LMFDB - Embedded newform 8015.2.a.h.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("8015.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$64.0000972201$
Analytic rank:	$1$
Dimension:	$38$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
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)

$f(q)$	$=$	$q-1.84626 q^{2} -2.48565 q^{3} +1.40867 q^{4} +1.00000 q^{5} +4.58916 q^{6} +1.00000 q^{7} +1.09175 q^{8} +3.17847 q^{9} +O(q^{10})$	\(q-1.84626 q^{2} -2.48565 q^{3} +1.40867 q^{4} +1.00000 q^{5} +4.58916 q^{6} +1.00000 q^{7} +1.09175 q^{8} +3.17847 q^{9} -1.84626 q^{10} +2.78106 q^{11} -3.50147 q^{12} -0.836383 q^{13} -1.84626 q^{14} -2.48565 q^{15} -4.83299 q^{16} +0.557984 q^{17} -5.86827 q^{18} -2.22396 q^{19} +1.40867 q^{20} -2.48565 q^{21} -5.13455 q^{22} +1.42029 q^{23} -2.71370 q^{24} +1.00000 q^{25} +1.54418 q^{26} -0.443611 q^{27} +1.40867 q^{28} +1.97051 q^{29} +4.58916 q^{30} +3.96581 q^{31} +6.73945 q^{32} -6.91275 q^{33} -1.03018 q^{34} +1.00000 q^{35} +4.47742 q^{36} +5.79173 q^{37} +4.10600 q^{38} +2.07896 q^{39} +1.09175 q^{40} -6.36683 q^{41} +4.58916 q^{42} +4.28567 q^{43} +3.91760 q^{44} +3.17847 q^{45} -2.62223 q^{46} +1.23880 q^{47} +12.0131 q^{48} +1.00000 q^{49} -1.84626 q^{50} -1.38695 q^{51} -1.17819 q^{52} -5.35412 q^{53} +0.819020 q^{54} +2.78106 q^{55} +1.09175 q^{56} +5.52799 q^{57} -3.63807 q^{58} -5.63267 q^{59} -3.50147 q^{60} -12.0042 q^{61} -7.32191 q^{62} +3.17847 q^{63} -2.77679 q^{64} -0.836383 q^{65} +12.7627 q^{66} -6.02699 q^{67} +0.786015 q^{68} -3.53036 q^{69} -1.84626 q^{70} -11.5013 q^{71} +3.47008 q^{72} +11.0362 q^{73} -10.6930 q^{74} -2.48565 q^{75} -3.13282 q^{76} +2.78106 q^{77} -3.83829 q^{78} -9.99086 q^{79} -4.83299 q^{80} -8.43274 q^{81} +11.7548 q^{82} -6.22897 q^{83} -3.50147 q^{84} +0.557984 q^{85} -7.91245 q^{86} -4.89800 q^{87} +3.03621 q^{88} +11.2752 q^{89} -5.86827 q^{90} -0.836383 q^{91} +2.00073 q^{92} -9.85763 q^{93} -2.28715 q^{94} -2.22396 q^{95} -16.7519 q^{96} +5.40278 q^{97} -1.84626 q^{98} +8.83951 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 38 q - 6 q^{2} - 9 q^{3} + 24 q^{4} + 38 q^{5} - 10 q^{6} + 38 q^{7} - 21 q^{8} + 13 q^{9}+O(q^{10}) $ 38 * q - 6 * q^2 - 9 * q^3 + 24 * q^4 + 38 * q^5 - 10 * q^6 + 38 * q^7 - 21 * q^8 + 13 * q^9	\( 38 q - 6 q^{2} - 9 q^{3} + 24 q^{4} + 38 q^{5} - 10 q^{6} + 38 q^{7} - 21 q^{8} + 13 q^{9} - 6 q^{10} - 18 q^{11} - 20 q^{12} - 25 q^{13} - 6 q^{14} - 9 q^{15} - 21 q^{17} - 7 q^{18} - 14 q^{19} + 24 q^{20} - 9 q^{21} - 11 q^{22} - 16 q^{23} - 10 q^{24} + 38 q^{25} - 21 q^{26} - 15 q^{27} + 24 q^{28} - 52 q^{29} - 10 q^{30} - 30 q^{31} - 8 q^{32} - 13 q^{33} - 9 q^{34} + 38 q^{35} - 16 q^{36} - 47 q^{37} - 10 q^{38} - 50 q^{39} - 21 q^{40} - 35 q^{41} - 10 q^{42} - 18 q^{43} - 22 q^{44} + 13 q^{45} - 17 q^{46} - 23 q^{47} - 13 q^{48} + 38 q^{49} - 6 q^{50} - 5 q^{51} - 41 q^{52} - 12 q^{53} + 35 q^{54} - 18 q^{55} - 21 q^{56} - 3 q^{57} - 16 q^{58} - 16 q^{59} - 20 q^{60} - 47 q^{61} + 14 q^{62} + 13 q^{63} - 55 q^{64} - 25 q^{65} - 6 q^{66} - 54 q^{67} + 31 q^{68} - 95 q^{69} - 6 q^{70} - 41 q^{71} - 59 q^{73} - q^{74} - 9 q^{75} - 23 q^{76} - 18 q^{77} + 19 q^{78} - 117 q^{79} - 38 q^{81} + 19 q^{82} - 21 q^{83} - 20 q^{84} - 21 q^{85} - 12 q^{86} - 14 q^{87} - 40 q^{88} - 96 q^{89} - 7 q^{90} - 25 q^{91} + 53 q^{92} - 53 q^{93} - 28 q^{94} - 14 q^{95} + 40 q^{96} - 70 q^{97} - 6 q^{98} - 52 q^{99}+O(q^{100}) \) 38 * q - 6 * q^2 - 9 * q^3 + 24 * q^4 + 38 * q^5 - 10 * q^6 + 38 * q^7 - 21 * q^8 + 13 * q^9 - 6 * q^10 - 18 * q^11 - 20 * q^12 - 25 * q^13 - 6 * q^14 - 9 * q^15 - 21 * q^17 - 7 * q^18 - 14 * q^19 + 24 * q^20 - 9 * q^21 - 11 * q^22 - 16 * q^23 - 10 * q^24 + 38 * q^25 - 21 * q^26 - 15 * q^27 + 24 * q^28 - 52 * q^29 - 10 * q^30 - 30 * q^31 - 8 * q^32 - 13 * q^33 - 9 * q^34 + 38 * q^35 - 16 * q^36 - 47 * q^37 - 10 * q^38 - 50 * q^39 - 21 * q^40 - 35 * q^41 - 10 * q^42 - 18 * q^43 - 22 * q^44 + 13 * q^45 - 17 * q^46 - 23 * q^47 - 13 * q^48 + 38 * q^49 - 6 * q^50 - 5 * q^51 - 41 * q^52 - 12 * q^53 + 35 * q^54 - 18 * q^55 - 21 * q^56 - 3 * q^57 - 16 * q^58 - 16 * q^59 - 20 * q^60 - 47 * q^61 + 14 * q^62 + 13 * q^63 - 55 * q^64 - 25 * q^65 - 6 * q^66 - 54 * q^67 + 31 * q^68 - 95 * q^69 - 6 * q^70 - 41 * q^71 - 59 * q^73 - q^74 - 9 * q^75 - 23 * q^76 - 18 * q^77 + 19 * q^78 - 117 * q^79 - 38 * q^81 + 19 * q^82 - 21 * q^83 - 20 * q^84 - 21 * q^85 - 12 * q^86 - 14 * q^87 - 40 * q^88 - 96 * q^89 - 7 * q^90 - 25 * q^91 + 53 * q^92 - 53 * q^93 - 28 * q^94 - 14 * q^95 + 40 * q^96 - 70 * q^97 - 6 * q^98 - 52 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.84626	−1.30550	−0.652751	−	0.757573i	$-0.726385\pi$
$2$	−1.84626	−1.30550	−0.652751	+	0.757573i	$0.726385\pi$
$3$	−2.48565	−1.43509	−0.717546	−	0.696511i	$-0.754735\pi$
$3$	−2.48565	−1.43509	−0.717546	+	0.696511i	$0.754735\pi$
$4$	1.40867	0.704335
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	4.58916	1.87352
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	1.09175	0.385991
$9$	3.17847	1.05949
$10$	−1.84626	−0.583838
$11$	2.78106	0.838521	0.419260	−	0.907866i	$-0.362289\pi$
$11$	2.78106	0.838521	0.419260	+	0.907866i	$0.362289\pi$
$12$	−3.50147	−1.01079
$13$	−0.836383	−0.231971	−0.115985	−	0.993251i	$-0.537003\pi$
$13$	−0.836383	−0.231971	−0.115985	+	0.993251i	$0.537003\pi$
$14$	−1.84626	−0.493433
$15$	−2.48565	−0.641793
$16$	−4.83299	−1.20825
$17$	0.557984	0.135331	0.0676655	−	0.997708i	$-0.478445\pi$
$17$	0.557984	0.135331	0.0676655	+	0.997708i	$0.478445\pi$
$18$	−5.86827	−1.38317
$19$	−2.22396	−0.510211	−0.255105	−	0.966913i	$-0.582110\pi$
$19$	−2.22396	−0.510211	−0.255105	+	0.966913i	$0.582110\pi$
$20$	1.40867	0.314988
$21$	−2.48565	−0.542414
$22$	−5.13455	−1.09469
$23$	1.42029	0.296152	0.148076	−	0.988976i	$-0.452692\pi$
$23$	1.42029	0.296152	0.148076	+	0.988976i	$0.452692\pi$
$24$	−2.71370	−0.553932
$25$	1.00000	0.200000
$26$	1.54418	0.302839
$27$	−0.443611	−0.0853730
$28$	1.40867	0.266214
$29$	1.97051	0.365914	0.182957	−	0.983121i	$-0.441433\pi$
$29$	1.97051	0.365914	0.182957	+	0.983121i	$0.441433\pi$
$30$	4.58916	0.837862
$31$	3.96581	0.712281	0.356140	−	0.934432i	$-0.384093\pi$
$31$	3.96581	0.712281	0.356140	+	0.934432i	$0.384093\pi$
$32$	6.73945	1.19138
$33$	−6.91275	−1.20335
$34$	−1.03018	−0.176675
$35$	1.00000	0.169031
$36$	4.47742	0.746236
$37$	5.79173	0.952154	0.476077	−	0.879404i	$-0.342058\pi$
$37$	5.79173	0.952154	0.476077	+	0.879404i	$0.342058\pi$
$38$	4.10600	0.666081
$39$	2.07896	0.332900
$40$	1.09175	0.172620
$41$	−6.36683	−0.994332	−0.497166	−	0.867655i	$-0.665626\pi$
$41$	−6.36683	−0.994332	−0.497166	+	0.867655i	$0.665626\pi$
$42$	4.58916	0.708122
$43$	4.28567	0.653558	0.326779	−	0.945101i	$-0.394037\pi$
$43$	4.28567	0.653558	0.326779	+	0.945101i	$0.394037\pi$
$44$	3.91760	0.590600
$45$	3.17847	0.473818
$46$	−2.62223	−0.386627
$47$	1.23880	0.180698	0.0903491	−	0.995910i	$-0.471202\pi$
$47$	1.23880	0.180698	0.0903491	+	0.995910i	$0.471202\pi$
$48$	12.0131	1.73395
$49$	1.00000	0.142857
$50$	−1.84626	−0.261100
$51$	−1.38695	−0.194212
$52$	−1.17819	−0.163385
$53$	−5.35412	−0.735445	−0.367722	−	0.929936i	$-0.619862\pi$
$53$	−5.35412	−0.735445	−0.367722	+	0.929936i	$0.619862\pi$
$54$	0.819020	0.111455
$55$	2.78106	0.374998
$56$	1.09175	0.145891
$57$	5.52799	0.732200
$58$	−3.63807	−0.477701
$59$	−5.63267	−0.733311	−0.366656	−	0.930357i	$-0.619497\pi$
$59$	−5.63267	−0.733311	−0.366656	+	0.930357i	$0.619497\pi$
$60$	−3.50147	−0.452037
$61$	−12.0042	−1.53699	−0.768493	−	0.639858i	$-0.778993\pi$
$61$	−12.0042	−1.53699	−0.768493	+	0.639858i	$0.778993\pi$
$62$	−7.32191	−0.929884
$63$	3.17847	0.400449
$64$	−2.77679	−0.347099
$65$	−0.836383	−0.103741
$66$	12.7627	1.57098
$67$	−6.02699	−0.736315	−0.368157	−	0.929764i	$-0.620011\pi$
$67$	−6.02699	−0.736315	−0.368157	+	0.929764i	$0.620011\pi$
$68$	0.786015	0.0953183
$69$	−3.53036	−0.425005
$70$	−1.84626	−0.220670
$71$	−11.5013	−1.36495	−0.682477	−	0.730907i	$-0.739097\pi$
$71$	−11.5013	−1.36495	−0.682477	+	0.730907i	$0.739097\pi$
$72$	3.47008	0.408953
$73$	11.0362	1.29169	0.645844	−	0.763470i	$-0.276506\pi$
$73$	11.0362	1.29169	0.645844	+	0.763470i	$0.276506\pi$
$74$	−10.6930	−1.24304
$75$	−2.48565	−0.287018
$76$	−3.13282	−0.359360
$77$	2.78106	0.316931
$78$	−3.83829	−0.434601
$79$	−9.99086	−1.12406	−0.562030	−	0.827117i	$-0.689979\pi$
$79$	−9.99086	−1.12406	−0.562030	+	0.827117i	$0.689979\pi$
$80$	−4.83299	−0.540345
$81$	−8.43274	−0.936971
$82$	11.7548	1.29810
$83$	−6.22897	−0.683719	−0.341859	−	0.939751i	$-0.611057\pi$
$83$	−6.22897	−0.683719	−0.341859	+	0.939751i	$0.611057\pi$
$84$	−3.50147	−0.382041
$85$	0.557984	0.0605218
$86$	−7.91245	−0.853222
$87$	−4.89800	−0.525120
$88$	3.03621	0.323661
$89$	11.2752	1.19517	0.597585	−	0.801806i	$-0.296127\pi$
$89$	11.2752	1.19517	0.597585	+	0.801806i	$0.296127\pi$
$90$	−5.86827	−0.618570
$91$	−0.836383	−0.0876768
$92$	2.00073	0.208590
$93$	−9.85763	−1.02219
$94$	−2.28715	−0.235902
$95$	−2.22396	−0.228173
$96$	−16.7519	−1.70974
$97$	5.40278	0.548569	0.274285	−	0.961649i	$-0.411559\pi$
$97$	5.40278	0.548569	0.274285	+	0.961649i	$0.411559\pi$
$98$	−1.84626	−0.186500
$99$	8.83951	0.888404
$100$	1.40867	0.140867
$101$	−3.74115	−0.372259	−0.186129	−	0.982525i	$-0.559594\pi$
$101$	−3.74115	−0.372259	−0.186129	+	0.982525i	$0.559594\pi$
$102$	2.56067	0.253545
$103$	−9.96398	−0.981780	−0.490890	−	0.871221i	$-0.663328\pi$
$103$	−9.96398	−0.981780	−0.490890	+	0.871221i	$0.663328\pi$
$104$	−0.913119	−0.0895387
$105$	−2.48565	−0.242575
$106$	9.88509	0.960124
$107$	−17.1030	−1.65341	−0.826707	−	0.562633i	$-0.809788\pi$
$107$	−17.1030	−1.65341	−0.826707	+	0.562633i	$0.809788\pi$
$108$	−0.624902	−0.0601312
$109$	−15.8171	−1.51500	−0.757500	−	0.652835i	$-0.773579\pi$
$109$	−15.8171	−1.51500	−0.757500	+	0.652835i	$0.773579\pi$
$110$	−5.13455	−0.489561
$111$	−14.3962	−1.36643
$112$	−4.83299	−0.456674
$113$	−6.16884	−0.580316	−0.290158	−	0.956979i	$-0.593708\pi$
$113$	−6.16884	−0.580316	−0.290158	+	0.956979i	$0.593708\pi$
$114$	−10.2061	−0.955888
$115$	1.42029	0.132443
$116$	2.77580	0.257726
$117$	−2.65842	−0.245771
$118$	10.3994	0.957339
$119$	0.557984	0.0511503
$120$	−2.71370	−0.247726
$121$	−3.26571	−0.296883
$122$	22.1629	2.00654
$123$	15.8257	1.42696
$124$	5.58652	0.501684
$125$	1.00000	0.0894427
$126$	−5.86827	−0.522787
$127$	1.04890	0.0930752	0.0465376	−	0.998917i	$-0.485181\pi$
$127$	1.04890	0.0930752	0.0465376	+	0.998917i	$0.485181\pi$
$128$	−8.35222	−0.738239
$129$	−10.6527	−0.937916
$130$	1.54418	0.135434
$131$	11.8079	1.03166	0.515831	−	0.856690i	$-0.327483\pi$
$131$	11.8079	1.03166	0.515831	+	0.856690i	$0.327483\pi$
$132$	−9.73778	−0.847565
$133$	−2.22396	−0.192842
$134$	11.1274	0.961260
$135$	−0.443611	−0.0381799
$136$	0.609177	0.0522365
$137$	−10.9200	−0.932954	−0.466477	−	0.884533i	$-0.654477\pi$
$137$	−10.9200	−0.932954	−0.466477	+	0.884533i	$0.654477\pi$
$138$	6.51795	0.554845
$139$	16.4312	1.39367	0.696837	−	0.717230i	$-0.254590\pi$
$139$	16.4312	1.39367	0.696837	+	0.717230i	$0.254590\pi$
$140$	1.40867	0.119054
$141$	−3.07924	−0.259319
$142$	21.2344	1.78195
$143$	−2.32603	−0.194512
$144$	−15.3615	−1.28013
$145$	1.97051	0.163642
$146$	−20.3756	−1.68630
$147$	−2.48565	−0.205013
$148$	8.15864	0.670636
$149$	−4.60058	−0.376894	−0.188447	−	0.982083i	$-0.560345\pi$
$149$	−4.60058	−0.376894	−0.188447	+	0.982083i	$0.560345\pi$
$150$	4.58916	0.374703
$151$	−10.5145	−0.855655	−0.427827	−	0.903860i	$-0.640721\pi$
$151$	−10.5145	−0.855655	−0.427827	+	0.903860i	$0.640721\pi$
$152$	−2.42800	−0.196937
$153$	1.77353	0.143382
$154$	−5.13455	−0.413754
$155$	3.96581	0.318542
$156$	2.92857	0.234473
$157$	21.0819	1.68252	0.841259	−	0.540632i	$-0.181815\pi$
$157$	21.0819	1.68252	0.841259	+	0.540632i	$0.181815\pi$
$158$	18.4457	1.46746
$159$	13.3085	1.05543
$160$	6.73945	0.532800
$161$	1.42029	0.111935
$162$	15.5690	1.22322
$163$	8.50012	0.665781	0.332890	−	0.942966i	$-0.391976\pi$
$163$	8.50012	0.665781	0.332890	+	0.942966i	$0.391976\pi$
$164$	−8.96877	−0.700343
$165$	−6.91275	−0.538157
$166$	11.5003	0.892596
$167$	1.92712	0.149125	0.0745627	−	0.997216i	$-0.476244\pi$
$167$	1.92712	0.149125	0.0745627	+	0.997216i	$0.476244\pi$
$168$	−2.71370	−0.209367
$169$	−12.3005	−0.946189
$170$	−1.03018	−0.0790114
$171$	−7.06878	−0.540563
$172$	6.03709	0.460324
$173$	9.02584	0.686222	0.343111	−	0.939295i	$-0.388519\pi$
$173$	9.02584	0.686222	0.343111	+	0.939295i	$0.388519\pi$
$174$	9.04297	0.685546
$175$	1.00000	0.0755929
$176$	−13.4408	−1.01314
$177$	14.0009	1.05237
$178$	−20.8170	−1.56030
$179$	−1.03300	−0.0772097	−0.0386049	−	0.999255i	$-0.512291\pi$
$179$	−1.03300	−0.0772097	−0.0386049	+	0.999255i	$0.512291\pi$
$180$	4.47742	0.333727
$181$	−14.2057	−1.05590	−0.527950	−	0.849276i	$-0.677039\pi$
$181$	−14.2057	−1.05590	−0.527950	+	0.849276i	$0.677039\pi$
$182$	1.54418	0.114462
$183$	29.8384	2.20572
$184$	1.55060	0.114312
$185$	5.79173	0.425816
$186$	18.1997	1.33447
$187$	1.55179	0.113478
$188$	1.74507	0.127272
$189$	−0.443611	−0.0322679
$190$	4.10600	0.297881
$191$	−2.05893	−0.148979	−0.0744894	−	0.997222i	$-0.523733\pi$
$191$	−2.05893	−0.148979	−0.0744894	+	0.997222i	$0.523733\pi$
$192$	6.90215	0.498119
$193$	1.11134	0.0799957	0.0399978	−	0.999200i	$-0.487265\pi$
$193$	1.11134	0.0799957	0.0399978	+	0.999200i	$0.487265\pi$
$194$	−9.97493	−0.716158
$195$	2.07896	0.148877
$196$	1.40867	0.100619
$197$	3.81098	0.271521	0.135761	−	0.990742i	$-0.456652\pi$
$197$	3.81098	0.271521	0.135761	+	0.990742i	$0.456652\pi$
$198$	−16.3200	−1.15981
$199$	14.2671	1.01137	0.505684	−	0.862719i	$-0.331240\pi$
$199$	14.2671	1.01137	0.505684	+	0.862719i	$0.331240\pi$
$200$	1.09175	0.0771982
$201$	14.9810	1.05668
$202$	6.90713	0.485984
$203$	1.97051	0.138302
$204$	−1.95376	−0.136791
$205$	−6.36683	−0.444679
$206$	18.3961	1.28172
$207$	4.51436	0.313770
$208$	4.04223	0.280278
$209$	−6.18496	−0.427822
$210$	4.58916	0.316682
$211$	−0.687649	−0.0473397	−0.0236698	−	0.999720i	$-0.507535\pi$
$211$	−0.687649	−0.0473397	−0.0236698	+	0.999720i	$0.507535\pi$
$212$	−7.54219	−0.518000
$213$	28.5883	1.95884
$214$	31.5766	2.15853
$215$	4.28567	0.292280
$216$	−0.484311	−0.0329532
$217$	3.96581	0.269217
$218$	29.2024	1.97784
$219$	−27.4321	−1.85369
$220$	3.91760	0.264124
$221$	−0.466688	−0.0313928
$222$	26.5792	1.78388
$223$	20.1904	1.35205	0.676025	−	0.736878i	$-0.263701\pi$
$223$	20.1904	1.35205	0.676025	+	0.736878i	$0.263701\pi$
$224$	6.73945	0.450299
$225$	3.17847	0.211898
$226$	11.3893	0.757603
$227$	23.2959	1.54620	0.773101	−	0.634283i	$-0.218705\pi$
$227$	23.2959	1.54620	0.773101	+	0.634283i	$0.218705\pi$
$228$	7.78711	0.515714
$229$	−1.00000	−0.0660819
$229$	−1.00000	−0.0660819
$230$	−2.62223	−0.172905
$231$	−6.91275	−0.454825
$232$	2.15130	0.141239
$233$	−28.8625	−1.89085	−0.945423	−	0.325847i	$-0.894351\pi$
$233$	−28.8625	−1.89085	−0.945423	+	0.325847i	$0.894351\pi$
$234$	4.90813	0.320854
$235$	1.23880	0.0808107
$236$	−7.93458	−0.516497
$237$	24.8338	1.61313
$238$	−1.03018	−0.0667768
$239$	3.35377	0.216938	0.108469	−	0.994100i	$-0.465405\pi$
$239$	3.35377	0.216938	0.108469	+	0.994100i	$0.465405\pi$
$240$	12.0131	0.775444
$241$	−20.6760	−1.33186	−0.665928	−	0.746016i	$-0.731964\pi$
$241$	−20.6760	−1.33186	−0.665928	+	0.746016i	$0.731964\pi$
$242$	6.02935	0.387581
$243$	22.2917	1.43001
$244$	−16.9100	−1.08255
$245$	1.00000	0.0638877
$246$	−29.2184	−1.86290
$247$	1.86008	0.118354
$248$	4.32966	0.274934
$249$	15.4831	0.981199
$250$	−1.84626	−0.116768
$251$	−9.54634	−0.602560	−0.301280	−	0.953536i	$-0.597414\pi$
$251$	−9.54634	−0.602560	−0.301280	+	0.953536i	$0.597414\pi$
$252$	4.47742	0.282051
$253$	3.94992	0.248330
$254$	−1.93655	−0.121510
$255$	−1.38695	−0.0868544
$256$	20.9740	1.31087
$257$	−10.7155	−0.668413	−0.334206	−	0.942500i	$-0.608468\pi$
$257$	−10.7155	−0.668413	−0.334206	+	0.942500i	$0.608468\pi$
$258$	19.6676	1.22445
$259$	5.79173	0.359881
$260$	−1.17819	−0.0730681
$261$	6.26320	0.387682
$262$	−21.8005	−1.34684
$263$	28.2376	1.74120	0.870601	−	0.491990i	$-0.163730\pi$
$263$	28.2376	1.74120	0.870601	+	0.491990i	$0.163730\pi$
$264$	−7.54697	−0.464484
$265$	−5.35412	−0.328901
$266$	4.10600	0.251755
$267$	−28.0263	−1.71518
$268$	−8.49005	−0.518612
$269$	22.2806	1.35847	0.679236	−	0.733920i	$-0.262311\pi$
$269$	22.2806	1.35847	0.679236	+	0.733920i	$0.262311\pi$
$270$	0.819020	0.0498440
$271$	−21.4319	−1.30190	−0.650948	−	0.759122i	$-0.725629\pi$
$271$	−21.4319	−1.30190	−0.650948	+	0.759122i	$0.725629\pi$
$272$	−2.69673	−0.163513
$273$	2.07896	0.125824
$274$	20.1611	1.21797
$275$	2.78106	0.167704
$276$	−4.97311	−0.299346
$277$	4.86718	0.292441	0.146220	−	0.989252i	$-0.453289\pi$
$277$	4.86718	0.292441	0.146220	+	0.989252i	$0.453289\pi$
$278$	−30.3362	−1.81944
$279$	12.6052	0.754654
$280$	1.09175	0.0652444
$281$	30.3356	1.80967	0.904836	−	0.425761i	$-0.139994\pi$
$281$	30.3356	1.80967	0.904836	+	0.425761i	$0.139994\pi$
$282$	5.68507	0.338541
$283$	−8.58640	−0.510409	−0.255204	−	0.966887i	$-0.582143\pi$
$283$	−8.58640	−0.510409	−0.255204	+	0.966887i	$0.582143\pi$
$284$	−16.2016	−0.961386
$285$	5.52799	0.327450
$286$	4.29445	0.253936
$287$	−6.36683	−0.375822
$288$	21.4211	1.26225
$289$	−16.6887	−0.981686
$290$	−3.63807	−0.213635
$291$	−13.4294	−0.787247
$292$	15.5463	0.909781
$293$	−20.4260	−1.19330	−0.596650	−	0.802501i	$-0.703502\pi$
$293$	−20.4260	−1.19330	−0.596650	+	0.802501i	$0.703502\pi$
$294$	4.58916	0.267645
$295$	−5.63267	−0.327947
$296$	6.32310	0.367523
$297$	−1.23371	−0.0715870
$298$	8.49386	0.492036
$299$	−1.18791	−0.0686986
$300$	−3.50147	−0.202157
$301$	4.28567	0.247022
$302$	19.4124	1.11706
$303$	9.29920	0.534225
$304$	10.7484	0.616461
$305$	−12.0042	−0.687361
$306$	−3.27440	−0.187185
$307$	2.51120	0.143321	0.0716607	−	0.997429i	$-0.477170\pi$
$307$	2.51120	0.143321	0.0716607	+	0.997429i	$0.477170\pi$
$308$	3.91760	0.223226
$309$	24.7670	1.40895
$310$	−7.32191	−0.415857
$311$	−4.14564	−0.235078	−0.117539	−	0.993068i	$-0.537500\pi$
$311$	−4.14564	−0.235078	−0.117539	+	0.993068i	$0.537500\pi$
$312$	2.26970	0.128496
$313$	−9.30833	−0.526138	−0.263069	−	0.964777i	$-0.584735\pi$
$313$	−9.30833	−0.526138	−0.263069	+	0.964777i	$0.584735\pi$
$314$	−38.9226	−2.19653
$315$	3.17847	0.179086
$316$	−14.0738	−0.791715
$317$	−22.5962	−1.26913	−0.634566	−	0.772869i	$-0.718821\pi$
$317$	−22.5962	−1.26913	−0.634566	+	0.772869i	$0.718821\pi$
$318$	−24.5709	−1.37787
$319$	5.48010	0.306827
$320$	−2.77679	−0.155228
$321$	42.5122	2.37280
$322$	−2.62223	−0.146131
$323$	−1.24093	−0.0690473
$324$	−11.8790	−0.659942
$325$	−0.836383	−0.0463942
$326$	−15.6934	−0.869178
$327$	39.3157	2.17416
$328$	−6.95097	−0.383803
$329$	1.23880	0.0682975
$330$	12.7627	0.702564
$331$	−34.7370	−1.90932	−0.954658	−	0.297704i	$-0.903779\pi$
$331$	−34.7370	−1.90932	−0.954658	+	0.297704i	$0.903779\pi$
$332$	−8.77457	−0.481567
$333$	18.4088	1.00880
$334$	−3.55797	−0.194683
$335$	−6.02699	−0.329290
$336$	12.0131	0.655370
$337$	0.276895	0.0150834	0.00754171	−	0.999972i	$-0.497599\pi$
$337$	0.276895	0.0150834	0.00754171	+	0.999972i	$0.497599\pi$
$338$	22.7098	1.23525
$339$	15.3336	0.832806
$340$	0.786015	0.0426277
$341$	11.0292	0.597262
$342$	13.0508	0.705706
$343$	1.00000	0.0539949
$344$	4.67887	0.252268
$345$	−3.53036	−0.190068
$346$	−16.6640	−0.895864
$347$	9.97275	0.535365	0.267683	−	0.963507i	$-0.413742\pi$
$347$	9.97275	0.535365	0.267683	+	0.963507i	$0.413742\pi$
$348$	−6.89966	−0.369861
$349$	−0.947313	−0.0507085	−0.0253543	−	0.999679i	$-0.508071\pi$
$349$	−0.947313	−0.0507085	−0.0253543	+	0.999679i	$0.508071\pi$
$350$	−1.84626	−0.0986867
$351$	0.371029	0.0198040
$352$	18.7428	0.998995
$353$	9.15858	0.487462	0.243731	−	0.969843i	$-0.421629\pi$
$353$	9.15858	0.487462	0.243731	+	0.969843i	$0.421629\pi$
$354$	−25.8492	−1.37387
$355$	−11.5013	−0.610426
$356$	15.8831	0.841801
$357$	−1.38695	−0.0734054
$358$	1.90718	0.100797
$359$	−17.1522	−0.905257	−0.452628	−	0.891699i	$-0.649514\pi$
$359$	−17.1522	−0.905257	−0.452628	+	0.891699i	$0.649514\pi$
$360$	3.47008	0.182889
$361$	−14.0540	−0.739685
$362$	26.2273	1.37848
$363$	8.11742	0.426054
$364$	−1.17819	−0.0617539
$365$	11.0362	0.577660
$366$	−55.0894	−2.87957
$367$	−16.1693	−0.844030	−0.422015	−	0.906589i	$-0.638677\pi$
$367$	−16.1693	−0.844030	−0.422015	+	0.906589i	$0.638677\pi$
$368$	−6.86427	−0.357825
$369$	−20.2368	−1.05348
$370$	−10.6930	−0.555904
$371$	−5.35412	−0.277972
$372$	−13.8862	−0.719963
$373$	18.3790	0.951628	0.475814	−	0.879546i	$-0.342154\pi$
$373$	18.3790	0.951628	0.475814	+	0.879546i	$0.342154\pi$
$374$	−2.86500	−0.148145
$375$	−2.48565	−0.128359
$376$	1.35246	0.0697478
$377$	−1.64810	−0.0848814
$378$	0.819020	0.0421259
$379$	20.8271	1.06982	0.534909	−	0.844910i	$-0.320346\pi$
$379$	20.8271	1.06982	0.534909	+	0.844910i	$0.320346\pi$
$380$	−3.13282	−0.160710
$381$	−2.60721	−0.133572
$382$	3.80131	0.194492
$383$	−12.2644	−0.626680	−0.313340	−	0.949641i	$-0.601448\pi$
$383$	−12.2644	−0.626680	−0.313340	+	0.949641i	$0.601448\pi$
$384$	20.7607	1.05944
$385$	2.78106	0.141736
$386$	−2.05181	−0.104435
$387$	13.6219	0.692438
$388$	7.61074	0.386377
$389$	15.1596	0.768623	0.384311	−	0.923204i	$-0.374439\pi$
$389$	15.1596	0.768623	0.384311	+	0.923204i	$0.374439\pi$
$390$	−3.83829	−0.194360
$391$	0.792501	0.0400785
$392$	1.09175	0.0551416
$393$	−29.3504	−1.48053
$394$	−7.03606	−0.354472
$395$	−9.99086	−0.502695
$396$	12.4520	0.625734
$397$	0.989546	0.0496639	0.0248319	−	0.999692i	$-0.492095\pi$
$397$	0.989546	0.0496639	0.0248319	+	0.999692i	$0.492095\pi$
$398$	−26.3407	−1.32034
$399$	5.52799	0.276745
$400$	−4.83299	−0.241649
$401$	−24.7212	−1.23452	−0.617259	−	0.786760i	$-0.711757\pi$
$401$	−24.7212	−1.23452	−0.617259	+	0.786760i	$0.711757\pi$
$402$	−27.6588	−1.37950
$403$	−3.31694	−0.165228
$404$	−5.27005	−0.262195
$405$	−8.43274	−0.419026
$406$	−3.63807	−0.180554
$407$	16.1071	0.798401
$408$	−1.51420	−0.0749642
$409$	17.3902	0.859892	0.429946	−	0.902855i	$-0.358533\pi$
$409$	17.3902	0.859892	0.429946	+	0.902855i	$0.358533\pi$
$410$	11.7548	0.580529
$411$	27.1432	1.33888
$412$	−14.0360	−0.691503
$413$	−5.63267	−0.277166
$414$	−8.33468	−0.409627
$415$	−6.22897	−0.305768
$416$	−5.63676	−0.276365
$417$	−40.8422	−2.00005
$418$	11.4190	0.558523
$419$	20.5325	1.00308	0.501538	−	0.865136i	$-0.332768\pi$
$419$	20.5325	1.00308	0.501538	+	0.865136i	$0.332768\pi$
$420$	−3.50147	−0.170854
$421$	16.5983	0.808950	0.404475	−	0.914549i	$-0.367454\pi$
$421$	16.5983	0.808950	0.404475	+	0.914549i	$0.367454\pi$
$422$	1.26958	0.0618020
$423$	3.93750	0.191448
$424$	−5.84534	−0.283875
$425$	0.557984	0.0270662
$426$	−52.7813	−2.55726
$427$	−12.0042	−0.580926
$428$	−24.0926	−1.16456
$429$	5.78171	0.279143
$430$	−7.91245	−0.381572
$431$	36.4665	1.75653	0.878264	−	0.478176i	$-0.158702\pi$
$431$	36.4665	1.75653	0.878264	+	0.478176i	$0.158702\pi$
$432$	2.14397	0.103152
$433$	−13.8140	−0.663856	−0.331928	−	0.943305i	$-0.607699\pi$
$433$	−13.8140	−0.663856	−0.331928	+	0.943305i	$0.607699\pi$
$434$	−7.32191	−0.351463
$435$	−4.89800	−0.234841
$436$	−22.2810	−1.06707
$437$	−3.15867	−0.151100
$438$	50.6468	2.42000
$439$	−33.1732	−1.58327	−0.791635	−	0.610994i	$-0.790770\pi$
$439$	−33.1732	−1.58327	−0.791635	+	0.610994i	$0.790770\pi$
$440$	3.03621	0.144746
$441$	3.17847	0.151356
$442$	0.861627	0.0409834
$443$	16.3700	0.777762	0.388881	−	0.921288i	$-0.372862\pi$
$443$	16.3700	0.777762	0.388881	+	0.921288i	$0.372862\pi$
$444$	−20.2795	−0.962424
$445$	11.2752	0.534496
$446$	−37.2767	−1.76510
$447$	11.4354	0.540878
$448$	−2.77679	−0.131191
$449$	23.1134	1.09079	0.545395	−	0.838179i	$-0.316380\pi$
$449$	23.1134	1.09079	0.545395	+	0.838179i	$0.316380\pi$
$450$	−5.86827	−0.276633
$451$	−17.7065	−0.833768
$452$	−8.68986	−0.408737
$453$	26.1353	1.22794
$454$	−43.0102	−2.01857
$455$	−0.836383	−0.0392103
$456$	6.03516	0.282622
$457$	−9.55171	−0.446810	−0.223405	−	0.974726i	$-0.571717\pi$
$457$	−9.55171	−0.446810	−0.223405	+	0.974726i	$0.571717\pi$
$458$	1.84626	0.0862700
$459$	−0.247528	−0.0115536
$460$	2.00073	0.0932844
$461$	17.5115	0.815590	0.407795	−	0.913074i	$-0.366298\pi$
$461$	17.5115	0.815590	0.407795	+	0.913074i	$0.366298\pi$
$462$	12.7627	0.593775
$463$	35.1700	1.63449	0.817244	−	0.576292i	$-0.195501\pi$
$463$	35.1700	1.63449	0.817244	+	0.576292i	$0.195501\pi$
$464$	−9.52344	−0.442115
$465$	−9.85763	−0.457137
$466$	53.2876	2.46850
$467$	−15.8783	−0.734759	−0.367380	−	0.930071i	$-0.619745\pi$
$467$	−15.8783	−0.734759	−0.367380	+	0.930071i	$0.619745\pi$
$468$	−3.74483	−0.173105
$469$	−6.02699	−0.278301
$470$	−2.28715	−0.105498
$471$	−52.4023	−2.41457
$472$	−6.14945	−0.283051
$473$	11.9187	0.548022
$474$	−45.8496	−2.10594
$475$	−2.22396	−0.102042
$476$	0.786015	0.0360269
$477$	−17.0179	−0.779196
$478$	−6.19193	−0.283212
$479$	14.9623	0.683645	0.341823	−	0.939764i	$-0.388956\pi$
$479$	14.9623	0.683645	0.341823	+	0.939764i	$0.388956\pi$
$480$	−16.7519	−0.764618
$481$	−4.84410	−0.220872
$482$	38.1732	1.73874
$483$	−3.53036	−0.160637
$484$	−4.60031	−0.209105
$485$	5.40278	0.245328
$486$	−41.1562	−1.86689
$487$	−22.2647	−1.00891	−0.504454	−	0.863438i	$-0.668306\pi$
$487$	−22.2647	−1.00891	−0.504454	+	0.863438i	$0.668306\pi$
$488$	−13.1056	−0.593262
$489$	−21.1283	−0.955457
$490$	−1.84626	−0.0834055
$491$	−37.1441	−1.67629	−0.838144	−	0.545448i	$-0.816359\pi$
$491$	−37.1441	−1.67629	−0.838144	+	0.545448i	$0.816359\pi$
$492$	22.2932	1.00506
$493$	1.09951	0.0495195
$494$	−3.43419	−0.154512
$495$	8.83951	0.397306
$496$	−19.1667	−0.860611
$497$	−11.5013	−0.515904
$498$	−28.5857	−1.28096
$499$	−33.2857	−1.49007	−0.745036	−	0.667024i	$-0.767568\pi$
$499$	−33.2857	−1.49007	−0.745036	+	0.667024i	$0.767568\pi$
$500$	1.40867	0.0629977
$501$	−4.79016	−0.214009
$502$	17.6250	0.786643
$503$	−19.2391	−0.857829	−0.428915	−	0.903345i	$-0.641104\pi$
$503$	−19.2391	−0.857829	−0.428915	+	0.903345i	$0.641104\pi$
$504$	3.47008	0.154570
$505$	−3.74115	−0.166479
$506$	−7.29258	−0.324195
$507$	30.5747	1.35787
$508$	1.47756	0.0655562
$509$	−27.8667	−1.23517	−0.617584	−	0.786505i	$-0.711888\pi$
$509$	−27.8667	−1.23517	−0.617584	+	0.786505i	$0.711888\pi$
$510$	2.56067	0.113389
$511$	11.0362	0.488212
$512$	−22.0189	−0.973107
$513$	0.986572	0.0435582
$514$	19.7835	0.872614
$515$	−9.96398	−0.439066
$516$	−15.0061	−0.660608
$517$	3.44519	0.151519
$518$	−10.6930	−0.469825
$519$	−22.4351	−0.984792
$520$	−0.913119	−0.0400429
$521$	19.8124	0.867997	0.433998	−	0.900914i	$-0.357102\pi$
$521$	19.8124	0.867997	0.433998	+	0.900914i	$0.357102\pi$
$522$	−11.5635	−0.506120
$523$	−7.01034	−0.306541	−0.153270	−	0.988184i	$-0.548981\pi$
$523$	−7.01034	−0.306541	−0.153270	+	0.988184i	$0.548981\pi$
$524$	16.6335	0.726636
$525$	−2.48565	−0.108483
$526$	−52.1338	−2.27314
$527$	2.21286	0.0963936
$528$	33.4092	1.45395
$529$	−20.9828	−0.912294
$530$	9.88509	0.429381
$531$	−17.9033	−0.776936
$532$	−3.13282	−0.135825
$533$	5.32511	0.230656
$534$	51.7437	2.23917
$535$	−17.1030	−0.739429
$536$	−6.57995	−0.284211
$537$	2.56767	0.110803
$538$	−41.1358	−1.77349
$539$	2.78106	0.119789
$540$	−0.624902	−0.0268915
$541$	23.5564	1.01277	0.506385	−	0.862307i	$-0.330981\pi$
$541$	23.5564	1.01277	0.506385	+	0.862307i	$0.330981\pi$
$542$	39.5689	1.69963
$543$	35.3104	1.51531
$544$	3.76050	0.161230
$545$	−15.8171	−0.677529
$546$	−3.83829	−0.164264
$547$	20.9400	0.895332	0.447666	−	0.894201i	$-0.352255\pi$
$547$	20.9400	0.895332	0.447666	+	0.894201i	$0.352255\pi$
$548$	−15.3826	−0.657113
$549$	−38.1551	−1.62842
$550$	−5.13455	−0.218938
$551$	−4.38232	−0.186693
$552$	−3.85426	−0.164048
$553$	−9.99086	−0.424855
$554$	−8.98607	−0.381782
$555$	−14.3962	−0.611086
$556$	23.1461	0.981614
$557$	5.71955	0.242345	0.121173	−	0.992631i	$-0.461335\pi$
$557$	5.71955	0.242345	0.121173	+	0.992631i	$0.461335\pi$
$558$	−23.2725	−0.985202
$559$	−3.58446	−0.151607
$560$	−4.83299	−0.204231
$561$	−3.85720	−0.162851
$562$	−56.0074	−2.36253
$563$	7.35417	0.309941	0.154971	−	0.987919i	$-0.450472\pi$
$563$	7.35417	0.309941	0.154971	+	0.987919i	$0.450472\pi$
$564$	−4.33763	−0.182647
$565$	−6.16884	−0.259525
$566$	15.8527	0.666340
$567$	−8.43274	−0.354142
$568$	−12.5565	−0.526860
$569$	12.0493	0.505131	0.252566	−	0.967580i	$-0.418726\pi$
$569$	12.0493	0.505131	0.252566	+	0.967580i	$0.418726\pi$
$570$	−10.2061	−0.427486
$571$	−1.40329	−0.0587257	−0.0293628	−	0.999569i	$-0.509348\pi$
$571$	−1.40329	−0.0587257	−0.0293628	+	0.999569i	$0.509348\pi$
$572$	−3.27661	−0.137002
$573$	5.11778	0.213798
$574$	11.7548	0.490637
$575$	1.42029	0.0592304
$576$	−8.82595	−0.367748
$577$	26.7058	1.11178	0.555888	−	0.831258i	$-0.312379\pi$
$577$	26.7058	1.11178	0.555888	+	0.831258i	$0.312379\pi$
$578$	30.8116	1.28159
$579$	−2.76239	−0.114801
$580$	2.77580	0.115259
$581$	−6.22897	−0.258421
$582$	24.7942	1.02775
$583$	−14.8901	−0.616686
$584$	12.0487	0.498580
$585$	−2.65842	−0.109912
$586$	37.7117	1.55786
$587$	30.0956	1.24218	0.621089	−	0.783740i	$-0.286691\pi$
$587$	30.0956	1.24218	0.621089	+	0.783740i	$0.286691\pi$
$588$	−3.50147	−0.144398
$589$	−8.81980	−0.363413
$590$	10.3994	0.428135
$591$	−9.47278	−0.389658
$592$	−27.9914	−1.15044
$593$	12.5158	0.513964	0.256982	−	0.966416i	$-0.417272\pi$
$593$	12.5158	0.513964	0.256982	+	0.966416i	$0.417272\pi$
$594$	2.27774	0.0934570
$595$	0.557984	0.0228751
$596$	−6.48070	−0.265460
$597$	−35.4630	−1.45141
$598$	2.19319	0.0896862
$599$	−25.7777	−1.05325	−0.526624	−	0.850098i	$-0.676542\pi$
$599$	−25.7777	−1.05325	−0.526624	+	0.850098i	$0.676542\pi$
$600$	−2.71370	−0.110786
$601$	−15.3895	−0.627750	−0.313875	−	0.949464i	$-0.601627\pi$
$601$	−15.3895	−0.627750	−0.313875	+	0.949464i	$0.601627\pi$
$602$	−7.91245	−0.322487
$603$	−19.1566	−0.780118
$604$	−14.8114	−0.602668
$605$	−3.26571	−0.132770
$606$	−17.1687	−0.697432
$607$	22.5311	0.914510	0.457255	−	0.889336i	$-0.348833\pi$
$607$	22.5311	0.914510	0.457255	+	0.889336i	$0.348833\pi$
$608$	−14.9883	−0.607854
$609$	−4.89800	−0.198477
$610$	22.1629	0.897351
$611$	−1.03612	−0.0419167
$612$	2.49832	0.100989
$613$	−44.6177	−1.80209	−0.901047	−	0.433722i	$-0.857200\pi$
$613$	−44.6177	−1.80209	−0.901047	+	0.433722i	$0.857200\pi$
$614$	−4.63632	−0.187106
$615$	15.8257	0.638155
$616$	3.03621	0.122333
$617$	22.7062	0.914116	0.457058	−	0.889437i	$-0.348903\pi$
$617$	22.7062	0.914116	0.457058	+	0.889437i	$0.348903\pi$
$618$	−45.7263	−1.83938
$619$	4.90674	0.197219	0.0986093	−	0.995126i	$-0.468561\pi$
$619$	4.90674	0.197219	0.0986093	+	0.995126i	$0.468561\pi$
$620$	5.58652	0.224360
$621$	−0.630058	−0.0252834
$622$	7.65393	0.306895
$623$	11.2752	0.451732
$624$	−10.0476	−0.402225
$625$	1.00000	0.0400000
$626$	17.1856	0.686874
$627$	15.3737	0.613965
$628$	29.6975	1.18506
$629$	3.23169	0.128856
$630$	−5.86827	−0.233798
$631$	5.95293	0.236982	0.118491	−	0.992955i	$-0.462194\pi$
$631$	5.95293	0.236982	0.118491	+	0.992955i	$0.462194\pi$
$632$	−10.9075	−0.433877
$633$	1.70926	0.0679368
$634$	41.7185	1.65685
$635$	1.04890	0.0416245
$636$	18.7473	0.743377
$637$	−0.836383	−0.0331387
$638$	−10.1177	−0.400563
$639$	−36.5566	−1.44616
$640$	−8.35222	−0.330151
$641$	−29.9317	−1.18223	−0.591116	−	0.806587i	$-0.701312\pi$
$641$	−29.9317	−1.18223	−0.591116	+	0.806587i	$0.701312\pi$
$642$	−78.4886	−3.09770
$643$	−15.1716	−0.598308	−0.299154	−	0.954205i	$-0.596704\pi$
$643$	−15.1716	−0.598308	−0.299154	+	0.954205i	$0.596704\pi$
$644$	2.00073	0.0788397
$645$	−10.6527	−0.419449
$646$	2.29108	0.0901414
$647$	17.3267	0.681183	0.340592	−	0.940211i	$-0.389373\pi$
$647$	17.3267	0.681183	0.340592	+	0.940211i	$0.389373\pi$
$648$	−9.20642	−0.361662
$649$	−15.6648	−0.614897
$650$	1.54418	0.0605677
$651$	−9.85763	−0.386351
$652$	11.9739	0.468933
$653$	−32.7409	−1.28125	−0.640624	−	0.767854i	$-0.721324\pi$
$653$	−32.7409	−1.28125	−0.640624	+	0.767854i	$0.721324\pi$
$654$	−72.5870	−2.83838
$655$	11.8079	0.461373
$656$	30.7708	1.20140
$657$	35.0782	1.36853
$658$	−2.28715	−0.0891625
$659$	44.5129	1.73398	0.866988	−	0.498328i	$-0.166053\pi$
$659$	44.5129	1.73398	0.866988	+	0.498328i	$0.166053\pi$
$660$	−9.73778	−0.379043
$661$	−30.1593	−1.17306	−0.586531	−	0.809927i	$-0.699507\pi$
$661$	−30.1593	−1.17306	−0.586531	+	0.809927i	$0.699507\pi$
$662$	64.1334	2.49262
$663$	1.16002	0.0450516
$664$	−6.80046	−0.263909
$665$	−2.22396	−0.0862414
$666$	−33.9875	−1.31699
$667$	2.79870	0.108366
$668$	2.71468	0.105034
$669$	−50.1864	−1.94032
$670$	11.1274	0.429889
$671$	−33.3845	−1.28879
$672$	−16.7519	−0.646220
$673$	−10.1449	−0.391057	−0.195529	−	0.980698i	$-0.562642\pi$
$673$	−10.1449	−0.391057	−0.195529	+	0.980698i	$0.562642\pi$
$674$	−0.511219	−0.0196914
$675$	−0.443611	−0.0170746
$676$	−17.3273	−0.666435
$677$	6.14780	0.236279	0.118139	−	0.992997i	$-0.462307\pi$
$677$	6.14780	0.236279	0.118139	+	0.992997i	$0.462307\pi$
$678$	−28.3098	−1.08723
$679$	5.40278	0.207340
$680$	0.609177	0.0233609
$681$	−57.9055	−2.21894
$682$	−20.3627	−0.779727
$683$	20.1499	0.771016	0.385508	−	0.922704i	$-0.374026\pi$
$683$	20.1499	0.771016	0.385508	+	0.922704i	$0.374026\pi$
$684$	−9.95758	−0.380738
$685$	−10.9200	−0.417230
$686$	−1.84626	−0.0704905
$687$	2.48565	0.0948336
$688$	−20.7126	−0.789660
$689$	4.47809	0.170602
$690$	6.51795	0.248134
$691$	−14.7150	−0.559784	−0.279892	−	0.960032i	$-0.590299\pi$
$691$	−14.7150	−0.559784	−0.279892	+	0.960032i	$0.590299\pi$
$692$	12.7144	0.483330
$693$	8.83951	0.335785
$694$	−18.4123	−0.698921
$695$	16.4312	0.623270
$696$	−5.34737	−0.202692
$697$	−3.55259	−0.134564
$698$	1.74898	0.0662000
$699$	71.7421	2.71354
$700$	1.40867	0.0532427
$701$	9.85029	0.372040	0.186020	−	0.982546i	$-0.440441\pi$
$701$	9.85029	0.372040	0.186020	+	0.982546i	$0.440441\pi$
$702$	−0.685015	−0.0258542
$703$	−12.8806	−0.485799
$704$	−7.72243	−0.291050
$705$	−3.07924	−0.115971
$706$	−16.9091	−0.636382
$707$	−3.74115	−0.140700
$708$	19.7226	0.741221
$709$	−36.6551	−1.37661	−0.688305	−	0.725422i	$-0.741645\pi$
$709$	−36.6551	−1.37661	−0.688305	+	0.725422i	$0.741645\pi$
$710$	21.2344	0.796913
$711$	−31.7556	−1.19093
$712$	12.3097	0.461325
$713$	5.63262	0.210943
$714$	2.56067	0.0958309
$715$	−2.32603	−0.0869886
$716$	−1.45515	−0.0543815
$717$	−8.33631	−0.311325
$718$	31.6673	1.18181
$719$	35.7674	1.33390	0.666949	−	0.745104i	$-0.267600\pi$
$719$	35.7674	1.33390	0.666949	+	0.745104i	$0.267600\pi$
$720$	−15.3615	−0.572489
$721$	−9.96398	−0.371078
$722$	25.9473	0.965660
$723$	51.3933	1.91134
$724$	−20.0111	−0.743707
$725$	1.97051	0.0731828
$726$	−14.9869	−0.556215
$727$	14.7549	0.547230	0.273615	−	0.961839i	$-0.411781\pi$
$727$	14.7549	0.547230	0.273615	+	0.961839i	$0.411781\pi$
$728$	−0.913119	−0.0338424
$729$	−30.1112	−1.11523
$730$	−20.3756	−0.754137
$731$	2.39133	0.0884466
$732$	42.0324	1.55356
$733$	30.0881	1.11133	0.555665	−	0.831406i	$-0.312464\pi$
$733$	30.0881	1.11133	0.555665	+	0.831406i	$0.312464\pi$
$734$	29.8527	1.10188
$735$	−2.48565	−0.0916847
$736$	9.57201	0.352829
$737$	−16.7614	−0.617415
$738$	37.3623	1.37533
$739$	6.90296	0.253929	0.126965	−	0.991907i	$-0.459476\pi$
$739$	6.90296	0.253929	0.126965	+	0.991907i	$0.459476\pi$
$740$	8.15864	0.299917
$741$	−4.62351	−0.169849
$742$	9.88509	0.362893
$743$	6.98647	0.256309	0.128154	−	0.991754i	$-0.459095\pi$
$743$	6.98647	0.256309	0.128154	+	0.991754i	$0.459095\pi$
$744$	−10.7620	−0.394555
$745$	−4.60058	−0.168552
$746$	−33.9323	−1.24235
$747$	−19.7986	−0.724393
$748$	2.18595	0.0799264
$749$	−17.1030	−0.624932
$750$	4.58916	0.167572
$751$	37.8299	1.38043	0.690217	−	0.723603i	$-0.257515\pi$
$751$	37.8299	1.38043	0.690217	+	0.723603i	$0.257515\pi$
$752$	−5.98713	−0.218328
$753$	23.7289	0.864729
$754$	3.04282	0.110813
$755$	−10.5145	−0.382660
$756$	−0.624902	−0.0227275
$757$	−41.2687	−1.49994	−0.749969	−	0.661473i	$-0.769931\pi$
$757$	−41.2687	−1.49994	−0.749969	+	0.661473i	$0.769931\pi$
$758$	−38.4523	−1.39665
$759$	−9.81814	−0.356376
$760$	−2.42800	−0.0880728
$761$	4.08239	0.147987	0.0739934	−	0.997259i	$-0.476426\pi$
$761$	4.08239	0.147987	0.0739934	+	0.997259i	$0.476426\pi$
$762$	4.81359	0.174378
$763$	−15.8171	−0.572616
$764$	−2.90035	−0.104931
$765$	1.77353	0.0641222
$766$	22.6432	0.818131
$767$	4.71107	0.170107
$768$	−52.1340	−1.88122
$769$	−3.68497	−0.132884	−0.0664418	−	0.997790i	$-0.521165\pi$
$769$	−3.68497	−0.132884	−0.0664418	+	0.997790i	$0.521165\pi$
$770$	−5.13455	−0.185036
$771$	26.6349	0.959234
$772$	1.56551	0.0563438
$773$	−34.3487	−1.23544	−0.617719	−	0.786399i	$-0.711943\pi$
$773$	−34.3487	−1.23544	−0.617719	+	0.786399i	$0.711943\pi$
$774$	−25.1495	−0.903979
$775$	3.96581	0.142456
$776$	5.89847	0.211743
$777$	−14.3962	−0.516462
$778$	−27.9886	−1.00344
$779$	14.1596	0.507319
$780$	2.92857	0.104860
$781$	−31.9858	−1.14454
$782$	−1.46316	−0.0523226
$783$	−0.874138	−0.0312392
$784$	−4.83299	−0.172607
$785$	21.0819	0.752445
$786$	54.1883	1.93283
$787$	−40.9882	−1.46107	−0.730535	−	0.682875i	$-0.760729\pi$
$787$	−40.9882	−1.46107	−0.730535	+	0.682875i	$0.760729\pi$
$788$	5.36842	0.191242
$789$	−70.1887	−2.49879
$790$	18.4457	0.656269
$791$	−6.16884	−0.219339
$792$	9.65051	0.342916
$793$	10.0401	0.356536
$794$	−1.82696	−0.0648363
$795$	13.3085	0.472003
$796$	20.0976	0.712342
$797$	13.3692	0.473562	0.236781	−	0.971563i	$-0.423908\pi$
$797$	13.3692	0.473562	0.236781	+	0.971563i	$0.423908\pi$
$798$	−10.2061	−0.361292
$799$	0.691233	0.0244540
$800$	6.73945	0.238276
$801$	35.8379	1.26627
$802$	45.6417	1.61167
$803$	30.6923	1.08311
$804$	21.1033	0.744257
$805$	1.42029	0.0500588
$806$	6.12392	0.215706
$807$	−55.3818	−1.94953
$808$	−4.08439	−0.143688
$809$	−2.91653	−0.102540	−0.0512698	−	0.998685i	$-0.516327\pi$
$809$	−2.91653	−0.102540	−0.0512698	+	0.998685i	$0.516327\pi$
$810$	15.5690	0.547040
$811$	11.4470	0.401958	0.200979	−	0.979596i	$-0.435588\pi$
$811$	11.4470	0.401958	0.200979	+	0.979596i	$0.435588\pi$
$812$	2.77580	0.0974113
$813$	53.2723	1.86834
$814$	−29.7379	−1.04231
$815$	8.50012	0.297746
$816$	6.70313	0.234657
$817$	−9.53114	−0.333453
$818$	−32.1069	−1.12259
$819$	−2.65842	−0.0928926
$820$	−8.96877	−0.313203
$821$	−39.3897	−1.37471	−0.687356	−	0.726321i	$-0.741229\pi$
$821$	−39.3897	−1.37471	−0.687356	+	0.726321i	$0.741229\pi$
$822$	−50.1134	−1.74790
$823$	−40.8705	−1.42465	−0.712327	−	0.701847i	$-0.752359\pi$
$823$	−40.8705	−1.42465	−0.712327	+	0.701847i	$0.752359\pi$
$824$	−10.8781	−0.378958
$825$	−6.91275	−0.240671
$826$	10.3994	0.361840
$827$	−5.78144	−0.201040	−0.100520	−	0.994935i	$-0.532051\pi$
$827$	−5.78144	−0.201040	−0.100520	+	0.994935i	$0.532051\pi$
$828$	6.35925	0.220999
$829$	−6.58933	−0.228857	−0.114428	−	0.993431i	$-0.536504\pi$
$829$	−6.58933	−0.228857	−0.114428	+	0.993431i	$0.536504\pi$
$830$	11.5003	0.399181
$831$	−12.0981	−0.419679
$832$	2.32246	0.0805170
$833$	0.557984	0.0193330
$834$	75.4052	2.61107
$835$	1.92712	0.0666909
$836$	−8.71257	−0.301330
$837$	−1.75928	−0.0608095
$838$	−37.9082	−1.30952
$839$	17.3648	0.599499	0.299750	−	0.954018i	$-0.403097\pi$
$839$	17.3648	0.599499	0.299750	+	0.954018i	$0.403097\pi$
$840$	−2.71370	−0.0936317
$841$	−25.1171	−0.866107
$842$	−30.6447	−1.05609
$843$	−75.4038	−2.59705
$844$	−0.968670	−0.0333430
$845$	−12.3005	−0.423149
$846$	−7.26964	−0.249935
$847$	−3.26571	−0.112211
$848$	25.8764	0.888599
$849$	21.3428	0.732484
$850$	−1.03018	−0.0353350
$851$	8.22596	0.281982
$852$	40.2715	1.37968
$853$	−34.7609	−1.19019	−0.595096	−	0.803655i	$-0.702886\pi$
$853$	−34.7609	−1.19019	−0.595096	+	0.803655i	$0.702886\pi$
$854$	22.1629	0.758400
$855$	−7.06878	−0.241747
$856$	−18.6722	−0.638202
$857$	−49.7173	−1.69831	−0.849156	−	0.528143i	$-0.822889\pi$
$857$	−49.7173	−1.69831	−0.849156	+	0.528143i	$0.822889\pi$
$858$	−10.6745	−0.364422
$859$	10.0223	0.341955	0.170978	−	0.985275i	$-0.445307\pi$
$859$	10.0223	0.341955	0.170978	+	0.985275i	$0.445307\pi$
$860$	6.03709	0.205863
$861$	15.8257	0.539339
$862$	−67.3265	−2.29315
$863$	−48.5192	−1.65161	−0.825807	−	0.563953i	$-0.809280\pi$
$863$	−48.5192	−1.65161	−0.825807	+	0.563953i	$0.809280\pi$
$864$	−2.98969	−0.101711
$865$	9.02584	0.306888
$866$	25.5041	0.866666
$867$	41.4822	1.40881
$868$	5.58652	0.189619
$869$	−27.7852	−0.942547
$870$	9.04297	0.306585
$871$	5.04088	0.170804
$872$	−17.2682	−0.584776
$873$	17.1726	0.581203
$874$	5.83173	0.197261
$875$	1.00000	0.0338062
$876$	−38.6428	−1.30562
$877$	−22.6186	−0.763774	−0.381887	−	0.924209i	$-0.624726\pi$
$877$	−22.6186	−0.763774	−0.381887	+	0.924209i	$0.624726\pi$
$878$	61.2463	2.06696
$879$	50.7720	1.71250
$880$	−13.4408	−0.453090
$881$	−20.5934	−0.693810	−0.346905	−	0.937900i	$-0.612767\pi$
$881$	−20.5934	−0.693810	−0.346905	+	0.937900i	$0.612767\pi$
$882$	−5.86827	−0.197595
$883$	35.8005	1.20478	0.602391	−	0.798201i	$-0.294215\pi$
$883$	35.8005	1.20478	0.602391	+	0.798201i	$0.294215\pi$
$884$	−0.657410	−0.0221111
$885$	14.0009	0.470634
$886$	−30.2232	−1.01537
$887$	54.9178	1.84396	0.921980	−	0.387237i	$-0.126571\pi$
$887$	54.9178	1.84396	0.921980	+	0.387237i	$0.126571\pi$
$888$	−15.7170	−0.527429
$889$	1.04890	0.0351791
$890$	−20.8170	−0.697786
$891$	−23.4520	−0.785670
$892$	28.4417	0.952297
$893$	−2.75505	−0.0921942
$894$	−21.1128	−0.706117
$895$	−1.03300	−0.0345292
$896$	−8.35222	−0.279028
$897$	2.95273	0.0985889
$898$	−42.6733	−1.42403
$899$	7.81466	0.260633
$900$	4.47742	0.149247
$901$	−2.98751	−0.0995284
$902$	32.6908	1.08849
$903$	−10.6527	−0.354499
$904$	−6.73481	−0.223997
$905$	−14.2057	−0.472212
$906$	−48.2525	−1.60308
$907$	11.6990	0.388459	0.194230	−	0.980956i	$-0.437779\pi$
$907$	11.6990	0.388459	0.194230	+	0.980956i	$0.437779\pi$
$908$	32.8162	1.08904
$909$	−11.8911	−0.394404
$910$	1.54418	0.0511891
$911$	−41.5147	−1.37544	−0.687722	−	0.725974i	$-0.741389\pi$
$911$	−41.5147	−1.37544	−0.687722	+	0.725974i	$0.741389\pi$
$912$	−26.7167	−0.884678
$913$	−17.3231	−0.573312
$914$	17.6349	0.583311
$915$	29.8384	0.986426
$916$	−1.40867	−0.0465438
$917$	11.8079	0.389932
$918$	0.457000	0.0150832
$919$	−57.7249	−1.90417	−0.952085	−	0.305834i	$-0.901065\pi$
$919$	−57.7249	−1.90417	−0.952085	+	0.305834i	$0.901065\pi$
$920$	1.55060	0.0511218
$921$	−6.24196	−0.205680
$922$	−32.3307	−1.06475
$923$	9.61951	0.316630
$924$	−9.73778	−0.320350
$925$	5.79173	0.190431
$926$	−64.9329	−2.13383
$927$	−31.6702	−1.04019
$928$	13.2801	0.435942
$929$	10.9451	0.359099	0.179549	−	0.983749i	$-0.442536\pi$
$929$	10.9451	0.359099	0.179549	+	0.983749i	$0.442536\pi$
$930$	18.1997	0.596793
$931$	−2.22396	−0.0728873
$932$	−40.6578	−1.33179
$933$	10.3046	0.337358
$934$	29.3154	0.959230
$935$	1.55179	0.0507488
$936$	−2.90232	−0.0948653
$937$	−16.4573	−0.537636	−0.268818	−	0.963191i	$-0.586633\pi$
$937$	−16.4573	−0.537636	−0.268818	+	0.963191i	$0.586633\pi$
$938$	11.1274	0.363322
$939$	23.1373	0.755056
$940$	1.74507	0.0569178
$941$	−29.2980	−0.955089	−0.477544	−	0.878608i	$-0.658473\pi$
$941$	−29.2980	−0.955089	−0.477544	+	0.878608i	$0.658473\pi$
$942$	96.7481	3.15223
$943$	−9.04277	−0.294473
$944$	27.2226	0.886021
$945$	−0.443611	−0.0144307
$946$	−22.0050	−0.715444
$947$	10.1181	0.328793	0.164397	−	0.986394i	$-0.447432\pi$
$947$	10.1181	0.328793	0.164397	+	0.986394i	$0.447432\pi$
$948$	34.9827	1.13618
$949$	−9.23048	−0.299634
$950$	4.10600	0.133216
$951$	56.1664	1.82132
$952$	0.609177	0.0197435
$953$	−28.7130	−0.930107	−0.465053	−	0.885283i	$-0.653965\pi$
$953$	−28.7130	−0.930107	−0.465053	+	0.885283i	$0.653965\pi$
$954$	31.4194	1.01724
$955$	−2.05893	−0.0666253
$956$	4.72436	0.152797
$957$	−13.6216	−0.440324
$958$	−27.6243	−0.892500
$959$	−10.9200	−0.352624
$960$	6.90215	0.222766
$961$	−15.2723	−0.492656
$962$	8.94347	0.288349
$963$	−54.3615	−1.75177
$964$	−29.1256	−0.938073
$965$	1.11134	0.0357752
$966$	6.51795	0.209712
$967$	−39.4360	−1.26818	−0.634089	−	0.773260i	$-0.718625\pi$
$967$	−39.4360	−1.26818	−0.634089	+	0.773260i	$0.718625\pi$
$968$	−3.56533	−0.114594
$969$	3.08453	0.0990893
$970$	−9.97493	−0.320276
$971$	−31.5360	−1.01204	−0.506019	−	0.862522i	$-0.668884\pi$
$971$	−31.5360	−1.01204	−0.506019	+	0.862522i	$0.668884\pi$
$972$	31.4017	1.00721
$973$	16.4312	0.526759
$974$	41.1063	1.31713
$975$	2.07896	0.0665799
$976$	58.0164	1.85706
$977$	−12.5307	−0.400892	−0.200446	−	0.979705i	$-0.564239\pi$
$977$	−12.5307	−0.400892	−0.200446	+	0.979705i	$0.564239\pi$
$978$	39.0084	1.24735
$979$	31.3570	1.00218
$980$	1.40867	0.0449983
$981$	−50.2740	−1.60513
$982$	68.5776	2.18840
$983$	20.2205	0.644935	0.322467	−	0.946581i	$-0.395488\pi$
$983$	20.2205	0.644935	0.322467	+	0.946581i	$0.395488\pi$
$984$	17.2777	0.550793
$985$	3.81098	0.121428
$986$	−2.02998	−0.0646478
$987$	−3.07924	−0.0980132
$988$	2.62024	0.0833610
$989$	6.08691	0.193552
$990$	−16.3200	−0.518684
$991$	−23.6381	−0.750889	−0.375444	−	0.926845i	$-0.622510\pi$
$991$	−23.6381	−0.750889	−0.375444	+	0.926845i	$0.622510\pi$
$992$	26.7274	0.848596
$993$	86.3440	2.74005
$994$	21.2344	0.673514
$995$	14.2671	0.452297
$996$	21.8105	0.691093
$997$	0.922137	0.0292044	0.0146022	−	0.999893i	$-0.495352\pi$
$997$	0.922137	0.0292044	0.0146022	+	0.999893i	$0.495352\pi$
$998$	61.4540	1.94529
$999$	−2.56927	−0.0812882

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8015.2.a.h.1.8	✓	38

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8015.2.a.h.1.8	✓	38	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-1.84626 q^{2} -2.48565 q^{3} +1.40867 q^{4} +1.00000 q^{5} +4.58916 q^{6} +1.00000 q^{7} +1.09175 q^{8} +3.17847 q^{9} +O(q^{10})\)	\(q-1.84626 q^{2} -2.48565 q^{3} +1.40867 q^{4} +1.00000 q^{5} +4.58916 q^{6} +1.00000 q^{7} +1.09175 q^{8} +3.17847 q^{9} -1.84626 q^{10} +2.78106 q^{11} -3.50147 q^{12} -0.836383 q^{13} -1.84626 q^{14} -2.48565 q^{15} -4.83299 q^{16} +0.557984 q^{17} -5.86827 q^{18} -2.22396 q^{19} +1.40867 q^{20} -2.48565 q^{21} -5.13455 q^{22} +1.42029 q^{23} -2.71370 q^{24} +1.00000 q^{25} +1.54418 q^{26} -0.443611 q^{27} +1.40867 q^{28} +1.97051 q^{29} +4.58916 q^{30} +3.96581 q^{31} +6.73945 q^{32} -6.91275 q^{33} -1.03018 q^{34} +1.00000 q^{35} +4.47742 q^{36} +5.79173 q^{37} +4.10600 q^{38} +2.07896 q^{39} +1.09175 q^{40} -6.36683 q^{41} +4.58916 q^{42} +4.28567 q^{43} +3.91760 q^{44} +3.17847 q^{45} -2.62223 q^{46} +1.23880 q^{47} +12.0131 q^{48} +1.00000 q^{49} -1.84626 q^{50} -1.38695 q^{51} -1.17819 q^{52} -5.35412 q^{53} +0.819020 q^{54} +2.78106 q^{55} +1.09175 q^{56} +5.52799 q^{57} -3.63807 q^{58} -5.63267 q^{59} -3.50147 q^{60} -12.0042 q^{61} -7.32191 q^{62} +3.17847 q^{63} -2.77679 q^{64} -0.836383 q^{65} +12.7627 q^{66} -6.02699 q^{67} +0.786015 q^{68} -3.53036 q^{69} -1.84626 q^{70} -11.5013 q^{71} +3.47008 q^{72} +11.0362 q^{73} -10.6930 q^{74} -2.48565 q^{75} -3.13282 q^{76} +2.78106 q^{77} -3.83829 q^{78} -9.99086 q^{79} -4.83299 q^{80} -8.43274 q^{81} +11.7548 q^{82} -6.22897 q^{83} -3.50147 q^{84} +0.557984 q^{85} -7.91245 q^{86} -4.89800 q^{87} +3.03621 q^{88} +11.2752 q^{89} -5.86827 q^{90} -0.836383 q^{91} +2.00073 q^{92} -9.85763 q^{93} -2.28715 q^{94} -2.22396 q^{95} -16.7519 q^{96} +5.40278 q^{97} -1.84626 q^{98} +8.83951 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 38 q - 6 q^{2} - 9 q^{3} + 24 q^{4} + 38 q^{5} - 10 q^{6} + 38 q^{7} - 21 q^{8} + 13 q^{9}+O(q^{10}) \) 38 * q - 6 * q^2 - 9 * q^3 + 24 * q^4 + 38 * q^5 - 10 * q^6 + 38 * q^7 - 21 * q^8 + 13 * q^9	\( 38 q - 6 q^{2} - 9 q^{3} + 24 q^{4} + 38 q^{5} - 10 q^{6} + 38 q^{7} - 21 q^{8} + 13 q^{9} - 6 q^{10} - 18 q^{11} - 20 q^{12} - 25 q^{13} - 6 q^{14} - 9 q^{15} - 21 q^{17} - 7 q^{18} - 14 q^{19} + 24 q^{20} - 9 q^{21} - 11 q^{22} - 16 q^{23} - 10 q^{24} + 38 q^{25} - 21 q^{26} - 15 q^{27} + 24 q^{28} - 52 q^{29} - 10 q^{30} - 30 q^{31} - 8 q^{32} - 13 q^{33} - 9 q^{34} + 38 q^{35} - 16 q^{36} - 47 q^{37} - 10 q^{38} - 50 q^{39} - 21 q^{40} - 35 q^{41} - 10 q^{42} - 18 q^{43} - 22 q^{44} + 13 q^{45} - 17 q^{46} - 23 q^{47} - 13 q^{48} + 38 q^{49} - 6 q^{50} - 5 q^{51} - 41 q^{52} - 12 q^{53} + 35 q^{54} - 18 q^{55} - 21 q^{56} - 3 q^{57} - 16 q^{58} - 16 q^{59} - 20 q^{60} - 47 q^{61} + 14 q^{62} + 13 q^{63} - 55 q^{64} - 25 q^{65} - 6 q^{66} - 54 q^{67} + 31 q^{68} - 95 q^{69} - 6 q^{70} - 41 q^{71} - 59 q^{73} - q^{74} - 9 q^{75} - 23 q^{76} - 18 q^{77} + 19 q^{78} - 117 q^{79} - 38 q^{81} + 19 q^{82} - 21 q^{83} - 20 q^{84} - 21 q^{85} - 12 q^{86} - 14 q^{87} - 40 q^{88} - 96 q^{89} - 7 q^{90} - 25 q^{91} + 53 q^{92} - 53 q^{93} - 28 q^{94} - 14 q^{95} + 40 q^{96} - 70 q^{97} - 6 q^{98} - 52 q^{99}+O(q^{100}) \) 38 * q - 6 * q^2 - 9 * q^3 + 24 * q^4 + 38 * q^5 - 10 * q^6 + 38 * q^7 - 21 * q^8 + 13 * q^9 - 6 * q^10 - 18 * q^11 - 20 * q^12 - 25 * q^13 - 6 * q^14 - 9 * q^15 - 21 * q^17 - 7 * q^18 - 14 * q^19 + 24 * q^20 - 9 * q^21 - 11 * q^22 - 16 * q^23 - 10 * q^24 + 38 * q^25 - 21 * q^26 - 15 * q^27 + 24 * q^28 - 52 * q^29 - 10 * q^30 - 30 * q^31 - 8 * q^32 - 13 * q^33 - 9 * q^34 + 38 * q^35 - 16 * q^36 - 47 * q^37 - 10 * q^38 - 50 * q^39 - 21 * q^40 - 35 * q^41 - 10 * q^42 - 18 * q^43 - 22 * q^44 + 13 * q^45 - 17 * q^46 - 23 * q^47 - 13 * q^48 + 38 * q^49 - 6 * q^50 - 5 * q^51 - 41 * q^52 - 12 * q^53 + 35 * q^54 - 18 * q^55 - 21 * q^56 - 3 * q^57 - 16 * q^58 - 16 * q^59 - 20 * q^60 - 47 * q^61 + 14 * q^62 + 13 * q^63 - 55 * q^64 - 25 * q^65 - 6 * q^66 - 54 * q^67 + 31 * q^68 - 95 * q^69 - 6 * q^70 - 41 * q^71 - 59 * q^73 - q^74 - 9 * q^75 - 23 * q^76 - 18 * q^77 + 19 * q^78 - 117 * q^79 - 38 * q^81 + 19 * q^82 - 21 * q^83 - 20 * q^84 - 21 * q^85 - 12 * q^86 - 14 * q^87 - 40 * q^88 - 96 * q^89 - 7 * q^90 - 25 * q^91 + 53 * q^92 - 53 * q^93 - 28 * q^94 - 14 * q^95 + 40 * q^96 - 70 * q^97 - 6 * q^98 - 52 * q^99

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