LMFDB - Embedded newform 2541.2.a.br.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2541,2,Mod(1,2541)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2541, 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("2541.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2541 = 3 \cdot 7 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2541.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:	$20.2899871536$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 19x^{8} - x^{7} + 124x^{6} + 6x^{5} - 316x^{4} + 17x^{3} + 253x^{2} - 70x - 11 $ x^10 - 19x^8 - x^7 + 124x^6 + 6x^5 - 316x^4 + 17x^3 + 253x^2 - 70*x - 11
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 231)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$-1.33330$ of defining polynomial
Character	$\chi$	$=$	2541.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.33330 q^{2} +1.00000 q^{3} -0.222305 q^{4} -0.873210 q^{5} +1.33330 q^{6} +1.00000 q^{7} -2.96300 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.33330 q^{2} +1.00000 q^{3} -0.222305 q^{4} -0.873210 q^{5} +1.33330 q^{6} +1.00000 q^{7} -2.96300 q^{8} +1.00000 q^{9} -1.16425 q^{10} -0.222305 q^{12} -0.0395440 q^{13} +1.33330 q^{14} -0.873210 q^{15} -3.50597 q^{16} -2.04633 q^{17} +1.33330 q^{18} +5.69421 q^{19} +0.194119 q^{20} +1.00000 q^{21} +5.97870 q^{23} -2.96300 q^{24} -4.23750 q^{25} -0.0527241 q^{26} +1.00000 q^{27} -0.222305 q^{28} +4.67254 q^{29} -1.16425 q^{30} +7.47891 q^{31} +1.25149 q^{32} -2.72838 q^{34} -0.873210 q^{35} -0.222305 q^{36} +11.5704 q^{37} +7.59210 q^{38} -0.0395440 q^{39} +2.58733 q^{40} +6.14882 q^{41} +1.33330 q^{42} +1.79689 q^{43} -0.873210 q^{45} +7.97142 q^{46} +6.04773 q^{47} -3.50597 q^{48} +1.00000 q^{49} -5.64987 q^{50} -2.04633 q^{51} +0.00879083 q^{52} -0.124401 q^{53} +1.33330 q^{54} -2.96300 q^{56} +5.69421 q^{57} +6.22991 q^{58} -14.3460 q^{59} +0.194119 q^{60} -7.55944 q^{61} +9.97165 q^{62} +1.00000 q^{63} +8.68056 q^{64} +0.0345302 q^{65} +4.85938 q^{67} +0.454910 q^{68} +5.97870 q^{69} -1.16425 q^{70} -11.2503 q^{71} -2.96300 q^{72} -0.612954 q^{73} +15.4269 q^{74} -4.23750 q^{75} -1.26585 q^{76} -0.0527241 q^{78} +0.155227 q^{79} +3.06145 q^{80} +1.00000 q^{81} +8.19824 q^{82} -8.91599 q^{83} -0.222305 q^{84} +1.78688 q^{85} +2.39580 q^{86} +4.67254 q^{87} +5.17689 q^{89} -1.16425 q^{90} -0.0395440 q^{91} -1.32910 q^{92} +7.47891 q^{93} +8.06345 q^{94} -4.97224 q^{95} +1.25149 q^{96} +7.94222 q^{97} +1.33330 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 10 q^{3} + 18 q^{4} + 5 q^{5} + 10 q^{7} - 3 q^{8} + 10 q^{9}+O(q^{10}) $ 10 * q + 10 * q^3 + 18 * q^4 + 5 * q^5 + 10 * q^7 - 3 * q^8 + 10 * q^9	$ 10 q + 10 q^{3} + 18 q^{4} + 5 q^{5} + 10 q^{7} - 3 q^{8} + 10 q^{9} - 6 q^{10} + 18 q^{12} + 6 q^{13} + 5 q^{15} + 38 q^{16} + 8 q^{17} + 7 q^{20} + 10 q^{21} - 3 q^{24} + 31 q^{25} + q^{26} + 10 q^{27} + 18 q^{28} - 14 q^{29} - 6 q^{30} + 26 q^{31} - 41 q^{32} + 21 q^{34} + 5 q^{35} + 18 q^{36} + 24 q^{37} + 8 q^{38} + 6 q^{39} - 5 q^{40} + 19 q^{41} - 6 q^{43} + 5 q^{45} - q^{46} + 15 q^{47} + 38 q^{48} + 10 q^{49} - q^{50} + 8 q^{51} - 25 q^{52} - q^{53} - 3 q^{56} + 11 q^{58} + 23 q^{59} + 7 q^{60} + 11 q^{62} + 10 q^{63} + 53 q^{64} - 29 q^{65} + 38 q^{67} + 87 q^{68} - 6 q^{70} + 26 q^{71} - 3 q^{72} - q^{73} - 39 q^{74} + 31 q^{75} - 2 q^{76} + q^{78} + 5 q^{79} + 6 q^{80} + 10 q^{81} + 5 q^{82} + 6 q^{83} + 18 q^{84} - q^{85} - 41 q^{86} - 14 q^{87} - 9 q^{89} - 6 q^{90} + 6 q^{91} - 48 q^{92} + 26 q^{93} - 42 q^{95} - 41 q^{96} + 24 q^{97}+O(q^{100}) $ 10 * q + 10 * q^3 + 18 * q^4 + 5 * q^5 + 10 * q^7 - 3 * q^8 + 10 * q^9 - 6 * q^10 + 18 * q^12 + 6 * q^13 + 5 * q^15 + 38 * q^16 + 8 * q^17 + 7 * q^20 + 10 * q^21 - 3 * q^24 + 31 * q^25 + q^26 + 10 * q^27 + 18 * q^28 - 14 * q^29 - 6 * q^30 + 26 * q^31 - 41 * q^32 + 21 * q^34 + 5 * q^35 + 18 * q^36 + 24 * q^37 + 8 * q^38 + 6 * q^39 - 5 * q^40 + 19 * q^41 - 6 * q^43 + 5 * q^45 - q^46 + 15 * q^47 + 38 * q^48 + 10 * q^49 - q^50 + 8 * q^51 - 25 * q^52 - q^53 - 3 * q^56 + 11 * q^58 + 23 * q^59 + 7 * q^60 + 11 * q^62 + 10 * q^63 + 53 * q^64 - 29 * q^65 + 38 * q^67 + 87 * q^68 - 6 * q^70 + 26 * q^71 - 3 * q^72 - q^73 - 39 * q^74 + 31 * q^75 - 2 * q^76 + q^78 + 5 * q^79 + 6 * q^80 + 10 * q^81 + 5 * q^82 + 6 * q^83 + 18 * q^84 - q^85 - 41 * q^86 - 14 * q^87 - 9 * q^89 - 6 * q^90 + 6 * q^91 - 48 * q^92 + 26 * q^93 - 42 * q^95 - 41 * q^96 + 24 * q^97

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 $

$2$	1.33330	0.942787	0.471394	−	0.881923i	$-0.343751\pi$
$2$	1.33330	0.942787	0.471394	+	0.881923i	$0.343751\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−0.222305	−0.111152
$5$	−0.873210	−0.390512	−0.195256	−	0.980752i	$-0.562554\pi$
$5$	−0.873210	−0.390512	−0.195256	+	0.980752i	$0.562554\pi$
$6$	1.33330	0.544318
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−2.96300	−1.04758
$9$	1.00000	0.333333
$10$	−1.16425	−0.368169
$11$	0	0
$11$	0	0
$12$	−0.222305	−0.0641739
$13$	−0.0395440	−0.0109675	−0.00548377	−	0.999985i	$-0.501746\pi$
$13$	−0.0395440	−0.0109675	−0.00548377	+	0.999985i	$0.501746\pi$
$14$	1.33330	0.356340
$15$	−0.873210	−0.225462
$16$	−3.50597	−0.876493
$17$	−2.04633	−0.496308	−0.248154	−	0.968721i	$-0.579824\pi$
$17$	−2.04633	−0.496308	−0.248154	+	0.968721i	$0.579824\pi$
$18$	1.33330	0.314262
$19$	5.69421	1.30634	0.653170	−	0.757211i	$-0.273439\pi$
$19$	5.69421	1.30634	0.653170	+	0.757211i	$0.273439\pi$
$20$	0.194119	0.0434063
$21$	1.00000	0.218218
$22$	0	0
$23$	5.97870	1.24665	0.623323	−	0.781965i	$-0.285782\pi$
$23$	5.97870	1.24665	0.623323	+	0.781965i	$0.285782\pi$
$24$	−2.96300	−0.604821
$25$	−4.23750	−0.847501
$26$	−0.0527241	−0.0103401
$27$	1.00000	0.192450
$28$	−0.222305	−0.0420117
$29$	4.67254	0.867669	0.433834	−	0.900993i	$-0.357160\pi$
$29$	4.67254	0.867669	0.433834	+	0.900993i	$0.357160\pi$
$30$	−1.16425	−0.212563
$31$	7.47891	1.34325	0.671626	−	0.740890i	$-0.265596\pi$
$31$	7.47891	1.34325	0.671626	+	0.740890i	$0.265596\pi$
$32$	1.25149	0.221234
$33$	0	0
$34$	−2.72838	−0.467913
$35$	−0.873210	−0.147600
$36$	−0.222305	−0.0370508
$37$	11.5704	1.90217	0.951085	−	0.308930i	$-0.0999708\pi$
$37$	11.5704	1.90217	0.951085	+	0.308930i	$0.0999708\pi$
$38$	7.59210	1.23160
$39$	−0.0395440	−0.00633211
$40$	2.58733	0.409092
$41$	6.14882	0.960285	0.480142	−	0.877191i	$-0.340585\pi$
$41$	6.14882	0.960285	0.480142	+	0.877191i	$0.340585\pi$
$42$	1.33330	0.205733
$43$	1.79689	0.274024	0.137012	−	0.990569i	$-0.456250\pi$
$43$	1.79689	0.274024	0.137012	+	0.990569i	$0.456250\pi$
$44$	0	0
$45$	−0.873210	−0.130171
$46$	7.97142	1.17532
$47$	6.04773	0.882152	0.441076	−	0.897470i	$-0.354597\pi$
$47$	6.04773	0.882152	0.441076	+	0.897470i	$0.354597\pi$
$48$	−3.50597	−0.506043
$49$	1.00000	0.142857
$50$	−5.64987	−0.799013
$51$	−2.04633	−0.286544
$52$	0.00879083	0.00121907
$53$	−0.124401	−0.0170878	−0.00854390	−	0.999964i	$-0.502720\pi$
$53$	−0.124401	−0.0170878	−0.00854390	+	0.999964i	$0.502720\pi$
$54$	1.33330	0.181439
$55$	0	0
$56$	−2.96300	−0.395948
$57$	5.69421	0.754216
$58$	6.22991	0.818027
$59$	−14.3460	−1.86769	−0.933845	−	0.357679i	$-0.883568\pi$
$59$	−14.3460	−1.86769	−0.933845	+	0.357679i	$0.883568\pi$
$60$	0.194119	0.0250607
$61$	−7.55944	−0.967887	−0.483944	−	0.875099i	$-0.660796\pi$
$61$	−7.55944	−0.967887	−0.483944	+	0.875099i	$0.660796\pi$
$62$	9.97165	1.26640
$63$	1.00000	0.125988
$64$	8.68056	1.08507
$65$	0.0345302	0.00428295
$66$	0	0
$67$	4.85938	0.593668	0.296834	−	0.954929i	$-0.404069\pi$
$67$	4.85938	0.593668	0.296834	+	0.954929i	$0.404069\pi$
$68$	0.454910	0.0551659
$69$	5.97870	0.719751
$70$	−1.16425	−0.139155
$71$	−11.2503	−1.33516	−0.667582	−	0.744536i	$-0.732671\pi$
$71$	−11.2503	−1.33516	−0.667582	+	0.744536i	$0.732671\pi$
$72$	−2.96300	−0.349193
$73$	−0.612954	−0.0717409	−0.0358704	−	0.999356i	$-0.511420\pi$
$73$	−0.612954	−0.0717409	−0.0358704	+	0.999356i	$0.511420\pi$
$74$	15.4269	1.79334
$75$	−4.23750	−0.489305
$76$	−1.26585	−0.145203
$77$	0	0
$78$	−0.0527241	−0.00596983
$79$	0.155227	0.0174644	0.00873220	−	0.999962i	$-0.497220\pi$
$79$	0.155227	0.0174644	0.00873220	+	0.999962i	$0.497220\pi$
$80$	3.06145	0.342281
$81$	1.00000	0.111111
$82$	8.19824	0.905344
$83$	−8.91599	−0.978657	−0.489328	−	0.872100i	$-0.662758\pi$
$83$	−8.91599	−0.978657	−0.489328	+	0.872100i	$0.662758\pi$
$84$	−0.222305	−0.0242555
$85$	1.78688	0.193814
$86$	2.39580	0.258346
$87$	4.67254	0.500949
$88$	0	0
$89$	5.17689	0.548749	0.274374	−	0.961623i	$-0.411529\pi$
$89$	5.17689	0.548749	0.274374	+	0.961623i	$0.411529\pi$
$90$	−1.16425	−0.122723
$91$	−0.0395440	−0.00414534
$92$	−1.32910	−0.138568
$93$	7.47891	0.775527
$94$	8.06345	0.831682
$95$	−4.97224	−0.510141
$96$	1.25149	0.127730
$97$	7.94222	0.806410	0.403205	−	0.915110i	$-0.367896\pi$
$97$	7.94222	0.806410	0.403205	+	0.915110i	$0.367896\pi$
$98$	1.33330	0.134684
$99$	0	0
$100$	0.942018	0.0942018
$101$	9.09560	0.905046	0.452523	−	0.891753i	$-0.350524\pi$
$101$	9.09560	0.905046	0.452523	+	0.891753i	$0.350524\pi$
$102$	−2.72838	−0.270150
$103$	3.43750	0.338707	0.169354	−	0.985555i	$-0.445832\pi$
$103$	3.43750	0.338707	0.169354	+	0.985555i	$0.445832\pi$
$104$	0.117169	0.0114894
$105$	−0.873210	−0.0852166
$106$	−0.165864	−0.0161102
$107$	−3.29161	−0.318212	−0.159106	−	0.987262i	$-0.550861\pi$
$107$	−3.29161	−0.318212	−0.159106	+	0.987262i	$0.550861\pi$
$108$	−0.222305	−0.0213913
$109$	−9.99510	−0.957357	−0.478678	−	0.877990i	$-0.658884\pi$
$109$	−9.99510	−0.957357	−0.478678	+	0.877990i	$0.658884\pi$
$110$	0	0
$111$	11.5704	1.09822
$112$	−3.50597	−0.331283
$113$	4.40261	0.414163	0.207081	−	0.978324i	$-0.433603\pi$
$113$	4.40261	0.414163	0.207081	+	0.978324i	$0.433603\pi$
$114$	7.59210	0.711065
$115$	−5.22067	−0.486830
$116$	−1.03873	−0.0964435
$117$	−0.0395440	−0.00365585
$118$	−19.1275	−1.76083
$119$	−2.04633	−0.187587
$120$	2.58733	0.236190
$121$	0	0
$122$	−10.0790	−0.912512
$123$	6.14882	0.554421
$124$	−1.66260	−0.149306
$125$	8.06628	0.721470
$126$	1.33330	0.118780
$127$	−12.9823	−1.15200	−0.575998	−	0.817451i	$-0.695386\pi$
$127$	−12.9823	−1.15200	−0.575998	+	0.817451i	$0.695386\pi$
$128$	9.07082	0.801755
$129$	1.79689	0.158208
$130$	0.0460393	0.00403791
$131$	−18.1255	−1.58363	−0.791817	−	0.610758i	$-0.790865\pi$
$131$	−18.1255	−1.58363	−0.791817	+	0.610758i	$0.790865\pi$
$132$	0	0
$133$	5.69421	0.493750
$134$	6.47902	0.559702
$135$	−0.873210	−0.0751540
$136$	6.06329	0.519923
$137$	5.20699	0.444863	0.222431	−	0.974948i	$-0.428601\pi$
$137$	5.20699	0.444863	0.222431	+	0.974948i	$0.428601\pi$
$138$	7.97142	0.678572
$139$	18.1482	1.53931	0.769657	−	0.638458i	$-0.220427\pi$
$139$	18.1482	1.53931	0.769657	+	0.638458i	$0.220427\pi$
$140$	0.194119	0.0164061
$141$	6.04773	0.509311
$142$	−15.0000	−1.25878
$143$	0	0
$144$	−3.50597	−0.292164
$145$	−4.08011	−0.338835
$146$	−0.817253	−0.0676364
$147$	1.00000	0.0824786
$148$	−2.57217	−0.211431
$149$	−11.0495	−0.905212	−0.452606	−	0.891711i	$-0.649506\pi$
$149$	−11.0495	−0.905212	−0.452606	+	0.891711i	$0.649506\pi$
$150$	−5.64987	−0.461310
$151$	−15.9314	−1.29648	−0.648240	−	0.761436i	$-0.724495\pi$
$151$	−15.9314	−1.29648	−0.648240	+	0.761436i	$0.724495\pi$
$152$	−16.8720	−1.36850
$153$	−2.04633	−0.165436
$154$	0	0
$155$	−6.53066	−0.524555
$156$	0.00879083	0.000703830 0
$157$	16.0035	1.27722	0.638610	−	0.769531i	$-0.279510\pi$
$157$	16.0035	1.27722	0.638610	+	0.769531i	$0.279510\pi$
$158$	0.206964	0.0164652
$159$	−0.124401	−0.00986564
$160$	−1.09281	−0.0863945
$161$	5.97870	0.471188
$162$	1.33330	0.104754
$163$	22.0034	1.72344	0.861721	−	0.507383i	$-0.169387\pi$
$163$	22.0034	1.72344	0.861721	+	0.507383i	$0.169387\pi$
$164$	−1.36691	−0.106738
$165$	0	0
$166$	−11.8877	−0.922665
$167$	4.72101	0.365323	0.182661	−	0.983176i	$-0.441529\pi$
$167$	4.72101	0.365323	0.182661	+	0.983176i	$0.441529\pi$
$168$	−2.96300	−0.228601
$169$	−12.9984	−0.999880
$170$	2.38245	0.182725
$171$	5.69421	0.435447
$172$	−0.399458	−0.0304584
$173$	9.47572	0.720426	0.360213	−	0.932870i	$-0.382704\pi$
$173$	9.47572	0.720426	0.360213	+	0.932870i	$0.382704\pi$
$174$	6.22991	0.472288
$175$	−4.23750	−0.320325
$176$	0	0
$177$	−14.3460	−1.07831
$178$	6.90235	0.517353
$179$	17.7185	1.32434	0.662170	−	0.749353i	$-0.269636\pi$
$179$	17.7185	1.32434	0.662170	+	0.749353i	$0.269636\pi$
$180$	0.194119	0.0144688
$181$	16.2742	1.20965	0.604826	−	0.796358i	$-0.293243\pi$
$181$	16.2742	1.20965	0.604826	+	0.796358i	$0.293243\pi$
$182$	−0.0527241	−0.00390817
$183$	−7.55944	−0.558810
$184$	−17.7149	−1.30596
$185$	−10.1034	−0.742819
$186$	9.97165	0.731157
$187$	0	0
$188$	−1.34444	−0.0980534
$189$	1.00000	0.0727393
$190$	−6.62950	−0.480954
$191$	6.44604	0.466419	0.233210	−	0.972426i	$-0.425077\pi$
$191$	6.44604	0.466419	0.233210	+	0.972426i	$0.425077\pi$
$192$	8.68056	0.626465
$193$	1.81074	0.130340	0.0651701	−	0.997874i	$-0.479241\pi$
$193$	1.81074	0.130340	0.0651701	+	0.997874i	$0.479241\pi$
$194$	10.5894	0.760273
$195$	0.0345302	0.00247276
$196$	−0.222305	−0.0158789
$197$	6.85772	0.488592	0.244296	−	0.969701i	$-0.421443\pi$
$197$	6.85772	0.488592	0.244296	+	0.969701i	$0.421443\pi$
$198$	0	0
$199$	−5.07400	−0.359687	−0.179843	−	0.983695i	$-0.557559\pi$
$199$	−5.07400	−0.359687	−0.179843	+	0.983695i	$0.557559\pi$
$200$	12.5557	0.887825
$201$	4.85938	0.342754
$202$	12.1272	0.853266
$203$	4.67254	0.327948
$204$	0.454910	0.0318500
$205$	−5.36922	−0.375002
$206$	4.58323	0.319329
$207$	5.97870	0.415549
$208$	0.138640	0.00961296
$209$	0	0
$210$	−1.16425	−0.0803411
$211$	−8.10688	−0.558101	−0.279050	−	0.960276i	$-0.590020\pi$
$211$	−8.10688	−0.558101	−0.279050	+	0.960276i	$0.590020\pi$
$212$	0.0276550	0.00189935
$213$	−11.2503	−0.770857
$214$	−4.38871	−0.300006
$215$	−1.56907	−0.107009
$216$	−2.96300	−0.201607
$217$	7.47891	0.507702
$218$	−13.3265	−0.902583
$219$	−0.612954	−0.0414196
$220$	0	0
$221$	0.0809201	0.00544328
$222$	15.4269	1.03539
$223$	−16.2050	−1.08517	−0.542583	−	0.840002i	$-0.682554\pi$
$223$	−16.2050	−1.08517	−0.542583	+	0.840002i	$0.682554\pi$
$224$	1.25149	0.0836187
$225$	−4.23750	−0.282500
$226$	5.87001	0.390467
$227$	−23.6742	−1.57131	−0.785655	−	0.618665i	$-0.787674\pi$
$227$	−23.6742	−1.57131	−0.785655	+	0.618665i	$0.787674\pi$
$228$	−1.26585	−0.0838330
$229$	10.1567	0.671176	0.335588	−	0.942009i	$-0.391065\pi$
$229$	10.1567	0.671176	0.335588	+	0.942009i	$0.391065\pi$
$230$	−6.96073	−0.458977
$231$	0	0
$232$	−13.8448	−0.908952
$233$	−23.5158	−1.54057	−0.770287	−	0.637697i	$-0.779887\pi$
$233$	−23.5158	−1.54057	−0.770287	+	0.637697i	$0.779887\pi$
$234$	−0.0527241	−0.00344668
$235$	−5.28094	−0.344491
$236$	3.18919	0.207598
$237$	0.155227	0.0100831
$238$	−2.72838	−0.176854
$239$	−7.82554	−0.506192	−0.253096	−	0.967441i	$-0.581449\pi$
$239$	−7.82554	−0.506192	−0.253096	+	0.967441i	$0.581449\pi$
$240$	3.06145	0.197616
$241$	6.86139	0.441981	0.220991	−	0.975276i	$-0.429071\pi$
$241$	6.86139	0.441981	0.220991	+	0.975276i	$0.429071\pi$
$242$	0	0
$243$	1.00000	0.0641500
$244$	1.68050	0.107583
$245$	−0.873210	−0.0557874
$246$	8.19824	0.522701
$247$	−0.225172	−0.0143273
$248$	−22.1600	−1.40716
$249$	−8.91599	−0.565028
$250$	10.7548	0.680193
$251$	−2.56709	−0.162033	−0.0810166	−	0.996713i	$-0.525817\pi$
$251$	−2.56709	−0.162033	−0.0810166	+	0.996713i	$0.525817\pi$
$252$	−0.222305	−0.0140039
$253$	0	0
$254$	−17.3094	−1.08609
$255$	1.78688	0.111899
$256$	−5.26696	−0.329185
$257$	−19.5915	−1.22208	−0.611042	−	0.791598i	$-0.709250\pi$
$257$	−19.5915	−1.22208	−0.611042	+	0.791598i	$0.709250\pi$
$258$	2.39580	0.149156
$259$	11.5704	0.718953
$260$	−0.00767624	−0.000476060 0
$261$	4.67254	0.289223
$262$	−24.1668	−1.49303
$263$	26.5306	1.63595	0.817974	−	0.575255i	$-0.195097\pi$
$263$	26.5306	1.63595	0.817974	+	0.575255i	$0.195097\pi$
$264$	0	0
$265$	0.108628	0.00667298
$266$	7.59210	0.465501
$267$	5.17689	0.316820
$268$	−1.08026	−0.0659876
$269$	−17.1248	−1.04412	−0.522058	−	0.852910i	$-0.674836\pi$
$269$	−17.1248	−1.04412	−0.522058	+	0.852910i	$0.674836\pi$
$270$	−1.16425	−0.0708542
$271$	−5.29554	−0.321681	−0.160840	−	0.986980i	$-0.551420\pi$
$271$	−5.29554	−0.321681	−0.160840	+	0.986980i	$0.551420\pi$
$272$	7.17438	0.435010
$273$	−0.0395440	−0.00239331
$274$	6.94249	0.419411
$275$	0	0
$276$	−1.32910	−0.0800021
$277$	−2.45004	−0.147209	−0.0736044	−	0.997288i	$-0.523450\pi$
$277$	−2.45004	−0.147209	−0.0736044	+	0.997288i	$0.523450\pi$
$278$	24.1971	1.45125
$279$	7.47891	0.447751
$280$	2.58733	0.154622
$281$	−0.301746	−0.0180006	−0.00900031	−	0.999959i	$-0.502865\pi$
$281$	−0.301746	−0.0180006	−0.00900031	+	0.999959i	$0.502865\pi$
$282$	8.06345	0.480172
$283$	−24.0094	−1.42721	−0.713605	−	0.700548i	$-0.752939\pi$
$283$	−24.0094	−1.42721	−0.713605	+	0.700548i	$0.752939\pi$
$284$	2.50100	0.148407
$285$	−4.97224	−0.294530
$286$	0	0
$287$	6.14882	0.362954
$288$	1.25149	0.0737448
$289$	−12.8125	−0.753678
$290$	−5.44002	−0.319449
$291$	7.94222	0.465581
$292$	0.136263	0.00797418
$293$	1.96403	0.114740	0.0573700	−	0.998353i	$-0.481729\pi$
$293$	1.96403	0.114740	0.0573700	+	0.998353i	$0.481729\pi$
$294$	1.33330	0.0777598
$295$	12.5271	0.729354
$296$	−34.2833	−1.99268
$297$	0	0
$298$	−14.7324	−0.853422
$299$	−0.236422	−0.0136726
$300$	0.942018	0.0543874
$301$	1.79689	0.103571
$302$	−21.2414	−1.22230
$303$	9.09560	0.522529
$304$	−19.9637	−1.14500
$305$	6.60098	0.377971
$306$	−2.72838	−0.155971
$307$	−20.0180	−1.14249	−0.571243	−	0.820781i	$-0.693538\pi$
$307$	−20.0180	−1.14249	−0.571243	+	0.820781i	$0.693538\pi$
$308$	0	0
$309$	3.43750	0.195553
$310$	−8.70735	−0.494544
$311$	17.7041	1.00391	0.501954	−	0.864894i	$-0.332615\pi$
$311$	17.7041	1.00391	0.501954	+	0.864894i	$0.332615\pi$
$312$	0.117169	0.00663339
$313$	28.3315	1.60139	0.800697	−	0.599070i	$-0.204463\pi$
$313$	28.3315	1.60139	0.800697	+	0.599070i	$0.204463\pi$
$314$	21.3375	1.20415
$315$	−0.873210	−0.0491998
$316$	−0.0345077	−0.00194121
$317$	−21.9554	−1.23314	−0.616570	−	0.787300i	$-0.711478\pi$
$317$	−21.9554	−1.23314	−0.616570	+	0.787300i	$0.711478\pi$
$318$	−0.165864	−0.00930120
$319$	0	0
$320$	−7.57995	−0.423732
$321$	−3.29161	−0.183720
$322$	7.97142	0.444230
$323$	−11.6522	−0.648347
$324$	−0.222305	−0.0123503
$325$	0.167568	0.00929499
$326$	29.3372	1.62484
$327$	−9.99510	−0.552730
$328$	−18.2190	−1.00598
$329$	6.04773	0.333422
$330$	0	0
$331$	23.1465	1.27225	0.636123	−	0.771587i	$-0.280537\pi$
$331$	23.1465	1.27225	0.636123	+	0.771587i	$0.280537\pi$
$332$	1.98207	0.108780
$333$	11.5704	0.634057
$334$	6.29454	0.344422
$335$	−4.24326	−0.231834
$336$	−3.50597	−0.191266
$337$	−35.0111	−1.90717	−0.953587	−	0.301117i	$-0.902640\pi$
$337$	−35.0111	−1.90717	−0.953587	+	0.301117i	$0.902640\pi$
$338$	−17.3308	−0.942674
$339$	4.40261	0.239117
$340$	−0.397232	−0.0215429
$341$	0	0
$342$	7.59210	0.410534
$343$	1.00000	0.0539949
$344$	−5.32420	−0.287062
$345$	−5.22067	−0.281071
$346$	12.6340	0.679208
$347$	3.75958	0.201825	0.100912	−	0.994895i	$-0.467824\pi$
$347$	3.75958	0.201825	0.100912	+	0.994895i	$0.467824\pi$
$348$	−1.03873	−0.0556817
$349$	12.1740	0.651658	0.325829	−	0.945429i	$-0.394357\pi$
$349$	12.1740	0.651658	0.325829	+	0.945429i	$0.394357\pi$
$350$	−5.64987	−0.301998
$351$	−0.0395440	−0.00211070
$352$	0	0
$353$	−5.79059	−0.308202	−0.154101	−	0.988055i	$-0.549248\pi$
$353$	−5.79059	−0.308202	−0.154101	+	0.988055i	$0.549248\pi$
$354$	−19.1275	−1.01662
$355$	9.82387	0.521397
$356$	−1.15085	−0.0609948
$357$	−2.04633	−0.108303
$358$	23.6241	1.24857
$359$	−5.76086	−0.304046	−0.152023	−	0.988377i	$-0.548579\pi$
$359$	−5.76086	−0.304046	−0.152023	+	0.988377i	$0.548579\pi$
$360$	2.58733	0.136364
$361$	13.4240	0.706525
$362$	21.6984	1.14044
$363$	0	0
$364$	0.00879083	0.000460765 0
$365$	0.535238	0.0280156
$366$	−10.0790	−0.526839
$367$	14.2580	0.744263	0.372132	−	0.928180i	$-0.378627\pi$
$367$	14.2580	0.744263	0.372132	+	0.928180i	$0.378627\pi$
$368$	−20.9612	−1.09268
$369$	6.14882	0.320095
$370$	−13.4709	−0.700320
$371$	−0.124401	−0.00645858
$372$	−1.66260	−0.0862017
$373$	−32.2223	−1.66841	−0.834203	−	0.551458i	$-0.814072\pi$
$373$	−32.2223	−1.66841	−0.834203	+	0.551458i	$0.814072\pi$
$374$	0	0
$375$	8.06628	0.416541
$376$	−17.9195	−0.924125
$377$	−0.184771	−0.00951619
$378$	1.33330	0.0685777
$379$	−28.5774	−1.46792	−0.733960	−	0.679193i	$-0.762330\pi$
$379$	−28.5774	−1.46792	−0.733960	+	0.679193i	$0.762330\pi$
$380$	1.10535	0.0567035
$381$	−12.9823	−0.665105
$382$	8.59452	0.439734
$383$	−20.1613	−1.03019	−0.515097	−	0.857132i	$-0.672244\pi$
$383$	−20.1613	−1.03019	−0.515097	+	0.857132i	$0.672244\pi$
$384$	9.07082	0.462894
$385$	0	0
$386$	2.41427	0.122883
$387$	1.79689	0.0913412
$388$	−1.76559	−0.0896345
$389$	−16.5608	−0.839663	−0.419832	−	0.907602i	$-0.637911\pi$
$389$	−16.5608	−0.839663	−0.419832	+	0.907602i	$0.637911\pi$
$390$	0.0460393	0.00233129
$391$	−12.2344	−0.618721
$392$	−2.96300	−0.149654
$393$	−18.1255	−0.914312
$394$	9.14342	0.460639
$395$	−0.135546	−0.00682005
$396$	0	0
$397$	30.9920	1.55545	0.777723	−	0.628607i	$-0.216375\pi$
$397$	30.9920	1.55545	0.777723	+	0.628607i	$0.216375\pi$
$398$	−6.76518	−0.339108
$399$	5.69421	0.285067
$400$	14.8566	0.742828
$401$	3.48264	0.173915	0.0869574	−	0.996212i	$-0.472286\pi$
$401$	3.48264	0.173915	0.0869574	+	0.996212i	$0.472286\pi$
$402$	6.47902	0.323144
$403$	−0.295746	−0.0147322
$404$	−2.02200	−0.100598
$405$	−0.873210	−0.0433902
$406$	6.22991	0.309185
$407$	0	0
$408$	6.06329	0.300177
$409$	26.5883	1.31471	0.657353	−	0.753583i	$-0.271676\pi$
$409$	26.5883	1.31471	0.657353	+	0.753583i	$0.271676\pi$
$410$	−7.15879	−0.353547
$411$	5.20699	0.256842
$412$	−0.764174	−0.0376481
$413$	−14.3460	−0.705920
$414$	7.97142	0.391774
$415$	7.78553	0.382177
$416$	−0.0494889	−0.00242639
$417$	18.1482	0.888723
$418$	0	0
$419$	29.1491	1.42402	0.712012	−	0.702167i	$-0.247784\pi$
$419$	29.1491	1.42402	0.712012	+	0.702167i	$0.247784\pi$
$420$	0.194119	0.00947204
$421$	−19.9909	−0.974297	−0.487148	−	0.873319i	$-0.661963\pi$
$421$	−19.9909	−0.974297	−0.487148	+	0.873319i	$0.661963\pi$
$422$	−10.8089	−0.526170
$423$	6.04773	0.294051
$424$	0.368601	0.0179008
$425$	8.67134	0.420622
$426$	−15.0000	−0.726754
$427$	−7.55944	−0.365827
$428$	0.731740	0.0353700
$429$	0	0
$430$	−2.09204	−0.100887
$431$	−16.9285	−0.815417	−0.407709	−	0.913112i	$-0.633672\pi$
$431$	−16.9285	−0.815417	−0.407709	+	0.913112i	$0.633672\pi$
$432$	−3.50597	−0.168681
$433$	−8.55148	−0.410958	−0.205479	−	0.978662i	$-0.565875\pi$
$433$	−8.55148	−0.410958	−0.205479	+	0.978662i	$0.565875\pi$
$434$	9.97165	0.478654
$435$	−4.08011	−0.195626
$436$	2.22196	0.106413
$437$	34.0440	1.62854
$438$	−0.817253	−0.0390499
$439$	33.9408	1.61990	0.809952	−	0.586496i	$-0.199493\pi$
$439$	33.9408	1.61990	0.809952	+	0.586496i	$0.199493\pi$
$440$	0	0
$441$	1.00000	0.0476190
$442$	0.107891	0.00513185
$443$	−35.1601	−1.67051	−0.835254	−	0.549864i	$-0.814680\pi$
$443$	−35.1601	−1.67051	−0.835254	+	0.549864i	$0.814680\pi$
$444$	−2.57217	−0.122070
$445$	−4.52051	−0.214293
$446$	−21.6061	−1.02308
$447$	−11.0495	−0.522624
$448$	8.68056	0.410118
$449$	−1.92800	−0.0909879	−0.0454939	−	0.998965i	$-0.514486\pi$
$449$	−1.92800	−0.0909879	−0.0454939	+	0.998965i	$0.514486\pi$
$450$	−5.64987	−0.266338
$451$	0	0
$452$	−0.978723	−0.0460352
$453$	−15.9314	−0.748523
$454$	−31.5648	−1.48141
$455$	0.0345302	0.00161880
$456$	−16.8720	−0.790102
$457$	7.65166	0.357930	0.178965	−	0.983855i	$-0.442725\pi$
$457$	7.65166	0.357930	0.178965	+	0.983855i	$0.442725\pi$
$458$	13.5420	0.632776
$459$	−2.04633	−0.0955146
$460$	1.16058	0.0541123
$461$	−40.7525	−1.89803	−0.949017	−	0.315224i	$-0.897920\pi$
$461$	−40.7525	−1.89803	−0.949017	+	0.315224i	$0.897920\pi$
$462$	0	0
$463$	−8.37407	−0.389176	−0.194588	−	0.980885i	$-0.562337\pi$
$463$	−8.37407	−0.389176	−0.194588	+	0.980885i	$0.562337\pi$
$464$	−16.3818	−0.760505
$465$	−6.53066	−0.302852
$466$	−31.3537	−1.45243
$467$	9.49614	0.439429	0.219714	−	0.975564i	$-0.429487\pi$
$467$	9.49614	0.439429	0.219714	+	0.975564i	$0.429487\pi$
$468$	0.00879083	0.000406356 0
$469$	4.85938	0.224385
$470$	−7.04109	−0.324781
$471$	16.0035	0.737403
$472$	42.5072	1.95655
$473$	0	0
$474$	0.206964	0.00950619
$475$	−24.1292	−1.10712
$476$	0.454910	0.0208507
$477$	−0.124401	−0.00569593
$478$	−10.4338	−0.477232
$479$	36.2983	1.65851	0.829256	−	0.558869i	$-0.188765\pi$
$479$	36.2983	1.65851	0.829256	+	0.558869i	$0.188765\pi$
$480$	−1.09281	−0.0498799
$481$	−0.457542	−0.0208621
$482$	9.14831	0.416694
$483$	5.97870	0.272040
$484$	0	0
$485$	−6.93523	−0.314912
$486$	1.33330	0.0604798
$487$	5.36736	0.243218	0.121609	−	0.992578i	$-0.461195\pi$
$487$	5.36736	0.243218	0.121609	+	0.992578i	$0.461195\pi$
$488$	22.3987	1.01394
$489$	22.0034	0.995030
$490$	−1.16425	−0.0525956
$491$	−23.0614	−1.04075	−0.520373	−	0.853939i	$-0.674207\pi$
$491$	−23.0614	−1.04075	−0.520373	+	0.853939i	$0.674207\pi$
$492$	−1.36691	−0.0616252
$493$	−9.56156	−0.430631
$494$	−0.300222	−0.0135076
$495$	0	0
$496$	−26.2208	−1.17735
$497$	−11.2503	−0.504644
$498$	−11.8877	−0.532701
$499$	33.1392	1.48351	0.741756	−	0.670670i	$-0.233993\pi$
$499$	33.1392	1.48351	0.741756	+	0.670670i	$0.233993\pi$
$500$	−1.79318	−0.0801932
$501$	4.72101	0.210919
$502$	−3.42270	−0.152763
$503$	18.1118	0.807563	0.403782	−	0.914855i	$-0.367696\pi$
$503$	18.1118	0.807563	0.403782	+	0.914855i	$0.367696\pi$
$504$	−2.96300	−0.131983
$505$	−7.94237	−0.353431
$506$	0	0
$507$	−12.9984	−0.577281
$508$	2.88604	0.128047
$509$	−15.5919	−0.691100	−0.345550	−	0.938400i	$-0.612308\pi$
$509$	−15.5919	−0.691100	−0.345550	+	0.938400i	$0.612308\pi$
$510$	2.38245	0.105497
$511$	−0.612954	−0.0271155
$512$	−25.1641	−1.11211
$513$	5.69421	0.251405
$514$	−26.1214	−1.15217
$515$	−3.00166	−0.132269
$516$	−0.399458	−0.0175852
$517$	0	0
$518$	15.4269	0.677819
$519$	9.47572	0.415938
$520$	−0.102313	−0.00448673
$521$	−15.4692	−0.677716	−0.338858	−	0.940838i	$-0.610041\pi$
$521$	−15.4692	−0.677716	−0.338858	+	0.940838i	$0.610041\pi$
$522$	6.22991	0.272676
$523$	17.3464	0.758504	0.379252	−	0.925293i	$-0.376181\pi$
$523$	17.3464	0.758504	0.379252	+	0.925293i	$0.376181\pi$
$524$	4.02940	0.176025
$525$	−4.23750	−0.184940
$526$	35.3733	1.54235
$527$	−15.3043	−0.666667
$528$	0	0
$529$	12.7449	0.554126
$530$	0.144834	0.00629120
$531$	−14.3460	−0.622563
$532$	−1.26585	−0.0548816
$533$	−0.243149	−0.0105320
$534$	6.90235	0.298694
$535$	2.87427	0.124265
$536$	−14.3984	−0.621914
$537$	17.7185	0.764608
$538$	−22.8325	−0.984380
$539$	0	0
$540$	0.194119	0.00835355
$541$	−30.2945	−1.30246	−0.651232	−	0.758879i	$-0.725748\pi$
$541$	−30.2945	−1.30246	−0.651232	+	0.758879i	$0.725748\pi$
$542$	−7.06055	−0.303277
$543$	16.2742	0.698393
$544$	−2.56096	−0.109800
$545$	8.72782	0.373859
$546$	−0.0527241	−0.00225638
$547$	30.4490	1.30191	0.650954	−	0.759118i	$-0.274369\pi$
$547$	30.4490	1.30191	0.650954	+	0.759118i	$0.274369\pi$
$548$	−1.15754	−0.0494476
$549$	−7.55944	−0.322629
$550$	0	0
$551$	26.6064	1.13347
$552$	−17.7149	−0.753997
$553$	0.155227	0.00660092
$554$	−3.26665	−0.138787
$555$	−10.1034	−0.428867
$556$	−4.03445	−0.171099
$557$	−7.17456	−0.303996	−0.151998	−	0.988381i	$-0.548571\pi$
$557$	−7.17456	−0.303996	−0.151998	+	0.988381i	$0.548571\pi$
$558$	9.97165	0.422134
$559$	−0.0710563	−0.00300536
$560$	3.06145	0.129370
$561$	0	0
$562$	−0.402318	−0.0169708
$563$	−9.01364	−0.379880	−0.189940	−	0.981796i	$-0.560829\pi$
$563$	−9.01364	−0.379880	−0.189940	+	0.981796i	$0.560829\pi$
$564$	−1.34444	−0.0566112
$565$	−3.84441	−0.161735
$566$	−32.0118	−1.34556
$567$	1.00000	0.0419961
$568$	33.3347	1.39869
$569$	−7.45999	−0.312739	−0.156370	−	0.987699i	$-0.549979\pi$
$569$	−7.45999	−0.312739	−0.156370	+	0.987699i	$0.549979\pi$
$570$	−6.62950	−0.277679
$571$	37.5921	1.57318	0.786590	−	0.617475i	$-0.211844\pi$
$571$	37.5921	1.57318	0.786590	+	0.617475i	$0.211844\pi$
$572$	0	0
$573$	6.44604	0.269287
$574$	8.19824	0.342188
$575$	−25.3348	−1.05653
$576$	8.68056	0.361690
$577$	−12.1230	−0.504688	−0.252344	−	0.967638i	$-0.581201\pi$
$577$	−12.1230	−0.504688	−0.252344	+	0.967638i	$0.581201\pi$
$578$	−17.0830	−0.710558
$579$	1.81074	0.0752519
$580$	0.907029	0.0376623
$581$	−8.91599	−0.369897
$582$	10.5894	0.438944
$583$	0	0
$584$	1.81619	0.0751543
$585$	0.0345302	0.00142765
$586$	2.61865	0.108175
$587$	−1.28073	−0.0528615	−0.0264307	−	0.999651i	$-0.508414\pi$
$587$	−1.28073	−0.0528615	−0.0264307	+	0.999651i	$0.508414\pi$
$588$	−0.222305	−0.00916770
$589$	42.5865	1.75474
$590$	16.7024	0.687626
$591$	6.85772	0.282089
$592$	−40.5656	−1.66724
$593$	24.7324	1.01564	0.507819	−	0.861464i	$-0.330452\pi$
$593$	24.7324	1.01564	0.507819	+	0.861464i	$0.330452\pi$
$594$	0	0
$595$	1.78688	0.0732548
$596$	2.45636	0.100617
$597$	−5.07400	−0.207665
$598$	−0.315222	−0.0128904
$599$	−27.9003	−1.13998	−0.569988	−	0.821653i	$-0.693052\pi$
$599$	−27.9003	−1.13998	−0.569988	+	0.821653i	$0.693052\pi$
$600$	12.5557	0.512586
$601$	34.4256	1.40425	0.702124	−	0.712055i	$-0.252235\pi$
$601$	34.4256	1.40425	0.702124	+	0.712055i	$0.252235\pi$
$602$	2.39580	0.0976456
$603$	4.85938	0.197889
$604$	3.54163	0.144107
$605$	0	0
$606$	12.1272	0.492633
$607$	26.4243	1.07253	0.536264	−	0.844050i	$-0.319835\pi$
$607$	26.4243	1.07253	0.536264	+	0.844050i	$0.319835\pi$
$608$	7.12624	0.289007
$609$	4.67254	0.189341
$610$	8.80111	0.356346
$611$	−0.239152	−0.00967503
$612$	0.454910	0.0183886
$613$	39.6007	1.59946	0.799729	−	0.600361i	$-0.204976\pi$
$613$	39.6007	1.59946	0.799729	+	0.600361i	$0.204976\pi$
$614$	−26.6900	−1.07712
$615$	−5.36922	−0.216508
$616$	0	0
$617$	17.0640	0.686971	0.343486	−	0.939158i	$-0.388392\pi$
$617$	17.0640	0.686971	0.343486	+	0.939158i	$0.388392\pi$
$618$	4.58323	0.184364
$619$	29.2807	1.17689	0.588445	−	0.808538i	$-0.299741\pi$
$619$	29.2807	1.17689	0.588445	+	0.808538i	$0.299741\pi$
$620$	1.45180	0.0583056
$621$	5.97870	0.239917
$622$	23.6049	0.946471
$623$	5.17689	0.207408
$624$	0.138640	0.00555005
$625$	14.1440	0.565758
$626$	37.7745	1.50977
$627$	0	0
$628$	−3.55766	−0.141966
$629$	−23.6770	−0.944062
$630$	−1.16425	−0.0463850
$631$	−40.2944	−1.60410	−0.802048	−	0.597260i	$-0.796256\pi$
$631$	−40.2944	−1.60410	−0.802048	+	0.597260i	$0.796256\pi$
$632$	−0.459938	−0.0182954
$633$	−8.10688	−0.322220
$634$	−29.2732	−1.16259
$635$	11.3363	0.449867
$636$	0.0276550	0.00109659
$637$	−0.0395440	−0.00156679
$638$	0	0
$639$	−11.2503	−0.445055
$640$	−7.92074	−0.313095
$641$	−12.5572	−0.495980	−0.247990	−	0.968763i	$-0.579770\pi$
$641$	−12.5572	−0.495980	−0.247990	+	0.968763i	$0.579770\pi$
$642$	−4.38871	−0.173208
$643$	−4.13705	−0.163149	−0.0815747	−	0.996667i	$-0.525995\pi$
$643$	−4.13705	−0.163149	−0.0815747	+	0.996667i	$0.525995\pi$
$644$	−1.32910	−0.0523737
$645$	−1.56907	−0.0617819
$646$	−15.5359	−0.611254
$647$	−37.6088	−1.47856	−0.739278	−	0.673400i	$-0.764833\pi$
$647$	−37.6088	−1.47856	−0.739278	+	0.673400i	$0.764833\pi$
$648$	−2.96300	−0.116398
$649$	0	0
$650$	0.223419	0.00876320
$651$	7.47891	0.293122
$652$	−4.89147	−0.191565
$653$	6.02137	0.235634	0.117817	−	0.993035i	$-0.462410\pi$
$653$	6.02137	0.235634	0.117817	+	0.993035i	$0.462410\pi$
$654$	−13.3265	−0.521107
$655$	15.8274	0.618428
$656$	−21.5576	−0.841682
$657$	−0.612954	−0.0239136
$658$	8.06345	0.314346
$659$	38.6192	1.50439	0.752195	−	0.658940i	$-0.228995\pi$
$659$	38.6192	1.50439	0.752195	+	0.658940i	$0.228995\pi$
$660$	0	0
$661$	43.0833	1.67575	0.837874	−	0.545864i	$-0.183798\pi$
$661$	43.0833	1.67575	0.837874	+	0.545864i	$0.183798\pi$
$662$	30.8613	1.19946
$663$	0.0809201	0.00314268
$664$	26.4181	1.02522
$665$	−4.97224	−0.192815
$666$	15.4269	0.597780
$667$	27.9357	1.08168
$668$	−1.04950	−0.0406066
$669$	−16.2050	−0.626521
$670$	−5.65755	−0.218570
$671$	0	0
$672$	1.25149	0.0482773
$673$	21.0171	0.810149	0.405075	−	0.914284i	$-0.367246\pi$
$673$	21.0171	0.810149	0.405075	+	0.914284i	$0.367246\pi$
$674$	−46.6803	−1.79806
$675$	−4.23750	−0.163102
$676$	2.88962	0.111139
$677$	23.8886	0.918115	0.459057	−	0.888407i	$-0.348187\pi$
$677$	23.8886	0.918115	0.459057	+	0.888407i	$0.348187\pi$
$678$	5.87001	0.225437
$679$	7.94222	0.304794
$680$	−5.29453	−0.203036
$681$	−23.6742	−0.907196
$682$	0	0
$683$	−13.5672	−0.519134	−0.259567	−	0.965725i	$-0.583580\pi$
$683$	−13.5672	−0.519134	−0.259567	+	0.965725i	$0.583580\pi$
$684$	−1.26585	−0.0484010
$685$	−4.54679	−0.173724
$686$	1.33330	0.0509057
$687$	10.1567	0.387504
$688$	−6.29985	−0.240180
$689$	0.00491932	0.000187411 0
$690$	−6.96073	−0.264990
$691$	−4.91171	−0.186850	−0.0934251	−	0.995626i	$-0.529782\pi$
$691$	−4.91171	−0.186850	−0.0934251	+	0.995626i	$0.529782\pi$
$692$	−2.10650	−0.0800771
$693$	0	0
$694$	5.01266	0.190278
$695$	−15.8472	−0.601120
$696$	−13.8448	−0.524784
$697$	−12.5825	−0.476597
$698$	16.2316	0.614375
$699$	−23.5158	−0.889451
$700$	0.942018	0.0356049
$701$	−36.9242	−1.39461	−0.697304	−	0.716775i	$-0.745617\pi$
$701$	−36.9242	−1.39461	−0.697304	+	0.716775i	$0.745617\pi$
$702$	−0.0527241	−0.00198994
$703$	65.8845	2.48488
$704$	0	0
$705$	−5.28094	−0.198892
$706$	−7.72061	−0.290569
$707$	9.09560	0.342075
$708$	3.18919	0.119857
$709$	0.489376	0.0183789	0.00918945	−	0.999958i	$-0.497075\pi$
$709$	0.489376	0.0183789	0.00918945	+	0.999958i	$0.497075\pi$
$710$	13.0982	0.491566
$711$	0.155227	0.00582146
$712$	−15.3391	−0.574858
$713$	44.7142	1.67456
$714$	−2.72838	−0.102107
$715$	0	0
$716$	−3.93890	−0.147204
$717$	−7.82554	−0.292250
$718$	−7.68096	−0.286651
$719$	10.1392	0.378127	0.189064	−	0.981965i	$-0.439455\pi$
$719$	10.1392	0.378127	0.189064	+	0.981965i	$0.439455\pi$
$720$	3.06145	0.114094
$721$	3.43750	0.128019
$722$	17.8982	0.666103
$723$	6.86139	0.255178
$724$	−3.61784	−0.134456
$725$	−19.7999	−0.735350
$726$	0	0
$727$	−10.5834	−0.392516	−0.196258	−	0.980552i	$-0.562879\pi$
$727$	−10.5834	−0.392516	−0.196258	+	0.980552i	$0.562879\pi$
$728$	0.117169	0.00434257
$729$	1.00000	0.0370370
$730$	0.713634	0.0264128
$731$	−3.67704	−0.136000
$732$	1.68050	0.0621131
$733$	−12.5752	−0.464475	−0.232238	−	0.972659i	$-0.574605\pi$
$733$	−12.5752	−0.464475	−0.232238	+	0.972659i	$0.574605\pi$
$734$	19.0103	0.701682
$735$	−0.873210	−0.0322089
$736$	7.48229	0.275801
$737$	0	0
$738$	8.19824	0.301781
$739$	1.39740	0.0514043	0.0257022	−	0.999670i	$-0.491818\pi$
$739$	1.39740	0.0514043	0.0257022	+	0.999670i	$0.491818\pi$
$740$	2.24604	0.0825662
$741$	−0.225172	−0.00827189
$742$	−0.165864	−0.00608907
$743$	−24.1170	−0.884767	−0.442383	−	0.896826i	$-0.645867\pi$
$743$	−24.1170	−0.884767	−0.442383	+	0.896826i	$0.645867\pi$
$744$	−22.1600	−0.812427
$745$	9.64856	0.353496
$746$	−42.9620	−1.57295
$747$	−8.91599	−0.326219
$748$	0	0
$749$	−3.29161	−0.120273
$750$	10.7548	0.392710
$751$	−19.2248	−0.701523	−0.350762	−	0.936465i	$-0.614077\pi$
$751$	−19.2248	−0.701523	−0.350762	+	0.936465i	$0.614077\pi$
$752$	−21.2032	−0.773200
$753$	−2.56709	−0.0935499
$754$	−0.246355	−0.00897174
$755$	13.9115	0.506290
$756$	−0.222305	−0.00808515
$757$	−42.4814	−1.54401	−0.772006	−	0.635615i	$-0.780747\pi$
$757$	−42.4814	−1.54401	−0.772006	+	0.635615i	$0.780747\pi$
$758$	−38.1023	−1.38394
$759$	0	0
$760$	14.7328	0.534414
$761$	−14.7018	−0.532939	−0.266470	−	0.963843i	$-0.585857\pi$
$761$	−14.7018	−0.532939	−0.266470	+	0.963843i	$0.585857\pi$
$762$	−17.3094	−0.627052
$763$	−9.99510	−0.361847
$764$	−1.43299	−0.0518437
$765$	1.78688	0.0646047
$766$	−26.8811	−0.971254
$767$	0.567298	0.0204839
$768$	−5.26696	−0.190055
$769$	45.4931	1.64052	0.820262	−	0.571988i	$-0.193828\pi$
$769$	45.4931	1.64052	0.820262	+	0.571988i	$0.193828\pi$
$770$	0	0
$771$	−19.5915	−0.705571
$772$	−0.402537	−0.0144876
$773$	6.05381	0.217741	0.108870	−	0.994056i	$-0.465277\pi$
$773$	6.05381	0.217741	0.108870	+	0.994056i	$0.465277\pi$
$774$	2.39580	0.0861153
$775$	−31.6919	−1.13841
$776$	−23.5328	−0.844779
$777$	11.5704	0.415087
$778$	−22.0805	−0.791624
$779$	35.0127	1.25446
$780$	−0.00767624	−0.000274854 0
$781$	0	0
$782$	−16.3122	−0.583322
$783$	4.67254	0.166983
$784$	−3.50597	−0.125213
$785$	−13.9744	−0.498769
$786$	−24.1668	−0.862002
$787$	−54.7630	−1.95209	−0.976046	−	0.217566i	$-0.930188\pi$
$787$	−54.7630	−1.95209	−0.976046	+	0.217566i	$0.930188\pi$
$788$	−1.52451	−0.0543083
$789$	26.5306	0.944515
$790$	−0.180723	−0.00642985
$791$	4.40261	0.156539
$792$	0	0
$793$	0.298931	0.0106153
$794$	41.3218	1.46645
$795$	0.108628	0.00385265
$796$	1.12798	0.0399801
$797$	−43.2922	−1.53349	−0.766744	−	0.641953i	$-0.778124\pi$
$797$	−43.2922	−1.53349	−0.766744	+	0.641953i	$0.778124\pi$
$798$	7.59210	0.268757
$799$	−12.3757	−0.437819
$800$	−5.30319	−0.187496
$801$	5.17689	0.182916
$802$	4.64342	0.163965
$803$	0	0
$804$	−1.08026	−0.0380980
$805$	−5.22067	−0.184004
$806$	−0.394319	−0.0138893
$807$	−17.1248	−0.602821
$808$	−26.9503	−0.948108
$809$	15.5173	0.545559	0.272779	−	0.962077i	$-0.412057\pi$
$809$	15.5173	0.545559	0.272779	+	0.962077i	$0.412057\pi$
$810$	−1.16425	−0.0409077
$811$	−41.4421	−1.45523	−0.727615	−	0.685986i	$-0.759371\pi$
$811$	−41.4421	−1.45523	−0.727615	+	0.685986i	$0.759371\pi$
$812$	−1.03873	−0.0364522
$813$	−5.29554	−0.185723
$814$	0	0
$815$	−19.2136	−0.673024
$816$	7.17438	0.251153
$817$	10.2319	0.357968
$818$	35.4502	1.23949
$819$	−0.0395440	−0.00138178
$820$	1.19360	0.0416824
$821$	40.0922	1.39923	0.699613	−	0.714522i	$-0.253356\pi$
$821$	40.0922	1.39923	0.699613	+	0.714522i	$0.253356\pi$
$822$	6.94249	0.242147
$823$	4.23033	0.147460	0.0737301	−	0.997278i	$-0.476510\pi$
$823$	4.23033	0.147460	0.0737301	+	0.997278i	$0.476510\pi$
$824$	−10.1853	−0.354823
$825$	0	0
$826$	−19.1275	−0.665532
$827$	−47.6889	−1.65830	−0.829152	−	0.559023i	$-0.811176\pi$
$827$	−47.6889	−1.65830	−0.829152	+	0.559023i	$0.811176\pi$
$828$	−1.32910	−0.0461893
$829$	4.68523	0.162725	0.0813624	−	0.996685i	$-0.474073\pi$
$829$	4.68523	0.162725	0.0813624	+	0.996685i	$0.474073\pi$
$830$	10.3805	0.360311
$831$	−2.45004	−0.0849911
$832$	−0.343264	−0.0119005
$833$	−2.04633	−0.0709012
$834$	24.1971	0.837877
$835$	−4.12244	−0.142663
$836$	0	0
$837$	7.47891	0.258509
$838$	38.8645	1.34255
$839$	−6.93707	−0.239494	−0.119747	−	0.992804i	$-0.538208\pi$
$839$	−6.93707	−0.239494	−0.119747	+	0.992804i	$0.538208\pi$
$840$	2.58733	0.0892712
$841$	−7.16738	−0.247151
$842$	−26.6539	−0.918555
$843$	−0.301746	−0.0103927
$844$	1.80220	0.0620343
$845$	11.3504	0.390465
$846$	8.06345	0.277227
$847$	0	0
$848$	0.436146	0.0149773
$849$	−24.0094	−0.824000
$850$	11.5615	0.396557
$851$	69.1763	2.37133
$852$	2.50100	0.0856827
$853$	6.23883	0.213613	0.106807	−	0.994280i	$-0.465937\pi$
$853$	6.23883	0.213613	0.106807	+	0.994280i	$0.465937\pi$
$854$	−10.0790	−0.344897
$855$	−4.97224	−0.170047
$856$	9.75304	0.333352
$857$	−26.5684	−0.907559	−0.453779	−	0.891114i	$-0.649925\pi$
$857$	−26.5684	−0.907559	−0.453779	+	0.891114i	$0.649925\pi$
$858$	0	0
$859$	44.6475	1.52335	0.761677	−	0.647957i	$-0.224377\pi$
$859$	44.6475	1.52335	0.761677	+	0.647957i	$0.224377\pi$
$860$	0.348811	0.0118944
$861$	6.14882	0.209551
$862$	−22.5708	−0.768765
$863$	−21.2309	−0.722707	−0.361353	−	0.932429i	$-0.617685\pi$
$863$	−21.2309	−0.722707	−0.361353	+	0.932429i	$0.617685\pi$
$864$	1.25149	0.0425766
$865$	−8.27430	−0.281335
$866$	−11.4017	−0.387446
$867$	−12.8125	−0.435136
$868$	−1.66260	−0.0564323
$869$	0	0
$870$	−5.44002	−0.184434
$871$	−0.192159	−0.00651107
$872$	29.6155	1.00291
$873$	7.94222	0.268803
$874$	45.3909	1.53537
$875$	8.06628	0.272690
$876$	0.136263	0.00460389
$877$	−9.63512	−0.325355	−0.162677	−	0.986679i	$-0.552013\pi$
$877$	−9.63512	−0.325355	−0.162677	+	0.986679i	$0.552013\pi$
$878$	45.2533	1.52722
$879$	1.96403	0.0662452
$880$	0	0
$881$	−38.9952	−1.31378	−0.656891	−	0.753985i	$-0.728129\pi$
$881$	−38.9952	−1.31378	−0.656891	+	0.753985i	$0.728129\pi$
$882$	1.33330	0.0448946
$883$	14.8304	0.499081	0.249541	−	0.968364i	$-0.419720\pi$
$883$	14.8304	0.499081	0.249541	+	0.968364i	$0.419720\pi$
$884$	−0.0179889	−0.000605034 0
$885$	12.5271	0.421093
$886$	−46.8791	−1.57493
$887$	17.6091	0.591254	0.295627	−	0.955303i	$-0.404471\pi$
$887$	17.6091	0.591254	0.295627	+	0.955303i	$0.404471\pi$
$888$	−34.2833	−1.15047
$889$	−12.9823	−0.435413
$890$	−6.02721	−0.202032
$891$	0	0
$892$	3.60245	0.120619
$893$	34.4370	1.15239
$894$	−14.7324	−0.492724
$895$	−15.4720	−0.517170
$896$	9.07082	0.303035
$897$	−0.236422	−0.00789390
$898$	−2.57060	−0.0857822
$899$	34.9455	1.16550
$900$	0.942018	0.0314006
$901$	0.254566	0.00848081
$902$	0	0
$903$	1.79689	0.0597968
$904$	−13.0450	−0.433869
$905$	−14.2108	−0.472383
$906$	−21.2414	−0.705698
$907$	46.0126	1.52782	0.763911	−	0.645322i	$-0.223277\pi$
$907$	46.0126	1.52782	0.763911	+	0.645322i	$0.223277\pi$
$908$	5.26289	0.174655
$909$	9.09560	0.301682
$910$	0.0460393	0.00152619
$911$	19.5000	0.646064	0.323032	−	0.946388i	$-0.395298\pi$
$911$	19.5000	0.646064	0.323032	+	0.946388i	$0.395298\pi$
$912$	−19.9637	−0.661065
$913$	0	0
$914$	10.2020	0.337451
$915$	6.60098	0.218222
$916$	−2.25789	−0.0746029
$917$	−18.1255	−0.598558
$918$	−2.72838	−0.0900499
$919$	−11.7377	−0.387191	−0.193596	−	0.981081i	$-0.562015\pi$
$919$	−11.7377	−0.387191	−0.193596	+	0.981081i	$0.562015\pi$
$920$	15.4689	0.509993
$921$	−20.0180	−0.659614
$922$	−54.3354	−1.78944
$923$	0.444882	0.0146435
$924$	0	0
$925$	−49.0298	−1.61209
$926$	−11.1652	−0.366910
$927$	3.43750	0.112902
$928$	5.84764	0.191958
$929$	35.6903	1.17096	0.585480	−	0.810687i	$-0.300906\pi$
$929$	35.6903	1.17096	0.585480	+	0.810687i	$0.300906\pi$
$930$	−8.70735	−0.285525
$931$	5.69421	0.186620
$932$	5.22769	0.171239
$933$	17.7041	0.579606
$934$	12.6612	0.414288
$935$	0	0
$936$	0.117169	0.00382979
$937$	−35.3541	−1.15497	−0.577485	−	0.816402i	$-0.695966\pi$
$937$	−35.3541	−1.15497	−0.577485	+	0.816402i	$0.695966\pi$
$938$	6.47902	0.211548
$939$	28.3315	0.924565
$940$	1.17398	0.0382910
$941$	30.5431	0.995678	0.497839	−	0.867270i	$-0.334127\pi$
$941$	30.5431	0.995678	0.497839	+	0.867270i	$0.334127\pi$
$942$	21.3375	0.695214
$943$	36.7620	1.19713
$944$	50.2966	1.63702
$945$	−0.873210	−0.0284055
$946$	0	0
$947$	38.9527	1.26579	0.632897	−	0.774236i	$-0.281866\pi$
$947$	38.9527	1.26579	0.632897	+	0.774236i	$0.281866\pi$
$948$	−0.0345077	−0.00112076
$949$	0.0242387	0.000786821 0
$950$	−32.1715	−1.04378
$951$	−21.9554	−0.711953
$952$	6.06329	0.196512
$953$	−35.2846	−1.14298	−0.571490	−	0.820609i	$-0.693634\pi$
$953$	−35.2846	−1.14298	−0.571490	+	0.820609i	$0.693634\pi$
$954$	−0.165864	−0.00537005
$955$	−5.62875	−0.182142
$956$	1.73966	0.0562645
$957$	0	0
$958$	48.3966	1.56362
$959$	5.20699	0.168142
$960$	−7.57995	−0.244642
$961$	24.9341	0.804326
$962$	−0.610042	−0.0196685
$963$	−3.29161	−0.106071
$964$	−1.52532	−0.0491273
$965$	−1.58116	−0.0508993
$966$	7.97142	0.256476
$967$	−31.4791	−1.01230	−0.506150	−	0.862445i	$-0.668932\pi$
$967$	−31.4791	−1.01230	−0.506150	+	0.862445i	$0.668932\pi$
$968$	0	0
$969$	−11.6522	−0.374324
$970$	−9.24675	−0.296895
$971$	−34.4771	−1.10642	−0.553211	−	0.833041i	$-0.686598\pi$
$971$	−34.4771	−1.10642	−0.553211	+	0.833041i	$0.686598\pi$
$972$	−0.222305	−0.00713044
$973$	18.1482	0.581806
$974$	7.15631	0.229303
$975$	0.167568	0.00536647
$976$	26.5032	0.848346
$977$	5.51932	0.176579	0.0882894	−	0.996095i	$-0.471860\pi$
$977$	5.51932	0.176579	0.0882894	+	0.996095i	$0.471860\pi$
$978$	29.3372	0.938101
$979$	0	0
$980$	0.194119	0.00620090
$981$	−9.99510	−0.319119
$982$	−30.7478	−0.981202
$983$	−33.0076	−1.05278	−0.526390	−	0.850243i	$-0.676455\pi$
$983$	−33.0076	−1.05278	−0.526390	+	0.850243i	$0.676455\pi$
$984$	−18.2190	−0.580800
$985$	−5.98823	−0.190801
$986$	−12.7485	−0.405993
$987$	6.04773	0.192501
$988$	0.0500568	0.00159252
$989$	10.7431	0.341610
$990$	0	0
$991$	−40.9399	−1.30050	−0.650249	−	0.759721i	$-0.725335\pi$
$991$	−40.9399	−1.30050	−0.650249	+	0.759721i	$0.725335\pi$
$992$	9.35978	0.297173
$993$	23.1465	0.734532
$994$	−15.0000	−0.475772
$995$	4.43067	0.140462
$996$	1.98207	0.0628042
$997$	37.8795	1.19966	0.599828	−	0.800129i	$-0.295236\pi$
$997$	37.8795	1.19966	0.599828	+	0.800129i	$0.295236\pi$
$998$	44.1845	1.39864
$999$	11.5704	0.366073

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2541.2.a.br.1.7		10
3.2	odd	2		7623.2.a.cy.1.4		10
11.2	odd	10		231.2.j.g.169.4	✓	20
11.6	odd	10		231.2.j.g.190.4	yes	20
11.10	odd	2		2541.2.a.bq.1.4		10
33.2	even	10		693.2.m.j.631.2		20
33.17	even	10		693.2.m.j.190.2		20
33.32	even	2		7623.2.a.cx.1.7		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.j.g.169.4	✓	20	11.2	odd	10
231.2.j.g.190.4	yes	20	11.6	odd	10
693.2.m.j.190.2		20	33.17	even	10
693.2.m.j.631.2		20	33.2	even	10
2541.2.a.bq.1.4		10	11.10	odd	2
2541.2.a.br.1.7		10	1.1	even	1	trivial
7623.2.a.cx.1.7		10	33.32	even	2
7623.2.a.cy.1.4		10	3.2	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:	\( N \)	\(=\)	\( 2541 = 3 \cdot 7 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2541.a (trivial)

\(f(q)\)	\(=\)	\(q+1.33330 q^{2} +1.00000 q^{3} -0.222305 q^{4} -0.873210 q^{5} +1.33330 q^{6} +1.00000 q^{7} -2.96300 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.33330 q^{2} +1.00000 q^{3} -0.222305 q^{4} -0.873210 q^{5} +1.33330 q^{6} +1.00000 q^{7} -2.96300 q^{8} +1.00000 q^{9} -1.16425 q^{10} -0.222305 q^{12} -0.0395440 q^{13} +1.33330 q^{14} -0.873210 q^{15} -3.50597 q^{16} -2.04633 q^{17} +1.33330 q^{18} +5.69421 q^{19} +0.194119 q^{20} +1.00000 q^{21} +5.97870 q^{23} -2.96300 q^{24} -4.23750 q^{25} -0.0527241 q^{26} +1.00000 q^{27} -0.222305 q^{28} +4.67254 q^{29} -1.16425 q^{30} +7.47891 q^{31} +1.25149 q^{32} -2.72838 q^{34} -0.873210 q^{35} -0.222305 q^{36} +11.5704 q^{37} +7.59210 q^{38} -0.0395440 q^{39} +2.58733 q^{40} +6.14882 q^{41} +1.33330 q^{42} +1.79689 q^{43} -0.873210 q^{45} +7.97142 q^{46} +6.04773 q^{47} -3.50597 q^{48} +1.00000 q^{49} -5.64987 q^{50} -2.04633 q^{51} +0.00879083 q^{52} -0.124401 q^{53} +1.33330 q^{54} -2.96300 q^{56} +5.69421 q^{57} +6.22991 q^{58} -14.3460 q^{59} +0.194119 q^{60} -7.55944 q^{61} +9.97165 q^{62} +1.00000 q^{63} +8.68056 q^{64} +0.0345302 q^{65} +4.85938 q^{67} +0.454910 q^{68} +5.97870 q^{69} -1.16425 q^{70} -11.2503 q^{71} -2.96300 q^{72} -0.612954 q^{73} +15.4269 q^{74} -4.23750 q^{75} -1.26585 q^{76} -0.0527241 q^{78} +0.155227 q^{79} +3.06145 q^{80} +1.00000 q^{81} +8.19824 q^{82} -8.91599 q^{83} -0.222305 q^{84} +1.78688 q^{85} +2.39580 q^{86} +4.67254 q^{87} +5.17689 q^{89} -1.16425 q^{90} -0.0395440 q^{91} -1.32910 q^{92} +7.47891 q^{93} +8.06345 q^{94} -4.97224 q^{95} +1.25149 q^{96} +7.94222 q^{97} +1.33330 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 10 q^{3} + 18 q^{4} + 5 q^{5} + 10 q^{7} - 3 q^{8} + 10 q^{9}+O(q^{10}) \) 10 * q + 10 * q^3 + 18 * q^4 + 5 * q^5 + 10 * q^7 - 3 * q^8 + 10 * q^9	\( 10 q + 10 q^{3} + 18 q^{4} + 5 q^{5} + 10 q^{7} - 3 q^{8} + 10 q^{9} - 6 q^{10} + 18 q^{12} + 6 q^{13} + 5 q^{15} + 38 q^{16} + 8 q^{17} + 7 q^{20} + 10 q^{21} - 3 q^{24} + 31 q^{25} + q^{26} + 10 q^{27} + 18 q^{28} - 14 q^{29} - 6 q^{30} + 26 q^{31} - 41 q^{32} + 21 q^{34} + 5 q^{35} + 18 q^{36} + 24 q^{37} + 8 q^{38} + 6 q^{39} - 5 q^{40} + 19 q^{41} - 6 q^{43} + 5 q^{45} - q^{46} + 15 q^{47} + 38 q^{48} + 10 q^{49} - q^{50} + 8 q^{51} - 25 q^{52} - q^{53} - 3 q^{56} + 11 q^{58} + 23 q^{59} + 7 q^{60} + 11 q^{62} + 10 q^{63} + 53 q^{64} - 29 q^{65} + 38 q^{67} + 87 q^{68} - 6 q^{70} + 26 q^{71} - 3 q^{72} - q^{73} - 39 q^{74} + 31 q^{75} - 2 q^{76} + q^{78} + 5 q^{79} + 6 q^{80} + 10 q^{81} + 5 q^{82} + 6 q^{83} + 18 q^{84} - q^{85} - 41 q^{86} - 14 q^{87} - 9 q^{89} - 6 q^{90} + 6 q^{91} - 48 q^{92} + 26 q^{93} - 42 q^{95} - 41 q^{96} + 24 q^{97}+O(q^{100}) \) 10 * q + 10 * q^3 + 18 * q^4 + 5 * q^5 + 10 * q^7 - 3 * q^8 + 10 * q^9 - 6 * q^10 + 18 * q^12 + 6 * q^13 + 5 * q^15 + 38 * q^16 + 8 * q^17 + 7 * q^20 + 10 * q^21 - 3 * q^24 + 31 * q^25 + q^26 + 10 * q^27 + 18 * q^28 - 14 * q^29 - 6 * q^30 + 26 * q^31 - 41 * q^32 + 21 * q^34 + 5 * q^35 + 18 * q^36 + 24 * q^37 + 8 * q^38 + 6 * q^39 - 5 * q^40 + 19 * q^41 - 6 * q^43 + 5 * q^45 - q^46 + 15 * q^47 + 38 * q^48 + 10 * q^49 - q^50 + 8 * q^51 - 25 * q^52 - q^53 - 3 * q^56 + 11 * q^58 + 23 * q^59 + 7 * q^60 + 11 * q^62 + 10 * q^63 + 53 * q^64 - 29 * q^65 + 38 * q^67 + 87 * q^68 - 6 * q^70 + 26 * q^71 - 3 * q^72 - q^73 - 39 * q^74 + 31 * q^75 - 2 * q^76 + q^78 + 5 * q^79 + 6 * q^80 + 10 * q^81 + 5 * q^82 + 6 * q^83 + 18 * q^84 - q^85 - 41 * q^86 - 14 * q^87 - 9 * q^89 - 6 * q^90 + 6 * q^91 - 48 * q^92 + 26 * q^93 - 42 * q^95 - 41 * q^96 + 24 * q^97

Introduction

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