LMFDB - Embedded newform 8015.2.a.l.1.27

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			1.27
Character	$\chi$	$=$	8015.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.521477 q^{2} +2.21540 q^{3} -1.72806 q^{4} -1.00000 q^{5} -1.15528 q^{6} -1.00000 q^{7} +1.94410 q^{8} +1.90801 q^{9} +O(q^{10})$	\(q-0.521477 q^{2} +2.21540 q^{3} -1.72806 q^{4} -1.00000 q^{5} -1.15528 q^{6} -1.00000 q^{7} +1.94410 q^{8} +1.90801 q^{9} +0.521477 q^{10} +1.94603 q^{11} -3.82835 q^{12} +1.76780 q^{13} +0.521477 q^{14} -2.21540 q^{15} +2.44232 q^{16} +3.17335 q^{17} -0.994983 q^{18} +8.00800 q^{19} +1.72806 q^{20} -2.21540 q^{21} -1.01481 q^{22} +8.06739 q^{23} +4.30696 q^{24} +1.00000 q^{25} -0.921868 q^{26} -2.41920 q^{27} +1.72806 q^{28} -9.38093 q^{29} +1.15528 q^{30} +4.44905 q^{31} -5.16181 q^{32} +4.31124 q^{33} -1.65483 q^{34} +1.00000 q^{35} -3.29716 q^{36} -5.76682 q^{37} -4.17599 q^{38} +3.91639 q^{39} -1.94410 q^{40} -2.45236 q^{41} +1.15528 q^{42} +5.49412 q^{43} -3.36286 q^{44} -1.90801 q^{45} -4.20696 q^{46} -7.29838 q^{47} +5.41073 q^{48} +1.00000 q^{49} -0.521477 q^{50} +7.03024 q^{51} -3.05487 q^{52} -3.09207 q^{53} +1.26156 q^{54} -1.94603 q^{55} -1.94410 q^{56} +17.7409 q^{57} +4.89194 q^{58} -4.07297 q^{59} +3.82835 q^{60} +13.1374 q^{61} -2.32008 q^{62} -1.90801 q^{63} -2.19288 q^{64} -1.76780 q^{65} -2.24821 q^{66} +2.43612 q^{67} -5.48374 q^{68} +17.8725 q^{69} -0.521477 q^{70} -2.59448 q^{71} +3.70936 q^{72} +14.4455 q^{73} +3.00726 q^{74} +2.21540 q^{75} -13.8383 q^{76} -1.94603 q^{77} -2.04231 q^{78} +1.80474 q^{79} -2.44232 q^{80} -11.0835 q^{81} +1.27885 q^{82} -6.57950 q^{83} +3.82835 q^{84} -3.17335 q^{85} -2.86506 q^{86} -20.7825 q^{87} +3.78327 q^{88} -11.5305 q^{89} +0.994983 q^{90} -1.76780 q^{91} -13.9410 q^{92} +9.85644 q^{93} +3.80594 q^{94} -8.00800 q^{95} -11.4355 q^{96} +4.26564 q^{97} -0.521477 q^{98} +3.71304 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−0.521477	−0.368740	−0.184370	−	0.982857i	$-0.559024\pi$
$2$	−0.521477	−0.368740	−0.184370	+	0.982857i	$0.559024\pi$
$3$	2.21540	1.27906	0.639532	−	0.768765i	$-0.279128\pi$
$3$	2.21540	1.27906	0.639532	+	0.768765i	$0.279128\pi$
$4$	−1.72806	−0.864031
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−1.15528	−0.471642
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	1.94410	0.687342
$9$	1.90801	0.636003
$10$	0.521477	0.164905
$11$	1.94603	0.586750	0.293375	−	0.955997i	$-0.405222\pi$
$11$	1.94603	0.586750	0.293375	+	0.955997i	$0.405222\pi$
$12$	−3.82835	−1.10515
$13$	1.76780	0.490300	0.245150	−	0.969485i	$-0.421163\pi$
$13$	1.76780	0.490300	0.245150	+	0.969485i	$0.421163\pi$
$14$	0.521477	0.139371
$15$	−2.21540	−0.572015
$16$	2.44232	0.610580
$17$	3.17335	0.769649	0.384825	−	0.922990i	$-0.374262\pi$
$17$	3.17335	0.769649	0.384825	+	0.922990i	$0.374262\pi$
$18$	−0.994983	−0.234520
$19$	8.00800	1.83716	0.918580	−	0.395234i	$-0.129337\pi$
$19$	8.00800	1.83716	0.918580	+	0.395234i	$0.129337\pi$
$20$	1.72806	0.386406
$21$	−2.21540	−0.483441
$22$	−1.01481	−0.216358
$23$	8.06739	1.68217	0.841084	−	0.540905i	$-0.181918\pi$
$23$	8.06739	1.68217	0.841084	+	0.540905i	$0.181918\pi$
$24$	4.30696	0.879155
$25$	1.00000	0.200000
$26$	−0.921868	−0.180793
$27$	−2.41920	−0.465575
$28$	1.72806	0.326573
$29$	−9.38093	−1.74199	−0.870997	−	0.491288i	$-0.836526\pi$
$29$	−9.38093	−1.74199	−0.870997	+	0.491288i	$0.836526\pi$
$30$	1.15528	0.210925
$31$	4.44905	0.799074	0.399537	−	0.916717i	$-0.369171\pi$
$31$	4.44905	0.799074	0.399537	+	0.916717i	$0.369171\pi$
$32$	−5.16181	−0.912488
$33$	4.31124	0.750490
$34$	−1.65483	−0.283800
$35$	1.00000	0.169031
$36$	−3.29716	−0.549527
$37$	−5.76682	−0.948060	−0.474030	−	0.880509i	$-0.657201\pi$
$37$	−5.76682	−0.948060	−0.474030	+	0.880509i	$0.657201\pi$
$38$	−4.17599	−0.677434
$39$	3.91639	0.627125
$40$	−1.94410	−0.307389
$41$	−2.45236	−0.382994	−0.191497	−	0.981493i	$-0.561334\pi$
$41$	−2.45236	−0.382994	−0.191497	+	0.981493i	$0.561334\pi$
$42$	1.15528	0.178264
$43$	5.49412	0.837845	0.418923	−	0.908022i	$-0.362408\pi$
$43$	5.49412	0.837845	0.418923	+	0.908022i	$0.362408\pi$
$44$	−3.36286	−0.506970
$45$	−1.90801	−0.284429
$46$	−4.20696	−0.620282
$47$	−7.29838	−1.06458	−0.532289	−	0.846563i	$-0.678668\pi$
$47$	−7.29838	−1.06458	−0.532289	+	0.846563i	$0.678668\pi$
$48$	5.41073	0.780971
$49$	1.00000	0.142857
$50$	−0.521477	−0.0737480
$51$	7.03024	0.984431
$52$	−3.05487	−0.423634
$53$	−3.09207	−0.424729	−0.212364	−	0.977191i	$-0.568116\pi$
$53$	−3.09207	−0.424729	−0.212364	+	0.977191i	$0.568116\pi$
$54$	1.26156	0.171676
$55$	−1.94603	−0.262402
$56$	−1.94410	−0.259791
$57$	17.7409	2.34985
$58$	4.89194	0.642343
$59$	−4.07297	−0.530255	−0.265128	−	0.964213i	$-0.585414\pi$
$59$	−4.07297	−0.530255	−0.265128	+	0.964213i	$0.585414\pi$
$60$	3.82835	0.494238
$61$	13.1374	1.68207	0.841033	−	0.540983i	$-0.181948\pi$
$61$	13.1374	1.68207	0.841033	+	0.540983i	$0.181948\pi$
$62$	−2.32008	−0.294650
$63$	−1.90801	−0.240387
$64$	−2.19288	−0.274110
$65$	−1.76780	−0.219269
$66$	−2.24821	−0.276736
$67$	2.43612	0.297620	0.148810	−	0.988866i	$-0.452456\pi$
$67$	2.43612	0.297620	0.148810	+	0.988866i	$0.452456\pi$
$68$	−5.48374	−0.665001
$69$	17.8725	2.15160
$70$	−0.521477	−0.0623284
$71$	−2.59448	−0.307909	−0.153954	−	0.988078i	$-0.549201\pi$
$71$	−2.59448	−0.307909	−0.153954	+	0.988078i	$0.549201\pi$
$72$	3.70936	0.437152
$73$	14.4455	1.69071	0.845357	−	0.534202i	$-0.179388\pi$
$73$	14.4455	1.69071	0.845357	+	0.534202i	$0.179388\pi$
$74$	3.00726	0.349587
$75$	2.21540	0.255813
$76$	−13.8383	−1.58736
$77$	−1.94603	−0.221771
$78$	−2.04231	−0.231246
$79$	1.80474	0.203050	0.101525	−	0.994833i	$-0.467628\pi$
$79$	1.80474	0.203050	0.101525	+	0.994833i	$0.467628\pi$
$80$	−2.44232	−0.273060
$81$	−11.0835	−1.23150
$82$	1.27885	0.141225
$83$	−6.57950	−0.722194	−0.361097	−	0.932528i	$-0.617598\pi$
$83$	−6.57950	−0.722194	−0.361097	+	0.932528i	$0.617598\pi$
$84$	3.82835	0.417708
$85$	−3.17335	−0.344198
$86$	−2.86506	−0.308947
$87$	−20.7825	−2.22812
$88$	3.78327	0.403298
$89$	−11.5305	−1.22223	−0.611115	−	0.791542i	$-0.709279\pi$
$89$	−11.5305	−1.22223	−0.611115	+	0.791542i	$0.709279\pi$
$90$	0.994983	0.104880
$91$	−1.76780	−0.185316
$92$	−13.9410	−1.45344
$93$	9.85644	1.02207
$94$	3.80594	0.392552
$95$	−8.00800	−0.821603
$96$	−11.4355	−1.16713
$97$	4.26564	0.433110	0.216555	−	0.976270i	$-0.430518\pi$
$97$	4.26564	0.433110	0.216555	+	0.976270i	$0.430518\pi$
$98$	−0.521477	−0.0526771
$99$	3.71304	0.373175
$100$	−1.72806	−0.172806
$101$	8.68195	0.863886	0.431943	−	0.901901i	$-0.357828\pi$
$101$	8.68195	0.863886	0.431943	+	0.901901i	$0.357828\pi$
$102$	−3.66611	−0.362999
$103$	−6.86999	−0.676920	−0.338460	−	0.940981i	$-0.609906\pi$
$103$	−6.86999	−0.676920	−0.338460	+	0.940981i	$0.609906\pi$
$104$	3.43678	0.337004
$105$	2.21540	0.216201
$106$	1.61244	0.156614
$107$	12.2170	1.18106	0.590532	−	0.807014i	$-0.298918\pi$
$107$	12.2170	1.18106	0.590532	+	0.807014i	$0.298918\pi$
$108$	4.18052	0.402271
$109$	10.0997	0.967372	0.483686	−	0.875242i	$-0.339298\pi$
$109$	10.0997	0.967372	0.483686	+	0.875242i	$0.339298\pi$
$110$	1.01481	0.0967582
$111$	−12.7758	−1.21263
$112$	−2.44232	−0.230778
$113$	0.766277	0.0720853	0.0360426	−	0.999350i	$-0.488525\pi$
$113$	0.766277	0.0720853	0.0360426	+	0.999350i	$0.488525\pi$
$114$	−9.25149	−0.866481
$115$	−8.06739	−0.752288
$116$	16.2108	1.50514
$117$	3.37298	0.311833
$118$	2.12396	0.195526
$119$	−3.17335	−0.290900
$120$	−4.30696	−0.393170
$121$	−7.21297	−0.655725
$122$	−6.85083	−0.620245
$123$	−5.43296	−0.489874
$124$	−7.68824	−0.690424
$125$	−1.00000	−0.0894427
$126$	0.994983	0.0886401
$127$	7.76968	0.689447	0.344724	−	0.938704i	$-0.387973\pi$
$127$	7.76968	0.689447	0.344724	+	0.938704i	$0.387973\pi$
$128$	11.4672	1.01356
$129$	12.1717	1.07166
$130$	0.921868	0.0808532
$131$	4.15239	0.362796	0.181398	−	0.983410i	$-0.441938\pi$
$131$	4.15239	0.362796	0.181398	+	0.983410i	$0.441938\pi$
$132$	−7.45009	−0.648447
$133$	−8.00800	−0.694381
$134$	−1.27038	−0.109744
$135$	2.41920	0.208211
$136$	6.16930	0.529013
$137$	−14.4146	−1.23152	−0.615760	−	0.787934i	$-0.711151\pi$
$137$	−14.4146	−1.23152	−0.615760	+	0.787934i	$0.711151\pi$
$138$	−9.32011	−0.793380
$139$	−14.0854	−1.19470	−0.597352	−	0.801979i	$-0.703781\pi$
$139$	−14.0854	−1.19470	−0.597352	+	0.801979i	$0.703781\pi$
$140$	−1.72806	−0.146048
$141$	−16.1688	−1.36166
$142$	1.35296	0.113538
$143$	3.44019	0.287684
$144$	4.65997	0.388331
$145$	9.38093	0.779044
$146$	−7.53297	−0.623433
$147$	2.21540	0.182723
$148$	9.96542	0.819153
$149$	11.5097	0.942914	0.471457	−	0.881889i	$-0.343728\pi$
$149$	11.5097	0.942914	0.471457	+	0.881889i	$0.343728\pi$
$150$	−1.15528	−0.0943283
$151$	−10.4398	−0.849578	−0.424789	−	0.905292i	$-0.639652\pi$
$151$	−10.4398	−0.849578	−0.424789	+	0.905292i	$0.639652\pi$
$152$	15.5683	1.26276
$153$	6.05478	0.489500
$154$	1.01481	0.0817756
$155$	−4.44905	−0.357357
$156$	−6.76777	−0.541855
$157$	−24.6599	−1.96807	−0.984036	−	0.177967i	$-0.943048\pi$
$157$	−24.6599	−1.96807	−0.984036	+	0.177967i	$0.943048\pi$
$158$	−0.941133	−0.0748725
$159$	−6.85018	−0.543255
$160$	5.16181	0.408077
$161$	−8.06739	−0.635800
$162$	5.77980	0.454104
$163$	16.1527	1.26518	0.632589	−	0.774487i	$-0.281992\pi$
$163$	16.1527	1.26518	0.632589	+	0.774487i	$0.281992\pi$
$164$	4.23783	0.330919
$165$	−4.31124	−0.335629
$166$	3.43106	0.266302
$167$	12.4168	0.960842	0.480421	−	0.877038i	$-0.340484\pi$
$167$	12.4168	0.960842	0.480421	+	0.877038i	$0.340484\pi$
$168$	−4.30696	−0.332289
$169$	−9.87488	−0.759606
$170$	1.65483	0.126919
$171$	15.2793	1.16844
$172$	−9.49418	−0.723924
$173$	−14.6928	−1.11707	−0.558536	−	0.829480i	$-0.688637\pi$
$173$	−14.6928	−1.11707	−0.558536	+	0.829480i	$0.688637\pi$
$174$	10.8376	0.821597
$175$	−1.00000	−0.0755929
$176$	4.75283	0.358258
$177$	−9.02327	−0.678230
$178$	6.01288	0.450685
$179$	9.42205	0.704237	0.352119	−	0.935955i	$-0.385461\pi$
$179$	9.42205	0.704237	0.352119	+	0.935955i	$0.385461\pi$
$180$	3.29716	0.245756
$181$	20.6969	1.53839	0.769194	−	0.639016i	$-0.220658\pi$
$181$	20.6969	1.53839	0.769194	+	0.639016i	$0.220658\pi$
$182$	0.921868	0.0683334
$183$	29.1045	2.15147
$184$	15.6838	1.15622
$185$	5.76682	0.423985
$186$	−5.13991	−0.376876
$187$	6.17542	0.451592
$188$	12.6120	0.919828
$189$	2.41920	0.175971
$190$	4.17599	0.302958
$191$	19.0734	1.38010	0.690052	−	0.723760i	$-0.257588\pi$
$191$	19.0734	1.38010	0.690052	+	0.723760i	$0.257588\pi$
$192$	−4.85811	−0.350604
$193$	23.5476	1.69499	0.847496	−	0.530802i	$-0.178109\pi$
$193$	23.5476	1.69499	0.847496	+	0.530802i	$0.178109\pi$
$194$	−2.22443	−0.159705
$195$	−3.91639	−0.280459
$196$	−1.72806	−0.123433
$197$	10.3337	0.736243	0.368121	−	0.929778i	$-0.380001\pi$
$197$	10.3337	0.736243	0.368121	+	0.929778i	$0.380001\pi$
$198$	−1.93627	−0.137604
$199$	−4.58436	−0.324976	−0.162488	−	0.986710i	$-0.551952\pi$
$199$	−4.58436	−0.324976	−0.162488	+	0.986710i	$0.551952\pi$
$200$	1.94410	0.137468
$201$	5.39700	0.380675
$202$	−4.52743	−0.318549
$203$	9.38093	0.658412
$204$	−12.1487	−0.850578
$205$	2.45236	0.171280
$206$	3.58254	0.249607
$207$	15.3927	1.06986
$208$	4.31754	0.299368
$209$	15.5838	1.07795
$210$	−1.15528	−0.0797220
$211$	9.78267	0.673467	0.336733	−	0.941600i	$-0.390678\pi$
$211$	9.78267	0.673467	0.336733	+	0.941600i	$0.390678\pi$
$212$	5.34329	0.366979
$213$	−5.74783	−0.393835
$214$	−6.37089	−0.435505
$215$	−5.49412	−0.374696
$216$	−4.70316	−0.320009
$217$	−4.44905	−0.302021
$218$	−5.26674	−0.356709
$219$	32.0025	2.16253
$220$	3.36286	0.226724
$221$	5.60985	0.377359
$222$	6.66230	0.447144
$223$	4.86837	0.326010	0.163005	−	0.986625i	$-0.447881\pi$
$223$	4.86837	0.326010	0.163005	+	0.986625i	$0.447881\pi$
$224$	5.16181	0.344888
$225$	1.90801	0.127201
$226$	−0.399596	−0.0265807
$227$	21.3861	1.41944	0.709722	−	0.704482i	$-0.248820\pi$
$227$	21.3861	1.41944	0.709722	+	0.704482i	$0.248820\pi$
$228$	−30.6574	−2.03034
$229$	1.00000	0.0660819
$229$	1.00000	0.0660819
$230$	4.20696	0.277399
$231$	−4.31124	−0.283659
$232$	−18.2374	−1.19735
$233$	3.40775	0.223249	0.111624	−	0.993750i	$-0.464395\pi$
$233$	3.40775	0.223249	0.111624	+	0.993750i	$0.464395\pi$
$234$	−1.75893	−0.114985
$235$	7.29838	0.476094
$236$	7.03834	0.458157
$237$	3.99824	0.259713
$238$	1.65483	0.107266
$239$	13.2065	0.854255	0.427127	−	0.904191i	$-0.359526\pi$
$239$	13.2065	0.854255	0.427127	+	0.904191i	$0.359526\pi$
$240$	−5.41073	−0.349261
$241$	20.7817	1.33867	0.669334	−	0.742962i	$-0.266580\pi$
$241$	20.7817	1.33867	0.669334	+	0.742962i	$0.266580\pi$
$242$	3.76140	0.241792
$243$	−17.2969	−1.10960
$244$	−22.7022	−1.45336
$245$	−1.00000	−0.0638877
$246$	2.83316	0.180636
$247$	14.1566	0.900760
$248$	8.64939	0.549237
$249$	−14.5762	−0.923732
$250$	0.521477	0.0329811
$251$	22.6681	1.43080	0.715400	−	0.698715i	$-0.246244\pi$
$251$	22.6681	1.43080	0.715400	+	0.698715i	$0.246244\pi$
$252$	3.29716	0.207702
$253$	15.6994	0.987011
$254$	−4.05171	−0.254227
$255$	−7.03024	−0.440251
$256$	−1.59410	−0.0996311
$257$	6.45052	0.402372	0.201186	−	0.979553i	$-0.435520\pi$
$257$	6.45052	0.402372	0.201186	+	0.979553i	$0.435520\pi$
$258$	−6.34725	−0.395163
$259$	5.76682	0.358333
$260$	3.05487	0.189455
$261$	−17.8989	−1.10791
$262$	−2.16537	−0.133777
$263$	5.20949	0.321231	0.160616	−	0.987017i	$-0.448652\pi$
$263$	5.20949	0.321231	0.160616	+	0.987017i	$0.448652\pi$
$264$	8.38147	0.515844
$265$	3.09207	0.189944
$266$	4.17599	0.256046
$267$	−25.5447	−1.56331
$268$	−4.20977	−0.257153
$269$	−22.1049	−1.34776	−0.673881	−	0.738840i	$-0.735374\pi$
$269$	−22.1049	−1.34776	−0.673881	+	0.738840i	$0.735374\pi$
$270$	−1.26156	−0.0767758
$271$	−2.22456	−0.135132	−0.0675661	−	0.997715i	$-0.521523\pi$
$271$	−2.22456	−0.135132	−0.0675661	+	0.997715i	$0.521523\pi$
$272$	7.75033	0.469933
$273$	−3.91639	−0.237031
$274$	7.51686	0.454110
$275$	1.94603	0.117350
$276$	−30.8848	−1.85905
$277$	−26.0570	−1.56562	−0.782808	−	0.622264i	$-0.786213\pi$
$277$	−26.0570	−1.56562	−0.782808	+	0.622264i	$0.786213\pi$
$278$	7.34519	0.440535
$279$	8.48884	0.508213
$280$	1.94410	0.116182
$281$	−28.3543	−1.69148	−0.845739	−	0.533597i	$-0.820840\pi$
$281$	−28.3543	−1.69148	−0.845739	+	0.533597i	$0.820840\pi$
$282$	8.43168	0.502099
$283$	7.94287	0.472154	0.236077	−	0.971734i	$-0.424138\pi$
$283$	7.94287	0.472154	0.236077	+	0.971734i	$0.424138\pi$
$284$	4.48343	0.266043
$285$	−17.7409	−1.05088
$286$	−1.79398	−0.106080
$287$	2.45236	0.144758
$288$	−9.84879	−0.580345
$289$	−6.92987	−0.407640
$290$	−4.89194	−0.287264
$291$	9.45011	0.553975
$292$	−24.9627	−1.46083
$293$	4.74681	0.277311	0.138656	−	0.990341i	$-0.455722\pi$
$293$	4.74681	0.277311	0.138656	+	0.990341i	$0.455722\pi$
$294$	−1.15528	−0.0673774
$295$	4.07297	0.237137
$296$	−11.2113	−0.651642
$297$	−4.70783	−0.273176
$298$	−6.00206	−0.347690
$299$	14.2616	0.824767
$300$	−3.82835	−0.221030
$301$	−5.49412	−0.316676
$302$	5.44411	0.313273
$303$	19.2340	1.10497
$304$	19.5581	1.12173
$305$	−13.1374	−0.752243
$306$	−3.15743	−0.180498
$307$	21.7657	1.24224	0.621118	−	0.783717i	$-0.286679\pi$
$307$	21.7657	1.24224	0.621118	+	0.783717i	$0.286679\pi$
$308$	3.36286	0.191617
$309$	−15.2198	−0.865823
$310$	2.32008	0.131772
$311$	−3.62981	−0.205828	−0.102914	−	0.994690i	$-0.532817\pi$
$311$	−3.62981	−0.205828	−0.102914	+	0.994690i	$0.532817\pi$
$312$	7.61385	0.431050
$313$	−31.8759	−1.80173	−0.900865	−	0.434099i	$-0.857067\pi$
$313$	−31.8759	−1.80173	−0.900865	+	0.434099i	$0.857067\pi$
$314$	12.8596	0.725707
$315$	1.90801	0.107504
$316$	−3.11871	−0.175441
$317$	−11.3583	−0.637948	−0.318974	−	0.947763i	$-0.603338\pi$
$317$	−11.3583	−0.637948	−0.318974	+	0.947763i	$0.603338\pi$
$318$	3.57221	0.200320
$319$	−18.2556	−1.02211
$320$	2.19288	0.122586
$321$	27.0656	1.51066
$322$	4.20696	0.234445
$323$	25.4121	1.41397
$324$	19.1530	1.06406
$325$	1.76780	0.0980600
$326$	−8.42327	−0.466522
$327$	22.3748	1.23733
$328$	−4.76762	−0.263248
$329$	7.29838	0.402373
$330$	2.24821	0.123760
$331$	−5.58681	−0.307079	−0.153540	−	0.988143i	$-0.549067\pi$
$331$	−5.58681	−0.307079	−0.153540	+	0.988143i	$0.549067\pi$
$332$	11.3698	0.623998
$333$	−11.0032	−0.602969
$334$	−6.47508	−0.354301
$335$	−2.43612	−0.133100
$336$	−5.41073	−0.295179
$337$	34.2765	1.86716	0.933579	−	0.358371i	$-0.116668\pi$
$337$	34.2765	1.86716	0.933579	+	0.358371i	$0.116668\pi$
$338$	5.14952	0.280097
$339$	1.69761	0.0922016
$340$	5.48374	0.297397
$341$	8.65799	0.468856
$342$	−7.96782	−0.430850
$343$	−1.00000	−0.0539949
$344$	10.6811	0.575887
$345$	−17.8725	−0.962224
$346$	7.66195	0.411909
$347$	−6.91428	−0.371178	−0.185589	−	0.982627i	$-0.559419\pi$
$347$	−6.91428	−0.371178	−0.185589	+	0.982627i	$0.559419\pi$
$348$	35.9135	1.92517
$349$	−34.7541	−1.86035	−0.930173	−	0.367123i	$-0.880343\pi$
$349$	−34.7541	−1.86035	−0.930173	+	0.367123i	$0.880343\pi$
$350$	0.521477	0.0278741
$351$	−4.27666	−0.228271
$352$	−10.0450	−0.535402
$353$	−3.26561	−0.173811	−0.0869054	−	0.996217i	$-0.527698\pi$
$353$	−3.26561	−0.173811	−0.0869054	+	0.996217i	$0.527698\pi$
$354$	4.70542	0.250090
$355$	2.59448	0.137701
$356$	19.9254	1.05604
$357$	−7.03024	−0.372080
$358$	−4.91338	−0.259680
$359$	24.6523	1.30110	0.650550	−	0.759463i	$-0.274538\pi$
$359$	24.6523	1.30110	0.650550	+	0.759463i	$0.274538\pi$
$360$	−3.70936	−0.195500
$361$	45.1280	2.37516
$362$	−10.7929	−0.567265
$363$	−15.9796	−0.838713
$364$	3.05487	0.160119
$365$	−14.4455	−0.756110
$366$	−15.1773	−0.793333
$367$	10.6833	0.557665	0.278832	−	0.960340i	$-0.410053\pi$
$367$	10.6833	0.557665	0.278832	+	0.960340i	$0.410053\pi$
$368$	19.7032	1.02710
$369$	−4.67912	−0.243585
$370$	−3.00726	−0.156340
$371$	3.09207	0.160532
$372$	−17.0325	−0.883096
$373$	−16.3923	−0.848761	−0.424381	−	0.905484i	$-0.639508\pi$
$373$	−16.3923	−0.848761	−0.424381	+	0.905484i	$0.639508\pi$
$374$	−3.22034	−0.166520
$375$	−2.21540	−0.114403
$376$	−14.1888	−0.731730
$377$	−16.5836	−0.854100
$378$	−1.26156	−0.0648874
$379$	36.8033	1.89046	0.945228	−	0.326410i	$-0.105839\pi$
$379$	36.8033	1.89046	0.945228	+	0.326410i	$0.105839\pi$
$380$	13.8383	0.709891
$381$	17.2130	0.881847
$382$	−9.94634	−0.508899
$383$	−17.1835	−0.878036	−0.439018	−	0.898478i	$-0.644674\pi$
$383$	−17.1835	−0.878036	−0.439018	+	0.898478i	$0.644674\pi$
$384$	25.4044	1.29641
$385$	1.94603	0.0991788
$386$	−12.2795	−0.625011
$387$	10.4828	0.532872
$388$	−7.37129	−0.374220
$389$	32.5302	1.64935	0.824675	−	0.565608i	$-0.191358\pi$
$389$	32.5302	1.64935	0.824675	+	0.565608i	$0.191358\pi$
$390$	2.04231	0.103416
$391$	25.6006	1.29468
$392$	1.94410	0.0981918
$393$	9.19921	0.464039
$394$	−5.38876	−0.271482
$395$	−1.80474	−0.0908066
$396$	−6.41637	−0.322435
$397$	−9.64015	−0.483825	−0.241913	−	0.970298i	$-0.577775\pi$
$397$	−9.64015	−0.483825	−0.241913	+	0.970298i	$0.577775\pi$
$398$	2.39064	0.119832
$399$	−17.7409	−0.888158
$400$	2.44232	0.122116
$401$	−22.6165	−1.12941	−0.564707	−	0.825291i	$-0.691011\pi$
$401$	−22.6165	−1.12941	−0.564707	+	0.825291i	$0.691011\pi$
$402$	−2.81441	−0.140370
$403$	7.86505	0.391786
$404$	−15.0029	−0.746424
$405$	11.0835	0.550745
$406$	−4.89194	−0.242783
$407$	−11.2224	−0.556274
$408$	13.6675	0.676641
$409$	33.3648	1.64979	0.824893	−	0.565289i	$-0.191236\pi$
$409$	33.3648	1.64979	0.824893	+	0.565289i	$0.191236\pi$
$410$	−1.27885	−0.0631578
$411$	−31.9341	−1.57519
$412$	11.8718	0.584880
$413$	4.07297	0.200418
$414$	−8.02692	−0.394501
$415$	6.57950	0.322975
$416$	−9.12506	−0.447393
$417$	−31.2047	−1.52810
$418$	−8.12659	−0.397484
$419$	40.1626	1.96207	0.981036	−	0.193824i	$-0.0620892\pi$
$419$	40.1626	1.96207	0.981036	+	0.193824i	$0.0620892\pi$
$420$	−3.82835	−0.186805
$421$	−6.45628	−0.314660	−0.157330	−	0.987546i	$-0.550289\pi$
$421$	−6.45628	−0.314660	−0.157330	+	0.987546i	$0.550289\pi$
$422$	−5.10144	−0.248334
$423$	−13.9254	−0.677075
$424$	−6.01129	−0.291934
$425$	3.17335	0.153930
$426$	2.99736	0.145223
$427$	−13.1374	−0.635761
$428$	−21.1118	−1.02048
$429$	7.62142	0.367965
$430$	2.86506	0.138165
$431$	−6.82850	−0.328917	−0.164459	−	0.986384i	$-0.552588\pi$
$431$	−6.82850	−0.328917	−0.164459	+	0.986384i	$0.552588\pi$
$432$	−5.90846	−0.284271
$433$	−1.09315	−0.0525335	−0.0262667	−	0.999655i	$-0.508362\pi$
$433$	−1.09315	−0.0525335	−0.0262667	+	0.999655i	$0.508362\pi$
$434$	2.32008	0.111367
$435$	20.7825	0.996446
$436$	−17.4528	−0.835839
$437$	64.6036	3.09041
$438$	−16.6886	−0.797411
$439$	23.0556	1.10038	0.550192	−	0.835038i	$-0.314554\pi$
$439$	23.0556	1.10038	0.550192	+	0.835038i	$0.314554\pi$
$440$	−3.78327	−0.180360
$441$	1.90801	0.0908576
$442$	−2.92541	−0.139147
$443$	12.2707	0.582999	0.291500	−	0.956571i	$-0.405846\pi$
$443$	12.2707	0.582999	0.291500	+	0.956571i	$0.405846\pi$
$444$	22.0774	1.04775
$445$	11.5305	0.546598
$446$	−2.53874	−0.120213
$447$	25.4987	1.20605
$448$	2.19288	0.103604
$449$	−20.3262	−0.959254	−0.479627	−	0.877473i	$-0.659228\pi$
$449$	−20.3262	−0.959254	−0.479627	+	0.877473i	$0.659228\pi$
$450$	−0.994983	−0.0469040
$451$	−4.77236	−0.224722
$452$	−1.32417	−0.0622839
$453$	−23.1283	−1.08666
$454$	−11.1523	−0.523406
$455$	1.76780	0.0828758
$456$	34.4901	1.61515
$457$	21.2711	0.995022	0.497511	−	0.867458i	$-0.334247\pi$
$457$	21.2711	0.995022	0.497511	+	0.867458i	$0.334247\pi$
$458$	−0.521477	−0.0243670
$459$	−7.67695	−0.358329
$460$	13.9410	0.650000
$461$	29.7055	1.38352	0.691762	−	0.722126i	$-0.256835\pi$
$461$	29.7055	1.38352	0.691762	+	0.722126i	$0.256835\pi$
$462$	2.24821	0.104596
$463$	−7.63301	−0.354736	−0.177368	−	0.984145i	$-0.556758\pi$
$463$	−7.63301	−0.354736	−0.177368	+	0.984145i	$0.556758\pi$
$464$	−22.9112	−1.06363
$465$	−9.85644	−0.457082
$466$	−1.77706	−0.0823208
$467$	−10.7663	−0.498205	−0.249103	−	0.968477i	$-0.580136\pi$
$467$	−10.7663	−0.498205	−0.249103	+	0.968477i	$0.580136\pi$
$468$	−5.82873	−0.269433
$469$	−2.43612	−0.112490
$470$	−3.80594	−0.175555
$471$	−54.6316	−2.51729
$472$	−7.91825	−0.364467
$473$	10.6917	0.491606
$474$	−2.08499	−0.0957667
$475$	8.00800	0.367432
$476$	5.48374	0.251347
$477$	−5.89970	−0.270129
$478$	−6.88686	−0.314998
$479$	−18.1989	−0.831528	−0.415764	−	0.909472i	$-0.636486\pi$
$479$	−18.1989	−0.831528	−0.415764	+	0.909472i	$0.636486\pi$
$480$	11.4355	0.521956
$481$	−10.1946	−0.464834
$482$	−10.8372	−0.493620
$483$	−17.8725	−0.813228
$484$	12.4645	0.566566
$485$	−4.26564	−0.193693
$486$	9.01993	0.409152
$487$	12.6195	0.571843	0.285922	−	0.958253i	$-0.407700\pi$
$487$	12.6195	0.571843	0.285922	+	0.958253i	$0.407700\pi$
$488$	25.5403	1.15616
$489$	35.7848	1.61824
$490$	0.521477	0.0235579
$491$	14.2955	0.645146	0.322573	−	0.946545i	$-0.395452\pi$
$491$	14.2955	0.645146	0.322573	+	0.946545i	$0.395452\pi$
$492$	9.38849	0.423266
$493$	−29.7689	−1.34073
$494$	−7.38232	−0.332146
$495$	−3.71304	−0.166889
$496$	10.8660	0.487899
$497$	2.59448	0.116379
$498$	7.60118	0.340617
$499$	0.229430	0.0102707	0.00513534	−	0.999987i	$-0.498365\pi$
$499$	0.229430	0.0102707	0.00513534	+	0.999987i	$0.498365\pi$
$500$	1.72806	0.0772813
$501$	27.5083	1.22898
$502$	−11.8209	−0.527593
$503$	22.2710	0.993014	0.496507	−	0.868033i	$-0.334616\pi$
$503$	22.2710	0.993014	0.496507	+	0.868033i	$0.334616\pi$
$504$	−3.70936	−0.165228
$505$	−8.68195	−0.386342
$506$	−8.18686	−0.363950
$507$	−21.8768	−0.971584
$508$	−13.4265	−0.595704
$509$	35.8978	1.59114	0.795570	−	0.605862i	$-0.207171\pi$
$509$	35.8978	1.59114	0.795570	+	0.605862i	$0.207171\pi$
$510$	3.66611	0.162338
$511$	−14.4455	−0.639030
$512$	−22.1030	−0.976825
$513$	−19.3729	−0.855336
$514$	−3.36380	−0.148371
$515$	6.86999	0.302728
$516$	−21.0334	−0.925945
$517$	−14.2029	−0.624641
$518$	−3.00726	−0.132132
$519$	−32.5505	−1.42881
$520$	−3.43678	−0.150713
$521$	−29.5646	−1.29525	−0.647625	−	0.761960i	$-0.724237\pi$
$521$	−29.5646	−1.29525	−0.647625	+	0.761960i	$0.724237\pi$
$522$	9.33386	0.408532
$523$	19.2331	0.841004	0.420502	−	0.907292i	$-0.361854\pi$
$523$	19.2331	0.841004	0.420502	+	0.907292i	$0.361854\pi$
$524$	−7.17558	−0.313467
$525$	−2.21540	−0.0966881
$526$	−2.71663	−0.118451
$527$	14.1184	0.615007
$528$	10.5294	0.458235
$529$	42.0828	1.82969
$530$	−1.61244	−0.0700401
$531$	−7.77126	−0.337244
$532$	13.8383	0.599967
$533$	−4.33528	−0.187782
$534$	13.3210	0.576454
$535$	−12.2170	−0.528188
$536$	4.73606	0.204567
$537$	20.8736	0.900764
$538$	11.5272	0.496973
$539$	1.94603	0.0838214
$540$	−4.18052	−0.179901
$541$	−28.0213	−1.20473	−0.602365	−	0.798221i	$-0.705775\pi$
$541$	−28.0213	−1.20473	−0.602365	+	0.798221i	$0.705775\pi$
$542$	1.16005	0.0498286
$543$	45.8519	1.96770
$544$	−16.3802	−0.702296
$545$	−10.0997	−0.432622
$546$	2.04231	0.0874028
$547$	−4.05384	−0.173330	−0.0866648	−	0.996238i	$-0.527621\pi$
$547$	−4.05384	−0.173330	−0.0866648	+	0.996238i	$0.527621\pi$
$548$	24.9093	1.06407
$549$	25.0662	1.06980
$550$	−1.01481	−0.0432716
$551$	−75.1224	−3.20032
$552$	34.7459	1.47889
$553$	−1.80474	−0.0767456
$554$	13.5881	0.577305
$555$	12.7758	0.542304
$556$	24.3404	1.03226
$557$	−5.90559	−0.250228	−0.125114	−	0.992142i	$-0.539930\pi$
$557$	−5.90559	−0.250228	−0.125114	+	0.992142i	$0.539930\pi$
$558$	−4.42673	−0.187399
$559$	9.71252	0.410796
$560$	2.44232	0.103207
$561$	13.6811	0.577614
$562$	14.7861	0.623715
$563$	−0.508143	−0.0214157	−0.0107078	−	0.999943i	$-0.503408\pi$
$563$	−0.508143	−0.0214157	−0.0107078	+	0.999943i	$0.503408\pi$
$564$	27.9408	1.17652
$565$	−0.766277	−0.0322375
$566$	−4.14202	−0.174102
$567$	11.0835	0.465464
$568$	−5.04393	−0.211639
$569$	−42.1989	−1.76907	−0.884535	−	0.466474i	$-0.845524\pi$
$569$	−42.1989	−1.76907	−0.884535	+	0.466474i	$0.845524\pi$
$570$	9.25149	0.387502
$571$	24.4134	1.02167	0.510834	−	0.859680i	$-0.329337\pi$
$571$	24.4134	1.02167	0.510834	+	0.859680i	$0.329337\pi$
$572$	−5.94487	−0.248567
$573$	42.2553	1.76524
$574$	−1.27885	−0.0533781
$575$	8.06739	0.336433
$576$	−4.18404	−0.174335
$577$	17.7582	0.739285	0.369643	−	0.929174i	$-0.379480\pi$
$577$	17.7582	0.739285	0.369643	+	0.929174i	$0.379480\pi$
$578$	3.61377	0.150313
$579$	52.1674	2.16800
$580$	−16.2108	−0.673118
$581$	6.57950	0.272964
$582$	−4.92801	−0.204273
$583$	−6.01726	−0.249209
$584$	28.0834	1.16210
$585$	−3.37298	−0.139456
$586$	−2.47535	−0.102256
$587$	−10.6472	−0.439455	−0.219728	−	0.975561i	$-0.570517\pi$
$587$	−10.6472	−0.439455	−0.219728	+	0.975561i	$0.570517\pi$
$588$	−3.82835	−0.157879
$589$	35.6280	1.46803
$590$	−2.12396	−0.0874420
$591$	22.8932	0.941701
$592$	−14.0844	−0.578867
$593$	−39.3692	−1.61670	−0.808349	−	0.588703i	$-0.799639\pi$
$593$	−39.3692	−1.61670	−0.808349	+	0.588703i	$0.799639\pi$
$594$	2.45502	0.100731
$595$	3.17335	0.130095
$596$	−19.8895	−0.814707
$597$	−10.1562	−0.415666
$598$	−7.43707	−0.304124
$599$	24.1593	0.987124	0.493562	−	0.869711i	$-0.335695\pi$
$599$	24.1593	0.987124	0.493562	+	0.869711i	$0.335695\pi$
$600$	4.30696	0.175831
$601$	22.0904	0.901085	0.450542	−	0.892755i	$-0.351231\pi$
$601$	22.0904	0.901085	0.450542	+	0.892755i	$0.351231\pi$
$602$	2.86506	0.116771
$603$	4.64815	0.189287
$604$	18.0406	0.734061
$605$	7.21297	0.293249
$606$	−10.0301	−0.407445
$607$	−17.0574	−0.692337	−0.346169	−	0.938172i	$-0.612518\pi$
$607$	−17.0574	−0.692337	−0.346169	+	0.938172i	$0.612518\pi$
$608$	−41.3358	−1.67639
$609$	20.7825	0.842151
$610$	6.85083	0.277382
$611$	−12.9021	−0.521963
$612$	−10.4630	−0.422943
$613$	−39.5793	−1.59859	−0.799296	−	0.600937i	$-0.794794\pi$
$613$	−39.5793	−1.59859	−0.799296	+	0.600937i	$0.794794\pi$
$614$	−11.3503	−0.458062
$615$	5.43296	0.219078
$616$	−3.78327	−0.152432
$617$	−46.6979	−1.87999	−0.939994	−	0.341191i	$-0.889170\pi$
$617$	−46.6979	−1.87999	−0.939994	+	0.341191i	$0.889170\pi$
$618$	7.93677	0.319264
$619$	−7.43674	−0.298908	−0.149454	−	0.988769i	$-0.547752\pi$
$619$	−7.43674	−0.298908	−0.149454	+	0.988769i	$0.547752\pi$
$620$	7.68824	0.308767
$621$	−19.5166	−0.783175
$622$	1.89286	0.0758968
$623$	11.5305	0.461959
$624$	9.56510	0.382910
$625$	1.00000	0.0400000
$626$	16.6225	0.664370
$627$	34.5244	1.37877
$628$	42.6138	1.70048
$629$	−18.3001	−0.729674
$630$	−0.994983	−0.0396411
$631$	30.6502	1.22016	0.610082	−	0.792338i	$-0.291136\pi$
$631$	30.6502	1.22016	0.610082	+	0.792338i	$0.291136\pi$
$632$	3.50860	0.139565
$633$	21.6726	0.861407
$634$	5.92311	0.235237
$635$	−7.76968	−0.308330
$636$	11.8375	0.469389
$637$	1.76780	0.0700429
$638$	9.51985	0.376894
$639$	−4.95030	−0.195831
$640$	−11.4672	−0.453279
$641$	−24.8632	−0.982039	−0.491020	−	0.871149i	$-0.663376\pi$
$641$	−24.8632	−0.982039	−0.491020	+	0.871149i	$0.663376\pi$
$642$	−14.1141	−0.557039
$643$	27.4053	1.08076	0.540380	−	0.841421i	$-0.318281\pi$
$643$	27.4053	1.08076	0.540380	+	0.841421i	$0.318281\pi$
$644$	13.9410	0.549350
$645$	−12.1717	−0.479260
$646$	−13.2518	−0.521387
$647$	−38.7464	−1.52328	−0.761639	−	0.648001i	$-0.775605\pi$
$647$	−38.7464	−1.52328	−0.761639	+	0.648001i	$0.775605\pi$
$648$	−21.5475	−0.846464
$649$	−7.92611	−0.311127
$650$	−0.921868	−0.0361586
$651$	−9.85644	−0.386305
$652$	−27.9129	−1.09315
$653$	0.501317	0.0196180	0.00980902	−	0.999952i	$-0.496878\pi$
$653$	0.501317	0.0196180	0.00980902	+	0.999952i	$0.496878\pi$
$654$	−11.6680	−0.456253
$655$	−4.15239	−0.162247
$656$	−5.98945	−0.233849
$657$	27.5621	1.07530
$658$	−3.80594	−0.148371
$659$	−8.28075	−0.322572	−0.161286	−	0.986908i	$-0.551564\pi$
$659$	−8.28075	−0.322572	−0.161286	+	0.986908i	$0.551564\pi$
$660$	7.45009	0.289994
$661$	−40.6226	−1.58003	−0.790017	−	0.613085i	$-0.789928\pi$
$661$	−40.6226	−1.58003	−0.790017	+	0.613085i	$0.789928\pi$
$662$	2.91339	0.113232
$663$	12.4281	0.482666
$664$	−12.7912	−0.496395
$665$	8.00800	0.310537
$666$	5.73789	0.222339
$667$	−75.6796	−2.93033
$668$	−21.4570	−0.830198
$669$	10.7854	0.416987
$670$	1.27038	0.0490792
$671$	25.5657	0.986952
$672$	11.4355	0.441134
$673$	−0.619618	−0.0238845	−0.0119423	−	0.999929i	$-0.503801\pi$
$673$	−0.619618	−0.0238845	−0.0119423	+	0.999929i	$0.503801\pi$
$674$	−17.8744	−0.688496
$675$	−2.41920	−0.0931150
$676$	17.0644	0.656323
$677$	3.34551	0.128578	0.0642892	−	0.997931i	$-0.479522\pi$
$677$	3.34551	0.128578	0.0642892	+	0.997931i	$0.479522\pi$
$678$	−0.885265	−0.0339984
$679$	−4.26564	−0.163700
$680$	−6.16930	−0.236582
$681$	47.3788	1.81556
$682$	−4.51494	−0.172886
$683$	−27.2802	−1.04385	−0.521923	−	0.852993i	$-0.674785\pi$
$683$	−27.2802	−1.04385	−0.521923	+	0.852993i	$0.674785\pi$
$684$	−26.4036	−1.00957
$685$	14.4146	0.550752
$686$	0.521477	0.0199101
$687$	2.21540	0.0845229
$688$	13.4184	0.511572
$689$	−5.46617	−0.208245
$690$	9.32011	0.354810
$691$	−44.1591	−1.67989	−0.839946	−	0.542670i	$-0.817413\pi$
$691$	−44.1591	−1.67989	−0.839946	+	0.542670i	$0.817413\pi$
$692$	25.3901	0.965185
$693$	−3.71304	−0.141047
$694$	3.60564	0.136868
$695$	14.0854	0.534288
$696$	−40.4033	−1.53148
$697$	−7.78218	−0.294771
$698$	18.1235	0.685983
$699$	7.54953	0.285550
$700$	1.72806	0.0653146
$701$	−16.0814	−0.607388	−0.303694	−	0.952770i	$-0.598220\pi$
$701$	−16.0814	−0.607388	−0.303694	+	0.952770i	$0.598220\pi$
$702$	2.23018	0.0841727
$703$	−46.1807	−1.74174
$704$	−4.26741	−0.160834
$705$	16.1688	0.608954
$706$	1.70294	0.0640910
$707$	−8.68195	−0.326518
$708$	15.5928	0.586012
$709$	49.1375	1.84540	0.922699	−	0.385522i	$-0.125979\pi$
$709$	49.1375	1.84540	0.922699	+	0.385522i	$0.125979\pi$
$710$	−1.35296	−0.0507758
$711$	3.44347	0.129140
$712$	−22.4164	−0.840090
$713$	35.8923	1.34418
$714$	3.66611	0.137201
$715$	−3.44019	−0.128656
$716$	−16.2819	−0.608483
$717$	29.2576	1.09265
$718$	−12.8556	−0.479768
$719$	−41.6531	−1.55340	−0.776699	−	0.629872i	$-0.783107\pi$
$719$	−41.6531	−1.55340	−0.776699	+	0.629872i	$0.783107\pi$
$720$	−4.65997	−0.173667
$721$	6.86999	0.255852
$722$	−23.5332	−0.875816
$723$	46.0399	1.71224
$724$	−35.7655	−1.32921
$725$	−9.38093	−0.348399
$726$	8.33301	0.309267
$727$	−32.1494	−1.19235	−0.596177	−	0.802853i	$-0.703314\pi$
$727$	−32.1494	−1.19235	−0.596177	+	0.802853i	$0.703314\pi$
$728$	−3.43678	−0.127376
$729$	−5.06899	−0.187740
$730$	7.53297	0.278808
$731$	17.4347	0.644847
$732$	−50.2945	−1.85894
$733$	5.04428	0.186315	0.0931575	−	0.995651i	$-0.470304\pi$
$733$	5.04428	0.186315	0.0931575	+	0.995651i	$0.470304\pi$
$734$	−5.57111	−0.205633
$735$	−2.21540	−0.0817164
$736$	−41.6423	−1.53496
$737$	4.74077	0.174628
$738$	2.44005	0.0898197
$739$	2.82188	0.103805	0.0519023	−	0.998652i	$-0.483472\pi$
$739$	2.82188	0.103805	0.0519023	+	0.998652i	$0.483472\pi$
$740$	−9.96542	−0.366336
$741$	31.3625	1.15213
$742$	−1.61244	−0.0591947
$743$	28.1231	1.03174	0.515869	−	0.856668i	$-0.327469\pi$
$743$	28.1231	1.03174	0.515869	+	0.856668i	$0.327469\pi$
$744$	19.1619	0.702509
$745$	−11.5097	−0.421684
$746$	8.54821	0.312972
$747$	−12.5538	−0.459318
$748$	−10.6715	−0.390189
$749$	−12.2170	−0.446400
$750$	1.15528	0.0421849
$751$	−20.6063	−0.751934	−0.375967	−	0.926633i	$-0.622689\pi$
$751$	−20.6063	−0.751934	−0.375967	+	0.926633i	$0.622689\pi$
$752$	−17.8250	−0.650010
$753$	50.2191	1.83008
$754$	8.64798	0.314941
$755$	10.4398	0.379943
$756$	−4.18052	−0.152044
$757$	−21.1983	−0.770466	−0.385233	−	0.922819i	$-0.625879\pi$
$757$	−21.1983	−0.770466	−0.385233	+	0.922819i	$0.625879\pi$
$758$	−19.1920	−0.697087
$759$	34.7804	1.26245
$760$	−15.5683	−0.564723
$761$	40.4281	1.46552	0.732759	−	0.680489i	$-0.238232\pi$
$761$	40.4281	1.46552	0.732759	+	0.680489i	$0.238232\pi$
$762$	−8.97616	−0.325172
$763$	−10.0997	−0.365632
$764$	−32.9600	−1.19245
$765$	−6.05478	−0.218911
$766$	8.96080	0.323767
$767$	−7.20020	−0.259984
$768$	−3.53157	−0.127434
$769$	24.4831	0.882885	0.441442	−	0.897290i	$-0.354467\pi$
$769$	24.4831	0.882885	0.441442	+	0.897290i	$0.354467\pi$
$770$	−1.01481	−0.0365712
$771$	14.2905	0.514660
$772$	−40.6917	−1.46453
$773$	−34.9088	−1.25558	−0.627792	−	0.778381i	$-0.716041\pi$
$773$	−34.9088	−1.25558	−0.627792	+	0.778381i	$0.716041\pi$
$774$	−5.46656	−0.196491
$775$	4.44905	0.159815
$776$	8.29282	0.297695
$777$	12.7758	0.458330
$778$	−16.9638	−0.608181
$779$	−19.6385	−0.703621
$780$	6.76777	0.242325
$781$	−5.04894	−0.180665
$782$	−13.3501	−0.477400
$783$	22.6943	0.811029
$784$	2.44232	0.0872258
$785$	24.6599	0.880149
$786$	−4.79718	−0.171110
$787$	−3.32851	−0.118648	−0.0593242	−	0.998239i	$-0.518895\pi$
$787$	−3.32851	−0.118648	−0.0593242	+	0.998239i	$0.518895\pi$
$788$	−17.8572	−0.636137
$789$	11.5411	0.410875
$790$	0.941133	0.0334840
$791$	−0.766277	−0.0272457
$792$	7.21852	0.256499
$793$	23.2243	0.824718
$794$	5.02712	0.178406
$795$	6.85018	0.242951
$796$	7.92205	0.280790
$797$	23.6805	0.838807	0.419403	−	0.907800i	$-0.362239\pi$
$797$	23.6805	0.838807	0.419403	+	0.907800i	$0.362239\pi$
$798$	9.25149	0.327499
$799$	−23.1603	−0.819352
$800$	−5.16181	−0.182498
$801$	−22.0003	−0.777342
$802$	11.7940	0.416460
$803$	28.1113	0.992026
$804$	−9.32634	−0.328915
$805$	8.06739	0.284338
$806$	−4.10144	−0.144467
$807$	−48.9713	−1.72387
$808$	16.8786	0.593786
$809$	−24.5365	−0.862658	−0.431329	−	0.902195i	$-0.641955\pi$
$809$	−24.5365	−0.862658	−0.431329	+	0.902195i	$0.641955\pi$
$810$	−5.77980	−0.203082
$811$	−14.8574	−0.521715	−0.260858	−	0.965377i	$-0.584005\pi$
$811$	−14.8574	−0.521715	−0.260858	+	0.965377i	$0.584005\pi$
$812$	−16.2108	−0.568888
$813$	−4.92829	−0.172843
$814$	5.85222	0.205120
$815$	−16.1527	−0.565805
$816$	17.1701	0.601074
$817$	43.9969	1.53926
$818$	−17.3990	−0.608341
$819$	−3.37298	−0.117862
$820$	−4.23783	−0.147991
$821$	5.58022	0.194751	0.0973755	−	0.995248i	$-0.468955\pi$
$821$	5.58022	0.194751	0.0973755	+	0.995248i	$0.468955\pi$
$822$	16.6529	0.580836
$823$	−28.1659	−0.981802	−0.490901	−	0.871215i	$-0.663332\pi$
$823$	−28.1659	−0.981802	−0.490901	+	0.871215i	$0.663332\pi$
$824$	−13.3559	−0.465276
$825$	4.31124	0.150098
$826$	−2.12396	−0.0739020
$827$	40.2445	1.39944	0.699719	−	0.714418i	$-0.253308\pi$
$827$	40.2445	1.39944	0.699719	+	0.714418i	$0.253308\pi$
$828$	−26.5995	−0.924396
$829$	12.7795	0.443849	0.221925	−	0.975064i	$-0.428766\pi$
$829$	12.7795	0.443849	0.221925	+	0.975064i	$0.428766\pi$
$830$	−3.43106	−0.119094
$831$	−57.7268	−2.00252
$832$	−3.87658	−0.134396
$833$	3.17335	0.109950
$834$	16.2725	0.563472
$835$	−12.4168	−0.429702
$836$	−26.9298	−0.931385
$837$	−10.7631	−0.372028
$838$	−20.9439	−0.723494
$839$	31.7421	1.09586	0.547929	−	0.836525i	$-0.315416\pi$
$839$	31.7421	1.09586	0.547929	+	0.836525i	$0.315416\pi$
$840$	4.30696	0.148604
$841$	59.0018	2.03454
$842$	3.36680	0.116028
$843$	−62.8163	−2.16351
$844$	−16.9051	−0.581896
$845$	9.87488	0.339706
$846$	7.26176	0.249665
$847$	7.21297	0.247841
$848$	−7.55183	−0.259331
$849$	17.5966	0.603915
$850$	−1.65483	−0.0567601
$851$	−46.5232	−1.59479
$852$	9.93260	0.340285
$853$	−50.8267	−1.74027	−0.870137	−	0.492809i	$-0.835970\pi$
$853$	−50.8267	−1.74027	−0.870137	+	0.492809i	$0.835970\pi$
$854$	6.85083	0.234431
$855$	−15.2793	−0.522542
$856$	23.7511	0.811795
$857$	49.9930	1.70773	0.853864	−	0.520496i	$-0.174253\pi$
$857$	49.9930	1.70773	0.853864	+	0.520496i	$0.174253\pi$
$858$	−3.97439	−0.135684
$859$	9.67641	0.330155	0.165077	−	0.986281i	$-0.447213\pi$
$859$	9.67641	0.330155	0.165077	+	0.986281i	$0.447213\pi$
$860$	9.49418	0.323749
$861$	5.43296	0.185155
$862$	3.56090	0.121285
$863$	38.3629	1.30589	0.652944	−	0.757406i	$-0.273534\pi$
$863$	38.3629	1.30589	0.652944	+	0.757406i	$0.273534\pi$
$864$	12.4874	0.424831
$865$	14.6928	0.499570
$866$	0.570053	0.0193712
$867$	−15.3525	−0.521397
$868$	7.68824	0.260956
$869$	3.51209	0.119139
$870$	−10.8376	−0.367429
$871$	4.30659	0.145923
$872$	19.6347	0.664916
$873$	8.13888	0.275459
$874$	−33.6893	−1.13956
$875$	1.00000	0.0338062
$876$	−55.3023	−1.86849
$877$	−32.2934	−1.09047	−0.545236	−	0.838283i	$-0.683560\pi$
$877$	−32.2934	−1.09047	−0.545236	+	0.838283i	$0.683560\pi$
$878$	−12.0230	−0.405755
$879$	10.5161	0.354699
$880$	−4.75283	−0.160218
$881$	−4.98135	−0.167826	−0.0839130	−	0.996473i	$-0.526742\pi$
$881$	−4.98135	−0.167826	−0.0839130	+	0.996473i	$0.526742\pi$
$882$	−0.994983	−0.0335028
$883$	−8.17252	−0.275027	−0.137514	−	0.990500i	$-0.543911\pi$
$883$	−8.17252	−0.275027	−0.137514	+	0.990500i	$0.543911\pi$
$884$	−9.69417	−0.326050
$885$	9.02327	0.303314
$886$	−6.39890	−0.214975
$887$	−15.3734	−0.516187	−0.258094	−	0.966120i	$-0.583094\pi$
$887$	−15.3734	−0.516187	−0.258094	+	0.966120i	$0.583094\pi$
$888$	−24.8375	−0.833491
$889$	−7.76968	−0.260587
$890$	−6.01288	−0.201552
$891$	−21.5689	−0.722584
$892$	−8.41284	−0.281683
$893$	−58.4454	−1.95580
$894$	−13.2970	−0.444717
$895$	−9.42205	−0.314944
$896$	−11.4672	−0.383091
$897$	31.5951	1.05493
$898$	10.5997	0.353715
$899$	−41.7362	−1.39198
$900$	−3.29716	−0.109905
$901$	−9.81221	−0.326892
$902$	2.48868	0.0828638
$903$	−12.1717	−0.405048
$904$	1.48972	0.0495473
$905$	−20.6969	−0.687988
$906$	12.0609	0.400696
$907$	45.3723	1.50656	0.753281	−	0.657698i	$-0.228470\pi$
$907$	45.3723	1.50656	0.753281	+	0.657698i	$0.228470\pi$
$908$	−36.9565	−1.22644
$909$	16.5652	0.549434
$910$	−0.921868	−0.0305596
$911$	−11.3484	−0.375988	−0.187994	−	0.982170i	$-0.560199\pi$
$911$	−11.3484	−0.375988	−0.187994	+	0.982170i	$0.560199\pi$
$912$	43.3291	1.43477
$913$	−12.8039	−0.423747
$914$	−11.0924	−0.366904
$915$	−29.1045	−0.962167
$916$	−1.72806	−0.0570968
$917$	−4.15239	−0.137124
$918$	4.00335	0.132130
$919$	1.39304	0.0459520	0.0229760	−	0.999736i	$-0.492686\pi$
$919$	1.39304	0.0459520	0.0229760	+	0.999736i	$0.492686\pi$
$920$	−15.6838	−0.517080
$921$	48.2199	1.58890
$922$	−15.4907	−0.510160
$923$	−4.58654	−0.150968
$924$	7.45009	0.245090
$925$	−5.76682	−0.189612
$926$	3.98044	0.130805
$927$	−13.1080	−0.430523
$928$	48.4226	1.58955
$929$	−11.5469	−0.378842	−0.189421	−	0.981896i	$-0.560661\pi$
$929$	−11.5469	−0.378842	−0.189421	+	0.981896i	$0.560661\pi$
$930$	5.13991	0.168544
$931$	8.00800	0.262452
$932$	−5.88880	−0.192894
$933$	−8.04149	−0.263267
$934$	5.61438	0.183708
$935$	−6.17542	−0.201958
$936$	6.55741	0.214336
$937$	19.9882	0.652986	0.326493	−	0.945200i	$-0.394133\pi$
$937$	19.9882	0.652986	0.326493	+	0.945200i	$0.394133\pi$
$938$	1.27038	0.0414795
$939$	−70.6179	−2.30453
$940$	−12.6120	−0.411360
$941$	−13.2560	−0.432134	−0.216067	−	0.976379i	$-0.569323\pi$
$941$	−13.2560	−0.432134	−0.216067	+	0.976379i	$0.569323\pi$
$942$	28.4891	0.928225
$943$	−19.7841	−0.644260
$944$	−9.94750	−0.323764
$945$	−2.41920	−0.0786965
$946$	−5.57548	−0.181275
$947$	59.6926	1.93975	0.969875	−	0.243603i	$-0.0783294\pi$
$947$	59.6926	1.93975	0.969875	+	0.243603i	$0.0783294\pi$
$948$	−6.90920	−0.224400
$949$	25.5367	0.828957
$950$	−4.17599	−0.135487
$951$	−25.1633	−0.815976
$952$	−6.16930	−0.199948
$953$	42.0824	1.36318	0.681592	−	0.731733i	$-0.261288\pi$
$953$	42.0824	1.36318	0.681592	+	0.731733i	$0.261288\pi$
$954$	3.07656	0.0996073
$955$	−19.0734	−0.617201
$956$	−22.8216	−0.738103
$957$	−40.4434	−1.30735
$958$	9.49030	0.306618
$959$	14.4146	0.465471
$960$	4.85811	0.156795
$961$	−11.2059	−0.361482
$962$	5.31625	0.171403
$963$	23.3102	0.751160
$964$	−35.9121	−1.15665
$965$	−23.5476	−0.758023
$966$	9.32011	0.299870
$967$	−1.19110	−0.0383031	−0.0191516	−	0.999817i	$-0.506097\pi$
$967$	−1.19110	−0.0383031	−0.0191516	+	0.999817i	$0.506097\pi$
$968$	−14.0227	−0.450707
$969$	56.2981	1.80856
$970$	2.22443	0.0714222
$971$	−6.86428	−0.220285	−0.110143	−	0.993916i	$-0.535131\pi$
$971$	−6.86428	−0.220285	−0.110143	+	0.993916i	$0.535131\pi$
$972$	29.8901	0.958725
$973$	14.0854	0.451556
$974$	−6.58077	−0.210861
$975$	3.91639	0.125425
$976$	32.0857	1.02704
$977$	12.0593	0.385812	0.192906	−	0.981217i	$-0.438209\pi$
$977$	12.0593	0.385812	0.192906	+	0.981217i	$0.438209\pi$
$978$	−18.6609	−0.596711
$979$	−22.4387	−0.717143
$980$	1.72806	0.0552009
$981$	19.2703	0.615252
$982$	−7.45476	−0.237891
$983$	8.91972	0.284495	0.142247	−	0.989831i	$-0.454567\pi$
$983$	8.91972	0.284495	0.142247	+	0.989831i	$0.454567\pi$
$984$	−10.5622	−0.336711
$985$	−10.3337	−0.329258
$986$	15.5238	0.494379
$987$	16.1688	0.514660
$988$	−24.4634	−0.778285
$989$	44.3232	1.40940
$990$	1.93627	0.0615386
$991$	−13.1220	−0.416833	−0.208417	−	0.978040i	$-0.566831\pi$
$991$	−13.1220	−0.416833	−0.208417	+	0.978040i	$0.566831\pi$
$992$	−22.9652	−0.729145
$993$	−12.3770	−0.392774
$994$	−1.35296	−0.0429134
$995$	4.58436	0.145334
$996$	25.1887	0.798133
$997$	−41.2787	−1.30731	−0.653655	−	0.756793i	$-0.726765\pi$
$997$	−41.2787	−1.30731	−0.653655	+	0.756793i	$0.726765\pi$
$998$	−0.119642	−0.00378721
$999$	13.9511	0.441393

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8015.2.a.l.1.27	✓	62

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8015.2.a.l.1.27	✓	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)

\(f(q)\)	\(=\)	\(q-0.521477 q^{2} +2.21540 q^{3} -1.72806 q^{4} -1.00000 q^{5} -1.15528 q^{6} -1.00000 q^{7} +1.94410 q^{8} +1.90801 q^{9} +O(q^{10})\)	\(q-0.521477 q^{2} +2.21540 q^{3} -1.72806 q^{4} -1.00000 q^{5} -1.15528 q^{6} -1.00000 q^{7} +1.94410 q^{8} +1.90801 q^{9} +0.521477 q^{10} +1.94603 q^{11} -3.82835 q^{12} +1.76780 q^{13} +0.521477 q^{14} -2.21540 q^{15} +2.44232 q^{16} +3.17335 q^{17} -0.994983 q^{18} +8.00800 q^{19} +1.72806 q^{20} -2.21540 q^{21} -1.01481 q^{22} +8.06739 q^{23} +4.30696 q^{24} +1.00000 q^{25} -0.921868 q^{26} -2.41920 q^{27} +1.72806 q^{28} -9.38093 q^{29} +1.15528 q^{30} +4.44905 q^{31} -5.16181 q^{32} +4.31124 q^{33} -1.65483 q^{34} +1.00000 q^{35} -3.29716 q^{36} -5.76682 q^{37} -4.17599 q^{38} +3.91639 q^{39} -1.94410 q^{40} -2.45236 q^{41} +1.15528 q^{42} +5.49412 q^{43} -3.36286 q^{44} -1.90801 q^{45} -4.20696 q^{46} -7.29838 q^{47} +5.41073 q^{48} +1.00000 q^{49} -0.521477 q^{50} +7.03024 q^{51} -3.05487 q^{52} -3.09207 q^{53} +1.26156 q^{54} -1.94603 q^{55} -1.94410 q^{56} +17.7409 q^{57} +4.89194 q^{58} -4.07297 q^{59} +3.82835 q^{60} +13.1374 q^{61} -2.32008 q^{62} -1.90801 q^{63} -2.19288 q^{64} -1.76780 q^{65} -2.24821 q^{66} +2.43612 q^{67} -5.48374 q^{68} +17.8725 q^{69} -0.521477 q^{70} -2.59448 q^{71} +3.70936 q^{72} +14.4455 q^{73} +3.00726 q^{74} +2.21540 q^{75} -13.8383 q^{76} -1.94603 q^{77} -2.04231 q^{78} +1.80474 q^{79} -2.44232 q^{80} -11.0835 q^{81} +1.27885 q^{82} -6.57950 q^{83} +3.82835 q^{84} -3.17335 q^{85} -2.86506 q^{86} -20.7825 q^{87} +3.78327 q^{88} -11.5305 q^{89} +0.994983 q^{90} -1.76780 q^{91} -13.9410 q^{92} +9.85644 q^{93} +3.80594 q^{94} -8.00800 q^{95} -11.4355 q^{96} +4.26564 q^{97} -0.521477 q^{98} +3.71304 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 62 q + 2 q^{2} + 11 q^{3} + 64 q^{4} - 62 q^{5} + 3 q^{6} - 62 q^{7} + 15 q^{8} + 69 q^{9}+O(q^{10}) \) 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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