LMFDB - Embedded newform 975.2.bc.f.901.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [975,2,Mod(751,975)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(975, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 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("975.751");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 975 = 3 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	975.bc (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:	$7.78541419707$
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:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			901.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	975.901
Dual form			975.2.bc.f.751.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.50000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-1.50000 + 0.866025i) q^{6} +(1.50000 - 0.866025i) q^{7} -1.73205i q^{8} +(-0.500000 - 0.866025i) q^{9} +(3.00000 + 1.73205i) q^{11} -1.00000 q^{12} +(1.00000 - 3.46410i) q^{13} +3.00000 q^{14} +(2.50000 - 4.33013i) q^{16} +(3.00000 + 5.19615i) q^{17} -1.73205i q^{18} +(1.50000 - 0.866025i) q^{19} +1.73205i q^{21} +(3.00000 + 5.19615i) q^{22} +(-3.00000 + 5.19615i) q^{23} +(1.50000 + 0.866025i) q^{24} +(4.50000 - 4.33013i) q^{26} +1.00000 q^{27} +(1.50000 + 0.866025i) q^{28} +(3.00000 - 5.19615i) q^{29} -3.46410i q^{31} +(4.50000 - 2.59808i) q^{32} +(-3.00000 + 1.73205i) q^{33} +10.3923i q^{34} +(0.500000 - 0.866025i) q^{36} +(6.00000 + 3.46410i) q^{37} +3.00000 q^{38} +(2.50000 + 2.59808i) q^{39} +(-3.00000 - 1.73205i) q^{41} +(-1.50000 + 2.59808i) q^{42} +(2.50000 + 4.33013i) q^{43} +3.46410i q^{44} +(-9.00000 + 5.19615i) q^{46} +6.92820i q^{47} +(2.50000 + 4.33013i) q^{48} +(-2.00000 + 3.46410i) q^{49} -6.00000 q^{51} +(3.50000 - 0.866025i) q^{52} -12.0000 q^{53} +(1.50000 + 0.866025i) q^{54} +(-1.50000 - 2.59808i) q^{56} +1.73205i q^{57} +(9.00000 - 5.19615i) q^{58} +(9.00000 - 5.19615i) q^{59} +(1.00000 + 1.73205i) q^{61} +(3.00000 - 5.19615i) q^{62} +(-1.50000 - 0.866025i) q^{63} -1.00000 q^{64} -6.00000 q^{66} +(-7.50000 - 4.33013i) q^{67} +(-3.00000 + 5.19615i) q^{68} +(-3.00000 - 5.19615i) q^{69} +(3.00000 - 1.73205i) q^{71} +(-1.50000 + 0.866025i) q^{72} -8.66025i q^{73} +(6.00000 + 10.3923i) q^{74} +(1.50000 + 0.866025i) q^{76} +6.00000 q^{77} +(1.50000 + 6.06218i) q^{78} -11.0000 q^{79} +(-0.500000 + 0.866025i) q^{81} +(-3.00000 - 5.19615i) q^{82} +3.46410i q^{83} +(-1.50000 + 0.866025i) q^{84} +8.66025i q^{86} +(3.00000 + 5.19615i) q^{87} +(3.00000 - 5.19615i) q^{88} +(-3.00000 - 1.73205i) q^{89} +(-1.50000 - 6.06218i) q^{91} -6.00000 q^{92} +(3.00000 + 1.73205i) q^{93} +(-6.00000 + 10.3923i) q^{94} +5.19615i q^{96} +(-6.00000 + 3.46410i) q^{97} +(-6.00000 + 3.46410i) q^{98} -3.46410i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 3 q^{2} - q^{3} + q^{4} - 3 q^{6} + 3 q^{7} - q^{9} + 6 q^{11} - 2 q^{12} + 2 q^{13} + 6 q^{14} + 5 q^{16} + 6 q^{17} + 3 q^{19} + 6 q^{22} - 6 q^{23} + 3 q^{24} + 9 q^{26} + 2 q^{27} + 3 q^{28}+ \cdots - 12 q^{98}+O(q^{100}) $ 2 * q + 3 * q^2 - q^3 + q^4 - 3 * q^6 + 3 * q^7 - q^9 + 6 * q^11 - 2 * q^12 + 2 * q^13 + 6 * q^14 + 5 * q^16 + 6 * q^17 + 3 * q^19 + 6 * q^22 - 6 * q^23 + 3 * q^24 + 9 * q^26 + 2 * q^27 + 3 * q^28 + 6 * q^29 + 9 * q^32 - 6 * q^33 + q^36 + 12 * q^37 + 6 * q^38 + 5 * q^39 - 6 * q^41 - 3 * q^42 + 5 * q^43 - 18 * q^46 + 5 * q^48 - 4 * q^49 - 12 * q^51 + 7 * q^52 - 24 * q^53 + 3 * q^54 - 3 * q^56 + 18 * q^58 + 18 * q^59 + 2 * q^61 + 6 * q^62 - 3 * q^63 - 2 * q^64 - 12 * q^66 - 15 * q^67 - 6 * q^68 - 6 * q^69 + 6 * q^71 - 3 * q^72 + 12 * q^74 + 3 * q^76 + 12 * q^77 + 3 * q^78 - 22 * q^79 - q^81 - 6 * q^82 - 3 * q^84 + 6 * q^87 + 6 * q^88 - 6 * q^89 - 3 * q^91 - 12 * q^92 + 6 * q^93 - 12 * q^94 - 12 * q^97 - 12 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/975\mathbb{Z}\right)^\times$.

$n$	$301$	$326$	$352$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$	1.50000	+	0.866025i	1.06066	+	0.612372i	0.925615	−	0.378467i	$-0.123549\pi$
$2$	1.50000	+	0.866025i	1.06066	+	0.612372i	0.135045	+	0.990839i	$0.456882\pi$
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$		0			0
$5$		0			0
$6$	−1.50000	+	0.866025i	−0.612372	+	0.353553i
$7$	1.50000	−	0.866025i	0.566947	−	0.327327i	−0.188982	−	0.981981i	$-0.560519\pi$
$7$	1.50000	−	0.866025i	0.566947	−	0.327327i	0.755929	+	0.654654i	$0.227186\pi$
$8$		−	1.73205i		−	0.612372i
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$		0			0
$11$	3.00000	+	1.73205i	0.904534	+	0.522233i	0.878668	−	0.477432i	$-0.158432\pi$
$11$	3.00000	+	1.73205i	0.904534	+	0.522233i	0.0258656	+	0.999665i	$0.491766\pi$
$12$	−1.00000			−0.288675
$13$	1.00000	−	3.46410i	0.277350	−	0.960769i
$13$	1.00000	−	3.46410i	0.277350	−	0.960769i
$14$	3.00000			0.801784
$15$		0			0
$16$	2.50000	−	4.33013i	0.625000	−	1.08253i
$17$	3.00000	+	5.19615i	0.727607	+	1.26025i	0.957892	+	0.287129i	$0.0927008\pi$
$17$	3.00000	+	5.19615i	0.727607	+	1.26025i	−0.230285	+	0.973123i	$0.573966\pi$
$18$		−	1.73205i		−	0.408248i
$19$	1.50000	−	0.866025i	0.344124	−	0.198680i	−0.317970	−	0.948101i	$-0.603001\pi$
$19$	1.50000	−	0.866025i	0.344124	−	0.198680i	0.662094	+	0.749421i	$0.269668\pi$
$20$		0			0
$21$			1.73205i			0.377964i
$22$	3.00000	+	5.19615i	0.639602	+	1.10782i
$23$	−3.00000	+	5.19615i	−0.625543	+	1.08347i	0.362892	+	0.931831i	$0.381789\pi$
$23$	−3.00000	+	5.19615i	−0.625543	+	1.08347i	−0.988436	+	0.151642i	$0.951544\pi$
$24$	1.50000	+	0.866025i	0.306186	+	0.176777i
$25$		0			0
$26$	4.50000	−	4.33013i	0.882523	−	0.849208i
$27$	1.00000			0.192450
$28$	1.50000	+	0.866025i	0.283473	+	0.163663i
$29$	3.00000	−	5.19615i	0.557086	−	0.964901i	−0.440652	−	0.897678i	$-0.645253\pi$
$29$	3.00000	−	5.19615i	0.557086	−	0.964901i	0.997738	−	0.0672232i	$-0.0214140\pi$
$30$		0			0
$31$		−	3.46410i		−	0.622171i	−0.950382	−	0.311086i	$-0.899307\pi$
$31$		−	3.46410i		−	0.622171i	0.950382	−	0.311086i	$-0.100693\pi$
$32$	4.50000	−	2.59808i	0.795495	−	0.459279i
$33$	−3.00000	+	1.73205i	−0.522233	+	0.301511i
$34$			10.3923i			1.78227i
$35$		0			0
$36$	0.500000	−	0.866025i	0.0833333	−	0.144338i
$37$	6.00000	+	3.46410i	0.986394	+	0.569495i	0.904194	−	0.427121i	$-0.140472\pi$
$37$	6.00000	+	3.46410i	0.986394	+	0.569495i	0.0821995	+	0.996616i	$0.473806\pi$
$38$	3.00000			0.486664
$39$	2.50000	+	2.59808i	0.400320	+	0.416025i
$40$		0			0
$41$	−3.00000	−	1.73205i	−0.468521	−	0.270501i	0.247099	−	0.968990i	$-0.420523\pi$
$41$	−3.00000	−	1.73205i	−0.468521	−	0.270501i	−0.715621	+	0.698489i	$0.753856\pi$
$42$	−1.50000	+	2.59808i	−0.231455	+	0.400892i
$43$	2.50000	+	4.33013i	0.381246	+	0.660338i	0.991241	−	0.132068i	$-0.0421616\pi$
$43$	2.50000	+	4.33013i	0.381246	+	0.660338i	−0.609994	+	0.792406i	$0.708828\pi$
$44$			3.46410i			0.522233i
$45$		0			0
$46$	−9.00000	+	5.19615i	−1.32698	+	0.766131i
$47$			6.92820i			1.01058i	0.862949	+	0.505291i	$0.168615\pi$
$47$			6.92820i			1.01058i	−0.862949	+	0.505291i	$0.831385\pi$
$48$	2.50000	+	4.33013i	0.360844	+	0.625000i
$49$	−2.00000	+	3.46410i	−0.285714	+	0.494872i
$50$		0			0
$51$	−6.00000			−0.840168
$52$	3.50000	−	0.866025i	0.485363	−	0.120096i
$53$	−12.0000			−1.64833			−0.824163	−	0.566352i	$-0.808354\pi$
$53$	−12.0000			−1.64833			−0.824163	+	0.566352i	$0.808354\pi$
$54$	1.50000	+	0.866025i	0.204124	+	0.117851i
$55$		0			0
$56$	−1.50000	−	2.59808i	−0.200446	−	0.347183i
$57$			1.73205i			0.229416i
$58$	9.00000	−	5.19615i	1.18176	−	0.682288i
$59$	9.00000	−	5.19615i	1.17170	−	0.676481i	0.217620	−	0.976034i	$-0.430171\pi$
$59$	9.00000	−	5.19615i	1.17170	−	0.676481i	0.954080	+	0.299552i	$0.0968372\pi$
$60$		0			0
$61$	1.00000	+	1.73205i	0.128037	+	0.221766i	0.922916	−	0.385002i	$-0.125799\pi$
$61$	1.00000	+	1.73205i	0.128037	+	0.221766i	−0.794879	+	0.606768i	$0.792466\pi$
$62$	3.00000	−	5.19615i	0.381000	−	0.659912i
$63$	−1.50000	−	0.866025i	−0.188982	−	0.109109i
$64$	−1.00000			−0.125000
$65$		0			0
$66$	−6.00000			−0.738549
$67$	−7.50000	−	4.33013i	−0.916271	−	0.529009i	−0.0338274	−	0.999428i	$-0.510770\pi$
$67$	−7.50000	−	4.33013i	−0.916271	−	0.529009i	−0.882443	+	0.470418i	$0.844103\pi$
$68$	−3.00000	+	5.19615i	−0.363803	+	0.630126i
$69$	−3.00000	−	5.19615i	−0.361158	−	0.625543i
$70$		0			0
$71$	3.00000	−	1.73205i	0.356034	−	0.205557i	−0.311305	−	0.950310i	$-0.600766\pi$
$71$	3.00000	−	1.73205i	0.356034	−	0.205557i	0.667340	+	0.744753i	$0.267433\pi$
$72$	−1.50000	+	0.866025i	−0.176777	+	0.102062i
$73$		−	8.66025i		−	1.01361i	−0.862062	−	0.506803i	$-0.830827\pi$
$73$		−	8.66025i		−	1.01361i	0.862062	−	0.506803i	$-0.169173\pi$
$74$	6.00000	+	10.3923i	0.697486	+	1.20808i
$75$		0			0
$76$	1.50000	+	0.866025i	0.172062	+	0.0993399i
$77$	6.00000			0.683763
$78$	1.50000	+	6.06218i	0.169842	+	0.686406i
$79$	−11.0000			−1.23760			−0.618798	−	0.785550i	$-0.712380\pi$
$79$	−11.0000			−1.23760			−0.618798	+	0.785550i	$0.712380\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−3.00000	−	5.19615i	−0.331295	−	0.573819i
$83$			3.46410i			0.380235i	0.981761	+	0.190117i	$0.0608868\pi$
$83$			3.46410i			0.380235i	−0.981761	+	0.190117i	$0.939113\pi$
$84$	−1.50000	+	0.866025i	−0.163663	+	0.0944911i
$85$		0			0
$86$			8.66025i			0.933859i
$87$	3.00000	+	5.19615i	0.321634	+	0.557086i
$88$	3.00000	−	5.19615i	0.319801	−	0.553912i
$89$	−3.00000	−	1.73205i	−0.317999	−	0.183597i	0.332501	−	0.943103i	$-0.392107\pi$
$89$	−3.00000	−	1.73205i	−0.317999	−	0.183597i	−0.650500	+	0.759506i	$0.725441\pi$
$90$		0			0
$91$	−1.50000	−	6.06218i	−0.157243	−	0.635489i
$92$	−6.00000			−0.625543
$93$	3.00000	+	1.73205i	0.311086	+	0.179605i
$94$	−6.00000	+	10.3923i	−0.618853	+	1.07188i
$95$		0			0
$96$			5.19615i			0.530330i
$97$	−6.00000	+	3.46410i	−0.609208	+	0.351726i	−0.772655	−	0.634826i	$-0.781072\pi$
$97$	−6.00000	+	3.46410i	−0.609208	+	0.351726i	0.163448	+	0.986552i	$0.447739\pi$
$98$	−6.00000	+	3.46410i	−0.606092	+	0.349927i
$99$		−	3.46410i		−	0.348155i
$100$		0			0
$101$	3.00000	−	5.19615i	0.298511	−	0.517036i	−0.677284	−	0.735721i	$-0.736843\pi$
$101$	3.00000	−	5.19615i	0.298511	−	0.517036i	0.975796	+	0.218685i	$0.0701767\pi$
$102$	−9.00000	−	5.19615i	−0.891133	−	0.514496i
$103$	13.0000			1.28093			0.640464	−	0.767988i	$-0.278742\pi$
$103$	13.0000			1.28093			0.640464	+	0.767988i	$0.278742\pi$
$104$	−6.00000	−	1.73205i	−0.588348	−	0.169842i
$105$		0			0
$106$	−18.0000	−	10.3923i	−1.74831	−	1.00939i
$107$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$107$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$108$	0.500000	+	0.866025i	0.0481125	+	0.0833333i
$109$		−	13.8564i		−	1.32720i	−0.748086	−	0.663602i	$-0.769027\pi$
$109$		−	13.8564i		−	1.32720i	0.748086	−	0.663602i	$-0.230973\pi$
$110$		0			0
$111$	−6.00000	+	3.46410i	−0.569495	+	0.328798i
$112$		−	8.66025i		−	0.818317i
$113$	6.00000	+	10.3923i	0.564433	+	0.977626i	0.997102	+	0.0760733i	$0.0242383\pi$
$113$	6.00000	+	10.3923i	0.564433	+	0.977626i	−0.432670	+	0.901553i	$0.642428\pi$
$114$	−1.50000	+	2.59808i	−0.140488	+	0.243332i
$115$		0			0
$116$	6.00000			0.557086
$117$	−3.50000	+	0.866025i	−0.323575	+	0.0800641i
$118$	18.0000			1.65703
$119$	9.00000	+	5.19615i	0.825029	+	0.476331i
$120$		0			0
$121$	0.500000	+	0.866025i	0.0454545	+	0.0787296i
$122$			3.46410i			0.313625i
$123$	3.00000	−	1.73205i	0.270501	−	0.156174i
$124$	3.00000	−	1.73205i	0.269408	−	0.155543i
$125$		0			0
$126$	−1.50000	−	2.59808i	−0.133631	−	0.231455i
$127$	0.500000	−	0.866025i	0.0443678	−	0.0768473i	−0.842989	−	0.537931i	$-0.819206\pi$
$127$	0.500000	−	0.866025i	0.0443678	−	0.0768473i	0.887357	+	0.461084i	$0.152539\pi$
$128$	−10.5000	−	6.06218i	−0.928078	−	0.535826i
$129$	−5.00000			−0.440225
$130$		0			0
$131$	−12.0000			−1.04844			−0.524222	−	0.851581i	$-0.675644\pi$
$131$	−12.0000			−1.04844			−0.524222	+	0.851581i	$0.675644\pi$
$132$	−3.00000	−	1.73205i	−0.261116	−	0.150756i
$133$	1.50000	−	2.59808i	0.130066	−	0.225282i
$134$	−7.50000	−	12.9904i	−0.647901	−	1.12220i
$135$		0			0
$136$	9.00000	−	5.19615i	0.771744	−	0.445566i
$137$	9.00000	−	5.19615i	0.768922	−	0.443937i	−0.0635680	−	0.997978i	$-0.520248\pi$
$137$	9.00000	−	5.19615i	0.768922	−	0.443937i	0.832490	+	0.554040i	$0.186915\pi$
$138$		−	10.3923i		−	0.884652i
$139$	−2.50000	−	4.33013i	−0.212047	−	0.367277i	0.740308	−	0.672268i	$-0.234680\pi$
$139$	−2.50000	−	4.33013i	−0.212047	−	0.367277i	−0.952355	+	0.304991i	$0.901346\pi$
$140$		0			0
$141$	−6.00000	−	3.46410i	−0.505291	−	0.291730i
$142$	6.00000			0.503509
$143$	9.00000	−	8.66025i	0.752618	−	0.724207i
$144$	−5.00000			−0.416667
$145$		0			0
$146$	7.50000	−	12.9904i	0.620704	−	1.07509i
$147$	−2.00000	−	3.46410i	−0.164957	−	0.285714i
$148$			6.92820i			0.569495i
$149$	3.00000	−	1.73205i	0.245770	−	0.141895i	−0.372056	−	0.928210i	$-0.621347\pi$
$149$	3.00000	−	1.73205i	0.245770	−	0.141895i	0.617826	+	0.786315i	$0.288014\pi$
$150$		0			0
$151$			8.66025i			0.704761i	0.935857	+	0.352381i	$0.114628\pi$
$151$			8.66025i			0.704761i	−0.935857	+	0.352381i	$0.885372\pi$
$152$	−1.50000	−	2.59808i	−0.121666	−	0.210732i
$153$	3.00000	−	5.19615i	0.242536	−	0.420084i
$154$	9.00000	+	5.19615i	0.725241	+	0.418718i
$155$		0			0
$156$	−1.00000	+	3.46410i	−0.0800641	+	0.277350i
$157$	−23.0000			−1.83560			−0.917800	−	0.397043i	$-0.870036\pi$
$157$	−23.0000			−1.83560			−0.917800	+	0.397043i	$0.870036\pi$
$158$	−16.5000	−	9.52628i	−1.31267	−	0.757870i
$159$	6.00000	−	10.3923i	0.475831	−	0.824163i
$160$		0			0
$161$			10.3923i			0.819028i
$162$	−1.50000	+	0.866025i	−0.117851	+	0.0680414i
$163$	−21.0000	+	12.1244i	−1.64485	+	0.949653i	−0.665771	+	0.746156i	$0.731897\pi$
$163$	−21.0000	+	12.1244i	−1.64485	+	0.949653i	−0.979076	+	0.203497i	$0.934769\pi$
$164$		−	3.46410i		−	0.270501i
$165$		0			0
$166$	−3.00000	+	5.19615i	−0.232845	+	0.403300i
$167$	−3.00000	−	1.73205i	−0.232147	−	0.134030i	0.379415	−	0.925227i	$-0.376125\pi$
$167$	−3.00000	−	1.73205i	−0.232147	−	0.134030i	−0.611562	+	0.791196i	$0.709459\pi$
$168$	3.00000			0.231455
$169$	−11.0000	−	6.92820i	−0.846154	−	0.532939i
$170$		0			0
$171$	−1.50000	−	0.866025i	−0.114708	−	0.0662266i
$172$	−2.50000	+	4.33013i	−0.190623	+	0.330169i
$173$	12.0000	+	20.7846i	0.912343	+	1.58022i	0.810745	+	0.585399i	$0.199062\pi$
$173$	12.0000	+	20.7846i	0.912343	+	1.58022i	0.101598	+	0.994826i	$0.467605\pi$
$174$			10.3923i			0.787839i
$175$		0			0
$176$	15.0000	−	8.66025i	1.13067	−	0.652791i
$177$			10.3923i			0.781133i
$178$	−3.00000	−	5.19615i	−0.224860	−	0.389468i
$179$	−6.00000	+	10.3923i	−0.448461	+	0.776757i	−0.998286	−	0.0585225i	$-0.981361\pi$
$179$	−6.00000	+	10.3923i	−0.448461	+	0.776757i	0.549825	+	0.835280i	$0.314694\pi$
$180$		0			0
$181$	17.0000			1.26360			0.631800	−	0.775131i	$-0.282316\pi$
$181$	17.0000			1.26360			0.631800	+	0.775131i	$0.282316\pi$
$182$	3.00000	−	10.3923i	0.222375	−	0.770329i
$183$	−2.00000			−0.147844
$184$	9.00000	+	5.19615i	0.663489	+	0.383065i
$185$		0			0
$186$	3.00000	+	5.19615i	0.219971	+	0.381000i
$187$			20.7846i			1.51992i
$188$	−6.00000	+	3.46410i	−0.437595	+	0.252646i
$189$	1.50000	−	0.866025i	0.109109	−	0.0629941i
$190$		0			0
$191$	3.00000	+	5.19615i	0.217072	+	0.375980i	0.953912	−	0.300088i	$-0.0970159\pi$
$191$	3.00000	+	5.19615i	0.217072	+	0.375980i	−0.736839	+	0.676068i	$0.763683\pi$
$192$	0.500000	−	0.866025i	0.0360844	−	0.0625000i
$193$	−19.5000	−	11.2583i	−1.40364	−	0.810392i	−0.408877	−	0.912590i	$-0.634079\pi$
$193$	−19.5000	−	11.2583i	−1.40364	−	0.810392i	−0.994764	+	0.102197i	$0.967413\pi$
$194$	−12.0000			−0.861550
$195$		0			0
$196$	−4.00000			−0.285714
$197$	−18.0000	−	10.3923i	−1.28245	−	0.740421i	−0.305152	−	0.952304i	$-0.598707\pi$
$197$	−18.0000	−	10.3923i	−1.28245	−	0.740421i	−0.977295	+	0.211883i	$0.932041\pi$
$198$	3.00000	−	5.19615i	0.213201	−	0.369274i
$199$	−12.5000	−	21.6506i	−0.886102	−	1.53477i	−0.844446	−	0.535641i	$-0.820070\pi$
$199$	−12.5000	−	21.6506i	−0.886102	−	1.53477i	−0.0416556	−	0.999132i	$-0.513263\pi$
$200$		0			0
$201$	7.50000	−	4.33013i	0.529009	−	0.305424i
$202$	9.00000	−	5.19615i	0.633238	−	0.365600i
$203$		−	10.3923i		−	0.729397i
$204$	−3.00000	−	5.19615i	−0.210042	−	0.363803i
$205$		0			0
$206$	19.5000	+	11.2583i	1.35863	+	0.784405i
$207$	6.00000			0.417029
$208$	−12.5000	−	12.9904i	−0.866719	−	0.900721i
$209$	6.00000			0.415029
$210$		0			0
$211$	−8.00000	+	13.8564i	−0.550743	+	0.953914i	0.447478	+	0.894295i	$0.352322\pi$
$211$	−8.00000	+	13.8564i	−0.550743	+	0.953914i	−0.998221	+	0.0596196i	$0.981011\pi$
$212$	−6.00000	−	10.3923i	−0.412082	−	0.713746i
$213$			3.46410i			0.237356i
$214$		0			0
$215$		0			0
$216$		−	1.73205i		−	0.117851i
$217$	−3.00000	−	5.19615i	−0.203653	−	0.352738i
$218$	12.0000	−	20.7846i	0.812743	−	1.40771i
$219$	7.50000	+	4.33013i	0.506803	+	0.292603i
$220$		0			0
$221$	21.0000	−	5.19615i	1.41261	−	0.349531i
$222$	−12.0000			−0.805387
$223$	7.50000	+	4.33013i	0.502237	+	0.289967i	0.729637	−	0.683835i	$-0.239689\pi$
$223$	7.50000	+	4.33013i	0.502237	+	0.289967i	−0.227400	+	0.973801i	$0.573022\pi$
$224$	4.50000	−	7.79423i	0.300669	−	0.520774i
$225$		0			0
$226$			20.7846i			1.38257i
$227$	24.0000	−	13.8564i	1.59294	−	0.919682i	0.600136	−	0.799898i	$-0.295113\pi$
$227$	24.0000	−	13.8564i	1.59294	−	0.919682i	0.992800	−	0.119784i	$-0.0382202\pi$
$228$	−1.50000	+	0.866025i	−0.0993399	+	0.0573539i
$229$			1.73205i			0.114457i	0.998361	+	0.0572286i	$0.0182264\pi$
$229$			1.73205i			0.114457i	−0.998361	+	0.0572286i	$0.981774\pi$
$230$		0			0
$231$	−3.00000	+	5.19615i	−0.197386	+	0.341882i
$232$	−9.00000	−	5.19615i	−0.590879	−	0.341144i
$233$	−24.0000			−1.57229			−0.786146	−	0.618041i	$-0.787927\pi$
$233$	−24.0000			−1.57229			−0.786146	+	0.618041i	$0.787927\pi$
$234$	−6.00000	−	1.73205i	−0.392232	−	0.113228i
$235$		0			0
$236$	9.00000	+	5.19615i	0.585850	+	0.338241i
$237$	5.50000	−	9.52628i	0.357263	−	0.618798i
$238$	9.00000	+	15.5885i	0.583383	+	1.01045i
$239$		−	10.3923i		−	0.672222i	−0.941822	−	0.336111i	$-0.890888\pi$
$239$		−	10.3923i		−	0.672222i	0.941822	−	0.336111i	$-0.109112\pi$
$240$		0			0
$241$	−16.5000	+	9.52628i	−1.06286	+	0.613642i	−0.926222	−	0.376980i	$-0.876963\pi$
$241$	−16.5000	+	9.52628i	−1.06286	+	0.613642i	−0.136637	+	0.990621i	$0.543629\pi$
$242$			1.73205i			0.111340i
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$	−1.00000	+	1.73205i	−0.0640184	+	0.110883i
$245$		0			0
$246$	6.00000			0.382546
$247$	−1.50000	−	6.06218i	−0.0954427	−	0.385727i
$248$	−6.00000			−0.381000
$249$	−3.00000	−	1.73205i	−0.190117	−	0.109764i
$250$		0			0
$251$	12.0000	+	20.7846i	0.757433	+	1.31191i	0.944156	+	0.329500i	$0.106880\pi$
$251$	12.0000	+	20.7846i	0.757433	+	1.31191i	−0.186722	+	0.982413i	$0.559786\pi$
$252$		−	1.73205i		−	0.109109i
$253$	−18.0000	+	10.3923i	−1.13165	+	0.653359i
$254$	1.50000	−	0.866025i	0.0941184	−	0.0543393i
$255$		0			0
$256$	−9.50000	−	16.4545i	−0.593750	−	1.02841i
$257$	−6.00000	+	10.3923i	−0.374270	+	0.648254i	−0.990217	−	0.139533i	$-0.955440\pi$
$257$	−6.00000	+	10.3923i	−0.374270	+	0.648254i	0.615948	+	0.787787i	$0.288773\pi$
$258$	−7.50000	−	4.33013i	−0.466930	−	0.269582i
$259$	12.0000			0.745644
$260$		0			0
$261$	−6.00000			−0.371391
$262$	−18.0000	−	10.3923i	−1.11204	−	0.642039i
$263$	−3.00000	+	5.19615i	−0.184988	+	0.320408i	−0.943572	−	0.331166i	$-0.892558\pi$
$263$	−3.00000	+	5.19615i	−0.184988	+	0.320408i	0.758585	+	0.651575i	$0.225891\pi$
$264$	3.00000	+	5.19615i	0.184637	+	0.319801i
$265$		0			0
$266$	4.50000	−	2.59808i	0.275913	−	0.159298i
$267$	3.00000	−	1.73205i	0.183597	−	0.106000i
$268$		−	8.66025i		−	0.529009i
$269$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$269$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$270$		0			0
$271$	7.50000	+	4.33013i	0.455593	+	0.263036i	0.710189	−	0.704011i	$-0.248609\pi$
$271$	7.50000	+	4.33013i	0.455593	+	0.263036i	−0.254597	+	0.967047i	$0.581943\pi$
$272$	30.0000			1.81902
$273$	6.00000	+	1.73205i	0.363137	+	0.104828i
$274$	18.0000			1.08742
$275$		0			0
$276$	3.00000	−	5.19615i	0.180579	−	0.312772i
$277$	8.50000	+	14.7224i	0.510716	+	0.884585i	0.999923	+	0.0124177i	$0.00395278\pi$
$277$	8.50000	+	14.7224i	0.510716	+	0.884585i	−0.489207	+	0.872167i	$0.662714\pi$
$278$		−	8.66025i		−	0.519408i
$279$	−3.00000	+	1.73205i	−0.179605	+	0.103695i
$280$		0			0
$281$		−	3.46410i		−	0.206651i	−0.994648	−	0.103325i	$-0.967052\pi$
$281$		−	3.46410i		−	0.206651i	0.994648	−	0.103325i	$-0.0329483\pi$
$282$	−6.00000	−	10.3923i	−0.357295	−	0.618853i
$283$	2.00000	−	3.46410i	0.118888	−	0.205919i	−0.800439	−	0.599414i	$-0.795400\pi$
$283$	2.00000	−	3.46410i	0.118888	−	0.205919i	0.919327	+	0.393494i	$0.128734\pi$
$284$	3.00000	+	1.73205i	0.178017	+	0.102778i
$285$		0			0
$286$	21.0000	−	5.19615i	1.24176	−	0.307255i
$287$	−6.00000			−0.354169
$288$	−4.50000	−	2.59808i	−0.265165	−	0.153093i
$289$	−9.50000	+	16.4545i	−0.558824	+	0.967911i
$290$		0			0
$291$		−	6.92820i		−	0.406138i
$292$	7.50000	−	4.33013i	0.438904	−	0.253402i
$293$	−6.00000	+	3.46410i	−0.350524	+	0.202375i	−0.664916	−	0.746918i	$-0.731533\pi$
$293$	−6.00000	+	3.46410i	−0.350524	+	0.202375i	0.314392	+	0.949293i	$0.398199\pi$
$294$		−	6.92820i		−	0.404061i
$295$		0			0
$296$	6.00000	−	10.3923i	0.348743	−	0.604040i
$297$	3.00000	+	1.73205i	0.174078	+	0.100504i
$298$	6.00000			0.347571
$299$	15.0000	+	15.5885i	0.867472	+	0.901504i
$300$		0			0
$301$	7.50000	+	4.33013i	0.432293	+	0.249584i
$302$	−7.50000	+	12.9904i	−0.431577	+	0.747512i
$303$	3.00000	+	5.19615i	0.172345	+	0.298511i
$304$		−	8.66025i		−	0.496700i
$305$		0			0
$306$	9.00000	−	5.19615i	0.514496	−	0.297044i
$307$		−	10.3923i		−	0.593120i	−0.955014	−	0.296560i	$-0.904160\pi$
$307$		−	10.3923i		−	0.593120i	0.955014	−	0.296560i	$-0.0958395\pi$
$308$	3.00000	+	5.19615i	0.170941	+	0.296078i
$309$	−6.50000	+	11.2583i	−0.369772	+	0.640464i
$310$		0			0
$311$	12.0000			0.680458			0.340229	−	0.940343i	$-0.389495\pi$
$311$	12.0000			0.680458			0.340229	+	0.940343i	$0.389495\pi$
$312$	4.50000	−	4.33013i	0.254762	−	0.245145i
$313$	−25.0000			−1.41308			−0.706542	−	0.707671i	$-0.749746\pi$
$313$	−25.0000			−1.41308			−0.706542	+	0.707671i	$0.749746\pi$
$314$	−34.5000	−	19.9186i	−1.94695	−	1.12407i
$315$		0			0
$316$	−5.50000	−	9.52628i	−0.309399	−	0.535895i
$317$			6.92820i			0.389127i	0.980890	+	0.194563i	$0.0623290\pi$
$317$			6.92820i			0.389127i	−0.980890	+	0.194563i	$0.937671\pi$
$318$	18.0000	−	10.3923i	1.00939	−	0.582772i
$319$	18.0000	−	10.3923i	1.00781	−	0.581857i
$320$		0			0
$321$		0			0
$322$	−9.00000	+	15.5885i	−0.501550	+	0.868711i
$323$	9.00000	+	5.19615i	0.500773	+	0.289122i
$324$	−1.00000			−0.0555556
$325$		0			0
$326$	−42.0000			−2.32616
$327$	12.0000	+	6.92820i	0.663602	+	0.383131i
$328$	−3.00000	+	5.19615i	−0.165647	+	0.286910i
$329$	6.00000	+	10.3923i	0.330791	+	0.572946i
$330$		0			0
$331$	4.50000	−	2.59808i	0.247342	−	0.142803i	−0.371204	−	0.928551i	$-0.621055\pi$
$331$	4.50000	−	2.59808i	0.247342	−	0.142803i	0.618547	+	0.785748i	$0.287722\pi$
$332$	−3.00000	+	1.73205i	−0.164646	+	0.0950586i
$333$		−	6.92820i		−	0.379663i
$334$	−3.00000	−	5.19615i	−0.164153	−	0.284321i
$335$		0			0
$336$	7.50000	+	4.33013i	0.409159	+	0.236228i
$337$	−19.0000			−1.03500			−0.517498	−	0.855684i	$-0.673136\pi$
$337$	−19.0000			−1.03500			−0.517498	+	0.855684i	$0.673136\pi$
$338$	−10.5000	−	19.9186i	−0.571125	−	1.08343i
$339$	−12.0000			−0.651751
$340$		0			0
$341$	6.00000	−	10.3923i	0.324918	−	0.562775i
$342$	−1.50000	−	2.59808i	−0.0811107	−	0.140488i
$343$			19.0526i			1.02874i
$344$	7.50000	−	4.33013i	0.404373	−	0.233465i
$345$		0			0
$346$			41.5692i			2.23478i
$347$	−12.0000	−	20.7846i	−0.644194	−	1.11578i	−0.984487	−	0.175457i	$-0.943860\pi$
$347$	−12.0000	−	20.7846i	−0.644194	−	1.11578i	0.340293	−	0.940319i	$-0.389474\pi$
$348$	−3.00000	+	5.19615i	−0.160817	+	0.278543i
$349$	−10.5000	−	6.06218i	−0.562052	−	0.324501i	0.191917	−	0.981411i	$-0.438530\pi$
$349$	−10.5000	−	6.06218i	−0.562052	−	0.324501i	−0.753969	+	0.656910i	$0.771863\pi$
$350$		0			0
$351$	1.00000	−	3.46410i	0.0533761	−	0.184900i
$352$	18.0000			0.959403
$353$	21.0000	+	12.1244i	1.11772	+	0.645314i	0.940817	−	0.338914i	$-0.110060\pi$
$353$	21.0000	+	12.1244i	1.11772	+	0.645314i	0.176900	+	0.984229i	$0.443393\pi$
$354$	−9.00000	+	15.5885i	−0.478345	+	0.828517i
$355$		0			0
$356$		−	3.46410i		−	0.183597i
$357$	−9.00000	+	5.19615i	−0.476331	+	0.275010i
$358$	−18.0000	+	10.3923i	−0.951330	+	0.549250i
$359$			27.7128i			1.46263i	0.682042	+	0.731313i	$0.261092\pi$
$359$			27.7128i			1.46263i	−0.682042	+	0.731313i	$0.738908\pi$
$360$		0			0
$361$	−8.00000	+	13.8564i	−0.421053	+	0.729285i
$362$	25.5000	+	14.7224i	1.34025	+	0.773794i
$363$	−1.00000			−0.0524864
$364$	4.50000	−	4.33013i	0.235864	−	0.226960i
$365$		0			0
$366$	−3.00000	−	1.73205i	−0.156813	−	0.0905357i
$367$	17.5000	−	30.3109i	0.913493	−	1.58222i	0.104399	−	0.994535i	$-0.466708\pi$
$367$	17.5000	−	30.3109i	0.913493	−	1.58222i	0.809093	−	0.587680i	$-0.199959\pi$
$368$	15.0000	+	25.9808i	0.781929	+	1.35434i
$369$			3.46410i			0.180334i
$370$		0			0
$371$	−18.0000	+	10.3923i	−0.934513	+	0.539542i
$372$			3.46410i			0.179605i
$373$	18.5000	+	32.0429i	0.957894	+	1.65912i	0.727603	+	0.685999i	$0.240634\pi$
$373$	18.5000	+	32.0429i	0.957894	+	1.65912i	0.230291	+	0.973122i	$0.426032\pi$
$374$	−18.0000	+	31.1769i	−0.930758	+	1.61212i
$375$		0			0
$376$	12.0000			0.618853
$377$	−15.0000	−	15.5885i	−0.772539	−	0.802846i
$378$	3.00000			0.154303
$379$	22.5000	+	12.9904i	1.15575	+	0.667271i	0.950281	−	0.311393i	$-0.100796\pi$
$379$	22.5000	+	12.9904i	1.15575	+	0.667271i	0.205466	+	0.978664i	$0.434129\pi$
$380$		0			0
$381$	0.500000	+	0.866025i	0.0256158	+	0.0443678i
$382$			10.3923i			0.531717i
$383$	24.0000	−	13.8564i	1.22634	−	0.708029i	0.260080	−	0.965587i	$-0.416251\pi$
$383$	24.0000	−	13.8564i	1.22634	−	0.708029i	0.966263	+	0.257558i	$0.0829178\pi$
$384$	10.5000	−	6.06218i	0.535826	−	0.309359i
$385$		0			0
$386$	−19.5000	−	33.7750i	−0.992524	−	1.71910i
$387$	2.50000	−	4.33013i	0.127082	−	0.220113i
$388$	−6.00000	−	3.46410i	−0.304604	−	0.175863i
$389$	−12.0000			−0.608424			−0.304212	−	0.952604i	$-0.598393\pi$
$389$	−12.0000			−0.608424			−0.304212	+	0.952604i	$0.598393\pi$
$390$		0			0
$391$	−36.0000			−1.82060
$392$	6.00000	+	3.46410i	0.303046	+	0.174964i
$393$	6.00000	−	10.3923i	0.302660	−	0.524222i
$394$	−18.0000	−	31.1769i	−0.906827	−	1.57067i
$395$		0			0
$396$	3.00000	−	1.73205i	0.150756	−	0.0870388i
$397$	−22.5000	+	12.9904i	−1.12924	+	0.651969i	−0.943744	−	0.330676i	$-0.892723\pi$
$397$	−22.5000	+	12.9904i	−1.12924	+	0.651969i	−0.185498	+	0.982645i	$0.559390\pi$
$398$		−	43.3013i		−	2.17050i
$399$	1.50000	+	2.59808i	0.0750939	+	0.130066i
$400$		0			0
$401$	−6.00000	−	3.46410i	−0.299626	−	0.172989i	0.342649	−	0.939463i	$-0.388676\pi$
$401$	−6.00000	−	3.46410i	−0.299626	−	0.172989i	−0.642275	+	0.766475i	$0.722009\pi$
$402$	15.0000			0.748132
$403$	−12.0000	−	3.46410i	−0.597763	−	0.172559i
$404$	6.00000			0.298511
$405$		0			0
$406$	9.00000	−	15.5885i	0.446663	−	0.773642i
$407$	12.0000	+	20.7846i	0.594818	+	1.03025i
$408$			10.3923i			0.514496i
$409$	−30.0000	+	17.3205i	−1.48340	+	0.856444i	−0.999822	−	0.0188549i	$-0.993998\pi$
$409$	−30.0000	+	17.3205i	−1.48340	+	0.856444i	−0.483582	+	0.875299i	$0.660665\pi$
$410$		0			0
$411$			10.3923i			0.512615i
$412$	6.50000	+	11.2583i	0.320232	+	0.554658i
$413$	9.00000	−	15.5885i	0.442861	−	0.767058i
$414$	9.00000	+	5.19615i	0.442326	+	0.255377i
$415$		0			0
$416$	−4.50000	−	18.1865i	−0.220631	−	0.891668i
$417$	5.00000			0.244851
$418$	9.00000	+	5.19615i	0.440204	+	0.254152i
$419$	6.00000	−	10.3923i	0.293119	−	0.507697i	−0.681426	−	0.731887i	$-0.738640\pi$
$419$	6.00000	−	10.3923i	0.293119	−	0.507697i	0.974546	+	0.224189i	$0.0719734\pi$
$420$		0			0
$421$		−	5.19615i		−	0.253245i	−0.991951	−	0.126622i	$-0.959586\pi$
$421$		−	5.19615i		−	0.253245i	0.991951	−	0.126622i	$-0.0404137\pi$
$422$	−24.0000	+	13.8564i	−1.16830	+	0.674519i
$423$	6.00000	−	3.46410i	0.291730	−	0.168430i
$424$			20.7846i			1.00939i
$425$		0			0
$426$	−3.00000	+	5.19615i	−0.145350	+	0.251754i
$427$	3.00000	+	1.73205i	0.145180	+	0.0838198i
$428$		0			0
$429$	3.00000	+	12.1244i	0.144841	+	0.585369i
$430$		0			0
$431$	−24.0000	−	13.8564i	−1.15604	−	0.667440i	−0.205688	−	0.978618i	$-0.565943\pi$
$431$	−24.0000	−	13.8564i	−1.15604	−	0.667440i	−0.950352	+	0.311178i	$0.899276\pi$
$432$	2.50000	−	4.33013i	0.120281	−	0.208333i
$433$	−1.00000	−	1.73205i	−0.0480569	−	0.0832370i	0.840996	−	0.541041i	$-0.181970\pi$
$433$	−1.00000	−	1.73205i	−0.0480569	−	0.0832370i	−0.889053	+	0.457804i	$0.848636\pi$
$434$		−	10.3923i		−	0.498847i
$435$		0			0
$436$	12.0000	−	6.92820i	0.574696	−	0.331801i
$437$			10.3923i			0.497131i
$438$	7.50000	+	12.9904i	0.358364	+	0.620704i
$439$	15.5000	−	26.8468i	0.739775	−	1.28133i	−0.212822	−	0.977091i	$-0.568265\pi$
$439$	15.5000	−	26.8468i	0.739775	−	1.28133i	0.952597	−	0.304236i	$-0.0984012\pi$
$440$		0			0
$441$	4.00000			0.190476
$442$	36.0000	+	10.3923i	1.71235	+	0.494312i
$443$	18.0000			0.855206			0.427603	−	0.903967i	$-0.359358\pi$
$443$	18.0000			0.855206			0.427603	+	0.903967i	$0.359358\pi$
$444$	−6.00000	−	3.46410i	−0.284747	−	0.164399i
$445$		0			0
$446$	7.50000	+	12.9904i	0.355135	+	0.615112i
$447$			3.46410i			0.163846i
$448$	−1.50000	+	0.866025i	−0.0708683	+	0.0409159i
$449$	24.0000	−	13.8564i	1.13263	−	0.653924i	0.188035	−	0.982162i	$-0.439788\pi$
$449$	24.0000	−	13.8564i	1.13263	−	0.653924i	0.944595	+	0.328238i	$0.106455\pi$
$450$		0			0
$451$	−6.00000	−	10.3923i	−0.282529	−	0.489355i
$452$	−6.00000	+	10.3923i	−0.282216	+	0.488813i
$453$	−7.50000	−	4.33013i	−0.352381	−	0.203447i
$454$	48.0000			2.25275
$455$		0			0
$456$	3.00000			0.140488
$457$	1.50000	+	0.866025i	0.0701670	+	0.0405110i	0.534673	−	0.845059i	$-0.320435\pi$
$457$	1.50000	+	0.866025i	0.0701670	+	0.0405110i	−0.464506	+	0.885570i	$0.653768\pi$
$458$	−1.50000	+	2.59808i	−0.0700904	+	0.121400i
$459$	3.00000	+	5.19615i	0.140028	+	0.242536i
$460$		0			0
$461$	−21.0000	+	12.1244i	−0.978068	+	0.564688i	−0.901686	−	0.432391i	$-0.857670\pi$
$461$	−21.0000	+	12.1244i	−0.978068	+	0.564688i	−0.0763814	+	0.997079i	$0.524337\pi$
$462$	−9.00000	+	5.19615i	−0.418718	+	0.241747i
$463$			15.5885i			0.724457i	0.932089	+	0.362229i	$0.117984\pi$
$463$			15.5885i			0.724457i	−0.932089	+	0.362229i	$0.882016\pi$
$464$	−15.0000	−	25.9808i	−0.696358	−	1.20613i
$465$		0			0
$466$	−36.0000	−	20.7846i	−1.66767	−	0.962828i
$467$	−18.0000			−0.832941			−0.416470	−	0.909149i	$-0.636733\pi$
$467$	−18.0000			−0.832941			−0.416470	+	0.909149i	$0.636733\pi$
$468$	−2.50000	−	2.59808i	−0.115563	−	0.120096i
$469$	−15.0000			−0.692636
$470$		0			0
$471$	11.5000	−	19.9186i	0.529892	−	0.917800i
$472$	−9.00000	−	15.5885i	−0.414259	−	0.717517i
$473$			17.3205i			0.796398i
$474$	16.5000	−	9.52628i	0.757870	−	0.437557i
$475$		0			0
$476$			10.3923i			0.476331i
$477$	6.00000	+	10.3923i	0.274721	+	0.475831i
$478$	9.00000	−	15.5885i	0.411650	−	0.712999i
$479$	18.0000	+	10.3923i	0.822441	+	0.474837i	0.851258	−	0.524748i	$-0.175841\pi$
$479$	18.0000	+	10.3923i	0.822441	+	0.474837i	−0.0288165	+	0.999585i	$0.509174\pi$
$480$		0			0
$481$	18.0000	−	17.3205i	0.820729	−	0.789747i
$482$	−33.0000			−1.50311
$483$	−9.00000	−	5.19615i	−0.409514	−	0.236433i
$484$	−0.500000	+	0.866025i	−0.0227273	+	0.0393648i
$485$		0			0
$486$		−	1.73205i		−	0.0785674i
$487$	22.5000	−	12.9904i	1.01957	−	0.588650i	0.105592	−	0.994410i	$-0.466326\pi$
$487$	22.5000	−	12.9904i	1.01957	−	0.588650i	0.913980	+	0.405759i	$0.132993\pi$
$488$	3.00000	−	1.73205i	0.135804	−	0.0784063i
$489$		−	24.2487i		−	1.09656i
$490$		0			0
$491$	−15.0000	+	25.9808i	−0.676941	+	1.17250i	0.298957	+	0.954267i	$0.403361\pi$
$491$	−15.0000	+	25.9808i	−0.676941	+	1.17250i	−0.975898	+	0.218229i	$0.929972\pi$
$492$	3.00000	+	1.73205i	0.135250	+	0.0780869i
$493$	36.0000			1.62136
$494$	3.00000	−	10.3923i	0.134976	−	0.467572i
$495$		0			0
$496$	−15.0000	−	8.66025i	−0.673520	−	0.388857i
$497$	3.00000	−	5.19615i	0.134568	−	0.233079i
$498$	−3.00000	−	5.19615i	−0.134433	−	0.232845i
$499$			32.9090i			1.47321i	0.676325	+	0.736604i	$0.263572\pi$
$499$			32.9090i			1.47321i	−0.676325	+	0.736604i	$0.736428\pi$
$500$		0			0
$501$	3.00000	−	1.73205i	0.134030	−	0.0773823i
$502$			41.5692i			1.85533i
$503$	−3.00000	−	5.19615i	−0.133763	−	0.231685i	0.791361	−	0.611349i	$-0.209373\pi$
$503$	−3.00000	−	5.19615i	−0.133763	−	0.231685i	−0.925124	+	0.379664i	$0.876040\pi$
$504$	−1.50000	+	2.59808i	−0.0668153	+	0.115728i
$505$		0			0
$506$	−36.0000			−1.60040
$507$	11.5000	−	6.06218i	0.510733	−	0.269231i
$508$	1.00000			0.0443678
$509$	−9.00000	−	5.19615i	−0.398918	−	0.230315i	0.287099	−	0.957901i	$-0.407309\pi$
$509$	−9.00000	−	5.19615i	−0.398918	−	0.230315i	−0.686017	+	0.727586i	$0.740642\pi$
$510$		0			0
$511$	−7.50000	−	12.9904i	−0.331780	−	0.574661i
$512$		−	8.66025i		−	0.382733i
$513$	1.50000	−	0.866025i	0.0662266	−	0.0382360i
$514$	−18.0000	+	10.3923i	−0.793946	+	0.458385i
$515$		0			0
$516$	−2.50000	−	4.33013i	−0.110056	−	0.190623i
$517$	−12.0000	+	20.7846i	−0.527759	+	0.914106i
$518$	18.0000	+	10.3923i	0.790875	+	0.456612i
$519$	−24.0000			−1.05348
$520$		0			0
$521$	−6.00000			−0.262865			−0.131432	−	0.991325i	$-0.541958\pi$
$521$	−6.00000			−0.262865			−0.131432	+	0.991325i	$0.541958\pi$
$522$	−9.00000	−	5.19615i	−0.393919	−	0.227429i
$523$	14.5000	−	25.1147i	0.634041	−	1.09819i	−0.352677	−	0.935745i	$-0.614728\pi$
$523$	14.5000	−	25.1147i	0.634041	−	1.09819i	0.986718	−	0.162446i	$-0.0519382\pi$
$524$	−6.00000	−	10.3923i	−0.262111	−	0.453990i
$525$		0			0
$526$	−9.00000	+	5.19615i	−0.392419	+	0.226563i
$527$	18.0000	−	10.3923i	0.784092	−	0.452696i
$528$			17.3205i			0.753778i
$529$	−6.50000	−	11.2583i	−0.282609	−	0.489493i
$530$		0			0
$531$	−9.00000	−	5.19615i	−0.390567	−	0.225494i
$532$	3.00000			0.130066
$533$	−9.00000	+	8.66025i	−0.389833	+	0.375117i
$534$	6.00000			0.259645
$535$		0			0
$536$	−7.50000	+	12.9904i	−0.323951	+	0.561099i
$537$	−6.00000	−	10.3923i	−0.258919	−	0.448461i
$538$		0			0
$539$	−12.0000	+	6.92820i	−0.516877	+	0.298419i
$540$		0			0
$541$			6.92820i			0.297867i	0.988847	+	0.148933i	$0.0475840\pi$
$541$			6.92820i			0.297867i	−0.988847	+	0.148933i	$0.952416\pi$
$542$	7.50000	+	12.9904i	0.322153	+	0.557985i
$543$	−8.50000	+	14.7224i	−0.364770	+	0.631800i
$544$	27.0000	+	15.5885i	1.15762	+	0.668350i
$545$		0			0
$546$	7.50000	+	7.79423i	0.320970	+	0.333562i
$547$	−17.0000			−0.726868			−0.363434	−	0.931620i	$-0.618396\pi$
$547$	−17.0000			−0.726868			−0.363434	+	0.931620i	$0.618396\pi$
$548$	9.00000	+	5.19615i	0.384461	+	0.221969i
$549$	1.00000	−	1.73205i	0.0426790	−	0.0739221i
$550$		0			0
$551$		−	10.3923i		−	0.442727i
$552$	−9.00000	+	5.19615i	−0.383065	+	0.221163i
$553$	−16.5000	+	9.52628i	−0.701651	+	0.405099i
$554$			29.4449i			1.25099i
$555$		0			0
$556$	2.50000	−	4.33013i	0.106024	−	0.183638i
$557$	−33.0000	−	19.0526i	−1.39825	−	0.807283i	−0.404045	−	0.914739i	$-0.632396\pi$
$557$	−33.0000	−	19.0526i	−1.39825	−	0.807283i	−0.994210	+	0.107456i	$0.965729\pi$
$558$	−6.00000			−0.254000
$559$	17.5000	−	4.33013i	0.740171	−	0.183145i
$560$		0			0
$561$	−18.0000	−	10.3923i	−0.759961	−	0.438763i
$562$	3.00000	−	5.19615i	0.126547	−	0.219186i
$563$	18.0000	+	31.1769i	0.758610	+	1.31395i	0.943560	+	0.331202i	$0.107454\pi$
$563$	18.0000	+	31.1769i	0.758610	+	1.31395i	−0.184950	+	0.982748i	$0.559212\pi$
$564$		−	6.92820i		−	0.291730i
$565$		0			0
$566$	6.00000	−	3.46410i	0.252199	−	0.145607i
$567$			1.73205i			0.0727393i
$568$	−3.00000	−	5.19615i	−0.125877	−	0.218026i
$569$	−3.00000	+	5.19615i	−0.125767	+	0.217834i	−0.922032	−	0.387113i	$-0.873472\pi$
$569$	−3.00000	+	5.19615i	−0.125767	+	0.217834i	0.796266	+	0.604947i	$0.206806\pi$
$570$		0			0
$571$	19.0000			0.795125			0.397563	−	0.917575i	$-0.369856\pi$
$571$	19.0000			0.795125			0.397563	+	0.917575i	$0.369856\pi$
$572$	12.0000	+	3.46410i	0.501745	+	0.144841i
$573$	−6.00000			−0.250654
$574$	−9.00000	−	5.19615i	−0.375653	−	0.216883i
$575$		0			0
$576$	0.500000	+	0.866025i	0.0208333	+	0.0360844i
$577$			1.73205i			0.0721062i	0.999350	+	0.0360531i	$0.0114785\pi$
$577$			1.73205i			0.0721062i	−0.999350	+	0.0360531i	$0.988521\pi$
$578$	−28.5000	+	16.4545i	−1.18544	+	0.684416i
$579$	19.5000	−	11.2583i	0.810392	−	0.467880i
$580$		0			0
$581$	3.00000	+	5.19615i	0.124461	+	0.215573i
$582$	6.00000	−	10.3923i	0.248708	−	0.430775i
$583$	−36.0000	−	20.7846i	−1.49097	−	0.860811i
$584$	−15.0000			−0.620704
$585$		0			0
$586$	−12.0000			−0.495715
$587$	36.0000	+	20.7846i	1.48588	+	0.857873i	0.999871	−	0.0160815i	$-0.00511913\pi$
$587$	36.0000	+	20.7846i	1.48588	+	0.857873i	0.486008	+	0.873954i	$0.338452\pi$
$588$	2.00000	−	3.46410i	0.0824786	−	0.142857i
$589$	−3.00000	−	5.19615i	−0.123613	−	0.214104i
$590$		0			0
$591$	18.0000	−	10.3923i	0.740421	−	0.427482i
$592$	30.0000	−	17.3205i	1.23299	−	0.711868i
$593$		−	27.7128i		−	1.13803i	−0.822328	−	0.569014i	$-0.807325\pi$
$593$		−	27.7128i		−	1.13803i	0.822328	−	0.569014i	$-0.192675\pi$
$594$	3.00000	+	5.19615i	0.123091	+	0.213201i
$595$		0			0
$596$	3.00000	+	1.73205i	0.122885	+	0.0709476i
$597$	25.0000			1.02318
$598$	9.00000	+	36.3731i	0.368037	+	1.48741i
$599$	12.0000			0.490307			0.245153	−	0.969484i	$-0.421162\pi$
$599$	12.0000			0.490307			0.245153	+	0.969484i	$0.421162\pi$
$600$		0			0
$601$	5.50000	−	9.52628i	0.224350	−	0.388585i	−0.731774	−	0.681547i	$-0.761308\pi$
$601$	5.50000	−	9.52628i	0.224350	−	0.388585i	0.956124	+	0.292962i	$0.0946409\pi$
$602$	7.50000	+	12.9904i	0.305677	+	0.529448i
$603$			8.66025i			0.352673i
$604$	−7.50000	+	4.33013i	−0.305171	+	0.176190i
$605$		0			0
$606$			10.3923i			0.422159i
$607$	−2.00000	−	3.46410i	−0.0811775	−	0.140604i	0.822578	−	0.568652i	$-0.192535\pi$
$607$	−2.00000	−	3.46410i	−0.0811775	−	0.140604i	−0.903756	+	0.428048i	$0.859201\pi$
$608$	4.50000	−	7.79423i	0.182499	−	0.316098i
$609$	9.00000	+	5.19615i	0.364698	+	0.210559i
$610$		0			0
$611$	24.0000	+	6.92820i	0.970936	+	0.280285i
$612$	6.00000			0.242536
$613$	−1.50000	−	0.866025i	−0.0605844	−	0.0349784i	0.469402	−	0.882985i	$-0.344470\pi$
$613$	−1.50000	−	0.866025i	−0.0605844	−	0.0349784i	−0.529986	+	0.848006i	$0.677803\pi$
$614$	9.00000	−	15.5885i	0.363210	−	0.629099i
$615$		0			0
$616$		−	10.3923i		−	0.418718i
$617$	−21.0000	+	12.1244i	−0.845428	+	0.488108i	−0.859106	−	0.511798i	$-0.828980\pi$
$617$	−21.0000	+	12.1244i	−0.845428	+	0.488108i	0.0136775	+	0.999906i	$0.495646\pi$
$618$	−19.5000	+	11.2583i	−0.784405	+	0.452876i
$619$			19.0526i			0.765787i	0.923792	+	0.382893i	$0.125072\pi$
$619$			19.0526i			0.765787i	−0.923792	+	0.382893i	$0.874928\pi$
$620$		0			0
$621$	−3.00000	+	5.19615i	−0.120386	+	0.208514i
$622$	18.0000	+	10.3923i	0.721734	+	0.416693i
$623$	−6.00000			−0.240385
$624$	17.5000	−	4.33013i	0.700561	−	0.173344i
$625$		0			0
$626$	−37.5000	−	21.6506i	−1.49880	−	0.865333i
$627$	−3.00000	+	5.19615i	−0.119808	+	0.207514i
$628$	−11.5000	−	19.9186i	−0.458900	−	0.794838i
$629$			41.5692i			1.65747i
$630$		0			0
$631$	31.5000	−	18.1865i	1.25400	−	0.723994i	0.282095	−	0.959387i	$-0.408971\pi$
$631$	31.5000	−	18.1865i	1.25400	−	0.723994i	0.971900	+	0.235392i	$0.0756374\pi$
$632$			19.0526i			0.757870i
$633$	−8.00000	−	13.8564i	−0.317971	−	0.550743i
$634$	−6.00000	+	10.3923i	−0.238290	+	0.412731i
$635$		0			0
$636$	12.0000			0.475831
$637$	10.0000	+	10.3923i	0.396214	+	0.411758i
$638$	36.0000			1.42525
$639$	−3.00000	−	1.73205i	−0.118678	−	0.0685189i
$640$		0			0
$641$	−21.0000	−	36.3731i	−0.829450	−	1.43665i	−0.898470	−	0.439034i	$-0.855321\pi$
$641$	−21.0000	−	36.3731i	−0.829450	−	1.43665i	0.0690201	−	0.997615i	$-0.478013\pi$
$642$		0			0
$643$	19.5000	−	11.2583i	0.769005	−	0.443985i	−0.0635146	−	0.997981i	$-0.520231\pi$
$643$	19.5000	−	11.2583i	0.769005	−	0.443985i	0.832520	+	0.553996i	$0.186898\pi$
$644$	−9.00000	+	5.19615i	−0.354650	+	0.204757i
$645$		0			0
$646$	9.00000	+	15.5885i	0.354100	+	0.613320i
$647$	6.00000	−	10.3923i	0.235884	−	0.408564i	−0.723645	−	0.690172i	$-0.757535\pi$
$647$	6.00000	−	10.3923i	0.235884	−	0.408564i	0.959529	+	0.281609i	$0.0908680\pi$
$648$	1.50000	+	0.866025i	0.0589256	+	0.0340207i
$649$	36.0000			1.41312
$650$		0			0
$651$	6.00000			0.235159
$652$	−21.0000	−	12.1244i	−0.822423	−	0.474826i
$653$	−6.00000	+	10.3923i	−0.234798	+	0.406682i	−0.959214	−	0.282681i	$-0.908776\pi$
$653$	−6.00000	+	10.3923i	−0.234798	+	0.406682i	0.724416	+	0.689363i	$0.242110\pi$
$654$	12.0000	+	20.7846i	0.469237	+	0.812743i
$655$		0			0
$656$	−15.0000	+	8.66025i	−0.585652	+	0.338126i
$657$	−7.50000	+	4.33013i	−0.292603	+	0.168934i
$658$			20.7846i			0.810268i
$659$	9.00000	+	15.5885i	0.350590	+	0.607240i	0.986353	−	0.164644i	$-0.0526477\pi$
$659$	9.00000	+	15.5885i	0.350590	+	0.607240i	−0.635763	+	0.771885i	$0.719314\pi$
$660$		0			0
$661$	37.5000	+	21.6506i	1.45858	+	0.842112i	0.998942	−	0.0459936i	$-0.0146454\pi$
$661$	37.5000	+	21.6506i	1.45858	+	0.842112i	0.459639	+	0.888106i	$0.347979\pi$
$662$	9.00000			0.349795
$663$	−6.00000	+	20.7846i	−0.233021	+	0.807207i
$664$	6.00000			0.232845
$665$		0			0
$666$	6.00000	−	10.3923i	0.232495	−	0.402694i
$667$	18.0000	+	31.1769i	0.696963	+	1.20717i
$668$		−	3.46410i		−	0.134030i
$669$	−7.50000	+	4.33013i	−0.289967	+	0.167412i
$670$		0			0
$671$			6.92820i			0.267460i
$672$	4.50000	+	7.79423i	0.173591	+	0.300669i
$673$	23.5000	−	40.7032i	0.905858	−	1.56899i	0.0860977	−	0.996287i	$-0.472560\pi$
$673$	23.5000	−	40.7032i	0.905858	−	1.56899i	0.819761	−	0.572706i	$-0.194106\pi$
$674$	−28.5000	−	16.4545i	−1.09778	−	0.633803i
$675$		0			0
$676$	0.500000	−	12.9904i	0.0192308	−	0.499630i
$677$	24.0000			0.922395			0.461197	−	0.887298i	$-0.347420\pi$
$677$	24.0000			0.922395			0.461197	+	0.887298i	$0.347420\pi$
$678$	−18.0000	−	10.3923i	−0.691286	−	0.399114i
$679$	−6.00000	+	10.3923i	−0.230259	+	0.398820i
$680$		0			0
$681$			27.7128i			1.06196i
$682$	18.0000	−	10.3923i	0.689256	−	0.397942i
$683$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$683$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$684$		−	1.73205i		−	0.0662266i
$685$		0			0
$686$	−16.5000	+	28.5788i	−0.629973	+	1.09115i
$687$	−1.50000	−	0.866025i	−0.0572286	−	0.0330409i
$688$	25.0000			0.953116
$689$	−12.0000	+	41.5692i	−0.457164	+	1.58366i
$690$		0			0
$691$	−4.50000	−	2.59808i	−0.171188	−	0.0988355i	0.411958	−	0.911203i	$-0.364845\pi$
$691$	−4.50000	−	2.59808i	−0.171188	−	0.0988355i	−0.583146	+	0.812367i	$0.698178\pi$
$692$	−12.0000	+	20.7846i	−0.456172	+	0.790112i
$693$	−3.00000	−	5.19615i	−0.113961	−	0.197386i
$694$		−	41.5692i		−	1.57795i
$695$		0			0
$696$	9.00000	−	5.19615i	0.341144	−	0.196960i
$697$		−	20.7846i		−	0.787273i
$698$	−10.5000	−	18.1865i	−0.397431	−	0.688370i
$699$	12.0000	−	20.7846i	0.453882	−	0.786146i
$700$		0			0
$701$	30.0000			1.13308			0.566542	−	0.824033i	$-0.308281\pi$
$701$	30.0000			1.13308			0.566542	+	0.824033i	$0.308281\pi$
$702$	4.50000	−	4.33013i	0.169842	−	0.163430i
$703$	12.0000			0.452589
$704$	−3.00000	−	1.73205i	−0.113067	−	0.0652791i
$705$		0			0
$706$	21.0000	+	36.3731i	0.790345	+	1.36892i
$707$		−	10.3923i		−	0.390843i
$708$	−9.00000	+	5.19615i	−0.338241	+	0.195283i
$709$	−31.5000	+	18.1865i	−1.18301	+	0.683010i	−0.956708	−	0.291048i	$-0.905996\pi$
$709$	−31.5000	+	18.1865i	−1.18301	+	0.683010i	−0.226299	+	0.974058i	$0.572663\pi$
$710$		0			0
$711$	5.50000	+	9.52628i	0.206266	+	0.357263i
$712$	−3.00000	+	5.19615i	−0.112430	+	0.194734i
$713$	18.0000	+	10.3923i	0.674105	+	0.389195i
$714$	−18.0000			−0.673633
$715$		0			0
$716$	−12.0000			−0.448461
$717$	9.00000	+	5.19615i	0.336111	+	0.194054i
$718$	−24.0000	+	41.5692i	−0.895672	+	1.55135i
$719$	3.00000	+	5.19615i	0.111881	+	0.193784i	0.916529	−	0.399969i	$-0.130979\pi$
$719$	3.00000	+	5.19615i	0.111881	+	0.193784i	−0.804648	+	0.593753i	$0.797646\pi$
$720$		0			0
$721$	19.5000	−	11.2583i	0.726218	−	0.419282i
$722$	−24.0000	+	13.8564i	−0.893188	+	0.515682i
$723$		−	19.0526i		−	0.708572i
$724$	8.50000	+	14.7224i	0.315900	+	0.547155i
$725$		0			0
$726$	−1.50000	−	0.866025i	−0.0556702	−	0.0321412i
$727$	17.0000			0.630495			0.315248	−	0.949009i	$-0.397912\pi$
$727$	17.0000			0.630495			0.315248	+	0.949009i	$0.397912\pi$
$728$	−10.5000	+	2.59808i	−0.389156	+	0.0962911i
$729$	1.00000			0.0370370
$730$		0			0
$731$	−15.0000	+	25.9808i	−0.554795	+	0.960933i
$732$	−1.00000	−	1.73205i	−0.0369611	−	0.0640184i
$733$		−	46.7654i		−	1.72732i	−0.504076	−	0.863659i	$-0.668167\pi$
$733$		−	46.7654i		−	1.72732i	0.504076	−	0.863659i	$-0.331833\pi$
$734$	52.5000	−	30.3109i	1.93781	−	1.11880i
$735$		0			0
$736$			31.1769i			1.14920i
$737$	−15.0000	−	25.9808i	−0.552532	−	0.957014i
$738$	−3.00000	+	5.19615i	−0.110432	+	0.191273i
$739$	−21.0000	−	12.1244i	−0.772497	−	0.446002i	0.0612673	−	0.998121i	$-0.480486\pi$
$739$	−21.0000	−	12.1244i	−0.772497	−	0.446002i	−0.833765	+	0.552120i	$0.813819\pi$
$740$		0			0
$741$	6.00000	+	1.73205i	0.220416	+	0.0636285i
$742$	−36.0000			−1.32160
$743$	3.00000	+	1.73205i	0.110059	+	0.0635428i	0.554019	−	0.832504i	$-0.313093\pi$
$743$	3.00000	+	1.73205i	0.110059	+	0.0635428i	−0.443960	+	0.896047i	$0.646427\pi$
$744$	3.00000	−	5.19615i	0.109985	−	0.190500i
$745$		0			0
$746$			64.0859i			2.34635i
$747$	3.00000	−	1.73205i	0.109764	−	0.0633724i
$748$	−18.0000	+	10.3923i	−0.658145	+	0.379980i
$749$		0			0
$750$		0			0
$751$	20.0000	−	34.6410i	0.729810	−	1.26407i	−0.227153	−	0.973859i	$-0.572942\pi$
$751$	20.0000	−	34.6410i	0.729810	−	1.26407i	0.956963	−	0.290209i	$-0.0937250\pi$
$752$	30.0000	+	17.3205i	1.09399	+	0.631614i
$753$	−24.0000			−0.874609
$754$	−9.00000	−	36.3731i	−0.327761	−	1.32463i
$755$		0			0
$756$	1.50000	+	0.866025i	0.0545545	+	0.0314970i
$757$	21.5000	−	37.2391i	0.781431	−	1.35348i	−0.149677	−	0.988735i	$-0.547824\pi$
$757$	21.5000	−	37.2391i	0.781431	−	1.35348i	0.931108	−	0.364743i	$-0.118843\pi$
$758$	22.5000	+	38.9711i	0.817237	+	1.41550i
$759$		−	20.7846i		−	0.754434i
$760$		0			0
$761$	39.0000	−	22.5167i	1.41375	−	0.816228i	0.418010	−	0.908443i	$-0.362728\pi$
$761$	39.0000	−	22.5167i	1.41375	−	0.816228i	0.995739	+	0.0922143i	$0.0293945\pi$
$762$			1.73205i			0.0627456i
$763$	−12.0000	−	20.7846i	−0.434429	−	0.752453i
$764$	−3.00000	+	5.19615i	−0.108536	+	0.187990i
$765$		0			0
$766$	48.0000			1.73431
$767$	−9.00000	−	36.3731i	−0.324971	−	1.31336i
$768$	19.0000			0.685603
$769$	13.5000	+	7.79423i	0.486822	+	0.281067i	0.723255	−	0.690581i	$-0.242645\pi$
$769$	13.5000	+	7.79423i	0.486822	+	0.281067i	−0.236433	+	0.971648i	$0.575978\pi$
$770$		0			0
$771$	−6.00000	−	10.3923i	−0.216085	−	0.374270i
$772$		−	22.5167i		−	0.810392i
$773$	−24.0000	+	13.8564i	−0.863220	+	0.498380i	−0.865089	−	0.501618i	$-0.832738\pi$
$773$	−24.0000	+	13.8564i	−0.863220	+	0.498380i	0.00186926	+	0.999998i	$0.499405\pi$
$774$	7.50000	−	4.33013i	0.269582	−	0.155643i
$775$		0			0
$776$	6.00000	+	10.3923i	0.215387	+	0.373062i
$777$	−6.00000	+	10.3923i	−0.215249	+	0.372822i
$778$	−18.0000	−	10.3923i	−0.645331	−	0.372582i
$779$	−6.00000			−0.214972
$780$		0			0
$781$	12.0000			0.429394
$782$	−54.0000	−	31.1769i	−1.93104	−	1.11488i
$783$	3.00000	−	5.19615i	0.107211	−	0.185695i
$784$	10.0000	+	17.3205i	0.357143	+	0.618590i
$785$		0			0
$786$	18.0000	−	10.3923i	0.642039	−	0.370681i
$787$	45.0000	−	25.9808i	1.60408	−	0.926114i	0.613417	−	0.789759i	$-0.289795\pi$
$787$	45.0000	−	25.9808i	1.60408	−	0.926114i	0.990660	−	0.136355i	$-0.0435387\pi$
$788$		−	20.7846i		−	0.740421i
$789$	−3.00000	−	5.19615i	−0.106803	−	0.184988i
$790$		0			0
$791$	18.0000	+	10.3923i	0.640006	+	0.369508i
$792$	−6.00000			−0.213201
$793$	7.00000	−	1.73205i	0.248577	−	0.0615069i
$794$	−45.0000			−1.59699
$795$		0			0
$796$	12.5000	−	21.6506i	0.443051	−	0.767386i
$797$	−15.0000	−	25.9808i	−0.531327	−	0.920286i	−0.999331	−	0.0365596i	$-0.988360\pi$
$797$	−15.0000	−	25.9808i	−0.531327	−	0.920286i	0.468004	−	0.883726i	$-0.344973\pi$
$798$			5.19615i			0.183942i
$799$	−36.0000	+	20.7846i	−1.27359	+	0.735307i
$800$		0			0
$801$			3.46410i			0.122398i
$802$	−6.00000	−	10.3923i	−0.211867	−	0.366965i
$803$	15.0000	−	25.9808i	0.529339	−	0.916841i
$804$	7.50000	+	4.33013i	0.264505	+	0.152712i
$805$		0			0
$806$	−15.0000	−	15.5885i	−0.528352	−	0.549080i
$807$		0			0
$808$	−9.00000	−	5.19615i	−0.316619	−	0.182800i
$809$	12.0000	−	20.7846i	0.421898	−	0.730748i	−0.574228	−	0.818696i	$-0.694698\pi$
$809$	12.0000	−	20.7846i	0.421898	−	0.730748i	0.996125	+	0.0879478i	$0.0280309\pi$
$810$		0			0
$811$		−	5.19615i		−	0.182462i	−0.995830	−	0.0912308i	$-0.970920\pi$
$811$		−	5.19615i		−	0.182462i	0.995830	−	0.0912308i	$-0.0290801\pi$
$812$	9.00000	−	5.19615i	0.315838	−	0.182349i
$813$	−7.50000	+	4.33013i	−0.263036	+	0.151864i
$814$			41.5692i			1.45700i
$815$		0			0
$816$	−15.0000	+	25.9808i	−0.525105	+	0.909509i
$817$	7.50000	+	4.33013i	0.262392	+	0.151492i
$818$	−60.0000			−2.09785
$819$	−4.50000	+	4.33013i	−0.157243	+	0.151307i
$820$		0			0
$821$	6.00000	+	3.46410i	0.209401	+	0.120898i	0.601033	−	0.799224i	$-0.294756\pi$
$821$	6.00000	+	3.46410i	0.209401	+	0.120898i	−0.391632	+	0.920122i	$0.628089\pi$
$822$	−9.00000	+	15.5885i	−0.313911	+	0.543710i
$823$	−18.5000	−	32.0429i	−0.644869	−	1.11695i	−0.984332	−	0.176327i	$-0.943578\pi$
$823$	−18.5000	−	32.0429i	−0.644869	−	1.11695i	0.339462	−	0.940620i	$-0.389755\pi$
$824$		−	22.5167i		−	0.784405i
$825$		0			0
$826$	27.0000	−	15.5885i	0.939450	−	0.542392i
$827$			48.4974i			1.68642i	0.537584	+	0.843210i	$0.319337\pi$
$827$			48.4974i			1.68642i	−0.537584	+	0.843210i	$0.680663\pi$
$828$	3.00000	+	5.19615i	0.104257	+	0.180579i
$829$	20.5000	−	35.5070i	0.711994	−	1.23321i	−0.252113	−	0.967698i	$-0.581125\pi$
$829$	20.5000	−	35.5070i	0.711994	−	1.23321i	0.964107	−	0.265513i	$-0.0855412\pi$
$830$		0			0
$831$	−17.0000			−0.589723
$832$	−1.00000	+	3.46410i	−0.0346688	+	0.120096i
$833$	−24.0000			−0.831551
$834$	7.50000	+	4.33013i	0.259704	+	0.149940i
$835$		0			0
$836$	3.00000	+	5.19615i	0.103757	+	0.179713i
$837$		−	3.46410i		−	0.119737i
$838$	18.0000	−	10.3923i	0.621800	−	0.358996i
$839$	12.0000	−	6.92820i	0.414286	−	0.239188i	−0.278344	−	0.960482i	$-0.589785\pi$
$839$	12.0000	−	6.92820i	0.414286	−	0.239188i	0.692630	+	0.721293i	$0.256452\pi$
$840$		0			0
$841$	−3.50000	−	6.06218i	−0.120690	−	0.209041i
$842$	4.50000	−	7.79423i	0.155080	−	0.268607i
$843$	3.00000	+	1.73205i	0.103325	+	0.0596550i
$844$	−16.0000			−0.550743
$845$		0			0
$846$	12.0000			0.412568
$847$	1.50000	+	0.866025i	0.0515406	+	0.0297570i
$848$	−30.0000	+	51.9615i	−1.03020	+	1.78437i
$849$	2.00000	+	3.46410i	0.0686398	+	0.118888i
$850$		0			0
$851$	−36.0000	+	20.7846i	−1.23406	+	0.712487i
$852$	−3.00000	+	1.73205i	−0.102778	+	0.0593391i
$853$		0			0		1.00000			$0$
$853$		0			0		−1.00000			$\pi$
$854$	3.00000	+	5.19615i	0.102658	+	0.177809i
$855$		0			0
$856$		0			0
$857$	−42.0000			−1.43469			−0.717346	−	0.696717i	$-0.754643\pi$
$857$	−42.0000			−1.43469			−0.717346	+	0.696717i	$0.754643\pi$
$858$	−6.00000	+	20.7846i	−0.204837	+	0.709575i
$859$	1.00000			0.0341196			0.0170598	−	0.999854i	$-0.494569\pi$
$859$	1.00000			0.0341196			0.0170598	+	0.999854i	$0.494569\pi$
$860$		0			0
$861$	3.00000	−	5.19615i	0.102240	−	0.177084i
$862$	−24.0000	−	41.5692i	−0.817443	−	1.41585i
$863$		−	20.7846i		−	0.707516i	−0.935337	−	0.353758i	$-0.884904\pi$
$863$		−	20.7846i		−	0.707516i	0.935337	−	0.353758i	$-0.115096\pi$
$864$	4.50000	−	2.59808i	0.153093	−	0.0883883i
$865$		0			0
$866$		−	3.46410i		−	0.117715i
$867$	−9.50000	−	16.4545i	−0.322637	−	0.558824i
$868$	3.00000	−	5.19615i	0.101827	−	0.176369i
$869$	−33.0000	−	19.0526i	−1.11945	−	0.646314i
$870$		0			0
$871$	−22.5000	+	21.6506i	−0.762383	+	0.733604i
$872$	−24.0000			−0.812743
$873$	6.00000	+	3.46410i	0.203069	+	0.117242i
$874$	−9.00000	+	15.5885i	−0.304430	+	0.527287i
$875$		0			0
$876$			8.66025i			0.292603i
$877$	13.5000	−	7.79423i	0.455863	−	0.263192i	−0.254440	−	0.967088i	$-0.581891\pi$
$877$	13.5000	−	7.79423i	0.455863	−	0.263192i	0.710303	+	0.703896i	$0.248558\pi$
$878$	46.5000	−	26.8468i	1.56930	−	0.906035i
$879$		−	6.92820i		−	0.233682i
$880$		0			0
$881$	6.00000	−	10.3923i	0.202145	−	0.350126i	−0.747074	−	0.664741i	$-0.768542\pi$
$881$	6.00000	−	10.3923i	0.202145	−	0.350126i	0.949219	+	0.314615i	$0.101875\pi$
$882$	6.00000	+	3.46410i	0.202031	+	0.116642i
$883$	−16.0000			−0.538443			−0.269221	−	0.963078i	$-0.586766\pi$
$883$	−16.0000			−0.538443			−0.269221	+	0.963078i	$0.586766\pi$
$884$	15.0000	+	15.5885i	0.504505	+	0.524297i
$885$		0			0
$886$	27.0000	+	15.5885i	0.907083	+	0.523704i
$887$	−12.0000	+	20.7846i	−0.402921	+	0.697879i	−0.994077	−	0.108678i	$-0.965338\pi$
$887$	−12.0000	+	20.7846i	−0.402921	+	0.697879i	0.591156	+	0.806557i	$0.298672\pi$
$888$	6.00000	+	10.3923i	0.201347	+	0.348743i
$889$		−	1.73205i		−	0.0580911i
$890$		0			0
$891$	−3.00000	+	1.73205i	−0.100504	+	0.0580259i
$892$			8.66025i			0.289967i
$893$	6.00000	+	10.3923i	0.200782	+	0.347765i
$894$	−3.00000	+	5.19615i	−0.100335	+	0.173785i
$895$		0			0
$896$	−21.0000			−0.701561
$897$	−21.0000	+	5.19615i	−0.701170	+	0.173494i
$898$	48.0000			1.60178
$899$	−18.0000	−	10.3923i	−0.600334	−	0.346603i
$900$		0			0
$901$	−36.0000	−	62.3538i	−1.19933	−	2.07731i
$902$		−	20.7846i		−	0.692052i
$903$	−7.50000	+	4.33013i	−0.249584	+	0.144098i
$904$	18.0000	−	10.3923i	0.598671	−	0.345643i
$905$		0			0
$906$	−7.50000	−	12.9904i	−0.249171	−	0.431577i
$907$	−4.00000	+	6.92820i	−0.132818	+	0.230047i	−0.924762	−	0.380547i	$-0.875736\pi$
$907$	−4.00000	+	6.92820i	−0.132818	+	0.230047i	0.791944	+	0.610594i	$0.209069\pi$
$908$	24.0000	+	13.8564i	0.796468	+	0.459841i
$909$	−6.00000			−0.199007
$910$		0			0
$911$	−30.0000			−0.993944			−0.496972	−	0.867766i	$-0.665555\pi$
$911$	−30.0000			−0.993944			−0.496972	+	0.867766i	$0.665555\pi$
$912$	7.50000	+	4.33013i	0.248350	+	0.143385i
$913$	−6.00000	+	10.3923i	−0.198571	+	0.343935i
$914$	1.50000	+	2.59808i	0.0496156	+	0.0859367i
$915$		0			0
$916$	−1.50000	+	0.866025i	−0.0495614	+	0.0286143i
$917$	−18.0000	+	10.3923i	−0.594412	+	0.343184i
$918$			10.3923i			0.342997i
$919$	−21.5000	−	37.2391i	−0.709220	−	1.22840i	−0.965147	−	0.261708i	$-0.915714\pi$
$919$	−21.5000	−	37.2391i	−0.709220	−	1.22840i	0.255927	−	0.966696i	$-0.417619\pi$
$920$		0			0
$921$	9.00000	+	5.19615i	0.296560	+	0.171219i
$922$	−42.0000			−1.38320
$923$	−3.00000	−	12.1244i	−0.0987462	−	0.399078i
$924$	−6.00000			−0.197386
$925$		0			0
$926$	−13.5000	+	23.3827i	−0.443638	+	0.768403i
$927$	−6.50000	−	11.2583i	−0.213488	−	0.369772i
$928$		−	31.1769i		−	1.02343i
$929$	27.0000	−	15.5885i	0.885841	−	0.511441i	0.0132613	−	0.999912i	$-0.495779\pi$
$929$	27.0000	−	15.5885i	0.885841	−	0.511441i	0.872580	+	0.488471i	$0.162445\pi$
$930$		0			0
$931$			6.92820i			0.227063i
$932$	−12.0000	−	20.7846i	−0.393073	−	0.680823i
$933$	−6.00000	+	10.3923i	−0.196431	+	0.340229i
$934$	−27.0000	−	15.5885i	−0.883467	−	0.510070i
$935$		0			0
$936$	1.50000	+	6.06218i	0.0490290	+	0.198148i
$937$	−13.0000			−0.424691			−0.212346	−	0.977195i	$-0.568110\pi$
$937$	−13.0000			−0.424691			−0.212346	+	0.977195i	$0.568110\pi$
$938$	−22.5000	−	12.9904i	−0.734651	−	0.424151i
$939$	12.5000	−	21.6506i	0.407922	−	0.706542i
$940$		0			0
$941$		0			0		1.00000			$0$
$941$		0			0		−1.00000			$\pi$
$942$	34.5000	−	19.9186i	1.12407	−	0.648983i
$943$	18.0000	−	10.3923i	0.586161	−	0.338420i
$944$		−	51.9615i		−	1.69120i
$945$		0			0
$946$	−15.0000	+	25.9808i	−0.487692	+	0.844707i
$947$	27.0000	+	15.5885i	0.877382	+	0.506557i	0.869794	−	0.493414i	$-0.164251\pi$
$947$	27.0000	+	15.5885i	0.877382	+	0.506557i	0.00758776	+	0.999971i	$0.497585\pi$
$948$	11.0000			0.357263
$949$	−30.0000	−	8.66025i	−0.973841	−	0.281124i
$950$		0			0
$951$	−6.00000	−	3.46410i	−0.194563	−	0.112331i
$952$	9.00000	−	15.5885i	0.291692	−	0.505225i
$953$	−27.0000	−	46.7654i	−0.874616	−	1.51488i	−0.857171	−	0.515031i	$-0.827780\pi$
$953$	−27.0000	−	46.7654i	−0.874616	−	1.51488i	−0.0174443	−	0.999848i	$-0.505553\pi$
$954$			20.7846i			0.672927i
$955$		0			0
$956$	9.00000	−	5.19615i	0.291081	−	0.168056i
$957$			20.7846i			0.671871i
$958$	18.0000	+	31.1769i	0.581554	+	1.00728i
$959$	9.00000	−	15.5885i	0.290625	−	0.503378i
$960$		0			0
$961$	19.0000			0.612903
$962$	42.0000	−	10.3923i	1.35413	−	0.335061i
$963$		0			0
$964$	−16.5000	−	9.52628i	−0.531429	−	0.306821i
$965$		0			0
$966$	−9.00000	−	15.5885i	−0.289570	−	0.501550i
$967$		−	10.3923i		−	0.334194i	−0.985940	−	0.167097i	$-0.946561\pi$
$967$		−	10.3923i		−	0.334194i	0.985940	−	0.167097i	$-0.0534393\pi$
$968$	1.50000	−	0.866025i	0.0482118	−	0.0278351i
$969$	−9.00000	+	5.19615i	−0.289122	+	0.166924i
$970$		0			0
$971$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$971$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$972$	0.500000	−	0.866025i	0.0160375	−	0.0277778i
$973$	−7.50000	−	4.33013i	−0.240439	−	0.138817i
$974$	45.0000			1.44189
$975$		0			0
$976$	10.0000			0.320092
$977$	6.00000	+	3.46410i	0.191957	+	0.110826i	0.592898	−	0.805277i	$-0.297984\pi$
$977$	6.00000	+	3.46410i	0.191957	+	0.110826i	−0.400941	+	0.916104i	$0.631317\pi$
$978$	21.0000	−	36.3731i	0.671506	−	1.16308i
$979$	−6.00000	−	10.3923i	−0.191761	−	0.332140i
$980$		0			0
$981$	−12.0000	+	6.92820i	−0.383131	+	0.221201i
$982$	−45.0000	+	25.9808i	−1.43601	+	0.829079i
$983$		−	31.1769i		−	0.994389i	−0.867639	−	0.497195i	$-0.834364\pi$
$983$		−	31.1769i		−	0.994389i	0.867639	−	0.497195i	$-0.165636\pi$
$984$	−3.00000	−	5.19615i	−0.0956365	−	0.165647i
$985$		0			0
$986$	54.0000	+	31.1769i	1.71971	+	0.992875i
$987$	−12.0000			−0.381964
$988$	4.50000	−	4.33013i	0.143164	−	0.137760i
$989$	−30.0000			−0.953945
$990$		0			0
$991$	−23.5000	+	40.7032i	−0.746502	+	1.29298i	0.202988	+	0.979181i	$0.434935\pi$
$991$	−23.5000	+	40.7032i	−0.746502	+	1.29298i	−0.949490	+	0.313798i	$0.898398\pi$
$992$	−9.00000	−	15.5885i	−0.285750	−	0.494934i
$993$			5.19615i			0.164895i
$994$	9.00000	−	5.19615i	0.285463	−	0.164812i
$995$		0			0
$996$		−	3.46410i		−	0.109764i
$997$	−0.500000	−	0.866025i	−0.0158352	−	0.0274273i	0.857999	−	0.513651i	$-0.171707\pi$
$997$	−0.500000	−	0.866025i	−0.0158352	−	0.0274273i	−0.873834	+	0.486224i	$0.838374\pi$
$998$	−28.5000	+	49.3634i	−0.902152	+	1.56257i
$999$	6.00000	+	3.46410i	0.189832	+	0.109599i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	975.2.bc.f.901.1	yes	2
5.2	odd	4		975.2.w.b.199.1		4
5.3	odd	4		975.2.w.b.199.2		4
5.4	even	2		975.2.bc.b.901.1	yes	2
13.10	even	6	inner	975.2.bc.f.751.1	yes	2
65.23	odd	12		975.2.w.b.49.1		4
65.49	even	6		975.2.bc.b.751.1	✓	2
65.62	odd	12		975.2.w.b.49.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
975.2.w.b.49.1		4	65.23	odd	12
975.2.w.b.49.2		4	65.62	odd	12
975.2.w.b.199.1		4	5.2	odd	4
975.2.w.b.199.2		4	5.3	odd	4
975.2.bc.b.751.1	✓	2	65.49	even	6
975.2.bc.b.901.1	yes	2	5.4	even	2
975.2.bc.f.751.1	yes	2	13.10	even	6	inner
975.2.bc.f.901.1	yes	2	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 975 = 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	975.bc (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.50000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-1.50000 + 0.866025i) q^{6} +(1.50000 - 0.866025i) q^{7} -1.73205i q^{8} +(-0.500000 - 0.866025i) q^{9} +(3.00000 + 1.73205i) q^{11} -1.00000 q^{12} +(1.00000 - 3.46410i) q^{13} +3.00000 q^{14} +(2.50000 - 4.33013i) q^{16} +(3.00000 + 5.19615i) q^{17} -1.73205i q^{18} +(1.50000 - 0.866025i) q^{19} +1.73205i q^{21} +(3.00000 + 5.19615i) q^{22} +(-3.00000 + 5.19615i) q^{23} +(1.50000 + 0.866025i) q^{24} +(4.50000 - 4.33013i) q^{26} +1.00000 q^{27} +(1.50000 + 0.866025i) q^{28} +(3.00000 - 5.19615i) q^{29} -3.46410i q^{31} +(4.50000 - 2.59808i) q^{32} +(-3.00000 + 1.73205i) q^{33} +10.3923i q^{34} +(0.500000 - 0.866025i) q^{36} +(6.00000 + 3.46410i) q^{37} +3.00000 q^{38} +(2.50000 + 2.59808i) q^{39} +(-3.00000 - 1.73205i) q^{41} +(-1.50000 + 2.59808i) q^{42} +(2.50000 + 4.33013i) q^{43} +3.46410i q^{44} +(-9.00000 + 5.19615i) q^{46} +6.92820i q^{47} +(2.50000 + 4.33013i) q^{48} +(-2.00000 + 3.46410i) q^{49} -6.00000 q^{51} +(3.50000 - 0.866025i) q^{52} -12.0000 q^{53} +(1.50000 + 0.866025i) q^{54} +(-1.50000 - 2.59808i) q^{56} +1.73205i q^{57} +(9.00000 - 5.19615i) q^{58} +(9.00000 - 5.19615i) q^{59} +(1.00000 + 1.73205i) q^{61} +(3.00000 - 5.19615i) q^{62} +(-1.50000 - 0.866025i) q^{63} -1.00000 q^{64} -6.00000 q^{66} +(-7.50000 - 4.33013i) q^{67} +(-3.00000 + 5.19615i) q^{68} +(-3.00000 - 5.19615i) q^{69} +(3.00000 - 1.73205i) q^{71} +(-1.50000 + 0.866025i) q^{72} -8.66025i q^{73} +(6.00000 + 10.3923i) q^{74} +(1.50000 + 0.866025i) q^{76} +6.00000 q^{77} +(1.50000 + 6.06218i) q^{78} -11.0000 q^{79} +(-0.500000 + 0.866025i) q^{81} +(-3.00000 - 5.19615i) q^{82} +3.46410i q^{83} +(-1.50000 + 0.866025i) q^{84} +8.66025i q^{86} +(3.00000 + 5.19615i) q^{87} +(3.00000 - 5.19615i) q^{88} +(-3.00000 - 1.73205i) q^{89} +(-1.50000 - 6.06218i) q^{91} -6.00000 q^{92} +(3.00000 + 1.73205i) q^{93} +(-6.00000 + 10.3923i) q^{94} +5.19615i q^{96} +(-6.00000 + 3.46410i) q^{97} +(-6.00000 + 3.46410i) q^{98} -3.46410i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 3 q^{2} - q^{3} + q^{4} - 3 q^{6} + 3 q^{7} - q^{9} + 6 q^{11} - 2 q^{12} + 2 q^{13} + 6 q^{14} + 5 q^{16} + 6 q^{17} + 3 q^{19} + 6 q^{22} - 6 q^{23} + 3 q^{24} + 9 q^{26} + 2 q^{27} + 3 q^{28}+ \cdots - 12 q^{98}+O(q^{100}) \) 2 * q + 3 * q^2 - q^3 + q^4 - 3 * q^6 + 3 * q^7 - q^9 + 6 * q^11 - 2 * q^12 + 2 * q^13 + 6 * q^14 + 5 * q^16 + 6 * q^17 + 3 * q^19 + 6 * q^22 - 6 * q^23 + 3 * q^24 + 9 * q^26 + 2 * q^27 + 3 * q^28 + 6 * q^29 + 9 * q^32 - 6 * q^33 + q^36 + 12 * q^37 + 6 * q^38 + 5 * q^39 - 6 * q^41 - 3 * q^42 + 5 * q^43 - 18 * q^46 + 5 * q^48 - 4 * q^49 - 12 * q^51 + 7 * q^52 - 24 * q^53 + 3 * q^54 - 3 * q^56 + 18 * q^58 + 18 * q^59 + 2 * q^61 + 6 * q^62 - 3 * q^63 - 2 * q^64 - 12 * q^66 - 15 * q^67 - 6 * q^68 - 6 * q^69 + 6 * q^71 - 3 * q^72 + 12 * q^74 + 3 * q^76 + 12 * q^77 + 3 * q^78 - 22 * q^79 - q^81 - 6 * q^82 - 3 * q^84 + 6 * q^87 + 6 * q^88 - 6 * q^89 - 3 * q^91 - 12 * q^92 + 6 * q^93 - 12 * q^94 - 12 * q^97 - 12 * q^98

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