LMFDB - Embedded newform 8002.2.a.e.1.18

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			1.18
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)

$f(q)$	$=$	$q-1.00000 q^{2} -1.70235 q^{3} +1.00000 q^{4} +4.07630 q^{5} +1.70235 q^{6} +1.03752 q^{7} -1.00000 q^{8} -0.101993 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.70235 q^{3} +1.00000 q^{4} +4.07630 q^{5} +1.70235 q^{6} +1.03752 q^{7} -1.00000 q^{8} -0.101993 q^{9} -4.07630 q^{10} -1.31126 q^{11} -1.70235 q^{12} +2.37232 q^{13} -1.03752 q^{14} -6.93930 q^{15} +1.00000 q^{16} -5.13379 q^{17} +0.101993 q^{18} +4.46798 q^{19} +4.07630 q^{20} -1.76623 q^{21} +1.31126 q^{22} +0.760254 q^{23} +1.70235 q^{24} +11.6162 q^{25} -2.37232 q^{26} +5.28069 q^{27} +1.03752 q^{28} +5.15882 q^{29} +6.93930 q^{30} -0.698242 q^{31} -1.00000 q^{32} +2.23223 q^{33} +5.13379 q^{34} +4.22925 q^{35} -0.101993 q^{36} -7.91187 q^{37} -4.46798 q^{38} -4.03853 q^{39} -4.07630 q^{40} +3.27999 q^{41} +1.76623 q^{42} +5.83497 q^{43} -1.31126 q^{44} -0.415754 q^{45} -0.760254 q^{46} -2.17474 q^{47} -1.70235 q^{48} -5.92355 q^{49} -11.6162 q^{50} +8.73953 q^{51} +2.37232 q^{52} -0.495898 q^{53} -5.28069 q^{54} -5.34510 q^{55} -1.03752 q^{56} -7.60608 q^{57} -5.15882 q^{58} -1.42763 q^{59} -6.93930 q^{60} -10.1785 q^{61} +0.698242 q^{62} -0.105820 q^{63} +1.00000 q^{64} +9.67029 q^{65} -2.23223 q^{66} +15.5856 q^{67} -5.13379 q^{68} -1.29422 q^{69} -4.22925 q^{70} -7.14382 q^{71} +0.101993 q^{72} -8.35550 q^{73} +7.91187 q^{74} -19.7749 q^{75} +4.46798 q^{76} -1.36046 q^{77} +4.03853 q^{78} +6.98878 q^{79} +4.07630 q^{80} -8.68362 q^{81} -3.27999 q^{82} +9.52981 q^{83} -1.76623 q^{84} -20.9269 q^{85} -5.83497 q^{86} -8.78213 q^{87} +1.31126 q^{88} +15.9239 q^{89} +0.415754 q^{90} +2.46133 q^{91} +0.760254 q^{92} +1.18865 q^{93} +2.17474 q^{94} +18.2128 q^{95} +1.70235 q^{96} +6.80293 q^{97} +5.92355 q^{98} +0.133740 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−1.70235	−0.982854	−0.491427	−	0.870919i	$-0.663525\pi$
$3$	−1.70235	−0.982854	−0.491427	+	0.870919i	$0.663525\pi$
$4$	1.00000	0.500000
$5$	4.07630	1.82298	0.911489	−	0.411325i	$-0.134934\pi$
$5$	4.07630	1.82298	0.911489	+	0.411325i	$0.134934\pi$
$6$	1.70235	0.694983
$7$	1.03752	0.392146	0.196073	−	0.980589i	$-0.437181\pi$
$7$	1.03752	0.392146	0.196073	+	0.980589i	$0.437181\pi$
$8$	−1.00000	−0.353553
$9$	−0.101993	−0.0339977
$10$	−4.07630	−1.28904
$11$	−1.31126	−0.395361	−0.197680	−	0.980267i	$-0.563341\pi$
$11$	−1.31126	−0.395361	−0.197680	+	0.980267i	$0.563341\pi$
$12$	−1.70235	−0.491427
$13$	2.37232	0.657963	0.328982	−	0.944336i	$-0.393295\pi$
$13$	2.37232	0.657963	0.328982	+	0.944336i	$0.393295\pi$
$14$	−1.03752	−0.277289
$15$	−6.93930	−1.79172
$16$	1.00000	0.250000
$17$	−5.13379	−1.24513	−0.622564	−	0.782569i	$-0.713909\pi$
$17$	−5.13379	−1.24513	−0.622564	+	0.782569i	$0.713909\pi$
$18$	0.101993	0.0240400
$19$	4.46798	1.02503	0.512513	−	0.858680i	$-0.328715\pi$
$19$	4.46798	1.02503	0.512513	+	0.858680i	$0.328715\pi$
$20$	4.07630	0.911489
$21$	−1.76623	−0.385423
$22$	1.31126	0.279562
$23$	0.760254	0.158524	0.0792619	−	0.996854i	$-0.474744\pi$
$23$	0.760254	0.158524	0.0792619	+	0.996854i	$0.474744\pi$
$24$	1.70235	0.347491
$25$	11.6162	2.32325
$26$	−2.37232	−0.465250
$27$	5.28069	1.01627
$28$	1.03752	0.196073
$29$	5.15882	0.957969	0.478984	−	0.877823i	$-0.341005\pi$
$29$	5.15882	0.957969	0.478984	+	0.877823i	$0.341005\pi$
$30$	6.93930	1.26694
$31$	−0.698242	−0.125408	−0.0627040	−	0.998032i	$-0.519972\pi$
$31$	−0.698242	−0.125408	−0.0627040	+	0.998032i	$0.519972\pi$
$32$	−1.00000	−0.176777
$33$	2.23223	0.388582
$34$	5.13379	0.880438
$35$	4.22925	0.714874
$36$	−0.101993	−0.0169988
$37$	−7.91187	−1.30070	−0.650352	−	0.759633i	$-0.725379\pi$
$37$	−7.91187	−1.30070	−0.650352	+	0.759633i	$0.725379\pi$
$38$	−4.46798	−0.724802
$39$	−4.03853	−0.646682
$40$	−4.07630	−0.644520
$41$	3.27999	0.512249	0.256124	−	0.966644i	$-0.417554\pi$
$41$	3.27999	0.512249	0.256124	+	0.966644i	$0.417554\pi$
$42$	1.76623	0.272535
$43$	5.83497	0.889824	0.444912	−	0.895574i	$-0.353235\pi$
$43$	5.83497	0.889824	0.444912	+	0.895574i	$0.353235\pi$
$44$	−1.31126	−0.197680
$45$	−0.415754	−0.0619770
$46$	−0.760254	−0.112093
$47$	−2.17474	−0.317219	−0.158610	−	0.987341i	$-0.550701\pi$
$47$	−2.17474	−0.317219	−0.158610	+	0.987341i	$0.550701\pi$
$48$	−1.70235	−0.245714
$49$	−5.92355	−0.846221
$50$	−11.6162	−1.64278
$51$	8.73953	1.22378
$52$	2.37232	0.328982
$53$	−0.495898	−0.0681169	−0.0340584	−	0.999420i	$-0.510843\pi$
$53$	−0.495898	−0.0681169	−0.0340584	+	0.999420i	$0.510843\pi$
$54$	−5.28069	−0.718611
$55$	−5.34510	−0.720734
$56$	−1.03752	−0.138645
$57$	−7.60608	−1.00745
$58$	−5.15882	−0.677386
$59$	−1.42763	−0.185862	−0.0929309	−	0.995673i	$-0.529624\pi$
$59$	−1.42763	−0.185862	−0.0929309	+	0.995673i	$0.529624\pi$
$60$	−6.93930	−0.895860
$61$	−10.1785	−1.30323	−0.651613	−	0.758551i	$-0.725908\pi$
$61$	−10.1785	−1.30323	−0.651613	+	0.758551i	$0.725908\pi$
$62$	0.698242	0.0886768
$63$	−0.105820	−0.0133321
$64$	1.00000	0.125000
$65$	9.67029	1.19945
$66$	−2.23223	−0.274769
$67$	15.5856	1.90408	0.952042	−	0.305966i	$-0.0989794\pi$
$67$	15.5856	1.90408	0.952042	+	0.305966i	$0.0989794\pi$
$68$	−5.13379	−0.622564
$69$	−1.29422	−0.155806
$70$	−4.22925	−0.505492
$71$	−7.14382	−0.847815	−0.423907	−	0.905706i	$-0.639342\pi$
$71$	−7.14382	−0.847815	−0.423907	+	0.905706i	$0.639342\pi$
$72$	0.101993	0.0120200
$73$	−8.35550	−0.977937	−0.488969	−	0.872301i	$-0.662627\pi$
$73$	−8.35550	−0.977937	−0.488969	+	0.872301i	$0.662627\pi$
$74$	7.91187	0.919737
$75$	−19.7749	−2.28341
$76$	4.46798	0.512513
$77$	−1.36046	−0.155039
$78$	4.03853	0.457273
$79$	6.98878	0.786299	0.393150	−	0.919475i	$-0.371385\pi$
$79$	6.98878	0.786299	0.393150	+	0.919475i	$0.371385\pi$
$80$	4.07630	0.455744
$81$	−8.68362	−0.964846
$82$	−3.27999	−0.362215
$83$	9.52981	1.04603	0.523016	−	0.852323i	$-0.324807\pi$
$83$	9.52981	1.04603	0.523016	+	0.852323i	$0.324807\pi$
$84$	−1.76623	−0.192711
$85$	−20.9269	−2.26984
$86$	−5.83497	−0.629201
$87$	−8.78213	−0.941543
$88$	1.31126	0.139781
$89$	15.9239	1.68792	0.843962	−	0.536402i	$-0.180217\pi$
$89$	15.9239	1.68792	0.843962	+	0.536402i	$0.180217\pi$
$90$	0.415754	0.0438244
$91$	2.46133	0.258018
$92$	0.760254	0.0792619
$93$	1.18865	0.123258
$94$	2.17474	0.224308
$95$	18.2128	1.86860
$96$	1.70235	0.173746
$97$	6.80293	0.690733	0.345367	−	0.938468i	$-0.387755\pi$
$97$	6.80293	0.690733	0.345367	+	0.938468i	$0.387755\pi$
$98$	5.92355	0.598369
$99$	0.133740	0.0134413
$100$	11.6162	1.16162
$101$	10.7348	1.06815	0.534076	−	0.845436i	$-0.320660\pi$
$101$	10.7348	1.06815	0.534076	+	0.845436i	$0.320660\pi$
$102$	−8.73953	−0.865342
$103$	−8.94582	−0.881458	−0.440729	−	0.897640i	$-0.645280\pi$
$103$	−8.94582	−0.881458	−0.440729	+	0.897640i	$0.645280\pi$
$104$	−2.37232	−0.232625
$105$	−7.19968	−0.702617
$106$	0.495898	0.0481659
$107$	−1.15600	−0.111755	−0.0558776	−	0.998438i	$-0.517796\pi$
$107$	−1.15600	−0.111755	−0.0558776	+	0.998438i	$0.517796\pi$
$108$	5.28069	0.508134
$109$	11.5722	1.10842	0.554208	−	0.832378i	$-0.313021\pi$
$109$	11.5722	1.10842	0.554208	+	0.832378i	$0.313021\pi$
$110$	5.34510	0.509636
$111$	13.4688	1.27840
$112$	1.03752	0.0980366
$113$	12.7261	1.19717	0.598584	−	0.801060i	$-0.295730\pi$
$113$	12.7261	1.19717	0.598584	+	0.801060i	$0.295730\pi$
$114$	7.60608	0.712375
$115$	3.09902	0.288985
$116$	5.15882	0.478984
$117$	−0.241960	−0.0223692
$118$	1.42763	0.131424
$119$	−5.32642	−0.488272
$120$	6.93930	0.633469
$121$	−9.28059	−0.843690
$122$	10.1785	0.921521
$123$	−5.58371	−0.503466
$124$	−0.698242	−0.0627040
$125$	26.9697	2.41225
$126$	0.105820	0.00942720
$127$	15.6377	1.38762	0.693811	−	0.720157i	$-0.255930\pi$
$127$	15.6377	1.38762	0.693811	+	0.720157i	$0.255930\pi$
$128$	−1.00000	−0.0883883
$129$	−9.93318	−0.874567
$130$	−9.67029	−0.848141
$131$	9.26329	0.809338	0.404669	−	0.914463i	$-0.367387\pi$
$131$	9.26329	0.809338	0.404669	+	0.914463i	$0.367387\pi$
$132$	2.23223	0.194291
$133$	4.63563	0.401960
$134$	−15.5856	−1.34639
$135$	21.5257	1.85264
$136$	5.13379	0.440219
$137$	−0.0402046	−0.00343491	−0.00171746	−	0.999999i	$-0.500547\pi$
$137$	−0.0402046	−0.00343491	−0.00171746	+	0.999999i	$0.500547\pi$
$138$	1.29422	0.110171
$139$	−19.9509	−1.69221	−0.846105	−	0.533016i	$-0.821058\pi$
$139$	−19.9509	−1.69221	−0.846105	+	0.533016i	$0.821058\pi$
$140$	4.22925	0.357437
$141$	3.70218	0.311780
$142$	7.14382	0.599496
$143$	−3.11074	−0.260133
$144$	−0.101993	−0.00849942
$145$	21.0289	1.74635
$146$	8.35550	0.691506
$147$	10.0840	0.831712
$148$	−7.91187	−0.650352
$149$	−12.8354	−1.05152	−0.525760	−	0.850633i	$-0.676219\pi$
$149$	−12.8354	−1.05152	−0.525760	+	0.850633i	$0.676219\pi$
$150$	19.7749	1.61462
$151$	−16.1459	−1.31393	−0.656967	−	0.753919i	$-0.728161\pi$
$151$	−16.1459	−1.31393	−0.656967	+	0.753919i	$0.728161\pi$
$152$	−4.46798	−0.362401
$153$	0.523611	0.0423314
$154$	1.36046	0.109629
$155$	−2.84624	−0.228616
$156$	−4.03853	−0.323341
$157$	12.0959	0.965358	0.482679	−	0.875797i	$-0.339664\pi$
$157$	12.0959	0.965358	0.482679	+	0.875797i	$0.339664\pi$
$158$	−6.98878	−0.555998
$159$	0.844194	0.0669490
$160$	−4.07630	−0.322260
$161$	0.788780	0.0621646
$162$	8.68362	0.682249
$163$	1.88880	0.147942	0.0739709	−	0.997260i	$-0.476433\pi$
$163$	1.88880	0.147942	0.0739709	+	0.997260i	$0.476433\pi$
$164$	3.27999	0.256124
$165$	9.09925	0.708376
$166$	−9.52981	−0.739657
$167$	6.55728	0.507418	0.253709	−	0.967281i	$-0.418349\pi$
$167$	6.55728	0.507418	0.253709	+	0.967281i	$0.418349\pi$
$168$	1.76623	0.136268
$169$	−7.37210	−0.567085
$170$	20.9269	1.60502
$171$	−0.455703	−0.0348485
$172$	5.83497	0.444912
$173$	9.61367	0.730914	0.365457	−	0.930828i	$-0.380913\pi$
$173$	9.61367	0.730914	0.365457	+	0.930828i	$0.380913\pi$
$174$	8.78213	0.665772
$175$	12.0521	0.911053
$176$	−1.31126	−0.0988402
$177$	2.43033	0.182675
$178$	−15.9239	−1.19354
$179$	10.3741	0.775400	0.387700	−	0.921786i	$-0.373270\pi$
$179$	10.3741	0.775400	0.387700	+	0.921786i	$0.373270\pi$
$180$	−0.415754	−0.0309885
$181$	−5.78228	−0.429793	−0.214897	−	0.976637i	$-0.568941\pi$
$181$	−5.78228	−0.429793	−0.214897	+	0.976637i	$0.568941\pi$
$182$	−2.46133	−0.182446
$183$	17.3274	1.28088
$184$	−0.760254	−0.0560466
$185$	−32.2512	−2.37115
$186$	−1.18865	−0.0871564
$187$	6.73175	0.492274
$188$	−2.17474	−0.158610
$189$	5.47883	0.398526
$190$	−18.2128	−1.32130
$191$	8.94259	0.647063	0.323532	−	0.946217i	$-0.395130\pi$
$191$	8.94259	0.647063	0.323532	+	0.946217i	$0.395130\pi$
$192$	−1.70235	−0.122857
$193$	−17.8248	−1.28305	−0.641527	−	0.767100i	$-0.721699\pi$
$193$	−17.8248	−1.28305	−0.641527	+	0.767100i	$0.721699\pi$
$194$	−6.80293	−0.488422
$195$	−16.4623	−1.17889
$196$	−5.92355	−0.423111
$197$	18.6669	1.32996	0.664982	−	0.746859i	$-0.268439\pi$
$197$	18.6669	1.32996	0.664982	+	0.746859i	$0.268439\pi$
$198$	−0.133740	−0.00950447
$199$	13.4208	0.951375	0.475687	−	0.879614i	$-0.342199\pi$
$199$	13.4208	0.951375	0.475687	+	0.879614i	$0.342199\pi$
$200$	−11.6162	−0.821392
$201$	−26.5322	−1.87144
$202$	−10.7348	−0.755298
$203$	5.35239	0.375664
$204$	8.73953	0.611889
$205$	13.3702	0.933818
$206$	8.94582	0.623285
$207$	−0.0775406	−0.00538944
$208$	2.37232	0.164491
$209$	−5.85870	−0.405255
$210$	7.19968	0.496825
$211$	−3.72585	−0.256498	−0.128249	−	0.991742i	$-0.540936\pi$
$211$	−3.72585	−0.256498	−0.128249	+	0.991742i	$0.540936\pi$
$212$	−0.495898	−0.0340584
$213$	12.1613	0.833278
$214$	1.15600	0.0790228
$215$	23.7851	1.62213
$216$	−5.28069	−0.359305
$217$	−0.724441	−0.0491783
$218$	−11.5722	−0.783768
$219$	14.2240	0.961170
$220$	−5.34510	−0.360367
$221$	−12.1790	−0.819248
$222$	−13.4688	−0.903967
$223$	−3.81823	−0.255688	−0.127844	−	0.991794i	$-0.540806\pi$
$223$	−3.81823	−0.255688	−0.127844	+	0.991794i	$0.540806\pi$
$224$	−1.03752	−0.0693223
$225$	−1.18477	−0.0789850
$226$	−12.7261	−0.846526
$227$	15.3243	1.01711	0.508554	−	0.861030i	$-0.330180\pi$
$227$	15.3243	1.01711	0.508554	+	0.861030i	$0.330180\pi$
$228$	−7.60608	−0.503725
$229$	19.0411	1.25827	0.629136	−	0.777295i	$-0.283409\pi$
$229$	19.0411	1.25827	0.629136	+	0.777295i	$0.283409\pi$
$230$	−3.09902	−0.204344
$231$	2.31599	0.152381
$232$	−5.15882	−0.338693
$233$	−12.6530	−0.828928	−0.414464	−	0.910066i	$-0.636031\pi$
$233$	−12.6530	−0.828928	−0.414464	+	0.910066i	$0.636031\pi$
$234$	0.241960	0.0158174
$235$	−8.86491	−0.578283
$236$	−1.42763	−0.0929309
$237$	−11.8974	−0.772818
$238$	5.32642	0.345261
$239$	−3.96287	−0.256337	−0.128169	−	0.991752i	$-0.540910\pi$
$239$	−3.96287	−0.256337	−0.128169	+	0.991752i	$0.540910\pi$
$240$	−6.93930	−0.447930
$241$	−20.3938	−1.31368	−0.656841	−	0.754029i	$-0.728108\pi$
$241$	−20.3938	−1.31368	−0.656841	+	0.754029i	$0.728108\pi$
$242$	9.28059	0.596579
$243$	−1.05948	−0.0679656
$244$	−10.1785	−0.651613
$245$	−24.1462	−1.54264
$246$	5.58371	0.356004
$247$	10.5995	0.674429
$248$	0.698242	0.0443384
$249$	−16.2231	−1.02810
$250$	−26.9697	−1.70572
$251$	25.6553	1.61935	0.809674	−	0.586880i	$-0.199644\pi$
$251$	25.6553	1.61935	0.809674	+	0.586880i	$0.199644\pi$
$252$	−0.105820	−0.00666603
$253$	−0.996893	−0.0626741
$254$	−15.6377	−0.981196
$255$	35.6249	2.23092
$256$	1.00000	0.0625000
$257$	−21.0779	−1.31480	−0.657402	−	0.753540i	$-0.728345\pi$
$257$	−21.0779	−1.31480	−0.657402	+	0.753540i	$0.728345\pi$
$258$	9.93318	0.618413
$259$	−8.20874	−0.510066
$260$	9.67029	0.599726
$261$	−0.526164	−0.0325687
$262$	−9.26329	−0.572288
$263$	15.9581	0.984019	0.492009	−	0.870590i	$-0.336263\pi$
$263$	15.9581	0.984019	0.492009	+	0.870590i	$0.336263\pi$
$264$	−2.23223	−0.137384
$265$	−2.02143	−0.124176
$266$	−4.63563	−0.284229
$267$	−27.1080	−1.65898
$268$	15.5856	0.952042
$269$	−7.34367	−0.447752	−0.223876	−	0.974618i	$-0.571871\pi$
$269$	−7.34367	−0.447752	−0.223876	+	0.974618i	$0.571871\pi$
$270$	−21.5257	−1.31001
$271$	−3.56307	−0.216441	−0.108221	−	0.994127i	$-0.534515\pi$
$271$	−3.56307	−0.216441	−0.108221	+	0.994127i	$0.534515\pi$
$272$	−5.13379	−0.311282
$273$	−4.19006	−0.253594
$274$	0.0402046	0.00242885
$275$	−15.2319	−0.918520
$276$	−1.29422	−0.0779029
$277$	−6.73812	−0.404855	−0.202427	−	0.979297i	$-0.564883\pi$
$277$	−6.73812	−0.404855	−0.202427	+	0.979297i	$0.564883\pi$
$278$	19.9509	1.19657
$279$	0.0712158	0.00426358
$280$	−4.22925	−0.252746
$281$	−24.8932	−1.48501	−0.742503	−	0.669843i	$-0.766361\pi$
$281$	−24.8932	−1.48501	−0.742503	+	0.669843i	$0.766361\pi$
$282$	−3.70218	−0.220462
$283$	5.60601	0.333243	0.166621	−	0.986021i	$-0.446714\pi$
$283$	5.60601	0.333243	0.166621	+	0.986021i	$0.446714\pi$
$284$	−7.14382	−0.423907
$285$	−31.0047	−1.83656
$286$	3.11074	0.183942
$287$	3.40306	0.200877
$288$	0.101993	0.00601000
$289$	9.35582	0.550342
$290$	−21.0289	−1.23486
$291$	−11.5810	−0.678890
$292$	−8.35550	−0.488969
$293$	2.56147	0.149643	0.0748214	−	0.997197i	$-0.476161\pi$
$293$	2.56147	0.149643	0.0748214	+	0.997197i	$0.476161\pi$
$294$	−10.0840	−0.588109
$295$	−5.81946	−0.338822
$296$	7.91187	0.459868
$297$	−6.92437	−0.401793
$298$	12.8354	0.743537
$299$	1.80356	0.104303
$300$	−19.7749	−1.14171
$301$	6.05391	0.348941
$302$	16.1459	0.929092
$303$	−18.2744	−1.04984
$304$	4.46798	0.256256
$305$	−41.4907	−2.37575
$306$	−0.523611	−0.0299329
$307$	6.62710	0.378228	0.189114	−	0.981955i	$-0.439438\pi$
$307$	6.62710	0.378228	0.189114	+	0.981955i	$0.439438\pi$
$308$	−1.36046	−0.0775196
$309$	15.2289	0.866344
$310$	2.84624	0.161656
$311$	14.4722	0.820643	0.410321	−	0.911941i	$-0.365417\pi$
$311$	14.4722	0.820643	0.410321	+	0.911941i	$0.365417\pi$
$312$	4.03853	0.228637
$313$	−30.8995	−1.74655	−0.873273	−	0.487232i	$-0.838007\pi$
$313$	−30.8995	−1.74655	−0.873273	+	0.487232i	$0.838007\pi$
$314$	−12.0959	−0.682611
$315$	−0.431354	−0.0243041
$316$	6.98878	0.393150
$317$	−11.4870	−0.645175	−0.322588	−	0.946540i	$-0.604553\pi$
$317$	−11.4870	−0.645175	−0.322588	+	0.946540i	$0.604553\pi$
$318$	−0.844194	−0.0473401
$319$	−6.76457	−0.378743
$320$	4.07630	0.227872
$321$	1.96793	0.109839
$322$	−0.788780	−0.0439570
$323$	−22.9377	−1.27629
$324$	−8.68362	−0.482423
$325$	27.5574	1.52861
$326$	−1.88880	−0.104611
$327$	−19.7000	−1.08941
$328$	−3.27999	−0.181107
$329$	−2.25634	−0.124396
$330$	−9.09925	−0.500897
$331$	9.23886	0.507814	0.253907	−	0.967229i	$-0.418284\pi$
$331$	9.23886	0.507814	0.253907	+	0.967229i	$0.418284\pi$
$332$	9.52981	0.523016
$333$	0.806956	0.0442209
$334$	−6.55728	−0.358799
$335$	63.5316	3.47110
$336$	−1.76623	−0.0963557
$337$	10.4779	0.570767	0.285384	−	0.958413i	$-0.407879\pi$
$337$	10.4779	0.570767	0.285384	+	0.958413i	$0.407879\pi$
$338$	7.37210	0.400989
$339$	−21.6643	−1.17664
$340$	−20.9269	−1.13492
$341$	0.915579	0.0495814
$342$	0.455703	0.0246416
$343$	−13.4085	−0.723989
$344$	−5.83497	−0.314600
$345$	−5.27563	−0.284030
$346$	−9.61367	−0.516834
$347$	13.3901	0.718818	0.359409	−	0.933180i	$-0.382978\pi$
$347$	13.3901	0.718818	0.359409	+	0.933180i	$0.382978\pi$
$348$	−8.78213	−0.470772
$349$	28.3325	1.51660	0.758301	−	0.651905i	$-0.226030\pi$
$349$	28.3325	1.51660	0.758301	+	0.651905i	$0.226030\pi$
$350$	−12.0521	−0.644211
$351$	12.5275	0.668667
$352$	1.31126	0.0698906
$353$	7.38649	0.393143	0.196572	−	0.980489i	$-0.437019\pi$
$353$	7.38649	0.393143	0.196572	+	0.980489i	$0.437019\pi$
$354$	−2.43033	−0.129171
$355$	−29.1203	−1.54555
$356$	15.9239	0.843962
$357$	9.06745	0.479900
$358$	−10.3741	−0.548291
$359$	−17.7601	−0.937341	−0.468670	−	0.883373i	$-0.655267\pi$
$359$	−17.7601	−0.937341	−0.468670	+	0.883373i	$0.655267\pi$
$360$	0.415754	0.0219122
$361$	0.962862	0.0506770
$362$	5.78228	0.303910
$363$	15.7988	0.829224
$364$	2.46133	0.129009
$365$	−34.0595	−1.78276
$366$	−17.3274	−0.905720
$367$	29.5891	1.54454	0.772269	−	0.635296i	$-0.219122\pi$
$367$	29.5891	1.54454	0.772269	+	0.635296i	$0.219122\pi$
$368$	0.760254	0.0396310
$369$	−0.334536	−0.0174153
$370$	32.2512	1.67666
$371$	−0.514505	−0.0267118
$372$	1.18865	0.0616289
$373$	29.1942	1.51162	0.755810	−	0.654791i	$-0.227243\pi$
$373$	29.1942	1.51162	0.755810	+	0.654791i	$0.227243\pi$
$374$	−6.73175	−0.348091
$375$	−45.9120	−2.37089
$376$	2.17474	0.112154
$377$	12.2384	0.630308
$378$	−5.47883	−0.281801
$379$	8.17757	0.420054	0.210027	−	0.977696i	$-0.432645\pi$
$379$	8.17757	0.420054	0.210027	+	0.977696i	$0.432645\pi$
$380$	18.2128	0.934299
$381$	−26.6209	−1.36383
$382$	−8.94259	−0.457543
$383$	7.06134	0.360818	0.180409	−	0.983592i	$-0.442258\pi$
$383$	7.06134	0.360818	0.180409	+	0.983592i	$0.442258\pi$
$384$	1.70235	0.0868729
$385$	−5.54566	−0.282633
$386$	17.8248	0.907256
$387$	−0.595126	−0.0302520
$388$	6.80293	0.345367
$389$	4.21852	0.213888	0.106944	−	0.994265i	$-0.465894\pi$
$389$	4.21852	0.213888	0.106944	+	0.994265i	$0.465894\pi$
$390$	16.4623	0.833598
$391$	−3.90298	−0.197382
$392$	5.92355	0.299184
$393$	−15.7694	−0.795461
$394$	−18.6669	−0.940427
$395$	28.4884	1.43341
$396$	0.133740	0.00672067
$397$	10.9084	0.547478	0.273739	−	0.961804i	$-0.411740\pi$
$397$	10.9084	0.547478	0.273739	+	0.961804i	$0.411740\pi$
$398$	−13.4208	−0.672723
$399$	−7.89148	−0.395068
$400$	11.6162	0.580812
$401$	25.6705	1.28192	0.640961	−	0.767574i	$-0.278536\pi$
$401$	25.6705	1.28192	0.640961	+	0.767574i	$0.278536\pi$
$402$	26.5322	1.32331
$403$	−1.65645	−0.0825138
$404$	10.7348	0.534076
$405$	−35.3970	−1.75889
$406$	−5.35239	−0.265635
$407$	10.3745	0.514247
$408$	−8.73953	−0.432671
$409$	27.2787	1.34885	0.674424	−	0.738345i	$-0.264392\pi$
$409$	27.2787	1.34885	0.674424	+	0.738345i	$0.264392\pi$
$410$	−13.3702	−0.660309
$411$	0.0684424	0.00337602
$412$	−8.94582	−0.440729
$413$	−1.48120	−0.0728850
$414$	0.0775406	0.00381091
$415$	38.8464	1.90689
$416$	−2.37232	−0.116313
$417$	33.9634	1.66320
$418$	5.85870	0.286558
$419$	11.8089	0.576901	0.288451	−	0.957495i	$-0.406860\pi$
$419$	11.8089	0.576901	0.288451	+	0.957495i	$0.406860\pi$
$420$	−7.19968	−0.351308
$421$	−38.9584	−1.89871	−0.949357	−	0.314198i	$-0.898264\pi$
$421$	−38.9584	−1.89871	−0.949357	+	0.314198i	$0.898264\pi$
$422$	3.72585	0.181371
$423$	0.221809	0.0107847
$424$	0.495898	0.0240830
$425$	−59.6353	−2.89274
$426$	−12.1613	−0.589217
$427$	−10.5604	−0.511056
$428$	−1.15600	−0.0558776
$429$	5.29557	0.255673
$430$	−23.7851	−1.14702
$431$	10.2463	0.493547	0.246774	−	0.969073i	$-0.420630\pi$
$431$	10.2463	0.493547	0.246774	+	0.969073i	$0.420630\pi$
$432$	5.28069	0.254067
$433$	−4.12687	−0.198325	−0.0991623	−	0.995071i	$-0.531616\pi$
$433$	−4.12687	−0.198325	−0.0991623	+	0.995071i	$0.531616\pi$
$434$	0.724441	0.0347743
$435$	−35.7986	−1.71641
$436$	11.5722	0.554208
$437$	3.39680	0.162491
$438$	−14.2240	−0.679650
$439$	−19.6791	−0.939233	−0.469616	−	0.882871i	$-0.655608\pi$
$439$	−19.6791	−0.939233	−0.469616	+	0.882871i	$0.655608\pi$
$440$	5.34510	0.254818
$441$	0.604161	0.0287696
$442$	12.1790	0.579296
$443$	1.80713	0.0858591	0.0429296	−	0.999078i	$-0.486331\pi$
$443$	1.80713	0.0858591	0.0429296	+	0.999078i	$0.486331\pi$
$444$	13.4688	0.639201
$445$	64.9104	3.07705
$446$	3.81823	0.180798
$447$	21.8505	1.03349
$448$	1.03752	0.0490183
$449$	−19.7178	−0.930540	−0.465270	−	0.885169i	$-0.654043\pi$
$449$	−19.7178	−0.930540	−0.465270	+	0.885169i	$0.654043\pi$
$450$	1.18477	0.0558508
$451$	−4.30093	−0.202523
$452$	12.7261	0.598584
$453$	27.4860	1.29141
$454$	−15.3243	−0.719205
$455$	10.0331	0.470361
$456$	7.60608	0.356188
$457$	24.0627	1.12561	0.562804	−	0.826591i	$-0.309723\pi$
$457$	24.0627	1.12561	0.562804	+	0.826591i	$0.309723\pi$
$458$	−19.0411	−0.889733
$459$	−27.1100	−1.26538
$460$	3.09902	0.144493
$461$	−9.06197	−0.422058	−0.211029	−	0.977480i	$-0.567681\pi$
$461$	−9.06197	−0.422058	−0.211029	+	0.977480i	$0.567681\pi$
$462$	−2.31599	−0.107750
$463$	−27.5234	−1.27912	−0.639560	−	0.768741i	$-0.720883\pi$
$463$	−27.5234	−1.27912	−0.639560	+	0.768741i	$0.720883\pi$
$464$	5.15882	0.239492
$465$	4.84531	0.224696
$466$	12.6530	0.586140
$467$	3.53732	0.163688	0.0818438	−	0.996645i	$-0.473919\pi$
$467$	3.53732	0.163688	0.0818438	+	0.996645i	$0.473919\pi$
$468$	−0.241960	−0.0111846
$469$	16.1704	0.746680
$470$	8.86491	0.408908
$471$	−20.5915	−0.948806
$472$	1.42763	0.0657121
$473$	−7.65118	−0.351802
$474$	11.8974	0.546465
$475$	51.9011	2.38139
$476$	−5.32642	−0.244136
$477$	0.0505782	0.00231582
$478$	3.96287	0.181258
$479$	−1.80306	−0.0823839	−0.0411919	−	0.999151i	$-0.513116\pi$
$479$	−1.80306	−0.0823839	−0.0411919	+	0.999151i	$0.513116\pi$
$480$	6.93930	0.316734
$481$	−18.7695	−0.855815
$482$	20.3938	0.928913
$483$	−1.34278	−0.0610987
$484$	−9.28059	−0.421845
$485$	27.7308	1.25919
$486$	1.05948	0.0480589
$487$	13.8396	0.627131	0.313565	−	0.949567i	$-0.398477\pi$
$487$	13.8396	0.627131	0.313565	+	0.949567i	$0.398477\pi$
$488$	10.1785	0.460760
$489$	−3.21540	−0.145405
$490$	24.1462	1.09081
$491$	40.3124	1.81927	0.909636	−	0.415406i	$-0.136360\pi$
$491$	40.3124	1.81927	0.909636	+	0.415406i	$0.136360\pi$
$492$	−5.58371	−0.251733
$493$	−26.4843	−1.19279
$494$	−10.5995	−0.476893
$495$	0.545163	0.0245033
$496$	−0.698242	−0.0313520
$497$	−7.41186	−0.332468
$498$	16.2231	0.726975
$499$	32.4731	1.45370	0.726848	−	0.686798i	$-0.240985\pi$
$499$	32.4731	1.45370	0.726848	+	0.686798i	$0.240985\pi$
$500$	26.9697	1.20612
$501$	−11.1628	−0.498718
$502$	−25.6553	−1.14505
$503$	−42.9514	−1.91511	−0.957553	−	0.288257i	$-0.906924\pi$
$503$	−42.9514	−1.91511	−0.957553	+	0.288257i	$0.906924\pi$
$504$	0.105820	0.00471360
$505$	43.7583	1.94722
$506$	0.996893	0.0443173
$507$	12.5499	0.557361
$508$	15.6377	0.693811
$509$	−34.6615	−1.53634	−0.768172	−	0.640244i	$-0.778833\pi$
$509$	−34.6615	−1.53634	−0.768172	+	0.640244i	$0.778833\pi$
$510$	−35.6249	−1.57750
$511$	−8.66902	−0.383495
$512$	−1.00000	−0.0441942
$513$	23.5940	1.04170
$514$	21.0779	0.929706
$515$	−36.4658	−1.60688
$516$	−9.93318	−0.437284
$517$	2.85166	0.125416
$518$	8.20874	0.360671
$519$	−16.3659	−0.718382
$520$	−9.67029	−0.424070
$521$	28.1674	1.23404	0.617019	−	0.786949i	$-0.288340\pi$
$521$	28.1674	1.23404	0.617019	+	0.786949i	$0.288340\pi$
$522$	0.526164	0.0230296
$523$	13.8014	0.603492	0.301746	−	0.953388i	$-0.402431\pi$
$523$	13.8014	0.603492	0.301746	+	0.953388i	$0.402431\pi$
$524$	9.26329	0.404669
$525$	−20.5169	−0.895432
$526$	−15.9581	−0.695806
$527$	3.58463	0.156149
$528$	2.23223	0.0971455
$529$	−22.4220	−0.974870
$530$	2.02143	0.0878053
$531$	0.145609	0.00631887
$532$	4.63563	0.200980
$533$	7.78119	0.337041
$534$	27.1080	1.17308
$535$	−4.71222	−0.203727
$536$	−15.5856	−0.673196
$537$	−17.6605	−0.762105
$538$	7.34367	0.316608
$539$	7.76733	0.334563
$540$	21.5257	0.926318
$541$	29.4943	1.26806	0.634030	−	0.773309i	$-0.281400\pi$
$541$	29.4943	1.26806	0.634030	+	0.773309i	$0.281400\pi$
$542$	3.56307	0.153047
$543$	9.84348	0.422424
$544$	5.13379	0.220110
$545$	47.1718	2.02062
$546$	4.19006	0.179318
$547$	12.4292	0.531434	0.265717	−	0.964051i	$-0.414391\pi$
$547$	12.4292	0.531434	0.265717	+	0.964051i	$0.414391\pi$
$548$	−0.0402046	−0.00171746
$549$	1.03814	0.0443067
$550$	15.2319	0.649492
$551$	23.0495	0.981942
$552$	1.29422	0.0550857
$553$	7.25101	0.308344
$554$	6.73812	0.286275
$555$	54.9029	2.33050
$556$	−19.9509	−0.846105
$557$	−35.5304	−1.50547	−0.752736	−	0.658322i	$-0.771267\pi$
$557$	−35.5304	−1.50547	−0.752736	+	0.658322i	$0.771267\pi$
$558$	−0.0712158	−0.00301481
$559$	13.8424	0.585472
$560$	4.22925	0.178718
$561$	−11.4598	−0.483834
$562$	24.8932	1.05006
$563$	−7.98426	−0.336497	−0.168248	−	0.985745i	$-0.553811\pi$
$563$	−7.98426	−0.336497	−0.168248	+	0.985745i	$0.553811\pi$
$564$	3.70218	0.155890
$565$	51.8753	2.18241
$566$	−5.60601	−0.235638
$567$	−9.00944	−0.378361
$568$	7.14382	0.299748
$569$	−2.21774	−0.0929727	−0.0464863	−	0.998919i	$-0.514802\pi$
$569$	−2.21774	−0.0929727	−0.0464863	+	0.998919i	$0.514802\pi$
$570$	31.0047	1.29864
$571$	−33.0788	−1.38431	−0.692153	−	0.721751i	$-0.743338\pi$
$571$	−33.0788	−1.38431	−0.692153	+	0.721751i	$0.743338\pi$
$572$	−3.11074	−0.130066
$573$	−15.2235	−0.635969
$574$	−3.40306	−0.142041
$575$	8.83128	0.368290
$576$	−0.101993	−0.00424971
$577$	−36.2739	−1.51010	−0.755050	−	0.655667i	$-0.772388\pi$
$577$	−36.2739	−1.51010	−0.755050	+	0.655667i	$0.772388\pi$
$578$	−9.35582	−0.389151
$579$	30.3440	1.26106
$580$	21.0289	0.873177
$581$	9.88739	0.410198
$582$	11.5810	0.480048
$583$	0.650253	0.0269307
$584$	8.35550	0.345753
$585$	−0.986302	−0.0407786
$586$	−2.56147	−0.105813
$587$	45.8702	1.89326	0.946632	−	0.322315i	$-0.104461\pi$
$587$	45.8702	1.89326	0.946632	+	0.322315i	$0.104461\pi$
$588$	10.0840	0.415856
$589$	−3.11973	−0.128546
$590$	5.81946	0.239583
$591$	−31.7777	−1.30716
$592$	−7.91187	−0.325176
$593$	−26.2469	−1.07783	−0.538916	−	0.842360i	$-0.681166\pi$
$593$	−26.2469	−1.07783	−0.538916	+	0.842360i	$0.681166\pi$
$594$	6.92437	0.284110
$595$	−21.7121	−0.890109
$596$	−12.8354	−0.525760
$597$	−22.8469	−0.935062
$598$	−1.80356	−0.0737533
$599$	−14.9251	−0.609824	−0.304912	−	0.952381i	$-0.598627\pi$
$599$	−14.9251	−0.609824	−0.304912	+	0.952381i	$0.598627\pi$
$600$	19.7749	0.807308
$601$	−26.5058	−1.08120	−0.540598	−	0.841281i	$-0.681802\pi$
$601$	−26.5058	−1.08120	−0.540598	+	0.841281i	$0.681802\pi$
$602$	−6.05391	−0.246739
$603$	−1.58962	−0.0647345
$604$	−16.1459	−0.656967
$605$	−37.8305	−1.53803
$606$	18.2744	0.742348
$607$	−24.2897	−0.985888	−0.492944	−	0.870061i	$-0.664079\pi$
$607$	−24.2897	−0.985888	−0.492944	+	0.870061i	$0.664079\pi$
$608$	−4.46798	−0.181201
$609$	−9.11165	−0.369223
$610$	41.4907	1.67991
$611$	−5.15919	−0.208718
$612$	0.523611	0.0211657
$613$	8.53805	0.344848	0.172424	−	0.985023i	$-0.444840\pi$
$613$	8.53805	0.344848	0.172424	+	0.985023i	$0.444840\pi$
$614$	−6.62710	−0.267448
$615$	−22.7609	−0.917807
$616$	1.36046	0.0548147
$617$	−32.7930	−1.32019	−0.660097	−	0.751180i	$-0.729485\pi$
$617$	−32.7930	−1.32019	−0.660097	+	0.751180i	$0.729485\pi$
$618$	−15.2289	−0.612598
$619$	−14.8820	−0.598158	−0.299079	−	0.954228i	$-0.596679\pi$
$619$	−14.8820	−0.598158	−0.299079	+	0.954228i	$0.596679\pi$
$620$	−2.84624	−0.114308
$621$	4.01466	0.161103
$622$	−14.4722	−0.580282
$623$	16.5213	0.661914
$624$	−4.03853	−0.161670
$625$	51.8557	2.07423
$626$	30.8995	1.23499
$627$	9.97358	0.398306
$628$	12.0959	0.482679
$629$	40.6179	1.61954
$630$	0.431354	0.0171856
$631$	29.2178	1.16314	0.581572	−	0.813495i	$-0.302438\pi$
$631$	29.2178	1.16314	0.581572	+	0.813495i	$0.302438\pi$
$632$	−6.98878	−0.277999
$633$	6.34271	0.252100
$634$	11.4870	0.456208
$635$	63.7440	2.52960
$636$	0.844194	0.0334745
$637$	−14.0526	−0.556782
$638$	6.76457	0.267812
$639$	0.728620	0.0288237
$640$	−4.07630	−0.161130
$641$	1.52056	0.0600584	0.0300292	−	0.999549i	$-0.490440\pi$
$641$	1.52056	0.0600584	0.0300292	+	0.999549i	$0.490440\pi$
$642$	−1.96793	−0.0776679
$643$	30.5898	1.20634	0.603172	−	0.797611i	$-0.293903\pi$
$643$	30.5898	1.20634	0.603172	+	0.797611i	$0.293903\pi$
$644$	0.788780	0.0310823
$645$	−40.4906	−1.59432
$646$	22.9377	0.902471
$647$	1.90178	0.0747669	0.0373834	−	0.999301i	$-0.488098\pi$
$647$	1.90178	0.0747669	0.0373834	+	0.999301i	$0.488098\pi$
$648$	8.68362	0.341125
$649$	1.87200	0.0734825
$650$	−27.5574	−1.08089
$651$	1.23325	0.0483351
$652$	1.88880	0.0739709
$653$	24.2031	0.947139	0.473569	−	0.880756i	$-0.342965\pi$
$653$	24.2031	0.947139	0.473569	+	0.880756i	$0.342965\pi$
$654$	19.7000	0.770330
$655$	37.7600	1.47540
$656$	3.27999	0.128062
$657$	0.852203	0.0332476
$658$	2.25634	0.0879615
$659$	27.2315	1.06079	0.530395	−	0.847751i	$-0.322044\pi$
$659$	27.2315	1.06079	0.530395	+	0.847751i	$0.322044\pi$
$660$	9.09925	0.354188
$661$	16.3279	0.635081	0.317541	−	0.948245i	$-0.397143\pi$
$661$	16.3279	0.635081	0.317541	+	0.948245i	$0.397143\pi$
$662$	−9.23886	−0.359079
$663$	20.7330	0.805201
$664$	−9.52981	−0.369828
$665$	18.8962	0.732764
$666$	−0.806956	−0.0312689
$667$	3.92201	0.151861
$668$	6.55728	0.253709
$669$	6.49998	0.251304
$670$	−63.5316	−2.45444
$671$	13.3467	0.515245
$672$	1.76623	0.0681338
$673$	20.0018	0.771012	0.385506	−	0.922705i	$-0.374027\pi$
$673$	20.0018	0.771012	0.385506	+	0.922705i	$0.374027\pi$
$674$	−10.4779	−0.403593
$675$	61.3417	2.36104
$676$	−7.37210	−0.283542
$677$	−15.5543	−0.597799	−0.298899	−	0.954285i	$-0.596619\pi$
$677$	−15.5543	−0.597799	−0.298899	+	0.954285i	$0.596619\pi$
$678$	21.6643	0.832011
$679$	7.05819	0.270869
$680$	20.9269	0.802509
$681$	−26.0874	−0.999670
$682$	−0.915579	−0.0350593
$683$	−22.9697	−0.878910	−0.439455	−	0.898265i	$-0.644828\pi$
$683$	−22.9697	−0.878910	−0.439455	+	0.898265i	$0.644828\pi$
$684$	−0.455703	−0.0174242
$685$	−0.163886	−0.00626176
$686$	13.4085	0.511938
$687$	−32.4147	−1.23670
$688$	5.83497	0.222456
$689$	−1.17643	−0.0448184
$690$	5.27563	0.200840
$691$	−26.6472	−1.01371	−0.506854	−	0.862032i	$-0.669192\pi$
$691$	−26.6472	−1.01371	−0.506854	+	0.862032i	$0.669192\pi$
$692$	9.61367	0.365457
$693$	0.138758	0.00527098
$694$	−13.3901	−0.508281
$695$	−81.3257	−3.08486
$696$	8.78213	0.332886
$697$	−16.8388	−0.637815
$698$	−28.3325	−1.07240
$699$	21.5399	0.814715
$700$	12.0521	0.455526
$701$	9.42887	0.356124	0.178062	−	0.984019i	$-0.443017\pi$
$701$	9.42887	0.356124	0.178062	+	0.984019i	$0.443017\pi$
$702$	−12.5275	−0.472819
$703$	−35.3501	−1.33325
$704$	−1.31126	−0.0494201
$705$	15.0912	0.568368
$706$	−7.38649	−0.277994
$707$	11.1376	0.418872
$708$	2.43033	0.0913375
$709$	−31.0011	−1.16427	−0.582135	−	0.813092i	$-0.697783\pi$
$709$	−31.0011	−1.16427	−0.582135	+	0.813092i	$0.697783\pi$
$710$	29.1203	1.09287
$711$	−0.712807	−0.0267324
$712$	−15.9239	−0.596772
$713$	−0.530841	−0.0198802
$714$	−9.06745	−0.339341
$715$	−12.6803	−0.474216
$716$	10.3741	0.387700
$717$	6.74621	0.251942
$718$	17.7601	0.662800
$719$	22.9014	0.854080	0.427040	−	0.904233i	$-0.359556\pi$
$719$	22.9014	0.854080	0.427040	+	0.904233i	$0.359556\pi$
$720$	−0.415754	−0.0154943
$721$	−9.28148	−0.345660
$722$	−0.962862	−0.0358340
$723$	34.7175	1.29116
$724$	−5.78228	−0.214897
$725$	59.9260	2.22560
$726$	−15.7988	−0.586350
$727$	−26.5340	−0.984092	−0.492046	−	0.870569i	$-0.663751\pi$
$727$	−26.5340	−0.984092	−0.492046	+	0.870569i	$0.663751\pi$
$728$	−2.46133	−0.0912231
$729$	27.8545	1.03165
$730$	34.0595	1.26060
$731$	−29.9555	−1.10794
$732$	17.3274	0.640441
$733$	4.32778	0.159850	0.0799250	−	0.996801i	$-0.474532\pi$
$733$	4.32778	0.159850	0.0799250	+	0.996801i	$0.474532\pi$
$734$	−29.5891	−1.09215
$735$	41.1053	1.51619
$736$	−0.760254	−0.0280233
$737$	−20.4368	−0.752800
$738$	0.334536	0.0123145
$739$	28.1923	1.03707	0.518536	−	0.855056i	$-0.326477\pi$
$739$	28.1923	1.03707	0.518536	+	0.855056i	$0.326477\pi$
$740$	−32.2512	−1.18558
$741$	−18.0441	−0.662865
$742$	0.514505	0.0188881
$743$	7.65119	0.280695	0.140348	−	0.990102i	$-0.455178\pi$
$743$	7.65119	0.280695	0.140348	+	0.990102i	$0.455178\pi$
$744$	−1.18865	−0.0435782
$745$	−52.3211	−1.91690
$746$	−29.1942	−1.06888
$747$	−0.971975	−0.0355627
$748$	6.73175	0.246137
$749$	−1.19938	−0.0438244
$750$	45.9120	1.67647
$751$	37.7778	1.37853	0.689266	−	0.724508i	$-0.257933\pi$
$751$	37.7778	1.37853	0.689266	+	0.724508i	$0.257933\pi$
$752$	−2.17474	−0.0793048
$753$	−43.6744	−1.59158
$754$	−12.2384	−0.445695
$755$	−65.8156	−2.39527
$756$	5.47883	0.199263
$757$	1.13336	0.0411928	0.0205964	−	0.999788i	$-0.493443\pi$
$757$	1.13336	0.0411928	0.0205964	+	0.999788i	$0.493443\pi$
$758$	−8.17757	−0.297023
$759$	1.69706	0.0615995
$760$	−18.2128	−0.660649
$761$	1.72037	0.0623634	0.0311817	−	0.999514i	$-0.490073\pi$
$761$	1.72037	0.0623634	0.0311817	+	0.999514i	$0.490073\pi$
$762$	26.6209	0.964373
$763$	12.0064	0.434661
$764$	8.94259	0.323532
$765$	2.13440	0.0771693
$766$	−7.06134	−0.255137
$767$	−3.38680	−0.122290
$768$	−1.70235	−0.0614284
$769$	30.1413	1.08692	0.543461	−	0.839435i	$-0.317114\pi$
$769$	30.1413	1.08692	0.543461	+	0.839435i	$0.317114\pi$
$770$	5.54566	0.199852
$771$	35.8820	1.29226
$772$	−17.8248	−0.641527
$773$	48.2615	1.73585	0.867924	−	0.496698i	$-0.165454\pi$
$773$	48.2615	1.73585	0.867924	+	0.496698i	$0.165454\pi$
$774$	0.595126	0.0213914
$775$	−8.11094	−0.291354
$776$	−6.80293	−0.244211
$777$	13.9742	0.501321
$778$	−4.21852	−0.151241
$779$	14.6549	0.525068
$780$	−16.4623	−0.589443
$781$	9.36742	0.335193
$782$	3.90298	0.139570
$783$	27.2421	0.973554
$784$	−5.92355	−0.211555
$785$	49.3065	1.75983
$786$	15.7694	0.562476
$787$	−46.3501	−1.65220	−0.826101	−	0.563522i	$-0.809446\pi$
$787$	−46.3501	−1.65220	−0.826101	+	0.563522i	$0.809446\pi$
$788$	18.6669	0.664982
$789$	−27.1663	−0.967147
$790$	−28.4884	−1.01357
$791$	13.2036	0.469465
$792$	−0.133740	−0.00475223
$793$	−24.1467	−0.857475
$794$	−10.9084	−0.387125
$795$	3.44119	0.122046
$796$	13.4208	0.475687
$797$	37.0247	1.31148	0.655741	−	0.754985i	$-0.272356\pi$
$797$	37.0247	1.31148	0.655741	+	0.754985i	$0.272356\pi$
$798$	7.89148	0.279355
$799$	11.1647	0.394978
$800$	−11.6162	−0.410696
$801$	−1.62412	−0.0573855
$802$	−25.6705	−0.906455
$803$	10.9563	0.386638
$804$	−26.5322	−0.935719
$805$	3.21530	0.113325
$806$	1.65645	0.0583461
$807$	12.5015	0.440075
$808$	−10.7348	−0.377649
$809$	−10.3362	−0.363402	−0.181701	−	0.983354i	$-0.558160\pi$
$809$	−10.3362	−0.363402	−0.181701	+	0.983354i	$0.558160\pi$
$810$	35.3970	1.24373
$811$	31.7218	1.11390	0.556951	−	0.830545i	$-0.311971\pi$
$811$	31.7218	1.11390	0.556951	+	0.830545i	$0.311971\pi$
$812$	5.35239	0.187832
$813$	6.06561	0.212730
$814$	−10.3745	−0.363628
$815$	7.69930	0.269695
$816$	8.73953	0.305945
$817$	26.0705	0.912092
$818$	−27.2787	−0.953779
$819$	−0.251039	−0.00877201
$820$	13.3702	0.466909
$821$	0.280146	0.00977716	0.00488858	−	0.999988i	$-0.498444\pi$
$821$	0.280146	0.00977716	0.00488858	+	0.999988i	$0.498444\pi$
$822$	−0.0684424	−0.00238720
$823$	36.5580	1.27433	0.637167	−	0.770726i	$-0.280106\pi$
$823$	36.5580	1.27433	0.637167	+	0.770726i	$0.280106\pi$
$824$	8.94582	0.311642
$825$	25.9301	0.902771
$826$	1.48120	0.0515375
$827$	36.4356	1.26699	0.633495	−	0.773747i	$-0.281620\pi$
$827$	36.4356	1.26699	0.633495	+	0.773747i	$0.281620\pi$
$828$	−0.0775406	−0.00269472
$829$	1.02705	0.0356708	0.0178354	−	0.999841i	$-0.494323\pi$
$829$	1.02705	0.0356708	0.0178354	+	0.999841i	$0.494323\pi$
$830$	−38.8464	−1.34838
$831$	11.4707	0.397913
$832$	2.37232	0.0822454
$833$	30.4103	1.05365
$834$	−33.9634	−1.17606
$835$	26.7295	0.925011
$836$	−5.85870	−0.202627
$837$	−3.68720	−0.127448
$838$	−11.8089	−0.407931
$839$	12.2991	0.424614	0.212307	−	0.977203i	$-0.431902\pi$
$839$	12.2991	0.424614	0.212307	+	0.977203i	$0.431902\pi$
$840$	7.19968	0.248413
$841$	−2.38659	−0.0822962
$842$	38.9584	1.34259
$843$	42.3771	1.45954
$844$	−3.72585	−0.128249
$845$	−30.0509	−1.03378
$846$	−0.221809	−0.00762594
$847$	−9.62881	−0.330850
$848$	−0.495898	−0.0170292
$849$	−9.54342	−0.327529
$850$	59.6353	2.04547
$851$	−6.01503	−0.206193
$852$	12.1613	0.416639
$853$	31.0343	1.06260	0.531298	−	0.847185i	$-0.321705\pi$
$853$	31.0343	1.06260	0.531298	+	0.847185i	$0.321705\pi$
$854$	10.5604	0.361371
$855$	−1.85758	−0.0635280
$856$	1.15600	0.0395114
$857$	33.9058	1.15820	0.579101	−	0.815256i	$-0.303404\pi$
$857$	33.9058	1.15820	0.579101	+	0.815256i	$0.303404\pi$
$858$	−5.29557	−0.180788
$859$	7.08003	0.241568	0.120784	−	0.992679i	$-0.461459\pi$
$859$	7.08003	0.241568	0.120784	+	0.992679i	$0.461459\pi$
$860$	23.7851	0.811065
$861$	−5.79322	−0.197432
$862$	−10.2463	−0.348991
$863$	5.77788	0.196681	0.0983406	−	0.995153i	$-0.468647\pi$
$863$	5.77788	0.196681	0.0983406	+	0.995153i	$0.468647\pi$
$864$	−5.28069	−0.179653
$865$	39.1882	1.33244
$866$	4.12687	0.140237
$867$	−15.9269	−0.540906
$868$	−0.724441	−0.0245891
$869$	−9.16413	−0.310872
$870$	35.7986	1.21369
$871$	36.9740	1.25282
$872$	−11.5722	−0.391884
$873$	−0.693852	−0.0234833
$874$	−3.39680	−0.114898
$875$	27.9817	0.945954
$876$	14.2240	0.480585
$877$	49.2301	1.66238	0.831191	−	0.555986i	$-0.187659\pi$
$877$	49.2301	1.66238	0.831191	+	0.555986i	$0.187659\pi$
$878$	19.6791	0.664138
$879$	−4.36053	−0.147077
$880$	−5.34510	−0.180183
$881$	17.9217	0.603797	0.301899	−	0.953340i	$-0.402380\pi$
$881$	17.9217	0.603797	0.301899	+	0.953340i	$0.402380\pi$
$882$	−0.604161	−0.0203432
$883$	7.95247	0.267622	0.133811	−	0.991007i	$-0.457278\pi$
$883$	7.95247	0.267622	0.133811	+	0.991007i	$0.457278\pi$
$884$	−12.1790	−0.409624
$885$	9.90677	0.333012
$886$	−1.80713	−0.0607116
$887$	−33.8122	−1.13530	−0.567652	−	0.823269i	$-0.692148\pi$
$887$	−33.8122	−1.13530	−0.567652	+	0.823269i	$0.692148\pi$
$888$	−13.4688	−0.451984
$889$	16.2245	0.544151
$890$	−64.9104	−2.17580
$891$	11.3865	0.381462
$892$	−3.81823	−0.127844
$893$	−9.71672	−0.325158
$894$	−21.8505	−0.730789
$895$	42.2881	1.41354
$896$	−1.03752	−0.0346612
$897$	−3.07030	−0.102514
$898$	19.7178	0.657991
$899$	−3.60210	−0.120137
$900$	−1.18477	−0.0394925
$901$	2.54584	0.0848142
$902$	4.30093	0.143205
$903$	−10.3059	−0.342958
$904$	−12.7261	−0.423263
$905$	−23.5703	−0.783503
$906$	−27.4860	−0.913162
$907$	−46.1789	−1.53335	−0.766673	−	0.642038i	$-0.778089\pi$
$907$	−46.1789	−1.53335	−0.766673	+	0.642038i	$0.778089\pi$
$908$	15.3243	0.508554
$909$	−1.09487	−0.0363147
$910$	−10.0331	−0.332595
$911$	18.2569	0.604877	0.302438	−	0.953169i	$-0.402199\pi$
$911$	18.2569	0.604877	0.302438	+	0.953169i	$0.402199\pi$
$912$	−7.60608	−0.251863
$913$	−12.4961	−0.413560
$914$	−24.0627	−0.795925
$915$	70.6319	2.33502
$916$	19.0411	0.629136
$917$	9.61087	0.317379
$918$	27.1100	0.894762
$919$	−35.1701	−1.16015	−0.580077	−	0.814562i	$-0.696977\pi$
$919$	−35.1701	−1.16015	−0.580077	+	0.814562i	$0.696977\pi$
$920$	−3.09902	−0.102172
$921$	−11.2817	−0.371743
$922$	9.06197	0.298440
$923$	−16.9474	−0.557831
$924$	2.31599	0.0761905
$925$	−91.9062	−3.02186
$926$	27.5234	0.904475
$927$	0.912411	0.0299675
$928$	−5.15882	−0.169347
$929$	11.4417	0.375389	0.187695	−	0.982227i	$-0.439898\pi$
$929$	11.4417	0.375389	0.187695	+	0.982227i	$0.439898\pi$
$930$	−4.84531	−0.158884
$931$	−26.4663	−0.867398
$932$	−12.6530	−0.414464
$933$	−24.6368	−0.806572
$934$	−3.53732	−0.115745
$935$	27.4406	0.897405
$936$	0.241960	0.00790871
$937$	29.1310	0.951669	0.475835	−	0.879535i	$-0.342146\pi$
$937$	29.1310	0.951669	0.475835	+	0.879535i	$0.342146\pi$
$938$	−16.1704	−0.527982
$939$	52.6019	1.71660
$940$	−8.86491	−0.289142
$941$	−9.40037	−0.306443	−0.153222	−	0.988192i	$-0.548965\pi$
$941$	−9.40037	−0.306443	−0.153222	+	0.988192i	$0.548965\pi$
$942$	20.5915	0.670907
$943$	2.49363	0.0812036
$944$	−1.42763	−0.0464655
$945$	22.3334	0.726504
$946$	7.65118	0.248761
$947$	55.4521	1.80195	0.900976	−	0.433870i	$-0.142852\pi$
$947$	55.4521	1.80195	0.900976	+	0.433870i	$0.142852\pi$
$948$	−11.8974	−0.386409
$949$	−19.8219	−0.643447
$950$	−51.9011	−1.68389
$951$	19.5550	0.634113
$952$	5.32642	0.172630
$953$	35.5889	1.15284	0.576419	−	0.817154i	$-0.304449\pi$
$953$	35.5889	1.15284	0.576419	+	0.817154i	$0.304449\pi$
$954$	−0.0505782	−0.00163753
$955$	36.4527	1.17958
$956$	−3.96287	−0.128169
$957$	11.5157	0.372249
$958$	1.80306	0.0582542
$959$	−0.0417131	−0.00134699
$960$	−6.93930	−0.223965
$961$	−30.5125	−0.984273
$962$	18.7695	0.605153
$963$	0.117904	0.00379942
$964$	−20.3938	−0.656841
$965$	−72.6591	−2.33898
$966$	1.34278	0.0432033
$967$	42.8153	1.37685	0.688424	−	0.725308i	$-0.258303\pi$
$967$	42.8153	1.37685	0.688424	+	0.725308i	$0.258303\pi$
$968$	9.28059	0.298289
$969$	39.0481	1.25440
$970$	−27.7308	−0.890382
$971$	2.86244	0.0918601	0.0459300	−	0.998945i	$-0.485375\pi$
$971$	2.86244	0.0918601	0.0459300	+	0.998945i	$0.485375\pi$
$972$	−1.05948	−0.0339828
$973$	−20.6995	−0.663594
$974$	−13.8396	−0.443448
$975$	−46.9125	−1.50240
$976$	−10.1785	−0.325807
$977$	−10.5258	−0.336750	−0.168375	−	0.985723i	$-0.553852\pi$
$977$	−10.5258	−0.336750	−0.168375	+	0.985723i	$0.553852\pi$
$978$	3.21540	0.102817
$979$	−20.8804	−0.667339
$980$	−24.1462	−0.771321
$981$	−1.18028	−0.0376836
$982$	−40.3124	−1.28642
$983$	−9.29329	−0.296410	−0.148205	−	0.988957i	$-0.547350\pi$
$983$	−9.29329	−0.296410	−0.148205	+	0.988957i	$0.547350\pi$
$984$	5.58371	0.178002
$985$	76.0921	2.42450
$986$	26.4843	0.843432
$987$	3.84110	0.122263
$988$	10.5995	0.337214
$989$	4.43606	0.141058
$990$	−0.545163	−0.0173264
$991$	9.97620	0.316904	0.158452	−	0.987367i	$-0.449350\pi$
$991$	9.97620	0.316904	0.158452	+	0.987367i	$0.449350\pi$
$992$	0.698242	0.0221692
$993$	−15.7278	−0.499107
$994$	7.41186	0.235090
$995$	54.7072	1.73433
$996$	−16.2231	−0.514049
$997$	52.2680	1.65535	0.827673	−	0.561211i	$-0.189664\pi$
$997$	52.2680	1.65535	0.827673	+	0.561211i	$0.189664\pi$
$998$	−32.4731	−1.02792
$999$	−41.7801	−1.32187

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8002.2.a.e.1.18	✓	77

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8002.2.a.e.1.18	✓	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.70235 q^{3} +1.00000 q^{4} +4.07630 q^{5} +1.70235 q^{6} +1.03752 q^{7} -1.00000 q^{8} -0.101993 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.70235 q^{3} +1.00000 q^{4} +4.07630 q^{5} +1.70235 q^{6} +1.03752 q^{7} -1.00000 q^{8} -0.101993 q^{9} -4.07630 q^{10} -1.31126 q^{11} -1.70235 q^{12} +2.37232 q^{13} -1.03752 q^{14} -6.93930 q^{15} +1.00000 q^{16} -5.13379 q^{17} +0.101993 q^{18} +4.46798 q^{19} +4.07630 q^{20} -1.76623 q^{21} +1.31126 q^{22} +0.760254 q^{23} +1.70235 q^{24} +11.6162 q^{25} -2.37232 q^{26} +5.28069 q^{27} +1.03752 q^{28} +5.15882 q^{29} +6.93930 q^{30} -0.698242 q^{31} -1.00000 q^{32} +2.23223 q^{33} +5.13379 q^{34} +4.22925 q^{35} -0.101993 q^{36} -7.91187 q^{37} -4.46798 q^{38} -4.03853 q^{39} -4.07630 q^{40} +3.27999 q^{41} +1.76623 q^{42} +5.83497 q^{43} -1.31126 q^{44} -0.415754 q^{45} -0.760254 q^{46} -2.17474 q^{47} -1.70235 q^{48} -5.92355 q^{49} -11.6162 q^{50} +8.73953 q^{51} +2.37232 q^{52} -0.495898 q^{53} -5.28069 q^{54} -5.34510 q^{55} -1.03752 q^{56} -7.60608 q^{57} -5.15882 q^{58} -1.42763 q^{59} -6.93930 q^{60} -10.1785 q^{61} +0.698242 q^{62} -0.105820 q^{63} +1.00000 q^{64} +9.67029 q^{65} -2.23223 q^{66} +15.5856 q^{67} -5.13379 q^{68} -1.29422 q^{69} -4.22925 q^{70} -7.14382 q^{71} +0.101993 q^{72} -8.35550 q^{73} +7.91187 q^{74} -19.7749 q^{75} +4.46798 q^{76} -1.36046 q^{77} +4.03853 q^{78} +6.98878 q^{79} +4.07630 q^{80} -8.68362 q^{81} -3.27999 q^{82} +9.52981 q^{83} -1.76623 q^{84} -20.9269 q^{85} -5.83497 q^{86} -8.78213 q^{87} +1.31126 q^{88} +15.9239 q^{89} +0.415754 q^{90} +2.46133 q^{91} +0.760254 q^{92} +1.18865 q^{93} +2.17474 q^{94} +18.2128 q^{95} +1.70235 q^{96} +6.80293 q^{97} +5.92355 q^{98} +0.133740 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 77 q - 77 q^{2} + 10 q^{3} + 77 q^{4} + 18 q^{5} - 10 q^{6} + 21 q^{7} - 77 q^{8} + 71 q^{9}+O(q^{10}) \) 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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