LMFDB - Embedded newform 966.2.i.f.277.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(277,966)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(966, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4, 0]))

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

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

chi := DirichletCharacter("966.277");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.i (of order $3$, 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:	$7.71354883526$
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:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			277.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	966.277
Dual form			966.2.i.f.415.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} -1.00000 q^{6} +(-0.500000 - 2.59808i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} -1.00000 q^{6} +(-0.500000 - 2.59808i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(1.50000 - 2.59808i) q^{11} +(-0.500000 - 0.866025i) q^{12} +2.00000 q^{13} +(2.00000 - 1.73205i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(1.50000 - 2.59808i) q^{17} +(0.500000 - 0.866025i) q^{18} +(-1.00000 - 1.73205i) q^{19} +(2.50000 + 0.866025i) q^{21} +3.00000 q^{22} +(0.500000 + 0.866025i) q^{23} +(0.500000 - 0.866025i) q^{24} +(2.50000 - 4.33013i) q^{25} +(1.00000 + 1.73205i) q^{26} +1.00000 q^{27} +(2.50000 + 0.866025i) q^{28} +3.00000 q^{29} +(-1.00000 + 1.73205i) q^{31} +(0.500000 - 0.866025i) q^{32} +(1.50000 + 2.59808i) q^{33} +3.00000 q^{34} +1.00000 q^{36} +(-1.00000 - 1.73205i) q^{37} +(1.00000 - 1.73205i) q^{38} +(-1.00000 + 1.73205i) q^{39} +6.00000 q^{41} +(0.500000 + 2.59808i) q^{42} +2.00000 q^{43} +(1.50000 + 2.59808i) q^{44} +(-0.500000 + 0.866025i) q^{46} +(1.50000 + 2.59808i) q^{47} +1.00000 q^{48} +(-6.50000 + 2.59808i) q^{49} +5.00000 q^{50} +(1.50000 + 2.59808i) q^{51} +(-1.00000 + 1.73205i) q^{52} +(3.00000 - 5.19615i) q^{53} +(0.500000 + 0.866025i) q^{54} +(0.500000 + 2.59808i) q^{56} +2.00000 q^{57} +(1.50000 + 2.59808i) q^{58} +(-1.00000 - 1.73205i) q^{61} -2.00000 q^{62} +(-2.00000 + 1.73205i) q^{63} +1.00000 q^{64} +(-1.50000 + 2.59808i) q^{66} +(-1.00000 + 1.73205i) q^{67} +(1.50000 + 2.59808i) q^{68} -1.00000 q^{69} +3.00000 q^{71} +(0.500000 + 0.866025i) q^{72} +(-5.50000 + 9.52628i) q^{73} +(1.00000 - 1.73205i) q^{74} +(2.50000 + 4.33013i) q^{75} +2.00000 q^{76} +(-7.50000 - 2.59808i) q^{77} -2.00000 q^{78} +(-5.50000 - 9.52628i) q^{79} +(-0.500000 + 0.866025i) q^{81} +(3.00000 + 5.19615i) q^{82} +(-2.00000 + 1.73205i) q^{84} +(1.00000 + 1.73205i) q^{86} +(-1.50000 + 2.59808i) q^{87} +(-1.50000 + 2.59808i) q^{88} +(3.00000 + 5.19615i) q^{89} +(-1.00000 - 5.19615i) q^{91} -1.00000 q^{92} +(-1.00000 - 1.73205i) q^{93} +(-1.50000 + 2.59808i) q^{94} +(0.500000 + 0.866025i) q^{96} +8.00000 q^{97} +(-5.50000 - 4.33013i) q^{98} -3.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} - q^{3} - q^{4} - 2 q^{6} - q^{7} - 2 q^{8} - q^{9}+O(q^{10}) $ 2 * q + q^2 - q^3 - q^4 - 2 * q^6 - q^7 - 2 * q^8 - q^9	$ 2 q + q^{2} - q^{3} - q^{4} - 2 q^{6} - q^{7} - 2 q^{8} - q^{9} + 3 q^{11} - q^{12} + 4 q^{13} + 4 q^{14} - q^{16} + 3 q^{17} + q^{18} - 2 q^{19} + 5 q^{21} + 6 q^{22} + q^{23} + q^{24} + 5 q^{25} + 2 q^{26} + 2 q^{27} + 5 q^{28} + 6 q^{29} - 2 q^{31} + q^{32} + 3 q^{33} + 6 q^{34} + 2 q^{36} - 2 q^{37} + 2 q^{38} - 2 q^{39} + 12 q^{41} + q^{42} + 4 q^{43} + 3 q^{44} - q^{46} + 3 q^{47} + 2 q^{48} - 13 q^{49} + 10 q^{50} + 3 q^{51} - 2 q^{52} + 6 q^{53} + q^{54} + q^{56} + 4 q^{57} + 3 q^{58} - 2 q^{61} - 4 q^{62} - 4 q^{63} + 2 q^{64} - 3 q^{66} - 2 q^{67} + 3 q^{68} - 2 q^{69} + 6 q^{71} + q^{72} - 11 q^{73} + 2 q^{74} + 5 q^{75} + 4 q^{76} - 15 q^{77} - 4 q^{78} - 11 q^{79} - q^{81} + 6 q^{82} - 4 q^{84} + 2 q^{86} - 3 q^{87} - 3 q^{88} + 6 q^{89} - 2 q^{91} - 2 q^{92} - 2 q^{93} - 3 q^{94} + q^{96} + 16 q^{97} - 11 q^{98} - 6 q^{99}+O(q^{100}) $ 2 * q + q^2 - q^3 - q^4 - 2 * q^6 - q^7 - 2 * q^8 - q^9 + 3 * q^11 - q^12 + 4 * q^13 + 4 * q^14 - q^16 + 3 * q^17 + q^18 - 2 * q^19 + 5 * q^21 + 6 * q^22 + q^23 + q^24 + 5 * q^25 + 2 * q^26 + 2 * q^27 + 5 * q^28 + 6 * q^29 - 2 * q^31 + q^32 + 3 * q^33 + 6 * q^34 + 2 * q^36 - 2 * q^37 + 2 * q^38 - 2 * q^39 + 12 * q^41 + q^42 + 4 * q^43 + 3 * q^44 - q^46 + 3 * q^47 + 2 * q^48 - 13 * q^49 + 10 * q^50 + 3 * q^51 - 2 * q^52 + 6 * q^53 + q^54 + q^56 + 4 * q^57 + 3 * q^58 - 2 * q^61 - 4 * q^62 - 4 * q^63 + 2 * q^64 - 3 * q^66 - 2 * q^67 + 3 * q^68 - 2 * q^69 + 6 * q^71 + q^72 - 11 * q^73 + 2 * q^74 + 5 * q^75 + 4 * q^76 - 15 * q^77 - 4 * q^78 - 11 * q^79 - q^81 + 6 * q^82 - 4 * q^84 + 2 * q^86 - 3 * q^87 - 3 * q^88 + 6 * q^89 - 2 * q^91 - 2 * q^92 - 2 * q^93 - 3 * q^94 + q^96 + 16 * q^97 - 11 * q^98 - 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/966\mathbb{Z}\right)^\times$.

$n$	$323$	$829$	$925$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$5$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$6$	−1.00000			−0.408248
$7$	−0.500000	−	2.59808i	−0.188982	−	0.981981i
$7$	−0.500000	−	2.59808i	−0.188982	−	0.981981i
$8$	−1.00000			−0.353553
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$		0			0
$11$	1.50000	−	2.59808i	0.452267	−	0.783349i	−0.546259	−	0.837616i	$-0.683949\pi$
$11$	1.50000	−	2.59808i	0.452267	−	0.783349i	0.998526	+	0.0542666i	$0.0172821\pi$
$12$	−0.500000	−	0.866025i	−0.144338	−	0.250000i
$13$	2.00000			0.554700			0.277350	−	0.960769i	$-0.410544\pi$
$13$	2.00000			0.554700			0.277350	+	0.960769i	$0.410544\pi$
$14$	2.00000	−	1.73205i	0.534522	−	0.462910i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	1.50000	−	2.59808i	0.363803	−	0.630126i	−0.624780	−	0.780801i	$-0.714811\pi$
$17$	1.50000	−	2.59808i	0.363803	−	0.630126i	0.988583	+	0.150675i	$0.0481447\pi$
$18$	0.500000	−	0.866025i	0.117851	−	0.204124i
$19$	−1.00000	−	1.73205i	−0.229416	−	0.397360i	0.728219	−	0.685344i	$-0.240348\pi$
$19$	−1.00000	−	1.73205i	−0.229416	−	0.397360i	−0.957635	+	0.287984i	$0.907015\pi$
$20$		0			0
$21$	2.50000	+	0.866025i	0.545545	+	0.188982i
$22$	3.00000			0.639602
$23$	0.500000	+	0.866025i	0.104257	+	0.180579i
$23$	0.500000	+	0.866025i	0.104257	+	0.180579i
$24$	0.500000	−	0.866025i	0.102062	−	0.176777i
$25$	2.50000	−	4.33013i	0.500000	−	0.866025i
$26$	1.00000	+	1.73205i	0.196116	+	0.339683i
$27$	1.00000			0.192450
$28$	2.50000	+	0.866025i	0.472456	+	0.163663i
$29$	3.00000			0.557086			0.278543	−	0.960424i	$-0.410149\pi$
$29$	3.00000			0.557086			0.278543	+	0.960424i	$0.410149\pi$
$30$		0			0
$31$	−1.00000	+	1.73205i	−0.179605	+	0.311086i	−0.941745	−	0.336327i	$-0.890815\pi$
$31$	−1.00000	+	1.73205i	−0.179605	+	0.311086i	0.762140	+	0.647412i	$0.224149\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	1.50000	+	2.59808i	0.261116	+	0.452267i
$34$	3.00000			0.514496
$35$		0			0
$36$	1.00000			0.166667
$37$	−1.00000	−	1.73205i	−0.164399	−	0.284747i	0.772043	−	0.635571i	$-0.219235\pi$
$37$	−1.00000	−	1.73205i	−0.164399	−	0.284747i	−0.936442	+	0.350823i	$0.885902\pi$
$38$	1.00000	−	1.73205i	0.162221	−	0.280976i
$39$	−1.00000	+	1.73205i	−0.160128	+	0.277350i
$40$		0			0
$41$	6.00000			0.937043			0.468521	−	0.883452i	$-0.344787\pi$
$41$	6.00000			0.937043			0.468521	+	0.883452i	$0.344787\pi$
$42$	0.500000	+	2.59808i	0.0771517	+	0.400892i
$43$	2.00000			0.304997			0.152499	−	0.988304i	$-0.451268\pi$
$43$	2.00000			0.304997			0.152499	+	0.988304i	$0.451268\pi$
$44$	1.50000	+	2.59808i	0.226134	+	0.391675i
$45$		0			0
$46$	−0.500000	+	0.866025i	−0.0737210	+	0.127688i
$47$	1.50000	+	2.59808i	0.218797	+	0.378968i	0.954441	−	0.298401i	$-0.0964533\pi$
$47$	1.50000	+	2.59808i	0.218797	+	0.378968i	−0.735643	+	0.677369i	$0.763120\pi$
$48$	1.00000			0.144338
$49$	−6.50000	+	2.59808i	−0.928571	+	0.371154i
$50$	5.00000			0.707107
$51$	1.50000	+	2.59808i	0.210042	+	0.363803i
$52$	−1.00000	+	1.73205i	−0.138675	+	0.240192i
$53$	3.00000	−	5.19615i	0.412082	−	0.713746i	−0.583036	−	0.812447i	$-0.698135\pi$
$53$	3.00000	−	5.19615i	0.412082	−	0.713746i	0.995117	+	0.0987002i	$0.0314685\pi$
$54$	0.500000	+	0.866025i	0.0680414	+	0.117851i
$55$		0			0
$56$	0.500000	+	2.59808i	0.0668153	+	0.347183i
$57$	2.00000			0.264906
$58$	1.50000	+	2.59808i	0.196960	+	0.341144i
$59$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$59$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$60$		0			0
$61$	−1.00000	−	1.73205i	−0.128037	−	0.221766i	0.794879	−	0.606768i	$-0.207534\pi$
$61$	−1.00000	−	1.73205i	−0.128037	−	0.221766i	−0.922916	+	0.385002i	$0.874201\pi$
$62$	−2.00000			−0.254000
$63$	−2.00000	+	1.73205i	−0.251976	+	0.218218i
$64$	1.00000			0.125000
$65$		0			0
$66$	−1.50000	+	2.59808i	−0.184637	+	0.319801i
$67$	−1.00000	+	1.73205i	−0.122169	+	0.211604i	−0.920623	−	0.390453i	$-0.872318\pi$
$67$	−1.00000	+	1.73205i	−0.122169	+	0.211604i	0.798454	+	0.602056i	$0.205652\pi$
$68$	1.50000	+	2.59808i	0.181902	+	0.315063i
$69$	−1.00000			−0.120386
$70$		0			0
$71$	3.00000			0.356034			0.178017	−	0.984027i	$-0.443032\pi$
$71$	3.00000			0.356034			0.178017	+	0.984027i	$0.443032\pi$
$72$	0.500000	+	0.866025i	0.0589256	+	0.102062i
$73$	−5.50000	+	9.52628i	−0.643726	+	1.11497i	0.340868	+	0.940111i	$0.389279\pi$
$73$	−5.50000	+	9.52628i	−0.643726	+	1.11497i	−0.984594	+	0.174855i	$0.944054\pi$
$74$	1.00000	−	1.73205i	0.116248	−	0.201347i
$75$	2.50000	+	4.33013i	0.288675	+	0.500000i
$76$	2.00000			0.229416
$77$	−7.50000	−	2.59808i	−0.854704	−	0.296078i
$78$	−2.00000			−0.226455
$79$	−5.50000	−	9.52628i	−0.618798	−	1.07179i	−0.989705	−	0.143120i	$-0.954286\pi$
$79$	−5.50000	−	9.52628i	−0.618798	−	1.07179i	0.370907	−	0.928670i	$-0.379047\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	3.00000	+	5.19615i	0.331295	+	0.573819i
$83$		0			0			−	1.00000i	$-0.5\pi$
$83$		0			0				1.00000i	$0.5\pi$
$84$	−2.00000	+	1.73205i	−0.218218	+	0.188982i
$85$		0			0
$86$	1.00000	+	1.73205i	0.107833	+	0.186772i
$87$	−1.50000	+	2.59808i	−0.160817	+	0.278543i
$88$	−1.50000	+	2.59808i	−0.159901	+	0.276956i
$89$	3.00000	+	5.19615i	0.317999	+	0.550791i	0.980071	−	0.198650i	$-0.0636557\pi$
$89$	3.00000	+	5.19615i	0.317999	+	0.550791i	−0.662071	+	0.749441i	$0.730322\pi$
$90$		0			0
$91$	−1.00000	−	5.19615i	−0.104828	−	0.544705i
$92$	−1.00000			−0.104257
$93$	−1.00000	−	1.73205i	−0.103695	−	0.179605i
$94$	−1.50000	+	2.59808i	−0.154713	+	0.267971i
$95$		0			0
$96$	0.500000	+	0.866025i	0.0510310	+	0.0883883i
$97$	8.00000			0.812277			0.406138	−	0.913812i	$-0.366875\pi$
$97$	8.00000			0.812277			0.406138	+	0.913812i	$0.366875\pi$
$98$	−5.50000	−	4.33013i	−0.555584	−	0.437409i
$99$	−3.00000			−0.301511
$100$	2.50000	+	4.33013i	0.250000	+	0.433013i
$101$	1.50000	−	2.59808i	0.149256	−	0.258518i	−0.781697	−	0.623658i	$-0.785646\pi$
$101$	1.50000	−	2.59808i	0.149256	−	0.258518i	0.930953	+	0.365140i	$0.118979\pi$
$102$	−1.50000	+	2.59808i	−0.148522	+	0.257248i
$103$	−2.50000	−	4.33013i	−0.246332	−	0.426660i	0.716173	−	0.697923i	$-0.245892\pi$
$103$	−2.50000	−	4.33013i	−0.246332	−	0.426660i	−0.962505	+	0.271263i	$0.912559\pi$
$104$	−2.00000			−0.196116
$105$		0			0
$106$	6.00000			0.582772
$107$	−6.00000	−	10.3923i	−0.580042	−	1.00466i	−0.995474	−	0.0950377i	$-0.969703\pi$
$107$	−6.00000	−	10.3923i	−0.580042	−	1.00466i	0.415432	−	0.909624i	$-0.363630\pi$
$108$	−0.500000	+	0.866025i	−0.0481125	+	0.0833333i
$109$	0.500000	−	0.866025i	0.0478913	−	0.0829502i	−0.841086	−	0.540901i	$-0.818083\pi$
$109$	0.500000	−	0.866025i	0.0478913	−	0.0829502i	0.888977	+	0.457951i	$0.151417\pi$
$110$		0			0
$111$	2.00000			0.189832
$112$	−2.00000	+	1.73205i	−0.188982	+	0.163663i
$113$	18.0000			1.69330			0.846649	−	0.532152i	$-0.178617\pi$
$113$	18.0000			1.69330			0.846649	+	0.532152i	$0.178617\pi$
$114$	1.00000	+	1.73205i	0.0936586	+	0.162221i
$115$		0			0
$116$	−1.50000	+	2.59808i	−0.139272	+	0.241225i
$117$	−1.00000	−	1.73205i	−0.0924500	−	0.160128i
$118$		0			0
$119$	−7.50000	−	2.59808i	−0.687524	−	0.238165i
$120$		0			0
$121$	1.00000	+	1.73205i	0.0909091	+	0.157459i
$122$	1.00000	−	1.73205i	0.0905357	−	0.156813i
$123$	−3.00000	+	5.19615i	−0.270501	+	0.468521i
$124$	−1.00000	−	1.73205i	−0.0898027	−	0.155543i
$125$		0			0
$126$	−2.50000	−	0.866025i	−0.222718	−	0.0771517i
$127$	2.00000			0.177471			0.0887357	−	0.996055i	$-0.471717\pi$
$127$	2.00000			0.177471			0.0887357	+	0.996055i	$0.471717\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	−1.00000	+	1.73205i	−0.0880451	+	0.152499i
$130$		0			0
$131$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$131$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$132$	−3.00000			−0.261116
$133$	−4.00000	+	3.46410i	−0.346844	+	0.300376i
$134$	−2.00000			−0.172774
$135$		0			0
$136$	−1.50000	+	2.59808i	−0.128624	+	0.222783i
$137$	10.5000	−	18.1865i	0.897076	−	1.55378i	0.0658609	−	0.997829i	$-0.479021\pi$
$137$	10.5000	−	18.1865i	0.897076	−	1.55378i	0.831215	−	0.555952i	$-0.187646\pi$
$138$	−0.500000	−	0.866025i	−0.0425628	−	0.0737210i
$139$	−13.0000			−1.10265			−0.551323	−	0.834292i	$-0.685877\pi$
$139$	−13.0000			−1.10265			−0.551323	+	0.834292i	$0.685877\pi$
$140$		0			0
$141$	−3.00000			−0.252646
$142$	1.50000	+	2.59808i	0.125877	+	0.218026i
$143$	3.00000	−	5.19615i	0.250873	−	0.434524i
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$		0			0
$146$	−11.0000			−0.910366
$147$	1.00000	−	6.92820i	0.0824786	−	0.571429i
$148$	2.00000			0.164399
$149$	−6.00000	−	10.3923i	−0.491539	−	0.851371i	0.508413	−	0.861113i	$-0.330232\pi$
$149$	−6.00000	−	10.3923i	−0.491539	−	0.851371i	−0.999953	+	0.00974235i	$0.996899\pi$
$150$	−2.50000	+	4.33013i	−0.204124	+	0.353553i
$151$	2.00000	−	3.46410i	0.162758	−	0.281905i	−0.773099	−	0.634285i	$-0.781294\pi$
$151$	2.00000	−	3.46410i	0.162758	−	0.281905i	0.935857	+	0.352381i	$0.114628\pi$
$152$	1.00000	+	1.73205i	0.0811107	+	0.140488i
$153$	−3.00000			−0.242536
$154$	−1.50000	−	7.79423i	−0.120873	−	0.628077i
$155$		0			0
$156$	−1.00000	−	1.73205i	−0.0800641	−	0.138675i
$157$	−11.5000	+	19.9186i	−0.917800	+	1.58968i	−0.115050	+	0.993360i	$0.536703\pi$
$157$	−11.5000	+	19.9186i	−0.917800	+	1.58968i	−0.802749	+	0.596316i	$0.796630\pi$
$158$	5.50000	−	9.52628i	0.437557	−	0.757870i
$159$	3.00000	+	5.19615i	0.237915	+	0.412082i
$160$		0			0
$161$	2.00000	−	1.73205i	0.157622	−	0.136505i
$162$	−1.00000			−0.0785674
$163$	−11.5000	−	19.9186i	−0.900750	−	1.56014i	−0.826523	−	0.562902i	$-0.809685\pi$
$163$	−11.5000	−	19.9186i	−0.900750	−	1.56014i	−0.0742262	−	0.997241i	$-0.523649\pi$
$164$	−3.00000	+	5.19615i	−0.234261	+	0.405751i
$165$		0			0
$166$		0			0
$167$		0			0			−	1.00000i	$-0.5\pi$
$167$		0			0				1.00000i	$0.5\pi$
$168$	−2.50000	−	0.866025i	−0.192879	−	0.0668153i
$169$	−9.00000			−0.692308
$170$		0			0
$171$	−1.00000	+	1.73205i	−0.0764719	+	0.132453i
$172$	−1.00000	+	1.73205i	−0.0762493	+	0.132068i
$173$	7.50000	+	12.9904i	0.570214	+	0.987640i	0.996544	+	0.0830722i	$0.0264732\pi$
$173$	7.50000	+	12.9904i	0.570214	+	0.987640i	−0.426329	+	0.904568i	$0.640193\pi$
$174$	−3.00000			−0.227429
$175$	−12.5000	−	4.33013i	−0.944911	−	0.327327i
$176$	−3.00000			−0.226134
$177$		0			0
$178$	−3.00000	+	5.19615i	−0.224860	+	0.389468i
$179$	−3.00000	+	5.19615i	−0.224231	+	0.388379i	−0.956088	−	0.293079i	$-0.905320\pi$
$179$	−3.00000	+	5.19615i	−0.224231	+	0.388379i	0.731858	+	0.681457i	$0.238654\pi$
$180$		0			0
$181$	11.0000			0.817624			0.408812	−	0.912619i	$-0.365943\pi$
$181$	11.0000			0.817624			0.408812	+	0.912619i	$0.365943\pi$
$182$	4.00000	−	3.46410i	0.296500	−	0.256776i
$183$	2.00000			0.147844
$184$	−0.500000	−	0.866025i	−0.0368605	−	0.0638442i
$185$		0			0
$186$	1.00000	−	1.73205i	0.0733236	−	0.127000i
$187$	−4.50000	−	7.79423i	−0.329073	−	0.569970i
$188$	−3.00000			−0.218797
$189$	−0.500000	−	2.59808i	−0.0363696	−	0.188982i
$190$		0			0
$191$	−6.00000	−	10.3923i	−0.434145	−	0.751961i	0.563081	−	0.826402i	$-0.309616\pi$
$191$	−6.00000	−	10.3923i	−0.434145	−	0.751961i	−0.997225	+	0.0744412i	$0.976283\pi$
$192$	−0.500000	+	0.866025i	−0.0360844	+	0.0625000i
$193$	−7.00000	+	12.1244i	−0.503871	+	0.872730i	0.496119	+	0.868255i	$0.334758\pi$
$193$	−7.00000	+	12.1244i	−0.503871	+	0.872730i	−0.999990	+	0.00447566i	$0.998575\pi$
$194$	4.00000	+	6.92820i	0.287183	+	0.497416i
$195$		0			0
$196$	1.00000	−	6.92820i	0.0714286	−	0.494872i
$197$	15.0000			1.06871			0.534353	−	0.845262i	$-0.320555\pi$
$197$	15.0000			1.06871			0.534353	+	0.845262i	$0.320555\pi$
$198$	−1.50000	−	2.59808i	−0.106600	−	0.184637i
$199$	−8.50000	+	14.7224i	−0.602549	+	1.04365i	0.389885	+	0.920864i	$0.372515\pi$
$199$	−8.50000	+	14.7224i	−0.602549	+	1.04365i	−0.992434	+	0.122782i	$0.960818\pi$
$200$	−2.50000	+	4.33013i	−0.176777	+	0.306186i
$201$	−1.00000	−	1.73205i	−0.0705346	−	0.122169i
$202$	3.00000			0.211079
$203$	−1.50000	−	7.79423i	−0.105279	−	0.547048i
$204$	−3.00000			−0.210042
$205$		0			0
$206$	2.50000	−	4.33013i	0.174183	−	0.301694i
$207$	0.500000	−	0.866025i	0.0347524	−	0.0601929i
$208$	−1.00000	−	1.73205i	−0.0693375	−	0.120096i
$209$	−6.00000			−0.415029
$210$		0			0
$211$	−19.0000			−1.30801			−0.654007	−	0.756489i	$-0.726913\pi$
$211$	−19.0000			−1.30801			−0.654007	+	0.756489i	$0.726913\pi$
$212$	3.00000	+	5.19615i	0.206041	+	0.356873i
$213$	−1.50000	+	2.59808i	−0.102778	+	0.178017i
$214$	6.00000	−	10.3923i	0.410152	−	0.710403i
$215$		0			0
$216$	−1.00000			−0.0680414
$217$	5.00000	+	1.73205i	0.339422	+	0.117579i
$218$	1.00000			0.0677285
$219$	−5.50000	−	9.52628i	−0.371656	−	0.643726i
$220$		0			0
$221$	3.00000	−	5.19615i	0.201802	−	0.349531i
$222$	1.00000	+	1.73205i	0.0671156	+	0.116248i
$223$	−10.0000			−0.669650			−0.334825	−	0.942280i	$-0.608677\pi$
$223$	−10.0000			−0.669650			−0.334825	+	0.942280i	$0.608677\pi$
$224$	−2.50000	−	0.866025i	−0.167038	−	0.0578638i
$225$	−5.00000			−0.333333
$226$	9.00000	+	15.5885i	0.598671	+	1.03693i
$227$	1.50000	−	2.59808i	0.0995585	−	0.172440i	−0.811943	−	0.583736i	$-0.801590\pi$
$227$	1.50000	−	2.59808i	0.0995585	−	0.172440i	0.911502	+	0.411296i	$0.134924\pi$
$228$	−1.00000	+	1.73205i	−0.0662266	+	0.114708i
$229$	0.500000	+	0.866025i	0.0330409	+	0.0572286i	0.882073	−	0.471113i	$-0.156147\pi$
$229$	0.500000	+	0.866025i	0.0330409	+	0.0572286i	−0.849032	+	0.528341i	$0.822814\pi$
$230$		0			0
$231$	6.00000	−	5.19615i	0.394771	−	0.341882i
$232$	−3.00000			−0.196960
$233$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$233$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$234$	1.00000	−	1.73205i	0.0653720	−	0.113228i
$235$		0			0
$236$		0			0
$237$	11.0000			0.714527
$238$	−1.50000	−	7.79423i	−0.0972306	−	0.505225i
$239$	15.0000			0.970269			0.485135	−	0.874439i	$-0.338771\pi$
$239$	15.0000			0.970269			0.485135	+	0.874439i	$0.338771\pi$
$240$		0			0
$241$	−1.00000	+	1.73205i	−0.0644157	+	0.111571i	−0.896435	−	0.443176i	$-0.853852\pi$
$241$	−1.00000	+	1.73205i	−0.0644157	+	0.111571i	0.832019	+	0.554747i	$0.187185\pi$
$242$	−1.00000	+	1.73205i	−0.0642824	+	0.111340i
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$	2.00000			0.128037
$245$		0			0
$246$	−6.00000			−0.382546
$247$	−2.00000	−	3.46410i	−0.127257	−	0.220416i
$248$	1.00000	−	1.73205i	0.0635001	−	0.109985i
$249$		0			0
$250$		0			0
$251$	3.00000			0.189358			0.0946792	−	0.995508i	$-0.469817\pi$
$251$	3.00000			0.189358			0.0946792	+	0.995508i	$0.469817\pi$
$252$	−0.500000	−	2.59808i	−0.0314970	−	0.163663i
$253$	3.00000			0.188608
$254$	1.00000	+	1.73205i	0.0627456	+	0.108679i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−3.00000	−	5.19615i	−0.187135	−	0.324127i	0.757159	−	0.653231i	$-0.226587\pi$
$257$	−3.00000	−	5.19615i	−0.187135	−	0.324127i	−0.944294	+	0.329104i	$0.893253\pi$
$258$	−2.00000			−0.124515
$259$	−4.00000	+	3.46410i	−0.248548	+	0.215249i
$260$		0			0
$261$	−1.50000	−	2.59808i	−0.0928477	−	0.160817i
$262$		0			0
$263$	−12.0000	+	20.7846i	−0.739952	+	1.28163i	0.212565	+	0.977147i	$0.431818\pi$
$263$	−12.0000	+	20.7846i	−0.739952	+	1.28163i	−0.952517	+	0.304487i	$0.901515\pi$
$264$	−1.50000	−	2.59808i	−0.0923186	−	0.159901i
$265$		0			0
$266$	−5.00000	−	1.73205i	−0.306570	−	0.106199i
$267$	−6.00000			−0.367194
$268$	−1.00000	−	1.73205i	−0.0610847	−	0.105802i
$269$	−7.50000	+	12.9904i	−0.457283	+	0.792038i	−0.998816	−	0.0486418i	$-0.984511\pi$
$269$	−7.50000	+	12.9904i	−0.457283	+	0.792038i	0.541533	+	0.840679i	$0.317844\pi$
$270$		0			0
$271$	11.0000	+	19.0526i	0.668202	+	1.15736i	0.978406	+	0.206691i	$0.0662693\pi$
$271$	11.0000	+	19.0526i	0.668202	+	1.15736i	−0.310204	+	0.950670i	$0.600397\pi$
$272$	−3.00000			−0.181902
$273$	5.00000	+	1.73205i	0.302614	+	0.104828i
$274$	21.0000			1.26866
$275$	−7.50000	−	12.9904i	−0.452267	−	0.783349i
$276$	0.500000	−	0.866025i	0.0300965	−	0.0521286i
$277$	−4.00000	+	6.92820i	−0.240337	+	0.416275i	−0.960810	−	0.277207i	$-0.910591\pi$
$277$	−4.00000	+	6.92820i	−0.240337	+	0.416275i	0.720473	+	0.693482i	$0.243925\pi$
$278$	−6.50000	−	11.2583i	−0.389844	−	0.675230i
$279$	2.00000			0.119737
$280$		0			0
$281$	−3.00000			−0.178965			−0.0894825	−	0.995988i	$-0.528521\pi$
$281$	−3.00000			−0.178965			−0.0894825	+	0.995988i	$0.528521\pi$
$282$	−1.50000	−	2.59808i	−0.0893237	−	0.154713i
$283$	−4.00000	+	6.92820i	−0.237775	+	0.411839i	−0.960076	−	0.279741i	$-0.909752\pi$
$283$	−4.00000	+	6.92820i	−0.237775	+	0.411839i	0.722300	+	0.691580i	$0.243085\pi$
$284$	−1.50000	+	2.59808i	−0.0890086	+	0.154167i
$285$		0			0
$286$	6.00000			0.354787
$287$	−3.00000	−	15.5885i	−0.177084	−	0.920158i
$288$	−1.00000			−0.0589256
$289$	4.00000	+	6.92820i	0.235294	+	0.407541i
$290$		0			0
$291$	−4.00000	+	6.92820i	−0.234484	+	0.406138i
$292$	−5.50000	−	9.52628i	−0.321863	−	0.557483i
$293$		0			0			−	1.00000i	$-0.5\pi$
$293$		0			0				1.00000i	$0.5\pi$
$294$	6.50000	−	2.59808i	0.379088	−	0.151523i
$295$		0			0
$296$	1.00000	+	1.73205i	0.0581238	+	0.100673i
$297$	1.50000	−	2.59808i	0.0870388	−	0.150756i
$298$	6.00000	−	10.3923i	0.347571	−	0.602010i
$299$	1.00000	+	1.73205i	0.0578315	+	0.100167i
$300$	−5.00000			−0.288675
$301$	−1.00000	−	5.19615i	−0.0576390	−	0.299501i
$302$	4.00000			0.230174
$303$	1.50000	+	2.59808i	0.0861727	+	0.149256i
$304$	−1.00000	+	1.73205i	−0.0573539	+	0.0993399i
$305$		0			0
$306$	−1.50000	−	2.59808i	−0.0857493	−	0.148522i
$307$	11.0000			0.627803			0.313902	−	0.949456i	$-0.398364\pi$
$307$	11.0000			0.627803			0.313902	+	0.949456i	$0.398364\pi$
$308$	6.00000	−	5.19615i	0.341882	−	0.296078i
$309$	5.00000			0.284440
$310$		0			0
$311$	1.50000	−	2.59808i	0.0850572	−	0.147323i	−0.820358	−	0.571850i	$-0.806226\pi$
$311$	1.50000	−	2.59808i	0.0850572	−	0.147323i	0.905416	+	0.424526i	$0.139559\pi$
$312$	1.00000	−	1.73205i	0.0566139	−	0.0980581i
$313$	−4.00000	−	6.92820i	−0.226093	−	0.391605i	0.730554	−	0.682855i	$-0.239262\pi$
$313$	−4.00000	−	6.92820i	−0.226093	−	0.391605i	−0.956647	+	0.291250i	$0.905929\pi$
$314$	−23.0000			−1.29797
$315$		0			0
$316$	11.0000			0.618798
$317$	9.00000	+	15.5885i	0.505490	+	0.875535i	0.999980	+	0.00635137i	$0.00202172\pi$
$317$	9.00000	+	15.5885i	0.505490	+	0.875535i	−0.494489	+	0.869184i	$0.664645\pi$
$318$	−3.00000	+	5.19615i	−0.168232	+	0.291386i
$319$	4.50000	−	7.79423i	0.251952	−	0.436393i
$320$		0			0
$321$	12.0000			0.669775
$322$	2.50000	+	0.866025i	0.139320	+	0.0482617i
$323$	−6.00000			−0.333849
$324$	−0.500000	−	0.866025i	−0.0277778	−	0.0481125i
$325$	5.00000	−	8.66025i	0.277350	−	0.480384i
$326$	11.5000	−	19.9186i	0.636926	−	1.10319i
$327$	0.500000	+	0.866025i	0.0276501	+	0.0478913i
$328$	−6.00000			−0.331295
$329$	6.00000	−	5.19615i	0.330791	−	0.286473i
$330$		0			0
$331$	−4.00000	−	6.92820i	−0.219860	−	0.380808i	0.734905	−	0.678170i	$-0.237227\pi$
$331$	−4.00000	−	6.92820i	−0.219860	−	0.380808i	−0.954765	+	0.297361i	$0.903893\pi$
$332$		0			0
$333$	−1.00000	+	1.73205i	−0.0547997	+	0.0949158i
$334$		0			0
$335$		0			0
$336$	−0.500000	−	2.59808i	−0.0272772	−	0.141737i
$337$	14.0000			0.762629			0.381314	−	0.924445i	$-0.375472\pi$
$337$	14.0000			0.762629			0.381314	+	0.924445i	$0.375472\pi$
$338$	−4.50000	−	7.79423i	−0.244768	−	0.423950i
$339$	−9.00000	+	15.5885i	−0.488813	+	0.846649i
$340$		0			0
$341$	3.00000	+	5.19615i	0.162459	+	0.281387i
$342$	−2.00000			−0.108148
$343$	10.0000	+	15.5885i	0.539949	+	0.841698i
$344$	−2.00000			−0.107833
$345$		0			0
$346$	−7.50000	+	12.9904i	−0.403202	+	0.698367i
$347$	−3.00000	+	5.19615i	−0.161048	+	0.278944i	−0.935245	−	0.354001i	$-0.884821\pi$
$347$	−3.00000	+	5.19615i	−0.161048	+	0.278944i	0.774197	+	0.632945i	$0.218154\pi$
$348$	−1.50000	−	2.59808i	−0.0804084	−	0.139272i
$349$	−22.0000			−1.17763			−0.588817	−	0.808267i	$-0.700406\pi$
$349$	−22.0000			−1.17763			−0.588817	+	0.808267i	$0.700406\pi$
$350$	−2.50000	−	12.9904i	−0.133631	−	0.694365i
$351$	2.00000			0.106752
$352$	−1.50000	−	2.59808i	−0.0799503	−	0.138478i
$353$	9.00000	−	15.5885i	0.479022	−	0.829690i	−0.520689	−	0.853746i	$-0.674325\pi$
$353$	9.00000	−	15.5885i	0.479022	−	0.829690i	0.999711	+	0.0240566i	$0.00765819\pi$
$354$		0			0
$355$		0			0
$356$	−6.00000			−0.317999
$357$	6.00000	−	5.19615i	0.317554	−	0.275010i
$358$	−6.00000			−0.317110
$359$	6.00000	+	10.3923i	0.316668	+	0.548485i	0.979791	−	0.200026i	$-0.0641026\pi$
$359$	6.00000	+	10.3923i	0.316668	+	0.548485i	−0.663123	+	0.748511i	$0.730769\pi$
$360$		0			0
$361$	7.50000	−	12.9904i	0.394737	−	0.683704i
$362$	5.50000	+	9.52628i	0.289074	+	0.500690i
$363$	−2.00000			−0.104973
$364$	5.00000	+	1.73205i	0.262071	+	0.0907841i
$365$		0			0
$366$	1.00000	+	1.73205i	0.0522708	+	0.0905357i
$367$	−4.00000	+	6.92820i	−0.208798	+	0.361649i	−0.951336	−	0.308155i	$-0.900289\pi$
$367$	−4.00000	+	6.92820i	−0.208798	+	0.361649i	0.742538	+	0.669804i	$0.233622\pi$
$368$	0.500000	−	0.866025i	0.0260643	−	0.0451447i
$369$	−3.00000	−	5.19615i	−0.156174	−	0.270501i
$370$		0			0
$371$	−15.0000	−	5.19615i	−0.778761	−	0.269771i
$372$	2.00000			0.103695
$373$	6.50000	+	11.2583i	0.336557	+	0.582934i	0.983783	−	0.179364i	$-0.0574041\pi$
$373$	6.50000	+	11.2583i	0.336557	+	0.582934i	−0.647225	+	0.762299i	$0.724071\pi$
$374$	4.50000	−	7.79423i	0.232689	−	0.403030i
$375$		0			0
$376$	−1.50000	−	2.59808i	−0.0773566	−	0.133986i
$377$	6.00000			0.309016
$378$	2.00000	−	1.73205i	0.102869	−	0.0890871i
$379$	20.0000			1.02733			0.513665	−	0.857991i	$-0.328287\pi$
$379$	20.0000			1.02733			0.513665	+	0.857991i	$0.328287\pi$
$380$		0			0
$381$	−1.00000	+	1.73205i	−0.0512316	+	0.0887357i
$382$	6.00000	−	10.3923i	0.306987	−	0.531717i
$383$	3.00000	+	5.19615i	0.153293	+	0.265511i	0.932436	−	0.361335i	$-0.117679\pi$
$383$	3.00000	+	5.19615i	0.153293	+	0.265511i	−0.779143	+	0.626846i	$0.784346\pi$
$384$	−1.00000			−0.0510310
$385$		0			0
$386$	−14.0000			−0.712581
$387$	−1.00000	−	1.73205i	−0.0508329	−	0.0880451i
$388$	−4.00000	+	6.92820i	−0.203069	+	0.351726i
$389$	−12.0000	+	20.7846i	−0.608424	+	1.05382i	0.383076	+	0.923717i	$0.374865\pi$
$389$	−12.0000	+	20.7846i	−0.608424	+	1.05382i	−0.991500	+	0.130105i	$0.958469\pi$
$390$		0			0
$391$	3.00000			0.151717
$392$	6.50000	−	2.59808i	0.328300	−	0.131223i
$393$		0			0
$394$	7.50000	+	12.9904i	0.377845	+	0.654446i
$395$		0			0
$396$	1.50000	−	2.59808i	0.0753778	−	0.130558i
$397$	17.0000	+	29.4449i	0.853206	+	1.47780i	0.878300	+	0.478110i	$0.158678\pi$
$397$	17.0000	+	29.4449i	0.853206	+	1.47780i	−0.0250943	+	0.999685i	$0.507989\pi$
$398$	−17.0000			−0.852133
$399$	−1.00000	−	5.19615i	−0.0500626	−	0.260133i
$400$	−5.00000			−0.250000
$401$	7.50000	+	12.9904i	0.374532	+	0.648709i	0.990257	−	0.139253i	$-0.0444700\pi$
$401$	7.50000	+	12.9904i	0.374532	+	0.648709i	−0.615725	+	0.787961i	$0.711137\pi$
$402$	1.00000	−	1.73205i	0.0498755	−	0.0863868i
$403$	−2.00000	+	3.46410i	−0.0996271	+	0.172559i
$404$	1.50000	+	2.59808i	0.0746278	+	0.129259i
$405$		0			0
$406$	6.00000	−	5.19615i	0.297775	−	0.257881i
$407$	−6.00000			−0.297409
$408$	−1.50000	−	2.59808i	−0.0742611	−	0.128624i
$409$	−14.5000	+	25.1147i	−0.716979	+	1.24184i	0.245212	+	0.969469i	$0.421142\pi$
$409$	−14.5000	+	25.1147i	−0.716979	+	1.24184i	−0.962191	+	0.272374i	$0.912191\pi$
$410$		0			0
$411$	10.5000	+	18.1865i	0.517927	+	0.897076i
$412$	5.00000			0.246332
$413$		0			0
$414$	1.00000			0.0491473
$415$		0			0
$416$	1.00000	−	1.73205i	0.0490290	−	0.0849208i
$417$	6.50000	−	11.2583i	0.318306	−	0.551323i
$418$	−3.00000	−	5.19615i	−0.146735	−	0.254152i
$419$	−21.0000			−1.02592			−0.512959	−	0.858413i	$-0.671451\pi$
$419$	−21.0000			−1.02592			−0.512959	+	0.858413i	$0.671451\pi$
$420$		0			0
$421$	17.0000			0.828529			0.414265	−	0.910156i	$-0.364039\pi$
$421$	17.0000			0.828529			0.414265	+	0.910156i	$0.364039\pi$
$422$	−9.50000	−	16.4545i	−0.462453	−	0.800992i
$423$	1.50000	−	2.59808i	0.0729325	−	0.126323i
$424$	−3.00000	+	5.19615i	−0.145693	+	0.252347i
$425$	−7.50000	−	12.9904i	−0.363803	−	0.630126i
$426$	−3.00000			−0.145350
$427$	−4.00000	+	3.46410i	−0.193574	+	0.167640i
$428$	12.0000			0.580042
$429$	3.00000	+	5.19615i	0.144841	+	0.250873i
$430$		0			0
$431$	−15.0000	+	25.9808i	−0.722525	+	1.25145i	0.237460	+	0.971397i	$0.423685\pi$
$431$	−15.0000	+	25.9808i	−0.722525	+	1.25145i	−0.959985	+	0.280052i	$0.909648\pi$
$432$	−0.500000	−	0.866025i	−0.0240563	−	0.0416667i
$433$	2.00000			0.0961139			0.0480569	−	0.998845i	$-0.484697\pi$
$433$	2.00000			0.0961139			0.0480569	+	0.998845i	$0.484697\pi$
$434$	1.00000	+	5.19615i	0.0480015	+	0.249423i
$435$		0			0
$436$	0.500000	+	0.866025i	0.0239457	+	0.0414751i
$437$	1.00000	−	1.73205i	0.0478365	−	0.0828552i
$438$	5.50000	−	9.52628i	0.262800	−	0.455183i
$439$	−4.00000	−	6.92820i	−0.190910	−	0.330665i	0.754642	−	0.656136i	$-0.227810\pi$
$439$	−4.00000	−	6.92820i	−0.190910	−	0.330665i	−0.945552	+	0.325471i	$0.894477\pi$
$440$		0			0
$441$	5.50000	+	4.33013i	0.261905	+	0.206197i
$442$	6.00000			0.285391
$443$	12.0000	+	20.7846i	0.570137	+	0.987507i	0.996551	+	0.0829786i	$0.0264433\pi$
$443$	12.0000	+	20.7846i	0.570137	+	0.987507i	−0.426414	+	0.904528i	$0.640223\pi$
$444$	−1.00000	+	1.73205i	−0.0474579	+	0.0821995i
$445$		0			0
$446$	−5.00000	−	8.66025i	−0.236757	−	0.410075i
$447$	12.0000			0.567581
$448$	−0.500000	−	2.59808i	−0.0236228	−	0.122748i
$449$	12.0000			0.566315			0.283158	−	0.959073i	$-0.408618\pi$
$449$	12.0000			0.566315			0.283158	+	0.959073i	$0.408618\pi$
$450$	−2.50000	−	4.33013i	−0.117851	−	0.204124i
$451$	9.00000	−	15.5885i	0.423793	−	0.734032i
$452$	−9.00000	+	15.5885i	−0.423324	+	0.733219i
$453$	2.00000	+	3.46410i	0.0939682	+	0.162758i
$454$	3.00000			0.140797
$455$		0			0
$456$	−2.00000			−0.0936586
$457$	−10.0000	−	17.3205i	−0.467780	−	0.810219i	0.531542	−	0.847032i	$-0.321613\pi$
$457$	−10.0000	−	17.3205i	−0.467780	−	0.810219i	−0.999322	+	0.0368128i	$0.988279\pi$
$458$	−0.500000	+	0.866025i	−0.0233635	+	0.0404667i
$459$	1.50000	−	2.59808i	0.0700140	−	0.121268i
$460$		0			0
$461$	−30.0000			−1.39724			−0.698620	−	0.715493i	$-0.746202\pi$
$461$	−30.0000			−1.39724			−0.698620	+	0.715493i	$0.746202\pi$
$462$	7.50000	+	2.59808i	0.348932	+	0.120873i
$463$	32.0000			1.48717			0.743583	−	0.668644i	$-0.233125\pi$
$463$	32.0000			1.48717			0.743583	+	0.668644i	$0.233125\pi$
$464$	−1.50000	−	2.59808i	−0.0696358	−	0.120613i
$465$		0			0
$466$		0			0
$467$	10.5000	+	18.1865i	0.485882	+	0.841572i	0.999868	−	0.0162260i	$-0.00516512\pi$
$467$	10.5000	+	18.1865i	0.485882	+	0.841572i	−0.513986	+	0.857798i	$0.671832\pi$
$468$	2.00000			0.0924500
$469$	5.00000	+	1.73205i	0.230879	+	0.0799787i
$470$		0			0
$471$	−11.5000	−	19.9186i	−0.529892	−	0.917800i
$472$		0			0
$473$	3.00000	−	5.19615i	0.137940	−	0.238919i
$474$	5.50000	+	9.52628i	0.252623	+	0.437557i
$475$	−10.0000			−0.458831
$476$	6.00000	−	5.19615i	0.275010	−	0.238165i
$477$	−6.00000			−0.274721
$478$	7.50000	+	12.9904i	0.343042	+	0.594166i
$479$	−15.0000	+	25.9808i	−0.685367	+	1.18709i	0.287954	+	0.957644i	$0.407025\pi$
$479$	−15.0000	+	25.9808i	−0.685367	+	1.18709i	−0.973321	+	0.229447i	$0.926308\pi$
$480$		0			0
$481$	−2.00000	−	3.46410i	−0.0911922	−	0.157949i
$482$	−2.00000			−0.0910975
$483$	0.500000	+	2.59808i	0.0227508	+	0.118217i
$484$	−2.00000			−0.0909091
$485$		0			0
$486$	0.500000	−	0.866025i	0.0226805	−	0.0392837i
$487$	−1.00000	+	1.73205i	−0.0453143	+	0.0784867i	−0.887793	−	0.460243i	$-0.847762\pi$
$487$	−1.00000	+	1.73205i	−0.0453143	+	0.0784867i	0.842479	+	0.538730i	$0.181096\pi$
$488$	1.00000	+	1.73205i	0.0452679	+	0.0784063i
$489$	23.0000			1.04010
$490$		0			0
$491$		0			0			−	1.00000i	$-0.5\pi$
$491$		0			0				1.00000i	$0.5\pi$
$492$	−3.00000	−	5.19615i	−0.135250	−	0.234261i
$493$	4.50000	−	7.79423i	0.202670	−	0.351034i
$494$	2.00000	−	3.46410i	0.0899843	−	0.155857i
$495$		0			0
$496$	2.00000			0.0898027
$497$	−1.50000	−	7.79423i	−0.0672842	−	0.349619i
$498$		0			0
$499$	−17.5000	−	30.3109i	−0.783408	−	1.35690i	−0.929946	−	0.367697i	$-0.880146\pi$
$499$	−17.5000	−	30.3109i	−0.783408	−	1.35690i	0.146538	−	0.989205i	$-0.453187\pi$
$500$		0			0
$501$		0			0
$502$	1.50000	+	2.59808i	0.0669483	+	0.115958i
$503$	30.0000			1.33763			0.668817	−	0.743427i	$-0.266801\pi$
$503$	30.0000			1.33763			0.668817	+	0.743427i	$0.266801\pi$
$504$	2.00000	−	1.73205i	0.0890871	−	0.0771517i
$505$		0			0
$506$	1.50000	+	2.59808i	0.0666831	+	0.115499i
$507$	4.50000	−	7.79423i	0.199852	−	0.346154i
$508$	−1.00000	+	1.73205i	−0.0443678	+	0.0768473i
$509$	10.5000	+	18.1865i	0.465404	+	0.806104i	0.999220	−	0.0394971i	$-0.0125756\pi$
$509$	10.5000	+	18.1865i	0.465404	+	0.806104i	−0.533815	+	0.845601i	$0.679242\pi$
$510$		0			0
$511$	27.5000	+	9.52628i	1.21653	+	0.421418i
$512$	−1.00000			−0.0441942
$513$	−1.00000	−	1.73205i	−0.0441511	−	0.0764719i
$514$	3.00000	−	5.19615i	0.132324	−	0.229192i
$515$		0			0
$516$	−1.00000	−	1.73205i	−0.0440225	−	0.0762493i
$517$	9.00000			0.395820
$518$	−5.00000	−	1.73205i	−0.219687	−	0.0761019i
$519$	−15.0000			−0.658427
$520$		0			0
$521$	21.0000	−	36.3731i	0.920027	−	1.59353i	0.120656	−	0.992694i	$-0.461500\pi$
$521$	21.0000	−	36.3731i	0.920027	−	1.59353i	0.799370	−	0.600839i	$-0.205167\pi$
$522$	1.50000	−	2.59808i	0.0656532	−	0.113715i
$523$	11.0000	+	19.0526i	0.480996	+	0.833110i	0.999762	−	0.0218062i	$-0.00694167\pi$
$523$	11.0000	+	19.0526i	0.480996	+	0.833110i	−0.518766	+	0.854916i	$0.673608\pi$
$524$		0			0
$525$	10.0000	−	8.66025i	0.436436	−	0.377964i
$526$	−24.0000			−1.04645
$527$	3.00000	+	5.19615i	0.130682	+	0.226348i
$528$	1.50000	−	2.59808i	0.0652791	−	0.113067i
$529$	−0.500000	+	0.866025i	−0.0217391	+	0.0376533i
$530$		0			0
$531$		0			0
$532$	−1.00000	−	5.19615i	−0.0433555	−	0.225282i
$533$	12.0000			0.519778
$534$	−3.00000	−	5.19615i	−0.129823	−	0.224860i
$535$		0			0
$536$	1.00000	−	1.73205i	0.0431934	−	0.0748132i
$537$	−3.00000	−	5.19615i	−0.129460	−	0.224231i
$538$	−15.0000			−0.646696
$539$	−3.00000	+	20.7846i	−0.129219	+	0.895257i
$540$		0			0
$541$	−10.0000	−	17.3205i	−0.429934	−	0.744667i	0.566933	−	0.823764i	$-0.308130\pi$
$541$	−10.0000	−	17.3205i	−0.429934	−	0.744667i	−0.996867	+	0.0790969i	$0.974796\pi$
$542$	−11.0000	+	19.0526i	−0.472490	+	0.818377i
$543$	−5.50000	+	9.52628i	−0.236028	+	0.408812i
$544$	−1.50000	−	2.59808i	−0.0643120	−	0.111392i
$545$		0			0
$546$	1.00000	+	5.19615i	0.0427960	+	0.222375i
$547$	17.0000			0.726868			0.363434	−	0.931620i	$-0.381604\pi$
$547$	17.0000			0.726868			0.363434	+	0.931620i	$0.381604\pi$
$548$	10.5000	+	18.1865i	0.448538	+	0.776890i
$549$	−1.00000	+	1.73205i	−0.0426790	+	0.0739221i
$550$	7.50000	−	12.9904i	0.319801	−	0.553912i
$551$	−3.00000	−	5.19615i	−0.127804	−	0.221364i
$552$	1.00000			0.0425628
$553$	−22.0000	+	19.0526i	−0.935535	+	0.810197i
$554$	−8.00000			−0.339887
$555$		0			0
$556$	6.50000	−	11.2583i	0.275661	−	0.477460i
$557$	−15.0000	+	25.9808i	−0.635570	+	1.10084i	0.350824	+	0.936442i	$0.385902\pi$
$557$	−15.0000	+	25.9808i	−0.635570	+	1.10084i	−0.986394	+	0.164399i	$0.947432\pi$
$558$	1.00000	+	1.73205i	0.0423334	+	0.0733236i
$559$	4.00000			0.169182
$560$		0			0
$561$	9.00000			0.379980
$562$	−1.50000	−	2.59808i	−0.0632737	−	0.109593i
$563$	4.50000	−	7.79423i	0.189652	−	0.328488i	−0.755482	−	0.655169i	$-0.772597\pi$
$563$	4.50000	−	7.79423i	0.189652	−	0.328488i	0.945134	+	0.326682i	$0.105931\pi$
$564$	1.50000	−	2.59808i	0.0631614	−	0.109399i
$565$		0			0
$566$	−8.00000			−0.336265
$567$	2.50000	+	0.866025i	0.104990	+	0.0363696i
$568$	−3.00000			−0.125877
$569$	3.00000	+	5.19615i	0.125767	+	0.217834i	0.922032	−	0.387113i	$-0.126528\pi$
$569$	3.00000	+	5.19615i	0.125767	+	0.217834i	−0.796266	+	0.604947i	$0.793194\pi$
$570$		0			0
$571$	2.00000	−	3.46410i	0.0836974	−	0.144968i	−0.821138	−	0.570730i	$-0.806660\pi$
$571$	2.00000	−	3.46410i	0.0836974	−	0.144968i	0.904835	+	0.425762i	$0.139994\pi$
$572$	3.00000	+	5.19615i	0.125436	+	0.217262i
$573$	12.0000			0.501307
$574$	12.0000	−	10.3923i	0.500870	−	0.433766i
$575$	5.00000			0.208514
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	15.5000	−	26.8468i	0.645273	−	1.11765i	−0.338965	−	0.940799i	$-0.610077\pi$
$577$	15.5000	−	26.8468i	0.645273	−	1.11765i	0.984238	−	0.176847i	$-0.0565899\pi$
$578$	−4.00000	+	6.92820i	−0.166378	+	0.288175i
$579$	−7.00000	−	12.1244i	−0.290910	−	0.503871i
$580$		0			0
$581$		0			0
$582$	−8.00000			−0.331611
$583$	−9.00000	−	15.5885i	−0.372742	−	0.645608i
$584$	5.50000	−	9.52628i	0.227592	−	0.394200i
$585$		0			0
$586$		0			0
$587$	−12.0000			−0.495293			−0.247647	−	0.968850i	$-0.579657\pi$
$587$	−12.0000			−0.495293			−0.247647	+	0.968850i	$0.579657\pi$
$588$	5.50000	+	4.33013i	0.226816	+	0.178571i
$589$	4.00000			0.164817
$590$		0			0
$591$	−7.50000	+	12.9904i	−0.308509	+	0.534353i
$592$	−1.00000	+	1.73205i	−0.0410997	+	0.0711868i
$593$	21.0000	+	36.3731i	0.862367	+	1.49366i	0.869638	+	0.493689i	$0.164352\pi$
$593$	21.0000	+	36.3731i	0.862367	+	1.49366i	−0.00727173	+	0.999974i	$0.502315\pi$
$594$	3.00000			0.123091
$595$		0			0
$596$	12.0000			0.491539
$597$	−8.50000	−	14.7224i	−0.347882	−	0.602549i
$598$	−1.00000	+	1.73205i	−0.0408930	+	0.0708288i
$599$	−7.50000	+	12.9904i	−0.306442	+	0.530773i	−0.977581	−	0.210558i	$-0.932472\pi$
$599$	−7.50000	+	12.9904i	−0.306442	+	0.530773i	0.671140	+	0.741331i	$0.265805\pi$
$600$	−2.50000	−	4.33013i	−0.102062	−	0.176777i
$601$	26.0000			1.06056			0.530281	−	0.847822i	$-0.322086\pi$
$601$	26.0000			1.06056			0.530281	+	0.847822i	$0.322086\pi$
$602$	4.00000	−	3.46410i	0.163028	−	0.141186i
$603$	2.00000			0.0814463
$604$	2.00000	+	3.46410i	0.0813788	+	0.140952i
$605$		0			0
$606$	−1.50000	+	2.59808i	−0.0609333	+	0.105540i
$607$	−7.00000	−	12.1244i	−0.284121	−	0.492112i	0.688274	−	0.725450i	$-0.258368\pi$
$607$	−7.00000	−	12.1244i	−0.284121	−	0.492112i	−0.972396	+	0.233338i	$0.925035\pi$
$608$	−2.00000			−0.0811107
$609$	7.50000	+	2.59808i	0.303915	+	0.105279i
$610$		0			0
$611$	3.00000	+	5.19615i	0.121367	+	0.210214i
$612$	1.50000	−	2.59808i	0.0606339	−	0.105021i
$613$	−2.50000	+	4.33013i	−0.100974	+	0.174892i	−0.912086	−	0.409998i	$-0.865529\pi$
$613$	−2.50000	+	4.33013i	−0.100974	+	0.174892i	0.811112	+	0.584891i	$0.198863\pi$
$614$	5.50000	+	9.52628i	0.221962	+	0.384449i
$615$		0			0
$616$	7.50000	+	2.59808i	0.302184	+	0.104679i
$617$	33.0000			1.32853			0.664265	−	0.747497i	$-0.268745\pi$
$617$	33.0000			1.32853			0.664265	+	0.747497i	$0.268745\pi$
$618$	2.50000	+	4.33013i	0.100565	+	0.174183i
$619$	−16.0000	+	27.7128i	−0.643094	+	1.11387i	0.341644	+	0.939829i	$0.389016\pi$
$619$	−16.0000	+	27.7128i	−0.643094	+	1.11387i	−0.984738	+	0.174042i	$0.944317\pi$
$620$		0			0
$621$	0.500000	+	0.866025i	0.0200643	+	0.0347524i
$622$	3.00000			0.120289
$623$	12.0000	−	10.3923i	0.480770	−	0.416359i
$624$	2.00000			0.0800641
$625$	−12.5000	−	21.6506i	−0.500000	−	0.866025i
$626$	4.00000	−	6.92820i	0.159872	−	0.276907i
$627$	3.00000	−	5.19615i	0.119808	−	0.207514i
$628$	−11.5000	−	19.9186i	−0.458900	−	0.794838i
$629$	−6.00000			−0.239236
$630$		0			0
$631$	17.0000			0.676759			0.338380	−	0.941010i	$-0.390121\pi$
$631$	17.0000			0.676759			0.338380	+	0.941010i	$0.390121\pi$
$632$	5.50000	+	9.52628i	0.218778	+	0.378935i
$633$	9.50000	−	16.4545i	0.377591	−	0.654007i
$634$	−9.00000	+	15.5885i	−0.357436	+	0.619097i
$635$		0			0
$636$	−6.00000			−0.237915
$637$	−13.0000	+	5.19615i	−0.515079	+	0.205879i
$638$	9.00000			0.356313
$639$	−1.50000	−	2.59808i	−0.0593391	−	0.102778i
$640$		0			0
$641$	1.50000	−	2.59808i	0.0592464	−	0.102618i	−0.834881	−	0.550431i	$-0.814464\pi$
$641$	1.50000	−	2.59808i	0.0592464	−	0.102618i	0.894127	+	0.447813i	$0.147797\pi$
$642$	6.00000	+	10.3923i	0.236801	+	0.410152i
$643$	−28.0000			−1.10421			−0.552106	−	0.833774i	$-0.686176\pi$
$643$	−28.0000			−1.10421			−0.552106	+	0.833774i	$0.686176\pi$
$644$	0.500000	+	2.59808i	0.0197028	+	0.102379i
$645$		0			0
$646$	−3.00000	−	5.19615i	−0.118033	−	0.204440i
$647$	7.50000	−	12.9904i	0.294855	−	0.510705i	−0.680096	−	0.733123i	$-0.738062\pi$
$647$	7.50000	−	12.9904i	0.294855	−	0.510705i	0.974951	+	0.222419i	$0.0713952\pi$
$648$	0.500000	−	0.866025i	0.0196419	−	0.0340207i
$649$		0			0
$650$	10.0000			0.392232
$651$	−4.00000	+	3.46410i	−0.156772	+	0.135769i
$652$	23.0000			0.900750
$653$	−1.50000	−	2.59808i	−0.0586995	−	0.101671i	0.835182	−	0.549973i	$-0.185362\pi$
$653$	−1.50000	−	2.59808i	−0.0586995	−	0.101671i	−0.893882	+	0.448303i	$0.852029\pi$
$654$	−0.500000	+	0.866025i	−0.0195515	+	0.0338643i
$655$		0			0
$656$	−3.00000	−	5.19615i	−0.117130	−	0.202876i
$657$	11.0000			0.429151
$658$	7.50000	+	2.59808i	0.292380	+	0.101284i
$659$	3.00000			0.116863			0.0584317	−	0.998291i	$-0.481390\pi$
$659$	3.00000			0.116863			0.0584317	+	0.998291i	$0.481390\pi$
$660$		0			0
$661$	−2.50000	+	4.33013i	−0.0972387	+	0.168422i	−0.910541	−	0.413419i	$-0.864334\pi$
$661$	−2.50000	+	4.33013i	−0.0972387	+	0.168422i	0.813302	+	0.581842i	$0.197668\pi$
$662$	4.00000	−	6.92820i	0.155464	−	0.269272i
$663$	3.00000	+	5.19615i	0.116510	+	0.201802i
$664$		0			0
$665$		0			0
$666$	−2.00000			−0.0774984
$667$	1.50000	+	2.59808i	0.0580802	+	0.100598i
$668$		0			0
$669$	5.00000	−	8.66025i	0.193311	−	0.334825i
$670$		0			0
$671$	−6.00000			−0.231627
$672$	2.00000	−	1.73205i	0.0771517	−	0.0668153i
$673$	−19.0000			−0.732396			−0.366198	−	0.930537i	$-0.619341\pi$
$673$	−19.0000			−0.732396			−0.366198	+	0.930537i	$0.619341\pi$
$674$	7.00000	+	12.1244i	0.269630	+	0.467013i
$675$	2.50000	−	4.33013i	0.0962250	−	0.166667i
$676$	4.50000	−	7.79423i	0.173077	−	0.299778i
$677$	9.00000	+	15.5885i	0.345898	+	0.599113i	0.985517	−	0.169580i	$-0.0542410\pi$
$677$	9.00000	+	15.5885i	0.345898	+	0.599113i	−0.639618	+	0.768693i	$0.720908\pi$
$678$	−18.0000			−0.691286
$679$	−4.00000	−	20.7846i	−0.153506	−	0.797640i
$680$		0			0
$681$	1.50000	+	2.59808i	0.0574801	+	0.0995585i
$682$	−3.00000	+	5.19615i	−0.114876	+	0.198971i
$683$	−24.0000	+	41.5692i	−0.918334	+	1.59060i	−0.116390	+	0.993204i	$0.537132\pi$
$683$	−24.0000	+	41.5692i	−0.918334	+	1.59060i	−0.801945	+	0.597398i	$0.796201\pi$
$684$	−1.00000	−	1.73205i	−0.0382360	−	0.0662266i
$685$		0			0
$686$	−8.50000	+	16.4545i	−0.324532	+	0.628235i
$687$	−1.00000			−0.0381524
$688$	−1.00000	−	1.73205i	−0.0381246	−	0.0660338i
$689$	6.00000	−	10.3923i	0.228582	−	0.395915i
$690$		0			0
$691$	−8.50000	−	14.7224i	−0.323355	−	0.560068i	0.657823	−	0.753173i	$-0.271478\pi$
$691$	−8.50000	−	14.7224i	−0.323355	−	0.560068i	−0.981178	+	0.193105i	$0.938144\pi$
$692$	−15.0000			−0.570214
$693$	1.50000	+	7.79423i	0.0569803	+	0.296078i
$694$	−6.00000			−0.227757
$695$		0			0
$696$	1.50000	−	2.59808i	0.0568574	−	0.0984798i
$697$	9.00000	−	15.5885i	0.340899	−	0.590455i
$698$	−11.0000	−	19.0526i	−0.416356	−	0.721150i
$699$		0			0
$700$	10.0000	−	8.66025i	0.377964	−	0.327327i
$701$	−42.0000			−1.58632			−0.793159	−	0.609015i	$-0.791565\pi$
$701$	−42.0000			−1.58632			−0.793159	+	0.609015i	$0.791565\pi$
$702$	1.00000	+	1.73205i	0.0377426	+	0.0653720i
$703$	−2.00000	+	3.46410i	−0.0754314	+	0.130651i
$704$	1.50000	−	2.59808i	0.0565334	−	0.0979187i
$705$		0			0
$706$	18.0000			0.677439
$707$	−7.50000	−	2.59808i	−0.282067	−	0.0977107i
$708$		0			0
$709$	15.5000	+	26.8468i	0.582115	+	1.00825i	0.995228	+	0.0975728i	$0.0311079\pi$
$709$	15.5000	+	26.8468i	0.582115	+	1.00825i	−0.413114	+	0.910679i	$0.635559\pi$
$710$		0			0
$711$	−5.50000	+	9.52628i	−0.206266	+	0.357263i
$712$	−3.00000	−	5.19615i	−0.112430	−	0.194734i
$713$	−2.00000			−0.0749006
$714$	7.50000	+	2.59808i	0.280680	+	0.0972306i
$715$		0			0
$716$	−3.00000	−	5.19615i	−0.112115	−	0.194189i
$717$	−7.50000	+	12.9904i	−0.280093	+	0.485135i
$718$	−6.00000	+	10.3923i	−0.223918	+	0.387837i
$719$	24.0000	+	41.5692i	0.895049	+	1.55027i	0.833744	+	0.552151i	$0.186193\pi$
$719$	24.0000	+	41.5692i	0.895049	+	1.55027i	0.0613050	+	0.998119i	$0.480474\pi$
$720$		0			0
$721$	−10.0000	+	8.66025i	−0.372419	+	0.322525i
$722$	15.0000			0.558242
$723$	−1.00000	−	1.73205i	−0.0371904	−	0.0644157i
$724$	−5.50000	+	9.52628i	−0.204406	+	0.354041i
$725$	7.50000	−	12.9904i	0.278543	−	0.482451i
$726$	−1.00000	−	1.73205i	−0.0371135	−	0.0642824i
$727$	23.0000			0.853023			0.426511	−	0.904482i	$-0.359742\pi$
$727$	23.0000			0.853023			0.426511	+	0.904482i	$0.359742\pi$
$728$	1.00000	+	5.19615i	0.0370625	+	0.192582i
$729$	1.00000			0.0370370
$730$		0			0
$731$	3.00000	−	5.19615i	0.110959	−	0.192187i
$732$	−1.00000	+	1.73205i	−0.0369611	+	0.0640184i
$733$	−20.5000	−	35.5070i	−0.757185	−	1.31148i	−0.944281	−	0.329141i	$-0.893241\pi$
$733$	−20.5000	−	35.5070i	−0.757185	−	1.31148i	0.187096	−	0.982342i	$-0.440092\pi$
$734$	−8.00000			−0.295285
$735$		0			0
$736$	1.00000			0.0368605
$737$	3.00000	+	5.19615i	0.110506	+	0.191403i
$738$	3.00000	−	5.19615i	0.110432	−	0.191273i
$739$	12.5000	−	21.6506i	0.459820	−	0.796431i	−0.539131	−	0.842222i	$-0.681247\pi$
$739$	12.5000	−	21.6506i	0.459820	−	0.796431i	0.998951	+	0.0457903i	$0.0145806\pi$
$740$		0			0
$741$	4.00000			0.146944
$742$	−3.00000	−	15.5885i	−0.110133	−	0.572270i
$743$	−12.0000			−0.440237			−0.220119	−	0.975473i	$-0.570644\pi$
$743$	−12.0000			−0.440237			−0.220119	+	0.975473i	$0.570644\pi$
$744$	1.00000	+	1.73205i	0.0366618	+	0.0635001i
$745$		0			0
$746$	−6.50000	+	11.2583i	−0.237982	+	0.412197i
$747$		0			0
$748$	9.00000			0.329073
$749$	−24.0000	+	20.7846i	−0.876941	+	0.759453i
$750$		0			0
$751$	−16.0000	−	27.7128i	−0.583848	−	1.01125i	−0.995018	−	0.0996961i	$-0.968213\pi$
$751$	−16.0000	−	27.7128i	−0.583848	−	1.01125i	0.411170	−	0.911559i	$-0.365120\pi$
$752$	1.50000	−	2.59808i	0.0546994	−	0.0947421i
$753$	−1.50000	+	2.59808i	−0.0546630	+	0.0946792i
$754$	3.00000	+	5.19615i	0.109254	+	0.189233i
$755$		0			0
$756$	2.50000	+	0.866025i	0.0909241	+	0.0314970i
$757$	38.0000			1.38113			0.690567	−	0.723269i	$-0.257361\pi$
$757$	38.0000			1.38113			0.690567	+	0.723269i	$0.257361\pi$
$758$	10.0000	+	17.3205i	0.363216	+	0.629109i
$759$	−1.50000	+	2.59808i	−0.0544466	+	0.0943042i
$760$		0			0
$761$	−24.0000	−	41.5692i	−0.869999	−	1.50688i	−0.861996	−	0.506915i	$-0.830786\pi$
$761$	−24.0000	−	41.5692i	−0.869999	−	1.50688i	−0.00800331	−	0.999968i	$-0.502548\pi$
$762$	−2.00000			−0.0724524
$763$	−2.50000	−	0.866025i	−0.0905061	−	0.0313522i
$764$	12.0000			0.434145
$765$		0			0
$766$	−3.00000	+	5.19615i	−0.108394	+	0.187745i
$767$		0			0
$768$	−0.500000	−	0.866025i	−0.0180422	−	0.0312500i
$769$	14.0000			0.504853			0.252426	−	0.967616i	$-0.418771\pi$
$769$	14.0000			0.504853			0.252426	+	0.967616i	$0.418771\pi$
$770$		0			0
$771$	6.00000			0.216085
$772$	−7.00000	−	12.1244i	−0.251936	−	0.436365i
$773$	18.0000	−	31.1769i	0.647415	−	1.12136i	−0.336323	−	0.941747i	$-0.609183\pi$
$773$	18.0000	−	31.1769i	0.647415	−	1.12136i	0.983738	−	0.179609i	$-0.0574833\pi$
$774$	1.00000	−	1.73205i	0.0359443	−	0.0622573i
$775$	5.00000	+	8.66025i	0.179605	+	0.311086i
$776$	−8.00000			−0.287183
$777$	−1.00000	−	5.19615i	−0.0358748	−	0.186411i
$778$	−24.0000			−0.860442
$779$	−6.00000	−	10.3923i	−0.214972	−	0.372343i
$780$		0			0
$781$	4.50000	−	7.79423i	0.161023	−	0.278899i
$782$	1.50000	+	2.59808i	0.0536399	+	0.0929070i
$783$	3.00000			0.107211
$784$	5.50000	+	4.33013i	0.196429	+	0.154647i
$785$		0			0
$786$		0			0
$787$	20.0000	−	34.6410i	0.712923	−	1.23482i	−0.250832	−	0.968031i	$-0.580704\pi$
$787$	20.0000	−	34.6410i	0.712923	−	1.23482i	0.963755	−	0.266788i	$-0.0859624\pi$
$788$	−7.50000	+	12.9904i	−0.267176	+	0.462763i
$789$	−12.0000	−	20.7846i	−0.427211	−	0.739952i
$790$		0			0
$791$	−9.00000	−	46.7654i	−0.320003	−	1.66279i
$792$	3.00000			0.106600
$793$	−2.00000	−	3.46410i	−0.0710221	−	0.123014i
$794$	−17.0000	+	29.4449i	−0.603307	+	1.04496i
$795$		0			0
$796$	−8.50000	−	14.7224i	−0.301275	−	0.521823i
$797$	30.0000			1.06265			0.531327	−	0.847167i	$-0.321693\pi$
$797$	30.0000			1.06265			0.531327	+	0.847167i	$0.321693\pi$
$798$	4.00000	−	3.46410i	0.141598	−	0.122628i
$799$	9.00000			0.318397
$800$	−2.50000	−	4.33013i	−0.0883883	−	0.153093i
$801$	3.00000	−	5.19615i	0.106000	−	0.183597i
$802$	−7.50000	+	12.9904i	−0.264834	+	0.458706i
$803$	16.5000	+	28.5788i	0.582272	+	1.00853i
$804$	2.00000			0.0705346
$805$		0			0
$806$	−4.00000			−0.140894
$807$	−7.50000	−	12.9904i	−0.264013	−	0.457283i
$808$	−1.50000	+	2.59808i	−0.0527698	+	0.0914000i
$809$	−15.0000	+	25.9808i	−0.527372	+	0.913435i	0.472119	+	0.881535i	$0.343489\pi$
$809$	−15.0000	+	25.9808i	−0.527372	+	0.913435i	−0.999491	+	0.0319002i	$0.989844\pi$
$810$		0			0
$811$	−7.00000			−0.245803			−0.122902	−	0.992419i	$-0.539220\pi$
$811$	−7.00000			−0.245803			−0.122902	+	0.992419i	$0.539220\pi$
$812$	7.50000	+	2.59808i	0.263198	+	0.0911746i
$813$	−22.0000			−0.771574
$814$	−3.00000	−	5.19615i	−0.105150	−	0.182125i
$815$		0			0
$816$	1.50000	−	2.59808i	0.0525105	−	0.0909509i
$817$	−2.00000	−	3.46410i	−0.0699711	−	0.121194i
$818$	−29.0000			−1.01396
$819$	−4.00000	+	3.46410i	−0.139771	+	0.121046i
$820$		0			0
$821$	−16.5000	−	28.5788i	−0.575854	−	0.997408i	−0.995948	−	0.0899279i	$-0.971336\pi$
$821$	−16.5000	−	28.5788i	−0.575854	−	0.997408i	0.420094	−	0.907480i	$-0.361997\pi$
$822$	−10.5000	+	18.1865i	−0.366230	+	0.634328i
$823$	11.0000	−	19.0526i	0.383436	−	0.664130i	−0.608115	−	0.793849i	$-0.708074\pi$
$823$	11.0000	−	19.0526i	0.383436	−	0.664130i	0.991551	+	0.129719i	$0.0414074\pi$
$824$	2.50000	+	4.33013i	0.0870916	+	0.150847i
$825$	15.0000			0.522233
$826$		0			0
$827$	−21.0000			−0.730242			−0.365121	−	0.930960i	$-0.618972\pi$
$827$	−21.0000			−0.730242			−0.365121	+	0.930960i	$0.618972\pi$
$828$	0.500000	+	0.866025i	0.0173762	+	0.0300965i
$829$	−19.0000	+	32.9090i	−0.659897	+	1.14298i	0.320745	+	0.947166i	$0.396067\pi$
$829$	−19.0000	+	32.9090i	−0.659897	+	1.14298i	−0.980642	+	0.195810i	$0.937266\pi$
$830$		0			0
$831$	−4.00000	−	6.92820i	−0.138758	−	0.240337i
$832$	2.00000			0.0693375
$833$	−3.00000	+	20.7846i	−0.103944	+	0.720144i
$834$	13.0000			0.450153
$835$		0			0
$836$	3.00000	−	5.19615i	0.103757	−	0.179713i
$837$	−1.00000	+	1.73205i	−0.0345651	+	0.0598684i
$838$	−10.5000	−	18.1865i	−0.362716	−	0.628243i
$839$	−36.0000			−1.24286			−0.621429	−	0.783470i	$-0.713448\pi$
$839$	−36.0000			−1.24286			−0.621429	+	0.783470i	$0.713448\pi$
$840$		0			0
$841$	−20.0000			−0.689655
$842$	8.50000	+	14.7224i	0.292929	+	0.507369i
$843$	1.50000	−	2.59808i	0.0516627	−	0.0894825i
$844$	9.50000	−	16.4545i	0.327003	−	0.566387i
$845$		0			0
$846$	3.00000			0.103142
$847$	4.00000	−	3.46410i	0.137442	−	0.119028i
$848$	−6.00000			−0.206041
$849$	−4.00000	−	6.92820i	−0.137280	−	0.237775i
$850$	7.50000	−	12.9904i	0.257248	−	0.445566i
$851$	1.00000	−	1.73205i	0.0342796	−	0.0593739i
$852$	−1.50000	−	2.59808i	−0.0513892	−	0.0890086i
$853$	−46.0000			−1.57501			−0.787505	−	0.616308i	$-0.788628\pi$
$853$	−46.0000			−1.57501			−0.787505	+	0.616308i	$0.788628\pi$
$854$	−5.00000	−	1.73205i	−0.171096	−	0.0592696i
$855$		0			0
$856$	6.00000	+	10.3923i	0.205076	+	0.355202i
$857$	9.00000	−	15.5885i	0.307434	−	0.532492i	−0.670366	−	0.742030i	$-0.733863\pi$
$857$	9.00000	−	15.5885i	0.307434	−	0.532492i	0.977800	+	0.209539i	$0.0671963\pi$
$858$	−3.00000	+	5.19615i	−0.102418	+	0.177394i
$859$	−5.50000	−	9.52628i	−0.187658	−	0.325032i	0.756811	−	0.653633i	$-0.226756\pi$
$859$	−5.50000	−	9.52628i	−0.187658	−	0.325032i	−0.944469	+	0.328601i	$0.893423\pi$
$860$		0			0
$861$	15.0000	+	5.19615i	0.511199	+	0.177084i
$862$	−30.0000			−1.02180
$863$	−1.50000	−	2.59808i	−0.0510606	−	0.0884395i	0.839365	−	0.543568i	$-0.182927\pi$
$863$	−1.50000	−	2.59808i	−0.0510606	−	0.0884395i	−0.890426	+	0.455128i	$0.849593\pi$
$864$	0.500000	−	0.866025i	0.0170103	−	0.0294628i
$865$		0			0
$866$	1.00000	+	1.73205i	0.0339814	+	0.0588575i
$867$	−8.00000			−0.271694
$868$	−4.00000	+	3.46410i	−0.135769	+	0.117579i
$869$	−33.0000			−1.11945
$870$		0			0
$871$	−2.00000	+	3.46410i	−0.0677674	+	0.117377i
$872$	−0.500000	+	0.866025i	−0.0169321	+	0.0293273i
$873$	−4.00000	−	6.92820i	−0.135379	−	0.234484i
$874$	2.00000			0.0676510
$875$		0			0
$876$	11.0000			0.371656
$877$	2.00000	+	3.46410i	0.0675352	+	0.116974i	0.897816	−	0.440371i	$-0.145153\pi$
$877$	2.00000	+	3.46410i	0.0675352	+	0.116974i	−0.830281	+	0.557346i	$0.811820\pi$
$878$	4.00000	−	6.92820i	0.134993	−	0.233816i
$879$		0			0
$880$		0			0
$881$	−15.0000			−0.505363			−0.252681	−	0.967550i	$-0.581312\pi$
$881$	−15.0000			−0.505363			−0.252681	+	0.967550i	$0.581312\pi$
$882$	−1.00000	+	6.92820i	−0.0336718	+	0.233285i
$883$	20.0000			0.673054			0.336527	−	0.941674i	$-0.390748\pi$
$883$	20.0000			0.673054			0.336527	+	0.941674i	$0.390748\pi$
$884$	3.00000	+	5.19615i	0.100901	+	0.174766i
$885$		0			0
$886$	−12.0000	+	20.7846i	−0.403148	+	0.698273i
$887$	−13.5000	−	23.3827i	−0.453286	−	0.785114i	0.545302	−	0.838240i	$-0.316415\pi$
$887$	−13.5000	−	23.3827i	−0.453286	−	0.785114i	−0.998588	+	0.0531258i	$0.983082\pi$
$888$	−2.00000			−0.0671156
$889$	−1.00000	−	5.19615i	−0.0335389	−	0.174273i
$890$		0			0
$891$	1.50000	+	2.59808i	0.0502519	+	0.0870388i
$892$	5.00000	−	8.66025i	0.167412	−	0.289967i
$893$	3.00000	−	5.19615i	0.100391	−	0.173883i
$894$	6.00000	+	10.3923i	0.200670	+	0.347571i
$895$		0			0
$896$	2.00000	−	1.73205i	0.0668153	−	0.0578638i
$897$	−2.00000			−0.0667781
$898$	6.00000	+	10.3923i	0.200223	+	0.346796i
$899$	−3.00000	+	5.19615i	−0.100056	+	0.173301i
$900$	2.50000	−	4.33013i	0.0833333	−	0.144338i
$901$	−9.00000	−	15.5885i	−0.299833	−	0.519327i
$902$	18.0000			0.599334
$903$	5.00000	+	1.73205i	0.166390	+	0.0576390i
$904$	−18.0000			−0.598671
$905$		0			0
$906$	−2.00000	+	3.46410i	−0.0664455	+	0.115087i
$907$	−22.0000	+	38.1051i	−0.730498	+	1.26526i	0.226173	+	0.974087i	$0.427379\pi$
$907$	−22.0000	+	38.1051i	−0.730498	+	1.26526i	−0.956671	+	0.291172i	$0.905955\pi$
$908$	1.50000	+	2.59808i	0.0497792	+	0.0862202i
$909$	−3.00000			−0.0995037
$910$		0			0
$911$	−24.0000			−0.795155			−0.397578	−	0.917568i	$-0.630149\pi$
$911$	−24.0000			−0.795155			−0.397578	+	0.917568i	$0.630149\pi$
$912$	−1.00000	−	1.73205i	−0.0331133	−	0.0573539i
$913$		0			0
$914$	10.0000	−	17.3205i	0.330771	−	0.572911i
$915$		0			0
$916$	−1.00000			−0.0330409
$917$		0			0
$918$	3.00000			0.0990148
$919$	−14.5000	−	25.1147i	−0.478311	−	0.828459i	0.521380	−	0.853325i	$-0.325417\pi$
$919$	−14.5000	−	25.1147i	−0.478311	−	0.828459i	−0.999691	+	0.0248659i	$0.992084\pi$
$920$		0			0
$921$	−5.50000	+	9.52628i	−0.181231	+	0.313902i
$922$	−15.0000	−	25.9808i	−0.493999	−	0.855631i
$923$	6.00000			0.197492
$924$	1.50000	+	7.79423i	0.0493464	+	0.256411i
$925$	−10.0000			−0.328798
$926$	16.0000	+	27.7128i	0.525793	+	0.910700i
$927$	−2.50000	+	4.33013i	−0.0821108	+	0.142220i
$928$	1.50000	−	2.59808i	0.0492399	−	0.0852860i
$929$	−21.0000	−	36.3731i	−0.688988	−	1.19336i	−0.972166	−	0.234294i	$-0.924722\pi$
$929$	−21.0000	−	36.3731i	−0.688988	−	1.19336i	0.283178	−	0.959067i	$-0.408611\pi$
$930$		0			0
$931$	11.0000	+	8.66025i	0.360510	+	0.283828i
$932$		0			0
$933$	1.50000	+	2.59808i	0.0491078	+	0.0850572i
$934$	−10.5000	+	18.1865i	−0.343570	+	0.595082i
$935$		0			0
$936$	1.00000	+	1.73205i	0.0326860	+	0.0566139i
$937$	38.0000			1.24141			0.620703	−	0.784046i	$-0.286847\pi$
$937$	38.0000			1.24141			0.620703	+	0.784046i	$0.286847\pi$
$938$	1.00000	+	5.19615i	0.0326512	+	0.169660i
$939$	8.00000			0.261070
$940$		0			0
$941$	−27.0000	+	46.7654i	−0.880175	+	1.52451i	−0.0290288	+	0.999579i	$0.509241\pi$
$941$	−27.0000	+	46.7654i	−0.880175	+	1.52451i	−0.851146	+	0.524929i	$0.824092\pi$
$942$	11.5000	−	19.9186i	0.374690	−	0.648983i
$943$	3.00000	+	5.19615i	0.0976934	+	0.169210i
$944$		0			0
$945$		0			0
$946$	6.00000			0.195077
$947$	3.00000	+	5.19615i	0.0974869	+	0.168852i	0.910644	−	0.413192i	$-0.135586\pi$
$947$	3.00000	+	5.19615i	0.0974869	+	0.168852i	−0.813157	+	0.582045i	$0.802253\pi$
$948$	−5.50000	+	9.52628i	−0.178632	+	0.309399i
$949$	−11.0000	+	19.0526i	−0.357075	+	0.618472i
$950$	−5.00000	−	8.66025i	−0.162221	−	0.280976i
$951$	−18.0000			−0.583690
$952$	7.50000	+	2.59808i	0.243076	+	0.0842041i
$953$	33.0000			1.06897			0.534487	−	0.845176i	$-0.320505\pi$
$953$	33.0000			1.06897			0.534487	+	0.845176i	$0.320505\pi$
$954$	−3.00000	−	5.19615i	−0.0971286	−	0.168232i
$955$		0			0
$956$	−7.50000	+	12.9904i	−0.242567	+	0.420139i
$957$	4.50000	+	7.79423i	0.145464	+	0.251952i
$958$	−30.0000			−0.969256
$959$	−52.5000	−	18.1865i	−1.69531	−	0.587274i
$960$		0			0
$961$	13.5000	+	23.3827i	0.435484	+	0.754280i
$962$	2.00000	−	3.46410i	0.0644826	−	0.111687i
$963$	−6.00000	+	10.3923i	−0.193347	+	0.334887i
$964$	−1.00000	−	1.73205i	−0.0322078	−	0.0557856i
$965$		0			0
$966$	−2.00000	+	1.73205i	−0.0643489	+	0.0557278i
$967$	14.0000			0.450210			0.225105	−	0.974335i	$-0.427728\pi$
$967$	14.0000			0.450210			0.225105	+	0.974335i	$0.427728\pi$
$968$	−1.00000	−	1.73205i	−0.0321412	−	0.0556702i
$969$	3.00000	−	5.19615i	0.0963739	−	0.166924i
$970$		0			0
$971$	−22.5000	−	38.9711i	−0.722059	−	1.25064i	−0.960173	−	0.279406i	$-0.909862\pi$
$971$	−22.5000	−	38.9711i	−0.722059	−	1.25064i	0.238114	−	0.971237i	$-0.423471\pi$
$972$	1.00000			0.0320750
$973$	6.50000	+	33.7750i	0.208380	+	1.08278i
$974$	−2.00000			−0.0640841
$975$	5.00000	+	8.66025i	0.160128	+	0.277350i
$976$	−1.00000	+	1.73205i	−0.0320092	+	0.0554416i
$977$	−9.00000	+	15.5885i	−0.287936	+	0.498719i	−0.973317	−	0.229465i	$-0.926302\pi$
$977$	−9.00000	+	15.5885i	−0.287936	+	0.498719i	0.685381	+	0.728184i	$0.259636\pi$
$978$	11.5000	+	19.9186i	0.367729	+	0.636926i
$979$	18.0000			0.575282
$980$		0			0
$981$	−1.00000			−0.0319275
$982$		0			0
$983$	9.00000	−	15.5885i	0.287055	−	0.497195i	−0.686050	−	0.727554i	$-0.740657\pi$
$983$	9.00000	−	15.5885i	0.287055	−	0.497195i	0.973106	+	0.230360i	$0.0739903\pi$
$984$	3.00000	−	5.19615i	0.0956365	−	0.165647i
$985$		0			0
$986$	9.00000			0.286618
$987$	1.50000	+	7.79423i	0.0477455	+	0.248093i
$988$	4.00000			0.127257
$989$	1.00000	+	1.73205i	0.0317982	+	0.0550760i
$990$		0			0
$991$	20.0000	−	34.6410i	0.635321	−	1.10041i	−0.351126	−	0.936328i	$-0.614201\pi$
$991$	20.0000	−	34.6410i	0.635321	−	1.10041i	0.986447	−	0.164080i	$-0.0524655\pi$
$992$	1.00000	+	1.73205i	0.0317500	+	0.0549927i
$993$	8.00000			0.253872
$994$	6.00000	−	5.19615i	0.190308	−	0.164812i
$995$		0			0
$996$		0			0
$997$	26.0000	−	45.0333i	0.823428	−	1.42622i	−0.0796863	−	0.996820i	$-0.525392\pi$
$997$	26.0000	−	45.0333i	0.823428	−	1.42622i	0.903115	−	0.429400i	$-0.141275\pi$
$998$	17.5000	−	30.3109i	0.553953	−	0.959474i
$999$	−1.00000	−	1.73205i	−0.0316386	−	0.0547997i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.i.f.277.1	✓	2
7.2	even	3	inner	966.2.i.f.415.1	yes	2
7.3	odd	6		6762.2.a.e.1.1		1
7.4	even	3		6762.2.a.o.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.i.f.277.1	✓	2	1.1	even	1	trivial
966.2.i.f.415.1	yes	2	7.2	even	3	inner
6762.2.a.e.1.1		1	7.3	odd	6
6762.2.a.o.1.1		1	7.4	even	3

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:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	966.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} -1.00000 q^{6} +(-0.500000 - 2.59808i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} -1.00000 q^{6} +(-0.500000 - 2.59808i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(1.50000 - 2.59808i) q^{11} +(-0.500000 - 0.866025i) q^{12} +2.00000 q^{13} +(2.00000 - 1.73205i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(1.50000 - 2.59808i) q^{17} +(0.500000 - 0.866025i) q^{18} +(-1.00000 - 1.73205i) q^{19} +(2.50000 + 0.866025i) q^{21} +3.00000 q^{22} +(0.500000 + 0.866025i) q^{23} +(0.500000 - 0.866025i) q^{24} +(2.50000 - 4.33013i) q^{25} +(1.00000 + 1.73205i) q^{26} +1.00000 q^{27} +(2.50000 + 0.866025i) q^{28} +3.00000 q^{29} +(-1.00000 + 1.73205i) q^{31} +(0.500000 - 0.866025i) q^{32} +(1.50000 + 2.59808i) q^{33} +3.00000 q^{34} +1.00000 q^{36} +(-1.00000 - 1.73205i) q^{37} +(1.00000 - 1.73205i) q^{38} +(-1.00000 + 1.73205i) q^{39} +6.00000 q^{41} +(0.500000 + 2.59808i) q^{42} +2.00000 q^{43} +(1.50000 + 2.59808i) q^{44} +(-0.500000 + 0.866025i) q^{46} +(1.50000 + 2.59808i) q^{47} +1.00000 q^{48} +(-6.50000 + 2.59808i) q^{49} +5.00000 q^{50} +(1.50000 + 2.59808i) q^{51} +(-1.00000 + 1.73205i) q^{52} +(3.00000 - 5.19615i) q^{53} +(0.500000 + 0.866025i) q^{54} +(0.500000 + 2.59808i) q^{56} +2.00000 q^{57} +(1.50000 + 2.59808i) q^{58} +(-1.00000 - 1.73205i) q^{61} -2.00000 q^{62} +(-2.00000 + 1.73205i) q^{63} +1.00000 q^{64} +(-1.50000 + 2.59808i) q^{66} +(-1.00000 + 1.73205i) q^{67} +(1.50000 + 2.59808i) q^{68} -1.00000 q^{69} +3.00000 q^{71} +(0.500000 + 0.866025i) q^{72} +(-5.50000 + 9.52628i) q^{73} +(1.00000 - 1.73205i) q^{74} +(2.50000 + 4.33013i) q^{75} +2.00000 q^{76} +(-7.50000 - 2.59808i) q^{77} -2.00000 q^{78} +(-5.50000 - 9.52628i) q^{79} +(-0.500000 + 0.866025i) q^{81} +(3.00000 + 5.19615i) q^{82} +(-2.00000 + 1.73205i) q^{84} +(1.00000 + 1.73205i) q^{86} +(-1.50000 + 2.59808i) q^{87} +(-1.50000 + 2.59808i) q^{88} +(3.00000 + 5.19615i) q^{89} +(-1.00000 - 5.19615i) q^{91} -1.00000 q^{92} +(-1.00000 - 1.73205i) q^{93} +(-1.50000 + 2.59808i) q^{94} +(0.500000 + 0.866025i) q^{96} +8.00000 q^{97} +(-5.50000 - 4.33013i) q^{98} -3.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} - q^{3} - q^{4} - 2 q^{6} - q^{7} - 2 q^{8} - q^{9}+O(q^{10}) \) 2 * q + q^2 - q^3 - q^4 - 2 * q^6 - q^7 - 2 * q^8 - q^9	\( 2 q + q^{2} - q^{3} - q^{4} - 2 q^{6} - q^{7} - 2 q^{8} - q^{9} + 3 q^{11} - q^{12} + 4 q^{13} + 4 q^{14} - q^{16} + 3 q^{17} + q^{18} - 2 q^{19} + 5 q^{21} + 6 q^{22} + q^{23} + q^{24} + 5 q^{25} + 2 q^{26} + 2 q^{27} + 5 q^{28} + 6 q^{29} - 2 q^{31} + q^{32} + 3 q^{33} + 6 q^{34} + 2 q^{36} - 2 q^{37} + 2 q^{38} - 2 q^{39} + 12 q^{41} + q^{42} + 4 q^{43} + 3 q^{44} - q^{46} + 3 q^{47} + 2 q^{48} - 13 q^{49} + 10 q^{50} + 3 q^{51} - 2 q^{52} + 6 q^{53} + q^{54} + q^{56} + 4 q^{57} + 3 q^{58} - 2 q^{61} - 4 q^{62} - 4 q^{63} + 2 q^{64} - 3 q^{66} - 2 q^{67} + 3 q^{68} - 2 q^{69} + 6 q^{71} + q^{72} - 11 q^{73} + 2 q^{74} + 5 q^{75} + 4 q^{76} - 15 q^{77} - 4 q^{78} - 11 q^{79} - q^{81} + 6 q^{82} - 4 q^{84} + 2 q^{86} - 3 q^{87} - 3 q^{88} + 6 q^{89} - 2 q^{91} - 2 q^{92} - 2 q^{93} - 3 q^{94} + q^{96} + 16 q^{97} - 11 q^{98} - 6 q^{99}+O(q^{100}) \) 2 * q + q^2 - q^3 - q^4 - 2 * q^6 - q^7 - 2 * q^8 - q^9 + 3 * q^11 - q^12 + 4 * q^13 + 4 * q^14 - q^16 + 3 * q^17 + q^18 - 2 * q^19 + 5 * q^21 + 6 * q^22 + q^23 + q^24 + 5 * q^25 + 2 * q^26 + 2 * q^27 + 5 * q^28 + 6 * q^29 - 2 * q^31 + q^32 + 3 * q^33 + 6 * q^34 + 2 * q^36 - 2 * q^37 + 2 * q^38 - 2 * q^39 + 12 * q^41 + q^42 + 4 * q^43 + 3 * q^44 - q^46 + 3 * q^47 + 2 * q^48 - 13 * q^49 + 10 * q^50 + 3 * q^51 - 2 * q^52 + 6 * q^53 + q^54 + q^56 + 4 * q^57 + 3 * q^58 - 2 * q^61 - 4 * q^62 - 4 * q^63 + 2 * q^64 - 3 * q^66 - 2 * q^67 + 3 * q^68 - 2 * q^69 + 6 * q^71 + q^72 - 11 * q^73 + 2 * q^74 + 5 * q^75 + 4 * q^76 - 15 * q^77 - 4 * q^78 - 11 * q^79 - q^81 + 6 * q^82 - 4 * q^84 + 2 * q^86 - 3 * q^87 - 3 * q^88 + 6 * q^89 - 2 * q^91 - 2 * q^92 - 2 * q^93 - 3 * q^94 + q^96 + 16 * q^97 - 11 * q^98 - 6 * q^99

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