LMFDB - Embedded newform 8002.2.a.e.1.32

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			1.32
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)

$f(q)$	$=$	$q-1.00000 q^{2} -0.430836 q^{3} +1.00000 q^{4} +3.21990 q^{5} +0.430836 q^{6} -1.66507 q^{7} -1.00000 q^{8} -2.81438 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -0.430836 q^{3} +1.00000 q^{4} +3.21990 q^{5} +0.430836 q^{6} -1.66507 q^{7} -1.00000 q^{8} -2.81438 q^{9} -3.21990 q^{10} +6.41029 q^{11} -0.430836 q^{12} -5.13198 q^{13} +1.66507 q^{14} -1.38725 q^{15} +1.00000 q^{16} +0.346537 q^{17} +2.81438 q^{18} -5.33722 q^{19} +3.21990 q^{20} +0.717371 q^{21} -6.41029 q^{22} -3.79422 q^{23} +0.430836 q^{24} +5.36774 q^{25} +5.13198 q^{26} +2.50505 q^{27} -1.66507 q^{28} -5.37935 q^{29} +1.38725 q^{30} -3.98254 q^{31} -1.00000 q^{32} -2.76178 q^{33} -0.346537 q^{34} -5.36134 q^{35} -2.81438 q^{36} -2.63552 q^{37} +5.33722 q^{38} +2.21104 q^{39} -3.21990 q^{40} +1.77231 q^{41} -0.717371 q^{42} +4.72304 q^{43} +6.41029 q^{44} -9.06201 q^{45} +3.79422 q^{46} -1.32087 q^{47} -0.430836 q^{48} -4.22755 q^{49} -5.36774 q^{50} -0.149301 q^{51} -5.13198 q^{52} +13.3415 q^{53} -2.50505 q^{54} +20.6405 q^{55} +1.66507 q^{56} +2.29947 q^{57} +5.37935 q^{58} +2.71462 q^{59} -1.38725 q^{60} +6.49092 q^{61} +3.98254 q^{62} +4.68613 q^{63} +1.00000 q^{64} -16.5244 q^{65} +2.76178 q^{66} +2.12793 q^{67} +0.346537 q^{68} +1.63469 q^{69} +5.36134 q^{70} -12.3761 q^{71} +2.81438 q^{72} +15.3852 q^{73} +2.63552 q^{74} -2.31261 q^{75} -5.33722 q^{76} -10.6736 q^{77} -2.21104 q^{78} +9.28208 q^{79} +3.21990 q^{80} +7.36388 q^{81} -1.77231 q^{82} +14.8405 q^{83} +0.717371 q^{84} +1.11581 q^{85} -4.72304 q^{86} +2.31762 q^{87} -6.41029 q^{88} -2.41664 q^{89} +9.06201 q^{90} +8.54509 q^{91} -3.79422 q^{92} +1.71582 q^{93} +1.32087 q^{94} -17.1853 q^{95} +0.430836 q^{96} +13.9184 q^{97} +4.22755 q^{98} -18.0410 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−0.430836	−0.248743	−0.124372	−	0.992236i	$-0.539692\pi$
$3$	−0.430836	−0.248743	−0.124372	+	0.992236i	$0.539692\pi$
$4$	1.00000	0.500000
$5$	3.21990	1.43998	0.719991	−	0.693984i	$-0.244146\pi$
$5$	3.21990	1.43998	0.719991	+	0.693984i	$0.244146\pi$
$6$	0.430836	0.175888
$7$	−1.66507	−0.629336	−0.314668	−	0.949202i	$-0.601893\pi$
$7$	−1.66507	−0.629336	−0.314668	+	0.949202i	$0.601893\pi$
$8$	−1.00000	−0.353553
$9$	−2.81438	−0.938127
$10$	−3.21990	−1.01822
$11$	6.41029	1.93278	0.966388	−	0.257090i	$-0.0827636\pi$
$11$	6.41029	1.93278	0.966388	+	0.257090i	$0.0827636\pi$
$12$	−0.430836	−0.124372
$13$	−5.13198	−1.42335	−0.711677	−	0.702506i	$-0.752064\pi$
$13$	−5.13198	−1.42335	−0.711677	+	0.702506i	$0.752064\pi$
$14$	1.66507	0.445008
$15$	−1.38725	−0.358186
$16$	1.00000	0.250000
$17$	0.346537	0.0840476	0.0420238	−	0.999117i	$-0.486619\pi$
$17$	0.346537	0.0840476	0.0420238	+	0.999117i	$0.486619\pi$
$18$	2.81438	0.663356
$19$	−5.33722	−1.22444	−0.612221	−	0.790687i	$-0.709724\pi$
$19$	−5.33722	−1.22444	−0.612221	+	0.790687i	$0.709724\pi$
$20$	3.21990	0.719991
$21$	0.717371	0.156543
$22$	−6.41029	−1.36668
$23$	−3.79422	−0.791149	−0.395574	−	0.918434i	$-0.629454\pi$
$23$	−3.79422	−0.791149	−0.395574	+	0.918434i	$0.629454\pi$
$24$	0.430836	0.0879441
$25$	5.36774	1.07355
$26$	5.13198	1.00646
$27$	2.50505	0.482096
$28$	−1.66507	−0.314668
$29$	−5.37935	−0.998919	−0.499460	−	0.866337i	$-0.666468\pi$
$29$	−5.37935	−0.998919	−0.499460	+	0.866337i	$0.666468\pi$
$30$	1.38725	0.253276
$31$	−3.98254	−0.715285	−0.357643	−	0.933859i	$-0.616419\pi$
$31$	−3.98254	−0.715285	−0.357643	+	0.933859i	$0.616419\pi$
$32$	−1.00000	−0.176777
$33$	−2.76178	−0.480765
$34$	−0.346537	−0.0594306
$35$	−5.36134	−0.906233
$36$	−2.81438	−0.469063
$37$	−2.63552	−0.433277	−0.216639	−	0.976252i	$-0.569509\pi$
$37$	−2.63552	−0.433277	−0.216639	+	0.976252i	$0.569509\pi$
$38$	5.33722	0.865811
$39$	2.21104	0.354050
$40$	−3.21990	−0.509110
$41$	1.77231	0.276788	0.138394	−	0.990377i	$-0.455806\pi$
$41$	1.77231	0.276788	0.138394	+	0.990377i	$0.455806\pi$
$42$	−0.717371	−0.110693
$43$	4.72304	0.720257	0.360128	−	0.932903i	$-0.382733\pi$
$43$	4.72304	0.720257	0.360128	+	0.932903i	$0.382733\pi$
$44$	6.41029	0.966388
$45$	−9.06201	−1.35089
$46$	3.79422	0.559427
$47$	−1.32087	−0.192669	−0.0963345	−	0.995349i	$-0.530712\pi$
$47$	−1.32087	−0.192669	−0.0963345	+	0.995349i	$0.530712\pi$
$48$	−0.430836	−0.0621858
$49$	−4.22755	−0.603936
$50$	−5.36774	−0.759112
$51$	−0.149301	−0.0209063
$52$	−5.13198	−0.711677
$53$	13.3415	1.83260	0.916300	−	0.400493i	$-0.131161\pi$
$53$	13.3415	1.83260	0.916300	+	0.400493i	$0.131161\pi$
$54$	−2.50505	−0.340893
$55$	20.6405	2.78316
$56$	1.66507	0.222504
$57$	2.29947	0.304572
$58$	5.37935	0.706343
$59$	2.71462	0.353414	0.176707	−	0.984263i	$-0.443455\pi$
$59$	2.71462	0.353414	0.176707	+	0.984263i	$0.443455\pi$
$60$	−1.38725	−0.179093
$61$	6.49092	0.831078	0.415539	−	0.909575i	$-0.363593\pi$
$61$	6.49092	0.831078	0.415539	+	0.909575i	$0.363593\pi$
$62$	3.98254	0.505783
$63$	4.68613	0.590397
$64$	1.00000	0.125000
$65$	−16.5244	−2.04960
$66$	2.76178	0.339952
$67$	2.12793	0.259968	0.129984	−	0.991516i	$-0.458507\pi$
$67$	2.12793	0.259968	0.129984	+	0.991516i	$0.458507\pi$
$68$	0.346537	0.0420238
$69$	1.63469	0.196793
$70$	5.36134	0.640803
$71$	−12.3761	−1.46878	−0.734389	−	0.678729i	$-0.762531\pi$
$71$	−12.3761	−1.46878	−0.734389	+	0.678729i	$0.762531\pi$
$72$	2.81438	0.331678
$73$	15.3852	1.80071	0.900353	−	0.435160i	$-0.143308\pi$
$73$	15.3852	1.80071	0.900353	+	0.435160i	$0.143308\pi$
$74$	2.63552	0.306373
$75$	−2.31261	−0.267038
$76$	−5.33722	−0.612221
$77$	−10.6736	−1.21637
$78$	−2.21104	−0.250351
$79$	9.28208	1.04432	0.522158	−	0.852849i	$-0.325127\pi$
$79$	9.28208	1.04432	0.522158	+	0.852849i	$0.325127\pi$
$80$	3.21990	0.359995
$81$	7.36388	0.818209
$82$	−1.77231	−0.195719
$83$	14.8405	1.62896	0.814480	−	0.580192i	$-0.197022\pi$
$83$	14.8405	1.62896	0.814480	+	0.580192i	$0.197022\pi$
$84$	0.717371	0.0782716
$85$	1.11581	0.121027
$86$	−4.72304	−0.509299
$87$	2.31762	0.248475
$88$	−6.41029	−0.683339
$89$	−2.41664	−0.256164	−0.128082	−	0.991764i	$-0.540882\pi$
$89$	−2.41664	−0.256164	−0.128082	+	0.991764i	$0.540882\pi$
$90$	9.06201	0.955220
$91$	8.54509	0.895769
$92$	−3.79422	−0.395574
$93$	1.71582	0.177922
$94$	1.32087	0.136237
$95$	−17.1853	−1.76317
$96$	0.430836	0.0439720
$97$	13.9184	1.41320	0.706601	−	0.707612i	$-0.250228\pi$
$97$	13.9184	1.41320	0.706601	+	0.707612i	$0.250228\pi$
$98$	4.22755	0.427047
$99$	−18.0410	−1.81319
$100$	5.36774	0.536774
$101$	15.3101	1.52341	0.761707	−	0.647921i	$-0.224361\pi$
$101$	15.3101	1.52341	0.761707	+	0.647921i	$0.224361\pi$
$102$	0.149301	0.0147830
$103$	−3.76917	−0.371387	−0.185694	−	0.982608i	$-0.559453\pi$
$103$	−3.76917	−0.371387	−0.185694	+	0.982608i	$0.559453\pi$
$104$	5.13198	0.503232
$105$	2.30986	0.225419
$106$	−13.3415	−1.29584
$107$	−11.4042	−1.10249	−0.551245	−	0.834344i	$-0.685847\pi$
$107$	−11.4042	−1.10249	−0.551245	+	0.834344i	$0.685847\pi$
$108$	2.50505	0.241048
$109$	−15.3671	−1.47191	−0.735953	−	0.677033i	$-0.763265\pi$
$109$	−15.3671	−1.47191	−0.735953	+	0.677033i	$0.763265\pi$
$110$	−20.6405	−1.96799
$111$	1.13548	0.107775
$112$	−1.66507	−0.157334
$113$	−18.9781	−1.78531	−0.892653	−	0.450744i	$-0.851159\pi$
$113$	−18.9781	−1.78531	−0.892653	+	0.450744i	$0.851159\pi$
$114$	−2.29947	−0.215365
$115$	−12.2170	−1.13924
$116$	−5.37935	−0.499460
$117$	14.4433	1.33529
$118$	−2.71462	−0.249901
$119$	−0.577008	−0.0528942
$120$	1.38725	0.126638
$121$	30.0918	2.73562
$122$	−6.49092	−0.587661
$123$	−0.763575	−0.0688493
$124$	−3.98254	−0.357643
$125$	1.18407	0.105906
$126$	−4.68613	−0.417474
$127$	22.1879	1.96885	0.984427	−	0.175791i	$-0.0562484\pi$
$127$	22.1879	1.96885	0.984427	+	0.175791i	$0.0562484\pi$
$128$	−1.00000	−0.0883883
$129$	−2.03486	−0.179159
$130$	16.5244	1.44929
$131$	6.03625	0.527390	0.263695	−	0.964606i	$-0.415059\pi$
$131$	6.03625	0.527390	0.263695	+	0.964606i	$0.415059\pi$
$132$	−2.76178	−0.240382
$133$	8.88683	0.770586
$134$	−2.12793	−0.183825
$135$	8.06599	0.694210
$136$	−0.346537	−0.0297153
$137$	15.4802	1.32256	0.661280	−	0.750139i	$-0.270013\pi$
$137$	15.4802	1.32256	0.661280	+	0.750139i	$0.270013\pi$
$138$	−1.63469	−0.139154
$139$	−6.73712	−0.571435	−0.285718	−	0.958314i	$-0.592232\pi$
$139$	−6.73712	−0.571435	−0.285718	+	0.958314i	$0.592232\pi$
$140$	−5.36134	−0.453116
$141$	0.569079	0.0479251
$142$	12.3761	1.03858
$143$	−32.8975	−2.75102
$144$	−2.81438	−0.234532
$145$	−17.3209	−1.43843
$146$	−15.3852	−1.27329
$147$	1.82138	0.150225
$148$	−2.63552	−0.216639
$149$	22.2293	1.82109	0.910547	−	0.413405i	$-0.135661\pi$
$149$	22.2293	1.82109	0.910547	+	0.413405i	$0.135661\pi$
$150$	2.31261	0.188824
$151$	8.84387	0.719704	0.359852	−	0.933009i	$-0.382827\pi$
$151$	8.84387	0.719704	0.359852	+	0.933009i	$0.382827\pi$
$152$	5.33722	0.432906
$153$	−0.975287	−0.0788473
$154$	10.6736	0.860100
$155$	−12.8234	−1.03000
$156$	2.21104	0.177025
$157$	22.9867	1.83454	0.917271	−	0.398265i	$-0.130387\pi$
$157$	22.9867	1.83454	0.917271	+	0.398265i	$0.130387\pi$
$158$	−9.28208	−0.738442
$159$	−5.74801	−0.455847
$160$	−3.21990	−0.254555
$161$	6.31762	0.497899
$162$	−7.36388	−0.578561
$163$	15.7707	1.23526	0.617629	−	0.786469i	$-0.288093\pi$
$163$	15.7707	1.23526	0.617629	+	0.786469i	$0.288093\pi$
$164$	1.77231	0.138394
$165$	−8.89266	−0.692293
$166$	−14.8405	−1.15185
$167$	6.52186	0.504677	0.252338	−	0.967639i	$-0.418800\pi$
$167$	6.52186	0.504677	0.252338	+	0.967639i	$0.418800\pi$
$168$	−0.717371	−0.0553464
$169$	13.3372	1.02594
$170$	−1.11581	−0.0855790
$171$	15.0210	1.14868
$172$	4.72304	0.360128
$173$	0.353625	0.0268856	0.0134428	−	0.999910i	$-0.495721\pi$
$173$	0.353625	0.0268856	0.0134428	+	0.999910i	$0.495721\pi$
$174$	−2.31762	−0.175698
$175$	−8.93764	−0.675622
$176$	6.41029	0.483194
$177$	−1.16956	−0.0879094
$178$	2.41664	0.181135
$179$	17.9969	1.34515	0.672577	−	0.740027i	$-0.265187\pi$
$179$	17.9969	1.34515	0.672577	+	0.740027i	$0.265187\pi$
$180$	−9.06201	−0.675443
$181$	13.3210	0.990144	0.495072	−	0.868852i	$-0.335142\pi$
$181$	13.3210	0.990144	0.495072	+	0.868852i	$0.335142\pi$
$182$	−8.54509	−0.633404
$183$	−2.79652	−0.206725
$184$	3.79422	0.279713
$185$	−8.48611	−0.623911
$186$	−1.71582	−0.125810
$187$	2.22140	0.162445
$188$	−1.32087	−0.0963345
$189$	−4.17107	−0.303401
$190$	17.1853	1.24675
$191$	9.04823	0.654707	0.327353	−	0.944902i	$-0.393843\pi$
$191$	9.04823	0.654707	0.327353	+	0.944902i	$0.393843\pi$
$192$	−0.430836	−0.0310929
$193$	0.428768	0.0308634	0.0154317	−	0.999881i	$-0.495088\pi$
$193$	0.428768	0.0308634	0.0154317	+	0.999881i	$0.495088\pi$
$194$	−13.9184	−0.999284
$195$	7.11933	0.509826
$196$	−4.22755	−0.301968
$197$	−3.17267	−0.226044	−0.113022	−	0.993593i	$-0.536053\pi$
$197$	−3.17267	−0.226044	−0.113022	+	0.993593i	$0.536053\pi$
$198$	18.0410	1.28212
$199$	9.57760	0.678938	0.339469	−	0.940617i	$-0.389753\pi$
$199$	9.57760	0.678938	0.339469	+	0.940617i	$0.389753\pi$
$200$	−5.36774	−0.379556
$201$	−0.916790	−0.0646653
$202$	−15.3101	−1.07722
$203$	8.95697	0.628656
$204$	−0.149301	−0.0104531
$205$	5.70666	0.398570
$206$	3.76917	0.262610
$207$	10.6784	0.742198
$208$	−5.13198	−0.355839
$209$	−34.2131	−2.36657
$210$	−2.30986	−0.159396
$211$	−9.31513	−0.641280	−0.320640	−	0.947201i	$-0.603898\pi$
$211$	−9.31513	−0.641280	−0.320640	+	0.947201i	$0.603898\pi$
$212$	13.3415	0.916300
$213$	5.33209	0.365349
$214$	11.4042	0.779578
$215$	15.2077	1.03716
$216$	−2.50505	−0.170447
$217$	6.63119	0.450155
$218$	15.3671	1.04079
$219$	−6.62852	−0.447914
$220$	20.6405	1.39158
$221$	−1.77842	−0.119630
$222$	−1.13548	−0.0762083
$223$	−5.20271	−0.348399	−0.174200	−	0.984710i	$-0.555734\pi$
$223$	−5.20271	−0.348399	−0.174200	+	0.984710i	$0.555734\pi$
$224$	1.66507	0.111252
$225$	−15.1068	−1.00712
$226$	18.9781	1.26240
$227$	15.3105	1.01619	0.508097	−	0.861300i	$-0.330349\pi$
$227$	15.3105	1.01619	0.508097	+	0.861300i	$0.330349\pi$
$228$	2.29947	0.152286
$229$	−21.2612	−1.40498	−0.702491	−	0.711693i	$-0.747929\pi$
$229$	−21.2612	−1.40498	−0.702491	+	0.711693i	$0.747929\pi$
$230$	12.2170	0.805564
$231$	4.59856	0.302563
$232$	5.37935	0.353171
$233$	−11.8182	−0.774234	−0.387117	−	0.922031i	$-0.626529\pi$
$233$	−11.8182	−0.774234	−0.387117	+	0.922031i	$0.626529\pi$
$234$	−14.4433	−0.944191
$235$	−4.25307	−0.277440
$236$	2.71462	0.176707
$237$	−3.99905	−0.259766
$238$	0.577008	0.0374018
$239$	13.2607	0.857765	0.428883	−	0.903360i	$-0.358907\pi$
$239$	13.2607	0.857765	0.428883	+	0.903360i	$0.358907\pi$
$240$	−1.38725	−0.0895465
$241$	−9.86428	−0.635414	−0.317707	−	0.948189i	$-0.602913\pi$
$241$	−9.86428	−0.635414	−0.317707	+	0.948189i	$0.602913\pi$
$242$	−30.0918	−1.93437
$243$	−10.6878	−0.685620
$244$	6.49092	0.415539
$245$	−13.6123	−0.869657
$246$	0.763575	0.0486838
$247$	27.3905	1.74282
$248$	3.98254	0.252891
$249$	−6.39384	−0.405193
$250$	−1.18407	−0.0748871
$251$	−11.0639	−0.698348	−0.349174	−	0.937058i	$-0.613538\pi$
$251$	−11.0639	−0.698348	−0.349174	+	0.937058i	$0.613538\pi$
$252$	4.68613	0.295199
$253$	−24.3220	−1.52911
$254$	−22.1879	−1.39219
$255$	−0.480733	−0.0301047
$256$	1.00000	0.0625000
$257$	−16.8459	−1.05082	−0.525408	−	0.850850i	$-0.676087\pi$
$257$	−16.8459	−1.05082	−0.525408	+	0.850850i	$0.676087\pi$
$258$	2.03486	0.126685
$259$	4.38832	0.272677
$260$	−16.5244	−1.02480
$261$	15.1395	0.937113
$262$	−6.03625	−0.372921
$263$	−6.60882	−0.407517	−0.203759	−	0.979021i	$-0.565316\pi$
$263$	−6.60882	−0.407517	−0.203759	+	0.979021i	$0.565316\pi$
$264$	2.76178	0.169976
$265$	42.9583	2.63891
$266$	−8.88683	−0.544886
$267$	1.04118	0.0637190
$268$	2.12793	0.129984
$269$	−18.4546	−1.12519	−0.562597	−	0.826731i	$-0.690198\pi$
$269$	−18.4546	−1.12519	−0.562597	+	0.826731i	$0.690198\pi$
$270$	−8.06599	−0.490880
$271$	16.6994	1.01442	0.507208	−	0.861824i	$-0.330678\pi$
$271$	16.6994	1.01442	0.507208	+	0.861824i	$0.330678\pi$
$272$	0.346537	0.0210119
$273$	−3.68153	−0.222817
$274$	−15.4802	−0.935191
$275$	34.4087	2.07492
$276$	1.63469	0.0983965
$277$	10.9665	0.658910	0.329455	−	0.944171i	$-0.393135\pi$
$277$	10.9665	0.658910	0.329455	+	0.944171i	$0.393135\pi$
$278$	6.73712	0.404066
$279$	11.2084	0.671028
$280$	5.36134	0.320402
$281$	3.40196	0.202944	0.101472	−	0.994838i	$-0.467645\pi$
$281$	3.40196	0.202944	0.101472	+	0.994838i	$0.467645\pi$
$282$	−0.569079	−0.0338882
$283$	31.8016	1.89041	0.945205	−	0.326476i	$-0.105861\pi$
$283$	31.8016	1.89041	0.945205	+	0.326476i	$0.105861\pi$
$284$	−12.3761	−0.734389
$285$	7.40405	0.438578
$286$	32.8975	1.94527
$287$	−2.95102	−0.174193
$288$	2.81438	0.165839
$289$	−16.8799	−0.992936
$290$	17.3209	1.01712
$291$	−5.99656	−0.351524
$292$	15.3852	0.900353
$293$	−29.3298	−1.71346	−0.856732	−	0.515762i	$-0.827509\pi$
$293$	−29.3298	−1.71346	−0.856732	+	0.515762i	$0.827509\pi$
$294$	−1.82138	−0.106225
$295$	8.74081	0.508910
$296$	2.63552	0.153187
$297$	16.0581	0.931783
$298$	−22.2293	−1.28771
$299$	19.4718	1.12609
$300$	−2.31261	−0.133519
$301$	−7.86418	−0.453284
$302$	−8.84387	−0.508907
$303$	−6.59616	−0.378939
$304$	−5.33722	−0.306111
$305$	20.9001	1.19674
$306$	0.975287	0.0557535
$307$	−34.0410	−1.94282	−0.971410	−	0.237408i	$-0.923702\pi$
$307$	−34.0410	−1.94282	−0.971410	+	0.237408i	$0.923702\pi$
$308$	−10.6736	−0.608183
$309$	1.62389	0.0923801
$310$	12.8234	0.728318
$311$	−11.2570	−0.638324	−0.319162	−	0.947700i	$-0.603401\pi$
$311$	−11.2570	−0.638324	−0.319162	+	0.947700i	$0.603401\pi$
$312$	−2.21104	−0.125176
$313$	−14.0885	−0.796328	−0.398164	−	0.917314i	$-0.630352\pi$
$313$	−14.0885	−0.796328	−0.398164	+	0.917314i	$0.630352\pi$
$314$	−22.9867	−1.29722
$315$	15.0889	0.850161
$316$	9.28208	0.522158
$317$	29.8724	1.67780	0.838901	−	0.544284i	$-0.183199\pi$
$317$	29.8724	1.67780	0.838901	+	0.544284i	$0.183199\pi$
$318$	5.74801	0.322333
$319$	−34.4832	−1.93069
$320$	3.21990	0.179998
$321$	4.91336	0.274237
$322$	−6.31762	−0.352067
$323$	−1.84954	−0.102911
$324$	7.36388	0.409104
$325$	−27.5471	−1.52804
$326$	−15.7707	−0.873460
$327$	6.62072	0.366127
$328$	−1.77231	−0.0978595
$329$	2.19934	0.121254
$330$	8.89266	0.489525
$331$	−13.2780	−0.729824	−0.364912	−	0.931042i	$-0.618901\pi$
$331$	−13.2780	−0.729824	−0.364912	+	0.931042i	$0.618901\pi$
$332$	14.8405	0.814480
$333$	7.41736	0.406469
$334$	−6.52186	−0.356860
$335$	6.85172	0.374349
$336$	0.717371	0.0391358
$337$	−31.5319	−1.71765	−0.858825	−	0.512269i	$-0.828805\pi$
$337$	−31.5319	−1.71765	−0.858825	+	0.512269i	$0.828805\pi$
$338$	−13.3372	−0.725449
$339$	8.17644	0.444083
$340$	1.11581	0.0605135
$341$	−25.5292	−1.38249
$342$	−15.0210	−0.812241
$343$	18.6946	1.00941
$344$	−4.72304	−0.254649
$345$	5.26352	0.283378
$346$	−0.353625	−0.0190110
$347$	−33.5689	−1.80207	−0.901037	−	0.433743i	$-0.857193\pi$
$347$	−33.5689	−1.80207	−0.901037	+	0.433743i	$0.857193\pi$
$348$	2.31762	0.124237
$349$	−13.1300	−0.702831	−0.351415	−	0.936220i	$-0.614300\pi$
$349$	−13.1300	−0.702831	−0.351415	+	0.936220i	$0.614300\pi$
$350$	8.93764	0.477737
$351$	−12.8558	−0.686194
$352$	−6.41029	−0.341670
$353$	−18.5602	−0.987861	−0.493931	−	0.869501i	$-0.664440\pi$
$353$	−18.5602	−0.987861	−0.493931	+	0.869501i	$0.664440\pi$
$354$	1.16956	0.0621613
$355$	−39.8499	−2.11501
$356$	−2.41664	−0.128082
$357$	0.248596	0.0131571
$358$	−17.9969	−0.951168
$359$	9.93063	0.524119	0.262059	−	0.965052i	$-0.415598\pi$
$359$	9.93063	0.524119	0.262059	+	0.965052i	$0.415598\pi$
$360$	9.06201	0.477610
$361$	9.48591	0.499258
$362$	−13.3210	−0.700137
$363$	−12.9646	−0.680467
$364$	8.54509	0.447884
$365$	49.5389	2.59298
$366$	2.79652	0.146177
$367$	36.9824	1.93047	0.965233	−	0.261393i	$-0.0841817\pi$
$367$	36.9824	1.93047	0.965233	+	0.261393i	$0.0841817\pi$
$368$	−3.79422	−0.197787
$369$	−4.98795	−0.259663
$370$	8.48611	0.441172
$371$	−22.2145	−1.15332
$372$	1.71582	0.0889612
$373$	22.9988	1.19083	0.595416	−	0.803417i	$-0.296987\pi$
$373$	22.9988	1.19083	0.595416	+	0.803417i	$0.296987\pi$
$374$	−2.22140	−0.114866
$375$	−0.510140	−0.0263435
$376$	1.32087	0.0681187
$377$	27.6067	1.42182
$378$	4.17107	0.214537
$379$	14.2022	0.729518	0.364759	−	0.931102i	$-0.381151\pi$
$379$	14.2022	0.729518	0.364759	+	0.931102i	$0.381151\pi$
$380$	−17.1853	−0.881587
$381$	−9.55934	−0.489740
$382$	−9.04823	−0.462948
$383$	4.98375	0.254658	0.127329	−	0.991861i	$-0.459360\pi$
$383$	4.98375	0.254658	0.127329	+	0.991861i	$0.459360\pi$
$384$	0.430836	0.0219860
$385$	−34.3678	−1.75154
$386$	−0.428768	−0.0218237
$387$	−13.2924	−0.675692
$388$	13.9184	0.706601
$389$	−14.0391	−0.711810	−0.355905	−	0.934522i	$-0.615827\pi$
$389$	−14.0391	−0.711810	−0.355905	+	0.934522i	$0.615827\pi$
$390$	−7.11933	−0.360501
$391$	−1.31484	−0.0664942
$392$	4.22755	0.213524
$393$	−2.60064	−0.131185
$394$	3.17267	0.159837
$395$	29.8873	1.50379
$396$	−18.0410	−0.906594
$397$	24.7779	1.24357	0.621784	−	0.783189i	$-0.286408\pi$
$397$	24.7779	1.24357	0.621784	+	0.783189i	$0.286408\pi$
$398$	−9.57760	−0.480082
$399$	−3.82877	−0.191678
$400$	5.36774	0.268387
$401$	−22.5600	−1.12659	−0.563296	−	0.826255i	$-0.690467\pi$
$401$	−22.5600	−1.12659	−0.563296	+	0.826255i	$0.690467\pi$
$402$	0.916790	0.0457253
$403$	20.4383	1.01810
$404$	15.3101	0.761707
$405$	23.7109	1.17821
$406$	−8.95697	−0.444527
$407$	−16.8945	−0.837428
$408$	0.149301	0.00739149
$409$	−20.2629	−1.00193	−0.500967	−	0.865466i	$-0.667022\pi$
$409$	−20.2629	−1.00193	−0.500967	+	0.865466i	$0.667022\pi$
$410$	−5.70666	−0.281832
$411$	−6.66942	−0.328978
$412$	−3.76917	−0.185694
$413$	−4.52003	−0.222416
$414$	−10.6784	−0.524813
$415$	47.7850	2.34567
$416$	5.13198	0.251616
$417$	2.90260	0.142141
$418$	34.2131	1.67342
$419$	−33.7256	−1.64760	−0.823802	−	0.566877i	$-0.808151\pi$
$419$	−33.7256	−1.64760	−0.823802	+	0.566877i	$0.808151\pi$
$420$	2.30986	0.112710
$421$	−9.03190	−0.440188	−0.220094	−	0.975479i	$-0.570636\pi$
$421$	−9.03190	−0.440188	−0.220094	+	0.975479i	$0.570636\pi$
$422$	9.31513	0.453453
$423$	3.71743	0.180748
$424$	−13.3415	−0.647922
$425$	1.86012	0.0902291
$426$	−5.33209	−0.258341
$427$	−10.8078	−0.523027
$428$	−11.4042	−0.551245
$429$	14.1734	0.684299
$430$	−15.2077	−0.733381
$431$	28.2092	1.35879	0.679395	−	0.733773i	$-0.262242\pi$
$431$	28.2092	1.35879	0.679395	+	0.733773i	$0.262242\pi$
$432$	2.50505	0.120524
$433$	19.3915	0.931898	0.465949	−	0.884811i	$-0.345713\pi$
$433$	19.3915	0.931898	0.465949	+	0.884811i	$0.345713\pi$
$434$	−6.63119	−0.318308
$435$	7.46249	0.357799
$436$	−15.3671	−0.735953
$437$	20.2506	0.968716
$438$	6.62852	0.316723
$439$	−34.0749	−1.62631	−0.813153	−	0.582050i	$-0.802251\pi$
$439$	−34.0749	−1.62631	−0.813153	+	0.582050i	$0.802251\pi$
$440$	−20.6405	−0.983996
$441$	11.8979	0.566568
$442$	1.77842	0.0845909
$443$	11.6550	0.553745	0.276873	−	0.960907i	$-0.410702\pi$
$443$	11.6550	0.553745	0.276873	+	0.960907i	$0.410702\pi$
$444$	1.13548	0.0538874
$445$	−7.78134	−0.368871
$446$	5.20271	0.246356
$447$	−9.57718	−0.452985
$448$	−1.66507	−0.0786670
$449$	18.0920	0.853812	0.426906	−	0.904296i	$-0.359603\pi$
$449$	18.0920	0.853812	0.426906	+	0.904296i	$0.359603\pi$
$450$	15.1068	0.712144
$451$	11.3610	0.534970
$452$	−18.9781	−0.892653
$453$	−3.81026	−0.179022
$454$	−15.3105	−0.718558
$455$	27.5143	1.28989
$456$	−2.29947	−0.107682
$457$	10.5397	0.493025	0.246513	−	0.969140i	$-0.420715\pi$
$457$	10.5397	0.493025	0.246513	+	0.969140i	$0.420715\pi$
$458$	21.2612	0.993472
$459$	0.868091	0.0405190
$460$	−12.2170	−0.569620
$461$	−2.02145	−0.0941485	−0.0470742	−	0.998891i	$-0.514990\pi$
$461$	−2.02145	−0.0941485	−0.0470742	+	0.998891i	$0.514990\pi$
$462$	−4.59856	−0.213944
$463$	10.1366	0.471090	0.235545	−	0.971863i	$-0.424313\pi$
$463$	10.1366	0.471090	0.235545	+	0.971863i	$0.424313\pi$
$464$	−5.37935	−0.249730
$465$	5.52477	0.256205
$466$	11.8182	0.547466
$467$	35.3455	1.63560	0.817798	−	0.575505i	$-0.195194\pi$
$467$	35.3455	1.63560	0.817798	+	0.575505i	$0.195194\pi$
$468$	14.4433	0.667644
$469$	−3.54315	−0.163607
$470$	4.25307	0.196179
$471$	−9.90352	−0.456330
$472$	−2.71462	−0.124951
$473$	30.2761	1.39209
$474$	3.99905	0.183683
$475$	−28.6488	−1.31450
$476$	−0.577008	−0.0264471
$477$	−37.5481	−1.71921
$478$	−13.2607	−0.606532
$479$	−11.9146	−0.544394	−0.272197	−	0.962242i	$-0.587750\pi$
$479$	−11.9146	−0.544394	−0.272197	+	0.962242i	$0.587750\pi$
$480$	1.38725	0.0633189
$481$	13.5255	0.616707
$482$	9.86428	0.449306
$483$	−2.72186	−0.123849
$484$	30.0918	1.36781
$485$	44.8159	2.03498
$486$	10.6878	0.484807
$487$	−13.5732	−0.615058	−0.307529	−	0.951539i	$-0.599502\pi$
$487$	−13.5732	−0.615058	−0.307529	+	0.951539i	$0.599502\pi$
$488$	−6.49092	−0.293830
$489$	−6.79460	−0.307262
$490$	13.6123	0.614940
$491$	6.73450	0.303924	0.151962	−	0.988386i	$-0.451441\pi$
$491$	6.73450	0.303924	0.151962	+	0.988386i	$0.451441\pi$
$492$	−0.763575	−0.0344246
$493$	−1.86414	−0.0839568
$494$	−27.3905	−1.23236
$495$	−58.0901	−2.61096
$496$	−3.98254	−0.178821
$497$	20.6071	0.924355
$498$	6.39384	0.286515
$499$	−15.0255	−0.672632	−0.336316	−	0.941749i	$-0.609181\pi$
$499$	−15.0255	−0.672632	−0.336316	+	0.941749i	$0.609181\pi$
$500$	1.18407	0.0529532
$501$	−2.80985	−0.125535
$502$	11.0639	0.493807
$503$	9.52402	0.424655	0.212327	−	0.977199i	$-0.431896\pi$
$503$	9.52402	0.424655	0.212327	+	0.977199i	$0.431896\pi$
$504$	−4.68613	−0.208737
$505$	49.2970	2.19369
$506$	24.3220	1.08125
$507$	−5.74615	−0.255196
$508$	22.1879	0.984427
$509$	9.02641	0.400089	0.200044	−	0.979787i	$-0.435891\pi$
$509$	9.02641	0.400089	0.200044	+	0.979787i	$0.435891\pi$
$510$	0.480733	0.0212872
$511$	−25.6175	−1.13325
$512$	−1.00000	−0.0441942
$513$	−13.3700	−0.590299
$514$	16.8459	0.743039
$515$	−12.1363	−0.534791
$516$	−2.03486	−0.0895796
$517$	−8.46717	−0.372386
$518$	−4.38832	−0.192812
$519$	−0.152354	−0.00668761
$520$	16.5244	0.724645
$521$	33.1915	1.45414	0.727072	−	0.686561i	$-0.240880\pi$
$521$	33.1915	1.45414	0.727072	+	0.686561i	$0.240880\pi$
$522$	−15.1395	−0.662639
$523$	20.5662	0.899299	0.449649	−	0.893205i	$-0.351549\pi$
$523$	20.5662	0.899299	0.449649	+	0.893205i	$0.351549\pi$
$524$	6.03625	0.263695
$525$	3.85066	0.168056
$526$	6.60882	0.288158
$527$	−1.38010	−0.0601180
$528$	−2.76178	−0.120191
$529$	−8.60392	−0.374084
$530$	−42.9583	−1.86599
$531$	−7.63999	−0.331547
$532$	8.88683	0.385293
$533$	−9.09546	−0.393968
$534$	−1.04118	−0.0450561
$535$	−36.7205	−1.58756
$536$	−2.12793	−0.0919126
$537$	−7.75373	−0.334598
$538$	18.4546	0.795632
$539$	−27.0998	−1.16727
$540$	8.06599	0.347105
$541$	20.9894	0.902403	0.451201	−	0.892422i	$-0.350996\pi$
$541$	20.9894	0.902403	0.451201	+	0.892422i	$0.350996\pi$
$542$	−16.6994	−0.717300
$543$	−5.73918	−0.246292
$544$	−0.346537	−0.0148577
$545$	−49.4806	−2.11952
$546$	3.68153	0.157555
$547$	21.3169	0.911444	0.455722	−	0.890122i	$-0.349381\pi$
$547$	21.3169	0.911444	0.455722	+	0.890122i	$0.349381\pi$
$548$	15.4802	0.661280
$549$	−18.2679	−0.779656
$550$	−34.4087	−1.46719
$551$	28.7107	1.22312
$552$	−1.63469	−0.0695768
$553$	−15.4553	−0.657225
$554$	−10.9665	−0.465920
$555$	3.65612	0.155194
$556$	−6.73712	−0.285718
$557$	32.8735	1.39290	0.696448	−	0.717607i	$-0.254763\pi$
$557$	32.8735	1.39290	0.696448	+	0.717607i	$0.254763\pi$
$558$	−11.2084	−0.474488
$559$	−24.2385	−1.02518
$560$	−5.36134	−0.226558
$561$	−0.957061	−0.0404071
$562$	−3.40196	−0.143503
$563$	7.03603	0.296533	0.148267	−	0.988947i	$-0.452631\pi$
$563$	7.03603	0.296533	0.148267	+	0.988947i	$0.452631\pi$
$564$	0.569079	0.0239626
$565$	−61.1074	−2.57081
$566$	−31.8016	−1.33672
$567$	−12.2613	−0.514928
$568$	12.3761	0.519291
$569$	−35.5151	−1.48887	−0.744435	−	0.667694i	$-0.767281\pi$
$569$	−35.5151	−1.48887	−0.744435	+	0.667694i	$0.767281\pi$
$570$	−7.40405	−0.310121
$571$	−27.6696	−1.15794	−0.578968	−	0.815350i	$-0.696545\pi$
$571$	−27.6696	−1.15794	−0.578968	+	0.815350i	$0.696545\pi$
$572$	−32.8975	−1.37551
$573$	−3.89830	−0.162854
$574$	2.95102	0.123173
$575$	−20.3663	−0.849335
$576$	−2.81438	−0.117266
$577$	−20.1828	−0.840220	−0.420110	−	0.907473i	$-0.638009\pi$
$577$	−20.1828	−0.840220	−0.420110	+	0.907473i	$0.638009\pi$
$578$	16.8799	0.702112
$579$	−0.184729	−0.00767706
$580$	−17.3209	−0.719213
$581$	−24.7105	−1.02516
$582$	5.99656	0.248565
$583$	85.5231	3.54200
$584$	−15.3852	−0.636646
$585$	46.5061	1.92279
$586$	29.3298	1.21160
$587$	22.9801	0.948492	0.474246	−	0.880392i	$-0.342721\pi$
$587$	22.9801	0.948492	0.474246	+	0.880392i	$0.342721\pi$
$588$	1.82138	0.0751125
$589$	21.2557	0.875825
$590$	−8.74081	−0.359854
$591$	1.36690	0.0562268
$592$	−2.63552	−0.108319
$593$	−9.05053	−0.371661	−0.185830	−	0.982582i	$-0.559497\pi$
$593$	−9.05053	−0.371661	−0.185830	+	0.982582i	$0.559497\pi$
$594$	−16.0581	−0.658870
$595$	−1.85790	−0.0761667
$596$	22.2293	0.910547
$597$	−4.12638	−0.168881
$598$	−19.4718	−0.796263
$599$	21.0063	0.858293	0.429146	−	0.903235i	$-0.358814\pi$
$599$	21.0063	0.858293	0.429146	+	0.903235i	$0.358814\pi$
$600$	2.31261	0.0944121
$601$	−6.83608	−0.278850	−0.139425	−	0.990233i	$-0.544525\pi$
$601$	−6.83608	−0.278850	−0.139425	+	0.990233i	$0.544525\pi$
$602$	7.86418	0.320520
$603$	−5.98881	−0.243883
$604$	8.84387	0.359852
$605$	96.8925	3.93924
$606$	6.59616	0.267951
$607$	−25.6801	−1.04232	−0.521161	−	0.853459i	$-0.674501\pi$
$607$	−25.6801	−1.04232	−0.521161	+	0.853459i	$0.674501\pi$
$608$	5.33722	0.216453
$609$	−3.85899	−0.156374
$610$	−20.9001	−0.846220
$611$	6.77868	0.274236
$612$	−0.975287	−0.0394237
$613$	14.3984	0.581547	0.290774	−	0.956792i	$-0.406087\pi$
$613$	14.3984	0.581547	0.290774	+	0.956792i	$0.406087\pi$
$614$	34.0410	1.37378
$615$	−2.45863	−0.0991417
$616$	10.6736	0.430050
$617$	−46.1049	−1.85611	−0.928057	−	0.372439i	$-0.878522\pi$
$617$	−46.1049	−1.85611	−0.928057	+	0.372439i	$0.878522\pi$
$618$	−1.62389	−0.0653226
$619$	13.8443	0.556448	0.278224	−	0.960516i	$-0.410254\pi$
$619$	13.8443	0.556448	0.278224	+	0.960516i	$0.410254\pi$
$620$	−12.8234	−0.514999
$621$	−9.50468	−0.381410
$622$	11.2570	0.451363
$623$	4.02387	0.161213
$624$	2.21104	0.0885125
$625$	−23.0261	−0.921044
$626$	14.0885	0.563089
$627$	14.7402	0.588669
$628$	22.9867	0.917271
$629$	−0.913307	−0.0364159
$630$	−15.0889	−0.601155
$631$	21.6071	0.860165	0.430082	−	0.902790i	$-0.358485\pi$
$631$	21.6071	0.860165	0.430082	+	0.902790i	$0.358485\pi$
$632$	−9.28208	−0.369221
$633$	4.01329	0.159514
$634$	−29.8724	−1.18638
$635$	71.4426	2.83511
$636$	−5.74801	−0.227924
$637$	21.6957	0.859615
$638$	34.4832	1.36520
$639$	34.8312	1.37790
$640$	−3.21990	−0.127278
$641$	−43.8721	−1.73284	−0.866421	−	0.499314i	$-0.833585\pi$
$641$	−43.8721	−1.73284	−0.866421	+	0.499314i	$0.833585\pi$
$642$	−4.91336	−0.193915
$643$	0.0509698	0.00201005	0.00100503	−	0.999999i	$-0.499680\pi$
$643$	0.0509698	0.00201005	0.00100503	+	0.999999i	$0.499680\pi$
$644$	6.31762	0.248949
$645$	−6.55203	−0.257986
$646$	1.84954	0.0727694
$647$	21.5299	0.846426	0.423213	−	0.906030i	$-0.360902\pi$
$647$	21.5299	0.846426	0.423213	+	0.906030i	$0.360902\pi$
$648$	−7.36388	−0.289280
$649$	17.4015	0.683070
$650$	27.5471	1.08049
$651$	−2.85696	−0.111973
$652$	15.7707	0.617629
$653$	−22.0984	−0.864776	−0.432388	−	0.901688i	$-0.642329\pi$
$653$	−22.0984	−0.864776	−0.432388	+	0.901688i	$0.642329\pi$
$654$	−6.62072	−0.258891
$655$	19.4361	0.759432
$656$	1.77231	0.0691971
$657$	−43.2999	−1.68929
$658$	−2.19934	−0.0857392
$659$	−0.700233	−0.0272772	−0.0136386	−	0.999907i	$-0.504341\pi$
$659$	−0.700233	−0.0272772	−0.0136386	+	0.999907i	$0.504341\pi$
$660$	−8.89266	−0.346146
$661$	−21.5048	−0.836440	−0.418220	−	0.908346i	$-0.637346\pi$
$661$	−21.5048	−0.836440	−0.418220	+	0.908346i	$0.637346\pi$
$662$	13.2780	0.516063
$663$	0.766208	0.0297571
$664$	−14.8405	−0.575924
$665$	28.6147	1.10963
$666$	−7.41736	−0.287417
$667$	20.4104	0.790294
$668$	6.52186	0.252338
$669$	2.24152	0.0866620
$670$	−6.85172	−0.264705
$671$	41.6087	1.60629
$672$	−0.717371	−0.0276732
$673$	21.7786	0.839503	0.419752	−	0.907639i	$-0.362117\pi$
$673$	21.7786	0.839503	0.419752	+	0.907639i	$0.362117\pi$
$674$	31.5319	1.21456
$675$	13.4464	0.517553
$676$	13.3372	0.512970
$677$	37.0274	1.42308	0.711540	−	0.702645i	$-0.247998\pi$
$677$	37.0274	1.42308	0.711540	+	0.702645i	$0.247998\pi$
$678$	−8.17644	−0.314014
$679$	−23.1751	−0.889379
$680$	−1.11581	−0.0427895
$681$	−6.59633	−0.252772
$682$	25.5292	0.977565
$683$	24.0444	0.920034	0.460017	−	0.887910i	$-0.347843\pi$
$683$	24.0444	0.920034	0.460017	+	0.887910i	$0.347843\pi$
$684$	15.0210	0.574341
$685$	49.8446	1.90446
$686$	−18.6946	−0.713764
$687$	9.16011	0.349480
$688$	4.72304	0.180064
$689$	−68.4684	−2.60844
$690$	−5.26352	−0.200379
$691$	−12.4150	−0.472287	−0.236144	−	0.971718i	$-0.575884\pi$
$691$	−12.4150	−0.472287	−0.236144	+	0.971718i	$0.575884\pi$
$692$	0.353625	0.0134428
$693$	30.0395	1.14110
$694$	33.5689	1.27426
$695$	−21.6928	−0.822857
$696$	−2.31762	−0.0878490
$697$	0.614171	0.0232634
$698$	13.1300	0.496976
$699$	5.09169	0.192586
$700$	−8.93764	−0.337811
$701$	22.2919	0.841955	0.420977	−	0.907071i	$-0.361687\pi$
$701$	22.2919	0.841955	0.420977	+	0.907071i	$0.361687\pi$
$702$	12.8558	0.485212
$703$	14.0664	0.530523
$704$	6.41029	0.241597
$705$	1.83238	0.0690113
$706$	18.5602	0.698523
$707$	−25.4924	−0.958740
$708$	−1.16956	−0.0439547
$709$	−11.1300	−0.417996	−0.208998	−	0.977916i	$-0.567020\pi$
$709$	−11.1300	−0.417996	−0.208998	+	0.977916i	$0.567020\pi$
$710$	39.8499	1.49554
$711$	−26.1233	−0.979700
$712$	2.41664	0.0905675
$713$	15.1106	0.565897
$714$	−0.248596	−0.00930346
$715$	−105.926	−3.96143
$716$	17.9969	0.672577
$717$	−5.71320	−0.213363
$718$	−9.93063	−0.370608
$719$	6.05829	0.225936	0.112968	−	0.993599i	$-0.463964\pi$
$719$	6.05829	0.225936	0.112968	+	0.993599i	$0.463964\pi$
$720$	−9.06201	−0.337721
$721$	6.27592	0.233727
$722$	−9.48591	−0.353029
$723$	4.24989	0.158055
$724$	13.3210	0.495072
$725$	−28.8749	−1.07239
$726$	12.9646	0.481163
$727$	−37.9377	−1.40703	−0.703515	−	0.710680i	$-0.748387\pi$
$727$	−37.9377	−1.40703	−0.703515	+	0.710680i	$0.748387\pi$
$728$	−8.54509	−0.316702
$729$	−17.4870	−0.647665
$730$	−49.5389	−1.83352
$731$	1.63671	0.0605359
$732$	−2.79652	−0.103363
$733$	1.63815	0.0605065	0.0302532	−	0.999542i	$-0.490369\pi$
$733$	1.63815	0.0605065	0.0302532	+	0.999542i	$0.490369\pi$
$734$	−36.9824	−1.36505
$735$	5.86466	0.216321
$736$	3.79422	0.139857
$737$	13.6407	0.502460
$738$	4.98795	0.183609
$739$	40.1599	1.47731	0.738654	−	0.674085i	$-0.235462\pi$
$739$	40.1599	1.47731	0.738654	+	0.674085i	$0.235462\pi$
$740$	−8.48611	−0.311956
$741$	−11.8008	−0.433514
$742$	22.2145	0.815521
$743$	−16.1533	−0.592608	−0.296304	−	0.955094i	$-0.595754\pi$
$743$	−16.1533	−0.592608	−0.296304	+	0.955094i	$0.595754\pi$
$744$	−1.71582	−0.0629051
$745$	71.5760	2.62234
$746$	−22.9988	−0.842046
$747$	−41.7669	−1.52817
$748$	2.22140	0.0812226
$749$	18.9888	0.693836
$750$	0.510140	0.0186277
$751$	−27.9529	−1.02002	−0.510008	−	0.860170i	$-0.670358\pi$
$751$	−27.9529	−1.02002	−0.510008	+	0.860170i	$0.670358\pi$
$752$	−1.32087	−0.0481672
$753$	4.76674	0.173710
$754$	−27.6067	−1.00538
$755$	28.4763	1.03636
$756$	−4.17107	−0.151700
$757$	−17.8384	−0.648348	−0.324174	−	0.945997i	$-0.605086\pi$
$757$	−17.8384	−0.648348	−0.324174	+	0.945997i	$0.605086\pi$
$758$	−14.2022	−0.515847
$759$	10.4788	0.380357
$760$	17.1853	0.623376
$761$	−33.0325	−1.19743	−0.598713	−	0.800964i	$-0.704321\pi$
$761$	−33.0325	−1.19743	−0.598713	+	0.800964i	$0.704321\pi$
$762$	9.55934	0.346298
$763$	25.5873	0.926323
$764$	9.04823	0.327353
$765$	−3.14032	−0.113539
$766$	−4.98375	−0.180070
$767$	−13.9314	−0.503034
$768$	−0.430836	−0.0155465
$769$	−4.59964	−0.165867	−0.0829336	−	0.996555i	$-0.526429\pi$
$769$	−4.59964	−0.165867	−0.0829336	+	0.996555i	$0.526429\pi$
$770$	34.3678	1.23853
$771$	7.25780	0.261383
$772$	0.428768	0.0154317
$773$	18.1288	0.652047	0.326023	−	0.945362i	$-0.394291\pi$
$773$	18.1288	0.652047	0.326023	+	0.945362i	$0.394291\pi$
$774$	13.2924	0.477787
$775$	−21.3772	−0.767892
$776$	−13.9184	−0.499642
$777$	−1.89065	−0.0678266
$778$	14.0391	0.503326
$779$	−9.45921	−0.338911
$780$	7.11933	0.254913
$781$	−79.3347	−2.83882
$782$	1.31484	0.0470185
$783$	−13.4755	−0.481575
$784$	−4.22755	−0.150984
$785$	74.0149	2.64171
$786$	2.60064	0.0927616
$787$	12.8235	0.457109	0.228554	−	0.973531i	$-0.426600\pi$
$787$	12.8235	0.457109	0.228554	+	0.973531i	$0.426600\pi$
$788$	−3.17267	−0.113022
$789$	2.84732	0.101367
$790$	−29.8873	−1.06334
$791$	31.5998	1.12356
$792$	18.0410	0.641059
$793$	−33.3113	−1.18292
$794$	−24.7779	−0.879336
$795$	−18.5080	−0.656411
$796$	9.57760	0.339469
$797$	−5.74727	−0.203579	−0.101789	−	0.994806i	$-0.532457\pi$
$797$	−5.74727	−0.203579	−0.101789	+	0.994806i	$0.532457\pi$
$798$	3.82877	0.135537
$799$	−0.457731	−0.0161934
$800$	−5.36774	−0.189778
$801$	6.80135	0.240314
$802$	22.5600	0.796620
$803$	98.6238	3.48036
$804$	−0.916790	−0.0323327
$805$	20.3421	0.716965
$806$	−20.4383	−0.719909
$807$	7.95089	0.279884
$808$	−15.3101	−0.538608
$809$	10.8269	0.380654	0.190327	−	0.981721i	$-0.439045\pi$
$809$	10.8269	0.380654	0.190327	+	0.981721i	$0.439045\pi$
$810$	−23.7109	−0.833117
$811$	18.4968	0.649509	0.324755	−	0.945798i	$-0.394718\pi$
$811$	18.4968	0.649509	0.324755	+	0.945798i	$0.394718\pi$
$812$	8.95697	0.314328
$813$	−7.19470	−0.252329
$814$	16.8945	0.592151
$815$	50.7801	1.77875
$816$	−0.149301	−0.00522657
$817$	−25.2079	−0.881913
$818$	20.2629	0.708475
$819$	−24.0491	−0.840345
$820$	5.70666	0.199285
$821$	48.4234	1.68999	0.844995	−	0.534774i	$-0.179603\pi$
$821$	48.4234	1.68999	0.844995	+	0.534774i	$0.179603\pi$
$822$	6.66942	0.232623
$823$	49.3142	1.71898	0.859492	−	0.511149i	$-0.170780\pi$
$823$	49.3142	1.71898	0.859492	+	0.511149i	$0.170780\pi$
$824$	3.76917	0.131305
$825$	−14.8245	−0.516124
$826$	4.52003	0.157272
$827$	−33.3655	−1.16023	−0.580115	−	0.814534i	$-0.696993\pi$
$827$	−33.3655	−1.16023	−0.580115	+	0.814534i	$0.696993\pi$
$828$	10.6784	0.371099
$829$	47.8374	1.66146	0.830730	−	0.556675i	$-0.187923\pi$
$829$	47.8374	1.66146	0.830730	+	0.556675i	$0.187923\pi$
$830$	−47.7850	−1.65864
$831$	−4.72474	−0.163900
$832$	−5.13198	−0.177919
$833$	−1.46500	−0.0507594
$834$	−2.90260	−0.100509
$835$	20.9997	0.726725
$836$	−34.2131	−1.18329
$837$	−9.97644	−0.344836
$838$	33.7256	1.16503
$839$	18.6530	0.643972	0.321986	−	0.946744i	$-0.395650\pi$
$839$	18.6530	0.643972	0.321986	+	0.946744i	$0.395650\pi$
$840$	−2.30986	−0.0796978
$841$	−0.0626434	−0.00216012
$842$	9.03190	0.311260
$843$	−1.46569	−0.0504809
$844$	−9.31513	−0.320640
$845$	42.9444	1.47733
$846$	−3.71743	−0.127808
$847$	−50.1049	−1.72162
$848$	13.3415	0.458150
$849$	−13.7013	−0.470227
$850$	−1.86012	−0.0638016
$851$	9.99974	0.342787
$852$	5.33209	0.182674
$853$	32.1345	1.10027	0.550133	−	0.835077i	$-0.314577\pi$
$853$	32.1345	1.10027	0.550133	+	0.835077i	$0.314577\pi$
$854$	10.8078	0.369836
$855$	48.3660	1.65408
$856$	11.4042	0.389789
$857$	−38.7203	−1.32266	−0.661330	−	0.750096i	$-0.730007\pi$
$857$	−38.7203	−1.32266	−0.661330	+	0.750096i	$0.730007\pi$
$858$	−14.1734	−0.483873
$859$	−41.8542	−1.42805	−0.714023	−	0.700122i	$-0.753129\pi$
$859$	−41.8542	−1.42805	−0.714023	+	0.700122i	$0.753129\pi$
$860$	15.2077	0.518578
$861$	1.27140	0.0433293
$862$	−28.2092	−0.960809
$863$	−25.8365	−0.879485	−0.439742	−	0.898124i	$-0.644930\pi$
$863$	−25.8365	−0.879485	−0.439742	+	0.898124i	$0.644930\pi$
$864$	−2.50505	−0.0852234
$865$	1.13864	0.0387148
$866$	−19.3915	−0.658952
$867$	7.27248	0.246986
$868$	6.63119	0.225077
$869$	59.5008	2.01843
$870$	−7.46249	−0.253002
$871$	−10.9205	−0.370027
$872$	15.3671	0.520397
$873$	−39.1717	−1.32576
$874$	−20.2506	−0.684985
$875$	−1.97155	−0.0666507
$876$	−6.62852	−0.223957
$877$	16.8305	0.568325	0.284163	−	0.958776i	$-0.408284\pi$
$877$	16.8305	0.568325	0.284163	+	0.958776i	$0.408284\pi$
$878$	34.0749	1.14997
$879$	12.6363	0.426213
$880$	20.6405	0.695790
$881$	−15.1656	−0.510941	−0.255471	−	0.966817i	$-0.582230\pi$
$881$	−15.1656	−0.510941	−0.255471	+	0.966817i	$0.582230\pi$
$882$	−11.8979	−0.400624
$883$	−42.7417	−1.43837	−0.719186	−	0.694818i	$-0.755485\pi$
$883$	−42.7417	−1.43837	−0.719186	+	0.694818i	$0.755485\pi$
$884$	−1.77842	−0.0598148
$885$	−3.76586	−0.126588
$886$	−11.6550	−0.391557
$887$	45.3517	1.52276	0.761381	−	0.648305i	$-0.224522\pi$
$887$	45.3517	1.52276	0.761381	+	0.648305i	$0.224522\pi$
$888$	−1.13548	−0.0381042
$889$	−36.9443	−1.23907
$890$	7.78134	0.260831
$891$	47.2046	1.58141
$892$	−5.20271	−0.174200
$893$	7.04978	0.235912
$894$	9.57718	0.320309
$895$	57.9483	1.93700
$896$	1.66507	0.0556260
$897$	−8.38917	−0.280106
$898$	−18.0920	−0.603736
$899$	21.4235	0.714512
$900$	−15.1068	−0.503562
$901$	4.62333	0.154026
$902$	−11.3610	−0.378281
$903$	3.38817	0.112751
$904$	18.9781	0.631201
$905$	42.8923	1.42579
$906$	3.81026	0.126587
$907$	52.6328	1.74764	0.873822	−	0.486247i	$-0.161634\pi$
$907$	52.6328	1.74764	0.873822	+	0.486247i	$0.161634\pi$
$908$	15.3105	0.508097
$909$	−43.0885	−1.42916
$910$	−27.5143	−0.912090
$911$	13.3122	0.441053	0.220526	−	0.975381i	$-0.429222\pi$
$911$	13.3122	0.441053	0.220526	+	0.975381i	$0.429222\pi$
$912$	2.29947	0.0761430
$913$	95.1321	3.14841
$914$	−10.5397	−0.348621
$915$	−9.00452	−0.297680
$916$	−21.2612	−0.702491
$917$	−10.0508	−0.331906
$918$	−0.868091	−0.0286513
$919$	46.3706	1.52963	0.764813	−	0.644252i	$-0.222831\pi$
$919$	46.3706	1.52963	0.764813	+	0.644252i	$0.222831\pi$
$920$	12.2170	0.402782
$921$	14.6661	0.483264
$922$	2.02145	0.0665730
$923$	63.5141	2.09059
$924$	4.59856	0.151281
$925$	−14.1468	−0.465144
$926$	−10.1366	−0.333111
$927$	10.6079	0.348408
$928$	5.37935	0.176586
$929$	26.5038	0.869560	0.434780	−	0.900537i	$-0.356826\pi$
$929$	26.5038	0.869560	0.434780	+	0.900537i	$0.356826\pi$
$930$	−5.52477	−0.181164
$931$	22.5634	0.739485
$932$	−11.8182	−0.387117
$933$	4.84991	0.158779
$934$	−35.3455	−1.15654
$935$	7.15269	0.233918
$936$	−14.4433	−0.472095
$937$	18.2665	0.596741	0.298371	−	0.954450i	$-0.403557\pi$
$937$	18.2665	0.596741	0.298371	+	0.954450i	$0.403557\pi$
$938$	3.54315	0.115688
$939$	6.06983	0.198081
$940$	−4.25307	−0.138720
$941$	−15.8153	−0.515565	−0.257782	−	0.966203i	$-0.582992\pi$
$941$	−15.8153	−0.515565	−0.257782	+	0.966203i	$0.582992\pi$
$942$	9.90352	0.322674
$943$	−6.72453	−0.218981
$944$	2.71462	0.0883535
$945$	−13.4304	−0.436891
$946$	−30.2761	−0.984360
$947$	48.8300	1.58676	0.793381	−	0.608726i	$-0.208319\pi$
$947$	48.8300	1.58676	0.793381	+	0.608726i	$0.208319\pi$
$948$	−3.99905	−0.129883
$949$	−78.9567	−2.56304
$950$	28.6488	0.929489
$951$	−12.8701	−0.417342
$952$	0.577008	0.0187009
$953$	−54.4046	−1.76234	−0.881169	−	0.472802i	$-0.843243\pi$
$953$	−54.4046	−1.76234	−0.881169	+	0.472802i	$0.843243\pi$
$954$	37.5481	1.21567
$955$	29.1344	0.942766
$956$	13.2607	0.428883
$957$	14.8566	0.480245
$958$	11.9146	0.384945
$959$	−25.7755	−0.832335
$960$	−1.38725	−0.0447732
$961$	−15.1394	−0.488367
$962$	−13.5255	−0.436078
$963$	32.0959	1.03427
$964$	−9.86428	−0.317707
$965$	1.38059	0.0444427
$966$	2.72186	0.0875744
$967$	27.1063	0.871680	0.435840	−	0.900024i	$-0.356451\pi$
$967$	27.1063	0.871680	0.435840	+	0.900024i	$0.356451\pi$
$968$	−30.0918	−0.967187
$969$	0.796851	0.0255985
$970$	−44.8159	−1.43895
$971$	12.0564	0.386908	0.193454	−	0.981109i	$-0.438031\pi$
$971$	12.0564	0.386908	0.193454	+	0.981109i	$0.438031\pi$
$972$	−10.6878	−0.342810
$973$	11.2178	0.359625
$974$	13.5732	0.434912
$975$	11.8683	0.380089
$976$	6.49092	0.207769
$977$	−55.2757	−1.76843	−0.884214	−	0.467083i	$-0.845305\pi$
$977$	−55.2757	−1.76843	−0.884214	+	0.467083i	$0.845305\pi$
$978$	6.79460	0.217267
$979$	−15.4914	−0.495107
$980$	−13.6123	−0.434828
$981$	43.2490	1.38083
$982$	−6.73450	−0.214907
$983$	39.6479	1.26457	0.632287	−	0.774735i	$-0.282117\pi$
$983$	39.6479	1.26457	0.632287	+	0.774735i	$0.282117\pi$
$984$	0.763575	0.0243419
$985$	−10.2157	−0.325499
$986$	1.86414	0.0593664
$987$	−0.947555	−0.0301610
$988$	27.3905	0.871408
$989$	−17.9202	−0.569830
$990$	58.0901	1.84623
$991$	41.5899	1.32115	0.660574	−	0.750761i	$-0.270313\pi$
$991$	41.5899	1.32115	0.660574	+	0.750761i	$0.270313\pi$
$992$	3.98254	0.126446
$993$	5.72063	0.181539
$994$	−20.6071	−0.653618
$995$	30.8389	0.977658
$996$	−6.39384	−0.202596
$997$	1.47031	0.0465653	0.0232826	−	0.999729i	$-0.492588\pi$
$997$	1.47031	0.0465653	0.0232826	+	0.999729i	$0.492588\pi$
$998$	15.0255	0.475623
$999$	−6.60210	−0.208881

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8002.2.a.e.1.32	✓	77

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8002.2.a.e.1.32	✓	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -0.430836 q^{3} +1.00000 q^{4} +3.21990 q^{5} +0.430836 q^{6} -1.66507 q^{7} -1.00000 q^{8} -2.81438 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -0.430836 q^{3} +1.00000 q^{4} +3.21990 q^{5} +0.430836 q^{6} -1.66507 q^{7} -1.00000 q^{8} -2.81438 q^{9} -3.21990 q^{10} +6.41029 q^{11} -0.430836 q^{12} -5.13198 q^{13} +1.66507 q^{14} -1.38725 q^{15} +1.00000 q^{16} +0.346537 q^{17} +2.81438 q^{18} -5.33722 q^{19} +3.21990 q^{20} +0.717371 q^{21} -6.41029 q^{22} -3.79422 q^{23} +0.430836 q^{24} +5.36774 q^{25} +5.13198 q^{26} +2.50505 q^{27} -1.66507 q^{28} -5.37935 q^{29} +1.38725 q^{30} -3.98254 q^{31} -1.00000 q^{32} -2.76178 q^{33} -0.346537 q^{34} -5.36134 q^{35} -2.81438 q^{36} -2.63552 q^{37} +5.33722 q^{38} +2.21104 q^{39} -3.21990 q^{40} +1.77231 q^{41} -0.717371 q^{42} +4.72304 q^{43} +6.41029 q^{44} -9.06201 q^{45} +3.79422 q^{46} -1.32087 q^{47} -0.430836 q^{48} -4.22755 q^{49} -5.36774 q^{50} -0.149301 q^{51} -5.13198 q^{52} +13.3415 q^{53} -2.50505 q^{54} +20.6405 q^{55} +1.66507 q^{56} +2.29947 q^{57} +5.37935 q^{58} +2.71462 q^{59} -1.38725 q^{60} +6.49092 q^{61} +3.98254 q^{62} +4.68613 q^{63} +1.00000 q^{64} -16.5244 q^{65} +2.76178 q^{66} +2.12793 q^{67} +0.346537 q^{68} +1.63469 q^{69} +5.36134 q^{70} -12.3761 q^{71} +2.81438 q^{72} +15.3852 q^{73} +2.63552 q^{74} -2.31261 q^{75} -5.33722 q^{76} -10.6736 q^{77} -2.21104 q^{78} +9.28208 q^{79} +3.21990 q^{80} +7.36388 q^{81} -1.77231 q^{82} +14.8405 q^{83} +0.717371 q^{84} +1.11581 q^{85} -4.72304 q^{86} +2.31762 q^{87} -6.41029 q^{88} -2.41664 q^{89} +9.06201 q^{90} +8.54509 q^{91} -3.79422 q^{92} +1.71582 q^{93} +1.32087 q^{94} -17.1853 q^{95} +0.430836 q^{96} +13.9184 q^{97} +4.22755 q^{98} -18.0410 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 77 q - 77 q^{2} + 10 q^{3} + 77 q^{4} + 18 q^{5} - 10 q^{6} + 21 q^{7} - 77 q^{8} + 71 q^{9}+O(q^{10}) \) 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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