LMFDB - Embedded newform 8002.2.a.d.1.41

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			1.41
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)

$f(q)$	$=$	$q+1.00000 q^{2} +0.228484 q^{3} +1.00000 q^{4} -2.86156 q^{5} +0.228484 q^{6} -2.87452 q^{7} +1.00000 q^{8} -2.94779 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +0.228484 q^{3} +1.00000 q^{4} -2.86156 q^{5} +0.228484 q^{6} -2.87452 q^{7} +1.00000 q^{8} -2.94779 q^{9} -2.86156 q^{10} +1.71198 q^{11} +0.228484 q^{12} +2.29301 q^{13} -2.87452 q^{14} -0.653821 q^{15} +1.00000 q^{16} -0.00285689 q^{17} -2.94779 q^{18} +6.57861 q^{19} -2.86156 q^{20} -0.656783 q^{21} +1.71198 q^{22} +5.25023 q^{23} +0.228484 q^{24} +3.18852 q^{25} +2.29301 q^{26} -1.35898 q^{27} -2.87452 q^{28} -2.16156 q^{29} -0.653821 q^{30} -5.70627 q^{31} +1.00000 q^{32} +0.391161 q^{33} -0.00285689 q^{34} +8.22561 q^{35} -2.94779 q^{36} -2.32893 q^{37} +6.57861 q^{38} +0.523917 q^{39} -2.86156 q^{40} +9.84518 q^{41} -0.656783 q^{42} -0.814891 q^{43} +1.71198 q^{44} +8.43529 q^{45} +5.25023 q^{46} -4.46195 q^{47} +0.228484 q^{48} +1.26287 q^{49} +3.18852 q^{50} -0.000652753 q^{51} +2.29301 q^{52} +1.34178 q^{53} -1.35898 q^{54} -4.89894 q^{55} -2.87452 q^{56} +1.50311 q^{57} -2.16156 q^{58} +5.60252 q^{59} -0.653821 q^{60} -4.10414 q^{61} -5.70627 q^{62} +8.47350 q^{63} +1.00000 q^{64} -6.56158 q^{65} +0.391161 q^{66} -3.15087 q^{67} -0.00285689 q^{68} +1.19960 q^{69} +8.22561 q^{70} -4.23036 q^{71} -2.94779 q^{72} -12.0681 q^{73} -2.32893 q^{74} +0.728527 q^{75} +6.57861 q^{76} -4.92113 q^{77} +0.523917 q^{78} -5.46316 q^{79} -2.86156 q^{80} +8.53288 q^{81} +9.84518 q^{82} -1.27109 q^{83} -0.656783 q^{84} +0.00817515 q^{85} -0.814891 q^{86} -0.493882 q^{87} +1.71198 q^{88} -4.40121 q^{89} +8.43529 q^{90} -6.59130 q^{91} +5.25023 q^{92} -1.30379 q^{93} -4.46195 q^{94} -18.8251 q^{95} +0.228484 q^{96} -6.29388 q^{97} +1.26287 q^{98} -5.04657 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	0.228484	0.131915	0.0659577	−	0.997822i	$-0.478990\pi$
$3$	0.228484	0.131915	0.0659577	+	0.997822i	$0.478990\pi$
$4$	1.00000	0.500000
$5$	−2.86156	−1.27973	−0.639864	−	0.768488i	$-0.721009\pi$
$5$	−2.86156	−1.27973	−0.639864	+	0.768488i	$0.721009\pi$
$6$	0.228484	0.0932783
$7$	−2.87452	−1.08647	−0.543233	−	0.839582i	$-0.682800\pi$
$7$	−2.87452	−1.08647	−0.543233	+	0.839582i	$0.682800\pi$
$8$	1.00000	0.353553
$9$	−2.94779	−0.982598
$10$	−2.86156	−0.904904
$11$	1.71198	0.516182	0.258091	−	0.966121i	$-0.416907\pi$
$11$	1.71198	0.516182	0.258091	+	0.966121i	$0.416907\pi$
$12$	0.228484	0.0659577
$13$	2.29301	0.635966	0.317983	−	0.948096i	$-0.396994\pi$
$13$	2.29301	0.635966	0.317983	+	0.948096i	$0.396994\pi$
$14$	−2.87452	−0.768248
$15$	−0.653821	−0.168816
$16$	1.00000	0.250000
$17$	−0.00285689	−0.000692896 0	−0.000346448	−	1.00000i	$-0.500110\pi$
$17$	−0.00285689	−0.000692896 0	−0.000346448		1.00000i	$0.500110\pi$
$18$	−2.94779	−0.694802
$19$	6.57861	1.50924	0.754618	−	0.656165i	$-0.227822\pi$
$19$	6.57861	1.50924	0.754618	+	0.656165i	$0.227822\pi$
$20$	−2.86156	−0.639864
$21$	−0.656783	−0.143322
$22$	1.71198	0.364996
$23$	5.25023	1.09475	0.547375	−	0.836888i	$-0.315627\pi$
$23$	5.25023	1.09475	0.547375	+	0.836888i	$0.315627\pi$
$24$	0.228484	0.0466392
$25$	3.18852	0.637704
$26$	2.29301	0.449696
$27$	−1.35898	−0.261535
$28$	−2.87452	−0.543233
$29$	−2.16156	−0.401391	−0.200696	−	0.979654i	$-0.564320\pi$
$29$	−2.16156	−0.401391	−0.200696	+	0.979654i	$0.564320\pi$
$30$	−0.653821	−0.119371
$31$	−5.70627	−1.02488	−0.512438	−	0.858724i	$-0.671258\pi$
$31$	−5.70627	−1.02488	−0.512438	+	0.858724i	$0.671258\pi$
$32$	1.00000	0.176777
$33$	0.391161	0.0680924
$34$	−0.00285689	−0.000489952 0
$35$	8.22561	1.39038
$36$	−2.94779	−0.491299
$37$	−2.32893	−0.382873	−0.191437	−	0.981505i	$-0.561315\pi$
$37$	−2.32893	−0.382873	−0.191437	+	0.981505i	$0.561315\pi$
$38$	6.57861	1.06719
$39$	0.523917	0.0838938
$40$	−2.86156	−0.452452
$41$	9.84518	1.53756	0.768779	−	0.639514i	$-0.220865\pi$
$41$	9.84518	1.53756	0.768779	+	0.639514i	$0.220865\pi$
$42$	−0.656783	−0.101344
$43$	−0.814891	−0.124270	−0.0621348	−	0.998068i	$-0.519791\pi$
$43$	−0.814891	−0.124270	−0.0621348	+	0.998068i	$0.519791\pi$
$44$	1.71198	0.258091
$45$	8.43529	1.25746
$46$	5.25023	0.774105
$47$	−4.46195	−0.650842	−0.325421	−	0.945569i	$-0.605506\pi$
$47$	−4.46195	−0.650842	−0.325421	+	0.945569i	$0.605506\pi$
$48$	0.228484	0.0329789
$49$	1.26287	0.180409
$50$	3.18852	0.450925
$51$	−0.000652753 0	−9.14038e−5 0
$52$	2.29301	0.317983
$53$	1.34178	0.184308	0.0921541	−	0.995745i	$-0.470625\pi$
$53$	1.34178	0.184308	0.0921541	+	0.995745i	$0.470625\pi$
$54$	−1.35898	−0.184933
$55$	−4.89894	−0.660572
$56$	−2.87452	−0.384124
$57$	1.50311	0.199092
$58$	−2.16156	−0.283826
$59$	5.60252	0.729386	0.364693	−	0.931128i	$-0.381174\pi$
$59$	5.60252	0.729386	0.364693	+	0.931128i	$0.381174\pi$
$60$	−0.653821	−0.0844080
$61$	−4.10414	−0.525481	−0.262741	−	0.964866i	$-0.584626\pi$
$61$	−4.10414	−0.525481	−0.262741	+	0.964866i	$0.584626\pi$
$62$	−5.70627	−0.724697
$63$	8.47350	1.06756
$64$	1.00000	0.125000
$65$	−6.56158	−0.813864
$66$	0.391161	0.0481486
$67$	−3.15087	−0.384940	−0.192470	−	0.981303i	$-0.561650\pi$
$67$	−3.15087	−0.384940	−0.192470	+	0.981303i	$0.561650\pi$
$68$	−0.00285689	−0.000346448 0
$69$	1.19960	0.144414
$70$	8.22561	0.983148
$71$	−4.23036	−0.502051	−0.251025	−	0.967980i	$-0.580768\pi$
$71$	−4.23036	−0.502051	−0.251025	+	0.967980i	$0.580768\pi$
$72$	−2.94779	−0.347401
$73$	−12.0681	−1.41247	−0.706234	−	0.707978i	$-0.749607\pi$
$73$	−12.0681	−1.41247	−0.706234	+	0.707978i	$0.749607\pi$
$74$	−2.32893	−0.270732
$75$	0.728527	0.0841231
$76$	6.57861	0.754618
$77$	−4.92113	−0.560814
$78$	0.523917	0.0593219
$79$	−5.46316	−0.614654	−0.307327	−	0.951604i	$-0.599434\pi$
$79$	−5.46316	−0.614654	−0.307327	+	0.951604i	$0.599434\pi$
$80$	−2.86156	−0.319932
$81$	8.53288	0.948098
$82$	9.84518	1.08722
$83$	−1.27109	−0.139520	−0.0697601	−	0.997564i	$-0.522223\pi$
$83$	−1.27109	−0.139520	−0.0697601	+	0.997564i	$0.522223\pi$
$84$	−0.656783	−0.0716609
$85$	0.00817515	0.000886719 0
$86$	−0.814891	−0.0878719
$87$	−0.493882	−0.0529497
$88$	1.71198	0.182498
$89$	−4.40121	−0.466527	−0.233264	−	0.972414i	$-0.574940\pi$
$89$	−4.40121	−0.466527	−0.233264	+	0.972414i	$0.574940\pi$
$90$	8.43529	0.889158
$91$	−6.59130	−0.690956
$92$	5.25023	0.547375
$93$	−1.30379	−0.135197
$94$	−4.46195	−0.460215
$95$	−18.8251	−1.93141
$96$	0.228484	0.0233196
$97$	−6.29388	−0.639046	−0.319523	−	0.947578i	$-0.603523\pi$
$97$	−6.29388	−0.639046	−0.319523	+	0.947578i	$0.603523\pi$
$98$	1.26287	0.127569
$99$	−5.04657	−0.507199
$100$	3.18852	0.318852
$101$	8.43645	0.839458	0.419729	−	0.907649i	$-0.362125\pi$
$101$	8.43645	0.839458	0.419729	+	0.907649i	$0.362125\pi$
$102$	−0.000652753 0	−6.46322e−5 0
$103$	13.1571	1.29641	0.648204	−	0.761467i	$-0.275520\pi$
$103$	13.1571	1.29641	0.648204	+	0.761467i	$0.275520\pi$
$104$	2.29301	0.224848
$105$	1.87942	0.183413
$106$	1.34178	0.130326
$107$	−10.0205	−0.968715	−0.484357	−	0.874870i	$-0.660947\pi$
$107$	−10.0205	−0.968715	−0.484357	+	0.874870i	$0.660947\pi$
$108$	−1.35898	−0.130768
$109$	14.9992	1.43667	0.718333	−	0.695700i	$-0.244905\pi$
$109$	14.9992	1.43667	0.718333	+	0.695700i	$0.244905\pi$
$110$	−4.89894	−0.467095
$111$	−0.532123	−0.0505069
$112$	−2.87452	−0.271617
$113$	−16.0621	−1.51100	−0.755498	−	0.655151i	$-0.772605\pi$
$113$	−16.0621	−1.51100	−0.755498	+	0.655151i	$0.772605\pi$
$114$	1.50311	0.140779
$115$	−15.0239	−1.40098
$116$	−2.16156	−0.200696
$117$	−6.75932	−0.624899
$118$	5.60252	0.515754
$119$	0.00821217	0.000752809 0
$120$	−0.653821	−0.0596854
$121$	−8.06912	−0.733556
$122$	−4.10414	−0.371571
$123$	2.24947	0.202828
$124$	−5.70627	−0.512438
$125$	5.18365	0.463640
$126$	8.47350	0.754879
$127$	−7.54873	−0.669841	−0.334921	−	0.942246i	$-0.608709\pi$
$127$	−7.54873	−0.669841	−0.334921	+	0.942246i	$0.608709\pi$
$128$	1.00000	0.0883883
$129$	−0.186190	−0.0163931
$130$	−6.56158	−0.575489
$131$	−19.4882	−1.70269	−0.851345	−	0.524606i	$-0.824213\pi$
$131$	−19.4882	−1.70269	−0.851345	+	0.524606i	$0.824213\pi$
$132$	0.391161	0.0340462
$133$	−18.9103	−1.63973
$134$	−3.15087	−0.272194
$135$	3.88880	0.334694
$136$	−0.00285689	−0.000244976 0
$137$	5.86215	0.500837	0.250419	−	0.968138i	$-0.419432\pi$
$137$	5.86215	0.500837	0.250419	+	0.968138i	$0.419432\pi$
$138$	1.19960	0.102116
$139$	4.13262	0.350524	0.175262	−	0.984522i	$-0.443923\pi$
$139$	4.13262	0.350524	0.175262	+	0.984522i	$0.443923\pi$
$140$	8.22561	0.695191
$141$	−1.01949	−0.0858562
$142$	−4.23036	−0.355004
$143$	3.92559	0.328274
$144$	−2.94779	−0.245650
$145$	6.18543	0.513672
$146$	−12.0681	−0.998766
$147$	0.288545	0.0237988
$148$	−2.32893	−0.191437
$149$	7.59182	0.621946	0.310973	−	0.950419i	$-0.399345\pi$
$149$	7.59182	0.621946	0.310973	+	0.950419i	$0.399345\pi$
$150$	0.728527	0.0594840
$151$	14.7747	1.20235	0.601173	−	0.799119i	$-0.294700\pi$
$151$	14.7747	1.20235	0.601173	+	0.799119i	$0.294700\pi$
$152$	6.57861	0.533595
$153$	0.00842151	0.000680839 0
$154$	−4.92113	−0.396556
$155$	16.3288	1.31156
$156$	0.523917	0.0419469
$157$	−22.6549	−1.80805	−0.904027	−	0.427475i	$-0.859403\pi$
$157$	−22.6549	−1.80805	−0.904027	+	0.427475i	$0.859403\pi$
$158$	−5.46316	−0.434626
$159$	0.306577	0.0243131
$160$	−2.86156	−0.226226
$161$	−15.0919	−1.18941
$162$	8.53288	0.670406
$163$	−18.2066	−1.42605	−0.713026	−	0.701138i	$-0.752676\pi$
$163$	−18.2066	−1.42605	−0.713026	+	0.701138i	$0.752676\pi$
$164$	9.84518	0.768779
$165$	−1.11933	−0.0871397
$166$	−1.27109	−0.0986556
$167$	−4.28532	−0.331608	−0.165804	−	0.986159i	$-0.553022\pi$
$167$	−4.28532	−0.331608	−0.165804	+	0.986159i	$0.553022\pi$
$168$	−0.656783	−0.0506719
$169$	−7.74211	−0.595547
$170$	0.00817515	0.000627005 0
$171$	−19.3924	−1.48297
$172$	−0.814891	−0.0621348
$173$	14.6495	1.11378	0.556891	−	0.830586i	$-0.311994\pi$
$173$	14.6495	1.11378	0.556891	+	0.830586i	$0.311994\pi$
$174$	−0.493882	−0.0374411
$175$	−9.16547	−0.692844
$176$	1.71198	0.129045
$177$	1.28009	0.0962173
$178$	−4.40121	−0.329884
$179$	−7.24658	−0.541635	−0.270817	−	0.962631i	$-0.587294\pi$
$179$	−7.24658	−0.541635	−0.270817	+	0.962631i	$0.587294\pi$
$180$	8.43529	0.628729
$181$	−0.667831	−0.0496395	−0.0248197	−	0.999692i	$-0.507901\pi$
$181$	−0.667831	−0.0496395	−0.0248197	+	0.999692i	$0.507901\pi$
$182$	−6.59130	−0.488580
$183$	−0.937732	−0.0693191
$184$	5.25023	0.387052
$185$	6.66436	0.489974
$186$	−1.30379	−0.0955987
$187$	−0.00489093	−0.000357661 0
$188$	−4.46195	−0.325421
$189$	3.90641	0.284149
$190$	−18.8251	−1.36571
$191$	−9.99876	−0.723485	−0.361742	−	0.932278i	$-0.617818\pi$
$191$	−9.99876	−0.723485	−0.361742	+	0.932278i	$0.617818\pi$
$192$	0.228484	0.0164894
$193$	17.1831	1.23687	0.618433	−	0.785837i	$-0.287768\pi$
$193$	17.1831	1.23687	0.618433	+	0.785837i	$0.287768\pi$
$194$	−6.29388	−0.451874
$195$	−1.49922	−0.107361
$196$	1.26287	0.0902047
$197$	−1.24154	−0.0884559	−0.0442280	−	0.999021i	$-0.514083\pi$
$197$	−1.24154	−0.0884559	−0.0442280	+	0.999021i	$0.514083\pi$
$198$	−5.04657	−0.358644
$199$	15.0369	1.06594	0.532970	−	0.846134i	$-0.321076\pi$
$199$	15.0369	1.06594	0.532970	+	0.846134i	$0.321076\pi$
$200$	3.18852	0.225463
$201$	−0.719924	−0.0507795
$202$	8.43645	0.593587
$203$	6.21344	0.436098
$204$	−0.000652753 0	−4.57019e−5 0
$205$	−28.1726	−1.96766
$206$	13.1571	0.916699
$207$	−15.4766	−1.07570
$208$	2.29301	0.158992
$209$	11.2625	0.779040
$210$	1.87942	0.129692
$211$	−25.0392	−1.72377	−0.861885	−	0.507103i	$-0.830716\pi$
$211$	−25.0392	−1.72377	−0.861885	+	0.507103i	$0.830716\pi$
$212$	1.34178	0.0921541
$213$	−0.966570	−0.0662283
$214$	−10.0205	−0.684985
$215$	2.33186	0.159031
$216$	−1.35898	−0.0924667
$217$	16.4028	1.11349
$218$	14.9992	1.01588
$219$	−2.75738	−0.186326
$220$	−4.89894	−0.330286
$221$	−0.00655086	−0.000440659 0
$222$	−0.532123	−0.0357138
$223$	−23.3442	−1.56325	−0.781623	−	0.623751i	$-0.785608\pi$
$223$	−23.3442	−1.56325	−0.781623	+	0.623751i	$0.785608\pi$
$224$	−2.87452	−0.192062
$225$	−9.39911	−0.626607
$226$	−16.0621	−1.06844
$227$	−15.6182	−1.03662	−0.518309	−	0.855194i	$-0.673438\pi$
$227$	−15.6182	−1.03662	−0.518309	+	0.855194i	$0.673438\pi$
$228$	1.50311	0.0995458
$229$	5.39074	0.356230	0.178115	−	0.984010i	$-0.443000\pi$
$229$	5.39074	0.356230	0.178115	+	0.984010i	$0.443000\pi$
$230$	−15.0239	−0.990644
$231$	−1.12440	−0.0739801
$232$	−2.16156	−0.141913
$233$	−24.8832	−1.63015	−0.815076	−	0.579354i	$-0.803305\pi$
$233$	−24.8832	−1.63015	−0.815076	+	0.579354i	$0.803305\pi$
$234$	−6.75932	−0.441871
$235$	12.7681	0.832901
$236$	5.60252	0.364693
$237$	−1.24825	−0.0810823
$238$	0.00821217	0.000532316 0
$239$	4.29204	0.277629	0.138815	−	0.990318i	$-0.455671\pi$
$239$	4.29204	0.277629	0.138815	+	0.990318i	$0.455671\pi$
$240$	−0.653821	−0.0422040
$241$	−24.2927	−1.56483	−0.782414	−	0.622758i	$-0.786012\pi$
$241$	−24.2927	−1.56483	−0.782414	+	0.622758i	$0.786012\pi$
$242$	−8.06912	−0.518703
$243$	6.02656	0.386604
$244$	−4.10414	−0.262741
$245$	−3.61377	−0.230875
$246$	2.24947	0.143421
$247$	15.0848	0.959823
$248$	−5.70627	−0.362348
$249$	−0.290424	−0.0184049
$250$	5.18365	0.327843
$251$	−3.25091	−0.205196	−0.102598	−	0.994723i	$-0.532715\pi$
$251$	−3.25091	−0.205196	−0.102598	+	0.994723i	$0.532715\pi$
$252$	8.47350	0.533780
$253$	8.98830	0.565090
$254$	−7.54873	−0.473649
$255$	0.00186789	0.000116972 0
$256$	1.00000	0.0625000
$257$	−23.6245	−1.47366	−0.736829	−	0.676079i	$-0.763678\pi$
$257$	−23.6245	−1.47366	−0.736829	+	0.676079i	$0.763678\pi$
$258$	−0.186190	−0.0115917
$259$	6.69455	0.415979
$260$	−6.56158	−0.406932
$261$	6.37183	0.394406
$262$	−19.4882	−1.20398
$263$	−25.3014	−1.56015	−0.780075	−	0.625686i	$-0.784819\pi$
$263$	−25.3014	−1.56015	−0.780075	+	0.625686i	$0.784819\pi$
$264$	0.391161	0.0240743
$265$	−3.83959	−0.235864
$266$	−18.9103	−1.15947
$267$	−1.00561	−0.0615421
$268$	−3.15087	−0.192470
$269$	1.69021	0.103054	0.0515270	−	0.998672i	$-0.483591\pi$
$269$	1.69021	0.103054	0.0515270	+	0.998672i	$0.483591\pi$
$270$	3.88880	0.236665
$271$	−22.8070	−1.38543	−0.692714	−	0.721212i	$-0.743585\pi$
$271$	−22.8070	−1.38543	−0.692714	+	0.721212i	$0.743585\pi$
$272$	−0.00285689	−0.000173224 0
$273$	−1.50601	−0.0911478
$274$	5.86215	0.354145
$275$	5.45869	0.329171
$276$	1.19960	0.0722072
$277$	24.5128	1.47283	0.736417	−	0.676528i	$-0.236516\pi$
$277$	24.5128	1.47283	0.736417	+	0.676528i	$0.236516\pi$
$278$	4.13262	0.247858
$279$	16.8209	1.00704
$280$	8.22561	0.491574
$281$	−29.3352	−1.74999	−0.874996	−	0.484130i	$-0.839136\pi$
$281$	−29.3352	−1.74999	−0.874996	+	0.484130i	$0.839136\pi$
$282$	−1.01949	−0.0607095
$283$	−26.5643	−1.57908	−0.789542	−	0.613697i	$-0.789682\pi$
$283$	−26.5643	−1.57908	−0.789542	+	0.613697i	$0.789682\pi$
$284$	−4.23036	−0.251025
$285$	−4.30123	−0.254783
$286$	3.92559	0.232125
$287$	−28.3002	−1.67051
$288$	−2.94779	−0.173700
$289$	−17.0000	−1.00000
$290$	6.18543	0.363221
$291$	−1.43805	−0.0843001
$292$	−12.0681	−0.706234
$293$	19.8935	1.16219	0.581096	−	0.813835i	$-0.302624\pi$
$293$	19.8935	1.16219	0.581096	+	0.813835i	$0.302624\pi$
$294$	0.288545	0.0168283
$295$	−16.0319	−0.933416
$296$	−2.32893	−0.135366
$297$	−2.32654	−0.135000
$298$	7.59182	0.439783
$299$	12.0388	0.696224
$300$	0.728527	0.0420615
$301$	2.34242	0.135015
$302$	14.7747	0.850188
$303$	1.92760	0.110738
$304$	6.57861	0.377309
$305$	11.7442	0.672473
$306$	0.00842151	0.000481426 0
$307$	12.8373	0.732662	0.366331	−	0.930485i	$-0.380614\pi$
$307$	12.8373	0.732662	0.366331	+	0.930485i	$0.380614\pi$
$308$	−4.92113	−0.280407
$309$	3.00619	0.171016
$310$	16.3288	0.927415
$311$	5.28053	0.299431	0.149716	−	0.988729i	$-0.452164\pi$
$311$	5.28053	0.299431	0.149716	+	0.988729i	$0.452164\pi$
$312$	0.523917	0.0296609
$313$	−26.2530	−1.48390	−0.741952	−	0.670453i	$-0.766100\pi$
$313$	−26.2530	−1.48390	−0.741952	+	0.670453i	$0.766100\pi$
$314$	−22.6549	−1.27849
$315$	−24.2474	−1.36619
$316$	−5.46316	−0.307327
$317$	−21.0186	−1.18052	−0.590261	−	0.807213i	$-0.700975\pi$
$317$	−21.0186	−1.18052	−0.590261	+	0.807213i	$0.700975\pi$
$318$	0.306577	0.0171920
$319$	−3.70055	−0.207191
$320$	−2.86156	−0.159966
$321$	−2.28952	−0.127788
$322$	−15.0919	−0.841039
$323$	−0.0187943	−0.00104574
$324$	8.53288	0.474049
$325$	7.31131	0.405558
$326$	−18.2066	−1.00837
$327$	3.42709	0.189518
$328$	9.84518	0.543609
$329$	12.8260	0.707118
$330$	−1.11933	−0.0616171
$331$	26.4896	1.45600	0.728001	−	0.685576i	$-0.240450\pi$
$331$	26.4896	1.45600	0.728001	+	0.685576i	$0.240450\pi$
$332$	−1.27109	−0.0697601
$333$	6.86520	0.376211
$334$	−4.28532	−0.234482
$335$	9.01639	0.492618
$336$	−0.656783	−0.0358304
$337$	28.1371	1.53273	0.766363	−	0.642408i	$-0.222065\pi$
$337$	28.1371	1.53273	0.766363	+	0.642408i	$0.222065\pi$
$338$	−7.74211	−0.421115
$339$	−3.66994	−0.199324
$340$	0.00817515	0.000443360 0
$341$	−9.76902	−0.529022
$342$	−19.3924	−1.04862
$343$	16.4915	0.890458
$344$	−0.814891	−0.0439360
$345$	−3.43271	−0.184811
$346$	14.6495	0.787562
$347$	2.34417	0.125842	0.0629209	−	0.998019i	$-0.479958\pi$
$347$	2.34417	0.125842	0.0629209	+	0.998019i	$0.479958\pi$
$348$	−0.493882	−0.0264749
$349$	26.7719	1.43307	0.716535	−	0.697552i	$-0.245727\pi$
$349$	26.7719	1.43307	0.716535	+	0.697552i	$0.245727\pi$
$350$	−9.16547	−0.489915
$351$	−3.11615	−0.166328
$352$	1.71198	0.0912489
$353$	−8.37917	−0.445978	−0.222989	−	0.974821i	$-0.571581\pi$
$353$	−8.37917	−0.445978	−0.222989	+	0.974821i	$0.571581\pi$
$354$	1.28009	0.0680359
$355$	12.1054	0.642489
$356$	−4.40121	−0.233264
$357$	0.00187635	9.93071e−5 0
$358$	−7.24658	−0.382994
$359$	22.8457	1.20575	0.602875	−	0.797836i	$-0.294022\pi$
$359$	22.8457	1.20575	0.602875	+	0.797836i	$0.294022\pi$
$360$	8.43529	0.444579
$361$	24.2780	1.27779
$362$	−0.667831	−0.0351004
$363$	−1.84367	−0.0967674
$364$	−6.59130	−0.345478
$365$	34.5337	1.80758
$366$	−0.937732	−0.0490160
$367$	9.27781	0.484297	0.242149	−	0.970239i	$-0.422148\pi$
$367$	9.27781	0.484297	0.242149	+	0.970239i	$0.422148\pi$
$368$	5.25023	0.273687
$369$	−29.0216	−1.51080
$370$	6.66436	0.346464
$371$	−3.85699	−0.200245
$372$	−1.30379	−0.0675985
$373$	19.1523	0.991668	0.495834	−	0.868417i	$-0.334862\pi$
$373$	19.1523	0.991668	0.495834	+	0.868417i	$0.334862\pi$
$374$	−0.00489093	−0.000252904 0
$375$	1.18438	0.0611613
$376$	−4.46195	−0.230108
$377$	−4.95647	−0.255271
$378$	3.90641	0.200924
$379$	−17.8227	−0.915490	−0.457745	−	0.889084i	$-0.651343\pi$
$379$	−17.8227	−0.915490	−0.457745	+	0.889084i	$0.651343\pi$
$380$	−18.8251	−0.965706
$381$	−1.72477	−0.0883624
$382$	−9.99876	−0.511581
$383$	−20.3896	−1.04186	−0.520929	−	0.853600i	$-0.674414\pi$
$383$	−20.3896	−1.04186	−0.520929	+	0.853600i	$0.674414\pi$
$384$	0.228484	0.0116598
$385$	14.0821	0.717690
$386$	17.1831	0.874596
$387$	2.40213	0.122107
$388$	−6.29388	−0.319523
$389$	−26.2163	−1.32922	−0.664611	−	0.747190i	$-0.731403\pi$
$389$	−26.2163	−1.32922	−0.664611	+	0.747190i	$0.731403\pi$
$390$	−1.49922	−0.0759159
$391$	−0.0149993	−0.000758548 0
$392$	1.26287	0.0637844
$393$	−4.45274	−0.224611
$394$	−1.24154	−0.0625478
$395$	15.6332	0.786590
$396$	−5.04657	−0.253600
$397$	17.4064	0.873603	0.436801	−	0.899558i	$-0.356111\pi$
$397$	17.4064	0.873603	0.436801	+	0.899558i	$0.356111\pi$
$398$	15.0369	0.753733
$399$	−4.32071	−0.216306
$400$	3.18852	0.159426
$401$	27.6890	1.38272	0.691360	−	0.722510i	$-0.257012\pi$
$401$	27.6890	1.38272	0.691360	+	0.722510i	$0.257012\pi$
$402$	−0.719924	−0.0359065
$403$	−13.0845	−0.651786
$404$	8.43645	0.419729
$405$	−24.4173	−1.21331
$406$	6.21344	0.308368
$407$	−3.98708	−0.197632
$408$	−0.000652753 0	−3.23161e−5 0
$409$	−18.1930	−0.899587	−0.449793	−	0.893133i	$-0.648502\pi$
$409$	−18.1930	−0.899587	−0.449793	+	0.893133i	$0.648502\pi$
$410$	−28.1726	−1.39134
$411$	1.33941	0.0660682
$412$	13.1571	0.648204
$413$	−16.1046	−0.792453
$414$	−15.4766	−0.760634
$415$	3.63730	0.178548
$416$	2.29301	0.112424
$417$	0.944239	0.0462396
$418$	11.2625	0.550864
$419$	−32.0174	−1.56415	−0.782075	−	0.623184i	$-0.785839\pi$
$419$	−32.0174	−1.56415	−0.782075	+	0.623184i	$0.785839\pi$
$420$	1.87942	0.0917064
$421$	31.1183	1.51661	0.758306	−	0.651899i	$-0.226028\pi$
$421$	31.1183	1.51661	0.758306	+	0.651899i	$0.226028\pi$
$422$	−25.0392	−1.21889
$423$	13.1529	0.639517
$424$	1.34178	0.0651628
$425$	−0.00910924	−0.000441863 0
$426$	−0.966570	−0.0468305
$427$	11.7974	0.570918
$428$	−10.0205	−0.484357
$429$	0.896935	0.0433044
$430$	2.33186	0.112452
$431$	−17.2067	−0.828816	−0.414408	−	0.910091i	$-0.636011\pi$
$431$	−17.2067	−0.828816	−0.414408	+	0.910091i	$0.636011\pi$
$432$	−1.35898	−0.0653838
$433$	26.6126	1.27892	0.639460	−	0.768825i	$-0.279158\pi$
$433$	26.6126	1.27892	0.639460	+	0.768825i	$0.279158\pi$
$434$	16.4028	0.787359
$435$	1.41327	0.0677612
$436$	14.9992	0.718333
$437$	34.5392	1.65223
$438$	−2.75738	−0.131753
$439$	15.4361	0.736725	0.368363	−	0.929682i	$-0.379919\pi$
$439$	15.4361	0.736725	0.368363	+	0.929682i	$0.379919\pi$
$440$	−4.89894	−0.233548
$441$	−3.72267	−0.177270
$442$	−0.00655086	−0.000311593 0
$443$	10.3719	0.492785	0.246393	−	0.969170i	$-0.420755\pi$
$443$	10.3719	0.492785	0.246393	+	0.969170i	$0.420755\pi$
$444$	−0.532123	−0.0252535
$445$	12.5943	0.597028
$446$	−23.3442	−1.10538
$447$	1.73461	0.0820444
$448$	−2.87452	−0.135808
$449$	−34.0731	−1.60801	−0.804004	−	0.594624i	$-0.797301\pi$
$449$	−34.0731	−1.60801	−0.804004	+	0.594624i	$0.797301\pi$
$450$	−9.39911	−0.443078
$451$	16.8548	0.793660
$452$	−16.0621	−0.755498
$453$	3.37578	0.158608
$454$	−15.6182	−0.732999
$455$	18.8614	0.884236
$456$	1.50311	0.0703895
$457$	−13.7577	−0.643556	−0.321778	−	0.946815i	$-0.604281\pi$
$457$	−13.7577	−0.643556	−0.321778	+	0.946815i	$0.604281\pi$
$458$	5.39074	0.251893
$459$	0.00388244	0.000181217 0
$460$	−15.0239	−0.700491
$461$	13.3448	0.621530	0.310765	−	0.950487i	$-0.399415\pi$
$461$	13.3448	0.621530	0.310765	+	0.950487i	$0.399415\pi$
$462$	−1.12440	−0.0523118
$463$	10.0846	0.468669	0.234334	−	0.972156i	$-0.424709\pi$
$463$	10.0846	0.468669	0.234334	+	0.972156i	$0.424709\pi$
$464$	−2.16156	−0.100348
$465$	3.73088	0.173015
$466$	−24.8832	−1.15269
$467$	−4.91763	−0.227561	−0.113780	−	0.993506i	$-0.536296\pi$
$467$	−4.91763	−0.227561	−0.113780	+	0.993506i	$0.536296\pi$
$468$	−6.75932	−0.312450
$469$	9.05723	0.418224
$470$	12.7681	0.588950
$471$	−5.17628	−0.238510
$472$	5.60252	0.257877
$473$	−1.39508	−0.0641457
$474$	−1.24825	−0.0573339
$475$	20.9760	0.962446
$476$	0.00821217	0.000376404 0
$477$	−3.95530	−0.181101
$478$	4.29204	0.196313
$479$	10.5277	0.481024	0.240512	−	0.970646i	$-0.422685\pi$
$479$	10.5277	0.481024	0.240512	+	0.970646i	$0.422685\pi$
$480$	−0.653821	−0.0298427
$481$	−5.34025	−0.243494
$482$	−24.2927	−1.10650
$483$	−3.44826	−0.156901
$484$	−8.06912	−0.366778
$485$	18.0103	0.817806
$486$	6.02656	0.273370
$487$	7.37695	0.334282	0.167141	−	0.985933i	$-0.446547\pi$
$487$	7.37695	0.334282	0.167141	+	0.985933i	$0.446547\pi$
$488$	−4.10414	−0.185786
$489$	−4.15992	−0.188118
$490$	−3.61377	−0.163253
$491$	31.0195	1.39989	0.699945	−	0.714197i	$-0.253208\pi$
$491$	31.0195	1.39989	0.699945	+	0.714197i	$0.253208\pi$
$492$	2.24947	0.101414
$493$	0.00617532	0.000278123 0
$494$	15.0848	0.678697
$495$	14.4411	0.649077
$496$	−5.70627	−0.256219
$497$	12.1602	0.545462
$498$	−0.290424	−0.0130142
$499$	43.4980	1.94724	0.973619	−	0.228180i	$-0.0732774\pi$
$499$	43.4980	1.94724	0.973619	+	0.228180i	$0.0732774\pi$
$500$	5.18365	0.231820
$501$	−0.979127	−0.0437442
$502$	−3.25091	−0.145095
$503$	−2.00122	−0.0892298	−0.0446149	−	0.999004i	$-0.514206\pi$
$503$	−2.00122	−0.0892298	−0.0446149	+	0.999004i	$0.514206\pi$
$504$	8.47350	0.377440
$505$	−24.1414	−1.07428
$506$	8.98830	0.399579
$507$	−1.76895	−0.0785618
$508$	−7.54873	−0.334921
$509$	14.3106	0.634307	0.317153	−	0.948374i	$-0.397273\pi$
$509$	14.3106	0.634307	0.317153	+	0.948374i	$0.397273\pi$
$510$	0.00186789	8.27117e−5 0
$511$	34.6901	1.53460
$512$	1.00000	0.0441942
$513$	−8.94018	−0.394718
$514$	−23.6245	−1.04203
$515$	−37.6498	−1.65905
$516$	−0.186190	−0.00819655
$517$	−7.63878	−0.335953
$518$	6.69455	0.294142
$519$	3.34718	0.146925
$520$	−6.56158	−0.287744
$521$	−33.3079	−1.45925	−0.729623	−	0.683850i	$-0.760304\pi$
$521$	−33.3079	−1.45925	−0.729623	+	0.683850i	$0.760304\pi$
$522$	6.37183	0.278887
$523$	−27.4400	−1.19987	−0.599934	−	0.800049i	$-0.704807\pi$
$523$	−27.4400	−1.19987	−0.599934	+	0.800049i	$0.704807\pi$
$524$	−19.4882	−0.851345
$525$	−2.09417	−0.0913969
$526$	−25.3014	−1.10319
$527$	0.0163021	0.000710133 0
$528$	0.391161	0.0170231
$529$	4.56495	0.198476
$530$	−3.83959	−0.166781
$531$	−16.5151	−0.716693
$532$	−18.9103	−0.819867
$533$	22.5751	0.977835
$534$	−1.00561	−0.0435169
$535$	28.6741	1.23969
$536$	−3.15087	−0.136097
$537$	−1.65573	−0.0714500
$538$	1.69021	0.0728702
$539$	2.16200	0.0931241
$540$	3.88880	0.167347
$541$	−26.0367	−1.11941	−0.559703	−	0.828693i	$-0.689085\pi$
$541$	−26.0367	−1.11941	−0.559703	+	0.828693i	$0.689085\pi$
$542$	−22.8070	−0.979646
$543$	−0.152589	−0.00654822
$544$	−0.00285689	−0.000122488 0
$545$	−42.9212	−1.83854
$546$	−1.50601	−0.0644512
$547$	8.44955	0.361277	0.180638	−	0.983550i	$-0.442184\pi$
$547$	8.44955	0.361277	0.180638	+	0.983550i	$0.442184\pi$
$548$	5.86215	0.250419
$549$	12.0982	0.516337
$550$	5.45869	0.232759
$551$	−14.2200	−0.605794
$552$	1.19960	0.0510582
$553$	15.7040	0.667801
$554$	24.5128	1.04145
$555$	1.52270	0.0646351
$556$	4.13262	0.175262
$557$	27.4064	1.16125	0.580623	−	0.814172i	$-0.302809\pi$
$557$	27.4064	1.16125	0.580623	+	0.814172i	$0.302809\pi$
$558$	16.8209	0.712086
$559$	−1.86855	−0.0790313
$560$	8.22561	0.347595
$561$	−0.00111750	−4.71810e−5 0
$562$	−29.3352	−1.23743
$563$	28.2522	1.19069	0.595345	−	0.803471i	$-0.297016\pi$
$563$	28.2522	1.19069	0.595345	+	0.803471i	$0.297016\pi$
$564$	−1.01949	−0.0429281
$565$	45.9627	1.93366
$566$	−26.5643	−1.11658
$567$	−24.5279	−1.03008
$568$	−4.23036	−0.177502
$569$	−9.12837	−0.382681	−0.191341	−	0.981524i	$-0.561284\pi$
$569$	−9.12837	−0.382681	−0.191341	+	0.981524i	$0.561284\pi$
$570$	−4.30123	−0.180159
$571$	−37.9007	−1.58609	−0.793047	−	0.609161i	$-0.791506\pi$
$571$	−37.9007	−1.58609	−0.793047	+	0.609161i	$0.791506\pi$
$572$	3.92559	0.164137
$573$	−2.28456	−0.0954389
$574$	−28.3002	−1.18123
$575$	16.7405	0.698126
$576$	−2.94779	−0.122825
$577$	0.215244	0.00896073	0.00448037	−	0.999990i	$-0.498574\pi$
$577$	0.215244	0.00896073	0.00448037	+	0.999990i	$0.498574\pi$
$578$	−17.0000	−0.707106
$579$	3.92607	0.163162
$580$	6.18543	0.256836
$581$	3.65377	0.151584
$582$	−1.43805	−0.0596092
$583$	2.29711	0.0951366
$584$	−12.0681	−0.499383
$585$	19.3422	0.799701
$586$	19.8935	0.821793
$587$	−31.2556	−1.29006	−0.645029	−	0.764158i	$-0.723155\pi$
$587$	−31.2556	−1.29006	−0.645029	+	0.764158i	$0.723155\pi$
$588$	0.288545	0.0118994
$589$	−37.5393	−1.54678
$590$	−16.0319	−0.660025
$591$	−0.283672	−0.0116687
$592$	−2.32893	−0.0957183
$593$	−10.7545	−0.441635	−0.220817	−	0.975315i	$-0.570872\pi$
$593$	−10.7545	−0.441635	−0.220817	+	0.975315i	$0.570872\pi$
$594$	−2.32654	−0.0954593
$595$	−0.0234996	−0.000963391 0
$596$	7.59182	0.310973
$597$	3.43570	0.140614
$598$	12.0388	0.492304
$599$	−29.2331	−1.19443	−0.597216	−	0.802081i	$-0.703726\pi$
$599$	−29.2331	−1.19443	−0.597216	+	0.802081i	$0.703726\pi$
$600$	0.728527	0.0297420
$601$	44.9345	1.83292	0.916458	−	0.400131i	$-0.131036\pi$
$601$	44.9345	1.83292	0.916458	+	0.400131i	$0.131036\pi$
$602$	2.34242	0.0954699
$603$	9.28811	0.378241
$604$	14.7747	0.601173
$605$	23.0903	0.938753
$606$	1.92760	0.0783033
$607$	12.0192	0.487844	0.243922	−	0.969795i	$-0.421566\pi$
$607$	12.0192	0.487844	0.243922	+	0.969795i	$0.421566\pi$
$608$	6.57861	0.266798
$609$	1.41967	0.0575281
$610$	11.7442	0.475510
$611$	−10.2313	−0.413914
$612$	0.00842151	0.000340419 0
$613$	−12.0076	−0.484981	−0.242491	−	0.970154i	$-0.577964\pi$
$613$	−12.0076	−0.484981	−0.242491	+	0.970154i	$0.577964\pi$
$614$	12.8373	0.518071
$615$	−6.43699	−0.259564
$616$	−4.92113	−0.198278
$617$	15.4553	0.622207	0.311103	−	0.950376i	$-0.399301\pi$
$617$	15.4553	0.622207	0.311103	+	0.950376i	$0.399301\pi$
$618$	3.00619	0.120927
$619$	−4.85412	−0.195103	−0.0975517	−	0.995230i	$-0.531101\pi$
$619$	−4.85412	−0.195103	−0.0975517	+	0.995230i	$0.531101\pi$
$620$	16.3288	0.655781
$621$	−7.13495	−0.286316
$622$	5.28053	0.211730
$623$	12.6514	0.506866
$624$	0.523917	0.0209734
$625$	−30.7759	−1.23104
$626$	−26.2530	−1.04928
$627$	2.57329	0.102767
$628$	−22.6549	−0.904027
$629$	0.00665348	0.000265292 0
$630$	−24.2474	−0.966040
$631$	−10.6442	−0.423739	−0.211869	−	0.977298i	$-0.567955\pi$
$631$	−10.6442	−0.423739	−0.211869	+	0.977298i	$0.567955\pi$
$632$	−5.46316	−0.217313
$633$	−5.72107	−0.227392
$634$	−21.0186	−0.834755
$635$	21.6011	0.857215
$636$	0.306577	0.0121566
$637$	2.89576	0.114734
$638$	−3.70055	−0.146506
$639$	12.4702	0.493314
$640$	−2.86156	−0.113113
$641$	9.55764	0.377504	0.188752	−	0.982025i	$-0.439556\pi$
$641$	9.55764	0.377504	0.188752	+	0.982025i	$0.439556\pi$
$642$	−2.28952	−0.0903601
$643$	24.7853	0.977436	0.488718	−	0.872442i	$-0.337465\pi$
$643$	24.7853	0.977436	0.488718	+	0.872442i	$0.337465\pi$
$644$	−15.0919	−0.594704
$645$	0.532793	0.0209787
$646$	−0.0187943	−0.000739453 0
$647$	10.4593	0.411198	0.205599	−	0.978636i	$-0.434086\pi$
$647$	10.4593	0.411198	0.205599	+	0.978636i	$0.434086\pi$
$648$	8.53288	0.335203
$649$	9.59141	0.376496
$650$	7.31131	0.286773
$651$	3.74778	0.146887
$652$	−18.2066	−0.713026
$653$	12.8362	0.502318	0.251159	−	0.967946i	$-0.419188\pi$
$653$	12.8362	0.502318	0.251159	+	0.967946i	$0.419188\pi$
$654$	3.42709	0.134010
$655$	55.7666	2.17898
$656$	9.84518	0.384390
$657$	35.5744	1.38789
$658$	12.8260	0.500008
$659$	25.5068	0.993602	0.496801	−	0.867864i	$-0.334508\pi$
$659$	25.5068	0.993602	0.496801	+	0.867864i	$0.334508\pi$
$660$	−1.11933	−0.0435699
$661$	−1.98990	−0.0773981	−0.0386991	−	0.999251i	$-0.512321\pi$
$661$	−1.98990	−0.0773981	−0.0386991	+	0.999251i	$0.512321\pi$
$662$	26.4896	1.02955
$663$	−0.00149677	−5.81297e−5 0
$664$	−1.27109	−0.0493278
$665$	54.1130	2.09841
$666$	6.86520	0.266021
$667$	−11.3487	−0.439423
$668$	−4.28532	−0.165804
$669$	−5.33379	−0.206216
$670$	9.01639	0.348334
$671$	−7.02621	−0.271244
$672$	−0.656783	−0.0253359
$673$	22.1068	0.852154	0.426077	−	0.904687i	$-0.359895\pi$
$673$	22.1068	0.852154	0.426077	+	0.904687i	$0.359895\pi$
$674$	28.1371	1.08380
$675$	−4.33313	−0.166782
$676$	−7.74211	−0.297773
$677$	−16.5222	−0.634999	−0.317500	−	0.948258i	$-0.602843\pi$
$677$	−16.5222	−0.634999	−0.317500	+	0.948258i	$0.602843\pi$
$678$	−3.66994	−0.140943
$679$	18.0919	0.694303
$680$	0.00817515	0.000313503 0
$681$	−3.56852	−0.136746
$682$	−9.76902	−0.374075
$683$	32.5662	1.24611	0.623055	−	0.782178i	$-0.285891\pi$
$683$	32.5662	1.24611	0.623055	+	0.782178i	$0.285891\pi$
$684$	−19.3924	−0.741486
$685$	−16.7749	−0.640935
$686$	16.4915	0.629649
$687$	1.23170	0.0469923
$688$	−0.814891	−0.0310674
$689$	3.07672	0.117214
$690$	−3.43271	−0.130681
$691$	−23.5571	−0.896153	−0.448077	−	0.893995i	$-0.647891\pi$
$691$	−23.5571	−0.896153	−0.448077	+	0.893995i	$0.647891\pi$
$692$	14.6495	0.556891
$693$	14.5065	0.551055
$694$	2.34417	0.0889836
$695$	−11.8257	−0.448576
$696$	−0.493882	−0.0187205
$697$	−0.0281265	−0.00106537
$698$	26.7719	1.01333
$699$	−5.68542	−0.215042
$700$	−9.16547	−0.346422
$701$	39.9574	1.50917	0.754586	−	0.656201i	$-0.227838\pi$
$701$	39.9574	1.50917	0.754586	+	0.656201i	$0.227838\pi$
$702$	−3.11615	−0.117611
$703$	−15.3211	−0.577846
$704$	1.71198	0.0645227
$705$	2.91732	0.109873
$706$	−8.37917	−0.315354
$707$	−24.2507	−0.912043
$708$	1.28009	0.0481086
$709$	−8.01785	−0.301117	−0.150558	−	0.988601i	$-0.548107\pi$
$709$	−8.01785	−0.301117	−0.150558	+	0.988601i	$0.548107\pi$
$710$	12.1054	0.454308
$711$	16.1043	0.603958
$712$	−4.40121	−0.164942
$713$	−29.9592	−1.12198
$714$	0.00187635	7.02207e−5 0
$715$	−11.2333	−0.420102
$716$	−7.24658	−0.270817
$717$	0.980664	0.0366236
$718$	22.8457	0.852594
$719$	5.13811	0.191619	0.0958096	−	0.995400i	$-0.469456\pi$
$719$	5.13811	0.191619	0.0958096	+	0.995400i	$0.469456\pi$
$720$	8.43529	0.314365
$721$	−37.8203	−1.40850
$722$	24.2780	0.903535
$723$	−5.55049	−0.206425
$724$	−0.667831	−0.0248197
$725$	−6.89217	−0.255969
$726$	−1.84367	−0.0684249
$727$	16.8573	0.625201	0.312601	−	0.949885i	$-0.398800\pi$
$727$	16.8573	0.625201	0.312601	+	0.949885i	$0.398800\pi$
$728$	−6.59130	−0.244290
$729$	−24.2217	−0.897099
$730$	34.5337	1.27815
$731$	0.00232805	8.61060e−5 0
$732$	−0.937732	−0.0346596
$733$	−38.7645	−1.43180	−0.715899	−	0.698204i	$-0.753983\pi$
$733$	−38.7645	−1.43180	−0.715899	+	0.698204i	$0.753983\pi$
$734$	9.27781	0.342450
$735$	−0.825689	−0.0304560
$736$	5.25023	0.193526
$737$	−5.39423	−0.198699
$738$	−29.0216	−1.06830
$739$	39.5516	1.45493	0.727464	−	0.686146i	$-0.240699\pi$
$739$	39.5516	1.45493	0.727464	+	0.686146i	$0.240699\pi$
$740$	6.66436	0.244987
$741$	3.44664	0.126615
$742$	−3.85699	−0.141594
$743$	−26.1252	−0.958440	−0.479220	−	0.877695i	$-0.659080\pi$
$743$	−26.1252	−0.958440	−0.479220	+	0.877695i	$0.659080\pi$
$744$	−1.30379	−0.0477993
$745$	−21.7245	−0.795922
$746$	19.1523	0.701215
$747$	3.74691	0.137092
$748$	−0.00489093	−0.000178830 0
$749$	28.8040	1.05248
$750$	1.18438	0.0432476
$751$	26.0099	0.949114	0.474557	−	0.880225i	$-0.342608\pi$
$751$	26.0099	0.949114	0.474557	+	0.880225i	$0.342608\pi$
$752$	−4.46195	−0.162711
$753$	−0.742782	−0.0270685
$754$	−4.95647	−0.180504
$755$	−42.2786	−1.53868
$756$	3.90641	0.142075
$757$	47.0873	1.71142	0.855709	−	0.517457i	$-0.173121\pi$
$757$	47.0873	1.71142	0.855709	+	0.517457i	$0.173121\pi$
$758$	−17.8227	−0.647349
$759$	2.05369	0.0745441
$760$	−18.8251	−0.682857
$761$	−16.6714	−0.604338	−0.302169	−	0.953254i	$-0.597711\pi$
$761$	−16.6714	−0.604338	−0.302169	+	0.953254i	$0.597711\pi$
$762$	−1.72477	−0.0624817
$763$	−43.1156	−1.56089
$764$	−9.99876	−0.361742
$765$	−0.0240987	−0.000871289 0
$766$	−20.3896	−0.736705
$767$	12.8466	0.463865
$768$	0.228484	0.00824472
$769$	17.4308	0.628572	0.314286	−	0.949328i	$-0.398235\pi$
$769$	17.4308	0.628572	0.314286	+	0.949328i	$0.398235\pi$
$770$	14.0821	0.507483
$771$	−5.39784	−0.194398
$772$	17.1831	0.618433
$773$	−12.2444	−0.440400	−0.220200	−	0.975455i	$-0.570671\pi$
$773$	−12.2444	−0.440400	−0.220200	+	0.975455i	$0.570671\pi$
$774$	2.40213	0.0863428
$775$	−18.1946	−0.653568
$776$	−6.29388	−0.225937
$777$	1.52960	0.0548741
$778$	−26.2163	−0.939901
$779$	64.7675	2.32054
$780$	−1.49922	−0.0536806
$781$	−7.24229	−0.259150
$782$	−0.0149993	−0.000536374 0
$783$	2.93751	0.104978
$784$	1.26287	0.0451024
$785$	64.8282	2.31382
$786$	−4.45274	−0.158824
$787$	24.1515	0.860908	0.430454	−	0.902613i	$-0.358353\pi$
$787$	24.1515	0.860908	0.430454	+	0.902613i	$0.358353\pi$
$788$	−1.24154	−0.0442280
$789$	−5.78097	−0.205808
$790$	15.6332	0.556203
$791$	46.1708	1.64165
$792$	−5.04657	−0.179322
$793$	−9.41083	−0.334188
$794$	17.4064	0.617730
$795$	−0.877287	−0.0311142
$796$	15.0369	0.532970
$797$	−13.0685	−0.462911	−0.231455	−	0.972846i	$-0.574349\pi$
$797$	−13.0685	−0.462911	−0.231455	+	0.972846i	$0.574349\pi$
$798$	−4.32071	−0.152952
$799$	0.0127473	0.000450966 0
$800$	3.18852	0.112731
$801$	12.9739	0.458409
$802$	27.6890	0.977731
$803$	−20.6604	−0.729091
$804$	−0.719924	−0.0253898
$805$	43.1864	1.52212
$806$	−13.0845	−0.460883
$807$	0.386187	0.0135944
$808$	8.43645	0.296793
$809$	46.1265	1.62172	0.810861	−	0.585239i	$-0.198999\pi$
$809$	46.1265	1.62172	0.810861	+	0.585239i	$0.198999\pi$
$810$	−24.4173	−0.857938
$811$	30.1520	1.05878	0.529389	−	0.848379i	$-0.322421\pi$
$811$	30.1520	1.05878	0.529389	+	0.848379i	$0.322421\pi$
$812$	6.21344	0.218049
$813$	−5.21105	−0.182759
$814$	−3.98708	−0.139747
$815$	52.0993	1.82496
$816$	−0.000652753 0	−2.28509e−5 0
$817$	−5.36084	−0.187552
$818$	−18.1930	−0.636104
$819$	19.4298	0.678932
$820$	−28.1726	−0.983828
$821$	−49.5367	−1.72884	−0.864422	−	0.502768i	$-0.832315\pi$
$821$	−49.5367	−1.72884	−0.864422	+	0.502768i	$0.832315\pi$
$822$	1.33941	0.0467172
$823$	27.6156	0.962618	0.481309	−	0.876551i	$-0.340162\pi$
$823$	27.6156	0.962618	0.481309	+	0.876551i	$0.340162\pi$
$824$	13.1571	0.458349
$825$	1.24722	0.0434228
$826$	−16.1046	−0.560349
$827$	−51.9497	−1.80647	−0.903234	−	0.429149i	$-0.858814\pi$
$827$	−51.9497	−1.80647	−0.903234	+	0.429149i	$0.858814\pi$
$828$	−15.4766	−0.537849
$829$	−39.4906	−1.37156	−0.685782	−	0.727807i	$-0.740540\pi$
$829$	−39.4906	−1.37156	−0.685782	+	0.727807i	$0.740540\pi$
$830$	3.63730	0.126252
$831$	5.60080	0.194289
$832$	2.29301	0.0794958
$833$	−0.00360786	−0.000125005 0
$834$	0.944239	0.0326963
$835$	12.2627	0.424368
$836$	11.2625	0.389520
$837$	7.75469	0.268041
$838$	−32.0174	−1.10602
$839$	−5.65381	−0.195191	−0.0975957	−	0.995226i	$-0.531115\pi$
$839$	−5.65381	−0.195191	−0.0975957	+	0.995226i	$0.531115\pi$
$840$	1.87942	0.0648462
$841$	−24.3277	−0.838885
$842$	31.1183	1.07241
$843$	−6.70264	−0.230851
$844$	−25.0392	−0.861885
$845$	22.1545	0.762138
$846$	13.1529	0.452207
$847$	23.1948	0.796984
$848$	1.34178	0.0460771
$849$	−6.06952	−0.208306
$850$	−0.00910924	−0.000312444 0
$851$	−12.2274	−0.419150
$852$	−0.966570	−0.0331141
$853$	40.9300	1.40142	0.700708	−	0.713448i	$-0.252867\pi$
$853$	40.9300	1.40142	0.700708	+	0.713448i	$0.252867\pi$
$854$	11.7974	0.403700
$855$	55.4924	1.89780
$856$	−10.0205	−0.342492
$857$	−49.9689	−1.70690	−0.853452	−	0.521171i	$-0.825495\pi$
$857$	−49.9689	−1.70690	−0.853452	+	0.521171i	$0.825495\pi$
$858$	0.896935	0.0306209
$859$	22.0396	0.751983	0.375991	−	0.926623i	$-0.377302\pi$
$859$	22.0396	0.751983	0.375991	+	0.926623i	$0.377302\pi$
$860$	2.33186	0.0795157
$861$	−6.46614	−0.220365
$862$	−17.2067	−0.586061
$863$	−31.3074	−1.06572	−0.532858	−	0.846205i	$-0.678882\pi$
$863$	−31.3074	−1.06572	−0.532858	+	0.846205i	$0.678882\pi$
$864$	−1.35898	−0.0462334
$865$	−41.9204	−1.42534
$866$	26.6126	0.904332
$867$	−3.88423	−0.131915
$868$	16.4028	0.556747
$869$	−9.35283	−0.317273
$870$	1.41327	0.0479144
$871$	−7.22497	−0.244809
$872$	14.9992	0.507938
$873$	18.5531	0.627926
$874$	34.5392	1.16831
$875$	−14.9005	−0.503729
$876$	−2.75738	−0.0931632
$877$	−20.8375	−0.703633	−0.351817	−	0.936069i	$-0.614436\pi$
$877$	−20.8375	−0.703633	−0.351817	+	0.936069i	$0.614436\pi$
$878$	15.4361	0.520943
$879$	4.54535	0.153311
$880$	−4.89894	−0.165143
$881$	−35.2874	−1.18886	−0.594432	−	0.804146i	$-0.702623\pi$
$881$	−35.2874	−1.18886	−0.594432	+	0.804146i	$0.702623\pi$
$882$	−3.72267	−0.125349
$883$	20.6225	0.694004	0.347002	−	0.937864i	$-0.387200\pi$
$883$	20.6225	0.694004	0.347002	+	0.937864i	$0.387200\pi$
$884$	−0.00655086	−0.000220329 0
$885$	−3.66305	−0.123132
$886$	10.3719	0.348452
$887$	7.98379	0.268070	0.134035	−	0.990977i	$-0.457207\pi$
$887$	7.98379	0.268070	0.134035	+	0.990977i	$0.457207\pi$
$888$	−0.532123	−0.0178569
$889$	21.6990	0.727760
$890$	12.5943	0.422162
$891$	14.6081	0.489391
$892$	−23.3442	−0.781623
$893$	−29.3534	−0.982274
$894$	1.73461	0.0580141
$895$	20.7365	0.693145
$896$	−2.87452	−0.0960310
$897$	2.75068	0.0918427
$898$	−34.0731	−1.13703
$899$	12.3344	0.411376
$900$	−9.39911	−0.313304
$901$	−0.00383332	−0.000127707 0
$902$	16.8548	0.561202
$903$	0.535206	0.0178105
$904$	−16.0621	−0.534218
$905$	1.91104	0.0635251
$906$	3.37578	0.112153
$907$	7.92362	0.263100	0.131550	−	0.991310i	$-0.458005\pi$
$907$	7.92362	0.263100	0.131550	+	0.991310i	$0.458005\pi$
$908$	−15.6182	−0.518309
$909$	−24.8689	−0.824850
$910$	18.8614	0.625249
$911$	12.9251	0.428227	0.214114	−	0.976809i	$-0.431314\pi$
$911$	12.9251	0.428227	0.214114	+	0.976809i	$0.431314\pi$
$912$	1.50311	0.0497729
$913$	−2.17608	−0.0720177
$914$	−13.7577	−0.455063
$915$	2.68337	0.0887096
$916$	5.39074	0.178115
$917$	56.0192	1.84992
$918$	0.00388244	0.000128140 0
$919$	−3.70327	−0.122160	−0.0610798	−	0.998133i	$-0.519454\pi$
$919$	−3.70327	−0.122160	−0.0610798	+	0.998133i	$0.519454\pi$
$920$	−15.0239	−0.495322
$921$	2.93312	0.0966495
$922$	13.3448	0.439488
$923$	−9.70025	−0.319287
$924$	−1.12440	−0.0369900
$925$	−7.42583	−0.244160
$926$	10.0846	0.331399
$927$	−38.7844	−1.27385
$928$	−2.16156	−0.0709566
$929$	−23.0287	−0.755548	−0.377774	−	0.925898i	$-0.623310\pi$
$929$	−23.0287	−0.755548	−0.377774	+	0.925898i	$0.623310\pi$
$930$	3.73088	0.122340
$931$	8.30790	0.272280
$932$	−24.8832	−0.815076
$933$	1.20652	0.0394996
$934$	−4.91763	−0.160910
$935$	0.0139957	0.000457708 0
$936$	−6.75932	−0.220935
$937$	−27.4060	−0.895314	−0.447657	−	0.894205i	$-0.647741\pi$
$937$	−27.4060	−0.895314	−0.447657	+	0.894205i	$0.647741\pi$
$938$	9.05723	0.295729
$939$	−5.99839	−0.195750
$940$	12.7681	0.416451
$941$	4.53005	0.147675	0.0738377	−	0.997270i	$-0.476475\pi$
$941$	4.53005	0.147675	0.0738377	+	0.997270i	$0.476475\pi$
$942$	−5.17628	−0.168652
$943$	51.6895	1.68324
$944$	5.60252	0.182346
$945$	−11.1784	−0.363634
$946$	−1.39508	−0.0453579
$947$	16.4409	0.534258	0.267129	−	0.963661i	$-0.413925\pi$
$947$	16.4409	0.534258	0.267129	+	0.963661i	$0.413925\pi$
$948$	−1.24825	−0.0405412
$949$	−27.6723	−0.898282
$950$	20.9760	0.680552
$951$	−4.80242	−0.155729
$952$	0.00821217	0.000266158 0
$953$	56.6555	1.83525	0.917626	−	0.397445i	$-0.130103\pi$
$953$	56.6555	1.83525	0.917626	+	0.397445i	$0.130103\pi$
$954$	−3.95530	−0.128058
$955$	28.6120	0.925864
$956$	4.29204	0.138815
$957$	−0.845517	−0.0273317
$958$	10.5277	0.340135
$959$	−16.8509	−0.544143
$960$	−0.653821	−0.0211020
$961$	1.56148	0.0503703
$962$	−5.34025	−0.172177
$963$	29.5383	0.951857
$964$	−24.2927	−0.782414
$965$	−49.1704	−1.58285
$966$	−3.44826	−0.110946
$967$	−32.1365	−1.03344	−0.516720	−	0.856154i	$-0.672847\pi$
$967$	−32.1365	−1.03344	−0.516720	+	0.856154i	$0.672847\pi$
$968$	−8.06912	−0.259351
$969$	−0.00429421	−0.000137950 0
$970$	18.0103	0.578276
$971$	−40.6310	−1.30391	−0.651956	−	0.758257i	$-0.726051\pi$
$971$	−40.6310	−1.30391	−0.651956	+	0.758257i	$0.726051\pi$
$972$	6.02656	0.193302
$973$	−11.8793	−0.380833
$974$	7.37695	0.236373
$975$	1.67052	0.0534994
$976$	−4.10414	−0.131370
$977$	−16.9424	−0.542034	−0.271017	−	0.962575i	$-0.587360\pi$
$977$	−16.9424	−0.542034	−0.271017	+	0.962575i	$0.587360\pi$
$978$	−4.15992	−0.133020
$979$	−7.53479	−0.240813
$980$	−3.61377	−0.115438
$981$	−44.2147	−1.41167
$982$	31.0195	0.989871
$983$	−58.4467	−1.86416	−0.932080	−	0.362252i	$-0.882008\pi$
$983$	−58.4467	−1.86416	−0.932080	+	0.362252i	$0.882008\pi$
$984$	2.24947	0.0717104
$985$	3.55273	0.113200
$986$	0.00617532	0.000196662 0
$987$	2.93053	0.0932799
$988$	15.0848	0.479911
$989$	−4.27837	−0.136044
$990$	14.4411	0.458967
$991$	−46.1093	−1.46471	−0.732354	−	0.680924i	$-0.761578\pi$
$991$	−46.1093	−1.46471	−0.732354	+	0.680924i	$0.761578\pi$
$992$	−5.70627	−0.181174
$993$	6.05247	0.192069
$994$	12.1602	0.385700
$995$	−43.0290	−1.36411
$996$	−0.290424	−0.00920243
$997$	−54.6390	−1.73043	−0.865217	−	0.501398i	$-0.832819\pi$
$997$	−54.6390	−1.73043	−0.865217	+	0.501398i	$0.832819\pi$
$998$	43.4980	1.37691
$999$	3.16496	0.100135

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8002.2.a.d.1.41	✓	69

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8002.2.a.d.1.41	✓	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +0.228484 q^{3} +1.00000 q^{4} -2.86156 q^{5} +0.228484 q^{6} -2.87452 q^{7} +1.00000 q^{8} -2.94779 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +0.228484 q^{3} +1.00000 q^{4} -2.86156 q^{5} +0.228484 q^{6} -2.87452 q^{7} +1.00000 q^{8} -2.94779 q^{9} -2.86156 q^{10} +1.71198 q^{11} +0.228484 q^{12} +2.29301 q^{13} -2.87452 q^{14} -0.653821 q^{15} +1.00000 q^{16} -0.00285689 q^{17} -2.94779 q^{18} +6.57861 q^{19} -2.86156 q^{20} -0.656783 q^{21} +1.71198 q^{22} +5.25023 q^{23} +0.228484 q^{24} +3.18852 q^{25} +2.29301 q^{26} -1.35898 q^{27} -2.87452 q^{28} -2.16156 q^{29} -0.653821 q^{30} -5.70627 q^{31} +1.00000 q^{32} +0.391161 q^{33} -0.00285689 q^{34} +8.22561 q^{35} -2.94779 q^{36} -2.32893 q^{37} +6.57861 q^{38} +0.523917 q^{39} -2.86156 q^{40} +9.84518 q^{41} -0.656783 q^{42} -0.814891 q^{43} +1.71198 q^{44} +8.43529 q^{45} +5.25023 q^{46} -4.46195 q^{47} +0.228484 q^{48} +1.26287 q^{49} +3.18852 q^{50} -0.000652753 q^{51} +2.29301 q^{52} +1.34178 q^{53} -1.35898 q^{54} -4.89894 q^{55} -2.87452 q^{56} +1.50311 q^{57} -2.16156 q^{58} +5.60252 q^{59} -0.653821 q^{60} -4.10414 q^{61} -5.70627 q^{62} +8.47350 q^{63} +1.00000 q^{64} -6.56158 q^{65} +0.391161 q^{66} -3.15087 q^{67} -0.00285689 q^{68} +1.19960 q^{69} +8.22561 q^{70} -4.23036 q^{71} -2.94779 q^{72} -12.0681 q^{73} -2.32893 q^{74} +0.728527 q^{75} +6.57861 q^{76} -4.92113 q^{77} +0.523917 q^{78} -5.46316 q^{79} -2.86156 q^{80} +8.53288 q^{81} +9.84518 q^{82} -1.27109 q^{83} -0.656783 q^{84} +0.00817515 q^{85} -0.814891 q^{86} -0.493882 q^{87} +1.71198 q^{88} -4.40121 q^{89} +8.43529 q^{90} -6.59130 q^{91} +5.25023 q^{92} -1.30379 q^{93} -4.46195 q^{94} -18.8251 q^{95} +0.228484 q^{96} -6.29388 q^{97} +1.26287 q^{98} -5.04657 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 69 q + 69 q^{2} - 25 q^{3} + 69 q^{4} - 33 q^{5} - 25 q^{6} - 19 q^{7} + 69 q^{8} + 54 q^{9}+O(q^{10}) \) 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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