LMFDB - Embedded newform 2011.2.a.b.1.68

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2011,2,Mod(1,2011)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2011, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("2011.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2011 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2011.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:	$16.0579158465$
Analytic rank:	$0$
Dimension:	$90$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.68
Character	$\chi$	$=$	2011.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.70485 q^{2} +3.05957 q^{3} +0.906523 q^{4} +3.01399 q^{5} +5.21612 q^{6} -2.00394 q^{7} -1.86422 q^{8} +6.36098 q^{9} +O(q^{10})$	\(q+1.70485 q^{2} +3.05957 q^{3} +0.906523 q^{4} +3.01399 q^{5} +5.21612 q^{6} -2.00394 q^{7} -1.86422 q^{8} +6.36098 q^{9} +5.13841 q^{10} -1.57364 q^{11} +2.77357 q^{12} +3.75621 q^{13} -3.41642 q^{14} +9.22152 q^{15} -4.99126 q^{16} +2.92170 q^{17} +10.8445 q^{18} +2.90713 q^{19} +2.73225 q^{20} -6.13119 q^{21} -2.68282 q^{22} -5.84789 q^{23} -5.70371 q^{24} +4.08414 q^{25} +6.40378 q^{26} +10.2832 q^{27} -1.81662 q^{28} -5.63779 q^{29} +15.7213 q^{30} -1.02535 q^{31} -4.78093 q^{32} -4.81466 q^{33} +4.98106 q^{34} -6.03985 q^{35} +5.76637 q^{36} +5.96990 q^{37} +4.95622 q^{38} +11.4924 q^{39} -5.61873 q^{40} +3.82577 q^{41} -10.4528 q^{42} -12.2255 q^{43} -1.42654 q^{44} +19.1719 q^{45} -9.96978 q^{46} -1.27493 q^{47} -15.2711 q^{48} -2.98423 q^{49} +6.96285 q^{50} +8.93914 q^{51} +3.40509 q^{52} -9.99846 q^{53} +17.5313 q^{54} -4.74293 q^{55} +3.73578 q^{56} +8.89457 q^{57} -9.61161 q^{58} +9.24496 q^{59} +8.35952 q^{60} +5.48640 q^{61} -1.74807 q^{62} -12.7470 q^{63} +1.83174 q^{64} +11.3212 q^{65} -8.20828 q^{66} -8.76726 q^{67} +2.64858 q^{68} -17.8920 q^{69} -10.2971 q^{70} +11.0496 q^{71} -11.8582 q^{72} -13.2043 q^{73} +10.1778 q^{74} +12.4957 q^{75} +2.63538 q^{76} +3.15347 q^{77} +19.5928 q^{78} +7.74308 q^{79} -15.0436 q^{80} +12.3791 q^{81} +6.52237 q^{82} +7.33603 q^{83} -5.55807 q^{84} +8.80596 q^{85} -20.8427 q^{86} -17.2492 q^{87} +2.93360 q^{88} +9.48918 q^{89} +32.6853 q^{90} -7.52721 q^{91} -5.30124 q^{92} -3.13714 q^{93} -2.17357 q^{94} +8.76205 q^{95} -14.6276 q^{96} -1.49630 q^{97} -5.08767 q^{98} -10.0099 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 90 q + 11 q^{2} + 9 q^{3} + 95 q^{4} + 47 q^{5} + 20 q^{6} + 4 q^{7} + 33 q^{8} + 109 q^{9}+O(q^{10}) $ 90 * q + 11 * q^2 + 9 * q^3 + 95 * q^4 + 47 * q^5 + 20 * q^6 + 4 * q^7 + 33 * q^8 + 109 * q^9	\( 90 q + 11 q^{2} + 9 q^{3} + 95 q^{4} + 47 q^{5} + 20 q^{6} + 4 q^{7} + 33 q^{8} + 109 q^{9} + 19 q^{10} + 24 q^{11} + 14 q^{12} + 36 q^{13} + 43 q^{14} + 4 q^{15} + 93 q^{16} + 55 q^{17} + 18 q^{18} + 15 q^{19} + 76 q^{20} + 65 q^{21} - 3 q^{22} + 30 q^{23} + 46 q^{24} + 107 q^{25} + 38 q^{26} + 21 q^{27} + 2 q^{28} + 149 q^{29} + q^{30} + 33 q^{31} + 67 q^{32} + 13 q^{33} + 15 q^{34} + 34 q^{35} + 103 q^{36} + 23 q^{37} + 38 q^{38} + 32 q^{39} + 43 q^{40} + 144 q^{41} - 20 q^{42} - 5 q^{43} + 37 q^{44} + 103 q^{45} + 8 q^{46} + 28 q^{47} + 12 q^{48} + 114 q^{49} + 67 q^{50} + 11 q^{51} + 59 q^{52} + 59 q^{53} + 38 q^{54} + 3 q^{55} + 106 q^{56} + 2 q^{57} - 5 q^{58} + 86 q^{59} - 28 q^{60} + 113 q^{61} + 12 q^{62} - 29 q^{63} + 71 q^{64} + 51 q^{65} + 15 q^{66} - 14 q^{67} + 96 q^{68} + 116 q^{69} - 24 q^{70} + 47 q^{71} + 13 q^{72} + 22 q^{73} + 57 q^{74} + 7 q^{75} + 2 q^{76} + 100 q^{77} - 34 q^{78} + 18 q^{79} + 100 q^{80} + 154 q^{81} - 4 q^{82} + 24 q^{83} + 35 q^{84} + 30 q^{85} - q^{86} + 49 q^{87} - 74 q^{88} + 97 q^{89} + 22 q^{90} - 25 q^{91} + 23 q^{92} + 32 q^{93} + 21 q^{94} + 56 q^{95} + 29 q^{96} + 26 q^{97} + 15 q^{98} - 11 q^{99}+O(q^{100}) \) 90 * q + 11 * q^2 + 9 * q^3 + 95 * q^4 + 47 * q^5 + 20 * q^6 + 4 * q^7 + 33 * q^8 + 109 * q^9 + 19 * q^10 + 24 * q^11 + 14 * q^12 + 36 * q^13 + 43 * q^14 + 4 * q^15 + 93 * q^16 + 55 * q^17 + 18 * q^18 + 15 * q^19 + 76 * q^20 + 65 * q^21 - 3 * q^22 + 30 * q^23 + 46 * q^24 + 107 * q^25 + 38 * q^26 + 21 * q^27 + 2 * q^28 + 149 * q^29 + q^30 + 33 * q^31 + 67 * q^32 + 13 * q^33 + 15 * q^34 + 34 * q^35 + 103 * q^36 + 23 * q^37 + 38 * q^38 + 32 * q^39 + 43 * q^40 + 144 * q^41 - 20 * q^42 - 5 * q^43 + 37 * q^44 + 103 * q^45 + 8 * q^46 + 28 * q^47 + 12 * q^48 + 114 * q^49 + 67 * q^50 + 11 * q^51 + 59 * q^52 + 59 * q^53 + 38 * q^54 + 3 * q^55 + 106 * q^56 + 2 * q^57 - 5 * q^58 + 86 * q^59 - 28 * q^60 + 113 * q^61 + 12 * q^62 - 29 * q^63 + 71 * q^64 + 51 * q^65 + 15 * q^66 - 14 * q^67 + 96 * q^68 + 116 * q^69 - 24 * q^70 + 47 * q^71 + 13 * q^72 + 22 * q^73 + 57 * q^74 + 7 * q^75 + 2 * q^76 + 100 * q^77 - 34 * q^78 + 18 * q^79 + 100 * q^80 + 154 * q^81 - 4 * q^82 + 24 * q^83 + 35 * q^84 + 30 * q^85 - q^86 + 49 * q^87 - 74 * q^88 + 97 * q^89 + 22 * q^90 - 25 * q^91 + 23 * q^92 + 32 * q^93 + 21 * q^94 + 56 * q^95 + 29 * q^96 + 26 * q^97 + 15 * q^98 - 11 * q^99

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 $

$2$	1.70485	1.20551	0.602756	−	0.797925i	$-0.294069\pi$
$2$	1.70485	1.20551	0.602756	+	0.797925i	$0.294069\pi$
$3$	3.05957	1.76644	0.883222	−	0.468955i	$-0.155369\pi$
$3$	3.05957	1.76644	0.883222	+	0.468955i	$0.155369\pi$
$4$	0.906523	0.453261
$5$	3.01399	1.34790	0.673949	−	0.738778i	$-0.264597\pi$
$5$	3.01399	1.34790	0.673949	+	0.738778i	$0.264597\pi$
$6$	5.21612	2.12947
$7$	−2.00394	−0.757418	−0.378709	−	0.925516i	$-0.623632\pi$
$7$	−2.00394	−0.757418	−0.378709	+	0.925516i	$0.623632\pi$
$8$	−1.86422	−0.659100
$9$	6.36098	2.12033
$10$	5.13841	1.62491
$11$	−1.57364	−0.474469	−0.237235	−	0.971452i	$-0.576241\pi$
$11$	−1.57364	−0.474469	−0.237235	+	0.971452i	$0.576241\pi$
$12$	2.77357	0.800661
$13$	3.75621	1.04178	0.520892	−	0.853622i	$-0.325599\pi$
$13$	3.75621	1.04178	0.520892	+	0.853622i	$0.325599\pi$
$14$	−3.41642	−0.913077
$15$	9.22152	2.38099
$16$	−4.99126	−1.24782
$17$	2.92170	0.708615	0.354308	−	0.935129i	$-0.384717\pi$
$17$	2.92170	0.708615	0.354308	+	0.935129i	$0.384717\pi$
$18$	10.8445	2.55608
$19$	2.90713	0.666941	0.333470	−	0.942761i	$-0.391780\pi$
$19$	2.90713	0.666941	0.333470	+	0.942761i	$0.391780\pi$
$20$	2.73225	0.610950
$21$	−6.13119	−1.33794
$22$	−2.68282	−0.571979
$23$	−5.84789	−1.21937	−0.609684	−	0.792644i	$-0.708704\pi$
$23$	−5.84789	−1.21937	−0.609684	+	0.792644i	$0.708704\pi$
$24$	−5.70371	−1.16426
$25$	4.08414	0.816827
$26$	6.40378	1.25588
$27$	10.2832	1.97899
$28$	−1.81662	−0.343308
$29$	−5.63779	−1.04691	−0.523456	−	0.852053i	$-0.675358\pi$
$29$	−5.63779	−1.04691	−0.523456	+	0.852053i	$0.675358\pi$
$30$	15.7213	2.87031
$31$	−1.02535	−0.184159	−0.0920793	−	0.995752i	$-0.529351\pi$
$31$	−1.02535	−0.184159	−0.0920793	+	0.995752i	$0.529351\pi$
$32$	−4.78093	−0.845157
$33$	−4.81466	−0.838124
$34$	4.98106	0.854245
$35$	−6.03985	−1.02092
$36$	5.76637	0.961062
$37$	5.96990	0.981445	0.490723	−	0.871316i	$-0.336733\pi$
$37$	5.96990	0.981445	0.490723	+	0.871316i	$0.336733\pi$
$38$	4.95622	0.804006
$39$	11.4924	1.84025
$40$	−5.61873	−0.888400
$41$	3.82577	0.597485	0.298742	−	0.954334i	$-0.403433\pi$
$41$	3.82577	0.597485	0.298742	+	0.954334i	$0.403433\pi$
$42$	−10.4528	−1.61290
$43$	−12.2255	−1.86437	−0.932187	−	0.361978i	$-0.882102\pi$
$43$	−12.2255	−1.86437	−0.932187	+	0.361978i	$0.882102\pi$
$44$	−1.42654	−0.215059
$45$	19.1719	2.85798
$46$	−9.96978	−1.46996
$47$	−1.27493	−0.185968	−0.0929840	−	0.995668i	$-0.529641\pi$
$47$	−1.27493	−0.185968	−0.0929840	+	0.995668i	$0.529641\pi$
$48$	−15.2711	−2.20420
$49$	−2.98423	−0.426319
$50$	6.96285	0.984696
$51$	8.93914	1.25173
$52$	3.40509	0.472201
$53$	−9.99846	−1.37339	−0.686697	−	0.726944i	$-0.740940\pi$
$53$	−9.99846	−1.37339	−0.686697	+	0.726944i	$0.740940\pi$
$54$	17.5313	2.38570
$55$	−4.74293	−0.639536
$56$	3.73578	0.499214
$57$	8.89457	1.17811
$58$	−9.61161	−1.26207
$59$	9.24496	1.20359	0.601795	−	0.798650i	$-0.294452\pi$
$59$	9.24496	1.20359	0.601795	+	0.798650i	$0.294452\pi$
$60$	8.35952	1.07921
$61$	5.48640	0.702462	0.351231	−	0.936289i	$-0.385763\pi$
$61$	5.48640	0.702462	0.351231	+	0.936289i	$0.385763\pi$
$62$	−1.74807	−0.222006
$63$	−12.7470	−1.60597
$64$	1.83174	0.228967
$65$	11.3212	1.40422
$66$	−8.20828	−1.01037
$67$	−8.76726	−1.07109	−0.535546	−	0.844506i	$-0.679894\pi$
$67$	−8.76726	−1.07109	−0.535546	+	0.844506i	$0.679894\pi$
$68$	2.64858	0.321188
$69$	−17.8920	−2.15395
$70$	−10.2971	−1.23073
$71$	11.0496	1.31135	0.655675	−	0.755043i	$-0.272384\pi$
$71$	11.0496	1.31135	0.655675	+	0.755043i	$0.272384\pi$
$72$	−11.8582	−1.39751
$73$	−13.2043	−1.54544	−0.772721	−	0.634745i	$-0.781105\pi$
$73$	−13.2043	−1.54544	−0.772721	+	0.634745i	$0.781105\pi$
$74$	10.1778	1.18315
$75$	12.4957	1.44288
$76$	2.63538	0.302299
$77$	3.15347	0.359371
$78$	19.5928	2.21845
$79$	7.74308	0.871165	0.435582	−	0.900149i	$-0.356542\pi$
$79$	7.74308	0.871165	0.435582	+	0.900149i	$0.356542\pi$
$80$	−15.0436	−1.68193
$81$	12.3791	1.37546
$82$	6.52237	0.720276
$83$	7.33603	0.805234	0.402617	−	0.915368i	$-0.368101\pi$
$83$	7.33603	0.805234	0.402617	+	0.915368i	$0.368101\pi$
$84$	−5.55807	−0.606435
$85$	8.80596	0.955141
$86$	−20.8427	−2.24753
$87$	−17.2492	−1.84931
$88$	2.93360	0.312723
$89$	9.48918	1.00585	0.502925	−	0.864330i	$-0.332257\pi$
$89$	9.48918	1.00585	0.502925	+	0.864330i	$0.332257\pi$
$90$	32.6853	3.44533
$91$	−7.52721	−0.789066
$92$	−5.30124	−0.552693
$93$	−3.13714	−0.325306
$94$	−2.17357	−0.224187
$95$	8.76205	0.898968
$96$	−14.6276	−1.49292
$97$	−1.49630	−0.151926	−0.0759631	−	0.997111i	$-0.524203\pi$
$97$	−1.49630	−0.151926	−0.0759631	+	0.997111i	$0.524203\pi$
$98$	−5.08767	−0.513933
$99$	−10.0099	−1.00603
$100$	3.70236	0.370236
$101$	9.73974	0.969140	0.484570	−	0.874752i	$-0.338976\pi$
$101$	9.73974	0.969140	0.484570	+	0.874752i	$0.338976\pi$
$102$	15.2399	1.50898
$103$	−9.92776	−0.978211	−0.489106	−	0.872225i	$-0.662677\pi$
$103$	−9.92776	−0.978211	−0.489106	+	0.872225i	$0.662677\pi$
$104$	−7.00239	−0.686640
$105$	−18.4794	−1.80340
$106$	−17.0459	−1.65564
$107$	−18.2036	−1.75981	−0.879904	−	0.475151i	$-0.842393\pi$
$107$	−18.2036	−1.75981	−0.879904	+	0.475151i	$0.842393\pi$
$108$	9.32192	0.897002
$109$	13.6318	1.30569	0.652846	−	0.757490i	$-0.273575\pi$
$109$	13.6318	1.30569	0.652846	+	0.757490i	$0.273575\pi$
$110$	−8.08599	−0.770969
$111$	18.2653	1.73367
$112$	10.0022	0.945117
$113$	0.728157	0.0684992	0.0342496	−	0.999413i	$-0.489096\pi$
$113$	0.728157	0.0684992	0.0342496	+	0.999413i	$0.489096\pi$
$114$	15.1639	1.42023
$115$	−17.6255	−1.64358
$116$	−5.11079	−0.474525
$117$	23.8932	2.20892
$118$	15.7613	1.45094
$119$	−5.85490	−0.536718
$120$	−17.1909	−1.56931
$121$	−8.52367	−0.774879
$122$	9.35351	0.846827
$123$	11.7052	1.05542
$124$	−0.929505	−0.0834720
$125$	−2.76040	−0.246898
$126$	−21.7318	−1.93602
$127$	0.868624	0.0770779	0.0385389	−	0.999257i	$-0.487730\pi$
$127$	0.868624	0.0770779	0.0385389	+	0.999257i	$0.487730\pi$
$128$	12.6847	1.12118
$129$	−37.4048	−3.29331
$130$	19.3009	1.69280
$131$	−4.24124	−0.370558	−0.185279	−	0.982686i	$-0.559319\pi$
$131$	−4.24124	−0.370558	−0.185279	+	0.982686i	$0.559319\pi$
$132$	−4.36460	−0.379889
$133$	−5.82571	−0.505153
$134$	−14.9469	−1.29121
$135$	30.9933	2.66748
$136$	−5.44668	−0.467049
$137$	−19.3980	−1.65729	−0.828643	−	0.559777i	$-0.810887\pi$
$137$	−19.3980	−1.65729	−0.828643	+	0.559777i	$0.810887\pi$
$138$	−30.5033	−2.59661
$139$	8.71195	0.738938	0.369469	−	0.929243i	$-0.379540\pi$
$139$	8.71195	0.738938	0.369469	+	0.929243i	$0.379540\pi$
$140$	−5.47526	−0.462744
$141$	−3.90075	−0.328502
$142$	18.8380	1.58085
$143$	−5.91091	−0.494295
$144$	−31.7493	−2.64578
$145$	−16.9923	−1.41113
$146$	−22.5113	−1.86305
$147$	−9.13047	−0.753068
$148$	5.41185	0.444851
$149$	−1.59523	−0.130686	−0.0653431	−	0.997863i	$-0.520814\pi$
$149$	−1.59523	−0.130686	−0.0653431	+	0.997863i	$0.520814\pi$
$150$	21.3033	1.73941
$151$	12.8613	1.04664	0.523319	−	0.852137i	$-0.324694\pi$
$151$	12.8613	1.04664	0.523319	+	0.852137i	$0.324694\pi$
$152$	−5.41952	−0.439581
$153$	18.5848	1.50250
$154$	5.37621	0.433227
$155$	−3.09040	−0.248227
$156$	10.4181	0.834116
$157$	−18.3877	−1.46750	−0.733749	−	0.679420i	$-0.762231\pi$
$157$	−18.3877	−1.46750	−0.733749	+	0.679420i	$0.762231\pi$
$158$	13.2008	1.05020
$159$	−30.5910	−2.42602
$160$	−14.4097	−1.13919
$161$	11.7188	0.923571
$162$	21.1046	1.65813
$163$	−4.88239	−0.382418	−0.191209	−	0.981549i	$-0.561241\pi$
$163$	−4.88239	−0.382418	−0.191209	+	0.981549i	$0.561241\pi$
$164$	3.46815	0.270817
$165$	−14.5113	−1.12971
$166$	12.5069	0.970721
$167$	−18.5032	−1.43182	−0.715908	−	0.698194i	$-0.753987\pi$
$167$	−18.5032	−1.43182	−0.715908	+	0.698194i	$0.753987\pi$
$168$	11.4299	0.881834
$169$	1.10909	0.0853146
$170$	15.0129	1.15143
$171$	18.4922	1.41413
$172$	−11.0827	−0.845049
$173$	5.19162	0.394712	0.197356	−	0.980332i	$-0.436765\pi$
$173$	5.19162	0.394712	0.197356	+	0.980332i	$0.436765\pi$
$174$	−29.4074	−2.22937
$175$	−8.18436	−0.618679
$176$	7.85444	0.592050
$177$	28.2856	2.12608
$178$	16.1776	1.21257
$179$	−2.68169	−0.200439	−0.100220	−	0.994965i	$-0.531955\pi$
$179$	−2.68169	−0.200439	−0.100220	+	0.994965i	$0.531955\pi$
$180$	17.3798	1.29541
$181$	16.9412	1.25923	0.629616	−	0.776906i	$-0.283212\pi$
$181$	16.9412	1.25923	0.629616	+	0.776906i	$0.283212\pi$
$182$	−12.8328	−0.951229
$183$	16.7860	1.24086
$184$	10.9017	0.803686
$185$	17.9932	1.32289
$186$	−5.34836	−0.392161
$187$	−4.59769	−0.336216
$188$	−1.15576	−0.0842921
$189$	−20.6068	−1.49893
$190$	14.9380	1.08372
$191$	−5.98018	−0.432711	−0.216355	−	0.976315i	$-0.569417\pi$
$191$	−5.98018	−0.432711	−0.216355	+	0.976315i	$0.569417\pi$
$192$	5.60434	0.404458
$193$	22.1179	1.59208	0.796041	−	0.605242i	$-0.206924\pi$
$193$	22.1179	1.59208	0.796041	+	0.605242i	$0.206924\pi$
$194$	−2.55097	−0.183149
$195$	34.6379	2.48047
$196$	−2.70527	−0.193234
$197$	−0.902354	−0.0642901	−0.0321450	−	0.999483i	$-0.510234\pi$
$197$	−0.902354	−0.0642901	−0.0321450	+	0.999483i	$0.510234\pi$
$198$	−17.0654	−1.21278
$199$	11.6185	0.823614	0.411807	−	0.911271i	$-0.364898\pi$
$199$	11.6185	0.823614	0.411807	+	0.911271i	$0.364898\pi$
$200$	−7.61372	−0.538371
$201$	−26.8241	−1.89202
$202$	16.6048	1.16831
$203$	11.2978	0.792950
$204$	8.10353	0.567361
$205$	11.5308	0.805348
$206$	−16.9254	−1.17925
$207$	−37.1983	−2.58546
$208$	−18.7482	−1.29995
$209$	−4.57476	−0.316443
$210$	−31.5046	−2.17402
$211$	−15.0508	−1.03614	−0.518071	−	0.855338i	$-0.673350\pi$
$211$	−15.0508	−1.03614	−0.518071	+	0.855338i	$0.673350\pi$
$212$	−9.06383	−0.622507
$213$	33.8072	2.31643
$214$	−31.0345	−2.12147
$215$	−36.8476	−2.51298
$216$	−19.1700	−1.30436
$217$	2.05474	0.139485
$218$	23.2403	1.57403
$219$	−40.3994	−2.72994
$220$	−4.29957	−0.289877
$221$	10.9745	0.738224
$222$	31.1397	2.08996
$223$	−16.1468	−1.08127	−0.540636	−	0.841257i	$-0.681816\pi$
$223$	−16.1468	−1.08127	−0.540636	+	0.841257i	$0.681816\pi$
$224$	9.58069	0.640137
$225$	25.9791	1.73194
$226$	1.24140	0.0825767
$227$	−11.3211	−0.751406	−0.375703	−	0.926740i	$-0.622599\pi$
$227$	−11.3211	−0.751406	−0.375703	+	0.926740i	$0.622599\pi$
$228$	8.06313	0.533994
$229$	9.75835	0.644850	0.322425	−	0.946595i	$-0.395502\pi$
$229$	9.75835	0.644850	0.322425	+	0.946595i	$0.395502\pi$
$230$	−30.0488	−1.98136
$231$	9.64827	0.634810
$232$	10.5101	0.690020
$233$	16.0916	1.05420	0.527098	−	0.849804i	$-0.323280\pi$
$233$	16.0916	1.05420	0.527098	+	0.849804i	$0.323280\pi$
$234$	40.7343	2.66289
$235$	−3.84263	−0.250666
$236$	8.38076	0.545541
$237$	23.6905	1.53886
$238$	−9.98174	−0.647020
$239$	−15.2027	−0.983382	−0.491691	−	0.870770i	$-0.663621\pi$
$239$	−15.2027	−0.983382	−0.491691	+	0.870770i	$0.663621\pi$
$240$	−46.0270	−2.97103
$241$	−22.7794	−1.46735	−0.733675	−	0.679500i	$-0.762197\pi$
$241$	−22.7794	−1.46735	−0.733675	+	0.679500i	$0.762197\pi$
$242$	−14.5316	−0.934126
$243$	7.02533	0.450675
$244$	4.97355	0.318399
$245$	−8.99444	−0.574634
$246$	19.9557	1.27233
$247$	10.9198	0.694809
$248$	1.91148	0.121379
$249$	22.4451	1.42240
$250$	−4.70608	−0.297638
$251$	11.1140	0.701508	0.350754	−	0.936468i	$-0.385925\pi$
$251$	11.1140	0.701508	0.350754	+	0.936468i	$0.385925\pi$
$252$	−11.5555	−0.727925
$253$	9.20245	0.578553
$254$	1.48088	0.0929184
$255$	26.9425	1.68720
$256$	17.9621	1.12263
$257$	27.8639	1.73810	0.869052	−	0.494721i	$-0.164730\pi$
$257$	27.8639	1.73810	0.869052	+	0.494721i	$0.164730\pi$
$258$	−63.7697	−3.97013
$259$	−11.9633	−0.743364
$260$	10.2629	0.636478
$261$	−35.8619	−2.21980
$262$	−7.23068	−0.446713
$263$	−1.29086	−0.0795980	−0.0397990	−	0.999208i	$-0.512672\pi$
$263$	−1.29086	−0.0795980	−0.0397990	+	0.999208i	$0.512672\pi$
$264$	8.97557	0.552408
$265$	−30.1353	−1.85119
$266$	−9.93197	−0.608968
$267$	29.0328	1.77678
$268$	−7.94772	−0.485484
$269$	12.7376	0.776625	0.388312	−	0.921528i	$-0.373058\pi$
$269$	12.7376	0.776625	0.388312	+	0.921528i	$0.373058\pi$
$270$	52.8391	3.21568
$271$	20.5660	1.24929	0.624646	−	0.780908i	$-0.285243\pi$
$271$	20.5660	1.24929	0.624646	+	0.780908i	$0.285243\pi$
$272$	−14.5829	−0.884221
$273$	−23.0300	−1.39384
$274$	−33.0708	−1.99788
$275$	−6.42695	−0.387560
$276$	−16.2195	−0.976301
$277$	5.15772	0.309897	0.154949	−	0.987923i	$-0.450479\pi$
$277$	5.15772	0.309897	0.154949	+	0.987923i	$0.450479\pi$
$278$	14.8526	0.890800
$279$	−6.52224	−0.390477
$280$	11.2596	0.672890
$281$	33.0794	1.97335	0.986675	−	0.162704i	$-0.0520216\pi$
$281$	33.0794	1.97335	0.986675	+	0.162704i	$0.0520216\pi$
$282$	−6.65020	−0.396014
$283$	6.95079	0.413181	0.206591	−	0.978427i	$-0.433763\pi$
$283$	6.95079	0.413181	0.206591	+	0.978427i	$0.433763\pi$
$284$	10.0168	0.594385
$285$	26.8081	1.58798
$286$	−10.0772	−0.595879
$287$	−7.66661	−0.452546
$288$	−30.4114	−1.79201
$289$	−8.46370	−0.497864
$290$	−28.9693	−1.70114
$291$	−4.57803	−0.268369
$292$	−11.9700	−0.700490
$293$	27.0335	1.57931	0.789656	−	0.613550i	$-0.210259\pi$
$293$	27.0335	1.57931	0.789656	+	0.613550i	$0.210259\pi$
$294$	−15.5661	−0.907834
$295$	27.8642	1.62232
$296$	−11.1292	−0.646871
$297$	−16.1820	−0.938972
$298$	−2.71963	−0.157544
$299$	−21.9659	−1.27032
$300$	11.3276	0.654002
$301$	24.4992	1.41211
$302$	21.9266	1.26173
$303$	29.7994	1.71193
$304$	−14.5102	−0.832219
$305$	16.5360	0.946846
$306$	31.6844	1.81128
$307$	−10.5250	−0.600696	−0.300348	−	0.953830i	$-0.597103\pi$
$307$	−10.5250	−0.600696	−0.300348	+	0.953830i	$0.597103\pi$
$308$	2.85869	0.162889
$309$	−30.3747	−1.72796
$310$	−5.26868	−0.299241
$311$	6.67044	0.378246	0.189123	−	0.981953i	$-0.439436\pi$
$311$	6.67044	0.378246	0.189123	+	0.981953i	$0.439436\pi$
$312$	−21.4243	−1.21291
$313$	4.75050	0.268514	0.134257	−	0.990947i	$-0.457135\pi$
$313$	4.75050	0.268514	0.134257	+	0.990947i	$0.457135\pi$
$314$	−31.3483	−1.76909
$315$	−38.4194	−2.16469
$316$	7.01928	0.394865
$317$	−9.37221	−0.526396	−0.263198	−	0.964742i	$-0.584777\pi$
$317$	−9.37221	−0.526396	−0.263198	+	0.964742i	$0.584777\pi$
$318$	−52.1532	−2.92460
$319$	8.87184	0.496728
$320$	5.52084	0.308625
$321$	−55.6952	−3.10860
$322$	19.9788	1.11338
$323$	8.49374	0.472604
$324$	11.2220	0.623442
$325$	15.3409	0.850958
$326$	−8.32375	−0.461010
$327$	41.7076	2.30643
$328$	−7.13207	−0.393803
$329$	2.55489	0.140855
$330$	−24.7397	−1.36187
$331$	17.6026	0.967528	0.483764	−	0.875198i	$-0.339269\pi$
$331$	17.6026	0.967528	0.483764	+	0.875198i	$0.339269\pi$
$332$	6.65028	0.364982
$333$	37.9744	2.08098
$334$	−31.5452	−1.72607
$335$	−26.4244	−1.44372
$336$	30.6024	1.66950
$337$	−4.50731	−0.245529	−0.122765	−	0.992436i	$-0.539176\pi$
$337$	−4.50731	−0.245529	−0.122765	+	0.992436i	$0.539176\pi$
$338$	1.89084	0.102848
$339$	2.22785	0.121000
$340$	7.98281	0.432928
$341$	1.61353	0.0873777
$342$	31.5264	1.70475
$343$	20.0078	1.08032
$344$	22.7910	1.22881
$345$	−53.9264	−2.90330
$346$	8.85096	0.475830
$347$	−11.5404	−0.619519	−0.309759	−	0.950815i	$-0.600248\pi$
$347$	−11.5404	−0.619519	−0.309759	+	0.950815i	$0.600248\pi$
$348$	−15.6368	−0.838222
$349$	32.4286	1.73587	0.867933	−	0.496682i	$-0.165448\pi$
$349$	32.4286	1.73587	0.867933	+	0.496682i	$0.165448\pi$
$350$	−13.9531	−0.745826
$351$	38.6257	2.06169
$352$	7.52345	0.401001
$353$	−7.74513	−0.412232	−0.206116	−	0.978528i	$-0.566082\pi$
$353$	−7.74513	−0.412232	−0.206116	+	0.978528i	$0.566082\pi$
$354$	48.2228	2.56301
$355$	33.3035	1.76757
$356$	8.60216	0.455913
$357$	−17.9135	−0.948082
$358$	−4.57189	−0.241632
$359$	11.8943	0.627758	0.313879	−	0.949463i	$-0.398371\pi$
$359$	11.8943	0.627758	0.313879	+	0.949463i	$0.398371\pi$
$360$	−35.7406	−1.88370
$361$	−10.5486	−0.555190
$362$	28.8823	1.51802
$363$	−26.0788	−1.36878
$364$	−6.82359	−0.357653
$365$	−39.7975	−2.08310
$366$	28.6177	1.49587
$367$	−21.6638	−1.13084	−0.565422	−	0.824802i	$-0.691287\pi$
$367$	−21.6638	−1.13084	−0.565422	+	0.824802i	$0.691287\pi$
$368$	29.1883	1.52155
$369$	24.3356	1.26686
$370$	30.6758	1.59476
$371$	20.0363	1.04023
$372$	−2.84389	−0.147449
$373$	17.7483	0.918971	0.459486	−	0.888185i	$-0.348034\pi$
$373$	17.7483	0.918971	0.459486	+	0.888185i	$0.348034\pi$
$374$	−7.83838	−0.405313
$375$	−8.44564	−0.436131
$376$	2.37675	0.122572
$377$	−21.1767	−1.09066
$378$	−35.1316	−1.80697
$379$	−1.66104	−0.0853221	−0.0426610	−	0.999090i	$-0.513584\pi$
$379$	−1.66104	−0.0853221	−0.0426610	+	0.999090i	$0.513584\pi$
$380$	7.94300	0.407467
$381$	2.65762	0.136154
$382$	−10.1953	−0.521638
$383$	−28.0017	−1.43082	−0.715410	−	0.698704i	$-0.753760\pi$
$383$	−28.0017	−1.43082	−0.715410	+	0.698704i	$0.753760\pi$
$384$	38.8098	1.98050
$385$	9.50453	0.484396
$386$	37.7078	1.91928
$387$	−77.7662	−3.95308
$388$	−1.35643	−0.0688623
$389$	17.0819	0.866088	0.433044	−	0.901373i	$-0.357440\pi$
$389$	17.0819	0.866088	0.433044	+	0.901373i	$0.357440\pi$
$390$	59.0526	2.99024
$391$	−17.0857	−0.864063
$392$	5.56326	0.280987
$393$	−12.9764	−0.654571
$394$	−1.53838	−0.0775025
$395$	23.3376	1.17424
$396$	−9.07418	−0.455995
$397$	−10.7081	−0.537424	−0.268712	−	0.963221i	$-0.586598\pi$
$397$	−10.7081	−0.537424	−0.268712	+	0.963221i	$0.586598\pi$
$398$	19.8079	0.992878
$399$	−17.8242	−0.892324
$400$	−20.3850	−1.01925
$401$	4.77147	0.238276	0.119138	−	0.992878i	$-0.461987\pi$
$401$	4.77147	0.238276	0.119138	+	0.992878i	$0.461987\pi$
$402$	−45.7311	−2.28086
$403$	−3.85143	−0.191854
$404$	8.82929	0.439274
$405$	37.3105	1.85398
$406$	19.2611	0.955911
$407$	−9.39446	−0.465666
$408$	−16.6645	−0.825015
$409$	7.59875	0.375734	0.187867	−	0.982194i	$-0.439843\pi$
$409$	7.59875	0.375734	0.187867	+	0.982194i	$0.439843\pi$
$410$	19.6584	0.970858
$411$	−59.3497	−2.92750
$412$	−8.99974	−0.443385
$413$	−18.5263	−0.911621
$414$	−63.4176	−3.11680
$415$	22.1107	1.08537
$416$	−17.9582	−0.880472
$417$	26.6548	1.30529
$418$	−7.79930	−0.381476
$419$	−8.20149	−0.400669	−0.200334	−	0.979728i	$-0.564203\pi$
$419$	−8.20149	−0.400669	−0.200334	+	0.979728i	$0.564203\pi$
$420$	−16.7520	−0.817412
$421$	8.42076	0.410403	0.205201	−	0.978720i	$-0.434215\pi$
$421$	8.42076	0.410403	0.205201	+	0.978720i	$0.434215\pi$
$422$	−25.6595	−1.24908
$423$	−8.10982	−0.394313
$424$	18.6393	0.905205
$425$	11.9326	0.578816
$426$	57.6362	2.79248
$427$	−10.9944	−0.532057
$428$	−16.5020	−0.797653
$429$	−18.0848	−0.873144
$430$	−62.8197	−3.02944
$431$	5.03130	0.242349	0.121175	−	0.992631i	$-0.461334\pi$
$431$	5.03130	0.242349	0.121175	+	0.992631i	$0.461334\pi$
$432$	−51.3259	−2.46942
$433$	15.3717	0.738715	0.369358	−	0.929287i	$-0.379578\pi$
$433$	15.3717	0.738715	0.369358	+	0.929287i	$0.379578\pi$
$434$	3.50303	0.168151
$435$	−51.9890	−2.49268
$436$	12.3576	0.591820
$437$	−17.0006	−0.813247
$438$	−68.8750	−3.29098
$439$	−2.43507	−0.116220	−0.0581098	−	0.998310i	$-0.518507\pi$
$439$	−2.43507	−0.116220	−0.0581098	+	0.998310i	$0.518507\pi$
$440$	8.84185	0.421519
$441$	−18.9826	−0.903935
$442$	18.7099	0.889939
$443$	−31.4312	−1.49334	−0.746670	−	0.665194i	$-0.768349\pi$
$443$	−31.4312	−1.49334	−0.746670	+	0.665194i	$0.768349\pi$
$444$	16.5579	0.785805
$445$	28.6003	1.35578
$446$	−27.5280	−1.30349
$447$	−4.88071	−0.230850
$448$	−3.67069	−0.173424
$449$	−8.01251	−0.378134	−0.189067	−	0.981964i	$-0.560546\pi$
$449$	−8.01251	−0.378134	−0.189067	+	0.981964i	$0.560546\pi$
$450$	44.2906	2.08788
$451$	−6.02037	−0.283488
$452$	0.660091	0.0310481
$453$	39.3501	1.84883
$454$	−19.3008	−0.905830
$455$	−22.6869	−1.06358
$456$	−16.5814	−0.776495
$457$	−18.4703	−0.864003	−0.432001	−	0.901873i	$-0.642192\pi$
$457$	−18.4703	−0.864003	−0.432001	+	0.901873i	$0.642192\pi$
$458$	16.6366	0.777375
$459$	30.0443	1.40235
$460$	−15.9779	−0.744973
$461$	−27.0180	−1.25835	−0.629176	−	0.777263i	$-0.716608\pi$
$461$	−27.0180	−1.25835	−0.629176	+	0.777263i	$0.716608\pi$
$462$	16.4489	0.765271
$463$	3.73029	0.173361	0.0866807	−	0.996236i	$-0.472374\pi$
$463$	3.73029	0.173361	0.0866807	+	0.996236i	$0.472374\pi$
$464$	28.1397	1.30635
$465$	−9.45530	−0.438479
$466$	27.4338	1.27085
$467$	32.0915	1.48502	0.742508	−	0.669837i	$-0.233636\pi$
$467$	32.0915	1.48502	0.742508	+	0.669837i	$0.233636\pi$
$468$	21.6597	1.00122
$469$	17.5691	0.811263
$470$	−6.55113	−0.302181
$471$	−56.2585	−2.59225
$472$	−17.2346	−0.793287
$473$	19.2385	0.884588
$474$	40.3888	1.85512
$475$	11.8731	0.544776
$476$	−5.30760	−0.243273
$477$	−63.6000	−2.91204
$478$	−25.9184	−1.18548
$479$	−13.1134	−0.599166	−0.299583	−	0.954070i	$-0.596848\pi$
$479$	−13.1134	−0.599166	−0.299583	+	0.954070i	$0.596848\pi$
$480$	−44.0875	−2.01231
$481$	22.4242	1.02245
$482$	−38.8355	−1.76891
$483$	35.8545	1.63144
$484$	−7.72690	−0.351223
$485$	−4.50983	−0.204781
$486$	11.9772	0.543295
$487$	38.9869	1.76666	0.883332	−	0.468748i	$-0.155295\pi$
$487$	38.9869	1.76666	0.883332	+	0.468748i	$0.155295\pi$
$488$	−10.2278	−0.462993
$489$	−14.9380	−0.675521
$490$	−15.3342	−0.692729
$491$	21.7703	0.982481	0.491240	−	0.871024i	$-0.336544\pi$
$491$	21.7703	0.982481	0.491240	+	0.871024i	$0.336544\pi$
$492$	10.6110	0.478383
$493$	−16.4719	−0.741858
$494$	18.6166	0.837601
$495$	−30.1697	−1.35603
$496$	5.11780	0.229796
$497$	−22.1428	−0.993240
$498$	38.2656	1.71472
$499$	7.13493	0.319403	0.159702	−	0.987165i	$-0.448947\pi$
$499$	7.13493	0.319403	0.159702	+	0.987165i	$0.448947\pi$
$500$	−2.50237	−0.111909
$501$	−56.6117	−2.52923
$502$	18.9477	0.845677
$503$	21.7326	0.969010	0.484505	−	0.874788i	$-0.339000\pi$
$503$	21.7326	0.969010	0.484505	+	0.874788i	$0.339000\pi$
$504$	23.7632	1.05850
$505$	29.3555	1.30630
$506$	15.6888	0.697453
$507$	3.39334	0.150704
$508$	0.787427	0.0349364
$509$	12.5617	0.556789	0.278394	−	0.960467i	$-0.410198\pi$
$509$	12.5617	0.556789	0.278394	+	0.960467i	$0.410198\pi$
$510$	45.9329	2.03395
$511$	26.4605	1.17055
$512$	5.25329	0.232165
$513$	29.8945	1.31987
$514$	47.5039	2.09531
$515$	−29.9222	−1.31853
$516$	−33.9083	−1.49273
$517$	2.00628	0.0882361
$518$	−20.3957	−0.896135
$519$	15.8841	0.697237
$520$	−21.1051	−0.925521
$521$	−13.8376	−0.606237	−0.303118	−	0.952953i	$-0.598028\pi$
$521$	−13.8376	−0.606237	−0.303118	+	0.952953i	$0.598028\pi$
$522$	−61.1392	−2.67599
$523$	0.482590	0.0211022	0.0105511	−	0.999944i	$-0.496641\pi$
$523$	0.482590	0.0211022	0.0105511	+	0.999944i	$0.496641\pi$
$524$	−3.84478	−0.167960
$525$	−25.0406	−1.09286
$526$	−2.20073	−0.0959564
$527$	−2.99577	−0.130498
$528$	24.0312	1.04582
$529$	11.1978	0.486860
$530$	−51.3762	−2.23164
$531$	58.8070	2.55201
$532$	−5.28113	−0.228966
$533$	14.3704	0.622450
$534$	49.4967	2.14193
$535$	−54.8655	−2.37204
$536$	16.3441	0.705957
$537$	−8.20483	−0.354065
$538$	21.7157	0.936231
$539$	4.69610	0.202275
$540$	28.0962	1.20907
$541$	37.5889	1.61607	0.808036	−	0.589133i	$-0.200531\pi$
$541$	37.5889	1.61607	0.808036	+	0.589133i	$0.200531\pi$
$542$	35.0619	1.50604
$543$	51.8329	2.22436
$544$	−13.9684	−0.598891
$545$	41.0862	1.75994
$546$	−39.2628	−1.68029
$547$	−3.98225	−0.170269	−0.0851343	−	0.996369i	$-0.527132\pi$
$547$	−3.98225	−0.170269	−0.0851343	+	0.996369i	$0.527132\pi$
$548$	−17.5848	−0.751184
$549$	34.8989	1.48945
$550$	−10.9570	−0.467208
$551$	−16.3898	−0.698228
$552$	33.3546	1.41967
$553$	−15.5167	−0.659835
$554$	8.79315	0.373585
$555$	55.0515	2.33681
$556$	7.89759	0.334932
$557$	−4.62197	−0.195839	−0.0979197	−	0.995194i	$-0.531219\pi$
$557$	−4.62197	−0.195839	−0.0979197	+	0.995194i	$0.531219\pi$
$558$	−11.1195	−0.470724
$559$	−45.9216	−1.94228
$560$	30.1465	1.27392
$561$	−14.0670	−0.593907
$562$	56.3955	2.37890
$563$	−18.2006	−0.767064	−0.383532	−	0.923528i	$-0.625292\pi$
$563$	−18.2006	−0.767064	−0.383532	+	0.923528i	$0.625292\pi$
$564$	−3.53612	−0.148897
$565$	2.19466	0.0923300
$566$	11.8501	0.498096
$567$	−24.8070	−1.04180
$568$	−20.5989	−0.864312
$569$	17.2658	0.723820	0.361910	−	0.932213i	$-0.382125\pi$
$569$	17.2658	0.723820	0.361910	+	0.932213i	$0.382125\pi$
$570$	45.7039	1.91433
$571$	44.8904	1.87860	0.939302	−	0.343091i	$-0.111474\pi$
$571$	44.8904	1.87860	0.939302	+	0.343091i	$0.111474\pi$
$572$	−5.35837	−0.224045
$573$	−18.2968	−0.764359
$574$	−13.0704	−0.545549
$575$	−23.8836	−0.996014
$576$	11.6517	0.485486
$577$	28.6252	1.19168	0.595841	−	0.803102i	$-0.296819\pi$
$577$	28.6252	1.19168	0.595841	+	0.803102i	$0.296819\pi$
$578$	−14.4294	−0.600182
$579$	67.6714	2.81233
$580$	−15.4039	−0.639611
$581$	−14.7010	−0.609899
$582$	−7.80487	−0.323522
$583$	15.7340	0.651634
$584$	24.6156	1.01860
$585$	72.0137	2.97740
$586$	46.0881	1.90388
$587$	20.5271	0.847245	0.423623	−	0.905839i	$-0.360758\pi$
$587$	20.5271	0.847245	0.423623	+	0.905839i	$0.360758\pi$
$588$	−8.27698	−0.341337
$589$	−2.98083	−0.122823
$590$	47.5044	1.95572
$591$	−2.76082	−0.113565
$592$	−29.7973	−1.22466
$593$	6.29815	0.258634	0.129317	−	0.991603i	$-0.458722\pi$
$593$	6.29815	0.258634	0.129317	+	0.991603i	$0.458722\pi$
$594$	−27.5879	−1.13194
$595$	−17.6466	−0.723440
$596$	−1.44611	−0.0592350
$597$	35.5477	1.45487
$598$	−37.4486	−1.53139
$599$	36.5777	1.49452	0.747261	−	0.664530i	$-0.231368\pi$
$599$	36.5777	1.49452	0.747261	+	0.664530i	$0.231368\pi$
$600$	−23.2947	−0.951003
$601$	−35.5216	−1.44896	−0.724479	−	0.689297i	$-0.757920\pi$
$601$	−35.5216	−1.44896	−0.724479	+	0.689297i	$0.757920\pi$
$602$	41.7675	1.70232
$603$	−55.7684	−2.27106
$604$	11.6591	0.474400
$605$	−25.6902	−1.04446
$606$	50.8036	2.06376
$607$	−27.5656	−1.11885	−0.559427	−	0.828880i	$-0.688979\pi$
$607$	−27.5656	−1.11885	−0.559427	+	0.828880i	$0.688979\pi$
$608$	−13.8988	−0.563670
$609$	34.5664	1.40070
$610$	28.1914	1.14144
$611$	−4.78891	−0.193739
$612$	16.8476	0.681023
$613$	35.7085	1.44225	0.721126	−	0.692804i	$-0.243625\pi$
$613$	35.7085	1.44225	0.721126	+	0.692804i	$0.243625\pi$
$614$	−17.9436	−0.724147
$615$	35.2794	1.42260
$616$	−5.87876	−0.236862
$617$	31.0167	1.24869	0.624343	−	0.781151i	$-0.285367\pi$
$617$	31.0167	1.24869	0.624343	+	0.781151i	$0.285367\pi$
$618$	−51.7844	−2.08307
$619$	11.9413	0.479961	0.239980	−	0.970778i	$-0.422859\pi$
$619$	11.9413	0.479961	0.239980	+	0.970778i	$0.422859\pi$
$620$	−2.80152	−0.112512
$621$	−60.1347	−2.41312
$622$	11.3721	0.455981
$623$	−19.0157	−0.761849
$624$	−57.3615	−2.29630
$625$	−28.7405	−1.14962
$626$	8.09891	0.323698
$627$	−13.9968	−0.558979
$628$	−16.6689	−0.665160
$629$	17.4422	0.695467
$630$	−65.4994	−2.60956
$631$	−22.4146	−0.892311	−0.446155	−	0.894956i	$-0.647207\pi$
$631$	−22.4146	−0.892311	−0.446155	+	0.894956i	$0.647207\pi$
$632$	−14.4348	−0.574185
$633$	−46.0491	−1.83029
$634$	−15.9782	−0.634577
$635$	2.61802	0.103893
$636$	−27.7315	−1.09962
$637$	−11.2094	−0.444132
$638$	15.1252	0.598812
$639$	70.2865	2.78049
$640$	38.2316	1.51124
$641$	−44.1524	−1.74392	−0.871958	−	0.489580i	$-0.837150\pi$
$641$	−44.1524	−1.74392	−0.871958	+	0.489580i	$0.837150\pi$
$642$	−94.9522	−3.74746
$643$	−29.5796	−1.16650	−0.583252	−	0.812291i	$-0.698220\pi$
$643$	−29.5796	−1.16650	−0.583252	+	0.812291i	$0.698220\pi$
$644$	10.6234	0.418619
$645$	−112.738	−4.43905
$646$	14.4806	0.569731
$647$	7.50397	0.295011	0.147506	−	0.989061i	$-0.452876\pi$
$647$	7.50397	0.295011	0.147506	+	0.989061i	$0.452876\pi$
$648$	−23.0774	−0.906565
$649$	−14.5482	−0.571067
$650$	26.1539	1.02584
$651$	6.28663	0.246393
$652$	−4.42600	−0.173335
$653$	−12.1832	−0.476765	−0.238382	−	0.971171i	$-0.576617\pi$
$653$	−12.1832	−0.476765	−0.238382	+	0.971171i	$0.576617\pi$
$654$	71.1053	2.78044
$655$	−12.7830	−0.499475
$656$	−19.0954	−0.745551
$657$	−83.9921	−3.27684
$658$	4.35570	0.169803
$659$	36.2155	1.41076	0.705378	−	0.708832i	$-0.250777\pi$
$659$	36.2155	1.41076	0.705378	+	0.708832i	$0.250777\pi$
$660$	−13.1548	−0.512052
$661$	−50.6944	−1.97178	−0.985892	−	0.167382i	$-0.946469\pi$
$661$	−50.6944	−1.97178	−0.985892	+	0.167382i	$0.946469\pi$
$662$	30.0099	1.16637
$663$	33.5772	1.30403
$664$	−13.6760	−0.530730
$665$	−17.5586	−0.680894
$666$	64.7408	2.50865
$667$	32.9692	1.27657
$668$	−16.7735	−0.648987
$669$	−49.4024	−1.91001
$670$	−45.0498	−1.74042
$671$	−8.63361	−0.333297
$672$	29.3128	1.13077
$673$	16.2806	0.627570	0.313785	−	0.949494i	$-0.398403\pi$
$673$	16.2806	0.627570	0.313785	+	0.949494i	$0.398403\pi$
$674$	−7.68431	−0.295988
$675$	41.9978	1.61650
$676$	1.00542	0.0386698
$677$	6.50254	0.249913	0.124956	−	0.992162i	$-0.460121\pi$
$677$	6.50254	0.249913	0.124956	+	0.992162i	$0.460121\pi$
$678$	3.79815	0.145867
$679$	2.99849	0.115072
$680$	−16.4162	−0.629534
$681$	−34.6376	−1.32732
$682$	2.75083	0.105335
$683$	−23.0374	−0.881503	−0.440751	−	0.897629i	$-0.645288\pi$
$683$	−23.0374	−0.881503	−0.440751	+	0.897629i	$0.645288\pi$
$684$	16.7636	0.640972
$685$	−58.4655	−2.23385
$686$	34.1103	1.30234
$687$	29.8564	1.13909
$688$	61.0208	2.32639
$689$	−37.5563	−1.43078
$690$	−91.9366	−3.49997
$691$	13.8522	0.526963	0.263482	−	0.964664i	$-0.415129\pi$
$691$	13.8522	0.526963	0.263482	+	0.964664i	$0.415129\pi$
$692$	4.70633	0.178908
$693$	20.0592	0.761985
$694$	−19.6746	−0.746838
$695$	26.2577	0.996013
$696$	32.1563	1.21888
$697$	11.1777	0.423387
$698$	55.2861	2.09261
$699$	49.2334	1.86218
$700$	−7.41931	−0.280424
$701$	13.5036	0.510024	0.255012	−	0.966938i	$-0.417921\pi$
$701$	13.5036	0.510024	0.255012	+	0.966938i	$0.417921\pi$
$702$	65.8511	2.48539
$703$	17.3553	0.654566
$704$	−2.88249	−0.108638
$705$	−11.7568	−0.442787
$706$	−13.2043	−0.496951
$707$	−19.5178	−0.734044
$708$	25.6415	0.963668
$709$	0.412771	0.0155019	0.00775097	−	0.999970i	$-0.497533\pi$
$709$	0.412771	0.0155019	0.00775097	+	0.999970i	$0.497533\pi$
$710$	56.7776	2.13082
$711$	49.2536	1.84715
$712$	−17.6899	−0.662957
$713$	5.99614	0.224557
$714$	−30.5398	−1.14292
$715$	−17.8154	−0.666259
$716$	−2.43102	−0.0908513
$717$	−46.5138	−1.73709
$718$	20.2781	0.756771
$719$	−17.7476	−0.661874	−0.330937	−	0.943653i	$-0.607365\pi$
$719$	−17.7476	−0.661874	−0.330937	+	0.943653i	$0.607365\pi$
$720$	−95.6921	−3.56623
$721$	19.8946	0.740914
$722$	−17.9838	−0.669289
$723$	−69.6952	−2.59199
$724$	15.3576	0.570761
$725$	−23.0255	−0.855147
$726$	−44.4605	−1.65008
$727$	−40.7029	−1.50959	−0.754794	−	0.655962i	$-0.772263\pi$
$727$	−40.7029	−1.50959	−0.754794	+	0.655962i	$0.772263\pi$
$728$	14.0324	0.520074
$729$	−15.6429	−0.579365
$730$	−67.8489	−2.51120
$731$	−35.7192	−1.32112
$732$	15.2169	0.562434
$733$	−26.3236	−0.972285	−0.486142	−	0.873880i	$-0.661596\pi$
$733$	−26.3236	−0.972285	−0.486142	+	0.873880i	$0.661596\pi$
$734$	−36.9337	−1.36325
$735$	−27.5191	−1.01506
$736$	27.9583	1.03056
$737$	13.7965	0.508200
$738$	41.4887	1.52722
$739$	−8.19491	−0.301455	−0.150727	−	0.988575i	$-0.548162\pi$
$739$	−8.19491	−0.301455	−0.150727	+	0.988575i	$0.548162\pi$
$740$	16.3113	0.599614
$741$	33.4098	1.22734
$742$	34.1589	1.25401
$743$	45.7357	1.67788	0.838939	−	0.544225i	$-0.183176\pi$
$743$	45.7357	1.67788	0.838939	+	0.544225i	$0.183176\pi$
$744$	5.84831	0.214409
$745$	−4.80800	−0.176151
$746$	30.2582	1.10783
$747$	46.6644	1.70736
$748$	−4.16791	−0.152394
$749$	36.4789	1.33291
$750$	−14.3986	−0.525762
$751$	−36.4108	−1.32865	−0.664324	−	0.747445i	$-0.731280\pi$
$751$	−36.4108	−1.32865	−0.664324	+	0.747445i	$0.731280\pi$
$752$	6.36352	0.232054
$753$	34.0040	1.23918
$754$	−36.1032	−1.31480
$755$	38.7638	1.41076
$756$	−18.6805	−0.679405
$757$	19.3712	0.704059	0.352029	−	0.935989i	$-0.385492\pi$
$757$	19.3712	0.704059	0.352029	+	0.935989i	$0.385492\pi$
$758$	−2.83184	−0.102857
$759$	28.1556	1.02198
$760$	−16.3344	−0.592510
$761$	−1.15815	−0.0419829	−0.0209914	−	0.999780i	$-0.506682\pi$
$761$	−1.15815	−0.0419829	−0.0209914	+	0.999780i	$0.506682\pi$
$762$	4.53084	0.164135
$763$	−27.3174	−0.988954
$764$	−5.42117	−0.196131
$765$	56.0145	2.02521
$766$	−47.7388	−1.72487
$767$	34.7260	1.25388
$768$	54.9563	1.98306
$769$	11.0641	0.398982	0.199491	−	0.979900i	$-0.436071\pi$
$769$	11.0641	0.398982	0.199491	+	0.979900i	$0.436071\pi$
$770$	16.2038	0.583946
$771$	85.2517	3.07026
$772$	20.0504	0.721630
$773$	−5.83405	−0.209836	−0.104918	−	0.994481i	$-0.533458\pi$
$773$	−5.83405	−0.209836	−0.104918	+	0.994481i	$0.533458\pi$
$774$	−132.580	−4.76549
$775$	−4.18768	−0.150426
$776$	2.78943	0.100135
$777$	−36.6026	−1.31311
$778$	29.1222	1.04408
$779$	11.1220	0.398487
$780$	31.4001	1.12430
$781$	−17.3881	−0.622196
$782$	−29.1287	−1.04164
$783$	−57.9743	−2.07183
$784$	14.8951	0.531967
$785$	−55.4204	−1.97804
$786$	−22.1228	−0.789094
$787$	−8.64828	−0.308278	−0.154139	−	0.988049i	$-0.549260\pi$
$787$	−8.64828	−0.308278	−0.154139	+	0.988049i	$0.549260\pi$
$788$	−0.818005	−0.0291402
$789$	−3.94949	−0.140605
$790$	39.7871	1.41556
$791$	−1.45918	−0.0518825
$792$	18.6606	0.663075
$793$	20.6081	0.731814
$794$	−18.2557	−0.647872
$795$	−92.2010	−3.27003
$796$	10.5324	0.373313
$797$	−29.1136	−1.03126	−0.515629	−	0.856812i	$-0.672442\pi$
$797$	−29.1136	−1.03126	−0.515629	+	0.856812i	$0.672442\pi$
$798$	−30.3876	−1.07571
$799$	−3.72496	−0.131780
$800$	−19.5260	−0.690348
$801$	60.3605	2.13273
$802$	8.13465	0.287245
$803$	20.7787	0.733265
$804$	−24.3166	−0.857581
$805$	35.3204	1.24488
$806$	−6.56613	−0.231282
$807$	38.9716	1.37186
$808$	−18.1570	−0.638761
$809$	−31.7846	−1.11749	−0.558743	−	0.829341i	$-0.688716\pi$
$809$	−31.7846	−1.11749	−0.558743	+	0.829341i	$0.688716\pi$
$810$	63.6090	2.23499
$811$	14.3202	0.502850	0.251425	−	0.967877i	$-0.419101\pi$
$811$	14.3202	0.502850	0.251425	+	0.967877i	$0.419101\pi$
$812$	10.2417	0.359413
$813$	62.9230	2.20681
$814$	−16.0162	−0.561366
$815$	−14.7155	−0.515461
$816$	−44.6176	−1.56193
$817$	−35.5411	−1.24343
$818$	12.9547	0.452952
$819$	−47.8804	−1.67308
$820$	10.4530	0.365033
$821$	7.72980	0.269772	0.134886	−	0.990861i	$-0.456933\pi$
$821$	7.72980	0.269772	0.134886	+	0.990861i	$0.456933\pi$
$822$	−101.182	−3.52914
$823$	−3.99506	−0.139259	−0.0696295	−	0.997573i	$-0.522182\pi$
$823$	−3.99506	−0.139259	−0.0696295	+	0.997573i	$0.522182\pi$
$824$	18.5075	0.644739
$825$	−19.6637	−0.684603
$826$	−31.5846	−1.09897
$827$	−44.9918	−1.56452	−0.782259	−	0.622953i	$-0.785933\pi$
$827$	−44.9918	−1.56452	−0.782259	+	0.622953i	$0.785933\pi$
$828$	−33.7211	−1.17189
$829$	46.6492	1.62019	0.810096	−	0.586297i	$-0.199415\pi$
$829$	46.6492	1.62019	0.810096	+	0.586297i	$0.199415\pi$
$830$	37.6956	1.30843
$831$	15.7804	0.547416
$832$	6.88039	0.238535
$833$	−8.71901	−0.302096
$834$	45.4426	1.57355
$835$	−55.7683	−1.92994
$836$	−4.14713	−0.143431
$837$	−10.5439	−0.364449
$838$	−13.9823	−0.483012
$839$	33.6510	1.16176	0.580880	−	0.813989i	$-0.302709\pi$
$839$	33.6510	1.16176	0.580880	+	0.813989i	$0.302709\pi$
$840$	34.4495	1.18862
$841$	2.78472	0.0960250
$842$	14.3562	0.494746
$843$	101.209	3.48581
$844$	−13.6439	−0.469643
$845$	3.34279	0.114995
$846$	−13.8260	−0.475349
$847$	17.0809	0.586907
$848$	49.9049	1.71374
$849$	21.2664	0.729862
$850$	20.3433	0.697771
$851$	−34.9113	−1.19674
$852$	30.6470	1.04995
$853$	−56.3480	−1.92932	−0.964660	−	0.263499i	$-0.915124\pi$
$853$	−56.3480	−1.92932	−0.964660	+	0.263499i	$0.915124\pi$
$854$	−18.7439	−0.641401
$855$	55.7352	1.90611
$856$	33.9355	1.15989
$857$	−42.7863	−1.46155	−0.730777	−	0.682617i	$-0.760842\pi$
$857$	−42.7863	−1.46155	−0.730777	+	0.682617i	$0.760842\pi$
$858$	−30.8320	−1.05259
$859$	−13.8783	−0.473521	−0.236761	−	0.971568i	$-0.576086\pi$
$859$	−13.8783	−0.473521	−0.236761	+	0.971568i	$0.576086\pi$
$860$	−33.4032	−1.13904
$861$	−23.4565	−0.799397
$862$	8.57762	0.292155
$863$	26.0166	0.885615	0.442807	−	0.896617i	$-0.353983\pi$
$863$	26.0166	0.885615	0.442807	+	0.896617i	$0.353983\pi$
$864$	−49.1631	−1.67256
$865$	15.6475	0.532031
$866$	26.2064	0.890531
$867$	−25.8953	−0.879450
$868$	1.86267	0.0632232
$869$	−12.1848	−0.413341
$870$	−88.6336	−3.00496
$871$	−32.9316	−1.11585
$872$	−25.4127	−0.860583
$873$	−9.51793	−0.322133
$874$	−28.9834	−0.980379
$875$	5.53167	0.187005
$876$	−36.6230	−1.23738
$877$	−35.9629	−1.21438	−0.607190	−	0.794557i	$-0.707703\pi$
$877$	−35.9629	−1.21438	−0.607190	+	0.794557i	$0.707703\pi$
$878$	−4.15144	−0.140104
$879$	82.7108	2.78977
$880$	23.6732	0.798023
$881$	−15.8792	−0.534983	−0.267491	−	0.963560i	$-0.586195\pi$
$881$	−15.8792	−0.534983	−0.267491	+	0.963560i	$0.586195\pi$
$882$	−32.3626	−1.08971
$883$	27.7258	0.933046	0.466523	−	0.884509i	$-0.345506\pi$
$883$	27.7258	0.933046	0.466523	+	0.884509i	$0.345506\pi$
$884$	9.94863	0.334609
$885$	85.2525	2.86573
$886$	−53.5855	−1.80024
$887$	36.8196	1.23628	0.618140	−	0.786068i	$-0.287886\pi$
$887$	36.8196	1.23628	0.618140	+	0.786068i	$0.287886\pi$
$888$	−34.0506	−1.14266
$889$	−1.74067	−0.0583801
$890$	48.7593	1.63441
$891$	−19.4802	−0.652613
$892$	−14.6375	−0.490099
$893$	−3.70639	−0.124030
$894$	−8.32090	−0.278292
$895$	−8.08260	−0.270171
$896$	−25.4194	−0.849202
$897$	−67.2062	−2.24395
$898$	−13.6602	−0.455845
$899$	5.78072	0.192798
$900$	23.5507	0.785022
$901$	−29.2125	−0.973208
$902$	−10.2639	−0.341749
$903$	74.9570	2.49441
$904$	−1.35744	−0.0451479
$905$	51.0607	1.69732
$906$	67.0860	2.22878
$907$	−29.3772	−0.975453	−0.487726	−	0.872997i	$-0.662174\pi$
$907$	−29.3772	−0.975453	−0.487726	+	0.872997i	$0.662174\pi$
$908$	−10.2628	−0.340583
$909$	61.9543	2.05489
$910$	−38.6779	−1.28216
$911$	−19.3887	−0.642376	−0.321188	−	0.947015i	$-0.604082\pi$
$911$	−19.3887	−0.642376	−0.321188	+	0.947015i	$0.604082\pi$
$912$	−44.3951	−1.47007
$913$	−11.5443	−0.382059
$914$	−31.4891	−1.04157
$915$	50.5930	1.67255
$916$	8.84617	0.292286
$917$	8.49917	0.280667
$918$	51.2210	1.69055
$919$	−16.8524	−0.555908	−0.277954	−	0.960594i	$-0.589656\pi$
$919$	−16.8524	−0.555908	−0.277954	+	0.960594i	$0.589656\pi$
$920$	32.8577	1.08329
$921$	−32.2021	−1.06110
$922$	−46.0617	−1.51696
$923$	41.5047	1.36614
$924$	8.74638	0.287735
$925$	24.3819	0.801672
$926$	6.35960	0.208989
$927$	−63.1503	−2.07413
$928$	26.9539	0.884805
$929$	44.9076	1.47337	0.736685	−	0.676236i	$-0.236390\pi$
$929$	44.9076	1.47337	0.736685	+	0.676236i	$0.236390\pi$
$930$	−16.1199	−0.528592
$931$	−8.67554	−0.284329
$932$	14.5874	0.477827
$933$	20.4087	0.668151
$934$	54.7112	1.79021
$935$	−13.8574	−0.453185
$936$	−44.5420	−1.45590
$937$	57.0727	1.86448	0.932242	−	0.361836i	$-0.117850\pi$
$937$	57.0727	1.86448	0.932242	+	0.361836i	$0.117850\pi$
$938$	29.9526	0.977989
$939$	14.5345	0.474316
$940$	−3.48344	−0.113617
$941$	4.88163	0.159137	0.0795684	−	0.996829i	$-0.474646\pi$
$941$	4.88163	0.159137	0.0795684	+	0.996829i	$0.474646\pi$
$942$	−95.9124	−3.12500
$943$	−22.3727	−0.728554
$944$	−46.1440	−1.50186
$945$	−62.1087	−2.02040
$946$	32.7989	1.06638
$947$	−30.3198	−0.985260	−0.492630	−	0.870239i	$-0.663964\pi$
$947$	−30.3198	−0.985260	−0.492630	+	0.870239i	$0.663964\pi$
$948$	21.4760	0.697508
$949$	−49.5980	−1.61002
$950$	20.2419	0.656734
$951$	−28.6750	−0.929849
$952$	10.9148	0.353751
$953$	30.1655	0.977157	0.488579	−	0.872520i	$-0.337516\pi$
$953$	30.1655	0.977157	0.488579	+	0.872520i	$0.337516\pi$
$954$	−108.429	−3.51051
$955$	−18.0242	−0.583249
$956$	−13.7816	−0.445729
$957$	27.1440	0.877442
$958$	−22.3564	−0.722303
$959$	38.8725	1.25526
$960$	16.8914	0.545168
$961$	−29.9487	−0.966086
$962$	38.2299	1.23258
$963$	−115.793	−3.73137
$964$	−20.6501	−0.665094
$965$	66.6632	2.14596
$966$	61.1267	1.96672
$967$	41.2781	1.32741	0.663707	−	0.747993i	$-0.268982\pi$
$967$	41.2781	1.32741	0.663707	+	0.747993i	$0.268982\pi$
$968$	15.8900	0.510723
$969$	25.9872	0.834830
$970$	−7.68860	−0.246866
$971$	30.8224	0.989138	0.494569	−	0.869138i	$-0.335326\pi$
$971$	30.8224	0.989138	0.494569	+	0.869138i	$0.335326\pi$
$972$	6.36862	0.204274
$973$	−17.4582	−0.559685
$974$	66.4669	2.12974
$975$	46.9365	1.50317
$976$	−27.3841	−0.876543
$977$	−1.85619	−0.0593849	−0.0296925	−	0.999559i	$-0.509453\pi$
$977$	−1.85619	−0.0593849	−0.0296925	+	0.999559i	$0.509453\pi$
$978$	−25.4671	−0.814349
$979$	−14.9325	−0.477245
$980$	−8.15367	−0.260459
$981$	86.7118	2.76849
$982$	37.1152	1.18439
$983$	−6.82470	−0.217674	−0.108837	−	0.994060i	$-0.534713\pi$
$983$	−6.82470	−0.217674	−0.108837	+	0.994060i	$0.534713\pi$
$984$	−21.8211	−0.695630
$985$	−2.71969	−0.0866564
$986$	−28.0822	−0.894319
$987$	7.81686	0.248813
$988$	9.89902	0.314930
$989$	71.4934	2.27336
$990$	−51.4348	−1.63471
$991$	−5.52409	−0.175479	−0.0877393	−	0.996143i	$-0.527964\pi$
$991$	−5.52409	−0.175479	−0.0877393	+	0.996143i	$0.527964\pi$
$992$	4.90214	0.155643
$993$	53.8565	1.70909
$994$	−37.7502	−1.19736
$995$	35.0181	1.11015
$996$	20.3470	0.644720
$997$	−1.44527	−0.0457720	−0.0228860	−	0.999738i	$-0.507285\pi$
$997$	−1.44527	−0.0457720	−0.0228860	+	0.999738i	$0.507285\pi$
$998$	12.1640	0.385045
$999$	61.3894	1.94227

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2011.2.a.b.1.68	✓	90

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2011.2.a.b.1.68	✓	90	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 2011 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2011.a (trivial)

\(f(q)\)	\(=\)	\(q+1.70485 q^{2} +3.05957 q^{3} +0.906523 q^{4} +3.01399 q^{5} +5.21612 q^{6} -2.00394 q^{7} -1.86422 q^{8} +6.36098 q^{9} +O(q^{10})\)	\(q+1.70485 q^{2} +3.05957 q^{3} +0.906523 q^{4} +3.01399 q^{5} +5.21612 q^{6} -2.00394 q^{7} -1.86422 q^{8} +6.36098 q^{9} +5.13841 q^{10} -1.57364 q^{11} +2.77357 q^{12} +3.75621 q^{13} -3.41642 q^{14} +9.22152 q^{15} -4.99126 q^{16} +2.92170 q^{17} +10.8445 q^{18} +2.90713 q^{19} +2.73225 q^{20} -6.13119 q^{21} -2.68282 q^{22} -5.84789 q^{23} -5.70371 q^{24} +4.08414 q^{25} +6.40378 q^{26} +10.2832 q^{27} -1.81662 q^{28} -5.63779 q^{29} +15.7213 q^{30} -1.02535 q^{31} -4.78093 q^{32} -4.81466 q^{33} +4.98106 q^{34} -6.03985 q^{35} +5.76637 q^{36} +5.96990 q^{37} +4.95622 q^{38} +11.4924 q^{39} -5.61873 q^{40} +3.82577 q^{41} -10.4528 q^{42} -12.2255 q^{43} -1.42654 q^{44} +19.1719 q^{45} -9.96978 q^{46} -1.27493 q^{47} -15.2711 q^{48} -2.98423 q^{49} +6.96285 q^{50} +8.93914 q^{51} +3.40509 q^{52} -9.99846 q^{53} +17.5313 q^{54} -4.74293 q^{55} +3.73578 q^{56} +8.89457 q^{57} -9.61161 q^{58} +9.24496 q^{59} +8.35952 q^{60} +5.48640 q^{61} -1.74807 q^{62} -12.7470 q^{63} +1.83174 q^{64} +11.3212 q^{65} -8.20828 q^{66} -8.76726 q^{67} +2.64858 q^{68} -17.8920 q^{69} -10.2971 q^{70} +11.0496 q^{71} -11.8582 q^{72} -13.2043 q^{73} +10.1778 q^{74} +12.4957 q^{75} +2.63538 q^{76} +3.15347 q^{77} +19.5928 q^{78} +7.74308 q^{79} -15.0436 q^{80} +12.3791 q^{81} +6.52237 q^{82} +7.33603 q^{83} -5.55807 q^{84} +8.80596 q^{85} -20.8427 q^{86} -17.2492 q^{87} +2.93360 q^{88} +9.48918 q^{89} +32.6853 q^{90} -7.52721 q^{91} -5.30124 q^{92} -3.13714 q^{93} -2.17357 q^{94} +8.76205 q^{95} -14.6276 q^{96} -1.49630 q^{97} -5.08767 q^{98} -10.0099 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 90 q + 11 q^{2} + 9 q^{3} + 95 q^{4} + 47 q^{5} + 20 q^{6} + 4 q^{7} + 33 q^{8} + 109 q^{9}+O(q^{10}) \) 90 * q + 11 * q^2 + 9 * q^3 + 95 * q^4 + 47 * q^5 + 20 * q^6 + 4 * q^7 + 33 * q^8 + 109 * q^9	\( 90 q + 11 q^{2} + 9 q^{3} + 95 q^{4} + 47 q^{5} + 20 q^{6} + 4 q^{7} + 33 q^{8} + 109 q^{9} + 19 q^{10} + 24 q^{11} + 14 q^{12} + 36 q^{13} + 43 q^{14} + 4 q^{15} + 93 q^{16} + 55 q^{17} + 18 q^{18} + 15 q^{19} + 76 q^{20} + 65 q^{21} - 3 q^{22} + 30 q^{23} + 46 q^{24} + 107 q^{25} + 38 q^{26} + 21 q^{27} + 2 q^{28} + 149 q^{29} + q^{30} + 33 q^{31} + 67 q^{32} + 13 q^{33} + 15 q^{34} + 34 q^{35} + 103 q^{36} + 23 q^{37} + 38 q^{38} + 32 q^{39} + 43 q^{40} + 144 q^{41} - 20 q^{42} - 5 q^{43} + 37 q^{44} + 103 q^{45} + 8 q^{46} + 28 q^{47} + 12 q^{48} + 114 q^{49} + 67 q^{50} + 11 q^{51} + 59 q^{52} + 59 q^{53} + 38 q^{54} + 3 q^{55} + 106 q^{56} + 2 q^{57} - 5 q^{58} + 86 q^{59} - 28 q^{60} + 113 q^{61} + 12 q^{62} - 29 q^{63} + 71 q^{64} + 51 q^{65} + 15 q^{66} - 14 q^{67} + 96 q^{68} + 116 q^{69} - 24 q^{70} + 47 q^{71} + 13 q^{72} + 22 q^{73} + 57 q^{74} + 7 q^{75} + 2 q^{76} + 100 q^{77} - 34 q^{78} + 18 q^{79} + 100 q^{80} + 154 q^{81} - 4 q^{82} + 24 q^{83} + 35 q^{84} + 30 q^{85} - q^{86} + 49 q^{87} - 74 q^{88} + 97 q^{89} + 22 q^{90} - 25 q^{91} + 23 q^{92} + 32 q^{93} + 21 q^{94} + 56 q^{95} + 29 q^{96} + 26 q^{97} + 15 q^{98} - 11 q^{99}+O(q^{100}) \) 90 * q + 11 * q^2 + 9 * q^3 + 95 * q^4 + 47 * q^5 + 20 * q^6 + 4 * q^7 + 33 * q^8 + 109 * q^9 + 19 * q^10 + 24 * q^11 + 14 * q^12 + 36 * q^13 + 43 * q^14 + 4 * q^15 + 93 * q^16 + 55 * q^17 + 18 * q^18 + 15 * q^19 + 76 * q^20 + 65 * q^21 - 3 * q^22 + 30 * q^23 + 46 * q^24 + 107 * q^25 + 38 * q^26 + 21 * q^27 + 2 * q^28 + 149 * q^29 + q^30 + 33 * q^31 + 67 * q^32 + 13 * q^33 + 15 * q^34 + 34 * q^35 + 103 * q^36 + 23 * q^37 + 38 * q^38 + 32 * q^39 + 43 * q^40 + 144 * q^41 - 20 * q^42 - 5 * q^43 + 37 * q^44 + 103 * q^45 + 8 * q^46 + 28 * q^47 + 12 * q^48 + 114 * q^49 + 67 * q^50 + 11 * q^51 + 59 * q^52 + 59 * q^53 + 38 * q^54 + 3 * q^55 + 106 * q^56 + 2 * q^57 - 5 * q^58 + 86 * q^59 - 28 * q^60 + 113 * q^61 + 12 * q^62 - 29 * q^63 + 71 * q^64 + 51 * q^65 + 15 * q^66 - 14 * q^67 + 96 * q^68 + 116 * q^69 - 24 * q^70 + 47 * q^71 + 13 * q^72 + 22 * q^73 + 57 * q^74 + 7 * q^75 + 2 * q^76 + 100 * q^77 - 34 * q^78 + 18 * q^79 + 100 * q^80 + 154 * q^81 - 4 * q^82 + 24 * q^83 + 35 * q^84 + 30 * q^85 - q^86 + 49 * q^87 - 74 * q^88 + 97 * q^89 + 22 * q^90 - 25 * q^91 + 23 * q^92 + 32 * q^93 + 21 * q^94 + 56 * q^95 + 29 * q^96 + 26 * q^97 + 15 * q^98 - 11 * q^99

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