LMFDB - Embedded newform 8015.2.a.h.1.15

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:	$1$
Dimension:	$38$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
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)

$f(q)$	$=$	$q-0.697175 q^{2} +1.52901 q^{3} -1.51395 q^{4} +1.00000 q^{5} -1.06599 q^{6} +1.00000 q^{7} +2.44984 q^{8} -0.662121 q^{9} +O(q^{10})$	\(q-0.697175 q^{2} +1.52901 q^{3} -1.51395 q^{4} +1.00000 q^{5} -1.06599 q^{6} +1.00000 q^{7} +2.44984 q^{8} -0.662121 q^{9} -0.697175 q^{10} +4.72403 q^{11} -2.31484 q^{12} +3.96239 q^{13} -0.697175 q^{14} +1.52901 q^{15} +1.31993 q^{16} -7.67249 q^{17} +0.461615 q^{18} +3.77701 q^{19} -1.51395 q^{20} +1.52901 q^{21} -3.29348 q^{22} -4.65029 q^{23} +3.74583 q^{24} +1.00000 q^{25} -2.76248 q^{26} -5.59943 q^{27} -1.51395 q^{28} -9.27644 q^{29} -1.06599 q^{30} -5.45181 q^{31} -5.81989 q^{32} +7.22311 q^{33} +5.34907 q^{34} +1.00000 q^{35} +1.00242 q^{36} -8.01914 q^{37} -2.63324 q^{38} +6.05854 q^{39} +2.44984 q^{40} -3.28226 q^{41} -1.06599 q^{42} +5.79720 q^{43} -7.15193 q^{44} -0.662121 q^{45} +3.24207 q^{46} +6.73188 q^{47} +2.01818 q^{48} +1.00000 q^{49} -0.697175 q^{50} -11.7313 q^{51} -5.99884 q^{52} +0.616816 q^{53} +3.90378 q^{54} +4.72403 q^{55} +2.44984 q^{56} +5.77510 q^{57} +6.46731 q^{58} +3.12917 q^{59} -2.31484 q^{60} -15.4538 q^{61} +3.80087 q^{62} -0.662121 q^{63} +1.41763 q^{64} +3.96239 q^{65} -5.03577 q^{66} -11.5684 q^{67} +11.6157 q^{68} -7.11035 q^{69} -0.697175 q^{70} -6.08557 q^{71} -1.62209 q^{72} -4.50621 q^{73} +5.59075 q^{74} +1.52901 q^{75} -5.71820 q^{76} +4.72403 q^{77} -4.22386 q^{78} -10.8522 q^{79} +1.31993 q^{80} -6.57523 q^{81} +2.28831 q^{82} -7.55862 q^{83} -2.31484 q^{84} -7.67249 q^{85} -4.04166 q^{86} -14.1838 q^{87} +11.5731 q^{88} -11.8723 q^{89} +0.461615 q^{90} +3.96239 q^{91} +7.04029 q^{92} -8.33589 q^{93} -4.69330 q^{94} +3.77701 q^{95} -8.89869 q^{96} -18.0736 q^{97} -0.697175 q^{98} -3.12788 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 38 q - 6 q^{2} - 9 q^{3} + 24 q^{4} + 38 q^{5} - 10 q^{6} + 38 q^{7} - 21 q^{8} + 13 q^{9}+O(q^{10}) $ 38 * q - 6 * q^2 - 9 * q^3 + 24 * q^4 + 38 * q^5 - 10 * q^6 + 38 * q^7 - 21 * q^8 + 13 * q^9	\( 38 q - 6 q^{2} - 9 q^{3} + 24 q^{4} + 38 q^{5} - 10 q^{6} + 38 q^{7} - 21 q^{8} + 13 q^{9} - 6 q^{10} - 18 q^{11} - 20 q^{12} - 25 q^{13} - 6 q^{14} - 9 q^{15} - 21 q^{17} - 7 q^{18} - 14 q^{19} + 24 q^{20} - 9 q^{21} - 11 q^{22} - 16 q^{23} - 10 q^{24} + 38 q^{25} - 21 q^{26} - 15 q^{27} + 24 q^{28} - 52 q^{29} - 10 q^{30} - 30 q^{31} - 8 q^{32} - 13 q^{33} - 9 q^{34} + 38 q^{35} - 16 q^{36} - 47 q^{37} - 10 q^{38} - 50 q^{39} - 21 q^{40} - 35 q^{41} - 10 q^{42} - 18 q^{43} - 22 q^{44} + 13 q^{45} - 17 q^{46} - 23 q^{47} - 13 q^{48} + 38 q^{49} - 6 q^{50} - 5 q^{51} - 41 q^{52} - 12 q^{53} + 35 q^{54} - 18 q^{55} - 21 q^{56} - 3 q^{57} - 16 q^{58} - 16 q^{59} - 20 q^{60} - 47 q^{61} + 14 q^{62} + 13 q^{63} - 55 q^{64} - 25 q^{65} - 6 q^{66} - 54 q^{67} + 31 q^{68} - 95 q^{69} - 6 q^{70} - 41 q^{71} - 59 q^{73} - q^{74} - 9 q^{75} - 23 q^{76} - 18 q^{77} + 19 q^{78} - 117 q^{79} - 38 q^{81} + 19 q^{82} - 21 q^{83} - 20 q^{84} - 21 q^{85} - 12 q^{86} - 14 q^{87} - 40 q^{88} - 96 q^{89} - 7 q^{90} - 25 q^{91} + 53 q^{92} - 53 q^{93} - 28 q^{94} - 14 q^{95} + 40 q^{96} - 70 q^{97} - 6 q^{98} - 52 q^{99}+O(q^{100}) \) 38 * q - 6 * q^2 - 9 * q^3 + 24 * q^4 + 38 * q^5 - 10 * q^6 + 38 * q^7 - 21 * q^8 + 13 * q^9 - 6 * q^10 - 18 * q^11 - 20 * q^12 - 25 * q^13 - 6 * q^14 - 9 * q^15 - 21 * q^17 - 7 * q^18 - 14 * q^19 + 24 * q^20 - 9 * q^21 - 11 * q^22 - 16 * q^23 - 10 * q^24 + 38 * q^25 - 21 * q^26 - 15 * q^27 + 24 * q^28 - 52 * q^29 - 10 * q^30 - 30 * q^31 - 8 * q^32 - 13 * q^33 - 9 * q^34 + 38 * q^35 - 16 * q^36 - 47 * q^37 - 10 * q^38 - 50 * q^39 - 21 * q^40 - 35 * q^41 - 10 * q^42 - 18 * q^43 - 22 * q^44 + 13 * q^45 - 17 * q^46 - 23 * q^47 - 13 * q^48 + 38 * q^49 - 6 * q^50 - 5 * q^51 - 41 * q^52 - 12 * q^53 + 35 * q^54 - 18 * q^55 - 21 * q^56 - 3 * q^57 - 16 * q^58 - 16 * q^59 - 20 * q^60 - 47 * q^61 + 14 * q^62 + 13 * q^63 - 55 * q^64 - 25 * q^65 - 6 * q^66 - 54 * q^67 + 31 * q^68 - 95 * q^69 - 6 * q^70 - 41 * q^71 - 59 * q^73 - q^74 - 9 * q^75 - 23 * q^76 - 18 * q^77 + 19 * q^78 - 117 * q^79 - 38 * q^81 + 19 * q^82 - 21 * q^83 - 20 * q^84 - 21 * q^85 - 12 * q^86 - 14 * q^87 - 40 * q^88 - 96 * q^89 - 7 * q^90 - 25 * q^91 + 53 * q^92 - 53 * q^93 - 28 * q^94 - 14 * q^95 + 40 * q^96 - 70 * q^97 - 6 * q^98 - 52 * 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 $

$2$	−0.697175	−0.492977	−0.246489	−	0.969146i	$-0.579277\pi$
$2$	−0.697175	−0.492977	−0.246489	+	0.969146i	$0.579277\pi$
$3$	1.52901	0.882776	0.441388	−	0.897316i	$-0.354486\pi$
$3$	1.52901	0.882776	0.441388	+	0.897316i	$0.354486\pi$
$4$	−1.51395	−0.756973
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−1.06599	−0.435189
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	2.44984	0.866148
$9$	−0.662121	−0.220707
$10$	−0.697175	−0.220466
$11$	4.72403	1.42435	0.712175	−	0.702002i	$-0.247710\pi$
$11$	4.72403	1.42435	0.712175	+	0.702002i	$0.247710\pi$
$12$	−2.31484	−0.668238
$13$	3.96239	1.09897	0.549484	−	0.835504i	$-0.314824\pi$
$13$	3.96239	1.09897	0.549484	+	0.835504i	$0.314824\pi$
$14$	−0.697175	−0.186328
$15$	1.52901	0.394789
$16$	1.31993	0.329982
$17$	−7.67249	−1.86085	−0.930426	−	0.366480i	$-0.880563\pi$
$17$	−7.67249	−1.86085	−0.930426	+	0.366480i	$0.880563\pi$
$18$	0.461615	0.108804
$19$	3.77701	0.866506	0.433253	−	0.901272i	$-0.357366\pi$
$19$	3.77701	0.866506	0.433253	+	0.901272i	$0.357366\pi$
$20$	−1.51395	−0.338529
$21$	1.52901	0.333658
$22$	−3.29348	−0.702172
$23$	−4.65029	−0.969652	−0.484826	−	0.874611i	$-0.661117\pi$
$23$	−4.65029	−0.969652	−0.484826	+	0.874611i	$0.661117\pi$
$24$	3.74583	0.764615
$25$	1.00000	0.200000
$26$	−2.76248	−0.541766
$27$	−5.59943	−1.07761
$28$	−1.51395	−0.286109
$29$	−9.27644	−1.72259	−0.861296	−	0.508104i	$-0.830347\pi$
$29$	−9.27644	−1.72259	−0.861296	+	0.508104i	$0.830347\pi$
$30$	−1.06599	−0.194622
$31$	−5.45181	−0.979175	−0.489587	−	0.871954i	$-0.662853\pi$
$31$	−5.45181	−0.979175	−0.489587	+	0.871954i	$0.662853\pi$
$32$	−5.81989	−1.02882
$33$	7.22311	1.25738
$34$	5.34907	0.917358
$35$	1.00000	0.169031
$36$	1.00242	0.167069
$37$	−8.01914	−1.31834	−0.659169	−	0.751994i	$-0.729092\pi$
$37$	−8.01914	−1.31834	−0.659169	+	0.751994i	$0.729092\pi$
$38$	−2.63324	−0.427168
$39$	6.05854	0.970142
$40$	2.44984	0.387353
$41$	−3.28226	−0.512603	−0.256302	−	0.966597i	$-0.582504\pi$
$41$	−3.28226	−0.512603	−0.256302	+	0.966597i	$0.582504\pi$
$42$	−1.06599	−0.164486
$43$	5.79720	0.884064	0.442032	−	0.896999i	$-0.354258\pi$
$43$	5.79720	0.884064	0.442032	+	0.896999i	$0.354258\pi$
$44$	−7.15193	−1.07819
$45$	−0.662121	−0.0987032
$46$	3.24207	0.478017
$47$	6.73188	0.981945	0.490973	−	0.871175i	$-0.336642\pi$
$47$	6.73188	0.981945	0.490973	+	0.871175i	$0.336642\pi$
$48$	2.01818	0.291300
$49$	1.00000	0.142857
$50$	−0.697175	−0.0985955
$51$	−11.7313	−1.64272
$52$	−5.99884	−0.831889
$53$	0.616816	0.0847263	0.0423631	−	0.999102i	$-0.486511\pi$
$53$	0.616816	0.0847263	0.0423631	+	0.999102i	$0.486511\pi$
$54$	3.90378	0.531238
$55$	4.72403	0.636989
$56$	2.44984	0.327373
$57$	5.77510	0.764931
$58$	6.46731	0.849199
$59$	3.12917	0.407383	0.203692	−	0.979035i	$-0.434706\pi$
$59$	3.12917	0.407383	0.203692	+	0.979035i	$0.434706\pi$
$60$	−2.31484	−0.298845
$61$	−15.4538	−1.97866	−0.989329	−	0.145696i	$-0.953458\pi$
$61$	−15.4538	−1.97866	−0.989329	+	0.145696i	$0.953458\pi$
$62$	3.80087	0.482711
$63$	−0.662121	−0.0834194
$64$	1.41763	0.177204
$65$	3.96239	0.491473
$66$	−5.03577	−0.619861
$67$	−11.5684	−1.41330	−0.706651	−	0.707563i	$-0.749795\pi$
$67$	−11.5684	−1.41330	−0.706651	+	0.707563i	$0.749795\pi$
$68$	11.6157	1.40862
$69$	−7.11035	−0.855985
$70$	−0.697175	−0.0833284
$71$	−6.08557	−0.722224	−0.361112	−	0.932522i	$-0.617603\pi$
$71$	−6.08557	−0.722224	−0.361112	+	0.932522i	$0.617603\pi$
$72$	−1.62209	−0.191165
$73$	−4.50621	−0.527411	−0.263706	−	0.964603i	$-0.584945\pi$
$73$	−4.50621	−0.527411	−0.263706	+	0.964603i	$0.584945\pi$
$74$	5.59075	0.649911
$75$	1.52901	0.176555
$76$	−5.71820	−0.655922
$77$	4.72403	0.538354
$78$	−4.22386	−0.478258
$79$	−10.8522	−1.22097	−0.610486	−	0.792027i	$-0.709026\pi$
$79$	−10.8522	−1.22097	−0.610486	+	0.792027i	$0.709026\pi$
$80$	1.31993	0.147572
$81$	−6.57523	−0.730581
$82$	2.28831	0.252702
$83$	−7.55862	−0.829666	−0.414833	−	0.909898i	$-0.636160\pi$
$83$	−7.55862	−0.829666	−0.414833	+	0.909898i	$0.636160\pi$
$84$	−2.31484	−0.252570
$85$	−7.67249	−0.832198
$86$	−4.04166	−0.435824
$87$	−14.1838	−1.52066
$88$	11.5731	1.23370
$89$	−11.8723	−1.25846	−0.629230	−	0.777219i	$-0.716630\pi$
$89$	−11.8723	−1.25846	−0.629230	+	0.777219i	$0.716630\pi$
$90$	0.461615	0.0486584
$91$	3.96239	0.415371
$92$	7.04029	0.734001
$93$	−8.33589	−0.864392
$94$	−4.69330	−0.484077
$95$	3.77701	0.387513
$96$	−8.89869	−0.908219
$97$	−18.0736	−1.83509	−0.917546	−	0.397630i	$-0.869833\pi$
$97$	−18.0736	−1.83509	−0.917546	+	0.397630i	$0.869833\pi$
$98$	−0.697175	−0.0704254
$99$	−3.12788	−0.314364
$100$	−1.51395	−0.151395
$101$	−0.220999	−0.0219902	−0.0109951	−	0.999940i	$-0.503500\pi$
$101$	−0.220999	−0.0219902	−0.0109951	+	0.999940i	$0.503500\pi$
$102$	8.17880	0.809822
$103$	1.92303	0.189481	0.0947407	−	0.995502i	$-0.469798\pi$
$103$	1.92303	0.189481	0.0947407	+	0.995502i	$0.469798\pi$
$104$	9.70720	0.951869
$105$	1.52901	0.149216
$106$	−0.430029	−0.0417681
$107$	12.3575	1.19465	0.597323	−	0.802001i	$-0.296231\pi$
$107$	12.3575	1.19465	0.597323	+	0.802001i	$0.296231\pi$
$108$	8.47723	0.815722
$109$	15.3280	1.46815	0.734076	−	0.679068i	$-0.237616\pi$
$109$	15.3280	1.46815	0.734076	+	0.679068i	$0.237616\pi$
$110$	−3.29348	−0.314021
$111$	−12.2614	−1.16380
$112$	1.31993	0.124721
$113$	7.45211	0.701035	0.350518	−	0.936556i	$-0.386006\pi$
$113$	7.45211	0.701035	0.350518	+	0.936556i	$0.386006\pi$
$114$	−4.02626	−0.377094
$115$	−4.65029	−0.433642
$116$	14.0440	1.30396
$117$	−2.62358	−0.242550
$118$	−2.18158	−0.200831
$119$	−7.67249	−0.703336
$120$	3.74583	0.341946
$121$	11.3165	1.02877
$122$	10.7740	0.975434
$123$	−5.01862	−0.452514
$124$	8.25376	0.741209
$125$	1.00000	0.0894427
$126$	0.461615	0.0411239
$127$	−14.1361	−1.25438	−0.627189	−	0.778867i	$-0.715795\pi$
$127$	−14.1361	−1.25438	−0.627189	+	0.778867i	$0.715795\pi$
$128$	10.6514	0.941464
$129$	8.86399	0.780430
$130$	−2.76248	−0.242285
$131$	−12.5790	−1.09903	−0.549516	−	0.835483i	$-0.685188\pi$
$131$	−12.5790	−1.09903	−0.549516	+	0.835483i	$0.685188\pi$
$132$	−10.9354	−0.951804
$133$	3.77701	0.327509
$134$	8.06518	0.696726
$135$	−5.59943	−0.481922
$136$	−18.7964	−1.61177
$137$	19.9479	1.70426	0.852130	−	0.523330i	$-0.175310\pi$
$137$	19.9479	1.70426	0.852130	+	0.523330i	$0.175310\pi$
$138$	4.95716	0.421981
$139$	16.1146	1.36682	0.683409	−	0.730036i	$-0.260497\pi$
$139$	16.1146	1.36682	0.683409	+	0.730036i	$0.260497\pi$
$140$	−1.51395	−0.127952
$141$	10.2931	0.866837
$142$	4.24271	0.356040
$143$	18.7184	1.56532
$144$	−0.873951	−0.0728293
$145$	−9.27644	−0.770366
$146$	3.14162	0.260002
$147$	1.52901	0.126111
$148$	12.1406	0.997947
$149$	16.9863	1.39158	0.695788	−	0.718247i	$-0.255055\pi$
$149$	16.9863	1.39158	0.695788	+	0.718247i	$0.255055\pi$
$150$	−1.06599	−0.0870377
$151$	−14.3955	−1.17149	−0.585745	−	0.810496i	$-0.699198\pi$
$151$	−14.3955	−1.17149	−0.585745	+	0.810496i	$0.699198\pi$
$152$	9.25307	0.750523
$153$	5.08012	0.410703
$154$	−3.29348	−0.265396
$155$	−5.45181	−0.437900
$156$	−9.17230	−0.734372
$157$	3.33463	0.266133	0.133066	−	0.991107i	$-0.457518\pi$
$157$	3.33463	0.266133	0.133066	+	0.991107i	$0.457518\pi$
$158$	7.56591	0.601911
$159$	0.943120	0.0747943
$160$	−5.81989	−0.460103
$161$	−4.65029	−0.366494
$162$	4.58409	0.360160
$163$	−19.3186	−1.51315	−0.756576	−	0.653905i	$-0.773129\pi$
$163$	−19.3186	−1.51315	−0.756576	+	0.653905i	$0.773129\pi$
$164$	4.96917	0.388027
$165$	7.22311	0.562318
$166$	5.26968	0.409007
$167$	6.67378	0.516433	0.258216	−	0.966087i	$-0.416865\pi$
$167$	6.67378	0.516433	0.258216	+	0.966087i	$0.416865\pi$
$168$	3.74583	0.288997
$169$	2.70050	0.207731
$170$	5.34907	0.410255
$171$	−2.50084	−0.191244
$172$	−8.77665	−0.669213
$173$	16.9132	1.28588	0.642942	−	0.765915i	$-0.277714\pi$
$173$	16.9132	1.28588	0.642942	+	0.765915i	$0.277714\pi$
$174$	9.88859	0.749652
$175$	1.00000	0.0755929
$176$	6.23538	0.470009
$177$	4.78454	0.359628
$178$	8.27707	0.620392
$179$	−10.5544	−0.788870	−0.394435	−	0.918924i	$-0.629060\pi$
$179$	−10.5544	−0.788870	−0.394435	+	0.918924i	$0.629060\pi$
$180$	1.00242	0.0747157
$181$	24.0123	1.78482	0.892411	−	0.451224i	$-0.149013\pi$
$181$	24.0123	1.78482	0.892411	+	0.451224i	$0.149013\pi$
$182$	−2.76248	−0.204768
$183$	−23.6291	−1.74671
$184$	−11.3924	−0.839862
$185$	−8.01914	−0.589579
$186$	5.81158	0.426126
$187$	−36.2451	−2.65050
$188$	−10.1917	−0.743306
$189$	−5.59943	−0.407298
$190$	−2.63324	−0.191035
$191$	−15.3915	−1.11369	−0.556845	−	0.830617i	$-0.687988\pi$
$191$	−15.3915	−1.11369	−0.556845	+	0.830617i	$0.687988\pi$
$192$	2.16758	0.156432
$193$	−4.36180	−0.313969	−0.156985	−	0.987601i	$-0.550177\pi$
$193$	−4.36180	−0.313969	−0.156985	+	0.987601i	$0.550177\pi$
$194$	12.6004	0.904659
$195$	6.05854	0.433861
$196$	−1.51395	−0.108139
$197$	26.8880	1.91569	0.957844	−	0.287287i	$-0.0927534\pi$
$197$	26.8880	1.91569	0.957844	+	0.287287i	$0.0927534\pi$
$198$	2.18068	0.154974
$199$	7.52248	0.533254	0.266627	−	0.963800i	$-0.414091\pi$
$199$	7.52248	0.533254	0.266627	+	0.963800i	$0.414091\pi$
$200$	2.44984	0.173230
$201$	−17.6882	−1.24763
$202$	0.154075	0.0108407
$203$	−9.27644	−0.651078
$204$	17.7606	1.24349
$205$	−3.28226	−0.229243
$206$	−1.34069	−0.0934101
$207$	3.07905	0.214009
$208$	5.23006	0.362639
$209$	17.8427	1.23421
$210$	−1.06599	−0.0735603
$211$	11.2297	0.773085	0.386542	−	0.922272i	$-0.373669\pi$
$211$	11.2297	0.773085	0.386542	+	0.922272i	$0.373669\pi$
$212$	−0.933827	−0.0641355
$213$	−9.30491	−0.637562
$214$	−8.61536	−0.588934
$215$	5.79720	0.395366
$216$	−13.7177	−0.933370
$217$	−5.45181	−0.370093
$218$	−10.6863	−0.723766
$219$	−6.89004	−0.465586
$220$	−7.15193	−0.482183
$221$	−30.4014	−2.04502
$222$	8.54832	0.573726
$223$	12.8827	0.862689	0.431344	−	0.902187i	$-0.358039\pi$
$223$	12.8827	0.862689	0.431344	+	0.902187i	$0.358039\pi$
$224$	−5.81989	−0.388858
$225$	−0.662121	−0.0441414
$226$	−5.19543	−0.345595
$227$	−4.31424	−0.286346	−0.143173	−	0.989698i	$-0.545731\pi$
$227$	−4.31424	−0.286346	−0.143173	+	0.989698i	$0.545731\pi$
$228$	−8.74319	−0.579032
$229$	−1.00000	−0.0660819
$229$	−1.00000	−0.0660819
$230$	3.24207	0.213776
$231$	7.22311	0.475246
$232$	−22.7258	−1.49202
$233$	−26.5574	−1.73983	−0.869916	−	0.493200i	$-0.835827\pi$
$233$	−26.5574	−1.73983	−0.869916	+	0.493200i	$0.835827\pi$
$234$	1.82909	0.119572
$235$	6.73188	0.439139
$236$	−4.73740	−0.308378
$237$	−16.5932	−1.07784
$238$	5.34907	0.346729
$239$	−15.8191	−1.02325	−0.511627	−	0.859208i	$-0.670957\pi$
$239$	−15.8191	−1.02325	−0.511627	+	0.859208i	$0.670957\pi$
$240$	2.01818	0.130273
$241$	11.9076	0.767038	0.383519	−	0.923533i	$-0.374712\pi$
$241$	11.9076	0.767038	0.383519	+	0.923533i	$0.374712\pi$
$242$	−7.88958	−0.507162
$243$	6.74467	0.432671
$244$	23.3963	1.49779
$245$	1.00000	0.0638877
$246$	3.49886	0.223079
$247$	14.9660	0.952263
$248$	−13.3561	−0.848111
$249$	−11.5572	−0.732409
$250$	−0.697175	−0.0440932
$251$	18.4242	1.16293	0.581464	−	0.813572i	$-0.302480\pi$
$251$	18.4242	1.16293	0.581464	+	0.813572i	$0.302480\pi$
$252$	1.00242	0.0631463
$253$	−21.9681	−1.38112
$254$	9.85535	0.618380
$255$	−11.7313	−0.734645
$256$	−10.2612	−0.641325
$257$	14.3553	0.895461	0.447731	−	0.894169i	$-0.352232\pi$
$257$	14.3553	0.895461	0.447731	+	0.894169i	$0.352232\pi$
$258$	−6.17975	−0.384735
$259$	−8.01914	−0.498285
$260$	−5.99884	−0.372032
$261$	6.14213	0.380188
$262$	8.76977	0.541798
$263$	1.11527	0.0687706	0.0343853	−	0.999409i	$-0.489053\pi$
$263$	1.11527	0.0687706	0.0343853	+	0.999409i	$0.489053\pi$
$264$	17.6954	1.08908
$265$	0.616816	0.0378907
$266$	−2.63324	−0.161454
$267$	−18.1529	−1.11094
$268$	17.5139	1.06983
$269$	3.80330	0.231891	0.115946	−	0.993256i	$-0.463010\pi$
$269$	3.80330	0.231891	0.115946	+	0.993256i	$0.463010\pi$
$270$	3.90378	0.237577
$271$	0.409385	0.0248684	0.0124342	−	0.999923i	$-0.496042\pi$
$271$	0.409385	0.0248684	0.0124342	+	0.999923i	$0.496042\pi$
$272$	−10.1271	−0.614047
$273$	6.05854	0.366679
$274$	−13.9072	−0.840162
$275$	4.72403	0.284870
$276$	10.7647	0.647958
$277$	6.04412	0.363156	0.181578	−	0.983377i	$-0.441880\pi$
$277$	6.04412	0.363156	0.181578	+	0.983377i	$0.441880\pi$
$278$	−11.2347	−0.673811
$279$	3.60976	0.216111
$280$	2.44984	0.146406
$281$	−11.2126	−0.668890	−0.334445	−	0.942415i	$-0.608549\pi$
$281$	−11.2126	−0.668890	−0.334445	+	0.942415i	$0.608549\pi$
$282$	−7.17611	−0.427331
$283$	−2.27925	−0.135487	−0.0677437	−	0.997703i	$-0.521580\pi$
$283$	−2.27925	−0.135487	−0.0677437	+	0.997703i	$0.521580\pi$
$284$	9.21323	0.546704
$285$	5.77510	0.342087
$286$	−13.0500	−0.771665
$287$	−3.28226	−0.193746
$288$	3.85347	0.227068
$289$	41.8671	2.46277
$290$	6.46731	0.379773
$291$	−27.6347	−1.61997
$292$	6.82215	0.399236
$293$	−1.80650	−0.105537	−0.0527686	−	0.998607i	$-0.516805\pi$
$293$	−1.80650	−0.105537	−0.0527686	+	0.998607i	$0.516805\pi$
$294$	−1.06599	−0.0621698
$295$	3.12917	0.182187
$296$	−19.6456	−1.14188
$297$	−26.4519	−1.53489
$298$	−11.8425	−0.686015
$299$	−18.4262	−1.06562
$300$	−2.31484	−0.133648
$301$	5.79720	0.334145
$302$	10.0362	0.577518
$303$	−0.337910	−0.0194124
$304$	4.98538	0.285931
$305$	−15.4538	−0.884883
$306$	−3.54173	−0.202467
$307$	−4.83422	−0.275903	−0.137952	−	0.990439i	$-0.544052\pi$
$307$	−4.83422	−0.275903	−0.137952	+	0.990439i	$0.544052\pi$
$308$	−7.15193	−0.407519
$309$	2.94033	0.167270
$310$	3.80087	0.215875
$311$	12.1972	0.691640	0.345820	−	0.938301i	$-0.387601\pi$
$311$	12.1972	0.691640	0.345820	+	0.938301i	$0.387601\pi$
$312$	14.8424	0.840287
$313$	−23.5400	−1.33056	−0.665278	−	0.746595i	$-0.731687\pi$
$313$	−23.5400	−1.33056	−0.665278	+	0.746595i	$0.731687\pi$
$314$	−2.32482	−0.131197
$315$	−0.662121	−0.0373063
$316$	16.4297	0.924243
$317$	−6.57897	−0.369512	−0.184756	−	0.982784i	$-0.559149\pi$
$317$	−6.57897	−0.369512	−0.184756	+	0.982784i	$0.559149\pi$
$318$	−0.657520	−0.0368719
$319$	−43.8222	−2.45357
$320$	1.41763	0.0792481
$321$	18.8948	1.05460
$322$	3.24207	0.180673
$323$	−28.9791	−1.61244
$324$	9.95455	0.553031
$325$	3.96239	0.219794
$326$	13.4685	0.745950
$327$	23.4366	1.29605
$328$	−8.04101	−0.443990
$329$	6.73188	0.371140
$330$	−5.03577	−0.277210
$331$	−0.273192	−0.0150160	−0.00750798	−	0.999972i	$-0.502390\pi$
$331$	−0.273192	−0.0150160	−0.00750798	+	0.999972i	$0.502390\pi$
$332$	11.4433	0.628035
$333$	5.30964	0.290967
$334$	−4.65280	−0.254590
$335$	−11.5684	−0.632048
$336$	2.01818	0.110101
$337$	−7.39241	−0.402690	−0.201345	−	0.979520i	$-0.564531\pi$
$337$	−7.39241	−0.402690	−0.201345	+	0.979520i	$0.564531\pi$
$338$	−1.88272	−0.102407
$339$	11.3944	0.618857
$340$	11.6157	0.629952
$341$	−25.7546	−1.39469
$342$	1.74352	0.0942790
$343$	1.00000	0.0539949
$344$	14.2022	0.765731
$345$	−7.11035	−0.382808
$346$	−11.7914	−0.633912
$347$	−17.8761	−0.959637	−0.479818	−	0.877368i	$-0.659297\pi$
$347$	−17.8761	−0.959637	−0.479818	+	0.877368i	$0.659297\pi$
$348$	21.4735	1.15110
$349$	−2.08842	−0.111790	−0.0558952	−	0.998437i	$-0.517801\pi$
$349$	−2.08842	−0.111790	−0.0558952	+	0.998437i	$0.517801\pi$
$350$	−0.697175	−0.0372656
$351$	−22.1871	−1.18426
$352$	−27.4934	−1.46540
$353$	5.59961	0.298037	0.149019	−	0.988834i	$-0.452389\pi$
$353$	5.59961	0.298037	0.149019	+	0.988834i	$0.452389\pi$
$354$	−3.33566	−0.177288
$355$	−6.08557	−0.322988
$356$	17.9740	0.952620
$357$	−11.7313	−0.620888
$358$	7.35824	0.388895
$359$	−18.8727	−0.996062	−0.498031	−	0.867159i	$-0.665943\pi$
$359$	−18.8727	−0.996062	−0.498031	+	0.867159i	$0.665943\pi$
$360$	−1.62209	−0.0854916
$361$	−4.73417	−0.249167
$362$	−16.7408	−0.879877
$363$	17.3031	0.908175
$364$	−5.99884	−0.314425
$365$	−4.50621	−0.235866
$366$	16.4736	0.861090
$367$	−11.4837	−0.599442	−0.299721	−	0.954027i	$-0.596894\pi$
$367$	−11.4837	−0.599442	−0.299721	+	0.954027i	$0.596894\pi$
$368$	−6.13804	−0.319967
$369$	2.17325	0.113135
$370$	5.59075	0.290649
$371$	0.616816	0.0320235
$372$	12.6201	0.654321
$373$	−22.3177	−1.15556	−0.577782	−	0.816191i	$-0.696082\pi$
$373$	−22.3177	−1.15556	−0.577782	+	0.816191i	$0.696082\pi$
$374$	25.2692	1.30664
$375$	1.52901	0.0789579
$376$	16.4920	0.850510
$377$	−36.7568	−1.89307
$378$	3.90378	0.200789
$379$	11.0784	0.569057	0.284528	−	0.958668i	$-0.408163\pi$
$379$	11.0784	0.569057	0.284528	+	0.958668i	$0.408163\pi$
$380$	−5.71820	−0.293337
$381$	−21.6143	−1.10733
$382$	10.7306	0.549024
$383$	−14.6265	−0.747379	−0.373689	−	0.927554i	$-0.621907\pi$
$383$	−14.6265	−0.747379	−0.373689	+	0.927554i	$0.621907\pi$
$384$	16.2862	0.831102
$385$	4.72403	0.240759
$386$	3.04094	0.154780
$387$	−3.83845	−0.195119
$388$	27.3624	1.38912
$389$	24.9412	1.26457	0.632285	−	0.774736i	$-0.282117\pi$
$389$	24.9412	1.26457	0.632285	+	0.774736i	$0.282117\pi$
$390$	−4.22386	−0.213884
$391$	35.6793	1.80438
$392$	2.44984	0.123735
$393$	−19.2334	−0.970199
$394$	−18.7456	−0.944391
$395$	−10.8522	−0.546035
$396$	4.73545	0.237965
$397$	−25.5977	−1.28471	−0.642357	−	0.766406i	$-0.722043\pi$
$397$	−25.5977	−1.28471	−0.642357	+	0.766406i	$0.722043\pi$
$398$	−5.24449	−0.262882
$399$	5.77510	0.289117
$400$	1.31993	0.0659963
$401$	6.45262	0.322228	0.161114	−	0.986936i	$-0.448491\pi$
$401$	6.45262	0.322228	0.161114	+	0.986936i	$0.448491\pi$
$402$	12.3318	0.615053
$403$	−21.6022	−1.07608
$404$	0.334580	0.0166460
$405$	−6.57523	−0.326726
$406$	6.46731	0.320967
$407$	−37.8827	−1.87778
$408$	−28.7399	−1.42283
$409$	−29.8785	−1.47740	−0.738699	−	0.674035i	$-0.764560\pi$
$409$	−29.8785	−1.47740	−0.738699	+	0.674035i	$0.764560\pi$
$410$	2.28831	0.113012
$411$	30.5005	1.50448
$412$	−2.91136	−0.143432
$413$	3.12917	0.153976
$414$	−2.14664	−0.105502
$415$	−7.55862	−0.371038
$416$	−23.0607	−1.13064
$417$	24.6393	1.20659
$418$	−12.4395	−0.608437
$419$	4.42251	0.216054	0.108027	−	0.994148i	$-0.465547\pi$
$419$	4.42251	0.216054	0.108027	+	0.994148i	$0.465547\pi$
$420$	−2.31484	−0.112953
$421$	14.6571	0.714342	0.357171	−	0.934039i	$-0.383741\pi$
$421$	14.6571	0.714342	0.357171	+	0.934039i	$0.383741\pi$
$422$	−7.82907	−0.381113
$423$	−4.45732	−0.216722
$424$	1.51110	0.0733855
$425$	−7.67249	−0.372170
$426$	6.48716	0.314304
$427$	−15.4538	−0.747863
$428$	−18.7086	−0.904315
$429$	28.6207	1.38182
$430$	−4.04166	−0.194906
$431$	31.6934	1.52662	0.763309	−	0.646034i	$-0.223573\pi$
$431$	31.6934	1.52662	0.763309	+	0.646034i	$0.223573\pi$
$432$	−7.39084	−0.355592
$433$	−5.39763	−0.259393	−0.129697	−	0.991554i	$-0.541400\pi$
$433$	−5.39763	−0.259393	−0.129697	+	0.991554i	$0.541400\pi$
$434$	3.80087	0.182448
$435$	−14.1838	−0.680061
$436$	−23.2057	−1.11135
$437$	−17.5642	−0.840210
$438$	4.80357	0.229523
$439$	−13.9974	−0.668059	−0.334030	−	0.942563i	$-0.608409\pi$
$439$	−13.9974	−0.668059	−0.334030	+	0.942563i	$0.608409\pi$
$440$	11.5731	0.551727
$441$	−0.662121	−0.0315296
$442$	21.1951	1.00815
$443$	38.7664	1.84185	0.920925	−	0.389740i	$-0.127435\pi$
$443$	38.7664	1.84185	0.920925	+	0.389740i	$0.127435\pi$
$444$	18.5631	0.880964
$445$	−11.8723	−0.562800
$446$	−8.98149	−0.425286
$447$	25.9723	1.22845
$448$	1.41763	0.0669769
$449$	33.9501	1.60220	0.801102	−	0.598528i	$-0.204248\pi$
$449$	33.9501	1.60220	0.801102	+	0.598528i	$0.204248\pi$
$450$	0.461615	0.0217607
$451$	−15.5055	−0.730126
$452$	−11.2821	−0.530665
$453$	−22.0109	−1.03416
$454$	3.00778	0.141162
$455$	3.96239	0.185760
$456$	14.1481	0.662543
$457$	37.7165	1.76430	0.882152	−	0.470965i	$-0.156094\pi$
$457$	37.7165	1.76430	0.882152	+	0.470965i	$0.156094\pi$
$458$	0.697175	0.0325769
$459$	42.9616	2.00527
$460$	7.04029	0.328255
$461$	6.69083	0.311623	0.155812	−	0.987787i	$-0.450201\pi$
$461$	6.69083	0.311623	0.155812	+	0.987787i	$0.450201\pi$
$462$	−5.03577	−0.234285
$463$	15.4960	0.720162	0.360081	−	0.932921i	$-0.382749\pi$
$463$	15.4960	0.720162	0.360081	+	0.932921i	$0.382749\pi$
$464$	−12.2442	−0.568424
$465$	−8.33589	−0.386568
$466$	18.5152	0.857698
$467$	−10.1618	−0.470230	−0.235115	−	0.971968i	$-0.575547\pi$
$467$	−10.1618	−0.470230	−0.235115	+	0.971968i	$0.575547\pi$
$468$	3.97196	0.183604
$469$	−11.5684	−0.534178
$470$	−4.69330	−0.216486
$471$	5.09869	0.234935
$472$	7.66596	0.352854
$473$	27.3862	1.25922
$474$	11.5684	0.531353
$475$	3.77701	0.173301
$476$	11.6157	0.532407
$477$	−0.408407	−0.0186997
$478$	11.0287	0.504441
$479$	−16.6931	−0.762728	−0.381364	−	0.924425i	$-0.624546\pi$
$479$	−16.6931	−0.762728	−0.381364	+	0.924425i	$0.624546\pi$
$480$	−8.89869	−0.406168
$481$	−31.7749	−1.44881
$482$	−8.30171	−0.378132
$483$	−7.11035	−0.323532
$484$	−17.1326	−0.778753
$485$	−18.0736	−0.820678
$486$	−4.70222	−0.213297
$487$	11.2992	0.512016	0.256008	−	0.966675i	$-0.417593\pi$
$487$	11.2992	0.512016	0.256008	+	0.966675i	$0.417593\pi$
$488$	−37.8593	−1.71381
$489$	−29.5384	−1.33577
$490$	−0.697175	−0.0314952
$491$	0.627792	0.0283319	0.0141659	−	0.999900i	$-0.495491\pi$
$491$	0.627792	0.0283319	0.0141659	+	0.999900i	$0.495491\pi$
$492$	7.59792	0.342541
$493$	71.1734	3.20549
$494$	−10.4339	−0.469444
$495$	−3.12788	−0.140588
$496$	−7.19600	−0.323110
$497$	−6.08557	−0.272975
$498$	8.05741	0.361061
$499$	−42.6652	−1.90996	−0.954978	−	0.296677i	$-0.904122\pi$
$499$	−42.6652	−1.90996	−0.954978	+	0.296677i	$0.904122\pi$
$500$	−1.51395	−0.0677057
$501$	10.2043	0.455894
$502$	−12.8449	−0.573297
$503$	3.64795	0.162654	0.0813270	−	0.996687i	$-0.474084\pi$
$503$	3.64795	0.162654	0.0813270	+	0.996687i	$0.474084\pi$
$504$	−1.62209	−0.0722536
$505$	−0.220999	−0.00983432
$506$	15.3156	0.680863
$507$	4.12910	0.183380
$508$	21.4013	0.949530
$509$	−39.5730	−1.75404	−0.877021	−	0.480452i	$-0.840473\pi$
$509$	−39.5730	−1.75404	−0.877021	+	0.480452i	$0.840473\pi$
$510$	8.17880	0.362163
$511$	−4.50621	−0.199343
$512$	−14.1490	−0.625305
$513$	−21.1491	−0.933756
$514$	−10.0082	−0.441442
$515$	1.92303	0.0847387
$516$	−13.4196	−0.590765
$517$	31.8016	1.39863
$518$	5.59075	0.245643
$519$	25.8604	1.13515
$520$	9.70720	0.425689
$521$	−20.0321	−0.877624	−0.438812	−	0.898579i	$-0.644601\pi$
$521$	−20.0321	−0.877624	−0.438812	+	0.898579i	$0.644601\pi$
$522$	−4.28214	−0.187424
$523$	−15.9562	−0.697716	−0.348858	−	0.937176i	$-0.613430\pi$
$523$	−15.9562	−0.697716	−0.348858	+	0.937176i	$0.613430\pi$
$524$	19.0439	0.831938
$525$	1.52901	0.0667316
$526$	−0.777540	−0.0339023
$527$	41.8290	1.82210
$528$	9.53397	0.414913
$529$	−1.37482	−0.0597747
$530$	−0.430029	−0.0186793
$531$	−2.07189	−0.0899123
$532$	−5.71820	−0.247915
$533$	−13.0056	−0.563334
$534$	12.6557	0.547667
$535$	12.3575	0.534262
$536$	−28.3406	−1.22413
$537$	−16.1377	−0.696395
$538$	−2.65157	−0.114317
$539$	4.72403	0.203479
$540$	8.47723	0.364802
$541$	−3.87099	−0.166427	−0.0832135	−	0.996532i	$-0.526518\pi$
$541$	−3.87099	−0.166427	−0.0832135	+	0.996532i	$0.526518\pi$
$542$	−0.285413	−0.0122595
$543$	36.7151	1.57560
$544$	44.6531	1.91449
$545$	15.3280	0.656577
$546$	−4.22386	−0.180765
$547$	−1.52917	−0.0653826	−0.0326913	−	0.999465i	$-0.510408\pi$
$547$	−1.52917	−0.0653826	−0.0326913	+	0.999465i	$0.510408\pi$
$548$	−30.2000	−1.29008
$549$	10.2323	0.436704
$550$	−3.29348	−0.140434
$551$	−35.0372	−1.49264
$552$	−17.4192	−0.741410
$553$	−10.8522	−0.461484
$554$	−4.21381	−0.179028
$555$	−12.2614	−0.520466
$556$	−24.3966	−1.03464
$557$	−24.3803	−1.03303	−0.516513	−	0.856279i	$-0.672770\pi$
$557$	−24.3803	−1.03303	−0.516513	+	0.856279i	$0.672770\pi$
$558$	−2.51664	−0.106538
$559$	22.9707	0.971558
$560$	1.31993	0.0557771
$561$	−55.4192	−2.33980
$562$	7.81717	0.329747
$563$	−43.5665	−1.83611	−0.918054	−	0.396455i	$-0.870240\pi$
$563$	−43.5665	−1.83611	−0.918054	+	0.396455i	$0.870240\pi$
$564$	−15.5832	−0.656173
$565$	7.45211	0.313513
$566$	1.58904	0.0667922
$567$	−6.57523	−0.276134
$568$	−14.9087	−0.625553
$569$	−9.99798	−0.419137	−0.209569	−	0.977794i	$-0.567206\pi$
$569$	−9.99798	−0.419137	−0.209569	+	0.977794i	$0.567206\pi$
$570$	−4.02626	−0.168641
$571$	46.3384	1.93920	0.969601	−	0.244692i	$-0.0786868\pi$
$571$	46.3384	1.93920	0.969601	+	0.244692i	$0.0786868\pi$
$572$	−28.3387	−1.18490
$573$	−23.5338	−0.983138
$574$	2.28831	0.0955123
$575$	−4.65029	−0.193930
$576$	−0.938645	−0.0391102
$577$	−34.4044	−1.43228	−0.716138	−	0.697959i	$-0.754092\pi$
$577$	−34.4044	−1.43228	−0.716138	+	0.697959i	$0.754092\pi$
$578$	−29.1887	−1.21409
$579$	−6.66925	−0.277164
$580$	14.0440	0.583147
$581$	−7.55862	−0.313584
$582$	19.2662	0.798611
$583$	2.91386	0.120680
$584$	−11.0395	−0.456816
$585$	−2.62358	−0.108472
$586$	1.25945	0.0520274
$587$	19.5261	0.805928	0.402964	−	0.915216i	$-0.367980\pi$
$587$	19.5261	0.805928	0.402964	+	0.915216i	$0.367980\pi$
$588$	−2.31484	−0.0954625
$589$	−20.5916	−0.848461
$590$	−2.18158	−0.0898142
$591$	41.1120	1.69112
$592$	−10.5847	−0.435028
$593$	48.4013	1.98760	0.993801	−	0.111173i	$-0.0354607\pi$
$593$	48.4013	1.98760	0.993801	+	0.111173i	$0.0354607\pi$
$594$	18.4416	0.756668
$595$	−7.67249	−0.314541
$596$	−25.7164	−1.05339
$597$	11.5020	0.470744
$598$	12.8463	0.525325
$599$	−18.0912	−0.739186	−0.369593	−	0.929194i	$-0.620503\pi$
$599$	−18.0912	−0.739186	−0.369593	+	0.929194i	$0.620503\pi$
$600$	3.74583	0.152923
$601$	4.90320	0.200006	0.100003	−	0.994987i	$-0.468115\pi$
$601$	4.90320	0.200006	0.100003	+	0.994987i	$0.468115\pi$
$602$	−4.04166	−0.164726
$603$	7.65966	0.311926
$604$	21.7940	0.886786
$605$	11.3165	0.460081
$606$	0.235583	0.00956989
$607$	11.5044	0.466951	0.233475	−	0.972363i	$-0.424990\pi$
$607$	11.5044	0.466951	0.233475	+	0.972363i	$0.424990\pi$
$608$	−21.9818	−0.891481
$609$	−14.1838	−0.574756
$610$	10.7740	0.436227
$611$	26.6743	1.07913
$612$	−7.69103	−0.310891
$613$	−10.8250	−0.437217	−0.218609	−	0.975813i	$-0.570152\pi$
$613$	−10.8250	−0.437217	−0.218609	+	0.975813i	$0.570152\pi$
$614$	3.37030	0.136014
$615$	−5.01862	−0.202370
$616$	11.5731	0.466294
$617$	−29.7309	−1.19692	−0.598461	−	0.801152i	$-0.704221\pi$
$617$	−29.7309	−1.19692	−0.598461	+	0.801152i	$0.704221\pi$
$618$	−2.04993	−0.0824601
$619$	−11.9115	−0.478763	−0.239382	−	0.970926i	$-0.576945\pi$
$619$	−11.9115	−0.478763	−0.239382	+	0.970926i	$0.576945\pi$
$620$	8.25376	0.331479
$621$	26.0390	1.04491
$622$	−8.50359	−0.340963
$623$	−11.8723	−0.475653
$624$	7.99683	0.320129
$625$	1.00000	0.0400000
$626$	16.4115	0.655935
$627$	27.2818	1.08953
$628$	−5.04845	−0.201455
$629$	61.5268	2.45323
$630$	0.461615	0.0183912
$631$	−15.6278	−0.622134	−0.311067	−	0.950388i	$-0.600686\pi$
$631$	−15.6278	−0.622134	−0.311067	+	0.950388i	$0.600686\pi$
$632$	−26.5862	−1.05754
$633$	17.1704	0.682460
$634$	4.58669	0.182161
$635$	−14.1361	−0.560975
$636$	−1.42783	−0.0566173
$637$	3.96239	0.156995
$638$	30.5518	1.20956
$639$	4.02938	0.159400
$640$	10.6514	0.421036
$641$	0.338520	0.0133707	0.00668537	−	0.999978i	$-0.497872\pi$
$641$	0.338520	0.0133707	0.00668537	+	0.999978i	$0.497872\pi$
$642$	−13.1730	−0.519896
$643$	22.7358	0.896614	0.448307	−	0.893880i	$-0.352027\pi$
$643$	22.7358	0.896614	0.448307	+	0.893880i	$0.352027\pi$
$644$	7.04029	0.277426
$645$	8.86399	0.349019
$646$	20.2035	0.794897
$647$	45.7352	1.79803	0.899017	−	0.437913i	$-0.144282\pi$
$647$	45.7352	1.79803	0.899017	+	0.437913i	$0.144282\pi$
$648$	−16.1082	−0.632792
$649$	14.7823	0.580256
$650$	−2.76248	−0.108353
$651$	−8.33589	−0.326709
$652$	29.2474	1.14542
$653$	−18.2643	−0.714736	−0.357368	−	0.933964i	$-0.616326\pi$
$653$	−18.2643	−0.714736	−0.357368	+	0.933964i	$0.616326\pi$
$654$	−16.3394	−0.638923
$655$	−12.5790	−0.491502
$656$	−4.33234	−0.169150
$657$	2.98365	0.116403
$658$	−4.69330	−0.182964
$659$	−39.9921	−1.55787	−0.778936	−	0.627104i	$-0.784240\pi$
$659$	−39.9921	−1.55787	−0.778936	+	0.627104i	$0.784240\pi$
$660$	−10.9354	−0.425660
$661$	−28.7096	−1.11667	−0.558337	−	0.829614i	$-0.688560\pi$
$661$	−28.7096	−1.11667	−0.558337	+	0.829614i	$0.688560\pi$
$662$	0.190462	0.00740253
$663$	−46.4841	−1.80529
$664$	−18.5174	−0.718614
$665$	3.77701	0.146466
$666$	−3.70175	−0.143440
$667$	43.1381	1.67031
$668$	−10.1037	−0.390926
$669$	19.6978	0.761561
$670$	8.06518	0.311585
$671$	−73.0044	−2.81830
$672$	−8.89869	−0.343274
$673$	−9.17514	−0.353676	−0.176838	−	0.984240i	$-0.556587\pi$
$673$	−9.17514	−0.353676	−0.176838	+	0.984240i	$0.556587\pi$
$674$	5.15381	0.198517
$675$	−5.59943	−0.215522
$676$	−4.08841	−0.157247
$677$	49.1575	1.88928	0.944639	−	0.328113i	$-0.106413\pi$
$677$	49.1575	1.88928	0.944639	+	0.328113i	$0.106413\pi$
$678$	−7.94387	−0.305083
$679$	−18.0736	−0.693600
$680$	−18.7964	−0.720807
$681$	−6.59653	−0.252780
$682$	17.9554	0.687550
$683$	3.98060	0.152313	0.0761567	−	0.997096i	$-0.475735\pi$
$683$	3.98060	0.152313	0.0761567	+	0.997096i	$0.475735\pi$
$684$	3.78614	0.144767
$685$	19.9479	0.762168
$686$	−0.697175	−0.0266183
$687$	−1.52901	−0.0583355
$688$	7.65187	0.291725
$689$	2.44406	0.0931115
$690$	4.95716	0.188716
$691$	−23.1412	−0.880331	−0.440166	−	0.897917i	$-0.645080\pi$
$691$	−23.1412	−0.880331	−0.440166	+	0.897917i	$0.645080\pi$
$692$	−25.6056	−0.973380
$693$	−3.12788	−0.118818
$694$	12.4627	0.473079
$695$	16.1146	0.611260
$696$	−34.7480	−1.31712
$697$	25.1831	0.953879
$698$	1.45599	0.0551102
$699$	−40.6066	−1.53588
$700$	−1.51395	−0.0572218
$701$	−5.00780	−0.189142	−0.0945709	−	0.995518i	$-0.530148\pi$
$701$	−5.00780	−0.189142	−0.0945709	+	0.995518i	$0.530148\pi$
$702$	15.4683	0.583813
$703$	−30.2884	−1.14235
$704$	6.69695	0.252401
$705$	10.2931	0.387661
$706$	−3.90391	−0.146926
$707$	−0.220999	−0.00831152
$708$	−7.24354	−0.272229
$709$	26.9826	1.01335	0.506676	−	0.862137i	$-0.330874\pi$
$709$	26.9826	1.01335	0.506676	+	0.862137i	$0.330874\pi$
$710$	4.24271	0.159226
$711$	7.18549	0.269477
$712$	−29.0852	−1.09001
$713$	25.3525	0.949459
$714$	8.17880	0.306084
$715$	18.7184	0.700030
$716$	15.9787	0.597153
$717$	−24.1876	−0.903303
$718$	13.1576	0.491036
$719$	−43.8113	−1.63388	−0.816942	−	0.576719i	$-0.804333\pi$
$719$	−43.8113	−1.63388	−0.816942	+	0.576719i	$0.804333\pi$
$720$	−0.873951	−0.0325702
$721$	1.92303	0.0716172
$722$	3.30055	0.122834
$723$	18.2069	0.677123
$724$	−36.3534	−1.35106
$725$	−9.27644	−0.344518
$726$	−12.0633	−0.447710
$727$	−9.47224	−0.351306	−0.175653	−	0.984452i	$-0.556204\pi$
$727$	−9.47224	−0.351306	−0.175653	+	0.984452i	$0.556204\pi$
$728$	9.70720	0.359773
$729$	30.0384	1.11253
$730$	3.14162	0.116276
$731$	−44.4789	−1.64511
$732$	35.7732	1.32221
$733$	13.4871	0.498158	0.249079	−	0.968483i	$-0.419872\pi$
$733$	13.4871	0.498158	0.249079	+	0.968483i	$0.419872\pi$
$734$	8.00612	0.295511
$735$	1.52901	0.0563985
$736$	27.0642	0.997599
$737$	−54.6494	−2.01304
$738$	−1.51514	−0.0557731
$739$	18.2183	0.670171	0.335086	−	0.942188i	$-0.391235\pi$
$739$	18.2183	0.670171	0.335086	+	0.942188i	$0.391235\pi$
$740$	12.1406	0.446296
$741$	22.8832	0.840634
$742$	−0.430029	−0.0157869
$743$	34.0968	1.25089	0.625445	−	0.780268i	$-0.284917\pi$
$743$	34.0968	1.25089	0.625445	+	0.780268i	$0.284917\pi$
$744$	−20.4216	−0.748691
$745$	16.9863	0.622332
$746$	15.5593	0.569667
$747$	5.00472	0.183113
$748$	54.8731	2.00636
$749$	12.3575	0.451534
$750$	−1.06599	−0.0389244
$751$	−22.9160	−0.836217	−0.418108	−	0.908397i	$-0.637307\pi$
$751$	−22.9160	−0.836217	−0.418108	+	0.908397i	$0.637307\pi$
$752$	8.88558	0.324024
$753$	28.1709	1.02660
$754$	25.6260	0.933242
$755$	−14.3955	−0.523906
$756$	8.47723	0.308314
$757$	−11.2025	−0.407163	−0.203581	−	0.979058i	$-0.565258\pi$
$757$	−11.2025	−0.407163	−0.203581	+	0.979058i	$0.565258\pi$
$758$	−7.72356	−0.280532
$759$	−33.5895	−1.21922
$760$	9.25307	0.335644
$761$	18.0174	0.653130	0.326565	−	0.945175i	$-0.394109\pi$
$761$	18.0174	0.653130	0.326565	+	0.945175i	$0.394109\pi$
$762$	15.0690	0.545891
$763$	15.3280	0.554909
$764$	23.3019	0.843033
$765$	5.08012	0.183672
$766$	10.1972	0.368441
$767$	12.3990	0.447701
$768$	−15.6895	−0.566146
$769$	−5.72651	−0.206503	−0.103252	−	0.994655i	$-0.532925\pi$
$769$	−5.72651	−0.206503	−0.103252	+	0.994655i	$0.532925\pi$
$770$	−3.29348	−0.118689
$771$	21.9495	0.790491
$772$	6.60353	0.237666
$773$	36.9155	1.32776	0.663879	−	0.747840i	$-0.268909\pi$
$773$	36.9155	1.32776	0.663879	+	0.747840i	$0.268909\pi$
$774$	2.67607	0.0961894
$775$	−5.45181	−0.195835
$776$	−44.2773	−1.58946
$777$	−12.2614	−0.439874
$778$	−17.3884	−0.623404
$779$	−12.3971	−0.444174
$780$	−9.17230	−0.328421
$781$	−28.7484	−1.02870
$782$	−24.8747	−0.889518
$783$	51.9428	1.85628
$784$	1.31993	0.0471402
$785$	3.33463	0.119018
$786$	13.4091	0.478286
$787$	−49.8936	−1.77852	−0.889258	−	0.457406i	$-0.848779\pi$
$787$	−49.8936	−1.77852	−0.889258	+	0.457406i	$0.848779\pi$
$788$	−40.7070	−1.45013
$789$	1.70526	0.0607090
$790$	7.56591	0.269183
$791$	7.45211	0.264967
$792$	−7.66280	−0.272286
$793$	−61.2340	−2.17448
$794$	17.8461	0.633335
$795$	0.943120	0.0334490
$796$	−11.3886	−0.403659
$797$	15.1048	0.535041	0.267520	−	0.963552i	$-0.413796\pi$
$797$	15.1048	0.535041	0.267520	+	0.963552i	$0.413796\pi$
$798$	−4.02626	−0.142528
$799$	−51.6503	−1.82725
$800$	−5.81989	−0.205764
$801$	7.86089	0.277751
$802$	−4.49860	−0.158851
$803$	−21.2875	−0.751218
$804$	26.7790	0.944421
$805$	−4.65029	−0.163901
$806$	15.0605	0.530484
$807$	5.81529	0.204708
$808$	−0.541411	−0.0190468
$809$	−40.8619	−1.43663	−0.718313	−	0.695720i	$-0.755086\pi$
$809$	−40.8619	−1.43663	−0.718313	+	0.695720i	$0.755086\pi$
$810$	4.58409	0.161069
$811$	23.9044	0.839398	0.419699	−	0.907663i	$-0.362136\pi$
$811$	23.9044	0.839398	0.419699	+	0.907663i	$0.362136\pi$
$812$	14.0440	0.492849
$813$	0.625955	0.0219532
$814$	26.4109	0.925701
$815$	−19.3186	−0.676702
$816$	−15.4845	−0.542066
$817$	21.8961	0.766047
$818$	20.8306	0.728324
$819$	−2.62358	−0.0916753
$820$	4.96917	0.173531
$821$	12.1283	0.423282	0.211641	−	0.977347i	$-0.432119\pi$
$821$	12.1283	0.423282	0.211641	+	0.977347i	$0.432119\pi$
$822$	−21.2642	−0.741675
$823$	4.96249	0.172981	0.0864907	−	0.996253i	$-0.472435\pi$
$823$	4.96249	0.172981	0.0864907	+	0.996253i	$0.472435\pi$
$824$	4.71110	0.164119
$825$	7.22311	0.251476
$826$	−2.18158	−0.0759069
$827$	−52.7248	−1.83342	−0.916710	−	0.399554i	$-0.869165\pi$
$827$	−52.7248	−1.83342	−0.916710	+	0.399554i	$0.869165\pi$
$828$	−4.66152	−0.161999
$829$	23.9696	0.832498	0.416249	−	0.909251i	$-0.363345\pi$
$829$	23.9696	0.832498	0.416249	+	0.909251i	$0.363345\pi$
$830$	5.26968	0.182913
$831$	9.24153	0.320585
$832$	5.61721	0.194742
$833$	−7.67249	−0.265836
$834$	−17.1779	−0.594824
$835$	6.67378	0.230956
$836$	−27.0130	−0.934262
$837$	30.5270	1.05517
$838$	−3.08326	−0.106510
$839$	44.4759	1.53548	0.767739	−	0.640763i	$-0.221382\pi$
$839$	44.4759	1.53548	0.767739	+	0.640763i	$0.221382\pi$
$840$	3.74583	0.129243
$841$	57.0523	1.96732
$842$	−10.2186	−0.352155
$843$	−17.1443	−0.590479
$844$	−17.0012	−0.585204
$845$	2.70050	0.0929001
$846$	3.10753	0.106839
$847$	11.3165	0.388839
$848$	0.814153	0.0279581
$849$	−3.48500	−0.119605
$850$	5.34907	0.183472
$851$	37.2913	1.27833
$852$	14.0871	0.482617
$853$	20.6686	0.707681	0.353841	−	0.935306i	$-0.384876\pi$
$853$	20.6686	0.707681	0.353841	+	0.935306i	$0.384876\pi$
$854$	10.7740	0.368679
$855$	−2.50084	−0.0855269
$856$	30.2739	1.03474
$857$	−28.4467	−0.971721	−0.485860	−	0.874037i	$-0.661494\pi$
$857$	−28.4467	−0.971721	−0.485860	+	0.874037i	$0.661494\pi$
$858$	−19.9537	−0.681207
$859$	−19.5899	−0.668400	−0.334200	−	0.942502i	$-0.608466\pi$
$859$	−19.5899	−0.668400	−0.334200	+	0.942502i	$0.608466\pi$
$860$	−8.77665	−0.299281
$861$	−5.01862	−0.171034
$862$	−22.0959	−0.752588
$863$	32.3277	1.10045	0.550224	−	0.835017i	$-0.314542\pi$
$863$	32.3277	1.10045	0.550224	+	0.835017i	$0.314542\pi$
$864$	32.5881	1.10867
$865$	16.9132	0.575065
$866$	3.76309	0.127875
$867$	64.0153	2.17407
$868$	8.25376	0.280151
$869$	−51.2663	−1.73909
$870$	9.88859	0.335255
$871$	−45.8383	−1.55317
$872$	37.5510	1.27164
$873$	11.9669	0.405018
$874$	12.2453	0.414204
$875$	1.00000	0.0338062
$876$	10.4312	0.352436
$877$	27.8378	0.940015	0.470008	−	0.882662i	$-0.344251\pi$
$877$	27.8378	0.940015	0.470008	+	0.882662i	$0.344251\pi$
$878$	9.75864	0.329338
$879$	−2.76217	−0.0931656
$880$	6.23538	0.210195
$881$	−23.8446	−0.803345	−0.401672	−	0.915783i	$-0.631571\pi$
$881$	−23.8446	−0.803345	−0.401672	+	0.915783i	$0.631571\pi$
$882$	0.461615	0.0155434
$883$	39.9582	1.34470	0.672350	−	0.740234i	$-0.265285\pi$
$883$	39.9582	1.34470	0.672350	+	0.740234i	$0.265285\pi$
$884$	46.0260	1.54802
$885$	4.78454	0.160831
$886$	−27.0270	−0.907990
$887$	−29.6297	−0.994869	−0.497434	−	0.867502i	$-0.665724\pi$
$887$	−29.6297	−0.994869	−0.497434	+	0.867502i	$0.665724\pi$
$888$	−30.0384	−1.00802
$889$	−14.1361	−0.474110
$890$	8.27707	0.277448
$891$	−31.0616	−1.04060
$892$	−19.5037	−0.653032
$893$	25.4264	0.850862
$894$	−18.1073	−0.605598
$895$	−10.5544	−0.352793
$896$	10.6514	0.355840
$897$	−28.1739	−0.940701
$898$	−23.6692	−0.789850
$899$	50.5734	1.68672
$900$	1.00242	0.0334139
$901$	−4.73252	−0.157663
$902$	10.8101	0.359936
$903$	8.86399	0.294975
$904$	18.2565	0.607201
$905$	24.0123	0.798196
$906$	15.3455	0.509819
$907$	−16.7706	−0.556859	−0.278429	−	0.960457i	$-0.589814\pi$
$907$	−16.7706	−0.556859	−0.278429	+	0.960457i	$0.589814\pi$
$908$	6.53153	0.216757
$909$	0.146328	0.00485339
$910$	−2.76248	−0.0915753
$911$	31.4051	1.04050	0.520248	−	0.854015i	$-0.325839\pi$
$911$	31.4051	1.04050	0.520248	+	0.854015i	$0.325839\pi$
$912$	7.62271	0.252413
$913$	−35.7072	−1.18173
$914$	−26.2950	−0.869762
$915$	−23.6291	−0.781153
$916$	1.51395	0.0500222
$917$	−12.5790	−0.415395
$918$	−29.9517	−0.988555
$919$	−28.0975	−0.926851	−0.463426	−	0.886136i	$-0.653380\pi$
$919$	−28.0975	−0.926851	−0.463426	+	0.886136i	$0.653380\pi$
$920$	−11.3924	−0.375598
$921$	−7.39157	−0.243561
$922$	−4.66468	−0.153623
$923$	−24.1134	−0.793701
$924$	−10.9354	−0.359748
$925$	−8.01914	−0.263668
$926$	−10.8035	−0.355024
$927$	−1.27328	−0.0418199
$928$	53.9879	1.77224
$929$	49.3619	1.61951	0.809756	−	0.586767i	$-0.199599\pi$
$929$	49.3619	1.61951	0.809756	+	0.586767i	$0.199599\pi$
$930$	5.81158	0.190569
$931$	3.77701	0.123787
$932$	40.2065	1.31701
$933$	18.6497	0.610563
$934$	7.08453	0.231813
$935$	−36.2451	−1.18534
$936$	−6.42734	−0.210084
$937$	37.9770	1.24066	0.620328	−	0.784343i	$-0.287000\pi$
$937$	37.9770	1.24066	0.620328	+	0.784343i	$0.287000\pi$
$938$	8.06518	0.263338
$939$	−35.9929	−1.17458
$940$	−10.1917	−0.332417
$941$	29.0378	0.946605	0.473303	−	0.880900i	$-0.343062\pi$
$941$	29.0378	0.946605	0.473303	+	0.880900i	$0.343062\pi$
$942$	−3.55468	−0.115818
$943$	15.2635	0.497047
$944$	4.13027	0.134429
$945$	−5.59943	−0.182149
$946$	−19.0930	−0.620765
$947$	54.8824	1.78344	0.891720	−	0.452588i	$-0.149499\pi$
$947$	54.8824	1.78344	0.891720	+	0.452588i	$0.149499\pi$
$948$	25.1212	0.815899
$949$	−17.8553	−0.579608
$950$	−2.63324	−0.0854336
$951$	−10.0593	−0.326196
$952$	−18.7964	−0.609193
$953$	41.8487	1.35561	0.677806	−	0.735241i	$-0.262931\pi$
$953$	41.8487	1.35561	0.677806	+	0.735241i	$0.262931\pi$
$954$	0.284731	0.00921852
$955$	−15.3915	−0.498057
$956$	23.9493	0.774575
$957$	−67.0047	−2.16595
$958$	11.6380	0.376008
$959$	19.9479	0.644150
$960$	2.16758	0.0699583
$961$	−1.27771	−0.0412166
$962$	22.1527	0.714232
$963$	−8.18217	−0.263667
$964$	−18.0275	−0.580627
$965$	−4.36180	−0.140411
$966$	4.95716	0.159494
$967$	15.2877	0.491620	0.245810	−	0.969318i	$-0.420946\pi$
$967$	15.2877	0.491620	0.245810	+	0.969318i	$0.420946\pi$
$968$	27.7236	0.891069
$969$	−44.3094	−1.42342
$970$	12.6004	0.404576
$971$	28.8325	0.925281	0.462640	−	0.886546i	$-0.346902\pi$
$971$	28.8325	0.925281	0.462640	+	0.886546i	$0.346902\pi$
$972$	−10.2111	−0.327520
$973$	16.1146	0.516609
$974$	−7.87753	−0.252412
$975$	6.05854	0.194028
$976$	−20.3979	−0.652921
$977$	3.95679	0.126589	0.0632945	−	0.997995i	$-0.479839\pi$
$977$	3.95679	0.126589	0.0632945	+	0.997995i	$0.479839\pi$
$978$	20.5935	0.658507
$979$	−56.0851	−1.79249
$980$	−1.51395	−0.0483612
$981$	−10.1490	−0.324031
$982$	−0.437681	−0.0139670
$983$	−13.0285	−0.415544	−0.207772	−	0.978177i	$-0.566621\pi$
$983$	−13.0285	−0.415544	−0.207772	+	0.978177i	$0.566621\pi$
$984$	−12.2948	−0.391944
$985$	26.8880	0.856722
$986$	−49.6203	−1.58023
$987$	10.2931	0.327634
$988$	−22.6577	−0.720837
$989$	−26.9586	−0.857235
$990$	2.18068	0.0693066
$991$	56.4201	1.79225	0.896123	−	0.443807i	$-0.146372\pi$
$991$	56.4201	1.79225	0.896123	+	0.443807i	$0.146372\pi$
$992$	31.7290	1.00740
$993$	−0.417713	−0.0132557
$994$	4.24271	0.134571
$995$	7.52248	0.238479
$996$	17.4970	0.554414
$997$	−47.6258	−1.50832	−0.754162	−	0.656689i	$-0.771956\pi$
$997$	−47.6258	−1.50832	−0.754162	+	0.656689i	$0.771956\pi$
$998$	29.7451	0.941565
$999$	44.9026	1.42066

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8015.2.a.h.1.15	✓	38

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8015.2.a.h.1.15	✓	38	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)

\(f(q)\)	\(=\)	\(q-0.697175 q^{2} +1.52901 q^{3} -1.51395 q^{4} +1.00000 q^{5} -1.06599 q^{6} +1.00000 q^{7} +2.44984 q^{8} -0.662121 q^{9} +O(q^{10})\)	\(q-0.697175 q^{2} +1.52901 q^{3} -1.51395 q^{4} +1.00000 q^{5} -1.06599 q^{6} +1.00000 q^{7} +2.44984 q^{8} -0.662121 q^{9} -0.697175 q^{10} +4.72403 q^{11} -2.31484 q^{12} +3.96239 q^{13} -0.697175 q^{14} +1.52901 q^{15} +1.31993 q^{16} -7.67249 q^{17} +0.461615 q^{18} +3.77701 q^{19} -1.51395 q^{20} +1.52901 q^{21} -3.29348 q^{22} -4.65029 q^{23} +3.74583 q^{24} +1.00000 q^{25} -2.76248 q^{26} -5.59943 q^{27} -1.51395 q^{28} -9.27644 q^{29} -1.06599 q^{30} -5.45181 q^{31} -5.81989 q^{32} +7.22311 q^{33} +5.34907 q^{34} +1.00000 q^{35} +1.00242 q^{36} -8.01914 q^{37} -2.63324 q^{38} +6.05854 q^{39} +2.44984 q^{40} -3.28226 q^{41} -1.06599 q^{42} +5.79720 q^{43} -7.15193 q^{44} -0.662121 q^{45} +3.24207 q^{46} +6.73188 q^{47} +2.01818 q^{48} +1.00000 q^{49} -0.697175 q^{50} -11.7313 q^{51} -5.99884 q^{52} +0.616816 q^{53} +3.90378 q^{54} +4.72403 q^{55} +2.44984 q^{56} +5.77510 q^{57} +6.46731 q^{58} +3.12917 q^{59} -2.31484 q^{60} -15.4538 q^{61} +3.80087 q^{62} -0.662121 q^{63} +1.41763 q^{64} +3.96239 q^{65} -5.03577 q^{66} -11.5684 q^{67} +11.6157 q^{68} -7.11035 q^{69} -0.697175 q^{70} -6.08557 q^{71} -1.62209 q^{72} -4.50621 q^{73} +5.59075 q^{74} +1.52901 q^{75} -5.71820 q^{76} +4.72403 q^{77} -4.22386 q^{78} -10.8522 q^{79} +1.31993 q^{80} -6.57523 q^{81} +2.28831 q^{82} -7.55862 q^{83} -2.31484 q^{84} -7.67249 q^{85} -4.04166 q^{86} -14.1838 q^{87} +11.5731 q^{88} -11.8723 q^{89} +0.461615 q^{90} +3.96239 q^{91} +7.04029 q^{92} -8.33589 q^{93} -4.69330 q^{94} +3.77701 q^{95} -8.89869 q^{96} -18.0736 q^{97} -0.697175 q^{98} -3.12788 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 38 q - 6 q^{2} - 9 q^{3} + 24 q^{4} + 38 q^{5} - 10 q^{6} + 38 q^{7} - 21 q^{8} + 13 q^{9}+O(q^{10}) \) 38 * q - 6 * q^2 - 9 * q^3 + 24 * q^4 + 38 * q^5 - 10 * q^6 + 38 * q^7 - 21 * q^8 + 13 * q^9	\( 38 q - 6 q^{2} - 9 q^{3} + 24 q^{4} + 38 q^{5} - 10 q^{6} + 38 q^{7} - 21 q^{8} + 13 q^{9} - 6 q^{10} - 18 q^{11} - 20 q^{12} - 25 q^{13} - 6 q^{14} - 9 q^{15} - 21 q^{17} - 7 q^{18} - 14 q^{19} + 24 q^{20} - 9 q^{21} - 11 q^{22} - 16 q^{23} - 10 q^{24} + 38 q^{25} - 21 q^{26} - 15 q^{27} + 24 q^{28} - 52 q^{29} - 10 q^{30} - 30 q^{31} - 8 q^{32} - 13 q^{33} - 9 q^{34} + 38 q^{35} - 16 q^{36} - 47 q^{37} - 10 q^{38} - 50 q^{39} - 21 q^{40} - 35 q^{41} - 10 q^{42} - 18 q^{43} - 22 q^{44} + 13 q^{45} - 17 q^{46} - 23 q^{47} - 13 q^{48} + 38 q^{49} - 6 q^{50} - 5 q^{51} - 41 q^{52} - 12 q^{53} + 35 q^{54} - 18 q^{55} - 21 q^{56} - 3 q^{57} - 16 q^{58} - 16 q^{59} - 20 q^{60} - 47 q^{61} + 14 q^{62} + 13 q^{63} - 55 q^{64} - 25 q^{65} - 6 q^{66} - 54 q^{67} + 31 q^{68} - 95 q^{69} - 6 q^{70} - 41 q^{71} - 59 q^{73} - q^{74} - 9 q^{75} - 23 q^{76} - 18 q^{77} + 19 q^{78} - 117 q^{79} - 38 q^{81} + 19 q^{82} - 21 q^{83} - 20 q^{84} - 21 q^{85} - 12 q^{86} - 14 q^{87} - 40 q^{88} - 96 q^{89} - 7 q^{90} - 25 q^{91} + 53 q^{92} - 53 q^{93} - 28 q^{94} - 14 q^{95} + 40 q^{96} - 70 q^{97} - 6 q^{98} - 52 q^{99}+O(q^{100}) \) 38 * q - 6 * q^2 - 9 * q^3 + 24 * q^4 + 38 * q^5 - 10 * q^6 + 38 * q^7 - 21 * q^8 + 13 * q^9 - 6 * q^10 - 18 * q^11 - 20 * q^12 - 25 * q^13 - 6 * q^14 - 9 * q^15 - 21 * q^17 - 7 * q^18 - 14 * q^19 + 24 * q^20 - 9 * q^21 - 11 * q^22 - 16 * q^23 - 10 * q^24 + 38 * q^25 - 21 * q^26 - 15 * q^27 + 24 * q^28 - 52 * q^29 - 10 * q^30 - 30 * q^31 - 8 * q^32 - 13 * q^33 - 9 * q^34 + 38 * q^35 - 16 * q^36 - 47 * q^37 - 10 * q^38 - 50 * q^39 - 21 * q^40 - 35 * q^41 - 10 * q^42 - 18 * q^43 - 22 * q^44 + 13 * q^45 - 17 * q^46 - 23 * q^47 - 13 * q^48 + 38 * q^49 - 6 * q^50 - 5 * q^51 - 41 * q^52 - 12 * q^53 + 35 * q^54 - 18 * q^55 - 21 * q^56 - 3 * q^57 - 16 * q^58 - 16 * q^59 - 20 * q^60 - 47 * q^61 + 14 * q^62 + 13 * q^63 - 55 * q^64 - 25 * q^65 - 6 * q^66 - 54 * q^67 + 31 * q^68 - 95 * q^69 - 6 * q^70 - 41 * q^71 - 59 * q^73 - q^74 - 9 * q^75 - 23 * q^76 - 18 * q^77 + 19 * q^78 - 117 * q^79 - 38 * q^81 + 19 * q^82 - 21 * q^83 - 20 * q^84 - 21 * q^85 - 12 * q^86 - 14 * q^87 - 40 * q^88 - 96 * q^89 - 7 * q^90 - 25 * q^91 + 53 * q^92 - 53 * q^93 - 28 * q^94 - 14 * q^95 + 40 * q^96 - 70 * q^97 - 6 * q^98 - 52 * q^99

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