LMFDB - Embedded newform 8002.2.a.d.1.42

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:	$1$
Dimension:	$69$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.42
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)

$f(q)$	$=$	$q+1.00000 q^{2} +0.233596 q^{3} +1.00000 q^{4} +1.44908 q^{5} +0.233596 q^{6} -1.89084 q^{7} +1.00000 q^{8} -2.94543 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +0.233596 q^{3} +1.00000 q^{4} +1.44908 q^{5} +0.233596 q^{6} -1.89084 q^{7} +1.00000 q^{8} -2.94543 q^{9} +1.44908 q^{10} -0.939692 q^{11} +0.233596 q^{12} +6.04214 q^{13} -1.89084 q^{14} +0.338500 q^{15} +1.00000 q^{16} -5.41499 q^{17} -2.94543 q^{18} -3.73800 q^{19} +1.44908 q^{20} -0.441692 q^{21} -0.939692 q^{22} +7.85958 q^{23} +0.233596 q^{24} -2.90016 q^{25} +6.04214 q^{26} -1.38883 q^{27} -1.89084 q^{28} +1.50996 q^{29} +0.338500 q^{30} -5.85679 q^{31} +1.00000 q^{32} -0.219508 q^{33} -5.41499 q^{34} -2.73998 q^{35} -2.94543 q^{36} -7.71700 q^{37} -3.73800 q^{38} +1.41142 q^{39} +1.44908 q^{40} -7.43039 q^{41} -0.441692 q^{42} -2.20301 q^{43} -0.939692 q^{44} -4.26818 q^{45} +7.85958 q^{46} +4.74613 q^{47} +0.233596 q^{48} -3.42474 q^{49} -2.90016 q^{50} -1.26492 q^{51} +6.04214 q^{52} +10.8344 q^{53} -1.38883 q^{54} -1.36169 q^{55} -1.89084 q^{56} -0.873180 q^{57} +1.50996 q^{58} -2.40412 q^{59} +0.338500 q^{60} -15.6010 q^{61} -5.85679 q^{62} +5.56933 q^{63} +1.00000 q^{64} +8.75557 q^{65} -0.219508 q^{66} -4.63587 q^{67} -5.41499 q^{68} +1.83597 q^{69} -2.73998 q^{70} -3.65545 q^{71} -2.94543 q^{72} -0.689342 q^{73} -7.71700 q^{74} -0.677465 q^{75} -3.73800 q^{76} +1.77680 q^{77} +1.41142 q^{78} +4.69846 q^{79} +1.44908 q^{80} +8.51187 q^{81} -7.43039 q^{82} -9.07398 q^{83} -0.441692 q^{84} -7.84676 q^{85} -2.20301 q^{86} +0.352721 q^{87} -0.939692 q^{88} +15.6008 q^{89} -4.26818 q^{90} -11.4247 q^{91} +7.85958 q^{92} -1.36812 q^{93} +4.74613 q^{94} -5.41666 q^{95} +0.233596 q^{96} -17.1560 q^{97} -3.42474 q^{98} +2.76780 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 69 q + 69 q^{2} - 25 q^{3} + 69 q^{4} - 33 q^{5} - 25 q^{6} - 19 q^{7} + 69 q^{8} + 54 q^{9}+O(q^{10}) $ 69 * q + 69 * q^2 - 25 * q^3 + 69 * q^4 - 33 * q^5 - 25 * q^6 - 19 * q^7 + 69 * q^8 + 54 * q^9	\( 69 q + 69 q^{2} - 25 q^{3} + 69 q^{4} - 33 q^{5} - 25 q^{6} - 19 q^{7} + 69 q^{8} + 54 q^{9} - 33 q^{10} - 30 q^{11} - 25 q^{12} - 58 q^{13} - 19 q^{14} + 2 q^{15} + 69 q^{16} - 80 q^{17} + 54 q^{18} - 40 q^{19} - 33 q^{20} - 32 q^{21} - 30 q^{22} - 45 q^{23} - 25 q^{24} + 42 q^{25} - 58 q^{26} - 76 q^{27} - 19 q^{28} - 44 q^{29} + 2 q^{30} - 12 q^{31} + 69 q^{32} - 41 q^{33} - 80 q^{34} - 49 q^{35} + 54 q^{36} - 47 q^{37} - 40 q^{38} - 14 q^{39} - 33 q^{40} - 94 q^{41} - 32 q^{42} - 10 q^{43} - 30 q^{44} - 89 q^{45} - 45 q^{46} - 85 q^{47} - 25 q^{48} + 32 q^{49} + 42 q^{50} - 10 q^{51} - 58 q^{52} - 41 q^{53} - 76 q^{54} - 27 q^{55} - 19 q^{56} - 72 q^{57} - 44 q^{58} - 75 q^{59} + 2 q^{60} - 98 q^{61} - 12 q^{62} - 61 q^{63} + 69 q^{64} - 47 q^{65} - 41 q^{66} - 22 q^{67} - 80 q^{68} - 74 q^{69} - 49 q^{70} - 22 q^{71} + 54 q^{72} - 129 q^{73} - 47 q^{74} - 106 q^{75} - 40 q^{76} - 108 q^{77} - 14 q^{78} + 21 q^{79} - 33 q^{80} + 13 q^{81} - 94 q^{82} - 111 q^{83} - 32 q^{84} - 67 q^{85} - 10 q^{86} - 38 q^{87} - 30 q^{88} - 112 q^{89} - 89 q^{90} - 55 q^{91} - 45 q^{92} - 90 q^{93} - 85 q^{94} - 38 q^{95} - 25 q^{96} - 98 q^{97} + 32 q^{98} - 51 q^{99}+O(q^{100}) \) 69 * q + 69 * q^2 - 25 * q^3 + 69 * q^4 - 33 * q^5 - 25 * q^6 - 19 * q^7 + 69 * q^8 + 54 * q^9 - 33 * q^10 - 30 * q^11 - 25 * q^12 - 58 * q^13 - 19 * q^14 + 2 * q^15 + 69 * q^16 - 80 * q^17 + 54 * q^18 - 40 * q^19 - 33 * q^20 - 32 * q^21 - 30 * q^22 - 45 * q^23 - 25 * q^24 + 42 * q^25 - 58 * q^26 - 76 * q^27 - 19 * q^28 - 44 * q^29 + 2 * q^30 - 12 * q^31 + 69 * q^32 - 41 * q^33 - 80 * q^34 - 49 * q^35 + 54 * q^36 - 47 * q^37 - 40 * q^38 - 14 * q^39 - 33 * q^40 - 94 * q^41 - 32 * q^42 - 10 * q^43 - 30 * q^44 - 89 * q^45 - 45 * q^46 - 85 * q^47 - 25 * q^48 + 32 * q^49 + 42 * q^50 - 10 * q^51 - 58 * q^52 - 41 * q^53 - 76 * q^54 - 27 * q^55 - 19 * q^56 - 72 * q^57 - 44 * q^58 - 75 * q^59 + 2 * q^60 - 98 * q^61 - 12 * q^62 - 61 * q^63 + 69 * q^64 - 47 * q^65 - 41 * q^66 - 22 * q^67 - 80 * q^68 - 74 * q^69 - 49 * q^70 - 22 * q^71 + 54 * q^72 - 129 * q^73 - 47 * q^74 - 106 * q^75 - 40 * q^76 - 108 * q^77 - 14 * q^78 + 21 * q^79 - 33 * q^80 + 13 * q^81 - 94 * q^82 - 111 * q^83 - 32 * q^84 - 67 * q^85 - 10 * q^86 - 38 * q^87 - 30 * q^88 - 112 * q^89 - 89 * q^90 - 55 * q^91 - 45 * q^92 - 90 * q^93 - 85 * q^94 - 38 * q^95 - 25 * q^96 - 98 * q^97 + 32 * q^98 - 51 * 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
$3$	0.233596	0.134867	0.0674333	−	0.997724i	$-0.478519\pi$
$3$	0.233596	0.134867	0.0674333	+	0.997724i	$0.478519\pi$
$4$	1.00000	0.500000
$5$	1.44908	0.648050	0.324025	−	0.946049i	$-0.394964\pi$
$5$	1.44908	0.648050	0.324025	+	0.946049i	$0.394964\pi$
$6$	0.233596	0.0953651
$7$	−1.89084	−0.714669	−0.357334	−	0.933976i	$-0.616314\pi$
$7$	−1.89084	−0.714669	−0.357334	+	0.933976i	$0.616314\pi$
$8$	1.00000	0.353553
$9$	−2.94543	−0.981811
$10$	1.44908	0.458240
$11$	−0.939692	−0.283328	−0.141664	−	0.989915i	$-0.545245\pi$
$11$	−0.939692	−0.283328	−0.141664	+	0.989915i	$0.545245\pi$
$12$	0.233596	0.0674333
$13$	6.04214	1.67579	0.837895	−	0.545832i	$-0.183786\pi$
$13$	6.04214	1.67579	0.837895	+	0.545832i	$0.183786\pi$
$14$	−1.89084	−0.505347
$15$	0.338500	0.0874003
$16$	1.00000	0.250000
$17$	−5.41499	−1.31333	−0.656664	−	0.754184i	$-0.728033\pi$
$17$	−5.41499	−1.31333	−0.656664	+	0.754184i	$0.728033\pi$
$18$	−2.94543	−0.694245
$19$	−3.73800	−0.857555	−0.428777	−	0.903410i	$-0.641056\pi$
$19$	−3.73800	−0.857555	−0.428777	+	0.903410i	$0.641056\pi$
$20$	1.44908	0.324025
$21$	−0.441692	−0.0963850
$22$	−0.939692	−0.200343
$23$	7.85958	1.63884	0.819418	−	0.573196i	$-0.194297\pi$
$23$	7.85958	1.63884	0.819418	+	0.573196i	$0.194297\pi$
$24$	0.233596	0.0476826
$25$	−2.90016	−0.580032
$26$	6.04214	1.18496
$27$	−1.38883	−0.267280
$28$	−1.89084	−0.357334
$29$	1.50996	0.280393	0.140196	−	0.990124i	$-0.455227\pi$
$29$	1.50996	0.280393	0.140196	+	0.990124i	$0.455227\pi$
$30$	0.338500	0.0618013
$31$	−5.85679	−1.05191	−0.525955	−	0.850512i	$-0.676292\pi$
$31$	−5.85679	−1.05191	−0.525955	+	0.850512i	$0.676292\pi$
$32$	1.00000	0.176777
$33$	−0.219508	−0.0382115
$34$	−5.41499	−0.928663
$35$	−2.73998	−0.463141
$36$	−2.94543	−0.490905
$37$	−7.71700	−1.26867	−0.634334	−	0.773059i	$-0.718726\pi$
$37$	−7.71700	−1.26867	−0.634334	+	0.773059i	$0.718726\pi$
$38$	−3.73800	−0.606383
$39$	1.41142	0.226008
$40$	1.44908	0.229120
$41$	−7.43039	−1.16043	−0.580216	−	0.814463i	$-0.697032\pi$
$41$	−7.43039	−1.16043	−0.580216	+	0.814463i	$0.697032\pi$
$42$	−0.441692	−0.0681545
$43$	−2.20301	−0.335956	−0.167978	−	0.985791i	$-0.553724\pi$
$43$	−2.20301	−0.335956	−0.167978	+	0.985791i	$0.553724\pi$
$44$	−0.939692	−0.141664
$45$	−4.26818	−0.636262
$46$	7.85958	1.15883
$47$	4.74613	0.692294	0.346147	−	0.938180i	$-0.387490\pi$
$47$	4.74613	0.692294	0.346147	+	0.938180i	$0.387490\pi$
$48$	0.233596	0.0337167
$49$	−3.42474	−0.489248
$50$	−2.90016	−0.410144
$51$	−1.26492	−0.177124
$52$	6.04214	0.837895
$53$	10.8344	1.48822	0.744112	−	0.668055i	$-0.232873\pi$
$53$	10.8344	1.48822	0.744112	+	0.668055i	$0.232873\pi$
$54$	−1.38883	−0.188996
$55$	−1.36169	−0.183611
$56$	−1.89084	−0.252674
$57$	−0.873180	−0.115656
$58$	1.50996	0.198268
$59$	−2.40412	−0.312989	−0.156495	−	0.987679i	$-0.550019\pi$
$59$	−2.40412	−0.312989	−0.156495	+	0.987679i	$0.550019\pi$
$60$	0.338500	0.0437001
$61$	−15.6010	−1.99750	−0.998749	−	0.0500095i	$-0.984075\pi$
$61$	−15.6010	−1.99750	−0.998749	+	0.0500095i	$0.984075\pi$
$62$	−5.85679	−0.743813
$63$	5.56933	0.701670
$64$	1.00000	0.125000
$65$	8.75557	1.08599
$66$	−0.219508	−0.0270196
$67$	−4.63587	−0.566361	−0.283181	−	0.959067i	$-0.591390\pi$
$67$	−4.63587	−0.566361	−0.283181	+	0.959067i	$0.591390\pi$
$68$	−5.41499	−0.656664
$69$	1.83597	0.221024
$70$	−2.73998	−0.327490
$71$	−3.65545	−0.433823	−0.216911	−	0.976191i	$-0.569598\pi$
$71$	−3.65545	−0.433823	−0.216911	+	0.976191i	$0.569598\pi$
$72$	−2.94543	−0.347123
$73$	−0.689342	−0.0806814	−0.0403407	−	0.999186i	$-0.512844\pi$
$73$	−0.689342	−0.0806814	−0.0403407	+	0.999186i	$0.512844\pi$
$74$	−7.71700	−0.897083
$75$	−0.677465	−0.0782269
$76$	−3.73800	−0.428777
$77$	1.77680	0.202486
$78$	1.41142	0.159812
$79$	4.69846	0.528618	0.264309	−	0.964438i	$-0.414856\pi$
$79$	4.69846	0.528618	0.264309	+	0.964438i	$0.414856\pi$
$80$	1.44908	0.162012
$81$	8.51187	0.945764
$82$	−7.43039	−0.820549
$83$	−9.07398	−0.995998	−0.497999	−	0.867178i	$-0.665932\pi$
$83$	−9.07398	−0.995998	−0.497999	+	0.867178i	$0.665932\pi$
$84$	−0.441692	−0.0481925
$85$	−7.84676	−0.851101
$86$	−2.20301	−0.237557
$87$	0.352721	0.0378156
$88$	−0.939692	−0.100172
$89$	15.6008	1.65368	0.826842	−	0.562435i	$-0.190135\pi$
$89$	15.6008	1.65368	0.826842	+	0.562435i	$0.190135\pi$
$90$	−4.26818	−0.449905
$91$	−11.4247	−1.19763
$92$	7.85958	0.819418
$93$	−1.36812	−0.141868
$94$	4.74613	0.489526
$95$	−5.41666	−0.555738
$96$	0.233596	0.0238413
$97$	−17.1560	−1.74193	−0.870963	−	0.491348i	$-0.836504\pi$
$97$	−17.1560	−1.74193	−0.870963	+	0.491348i	$0.836504\pi$
$98$	−3.42474	−0.345951
$99$	2.76780	0.278174
$100$	−2.90016	−0.290016
$101$	1.55666	0.154893	0.0774466	−	0.996997i	$-0.475323\pi$
$101$	1.55666	0.154893	0.0774466	+	0.996997i	$0.475323\pi$
$102$	−1.26492	−0.125246
$103$	−2.94911	−0.290585	−0.145292	−	0.989389i	$-0.546412\pi$
$103$	−2.94911	−0.290585	−0.145292	+	0.989389i	$0.546412\pi$
$104$	6.04214	0.592481
$105$	−0.640048	−0.0624623
$106$	10.8344	1.05233
$107$	8.28765	0.801198	0.400599	−	0.916254i	$-0.368802\pi$
$107$	8.28765	0.801198	0.400599	+	0.916254i	$0.368802\pi$
$108$	−1.38883	−0.133640
$109$	5.60706	0.537059	0.268530	−	0.963271i	$-0.413462\pi$
$109$	5.60706	0.537059	0.268530	+	0.963271i	$0.413462\pi$
$110$	−1.36169	−0.129832
$111$	−1.80266	−0.171101
$112$	−1.89084	−0.178667
$113$	14.9758	1.40880	0.704401	−	0.709803i	$-0.251216\pi$
$113$	14.9758	1.40880	0.704401	+	0.709803i	$0.251216\pi$
$114$	−0.873180	−0.0817808
$115$	11.3892	1.06205
$116$	1.50996	0.140196
$117$	−17.7967	−1.64531
$118$	−2.40412	−0.221317
$119$	10.2389	0.938594
$120$	0.338500	0.0309007
$121$	−10.1170	−0.919725
$122$	−15.6010	−1.41244
$123$	−1.73571	−0.156504
$124$	−5.85679	−0.525955
$125$	−11.4480	−1.02394
$126$	5.56933	0.496155
$127$	−18.3296	−1.62649	−0.813246	−	0.581920i	$-0.802302\pi$
$127$	−18.3296	−1.62649	−0.813246	+	0.581920i	$0.802302\pi$
$128$	1.00000	0.0883883
$129$	−0.514614	−0.0453092
$130$	8.75557	0.767914
$131$	−7.01646	−0.613031	−0.306515	−	0.951866i	$-0.599163\pi$
$131$	−7.01646	−0.613031	−0.306515	+	0.951866i	$0.599163\pi$
$132$	−0.219508	−0.0191057
$133$	7.06794	0.612868
$134$	−4.63587	−0.400478
$135$	−2.01253	−0.173211
$136$	−5.41499	−0.464331
$137$	16.1050	1.37594	0.687972	−	0.725737i	$-0.258501\pi$
$137$	16.1050	1.37594	0.687972	+	0.725737i	$0.258501\pi$
$138$	1.83597	0.156288
$139$	−15.3670	−1.30341	−0.651704	−	0.758473i	$-0.725946\pi$
$139$	−15.3670	−1.30341	−0.651704	+	0.758473i	$0.725946\pi$
$140$	−2.73998	−0.231570
$141$	1.10868	0.0933674
$142$	−3.65545	−0.306759
$143$	−5.67776	−0.474798
$144$	−2.94543	−0.245453
$145$	2.18806	0.181708
$146$	−0.689342	−0.0570503
$147$	−0.800005	−0.0659833
$148$	−7.71700	−0.634334
$149$	−0.331975	−0.0271964	−0.0135982	−	0.999908i	$-0.504329\pi$
$149$	−0.331975	−0.0271964	−0.0135982	+	0.999908i	$0.504329\pi$
$150$	−0.677465	−0.0553148
$151$	9.10288	0.740782	0.370391	−	0.928876i	$-0.379224\pi$
$151$	9.10288	0.740782	0.370391	+	0.928876i	$0.379224\pi$
$152$	−3.73800	−0.303191
$153$	15.9495	1.28944
$154$	1.77680	0.143179
$155$	−8.48697	−0.681690
$156$	1.41142	0.113004
$157$	9.17898	0.732563	0.366281	−	0.930504i	$-0.380631\pi$
$157$	9.17898	0.732563	0.366281	+	0.930504i	$0.380631\pi$
$158$	4.69846	0.373789
$159$	2.53088	0.200712
$160$	1.44908	0.114560
$161$	−14.8612	−1.17123
$162$	8.51187	0.668756
$163$	7.61930	0.596790	0.298395	−	0.954443i	$-0.403549\pi$
$163$	7.61930	0.596790	0.298395	+	0.954443i	$0.403549\pi$
$164$	−7.43039	−0.580216
$165$	−0.318086	−0.0247629
$166$	−9.07398	−0.704277
$167$	−8.57418	−0.663490	−0.331745	−	0.943369i	$-0.607637\pi$
$167$	−8.57418	−0.663490	−0.331745	+	0.943369i	$0.607637\pi$
$168$	−0.441692	−0.0340772
$169$	23.5075	1.80827
$170$	−7.84676	−0.601819
$171$	11.0100	0.841957
$172$	−2.20301	−0.167978
$173$	−18.0437	−1.37184	−0.685920	−	0.727677i	$-0.740600\pi$
$173$	−18.0437	−1.37184	−0.685920	+	0.727677i	$0.740600\pi$
$174$	0.352721	0.0267397
$175$	5.48373	0.414531
$176$	−0.939692	−0.0708320
$177$	−0.561592	−0.0422118
$178$	15.6008	1.16933
$179$	−14.9677	−1.11874	−0.559370	−	0.828918i	$-0.688957\pi$
$179$	−14.9677	−1.11874	−0.559370	+	0.828918i	$0.688957\pi$
$180$	−4.26818	−0.318131
$181$	−3.99572	−0.297000	−0.148500	−	0.988912i	$-0.547444\pi$
$181$	−3.99572	−0.297000	−0.148500	+	0.988912i	$0.547444\pi$
$182$	−11.4247	−0.846855
$183$	−3.64432	−0.269396
$184$	7.85958	0.579416
$185$	−11.1826	−0.822160
$186$	−1.36812	−0.100316
$187$	5.08842	0.372102
$188$	4.74613	0.346147
$189$	2.62605	0.191017
$190$	−5.41666	−0.392966
$191$	19.0836	1.38084	0.690420	−	0.723409i	$-0.257426\pi$
$191$	19.0836	1.38084	0.690420	+	0.723409i	$0.257426\pi$
$192$	0.233596	0.0168583
$193$	−23.3943	−1.68396	−0.841980	−	0.539508i	$-0.818610\pi$
$193$	−23.3943	−1.68396	−0.841980	+	0.539508i	$0.818610\pi$
$194$	−17.1560	−1.23173
$195$	2.04526	0.146464
$196$	−3.42474	−0.244624
$197$	−12.5059	−0.891006	−0.445503	−	0.895280i	$-0.646975\pi$
$197$	−12.5059	−0.891006	−0.445503	+	0.895280i	$0.646975\pi$
$198$	2.76780	0.196699
$199$	−27.4625	−1.94676	−0.973381	−	0.229193i	$-0.926391\pi$
$199$	−27.4625	−1.94676	−0.973381	+	0.229193i	$0.926391\pi$
$200$	−2.90016	−0.205072
$201$	−1.08292	−0.0763832
$202$	1.55666	0.109526
$203$	−2.85509	−0.200388
$204$	−1.26492	−0.0885620
$205$	−10.7673	−0.752017
$206$	−2.94911	−0.205474
$207$	−23.1499	−1.60903
$208$	6.04214	0.418947
$209$	3.51257	0.242969
$210$	−0.640048	−0.0441675
$211$	9.01215	0.620422	0.310211	−	0.950668i	$-0.399600\pi$
$211$	9.01215	0.620422	0.310211	+	0.950668i	$0.399600\pi$
$212$	10.8344	0.744112
$213$	−0.853899	−0.0585082
$214$	8.28765	0.566532
$215$	−3.19234	−0.217716
$216$	−1.38883	−0.0944978
$217$	11.0742	0.751768
$218$	5.60706	0.379758
$219$	−0.161027	−0.0108812
$220$	−1.36169	−0.0918053
$221$	−32.7181	−2.20086
$222$	−1.80266	−0.120987
$223$	12.6460	0.846840	0.423420	−	0.905933i	$-0.360829\pi$
$223$	12.6460	0.846840	0.423420	+	0.905933i	$0.360829\pi$
$224$	−1.89084	−0.126337
$225$	8.54222	0.569482
$226$	14.9758	0.996173
$227$	9.60763	0.637681	0.318840	−	0.947808i	$-0.396707\pi$
$227$	9.60763	0.637681	0.318840	+	0.947808i	$0.396707\pi$
$228$	−0.873180	−0.0578278
$229$	−24.5336	−1.62122	−0.810612	−	0.585583i	$-0.800866\pi$
$229$	−24.5336	−1.62122	−0.810612	+	0.585583i	$0.800866\pi$
$230$	11.3892	0.750981
$231$	0.415054	0.0273086
$232$	1.50996	0.0991338
$233$	1.49690	0.0980653	0.0490327	−	0.998797i	$-0.484386\pi$
$233$	1.49690	0.0980653	0.0490327	+	0.998797i	$0.484386\pi$
$234$	−17.7967	−1.16341
$235$	6.87754	0.448641
$236$	−2.40412	−0.156495
$237$	1.09754	0.0712929
$238$	10.2389	0.663686
$239$	13.2936	0.859892	0.429946	−	0.902855i	$-0.358533\pi$
$239$	13.2936	0.859892	0.429946	+	0.902855i	$0.358533\pi$
$240$	0.338500	0.0218501
$241$	−14.9697	−0.964286	−0.482143	−	0.876092i	$-0.660141\pi$
$241$	−14.9697	−0.964286	−0.482143	+	0.876092i	$0.660141\pi$
$242$	−10.1170	−0.650344
$243$	6.15483	0.394832
$244$	−15.6010	−0.998749
$245$	−4.96273	−0.317057
$246$	−1.73571	−0.110665
$247$	−22.5855	−1.43708
$248$	−5.85679	−0.371906
$249$	−2.11964	−0.134327
$250$	−11.4480	−0.724034
$251$	−17.4057	−1.09864	−0.549320	−	0.835612i	$-0.685113\pi$
$251$	−17.4057	−1.09864	−0.549320	+	0.835612i	$0.685113\pi$
$252$	5.56933	0.350835
$253$	−7.38559	−0.464328
$254$	−18.3296	−1.15010
$255$	−1.83297	−0.114785
$256$	1.00000	0.0625000
$257$	−2.78066	−0.173453	−0.0867264	−	0.996232i	$-0.527641\pi$
$257$	−2.78066	−0.173453	−0.0867264	+	0.996232i	$0.527641\pi$
$258$	−0.514614	−0.0320385
$259$	14.5916	0.906677
$260$	8.75557	0.542997
$261$	−4.44749	−0.275293
$262$	−7.01646	−0.433478
$263$	−10.8994	−0.672083	−0.336042	−	0.941847i	$-0.609088\pi$
$263$	−10.8994	−0.672083	−0.336042	+	0.941847i	$0.609088\pi$
$264$	−0.219508	−0.0135098
$265$	15.7000	0.964443
$266$	7.06794	0.433363
$267$	3.64429	0.223027
$268$	−4.63587	−0.283181
$269$	−24.4383	−1.49003	−0.745015	−	0.667048i	$-0.767558\pi$
$269$	−24.4383	−1.49003	−0.745015	+	0.667048i	$0.767558\pi$
$270$	−2.01253	−0.122479
$271$	−28.7484	−1.74634	−0.873169	−	0.487418i	$-0.837939\pi$
$271$	−28.7484	−1.74634	−0.873169	+	0.487418i	$0.837939\pi$
$272$	−5.41499	−0.328332
$273$	−2.66876	−0.161521
$274$	16.1050	0.972940
$275$	2.72526	0.164339
$276$	1.83597	0.110512
$277$	26.5346	1.59431	0.797155	−	0.603774i	$-0.206337\pi$
$277$	26.5346	1.59431	0.797155	+	0.603774i	$0.206337\pi$
$278$	−15.3670	−0.921649
$279$	17.2508	1.03278
$280$	−2.73998	−0.163745
$281$	14.8705	0.887099	0.443550	−	0.896250i	$-0.353719\pi$
$281$	14.8705	0.887099	0.443550	+	0.896250i	$0.353719\pi$
$282$	1.10868	0.0660207
$283$	22.3236	1.32700	0.663500	−	0.748177i	$-0.269070\pi$
$283$	22.3236	1.32700	0.663500	+	0.748177i	$0.269070\pi$
$284$	−3.65545	−0.216911
$285$	−1.26531	−0.0749505
$286$	−5.67776	−0.335733
$287$	14.0497	0.829325
$288$	−2.94543	−0.173561
$289$	12.3221	0.724828
$290$	2.18806	0.128487
$291$	−4.00757	−0.234928
$292$	−0.689342	−0.0403407
$293$	2.43431	0.142214	0.0711070	−	0.997469i	$-0.477347\pi$
$293$	2.43431	0.142214	0.0711070	+	0.997469i	$0.477347\pi$
$294$	−0.800005	−0.0466572
$295$	−3.48377	−0.202833
$296$	−7.71700	−0.448542
$297$	1.30507	0.0757280
$298$	−0.331975	−0.0192308
$299$	47.4887	2.74634
$300$	−0.677465	−0.0391135
$301$	4.16553	0.240097
$302$	9.10288	0.523812
$303$	0.363629	0.0208899
$304$	−3.73800	−0.214389
$305$	−22.6071	−1.29448
$306$	15.9495	0.911771
$307$	32.6809	1.86520	0.932600	−	0.360912i	$-0.117535\pi$
$307$	32.6809	1.86520	0.932600	+	0.360912i	$0.117535\pi$
$308$	1.77680	0.101243
$309$	−0.688900	−0.0391902
$310$	−8.48697	−0.482028
$311$	0.0458777	0.00260148	0.00130074	−	0.999999i	$-0.499586\pi$
$311$	0.0458777	0.00260148	0.00130074	+	0.999999i	$0.499586\pi$
$312$	1.41142	0.0799059
$313$	−6.07515	−0.343388	−0.171694	−	0.985150i	$-0.554924\pi$
$313$	−6.07515	−0.343388	−0.171694	+	0.985150i	$0.554924\pi$
$314$	9.17898	0.518000
$315$	8.07042	0.454717
$316$	4.69846	0.264309
$317$	−2.61523	−0.146886	−0.0734431	−	0.997299i	$-0.523399\pi$
$317$	−2.61523	−0.146886	−0.0734431	+	0.997299i	$0.523399\pi$
$318$	2.53088	0.141925
$319$	−1.41890	−0.0794431
$320$	1.44908	0.0810062
$321$	1.93596	0.108055
$322$	−14.8612	−0.828182
$323$	20.2412	1.12625
$324$	8.51187	0.472882
$325$	−17.5232	−0.972011
$326$	7.61930	0.421994
$327$	1.30979	0.0724314
$328$	−7.43039	−0.410275
$329$	−8.97416	−0.494761
$330$	−0.318086	−0.0175100
$331$	1.45542	0.0799970	0.0399985	−	0.999200i	$-0.487265\pi$
$331$	1.45542	0.0799970	0.0399985	+	0.999200i	$0.487265\pi$
$332$	−9.07398	−0.497999
$333$	22.7299	1.24559
$334$	−8.57418	−0.469158
$335$	−6.71775	−0.367030
$336$	−0.441692	−0.0240963
$337$	−7.43243	−0.404870	−0.202435	−	0.979296i	$-0.564885\pi$
$337$	−7.43243	−0.404870	−0.202435	+	0.979296i	$0.564885\pi$
$338$	23.5075	1.27864
$339$	3.49828	0.190000
$340$	−7.84676	−0.425551
$341$	5.50358	0.298036
$342$	11.0100	0.595353
$343$	19.7115	1.06432
$344$	−2.20301	−0.118778
$345$	2.66047	0.143235
$346$	−18.0437	−0.970037
$347$	−1.74290	−0.0935637	−0.0467818	−	0.998905i	$-0.514897\pi$
$347$	−1.74290	−0.0935637	−0.0467818	+	0.998905i	$0.514897\pi$
$348$	0.352721	0.0189078
$349$	−3.79597	−0.203193	−0.101597	−	0.994826i	$-0.532395\pi$
$349$	−3.79597	−0.203193	−0.101597	+	0.994826i	$0.532395\pi$
$350$	5.48373	0.293117
$351$	−8.39150	−0.447905
$352$	−0.939692	−0.0500858
$353$	−1.95883	−0.104258	−0.0521290	−	0.998640i	$-0.516601\pi$
$353$	−1.95883	−0.104258	−0.0521290	+	0.998640i	$0.516601\pi$
$354$	−0.561592	−0.0298483
$355$	−5.29706	−0.281138
$356$	15.6008	0.826842
$357$	2.39175	0.126585
$358$	−14.9677	−0.791069
$359$	−4.19700	−0.221509	−0.110755	−	0.993848i	$-0.535327\pi$
$359$	−4.19700	−0.221509	−0.110755	+	0.993848i	$0.535327\pi$
$360$	−4.26818	−0.224953
$361$	−5.02739	−0.264600
$362$	−3.99572	−0.210010
$363$	−2.36328	−0.124040
$364$	−11.4247	−0.598817
$365$	−0.998914	−0.0522855
$366$	−3.64432	−0.190492
$367$	−13.8472	−0.722820	−0.361410	−	0.932407i	$-0.617705\pi$
$367$	−13.8472	−0.722820	−0.361410	+	0.932407i	$0.617705\pi$
$368$	7.85958	0.409709
$369$	21.8857	1.13932
$370$	−11.1826	−0.581355
$371$	−20.4861	−1.06359
$372$	−1.36812	−0.0709338
$373$	2.33116	0.120703	0.0603514	−	0.998177i	$-0.480778\pi$
$373$	2.33116	0.120703	0.0603514	+	0.998177i	$0.480778\pi$
$374$	5.08842	0.263116
$375$	−2.67420	−0.138095
$376$	4.74613	0.244763
$377$	9.12340	0.469879
$378$	2.62605	0.135069
$379$	2.94472	0.151260	0.0756300	−	0.997136i	$-0.475903\pi$
$379$	2.94472	0.151260	0.0756300	+	0.997136i	$0.475903\pi$
$380$	−5.41666	−0.277869
$381$	−4.28173	−0.219359
$382$	19.0836	0.976401
$383$	18.4399	0.942233	0.471117	−	0.882071i	$-0.343851\pi$
$383$	18.4399	0.942233	0.471117	+	0.882071i	$0.343851\pi$
$384$	0.233596	0.0119206
$385$	2.57474	0.131221
$386$	−23.3943	−1.19074
$387$	6.48882	0.329845
$388$	−17.1560	−0.870963
$389$	−0.517056	−0.0262158	−0.0131079	−	0.999914i	$-0.504172\pi$
$389$	−0.517056	−0.0262158	−0.0131079	+	0.999914i	$0.504172\pi$
$390$	2.04526	0.103566
$391$	−42.5595	−2.15233
$392$	−3.42474	−0.172975
$393$	−1.63902	−0.0826774
$394$	−12.5059	−0.630037
$395$	6.80845	0.342570
$396$	2.76780	0.139087
$397$	9.85730	0.494724	0.247362	−	0.968923i	$-0.420436\pi$
$397$	9.85730	0.494724	0.247362	+	0.968923i	$0.420436\pi$
$398$	−27.4625	−1.37657
$399$	1.65104	0.0826554
$400$	−2.90016	−0.145008
$401$	−33.6030	−1.67806	−0.839028	−	0.544089i	$-0.816875\pi$
$401$	−33.6030	−1.67806	−0.839028	+	0.544089i	$0.816875\pi$
$402$	−1.08292	−0.0540111
$403$	−35.3876	−1.76278
$404$	1.55666	0.0774466
$405$	12.3344	0.612902
$406$	−2.85509	−0.141696
$407$	7.25161	0.359449
$408$	−1.26492	−0.0626228
$409$	−5.08546	−0.251460	−0.125730	−	0.992065i	$-0.540127\pi$
$409$	−5.08546	−0.251460	−0.125730	+	0.992065i	$0.540127\pi$
$410$	−10.7673	−0.531757
$411$	3.76207	0.185569
$412$	−2.94911	−0.145292
$413$	4.54579	0.223684
$414$	−23.1499	−1.13775
$415$	−13.1489	−0.645456
$416$	6.04214	0.296240
$417$	−3.58966	−0.175786
$418$	3.51257	0.171805
$419$	22.8758	1.11756	0.558779	−	0.829317i	$-0.311270\pi$
$419$	22.8758	1.11756	0.558779	+	0.829317i	$0.311270\pi$
$420$	−0.640048	−0.0312311
$421$	7.98184	0.389011	0.194506	−	0.980901i	$-0.437690\pi$
$421$	7.98184	0.389011	0.194506	+	0.980901i	$0.437690\pi$
$422$	9.01215	0.438705
$423$	−13.9794	−0.679702
$424$	10.8344	0.526167
$425$	15.7043	0.761771
$426$	−0.853899	−0.0413715
$427$	29.4989	1.42755
$428$	8.28765	0.400599
$429$	−1.32630	−0.0640344
$430$	−3.19234	−0.153948
$431$	−6.86384	−0.330620	−0.165310	−	0.986242i	$-0.552862\pi$
$431$	−6.86384	−0.330620	−0.165310	+	0.986242i	$0.552862\pi$
$432$	−1.38883	−0.0668201
$433$	34.9443	1.67931	0.839657	−	0.543117i	$-0.182756\pi$
$433$	34.9443	1.67931	0.839657	+	0.543117i	$0.182756\pi$
$434$	11.0742	0.531580
$435$	0.511122	0.0245064
$436$	5.60706	0.268530
$437$	−29.3791	−1.40539
$438$	−0.161027	−0.00769419
$439$	38.6696	1.84560	0.922799	−	0.385282i	$-0.125896\pi$
$439$	38.6696	1.84560	0.922799	+	0.385282i	$0.125896\pi$
$440$	−1.36169	−0.0649161
$441$	10.0873	0.480349
$442$	−32.7181	−1.55624
$443$	8.58458	0.407865	0.203933	−	0.978985i	$-0.434628\pi$
$443$	8.58458	0.407865	0.203933	+	0.978985i	$0.434628\pi$
$444$	−1.80266	−0.0855505
$445$	22.6069	1.07167
$446$	12.6460	0.598806
$447$	−0.0775479	−0.00366789
$448$	−1.89084	−0.0893336
$449$	−21.0233	−0.992153	−0.496076	−	0.868279i	$-0.665226\pi$
$449$	−21.0233	−0.992153	−0.496076	+	0.868279i	$0.665226\pi$
$450$	8.54222	0.402684
$451$	6.98228	0.328783
$452$	14.9758	0.704401
$453$	2.12640	0.0999068
$454$	9.60763	0.450908
$455$	−16.5553	−0.776126
$456$	−0.873180	−0.0408904
$457$	−6.43147	−0.300851	−0.150426	−	0.988621i	$-0.548064\pi$
$457$	−6.43147	−0.300851	−0.150426	+	0.988621i	$0.548064\pi$
$458$	−24.5336	−1.14638
$459$	7.52049	0.351026
$460$	11.3892	0.531024
$461$	−33.9388	−1.58069	−0.790343	−	0.612664i	$-0.790098\pi$
$461$	−33.9388	−1.58069	−0.790343	+	0.612664i	$0.790098\pi$
$462$	0.415054	0.0193101
$463$	19.5144	0.906910	0.453455	−	0.891279i	$-0.350191\pi$
$463$	19.5144	0.906910	0.453455	+	0.891279i	$0.350191\pi$
$464$	1.50996	0.0700982
$465$	−1.98252	−0.0919372
$466$	1.49690	0.0693426
$467$	3.62029	0.167527	0.0837636	−	0.996486i	$-0.473306\pi$
$467$	3.62029	0.167527	0.0837636	+	0.996486i	$0.473306\pi$
$468$	−17.7967	−0.822654
$469$	8.76566	0.404761
$470$	6.87754	0.317237
$471$	2.14417	0.0987983
$472$	−2.40412	−0.110658
$473$	2.07015	0.0951857
$474$	1.09754	0.0504117
$475$	10.8408	0.497409
$476$	10.2389	0.469297
$477$	−31.9121	−1.46115
$478$	13.2936	0.608035
$479$	−30.8619	−1.41012	−0.705059	−	0.709149i	$-0.749080\pi$
$479$	−30.8619	−1.41012	−0.705059	+	0.709149i	$0.749080\pi$
$480$	0.338500	0.0154503
$481$	−46.6272	−2.12602
$482$	−14.9697	−0.681853
$483$	−3.47151	−0.157959
$484$	−10.1170	−0.459863
$485$	−24.8604	−1.12885
$486$	6.15483	0.279189
$487$	22.7328	1.03012	0.515061	−	0.857154i	$-0.327769\pi$
$487$	22.7328	1.03012	0.515061	+	0.857154i	$0.327769\pi$
$488$	−15.6010	−0.706222
$489$	1.77984	0.0804870
$490$	−4.96273	−0.224193
$491$	−19.7022	−0.889146	−0.444573	−	0.895743i	$-0.646645\pi$
$491$	−19.7022	−0.889146	−0.444573	+	0.895743i	$0.646645\pi$
$492$	−1.73571	−0.0782518
$493$	−8.17642	−0.368247
$494$	−22.5855	−1.01617
$495$	4.01077	0.180271
$496$	−5.85679	−0.262978
$497$	6.91186	0.310039
$498$	−2.11964	−0.0949835
$499$	−21.2216	−0.950007	−0.475004	−	0.879984i	$-0.657553\pi$
$499$	−21.2216	−0.950007	−0.475004	+	0.879984i	$0.657553\pi$
$500$	−11.4480	−0.511969
$501$	−2.00289	−0.0894827
$502$	−17.4057	−0.776856
$503$	3.90122	0.173947	0.0869734	−	0.996211i	$-0.472280\pi$
$503$	3.90122	0.173947	0.0869734	+	0.996211i	$0.472280\pi$
$504$	5.56933	0.248078
$505$	2.25572	0.100378
$506$	−7.38559	−0.328330
$507$	5.49125	0.243875
$508$	−18.3296	−0.813246
$509$	−6.42296	−0.284693	−0.142346	−	0.989817i	$-0.545465\pi$
$509$	−6.42296	−0.284693	−0.142346	+	0.989817i	$0.545465\pi$
$510$	−1.83297	−0.0811654
$511$	1.30343	0.0576605
$512$	1.00000	0.0441942
$513$	5.19143	0.229207
$514$	−2.78066	−0.122650
$515$	−4.27351	−0.188313
$516$	−0.514614	−0.0226546
$517$	−4.45990	−0.196146
$518$	14.5916	0.641118
$519$	−4.21494	−0.185015
$520$	8.75557	0.383957
$521$	−38.1078	−1.66953	−0.834767	−	0.550603i	$-0.814398\pi$
$521$	−38.1078	−1.66953	−0.834767	+	0.550603i	$0.814398\pi$
$522$	−4.44749	−0.194661
$523$	44.9111	1.96383	0.981913	−	0.189330i	$-0.0606317\pi$
$523$	44.9111	1.96383	0.981913	+	0.189330i	$0.0606317\pi$
$524$	−7.01646	−0.306515
$525$	1.28098	0.0559064
$526$	−10.8994	−0.475235
$527$	31.7144	1.38150
$528$	−0.219508	−0.00955287
$529$	38.7731	1.68579
$530$	15.7000	0.681964
$531$	7.08117	0.307296
$532$	7.06794	0.306434
$533$	−44.8955	−1.94464
$534$	3.64429	0.157704
$535$	12.0095	0.519216
$536$	−4.63587	−0.200239
$537$	−3.49640	−0.150881
$538$	−24.4383	−1.05361
$539$	3.21820	0.138618
$540$	−2.01253	−0.0866054
$541$	−15.1678	−0.652116	−0.326058	−	0.945350i	$-0.605720\pi$
$541$	−15.1678	−0.652116	−0.326058	+	0.945350i	$0.605720\pi$
$542$	−28.7484	−1.23485
$543$	−0.933384	−0.0400554
$544$	−5.41499	−0.232166
$545$	8.12510	0.348041
$546$	−2.66876	−0.114213
$547$	36.6310	1.56623	0.783115	−	0.621877i	$-0.213630\pi$
$547$	36.6310	1.56623	0.783115	+	0.621877i	$0.213630\pi$
$548$	16.1050	0.687972
$549$	45.9516	1.96116
$550$	2.72526	0.116205
$551$	−5.64423	−0.240452
$552$	1.83597	0.0781439
$553$	−8.88401	−0.377787
$554$	26.5346	1.12735
$555$	−2.61220	−0.110882
$556$	−15.3670	−0.651704
$557$	43.1503	1.82834	0.914169	−	0.405333i	$-0.132844\pi$
$557$	43.1503	1.82834	0.914169	+	0.405333i	$0.132844\pi$
$558$	17.2508	0.730284
$559$	−13.3109	−0.562991
$560$	−2.73998	−0.115785
$561$	1.18863	0.0501842
$562$	14.8705	0.627274
$563$	13.0634	0.550555	0.275277	−	0.961365i	$-0.411230\pi$
$563$	13.0634	0.550555	0.275277	+	0.961365i	$0.411230\pi$
$564$	1.10868	0.0466837
$565$	21.7011	0.912973
$566$	22.3236	0.938330
$567$	−16.0946	−0.675908
$568$	−3.65545	−0.153379
$569$	−4.79322	−0.200942	−0.100471	−	0.994940i	$-0.532035\pi$
$569$	−4.79322	−0.200942	−0.100471	+	0.994940i	$0.532035\pi$
$570$	−1.26531	−0.0529980
$571$	−28.0979	−1.17586	−0.587929	−	0.808912i	$-0.700057\pi$
$571$	−28.0979	−1.17586	−0.587929	+	0.808912i	$0.700057\pi$
$572$	−5.67776	−0.237399
$573$	4.45785	0.186229
$574$	14.0497	0.586421
$575$	−22.7940	−0.950577
$576$	−2.94543	−0.122726
$577$	−8.52039	−0.354708	−0.177354	−	0.984147i	$-0.556754\pi$
$577$	−8.52039	−0.354708	−0.177354	+	0.984147i	$0.556754\pi$
$578$	12.3221	0.512531
$579$	−5.46482	−0.227110
$580$	2.18806	0.0908542
$581$	17.1574	0.711809
$582$	−4.00757	−0.166119
$583$	−10.1810	−0.421655
$584$	−0.689342	−0.0285252
$585$	−25.7889	−1.06624
$586$	2.43431	0.100560
$587$	31.0584	1.28192	0.640958	−	0.767576i	$-0.278537\pi$
$587$	31.0584	1.28192	0.640958	+	0.767576i	$0.278537\pi$
$588$	−0.800005	−0.0329916
$589$	21.8926	0.902071
$590$	−3.48377	−0.143424
$591$	−2.92132	−0.120167
$592$	−7.71700	−0.317167
$593$	13.4430	0.552037	0.276019	−	0.961152i	$-0.410985\pi$
$593$	13.4430	0.552037	0.276019	+	0.961152i	$0.410985\pi$
$594$	1.30507	0.0535477
$595$	14.8369	0.608256
$596$	−0.331975	−0.0135982
$597$	−6.41512	−0.262553
$598$	47.4887	1.94196
$599$	12.0032	0.490435	0.245218	−	0.969468i	$-0.421141\pi$
$599$	12.0032	0.490435	0.245218	+	0.969468i	$0.421141\pi$
$600$	−0.677465	−0.0276574
$601$	−36.6546	−1.49517	−0.747586	−	0.664165i	$-0.768787\pi$
$601$	−36.6546	−1.49517	−0.747586	+	0.664165i	$0.768787\pi$
$602$	4.16553	0.169774
$603$	13.6546	0.556060
$604$	9.10288	0.370391
$605$	−14.6603	−0.596028
$606$	0.363629	0.0147714
$607$	1.08002	0.0438367	0.0219183	−	0.999760i	$-0.493023\pi$
$607$	1.08002	0.0438367	0.0219183	+	0.999760i	$0.493023\pi$
$608$	−3.73800	−0.151596
$609$	−0.666937	−0.0270257
$610$	−22.6071	−0.915334
$611$	28.6768	1.16014
$612$	15.9495	0.644720
$613$	34.2504	1.38336	0.691680	−	0.722205i	$-0.256871\pi$
$613$	34.2504	1.38336	0.691680	+	0.722205i	$0.256871\pi$
$614$	32.6809	1.31890
$615$	−2.51519	−0.101422
$616$	1.77680	0.0715895
$617$	5.67697	0.228546	0.114273	−	0.993449i	$-0.463546\pi$
$617$	5.67697	0.228546	0.114273	+	0.993449i	$0.463546\pi$
$618$	−0.688900	−0.0277116
$619$	12.0182	0.483054	0.241527	−	0.970394i	$-0.422352\pi$
$619$	12.0182	0.483054	0.241527	+	0.970394i	$0.422352\pi$
$620$	−8.48697	−0.340845
$621$	−10.9156	−0.438029
$622$	0.0458777	0.00183953
$623$	−29.4986	−1.18184
$624$	1.41142	0.0565020
$625$	−2.08829	−0.0835314
$626$	−6.07515	−0.242812
$627$	0.820521	0.0327685
$628$	9.17898	0.366281
$629$	41.7875	1.66618
$630$	8.07042	0.321533
$631$	−8.99761	−0.358189	−0.179095	−	0.983832i	$-0.557317\pi$
$631$	−8.99761	−0.358189	−0.179095	+	0.983832i	$0.557317\pi$
$632$	4.69846	0.186895
$633$	2.10520	0.0836742
$634$	−2.61523	−0.103864
$635$	−26.5612	−1.05405
$636$	2.53088	0.100356
$637$	−20.6928	−0.819877
$638$	−1.41890	−0.0561748
$639$	10.7669	0.425932
$640$	1.44908	0.0572800
$641$	21.1860	0.836796	0.418398	−	0.908264i	$-0.362592\pi$
$641$	21.1860	0.836796	0.418398	+	0.908264i	$0.362592\pi$
$642$	1.93596	0.0764063
$643$	40.2717	1.58816	0.794080	−	0.607814i	$-0.207953\pi$
$643$	40.2717	1.58816	0.794080	+	0.607814i	$0.207953\pi$
$644$	−14.8612	−0.585613
$645$	−0.745718	−0.0293626
$646$	20.2412	0.796379
$647$	32.2828	1.26917	0.634584	−	0.772854i	$-0.281171\pi$
$647$	32.2828	1.26917	0.634584	+	0.772854i	$0.281171\pi$
$648$	8.51187	0.334378
$649$	2.25913	0.0886786
$650$	−17.5232	−0.687315
$651$	2.58689	0.101388
$652$	7.61930	0.298395
$653$	40.8264	1.59766	0.798831	−	0.601555i	$-0.205452\pi$
$653$	40.8264	1.59766	0.798831	+	0.601555i	$0.205452\pi$
$654$	1.30979	0.0512167
$655$	−10.1674	−0.397274
$656$	−7.43039	−0.290108
$657$	2.03041	0.0792139
$658$	−8.97416	−0.349849
$659$	−20.3750	−0.793696	−0.396848	−	0.917884i	$-0.629896\pi$
$659$	−20.3750	−0.793696	−0.396848	+	0.917884i	$0.629896\pi$
$660$	−0.318086	−0.0123815
$661$	16.7777	0.652579	0.326289	−	0.945270i	$-0.394202\pi$
$661$	16.7777	0.652579	0.326289	+	0.945270i	$0.394202\pi$
$662$	1.45542	0.0565664
$663$	−7.64282	−0.296823
$664$	−9.07398	−0.352139
$665$	10.2420	0.397169
$666$	22.7299	0.880766
$667$	11.8677	0.459518
$668$	−8.57418	−0.331745
$669$	2.95406	0.114211
$670$	−6.71775	−0.259529
$671$	14.6601	0.565947
$672$	−0.441692	−0.0170386
$673$	1.79889	0.0693422	0.0346711	−	0.999399i	$-0.488962\pi$
$673$	1.79889	0.0693422	0.0346711	+	0.999399i	$0.488962\pi$
$674$	−7.43243	−0.286286
$675$	4.02782	0.155031
$676$	23.5075	0.904135
$677$	−32.3486	−1.24326	−0.621629	−	0.783312i	$-0.713529\pi$
$677$	−32.3486	−1.24326	−0.621629	+	0.783312i	$0.713529\pi$
$678$	3.49828	0.134351
$679$	32.4392	1.24490
$680$	−7.84676	−0.300910
$681$	2.24430	0.0860018
$682$	5.50358	0.210743
$683$	13.1559	0.503398	0.251699	−	0.967806i	$-0.419011\pi$
$683$	13.1559	0.503398	0.251699	+	0.967806i	$0.419011\pi$
$684$	11.0100	0.420978
$685$	23.3375	0.891680
$686$	19.7115	0.752588
$687$	−5.73094	−0.218649
$688$	−2.20301	−0.0839890
$689$	65.4632	2.49395
$690$	2.66047	0.101282
$691$	24.2250	0.921562	0.460781	−	0.887514i	$-0.347569\pi$
$691$	24.2250	0.921562	0.460781	+	0.887514i	$0.347569\pi$
$692$	−18.0437	−0.685920
$693$	−5.23346	−0.198803
$694$	−1.74290	−0.0661595
$695$	−22.2680	−0.844673
$696$	0.352721	0.0133698
$697$	40.2355	1.52403
$698$	−3.79597	−0.143679
$699$	0.349670	0.0132257
$700$	5.48373	0.207265
$701$	−38.7958	−1.46530	−0.732648	−	0.680607i	$-0.761716\pi$
$701$	−38.7958	−1.46530	−0.732648	+	0.680607i	$0.761716\pi$
$702$	−8.39150	−0.316717
$703$	28.8461	1.08795
$704$	−0.939692	−0.0354160
$705$	1.60656	0.0605067
$706$	−1.95883	−0.0737215
$707$	−2.94338	−0.110697
$708$	−0.561592	−0.0211059
$709$	−19.8632	−0.745978	−0.372989	−	0.927836i	$-0.621667\pi$
$709$	−19.8632	−0.745978	−0.372989	+	0.927836i	$0.621667\pi$
$710$	−5.29706	−0.198795
$711$	−13.8390	−0.519002
$712$	15.6008	0.584665
$713$	−46.0319	−1.72391
$714$	2.39175	0.0895091
$715$	−8.22754	−0.307693
$716$	−14.9677	−0.559370
$717$	3.10533	0.115971
$718$	−4.19700	−0.156631
$719$	−12.1142	−0.451784	−0.225892	−	0.974152i	$-0.572530\pi$
$719$	−12.1142	−0.451784	−0.225892	+	0.974152i	$0.572530\pi$
$720$	−4.26818	−0.159066
$721$	5.57629	0.207672
$722$	−5.02739	−0.187100
$723$	−3.49687	−0.130050
$724$	−3.99572	−0.148500
$725$	−4.37913	−0.162637
$726$	−2.36328	−0.0877097
$727$	−11.3188	−0.419789	−0.209895	−	0.977724i	$-0.567312\pi$
$727$	−11.3188	−0.419789	−0.209895	+	0.977724i	$0.567312\pi$
$728$	−11.4247	−0.423428
$729$	−24.0979	−0.892514
$730$	−0.998914	−0.0369715
$731$	11.9293	0.441220
$732$	−3.64432	−0.134698
$733$	37.6123	1.38924	0.694621	−	0.719375i	$-0.255572\pi$
$733$	37.6123	1.38924	0.694621	+	0.719375i	$0.255572\pi$
$734$	−13.8472	−0.511111
$735$	−1.15927	−0.0427604
$736$	7.85958	0.289708
$737$	4.35629	0.160466
$738$	21.8857	0.805624
$739$	21.8775	0.804776	0.402388	−	0.915469i	$-0.368180\pi$
$739$	21.8775	0.804776	0.402388	+	0.915469i	$0.368180\pi$
$740$	−11.1826	−0.411080
$741$	−5.27588	−0.193814
$742$	−20.4861	−0.752070
$743$	−32.7663	−1.20208	−0.601040	−	0.799219i	$-0.705247\pi$
$743$	−32.7663	−1.20208	−0.601040	+	0.799219i	$0.705247\pi$
$744$	−1.36812	−0.0501578
$745$	−0.481059	−0.0176246
$746$	2.33116	0.0853497
$747$	26.7268	0.977882
$748$	5.08842	0.186051
$749$	−15.6706	−0.572591
$750$	−2.67420	−0.0976481
$751$	30.5841	1.11603	0.558016	−	0.829831i	$-0.311563\pi$
$751$	30.5841	1.11603	0.558016	+	0.829831i	$0.311563\pi$
$752$	4.74613	0.173074
$753$	−4.06591	−0.148170
$754$	9.12340	0.332255
$755$	13.1908	0.480063
$756$	2.62605	0.0955084
$757$	2.16699	0.0787605	0.0393802	−	0.999224i	$-0.487462\pi$
$757$	2.16699	0.0787605	0.0393802	+	0.999224i	$0.487462\pi$
$758$	2.94472	0.106957
$759$	−1.72524	−0.0626224
$760$	−5.41666	−0.196483
$761$	23.1274	0.838369	0.419185	−	0.907901i	$-0.362316\pi$
$761$	23.1274	0.838369	0.419185	+	0.907901i	$0.362316\pi$
$762$	−4.28173	−0.155111
$763$	−10.6020	−0.383820
$764$	19.0836	0.690420
$765$	23.1121	0.835620
$766$	18.4399	0.666260
$767$	−14.5260	−0.524504
$768$	0.233596	0.00842917
$769$	−13.3618	−0.481840	−0.240920	−	0.970545i	$-0.577449\pi$
$769$	−13.3618	−0.481840	−0.240920	+	0.970545i	$0.577449\pi$
$770$	2.57474	0.0927871
$771$	−0.649551	−0.0233930
$772$	−23.3943	−0.841980
$773$	−15.5960	−0.560948	−0.280474	−	0.959862i	$-0.590492\pi$
$773$	−15.5960	−0.560948	−0.280474	+	0.959862i	$0.590492\pi$
$774$	6.48882	0.233236
$775$	16.9856	0.610141
$776$	−17.1560	−0.615864
$777$	3.40854	0.122281
$778$	−0.517056	−0.0185374
$779$	27.7748	0.995134
$780$	2.04526	0.0732322
$781$	3.43500	0.122914
$782$	−42.5595	−1.52193
$783$	−2.09708	−0.0749434
$784$	−3.42474	−0.122312
$785$	13.3011	0.474737
$786$	−1.63902	−0.0584617
$787$	−38.6458	−1.37758	−0.688788	−	0.724963i	$-0.741857\pi$
$787$	−38.6458	−1.37758	−0.688788	+	0.724963i	$0.741857\pi$
$788$	−12.5059	−0.445503
$789$	−2.54604	−0.0906416
$790$	6.80845	0.242234
$791$	−28.3167	−1.00683
$792$	2.76780	0.0983495
$793$	−94.2632	−3.34738
$794$	9.85730	0.349822
$795$	3.66745	0.130071
$796$	−27.4625	−0.973381
$797$	−48.6046	−1.72166	−0.860831	−	0.508890i	$-0.830056\pi$
$797$	−48.6046	−1.72166	−0.860831	+	0.508890i	$0.830056\pi$
$798$	1.65104	0.0584462
$799$	−25.7002	−0.909209
$800$	−2.90016	−0.102536
$801$	−45.9512	−1.62360
$802$	−33.6030	−1.18656
$803$	0.647769	0.0228593
$804$	−1.08292	−0.0381916
$805$	−21.5351	−0.759012
$806$	−35.3876	−1.24647
$807$	−5.70869	−0.200955
$808$	1.55666	0.0547630
$809$	39.9071	1.40306	0.701530	−	0.712640i	$-0.252501\pi$
$809$	39.9071	1.40306	0.701530	+	0.712640i	$0.252501\pi$
$810$	12.3344	0.433387
$811$	38.1244	1.33873	0.669364	−	0.742935i	$-0.266567\pi$
$811$	38.1244	1.33873	0.669364	+	0.742935i	$0.266567\pi$
$812$	−2.85509	−0.100194
$813$	−6.71550	−0.235523
$814$	7.25161	0.254169
$815$	11.0410	0.386749
$816$	−1.26492	−0.0442810
$817$	8.23484	0.288101
$818$	−5.08546	−0.177809
$819$	33.6507	1.17585
$820$	−10.7673	−0.376009
$821$	−5.91303	−0.206366	−0.103183	−	0.994662i	$-0.532903\pi$
$821$	−5.91303	−0.206366	−0.103183	+	0.994662i	$0.532903\pi$
$822$	3.76207	0.131217
$823$	50.5663	1.76263	0.881315	−	0.472529i	$-0.156659\pi$
$823$	50.5663	1.76263	0.881315	+	0.472529i	$0.156659\pi$
$824$	−2.94911	−0.102737
$825$	0.636609	0.0221639
$826$	4.54579	0.158168
$827$	−41.6474	−1.44822	−0.724112	−	0.689683i	$-0.757750\pi$
$827$	−41.6474	−1.44822	−0.724112	+	0.689683i	$0.757750\pi$
$828$	−23.1499	−0.804514
$829$	7.02445	0.243969	0.121985	−	0.992532i	$-0.461074\pi$
$829$	7.02445	0.243969	0.121985	+	0.992532i	$0.461074\pi$
$830$	−13.1489	−0.456407
$831$	6.19838	0.215019
$832$	6.04214	0.209474
$833$	18.5449	0.642543
$834$	−3.58966	−0.124300
$835$	−12.4247	−0.429975
$836$	3.51257	0.121485
$837$	8.13408	0.281155
$838$	22.8758	0.790232
$839$	−8.11486	−0.280156	−0.140078	−	0.990140i	$-0.544735\pi$
$839$	−8.11486	−0.280156	−0.140078	+	0.990140i	$0.544735\pi$
$840$	−0.640048	−0.0220837
$841$	−26.7200	−0.921380
$842$	7.98184	0.275072
$843$	3.47369	0.119640
$844$	9.01215	0.310211
$845$	34.0643	1.17185
$846$	−13.9794	−0.480622
$847$	19.1295	0.657299
$848$	10.8344	0.372056
$849$	5.21470	0.178968
$850$	15.7043	0.538654
$851$	−60.6524	−2.07914
$852$	−0.853899	−0.0292541
$853$	−39.6057	−1.35607	−0.678036	−	0.735029i	$-0.737169\pi$
$853$	−39.6057	−1.35607	−0.678036	+	0.735029i	$0.737169\pi$
$854$	29.4989	1.00943
$855$	15.9544	0.545630
$856$	8.28765	0.283266
$857$	−7.75970	−0.265066	−0.132533	−	0.991179i	$-0.542311\pi$
$857$	−7.75970	−0.265066	−0.132533	+	0.991179i	$0.542311\pi$
$858$	−1.32630	−0.0452792
$859$	−30.3788	−1.03651	−0.518256	−	0.855226i	$-0.673419\pi$
$859$	−30.3788	−1.03651	−0.518256	+	0.855226i	$0.673419\pi$
$860$	−3.19234	−0.108858
$861$	3.28194	0.111848
$862$	−6.86384	−0.233783
$863$	−21.9868	−0.748438	−0.374219	−	0.927340i	$-0.622089\pi$
$863$	−21.9868	−0.748438	−0.374219	+	0.927340i	$0.622089\pi$
$864$	−1.38883	−0.0472489
$865$	−26.1469	−0.889020
$866$	34.9443	1.18745
$867$	2.87839	0.0977552
$868$	11.0742	0.375884
$869$	−4.41510	−0.149772
$870$	0.511122	0.0173286
$871$	−28.0106	−0.949102
$872$	5.60706	0.189879
$873$	50.5318	1.71024
$874$	−29.3791	−0.993762
$875$	21.6463	0.731777
$876$	−0.161027	−0.00544061
$877$	9.60501	0.324338	0.162169	−	0.986763i	$-0.448151\pi$
$877$	9.60501	0.324338	0.162169	+	0.986763i	$0.448151\pi$
$878$	38.6696	1.30503
$879$	0.568645	0.0191799
$880$	−1.36169	−0.0459026
$881$	28.0209	0.944048	0.472024	−	0.881586i	$-0.343523\pi$
$881$	28.0209	0.944048	0.472024	+	0.881586i	$0.343523\pi$
$882$	10.0873	0.339658
$883$	5.38272	0.181143	0.0905715	−	0.995890i	$-0.471131\pi$
$883$	5.38272	0.181143	0.0905715	+	0.995890i	$0.471131\pi$
$884$	−32.7181	−1.10043
$885$	−0.813793	−0.0273554
$886$	8.58458	0.288404
$887$	−17.5264	−0.588479	−0.294240	−	0.955732i	$-0.595066\pi$
$887$	−17.5264	−0.588479	−0.294240	+	0.955732i	$0.595066\pi$
$888$	−1.80266	−0.0604933
$889$	34.6583	1.16240
$890$	22.6069	0.757784
$891$	−7.99854	−0.267961
$892$	12.6460	0.423420
$893$	−17.7410	−0.593680
$894$	−0.0775479	−0.00259359
$895$	−21.6895	−0.724999
$896$	−1.89084	−0.0631684
$897$	11.0932	0.370390
$898$	−21.0233	−0.701558
$899$	−8.84352	−0.294948
$900$	8.54222	0.284741
$901$	−58.6683	−1.95452
$902$	6.98228	0.232485
$903$	0.973051	0.0323811
$904$	14.9758	0.498087
$905$	−5.79013	−0.192471
$906$	2.12640	0.0706448
$907$	−55.0265	−1.82712	−0.913562	−	0.406700i	$-0.866679\pi$
$907$	−55.0265	−1.82712	−0.913562	+	0.406700i	$0.866679\pi$
$908$	9.60763	0.318840
$909$	−4.58503	−0.152076
$910$	−16.5553	−0.548804
$911$	−6.06433	−0.200920	−0.100460	−	0.994941i	$-0.532031\pi$
$911$	−6.06433	−0.200920	−0.100460	+	0.994941i	$0.532031\pi$
$912$	−0.873180	−0.0289139
$913$	8.52675	0.282194
$914$	−6.43147	−0.212734
$915$	−5.28092	−0.174582
$916$	−24.5336	−0.810612
$917$	13.2670	0.438114
$918$	7.52049	0.248213
$919$	−35.3738	−1.16687	−0.583437	−	0.812158i	$-0.698293\pi$
$919$	−35.3738	−1.16687	−0.583437	+	0.812158i	$0.698293\pi$
$920$	11.3892	0.375490
$921$	7.63413	0.251553
$922$	−33.9388	−1.11771
$923$	−22.0868	−0.726995
$924$	0.415054	0.0136543
$925$	22.3805	0.735868
$926$	19.5144	0.641282
$927$	8.68641	0.285299
$928$	1.50996	0.0495669
$929$	44.7813	1.46923	0.734613	−	0.678486i	$-0.237364\pi$
$929$	44.7813	1.46923	0.734613	+	0.678486i	$0.237364\pi$
$930$	−1.98252	−0.0650094
$931$	12.8017	0.419557
$932$	1.49690	0.0490327
$933$	0.0107168	0.000350853 0
$934$	3.62029	0.118460
$935$	7.37355	0.241141
$936$	−17.7967	−0.581704
$937$	−12.1122	−0.395687	−0.197844	−	0.980234i	$-0.563394\pi$
$937$	−12.1122	−0.395687	−0.197844	+	0.980234i	$0.563394\pi$
$938$	8.76566	0.286209
$939$	−1.41913	−0.0463116
$940$	6.87754	0.224321
$941$	28.5058	0.929262	0.464631	−	0.885504i	$-0.346187\pi$
$941$	28.5058	0.929262	0.464631	+	0.885504i	$0.346187\pi$
$942$	2.14417	0.0698609
$943$	−58.3998	−1.90176
$944$	−2.40412	−0.0782474
$945$	3.80536	0.123788
$946$	2.07015	0.0673064
$947$	56.2754	1.82870	0.914352	−	0.404920i	$-0.132701\pi$
$947$	56.2754	1.82870	0.914352	+	0.404920i	$0.132701\pi$
$948$	1.09754	0.0356464
$949$	−4.16510	−0.135205
$950$	10.8408	0.351721
$951$	−0.610908	−0.0198100
$952$	10.2389	0.331843
$953$	−1.14976	−0.0372445	−0.0186223	−	0.999827i	$-0.505928\pi$
$953$	−1.14976	−0.0372445	−0.0186223	+	0.999827i	$0.505928\pi$
$954$	−31.9121	−1.03319
$955$	27.6537	0.894853
$956$	13.2936	0.429946
$957$	−0.331449	−0.0107142
$958$	−30.8619	−0.997104
$959$	−30.4520	−0.983345
$960$	0.338500	0.0109250
$961$	3.30197	0.106515
$962$	−46.6272	−1.50332
$963$	−24.4107	−0.786625
$964$	−14.9697	−0.482143
$965$	−33.9003	−1.09129
$966$	−3.47151	−0.111694
$967$	−43.8084	−1.40878	−0.704391	−	0.709812i	$-0.748780\pi$
$967$	−43.8084	−1.40878	−0.704391	+	0.709812i	$0.748780\pi$
$968$	−10.1170	−0.325172
$969$	4.72826	0.151894
$970$	−24.8604	−0.798221
$971$	39.3077	1.26144	0.630722	−	0.776009i	$-0.282759\pi$
$971$	39.3077	1.26144	0.630722	+	0.776009i	$0.282759\pi$
$972$	6.15483	0.197416
$973$	29.0564	0.931505
$974$	22.7328	0.728406
$975$	−4.09334	−0.131092
$976$	−15.6010	−0.499374
$977$	6.95840	0.222619	0.111309	−	0.993786i	$-0.464496\pi$
$977$	6.95840	0.222619	0.111309	+	0.993786i	$0.464496\pi$
$978$	1.77984	0.0569129
$979$	−14.6600	−0.468535
$980$	−4.96273	−0.158529
$981$	−16.5152	−0.527291
$982$	−19.7022	−0.628721
$983$	24.0849	0.768190	0.384095	−	0.923294i	$-0.374514\pi$
$983$	24.0849	0.768190	0.384095	+	0.923294i	$0.374514\pi$
$984$	−1.73571	−0.0553324
$985$	−18.1220	−0.577416
$986$	−8.17642	−0.260390
$987$	−2.09633	−0.0667268
$988$	−22.5855	−0.718541
$989$	−17.3147	−0.550577
$990$	4.01077	0.127471
$991$	36.9130	1.17258	0.586291	−	0.810101i	$-0.300588\pi$
$991$	36.9130	1.17258	0.586291	+	0.810101i	$0.300588\pi$
$992$	−5.85679	−0.185953
$993$	0.339980	0.0107889
$994$	6.91186	0.219231
$995$	−39.7954	−1.26160
$996$	−2.11964	−0.0671635
$997$	−28.6555	−0.907529	−0.453764	−	0.891122i	$-0.649919\pi$
$997$	−28.6555	−0.907529	−0.453764	+	0.891122i	$0.649919\pi$
$998$	−21.2216	−0.671757
$999$	10.7176	0.339090

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8002.2.a.d.1.42	✓	69

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8002.2.a.d.1.42	✓	69	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +0.233596 q^{3} +1.00000 q^{4} +1.44908 q^{5} +0.233596 q^{6} -1.89084 q^{7} +1.00000 q^{8} -2.94543 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +0.233596 q^{3} +1.00000 q^{4} +1.44908 q^{5} +0.233596 q^{6} -1.89084 q^{7} +1.00000 q^{8} -2.94543 q^{9} +1.44908 q^{10} -0.939692 q^{11} +0.233596 q^{12} +6.04214 q^{13} -1.89084 q^{14} +0.338500 q^{15} +1.00000 q^{16} -5.41499 q^{17} -2.94543 q^{18} -3.73800 q^{19} +1.44908 q^{20} -0.441692 q^{21} -0.939692 q^{22} +7.85958 q^{23} +0.233596 q^{24} -2.90016 q^{25} +6.04214 q^{26} -1.38883 q^{27} -1.89084 q^{28} +1.50996 q^{29} +0.338500 q^{30} -5.85679 q^{31} +1.00000 q^{32} -0.219508 q^{33} -5.41499 q^{34} -2.73998 q^{35} -2.94543 q^{36} -7.71700 q^{37} -3.73800 q^{38} +1.41142 q^{39} +1.44908 q^{40} -7.43039 q^{41} -0.441692 q^{42} -2.20301 q^{43} -0.939692 q^{44} -4.26818 q^{45} +7.85958 q^{46} +4.74613 q^{47} +0.233596 q^{48} -3.42474 q^{49} -2.90016 q^{50} -1.26492 q^{51} +6.04214 q^{52} +10.8344 q^{53} -1.38883 q^{54} -1.36169 q^{55} -1.89084 q^{56} -0.873180 q^{57} +1.50996 q^{58} -2.40412 q^{59} +0.338500 q^{60} -15.6010 q^{61} -5.85679 q^{62} +5.56933 q^{63} +1.00000 q^{64} +8.75557 q^{65} -0.219508 q^{66} -4.63587 q^{67} -5.41499 q^{68} +1.83597 q^{69} -2.73998 q^{70} -3.65545 q^{71} -2.94543 q^{72} -0.689342 q^{73} -7.71700 q^{74} -0.677465 q^{75} -3.73800 q^{76} +1.77680 q^{77} +1.41142 q^{78} +4.69846 q^{79} +1.44908 q^{80} +8.51187 q^{81} -7.43039 q^{82} -9.07398 q^{83} -0.441692 q^{84} -7.84676 q^{85} -2.20301 q^{86} +0.352721 q^{87} -0.939692 q^{88} +15.6008 q^{89} -4.26818 q^{90} -11.4247 q^{91} +7.85958 q^{92} -1.36812 q^{93} +4.74613 q^{94} -5.41666 q^{95} +0.233596 q^{96} -17.1560 q^{97} -3.42474 q^{98} +2.76780 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 69 q + 69 q^{2} - 25 q^{3} + 69 q^{4} - 33 q^{5} - 25 q^{6} - 19 q^{7} + 69 q^{8} + 54 q^{9}+O(q^{10}) \) 69 * q + 69 * q^2 - 25 * q^3 + 69 * q^4 - 33 * q^5 - 25 * q^6 - 19 * q^7 + 69 * q^8 + 54 * q^9	\( 69 q + 69 q^{2} - 25 q^{3} + 69 q^{4} - 33 q^{5} - 25 q^{6} - 19 q^{7} + 69 q^{8} + 54 q^{9} - 33 q^{10} - 30 q^{11} - 25 q^{12} - 58 q^{13} - 19 q^{14} + 2 q^{15} + 69 q^{16} - 80 q^{17} + 54 q^{18} - 40 q^{19} - 33 q^{20} - 32 q^{21} - 30 q^{22} - 45 q^{23} - 25 q^{24} + 42 q^{25} - 58 q^{26} - 76 q^{27} - 19 q^{28} - 44 q^{29} + 2 q^{30} - 12 q^{31} + 69 q^{32} - 41 q^{33} - 80 q^{34} - 49 q^{35} + 54 q^{36} - 47 q^{37} - 40 q^{38} - 14 q^{39} - 33 q^{40} - 94 q^{41} - 32 q^{42} - 10 q^{43} - 30 q^{44} - 89 q^{45} - 45 q^{46} - 85 q^{47} - 25 q^{48} + 32 q^{49} + 42 q^{50} - 10 q^{51} - 58 q^{52} - 41 q^{53} - 76 q^{54} - 27 q^{55} - 19 q^{56} - 72 q^{57} - 44 q^{58} - 75 q^{59} + 2 q^{60} - 98 q^{61} - 12 q^{62} - 61 q^{63} + 69 q^{64} - 47 q^{65} - 41 q^{66} - 22 q^{67} - 80 q^{68} - 74 q^{69} - 49 q^{70} - 22 q^{71} + 54 q^{72} - 129 q^{73} - 47 q^{74} - 106 q^{75} - 40 q^{76} - 108 q^{77} - 14 q^{78} + 21 q^{79} - 33 q^{80} + 13 q^{81} - 94 q^{82} - 111 q^{83} - 32 q^{84} - 67 q^{85} - 10 q^{86} - 38 q^{87} - 30 q^{88} - 112 q^{89} - 89 q^{90} - 55 q^{91} - 45 q^{92} - 90 q^{93} - 85 q^{94} - 38 q^{95} - 25 q^{96} - 98 q^{97} + 32 q^{98} - 51 q^{99}+O(q^{100}) \) 69 * q + 69 * q^2 - 25 * q^3 + 69 * q^4 - 33 * q^5 - 25 * q^6 - 19 * q^7 + 69 * q^8 + 54 * q^9 - 33 * q^10 - 30 * q^11 - 25 * q^12 - 58 * q^13 - 19 * q^14 + 2 * q^15 + 69 * q^16 - 80 * q^17 + 54 * q^18 - 40 * q^19 - 33 * q^20 - 32 * q^21 - 30 * q^22 - 45 * q^23 - 25 * q^24 + 42 * q^25 - 58 * q^26 - 76 * q^27 - 19 * q^28 - 44 * q^29 + 2 * q^30 - 12 * q^31 + 69 * q^32 - 41 * q^33 - 80 * q^34 - 49 * q^35 + 54 * q^36 - 47 * q^37 - 40 * q^38 - 14 * q^39 - 33 * q^40 - 94 * q^41 - 32 * q^42 - 10 * q^43 - 30 * q^44 - 89 * q^45 - 45 * q^46 - 85 * q^47 - 25 * q^48 + 32 * q^49 + 42 * q^50 - 10 * q^51 - 58 * q^52 - 41 * q^53 - 76 * q^54 - 27 * q^55 - 19 * q^56 - 72 * q^57 - 44 * q^58 - 75 * q^59 + 2 * q^60 - 98 * q^61 - 12 * q^62 - 61 * q^63 + 69 * q^64 - 47 * q^65 - 41 * q^66 - 22 * q^67 - 80 * q^68 - 74 * q^69 - 49 * q^70 - 22 * q^71 + 54 * q^72 - 129 * q^73 - 47 * q^74 - 106 * q^75 - 40 * q^76 - 108 * q^77 - 14 * q^78 + 21 * q^79 - 33 * q^80 + 13 * q^81 - 94 * q^82 - 111 * q^83 - 32 * q^84 - 67 * q^85 - 10 * q^86 - 38 * q^87 - 30 * q^88 - 112 * q^89 - 89 * q^90 - 55 * q^91 - 45 * q^92 - 90 * q^93 - 85 * q^94 - 38 * q^95 - 25 * q^96 - 98 * q^97 + 32 * q^98 - 51 * q^99

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