LMFDB - Embedded newform 8015.2.a.l.1.49

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("8015.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8015 = 5 \cdot 7 \cdot 229 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8015.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$64.0000972201$
Analytic rank:	$0$
Dimension:	$62$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.49
Character	$\chi$	$=$	8015.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.87567 q^{2} +1.33294 q^{3} +1.51815 q^{4} -1.00000 q^{5} +2.50015 q^{6} -1.00000 q^{7} -0.903793 q^{8} -1.22328 q^{9} +O(q^{10})$	\(q+1.87567 q^{2} +1.33294 q^{3} +1.51815 q^{4} -1.00000 q^{5} +2.50015 q^{6} -1.00000 q^{7} -0.903793 q^{8} -1.22328 q^{9} -1.87567 q^{10} -3.98252 q^{11} +2.02360 q^{12} +5.96900 q^{13} -1.87567 q^{14} -1.33294 q^{15} -4.73152 q^{16} +3.59235 q^{17} -2.29448 q^{18} +4.67846 q^{19} -1.51815 q^{20} -1.33294 q^{21} -7.46991 q^{22} +3.64241 q^{23} -1.20470 q^{24} +1.00000 q^{25} +11.1959 q^{26} -5.62936 q^{27} -1.51815 q^{28} -0.721455 q^{29} -2.50015 q^{30} -8.67804 q^{31} -7.06720 q^{32} -5.30845 q^{33} +6.73808 q^{34} +1.00000 q^{35} -1.85713 q^{36} +8.84089 q^{37} +8.77527 q^{38} +7.95630 q^{39} +0.903793 q^{40} +0.649730 q^{41} -2.50015 q^{42} +11.2509 q^{43} -6.04607 q^{44} +1.22328 q^{45} +6.83197 q^{46} -9.73223 q^{47} -6.30681 q^{48} +1.00000 q^{49} +1.87567 q^{50} +4.78838 q^{51} +9.06184 q^{52} +4.65742 q^{53} -10.5588 q^{54} +3.98252 q^{55} +0.903793 q^{56} +6.23609 q^{57} -1.35321 q^{58} +9.28342 q^{59} -2.02360 q^{60} +5.14011 q^{61} -16.2772 q^{62} +1.22328 q^{63} -3.79272 q^{64} -5.96900 q^{65} -9.95691 q^{66} +10.7240 q^{67} +5.45373 q^{68} +4.85510 q^{69} +1.87567 q^{70} +10.2206 q^{71} +1.10559 q^{72} +5.45139 q^{73} +16.5826 q^{74} +1.33294 q^{75} +7.10261 q^{76} +3.98252 q^{77} +14.9234 q^{78} +1.37256 q^{79} +4.73152 q^{80} -3.83373 q^{81} +1.21868 q^{82} -1.67954 q^{83} -2.02360 q^{84} -3.59235 q^{85} +21.1030 q^{86} -0.961653 q^{87} +3.59938 q^{88} +13.5816 q^{89} +2.29448 q^{90} -5.96900 q^{91} +5.52973 q^{92} -11.5673 q^{93} -18.2545 q^{94} -4.67846 q^{95} -9.42012 q^{96} -2.51699 q^{97} +1.87567 q^{98} +4.87175 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 62 q + 2 q^{2} + 11 q^{3} + 64 q^{4} - 62 q^{5} + 3 q^{6} - 62 q^{7} + 15 q^{8} + 69 q^{9}+O(q^{10}) $ 62 * q + 2 * q^2 + 11 * q^3 + 64 * q^4 - 62 * q^5 + 3 * q^6 - 62 * q^7 + 15 * q^8 + 69 * q^9	\( 62 q + 2 q^{2} + 11 q^{3} + 64 q^{4} - 62 q^{5} + 3 q^{6} - 62 q^{7} + 15 q^{8} + 69 q^{9} - 2 q^{10} - 13 q^{11} + 37 q^{12} + 31 q^{13} - 2 q^{14} - 11 q^{15} + 64 q^{16} + 30 q^{17} + 18 q^{18} + 20 q^{19} - 64 q^{20} - 11 q^{21} + 7 q^{22} + 29 q^{24} + 62 q^{25} + 59 q^{27} - 64 q^{28} - 29 q^{29} - 3 q^{30} + 20 q^{31} + 22 q^{32} + 72 q^{33} + 13 q^{34} + 62 q^{35} + 53 q^{36} + 35 q^{37} + 34 q^{38} - 6 q^{39} - 15 q^{40} + 13 q^{41} - 3 q^{42} - 4 q^{43} - 44 q^{44} - 69 q^{45} - 19 q^{46} + 58 q^{47} + 64 q^{48} + 62 q^{49} + 2 q^{50} - 30 q^{51} + 82 q^{52} + 18 q^{53} + 22 q^{54} + 13 q^{55} - 15 q^{56} + 21 q^{57} + 18 q^{58} - 11 q^{59} - 37 q^{60} + 24 q^{61} + 48 q^{62} - 69 q^{63} + 65 q^{64} - 31 q^{65} + 25 q^{66} - 6 q^{67} + 65 q^{68} + 27 q^{69} + 2 q^{70} - 35 q^{71} + 53 q^{72} + 116 q^{73} - 69 q^{74} + 11 q^{75} + 65 q^{76} + 13 q^{77} + 102 q^{78} - 83 q^{79} - 64 q^{80} + 126 q^{81} + 71 q^{82} + 84 q^{83} - 37 q^{84} - 30 q^{85} + 24 q^{86} + 49 q^{87} + 20 q^{88} - 16 q^{89} - 18 q^{90} - 31 q^{91} + 19 q^{92} + 65 q^{93} + 54 q^{94} - 20 q^{95} + 17 q^{96} + 155 q^{97} + 2 q^{98} + 6 q^{99}+O(q^{100}) \) 62 * q + 2 * q^2 + 11 * q^3 + 64 * q^4 - 62 * q^5 + 3 * q^6 - 62 * q^7 + 15 * q^8 + 69 * q^9 - 2 * q^10 - 13 * q^11 + 37 * q^12 + 31 * q^13 - 2 * q^14 - 11 * q^15 + 64 * q^16 + 30 * q^17 + 18 * q^18 + 20 * q^19 - 64 * q^20 - 11 * q^21 + 7 * q^22 + 29 * q^24 + 62 * q^25 + 59 * q^27 - 64 * q^28 - 29 * q^29 - 3 * q^30 + 20 * q^31 + 22 * q^32 + 72 * q^33 + 13 * q^34 + 62 * q^35 + 53 * q^36 + 35 * q^37 + 34 * q^38 - 6 * q^39 - 15 * q^40 + 13 * q^41 - 3 * q^42 - 4 * q^43 - 44 * q^44 - 69 * q^45 - 19 * q^46 + 58 * q^47 + 64 * q^48 + 62 * q^49 + 2 * q^50 - 30 * q^51 + 82 * q^52 + 18 * q^53 + 22 * q^54 + 13 * q^55 - 15 * q^56 + 21 * q^57 + 18 * q^58 - 11 * q^59 - 37 * q^60 + 24 * q^61 + 48 * q^62 - 69 * q^63 + 65 * q^64 - 31 * q^65 + 25 * q^66 - 6 * q^67 + 65 * q^68 + 27 * q^69 + 2 * q^70 - 35 * q^71 + 53 * q^72 + 116 * q^73 - 69 * q^74 + 11 * q^75 + 65 * q^76 + 13 * q^77 + 102 * q^78 - 83 * q^79 - 64 * q^80 + 126 * q^81 + 71 * q^82 + 84 * q^83 - 37 * q^84 - 30 * q^85 + 24 * q^86 + 49 * q^87 + 20 * q^88 - 16 * q^89 - 18 * q^90 - 31 * q^91 + 19 * q^92 + 65 * q^93 + 54 * q^94 - 20 * q^95 + 17 * q^96 + 155 * q^97 + 2 * q^98 + 6 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	1.87567	1.32630	0.663151	−	0.748486i	$-0.269219\pi$
$2$	1.87567	1.32630	0.663151	+	0.748486i	$0.269219\pi$
$3$	1.33294	0.769571	0.384785	−	0.923006i	$-0.374275\pi$
$3$	1.33294	0.769571	0.384785	+	0.923006i	$0.374275\pi$
$4$	1.51815	0.759075
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	2.50015	1.02068
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−0.903793	−0.319539
$9$	−1.22328	−0.407761
$10$	−1.87567	−0.593140
$11$	−3.98252	−1.20078	−0.600388	−	0.799709i	$-0.704987\pi$
$11$	−3.98252	−1.20078	−0.600388	+	0.799709i	$0.704987\pi$
$12$	2.02360	0.584162
$13$	5.96900	1.65550	0.827752	−	0.561094i	$-0.189620\pi$
$13$	5.96900	1.65550	0.827752	+	0.561094i	$0.189620\pi$
$14$	−1.87567	−0.501295
$15$	−1.33294	−0.344162
$16$	−4.73152	−1.18288
$17$	3.59235	0.871274	0.435637	−	0.900122i	$-0.356523\pi$
$17$	3.59235	0.871274	0.435637	+	0.900122i	$0.356523\pi$
$18$	−2.29448	−0.540814
$19$	4.67846	1.07331	0.536657	−	0.843801i	$-0.319687\pi$
$19$	4.67846	1.07331	0.536657	+	0.843801i	$0.319687\pi$
$20$	−1.51815	−0.339469
$21$	−1.33294	−0.290870
$22$	−7.46991	−1.59259
$23$	3.64241	0.759495	0.379748	−	0.925090i	$-0.376011\pi$
$23$	3.64241	0.759495	0.379748	+	0.925090i	$0.376011\pi$
$24$	−1.20470	−0.245908
$25$	1.00000	0.200000
$26$	11.1959	2.19570
$27$	−5.62936	−1.08337
$28$	−1.51815	−0.286903
$29$	−0.721455	−0.133971	−0.0669854	−	0.997754i	$-0.521338\pi$
$29$	−0.721455	−0.133971	−0.0669854	+	0.997754i	$0.521338\pi$
$30$	−2.50015	−0.456463
$31$	−8.67804	−1.55862	−0.779311	−	0.626638i	$-0.784431\pi$
$31$	−8.67804	−1.55862	−0.779311	+	0.626638i	$0.784431\pi$
$32$	−7.06720	−1.24932
$33$	−5.30845	−0.924082
$34$	6.73808	1.15557
$35$	1.00000	0.169031
$36$	−1.85713	−0.309521
$37$	8.84089	1.45343	0.726717	−	0.686937i	$-0.241045\pi$
$37$	8.84089	1.45343	0.726717	+	0.686937i	$0.241045\pi$
$38$	8.77527	1.42354
$39$	7.95630	1.27403
$40$	0.903793	0.142902
$41$	0.649730	0.101471	0.0507354	−	0.998712i	$-0.483843\pi$
$41$	0.649730	0.101471	0.0507354	+	0.998712i	$0.483843\pi$
$42$	−2.50015	−0.385782
$43$	11.2509	1.71574	0.857872	−	0.513863i	$-0.171786\pi$
$43$	11.2509	1.71574	0.857872	+	0.513863i	$0.171786\pi$
$44$	−6.04607	−0.911479
$45$	1.22328	0.182356
$46$	6.83197	1.00732
$47$	−9.73223	−1.41959	−0.709796	−	0.704407i	$-0.751213\pi$
$47$	−9.73223	−1.41959	−0.709796	+	0.704407i	$0.751213\pi$
$48$	−6.30681	−0.910310
$49$	1.00000	0.142857
$50$	1.87567	0.265260
$51$	4.78838	0.670507
$52$	9.06184	1.25665
$53$	4.65742	0.639746	0.319873	−	0.947460i	$-0.396360\pi$
$53$	4.65742	0.639746	0.319873	+	0.947460i	$0.396360\pi$
$54$	−10.5588	−1.43688
$55$	3.98252	0.537003
$56$	0.903793	0.120774
$57$	6.23609	0.825991
$58$	−1.35321	−0.177686
$59$	9.28342	1.20860	0.604299	−	0.796757i	$-0.293453\pi$
$59$	9.28342	1.20860	0.604299	+	0.796757i	$0.293453\pi$
$60$	−2.02360	−0.261245
$61$	5.14011	0.658124	0.329062	−	0.944308i	$-0.393268\pi$
$61$	5.14011	0.658124	0.329062	+	0.944308i	$0.393268\pi$
$62$	−16.2772	−2.06720
$63$	1.22328	0.154119
$64$	−3.79272	−0.474090
$65$	−5.96900	−0.740364
$66$	−9.95691	−1.22561
$67$	10.7240	1.31014	0.655071	−	0.755567i	$-0.272639\pi$
$67$	10.7240	1.31014	0.655071	+	0.755567i	$0.272639\pi$
$68$	5.45373	0.661362
$69$	4.85510	0.584485
$70$	1.87567	0.224186
$71$	10.2206	1.21296	0.606481	−	0.795098i	$-0.292580\pi$
$71$	10.2206	1.21296	0.606481	+	0.795098i	$0.292580\pi$
$72$	1.10559	0.130296
$73$	5.45139	0.638037	0.319018	−	0.947749i	$-0.396647\pi$
$73$	5.45139	0.638037	0.319018	+	0.947749i	$0.396647\pi$
$74$	16.5826	1.92769
$75$	1.33294	0.153914
$76$	7.10261	0.814725
$77$	3.98252	0.453851
$78$	14.9234	1.68974
$79$	1.37256	0.154425	0.0772123	−	0.997015i	$-0.475398\pi$
$79$	1.37256	0.154425	0.0772123	+	0.997015i	$0.475398\pi$
$80$	4.73152	0.529000
$81$	−3.83373	−0.425970
$82$	1.21868	0.134581
$83$	−1.67954	−0.184353	−0.0921767	−	0.995743i	$-0.529382\pi$
$83$	−1.67954	−0.184353	−0.0921767	+	0.995743i	$0.529382\pi$
$84$	−2.02360	−0.220792
$85$	−3.59235	−0.389646
$86$	21.1030	2.27559
$87$	−0.961653	−0.103100
$88$	3.59938	0.383695
$89$	13.5816	1.43964	0.719822	−	0.694159i	$-0.244224\pi$
$89$	13.5816	1.43964	0.719822	+	0.694159i	$0.244224\pi$
$90$	2.29448	0.241859
$91$	−5.96900	−0.625722
$92$	5.52973	0.576514
$93$	−11.5673	−1.19947
$94$	−18.2545	−1.88281
$95$	−4.67846	−0.480000
$96$	−9.42012	−0.961437
$97$	−2.51699	−0.255562	−0.127781	−	0.991802i	$-0.540785\pi$
$97$	−2.51699	−0.255562	−0.127781	+	0.991802i	$0.540785\pi$
$98$	1.87567	0.189472
$99$	4.87175	0.489630
$100$	1.51815	0.151815
$101$	−8.19186	−0.815120	−0.407560	−	0.913178i	$-0.633620\pi$
$101$	−8.19186	−0.815120	−0.407560	+	0.913178i	$0.633620\pi$
$102$	8.98143	0.889294
$103$	9.58693	0.944628	0.472314	−	0.881430i	$-0.343419\pi$
$103$	9.58693	0.944628	0.472314	+	0.881430i	$0.343419\pi$
$104$	−5.39474	−0.528998
$105$	1.33294	0.130081
$106$	8.73580	0.848496
$107$	2.59404	0.250775	0.125388	−	0.992108i	$-0.459983\pi$
$107$	2.59404	0.250775	0.125388	+	0.992108i	$0.459983\pi$
$108$	−8.54622	−0.822360
$109$	−8.95812	−0.858033	−0.429016	−	0.903297i	$-0.641140\pi$
$109$	−8.95812	−0.858033	−0.429016	+	0.903297i	$0.641140\pi$
$110$	7.46991	0.712228
$111$	11.7843	1.11852
$112$	4.73152	0.447087
$113$	−4.89637	−0.460611	−0.230306	−	0.973118i	$-0.573973\pi$
$113$	−4.89637	−0.460611	−0.230306	+	0.973118i	$0.573973\pi$
$114$	11.6969	1.09551
$115$	−3.64241	−0.339657
$116$	−1.09528	−0.101694
$117$	−7.30178	−0.675050
$118$	17.4127	1.60297
$119$	−3.59235	−0.329311
$120$	1.20470	0.109973
$121$	4.86050	0.441864
$122$	9.64117	0.872870
$123$	0.866048	0.0780889
$124$	−13.1746	−1.18311
$125$	−1.00000	−0.0894427
$126$	2.29448	0.204408
$127$	−17.1223	−1.51936	−0.759680	−	0.650298i	$-0.774644\pi$
$127$	−17.1223	−1.51936	−0.759680	+	0.650298i	$0.774644\pi$
$128$	7.02050	0.620531
$129$	14.9967	1.32039
$130$	−11.1959	−0.981945
$131$	6.84606	0.598143	0.299072	−	0.954231i	$-0.403323\pi$
$131$	6.84606	0.598143	0.299072	+	0.954231i	$0.403323\pi$
$132$	−8.05902	−0.701448
$133$	−4.67846	−0.405674
$134$	20.1147	1.73764
$135$	5.62936	0.484498
$136$	−3.24674	−0.278406
$137$	10.4683	0.894369	0.447184	−	0.894442i	$-0.352427\pi$
$137$	10.4683	0.894369	0.447184	+	0.894442i	$0.352427\pi$
$138$	9.10658	0.775203
$139$	−19.3425	−1.64061	−0.820306	−	0.571925i	$-0.806197\pi$
$139$	−19.3425	−1.64061	−0.820306	+	0.571925i	$0.806197\pi$
$140$	1.51815	0.128307
$141$	−12.9724	−1.09248
$142$	19.1705	1.60875
$143$	−23.7717	−1.98789
$144$	5.78799	0.482332
$145$	0.721455	0.0599136
$146$	10.2250	0.846229
$147$	1.33294	0.109939
$148$	13.4218	1.10326
$149$	−1.85795	−0.152209	−0.0761045	−	0.997100i	$-0.524248\pi$
$149$	−1.85795	−0.152209	−0.0761045	+	0.997100i	$0.524248\pi$
$150$	2.50015	0.204137
$151$	16.0060	1.30255	0.651274	−	0.758843i	$-0.274235\pi$
$151$	16.0060	1.30255	0.651274	+	0.758843i	$0.274235\pi$
$152$	−4.22836	−0.342966
$153$	−4.39447	−0.355272
$154$	7.46991	0.601943
$155$	8.67804	0.697037
$156$	12.0789	0.967082
$157$	19.6666	1.56957	0.784785	−	0.619768i	$-0.212773\pi$
$157$	19.6666	1.56957	0.784785	+	0.619768i	$0.212773\pi$
$158$	2.57446	0.204813
$159$	6.20804	0.492330
$160$	7.06720	0.558711
$161$	−3.64241	−0.287062
$162$	−7.19083	−0.564965
$163$	23.0762	1.80747	0.903736	−	0.428091i	$-0.140814\pi$
$163$	23.0762	1.80747	0.903736	+	0.428091i	$0.140814\pi$
$164$	0.986387	0.0770239
$165$	5.30845	0.413262
$166$	−3.15027	−0.244508
$167$	−20.4601	−1.58325	−0.791625	−	0.611007i	$-0.790765\pi$
$167$	−20.4601	−1.58325	−0.791625	+	0.611007i	$0.790765\pi$
$168$	1.20470	0.0929444
$169$	22.6290	1.74069
$170$	−6.73808	−0.516787
$171$	−5.72309	−0.437655
$172$	17.0805	1.30238
$173$	−15.8160	−1.20247	−0.601236	−	0.799072i	$-0.705325\pi$
$173$	−15.8160	−1.20247	−0.601236	+	0.799072i	$0.705325\pi$
$174$	−1.80375	−0.136742
$175$	−1.00000	−0.0755929
$176$	18.8434	1.42037
$177$	12.3742	0.930102
$178$	25.4746	1.90940
$179$	9.36766	0.700172	0.350086	−	0.936718i	$-0.386152\pi$
$179$	9.36766	0.700172	0.350086	+	0.936718i	$0.386152\pi$
$180$	1.85713	0.138422
$181$	18.4437	1.37091	0.685455	−	0.728115i	$-0.259603\pi$
$181$	18.4437	1.37091	0.685455	+	0.728115i	$0.259603\pi$
$182$	−11.1959	−0.829895
$183$	6.85144	0.506473
$184$	−3.29199	−0.242688
$185$	−8.84089	−0.649995
$186$	−21.6964	−1.59086
$187$	−14.3066	−1.04621
$188$	−14.7750	−1.07758
$189$	5.62936	0.409476
$190$	−8.77527	−0.636625
$191$	−20.1710	−1.45952	−0.729762	−	0.683701i	$-0.760369\pi$
$191$	−20.1710	−1.45952	−0.729762	+	0.683701i	$0.760369\pi$
$192$	−5.05545	−0.364846
$193$	−12.7911	−0.920723	−0.460361	−	0.887732i	$-0.652280\pi$
$193$	−12.7911	−0.920723	−0.460361	+	0.887732i	$0.652280\pi$
$194$	−4.72105	−0.338952
$195$	−7.95630	−0.569762
$196$	1.51815	0.108439
$197$	−8.69625	−0.619582	−0.309791	−	0.950805i	$-0.600259\pi$
$197$	−8.69625	−0.619582	−0.309791	+	0.950805i	$0.600259\pi$
$198$	9.13782	0.649396
$199$	19.3957	1.37493	0.687463	−	0.726219i	$-0.258724\pi$
$199$	19.3957	1.37493	0.687463	+	0.726219i	$0.258724\pi$
$200$	−0.903793	−0.0639078
$201$	14.2944	1.00825
$202$	−15.3652	−1.08109
$203$	0.721455	0.0506362
$204$	7.26948	0.508965
$205$	−0.649730	−0.0453791
$206$	17.9820	1.25286
$207$	−4.45570	−0.309692
$208$	−28.2425	−1.95826
$209$	−18.6321	−1.28881
$210$	2.50015	0.172527
$211$	−5.43974	−0.374487	−0.187244	−	0.982314i	$-0.559955\pi$
$211$	−5.43974	−0.374487	−0.187244	+	0.982314i	$0.559955\pi$
$212$	7.07067	0.485615
$213$	13.6234	0.933461
$214$	4.86557	0.332604
$215$	−11.2509	−0.767304
$216$	5.08778	0.346180
$217$	8.67804	0.589104
$218$	−16.8025	−1.13801
$219$	7.26635	0.491014
$220$	6.04607	0.407626
$221$	21.4428	1.44240
$222$	22.1036	1.48349
$223$	−25.2433	−1.69041	−0.845207	−	0.534439i	$-0.820523\pi$
$223$	−25.2433	−1.69041	−0.845207	+	0.534439i	$0.820523\pi$
$224$	7.06720	0.472197
$225$	−1.22328	−0.0815522
$226$	−9.18398	−0.610909
$227$	8.70283	0.577627	0.288814	−	0.957385i	$-0.406739\pi$
$227$	8.70283	0.577627	0.288814	+	0.957385i	$0.406739\pi$
$228$	9.46732	0.626989
$229$	1.00000	0.0660819
$229$	1.00000	0.0660819
$230$	−6.83197	−0.450487
$231$	5.30845	0.349270
$232$	0.652046	0.0428089
$233$	−24.1356	−1.58118	−0.790588	−	0.612348i	$-0.790225\pi$
$233$	−24.1356	−1.58118	−0.790588	+	0.612348i	$0.790225\pi$
$234$	−13.6958	−0.895319
$235$	9.73223	0.634861
$236$	14.0936	0.917417
$237$	1.82953	0.118841
$238$	−6.73808	−0.436765
$239$	1.86403	0.120574	0.0602869	−	0.998181i	$-0.480798\pi$
$239$	1.86403	0.120574	0.0602869	+	0.998181i	$0.480798\pi$
$240$	6.30681	0.407103
$241$	22.3650	1.44066	0.720329	−	0.693632i	$-0.243991\pi$
$241$	22.3650	1.44066	0.720329	+	0.693632i	$0.243991\pi$
$242$	9.11671	0.586044
$243$	11.7780	0.755557
$244$	7.80346	0.499565
$245$	−1.00000	−0.0638877
$246$	1.62442	0.103569
$247$	27.9258	1.77687
$248$	7.84315	0.498040
$249$	−2.23872	−0.141873
$250$	−1.87567	−0.118628
$251$	−13.2019	−0.833294	−0.416647	−	0.909068i	$-0.636795\pi$
$251$	−13.2019	−0.833294	−0.416647	+	0.909068i	$0.636795\pi$
$252$	1.85713	0.116988
$253$	−14.5060	−0.911984
$254$	−32.1159	−2.01513
$255$	−4.78838	−0.299860
$256$	20.7536	1.29710
$257$	26.4275	1.64850	0.824251	−	0.566224i	$-0.191596\pi$
$257$	26.4275	1.64850	0.824251	+	0.566224i	$0.191596\pi$
$258$	28.1289	1.75123
$259$	−8.84089	−0.549346
$260$	−9.06184	−0.561992
$261$	0.882543	0.0546281
$262$	12.8410	0.793318
$263$	8.99028	0.554364	0.277182	−	0.960817i	$-0.410599\pi$
$263$	8.99028	0.554364	0.277182	+	0.960817i	$0.410599\pi$
$264$	4.79774	0.295280
$265$	−4.65742	−0.286103
$266$	−8.77527	−0.538046
$267$	18.1034	1.10791
$268$	16.2806	0.994496
$269$	28.4526	1.73478	0.867392	−	0.497625i	$-0.165795\pi$
$269$	28.4526	1.73478	0.867392	+	0.497625i	$0.165795\pi$
$270$	10.5588	0.642591
$271$	3.67532	0.223260	0.111630	−	0.993750i	$-0.464393\pi$
$271$	3.67532	0.223260	0.111630	+	0.993750i	$0.464393\pi$
$272$	−16.9973	−1.03061
$273$	−7.95630	−0.481537
$274$	19.6351	1.18620
$275$	−3.98252	−0.240155
$276$	7.37077	0.443668
$277$	−5.23116	−0.314310	−0.157155	−	0.987574i	$-0.550232\pi$
$277$	−5.23116	−0.314310	−0.157155	+	0.987574i	$0.550232\pi$
$278$	−36.2803	−2.17595
$279$	10.6157	0.635545
$280$	−0.903793	−0.0540120
$281$	17.2831	1.03103	0.515513	−	0.856882i	$-0.327601\pi$
$281$	17.2831	1.03103	0.515513	+	0.856882i	$0.327601\pi$
$282$	−24.3321	−1.44895
$283$	−11.7370	−0.697693	−0.348847	−	0.937180i	$-0.613427\pi$
$283$	−11.7370	−0.697693	−0.348847	+	0.937180i	$0.613427\pi$
$284$	15.5164	0.920730
$285$	−6.23609	−0.369394
$286$	−44.5879	−2.63654
$287$	−0.649730	−0.0383523
$288$	8.64519	0.509422
$289$	−4.09499	−0.240882
$290$	1.35321	0.0794634
$291$	−3.35499	−0.196673
$292$	8.27602	0.484318
$293$	20.3986	1.19170	0.595850	−	0.803096i	$-0.296815\pi$
$293$	20.3986	1.19170	0.595850	+	0.803096i	$0.296815\pi$
$294$	2.50015	0.145812
$295$	−9.28342	−0.540502
$296$	−7.99033	−0.464429
$297$	22.4191	1.30089
$298$	−3.48490	−0.201875
$299$	21.7416	1.25735
$300$	2.02360	0.116832
$301$	−11.2509	−0.648490
$302$	30.0220	1.72757
$303$	−10.9192	−0.627293
$304$	−22.1363	−1.26960
$305$	−5.14011	−0.294322
$306$	−8.24258	−0.471197
$307$	−12.6110	−0.719750	−0.359875	−	0.933001i	$-0.617181\pi$
$307$	−12.6110	−0.719750	−0.359875	+	0.933001i	$0.617181\pi$
$308$	6.04607	0.344507
$309$	12.7788	0.726958
$310$	16.2772	0.924481
$311$	−9.49597	−0.538467	−0.269234	−	0.963075i	$-0.586770\pi$
$311$	−9.49597	−0.538467	−0.269234	+	0.963075i	$0.586770\pi$
$312$	−7.19084	−0.407101
$313$	−6.39603	−0.361525	−0.180762	−	0.983527i	$-0.557856\pi$
$313$	−6.39603	−0.361525	−0.180762	+	0.983527i	$0.557856\pi$
$314$	36.8882	2.08172
$315$	−1.22328	−0.0689242
$316$	2.08374	0.117220
$317$	−13.6302	−0.765546	−0.382773	−	0.923842i	$-0.625031\pi$
$317$	−13.6302	−0.765546	−0.382773	+	0.923842i	$0.625031\pi$
$318$	11.6443	0.652978
$319$	2.87321	0.160869
$320$	3.79272	0.212019
$321$	3.45769	0.192989
$322$	−6.83197	−0.380731
$323$	16.8067	0.935150
$324$	−5.82018	−0.323343
$325$	5.96900	0.331101
$326$	43.2835	2.39725
$327$	−11.9406	−0.660317
$328$	−0.587221	−0.0324239
$329$	9.73223	0.536555
$330$	9.95691	0.548110
$331$	−3.80067	−0.208904	−0.104452	−	0.994530i	$-0.533309\pi$
$331$	−3.80067	−0.208904	−0.104452	+	0.994530i	$0.533309\pi$
$332$	−2.54979	−0.139938
$333$	−10.8149	−0.592653
$334$	−38.3765	−2.09987
$335$	−10.7240	−0.585913
$336$	6.30681	0.344065
$337$	11.4549	0.623987	0.311993	−	0.950084i	$-0.399003\pi$
$337$	11.4549	0.623987	0.311993	+	0.950084i	$0.399003\pi$
$338$	42.4446	2.30868
$339$	−6.52654	−0.354473
$340$	−5.45373	−0.295770
$341$	34.5605	1.87156
$342$	−10.7346	−0.580463
$343$	−1.00000	−0.0539949
$344$	−10.1685	−0.548247
$345$	−4.85510	−0.261390
$346$	−29.6657	−1.59484
$347$	15.7027	0.842967	0.421483	−	0.906836i	$-0.361510\pi$
$347$	15.7027	0.842967	0.421483	+	0.906836i	$0.361510\pi$
$348$	−1.45993	−0.0782606
$349$	9.26458	0.495922	0.247961	−	0.968770i	$-0.420240\pi$
$349$	9.26458	0.495922	0.247961	+	0.968770i	$0.420240\pi$
$350$	−1.87567	−0.100259
$351$	−33.6017	−1.79353
$352$	28.1453	1.50015
$353$	−10.0029	−0.532402	−0.266201	−	0.963918i	$-0.585768\pi$
$353$	−10.0029	−0.532402	−0.266201	+	0.963918i	$0.585768\pi$
$354$	23.2100	1.23360
$355$	−10.2206	−0.542453
$356$	20.6189	1.09280
$357$	−4.78838	−0.253428
$358$	17.5707	0.928639
$359$	8.78137	0.463463	0.231731	−	0.972780i	$-0.425561\pi$
$359$	8.78137	0.463463	0.231731	+	0.972780i	$0.425561\pi$
$360$	−1.10559	−0.0582699
$361$	2.88803	0.152002
$362$	34.5944	1.81824
$363$	6.47873	0.340045
$364$	−9.06184	−0.474970
$365$	−5.45139	−0.285339
$366$	12.8511	0.671735
$367$	2.35664	0.123016	0.0615078	−	0.998107i	$-0.480409\pi$
$367$	2.35664	0.123016	0.0615078	+	0.998107i	$0.480409\pi$
$368$	−17.2341	−0.898392
$369$	−0.794803	−0.0413758
$370$	−16.5826	−0.862089
$371$	−4.65742	−0.241801
$372$	−17.5608	−0.910487
$373$	−7.72871	−0.400178	−0.200089	−	0.979778i	$-0.564123\pi$
$373$	−7.72871	−0.400178	−0.200089	+	0.979778i	$0.564123\pi$
$374$	−26.8346	−1.38758
$375$	−1.33294	−0.0688325
$376$	8.79592	0.453615
$377$	−4.30637	−0.221789
$378$	10.5588	0.543088
$379$	−4.60055	−0.236314	−0.118157	−	0.992995i	$-0.537699\pi$
$379$	−4.60055	−0.236314	−0.118157	+	0.992995i	$0.537699\pi$
$380$	−7.10261	−0.364356
$381$	−22.8229	−1.16925
$382$	−37.8343	−1.93577
$383$	−18.0940	−0.924559	−0.462279	−	0.886734i	$-0.652968\pi$
$383$	−18.0940	−0.924559	−0.462279	+	0.886734i	$0.652968\pi$
$384$	9.35788	0.477542
$385$	−3.98252	−0.202968
$386$	−23.9919	−1.22116
$387$	−13.7630	−0.699613
$388$	−3.82117	−0.193991
$389$	28.8310	1.46179	0.730894	−	0.682491i	$-0.239104\pi$
$389$	28.8310	1.46179	0.730894	+	0.682491i	$0.239104\pi$
$390$	−14.9234	−0.755676
$391$	13.0848	0.661728
$392$	−0.903793	−0.0456484
$393$	9.12536	0.460313
$394$	−16.3113	−0.821753
$395$	−1.37256	−0.0690607
$396$	7.39605	0.371666
$397$	−31.5028	−1.58108	−0.790539	−	0.612412i	$-0.790199\pi$
$397$	−31.5028	−1.58108	−0.790539	+	0.612412i	$0.790199\pi$
$398$	36.3800	1.82357
$399$	−6.23609	−0.312195
$400$	−4.73152	−0.236576
$401$	−9.95960	−0.497359	−0.248679	−	0.968586i	$-0.579997\pi$
$401$	−9.95960	−0.497359	−0.248679	+	0.968586i	$0.579997\pi$
$402$	26.8116	1.33724
$403$	−51.7992	−2.58030
$404$	−12.4365	−0.618737
$405$	3.83373	0.190500
$406$	1.35321	0.0671589
$407$	−35.2091	−1.74525
$408$	−4.32770	−0.214253
$409$	23.2826	1.15125	0.575626	−	0.817713i	$-0.304759\pi$
$409$	23.2826	1.15125	0.575626	+	0.817713i	$0.304759\pi$
$410$	−1.21868	−0.0601864
$411$	13.9536	0.688280
$412$	14.5544	0.717044
$413$	−9.28342	−0.456807
$414$	−8.35743	−0.410745
$415$	1.67954	0.0824453
$416$	−42.1841	−2.06825
$417$	−25.7824	−1.26257
$418$	−34.9477	−1.70935
$419$	−6.62465	−0.323636	−0.161818	−	0.986821i	$-0.551736\pi$
$419$	−6.62465	−0.323636	−0.161818	+	0.986821i	$0.551736\pi$
$420$	2.02360	0.0987414
$421$	37.2732	1.81658	0.908292	−	0.418337i	$-0.137387\pi$
$421$	37.2732	1.81658	0.908292	+	0.418337i	$0.137387\pi$
$422$	−10.2032	−0.496683
$423$	11.9053	0.578854
$424$	−4.20934	−0.204424
$425$	3.59235	0.174255
$426$	25.5531	1.23805
$427$	−5.14011	−0.248747
$428$	3.93814	0.190357
$429$	−31.6861	−1.52982
$430$	−21.1030	−1.01768
$431$	−26.5067	−1.27678	−0.638390	−	0.769713i	$-0.720399\pi$
$431$	−26.5067	−1.27678	−0.638390	+	0.769713i	$0.720399\pi$
$432$	26.6354	1.28150
$433$	−35.0450	−1.68416	−0.842079	−	0.539355i	$-0.818668\pi$
$433$	−35.0450	−1.68416	−0.842079	+	0.539355i	$0.818668\pi$
$434$	16.2772	0.781329
$435$	0.961653	0.0461077
$436$	−13.5998	−0.651311
$437$	17.0409	0.815176
$438$	13.6293	0.651233
$439$	−10.8227	−0.516541	−0.258270	−	0.966073i	$-0.583153\pi$
$439$	−10.8227	−0.516541	−0.258270	+	0.966073i	$0.583153\pi$
$440$	−3.59938	−0.171594
$441$	−1.22328	−0.0582516
$442$	40.2196	1.91305
$443$	−9.85659	−0.468301	−0.234150	−	0.972200i	$-0.575231\pi$
$443$	−9.85659	−0.468301	−0.234150	+	0.972200i	$0.575231\pi$
$444$	17.8904	0.849040
$445$	−13.5816	−0.643828
$446$	−47.3481	−2.24200
$447$	−2.47652	−0.117136
$448$	3.79272	0.179189
$449$	−40.7090	−1.92118	−0.960589	−	0.277972i	$-0.910338\pi$
$449$	−40.7090	−1.92118	−0.960589	+	0.277972i	$0.910338\pi$
$450$	−2.29448	−0.108163
$451$	−2.58756	−0.121844
$452$	−7.43342	−0.349639
$453$	21.3349	1.00240
$454$	16.3237	0.766107
$455$	5.96900	0.279831
$456$	−5.63614	−0.263936
$457$	−0.252709	−0.0118212	−0.00591061	−	0.999983i	$-0.501881\pi$
$457$	−0.252709	−0.0118212	−0.00591061	+	0.999983i	$0.501881\pi$
$458$	1.87567	0.0876445
$459$	−20.2227	−0.943914
$460$	−5.52973	−0.257825
$461$	−35.2872	−1.64349	−0.821745	−	0.569855i	$-0.806999\pi$
$461$	−35.2872	−1.64349	−0.821745	+	0.569855i	$0.806999\pi$
$462$	9.95691	0.463238
$463$	6.43317	0.298975	0.149487	−	0.988764i	$-0.452238\pi$
$463$	6.43317	0.298975	0.149487	+	0.988764i	$0.452238\pi$
$464$	3.41358	0.158471
$465$	11.5673	0.536419
$466$	−45.2705	−2.09712
$467$	−7.70547	−0.356567	−0.178283	−	0.983979i	$-0.557054\pi$
$467$	−7.70547	−0.356567	−0.178283	+	0.983979i	$0.557054\pi$
$468$	−11.0852	−0.512413
$469$	−10.7240	−0.495187
$470$	18.2545	0.842017
$471$	26.2144	1.20789
$472$	−8.39029	−0.386194
$473$	−44.8069	−2.06022
$474$	3.43160	0.157618
$475$	4.67846	0.214663
$476$	−5.45373	−0.249971
$477$	−5.69734	−0.260863
$478$	3.49630	0.159917
$479$	−27.3454	−1.24944	−0.624722	−	0.780847i	$-0.714788\pi$
$479$	−27.3454	−1.24944	−0.624722	+	0.780847i	$0.714788\pi$
$480$	9.42012	0.429968
$481$	52.7713	2.40616
$482$	41.9495	1.91075
$483$	−4.85510	−0.220915
$484$	7.37897	0.335408
$485$	2.51699	0.114291
$486$	22.0916	1.00210
$487$	2.57448	0.116661	0.0583305	−	0.998297i	$-0.481422\pi$
$487$	2.57448	0.116661	0.0583305	+	0.998297i	$0.481422\pi$
$488$	−4.64560	−0.210296
$489$	30.7592	1.39098
$490$	−1.87567	−0.0847343
$491$	−9.53520	−0.430318	−0.215159	−	0.976579i	$-0.569027\pi$
$491$	−9.53520	−0.430318	−0.215159	+	0.976579i	$0.569027\pi$
$492$	1.31479	0.0592753
$493$	−2.59172	−0.116725
$494$	52.3796	2.35667
$495$	−4.87175	−0.218969
$496$	41.0603	1.84366
$497$	−10.2206	−0.458457
$498$	−4.19910	−0.188166
$499$	4.30431	0.192687	0.0963436	−	0.995348i	$-0.469285\pi$
$499$	4.30431	0.192687	0.0963436	+	0.995348i	$0.469285\pi$
$500$	−1.51815	−0.0678937
$501$	−27.2720	−1.21842
$502$	−24.7624	−1.10520
$503$	−5.26391	−0.234706	−0.117353	−	0.993090i	$-0.537441\pi$
$503$	−5.26391	−0.234706	−0.117353	+	0.993090i	$0.537441\pi$
$504$	−1.10559	−0.0492471
$505$	8.19186	0.364533
$506$	−27.2085	−1.20957
$507$	30.1630	1.33959
$508$	−25.9942	−1.15331
$509$	30.6866	1.36016	0.680079	−	0.733138i	$-0.261945\pi$
$509$	30.6866	1.36016	0.680079	+	0.733138i	$0.261945\pi$
$510$	−8.98143	−0.397704
$511$	−5.45139	−0.241155
$512$	24.8860	1.09982
$513$	−26.3368	−1.16280
$514$	49.5694	2.18641
$515$	−9.58693	−0.422451
$516$	22.7672	1.00227
$517$	38.7588	1.70461
$518$	−16.5826	−0.728598
$519$	−21.0818	−0.925387
$520$	5.39474	0.236575
$521$	8.23917	0.360965	0.180482	−	0.983578i	$-0.442234\pi$
$521$	8.23917	0.360965	0.180482	+	0.983578i	$0.442234\pi$
$522$	1.65536	0.0724533
$523$	−27.1826	−1.18861	−0.594305	−	0.804239i	$-0.702573\pi$
$523$	−27.1826	−1.18861	−0.594305	+	0.804239i	$0.702573\pi$
$524$	10.3933	0.454035
$525$	−1.33294	−0.0581741
$526$	16.8628	0.735254
$527$	−31.1746	−1.35799
$528$	25.1170	1.09308
$529$	−9.73284	−0.423167
$530$	−8.73580	−0.379459
$531$	−11.3563	−0.492819
$532$	−7.10261	−0.307937
$533$	3.87824	0.167985
$534$	33.9560	1.46942
$535$	−2.59404	−0.112150
$536$	−9.69225	−0.418641
$537$	12.4865	0.538832
$538$	53.3677	2.30085
$539$	−3.98252	−0.171539
$540$	8.54622	0.367771
$541$	6.27326	0.269708	0.134854	−	0.990865i	$-0.456943\pi$
$541$	6.27326	0.269708	0.134854	+	0.990865i	$0.456943\pi$
$542$	6.89371	0.296110
$543$	24.5843	1.05501
$544$	−25.3879	−1.08850
$545$	8.95812	0.383724
$546$	−14.9234	−0.638663
$547$	13.9040	0.594494	0.297247	−	0.954801i	$-0.403932\pi$
$547$	13.9040	0.594494	0.297247	+	0.954801i	$0.403932\pi$
$548$	15.8925	0.678893
$549$	−6.28781	−0.268357
$550$	−7.46991	−0.318518
$551$	−3.37530	−0.143793
$552$	−4.38800	−0.186766
$553$	−1.37256	−0.0583670
$554$	−9.81195	−0.416870
$555$	−11.7843	−0.500217
$556$	−29.3649	−1.24535
$557$	26.6647	1.12982	0.564910	−	0.825153i	$-0.308911\pi$
$557$	26.6647	1.12982	0.564910	+	0.825153i	$0.308911\pi$
$558$	19.9116	0.842924
$559$	67.1566	2.84042
$560$	−4.73152	−0.199943
$561$	−19.0698	−0.805129
$562$	32.4175	1.36745
$563$	44.4070	1.87153	0.935766	−	0.352623i	$-0.114710\pi$
$563$	44.4070	1.87153	0.935766	+	0.352623i	$0.114710\pi$
$564$	−19.6941	−0.829271
$565$	4.89637	0.205992
$566$	−22.0148	−0.925352
$567$	3.83373	0.161002
$568$	−9.23731	−0.387589
$569$	−40.6265	−1.70315	−0.851576	−	0.524232i	$-0.824353\pi$
$569$	−40.6265	−1.70315	−0.851576	+	0.524232i	$0.824353\pi$
$570$	−11.6969	−0.489928
$571$	−12.9453	−0.541745	−0.270872	−	0.962615i	$-0.587312\pi$
$571$	−12.9453	−0.541745	−0.270872	+	0.962615i	$0.587312\pi$
$572$	−36.0890	−1.50896
$573$	−26.8867	−1.12321
$574$	−1.21868	−0.0508668
$575$	3.64241	0.151899
$576$	4.63957	0.193315
$577$	−15.9248	−0.662957	−0.331478	−	0.943463i	$-0.607547\pi$
$577$	−15.9248	−0.662957	−0.331478	+	0.943463i	$0.607547\pi$
$578$	−7.68086	−0.319482
$579$	−17.0497	−0.708561
$580$	1.09528	0.0454789
$581$	1.67954	0.0696790
$582$	−6.29286	−0.260847
$583$	−18.5483	−0.768192
$584$	−4.92693	−0.203878
$585$	7.30178	0.301891
$586$	38.2611	1.58055
$587$	48.2730	1.99244	0.996220	−	0.0868715i	$-0.0276870\pi$
$587$	48.2730	1.99244	0.996220	+	0.0868715i	$0.0276870\pi$
$588$	2.02360	0.0834517
$589$	−40.5999	−1.67289
$590$	−17.4127	−0.716868
$591$	−11.5915	−0.476812
$592$	−41.8308	−1.71924
$593$	−20.7831	−0.853459	−0.426730	−	0.904379i	$-0.640334\pi$
$593$	−20.7831	−0.853459	−0.426730	+	0.904379i	$0.640334\pi$
$594$	42.0509	1.72537
$595$	3.59235	0.147272
$596$	−2.82064	−0.115538
$597$	25.8532	1.05810
$598$	40.7801	1.66762
$599$	−26.1916	−1.07016	−0.535080	−	0.844801i	$-0.679719\pi$
$599$	−26.1916	−1.07016	−0.535080	+	0.844801i	$0.679719\pi$
$600$	−1.20470	−0.0491816
$601$	27.9876	1.14164	0.570819	−	0.821076i	$-0.306626\pi$
$601$	27.9876	1.14164	0.570819	+	0.821076i	$0.306626\pi$
$602$	−21.1030	−0.860093
$603$	−13.1185	−0.534225
$604$	24.2995	0.988731
$605$	−4.86050	−0.197607
$606$	−20.4809	−0.831979
$607$	10.0883	0.409473	0.204737	−	0.978817i	$-0.434366\pi$
$607$	10.0883	0.409473	0.204737	+	0.978817i	$0.434366\pi$
$608$	−33.0636	−1.34091
$609$	0.961653	0.0389681
$610$	−9.64117	−0.390359
$611$	−58.0917	−2.35014
$612$	−6.67146	−0.269678
$613$	5.68666	0.229682	0.114841	−	0.993384i	$-0.463364\pi$
$613$	5.68666	0.229682	0.114841	+	0.993384i	$0.463364\pi$
$614$	−23.6542	−0.954605
$615$	−0.866048	−0.0349224
$616$	−3.59938	−0.145023
$617$	48.2983	1.94441	0.972207	−	0.234122i	$-0.0752215\pi$
$617$	48.2983	1.94441	0.972207	+	0.234122i	$0.0752215\pi$
$618$	23.9688	0.964166
$619$	−20.3188	−0.816682	−0.408341	−	0.912830i	$-0.633892\pi$
$619$	−20.3188	−0.816682	−0.408341	+	0.912830i	$0.633892\pi$
$620$	13.1746	0.529103
$621$	−20.5045	−0.822815
$622$	−17.8113	−0.714170
$623$	−13.5816	−0.544134
$624$	−37.6454	−1.50702
$625$	1.00000	0.0400000
$626$	−11.9969	−0.479491
$627$	−24.8354	−0.991830
$628$	29.8569	1.19142
$629$	31.7596	1.26634
$630$	−2.29448	−0.0914142
$631$	−7.50510	−0.298773	−0.149387	−	0.988779i	$-0.547730\pi$
$631$	−7.50510	−0.298773	−0.149387	+	0.988779i	$0.547730\pi$
$632$	−1.24051	−0.0493447
$633$	−7.25082	−0.288194
$634$	−25.5657	−1.01534
$635$	17.1223	0.679478
$636$	9.42474	0.373715
$637$	5.96900	0.236501
$638$	5.38921	0.213361
$639$	−12.5027	−0.494599
$640$	−7.02050	−0.277510
$641$	−27.7754	−1.09706	−0.548532	−	0.836130i	$-0.684813\pi$
$641$	−27.7754	−1.09706	−0.548532	+	0.836130i	$0.684813\pi$
$642$	6.48550	0.255962
$643$	39.1522	1.54401	0.772006	−	0.635615i	$-0.219253\pi$
$643$	39.1522	1.54401	0.772006	+	0.635615i	$0.219253\pi$
$644$	−5.52973	−0.217902
$645$	−14.9967	−0.590495
$646$	31.5239	1.24029
$647$	−20.5738	−0.808841	−0.404421	−	0.914573i	$-0.632527\pi$
$647$	−20.5738	−0.808841	−0.404421	+	0.914573i	$0.632527\pi$
$648$	3.46490	0.136114
$649$	−36.9715	−1.45126
$650$	11.1959	0.439139
$651$	11.5673	0.453357
$652$	35.0332	1.37201
$653$	11.6861	0.457311	0.228655	−	0.973507i	$-0.426567\pi$
$653$	11.6861	0.457311	0.228655	+	0.973507i	$0.426567\pi$
$654$	−22.3967	−0.875779
$655$	−6.84606	−0.267498
$656$	−3.07421	−0.120028
$657$	−6.66859	−0.260166
$658$	18.2545	0.711634
$659$	6.77164	0.263785	0.131893	−	0.991264i	$-0.457895\pi$
$659$	6.77164	0.263785	0.131893	+	0.991264i	$0.457895\pi$
$660$	8.05902	0.313697
$661$	41.0778	1.59774	0.798870	−	0.601503i	$-0.205431\pi$
$661$	41.0778	1.59774	0.798870	+	0.601503i	$0.205431\pi$
$662$	−7.12881	−0.277069
$663$	28.5818	1.11003
$664$	1.51796	0.0589081
$665$	4.67846	0.181423
$666$	−20.2852	−0.786037
$667$	−2.62783	−0.101750
$668$	−31.0615	−1.20181
$669$	−33.6477	−1.30089
$670$	−20.1147	−0.777097
$671$	−20.4706	−0.790259
$672$	9.42012	0.363389
$673$	−11.9457	−0.460474	−0.230237	−	0.973135i	$-0.573950\pi$
$673$	−11.9457	−0.460474	−0.230237	+	0.973135i	$0.573950\pi$
$674$	21.4856	0.827594
$675$	−5.62936	−0.216674
$676$	34.3542	1.32132
$677$	−41.9092	−1.61070	−0.805351	−	0.592799i	$-0.798023\pi$
$677$	−41.9092	−1.61070	−0.805351	+	0.592799i	$0.798023\pi$
$678$	−12.2417	−0.470138
$679$	2.51699	0.0965933
$680$	3.24674	0.124507
$681$	11.6003	0.444525
$682$	64.8242	2.48225
$683$	−16.3476	−0.625522	−0.312761	−	0.949832i	$-0.601254\pi$
$683$	−16.3476	−0.625522	−0.312761	+	0.949832i	$0.601254\pi$
$684$	−8.68850	−0.332213
$685$	−10.4683	−0.399974
$686$	−1.87567	−0.0716135
$687$	1.33294	0.0508547
$688$	−53.2338	−2.02952
$689$	27.8002	1.05910
$690$	−9.10658	−0.346682
$691$	−15.6603	−0.595746	−0.297873	−	0.954605i	$-0.596277\pi$
$691$	−15.6603	−0.595746	−0.297873	+	0.954605i	$0.596277\pi$
$692$	−24.0111	−0.912766
$693$	−4.87175	−0.185063
$694$	29.4532	1.11803
$695$	19.3425	0.733704
$696$	0.869135	0.0329445
$697$	2.33406	0.0884088
$698$	17.3773	0.657742
$699$	−32.1712	−1.21683
$700$	−1.51815	−0.0573807
$701$	−2.99269	−0.113032	−0.0565161	−	0.998402i	$-0.517999\pi$
$701$	−2.99269	−0.113032	−0.0565161	+	0.998402i	$0.517999\pi$
$702$	−63.0258	−2.37876
$703$	41.3618	1.55999
$704$	15.1046	0.569276
$705$	12.9724	0.488570
$706$	−18.7622	−0.706125
$707$	8.19186	0.308086
$708$	18.7859	0.706017
$709$	15.1725	0.569817	0.284908	−	0.958555i	$-0.408037\pi$
$709$	15.1725	0.569817	0.284908	+	0.958555i	$0.408037\pi$
$710$	−19.1705	−0.719457
$711$	−1.67902	−0.0629683
$712$	−12.2749	−0.460022
$713$	−31.6090	−1.18377
$714$	−8.98143	−0.336122
$715$	23.7717	0.889011
$716$	14.2215	0.531483
$717$	2.48463	0.0927901
$718$	16.4710	0.614692
$719$	41.4674	1.54647	0.773236	−	0.634119i	$-0.218637\pi$
$719$	41.4674	1.54647	0.773236	+	0.634119i	$0.218637\pi$
$720$	−5.78799	−0.215706
$721$	−9.58693	−0.357036
$722$	5.41701	0.201600
$723$	29.8112	1.10869
$724$	28.0003	1.04062
$725$	−0.721455	−0.0267942
$726$	12.1520	0.451002
$727$	−37.3677	−1.38589	−0.692946	−	0.720989i	$-0.743688\pi$
$727$	−37.3677	−1.38589	−0.692946	+	0.720989i	$0.743688\pi$
$728$	5.39474	0.199942
$729$	27.2005	1.00742
$730$	−10.2250	−0.378445
$731$	40.4172	1.49488
$732$	10.4015	0.384451
$733$	21.9432	0.810491	0.405245	−	0.914208i	$-0.367186\pi$
$733$	21.9432	0.810491	0.405245	+	0.914208i	$0.367186\pi$
$734$	4.42029	0.163156
$735$	−1.33294	−0.0491661
$736$	−25.7416	−0.948850
$737$	−42.7085	−1.57319
$738$	−1.49079	−0.0548768
$739$	−46.7710	−1.72050	−0.860250	−	0.509872i	$-0.829693\pi$
$739$	−46.7710	−1.72050	−0.860250	+	0.509872i	$0.829693\pi$
$740$	−13.4218	−0.493395
$741$	37.2233	1.36743
$742$	−8.73580	−0.320701
$743$	−43.4227	−1.59303	−0.796513	−	0.604622i	$-0.793324\pi$
$743$	−43.4227	−1.59303	−0.796513	+	0.604622i	$0.793324\pi$
$744$	10.4544	0.383277
$745$	1.85795	0.0680699
$746$	−14.4965	−0.530756
$747$	2.05455	0.0751721
$748$	−21.7196	−0.794148
$749$	−2.59404	−0.0947842
$750$	−2.50015	−0.0912926
$751$	41.2913	1.50674	0.753371	−	0.657596i	$-0.228426\pi$
$751$	41.2913	1.50674	0.753371	+	0.657596i	$0.228426\pi$
$752$	46.0482	1.67921
$753$	−17.5972	−0.641279
$754$	−8.07733	−0.294159
$755$	−16.0060	−0.582517
$756$	8.54622	0.310823
$757$	50.2207	1.82530	0.912652	−	0.408738i	$-0.134031\pi$
$757$	50.2207	1.82530	0.912652	+	0.408738i	$0.134031\pi$
$758$	−8.62912	−0.313424
$759$	−19.3355	−0.701836
$760$	4.22836	0.153379
$761$	−53.1491	−1.92666	−0.963328	−	0.268328i	$-0.913529\pi$
$761$	−53.1491	−1.92666	−0.963328	+	0.268328i	$0.913529\pi$
$762$	−42.8084	−1.55078
$763$	8.95812	0.324306
$764$	−30.6226	−1.10789
$765$	4.39447	0.158882
$766$	−33.9384	−1.22624
$767$	55.4128	2.00084
$768$	27.6632	0.998210
$769$	17.9299	0.646567	0.323284	−	0.946302i	$-0.395213\pi$
$769$	17.9299	0.646567	0.323284	+	0.946302i	$0.395213\pi$
$770$	−7.46991	−0.269197
$771$	35.2262	1.26864
$772$	−19.4188	−0.698898
$773$	25.3712	0.912538	0.456269	−	0.889842i	$-0.349185\pi$
$773$	25.3712	0.912538	0.456269	+	0.889842i	$0.349185\pi$
$774$	−25.8149	−0.927898
$775$	−8.67804	−0.311724
$776$	2.27484	0.0816620
$777$	−11.7843	−0.422761
$778$	54.0774	1.93877
$779$	3.03974	0.108910
$780$	−12.0789	−0.432492
$781$	−40.7038	−1.45650
$782$	24.5429	0.877651
$783$	4.06133	0.145140
$784$	−4.73152	−0.168983
$785$	−19.6666	−0.701933
$786$	17.1162	0.610514
$787$	25.1792	0.897540	0.448770	−	0.893647i	$-0.351862\pi$
$787$	25.1792	0.897540	0.448770	+	0.893647i	$0.351862\pi$
$788$	−13.2022	−0.470309
$789$	11.9835	0.426622
$790$	−2.57446	−0.0915953
$791$	4.89637	0.174095
$792$	−4.40306	−0.156456
$793$	30.6813	1.08953
$794$	−59.0889	−2.09699
$795$	−6.20804	−0.220177
$796$	29.4456	1.04367
$797$	−4.44534	−0.157462	−0.0787310	−	0.996896i	$-0.525087\pi$
$797$	−4.44534	−0.157462	−0.0787310	+	0.996896i	$0.525087\pi$
$798$	−11.6969	−0.414065
$799$	−34.9616	−1.23685
$800$	−7.06720	−0.249863
$801$	−16.6141	−0.587030
$802$	−18.6810	−0.659648
$803$	−21.7103	−0.766139
$804$	21.7010	0.765335
$805$	3.64241	0.128378
$806$	−97.1584	−3.42226
$807$	37.9254	1.33504
$808$	7.40374	0.260463
$809$	−2.05911	−0.0723945	−0.0361973	−	0.999345i	$-0.511524\pi$
$809$	−2.05911	−0.0723945	−0.0361973	+	0.999345i	$0.511524\pi$
$810$	7.19083	0.252660
$811$	31.5492	1.10784	0.553921	−	0.832569i	$-0.313131\pi$
$811$	31.5492	1.10784	0.553921	+	0.832569i	$0.313131\pi$
$812$	1.09528	0.0384367
$813$	4.89897	0.171814
$814$	−66.0407	−2.31472
$815$	−23.0762	−0.808326
$816$	−22.6563	−0.793129
$817$	52.6369	1.84153
$818$	43.6706	1.52691
$819$	7.30178	0.255145
$820$	−0.986387	−0.0344461
$821$	−16.1075	−0.562156	−0.281078	−	0.959685i	$-0.590692\pi$
$821$	−16.1075	−0.562156	−0.281078	+	0.959685i	$0.590692\pi$
$822$	26.1724	0.912867
$823$	−9.34064	−0.325594	−0.162797	−	0.986660i	$-0.552052\pi$
$823$	−9.34064	−0.325594	−0.162797	+	0.986660i	$0.552052\pi$
$824$	−8.66460	−0.301846
$825$	−5.30845	−0.184816
$826$	−17.4127	−0.605864
$827$	10.5303	0.366174	0.183087	−	0.983097i	$-0.441391\pi$
$827$	10.5303	0.366174	0.183087	+	0.983097i	$0.441391\pi$
$828$	−6.76442	−0.235080
$829$	49.2567	1.71075	0.855377	−	0.518006i	$-0.173325\pi$
$829$	49.2567	1.71075	0.855377	+	0.518006i	$0.173325\pi$
$830$	3.15027	0.109347
$831$	−6.97280	−0.241884
$832$	−22.6387	−0.784857
$833$	3.59235	0.124468
$834$	−48.3593	−1.67454
$835$	20.4601	0.708051
$836$	−28.2863	−0.978303
$837$	48.8518	1.68857
$838$	−12.4257	−0.429238
$839$	34.3705	1.18660	0.593300	−	0.804981i	$-0.297825\pi$
$839$	34.3705	1.18660	0.593300	+	0.804981i	$0.297825\pi$
$840$	−1.20470	−0.0415660
$841$	−28.4795	−0.982052
$842$	69.9123	2.40934
$843$	23.0373	0.793447
$844$	−8.25834	−0.284264
$845$	−22.6290	−0.778461
$846$	22.3304	0.767735
$847$	−4.86050	−0.167009
$848$	−22.0367	−0.756743
$849$	−15.6447	−0.536924
$850$	6.73808	0.231114
$851$	32.2021	1.10388
$852$	20.6824	0.708567
$853$	12.3159	0.421689	0.210845	−	0.977520i	$-0.432379\pi$
$853$	12.3159	0.421689	0.210845	+	0.977520i	$0.432379\pi$
$854$	−9.64117	−0.329914
$855$	5.72309	0.195725
$856$	−2.34448	−0.0801326
$857$	6.74722	0.230481	0.115240	−	0.993338i	$-0.463236\pi$
$857$	6.74722	0.230481	0.115240	+	0.993338i	$0.463236\pi$
$858$	−59.4328	−2.02900
$859$	42.2635	1.44201	0.721006	−	0.692929i	$-0.243680\pi$
$859$	42.2635	1.44201	0.721006	+	0.692929i	$0.243680\pi$
$860$	−17.0805	−0.582441
$861$	−0.866048	−0.0295148
$862$	−49.7178	−1.69340
$863$	−43.1825	−1.46995	−0.734974	−	0.678095i	$-0.762806\pi$
$863$	−43.1825	−1.46995	−0.734974	+	0.678095i	$0.762806\pi$
$864$	39.7838	1.35347
$865$	15.8160	0.537762
$866$	−65.7331	−2.23370
$867$	−5.45835	−0.185375
$868$	13.1746	0.447174
$869$	−5.46623	−0.185429
$870$	1.80375	0.0611527
$871$	64.0114	2.16894
$872$	8.09629	0.274175
$873$	3.07899	0.104208
$874$	31.9631	1.08117
$875$	1.00000	0.0338062
$876$	11.0314	0.372717
$877$	−18.3276	−0.618881	−0.309440	−	0.950919i	$-0.600142\pi$
$877$	−18.3276	−0.618881	−0.309440	+	0.950919i	$0.600142\pi$
$878$	−20.2999	−0.685089
$879$	27.1900	0.917097
$880$	−18.8434	−0.635211
$881$	−17.9168	−0.603631	−0.301816	−	0.953366i	$-0.597593\pi$
$881$	−17.9168	−0.603631	−0.301816	+	0.953366i	$0.597593\pi$
$882$	−2.29448	−0.0772591
$883$	18.5031	0.622680	0.311340	−	0.950299i	$-0.399222\pi$
$883$	18.5031	0.622680	0.311340	+	0.950299i	$0.399222\pi$
$884$	32.5534	1.09489
$885$	−12.3742	−0.415954
$886$	−18.4877	−0.621108
$887$	−13.6331	−0.457754	−0.228877	−	0.973455i	$-0.573505\pi$
$887$	−13.6331	−0.457754	−0.228877	+	0.973455i	$0.573505\pi$
$888$	−10.6506	−0.357411
$889$	17.1223	0.574264
$890$	−25.4746	−0.853910
$891$	15.2679	0.511495
$892$	−38.3231	−1.28315
$893$	−45.5319	−1.52367
$894$	−4.64515	−0.155357
$895$	−9.36766	−0.313126
$896$	−7.02050	−0.234538
$897$	28.9801	0.967617
$898$	−76.3569	−2.54806
$899$	6.26081	0.208810
$900$	−1.85713	−0.0619042
$901$	16.7311	0.557394
$902$	−4.85343	−0.161601
$903$	−14.9967	−0.499059
$904$	4.42530	0.147183
$905$	−18.4437	−0.613089
$906$	40.0174	1.32949
$907$	8.76323	0.290978	0.145489	−	0.989360i	$-0.453524\pi$
$907$	8.76323	0.290978	0.145489	+	0.989360i	$0.453524\pi$
$908$	13.2122	0.438462
$909$	10.0210	0.332374
$910$	11.1959	0.371140
$911$	34.9953	1.15945	0.579723	−	0.814814i	$-0.303161\pi$
$911$	34.9953	1.15945	0.579723	+	0.814814i	$0.303161\pi$
$912$	−29.5062	−0.977048
$913$	6.68881	0.221367
$914$	−0.473999	−0.0156785
$915$	−6.85144	−0.226501
$916$	1.51815	0.0501611
$917$	−6.84606	−0.226077
$918$	−37.9311	−1.25191
$919$	−31.5112	−1.03946	−0.519729	−	0.854331i	$-0.673967\pi$
$919$	−31.5112	−1.03946	−0.519729	+	0.854331i	$0.673967\pi$
$920$	3.29199	0.108534
$921$	−16.8097	−0.553898
$922$	−66.1873	−2.17976
$923$	61.0068	2.00806
$924$	8.05902	0.265122
$925$	8.84089	0.290687
$926$	12.0665	0.396531
$927$	−11.7275	−0.385183
$928$	5.09867	0.167372
$929$	−23.0321	−0.755657	−0.377829	−	0.925876i	$-0.623329\pi$
$929$	−23.0321	−0.755657	−0.377829	+	0.925876i	$0.623329\pi$
$930$	21.6964	0.711453
$931$	4.67846	0.153330
$932$	−36.6415	−1.20023
$933$	−12.6575	−0.414389
$934$	−14.4529	−0.472915
$935$	14.3066	0.467877
$936$	6.59930	0.215705
$937$	−7.03558	−0.229842	−0.114921	−	0.993375i	$-0.536662\pi$
$937$	−7.03558	−0.229842	−0.114921	+	0.993375i	$0.536662\pi$
$938$	−20.1147	−0.656767
$939$	−8.52549	−0.278219
$940$	14.7750	0.481907
$941$	−17.1579	−0.559332	−0.279666	−	0.960097i	$-0.590224\pi$
$941$	−17.1579	−0.559332	−0.279666	+	0.960097i	$0.590224\pi$
$942$	49.1696	1.60203
$943$	2.36658	0.0770665
$944$	−43.9247	−1.42963
$945$	−5.62936	−0.183123
$946$	−84.0431	−2.73248
$947$	−23.3577	−0.759024	−0.379512	−	0.925187i	$-0.623908\pi$
$947$	−23.3577	−0.759024	−0.379512	+	0.925187i	$0.623908\pi$
$948$	2.77750	0.0902089
$949$	32.5393	1.05627
$950$	8.77527	0.284707
$951$	−18.1681	−0.589142
$952$	3.24674	0.105228
$953$	44.7601	1.44992	0.724961	−	0.688789i	$-0.241858\pi$
$953$	44.7601	1.44992	0.724961	+	0.688789i	$0.241858\pi$
$954$	−10.6864	−0.345984
$955$	20.1710	0.652719
$956$	2.82987	0.0915246
$957$	3.82981	0.123800
$958$	−51.2911	−1.65714
$959$	−10.4683	−0.338040
$960$	5.05545	0.163164
$961$	44.3083	1.42930
$962$	98.9817	3.19130
$963$	−3.17325	−0.102256
$964$	33.9535	1.09357
$965$	12.7911	0.411760
$966$	−9.10658	−0.292999
$967$	−8.91431	−0.286665	−0.143332	−	0.989675i	$-0.545782\pi$
$967$	−8.91431	−0.286665	−0.143332	+	0.989675i	$0.545782\pi$
$968$	−4.39288	−0.141193
$969$	22.4023	0.719664
$970$	4.72105	0.151584
$971$	−52.9146	−1.69811	−0.849056	−	0.528303i	$-0.822829\pi$
$971$	−52.9146	−1.69811	−0.849056	+	0.528303i	$0.822829\pi$
$972$	17.8807	0.573525
$973$	19.3425	0.620093
$974$	4.82889	0.154728
$975$	7.95630	0.254805
$976$	−24.3205	−0.778481
$977$	58.9420	1.88572	0.942861	−	0.333186i	$-0.108124\pi$
$977$	58.9420	1.88572	0.942861	+	0.333186i	$0.108124\pi$
$978$	57.6941	1.84485
$979$	−54.0889	−1.72869
$980$	−1.51815	−0.0484955
$981$	10.9583	0.349872
$982$	−17.8849	−0.570731
$983$	2.32910	0.0742869	0.0371434	−	0.999310i	$-0.488174\pi$
$983$	2.32910	0.0742869	0.0371434	+	0.999310i	$0.488174\pi$
$984$	−0.782728	−0.0249525
$985$	8.69625	0.277086
$986$	−4.86122	−0.154813
$987$	12.9724	0.412917
$988$	42.3955	1.34878
$989$	40.9803	1.30310
$990$	−9.13782	−0.290419
$991$	17.4309	0.553710	0.276855	−	0.960912i	$-0.410708\pi$
$991$	17.4309	0.553710	0.276855	+	0.960912i	$0.410708\pi$
$992$	61.3294	1.94721
$993$	−5.06605	−0.160766
$994$	−19.1705	−0.608052
$995$	−19.3957	−0.614886
$996$	−3.39871	−0.107692
$997$	2.64198	0.0836724	0.0418362	−	0.999124i	$-0.486679\pi$
$997$	2.64198	0.0836724	0.0418362	+	0.999124i	$0.486679\pi$
$998$	8.07347	0.255561
$999$	−49.7686	−1.57461

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8015.2.a.l.1.49	✓	62

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8015.2.a.l.1.49	✓	62	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 8015 = 5 \cdot 7 \cdot 229 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8015.a (trivial)

\(f(q)\)	\(=\)	\(q+1.87567 q^{2} +1.33294 q^{3} +1.51815 q^{4} -1.00000 q^{5} +2.50015 q^{6} -1.00000 q^{7} -0.903793 q^{8} -1.22328 q^{9} +O(q^{10})\)	\(q+1.87567 q^{2} +1.33294 q^{3} +1.51815 q^{4} -1.00000 q^{5} +2.50015 q^{6} -1.00000 q^{7} -0.903793 q^{8} -1.22328 q^{9} -1.87567 q^{10} -3.98252 q^{11} +2.02360 q^{12} +5.96900 q^{13} -1.87567 q^{14} -1.33294 q^{15} -4.73152 q^{16} +3.59235 q^{17} -2.29448 q^{18} +4.67846 q^{19} -1.51815 q^{20} -1.33294 q^{21} -7.46991 q^{22} +3.64241 q^{23} -1.20470 q^{24} +1.00000 q^{25} +11.1959 q^{26} -5.62936 q^{27} -1.51815 q^{28} -0.721455 q^{29} -2.50015 q^{30} -8.67804 q^{31} -7.06720 q^{32} -5.30845 q^{33} +6.73808 q^{34} +1.00000 q^{35} -1.85713 q^{36} +8.84089 q^{37} +8.77527 q^{38} +7.95630 q^{39} +0.903793 q^{40} +0.649730 q^{41} -2.50015 q^{42} +11.2509 q^{43} -6.04607 q^{44} +1.22328 q^{45} +6.83197 q^{46} -9.73223 q^{47} -6.30681 q^{48} +1.00000 q^{49} +1.87567 q^{50} +4.78838 q^{51} +9.06184 q^{52} +4.65742 q^{53} -10.5588 q^{54} +3.98252 q^{55} +0.903793 q^{56} +6.23609 q^{57} -1.35321 q^{58} +9.28342 q^{59} -2.02360 q^{60} +5.14011 q^{61} -16.2772 q^{62} +1.22328 q^{63} -3.79272 q^{64} -5.96900 q^{65} -9.95691 q^{66} +10.7240 q^{67} +5.45373 q^{68} +4.85510 q^{69} +1.87567 q^{70} +10.2206 q^{71} +1.10559 q^{72} +5.45139 q^{73} +16.5826 q^{74} +1.33294 q^{75} +7.10261 q^{76} +3.98252 q^{77} +14.9234 q^{78} +1.37256 q^{79} +4.73152 q^{80} -3.83373 q^{81} +1.21868 q^{82} -1.67954 q^{83} -2.02360 q^{84} -3.59235 q^{85} +21.1030 q^{86} -0.961653 q^{87} +3.59938 q^{88} +13.5816 q^{89} +2.29448 q^{90} -5.96900 q^{91} +5.52973 q^{92} -11.5673 q^{93} -18.2545 q^{94} -4.67846 q^{95} -9.42012 q^{96} -2.51699 q^{97} +1.87567 q^{98} +4.87175 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 62 q + 2 q^{2} + 11 q^{3} + 64 q^{4} - 62 q^{5} + 3 q^{6} - 62 q^{7} + 15 q^{8} + 69 q^{9}+O(q^{10}) \) 62 * q + 2 * q^2 + 11 * q^3 + 64 * q^4 - 62 * q^5 + 3 * q^6 - 62 * q^7 + 15 * q^8 + 69 * q^9	\( 62 q + 2 q^{2} + 11 q^{3} + 64 q^{4} - 62 q^{5} + 3 q^{6} - 62 q^{7} + 15 q^{8} + 69 q^{9} - 2 q^{10} - 13 q^{11} + 37 q^{12} + 31 q^{13} - 2 q^{14} - 11 q^{15} + 64 q^{16} + 30 q^{17} + 18 q^{18} + 20 q^{19} - 64 q^{20} - 11 q^{21} + 7 q^{22} + 29 q^{24} + 62 q^{25} + 59 q^{27} - 64 q^{28} - 29 q^{29} - 3 q^{30} + 20 q^{31} + 22 q^{32} + 72 q^{33} + 13 q^{34} + 62 q^{35} + 53 q^{36} + 35 q^{37} + 34 q^{38} - 6 q^{39} - 15 q^{40} + 13 q^{41} - 3 q^{42} - 4 q^{43} - 44 q^{44} - 69 q^{45} - 19 q^{46} + 58 q^{47} + 64 q^{48} + 62 q^{49} + 2 q^{50} - 30 q^{51} + 82 q^{52} + 18 q^{53} + 22 q^{54} + 13 q^{55} - 15 q^{56} + 21 q^{57} + 18 q^{58} - 11 q^{59} - 37 q^{60} + 24 q^{61} + 48 q^{62} - 69 q^{63} + 65 q^{64} - 31 q^{65} + 25 q^{66} - 6 q^{67} + 65 q^{68} + 27 q^{69} + 2 q^{70} - 35 q^{71} + 53 q^{72} + 116 q^{73} - 69 q^{74} + 11 q^{75} + 65 q^{76} + 13 q^{77} + 102 q^{78} - 83 q^{79} - 64 q^{80} + 126 q^{81} + 71 q^{82} + 84 q^{83} - 37 q^{84} - 30 q^{85} + 24 q^{86} + 49 q^{87} + 20 q^{88} - 16 q^{89} - 18 q^{90} - 31 q^{91} + 19 q^{92} + 65 q^{93} + 54 q^{94} - 20 q^{95} + 17 q^{96} + 155 q^{97} + 2 q^{98} + 6 q^{99}+O(q^{100}) \) 62 * q + 2 * q^2 + 11 * q^3 + 64 * q^4 - 62 * q^5 + 3 * q^6 - 62 * q^7 + 15 * q^8 + 69 * q^9 - 2 * q^10 - 13 * q^11 + 37 * q^12 + 31 * q^13 - 2 * q^14 - 11 * q^15 + 64 * q^16 + 30 * q^17 + 18 * q^18 + 20 * q^19 - 64 * q^20 - 11 * q^21 + 7 * q^22 + 29 * q^24 + 62 * q^25 + 59 * q^27 - 64 * q^28 - 29 * q^29 - 3 * q^30 + 20 * q^31 + 22 * q^32 + 72 * q^33 + 13 * q^34 + 62 * q^35 + 53 * q^36 + 35 * q^37 + 34 * q^38 - 6 * q^39 - 15 * q^40 + 13 * q^41 - 3 * q^42 - 4 * q^43 - 44 * q^44 - 69 * q^45 - 19 * q^46 + 58 * q^47 + 64 * q^48 + 62 * q^49 + 2 * q^50 - 30 * q^51 + 82 * q^52 + 18 * q^53 + 22 * q^54 + 13 * q^55 - 15 * q^56 + 21 * q^57 + 18 * q^58 - 11 * q^59 - 37 * q^60 + 24 * q^61 + 48 * q^62 - 69 * q^63 + 65 * q^64 - 31 * q^65 + 25 * q^66 - 6 * q^67 + 65 * q^68 + 27 * q^69 + 2 * q^70 - 35 * q^71 + 53 * q^72 + 116 * q^73 - 69 * q^74 + 11 * q^75 + 65 * q^76 + 13 * q^77 + 102 * q^78 - 83 * q^79 - 64 * q^80 + 126 * q^81 + 71 * q^82 + 84 * q^83 - 37 * q^84 - 30 * q^85 + 24 * q^86 + 49 * q^87 + 20 * q^88 - 16 * q^89 - 18 * q^90 - 31 * q^91 + 19 * q^92 + 65 * q^93 + 54 * q^94 - 20 * q^95 + 17 * q^96 + 155 * q^97 + 2 * q^98 + 6 * q^99

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