LMFDB - Embedded newform 8002.2.a.e.1.50

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8002,2,Mod(1,8002)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8002, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8002.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8002 = 2 \cdot 4001 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8002.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:	$63.8962916974$
Analytic rank:	$0$
Dimension:	$77$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.50
Character	$\chi$	$=$	8002.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.10632 q^{3} +1.00000 q^{4} +1.44569 q^{5} -1.10632 q^{6} +1.29319 q^{7} -1.00000 q^{8} -1.77605 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.10632 q^{3} +1.00000 q^{4} +1.44569 q^{5} -1.10632 q^{6} +1.29319 q^{7} -1.00000 q^{8} -1.77605 q^{9} -1.44569 q^{10} -2.10668 q^{11} +1.10632 q^{12} -4.79361 q^{13} -1.29319 q^{14} +1.59940 q^{15} +1.00000 q^{16} +3.77176 q^{17} +1.77605 q^{18} +1.29679 q^{19} +1.44569 q^{20} +1.43068 q^{21} +2.10668 q^{22} -4.54774 q^{23} -1.10632 q^{24} -2.90998 q^{25} +4.79361 q^{26} -5.28386 q^{27} +1.29319 q^{28} +6.76176 q^{29} -1.59940 q^{30} +7.63859 q^{31} -1.00000 q^{32} -2.33067 q^{33} -3.77176 q^{34} +1.86955 q^{35} -1.77605 q^{36} +0.754296 q^{37} -1.29679 q^{38} -5.30328 q^{39} -1.44569 q^{40} +7.90594 q^{41} -1.43068 q^{42} +7.11833 q^{43} -2.10668 q^{44} -2.56761 q^{45} +4.54774 q^{46} +3.20727 q^{47} +1.10632 q^{48} -5.32767 q^{49} +2.90998 q^{50} +4.17279 q^{51} -4.79361 q^{52} -2.85563 q^{53} +5.28386 q^{54} -3.04561 q^{55} -1.29319 q^{56} +1.43467 q^{57} -6.76176 q^{58} -7.10291 q^{59} +1.59940 q^{60} -6.80758 q^{61} -7.63859 q^{62} -2.29676 q^{63} +1.00000 q^{64} -6.93007 q^{65} +2.33067 q^{66} +11.8256 q^{67} +3.77176 q^{68} -5.03128 q^{69} -1.86955 q^{70} +7.55012 q^{71} +1.77605 q^{72} +5.57269 q^{73} -0.754296 q^{74} -3.21938 q^{75} +1.29679 q^{76} -2.72433 q^{77} +5.30328 q^{78} +3.77798 q^{79} +1.44569 q^{80} -0.517522 q^{81} -7.90594 q^{82} -16.1284 q^{83} +1.43068 q^{84} +5.45280 q^{85} -7.11833 q^{86} +7.48070 q^{87} +2.10668 q^{88} +10.9277 q^{89} +2.56761 q^{90} -6.19902 q^{91} -4.54774 q^{92} +8.45076 q^{93} -3.20727 q^{94} +1.87475 q^{95} -1.10632 q^{96} +13.3859 q^{97} +5.32767 q^{98} +3.74156 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 77 q - 77 q^{2} + 10 q^{3} + 77 q^{4} + 18 q^{5} - 10 q^{6} + 21 q^{7} - 77 q^{8} + 71 q^{9}+O(q^{10}) $ 77 * q - 77 * q^2 + 10 * q^3 + 77 * q^4 + 18 * q^5 - 10 * q^6 + 21 * q^7 - 77 * q^8 + 71 * q^9	\( 77 q - 77 q^{2} + 10 q^{3} + 77 q^{4} + 18 q^{5} - 10 q^{6} + 21 q^{7} - 77 q^{8} + 71 q^{9} - 18 q^{10} + 30 q^{11} + 10 q^{12} - 2 q^{13} - 21 q^{14} + 21 q^{15} + 77 q^{16} + 60 q^{17} - 71 q^{18} - 3 q^{19} + 18 q^{20} + 10 q^{21} - 30 q^{22} + 53 q^{23} - 10 q^{24} + 59 q^{25} + 2 q^{26} + 43 q^{27} + 21 q^{28} + 30 q^{29} - 21 q^{30} + 22 q^{31} - 77 q^{32} + 31 q^{33} - 60 q^{34} + 41 q^{35} + 71 q^{36} - 3 q^{37} + 3 q^{38} + 44 q^{39} - 18 q^{40} + 48 q^{41} - 10 q^{42} + 21 q^{43} + 30 q^{44} + 33 q^{45} - 53 q^{46} + 107 q^{47} + 10 q^{48} + 24 q^{49} - 59 q^{50} + 18 q^{51} - 2 q^{52} + 42 q^{53} - 43 q^{54} + 49 q^{55} - 21 q^{56} + 32 q^{57} - 30 q^{58} + 42 q^{59} + 21 q^{60} - 31 q^{61} - 22 q^{62} + 109 q^{63} + 77 q^{64} + 39 q^{65} - 31 q^{66} - q^{67} + 60 q^{68} - 33 q^{69} - 41 q^{70} + 58 q^{71} - 71 q^{72} + 35 q^{73} + 3 q^{74} + 34 q^{75} - 3 q^{76} + 86 q^{77} - 44 q^{78} + 25 q^{79} + 18 q^{80} + 53 q^{81} - 48 q^{82} + 107 q^{83} + 10 q^{84} + 21 q^{85} - 21 q^{86} + 100 q^{87} - 30 q^{88} + 34 q^{89} - 33 q^{90} - 51 q^{91} + 53 q^{92} + 48 q^{93} - 107 q^{94} + 118 q^{95} - 10 q^{96} - 13 q^{97} - 24 q^{98} + 63 q^{99}+O(q^{100}) \) 77 * q - 77 * q^2 + 10 * q^3 + 77 * q^4 + 18 * q^5 - 10 * q^6 + 21 * q^7 - 77 * q^8 + 71 * q^9 - 18 * q^10 + 30 * q^11 + 10 * q^12 - 2 * q^13 - 21 * q^14 + 21 * q^15 + 77 * q^16 + 60 * q^17 - 71 * q^18 - 3 * q^19 + 18 * q^20 + 10 * q^21 - 30 * q^22 + 53 * q^23 - 10 * q^24 + 59 * q^25 + 2 * q^26 + 43 * q^27 + 21 * q^28 + 30 * q^29 - 21 * q^30 + 22 * q^31 - 77 * q^32 + 31 * q^33 - 60 * q^34 + 41 * q^35 + 71 * q^36 - 3 * q^37 + 3 * q^38 + 44 * q^39 - 18 * q^40 + 48 * q^41 - 10 * q^42 + 21 * q^43 + 30 * q^44 + 33 * q^45 - 53 * q^46 + 107 * q^47 + 10 * q^48 + 24 * q^49 - 59 * q^50 + 18 * q^51 - 2 * q^52 + 42 * q^53 - 43 * q^54 + 49 * q^55 - 21 * q^56 + 32 * q^57 - 30 * q^58 + 42 * q^59 + 21 * q^60 - 31 * q^61 - 22 * q^62 + 109 * q^63 + 77 * q^64 + 39 * q^65 - 31 * q^66 - q^67 + 60 * q^68 - 33 * q^69 - 41 * q^70 + 58 * q^71 - 71 * q^72 + 35 * q^73 + 3 * q^74 + 34 * q^75 - 3 * q^76 + 86 * q^77 - 44 * q^78 + 25 * q^79 + 18 * q^80 + 53 * q^81 - 48 * q^82 + 107 * q^83 + 10 * q^84 + 21 * q^85 - 21 * q^86 + 100 * q^87 - 30 * q^88 + 34 * q^89 - 33 * q^90 - 51 * q^91 + 53 * q^92 + 48 * q^93 - 107 * q^94 + 118 * q^95 - 10 * q^96 - 13 * q^97 - 24 * q^98 + 63 * 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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	1.10632	0.638737	0.319368	−	0.947631i	$-0.396529\pi$
$3$	1.10632	0.638737	0.319368	+	0.947631i	$0.396529\pi$
$4$	1.00000	0.500000
$5$	1.44569	0.646532	0.323266	−	0.946308i	$-0.395219\pi$
$5$	1.44569	0.646532	0.323266	+	0.946308i	$0.395219\pi$
$6$	−1.10632	−0.451655
$7$	1.29319	0.488778	0.244389	−	0.969677i	$-0.421413\pi$
$7$	1.29319	0.488778	0.244389	+	0.969677i	$0.421413\pi$
$8$	−1.00000	−0.353553
$9$	−1.77605	−0.592015
$10$	−1.44569	−0.457167
$11$	−2.10668	−0.635188	−0.317594	−	0.948227i	$-0.602875\pi$
$11$	−2.10668	−0.635188	−0.317594	+	0.948227i	$0.602875\pi$
$12$	1.10632	0.319368
$13$	−4.79361	−1.32951	−0.664753	−	0.747063i	$-0.731463\pi$
$13$	−4.79361	−1.32951	−0.664753	+	0.747063i	$0.731463\pi$
$14$	−1.29319	−0.345619
$15$	1.59940	0.412964
$16$	1.00000	0.250000
$17$	3.77176	0.914786	0.457393	−	0.889265i	$-0.348783\pi$
$17$	3.77176	0.914786	0.457393	+	0.889265i	$0.348783\pi$
$18$	1.77605	0.418618
$19$	1.29679	0.297504	0.148752	−	0.988875i	$-0.452474\pi$
$19$	1.29679	0.297504	0.148752	+	0.988875i	$0.452474\pi$
$20$	1.44569	0.323266
$21$	1.43068	0.312201
$22$	2.10668	0.449146
$23$	−4.54774	−0.948269	−0.474135	−	0.880452i	$-0.657239\pi$
$23$	−4.54774	−0.948269	−0.474135	+	0.880452i	$0.657239\pi$
$24$	−1.10632	−0.225828
$25$	−2.90998	−0.581996
$26$	4.79361	0.940103
$27$	−5.28386	−1.01688
$28$	1.29319	0.244389
$29$	6.76176	1.25563	0.627814	−	0.778363i	$-0.283950\pi$
$29$	6.76176	1.25563	0.627814	+	0.778363i	$0.283950\pi$
$30$	−1.59940	−0.292010
$31$	7.63859	1.37193	0.685966	−	0.727634i	$-0.259380\pi$
$31$	7.63859	1.37193	0.685966	+	0.727634i	$0.259380\pi$
$32$	−1.00000	−0.176777
$33$	−2.33067	−0.405718
$34$	−3.77176	−0.646852
$35$	1.86955	0.316011
$36$	−1.77605	−0.296008
$37$	0.754296	0.124005	0.0620027	−	0.998076i	$-0.480251\pi$
$37$	0.754296	0.124005	0.0620027	+	0.998076i	$0.480251\pi$
$38$	−1.29679	−0.210367
$39$	−5.30328	−0.849205
$40$	−1.44569	−0.228584
$41$	7.90594	1.23470	0.617350	−	0.786688i	$-0.288206\pi$
$41$	7.90594	1.23470	0.617350	+	0.786688i	$0.288206\pi$
$42$	−1.43068	−0.220759
$43$	7.11833	1.08554	0.542768	−	0.839883i	$-0.317376\pi$
$43$	7.11833	1.08554	0.542768	+	0.839883i	$0.317376\pi$
$44$	−2.10668	−0.317594
$45$	−2.56761	−0.382757
$46$	4.54774	0.670528
$47$	3.20727	0.467828	0.233914	−	0.972257i	$-0.424847\pi$
$47$	3.20727	0.467828	0.233914	+	0.972257i	$0.424847\pi$
$48$	1.10632	0.159684
$49$	−5.32767	−0.761096
$50$	2.90998	0.411533
$51$	4.17279	0.584308
$52$	−4.79361	−0.664753
$53$	−2.85563	−0.392251	−0.196126	−	0.980579i	$-0.562836\pi$
$53$	−2.85563	−0.392251	−0.196126	+	0.980579i	$0.562836\pi$
$54$	5.28386	0.719042
$55$	−3.04561	−0.410670
$56$	−1.29319	−0.172809
$57$	1.43467	0.190027
$58$	−6.76176	−0.887863
$59$	−7.10291	−0.924720	−0.462360	−	0.886692i	$-0.652997\pi$
$59$	−7.10291	−0.924720	−0.462360	+	0.886692i	$0.652997\pi$
$60$	1.59940	0.206482
$61$	−6.80758	−0.871621	−0.435811	−	0.900038i	$-0.643538\pi$
$61$	−6.80758	−0.871621	−0.435811	+	0.900038i	$0.643538\pi$
$62$	−7.63859	−0.970102
$63$	−2.29676	−0.289364
$64$	1.00000	0.125000
$65$	−6.93007	−0.859569
$66$	2.33067	0.286886
$67$	11.8256	1.44472	0.722362	−	0.691515i	$-0.243057\pi$
$67$	11.8256	1.44472	0.722362	+	0.691515i	$0.243057\pi$
$68$	3.77176	0.457393
$69$	−5.03128	−0.605694
$70$	−1.86955	−0.223454
$71$	7.55012	0.896035	0.448017	−	0.894025i	$-0.352130\pi$
$71$	7.55012	0.896035	0.448017	+	0.894025i	$0.352130\pi$
$72$	1.77605	0.209309
$73$	5.57269	0.652234	0.326117	−	0.945329i	$-0.394260\pi$
$73$	5.57269	0.652234	0.326117	+	0.945329i	$0.394260\pi$
$74$	−0.754296	−0.0876851
$75$	−3.21938	−0.371742
$76$	1.29679	0.148752
$77$	−2.72433	−0.310466
$78$	5.30328	0.600479
$79$	3.77798	0.425056	0.212528	−	0.977155i	$-0.431830\pi$
$79$	3.77798	0.425056	0.212528	+	0.977155i	$0.431830\pi$
$80$	1.44569	0.161633
$81$	−0.517522	−0.0575025
$82$	−7.90594	−0.873065
$83$	−16.1284	−1.77032	−0.885161	−	0.465286i	$-0.845952\pi$
$83$	−16.1284	−1.77032	−0.885161	+	0.465286i	$0.845952\pi$
$84$	1.43068	0.156100
$85$	5.45280	0.591439
$86$	−7.11833	−0.767589
$87$	7.48070	0.802016
$88$	2.10668	0.224573
$89$	10.9277	1.15833	0.579165	−	0.815210i	$-0.303379\pi$
$89$	10.9277	1.15833	0.579165	+	0.815210i	$0.303379\pi$
$90$	2.56761	0.270650
$91$	−6.19902	−0.649834
$92$	−4.54774	−0.474135
$93$	8.45076	0.876303
$94$	−3.20727	−0.330804
$95$	1.87475	0.192346
$96$	−1.10632	−0.112914
$97$	13.3859	1.35914	0.679568	−	0.733613i	$-0.262167\pi$
$97$	13.3859	1.35914	0.679568	+	0.733613i	$0.262167\pi$
$98$	5.32767	0.538176
$99$	3.74156	0.376041
$100$	−2.90998	−0.290998
$101$	0.115379	0.0114807	0.00574033	−	0.999984i	$-0.498173\pi$
$101$	0.115379	0.0114807	0.00574033	+	0.999984i	$0.498173\pi$
$102$	−4.17279	−0.413168
$103$	0.784046	0.0772543	0.0386272	−	0.999254i	$-0.487702\pi$
$103$	0.784046	0.0772543	0.0386272	+	0.999254i	$0.487702\pi$
$104$	4.79361	0.470052
$105$	2.06833	0.201848
$106$	2.85563	0.277363
$107$	−13.7570	−1.32994	−0.664971	−	0.746869i	$-0.731556\pi$
$107$	−13.7570	−1.32994	−0.664971	+	0.746869i	$0.731556\pi$
$108$	−5.28386	−0.508439
$109$	−5.03372	−0.482143	−0.241072	−	0.970507i	$-0.577499\pi$
$109$	−5.03372	−0.482143	−0.241072	+	0.970507i	$0.577499\pi$
$110$	3.04561	0.290387
$111$	0.834496	0.0792069
$112$	1.29319	0.122195
$113$	19.8813	1.87027	0.935135	−	0.354291i	$-0.115278\pi$
$113$	19.8813	1.87027	0.935135	+	0.354291i	$0.115278\pi$
$114$	−1.43467	−0.134369
$115$	−6.57462	−0.613087
$116$	6.76176	0.627814
$117$	8.51366	0.787089
$118$	7.10291	0.653876
$119$	4.87759	0.447128
$120$	−1.59940	−0.146005
$121$	−6.56190	−0.596536
$122$	6.80758	0.616329
$123$	8.74653	0.788648
$124$	7.63859	0.685966
$125$	−11.4354	−1.02281
$126$	2.29676	0.204611
$127$	13.0650	1.15934	0.579668	−	0.814853i	$-0.303182\pi$
$127$	13.0650	1.15934	0.579668	+	0.814853i	$0.303182\pi$
$128$	−1.00000	−0.0883883
$129$	7.87518	0.693371
$130$	6.93007	0.607807
$131$	7.25576	0.633939	0.316970	−	0.948436i	$-0.397335\pi$
$131$	7.25576	0.633939	0.316970	+	0.948436i	$0.397335\pi$
$132$	−2.33067	−0.202859
$133$	1.67699	0.145413
$134$	−11.8256	−1.02157
$135$	−7.63882	−0.657445
$136$	−3.77176	−0.323426
$137$	−3.06446	−0.261815	−0.130907	−	0.991395i	$-0.541789\pi$
$137$	−3.06446	−0.261815	−0.130907	+	0.991395i	$0.541789\pi$
$138$	5.03128	0.428291
$139$	−11.5301	−0.977972	−0.488986	−	0.872292i	$-0.662633\pi$
$139$	−11.5301	−0.977972	−0.488986	+	0.872292i	$0.662633\pi$
$140$	1.86955	0.158006
$141$	3.54828	0.298819
$142$	−7.55012	−0.633592
$143$	10.0986	0.844487
$144$	−1.77605	−0.148004
$145$	9.77542	0.811804
$146$	−5.57269	−0.461199
$147$	−5.89413	−0.486140
$148$	0.754296	0.0620027
$149$	15.3231	1.25532	0.627659	−	0.778488i	$-0.284013\pi$
$149$	15.3231	1.25532	0.627659	+	0.778488i	$0.284013\pi$
$150$	3.21938	0.262861
$151$	−2.92246	−0.237827	−0.118913	−	0.992905i	$-0.537941\pi$
$151$	−2.92246	−0.237827	−0.118913	+	0.992905i	$0.537941\pi$
$152$	−1.29679	−0.105183
$153$	−6.69882	−0.541568
$154$	2.72433	0.219533
$155$	11.0430	0.886998
$156$	−5.30328	−0.424602
$157$	−1.37302	−0.109579	−0.0547896	−	0.998498i	$-0.517449\pi$
$157$	−1.37302	−0.109579	−0.0547896	+	0.998498i	$0.517449\pi$
$158$	−3.77798	−0.300560
$159$	−3.15925	−0.250545
$160$	−1.44569	−0.114292
$161$	−5.88107	−0.463494
$162$	0.517522	0.0406604
$163$	20.2095	1.58293	0.791465	−	0.611214i	$-0.209319\pi$
$163$	20.2095	1.58293	0.791465	+	0.611214i	$0.209319\pi$
$164$	7.90594	0.617350
$165$	−3.36943	−0.262310
$166$	16.1284	1.25181
$167$	18.0502	1.39676	0.698382	−	0.715726i	$-0.253904\pi$
$167$	18.0502	1.39676	0.698382	+	0.715726i	$0.253904\pi$
$168$	−1.43068	−0.110380
$169$	9.97865	0.767589
$170$	−5.45280	−0.418211
$171$	−2.30316	−0.176127
$172$	7.11833	0.542768
$173$	19.1299	1.45442	0.727211	−	0.686414i	$-0.240816\pi$
$173$	19.1299	1.45442	0.727211	+	0.686414i	$0.240816\pi$
$174$	−7.48070	−0.567111
$175$	−3.76315	−0.284467
$176$	−2.10668	−0.158797
$177$	−7.85812	−0.590653
$178$	−10.9277	−0.819063
$179$	−1.99996	−0.149484	−0.0747419	−	0.997203i	$-0.523813\pi$
$179$	−1.99996	−0.149484	−0.0747419	+	0.997203i	$0.523813\pi$
$180$	−2.56761	−0.191379
$181$	21.2929	1.58269	0.791345	−	0.611370i	$-0.209381\pi$
$181$	21.2929	1.58269	0.791345	+	0.611370i	$0.209381\pi$
$182$	6.19902	0.459502
$183$	−7.53139	−0.556736
$184$	4.54774	0.335264
$185$	1.09048	0.0801736
$186$	−8.45076	−0.619640
$187$	−7.94589	−0.581061
$188$	3.20727	0.233914
$189$	−6.83301	−0.497028
$190$	−1.87475	−0.136009
$191$	17.5295	1.26839	0.634195	−	0.773173i	$-0.281332\pi$
$191$	17.5295	1.26839	0.634195	+	0.773173i	$0.281332\pi$
$192$	1.10632	0.0798421
$193$	−9.12570	−0.656882	−0.328441	−	0.944524i	$-0.606523\pi$
$193$	−9.12570	−0.656882	−0.328441	+	0.944524i	$0.606523\pi$
$194$	−13.3859	−0.961054
$195$	−7.66691	−0.549039
$196$	−5.32767	−0.380548
$197$	−24.0210	−1.71143	−0.855714	−	0.517450i	$-0.826881\pi$
$197$	−24.0210	−1.71143	−0.855714	+	0.517450i	$0.826881\pi$
$198$	−3.74156	−0.265901
$199$	−8.81825	−0.625109	−0.312555	−	0.949900i	$-0.601185\pi$
$199$	−8.81825	−0.625109	−0.312555	+	0.949900i	$0.601185\pi$
$200$	2.90998	0.205767
$201$	13.0829	0.922798
$202$	−0.115379	−0.00811805
$203$	8.74422	0.613724
$204$	4.17279	0.292154
$205$	11.4295	0.798274
$206$	−0.784046	−0.0546270
$207$	8.07699	0.561390
$208$	−4.79361	−0.332377
$209$	−2.73192	−0.188971
$210$	−2.06833	−0.142728
$211$	12.3388	0.849435	0.424718	−	0.905326i	$-0.360373\pi$
$211$	12.3388	0.849435	0.424718	+	0.905326i	$0.360373\pi$
$212$	−2.85563	−0.196126
$213$	8.35289	0.572330
$214$	13.7570	0.940412
$215$	10.2909	0.701834
$216$	5.28386	0.359521
$217$	9.87812	0.670571
$218$	5.03372	0.340927
$219$	6.16520	0.416606
$220$	−3.04561	−0.205335
$221$	−18.0803	−1.21621
$222$	−0.834496	−0.0560077
$223$	18.0776	1.21056	0.605282	−	0.796011i	$-0.293060\pi$
$223$	18.0776	1.21056	0.605282	+	0.796011i	$0.293060\pi$
$224$	−1.29319	−0.0864046
$225$	5.16826	0.344550
$226$	−19.8813	−1.32248
$227$	11.0316	0.732196	0.366098	−	0.930576i	$-0.380694\pi$
$227$	11.0316	0.732196	0.366098	+	0.930576i	$0.380694\pi$
$228$	1.43467	0.0950133
$229$	−5.66794	−0.374548	−0.187274	−	0.982308i	$-0.559965\pi$
$229$	−5.66794	−0.374548	−0.187274	+	0.982308i	$0.559965\pi$
$230$	6.57462	0.433518
$231$	−3.01399	−0.198306
$232$	−6.76176	−0.443932
$233$	23.4166	1.53407	0.767036	−	0.641605i	$-0.221731\pi$
$233$	23.4166	1.53407	0.767036	+	0.641605i	$0.221731\pi$
$234$	−8.51366	−0.556556
$235$	4.63672	0.302466
$236$	−7.10291	−0.462360
$237$	4.17967	0.271499
$238$	−4.87759	−0.316167
$239$	−17.6308	−1.14044	−0.570221	−	0.821491i	$-0.693142\pi$
$239$	−17.6308	−1.14044	−0.570221	+	0.821491i	$0.693142\pi$
$240$	1.59940	0.103241
$241$	18.5269	1.19342	0.596712	−	0.802455i	$-0.296473\pi$
$241$	18.5269	1.19342	0.596712	+	0.802455i	$0.296473\pi$
$242$	6.56190	0.421815
$243$	15.2790	0.980150
$244$	−6.80758	−0.435811
$245$	−7.70216	−0.492073
$246$	−8.74653	−0.557659
$247$	−6.21629	−0.395533
$248$	−7.63859	−0.485051
$249$	−17.8432	−1.13077
$250$	11.4354	0.723237
$251$	2.02722	0.127957	0.0639784	−	0.997951i	$-0.479621\pi$
$251$	2.02722	0.127957	0.0639784	+	0.997951i	$0.479621\pi$
$252$	−2.29676	−0.144682
$253$	9.58063	0.602329
$254$	−13.0650	−0.819774
$255$	6.03256	0.377774
$256$	1.00000	0.0625000
$257$	12.8905	0.804090	0.402045	−	0.915620i	$-0.368300\pi$
$257$	12.8905	0.804090	0.402045	+	0.915620i	$0.368300\pi$
$258$	−7.87518	−0.490288
$259$	0.975445	0.0606112
$260$	−6.93007	−0.429785
$261$	−12.0092	−0.743351
$262$	−7.25576	−0.448263
$263$	0.549306	0.0338716	0.0169358	−	0.999857i	$-0.494609\pi$
$263$	0.549306	0.0338716	0.0169358	+	0.999857i	$0.494609\pi$
$264$	2.33067	0.143443
$265$	−4.12836	−0.253603
$266$	−1.67699	−0.102823
$267$	12.0895	0.739868
$268$	11.8256	0.722362
$269$	4.45852	0.271841	0.135920	−	0.990720i	$-0.456601\pi$
$269$	4.45852	0.271841	0.135920	+	0.990720i	$0.456601\pi$
$270$	7.63882	0.464884
$271$	12.7232	0.772879	0.386440	−	0.922315i	$-0.373705\pi$
$271$	12.7232	0.772879	0.386440	+	0.922315i	$0.373705\pi$
$272$	3.77176	0.228697
$273$	−6.85813	−0.415073
$274$	3.06446	0.185131
$275$	6.13039	0.369677
$276$	−5.03128	−0.302847
$277$	−6.68783	−0.401833	−0.200916	−	0.979608i	$-0.564392\pi$
$277$	−6.68783	−0.401833	−0.200916	+	0.979608i	$0.564392\pi$
$278$	11.5301	0.691530
$279$	−13.5665	−0.812205
$280$	−1.86955	−0.111727
$281$	13.6759	0.815833	0.407916	−	0.913019i	$-0.366255\pi$
$281$	13.6759	0.815833	0.407916	+	0.913019i	$0.366255\pi$
$282$	−3.54828	−0.211297
$283$	6.28239	0.373449	0.186725	−	0.982412i	$-0.440213\pi$
$283$	6.28239	0.373449	0.186725	+	0.982412i	$0.440213\pi$
$284$	7.55012	0.448017
$285$	2.07409	0.122858
$286$	−10.0986	−0.597142
$287$	10.2239	0.603495
$288$	1.77605	0.104655
$289$	−2.77382	−0.163166
$290$	−9.77542	−0.574032
$291$	14.8092	0.868130
$292$	5.57269	0.326117
$293$	−30.3334	−1.77210	−0.886049	−	0.463592i	$-0.846560\pi$
$293$	−30.3334	−1.77210	−0.886049	+	0.463592i	$0.846560\pi$
$294$	5.89413	0.343753
$295$	−10.2686	−0.597861
$296$	−0.754296	−0.0438426
$297$	11.1314	0.645909
$298$	−15.3231	−0.887644
$299$	21.8001	1.26073
$300$	−3.21938	−0.185871
$301$	9.20533	0.530586
$302$	2.92246	0.168169
$303$	0.127647	0.00733312
$304$	1.29679	0.0743759
$305$	−9.84165	−0.563531
$306$	6.69882	0.382946
$307$	−29.4825	−1.68266	−0.841328	−	0.540525i	$-0.818226\pi$
$307$	−29.4825	−1.68266	−0.841328	+	0.540525i	$0.818226\pi$
$308$	−2.72433	−0.155233
$309$	0.867409	0.0493452
$310$	−11.0430	−0.627203
$311$	6.68052	0.378818	0.189409	−	0.981898i	$-0.439343\pi$
$311$	6.68052	0.378818	0.189409	+	0.981898i	$0.439343\pi$
$312$	5.30328	0.300239
$313$	26.8049	1.51510	0.757551	−	0.652776i	$-0.226396\pi$
$313$	26.8049	1.51510	0.757551	+	0.652776i	$0.226396\pi$
$314$	1.37302	0.0774842
$315$	−3.32040	−0.187083
$316$	3.77798	0.212528
$317$	−17.3098	−0.972214	−0.486107	−	0.873899i	$-0.661583\pi$
$317$	−17.3098	−0.972214	−0.486107	+	0.873899i	$0.661583\pi$
$318$	3.15925	0.177162
$319$	−14.2449	−0.797560
$320$	1.44569	0.0808165
$321$	−15.2197	−0.849483
$322$	5.88107	0.327739
$323$	4.89118	0.272152
$324$	−0.517522	−0.0287512
$325$	13.9493	0.773768
$326$	−20.2095	−1.11930
$327$	−5.56893	−0.307963
$328$	−7.90594	−0.436532
$329$	4.14759	0.228664
$330$	3.36943	0.185481
$331$	−14.5070	−0.797376	−0.398688	−	0.917087i	$-0.630534\pi$
$331$	−14.5070	−0.797376	−0.398688	+	0.917087i	$0.630534\pi$
$332$	−16.1284	−0.885161
$333$	−1.33966	−0.0734131
$334$	−18.0502	−0.987661
$335$	17.0961	0.934061
$336$	1.43068	0.0780502
$337$	12.4094	0.675983	0.337992	−	0.941149i	$-0.390252\pi$
$337$	12.4094	0.675983	0.337992	+	0.941149i	$0.390252\pi$
$338$	−9.97865	−0.542767
$339$	21.9951	1.19461
$340$	5.45280	0.295719
$341$	−16.0921	−0.871434
$342$	2.30316	0.124540
$343$	−15.9420	−0.860786
$344$	−7.11833	−0.383795
$345$	−7.27367	−0.391601
$346$	−19.1299	−1.02843
$347$	14.5830	0.782854	0.391427	−	0.920209i	$-0.371982\pi$
$347$	14.5830	0.782854	0.391427	+	0.920209i	$0.371982\pi$
$348$	7.48070	0.401008
$349$	−12.3085	−0.658861	−0.329431	−	0.944180i	$-0.606857\pi$
$349$	−12.3085	−0.658861	−0.329431	+	0.944180i	$0.606857\pi$
$350$	3.76315	0.201149
$351$	25.3287	1.35195
$352$	2.10668	0.112286
$353$	1.24535	0.0662832	0.0331416	−	0.999451i	$-0.489449\pi$
$353$	1.24535	0.0662832	0.0331416	+	0.999451i	$0.489449\pi$
$354$	7.85812	0.417654
$355$	10.9151	0.579316
$356$	10.9277	0.579165
$357$	5.39620	0.285597
$358$	1.99996	0.105701
$359$	−9.43282	−0.497845	−0.248923	−	0.968523i	$-0.580076\pi$
$359$	−9.43282	−0.497845	−0.248923	+	0.968523i	$0.580076\pi$
$360$	2.56761	0.135325
$361$	−17.3183	−0.911492
$362$	−21.2929	−1.11913
$363$	−7.25959	−0.381030
$364$	−6.19902	−0.324917
$365$	8.05638	0.421690
$366$	7.53139	0.393672
$367$	−27.6736	−1.44455	−0.722275	−	0.691606i	$-0.756904\pi$
$367$	−27.6736	−1.44455	−0.722275	+	0.691606i	$0.756904\pi$
$368$	−4.54774	−0.237067
$369$	−14.0413	−0.730962
$370$	−1.09048	−0.0566913
$371$	−3.69286	−0.191724
$372$	8.45076	0.438152
$373$	37.8665	1.96065	0.980327	−	0.197379i	$-0.0632430\pi$
$373$	37.8665	1.96065	0.980327	+	0.197379i	$0.0632430\pi$
$374$	7.94589	0.410872
$375$	−12.6512	−0.653307
$376$	−3.20727	−0.165402
$377$	−32.4132	−1.66937
$378$	6.83301	0.351452
$379$	1.74405	0.0895859	0.0447930	−	0.998996i	$-0.485737\pi$
$379$	1.74405	0.0895859	0.0447930	+	0.998996i	$0.485737\pi$
$380$	1.87475	0.0961729
$381$	14.4542	0.740510
$382$	−17.5295	−0.896887
$383$	19.2505	0.983654	0.491827	−	0.870693i	$-0.336329\pi$
$383$	19.2505	0.983654	0.491827	+	0.870693i	$0.336329\pi$
$384$	−1.10632	−0.0564569
$385$	−3.93854	−0.200726
$386$	9.12570	0.464486
$387$	−12.6425	−0.642654
$388$	13.3859	0.679568
$389$	−2.37502	−0.120418	−0.0602092	−	0.998186i	$-0.519177\pi$
$389$	−2.37502	−0.120418	−0.0602092	+	0.998186i	$0.519177\pi$
$390$	7.66691	0.388229
$391$	−17.1530	−0.867464
$392$	5.32767	0.269088
$393$	8.02723	0.404920
$394$	24.0210	1.21016
$395$	5.46178	0.274812
$396$	3.74156	0.188020
$397$	−9.30781	−0.467146	−0.233573	−	0.972339i	$-0.575042\pi$
$397$	−9.30781	−0.467146	−0.233573	+	0.972339i	$0.575042\pi$
$398$	8.81825	0.442019
$399$	1.85529	0.0928809
$400$	−2.90998	−0.145499
$401$	−2.78835	−0.139244	−0.0696218	−	0.997573i	$-0.522179\pi$
$401$	−2.78835	−0.139244	−0.0696218	+	0.997573i	$0.522179\pi$
$402$	−13.0829	−0.652517
$403$	−36.6164	−1.82399
$404$	0.115379	0.00574033
$405$	−0.748177	−0.0371772
$406$	−8.74422	−0.433968
$407$	−1.58906	−0.0787668
$408$	−4.17279	−0.206584
$409$	−30.3477	−1.50060	−0.750299	−	0.661099i	$-0.770090\pi$
$409$	−30.3477	−1.50060	−0.750299	+	0.661099i	$0.770090\pi$
$410$	−11.4295	−0.564465
$411$	−3.39029	−0.167231
$412$	0.784046	0.0386272
$413$	−9.18538	−0.451983
$414$	−8.07699	−0.396963
$415$	−23.3167	−1.14457
$416$	4.79361	0.235026
$417$	−12.7561	−0.624667
$418$	2.73192	0.133622
$419$	−15.3987	−0.752274	−0.376137	−	0.926564i	$-0.622748\pi$
$419$	−15.3987	−0.752274	−0.376137	+	0.926564i	$0.622748\pi$
$420$	2.06833	0.100924
$421$	−10.2275	−0.498457	−0.249228	−	0.968445i	$-0.580177\pi$
$421$	−10.2275	−0.498457	−0.249228	+	0.968445i	$0.580177\pi$
$422$	−12.3388	−0.600641
$423$	−5.69626	−0.276961
$424$	2.85563	0.138682
$425$	−10.9757	−0.532402
$426$	−8.35289	−0.404699
$427$	−8.80347	−0.426030
$428$	−13.7570	−0.664971
$429$	11.1723	0.539405
$430$	−10.2909	−0.496271
$431$	13.7616	0.662875	0.331437	−	0.943477i	$-0.392466\pi$
$431$	13.7616	0.662875	0.331437	+	0.943477i	$0.392466\pi$
$432$	−5.28386	−0.254220
$433$	23.5973	1.13401	0.567007	−	0.823713i	$-0.308101\pi$
$433$	23.5973	1.13401	0.567007	+	0.823713i	$0.308101\pi$
$434$	−9.87812	−0.474165
$435$	10.8148	0.518529
$436$	−5.03372	−0.241072
$437$	−5.89746	−0.282114
$438$	−6.16520	−0.294585
$439$	3.15735	0.150692	0.0753461	−	0.997157i	$-0.475994\pi$
$439$	3.15735	0.150692	0.0753461	+	0.997157i	$0.475994\pi$
$440$	3.04561	0.145194
$441$	9.46219	0.450580
$442$	18.0803	0.859994
$443$	21.1557	1.00514	0.502569	−	0.864537i	$-0.332388\pi$
$443$	21.1557	1.00514	0.502569	+	0.864537i	$0.332388\pi$
$444$	0.834496	0.0396034
$445$	15.7980	0.748898
$446$	−18.0776	−0.855999
$447$	16.9523	0.801818
$448$	1.29319	0.0610973
$449$	−39.5257	−1.86533	−0.932667	−	0.360737i	$-0.882525\pi$
$449$	−39.5257	−1.86533	−0.932667	+	0.360737i	$0.882525\pi$
$450$	−5.16826	−0.243634
$451$	−16.6553	−0.784267
$452$	19.8813	0.935135
$453$	−3.23319	−0.151909
$454$	−11.0316	−0.517741
$455$	−8.96187	−0.420139
$456$	−1.43467	−0.0671845
$457$	−24.8316	−1.16157	−0.580786	−	0.814057i	$-0.697255\pi$
$457$	−24.8316	−1.16157	−0.580786	+	0.814057i	$0.697255\pi$
$458$	5.66794	0.264845
$459$	−19.9294	−0.930227
$460$	−6.57462	−0.306543
$461$	30.9331	1.44070	0.720350	−	0.693611i	$-0.243981\pi$
$461$	30.9331	1.44070	0.720350	+	0.693611i	$0.243981\pi$
$462$	3.01399	0.140224
$463$	−19.7672	−0.918658	−0.459329	−	0.888266i	$-0.651910\pi$
$463$	−19.7672	−0.918658	−0.459329	+	0.888266i	$0.651910\pi$
$464$	6.76176	0.313907
$465$	12.2172	0.566558
$466$	−23.4166	−1.08475
$467$	−22.3460	−1.03405	−0.517024	−	0.855971i	$-0.672960\pi$
$467$	−22.3460	−1.03405	−0.517024	+	0.855971i	$0.672960\pi$
$468$	8.51366	0.393544
$469$	15.2927	0.706150
$470$	−4.63672	−0.213876
$471$	−1.51901	−0.0699922
$472$	7.10291	0.326938
$473$	−14.9960	−0.689519
$474$	−4.17967	−0.191979
$475$	−3.77363	−0.173146
$476$	4.87759	0.223564
$477$	5.07173	0.232219
$478$	17.6308	0.806414
$479$	24.6104	1.12448	0.562238	−	0.826975i	$-0.309940\pi$
$479$	24.6104	1.12448	0.562238	+	0.826975i	$0.309940\pi$
$480$	−1.59940	−0.0730024
$481$	−3.61580	−0.164866
$482$	−18.5269	−0.843878
$483$	−6.50638	−0.296050
$484$	−6.56190	−0.298268
$485$	19.3519	0.878725
$486$	−15.2790	−0.693071
$487$	−10.0874	−0.457103	−0.228552	−	0.973532i	$-0.573399\pi$
$487$	−10.0874	−0.457103	−0.228552	+	0.973532i	$0.573399\pi$
$488$	6.80758	0.308165
$489$	22.3583	1.01108
$490$	7.70216	0.347948
$491$	20.2989	0.916075	0.458037	−	0.888933i	$-0.348553\pi$
$491$	20.2989	0.916075	0.458037	+	0.888933i	$0.348553\pi$
$492$	8.74653	0.394324
$493$	25.5038	1.14863
$494$	6.21629	0.279684
$495$	5.40914	0.243123
$496$	7.63859	0.342983
$497$	9.76372	0.437963
$498$	17.8432	0.799575
$499$	−25.9608	−1.16216	−0.581082	−	0.813845i	$-0.697370\pi$
$499$	−25.9608	−1.16216	−0.581082	+	0.813845i	$0.697370\pi$
$500$	−11.4354	−0.511406
$501$	19.9693	0.892164
$502$	−2.02722	−0.0904791
$503$	29.7449	1.32626	0.663129	−	0.748505i	$-0.269228\pi$
$503$	29.7449	1.32626	0.663129	+	0.748505i	$0.269228\pi$
$504$	2.29676	0.102306
$505$	0.166803	0.00742262
$506$	−9.58063	−0.425911
$507$	11.0396	0.490287
$508$	13.0650	0.579668
$509$	43.4722	1.92687	0.963436	−	0.267939i	$-0.0863426\pi$
$509$	43.4722	1.92687	0.963436	+	0.267939i	$0.0863426\pi$
$510$	−6.03256	−0.267126
$511$	7.20653	0.318798
$512$	−1.00000	−0.0441942
$513$	−6.85205	−0.302525
$514$	−12.8905	−0.568578
$515$	1.13349	0.0499474
$516$	7.87518	0.346686
$517$	−6.75669	−0.297159
$518$	−0.975445	−0.0428586
$519$	21.1639	0.928993
$520$	6.93007	0.303904
$521$	27.7317	1.21495	0.607474	−	0.794340i	$-0.292183\pi$
$521$	27.7317	1.21495	0.607474	+	0.794340i	$0.292183\pi$
$522$	12.0092	0.525629
$523$	−9.83909	−0.430233	−0.215117	−	0.976588i	$-0.569013\pi$
$523$	−9.83909	−0.430233	−0.215117	+	0.976588i	$0.569013\pi$
$524$	7.25576	0.316970
$525$	−4.16326	−0.181700
$526$	−0.549306	−0.0239509
$527$	28.8109	1.25502
$528$	−2.33067	−0.101429
$529$	−2.31807	−0.100785
$530$	4.12836	0.179324
$531$	12.6151	0.547448
$532$	1.67699	0.0727067
$533$	−37.8980	−1.64154
$534$	−12.0895	−0.523165
$535$	−19.8884	−0.859851
$536$	−11.8256	−0.510787
$537$	−2.21260	−0.0954808
$538$	−4.45852	−0.192220
$539$	11.2237	0.483439
$540$	−7.63882	−0.328723
$541$	−24.8380	−1.06787	−0.533934	−	0.845526i	$-0.679287\pi$
$541$	−24.8380	−1.06787	−0.533934	+	0.845526i	$0.679287\pi$
$542$	−12.7232	−0.546508
$543$	23.5569	1.01092
$544$	−3.77176	−0.161713
$545$	−7.27721	−0.311721
$546$	6.85813	0.293501
$547$	10.5774	0.452255	0.226128	−	0.974098i	$-0.427393\pi$
$547$	10.5774	0.452255	0.226128	+	0.974098i	$0.427393\pi$
$548$	−3.06446	−0.130907
$549$	12.0906	0.516013
$550$	−6.13039	−0.261401
$551$	8.76858	0.373554
$552$	5.03128	0.214145
$553$	4.88563	0.207758
$554$	6.68783	0.284139
$555$	1.20642	0.0512098
$556$	−11.5301	−0.488986
$557$	2.59324	0.109879	0.0549396	−	0.998490i	$-0.482503\pi$
$557$	2.59324	0.109879	0.0549396	+	0.998490i	$0.482503\pi$
$558$	13.5665	0.574315
$559$	−34.1225	−1.44323
$560$	1.86955	0.0790028
$561$	−8.79073	−0.371145
$562$	−13.6759	−0.576881
$563$	−21.2272	−0.894619	−0.447310	−	0.894379i	$-0.647618\pi$
$563$	−21.2272	−0.894619	−0.447310	+	0.894379i	$0.647618\pi$
$564$	3.54828	0.149410
$565$	28.7421	1.20919
$566$	−6.28239	−0.264069
$567$	−0.669253	−0.0281060
$568$	−7.55012	−0.316796
$569$	−7.45651	−0.312593	−0.156297	−	0.987710i	$-0.549956\pi$
$569$	−7.45651	−0.312593	−0.156297	+	0.987710i	$0.549956\pi$
$570$	−2.07409	−0.0868740
$571$	19.2418	0.805245	0.402623	−	0.915366i	$-0.368099\pi$
$571$	19.2418	0.805245	0.402623	+	0.915366i	$0.368099\pi$
$572$	10.0986	0.422243
$573$	19.3933	0.810167
$574$	−10.2239	−0.426735
$575$	13.2338	0.551889
$576$	−1.77605	−0.0740019
$577$	−14.2082	−0.591493	−0.295747	−	0.955266i	$-0.595568\pi$
$577$	−14.2082	−0.591493	−0.295747	+	0.955266i	$0.595568\pi$
$578$	2.77382	0.115376
$579$	−10.0960	−0.419575
$580$	9.77542	0.405902
$581$	−20.8570	−0.865295
$582$	−14.8092	−0.613860
$583$	6.01590	0.249153
$584$	−5.57269	−0.230600
$585$	12.3081	0.508878
$586$	30.3334	1.25306
$587$	1.66862	0.0688713	0.0344357	−	0.999407i	$-0.489037\pi$
$587$	1.66862	0.0688713	0.0344357	+	0.999407i	$0.489037\pi$
$588$	−5.89413	−0.243070
$589$	9.90564	0.408155
$590$	10.2686	0.422752
$591$	−26.5751	−1.09315
$592$	0.754296	0.0310014
$593$	30.9789	1.27215	0.636076	−	0.771626i	$-0.280556\pi$
$593$	30.9789	1.27215	0.636076	+	0.771626i	$0.280556\pi$
$594$	−11.1314	−0.456727
$595$	7.05148	0.289083
$596$	15.3231	0.627659
$597$	−9.75585	−0.399280
$598$	−21.8001	−0.891471
$599$	−24.2976	−0.992773	−0.496386	−	0.868102i	$-0.665340\pi$
$599$	−24.2976	−0.992773	−0.496386	+	0.868102i	$0.665340\pi$
$600$	3.21938	0.131431
$601$	−12.5673	−0.512631	−0.256316	−	0.966593i	$-0.582509\pi$
$601$	−12.5673	−0.512631	−0.256316	+	0.966593i	$0.582509\pi$
$602$	−9.20533	−0.375181
$603$	−21.0028	−0.855299
$604$	−2.92246	−0.118913
$605$	−9.48648	−0.385680
$606$	−0.127647	−0.00518530
$607$	−6.97183	−0.282978	−0.141489	−	0.989940i	$-0.545189\pi$
$607$	−6.97183	−0.282978	−0.141489	+	0.989940i	$0.545189\pi$
$608$	−1.29679	−0.0525917
$609$	9.67394	0.392008
$610$	9.84165	0.398477
$611$	−15.3744	−0.621981
$612$	−6.69882	−0.270784
$613$	18.4830	0.746521	0.373261	−	0.927727i	$-0.378240\pi$
$613$	18.4830	0.746521	0.373261	+	0.927727i	$0.378240\pi$
$614$	29.4825	1.18982
$615$	12.6448	0.509887
$616$	2.72433	0.109766
$617$	21.6968	0.873479	0.436739	−	0.899588i	$-0.356133\pi$
$617$	21.6968	0.873479	0.436739	+	0.899588i	$0.356133\pi$
$618$	−0.867409	−0.0348923
$619$	−28.5321	−1.14680	−0.573401	−	0.819275i	$-0.694376\pi$
$619$	−28.5321	−1.14680	−0.573401	+	0.819275i	$0.694376\pi$
$620$	11.0430	0.443499
$621$	24.0296	0.964275
$622$	−6.68052	−0.267865
$623$	14.1315	0.566167
$624$	−5.30328	−0.212301
$625$	−1.98212	−0.0792849
$626$	−26.8049	−1.07134
$627$	−3.02239	−0.120703
$628$	−1.37302	−0.0547896
$629$	2.84502	0.113439
$630$	3.32040	0.132288
$631$	−0.789685	−0.0314369	−0.0157184	−	0.999876i	$-0.505004\pi$
$631$	−0.789685	−0.0314369	−0.0157184	+	0.999876i	$0.505004\pi$
$632$	−3.77798	−0.150280
$633$	13.6507	0.542565
$634$	17.3098	0.687459
$635$	18.8880	0.749548
$636$	−3.15925	−0.125273
$637$	25.5387	1.01188
$638$	14.2449	0.563960
$639$	−13.4094	−0.530466
$640$	−1.44569	−0.0571459
$641$	44.7022	1.76563	0.882816	−	0.469720i	$-0.155645\pi$
$641$	44.7022	1.76563	0.882816	+	0.469720i	$0.155645\pi$
$642$	15.2197	0.600675
$643$	−6.81902	−0.268916	−0.134458	−	0.990919i	$-0.542929\pi$
$643$	−6.81902	−0.268916	−0.134458	+	0.990919i	$0.542929\pi$
$644$	−5.88107	−0.231747
$645$	11.3851	0.448287
$646$	−4.89118	−0.192441
$647$	−21.4787	−0.844413	−0.422207	−	0.906500i	$-0.638744\pi$
$647$	−21.4787	−0.844413	−0.422207	+	0.906500i	$0.638744\pi$
$648$	0.517522	0.0203302
$649$	14.9636	0.587371
$650$	−13.9493	−0.547136
$651$	10.9284	0.428318
$652$	20.2095	0.791465
$653$	−25.1927	−0.985868	−0.492934	−	0.870067i	$-0.664076\pi$
$653$	−25.1927	−0.985868	−0.492934	+	0.870067i	$0.664076\pi$
$654$	5.56893	0.217762
$655$	10.4896	0.409862
$656$	7.90594	0.308675
$657$	−9.89735	−0.386133
$658$	−4.14759	−0.161690
$659$	−7.22921	−0.281610	−0.140805	−	0.990037i	$-0.544969\pi$
$659$	−7.22921	−0.281610	−0.140805	+	0.990037i	$0.544969\pi$
$660$	−3.36943	−0.131155
$661$	19.6736	0.765214	0.382607	−	0.923911i	$-0.375026\pi$
$661$	19.6736	0.765214	0.382607	+	0.923911i	$0.375026\pi$
$662$	14.5070	0.563830
$663$	−20.0027	−0.776841
$664$	16.1284	0.625903
$665$	2.42441	0.0940145
$666$	1.33966	0.0519109
$667$	−30.7507	−1.19067
$668$	18.0502	0.698382
$669$	19.9997	0.773232
$670$	−17.0961	−0.660481
$671$	14.3414	0.553643
$672$	−1.43068	−0.0551898
$673$	−25.6479	−0.988653	−0.494326	−	0.869276i	$-0.664585\pi$
$673$	−25.6479	−0.988653	−0.494326	+	0.869276i	$0.664585\pi$
$674$	−12.4094	−0.477992
$675$	15.3759	0.591819
$676$	9.97865	0.383794
$677$	37.1134	1.42638	0.713192	−	0.700968i	$-0.247249\pi$
$677$	37.1134	1.42638	0.713192	+	0.700968i	$0.247249\pi$
$678$	−21.9951	−0.844717
$679$	17.3105	0.664316
$680$	−5.45280	−0.209105
$681$	12.2046	0.467680
$682$	16.0921	0.616197
$683$	24.9894	0.956191	0.478096	−	0.878308i	$-0.341327\pi$
$683$	24.9894	0.956191	0.478096	+	0.878308i	$0.341327\pi$
$684$	−2.30316	−0.0880634
$685$	−4.43026	−0.169272
$686$	15.9420	0.608667
$687$	−6.27058	−0.239237
$688$	7.11833	0.271384
$689$	13.6888	0.521500
$690$	7.27367	0.276904
$691$	−2.62521	−0.0998677	−0.0499339	−	0.998753i	$-0.515901\pi$
$691$	−2.62521	−0.0998677	−0.0499339	+	0.998753i	$0.515901\pi$
$692$	19.1299	0.727211
$693$	4.83853	0.183801
$694$	−14.5830	−0.553561
$695$	−16.6690	−0.632290
$696$	−7.48070	−0.283555
$697$	29.8193	1.12949
$698$	12.3085	0.465885
$699$	25.9063	0.979868
$700$	−3.76315	−0.142234
$701$	−34.5141	−1.30358	−0.651790	−	0.758400i	$-0.725982\pi$
$701$	−34.5141	−1.30358	−0.651790	+	0.758400i	$0.725982\pi$
$702$	−25.3287	−0.955971
$703$	0.978162	0.0368921
$704$	−2.10668	−0.0793985
$705$	5.12971	0.193196
$706$	−1.24535	−0.0468693
$707$	0.149207	0.00561150
$708$	−7.85812	−0.295326
$709$	−11.8276	−0.444197	−0.222098	−	0.975024i	$-0.571291\pi$
$709$	−11.8276	−0.444197	−0.222098	+	0.975024i	$0.571291\pi$
$710$	−10.9151	−0.409638
$711$	−6.70986	−0.251639
$712$	−10.9277	−0.409531
$713$	−34.7383	−1.30096
$714$	−5.39620	−0.201948
$715$	14.5994	0.545988
$716$	−1.99996	−0.0747419
$717$	−19.5054	−0.728442
$718$	9.43282	0.352030
$719$	6.74414	0.251514	0.125757	−	0.992061i	$-0.459864\pi$
$719$	6.74414	0.251514	0.125757	+	0.992061i	$0.459864\pi$
$720$	−2.56761	−0.0956893
$721$	1.01392	0.0377602
$722$	17.3183	0.644522
$723$	20.4968	0.762284
$724$	21.2929	0.791345
$725$	−19.6766	−0.730770
$726$	7.25959	0.269429
$727$	24.2784	0.900438	0.450219	−	0.892918i	$-0.351346\pi$
$727$	24.2784	0.900438	0.450219	+	0.892918i	$0.351346\pi$
$728$	6.19902	0.229751
$729$	18.4561	0.683560
$730$	−8.05638	−0.298180
$731$	26.8486	0.993033
$732$	−7.53139	−0.278368
$733$	−24.2269	−0.894841	−0.447421	−	0.894324i	$-0.647657\pi$
$733$	−24.2269	−0.894841	−0.447421	+	0.894324i	$0.647657\pi$
$734$	27.6736	1.02145
$735$	−8.52109	−0.314305
$736$	4.54774	0.167632
$737$	−24.9127	−0.917671
$738$	14.0413	0.516868
$739$	11.9689	0.440283	0.220142	−	0.975468i	$-0.429348\pi$
$739$	11.9689	0.440283	0.220142	+	0.975468i	$0.429348\pi$
$740$	1.09048	0.0400868
$741$	−6.87724	−0.252642
$742$	3.69286	0.135569
$743$	−32.9605	−1.20920	−0.604601	−	0.796528i	$-0.706668\pi$
$743$	−32.9605	−1.20920	−0.604601	+	0.796528i	$0.706668\pi$
$744$	−8.45076	−0.309820
$745$	22.1525	0.811604
$746$	−37.8665	−1.38639
$747$	28.6448	1.04806
$748$	−7.94589	−0.290531
$749$	−17.7904	−0.650047
$750$	12.6512	0.461958
$751$	−15.8818	−0.579534	−0.289767	−	0.957097i	$-0.593578\pi$
$751$	−15.8818	−0.579534	−0.289767	+	0.957097i	$0.593578\pi$
$752$	3.20727	0.116957
$753$	2.24276	0.0817307
$754$	32.4132	1.18042
$755$	−4.22498	−0.153763
$756$	−6.83301	−0.248514
$757$	−0.887632	−0.0322615	−0.0161308	−	0.999870i	$-0.505135\pi$
$757$	−0.887632	−0.0322615	−0.0161308	+	0.999870i	$0.505135\pi$
$758$	−1.74405	−0.0633468
$759$	10.5993	0.384730
$760$	−1.87475	−0.0680045
$761$	−5.75731	−0.208702	−0.104351	−	0.994541i	$-0.533277\pi$
$761$	−5.75731	−0.208702	−0.104351	+	0.994541i	$0.533277\pi$
$762$	−14.4542	−0.523620
$763$	−6.50954	−0.235661
$764$	17.5295	0.634195
$765$	−9.68442	−0.350141
$766$	−19.2505	−0.695549
$767$	34.0485	1.22942
$768$	1.10632	0.0399210
$769$	−28.0934	−1.01307	−0.506537	−	0.862218i	$-0.669075\pi$
$769$	−28.0934	−1.01307	−0.506537	+	0.862218i	$0.669075\pi$
$770$	3.93854	0.141935
$771$	14.2611	0.513602
$772$	−9.12570	−0.328441
$773$	−4.10253	−0.147558	−0.0737788	−	0.997275i	$-0.523506\pi$
$773$	−4.10253	−0.147558	−0.0737788	+	0.997275i	$0.523506\pi$
$774$	12.6425	0.454425
$775$	−22.2281	−0.798459
$776$	−13.3859	−0.480527
$777$	1.07916	0.0387146
$778$	2.37502	0.0851487
$779$	10.2523	0.367328
$780$	−7.66691	−0.274519
$781$	−15.9057	−0.569150
$782$	17.1530	0.613389
$783$	−35.7282	−1.27682
$784$	−5.32767	−0.190274
$785$	−1.98497	−0.0708465
$786$	−8.02723	−0.286322
$787$	11.6968	0.416945	0.208473	−	0.978028i	$-0.433151\pi$
$787$	11.6968	0.416945	0.208473	+	0.978028i	$0.433151\pi$
$788$	−24.0210	−0.855714
$789$	0.607710	0.0216351
$790$	−5.46178	−0.194322
$791$	25.7102	0.914148
$792$	−3.74156	−0.132951
$793$	32.6328	1.15883
$794$	9.30781	0.330322
$795$	−4.56730	−0.161986
$796$	−8.81825	−0.312555
$797$	35.3307	1.25148	0.625739	−	0.780033i	$-0.284798\pi$
$797$	35.3307	1.25148	0.625739	+	0.780033i	$0.284798\pi$
$798$	−1.85529	−0.0656767
$799$	12.0970	0.427963
$800$	2.90998	0.102883
$801$	−19.4080	−0.685749
$802$	2.78835	0.0984601
$803$	−11.7399	−0.414291
$804$	13.0829	0.461399
$805$	−8.50221	−0.299664
$806$	36.6164	1.28976
$807$	4.93257	0.173635
$808$	−0.115379	−0.00405902
$809$	18.2808	0.642718	0.321359	−	0.946958i	$-0.395860\pi$
$809$	18.2808	0.642718	0.321359	+	0.946958i	$0.395860\pi$
$810$	0.748177	0.0262883
$811$	−20.3273	−0.713787	−0.356894	−	0.934145i	$-0.616164\pi$
$811$	−20.3273	−0.713787	−0.356894	+	0.934145i	$0.616164\pi$
$812$	8.74422	0.306862
$813$	14.0760	0.493667
$814$	1.58906	0.0556965
$815$	29.2167	1.02342
$816$	4.17279	0.146077
$817$	9.23097	0.322951
$818$	30.3477	1.06108
$819$	11.0098	0.384712
$820$	11.4295	0.399137
$821$	29.4870	1.02910	0.514551	−	0.857460i	$-0.327959\pi$
$821$	29.4870	1.02910	0.514551	+	0.857460i	$0.327959\pi$
$822$	3.39029	0.118250
$823$	44.0387	1.53509	0.767546	−	0.640994i	$-0.221478\pi$
$823$	44.0387	1.53509	0.767546	+	0.640994i	$0.221478\pi$
$824$	−0.784046	−0.0273135
$825$	6.78221	0.236126
$826$	9.18538	0.319600
$827$	5.20538	0.181009	0.0905043	−	0.995896i	$-0.471152\pi$
$827$	5.20538	0.181009	0.0905043	+	0.995896i	$0.471152\pi$
$828$	8.07699	0.280695
$829$	28.0817	0.975316	0.487658	−	0.873035i	$-0.337851\pi$
$829$	28.0817	0.975316	0.487658	+	0.873035i	$0.337851\pi$
$830$	23.3167	0.809333
$831$	−7.39891	−0.256665
$832$	−4.79361	−0.166188
$833$	−20.0947	−0.696240
$834$	12.7561	0.441706
$835$	26.0949	0.903053
$836$	−2.73192	−0.0944854
$837$	−40.3612	−1.39509
$838$	15.3987	0.531938
$839$	−10.7282	−0.370379	−0.185189	−	0.982703i	$-0.559290\pi$
$839$	−10.7282	−0.370379	−0.185189	+	0.982703i	$0.559290\pi$
$840$	−2.06833	−0.0713640
$841$	16.7214	0.576602
$842$	10.2275	0.352462
$843$	15.1299	0.521102
$844$	12.3388	0.424718
$845$	14.4260	0.496271
$846$	5.69626	0.195841
$847$	−8.48576	−0.291574
$848$	−2.85563	−0.0980628
$849$	6.95036	0.238536
$850$	10.9757	0.376465
$851$	−3.43034	−0.117591
$852$	8.35289	0.286165
$853$	−14.7235	−0.504124	−0.252062	−	0.967711i	$-0.581109\pi$
$853$	−14.7235	−0.504124	−0.252062	+	0.967711i	$0.581109\pi$
$854$	8.80347	0.301248
$855$	−3.32965	−0.113872
$856$	13.7570	0.470206
$857$	42.2696	1.44390	0.721952	−	0.691943i	$-0.243245\pi$
$857$	42.2696	1.44390	0.721952	+	0.691943i	$0.243245\pi$
$858$	−11.1723	−0.381417
$859$	8.15916	0.278387	0.139193	−	0.990265i	$-0.455549\pi$
$859$	8.15916	0.278387	0.139193	+	0.990265i	$0.455549\pi$
$860$	10.2909	0.350917
$861$	11.3109	0.385474
$862$	−13.7616	−0.468723
$863$	31.2572	1.06401	0.532004	−	0.846742i	$-0.321439\pi$
$863$	31.2572	1.06401	0.532004	+	0.846742i	$0.321439\pi$
$864$	5.28386	0.179760
$865$	27.6560	0.940331
$866$	−23.5973	−0.801869
$867$	−3.06875	−0.104220
$868$	9.87812	0.335285
$869$	−7.95899	−0.269990
$870$	−10.8148	−0.366655
$871$	−56.6871	−1.92077
$872$	5.03372	0.170463
$873$	−23.7740	−0.804629
$874$	5.89746	0.199484
$875$	−14.7881	−0.499928
$876$	6.16520	0.208303
$877$	−25.1700	−0.849932	−0.424966	−	0.905209i	$-0.639714\pi$
$877$	−25.1700	−0.849932	−0.424966	+	0.905209i	$0.639714\pi$
$878$	−3.15735	−0.106555
$879$	−33.5586	−1.13190
$880$	−3.04561	−0.102667
$881$	−51.7576	−1.74376	−0.871879	−	0.489721i	$-0.837098\pi$
$881$	−51.7576	−1.74376	−0.871879	+	0.489721i	$0.837098\pi$
$882$	−9.46219	−0.318608
$883$	10.2736	0.345735	0.172867	−	0.984945i	$-0.444697\pi$
$883$	10.2736	0.345735	0.172867	+	0.984945i	$0.444697\pi$
$884$	−18.0803	−0.608107
$885$	−11.3604	−0.381876
$886$	−21.1557	−0.710740
$887$	−26.8140	−0.900328	−0.450164	−	0.892946i	$-0.648634\pi$
$887$	−26.8140	−0.900328	−0.450164	+	0.892946i	$0.648634\pi$
$888$	−0.834496	−0.0280039
$889$	16.8955	0.566658
$890$	−15.7980	−0.529551
$891$	1.09025	0.0365249
$892$	18.0776	0.605282
$893$	4.15915	0.139181
$894$	−16.9523	−0.566971
$895$	−2.89132	−0.0966462
$896$	−1.29319	−0.0432023
$897$	24.1180	0.805275
$898$	39.5257	1.31899
$899$	51.6504	1.72264
$900$	5.16826	0.172275
$901$	−10.7708	−0.358826
$902$	16.6553	0.554560
$903$	10.1841	0.338905
$904$	−19.8813	−0.661241
$905$	30.7830	1.02326
$906$	3.23319	0.107416
$907$	37.3396	1.23984	0.619921	−	0.784664i	$-0.287165\pi$
$907$	37.3396	1.23984	0.619921	+	0.784664i	$0.287165\pi$
$908$	11.0316	0.366098
$909$	−0.204919	−0.00679672
$910$	8.96187	0.297083
$911$	1.89150	0.0626682	0.0313341	−	0.999509i	$-0.490024\pi$
$911$	1.89150	0.0626682	0.0313341	+	0.999509i	$0.490024\pi$
$912$	1.43467	0.0475066
$913$	33.9774	1.12449
$914$	24.8316	0.821355
$915$	−10.8881	−0.359948
$916$	−5.66794	−0.187274
$917$	9.38306	0.309856
$918$	19.9294	0.657770
$919$	−9.24302	−0.304899	−0.152450	−	0.988311i	$-0.548716\pi$
$919$	−9.24302	−0.304899	−0.152450	+	0.988311i	$0.548716\pi$
$920$	6.57462	0.216759
$921$	−32.6172	−1.07477
$922$	−30.9331	−1.01873
$923$	−36.1923	−1.19128
$924$	−3.01399	−0.0991531
$925$	−2.19499	−0.0721707
$926$	19.7672	0.649589
$927$	−1.39250	−0.0457357
$928$	−6.76176	−0.221966
$929$	−36.9585	−1.21257	−0.606285	−	0.795247i	$-0.707341\pi$
$929$	−36.9585	−1.21257	−0.606285	+	0.795247i	$0.707341\pi$
$930$	−12.2172	−0.400617
$931$	−6.90886	−0.226429
$932$	23.4166	0.767036
$933$	7.39083	0.241965
$934$	22.3460	0.731183
$935$	−11.4873	−0.375675
$936$	−8.51366	−0.278278
$937$	−45.6735	−1.49209	−0.746044	−	0.665897i	$-0.768049\pi$
$937$	−45.6735	−1.49209	−0.746044	+	0.665897i	$0.768049\pi$
$938$	−15.2927	−0.499323
$939$	29.6549	0.967751
$940$	4.63672	0.151233
$941$	−27.9903	−0.912458	−0.456229	−	0.889862i	$-0.650800\pi$
$941$	−27.9903	−0.912458	−0.456229	+	0.889862i	$0.650800\pi$
$942$	1.51901	0.0494920
$943$	−35.9542	−1.17083
$944$	−7.10291	−0.231180
$945$	−9.87842	−0.321345
$946$	14.9960	0.487563
$947$	32.3865	1.05242	0.526210	−	0.850355i	$-0.323613\pi$
$947$	32.3865	1.05242	0.526210	+	0.850355i	$0.323613\pi$
$948$	4.17967	0.135749
$949$	−26.7133	−0.867150
$950$	3.77363	0.122433
$951$	−19.1502	−0.620989
$952$	−4.87759	−0.158084
$953$	−5.35643	−0.173512	−0.0867559	−	0.996230i	$-0.527650\pi$
$953$	−5.35643	−0.173512	−0.0867559	+	0.996230i	$0.527650\pi$
$954$	−5.07173	−0.164203
$955$	25.3422	0.820055
$956$	−17.6308	−0.570221
$957$	−15.7594	−0.509431
$958$	−24.6104	−0.795125
$959$	−3.96292	−0.127969
$960$	1.59940	0.0516205
$961$	27.3481	0.882197
$962$	3.61580	0.116578
$963$	24.4331	0.787347
$964$	18.5269	0.596712
$965$	−13.1929	−0.424696
$966$	6.50638	0.209339
$967$	23.5601	0.757643	0.378822	−	0.925470i	$-0.376329\pi$
$967$	23.5601	0.757643	0.378822	+	0.925470i	$0.376329\pi$
$968$	6.56190	0.210907
$969$	5.41123	0.173834
$970$	−19.3519	−0.621352
$971$	−8.85901	−0.284299	−0.142150	−	0.989845i	$-0.545401\pi$
$971$	−8.85901	−0.284299	−0.142150	+	0.989845i	$0.545401\pi$
$972$	15.2790	0.490075
$973$	−14.9106	−0.478012
$974$	10.0874	0.323221
$975$	15.4324	0.494234
$976$	−6.80758	−0.217905
$977$	−16.7091	−0.534572	−0.267286	−	0.963617i	$-0.586127\pi$
$977$	−16.7091	−0.534572	−0.267286	+	0.963617i	$0.586127\pi$
$978$	−22.3583	−0.714939
$979$	−23.0211	−0.735757
$980$	−7.70216	−0.246036
$981$	8.94012	0.285436
$982$	−20.2989	−0.647763
$983$	−3.44336	−0.109826	−0.0549130	−	0.998491i	$-0.517488\pi$
$983$	−3.44336	−0.109826	−0.0549130	+	0.998491i	$0.517488\pi$
$984$	−8.74653	−0.278829
$985$	−34.7270	−1.10649
$986$	−25.5038	−0.812205
$987$	4.58859	0.146056
$988$	−6.21629	−0.197767
$989$	−32.3723	−1.02938
$990$	−5.40914	−0.171914
$991$	13.8344	0.439464	0.219732	−	0.975560i	$-0.429482\pi$
$991$	13.8344	0.439464	0.219732	+	0.975560i	$0.429482\pi$
$992$	−7.63859	−0.242526
$993$	−16.0494	−0.509313
$994$	−9.76372	−0.309686
$995$	−12.7485	−0.404153
$996$	−17.8432	−0.565385
$997$	−15.0164	−0.475574	−0.237787	−	0.971317i	$-0.576422\pi$
$997$	−15.0164	−0.475574	−0.237787	+	0.971317i	$0.576422\pi$
$998$	25.9608	0.821773
$999$	−3.98559	−0.126099

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8002.2.a.e.1.50	✓	77

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8002.2.a.e.1.50	✓	77	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:	\( N \)	\(=\)	\( 8002 = 2 \cdot 4001 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8002.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.10632 q^{3} +1.00000 q^{4} +1.44569 q^{5} -1.10632 q^{6} +1.29319 q^{7} -1.00000 q^{8} -1.77605 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.10632 q^{3} +1.00000 q^{4} +1.44569 q^{5} -1.10632 q^{6} +1.29319 q^{7} -1.00000 q^{8} -1.77605 q^{9} -1.44569 q^{10} -2.10668 q^{11} +1.10632 q^{12} -4.79361 q^{13} -1.29319 q^{14} +1.59940 q^{15} +1.00000 q^{16} +3.77176 q^{17} +1.77605 q^{18} +1.29679 q^{19} +1.44569 q^{20} +1.43068 q^{21} +2.10668 q^{22} -4.54774 q^{23} -1.10632 q^{24} -2.90998 q^{25} +4.79361 q^{26} -5.28386 q^{27} +1.29319 q^{28} +6.76176 q^{29} -1.59940 q^{30} +7.63859 q^{31} -1.00000 q^{32} -2.33067 q^{33} -3.77176 q^{34} +1.86955 q^{35} -1.77605 q^{36} +0.754296 q^{37} -1.29679 q^{38} -5.30328 q^{39} -1.44569 q^{40} +7.90594 q^{41} -1.43068 q^{42} +7.11833 q^{43} -2.10668 q^{44} -2.56761 q^{45} +4.54774 q^{46} +3.20727 q^{47} +1.10632 q^{48} -5.32767 q^{49} +2.90998 q^{50} +4.17279 q^{51} -4.79361 q^{52} -2.85563 q^{53} +5.28386 q^{54} -3.04561 q^{55} -1.29319 q^{56} +1.43467 q^{57} -6.76176 q^{58} -7.10291 q^{59} +1.59940 q^{60} -6.80758 q^{61} -7.63859 q^{62} -2.29676 q^{63} +1.00000 q^{64} -6.93007 q^{65} +2.33067 q^{66} +11.8256 q^{67} +3.77176 q^{68} -5.03128 q^{69} -1.86955 q^{70} +7.55012 q^{71} +1.77605 q^{72} +5.57269 q^{73} -0.754296 q^{74} -3.21938 q^{75} +1.29679 q^{76} -2.72433 q^{77} +5.30328 q^{78} +3.77798 q^{79} +1.44569 q^{80} -0.517522 q^{81} -7.90594 q^{82} -16.1284 q^{83} +1.43068 q^{84} +5.45280 q^{85} -7.11833 q^{86} +7.48070 q^{87} +2.10668 q^{88} +10.9277 q^{89} +2.56761 q^{90} -6.19902 q^{91} -4.54774 q^{92} +8.45076 q^{93} -3.20727 q^{94} +1.87475 q^{95} -1.10632 q^{96} +13.3859 q^{97} +5.32767 q^{98} +3.74156 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 77 q - 77 q^{2} + 10 q^{3} + 77 q^{4} + 18 q^{5} - 10 q^{6} + 21 q^{7} - 77 q^{8} + 71 q^{9}+O(q^{10}) \) 77 * q - 77 * q^2 + 10 * q^3 + 77 * q^4 + 18 * q^5 - 10 * q^6 + 21 * q^7 - 77 * q^8 + 71 * q^9	\( 77 q - 77 q^{2} + 10 q^{3} + 77 q^{4} + 18 q^{5} - 10 q^{6} + 21 q^{7} - 77 q^{8} + 71 q^{9} - 18 q^{10} + 30 q^{11} + 10 q^{12} - 2 q^{13} - 21 q^{14} + 21 q^{15} + 77 q^{16} + 60 q^{17} - 71 q^{18} - 3 q^{19} + 18 q^{20} + 10 q^{21} - 30 q^{22} + 53 q^{23} - 10 q^{24} + 59 q^{25} + 2 q^{26} + 43 q^{27} + 21 q^{28} + 30 q^{29} - 21 q^{30} + 22 q^{31} - 77 q^{32} + 31 q^{33} - 60 q^{34} + 41 q^{35} + 71 q^{36} - 3 q^{37} + 3 q^{38} + 44 q^{39} - 18 q^{40} + 48 q^{41} - 10 q^{42} + 21 q^{43} + 30 q^{44} + 33 q^{45} - 53 q^{46} + 107 q^{47} + 10 q^{48} + 24 q^{49} - 59 q^{50} + 18 q^{51} - 2 q^{52} + 42 q^{53} - 43 q^{54} + 49 q^{55} - 21 q^{56} + 32 q^{57} - 30 q^{58} + 42 q^{59} + 21 q^{60} - 31 q^{61} - 22 q^{62} + 109 q^{63} + 77 q^{64} + 39 q^{65} - 31 q^{66} - q^{67} + 60 q^{68} - 33 q^{69} - 41 q^{70} + 58 q^{71} - 71 q^{72} + 35 q^{73} + 3 q^{74} + 34 q^{75} - 3 q^{76} + 86 q^{77} - 44 q^{78} + 25 q^{79} + 18 q^{80} + 53 q^{81} - 48 q^{82} + 107 q^{83} + 10 q^{84} + 21 q^{85} - 21 q^{86} + 100 q^{87} - 30 q^{88} + 34 q^{89} - 33 q^{90} - 51 q^{91} + 53 q^{92} + 48 q^{93} - 107 q^{94} + 118 q^{95} - 10 q^{96} - 13 q^{97} - 24 q^{98} + 63 q^{99}+O(q^{100}) \) 77 * q - 77 * q^2 + 10 * q^3 + 77 * q^4 + 18 * q^5 - 10 * q^6 + 21 * q^7 - 77 * q^8 + 71 * q^9 - 18 * q^10 + 30 * q^11 + 10 * q^12 - 2 * q^13 - 21 * q^14 + 21 * q^15 + 77 * q^16 + 60 * q^17 - 71 * q^18 - 3 * q^19 + 18 * q^20 + 10 * q^21 - 30 * q^22 + 53 * q^23 - 10 * q^24 + 59 * q^25 + 2 * q^26 + 43 * q^27 + 21 * q^28 + 30 * q^29 - 21 * q^30 + 22 * q^31 - 77 * q^32 + 31 * q^33 - 60 * q^34 + 41 * q^35 + 71 * q^36 - 3 * q^37 + 3 * q^38 + 44 * q^39 - 18 * q^40 + 48 * q^41 - 10 * q^42 + 21 * q^43 + 30 * q^44 + 33 * q^45 - 53 * q^46 + 107 * q^47 + 10 * q^48 + 24 * q^49 - 59 * q^50 + 18 * q^51 - 2 * q^52 + 42 * q^53 - 43 * q^54 + 49 * q^55 - 21 * q^56 + 32 * q^57 - 30 * q^58 + 42 * q^59 + 21 * q^60 - 31 * q^61 - 22 * q^62 + 109 * q^63 + 77 * q^64 + 39 * q^65 - 31 * q^66 - q^67 + 60 * q^68 - 33 * q^69 - 41 * q^70 + 58 * q^71 - 71 * q^72 + 35 * q^73 + 3 * q^74 + 34 * q^75 - 3 * q^76 + 86 * q^77 - 44 * q^78 + 25 * q^79 + 18 * q^80 + 53 * q^81 - 48 * q^82 + 107 * q^83 + 10 * q^84 + 21 * q^85 - 21 * q^86 + 100 * q^87 - 30 * q^88 + 34 * q^89 - 33 * q^90 - 51 * q^91 + 53 * q^92 + 48 * q^93 - 107 * q^94 + 118 * q^95 - 10 * q^96 - 13 * q^97 - 24 * q^98 + 63 * q^99

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