LMFDB - Embedded newform 2671.2.a.b.1.59

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2671,2,Mod(1,2671)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2671, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("2671.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2671 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2671.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:	$21.3280423799$
Analytic rank:	$0$
Dimension:	$122$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.59
Character	$\chi$	$=$	2671.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.0716716 q^{2} +2.79309 q^{3} -1.99486 q^{4} +2.81758 q^{5} +0.200185 q^{6} +0.519275 q^{7} -0.286318 q^{8} +4.80137 q^{9} +O(q^{10})$	\(q+0.0716716 q^{2} +2.79309 q^{3} -1.99486 q^{4} +2.81758 q^{5} +0.200185 q^{6} +0.519275 q^{7} -0.286318 q^{8} +4.80137 q^{9} +0.201940 q^{10} -3.70536 q^{11} -5.57184 q^{12} +5.65930 q^{13} +0.0372172 q^{14} +7.86975 q^{15} +3.96921 q^{16} +2.63035 q^{17} +0.344122 q^{18} +0.800678 q^{19} -5.62068 q^{20} +1.45038 q^{21} -0.265569 q^{22} -5.44047 q^{23} -0.799714 q^{24} +2.93873 q^{25} +0.405611 q^{26} +5.03141 q^{27} -1.03588 q^{28} +4.06812 q^{29} +0.564038 q^{30} +5.06221 q^{31} +0.857116 q^{32} -10.3494 q^{33} +0.188521 q^{34} +1.46310 q^{35} -9.57808 q^{36} +5.72799 q^{37} +0.0573859 q^{38} +15.8070 q^{39} -0.806723 q^{40} -3.33769 q^{41} +0.103951 q^{42} -12.3791 q^{43} +7.39169 q^{44} +13.5282 q^{45} -0.389927 q^{46} +4.66533 q^{47} +11.0864 q^{48} -6.73035 q^{49} +0.210624 q^{50} +7.34682 q^{51} -11.2895 q^{52} +3.16546 q^{53} +0.360609 q^{54} -10.4401 q^{55} -0.148678 q^{56} +2.23637 q^{57} +0.291569 q^{58} +8.34292 q^{59} -15.6991 q^{60} -0.267265 q^{61} +0.362817 q^{62} +2.49323 q^{63} -7.87698 q^{64} +15.9455 q^{65} -0.741759 q^{66} -8.12254 q^{67} -5.24719 q^{68} -15.1957 q^{69} +0.104862 q^{70} +8.31807 q^{71} -1.37472 q^{72} +5.43956 q^{73} +0.410534 q^{74} +8.20816 q^{75} -1.59724 q^{76} -1.92410 q^{77} +1.13291 q^{78} +11.8414 q^{79} +11.1835 q^{80} -0.350929 q^{81} -0.239217 q^{82} -8.79199 q^{83} -2.89332 q^{84} +7.41121 q^{85} -0.887232 q^{86} +11.3627 q^{87} +1.06091 q^{88} +7.73620 q^{89} +0.969590 q^{90} +2.93873 q^{91} +10.8530 q^{92} +14.1392 q^{93} +0.334372 q^{94} +2.25597 q^{95} +2.39400 q^{96} -6.57347 q^{97} -0.482375 q^{98} -17.7908 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 122 q + 14 q^{2} + 10 q^{3} + 128 q^{4} + 33 q^{5} + 22 q^{6} + 6 q^{7} + 36 q^{8} + 162 q^{9}+O(q^{10}) $ 122 * q + 14 * q^2 + 10 * q^3 + 128 * q^4 + 33 * q^5 + 22 * q^6 + 6 * q^7 + 36 * q^8 + 162 * q^9	\( 122 q + 14 q^{2} + 10 q^{3} + 128 q^{4} + 33 q^{5} + 22 q^{6} + 6 q^{7} + 36 q^{8} + 162 q^{9} + 16 q^{10} + 43 q^{11} + 23 q^{12} + 25 q^{13} + 45 q^{14} + 12 q^{15} + 132 q^{16} + 103 q^{17} + 30 q^{18} + 37 q^{19} + 63 q^{20} + 81 q^{21} + 15 q^{23} + 60 q^{24} + 151 q^{25} + 59 q^{26} + 22 q^{27} - 3 q^{28} + 80 q^{29} - 9 q^{30} + 15 q^{31} + 66 q^{32} + 93 q^{33} + 30 q^{34} + 23 q^{35} + 162 q^{36} + 18 q^{37} + 41 q^{38} + 10 q^{39} + 29 q^{40} + 249 q^{41} - 8 q^{42} + 14 q^{43} + 100 q^{44} + 59 q^{45} + 11 q^{46} + 57 q^{47} + 33 q^{48} + 180 q^{49} + 63 q^{50} + 26 q^{51} + 31 q^{52} + 65 q^{53} + 65 q^{54} - 8 q^{55} + 120 q^{56} + 57 q^{57} - 31 q^{58} + 108 q^{59} - q^{60} + 70 q^{61} + 25 q^{62} - 7 q^{63} + 100 q^{64} + 171 q^{65} + 12 q^{66} - 6 q^{67} + 184 q^{68} + 64 q^{69} - 24 q^{70} + 47 q^{71} + 53 q^{72} + 76 q^{73} + 66 q^{74} + 40 q^{75} + 32 q^{76} + 73 q^{77} - 19 q^{78} + 8 q^{79} + 115 q^{80} + 250 q^{81} - 13 q^{82} + 116 q^{83} + 159 q^{84} + 31 q^{85} + 91 q^{86} + 25 q^{87} - 43 q^{88} + 361 q^{89} + 32 q^{90} + 7 q^{91} + 5 q^{92} + 18 q^{93} + 23 q^{94} + 42 q^{95} + 77 q^{96} + 79 q^{97} + 56 q^{98} + 74 q^{99}+O(q^{100}) \) 122 * q + 14 * q^2 + 10 * q^3 + 128 * q^4 + 33 * q^5 + 22 * q^6 + 6 * q^7 + 36 * q^8 + 162 * q^9 + 16 * q^10 + 43 * q^11 + 23 * q^12 + 25 * q^13 + 45 * q^14 + 12 * q^15 + 132 * q^16 + 103 * q^17 + 30 * q^18 + 37 * q^19 + 63 * q^20 + 81 * q^21 + 15 * q^23 + 60 * q^24 + 151 * q^25 + 59 * q^26 + 22 * q^27 - 3 * q^28 + 80 * q^29 - 9 * q^30 + 15 * q^31 + 66 * q^32 + 93 * q^33 + 30 * q^34 + 23 * q^35 + 162 * q^36 + 18 * q^37 + 41 * q^38 + 10 * q^39 + 29 * q^40 + 249 * q^41 - 8 * q^42 + 14 * q^43 + 100 * q^44 + 59 * q^45 + 11 * q^46 + 57 * q^47 + 33 * q^48 + 180 * q^49 + 63 * q^50 + 26 * q^51 + 31 * q^52 + 65 * q^53 + 65 * q^54 - 8 * q^55 + 120 * q^56 + 57 * q^57 - 31 * q^58 + 108 * q^59 - q^60 + 70 * q^61 + 25 * q^62 - 7 * q^63 + 100 * q^64 + 171 * q^65 + 12 * q^66 - 6 * q^67 + 184 * q^68 + 64 * q^69 - 24 * q^70 + 47 * q^71 + 53 * q^72 + 76 * q^73 + 66 * q^74 + 40 * q^75 + 32 * q^76 + 73 * q^77 - 19 * q^78 + 8 * q^79 + 115 * q^80 + 250 * q^81 - 13 * q^82 + 116 * q^83 + 159 * q^84 + 31 * q^85 + 91 * q^86 + 25 * q^87 - 43 * q^88 + 361 * q^89 + 32 * q^90 + 7 * q^91 + 5 * q^92 + 18 * q^93 + 23 * q^94 + 42 * q^95 + 77 * q^96 + 79 * q^97 + 56 * q^98 + 74 * 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 $

$2$	0.0716716	0.0506795	0.0253397	−	0.999679i	$-0.491933\pi$
$2$	0.0716716	0.0506795	0.0253397	+	0.999679i	$0.491933\pi$
$3$	2.79309	1.61259	0.806297	−	0.591511i	$-0.201468\pi$
$3$	2.79309	1.61259	0.806297	+	0.591511i	$0.201468\pi$
$4$	−1.99486	−0.997432
$5$	2.81758	1.26006	0.630029	−	0.776572i	$-0.283043\pi$
$5$	2.81758	1.26006	0.630029	+	0.776572i	$0.283043\pi$
$6$	0.200185	0.0817254
$7$	0.519275	0.196267	0.0981337	−	0.995173i	$-0.468713\pi$
$7$	0.519275	0.196267	0.0981337	+	0.995173i	$0.468713\pi$
$8$	−0.286318	−0.101229
$9$	4.80137	1.60046
$10$	0.201940	0.0638591
$11$	−3.70536	−1.11721	−0.558604	−	0.829434i	$-0.688663\pi$
$11$	−3.70536	−1.11721	−0.558604	+	0.829434i	$0.688663\pi$
$12$	−5.57184	−1.60845
$13$	5.65930	1.56961	0.784804	−	0.619744i	$-0.212763\pi$
$13$	5.65930	1.56961	0.784804	+	0.619744i	$0.212763\pi$
$14$	0.0372172	0.00994673
$15$	7.86975	2.03196
$16$	3.96921	0.992301
$17$	2.63035	0.637954	0.318977	−	0.947762i	$-0.396661\pi$
$17$	2.63035	0.637954	0.318977	+	0.947762i	$0.396661\pi$
$18$	0.344122	0.0811104
$19$	0.800678	0.183688	0.0918441	−	0.995773i	$-0.470724\pi$
$19$	0.800678	0.183688	0.0918441	+	0.995773i	$0.470724\pi$
$20$	−5.62068	−1.25682
$21$	1.45038	0.316500
$22$	−0.265569	−0.0566195
$23$	−5.44047	−1.13442	−0.567208	−	0.823575i	$-0.691976\pi$
$23$	−5.44047	−1.13442	−0.567208	+	0.823575i	$0.691976\pi$
$24$	−0.799714	−0.163241
$25$	2.93873	0.587747
$26$	0.405611	0.0795469
$27$	5.03141	0.968295
$28$	−1.03588	−0.195763
$29$	4.06812	0.755432	0.377716	−	0.925922i	$-0.376710\pi$
$29$	4.06812	0.755432	0.377716	+	0.925922i	$0.376710\pi$
$30$	0.564038	0.102979
$31$	5.06221	0.909200	0.454600	−	0.890696i	$-0.349782\pi$
$31$	5.06221	0.909200	0.454600	+	0.890696i	$0.349782\pi$
$32$	0.857116	0.151518
$33$	−10.3494	−1.80160
$34$	0.188521	0.0323312
$35$	1.46310	0.247308
$36$	−9.57808	−1.59635
$37$	5.72799	0.941676	0.470838	−	0.882220i	$-0.343952\pi$
$37$	5.72799	0.941676	0.470838	+	0.882220i	$0.343952\pi$
$38$	0.0573859	0.00930922
$39$	15.8070	2.53114
$40$	−0.806723	−0.127554
$41$	−3.33769	−0.521259	−0.260630	−	0.965439i	$-0.583930\pi$
$41$	−3.33769	−0.521259	−0.260630	+	0.965439i	$0.583930\pi$
$42$	0.103951	0.0160400
$43$	−12.3791	−1.88780	−0.943900	−	0.330231i	$-0.892873\pi$
$43$	−12.3791	−1.88780	−0.943900	+	0.330231i	$0.892873\pi$
$44$	7.39169	1.11434
$45$	13.5282	2.01667
$46$	−0.389927	−0.0574916
$47$	4.66533	0.680508	0.340254	−	0.940334i	$-0.389487\pi$
$47$	4.66533	0.680508	0.340254	+	0.940334i	$0.389487\pi$
$48$	11.0864	1.60018
$49$	−6.73035	−0.961479
$50$	0.210624	0.0297867
$51$	7.34682	1.02876
$52$	−11.2895	−1.56558
$53$	3.16546	0.434809	0.217404	−	0.976082i	$-0.430241\pi$
$53$	3.16546	0.434809	0.217404	+	0.976082i	$0.430241\pi$
$54$	0.360609	0.0490727
$55$	−10.4401	−1.40775
$56$	−0.148678	−0.0198679
$57$	2.23637	0.296214
$58$	0.291569	0.0382849
$59$	8.34292	1.08616	0.543078	−	0.839682i	$-0.317259\pi$
$59$	8.34292	1.08616	0.543078	+	0.839682i	$0.317259\pi$
$60$	−15.6991	−2.02674
$61$	−0.267265	−0.0342198	−0.0171099	−	0.999854i	$-0.505447\pi$
$61$	−0.267265	−0.0342198	−0.0171099	+	0.999854i	$0.505447\pi$
$62$	0.362817	0.0460778
$63$	2.49323	0.314118
$64$	−7.87698	−0.984623
$65$	15.9455	1.97780
$66$	−0.741759	−0.0913043
$67$	−8.12254	−0.992326	−0.496163	−	0.868229i	$-0.665258\pi$
$67$	−8.12254	−0.992326	−0.496163	+	0.868229i	$0.665258\pi$
$68$	−5.24719	−0.636315
$69$	−15.1957	−1.82935
$70$	0.104862	0.0125335
$71$	8.31807	0.987174	0.493587	−	0.869697i	$-0.335686\pi$
$71$	8.31807	0.987174	0.493587	+	0.869697i	$0.335686\pi$
$72$	−1.37472	−0.162012
$73$	5.43956	0.636652	0.318326	−	0.947981i	$-0.396879\pi$
$73$	5.43956	0.636652	0.318326	+	0.947981i	$0.396879\pi$
$74$	0.410534	0.0477236
$75$	8.20816	0.947797
$76$	−1.59724	−0.183216
$77$	−1.92410	−0.219272
$78$	1.13291	0.128277
$79$	11.8414	1.33227	0.666133	−	0.745833i	$-0.267948\pi$
$79$	11.8414	1.33227	0.666133	+	0.745833i	$0.267948\pi$
$80$	11.1835	1.25036
$81$	−0.350929	−0.0389921
$82$	−0.239217	−0.0264172
$83$	−8.79199	−0.965046	−0.482523	−	0.875883i	$-0.660279\pi$
$83$	−8.79199	−0.965046	−0.482523	+	0.875883i	$0.660279\pi$
$84$	−2.89332	−0.315687
$85$	7.41121	0.803859
$86$	−0.887232	−0.0956727
$87$	11.3627	1.21820
$88$	1.06091	0.113094
$89$	7.73620	0.820036	0.410018	−	0.912078i	$-0.365523\pi$
$89$	7.73620	0.820036	0.410018	+	0.912078i	$0.365523\pi$
$90$	0.969590	0.102204
$91$	2.93873	0.308063
$92$	10.8530	1.13150
$93$	14.1392	1.46617
$94$	0.334372	0.0344878
$95$	2.25597	0.231458
$96$	2.39400	0.244337
$97$	−6.57347	−0.667435	−0.333717	−	0.942673i	$-0.608303\pi$
$97$	−6.57347	−0.667435	−0.333717	+	0.942673i	$0.608303\pi$
$98$	−0.482375	−0.0487272
$99$	−17.7908	−1.78804
$100$	−5.86237	−0.586237
$101$	15.5920	1.55147	0.775733	−	0.631062i	$-0.217380\pi$
$101$	15.5920	1.55147	0.775733	+	0.631062i	$0.217380\pi$
$102$	0.526558	0.0521370
$103$	5.46017	0.538007	0.269003	−	0.963139i	$-0.413306\pi$
$103$	5.46017	0.538007	0.269003	+	0.963139i	$0.413306\pi$
$104$	−1.62036	−0.158890
$105$	4.08656	0.398808
$106$	0.226873	0.0220359
$107$	−8.85477	−0.856023	−0.428012	−	0.903773i	$-0.640786\pi$
$107$	−8.85477	−0.856023	−0.428012	+	0.903773i	$0.640786\pi$
$108$	−10.0370	−0.965808
$109$	−2.32146	−0.222356	−0.111178	−	0.993801i	$-0.535462\pi$
$109$	−2.32146	−0.222356	−0.111178	+	0.993801i	$0.535462\pi$
$110$	−0.748261	−0.0713439
$111$	15.9988	1.51854
$112$	2.06111	0.194756
$113$	−4.01639	−0.377830	−0.188915	−	0.981993i	$-0.560497\pi$
$113$	−4.01639	−0.377830	−0.188915	+	0.981993i	$0.560497\pi$
$114$	0.160284	0.0150120
$115$	−15.3289	−1.42943
$116$	−8.11535	−0.753491
$117$	27.1724	2.51209
$118$	0.597950	0.0550458
$119$	1.36587	0.125210
$120$	−2.25325	−0.205693
$121$	2.72969	0.248154
$122$	−0.0191553	−0.00173424
$123$	−9.32248	−0.840580
$124$	−10.0984	−0.906865
$125$	−5.80777	−0.519463
$126$	0.178694	0.0159193
$127$	−16.6794	−1.48006	−0.740028	−	0.672576i	$-0.765188\pi$
$127$	−16.6794	−1.48006	−0.740028	+	0.672576i	$0.765188\pi$
$128$	−2.27879	−0.201418
$129$	−34.5761	−3.04426
$130$	1.14284	0.100234
$131$	10.5483	0.921607	0.460804	−	0.887502i	$-0.347561\pi$
$131$	10.5483	0.921607	0.460804	+	0.887502i	$0.347561\pi$
$132$	20.6457	1.79698
$133$	0.415772	0.0360520
$134$	−0.582155	−0.0502905
$135$	14.1764	1.22011
$136$	−0.753117	−0.0645793
$137$	−8.21313	−0.701695	−0.350847	−	0.936433i	$-0.614106\pi$
$137$	−8.21313	−0.701695	−0.350847	+	0.936433i	$0.614106\pi$
$138$	−1.08910	−0.0927106
$139$	1.95916	0.166174	0.0830870	−	0.996542i	$-0.473522\pi$
$139$	1.95916	0.166174	0.0830870	+	0.996542i	$0.473522\pi$
$140$	−2.91868	−0.246673
$141$	13.0307	1.09738
$142$	0.596170	0.0500294
$143$	−20.9698	−1.75358
$144$	19.0576	1.58814
$145$	11.4622	0.951888
$146$	0.389862	0.0322652
$147$	−18.7985	−1.55048
$148$	−11.4266	−0.939257
$149$	5.85060	0.479300	0.239650	−	0.970859i	$-0.422967\pi$
$149$	5.85060	0.479300	0.239650	+	0.970859i	$0.422967\pi$
$150$	0.588292	0.0480338
$151$	0.261759	0.0213016	0.0106508	−	0.999943i	$-0.496610\pi$
$151$	0.261759	0.0213016	0.0106508	+	0.999943i	$0.496610\pi$
$152$	−0.229249	−0.0185945
$153$	12.6293	1.02102
$154$	−0.137903	−0.0111126
$155$	14.2632	1.14565
$156$	−31.5327	−2.52464
$157$	5.38912	0.430099	0.215049	−	0.976603i	$-0.431009\pi$
$157$	5.38912	0.430099	0.215049	+	0.976603i	$0.431009\pi$
$158$	0.848695	0.0675186
$159$	8.84142	0.701170
$160$	2.41499	0.190922
$161$	−2.82510	−0.222649
$162$	−0.0251516	−0.00197610
$163$	−11.6850	−0.915240	−0.457620	−	0.889148i	$-0.651298\pi$
$163$	−11.6850	−0.915240	−0.457620	+	0.889148i	$0.651298\pi$
$164$	6.65823	0.519921
$165$	−29.1603	−2.27012
$166$	−0.630136	−0.0489080
$167$	3.99915	0.309464	0.154732	−	0.987957i	$-0.450549\pi$
$167$	3.99915	0.309464	0.154732	+	0.987957i	$0.450549\pi$
$168$	−0.415271	−0.0320389
$169$	19.0277	1.46367
$170$	0.531173	0.0407391
$171$	3.84436	0.293985
$172$	24.6947	1.88295
$173$	1.68692	0.128254	0.0641271	−	0.997942i	$-0.479574\pi$
$173$	1.68692	0.128254	0.0641271	+	0.997942i	$0.479574\pi$
$174$	0.814379	0.0617379
$175$	1.52601	0.115356
$176$	−14.7073	−1.10861
$177$	23.3026	1.75153
$178$	0.554466	0.0415590
$179$	−26.1739	−1.95633	−0.978165	−	0.207832i	$-0.933359\pi$
$179$	−26.1739	−1.95633	−0.978165	+	0.207832i	$0.933359\pi$
$180$	−26.9870	−2.01149
$181$	5.92571	0.440454	0.220227	−	0.975449i	$-0.429320\pi$
$181$	5.92571	0.440454	0.220227	+	0.975449i	$0.429320\pi$
$182$	0.210624	0.0156125
$183$	−0.746496	−0.0551826
$184$	1.55770	0.114836
$185$	16.1390	1.18657
$186$	1.01338	0.0743047
$187$	−9.74640	−0.712727
$188$	−9.30669	−0.678760
$189$	2.61268	0.190045
$190$	0.161689	0.0117302
$191$	6.85743	0.496186	0.248093	−	0.968736i	$-0.420196\pi$
$191$	6.85743	0.496186	0.248093	+	0.968736i	$0.420196\pi$
$192$	−22.0011	−1.58780
$193$	−13.5459	−0.975057	−0.487529	−	0.873107i	$-0.662102\pi$
$193$	−13.5459	−0.975057	−0.487529	+	0.873107i	$0.662102\pi$
$194$	−0.471131	−0.0338252
$195$	44.5373	3.18938
$196$	13.4261	0.959010
$197$	−10.9642	−0.781169	−0.390585	−	0.920567i	$-0.627727\pi$
$197$	−10.9642	−0.781169	−0.390585	+	0.920567i	$0.627727\pi$
$198$	−1.27510	−0.0906172
$199$	12.6538	0.897004	0.448502	−	0.893782i	$-0.351958\pi$
$199$	12.6538	0.897004	0.448502	+	0.893782i	$0.351958\pi$
$200$	−0.841413	−0.0594969
$201$	−22.6870	−1.60022
$202$	1.11751	0.0786274
$203$	2.11247	0.148267
$204$	−14.6559	−1.02612
$205$	−9.40419	−0.656817
$206$	0.391339	0.0272659
$207$	−26.1217	−1.81559
$208$	22.4629	1.55752
$209$	−2.96680	−0.205218
$210$	0.292891	0.0202114
$211$	7.08084	0.487465	0.243733	−	0.969842i	$-0.421628\pi$
$211$	7.08084	0.487465	0.243733	+	0.969842i	$0.421628\pi$
$212$	−6.31465	−0.433692
$213$	23.2332	1.59191
$214$	−0.634636	−0.0433828
$215$	−34.8792	−2.37874
$216$	−1.44058	−0.0980193
$217$	2.62868	0.178446
$218$	−0.166383	−0.0112689
$219$	15.1932	1.02666
$220$	20.8266	1.40413
$221$	14.8860	1.00134
$222$	1.14666	0.0769588
$223$	−19.7828	−1.32475	−0.662377	−	0.749170i	$-0.730452\pi$
$223$	−19.7828	−1.32475	−0.662377	+	0.749170i	$0.730452\pi$
$224$	0.445079	0.0297381
$225$	14.1100	0.940664
$226$	−0.287861	−0.0191482
$227$	−14.1558	−0.939554	−0.469777	−	0.882785i	$-0.655666\pi$
$227$	−14.1558	−0.939554	−0.469777	+	0.882785i	$0.655666\pi$
$228$	−4.46125	−0.295454
$229$	−12.3518	−0.816232	−0.408116	−	0.912930i	$-0.633814\pi$
$229$	−12.3518	−0.816232	−0.408116	+	0.912930i	$0.633814\pi$
$230$	−1.09865	−0.0724428
$231$	−5.37419	−0.353596
$232$	−1.16478	−0.0764714
$233$	5.58100	0.365624	0.182812	−	0.983148i	$-0.441480\pi$
$233$	5.58100	0.365624	0.182812	+	0.983148i	$0.441480\pi$
$234$	1.94749	0.127312
$235$	13.1449	0.857480
$236$	−16.6430	−1.08337
$237$	33.0743	2.14840
$238$	0.0978944	0.00634555
$239$	−6.83699	−0.442248	−0.221124	−	0.975246i	$-0.570973\pi$
$239$	−6.83699	−0.442248	−0.221124	+	0.975246i	$0.570973\pi$
$240$	31.2367	2.01632
$241$	18.8253	1.21264	0.606321	−	0.795220i	$-0.292645\pi$
$241$	18.8253	1.21264	0.606321	+	0.795220i	$0.292645\pi$
$242$	0.195641	0.0125763
$243$	−16.0744	−1.03117
$244$	0.533157	0.0341319
$245$	−18.9633	−1.21152
$246$	−0.668157	−0.0426001
$247$	4.53128	0.288319
$248$	−1.44940	−0.0920372
$249$	−24.5568	−1.55623
$250$	−0.416252	−0.0263261
$251$	−12.4435	−0.785430	−0.392715	−	0.919660i	$-0.628464\pi$
$251$	−12.4435	−0.785430	−0.392715	+	0.919660i	$0.628464\pi$
$252$	−4.97366	−0.313311
$253$	20.1589	1.26738
$254$	−1.19544	−0.0750084
$255$	20.7002	1.29630
$256$	15.5906	0.974415
$257$	13.2664	0.827534	0.413767	−	0.910383i	$-0.364213\pi$
$257$	13.2664	0.827534	0.413767	+	0.910383i	$0.364213\pi$
$258$	−2.47812	−0.154281
$259$	2.97440	0.184820
$260$	−31.8091	−1.97272
$261$	19.5326	1.20904
$262$	0.756012	0.0467066
$263$	−7.32031	−0.451390	−0.225695	−	0.974198i	$-0.572465\pi$
$263$	−7.32031	−0.451390	−0.225695	+	0.974198i	$0.572465\pi$
$264$	2.96323	0.182374
$265$	8.91891	0.547885
$266$	0.0297990	0.00182710
$267$	21.6079	1.32238
$268$	16.2034	0.989777
$269$	7.65138	0.466513	0.233256	−	0.972415i	$-0.425062\pi$
$269$	7.65138	0.466513	0.233256	+	0.972415i	$0.425062\pi$
$270$	1.01604	0.0618344
$271$	−8.72422	−0.529959	−0.264979	−	0.964254i	$-0.585365\pi$
$271$	−8.72422	−0.529959	−0.264979	+	0.964254i	$0.585365\pi$
$272$	10.4404	0.633042
$273$	8.20816	0.496781
$274$	−0.588648	−0.0355615
$275$	−10.8891	−0.656635
$276$	30.3134	1.82465
$277$	−19.4444	−1.16830	−0.584149	−	0.811646i	$-0.698572\pi$
$277$	−19.4444	−1.16830	−0.584149	+	0.811646i	$0.698572\pi$
$278$	0.140416	0.00842161
$279$	24.3056	1.45514
$280$	−0.418911	−0.0250347
$281$	2.64456	0.157761	0.0788806	−	0.996884i	$-0.474865\pi$
$281$	2.64456	0.157761	0.0788806	+	0.996884i	$0.474865\pi$
$282$	0.933931	0.0556148
$283$	−7.79444	−0.463332	−0.231666	−	0.972795i	$-0.574418\pi$
$283$	−7.79444	−0.463332	−0.231666	+	0.972795i	$0.574418\pi$
$284$	−16.5934	−0.984638
$285$	6.30114	0.373247
$286$	−1.50294	−0.0888705
$287$	−1.73318	−0.102306
$288$	4.11533	0.242498
$289$	−10.0813	−0.593015
$290$	0.821518	0.0482412
$291$	−18.3603	−1.07630
$292$	−10.8512	−0.635017
$293$	9.75014	0.569609	0.284805	−	0.958586i	$-0.408071\pi$
$293$	9.75014	0.569609	0.284805	+	0.958586i	$0.408071\pi$
$294$	−1.34732	−0.0785772
$295$	23.5068	1.36862
$296$	−1.64003	−0.0953247
$297$	−18.6432	−1.08179
$298$	0.419322	0.0242907
$299$	−30.7893	−1.78059
$300$	−16.3742	−0.945362
$301$	−6.42817	−0.370514
$302$	0.0187607	0.00107956
$303$	43.5500	2.50188
$304$	3.17806	0.182274
$305$	−0.753039	−0.0431189
$306$	0.905162	0.0517447
$307$	−8.34685	−0.476380	−0.238190	−	0.971219i	$-0.576554\pi$
$307$	−8.34685	−0.476380	−0.238190	+	0.971219i	$0.576554\pi$
$308$	3.83832	0.218708
$309$	15.2508	0.867586
$310$	1.02226	0.0580607
$311$	15.5148	0.879762	0.439881	−	0.898056i	$-0.355021\pi$
$311$	15.5148	0.879762	0.439881	+	0.898056i	$0.355021\pi$
$312$	−4.52582	−0.256224
$313$	25.2206	1.42555	0.712776	−	0.701391i	$-0.247437\pi$
$313$	25.2206	1.42555	0.712776	+	0.701391i	$0.247437\pi$
$314$	0.386247	0.0217972
$315$	7.02487	0.395807
$316$	−23.6221	−1.32884
$317$	−7.32914	−0.411645	−0.205823	−	0.978589i	$-0.565987\pi$
$317$	−7.32914	−0.411645	−0.205823	+	0.978589i	$0.565987\pi$
$318$	0.633678	0.0355349
$319$	−15.0739	−0.843974
$320$	−22.1940	−1.24068
$321$	−24.7322	−1.38042
$322$	−0.202479	−0.0112837
$323$	2.10606	0.117185
$324$	0.700055	0.0388920
$325$	16.6312	0.922532
$326$	−0.837483	−0.0463839
$327$	−6.48406	−0.358569
$328$	0.955641	0.0527665
$329$	2.42259	0.133562
$330$	−2.08996	−0.115049
$331$	4.63200	0.254598	0.127299	−	0.991864i	$-0.459369\pi$
$331$	4.63200	0.254598	0.127299	+	0.991864i	$0.459369\pi$
$332$	17.5388	0.962567
$333$	27.5022	1.50711
$334$	0.286626	0.0156835
$335$	−22.8859	−1.25039
$336$	5.75687	0.314063
$337$	−15.6246	−0.851126	−0.425563	−	0.904929i	$-0.639924\pi$
$337$	−15.6246	−0.851126	−0.425563	+	0.904929i	$0.639924\pi$
$338$	1.36375	0.0741781
$339$	−11.2182	−0.609287
$340$	−14.7844	−0.801794
$341$	−18.7573	−1.01577
$342$	0.275531	0.0148990
$343$	−7.12983	−0.384974
$344$	3.54437	0.191100
$345$	−42.8151	−2.30509
$346$	0.120904	0.00649985
$347$	3.90517	0.209641	0.104820	−	0.994491i	$-0.466573\pi$
$347$	3.90517	0.209641	0.104820	+	0.994491i	$0.466573\pi$
$348$	−22.6669	−1.21508
$349$	−1.02994	−0.0551312	−0.0275656	−	0.999620i	$-0.508776\pi$
$349$	−1.02994	−0.0551312	−0.0275656	+	0.999620i	$0.508776\pi$
$350$	0.109372	0.00584616
$351$	28.4743	1.51984
$352$	−3.17592	−0.169277
$353$	−19.6624	−1.04652	−0.523262	−	0.852172i	$-0.675285\pi$
$353$	−19.6624	−1.04652	−0.523262	+	0.852172i	$0.675285\pi$
$354$	1.67013	0.0887665
$355$	23.4368	1.24390
$356$	−15.4327	−0.817929
$357$	3.81502	0.201912
$358$	−1.87592	−0.0991457
$359$	−36.2509	−1.91325	−0.956625	−	0.291324i	$-0.905904\pi$
$359$	−36.2509	−1.91325	−0.956625	+	0.291324i	$0.905904\pi$
$360$	−3.87338	−0.204145
$361$	−18.3589	−0.966259
$362$	0.424705	0.0223220
$363$	7.62429	0.400171
$364$	−5.86237	−0.307272
$365$	15.3264	0.802219
$366$	−0.0535026	−0.00279662
$367$	−30.7002	−1.60254	−0.801268	−	0.598305i	$-0.795841\pi$
$367$	−30.7002	−1.60254	−0.801268	+	0.598305i	$0.795841\pi$
$368$	−21.5943	−1.12568
$369$	−16.0255	−0.834254
$370$	1.15671	0.0601345
$371$	1.64374	0.0853388
$372$	−28.2058	−1.46240
$373$	9.15627	0.474093	0.237047	−	0.971498i	$-0.423821\pi$
$373$	9.15627	0.474093	0.237047	+	0.971498i	$0.423821\pi$
$374$	−0.698540	−0.0361206
$375$	−16.2217	−0.837683
$376$	−1.33577	−0.0688870
$377$	23.0228	1.18573
$378$	0.187255	0.00963137
$379$	−10.2851	−0.528308	−0.264154	−	0.964481i	$-0.585093\pi$
$379$	−10.2851	−0.528308	−0.264154	+	0.964481i	$0.585093\pi$
$380$	−4.50036	−0.230863
$381$	−46.5871	−2.38673
$382$	0.491483	0.0251464
$383$	6.80400	0.347668	0.173834	−	0.984775i	$-0.444384\pi$
$383$	6.80400	0.347668	0.173834	+	0.984775i	$0.444384\pi$
$384$	−6.36487	−0.324806
$385$	−5.42130	−0.276295
$386$	−0.970858	−0.0494154
$387$	−59.4369	−3.02135
$388$	13.1132	0.665721
$389$	9.09929	0.461352	0.230676	−	0.973031i	$-0.425906\pi$
$389$	9.09929	0.461352	0.230676	+	0.973031i	$0.425906\pi$
$390$	3.19206	0.161636
$391$	−14.3103	−0.723705
$392$	1.92702	0.0973293
$393$	29.4623	1.48618
$394$	−0.785824	−0.0395892
$395$	33.3642	1.67873
$396$	35.4903	1.78345
$397$	−33.0986	−1.66117	−0.830586	−	0.556891i	$-0.811994\pi$
$397$	−33.0986	−1.66117	−0.830586	+	0.556891i	$0.811994\pi$
$398$	0.906918	0.0454597
$399$	1.16129	0.0581372
$400$	11.6644	0.583222
$401$	9.38404	0.468616	0.234308	−	0.972162i	$-0.424718\pi$
$401$	9.38404	0.468616	0.234308	+	0.972162i	$0.424718\pi$
$402$	−1.62601	−0.0810982
$403$	28.6486	1.42709
$404$	−31.1040	−1.54748
$405$	−0.988769	−0.0491323
$406$	0.151404	0.00751407
$407$	−21.2243	−1.05205
$408$	−2.10353	−0.104140
$409$	−5.04819	−0.249617	−0.124808	−	0.992181i	$-0.539832\pi$
$409$	−5.04819	−0.249617	−0.124808	+	0.992181i	$0.539832\pi$
$410$	−0.674013	−0.0332871
$411$	−22.9400	−1.13155
$412$	−10.8923	−0.536625
$413$	4.33227	0.213177
$414$	−1.87219	−0.0920129
$415$	−24.7721	−1.21601
$416$	4.85068	0.237824
$417$	5.47213	0.267971
$418$	−0.212635	−0.0104003
$419$	33.9579	1.65895	0.829476	−	0.558542i	$-0.188639\pi$
$419$	33.9579	1.65895	0.829476	+	0.558542i	$0.188639\pi$
$420$	−8.15214	−0.397784
$421$	0.189023	0.00921241	0.00460621	−	0.999989i	$-0.498534\pi$
$421$	0.189023	0.00921241	0.00460621	+	0.999989i	$0.498534\pi$
$422$	0.507495	0.0247045
$423$	22.4000	1.08912
$424$	−0.906328	−0.0440152
$425$	7.72990	0.374955
$426$	1.66516	0.0806771
$427$	−0.138784	−0.00671623
$428$	17.6641	0.853825
$429$	−58.5705	−2.82781
$430$	−2.49984	−0.120553
$431$	23.2539	1.12010	0.560049	−	0.828459i	$-0.310782\pi$
$431$	23.2539	1.12010	0.560049	+	0.828459i	$0.310782\pi$
$432$	19.9707	0.960840
$433$	37.7471	1.81401	0.907005	−	0.421120i	$-0.138363\pi$
$433$	37.7471	1.81401	0.907005	+	0.421120i	$0.138363\pi$
$434$	0.188402	0.00904357
$435$	32.0151	1.53501
$436$	4.63099	0.221784
$437$	−4.35606	−0.208379
$438$	1.08892	0.0520307
$439$	20.3729	0.972346	0.486173	−	0.873863i	$-0.338392\pi$
$439$	20.3729	0.972346	0.486173	+	0.873863i	$0.338392\pi$
$440$	2.98920	0.142505
$441$	−32.3149	−1.53881
$442$	1.06690	0.0507473
$443$	20.8107	0.988748	0.494374	−	0.869249i	$-0.335397\pi$
$443$	20.8107	0.988748	0.494374	+	0.869249i	$0.335397\pi$
$444$	−31.9154	−1.51464
$445$	21.7973	1.03329
$446$	−1.41787	−0.0671379
$447$	16.3413	0.772916
$448$	−4.09032	−0.193249
$449$	6.25892	0.295377	0.147688	−	0.989034i	$-0.452817\pi$
$449$	6.25892	0.295377	0.147688	+	0.989034i	$0.452817\pi$
$450$	1.01128	0.0476723
$451$	12.3673	0.582355
$452$	8.01215	0.376860
$453$	0.731117	0.0343509
$454$	−1.01457	−0.0476161
$455$	8.28011	0.388177
$456$	−0.640313	−0.0299854
$457$	−26.0681	−1.21942	−0.609708	−	0.792626i	$-0.708713\pi$
$457$	−26.0681	−1.21942	−0.609708	+	0.792626i	$0.708713\pi$
$458$	−0.885276	−0.0413662
$459$	13.2344	0.617727
$460$	30.5791	1.42576
$461$	16.0509	0.747563	0.373782	−	0.927517i	$-0.378061\pi$
$461$	16.0509	0.747563	0.373782	+	0.927517i	$0.378061\pi$
$462$	−0.385177	−0.0179201
$463$	−23.2062	−1.07848	−0.539242	−	0.842151i	$-0.681289\pi$
$463$	−23.2062	−1.07848	−0.539242	+	0.842151i	$0.681289\pi$
$464$	16.1472	0.749616
$465$	39.8384	1.84746
$466$	0.399999	0.0185296
$467$	−33.4722	−1.54891	−0.774455	−	0.632629i	$-0.781976\pi$
$467$	−33.4722	−1.54891	−0.774455	+	0.632629i	$0.781976\pi$
$468$	−54.2053	−2.50564
$469$	−4.21783	−0.194761
$470$	0.942117	0.0434566
$471$	15.0523	0.693574
$472$	−2.38873	−0.109950
$473$	45.8692	2.10907
$474$	2.37049	0.108880
$475$	2.35298	0.107962
$476$	−2.72473	−0.124888
$477$	15.1985	0.695893
$478$	−0.490018	−0.0224129
$479$	1.98479	0.0906874	0.0453437	−	0.998971i	$-0.485562\pi$
$479$	1.98479	0.0906874	0.0453437	+	0.998971i	$0.485562\pi$
$480$	6.74529	0.307879
$481$	32.4164	1.47806
$482$	1.34924	0.0614561
$483$	−7.89076	−0.359042
$484$	−5.44536	−0.247517
$485$	−18.5213	−0.841007
$486$	−1.15208	−0.0522593
$487$	−13.1010	−0.593665	−0.296833	−	0.954930i	$-0.595930\pi$
$487$	−13.1010	−0.593665	−0.296833	+	0.954930i	$0.595930\pi$
$488$	0.0765228	0.00346403
$489$	−32.6373	−1.47591
$490$	−1.35913	−0.0613992
$491$	0.429622	0.0193886	0.00969428	−	0.999953i	$-0.496914\pi$
$491$	0.429622	0.0193886	0.00969428	+	0.999953i	$0.496914\pi$
$492$	18.5971	0.838421
$493$	10.7006	0.481931
$494$	0.324764	0.0146118
$495$	−50.1270	−2.25304
$496$	20.0930	0.902201
$497$	4.31937	0.193750
$498$	−1.76003	−0.0788687
$499$	−42.7660	−1.91447	−0.957234	−	0.289316i	$-0.906572\pi$
$499$	−42.7660	−1.91447	−0.957234	+	0.289316i	$0.906572\pi$
$500$	11.5857	0.518129
$501$	11.1700	0.499039
$502$	−0.891849	−0.0398052
$503$	31.6415	1.41082	0.705412	−	0.708798i	$-0.250762\pi$
$503$	31.6415	1.41082	0.705412	+	0.708798i	$0.250762\pi$
$504$	−0.713858	−0.0317978
$505$	43.9317	1.95494
$506$	1.44482	0.0642301
$507$	53.1462	2.36031
$508$	33.2731	1.47625
$509$	6.15969	0.273023	0.136512	−	0.990638i	$-0.456411\pi$
$509$	6.15969	0.273023	0.136512	+	0.990638i	$0.456411\pi$
$510$	1.48362	0.0656957
$511$	2.82463	0.124954
$512$	5.67498	0.250801
$513$	4.02854	0.177864
$514$	0.950822	0.0419390
$515$	15.3844	0.677920
$516$	68.9746	3.03644
$517$	−17.2867	−0.760269
$518$	0.213180	0.00936659
$519$	4.71173	0.206822
$520$	−4.56549	−0.200210
$521$	24.0824	1.05507	0.527535	−	0.849533i	$-0.323116\pi$
$521$	24.0824	1.05507	0.527535	+	0.849533i	$0.323116\pi$
$522$	1.39993	0.0612733
$523$	−8.14337	−0.356085	−0.178042	−	0.984023i	$-0.556976\pi$
$523$	−8.14337	−0.356085	−0.178042	+	0.984023i	$0.556976\pi$
$524$	−21.0424	−0.919240
$525$	4.26229	0.186022
$526$	−0.524659	−0.0228762
$527$	13.3154	0.580028
$528$	−41.0790	−1.78773
$529$	6.59869	0.286900
$530$	0.639233	0.0277665
$531$	40.0575	1.73835
$532$	−0.829408	−0.0359594
$533$	−18.8890	−0.818173
$534$	1.54867	0.0670177
$535$	−24.9490	−1.07864
$536$	2.32563	0.100452
$537$	−73.1062	−3.15476
$538$	0.548386	0.0236426
$539$	24.9384	1.07417
$540$	−28.2799	−1.21697
$541$	−13.9379	−0.599235	−0.299618	−	0.954059i	$-0.596859\pi$
$541$	−13.9379	−0.599235	−0.299618	+	0.954059i	$0.596859\pi$
$542$	−0.625279	−0.0268580
$543$	16.5511	0.710274
$544$	2.25451	0.0966615
$545$	−6.54089	−0.280181
$546$	0.588292	0.0251766
$547$	38.5319	1.64750	0.823752	−	0.566950i	$-0.191877\pi$
$547$	38.5319	1.64750	0.823752	+	0.566950i	$0.191877\pi$
$548$	16.3841	0.699893
$549$	−1.28324	−0.0547673
$550$	−0.780437	−0.0332779
$551$	3.25726	0.138764
$552$	4.35082	0.185183
$553$	6.14896	0.261481
$554$	−1.39361	−0.0592088
$555$	45.0779	1.91345
$556$	−3.90826	−0.165747
$557$	35.2921	1.49538	0.747688	−	0.664050i	$-0.231164\pi$
$557$	35.2921	1.49538	0.747688	+	0.664050i	$0.231164\pi$
$558$	1.74202	0.0737456
$559$	−70.0573	−2.96311
$560$	5.80733	0.245404
$561$	−27.2226	−1.14934
$562$	0.189540	0.00799525
$563$	−44.5330	−1.87684	−0.938422	−	0.345492i	$-0.887712\pi$
$563$	−44.5330	−1.87684	−0.938422	+	0.345492i	$0.887712\pi$
$564$	−25.9945	−1.09456
$565$	−11.3165	−0.476088
$566$	−0.558640	−0.0234814
$567$	−0.182229	−0.00765288
$568$	−2.38162	−0.0999304
$569$	−46.5177	−1.95012	−0.975061	−	0.221937i	$-0.928762\pi$
$569$	−46.5177	−1.95012	−0.975061	+	0.221937i	$0.928762\pi$
$570$	0.451613	0.0189160
$571$	28.1128	1.17648	0.588242	−	0.808685i	$-0.299820\pi$
$571$	28.1128	1.17648	0.588242	+	0.808685i	$0.299820\pi$
$572$	41.8318	1.74908
$573$	19.1534	0.800146
$574$	−0.124220	−0.00518483
$575$	−15.9881	−0.666749
$576$	−37.8203	−1.57585
$577$	−38.8640	−1.61793	−0.808964	−	0.587858i	$-0.799971\pi$
$577$	−38.8640	−1.61793	−0.808964	+	0.587858i	$0.799971\pi$
$578$	−0.722540	−0.0300537
$579$	−37.8351	−1.57237
$580$	−22.8656	−0.949443
$581$	−4.56546	−0.189407
$582$	−1.31591	−0.0545464
$583$	−11.7292	−0.485772
$584$	−1.55745	−0.0644475
$585$	76.5604	3.16538
$586$	0.698808	0.0288675
$587$	−31.6699	−1.30716	−0.653578	−	0.756859i	$-0.726733\pi$
$587$	−31.6699	−1.30716	−0.653578	+	0.756859i	$0.726733\pi$
$588$	37.5005	1.54649
$589$	4.05320	0.167009
$590$	1.68477	0.0693609
$591$	−30.6241	−1.25971
$592$	22.7356	0.934426
$593$	−12.5572	−0.515663	−0.257832	−	0.966190i	$-0.583008\pi$
$593$	−12.5572	−0.515663	−0.257832	+	0.966190i	$0.583008\pi$
$594$	−1.33619	−0.0548244
$595$	3.84846	0.157771
$596$	−11.6712	−0.478069
$597$	35.3432	1.44650
$598$	−2.20672	−0.0902393
$599$	−41.1485	−1.68128	−0.840641	−	0.541592i	$-0.817822\pi$
$599$	−41.1485	−1.68128	−0.840641	+	0.541592i	$0.817822\pi$
$600$	−2.35015	−0.0959443
$601$	15.2495	0.622038	0.311019	−	0.950404i	$-0.399330\pi$
$601$	15.2495	0.622038	0.311019	+	0.950404i	$0.399330\pi$
$602$	−0.460717	−0.0187774
$603$	−38.9993	−1.58818
$604$	−0.522173	−0.0212469
$605$	7.69112	0.312688
$606$	3.12130	0.126794
$607$	10.3308	0.419314	0.209657	−	0.977775i	$-0.432765\pi$
$607$	10.3308	0.419314	0.209657	+	0.977775i	$0.432765\pi$
$608$	0.686274	0.0278321
$609$	5.90034	0.239094
$610$	−0.0539715	−0.00218524
$611$	26.4025	1.06813
$612$	−25.1937	−1.01840
$613$	25.8809	1.04532	0.522659	−	0.852542i	$-0.324940\pi$
$613$	25.8809	1.04532	0.522659	+	0.852542i	$0.324940\pi$
$614$	−0.598232	−0.0241427
$615$	−26.2668	−1.05918
$616$	0.550905	0.0221966
$617$	−46.7870	−1.88358	−0.941788	−	0.336208i	$-0.890856\pi$
$617$	−46.7870	−1.88358	−0.941788	+	0.336208i	$0.890856\pi$
$618$	1.09305	0.0439688
$619$	37.1460	1.49302	0.746511	−	0.665373i	$-0.231727\pi$
$619$	37.1460	1.49302	0.746511	+	0.665373i	$0.231727\pi$
$620$	−28.4531	−1.14270
$621$	−27.3732	−1.09845
$622$	1.11197	0.0445859
$623$	4.01721	0.160946
$624$	62.7411	2.51165
$625$	−31.0575	−1.24230
$626$	1.80760	0.0722463
$627$	−8.28656	−0.330933
$628$	−10.7506	−0.428994
$629$	15.0666	0.600746
$630$	0.503484	0.0200593
$631$	−1.19389	−0.0475280	−0.0237640	−	0.999718i	$-0.507565\pi$
$631$	−1.19389	−0.0475280	−0.0237640	+	0.999718i	$0.507565\pi$
$632$	−3.39042	−0.134864
$633$	19.7775	0.786083
$634$	−0.525291	−0.0208620
$635$	−46.9954	−1.86496
$636$	−17.6374	−0.699369
$637$	−38.0891	−1.50915
$638$	−1.08037	−0.0427722
$639$	39.9382	1.57993
$640$	−6.42066	−0.253799
$641$	−9.54804	−0.377125	−0.188562	−	0.982061i	$-0.560383\pi$
$641$	−9.54804	−0.377125	−0.188562	+	0.982061i	$0.560383\pi$
$642$	−1.77260	−0.0699588
$643$	14.1353	0.557443	0.278722	−	0.960372i	$-0.410089\pi$
$643$	14.1353	0.557443	0.278722	+	0.960372i	$0.410089\pi$
$644$	5.63568	0.222077
$645$	−97.4208	−3.83594
$646$	0.150945	0.00593885
$647$	47.1123	1.85218	0.926089	−	0.377306i	$-0.123150\pi$
$647$	47.1123	1.85218	0.926089	+	0.377306i	$0.123150\pi$
$648$	0.100477	0.00394712
$649$	−30.9135	−1.21346
$650$	1.19198	0.0467534
$651$	7.34215	0.287761
$652$	23.3100	0.912889
$653$	−18.4801	−0.723182	−0.361591	−	0.932337i	$-0.617766\pi$
$653$	−18.4801	−0.723182	−0.361591	+	0.932337i	$0.617766\pi$
$654$	−0.464723	−0.0181721
$655$	29.7206	1.16128
$656$	−13.2480	−0.517246
$657$	26.1174	1.01894
$658$	0.173631	0.00676883
$659$	−45.7369	−1.78166	−0.890828	−	0.454341i	$-0.849875\pi$
$659$	−45.7369	−1.78166	−0.890828	+	0.454341i	$0.849875\pi$
$660$	58.1708	2.26429
$661$	25.5958	0.995563	0.497781	−	0.867303i	$-0.334148\pi$
$661$	25.5958	0.995563	0.497781	+	0.867303i	$0.334148\pi$
$662$	0.331983	0.0129029
$663$	41.5779	1.61475
$664$	2.51731	0.0976904
$665$	1.17147	0.0454276
$666$	1.97113	0.0763796
$667$	−22.1325	−0.856974
$668$	−7.97776	−0.308669
$669$	−55.2552	−2.13629
$670$	−1.64027	−0.0633690
$671$	0.990313	0.0382306
$672$	1.24315	0.0479554
$673$	−22.2301	−0.856909	−0.428454	−	0.903563i	$-0.640942\pi$
$673$	−22.2301	−0.856909	−0.428454	+	0.903563i	$0.640942\pi$
$674$	−1.11984	−0.0431346
$675$	14.7860	0.569112
$676$	−37.9577	−1.45991
$677$	−14.3478	−0.551430	−0.275715	−	0.961239i	$-0.588915\pi$
$677$	−14.3478	−0.551430	−0.275715	+	0.961239i	$0.588915\pi$
$678$	−0.804023	−0.0308783
$679$	−3.41344	−0.130996
$680$	−2.12196	−0.0813736
$681$	−39.5385	−1.51512
$682$	−1.34437	−0.0514785
$683$	−18.8301	−0.720514	−0.360257	−	0.932853i	$-0.617311\pi$
$683$	−18.8301	−0.720514	−0.360257	+	0.932853i	$0.617311\pi$
$684$	−7.66897	−0.293230
$685$	−23.1411	−0.884176
$686$	−0.511006	−0.0195103
$687$	−34.4998	−1.31625
$688$	−49.1353	−1.87327
$689$	17.9143	0.682480
$690$	−3.06863	−0.116821
$691$	−43.7482	−1.66426	−0.832130	−	0.554581i	$-0.812879\pi$
$691$	−43.7482	−1.66426	−0.832130	+	0.554581i	$0.812879\pi$
$692$	−3.36518	−0.127925
$693$	−9.23832	−0.350935
$694$	0.279890	0.0106245
$695$	5.52009	0.209389
$696$	−3.25333	−0.123317
$697$	−8.77929	−0.332539
$698$	−0.0738172	−0.00279402
$699$	15.5883	0.589602
$700$	−3.04418	−0.115059
$701$	−10.6458	−0.402087	−0.201044	−	0.979582i	$-0.564433\pi$
$701$	−10.6458	−0.402087	−0.201044	+	0.979582i	$0.564433\pi$
$702$	2.04080	0.0770249
$703$	4.58628	0.172975
$704$	29.1870	1.10003
$705$	36.7150	1.38277
$706$	−1.40923	−0.0530372
$707$	8.09655	0.304502
$708$	−46.4854	−1.74703
$709$	−12.0326	−0.451894	−0.225947	−	0.974140i	$-0.572548\pi$
$709$	−12.0326	−0.451894	−0.225947	+	0.974140i	$0.572548\pi$
$710$	1.67975	0.0630400
$711$	56.8552	2.13224
$712$	−2.21501	−0.0830112
$713$	−27.5408	−1.03141
$714$	0.273428	0.0102328
$715$	−59.0839	−2.20961
$716$	52.2133	1.95130
$717$	−19.0964	−0.713167
$718$	−2.59816	−0.0969624
$719$	40.1625	1.49781	0.748905	−	0.662677i	$-0.230580\pi$
$719$	40.1625	1.49781	0.748905	+	0.662677i	$0.230580\pi$
$720$	53.6963	2.00114
$721$	2.83533	0.105593
$722$	−1.31581	−0.0489695
$723$	52.5808	1.95550
$724$	−11.8210	−0.439323
$725$	11.9551	0.444003
$726$	0.546445	0.0202805
$727$	−50.8367	−1.88543	−0.942714	−	0.333602i	$-0.891736\pi$
$727$	−50.8367	−1.88543	−0.942714	+	0.333602i	$0.891736\pi$
$728$	−0.841413	−0.0311848
$729$	−43.8445	−1.62387
$730$	1.09847	0.0406560
$731$	−32.5615	−1.20433
$732$	1.48916	0.0550409
$733$	34.7493	1.28350	0.641748	−	0.766916i	$-0.278210\pi$
$733$	34.7493	1.28350	0.641748	+	0.766916i	$0.278210\pi$
$734$	−2.20033	−0.0812157
$735$	−52.9662	−1.95369
$736$	−4.66311	−0.171885
$737$	30.0969	1.10863
$738$	−1.14857	−0.0422795
$739$	−19.3680	−0.712465	−0.356233	−	0.934397i	$-0.615939\pi$
$739$	−19.3680	−0.712465	−0.356233	+	0.934397i	$0.615939\pi$
$740$	−32.1952	−1.18352
$741$	12.6563	0.464941
$742$	0.117810	0.00432493
$743$	−14.1775	−0.520123	−0.260062	−	0.965592i	$-0.583743\pi$
$743$	−14.1775	−0.520123	−0.260062	+	0.965592i	$0.583743\pi$
$744$	−4.04832	−0.148419
$745$	16.4845	0.603946
$746$	0.656244	0.0240268
$747$	−42.2136	−1.54452
$748$	19.4427	0.710897
$749$	−4.59806	−0.168009
$750$	−1.16263	−0.0424533
$751$	47.5235	1.73416	0.867079	−	0.498170i	$-0.165994\pi$
$751$	47.5235	1.73416	0.867079	+	0.498170i	$0.165994\pi$
$752$	18.5176	0.675269
$753$	−34.7560	−1.26658
$754$	1.65008	0.0600923
$755$	0.737526	0.0268413
$756$	−5.21195	−0.189557
$757$	6.38477	0.232058	0.116029	−	0.993246i	$-0.462983\pi$
$757$	6.38477	0.232058	0.116029	+	0.993246i	$0.462983\pi$
$758$	−0.737147	−0.0267744
$759$	56.3057	2.04377
$760$	−0.645926	−0.0234302
$761$	−24.5431	−0.889687	−0.444843	−	0.895608i	$-0.646741\pi$
$761$	−24.5431	−0.889687	−0.444843	+	0.895608i	$0.646741\pi$
$762$	−3.33897	−0.120958
$763$	−1.20548	−0.0436411
$764$	−13.6796	−0.494911
$765$	35.5840	1.28654
$766$	0.487654	0.0176196
$767$	47.2151	1.70484
$768$	43.5461	1.57133
$769$	48.7072	1.75643	0.878213	−	0.478269i	$-0.158736\pi$
$769$	48.7072	1.75643	0.878213	+	0.478269i	$0.158736\pi$
$770$	−0.388553	−0.0140025
$771$	37.0542	1.33448
$772$	27.0223	0.972553
$773$	−18.3415	−0.659698	−0.329849	−	0.944034i	$-0.606998\pi$
$773$	−18.3415	−0.659698	−0.329849	+	0.944034i	$0.606998\pi$
$774$	−4.25993	−0.153120
$775$	14.8765	0.534379
$776$	1.88210	0.0675636
$777$	8.30778	0.298040
$778$	0.652160	0.0233811
$779$	−2.67242	−0.0957492
$780$	−88.8459	−3.18119
$781$	−30.8215	−1.10288
$782$	−1.02564	−0.0366770
$783$	20.4684	0.731481
$784$	−26.7142	−0.954077
$785$	15.1843	0.541949
$786$	2.11161	0.0753187
$787$	−2.65257	−0.0945541	−0.0472770	−	0.998882i	$-0.515054\pi$
$787$	−2.65257	−0.0945541	−0.0472770	+	0.998882i	$0.515054\pi$
$788$	21.8721	0.779163
$789$	−20.4463	−0.727909
$790$	2.39126	0.0850773
$791$	−2.08561	−0.0741558
$792$	5.09384	0.181002
$793$	−1.51253	−0.0537117
$794$	−2.37223	−0.0841873
$795$	24.9114	0.883515
$796$	−25.2426	−0.894700
$797$	12.6816	0.449205	0.224603	−	0.974450i	$-0.427892\pi$
$797$	12.6816	0.449205	0.224603	+	0.974450i	$0.427892\pi$
$798$	0.0832315	0.00294636
$799$	12.2715	0.434133
$800$	2.51883	0.0890542
$801$	37.1444	1.31243
$802$	0.672569	0.0237492
$803$	−20.1555	−0.711273
$804$	45.2575	1.59611
$805$	−7.95993	−0.280551
$806$	2.05329	0.0723241
$807$	21.3710	0.752295
$808$	−4.46428	−0.157053
$809$	−28.4227	−0.999290	−0.499645	−	0.866230i	$-0.666536\pi$
$809$	−28.4227	−0.999290	−0.499645	+	0.866230i	$0.666536\pi$
$810$	−0.0708666	−0.00249000
$811$	−39.2445	−1.37806	−0.689031	−	0.724732i	$-0.741963\pi$
$811$	−39.2445	−1.37806	−0.689031	+	0.724732i	$0.741963\pi$
$812$	−4.21410	−0.147886
$813$	−24.3676	−0.854608
$814$	−1.52118	−0.0533172
$815$	−32.9234	−1.15326
$816$	29.1610	1.02084
$817$	−9.91171	−0.346767
$818$	−0.361812	−0.0126504
$819$	14.1100	0.493042
$820$	18.7601	0.655130
$821$	−17.5299	−0.611799	−0.305899	−	0.952064i	$-0.598957\pi$
$821$	−17.5299	−0.611799	−0.305899	+	0.952064i	$0.598957\pi$
$822$	−1.64415	−0.0573463
$823$	−1.46962	−0.0512276	−0.0256138	−	0.999672i	$-0.508154\pi$
$823$	−1.46962	−0.0512276	−0.0256138	+	0.999672i	$0.508154\pi$
$824$	−1.56335	−0.0544618
$825$	−30.4142	−1.05889
$826$	0.310500	0.0108037
$827$	45.6957	1.58899	0.794497	−	0.607268i	$-0.207734\pi$
$827$	45.6957	1.58899	0.794497	+	0.607268i	$0.207734\pi$
$828$	52.1093	1.81092
$829$	−5.83152	−0.202537	−0.101268	−	0.994859i	$-0.532290\pi$
$829$	−5.83152	−0.202537	−0.101268	+	0.994859i	$0.532290\pi$
$830$	−1.77545	−0.0616269
$831$	−54.3100	−1.88399
$832$	−44.5782	−1.54547
$833$	−17.7032	−0.613379
$834$	0.392196	0.0135806
$835$	11.2679	0.389942
$836$	5.91836	0.204691
$837$	25.4701	0.880374
$838$	2.43382	0.0840748
$839$	43.9918	1.51877	0.759383	−	0.650644i	$-0.225501\pi$
$839$	43.9918	1.51877	0.759383	+	0.650644i	$0.225501\pi$
$840$	−1.17006	−0.0403708
$841$	−12.4504	−0.429323
$842$	0.0135476	0.000466880 0
$843$	7.38650	0.254405
$844$	−14.1253	−0.486213
$845$	53.6121	1.84431
$846$	1.60544	0.0551963
$847$	1.41746	0.0487045
$848$	12.5643	0.431461
$849$	−21.7706	−0.747166
$850$	0.554014	0.0190025
$851$	−31.1629	−1.06825
$852$	−46.3470	−1.58782
$853$	12.0655	0.413116	0.206558	−	0.978434i	$-0.433774\pi$
$853$	12.0655	0.413116	0.206558	+	0.978434i	$0.433774\pi$
$854$	−0.00994687	−0.000340375 0
$855$	10.8318	0.370439
$856$	2.53528	0.0866542
$857$	9.71810	0.331964	0.165982	−	0.986129i	$-0.446921\pi$
$857$	9.71810	0.331964	0.165982	+	0.986129i	$0.446921\pi$
$858$	−4.19784	−0.143312
$859$	−38.6123	−1.31743	−0.658717	−	0.752391i	$-0.728900\pi$
$859$	−38.6123	−1.31743	−0.658717	+	0.752391i	$0.728900\pi$
$860$	69.5791	2.37263
$861$	−4.84093	−0.164978
$862$	1.66664	0.0567660
$863$	51.9259	1.76758	0.883789	−	0.467886i	$-0.154984\pi$
$863$	51.9259	1.76758	0.883789	+	0.467886i	$0.154984\pi$
$864$	4.31250	0.146714
$865$	4.75303	0.161608
$866$	2.70539	0.0919330
$867$	−28.1579	−0.956292
$868$	−5.24386	−0.177988
$869$	−43.8768	−1.48842
$870$	2.29458	0.0777934
$871$	−45.9679	−1.55756
$872$	0.664676	0.0225088
$873$	−31.5617	−1.06820
$874$	−0.312206	−0.0105605
$875$	−3.01583	−0.101954
$876$	−30.3084	−1.02402
$877$	−16.2980	−0.550343	−0.275172	−	0.961395i	$-0.588735\pi$
$877$	−16.2980	−0.550343	−0.275172	+	0.961395i	$0.588735\pi$
$878$	1.46016	0.0492780
$879$	27.2331	0.918548
$880$	−41.4390	−1.39691
$881$	−3.24524	−0.109335	−0.0546674	−	0.998505i	$-0.517410\pi$
$881$	−3.24524	−0.109335	−0.0546674	+	0.998505i	$0.517410\pi$
$882$	−2.31606	−0.0779859
$883$	−16.6948	−0.561824	−0.280912	−	0.959734i	$-0.590637\pi$
$883$	−16.6948	−0.561824	−0.280912	+	0.959734i	$0.590637\pi$
$884$	−29.6954	−0.998766
$885$	65.6567	2.20703
$886$	1.49154	0.0501092
$887$	−11.0378	−0.370613	−0.185306	−	0.982681i	$-0.559328\pi$
$887$	−11.0378	−0.370613	−0.185306	+	0.982681i	$0.559328\pi$
$888$	−4.58075	−0.153720
$889$	−8.66118	−0.290487
$890$	1.56225	0.0523667
$891$	1.30032	0.0435623
$892$	39.4640	1.32135
$893$	3.73543	0.125001
$894$	1.17121	0.0391710
$895$	−73.7469	−2.46509
$896$	−1.18332	−0.0395318
$897$	−85.9973	−2.87137
$898$	0.448587	0.0149695
$899$	20.5937	0.686839
$900$	−28.1474	−0.938248
$901$	8.32626	0.277388
$902$	0.886387	0.0295135
$903$	−17.9545	−0.597488
$904$	1.14997	0.0382473
$905$	16.6961	0.554998
$906$	0.0524003	0.00174088
$907$	12.5442	0.416522	0.208261	−	0.978073i	$-0.433220\pi$
$907$	12.5442	0.416522	0.208261	+	0.978073i	$0.433220\pi$
$908$	28.2389	0.937140
$909$	74.8632	2.48306
$910$	0.593448	0.0196726
$911$	23.9424	0.793247	0.396624	−	0.917981i	$-0.370182\pi$
$911$	23.9424	0.793247	0.396624	+	0.917981i	$0.370182\pi$
$912$	8.87661	0.293934
$913$	32.5775	1.07816
$914$	−1.86834	−0.0617993
$915$	−2.10331	−0.0695333
$916$	24.6402	0.814136
$917$	5.47746	0.180882
$918$	0.948528	0.0313061
$919$	49.0324	1.61743	0.808715	−	0.588200i	$-0.200163\pi$
$919$	49.0324	1.61743	0.808715	+	0.588200i	$0.200163\pi$
$920$	4.38895	0.144699
$921$	−23.3135	−0.768207
$922$	1.15039	0.0378861
$923$	47.0745	1.54948
$924$	10.7208	0.352688
$925$	16.8330	0.553467
$926$	−1.66323	−0.0546570
$927$	26.2163	0.861057
$928$	3.48685	0.114462
$929$	1.01000	0.0331369	0.0165685	−	0.999863i	$-0.494726\pi$
$929$	1.01000	0.0331369	0.0165685	+	0.999863i	$0.494726\pi$
$930$	2.85528	0.0936283
$931$	−5.38885	−0.176612
$932$	−11.1333	−0.364685
$933$	43.3342	1.41870
$934$	−2.39901	−0.0784979
$935$	−27.4612	−0.898078
$936$	−7.77996	−0.254296
$937$	−24.2026	−0.790665	−0.395332	−	0.918538i	$-0.629371\pi$
$937$	−24.2026	−0.790665	−0.395332	+	0.918538i	$0.629371\pi$
$938$	−0.302298	−0.00987040
$939$	70.4435	2.29884
$940$	−26.2223	−0.855277
$941$	12.9943	0.423601	0.211801	−	0.977313i	$-0.432067\pi$
$941$	12.9943	0.423601	0.211801	+	0.977313i	$0.432067\pi$
$942$	1.07882	0.0351500
$943$	18.1586	0.591325
$944$	33.1148	1.07779
$945$	7.36143	0.239467
$946$	3.28752	0.106886
$947$	31.7016	1.03016	0.515082	−	0.857141i	$-0.327761\pi$
$947$	31.7016	1.03016	0.515082	+	0.857141i	$0.327761\pi$
$948$	−65.9786	−2.14289
$949$	30.7841	0.999295
$950$	0.168642	0.00547146
$951$	−20.4710	−0.663816
$952$	−0.391075	−0.0126748
$953$	−6.78079	−0.219651	−0.109826	−	0.993951i	$-0.535029\pi$
$953$	−6.78079	−0.219651	−0.109826	+	0.993951i	$0.535029\pi$
$954$	1.08930	0.0352675
$955$	19.3213	0.625223
$956$	13.6389	0.441112
$957$	−42.1027	−1.36099
$958$	0.142253	0.00459599
$959$	−4.26487	−0.137720
$960$	−61.9899	−2.00072
$961$	−5.37401	−0.173355
$962$	2.32334	0.0749074
$963$	−42.5151	−1.37003
$964$	−37.5539	−1.20953
$965$	−38.1667	−1.22863
$966$	−0.565544	−0.0181961
$967$	−8.76190	−0.281764	−0.140882	−	0.990026i	$-0.544994\pi$
$967$	−8.76190	−0.281764	−0.140882	+	0.990026i	$0.544994\pi$
$968$	−0.781561	−0.0251203
$969$	5.88244	0.188971
$970$	−1.32745	−0.0426218
$971$	12.8301	0.411737	0.205868	−	0.978580i	$-0.433998\pi$
$971$	12.8301	0.411737	0.205868	+	0.978580i	$0.433998\pi$
$972$	32.0662	1.02852
$973$	1.01734	0.0326146
$974$	−0.938973	−0.0300866
$975$	46.4525	1.48767
$976$	−1.06083	−0.0339563
$977$	61.6583	1.97262	0.986312	−	0.164888i	$-0.0527264\pi$
$977$	61.6583	1.97262	0.986312	+	0.164888i	$0.0527264\pi$
$978$	−2.33917	−0.0747983
$979$	−28.6654	−0.916150
$980$	37.8292	1.20841
$981$	−11.1462	−0.355871
$982$	0.0307917	0.000982602 0
$983$	−2.97661	−0.0949393	−0.0474696	−	0.998873i	$-0.515116\pi$
$983$	−2.97661	−0.0949393	−0.0474696	+	0.998873i	$0.515116\pi$
$984$	2.66920	0.0850908
$985$	−30.8926	−0.984319
$986$	0.766929	0.0244240
$987$	6.76651	0.215381
$988$	−9.03929	−0.287578
$989$	67.3483	2.14155
$990$	−3.59268	−0.114183
$991$	−26.9979	−0.857617	−0.428809	−	0.903395i	$-0.641067\pi$
$991$	−26.9979	−0.857617	−0.428809	+	0.903395i	$0.641067\pi$
$992$	4.33890	0.137760
$993$	12.9376	0.410562
$994$	0.309576	0.00981915
$995$	35.6530	1.13028
$996$	48.9875	1.55223
$997$	−34.0026	−1.07687	−0.538436	−	0.842666i	$-0.680985\pi$
$997$	−34.0026	−1.07687	−0.538436	+	0.842666i	$0.680985\pi$
$998$	−3.06510	−0.0970242
$999$	28.8198	0.911820

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2671.2.a.b.1.59	✓	122

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2671.2.a.b.1.59	✓	122	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:	\( N \)	\(=\)	\( 2671 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2671.a (trivial)

\(f(q)\)	\(=\)	\(q+0.0716716 q^{2} +2.79309 q^{3} -1.99486 q^{4} +2.81758 q^{5} +0.200185 q^{6} +0.519275 q^{7} -0.286318 q^{8} +4.80137 q^{9} +O(q^{10})\)	\(q+0.0716716 q^{2} +2.79309 q^{3} -1.99486 q^{4} +2.81758 q^{5} +0.200185 q^{6} +0.519275 q^{7} -0.286318 q^{8} +4.80137 q^{9} +0.201940 q^{10} -3.70536 q^{11} -5.57184 q^{12} +5.65930 q^{13} +0.0372172 q^{14} +7.86975 q^{15} +3.96921 q^{16} +2.63035 q^{17} +0.344122 q^{18} +0.800678 q^{19} -5.62068 q^{20} +1.45038 q^{21} -0.265569 q^{22} -5.44047 q^{23} -0.799714 q^{24} +2.93873 q^{25} +0.405611 q^{26} +5.03141 q^{27} -1.03588 q^{28} +4.06812 q^{29} +0.564038 q^{30} +5.06221 q^{31} +0.857116 q^{32} -10.3494 q^{33} +0.188521 q^{34} +1.46310 q^{35} -9.57808 q^{36} +5.72799 q^{37} +0.0573859 q^{38} +15.8070 q^{39} -0.806723 q^{40} -3.33769 q^{41} +0.103951 q^{42} -12.3791 q^{43} +7.39169 q^{44} +13.5282 q^{45} -0.389927 q^{46} +4.66533 q^{47} +11.0864 q^{48} -6.73035 q^{49} +0.210624 q^{50} +7.34682 q^{51} -11.2895 q^{52} +3.16546 q^{53} +0.360609 q^{54} -10.4401 q^{55} -0.148678 q^{56} +2.23637 q^{57} +0.291569 q^{58} +8.34292 q^{59} -15.6991 q^{60} -0.267265 q^{61} +0.362817 q^{62} +2.49323 q^{63} -7.87698 q^{64} +15.9455 q^{65} -0.741759 q^{66} -8.12254 q^{67} -5.24719 q^{68} -15.1957 q^{69} +0.104862 q^{70} +8.31807 q^{71} -1.37472 q^{72} +5.43956 q^{73} +0.410534 q^{74} +8.20816 q^{75} -1.59724 q^{76} -1.92410 q^{77} +1.13291 q^{78} +11.8414 q^{79} +11.1835 q^{80} -0.350929 q^{81} -0.239217 q^{82} -8.79199 q^{83} -2.89332 q^{84} +7.41121 q^{85} -0.887232 q^{86} +11.3627 q^{87} +1.06091 q^{88} +7.73620 q^{89} +0.969590 q^{90} +2.93873 q^{91} +10.8530 q^{92} +14.1392 q^{93} +0.334372 q^{94} +2.25597 q^{95} +2.39400 q^{96} -6.57347 q^{97} -0.482375 q^{98} -17.7908 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 122 q + 14 q^{2} + 10 q^{3} + 128 q^{4} + 33 q^{5} + 22 q^{6} + 6 q^{7} + 36 q^{8} + 162 q^{9}+O(q^{10}) \) 122 * q + 14 * q^2 + 10 * q^3 + 128 * q^4 + 33 * q^5 + 22 * q^6 + 6 * q^7 + 36 * q^8 + 162 * q^9	\( 122 q + 14 q^{2} + 10 q^{3} + 128 q^{4} + 33 q^{5} + 22 q^{6} + 6 q^{7} + 36 q^{8} + 162 q^{9} + 16 q^{10} + 43 q^{11} + 23 q^{12} + 25 q^{13} + 45 q^{14} + 12 q^{15} + 132 q^{16} + 103 q^{17} + 30 q^{18} + 37 q^{19} + 63 q^{20} + 81 q^{21} + 15 q^{23} + 60 q^{24} + 151 q^{25} + 59 q^{26} + 22 q^{27} - 3 q^{28} + 80 q^{29} - 9 q^{30} + 15 q^{31} + 66 q^{32} + 93 q^{33} + 30 q^{34} + 23 q^{35} + 162 q^{36} + 18 q^{37} + 41 q^{38} + 10 q^{39} + 29 q^{40} + 249 q^{41} - 8 q^{42} + 14 q^{43} + 100 q^{44} + 59 q^{45} + 11 q^{46} + 57 q^{47} + 33 q^{48} + 180 q^{49} + 63 q^{50} + 26 q^{51} + 31 q^{52} + 65 q^{53} + 65 q^{54} - 8 q^{55} + 120 q^{56} + 57 q^{57} - 31 q^{58} + 108 q^{59} - q^{60} + 70 q^{61} + 25 q^{62} - 7 q^{63} + 100 q^{64} + 171 q^{65} + 12 q^{66} - 6 q^{67} + 184 q^{68} + 64 q^{69} - 24 q^{70} + 47 q^{71} + 53 q^{72} + 76 q^{73} + 66 q^{74} + 40 q^{75} + 32 q^{76} + 73 q^{77} - 19 q^{78} + 8 q^{79} + 115 q^{80} + 250 q^{81} - 13 q^{82} + 116 q^{83} + 159 q^{84} + 31 q^{85} + 91 q^{86} + 25 q^{87} - 43 q^{88} + 361 q^{89} + 32 q^{90} + 7 q^{91} + 5 q^{92} + 18 q^{93} + 23 q^{94} + 42 q^{95} + 77 q^{96} + 79 q^{97} + 56 q^{98} + 74 q^{99}+O(q^{100}) \) 122 * q + 14 * q^2 + 10 * q^3 + 128 * q^4 + 33 * q^5 + 22 * q^6 + 6 * q^7 + 36 * q^8 + 162 * q^9 + 16 * q^10 + 43 * q^11 + 23 * q^12 + 25 * q^13 + 45 * q^14 + 12 * q^15 + 132 * q^16 + 103 * q^17 + 30 * q^18 + 37 * q^19 + 63 * q^20 + 81 * q^21 + 15 * q^23 + 60 * q^24 + 151 * q^25 + 59 * q^26 + 22 * q^27 - 3 * q^28 + 80 * q^29 - 9 * q^30 + 15 * q^31 + 66 * q^32 + 93 * q^33 + 30 * q^34 + 23 * q^35 + 162 * q^36 + 18 * q^37 + 41 * q^38 + 10 * q^39 + 29 * q^40 + 249 * q^41 - 8 * q^42 + 14 * q^43 + 100 * q^44 + 59 * q^45 + 11 * q^46 + 57 * q^47 + 33 * q^48 + 180 * q^49 + 63 * q^50 + 26 * q^51 + 31 * q^52 + 65 * q^53 + 65 * q^54 - 8 * q^55 + 120 * q^56 + 57 * q^57 - 31 * q^58 + 108 * q^59 - q^60 + 70 * q^61 + 25 * q^62 - 7 * q^63 + 100 * q^64 + 171 * q^65 + 12 * q^66 - 6 * q^67 + 184 * q^68 + 64 * q^69 - 24 * q^70 + 47 * q^71 + 53 * q^72 + 76 * q^73 + 66 * q^74 + 40 * q^75 + 32 * q^76 + 73 * q^77 - 19 * q^78 + 8 * q^79 + 115 * q^80 + 250 * q^81 - 13 * q^82 + 116 * q^83 + 159 * q^84 + 31 * q^85 + 91 * q^86 + 25 * q^87 - 43 * q^88 + 361 * q^89 + 32 * q^90 + 7 * q^91 + 5 * q^92 + 18 * q^93 + 23 * q^94 + 42 * q^95 + 77 * q^96 + 79 * q^97 + 56 * q^98 + 74 * q^99

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