LMFDB - Embedded newform 8031.2.a.a.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8031,2,Mod(1,8031)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8031, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("8031.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8031 = 3 \cdot 2677 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8031.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:	$64.1278578633$
Analytic rank:	$1$
Dimension:	$92$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Character	$\chi$	$=$	8031.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.36612 q^{2} +1.00000 q^{3} +3.59855 q^{4} -2.41373 q^{5} -2.36612 q^{6} -0.423916 q^{7} -3.78236 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.36612 q^{2} +1.00000 q^{3} +3.59855 q^{4} -2.41373 q^{5} -2.36612 q^{6} -0.423916 q^{7} -3.78236 q^{8} +1.00000 q^{9} +5.71118 q^{10} -2.13709 q^{11} +3.59855 q^{12} -5.25833 q^{13} +1.00304 q^{14} -2.41373 q^{15} +1.75245 q^{16} +2.19385 q^{17} -2.36612 q^{18} +3.20892 q^{19} -8.68591 q^{20} -0.423916 q^{21} +5.05661 q^{22} +4.87499 q^{23} -3.78236 q^{24} +0.826077 q^{25} +12.4419 q^{26} +1.00000 q^{27} -1.52548 q^{28} +2.13255 q^{29} +5.71118 q^{30} +0.554654 q^{31} +3.41821 q^{32} -2.13709 q^{33} -5.19093 q^{34} +1.02322 q^{35} +3.59855 q^{36} -5.83328 q^{37} -7.59271 q^{38} -5.25833 q^{39} +9.12959 q^{40} +0.276934 q^{41} +1.00304 q^{42} -8.49587 q^{43} -7.69040 q^{44} -2.41373 q^{45} -11.5348 q^{46} +6.03505 q^{47} +1.75245 q^{48} -6.82030 q^{49} -1.95460 q^{50} +2.19385 q^{51} -18.9223 q^{52} +6.21935 q^{53} -2.36612 q^{54} +5.15834 q^{55} +1.60340 q^{56} +3.20892 q^{57} -5.04588 q^{58} +10.8086 q^{59} -8.68591 q^{60} +1.06559 q^{61} -1.31238 q^{62} -0.423916 q^{63} -11.5928 q^{64} +12.6922 q^{65} +5.05661 q^{66} +4.85513 q^{67} +7.89468 q^{68} +4.87499 q^{69} -2.42106 q^{70} -3.58389 q^{71} -3.78236 q^{72} -1.07364 q^{73} +13.8023 q^{74} +0.826077 q^{75} +11.5475 q^{76} +0.905944 q^{77} +12.4419 q^{78} -0.303028 q^{79} -4.22993 q^{80} +1.00000 q^{81} -0.655260 q^{82} +11.2037 q^{83} -1.52548 q^{84} -5.29536 q^{85} +20.1023 q^{86} +2.13255 q^{87} +8.08323 q^{88} -5.20373 q^{89} +5.71118 q^{90} +2.22909 q^{91} +17.5429 q^{92} +0.554654 q^{93} -14.2797 q^{94} -7.74546 q^{95} +3.41821 q^{96} +5.56916 q^{97} +16.1377 q^{98} -2.13709 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 92 q - 6 q^{2} + 92 q^{3} + 70 q^{4} - 18 q^{5} - 6 q^{6} - 42 q^{7} - 15 q^{8} + 92 q^{9}+O(q^{10}) $ 92 * q - 6 * q^2 + 92 * q^3 + 70 * q^4 - 18 * q^5 - 6 * q^6 - 42 * q^7 - 15 * q^8 + 92 * q^9	\( 92 q - 6 q^{2} + 92 q^{3} + 70 q^{4} - 18 q^{5} - 6 q^{6} - 42 q^{7} - 15 q^{8} + 92 q^{9} - 44 q^{10} - 24 q^{11} + 70 q^{12} - 48 q^{13} - 29 q^{14} - 18 q^{15} + 26 q^{16} - 69 q^{17} - 6 q^{18} - 74 q^{19} - 42 q^{20} - 42 q^{21} - 62 q^{22} - 19 q^{23} - 15 q^{24} + 16 q^{25} - 27 q^{26} + 92 q^{27} - 101 q^{28} - 54 q^{29} - 44 q^{30} - 67 q^{31} - 36 q^{32} - 24 q^{33} - 63 q^{34} - 31 q^{35} + 70 q^{36} - 70 q^{37} - 18 q^{38} - 48 q^{39} - 125 q^{40} - 98 q^{41} - 29 q^{42} - 159 q^{43} - 52 q^{44} - 18 q^{45} - 68 q^{46} - 15 q^{47} + 26 q^{48} - 28 q^{49} - 7 q^{50} - 69 q^{51} - 98 q^{52} - 23 q^{53} - 6 q^{54} - 93 q^{55} - 48 q^{56} - 74 q^{57} - 37 q^{58} - 36 q^{59} - 42 q^{60} - 172 q^{61} - 26 q^{62} - 42 q^{63} - 23 q^{64} - 66 q^{65} - 62 q^{66} - 143 q^{67} - 74 q^{68} - 19 q^{69} - 30 q^{70} - 9 q^{71} - 15 q^{72} - 134 q^{73} - 19 q^{74} + 16 q^{75} - 157 q^{76} - 25 q^{77} - 27 q^{78} - 138 q^{79} - 29 q^{80} + 92 q^{81} - 61 q^{82} - 24 q^{83} - 101 q^{84} - 84 q^{85} + 14 q^{86} - 54 q^{87} - 140 q^{88} - 148 q^{89} - 44 q^{90} - 115 q^{91} - 12 q^{92} - 67 q^{93} - 79 q^{94} - 10 q^{95} - 36 q^{96} - 165 q^{97} + 36 q^{98} - 24 q^{99}+O(q^{100}) \) 92 * q - 6 * q^2 + 92 * q^3 + 70 * q^4 - 18 * q^5 - 6 * q^6 - 42 * q^7 - 15 * q^8 + 92 * q^9 - 44 * q^10 - 24 * q^11 + 70 * q^12 - 48 * q^13 - 29 * q^14 - 18 * q^15 + 26 * q^16 - 69 * q^17 - 6 * q^18 - 74 * q^19 - 42 * q^20 - 42 * q^21 - 62 * q^22 - 19 * q^23 - 15 * q^24 + 16 * q^25 - 27 * q^26 + 92 * q^27 - 101 * q^28 - 54 * q^29 - 44 * q^30 - 67 * q^31 - 36 * q^32 - 24 * q^33 - 63 * q^34 - 31 * q^35 + 70 * q^36 - 70 * q^37 - 18 * q^38 - 48 * q^39 - 125 * q^40 - 98 * q^41 - 29 * q^42 - 159 * q^43 - 52 * q^44 - 18 * q^45 - 68 * q^46 - 15 * q^47 + 26 * q^48 - 28 * q^49 - 7 * q^50 - 69 * q^51 - 98 * q^52 - 23 * q^53 - 6 * q^54 - 93 * q^55 - 48 * q^56 - 74 * q^57 - 37 * q^58 - 36 * q^59 - 42 * q^60 - 172 * q^61 - 26 * q^62 - 42 * q^63 - 23 * q^64 - 66 * q^65 - 62 * q^66 - 143 * q^67 - 74 * q^68 - 19 * q^69 - 30 * q^70 - 9 * q^71 - 15 * q^72 - 134 * q^73 - 19 * q^74 + 16 * q^75 - 157 * q^76 - 25 * q^77 - 27 * q^78 - 138 * q^79 - 29 * q^80 + 92 * q^81 - 61 * q^82 - 24 * q^83 - 101 * q^84 - 84 * q^85 + 14 * q^86 - 54 * q^87 - 140 * q^88 - 148 * q^89 - 44 * q^90 - 115 * q^91 - 12 * q^92 - 67 * q^93 - 79 * q^94 - 10 * q^95 - 36 * q^96 - 165 * q^97 + 36 * q^98 - 24 * 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 $

$2$	−2.36612	−1.67310	−0.836552	−	0.547888i	$-0.815432\pi$
$2$	−2.36612	−1.67310	−0.836552	+	0.547888i	$0.815432\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	3.59855	1.79927
$5$	−2.41373	−1.07945	−0.539726	−	0.841841i	$-0.681472\pi$
$5$	−2.41373	−1.07945	−0.539726	+	0.841841i	$0.681472\pi$
$6$	−2.36612	−0.965966
$7$	−0.423916	−0.160225	−0.0801125	−	0.996786i	$-0.525528\pi$
$7$	−0.423916	−0.160225	−0.0801125	+	0.996786i	$0.525528\pi$
$8$	−3.78236	−1.33727
$9$	1.00000	0.333333
$10$	5.71118	1.80603
$11$	−2.13709	−0.644355	−0.322178	−	0.946679i	$-0.604415\pi$
$11$	−2.13709	−0.644355	−0.322178	+	0.946679i	$0.604415\pi$
$12$	3.59855	1.03881
$13$	−5.25833	−1.45840	−0.729199	−	0.684302i	$-0.760107\pi$
$13$	−5.25833	−1.45840	−0.729199	+	0.684302i	$0.760107\pi$
$14$	1.00304	0.268073
$15$	−2.41373	−0.623222
$16$	1.75245	0.438112
$17$	2.19385	0.532087	0.266044	−	0.963961i	$-0.414283\pi$
$17$	2.19385	0.532087	0.266044	+	0.963961i	$0.414283\pi$
$18$	−2.36612	−0.557701
$19$	3.20892	0.736177	0.368088	−	0.929791i	$-0.380012\pi$
$19$	3.20892	0.736177	0.368088	+	0.929791i	$0.380012\pi$
$20$	−8.68591	−1.94223
$21$	−0.423916	−0.0925060
$22$	5.05661	1.07807
$23$	4.87499	1.01651	0.508253	−	0.861208i	$-0.330292\pi$
$23$	4.87499	1.01651	0.508253	+	0.861208i	$0.330292\pi$
$24$	−3.78236	−0.772072
$25$	0.826077	0.165215
$26$	12.4419	2.44005
$27$	1.00000	0.192450
$28$	−1.52548	−0.288289
$29$	2.13255	0.396004	0.198002	−	0.980202i	$-0.436555\pi$
$29$	2.13255	0.396004	0.198002	+	0.980202i	$0.436555\pi$
$30$	5.71118	1.04271
$31$	0.554654	0.0996187	0.0498094	−	0.998759i	$-0.484139\pi$
$31$	0.554654	0.0996187	0.0498094	+	0.998759i	$0.484139\pi$
$32$	3.41821	0.604261
$33$	−2.13709	−0.372019
$34$	−5.19093	−0.890237
$35$	1.02322	0.172955
$36$	3.59855	0.599758
$37$	−5.83328	−0.958986	−0.479493	−	0.877546i	$-0.659179\pi$
$37$	−5.83328	−0.958986	−0.479493	+	0.877546i	$0.659179\pi$
$38$	−7.59271	−1.23170
$39$	−5.25833	−0.842007
$40$	9.12959	1.44352
$41$	0.276934	0.0432498	0.0216249	−	0.999766i	$-0.493116\pi$
$41$	0.276934	0.0432498	0.0216249	+	0.999766i	$0.493116\pi$
$42$	1.00304	0.154772
$43$	−8.49587	−1.29561	−0.647804	−	0.761807i	$-0.724313\pi$
$43$	−8.49587	−1.29561	−0.647804	+	0.761807i	$0.724313\pi$
$44$	−7.69040	−1.15937
$45$	−2.41373	−0.359817
$46$	−11.5348	−1.70072
$47$	6.03505	0.880302	0.440151	−	0.897924i	$-0.354925\pi$
$47$	6.03505	0.880302	0.440151	+	0.897924i	$0.354925\pi$
$48$	1.75245	0.252944
$49$	−6.82030	−0.974328
$50$	−1.95460	−0.276423
$51$	2.19385	0.307201
$52$	−18.9223	−2.62406
$53$	6.21935	0.854294	0.427147	−	0.904182i	$-0.359519\pi$
$53$	6.21935	0.854294	0.427147	+	0.904182i	$0.359519\pi$
$54$	−2.36612	−0.321989
$55$	5.15834	0.695550
$56$	1.60340	0.214264
$57$	3.20892	0.425032
$58$	−5.04588	−0.662556
$59$	10.8086	1.40716	0.703581	−	0.710615i	$-0.251583\pi$
$59$	10.8086	1.40716	0.703581	+	0.710615i	$0.251583\pi$
$60$	−8.68591	−1.12135
$61$	1.06559	0.136435	0.0682174	−	0.997670i	$-0.478269\pi$
$61$	1.06559	0.136435	0.0682174	+	0.997670i	$0.478269\pi$
$62$	−1.31238	−0.166672
$63$	−0.423916	−0.0534083
$64$	−11.5928	−1.44910
$65$	12.6922	1.57427
$66$	5.05661	0.622426
$67$	4.85513	0.593149	0.296575	−	0.955010i	$-0.404156\pi$
$67$	4.85513	0.593149	0.296575	+	0.955010i	$0.404156\pi$
$68$	7.89468	0.957371
$69$	4.87499	0.586880
$70$	−2.42106	−0.289372
$71$	−3.58389	−0.425329	−0.212665	−	0.977125i	$-0.568214\pi$
$71$	−3.58389	−0.425329	−0.212665	+	0.977125i	$0.568214\pi$
$72$	−3.78236	−0.445756
$73$	−1.07364	−0.125660	−0.0628298	−	0.998024i	$-0.520013\pi$
$73$	−1.07364	−0.125660	−0.0628298	+	0.998024i	$0.520013\pi$
$74$	13.8023	1.60448
$75$	0.826077	0.0953872
$76$	11.5475	1.32458
$77$	0.905944	0.103242
$78$	12.4419	1.40876
$79$	−0.303028	−0.0340933	−0.0170466	−	0.999855i	$-0.505426\pi$
$79$	−0.303028	−0.0340933	−0.0170466	+	0.999855i	$0.505426\pi$
$80$	−4.22993	−0.472921
$81$	1.00000	0.111111
$82$	−0.655260	−0.0723614
$83$	11.2037	1.22976	0.614882	−	0.788619i	$-0.289204\pi$
$83$	11.2037	1.22976	0.614882	+	0.788619i	$0.289204\pi$
$84$	−1.52548	−0.166444
$85$	−5.29536	−0.574363
$86$	20.1023	2.16769
$87$	2.13255	0.228633
$88$	8.08323	0.861675
$89$	−5.20373	−0.551594	−0.275797	−	0.961216i	$-0.588942\pi$
$89$	−5.20373	−0.551594	−0.275797	+	0.961216i	$0.588942\pi$
$90$	5.71118	0.602011
$91$	2.22909	0.233672
$92$	17.5429	1.82897
$93$	0.554654	0.0575149
$94$	−14.2797	−1.47284
$95$	−7.74546	−0.794667
$96$	3.41821	0.348870
$97$	5.56916	0.565462	0.282731	−	0.959199i	$-0.408760\pi$
$97$	5.56916	0.565462	0.282731	+	0.959199i	$0.408760\pi$
$98$	16.1377	1.63015
$99$	−2.13709	−0.214785
$100$	2.97268	0.297268
$101$	10.7912	1.07377	0.536885	−	0.843656i	$-0.319601\pi$
$101$	10.7912	1.07377	0.536885	+	0.843656i	$0.319601\pi$
$102$	−5.19093	−0.513979
$103$	−7.99310	−0.787583	−0.393792	−	0.919200i	$-0.628837\pi$
$103$	−7.99310	−0.787583	−0.393792	+	0.919200i	$0.628837\pi$
$104$	19.8889	1.95027
$105$	1.02322	0.0998557
$106$	−14.7158	−1.42932
$107$	−9.58272	−0.926396	−0.463198	−	0.886255i	$-0.653298\pi$
$107$	−9.58272	−0.926396	−0.463198	+	0.886255i	$0.653298\pi$
$108$	3.59855	0.346270
$109$	15.4187	1.47684	0.738420	−	0.674341i	$-0.235572\pi$
$109$	15.4187	1.47684	0.738420	+	0.674341i	$0.235572\pi$
$110$	−12.2053	−1.16373
$111$	−5.83328	−0.553671
$112$	−0.742890	−0.0701965
$113$	−13.6095	−1.28027	−0.640135	−	0.768262i	$-0.721122\pi$
$113$	−13.6095	−1.28027	−0.640135	+	0.768262i	$0.721122\pi$
$114$	−7.59271	−0.711122
$115$	−11.7669	−1.09727
$116$	7.67408	0.712520
$117$	−5.25833	−0.486133
$118$	−25.5745	−2.35433
$119$	−0.930008	−0.0852537
$120$	9.12959	0.833414
$121$	−6.43287	−0.584806
$122$	−2.52132	−0.228269
$123$	0.276934	0.0249703
$124$	1.99595	0.179241
$125$	10.0747	0.901109
$126$	1.00304	0.0893577
$127$	19.7685	1.75417	0.877084	−	0.480338i	$-0.159486\pi$
$127$	19.7685	1.75417	0.877084	+	0.480338i	$0.159486\pi$
$128$	20.5936	1.82024
$129$	−8.49587	−0.748020
$130$	−30.0313	−2.63392
$131$	−4.24106	−0.370543	−0.185271	−	0.982687i	$-0.559316\pi$
$131$	−4.24106	−0.370543	−0.185271	+	0.982687i	$0.559316\pi$
$132$	−7.69040	−0.669364
$133$	−1.36031	−0.117954
$134$	−11.4879	−0.992399
$135$	−2.41373	−0.207741
$136$	−8.29795	−0.711543
$137$	19.1481	1.63593	0.817967	−	0.575265i	$-0.195101\pi$
$137$	19.1481	1.63593	0.817967	+	0.575265i	$0.195101\pi$
$138$	−11.5348	−0.981910
$139$	10.4304	0.884692	0.442346	−	0.896845i	$-0.354146\pi$
$139$	10.4304	0.884692	0.442346	+	0.896845i	$0.354146\pi$
$140$	3.68209	0.311194
$141$	6.03505	0.508243
$142$	8.47993	0.711620
$143$	11.2375	0.939727
$144$	1.75245	0.146037
$145$	−5.14739	−0.427468
$146$	2.54036	0.210241
$147$	−6.82030	−0.562528
$148$	−20.9913	−1.72548
$149$	−20.2545	−1.65932	−0.829658	−	0.558272i	$-0.811465\pi$
$149$	−20.2545	−1.65932	−0.829658	+	0.558272i	$0.811465\pi$
$150$	−1.95460	−0.159593
$151$	−21.9733	−1.78816	−0.894081	−	0.447905i	$-0.852170\pi$
$151$	−21.9733	−1.78816	−0.894081	+	0.447905i	$0.852170\pi$
$152$	−12.1373	−0.984465
$153$	2.19385	0.177362
$154$	−2.14358	−0.172734
$155$	−1.33878	−0.107534
$156$	−18.9223	−1.51500
$157$	18.4819	1.47502	0.737508	−	0.675338i	$-0.236002\pi$
$157$	18.4819	1.47502	0.737508	+	0.675338i	$0.236002\pi$
$158$	0.717001	0.0570415
$159$	6.21935	0.493227
$160$	−8.25063	−0.652270
$161$	−2.06658	−0.162870
$162$	−2.36612	−0.185900
$163$	−16.2270	−1.27100	−0.635500	−	0.772101i	$-0.719206\pi$
$163$	−16.2270	−1.27100	−0.635500	+	0.772101i	$0.719206\pi$
$164$	0.996560	0.0778182
$165$	5.15834	0.401576
$166$	−26.5093	−2.05752
$167$	−9.75977	−0.755234	−0.377617	−	0.925962i	$-0.623256\pi$
$167$	−9.75977	−0.755234	−0.377617	+	0.925962i	$0.623256\pi$
$168$	1.60340	0.123705
$169$	14.6500	1.12693
$170$	12.5295	0.960968
$171$	3.20892	0.245392
$172$	−30.5728	−2.33115
$173$	5.17943	0.393785	0.196892	−	0.980425i	$-0.436915\pi$
$173$	5.17943	0.393785	0.196892	+	0.980425i	$0.436915\pi$
$174$	−5.04588	−0.382527
$175$	−0.350187	−0.0264717
$176$	−3.74513	−0.282300
$177$	10.8086	0.812426
$178$	12.3127	0.922874
$179$	−12.6301	−0.944018	−0.472009	−	0.881594i	$-0.656471\pi$
$179$	−12.6301	−0.944018	−0.472009	+	0.881594i	$0.656471\pi$
$180$	−8.68591	−0.647410
$181$	0.150038	0.0111522	0.00557611	−	0.999984i	$-0.498225\pi$
$181$	0.150038	0.0111522	0.00557611	+	0.999984i	$0.498225\pi$
$182$	−5.27430	−0.390957
$183$	1.06559	0.0787707
$184$	−18.4390	−1.35934
$185$	14.0800	1.03518
$186$	−1.31238	−0.0962284
$187$	−4.68845	−0.342853
$188$	21.7174	1.58390
$189$	−0.423916	−0.0308353
$190$	18.3267	1.32956
$191$	−14.4496	−1.04554	−0.522769	−	0.852474i	$-0.675101\pi$
$191$	−14.4496	−1.04554	−0.522769	+	0.852474i	$0.675101\pi$
$192$	−11.5928	−0.836640
$193$	−13.7119	−0.987002	−0.493501	−	0.869745i	$-0.664283\pi$
$193$	−13.7119	−0.987002	−0.493501	+	0.869745i	$0.664283\pi$
$194$	−13.1773	−0.946077
$195$	12.6922	0.908905
$196$	−24.5432	−1.75308
$197$	11.8522	0.844437	0.422218	−	0.906494i	$-0.361252\pi$
$197$	11.8522	0.844437	0.422218	+	0.906494i	$0.361252\pi$
$198$	5.05661	0.359358
$199$	2.91671	0.206760	0.103380	−	0.994642i	$-0.467034\pi$
$199$	2.91671	0.206760	0.103380	+	0.994642i	$0.467034\pi$
$200$	−3.12452	−0.220937
$201$	4.85513	0.342455
$202$	−25.5334	−1.79653
$203$	−0.904021	−0.0634498
$204$	7.89468	0.552738
$205$	−0.668443	−0.0466861
$206$	18.9127	1.31771
$207$	4.87499	0.338835
$208$	−9.21495	−0.638942
$209$	−6.85774	−0.474360
$210$	−2.42106	−0.167069
$211$	0.00251402	0.000173072 0	8.65361e−5	−	1.00000i	$-0.499972\pi$
$211$	0.00251402	0.000173072 0	8.65361e−5		1.00000i	$0.499972\pi$
$212$	22.3806	1.53711
$213$	−3.58389	−0.245564
$214$	22.6739	1.54996
$215$	20.5067	1.39855
$216$	−3.78236	−0.257357
$217$	−0.235126	−0.0159614
$218$	−36.4825	−2.47091
$219$	−1.07364	−0.0725496
$220$	18.5625	1.25149
$221$	−11.5360	−0.775995
$222$	13.8023	0.926348
$223$	19.9172	1.33376	0.666879	−	0.745166i	$-0.267630\pi$
$223$	19.9172	1.33376	0.666879	+	0.745166i	$0.267630\pi$
$224$	−1.44903	−0.0968177
$225$	0.826077	0.0550718
$226$	32.2017	2.14202
$227$	7.59943	0.504392	0.252196	−	0.967676i	$-0.418847\pi$
$227$	7.59943	0.504392	0.252196	+	0.967676i	$0.418847\pi$
$228$	11.5475	0.764749
$229$	−8.28408	−0.547427	−0.273714	−	0.961811i	$-0.588252\pi$
$229$	−8.28408	−0.547427	−0.273714	+	0.961811i	$0.588252\pi$
$230$	27.8419	1.83584
$231$	0.905944	0.0596067
$232$	−8.06607	−0.529564
$233$	−18.6171	−1.21964	−0.609822	−	0.792539i	$-0.708759\pi$
$233$	−18.6171	−1.21964	−0.609822	+	0.792539i	$0.708759\pi$
$234$	12.4419	0.813350
$235$	−14.5670	−0.950243
$236$	38.8953	2.53187
$237$	−0.303028	−0.0196838
$238$	2.20052	0.142638
$239$	−21.9934	−1.42264	−0.711318	−	0.702870i	$-0.751901\pi$
$239$	−21.9934	−1.42264	−0.711318	+	0.702870i	$0.751901\pi$
$240$	−4.22993	−0.273041
$241$	26.3772	1.69910	0.849551	−	0.527506i	$-0.176873\pi$
$241$	26.3772	1.69910	0.849551	+	0.527506i	$0.176873\pi$
$242$	15.2210	0.978441
$243$	1.00000	0.0641500
$244$	3.83457	0.245483
$245$	16.4623	1.05174
$246$	−0.655260	−0.0417779
$247$	−16.8736	−1.07364
$248$	−2.09790	−0.133217
$249$	11.2037	0.710004
$250$	−23.8380	−1.50765
$251$	−1.06472	−0.0672044	−0.0336022	−	0.999435i	$-0.510698\pi$
$251$	−1.06472	−0.0672044	−0.0336022	+	0.999435i	$0.510698\pi$
$252$	−1.52548	−0.0960962
$253$	−10.4183	−0.654991
$254$	−46.7746	−2.93490
$255$	−5.29536	−0.331608
$256$	−25.5415	−1.59634
$257$	−23.2264	−1.44882	−0.724411	−	0.689368i	$-0.757888\pi$
$257$	−23.2264	−1.44882	−0.724411	+	0.689368i	$0.757888\pi$
$258$	20.1023	1.25151
$259$	2.47282	0.153654
$260$	45.6734	2.83254
$261$	2.13255	0.132001
$262$	10.0349	0.619956
$263$	22.2121	1.36966	0.684829	−	0.728704i	$-0.259877\pi$
$263$	22.2121	1.36966	0.684829	+	0.728704i	$0.259877\pi$
$264$	8.08323	0.497489
$265$	−15.0118	−0.922169
$266$	3.21867	0.197349
$267$	−5.20373	−0.318463
$268$	17.4714	1.06724
$269$	−2.04284	−0.124554	−0.0622770	−	0.998059i	$-0.519836\pi$
$269$	−2.04284	−0.124554	−0.0622770	+	0.998059i	$0.519836\pi$
$270$	5.71118	0.347571
$271$	11.9706	0.727160	0.363580	−	0.931563i	$-0.381554\pi$
$271$	11.9706	0.727160	0.363580	+	0.931563i	$0.381554\pi$
$272$	3.84461	0.233114
$273$	2.22909	0.134911
$274$	−45.3068	−2.73709
$275$	−1.76540	−0.106458
$276$	17.5429	1.05596
$277$	9.52681	0.572410	0.286205	−	0.958168i	$-0.407606\pi$
$277$	9.52681	0.572410	0.286205	+	0.958168i	$0.407606\pi$
$278$	−24.6795	−1.48018
$279$	0.554654	0.0332062
$280$	−3.87018	−0.231287
$281$	3.93029	0.234462	0.117231	−	0.993105i	$-0.462598\pi$
$281$	3.93029	0.234462	0.117231	+	0.993105i	$0.462598\pi$
$282$	−14.2797	−0.850342
$283$	−30.9124	−1.83755	−0.918777	−	0.394778i	$-0.870822\pi$
$283$	−30.9124	−1.83755	−0.918777	+	0.394778i	$0.870822\pi$
$284$	−12.8968	−0.765284
$285$	−7.74546	−0.458801
$286$	−26.5893	−1.57226
$287$	−0.117397	−0.00692970
$288$	3.41821	0.201420
$289$	−12.1870	−0.716883
$290$	12.1794	0.715197
$291$	5.56916	0.326470
$292$	−3.86353	−0.226096
$293$	−10.4683	−0.611567	−0.305783	−	0.952101i	$-0.598918\pi$
$293$	−10.4683	−0.611567	−0.305783	+	0.952101i	$0.598918\pi$
$294$	16.1377	0.941168
$295$	−26.0891	−1.51896
$296$	22.0636	1.28242
$297$	−2.13709	−0.124006
$298$	47.9248	2.77621
$299$	−25.6343	−1.48247
$300$	2.97268	0.171628
$301$	3.60153	0.207589
$302$	51.9916	2.99178
$303$	10.7912	0.619941
$304$	5.62347	0.322528
$305$	−2.57204	−0.147275
$306$	−5.19093	−0.296746
$307$	9.57619	0.546542	0.273271	−	0.961937i	$-0.411894\pi$
$307$	9.57619	0.546542	0.273271	+	0.961937i	$0.411894\pi$
$308$	3.26008	0.185760
$309$	−7.99310	−0.454711
$310$	3.16773	0.179915
$311$	−26.4810	−1.50160	−0.750801	−	0.660528i	$-0.770332\pi$
$311$	−26.4810	−1.50160	−0.750801	+	0.660528i	$0.770332\pi$
$312$	19.8889	1.12599
$313$	26.1714	1.47929	0.739647	−	0.672995i	$-0.234992\pi$
$313$	26.1714	1.47929	0.739647	+	0.672995i	$0.234992\pi$
$314$	−43.7305	−2.46785
$315$	1.02322	0.0576517
$316$	−1.09046	−0.0613431
$317$	8.41074	0.472394	0.236197	−	0.971705i	$-0.424099\pi$
$317$	8.41074	0.472394	0.236197	+	0.971705i	$0.424099\pi$
$318$	−14.7158	−0.825219
$319$	−4.55744	−0.255168
$320$	27.9819	1.56424
$321$	−9.58272	−0.534855
$322$	4.88979	0.272498
$323$	7.03990	0.391710
$324$	3.59855	0.199919
$325$	−4.34379	−0.240950
$326$	38.3952	2.12651
$327$	15.4187	0.852654
$328$	−1.04746	−0.0578365
$329$	−2.55835	−0.141046
$330$	−12.2053	−0.671878
$331$	3.04912	0.167595	0.0837975	−	0.996483i	$-0.473295\pi$
$331$	3.04912	0.167595	0.0837975	+	0.996483i	$0.473295\pi$
$332$	40.3170	2.21268
$333$	−5.83328	−0.319662
$334$	23.0928	1.26358
$335$	−11.7190	−0.640276
$336$	−0.742890	−0.0405280
$337$	−14.6204	−0.796425	−0.398212	−	0.917293i	$-0.630369\pi$
$337$	−14.6204	−0.796425	−0.398212	+	0.917293i	$0.630369\pi$
$338$	−34.6638	−1.88546
$339$	−13.6095	−0.739164
$340$	−19.0556	−1.03344
$341$	−1.18534	−0.0641899
$342$	−7.59271	−0.410567
$343$	5.85864	0.316337
$344$	32.1345	1.73258
$345$	−11.7669	−0.633508
$346$	−12.2552	−0.658842
$347$	−23.1015	−1.24015	−0.620075	−	0.784542i	$-0.712898\pi$
$347$	−23.1015	−1.24015	−0.620075	+	0.784542i	$0.712898\pi$
$348$	7.67408	0.411374
$349$	−36.9724	−1.97909	−0.989545	−	0.144226i	$-0.953931\pi$
$349$	−36.9724	−1.97909	−0.989545	+	0.144226i	$0.953931\pi$
$350$	0.828587	0.0442898
$351$	−5.25833	−0.280669
$352$	−7.30501	−0.389359
$353$	27.1124	1.44305	0.721525	−	0.692389i	$-0.243442\pi$
$353$	27.1124	1.44305	0.721525	+	0.692389i	$0.243442\pi$
$354$	−25.5745	−1.35927
$355$	8.65053	0.459123
$356$	−18.7259	−0.992469
$357$	−0.930008	−0.0492213
$358$	29.8844	1.57944
$359$	−22.3933	−1.18187	−0.590935	−	0.806719i	$-0.701241\pi$
$359$	−22.3933	−1.18187	−0.590935	+	0.806719i	$0.701241\pi$
$360$	9.12959	0.481172
$361$	−8.70283	−0.458043
$362$	−0.355008	−0.0186588
$363$	−6.43287	−0.337638
$364$	8.02148	0.420440
$365$	2.59146	0.135643
$366$	−2.52132	−0.131791
$367$	−20.9026	−1.09111	−0.545553	−	0.838076i	$-0.683680\pi$
$367$	−20.9026	−1.09111	−0.545553	+	0.838076i	$0.683680\pi$
$368$	8.54316	0.445343
$369$	0.276934	0.0144166
$370$	−33.3149	−1.73196
$371$	−2.63648	−0.136879
$372$	1.99595	0.103485
$373$	−31.8866	−1.65103	−0.825514	−	0.564382i	$-0.809115\pi$
$373$	−31.8866	−1.65103	−0.825514	+	0.564382i	$0.809115\pi$
$374$	11.0935	0.573629
$375$	10.0747	0.520256
$376$	−22.8267	−1.17720
$377$	−11.2136	−0.577532
$378$	1.00304	0.0515907
$379$	1.64967	0.0847380	0.0423690	−	0.999102i	$-0.486509\pi$
$379$	1.64967	0.0847380	0.0423690	+	0.999102i	$0.486509\pi$
$380$	−27.8724	−1.42982
$381$	19.7685	1.01277
$382$	34.1896	1.74929
$383$	−22.3576	−1.14242	−0.571209	−	0.820805i	$-0.693525\pi$
$383$	−22.3576	−1.14242	−0.571209	+	0.820805i	$0.693525\pi$
$384$	20.5936	1.05091
$385$	−2.18670	−0.111445
$386$	32.4440	1.65136
$387$	−8.49587	−0.431870
$388$	20.0409	1.01742
$389$	0.913103	0.0462961	0.0231481	−	0.999732i	$-0.492631\pi$
$389$	0.913103	0.0462961	0.0231481	+	0.999732i	$0.492631\pi$
$390$	−30.0313	−1.52069
$391$	10.6950	0.540870
$392$	25.7968	1.30294
$393$	−4.24106	−0.213933
$394$	−28.0439	−1.41283
$395$	0.731426	0.0368020
$396$	−7.69040	−0.386457
$397$	−10.6023	−0.532112	−0.266056	−	0.963958i	$-0.585721\pi$
$397$	−10.6023	−0.532112	−0.266056	+	0.963958i	$0.585721\pi$
$398$	−6.90130	−0.345931
$399$	−1.36031	−0.0681008
$400$	1.44766	0.0723829
$401$	26.7693	1.33679	0.668397	−	0.743805i	$-0.266981\pi$
$401$	26.7693	1.33679	0.668397	+	0.743805i	$0.266981\pi$
$402$	−11.4879	−0.572962
$403$	−2.91655	−0.145284
$404$	38.8328	1.93200
$405$	−2.41373	−0.119939
$406$	2.13903	0.106158
$407$	12.4662	0.617928
$408$	−8.29795	−0.410810
$409$	16.3611	0.809007	0.404503	−	0.914537i	$-0.367444\pi$
$409$	16.3611	0.809007	0.404503	+	0.914537i	$0.367444\pi$
$410$	1.58162	0.0781106
$411$	19.1481	0.944507
$412$	−28.7635	−1.41708
$413$	−4.58194	−0.225463
$414$	−11.5348	−0.566906
$415$	−27.0426	−1.32747
$416$	−17.9741	−0.881253
$417$	10.4304	0.510777
$418$	16.2263	0.793653
$419$	26.5353	1.29633	0.648167	−	0.761498i	$-0.275536\pi$
$419$	26.5353	1.29633	0.648167	+	0.761498i	$0.275536\pi$
$420$	3.68209	0.179668
$421$	10.0034	0.487536	0.243768	−	0.969834i	$-0.421616\pi$
$421$	10.0034	0.487536	0.243768	+	0.969834i	$0.421616\pi$
$422$	−0.00594848	−0.000289568 0
$423$	6.03505	0.293434
$424$	−23.5238	−1.14242
$425$	1.81229	0.0879091
$426$	8.47993	0.410854
$427$	−0.451720	−0.0218603
$428$	−34.4839	−1.66684
$429$	11.2375	0.542552
$430$	−48.5215	−2.33991
$431$	−5.75069	−0.277001	−0.138501	−	0.990362i	$-0.544228\pi$
$431$	−5.75069	−0.277001	−0.138501	+	0.990362i	$0.544228\pi$
$432$	1.75245	0.0843147
$433$	−40.6349	−1.95279	−0.976394	−	0.215998i	$-0.930699\pi$
$433$	−40.6349	−1.95279	−0.976394	+	0.215998i	$0.930699\pi$
$434$	0.556338	0.0267051
$435$	−5.14739	−0.246799
$436$	55.4848	2.65724
$437$	15.6434	0.748328
$438$	2.54036	0.121383
$439$	−1.07601	−0.0513552	−0.0256776	−	0.999670i	$-0.508174\pi$
$439$	−1.07601	−0.0513552	−0.0256776	+	0.999670i	$0.508174\pi$
$440$	−19.5107	−0.930137
$441$	−6.82030	−0.324776
$442$	27.2956	1.29832
$443$	−25.1636	−1.19556	−0.597780	−	0.801660i	$-0.703951\pi$
$443$	−25.1636	−1.19556	−0.597780	+	0.801660i	$0.703951\pi$
$444$	−20.9913	−0.996205
$445$	12.5604	0.595419
$446$	−47.1267	−2.23151
$447$	−20.2545	−0.958007
$448$	4.91438	0.232182
$449$	−1.00618	−0.0474845	−0.0237422	−	0.999718i	$-0.507558\pi$
$449$	−1.00618	−0.0474845	−0.0237422	+	0.999718i	$0.507558\pi$
$450$	−1.95460	−0.0921408
$451$	−0.591831	−0.0278682
$452$	−48.9743	−2.30356
$453$	−21.9733	−1.03240
$454$	−17.9812	−0.843900
$455$	−5.38041	−0.252238
$456$	−12.1373	−0.568381
$457$	8.61204	0.402854	0.201427	−	0.979504i	$-0.435442\pi$
$457$	8.61204	0.402854	0.201427	+	0.979504i	$0.435442\pi$
$458$	19.6012	0.915902
$459$	2.19385	0.102400
$460$	−42.3437	−1.97429
$461$	−3.55101	−0.165387	−0.0826936	−	0.996575i	$-0.526352\pi$
$461$	−3.55101	−0.165387	−0.0826936	+	0.996575i	$0.526352\pi$
$462$	−2.14358	−0.0997282
$463$	−25.8210	−1.20000	−0.600001	−	0.799999i	$-0.704833\pi$
$463$	−25.8210	−1.20000	−0.600001	+	0.799999i	$0.704833\pi$
$464$	3.73718	0.173494
$465$	−1.33878	−0.0620845
$466$	44.0503	2.04059
$467$	32.6996	1.51316	0.756579	−	0.653903i	$-0.226869\pi$
$467$	32.6996	1.51316	0.756579	+	0.653903i	$0.226869\pi$
$468$	−18.9223	−0.874686
$469$	−2.05817	−0.0950373
$470$	34.4672	1.58986
$471$	18.4819	0.851601
$472$	−40.8821	−1.88175
$473$	18.1564	0.834833
$474$	0.717001	0.0329330
$475$	2.65082	0.121628
$476$	−3.34668	−0.153395
$477$	6.21935	0.284765
$478$	52.0392	2.38022
$479$	−1.44887	−0.0662004	−0.0331002	−	0.999452i	$-0.510538\pi$
$479$	−1.44887	−0.0662004	−0.0331002	+	0.999452i	$0.510538\pi$
$480$	−8.25063	−0.376588
$481$	30.6733	1.39858
$482$	−62.4117	−2.84277
$483$	−2.06658	−0.0940328
$484$	−23.1490	−1.05223
$485$	−13.4424	−0.610389
$486$	−2.36612	−0.107330
$487$	6.57418	0.297905	0.148952	−	0.988844i	$-0.452410\pi$
$487$	6.57418	0.297905	0.148952	+	0.988844i	$0.452410\pi$
$488$	−4.03045	−0.182450
$489$	−16.2270	−0.733812
$490$	−38.9519	−1.75967
$491$	−1.83169	−0.0826632	−0.0413316	−	0.999145i	$-0.513160\pi$
$491$	−1.83169	−0.0826632	−0.0413316	+	0.999145i	$0.513160\pi$
$492$	0.996560	0.0449284
$493$	4.67850	0.210709
$494$	39.9250	1.79631
$495$	5.15834	0.231850
$496$	0.972002	0.0436442
$497$	1.51927	0.0681484
$498$	−26.5093	−1.18791
$499$	36.7768	1.64636	0.823178	−	0.567784i	$-0.192199\pi$
$499$	36.7768	1.64636	0.823178	+	0.567784i	$0.192199\pi$
$500$	36.2543	1.62134
$501$	−9.75977	−0.436034
$502$	2.51926	0.112440
$503$	38.7217	1.72652	0.863259	−	0.504762i	$-0.168420\pi$
$503$	38.7217	1.72652	0.863259	+	0.504762i	$0.168420\pi$
$504$	1.60340	0.0714212
$505$	−26.0471	−1.15908
$506$	24.6509	1.09587
$507$	14.6500	0.650631
$508$	71.1377	3.15623
$509$	8.83016	0.391390	0.195695	−	0.980665i	$-0.437304\pi$
$509$	8.83016	0.391390	0.195695	+	0.980665i	$0.437304\pi$
$510$	12.5295	0.554815
$511$	0.455131	0.0201338
$512$	19.2470	0.850607
$513$	3.20892	0.141677
$514$	54.9565	2.42403
$515$	19.2932	0.850158
$516$	−30.5728	−1.34589
$517$	−12.8974	−0.567227
$518$	−5.85100	−0.257078
$519$	5.17943	0.227352
$520$	−48.0064	−2.10522
$521$	22.7764	0.997854	0.498927	−	0.866644i	$-0.333728\pi$
$521$	22.7764	0.997854	0.498927	+	0.866644i	$0.333728\pi$
$522$	−5.04588	−0.220852
$523$	−6.22979	−0.272410	−0.136205	−	0.990681i	$-0.543491\pi$
$523$	−6.22979	−0.272410	−0.136205	+	0.990681i	$0.543491\pi$
$524$	−15.2616	−0.666708
$525$	−0.350187	−0.0152834
$526$	−52.5566	−2.29158
$527$	1.21683	0.0530059
$528$	−3.74513	−0.162986
$529$	0.765502	0.0332827
$530$	35.5198	1.54288
$531$	10.8086	0.469054
$532$	−4.89515	−0.212232
$533$	−1.45621	−0.0630754
$534$	12.3127	0.532822
$535$	23.1301	1.00000
$536$	−18.3639	−0.793199
$537$	−12.6301	−0.545029
$538$	4.83361	0.208392
$539$	14.5756	0.627814
$540$	−8.68591	−0.373782
$541$	−38.5766	−1.65854	−0.829268	−	0.558851i	$-0.811242\pi$
$541$	−38.5766	−1.65854	−0.829268	+	0.558851i	$0.811242\pi$
$542$	−28.3239	−1.21661
$543$	0.150038	0.00643874
$544$	7.49906	0.321519
$545$	−37.2164	−1.59418
$546$	−5.27430	−0.225719
$547$	−34.9694	−1.49518	−0.747592	−	0.664158i	$-0.768790\pi$
$547$	−34.9694	−1.49518	−0.747592	+	0.664158i	$0.768790\pi$
$548$	68.9054	2.94349
$549$	1.06559	0.0454783
$550$	4.17715	0.178114
$551$	6.84318	0.291529
$552$	−18.4390	−0.784815
$553$	0.128458	0.00546260
$554$	−22.5416	−0.957701
$555$	14.0800	0.597661
$556$	37.5341	1.59180
$557$	21.9130	0.928485	0.464243	−	0.885708i	$-0.346327\pi$
$557$	21.9130	0.928485	0.464243	+	0.885708i	$0.346327\pi$
$558$	−1.31238	−0.0555575
$559$	44.6741	1.88951
$560$	1.79313	0.0757737
$561$	−4.68845	−0.197947
$562$	−9.29957	−0.392278
$563$	−39.2207	−1.65295	−0.826477	−	0.562970i	$-0.809659\pi$
$563$	−39.2207	−1.65295	−0.826477	+	0.562970i	$0.809659\pi$
$564$	21.7174	0.914468
$565$	32.8495	1.38199
$566$	73.1427	3.07442
$567$	−0.423916	−0.0178028
$568$	13.5556	0.568779
$569$	−42.3523	−1.77550	−0.887751	−	0.460325i	$-0.847733\pi$
$569$	−42.3523	−1.77550	−0.887751	+	0.460325i	$0.847733\pi$
$570$	18.3267	0.767622
$571$	17.0044	0.711614	0.355807	−	0.934560i	$-0.384206\pi$
$571$	17.0044	0.711614	0.355807	+	0.934560i	$0.384206\pi$
$572$	40.4387	1.69083
$573$	−14.4496	−0.603642
$574$	0.277775	0.0115941
$575$	4.02712	0.167942
$576$	−11.5928	−0.483034
$577$	−26.9501	−1.12195	−0.560973	−	0.827834i	$-0.689573\pi$
$577$	−26.9501	−1.12195	−0.560973	+	0.827834i	$0.689573\pi$
$578$	28.8360	1.19942
$579$	−13.7119	−0.569846
$580$	−18.5231	−0.769131
$581$	−4.74942	−0.197039
$582$	−13.1773	−0.546218
$583$	−13.2913	−0.550469
$584$	4.06088	0.168040
$585$	12.6922	0.524757
$586$	24.7694	1.02321
$587$	−8.32757	−0.343716	−0.171858	−	0.985122i	$-0.554977\pi$
$587$	−8.32757	−0.343716	−0.171858	+	0.985122i	$0.554977\pi$
$588$	−24.5432	−1.01214
$589$	1.77984	0.0733370
$590$	61.7300	2.54138
$591$	11.8522	0.487536
$592$	−10.2225	−0.420143
$593$	18.0855	0.742684	0.371342	−	0.928496i	$-0.378898\pi$
$593$	18.0855	0.742684	0.371342	+	0.928496i	$0.378898\pi$
$594$	5.05661	0.207475
$595$	2.24479	0.0920273
$596$	−72.8869	−2.98556
$597$	2.91671	0.119373
$598$	60.6539	2.48032
$599$	44.7037	1.82654	0.913271	−	0.407353i	$-0.133548\pi$
$599$	44.7037	1.82654	0.913271	+	0.407353i	$0.133548\pi$
$600$	−3.12452	−0.127558
$601$	−40.1438	−1.63750	−0.818750	−	0.574150i	$-0.805333\pi$
$601$	−40.1438	−1.63750	−0.818750	+	0.574150i	$0.805333\pi$
$602$	−8.52168	−0.347318
$603$	4.85513	0.197716
$604$	−79.0720	−3.21739
$605$	15.5272	0.631270
$606$	−25.5334	−1.03722
$607$	37.8162	1.53491	0.767455	−	0.641102i	$-0.221523\pi$
$607$	37.8162	1.53491	0.767455	+	0.641102i	$0.221523\pi$
$608$	10.9688	0.444843
$609$	−0.904021	−0.0366328
$610$	6.08577	0.246406
$611$	−31.7343	−1.28383
$612$	7.89468	0.319124
$613$	38.0681	1.53756	0.768778	−	0.639515i	$-0.220865\pi$
$613$	38.0681	1.53756	0.768778	+	0.639515i	$0.220865\pi$
$614$	−22.6585	−0.914421
$615$	−0.668443	−0.0269542
$616$	−3.42661	−0.138062
$617$	0.964824	0.0388423	0.0194212	−	0.999811i	$-0.493818\pi$
$617$	0.964824	0.0388423	0.0194212	+	0.999811i	$0.493818\pi$
$618$	18.9127	0.760779
$619$	−40.8802	−1.64311	−0.821557	−	0.570126i	$-0.806894\pi$
$619$	−40.8802	−1.64311	−0.821557	+	0.570126i	$0.806894\pi$
$620$	−4.81767	−0.193482
$621$	4.87499	0.195627
$622$	62.6575	2.51234
$623$	2.20594	0.0883792
$624$	−9.21495	−0.368893
$625$	−28.4480	−1.13792
$626$	−61.9248	−2.47501
$627$	−6.85774	−0.273872
$628$	66.5080	2.65396
$629$	−12.7974	−0.510264
$630$	−2.42106	−0.0964573
$631$	15.5109	0.617481	0.308740	−	0.951146i	$-0.400093\pi$
$631$	15.5109	0.617481	0.308740	+	0.951146i	$0.400093\pi$
$632$	1.14616	0.0455918
$633$	0.00251402	9.99233e−5 0
$634$	−19.9009	−0.790365
$635$	−47.7157	−1.89354
$636$	22.3806	0.887450
$637$	35.8634	1.42096
$638$	10.7835	0.426922
$639$	−3.58389	−0.141776
$640$	−49.7074	−1.96486
$641$	−14.8269	−0.585627	−0.292813	−	0.956170i	$-0.594591\pi$
$641$	−14.8269	−0.585627	−0.292813	+	0.956170i	$0.594591\pi$
$642$	22.6739	0.894868
$643$	34.6976	1.36834	0.684170	−	0.729322i	$-0.260165\pi$
$643$	34.6976	1.36834	0.684170	+	0.729322i	$0.260165\pi$
$644$	−7.43670	−0.293047
$645$	20.5067	0.807451
$646$	−16.6573	−0.655372
$647$	−29.9407	−1.17709	−0.588546	−	0.808464i	$-0.700299\pi$
$647$	−29.9407	−1.17709	−0.588546	+	0.808464i	$0.700299\pi$
$648$	−3.78236	−0.148585
$649$	−23.0989	−0.906713
$650$	10.2779	0.403134
$651$	−0.235126	−0.00921533
$652$	−58.3938	−2.28688
$653$	31.8490	1.24635	0.623173	−	0.782084i	$-0.285843\pi$
$653$	31.8490	1.24635	0.623173	+	0.782084i	$0.285843\pi$
$654$	−36.4825	−1.42658
$655$	10.2368	0.399983
$656$	0.485312	0.0189483
$657$	−1.07364	−0.0418865
$658$	6.05338	0.235985
$659$	−26.0311	−1.01403	−0.507014	−	0.861938i	$-0.669251\pi$
$659$	−26.0311	−1.01403	−0.507014	+	0.861938i	$0.669251\pi$
$660$	18.5625	0.722546
$661$	23.7766	0.924803	0.462402	−	0.886671i	$-0.346988\pi$
$661$	23.7766	0.924803	0.462402	+	0.886671i	$0.346988\pi$
$662$	−7.21461	−0.280404
$663$	−11.5360	−0.448021
$664$	−42.3764	−1.64452
$665$	3.28342	0.127326
$666$	13.8023	0.534827
$667$	10.3962	0.402541
$668$	−35.1210	−1.35887
$669$	19.9172	0.770045
$670$	27.7285	1.07125
$671$	−2.27726	−0.0879125
$672$	−1.44903	−0.0558977
$673$	47.3953	1.82696	0.913478	−	0.406888i	$-0.133386\pi$
$673$	47.3953	1.82696	0.913478	+	0.406888i	$0.133386\pi$
$674$	34.5937	1.33250
$675$	0.826077	0.0317957
$676$	52.7188	2.02765
$677$	14.6697	0.563802	0.281901	−	0.959443i	$-0.409035\pi$
$677$	14.6697	0.563802	0.281901	+	0.959443i	$0.409035\pi$
$678$	32.2017	1.23670
$679$	−2.36085	−0.0906012
$680$	20.0290	0.768076
$681$	7.59943	0.291211
$682$	2.80467	0.107396
$683$	−9.20632	−0.352270	−0.176135	−	0.984366i	$-0.556360\pi$
$683$	−9.20632	−0.352270	−0.176135	+	0.984366i	$0.556360\pi$
$684$	11.5475	0.441528
$685$	−46.2183	−1.76591
$686$	−13.8623	−0.529264
$687$	−8.28408	−0.316057
$688$	−14.8886	−0.567622
$689$	−32.7034	−1.24590
$690$	27.8419	1.05992
$691$	−15.9698	−0.607518	−0.303759	−	0.952749i	$-0.598242\pi$
$691$	−15.9698	−0.607518	−0.303759	+	0.952749i	$0.598242\pi$
$692$	18.6384	0.708526
$693$	0.905944	0.0344140
$694$	54.6609	2.07490
$695$	−25.1760	−0.954982
$696$	−8.06607	−0.305744
$697$	0.607552	0.0230127
$698$	87.4814	3.31122
$699$	−18.6171	−0.704162
$700$	−1.26016	−0.0476298
$701$	8.84824	0.334194	0.167097	−	0.985941i	$-0.446561\pi$
$701$	8.84824	0.334194	0.167097	+	0.985941i	$0.446561\pi$
$702$	12.4419	0.469588
$703$	−18.7185	−0.705983
$704$	24.7748	0.933737
$705$	−14.5670	−0.548623
$706$	−64.1514	−2.41437
$707$	−4.57458	−0.172045
$708$	38.8953	1.46178
$709$	−49.5130	−1.85950	−0.929751	−	0.368190i	$-0.879978\pi$
$709$	−49.5130	−1.85950	−0.929751	+	0.368190i	$0.879978\pi$
$710$	−20.4682	−0.768159
$711$	−0.303028	−0.0113644
$712$	19.6824	0.737629
$713$	2.70393	0.101263
$714$	2.20052	0.0823522
$715$	−27.1243	−1.01439
$716$	−45.4500	−1.69855
$717$	−21.9934	−0.821359
$718$	52.9852	1.97739
$719$	27.2446	1.01605	0.508025	−	0.861342i	$-0.330376\pi$
$719$	27.2446	1.01605	0.508025	+	0.861342i	$0.330376\pi$
$720$	−4.22993	−0.157640
$721$	3.38840	0.126191
$722$	20.5920	0.766354
$723$	26.3772	0.980977
$724$	0.539918	0.0200659
$725$	1.76165	0.0654261
$726$	15.2210	0.564903
$727$	−33.0650	−1.22631	−0.613157	−	0.789961i	$-0.710101\pi$
$727$	−33.0650	−1.22631	−0.613157	+	0.789961i	$0.710101\pi$
$728$	−8.43122	−0.312482
$729$	1.00000	0.0370370
$730$	−6.13172	−0.226945
$731$	−18.6387	−0.689377
$732$	3.83457	0.141730
$733$	15.3524	0.567055	0.283528	−	0.958964i	$-0.408495\pi$
$733$	15.3524	0.567055	0.283528	+	0.958964i	$0.408495\pi$
$734$	49.4581	1.82553
$735$	16.4623	0.607222
$736$	16.6637	0.614234
$737$	−10.3758	−0.382199
$738$	−0.655260	−0.0241205
$739$	−47.1988	−1.73623	−0.868117	−	0.496359i	$-0.834670\pi$
$739$	−47.1988	−1.73623	−0.868117	+	0.496359i	$0.834670\pi$
$740$	50.6674	1.86257
$741$	−16.8736	−0.619866
$742$	6.23824	0.229013
$743$	−23.2158	−0.851705	−0.425853	−	0.904793i	$-0.640026\pi$
$743$	−23.2158	−0.851705	−0.425853	+	0.904793i	$0.640026\pi$
$744$	−2.09790	−0.0769128
$745$	48.8889	1.79115
$746$	75.4478	2.76234
$747$	11.2037	0.409921
$748$	−16.8716	−0.616887
$749$	4.06226	0.148432
$750$	−23.8380	−0.870441
$751$	−28.1118	−1.02581	−0.512907	−	0.858444i	$-0.671432\pi$
$751$	−28.1118	−1.02581	−0.512907	+	0.858444i	$0.671432\pi$
$752$	10.5761	0.385671
$753$	−1.06472	−0.0388005
$754$	26.5329	0.966271
$755$	53.0376	1.93023
$756$	−1.52548	−0.0554812
$757$	52.2757	1.89999	0.949996	−	0.312263i	$-0.101087\pi$
$757$	52.2757	1.89999	0.949996	+	0.312263i	$0.101087\pi$
$758$	−3.90333	−0.141775
$759$	−10.4183	−0.378159
$760$	29.2961	1.06268
$761$	−39.6526	−1.43741	−0.718703	−	0.695317i	$-0.755264\pi$
$761$	−39.6526	−1.43741	−0.718703	+	0.695317i	$0.755264\pi$
$762$	−46.7746	−1.69447
$763$	−6.53621	−0.236627
$764$	−51.9977	−1.88121
$765$	−5.29536	−0.191454
$766$	52.9008	1.91138
$767$	−56.8353	−2.05220
$768$	−25.5415	−0.921648
$769$	3.75182	0.135294	0.0676471	−	0.997709i	$-0.478451\pi$
$769$	3.75182	0.135294	0.0676471	+	0.997709i	$0.478451\pi$
$770$	5.17401	0.186458
$771$	−23.2264	−0.836478
$772$	−49.3428	−1.77589
$773$	37.0837	1.33381	0.666903	−	0.745144i	$-0.267619\pi$
$773$	37.0837	1.33381	0.666903	+	0.745144i	$0.267619\pi$
$774$	20.1023	0.722562
$775$	0.458187	0.0164586
$776$	−21.0646	−0.756174
$777$	2.47282	0.0887119
$778$	−2.16052	−0.0774582
$779$	0.888659	0.0318395
$780$	45.6734	1.63537
$781$	7.65908	0.274063
$782$	−25.3057	−0.904931
$783$	2.13255	0.0762111
$784$	−11.9522	−0.426865
$785$	−44.6103	−1.59221
$786$	10.0349	0.357932
$787$	−19.4794	−0.694365	−0.347182	−	0.937798i	$-0.612862\pi$
$787$	−19.4794	−0.694365	−0.347182	+	0.937798i	$0.612862\pi$
$788$	42.6508	1.51937
$789$	22.2121	0.790772
$790$	−1.73064	−0.0615736
$791$	5.76926	0.205131
$792$	8.08323	0.287225
$793$	−5.60322	−0.198976
$794$	25.0863	0.890279
$795$	−15.0118	−0.532414
$796$	10.4959	0.372018
$797$	−46.9849	−1.66429	−0.832145	−	0.554558i	$-0.812887\pi$
$797$	−46.9849	−1.66429	−0.832145	+	0.554558i	$0.812887\pi$
$798$	3.21867	0.113940
$799$	13.2400	0.468398
$800$	2.82371	0.0998332
$801$	−5.20373	−0.183865
$802$	−63.3394	−2.23659
$803$	2.29445	0.0809694
$804$	17.4714	0.616170
$805$	4.98817	0.175810
$806$	6.90093	0.243075
$807$	−2.04284	−0.0719113
$808$	−40.8164	−1.43592
$809$	−23.2781	−0.818415	−0.409208	−	0.912441i	$-0.634195\pi$
$809$	−23.2781	−0.818415	−0.409208	+	0.912441i	$0.634195\pi$
$810$	5.71118	0.200670
$811$	−33.5174	−1.17696	−0.588478	−	0.808514i	$-0.700273\pi$
$811$	−33.5174	−1.17696	−0.588478	+	0.808514i	$0.700273\pi$
$812$	−3.25316	−0.114164
$813$	11.9706	0.419826
$814$	−29.4966	−1.03386
$815$	39.1677	1.37198
$816$	3.84461	0.134588
$817$	−27.2626	−0.953797
$818$	−38.7125	−1.35355
$819$	2.22909	0.0778906
$820$	−2.40542	−0.0840010
$821$	−13.1908	−0.460363	−0.230181	−	0.973148i	$-0.573932\pi$
$821$	−13.1908	−0.460363	−0.230181	+	0.973148i	$0.573932\pi$
$822$	−45.3068	−1.58026
$823$	−46.6379	−1.62570	−0.812848	−	0.582477i	$-0.802084\pi$
$823$	−46.6379	−1.62570	−0.812848	+	0.582477i	$0.802084\pi$
$824$	30.2328	1.05321
$825$	−1.76540	−0.0614633
$826$	10.8414	0.377222
$827$	−15.8273	−0.550369	−0.275184	−	0.961391i	$-0.588739\pi$
$827$	−15.8273	−0.550369	−0.275184	+	0.961391i	$0.588739\pi$
$828$	17.5429	0.609657
$829$	−5.62270	−0.195284	−0.0976422	−	0.995222i	$-0.531130\pi$
$829$	−5.62270	−0.195284	−0.0976422	+	0.995222i	$0.531130\pi$
$830$	63.9862	2.22099
$831$	9.52681	0.330481
$832$	60.9589	2.11337
$833$	−14.9627	−0.518428
$834$	−24.6795	−0.854582
$835$	23.5574	0.815238
$836$	−24.6779	−0.853503
$837$	0.554654	0.0191716
$838$	−62.7858	−2.16890
$839$	9.05095	0.312473	0.156237	−	0.987720i	$-0.450064\pi$
$839$	9.05095	0.312473	0.156237	+	0.987720i	$0.450064\pi$
$840$	−3.87018	−0.133534
$841$	−24.4522	−0.843180
$842$	−23.6693	−0.815698
$843$	3.93029	0.135366
$844$	0.00904682	0.000311404 0
$845$	−35.3612	−1.21646
$846$	−14.2797	−0.490945
$847$	2.72699	0.0937006
$848$	10.8991	0.374276
$849$	−30.9124	−1.06091
$850$	−4.28811	−0.147081
$851$	−28.4372	−0.974814
$852$	−12.8968	−0.441837
$853$	−49.9408	−1.70994	−0.854971	−	0.518676i	$-0.826425\pi$
$853$	−49.9408	−1.70994	−0.854971	+	0.518676i	$0.826425\pi$
$854$	1.06883	0.0365745
$855$	−7.74546	−0.264889
$856$	36.2453	1.23884
$857$	2.90242	0.0991449	0.0495725	−	0.998771i	$-0.484214\pi$
$857$	2.90242	0.0991449	0.0495725	+	0.998771i	$0.484214\pi$
$858$	−26.5893	−0.907745
$859$	−21.7733	−0.742896	−0.371448	−	0.928454i	$-0.621139\pi$
$859$	−21.7733	−0.742896	−0.371448	+	0.928454i	$0.621139\pi$
$860$	73.7944	2.51637
$861$	−0.117397	−0.00400086
$862$	13.6069	0.463451
$863$	−34.8241	−1.18543	−0.592713	−	0.805414i	$-0.701943\pi$
$863$	−34.8241	−1.18543	−0.592713	+	0.805414i	$0.701943\pi$
$864$	3.41821	0.116290
$865$	−12.5017	−0.425071
$866$	96.1472	3.26721
$867$	−12.1870	−0.413893
$868$	−0.846113	−0.0287190
$869$	0.647596	0.0219682
$870$	12.1794	0.412919
$871$	−25.5299	−0.865048
$872$	−58.3190	−1.97493
$873$	5.56916	0.188487
$874$	−37.0144	−1.25203
$875$	−4.27083	−0.144380
$876$	−3.86353	−0.130536
$877$	−32.3924	−1.09381	−0.546907	−	0.837194i	$-0.684195\pi$
$877$	−32.3924	−1.09381	−0.546907	+	0.837194i	$0.684195\pi$
$878$	2.54598	0.0859226
$879$	−10.4683	−0.353088
$880$	9.03972	0.304729
$881$	3.36165	0.113257	0.0566285	−	0.998395i	$-0.481965\pi$
$881$	3.36165	0.113257	0.0566285	+	0.998395i	$0.481965\pi$
$882$	16.1377	0.543384
$883$	−14.7375	−0.495955	−0.247977	−	0.968766i	$-0.579766\pi$
$883$	−14.7375	−0.495955	−0.247977	+	0.968766i	$0.579766\pi$
$884$	−41.5128	−1.39623
$885$	−26.0891	−0.876974
$886$	59.5403	2.00030
$887$	−32.4647	−1.09006	−0.545029	−	0.838417i	$-0.683481\pi$
$887$	−32.4647	−1.09006	−0.545029	+	0.838417i	$0.683481\pi$
$888$	22.0636	0.740406
$889$	−8.38016	−0.281062
$890$	−29.7194	−0.996198
$891$	−2.13709	−0.0715950
$892$	71.6731	2.39979
$893$	19.3660	0.648058
$894$	47.9248	1.60284
$895$	30.4856	1.01902
$896$	−8.72996	−0.291648
$897$	−25.6343	−0.855904
$898$	2.38074	0.0794464
$899$	1.18283	0.0394495
$900$	2.97268	0.0990893
$901$	13.6443	0.454559
$902$	1.40035	0.0466264
$903$	3.60153	0.119852
$904$	51.4759	1.71206
$905$	−0.362150	−0.0120383
$906$	51.9916	1.72730
$907$	14.0092	0.465166	0.232583	−	0.972577i	$-0.425282\pi$
$907$	14.0092	0.465166	0.232583	+	0.972577i	$0.425282\pi$
$908$	27.3469	0.907539
$909$	10.7912	0.357923
$910$	12.7307	0.422019
$911$	−49.1430	−1.62818	−0.814090	−	0.580739i	$-0.802764\pi$
$911$	−49.1430	−1.62818	−0.814090	+	0.580739i	$0.802764\pi$
$912$	5.62347	0.186212
$913$	−23.9432	−0.792405
$914$	−20.3772	−0.674017
$915$	−2.57204	−0.0850291
$916$	−29.8107	−0.984972
$917$	1.79785	0.0593703
$918$	−5.19093	−0.171326
$919$	−32.9659	−1.08744	−0.543722	−	0.839265i	$-0.682985\pi$
$919$	−32.9659	−1.08744	−0.543722	+	0.839265i	$0.682985\pi$
$920$	44.5066	1.46734
$921$	9.57619	0.315546
$922$	8.40214	0.276710
$923$	18.8453	0.620300
$924$	3.26008	0.107249
$925$	−4.81874	−0.158439
$926$	61.0956	2.00773
$927$	−7.99310	−0.262528
$928$	7.28951	0.239290
$929$	−35.0516	−1.15001	−0.575003	−	0.818151i	$-0.694999\pi$
$929$	−35.0516	−1.15001	−0.575003	+	0.818151i	$0.694999\pi$
$930$	3.16773	0.103874
$931$	−21.8858	−0.717278
$932$	−66.9943	−2.19447
$933$	−26.4810	−0.866951
$934$	−77.3714	−2.53167
$935$	11.3166	0.370094
$936$	19.8889	0.650089
$937$	−39.7073	−1.29718	−0.648591	−	0.761138i	$-0.724641\pi$
$937$	−39.7073	−1.29718	−0.648591	+	0.761138i	$0.724641\pi$
$938$	4.86988	0.159007
$939$	26.1714	0.854071
$940$	−52.4199	−1.70975
$941$	−37.2961	−1.21582	−0.607909	−	0.794007i	$-0.707992\pi$
$941$	−37.2961	−1.21582	−0.607909	+	0.794007i	$0.707992\pi$
$942$	−43.7305	−1.42482
$943$	1.35005	0.0439636
$944$	18.9415	0.616495
$945$	1.02322	0.0332852
$946$	−42.9603	−1.39676
$947$	13.7155	0.445693	0.222846	−	0.974854i	$-0.428465\pi$
$947$	13.7155	0.445693	0.222846	+	0.974854i	$0.428465\pi$
$948$	−1.09046	−0.0354165
$949$	5.64553	0.183262
$950$	−6.27216	−0.203496
$951$	8.41074	0.272737
$952$	3.51763	0.114007
$953$	18.5367	0.600461	0.300231	−	0.953867i	$-0.402936\pi$
$953$	18.5367	0.600461	0.300231	+	0.953867i	$0.402936\pi$
$954$	−14.7158	−0.476440
$955$	34.8775	1.12861
$956$	−79.1444	−2.55971
$957$	−4.55744	−0.147321
$958$	3.42820	0.110760
$959$	−8.11719	−0.262118
$960$	27.9819	0.903112
$961$	−30.6924	−0.990076
$962$	−72.5769	−2.33997
$963$	−9.58272	−0.308799
$964$	94.9195	3.05715
$965$	33.0967	1.06542
$966$	4.88979	0.157327
$967$	14.7081	0.472981	0.236490	−	0.971634i	$-0.424003\pi$
$967$	14.7081	0.472981	0.236490	+	0.971634i	$0.424003\pi$
$968$	24.3314	0.782042
$969$	7.03990	0.226154
$970$	31.8065	1.02124
$971$	−23.1702	−0.743568	−0.371784	−	0.928319i	$-0.621254\pi$
$971$	−23.1702	−0.743568	−0.371784	+	0.928319i	$0.621254\pi$
$972$	3.59855	0.115423
$973$	−4.42159	−0.141750
$974$	−15.5553	−0.498425
$975$	−4.34379	−0.139113
$976$	1.86739	0.0597737
$977$	−22.0530	−0.705537	−0.352769	−	0.935711i	$-0.614760\pi$
$977$	−22.0530	−0.705537	−0.352769	+	0.935711i	$0.614760\pi$
$978$	38.3952	1.22774
$979$	11.1208	0.355423
$980$	59.2405	1.89237
$981$	15.4187	0.492280
$982$	4.33402	0.138304
$983$	40.0677	1.27796	0.638980	−	0.769223i	$-0.279357\pi$
$983$	40.0677	1.27796	0.638980	+	0.769223i	$0.279357\pi$
$984$	−1.04746	−0.0333919
$985$	−28.6081	−0.911528
$986$	−11.0699	−0.352538
$987$	−2.55835	−0.0814332
$988$	−60.7203	−1.93177
$989$	−41.4173	−1.31699
$990$	−12.2053	−0.387909
$991$	−3.87017	−0.122940	−0.0614701	−	0.998109i	$-0.519579\pi$
$991$	−3.87017	−0.122940	−0.0614701	+	0.998109i	$0.519579\pi$
$992$	1.89592	0.0601957
$993$	3.04912	0.0967610
$994$	−3.59478	−0.114019
$995$	−7.04014	−0.223187
$996$	40.3170	1.27749
$997$	14.9808	0.474447	0.237224	−	0.971455i	$-0.423763\pi$
$997$	14.9808	0.474447	0.237224	+	0.971455i	$0.423763\pi$
$998$	−87.0185	−2.75452
$999$	−5.83328	−0.184557

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8031.2.a.a.1.10	✓	92

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8031.2.a.a.1.10	✓	92	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:	\( N \)	\(=\)	\( 8031 = 3 \cdot 2677 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8031.a (trivial)

\(f(q)\)	\(=\)	\(q-2.36612 q^{2} +1.00000 q^{3} +3.59855 q^{4} -2.41373 q^{5} -2.36612 q^{6} -0.423916 q^{7} -3.78236 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.36612 q^{2} +1.00000 q^{3} +3.59855 q^{4} -2.41373 q^{5} -2.36612 q^{6} -0.423916 q^{7} -3.78236 q^{8} +1.00000 q^{9} +5.71118 q^{10} -2.13709 q^{11} +3.59855 q^{12} -5.25833 q^{13} +1.00304 q^{14} -2.41373 q^{15} +1.75245 q^{16} +2.19385 q^{17} -2.36612 q^{18} +3.20892 q^{19} -8.68591 q^{20} -0.423916 q^{21} +5.05661 q^{22} +4.87499 q^{23} -3.78236 q^{24} +0.826077 q^{25} +12.4419 q^{26} +1.00000 q^{27} -1.52548 q^{28} +2.13255 q^{29} +5.71118 q^{30} +0.554654 q^{31} +3.41821 q^{32} -2.13709 q^{33} -5.19093 q^{34} +1.02322 q^{35} +3.59855 q^{36} -5.83328 q^{37} -7.59271 q^{38} -5.25833 q^{39} +9.12959 q^{40} +0.276934 q^{41} +1.00304 q^{42} -8.49587 q^{43} -7.69040 q^{44} -2.41373 q^{45} -11.5348 q^{46} +6.03505 q^{47} +1.75245 q^{48} -6.82030 q^{49} -1.95460 q^{50} +2.19385 q^{51} -18.9223 q^{52} +6.21935 q^{53} -2.36612 q^{54} +5.15834 q^{55} +1.60340 q^{56} +3.20892 q^{57} -5.04588 q^{58} +10.8086 q^{59} -8.68591 q^{60} +1.06559 q^{61} -1.31238 q^{62} -0.423916 q^{63} -11.5928 q^{64} +12.6922 q^{65} +5.05661 q^{66} +4.85513 q^{67} +7.89468 q^{68} +4.87499 q^{69} -2.42106 q^{70} -3.58389 q^{71} -3.78236 q^{72} -1.07364 q^{73} +13.8023 q^{74} +0.826077 q^{75} +11.5475 q^{76} +0.905944 q^{77} +12.4419 q^{78} -0.303028 q^{79} -4.22993 q^{80} +1.00000 q^{81} -0.655260 q^{82} +11.2037 q^{83} -1.52548 q^{84} -5.29536 q^{85} +20.1023 q^{86} +2.13255 q^{87} +8.08323 q^{88} -5.20373 q^{89} +5.71118 q^{90} +2.22909 q^{91} +17.5429 q^{92} +0.554654 q^{93} -14.2797 q^{94} -7.74546 q^{95} +3.41821 q^{96} +5.56916 q^{97} +16.1377 q^{98} -2.13709 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 92 q - 6 q^{2} + 92 q^{3} + 70 q^{4} - 18 q^{5} - 6 q^{6} - 42 q^{7} - 15 q^{8} + 92 q^{9}+O(q^{10}) \) 92 * q - 6 * q^2 + 92 * q^3 + 70 * q^4 - 18 * q^5 - 6 * q^6 - 42 * q^7 - 15 * q^8 + 92 * q^9	\( 92 q - 6 q^{2} + 92 q^{3} + 70 q^{4} - 18 q^{5} - 6 q^{6} - 42 q^{7} - 15 q^{8} + 92 q^{9} - 44 q^{10} - 24 q^{11} + 70 q^{12} - 48 q^{13} - 29 q^{14} - 18 q^{15} + 26 q^{16} - 69 q^{17} - 6 q^{18} - 74 q^{19} - 42 q^{20} - 42 q^{21} - 62 q^{22} - 19 q^{23} - 15 q^{24} + 16 q^{25} - 27 q^{26} + 92 q^{27} - 101 q^{28} - 54 q^{29} - 44 q^{30} - 67 q^{31} - 36 q^{32} - 24 q^{33} - 63 q^{34} - 31 q^{35} + 70 q^{36} - 70 q^{37} - 18 q^{38} - 48 q^{39} - 125 q^{40} - 98 q^{41} - 29 q^{42} - 159 q^{43} - 52 q^{44} - 18 q^{45} - 68 q^{46} - 15 q^{47} + 26 q^{48} - 28 q^{49} - 7 q^{50} - 69 q^{51} - 98 q^{52} - 23 q^{53} - 6 q^{54} - 93 q^{55} - 48 q^{56} - 74 q^{57} - 37 q^{58} - 36 q^{59} - 42 q^{60} - 172 q^{61} - 26 q^{62} - 42 q^{63} - 23 q^{64} - 66 q^{65} - 62 q^{66} - 143 q^{67} - 74 q^{68} - 19 q^{69} - 30 q^{70} - 9 q^{71} - 15 q^{72} - 134 q^{73} - 19 q^{74} + 16 q^{75} - 157 q^{76} - 25 q^{77} - 27 q^{78} - 138 q^{79} - 29 q^{80} + 92 q^{81} - 61 q^{82} - 24 q^{83} - 101 q^{84} - 84 q^{85} + 14 q^{86} - 54 q^{87} - 140 q^{88} - 148 q^{89} - 44 q^{90} - 115 q^{91} - 12 q^{92} - 67 q^{93} - 79 q^{94} - 10 q^{95} - 36 q^{96} - 165 q^{97} + 36 q^{98} - 24 q^{99}+O(q^{100}) \) 92 * q - 6 * q^2 + 92 * q^3 + 70 * q^4 - 18 * q^5 - 6 * q^6 - 42 * q^7 - 15 * q^8 + 92 * q^9 - 44 * q^10 - 24 * q^11 + 70 * q^12 - 48 * q^13 - 29 * q^14 - 18 * q^15 + 26 * q^16 - 69 * q^17 - 6 * q^18 - 74 * q^19 - 42 * q^20 - 42 * q^21 - 62 * q^22 - 19 * q^23 - 15 * q^24 + 16 * q^25 - 27 * q^26 + 92 * q^27 - 101 * q^28 - 54 * q^29 - 44 * q^30 - 67 * q^31 - 36 * q^32 - 24 * q^33 - 63 * q^34 - 31 * q^35 + 70 * q^36 - 70 * q^37 - 18 * q^38 - 48 * q^39 - 125 * q^40 - 98 * q^41 - 29 * q^42 - 159 * q^43 - 52 * q^44 - 18 * q^45 - 68 * q^46 - 15 * q^47 + 26 * q^48 - 28 * q^49 - 7 * q^50 - 69 * q^51 - 98 * q^52 - 23 * q^53 - 6 * q^54 - 93 * q^55 - 48 * q^56 - 74 * q^57 - 37 * q^58 - 36 * q^59 - 42 * q^60 - 172 * q^61 - 26 * q^62 - 42 * q^63 - 23 * q^64 - 66 * q^65 - 62 * q^66 - 143 * q^67 - 74 * q^68 - 19 * q^69 - 30 * q^70 - 9 * q^71 - 15 * q^72 - 134 * q^73 - 19 * q^74 + 16 * q^75 - 157 * q^76 - 25 * q^77 - 27 * q^78 - 138 * q^79 - 29 * q^80 + 92 * q^81 - 61 * q^82 - 24 * q^83 - 101 * q^84 - 84 * q^85 + 14 * q^86 - 54 * q^87 - 140 * q^88 - 148 * q^89 - 44 * q^90 - 115 * q^91 - 12 * q^92 - 67 * q^93 - 79 * q^94 - 10 * q^95 - 36 * q^96 - 165 * q^97 + 36 * q^98 - 24 * q^99

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