LMFDB - Embedded newform 966.2.a.p.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(1,966)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(966, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("966.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.a (trivial)

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:	yes
Analytic conductor:	$7.71354883526$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{10})^+$
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:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-0.618034$ of defining polynomial
Character	$\chi$	$=$	966.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +2.00000 q^{5} +1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +2.00000 q^{5} +1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +2.00000 q^{10} +1.00000 q^{12} +4.47214 q^{13} +1.00000 q^{14} +2.00000 q^{15} +1.00000 q^{16} -4.47214 q^{17} +1.00000 q^{18} -6.47214 q^{19} +2.00000 q^{20} +1.00000 q^{21} -1.00000 q^{23} +1.00000 q^{24} -1.00000 q^{25} +4.47214 q^{26} +1.00000 q^{27} +1.00000 q^{28} -2.00000 q^{29} +2.00000 q^{30} +6.47214 q^{31} +1.00000 q^{32} -4.47214 q^{34} +2.00000 q^{35} +1.00000 q^{36} -10.9443 q^{37} -6.47214 q^{38} +4.47214 q^{39} +2.00000 q^{40} -6.00000 q^{41} +1.00000 q^{42} +12.9443 q^{43} +2.00000 q^{45} -1.00000 q^{46} +6.47214 q^{47} +1.00000 q^{48} +1.00000 q^{49} -1.00000 q^{50} -4.47214 q^{51} +4.47214 q^{52} +6.94427 q^{53} +1.00000 q^{54} +1.00000 q^{56} -6.47214 q^{57} -2.00000 q^{58} +4.00000 q^{59} +2.00000 q^{60} -6.00000 q^{61} +6.47214 q^{62} +1.00000 q^{63} +1.00000 q^{64} +8.94427 q^{65} -12.9443 q^{67} -4.47214 q^{68} -1.00000 q^{69} +2.00000 q^{70} -12.9443 q^{71} +1.00000 q^{72} -2.94427 q^{73} -10.9443 q^{74} -1.00000 q^{75} -6.47214 q^{76} +4.47214 q^{78} +12.9443 q^{79} +2.00000 q^{80} +1.00000 q^{81} -6.00000 q^{82} -6.47214 q^{83} +1.00000 q^{84} -8.94427 q^{85} +12.9443 q^{86} -2.00000 q^{87} -17.4164 q^{89} +2.00000 q^{90} +4.47214 q^{91} -1.00000 q^{92} +6.47214 q^{93} +6.47214 q^{94} -12.9443 q^{95} +1.00000 q^{96} +8.47214 q^{97} +1.00000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} + 2 q^{3} + 2 q^{4} + 4 q^{5} + 2 q^{6} + 2 q^{7} + 2 q^{8} + 2 q^{9}+O(q^{10}) $ 2 * q + 2 * q^2 + 2 * q^3 + 2 * q^4 + 4 * q^5 + 2 * q^6 + 2 * q^7 + 2 * q^8 + 2 * q^9	$ 2 q + 2 q^{2} + 2 q^{3} + 2 q^{4} + 4 q^{5} + 2 q^{6} + 2 q^{7} + 2 q^{8} + 2 q^{9} + 4 q^{10} + 2 q^{12} + 2 q^{14} + 4 q^{15} + 2 q^{16} + 2 q^{18} - 4 q^{19} + 4 q^{20} + 2 q^{21} - 2 q^{23} + 2 q^{24} - 2 q^{25} + 2 q^{27} + 2 q^{28} - 4 q^{29} + 4 q^{30} + 4 q^{31} + 2 q^{32} + 4 q^{35} + 2 q^{36} - 4 q^{37} - 4 q^{38} + 4 q^{40} - 12 q^{41} + 2 q^{42} + 8 q^{43} + 4 q^{45} - 2 q^{46} + 4 q^{47} + 2 q^{48} + 2 q^{49} - 2 q^{50} - 4 q^{53} + 2 q^{54} + 2 q^{56} - 4 q^{57} - 4 q^{58} + 8 q^{59} + 4 q^{60} - 12 q^{61} + 4 q^{62} + 2 q^{63} + 2 q^{64} - 8 q^{67} - 2 q^{69} + 4 q^{70} - 8 q^{71} + 2 q^{72} + 12 q^{73} - 4 q^{74} - 2 q^{75} - 4 q^{76} + 8 q^{79} + 4 q^{80} + 2 q^{81} - 12 q^{82} - 4 q^{83} + 2 q^{84} + 8 q^{86} - 4 q^{87} - 8 q^{89} + 4 q^{90} - 2 q^{92} + 4 q^{93} + 4 q^{94} - 8 q^{95} + 2 q^{96} + 8 q^{97} + 2 q^{98}+O(q^{100}) $ 2 * q + 2 * q^2 + 2 * q^3 + 2 * q^4 + 4 * q^5 + 2 * q^6 + 2 * q^7 + 2 * q^8 + 2 * q^9 + 4 * q^10 + 2 * q^12 + 2 * q^14 + 4 * q^15 + 2 * q^16 + 2 * q^18 - 4 * q^19 + 4 * q^20 + 2 * q^21 - 2 * q^23 + 2 * q^24 - 2 * q^25 + 2 * q^27 + 2 * q^28 - 4 * q^29 + 4 * q^30 + 4 * q^31 + 2 * q^32 + 4 * q^35 + 2 * q^36 - 4 * q^37 - 4 * q^38 + 4 * q^40 - 12 * q^41 + 2 * q^42 + 8 * q^43 + 4 * q^45 - 2 * q^46 + 4 * q^47 + 2 * q^48 + 2 * q^49 - 2 * q^50 - 4 * q^53 + 2 * q^54 + 2 * q^56 - 4 * q^57 - 4 * q^58 + 8 * q^59 + 4 * q^60 - 12 * q^61 + 4 * q^62 + 2 * q^63 + 2 * q^64 - 8 * q^67 - 2 * q^69 + 4 * q^70 - 8 * q^71 + 2 * q^72 + 12 * q^73 - 4 * q^74 - 2 * q^75 - 4 * q^76 + 8 * q^79 + 4 * q^80 + 2 * q^81 - 12 * q^82 - 4 * q^83 + 2 * q^84 + 8 * q^86 - 4 * q^87 - 8 * q^89 + 4 * q^90 - 2 * q^92 + 4 * q^93 + 4 * q^94 - 8 * q^95 + 2 * q^96 + 8 * q^97 + 2 * q^98

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	2.00000	0.894427	0.447214	−	0.894427i	$-0.352416\pi$
$5$	2.00000	0.894427	0.447214	+	0.894427i	$0.352416\pi$
$6$	1.00000	0.408248
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	2.00000	0.632456
$11$	0	0		−	1.00000i	$-0.5\pi$
$11$	0	0			1.00000i	$0.5\pi$
$12$	1.00000	0.288675
$13$	4.47214	1.24035	0.620174	−	0.784465i	$-0.287062\pi$
$13$	4.47214	1.24035	0.620174	+	0.784465i	$0.287062\pi$
$14$	1.00000	0.267261
$15$	2.00000	0.516398
$16$	1.00000	0.250000
$17$	−4.47214	−1.08465	−0.542326	−	0.840168i	$-0.682456\pi$
$17$	−4.47214	−1.08465	−0.542326	+	0.840168i	$0.682456\pi$
$18$	1.00000	0.235702
$19$	−6.47214	−1.48481	−0.742405	−	0.669951i	$-0.766315\pi$
$19$	−6.47214	−1.48481	−0.742405	+	0.669951i	$0.766315\pi$
$20$	2.00000	0.447214
$21$	1.00000	0.218218
$22$	0	0
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	1.00000	0.204124
$25$	−1.00000	−0.200000
$26$	4.47214	0.877058
$27$	1.00000	0.192450
$28$	1.00000	0.188982
$29$	−2.00000	−0.371391	−0.185695	−	0.982607i	$-0.559454\pi$
$29$	−2.00000	−0.371391	−0.185695	+	0.982607i	$0.559454\pi$
$30$	2.00000	0.365148
$31$	6.47214	1.16243	0.581215	−	0.813750i	$-0.302578\pi$
$31$	6.47214	1.16243	0.581215	+	0.813750i	$0.302578\pi$
$32$	1.00000	0.176777
$33$	0	0
$34$	−4.47214	−0.766965
$35$	2.00000	0.338062
$36$	1.00000	0.166667
$37$	−10.9443	−1.79923	−0.899614	−	0.436687i	$-0.856152\pi$
$37$	−10.9443	−1.79923	−0.899614	+	0.436687i	$0.856152\pi$
$38$	−6.47214	−1.04992
$39$	4.47214	0.716115
$40$	2.00000	0.316228
$41$	−6.00000	−0.937043	−0.468521	−	0.883452i	$-0.655213\pi$
$41$	−6.00000	−0.937043	−0.468521	+	0.883452i	$0.655213\pi$
$42$	1.00000	0.154303
$43$	12.9443	1.97398	0.986991	−	0.160773i	$-0.0513986\pi$
$43$	12.9443	1.97398	0.986991	+	0.160773i	$0.0513986\pi$
$44$	0	0
$45$	2.00000	0.298142
$46$	−1.00000	−0.147442
$47$	6.47214	0.944058	0.472029	−	0.881583i	$-0.343522\pi$
$47$	6.47214	0.944058	0.472029	+	0.881583i	$0.343522\pi$
$48$	1.00000	0.144338
$49$	1.00000	0.142857
$50$	−1.00000	−0.141421
$51$	−4.47214	−0.626224
$52$	4.47214	0.620174
$53$	6.94427	0.953869	0.476935	−	0.878939i	$-0.341748\pi$
$53$	6.94427	0.953869	0.476935	+	0.878939i	$0.341748\pi$
$54$	1.00000	0.136083
$55$	0	0
$56$	1.00000	0.133631
$57$	−6.47214	−0.857255
$58$	−2.00000	−0.262613
$59$	4.00000	0.520756	0.260378	−	0.965507i	$-0.416153\pi$
$59$	4.00000	0.520756	0.260378	+	0.965507i	$0.416153\pi$
$60$	2.00000	0.258199
$61$	−6.00000	−0.768221	−0.384111	−	0.923287i	$-0.625492\pi$
$61$	−6.00000	−0.768221	−0.384111	+	0.923287i	$0.625492\pi$
$62$	6.47214	0.821962
$63$	1.00000	0.125988
$64$	1.00000	0.125000
$65$	8.94427	1.10940
$66$	0	0
$67$	−12.9443	−1.58139	−0.790697	−	0.612207i	$-0.790282\pi$
$67$	−12.9443	−1.58139	−0.790697	+	0.612207i	$0.790282\pi$
$68$	−4.47214	−0.542326
$69$	−1.00000	−0.120386
$70$	2.00000	0.239046
$71$	−12.9443	−1.53620	−0.768101	−	0.640328i	$-0.778798\pi$
$71$	−12.9443	−1.53620	−0.768101	+	0.640328i	$0.778798\pi$
$72$	1.00000	0.117851
$73$	−2.94427	−0.344601	−0.172300	−	0.985044i	$-0.555120\pi$
$73$	−2.94427	−0.344601	−0.172300	+	0.985044i	$0.555120\pi$
$74$	−10.9443	−1.27225
$75$	−1.00000	−0.115470
$76$	−6.47214	−0.742405
$77$	0	0
$78$	4.47214	0.506370
$79$	12.9443	1.45634	0.728172	−	0.685394i	$-0.240370\pi$
$79$	12.9443	1.45634	0.728172	+	0.685394i	$0.240370\pi$
$80$	2.00000	0.223607
$81$	1.00000	0.111111
$82$	−6.00000	−0.662589
$83$	−6.47214	−0.710409	−0.355205	−	0.934789i	$-0.615589\pi$
$83$	−6.47214	−0.710409	−0.355205	+	0.934789i	$0.615589\pi$
$84$	1.00000	0.109109
$85$	−8.94427	−0.970143
$86$	12.9443	1.39582
$87$	−2.00000	−0.214423
$88$	0	0
$89$	−17.4164	−1.84614	−0.923068	−	0.384637i	$-0.874327\pi$
$89$	−17.4164	−1.84614	−0.923068	+	0.384637i	$0.874327\pi$
$90$	2.00000	0.210819
$91$	4.47214	0.468807
$92$	−1.00000	−0.104257
$93$	6.47214	0.671129
$94$	6.47214	0.667550
$95$	−12.9443	−1.32805
$96$	1.00000	0.102062
$97$	8.47214	0.860215	0.430108	−	0.902778i	$-0.358476\pi$
$97$	8.47214	0.860215	0.430108	+	0.902778i	$0.358476\pi$
$98$	1.00000	0.101015
$99$	0	0
$100$	−1.00000	−0.100000
$101$	17.4164	1.73300	0.866499	−	0.499179i	$-0.166365\pi$
$101$	17.4164	1.73300	0.866499	+	0.499179i	$0.166365\pi$
$102$	−4.47214	−0.442807
$103$	12.9443	1.27544	0.637719	−	0.770270i	$-0.279878\pi$
$103$	12.9443	1.27544	0.637719	+	0.770270i	$0.279878\pi$
$104$	4.47214	0.438529
$105$	2.00000	0.195180
$106$	6.94427	0.674487
$107$	−8.00000	−0.773389	−0.386695	−	0.922208i	$-0.626383\pi$
$107$	−8.00000	−0.773389	−0.386695	+	0.922208i	$0.626383\pi$
$108$	1.00000	0.0962250
$109$	14.9443	1.43140	0.715701	−	0.698407i	$-0.246107\pi$
$109$	14.9443	1.43140	0.715701	+	0.698407i	$0.246107\pi$
$110$	0	0
$111$	−10.9443	−1.03878
$112$	1.00000	0.0944911
$113$	−1.05573	−0.0993145	−0.0496573	−	0.998766i	$-0.515813\pi$
$113$	−1.05573	−0.0993145	−0.0496573	+	0.998766i	$0.515813\pi$
$114$	−6.47214	−0.606171
$115$	−2.00000	−0.186501
$116$	−2.00000	−0.185695
$117$	4.47214	0.413449
$118$	4.00000	0.368230
$119$	−4.47214	−0.409960
$120$	2.00000	0.182574
$121$	−11.0000	−1.00000
$122$	−6.00000	−0.543214
$123$	−6.00000	−0.541002
$124$	6.47214	0.581215
$125$	−12.0000	−1.07331
$126$	1.00000	0.0890871
$127$	3.05573	0.271152	0.135576	−	0.990767i	$-0.456712\pi$
$127$	3.05573	0.271152	0.135576	+	0.990767i	$0.456712\pi$
$128$	1.00000	0.0883883
$129$	12.9443	1.13968
$130$	8.94427	0.784465
$131$	12.0000	1.04844	0.524222	−	0.851581i	$-0.324356\pi$
$131$	12.0000	1.04844	0.524222	+	0.851581i	$0.324356\pi$
$132$	0	0
$133$	−6.47214	−0.561205
$134$	−12.9443	−1.11821
$135$	2.00000	0.172133
$136$	−4.47214	−0.383482
$137$	−14.0000	−1.19610	−0.598050	−	0.801459i	$-0.704058\pi$
$137$	−14.0000	−1.19610	−0.598050	+	0.801459i	$0.704058\pi$
$138$	−1.00000	−0.0851257
$139$	−8.94427	−0.758643	−0.379322	−	0.925265i	$-0.623843\pi$
$139$	−8.94427	−0.758643	−0.379322	+	0.925265i	$0.623843\pi$
$140$	2.00000	0.169031
$141$	6.47214	0.545052
$142$	−12.9443	−1.08626
$143$	0	0
$144$	1.00000	0.0833333
$145$	−4.00000	−0.332182
$146$	−2.94427	−0.243670
$147$	1.00000	0.0824786
$148$	−10.9443	−0.899614
$149$	−18.9443	−1.55198	−0.775988	−	0.630748i	$-0.782748\pi$
$149$	−18.9443	−1.55198	−0.775988	+	0.630748i	$0.782748\pi$
$150$	−1.00000	−0.0816497
$151$	−12.9443	−1.05339	−0.526695	−	0.850054i	$-0.676569\pi$
$151$	−12.9443	−1.05339	−0.526695	+	0.850054i	$0.676569\pi$
$152$	−6.47214	−0.524960
$153$	−4.47214	−0.361551
$154$	0	0
$155$	12.9443	1.03971
$156$	4.47214	0.358057
$157$	14.9443	1.19268	0.596341	−	0.802731i	$-0.296620\pi$
$157$	14.9443	1.19268	0.596341	+	0.802731i	$0.296620\pi$
$158$	12.9443	1.02979
$159$	6.94427	0.550717
$160$	2.00000	0.158114
$161$	−1.00000	−0.0788110
$162$	1.00000	0.0785674
$163$	8.94427	0.700569	0.350285	−	0.936643i	$-0.386085\pi$
$163$	8.94427	0.700569	0.350285	+	0.936643i	$0.386085\pi$
$164$	−6.00000	−0.468521
$165$	0	0
$166$	−6.47214	−0.502335
$167$	11.4164	0.883428	0.441714	−	0.897156i	$-0.354371\pi$
$167$	11.4164	0.883428	0.441714	+	0.897156i	$0.354371\pi$
$168$	1.00000	0.0771517
$169$	7.00000	0.538462
$170$	−8.94427	−0.685994
$171$	−6.47214	−0.494937
$172$	12.9443	0.986991
$173$	−8.47214	−0.644125	−0.322062	−	0.946718i	$-0.604376\pi$
$173$	−8.47214	−0.644125	−0.322062	+	0.946718i	$0.604376\pi$
$174$	−2.00000	−0.151620
$175$	−1.00000	−0.0755929
$176$	0	0
$177$	4.00000	0.300658
$178$	−17.4164	−1.30541
$179$	−20.0000	−1.49487	−0.747435	−	0.664335i	$-0.768715\pi$
$179$	−20.0000	−1.49487	−0.747435	+	0.664335i	$0.768715\pi$
$180$	2.00000	0.149071
$181$	2.00000	0.148659	0.0743294	−	0.997234i	$-0.476318\pi$
$181$	2.00000	0.148659	0.0743294	+	0.997234i	$0.476318\pi$
$182$	4.47214	0.331497
$183$	−6.00000	−0.443533
$184$	−1.00000	−0.0737210
$185$	−21.8885	−1.60928
$186$	6.47214	0.474560
$187$	0	0
$188$	6.47214	0.472029
$189$	1.00000	0.0727393
$190$	−12.9443	−0.939076
$191$	−20.9443	−1.51547	−0.757737	−	0.652560i	$-0.773695\pi$
$191$	−20.9443	−1.51547	−0.757737	+	0.652560i	$0.773695\pi$
$192$	1.00000	0.0721688
$193$	−23.8885	−1.71954	−0.859768	−	0.510686i	$-0.829392\pi$
$193$	−23.8885	−1.71954	−0.859768	+	0.510686i	$0.829392\pi$
$194$	8.47214	0.608264
$195$	8.94427	0.640513
$196$	1.00000	0.0714286
$197$	2.94427	0.209771	0.104885	−	0.994484i	$-0.466552\pi$
$197$	2.94427	0.209771	0.104885	+	0.994484i	$0.466552\pi$
$198$	0	0
$199$	20.9443	1.48470	0.742350	−	0.670012i	$-0.233711\pi$
$199$	20.9443	1.48470	0.742350	+	0.670012i	$0.233711\pi$
$200$	−1.00000	−0.0707107
$201$	−12.9443	−0.913019
$202$	17.4164	1.22541
$203$	−2.00000	−0.140372
$204$	−4.47214	−0.313112
$205$	−12.0000	−0.838116
$206$	12.9443	0.901870
$207$	−1.00000	−0.0695048
$208$	4.47214	0.310087
$209$	0	0
$210$	2.00000	0.138013
$211$	16.9443	1.16649	0.583246	−	0.812296i	$-0.301782\pi$
$211$	16.9443	1.16649	0.583246	+	0.812296i	$0.301782\pi$
$212$	6.94427	0.476935
$213$	−12.9443	−0.886927
$214$	−8.00000	−0.546869
$215$	25.8885	1.76558
$216$	1.00000	0.0680414
$217$	6.47214	0.439357
$218$	14.9443	1.01215
$219$	−2.94427	−0.198955
$220$	0	0
$221$	−20.0000	−1.34535
$222$	−10.9443	−0.734531
$223$	9.52786	0.638033	0.319016	−	0.947749i	$-0.396647\pi$
$223$	9.52786	0.638033	0.319016	+	0.947749i	$0.396647\pi$
$224$	1.00000	0.0668153
$225$	−1.00000	−0.0666667
$226$	−1.05573	−0.0702260
$227$	14.4721	0.960549	0.480275	−	0.877118i	$-0.340537\pi$
$227$	14.4721	0.960549	0.480275	+	0.877118i	$0.340537\pi$
$228$	−6.47214	−0.428628
$229$	−14.0000	−0.925146	−0.462573	−	0.886581i	$-0.653074\pi$
$229$	−14.0000	−0.925146	−0.462573	+	0.886581i	$0.653074\pi$
$230$	−2.00000	−0.131876
$231$	0	0
$232$	−2.00000	−0.131306
$233$	−6.00000	−0.393073	−0.196537	−	0.980497i	$-0.562969\pi$
$233$	−6.00000	−0.393073	−0.196537	+	0.980497i	$0.562969\pi$
$234$	4.47214	0.292353
$235$	12.9443	0.844391
$236$	4.00000	0.260378
$237$	12.9443	0.840821
$238$	−4.47214	−0.289886
$239$	3.05573	0.197659	0.0988293	−	0.995104i	$-0.468490\pi$
$239$	3.05573	0.197659	0.0988293	+	0.995104i	$0.468490\pi$
$240$	2.00000	0.129099
$241$	11.5279	0.742575	0.371288	−	0.928518i	$-0.378916\pi$
$241$	11.5279	0.742575	0.371288	+	0.928518i	$0.378916\pi$
$242$	−11.0000	−0.707107
$243$	1.00000	0.0641500
$244$	−6.00000	−0.384111
$245$	2.00000	0.127775
$246$	−6.00000	−0.382546
$247$	−28.9443	−1.84168
$248$	6.47214	0.410981
$249$	−6.47214	−0.410155
$250$	−12.0000	−0.758947
$251$	−14.4721	−0.913473	−0.456737	−	0.889602i	$-0.650982\pi$
$251$	−14.4721	−0.913473	−0.456737	+	0.889602i	$0.650982\pi$
$252$	1.00000	0.0629941
$253$	0	0
$254$	3.05573	0.191733
$255$	−8.94427	−0.560112
$256$	1.00000	0.0625000
$257$	14.9443	0.932198	0.466099	−	0.884733i	$-0.345659\pi$
$257$	14.9443	0.932198	0.466099	+	0.884733i	$0.345659\pi$
$258$	12.9443	0.805875
$259$	−10.9443	−0.680044
$260$	8.94427	0.554700
$261$	−2.00000	−0.123797
$262$	12.0000	0.741362
$263$	−24.0000	−1.47990	−0.739952	−	0.672660i	$-0.765152\pi$
$263$	−24.0000	−1.47990	−0.739952	+	0.672660i	$0.765152\pi$
$264$	0	0
$265$	13.8885	0.853166
$266$	−6.47214	−0.396832
$267$	−17.4164	−1.06587
$268$	−12.9443	−0.790697
$269$	7.52786	0.458982	0.229491	−	0.973311i	$-0.426294\pi$
$269$	7.52786	0.458982	0.229491	+	0.973311i	$0.426294\pi$
$270$	2.00000	0.121716
$271$	−11.4164	−0.693497	−0.346749	−	0.937958i	$-0.612714\pi$
$271$	−11.4164	−0.693497	−0.346749	+	0.937958i	$0.612714\pi$
$272$	−4.47214	−0.271163
$273$	4.47214	0.270666
$274$	−14.0000	−0.845771
$275$	0	0
$276$	−1.00000	−0.0601929
$277$	23.8885	1.43532	0.717662	−	0.696392i	$-0.245212\pi$
$277$	23.8885	1.43532	0.717662	+	0.696392i	$0.245212\pi$
$278$	−8.94427	−0.536442
$279$	6.47214	0.387477
$280$	2.00000	0.119523
$281$	10.0000	0.596550	0.298275	−	0.954480i	$-0.403589\pi$
$281$	10.0000	0.596550	0.298275	+	0.954480i	$0.403589\pi$
$282$	6.47214	0.385410
$283$	9.52786	0.566373	0.283186	−	0.959065i	$-0.408609\pi$
$283$	9.52786	0.566373	0.283186	+	0.959065i	$0.408609\pi$
$284$	−12.9443	−0.768101
$285$	−12.9443	−0.766752
$286$	0	0
$287$	−6.00000	−0.354169
$288$	1.00000	0.0589256
$289$	3.00000	0.176471
$290$	−4.00000	−0.234888
$291$	8.47214	0.496645
$292$	−2.94427	−0.172300
$293$	−7.88854	−0.460854	−0.230427	−	0.973090i	$-0.574012\pi$
$293$	−7.88854	−0.460854	−0.230427	+	0.973090i	$0.574012\pi$
$294$	1.00000	0.0583212
$295$	8.00000	0.465778
$296$	−10.9443	−0.636123
$297$	0	0
$298$	−18.9443	−1.09741
$299$	−4.47214	−0.258630
$300$	−1.00000	−0.0577350
$301$	12.9443	0.746095
$302$	−12.9443	−0.744859
$303$	17.4164	1.00055
$304$	−6.47214	−0.371202
$305$	−12.0000	−0.687118
$306$	−4.47214	−0.255655
$307$	7.05573	0.402692	0.201346	−	0.979520i	$-0.435468\pi$
$307$	7.05573	0.402692	0.201346	+	0.979520i	$0.435468\pi$
$308$	0	0
$309$	12.9443	0.736374
$310$	12.9443	0.735185
$311$	6.47214	0.367001	0.183501	−	0.983020i	$-0.441257\pi$
$311$	6.47214	0.367001	0.183501	+	0.983020i	$0.441257\pi$
$312$	4.47214	0.253185
$313$	13.4164	0.758340	0.379170	−	0.925327i	$-0.376210\pi$
$313$	13.4164	0.758340	0.379170	+	0.925327i	$0.376210\pi$
$314$	14.9443	0.843354
$315$	2.00000	0.112687
$316$	12.9443	0.728172
$317$	−30.9443	−1.73800	−0.869002	−	0.494809i	$-0.835238\pi$
$317$	−30.9443	−1.73800	−0.869002	+	0.494809i	$0.835238\pi$
$318$	6.94427	0.389415
$319$	0	0
$320$	2.00000	0.111803
$321$	−8.00000	−0.446516
$322$	−1.00000	−0.0557278
$323$	28.9443	1.61050
$324$	1.00000	0.0555556
$325$	−4.47214	−0.248069
$326$	8.94427	0.495377
$327$	14.9443	0.826420
$328$	−6.00000	−0.331295
$329$	6.47214	0.356820
$330$	0	0
$331$	21.8885	1.20310	0.601552	−	0.798834i	$-0.294549\pi$
$331$	21.8885	1.20310	0.601552	+	0.798834i	$0.294549\pi$
$332$	−6.47214	−0.355205
$333$	−10.9443	−0.599742
$334$	11.4164	0.624678
$335$	−25.8885	−1.41444
$336$	1.00000	0.0545545
$337$	14.9443	0.814066	0.407033	−	0.913413i	$-0.366563\pi$
$337$	14.9443	0.814066	0.407033	+	0.913413i	$0.366563\pi$
$338$	7.00000	0.380750
$339$	−1.05573	−0.0573393
$340$	−8.94427	−0.485071
$341$	0	0
$342$	−6.47214	−0.349973
$343$	1.00000	0.0539949
$344$	12.9443	0.697908
$345$	−2.00000	−0.107676
$346$	−8.47214	−0.455465
$347$	16.9443	0.909616	0.454808	−	0.890589i	$-0.349708\pi$
$347$	16.9443	0.909616	0.454808	+	0.890589i	$0.349708\pi$
$348$	−2.00000	−0.107211
$349$	15.5279	0.831188	0.415594	−	0.909550i	$-0.363574\pi$
$349$	15.5279	0.831188	0.415594	+	0.909550i	$0.363574\pi$
$350$	−1.00000	−0.0534522
$351$	4.47214	0.238705
$352$	0	0
$353$	2.00000	0.106449	0.0532246	−	0.998583i	$-0.483050\pi$
$353$	2.00000	0.106449	0.0532246	+	0.998583i	$0.483050\pi$
$354$	4.00000	0.212598
$355$	−25.8885	−1.37402
$356$	−17.4164	−0.923068
$357$	−4.47214	−0.236691
$358$	−20.0000	−1.05703
$359$	22.8328	1.20507	0.602535	−	0.798092i	$-0.294157\pi$
$359$	22.8328	1.20507	0.602535	+	0.798092i	$0.294157\pi$
$360$	2.00000	0.105409
$361$	22.8885	1.20466
$362$	2.00000	0.105118
$363$	−11.0000	−0.577350
$364$	4.47214	0.234404
$365$	−5.88854	−0.308220
$366$	−6.00000	−0.313625
$367$	−22.8328	−1.19186	−0.595932	−	0.803035i	$-0.703217\pi$
$367$	−22.8328	−1.19186	−0.595932	+	0.803035i	$0.703217\pi$
$368$	−1.00000	−0.0521286
$369$	−6.00000	−0.312348
$370$	−21.8885	−1.13793
$371$	6.94427	0.360529
$372$	6.47214	0.335565
$373$	−10.9443	−0.566673	−0.283336	−	0.959021i	$-0.591441\pi$
$373$	−10.9443	−0.566673	−0.283336	+	0.959021i	$0.591441\pi$
$374$	0	0
$375$	−12.0000	−0.619677
$376$	6.47214	0.333775
$377$	−8.94427	−0.460653
$378$	1.00000	0.0514344
$379$	24.0000	1.23280	0.616399	−	0.787434i	$-0.288591\pi$
$379$	24.0000	1.23280	0.616399	+	0.787434i	$0.288591\pi$
$380$	−12.9443	−0.664027
$381$	3.05573	0.156550
$382$	−20.9443	−1.07160
$383$	16.0000	0.817562	0.408781	−	0.912633i	$-0.365954\pi$
$383$	16.0000	0.817562	0.408781	+	0.912633i	$0.365954\pi$
$384$	1.00000	0.0510310
$385$	0	0
$386$	−23.8885	−1.21589
$387$	12.9443	0.657994
$388$	8.47214	0.430108
$389$	−1.05573	−0.0535275	−0.0267638	−	0.999642i	$-0.508520\pi$
$389$	−1.05573	−0.0535275	−0.0267638	+	0.999642i	$0.508520\pi$
$390$	8.94427	0.452911
$391$	4.47214	0.226166
$392$	1.00000	0.0505076
$393$	12.0000	0.605320
$394$	2.94427	0.148330
$395$	25.8885	1.30259
$396$	0	0
$397$	−27.5279	−1.38158	−0.690792	−	0.723054i	$-0.742738\pi$
$397$	−27.5279	−1.38158	−0.690792	+	0.723054i	$0.742738\pi$
$398$	20.9443	1.04984
$399$	−6.47214	−0.324012
$400$	−1.00000	−0.0500000
$401$	−22.0000	−1.09863	−0.549314	−	0.835616i	$-0.685111\pi$
$401$	−22.0000	−1.09863	−0.549314	+	0.835616i	$0.685111\pi$
$402$	−12.9443	−0.645602
$403$	28.9443	1.44182
$404$	17.4164	0.866499
$405$	2.00000	0.0993808
$406$	−2.00000	−0.0992583
$407$	0	0
$408$	−4.47214	−0.221404
$409$	19.8885	0.983425	0.491713	−	0.870758i	$-0.336371\pi$
$409$	19.8885	0.983425	0.491713	+	0.870758i	$0.336371\pi$
$410$	−12.0000	−0.592638
$411$	−14.0000	−0.690569
$412$	12.9443	0.637719
$413$	4.00000	0.196827
$414$	−1.00000	−0.0491473
$415$	−12.9443	−0.635409
$416$	4.47214	0.219265
$417$	−8.94427	−0.438003
$418$	0	0
$419$	19.4164	0.948554	0.474277	−	0.880376i	$-0.342710\pi$
$419$	19.4164	0.948554	0.474277	+	0.880376i	$0.342710\pi$
$420$	2.00000	0.0975900
$421$	−20.8328	−1.01533	−0.507665	−	0.861555i	$-0.669491\pi$
$421$	−20.8328	−1.01533	−0.507665	+	0.861555i	$0.669491\pi$
$422$	16.9443	0.824834
$423$	6.47214	0.314686
$424$	6.94427	0.337244
$425$	4.47214	0.216930
$426$	−12.9443	−0.627152
$427$	−6.00000	−0.290360
$428$	−8.00000	−0.386695
$429$	0	0
$430$	25.8885	1.24846
$431$	−17.8885	−0.861661	−0.430830	−	0.902433i	$-0.641779\pi$
$431$	−17.8885	−0.861661	−0.430830	+	0.902433i	$0.641779\pi$
$432$	1.00000	0.0481125
$433$	−1.41641	−0.0680682	−0.0340341	−	0.999421i	$-0.510835\pi$
$433$	−1.41641	−0.0680682	−0.0340341	+	0.999421i	$0.510835\pi$
$434$	6.47214	0.310672
$435$	−4.00000	−0.191785
$436$	14.9443	0.715701
$437$	6.47214	0.309604
$438$	−2.94427	−0.140683
$439$	−16.3607	−0.780853	−0.390426	−	0.920634i	$-0.627672\pi$
$439$	−16.3607	−0.780853	−0.390426	+	0.920634i	$0.627672\pi$
$440$	0	0
$441$	1.00000	0.0476190
$442$	−20.0000	−0.951303
$443$	−18.8328	−0.894774	−0.447387	−	0.894340i	$-0.647645\pi$
$443$	−18.8328	−0.894774	−0.447387	+	0.894340i	$0.647645\pi$
$444$	−10.9443	−0.519392
$445$	−34.8328	−1.65123
$446$	9.52786	0.451157
$447$	−18.9443	−0.896033
$448$	1.00000	0.0472456
$449$	18.0000	0.849473	0.424736	−	0.905317i	$-0.360367\pi$
$449$	18.0000	0.849473	0.424736	+	0.905317i	$0.360367\pi$
$450$	−1.00000	−0.0471405
$451$	0	0
$452$	−1.05573	−0.0496573
$453$	−12.9443	−0.608175
$454$	14.4721	0.679211
$455$	8.94427	0.419314
$456$	−6.47214	−0.303086
$457$	2.00000	0.0935561	0.0467780	−	0.998905i	$-0.485105\pi$
$457$	2.00000	0.0935561	0.0467780	+	0.998905i	$0.485105\pi$
$458$	−14.0000	−0.654177
$459$	−4.47214	−0.208741
$460$	−2.00000	−0.0932505
$461$	33.4164	1.55636	0.778179	−	0.628043i	$-0.216144\pi$
$461$	33.4164	1.55636	0.778179	+	0.628043i	$0.216144\pi$
$462$	0	0
$463$	41.8885	1.94673	0.973363	−	0.229270i	$-0.0736339\pi$
$463$	41.8885	1.94673	0.973363	+	0.229270i	$0.0736339\pi$
$464$	−2.00000	−0.0928477
$465$	12.9443	0.600276
$466$	−6.00000	−0.277945
$467$	−29.3050	−1.35607	−0.678036	−	0.735029i	$-0.737169\pi$
$467$	−29.3050	−1.35607	−0.678036	+	0.735029i	$0.737169\pi$
$468$	4.47214	0.206725
$469$	−12.9443	−0.597711
$470$	12.9443	0.597075
$471$	14.9443	0.688596
$472$	4.00000	0.184115
$473$	0	0
$474$	12.9443	0.594550
$475$	6.47214	0.296962
$476$	−4.47214	−0.204980
$477$	6.94427	0.317956
$478$	3.05573	0.139766
$479$	12.9443	0.591439	0.295719	−	0.955275i	$-0.404441\pi$
$479$	12.9443	0.591439	0.295719	+	0.955275i	$0.404441\pi$
$480$	2.00000	0.0912871
$481$	−48.9443	−2.23167
$482$	11.5279	0.525080
$483$	−1.00000	−0.0455016
$484$	−11.0000	−0.500000
$485$	16.9443	0.769400
$486$	1.00000	0.0453609
$487$	24.0000	1.08754	0.543772	−	0.839233i	$-0.316996\pi$
$487$	24.0000	1.08754	0.543772	+	0.839233i	$0.316996\pi$
$488$	−6.00000	−0.271607
$489$	8.94427	0.404474
$490$	2.00000	0.0903508
$491$	23.0557	1.04049	0.520245	−	0.854017i	$-0.325841\pi$
$491$	23.0557	1.04049	0.520245	+	0.854017i	$0.325841\pi$
$492$	−6.00000	−0.270501
$493$	8.94427	0.402830
$494$	−28.9443	−1.30226
$495$	0	0
$496$	6.47214	0.290607
$497$	−12.9443	−0.580630
$498$	−6.47214	−0.290023
$499$	15.0557	0.673987	0.336993	−	0.941507i	$-0.390590\pi$
$499$	15.0557	0.673987	0.336993	+	0.941507i	$0.390590\pi$
$500$	−12.0000	−0.536656
$501$	11.4164	0.510047
$502$	−14.4721	−0.645923
$503$	25.8885	1.15431	0.577157	−	0.816634i	$-0.304162\pi$
$503$	25.8885	1.15431	0.577157	+	0.816634i	$0.304162\pi$
$504$	1.00000	0.0445435
$505$	34.8328	1.55004
$506$	0	0
$507$	7.00000	0.310881
$508$	3.05573	0.135576
$509$	33.4164	1.48116	0.740578	−	0.671970i	$-0.234552\pi$
$509$	33.4164	1.48116	0.740578	+	0.671970i	$0.234552\pi$
$510$	−8.94427	−0.396059
$511$	−2.94427	−0.130247
$512$	1.00000	0.0441942
$513$	−6.47214	−0.285752
$514$	14.9443	0.659164
$515$	25.8885	1.14079
$516$	12.9443	0.569840
$517$	0	0
$518$	−10.9443	−0.480864
$519$	−8.47214	−0.371885
$520$	8.94427	0.392232
$521$	6.58359	0.288432	0.144216	−	0.989546i	$-0.453934\pi$
$521$	6.58359	0.288432	0.144216	+	0.989546i	$0.453934\pi$
$522$	−2.00000	−0.0875376
$523$	37.3050	1.63123	0.815616	−	0.578594i	$-0.196398\pi$
$523$	37.3050	1.63123	0.815616	+	0.578594i	$0.196398\pi$
$524$	12.0000	0.524222
$525$	−1.00000	−0.0436436
$526$	−24.0000	−1.04645
$527$	−28.9443	−1.26083
$528$	0	0
$529$	1.00000	0.0434783
$530$	13.8885	0.603280
$531$	4.00000	0.173585
$532$	−6.47214	−0.280603
$533$	−26.8328	−1.16226
$534$	−17.4164	−0.753682
$535$	−16.0000	−0.691740
$536$	−12.9443	−0.559107
$537$	−20.0000	−0.863064
$538$	7.52786	0.324549
$539$	0	0
$540$	2.00000	0.0860663
$541$	−10.0000	−0.429934	−0.214967	−	0.976621i	$-0.568964\pi$
$541$	−10.0000	−0.429934	−0.214967	+	0.976621i	$0.568964\pi$
$542$	−11.4164	−0.490377
$543$	2.00000	0.0858282
$544$	−4.47214	−0.191741
$545$	29.8885	1.28028
$546$	4.47214	0.191390
$547$	20.0000	0.855138	0.427569	−	0.903983i	$-0.359370\pi$
$547$	20.0000	0.855138	0.427569	+	0.903983i	$0.359370\pi$
$548$	−14.0000	−0.598050
$549$	−6.00000	−0.256074
$550$	0	0
$551$	12.9443	0.551445
$552$	−1.00000	−0.0425628
$553$	12.9443	0.550446
$554$	23.8885	1.01493
$555$	−21.8885	−0.929117
$556$	−8.94427	−0.379322
$557$	−34.9443	−1.48064	−0.740318	−	0.672257i	$-0.765325\pi$
$557$	−34.9443	−1.48064	−0.740318	+	0.672257i	$0.765325\pi$
$558$	6.47214	0.273987
$559$	57.8885	2.44842
$560$	2.00000	0.0845154
$561$	0	0
$562$	10.0000	0.421825
$563$	17.5279	0.738711	0.369356	−	0.929288i	$-0.379578\pi$
$563$	17.5279	0.738711	0.369356	+	0.929288i	$0.379578\pi$
$564$	6.47214	0.272526
$565$	−2.11146	−0.0888296
$566$	9.52786	0.400486
$567$	1.00000	0.0419961
$568$	−12.9443	−0.543130
$569$	27.8885	1.16915	0.584574	−	0.811340i	$-0.301262\pi$
$569$	27.8885	1.16915	0.584574	+	0.811340i	$0.301262\pi$
$570$	−12.9443	−0.542176
$571$	4.94427	0.206911	0.103456	−	0.994634i	$-0.467010\pi$
$571$	4.94427	0.206911	0.103456	+	0.994634i	$0.467010\pi$
$572$	0	0
$573$	−20.9443	−0.874960
$574$	−6.00000	−0.250435
$575$	1.00000	0.0417029
$576$	1.00000	0.0416667
$577$	14.9443	0.622138	0.311069	−	0.950387i	$-0.399313\pi$
$577$	14.9443	0.622138	0.311069	+	0.950387i	$0.399313\pi$
$578$	3.00000	0.124784
$579$	−23.8885	−0.992774
$580$	−4.00000	−0.166091
$581$	−6.47214	−0.268509
$582$	8.47214	0.351181
$583$	0	0
$584$	−2.94427	−0.121835
$585$	8.94427	0.369800
$586$	−7.88854	−0.325873
$587$	16.9443	0.699365	0.349682	−	0.936868i	$-0.386289\pi$
$587$	16.9443	0.699365	0.349682	+	0.936868i	$0.386289\pi$
$588$	1.00000	0.0412393
$589$	−41.8885	−1.72599
$590$	8.00000	0.329355
$591$	2.94427	0.121111
$592$	−10.9443	−0.449807
$593$	24.8328	1.01976	0.509881	−	0.860245i	$-0.329690\pi$
$593$	24.8328	1.01976	0.509881	+	0.860245i	$0.329690\pi$
$594$	0	0
$595$	−8.94427	−0.366679
$596$	−18.9443	−0.775988
$597$	20.9443	0.857192
$598$	−4.47214	−0.182879
$599$	−1.88854	−0.0771638	−0.0385819	−	0.999255i	$-0.512284\pi$
$599$	−1.88854	−0.0771638	−0.0385819	+	0.999255i	$0.512284\pi$
$600$	−1.00000	−0.0408248
$601$	−12.8328	−0.523461	−0.261731	−	0.965141i	$-0.584293\pi$
$601$	−12.8328	−0.523461	−0.261731	+	0.965141i	$0.584293\pi$
$602$	12.9443	0.527569
$603$	−12.9443	−0.527132
$604$	−12.9443	−0.526695
$605$	−22.0000	−0.894427
$606$	17.4164	0.707493
$607$	16.3607	0.664060	0.332030	−	0.943269i	$-0.392267\pi$
$607$	16.3607	0.664060	0.332030	+	0.943269i	$0.392267\pi$
$608$	−6.47214	−0.262480
$609$	−2.00000	−0.0810441
$610$	−12.0000	−0.485866
$611$	28.9443	1.17096
$612$	−4.47214	−0.180775
$613$	−12.8328	−0.518313	−0.259156	−	0.965835i	$-0.583444\pi$
$613$	−12.8328	−0.518313	−0.259156	+	0.965835i	$0.583444\pi$
$614$	7.05573	0.284746
$615$	−12.0000	−0.483887
$616$	0	0
$617$	26.0000	1.04672	0.523360	−	0.852111i	$-0.324678\pi$
$617$	26.0000	1.04672	0.523360	+	0.852111i	$0.324678\pi$
$618$	12.9443	0.520695
$619$	−25.5279	−1.02605	−0.513026	−	0.858373i	$-0.671475\pi$
$619$	−25.5279	−1.02605	−0.513026	+	0.858373i	$0.671475\pi$
$620$	12.9443	0.519854
$621$	−1.00000	−0.0401286
$622$	6.47214	0.259509
$623$	−17.4164	−0.697774
$624$	4.47214	0.179029
$625$	−19.0000	−0.760000
$626$	13.4164	0.536228
$627$	0	0
$628$	14.9443	0.596341
$629$	48.9443	1.95154
$630$	2.00000	0.0796819
$631$	−28.9443	−1.15225	−0.576127	−	0.817360i	$-0.695436\pi$
$631$	−28.9443	−1.15225	−0.576127	+	0.817360i	$0.695436\pi$
$632$	12.9443	0.514895
$633$	16.9443	0.673474
$634$	−30.9443	−1.22895
$635$	6.11146	0.242526
$636$	6.94427	0.275358
$637$	4.47214	0.177192
$638$	0	0
$639$	−12.9443	−0.512067
$640$	2.00000	0.0790569
$641$	10.0000	0.394976	0.197488	−	0.980305i	$-0.436722\pi$
$641$	10.0000	0.394976	0.197488	+	0.980305i	$0.436722\pi$
$642$	−8.00000	−0.315735
$643$	−1.52786	−0.0602531	−0.0301265	−	0.999546i	$-0.509591\pi$
$643$	−1.52786	−0.0602531	−0.0301265	+	0.999546i	$0.509591\pi$
$644$	−1.00000	−0.0394055
$645$	25.8885	1.01936
$646$	28.9443	1.13880
$647$	−32.3607	−1.27223	−0.636115	−	0.771594i	$-0.719460\pi$
$647$	−32.3607	−1.27223	−0.636115	+	0.771594i	$0.719460\pi$
$648$	1.00000	0.0392837
$649$	0	0
$650$	−4.47214	−0.175412
$651$	6.47214	0.253663
$652$	8.94427	0.350285
$653$	6.00000	0.234798	0.117399	−	0.993085i	$-0.462544\pi$
$653$	6.00000	0.234798	0.117399	+	0.993085i	$0.462544\pi$
$654$	14.9443	0.584367
$655$	24.0000	0.937758
$656$	−6.00000	−0.234261
$657$	−2.94427	−0.114867
$658$	6.47214	0.252310
$659$	−6.83282	−0.266169	−0.133084	−	0.991105i	$-0.542488\pi$
$659$	−6.83282	−0.266169	−0.133084	+	0.991105i	$0.542488\pi$
$660$	0	0
$661$	−30.0000	−1.16686	−0.583432	−	0.812162i	$-0.698291\pi$
$661$	−30.0000	−1.16686	−0.583432	+	0.812162i	$0.698291\pi$
$662$	21.8885	0.850722
$663$	−20.0000	−0.776736
$664$	−6.47214	−0.251168
$665$	−12.9443	−0.501957
$666$	−10.9443	−0.424082
$667$	2.00000	0.0774403
$668$	11.4164	0.441714
$669$	9.52786	0.368369
$670$	−25.8885	−1.00016
$671$	0	0
$672$	1.00000	0.0385758
$673$	−30.0000	−1.15642	−0.578208	−	0.815890i	$-0.696248\pi$
$673$	−30.0000	−1.15642	−0.578208	+	0.815890i	$0.696248\pi$
$674$	14.9443	0.575632
$675$	−1.00000	−0.0384900
$676$	7.00000	0.269231
$677$	−39.8885	−1.53304	−0.766521	−	0.642220i	$-0.778014\pi$
$677$	−39.8885	−1.53304	−0.766521	+	0.642220i	$0.778014\pi$
$678$	−1.05573	−0.0405450
$679$	8.47214	0.325131
$680$	−8.94427	−0.342997
$681$	14.4721	0.554573
$682$	0	0
$683$	−0.944272	−0.0361316	−0.0180658	−	0.999837i	$-0.505751\pi$
$683$	−0.944272	−0.0361316	−0.0180658	+	0.999837i	$0.505751\pi$
$684$	−6.47214	−0.247468
$685$	−28.0000	−1.06983
$686$	1.00000	0.0381802
$687$	−14.0000	−0.534133
$688$	12.9443	0.493496
$689$	31.0557	1.18313
$690$	−2.00000	−0.0761387
$691$	−32.9443	−1.25326	−0.626630	−	0.779317i	$-0.715566\pi$
$691$	−32.9443	−1.25326	−0.626630	+	0.779317i	$0.715566\pi$
$692$	−8.47214	−0.322062
$693$	0	0
$694$	16.9443	0.643196
$695$	−17.8885	−0.678551
$696$	−2.00000	−0.0758098
$697$	26.8328	1.01637
$698$	15.5279	0.587738
$699$	−6.00000	−0.226941
$700$	−1.00000	−0.0377964
$701$	32.8328	1.24008	0.620039	−	0.784571i	$-0.287117\pi$
$701$	32.8328	1.24008	0.620039	+	0.784571i	$0.287117\pi$
$702$	4.47214	0.168790
$703$	70.8328	2.67151
$704$	0	0
$705$	12.9443	0.487509
$706$	2.00000	0.0752710
$707$	17.4164	0.655011
$708$	4.00000	0.150329
$709$	−10.9443	−0.411021	−0.205510	−	0.978655i	$-0.565885\pi$
$709$	−10.9443	−0.411021	−0.205510	+	0.978655i	$0.565885\pi$
$710$	−25.8885	−0.971580
$711$	12.9443	0.485448
$712$	−17.4164	−0.652707
$713$	−6.47214	−0.242383
$714$	−4.47214	−0.167365
$715$	0	0
$716$	−20.0000	−0.747435
$717$	3.05573	0.114118
$718$	22.8328	0.852113
$719$	−14.4721	−0.539720	−0.269860	−	0.962900i	$-0.586977\pi$
$719$	−14.4721	−0.539720	−0.269860	+	0.962900i	$0.586977\pi$
$720$	2.00000	0.0745356
$721$	12.9443	0.482070
$722$	22.8885	0.851823
$723$	11.5279	0.428726
$724$	2.00000	0.0743294
$725$	2.00000	0.0742781
$726$	−11.0000	−0.408248
$727$	20.9443	0.776780	0.388390	−	0.921495i	$-0.373031\pi$
$727$	20.9443	0.776780	0.388390	+	0.921495i	$0.373031\pi$
$728$	4.47214	0.165748
$729$	1.00000	0.0370370
$730$	−5.88854	−0.217945
$731$	−57.8885	−2.14109
$732$	−6.00000	−0.221766
$733$	−33.0557	−1.22094	−0.610471	−	0.792039i	$-0.709020\pi$
$733$	−33.0557	−1.22094	−0.610471	+	0.792039i	$0.709020\pi$
$734$	−22.8328	−0.842775
$735$	2.00000	0.0737711
$736$	−1.00000	−0.0368605
$737$	0	0
$738$	−6.00000	−0.220863
$739$	8.94427	0.329020	0.164510	−	0.986375i	$-0.447396\pi$
$739$	8.94427	0.329020	0.164510	+	0.986375i	$0.447396\pi$
$740$	−21.8885	−0.804639
$741$	−28.9443	−1.06329
$742$	6.94427	0.254932
$743$	30.8328	1.13115	0.565573	−	0.824698i	$-0.308655\pi$
$743$	30.8328	1.13115	0.565573	+	0.824698i	$0.308655\pi$
$744$	6.47214	0.237280
$745$	−37.8885	−1.38813
$746$	−10.9443	−0.400698
$747$	−6.47214	−0.236803
$748$	0	0
$749$	−8.00000	−0.292314
$750$	−12.0000	−0.438178
$751$	−17.8885	−0.652762	−0.326381	−	0.945238i	$-0.605829\pi$
$751$	−17.8885	−0.652762	−0.326381	+	0.945238i	$0.605829\pi$
$752$	6.47214	0.236015
$753$	−14.4721	−0.527394
$754$	−8.94427	−0.325731
$755$	−25.8885	−0.942181
$756$	1.00000	0.0363696
$757$	−25.0557	−0.910666	−0.455333	−	0.890321i	$-0.650480\pi$
$757$	−25.0557	−0.910666	−0.455333	+	0.890321i	$0.650480\pi$
$758$	24.0000	0.871719
$759$	0	0
$760$	−12.9443	−0.469538
$761$	38.9443	1.41173	0.705864	−	0.708347i	$-0.250559\pi$
$761$	38.9443	1.41173	0.705864	+	0.708347i	$0.250559\pi$
$762$	3.05573	0.110697
$763$	14.9443	0.541019
$764$	−20.9443	−0.757737
$765$	−8.94427	−0.323381
$766$	16.0000	0.578103
$767$	17.8885	0.645918
$768$	1.00000	0.0360844
$769$	−14.3607	−0.517859	−0.258930	−	0.965896i	$-0.583370\pi$
$769$	−14.3607	−0.517859	−0.258930	+	0.965896i	$0.583370\pi$
$770$	0	0
$771$	14.9443	0.538205
$772$	−23.8885	−0.859768
$773$	22.9443	0.825248	0.412624	−	0.910901i	$-0.364612\pi$
$773$	22.9443	0.825248	0.412624	+	0.910901i	$0.364612\pi$
$774$	12.9443	0.465272
$775$	−6.47214	−0.232486
$776$	8.47214	0.304132
$777$	−10.9443	−0.392624
$778$	−1.05573	−0.0378497
$779$	38.8328	1.39133
$780$	8.94427	0.320256
$781$	0	0
$782$	4.47214	0.159923
$783$	−2.00000	−0.0714742
$784$	1.00000	0.0357143
$785$	29.8885	1.06677
$786$	12.0000	0.428026
$787$	−27.4164	−0.977289	−0.488645	−	0.872483i	$-0.662509\pi$
$787$	−27.4164	−0.977289	−0.488645	+	0.872483i	$0.662509\pi$
$788$	2.94427	0.104885
$789$	−24.0000	−0.854423
$790$	25.8885	0.921073
$791$	−1.05573	−0.0375374
$792$	0	0
$793$	−26.8328	−0.952861
$794$	−27.5279	−0.976927
$795$	13.8885	0.492576
$796$	20.9443	0.742350
$797$	24.8328	0.879623	0.439812	−	0.898090i	$-0.355045\pi$
$797$	24.8328	0.879623	0.439812	+	0.898090i	$0.355045\pi$
$798$	−6.47214	−0.229111
$799$	−28.9443	−1.02397
$800$	−1.00000	−0.0353553
$801$	−17.4164	−0.615379
$802$	−22.0000	−0.776847
$803$	0	0
$804$	−12.9443	−0.456509
$805$	−2.00000	−0.0704907
$806$	28.9443	1.01952
$807$	7.52786	0.264993
$808$	17.4164	0.612707
$809$	0.111456	0.00391859	0.00195930	−	0.999998i	$-0.499376\pi$
$809$	0.111456	0.00391859	0.00195930	+	0.999998i	$0.499376\pi$
$810$	2.00000	0.0702728
$811$	−2.11146	−0.0741433	−0.0370716	−	0.999313i	$-0.511803\pi$
$811$	−2.11146	−0.0741433	−0.0370716	+	0.999313i	$0.511803\pi$
$812$	−2.00000	−0.0701862
$813$	−11.4164	−0.400391
$814$	0	0
$815$	17.8885	0.626608
$816$	−4.47214	−0.156556
$817$	−83.7771	−2.93099
$818$	19.8885	0.695387
$819$	4.47214	0.156269
$820$	−12.0000	−0.419058
$821$	36.8328	1.28547	0.642737	−	0.766087i	$-0.277799\pi$
$821$	36.8328	1.28547	0.642737	+	0.766087i	$0.277799\pi$
$822$	−14.0000	−0.488306
$823$	3.05573	0.106516	0.0532580	−	0.998581i	$-0.483039\pi$
$823$	3.05573	0.106516	0.0532580	+	0.998581i	$0.483039\pi$
$824$	12.9443	0.450935
$825$	0	0
$826$	4.00000	0.139178
$827$	−1.88854	−0.0656711	−0.0328356	−	0.999461i	$-0.510454\pi$
$827$	−1.88854	−0.0656711	−0.0328356	+	0.999461i	$0.510454\pi$
$828$	−1.00000	−0.0347524
$829$	−13.4164	−0.465971	−0.232986	−	0.972480i	$-0.574849\pi$
$829$	−13.4164	−0.465971	−0.232986	+	0.972480i	$0.574849\pi$
$830$	−12.9443	−0.449302
$831$	23.8885	0.828684
$832$	4.47214	0.155043
$833$	−4.47214	−0.154950
$834$	−8.94427	−0.309715
$835$	22.8328	0.790162
$836$	0	0
$837$	6.47214	0.223710
$838$	19.4164	0.670729
$839$	−24.0000	−0.828572	−0.414286	−	0.910147i	$-0.635969\pi$
$839$	−24.0000	−0.828572	−0.414286	+	0.910147i	$0.635969\pi$
$840$	2.00000	0.0690066
$841$	−25.0000	−0.862069
$842$	−20.8328	−0.717946
$843$	10.0000	0.344418
$844$	16.9443	0.583246
$845$	14.0000	0.481615
$846$	6.47214	0.222517
$847$	−11.0000	−0.377964
$848$	6.94427	0.238467
$849$	9.52786	0.326995
$850$	4.47214	0.153393
$851$	10.9443	0.375165
$852$	−12.9443	−0.443463
$853$	38.3607	1.31344	0.656722	−	0.754132i	$-0.271942\pi$
$853$	38.3607	1.31344	0.656722	+	0.754132i	$0.271942\pi$
$854$	−6.00000	−0.205316
$855$	−12.9443	−0.442685
$856$	−8.00000	−0.273434
$857$	−12.1115	−0.413719	−0.206860	−	0.978371i	$-0.566324\pi$
$857$	−12.1115	−0.413719	−0.206860	+	0.978371i	$0.566324\pi$
$858$	0	0
$859$	15.0557	0.513695	0.256847	−	0.966452i	$-0.417316\pi$
$859$	15.0557	0.513695	0.256847	+	0.966452i	$0.417316\pi$
$860$	25.8885	0.882792
$861$	−6.00000	−0.204479
$862$	−17.8885	−0.609286
$863$	3.05573	0.104018	0.0520091	−	0.998647i	$-0.483438\pi$
$863$	3.05573	0.104018	0.0520091	+	0.998647i	$0.483438\pi$
$864$	1.00000	0.0340207
$865$	−16.9443	−0.576123
$866$	−1.41641	−0.0481315
$867$	3.00000	0.101885
$868$	6.47214	0.219679
$869$	0	0
$870$	−4.00000	−0.135613
$871$	−57.8885	−1.96148
$872$	14.9443	0.506077
$873$	8.47214	0.286738
$874$	6.47214	0.218923
$875$	−12.0000	−0.405674
$876$	−2.94427	−0.0994777
$877$	54.7214	1.84781	0.923905	−	0.382623i	$-0.124979\pi$
$877$	54.7214	1.84781	0.923905	+	0.382623i	$0.124979\pi$
$878$	−16.3607	−0.552146
$879$	−7.88854	−0.266074
$880$	0	0
$881$	−22.3607	−0.753350	−0.376675	−	0.926345i	$-0.622933\pi$
$881$	−22.3607	−0.753350	−0.376675	+	0.926345i	$0.622933\pi$
$882$	1.00000	0.0336718
$883$	−50.8328	−1.71066	−0.855330	−	0.518083i	$-0.826646\pi$
$883$	−50.8328	−1.71066	−0.855330	+	0.518083i	$0.826646\pi$
$884$	−20.0000	−0.672673
$885$	8.00000	0.268917
$886$	−18.8328	−0.632701
$887$	−14.4721	−0.485927	−0.242963	−	0.970035i	$-0.578119\pi$
$887$	−14.4721	−0.485927	−0.242963	+	0.970035i	$0.578119\pi$
$888$	−10.9443	−0.367266
$889$	3.05573	0.102486
$890$	−34.8328	−1.16760
$891$	0	0
$892$	9.52786	0.319016
$893$	−41.8885	−1.40175
$894$	−18.9443	−0.633591
$895$	−40.0000	−1.33705
$896$	1.00000	0.0334077
$897$	−4.47214	−0.149320
$898$	18.0000	0.600668
$899$	−12.9443	−0.431716
$900$	−1.00000	−0.0333333
$901$	−31.0557	−1.03462
$902$	0	0
$903$	12.9443	0.430758
$904$	−1.05573	−0.0351130
$905$	4.00000	0.132964
$906$	−12.9443	−0.430045
$907$	−6.11146	−0.202928	−0.101464	−	0.994839i	$-0.532353\pi$
$907$	−6.11146	−0.202928	−0.101464	+	0.994839i	$0.532353\pi$
$908$	14.4721	0.480275
$909$	17.4164	0.577666
$910$	8.94427	0.296500
$911$	40.7214	1.34916	0.674579	−	0.738202i	$-0.264325\pi$
$911$	40.7214	1.34916	0.674579	+	0.738202i	$0.264325\pi$
$912$	−6.47214	−0.214314
$913$	0	0
$914$	2.00000	0.0661541
$915$	−12.0000	−0.396708
$916$	−14.0000	−0.462573
$917$	12.0000	0.396275
$918$	−4.47214	−0.147602
$919$	52.9443	1.74647	0.873235	−	0.487299i	$-0.162018\pi$
$919$	52.9443	1.74647	0.873235	+	0.487299i	$0.162018\pi$
$920$	−2.00000	−0.0659380
$921$	7.05573	0.232494
$922$	33.4164	1.10051
$923$	−57.8885	−1.90542
$924$	0	0
$925$	10.9443	0.359845
$926$	41.8885	1.37654
$927$	12.9443	0.425146
$928$	−2.00000	−0.0656532
$929$	18.0000	0.590561	0.295280	−	0.955411i	$-0.404587\pi$
$929$	18.0000	0.590561	0.295280	+	0.955411i	$0.404587\pi$
$930$	12.9443	0.424459
$931$	−6.47214	−0.212116
$932$	−6.00000	−0.196537
$933$	6.47214	0.211888
$934$	−29.3050	−0.958887
$935$	0	0
$936$	4.47214	0.146176
$937$	−40.2492	−1.31488	−0.657442	−	0.753505i	$-0.728362\pi$
$937$	−40.2492	−1.31488	−0.657442	+	0.753505i	$0.728362\pi$
$938$	−12.9443	−0.422645
$939$	13.4164	0.437828
$940$	12.9443	0.422196
$941$	−6.00000	−0.195594	−0.0977972	−	0.995206i	$-0.531180\pi$
$941$	−6.00000	−0.195594	−0.0977972	+	0.995206i	$0.531180\pi$
$942$	14.9443	0.486911
$943$	6.00000	0.195387
$944$	4.00000	0.130189
$945$	2.00000	0.0650600
$946$	0	0
$947$	−16.9443	−0.550615	−0.275307	−	0.961356i	$-0.588780\pi$
$947$	−16.9443	−0.550615	−0.275307	+	0.961356i	$0.588780\pi$
$948$	12.9443	0.420410
$949$	−13.1672	−0.427425
$950$	6.47214	0.209984
$951$	−30.9443	−1.00344
$952$	−4.47214	−0.144943
$953$	−26.9443	−0.872811	−0.436405	−	0.899750i	$-0.643749\pi$
$953$	−26.9443	−0.872811	−0.436405	+	0.899750i	$0.643749\pi$
$954$	6.94427	0.224829
$955$	−41.8885	−1.35548
$956$	3.05573	0.0988293
$957$	0	0
$958$	12.9443	0.418210
$959$	−14.0000	−0.452084
$960$	2.00000	0.0645497
$961$	10.8885	0.351243
$962$	−48.9443	−1.57803
$963$	−8.00000	−0.257796
$964$	11.5279	0.371288
$965$	−47.7771	−1.53800
$966$	−1.00000	−0.0321745
$967$	−16.0000	−0.514525	−0.257263	−	0.966342i	$-0.582821\pi$
$967$	−16.0000	−0.514525	−0.257263	+	0.966342i	$0.582821\pi$
$968$	−11.0000	−0.353553
$969$	28.9443	0.929824
$970$	16.9443	0.544048
$971$	3.41641	0.109638	0.0548189	−	0.998496i	$-0.482542\pi$
$971$	3.41641	0.109638	0.0548189	+	0.998496i	$0.482542\pi$
$972$	1.00000	0.0320750
$973$	−8.94427	−0.286740
$974$	24.0000	0.769010
$975$	−4.47214	−0.143223
$976$	−6.00000	−0.192055
$977$	−6.00000	−0.191957	−0.0959785	−	0.995383i	$-0.530598\pi$
$977$	−6.00000	−0.191957	−0.0959785	+	0.995383i	$0.530598\pi$
$978$	8.94427	0.286006
$979$	0	0
$980$	2.00000	0.0638877
$981$	14.9443	0.477134
$982$	23.0557	0.735738
$983$	−57.8885	−1.84636	−0.923179	−	0.384371i	$-0.874419\pi$
$983$	−57.8885	−1.84636	−0.923179	+	0.384371i	$0.874419\pi$
$984$	−6.00000	−0.191273
$985$	5.88854	0.187625
$986$	8.94427	0.284844
$987$	6.47214	0.206010
$988$	−28.9443	−0.920840
$989$	−12.9443	−0.411604
$990$	0	0
$991$	43.0557	1.36771	0.683855	−	0.729618i	$-0.260302\pi$
$991$	43.0557	1.36771	0.683855	+	0.729618i	$0.260302\pi$
$992$	6.47214	0.205491
$993$	21.8885	0.694612
$994$	−12.9443	−0.410567
$995$	41.8885	1.32796
$996$	−6.47214	−0.205077
$997$	−1.63932	−0.0519178	−0.0259589	−	0.999663i	$-0.508264\pi$
$997$	−1.63932	−0.0519178	−0.0259589	+	0.999663i	$0.508264\pi$
$998$	15.0557	0.476581
$999$	−10.9443	−0.346261

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.a.p.1.2	✓	2
3.2	odd	2		2898.2.a.v.1.2		2
4.3	odd	2		7728.2.a.bd.1.2		2
7.6	odd	2		6762.2.a.bz.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.a.p.1.2	✓	2	1.1	even	1	trivial
2898.2.a.v.1.2		2	3.2	odd	2
6762.2.a.bz.1.1		2	7.6	odd	2
7728.2.a.bd.1.2		2	4.3	odd	2

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.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +2.00000 q^{5} +1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +2.00000 q^{5} +1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +2.00000 q^{10} +1.00000 q^{12} +4.47214 q^{13} +1.00000 q^{14} +2.00000 q^{15} +1.00000 q^{16} -4.47214 q^{17} +1.00000 q^{18} -6.47214 q^{19} +2.00000 q^{20} +1.00000 q^{21} -1.00000 q^{23} +1.00000 q^{24} -1.00000 q^{25} +4.47214 q^{26} +1.00000 q^{27} +1.00000 q^{28} -2.00000 q^{29} +2.00000 q^{30} +6.47214 q^{31} +1.00000 q^{32} -4.47214 q^{34} +2.00000 q^{35} +1.00000 q^{36} -10.9443 q^{37} -6.47214 q^{38} +4.47214 q^{39} +2.00000 q^{40} -6.00000 q^{41} +1.00000 q^{42} +12.9443 q^{43} +2.00000 q^{45} -1.00000 q^{46} +6.47214 q^{47} +1.00000 q^{48} +1.00000 q^{49} -1.00000 q^{50} -4.47214 q^{51} +4.47214 q^{52} +6.94427 q^{53} +1.00000 q^{54} +1.00000 q^{56} -6.47214 q^{57} -2.00000 q^{58} +4.00000 q^{59} +2.00000 q^{60} -6.00000 q^{61} +6.47214 q^{62} +1.00000 q^{63} +1.00000 q^{64} +8.94427 q^{65} -12.9443 q^{67} -4.47214 q^{68} -1.00000 q^{69} +2.00000 q^{70} -12.9443 q^{71} +1.00000 q^{72} -2.94427 q^{73} -10.9443 q^{74} -1.00000 q^{75} -6.47214 q^{76} +4.47214 q^{78} +12.9443 q^{79} +2.00000 q^{80} +1.00000 q^{81} -6.00000 q^{82} -6.47214 q^{83} +1.00000 q^{84} -8.94427 q^{85} +12.9443 q^{86} -2.00000 q^{87} -17.4164 q^{89} +2.00000 q^{90} +4.47214 q^{91} -1.00000 q^{92} +6.47214 q^{93} +6.47214 q^{94} -12.9443 q^{95} +1.00000 q^{96} +8.47214 q^{97} +1.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} + 2 q^{3} + 2 q^{4} + 4 q^{5} + 2 q^{6} + 2 q^{7} + 2 q^{8} + 2 q^{9}+O(q^{10}) \) 2 * q + 2 * q^2 + 2 * q^3 + 2 * q^4 + 4 * q^5 + 2 * q^6 + 2 * q^7 + 2 * q^8 + 2 * q^9	\( 2 q + 2 q^{2} + 2 q^{3} + 2 q^{4} + 4 q^{5} + 2 q^{6} + 2 q^{7} + 2 q^{8} + 2 q^{9} + 4 q^{10} + 2 q^{12} + 2 q^{14} + 4 q^{15} + 2 q^{16} + 2 q^{18} - 4 q^{19} + 4 q^{20} + 2 q^{21} - 2 q^{23} + 2 q^{24} - 2 q^{25} + 2 q^{27} + 2 q^{28} - 4 q^{29} + 4 q^{30} + 4 q^{31} + 2 q^{32} + 4 q^{35} + 2 q^{36} - 4 q^{37} - 4 q^{38} + 4 q^{40} - 12 q^{41} + 2 q^{42} + 8 q^{43} + 4 q^{45} - 2 q^{46} + 4 q^{47} + 2 q^{48} + 2 q^{49} - 2 q^{50} - 4 q^{53} + 2 q^{54} + 2 q^{56} - 4 q^{57} - 4 q^{58} + 8 q^{59} + 4 q^{60} - 12 q^{61} + 4 q^{62} + 2 q^{63} + 2 q^{64} - 8 q^{67} - 2 q^{69} + 4 q^{70} - 8 q^{71} + 2 q^{72} + 12 q^{73} - 4 q^{74} - 2 q^{75} - 4 q^{76} + 8 q^{79} + 4 q^{80} + 2 q^{81} - 12 q^{82} - 4 q^{83} + 2 q^{84} + 8 q^{86} - 4 q^{87} - 8 q^{89} + 4 q^{90} - 2 q^{92} + 4 q^{93} + 4 q^{94} - 8 q^{95} + 2 q^{96} + 8 q^{97} + 2 q^{98}+O(q^{100}) \) 2 * q + 2 * q^2 + 2 * q^3 + 2 * q^4 + 4 * q^5 + 2 * q^6 + 2 * q^7 + 2 * q^8 + 2 * q^9 + 4 * q^10 + 2 * q^12 + 2 * q^14 + 4 * q^15 + 2 * q^16 + 2 * q^18 - 4 * q^19 + 4 * q^20 + 2 * q^21 - 2 * q^23 + 2 * q^24 - 2 * q^25 + 2 * q^27 + 2 * q^28 - 4 * q^29 + 4 * q^30 + 4 * q^31 + 2 * q^32 + 4 * q^35 + 2 * q^36 - 4 * q^37 - 4 * q^38 + 4 * q^40 - 12 * q^41 + 2 * q^42 + 8 * q^43 + 4 * q^45 - 2 * q^46 + 4 * q^47 + 2 * q^48 + 2 * q^49 - 2 * q^50 - 4 * q^53 + 2 * q^54 + 2 * q^56 - 4 * q^57 - 4 * q^58 + 8 * q^59 + 4 * q^60 - 12 * q^61 + 4 * q^62 + 2 * q^63 + 2 * q^64 - 8 * q^67 - 2 * q^69 + 4 * q^70 - 8 * q^71 + 2 * q^72 + 12 * q^73 - 4 * q^74 - 2 * q^75 - 4 * q^76 + 8 * q^79 + 4 * q^80 + 2 * q^81 - 12 * q^82 - 4 * q^83 + 2 * q^84 + 8 * q^86 - 4 * q^87 - 8 * q^89 + 4 * q^90 - 2 * q^92 + 4 * q^93 + 4 * q^94 - 8 * q^95 + 2 * q^96 + 8 * q^97 + 2 * q^98

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