LMFDB - Embedded newform 8002.2.a.e.1.10

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			1.10
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)

$f(q)$	$=$	$q-1.00000 q^{2} -2.45617 q^{3} +1.00000 q^{4} +0.358646 q^{5} +2.45617 q^{6} -1.91182 q^{7} -1.00000 q^{8} +3.03279 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.45617 q^{3} +1.00000 q^{4} +0.358646 q^{5} +2.45617 q^{6} -1.91182 q^{7} -1.00000 q^{8} +3.03279 q^{9} -0.358646 q^{10} +5.12829 q^{11} -2.45617 q^{12} +3.67709 q^{13} +1.91182 q^{14} -0.880897 q^{15} +1.00000 q^{16} +3.57578 q^{17} -3.03279 q^{18} -7.77991 q^{19} +0.358646 q^{20} +4.69577 q^{21} -5.12829 q^{22} -0.723070 q^{23} +2.45617 q^{24} -4.87137 q^{25} -3.67709 q^{26} -0.0805476 q^{27} -1.91182 q^{28} +0.330291 q^{29} +0.880897 q^{30} +7.74033 q^{31} -1.00000 q^{32} -12.5960 q^{33} -3.57578 q^{34} -0.685668 q^{35} +3.03279 q^{36} +6.25420 q^{37} +7.77991 q^{38} -9.03159 q^{39} -0.358646 q^{40} -2.75424 q^{41} -4.69577 q^{42} +10.5331 q^{43} +5.12829 q^{44} +1.08770 q^{45} +0.723070 q^{46} +1.93642 q^{47} -2.45617 q^{48} -3.34493 q^{49} +4.87137 q^{50} -8.78273 q^{51} +3.67709 q^{52} -8.76896 q^{53} +0.0805476 q^{54} +1.83924 q^{55} +1.91182 q^{56} +19.1088 q^{57} -0.330291 q^{58} +4.14217 q^{59} -0.880897 q^{60} +13.8353 q^{61} -7.74033 q^{62} -5.79817 q^{63} +1.00000 q^{64} +1.31877 q^{65} +12.5960 q^{66} +10.2792 q^{67} +3.57578 q^{68} +1.77599 q^{69} +0.685668 q^{70} +11.3216 q^{71} -3.03279 q^{72} +2.13860 q^{73} -6.25420 q^{74} +11.9649 q^{75} -7.77991 q^{76} -9.80438 q^{77} +9.03159 q^{78} +2.66262 q^{79} +0.358646 q^{80} -8.90054 q^{81} +2.75424 q^{82} +16.1458 q^{83} +4.69577 q^{84} +1.28244 q^{85} -10.5331 q^{86} -0.811252 q^{87} -5.12829 q^{88} +6.65673 q^{89} -1.08770 q^{90} -7.02996 q^{91} -0.723070 q^{92} -19.0116 q^{93} -1.93642 q^{94} -2.79023 q^{95} +2.45617 q^{96} -15.5223 q^{97} +3.34493 q^{98} +15.5530 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−2.45617	−1.41807	−0.709037	−	0.705172i	$-0.750870\pi$
$3$	−2.45617	−1.41807	−0.709037	+	0.705172i	$0.750870\pi$
$4$	1.00000	0.500000
$5$	0.358646	0.160391	0.0801957	−	0.996779i	$-0.474445\pi$
$5$	0.358646	0.160391	0.0801957	+	0.996779i	$0.474445\pi$
$6$	2.45617	1.00273
$7$	−1.91182	−0.722602	−0.361301	−	0.932449i	$-0.617667\pi$
$7$	−1.91182	−0.722602	−0.361301	+	0.932449i	$0.617667\pi$
$8$	−1.00000	−0.353553
$9$	3.03279	1.01093
$10$	−0.358646	−0.113414
$11$	5.12829	1.54624	0.773118	−	0.634262i	$-0.218696\pi$
$11$	5.12829	1.54624	0.773118	+	0.634262i	$0.218696\pi$
$12$	−2.45617	−0.709037
$13$	3.67709	1.01984	0.509921	−	0.860221i	$-0.329675\pi$
$13$	3.67709	1.01984	0.509921	+	0.860221i	$0.329675\pi$
$14$	1.91182	0.510957
$15$	−0.880897	−0.227447
$16$	1.00000	0.250000
$17$	3.57578	0.867254	0.433627	−	0.901093i	$-0.357234\pi$
$17$	3.57578	0.867254	0.433627	+	0.901093i	$0.357234\pi$
$18$	−3.03279	−0.714836
$19$	−7.77991	−1.78483	−0.892417	−	0.451211i	$-0.850992\pi$
$19$	−7.77991	−1.78483	−0.892417	+	0.451211i	$0.850992\pi$
$20$	0.358646	0.0801957
$21$	4.69577	1.02470
$22$	−5.12829	−1.09335
$23$	−0.723070	−0.150771	−0.0753853	−	0.997154i	$-0.524019\pi$
$23$	−0.723070	−0.150771	−0.0753853	+	0.997154i	$0.524019\pi$
$24$	2.45617	0.501365
$25$	−4.87137	−0.974275
$26$	−3.67709	−0.721138
$27$	−0.0805476	−0.0155014
$28$	−1.91182	−0.361301
$29$	0.330291	0.0613335	0.0306667	−	0.999530i	$-0.490237\pi$
$29$	0.330291	0.0613335	0.0306667	+	0.999530i	$0.490237\pi$
$30$	0.880897	0.160829
$31$	7.74033	1.39021	0.695103	−	0.718911i	$-0.255359\pi$
$31$	7.74033	1.39021	0.695103	+	0.718911i	$0.255359\pi$
$32$	−1.00000	−0.176777
$33$	−12.5960	−2.19268
$34$	−3.57578	−0.613241
$35$	−0.685668	−0.115899
$36$	3.03279	0.505466
$37$	6.25420	1.02818	0.514092	−	0.857735i	$-0.328129\pi$
$37$	6.25420	1.02818	0.514092	+	0.857735i	$0.328129\pi$
$38$	7.77991	1.26207
$39$	−9.03159	−1.44621
$40$	−0.358646	−0.0567069
$41$	−2.75424	−0.430140	−0.215070	−	0.976599i	$-0.568998\pi$
$41$	−2.75424	−0.430140	−0.215070	+	0.976599i	$0.568998\pi$
$42$	−4.69577	−0.724574
$43$	10.5331	1.60628	0.803142	−	0.595788i	$-0.203160\pi$
$43$	10.5331	1.60628	0.803142	+	0.595788i	$0.203160\pi$
$44$	5.12829	0.773118
$45$	1.08770	0.162145
$46$	0.723070	0.106611
$47$	1.93642	0.282456	0.141228	−	0.989977i	$-0.454895\pi$
$47$	1.93642	0.282456	0.141228	+	0.989977i	$0.454895\pi$
$48$	−2.45617	−0.354518
$49$	−3.34493	−0.477847
$50$	4.87137	0.688916
$51$	−8.78273	−1.22983
$52$	3.67709	0.509921
$53$	−8.76896	−1.20451	−0.602255	−	0.798304i	$-0.705731\pi$
$53$	−8.76896	−1.20451	−0.602255	+	0.798304i	$0.705731\pi$
$54$	0.0805476	0.0109611
$55$	1.83924	0.248003
$56$	1.91182	0.255478
$57$	19.1088	2.53103
$58$	−0.330291	−0.0433693
$59$	4.14217	0.539265	0.269632	−	0.962963i	$-0.413098\pi$
$59$	4.14217	0.539265	0.269632	+	0.962963i	$0.413098\pi$
$60$	−0.880897	−0.113723
$61$	13.8353	1.77142	0.885712	−	0.464235i	$-0.153671\pi$
$61$	13.8353	1.77142	0.885712	+	0.464235i	$0.153671\pi$
$62$	−7.74033	−0.983023
$63$	−5.79817	−0.730501
$64$	1.00000	0.125000
$65$	1.31877	0.163574
$66$	12.5960	1.55046
$67$	10.2792	1.25580	0.627901	−	0.778293i	$-0.283914\pi$
$67$	10.2792	1.25580	0.627901	+	0.778293i	$0.283914\pi$
$68$	3.57578	0.433627
$69$	1.77599	0.213804
$70$	0.685668	0.0819530
$71$	11.3216	1.34363	0.671815	−	0.740719i	$-0.265515\pi$
$71$	11.3216	1.34363	0.671815	+	0.740719i	$0.265515\pi$
$72$	−3.03279	−0.357418
$73$	2.13860	0.250304	0.125152	−	0.992138i	$-0.460058\pi$
$73$	2.13860	0.250304	0.125152	+	0.992138i	$0.460058\pi$
$74$	−6.25420	−0.727035
$75$	11.9649	1.38159
$76$	−7.77991	−0.892417
$77$	−9.80438	−1.11731
$78$	9.03159	1.02263
$79$	2.66262	0.299569	0.149784	−	0.988719i	$-0.452142\pi$
$79$	2.66262	0.299569	0.149784	+	0.988719i	$0.452142\pi$
$80$	0.358646	0.0400978
$81$	−8.90054	−0.988949
$82$	2.75424	0.304155
$83$	16.1458	1.77223	0.886115	−	0.463466i	$-0.153395\pi$
$83$	16.1458	1.77223	0.886115	+	0.463466i	$0.153395\pi$
$84$	4.69577	0.512351
$85$	1.28244	0.139100
$86$	−10.5331	−1.13581
$87$	−0.811252	−0.0869753
$88$	−5.12829	−0.546677
$89$	6.65673	0.705612	0.352806	−	0.935697i	$-0.385228\pi$
$89$	6.65673	0.705612	0.352806	+	0.935697i	$0.385228\pi$
$90$	−1.08770	−0.114654
$91$	−7.02996	−0.736940
$92$	−0.723070	−0.0753853
$93$	−19.0116	−1.97141
$94$	−1.93642	−0.199726
$95$	−2.79023	−0.286272
$96$	2.45617	0.250682
$97$	−15.5223	−1.57605	−0.788025	−	0.615644i	$-0.788896\pi$
$97$	−15.5223	−1.57605	−0.788025	+	0.615644i	$0.788896\pi$
$98$	3.34493	0.337889
$99$	15.5530	1.56314
$100$	−4.87137	−0.487137
$101$	−17.1278	−1.70428	−0.852142	−	0.523310i	$-0.824697\pi$
$101$	−17.1278	−1.70428	−0.852142	+	0.523310i	$0.824697\pi$
$102$	8.78273	0.869620
$103$	0.0678555	0.00668600	0.00334300	−	0.999994i	$-0.498936\pi$
$103$	0.0678555	0.00668600	0.00334300	+	0.999994i	$0.498936\pi$
$104$	−3.67709	−0.360569
$105$	1.68412	0.164353
$106$	8.76896	0.851717
$107$	−9.95374	−0.962264	−0.481132	−	0.876648i	$-0.659774\pi$
$107$	−9.95374	−0.962264	−0.481132	+	0.876648i	$0.659774\pi$
$108$	−0.0805476	−0.00775069
$109$	−12.1877	−1.16737	−0.583685	−	0.811980i	$-0.698390\pi$
$109$	−12.1877	−1.16737	−0.583685	+	0.811980i	$0.698390\pi$
$110$	−1.83924	−0.175365
$111$	−15.3614	−1.45804
$112$	−1.91182	−0.180650
$113$	0.0565757	0.00532220	0.00266110	−	0.999996i	$-0.499153\pi$
$113$	0.0565757	0.00532220	0.00266110	+	0.999996i	$0.499153\pi$
$114$	−19.1088	−1.78971
$115$	−0.259326	−0.0241823
$116$	0.330291	0.0306667
$117$	11.1519	1.03099
$118$	−4.14217	−0.381318
$119$	−6.83626	−0.626679
$120$	0.880897	0.0804145
$121$	15.2993	1.39085
$122$	−13.8353	−1.25259
$123$	6.76490	0.609971
$124$	7.74033	0.695103
$125$	−3.54033	−0.316656
$126$	5.79817	0.516542
$127$	1.91398	0.169838	0.0849190	−	0.996388i	$-0.472937\pi$
$127$	1.91398	0.169838	0.0849190	+	0.996388i	$0.472937\pi$
$128$	−1.00000	−0.0883883
$129$	−25.8712	−2.27783
$130$	−1.31877	−0.115664
$131$	−5.97806	−0.522305	−0.261153	−	0.965297i	$-0.584103\pi$
$131$	−5.97806	−0.522305	−0.261153	+	0.965297i	$0.584103\pi$
$132$	−12.5960	−1.09634
$133$	14.8738	1.28972
$134$	−10.2792	−0.887986
$135$	−0.0288880	−0.00248629
$136$	−3.57578	−0.306620
$137$	−8.64368	−0.738480	−0.369240	−	0.929334i	$-0.620382\pi$
$137$	−8.64368	−0.738480	−0.369240	+	0.929334i	$0.620382\pi$
$138$	−1.77599	−0.151182
$139$	−6.52529	−0.553468	−0.276734	−	0.960947i	$-0.589252\pi$
$139$	−6.52529	−0.553468	−0.276734	+	0.960947i	$0.589252\pi$
$140$	−0.685668	−0.0579495
$141$	−4.75618	−0.400543
$142$	−11.3216	−0.950090
$143$	18.8572	1.57692
$144$	3.03279	0.252733
$145$	0.118457	0.00983735
$146$	−2.13860	−0.176992
$147$	8.21573	0.677622
$148$	6.25420	0.514092
$149$	−8.17522	−0.669740	−0.334870	−	0.942264i	$-0.608692\pi$
$149$	−8.17522	−0.669740	−0.334870	+	0.942264i	$0.608692\pi$
$150$	−11.9649	−0.976934
$151$	−8.63009	−0.702307	−0.351153	−	0.936318i	$-0.614210\pi$
$151$	−8.63009	−0.702307	−0.351153	+	0.936318i	$0.614210\pi$
$152$	7.77991	0.631034
$153$	10.8446	0.876734
$154$	9.80438	0.790060
$155$	2.77604	0.222977
$156$	−9.03159	−0.723106
$157$	−0.895203	−0.0714450	−0.0357225	−	0.999362i	$-0.511373\pi$
$157$	−0.895203	−0.0714450	−0.0357225	+	0.999362i	$0.511373\pi$
$158$	−2.66262	−0.211827
$159$	21.5381	1.70808
$160$	−0.358646	−0.0283534
$161$	1.38238	0.108947
$162$	8.90054	0.699293
$163$	12.6311	0.989341	0.494671	−	0.869081i	$-0.335289\pi$
$163$	12.6311	0.989341	0.494671	+	0.869081i	$0.335289\pi$
$164$	−2.75424	−0.215070
$165$	−4.51749	−0.351686
$166$	−16.1458	−1.25316
$167$	−8.71988	−0.674764	−0.337382	−	0.941368i	$-0.609541\pi$
$167$	−8.71988	−0.674764	−0.337382	+	0.941368i	$0.609541\pi$
$168$	−4.69577	−0.362287
$169$	0.521025	0.0400789
$170$	−1.28244	−0.0983585
$171$	−23.5949	−1.80435
$172$	10.5331	0.803142
$173$	4.33803	0.329815	0.164907	−	0.986309i	$-0.447268\pi$
$173$	4.33803	0.329815	0.164907	+	0.986309i	$0.447268\pi$
$174$	0.811252	0.0615008
$175$	9.31321	0.704013
$176$	5.12829	0.386559
$177$	−10.1739	−0.764717
$178$	−6.65673	−0.498943
$179$	−1.50661	−0.112609	−0.0563047	−	0.998414i	$-0.517932\pi$
$179$	−1.50661	−0.112609	−0.0563047	+	0.998414i	$0.517932\pi$
$180$	1.08770	0.0810723
$181$	8.54956	0.635484	0.317742	−	0.948177i	$-0.397075\pi$
$181$	8.54956	0.635484	0.317742	+	0.948177i	$0.397075\pi$
$182$	7.02996	0.521095
$183$	−33.9818	−2.51201
$184$	0.723070	0.0533055
$185$	2.24304	0.164912
$186$	19.0116	1.39400
$187$	18.3376	1.34098
$188$	1.93642	0.141228
$189$	0.153993	0.0112013
$190$	2.79023	0.202425
$191$	−3.47248	−0.251260	−0.125630	−	0.992077i	$-0.540095\pi$
$191$	−3.47248	−0.251260	−0.125630	+	0.992077i	$0.540095\pi$
$192$	−2.45617	−0.177259
$193$	−25.1942	−1.81352	−0.906758	−	0.421652i	$-0.861450\pi$
$193$	−25.1942	−1.81352	−0.906758	+	0.421652i	$0.861450\pi$
$194$	15.5223	1.11444
$195$	−3.23914	−0.231960
$196$	−3.34493	−0.238923
$197$	19.7918	1.41011	0.705055	−	0.709152i	$-0.250922\pi$
$197$	19.7918	1.41011	0.705055	+	0.709152i	$0.250922\pi$
$198$	−15.5530	−1.10531
$199$	0.695954	0.0493349	0.0246674	−	0.999696i	$-0.492147\pi$
$199$	0.695954	0.0493349	0.0246674	+	0.999696i	$0.492147\pi$
$200$	4.87137	0.344458
$201$	−25.2475	−1.78082
$202$	17.1278	1.20511
$203$	−0.631458	−0.0443197
$204$	−8.78273	−0.614914
$205$	−0.987798	−0.0689908
$206$	−0.0678555	−0.00472772
$207$	−2.19292	−0.152419
$208$	3.67709	0.254961
$209$	−39.8976	−2.75978
$210$	−1.68412	−0.116215
$211$	12.5891	0.866671	0.433336	−	0.901233i	$-0.357336\pi$
$211$	12.5891	0.866671	0.433336	+	0.901233i	$0.357336\pi$
$212$	−8.76896	−0.602255
$213$	−27.8079	−1.90537
$214$	9.95374	0.680423
$215$	3.77766	0.257634
$216$	0.0805476	0.00548057
$217$	−14.7982	−1.00456
$218$	12.1877	0.825455
$219$	−5.25277	−0.354949
$220$	1.83924	0.124001
$221$	13.1485	0.884462
$222$	15.3614	1.03099
$223$	18.6690	1.25017	0.625083	−	0.780558i	$-0.285065\pi$
$223$	18.6690	1.25017	0.625083	+	0.780558i	$0.285065\pi$
$224$	1.91182	0.127739
$225$	−14.7739	−0.984925
$226$	−0.0565757	−0.00376336
$227$	−6.28244	−0.416980	−0.208490	−	0.978024i	$-0.566855\pi$
$227$	−6.28244	−0.416980	−0.208490	+	0.978024i	$0.566855\pi$
$228$	19.1088	1.26551
$229$	11.4404	0.756003	0.378001	−	0.925805i	$-0.376611\pi$
$229$	11.4404	0.756003	0.378001	+	0.925805i	$0.376611\pi$
$230$	0.259326	0.0170995
$231$	24.0813	1.58443
$232$	−0.330291	−0.0216847
$233$	24.7109	1.61886	0.809432	−	0.587214i	$-0.199775\pi$
$233$	24.7109	1.61886	0.809432	+	0.587214i	$0.199775\pi$
$234$	−11.1519	−0.729021
$235$	0.694489	0.0453035
$236$	4.14217	0.269632
$237$	−6.53987	−0.424810
$238$	6.83626	0.443129
$239$	−11.3472	−0.733988	−0.366994	−	0.930223i	$-0.619613\pi$
$239$	−11.3472	−0.733988	−0.366994	+	0.930223i	$0.619613\pi$
$240$	−0.880897	−0.0568616
$241$	−20.3946	−1.31373	−0.656866	−	0.754007i	$-0.728118\pi$
$241$	−20.3946	−1.31373	−0.656866	+	0.754007i	$0.728118\pi$
$242$	−15.2993	−0.983477
$243$	22.1029	1.41790
$244$	13.8353	0.885712
$245$	−1.19964	−0.0766425
$246$	−6.76490	−0.431314
$247$	−28.6075	−1.82025
$248$	−7.74033	−0.491512
$249$	−39.6568	−2.51315
$250$	3.54033	0.223910
$251$	−3.23769	−0.204361	−0.102180	−	0.994766i	$-0.532582\pi$
$251$	−3.23769	−0.204361	−0.102180	+	0.994766i	$0.532582\pi$
$252$	−5.79817	−0.365250
$253$	−3.70811	−0.233127
$254$	−1.91398	−0.120094
$255$	−3.14989	−0.197254
$256$	1.00000	0.0625000
$257$	−23.2428	−1.44985	−0.724924	−	0.688829i	$-0.758125\pi$
$257$	−23.2428	−1.44985	−0.724924	+	0.688829i	$0.758125\pi$
$258$	25.8712	1.61067
$259$	−11.9569	−0.742967
$260$	1.31877	0.0817869
$261$	1.00170	0.0620039
$262$	5.97806	0.369326
$263$	15.4903	0.955174	0.477587	−	0.878584i	$-0.341511\pi$
$263$	15.4903	0.955174	0.477587	+	0.878584i	$0.341511\pi$
$264$	12.5960	0.775228
$265$	−3.14495	−0.193193
$266$	−14.8738	−0.911973
$267$	−16.3501	−1.00061
$268$	10.2792	0.627901
$269$	−2.11017	−0.128659	−0.0643297	−	0.997929i	$-0.520491\pi$
$269$	−2.11017	−0.128659	−0.0643297	+	0.997929i	$0.520491\pi$
$270$	0.0288880	0.00175807
$271$	26.5888	1.61515	0.807577	−	0.589762i	$-0.200778\pi$
$271$	26.5888	1.61515	0.807577	+	0.589762i	$0.200778\pi$
$272$	3.57578	0.216813
$273$	17.2668	1.04503
$274$	8.64368	0.522184
$275$	−24.9818	−1.50646
$276$	1.77599	0.106902
$277$	−13.0767	−0.785704	−0.392852	−	0.919602i	$-0.628512\pi$
$277$	−13.0767	−0.785704	−0.392852	+	0.919602i	$0.628512\pi$
$278$	6.52529	0.391361
$279$	23.4748	1.40540
$280$	0.685668	0.0409765
$281$	16.5235	0.985707	0.492854	−	0.870112i	$-0.335954\pi$
$281$	16.5235	0.985707	0.492854	+	0.870112i	$0.335954\pi$
$282$	4.75618	0.283227
$283$	23.5299	1.39871	0.699353	−	0.714777i	$-0.253472\pi$
$283$	23.5299	1.39871	0.699353	+	0.714777i	$0.253472\pi$
$284$	11.3216	0.671815
$285$	6.85330	0.405955
$286$	−18.8572	−1.11505
$287$	5.26563	0.310820
$288$	−3.03279	−0.178709
$289$	−4.21381	−0.247871
$290$	−0.118457	−0.00695606
$291$	38.1254	2.23495
$292$	2.13860	0.125152
$293$	10.6440	0.621828	0.310914	−	0.950438i	$-0.399365\pi$
$293$	10.6440	0.621828	0.310914	+	0.950438i	$0.399365\pi$
$294$	−8.21573	−0.479151
$295$	1.48557	0.0864934
$296$	−6.25420	−0.363518
$297$	−0.413071	−0.0239688
$298$	8.17522	0.473578
$299$	−2.65880	−0.153762
$300$	11.9649	0.690796
$301$	−20.1375	−1.16070
$302$	8.63009	0.496606
$303$	42.0690	2.41680
$304$	−7.77991	−0.446209
$305$	4.96196	0.284121
$306$	−10.8446	−0.619944
$307$	−22.2739	−1.27124	−0.635619	−	0.772003i	$-0.719255\pi$
$307$	−22.2739	−1.27124	−0.635619	+	0.772003i	$0.719255\pi$
$308$	−9.80438	−0.558657
$309$	−0.166665	−0.00948124
$310$	−2.77604	−0.157668
$311$	−34.2323	−1.94114	−0.970568	−	0.240828i	$-0.922581\pi$
$311$	−34.2323	−1.94114	−0.970568	+	0.240828i	$0.922581\pi$
$312$	9.03159	0.511313
$313$	−10.5955	−0.598896	−0.299448	−	0.954113i	$-0.596802\pi$
$313$	−10.5955	−0.598896	−0.299448	+	0.954113i	$0.596802\pi$
$314$	0.895203	0.0505192
$315$	−2.07949	−0.117166
$316$	2.66262	0.149784
$317$	−3.74670	−0.210436	−0.105218	−	0.994449i	$-0.533554\pi$
$317$	−3.74670	−0.210436	−0.105218	+	0.994449i	$0.533554\pi$
$318$	−21.5381	−1.20780
$319$	1.69383	0.0948360
$320$	0.358646	0.0200489
$321$	24.4481	1.36456
$322$	−1.38238	−0.0770372
$323$	−27.8192	−1.54790
$324$	−8.90054	−0.494475
$325$	−17.9125	−0.993607
$326$	−12.6311	−0.699570
$327$	29.9351	1.65542
$328$	2.75424	0.152078
$329$	−3.70209	−0.204103
$330$	4.51749	0.248680
$331$	28.1086	1.54499	0.772494	−	0.635023i	$-0.219009\pi$
$331$	28.1086	1.54499	0.772494	+	0.635023i	$0.219009\pi$
$332$	16.1458	0.886115
$333$	18.9677	1.03942
$334$	8.71988	0.477130
$335$	3.68658	0.201420
$336$	4.69577	0.256176
$337$	27.0540	1.47373	0.736863	−	0.676042i	$-0.236306\pi$
$337$	27.0540	1.47373	0.736863	+	0.676042i	$0.236306\pi$
$338$	−0.521025	−0.0283400
$339$	−0.138960	−0.00754726
$340$	1.28244	0.0695500
$341$	39.6946	2.14959
$342$	23.5949	1.27586
$343$	19.7777	1.06789
$344$	−10.5331	−0.567907
$345$	0.636950	0.0342923
$346$	−4.33803	−0.233214
$347$	14.3269	0.769109	0.384555	−	0.923102i	$-0.374355\pi$
$347$	14.3269	0.769109	0.384555	+	0.923102i	$0.374355\pi$
$348$	−0.811252	−0.0434877
$349$	−28.2450	−1.51192	−0.755959	−	0.654618i	$-0.772829\pi$
$349$	−28.2450	−1.51192	−0.755959	+	0.654618i	$0.772829\pi$
$350$	−9.31321	−0.497812
$351$	−0.296181	−0.0158090
$352$	−5.12829	−0.273339
$353$	29.7589	1.58391	0.791954	−	0.610581i	$-0.209064\pi$
$353$	29.7589	1.58391	0.791954	+	0.610581i	$0.209064\pi$
$354$	10.1739	0.540736
$355$	4.06046	0.215507
$356$	6.65673	0.352806
$357$	16.7910	0.888676
$358$	1.50661	0.0796269
$359$	−7.83656	−0.413598	−0.206799	−	0.978383i	$-0.566305\pi$
$359$	−7.83656	−0.413598	−0.206799	+	0.978383i	$0.566305\pi$
$360$	−1.08770	−0.0573268
$361$	41.5271	2.18563
$362$	−8.54956	−0.449355
$363$	−37.5778	−1.97232
$364$	−7.02996	−0.368470
$365$	0.767000	0.0401466
$366$	33.9818	1.77626
$367$	−11.8807	−0.620170	−0.310085	−	0.950709i	$-0.600357\pi$
$367$	−11.8807	−0.620170	−0.310085	+	0.950709i	$0.600357\pi$
$368$	−0.723070	−0.0376926
$369$	−8.35305	−0.434842
$370$	−2.24304	−0.116610
$371$	16.7647	0.870381
$372$	−19.0116	−0.985706
$373$	16.2587	0.841845	0.420923	−	0.907097i	$-0.361706\pi$
$373$	16.2587	0.841845	0.420923	+	0.907097i	$0.361706\pi$
$374$	−18.3376	−0.948215
$375$	8.69566	0.449042
$376$	−1.93642	−0.0998632
$377$	1.21451	0.0625505
$378$	−0.153993	−0.00792053
$379$	−30.0310	−1.54259	−0.771294	−	0.636479i	$-0.780390\pi$
$379$	−30.0310	−1.54259	−0.771294	+	0.636479i	$0.780390\pi$
$380$	−2.79023	−0.143136
$381$	−4.70106	−0.240843
$382$	3.47248	0.177667
$383$	6.22357	0.318010	0.159005	−	0.987278i	$-0.449171\pi$
$383$	6.22357	0.318010	0.159005	+	0.987278i	$0.449171\pi$
$384$	2.45617	0.125341
$385$	−3.51630	−0.179207
$386$	25.1942	1.28235
$387$	31.9447	1.62384
$388$	−15.5223	−0.788025
$389$	−27.8418	−1.41164	−0.705818	−	0.708393i	$-0.749420\pi$
$389$	−27.8418	−1.41164	−0.705818	+	0.708393i	$0.749420\pi$
$390$	3.23914	0.164020
$391$	−2.58554	−0.130756
$392$	3.34493	0.168944
$393$	14.6832	0.740667
$394$	−19.7918	−0.997099
$395$	0.954939	0.0480482
$396$	15.5530	0.781569
$397$	−5.78872	−0.290527	−0.145264	−	0.989393i	$-0.546403\pi$
$397$	−5.78872	−0.290527	−0.145264	+	0.989393i	$0.546403\pi$
$398$	−0.695954	−0.0348850
$399$	−36.5327	−1.82892
$400$	−4.87137	−0.243569
$401$	17.4983	0.873821	0.436911	−	0.899505i	$-0.356073\pi$
$401$	17.4983	0.873821	0.436911	+	0.899505i	$0.356073\pi$
$402$	25.2475	1.25923
$403$	28.4619	1.41779
$404$	−17.1278	−0.852142
$405$	−3.19214	−0.158619
$406$	0.631458	0.0313387
$407$	32.0733	1.58981
$408$	8.78273	0.434810
$409$	29.7803	1.47254	0.736270	−	0.676687i	$-0.236585\pi$
$409$	29.7803	1.47254	0.736270	+	0.676687i	$0.236585\pi$
$410$	0.987798	0.0487839
$411$	21.2304	1.04722
$412$	0.0678555	0.00334300
$413$	−7.91910	−0.389674
$414$	2.19292	0.107776
$415$	5.79062	0.284250
$416$	−3.67709	−0.180284
$417$	16.0273	0.784858
$418$	39.8976	1.95146
$419$	20.3335	0.993356	0.496678	−	0.867935i	$-0.334553\pi$
$419$	20.3335	0.993356	0.496678	+	0.867935i	$0.334553\pi$
$420$	1.68412	0.0821767
$421$	−22.2050	−1.08220	−0.541102	−	0.840957i	$-0.681993\pi$
$421$	−22.2050	−1.08220	−0.541102	+	0.840957i	$0.681993\pi$
$422$	−12.5891	−0.612829
$423$	5.87276	0.285543
$424$	8.76896	0.425859
$425$	−17.4189	−0.844943
$426$	27.8079	1.34730
$427$	−26.4506	−1.28003
$428$	−9.95374	−0.481132
$429$	−46.3166	−2.23618
$430$	−3.77766	−0.182175
$431$	−30.6666	−1.47716	−0.738579	−	0.674167i	$-0.764503\pi$
$431$	−30.6666	−1.47716	−0.738579	+	0.674167i	$0.764503\pi$
$432$	−0.0805476	−0.00387535
$433$	−21.6081	−1.03842	−0.519210	−	0.854646i	$-0.673774\pi$
$433$	−21.6081	−1.03842	−0.519210	+	0.854646i	$0.673774\pi$
$434$	14.7982	0.710334
$435$	−0.290952	−0.0139501
$436$	−12.1877	−0.583685
$437$	5.62542	0.269101
$438$	5.25277	0.250987
$439$	0.409379	0.0195386	0.00976930	−	0.999952i	$-0.496890\pi$
$439$	0.409379	0.0195386	0.00976930	+	0.999952i	$0.496890\pi$
$440$	−1.83924	−0.0876823
$441$	−10.1445	−0.483070
$442$	−13.1485	−0.625409
$443$	−13.5597	−0.644241	−0.322121	−	0.946699i	$-0.604396\pi$
$443$	−13.5597	−0.644241	−0.322121	+	0.946699i	$0.604396\pi$
$444$	−15.3614	−0.729020
$445$	2.38741	0.113174
$446$	−18.6690	−0.884001
$447$	20.0798	0.949740
$448$	−1.91182	−0.0903252
$449$	3.71919	0.175519	0.0877597	−	0.996142i	$-0.472029\pi$
$449$	3.71919	0.175519	0.0877597	+	0.996142i	$0.472029\pi$
$450$	14.7739	0.696447
$451$	−14.1245	−0.665099
$452$	0.0565757	0.00266110
$453$	21.1970	0.995923
$454$	6.28244	0.294849
$455$	−2.52127	−0.118199
$456$	−19.1088	−0.894853
$457$	20.8371	0.974720	0.487360	−	0.873201i	$-0.337960\pi$
$457$	20.8371	0.974720	0.487360	+	0.873201i	$0.337960\pi$
$458$	−11.4404	−0.534575
$459$	−0.288020	−0.0134436
$460$	−0.259326	−0.0120911
$461$	−22.4406	−1.04516	−0.522582	−	0.852589i	$-0.675031\pi$
$461$	−22.4406	−1.04516	−0.522582	+	0.852589i	$0.675031\pi$
$462$	−24.0813	−1.12036
$463$	−18.5063	−0.860062	−0.430031	−	0.902814i	$-0.641497\pi$
$463$	−18.5063	−0.860062	−0.430031	+	0.902814i	$0.641497\pi$
$464$	0.330291	0.0153334
$465$	−6.81844	−0.316197
$466$	−24.7109	−1.14471
$467$	29.4384	1.36225	0.681124	−	0.732168i	$-0.261492\pi$
$467$	29.4384	1.36225	0.681124	+	0.732168i	$0.261492\pi$
$468$	11.1519	0.515495
$469$	−19.6520	−0.907444
$470$	−0.694489	−0.0320344
$471$	2.19877	0.101314
$472$	−4.14217	−0.190659
$473$	54.0168	2.48369
$474$	6.53987	0.300386
$475$	37.8989	1.73892
$476$	−6.83626	−0.313339
$477$	−26.5945	−1.21768
$478$	11.3472	0.519008
$479$	−15.8363	−0.723581	−0.361790	−	0.932259i	$-0.617834\pi$
$479$	−15.8363	−0.723581	−0.361790	+	0.932259i	$0.617834\pi$
$480$	0.880897	0.0402073
$481$	22.9973	1.04859
$482$	20.3946	0.928949
$483$	−3.39538	−0.154495
$484$	15.2993	0.695423
$485$	−5.56700	−0.252785
$486$	−22.1029	−1.00261
$487$	−22.4529	−1.01744	−0.508719	−	0.860933i	$-0.669881\pi$
$487$	−22.4529	−1.01744	−0.508719	+	0.860933i	$0.669881\pi$
$488$	−13.8353	−0.626293
$489$	−31.0241	−1.40296
$490$	1.19964	0.0541944
$491$	−0.215708	−0.00973478	−0.00486739	−	0.999988i	$-0.501549\pi$
$491$	−0.215708	−0.00973478	−0.00486739	+	0.999988i	$0.501549\pi$
$492$	6.76490	0.304985
$493$	1.18105	0.0531917
$494$	28.6075	1.28711
$495$	5.57803	0.250714
$496$	7.74033	0.347551
$497$	−21.6450	−0.970910
$498$	39.6568	1.77707
$499$	15.1384	0.677687	0.338843	−	0.940843i	$-0.389964\pi$
$499$	15.1384	0.677687	0.338843	+	0.940843i	$0.389964\pi$
$500$	−3.54033	−0.158328
$501$	21.4175	0.956865
$502$	3.23769	0.144505
$503$	16.6980	0.744528	0.372264	−	0.928127i	$-0.378582\pi$
$503$	16.6980	0.744528	0.372264	+	0.928127i	$0.378582\pi$
$504$	5.79817	0.258271
$505$	−6.14283	−0.273352
$506$	3.70811	0.164846
$507$	−1.27973	−0.0568348
$508$	1.91398	0.0849190
$509$	33.9377	1.50426	0.752132	−	0.659013i	$-0.229026\pi$
$509$	33.9377	1.50426	0.752132	+	0.659013i	$0.229026\pi$
$510$	3.14989	0.139480
$511$	−4.08863	−0.180870
$512$	−1.00000	−0.0441942
$513$	0.626653	0.0276674
$514$	23.2428	1.02520
$515$	0.0243361	0.00107238
$516$	−25.8712	−1.13891
$517$	9.93051	0.436743
$518$	11.9569	0.525357
$519$	−10.6550	−0.467701
$520$	−1.31877	−0.0578321
$521$	29.4692	1.29107	0.645534	−	0.763731i	$-0.276635\pi$
$521$	29.4692	1.29107	0.645534	+	0.763731i	$0.276635\pi$
$522$	−1.00170	−0.0438434
$523$	35.0301	1.53176	0.765881	−	0.642983i	$-0.222303\pi$
$523$	35.0301	1.53176	0.765881	+	0.642983i	$0.222303\pi$
$524$	−5.97806	−0.261153
$525$	−22.8749	−0.998341
$526$	−15.4903	−0.675410
$527$	27.6777	1.20566
$528$	−12.5960	−0.548169
$529$	−22.4772	−0.977268
$530$	3.14495	0.136608
$531$	12.5624	0.545160
$532$	14.8738	0.644862
$533$	−10.1276	−0.438676
$534$	16.3501	0.707537
$535$	−3.56987	−0.154339
$536$	−10.2792	−0.443993
$537$	3.70050	0.159688
$538$	2.11017	0.0909759
$539$	−17.1537	−0.738864
$540$	−0.0288880	−0.00124314
$541$	−21.7312	−0.934297	−0.467149	−	0.884179i	$-0.654719\pi$
$541$	−21.7312	−0.934297	−0.467149	+	0.884179i	$0.654719\pi$
$542$	−26.5888	−1.14209
$543$	−20.9992	−0.901162
$544$	−3.57578	−0.153310
$545$	−4.37107	−0.187236
$546$	−17.2668	−0.738951
$547$	10.9312	0.467383	0.233692	−	0.972311i	$-0.424919\pi$
$547$	10.9312	0.467383	0.233692	+	0.972311i	$0.424919\pi$
$548$	−8.64368	−0.369240
$549$	41.9595	1.79079
$550$	24.9818	1.06523
$551$	−2.56963	−0.109470
$552$	−1.77599	−0.0755910
$553$	−5.09047	−0.216469
$554$	13.0767	0.555577
$555$	−5.50930	−0.233857
$556$	−6.52529	−0.276734
$557$	41.0887	1.74098	0.870492	−	0.492183i	$-0.163801\pi$
$557$	41.0887	1.74098	0.870492	+	0.492183i	$0.163801\pi$
$558$	−23.4748	−0.993769
$559$	38.7312	1.63816
$560$	−0.685668	−0.0289748
$561$	−45.0404	−1.90161
$562$	−16.5235	−0.697000
$563$	30.3308	1.27829	0.639145	−	0.769086i	$-0.279288\pi$
$563$	30.3308	1.27829	0.639145	+	0.769086i	$0.279288\pi$
$564$	−4.75618	−0.200271
$565$	0.0202906	0.000853634 0
$566$	−23.5299	−0.989034
$567$	17.0163	0.714616
$568$	−11.3216	−0.475045
$569$	35.7618	1.49921	0.749605	−	0.661885i	$-0.230243\pi$
$569$	35.7618	1.49921	0.749605	+	0.661885i	$0.230243\pi$
$570$	−6.85330	−0.287053
$571$	33.2767	1.39259	0.696293	−	0.717757i	$-0.254831\pi$
$571$	33.2767	1.39259	0.696293	+	0.717757i	$0.254831\pi$
$572$	18.8572	0.788459
$573$	8.52901	0.356304
$574$	−5.26563	−0.219783
$575$	3.52235	0.146892
$576$	3.03279	0.126366
$577$	−12.5284	−0.521563	−0.260782	−	0.965398i	$-0.583980\pi$
$577$	−12.5284	−0.521563	−0.260782	+	0.965398i	$0.583980\pi$
$578$	4.21381	0.175272
$579$	61.8813	2.57170
$580$	0.118457	0.00491868
$581$	−30.8679	−1.28062
$582$	−38.1254	−1.58035
$583$	−44.9698	−1.86246
$584$	−2.13860	−0.0884958
$585$	3.99957	0.165362
$586$	−10.6440	−0.439699
$587$	1.98145	0.0817833	0.0408917	−	0.999164i	$-0.486980\pi$
$587$	1.98145	0.0817833	0.0408917	+	0.999164i	$0.486980\pi$
$588$	8.21573	0.338811
$589$	−60.2191	−2.48129
$590$	−1.48557	−0.0611601
$591$	−48.6122	−1.99964
$592$	6.25420	0.257046
$593$	3.55257	0.145886	0.0729432	−	0.997336i	$-0.476761\pi$
$593$	3.55257	0.145886	0.0729432	+	0.997336i	$0.476761\pi$
$594$	0.413071	0.0169485
$595$	−2.45180	−0.100514
$596$	−8.17522	−0.334870
$597$	−1.70939	−0.0699605
$598$	2.65880	0.108726
$599$	−7.42041	−0.303190	−0.151595	−	0.988443i	$-0.548441\pi$
$599$	−7.42041	−0.303190	−0.151595	+	0.988443i	$0.548441\pi$
$600$	−11.9649	−0.488467
$601$	−38.9084	−1.58711	−0.793553	−	0.608501i	$-0.791771\pi$
$601$	−38.9084	−1.58711	−0.793553	+	0.608501i	$0.791771\pi$
$602$	20.1375	0.820741
$603$	31.1746	1.26953
$604$	−8.63009	−0.351153
$605$	5.48704	0.223080
$606$	−42.0690	−1.70894
$607$	−23.2176	−0.942373	−0.471187	−	0.882033i	$-0.656174\pi$
$607$	−23.2176	−0.942373	−0.471187	+	0.882033i	$0.656174\pi$
$608$	7.77991	0.315517
$609$	1.55097	0.0628485
$610$	−4.96196	−0.200904
$611$	7.12040	0.288060
$612$	10.8446	0.438367
$613$	8.72008	0.352201	0.176100	−	0.984372i	$-0.443652\pi$
$613$	8.72008	0.352201	0.176100	+	0.984372i	$0.443652\pi$
$614$	22.2739	0.898901
$615$	2.42620	0.0978340
$616$	9.80438	0.395030
$617$	−3.00235	−0.120870	−0.0604351	−	0.998172i	$-0.519249\pi$
$617$	−3.00235	−0.120870	−0.0604351	+	0.998172i	$0.519249\pi$
$618$	0.166665	0.00670425
$619$	38.8483	1.56145	0.780723	−	0.624877i	$-0.214851\pi$
$619$	38.8483	1.56145	0.780723	+	0.624877i	$0.214851\pi$
$620$	2.77604	0.111488
$621$	0.0582415	0.00233715
$622$	34.2323	1.37259
$623$	−12.7265	−0.509876
$624$	−9.03159	−0.361553
$625$	23.0871	0.923486
$626$	10.5955	0.423483
$627$	97.9955	3.91356
$628$	−0.895203	−0.0357225
$629$	22.3636	0.891696
$630$	2.07949	0.0828488
$631$	16.8132	0.669321	0.334661	−	0.942339i	$-0.391378\pi$
$631$	16.8132	0.669321	0.334661	+	0.942339i	$0.391378\pi$
$632$	−2.66262	−0.105914
$633$	−30.9211	−1.22900
$634$	3.74670	0.148801
$635$	0.686440	0.0272406
$636$	21.5381	0.854041
$637$	−12.2996	−0.487328
$638$	−1.69383	−0.0670592
$639$	34.3362	1.35832
$640$	−0.358646	−0.0141767
$641$	24.6632	0.974137	0.487068	−	0.873364i	$-0.338066\pi$
$641$	24.6632	0.974137	0.487068	+	0.873364i	$0.338066\pi$
$642$	−24.4481	−0.964890
$643$	31.4955	1.24206	0.621030	−	0.783787i	$-0.286714\pi$
$643$	31.4955	1.24206	0.621030	+	0.783787i	$0.286714\pi$
$644$	1.38238	0.0544735
$645$	−9.27858	−0.365344
$646$	27.8192	1.09453
$647$	3.61562	0.142144	0.0710722	−	0.997471i	$-0.477358\pi$
$647$	3.61562	0.142144	0.0710722	+	0.997471i	$0.477358\pi$
$648$	8.90054	0.349646
$649$	21.2422	0.833831
$650$	17.9125	0.702586
$651$	36.3469	1.42455
$652$	12.6311	0.494671
$653$	32.6830	1.27898	0.639492	−	0.768797i	$-0.279145\pi$
$653$	32.6830	1.27898	0.639492	+	0.768797i	$0.279145\pi$
$654$	−29.9351	−1.17056
$655$	−2.14401	−0.0837733
$656$	−2.75424	−0.107535
$657$	6.48593	0.253040
$658$	3.70209	0.144323
$659$	−6.75197	−0.263020	−0.131510	−	0.991315i	$-0.541982\pi$
$659$	−6.75197	−0.263020	−0.131510	+	0.991315i	$0.541982\pi$
$660$	−4.51749	−0.175843
$661$	26.3807	1.02609	0.513044	−	0.858362i	$-0.328518\pi$
$661$	26.3807	1.02609	0.513044	+	0.858362i	$0.328518\pi$
$662$	−28.1086	−1.09247
$663$	−32.2949	−1.25423
$664$	−16.1458	−0.626578
$665$	5.33444	0.206861
$666$	−18.9677	−0.734983
$667$	−0.238823	−0.00924728
$668$	−8.71988	−0.337382
$669$	−45.8542	−1.77283
$670$	−3.68658	−0.142425
$671$	70.9512	2.73904
$672$	−4.69577	−0.181143
$673$	11.5529	0.445330	0.222665	−	0.974895i	$-0.428524\pi$
$673$	11.5529	0.445330	0.222665	+	0.974895i	$0.428524\pi$
$674$	−27.0540	−1.04208
$675$	0.392377	0.0151026
$676$	0.521025	0.0200394
$677$	26.6911	1.02582	0.512910	−	0.858442i	$-0.328567\pi$
$677$	26.6911	1.02582	0.512910	+	0.858442i	$0.328567\pi$
$678$	0.138960	0.00533672
$679$	29.6759	1.13886
$680$	−1.28244	−0.0491793
$681$	15.4308	0.591308
$682$	−39.6946	−1.51999
$683$	−35.6474	−1.36401	−0.682005	−	0.731347i	$-0.738892\pi$
$683$	−35.6474	−1.36401	−0.682005	+	0.731347i	$0.738892\pi$
$684$	−23.5949	−0.902173
$685$	−3.10002	−0.118446
$686$	−19.7777	−0.755116
$687$	−28.0996	−1.07207
$688$	10.5331	0.401571
$689$	−32.2443	−1.22841
$690$	−0.636950	−0.0242483
$691$	−38.6427	−1.47004	−0.735018	−	0.678048i	$-0.762826\pi$
$691$	−38.6427	−1.47004	−0.735018	+	0.678048i	$0.762826\pi$
$692$	4.33803	0.164907
$693$	−29.7347	−1.12953
$694$	−14.3269	−0.543843
$695$	−2.34027	−0.0887715
$696$	0.811252	0.0307504
$697$	−9.84856	−0.373041
$698$	28.2450	1.06909
$699$	−60.6942	−2.29567
$700$	9.31321	0.352006
$701$	−11.9512	−0.451392	−0.225696	−	0.974198i	$-0.572466\pi$
$701$	−11.9512	−0.451392	−0.225696	+	0.974198i	$0.572466\pi$
$702$	0.296181	0.0111786
$703$	−48.6571	−1.83514
$704$	5.12829	0.193280
$705$	−1.70579	−0.0642436
$706$	−29.7589	−1.11999
$707$	32.7454	1.23152
$708$	−10.1739	−0.382358
$709$	−3.26106	−0.122472	−0.0612358	−	0.998123i	$-0.519504\pi$
$709$	−3.26106	−0.122472	−0.0612358	+	0.998123i	$0.519504\pi$
$710$	−4.06046	−0.152386
$711$	8.07519	0.302843
$712$	−6.65673	−0.249471
$713$	−5.59681	−0.209602
$714$	−16.7910	−0.628389
$715$	6.76305	0.252924
$716$	−1.50661	−0.0563047
$717$	27.8706	1.04085
$718$	7.83656	0.292458
$719$	8.47916	0.316219	0.158110	−	0.987422i	$-0.449460\pi$
$719$	8.47916	0.316219	0.158110	+	0.987422i	$0.449460\pi$
$720$	1.08770	0.0405361
$721$	−0.129728	−0.00483132
$722$	−41.5271	−1.54548
$723$	50.0927	1.86297
$724$	8.54956	0.317742
$725$	−1.60897	−0.0597556
$726$	37.5778	1.39464
$727$	34.0631	1.26333	0.631665	−	0.775242i	$-0.282372\pi$
$727$	34.0631	1.26333	0.631665	+	0.775242i	$0.282372\pi$
$728$	7.02996	0.260548
$729$	−27.5870	−1.02174
$730$	−0.767000	−0.0283879
$731$	37.6641	1.39306
$732$	−33.9818	−1.25600
$733$	−6.23377	−0.230250	−0.115125	−	0.993351i	$-0.536727\pi$
$733$	−6.23377	−0.230250	−0.115125	+	0.993351i	$0.536727\pi$
$734$	11.8807	0.438526
$735$	2.94654	0.108685
$736$	0.723070	0.0266527
$737$	52.7146	1.94177
$738$	8.35305	0.307480
$739$	−23.9882	−0.882418	−0.441209	−	0.897404i	$-0.645450\pi$
$739$	−23.9882	−0.882418	−0.441209	+	0.897404i	$0.645450\pi$
$740$	2.24304	0.0824558
$741$	70.2650	2.58125
$742$	−16.7647	−0.615452
$743$	−21.4444	−0.786717	−0.393359	−	0.919385i	$-0.628687\pi$
$743$	−21.4444	−0.786717	−0.393359	+	0.919385i	$0.628687\pi$
$744$	19.0116	0.697000
$745$	−2.93201	−0.107420
$746$	−16.2587	−0.595274
$747$	48.9668	1.79160
$748$	18.3376	0.670489
$749$	19.0298	0.695334
$750$	−8.69566	−0.317521
$751$	−32.9586	−1.20268	−0.601338	−	0.798995i	$-0.705365\pi$
$751$	−32.9586	−1.20268	−0.601338	+	0.798995i	$0.705365\pi$
$752$	1.93642	0.0706140
$753$	7.95232	0.289799
$754$	−1.21451	−0.0442299
$755$	−3.09515	−0.112644
$756$	0.153993	0.00560066
$757$	5.29760	0.192544	0.0962722	−	0.995355i	$-0.469308\pi$
$757$	5.29760	0.192544	0.0962722	+	0.995355i	$0.469308\pi$
$758$	30.0310	1.09077
$759$	9.10777	0.330591
$760$	2.79023	0.101212
$761$	38.7255	1.40380	0.701900	−	0.712276i	$-0.252335\pi$
$761$	38.7255	1.40380	0.701900	+	0.712276i	$0.252335\pi$
$762$	4.70106	0.170302
$763$	23.3007	0.843543
$764$	−3.47248	−0.125630
$765$	3.88937	0.140620
$766$	−6.22357	−0.224867
$767$	15.2312	0.549965
$768$	−2.45617	−0.0886296
$769$	−46.1948	−1.66583	−0.832913	−	0.553404i	$-0.813329\pi$
$769$	−46.1948	−1.66583	−0.832913	+	0.553404i	$0.813329\pi$
$770$	3.51630	0.126719
$771$	57.0884	2.05599
$772$	−25.1942	−0.906758
$773$	−0.152902	−0.00549949	−0.00274975	−	0.999996i	$-0.500875\pi$
$773$	−0.152902	−0.00549949	−0.00274975	+	0.999996i	$0.500875\pi$
$774$	−31.9447	−1.14823
$775$	−37.7061	−1.35444
$776$	15.5223	0.557218
$777$	29.3683	1.05358
$778$	27.8418	0.998177
$779$	21.4278	0.767729
$780$	−3.23914	−0.115980
$781$	58.0606	2.07757
$782$	2.58554	0.0924587
$783$	−0.0266041	−0.000950753 0
$784$	−3.34493	−0.119462
$785$	−0.321061	−0.0114592
$786$	−14.6832	−0.523731
$787$	−49.4510	−1.76274	−0.881369	−	0.472429i	$-0.843377\pi$
$787$	−49.4510	−1.76274	−0.881369	+	0.472429i	$0.843377\pi$
$788$	19.7918	0.705055
$789$	−38.0469	−1.35451
$790$	−0.954939	−0.0339752
$791$	−0.108163	−0.00384583
$792$	−15.5530	−0.552653
$793$	50.8736	1.80657
$794$	5.78872	0.205434
$795$	7.72455	0.273962
$796$	0.695954	0.0246674
$797$	41.4911	1.46969	0.734845	−	0.678235i	$-0.237255\pi$
$797$	41.4911	1.46969	0.734845	+	0.678235i	$0.237255\pi$
$798$	36.5327	1.29324
$799$	6.92421	0.244961
$800$	4.87137	0.172229
$801$	20.1885	0.713325
$802$	−17.4983	−0.617885
$803$	10.9673	0.387029
$804$	−25.2475	−0.890409
$805$	0.495786	0.0174742
$806$	−28.4619	−1.00253
$807$	5.18295	0.182448
$808$	17.1278	0.602555
$809$	19.0841	0.670961	0.335480	−	0.942047i	$-0.391101\pi$
$809$	19.0841	0.670961	0.335480	+	0.942047i	$0.391101\pi$
$810$	3.19214	0.112160
$811$	−47.1843	−1.65687	−0.828433	−	0.560088i	$-0.810767\pi$
$811$	−47.1843	−1.65687	−0.828433	+	0.560088i	$0.810767\pi$
$812$	−0.631458	−0.0221598
$813$	−65.3067	−2.29041
$814$	−32.0733	−1.12417
$815$	4.53008	0.158682
$816$	−8.78273	−0.307457
$817$	−81.9467	−2.86695
$818$	−29.7803	−1.04124
$819$	−21.3204	−0.744996
$820$	−0.987798	−0.0344954
$821$	25.2469	0.881123	0.440562	−	0.897722i	$-0.354779\pi$
$821$	25.2469	0.881123	0.440562	+	0.897722i	$0.354779\pi$
$822$	−21.2304	−0.740495
$823$	25.6178	0.892980	0.446490	−	0.894789i	$-0.352674\pi$
$823$	25.6178	0.892980	0.446490	+	0.894789i	$0.352674\pi$
$824$	−0.0678555	−0.00236386
$825$	61.3596	2.13627
$826$	7.91910	0.275541
$827$	−0.457860	−0.0159213	−0.00796067	−	0.999968i	$-0.502534\pi$
$827$	−0.457860	−0.0159213	−0.00796067	+	0.999968i	$0.502534\pi$
$828$	−2.19292	−0.0762094
$829$	−2.95124	−0.102501	−0.0512504	−	0.998686i	$-0.516321\pi$
$829$	−2.95124	−0.102501	−0.0512504	+	0.998686i	$0.516321\pi$
$830$	−5.79062	−0.200995
$831$	32.1187	1.11419
$832$	3.67709	0.127480
$833$	−11.9607	−0.414414
$834$	−16.0273	−0.554979
$835$	−3.12735	−0.108226
$836$	−39.8976	−1.37989
$837$	−0.623465	−0.0215501
$838$	−20.3335	−0.702409
$839$	53.5531	1.84886	0.924428	−	0.381356i	$-0.124543\pi$
$839$	53.5531	1.84886	0.924428	+	0.381356i	$0.124543\pi$
$840$	−1.68412	−0.0581077
$841$	−28.8909	−0.996238
$842$	22.2050	0.765234
$843$	−40.5845	−1.39780
$844$	12.5891	0.433336
$845$	0.186864	0.00642830
$846$	−5.87276	−0.201910
$847$	−29.2496	−1.00503
$848$	−8.76896	−0.301127
$849$	−57.7935	−1.98347
$850$	17.4189	0.597465
$851$	−4.52222	−0.155020
$852$	−27.8079	−0.952683
$853$	−4.09284	−0.140136	−0.0700680	−	0.997542i	$-0.522322\pi$
$853$	−4.09284	−0.140136	−0.0700680	+	0.997542i	$0.522322\pi$
$854$	26.4506	0.905121
$855$	−8.46220	−0.289401
$856$	9.95374	0.340212
$857$	5.08447	0.173682	0.0868411	−	0.996222i	$-0.472323\pi$
$857$	5.08447	0.173682	0.0868411	+	0.996222i	$0.472323\pi$
$858$	46.3166	1.58122
$859$	−16.9189	−0.577265	−0.288632	−	0.957440i	$-0.593201\pi$
$859$	−16.9189	−0.577265	−0.288632	+	0.957440i	$0.593201\pi$
$860$	3.77766	0.128817
$861$	−12.9333	−0.440766
$862$	30.6666	1.04451
$863$	41.0261	1.39654	0.698272	−	0.715832i	$-0.253952\pi$
$863$	41.0261	1.39654	0.698272	+	0.715832i	$0.253952\pi$
$864$	0.0805476	0.00274028
$865$	1.55582	0.0528994
$866$	21.6081	0.734274
$867$	10.3499	0.351500
$868$	−14.7982	−0.502282
$869$	13.6547	0.463204
$870$	0.290952	0.00986420
$871$	37.7975	1.28072
$872$	12.1877	0.412727
$873$	−47.0759	−1.59328
$874$	−5.62542	−0.190283
$875$	6.76848	0.228817
$876$	−5.25277	−0.177475
$877$	16.3670	0.552673	0.276337	−	0.961061i	$-0.410880\pi$
$877$	16.3670	0.552673	0.276337	+	0.961061i	$0.410880\pi$
$878$	−0.409379	−0.0138159
$879$	−26.1435	−0.881797
$880$	1.83924	0.0620007
$881$	30.8066	1.03790	0.518951	−	0.854804i	$-0.326323\pi$
$881$	30.8066	1.03790	0.518951	+	0.854804i	$0.326323\pi$
$882$	10.1445	0.341582
$883$	18.4888	0.622197	0.311098	−	0.950378i	$-0.399303\pi$
$883$	18.4888	0.622197	0.311098	+	0.950378i	$0.399303\pi$
$884$	13.1485	0.442231
$885$	−3.64883	−0.122654
$886$	13.5597	0.455547
$887$	−0.118637	−0.00398344	−0.00199172	−	0.999998i	$-0.500634\pi$
$887$	−0.118637	−0.00398344	−0.00199172	+	0.999998i	$0.500634\pi$
$888$	15.3614	0.515495
$889$	−3.65919	−0.122725
$890$	−2.38741	−0.0800261
$891$	−45.6445	−1.52915
$892$	18.6690	0.625083
$893$	−15.0652	−0.504137
$894$	−20.0798	−0.671568
$895$	−0.540340	−0.0180616
$896$	1.91182	0.0638696
$897$	6.53047	0.218046
$898$	−3.71919	−0.124111
$899$	2.55656	0.0852661
$900$	−14.7739	−0.492462
$901$	−31.3559	−1.04462
$902$	14.1245	0.470296
$903$	49.4611	1.64596
$904$	−0.0565757	−0.00188168
$905$	3.06626	0.101926
$906$	−21.1970	−0.704224
$907$	12.8960	0.428203	0.214102	−	0.976811i	$-0.431318\pi$
$907$	12.8960	0.428203	0.214102	+	0.976811i	$0.431318\pi$
$908$	−6.28244	−0.208490
$909$	−51.9452	−1.72291
$910$	2.52127	0.0835792
$911$	−6.76255	−0.224053	−0.112027	−	0.993705i	$-0.535734\pi$
$911$	−6.76255	−0.224053	−0.112027	+	0.993705i	$0.535734\pi$
$912$	19.1088	0.632756
$913$	82.8001	2.74029
$914$	−20.8371	−0.689231
$915$	−12.1874	−0.402904
$916$	11.4404	0.378001
$917$	11.4290	0.377419
$918$	0.288020	0.00950608
$919$	−15.3379	−0.505952	−0.252976	−	0.967473i	$-0.581409\pi$
$919$	−15.3379	−0.505952	−0.252976	+	0.967473i	$0.581409\pi$
$920$	0.259326	0.00854973
$921$	54.7086	1.80271
$922$	22.4406	0.739042
$923$	41.6307	1.37029
$924$	24.0813	0.792216
$925$	−30.4665	−1.00173
$926$	18.5063	0.608156
$927$	0.205792	0.00675909
$928$	−0.330291	−0.0108423
$929$	8.29140	0.272032	0.136016	−	0.990707i	$-0.456570\pi$
$929$	8.29140	0.272032	0.136016	+	0.990707i	$0.456570\pi$
$930$	6.81844	0.223585
$931$	26.0232	0.852877
$932$	24.7109	0.809432
$933$	84.0805	2.75267
$934$	−29.4384	−0.963254
$935$	6.57671	0.215081
$936$	−11.1519	−0.364510
$937$	28.3171	0.925078	0.462539	−	0.886599i	$-0.346939\pi$
$937$	28.3171	0.925078	0.462539	+	0.886599i	$0.346939\pi$
$938$	19.6520	0.641660
$939$	26.0245	0.849278
$940$	0.694489	0.0226517
$941$	52.5776	1.71398	0.856990	−	0.515334i	$-0.172332\pi$
$941$	52.5776	1.71398	0.856990	+	0.515334i	$0.172332\pi$
$942$	−2.19877	−0.0716400
$943$	1.99151	0.0648525
$944$	4.14217	0.134816
$945$	0.0552289	0.00179660
$946$	−54.0168	−1.75624
$947$	−31.0785	−1.00992	−0.504958	−	0.863144i	$-0.668492\pi$
$947$	−31.0785	−1.00992	−0.504958	+	0.863144i	$0.668492\pi$
$948$	−6.53987	−0.212405
$949$	7.86383	0.255271
$950$	−37.8989	−1.22960
$951$	9.20255	0.298413
$952$	6.83626	0.221564
$953$	30.1400	0.976329	0.488165	−	0.872752i	$-0.337667\pi$
$953$	30.1400	0.976329	0.488165	+	0.872752i	$0.337667\pi$
$954$	26.5945	0.861027
$955$	−1.24539	−0.0402998
$956$	−11.3472	−0.366994
$957$	−4.16033	−0.134484
$958$	15.8363	0.511649
$959$	16.5252	0.533627
$960$	−0.880897	−0.0284308
$961$	28.9128	0.932670
$962$	−22.9973	−0.741462
$963$	−30.1876	−0.972783
$964$	−20.3946	−0.656866
$965$	−9.03578	−0.290872
$966$	3.39538	0.109244
$967$	15.9836	0.513999	0.257000	−	0.966412i	$-0.417266\pi$
$967$	15.9836	0.513999	0.257000	+	0.966412i	$0.417266\pi$
$968$	−15.2993	−0.491739
$969$	68.3289	2.19504
$970$	5.56700	0.178746
$971$	−8.63180	−0.277008	−0.138504	−	0.990362i	$-0.544229\pi$
$971$	−8.63180	−0.277008	−0.138504	+	0.990362i	$0.544229\pi$
$972$	22.1029	0.708952
$973$	12.4752	0.399937
$974$	22.4529	0.719437
$975$	43.9962	1.40901
$976$	13.8353	0.442856
$977$	11.0749	0.354317	0.177159	−	0.984182i	$-0.443309\pi$
$977$	11.0749	0.354317	0.177159	+	0.984182i	$0.443309\pi$
$978$	31.0241	0.992041
$979$	34.1376	1.09104
$980$	−1.19964	−0.0383212
$981$	−36.9628	−1.18013
$982$	0.215708	0.00688353
$983$	3.07802	0.0981737	0.0490868	−	0.998795i	$-0.484369\pi$
$983$	3.07802	0.0981737	0.0490868	+	0.998795i	$0.484369\pi$
$984$	−6.76490	−0.215657
$985$	7.09826	0.226169
$986$	−1.18105	−0.0376122
$987$	9.09299	0.289433
$988$	−28.6075	−0.910125
$989$	−7.61618	−0.242180
$990$	−5.57803	−0.177281
$991$	−57.9932	−1.84221	−0.921107	−	0.389310i	$-0.872714\pi$
$991$	−57.9932	−1.84221	−0.921107	+	0.389310i	$0.872714\pi$
$992$	−7.74033	−0.245756
$993$	−69.0396	−2.19090
$994$	21.6450	0.686537
$995$	0.249601	0.00791289
$996$	−39.6568	−1.25658
$997$	−26.2100	−0.830080	−0.415040	−	0.909803i	$-0.636232\pi$
$997$	−26.2100	−0.830080	−0.415040	+	0.909803i	$0.636232\pi$
$998$	−15.1384	−0.479197
$999$	−0.503760	−0.0159383

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8002.2.a.e.1.10	✓	77

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8002.2.a.e.1.10	✓	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.45617 q^{3} +1.00000 q^{4} +0.358646 q^{5} +2.45617 q^{6} -1.91182 q^{7} -1.00000 q^{8} +3.03279 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.45617 q^{3} +1.00000 q^{4} +0.358646 q^{5} +2.45617 q^{6} -1.91182 q^{7} -1.00000 q^{8} +3.03279 q^{9} -0.358646 q^{10} +5.12829 q^{11} -2.45617 q^{12} +3.67709 q^{13} +1.91182 q^{14} -0.880897 q^{15} +1.00000 q^{16} +3.57578 q^{17} -3.03279 q^{18} -7.77991 q^{19} +0.358646 q^{20} +4.69577 q^{21} -5.12829 q^{22} -0.723070 q^{23} +2.45617 q^{24} -4.87137 q^{25} -3.67709 q^{26} -0.0805476 q^{27} -1.91182 q^{28} +0.330291 q^{29} +0.880897 q^{30} +7.74033 q^{31} -1.00000 q^{32} -12.5960 q^{33} -3.57578 q^{34} -0.685668 q^{35} +3.03279 q^{36} +6.25420 q^{37} +7.77991 q^{38} -9.03159 q^{39} -0.358646 q^{40} -2.75424 q^{41} -4.69577 q^{42} +10.5331 q^{43} +5.12829 q^{44} +1.08770 q^{45} +0.723070 q^{46} +1.93642 q^{47} -2.45617 q^{48} -3.34493 q^{49} +4.87137 q^{50} -8.78273 q^{51} +3.67709 q^{52} -8.76896 q^{53} +0.0805476 q^{54} +1.83924 q^{55} +1.91182 q^{56} +19.1088 q^{57} -0.330291 q^{58} +4.14217 q^{59} -0.880897 q^{60} +13.8353 q^{61} -7.74033 q^{62} -5.79817 q^{63} +1.00000 q^{64} +1.31877 q^{65} +12.5960 q^{66} +10.2792 q^{67} +3.57578 q^{68} +1.77599 q^{69} +0.685668 q^{70} +11.3216 q^{71} -3.03279 q^{72} +2.13860 q^{73} -6.25420 q^{74} +11.9649 q^{75} -7.77991 q^{76} -9.80438 q^{77} +9.03159 q^{78} +2.66262 q^{79} +0.358646 q^{80} -8.90054 q^{81} +2.75424 q^{82} +16.1458 q^{83} +4.69577 q^{84} +1.28244 q^{85} -10.5331 q^{86} -0.811252 q^{87} -5.12829 q^{88} +6.65673 q^{89} -1.08770 q^{90} -7.02996 q^{91} -0.723070 q^{92} -19.0116 q^{93} -1.93642 q^{94} -2.79023 q^{95} +2.45617 q^{96} -15.5223 q^{97} +3.34493 q^{98} +15.5530 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 77 q - 77 q^{2} + 10 q^{3} + 77 q^{4} + 18 q^{5} - 10 q^{6} + 21 q^{7} - 77 q^{8} + 71 q^{9}+O(q^{10}) \) 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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