LMFDB - Embedded newform 8015.2.a.j.1.2

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:	$45$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Character	$\chi$	$=$	8015.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.58820 q^{2} +1.46821 q^{3} +4.69879 q^{4} -1.00000 q^{5} -3.80002 q^{6} +1.00000 q^{7} -6.98503 q^{8} -0.844367 q^{9} +O(q^{10})$	\(q-2.58820 q^{2} +1.46821 q^{3} +4.69879 q^{4} -1.00000 q^{5} -3.80002 q^{6} +1.00000 q^{7} -6.98503 q^{8} -0.844367 q^{9} +2.58820 q^{10} +3.30944 q^{11} +6.89880 q^{12} +1.30961 q^{13} -2.58820 q^{14} -1.46821 q^{15} +8.68108 q^{16} +6.35843 q^{17} +2.18539 q^{18} -2.58012 q^{19} -4.69879 q^{20} +1.46821 q^{21} -8.56551 q^{22} -5.17298 q^{23} -10.2555 q^{24} +1.00000 q^{25} -3.38954 q^{26} -5.64433 q^{27} +4.69879 q^{28} +3.24075 q^{29} +3.80002 q^{30} -3.58032 q^{31} -8.49834 q^{32} +4.85895 q^{33} -16.4569 q^{34} -1.00000 q^{35} -3.96751 q^{36} +6.54685 q^{37} +6.67789 q^{38} +1.92278 q^{39} +6.98503 q^{40} -1.04697 q^{41} -3.80002 q^{42} -9.04119 q^{43} +15.5504 q^{44} +0.844367 q^{45} +13.3887 q^{46} -2.12712 q^{47} +12.7456 q^{48} +1.00000 q^{49} -2.58820 q^{50} +9.33550 q^{51} +6.15359 q^{52} -7.79670 q^{53} +14.6087 q^{54} -3.30944 q^{55} -6.98503 q^{56} -3.78816 q^{57} -8.38772 q^{58} -7.35180 q^{59} -6.89880 q^{60} -13.6865 q^{61} +9.26661 q^{62} -0.844367 q^{63} +4.63326 q^{64} -1.30961 q^{65} -12.5759 q^{66} -7.75990 q^{67} +29.8770 q^{68} -7.59501 q^{69} +2.58820 q^{70} +10.5663 q^{71} +5.89793 q^{72} -6.30888 q^{73} -16.9446 q^{74} +1.46821 q^{75} -12.1235 q^{76} +3.30944 q^{77} -4.97654 q^{78} -11.1866 q^{79} -8.68108 q^{80} -5.75394 q^{81} +2.70976 q^{82} -10.2414 q^{83} +6.89880 q^{84} -6.35843 q^{85} +23.4004 q^{86} +4.75809 q^{87} -23.1166 q^{88} +6.92006 q^{89} -2.18539 q^{90} +1.30961 q^{91} -24.3068 q^{92} -5.25666 q^{93} +5.50541 q^{94} +2.58012 q^{95} -12.4773 q^{96} -9.19452 q^{97} -2.58820 q^{98} -2.79438 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 45 q - 6 q^{2} + 34 q^{4} - 45 q^{5} + q^{6} + 45 q^{7} - 15 q^{8} + 29 q^{9}+O(q^{10}) $ 45 * q - 6 * q^2 + 34 * q^4 - 45 * q^5 + q^6 + 45 * q^7 - 15 * q^8 + 29 * q^9	\( 45 q - 6 q^{2} + 34 q^{4} - 45 q^{5} + q^{6} + 45 q^{7} - 15 q^{8} + 29 q^{9} + 6 q^{10} - q^{11} - 3 q^{12} - 21 q^{13} - 6 q^{14} + 8 q^{16} - 7 q^{17} - 36 q^{18} - 20 q^{19} - 34 q^{20} - 34 q^{22} - 22 q^{23} - 11 q^{24} + 45 q^{25} - q^{26} + 12 q^{27} + 34 q^{28} + 10 q^{29} - q^{30} - 27 q^{31} - 26 q^{32} - 39 q^{33} - 13 q^{34} - 45 q^{35} - 3 q^{36} - 72 q^{37} + 2 q^{38} - 37 q^{39} + 15 q^{40} - 4 q^{41} + q^{42} - 49 q^{43} + 5 q^{44} - 29 q^{45} - 67 q^{46} + 2 q^{47} + 8 q^{48} + 45 q^{49} - 6 q^{50} - 49 q^{51} - 47 q^{52} - 35 q^{53} - 12 q^{54} + q^{55} - 15 q^{56} - 77 q^{57} - 50 q^{58} + 4 q^{59} + 3 q^{60} - 36 q^{61} + 17 q^{62} + 29 q^{63} + 5 q^{64} + 21 q^{65} - 8 q^{66} - 80 q^{67} + 27 q^{68} + 9 q^{69} + 6 q^{70} - 12 q^{71} - 97 q^{72} - 55 q^{73} + 32 q^{74} - 37 q^{76} - q^{77} + 20 q^{78} - 94 q^{79} - 8 q^{80} - 19 q^{81} - 36 q^{82} + 24 q^{83} - 3 q^{84} + 7 q^{85} - 3 q^{86} - 4 q^{87} - 95 q^{88} + q^{89} + 36 q^{90} - 21 q^{91} - 65 q^{92} - 71 q^{93} - 53 q^{94} + 20 q^{95} - 13 q^{96} - 110 q^{97} - 6 q^{98} - 27 q^{99}+O(q^{100}) \) 45 * q - 6 * q^2 + 34 * q^4 - 45 * q^5 + q^6 + 45 * q^7 - 15 * q^8 + 29 * q^9 + 6 * q^10 - q^11 - 3 * q^12 - 21 * q^13 - 6 * q^14 + 8 * q^16 - 7 * q^17 - 36 * q^18 - 20 * q^19 - 34 * q^20 - 34 * q^22 - 22 * q^23 - 11 * q^24 + 45 * q^25 - q^26 + 12 * q^27 + 34 * q^28 + 10 * q^29 - q^30 - 27 * q^31 - 26 * q^32 - 39 * q^33 - 13 * q^34 - 45 * q^35 - 3 * q^36 - 72 * q^37 + 2 * q^38 - 37 * q^39 + 15 * q^40 - 4 * q^41 + q^42 - 49 * q^43 + 5 * q^44 - 29 * q^45 - 67 * q^46 + 2 * q^47 + 8 * q^48 + 45 * q^49 - 6 * q^50 - 49 * q^51 - 47 * q^52 - 35 * q^53 - 12 * q^54 + q^55 - 15 * q^56 - 77 * q^57 - 50 * q^58 + 4 * q^59 + 3 * q^60 - 36 * q^61 + 17 * q^62 + 29 * q^63 + 5 * q^64 + 21 * q^65 - 8 * q^66 - 80 * q^67 + 27 * q^68 + 9 * q^69 + 6 * q^70 - 12 * q^71 - 97 * q^72 - 55 * q^73 + 32 * q^74 - 37 * q^76 - q^77 + 20 * q^78 - 94 * q^79 - 8 * q^80 - 19 * q^81 - 36 * q^82 + 24 * q^83 - 3 * q^84 + 7 * q^85 - 3 * q^86 - 4 * q^87 - 95 * q^88 + q^89 + 36 * q^90 - 21 * q^91 - 65 * q^92 - 71 * q^93 - 53 * q^94 + 20 * q^95 - 13 * q^96 - 110 * q^97 - 6 * q^98 - 27 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.58820	−1.83014	−0.915068	−	0.403300i	$-0.867863\pi$
$2$	−2.58820	−1.83014	−0.915068	+	0.403300i	$0.867863\pi$
$3$	1.46821	0.847670	0.423835	−	0.905739i	$-0.360684\pi$
$3$	1.46821	0.847670	0.423835	+	0.905739i	$0.360684\pi$
$4$	4.69879	2.34940
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−3.80002	−1.55135
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−6.98503	−2.46958
$9$	−0.844367	−0.281456
$10$	2.58820	0.818462
$11$	3.30944	0.997835	0.498917	−	0.866650i	$-0.333731\pi$
$11$	3.30944	0.997835	0.498917	+	0.866650i	$0.333731\pi$
$12$	6.89880	1.99151
$13$	1.30961	0.363221	0.181610	−	0.983371i	$-0.441869\pi$
$13$	1.30961	0.363221	0.181610	+	0.983371i	$0.441869\pi$
$14$	−2.58820	−0.691726
$15$	−1.46821	−0.379090
$16$	8.68108	2.17027
$17$	6.35843	1.54215	0.771073	−	0.636747i	$-0.219720\pi$
$17$	6.35843	1.54215	0.771073	+	0.636747i	$0.219720\pi$
$18$	2.18539	0.515102
$19$	−2.58012	−0.591921	−0.295961	−	0.955200i	$-0.595640\pi$
$19$	−2.58012	−0.591921	−0.295961	+	0.955200i	$0.595640\pi$
$20$	−4.69879	−1.05068
$21$	1.46821	0.320389
$22$	−8.56551	−1.82617
$23$	−5.17298	−1.07864	−0.539321	−	0.842100i	$-0.681319\pi$
$23$	−5.17298	−1.07864	−0.539321	+	0.842100i	$0.681319\pi$
$24$	−10.2555	−2.09339
$25$	1.00000	0.200000
$26$	−3.38954	−0.664743
$27$	−5.64433	−1.08625
$28$	4.69879	0.887989
$29$	3.24075	0.601792	0.300896	−	0.953657i	$-0.402714\pi$
$29$	3.24075	0.601792	0.300896	+	0.953657i	$0.402714\pi$
$30$	3.80002	0.693785
$31$	−3.58032	−0.643045	−0.321523	−	0.946902i	$-0.604195\pi$
$31$	−3.58032	−0.643045	−0.321523	+	0.946902i	$0.604195\pi$
$32$	−8.49834	−1.50231
$33$	4.85895	0.845835
$34$	−16.4569	−2.82234
$35$	−1.00000	−0.169031
$36$	−3.96751	−0.661251
$37$	6.54685	1.07630	0.538148	−	0.842851i	$-0.319124\pi$
$37$	6.54685	1.07630	0.538148	+	0.842851i	$0.319124\pi$
$38$	6.67789	1.08330
$39$	1.92278	0.307891
$40$	6.98503	1.10443
$41$	−1.04697	−0.163509	−0.0817543	−	0.996653i	$-0.526052\pi$
$41$	−1.04697	−0.163509	−0.0817543	+	0.996653i	$0.526052\pi$
$42$	−3.80002	−0.586356
$43$	−9.04119	−1.37877	−0.689384	−	0.724396i	$-0.742119\pi$
$43$	−9.04119	−1.37877	−0.689384	+	0.724396i	$0.742119\pi$
$44$	15.5504	2.34431
$45$	0.844367	0.125871
$46$	13.3887	1.97406
$47$	−2.12712	−0.310272	−0.155136	−	0.987893i	$-0.549582\pi$
$47$	−2.12712	−0.310272	−0.155136	+	0.987893i	$0.549582\pi$
$48$	12.7456	1.83967
$49$	1.00000	0.142857
$50$	−2.58820	−0.366027
$51$	9.33550	1.30723
$52$	6.15359	0.853349
$53$	−7.79670	−1.07096	−0.535480	−	0.844548i	$-0.679869\pi$
$53$	−7.79670	−1.07096	−0.535480	+	0.844548i	$0.679869\pi$
$54$	14.6087	1.98799
$55$	−3.30944	−0.446245
$56$	−6.98503	−0.933413
$57$	−3.78816	−0.501754
$58$	−8.38772	−1.10136
$59$	−7.35180	−0.957123	−0.478561	−	0.878054i	$-0.658842\pi$
$59$	−7.35180	−0.957123	−0.478561	+	0.878054i	$0.658842\pi$
$60$	−6.89880	−0.890632
$61$	−13.6865	−1.75238	−0.876190	−	0.481966i	$-0.839923\pi$
$61$	−13.6865	−1.75238	−0.876190	+	0.481966i	$0.839923\pi$
$62$	9.26661	1.17686
$63$	−0.844367	−0.106380
$64$	4.63326	0.579158
$65$	−1.30961	−0.162437
$66$	−12.5759	−1.54799
$67$	−7.75990	−0.948022	−0.474011	−	0.880519i	$-0.657194\pi$
$67$	−7.75990	−0.948022	−0.474011	+	0.880519i	$0.657194\pi$
$68$	29.8770	3.62311
$69$	−7.59501	−0.914332
$70$	2.58820	0.309349
$71$	10.5663	1.25399	0.626995	−	0.779024i	$-0.284285\pi$
$71$	10.5663	1.25399	0.626995	+	0.779024i	$0.284285\pi$
$72$	5.89793	0.695077
$73$	−6.30888	−0.738399	−0.369199	−	0.929350i	$-0.620368\pi$
$73$	−6.30888	−0.738399	−0.369199	+	0.929350i	$0.620368\pi$
$74$	−16.9446	−1.96977
$75$	1.46821	0.169534
$76$	−12.1235	−1.39066
$77$	3.30944	0.377146
$78$	−4.97654	−0.563483
$79$	−11.1866	−1.25859	−0.629297	−	0.777165i	$-0.716657\pi$
$79$	−11.1866	−1.25859	−0.629297	+	0.777165i	$0.716657\pi$
$80$	−8.68108	−0.970574
$81$	−5.75394	−0.639327
$82$	2.70976	0.299243
$83$	−10.2414	−1.12414	−0.562071	−	0.827089i	$-0.689995\pi$
$83$	−10.2414	−1.12414	−0.562071	+	0.827089i	$0.689995\pi$
$84$	6.89880	0.752721
$85$	−6.35843	−0.689669
$86$	23.4004	2.52333
$87$	4.75809	0.510121
$88$	−23.1166	−2.46423
$89$	6.92006	0.733525	0.366762	−	0.930315i	$-0.380466\pi$
$89$	6.92006	0.733525	0.366762	+	0.930315i	$0.380466\pi$
$90$	−2.18539	−0.230361
$91$	1.30961	0.137284
$92$	−24.3068	−2.53416
$93$	−5.25666	−0.545090
$94$	5.50541	0.567840
$95$	2.58012	0.264715
$96$	−12.4773	−1.27346
$97$	−9.19452	−0.933562	−0.466781	−	0.884373i	$-0.654586\pi$
$97$	−9.19452	−0.933562	−0.466781	+	0.884373i	$0.654586\pi$
$98$	−2.58820	−0.261448
$99$	−2.79438	−0.280846
$100$	4.69879	0.469879
$101$	−9.68009	−0.963205	−0.481602	−	0.876390i	$-0.659945\pi$
$101$	−9.68009	−0.963205	−0.481602	+	0.876390i	$0.659945\pi$
$102$	−24.1622	−2.39241
$103$	13.7104	1.35093	0.675465	−	0.737392i	$-0.263943\pi$
$103$	13.7104	1.35093	0.675465	+	0.737392i	$0.263943\pi$
$104$	−9.14766	−0.897002
$105$	−1.46821	−0.143282
$106$	20.1794	1.96000
$107$	−2.06496	−0.199628	−0.0998138	−	0.995006i	$-0.531825\pi$
$107$	−2.06496	−0.199628	−0.0998138	+	0.995006i	$0.531825\pi$
$108$	−26.5215	−2.55204
$109$	4.02183	0.385221	0.192611	−	0.981275i	$-0.438305\pi$
$109$	4.02183	0.385221	0.192611	+	0.981275i	$0.438305\pi$
$110$	8.56551	0.816689
$111$	9.61213	0.912343
$112$	8.68108	0.820285
$113$	13.5413	1.27386	0.636931	−	0.770921i	$-0.280204\pi$
$113$	13.5413	1.27386	0.636931	+	0.770921i	$0.280204\pi$
$114$	9.80452	0.918278
$115$	5.17298	0.482383
$116$	15.2276	1.41385
$117$	−1.10579	−0.102230
$118$	19.0280	1.75166
$119$	6.35843	0.582876
$120$	10.2555	0.936192
$121$	−0.0475831	−0.00432574
$122$	35.4235	3.20709
$123$	−1.53716	−0.138601
$124$	−16.8232	−1.51077
$125$	−1.00000	−0.0894427
$126$	2.18539	0.194690
$127$	−17.7535	−1.57537	−0.787685	−	0.616078i	$-0.788721\pi$
$127$	−17.7535	−1.57537	−0.787685	+	0.616078i	$0.788721\pi$
$128$	5.00485	0.442370
$129$	−13.2743	−1.16874
$130$	3.38954	0.297282
$131$	17.9474	1.56807	0.784034	−	0.620717i	$-0.213159\pi$
$131$	17.9474	1.56807	0.784034	+	0.620717i	$0.213159\pi$
$132$	22.8312	1.98720
$133$	−2.58012	−0.223725
$134$	20.0842	1.73501
$135$	5.64433	0.485786
$136$	−44.4138	−3.80845
$137$	−5.68269	−0.485505	−0.242753	−	0.970088i	$-0.578050\pi$
$137$	−5.68269	−0.485505	−0.242753	+	0.970088i	$0.578050\pi$
$138$	19.6574	1.67335
$139$	16.8589	1.42995	0.714976	−	0.699149i	$-0.246438\pi$
$139$	16.8589	1.42995	0.714976	+	0.699149i	$0.246438\pi$
$140$	−4.69879	−0.397121
$141$	−3.12305	−0.263008
$142$	−27.3477	−2.29497
$143$	4.33408	0.362434
$144$	−7.33001	−0.610835
$145$	−3.24075	−0.269130
$146$	16.3287	1.35137
$147$	1.46821	0.121096
$148$	30.7623	2.52865
$149$	10.8233	0.886677	0.443338	−	0.896354i	$-0.353794\pi$
$149$	10.8233	0.886677	0.443338	+	0.896354i	$0.353794\pi$
$150$	−3.80002	−0.310270
$151$	5.59589	0.455387	0.227693	−	0.973733i	$-0.426882\pi$
$151$	5.59589	0.455387	0.227693	+	0.973733i	$0.426882\pi$
$152$	18.0222	1.46180
$153$	−5.36885	−0.434046
$154$	−8.56551	−0.690229
$155$	3.58032	0.287579
$156$	9.03475	0.723359
$157$	10.7298	0.856331	0.428166	−	0.903700i	$-0.359160\pi$
$157$	10.7298	0.856331	0.428166	+	0.903700i	$0.359160\pi$
$158$	28.9533	2.30340
$159$	−11.4472	−0.907820
$160$	8.49834	0.671852
$161$	−5.17298	−0.407688
$162$	14.8924	1.17006
$163$	9.82482	0.769539	0.384770	−	0.923013i	$-0.374281\pi$
$163$	9.82482	0.769539	0.384770	+	0.923013i	$0.374281\pi$
$164$	−4.91948	−0.384146
$165$	−4.85895	−0.378269
$166$	26.5069	2.05733
$167$	0.958810	0.0741950	0.0370975	−	0.999312i	$-0.488189\pi$
$167$	0.958810	0.0741950	0.0370975	+	0.999312i	$0.488189\pi$
$168$	−10.2555	−0.791227
$169$	−11.2849	−0.868071
$170$	16.4569	1.26219
$171$	2.17857	0.166600
$172$	−42.4827	−3.23928
$173$	−0.0544665	−0.00414101	−0.00207051	−	0.999998i	$-0.500659\pi$
$173$	−0.0544665	−0.00414101	−0.00207051	+	0.999998i	$0.500659\pi$
$174$	−12.3149	−0.933591
$175$	1.00000	0.0755929
$176$	28.7295	2.16557
$177$	−10.7940	−0.811324
$178$	−17.9105	−1.34245
$179$	−2.85793	−0.213612	−0.106806	−	0.994280i	$-0.534062\pi$
$179$	−2.85793	−0.213612	−0.106806	+	0.994280i	$0.534062\pi$
$180$	3.96751	0.295720
$181$	−19.5146	−1.45051	−0.725254	−	0.688482i	$-0.758277\pi$
$181$	−19.5146	−1.45051	−0.725254	+	0.688482i	$0.758277\pi$
$182$	−3.38954	−0.251249
$183$	−20.0947	−1.48544
$184$	36.1334	2.66379
$185$	−6.54685	−0.481334
$186$	13.6053	0.997589
$187$	21.0429	1.53881
$188$	−9.99488	−0.728952
$189$	−5.64433	−0.410564
$190$	−6.67789	−0.484465
$191$	−19.4287	−1.40581	−0.702907	−	0.711282i	$-0.748115\pi$
$191$	−19.4287	−1.40581	−0.702907	+	0.711282i	$0.748115\pi$
$192$	6.80259	0.490935
$193$	−23.7513	−1.70965	−0.854827	−	0.518912i	$-0.826337\pi$
$193$	−23.7513	−1.70965	−0.854827	+	0.518912i	$0.826337\pi$
$194$	23.7973	1.70854
$195$	−1.92278	−0.137693
$196$	4.69879	0.335628
$197$	−13.8588	−0.987399	−0.493699	−	0.869633i	$-0.664356\pi$
$197$	−13.8588	−0.987399	−0.493699	+	0.869633i	$0.664356\pi$
$198$	7.23243	0.513987
$199$	2.71572	0.192512	0.0962562	−	0.995357i	$-0.469313\pi$
$199$	2.71572	0.192512	0.0962562	+	0.995357i	$0.469313\pi$
$200$	−6.98503	−0.493916
$201$	−11.3931	−0.803610
$202$	25.0540	1.76280
$203$	3.24075	0.227456
$204$	43.8656	3.07120
$205$	1.04697	0.0731232
$206$	−35.4854	−2.47238
$207$	4.36790	0.303590
$208$	11.3688	0.788286
$209$	−8.53878	−0.590640
$210$	3.80002	0.262226
$211$	−10.1857	−0.701215	−0.350608	−	0.936522i	$-0.614025\pi$
$211$	−10.1857	−0.701215	−0.350608	+	0.936522i	$0.614025\pi$
$212$	−36.6351	−2.51611
$213$	15.5135	1.06297
$214$	5.34455	0.365346
$215$	9.04119	0.616604
$216$	39.4258	2.68258
$217$	−3.58032	−0.243048
$218$	−10.4093	−0.705007
$219$	−9.26275	−0.625918
$220$	−15.5504	−1.04841
$221$	8.32707	0.560139
$222$	−24.8782	−1.66971
$223$	−13.9892	−0.936787	−0.468393	−	0.883520i	$-0.655167\pi$
$223$	−13.9892	−0.936787	−0.468393	+	0.883520i	$0.655167\pi$
$224$	−8.49834	−0.567819
$225$	−0.844367	−0.0562911
$226$	−35.0477	−2.33134
$227$	−13.2772	−0.881235	−0.440618	−	0.897695i	$-0.645241\pi$
$227$	−13.2772	−0.881235	−0.440618	+	0.897695i	$0.645241\pi$
$228$	−17.7998	−1.17882
$229$	1.00000	0.0660819
$229$	1.00000	0.0660819
$230$	−13.3887	−0.882827
$231$	4.85895	0.319695
$232$	−22.6367	−1.48617
$233$	−10.2119	−0.669003	−0.334501	−	0.942395i	$-0.608568\pi$
$233$	−10.2119	−0.669003	−0.334501	+	0.942395i	$0.608568\pi$
$234$	2.86201	0.187096
$235$	2.12712	0.138758
$236$	−34.5446	−2.24866
$237$	−16.4243	−1.06687
$238$	−16.4569	−1.06674
$239$	27.6165	1.78636	0.893181	−	0.449696i	$-0.148468\pi$
$239$	27.6165	1.78636	0.893181	+	0.449696i	$0.148468\pi$
$240$	−12.7456	−0.822726
$241$	15.8374	1.02018	0.510088	−	0.860123i	$-0.329613\pi$
$241$	15.8374	1.02018	0.510088	+	0.860123i	$0.329613\pi$
$242$	0.123155	0.00791669
$243$	8.48500	0.544313
$244$	−64.3102	−4.11704
$245$	−1.00000	−0.0638877
$246$	3.97849	0.253659
$247$	−3.37896	−0.214998
$248$	25.0087	1.58805
$249$	−15.0365	−0.952901
$250$	2.58820	0.163692
$251$	26.8946	1.69757	0.848785	−	0.528738i	$-0.177335\pi$
$251$	26.8946	1.69757	0.848785	+	0.528738i	$0.177335\pi$
$252$	−3.96751	−0.249929
$253$	−17.1197	−1.07631
$254$	45.9497	2.88314
$255$	−9.33550	−0.584611
$256$	−22.2201	−1.38876
$257$	26.7343	1.66764	0.833819	−	0.552038i	$-0.186150\pi$
$257$	26.7343	1.66764	0.833819	+	0.552038i	$0.186150\pi$
$258$	34.3567	2.13895
$259$	6.54685	0.406801
$260$	−6.15359	−0.381629
$261$	−2.73638	−0.169378
$262$	−46.4514	−2.86978
$263$	23.0169	1.41928	0.709642	−	0.704562i	$-0.248857\pi$
$263$	23.0169	1.41928	0.709642	+	0.704562i	$0.248857\pi$
$264$	−33.9399	−2.08886
$265$	7.79670	0.478948
$266$	6.67789	0.409447
$267$	10.1601	0.621787
$268$	−36.4622	−2.22728
$269$	14.4145	0.878867	0.439433	−	0.898275i	$-0.355179\pi$
$269$	14.4145	0.878867	0.439433	+	0.898275i	$0.355179\pi$
$270$	−14.6087	−0.889055
$271$	27.7381	1.68497	0.842486	−	0.538718i	$-0.181091\pi$
$271$	27.7381	1.68497	0.842486	+	0.538718i	$0.181091\pi$
$272$	55.1980	3.34687
$273$	1.92278	0.116372
$274$	14.7080	0.888541
$275$	3.30944	0.199567
$276$	−35.6874	−2.14813
$277$	−30.6920	−1.84410	−0.922052	−	0.387067i	$-0.873488\pi$
$277$	−30.6920	−1.84410	−0.922052	+	0.387067i	$0.873488\pi$
$278$	−43.6342	−2.61700
$279$	3.02311	0.180989
$280$	6.98503	0.417435
$281$	−14.7863	−0.882080	−0.441040	−	0.897488i	$-0.645390\pi$
$281$	−14.7863	−0.882080	−0.441040	+	0.897488i	$0.645390\pi$
$282$	8.08308	0.481340
$283$	−12.3834	−0.736119	−0.368060	−	0.929802i	$-0.619978\pi$
$283$	−12.3834	−0.736119	−0.368060	+	0.929802i	$0.619978\pi$
$284$	49.6489	2.94612
$285$	3.78816	0.224391
$286$	−11.2175	−0.663304
$287$	−1.04697	−0.0618004
$288$	7.17571	0.422833
$289$	23.4296	1.37821
$290$	8.38772	0.492544
$291$	−13.4995	−0.791352
$292$	−29.6441	−1.73479
$293$	−33.3049	−1.94569	−0.972846	−	0.231454i	$-0.925652\pi$
$293$	−33.3049	−1.94569	−0.972846	+	0.231454i	$0.925652\pi$
$294$	−3.80002	−0.221622
$295$	7.35180	0.428038
$296$	−45.7299	−2.65800
$297$	−18.6796	−1.08390
$298$	−28.0128	−1.62274
$299$	−6.77459	−0.391785
$300$	6.89880	0.398303
$301$	−9.04119	−0.521126
$302$	−14.4833	−0.833420
$303$	−14.2124	−0.816480
$304$	−22.3983	−1.28463
$305$	13.6865	0.783688
$306$	13.8957	0.794363
$307$	−32.9601	−1.88113	−0.940566	−	0.339612i	$-0.889704\pi$
$307$	−32.9601	−1.88113	−0.940566	+	0.339612i	$0.889704\pi$
$308$	15.5504	0.886066
$309$	20.1298	1.14514
$310$	−9.26661	−0.526308
$311$	−18.9997	−1.07737	−0.538686	−	0.842507i	$-0.681079\pi$
$311$	−18.9997	−1.07737	−0.538686	+	0.842507i	$0.681079\pi$
$312$	−13.4307	−0.760362
$313$	−23.6184	−1.33499	−0.667496	−	0.744614i	$-0.732634\pi$
$313$	−23.6184	−1.33499	−0.667496	+	0.744614i	$0.732634\pi$
$314$	−27.7709	−1.56720
$315$	0.844367	0.0475747
$316$	−52.5637	−2.95694
$317$	14.7533	0.828626	0.414313	−	0.910134i	$-0.364022\pi$
$317$	14.7533	0.828626	0.414313	+	0.910134i	$0.364022\pi$
$318$	29.6276	1.66143
$319$	10.7251	0.600489
$320$	−4.63326	−0.259007
$321$	−3.03180	−0.169218
$322$	13.3887	0.746125
$323$	−16.4055	−0.912829
$324$	−27.0366	−1.50203
$325$	1.30961	0.0726441
$326$	−25.4286	−1.40836
$327$	5.90488	0.326541
$328$	7.31308	0.403797
$329$	−2.12712	−0.117272
$330$	12.5759	0.692283
$331$	22.9658	1.26232	0.631158	−	0.775654i	$-0.282580\pi$
$331$	22.9658	1.26232	0.631158	+	0.775654i	$0.282580\pi$
$332$	−48.1223	−2.64106
$333$	−5.52794	−0.302929
$334$	−2.48160	−0.135787
$335$	7.75990	0.423968
$336$	12.7456	0.695331
$337$	7.65611	0.417055	0.208527	−	0.978017i	$-0.433133\pi$
$337$	7.65611	0.417055	0.208527	+	0.978017i	$0.433133\pi$
$338$	29.2077	1.58869
$339$	19.8815	1.07981
$340$	−29.8770	−1.62031
$341$	−11.8489	−0.641653
$342$	−5.63859	−0.304900
$343$	1.00000	0.0539949
$344$	63.1530	3.40498
$345$	7.59501	0.408902
$346$	0.140970	0.00757862
$347$	−9.74676	−0.523234	−0.261617	−	0.965172i	$-0.584256\pi$
$347$	−9.74676	−0.523234	−0.261617	+	0.965172i	$0.584256\pi$
$348$	22.3573	1.19848
$349$	3.75443	0.200970	0.100485	−	0.994939i	$-0.467961\pi$
$349$	3.75443	0.200970	0.100485	+	0.994939i	$0.467961\pi$
$350$	−2.58820	−0.138345
$351$	−7.39187	−0.394549
$352$	−28.1248	−1.49906
$353$	−21.3472	−1.13620	−0.568099	−	0.822960i	$-0.692321\pi$
$353$	−21.3472	−1.13620	−0.568099	+	0.822960i	$0.692321\pi$
$354$	27.9370	1.48483
$355$	−10.5663	−0.560801
$356$	32.5159	1.72334
$357$	9.33550	0.494087
$358$	7.39690	0.390938
$359$	−20.1077	−1.06124	−0.530622	−	0.847609i	$-0.678042\pi$
$359$	−20.1077	−1.06124	−0.530622	+	0.847609i	$0.678042\pi$
$360$	−5.89793	−0.310848
$361$	−12.3430	−0.649629
$362$	50.5077	2.65462
$363$	−0.0698619	−0.00366680
$364$	6.15359	0.322536
$365$	6.30888	0.330222
$366$	52.0091	2.71856
$367$	−8.12715	−0.424234	−0.212117	−	0.977244i	$-0.568036\pi$
$367$	−8.12715	−0.424234	−0.212117	+	0.977244i	$0.568036\pi$
$368$	−44.9071	−2.34094
$369$	0.884023	0.0460204
$370$	16.9446	0.880906
$371$	−7.79670	−0.404785
$372$	−24.7000	−1.28063
$373$	25.2048	1.30505	0.652526	−	0.757766i	$-0.273709\pi$
$373$	25.2048	1.30505	0.652526	+	0.757766i	$0.273709\pi$
$374$	−54.4632	−2.81623
$375$	−1.46821	−0.0758179
$376$	14.8580	0.766241
$377$	4.24412	0.218583
$378$	14.6087	0.751389
$379$	−6.01275	−0.308854	−0.154427	−	0.988004i	$-0.549353\pi$
$379$	−6.01275	−0.308854	−0.154427	+	0.988004i	$0.549353\pi$
$380$	12.1235	0.621921
$381$	−26.0659	−1.33539
$382$	50.2855	2.57283
$383$	−27.0990	−1.38470	−0.692348	−	0.721564i	$-0.743424\pi$
$383$	−27.0990	−1.38470	−0.692348	+	0.721564i	$0.743424\pi$
$384$	7.34815	0.374984
$385$	−3.30944	−0.168665
$386$	61.4731	3.12890
$387$	7.63408	0.388062
$388$	−43.2031	−2.19331
$389$	33.9506	1.72136	0.860682	−	0.509142i	$-0.170037\pi$
$389$	33.9506	1.72136	0.860682	+	0.509142i	$0.170037\pi$
$390$	4.97654	0.251997
$391$	−32.8921	−1.66342
$392$	−6.98503	−0.352797
$393$	26.3505	1.32920
$394$	35.8694	1.80707
$395$	11.1866	0.562860
$396$	−13.1302	−0.659819
$397$	38.5939	1.93697	0.968486	−	0.249068i	$-0.0801243\pi$
$397$	38.5939	1.93697	0.968486	+	0.249068i	$0.0801243\pi$
$398$	−7.02884	−0.352324
$399$	−3.78816	−0.189645
$400$	8.68108	0.434054
$401$	−32.3476	−1.61536	−0.807682	−	0.589619i	$-0.799278\pi$
$401$	−32.3476	−1.61536	−0.807682	+	0.589619i	$0.799278\pi$
$402$	29.4878	1.47072
$403$	−4.68883	−0.233567
$404$	−45.4847	−2.26295
$405$	5.75394	0.285916
$406$	−8.38772	−0.416275
$407$	21.6664	1.07397
$408$	−65.2087	−3.22831
$409$	−2.19880	−0.108724	−0.0543618	−	0.998521i	$-0.517312\pi$
$409$	−2.19880	−0.108724	−0.0543618	+	0.998521i	$0.517312\pi$
$410$	−2.70976	−0.133825
$411$	−8.34337	−0.411548
$412$	64.4225	3.17387
$413$	−7.35180	−0.361758
$414$	−11.3050	−0.555611
$415$	10.2414	0.502732
$416$	−11.1295	−0.545669
$417$	24.7523	1.21213
$418$	22.1001	1.08095
$419$	24.3169	1.18796	0.593978	−	0.804481i	$-0.297557\pi$
$419$	24.3169	1.18796	0.593978	+	0.804481i	$0.297557\pi$
$420$	−6.89880	−0.336627
$421$	−24.6203	−1.19992	−0.599960	−	0.800030i	$-0.704817\pi$
$421$	−24.6203	−1.19992	−0.599960	+	0.800030i	$0.704817\pi$
$422$	26.3628	1.28332
$423$	1.79607	0.0873277
$424$	54.4602	2.64482
$425$	6.35843	0.308429
$426$	−40.1521	−1.94538
$427$	−13.6865	−0.662337
$428$	−9.70284	−0.469005
$429$	6.36333	0.307225
$430$	−23.4004	−1.12847
$431$	35.5650	1.71311	0.856553	−	0.516059i	$-0.172602\pi$
$431$	35.5650	1.71311	0.856553	+	0.516059i	$0.172602\pi$
$432$	−48.9988	−2.35746
$433$	−13.7983	−0.663106	−0.331553	−	0.943437i	$-0.607573\pi$
$433$	−13.7983	−0.663106	−0.331553	+	0.943437i	$0.607573\pi$
$434$	9.26661	0.444811
$435$	−4.75809	−0.228133
$436$	18.8977	0.905038
$437$	13.3469	0.638471
$438$	23.9739	1.14552
$439$	21.4415	1.02335	0.511674	−	0.859179i	$-0.329025\pi$
$439$	21.4415	1.02335	0.511674	+	0.859179i	$0.329025\pi$
$440$	23.1166	1.10204
$441$	−0.844367	−0.0402079
$442$	−21.5521	−1.02513
$443$	6.24184	0.296559	0.148279	−	0.988946i	$-0.452627\pi$
$443$	6.24184	0.296559	0.148279	+	0.988946i	$0.452627\pi$
$444$	45.1654	2.14346
$445$	−6.92006	−0.328042
$446$	36.2069	1.71445
$447$	15.8908	0.751609
$448$	4.63326	0.218901
$449$	−33.5441	−1.58304	−0.791521	−	0.611142i	$-0.790711\pi$
$449$	−33.5441	−1.58304	−0.791521	+	0.611142i	$0.790711\pi$
$450$	2.18539	0.103020
$451$	−3.46487	−0.163155
$452$	63.6279	2.99281
$453$	8.21593	0.386018
$454$	34.3640	1.61278
$455$	−1.30961	−0.0613955
$456$	26.4604	1.23912
$457$	−14.7817	−0.691460	−0.345730	−	0.938334i	$-0.612369\pi$
$457$	−14.7817	−0.691460	−0.345730	+	0.938334i	$0.612369\pi$
$458$	−2.58820	−0.120939
$459$	−35.8891	−1.67516
$460$	24.3068	1.13331
$461$	−24.7340	−1.15198	−0.575990	−	0.817457i	$-0.695383\pi$
$461$	−24.7340	−1.15198	−0.575990	+	0.817457i	$0.695383\pi$
$462$	−12.5759	−0.585086
$463$	−21.7698	−1.01173	−0.505863	−	0.862614i	$-0.668826\pi$
$463$	−21.7698	−1.01173	−0.505863	+	0.862614i	$0.668826\pi$
$464$	28.1332	1.30605
$465$	5.25666	0.243772
$466$	26.4304	1.22437
$467$	34.2932	1.58690	0.793451	−	0.608634i	$-0.208282\pi$
$467$	34.2932	1.58690	0.793451	+	0.608634i	$0.208282\pi$
$468$	−5.19589	−0.240180
$469$	−7.75990	−0.358319
$470$	−5.50541	−0.253946
$471$	15.7536	0.725886
$472$	51.3525	2.36369
$473$	−29.9213	−1.37578
$474$	42.5094	1.95252
$475$	−2.58012	−0.118384
$476$	29.8770	1.36941
$477$	6.58328	0.301428
$478$	−71.4771	−3.26929
$479$	19.5425	0.892921	0.446460	−	0.894803i	$-0.352684\pi$
$479$	19.5425	0.892921	0.446460	+	0.894803i	$0.352684\pi$
$480$	12.4773	0.569509
$481$	8.57382	0.390933
$482$	−40.9903	−1.86706
$483$	−7.59501	−0.345585
$484$	−0.223583	−0.0101629
$485$	9.19452	0.417502
$486$	−21.9609	−0.996167
$487$	−4.93800	−0.223762	−0.111881	−	0.993722i	$-0.535688\pi$
$487$	−4.93800	−0.223762	−0.111881	+	0.993722i	$0.535688\pi$
$488$	95.6008	4.32764
$489$	14.4249	0.652315
$490$	2.58820	0.116923
$491$	19.4702	0.878679	0.439340	−	0.898321i	$-0.355212\pi$
$491$	19.4702	0.878679	0.439340	+	0.898321i	$0.355212\pi$
$492$	−7.22281	−0.325629
$493$	20.6061	0.928051
$494$	8.74543	0.393475
$495$	2.79438	0.125598
$496$	−31.0811	−1.39558
$497$	10.5663	0.473963
$498$	38.9176	1.74394
$499$	−3.49900	−0.156637	−0.0783183	−	0.996928i	$-0.524955\pi$
$499$	−3.49900	−0.156637	−0.0783183	+	0.996928i	$0.524955\pi$
$500$	−4.69879	−0.210136
$501$	1.40773	0.0628928
$502$	−69.6086	−3.10678
$503$	−8.70882	−0.388307	−0.194154	−	0.980971i	$-0.562196\pi$
$503$	−8.70882	−0.388307	−0.194154	+	0.980971i	$0.562196\pi$
$504$	5.89793	0.262714
$505$	9.68009	0.430758
$506$	44.3093	1.96979
$507$	−16.5686	−0.735838
$508$	−83.4201	−3.70117
$509$	−35.0541	−1.55375	−0.776873	−	0.629658i	$-0.783195\pi$
$509$	−35.0541	−1.55375	−0.776873	+	0.629658i	$0.783195\pi$
$510$	24.1622	1.06992
$511$	−6.30888	−0.279088
$512$	47.5004	2.09924
$513$	14.5631	0.642975
$514$	−69.1937	−3.05200
$515$	−13.7104	−0.604154
$516$	−62.3734	−2.74584
$517$	−7.03957	−0.309600
$518$	−16.9446	−0.744502
$519$	−0.0799682	−0.00351021
$520$	9.14766	0.401152
$521$	−27.3496	−1.19821	−0.599104	−	0.800671i	$-0.704477\pi$
$521$	−27.3496	−1.19821	−0.599104	+	0.800671i	$0.704477\pi$
$522$	7.08231	0.309984
$523$	13.5770	0.593680	0.296840	−	0.954927i	$-0.404067\pi$
$523$	13.5770	0.593680	0.296840	+	0.954927i	$0.404067\pi$
$524$	84.3310	3.68402
$525$	1.46821	0.0640778
$526$	−59.5725	−2.59748
$527$	−22.7652	−0.991670
$528$	42.1809	1.83569
$529$	3.75976	0.163468
$530$	−20.1794	−0.876539
$531$	6.20762	0.269388
$532$	−12.1235	−0.525619
$533$	−1.37112	−0.0593897
$534$	−26.2964	−1.13795
$535$	2.06496	0.0892762
$536$	54.2031	2.34122
$537$	−4.19603	−0.181072
$538$	−37.3076	−1.60845
$539$	3.30944	0.142548
$540$	26.5215	1.14131
$541$	0.184722	0.00794183	0.00397092	−	0.999992i	$-0.498736\pi$
$541$	0.184722	0.00794183	0.00397092	+	0.999992i	$0.498736\pi$
$542$	−71.7919	−3.08373
$543$	−28.6514	−1.22955
$544$	−54.0361	−2.31678
$545$	−4.02183	−0.172276
$546$	−4.97654	−0.212976
$547$	14.8920	0.636738	0.318369	−	0.947967i	$-0.396865\pi$
$547$	14.8920	0.636738	0.318369	+	0.947967i	$0.396865\pi$
$548$	−26.7018	−1.14064
$549$	11.5565	0.493217
$550$	−8.56551	−0.365235
$551$	−8.36154	−0.356213
$552$	53.0514	2.25802
$553$	−11.1866	−0.475704
$554$	79.4371	3.37496
$555$	−9.61213	−0.408012
$556$	79.2164	3.35952
$557$	35.7126	1.51319	0.756596	−	0.653883i	$-0.226861\pi$
$557$	35.7126	1.51319	0.756596	+	0.653883i	$0.226861\pi$
$558$	−7.82442	−0.331234
$559$	−11.8404	−0.500797
$560$	−8.68108	−0.366842
$561$	30.8953	1.30440
$562$	38.2701	1.61433
$563$	−25.5949	−1.07870	−0.539349	−	0.842083i	$-0.681330\pi$
$563$	−25.5949	−1.07870	−0.539349	+	0.842083i	$0.681330\pi$
$564$	−14.6746	−0.617910
$565$	−13.5413	−0.569688
$566$	32.0509	1.34720
$567$	−5.75394	−0.241643
$568$	−73.8059	−3.09683
$569$	−14.3236	−0.600477	−0.300238	−	0.953864i	$-0.597066\pi$
$569$	−14.3236	−0.600477	−0.300238	+	0.953864i	$0.597066\pi$
$570$	−9.80452	−0.410666
$571$	19.3741	0.810780	0.405390	−	0.914144i	$-0.367136\pi$
$571$	19.3741	0.810780	0.405390	+	0.914144i	$0.367136\pi$
$572$	20.3650	0.851502
$573$	−28.5254	−1.19167
$574$	2.70976	0.113103
$575$	−5.17298	−0.215728
$576$	−3.91217	−0.163007
$577$	−17.9091	−0.745567	−0.372783	−	0.927918i	$-0.621597\pi$
$577$	−17.9091	−0.745567	−0.372783	+	0.927918i	$0.621597\pi$
$578$	−60.6407	−2.52232
$579$	−34.8718	−1.44922
$580$	−15.2276	−0.632292
$581$	−10.2414	−0.424886
$582$	34.9393	1.44828
$583$	−25.8027	−1.06864
$584$	44.0677	1.82353
$585$	1.10579	0.0457189
$586$	86.1998	3.56088
$587$	31.1533	1.28583	0.642917	−	0.765936i	$-0.277724\pi$
$587$	31.1533	1.28583	0.642917	+	0.765936i	$0.277724\pi$
$588$	6.89880	0.284502
$589$	9.23768	0.380632
$590$	−19.0280	−0.783368
$591$	−20.3476	−0.836988
$592$	56.8337	2.33585
$593$	10.0382	0.412220	0.206110	−	0.978529i	$-0.433920\pi$
$593$	10.0382	0.412220	0.206110	+	0.978529i	$0.433920\pi$
$594$	48.3466	1.98368
$595$	−6.35843	−0.260670
$596$	50.8563	2.08316
$597$	3.98724	0.163187
$598$	17.5340	0.717019
$599$	40.5363	1.65627	0.828134	−	0.560531i	$-0.189403\pi$
$599$	40.5363	1.65627	0.828134	+	0.560531i	$0.189403\pi$
$600$	−10.2555	−0.418678
$601$	12.1237	0.494534	0.247267	−	0.968947i	$-0.420467\pi$
$601$	12.1237	0.494534	0.247267	+	0.968947i	$0.420467\pi$
$602$	23.4004	0.953731
$603$	6.55220	0.266826
$604$	26.2939	1.06988
$605$	0.0475831	0.00193453
$606$	36.7845	1.49427
$607$	−0.404918	−0.0164351	−0.00821756	−	0.999966i	$-0.502616\pi$
$607$	−0.404918	−0.0164351	−0.00821756	+	0.999966i	$0.502616\pi$
$608$	21.9268	0.889248
$609$	4.75809	0.192808
$610$	−35.4235	−1.43426
$611$	−2.78569	−0.112697
$612$	−25.2271	−1.01975
$613$	−15.0783	−0.609008	−0.304504	−	0.952511i	$-0.598491\pi$
$613$	−15.0783	−0.609008	−0.304504	+	0.952511i	$0.598491\pi$
$614$	85.3074	3.44273
$615$	1.53716	0.0619844
$616$	−23.1166	−0.931392
$617$	−3.88533	−0.156418	−0.0782088	−	0.996937i	$-0.524920\pi$
$617$	−3.88533	−0.156418	−0.0782088	+	0.996937i	$0.524920\pi$
$618$	−52.0999	−2.09577
$619$	−9.17471	−0.368763	−0.184381	−	0.982855i	$-0.559028\pi$
$619$	−9.17471	−0.368763	−0.184381	+	0.982855i	$0.559028\pi$
$620$	16.8232	0.675636
$621$	29.1980	1.17168
$622$	49.1750	1.97174
$623$	6.92006	0.277246
$624$	16.6918	0.668207
$625$	1.00000	0.0400000
$626$	61.1292	2.44322
$627$	−12.5367	−0.500667
$628$	50.4171	2.01186
$629$	41.6277	1.65980
$630$	−2.18539	−0.0870681
$631$	31.6778	1.26107	0.630537	−	0.776159i	$-0.282835\pi$
$631$	31.6778	1.26107	0.630537	+	0.776159i	$0.282835\pi$
$632$	78.1389	3.10820
$633$	−14.9548	−0.594399
$634$	−38.1844	−1.51650
$635$	17.7535	0.704527
$636$	−53.7879	−2.13283
$637$	1.30961	0.0518887
$638$	−27.7587	−1.09898
$639$	−8.92183	−0.352942
$640$	−5.00485	−0.197834
$641$	1.60494	0.0633914	0.0316957	−	0.999498i	$-0.489909\pi$
$641$	1.60494	0.0633914	0.0316957	+	0.999498i	$0.489909\pi$
$642$	7.84690	0.309693
$643$	−33.6042	−1.32522	−0.662610	−	0.748965i	$-0.730551\pi$
$643$	−33.6042	−1.32522	−0.662610	+	0.748965i	$0.730551\pi$
$644$	−24.3068	−0.957822
$645$	13.2743	0.522677
$646$	42.4609	1.67060
$647$	−35.7734	−1.40640	−0.703200	−	0.710992i	$-0.748246\pi$
$647$	−35.7734	−1.40640	−0.703200	+	0.710992i	$0.748246\pi$
$648$	40.1914	1.57887
$649$	−24.3304	−0.955051
$650$	−3.38954	−0.132949
$651$	−5.25666	−0.206025
$652$	46.1648	1.80795
$653$	−6.39741	−0.250350	−0.125175	−	0.992135i	$-0.539949\pi$
$653$	−6.39741	−0.250350	−0.125175	+	0.992135i	$0.539949\pi$
$654$	−15.2830	−0.597614
$655$	−17.9474	−0.701262
$656$	−9.08879	−0.354858
$657$	5.32701	0.207826
$658$	5.50541	0.214623
$659$	39.2600	1.52935	0.764676	−	0.644415i	$-0.222899\pi$
$659$	39.2600	1.52935	0.764676	+	0.644415i	$0.222899\pi$
$660$	−22.8312	−0.888703
$661$	3.71549	0.144516	0.0722578	−	0.997386i	$-0.476980\pi$
$661$	3.71549	0.144516	0.0722578	+	0.997386i	$0.476980\pi$
$662$	−59.4403	−2.31021
$663$	12.2259	0.474813
$664$	71.5366	2.77616
$665$	2.58012	0.100053
$666$	14.3074	0.554402
$667$	−16.7643	−0.649118
$668$	4.50525	0.174313
$669$	−20.5391	−0.794086
$670$	−20.0842	−0.775920
$671$	−45.2948	−1.74859
$672$	−12.4773	−0.481323
$673$	17.0496	0.657213	0.328607	−	0.944467i	$-0.393421\pi$
$673$	17.0496	0.657213	0.328607	+	0.944467i	$0.393421\pi$
$674$	−19.8156	−0.763267
$675$	−5.64433	−0.217250
$676$	−53.0255	−2.03944
$677$	−23.4431	−0.900990	−0.450495	−	0.892779i	$-0.648752\pi$
$677$	−23.4431	−0.900990	−0.450495	+	0.892779i	$0.648752\pi$
$678$	−51.4573	−1.97621
$679$	−9.19452	−0.352853
$680$	44.4138	1.70319
$681$	−19.4936	−0.746997
$682$	30.6673	1.17431
$683$	14.9359	0.571507	0.285753	−	0.958303i	$-0.407756\pi$
$683$	14.9359	0.571507	0.285753	+	0.958303i	$0.407756\pi$
$684$	10.2367	0.391409
$685$	5.68269	0.217125
$686$	−2.58820	−0.0988180
$687$	1.46821	0.0560156
$688$	−78.4873	−2.99230
$689$	−10.2106	−0.388995
$690$	−19.6574	−0.748346
$691$	31.9138	1.21406	0.607030	−	0.794679i	$-0.292361\pi$
$691$	31.9138	1.21406	0.607030	+	0.794679i	$0.292361\pi$
$692$	−0.255927	−0.00972889
$693$	−2.79438	−0.106150
$694$	25.2266	0.957589
$695$	−16.8589	−0.639494
$696$	−33.2354	−1.25978
$697$	−6.65706	−0.252154
$698$	−9.71723	−0.367802
$699$	−14.9932	−0.567093
$700$	4.69879	0.177598
$701$	−9.07415	−0.342726	−0.171363	−	0.985208i	$-0.554817\pi$
$701$	−9.07415	−0.342726	−0.171363	+	0.985208i	$0.554817\pi$
$702$	19.1317	0.722078
$703$	−16.8917	−0.637082
$704$	15.3335	0.577904
$705$	3.12305	0.117621
$706$	55.2509	2.07940
$707$	−9.68009	−0.364057
$708$	−50.7186	−1.90612
$709$	−13.6151	−0.511326	−0.255663	−	0.966766i	$-0.582294\pi$
$709$	−13.6151	−0.511326	−0.255663	+	0.966766i	$0.582294\pi$
$710$	27.3477	1.02634
$711$	9.44562	0.354238
$712$	−48.3368	−1.81150
$713$	18.5210	0.693615
$714$	−24.1622	−0.904246
$715$	−4.33408	−0.162085
$716$	−13.4288	−0.501858
$717$	40.5468	1.51425
$718$	52.0428	1.94222
$719$	−25.1083	−0.936383	−0.468192	−	0.883627i	$-0.655094\pi$
$719$	−25.1083	−0.936383	−0.468192	+	0.883627i	$0.655094\pi$
$720$	7.33001	0.273174
$721$	13.7104	0.510603
$722$	31.9461	1.18891
$723$	23.2526	0.864772
$724$	−91.6950	−3.40782
$725$	3.24075	0.120358
$726$	0.180817	0.00671074
$727$	−50.4802	−1.87221	−0.936104	−	0.351723i	$-0.885596\pi$
$727$	−50.4802	−1.87221	−0.936104	+	0.351723i	$0.885596\pi$
$728$	−9.14766	−0.339035
$729$	29.7196	1.10072
$730$	−16.3287	−0.604351
$731$	−57.4878	−2.12626
$732$	−94.4207	−3.48989
$733$	−35.7783	−1.32150	−0.660750	−	0.750606i	$-0.729762\pi$
$733$	−35.7783	−1.32150	−0.660750	+	0.750606i	$0.729762\pi$
$734$	21.0347	0.776405
$735$	−1.46821	−0.0541556
$736$	43.9618	1.62045
$737$	−25.6809	−0.945970
$738$	−2.28803	−0.0842236
$739$	−18.0405	−0.663631	−0.331815	−	0.943344i	$-0.607661\pi$
$739$	−18.0405	−0.663631	−0.331815	+	0.943344i	$0.607661\pi$
$740$	−30.7623	−1.13084
$741$	−4.96101	−0.182247
$742$	20.1794	0.740811
$743$	−14.5038	−0.532093	−0.266047	−	0.963960i	$-0.585718\pi$
$743$	−14.5038	−0.532093	−0.266047	+	0.963960i	$0.585718\pi$
$744$	36.7179	1.34614
$745$	−10.8233	−0.396534
$746$	−65.2350	−2.38842
$747$	8.64752	0.316396
$748$	98.8761	3.61527
$749$	−2.06496	−0.0754522
$750$	3.80002	0.138757
$751$	36.8032	1.34297	0.671484	−	0.741019i	$-0.265657\pi$
$751$	36.8032	1.34297	0.671484	+	0.741019i	$0.265657\pi$
$752$	−18.4657	−0.673373
$753$	39.4868	1.43898
$754$	−10.9846	−0.400037
$755$	−5.59589	−0.203655
$756$	−26.5215	−0.964579
$757$	18.5114	0.672808	0.336404	−	0.941718i	$-0.390789\pi$
$757$	18.5114	0.672808	0.336404	+	0.941718i	$0.390789\pi$
$758$	15.5622	0.565245
$759$	−25.1353	−0.912352
$760$	−18.0222	−0.653735
$761$	−2.02193	−0.0732951	−0.0366475	−	0.999328i	$-0.511668\pi$
$761$	−2.02193	−0.0732951	−0.0366475	+	0.999328i	$0.511668\pi$
$762$	67.4637	2.44395
$763$	4.02183	0.145600
$764$	−91.2917	−3.30282
$765$	5.36885	0.194111
$766$	70.1378	2.53418
$767$	−9.62799	−0.347647
$768$	−32.6237	−1.17721
$769$	−27.4327	−0.989247	−0.494624	−	0.869107i	$-0.664694\pi$
$769$	−27.4327	−0.989247	−0.494624	+	0.869107i	$0.664694\pi$
$770$	8.56551	0.308680
$771$	39.2515	1.41361
$772$	−111.602	−4.01666
$773$	−18.8820	−0.679140	−0.339570	−	0.940581i	$-0.610282\pi$
$773$	−18.8820	−0.679140	−0.339570	+	0.940581i	$0.610282\pi$
$774$	−19.7586	−0.710207
$775$	−3.58032	−0.128609
$776$	64.2239	2.30551
$777$	9.61213	0.344833
$778$	−87.8711	−3.15033
$779$	2.70130	0.0967842
$780$	−9.03475	−0.323496
$781$	34.9686	1.25127
$782$	85.1313	3.04429
$783$	−18.2919	−0.653697
$784$	8.68108	0.310038
$785$	−10.7298	−0.382963
$786$	−68.2003	−2.43263
$787$	37.6170	1.34090	0.670451	−	0.741954i	$-0.266101\pi$
$787$	37.6170	1.34090	0.670451	+	0.741954i	$0.266101\pi$
$788$	−65.1197	−2.31979
$789$	33.7936	1.20308
$790$	−28.9533	−1.03011
$791$	13.5413	0.481474
$792$	19.5189	0.693572
$793$	−17.9240	−0.636501
$794$	−99.8888	−3.54492
$795$	11.4472	0.405990
$796$	12.7606	0.452288
$797$	−1.62791	−0.0576636	−0.0288318	−	0.999584i	$-0.509179\pi$
$797$	−1.62791	−0.0576636	−0.0288318	+	0.999584i	$0.509179\pi$
$798$	9.80452	0.347076
$799$	−13.5251	−0.478484
$800$	−8.49834	−0.300462
$801$	−5.84307	−0.206455
$802$	83.7222	2.95633
$803$	−20.8789	−0.736800
$804$	−53.5340	−1.88800
$805$	5.17298	0.182324
$806$	12.1356	0.427460
$807$	21.1635	0.744989
$808$	67.6157	2.37871
$809$	30.2464	1.06341	0.531703	−	0.846931i	$-0.321552\pi$
$809$	30.2464	1.06341	0.531703	+	0.846931i	$0.321552\pi$
$810$	−14.8924	−0.523265
$811$	−25.8569	−0.907959	−0.453980	−	0.891012i	$-0.649996\pi$
$811$	−25.8569	−0.907959	−0.453980	+	0.891012i	$0.649996\pi$
$812$	15.2276	0.534384
$813$	40.7253	1.42830
$814$	−56.0771	−1.96550
$815$	−9.82482	−0.344148
$816$	81.0422	2.83704
$817$	23.3274	0.816123
$818$	5.69094	0.198979
$819$	−1.10579	−0.0386395
$820$	4.91948	0.171796
$821$	−21.9341	−0.765504	−0.382752	−	0.923851i	$-0.625024\pi$
$821$	−21.9341	−0.765504	−0.382752	+	0.923851i	$0.625024\pi$
$822$	21.5943	0.753189
$823$	−42.7857	−1.49141	−0.745707	−	0.666274i	$-0.767888\pi$
$823$	−42.7857	−1.49141	−0.745707	+	0.666274i	$0.767888\pi$
$824$	−95.7678	−3.33623
$825$	4.85895	0.169167
$826$	19.0280	0.662067
$827$	−47.1666	−1.64014	−0.820071	−	0.572261i	$-0.806066\pi$
$827$	−47.1666	−1.64014	−0.820071	+	0.572261i	$0.806066\pi$
$828$	20.5238	0.713253
$829$	16.0195	0.556380	0.278190	−	0.960526i	$-0.410266\pi$
$829$	16.0195	0.556380	0.278190	+	0.960526i	$0.410266\pi$
$830$	−26.5069	−0.920067
$831$	−45.0622	−1.56319
$832$	6.06777	0.210362
$833$	6.35843	0.220307
$834$	−64.0640	−2.21836
$835$	−0.958810	−0.0331810
$836$	−40.1220	−1.38765
$837$	20.2085	0.698509
$838$	−62.9370	−2.17412
$839$	46.8453	1.61728	0.808639	−	0.588305i	$-0.200204\pi$
$839$	46.8453	1.61728	0.808639	+	0.588305i	$0.200204\pi$
$840$	10.2555	0.353847
$841$	−18.4975	−0.637846
$842$	63.7223	2.19601
$843$	−21.7094	−0.747712
$844$	−47.8607	−1.64743
$845$	11.2849	0.388213
$846$	−4.64858	−0.159822
$847$	−0.0475831	−0.00163498
$848$	−67.6838	−2.32427
$849$	−18.1815	−0.623986
$850$	−16.4569	−0.564467
$851$	−33.8667	−1.16094
$852$	72.8948	2.49734
$853$	24.3405	0.833401	0.416701	−	0.909044i	$-0.363186\pi$
$853$	24.3405	0.833401	0.416701	+	0.909044i	$0.363186\pi$
$854$	35.4235	1.21217
$855$	−2.17857	−0.0745056
$856$	14.4238	0.492996
$857$	47.1618	1.61102	0.805509	−	0.592584i	$-0.201892\pi$
$857$	47.1618	1.61102	0.805509	+	0.592584i	$0.201892\pi$
$858$	−16.4696	−0.562263
$859$	−19.4134	−0.662377	−0.331189	−	0.943565i	$-0.607450\pi$
$859$	−19.4134	−0.662377	−0.331189	+	0.943565i	$0.607450\pi$
$860$	42.4827	1.44865
$861$	−1.53716	−0.0523864
$862$	−92.0494	−3.13522
$863$	−26.0201	−0.885736	−0.442868	−	0.896587i	$-0.646039\pi$
$863$	−26.0201	−0.885736	−0.442868	+	0.896587i	$0.646039\pi$
$864$	47.9674	1.63188
$865$	0.0544665	0.00185192
$866$	35.7129	1.21357
$867$	34.3996	1.16827
$868$	−16.8232	−0.571017
$869$	−37.0215	−1.25587
$870$	12.3149	0.417514
$871$	−10.1624	−0.344341
$872$	−28.0926	−0.951335
$873$	7.76355	0.262756
$874$	−34.5446	−1.16849
$875$	−1.00000	−0.0338062
$876$	−43.5237	−1.47053
$877$	3.49564	0.118039	0.0590197	−	0.998257i	$-0.481203\pi$
$877$	3.49564	0.118039	0.0590197	+	0.998257i	$0.481203\pi$
$878$	−55.4951	−1.87287
$879$	−48.8985	−1.64930
$880$	−28.7295	−0.968472
$881$	−52.7103	−1.77586	−0.887928	−	0.459983i	$-0.847855\pi$
$881$	−52.7103	−1.77586	−0.887928	+	0.459983i	$0.847855\pi$
$882$	2.18539	0.0735860
$883$	−53.7748	−1.80967	−0.904833	−	0.425767i	$-0.860004\pi$
$883$	−53.7748	−1.80967	−0.904833	+	0.425767i	$0.860004\pi$
$884$	39.1272	1.31599
$885$	10.7940	0.362835
$886$	−16.1551	−0.542743
$887$	16.9372	0.568695	0.284347	−	0.958721i	$-0.408223\pi$
$887$	16.9372	0.568695	0.284347	+	0.958721i	$0.408223\pi$
$888$	−67.1410	−2.25310
$889$	−17.7535	−0.595434
$890$	17.9105	0.600362
$891$	−19.0424	−0.637943
$892$	−65.7324	−2.20088
$893$	5.48823	0.183656
$894$	−41.1286	−1.37555
$895$	2.85793	0.0955300
$896$	5.00485	0.167200
$897$	−9.94651	−0.332104
$898$	86.8189	2.89718
$899$	−11.6029	−0.386979
$900$	−3.96751	−0.132250
$901$	−49.5748	−1.65158
$902$	8.96779	0.298595
$903$	−13.2743	−0.441743
$904$	−94.5865	−3.14590
$905$	19.5146	0.648686
$906$	−21.2645	−0.706465
$907$	−23.4489	−0.778608	−0.389304	−	0.921109i	$-0.627284\pi$
$907$	−23.4489	−0.778608	−0.389304	+	0.921109i	$0.627284\pi$
$908$	−62.3866	−2.07037
$909$	8.17354	0.271099
$910$	3.38954	0.112362
$911$	−5.70048	−0.188865	−0.0944327	−	0.995531i	$-0.530104\pi$
$911$	−5.70048	−0.188865	−0.0944327	+	0.995531i	$0.530104\pi$
$912$	−32.8853	−1.08894
$913$	−33.8934	−1.12171
$914$	38.2581	1.26547
$915$	20.0947	0.664309
$916$	4.69879	0.155253
$917$	17.9474	0.592674
$918$	92.8882	3.06577
$919$	10.3870	0.342636	0.171318	−	0.985216i	$-0.445197\pi$
$919$	10.3870	0.342636	0.171318	+	0.985216i	$0.445197\pi$
$920$	−36.1334	−1.19128
$921$	−48.3922	−1.59458
$922$	64.0167	2.10828
$923$	13.8377	0.455475
$924$	22.8312	0.751091
$925$	6.54685	0.215259
$926$	56.3445	1.85160
$927$	−11.5766	−0.380227
$928$	−27.5410	−0.904077
$929$	40.0540	1.31413	0.657065	−	0.753834i	$-0.271798\pi$
$929$	40.0540	1.31413	0.657065	+	0.753834i	$0.271798\pi$
$930$	−13.6053	−0.446135
$931$	−2.58012	−0.0845602
$932$	−47.9835	−1.57175
$933$	−27.8954	−0.913255
$934$	−88.7578	−2.90425
$935$	−21.0429	−0.688175
$936$	7.72398	0.252466
$937$	11.8219	0.386204	0.193102	−	0.981179i	$-0.438145\pi$
$937$	11.8219	0.386204	0.193102	+	0.981179i	$0.438145\pi$
$938$	20.0842	0.655772
$939$	−34.6767	−1.13163
$940$	9.99488	0.325997
$941$	4.02767	0.131298	0.0656492	−	0.997843i	$-0.479088\pi$
$941$	4.02767	0.131298	0.0656492	+	0.997843i	$0.479088\pi$
$942$	−40.7734	−1.32847
$943$	5.41594	0.176367
$944$	−63.8216	−2.07721
$945$	5.64433	0.183610
$946$	77.4424	2.51787
$947$	11.2749	0.366384	0.183192	−	0.983077i	$-0.441357\pi$
$947$	11.2749	0.366384	0.183192	+	0.983077i	$0.441357\pi$
$948$	−77.1744	−2.50651
$949$	−8.26218	−0.268202
$950$	6.67789	0.216659
$951$	21.6609	0.702401
$952$	−44.4138	−1.43946
$953$	−25.1313	−0.814083	−0.407041	−	0.913410i	$-0.633440\pi$
$953$	−25.1313	−0.814083	−0.407041	+	0.913410i	$0.633440\pi$
$954$	−17.0389	−0.551653
$955$	19.4287	0.628699
$956$	129.764	4.19688
$957$	15.7466	0.509016
$958$	−50.5800	−1.63417
$959$	−5.68269	−0.183504
$960$	−6.80259	−0.219553
$961$	−18.1813	−0.586493
$962$	−22.1908	−0.715460
$963$	1.74359	0.0561863
$964$	74.4166	2.39680
$965$	23.7513	0.764581
$966$	19.6574	0.632468
$967$	−15.1520	−0.487256	−0.243628	−	0.969869i	$-0.578338\pi$
$967$	−15.1520	−0.487256	−0.243628	+	0.969869i	$0.578338\pi$
$968$	0.332369	0.0106828
$969$	−24.0867	−0.773778
$970$	−23.7973	−0.764084
$971$	−17.0214	−0.546244	−0.273122	−	0.961979i	$-0.588056\pi$
$971$	−17.0214	−0.546244	−0.273122	+	0.961979i	$0.588056\pi$
$972$	39.8693	1.27881
$973$	16.8589	0.540471
$974$	12.7806	0.409515
$975$	1.92278	0.0615782
$976$	−118.814	−3.80314
$977$	36.8747	1.17973	0.589863	−	0.807504i	$-0.299182\pi$
$977$	36.8747	1.17973	0.589863	+	0.807504i	$0.299182\pi$
$978$	−37.3345	−1.19383
$979$	22.9015	0.731937
$980$	−4.69879	−0.150097
$981$	−3.39590	−0.108423
$982$	−50.3929	−1.60810
$983$	−7.88227	−0.251405	−0.125703	−	0.992068i	$-0.540119\pi$
$983$	−7.88227	−0.251405	−0.125703	+	0.992068i	$0.540119\pi$
$984$	10.7371	0.342287
$985$	13.8588	0.441578
$986$	−53.3327	−1.69846
$987$	−3.12305	−0.0994077
$988$	−15.8770	−0.505116
$989$	46.7699	1.48720
$990$	−7.23243	−0.229862
$991$	35.1519	1.11664	0.558318	−	0.829627i	$-0.311447\pi$
$991$	35.1519	1.11664	0.558318	+	0.829627i	$0.311447\pi$
$992$	30.4268	0.966052
$993$	33.7186	1.07003
$994$	−27.3477	−0.867417
$995$	−2.71572	−0.0860942
$996$	−70.6536	−2.23874
$997$	−2.35526	−0.0745918	−0.0372959	−	0.999304i	$-0.511874\pi$
$997$	−2.35526	−0.0745918	−0.0372959	+	0.999304i	$0.511874\pi$
$998$	9.05611	0.286666
$999$	−36.9526	−1.16913

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8015.2.a.j.1.2	✓	45

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8015.2.a.j.1.2	✓	45	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-2.58820 q^{2} +1.46821 q^{3} +4.69879 q^{4} -1.00000 q^{5} -3.80002 q^{6} +1.00000 q^{7} -6.98503 q^{8} -0.844367 q^{9} +O(q^{10})\)	\(q-2.58820 q^{2} +1.46821 q^{3} +4.69879 q^{4} -1.00000 q^{5} -3.80002 q^{6} +1.00000 q^{7} -6.98503 q^{8} -0.844367 q^{9} +2.58820 q^{10} +3.30944 q^{11} +6.89880 q^{12} +1.30961 q^{13} -2.58820 q^{14} -1.46821 q^{15} +8.68108 q^{16} +6.35843 q^{17} +2.18539 q^{18} -2.58012 q^{19} -4.69879 q^{20} +1.46821 q^{21} -8.56551 q^{22} -5.17298 q^{23} -10.2555 q^{24} +1.00000 q^{25} -3.38954 q^{26} -5.64433 q^{27} +4.69879 q^{28} +3.24075 q^{29} +3.80002 q^{30} -3.58032 q^{31} -8.49834 q^{32} +4.85895 q^{33} -16.4569 q^{34} -1.00000 q^{35} -3.96751 q^{36} +6.54685 q^{37} +6.67789 q^{38} +1.92278 q^{39} +6.98503 q^{40} -1.04697 q^{41} -3.80002 q^{42} -9.04119 q^{43} +15.5504 q^{44} +0.844367 q^{45} +13.3887 q^{46} -2.12712 q^{47} +12.7456 q^{48} +1.00000 q^{49} -2.58820 q^{50} +9.33550 q^{51} +6.15359 q^{52} -7.79670 q^{53} +14.6087 q^{54} -3.30944 q^{55} -6.98503 q^{56} -3.78816 q^{57} -8.38772 q^{58} -7.35180 q^{59} -6.89880 q^{60} -13.6865 q^{61} +9.26661 q^{62} -0.844367 q^{63} +4.63326 q^{64} -1.30961 q^{65} -12.5759 q^{66} -7.75990 q^{67} +29.8770 q^{68} -7.59501 q^{69} +2.58820 q^{70} +10.5663 q^{71} +5.89793 q^{72} -6.30888 q^{73} -16.9446 q^{74} +1.46821 q^{75} -12.1235 q^{76} +3.30944 q^{77} -4.97654 q^{78} -11.1866 q^{79} -8.68108 q^{80} -5.75394 q^{81} +2.70976 q^{82} -10.2414 q^{83} +6.89880 q^{84} -6.35843 q^{85} +23.4004 q^{86} +4.75809 q^{87} -23.1166 q^{88} +6.92006 q^{89} -2.18539 q^{90} +1.30961 q^{91} -24.3068 q^{92} -5.25666 q^{93} +5.50541 q^{94} +2.58012 q^{95} -12.4773 q^{96} -9.19452 q^{97} -2.58820 q^{98} -2.79438 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 45 q - 6 q^{2} + 34 q^{4} - 45 q^{5} + q^{6} + 45 q^{7} - 15 q^{8} + 29 q^{9}+O(q^{10}) \) 45 * q - 6 * q^2 + 34 * q^4 - 45 * q^5 + q^6 + 45 * q^7 - 15 * q^8 + 29 * q^9	\( 45 q - 6 q^{2} + 34 q^{4} - 45 q^{5} + q^{6} + 45 q^{7} - 15 q^{8} + 29 q^{9} + 6 q^{10} - q^{11} - 3 q^{12} - 21 q^{13} - 6 q^{14} + 8 q^{16} - 7 q^{17} - 36 q^{18} - 20 q^{19} - 34 q^{20} - 34 q^{22} - 22 q^{23} - 11 q^{24} + 45 q^{25} - q^{26} + 12 q^{27} + 34 q^{28} + 10 q^{29} - q^{30} - 27 q^{31} - 26 q^{32} - 39 q^{33} - 13 q^{34} - 45 q^{35} - 3 q^{36} - 72 q^{37} + 2 q^{38} - 37 q^{39} + 15 q^{40} - 4 q^{41} + q^{42} - 49 q^{43} + 5 q^{44} - 29 q^{45} - 67 q^{46} + 2 q^{47} + 8 q^{48} + 45 q^{49} - 6 q^{50} - 49 q^{51} - 47 q^{52} - 35 q^{53} - 12 q^{54} + q^{55} - 15 q^{56} - 77 q^{57} - 50 q^{58} + 4 q^{59} + 3 q^{60} - 36 q^{61} + 17 q^{62} + 29 q^{63} + 5 q^{64} + 21 q^{65} - 8 q^{66} - 80 q^{67} + 27 q^{68} + 9 q^{69} + 6 q^{70} - 12 q^{71} - 97 q^{72} - 55 q^{73} + 32 q^{74} - 37 q^{76} - q^{77} + 20 q^{78} - 94 q^{79} - 8 q^{80} - 19 q^{81} - 36 q^{82} + 24 q^{83} - 3 q^{84} + 7 q^{85} - 3 q^{86} - 4 q^{87} - 95 q^{88} + q^{89} + 36 q^{90} - 21 q^{91} - 65 q^{92} - 71 q^{93} - 53 q^{94} + 20 q^{95} - 13 q^{96} - 110 q^{97} - 6 q^{98} - 27 q^{99}+O(q^{100}) \) 45 * q - 6 * q^2 + 34 * q^4 - 45 * q^5 + q^6 + 45 * q^7 - 15 * q^8 + 29 * q^9 + 6 * q^10 - q^11 - 3 * q^12 - 21 * q^13 - 6 * q^14 + 8 * q^16 - 7 * q^17 - 36 * q^18 - 20 * q^19 - 34 * q^20 - 34 * q^22 - 22 * q^23 - 11 * q^24 + 45 * q^25 - q^26 + 12 * q^27 + 34 * q^28 + 10 * q^29 - q^30 - 27 * q^31 - 26 * q^32 - 39 * q^33 - 13 * q^34 - 45 * q^35 - 3 * q^36 - 72 * q^37 + 2 * q^38 - 37 * q^39 + 15 * q^40 - 4 * q^41 + q^42 - 49 * q^43 + 5 * q^44 - 29 * q^45 - 67 * q^46 + 2 * q^47 + 8 * q^48 + 45 * q^49 - 6 * q^50 - 49 * q^51 - 47 * q^52 - 35 * q^53 - 12 * q^54 + q^55 - 15 * q^56 - 77 * q^57 - 50 * q^58 + 4 * q^59 + 3 * q^60 - 36 * q^61 + 17 * q^62 + 29 * q^63 + 5 * q^64 + 21 * q^65 - 8 * q^66 - 80 * q^67 + 27 * q^68 + 9 * q^69 + 6 * q^70 - 12 * q^71 - 97 * q^72 - 55 * q^73 + 32 * q^74 - 37 * q^76 - q^77 + 20 * q^78 - 94 * q^79 - 8 * q^80 - 19 * q^81 - 36 * q^82 + 24 * q^83 - 3 * q^84 + 7 * q^85 - 3 * q^86 - 4 * q^87 - 95 * q^88 + q^89 + 36 * q^90 - 21 * q^91 - 65 * q^92 - 71 * q^93 - 53 * q^94 + 20 * q^95 - 13 * q^96 - 110 * q^97 - 6 * q^98 - 27 * q^99

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