LMFDB - Embedded newform 4017.2.a.l.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4017,2,Mod(1,4017)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4017, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("4017.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4017 = 3 \cdot 13 \cdot 103 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4017.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:	$32.0759064919$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Character	$\chi$	$=$	4017.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.93942 q^{2} +1.00000 q^{3} +1.76133 q^{4} +0.142452 q^{5} -1.93942 q^{6} +3.99599 q^{7} +0.462872 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.93942 q^{2} +1.00000 q^{3} +1.76133 q^{4} +0.142452 q^{5} -1.93942 q^{6} +3.99599 q^{7} +0.462872 q^{8} +1.00000 q^{9} -0.276273 q^{10} +2.93562 q^{11} +1.76133 q^{12} -1.00000 q^{13} -7.74989 q^{14} +0.142452 q^{15} -4.42037 q^{16} -5.84525 q^{17} -1.93942 q^{18} +6.34942 q^{19} +0.250905 q^{20} +3.99599 q^{21} -5.69339 q^{22} -4.92732 q^{23} +0.462872 q^{24} -4.97971 q^{25} +1.93942 q^{26} +1.00000 q^{27} +7.03828 q^{28} +0.367041 q^{29} -0.276273 q^{30} +2.31723 q^{31} +7.64719 q^{32} +2.93562 q^{33} +11.3364 q^{34} +0.569236 q^{35} +1.76133 q^{36} +2.13124 q^{37} -12.3142 q^{38} -1.00000 q^{39} +0.0659368 q^{40} +3.03097 q^{41} -7.74989 q^{42} +3.61371 q^{43} +5.17061 q^{44} +0.142452 q^{45} +9.55612 q^{46} +6.96178 q^{47} -4.42037 q^{48} +8.96796 q^{49} +9.65772 q^{50} -5.84525 q^{51} -1.76133 q^{52} +4.59875 q^{53} -1.93942 q^{54} +0.418184 q^{55} +1.84963 q^{56} +6.34942 q^{57} -0.711845 q^{58} -6.80950 q^{59} +0.250905 q^{60} +8.96615 q^{61} -4.49408 q^{62} +3.99599 q^{63} -5.99035 q^{64} -0.142452 q^{65} -5.69339 q^{66} +9.34845 q^{67} -10.2954 q^{68} -4.92732 q^{69} -1.10398 q^{70} -8.00921 q^{71} +0.462872 q^{72} +13.2935 q^{73} -4.13337 q^{74} -4.97971 q^{75} +11.1835 q^{76} +11.7307 q^{77} +1.93942 q^{78} -6.54860 q^{79} -0.629689 q^{80} +1.00000 q^{81} -5.87831 q^{82} +15.7516 q^{83} +7.03828 q^{84} -0.832665 q^{85} -7.00850 q^{86} +0.367041 q^{87} +1.35882 q^{88} +9.79112 q^{89} -0.276273 q^{90} -3.99599 q^{91} -8.67866 q^{92} +2.31723 q^{93} -13.5018 q^{94} +0.904485 q^{95} +7.64719 q^{96} -15.8448 q^{97} -17.3926 q^{98} +2.93562 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 5 q^{2} + 32 q^{3} + 45 q^{4} + q^{5} + 5 q^{6} + 11 q^{7} + 12 q^{8} + 32 q^{9}+O(q^{10}) $ 32 * q + 5 * q^2 + 32 * q^3 + 45 * q^4 + q^5 + 5 * q^6 + 11 * q^7 + 12 * q^8 + 32 * q^9	\( 32 q + 5 q^{2} + 32 q^{3} + 45 q^{4} + q^{5} + 5 q^{6} + 11 q^{7} + 12 q^{8} + 32 q^{9} + 16 q^{10} + 3 q^{11} + 45 q^{12} - 32 q^{13} + 12 q^{14} + q^{15} + 75 q^{16} + 10 q^{17} + 5 q^{18} + 4 q^{20} + 11 q^{21} + 27 q^{22} + 53 q^{23} + 12 q^{24} + 67 q^{25} - 5 q^{26} + 32 q^{27} + 32 q^{28} + 6 q^{29} + 16 q^{30} + 12 q^{31} + 19 q^{32} + 3 q^{33} + 25 q^{34} + 16 q^{35} + 45 q^{36} + 36 q^{37} + 8 q^{38} - 32 q^{39} + 36 q^{40} - 19 q^{41} + 12 q^{42} + 43 q^{43} - 23 q^{44} + q^{45} + 11 q^{46} + 30 q^{47} + 75 q^{48} + 75 q^{49} + 28 q^{50} + 10 q^{51} - 45 q^{52} + 22 q^{53} + 5 q^{54} + 58 q^{55} + 60 q^{56} + 33 q^{58} - 24 q^{59} + 4 q^{60} + 47 q^{61} - 25 q^{62} + 11 q^{63} + 146 q^{64} - q^{65} + 27 q^{66} + 34 q^{67} + 58 q^{68} + 53 q^{69} - 35 q^{70} + 18 q^{71} + 12 q^{72} - 2 q^{73} - 20 q^{74} + 67 q^{75} + 24 q^{76} + 39 q^{77} - 5 q^{78} + 39 q^{79} + 2 q^{80} + 32 q^{81} + 64 q^{82} + 17 q^{83} + 32 q^{84} + 35 q^{85} - 13 q^{86} + 6 q^{87} + 55 q^{88} - 48 q^{89} + 16 q^{90} - 11 q^{91} + 39 q^{92} + 12 q^{93} + 58 q^{94} + 59 q^{95} + 19 q^{96} + 42 q^{97} + 16 q^{98} + 3 q^{99}+O(q^{100}) \) 32 * q + 5 * q^2 + 32 * q^3 + 45 * q^4 + q^5 + 5 * q^6 + 11 * q^7 + 12 * q^8 + 32 * q^9 + 16 * q^10 + 3 * q^11 + 45 * q^12 - 32 * q^13 + 12 * q^14 + q^15 + 75 * q^16 + 10 * q^17 + 5 * q^18 + 4 * q^20 + 11 * q^21 + 27 * q^22 + 53 * q^23 + 12 * q^24 + 67 * q^25 - 5 * q^26 + 32 * q^27 + 32 * q^28 + 6 * q^29 + 16 * q^30 + 12 * q^31 + 19 * q^32 + 3 * q^33 + 25 * q^34 + 16 * q^35 + 45 * q^36 + 36 * q^37 + 8 * q^38 - 32 * q^39 + 36 * q^40 - 19 * q^41 + 12 * q^42 + 43 * q^43 - 23 * q^44 + q^45 + 11 * q^46 + 30 * q^47 + 75 * q^48 + 75 * q^49 + 28 * q^50 + 10 * q^51 - 45 * q^52 + 22 * q^53 + 5 * q^54 + 58 * q^55 + 60 * q^56 + 33 * q^58 - 24 * q^59 + 4 * q^60 + 47 * q^61 - 25 * q^62 + 11 * q^63 + 146 * q^64 - q^65 + 27 * q^66 + 34 * q^67 + 58 * q^68 + 53 * q^69 - 35 * q^70 + 18 * q^71 + 12 * q^72 - 2 * q^73 - 20 * q^74 + 67 * q^75 + 24 * q^76 + 39 * q^77 - 5 * q^78 + 39 * q^79 + 2 * q^80 + 32 * q^81 + 64 * q^82 + 17 * q^83 + 32 * q^84 + 35 * q^85 - 13 * q^86 + 6 * q^87 + 55 * q^88 - 48 * q^89 + 16 * q^90 - 11 * q^91 + 39 * q^92 + 12 * q^93 + 58 * q^94 + 59 * q^95 + 19 * q^96 + 42 * q^97 + 16 * q^98 + 3 * 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 $

$2$	−1.93942	−1.37137	−0.685687	−	0.727896i	$-0.740498\pi$
$2$	−1.93942	−1.37137	−0.685687	+	0.727896i	$0.740498\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.76133	0.880667
$5$	0.142452	0.0637063	0.0318532	−	0.999493i	$-0.489859\pi$
$5$	0.142452	0.0637063	0.0318532	+	0.999493i	$0.489859\pi$
$6$	−1.93942	−0.791763
$7$	3.99599	1.51034	0.755172	−	0.655527i	$-0.227554\pi$
$7$	3.99599	1.51034	0.755172	+	0.655527i	$0.227554\pi$
$8$	0.462872	0.163650
$9$	1.00000	0.333333
$10$	−0.276273	−0.0873652
$11$	2.93562	0.885123	0.442561	−	0.896738i	$-0.354070\pi$
$11$	2.93562	0.885123	0.442561	+	0.896738i	$0.354070\pi$
$12$	1.76133	0.508453
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	−7.74989	−2.07125
$15$	0.142452	0.0367809
$16$	−4.42037	−1.10509
$17$	−5.84525	−1.41768	−0.708841	−	0.705369i	$-0.750782\pi$
$17$	−5.84525	−1.41768	−0.708841	+	0.705369i	$0.750782\pi$
$18$	−1.93942	−0.457125
$19$	6.34942	1.45666	0.728329	−	0.685228i	$-0.240297\pi$
$19$	6.34942	1.45666	0.728329	+	0.685228i	$0.240297\pi$
$20$	0.250905	0.0561041
$21$	3.99599	0.871997
$22$	−5.69339	−1.21383
$23$	−4.92732	−1.02742	−0.513709	−	0.857965i	$-0.671729\pi$
$23$	−4.92732	−1.02742	−0.513709	+	0.857965i	$0.671729\pi$
$24$	0.462872	0.0944833
$25$	−4.97971	−0.995942
$26$	1.93942	0.380351
$27$	1.00000	0.192450
$28$	7.03828	1.33011
$29$	0.367041	0.0681578	0.0340789	−	0.999419i	$-0.489150\pi$
$29$	0.367041	0.0681578	0.0340789	+	0.999419i	$0.489150\pi$
$30$	−0.276273	−0.0504403
$31$	2.31723	0.416187	0.208094	−	0.978109i	$-0.433274\pi$
$31$	2.31723	0.416187	0.208094	+	0.978109i	$0.433274\pi$
$32$	7.64719	1.35185
$33$	2.93562	0.511026
$34$	11.3364	1.94417
$35$	0.569236	0.0962184
$36$	1.76133	0.293556
$37$	2.13124	0.350374	0.175187	−	0.984535i	$-0.443947\pi$
$37$	2.13124	0.350374	0.175187	+	0.984535i	$0.443947\pi$
$38$	−12.3142	−1.99762
$39$	−1.00000	−0.160128
$40$	0.0659368	0.0104255
$41$	3.03097	0.473358	0.236679	−	0.971588i	$-0.423941\pi$
$41$	3.03097	0.473358	0.236679	+	0.971588i	$0.423941\pi$
$42$	−7.74989	−1.19583
$43$	3.61371	0.551086	0.275543	−	0.961289i	$-0.411142\pi$
$43$	3.61371	0.551086	0.275543	+	0.961289i	$0.411142\pi$
$44$	5.17061	0.779499
$45$	0.142452	0.0212354
$46$	9.55612	1.40897
$47$	6.96178	1.01548	0.507740	−	0.861510i	$-0.330481\pi$
$47$	6.96178	1.01548	0.507740	+	0.861510i	$0.330481\pi$
$48$	−4.42037	−0.638025
$49$	8.96796	1.28114
$50$	9.65772	1.36581
$51$	−5.84525	−0.818499
$52$	−1.76133	−0.244253
$53$	4.59875	0.631686	0.315843	−	0.948811i	$-0.397713\pi$
$53$	4.59875	0.631686	0.315843	+	0.948811i	$0.397713\pi$
$54$	−1.93942	−0.263921
$55$	0.418184	0.0563879
$56$	1.84963	0.247168
$57$	6.34942	0.841001
$58$	−0.711845	−0.0934698
$59$	−6.80950	−0.886521	−0.443261	−	0.896393i	$-0.646178\pi$
$59$	−6.80950	−0.886521	−0.443261	+	0.896393i	$0.646178\pi$
$60$	0.250905	0.0323917
$61$	8.96615	1.14800	0.573999	−	0.818856i	$-0.305391\pi$
$61$	8.96615	1.14800	0.573999	+	0.818856i	$0.305391\pi$
$62$	−4.49408	−0.570749
$63$	3.99599	0.503448
$64$	−5.99035	−0.748793
$65$	−0.142452	−0.0176690
$66$	−5.69339	−0.700808
$67$	9.34845	1.14209	0.571047	−	0.820917i	$-0.306537\pi$
$67$	9.34845	1.14209	0.571047	+	0.820917i	$0.306537\pi$
$68$	−10.2954	−1.24851
$69$	−4.92732	−0.593180
$70$	−1.10398	−0.131951
$71$	−8.00921	−0.950519	−0.475259	−	0.879846i	$-0.657646\pi$
$71$	−8.00921	−0.950519	−0.475259	+	0.879846i	$0.657646\pi$
$72$	0.462872	0.0545500
$73$	13.2935	1.55589	0.777943	−	0.628335i	$-0.216263\pi$
$73$	13.2935	1.55589	0.777943	+	0.628335i	$0.216263\pi$
$74$	−4.13337	−0.480494
$75$	−4.97971	−0.575007
$76$	11.1835	1.28283
$77$	11.7307	1.33684
$78$	1.93942	0.219596
$79$	−6.54860	−0.736775	−0.368388	−	0.929672i	$-0.620090\pi$
$79$	−6.54860	−0.736775	−0.368388	+	0.929672i	$0.620090\pi$
$80$	−0.629689	−0.0704014
$81$	1.00000	0.111111
$82$	−5.87831	−0.649151
$83$	15.7516	1.72896	0.864482	−	0.502664i	$-0.167647\pi$
$83$	15.7516	1.72896	0.864482	+	0.502664i	$0.167647\pi$
$84$	7.03828	0.767939
$85$	−0.832665	−0.0903152
$86$	−7.00850	−0.755746
$87$	0.367041	0.0393509
$88$	1.35882	0.144850
$89$	9.79112	1.03786	0.518928	−	0.854818i	$-0.326331\pi$
$89$	9.79112	1.03786	0.518928	+	0.854818i	$0.326331\pi$
$90$	−0.276273	−0.0291217
$91$	−3.99599	−0.418894
$92$	−8.67866	−0.904813
$93$	2.31723	0.240286
$94$	−13.5018	−1.39260
$95$	0.904485	0.0927982
$96$	7.64719	0.780488
$97$	−15.8448	−1.60879	−0.804397	−	0.594092i	$-0.797512\pi$
$97$	−15.8448	−1.60879	−0.804397	+	0.594092i	$0.797512\pi$
$98$	−17.3926	−1.75692
$99$	2.93562	0.295041
$100$	−8.77093	−0.877093
$101$	−9.24637	−0.920048	−0.460024	−	0.887906i	$-0.652159\pi$
$101$	−9.24637	−0.920048	−0.460024	+	0.887906i	$0.652159\pi$
$102$	11.3364	1.12247
$103$	−1.00000	−0.0985329
$103$	−1.00000	−0.0985329
$104$	−0.462872	−0.0453883
$105$	0.569236	0.0555517
$106$	−8.91888	−0.866278
$107$	4.47419	0.432536	0.216268	−	0.976334i	$-0.430612\pi$
$107$	4.47419	0.432536	0.216268	+	0.976334i	$0.430612\pi$
$108$	1.76133	0.169484
$109$	−1.47392	−0.141176	−0.0705880	−	0.997506i	$-0.522488\pi$
$109$	−1.47392	−0.141176	−0.0705880	+	0.997506i	$0.522488\pi$
$110$	−0.811033	−0.0773289
$111$	2.13124	0.202289
$112$	−17.6638	−1.66907
$113$	−19.1353	−1.80010	−0.900050	−	0.435787i	$-0.856470\pi$
$113$	−19.1353	−1.80010	−0.900050	+	0.435787i	$0.856470\pi$
$114$	−12.3142	−1.15333
$115$	−0.701905	−0.0654529
$116$	0.646482	0.0600243
$117$	−1.00000	−0.0924500
$118$	13.2065	1.21575
$119$	−23.3576	−2.14119
$120$	0.0659368	0.00601918
$121$	−2.38213	−0.216557
$122$	−17.3891	−1.57433
$123$	3.03097	0.273293
$124$	4.08142	0.366523
$125$	−1.42163	−0.127154
$126$	−7.74989	−0.690415
$127$	20.9076	1.85525	0.927624	−	0.373515i	$-0.121848\pi$
$127$	20.9076	1.85525	0.927624	+	0.373515i	$0.121848\pi$
$128$	−3.67661	−0.324969
$129$	3.61371	0.318170
$130$	0.276273	0.0242307
$131$	−10.2116	−0.892188	−0.446094	−	0.894986i	$-0.647185\pi$
$131$	−10.2116	−0.892188	−0.446094	+	0.894986i	$0.647185\pi$
$132$	5.17061	0.450044
$133$	25.3722	2.20005
$134$	−18.1305	−1.56624
$135$	0.142452	0.0122603
$136$	−2.70560	−0.232003
$137$	1.01658	0.0868519	0.0434259	−	0.999057i	$-0.486173\pi$
$137$	1.01658	0.0868519	0.0434259	+	0.999057i	$0.486173\pi$
$138$	9.55612	0.813471
$139$	6.32461	0.536446	0.268223	−	0.963357i	$-0.413564\pi$
$139$	6.32461	0.536446	0.268223	+	0.963357i	$0.413564\pi$
$140$	1.00261	0.0847364
$141$	6.96178	0.586287
$142$	15.5332	1.30352
$143$	−2.93562	−0.245489
$144$	−4.42037	−0.368364
$145$	0.0522856	0.00434208
$146$	−25.7816	−2.13370
$147$	8.96796	0.739665
$148$	3.75383	0.308563
$149$	21.2844	1.74369	0.871843	−	0.489786i	$-0.162925\pi$
$149$	21.2844	1.74369	0.871843	+	0.489786i	$0.162925\pi$
$150$	9.65772	0.788550
$151$	6.47214	0.526696	0.263348	−	0.964701i	$-0.415173\pi$
$151$	6.47214	0.526696	0.263348	+	0.964701i	$0.415173\pi$
$152$	2.93897	0.238382
$153$	−5.84525	−0.472560
$154$	−22.7507	−1.83331
$155$	0.330094	0.0265138
$156$	−1.76133	−0.141020
$157$	6.89735	0.550469	0.275234	−	0.961377i	$-0.411245\pi$
$157$	6.89735	0.550469	0.275234	+	0.961377i	$0.411245\pi$
$158$	12.7005	1.01039
$159$	4.59875	0.364704
$160$	1.08936	0.0861211
$161$	−19.6895	−1.55175
$162$	−1.93942	−0.152375
$163$	9.19942	0.720554	0.360277	−	0.932845i	$-0.382682\pi$
$163$	9.19942	0.720554	0.360277	+	0.932845i	$0.382682\pi$
$164$	5.33855	0.416871
$165$	0.418184	0.0325556
$166$	−30.5489	−2.37106
$167$	−14.3837	−1.11305	−0.556524	−	0.830832i	$-0.687865\pi$
$167$	−14.3837	−1.11305	−0.556524	+	0.830832i	$0.687865\pi$
$168$	1.84963	0.142702
$169$	1.00000	0.0769231
$170$	1.61488	0.123856
$171$	6.34942	0.485552
$172$	6.36496	0.485324
$173$	6.38389	0.485358	0.242679	−	0.970107i	$-0.421974\pi$
$173$	6.38389	0.485358	0.242679	+	0.970107i	$0.421974\pi$
$174$	−0.711845	−0.0539648
$175$	−19.8989	−1.50421
$176$	−12.9765	−0.978143
$177$	−6.80950	−0.511833
$178$	−18.9890	−1.42329
$179$	−4.60228	−0.343990	−0.171995	−	0.985098i	$-0.555021\pi$
$179$	−4.60228	−0.343990	−0.171995	+	0.985098i	$0.555021\pi$
$180$	0.250905	0.0187014
$181$	21.9624	1.63245	0.816227	−	0.577731i	$-0.196062\pi$
$181$	21.9624	1.63245	0.816227	+	0.577731i	$0.196062\pi$
$182$	7.74989	0.574460
$183$	8.96615	0.662797
$184$	−2.28072	−0.168137
$185$	0.303599	0.0223210
$186$	−4.49408	−0.329522
$187$	−17.1594	−1.25482
$188$	12.2620	0.894300
$189$	3.99599	0.290666
$190$	−1.75417	−0.127261
$191$	−0.581737	−0.0420930	−0.0210465	−	0.999778i	$-0.506700\pi$
$191$	−0.581737	−0.0420930	−0.0210465	+	0.999778i	$0.506700\pi$
$192$	−5.99035	−0.432316
$193$	11.7069	0.842678	0.421339	−	0.906903i	$-0.361560\pi$
$193$	11.7069	0.842678	0.421339	+	0.906903i	$0.361560\pi$
$194$	30.7296	2.20626
$195$	−0.142452	−0.0102012
$196$	15.7956	1.12826
$197$	6.66463	0.474835	0.237417	−	0.971408i	$-0.423699\pi$
$197$	6.66463	0.474835	0.237417	+	0.971408i	$0.423699\pi$
$198$	−5.69339	−0.404612
$199$	−16.2151	−1.14946	−0.574731	−	0.818343i	$-0.694893\pi$
$199$	−16.2151	−1.14946	−0.574731	+	0.818343i	$0.694893\pi$
$200$	−2.30497	−0.162986
$201$	9.34845	0.659389
$202$	17.9326	1.26173
$203$	1.46669	0.102942
$204$	−10.2954	−0.720825
$205$	0.431767	0.0301559
$206$	1.93942	0.135126
$207$	−4.92732	−0.342472
$208$	4.42037	0.306498
$209$	18.6395	1.28932
$210$	−1.10398	−0.0761822
$211$	4.11149	0.283047	0.141523	−	0.989935i	$-0.454800\pi$
$211$	4.11149	0.283047	0.141523	+	0.989935i	$0.454800\pi$
$212$	8.09993	0.556305
$213$	−8.00921	−0.548782
$214$	−8.67731	−0.593169
$215$	0.514780	0.0351077
$216$	0.462872	0.0314944
$217$	9.25965	0.628586
$218$	2.85854	0.193605
$219$	13.2935	0.898291
$220$	0.736562	0.0496590
$221$	5.84525	0.393194
$222$	−4.13337	−0.277413
$223$	−2.11772	−0.141813	−0.0709066	−	0.997483i	$-0.522589\pi$
$223$	−2.11772	−0.141813	−0.0709066	+	0.997483i	$0.522589\pi$
$224$	30.5581	2.04175
$225$	−4.97971	−0.331981
$226$	37.1114	2.46861
$227$	−20.5564	−1.36438	−0.682188	−	0.731176i	$-0.738972\pi$
$227$	−20.5564	−1.36438	−0.682188	+	0.731176i	$0.738972\pi$
$228$	11.1835	0.740642
$229$	−6.68613	−0.441832	−0.220916	−	0.975293i	$-0.570905\pi$
$229$	−6.68613	−0.441832	−0.220916	+	0.975293i	$0.570905\pi$
$230$	1.36129	0.0897605
$231$	11.7307	0.771825
$232$	0.169893	0.0111540
$233$	−1.71876	−0.112600	−0.0562999	−	0.998414i	$-0.517930\pi$
$233$	−1.71876	−0.112600	−0.0562999	+	0.998414i	$0.517930\pi$
$234$	1.93942	0.126784
$235$	0.991717	0.0646925
$236$	−11.9938	−0.780730
$237$	−6.54860	−0.425377
$238$	45.3001	2.93637
$239$	−19.0904	−1.23485	−0.617427	−	0.786628i	$-0.711825\pi$
$239$	−19.0904	−1.23485	−0.617427	+	0.786628i	$0.711825\pi$
$240$	−0.629689	−0.0406462
$241$	18.3258	1.18047	0.590233	−	0.807233i	$-0.299036\pi$
$241$	18.3258	1.18047	0.590233	+	0.807233i	$0.299036\pi$
$242$	4.61994	0.296981
$243$	1.00000	0.0641500
$244$	15.7924	1.01100
$245$	1.27750	0.0816165
$246$	−5.87831	−0.374787
$247$	−6.34942	−0.404004
$248$	1.07258	0.0681090
$249$	15.7516	0.998218
$250$	2.75712	0.174376
$251$	−8.43362	−0.532325	−0.266163	−	0.963928i	$-0.585756\pi$
$251$	−8.43362	−0.532325	−0.266163	+	0.963928i	$0.585756\pi$
$252$	7.03828	0.443370
$253$	−14.4647	−0.909390
$254$	−40.5485	−2.54424
$255$	−0.832665	−0.0521435
$256$	19.1112	1.19445
$257$	5.33270	0.332644	0.166322	−	0.986071i	$-0.446811\pi$
$257$	5.33270	0.332644	0.166322	+	0.986071i	$0.446811\pi$
$258$	−7.00850	−0.436330
$259$	8.51643	0.529185
$260$	−0.250905	−0.0155605
$261$	0.367041	0.0227193
$262$	19.8045	1.22352
$263$	−2.11890	−0.130657	−0.0653286	−	0.997864i	$-0.520810\pi$
$263$	−2.11890	−0.130657	−0.0653286	+	0.997864i	$0.520810\pi$
$264$	1.35882	0.0836294
$265$	0.655099	0.0402424
$266$	−49.2073	−3.01710
$267$	9.79112	0.599207
$268$	16.4657	1.00581
$269$	−0.550593	−0.0335702	−0.0167851	−	0.999859i	$-0.505343\pi$
$269$	−0.550593	−0.0335702	−0.0167851	+	0.999859i	$0.505343\pi$
$270$	−0.276273	−0.0168134
$271$	−5.02190	−0.305059	−0.152529	−	0.988299i	$-0.548742\pi$
$271$	−5.02190	−0.305059	−0.152529	+	0.988299i	$0.548742\pi$
$272$	25.8382	1.56667
$273$	−3.99599	−0.241848
$274$	−1.97156	−0.119106
$275$	−14.6185	−0.881531
$276$	−8.67866	−0.522394
$277$	9.59936	0.576770	0.288385	−	0.957515i	$-0.406882\pi$
$277$	9.59936	0.576770	0.288385	+	0.957515i	$0.406882\pi$
$278$	−12.2661	−0.735669
$279$	2.31723	0.138729
$280$	0.263483	0.0157461
$281$	17.1956	1.02580	0.512902	−	0.858447i	$-0.328570\pi$
$281$	17.1956	1.02580	0.512902	+	0.858447i	$0.328570\pi$
$282$	−13.5018	−0.804020
$283$	−19.5612	−1.16279	−0.581396	−	0.813621i	$-0.697493\pi$
$283$	−19.5612	−1.16279	−0.581396	+	0.813621i	$0.697493\pi$
$284$	−14.1069	−0.837091
$285$	0.904485	0.0535771
$286$	5.69339	0.336657
$287$	12.1117	0.714933
$288$	7.64719	0.450615
$289$	17.1670	1.00982
$290$	−0.101403	−0.00595462
$291$	−15.8448	−0.928838
$292$	23.4143	1.37022
$293$	29.6328	1.73117	0.865584	−	0.500764i	$-0.166948\pi$
$293$	29.6328	1.73117	0.865584	+	0.500764i	$0.166948\pi$
$294$	−17.3926	−1.01436
$295$	−0.970024	−0.0564770
$296$	0.986492	0.0573387
$297$	2.93562	0.170342
$298$	−41.2793	−2.39125
$299$	4.92732	0.284954
$300$	−8.77093	−0.506390
$301$	14.4404	0.832329
$302$	−12.5522	−0.722297
$303$	−9.24637	−0.531190
$304$	−28.0668	−1.60974
$305$	1.27724	0.0731347
$306$	11.3364	0.648057
$307$	31.0591	1.77264	0.886319	−	0.463075i	$-0.153254\pi$
$307$	31.0591	1.77264	0.886319	+	0.463075i	$0.153254\pi$
$308$	20.6617	1.17731
$309$	−1.00000	−0.0568880
$310$	−0.640189	−0.0363603
$311$	−0.666546	−0.0377964	−0.0188982	−	0.999821i	$-0.506016\pi$
$311$	−0.666546	−0.0377964	−0.0188982	+	0.999821i	$0.506016\pi$
$312$	−0.462872	−0.0262050
$313$	−9.96814	−0.563433	−0.281716	−	0.959498i	$-0.590904\pi$
$313$	−9.96814	−0.563433	−0.281716	+	0.959498i	$0.590904\pi$
$314$	−13.3768	−0.754898
$315$	0.569236	0.0320728
$316$	−11.5343	−0.648854
$317$	−23.0829	−1.29646	−0.648232	−	0.761443i	$-0.724491\pi$
$317$	−23.0829	−1.29646	−0.648232	+	0.761443i	$0.724491\pi$
$318$	−8.91888	−0.500146
$319$	1.07749	0.0603280
$320$	−0.853335	−0.0477029
$321$	4.47419	0.249725
$322$	38.1862	2.12803
$323$	−37.1140	−2.06508
$324$	1.76133	0.0978519
$325$	4.97971	0.276224
$326$	−17.8415	−0.988149
$327$	−1.47392	−0.0815079
$328$	1.40295	0.0774650
$329$	27.8192	1.53372
$330$	−0.811033	−0.0446459
$331$	−33.5169	−1.84226	−0.921128	−	0.389260i	$-0.872731\pi$
$331$	−33.5169	−1.84226	−0.921128	+	0.389260i	$0.872731\pi$
$332$	27.7439	1.52264
$333$	2.13124	0.116791
$334$	27.8961	1.52640
$335$	1.33170	0.0727586
$336$	−17.6638	−0.963637
$337$	−27.1914	−1.48121	−0.740604	−	0.671941i	$-0.765461\pi$
$337$	−27.1914	−1.48121	−0.740604	+	0.671941i	$0.765461\pi$
$338$	−1.93942	−0.105490
$339$	−19.1353	−1.03929
$340$	−1.46660	−0.0795377
$341$	6.80252	0.368377
$342$	−12.3142	−0.665874
$343$	7.86394	0.424613
$344$	1.67269	0.0901852
$345$	−0.701905	−0.0377893
$346$	−12.3810	−0.665608
$347$	8.21826	0.441179	0.220590	−	0.975367i	$-0.429202\pi$
$347$	8.21826	0.441179	0.220590	+	0.975367i	$0.429202\pi$
$348$	0.646482	0.0346551
$349$	−3.77081	−0.201847	−0.100923	−	0.994894i	$-0.532180\pi$
$349$	−3.77081	−0.201847	−0.100923	+	0.994894i	$0.532180\pi$
$350$	38.5922	2.06284
$351$	−1.00000	−0.0533761
$352$	22.4493	1.19655
$353$	1.41745	0.0754431	0.0377216	−	0.999288i	$-0.487990\pi$
$353$	1.41745	0.0754431	0.0377216	+	0.999288i	$0.487990\pi$
$354$	13.2065	0.701915
$355$	−1.14093	−0.0605540
$356$	17.2454	0.914006
$357$	−23.3576	−1.23621
$358$	8.92573	0.471740
$359$	2.79126	0.147317	0.0736585	−	0.997284i	$-0.476533\pi$
$359$	2.79126	0.147317	0.0736585	+	0.997284i	$0.476533\pi$
$360$	0.0659368	0.00347518
$361$	21.3152	1.12185
$362$	−42.5943	−2.23871
$363$	−2.38213	−0.125029
$364$	−7.03828	−0.368906
$365$	1.89368	0.0991198
$366$	−17.3891	−0.908943
$367$	1.07855	0.0562997	0.0281498	−	0.999604i	$-0.491038\pi$
$367$	1.07855	0.0562997	0.0281498	+	0.999604i	$0.491038\pi$
$368$	21.7806	1.13539
$369$	3.03097	0.157786
$370$	−0.588805	−0.0306105
$371$	18.3766	0.954063
$372$	4.08142	0.211612
$373$	1.21783	0.0630566	0.0315283	−	0.999503i	$-0.489963\pi$
$373$	1.21783	0.0630566	0.0315283	+	0.999503i	$0.489963\pi$
$374$	33.2793	1.72083
$375$	−1.42163	−0.0734124
$376$	3.22241	0.166183
$377$	−0.367041	−0.0189036
$378$	−7.74989	−0.398611
$379$	22.2891	1.14492	0.572458	−	0.819934i	$-0.305990\pi$
$379$	22.2891	1.14492	0.572458	+	0.819934i	$0.305990\pi$
$380$	1.59310	0.0817244
$381$	20.9076	1.07113
$382$	1.12823	0.0577253
$383$	20.7349	1.05950	0.529751	−	0.848153i	$-0.322285\pi$
$383$	20.7349	1.05950	0.529751	+	0.848153i	$0.322285\pi$
$384$	−3.67661	−0.187621
$385$	1.67106	0.0851651
$386$	−22.7045	−1.15563
$387$	3.61371	0.183695
$388$	−27.9080	−1.41681
$389$	9.18953	0.465927	0.232964	−	0.972485i	$-0.425158\pi$
$389$	9.18953	0.465927	0.232964	+	0.972485i	$0.425158\pi$
$390$	0.276273	0.0139896
$391$	28.8014	1.45655
$392$	4.15101	0.209658
$393$	−10.2116	−0.515105
$394$	−12.9255	−0.651176
$395$	−0.932859	−0.0469372
$396$	5.17061	0.259833
$397$	14.5739	0.731443	0.365722	−	0.930724i	$-0.380822\pi$
$397$	14.5739	0.731443	0.365722	+	0.930724i	$0.380822\pi$
$398$	31.4479	1.57634
$399$	25.3722	1.27020
$400$	22.0121	1.10061
$401$	8.07611	0.403301	0.201651	−	0.979457i	$-0.435369\pi$
$401$	8.07611	0.403301	0.201651	+	0.979457i	$0.435369\pi$
$402$	−18.1305	−0.904269
$403$	−2.31723	−0.115430
$404$	−16.2860	−0.810257
$405$	0.142452	0.00707848
$406$	−2.84453	−0.141172
$407$	6.25652	0.310124
$408$	−2.70560	−0.133947
$409$	−24.2237	−1.19778	−0.598891	−	0.800830i	$-0.704392\pi$
$409$	−24.2237	−1.19778	−0.598891	+	0.800830i	$0.704392\pi$
$410$	−0.837375	−0.0413550
$411$	1.01658	0.0501440
$412$	−1.76133	−0.0867747
$413$	−27.2107	−1.33895
$414$	9.55612	0.469658
$415$	2.24384	0.110146
$416$	−7.64719	−0.374934
$417$	6.32461	0.309718
$418$	−36.1497	−1.76814
$419$	−27.8301	−1.35959	−0.679795	−	0.733402i	$-0.737931\pi$
$419$	−27.8301	−1.35959	−0.679795	+	0.733402i	$0.737931\pi$
$420$	1.00261	0.0489226
$421$	11.1302	0.542453	0.271226	−	0.962516i	$-0.412571\pi$
$421$	11.1302	0.542453	0.271226	+	0.962516i	$0.412571\pi$
$422$	−7.97389	−0.388163
$423$	6.96178	0.338493
$424$	2.12863	0.103375
$425$	29.1076	1.41193
$426$	15.5332	0.752586
$427$	35.8287	1.73387
$428$	7.88054	0.380920
$429$	−2.93562	−0.141733
$430$	−0.998372	−0.0481458
$431$	−13.1624	−0.634009	−0.317005	−	0.948424i	$-0.602677\pi$
$431$	−13.1624	−0.634009	−0.317005	+	0.948424i	$0.602677\pi$
$432$	−4.42037	−0.212675
$433$	−14.3621	−0.690200	−0.345100	−	0.938566i	$-0.612155\pi$
$433$	−14.3621	−0.690200	−0.345100	+	0.938566i	$0.612155\pi$
$434$	−17.9583	−0.862026
$435$	0.0522856	0.00250690
$436$	−2.59607	−0.124329
$437$	−31.2856	−1.49659
$438$	−25.7816	−1.23189
$439$	−20.1325	−0.960871	−0.480436	−	0.877030i	$-0.659521\pi$
$439$	−20.1325	−0.960871	−0.480436	+	0.877030i	$0.659521\pi$
$440$	0.193566	0.00922788
$441$	8.96796	0.427046
$442$	−11.3364	−0.539216
$443$	−21.4665	−1.01991	−0.509953	−	0.860202i	$-0.670337\pi$
$443$	−21.4665	−1.01991	−0.509953	+	0.860202i	$0.670337\pi$
$444$	3.75383	0.178149
$445$	1.39476	0.0661180
$446$	4.10715	0.194479
$447$	21.2844	1.00672
$448$	−23.9374	−1.13094
$449$	2.99441	0.141315	0.0706574	−	0.997501i	$-0.477490\pi$
$449$	2.99441	0.141315	0.0706574	+	0.997501i	$0.477490\pi$
$450$	9.65772	0.455269
$451$	8.89778	0.418980
$452$	−33.7037	−1.58529
$453$	6.47214	0.304088
$454$	39.8674	1.87107
$455$	−0.569236	−0.0266862
$456$	2.93897	0.137630
$457$	−0.489822	−0.0229129	−0.0114564	−	0.999934i	$-0.503647\pi$
$457$	−0.489822	−0.0229129	−0.0114564	+	0.999934i	$0.503647\pi$
$458$	12.9672	0.605917
$459$	−5.84525	−0.272833
$460$	−1.23629	−0.0576423
$461$	−26.5860	−1.23823	−0.619116	−	0.785300i	$-0.712509\pi$
$461$	−26.5860	−1.23823	−0.619116	+	0.785300i	$0.712509\pi$
$462$	−22.7507	−1.05846
$463$	−3.01135	−0.139949	−0.0699746	−	0.997549i	$-0.522292\pi$
$463$	−3.01135	−0.139949	−0.0699746	+	0.997549i	$0.522292\pi$
$464$	−1.62246	−0.0753206
$465$	0.330094	0.0153077
$466$	3.33339	0.154417
$467$	21.4057	0.990536	0.495268	−	0.868740i	$-0.335070\pi$
$467$	21.4057	0.990536	0.495268	+	0.868740i	$0.335070\pi$
$468$	−1.76133	−0.0814177
$469$	37.3563	1.72496
$470$	−1.92335	−0.0887176
$471$	6.89735	0.317813
$472$	−3.15193	−0.145079
$473$	10.6085	0.487779
$474$	12.7005	0.583352
$475$	−31.6183	−1.45075
$476$	−41.1405	−1.88567
$477$	4.59875	0.210562
$478$	37.0242	1.69345
$479$	18.8469	0.861135	0.430568	−	0.902558i	$-0.358313\pi$
$479$	18.8469	0.861135	0.430568	+	0.902558i	$0.358313\pi$
$480$	1.08936	0.0497220
$481$	−2.13124	−0.0971763
$482$	−35.5413	−1.61886
$483$	−19.6895	−0.895905
$484$	−4.19573	−0.190715
$485$	−2.25712	−0.102490
$486$	−1.93942	−0.0879737
$487$	−38.2750	−1.73441	−0.867204	−	0.497954i	$-0.834085\pi$
$487$	−38.2750	−1.73441	−0.867204	+	0.497954i	$0.834085\pi$
$488$	4.15018	0.187870
$489$	9.19942	0.416012
$490$	−2.47760	−0.111927
$491$	−20.2926	−0.915794	−0.457897	−	0.889005i	$-0.651397\pi$
$491$	−20.2926	−0.915794	−0.457897	+	0.889005i	$0.651397\pi$
$492$	5.33855	0.240680
$493$	−2.14545	−0.0966260
$494$	12.3142	0.554041
$495$	0.418184	0.0187960
$496$	−10.2430	−0.459926
$497$	−32.0048	−1.43561
$498$	−30.5489	−1.36893
$499$	31.4646	1.40855	0.704273	−	0.709929i	$-0.251273\pi$
$499$	31.4646	1.40855	0.704273	+	0.709929i	$0.251273\pi$
$500$	−2.50396	−0.111980
$501$	−14.3837	−0.642618
$502$	16.3563	0.730017
$503$	−2.54774	−0.113598	−0.0567990	−	0.998386i	$-0.518089\pi$
$503$	−2.54774	−0.113598	−0.0567990	+	0.998386i	$0.518089\pi$
$504$	1.84963	0.0823892
$505$	−1.31716	−0.0586129
$506$	28.0531	1.24711
$507$	1.00000	0.0444116
$508$	36.8252	1.63386
$509$	−8.68625	−0.385011	−0.192506	−	0.981296i	$-0.561661\pi$
$509$	−8.68625	−0.385011	−0.192506	+	0.981296i	$0.561661\pi$
$510$	1.61488	0.0715083
$511$	53.1207	2.34992
$512$	−29.7113	−1.31307
$513$	6.34942	0.280334
$514$	−10.3423	−0.456180
$515$	−0.142452	−0.00627717
$516$	6.36496	0.280202
$517$	20.4371	0.898824
$518$	−16.5169	−0.725711
$519$	6.38389	0.280222
$520$	−0.0659368	−0.00289152
$521$	16.2017	0.709808	0.354904	−	0.934903i	$-0.384514\pi$
$521$	16.2017	0.709808	0.354904	+	0.934903i	$0.384514\pi$
$522$	−0.711845	−0.0311566
$523$	−0.328500	−0.0143643	−0.00718214	−	0.999974i	$-0.502286\pi$
$523$	−0.328500	−0.0143643	−0.00718214	+	0.999974i	$0.502286\pi$
$524$	−17.9860	−0.785721
$525$	−19.8989	−0.868458
$526$	4.10944	0.179180
$527$	−13.5448	−0.590021
$528$	−12.9765	−0.564731
$529$	1.27847	0.0555858
$530$	−1.27051	−0.0551874
$531$	−6.80950	−0.295507
$532$	44.6890	1.93751
$533$	−3.03097	−0.131286
$534$	−18.9890	−0.821736
$535$	0.637355	0.0275553
$536$	4.32713	0.186904
$537$	−4.60228	−0.198603
$538$	1.06783	0.0460373
$539$	26.3265	1.13396
$540$	0.250905	0.0107972
$541$	23.8408	1.02500	0.512498	−	0.858688i	$-0.328720\pi$
$541$	23.8408	1.02500	0.512498	+	0.858688i	$0.328720\pi$
$542$	9.73956	0.418350
$543$	21.9624	0.942498
$544$	−44.6998	−1.91649
$545$	−0.209962	−0.00899380
$546$	7.74989	0.331665
$547$	27.8127	1.18919	0.594593	−	0.804027i	$-0.297313\pi$
$547$	27.8127	1.18919	0.594593	+	0.804027i	$0.297313\pi$
$548$	1.79053	0.0764876
$549$	8.96615	0.382666
$550$	28.3514	1.20891
$551$	2.33050	0.0992825
$552$	−2.28072	−0.0970738
$553$	−26.1682	−1.11278
$554$	−18.6171	−0.790967
$555$	0.303599	0.0128871
$556$	11.1398	0.472431
$557$	33.4060	1.41546	0.707728	−	0.706485i	$-0.249720\pi$
$557$	33.4060	1.41546	0.707728	+	0.706485i	$0.249720\pi$
$558$	−4.49408	−0.190250
$559$	−3.61371	−0.152844
$560$	−2.51623	−0.106330
$561$	−17.1594	−0.724472
$562$	−33.3494	−1.40676
$563$	39.8457	1.67930	0.839648	−	0.543131i	$-0.182761\pi$
$563$	39.8457	1.67930	0.839648	+	0.543131i	$0.182761\pi$
$564$	12.2620	0.516324
$565$	−2.72586	−0.114678
$566$	37.9373	1.59462
$567$	3.99599	0.167816
$568$	−3.70724	−0.155552
$569$	1.46829	0.0615539	0.0307770	−	0.999526i	$-0.490202\pi$
$569$	1.46829	0.0615539	0.0307770	+	0.999526i	$0.490202\pi$
$570$	−1.75417	−0.0734742
$571$	22.4554	0.939728	0.469864	−	0.882739i	$-0.344303\pi$
$571$	22.4554	0.939728	0.469864	+	0.882739i	$0.344303\pi$
$572$	−5.17061	−0.216194
$573$	−0.581737	−0.0243024
$574$	−23.4897	−0.980441
$575$	24.5366	1.02325
$576$	−5.99035	−0.249598
$577$	−8.99005	−0.374261	−0.187130	−	0.982335i	$-0.559919\pi$
$577$	−8.99005	−0.374261	−0.187130	+	0.982335i	$0.559919\pi$
$578$	−33.2939	−1.38484
$579$	11.7069	0.486520
$580$	0.0920924	0.00382393
$581$	62.9433	2.61133
$582$	30.7296	1.27378
$583$	13.5002	0.559120
$584$	6.15319	0.254621
$585$	−0.142452	−0.00588965
$586$	−57.4704	−2.37408
$587$	10.3430	0.426902	0.213451	−	0.976954i	$-0.431530\pi$
$587$	10.3430	0.426902	0.213451	+	0.976954i	$0.431530\pi$
$588$	15.7956	0.651398
$589$	14.7131	0.606242
$590$	1.88128	0.0774511
$591$	6.66463	0.274146
$592$	−9.42088	−0.387196
$593$	28.3543	1.16437	0.582186	−	0.813056i	$-0.302198\pi$
$593$	28.3543	1.16437	0.582186	+	0.813056i	$0.302198\pi$
$594$	−5.69339	−0.233603
$595$	−3.32733	−0.136407
$596$	37.4889	1.53561
$597$	−16.2151	−0.663642
$598$	−9.55612	−0.390779
$599$	0.0621822	0.00254070	0.00127035	−	0.999999i	$-0.499596\pi$
$599$	0.0621822	0.00254070	0.00127035	+	0.999999i	$0.499596\pi$
$600$	−2.30497	−0.0940999
$601$	−33.3581	−1.36070	−0.680352	−	0.732885i	$-0.738173\pi$
$601$	−33.3581	−1.36070	−0.680352	+	0.732885i	$0.738173\pi$
$602$	−28.0059	−1.14144
$603$	9.34845	0.380698
$604$	11.3996	0.463844
$605$	−0.339338	−0.0137961
$606$	17.9326	0.728461
$607$	3.77004	0.153021	0.0765106	−	0.997069i	$-0.475622\pi$
$607$	3.77004	0.153021	0.0765106	+	0.997069i	$0.475622\pi$
$608$	48.5552	1.96918
$609$	1.46669	0.0594334
$610$	−2.47711	−0.100295
$611$	−6.96178	−0.281643
$612$	−10.2954	−0.416169
$613$	−4.20113	−0.169682	−0.0848410	−	0.996394i	$-0.527038\pi$
$613$	−4.20113	−0.169682	−0.0848410	+	0.996394i	$0.527038\pi$
$614$	−60.2366	−2.43095
$615$	0.431767	0.0174105
$616$	5.42982	0.218774
$617$	13.6836	0.550881	0.275440	−	0.961318i	$-0.411176\pi$
$617$	13.6836	0.550881	0.275440	+	0.961318i	$0.411176\pi$
$618$	1.93942	0.0780148
$619$	30.8520	1.24005	0.620024	−	0.784583i	$-0.287123\pi$
$619$	30.8520	1.24005	0.620024	+	0.784583i	$0.287123\pi$
$620$	0.581405	0.0233498
$621$	−4.92732	−0.197727
$622$	1.29271	0.0518330
$623$	39.1252	1.56752
$624$	4.42037	0.176956
$625$	24.6960	0.987841
$626$	19.3324	0.772677
$627$	18.6395	0.744390
$628$	12.1485	0.484780
$629$	−12.4576	−0.496719
$630$	−1.10398	−0.0439838
$631$	−12.0393	−0.479277	−0.239638	−	0.970862i	$-0.577029\pi$
$631$	−12.0393	−0.479277	−0.239638	+	0.970862i	$0.577029\pi$
$632$	−3.03116	−0.120573
$633$	4.11149	0.163417
$634$	44.7673	1.77794
$635$	2.97832	0.118191
$636$	8.09993	0.321183
$637$	−8.96796	−0.355323
$638$	−2.08971	−0.0827323
$639$	−8.00921	−0.316840
$640$	−0.523739	−0.0207026
$641$	−40.7836	−1.61086	−0.805428	−	0.592694i	$-0.798064\pi$
$641$	−40.7836	−1.61086	−0.805428	+	0.592694i	$0.798064\pi$
$642$	−8.67731	−0.342466
$643$	−39.7673	−1.56827	−0.784134	−	0.620592i	$-0.786892\pi$
$643$	−39.7673	−1.56827	−0.784134	+	0.620592i	$0.786892\pi$
$644$	−34.6798	−1.36658
$645$	0.514780	0.0202694
$646$	71.9794	2.83199
$647$	22.9307	0.901500	0.450750	−	0.892650i	$-0.351157\pi$
$647$	22.9307	0.901500	0.450750	+	0.892650i	$0.351157\pi$
$648$	0.462872	0.0181833
$649$	−19.9901	−0.784680
$650$	−9.65772	−0.378807
$651$	9.25965	0.362914
$652$	16.2032	0.634568
$653$	−27.1448	−1.06226	−0.531130	−	0.847290i	$-0.678232\pi$
$653$	−27.1448	−1.06226	−0.531130	+	0.847290i	$0.678232\pi$
$654$	2.85854	0.111778
$655$	−1.45465	−0.0568380
$656$	−13.3980	−0.523104
$657$	13.2935	0.518629
$658$	−53.9530	−2.10331
$659$	37.6387	1.46620	0.733098	−	0.680123i	$-0.238074\pi$
$659$	37.6387	1.46620	0.733098	+	0.680123i	$0.238074\pi$
$660$	0.736562	0.0286706
$661$	22.8347	0.888168	0.444084	−	0.895985i	$-0.353529\pi$
$661$	22.8347	0.888168	0.444084	+	0.895985i	$0.353529\pi$
$662$	65.0032	2.52642
$663$	5.84525	0.227011
$664$	7.29098	0.282945
$665$	3.61432	0.140157
$666$	−4.13337	−0.160165
$667$	−1.80853	−0.0700265
$668$	−25.3346	−0.980225
$669$	−2.11772	−0.0818759
$670$	−2.58272	−0.0997793
$671$	26.3212	1.01612
$672$	30.5581	1.17881
$673$	18.2767	0.704514	0.352257	−	0.935903i	$-0.385414\pi$
$673$	18.2767	0.704514	0.352257	+	0.935903i	$0.385414\pi$
$674$	52.7354	2.03129
$675$	−4.97971	−0.191669
$676$	1.76133	0.0677436
$677$	40.6025	1.56048	0.780239	−	0.625481i	$-0.215097\pi$
$677$	40.6025	1.56048	0.780239	+	0.625481i	$0.215097\pi$
$678$	37.1114	1.42525
$679$	−63.3157	−2.42983
$680$	−0.385417	−0.0147801
$681$	−20.5564	−0.787723
$682$	−13.1929	−0.505183
$683$	15.7742	0.603584	0.301792	−	0.953374i	$-0.402415\pi$
$683$	15.7742	0.603584	0.301792	+	0.953374i	$0.402415\pi$
$684$	11.1835	0.427610
$685$	0.144813	0.00553301
$686$	−15.2515	−0.582303
$687$	−6.68613	−0.255092
$688$	−15.9740	−0.609001
$689$	−4.59875	−0.175198
$690$	1.36129	0.0518232
$691$	34.5937	1.31600	0.658002	−	0.753016i	$-0.271402\pi$
$691$	34.5937	1.31600	0.658002	+	0.753016i	$0.271402\pi$
$692$	11.2442	0.427439
$693$	11.7307	0.445613
$694$	−15.9386	−0.605022
$695$	0.900951	0.0341750
$696$	0.169893	0.00643977
$697$	−17.7168	−0.671071
$698$	7.31317	0.276808
$699$	−1.71876	−0.0650096
$700$	−35.0486	−1.32471
$701$	−1.38508	−0.0523138	−0.0261569	−	0.999658i	$-0.508327\pi$
$701$	−1.38508	−0.0523138	−0.0261569	+	0.999658i	$0.508327\pi$
$702$	1.93942	0.0731985
$703$	13.5322	0.510375
$704$	−17.5854	−0.662774
$705$	0.991717	0.0373502
$706$	−2.74902	−0.103461
$707$	−36.9484	−1.38959
$708$	−11.9938	−0.450755
$709$	−46.5650	−1.74878	−0.874392	−	0.485220i	$-0.838739\pi$
$709$	−46.5650	−1.74878	−0.874392	+	0.485220i	$0.838739\pi$
$710$	2.21273	0.0830422
$711$	−6.54860	−0.245592
$712$	4.53203	0.169845
$713$	−11.4177	−0.427598
$714$	45.3001	1.69531
$715$	−0.418184	−0.0156392
$716$	−8.10615	−0.302941
$717$	−19.0904	−0.712943
$718$	−5.41342	−0.202027
$719$	−24.1577	−0.900931	−0.450466	−	0.892794i	$-0.648742\pi$
$719$	−24.1577	−0.900931	−0.450466	+	0.892794i	$0.648742\pi$
$720$	−0.629689	−0.0234671
$721$	−3.99599	−0.148819
$722$	−41.3389	−1.53848
$723$	18.3258	0.681542
$724$	38.6832	1.43765
$725$	−1.82776	−0.0678812
$726$	4.61994	0.171462
$727$	44.1100	1.63595	0.817975	−	0.575254i	$-0.195097\pi$
$727$	44.1100	1.63595	0.817975	+	0.575254i	$0.195097\pi$
$728$	−1.84963	−0.0685519
$729$	1.00000	0.0370370
$730$	−3.67263	−0.135930
$731$	−21.1231	−0.781265
$732$	15.7924	0.583704
$733$	−19.4985	−0.720192	−0.360096	−	0.932915i	$-0.617256\pi$
$733$	−19.4985	−0.720192	−0.360096	+	0.932915i	$0.617256\pi$
$734$	−2.09175	−0.0772079
$735$	1.27750	0.0471213
$736$	−37.6802	−1.38891
$737$	27.4435	1.01089
$738$	−5.87831	−0.216384
$739$	−47.7201	−1.75541	−0.877707	−	0.479199i	$-0.840927\pi$
$739$	−47.7201	−1.75541	−0.877707	+	0.479199i	$0.840927\pi$
$740$	0.534739	0.0196574
$741$	−6.34942	−0.233252
$742$	−35.6398	−1.30838
$743$	−48.9575	−1.79608	−0.898039	−	0.439916i	$-0.855008\pi$
$743$	−48.9575	−1.79608	−0.898039	+	0.439916i	$0.855008\pi$
$744$	1.07258	0.0393228
$745$	3.03200	0.111084
$746$	−2.36187	−0.0864742
$747$	15.7516	0.576321
$748$	−30.2235	−1.10508
$749$	17.8788	0.653278
$750$	2.75712	0.100676
$751$	−34.9723	−1.27616	−0.638078	−	0.769972i	$-0.720270\pi$
$751$	−34.9723	−1.27616	−0.638078	+	0.769972i	$0.720270\pi$
$752$	−30.7736	−1.12220
$753$	−8.43362	−0.307338
$754$	0.711845	0.0259239
$755$	0.921968	0.0335538
$756$	7.03828	0.255980
$757$	−47.9591	−1.74310	−0.871551	−	0.490305i	$-0.836885\pi$
$757$	−47.9591	−1.74310	−0.871551	+	0.490305i	$0.836885\pi$
$758$	−43.2279	−1.57011
$759$	−14.4647	−0.525037
$760$	0.418661	0.0151864
$761$	−23.0166	−0.834352	−0.417176	−	0.908826i	$-0.636980\pi$
$761$	−23.0166	−0.834352	−0.417176	+	0.908826i	$0.636980\pi$
$762$	−40.5485	−1.46892
$763$	−5.88977	−0.213224
$764$	−1.02463	−0.0370700
$765$	−0.832665	−0.0301051
$766$	−40.2135	−1.45297
$767$	6.80950	0.245877
$768$	19.1112	0.689615
$769$	−6.16029	−0.222146	−0.111073	−	0.993812i	$-0.535429\pi$
$769$	−6.16029	−0.222146	−0.111073	+	0.993812i	$0.535429\pi$
$770$	−3.24088	−0.116793
$771$	5.33270	0.192052
$772$	20.6197	0.742119
$773$	41.6617	1.49847	0.749234	−	0.662306i	$-0.230422\pi$
$773$	41.6617	1.49847	0.749234	+	0.662306i	$0.230422\pi$
$774$	−7.00850	−0.251915
$775$	−11.5391	−0.414498
$776$	−7.33411	−0.263279
$777$	8.51643	0.305525
$778$	−17.8223	−0.638961
$779$	19.2449	0.689520
$780$	−0.250905	−0.00898384
$781$	−23.5120	−0.841326
$782$	−55.8579	−1.99748
$783$	0.367041	0.0131170
$784$	−39.6417	−1.41577
$785$	0.982539	0.0350683
$786$	19.8045	0.706402
$787$	13.0640	0.465682	0.232841	−	0.972515i	$-0.425198\pi$
$787$	13.0640	0.465682	0.232841	+	0.972515i	$0.425198\pi$
$788$	11.7386	0.418172
$789$	−2.11890	−0.0754350
$790$	1.80920	0.0643685
$791$	−76.4646	−2.71877
$792$	1.35882	0.0482834
$793$	−8.96615	−0.318397
$794$	−28.2649	−1.00308
$795$	0.655099	0.0232340
$796$	−28.5603	−1.01229
$797$	4.71583	0.167043	0.0835216	−	0.996506i	$-0.473383\pi$
$797$	4.71583	0.167043	0.0835216	+	0.996506i	$0.473383\pi$
$798$	−49.2073	−1.74192
$799$	−40.6933	−1.43963
$800$	−38.0808	−1.34636
$801$	9.79112	0.345952
$802$	−15.6629	−0.553077
$803$	39.0247	1.37715
$804$	16.4657	0.580702
$805$	−2.80481	−0.0988564
$806$	4.49408	0.158297
$807$	−0.550593	−0.0193818
$808$	−4.27989	−0.150566
$809$	−26.5634	−0.933919	−0.466960	−	0.884279i	$-0.654651\pi$
$809$	−26.5634	−0.933919	−0.466960	+	0.884279i	$0.654651\pi$
$810$	−0.276273	−0.00970724
$811$	−2.04384	−0.0717690	−0.0358845	−	0.999356i	$-0.511425\pi$
$811$	−2.04384	−0.0717690	−0.0358845	+	0.999356i	$0.511425\pi$
$812$	2.58334	0.0906573
$813$	−5.02190	−0.176126
$814$	−12.1340	−0.425296
$815$	1.31047	0.0459038
$816$	25.8382	0.904517
$817$	22.9450	0.802744
$818$	46.9797	1.64261
$819$	−3.99599	−0.139631
$820$	0.760485	0.0265573
$821$	45.6933	1.59471	0.797353	−	0.603513i	$-0.206233\pi$
$821$	45.6933	1.59471	0.797353	+	0.603513i	$0.206233\pi$
$822$	−1.97156	−0.0687661
$823$	−23.3289	−0.813195	−0.406598	−	0.913607i	$-0.633285\pi$
$823$	−23.3289	−0.813195	−0.406598	+	0.913607i	$0.633285\pi$
$824$	−0.462872	−0.0161249
$825$	−14.6185	−0.508952
$826$	52.7729	1.83620
$827$	−12.3414	−0.429152	−0.214576	−	0.976707i	$-0.568837\pi$
$827$	−12.3414	−0.429152	−0.214576	+	0.976707i	$0.568837\pi$
$828$	−8.67866	−0.301604
$829$	−0.600041	−0.0208403	−0.0104201	−	0.999946i	$-0.503317\pi$
$829$	−0.600041	−0.0208403	−0.0104201	+	0.999946i	$0.503317\pi$
$830$	−4.35174	−0.151051
$831$	9.59936	0.332998
$832$	5.99035	0.207678
$833$	−52.4200	−1.81624
$834$	−12.2661	−0.424739
$835$	−2.04899	−0.0709082
$836$	32.8304	1.13546
$837$	2.31723	0.0800953
$838$	53.9742	1.86451
$839$	5.62774	0.194291	0.0971456	−	0.995270i	$-0.469029\pi$
$839$	5.62774	0.194291	0.0971456	+	0.995270i	$0.469029\pi$
$840$	0.263483	0.00909103
$841$	−28.8653	−0.995355
$842$	−21.5861	−0.743906
$843$	17.1956	0.592248
$844$	7.24171	0.249270
$845$	0.142452	0.00490049
$846$	−13.5018	−0.464201
$847$	−9.51898	−0.327076
$848$	−20.3282	−0.698072
$849$	−19.5612	−0.671338
$850$	−56.4518	−1.93628
$851$	−10.5013	−0.359980
$852$	−14.1069	−0.483294
$853$	−38.4798	−1.31752	−0.658762	−	0.752351i	$-0.728920\pi$
$853$	−38.4798	−1.31752	−0.658762	+	0.752351i	$0.728920\pi$
$854$	−69.4867	−2.37779
$855$	0.904485	0.0309327
$856$	2.07097	0.0707845
$857$	−0.610638	−0.0208590	−0.0104295	−	0.999946i	$-0.503320\pi$
$857$	−0.610638	−0.0208590	−0.0104295	+	0.999946i	$0.503320\pi$
$858$	5.69339	0.194369
$859$	−2.77294	−0.0946115	−0.0473057	−	0.998880i	$-0.515064\pi$
$859$	−2.77294	−0.0946115	−0.0473057	+	0.998880i	$0.515064\pi$
$860$	0.906699	0.0309182
$861$	12.1117	0.412767
$862$	25.5273	0.869464
$863$	−36.6108	−1.24625	−0.623123	−	0.782124i	$-0.714136\pi$
$863$	−36.6108	−1.24625	−0.623123	+	0.782124i	$0.714136\pi$
$864$	7.64719	0.260163
$865$	0.909395	0.0309204
$866$	27.8542	0.946523
$867$	17.1670	0.583020
$868$	16.3093	0.553575
$869$	−19.2242	−0.652137
$870$	−0.101403	−0.00343790
$871$	−9.34845	−0.316760
$872$	−0.682236	−0.0231034
$873$	−15.8448	−0.536265
$874$	60.6758	2.05239
$875$	−5.68081	−0.192046
$876$	23.4143	0.791096
$877$	49.0559	1.65650	0.828250	−	0.560358i	$-0.189337\pi$
$877$	49.0559	1.65650	0.828250	+	0.560358i	$0.189337\pi$
$878$	39.0453	1.31771
$879$	29.6328	0.999490
$880$	−1.84853	−0.0623139
$881$	−33.8801	−1.14145	−0.570725	−	0.821141i	$-0.693338\pi$
$881$	−33.8801	−1.14145	−0.570725	+	0.821141i	$0.693338\pi$
$882$	−17.3926	−0.585639
$883$	−52.6199	−1.77080	−0.885401	−	0.464828i	$-0.846116\pi$
$883$	−52.6199	−1.77080	−0.885401	+	0.464828i	$0.846116\pi$
$884$	10.2954	0.346273
$885$	−0.970024	−0.0326070
$886$	41.6325	1.39867
$887$	−53.1664	−1.78515	−0.892577	−	0.450895i	$-0.851105\pi$
$887$	−53.1664	−1.78515	−0.892577	+	0.450895i	$0.851105\pi$
$888$	0.986492	0.0331045
$889$	83.5465	2.80206
$890$	−2.70502	−0.0906725
$891$	2.93562	0.0983470
$892$	−3.73002	−0.124890
$893$	44.2033	1.47921
$894$	−41.2793	−1.38059
$895$	−0.655602	−0.0219144
$896$	−14.6917	−0.490815
$897$	4.92732	0.164518
$898$	−5.80740	−0.193796
$899$	0.850519	0.0283664
$900$	−8.77093	−0.292364
$901$	−26.8808	−0.895530
$902$	−17.2565	−0.574578
$903$	14.4404	0.480546
$904$	−8.85720	−0.294586
$905$	3.12858	0.103998
$906$	−12.5522	−0.417018
$907$	−15.3575	−0.509937	−0.254968	−	0.966949i	$-0.582065\pi$
$907$	−15.3575	−0.509937	−0.254968	+	0.966949i	$0.582065\pi$
$908$	−36.2067	−1.20156
$909$	−9.24637	−0.306683
$910$	1.10398	0.0365967
$911$	−3.87434	−0.128363	−0.0641813	−	0.997938i	$-0.520444\pi$
$911$	−3.87434	−0.128363	−0.0641813	+	0.997938i	$0.520444\pi$
$912$	−28.0668	−0.929384
$913$	46.2408	1.53035
$914$	0.949968	0.0314221
$915$	1.27724	0.0422243
$916$	−11.7765	−0.389107
$917$	−40.8053	−1.34751
$918$	11.3364	0.374156
$919$	17.7790	0.586474	0.293237	−	0.956040i	$-0.405268\pi$
$919$	17.7790	0.586474	0.293237	+	0.956040i	$0.405268\pi$
$920$	−0.324892	−0.0107114
$921$	31.0591	1.02343
$922$	51.5612	1.69808
$923$	8.00921	0.263626
$924$	20.6617	0.679721
$925$	−10.6130	−0.348952
$926$	5.84026	0.191923
$927$	−1.00000	−0.0328443
$928$	2.80683	0.0921388
$929$	56.9830	1.86955	0.934775	−	0.355240i	$-0.115601\pi$
$929$	56.9830	1.86955	0.934775	+	0.355240i	$0.115601\pi$
$930$	−0.640189	−0.0209926
$931$	56.9413	1.86618
$932$	−3.02732	−0.0991630
$933$	−0.666546	−0.0218218
$934$	−41.5145	−1.35840
$935$	−2.44439	−0.0799401
$936$	−0.462872	−0.0151294
$937$	−51.5166	−1.68297	−0.841487	−	0.540277i	$-0.818319\pi$
$937$	−51.5166	−1.68297	−0.841487	+	0.540277i	$0.818319\pi$
$938$	−72.4495	−2.36556
$939$	−9.96814	−0.325298
$940$	1.74674	0.0569725
$941$	27.3011	0.889989	0.444994	−	0.895533i	$-0.353206\pi$
$941$	27.3011	0.889989	0.444994	+	0.895533i	$0.353206\pi$
$942$	−13.3768	−0.435841
$943$	−14.9346	−0.486336
$944$	30.1005	0.979688
$945$	0.569236	0.0185172
$946$	−20.5743	−0.668928
$947$	−1.15498	−0.0375318	−0.0187659	−	0.999824i	$-0.505974\pi$
$947$	−1.15498	−0.0375318	−0.0187659	+	0.999824i	$0.505974\pi$
$948$	−11.5343	−0.374616
$949$	−13.2935	−0.431525
$950$	61.3210	1.98951
$951$	−23.0829	−0.748513
$952$	−10.8116	−0.350405
$953$	−27.7281	−0.898200	−0.449100	−	0.893482i	$-0.648255\pi$
$953$	−27.7281	−0.898200	−0.449100	+	0.893482i	$0.648255\pi$
$954$	−8.91888	−0.288759
$955$	−0.0828695	−0.00268159
$956$	−33.6245	−1.08750
$957$	1.07749	0.0348304
$958$	−36.5519	−1.18094
$959$	4.06223	0.131176
$960$	−0.853335	−0.0275413
$961$	−25.6304	−0.826788
$962$	4.13337	0.133265
$963$	4.47419	0.144179
$964$	32.2778	1.03960
$965$	1.66766	0.0536839
$966$	38.1862	1.22862
$967$	42.6668	1.37207	0.686035	−	0.727568i	$-0.259350\pi$
$967$	42.6668	1.37207	0.686035	+	0.727568i	$0.259350\pi$
$968$	−1.10262	−0.0354396
$969$	−37.1140	−1.19227
$970$	4.37749	0.140553
$971$	−33.7810	−1.08408	−0.542041	−	0.840352i	$-0.682348\pi$
$971$	−33.7810	−1.08408	−0.542041	+	0.840352i	$0.682348\pi$
$972$	1.76133	0.0564948
$973$	25.2731	0.810218
$974$	74.2312	2.37852
$975$	4.97971	0.159478
$976$	−39.6337	−1.26864
$977$	−40.6894	−1.30177	−0.650884	−	0.759177i	$-0.725602\pi$
$977$	−40.6894	−1.30177	−0.650884	+	0.759177i	$0.725602\pi$
$978$	−17.8415	−0.570508
$979$	28.7430	0.918630
$980$	2.25011	0.0718770
$981$	−1.47392	−0.0470586
$982$	39.3559	1.25590
$983$	−14.3943	−0.459107	−0.229553	−	0.973296i	$-0.573727\pi$
$983$	−14.3943	−0.459107	−0.229553	+	0.973296i	$0.573727\pi$
$984$	1.40295	0.0447244
$985$	0.949387	0.0302500
$986$	4.16091	0.132510
$987$	27.8192	0.885495
$988$	−11.1835	−0.355793
$989$	−17.8059	−0.566195
$990$	−0.811033	−0.0257763
$991$	−25.5793	−0.812553	−0.406277	−	0.913750i	$-0.633173\pi$
$991$	−25.5793	−0.812553	−0.406277	+	0.913750i	$0.633173\pi$
$992$	17.7203	0.562621
$993$	−33.5169	−1.06363
$994$	62.0705	1.96876
$995$	−2.30987	−0.0732279
$996$	27.7439	0.879098
$997$	47.5737	1.50667	0.753337	−	0.657635i	$-0.228443\pi$
$997$	47.5737	1.50667	0.753337	+	0.657635i	$0.228443\pi$
$998$	−61.0229	−1.93164
$999$	2.13124	0.0674295

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4017.2.a.l.1.5	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4017.2.a.l.1.5	✓	32	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:	\( N \)	\(=\)	\( 4017 = 3 \cdot 13 \cdot 103 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4017.a (trivial)

\(f(q)\)	\(=\)	\(q-1.93942 q^{2} +1.00000 q^{3} +1.76133 q^{4} +0.142452 q^{5} -1.93942 q^{6} +3.99599 q^{7} +0.462872 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.93942 q^{2} +1.00000 q^{3} +1.76133 q^{4} +0.142452 q^{5} -1.93942 q^{6} +3.99599 q^{7} +0.462872 q^{8} +1.00000 q^{9} -0.276273 q^{10} +2.93562 q^{11} +1.76133 q^{12} -1.00000 q^{13} -7.74989 q^{14} +0.142452 q^{15} -4.42037 q^{16} -5.84525 q^{17} -1.93942 q^{18} +6.34942 q^{19} +0.250905 q^{20} +3.99599 q^{21} -5.69339 q^{22} -4.92732 q^{23} +0.462872 q^{24} -4.97971 q^{25} +1.93942 q^{26} +1.00000 q^{27} +7.03828 q^{28} +0.367041 q^{29} -0.276273 q^{30} +2.31723 q^{31} +7.64719 q^{32} +2.93562 q^{33} +11.3364 q^{34} +0.569236 q^{35} +1.76133 q^{36} +2.13124 q^{37} -12.3142 q^{38} -1.00000 q^{39} +0.0659368 q^{40} +3.03097 q^{41} -7.74989 q^{42} +3.61371 q^{43} +5.17061 q^{44} +0.142452 q^{45} +9.55612 q^{46} +6.96178 q^{47} -4.42037 q^{48} +8.96796 q^{49} +9.65772 q^{50} -5.84525 q^{51} -1.76133 q^{52} +4.59875 q^{53} -1.93942 q^{54} +0.418184 q^{55} +1.84963 q^{56} +6.34942 q^{57} -0.711845 q^{58} -6.80950 q^{59} +0.250905 q^{60} +8.96615 q^{61} -4.49408 q^{62} +3.99599 q^{63} -5.99035 q^{64} -0.142452 q^{65} -5.69339 q^{66} +9.34845 q^{67} -10.2954 q^{68} -4.92732 q^{69} -1.10398 q^{70} -8.00921 q^{71} +0.462872 q^{72} +13.2935 q^{73} -4.13337 q^{74} -4.97971 q^{75} +11.1835 q^{76} +11.7307 q^{77} +1.93942 q^{78} -6.54860 q^{79} -0.629689 q^{80} +1.00000 q^{81} -5.87831 q^{82} +15.7516 q^{83} +7.03828 q^{84} -0.832665 q^{85} -7.00850 q^{86} +0.367041 q^{87} +1.35882 q^{88} +9.79112 q^{89} -0.276273 q^{90} -3.99599 q^{91} -8.67866 q^{92} +2.31723 q^{93} -13.5018 q^{94} +0.904485 q^{95} +7.64719 q^{96} -15.8448 q^{97} -17.3926 q^{98} +2.93562 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 5 q^{2} + 32 q^{3} + 45 q^{4} + q^{5} + 5 q^{6} + 11 q^{7} + 12 q^{8} + 32 q^{9}+O(q^{10}) \) 32 * q + 5 * q^2 + 32 * q^3 + 45 * q^4 + q^5 + 5 * q^6 + 11 * q^7 + 12 * q^8 + 32 * q^9	\( 32 q + 5 q^{2} + 32 q^{3} + 45 q^{4} + q^{5} + 5 q^{6} + 11 q^{7} + 12 q^{8} + 32 q^{9} + 16 q^{10} + 3 q^{11} + 45 q^{12} - 32 q^{13} + 12 q^{14} + q^{15} + 75 q^{16} + 10 q^{17} + 5 q^{18} + 4 q^{20} + 11 q^{21} + 27 q^{22} + 53 q^{23} + 12 q^{24} + 67 q^{25} - 5 q^{26} + 32 q^{27} + 32 q^{28} + 6 q^{29} + 16 q^{30} + 12 q^{31} + 19 q^{32} + 3 q^{33} + 25 q^{34} + 16 q^{35} + 45 q^{36} + 36 q^{37} + 8 q^{38} - 32 q^{39} + 36 q^{40} - 19 q^{41} + 12 q^{42} + 43 q^{43} - 23 q^{44} + q^{45} + 11 q^{46} + 30 q^{47} + 75 q^{48} + 75 q^{49} + 28 q^{50} + 10 q^{51} - 45 q^{52} + 22 q^{53} + 5 q^{54} + 58 q^{55} + 60 q^{56} + 33 q^{58} - 24 q^{59} + 4 q^{60} + 47 q^{61} - 25 q^{62} + 11 q^{63} + 146 q^{64} - q^{65} + 27 q^{66} + 34 q^{67} + 58 q^{68} + 53 q^{69} - 35 q^{70} + 18 q^{71} + 12 q^{72} - 2 q^{73} - 20 q^{74} + 67 q^{75} + 24 q^{76} + 39 q^{77} - 5 q^{78} + 39 q^{79} + 2 q^{80} + 32 q^{81} + 64 q^{82} + 17 q^{83} + 32 q^{84} + 35 q^{85} - 13 q^{86} + 6 q^{87} + 55 q^{88} - 48 q^{89} + 16 q^{90} - 11 q^{91} + 39 q^{92} + 12 q^{93} + 58 q^{94} + 59 q^{95} + 19 q^{96} + 42 q^{97} + 16 q^{98} + 3 q^{99}+O(q^{100}) \) 32 * q + 5 * q^2 + 32 * q^3 + 45 * q^4 + q^5 + 5 * q^6 + 11 * q^7 + 12 * q^8 + 32 * q^9 + 16 * q^10 + 3 * q^11 + 45 * q^12 - 32 * q^13 + 12 * q^14 + q^15 + 75 * q^16 + 10 * q^17 + 5 * q^18 + 4 * q^20 + 11 * q^21 + 27 * q^22 + 53 * q^23 + 12 * q^24 + 67 * q^25 - 5 * q^26 + 32 * q^27 + 32 * q^28 + 6 * q^29 + 16 * q^30 + 12 * q^31 + 19 * q^32 + 3 * q^33 + 25 * q^34 + 16 * q^35 + 45 * q^36 + 36 * q^37 + 8 * q^38 - 32 * q^39 + 36 * q^40 - 19 * q^41 + 12 * q^42 + 43 * q^43 - 23 * q^44 + q^45 + 11 * q^46 + 30 * q^47 + 75 * q^48 + 75 * q^49 + 28 * q^50 + 10 * q^51 - 45 * q^52 + 22 * q^53 + 5 * q^54 + 58 * q^55 + 60 * q^56 + 33 * q^58 - 24 * q^59 + 4 * q^60 + 47 * q^61 - 25 * q^62 + 11 * q^63 + 146 * q^64 - q^65 + 27 * q^66 + 34 * q^67 + 58 * q^68 + 53 * q^69 - 35 * q^70 + 18 * q^71 + 12 * q^72 - 2 * q^73 - 20 * q^74 + 67 * q^75 + 24 * q^76 + 39 * q^77 - 5 * q^78 + 39 * q^79 + 2 * q^80 + 32 * q^81 + 64 * q^82 + 17 * q^83 + 32 * q^84 + 35 * q^85 - 13 * q^86 + 6 * q^87 + 55 * q^88 - 48 * q^89 + 16 * q^90 - 11 * q^91 + 39 * q^92 + 12 * q^93 + 58 * q^94 + 59 * q^95 + 19 * q^96 + 42 * q^97 + 16 * q^98 + 3 * q^99

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