LMFDB - Embedded newform 8015.2.a.h.1.1

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			1.1
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)

$f(q)$	$=$	$q-2.60567 q^{2} -1.96600 q^{3} +4.78952 q^{4} +1.00000 q^{5} +5.12274 q^{6} +1.00000 q^{7} -7.26856 q^{8} +0.865151 q^{9} +O(q^{10})$	\(q-2.60567 q^{2} -1.96600 q^{3} +4.78952 q^{4} +1.00000 q^{5} +5.12274 q^{6} +1.00000 q^{7} -7.26856 q^{8} +0.865151 q^{9} -2.60567 q^{10} +0.861554 q^{11} -9.41618 q^{12} +1.22457 q^{13} -2.60567 q^{14} -1.96600 q^{15} +9.36043 q^{16} +6.95763 q^{17} -2.25430 q^{18} +3.11797 q^{19} +4.78952 q^{20} -1.96600 q^{21} -2.24492 q^{22} +5.50154 q^{23} +14.2900 q^{24} +1.00000 q^{25} -3.19082 q^{26} +4.19711 q^{27} +4.78952 q^{28} -7.82077 q^{29} +5.12274 q^{30} -7.87291 q^{31} -9.85307 q^{32} -1.69381 q^{33} -18.1293 q^{34} +1.00000 q^{35} +4.14366 q^{36} +1.73002 q^{37} -8.12441 q^{38} -2.40750 q^{39} -7.26856 q^{40} -4.72745 q^{41} +5.12274 q^{42} -8.26885 q^{43} +4.12643 q^{44} +0.865151 q^{45} -14.3352 q^{46} -0.377712 q^{47} -18.4026 q^{48} +1.00000 q^{49} -2.60567 q^{50} -13.6787 q^{51} +5.86508 q^{52} -0.141692 q^{53} -10.9363 q^{54} +0.861554 q^{55} -7.26856 q^{56} -6.12993 q^{57} +20.3783 q^{58} +4.69996 q^{59} -9.41618 q^{60} +2.58528 q^{61} +20.5142 q^{62} +0.865151 q^{63} +6.95299 q^{64} +1.22457 q^{65} +4.41352 q^{66} -0.162978 q^{67} +33.3237 q^{68} -10.8160 q^{69} -2.60567 q^{70} +2.32936 q^{71} -6.28840 q^{72} +4.98682 q^{73} -4.50786 q^{74} -1.96600 q^{75} +14.9336 q^{76} +0.861554 q^{77} +6.27314 q^{78} -8.99213 q^{79} +9.36043 q^{80} -10.8470 q^{81} +12.3182 q^{82} -9.60779 q^{83} -9.41618 q^{84} +6.95763 q^{85} +21.5459 q^{86} +15.3756 q^{87} -6.26225 q^{88} -7.56192 q^{89} -2.25430 q^{90} +1.22457 q^{91} +26.3497 q^{92} +15.4781 q^{93} +0.984193 q^{94} +3.11797 q^{95} +19.3711 q^{96} -9.53161 q^{97} -2.60567 q^{98} +0.745374 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.60567	−1.84249	−0.921243	−	0.388987i	$-0.872825\pi$
$2$	−2.60567	−1.84249	−0.921243	+	0.388987i	$0.872825\pi$
$3$	−1.96600	−1.13507	−0.567535	−	0.823349i	$-0.692103\pi$
$3$	−1.96600	−1.13507	−0.567535	+	0.823349i	$0.692103\pi$
$4$	4.78952	2.39476
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	5.12274	2.09135
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−7.26856	−2.56982
$9$	0.865151	0.288384
$10$	−2.60567	−0.823985
$11$	0.861554	0.259768	0.129884	−	0.991529i	$-0.458539\pi$
$11$	0.861554	0.259768	0.129884	+	0.991529i	$0.458539\pi$
$12$	−9.41618	−2.71822
$13$	1.22457	0.339634	0.169817	−	0.985476i	$-0.445682\pi$
$13$	1.22457	0.339634	0.169817	+	0.985476i	$0.445682\pi$
$14$	−2.60567	−0.696395
$15$	−1.96600	−0.507619
$16$	9.36043	2.34011
$17$	6.95763	1.68747	0.843736	−	0.536758i	$-0.180351\pi$
$17$	6.95763	1.68747	0.843736	+	0.536758i	$0.180351\pi$
$18$	−2.25430	−0.531343
$19$	3.11797	0.715312	0.357656	−	0.933853i	$-0.383576\pi$
$19$	3.11797	0.715312	0.357656	+	0.933853i	$0.383576\pi$
$20$	4.78952	1.07097
$21$	−1.96600	−0.429016
$22$	−2.24492	−0.478620
$23$	5.50154	1.14715	0.573576	−	0.819153i	$-0.305556\pi$
$23$	5.50154	1.14715	0.573576	+	0.819153i	$0.305556\pi$
$24$	14.2900	2.91693
$25$	1.00000	0.200000
$26$	−3.19082	−0.625770
$27$	4.19711	0.807734
$28$	4.78952	0.905133
$29$	−7.82077	−1.45228	−0.726140	−	0.687547i	$-0.758688\pi$
$29$	−7.82077	−1.45228	−0.726140	+	0.687547i	$0.758688\pi$
$30$	5.12274	0.935281
$31$	−7.87291	−1.41402	−0.707008	−	0.707205i	$-0.749956\pi$
$31$	−7.87291	−1.41402	−0.707008	+	0.707205i	$0.749956\pi$
$32$	−9.85307	−1.74179
$33$	−1.69381	−0.294855
$34$	−18.1293	−3.10915
$35$	1.00000	0.169031
$36$	4.14366	0.690609
$37$	1.73002	0.284413	0.142207	−	0.989837i	$-0.454580\pi$
$37$	1.73002	0.284413	0.142207	+	0.989837i	$0.454580\pi$
$38$	−8.12441	−1.31795
$39$	−2.40750	−0.385508
$40$	−7.26856	−1.14926
$41$	−4.72745	−0.738303	−0.369152	−	0.929369i	$-0.620352\pi$
$41$	−4.72745	−0.738303	−0.369152	+	0.929369i	$0.620352\pi$
$42$	5.12274	0.790457
$43$	−8.26885	−1.26099	−0.630494	−	0.776194i	$-0.717148\pi$
$43$	−8.26885	−1.26099	−0.630494	+	0.776194i	$0.717148\pi$
$44$	4.12643	0.622082
$45$	0.865151	0.128969
$46$	−14.3352	−2.11361
$47$	−0.377712	−0.0550950	−0.0275475	−	0.999620i	$-0.508770\pi$
$47$	−0.377712	−0.0550950	−0.0275475	+	0.999620i	$0.508770\pi$
$48$	−18.4026	−2.65618
$49$	1.00000	0.142857
$50$	−2.60567	−0.368497
$51$	−13.6787	−1.91540
$52$	5.86508	0.813340
$53$	−0.141692	−0.0194630	−0.00973148	−	0.999953i	$-0.503098\pi$
$53$	−0.141692	−0.0194630	−0.00973148	+	0.999953i	$0.503098\pi$
$54$	−10.9363	−1.48824
$55$	0.861554	0.116172
$56$	−7.26856	−0.971302
$57$	−6.12993	−0.811930
$58$	20.3783	2.67581
$59$	4.69996	0.611883	0.305942	−	0.952050i	$-0.401029\pi$
$59$	4.69996	0.611883	0.305942	+	0.952050i	$0.401029\pi$
$60$	−9.41618	−1.21562
$61$	2.58528	0.331012	0.165506	−	0.986209i	$-0.447074\pi$
$61$	2.58528	0.331012	0.165506	+	0.986209i	$0.447074\pi$
$62$	20.5142	2.60531
$63$	0.865151	0.108999
$64$	6.95299	0.869124
$65$	1.22457	0.151889
$66$	4.41352	0.543267
$67$	−0.162978	−0.0199109	−0.00995544	−	0.999950i	$-0.503169\pi$
$67$	−0.162978	−0.0199109	−0.00995544	+	0.999950i	$0.503169\pi$
$68$	33.3237	4.04109
$69$	−10.8160	−1.30210
$70$	−2.60567	−0.311437
$71$	2.32936	0.276444	0.138222	−	0.990401i	$-0.455861\pi$
$71$	2.32936	0.276444	0.138222	+	0.990401i	$0.455861\pi$
$72$	−6.28840	−0.741095
$73$	4.98682	0.583663	0.291832	−	0.956470i	$-0.405735\pi$
$73$	4.98682	0.583663	0.291832	+	0.956470i	$0.405735\pi$
$74$	−4.50786	−0.524028
$75$	−1.96600	−0.227014
$76$	14.9336	1.71300
$77$	0.861554	0.0981832
$78$	6.27314	0.710293
$79$	−8.99213	−1.01169	−0.505847	−	0.862623i	$-0.668820\pi$
$79$	−8.99213	−1.01169	−0.505847	+	0.862623i	$0.668820\pi$
$80$	9.36043	1.04653
$81$	−10.8470	−1.20522
$82$	12.3182	1.36031
$83$	−9.60779	−1.05459	−0.527296	−	0.849682i	$-0.676794\pi$
$83$	−9.60779	−1.05459	−0.527296	+	0.849682i	$0.676794\pi$
$84$	−9.41618	−1.02739
$85$	6.95763	0.754661
$86$	21.5459	2.32335
$87$	15.3756	1.64844
$88$	−6.26225	−0.667558
$89$	−7.56192	−0.801562	−0.400781	−	0.916174i	$-0.631261\pi$
$89$	−7.56192	−0.801562	−0.400781	+	0.916174i	$0.631261\pi$
$90$	−2.25430	−0.237624
$91$	1.22457	0.128369
$92$	26.3497	2.74715
$93$	15.4781	1.60501
$94$	0.984193	0.101512
$95$	3.11797	0.319897
$96$	19.3711	1.97706
$97$	−9.53161	−0.967789	−0.483894	−	0.875126i	$-0.660778\pi$
$97$	−9.53161	−0.967789	−0.483894	+	0.875126i	$0.660778\pi$
$98$	−2.60567	−0.263212
$99$	0.745374	0.0749129
$100$	4.78952	0.478952
$101$	−19.2461	−1.91506	−0.957531	−	0.288329i	$-0.906900\pi$
$101$	−19.2461	−1.91506	−0.957531	+	0.288329i	$0.906900\pi$
$102$	35.6421	3.52910
$103$	−18.1976	−1.79306	−0.896531	−	0.442981i	$-0.853921\pi$
$103$	−18.1976	−1.79306	−0.896531	+	0.442981i	$0.853921\pi$
$104$	−8.90083	−0.872798
$105$	−1.96600	−0.191862
$106$	0.369204	0.0358602
$107$	0.321158	0.0310475	0.0155237	−	0.999879i	$-0.495058\pi$
$107$	0.321158	0.0310475	0.0155237	+	0.999879i	$0.495058\pi$
$108$	20.1021	1.93433
$109$	0.0525574	0.00503408	0.00251704	−	0.999997i	$-0.499199\pi$
$109$	0.0525574	0.00503408	0.00251704	+	0.999997i	$0.499199\pi$
$110$	−2.24492	−0.214045
$111$	−3.40121	−0.322829
$112$	9.36043	0.884477
$113$	17.7908	1.67362	0.836808	−	0.547497i	$-0.184419\pi$
$113$	17.7908	1.67362	0.836808	+	0.547497i	$0.184419\pi$
$114$	15.9726	1.49597
$115$	5.50154	0.513022
$116$	−37.4577	−3.47786
$117$	1.05944	0.0979448
$118$	−12.2466	−1.12739
$119$	6.95763	0.637805
$120$	14.2900	1.30449
$121$	−10.2577	−0.932520
$122$	−6.73640	−0.609885
$123$	9.29415	0.838026
$124$	−37.7074	−3.38623
$125$	1.00000	0.0894427
$126$	−2.25430	−0.200829
$127$	13.6114	1.20781	0.603907	−	0.797055i	$-0.293610\pi$
$127$	13.6114	1.20781	0.603907	+	0.797055i	$0.293610\pi$
$128$	1.58894	0.140444
$129$	16.2566	1.43131
$130$	−3.19082	−0.279853
$131$	−9.86174	−0.861624	−0.430812	−	0.902442i	$-0.641773\pi$
$131$	−9.86174	−0.861624	−0.430812	+	0.902442i	$0.641773\pi$
$132$	−8.11255	−0.706107
$133$	3.11797	0.270363
$134$	0.424666	0.0366855
$135$	4.19711	0.361230
$136$	−50.5719	−4.33650
$137$	−20.2219	−1.72767	−0.863835	−	0.503775i	$-0.831944\pi$
$137$	−20.2219	−1.72767	−0.863835	+	0.503775i	$0.831944\pi$
$138$	28.1830	2.39910
$139$	1.45893	0.123745	0.0618725	−	0.998084i	$-0.480293\pi$
$139$	1.45893	0.123745	0.0618725	+	0.998084i	$0.480293\pi$
$140$	4.78952	0.404788
$141$	0.742582	0.0625366
$142$	−6.06954	−0.509345
$143$	1.05503	0.0882260
$144$	8.09818	0.674849
$145$	−7.82077	−0.649480
$146$	−12.9940	−1.07539
$147$	−1.96600	−0.162153
$148$	8.28595	0.681101
$149$	5.88646	0.482238	0.241119	−	0.970496i	$-0.422486\pi$
$149$	5.88646	0.482238	0.241119	+	0.970496i	$0.422486\pi$
$150$	5.12274	0.418270
$151$	−18.9288	−1.54040	−0.770201	−	0.637802i	$-0.779844\pi$
$151$	−18.9288	−1.54040	−0.770201	+	0.637802i	$0.779844\pi$
$152$	−22.6632	−1.83823
$153$	6.01940	0.486640
$154$	−2.24492	−0.180901
$155$	−7.87291	−0.632367
$156$	−11.5307	−0.923198
$157$	−19.0172	−1.51774	−0.758870	−	0.651242i	$-0.774248\pi$
$157$	−19.0172	−1.51774	−0.758870	+	0.651242i	$0.774248\pi$
$158$	23.4305	1.86403
$159$	0.278567	0.0220918
$160$	−9.85307	−0.778953
$161$	5.50154	0.433582
$162$	28.2636	2.22060
$163$	−7.16128	−0.560915	−0.280457	−	0.959866i	$-0.590486\pi$
$163$	−7.16128	−0.560915	−0.280457	+	0.959866i	$0.590486\pi$
$164$	−22.6422	−1.76806
$165$	−1.69381	−0.131863
$166$	25.0347	1.94307
$167$	3.28663	0.254327	0.127164	−	0.991882i	$-0.459413\pi$
$167$	3.28663	0.254327	0.127164	+	0.991882i	$0.459413\pi$
$168$	14.2900	1.10250
$169$	−11.5004	−0.884649
$170$	−18.1293	−1.39045
$171$	2.69752	0.206284
$172$	−39.6038	−3.01976
$173$	−20.6699	−1.57151	−0.785754	−	0.618540i	$-0.787725\pi$
$173$	−20.6699	−1.57151	−0.785754	+	0.618540i	$0.787725\pi$
$174$	−40.0638	−3.03723
$175$	1.00000	0.0755929
$176$	8.06451	0.607885
$177$	−9.24012	−0.694530
$178$	19.7039	1.47687
$179$	5.93604	0.443680	0.221840	−	0.975083i	$-0.428794\pi$
$179$	5.93604	0.443680	0.221840	+	0.975083i	$0.428794\pi$
$180$	4.14366	0.308850
$181$	−16.3490	−1.21521	−0.607606	−	0.794239i	$-0.707870\pi$
$181$	−16.3490	−1.21521	−0.607606	+	0.794239i	$0.707870\pi$
$182$	−3.19082	−0.236519
$183$	−5.08266	−0.375721
$184$	−39.9883	−2.94797
$185$	1.73002	0.127194
$186$	−40.3309	−2.95721
$187$	5.99437	0.438352
$188$	−1.80906	−0.131939
$189$	4.19711	0.305295
$190$	−8.12441	−0.589407
$191$	10.5424	0.762820	0.381410	−	0.924406i	$-0.375439\pi$
$191$	10.5424	0.762820	0.381410	+	0.924406i	$0.375439\pi$
$192$	−13.6696	−0.986516
$193$	−13.1762	−0.948441	−0.474220	−	0.880406i	$-0.657270\pi$
$193$	−13.1762	−0.948441	−0.474220	+	0.880406i	$0.657270\pi$
$194$	24.8362	1.78314
$195$	−2.40750	−0.172404
$196$	4.78952	0.342108
$197$	15.5258	1.10616	0.553082	−	0.833127i	$-0.313451\pi$
$197$	15.5258	1.10616	0.553082	+	0.833127i	$0.313451\pi$
$198$	−1.94220	−0.138026
$199$	−3.09386	−0.219318	−0.109659	−	0.993969i	$-0.534976\pi$
$199$	−3.09386	−0.219318	−0.109659	+	0.993969i	$0.534976\pi$
$200$	−7.26856	−0.513965
$201$	0.320414	0.0226002
$202$	50.1491	3.52848
$203$	−7.82077	−0.548910
$204$	−65.5143	−4.58692
$205$	−4.72745	−0.330179
$206$	47.4169	3.30369
$207$	4.75967	0.330820
$208$	11.4625	0.794779
$209$	2.68630	0.185815
$210$	5.12274	0.353503
$211$	7.48294	0.515147	0.257573	−	0.966259i	$-0.417077\pi$
$211$	7.48294	0.515147	0.257573	+	0.966259i	$0.417077\pi$
$212$	−0.678638	−0.0466090
$213$	−4.57952	−0.313783
$214$	−0.836830	−0.0572046
$215$	−8.26885	−0.563931
$216$	−30.5069	−2.07573
$217$	−7.87291	−0.534448
$218$	−0.136947	−0.00927523
$219$	−9.80409	−0.662499
$220$	4.12643	0.278204
$221$	8.52008	0.573122
$222$	8.86244	0.594808
$223$	0.935296	0.0626321	0.0313160	−	0.999510i	$-0.490030\pi$
$223$	0.935296	0.0626321	0.0313160	+	0.999510i	$0.490030\pi$
$224$	−9.85307	−0.658336
$225$	0.865151	0.0576768
$226$	−46.3569	−3.08361
$227$	2.79241	0.185338	0.0926692	−	0.995697i	$-0.470460\pi$
$227$	2.79241	0.185338	0.0926692	+	0.995697i	$0.470460\pi$
$228$	−29.3594	−1.94437
$229$	−1.00000	−0.0660819
$229$	−1.00000	−0.0660819
$230$	−14.3352	−0.945236
$231$	−1.69381	−0.111445
$232$	56.8457	3.73210
$233$	10.9435	0.716933	0.358467	−	0.933543i	$-0.383300\pi$
$233$	10.9435	0.716933	0.358467	+	0.933543i	$0.383300\pi$
$234$	−2.76054	−0.180462
$235$	−0.377712	−0.0246392
$236$	22.5105	1.46531
$237$	17.6785	1.14834
$238$	−18.1293	−1.17515
$239$	16.8269	1.08844	0.544221	−	0.838942i	$-0.316825\pi$
$239$	16.8269	1.08844	0.544221	+	0.838942i	$0.316825\pi$
$240$	−18.4026	−1.18788
$241$	7.76715	0.500326	0.250163	−	0.968204i	$-0.419516\pi$
$241$	7.76715	0.500326	0.250163	+	0.968204i	$0.419516\pi$
$242$	26.7282	1.71816
$243$	8.73379	0.560273
$244$	12.3823	0.792693
$245$	1.00000	0.0638877
$246$	−24.2175	−1.54405
$247$	3.81817	0.242944
$248$	57.2247	3.63377
$249$	18.8889	1.19704
$250$	−2.60567	−0.164797
$251$	24.2097	1.52810	0.764050	−	0.645157i	$-0.223208\pi$
$251$	24.2097	1.52810	0.764050	+	0.645157i	$0.223208\pi$
$252$	4.14366	0.261026
$253$	4.73988	0.297993
$254$	−35.4668	−2.22538
$255$	−13.6787	−0.856593
$256$	−18.0462	−1.12789
$257$	−12.6170	−0.787030	−0.393515	−	0.919318i	$-0.628741\pi$
$257$	−12.6170	−0.787030	−0.393515	+	0.919318i	$0.628741\pi$
$258$	−42.3592	−2.63717
$259$	1.73002	0.107498
$260$	5.86508	0.363737
$261$	−6.76615	−0.418814
$262$	25.6964	1.58753
$263$	−21.0124	−1.29568	−0.647840	−	0.761776i	$-0.724328\pi$
$263$	−21.0124	−1.29568	−0.647840	+	0.761776i	$0.724328\pi$
$264$	12.3116	0.757725
$265$	−0.141692	−0.00870410
$266$	−8.12441	−0.498140
$267$	14.8667	0.909829
$268$	−0.780584	−0.0476817
$269$	−5.93523	−0.361878	−0.180939	−	0.983494i	$-0.557914\pi$
$269$	−5.93523	−0.361878	−0.180939	+	0.983494i	$0.557914\pi$
$270$	−10.9363	−0.665561
$271$	7.44301	0.452131	0.226065	−	0.974112i	$-0.427414\pi$
$271$	7.44301	0.452131	0.226065	+	0.974112i	$0.427414\pi$
$272$	65.1264	3.94887
$273$	−2.40750	−0.145708
$274$	52.6915	3.18321
$275$	0.861554	0.0519536
$276$	−51.8035	−3.11821
$277$	−3.95539	−0.237656	−0.118828	−	0.992915i	$-0.537914\pi$
$277$	−3.95539	−0.237656	−0.118828	+	0.992915i	$0.537914\pi$
$278$	−3.80149	−0.227998
$279$	−6.81126	−0.407779
$280$	−7.26856	−0.434379
$281$	8.47584	0.505626	0.252813	−	0.967515i	$-0.418644\pi$
$281$	8.47584	0.505626	0.252813	+	0.967515i	$0.418644\pi$
$282$	−1.93492	−0.115223
$283$	27.2636	1.62065	0.810327	−	0.585979i	$-0.199290\pi$
$283$	27.2636	1.62065	0.810327	+	0.585979i	$0.199290\pi$
$284$	11.1565	0.662017
$285$	−6.12993	−0.363106
$286$	−2.74906	−0.162555
$287$	−4.72745	−0.279052
$288$	−8.52439	−0.502305
$289$	31.4086	1.84756
$290$	20.3783	1.19666
$291$	18.7391	1.09851
$292$	23.8845	1.39773
$293$	−2.35996	−0.137870	−0.0689352	−	0.997621i	$-0.521960\pi$
$293$	−2.35996	−0.137870	−0.0689352	+	0.997621i	$0.521960\pi$
$294$	5.12274	0.298764
$295$	4.69996	0.273642
$296$	−12.5747	−0.730892
$297$	3.61604	0.209824
$298$	−15.3382	−0.888517
$299$	6.73700	0.389611
$300$	−9.41618	−0.543643
$301$	−8.26885	−0.476609
$302$	49.3221	2.83817
$303$	37.8379	2.17373
$304$	29.1856	1.67391
$305$	2.58528	0.148033
$306$	−15.6846	−0.896627
$307$	2.66565	0.152137	0.0760683	−	0.997103i	$-0.475763\pi$
$307$	2.66565	0.152137	0.0760683	+	0.997103i	$0.475763\pi$
$308$	4.12643	0.235125
$309$	35.7764	2.03525
$310$	20.5142	1.16513
$311$	6.59436	0.373932	0.186966	−	0.982366i	$-0.440135\pi$
$311$	6.59436	0.373932	0.186966	+	0.982366i	$0.440135\pi$
$312$	17.4990	0.990687
$313$	−5.17264	−0.292375	−0.146187	−	0.989257i	$-0.546700\pi$
$313$	−5.17264	−0.292375	−0.146187	+	0.989257i	$0.546700\pi$
$314$	49.5526	2.79642
$315$	0.865151	0.0487458
$316$	−43.0679	−2.42276
$317$	26.2881	1.47649	0.738243	−	0.674535i	$-0.235656\pi$
$317$	26.2881	1.47649	0.738243	+	0.674535i	$0.235656\pi$
$318$	−0.725854	−0.0407039
$319$	−6.73801	−0.377256
$320$	6.95299	0.388684
$321$	−0.631395	−0.0352410
$322$	−14.3352	−0.798870
$323$	21.6937	1.20707
$324$	−51.9517	−2.88621
$325$	1.22457	0.0679267
$326$	18.6599	1.03348
$327$	−0.103328	−0.00571404
$328$	34.3617	1.89731
$329$	−0.377712	−0.0208239
$330$	4.41352	0.242956
$331$	−31.4426	−1.72824	−0.864120	−	0.503285i	$-0.832124\pi$
$331$	−31.4426	−1.72824	−0.864120	+	0.503285i	$0.832124\pi$
$332$	−46.0167	−2.52549
$333$	1.49673	0.0820202
$334$	−8.56387	−0.468594
$335$	−0.162978	−0.00890442
$336$	−18.4026	−1.00394
$337$	−20.2944	−1.10551	−0.552753	−	0.833345i	$-0.686423\pi$
$337$	−20.2944	−1.10551	−0.552753	+	0.833345i	$0.686423\pi$
$338$	29.9663	1.62995
$339$	−34.9766	−1.89967
$340$	33.3237	1.80723
$341$	−6.78294	−0.367317
$342$	−7.02885	−0.380076
$343$	1.00000	0.0539949
$344$	60.1026	3.24052
$345$	−10.8160	−0.582315
$346$	53.8591	2.89548
$347$	21.5231	1.15542	0.577710	−	0.816242i	$-0.303946\pi$
$347$	21.5231	1.15542	0.577710	+	0.816242i	$0.303946\pi$
$348$	73.6418	3.94761
$349$	−7.44752	−0.398657	−0.199328	−	0.979933i	$-0.563876\pi$
$349$	−7.44752	−0.398657	−0.199328	+	0.979933i	$0.563876\pi$
$350$	−2.60567	−0.139279
$351$	5.13964	0.274334
$352$	−8.48895	−0.452462
$353$	16.1037	0.857114	0.428557	−	0.903515i	$-0.359022\pi$
$353$	16.1037	0.857114	0.428557	+	0.903515i	$0.359022\pi$
$354$	24.0767	1.27966
$355$	2.32936	0.123630
$356$	−36.2179	−1.91955
$357$	−13.6787	−0.723953
$358$	−15.4674	−0.817475
$359$	−19.3250	−1.01993	−0.509966	−	0.860194i	$-0.670342\pi$
$359$	−19.3250	−1.01993	−0.509966	+	0.860194i	$0.670342\pi$
$360$	−6.28840	−0.331428
$361$	−9.27823	−0.488328
$362$	42.6001	2.23901
$363$	20.1667	1.05848
$364$	5.86508	0.307414
$365$	4.98682	0.261022
$366$	13.2437	0.692262
$367$	−27.9152	−1.45716	−0.728581	−	0.684959i	$-0.759820\pi$
$367$	−27.9152	−1.45716	−0.728581	+	0.684959i	$0.759820\pi$
$368$	51.4968	2.68446
$369$	−4.08996	−0.212915
$370$	−4.50786	−0.234352
$371$	−0.141692	−0.00735630
$372$	74.1328	3.84360
$373$	1.53000	0.0792202	0.0396101	−	0.999215i	$-0.487388\pi$
$373$	1.53000	0.0792202	0.0396101	+	0.999215i	$0.487388\pi$
$374$	−15.6193	−0.807657
$375$	−1.96600	−0.101524
$376$	2.74542	0.141584
$377$	−9.57705	−0.493243
$378$	−10.9363	−0.562502
$379$	−18.2557	−0.937732	−0.468866	−	0.883269i	$-0.655337\pi$
$379$	−18.2557	−0.937732	−0.468866	+	0.883269i	$0.655337\pi$
$380$	14.9336	0.766077
$381$	−26.7600	−1.37095
$382$	−27.4700	−1.40549
$383$	−29.4974	−1.50724	−0.753622	−	0.657308i	$-0.771695\pi$
$383$	−29.4974	−1.50724	−0.753622	+	0.657308i	$0.771695\pi$
$384$	−3.12386	−0.159414
$385$	0.861554	0.0439088
$386$	34.3327	1.74749
$387$	−7.15381	−0.363649
$388$	−45.6518	−2.31762
$389$	−0.159084	−0.00806586	−0.00403293	−	0.999992i	$-0.501284\pi$
$389$	−0.159084	−0.00806586	−0.00403293	+	0.999992i	$0.501284\pi$
$390$	6.27314	0.317653
$391$	38.2777	1.93579
$392$	−7.26856	−0.367118
$393$	19.3882	0.978004
$394$	−40.4550	−2.03809
$395$	−8.99213	−0.452443
$396$	3.56998	0.179398
$397$	12.2518	0.614899	0.307450	−	0.951564i	$-0.400524\pi$
$397$	12.2518	0.614899	0.307450	+	0.951564i	$0.400524\pi$
$398$	8.06158	0.404090
$399$	−6.12993	−0.306881
$400$	9.36043	0.468021
$401$	−13.7220	−0.685245	−0.342622	−	0.939473i	$-0.611315\pi$
$401$	−13.7220	−0.685245	−0.342622	+	0.939473i	$0.611315\pi$
$402$	−0.834892	−0.0416406
$403$	−9.64090	−0.480248
$404$	−92.1797	−4.58611
$405$	−10.8470	−0.538990
$406$	20.3783	1.01136
$407$	1.49050	0.0738816
$408$	99.4243	4.92224
$409$	14.0406	0.694263	0.347131	−	0.937817i	$-0.387156\pi$
$409$	14.0406	0.694263	0.347131	+	0.937817i	$0.387156\pi$
$410$	12.3182	0.608351
$411$	39.7562	1.96103
$412$	−87.1576	−4.29395
$413$	4.69996	0.231270
$414$	−12.4021	−0.609531
$415$	−9.60779	−0.471628
$416$	−12.0657	−0.591571
$417$	−2.86826	−0.140459
$418$	−6.99962	−0.342363
$419$	−22.4740	−1.09792	−0.548962	−	0.835847i	$-0.684977\pi$
$419$	−22.4740	−1.09792	−0.548962	+	0.835847i	$0.684977\pi$
$420$	−9.41618	−0.459463
$421$	14.5533	0.709283	0.354641	−	0.935002i	$-0.384603\pi$
$421$	14.5533	0.709283	0.354641	+	0.935002i	$0.384603\pi$
$422$	−19.4981	−0.949151
$423$	−0.326778	−0.0158885
$424$	1.02990	0.0500163
$425$	6.95763	0.337494
$426$	11.9327	0.578142
$427$	2.58528	0.125111
$428$	1.53819	0.0743512
$429$	−2.07419	−0.100143
$430$	21.5459	1.03904
$431$	−2.76627	−0.133247	−0.0666233	−	0.997778i	$-0.521223\pi$
$431$	−2.76627	−0.133247	−0.0666233	+	0.997778i	$0.521223\pi$
$432$	39.2867	1.89018
$433$	−4.28370	−0.205862	−0.102931	−	0.994689i	$-0.532822\pi$
$433$	−4.28370	−0.205862	−0.102931	+	0.994689i	$0.532822\pi$
$434$	20.5142	0.984713
$435$	15.3756	0.737205
$436$	0.251724	0.0120554
$437$	17.1537	0.820572
$438$	25.5462	1.22065
$439$	18.4232	0.879291	0.439646	−	0.898171i	$-0.355104\pi$
$439$	18.4232	0.879291	0.439646	+	0.898171i	$0.355104\pi$
$440$	−6.26225	−0.298541
$441$	0.865151	0.0411977
$442$	−22.2005	−1.05597
$443$	12.3138	0.585048	0.292524	−	0.956258i	$-0.405505\pi$
$443$	12.3138	0.585048	0.292524	+	0.956258i	$0.405505\pi$
$444$	−16.2902	−0.773097
$445$	−7.56192	−0.358469
$446$	−2.43707	−0.115399
$447$	−11.5728	−0.547374
$448$	6.95299	0.328498
$449$	15.0723	0.711307	0.355653	−	0.934618i	$-0.384258\pi$
$449$	15.0723	0.711307	0.355653	+	0.934618i	$0.384258\pi$
$450$	−2.25430	−0.106269
$451$	−4.07295	−0.191788
$452$	85.2092	4.00790
$453$	37.2139	1.74846
$454$	−7.27609	−0.341484
$455$	1.22457	0.0574086
$456$	44.5558	2.08652
$457$	−14.7545	−0.690189	−0.345094	−	0.938568i	$-0.612153\pi$
$457$	−14.7545	−0.690189	−0.345094	+	0.938568i	$0.612153\pi$
$458$	2.60567	0.121755
$459$	29.2019	1.36303
$460$	26.3497	1.22856
$461$	31.3884	1.46191	0.730953	−	0.682428i	$-0.239076\pi$
$461$	31.3884	1.46191	0.730953	+	0.682428i	$0.239076\pi$
$462$	4.41352	0.205336
$463$	−2.42654	−0.112771	−0.0563853	−	0.998409i	$-0.517958\pi$
$463$	−2.42654	−0.112771	−0.0563853	+	0.998409i	$0.517958\pi$
$464$	−73.2057	−3.39849
$465$	15.4781	0.717781
$466$	−28.5152	−1.32094
$467$	33.2715	1.53962	0.769811	−	0.638271i	$-0.220350\pi$
$467$	33.2715	1.53962	0.769811	+	0.638271i	$0.220350\pi$
$468$	5.07418	0.234554
$469$	−0.162978	−0.00752561
$470$	0.984193	0.0453974
$471$	37.3879	1.72274
$472$	−34.1619	−1.57243
$473$	−7.12406	−0.327565
$474$	−46.0644	−2.11581
$475$	3.11797	0.143062
$476$	33.3237	1.52739
$477$	−0.122585	−0.00561280
$478$	−43.8453	−2.00544
$479$	−16.3071	−0.745089	−0.372544	−	0.928014i	$-0.621515\pi$
$479$	−16.3071	−0.745089	−0.372544	+	0.928014i	$0.621515\pi$
$480$	19.3711	0.884167
$481$	2.11852	0.0965963
$482$	−20.2386	−0.921844
$483$	−10.8160	−0.492146
$484$	−49.1295	−2.23316
$485$	−9.53161	−0.432808
$486$	−22.7574	−1.03230
$487$	13.6642	0.619185	0.309592	−	0.950869i	$-0.399807\pi$
$487$	13.6642	0.619185	0.309592	+	0.950869i	$0.399807\pi$
$488$	−18.7913	−0.850641
$489$	14.0791	0.636678
$490$	−2.60567	−0.117712
$491$	−6.90374	−0.311562	−0.155781	−	0.987792i	$-0.549789\pi$
$491$	−6.90374	−0.311562	−0.155781	+	0.987792i	$0.549789\pi$
$492$	44.5145	2.00687
$493$	−54.4140	−2.45068
$494$	−9.94888	−0.447621
$495$	0.745374	0.0335021
$496$	−73.6938	−3.30895
$497$	2.32936	0.104486
$498$	−49.2182	−2.20552
$499$	−19.1296	−0.856360	−0.428180	−	0.903693i	$-0.640845\pi$
$499$	−19.1296	−0.856360	−0.428180	+	0.903693i	$0.640845\pi$
$500$	4.78952	0.214194
$501$	−6.46151	−0.288679
$502$	−63.0824	−2.81550
$503$	37.4808	1.67119	0.835593	−	0.549349i	$-0.185124\pi$
$503$	37.4808	1.67119	0.835593	+	0.549349i	$0.185124\pi$
$504$	−6.28840	−0.280108
$505$	−19.2461	−0.856442
$506$	−12.3506	−0.549049
$507$	22.6098	1.00414
$508$	65.1919	2.89242
$509$	38.4517	1.70434	0.852171	−	0.523263i	$-0.175285\pi$
$509$	38.4517	1.70434	0.852171	+	0.523263i	$0.175285\pi$
$510$	35.6421	1.57826
$511$	4.98682	0.220604
$512$	43.8446	1.93768
$513$	13.0865	0.577782
$514$	32.8759	1.45009
$515$	−18.1976	−0.801882
$516$	77.8610	3.42764
$517$	−0.325419	−0.0143119
$518$	−4.50786	−0.198064
$519$	40.6371	1.78377
$520$	−8.90083	−0.390327
$521$	−15.1576	−0.664068	−0.332034	−	0.943267i	$-0.607735\pi$
$521$	−15.1576	−0.664068	−0.332034	+	0.943267i	$0.607735\pi$
$522$	17.6304	0.771660
$523$	−29.2860	−1.28059	−0.640294	−	0.768130i	$-0.721188\pi$
$523$	−29.2860	−1.28059	−0.640294	+	0.768130i	$0.721188\pi$
$524$	−47.2330	−2.06338
$525$	−1.96600	−0.0858032
$526$	54.7514	2.38727
$527$	−54.7768	−2.38611
$528$	−15.8548	−0.689992
$529$	7.26698	0.315956
$530$	0.369204	0.0160372
$531$	4.06618	0.176457
$532$	14.9336	0.647453
$533$	−5.78907	−0.250753
$534$	−38.7378	−1.67635
$535$	0.321158	0.0138848
$536$	1.18461	0.0511674
$537$	−11.6702	−0.503608
$538$	15.4653	0.666755
$539$	0.861554	0.0371097
$540$	20.1021	0.865058
$541$	−43.2600	−1.85989	−0.929945	−	0.367697i	$-0.880146\pi$
$541$	−43.2600	−1.85989	−0.929945	+	0.367697i	$0.880146\pi$
$542$	−19.3940	−0.833045
$543$	32.1421	1.37935
$544$	−68.5540	−2.93923
$545$	0.0525574	0.00225131
$546$	6.27314	0.268466
$547$	13.2296	0.565655	0.282828	−	0.959171i	$-0.408728\pi$
$547$	13.2296	0.565655	0.282828	+	0.959171i	$0.408728\pi$
$548$	−96.8529	−4.13735
$549$	2.23666	0.0954584
$550$	−2.24492	−0.0957239
$551$	−24.3850	−1.03883
$552$	78.6169	3.34616
$553$	−8.99213	−0.382384
$554$	10.3064	0.437879
$555$	−3.40121	−0.144374
$556$	6.98757	0.296339
$557$	−17.8173	−0.754942	−0.377471	−	0.926021i	$-0.623206\pi$
$557$	−17.8173	−0.754942	−0.377471	+	0.926021i	$0.623206\pi$
$558$	17.7479	0.751328
$559$	−10.1258	−0.428274
$560$	9.36043	0.395550
$561$	−11.7849	−0.497560
$562$	−22.0852	−0.931610
$563$	8.00298	0.337285	0.168643	−	0.985677i	$-0.446062\pi$
$563$	8.00298	0.337285	0.168643	+	0.985677i	$0.446062\pi$
$564$	3.55661	0.149760
$565$	17.7908	0.748464
$566$	−71.0399	−2.98603
$567$	−10.8470	−0.455530
$568$	−16.9311	−0.710412
$569$	18.7212	0.784832	0.392416	−	0.919788i	$-0.371639\pi$
$569$	18.7212	0.784832	0.392416	+	0.919788i	$0.371639\pi$
$570$	15.9726	0.669018
$571$	−18.6431	−0.780190	−0.390095	−	0.920775i	$-0.627558\pi$
$571$	−18.6431	−0.780190	−0.390095	+	0.920775i	$0.627558\pi$
$572$	5.05308	0.211280
$573$	−20.7263	−0.865854
$574$	12.3182	0.514150
$575$	5.50154	0.229430
$576$	6.01539	0.250641
$577$	−35.5995	−1.48203	−0.741014	−	0.671490i	$-0.765655\pi$
$577$	−35.5995	−1.48203	−0.741014	+	0.671490i	$0.765655\pi$
$578$	−81.8404	−3.40411
$579$	25.9043	1.07655
$580$	−37.4577	−1.55535
$581$	−9.60779	−0.398598
$582$	−48.8280	−2.02399
$583$	−0.122076	−0.00505586
$584$	−36.2470	−1.49991
$585$	1.05944	0.0438022
$586$	6.14928	0.254024
$587$	−2.92781	−0.120843	−0.0604217	−	0.998173i	$-0.519245\pi$
$587$	−2.92781	−0.120843	−0.0604217	+	0.998173i	$0.519245\pi$
$588$	−9.41618	−0.388317
$589$	−24.5475	−1.01146
$590$	−12.2466	−0.504183
$591$	−30.5236	−1.25557
$592$	16.1937	0.665557
$593$	29.4624	1.20988	0.604939	−	0.796272i	$-0.293198\pi$
$593$	29.4624	1.20988	0.604939	+	0.796272i	$0.293198\pi$
$594$	−9.42220	−0.386597
$595$	6.95763	0.285235
$596$	28.1933	1.15484
$597$	6.08252	0.248941
$598$	−17.5544	−0.717853
$599$	−15.9038	−0.649810	−0.324905	−	0.945747i	$-0.605332\pi$
$599$	−15.9038	−0.649810	−0.324905	+	0.945747i	$0.605332\pi$
$600$	14.2900	0.583386
$601$	10.0525	0.410049	0.205025	−	0.978757i	$-0.434273\pi$
$601$	10.0525	0.410049	0.205025	+	0.978757i	$0.434273\pi$
$602$	21.5459	0.878146
$603$	−0.141000	−0.00574197
$604$	−90.6596	−3.68889
$605$	−10.2577	−0.417036
$606$	−98.5930	−4.00507
$607$	4.51800	0.183380	0.0916899	−	0.995788i	$-0.470773\pi$
$607$	4.51800	0.183380	0.0916899	+	0.995788i	$0.470773\pi$
$608$	−30.7216	−1.24593
$609$	15.3756	0.623052
$610$	−6.73640	−0.272749
$611$	−0.462533	−0.0187121
$612$	28.8300	1.16538
$613$	41.5370	1.67766	0.838832	−	0.544390i	$-0.183239\pi$
$613$	41.5370	1.67766	0.838832	+	0.544390i	$0.183239\pi$
$614$	−6.94580	−0.280310
$615$	9.29415	0.374776
$616$	−6.26225	−0.252313
$617$	−33.9438	−1.36652	−0.683262	−	0.730173i	$-0.739439\pi$
$617$	−33.9438	−1.36652	−0.683262	+	0.730173i	$0.739439\pi$
$618$	−93.2216	−3.74992
$619$	19.1929	0.771428	0.385714	−	0.922618i	$-0.373955\pi$
$619$	19.1929	0.771428	0.385714	+	0.922618i	$0.373955\pi$
$620$	−37.7074	−1.51437
$621$	23.0906	0.926593
$622$	−17.1827	−0.688964
$623$	−7.56192	−0.302962
$624$	−22.5352	−0.902129
$625$	1.00000	0.0400000
$626$	13.4782	0.538697
$627$	−5.28127	−0.210914
$628$	−91.0833	−3.63462
$629$	12.0368	0.479940
$630$	−2.25430	−0.0898134
$631$	7.92296	0.315408	0.157704	−	0.987486i	$-0.449591\pi$
$631$	7.92296	0.315408	0.157704	+	0.987486i	$0.449591\pi$
$632$	65.3598	2.59987
$633$	−14.7114	−0.584727
$634$	−68.4981	−2.72041
$635$	13.6114	0.540151
$636$	1.33420	0.0529045
$637$	1.22457	0.0485191
$638$	17.5570	0.695090
$639$	2.01525	0.0797220
$640$	1.58894	0.0628084
$641$	0.529885	0.0209292	0.0104646	−	0.999945i	$-0.496669\pi$
$641$	0.529885	0.0209292	0.0104646	+	0.999945i	$0.496669\pi$
$642$	1.64521	0.0649312
$643$	35.6898	1.40747	0.703734	−	0.710464i	$-0.251515\pi$
$643$	35.6898	1.40747	0.703734	+	0.710464i	$0.251515\pi$
$644$	26.3497	1.03832
$645$	16.2566	0.640101
$646$	−56.5266	−2.22401
$647$	9.22154	0.362536	0.181268	−	0.983434i	$-0.441980\pi$
$647$	9.22154	0.362536	0.181268	+	0.983434i	$0.441980\pi$
$648$	78.8418	3.09720
$649$	4.04927	0.158948
$650$	−3.19082	−0.125154
$651$	15.4781	0.606636
$652$	−34.2991	−1.34326
$653$	5.31820	0.208117	0.104059	−	0.994571i	$-0.466817\pi$
$653$	5.31820	0.208117	0.104059	+	0.994571i	$0.466817\pi$
$654$	0.269238	0.0105280
$655$	−9.86174	−0.385330
$656$	−44.2509	−1.72771
$657$	4.31436	0.168319
$658$	0.984193	0.0383678
$659$	−36.8728	−1.43636	−0.718180	−	0.695857i	$-0.755025\pi$
$659$	−36.8728	−1.43636	−0.718180	+	0.695857i	$0.755025\pi$
$660$	−8.11255	−0.315780
$661$	3.46496	0.134771	0.0673856	−	0.997727i	$-0.478534\pi$
$661$	3.46496	0.134771	0.0673856	+	0.997727i	$0.478534\pi$
$662$	81.9290	3.18426
$663$	−16.7505	−0.650534
$664$	69.8348	2.71011
$665$	3.11797	0.120910
$666$	−3.89998	−0.151121
$667$	−43.0263	−1.66599
$668$	15.7414	0.609052
$669$	−1.83879	−0.0710918
$670$	0.424666	0.0164063
$671$	2.22736	0.0859863
$672$	19.3711	0.747257
$673$	−13.0270	−0.502153	−0.251077	−	0.967967i	$-0.580785\pi$
$673$	−13.0270	−0.502153	−0.251077	+	0.967967i	$0.580785\pi$
$674$	52.8805	2.03688
$675$	4.19711	0.161547
$676$	−55.0815	−2.11852
$677$	−36.9142	−1.41873	−0.709364	−	0.704843i	$-0.751018\pi$
$677$	−36.9142	−1.41873	−0.709364	+	0.704843i	$0.751018\pi$
$678$	91.1376	3.50012
$679$	−9.53161	−0.365790
$680$	−50.5719	−1.93934
$681$	−5.48987	−0.210372
$682$	17.6741	0.676776
$683$	−28.4030	−1.08681	−0.543405	−	0.839471i	$-0.682865\pi$
$683$	−28.4030	−1.08681	−0.543405	+	0.839471i	$0.682865\pi$
$684$	12.9198	0.494001
$685$	−20.2219	−0.772638
$686$	−2.60567	−0.0994849
$687$	1.96600	0.0750075
$688$	−77.4000	−2.95085
$689$	−0.173512	−0.00661027
$690$	28.1830	1.07291
$691$	40.4448	1.53859	0.769297	−	0.638891i	$-0.220607\pi$
$691$	40.4448	1.53859	0.769297	+	0.638891i	$0.220607\pi$
$692$	−98.9990	−3.76338
$693$	0.745374	0.0283144
$694$	−56.0821	−2.12885
$695$	1.45893	0.0553404
$696$	−111.759	−4.23620
$697$	−32.8918	−1.24587
$698$	19.4058	0.734520
$699$	−21.5149	−0.813769
$700$	4.78952	0.181027
$701$	13.9795	0.527999	0.263999	−	0.964523i	$-0.414958\pi$
$701$	13.9795	0.527999	0.263999	+	0.964523i	$0.414958\pi$
$702$	−13.3922	−0.505456
$703$	5.39416	0.203444
$704$	5.99037	0.225771
$705$	0.742582	0.0279672
$706$	−41.9609	−1.57922
$707$	−19.2461	−0.723826
$708$	−44.2557	−1.66323
$709$	−17.5697	−0.659843	−0.329922	−	0.944008i	$-0.607022\pi$
$709$	−17.5697	−0.659843	−0.329922	+	0.944008i	$0.607022\pi$
$710$	−6.06954	−0.227786
$711$	−7.77955	−0.291756
$712$	54.9642	2.05987
$713$	−43.3132	−1.62209
$714$	35.6421	1.33387
$715$	1.05503	0.0394559
$716$	28.4307	1.06251
$717$	−33.0817	−1.23546
$718$	50.3545	1.87921
$719$	33.8977	1.26417	0.632086	−	0.774898i	$-0.282199\pi$
$719$	33.8977	1.26417	0.632086	+	0.774898i	$0.282199\pi$
$720$	8.09818	0.301802
$721$	−18.1976	−0.677714
$722$	24.1760	0.899738
$723$	−15.2702	−0.567905
$724$	−78.3038	−2.91014
$725$	−7.82077	−0.290456
$726$	−52.5477	−1.95023
$727$	52.3507	1.94158	0.970790	−	0.239930i	$-0.0771244\pi$
$727$	52.3507	1.94158	0.970790	+	0.239930i	$0.0771244\pi$
$728$	−8.90083	−0.329887
$729$	15.3703	0.569269
$730$	−12.9940	−0.480930
$731$	−57.5316	−2.12788
$732$	−24.3435	−0.899762
$733$	−6.19828	−0.228939	−0.114469	−	0.993427i	$-0.536517\pi$
$733$	−6.19828	−0.228939	−0.114469	+	0.993427i	$0.536517\pi$
$734$	72.7378	2.68480
$735$	−1.96600	−0.0725170
$736$	−54.2071	−1.99810
$737$	−0.140414	−0.00517221
$738$	10.6571	0.392292
$739$	37.6257	1.38408	0.692042	−	0.721858i	$-0.256711\pi$
$739$	37.6257	1.38408	0.692042	+	0.721858i	$0.256711\pi$
$740$	8.28595	0.304598
$741$	−7.50651	−0.275759
$742$	0.369204	0.0135539
$743$	0.272170	0.00998493	0.00499247	−	0.999988i	$-0.498411\pi$
$743$	0.272170	0.00998493	0.00499247	+	0.999988i	$0.498411\pi$
$744$	−112.504	−4.12459
$745$	5.88646	0.215663
$746$	−3.98667	−0.145962
$747$	−8.31219	−0.304127
$748$	28.7101	1.04975
$749$	0.321158	0.0117348
$750$	5.12274	0.187056
$751$	−1.03379	−0.0377236	−0.0188618	−	0.999822i	$-0.506004\pi$
$751$	−1.03379	−0.0377236	−0.0188618	+	0.999822i	$0.506004\pi$
$752$	−3.53555	−0.128928
$753$	−47.5962	−1.73450
$754$	24.9546	0.908794
$755$	−18.9288	−0.688888
$756$	20.1021	0.731107
$757$	25.8640	0.940043	0.470022	−	0.882655i	$-0.344246\pi$
$757$	25.8640	0.940043	0.470022	+	0.882655i	$0.344246\pi$
$758$	47.5683	1.72776
$759$	−9.31859	−0.338243
$760$	−22.6632	−0.822080
$761$	−27.0394	−0.980177	−0.490088	−	0.871673i	$-0.663036\pi$
$761$	−27.0394	−0.980177	−0.490088	+	0.871673i	$0.663036\pi$
$762$	69.7276	2.52596
$763$	0.0525574	0.00190270
$764$	50.4929	1.82677
$765$	6.01940	0.217632
$766$	76.8604	2.77708
$767$	5.75542	0.207816
$768$	35.4789	1.28023
$769$	−9.19142	−0.331451	−0.165726	−	0.986172i	$-0.552997\pi$
$769$	−9.19142	−0.331451	−0.165726	+	0.986172i	$0.552997\pi$
$770$	−2.24492	−0.0809015
$771$	24.8051	0.893334
$772$	−63.1074	−2.27129
$773$	19.2364	0.691885	0.345942	−	0.938256i	$-0.387559\pi$
$773$	19.2364	0.691885	0.345942	+	0.938256i	$0.387559\pi$
$774$	18.6405	0.670018
$775$	−7.87291	−0.282803
$776$	69.2811	2.48705
$777$	−3.40121	−0.122018
$778$	0.414519	0.0148612
$779$	−14.7401	−0.528117
$780$	−11.5307	−0.412867
$781$	2.00687	0.0718114
$782$	−99.7390	−3.56666
$783$	−32.8246	−1.17306
$784$	9.36043	0.334301
$785$	−19.0172	−0.678754
$786$	−50.5192	−1.80196
$787$	−26.7471	−0.953431	−0.476715	−	0.879058i	$-0.658173\pi$
$787$	−26.7471	−0.953431	−0.476715	+	0.879058i	$0.658173\pi$
$788$	74.3609	2.64900
$789$	41.3104	1.47069
$790$	23.4305	0.833621
$791$	17.7908	0.632567
$792$	−5.41780	−0.192513
$793$	3.16585	0.112423
$794$	−31.9241	−1.13294
$795$	0.278567	0.00987976
$796$	−14.8181	−0.525213
$797$	54.3028	1.92350	0.961751	−	0.273924i	$-0.0883217\pi$
$797$	54.3028	1.92350	0.961751	+	0.273924i	$0.0883217\pi$
$798$	15.9726	0.565423
$799$	−2.62798	−0.0929712
$800$	−9.85307	−0.348359
$801$	−6.54220	−0.231157
$802$	35.7550	1.26255
$803$	4.29642	0.151617
$804$	1.53463	0.0541221
$805$	5.50154	0.193904
$806$	25.1210	0.884850
$807$	11.6687	0.410756
$808$	139.892	4.92137
$809$	−27.8908	−0.980588	−0.490294	−	0.871557i	$-0.663111\pi$
$809$	−27.8908	−0.980588	−0.490294	+	0.871557i	$0.663111\pi$
$810$	28.2636	0.993082
$811$	−18.5421	−0.651102	−0.325551	−	0.945525i	$-0.605550\pi$
$811$	−18.5421	−0.651102	−0.325551	+	0.945525i	$0.605550\pi$
$812$	−37.4577	−1.31451
$813$	−14.6329	−0.513200
$814$	−3.88376	−0.136126
$815$	−7.16128	−0.250849
$816$	−128.038	−4.48224
$817$	−25.7821	−0.902001
$818$	−36.5852	−1.27917
$819$	1.05944	0.0370197
$820$	−22.6422	−0.790699
$821$	46.1490	1.61061	0.805306	−	0.592860i	$-0.202001\pi$
$821$	46.1490	1.61061	0.805306	+	0.592860i	$0.202001\pi$
$822$	−103.591	−3.61317
$823$	12.1081	0.422063	0.211031	−	0.977479i	$-0.432318\pi$
$823$	12.1081	0.422063	0.211031	+	0.977479i	$0.432318\pi$
$824$	132.270	4.60785
$825$	−1.69381	−0.0589710
$826$	−12.2466	−0.426112
$827$	−27.7149	−0.963740	−0.481870	−	0.876243i	$-0.660042\pi$
$827$	−27.7149	−0.963740	−0.481870	+	0.876243i	$0.660042\pi$
$828$	22.7965	0.792233
$829$	−27.7817	−0.964898	−0.482449	−	0.875924i	$-0.660253\pi$
$829$	−27.7817	−0.964898	−0.482449	+	0.875924i	$0.660253\pi$
$830$	25.0347	0.868968
$831$	7.77629	0.269756
$832$	8.51440	0.295184
$833$	6.95763	0.241067
$834$	7.47373	0.258794
$835$	3.28663	0.113738
$836$	12.8661	0.444983
$837$	−33.0435	−1.14215
$838$	58.5597	2.02291
$839$	−27.9868	−0.966211	−0.483106	−	0.875562i	$-0.660491\pi$
$839$	−27.9868	−0.966211	−0.483106	+	0.875562i	$0.660491\pi$
$840$	14.2900	0.493051
$841$	32.1644	1.10912
$842$	−37.9210	−1.30684
$843$	−16.6635	−0.573921
$844$	35.8396	1.23365
$845$	−11.5004	−0.395627
$846$	0.851476	0.0292743
$847$	−10.2577	−0.352460
$848$	−1.32630	−0.0455454
$849$	−53.6002	−1.83955
$850$	−18.1293	−0.621829
$851$	9.51777	0.326265
$852$	−21.9337	−0.751435
$853$	−42.5893	−1.45823	−0.729115	−	0.684392i	$-0.760068\pi$
$853$	−42.5893	−1.45823	−0.729115	+	0.684392i	$0.760068\pi$
$854$	−6.73640	−0.230515
$855$	2.69752	0.0922532
$856$	−2.33435	−0.0797865
$857$	10.1515	0.346769	0.173385	−	0.984854i	$-0.444530\pi$
$857$	10.1515	0.346769	0.173385	+	0.984854i	$0.444530\pi$
$858$	5.40465	0.184512
$859$	16.3023	0.556226	0.278113	−	0.960548i	$-0.410291\pi$
$859$	16.3023	0.556226	0.278113	+	0.960548i	$0.410291\pi$
$860$	−39.6038	−1.35048
$861$	9.29415	0.316744
$862$	7.20799	0.245505
$863$	45.4698	1.54781	0.773905	−	0.633302i	$-0.218301\pi$
$863$	45.4698	1.54781	0.773905	+	0.633302i	$0.218301\pi$
$864$	−41.3544	−1.40691
$865$	−20.6699	−0.702799
$866$	11.1619	0.379297
$867$	−61.7492	−2.09711
$868$	−37.7074	−1.27987
$869$	−7.74720	−0.262806
$870$	−40.0638	−1.35829
$871$	−0.199577	−0.00676240
$872$	−0.382016	−0.0129367
$873$	−8.24629	−0.279095
$874$	−44.6968	−1.51189
$875$	1.00000	0.0338062
$876$	−46.9568	−1.58652
$877$	−43.8107	−1.47938	−0.739691	−	0.672946i	$-0.765028\pi$
$877$	−43.8107	−1.47938	−0.739691	+	0.672946i	$0.765028\pi$
$878$	−48.0048	−1.62008
$879$	4.63968	0.156493
$880$	8.06451	0.271855
$881$	42.5801	1.43456	0.717279	−	0.696786i	$-0.245387\pi$
$881$	42.5801	1.43456	0.717279	+	0.696786i	$0.245387\pi$
$882$	−2.25430	−0.0759062
$883$	8.43346	0.283809	0.141904	−	0.989880i	$-0.454677\pi$
$883$	8.43346	0.283809	0.141904	+	0.989880i	$0.454677\pi$
$884$	40.8070	1.37249
$885$	−9.24012	−0.310603
$886$	−32.0858	−1.07794
$887$	−17.6678	−0.593227	−0.296614	−	0.954998i	$-0.595857\pi$
$887$	−17.6678	−0.593227	−0.296614	+	0.954998i	$0.595857\pi$
$888$	24.7219	0.829613
$889$	13.6114	0.456511
$890$	19.7039	0.660475
$891$	−9.34525	−0.313078
$892$	4.47962	0.149989
$893$	−1.17770	−0.0394101
$894$	30.1548	1.00853
$895$	5.93604	0.198420
$896$	1.58894	0.0530828
$897$	−13.2449	−0.442236
$898$	−39.2735	−1.31057
$899$	61.5722	2.05355
$900$	4.14366	0.138122
$901$	−0.985843	−0.0328432
$902$	10.6128	0.353366
$903$	16.2566	0.540984
$904$	−129.313	−4.30089
$905$	−16.3490	−0.543459
$906$	−96.9672	−3.22152
$907$	−14.4602	−0.480142	−0.240071	−	0.970755i	$-0.577171\pi$
$907$	−14.4602	−0.480142	−0.240071	+	0.970755i	$0.577171\pi$
$908$	13.3743	0.443841
$909$	−16.6508	−0.552273
$910$	−3.19082	−0.105774
$911$	−3.60171	−0.119330	−0.0596650	−	0.998218i	$-0.519003\pi$
$911$	−3.60171	−0.119330	−0.0596650	+	0.998218i	$0.519003\pi$
$912$	−57.3788	−1.90000
$913$	−8.27763	−0.273950
$914$	38.4455	1.27166
$915$	−5.08266	−0.168028
$916$	−4.78952	−0.158250
$917$	−9.86174	−0.325663
$918$	−76.0906	−2.51136
$919$	40.9342	1.35029	0.675147	−	0.737683i	$-0.264080\pi$
$919$	40.9342	1.35029	0.675147	+	0.737683i	$0.264080\pi$
$920$	−39.9883	−1.31837
$921$	−5.24066	−0.172686
$922$	−81.7879	−2.69354
$923$	2.85246	0.0938897
$924$	−8.11255	−0.266883
$925$	1.73002	0.0568827
$926$	6.32275	0.207778
$927$	−15.7437	−0.517090
$928$	77.0586	2.52957
$929$	−41.0137	−1.34561	−0.672807	−	0.739818i	$-0.734912\pi$
$929$	−41.0137	−1.34561	−0.672807	+	0.739818i	$0.734912\pi$
$930$	−40.3309	−1.32250
$931$	3.11797	0.102187
$932$	52.4141	1.71688
$933$	−12.9645	−0.424439
$934$	−86.6946	−2.83673
$935$	5.99437	0.196037
$936$	−7.70056	−0.251701
$937$	−47.0458	−1.53692	−0.768459	−	0.639899i	$-0.778976\pi$
$937$	−47.0458	−1.53692	−0.768459	+	0.639899i	$0.778976\pi$
$938$	0.424666	0.0138658
$939$	10.1694	0.331866
$940$	−1.80906	−0.0590050
$941$	−52.9609	−1.72648	−0.863238	−	0.504797i	$-0.831567\pi$
$941$	−52.9609	−1.72648	−0.863238	+	0.504797i	$0.831567\pi$
$942$	−97.4204	−3.17413
$943$	−26.0083	−0.846945
$944$	43.9937	1.43187
$945$	4.19711	0.136532
$946$	18.5630	0.603534
$947$	−43.4800	−1.41291	−0.706455	−	0.707758i	$-0.749707\pi$
$947$	−43.4800	−1.41291	−0.706455	+	0.707758i	$0.749707\pi$
$948$	84.6715	2.75000
$949$	6.10669	0.198232
$950$	−8.12441	−0.263591
$951$	−51.6823	−1.67591
$952$	−50.5719	−1.63904
$953$	−51.4308	−1.66601	−0.833004	−	0.553266i	$-0.813381\pi$
$953$	−51.4308	−1.66601	−0.833004	+	0.553266i	$0.813381\pi$
$954$	0.319417	0.0103415
$955$	10.5424	0.341143
$956$	80.5927	2.60655
$957$	13.2469	0.428212
$958$	42.4908	1.37282
$959$	−20.2219	−0.652998
$960$	−13.6696	−0.441183
$961$	30.9827	0.999443
$962$	−5.52017	−0.177977
$963$	0.277850	0.00895359
$964$	37.2009	1.19816
$965$	−13.1762	−0.424156
$966$	28.1830	0.906773
$967$	−21.6845	−0.697327	−0.348664	−	0.937248i	$-0.613364\pi$
$967$	−21.6845	−0.697327	−0.348664	+	0.937248i	$0.613364\pi$
$968$	74.5588	2.39641
$969$	−42.6498	−1.37011
$970$	24.8362	0.797444
$971$	14.5938	0.468337	0.234169	−	0.972196i	$-0.424763\pi$
$971$	14.5938	0.468337	0.234169	+	0.972196i	$0.424763\pi$
$972$	41.8306	1.34172
$973$	1.45893	0.0467712
$974$	−35.6044	−1.14084
$975$	−2.40750	−0.0771016
$976$	24.1994	0.774602
$977$	−12.7465	−0.407795	−0.203898	−	0.978992i	$-0.565361\pi$
$977$	−12.7465	−0.407795	−0.203898	+	0.978992i	$0.565361\pi$
$978$	−36.6854	−1.17307
$979$	−6.51500	−0.208220
$980$	4.78952	0.152995
$981$	0.0454701	0.00145175
$982$	17.9889	0.574048
$983$	−8.99625	−0.286936	−0.143468	−	0.989655i	$-0.545825\pi$
$983$	−8.99625	−0.286936	−0.143468	+	0.989655i	$0.545825\pi$
$984$	−67.5551	−2.15358
$985$	15.5258	0.494692
$986$	141.785	4.51535
$987$	0.742582	0.0236366
$988$	18.2872	0.581792
$989$	−45.4915	−1.44654
$990$	−1.94220	−0.0617272
$991$	−5.35189	−0.170008	−0.0850042	−	0.996381i	$-0.527090\pi$
$991$	−5.35189	−0.170008	−0.0850042	+	0.996381i	$0.527090\pi$
$992$	77.5723	2.46292
$993$	61.8161	1.96167
$994$	−6.06954	−0.192514
$995$	−3.09386	−0.0980819
$996$	90.4687	2.86661
$997$	12.5738	0.398216	0.199108	−	0.979978i	$-0.436196\pi$
$997$	12.5738	0.398216	0.199108	+	0.979978i	$0.436196\pi$
$998$	49.8455	1.57783
$999$	7.26108	0.229730

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8015.2.a.h.1.1	✓	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)

\(f(q)\)	\(=\)	\(q-2.60567 q^{2} -1.96600 q^{3} +4.78952 q^{4} +1.00000 q^{5} +5.12274 q^{6} +1.00000 q^{7} -7.26856 q^{8} +0.865151 q^{9} +O(q^{10})\)	\(q-2.60567 q^{2} -1.96600 q^{3} +4.78952 q^{4} +1.00000 q^{5} +5.12274 q^{6} +1.00000 q^{7} -7.26856 q^{8} +0.865151 q^{9} -2.60567 q^{10} +0.861554 q^{11} -9.41618 q^{12} +1.22457 q^{13} -2.60567 q^{14} -1.96600 q^{15} +9.36043 q^{16} +6.95763 q^{17} -2.25430 q^{18} +3.11797 q^{19} +4.78952 q^{20} -1.96600 q^{21} -2.24492 q^{22} +5.50154 q^{23} +14.2900 q^{24} +1.00000 q^{25} -3.19082 q^{26} +4.19711 q^{27} +4.78952 q^{28} -7.82077 q^{29} +5.12274 q^{30} -7.87291 q^{31} -9.85307 q^{32} -1.69381 q^{33} -18.1293 q^{34} +1.00000 q^{35} +4.14366 q^{36} +1.73002 q^{37} -8.12441 q^{38} -2.40750 q^{39} -7.26856 q^{40} -4.72745 q^{41} +5.12274 q^{42} -8.26885 q^{43} +4.12643 q^{44} +0.865151 q^{45} -14.3352 q^{46} -0.377712 q^{47} -18.4026 q^{48} +1.00000 q^{49} -2.60567 q^{50} -13.6787 q^{51} +5.86508 q^{52} -0.141692 q^{53} -10.9363 q^{54} +0.861554 q^{55} -7.26856 q^{56} -6.12993 q^{57} +20.3783 q^{58} +4.69996 q^{59} -9.41618 q^{60} +2.58528 q^{61} +20.5142 q^{62} +0.865151 q^{63} +6.95299 q^{64} +1.22457 q^{65} +4.41352 q^{66} -0.162978 q^{67} +33.3237 q^{68} -10.8160 q^{69} -2.60567 q^{70} +2.32936 q^{71} -6.28840 q^{72} +4.98682 q^{73} -4.50786 q^{74} -1.96600 q^{75} +14.9336 q^{76} +0.861554 q^{77} +6.27314 q^{78} -8.99213 q^{79} +9.36043 q^{80} -10.8470 q^{81} +12.3182 q^{82} -9.60779 q^{83} -9.41618 q^{84} +6.95763 q^{85} +21.5459 q^{86} +15.3756 q^{87} -6.26225 q^{88} -7.56192 q^{89} -2.25430 q^{90} +1.22457 q^{91} +26.3497 q^{92} +15.4781 q^{93} +0.984193 q^{94} +3.11797 q^{95} +19.3711 q^{96} -9.53161 q^{97} -2.60567 q^{98} +0.745374 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 38 q - 6 q^{2} - 9 q^{3} + 24 q^{4} + 38 q^{5} - 10 q^{6} + 38 q^{7} - 21 q^{8} + 13 q^{9}+O(q^{10}) \) 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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