LMFDB - Embedded newform 735.2.i.f.226.1

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:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 105)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			226.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	735.226
Dual form			735.2.i.f.361.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 - 1.73205i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-1.00000 - 1.73205i) q^{4} +(0.500000 - 0.866025i) q^{5} +2.00000 q^{6} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(1.00000 - 1.73205i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-1.00000 - 1.73205i) q^{4} +(0.500000 - 0.866025i) q^{5} +2.00000 q^{6} +(-0.500000 + 0.866025i) q^{9} +(-1.00000 - 1.73205i) q^{10} +(3.00000 + 5.19615i) q^{11} +(1.00000 - 1.73205i) q^{12} +3.00000 q^{13} +1.00000 q^{15} +(2.00000 - 3.46410i) q^{16} +(-2.00000 - 3.46410i) q^{17} +(1.00000 + 1.73205i) q^{18} +(0.500000 - 0.866025i) q^{19} -2.00000 q^{20} +12.0000 q^{22} +(2.00000 - 3.46410i) q^{23} +(-0.500000 - 0.866025i) q^{25} +(3.00000 - 5.19615i) q^{26} -1.00000 q^{27} -8.00000 q^{29} +(1.00000 - 1.73205i) q^{30} +(0.500000 + 0.866025i) q^{31} +(-4.00000 - 6.92820i) q^{32} +(-3.00000 + 5.19615i) q^{33} -8.00000 q^{34} +2.00000 q^{36} +(-3.50000 + 6.06218i) q^{37} +(-1.00000 - 1.73205i) q^{38} +(1.50000 + 2.59808i) q^{39} +6.00000 q^{41} +1.00000 q^{43} +(6.00000 - 10.3923i) q^{44} +(0.500000 + 0.866025i) q^{45} +(-4.00000 - 6.92820i) q^{46} +(1.00000 - 1.73205i) q^{47} +4.00000 q^{48} -2.00000 q^{50} +(2.00000 - 3.46410i) q^{51} +(-3.00000 - 5.19615i) q^{52} +(-2.00000 - 3.46410i) q^{53} +(-1.00000 + 1.73205i) q^{54} +6.00000 q^{55} +1.00000 q^{57} +(-8.00000 + 13.8564i) q^{58} +(-4.00000 - 6.92820i) q^{59} +(-1.00000 - 1.73205i) q^{60} +(-7.00000 + 12.1244i) q^{61} +2.00000 q^{62} -8.00000 q^{64} +(1.50000 - 2.59808i) q^{65} +(6.00000 + 10.3923i) q^{66} +(-3.50000 - 6.06218i) q^{67} +(-4.00000 + 6.92820i) q^{68} +4.00000 q^{69} +6.00000 q^{71} +(0.500000 + 0.866025i) q^{73} +(7.00000 + 12.1244i) q^{74} +(0.500000 - 0.866025i) q^{75} -2.00000 q^{76} +6.00000 q^{78} +(0.500000 - 0.866025i) q^{79} +(-2.00000 - 3.46410i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(6.00000 - 10.3923i) q^{82} -2.00000 q^{83} -4.00000 q^{85} +(1.00000 - 1.73205i) q^{86} +(-4.00000 - 6.92820i) q^{87} +(-6.00000 + 10.3923i) q^{89} +2.00000 q^{90} -8.00000 q^{92} +(-0.500000 + 0.866025i) q^{93} +(-2.00000 - 3.46410i) q^{94} +(-0.500000 - 0.866025i) q^{95} +(4.00000 - 6.92820i) q^{96} +6.00000 q^{97} -6.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} + q^{3} - 2 q^{4} + q^{5} + 4 q^{6} - q^{9}+O(q^{10}) $ 2 * q + 2 * q^2 + q^3 - 2 * q^4 + q^5 + 4 * q^6 - q^9	$ 2 q + 2 q^{2} + q^{3} - 2 q^{4} + q^{5} + 4 q^{6} - q^{9} - 2 q^{10} + 6 q^{11} + 2 q^{12} + 6 q^{13} + 2 q^{15} + 4 q^{16} - 4 q^{17} + 2 q^{18} + q^{19} - 4 q^{20} + 24 q^{22} + 4 q^{23} - q^{25} + 6 q^{26} - 2 q^{27} - 16 q^{29} + 2 q^{30} + q^{31} - 8 q^{32} - 6 q^{33} - 16 q^{34} + 4 q^{36} - 7 q^{37} - 2 q^{38} + 3 q^{39} + 12 q^{41} + 2 q^{43} + 12 q^{44} + q^{45} - 8 q^{46} + 2 q^{47} + 8 q^{48} - 4 q^{50} + 4 q^{51} - 6 q^{52} - 4 q^{53} - 2 q^{54} + 12 q^{55} + 2 q^{57} - 16 q^{58} - 8 q^{59} - 2 q^{60} - 14 q^{61} + 4 q^{62} - 16 q^{64} + 3 q^{65} + 12 q^{66} - 7 q^{67} - 8 q^{68} + 8 q^{69} + 12 q^{71} + q^{73} + 14 q^{74} + q^{75} - 4 q^{76} + 12 q^{78} + q^{79} - 4 q^{80} - q^{81} + 12 q^{82} - 4 q^{83} - 8 q^{85} + 2 q^{86} - 8 q^{87} - 12 q^{89} + 4 q^{90} - 16 q^{92} - q^{93} - 4 q^{94} - q^{95} + 8 q^{96} + 12 q^{97} - 12 q^{99}+O(q^{100}) $ 2 * q + 2 * q^2 + q^3 - 2 * q^4 + q^5 + 4 * q^6 - q^9 - 2 * q^10 + 6 * q^11 + 2 * q^12 + 6 * q^13 + 2 * q^15 + 4 * q^16 - 4 * q^17 + 2 * q^18 + q^19 - 4 * q^20 + 24 * q^22 + 4 * q^23 - q^25 + 6 * q^26 - 2 * q^27 - 16 * q^29 + 2 * q^30 + q^31 - 8 * q^32 - 6 * q^33 - 16 * q^34 + 4 * q^36 - 7 * q^37 - 2 * q^38 + 3 * q^39 + 12 * q^41 + 2 * q^43 + 12 * q^44 + q^45 - 8 * q^46 + 2 * q^47 + 8 * q^48 - 4 * q^50 + 4 * q^51 - 6 * q^52 - 4 * q^53 - 2 * q^54 + 12 * q^55 + 2 * q^57 - 16 * q^58 - 8 * q^59 - 2 * q^60 - 14 * q^61 + 4 * q^62 - 16 * q^64 + 3 * q^65 + 12 * q^66 - 7 * q^67 - 8 * q^68 + 8 * q^69 + 12 * q^71 + q^73 + 14 * q^74 + q^75 - 4 * q^76 + 12 * q^78 + q^79 - 4 * q^80 - q^81 + 12 * q^82 - 4 * q^83 - 8 * q^85 + 2 * q^86 - 8 * q^87 - 12 * q^89 + 4 * q^90 - 16 * q^92 - q^93 - 4 * q^94 - q^95 + 8 * q^96 + 12 * q^97 - 12 * 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 $

$2$	1.00000	−	1.73205i	0.707107	−	1.22474i	−0.258819	−	0.965926i	$-0.583333\pi$
$2$	1.00000	−	1.73205i	0.707107	−	1.22474i	0.965926	−	0.258819i	$-0.0833333\pi$
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$	−1.00000	−	1.73205i	−0.500000	−	0.866025i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$6$	2.00000			0.816497
$7$		0			0
$7$		0			0
$8$		0			0
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	−1.00000	−	1.73205i	−0.316228	−	0.547723i
$11$	3.00000	+	5.19615i	0.904534	+	1.56670i	0.821541	+	0.570149i	$0.193114\pi$
$11$	3.00000	+	5.19615i	0.904534	+	1.56670i	0.0829925	+	0.996550i	$0.473552\pi$
$12$	1.00000	−	1.73205i	0.288675	−	0.500000i
$13$	3.00000			0.832050			0.416025	−	0.909353i	$-0.363423\pi$
$13$	3.00000			0.832050			0.416025	+	0.909353i	$0.363423\pi$
$14$		0			0
$15$	1.00000			0.258199
$16$	2.00000	−	3.46410i	0.500000	−	0.866025i
$17$	−2.00000	−	3.46410i	−0.485071	−	0.840168i	0.514782	−	0.857321i	$-0.327873\pi$
$17$	−2.00000	−	3.46410i	−0.485071	−	0.840168i	−0.999853	+	0.0171533i	$0.994540\pi$
$18$	1.00000	+	1.73205i	0.235702	+	0.408248i
$19$	0.500000	−	0.866025i	0.114708	−	0.198680i	−0.802955	−	0.596040i	$-0.796740\pi$
$19$	0.500000	−	0.866025i	0.114708	−	0.198680i	0.917663	+	0.397360i	$0.130073\pi$
$20$	−2.00000			−0.447214
$21$		0			0
$22$	12.0000			2.55841
$23$	2.00000	−	3.46410i	0.417029	−	0.722315i	−0.578610	−	0.815604i	$-0.696405\pi$
$23$	2.00000	−	3.46410i	0.417029	−	0.722315i	0.995639	+	0.0932891i	$0.0297381\pi$
$24$		0			0
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	3.00000	−	5.19615i	0.588348	−	1.01905i
$27$	−1.00000			−0.192450
$28$		0			0
$29$	−8.00000			−1.48556			−0.742781	−	0.669534i	$-0.766494\pi$
$29$	−8.00000			−1.48556			−0.742781	+	0.669534i	$0.766494\pi$
$30$	1.00000	−	1.73205i	0.182574	−	0.316228i
$31$	0.500000	+	0.866025i	0.0898027	+	0.155543i	0.907428	−	0.420208i	$-0.138043\pi$
$31$	0.500000	+	0.866025i	0.0898027	+	0.155543i	−0.817625	+	0.575751i	$0.804710\pi$
$32$	−4.00000	−	6.92820i	−0.707107	−	1.22474i
$33$	−3.00000	+	5.19615i	−0.522233	+	0.904534i
$34$	−8.00000			−1.37199
$35$		0			0
$36$	2.00000			0.333333
$37$	−3.50000	+	6.06218i	−0.575396	+	0.996616i	0.420602	+	0.907245i	$0.361819\pi$
$37$	−3.50000	+	6.06218i	−0.575396	+	0.996616i	−0.995998	+	0.0893706i	$0.971514\pi$
$38$	−1.00000	−	1.73205i	−0.162221	−	0.280976i
$39$	1.50000	+	2.59808i	0.240192	+	0.416025i
$40$		0			0
$41$	6.00000			0.937043			0.468521	−	0.883452i	$-0.344787\pi$
$41$	6.00000			0.937043			0.468521	+	0.883452i	$0.344787\pi$
$42$		0			0
$43$	1.00000			0.152499			0.0762493	−	0.997089i	$-0.475706\pi$
$43$	1.00000			0.152499			0.0762493	+	0.997089i	$0.475706\pi$
$44$	6.00000	−	10.3923i	0.904534	−	1.56670i
$45$	0.500000	+	0.866025i	0.0745356	+	0.129099i
$46$	−4.00000	−	6.92820i	−0.589768	−	1.02151i
$47$	1.00000	−	1.73205i	0.145865	−	0.252646i	−0.783830	−	0.620975i	$-0.786737\pi$
$47$	1.00000	−	1.73205i	0.145865	−	0.252646i	0.929695	+	0.368329i	$0.120070\pi$
$48$	4.00000			0.577350
$49$		0			0
$50$	−2.00000			−0.282843
$51$	2.00000	−	3.46410i	0.280056	−	0.485071i
$52$	−3.00000	−	5.19615i	−0.416025	−	0.720577i
$53$	−2.00000	−	3.46410i	−0.274721	−	0.475831i	0.695344	−	0.718677i	$-0.255252\pi$
$53$	−2.00000	−	3.46410i	−0.274721	−	0.475831i	−0.970065	+	0.242846i	$0.921919\pi$
$54$	−1.00000	+	1.73205i	−0.136083	+	0.235702i
$55$	6.00000			0.809040
$56$		0			0
$57$	1.00000			0.132453
$58$	−8.00000	+	13.8564i	−1.05045	+	1.81944i
$59$	−4.00000	−	6.92820i	−0.520756	−	0.901975i	−0.999709	−	0.0241347i	$-0.992317\pi$
$59$	−4.00000	−	6.92820i	−0.520756	−	0.901975i	0.478953	−	0.877841i	$-0.341016\pi$
$60$	−1.00000	−	1.73205i	−0.129099	−	0.223607i
$61$	−7.00000	+	12.1244i	−0.896258	+	1.55236i	−0.0640184	+	0.997949i	$0.520392\pi$
$61$	−7.00000	+	12.1244i	−0.896258	+	1.55236i	−0.832240	+	0.554416i	$0.812942\pi$
$62$	2.00000			0.254000
$63$		0			0
$64$	−8.00000			−1.00000
$65$	1.50000	−	2.59808i	0.186052	−	0.322252i
$66$	6.00000	+	10.3923i	0.738549	+	1.27920i
$67$	−3.50000	−	6.06218i	−0.427593	−	0.740613i	0.569066	−	0.822292i	$-0.307305\pi$
$67$	−3.50000	−	6.06218i	−0.427593	−	0.740613i	−0.996659	+	0.0816792i	$0.973972\pi$
$68$	−4.00000	+	6.92820i	−0.485071	+	0.840168i
$69$	4.00000			0.481543
$70$		0			0
$71$	6.00000			0.712069			0.356034	−	0.934473i	$-0.384129\pi$
$71$	6.00000			0.712069			0.356034	+	0.934473i	$0.384129\pi$
$72$		0			0
$73$	0.500000	+	0.866025i	0.0585206	+	0.101361i	0.893801	−	0.448463i	$-0.148028\pi$
$73$	0.500000	+	0.866025i	0.0585206	+	0.101361i	−0.835281	+	0.549823i	$0.814695\pi$
$74$	7.00000	+	12.1244i	0.813733	+	1.40943i
$75$	0.500000	−	0.866025i	0.0577350	−	0.100000i
$76$	−2.00000			−0.229416
$77$		0			0
$78$	6.00000			0.679366
$79$	0.500000	−	0.866025i	0.0562544	−	0.0974355i	−0.836527	−	0.547926i	$-0.815418\pi$
$79$	0.500000	−	0.866025i	0.0562544	−	0.0974355i	0.892781	+	0.450490i	$0.148751\pi$
$80$	−2.00000	−	3.46410i	−0.223607	−	0.387298i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	6.00000	−	10.3923i	0.662589	−	1.14764i
$83$	−2.00000			−0.219529			−0.109764	−	0.993958i	$-0.535010\pi$
$83$	−2.00000			−0.219529			−0.109764	+	0.993958i	$0.535010\pi$
$84$		0			0
$85$	−4.00000			−0.433861
$86$	1.00000	−	1.73205i	0.107833	−	0.186772i
$87$	−4.00000	−	6.92820i	−0.428845	−	0.742781i
$88$		0			0
$89$	−6.00000	+	10.3923i	−0.635999	+	1.10158i	0.350304	+	0.936636i	$0.386078\pi$
$89$	−6.00000	+	10.3923i	−0.635999	+	1.10158i	−0.986303	+	0.164946i	$0.947255\pi$
$90$	2.00000			0.210819
$91$		0			0
$92$	−8.00000			−0.834058
$93$	−0.500000	+	0.866025i	−0.0518476	+	0.0898027i
$94$	−2.00000	−	3.46410i	−0.206284	−	0.357295i
$95$	−0.500000	−	0.866025i	−0.0512989	−	0.0888523i
$96$	4.00000	−	6.92820i	0.408248	−	0.707107i
$97$	6.00000			0.609208			0.304604	−	0.952479i	$-0.401476\pi$
$97$	6.00000			0.609208			0.304604	+	0.952479i	$0.401476\pi$
$98$		0			0
$99$	−6.00000			−0.603023
$100$	−1.00000	+	1.73205i	−0.100000	+	0.173205i
$101$	−5.00000	−	8.66025i	−0.497519	−	0.861727i	0.502477	−	0.864590i	$-0.332422\pi$
$101$	−5.00000	−	8.66025i	−0.497519	−	0.861727i	−0.999996	+	0.00286291i	$0.999089\pi$
$102$	−4.00000	−	6.92820i	−0.396059	−	0.685994i
$103$	−9.50000	+	16.4545i	−0.936063	+	1.62131i	−0.163335	+	0.986571i	$0.552225\pi$
$103$	−9.50000	+	16.4545i	−0.936063	+	1.62131i	−0.772728	+	0.634738i	$0.781108\pi$
$104$		0			0
$105$		0			0
$106$	−8.00000			−0.777029
$107$	−6.00000	+	10.3923i	−0.580042	+	1.00466i	0.415432	+	0.909624i	$0.363630\pi$
$107$	−6.00000	+	10.3923i	−0.580042	+	1.00466i	−0.995474	+	0.0950377i	$0.969703\pi$
$108$	1.00000	+	1.73205i	0.0962250	+	0.166667i
$109$	7.50000	+	12.9904i	0.718370	+	1.24425i	0.961645	+	0.274296i	$0.0884447\pi$
$109$	7.50000	+	12.9904i	0.718370	+	1.24425i	−0.243276	+	0.969957i	$0.578222\pi$
$110$	6.00000	−	10.3923i	0.572078	−	0.990867i
$111$	−7.00000			−0.664411
$112$		0			0
$113$	−6.00000			−0.564433			−0.282216	−	0.959351i	$-0.591070\pi$
$113$	−6.00000			−0.564433			−0.282216	+	0.959351i	$0.591070\pi$
$114$	1.00000	−	1.73205i	0.0936586	−	0.162221i
$115$	−2.00000	−	3.46410i	−0.186501	−	0.323029i
$116$	8.00000	+	13.8564i	0.742781	+	1.28654i
$117$	−1.50000	+	2.59808i	−0.138675	+	0.240192i
$118$	−16.0000			−1.47292
$119$		0			0
$120$		0			0
$121$	−12.5000	+	21.6506i	−1.13636	+	1.96824i
$122$	14.0000	+	24.2487i	1.26750	+	2.19538i
$123$	3.00000	+	5.19615i	0.270501	+	0.468521i
$124$	1.00000	−	1.73205i	0.0898027	−	0.155543i
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	5.00000			0.443678			0.221839	−	0.975083i	$-0.428794\pi$
$127$	5.00000			0.443678			0.221839	+	0.975083i	$0.428794\pi$
$128$		0			0
$129$	0.500000	+	0.866025i	0.0440225	+	0.0762493i
$130$	−3.00000	−	5.19615i	−0.263117	−	0.455733i
$131$	1.00000	−	1.73205i	0.0873704	−	0.151330i	−0.819028	−	0.573753i	$-0.805487\pi$
$131$	1.00000	−	1.73205i	0.0873704	−	0.151330i	0.906399	+	0.422423i	$0.138820\pi$
$132$	12.0000			1.04447
$133$		0			0
$134$	−14.0000			−1.20942
$135$	−0.500000	+	0.866025i	−0.0430331	+	0.0745356i
$136$		0			0
$137$	−4.00000	−	6.92820i	−0.341743	−	0.591916i	0.643013	−	0.765855i	$-0.277684\pi$
$137$	−4.00000	−	6.92820i	−0.341743	−	0.591916i	−0.984757	+	0.173939i	$0.944351\pi$
$138$	4.00000	−	6.92820i	0.340503	−	0.589768i
$139$	−21.0000			−1.78120			−0.890598	−	0.454791i	$-0.849714\pi$
$139$	−21.0000			−1.78120			−0.890598	+	0.454791i	$0.849714\pi$
$140$		0			0
$141$	2.00000			0.168430
$142$	6.00000	−	10.3923i	0.503509	−	0.872103i
$143$	9.00000	+	15.5885i	0.752618	+	1.30357i
$144$	2.00000	+	3.46410i	0.166667	+	0.288675i
$145$	−4.00000	+	6.92820i	−0.332182	+	0.575356i
$146$	2.00000			0.165521
$147$		0			0
$148$	14.0000			1.15079
$149$	2.00000	−	3.46410i	0.163846	−	0.283790i	−0.772399	−	0.635138i	$-0.780943\pi$
$149$	2.00000	−	3.46410i	0.163846	−	0.283790i	0.936245	+	0.351348i	$0.114277\pi$
$150$	−1.00000	−	1.73205i	−0.0816497	−	0.141421i
$151$	−4.00000	−	6.92820i	−0.325515	−	0.563809i	0.656101	−	0.754673i	$-0.272204\pi$
$151$	−4.00000	−	6.92820i	−0.325515	−	0.563809i	−0.981617	+	0.190864i	$0.938871\pi$
$152$		0			0
$153$	4.00000			0.323381
$154$		0			0
$155$	1.00000			0.0803219
$156$	3.00000	−	5.19615i	0.240192	−	0.416025i
$157$	5.00000	+	8.66025i	0.399043	+	0.691164i	0.993608	−	0.112884i	$-0.0360089\pi$
$157$	5.00000	+	8.66025i	0.399043	+	0.691164i	−0.594565	+	0.804048i	$0.702676\pi$
$158$	−1.00000	−	1.73205i	−0.0795557	−	0.137795i
$159$	2.00000	−	3.46410i	0.158610	−	0.274721i
$160$	−8.00000			−0.632456
$161$		0			0
$162$	−2.00000			−0.157135
$163$	6.00000	−	10.3923i	0.469956	−	0.813988i	−0.529454	−	0.848339i	$-0.677603\pi$
$163$	6.00000	−	10.3923i	0.469956	−	0.813988i	0.999410	+	0.0343508i	$0.0109363\pi$
$164$	−6.00000	−	10.3923i	−0.468521	−	0.811503i
$165$	3.00000	+	5.19615i	0.233550	+	0.404520i
$166$	−2.00000	+	3.46410i	−0.155230	+	0.268866i
$167$	10.0000			0.773823			0.386912	−	0.922117i	$-0.373542\pi$
$167$	10.0000			0.773823			0.386912	+	0.922117i	$0.373542\pi$
$168$		0			0
$169$	−4.00000			−0.307692
$170$	−4.00000	+	6.92820i	−0.306786	+	0.531369i
$171$	0.500000	+	0.866025i	0.0382360	+	0.0662266i
$172$	−1.00000	−	1.73205i	−0.0762493	−	0.132068i
$173$	12.0000	−	20.7846i	0.912343	−	1.58022i	0.101598	−	0.994826i	$-0.467605\pi$
$173$	12.0000	−	20.7846i	0.912343	−	1.58022i	0.810745	−	0.585399i	$-0.199062\pi$
$174$	−16.0000			−1.21296
$175$		0			0
$176$	24.0000			1.80907
$177$	4.00000	−	6.92820i	0.300658	−	0.520756i
$178$	12.0000	+	20.7846i	0.899438	+	1.55787i
$179$	−9.00000	−	15.5885i	−0.672692	−	1.16514i	−0.977138	−	0.212607i	$-0.931805\pi$
$179$	−9.00000	−	15.5885i	−0.672692	−	1.16514i	0.304446	−	0.952529i	$-0.401529\pi$
$180$	1.00000	−	1.73205i	0.0745356	−	0.129099i
$181$	−13.0000			−0.966282			−0.483141	−	0.875542i	$-0.660504\pi$
$181$	−13.0000			−0.966282			−0.483141	+	0.875542i	$0.660504\pi$
$182$		0			0
$183$	−14.0000			−1.03491
$184$		0			0
$185$	3.50000	+	6.06218i	0.257325	+	0.445700i
$186$	1.00000	+	1.73205i	0.0733236	+	0.127000i
$187$	12.0000	−	20.7846i	0.877527	−	1.51992i
$188$	−4.00000			−0.291730
$189$		0			0
$190$	−2.00000			−0.145095
$191$	−5.00000	+	8.66025i	−0.361787	+	0.626634i	−0.988255	−	0.152813i	$-0.951167\pi$
$191$	−5.00000	+	8.66025i	−0.361787	+	0.626634i	0.626468	+	0.779447i	$0.284500\pi$
$192$	−4.00000	−	6.92820i	−0.288675	−	0.500000i
$193$	4.50000	+	7.79423i	0.323917	+	0.561041i	0.981293	−	0.192522i	$-0.0616668\pi$
$193$	4.50000	+	7.79423i	0.323917	+	0.561041i	−0.657376	+	0.753563i	$0.728333\pi$
$194$	6.00000	−	10.3923i	0.430775	−	0.746124i
$195$	3.00000			0.214834
$196$		0			0
$197$	12.0000			0.854965			0.427482	−	0.904024i	$-0.359401\pi$
$197$	12.0000			0.854965			0.427482	+	0.904024i	$0.359401\pi$
$198$	−6.00000	+	10.3923i	−0.426401	+	0.738549i
$199$	4.00000	+	6.92820i	0.283552	+	0.491127i	0.972257	−	0.233915i	$-0.0751537\pi$
$199$	4.00000	+	6.92820i	0.283552	+	0.491127i	−0.688705	+	0.725042i	$0.741820\pi$
$200$		0			0
$201$	3.50000	−	6.06218i	0.246871	−	0.427593i
$202$	−20.0000			−1.40720
$203$		0			0
$204$	−8.00000			−0.560112
$205$	3.00000	−	5.19615i	0.209529	−	0.362915i
$206$	19.0000	+	32.9090i	1.32379	+	2.29288i
$207$	2.00000	+	3.46410i	0.139010	+	0.240772i
$208$	6.00000	−	10.3923i	0.416025	−	0.720577i
$209$	6.00000			0.415029
$210$		0			0
$211$	−20.0000			−1.37686			−0.688428	−	0.725304i	$-0.741699\pi$
$211$	−20.0000			−1.37686			−0.688428	+	0.725304i	$0.741699\pi$
$212$	−4.00000	+	6.92820i	−0.274721	+	0.475831i
$213$	3.00000	+	5.19615i	0.205557	+	0.356034i
$214$	12.0000	+	20.7846i	0.820303	+	1.42081i
$215$	0.500000	−	0.866025i	0.0340997	−	0.0590624i
$216$		0			0
$217$		0			0
$218$	30.0000			2.03186
$219$	−0.500000	+	0.866025i	−0.0337869	+	0.0585206i
$220$	−6.00000	−	10.3923i	−0.404520	−	0.700649i
$221$	−6.00000	−	10.3923i	−0.403604	−	0.699062i
$222$	−7.00000	+	12.1244i	−0.469809	+	0.813733i
$223$	24.0000			1.60716			0.803579	−	0.595198i	$-0.202926\pi$
$223$	24.0000			1.60716			0.803579	+	0.595198i	$0.202926\pi$
$224$		0			0
$225$	1.00000			0.0666667
$226$	−6.00000	+	10.3923i	−0.399114	+	0.691286i
$227$	−5.00000	−	8.66025i	−0.331862	−	0.574801i	0.651015	−	0.759065i	$-0.274343\pi$
$227$	−5.00000	−	8.66025i	−0.331862	−	0.574801i	−0.982877	+	0.184263i	$0.941010\pi$
$228$	−1.00000	−	1.73205i	−0.0662266	−	0.114708i
$229$	6.50000	−	11.2583i	0.429532	−	0.743971i	−0.567300	−	0.823511i	$-0.692012\pi$
$229$	6.50000	−	11.2583i	0.429532	−	0.743971i	0.996832	+	0.0795401i	$0.0253452\pi$
$230$	−8.00000			−0.527504
$231$		0			0
$232$		0			0
$233$	−3.00000	+	5.19615i	−0.196537	+	0.340411i	−0.947403	−	0.320043i	$-0.896303\pi$
$233$	−3.00000	+	5.19615i	−0.196537	+	0.340411i	0.750867	+	0.660454i	$0.229636\pi$
$234$	3.00000	+	5.19615i	0.196116	+	0.339683i
$235$	−1.00000	−	1.73205i	−0.0652328	−	0.112987i
$236$	−8.00000	+	13.8564i	−0.520756	+	0.901975i
$237$	1.00000			0.0649570
$238$		0			0
$239$	14.0000			0.905585			0.452792	−	0.891616i	$-0.350428\pi$
$239$	14.0000			0.905585			0.452792	+	0.891616i	$0.350428\pi$
$240$	2.00000	−	3.46410i	0.129099	−	0.223607i
$241$	−9.00000	−	15.5885i	−0.579741	−	1.00414i	−0.995509	−	0.0946700i	$-0.969820\pi$
$241$	−9.00000	−	15.5885i	−0.579741	−	1.00414i	0.415768	−	0.909471i	$-0.363513\pi$
$242$	25.0000	+	43.3013i	1.60706	+	2.78351i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	28.0000			1.79252
$245$		0			0
$246$	12.0000			0.765092
$247$	1.50000	−	2.59808i	0.0954427	−	0.165312i
$248$		0			0
$249$	−1.00000	−	1.73205i	−0.0633724	−	0.109764i
$250$	−1.00000	+	1.73205i	−0.0632456	+	0.109545i
$251$	−12.0000			−0.757433			−0.378717	−	0.925513i	$-0.623635\pi$
$251$	−12.0000			−0.757433			−0.378717	+	0.925513i	$0.623635\pi$
$252$		0			0
$253$	24.0000			1.50887
$254$	5.00000	−	8.66025i	0.313728	−	0.543393i
$255$	−2.00000	−	3.46410i	−0.125245	−	0.216930i
$256$	−8.00000	−	13.8564i	−0.500000	−	0.866025i
$257$	−9.00000	+	15.5885i	−0.561405	+	0.972381i	0.435970	+	0.899961i	$0.356405\pi$
$257$	−9.00000	+	15.5885i	−0.561405	+	0.972381i	−0.997374	+	0.0724199i	$0.976928\pi$
$258$	2.00000			0.124515
$259$		0			0
$260$	−6.00000			−0.372104
$261$	4.00000	−	6.92820i	0.247594	−	0.428845i
$262$	−2.00000	−	3.46410i	−0.123560	−	0.214013i
$263$	−2.00000	−	3.46410i	−0.123325	−	0.213606i	0.797752	−	0.602986i	$-0.206023\pi$
$263$	−2.00000	−	3.46410i	−0.123325	−	0.213606i	−0.921077	+	0.389380i	$0.872689\pi$
$264$		0			0
$265$	−4.00000			−0.245718
$266$		0			0
$267$	−12.0000			−0.734388
$268$	−7.00000	+	12.1244i	−0.427593	+	0.740613i
$269$	−5.00000	−	8.66025i	−0.304855	−	0.528025i	0.672374	−	0.740212i	$-0.265275\pi$
$269$	−5.00000	−	8.66025i	−0.304855	−	0.528025i	−0.977229	+	0.212187i	$0.931941\pi$
$270$	1.00000	+	1.73205i	0.0608581	+	0.105409i
$271$	−12.0000	+	20.7846i	−0.728948	+	1.26258i	0.228380	+	0.973572i	$0.426657\pi$
$271$	−12.0000	+	20.7846i	−0.728948	+	1.26258i	−0.957328	+	0.289003i	$0.906676\pi$
$272$	−16.0000			−0.970143
$273$		0			0
$274$	−16.0000			−0.966595
$275$	3.00000	−	5.19615i	0.180907	−	0.313340i
$276$	−4.00000	−	6.92820i	−0.240772	−	0.417029i
$277$	3.50000	+	6.06218i	0.210295	+	0.364241i	0.951807	−	0.306699i	$-0.0992243\pi$
$277$	3.50000	+	6.06218i	0.210295	+	0.364241i	−0.741512	+	0.670940i	$0.765891\pi$
$278$	−21.0000	+	36.3731i	−1.25950	+	2.18151i
$279$	−1.00000			−0.0598684
$280$		0			0
$281$	−12.0000			−0.715860			−0.357930	−	0.933748i	$-0.616517\pi$
$281$	−12.0000			−0.715860			−0.357930	+	0.933748i	$0.616517\pi$
$282$	2.00000	−	3.46410i	0.119098	−	0.206284i
$283$	−3.50000	−	6.06218i	−0.208053	−	0.360359i	0.743048	−	0.669238i	$-0.233379\pi$
$283$	−3.50000	−	6.06218i	−0.208053	−	0.360359i	−0.951101	+	0.308879i	$0.900046\pi$
$284$	−6.00000	−	10.3923i	−0.356034	−	0.616670i
$285$	0.500000	−	0.866025i	0.0296174	−	0.0512989i
$286$	36.0000			2.12872
$287$		0			0
$288$	8.00000			0.471405
$289$	0.500000	−	0.866025i	0.0294118	−	0.0509427i
$290$	8.00000	+	13.8564i	0.469776	+	0.813676i
$291$	3.00000	+	5.19615i	0.175863	+	0.304604i
$292$	1.00000	−	1.73205i	0.0585206	−	0.101361i
$293$	16.0000			0.934730			0.467365	−	0.884064i	$-0.345203\pi$
$293$	16.0000			0.934730			0.467365	+	0.884064i	$0.345203\pi$
$294$		0			0
$295$	−8.00000			−0.465778
$296$		0			0
$297$	−3.00000	−	5.19615i	−0.174078	−	0.301511i
$298$	−4.00000	−	6.92820i	−0.231714	−	0.401340i
$299$	6.00000	−	10.3923i	0.346989	−	0.601003i
$300$	−2.00000			−0.115470
$301$		0			0
$302$	−16.0000			−0.920697
$303$	5.00000	−	8.66025i	0.287242	−	0.497519i
$304$	−2.00000	−	3.46410i	−0.114708	−	0.198680i
$305$	7.00000	+	12.1244i	0.400819	+	0.694239i
$306$	4.00000	−	6.92820i	0.228665	−	0.396059i
$307$	−3.00000			−0.171219			−0.0856095	−	0.996329i	$-0.527284\pi$
$307$	−3.00000			−0.171219			−0.0856095	+	0.996329i	$0.527284\pi$
$308$		0			0
$309$	−19.0000			−1.08087
$310$	1.00000	−	1.73205i	0.0567962	−	0.0983739i
$311$	3.00000	+	5.19615i	0.170114	+	0.294647i	0.938460	−	0.345389i	$-0.112253\pi$
$311$	3.00000	+	5.19615i	0.170114	+	0.294647i	−0.768345	+	0.640036i	$0.778920\pi$
$312$		0			0
$313$	5.50000	−	9.52628i	0.310878	−	0.538457i	−0.667674	−	0.744453i	$-0.732710\pi$
$313$	5.50000	−	9.52628i	0.310878	−	0.538457i	0.978553	+	0.205996i	$0.0660435\pi$
$314$	20.0000			1.12867
$315$		0			0
$316$	−2.00000			−0.112509
$317$	−10.0000	+	17.3205i	−0.561656	+	0.972817i	0.435696	+	0.900094i	$0.356502\pi$
$317$	−10.0000	+	17.3205i	−0.561656	+	0.972817i	−0.997352	+	0.0727229i	$0.976831\pi$
$318$	−4.00000	−	6.92820i	−0.224309	−	0.388514i
$319$	−24.0000	−	41.5692i	−1.34374	−	2.32743i
$320$	−4.00000	+	6.92820i	−0.223607	+	0.387298i
$321$	−12.0000			−0.669775
$322$		0			0
$323$	−4.00000			−0.222566
$324$	−1.00000	+	1.73205i	−0.0555556	+	0.0962250i
$325$	−1.50000	−	2.59808i	−0.0832050	−	0.144115i
$326$	−12.0000	−	20.7846i	−0.664619	−	1.15115i
$327$	−7.50000	+	12.9904i	−0.414751	+	0.718370i
$328$		0			0
$329$		0			0
$330$	12.0000			0.660578
$331$	4.50000	−	7.79423i	0.247342	−	0.428410i	−0.715445	−	0.698669i	$-0.753776\pi$
$331$	4.50000	−	7.79423i	0.247342	−	0.428410i	0.962788	+	0.270259i	$0.0871094\pi$
$332$	2.00000	+	3.46410i	0.109764	+	0.190117i
$333$	−3.50000	−	6.06218i	−0.191799	−	0.332205i
$334$	10.0000	−	17.3205i	0.547176	−	0.947736i
$335$	−7.00000			−0.382451
$336$		0			0
$337$	25.0000			1.36184			0.680918	−	0.732359i	$-0.261581\pi$
$337$	25.0000			1.36184			0.680918	+	0.732359i	$0.261581\pi$
$338$	−4.00000	+	6.92820i	−0.217571	+	0.376845i
$339$	−3.00000	−	5.19615i	−0.162938	−	0.282216i
$340$	4.00000	+	6.92820i	0.216930	+	0.375735i
$341$	−3.00000	+	5.19615i	−0.162459	+	0.281387i
$342$	2.00000			0.108148
$343$		0			0
$344$		0			0
$345$	2.00000	−	3.46410i	0.107676	−	0.186501i
$346$	−24.0000	−	41.5692i	−1.29025	−	2.23478i
$347$	−8.00000	−	13.8564i	−0.429463	−	0.743851i	0.567363	−	0.823468i	$-0.307964\pi$
$347$	−8.00000	−	13.8564i	−0.429463	−	0.743851i	−0.996826	+	0.0796169i	$0.974630\pi$
$348$	−8.00000	+	13.8564i	−0.428845	+	0.742781i
$349$	−2.00000			−0.107058			−0.0535288	−	0.998566i	$-0.517047\pi$
$349$	−2.00000			−0.107058			−0.0535288	+	0.998566i	$0.517047\pi$
$350$		0			0
$351$	−3.00000			−0.160128
$352$	24.0000	−	41.5692i	1.27920	−	2.21565i
$353$	−9.00000	−	15.5885i	−0.479022	−	0.829690i	0.520689	−	0.853746i	$-0.325675\pi$
$353$	−9.00000	−	15.5885i	−0.479022	−	0.829690i	−0.999711	+	0.0240566i	$0.992342\pi$
$354$	−8.00000	−	13.8564i	−0.425195	−	0.736460i
$355$	3.00000	−	5.19615i	0.159223	−	0.275783i
$356$	24.0000			1.27200
$357$		0			0
$358$	−36.0000			−1.90266
$359$	12.0000	−	20.7846i	0.633336	−	1.09697i	−0.353529	−	0.935423i	$-0.615019\pi$
$359$	12.0000	−	20.7846i	0.633336	−	1.09697i	0.986865	−	0.161546i	$-0.0516481\pi$
$360$		0			0
$361$	9.00000	+	15.5885i	0.473684	+	0.820445i
$362$	−13.0000	+	22.5167i	−0.683265	+	1.18345i
$363$	−25.0000			−1.31216
$364$		0			0
$365$	1.00000			0.0523424
$366$	−14.0000	+	24.2487i	−0.731792	+	1.26750i
$367$	9.50000	+	16.4545i	0.495896	+	0.858917i	0.999989	−	0.00473247i	$-0.00150640\pi$
$367$	9.50000	+	16.4545i	0.495896	+	0.858917i	−0.504093	+	0.863649i	$0.668173\pi$
$368$	−8.00000	−	13.8564i	−0.417029	−	0.722315i
$369$	−3.00000	+	5.19615i	−0.156174	+	0.270501i
$370$	14.0000			0.727825
$371$		0			0
$372$	2.00000			0.103695
$373$	−5.50000	+	9.52628i	−0.284779	+	0.493252i	−0.972556	−	0.232671i	$-0.925254\pi$
$373$	−5.50000	+	9.52628i	−0.284779	+	0.493252i	0.687776	+	0.725923i	$0.258587\pi$
$374$	−24.0000	−	41.5692i	−1.24101	−	2.14949i
$375$	−0.500000	−	0.866025i	−0.0258199	−	0.0447214i
$376$		0			0
$377$	−24.0000			−1.23606
$378$		0			0
$379$	11.0000			0.565032			0.282516	−	0.959263i	$-0.408831\pi$
$379$	11.0000			0.565032			0.282516	+	0.959263i	$0.408831\pi$
$380$	−1.00000	+	1.73205i	−0.0512989	+	0.0888523i
$381$	2.50000	+	4.33013i	0.128079	+	0.221839i
$382$	10.0000	+	17.3205i	0.511645	+	0.886194i
$383$	14.0000	−	24.2487i	0.715367	−	1.23905i	−0.247451	−	0.968900i	$-0.579593\pi$
$383$	14.0000	−	24.2487i	0.715367	−	1.23905i	0.962818	−	0.270151i	$-0.0870736\pi$
$384$		0			0
$385$		0			0
$386$	18.0000			0.916176
$387$	−0.500000	+	0.866025i	−0.0254164	+	0.0440225i
$388$	−6.00000	−	10.3923i	−0.304604	−	0.527589i
$389$	−3.00000	−	5.19615i	−0.152106	−	0.263455i	0.779895	−	0.625910i	$-0.215272\pi$
$389$	−3.00000	−	5.19615i	−0.152106	−	0.263455i	−0.932002	+	0.362454i	$0.881939\pi$
$390$	3.00000	−	5.19615i	0.151911	−	0.263117i
$391$	−16.0000			−0.809155
$392$		0			0
$393$	2.00000			0.100887
$394$	12.0000	−	20.7846i	0.604551	−	1.04711i
$395$	−0.500000	−	0.866025i	−0.0251577	−	0.0435745i
$396$	6.00000	+	10.3923i	0.301511	+	0.522233i
$397$	−18.5000	+	32.0429i	−0.928488	+	1.60819i	−0.142636	+	0.989775i	$0.545558\pi$
$397$	−18.5000	+	32.0429i	−0.928488	+	1.60819i	−0.785853	+	0.618414i	$0.787776\pi$
$398$	16.0000			0.802008
$399$		0			0
$400$	−4.00000			−0.200000
$401$	6.00000	−	10.3923i	0.299626	−	0.518967i	−0.676425	−	0.736512i	$-0.736472\pi$
$401$	6.00000	−	10.3923i	0.299626	−	0.518967i	0.976050	+	0.217545i	$0.0698049\pi$
$402$	−7.00000	−	12.1244i	−0.349128	−	0.604708i
$403$	1.50000	+	2.59808i	0.0747203	+	0.129419i
$404$	−10.0000	+	17.3205i	−0.497519	+	0.861727i
$405$	−1.00000			−0.0496904
$406$		0			0
$407$	−42.0000			−2.08186
$408$		0			0
$409$	2.50000	+	4.33013i	0.123617	+	0.214111i	0.921192	−	0.389109i	$-0.127217\pi$
$409$	2.50000	+	4.33013i	0.123617	+	0.214111i	−0.797574	+	0.603220i	$0.793884\pi$
$410$	−6.00000	−	10.3923i	−0.296319	−	0.513239i
$411$	4.00000	−	6.92820i	0.197305	−	0.341743i
$412$	38.0000			1.87213
$413$		0			0
$414$	8.00000			0.393179
$415$	−1.00000	+	1.73205i	−0.0490881	+	0.0850230i
$416$	−12.0000	−	20.7846i	−0.588348	−	1.01905i
$417$	−10.5000	−	18.1865i	−0.514187	−	0.890598i
$418$	6.00000	−	10.3923i	0.293470	−	0.508304i
$419$	−6.00000			−0.293119			−0.146560	−	0.989202i	$-0.546820\pi$
$419$	−6.00000			−0.293119			−0.146560	+	0.989202i	$0.546820\pi$
$420$		0			0
$421$	1.00000			0.0487370			0.0243685	−	0.999703i	$-0.492242\pi$
$421$	1.00000			0.0487370			0.0243685	+	0.999703i	$0.492242\pi$
$422$	−20.0000	+	34.6410i	−0.973585	+	1.68630i
$423$	1.00000	+	1.73205i	0.0486217	+	0.0842152i
$424$		0			0
$425$	−2.00000	+	3.46410i	−0.0970143	+	0.168034i
$426$	12.0000			0.581402
$427$		0			0
$428$	24.0000			1.16008
$429$	−9.00000	+	15.5885i	−0.434524	+	0.752618i
$430$	−1.00000	−	1.73205i	−0.0482243	−	0.0835269i
$431$	1.00000	+	1.73205i	0.0481683	+	0.0834300i	0.889104	−	0.457705i	$-0.151328\pi$
$431$	1.00000	+	1.73205i	0.0481683	+	0.0834300i	−0.840936	+	0.541135i	$0.817995\pi$
$432$	−2.00000	+	3.46410i	−0.0962250	+	0.166667i
$433$	5.00000			0.240285			0.120142	−	0.992757i	$-0.461665\pi$
$433$	5.00000			0.240285			0.120142	+	0.992757i	$0.461665\pi$
$434$		0			0
$435$	−8.00000			−0.383571
$436$	15.0000	−	25.9808i	0.718370	−	1.24425i
$437$	−2.00000	−	3.46410i	−0.0956730	−	0.165710i
$438$	1.00000	+	1.73205i	0.0477818	+	0.0827606i
$439$	8.00000	−	13.8564i	0.381819	−	0.661330i	−0.609503	−	0.792784i	$-0.708631\pi$
$439$	8.00000	−	13.8564i	0.381819	−	0.661330i	0.991322	+	0.131453i	$0.0419644\pi$
$440$		0			0
$441$		0			0
$442$	−24.0000			−1.14156
$443$	18.0000	−	31.1769i	0.855206	−	1.48126i	−0.0212481	−	0.999774i	$-0.506764\pi$
$443$	18.0000	−	31.1769i	0.855206	−	1.48126i	0.876454	−	0.481486i	$-0.159903\pi$
$444$	7.00000	+	12.1244i	0.332205	+	0.575396i
$445$	6.00000	+	10.3923i	0.284427	+	0.492642i
$446$	24.0000	−	41.5692i	1.13643	−	1.96836i
$447$	4.00000			0.189194
$448$		0			0
$449$	30.0000			1.41579			0.707894	−	0.706319i	$-0.249646\pi$
$449$	30.0000			1.41579			0.707894	+	0.706319i	$0.249646\pi$
$450$	1.00000	−	1.73205i	0.0471405	−	0.0816497i
$451$	18.0000	+	31.1769i	0.847587	+	1.46806i
$452$	6.00000	+	10.3923i	0.282216	+	0.488813i
$453$	4.00000	−	6.92820i	0.187936	−	0.325515i
$454$	−20.0000			−0.938647
$455$		0			0
$456$		0			0
$457$	7.50000	−	12.9904i	0.350835	−	0.607664i	−0.635561	−	0.772051i	$-0.719231\pi$
$457$	7.50000	−	12.9904i	0.350835	−	0.607664i	0.986396	+	0.164386i	$0.0525644\pi$
$458$	−13.0000	−	22.5167i	−0.607450	−	1.05213i
$459$	2.00000	+	3.46410i	0.0933520	+	0.161690i
$460$	−4.00000	+	6.92820i	−0.186501	+	0.323029i
$461$	8.00000			0.372597			0.186299	−	0.982493i	$-0.440351\pi$
$461$	8.00000			0.372597			0.186299	+	0.982493i	$0.440351\pi$
$462$		0			0
$463$	3.00000			0.139422			0.0697109	−	0.997567i	$-0.477792\pi$
$463$	3.00000			0.139422			0.0697109	+	0.997567i	$0.477792\pi$
$464$	−16.0000	+	27.7128i	−0.742781	+	1.28654i
$465$	0.500000	+	0.866025i	0.0231869	+	0.0401610i
$466$	6.00000	+	10.3923i	0.277945	+	0.481414i
$467$	11.0000	−	19.0526i	0.509019	−	0.881647i	−0.490926	−	0.871201i	$-0.663342\pi$
$467$	11.0000	−	19.0526i	0.509019	−	0.881647i	0.999945	−	0.0104461i	$-0.00332515\pi$
$468$	6.00000			0.277350
$469$		0			0
$470$	−4.00000			−0.184506
$471$	−5.00000	+	8.66025i	−0.230388	+	0.399043i
$472$		0			0
$473$	3.00000	+	5.19615i	0.137940	+	0.238919i
$474$	1.00000	−	1.73205i	0.0459315	−	0.0795557i
$475$	−1.00000			−0.0458831
$476$		0			0
$477$	4.00000			0.183147
$478$	14.0000	−	24.2487i	0.640345	−	1.10911i
$479$	−2.00000	−	3.46410i	−0.0913823	−	0.158279i	0.816711	−	0.577047i	$-0.195795\pi$
$479$	−2.00000	−	3.46410i	−0.0913823	−	0.158279i	−0.908093	+	0.418769i	$0.862462\pi$
$480$	−4.00000	−	6.92820i	−0.182574	−	0.316228i
$481$	−10.5000	+	18.1865i	−0.478759	+	0.829235i
$482$	−36.0000			−1.63976
$483$		0			0
$484$	50.0000			2.27273
$485$	3.00000	−	5.19615i	0.136223	−	0.235945i
$486$	−1.00000	−	1.73205i	−0.0453609	−	0.0785674i
$487$	6.50000	+	11.2583i	0.294543	+	0.510164i	0.974879	−	0.222737i	$-0.0714992\pi$
$487$	6.50000	+	11.2583i	0.294543	+	0.510164i	−0.680335	+	0.732901i	$0.738166\pi$
$488$		0			0
$489$	12.0000			0.542659
$490$		0			0
$491$	−12.0000			−0.541552			−0.270776	−	0.962642i	$-0.587280\pi$
$491$	−12.0000			−0.541552			−0.270776	+	0.962642i	$0.587280\pi$
$492$	6.00000	−	10.3923i	0.270501	−	0.468521i
$493$	16.0000	+	27.7128i	0.720604	+	1.24812i
$494$	−3.00000	−	5.19615i	−0.134976	−	0.233786i
$495$	−3.00000	+	5.19615i	−0.134840	+	0.233550i
$496$	4.00000			0.179605
$497$		0			0
$498$	−4.00000			−0.179244
$499$	−14.5000	+	25.1147i	−0.649109	+	1.12429i	0.334227	+	0.942493i	$0.391525\pi$
$499$	−14.5000	+	25.1147i	−0.649109	+	1.12429i	−0.983336	+	0.181797i	$0.941809\pi$
$500$	1.00000	+	1.73205i	0.0447214	+	0.0774597i
$501$	5.00000	+	8.66025i	0.223384	+	0.386912i
$502$	−12.0000	+	20.7846i	−0.535586	+	0.927663i
$503$	2.00000			0.0891756			0.0445878	−	0.999005i	$-0.485803\pi$
$503$	2.00000			0.0891756			0.0445878	+	0.999005i	$0.485803\pi$
$504$		0			0
$505$	−10.0000			−0.444994
$506$	24.0000	−	41.5692i	1.06693	−	1.84798i
$507$	−2.00000	−	3.46410i	−0.0888231	−	0.153846i
$508$	−5.00000	−	8.66025i	−0.221839	−	0.384237i
$509$	5.00000	−	8.66025i	0.221621	−	0.383859i	−0.733679	−	0.679496i	$-0.762199\pi$
$509$	5.00000	−	8.66025i	0.221621	−	0.383859i	0.955300	+	0.295637i	$0.0955319\pi$
$510$	−8.00000			−0.354246
$511$		0			0
$512$	−32.0000			−1.41421
$513$	−0.500000	+	0.866025i	−0.0220755	+	0.0382360i
$514$	18.0000	+	31.1769i	0.793946	+	1.37515i
$515$	9.50000	+	16.4545i	0.418620	+	0.725071i
$516$	1.00000	−	1.73205i	0.0440225	−	0.0762493i
$517$	12.0000			0.527759
$518$		0			0
$519$	24.0000			1.05348
$520$		0			0
$521$	2.00000	+	3.46410i	0.0876216	+	0.151765i	0.906505	−	0.422194i	$-0.138740\pi$
$521$	2.00000	+	3.46410i	0.0876216	+	0.151765i	−0.818884	+	0.573959i	$0.805407\pi$
$522$	−8.00000	−	13.8564i	−0.350150	−	0.606478i
$523$	5.50000	−	9.52628i	0.240498	−	0.416555i	−0.720358	−	0.693602i	$-0.756023\pi$
$523$	5.50000	−	9.52628i	0.240498	−	0.416555i	0.960856	+	0.277047i	$0.0893559\pi$
$524$	−4.00000			−0.174741
$525$		0			0
$526$	−8.00000			−0.348817
$527$	2.00000	−	3.46410i	0.0871214	−	0.150899i
$528$	12.0000	+	20.7846i	0.522233	+	0.904534i
$529$	3.50000	+	6.06218i	0.152174	+	0.263573i
$530$	−4.00000	+	6.92820i	−0.173749	+	0.300942i
$531$	8.00000			0.347170
$532$		0			0
$533$	18.0000			0.779667
$534$	−12.0000	+	20.7846i	−0.519291	+	0.899438i
$535$	6.00000	+	10.3923i	0.259403	+	0.449299i
$536$		0			0
$537$	9.00000	−	15.5885i	0.388379	−	0.672692i
$538$	−20.0000			−0.862261
$539$		0			0
$540$	2.00000			0.0860663
$541$	1.50000	−	2.59808i	0.0644900	−	0.111700i	−0.831978	−	0.554809i	$-0.812791\pi$
$541$	1.50000	−	2.59808i	0.0644900	−	0.111700i	0.896468	+	0.443109i	$0.146125\pi$
$542$	24.0000	+	41.5692i	1.03089	+	1.78555i
$543$	−6.50000	−	11.2583i	−0.278942	−	0.483141i
$544$	−16.0000	+	27.7128i	−0.685994	+	1.18818i
$545$	15.0000			0.642529
$546$		0			0
$547$	36.0000			1.53925			0.769624	−	0.638497i	$-0.220443\pi$
$547$	36.0000			1.53925			0.769624	+	0.638497i	$0.220443\pi$
$548$	−8.00000	+	13.8564i	−0.341743	+	0.591916i
$549$	−7.00000	−	12.1244i	−0.298753	−	0.517455i
$550$	−6.00000	−	10.3923i	−0.255841	−	0.443129i
$551$	−4.00000	+	6.92820i	−0.170406	+	0.295151i
$552$		0			0
$553$		0			0
$554$	14.0000			0.594803
$555$	−3.50000	+	6.06218i	−0.148567	+	0.257325i
$556$	21.0000	+	36.3731i	0.890598	+	1.54256i
$557$	5.00000	+	8.66025i	0.211857	+	0.366947i	0.952296	−	0.305177i	$-0.0987156\pi$
$557$	5.00000	+	8.66025i	0.211857	+	0.366947i	−0.740439	+	0.672124i	$0.765382\pi$
$558$	−1.00000	+	1.73205i	−0.0423334	+	0.0733236i
$559$	3.00000			0.126886
$560$		0			0
$561$	24.0000			1.01328
$562$	−12.0000	+	20.7846i	−0.506189	+	0.876746i
$563$	−13.0000	−	22.5167i	−0.547885	−	0.948964i	−0.998419	−	0.0562051i	$-0.982100\pi$
$563$	−13.0000	−	22.5167i	−0.547885	−	0.948964i	0.450535	−	0.892759i	$-0.351233\pi$
$564$	−2.00000	−	3.46410i	−0.0842152	−	0.145865i
$565$	−3.00000	+	5.19615i	−0.126211	+	0.218604i
$566$	−14.0000			−0.588464
$567$		0			0
$568$		0			0
$569$	−9.00000	+	15.5885i	−0.377300	+	0.653502i	−0.990668	−	0.136295i	$-0.956481\pi$
$569$	−9.00000	+	15.5885i	−0.377300	+	0.653502i	0.613369	+	0.789797i	$0.289814\pi$
$570$	−1.00000	−	1.73205i	−0.0418854	−	0.0725476i
$571$	1.50000	+	2.59808i	0.0627730	+	0.108726i	0.895704	−	0.444651i	$-0.146672\pi$
$571$	1.50000	+	2.59808i	0.0627730	+	0.108726i	−0.832931	+	0.553377i	$0.813339\pi$
$572$	18.0000	−	31.1769i	0.752618	−	1.30357i
$573$	−10.0000			−0.417756
$574$		0			0
$575$	−4.00000			−0.166812
$576$	4.00000	−	6.92820i	0.166667	−	0.288675i
$577$	−14.5000	−	25.1147i	−0.603643	−	1.04554i	−0.992264	−	0.124143i	$-0.960382\pi$
$577$	−14.5000	−	25.1147i	−0.603643	−	1.04554i	0.388621	−	0.921397i	$-0.372951\pi$
$578$	−1.00000	−	1.73205i	−0.0415945	−	0.0720438i
$579$	−4.50000	+	7.79423i	−0.187014	+	0.323917i
$580$	16.0000			0.664364
$581$		0			0
$582$	12.0000			0.497416
$583$	12.0000	−	20.7846i	0.496989	−	0.860811i
$584$		0			0
$585$	1.50000	+	2.59808i	0.0620174	+	0.107417i
$586$	16.0000	−	27.7128i	0.660954	−	1.14481i
$587$	−12.0000			−0.495293			−0.247647	−	0.968850i	$-0.579657\pi$
$587$	−12.0000			−0.495293			−0.247647	+	0.968850i	$0.579657\pi$
$588$		0			0
$589$	1.00000			0.0412043
$590$	−8.00000	+	13.8564i	−0.329355	+	0.570459i
$591$	6.00000	+	10.3923i	0.246807	+	0.427482i
$592$	14.0000	+	24.2487i	0.575396	+	0.996616i
$593$	−9.00000	+	15.5885i	−0.369586	+	0.640141i	−0.989501	−	0.144528i	$-0.953834\pi$
$593$	−9.00000	+	15.5885i	−0.369586	+	0.640141i	0.619915	+	0.784669i	$0.287167\pi$
$594$	−12.0000			−0.492366
$595$		0			0
$596$	−8.00000			−0.327693
$597$	−4.00000	+	6.92820i	−0.163709	+	0.283552i
$598$	−12.0000	−	20.7846i	−0.490716	−	0.849946i
$599$	2.00000	+	3.46410i	0.0817178	+	0.141539i	0.903988	−	0.427558i	$-0.140626\pi$
$599$	2.00000	+	3.46410i	0.0817178	+	0.141539i	−0.822270	+	0.569097i	$0.807293\pi$
$600$		0			0
$601$	33.0000			1.34610			0.673049	−	0.739598i	$-0.264984\pi$
$601$	33.0000			1.34610			0.673049	+	0.739598i	$0.264984\pi$
$602$		0			0
$603$	7.00000			0.285062
$604$	−8.00000	+	13.8564i	−0.325515	+	0.563809i
$605$	12.5000	+	21.6506i	0.508197	+	0.880223i
$606$	−10.0000	−	17.3205i	−0.406222	−	0.703598i
$607$	17.5000	−	30.3109i	0.710303	−	1.23028i	−0.254440	−	0.967088i	$-0.581891\pi$
$607$	17.5000	−	30.3109i	0.710303	−	1.23028i	0.964743	−	0.263193i	$-0.0847754\pi$
$608$	−8.00000			−0.324443
$609$		0			0
$610$	28.0000			1.13369
$611$	3.00000	−	5.19615i	0.121367	−	0.210214i
$612$	−4.00000	−	6.92820i	−0.161690	−	0.280056i
$613$	15.0000	+	25.9808i	0.605844	+	1.04935i	0.991917	+	0.126885i	$0.0404979\pi$
$613$	15.0000	+	25.9808i	0.605844	+	1.04935i	−0.386073	+	0.922468i	$0.626169\pi$
$614$	−3.00000	+	5.19615i	−0.121070	+	0.209700i
$615$	6.00000			0.241943
$616$		0			0
$617$	18.0000			0.724653			0.362326	−	0.932051i	$-0.381983\pi$
$617$	18.0000			0.724653			0.362326	+	0.932051i	$0.381983\pi$
$618$	−19.0000	+	32.9090i	−0.764292	+	1.32379i
$619$	1.50000	+	2.59808i	0.0602901	+	0.104425i	0.894595	−	0.446878i	$-0.147464\pi$
$619$	1.50000	+	2.59808i	0.0602901	+	0.104425i	−0.834305	+	0.551303i	$0.814131\pi$
$620$	−1.00000	−	1.73205i	−0.0401610	−	0.0695608i
$621$	−2.00000	+	3.46410i	−0.0802572	+	0.139010i
$622$	12.0000			0.481156
$623$		0			0
$624$	12.0000			0.480384
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−11.0000	−	19.0526i	−0.439648	−	0.761493i
$627$	3.00000	+	5.19615i	0.119808	+	0.207514i
$628$	10.0000	−	17.3205i	0.399043	−	0.691164i
$629$	28.0000			1.11643
$630$		0			0
$631$	24.0000			0.955425			0.477712	−	0.878516i	$-0.341466\pi$
$631$	24.0000			0.955425			0.477712	+	0.878516i	$0.341466\pi$
$632$		0			0
$633$	−10.0000	−	17.3205i	−0.397464	−	0.688428i
$634$	20.0000	+	34.6410i	0.794301	+	1.37577i
$635$	2.50000	−	4.33013i	0.0992095	−	0.171836i
$636$	−8.00000			−0.317221
$637$		0			0
$638$	−96.0000			−3.80068
$639$	−3.00000	+	5.19615i	−0.118678	+	0.205557i
$640$		0			0
$641$	−6.00000	−	10.3923i	−0.236986	−	0.410471i	0.722862	−	0.690992i	$-0.242826\pi$
$641$	−6.00000	−	10.3923i	−0.236986	−	0.410471i	−0.959848	+	0.280521i	$0.909493\pi$
$642$	−12.0000	+	20.7846i	−0.473602	+	0.820303i
$643$	−1.00000			−0.0394362			−0.0197181	−	0.999806i	$-0.506277\pi$
$643$	−1.00000			−0.0394362			−0.0197181	+	0.999806i	$0.506277\pi$
$644$		0			0
$645$	1.00000			0.0393750
$646$	−4.00000	+	6.92820i	−0.157378	+	0.272587i
$647$	15.0000	+	25.9808i	0.589711	+	1.02141i	0.994270	+	0.106897i	$0.0340916\pi$
$647$	15.0000	+	25.9808i	0.589711	+	1.02141i	−0.404559	+	0.914512i	$0.632575\pi$
$648$		0			0
$649$	24.0000	−	41.5692i	0.942082	−	1.63173i
$650$	−6.00000			−0.235339
$651$		0			0
$652$	−24.0000			−0.939913
$653$	−7.00000	+	12.1244i	−0.273931	+	0.474463i	−0.969865	−	0.243643i	$-0.921657\pi$
$653$	−7.00000	+	12.1244i	−0.273931	+	0.474463i	0.695934	+	0.718106i	$0.254991\pi$
$654$	15.0000	+	25.9808i	0.586546	+	1.01593i
$655$	−1.00000	−	1.73205i	−0.0390732	−	0.0676768i
$656$	12.0000	−	20.7846i	0.468521	−	0.811503i
$657$	−1.00000			−0.0390137
$658$		0			0
$659$	−12.0000			−0.467454			−0.233727	−	0.972302i	$-0.575092\pi$
$659$	−12.0000			−0.467454			−0.233727	+	0.972302i	$0.575092\pi$
$660$	6.00000	−	10.3923i	0.233550	−	0.404520i
$661$	11.5000	+	19.9186i	0.447298	+	0.774743i	0.998209	−	0.0598209i	$-0.0190530\pi$
$661$	11.5000	+	19.9186i	0.447298	+	0.774743i	−0.550911	+	0.834564i	$0.685720\pi$
$662$	−9.00000	−	15.5885i	−0.349795	−	0.605863i
$663$	6.00000	−	10.3923i	0.233021	−	0.403604i
$664$		0			0
$665$		0			0
$666$	−14.0000			−0.542489
$667$	−16.0000	+	27.7128i	−0.619522	+	1.07304i
$668$	−10.0000	−	17.3205i	−0.386912	−	0.670151i
$669$	12.0000	+	20.7846i	0.463947	+	0.803579i
$670$	−7.00000	+	12.1244i	−0.270434	+	0.468405i
$671$	−84.0000			−3.24278
$672$		0			0
$673$	−37.0000			−1.42625			−0.713123	−	0.701039i	$-0.752720\pi$
$673$	−37.0000			−1.42625			−0.713123	+	0.701039i	$0.752720\pi$
$674$	25.0000	−	43.3013i	0.962964	−	1.66790i
$675$	0.500000	+	0.866025i	0.0192450	+	0.0333333i
$676$	4.00000	+	6.92820i	0.153846	+	0.266469i
$677$	8.00000	−	13.8564i	0.307465	−	0.532545i	−0.670342	−	0.742052i	$-0.733853\pi$
$677$	8.00000	−	13.8564i	0.307465	−	0.532545i	0.977807	+	0.209507i	$0.0671860\pi$
$678$	−12.0000			−0.460857
$679$		0			0
$680$		0			0
$681$	5.00000	−	8.66025i	0.191600	−	0.331862i
$682$	6.00000	+	10.3923i	0.229752	+	0.397942i
$683$	24.0000	+	41.5692i	0.918334	+	1.59060i	0.801945	+	0.597398i	$0.203799\pi$
$683$	24.0000	+	41.5692i	0.918334	+	1.59060i	0.116390	+	0.993204i	$0.462868\pi$
$684$	1.00000	−	1.73205i	0.0382360	−	0.0662266i
$685$	−8.00000			−0.305664
$686$		0			0
$687$	13.0000			0.495981
$688$	2.00000	−	3.46410i	0.0762493	−	0.132068i
$689$	−6.00000	−	10.3923i	−0.228582	−	0.395915i
$690$	−4.00000	−	6.92820i	−0.152277	−	0.263752i
$691$	13.5000	−	23.3827i	0.513564	−	0.889519i	−0.486312	−	0.873785i	$-0.661658\pi$
$691$	13.5000	−	23.3827i	0.513564	−	0.889519i	0.999876	−	0.0157341i	$-0.00500851\pi$
$692$	−48.0000			−1.82469
$693$		0			0
$694$	−32.0000			−1.21470
$695$	−10.5000	+	18.1865i	−0.398288	+	0.689855i
$696$		0			0
$697$	−12.0000	−	20.7846i	−0.454532	−	0.787273i
$698$	−2.00000	+	3.46410i	−0.0757011	+	0.131118i
$699$	−6.00000			−0.226941
$700$		0			0
$701$	−44.0000			−1.66186			−0.830929	−	0.556379i	$-0.812190\pi$
$701$	−44.0000			−1.66186			−0.830929	+	0.556379i	$0.812190\pi$
$702$	−3.00000	+	5.19615i	−0.113228	+	0.196116i
$703$	3.50000	+	6.06218i	0.132005	+	0.228639i
$704$	−24.0000	−	41.5692i	−0.904534	−	1.56670i
$705$	1.00000	−	1.73205i	0.0376622	−	0.0652328i
$706$	−36.0000			−1.35488
$707$		0			0
$708$	−16.0000			−0.601317
$709$	13.0000	−	22.5167i	0.488225	−	0.845631i	−0.511683	−	0.859174i	$-0.670978\pi$
$709$	13.0000	−	22.5167i	0.488225	−	0.845631i	0.999908	+	0.0135434i	$0.00431112\pi$
$710$	−6.00000	−	10.3923i	−0.225176	−	0.390016i
$711$	0.500000	+	0.866025i	0.0187515	+	0.0324785i
$712$		0			0
$713$	4.00000			0.149801
$714$		0			0
$715$	18.0000			0.673162
$716$	−18.0000	+	31.1769i	−0.672692	+	1.16514i
$717$	7.00000	+	12.1244i	0.261420	+	0.452792i
$718$	−24.0000	−	41.5692i	−0.895672	−	1.55135i
$719$	−17.0000	+	29.4449i	−0.633993	+	1.09811i	0.352735	+	0.935723i	$0.385252\pi$
$719$	−17.0000	+	29.4449i	−0.633993	+	1.09811i	−0.986728	+	0.162385i	$0.948081\pi$
$720$	4.00000			0.149071
$721$		0			0
$722$	36.0000			1.33978
$723$	9.00000	−	15.5885i	0.334714	−	0.579741i
$724$	13.0000	+	22.5167i	0.483141	+	0.836825i
$725$	4.00000	+	6.92820i	0.148556	+	0.257307i
$726$	−25.0000	+	43.3013i	−0.927837	+	1.60706i
$727$	−7.00000			−0.259616			−0.129808	−	0.991539i	$-0.541436\pi$
$727$	−7.00000			−0.259616			−0.129808	+	0.991539i	$0.541436\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$	1.00000	−	1.73205i	0.0370117	−	0.0641061i
$731$	−2.00000	−	3.46410i	−0.0739727	−	0.128124i
$732$	14.0000	+	24.2487i	0.517455	+	0.896258i
$733$	−21.5000	+	37.2391i	−0.794121	+	1.37546i	0.129275	+	0.991609i	$0.458735\pi$
$733$	−21.5000	+	37.2391i	−0.794121	+	1.37546i	−0.923396	+	0.383849i	$0.874598\pi$
$734$	38.0000			1.40261
$735$		0			0
$736$	−32.0000			−1.17954
$737$	21.0000	−	36.3731i	0.773545	−	1.33982i
$738$	6.00000	+	10.3923i	0.220863	+	0.382546i
$739$	−20.5000	−	35.5070i	−0.754105	−	1.30615i	−0.945818	−	0.324697i	$-0.894738\pi$
$739$	−20.5000	−	35.5070i	−0.754105	−	1.30615i	0.191714	−	0.981451i	$-0.438596\pi$
$740$	7.00000	−	12.1244i	0.257325	−	0.445700i
$741$	3.00000			0.110208
$742$		0			0
$743$	6.00000			0.220119			0.110059	−	0.993925i	$-0.464896\pi$
$743$	6.00000			0.220119			0.110059	+	0.993925i	$0.464896\pi$
$744$		0			0
$745$	−2.00000	−	3.46410i	−0.0732743	−	0.126915i
$746$	11.0000	+	19.0526i	0.402739	+	0.697564i
$747$	1.00000	−	1.73205i	0.0365881	−	0.0633724i
$748$	−48.0000			−1.75505
$749$		0			0
$750$	−2.00000			−0.0730297
$751$	−14.5000	+	25.1147i	−0.529113	+	0.916450i	0.470311	+	0.882501i	$0.344142\pi$
$751$	−14.5000	+	25.1147i	−0.529113	+	0.916450i	−0.999424	+	0.0339490i	$0.989192\pi$
$752$	−4.00000	−	6.92820i	−0.145865	−	0.252646i
$753$	−6.00000	−	10.3923i	−0.218652	−	0.378717i
$754$	−24.0000	+	41.5692i	−0.874028	+	1.51386i
$755$	−8.00000			−0.291150
$756$		0			0
$757$	−22.0000			−0.799604			−0.399802	−	0.916602i	$-0.630921\pi$
$757$	−22.0000			−0.799604			−0.399802	+	0.916602i	$0.630921\pi$
$758$	11.0000	−	19.0526i	0.399538	−	0.692020i
$759$	12.0000	+	20.7846i	0.435572	+	0.754434i
$760$		0			0
$761$	−6.00000	+	10.3923i	−0.217500	+	0.376721i	−0.954043	−	0.299670i	$-0.903123\pi$
$761$	−6.00000	+	10.3923i	−0.217500	+	0.376721i	0.736543	+	0.676391i	$0.236457\pi$
$762$	10.0000			0.362262
$763$		0			0
$764$	20.0000			0.723575
$765$	2.00000	−	3.46410i	0.0723102	−	0.125245i
$766$	−28.0000	−	48.4974i	−1.01168	−	1.75228i
$767$	−12.0000	−	20.7846i	−0.433295	−	0.750489i
$768$	8.00000	−	13.8564i	0.288675	−	0.500000i
$769$	49.0000			1.76699			0.883493	−	0.468445i	$-0.155186\pi$
$769$	49.0000			1.76699			0.883493	+	0.468445i	$0.155186\pi$
$770$		0			0
$771$	−18.0000			−0.648254
$772$	9.00000	−	15.5885i	0.323917	−	0.561041i
$773$	9.00000	+	15.5885i	0.323708	+	0.560678i	0.981250	−	0.192740i	$-0.0617373\pi$
$773$	9.00000	+	15.5885i	0.323708	+	0.560678i	−0.657542	+	0.753418i	$0.728404\pi$
$774$	1.00000	+	1.73205i	0.0359443	+	0.0622573i
$775$	0.500000	−	0.866025i	0.0179605	−	0.0311086i
$776$		0			0
$777$		0			0
$778$	−12.0000			−0.430221
$779$	3.00000	−	5.19615i	0.107486	−	0.186171i
$780$	−3.00000	−	5.19615i	−0.107417	−	0.186052i
$781$	18.0000	+	31.1769i	0.644091	+	1.11560i
$782$	−16.0000	+	27.7128i	−0.572159	+	0.991008i
$783$	8.00000			0.285897
$784$		0			0
$785$	10.0000			0.356915
$786$	2.00000	−	3.46410i	0.0713376	−	0.123560i
$787$	−16.0000	−	27.7128i	−0.570338	−	0.987855i	−0.996531	−	0.0832226i	$-0.973479\pi$
$787$	−16.0000	−	27.7128i	−0.570338	−	0.987855i	0.426193	−	0.904632i	$-0.359855\pi$
$788$	−12.0000	−	20.7846i	−0.427482	−	0.740421i
$789$	2.00000	−	3.46410i	0.0712019	−	0.123325i
$790$	−2.00000			−0.0711568
$791$		0			0
$792$		0			0
$793$	−21.0000	+	36.3731i	−0.745732	+	1.29165i
$794$	37.0000	+	64.0859i	1.31308	+	2.27432i
$795$	−2.00000	−	3.46410i	−0.0709327	−	0.122859i
$796$	8.00000	−	13.8564i	0.283552	−	0.491127i
$797$	36.0000			1.27519			0.637593	−	0.770374i	$-0.279930\pi$
$797$	36.0000			1.27519			0.637593	+	0.770374i	$0.279930\pi$
$798$		0			0
$799$	−8.00000			−0.283020
$800$	−4.00000	+	6.92820i	−0.141421	+	0.244949i
$801$	−6.00000	−	10.3923i	−0.212000	−	0.367194i
$802$	−12.0000	−	20.7846i	−0.423735	−	0.733930i
$803$	−3.00000	+	5.19615i	−0.105868	+	0.183368i
$804$	−14.0000			−0.493742
$805$		0			0
$806$	6.00000			0.211341
$807$	5.00000	−	8.66025i	0.176008	−	0.304855i
$808$		0			0
$809$	21.0000	+	36.3731i	0.738321	+	1.27881i	0.953251	+	0.302180i	$0.0977142\pi$
$809$	21.0000	+	36.3731i	0.738321	+	1.27881i	−0.214930	+	0.976629i	$0.568952\pi$
$810$	−1.00000	+	1.73205i	−0.0351364	+	0.0608581i
$811$	48.0000			1.68551			0.842754	−	0.538299i	$-0.180933\pi$
$811$	48.0000			1.68551			0.842754	+	0.538299i	$0.180933\pi$
$812$		0			0
$813$	−24.0000			−0.841717
$814$	−42.0000	+	72.7461i	−1.47210	+	2.54975i
$815$	−6.00000	−	10.3923i	−0.210171	−	0.364027i
$816$	−8.00000	−	13.8564i	−0.280056	−	0.485071i
$817$	0.500000	−	0.866025i	0.0174928	−	0.0302984i
$818$	10.0000			0.349642
$819$		0			0
$820$	−12.0000			−0.419058
$821$	−27.0000	+	46.7654i	−0.942306	+	1.63212i	−0.181250	+	0.983437i	$0.558014\pi$
$821$	−27.0000	+	46.7654i	−0.942306	+	1.63212i	−0.761056	+	0.648686i	$0.775319\pi$
$822$	−8.00000	−	13.8564i	−0.279032	−	0.483298i
$823$	−4.00000	−	6.92820i	−0.139431	−	0.241502i	0.787850	−	0.615867i	$-0.211194\pi$
$823$	−4.00000	−	6.92820i	−0.139431	−	0.241502i	−0.927281	+	0.374365i	$0.877861\pi$
$824$		0			0
$825$	6.00000			0.208893
$826$		0			0
$827$	−30.0000			−1.04320			−0.521601	−	0.853189i	$-0.674665\pi$
$827$	−30.0000			−1.04320			−0.521601	+	0.853189i	$0.674665\pi$
$828$	4.00000	−	6.92820i	0.139010	−	0.240772i
$829$	28.5000	+	49.3634i	0.989846	+	1.71446i	0.618024	+	0.786159i	$0.287934\pi$
$829$	28.5000	+	49.3634i	0.989846	+	1.71446i	0.371822	+	0.928304i	$0.378733\pi$
$830$	2.00000	+	3.46410i	0.0694210	+	0.120241i
$831$	−3.50000	+	6.06218i	−0.121414	+	0.210295i
$832$	−24.0000			−0.832050
$833$		0			0
$834$	−42.0000			−1.45434
$835$	5.00000	−	8.66025i	0.173032	−	0.299700i
$836$	−6.00000	−	10.3923i	−0.207514	−	0.359425i
$837$	−0.500000	−	0.866025i	−0.0172825	−	0.0299342i
$838$	−6.00000	+	10.3923i	−0.207267	+	0.358996i
$839$	−24.0000			−0.828572			−0.414286	−	0.910147i	$-0.635969\pi$
$839$	−24.0000			−0.828572			−0.414286	+	0.910147i	$0.635969\pi$
$840$		0			0
$841$	35.0000			1.20690
$842$	1.00000	−	1.73205i	0.0344623	−	0.0596904i
$843$	−6.00000	−	10.3923i	−0.206651	−	0.357930i
$844$	20.0000	+	34.6410i	0.688428	+	1.19239i
$845$	−2.00000	+	3.46410i	−0.0688021	+	0.119169i
$846$	4.00000			0.137523
$847$		0			0
$848$	−16.0000			−0.549442
$849$	3.50000	−	6.06218i	0.120120	−	0.208053i
$850$	4.00000	+	6.92820i	0.137199	+	0.237635i
$851$	14.0000	+	24.2487i	0.479914	+	0.831235i
$852$	6.00000	−	10.3923i	0.205557	−	0.356034i
$853$	9.00000			0.308154			0.154077	−	0.988059i	$-0.450760\pi$
$853$	9.00000			0.308154			0.154077	+	0.988059i	$0.450760\pi$
$854$		0			0
$855$	1.00000			0.0341993
$856$		0			0
$857$	−6.00000	−	10.3923i	−0.204956	−	0.354994i	0.745163	−	0.666883i	$-0.232372\pi$
$857$	−6.00000	−	10.3923i	−0.204956	−	0.354994i	−0.950119	+	0.311888i	$0.899038\pi$
$858$	18.0000	+	31.1769i	0.614510	+	1.06436i
$859$	−20.0000	+	34.6410i	−0.682391	+	1.18194i	0.291858	+	0.956462i	$0.405727\pi$
$859$	−20.0000	+	34.6410i	−0.682391	+	1.18194i	−0.974249	+	0.225475i	$0.927607\pi$
$860$	−2.00000			−0.0681994
$861$		0			0
$862$	4.00000			0.136241
$863$	3.00000	−	5.19615i	0.102121	−	0.176879i	−0.810437	−	0.585826i	$-0.800770\pi$
$863$	3.00000	−	5.19615i	0.102121	−	0.176879i	0.912558	+	0.408946i	$0.134104\pi$
$864$	4.00000	+	6.92820i	0.136083	+	0.235702i
$865$	−12.0000	−	20.7846i	−0.408012	−	0.706698i
$866$	5.00000	−	8.66025i	0.169907	−	0.294287i
$867$	1.00000			0.0339618
$868$		0			0
$869$	6.00000			0.203536
$870$	−8.00000	+	13.8564i	−0.271225	+	0.469776i
$871$	−10.5000	−	18.1865i	−0.355779	−	0.616227i
$872$		0			0
$873$	−3.00000	+	5.19615i	−0.101535	+	0.175863i
$874$	−8.00000			−0.270604
$875$		0			0
$876$	2.00000			0.0675737
$877$	11.0000	−	19.0526i	0.371444	−	0.643359i	−0.618344	−	0.785907i	$-0.712196\pi$
$877$	11.0000	−	19.0526i	0.371444	−	0.643359i	0.989788	+	0.142548i	$0.0455296\pi$
$878$	−16.0000	−	27.7128i	−0.539974	−	0.935262i
$879$	8.00000	+	13.8564i	0.269833	+	0.467365i
$880$	12.0000	−	20.7846i	0.404520	−	0.700649i
$881$		0			0			−	1.00000i	$-0.5\pi$
$881$		0			0				1.00000i	$0.5\pi$
$882$		0			0
$883$	7.00000			0.235569			0.117784	−	0.993039i	$-0.462421\pi$
$883$	7.00000			0.235569			0.117784	+	0.993039i	$0.462421\pi$
$884$	−12.0000	+	20.7846i	−0.403604	+	0.699062i
$885$	−4.00000	−	6.92820i	−0.134459	−	0.232889i
$886$	−36.0000	−	62.3538i	−1.20944	−	2.09482i
$887$	5.00000	−	8.66025i	0.167884	−	0.290783i	−0.769792	−	0.638295i	$-0.779640\pi$
$887$	5.00000	−	8.66025i	0.167884	−	0.290783i	0.937676	+	0.347512i	$0.112973\pi$
$888$		0			0
$889$		0			0
$890$	24.0000			0.804482
$891$	3.00000	−	5.19615i	0.100504	−	0.174078i
$892$	−24.0000	−	41.5692i	−0.803579	−	1.39184i
$893$	−1.00000	−	1.73205i	−0.0334637	−	0.0579609i
$894$	4.00000	−	6.92820i	0.133780	−	0.231714i
$895$	−18.0000			−0.601674
$896$		0			0
$897$	12.0000			0.400668
$898$	30.0000	−	51.9615i	1.00111	−	1.73398i
$899$	−4.00000	−	6.92820i	−0.133407	−	0.231069i
$900$	−1.00000	−	1.73205i	−0.0333333	−	0.0577350i
$901$	−8.00000	+	13.8564i	−0.266519	+	0.461624i
$902$	72.0000			2.39734
$903$		0			0
$904$		0			0
$905$	−6.50000	+	11.2583i	−0.216067	+	0.374240i
$906$	−8.00000	−	13.8564i	−0.265782	−	0.460348i
$907$	−15.5000	−	26.8468i	−0.514669	−	0.891433i	−0.999855	−	0.0170220i	$-0.994581\pi$
$907$	−15.5000	−	26.8468i	−0.514669	−	0.891433i	0.485186	−	0.874411i	$-0.338752\pi$
$908$	−10.0000	+	17.3205i	−0.331862	+	0.574801i
$909$	10.0000			0.331679
$910$		0			0
$911$	12.0000			0.397578			0.198789	−	0.980042i	$-0.436299\pi$
$911$	12.0000			0.397578			0.198789	+	0.980042i	$0.436299\pi$
$912$	2.00000	−	3.46410i	0.0662266	−	0.114708i
$913$	−6.00000	−	10.3923i	−0.198571	−	0.343935i
$914$	−15.0000	−	25.9808i	−0.496156	−	0.859367i
$915$	−7.00000	+	12.1244i	−0.231413	+	0.400819i
$916$	−26.0000			−0.859064
$917$		0			0
$918$	8.00000			0.264039
$919$	4.50000	−	7.79423i	0.148441	−	0.257108i	−0.782210	−	0.623015i	$-0.785908\pi$
$919$	4.50000	−	7.79423i	0.148441	−	0.257108i	0.930652	+	0.365907i	$0.119241\pi$
$920$		0			0
$921$	−1.50000	−	2.59808i	−0.0494267	−	0.0856095i
$922$	8.00000	−	13.8564i	0.263466	−	0.456336i
$923$	18.0000			0.592477
$924$		0			0
$925$	7.00000			0.230159
$926$	3.00000	−	5.19615i	0.0985861	−	0.170756i
$927$	−9.50000	−	16.4545i	−0.312021	−	0.540436i
$928$	32.0000	+	55.4256i	1.05045	+	1.81944i
$929$	−7.00000	+	12.1244i	−0.229663	+	0.397787i	−0.957708	−	0.287742i	$-0.907096\pi$
$929$	−7.00000	+	12.1244i	−0.229663	+	0.397787i	0.728046	+	0.685529i	$0.240429\pi$
$930$	2.00000			0.0655826
$931$		0			0
$932$	12.0000			0.393073
$933$	−3.00000	+	5.19615i	−0.0982156	+	0.170114i
$934$	−22.0000	−	38.1051i	−0.719862	−	1.24684i
$935$	−12.0000	−	20.7846i	−0.392442	−	0.679729i
$936$		0			0
$937$	29.0000			0.947389			0.473694	−	0.880689i	$-0.342920\pi$
$937$	29.0000			0.947389			0.473694	+	0.880689i	$0.342920\pi$
$938$		0			0
$939$	11.0000			0.358971
$940$	−2.00000	+	3.46410i	−0.0652328	+	0.112987i
$941$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$941$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$942$	10.0000	+	17.3205i	0.325818	+	0.564333i
$943$	12.0000	−	20.7846i	0.390774	−	0.676840i
$944$	−32.0000			−1.04151
$945$		0			0
$946$	12.0000			0.390154
$947$	−13.0000	+	22.5167i	−0.422443	+	0.731693i	−0.996178	−	0.0873481i	$-0.972161\pi$
$947$	−13.0000	+	22.5167i	−0.422443	+	0.731693i	0.573735	+	0.819041i	$0.305494\pi$
$948$	−1.00000	−	1.73205i	−0.0324785	−	0.0562544i
$949$	1.50000	+	2.59808i	0.0486921	+	0.0843371i
$950$	−1.00000	+	1.73205i	−0.0324443	+	0.0561951i
$951$	−20.0000			−0.648544
$952$		0			0
$953$	4.00000			0.129573			0.0647864	−	0.997899i	$-0.479363\pi$
$953$	4.00000			0.129573			0.0647864	+	0.997899i	$0.479363\pi$
$954$	4.00000	−	6.92820i	0.129505	−	0.224309i
$955$	5.00000	+	8.66025i	0.161796	+	0.280239i
$956$	−14.0000	−	24.2487i	−0.452792	−	0.784259i
$957$	24.0000	−	41.5692i	0.775810	−	1.34374i
$958$	−8.00000			−0.258468
$959$		0			0
$960$	−8.00000			−0.258199
$961$	15.0000	−	25.9808i	0.483871	−	0.838089i
$962$	21.0000	+	36.3731i	0.677067	+	1.17271i
$963$	−6.00000	−	10.3923i	−0.193347	−	0.334887i
$964$	−18.0000	+	31.1769i	−0.579741	+	1.00414i
$965$	9.00000			0.289720
$966$		0			0
$967$	55.0000			1.76868			0.884340	−	0.466843i	$-0.154609\pi$
$967$	55.0000			1.76868			0.884340	+	0.466843i	$0.154609\pi$
$968$		0			0
$969$	−2.00000	−	3.46410i	−0.0642493	−	0.111283i
$970$	−6.00000	−	10.3923i	−0.192648	−	0.333677i
$971$	−26.0000	+	45.0333i	−0.834380	+	1.44519i	0.0601548	+	0.998189i	$0.480841\pi$
$971$	−26.0000	+	45.0333i	−0.834380	+	1.44519i	−0.894534	+	0.446999i	$0.852493\pi$
$972$	−2.00000			−0.0641500
$973$		0			0
$974$	26.0000			0.833094
$975$	1.50000	−	2.59808i	0.0480384	−	0.0832050i
$976$	28.0000	+	48.4974i	0.896258	+	1.55236i
$977$	11.0000	+	19.0526i	0.351921	+	0.609545i	0.986586	−	0.163242i	$-0.0521952\pi$
$977$	11.0000	+	19.0526i	0.351921	+	0.609545i	−0.634665	+	0.772787i	$0.718862\pi$
$978$	12.0000	−	20.7846i	0.383718	−	0.664619i
$979$	−72.0000			−2.30113
$980$		0			0
$981$	−15.0000			−0.478913
$982$	−12.0000	+	20.7846i	−0.382935	+	0.663264i
$983$	16.0000	+	27.7128i	0.510321	+	0.883901i	0.999928	+	0.0119587i	$0.00380665\pi$
$983$	16.0000	+	27.7128i	0.510321	+	0.883901i	−0.489608	+	0.871943i	$0.662860\pi$
$984$		0			0
$985$	6.00000	−	10.3923i	0.191176	−	0.331126i
$986$	64.0000			2.03818
$987$		0			0
$988$	−6.00000			−0.190885
$989$	2.00000	−	3.46410i	0.0635963	−	0.110152i
$990$	6.00000	+	10.3923i	0.190693	+	0.330289i
$991$	7.50000	+	12.9904i	0.238245	+	0.412653i	0.960211	−	0.279276i	$-0.0900944\pi$
$991$	7.50000	+	12.9904i	0.238245	+	0.412653i	−0.721966	+	0.691929i	$0.756761\pi$
$992$	4.00000	−	6.92820i	0.127000	−	0.219971i
$993$	9.00000			0.285606
$994$		0			0
$995$	8.00000			0.253617
$996$	−2.00000	+	3.46410i	−0.0633724	+	0.109764i
$997$	−12.5000	−	21.6506i	−0.395879	−	0.685682i	0.597334	−	0.801993i	$-0.296227\pi$
$997$	−12.5000	−	21.6506i	−0.395879	−	0.685682i	−0.993213	+	0.116310i	$0.962893\pi$
$998$	29.0000	+	50.2295i	0.917979	+	1.58999i
$999$	3.50000	−	6.06218i	0.110735	−	0.191799i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	735.2.i.f.226.1		2
7.2	even	3		735.2.a.a.1.1		1
7.3	odd	6		105.2.i.b.46.1	yes	2
7.4	even	3	inner	735.2.i.f.361.1		2
7.5	odd	6		735.2.a.b.1.1		1
7.6	odd	2		105.2.i.b.16.1	✓	2
21.2	odd	6		2205.2.a.m.1.1		1
21.5	even	6		2205.2.a.k.1.1		1
21.17	even	6		315.2.j.a.46.1		2
21.20	even	2		315.2.j.a.226.1		2
28.3	even	6		1680.2.bg.l.1201.1		2
28.27	even	2		1680.2.bg.l.961.1		2
35.3	even	12		525.2.r.d.424.2		4
35.9	even	6		3675.2.a.p.1.1		1
35.13	even	4		525.2.r.d.499.1		4
35.17	even	12		525.2.r.d.424.1		4
35.19	odd	6		3675.2.a.o.1.1		1
35.24	odd	6		525.2.i.a.151.1		2
35.27	even	4		525.2.r.d.499.2		4
35.34	odd	2		525.2.i.a.226.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.i.b.16.1	✓	2	7.6	odd	2
105.2.i.b.46.1	yes	2	7.3	odd	6
315.2.j.a.46.1		2	21.17	even	6
315.2.j.a.226.1		2	21.20	even	2
525.2.i.a.151.1		2	35.24	odd	6
525.2.i.a.226.1		2	35.34	odd	2
525.2.r.d.424.1		4	35.17	even	12
525.2.r.d.424.2		4	35.3	even	12
525.2.r.d.499.1		4	35.13	even	4
525.2.r.d.499.2		4	35.27	even	4
735.2.a.a.1.1		1	7.2	even	3
735.2.a.b.1.1		1	7.5	odd	6
735.2.i.f.226.1		2	1.1	even	1	trivial
735.2.i.f.361.1		2	7.4	even	3	inner
1680.2.bg.l.961.1		2	28.27	even	2
1680.2.bg.l.1201.1		2	28.3	even	6
2205.2.a.k.1.1		1	21.5	even	6
2205.2.a.m.1.1		1	21.2	odd	6
3675.2.a.o.1.1		1	35.19	odd	6
3675.2.a.p.1.1		1	35.9	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)

\(f(q)\)	\(=\)	\(q+(1.00000 - 1.73205i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-1.00000 - 1.73205i) q^{4} +(0.500000 - 0.866025i) q^{5} +2.00000 q^{6} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(1.00000 - 1.73205i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-1.00000 - 1.73205i) q^{4} +(0.500000 - 0.866025i) q^{5} +2.00000 q^{6} +(-0.500000 + 0.866025i) q^{9} +(-1.00000 - 1.73205i) q^{10} +(3.00000 + 5.19615i) q^{11} +(1.00000 - 1.73205i) q^{12} +3.00000 q^{13} +1.00000 q^{15} +(2.00000 - 3.46410i) q^{16} +(-2.00000 - 3.46410i) q^{17} +(1.00000 + 1.73205i) q^{18} +(0.500000 - 0.866025i) q^{19} -2.00000 q^{20} +12.0000 q^{22} +(2.00000 - 3.46410i) q^{23} +(-0.500000 - 0.866025i) q^{25} +(3.00000 - 5.19615i) q^{26} -1.00000 q^{27} -8.00000 q^{29} +(1.00000 - 1.73205i) q^{30} +(0.500000 + 0.866025i) q^{31} +(-4.00000 - 6.92820i) q^{32} +(-3.00000 + 5.19615i) q^{33} -8.00000 q^{34} +2.00000 q^{36} +(-3.50000 + 6.06218i) q^{37} +(-1.00000 - 1.73205i) q^{38} +(1.50000 + 2.59808i) q^{39} +6.00000 q^{41} +1.00000 q^{43} +(6.00000 - 10.3923i) q^{44} +(0.500000 + 0.866025i) q^{45} +(-4.00000 - 6.92820i) q^{46} +(1.00000 - 1.73205i) q^{47} +4.00000 q^{48} -2.00000 q^{50} +(2.00000 - 3.46410i) q^{51} +(-3.00000 - 5.19615i) q^{52} +(-2.00000 - 3.46410i) q^{53} +(-1.00000 + 1.73205i) q^{54} +6.00000 q^{55} +1.00000 q^{57} +(-8.00000 + 13.8564i) q^{58} +(-4.00000 - 6.92820i) q^{59} +(-1.00000 - 1.73205i) q^{60} +(-7.00000 + 12.1244i) q^{61} +2.00000 q^{62} -8.00000 q^{64} +(1.50000 - 2.59808i) q^{65} +(6.00000 + 10.3923i) q^{66} +(-3.50000 - 6.06218i) q^{67} +(-4.00000 + 6.92820i) q^{68} +4.00000 q^{69} +6.00000 q^{71} +(0.500000 + 0.866025i) q^{73} +(7.00000 + 12.1244i) q^{74} +(0.500000 - 0.866025i) q^{75} -2.00000 q^{76} +6.00000 q^{78} +(0.500000 - 0.866025i) q^{79} +(-2.00000 - 3.46410i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(6.00000 - 10.3923i) q^{82} -2.00000 q^{83} -4.00000 q^{85} +(1.00000 - 1.73205i) q^{86} +(-4.00000 - 6.92820i) q^{87} +(-6.00000 + 10.3923i) q^{89} +2.00000 q^{90} -8.00000 q^{92} +(-0.500000 + 0.866025i) q^{93} +(-2.00000 - 3.46410i) q^{94} +(-0.500000 - 0.866025i) q^{95} +(4.00000 - 6.92820i) q^{96} +6.00000 q^{97} -6.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} + q^{3} - 2 q^{4} + q^{5} + 4 q^{6} - q^{9}+O(q^{10}) \) 2 * q + 2 * q^2 + q^3 - 2 * q^4 + q^5 + 4 * q^6 - q^9	\( 2 q + 2 q^{2} + q^{3} - 2 q^{4} + q^{5} + 4 q^{6} - q^{9} - 2 q^{10} + 6 q^{11} + 2 q^{12} + 6 q^{13} + 2 q^{15} + 4 q^{16} - 4 q^{17} + 2 q^{18} + q^{19} - 4 q^{20} + 24 q^{22} + 4 q^{23} - q^{25} + 6 q^{26} - 2 q^{27} - 16 q^{29} + 2 q^{30} + q^{31} - 8 q^{32} - 6 q^{33} - 16 q^{34} + 4 q^{36} - 7 q^{37} - 2 q^{38} + 3 q^{39} + 12 q^{41} + 2 q^{43} + 12 q^{44} + q^{45} - 8 q^{46} + 2 q^{47} + 8 q^{48} - 4 q^{50} + 4 q^{51} - 6 q^{52} - 4 q^{53} - 2 q^{54} + 12 q^{55} + 2 q^{57} - 16 q^{58} - 8 q^{59} - 2 q^{60} - 14 q^{61} + 4 q^{62} - 16 q^{64} + 3 q^{65} + 12 q^{66} - 7 q^{67} - 8 q^{68} + 8 q^{69} + 12 q^{71} + q^{73} + 14 q^{74} + q^{75} - 4 q^{76} + 12 q^{78} + q^{79} - 4 q^{80} - q^{81} + 12 q^{82} - 4 q^{83} - 8 q^{85} + 2 q^{86} - 8 q^{87} - 12 q^{89} + 4 q^{90} - 16 q^{92} - q^{93} - 4 q^{94} - q^{95} + 8 q^{96} + 12 q^{97} - 12 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 + q^3 - 2 * q^4 + q^5 + 4 * q^6 - q^9 - 2 * q^10 + 6 * q^11 + 2 * q^12 + 6 * q^13 + 2 * q^15 + 4 * q^16 - 4 * q^17 + 2 * q^18 + q^19 - 4 * q^20 + 24 * q^22 + 4 * q^23 - q^25 + 6 * q^26 - 2 * q^27 - 16 * q^29 + 2 * q^30 + q^31 - 8 * q^32 - 6 * q^33 - 16 * q^34 + 4 * q^36 - 7 * q^37 - 2 * q^38 + 3 * q^39 + 12 * q^41 + 2 * q^43 + 12 * q^44 + q^45 - 8 * q^46 + 2 * q^47 + 8 * q^48 - 4 * q^50 + 4 * q^51 - 6 * q^52 - 4 * q^53 - 2 * q^54 + 12 * q^55 + 2 * q^57 - 16 * q^58 - 8 * q^59 - 2 * q^60 - 14 * q^61 + 4 * q^62 - 16 * q^64 + 3 * q^65 + 12 * q^66 - 7 * q^67 - 8 * q^68 + 8 * q^69 + 12 * q^71 + q^73 + 14 * q^74 + q^75 - 4 * q^76 + 12 * q^78 + q^79 - 4 * q^80 - q^81 + 12 * q^82 - 4 * q^83 - 8 * q^85 + 2 * q^86 - 8 * q^87 - 12 * q^89 + 4 * q^90 - 16 * q^92 - q^93 - 4 * q^94 - q^95 + 8 * q^96 + 12 * q^97 - 12 * q^99

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