LMFDB - Embedded newform 930.2.o.a.491.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(161,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 5]))

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

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

chi := DirichletCharacter("930.161");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.o (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			491.1
Root			$-0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	930.491
Dual form			930.2.o.a.161.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +(-1.50000 - 0.866025i) q^{3} -1.00000 q^{4} +(-0.866025 + 0.500000i) q^{5} +(-0.866025 + 1.50000i) q^{6} +(2.00000 - 3.46410i) q^{7} +1.00000i q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +(-1.50000 - 0.866025i) q^{3} -1.00000 q^{4} +(-0.866025 + 0.500000i) q^{5} +(-0.866025 + 1.50000i) q^{6} +(2.00000 - 3.46410i) q^{7} +1.00000i q^{8} +(1.50000 + 2.59808i) q^{9} +(0.500000 + 0.866025i) q^{10} +(2.59808 + 4.50000i) q^{11} +(1.50000 + 0.866025i) q^{12} +(-3.46410 - 2.00000i) q^{14} +1.73205 q^{15} +1.00000 q^{16} +(2.59808 - 4.50000i) q^{17} +(2.59808 - 1.50000i) q^{18} +(1.00000 - 1.73205i) q^{19} +(0.866025 - 0.500000i) q^{20} +(-6.00000 + 3.46410i) q^{21} +(4.50000 - 2.59808i) q^{22} +5.19615 q^{23} +(0.866025 - 1.50000i) q^{24} +(0.500000 - 0.866025i) q^{25} -5.19615i q^{27} +(-2.00000 + 3.46410i) q^{28} -1.73205i q^{30} +(2.00000 + 5.19615i) q^{31} -1.00000i q^{32} -9.00000i q^{33} +(-4.50000 - 2.59808i) q^{34} +4.00000i q^{35} +(-1.50000 - 2.59808i) q^{36} +(-4.50000 - 2.59808i) q^{37} +(-1.73205 - 1.00000i) q^{38} +(-0.500000 - 0.866025i) q^{40} +(5.19615 - 3.00000i) q^{41} +(3.46410 + 6.00000i) q^{42} +(-7.50000 - 4.33013i) q^{43} +(-2.59808 - 4.50000i) q^{44} +(-2.59808 - 1.50000i) q^{45} -5.19615i q^{46} +9.00000i q^{47} +(-1.50000 - 0.866025i) q^{48} +(-4.50000 - 7.79423i) q^{49} +(-0.866025 - 0.500000i) q^{50} +(-7.79423 + 4.50000i) q^{51} -5.19615 q^{54} +(-4.50000 - 2.59808i) q^{55} +(3.46410 + 2.00000i) q^{56} +(-3.00000 + 1.73205i) q^{57} +(-10.3923 - 6.00000i) q^{59} -1.73205 q^{60} -13.8564i q^{61} +(5.19615 - 2.00000i) q^{62} +12.0000 q^{63} -1.00000 q^{64} -9.00000 q^{66} +(-3.50000 - 6.06218i) q^{67} +(-2.59808 + 4.50000i) q^{68} +(-7.79423 - 4.50000i) q^{69} +4.00000 q^{70} +(5.19615 - 3.00000i) q^{71} +(-2.59808 + 1.50000i) q^{72} +(12.0000 - 6.92820i) q^{73} +(-2.59808 + 4.50000i) q^{74} +(-1.50000 + 0.866025i) q^{75} +(-1.00000 + 1.73205i) q^{76} +20.7846 q^{77} +(-1.50000 - 0.866025i) q^{79} +(-0.866025 + 0.500000i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(-3.00000 - 5.19615i) q^{82} +(6.00000 - 3.46410i) q^{84} +5.19615i q^{85} +(-4.33013 + 7.50000i) q^{86} +(-4.50000 + 2.59808i) q^{88} +10.3923 q^{89} +(-1.50000 + 2.59808i) q^{90} -5.19615 q^{92} +(1.50000 - 9.52628i) q^{93} +9.00000 q^{94} +2.00000i q^{95} +(-0.866025 + 1.50000i) q^{96} -4.00000 q^{97} +(-7.79423 + 4.50000i) q^{98} +(-7.79423 + 13.5000i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 6 q^{3} - 4 q^{4} + 8 q^{7} + 6 q^{9}+O(q^{10}) $ 4 * q - 6 * q^3 - 4 * q^4 + 8 * q^7 + 6 * q^9	$ 4 q - 6 q^{3} - 4 q^{4} + 8 q^{7} + 6 q^{9} + 2 q^{10} + 6 q^{12} + 4 q^{16} + 4 q^{19} - 24 q^{21} + 18 q^{22} + 2 q^{25} - 8 q^{28} + 8 q^{31} - 18 q^{34} - 6 q^{36} - 18 q^{37} - 2 q^{40} - 30 q^{43} - 6 q^{48} - 18 q^{49} - 18 q^{55} - 12 q^{57} + 48 q^{63} - 4 q^{64} - 36 q^{66} - 14 q^{67} + 16 q^{70} + 48 q^{73} - 6 q^{75} - 4 q^{76} - 6 q^{79} - 18 q^{81} - 12 q^{82} + 24 q^{84} - 18 q^{88} - 6 q^{90} + 6 q^{93} + 36 q^{94} - 16 q^{97}+O(q^{100}) $ 4 * q - 6 * q^3 - 4 * q^4 + 8 * q^7 + 6 * q^9 + 2 * q^10 + 6 * q^12 + 4 * q^16 + 4 * q^19 - 24 * q^21 + 18 * q^22 + 2 * q^25 - 8 * q^28 + 8 * q^31 - 18 * q^34 - 6 * q^36 - 18 * q^37 - 2 * q^40 - 30 * q^43 - 6 * q^48 - 18 * q^49 - 18 * q^55 - 12 * q^57 + 48 * q^63 - 4 * q^64 - 36 * q^66 - 14 * q^67 + 16 * q^70 + 48 * q^73 - 6 * q^75 - 4 * q^76 - 6 * q^79 - 18 * q^81 - 12 * q^82 + 24 * q^84 - 18 * q^88 - 6 * q^90 + 6 * q^93 + 36 * q^94 - 16 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$	−1.50000	−	0.866025i	−0.866025	−	0.500000i
$3$	−1.50000	−	0.866025i	−0.866025	−	0.500000i
$4$	−1.00000			−0.500000
$5$	−0.866025	+	0.500000i	−0.387298	+	0.223607i
$5$	−0.866025	+	0.500000i	−0.387298	+	0.223607i
$6$	−0.866025	+	1.50000i	−0.353553	+	0.612372i
$7$	2.00000	−	3.46410i	0.755929	−	1.30931i	−0.188982	−	0.981981i	$-0.560519\pi$
$7$	2.00000	−	3.46410i	0.755929	−	1.30931i	0.944911	−	0.327327i	$-0.106148\pi$
$8$			1.00000i			0.353553i
$9$	1.50000	+	2.59808i	0.500000	+	0.866025i
$10$	0.500000	+	0.866025i	0.158114	+	0.273861i
$11$	2.59808	+	4.50000i	0.783349	+	1.35680i	0.929980	+	0.367610i	$0.119824\pi$
$11$	2.59808	+	4.50000i	0.783349	+	1.35680i	−0.146631	+	0.989191i	$0.546843\pi$
$12$	1.50000	+	0.866025i	0.433013	+	0.250000i
$13$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$13$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$14$	−3.46410	−	2.00000i	−0.925820	−	0.534522i
$15$	1.73205			0.447214
$16$	1.00000			0.250000
$17$	2.59808	−	4.50000i	0.630126	−	1.09141i	−0.357400	−	0.933952i	$-0.616337\pi$
$17$	2.59808	−	4.50000i	0.630126	−	1.09141i	0.987526	−	0.157459i	$-0.0503301\pi$
$18$	2.59808	−	1.50000i	0.612372	−	0.353553i
$19$	1.00000	−	1.73205i	0.229416	−	0.397360i	−0.728219	−	0.685344i	$-0.759652\pi$
$19$	1.00000	−	1.73205i	0.229416	−	0.397360i	0.957635	+	0.287984i	$0.0929851\pi$
$20$	0.866025	−	0.500000i	0.193649	−	0.111803i
$21$	−6.00000	+	3.46410i	−1.30931	+	0.755929i
$22$	4.50000	−	2.59808i	0.959403	−	0.553912i
$23$	5.19615			1.08347			0.541736	−	0.840548i	$-0.317767\pi$
$23$	5.19615			1.08347			0.541736	+	0.840548i	$0.317767\pi$
$24$	0.866025	−	1.50000i	0.176777	−	0.306186i
$25$	0.500000	−	0.866025i	0.100000	−	0.173205i
$26$		0			0
$27$		−	5.19615i		−	1.00000i
$28$	−2.00000	+	3.46410i	−0.377964	+	0.654654i
$29$		0			0			−	1.00000i	$-0.5\pi$
$29$		0			0				1.00000i	$0.5\pi$
$30$		−	1.73205i		−	0.316228i
$31$	2.00000	+	5.19615i	0.359211	+	0.933257i
$31$	2.00000	+	5.19615i	0.359211	+	0.933257i
$32$		−	1.00000i		−	0.176777i
$33$		−	9.00000i		−	1.56670i
$34$	−4.50000	−	2.59808i	−0.771744	−	0.445566i
$35$			4.00000i			0.676123i
$36$	−1.50000	−	2.59808i	−0.250000	−	0.433013i
$37$	−4.50000	−	2.59808i	−0.739795	−	0.427121i	0.0821995	−	0.996616i	$-0.473806\pi$
$37$	−4.50000	−	2.59808i	−0.739795	−	0.427121i	−0.821995	+	0.569495i	$0.807139\pi$
$38$	−1.73205	−	1.00000i	−0.280976	−	0.162221i
$39$		0			0
$40$	−0.500000	−	0.866025i	−0.0790569	−	0.136931i
$41$	5.19615	−	3.00000i	0.811503	−	0.468521i	−0.0359748	−	0.999353i	$-0.511454\pi$
$41$	5.19615	−	3.00000i	0.811503	−	0.468521i	0.847477	+	0.530831i	$0.178120\pi$
$42$	3.46410	+	6.00000i	0.534522	+	0.925820i
$43$	−7.50000	−	4.33013i	−1.14374	−	0.660338i	−0.196385	−	0.980527i	$-0.562920\pi$
$43$	−7.50000	−	4.33013i	−1.14374	−	0.660338i	−0.947354	+	0.320189i	$0.896254\pi$
$44$	−2.59808	−	4.50000i	−0.391675	−	0.678401i
$45$	−2.59808	−	1.50000i	−0.387298	−	0.223607i
$46$		−	5.19615i		−	0.766131i
$47$			9.00000i			1.31278i	0.754420	+	0.656392i	$0.227918\pi$
$47$			9.00000i			1.31278i	−0.754420	+	0.656392i	$0.772082\pi$
$48$	−1.50000	−	0.866025i	−0.216506	−	0.125000i
$49$	−4.50000	−	7.79423i	−0.642857	−	1.11346i
$50$	−0.866025	−	0.500000i	−0.122474	−	0.0707107i
$51$	−7.79423	+	4.50000i	−1.09141	+	0.630126i
$52$		0			0
$53$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$53$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$54$	−5.19615			−0.707107
$55$	−4.50000	−	2.59808i	−0.606780	−	0.350325i
$56$	3.46410	+	2.00000i	0.462910	+	0.267261i
$57$	−3.00000	+	1.73205i	−0.397360	+	0.229416i
$58$		0			0
$59$	−10.3923	−	6.00000i	−1.35296	−	0.781133i	−0.364299	−	0.931282i	$-0.618692\pi$
$59$	−10.3923	−	6.00000i	−1.35296	−	0.781133i	−0.988663	+	0.150148i	$0.952025\pi$
$60$	−1.73205			−0.223607
$61$		−	13.8564i		−	1.77413i	−0.461644	−	0.887066i	$-0.652740\pi$
$61$		−	13.8564i		−	1.77413i	0.461644	−	0.887066i	$-0.347260\pi$
$62$	5.19615	−	2.00000i	0.659912	−	0.254000i
$63$	12.0000			1.51186
$64$	−1.00000			−0.125000
$65$		0			0
$66$	−9.00000			−1.10782
$67$	−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	$0.973972\pi$
$68$	−2.59808	+	4.50000i	−0.315063	+	0.545705i
$69$	−7.79423	−	4.50000i	−0.938315	−	0.541736i
$70$	4.00000			0.478091
$71$	5.19615	−	3.00000i	0.616670	−	0.356034i	−0.158901	−	0.987294i	$-0.550795\pi$
$71$	5.19615	−	3.00000i	0.616670	−	0.356034i	0.775571	+	0.631260i	$0.217462\pi$
$72$	−2.59808	+	1.50000i	−0.306186	+	0.176777i
$73$	12.0000	−	6.92820i	1.40449	−	0.810885i	0.409644	−	0.912245i	$-0.365653\pi$
$73$	12.0000	−	6.92820i	1.40449	−	0.810885i	0.994850	+	0.101361i	$0.0323196\pi$
$74$	−2.59808	+	4.50000i	−0.302020	+	0.523114i
$75$	−1.50000	+	0.866025i	−0.173205	+	0.100000i
$76$	−1.00000	+	1.73205i	−0.114708	+	0.198680i
$77$	20.7846			2.36863
$78$		0			0
$79$	−1.50000	−	0.866025i	−0.168763	−	0.0974355i	0.413239	−	0.910622i	$-0.364397\pi$
$79$	−1.50000	−	0.866025i	−0.168763	−	0.0974355i	−0.582003	+	0.813187i	$0.697731\pi$
$80$	−0.866025	+	0.500000i	−0.0968246	+	0.0559017i
$81$	−4.50000	+	7.79423i	−0.500000	+	0.866025i
$82$	−3.00000	−	5.19615i	−0.331295	−	0.573819i
$83$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$83$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$84$	6.00000	−	3.46410i	0.654654	−	0.377964i
$85$			5.19615i			0.563602i
$86$	−4.33013	+	7.50000i	−0.466930	+	0.808746i
$87$		0			0
$88$	−4.50000	+	2.59808i	−0.479702	+	0.276956i
$89$	10.3923			1.10158			0.550791	−	0.834643i	$-0.314326\pi$
$89$	10.3923			1.10158			0.550791	+	0.834643i	$0.314326\pi$
$90$	−1.50000	+	2.59808i	−0.158114	+	0.273861i
$91$		0			0
$92$	−5.19615			−0.541736
$93$	1.50000	−	9.52628i	0.155543	−	0.987829i
$94$	9.00000			0.928279
$95$			2.00000i			0.205196i
$96$	−0.866025	+	1.50000i	−0.0883883	+	0.153093i
$97$	−4.00000			−0.406138			−0.203069	−	0.979164i	$-0.565092\pi$
$97$	−4.00000			−0.406138			−0.203069	+	0.979164i	$0.565092\pi$
$98$	−7.79423	+	4.50000i	−0.787336	+	0.454569i
$99$	−7.79423	+	13.5000i	−0.783349	+	1.35680i
$100$	−0.500000	+	0.866025i	−0.0500000	+	0.0866025i
$101$		−	3.00000i		−	0.298511i	−0.988799	−	0.149256i	$-0.952312\pi$
$101$		−	3.00000i		−	0.298511i	0.988799	−	0.149256i	$-0.0476877\pi$
$102$	4.50000	+	7.79423i	0.445566	+	0.771744i
$103$	−2.00000	−	3.46410i	−0.197066	−	0.341328i	0.750510	−	0.660859i	$-0.229808\pi$
$103$	−2.00000	−	3.46410i	−0.197066	−	0.341328i	−0.947576	+	0.319531i	$0.896475\pi$
$104$		0			0
$105$	3.46410	−	6.00000i	0.338062	−	0.585540i
$106$		0			0
$107$	5.19615	+	3.00000i	0.502331	+	0.290021i	0.729676	−	0.683793i	$-0.239671\pi$
$107$	5.19615	+	3.00000i	0.502331	+	0.290021i	−0.227345	+	0.973814i	$0.573004\pi$
$108$			5.19615i			0.500000i
$109$	8.00000			0.766261			0.383131	−	0.923694i	$-0.374846\pi$
$109$	8.00000			0.766261			0.383131	+	0.923694i	$0.374846\pi$
$110$	−2.59808	+	4.50000i	−0.247717	+	0.429058i
$111$	4.50000	+	7.79423i	0.427121	+	0.739795i
$112$	2.00000	−	3.46410i	0.188982	−	0.327327i
$113$	−2.59808	+	1.50000i	−0.244406	+	0.141108i	−0.617200	−	0.786806i	$-0.711733\pi$
$113$	−2.59808	+	1.50000i	−0.244406	+	0.141108i	0.372794	+	0.927914i	$0.378400\pi$
$114$	1.73205	+	3.00000i	0.162221	+	0.280976i
$115$	−4.50000	+	2.59808i	−0.419627	+	0.242272i
$116$		0			0
$117$		0			0
$118$	−6.00000	+	10.3923i	−0.552345	+	0.956689i
$119$	−10.3923	−	18.0000i	−0.952661	−	1.65006i
$120$			1.73205i			0.158114i
$121$	−8.00000	+	13.8564i	−0.727273	+	1.25967i
$122$	−13.8564			−1.25450
$123$	−10.3923			−0.937043
$124$	−2.00000	−	5.19615i	−0.179605	−	0.466628i
$125$			1.00000i			0.0894427i
$126$		−	12.0000i		−	1.06904i
$127$	6.00000	+	3.46410i	0.532414	+	0.307389i	0.741999	−	0.670401i	$-0.233878\pi$
$127$	6.00000	+	3.46410i	0.532414	+	0.307389i	−0.209585	+	0.977790i	$0.567211\pi$
$128$			1.00000i			0.0883883i
$129$	7.50000	+	12.9904i	0.660338	+	1.14374i
$130$		0			0
$131$	7.79423	+	4.50000i	0.680985	+	0.393167i	0.800226	−	0.599699i	$-0.204713\pi$
$131$	7.79423	+	4.50000i	0.680985	+	0.393167i	−0.119241	+	0.992865i	$0.538046\pi$
$132$			9.00000i			0.783349i
$133$	−4.00000	−	6.92820i	−0.346844	−	0.600751i
$134$	−6.06218	+	3.50000i	−0.523692	+	0.302354i
$135$	2.59808	+	4.50000i	0.223607	+	0.387298i
$136$	4.50000	+	2.59808i	0.385872	+	0.222783i
$137$	7.79423	+	13.5000i	0.665906	+	1.15338i	0.979039	+	0.203674i	$0.0652881\pi$
$137$	7.79423	+	13.5000i	0.665906	+	1.15338i	−0.313133	+	0.949709i	$0.601379\pi$
$138$	−4.50000	+	7.79423i	−0.383065	+	0.663489i
$139$			13.8564i			1.17529i	0.809121	+	0.587643i	$0.199944\pi$
$139$			13.8564i			1.17529i	−0.809121	+	0.587643i	$0.800056\pi$
$140$		−	4.00000i		−	0.338062i
$141$	7.79423	−	13.5000i	0.656392	−	1.13691i
$142$	−3.00000	−	5.19615i	−0.251754	−	0.436051i
$143$		0			0
$144$	1.50000	+	2.59808i	0.125000	+	0.216506i
$145$		0			0
$146$	−6.92820	−	12.0000i	−0.573382	−	0.993127i
$147$			15.5885i			1.28571i
$148$	4.50000	+	2.59808i	0.369898	+	0.213561i
$149$	−15.5885	−	9.00000i	−1.27706	−	0.737309i	−0.300750	−	0.953703i	$-0.597237\pi$
$149$	−15.5885	−	9.00000i	−1.27706	−	0.737309i	−0.976306	+	0.216394i	$0.930570\pi$
$150$	0.866025	+	1.50000i	0.0707107	+	0.122474i
$151$			12.1244i			0.986666i	0.869841	+	0.493333i	$0.164222\pi$
$151$			12.1244i			0.986666i	−0.869841	+	0.493333i	$0.835778\pi$
$152$	1.73205	+	1.00000i	0.140488	+	0.0811107i
$153$	15.5885			1.26025
$154$		−	20.7846i		−	1.67487i
$155$	−4.33013	−	3.50000i	−0.347804	−	0.281127i
$156$		0			0
$157$	−2.00000			−0.159617			−0.0798087	−	0.996810i	$-0.525431\pi$
$157$	−2.00000			−0.159617			−0.0798087	+	0.996810i	$0.525431\pi$
$158$	−0.866025	+	1.50000i	−0.0688973	+	0.119334i
$159$		0			0
$160$	0.500000	+	0.866025i	0.0395285	+	0.0684653i
$161$	10.3923	−	18.0000i	0.819028	−	1.41860i
$162$	7.79423	+	4.50000i	0.612372	+	0.353553i
$163$	11.0000			0.861586			0.430793	−	0.902451i	$-0.358234\pi$
$163$	11.0000			0.861586			0.430793	+	0.902451i	$0.358234\pi$
$164$	−5.19615	+	3.00000i	−0.405751	+	0.234261i
$165$	4.50000	+	7.79423i	0.350325	+	0.606780i
$166$		0			0
$167$	5.19615	−	9.00000i	0.402090	−	0.696441i	−0.591888	−	0.806020i	$-0.701617\pi$
$167$	5.19615	−	9.00000i	0.402090	−	0.696441i	0.993978	+	0.109580i	$0.0349504\pi$
$168$	−3.46410	−	6.00000i	−0.267261	−	0.462910i
$169$	−6.50000	+	11.2583i	−0.500000	+	0.866025i
$170$	5.19615			0.398527
$171$	6.00000			0.458831
$172$	7.50000	+	4.33013i	0.571870	+	0.330169i
$173$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$173$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$174$		0			0
$175$	−2.00000	−	3.46410i	−0.151186	−	0.261861i
$176$	2.59808	+	4.50000i	0.195837	+	0.339200i
$177$	10.3923	+	18.0000i	0.781133	+	1.35296i
$178$		−	10.3923i		−	0.778936i
$179$	2.59808	−	4.50000i	0.194189	−	0.336346i	−0.752445	−	0.658655i	$-0.771126\pi$
$179$	2.59808	−	4.50000i	0.194189	−	0.336346i	0.946634	+	0.322309i	$0.104459\pi$
$180$	2.59808	+	1.50000i	0.193649	+	0.111803i
$181$	18.0000	−	10.3923i	1.33793	−	0.772454i	0.351429	−	0.936214i	$-0.385696\pi$
$181$	18.0000	−	10.3923i	1.33793	−	0.772454i	0.986500	+	0.163760i	$0.0523624\pi$
$182$		0			0
$183$	−12.0000	+	20.7846i	−0.887066	+	1.53644i
$184$			5.19615i			0.383065i
$185$	5.19615			0.382029
$186$	−9.52628	−	1.50000i	−0.698501	−	0.109985i
$187$	27.0000			1.97444
$188$		−	9.00000i		−	0.656392i
$189$	−18.0000	−	10.3923i	−1.30931	−	0.755929i
$190$	2.00000			0.145095
$191$	−5.19615	+	3.00000i	−0.375980	+	0.217072i	−0.676068	−	0.736839i	$-0.736317\pi$
$191$	−5.19615	+	3.00000i	−0.375980	+	0.217072i	0.300088	+	0.953912i	$0.402984\pi$
$192$	1.50000	+	0.866025i	0.108253	+	0.0625000i
$193$	10.0000	−	17.3205i	0.719816	−	1.24676i	−0.241257	−	0.970461i	$-0.577560\pi$
$193$	10.0000	−	17.3205i	0.719816	−	1.24676i	0.961073	−	0.276296i	$-0.0891071\pi$
$194$			4.00000i			0.287183i
$195$		0			0
$196$	4.50000	+	7.79423i	0.321429	+	0.556731i
$197$	5.19615	+	9.00000i	0.370211	+	0.641223i	0.989598	−	0.143862i	$-0.0459522\pi$
$197$	5.19615	+	9.00000i	0.370211	+	0.641223i	−0.619387	+	0.785086i	$0.712619\pi$
$198$	13.5000	+	7.79423i	0.959403	+	0.553912i
$199$	15.0000	−	8.66025i	1.06332	−	0.613909i	0.136973	−	0.990575i	$-0.456263\pi$
$199$	15.0000	−	8.66025i	1.06332	−	0.613909i	0.926349	+	0.376666i	$0.122929\pi$
$200$	0.866025	+	0.500000i	0.0612372	+	0.0353553i
$201$			12.1244i			0.855186i
$202$	−3.00000			−0.211079
$203$		0			0
$204$	7.79423	−	4.50000i	0.545705	−	0.315063i
$205$	−3.00000	+	5.19615i	−0.209529	+	0.362915i
$206$	−3.46410	+	2.00000i	−0.241355	+	0.139347i
$207$	7.79423	+	13.5000i	0.541736	+	0.938315i
$208$		0			0
$209$	10.3923			0.718851
$210$	−6.00000	−	3.46410i	−0.414039	−	0.239046i
$211$	−1.00000	+	1.73205i	−0.0688428	+	0.119239i	−0.898392	−	0.439194i	$-0.855264\pi$
$211$	−1.00000	+	1.73205i	−0.0688428	+	0.119239i	0.829549	+	0.558433i	$0.188597\pi$
$212$		0			0
$213$	−10.3923			−0.712069
$214$	3.00000	−	5.19615i	0.205076	−	0.355202i
$215$	8.66025			0.590624
$216$	5.19615			0.353553
$217$	22.0000	+	3.46410i	1.49346	+	0.235159i
$218$		−	8.00000i		−	0.541828i
$219$	−24.0000			−1.62177
$220$	4.50000	+	2.59808i	0.303390	+	0.175162i
$221$		0			0
$222$	7.79423	−	4.50000i	0.523114	−	0.302020i
$223$	−15.0000	−	8.66025i	−1.00447	−	0.579934i	−0.0949052	−	0.995486i	$-0.530255\pi$
$223$	−15.0000	−	8.66025i	−1.00447	−	0.579934i	−0.909569	+	0.415553i	$0.863588\pi$
$224$	−3.46410	−	2.00000i	−0.231455	−	0.133631i
$225$	3.00000			0.200000
$226$	1.50000	+	2.59808i	0.0997785	+	0.172821i
$227$	−15.5885	+	9.00000i	−1.03464	+	0.597351i	−0.918311	−	0.395860i	$-0.870447\pi$
$227$	−15.5885	+	9.00000i	−1.03464	+	0.597351i	−0.116331	+	0.993210i	$0.537113\pi$
$228$	3.00000	−	1.73205i	0.198680	−	0.114708i
$229$	15.0000	+	8.66025i	0.991228	+	0.572286i	0.905641	−	0.424045i	$-0.139390\pi$
$229$	15.0000	+	8.66025i	0.991228	+	0.572286i	0.0855868	+	0.996331i	$0.472724\pi$
$230$	2.59808	+	4.50000i	0.171312	+	0.296721i
$231$	−31.1769	−	18.0000i	−2.05129	−	1.18431i
$232$		0			0
$233$			3.00000i			0.196537i	0.995160	+	0.0982683i	$0.0313303\pi$
$233$			3.00000i			0.196537i	−0.995160	+	0.0982683i	$0.968670\pi$
$234$		0			0
$235$	−4.50000	−	7.79423i	−0.293548	−	0.508439i
$236$	10.3923	+	6.00000i	0.676481	+	0.390567i
$237$	1.50000	+	2.59808i	0.0974355	+	0.168763i
$238$	−18.0000	+	10.3923i	−1.16677	+	0.673633i
$239$	−5.19615	−	9.00000i	−0.336111	−	0.582162i	0.647586	−	0.761992i	$-0.275778\pi$
$239$	−5.19615	−	9.00000i	−0.336111	−	0.582162i	−0.983698	+	0.179830i	$0.942445\pi$
$240$	1.73205			0.111803
$241$	−24.0000	−	13.8564i	−1.54598	−	0.892570i	−0.998443	−	0.0557856i	$-0.982234\pi$
$241$	−24.0000	−	13.8564i	−1.54598	−	0.892570i	−0.547533	−	0.836784i	$-0.684433\pi$
$242$	13.8564	+	8.00000i	0.890724	+	0.514259i
$243$	13.5000	−	7.79423i	0.866025	−	0.500000i
$244$			13.8564i			0.887066i
$245$	7.79423	+	4.50000i	0.497955	+	0.287494i
$246$			10.3923i			0.662589i
$247$		0			0
$248$	−5.19615	+	2.00000i	−0.329956	+	0.127000i
$249$		0			0
$250$	1.00000			0.0632456
$251$	−12.9904	+	22.5000i	−0.819946	+	1.42019i	0.0857761	+	0.996314i	$0.472663\pi$
$251$	−12.9904	+	22.5000i	−0.819946	+	1.42019i	−0.905722	+	0.423873i	$0.860670\pi$
$252$	−12.0000			−0.755929
$253$	13.5000	+	23.3827i	0.848738	+	1.47006i
$254$	3.46410	−	6.00000i	0.217357	−	0.376473i
$255$	4.50000	−	7.79423i	0.281801	−	0.488094i
$256$	1.00000			0.0625000
$257$	2.59808	−	1.50000i	0.162064	−	0.0935674i	−0.416775	−	0.909010i	$-0.636840\pi$
$257$	2.59808	−	1.50000i	0.162064	−	0.0935674i	0.578838	+	0.815442i	$0.303506\pi$
$258$	12.9904	−	7.50000i	0.808746	−	0.466930i
$259$	−18.0000	+	10.3923i	−1.11847	+	0.645746i
$260$		0			0
$261$		0			0
$262$	4.50000	−	7.79423i	0.278011	−	0.481529i
$263$	−15.5885			−0.961225			−0.480613	−	0.876933i	$-0.659586\pi$
$263$	−15.5885			−0.961225			−0.480613	+	0.876933i	$0.659586\pi$
$264$	9.00000			0.553912
$265$		0			0
$266$	−6.92820	+	4.00000i	−0.424795	+	0.245256i
$267$	−15.5885	−	9.00000i	−0.953998	−	0.550791i
$268$	3.50000	+	6.06218i	0.213797	+	0.370306i
$269$	−12.9904	−	22.5000i	−0.792038	−	1.37185i	−0.924703	−	0.380688i	$-0.875687\pi$
$269$	−12.9904	−	22.5000i	−0.792038	−	1.37185i	0.132666	−	0.991161i	$-0.457646\pi$
$270$	4.50000	−	2.59808i	0.273861	−	0.158114i
$271$		−	31.1769i		−	1.89386i	−0.321436	−	0.946931i	$-0.604165\pi$
$271$		−	31.1769i		−	1.89386i	0.321436	−	0.946931i	$-0.395835\pi$
$272$	2.59808	−	4.50000i	0.157532	−	0.272853i
$273$		0			0
$274$	13.5000	−	7.79423i	0.815565	−	0.470867i
$275$	5.19615			0.313340
$276$	7.79423	+	4.50000i	0.469157	+	0.270868i
$277$			1.73205i			0.104069i	0.998645	+	0.0520344i	$0.0165706\pi$
$277$			1.73205i			0.104069i	−0.998645	+	0.0520344i	$0.983429\pi$
$278$	13.8564			0.831052
$279$	−10.5000	+	12.9904i	−0.628619	+	0.777714i
$280$	−4.00000			−0.239046
$281$			12.0000i			0.715860i	0.933748	+	0.357930i	$0.116517\pi$
$281$			12.0000i			0.715860i	−0.933748	+	0.357930i	$0.883483\pi$
$282$	−13.5000	−	7.79423i	−0.803913	−	0.464140i
$283$	−25.0000			−1.48610			−0.743048	−	0.669238i	$-0.766621\pi$
$283$	−25.0000			−1.48610			−0.743048	+	0.669238i	$0.766621\pi$
$284$	−5.19615	+	3.00000i	−0.308335	+	0.178017i
$285$	1.73205	−	3.00000i	0.102598	−	0.177705i
$286$		0			0
$287$		−	24.0000i		−	1.41668i
$288$	2.59808	−	1.50000i	0.153093	−	0.0883883i
$289$	−5.00000	−	8.66025i	−0.294118	−	0.509427i
$290$		0			0
$291$	6.00000	+	3.46410i	0.351726	+	0.203069i
$292$	−12.0000	+	6.92820i	−0.702247	+	0.405442i
$293$	15.5885	+	9.00000i	0.910687	+	0.525786i	0.880652	−	0.473763i	$-0.157105\pi$
$293$	15.5885	+	9.00000i	0.910687	+	0.525786i	0.0300351	+	0.999549i	$0.490438\pi$
$294$	15.5885			0.909137
$295$	12.0000			0.698667
$296$	2.59808	−	4.50000i	0.151010	−	0.261557i
$297$	23.3827	−	13.5000i	1.35680	−	0.783349i
$298$	−9.00000	+	15.5885i	−0.521356	+	0.903015i
$299$		0			0
$300$	1.50000	−	0.866025i	0.0866025	−	0.0500000i
$301$	−30.0000	+	17.3205i	−1.72917	+	0.998337i
$302$	12.1244			0.697678
$303$	−2.59808	+	4.50000i	−0.149256	+	0.258518i
$304$	1.00000	−	1.73205i	0.0573539	−	0.0993399i
$305$	6.92820	+	12.0000i	0.396708	+	0.687118i
$306$		−	15.5885i		−	0.891133i
$307$	−14.0000	+	24.2487i	−0.799022	+	1.38395i	0.121231	+	0.992624i	$0.461316\pi$
$307$	−14.0000	+	24.2487i	−0.799022	+	1.38395i	−0.920253	+	0.391323i	$0.872018\pi$
$308$	−20.7846			−1.18431
$309$			6.92820i			0.394132i
$310$	−3.50000	+	4.33013i	−0.198787	+	0.245935i
$311$			24.0000i			1.36092i	0.732787	+	0.680458i	$0.238219\pi$
$311$			24.0000i			1.36092i	−0.732787	+	0.680458i	$0.761781\pi$
$312$		0			0
$313$	−3.00000	−	1.73205i	−0.169570	−	0.0979013i	0.412813	−	0.910816i	$-0.364546\pi$
$313$	−3.00000	−	1.73205i	−0.169570	−	0.0979013i	−0.582383	+	0.812914i	$0.697880\pi$
$314$			2.00000i			0.112867i
$315$	−10.3923	+	6.00000i	−0.585540	+	0.338062i
$316$	1.50000	+	0.866025i	0.0843816	+	0.0487177i
$317$	−20.7846	−	12.0000i	−1.16738	−	0.673987i	−0.214318	−	0.976764i	$-0.568753\pi$
$317$	−20.7846	−	12.0000i	−1.16738	−	0.673987i	−0.953062	+	0.302777i	$0.902086\pi$
$318$		0			0
$319$		0			0
$320$	0.866025	−	0.500000i	0.0484123	−	0.0279508i
$321$	−5.19615	−	9.00000i	−0.290021	−	0.502331i
$322$	−18.0000	−	10.3923i	−1.00310	−	0.579141i
$323$	−5.19615	−	9.00000i	−0.289122	−	0.500773i
$324$	4.50000	−	7.79423i	0.250000	−	0.433013i
$325$		0			0
$326$		−	11.0000i		−	0.609234i
$327$	−12.0000	−	6.92820i	−0.663602	−	0.383131i
$328$	3.00000	+	5.19615i	0.165647	+	0.286910i
$329$	31.1769	+	18.0000i	1.71884	+	0.992372i
$330$	7.79423	−	4.50000i	0.429058	−	0.247717i
$331$	24.0000	−	13.8564i	1.31916	−	0.761617i	0.335566	−	0.942017i	$-0.391072\pi$
$331$	24.0000	−	13.8564i	1.31916	−	0.761617i	0.983593	+	0.180400i	$0.0577391\pi$
$332$		0			0
$333$		−	15.5885i		−	0.854242i
$334$	−9.00000	−	5.19615i	−0.492458	−	0.284321i
$335$	6.06218	+	3.50000i	0.331212	+	0.191225i
$336$	−6.00000	+	3.46410i	−0.327327	+	0.188982i
$337$			24.2487i			1.32091i	0.750865	+	0.660456i	$0.229637\pi$
$337$			24.2487i			1.32091i	−0.750865	+	0.660456i	$0.770363\pi$
$338$	11.2583	+	6.50000i	0.612372	+	0.353553i
$339$	5.19615			0.282216
$340$		−	5.19615i		−	0.281801i
$341$	−18.1865	+	22.5000i	−0.984856	+	1.21844i
$342$		−	6.00000i		−	0.324443i
$343$	−8.00000			−0.431959
$344$	4.33013	−	7.50000i	0.233465	−	0.404373i
$345$	9.00000			0.484544
$346$		0			0
$347$	−5.19615	+	9.00000i	−0.278944	+	0.483145i	−0.971123	−	0.238581i	$-0.923318\pi$
$347$	−5.19615	+	9.00000i	−0.278944	+	0.483145i	0.692179	+	0.721726i	$0.256651\pi$
$348$		0			0
$349$	10.0000			0.535288			0.267644	−	0.963518i	$-0.413755\pi$
$349$	10.0000			0.535288			0.267644	+	0.963518i	$0.413755\pi$
$350$	−3.46410	+	2.00000i	−0.185164	+	0.106904i
$351$		0			0
$352$	4.50000	−	2.59808i	0.239851	−	0.138478i
$353$	12.9904	−	22.5000i	0.691408	−	1.19755i	−0.279968	−	0.960009i	$-0.590324\pi$
$353$	12.9904	−	22.5000i	0.691408	−	1.19755i	0.971377	−	0.237545i	$-0.0763427\pi$
$354$	18.0000	−	10.3923i	0.956689	−	0.552345i
$355$	−3.00000	+	5.19615i	−0.159223	+	0.275783i
$356$	−10.3923			−0.550791
$357$			36.0000i			1.90532i
$358$	−4.50000	−	2.59808i	−0.237832	−	0.137313i
$359$	−25.9808	+	15.0000i	−1.37121	+	0.791670i	−0.991081	−	0.133263i	$-0.957455\pi$
$359$	−25.9808	+	15.0000i	−1.37121	+	0.791670i	−0.380131	+	0.924932i	$0.624121\pi$
$360$	1.50000	−	2.59808i	0.0790569	−	0.136931i
$361$	7.50000	+	12.9904i	0.394737	+	0.683704i
$362$	−10.3923	−	18.0000i	−0.546207	−	0.946059i
$363$	24.0000	−	13.8564i	1.25967	−	0.727273i
$364$		0			0
$365$	−6.92820	+	12.0000i	−0.362639	+	0.628109i
$366$	20.7846	+	12.0000i	1.08643	+	0.627250i
$367$	12.0000	−	6.92820i	0.626395	−	0.361649i	−0.152960	−	0.988232i	$-0.548880\pi$
$367$	12.0000	−	6.92820i	0.626395	−	0.361649i	0.779355	+	0.626583i	$0.215547\pi$
$368$	5.19615			0.270868
$369$	15.5885	+	9.00000i	0.811503	+	0.468521i
$370$		−	5.19615i		−	0.270135i
$371$		0			0
$372$	−1.50000	+	9.52628i	−0.0777714	+	0.493915i
$373$	23.0000			1.19089			0.595447	−	0.803394i	$-0.296975\pi$
$373$	23.0000			1.19089			0.595447	+	0.803394i	$0.296975\pi$
$374$		−	27.0000i		−	1.39614i
$375$	0.866025	−	1.50000i	0.0447214	−	0.0774597i
$376$	−9.00000			−0.464140
$377$		0			0
$378$	−10.3923	+	18.0000i	−0.534522	+	0.925820i
$379$	−4.00000	+	6.92820i	−0.205466	+	0.355878i	−0.950281	−	0.311393i	$-0.899204\pi$
$379$	−4.00000	+	6.92820i	−0.205466	+	0.355878i	0.744815	+	0.667271i	$0.232538\pi$
$380$		−	2.00000i		−	0.102598i
$381$	−6.00000	−	10.3923i	−0.307389	−	0.532414i
$382$	3.00000	+	5.19615i	0.153493	+	0.265858i
$383$	−7.79423	−	13.5000i	−0.398266	−	0.689818i	0.595246	−	0.803544i	$-0.297055\pi$
$383$	−7.79423	−	13.5000i	−0.398266	−	0.689818i	−0.993512	+	0.113726i	$0.963721\pi$
$384$	0.866025	−	1.50000i	0.0441942	−	0.0765466i
$385$	−18.0000	+	10.3923i	−0.917365	+	0.529641i
$386$	−17.3205	−	10.0000i	−0.881591	−	0.508987i
$387$		−	25.9808i		−	1.32068i
$388$	4.00000			0.203069
$389$	12.9904	−	22.5000i	0.658638	−	1.14080i	−0.322330	−	0.946627i	$-0.604466\pi$
$389$	12.9904	−	22.5000i	0.658638	−	1.14080i	0.980968	−	0.194168i	$-0.0622006\pi$
$390$		0			0
$391$	13.5000	−	23.3827i	0.682724	−	1.18251i
$392$	7.79423	−	4.50000i	0.393668	−	0.227284i
$393$	−7.79423	−	13.5000i	−0.393167	−	0.680985i
$394$	9.00000	−	5.19615i	0.453413	−	0.261778i
$395$	1.73205			0.0871489
$396$	7.79423	−	13.5000i	0.391675	−	0.678401i
$397$	12.5000	−	21.6506i	0.627357	−	1.08661i	−0.360723	−	0.932673i	$-0.617470\pi$
$397$	12.5000	−	21.6506i	0.627357	−	1.08661i	0.988080	−	0.153941i	$-0.0491966\pi$
$398$	−8.66025	−	15.0000i	−0.434099	−	0.751882i
$399$			13.8564i			0.693688i
$400$	0.500000	−	0.866025i	0.0250000	−	0.0433013i
$401$	−31.1769			−1.55690			−0.778450	−	0.627706i	$-0.783994\pi$
$401$	−31.1769			−1.55690			−0.778450	+	0.627706i	$0.783994\pi$
$402$	12.1244			0.604708
$403$		0			0
$404$			3.00000i			0.149256i
$405$		−	9.00000i		−	0.447214i
$406$		0			0
$407$		−	27.0000i		−	1.33834i
$408$	−4.50000	−	7.79423i	−0.222783	−	0.385872i
$409$	−22.5000	−	12.9904i	−1.11255	−	0.642333i	−0.173064	−	0.984911i	$-0.555367\pi$
$409$	−22.5000	−	12.9904i	−1.11255	−	0.642333i	−0.939490	+	0.342578i	$0.888700\pi$
$410$	5.19615	+	3.00000i	0.256620	+	0.148159i
$411$		−	27.0000i		−	1.33181i
$412$	2.00000	+	3.46410i	0.0985329	+	0.170664i
$413$	−41.5692	+	24.0000i	−2.04549	+	1.18096i
$414$	13.5000	−	7.79423i	0.663489	−	0.383065i
$415$		0			0
$416$		0			0
$417$	12.0000	−	20.7846i	0.587643	−	1.01783i
$418$		−	10.3923i		−	0.508304i
$419$			33.0000i			1.61216i	0.591810	+	0.806078i	$0.298414\pi$
$419$			33.0000i			1.61216i	−0.591810	+	0.806078i	$0.701586\pi$
$420$	−3.46410	+	6.00000i	−0.169031	+	0.292770i
$421$	7.00000	+	12.1244i	0.341159	+	0.590905i	0.984648	−	0.174550i	$-0.0558472\pi$
$421$	7.00000	+	12.1244i	0.341159	+	0.590905i	−0.643489	+	0.765455i	$0.722514\pi$
$422$	1.73205	+	1.00000i	0.0843149	+	0.0486792i
$423$	−23.3827	+	13.5000i	−1.13691	+	0.656392i
$424$		0			0
$425$	−2.59808	−	4.50000i	−0.126025	−	0.218282i
$426$			10.3923i			0.503509i
$427$	−48.0000	−	27.7128i	−2.32288	−	1.34112i
$428$	−5.19615	−	3.00000i	−0.251166	−	0.145010i
$429$		0			0
$430$		−	8.66025i		−	0.417635i
$431$	15.5885	+	9.00000i	0.750870	+	0.433515i	0.826008	−	0.563658i	$-0.190607\pi$
$431$	15.5885	+	9.00000i	0.750870	+	0.433515i	−0.0751385	+	0.997173i	$0.523940\pi$
$432$		−	5.19615i		−	0.250000i
$433$		−	13.8564i		−	0.665896i	−0.942945	−	0.332948i	$-0.891957\pi$
$433$		−	13.8564i		−	0.665896i	0.942945	−	0.332948i	$-0.108043\pi$
$434$	3.46410	−	22.0000i	0.166282	−	1.05603i
$435$		0			0
$436$	−8.00000			−0.383131
$437$	5.19615	−	9.00000i	0.248566	−	0.430528i
$438$			24.0000i			1.14676i
$439$	20.5000	+	35.5070i	0.978412	+	1.69466i	0.668184	+	0.743996i	$0.267072\pi$
$439$	20.5000	+	35.5070i	0.978412	+	1.69466i	0.310228	+	0.950662i	$0.399595\pi$
$440$	2.59808	−	4.50000i	0.123858	−	0.214529i
$441$	13.5000	−	23.3827i	0.642857	−	1.11346i
$442$		0			0
$443$	−20.7846	+	12.0000i	−0.987507	+	0.570137i	−0.904528	−	0.426414i	$-0.859777\pi$
$443$	−20.7846	+	12.0000i	−0.987507	+	0.570137i	−0.0829786	+	0.996551i	$0.526443\pi$
$444$	−4.50000	−	7.79423i	−0.213561	−	0.369898i
$445$	−9.00000	+	5.19615i	−0.426641	+	0.246321i
$446$	−8.66025	+	15.0000i	−0.410075	+	0.710271i
$447$	15.5885	+	27.0000i	0.737309	+	1.27706i
$448$	−2.00000	+	3.46410i	−0.0944911	+	0.163663i
$449$	−41.5692			−1.96177			−0.980886	−	0.194581i	$-0.937665\pi$
$449$	−41.5692			−1.96177			−0.980886	+	0.194581i	$0.937665\pi$
$450$		−	3.00000i		−	0.141421i
$451$	27.0000	+	15.5885i	1.27138	+	0.734032i
$452$	2.59808	−	1.50000i	0.122203	−	0.0705541i
$453$	10.5000	−	18.1865i	0.493333	−	0.854478i
$454$	9.00000	+	15.5885i	0.422391	+	0.731603i
$455$		0			0
$456$	−1.73205	−	3.00000i	−0.0811107	−	0.140488i
$457$			17.3205i			0.810219i	0.914268	+	0.405110i	$0.132767\pi$
$457$			17.3205i			0.810219i	−0.914268	+	0.405110i	$0.867233\pi$
$458$	8.66025	−	15.0000i	0.404667	−	0.700904i
$459$	−23.3827	−	13.5000i	−1.09141	−	0.630126i
$460$	4.50000	−	2.59808i	0.209814	−	0.121136i
$461$	15.5885			0.726027			0.363013	−	0.931784i	$-0.381748\pi$
$461$	15.5885			0.726027			0.363013	+	0.931784i	$0.381748\pi$
$462$	−18.0000	+	31.1769i	−0.837436	+	1.45048i
$463$			17.3205i			0.804952i	0.915430	+	0.402476i	$0.131850\pi$
$463$			17.3205i			0.804952i	−0.915430	+	0.402476i	$0.868150\pi$
$464$		0			0
$465$	3.46410	+	9.00000i	0.160644	+	0.417365i
$466$	3.00000			0.138972
$467$			42.0000i			1.94353i	0.235954	+	0.971764i	$0.424178\pi$
$467$			42.0000i			1.94353i	−0.235954	+	0.971764i	$0.575822\pi$
$468$		0			0
$469$	−28.0000			−1.29292
$470$	−7.79423	+	4.50000i	−0.359521	+	0.207570i
$471$	3.00000	+	1.73205i	0.138233	+	0.0798087i
$472$	6.00000	−	10.3923i	0.276172	−	0.478345i
$473$		−	45.0000i		−	2.06910i
$474$	2.59808	−	1.50000i	0.119334	−	0.0688973i
$475$	−1.00000	−	1.73205i	−0.0458831	−	0.0794719i
$476$	10.3923	+	18.0000i	0.476331	+	0.825029i
$477$		0			0
$478$	−9.00000	+	5.19615i	−0.411650	+	0.237666i
$479$	20.7846	+	12.0000i	0.949673	+	0.548294i	0.892979	−	0.450098i	$-0.148611\pi$
$479$	20.7846	+	12.0000i	0.949673	+	0.548294i	0.0566937	+	0.998392i	$0.481944\pi$
$480$		−	1.73205i		−	0.0790569i
$481$		0			0
$482$	−13.8564	+	24.0000i	−0.631142	+	1.09317i
$483$	−31.1769	+	18.0000i	−1.41860	+	0.819028i
$484$	8.00000	−	13.8564i	0.363636	−	0.629837i
$485$	3.46410	−	2.00000i	0.157297	−	0.0908153i
$486$	−7.79423	−	13.5000i	−0.353553	−	0.612372i
$487$	−15.0000	+	8.66025i	−0.679715	+	0.392434i	−0.799748	−	0.600336i	$-0.795033\pi$
$487$	−15.0000	+	8.66025i	−0.679715	+	0.392434i	0.120033	+	0.992770i	$0.461700\pi$
$488$	13.8564			0.627250
$489$	−16.5000	−	9.52628i	−0.746156	−	0.430793i
$490$	4.50000	−	7.79423i	0.203289	−	0.352107i
$491$	7.79423	+	13.5000i	0.351749	+	0.609246i	0.986556	−	0.163424i	$-0.0522539\pi$
$491$	7.79423	+	13.5000i	0.351749	+	0.609246i	−0.634807	+	0.772670i	$0.718921\pi$
$492$	10.3923			0.468521
$493$		0			0
$494$		0			0
$495$		−	15.5885i		−	0.700649i
$496$	2.00000	+	5.19615i	0.0898027	+	0.233314i
$497$		−	24.0000i		−	1.07655i
$498$		0			0
$499$	−18.0000	−	10.3923i	−0.805791	−	0.465223i	0.0397013	−	0.999212i	$-0.487359\pi$
$499$	−18.0000	−	10.3923i	−0.805791	−	0.465223i	−0.845492	+	0.533988i	$0.820693\pi$
$500$		−	1.00000i		−	0.0447214i
$501$	−15.5885	+	9.00000i	−0.696441	+	0.402090i
$502$	22.5000	+	12.9904i	1.00422	+	0.579789i
$503$	20.7846	+	12.0000i	0.926740	+	0.535054i	0.885779	−	0.464107i	$-0.153625\pi$
$503$	20.7846	+	12.0000i	0.926740	+	0.535054i	0.0409609	+	0.999161i	$0.486958\pi$
$504$			12.0000i			0.534522i
$505$	1.50000	+	2.59808i	0.0667491	+	0.115613i
$506$	23.3827	−	13.5000i	1.03949	−	0.600148i
$507$	19.5000	−	11.2583i	0.866025	−	0.500000i
$508$	−6.00000	−	3.46410i	−0.266207	−	0.153695i
$509$	18.1865	+	31.5000i	0.806104	+	1.39621i	0.915543	+	0.402219i	$0.131761\pi$
$509$	18.1865	+	31.5000i	0.806104	+	1.39621i	−0.109439	+	0.993993i	$0.534906\pi$
$510$	−7.79423	−	4.50000i	−0.345134	−	0.199263i
$511$		−	55.4256i		−	2.45189i
$512$		−	1.00000i		−	0.0441942i
$513$	−9.00000	−	5.19615i	−0.397360	−	0.229416i
$514$	−1.50000	−	2.59808i	−0.0661622	−	0.114596i
$515$	3.46410	+	2.00000i	0.152647	+	0.0881305i
$516$	−7.50000	−	12.9904i	−0.330169	−	0.571870i
$517$	−40.5000	+	23.3827i	−1.78119	+	1.02837i
$518$	10.3923	+	18.0000i	0.456612	+	0.790875i
$519$		0			0
$520$		0			0
$521$	15.5885	+	9.00000i	0.682943	+	0.394297i	0.800963	−	0.598714i	$-0.204321\pi$
$521$	15.5885	+	9.00000i	0.682943	+	0.394297i	−0.118020	+	0.993011i	$0.537655\pi$
$522$		0			0
$523$			19.0526i			0.833110i	0.909110	+	0.416555i	$0.136763\pi$
$523$			19.0526i			0.833110i	−0.909110	+	0.416555i	$0.863237\pi$
$524$	−7.79423	−	4.50000i	−0.340492	−	0.196583i
$525$			6.92820i			0.302372i
$526$			15.5885i			0.679689i
$527$	28.5788	+	4.50000i	1.24491	+	0.196023i
$528$		−	9.00000i		−	0.391675i
$529$	4.00000			0.173913
$530$		0			0
$531$		−	36.0000i		−	1.56227i
$532$	4.00000	+	6.92820i	0.173422	+	0.300376i
$533$		0			0
$534$	−9.00000	+	15.5885i	−0.389468	+	0.674579i
$535$	−6.00000			−0.259403
$536$	6.06218	−	3.50000i	0.261846	−	0.151177i
$537$	−7.79423	+	4.50000i	−0.336346	+	0.194189i
$538$	−22.5000	+	12.9904i	−0.970044	+	0.560055i
$539$	23.3827	−	40.5000i	1.00716	−	1.74446i
$540$	−2.59808	−	4.50000i	−0.111803	−	0.193649i
$541$	4.00000	−	6.92820i	0.171973	−	0.297867i	−0.767136	−	0.641484i	$-0.778319\pi$
$541$	4.00000	−	6.92820i	0.171973	−	0.297867i	0.939110	+	0.343617i	$0.111652\pi$
$542$	−31.1769			−1.33916
$543$	−36.0000			−1.54491
$544$	−4.50000	−	2.59808i	−0.192936	−	0.111392i
$545$	−6.92820	+	4.00000i	−0.296772	+	0.171341i
$546$		0			0
$547$	−9.50000	−	16.4545i	−0.406191	−	0.703543i	0.588269	−	0.808666i	$-0.299810\pi$
$547$	−9.50000	−	16.4545i	−0.406191	−	0.703543i	−0.994459	+	0.105123i	$0.966476\pi$
$548$	−7.79423	−	13.5000i	−0.332953	−	0.576691i
$549$	36.0000	−	20.7846i	1.53644	−	0.887066i
$550$		−	5.19615i		−	0.221565i
$551$		0			0
$552$	4.50000	−	7.79423i	0.191533	−	0.331744i
$553$	−6.00000	+	3.46410i	−0.255146	+	0.147309i
$554$	1.73205			0.0735878
$555$	−7.79423	−	4.50000i	−0.330847	−	0.191014i
$556$		−	13.8564i		−	0.587643i
$557$	−20.7846			−0.880672			−0.440336	−	0.897833i	$-0.645141\pi$
$557$	−20.7846			−0.880672			−0.440336	+	0.897833i	$0.645141\pi$
$558$	12.9904	+	10.5000i	0.549927	+	0.444500i
$559$		0			0
$560$			4.00000i			0.169031i
$561$	−40.5000	−	23.3827i	−1.70991	−	0.987218i
$562$	12.0000			0.506189
$563$	5.19615	−	3.00000i	0.218992	−	0.126435i	−0.386492	−	0.922293i	$-0.626313\pi$
$563$	5.19615	−	3.00000i	0.218992	−	0.126435i	0.605483	+	0.795858i	$0.292980\pi$
$564$	−7.79423	+	13.5000i	−0.328196	+	0.568453i
$565$	1.50000	−	2.59808i	0.0631055	−	0.109302i
$566$			25.0000i			1.05083i
$567$	18.0000	+	31.1769i	0.755929	+	1.30931i
$568$	3.00000	+	5.19615i	0.125877	+	0.218026i
$569$	−15.5885	−	27.0000i	−0.653502	−	1.13190i	−0.982267	−	0.187487i	$-0.939966\pi$
$569$	−15.5885	−	27.0000i	−0.653502	−	1.13190i	0.328765	−	0.944412i	$-0.393368\pi$
$570$	−3.00000	−	1.73205i	−0.125656	−	0.0725476i
$571$	27.0000	−	15.5885i	1.12991	−	0.652357i	0.186001	−	0.982549i	$-0.440447\pi$
$571$	27.0000	−	15.5885i	1.12991	−	0.652357i	0.943913	+	0.330193i	$0.107114\pi$
$572$		0			0
$573$	10.3923			0.434145
$574$	−24.0000			−1.00174
$575$	2.59808	−	4.50000i	0.108347	−	0.187663i
$576$	−1.50000	−	2.59808i	−0.0625000	−	0.108253i
$577$	13.0000	−	22.5167i	0.541197	−	0.937381i	−0.457639	−	0.889138i	$-0.651305\pi$
$577$	13.0000	−	22.5167i	0.541197	−	0.937381i	0.998836	−	0.0482425i	$-0.0153620\pi$
$578$	−8.66025	+	5.00000i	−0.360219	+	0.207973i
$579$	−30.0000	+	17.3205i	−1.24676	+	0.719816i
$580$		0			0
$581$		0			0
$582$	3.46410	−	6.00000i	0.143592	−	0.248708i
$583$		0			0
$584$	6.92820	+	12.0000i	0.286691	+	0.496564i
$585$		0			0
$586$	9.00000	−	15.5885i	0.371787	−	0.643953i
$587$	−10.3923			−0.428936			−0.214468	−	0.976731i	$-0.568802\pi$
$587$	−10.3923			−0.428936			−0.214468	+	0.976731i	$0.568802\pi$
$588$		−	15.5885i		−	0.642857i
$589$	11.0000	+	1.73205i	0.453247	+	0.0713679i
$590$		−	12.0000i		−	0.494032i
$591$		−	18.0000i		−	0.740421i
$592$	−4.50000	−	2.59808i	−0.184949	−	0.106780i
$593$		−	6.00000i		−	0.246390i	−0.992382	−	0.123195i	$-0.960686\pi$
$593$		−	6.00000i		−	0.246390i	0.992382	−	0.123195i	$-0.0393141\pi$
$594$	−13.5000	−	23.3827i	−0.553912	−	0.959403i
$595$	18.0000	+	10.3923i	0.737928	+	0.426043i
$596$	15.5885	+	9.00000i	0.638528	+	0.368654i
$597$	−30.0000			−1.22782
$598$		0			0
$599$	−5.19615	+	3.00000i	−0.212309	+	0.122577i	−0.602384	−	0.798206i	$-0.705782\pi$
$599$	−5.19615	+	3.00000i	−0.212309	+	0.122577i	0.390075	+	0.920783i	$0.372449\pi$
$600$	−0.866025	−	1.50000i	−0.0353553	−	0.0612372i
$601$	40.5000	+	23.3827i	1.65203	+	0.953800i	0.976236	+	0.216708i	$0.0695320\pi$
$601$	40.5000	+	23.3827i	1.65203	+	0.953800i	0.675793	+	0.737091i	$0.263801\pi$
$602$	17.3205	+	30.0000i	0.705931	+	1.22271i
$603$	10.5000	−	18.1865i	0.427593	−	0.740613i
$604$		−	12.1244i		−	0.493333i
$605$		−	16.0000i		−	0.650493i
$606$	4.50000	+	2.59808i	0.182800	+	0.105540i
$607$	1.00000	+	1.73205i	0.0405887	+	0.0703018i	0.885606	−	0.464437i	$-0.153743\pi$
$607$	1.00000	+	1.73205i	0.0405887	+	0.0703018i	−0.845017	+	0.534739i	$0.820410\pi$
$608$	−1.73205	−	1.00000i	−0.0702439	−	0.0405554i
$609$		0			0
$610$	12.0000	−	6.92820i	0.485866	−	0.280515i
$611$		0			0
$612$	−15.5885			−0.630126
$613$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$613$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$614$	24.2487	+	14.0000i	0.978598	+	0.564994i
$615$	9.00000	−	5.19615i	0.362915	−	0.209529i
$616$			20.7846i			0.837436i
$617$	−38.9711	−	22.5000i	−1.56892	−	0.905816i	−0.996295	−	0.0859976i	$-0.972592\pi$
$617$	−38.9711	−	22.5000i	−1.56892	−	0.905816i	−0.572624	−	0.819818i	$-0.694074\pi$
$618$	6.92820			0.278693
$619$			41.5692i			1.67081i	0.549636	+	0.835404i	$0.314766\pi$
$619$			41.5692i			1.67081i	−0.549636	+	0.835404i	$0.685234\pi$
$620$	4.33013	+	3.50000i	0.173902	+	0.140563i
$621$		−	27.0000i		−	1.08347i
$622$	24.0000			0.962312
$623$	20.7846	−	36.0000i	0.832718	−	1.44231i
$624$		0			0
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−1.73205	+	3.00000i	−0.0692267	+	0.119904i
$627$	−15.5885	−	9.00000i	−0.622543	−	0.359425i
$628$	2.00000			0.0798087
$629$	−23.3827	+	13.5000i	−0.932329	+	0.538280i
$630$	6.00000	+	10.3923i	0.239046	+	0.414039i
$631$	−10.5000	+	6.06218i	−0.417998	+	0.241331i	−0.694221	−	0.719762i	$-0.744251\pi$
$631$	−10.5000	+	6.06218i	−0.417998	+	0.241331i	0.276222	+	0.961094i	$0.410917\pi$
$632$	0.866025	−	1.50000i	0.0344486	−	0.0596668i
$633$	3.00000	−	1.73205i	0.119239	−	0.0688428i
$634$	−12.0000	+	20.7846i	−0.476581	+	0.825462i
$635$	−6.92820			−0.274937
$636$		0			0
$637$		0			0
$638$		0			0
$639$	15.5885	+	9.00000i	0.616670	+	0.356034i
$640$	−0.500000	−	0.866025i	−0.0197642	−	0.0342327i
$641$	−5.19615	−	9.00000i	−0.205236	−	0.355479i	0.744972	−	0.667096i	$-0.232463\pi$
$641$	−5.19615	−	9.00000i	−0.205236	−	0.355479i	−0.950208	+	0.311617i	$0.899129\pi$
$642$	−9.00000	+	5.19615i	−0.355202	+	0.205076i
$643$		−	3.46410i		−	0.136611i	−0.997664	−	0.0683054i	$-0.978241\pi$
$643$		−	3.46410i		−	0.136611i	0.997664	−	0.0683054i	$-0.0217592\pi$
$644$	−10.3923	+	18.0000i	−0.409514	+	0.709299i
$645$	−12.9904	−	7.50000i	−0.511496	−	0.295312i
$646$	−9.00000	+	5.19615i	−0.354100	+	0.204440i
$647$	31.1769			1.22569			0.612845	−	0.790203i	$-0.290025\pi$
$647$	31.1769			1.22569			0.612845	+	0.790203i	$0.290025\pi$
$648$	−7.79423	−	4.50000i	−0.306186	−	0.176777i
$649$		−	62.3538i		−	2.44760i
$650$		0			0
$651$	−30.0000	−	24.2487i	−1.17579	−	0.950382i
$652$	−11.0000			−0.430793
$653$			36.0000i			1.40879i	0.709809	+	0.704394i	$0.248781\pi$
$653$			36.0000i			1.40879i	−0.709809	+	0.704394i	$0.751219\pi$
$654$	−6.92820	+	12.0000i	−0.270914	+	0.469237i
$655$	−9.00000			−0.351659
$656$	5.19615	−	3.00000i	0.202876	−	0.117130i
$657$	36.0000	+	20.7846i	1.40449	+	0.810885i
$658$	18.0000	−	31.1769i	0.701713	−	1.21540i
$659$			39.0000i			1.51922i	0.650376	+	0.759612i	$0.274611\pi$
$659$			39.0000i			1.51922i	−0.650376	+	0.759612i	$0.725389\pi$
$660$	−4.50000	−	7.79423i	−0.175162	−	0.303390i
$661$	−7.00000	−	12.1244i	−0.272268	−	0.471583i	0.697174	−	0.716902i	$-0.254441\pi$
$661$	−7.00000	−	12.1244i	−0.272268	−	0.471583i	−0.969442	+	0.245319i	$0.921107\pi$
$662$	−13.8564	−	24.0000i	−0.538545	−	0.932786i
$663$		0			0
$664$		0			0
$665$	6.92820	+	4.00000i	0.268664	+	0.155113i
$666$	−15.5885			−0.604040
$667$		0			0
$668$	−5.19615	+	9.00000i	−0.201045	+	0.348220i
$669$	15.0000	+	25.9808i	0.579934	+	1.00447i
$670$	3.50000	−	6.06218i	0.135217	−	0.234202i
$671$	62.3538	−	36.0000i	2.40714	−	1.38976i
$672$	3.46410	+	6.00000i	0.133631	+	0.231455i
$673$	15.0000	−	8.66025i	0.578208	−	0.333828i	−0.182213	−	0.983259i	$-0.558326\pi$
$673$	15.0000	−	8.66025i	0.578208	−	0.333828i	0.760421	+	0.649431i	$0.224993\pi$
$674$	24.2487			0.934025
$675$	−4.50000	−	2.59808i	−0.173205	−	0.100000i
$676$	6.50000	−	11.2583i	0.250000	−	0.433013i
$677$	−10.3923	−	18.0000i	−0.399409	−	0.691796i	0.594244	−	0.804285i	$-0.297451\pi$
$677$	−10.3923	−	18.0000i	−0.399409	−	0.691796i	−0.993653	+	0.112488i	$0.964118\pi$
$678$		−	5.19615i		−	0.199557i
$679$	−8.00000	+	13.8564i	−0.307012	+	0.531760i
$680$	−5.19615			−0.199263
$681$	31.1769			1.19470
$682$	22.5000	+	18.1865i	0.861570	+	0.696398i
$683$		−	42.0000i		−	1.60709i	−0.595247	−	0.803543i	$-0.702946\pi$
$683$		−	42.0000i		−	1.60709i	0.595247	−	0.803543i	$-0.297054\pi$
$684$	−6.00000			−0.229416
$685$	−13.5000	−	7.79423i	−0.515808	−	0.297802i
$686$			8.00000i			0.305441i
$687$	−15.0000	−	25.9808i	−0.572286	−	0.991228i
$688$	−7.50000	−	4.33013i	−0.285935	−	0.165085i
$689$		0			0
$690$		−	9.00000i		−	0.342624i
$691$	5.00000	+	8.66025i	0.190209	+	0.329452i	0.945319	−	0.326146i	$-0.105750\pi$
$691$	5.00000	+	8.66025i	0.190209	+	0.329452i	−0.755110	+	0.655598i	$0.772417\pi$
$692$		0			0
$693$	31.1769	+	54.0000i	1.18431	+	2.05129i
$694$	9.00000	+	5.19615i	0.341635	+	0.197243i
$695$	−6.92820	−	12.0000i	−0.262802	−	0.455186i
$696$		0			0
$697$		−	31.1769i		−	1.18091i
$698$		−	10.0000i		−	0.378506i
$699$	2.59808	−	4.50000i	0.0982683	−	0.170206i
$700$	2.00000	+	3.46410i	0.0755929	+	0.130931i
$701$	33.7750	+	19.5000i	1.27566	+	0.736505i	0.976048	−	0.217555i	$-0.0698082\pi$
$701$	33.7750	+	19.5000i	1.27566	+	0.736505i	0.299616	+	0.954060i	$0.403142\pi$
$702$		0			0
$703$	−9.00000	+	5.19615i	−0.339441	+	0.195977i
$704$	−2.59808	−	4.50000i	−0.0979187	−	0.169600i
$705$			15.5885i			0.587095i
$706$	−22.5000	−	12.9904i	−0.846799	−	0.488899i
$707$	−10.3923	−	6.00000i	−0.390843	−	0.225653i
$708$	−10.3923	−	18.0000i	−0.390567	−	0.676481i
$709$			17.3205i			0.650485i	0.945631	+	0.325243i	$0.105446\pi$
$709$			17.3205i			0.650485i	−0.945631	+	0.325243i	$0.894554\pi$
$710$	5.19615	+	3.00000i	0.195008	+	0.112588i
$711$		−	5.19615i		−	0.194871i
$712$			10.3923i			0.389468i
$713$	10.3923	+	27.0000i	0.389195	+	1.01116i
$714$	36.0000			1.34727
$715$		0			0
$716$	−2.59808	+	4.50000i	−0.0970947	+	0.168173i
$717$			18.0000i			0.672222i
$718$	15.0000	+	25.9808i	0.559795	+	0.969593i
$719$	−5.19615	+	9.00000i	−0.193784	+	0.335643i	−0.946501	−	0.322700i	$-0.895409\pi$
$719$	−5.19615	+	9.00000i	−0.193784	+	0.335643i	0.752717	+	0.658344i	$0.228743\pi$
$720$	−2.59808	−	1.50000i	−0.0968246	−	0.0559017i
$721$	−16.0000			−0.595871
$722$	12.9904	−	7.50000i	0.483452	−	0.279121i
$723$	24.0000	+	41.5692i	0.892570	+	1.54598i
$724$	−18.0000	+	10.3923i	−0.668965	+	0.386227i
$725$		0			0
$726$	−13.8564	−	24.0000i	−0.514259	−	0.890724i
$727$	−16.0000	+	27.7128i	−0.593407	+	1.02781i	0.400362	+	0.916357i	$0.368884\pi$
$727$	−16.0000	+	27.7128i	−0.593407	+	1.02781i	−0.993770	+	0.111454i	$0.964449\pi$
$728$		0			0
$729$	−27.0000			−1.00000
$730$	12.0000	+	6.92820i	0.444140	+	0.256424i
$731$	−38.9711	+	22.5000i	−1.44140	+	0.832193i
$732$	12.0000	−	20.7846i	0.443533	−	0.768221i
$733$	14.5000	+	25.1147i	0.535570	+	0.927634i	0.999136	+	0.0415715i	$0.0132364\pi$
$733$	14.5000	+	25.1147i	0.535570	+	0.927634i	−0.463566	+	0.886062i	$0.653430\pi$
$734$	−6.92820	−	12.0000i	−0.255725	−	0.442928i
$735$	−7.79423	−	13.5000i	−0.287494	−	0.497955i
$736$		−	5.19615i		−	0.191533i
$737$	18.1865	−	31.5000i	0.669910	−	1.16032i
$738$	9.00000	−	15.5885i	0.331295	−	0.573819i
$739$	−3.00000	+	1.73205i	−0.110357	+	0.0637145i	−0.554162	−	0.832409i	$-0.686961\pi$
$739$	−3.00000	+	1.73205i	−0.110357	+	0.0637145i	0.443806	+	0.896123i	$0.353628\pi$
$740$	−5.19615			−0.191014
$741$		0			0
$742$		0			0
$743$	25.9808			0.953142			0.476571	−	0.879136i	$-0.341880\pi$
$743$	25.9808			0.953142			0.476571	+	0.879136i	$0.341880\pi$
$744$	9.52628	+	1.50000i	0.349250	+	0.0549927i
$745$	18.0000			0.659469
$746$		−	23.0000i		−	0.842090i
$747$		0			0
$748$	−27.0000			−0.987218
$749$	20.7846	−	12.0000i	0.759453	−	0.438470i
$750$	−1.50000	−	0.866025i	−0.0547723	−	0.0316228i
$751$	−3.50000	+	6.06218i	−0.127717	+	0.221212i	−0.922792	−	0.385299i	$-0.874098\pi$
$751$	−3.50000	+	6.06218i	−0.127717	+	0.221212i	0.795075	+	0.606511i	$0.207432\pi$
$752$			9.00000i			0.328196i
$753$	38.9711	−	22.5000i	1.42019	−	0.819946i
$754$		0			0
$755$	−6.06218	−	10.5000i	−0.220625	−	0.382134i
$756$	18.0000	+	10.3923i	0.654654	+	0.377964i
$757$	−43.5000	+	25.1147i	−1.58103	+	0.912811i	−0.586326	+	0.810075i	$0.699426\pi$
$757$	−43.5000	+	25.1147i	−1.58103	+	0.912811i	−0.994709	+	0.102735i	$0.967241\pi$
$758$	6.92820	+	4.00000i	0.251644	+	0.145287i
$759$		−	46.7654i		−	1.69748i
$760$	−2.00000			−0.0725476
$761$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$761$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$762$	−10.3923	+	6.00000i	−0.376473	+	0.217357i
$763$	16.0000	−	27.7128i	0.579239	−	1.00327i
$764$	5.19615	−	3.00000i	0.187990	−	0.108536i
$765$	−13.5000	+	7.79423i	−0.488094	+	0.281801i
$766$	−13.5000	+	7.79423i	−0.487775	+	0.281617i
$767$		0			0
$768$	−1.50000	−	0.866025i	−0.0541266	−	0.0312500i
$769$	−17.0000	+	29.4449i	−0.613036	+	1.06181i	0.377690	+	0.925932i	$0.376718\pi$
$769$	−17.0000	+	29.4449i	−0.613036	+	1.06181i	−0.990726	+	0.135877i	$0.956615\pi$
$770$	10.3923	+	18.0000i	0.374513	+	0.648675i
$771$	−5.19615			−0.187135
$772$	−10.0000	+	17.3205i	−0.359908	+	0.623379i
$773$	20.7846			0.747570			0.373785	−	0.927515i	$-0.378060\pi$
$773$	20.7846			0.747570			0.373785	+	0.927515i	$0.378060\pi$
$774$	−25.9808			−0.933859
$775$	5.50000	+	0.866025i	0.197566	+	0.0311086i
$776$		−	4.00000i		−	0.143592i
$777$	36.0000			1.29149
$778$	−22.5000	−	12.9904i	−0.806664	−	0.465728i
$779$		−	12.0000i		−	0.429945i
$780$		0			0
$781$	27.0000	+	15.5885i	0.966136	+	0.557799i
$782$	−23.3827	−	13.5000i	−0.836163	−	0.482759i
$783$		0			0
$784$	−4.50000	−	7.79423i	−0.160714	−	0.278365i
$785$	1.73205	−	1.00000i	0.0618195	−	0.0356915i
$786$	−13.5000	+	7.79423i	−0.481529	+	0.278011i
$787$	−22.5000	−	12.9904i	−0.802038	−	0.463057i	0.0421450	−	0.999112i	$-0.486581\pi$
$787$	−22.5000	−	12.9904i	−0.802038	−	0.463057i	−0.844183	+	0.536054i	$0.819914\pi$
$788$	−5.19615	−	9.00000i	−0.185105	−	0.320612i
$789$	23.3827	+	13.5000i	0.832446	+	0.480613i
$790$		−	1.73205i		−	0.0616236i
$791$			12.0000i			0.426671i
$792$	−13.5000	−	7.79423i	−0.479702	−	0.276956i
$793$		0			0
$794$	−21.6506	−	12.5000i	−0.768352	−	0.443608i
$795$		0			0
$796$	−15.0000	+	8.66025i	−0.531661	+	0.306955i
$797$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$797$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$798$	13.8564			0.490511
$799$	40.5000	+	23.3827i	1.43279	+	0.827220i
$800$	−0.866025	−	0.500000i	−0.0306186	−	0.0176777i
$801$	15.5885	+	27.0000i	0.550791	+	0.953998i
$802$			31.1769i			1.10090i
$803$	62.3538	+	36.0000i	2.20042	+	1.27041i
$804$		−	12.1244i		−	0.427593i
$805$			20.7846i			0.732561i
$806$		0			0
$807$			45.0000i			1.58408i
$808$	3.00000			0.105540
$809$	−10.3923	+	18.0000i	−0.365374	+	0.632846i	−0.988836	−	0.149007i	$-0.952392\pi$
$809$	−10.3923	+	18.0000i	−0.365374	+	0.632846i	0.623462	+	0.781854i	$0.285726\pi$
$810$	−9.00000			−0.316228
$811$	22.0000	+	38.1051i	0.772524	+	1.33805i	0.936175	+	0.351533i	$0.114340\pi$
$811$	22.0000	+	38.1051i	0.772524	+	1.33805i	−0.163651	+	0.986518i	$0.552327\pi$
$812$		0			0
$813$	−27.0000	+	46.7654i	−0.946931	+	1.64013i
$814$	−27.0000			−0.946350
$815$	−9.52628	+	5.50000i	−0.333691	+	0.192657i
$816$	−7.79423	+	4.50000i	−0.272853	+	0.157532i
$817$	−15.0000	+	8.66025i	−0.524784	+	0.302984i
$818$	−12.9904	+	22.5000i	−0.454198	+	0.786694i
$819$		0			0
$820$	3.00000	−	5.19615i	0.104765	−	0.181458i
$821$	5.19615			0.181347			0.0906735	−	0.995881i	$-0.471098\pi$
$821$	5.19615			0.181347			0.0906735	+	0.995881i	$0.471098\pi$
$822$	−27.0000			−0.941733
$823$	3.00000	+	1.73205i	0.104573	+	0.0603755i	0.551375	−	0.834258i	$-0.314104\pi$
$823$	3.00000	+	1.73205i	0.104573	+	0.0603755i	−0.446801	+	0.894633i	$0.647437\pi$
$824$	3.46410	−	2.00000i	0.120678	−	0.0696733i
$825$	−7.79423	−	4.50000i	−0.271360	−	0.156670i
$826$	24.0000	+	41.5692i	0.835067	+	1.44638i
$827$	−10.3923	−	18.0000i	−0.361376	−	0.625921i	0.626812	−	0.779171i	$-0.284360\pi$
$827$	−10.3923	−	18.0000i	−0.361376	−	0.625921i	−0.988188	+	0.153249i	$0.951026\pi$
$828$	−7.79423	−	13.5000i	−0.270868	−	0.469157i
$829$		−	51.9615i		−	1.80470i	−0.431006	−	0.902349i	$-0.641841\pi$
$829$		−	51.9615i		−	1.80470i	0.431006	−	0.902349i	$-0.358159\pi$
$830$		0			0
$831$	1.50000	−	2.59808i	0.0520344	−	0.0901263i
$832$		0			0
$833$	−46.7654			−1.62032
$834$	−20.7846	−	12.0000i	−0.719712	−	0.415526i
$835$			10.3923i			0.359641i
$836$	−10.3923			−0.359425
$837$	27.0000	−	10.3923i	0.933257	−	0.359211i
$838$	33.0000			1.13997
$839$		−	18.0000i		−	0.621429i	−0.950503	−	0.310715i	$-0.899432\pi$
$839$		−	18.0000i		−	0.621429i	0.950503	−	0.310715i	$-0.100568\pi$
$840$	6.00000	+	3.46410i	0.207020	+	0.119523i
$841$	−29.0000			−1.00000
$842$	12.1244	−	7.00000i	0.417833	−	0.241236i
$843$	10.3923	−	18.0000i	0.357930	−	0.619953i
$844$	1.00000	−	1.73205i	0.0344214	−	0.0596196i
$845$		−	13.0000i		−	0.447214i
$846$	13.5000	+	23.3827i	0.464140	+	0.803913i
$847$	32.0000	+	55.4256i	1.09953	+	1.90445i
$848$		0			0
$849$	37.5000	+	21.6506i	1.28700	+	0.743048i
$850$	−4.50000	+	2.59808i	−0.154349	+	0.0891133i
$851$	−23.3827	−	13.5000i	−0.801548	−	0.462774i
$852$	10.3923			0.356034
$853$	−14.0000			−0.479351			−0.239675	−	0.970853i	$-0.577041\pi$
$853$	−14.0000			−0.479351			−0.239675	+	0.970853i	$0.577041\pi$
$854$	−27.7128	+	48.0000i	−0.948313	+	1.64253i
$855$	−5.19615	+	3.00000i	−0.177705	+	0.102598i
$856$	−3.00000	+	5.19615i	−0.102538	+	0.177601i
$857$	−38.9711	+	22.5000i	−1.33123	+	0.768585i	−0.985488	−	0.169745i	$-0.945706\pi$
$857$	−38.9711	+	22.5000i	−1.33123	+	0.768585i	−0.345741	+	0.938330i	$0.612372\pi$
$858$		0			0
$859$	21.0000	−	12.1244i	0.716511	−	0.413678i	−0.0969563	−	0.995289i	$-0.530911\pi$
$859$	21.0000	−	12.1244i	0.716511	−	0.413678i	0.813467	+	0.581611i	$0.197577\pi$
$860$	−8.66025			−0.295312
$861$	−20.7846	+	36.0000i	−0.708338	+	1.22688i
$862$	9.00000	−	15.5885i	0.306541	−	0.530945i
$863$	7.79423	+	13.5000i	0.265319	+	0.459545i	0.967647	−	0.252308i	$-0.0811895\pi$
$863$	7.79423	+	13.5000i	0.265319	+	0.459545i	−0.702328	+	0.711853i	$0.747856\pi$
$864$	−5.19615			−0.176777
$865$		0			0
$866$	−13.8564			−0.470860
$867$			17.3205i			0.588235i
$868$	−22.0000	−	3.46410i	−0.746729	−	0.117579i
$869$		−	9.00000i		−	0.305304i
$870$		0			0
$871$		0			0
$872$			8.00000i			0.270914i
$873$	−6.00000	−	10.3923i	−0.203069	−	0.351726i
$874$	−9.00000	−	5.19615i	−0.304430	−	0.175762i
$875$	3.46410	+	2.00000i	0.117108	+	0.0676123i
$876$	24.0000			0.810885
$877$	−3.50000	−	6.06218i	−0.118187	−	0.204705i	0.800862	−	0.598848i	$-0.204375\pi$
$877$	−3.50000	−	6.06218i	−0.118187	−	0.204705i	−0.919049	+	0.394143i	$0.871041\pi$
$878$	35.5070	−	20.5000i	1.19830	−	0.691841i
$879$	−15.5885	−	27.0000i	−0.525786	−	0.910687i
$880$	−4.50000	−	2.59808i	−0.151695	−	0.0875811i
$881$	−10.3923	−	18.0000i	−0.350126	−	0.606435i	0.636146	−	0.771569i	$-0.280528\pi$
$881$	−10.3923	−	18.0000i	−0.350126	−	0.606435i	−0.986271	+	0.165134i	$0.947194\pi$
$882$	−23.3827	−	13.5000i	−0.787336	−	0.454569i
$883$		−	5.19615i		−	0.174864i	−0.996170	−	0.0874322i	$-0.972134\pi$
$883$		−	5.19615i		−	0.174864i	0.996170	−	0.0874322i	$-0.0278661\pi$
$884$		0			0
$885$	−18.0000	−	10.3923i	−0.605063	−	0.349334i
$886$	12.0000	+	20.7846i	0.403148	+	0.698273i
$887$	−28.5788	−	16.5000i	−0.959583	−	0.554016i	−0.0635387	−	0.997979i	$-0.520239\pi$
$887$	−28.5788	−	16.5000i	−0.959583	−	0.554016i	−0.896045	+	0.443964i	$0.853572\pi$
$888$	−7.79423	+	4.50000i	−0.261557	+	0.151010i
$889$	24.0000	−	13.8564i	0.804934	−	0.464729i
$890$	5.19615	+	9.00000i	0.174175	+	0.301681i
$891$	−46.7654			−1.56670
$892$	15.0000	+	8.66025i	0.502237	+	0.289967i
$893$	15.5885	+	9.00000i	0.521648	+	0.301174i
$894$	27.0000	−	15.5885i	0.903015	−	0.521356i
$895$			5.19615i			0.173688i
$896$	3.46410	+	2.00000i	0.115728	+	0.0668153i
$897$		0			0
$898$			41.5692i			1.38718i
$899$		0			0
$900$	−3.00000			−0.100000
$901$		0			0
$902$	15.5885	−	27.0000i	0.519039	−	0.899002i
$903$	60.0000			1.99667
$904$	−1.50000	−	2.59808i	−0.0498893	−	0.0864107i
$905$	−10.3923	+	18.0000i	−0.345452	+	0.598340i
$906$	−18.1865	−	10.5000i	−0.604207	−	0.348839i
$907$	4.00000			0.132818			0.0664089	−	0.997792i	$-0.478846\pi$
$907$	4.00000			0.132818			0.0664089	+	0.997792i	$0.478846\pi$
$908$	15.5885	−	9.00000i	0.517321	−	0.298675i
$909$	7.79423	−	4.50000i	0.258518	−	0.149256i
$910$		0			0
$911$	−15.5885	+	27.0000i	−0.516469	+	0.894550i	0.483349	+	0.875428i	$0.339420\pi$
$911$	−15.5885	+	27.0000i	−0.516469	+	0.894550i	−0.999817	+	0.0191219i	$0.993913\pi$
$912$	−3.00000	+	1.73205i	−0.0993399	+	0.0573539i
$913$		0			0
$914$	17.3205			0.572911
$915$		−	24.0000i		−	0.793416i
$916$	−15.0000	−	8.66025i	−0.495614	−	0.286143i
$917$	31.1769	−	18.0000i	1.02955	−	0.594412i
$918$	−13.5000	+	23.3827i	−0.445566	+	0.771744i
$919$	8.50000	+	14.7224i	0.280389	+	0.485648i	0.971481	−	0.237119i	$-0.0762032\pi$
$919$	8.50000	+	14.7224i	0.280389	+	0.485648i	−0.691091	+	0.722767i	$0.742870\pi$
$920$	−2.59808	−	4.50000i	−0.0856560	−	0.148361i
$921$	42.0000	−	24.2487i	1.38395	−	0.799022i
$922$		−	15.5885i		−	0.513378i
$923$		0			0
$924$	31.1769	+	18.0000i	1.02565	+	0.592157i
$925$	−4.50000	+	2.59808i	−0.147959	+	0.0854242i
$926$	17.3205			0.569187
$927$	6.00000	−	10.3923i	0.197066	−	0.341328i
$928$		0			0
$929$		0			0			−	1.00000i	$-0.5\pi$
$929$		0			0				1.00000i	$0.5\pi$
$930$	9.00000	−	3.46410i	0.295122	−	0.113592i
$931$	−18.0000			−0.589926
$932$		−	3.00000i		−	0.0982683i
$933$	20.7846	−	36.0000i	0.680458	−	1.17859i
$934$	42.0000			1.37428
$935$	−23.3827	+	13.5000i	−0.764696	+	0.441497i
$936$		0			0
$937$	−5.00000	+	8.66025i	−0.163343	+	0.282918i	−0.936066	−	0.351826i	$-0.885561\pi$
$937$	−5.00000	+	8.66025i	−0.163343	+	0.282918i	0.772723	+	0.634744i	$0.218894\pi$
$938$			28.0000i			0.914232i
$939$	3.00000	+	5.19615i	0.0979013	+	0.169570i
$940$	4.50000	+	7.79423i	0.146774	+	0.254220i
$941$	28.5788	+	49.5000i	0.931644	+	1.61365i	0.780513	+	0.625140i	$0.214958\pi$
$941$	28.5788	+	49.5000i	0.931644	+	1.61365i	0.151131	+	0.988514i	$0.451708\pi$
$942$	1.73205	−	3.00000i	0.0564333	−	0.0977453i
$943$	27.0000	−	15.5885i	0.879241	−	0.507630i
$944$	−10.3923	−	6.00000i	−0.338241	−	0.195283i
$945$	20.7846			0.676123
$946$	−45.0000			−1.46308
$947$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$947$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$948$	−1.50000	−	2.59808i	−0.0487177	−	0.0843816i
$949$		0			0
$950$	−1.73205	+	1.00000i	−0.0561951	+	0.0324443i
$951$	20.7846	+	36.0000i	0.673987	+	1.16738i
$952$	18.0000	−	10.3923i	0.583383	−	0.336817i
$953$	−20.7846			−0.673280			−0.336640	−	0.941634i	$-0.609290\pi$
$953$	−20.7846			−0.673280			−0.336640	+	0.941634i	$0.609290\pi$
$954$		0			0
$955$	3.00000	−	5.19615i	0.0970777	−	0.168144i
$956$	5.19615	+	9.00000i	0.168056	+	0.291081i
$957$		0			0
$958$	12.0000	−	20.7846i	0.387702	−	0.671520i
$959$	62.3538			2.01351
$960$	−1.73205			−0.0559017
$961$	−23.0000	+	20.7846i	−0.741935	+	0.670471i
$962$		0			0
$963$			18.0000i			0.580042i
$964$	24.0000	+	13.8564i	0.772988	+	0.446285i
$965$			20.0000i			0.643823i
$966$	18.0000	+	31.1769i	0.579141	+	1.00310i
$967$	3.00000	+	1.73205i	0.0964735	+	0.0556990i	0.547461	−	0.836831i	$-0.315595\pi$
$967$	3.00000	+	1.73205i	0.0964735	+	0.0556990i	−0.450987	+	0.892530i	$0.648928\pi$
$968$	−13.8564	−	8.00000i	−0.445362	−	0.257130i
$969$			18.0000i			0.578243i
$970$	−2.00000	−	3.46410i	−0.0642161	−	0.111226i
$971$	38.9711	−	22.5000i	1.25064	−	0.722059i	0.279406	−	0.960173i	$-0.409862\pi$
$971$	38.9711	−	22.5000i	1.25064	−	0.722059i	0.971237	+	0.238114i	$0.0765291\pi$
$972$	−13.5000	+	7.79423i	−0.433013	+	0.250000i
$973$	48.0000	+	27.7128i	1.53881	+	0.888432i
$974$	8.66025	+	15.0000i	0.277492	+	0.480631i
$975$		0			0
$976$		−	13.8564i		−	0.443533i
$977$		−	30.0000i		−	0.959785i	−0.877327	−	0.479893i	$-0.840676\pi$
$977$		−	30.0000i		−	0.959785i	0.877327	−	0.479893i	$-0.159324\pi$
$978$	−9.52628	+	16.5000i	−0.304617	+	0.527612i
$979$	27.0000	+	46.7654i	0.862924	+	1.49463i
$980$	−7.79423	−	4.50000i	−0.248978	−	0.143747i
$981$	12.0000	+	20.7846i	0.383131	+	0.663602i
$982$	13.5000	−	7.79423i	0.430802	−	0.248724i
$983$	5.19615	+	9.00000i	0.165732	+	0.287055i	0.936915	−	0.349558i	$-0.113668\pi$
$983$	5.19615	+	9.00000i	0.165732	+	0.287055i	−0.771183	+	0.636613i	$0.780335\pi$
$984$		−	10.3923i		−	0.331295i
$985$	−9.00000	−	5.19615i	−0.286764	−	0.165563i
$986$		0			0
$987$	−31.1769	−	54.0000i	−0.992372	−	1.71884i
$988$		0			0
$989$	−38.9711	−	22.5000i	−1.23921	−	0.715458i
$990$	−15.5885			−0.495434
$991$		−	38.1051i		−	1.21045i	−0.796055	−	0.605224i	$-0.793083\pi$
$991$		−	38.1051i		−	1.21045i	0.796055	−	0.605224i	$-0.206917\pi$
$992$	5.19615	−	2.00000i	0.164978	−	0.0635001i
$993$	−48.0000			−1.52323
$994$	−24.0000			−0.761234
$995$	−8.66025	+	15.0000i	−0.274549	+	0.475532i
$996$		0			0
$997$	−13.0000	−	22.5167i	−0.411714	−	0.713110i	0.583363	−	0.812211i	$-0.301736\pi$
$997$	−13.0000	−	22.5167i	−0.411714	−	0.713110i	−0.995077	+	0.0991016i	$0.968403\pi$
$998$	−10.3923	+	18.0000i	−0.328963	+	0.569780i
$999$	−13.5000	+	23.3827i	−0.427121	+	0.739795i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.o.a.491.1	yes	4
3.2	odd	2	inner	930.2.o.a.491.2	yes	4
31.6	odd	6	inner	930.2.o.a.161.1	✓	4
93.68	even	6	inner	930.2.o.a.161.2	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.o.a.161.1	✓	4	31.6	odd	6	inner
930.2.o.a.161.2	yes	4	93.68	even	6	inner
930.2.o.a.491.1	yes	4	1.1	even	1	trivial
930.2.o.a.491.2	yes	4	3.2	odd	2	inner

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:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.o (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(-1.50000 - 0.866025i) q^{3} -1.00000 q^{4} +(-0.866025 + 0.500000i) q^{5} +(-0.866025 + 1.50000i) q^{6} +(2.00000 - 3.46410i) q^{7} +1.00000i q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +(-1.50000 - 0.866025i) q^{3} -1.00000 q^{4} +(-0.866025 + 0.500000i) q^{5} +(-0.866025 + 1.50000i) q^{6} +(2.00000 - 3.46410i) q^{7} +1.00000i q^{8} +(1.50000 + 2.59808i) q^{9} +(0.500000 + 0.866025i) q^{10} +(2.59808 + 4.50000i) q^{11} +(1.50000 + 0.866025i) q^{12} +(-3.46410 - 2.00000i) q^{14} +1.73205 q^{15} +1.00000 q^{16} +(2.59808 - 4.50000i) q^{17} +(2.59808 - 1.50000i) q^{18} +(1.00000 - 1.73205i) q^{19} +(0.866025 - 0.500000i) q^{20} +(-6.00000 + 3.46410i) q^{21} +(4.50000 - 2.59808i) q^{22} +5.19615 q^{23} +(0.866025 - 1.50000i) q^{24} +(0.500000 - 0.866025i) q^{25} -5.19615i q^{27} +(-2.00000 + 3.46410i) q^{28} -1.73205i q^{30} +(2.00000 + 5.19615i) q^{31} -1.00000i q^{32} -9.00000i q^{33} +(-4.50000 - 2.59808i) q^{34} +4.00000i q^{35} +(-1.50000 - 2.59808i) q^{36} +(-4.50000 - 2.59808i) q^{37} +(-1.73205 - 1.00000i) q^{38} +(-0.500000 - 0.866025i) q^{40} +(5.19615 - 3.00000i) q^{41} +(3.46410 + 6.00000i) q^{42} +(-7.50000 - 4.33013i) q^{43} +(-2.59808 - 4.50000i) q^{44} +(-2.59808 - 1.50000i) q^{45} -5.19615i q^{46} +9.00000i q^{47} +(-1.50000 - 0.866025i) q^{48} +(-4.50000 - 7.79423i) q^{49} +(-0.866025 - 0.500000i) q^{50} +(-7.79423 + 4.50000i) q^{51} -5.19615 q^{54} +(-4.50000 - 2.59808i) q^{55} +(3.46410 + 2.00000i) q^{56} +(-3.00000 + 1.73205i) q^{57} +(-10.3923 - 6.00000i) q^{59} -1.73205 q^{60} -13.8564i q^{61} +(5.19615 - 2.00000i) q^{62} +12.0000 q^{63} -1.00000 q^{64} -9.00000 q^{66} +(-3.50000 - 6.06218i) q^{67} +(-2.59808 + 4.50000i) q^{68} +(-7.79423 - 4.50000i) q^{69} +4.00000 q^{70} +(5.19615 - 3.00000i) q^{71} +(-2.59808 + 1.50000i) q^{72} +(12.0000 - 6.92820i) q^{73} +(-2.59808 + 4.50000i) q^{74} +(-1.50000 + 0.866025i) q^{75} +(-1.00000 + 1.73205i) q^{76} +20.7846 q^{77} +(-1.50000 - 0.866025i) q^{79} +(-0.866025 + 0.500000i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(-3.00000 - 5.19615i) q^{82} +(6.00000 - 3.46410i) q^{84} +5.19615i q^{85} +(-4.33013 + 7.50000i) q^{86} +(-4.50000 + 2.59808i) q^{88} +10.3923 q^{89} +(-1.50000 + 2.59808i) q^{90} -5.19615 q^{92} +(1.50000 - 9.52628i) q^{93} +9.00000 q^{94} +2.00000i q^{95} +(-0.866025 + 1.50000i) q^{96} -4.00000 q^{97} +(-7.79423 + 4.50000i) q^{98} +(-7.79423 + 13.5000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 6 q^{3} - 4 q^{4} + 8 q^{7} + 6 q^{9}+O(q^{10}) \) 4 * q - 6 * q^3 - 4 * q^4 + 8 * q^7 + 6 * q^9	\( 4 q - 6 q^{3} - 4 q^{4} + 8 q^{7} + 6 q^{9} + 2 q^{10} + 6 q^{12} + 4 q^{16} + 4 q^{19} - 24 q^{21} + 18 q^{22} + 2 q^{25} - 8 q^{28} + 8 q^{31} - 18 q^{34} - 6 q^{36} - 18 q^{37} - 2 q^{40} - 30 q^{43} - 6 q^{48} - 18 q^{49} - 18 q^{55} - 12 q^{57} + 48 q^{63} - 4 q^{64} - 36 q^{66} - 14 q^{67} + 16 q^{70} + 48 q^{73} - 6 q^{75} - 4 q^{76} - 6 q^{79} - 18 q^{81} - 12 q^{82} + 24 q^{84} - 18 q^{88} - 6 q^{90} + 6 q^{93} + 36 q^{94} - 16 q^{97}+O(q^{100}) \) 4 * q - 6 * q^3 - 4 * q^4 + 8 * q^7 + 6 * q^9 + 2 * q^10 + 6 * q^12 + 4 * q^16 + 4 * q^19 - 24 * q^21 + 18 * q^22 + 2 * q^25 - 8 * q^28 + 8 * q^31 - 18 * q^34 - 6 * q^36 - 18 * q^37 - 2 * q^40 - 30 * q^43 - 6 * q^48 - 18 * q^49 - 18 * q^55 - 12 * q^57 + 48 * q^63 - 4 * q^64 - 36 * q^66 - 14 * q^67 + 16 * q^70 + 48 * q^73 - 6 * q^75 - 4 * q^76 - 6 * q^79 - 18 * q^81 - 12 * q^82 + 24 * q^84 - 18 * q^88 - 6 * q^90 + 6 * q^93 + 36 * q^94 - 16 * q^97

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