LMFDB - Embedded newform 8015.2.a.l.1.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8015,2,Mod(1,8015)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8015, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8015.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8015 = 5 \cdot 7 \cdot 229 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8015.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:	$64.0000972201$
Analytic rank:	$0$
Dimension:	$62$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.19
Character	$\chi$	$=$	8015.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.28523 q^{2} -0.829686 q^{3} -0.348175 q^{4} -1.00000 q^{5} +1.06634 q^{6} -1.00000 q^{7} +3.01795 q^{8} -2.31162 q^{9} +O(q^{10})$	\(q-1.28523 q^{2} -0.829686 q^{3} -0.348175 q^{4} -1.00000 q^{5} +1.06634 q^{6} -1.00000 q^{7} +3.01795 q^{8} -2.31162 q^{9} +1.28523 q^{10} -2.11972 q^{11} +0.288876 q^{12} +3.07149 q^{13} +1.28523 q^{14} +0.829686 q^{15} -3.18242 q^{16} -6.86780 q^{17} +2.97097 q^{18} -3.15147 q^{19} +0.348175 q^{20} +0.829686 q^{21} +2.72434 q^{22} -0.512282 q^{23} -2.50395 q^{24} +1.00000 q^{25} -3.94759 q^{26} +4.40698 q^{27} +0.348175 q^{28} +3.17302 q^{29} -1.06634 q^{30} +3.72476 q^{31} -1.94575 q^{32} +1.75871 q^{33} +8.82673 q^{34} +1.00000 q^{35} +0.804849 q^{36} -5.59920 q^{37} +4.05038 q^{38} -2.54838 q^{39} -3.01795 q^{40} -7.64566 q^{41} -1.06634 q^{42} -5.76988 q^{43} +0.738035 q^{44} +2.31162 q^{45} +0.658402 q^{46} -10.3490 q^{47} +2.64041 q^{48} +1.00000 q^{49} -1.28523 q^{50} +5.69812 q^{51} -1.06942 q^{52} +5.76232 q^{53} -5.66400 q^{54} +2.11972 q^{55} -3.01795 q^{56} +2.61473 q^{57} -4.07808 q^{58} -0.788910 q^{59} -0.288876 q^{60} +5.99308 q^{61} -4.78719 q^{62} +2.31162 q^{63} +8.86559 q^{64} -3.07149 q^{65} -2.26035 q^{66} -11.9757 q^{67} +2.39120 q^{68} +0.425033 q^{69} -1.28523 q^{70} -15.5425 q^{71} -6.97636 q^{72} +9.76873 q^{73} +7.19628 q^{74} -0.829686 q^{75} +1.09726 q^{76} +2.11972 q^{77} +3.27526 q^{78} -9.51566 q^{79} +3.18242 q^{80} +3.27846 q^{81} +9.82645 q^{82} -2.71309 q^{83} -0.288876 q^{84} +6.86780 q^{85} +7.41564 q^{86} -2.63261 q^{87} -6.39723 q^{88} -16.0539 q^{89} -2.97097 q^{90} -3.07149 q^{91} +0.178364 q^{92} -3.09038 q^{93} +13.3009 q^{94} +3.15147 q^{95} +1.61436 q^{96} -0.759265 q^{97} -1.28523 q^{98} +4.90000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 62 q + 2 q^{2} + 11 q^{3} + 64 q^{4} - 62 q^{5} + 3 q^{6} - 62 q^{7} + 15 q^{8} + 69 q^{9}+O(q^{10}) $ 62 * q + 2 * q^2 + 11 * q^3 + 64 * q^4 - 62 * q^5 + 3 * q^6 - 62 * q^7 + 15 * q^8 + 69 * q^9	\( 62 q + 2 q^{2} + 11 q^{3} + 64 q^{4} - 62 q^{5} + 3 q^{6} - 62 q^{7} + 15 q^{8} + 69 q^{9} - 2 q^{10} - 13 q^{11} + 37 q^{12} + 31 q^{13} - 2 q^{14} - 11 q^{15} + 64 q^{16} + 30 q^{17} + 18 q^{18} + 20 q^{19} - 64 q^{20} - 11 q^{21} + 7 q^{22} + 29 q^{24} + 62 q^{25} + 59 q^{27} - 64 q^{28} - 29 q^{29} - 3 q^{30} + 20 q^{31} + 22 q^{32} + 72 q^{33} + 13 q^{34} + 62 q^{35} + 53 q^{36} + 35 q^{37} + 34 q^{38} - 6 q^{39} - 15 q^{40} + 13 q^{41} - 3 q^{42} - 4 q^{43} - 44 q^{44} - 69 q^{45} - 19 q^{46} + 58 q^{47} + 64 q^{48} + 62 q^{49} + 2 q^{50} - 30 q^{51} + 82 q^{52} + 18 q^{53} + 22 q^{54} + 13 q^{55} - 15 q^{56} + 21 q^{57} + 18 q^{58} - 11 q^{59} - 37 q^{60} + 24 q^{61} + 48 q^{62} - 69 q^{63} + 65 q^{64} - 31 q^{65} + 25 q^{66} - 6 q^{67} + 65 q^{68} + 27 q^{69} + 2 q^{70} - 35 q^{71} + 53 q^{72} + 116 q^{73} - 69 q^{74} + 11 q^{75} + 65 q^{76} + 13 q^{77} + 102 q^{78} - 83 q^{79} - 64 q^{80} + 126 q^{81} + 71 q^{82} + 84 q^{83} - 37 q^{84} - 30 q^{85} + 24 q^{86} + 49 q^{87} + 20 q^{88} - 16 q^{89} - 18 q^{90} - 31 q^{91} + 19 q^{92} + 65 q^{93} + 54 q^{94} - 20 q^{95} + 17 q^{96} + 155 q^{97} + 2 q^{98} + 6 q^{99}+O(q^{100}) \) 62 * q + 2 * q^2 + 11 * q^3 + 64 * q^4 - 62 * q^5 + 3 * q^6 - 62 * q^7 + 15 * q^8 + 69 * q^9 - 2 * q^10 - 13 * q^11 + 37 * q^12 + 31 * q^13 - 2 * q^14 - 11 * q^15 + 64 * q^16 + 30 * q^17 + 18 * q^18 + 20 * q^19 - 64 * q^20 - 11 * q^21 + 7 * q^22 + 29 * q^24 + 62 * q^25 + 59 * q^27 - 64 * q^28 - 29 * q^29 - 3 * q^30 + 20 * q^31 + 22 * q^32 + 72 * q^33 + 13 * q^34 + 62 * q^35 + 53 * q^36 + 35 * q^37 + 34 * q^38 - 6 * q^39 - 15 * q^40 + 13 * q^41 - 3 * q^42 - 4 * q^43 - 44 * q^44 - 69 * q^45 - 19 * q^46 + 58 * q^47 + 64 * q^48 + 62 * q^49 + 2 * q^50 - 30 * q^51 + 82 * q^52 + 18 * q^53 + 22 * q^54 + 13 * q^55 - 15 * q^56 + 21 * q^57 + 18 * q^58 - 11 * q^59 - 37 * q^60 + 24 * q^61 + 48 * q^62 - 69 * q^63 + 65 * q^64 - 31 * q^65 + 25 * q^66 - 6 * q^67 + 65 * q^68 + 27 * q^69 + 2 * q^70 - 35 * q^71 + 53 * q^72 + 116 * q^73 - 69 * q^74 + 11 * q^75 + 65 * q^76 + 13 * q^77 + 102 * q^78 - 83 * q^79 - 64 * q^80 + 126 * q^81 + 71 * q^82 + 84 * q^83 - 37 * q^84 - 30 * q^85 + 24 * q^86 + 49 * q^87 + 20 * q^88 - 16 * q^89 - 18 * q^90 - 31 * q^91 + 19 * q^92 + 65 * q^93 + 54 * q^94 - 20 * q^95 + 17 * q^96 + 155 * q^97 + 2 * q^98 + 6 * 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 $

$2$	−1.28523	−0.908797	−0.454399	−	0.890798i	$-0.650146\pi$
$2$	−1.28523	−0.908797	−0.454399	+	0.890798i	$0.650146\pi$
$3$	−0.829686	−0.479019	−0.239510	−	0.970894i	$-0.576987\pi$
$3$	−0.829686	−0.479019	−0.239510	+	0.970894i	$0.576987\pi$
$4$	−0.348175	−0.174088
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	1.06634	0.435332
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	3.01795	1.06701
$9$	−2.31162	−0.770540
$10$	1.28523	0.406426
$11$	−2.11972	−0.639121	−0.319560	−	0.947566i	$-0.603535\pi$
$11$	−2.11972	−0.639121	−0.319560	+	0.947566i	$0.603535\pi$
$12$	0.288876	0.0833913
$13$	3.07149	0.851879	0.425940	−	0.904752i	$-0.359944\pi$
$13$	3.07149	0.851879	0.425940	+	0.904752i	$0.359944\pi$
$14$	1.28523	0.343493
$15$	0.829686	0.214224
$16$	−3.18242	−0.795606
$17$	−6.86780	−1.66569	−0.832843	−	0.553509i	$-0.813288\pi$
$17$	−6.86780	−1.66569	−0.832843	+	0.553509i	$0.813288\pi$
$18$	2.97097	0.700265
$19$	−3.15147	−0.722997	−0.361499	−	0.932373i	$-0.617735\pi$
$19$	−3.15147	−0.722997	−0.361499	+	0.932373i	$0.617735\pi$
$20$	0.348175	0.0778543
$21$	0.829686	0.181052
$22$	2.72434	0.580831
$23$	−0.512282	−0.106818	−0.0534091	−	0.998573i	$-0.517009\pi$
$23$	−0.512282	−0.106818	−0.0534091	+	0.998573i	$0.517009\pi$
$24$	−2.50395	−0.511117
$25$	1.00000	0.200000
$26$	−3.94759	−0.774186
$27$	4.40698	0.848123
$28$	0.348175	0.0657989
$29$	3.17302	0.589216	0.294608	−	0.955618i	$-0.404811\pi$
$29$	3.17302	0.589216	0.294608	+	0.955618i	$0.404811\pi$
$30$	−1.06634	−0.194686
$31$	3.72476	0.668987	0.334494	−	0.942398i	$-0.391435\pi$
$31$	3.72476	0.668987	0.334494	+	0.942398i	$0.391435\pi$
$32$	−1.94575	−0.343963
$33$	1.75871	0.306151
$34$	8.82673	1.51377
$35$	1.00000	0.169031
$36$	0.804849	0.134141
$37$	−5.59920	−0.920503	−0.460251	−	0.887789i	$-0.652241\pi$
$37$	−5.59920	−0.920503	−0.460251	+	0.887789i	$0.652241\pi$
$38$	4.05038	0.657058
$39$	−2.54838	−0.408067
$40$	−3.01795	−0.477180
$41$	−7.64566	−1.19405	−0.597025	−	0.802222i	$-0.703651\pi$
$41$	−7.64566	−1.19405	−0.597025	+	0.802222i	$0.703651\pi$
$42$	−1.06634	−0.164540
$43$	−5.76988	−0.879898	−0.439949	−	0.898023i	$-0.645003\pi$
$43$	−5.76988	−0.879898	−0.439949	+	0.898023i	$0.645003\pi$
$44$	0.738035	0.111263
$45$	2.31162	0.344596
$46$	0.658402	0.0970760
$47$	−10.3490	−1.50956	−0.754779	−	0.655979i	$-0.772256\pi$
$47$	−10.3490	−1.50956	−0.754779	+	0.655979i	$0.772256\pi$
$48$	2.64041	0.381111
$49$	1.00000	0.142857
$50$	−1.28523	−0.181759
$51$	5.69812	0.797896
$52$	−1.06942	−0.148302
$53$	5.76232	0.791516	0.395758	−	0.918355i	$-0.370482\pi$
$53$	5.76232	0.791516	0.395758	+	0.918355i	$0.370482\pi$
$54$	−5.66400	−0.770772
$55$	2.11972	0.285824
$56$	−3.01795	−0.403291
$57$	2.61473	0.346330
$58$	−4.07808	−0.535478
$59$	−0.788910	−0.102707	−0.0513537	−	0.998681i	$-0.516354\pi$
$59$	−0.788910	−0.102707	−0.0513537	+	0.998681i	$0.516354\pi$
$60$	−0.288876	−0.0372937
$61$	5.99308	0.767335	0.383668	−	0.923471i	$-0.374661\pi$
$61$	5.99308	0.767335	0.383668	+	0.923471i	$0.374661\pi$
$62$	−4.78719	−0.607974
$63$	2.31162	0.291237
$64$	8.86559	1.10820
$65$	−3.07149	−0.380972
$66$	−2.26035	−0.278230
$67$	−11.9757	−1.46306	−0.731530	−	0.681810i	$-0.761193\pi$
$67$	−11.9757	−1.46306	−0.731530	+	0.681810i	$0.761193\pi$
$68$	2.39120	0.289975
$69$	0.425033	0.0511680
$70$	−1.28523	−0.153615
$71$	−15.5425	−1.84455	−0.922276	−	0.386533i	$-0.873673\pi$
$71$	−15.5425	−1.84455	−0.922276	+	0.386533i	$0.873673\pi$
$72$	−6.97636	−0.822172
$73$	9.76873	1.14334	0.571672	−	0.820482i	$-0.306295\pi$
$73$	9.76873	1.14334	0.571672	+	0.820482i	$0.306295\pi$
$74$	7.19628	0.836550
$75$	−0.829686	−0.0958039
$76$	1.09726	0.125865
$77$	2.11972	0.241565
$78$	3.27526	0.370850
$79$	−9.51566	−1.07059	−0.535297	−	0.844664i	$-0.679800\pi$
$79$	−9.51566	−1.07059	−0.535297	+	0.844664i	$0.679800\pi$
$80$	3.18242	0.355806
$81$	3.27846	0.364273
$82$	9.82645	1.08515
$83$	−2.71309	−0.297801	−0.148900	−	0.988852i	$-0.547573\pi$
$83$	−2.71309	−0.297801	−0.148900	+	0.988852i	$0.547573\pi$
$84$	−0.288876	−0.0315190
$85$	6.86780	0.744918
$86$	7.41564	0.799649
$87$	−2.63261	−0.282246
$88$	−6.39723	−0.681947
$89$	−16.0539	−1.70171	−0.850856	−	0.525399i	$-0.823916\pi$
$89$	−16.0539	−1.70171	−0.850856	+	0.525399i	$0.823916\pi$
$90$	−2.97097	−0.313168
$91$	−3.07149	−0.321980
$92$	0.178364	0.0185957
$93$	−3.09038	−0.320458
$94$	13.3009	1.37188
$95$	3.15147	0.323334
$96$	1.61436	0.164765
$97$	−0.759265	−0.0770917	−0.0385458	−	0.999257i	$-0.512273\pi$
$97$	−0.759265	−0.0770917	−0.0385458	+	0.999257i	$0.512273\pi$
$98$	−1.28523	−0.129828
$99$	4.90000	0.492468
$100$	−0.348175	−0.0348175
$101$	−4.01405	−0.399413	−0.199706	−	0.979856i	$-0.563999\pi$
$101$	−4.01405	−0.399413	−0.199706	+	0.979856i	$0.563999\pi$
$102$	−7.32341	−0.725126
$103$	−17.0160	−1.67664	−0.838320	−	0.545178i	$-0.816462\pi$
$103$	−17.0160	−1.67664	−0.838320	+	0.545178i	$0.816462\pi$
$104$	9.26963	0.908962
$105$	−0.829686	−0.0809691
$106$	−7.40593	−0.719327
$107$	1.70018	0.164363	0.0821814	−	0.996617i	$-0.473811\pi$
$107$	1.70018	0.164363	0.0821814	+	0.996617i	$0.473811\pi$
$108$	−1.53440	−0.147648
$109$	11.6739	1.11816	0.559078	−	0.829115i	$-0.311155\pi$
$109$	11.6739	1.11816	0.559078	+	0.829115i	$0.311155\pi$
$110$	−2.72434	−0.259756
$111$	4.64558	0.440939
$112$	3.18242	0.300711
$113$	4.59727	0.432475	0.216237	−	0.976341i	$-0.430622\pi$
$113$	4.59727	0.432475	0.216237	+	0.976341i	$0.430622\pi$
$114$	−3.36054	−0.314744
$115$	0.512282	0.0477705
$116$	−1.10477	−0.102575
$117$	−7.10013	−0.656407
$118$	1.01393	0.0933402
$119$	6.86780	0.629570
$120$	2.50395	0.228579
$121$	−6.50677	−0.591524
$122$	−7.70250	−0.697352
$123$	6.34349	0.571974
$124$	−1.29687	−0.116462
$125$	−1.00000	−0.0894427
$126$	−2.97097	−0.264675
$127$	20.5253	1.82132	0.910662	−	0.413152i	$-0.135572\pi$
$127$	20.5253	1.82132	0.910662	+	0.413152i	$0.135572\pi$
$128$	−7.50285	−0.663165
$129$	4.78719	0.421488
$130$	3.94759	0.346226
$131$	13.3057	1.16252	0.581262	−	0.813717i	$-0.302559\pi$
$131$	13.3057	1.16252	0.581262	+	0.813717i	$0.302559\pi$
$132$	−0.612337	−0.0532971
$133$	3.15147	0.273267
$134$	15.3915	1.32962
$135$	−4.40698	−0.379292
$136$	−20.7267	−1.77730
$137$	−11.9618	−1.02197	−0.510983	−	0.859591i	$-0.670719\pi$
$137$	−11.9618	−1.02197	−0.510983	+	0.859591i	$0.670719\pi$
$138$	−0.546267	−0.0465013
$139$	−2.77551	−0.235416	−0.117708	−	0.993048i	$-0.537555\pi$
$139$	−2.77551	−0.235416	−0.117708	+	0.993048i	$0.537555\pi$
$140$	−0.348175	−0.0294262
$141$	8.58643	0.723107
$142$	19.9757	1.67632
$143$	−6.51072	−0.544454
$144$	7.35656	0.613047
$145$	−3.17302	−0.263505
$146$	−12.5551	−1.03907
$147$	−0.829686	−0.0684313
$148$	1.94950	0.160248
$149$	−11.2506	−0.921682	−0.460841	−	0.887483i	$-0.652452\pi$
$149$	−11.2506	−0.921682	−0.460841	+	0.887483i	$0.652452\pi$
$150$	1.06634	0.0870663
$151$	11.2784	0.917821	0.458911	−	0.888482i	$-0.348240\pi$
$151$	11.2784	0.917821	0.458911	+	0.888482i	$0.348240\pi$
$152$	−9.51099	−0.771444
$153$	15.8758	1.28348
$154$	−2.72434	−0.219534
$155$	−3.72476	−0.299180
$156$	0.887281	0.0710393
$157$	−16.1105	−1.28576	−0.642880	−	0.765967i	$-0.722261\pi$
$157$	−16.1105	−1.28576	−0.642880	+	0.765967i	$0.722261\pi$
$158$	12.2298	0.972954
$159$	−4.78092	−0.379151
$160$	1.94575	0.153825
$161$	0.512282	0.0403735
$162$	−4.21358	−0.331050
$163$	−23.8170	−1.86549	−0.932744	−	0.360539i	$-0.882593\pi$
$163$	−23.8170	−1.86549	−0.932744	+	0.360539i	$0.882593\pi$
$164$	2.66203	0.207869
$165$	−1.75871	−0.136915
$166$	3.48696	0.270641
$167$	−0.127154	−0.00983946	−0.00491973	−	0.999988i	$-0.501566\pi$
$167$	−0.127154	−0.00983946	−0.00491973	+	0.999988i	$0.501566\pi$
$168$	2.50395	0.193184
$169$	−3.56592	−0.274302
$170$	−8.82673	−0.676979
$171$	7.28501	0.557099
$172$	2.00893	0.153179
$173$	4.69164	0.356699	0.178349	−	0.983967i	$-0.442924\pi$
$173$	4.69164	0.356699	0.178349	+	0.983967i	$0.442924\pi$
$174$	3.38352	0.256504
$175$	−1.00000	−0.0755929
$176$	6.74586	0.508488
$177$	0.654548	0.0491988
$178$	20.6330	1.54651
$179$	4.51041	0.337124	0.168562	−	0.985691i	$-0.446088\pi$
$179$	4.51041	0.337124	0.168562	+	0.985691i	$0.446088\pi$
$180$	−0.804849	−0.0599899
$181$	−11.0214	−0.819214	−0.409607	−	0.912262i	$-0.634334\pi$
$181$	−11.0214	−0.819214	−0.409607	+	0.912262i	$0.634334\pi$
$182$	3.94759	0.292615
$183$	−4.97237	−0.367568
$184$	−1.54604	−0.113976
$185$	5.59920	0.411661
$186$	3.97187	0.291231
$187$	14.5578	1.06458
$188$	3.60327	0.262795
$189$	−4.40698	−0.320560
$190$	−4.05038	−0.293845
$191$	−15.9321	−1.15280	−0.576402	−	0.817166i	$-0.695544\pi$
$191$	−15.9321	−1.15280	−0.576402	+	0.817166i	$0.695544\pi$
$192$	−7.35566	−0.530849
$193$	12.7166	0.915363	0.457681	−	0.889116i	$-0.348680\pi$
$193$	12.7166	0.915363	0.457681	+	0.889116i	$0.348680\pi$
$194$	0.975833	0.0700607
$195$	2.54838	0.182493
$196$	−0.348175	−0.0248696
$197$	−23.1318	−1.64807	−0.824037	−	0.566536i	$-0.808283\pi$
$197$	−23.1318	−1.64807	−0.824037	+	0.566536i	$0.808283\pi$
$198$	−6.29764	−0.447554
$199$	−16.3500	−1.15902	−0.579509	−	0.814966i	$-0.696756\pi$
$199$	−16.3500	−1.15902	−0.579509	+	0.814966i	$0.696756\pi$
$200$	3.01795	0.213402
$201$	9.93603	0.700834
$202$	5.15899	0.362985
$203$	−3.17302	−0.222703
$204$	−1.98394	−0.138904
$205$	7.64566	0.533996
$206$	21.8696	1.52373
$207$	1.18420	0.0823077
$208$	−9.77480	−0.677760
$209$	6.68025	0.462083
$210$	1.06634	0.0735845
$211$	−1.13399	−0.0780671	−0.0390335	−	0.999238i	$-0.512428\pi$
$211$	−1.13399	−0.0780671	−0.0390335	+	0.999238i	$0.512428\pi$
$212$	−2.00630	−0.137793
$213$	12.8954	0.883576
$214$	−2.18513	−0.149372
$215$	5.76988	0.393502
$216$	13.3001	0.904954
$217$	−3.72476	−0.252853
$218$	−15.0037	−1.01618
$219$	−8.10498	−0.547684
$220$	−0.738035	−0.0497583
$221$	−21.0944	−1.41896
$222$	−5.97065	−0.400724
$223$	0.407893	0.0273145	0.0136573	−	0.999907i	$-0.495653\pi$
$223$	0.407893	0.0273145	0.0136573	+	0.999907i	$0.495653\pi$
$224$	1.94575	0.130006
$225$	−2.31162	−0.154108
$226$	−5.90856	−0.393032
$227$	16.7163	1.10950	0.554751	−	0.832016i	$-0.312813\pi$
$227$	16.7163	1.10950	0.554751	+	0.832016i	$0.312813\pi$
$228$	−0.910385	−0.0602917
$229$	1.00000	0.0660819
$229$	1.00000	0.0660819
$230$	−0.658402	−0.0434137
$231$	−1.75871	−0.115714
$232$	9.57603	0.628697
$233$	−25.0566	−1.64151	−0.820757	−	0.571278i	$-0.806448\pi$
$233$	−25.0566	−1.64151	−0.820757	+	0.571278i	$0.806448\pi$
$234$	9.12533	0.596541
$235$	10.3490	0.675095
$236$	0.274679	0.0178801
$237$	7.89501	0.512836
$238$	−8.82673	−0.572152
$239$	−9.02309	−0.583655	−0.291828	−	0.956471i	$-0.594263\pi$
$239$	−9.02309	−0.583655	−0.291828	+	0.956471i	$0.594263\pi$
$240$	−2.64041	−0.170438
$241$	2.89667	0.186591	0.0932955	−	0.995638i	$-0.470260\pi$
$241$	2.89667	0.186591	0.0932955	+	0.995638i	$0.470260\pi$
$242$	8.36272	0.537576
$243$	−15.9410	−1.02262
$244$	−2.08664	−0.133583
$245$	−1.00000	−0.0638877
$246$	−8.15287	−0.519808
$247$	−9.67973	−0.615906
$248$	11.2412	0.713815
$249$	2.25102	0.142652
$250$	1.28523	0.0812853
$251$	−23.8655	−1.50638	−0.753188	−	0.657805i	$-0.771485\pi$
$251$	−23.8655	−1.50638	−0.753188	+	0.657805i	$0.771485\pi$
$252$	−0.804849	−0.0507007
$253$	1.08590	0.0682697
$254$	−26.3798	−1.65521
$255$	−5.69812	−0.356830
$256$	−8.08826	−0.505516
$257$	−5.23631	−0.326632	−0.163316	−	0.986574i	$-0.552219\pi$
$257$	−5.23631	−0.326632	−0.163316	+	0.986574i	$0.552219\pi$
$258$	−6.15265	−0.383047
$259$	5.59920	0.347917
$260$	1.06942	0.0663225
$261$	−7.33483	−0.454014
$262$	−17.1009	−1.05650
$263$	2.68393	0.165498	0.0827491	−	0.996570i	$-0.473630\pi$
$263$	2.68393	0.165498	0.0827491	+	0.996570i	$0.473630\pi$
$264$	5.30769	0.326666
$265$	−5.76232	−0.353977
$266$	−4.05038	−0.248345
$267$	13.3197	0.815153
$268$	4.16963	0.254700
$269$	13.5689	0.827312	0.413656	−	0.910433i	$-0.364252\pi$
$269$	13.5689	0.827312	0.413656	+	0.910433i	$0.364252\pi$
$270$	5.66400	0.344700
$271$	−12.0364	−0.731159	−0.365579	−	0.930780i	$-0.619129\pi$
$271$	−12.0364	−0.731159	−0.365579	+	0.930780i	$0.619129\pi$
$272$	21.8563	1.32523
$273$	2.54838	0.154235
$274$	15.3737	0.928760
$275$	−2.11972	−0.127824
$276$	−0.147986	−0.00890771
$277$	5.00271	0.300584	0.150292	−	0.988642i	$-0.451979\pi$
$277$	5.00271	0.300584	0.150292	+	0.988642i	$0.451979\pi$
$278$	3.56718	0.213945
$279$	−8.61024	−0.515482
$280$	3.01795	0.180357
$281$	−0.978797	−0.0583901	−0.0291951	−	0.999574i	$-0.509294\pi$
$281$	−0.978797	−0.0583901	−0.0291951	+	0.999574i	$0.509294\pi$
$282$	−11.0356	−0.657158
$283$	−20.8717	−1.24069	−0.620347	−	0.784327i	$-0.713008\pi$
$283$	−20.8717	−1.24069	−0.620347	+	0.784327i	$0.713008\pi$
$284$	5.41150	0.321113
$285$	−2.61473	−0.154883
$286$	8.36780	0.494798
$287$	7.64566	0.451309
$288$	4.49783	0.265037
$289$	30.1667	1.77451
$290$	4.07808	0.239473
$291$	0.629952	0.0369284
$292$	−3.40123	−0.199042
$293$	27.8956	1.62968	0.814840	−	0.579686i	$-0.196825\pi$
$293$	27.8956	1.62968	0.814840	+	0.579686i	$0.196825\pi$
$294$	1.06634	0.0621902
$295$	0.788910	0.0459321
$296$	−16.8981	−0.982183
$297$	−9.34158	−0.542053
$298$	14.4596	0.837622
$299$	−1.57347	−0.0909962
$300$	0.288876	0.0166783
$301$	5.76988	0.332570
$302$	−14.4953	−0.834113
$303$	3.33040	0.191326
$304$	10.0293	0.575221
$305$	−5.99308	−0.343163
$306$	−20.4041	−1.16642
$307$	24.8123	1.41611	0.708055	−	0.706157i	$-0.249573\pi$
$307$	24.8123	1.41611	0.708055	+	0.706157i	$0.249573\pi$
$308$	−0.738035	−0.0420535
$309$	14.1180	0.803143
$310$	4.78719	0.271894
$311$	−8.78571	−0.498192	−0.249096	−	0.968479i	$-0.580133\pi$
$311$	−8.78571	−0.498192	−0.249096	+	0.968479i	$0.580133\pi$
$312$	−7.69088	−0.435410
$313$	−7.29795	−0.412505	−0.206252	−	0.978499i	$-0.566127\pi$
$313$	−7.29795	−0.412505	−0.206252	+	0.978499i	$0.566127\pi$
$314$	20.7058	1.16850
$315$	−2.31162	−0.130245
$316$	3.31311	0.186377
$317$	−12.0895	−0.679012	−0.339506	−	0.940604i	$-0.610260\pi$
$317$	−12.0895	−0.679012	−0.339506	+	0.940604i	$0.610260\pi$
$318$	6.14459	0.344572
$319$	−6.72593	−0.376580
$320$	−8.86559	−0.495601
$321$	−1.41062	−0.0787330
$322$	−0.658402	−0.0366913
$323$	21.6437	1.20429
$324$	−1.14148	−0.0634154
$325$	3.07149	0.170376
$326$	30.6104	1.69535
$327$	−9.68567	−0.535619
$328$	−23.0742	−1.27406
$329$	10.3490	0.570559
$330$	2.26035	0.124428
$331$	−13.5342	−0.743907	−0.371953	−	0.928251i	$-0.621312\pi$
$331$	−13.5342	−0.743907	−0.371953	+	0.928251i	$0.621312\pi$
$332$	0.944632	0.0518434
$333$	12.9432	0.709285
$334$	0.163422	0.00894208
$335$	11.9757	0.654300
$336$	−2.64041	−0.144046
$337$	−14.4378	−0.786476	−0.393238	−	0.919437i	$-0.628645\pi$
$337$	−14.4378	−0.786476	−0.393238	+	0.919437i	$0.628645\pi$
$338$	4.58304	0.249285
$339$	−3.81429	−0.207164
$340$	−2.39120	−0.129681
$341$	−7.89547	−0.427564
$342$	−9.36294	−0.506290
$343$	−1.00000	−0.0539949
$344$	−17.4132	−0.938858
$345$	−0.425033	−0.0228830
$346$	−6.02985	−0.324167
$347$	10.6126	0.569716	0.284858	−	0.958570i	$-0.408054\pi$
$347$	10.6126	0.569716	0.284858	+	0.958570i	$0.408054\pi$
$348$	0.916610	0.0491355
$349$	8.40627	0.449977	0.224989	−	0.974361i	$-0.427765\pi$
$349$	8.40627	0.449977	0.224989	+	0.974361i	$0.427765\pi$
$350$	1.28523	0.0686986
$351$	13.5360	0.722499
$352$	4.12445	0.219834
$353$	−2.25429	−0.119984	−0.0599920	−	0.998199i	$-0.519108\pi$
$353$	−2.25429	−0.119984	−0.0599920	+	0.998199i	$0.519108\pi$
$354$	−0.841247	−0.0447118
$355$	15.5425	0.824908
$356$	5.58957	0.296247
$357$	−5.69812	−0.301576
$358$	−5.79693	−0.306377
$359$	31.0720	1.63992	0.819958	−	0.572424i	$-0.193997\pi$
$359$	31.0720	1.63992	0.819958	+	0.572424i	$0.193997\pi$
$360$	6.97636	0.367687
$361$	−9.06822	−0.477275
$362$	14.1651	0.744500
$363$	5.39858	0.283352
$364$	1.06942	0.0560527
$365$	−9.76873	−0.511319
$366$	6.39066	0.334045
$367$	3.23848	0.169047	0.0845237	−	0.996421i	$-0.473063\pi$
$367$	3.23848	0.169047	0.0845237	+	0.996421i	$0.473063\pi$
$368$	1.63030	0.0849852
$369$	17.6739	0.920064
$370$	−7.19628	−0.374117
$371$	−5.76232	−0.299165
$372$	1.07599	0.0557877
$373$	29.2902	1.51659	0.758294	−	0.651913i	$-0.226033\pi$
$373$	29.2902	1.51659	0.758294	+	0.651913i	$0.226033\pi$
$374$	−18.7102	−0.967483
$375$	0.829686	0.0428448
$376$	−31.2328	−1.61071
$377$	9.74592	0.501941
$378$	5.66400	0.291324
$379$	7.33776	0.376916	0.188458	−	0.982081i	$-0.439651\pi$
$379$	7.33776	0.376916	0.188458	+	0.982081i	$0.439651\pi$
$380$	−1.09726	−0.0562885
$381$	−17.0295	−0.872449
$382$	20.4764	1.04766
$383$	34.1527	1.74512	0.872560	−	0.488506i	$-0.162458\pi$
$383$	34.1527	1.74512	0.872560	+	0.488506i	$0.162458\pi$
$384$	6.22501	0.317669
$385$	−2.11972	−0.108031
$386$	−16.3438	−0.831879
$387$	13.3378	0.677997
$388$	0.264357	0.0134207
$389$	−8.03852	−0.407569	−0.203785	−	0.979016i	$-0.565324\pi$
$389$	−8.03852	−0.407569	−0.203785	+	0.979016i	$0.565324\pi$
$390$	−3.27526	−0.165849
$391$	3.51825	0.177926
$392$	3.01795	0.152430
$393$	−11.0395	−0.556871
$394$	29.7298	1.49777
$395$	9.51566	0.478785
$396$	−1.70606	−0.0857326
$397$	15.9574	0.800879	0.400440	−	0.916323i	$-0.368857\pi$
$397$	15.9574	0.800879	0.400440	+	0.916323i	$0.368857\pi$
$398$	21.0135	1.05331
$399$	−2.61473	−0.130900
$400$	−3.18242	−0.159121
$401$	−7.11257	−0.355185	−0.177592	−	0.984104i	$-0.556831\pi$
$401$	−7.11257	−0.355185	−0.177592	+	0.984104i	$0.556831\pi$
$402$	−12.7701	−0.636916
$403$	11.4406	0.569897
$404$	1.39759	0.0695328
$405$	−3.27846	−0.162908
$406$	4.07808	0.202391
$407$	11.8688	0.588313
$408$	17.1967	0.851361
$409$	−25.6282	−1.26723	−0.633615	−	0.773648i	$-0.718430\pi$
$409$	−25.6282	−1.26723	−0.633615	+	0.773648i	$0.718430\pi$
$410$	−9.82645	−0.485294
$411$	9.92454	0.489542
$412$	5.92456	0.291882
$413$	0.788910	0.0388197
$414$	−1.52198	−0.0748010
$415$	2.71309	0.133181
$416$	−5.97636	−0.293015
$417$	2.30280	0.112769
$418$	−8.58568	−0.419939
$419$	−14.6556	−0.715975	−0.357987	−	0.933726i	$-0.616537\pi$
$419$	−14.6556	−0.715975	−0.357987	+	0.933726i	$0.616537\pi$
$420$	0.288876	0.0140957
$421$	33.3142	1.62363	0.811816	−	0.583913i	$-0.198479\pi$
$421$	33.3142	1.62363	0.811816	+	0.583913i	$0.198479\pi$
$422$	1.45744	0.0709471
$423$	23.9230	1.16318
$424$	17.3904	0.844553
$425$	−6.86780	−0.333137
$426$	−16.5736	−0.802991
$427$	−5.99308	−0.290025
$428$	−0.591961	−0.0286135
$429$	5.40185	0.260804
$430$	−7.41564	−0.357614
$431$	−0.525063	−0.0252914	−0.0126457	−	0.999920i	$-0.504025\pi$
$431$	−0.525063	−0.0252914	−0.0126457	+	0.999920i	$0.504025\pi$
$432$	−14.0249	−0.674772
$433$	−17.1908	−0.826136	−0.413068	−	0.910700i	$-0.635543\pi$
$433$	−17.1908	−0.826136	−0.413068	+	0.910700i	$0.635543\pi$
$434$	4.78719	0.229793
$435$	2.63261	0.126224
$436$	−4.06456	−0.194657
$437$	1.61444	0.0772292
$438$	10.4168	0.497734
$439$	37.5515	1.79224	0.896118	−	0.443816i	$-0.146376\pi$
$439$	37.5515	1.79224	0.896118	+	0.443816i	$0.146376\pi$
$440$	6.39723	0.304976
$441$	−2.31162	−0.110077
$442$	27.1112	1.28955
$443$	23.0067	1.09308	0.546541	−	0.837432i	$-0.315944\pi$
$443$	23.0067	1.09308	0.546541	+	0.837432i	$0.315944\pi$
$444$	−1.61747	−0.0767619
$445$	16.0539	0.761028
$446$	−0.524238	−0.0248234
$447$	9.33443	0.441504
$448$	−8.86559	−0.418860
$449$	−9.83944	−0.464352	−0.232176	−	0.972674i	$-0.574585\pi$
$449$	−9.83944	−0.464352	−0.232176	+	0.972674i	$0.574585\pi$
$450$	2.97097	0.140053
$451$	16.2067	0.763143
$452$	−1.60065	−0.0752884
$453$	−9.35751	−0.439654
$454$	−21.4844	−1.00831
$455$	3.07149	0.143994
$456$	7.89114	0.369536
$457$	2.68226	0.125471	0.0627354	−	0.998030i	$-0.480018\pi$
$457$	2.68226	0.125471	0.0627354	+	0.998030i	$0.480018\pi$
$458$	−1.28523	−0.0600550
$459$	−30.2662	−1.41271
$460$	−0.178364	−0.00831625
$461$	5.15966	0.240309	0.120155	−	0.992755i	$-0.461661\pi$
$461$	5.15966	0.240309	0.120155	+	0.992755i	$0.461661\pi$
$462$	2.26035	0.105161
$463$	22.1578	1.02976	0.514879	−	0.857263i	$-0.327837\pi$
$463$	22.1578	1.02976	0.514879	+	0.857263i	$0.327837\pi$
$464$	−10.0979	−0.468783
$465$	3.09038	0.143313
$466$	32.2036	1.49180
$467$	12.0699	0.558530	0.279265	−	0.960214i	$-0.409909\pi$
$467$	12.0699	0.558530	0.279265	+	0.960214i	$0.409909\pi$
$468$	2.47209	0.114272
$469$	11.9757	0.552984
$470$	−13.3009	−0.613524
$471$	13.3667	0.615904
$472$	−2.38089	−0.109590
$473$	12.2305	0.562361
$474$	−10.1469	−0.466064
$475$	−3.15147	−0.144599
$476$	−2.39120	−0.109600
$477$	−13.3203	−0.609895
$478$	11.5968	0.530425
$479$	1.77670	0.0811794	0.0405897	−	0.999176i	$-0.487076\pi$
$479$	1.77670	0.0811794	0.0405897	+	0.999176i	$0.487076\pi$
$480$	−1.61436	−0.0736851
$481$	−17.1979	−0.784157
$482$	−3.72290	−0.169573
$483$	−0.425033	−0.0193397
$484$	2.26549	0.102977
$485$	0.759265	0.0344765
$486$	20.4879	0.929352
$487$	14.6185	0.662427	0.331214	−	0.943556i	$-0.392542\pi$
$487$	14.6185	0.662427	0.331214	+	0.943556i	$0.392542\pi$
$488$	18.0868	0.818752
$489$	19.7606	0.893605
$490$	1.28523	0.0580609
$491$	4.77155	0.215337	0.107668	−	0.994187i	$-0.465662\pi$
$491$	4.77155	0.215337	0.107668	+	0.994187i	$0.465662\pi$
$492$	−2.20865	−0.0995735
$493$	−21.7917	−0.981448
$494$	12.4407	0.559734
$495$	−4.90000	−0.220239
$496$	−11.8538	−0.532250
$497$	15.5425	0.697175
$498$	−2.89308	−0.129642
$499$	−0.0416221	−0.00186326	−0.000931630	−	1.00000i	$-0.500297\pi$
$499$	−0.0416221	−0.00186326	−0.000931630		1.00000i	$0.500297\pi$
$500$	0.348175	0.0155709
$501$	0.105498	0.00471329
$502$	30.6727	1.36899
$503$	7.28459	0.324804	0.162402	−	0.986725i	$-0.448076\pi$
$503$	7.28459	0.324804	0.162402	+	0.986725i	$0.448076\pi$
$504$	6.97636	0.310752
$505$	4.01405	0.178623
$506$	−1.39563	−0.0620433
$507$	2.95860	0.131396
$508$	−7.14639	−0.317070
$509$	−24.6010	−1.09042	−0.545211	−	0.838299i	$-0.683550\pi$
$509$	−24.6010	−1.09042	−0.545211	+	0.838299i	$0.683550\pi$
$510$	7.32341	0.324286
$511$	−9.76873	−0.432143
$512$	25.4010	1.12258
$513$	−13.8885	−0.613191
$514$	6.72988	0.296842
$515$	17.0160	0.749816
$516$	−1.66678	−0.0733758
$517$	21.9370	0.964790
$518$	−7.19628	−0.316186
$519$	−3.89259	−0.170866
$520$	−9.26963	−0.406500
$521$	−20.4969	−0.897987	−0.448993	−	0.893535i	$-0.648217\pi$
$521$	−20.4969	−0.897987	−0.448993	+	0.893535i	$0.648217\pi$
$522$	9.42696	0.412607
$523$	16.0003	0.699643	0.349822	−	0.936816i	$-0.386242\pi$
$523$	16.0003	0.699643	0.349822	+	0.936816i	$0.386242\pi$
$524$	−4.63271	−0.202381
$525$	0.829686	0.0362105
$526$	−3.44948	−0.150404
$527$	−25.5809	−1.11432
$528$	−5.59695	−0.243576
$529$	−22.7376	−0.988590
$530$	7.40593	0.321693
$531$	1.82366	0.0791402
$532$	−1.09726	−0.0475724
$533$	−23.4836	−1.01719
$534$	−17.1189	−0.740809
$535$	−1.70018	−0.0735053
$536$	−36.1420	−1.56110
$537$	−3.74223	−0.161489
$538$	−17.4392	−0.751858
$539$	−2.11972	−0.0913030
$540$	1.53440	0.0660301
$541$	34.3532	1.47696	0.738481	−	0.674275i	$-0.235544\pi$
$541$	34.3532	1.47696	0.738481	+	0.674275i	$0.235544\pi$
$542$	15.4696	0.664475
$543$	9.14430	0.392420
$544$	13.3630	0.572935
$545$	−11.6739	−0.500055
$546$	−3.27526	−0.140168
$547$	2.07177	0.0885826	0.0442913	−	0.999019i	$-0.485897\pi$
$547$	2.07177	0.0885826	0.0442913	+	0.999019i	$0.485897\pi$
$548$	4.16480	0.177912
$549$	−13.8537	−0.591263
$550$	2.72434	0.116166
$551$	−9.99969	−0.426001
$552$	1.28273	0.0545966
$553$	9.51566	0.404647
$554$	−6.42965	−0.273170
$555$	−4.64558	−0.197194
$556$	0.966364	0.0409829
$557$	44.3290	1.87828	0.939139	−	0.343537i	$-0.111625\pi$
$557$	44.3290	1.87828	0.939139	+	0.343537i	$0.111625\pi$
$558$	11.0662	0.468468
$559$	−17.7221	−0.749567
$560$	−3.18242	−0.134482
$561$	−12.0784	−0.509952
$562$	1.25798	0.0530648
$563$	−0.434764	−0.0183231	−0.00916157	−	0.999958i	$-0.502916\pi$
$563$	−0.434764	−0.0183231	−0.00916157	+	0.999958i	$0.502916\pi$
$564$	−2.98958	−0.125884
$565$	−4.59727	−0.193409
$566$	26.8250	1.12754
$567$	−3.27846	−0.137682
$568$	−46.9064	−1.96815
$569$	−32.2191	−1.35069	−0.675347	−	0.737500i	$-0.736006\pi$
$569$	−32.2191	−1.35069	−0.675347	+	0.737500i	$0.736006\pi$
$570$	3.36054	0.140758
$571$	−30.2732	−1.26689	−0.633446	−	0.773787i	$-0.718360\pi$
$571$	−30.2732	−1.26689	−0.633446	+	0.773787i	$0.718360\pi$
$572$	2.26687	0.0947826
$573$	13.2186	0.552215
$574$	−9.82645	−0.410148
$575$	−0.512282	−0.0213636
$576$	−20.4939	−0.853912
$577$	−27.7311	−1.15446	−0.577231	−	0.816581i	$-0.695867\pi$
$577$	−27.7311	−1.15446	−0.577231	+	0.816581i	$0.695867\pi$
$578$	−38.7713	−1.61267
$579$	−10.5508	−0.438477
$580$	1.10477	0.0458730
$581$	2.71309	0.112558
$582$	−0.809635	−0.0335604
$583$	−12.2145	−0.505874
$584$	29.4816	1.21996
$585$	7.10013	0.293554
$586$	−35.8524	−1.48105
$587$	43.0865	1.77837	0.889184	−	0.457549i	$-0.151273\pi$
$587$	43.0865	1.77837	0.889184	+	0.457549i	$0.151273\pi$
$588$	0.288876	0.0119130
$589$	−11.7385	−0.483676
$590$	−1.01393	−0.0417430
$591$	19.1921	0.789459
$592$	17.8190	0.732358
$593$	−12.9793	−0.532997	−0.266499	−	0.963835i	$-0.585867\pi$
$593$	−12.9793	−0.532997	−0.266499	+	0.963835i	$0.585867\pi$
$594$	12.0061	0.492617
$595$	−6.86780	−0.281552
$596$	3.91717	0.160453
$597$	13.5653	0.555192
$598$	2.02228	0.0826971
$599$	−21.6877	−0.886136	−0.443068	−	0.896488i	$-0.646110\pi$
$599$	−21.6877	−0.886136	−0.443068	+	0.896488i	$0.646110\pi$
$600$	−2.50395	−0.102223
$601$	28.1572	1.14856	0.574278	−	0.818660i	$-0.305283\pi$
$601$	28.1572	1.14856	0.574278	+	0.818660i	$0.305283\pi$
$602$	−7.41564	−0.302239
$603$	27.6832	1.12735
$604$	−3.92685	−0.159781
$605$	6.50677	0.264538
$606$	−4.28034	−0.173877
$607$	39.8634	1.61801	0.809003	−	0.587804i	$-0.200007\pi$
$607$	39.8634	1.61801	0.809003	+	0.587804i	$0.200007\pi$
$608$	6.13197	0.248684
$609$	2.63261	0.106679
$610$	7.70250	0.311865
$611$	−31.7869	−1.28596
$612$	−5.52754	−0.223438
$613$	34.6287	1.39864	0.699319	−	0.714810i	$-0.253487\pi$
$613$	34.6287	1.39864	0.699319	+	0.714810i	$0.253487\pi$
$614$	−31.8896	−1.28696
$615$	−6.34349	−0.255794
$616$	6.39723	0.257752
$617$	10.7919	0.434465	0.217233	−	0.976120i	$-0.430297\pi$
$617$	10.7919	0.434465	0.217233	+	0.976120i	$0.430297\pi$
$618$	−18.1449	−0.729895
$619$	−7.55894	−0.303819	−0.151910	−	0.988394i	$-0.548542\pi$
$619$	−7.55894	−0.303819	−0.151910	+	0.988394i	$0.548542\pi$
$620$	1.29687	0.0520836
$621$	−2.25761	−0.0905949
$622$	11.2917	0.452755
$623$	16.0539	0.643186
$624$	8.11001	0.324660
$625$	1.00000	0.0400000
$626$	9.37957	0.374883
$627$	−5.54251	−0.221347
$628$	5.60929	0.223835
$629$	38.4542	1.53327
$630$	2.97097	0.118366
$631$	−36.1018	−1.43719	−0.718595	−	0.695429i	$-0.755214\pi$
$631$	−36.1018	−1.43719	−0.718595	+	0.695429i	$0.755214\pi$
$632$	−28.7178	−1.14233
$633$	0.940855	0.0373956
$634$	15.5378	0.617084
$635$	−20.5253	−0.814521
$636$	1.66460	0.0660055
$637$	3.07149	0.121697
$638$	8.64440	0.342235
$639$	35.9283	1.42130
$640$	7.50285	0.296576
$641$	−18.3572	−0.725067	−0.362534	−	0.931971i	$-0.618088\pi$
$641$	−18.3572	−0.725067	−0.362534	+	0.931971i	$0.618088\pi$
$642$	1.81297	0.0715523
$643$	15.1575	0.597753	0.298876	−	0.954292i	$-0.403388\pi$
$643$	15.1575	0.597753	0.298876	+	0.954292i	$0.403388\pi$
$644$	−0.178364	−0.00702852
$645$	−4.78719	−0.188495
$646$	−27.8172	−1.09445
$647$	−16.4182	−0.645467	−0.322733	−	0.946490i	$-0.604602\pi$
$647$	−16.4182	−0.645467	−0.322733	+	0.946490i	$0.604602\pi$
$648$	9.89422	0.388682
$649$	1.67227	0.0656424
$650$	−3.94759	−0.154837
$651$	3.09038	0.121122
$652$	8.29247	0.324758
$653$	39.9952	1.56513	0.782567	−	0.622566i	$-0.213910\pi$
$653$	39.9952	1.56513	0.782567	+	0.622566i	$0.213910\pi$
$654$	12.4483	0.486769
$655$	−13.3057	−0.519896
$656$	24.3317	0.949994
$657$	−22.5816	−0.880993
$658$	−13.3009	−0.518523
$659$	−46.2910	−1.80324	−0.901621	−	0.432527i	$-0.857622\pi$
$659$	−46.2910	−1.80324	−0.901621	+	0.432527i	$0.857622\pi$
$660$	0.612337	0.0238352
$661$	1.10700	0.0430572	0.0215286	−	0.999768i	$-0.493147\pi$
$661$	1.10700	0.0430572	0.0215286	+	0.999768i	$0.493147\pi$
$662$	17.3946	0.676060
$663$	17.5017	0.679711
$664$	−8.18799	−0.317756
$665$	−3.15147	−0.122209
$666$	−16.6351	−0.644596
$667$	−1.62548	−0.0629389
$668$	0.0442718	0.00171293
$669$	−0.338423	−0.0130842
$670$	−15.3915	−0.594626
$671$	−12.7037	−0.490420
$672$	−1.61436	−0.0622753
$673$	20.3284	0.783601	0.391801	−	0.920050i	$-0.371852\pi$
$673$	20.3284	0.783601	0.391801	+	0.920050i	$0.371852\pi$
$674$	18.5559	0.714747
$675$	4.40698	0.169625
$676$	1.24156	0.0477525
$677$	39.2118	1.50703	0.753516	−	0.657429i	$-0.228356\pi$
$677$	39.2118	1.50703	0.753516	+	0.657429i	$0.228356\pi$
$678$	4.90225	0.188270
$679$	0.759265	0.0291379
$680$	20.7267	0.794833
$681$	−13.8693	−0.531473
$682$	10.1475	0.388569
$683$	−4.94760	−0.189315	−0.0946573	−	0.995510i	$-0.530176\pi$
$683$	−4.94760	−0.189315	−0.0946573	+	0.995510i	$0.530176\pi$
$684$	−2.53646	−0.0969839
$685$	11.9618	0.457037
$686$	1.28523	0.0490704
$687$	−0.829686	−0.0316545
$688$	18.3622	0.700052
$689$	17.6989	0.674276
$690$	0.546267	0.0207960
$691$	−1.07221	−0.0407888	−0.0203944	−	0.999792i	$-0.506492\pi$
$691$	−1.07221	−0.0407888	−0.0203944	+	0.999792i	$0.506492\pi$
$692$	−1.63351	−0.0620968
$693$	−4.90000	−0.186136
$694$	−13.6397	−0.517757
$695$	2.77551	0.105281
$696$	−7.94510	−0.301158
$697$	52.5089	1.98891
$698$	−10.8040	−0.408938
$699$	20.7891	0.786317
$700$	0.348175	0.0131598
$701$	6.44084	0.243267	0.121634	−	0.992575i	$-0.461187\pi$
$701$	6.44084	0.243267	0.121634	+	0.992575i	$0.461187\pi$
$702$	−17.3969	−0.656605
$703$	17.6457	0.665521
$704$	−18.7926	−0.708273
$705$	−8.58643	−0.323383
$706$	2.89729	0.109041
$707$	4.01405	0.150964
$708$	−0.227897	−0.00856490
$709$	17.9478	0.674045	0.337023	−	0.941497i	$-0.390580\pi$
$709$	17.9478	0.674045	0.337023	+	0.941497i	$0.390580\pi$
$710$	−19.9757	−0.749675
$711$	21.9966	0.824937
$712$	−48.4500	−1.81574
$713$	−1.90813	−0.0714600
$714$	7.32341	0.274072
$715$	6.51072	0.243487
$716$	−1.57041	−0.0586891
$717$	7.48634	0.279582
$718$	−39.9347	−1.49035
$719$	20.0385	0.747311	0.373656	−	0.927568i	$-0.378104\pi$
$719$	20.0385	0.747311	0.373656	+	0.927568i	$0.378104\pi$
$720$	−7.35656	−0.274163
$721$	17.0160	0.633711
$722$	11.6548	0.433746
$723$	−2.40333	−0.0893807
$724$	3.83738	0.142615
$725$	3.17302	0.117843
$726$	−6.93843	−0.257509
$727$	−11.3970	−0.422692	−0.211346	−	0.977411i	$-0.567785\pi$
$727$	−11.3970	−0.422692	−0.211346	+	0.977411i	$0.567785\pi$
$728$	−9.26963	−0.343555
$729$	3.39068	0.125581
$730$	12.5551	0.464685
$731$	39.6264	1.46563
$732$	1.73126	0.0639891
$733$	−26.2293	−0.968800	−0.484400	−	0.874847i	$-0.660962\pi$
$733$	−26.2293	−0.968800	−0.484400	+	0.874847i	$0.660962\pi$
$734$	−4.16220	−0.153630
$735$	0.829686	0.0306034
$736$	0.996772	0.0367415
$737$	25.3851	0.935072
$738$	−22.7150	−0.836152
$739$	11.3041	0.415829	0.207914	−	0.978147i	$-0.433332\pi$
$739$	11.3041	0.415829	0.207914	+	0.978147i	$0.433332\pi$
$740$	−1.94950	−0.0716651
$741$	8.03114	0.295031
$742$	7.40593	0.271880
$743$	−17.7554	−0.651381	−0.325690	−	0.945476i	$-0.605597\pi$
$743$	−17.7554	−0.651381	−0.325690	+	0.945476i	$0.605597\pi$
$744$	−9.32664	−0.341931
$745$	11.2506	0.412189
$746$	−37.6447	−1.37827
$747$	6.27165	0.229468
$748$	−5.06868	−0.185329
$749$	−1.70018	−0.0621233
$750$	−1.06634	−0.0389372
$751$	49.1304	1.79279	0.896397	−	0.443251i	$-0.146175\pi$
$751$	49.1304	1.79279	0.896397	+	0.443251i	$0.146175\pi$
$752$	32.9349	1.20101
$753$	19.8009	0.721583
$754$	−12.5258	−0.456162
$755$	−11.2784	−0.410462
$756$	1.53440	0.0558056
$757$	32.2813	1.17328	0.586642	−	0.809846i	$-0.300450\pi$
$757$	32.2813	1.17328	0.586642	+	0.809846i	$0.300450\pi$
$758$	−9.43074	−0.342540
$759$	−0.900953	−0.0327025
$760$	9.51099	0.345000
$761$	3.15537	0.114382	0.0571910	−	0.998363i	$-0.481786\pi$
$761$	3.15537	0.114382	0.0571910	+	0.998363i	$0.481786\pi$
$762$	21.8869	0.792880
$763$	−11.6739	−0.422624
$764$	5.54715	0.200689
$765$	−15.8758	−0.573989
$766$	−43.8942	−1.58596
$767$	−2.42313	−0.0874943
$768$	6.71072	0.242152
$769$	14.3547	0.517644	0.258822	−	0.965925i	$-0.416666\pi$
$769$	14.3547	0.517644	0.258822	+	0.965925i	$0.416666\pi$
$770$	2.72434	0.0981784
$771$	4.34450	0.156463
$772$	−4.42761	−0.159353
$773$	9.99331	0.359435	0.179717	−	0.983718i	$-0.442482\pi$
$773$	9.99331	0.359435	0.179717	+	0.983718i	$0.442482\pi$
$774$	−17.1421	−0.616162
$775$	3.72476	0.133797
$776$	−2.29143	−0.0822574
$777$	−4.64558	−0.166659
$778$	10.3314	0.370398
$779$	24.0951	0.863296
$780$	−0.887281	−0.0317698
$781$	32.9457	1.17889
$782$	−4.52177	−0.161698
$783$	13.9834	0.499727
$784$	−3.18242	−0.113658
$785$	16.1105	0.575010
$786$	14.1884	0.506083
$787$	−13.4187	−0.478327	−0.239163	−	0.970979i	$-0.576873\pi$
$787$	−13.4187	−0.478327	−0.239163	+	0.970979i	$0.576873\pi$
$788$	8.05392	0.286909
$789$	−2.22682	−0.0792769
$790$	−12.2298	−0.435118
$791$	−4.59727	−0.163460
$792$	14.7880	0.525468
$793$	18.4077	0.653677
$794$	−20.5090	−0.727837
$795$	4.78092	0.169562
$796$	5.69265	0.201771
$797$	−3.57274	−0.126553	−0.0632765	−	0.997996i	$-0.520155\pi$
$797$	−3.57274	−0.126553	−0.0632765	+	0.997996i	$0.520155\pi$
$798$	3.36054	0.118962
$799$	71.0749	2.51445
$800$	−1.94575	−0.0687926
$801$	37.1106	1.31124
$802$	9.14131	0.322791
$803$	−20.7070	−0.730735
$804$	−3.45948	−0.122006
$805$	−0.512282	−0.0180556
$806$	−14.7038	−0.517920
$807$	−11.2579	−0.396298
$808$	−12.1142	−0.426176
$809$	−27.7845	−0.976851	−0.488425	−	0.872606i	$-0.662429\pi$
$809$	−27.7845	−0.976851	−0.488425	+	0.872606i	$0.662429\pi$
$810$	4.21358	0.148050
$811$	−0.586590	−0.0205980	−0.0102990	−	0.999947i	$-0.503278\pi$
$811$	−0.586590	−0.0205980	−0.0102990	+	0.999947i	$0.503278\pi$
$812$	1.10477	0.0387697
$813$	9.98643	0.350239
$814$	−15.2541	−0.534657
$815$	23.8170	0.834272
$816$	−18.1338	−0.634811
$817$	18.1836	0.636164
$818$	32.9382	1.15166
$819$	7.10013	0.248099
$820$	−2.66203	−0.0929620
$821$	27.8267	0.971158	0.485579	−	0.874193i	$-0.338609\pi$
$821$	27.8267	0.971158	0.485579	+	0.874193i	$0.338609\pi$
$822$	−12.7554	−0.444894
$823$	−49.6784	−1.73168	−0.865840	−	0.500321i	$-0.833215\pi$
$823$	−49.6784	−1.73168	−0.865840	+	0.500321i	$0.833215\pi$
$824$	−51.3536	−1.78899
$825$	1.75871	0.0612303
$826$	−1.01393	−0.0352793
$827$	−11.1529	−0.387823	−0.193912	−	0.981019i	$-0.562118\pi$
$827$	−11.1529	−0.387823	−0.193912	+	0.981019i	$0.562118\pi$
$828$	−0.412309	−0.0143287
$829$	23.5046	0.816349	0.408174	−	0.912904i	$-0.366166\pi$
$829$	23.5046	0.816349	0.408174	+	0.912904i	$0.366166\pi$
$830$	−3.48696	−0.121034
$831$	−4.15068	−0.143985
$832$	27.2306	0.944051
$833$	−6.86780	−0.237955
$834$	−2.95964	−0.102484
$835$	0.127154	0.00440034
$836$	−2.32590	−0.0804428
$837$	16.4150	0.567384
$838$	18.8359	0.650676
$839$	−9.87033	−0.340761	−0.170381	−	0.985378i	$-0.554500\pi$
$839$	−9.87033	−0.340761	−0.170381	+	0.985378i	$0.554500\pi$
$840$	−2.50395	−0.0863946
$841$	−18.9319	−0.652825
$842$	−42.8165	−1.47555
$843$	0.812094	0.0279700
$844$	0.394827	0.0135905
$845$	3.56592	0.122671
$846$	−30.7466	−1.05709
$847$	6.50677	0.223575
$848$	−18.3381	−0.629735
$849$	17.3170	0.594317
$850$	8.82673	0.302754
$851$	2.86837	0.0983264
$852$	−4.48985	−0.153820
$853$	5.39797	0.184823	0.0924115	−	0.995721i	$-0.470542\pi$
$853$	5.39797	0.184823	0.0924115	+	0.995721i	$0.470542\pi$
$854$	7.70250	0.263574
$855$	−7.28501	−0.249142
$856$	5.13107	0.175376
$857$	−32.0359	−1.09433	−0.547163	−	0.837026i	$-0.684292\pi$
$857$	−32.0359	−1.09433	−0.547163	+	0.837026i	$0.684292\pi$
$858$	−6.94264	−0.237018
$859$	9.28563	0.316822	0.158411	−	0.987373i	$-0.449363\pi$
$859$	9.28563	0.316822	0.158411	+	0.987373i	$0.449363\pi$
$860$	−2.00893	−0.0685039
$861$	−6.34349	−0.216186
$862$	0.674829	0.0229848
$863$	19.6009	0.667222	0.333611	−	0.942711i	$-0.391733\pi$
$863$	19.6009	0.667222	0.333611	+	0.942711i	$0.391733\pi$
$864$	−8.57487	−0.291723
$865$	−4.69164	−0.159521
$866$	22.0941	0.750790
$867$	−25.0289	−0.850026
$868$	1.29687	0.0440186
$869$	20.1706	0.684240
$870$	−3.38352	−0.114712
$871$	−36.7832	−1.24635
$872$	35.2313	1.19308
$873$	1.75513	0.0594023
$874$	−2.07493	−0.0701857
$875$	1.00000	0.0338062
$876$	2.82195	0.0953450
$877$	41.2933	1.39438	0.697188	−	0.716888i	$-0.254434\pi$
$877$	41.2933	1.39438	0.697188	+	0.716888i	$0.254434\pi$
$878$	−48.2625	−1.62878
$879$	−23.1446	−0.780649
$880$	−6.74586	−0.227403
$881$	31.7879	1.07096	0.535481	−	0.844547i	$-0.320130\pi$
$881$	31.7879	1.07096	0.535481	+	0.844547i	$0.320130\pi$
$882$	2.97097	0.100038
$883$	2.44560	0.0823009	0.0411504	−	0.999153i	$-0.486898\pi$
$883$	2.44560	0.0823009	0.0411504	+	0.999153i	$0.486898\pi$
$884$	7.34455	0.247024
$885$	−0.654548	−0.0220024
$886$	−29.5690	−0.993390
$887$	−7.18207	−0.241150	−0.120575	−	0.992704i	$-0.538474\pi$
$887$	−7.18207	−0.241150	−0.120575	+	0.992704i	$0.538474\pi$
$888$	14.0201	0.470485
$889$	−20.5253	−0.688396
$890$	−20.6330	−0.691621
$891$	−6.94942	−0.232814
$892$	−0.142018	−0.00475512
$893$	32.6146	1.09141
$894$	−11.9969	−0.401237
$895$	−4.51041	−0.150766
$896$	7.50285	0.250653
$897$	1.30549	0.0435889
$898$	12.6460	0.422002
$899$	11.8188	0.394178
$900$	0.804849	0.0268283
$901$	−39.5745	−1.31842
$902$	−20.8294	−0.693542
$903$	−4.78719	−0.159308
$904$	13.8743	0.461454
$905$	11.0214	0.366364
$906$	12.0266	0.399556
$907$	−16.9745	−0.563629	−0.281814	−	0.959469i	$-0.590936\pi$
$907$	−16.9745	−0.563629	−0.281814	+	0.959469i	$0.590936\pi$
$908$	−5.82022	−0.193151
$909$	9.27896	0.307764
$910$	−3.94759	−0.130861
$911$	−15.6286	−0.517800	−0.258900	−	0.965904i	$-0.583360\pi$
$911$	−15.6286	−0.517800	−0.258900	+	0.965904i	$0.583360\pi$
$912$	−8.32119	−0.275542
$913$	5.75101	0.190331
$914$	−3.44733	−0.114027
$915$	4.97237	0.164382
$916$	−0.348175	−0.0115040
$917$	−13.3057	−0.439393
$918$	38.8992	1.28386
$919$	−42.8669	−1.41405	−0.707023	−	0.707190i	$-0.749962\pi$
$919$	−42.8669	−1.41405	−0.707023	+	0.707190i	$0.749962\pi$
$920$	1.54604	0.0509715
$921$	−20.5864	−0.678345
$922$	−6.63136	−0.218392
$923$	−47.7386	−1.57134
$924$	0.612337	0.0201444
$925$	−5.59920	−0.184101
$926$	−28.4779	−0.935842
$927$	39.3346	1.29192
$928$	−6.17390	−0.202668
$929$	−4.58841	−0.150541	−0.0752704	−	0.997163i	$-0.523982\pi$
$929$	−4.58841	−0.150541	−0.0752704	+	0.997163i	$0.523982\pi$
$930$	−3.97187	−0.130243
$931$	−3.15147	−0.103285
$932$	8.72409	0.285767
$933$	7.28938	0.238644
$934$	−15.5127	−0.507590
$935$	−14.5578	−0.476092
$936$	−21.4279	−0.700392
$937$	36.5381	1.19365	0.596825	−	0.802372i	$-0.296429\pi$
$937$	36.5381	1.19365	0.596825	+	0.802372i	$0.296429\pi$
$938$	−15.3915	−0.502551
$939$	6.05501	0.197598
$940$	−3.60327	−0.117526
$941$	−40.5683	−1.32249	−0.661244	−	0.750171i	$-0.729971\pi$
$941$	−40.5683	−1.32249	−0.661244	+	0.750171i	$0.729971\pi$
$942$	−17.1793	−0.559732
$943$	3.91673	0.127546
$944$	2.51065	0.0817146
$945$	4.40698	0.143359
$946$	−15.7191	−0.511072
$947$	−21.5637	−0.700725	−0.350363	−	0.936614i	$-0.613942\pi$
$947$	−21.5637	−0.700725	−0.350363	+	0.936614i	$0.613942\pi$
$948$	−2.74884	−0.0892783
$949$	30.0046	0.973991
$950$	4.05038	0.131412
$951$	10.0305	0.325260
$952$	20.7267	0.671756
$953$	27.6494	0.895653	0.447826	−	0.894121i	$-0.352198\pi$
$953$	27.6494	0.895653	0.447826	+	0.894121i	$0.352198\pi$
$954$	17.1197	0.554271
$955$	15.9321	0.515549
$956$	3.14162	0.101607
$957$	5.58041	0.180389
$958$	−2.28347	−0.0737756
$959$	11.9618	0.386267
$960$	7.35566	0.237403
$961$	−17.1261	−0.552456
$962$	22.1033	0.712640
$963$	−3.93018	−0.126648
$964$	−1.00855	−0.0324832
$965$	−12.7166	−0.409363
$966$	0.546267	0.0175758
$967$	31.2170	1.00387	0.501936	−	0.864905i	$-0.332621\pi$
$967$	31.2170	1.00387	0.501936	+	0.864905i	$0.332621\pi$
$968$	−19.6371	−0.631161
$969$	−17.9575	−0.576877
$970$	−0.975833	−0.0313321
$971$	44.8773	1.44018	0.720090	−	0.693881i	$-0.244100\pi$
$971$	44.8773	1.44018	0.720090	+	0.693881i	$0.244100\pi$
$972$	5.55027	0.178025
$973$	2.77551	0.0889788
$974$	−18.7882	−0.602012
$975$	−2.54838	−0.0816134
$976$	−19.0725	−0.610496
$977$	49.4673	1.58260	0.791299	−	0.611429i	$-0.209405\pi$
$977$	49.4673	1.58260	0.791299	+	0.611429i	$0.209405\pi$
$978$	−25.3970	−0.812106
$979$	34.0299	1.08760
$980$	0.348175	0.0111220
$981$	−26.9856	−0.861585
$982$	−6.13255	−0.195698
$983$	15.3198	0.488626	0.244313	−	0.969696i	$-0.421438\pi$
$983$	15.3198	0.488626	0.244313	+	0.969696i	$0.421438\pi$
$984$	19.1444	0.610300
$985$	23.1318	0.737041
$986$	28.0074	0.891938
$987$	−8.58643	−0.273309
$988$	3.37024	0.107222
$989$	2.95580	0.0939891
$990$	6.29764	0.200152
$991$	−20.4127	−0.648431	−0.324215	−	0.945983i	$-0.605100\pi$
$991$	−20.4127	−0.648431	−0.324215	+	0.945983i	$0.605100\pi$
$992$	−7.24745	−0.230107
$993$	11.2291	0.356346
$994$	−19.9757	−0.633591
$995$	16.3500	0.518329
$996$	−0.783748	−0.0248340
$997$	−33.0932	−1.04807	−0.524036	−	0.851696i	$-0.675574\pi$
$997$	−33.0932	−1.04807	−0.524036	+	0.851696i	$0.675574\pi$
$998$	0.0534941	0.00169333
$999$	−24.6755	−0.780700

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8015.2.a.l.1.19	✓	62

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8015.2.a.l.1.19	✓	62	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:	\( N \)	\(=\)	\( 8015 = 5 \cdot 7 \cdot 229 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8015.a (trivial)

\(f(q)\)	\(=\)	\(q-1.28523 q^{2} -0.829686 q^{3} -0.348175 q^{4} -1.00000 q^{5} +1.06634 q^{6} -1.00000 q^{7} +3.01795 q^{8} -2.31162 q^{9} +O(q^{10})\)	\(q-1.28523 q^{2} -0.829686 q^{3} -0.348175 q^{4} -1.00000 q^{5} +1.06634 q^{6} -1.00000 q^{7} +3.01795 q^{8} -2.31162 q^{9} +1.28523 q^{10} -2.11972 q^{11} +0.288876 q^{12} +3.07149 q^{13} +1.28523 q^{14} +0.829686 q^{15} -3.18242 q^{16} -6.86780 q^{17} +2.97097 q^{18} -3.15147 q^{19} +0.348175 q^{20} +0.829686 q^{21} +2.72434 q^{22} -0.512282 q^{23} -2.50395 q^{24} +1.00000 q^{25} -3.94759 q^{26} +4.40698 q^{27} +0.348175 q^{28} +3.17302 q^{29} -1.06634 q^{30} +3.72476 q^{31} -1.94575 q^{32} +1.75871 q^{33} +8.82673 q^{34} +1.00000 q^{35} +0.804849 q^{36} -5.59920 q^{37} +4.05038 q^{38} -2.54838 q^{39} -3.01795 q^{40} -7.64566 q^{41} -1.06634 q^{42} -5.76988 q^{43} +0.738035 q^{44} +2.31162 q^{45} +0.658402 q^{46} -10.3490 q^{47} +2.64041 q^{48} +1.00000 q^{49} -1.28523 q^{50} +5.69812 q^{51} -1.06942 q^{52} +5.76232 q^{53} -5.66400 q^{54} +2.11972 q^{55} -3.01795 q^{56} +2.61473 q^{57} -4.07808 q^{58} -0.788910 q^{59} -0.288876 q^{60} +5.99308 q^{61} -4.78719 q^{62} +2.31162 q^{63} +8.86559 q^{64} -3.07149 q^{65} -2.26035 q^{66} -11.9757 q^{67} +2.39120 q^{68} +0.425033 q^{69} -1.28523 q^{70} -15.5425 q^{71} -6.97636 q^{72} +9.76873 q^{73} +7.19628 q^{74} -0.829686 q^{75} +1.09726 q^{76} +2.11972 q^{77} +3.27526 q^{78} -9.51566 q^{79} +3.18242 q^{80} +3.27846 q^{81} +9.82645 q^{82} -2.71309 q^{83} -0.288876 q^{84} +6.86780 q^{85} +7.41564 q^{86} -2.63261 q^{87} -6.39723 q^{88} -16.0539 q^{89} -2.97097 q^{90} -3.07149 q^{91} +0.178364 q^{92} -3.09038 q^{93} +13.3009 q^{94} +3.15147 q^{95} +1.61436 q^{96} -0.759265 q^{97} -1.28523 q^{98} +4.90000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 62 q + 2 q^{2} + 11 q^{3} + 64 q^{4} - 62 q^{5} + 3 q^{6} - 62 q^{7} + 15 q^{8} + 69 q^{9}+O(q^{10}) \) 62 * q + 2 * q^2 + 11 * q^3 + 64 * q^4 - 62 * q^5 + 3 * q^6 - 62 * q^7 + 15 * q^8 + 69 * q^9	\( 62 q + 2 q^{2} + 11 q^{3} + 64 q^{4} - 62 q^{5} + 3 q^{6} - 62 q^{7} + 15 q^{8} + 69 q^{9} - 2 q^{10} - 13 q^{11} + 37 q^{12} + 31 q^{13} - 2 q^{14} - 11 q^{15} + 64 q^{16} + 30 q^{17} + 18 q^{18} + 20 q^{19} - 64 q^{20} - 11 q^{21} + 7 q^{22} + 29 q^{24} + 62 q^{25} + 59 q^{27} - 64 q^{28} - 29 q^{29} - 3 q^{30} + 20 q^{31} + 22 q^{32} + 72 q^{33} + 13 q^{34} + 62 q^{35} + 53 q^{36} + 35 q^{37} + 34 q^{38} - 6 q^{39} - 15 q^{40} + 13 q^{41} - 3 q^{42} - 4 q^{43} - 44 q^{44} - 69 q^{45} - 19 q^{46} + 58 q^{47} + 64 q^{48} + 62 q^{49} + 2 q^{50} - 30 q^{51} + 82 q^{52} + 18 q^{53} + 22 q^{54} + 13 q^{55} - 15 q^{56} + 21 q^{57} + 18 q^{58} - 11 q^{59} - 37 q^{60} + 24 q^{61} + 48 q^{62} - 69 q^{63} + 65 q^{64} - 31 q^{65} + 25 q^{66} - 6 q^{67} + 65 q^{68} + 27 q^{69} + 2 q^{70} - 35 q^{71} + 53 q^{72} + 116 q^{73} - 69 q^{74} + 11 q^{75} + 65 q^{76} + 13 q^{77} + 102 q^{78} - 83 q^{79} - 64 q^{80} + 126 q^{81} + 71 q^{82} + 84 q^{83} - 37 q^{84} - 30 q^{85} + 24 q^{86} + 49 q^{87} + 20 q^{88} - 16 q^{89} - 18 q^{90} - 31 q^{91} + 19 q^{92} + 65 q^{93} + 54 q^{94} - 20 q^{95} + 17 q^{96} + 155 q^{97} + 2 q^{98} + 6 q^{99}+O(q^{100}) \) 62 * q + 2 * q^2 + 11 * q^3 + 64 * q^4 - 62 * q^5 + 3 * q^6 - 62 * q^7 + 15 * q^8 + 69 * q^9 - 2 * q^10 - 13 * q^11 + 37 * q^12 + 31 * q^13 - 2 * q^14 - 11 * q^15 + 64 * q^16 + 30 * q^17 + 18 * q^18 + 20 * q^19 - 64 * q^20 - 11 * q^21 + 7 * q^22 + 29 * q^24 + 62 * q^25 + 59 * q^27 - 64 * q^28 - 29 * q^29 - 3 * q^30 + 20 * q^31 + 22 * q^32 + 72 * q^33 + 13 * q^34 + 62 * q^35 + 53 * q^36 + 35 * q^37 + 34 * q^38 - 6 * q^39 - 15 * q^40 + 13 * q^41 - 3 * q^42 - 4 * q^43 - 44 * q^44 - 69 * q^45 - 19 * q^46 + 58 * q^47 + 64 * q^48 + 62 * q^49 + 2 * q^50 - 30 * q^51 + 82 * q^52 + 18 * q^53 + 22 * q^54 + 13 * q^55 - 15 * q^56 + 21 * q^57 + 18 * q^58 - 11 * q^59 - 37 * q^60 + 24 * q^61 + 48 * q^62 - 69 * q^63 + 65 * q^64 - 31 * q^65 + 25 * q^66 - 6 * q^67 + 65 * q^68 + 27 * q^69 + 2 * q^70 - 35 * q^71 + 53 * q^72 + 116 * q^73 - 69 * q^74 + 11 * q^75 + 65 * q^76 + 13 * q^77 + 102 * q^78 - 83 * q^79 - 64 * q^80 + 126 * q^81 + 71 * q^82 + 84 * q^83 - 37 * q^84 - 30 * q^85 + 24 * q^86 + 49 * q^87 + 20 * q^88 - 16 * q^89 - 18 * q^90 - 31 * q^91 + 19 * q^92 + 65 * q^93 + 54 * q^94 - 20 * q^95 + 17 * q^96 + 155 * q^97 + 2 * q^98 + 6 * q^99

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