LMFDB - Embedded newform 6026.2.a.i.1.23

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6026,2,Mod(1,6026)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6026, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("6026.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6026 = 2 \cdot 23 \cdot 131 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6026.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:	$48.1178522580$
Analytic rank:	$1$
Dimension:	$25$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.23
Character	$\chi$	$=$	6026.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +2.57908 q^{3} +1.00000 q^{4} +3.18188 q^{5} -2.57908 q^{6} -4.63578 q^{7} -1.00000 q^{8} +3.65168 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +2.57908 q^{3} +1.00000 q^{4} +3.18188 q^{5} -2.57908 q^{6} -4.63578 q^{7} -1.00000 q^{8} +3.65168 q^{9} -3.18188 q^{10} -1.26450 q^{11} +2.57908 q^{12} -4.01571 q^{13} +4.63578 q^{14} +8.20633 q^{15} +1.00000 q^{16} +1.91966 q^{17} -3.65168 q^{18} -4.81311 q^{19} +3.18188 q^{20} -11.9561 q^{21} +1.26450 q^{22} +1.00000 q^{23} -2.57908 q^{24} +5.12434 q^{25} +4.01571 q^{26} +1.68074 q^{27} -4.63578 q^{28} +2.52740 q^{29} -8.20633 q^{30} +0.522139 q^{31} -1.00000 q^{32} -3.26126 q^{33} -1.91966 q^{34} -14.7505 q^{35} +3.65168 q^{36} +0.765306 q^{37} +4.81311 q^{38} -10.3569 q^{39} -3.18188 q^{40} -3.04970 q^{41} +11.9561 q^{42} -12.2288 q^{43} -1.26450 q^{44} +11.6192 q^{45} -1.00000 q^{46} -4.23012 q^{47} +2.57908 q^{48} +14.4904 q^{49} -5.12434 q^{50} +4.95097 q^{51} -4.01571 q^{52} +2.15776 q^{53} -1.68074 q^{54} -4.02349 q^{55} +4.63578 q^{56} -12.4134 q^{57} -2.52740 q^{58} -12.2789 q^{59} +8.20633 q^{60} +7.28104 q^{61} -0.522139 q^{62} -16.9284 q^{63} +1.00000 q^{64} -12.7775 q^{65} +3.26126 q^{66} +0.101696 q^{67} +1.91966 q^{68} +2.57908 q^{69} +14.7505 q^{70} -12.4867 q^{71} -3.65168 q^{72} +7.43375 q^{73} -0.765306 q^{74} +13.2161 q^{75} -4.81311 q^{76} +5.86196 q^{77} +10.3569 q^{78} -8.28540 q^{79} +3.18188 q^{80} -6.62028 q^{81} +3.04970 q^{82} -12.4279 q^{83} -11.9561 q^{84} +6.10813 q^{85} +12.2288 q^{86} +6.51838 q^{87} +1.26450 q^{88} +12.0434 q^{89} -11.6192 q^{90} +18.6159 q^{91} +1.00000 q^{92} +1.34664 q^{93} +4.23012 q^{94} -15.3147 q^{95} -2.57908 q^{96} +4.39915 q^{97} -14.4904 q^{98} -4.61756 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 25 q - 25 q^{2} - 4 q^{3} + 25 q^{4} - 3 q^{5} + 4 q^{6} - 11 q^{7} - 25 q^{8} + 19 q^{9}+O(q^{10}) $ 25 * q - 25 * q^2 - 4 * q^3 + 25 * q^4 - 3 * q^5 + 4 * q^6 - 11 * q^7 - 25 * q^8 + 19 * q^9	\( 25 q - 25 q^{2} - 4 q^{3} + 25 q^{4} - 3 q^{5} + 4 q^{6} - 11 q^{7} - 25 q^{8} + 19 q^{9} + 3 q^{10} - 12 q^{11} - 4 q^{12} - 6 q^{13} + 11 q^{14} + 25 q^{16} + 8 q^{17} - 19 q^{18} - 23 q^{19} - 3 q^{20} - 16 q^{21} + 12 q^{22} + 25 q^{23} + 4 q^{24} + 4 q^{25} + 6 q^{26} - 13 q^{27} - 11 q^{28} - 7 q^{29} - 7 q^{31} - 25 q^{32} + 3 q^{33} - 8 q^{34} - 18 q^{35} + 19 q^{36} - 7 q^{37} + 23 q^{38} - 2 q^{39} + 3 q^{40} - 10 q^{41} + 16 q^{42} - 26 q^{43} - 12 q^{44} + 20 q^{45} - 25 q^{46} - 2 q^{47} - 4 q^{48} + 2 q^{49} - 4 q^{50} - 28 q^{51} - 6 q^{52} + 47 q^{53} + 13 q^{54} - 38 q^{55} + 11 q^{56} - 4 q^{57} + 7 q^{58} - 19 q^{59} - 26 q^{61} + 7 q^{62} - 15 q^{63} + 25 q^{64} + 13 q^{65} - 3 q^{66} - 34 q^{67} + 8 q^{68} - 4 q^{69} + 18 q^{70} - 10 q^{71} - 19 q^{72} - 22 q^{73} + 7 q^{74} - 8 q^{75} - 23 q^{76} + 28 q^{77} + 2 q^{78} - 21 q^{79} - 3 q^{80} - 27 q^{81} + 10 q^{82} - 16 q^{83} - 16 q^{84} - 42 q^{85} + 26 q^{86} - 17 q^{87} + 12 q^{88} + 27 q^{89} - 20 q^{90} - 26 q^{91} + 25 q^{92} - 27 q^{93} + 2 q^{94} + 4 q^{96} + 4 q^{97} - 2 q^{98} - 2 q^{99}+O(q^{100}) \) 25 * q - 25 * q^2 - 4 * q^3 + 25 * q^4 - 3 * q^5 + 4 * q^6 - 11 * q^7 - 25 * q^8 + 19 * q^9 + 3 * q^10 - 12 * q^11 - 4 * q^12 - 6 * q^13 + 11 * q^14 + 25 * q^16 + 8 * q^17 - 19 * q^18 - 23 * q^19 - 3 * q^20 - 16 * q^21 + 12 * q^22 + 25 * q^23 + 4 * q^24 + 4 * q^25 + 6 * q^26 - 13 * q^27 - 11 * q^28 - 7 * q^29 - 7 * q^31 - 25 * q^32 + 3 * q^33 - 8 * q^34 - 18 * q^35 + 19 * q^36 - 7 * q^37 + 23 * q^38 - 2 * q^39 + 3 * q^40 - 10 * q^41 + 16 * q^42 - 26 * q^43 - 12 * q^44 + 20 * q^45 - 25 * q^46 - 2 * q^47 - 4 * q^48 + 2 * q^49 - 4 * q^50 - 28 * q^51 - 6 * q^52 + 47 * q^53 + 13 * q^54 - 38 * q^55 + 11 * q^56 - 4 * q^57 + 7 * q^58 - 19 * q^59 - 26 * q^61 + 7 * q^62 - 15 * q^63 + 25 * q^64 + 13 * q^65 - 3 * q^66 - 34 * q^67 + 8 * q^68 - 4 * q^69 + 18 * q^70 - 10 * q^71 - 19 * q^72 - 22 * q^73 + 7 * q^74 - 8 * q^75 - 23 * q^76 + 28 * q^77 + 2 * q^78 - 21 * q^79 - 3 * q^80 - 27 * q^81 + 10 * q^82 - 16 * q^83 - 16 * q^84 - 42 * q^85 + 26 * q^86 - 17 * q^87 + 12 * q^88 + 27 * q^89 - 20 * q^90 - 26 * q^91 + 25 * q^92 - 27 * q^93 + 2 * q^94 + 4 * q^96 + 4 * q^97 - 2 * q^98 - 2 * 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
$3$	2.57908	1.48904	0.744518	−	0.667603i	$-0.232679\pi$
$3$	2.57908	1.48904	0.744518	+	0.667603i	$0.232679\pi$
$4$	1.00000	0.500000
$5$	3.18188	1.42298	0.711489	−	0.702697i	$-0.248021\pi$
$5$	3.18188	1.42298	0.711489	+	0.702697i	$0.248021\pi$
$6$	−2.57908	−1.05291
$7$	−4.63578	−1.75216	−0.876080	−	0.482167i	$-0.839850\pi$
$7$	−4.63578	−1.75216	−0.876080	+	0.482167i	$0.839850\pi$
$8$	−1.00000	−0.353553
$9$	3.65168	1.21723
$10$	−3.18188	−1.00620
$11$	−1.26450	−0.381262	−0.190631	−	0.981662i	$-0.561053\pi$
$11$	−1.26450	−0.381262	−0.190631	+	0.981662i	$0.561053\pi$
$12$	2.57908	0.744518
$13$	−4.01571	−1.11376	−0.556879	−	0.830594i	$-0.688001\pi$
$13$	−4.01571	−1.11376	−0.556879	+	0.830594i	$0.688001\pi$
$14$	4.63578	1.23896
$15$	8.20633	2.11887
$16$	1.00000	0.250000
$17$	1.91966	0.465587	0.232793	−	0.972526i	$-0.425213\pi$
$17$	1.91966	0.465587	0.232793	+	0.972526i	$0.425213\pi$
$18$	−3.65168	−0.860709
$19$	−4.81311	−1.10420	−0.552102	−	0.833777i	$-0.686174\pi$
$19$	−4.81311	−1.10420	−0.552102	+	0.833777i	$0.686174\pi$
$20$	3.18188	0.711489
$21$	−11.9561	−2.60903
$22$	1.26450	0.269593
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	−2.57908	−0.526454
$25$	5.12434	1.02487
$26$	4.01571	0.787546
$27$	1.68074	0.323458
$28$	−4.63578	−0.876080
$29$	2.52740	0.469326	0.234663	−	0.972077i	$-0.424601\pi$
$29$	2.52740	0.469326	0.234663	+	0.972077i	$0.424601\pi$
$30$	−8.20633	−1.49826
$31$	0.522139	0.0937789	0.0468894	−	0.998900i	$-0.485069\pi$
$31$	0.522139	0.0937789	0.0468894	+	0.998900i	$0.485069\pi$
$32$	−1.00000	−0.176777
$33$	−3.26126	−0.567713
$34$	−1.91966	−0.329219
$35$	−14.7505	−2.49328
$36$	3.65168	0.608613
$37$	0.765306	0.125815	0.0629077	−	0.998019i	$-0.479963\pi$
$37$	0.765306	0.125815	0.0629077	+	0.998019i	$0.479963\pi$
$38$	4.81311	0.780789
$39$	−10.3569	−1.65842
$40$	−3.18188	−0.503099
$41$	−3.04970	−0.476283	−0.238142	−	0.971230i	$-0.576538\pi$
$41$	−3.04970	−0.476283	−0.238142	+	0.971230i	$0.576538\pi$
$42$	11.9561	1.84486
$43$	−12.2288	−1.86488	−0.932438	−	0.361330i	$-0.882323\pi$
$43$	−12.2288	−1.86488	−0.932438	+	0.361330i	$0.882323\pi$
$44$	−1.26450	−0.190631
$45$	11.6192	1.73209
$46$	−1.00000	−0.147442
$47$	−4.23012	−0.617026	−0.308513	−	0.951220i	$-0.599831\pi$
$47$	−4.23012	−0.617026	−0.308513	+	0.951220i	$0.599831\pi$
$48$	2.57908	0.372259
$49$	14.4904	2.07006
$50$	−5.12434	−0.724691
$51$	4.95097	0.693275
$52$	−4.01571	−0.556879
$53$	2.15776	0.296391	0.148195	−	0.988958i	$-0.452654\pi$
$53$	2.15776	0.296391	0.148195	+	0.988958i	$0.452654\pi$
$54$	−1.68074	−0.228719
$55$	−4.02349	−0.542528
$56$	4.63578	0.619482
$57$	−12.4134	−1.64420
$58$	−2.52740	−0.331864
$59$	−12.2789	−1.59857	−0.799286	−	0.600950i	$-0.794789\pi$
$59$	−12.2789	−1.59857	−0.799286	+	0.600950i	$0.794789\pi$
$60$	8.20633	1.05943
$61$	7.28104	0.932242	0.466121	−	0.884721i	$-0.345651\pi$
$61$	7.28104	0.932242	0.466121	+	0.884721i	$0.345651\pi$
$62$	−0.522139	−0.0663117
$63$	−16.9284	−2.13277
$64$	1.00000	0.125000
$65$	−12.7775	−1.58485
$66$	3.26126	0.401434
$67$	0.101696	0.0124242	0.00621208	−	0.999981i	$-0.498023\pi$
$67$	0.101696	0.0124242	0.00621208	+	0.999981i	$0.498023\pi$
$68$	1.91966	0.232793
$69$	2.57908	0.310485
$70$	14.7505	1.76302
$71$	−12.4867	−1.48190	−0.740950	−	0.671560i	$-0.765625\pi$
$71$	−12.4867	−1.48190	−0.740950	+	0.671560i	$0.765625\pi$
$72$	−3.65168	−0.430355
$73$	7.43375	0.870055	0.435028	−	0.900417i	$-0.356739\pi$
$73$	7.43375	0.870055	0.435028	+	0.900417i	$0.356739\pi$
$74$	−0.765306	−0.0889650
$75$	13.2161	1.52606
$76$	−4.81311	−0.552102
$77$	5.86196	0.668032
$78$	10.3569	1.17268
$79$	−8.28540	−0.932181	−0.466090	−	0.884737i	$-0.654338\pi$
$79$	−8.28540	−0.932181	−0.466090	+	0.884737i	$0.654338\pi$
$80$	3.18188	0.355745
$81$	−6.62028	−0.735586
$82$	3.04970	0.336783
$83$	−12.4279	−1.36414	−0.682070	−	0.731287i	$-0.738920\pi$
$83$	−12.4279	−1.36414	−0.682070	+	0.731287i	$0.738920\pi$
$84$	−11.9561	−1.30451
$85$	6.10813	0.662520
$86$	12.2288	1.31867
$87$	6.51838	0.698843
$88$	1.26450	0.134797
$89$	12.0434	1.27660	0.638300	−	0.769788i	$-0.279638\pi$
$89$	12.0434	1.27660	0.638300	+	0.769788i	$0.279638\pi$
$90$	−11.6192	−1.22477
$91$	18.6159	1.95148
$92$	1.00000	0.104257
$93$	1.34664	0.139640
$94$	4.23012	0.436303
$95$	−15.3147	−1.57126
$96$	−2.57908	−0.263227
$97$	4.39915	0.446666	0.223333	−	0.974742i	$-0.428306\pi$
$97$	4.39915	0.446666	0.223333	+	0.974742i	$0.428306\pi$
$98$	−14.4904	−1.46375
$99$	−4.61756	−0.464083
$100$	5.12434	0.512434
$101$	−5.58300	−0.555530	−0.277765	−	0.960649i	$-0.589594\pi$
$101$	−5.58300	−0.555530	−0.277765	+	0.960649i	$0.589594\pi$
$102$	−4.95097	−0.490219
$103$	0.603124	0.0594276	0.0297138	−	0.999558i	$-0.490540\pi$
$103$	0.603124	0.0594276	0.0297138	+	0.999558i	$0.490540\pi$
$104$	4.01571	0.393773
$105$	−38.0427	−3.71259
$106$	−2.15776	−0.209580
$107$	7.82536	0.756506	0.378253	−	0.925702i	$-0.376525\pi$
$107$	7.82536	0.756506	0.378253	+	0.925702i	$0.376525\pi$
$108$	1.68074	0.161729
$109$	6.94165	0.664889	0.332445	−	0.943123i	$-0.392127\pi$
$109$	6.94165	0.664889	0.332445	+	0.943123i	$0.392127\pi$
$110$	4.02349	0.383625
$111$	1.97379	0.187344
$112$	−4.63578	−0.438040
$113$	6.28389	0.591138	0.295569	−	0.955321i	$-0.404491\pi$
$113$	6.28389	0.591138	0.295569	+	0.955321i	$0.404491\pi$
$114$	12.4134	1.16262
$115$	3.18188	0.296711
$116$	2.52740	0.234663
$117$	−14.6641	−1.35570
$118$	12.2789	1.13036
$119$	−8.89913	−0.815782
$120$	−8.20633	−0.749132
$121$	−9.40103	−0.854639
$122$	−7.28104	−0.659194
$123$	−7.86544	−0.709202
$124$	0.522139	0.0468894
$125$	0.395623	0.0353856
$126$	16.9284	1.50810
$127$	−1.94142	−0.172273	−0.0861365	−	0.996283i	$-0.527452\pi$
$127$	−1.94142	−0.172273	−0.0861365	+	0.996283i	$0.527452\pi$
$128$	−1.00000	−0.0883883
$129$	−31.5391	−2.77687
$130$	12.7775	1.12066
$131$	1.00000	0.0873704
$131$	1.00000	0.0873704
$132$	−3.26126	−0.283857
$133$	22.3125	1.93474
$134$	−0.101696	−0.00878520
$135$	5.34790	0.460274
$136$	−1.91966	−0.164610
$137$	−15.5009	−1.32433	−0.662165	−	0.749358i	$-0.730362\pi$
$137$	−15.5009	−1.32433	−0.662165	+	0.749358i	$0.730362\pi$
$138$	−2.57908	−0.219546
$139$	−16.5983	−1.40785	−0.703924	−	0.710275i	$-0.748571\pi$
$139$	−16.5983	−1.40785	−0.703924	+	0.710275i	$0.748571\pi$
$140$	−14.7505	−1.24664
$141$	−10.9098	−0.918774
$142$	12.4867	1.04786
$143$	5.07788	0.424634
$144$	3.65168	0.304307
$145$	8.04187	0.667841
$146$	−7.43375	−0.615222
$147$	37.3720	3.08239
$148$	0.765306	0.0629077
$149$	−12.9435	−1.06037	−0.530185	−	0.847882i	$-0.677878\pi$
$149$	−12.9435	−1.06037	−0.530185	+	0.847882i	$0.677878\pi$
$150$	−13.2161	−1.07909
$151$	−0.198299	−0.0161373	−0.00806866	−	0.999967i	$-0.502568\pi$
$151$	−0.198299	−0.0161373	−0.00806866	+	0.999967i	$0.502568\pi$
$152$	4.81311	0.390395
$153$	7.00999	0.566724
$154$	−5.86196	−0.472370
$155$	1.66138	0.133445
$156$	−10.3569	−0.829212
$157$	−10.3105	−0.822865	−0.411432	−	0.911440i	$-0.634971\pi$
$157$	−10.3105	−0.822865	−0.411432	+	0.911440i	$0.634971\pi$
$158$	8.28540	0.659151
$159$	5.56504	0.441336
$160$	−3.18188	−0.251549
$161$	−4.63578	−0.365350
$162$	6.62028	0.520138
$163$	16.1906	1.26815	0.634073	−	0.773273i	$-0.281382\pi$
$163$	16.1906	1.26815	0.634073	+	0.773273i	$0.281382\pi$
$164$	−3.04970	−0.238142
$165$	−10.3769	−0.807843
$166$	12.4279	0.964593
$167$	−7.78187	−0.602179	−0.301090	−	0.953596i	$-0.597350\pi$
$167$	−7.78187	−0.602179	−0.301090	+	0.953596i	$0.597350\pi$
$168$	11.9561	0.922430
$169$	3.12593	0.240456
$170$	−6.10813	−0.468472
$171$	−17.5759	−1.34407
$172$	−12.2288	−0.932438
$173$	18.0854	1.37501	0.687504	−	0.726180i	$-0.258706\pi$
$173$	18.0854	1.37501	0.687504	+	0.726180i	$0.258706\pi$
$174$	−6.51838	−0.494157
$175$	−23.7553	−1.79573
$176$	−1.26450	−0.0953156
$177$	−31.6682	−2.38033
$178$	−12.0434	−0.902692
$179$	−4.73453	−0.353875	−0.176938	−	0.984222i	$-0.556619\pi$
$179$	−4.73453	−0.353875	−0.176938	+	0.984222i	$0.556619\pi$
$180$	11.6192	0.866043
$181$	−10.9668	−0.815159	−0.407579	−	0.913170i	$-0.633627\pi$
$181$	−10.9668	−0.815159	−0.407579	+	0.913170i	$0.633627\pi$
$182$	−18.6159	−1.37991
$183$	18.7784	1.38814
$184$	−1.00000	−0.0737210
$185$	2.43511	0.179033
$186$	−1.34664	−0.0987405
$187$	−2.42742	−0.177511
$188$	−4.23012	−0.308513
$189$	−7.79152	−0.566750
$190$	15.3147	1.11105
$191$	−0.598396	−0.0432984	−0.0216492	−	0.999766i	$-0.506892\pi$
$191$	−0.598396	−0.0432984	−0.0216492	+	0.999766i	$0.506892\pi$
$192$	2.57908	0.186129
$193$	17.0801	1.22945	0.614727	−	0.788740i	$-0.289266\pi$
$193$	17.0801	1.22945	0.614727	+	0.788740i	$0.289266\pi$
$194$	−4.39915	−0.315841
$195$	−32.9542	−2.35990
$196$	14.4904	1.03503
$197$	−17.2637	−1.22999	−0.614995	−	0.788531i	$-0.710842\pi$
$197$	−17.2637	−1.22999	−0.614995	+	0.788531i	$0.710842\pi$
$198$	4.61756	0.328156
$199$	2.97675	0.211016	0.105508	−	0.994418i	$-0.466353\pi$
$199$	2.97675	0.211016	0.105508	+	0.994418i	$0.466353\pi$
$200$	−5.12434	−0.362345
$201$	0.262283	0.0185000
$202$	5.58300	0.392819
$203$	−11.7165	−0.822334
$204$	4.95097	0.346637
$205$	−9.70377	−0.677741
$206$	−0.603124	−0.0420217
$207$	3.65168	0.253809
$208$	−4.01571	−0.278439
$209$	6.08620	0.420991
$210$	38.0427	2.62520
$211$	9.20716	0.633847	0.316924	−	0.948451i	$-0.397350\pi$
$211$	9.20716	0.633847	0.316924	+	0.948451i	$0.397350\pi$
$212$	2.15776	0.148195
$213$	−32.2043	−2.20660
$214$	−7.82536	−0.534931
$215$	−38.9106	−2.65368
$216$	−1.68074	−0.114360
$217$	−2.42052	−0.164316
$218$	−6.94165	−0.470148
$219$	19.1723	1.29554
$220$	−4.02349	−0.271264
$221$	−7.70881	−0.518551
$222$	−1.97379	−0.132472
$223$	5.35944	0.358895	0.179447	−	0.983768i	$-0.442569\pi$
$223$	5.35944	0.358895	0.179447	+	0.983768i	$0.442569\pi$
$224$	4.63578	0.309741
$225$	18.7124	1.24750
$226$	−6.28389	−0.417998
$227$	−12.7222	−0.844399	−0.422200	−	0.906503i	$-0.638742\pi$
$227$	−12.7222	−0.844399	−0.422200	+	0.906503i	$0.638742\pi$
$228$	−12.4134	−0.822099
$229$	−21.3443	−1.41047	−0.705236	−	0.708973i	$-0.749159\pi$
$229$	−21.3443	−1.41047	−0.705236	+	0.708973i	$0.749159\pi$
$230$	−3.18188	−0.209807
$231$	15.1185	0.994724
$232$	−2.52740	−0.165932
$233$	−17.6050	−1.15334	−0.576671	−	0.816977i	$-0.695649\pi$
$233$	−17.6050	−1.15334	−0.576671	+	0.816977i	$0.695649\pi$
$234$	14.6641	0.958621
$235$	−13.4597	−0.878015
$236$	−12.2789	−0.799286
$237$	−21.3688	−1.38805
$238$	8.89913	0.576845
$239$	−9.43941	−0.610585	−0.305292	−	0.952259i	$-0.598754\pi$
$239$	−9.43941	−0.610585	−0.305292	+	0.952259i	$0.598754\pi$
$240$	8.20633	0.529716
$241$	−14.6685	−0.944884	−0.472442	−	0.881362i	$-0.656627\pi$
$241$	−14.6685	−0.944884	−0.472442	+	0.881362i	$0.656627\pi$
$242$	9.40103	0.604321
$243$	−22.1165	−1.41877
$244$	7.28104	0.466121
$245$	46.1068	2.94565
$246$	7.86544	0.501482
$247$	19.3281	1.22981
$248$	−0.522139	−0.0331558
$249$	−32.0526	−2.03125
$250$	−0.395623	−0.0250214
$251$	6.81039	0.429868	0.214934	−	0.976629i	$-0.431046\pi$
$251$	6.81039	0.429868	0.214934	+	0.976629i	$0.431046\pi$
$252$	−16.9284	−1.06639
$253$	−1.26450	−0.0794987
$254$	1.94142	0.121815
$255$	15.7534	0.986515
$256$	1.00000	0.0625000
$257$	3.89974	0.243259	0.121630	−	0.992576i	$-0.461188\pi$
$257$	3.89974	0.243259	0.121630	+	0.992576i	$0.461188\pi$
$258$	31.5391	1.96354
$259$	−3.54779	−0.220449
$260$	−12.7775	−0.792426
$261$	9.22925	0.571276
$262$	−1.00000	−0.0617802
$263$	27.1329	1.67309	0.836543	−	0.547901i	$-0.184573\pi$
$263$	27.1329	1.67309	0.836543	+	0.547901i	$0.184573\pi$
$264$	3.26126	0.200717
$265$	6.86571	0.421757
$266$	−22.3125	−1.36807
$267$	31.0610	1.90090
$268$	0.101696	0.00621208
$269$	−27.3085	−1.66503	−0.832514	−	0.554004i	$-0.813099\pi$
$269$	−27.3085	−1.66503	−0.832514	+	0.554004i	$0.813099\pi$
$270$	−5.34790	−0.325463
$271$	15.6380	0.949940	0.474970	−	0.880002i	$-0.342459\pi$
$271$	15.6380	0.949940	0.474970	+	0.880002i	$0.342459\pi$
$272$	1.91966	0.116397
$273$	48.0121	2.90582
$274$	15.5009	0.936442
$275$	−6.47974	−0.390743
$276$	2.57908	0.155243
$277$	−5.00116	−0.300491	−0.150245	−	0.988649i	$-0.548006\pi$
$277$	−5.00116	−0.300491	−0.150245	+	0.988649i	$0.548006\pi$
$278$	16.5983	0.995499
$279$	1.90668	0.114150
$280$	14.7505	0.881509
$281$	17.9021	1.06795	0.533974	−	0.845501i	$-0.320698\pi$
$281$	17.9021	1.06795	0.533974	+	0.845501i	$0.320698\pi$
$282$	10.9098	0.649671
$283$	23.5850	1.40199	0.700993	−	0.713169i	$-0.252741\pi$
$283$	23.5850	1.40199	0.700993	+	0.713169i	$0.252741\pi$
$284$	−12.4867	−0.740950
$285$	−39.4980	−2.33966
$286$	−5.07788	−0.300261
$287$	14.1377	0.834524
$288$	−3.65168	−0.215177
$289$	−13.3149	−0.783229
$290$	−8.04187	−0.472235
$291$	11.3458	0.665102
$292$	7.43375	0.435028
$293$	−15.4132	−0.900451	−0.450226	−	0.892915i	$-0.648656\pi$
$293$	−15.4132	−0.900451	−0.450226	+	0.892915i	$0.648656\pi$
$294$	−37.3720	−2.17958
$295$	−39.0698	−2.27473
$296$	−0.765306	−0.0444825
$297$	−2.12530	−0.123322
$298$	12.9435	0.749795
$299$	−4.01571	−0.232235
$300$	13.2161	0.763032
$301$	56.6900	3.26756
$302$	0.198299	0.0114108
$303$	−14.3990	−0.827203
$304$	−4.81311	−0.276051
$305$	23.1674	1.32656
$306$	−7.00999	−0.400735
$307$	−20.2983	−1.15848	−0.579242	−	0.815155i	$-0.696652\pi$
$307$	−20.2983	−1.15848	−0.579242	+	0.815155i	$0.696652\pi$
$308$	5.86196	0.334016
$309$	1.55551	0.0884898
$310$	−1.66138	−0.0943601
$311$	19.8432	1.12520	0.562601	−	0.826729i	$-0.309801\pi$
$311$	19.8432	1.12520	0.562601	+	0.826729i	$0.309801\pi$
$312$	10.3569	0.586342
$313$	25.1262	1.42022	0.710109	−	0.704092i	$-0.248646\pi$
$313$	25.1262	1.42022	0.710109	+	0.704092i	$0.248646\pi$
$314$	10.3105	0.581853
$315$	−53.8640	−3.03489
$316$	−8.28540	−0.466090
$317$	12.4634	0.700014	0.350007	−	0.936747i	$-0.386179\pi$
$317$	12.4634	0.700014	0.350007	+	0.936747i	$0.386179\pi$
$318$	−5.56504	−0.312072
$319$	−3.19591	−0.178936
$320$	3.18188	0.177872
$321$	20.1823	1.12646
$322$	4.63578	0.258342
$323$	−9.23955	−0.514102
$324$	−6.62028	−0.367793
$325$	−20.5778	−1.14145
$326$	−16.1906	−0.896715
$327$	17.9031	0.990044
$328$	3.04970	0.168392
$329$	19.6099	1.08113
$330$	10.3769	0.571231
$331$	0.508882	0.0279707	0.0139853	−	0.999902i	$-0.495548\pi$
$331$	0.508882	0.0279707	0.0139853	+	0.999902i	$0.495548\pi$
$332$	−12.4279	−0.682070
$333$	2.79465	0.153146
$334$	7.78187	0.425805
$335$	0.323584	0.0176793
$336$	−11.9561	−0.652257
$337$	5.04420	0.274775	0.137387	−	0.990517i	$-0.456129\pi$
$337$	5.04420	0.274775	0.137387	+	0.990517i	$0.456129\pi$
$338$	−3.12593	−0.170028
$339$	16.2067	0.880226
$340$	6.10813	0.331260
$341$	−0.660247	−0.0357544
$342$	17.5759	0.950398
$343$	−34.7240	−1.87492
$344$	12.2288	0.659333
$345$	8.20633	0.441814
$346$	−18.0854	−0.972278
$347$	25.9834	1.39486	0.697432	−	0.716651i	$-0.254326\pi$
$347$	25.9834	1.39486	0.697432	+	0.716651i	$0.254326\pi$
$348$	6.51838	0.349422
$349$	6.97080	0.373139	0.186569	−	0.982442i	$-0.440263\pi$
$349$	6.97080	0.373139	0.186569	+	0.982442i	$0.440263\pi$
$350$	23.7553	1.26977
$351$	−6.74935	−0.360254
$352$	1.26450	0.0673983
$353$	−22.1200	−1.17733	−0.588664	−	0.808378i	$-0.700346\pi$
$353$	−22.1200	−1.17733	−0.588664	+	0.808378i	$0.700346\pi$
$354$	31.6682	1.68315
$355$	−39.7312	−2.10871
$356$	12.0434	0.638300
$357$	−22.9516	−1.21473
$358$	4.73453	0.250227
$359$	16.8468	0.889141	0.444570	−	0.895744i	$-0.353356\pi$
$359$	16.8468	0.889141	0.444570	+	0.895744i	$0.353356\pi$
$360$	−11.6192	−0.612385
$361$	4.16602	0.219264
$362$	10.9668	0.576404
$363$	−24.2461	−1.27259
$364$	18.6159	0.975740
$365$	23.6533	1.23807
$366$	−18.7784	−0.981564
$367$	18.6376	0.972874	0.486437	−	0.873716i	$-0.338296\pi$
$367$	18.6376	0.972874	0.486437	+	0.873716i	$0.338296\pi$
$368$	1.00000	0.0521286
$369$	−11.1365	−0.579744
$370$	−2.43511	−0.126595
$371$	−10.0029	−0.519323
$372$	1.34664	0.0698201
$373$	4.41732	0.228720	0.114360	−	0.993439i	$-0.463518\pi$
$373$	4.41732	0.228720	0.114360	+	0.993439i	$0.463518\pi$
$374$	2.42742	0.125519
$375$	1.02034	0.0526903
$376$	4.23012	0.218152
$377$	−10.1493	−0.522716
$378$	7.79152	0.400753
$379$	3.49439	0.179495	0.0897473	−	0.995965i	$-0.471394\pi$
$379$	3.49439	0.179495	0.0897473	+	0.995965i	$0.471394\pi$
$380$	−15.3147	−0.785629
$381$	−5.00708	−0.256520
$382$	0.598396	0.0306166
$383$	−7.54019	−0.385286	−0.192643	−	0.981269i	$-0.561706\pi$
$383$	−7.54019	−0.385286	−0.192643	+	0.981269i	$0.561706\pi$
$384$	−2.57908	−0.131613
$385$	18.6520	0.950595
$386$	−17.0801	−0.869355
$387$	−44.6557	−2.26998
$388$	4.39915	0.223333
$389$	19.3998	0.983608	0.491804	−	0.870706i	$-0.336338\pi$
$389$	19.3998	0.983608	0.491804	+	0.870706i	$0.336338\pi$
$390$	32.9542	1.66870
$391$	1.91966	0.0970815
$392$	−14.4904	−0.731877
$393$	2.57908	0.130098
$394$	17.2637	0.869734
$395$	−26.3631	−1.32647
$396$	−4.61756	−0.232041
$397$	12.9038	0.647626	0.323813	−	0.946121i	$-0.395035\pi$
$397$	12.9038	0.647626	0.323813	+	0.946121i	$0.395035\pi$
$398$	−2.97675	−0.149211
$399$	57.5458	2.88090
$400$	5.12434	0.256217
$401$	8.17899	0.408439	0.204220	−	0.978925i	$-0.434534\pi$
$401$	8.17899	0.408439	0.204220	+	0.978925i	$0.434534\pi$
$402$	−0.262283	−0.0130815
$403$	−2.09676	−0.104447
$404$	−5.58300	−0.277765
$405$	−21.0649	−1.04672
$406$	11.7165	0.581478
$407$	−0.967732	−0.0479687
$408$	−4.95097	−0.245110
$409$	−7.02918	−0.347571	−0.173785	−	0.984784i	$-0.555600\pi$
$409$	−7.02918	−0.347571	−0.173785	+	0.984784i	$0.555600\pi$
$410$	9.70377	0.479235
$411$	−39.9781	−1.97197
$412$	0.603124	0.0297138
$413$	56.9221	2.80095
$414$	−3.65168	−0.179470
$415$	−39.5441	−1.94114
$416$	4.01571	0.196886
$417$	−42.8084	−2.09634
$418$	−6.08620	−0.297686
$419$	−16.6286	−0.812359	−0.406180	−	0.913793i	$-0.633139\pi$
$419$	−16.6286	−0.812359	−0.406180	+	0.913793i	$0.633139\pi$
$420$	−38.0427	−1.85629
$421$	−17.8737	−0.871110	−0.435555	−	0.900162i	$-0.643448\pi$
$421$	−17.8737	−0.871110	−0.435555	+	0.900162i	$0.643448\pi$
$422$	−9.20716	−0.448198
$423$	−15.4470	−0.751061
$424$	−2.15776	−0.104790
$425$	9.83700	0.477164
$426$	32.2043	1.56030
$427$	−33.7533	−1.63344
$428$	7.82536	0.378253
$429$	13.0963	0.632295
$430$	38.9106	1.87643
$431$	35.7376	1.72142	0.860709	−	0.509097i	$-0.170020\pi$
$431$	35.7376	1.72142	0.860709	+	0.509097i	$0.170020\pi$
$432$	1.68074	0.0808645
$433$	30.6289	1.47193	0.735965	−	0.677019i	$-0.236729\pi$
$433$	30.6289	1.47193	0.735965	+	0.677019i	$0.236729\pi$
$434$	2.42052	0.116189
$435$	20.7407	0.994439
$436$	6.94165	0.332445
$437$	−4.81311	−0.230242
$438$	−19.1723	−0.916087
$439$	14.6975	0.701475	0.350738	−	0.936474i	$-0.385931\pi$
$439$	14.6975	0.701475	0.350738	+	0.936474i	$0.385931\pi$
$440$	4.02349	0.191813
$441$	52.9144	2.51973
$442$	7.70881	0.366671
$443$	4.38204	0.208197	0.104099	−	0.994567i	$-0.466804\pi$
$443$	4.38204	0.208197	0.104099	+	0.994567i	$0.466804\pi$
$444$	1.97379	0.0936718
$445$	38.3207	1.81657
$446$	−5.35944	−0.253777
$447$	−33.3823	−1.57893
$448$	−4.63578	−0.219020
$449$	6.94912	0.327949	0.163975	−	0.986465i	$-0.447568\pi$
$449$	6.94912	0.327949	0.163975	+	0.986465i	$0.447568\pi$
$450$	−18.7124	−0.882113
$451$	3.85636	0.181589
$452$	6.28389	0.295569
$453$	−0.511429	−0.0240290
$454$	12.7222	0.597080
$455$	59.2336	2.77691
$456$	12.4134	0.581312
$457$	21.2429	0.993699	0.496849	−	0.867837i	$-0.334490\pi$
$457$	21.2429	0.993699	0.496849	+	0.867837i	$0.334490\pi$
$458$	21.3443	0.997354
$459$	3.22645	0.150598
$460$	3.18188	0.148356
$461$	3.90486	0.181867	0.0909337	−	0.995857i	$-0.471015\pi$
$461$	3.90486	0.181867	0.0909337	+	0.995857i	$0.471015\pi$
$462$	−15.1185	−0.703376
$463$	28.1482	1.30816	0.654079	−	0.756426i	$-0.273056\pi$
$463$	28.1482	1.30816	0.654079	+	0.756426i	$0.273056\pi$
$464$	2.52740	0.117332
$465$	4.28484	0.198705
$466$	17.6050	0.815536
$467$	12.7575	0.590347	0.295173	−	0.955444i	$-0.404623\pi$
$467$	12.7575	0.590347	0.295173	+	0.955444i	$0.404623\pi$
$468$	−14.6641	−0.677848
$469$	−0.471440	−0.0217691
$470$	13.4597	0.620850
$471$	−26.5916	−1.22528
$472$	12.2789	0.565181
$473$	15.4634	0.711007
$474$	21.3688	0.981500
$475$	−24.6640	−1.13166
$476$	−8.89913	−0.407891
$477$	7.87943	0.360774
$478$	9.43941	0.431749
$479$	24.6827	1.12778	0.563891	−	0.825849i	$-0.309304\pi$
$479$	24.6827	1.12778	0.563891	+	0.825849i	$0.309304\pi$
$480$	−8.20633	−0.374566
$481$	−3.07325	−0.140128
$482$	14.6685	0.668134
$483$	−11.9561	−0.544020
$484$	−9.40103	−0.427320
$485$	13.9976	0.635596
$486$	22.1165	1.00322
$487$	−0.455052	−0.0206204	−0.0103102	−	0.999947i	$-0.503282\pi$
$487$	−0.455052	−0.0206204	−0.0103102	+	0.999947i	$0.503282\pi$
$488$	−7.28104	−0.329597
$489$	41.7569	1.88831
$490$	−46.1068	−2.08289
$491$	−41.4264	−1.86955	−0.934773	−	0.355246i	$-0.884397\pi$
$491$	−41.4264	−1.86955	−0.934773	+	0.355246i	$0.884397\pi$
$492$	−7.86544	−0.354601
$493$	4.85175	0.218512
$494$	−19.3281	−0.869610
$495$	−14.6925	−0.660379
$496$	0.522139	0.0234447
$497$	57.8856	2.59653
$498$	32.0526	1.43631
$499$	36.2491	1.62273	0.811367	−	0.584537i	$-0.198724\pi$
$499$	36.2491	1.62273	0.811367	+	0.584537i	$0.198724\pi$
$500$	0.395623	0.0176928
$501$	−20.0701	−0.896666
$502$	−6.81039	−0.303962
$503$	25.4110	1.13302	0.566511	−	0.824054i	$-0.308293\pi$
$503$	25.4110	1.13302	0.566511	+	0.824054i	$0.308293\pi$
$504$	16.9284	0.754050
$505$	−17.7644	−0.790507
$506$	1.26450	0.0562141
$507$	8.06203	0.358047
$508$	−1.94142	−0.0861365
$509$	5.51587	0.244487	0.122243	−	0.992500i	$-0.460991\pi$
$509$	5.51587	0.244487	0.122243	+	0.992500i	$0.460991\pi$
$510$	−15.7534	−0.697572
$511$	−34.4612	−1.52447
$512$	−1.00000	−0.0441942
$513$	−8.08957	−0.357163
$514$	−3.89974	−0.172010
$515$	1.91907	0.0845642
$516$	−31.5391	−1.38843
$517$	5.34900	0.235249
$518$	3.54779	0.155881
$519$	46.6438	2.04744
$520$	12.7775	0.560330
$521$	36.4421	1.59656	0.798279	−	0.602287i	$-0.205744\pi$
$521$	36.4421	1.59656	0.798279	+	0.602287i	$0.205744\pi$
$522$	−9.22925	−0.403953
$523$	25.9366	1.13413	0.567064	−	0.823674i	$-0.308079\pi$
$523$	25.9366	1.13413	0.567064	+	0.823674i	$0.308079\pi$
$524$	1.00000	0.0436852
$525$	−61.2669	−2.67391
$526$	−27.1329	−1.18305
$527$	1.00233	0.0436622
$528$	−3.26126	−0.141928
$529$	1.00000	0.0434783
$530$	−6.86571	−0.298227
$531$	−44.8385	−1.94583
$532$	22.3125	0.967370
$533$	12.2467	0.530464
$534$	−31.0610	−1.34414
$535$	24.8993	1.07649
$536$	−0.101696	−0.00439260
$537$	−12.2107	−0.526932
$538$	27.3085	1.17735
$539$	−18.3232	−0.789236
$540$	5.34790	0.230137
$541$	−36.7916	−1.58180	−0.790898	−	0.611948i	$-0.790386\pi$
$541$	−36.7916	−1.58180	−0.790898	+	0.611948i	$0.790386\pi$
$542$	−15.6380	−0.671709
$543$	−28.2844	−1.21380
$544$	−1.91966	−0.0823049
$545$	22.0875	0.946123
$546$	−48.0121	−2.05473
$547$	−32.4155	−1.38599	−0.692994	−	0.720943i	$-0.743709\pi$
$547$	−32.4155	−1.38599	−0.692994	+	0.720943i	$0.743709\pi$
$548$	−15.5009	−0.662165
$549$	26.5880	1.13475
$550$	6.47974	0.276297
$551$	−12.1646	−0.518231
$552$	−2.57908	−0.109773
$553$	38.4093	1.63333
$554$	5.00116	0.212479
$555$	6.28035	0.266586
$556$	−16.5983	−0.703924
$557$	−14.2555	−0.604027	−0.302013	−	0.953304i	$-0.597659\pi$
$557$	−14.2555	−0.604027	−0.302013	+	0.953304i	$0.597659\pi$
$558$	−1.90668	−0.0807164
$559$	49.1073	2.07702
$560$	−14.7505	−0.623321
$561$	−6.26052	−0.264320
$562$	−17.9021	−0.755153
$563$	−35.0677	−1.47793	−0.738963	−	0.673746i	$-0.764684\pi$
$563$	−35.0677	−1.47793	−0.738963	+	0.673746i	$0.764684\pi$
$564$	−10.9098	−0.459387
$565$	19.9945	0.841177
$566$	−23.5850	−0.991353
$567$	30.6901	1.28886
$568$	12.4867	0.523931
$569$	−41.0737	−1.72190	−0.860949	−	0.508691i	$-0.830129\pi$
$569$	−41.0737	−1.72190	−0.860949	+	0.508691i	$0.830129\pi$
$570$	39.4980	1.65439
$571$	−24.7840	−1.03718	−0.518589	−	0.855023i	$-0.673543\pi$
$571$	−24.7840	−1.03718	−0.518589	+	0.855023i	$0.673543\pi$
$572$	5.07788	0.212317
$573$	−1.54331	−0.0644729
$574$	−14.1377	−0.590097
$575$	5.12434	0.213700
$576$	3.65168	0.152153
$577$	−3.85857	−0.160634	−0.0803172	−	0.996769i	$-0.525593\pi$
$577$	−3.85857	−0.160634	−0.0803172	+	0.996769i	$0.525593\pi$
$578$	13.3149	0.553827
$579$	44.0511	1.83070
$580$	8.04187	0.333921
$581$	57.6130	2.39019
$582$	−11.3458	−0.470298
$583$	−2.72849	−0.113003
$584$	−7.43375	−0.307611
$585$	−46.6593	−1.92912
$586$	15.4132	0.636715
$587$	−6.70358	−0.276686	−0.138343	−	0.990384i	$-0.544178\pi$
$587$	−6.70358	−0.276686	−0.138343	+	0.990384i	$0.544178\pi$
$588$	37.3720	1.54120
$589$	−2.51311	−0.103551
$590$	39.0698	1.60848
$591$	−44.5246	−1.83150
$592$	0.765306	0.0314539
$593$	−0.728522	−0.0299168	−0.0149584	−	0.999888i	$-0.504762\pi$
$593$	−0.728522	−0.0299168	−0.0149584	+	0.999888i	$0.504762\pi$
$594$	2.12530	0.0872020
$595$	−28.3159	−1.16084
$596$	−12.9435	−0.530185
$597$	7.67729	0.314211
$598$	4.01571	0.164215
$599$	−7.03375	−0.287391	−0.143696	−	0.989622i	$-0.545899\pi$
$599$	−7.03375	−0.287391	−0.143696	+	0.989622i	$0.545899\pi$
$600$	−13.2161	−0.539545
$601$	−34.3904	−1.40281	−0.701406	−	0.712762i	$-0.747444\pi$
$601$	−34.3904	−1.40281	−0.701406	+	0.712762i	$0.747444\pi$
$602$	−56.6900	−2.31051
$603$	0.371361	0.0151230
$604$	−0.198299	−0.00806866
$605$	−29.9129	−1.21613
$606$	14.3990	0.584921
$607$	−11.2417	−0.456285	−0.228143	−	0.973628i	$-0.573265\pi$
$607$	−11.2417	−0.456285	−0.228143	+	0.973628i	$0.573265\pi$
$608$	4.81311	0.195197
$609$	−30.2177	−1.22448
$610$	−23.1674	−0.938019
$611$	16.9869	0.687218
$612$	7.00999	0.283362
$613$	−16.6393	−0.672054	−0.336027	−	0.941852i	$-0.609083\pi$
$613$	−16.6393	−0.672054	−0.336027	+	0.941852i	$0.609083\pi$
$614$	20.2983	0.819172
$615$	−25.0268	−1.00918
$616$	−5.86196	−0.236185
$617$	−11.3528	−0.457046	−0.228523	−	0.973539i	$-0.573390\pi$
$617$	−11.3528	−0.457046	−0.228523	+	0.973539i	$0.573390\pi$
$618$	−1.55551	−0.0625717
$619$	−32.8619	−1.32083	−0.660416	−	0.750900i	$-0.729620\pi$
$619$	−32.8619	−1.32083	−0.660416	+	0.750900i	$0.729620\pi$
$620$	1.66138	0.0667227
$621$	1.68074	0.0674456
$622$	−19.8432	−0.795638
$623$	−55.8306	−2.23681
$624$	−10.3569	−0.414606
$625$	−24.3629	−0.974514
$626$	−25.1262	−1.00425
$627$	15.6968	0.626870
$628$	−10.3105	−0.411432
$629$	1.46913	0.0585780
$630$	53.8640	2.14599
$631$	50.0763	1.99351	0.996754	−	0.0805085i	$-0.0256544\pi$
$631$	50.0763	1.99351	0.996754	+	0.0805085i	$0.0256544\pi$
$632$	8.28540	0.329576
$633$	23.7461	0.943821
$634$	−12.4634	−0.494985
$635$	−6.17735	−0.245141
$636$	5.56504	0.220668
$637$	−58.1894	−2.30555
$638$	3.19591	0.126527
$639$	−45.5975	−1.80381
$640$	−3.18188	−0.125775
$641$	14.7646	0.583166	0.291583	−	0.956545i	$-0.405818\pi$
$641$	14.7646	0.583166	0.291583	+	0.956545i	$0.405818\pi$
$642$	−20.1823	−0.796531
$643$	−20.9006	−0.824239	−0.412119	−	0.911130i	$-0.635211\pi$
$643$	−20.9006	−0.824239	−0.412119	+	0.911130i	$0.635211\pi$
$644$	−4.63578	−0.182675
$645$	−100.354	−3.95142
$646$	9.23955	0.363525
$647$	33.6407	1.32255	0.661277	−	0.750142i	$-0.270015\pi$
$647$	33.6407	1.32255	0.661277	+	0.750142i	$0.270015\pi$
$648$	6.62028	0.260069
$649$	15.5267	0.609475
$650$	20.5778	0.807130
$651$	−6.24272	−0.244672
$652$	16.1906	0.634073
$653$	36.3428	1.42220	0.711101	−	0.703089i	$-0.248197\pi$
$653$	36.3428	1.42220	0.711101	+	0.703089i	$0.248197\pi$
$654$	−17.9031	−0.700067
$655$	3.18188	0.124326
$656$	−3.04970	−0.119071
$657$	27.1457	1.05905
$658$	−19.6099	−0.764473
$659$	−17.6843	−0.688884	−0.344442	−	0.938808i	$-0.611932\pi$
$659$	−17.6843	−0.688884	−0.344442	+	0.938808i	$0.611932\pi$
$660$	−10.3769	−0.403922
$661$	−0.661145	−0.0257156	−0.0128578	−	0.999917i	$-0.504093\pi$
$661$	−0.661145	−0.0257156	−0.0128578	+	0.999917i	$0.504093\pi$
$662$	−0.508882	−0.0197782
$663$	−19.8817	−0.772140
$664$	12.4279	0.482296
$665$	70.9956	2.75309
$666$	−2.79465	−0.108291
$667$	2.52740	0.0978613
$668$	−7.78187	−0.301090
$669$	13.8225	0.534407
$670$	−0.323584	−0.0125012
$671$	−9.20690	−0.355429
$672$	11.9561	0.461215
$673$	−4.04884	−0.156071	−0.0780356	−	0.996951i	$-0.524865\pi$
$673$	−4.04884	−0.156071	−0.0780356	+	0.996951i	$0.524865\pi$
$674$	−5.04420	−0.194295
$675$	8.61266	0.331501
$676$	3.12593	0.120228
$677$	−14.7033	−0.565092	−0.282546	−	0.959254i	$-0.591179\pi$
$677$	−14.7033	−0.565092	−0.282546	+	0.959254i	$0.591179\pi$
$678$	−16.2067	−0.622414
$679$	−20.3935	−0.782630
$680$	−6.10813	−0.234236
$681$	−32.8115	−1.25734
$682$	0.660247	0.0252821
$683$	−36.1811	−1.38443	−0.692216	−	0.721690i	$-0.743365\pi$
$683$	−36.1811	−1.38443	−0.692216	+	0.721690i	$0.743365\pi$
$684$	−17.5759	−0.672033
$685$	−49.3219	−1.88449
$686$	34.7240	1.32577
$687$	−55.0488	−2.10024
$688$	−12.2288	−0.466219
$689$	−8.66492	−0.330107
$690$	−8.20633	−0.312410
$691$	−17.7820	−0.676457	−0.338229	−	0.941064i	$-0.609828\pi$
$691$	−17.7820	−0.676457	−0.338229	+	0.941064i	$0.609828\pi$
$692$	18.0854	0.687504
$693$	21.4060	0.813146
$694$	−25.9834	−0.986318
$695$	−52.8137	−2.00334
$696$	−6.51838	−0.247078
$697$	−5.85439	−0.221751
$698$	−6.97080	−0.263849
$699$	−45.4048	−1.71737
$700$	−23.7553	−0.897865
$701$	32.8207	1.23962	0.619811	−	0.784751i	$-0.287209\pi$
$701$	32.8207	1.23962	0.619811	+	0.784751i	$0.287209\pi$
$702$	6.74935	0.254738
$703$	−3.68350	−0.138926
$704$	−1.26450	−0.0476578
$705$	−34.7138	−1.30740
$706$	22.1200	0.832496
$707$	25.8816	0.973376
$708$	−31.6682	−1.19017
$709$	12.9070	0.484733	0.242367	−	0.970185i	$-0.422076\pi$
$709$	12.9070	0.484733	0.242367	+	0.970185i	$0.422076\pi$
$710$	39.7312	1.49108
$711$	−30.2556	−1.13468
$712$	−12.0434	−0.451346
$713$	0.522139	0.0195543
$714$	22.9516	0.858942
$715$	16.1572	0.604245
$716$	−4.73453	−0.176938
$717$	−24.3450	−0.909182
$718$	−16.8468	−0.628717
$719$	2.76708	0.103194	0.0515972	−	0.998668i	$-0.483569\pi$
$719$	2.76708	0.103194	0.0515972	+	0.998668i	$0.483569\pi$
$720$	11.6192	0.433022
$721$	−2.79595	−0.104127
$722$	−4.16602	−0.155043
$723$	−37.8314	−1.40697
$724$	−10.9668	−0.407579
$725$	12.9512	0.480997
$726$	24.2461	0.899856
$727$	−12.9705	−0.481048	−0.240524	−	0.970643i	$-0.577319\pi$
$727$	−12.9705	−0.481048	−0.240524	+	0.970643i	$0.577319\pi$
$728$	−18.6159	−0.689953
$729$	−37.1794	−1.37702
$730$	−23.6533	−0.875447
$731$	−23.4752	−0.868261
$732$	18.7784	0.694070
$733$	45.9892	1.69865	0.849325	−	0.527870i	$-0.177009\pi$
$733$	45.9892	1.69865	0.849325	+	0.527870i	$0.177009\pi$
$734$	−18.6376	−0.687926
$735$	118.913	4.38618
$736$	−1.00000	−0.0368605
$737$	−0.128595	−0.00473686
$738$	11.1365	0.409941
$739$	14.6396	0.538526	0.269263	−	0.963067i	$-0.413220\pi$
$739$	14.6396	0.538526	0.269263	+	0.963067i	$0.413220\pi$
$740$	2.43511	0.0895163
$741$	49.8487	1.83124
$742$	10.0029	0.367217
$743$	−1.84270	−0.0676021	−0.0338011	−	0.999429i	$-0.510761\pi$
$743$	−1.84270	−0.0676021	−0.0338011	+	0.999429i	$0.510761\pi$
$744$	−1.34664	−0.0493702
$745$	−41.1845	−1.50888
$746$	−4.41732	−0.161730
$747$	−45.3827	−1.66047
$748$	−2.42742	−0.0887553
$749$	−36.2766	−1.32552
$750$	−1.02034	−0.0372577
$751$	8.35688	0.304947	0.152473	−	0.988308i	$-0.451276\pi$
$751$	8.35688	0.304947	0.152473	+	0.988308i	$0.451276\pi$
$752$	−4.23012	−0.154257
$753$	17.5646	0.640088
$754$	10.1493	0.369616
$755$	−0.630962	−0.0229630
$756$	−7.79152	−0.283375
$757$	4.87006	0.177005	0.0885027	−	0.996076i	$-0.471792\pi$
$757$	4.87006	0.177005	0.0885027	+	0.996076i	$0.471792\pi$
$758$	−3.49439	−0.126922
$759$	−3.26126	−0.118376
$760$	15.3147	0.555523
$761$	17.6309	0.639118	0.319559	−	0.947566i	$-0.396465\pi$
$761$	17.6309	0.639118	0.319559	+	0.947566i	$0.396465\pi$
$762$	5.00708	0.181387
$763$	−32.1799	−1.16499
$764$	−0.598396	−0.0216492
$765$	22.3049	0.806436
$766$	7.54019	0.272438
$767$	49.3084	1.78042
$768$	2.57908	0.0930647
$769$	−23.7617	−0.856870	−0.428435	−	0.903573i	$-0.640935\pi$
$769$	−23.7617	−0.856870	−0.428435	+	0.903573i	$0.640935\pi$
$770$	−18.6520	−0.672172
$771$	10.0578	0.362221
$772$	17.0801	0.614727
$773$	30.7698	1.10671	0.553356	−	0.832945i	$-0.313347\pi$
$773$	30.7698	1.10671	0.553356	+	0.832945i	$0.313347\pi$
$774$	44.6557	1.60512
$775$	2.67561	0.0961109
$776$	−4.39915	−0.157920
$777$	−9.15004	−0.328256
$778$	−19.3998	−0.695516
$779$	14.6785	0.525913
$780$	−32.9542	−1.17995
$781$	15.7895	0.564993
$782$	−1.91966	−0.0686470
$783$	4.24789	0.151807
$784$	14.4904	0.517515
$785$	−32.8066	−1.17092
$786$	−2.57908	−0.0919929
$787$	13.8216	0.492688	0.246344	−	0.969182i	$-0.420771\pi$
$787$	13.8216	0.492688	0.246344	+	0.969182i	$0.420771\pi$
$788$	−17.2637	−0.614995
$789$	69.9781	2.49129
$790$	26.3631	0.937958
$791$	−29.1307	−1.03577
$792$	4.61756	0.164078
$793$	−29.2385	−1.03829
$794$	−12.9038	−0.457940
$795$	17.7073	0.628012
$796$	2.97675	0.105508
$797$	−44.3676	−1.57158	−0.785790	−	0.618494i	$-0.787743\pi$
$797$	−44.3676	−1.57158	−0.785790	+	0.618494i	$0.787743\pi$
$798$	−57.5458	−2.03710
$799$	−8.12040	−0.287279
$800$	−5.12434	−0.181173
$801$	43.9787	1.55391
$802$	−8.17899	−0.288810
$803$	−9.40001	−0.331719
$804$	0.262283	0.00925000
$805$	−14.7505	−0.519886
$806$	2.09676	0.0738552
$807$	−70.4309	−2.47929
$808$	5.58300	0.196409
$809$	37.7839	1.32841	0.664205	−	0.747550i	$-0.268770\pi$
$809$	37.7839	1.32841	0.664205	+	0.747550i	$0.268770\pi$
$810$	21.0649	0.740145
$811$	−42.2368	−1.48313	−0.741567	−	0.670879i	$-0.765917\pi$
$811$	−42.2368	−1.48313	−0.741567	+	0.670879i	$0.765917\pi$
$812$	−11.7165	−0.411167
$813$	40.3317	1.41449
$814$	0.967732	0.0339190
$815$	51.5165	1.80454
$816$	4.95097	0.173319
$817$	58.8586	2.05920
$818$	7.02918	0.245770
$819$	67.9794	2.37539
$820$	−9.70377	−0.338870
$821$	−45.1451	−1.57557	−0.787787	−	0.615948i	$-0.788773\pi$
$821$	−45.1451	−1.57557	−0.787787	+	0.615948i	$0.788773\pi$
$822$	39.9781	1.39440
$823$	−47.1420	−1.64327	−0.821634	−	0.570015i	$-0.806937\pi$
$823$	−47.1420	−1.64327	−0.821634	+	0.570015i	$0.806937\pi$
$824$	−0.603124	−0.0210108
$825$	−16.7118	−0.581830
$826$	−56.9221	−1.98057
$827$	1.71919	0.0597820	0.0298910	−	0.999553i	$-0.490484\pi$
$827$	1.71919	0.0597820	0.0298910	+	0.999553i	$0.490484\pi$
$828$	3.65168	0.126905
$829$	−30.6313	−1.06387	−0.531935	−	0.846785i	$-0.678535\pi$
$829$	−30.6313	−1.06387	−0.531935	+	0.846785i	$0.678535\pi$
$830$	39.5441	1.37259
$831$	−12.8984	−0.447441
$832$	−4.01571	−0.139220
$833$	27.8167	0.963793
$834$	42.8084	1.48233
$835$	−24.7610	−0.856888
$836$	6.08620	0.210495
$837$	0.877578	0.0303335
$838$	16.6286	0.574425
$839$	−24.3648	−0.841167	−0.420583	−	0.907254i	$-0.638175\pi$
$839$	−24.3648	−0.841167	−0.420583	+	0.907254i	$0.638175\pi$
$840$	38.0427	1.31260
$841$	−22.6123	−0.779733
$842$	17.8737	0.615968
$843$	46.1710	1.59021
$844$	9.20716	0.316924
$845$	9.94631	0.342164
$846$	15.4470	0.531080
$847$	43.5811	1.49746
$848$	2.15776	0.0740976
$849$	60.8278	2.08761
$850$	−9.83700	−0.337406
$851$	0.765306	0.0262343
$852$	−32.2043	−1.10330
$853$	−16.5561	−0.566869	−0.283435	−	0.958992i	$-0.591474\pi$
$853$	−16.5561	−0.566869	−0.283435	+	0.958992i	$0.591474\pi$
$854$	33.7533	1.15501
$855$	−55.9244	−1.91258
$856$	−7.82536	−0.267465
$857$	−9.09095	−0.310541	−0.155271	−	0.987872i	$-0.549625\pi$
$857$	−9.09095	−0.310541	−0.155271	+	0.987872i	$0.549625\pi$
$858$	−13.0963	−0.447100
$859$	53.2686	1.81750	0.908750	−	0.417340i	$-0.137038\pi$
$859$	53.2686	1.81750	0.908750	+	0.417340i	$0.137038\pi$
$860$	−38.9106	−1.32684
$861$	36.4624	1.24264
$862$	−35.7376	−1.21723
$863$	27.6330	0.940638	0.470319	−	0.882496i	$-0.344139\pi$
$863$	27.6330	0.940638	0.470319	+	0.882496i	$0.344139\pi$
$864$	−1.68074	−0.0571798
$865$	57.5456	1.95661
$866$	−30.6289	−1.04081
$867$	−34.3402	−1.16626
$868$	−2.42052	−0.0821578
$869$	10.4769	0.355405
$870$	−20.7407	−0.703175
$871$	−0.408382	−0.0138375
$872$	−6.94165	−0.235074
$873$	16.0643	0.543694
$874$	4.81311	0.162806
$875$	−1.83402	−0.0620011
$876$	19.1723	0.647771
$877$	−3.57180	−0.120611	−0.0603056	−	0.998180i	$-0.519208\pi$
$877$	−3.57180	−0.120611	−0.0603056	+	0.998180i	$0.519208\pi$
$878$	−14.6975	−0.496018
$879$	−39.7521	−1.34080
$880$	−4.02349	−0.135632
$881$	−48.8597	−1.64613	−0.823063	−	0.567950i	$-0.807737\pi$
$881$	−48.8597	−1.64613	−0.823063	+	0.567950i	$0.807737\pi$
$882$	−52.9144	−1.78172
$883$	38.1933	1.28531	0.642654	−	0.766157i	$-0.277833\pi$
$883$	38.1933	1.28531	0.642654	+	0.766157i	$0.277833\pi$
$884$	−7.70881	−0.259275
$885$	−100.764	−3.38716
$886$	−4.38204	−0.147218
$887$	38.3584	1.28795	0.643975	−	0.765047i	$-0.277284\pi$
$887$	38.3584	1.28795	0.643975	+	0.765047i	$0.277284\pi$
$888$	−1.97379	−0.0662360
$889$	8.99998	0.301850
$890$	−38.3207	−1.28451
$891$	8.37136	0.280451
$892$	5.35944	0.179447
$893$	20.3600	0.681322
$894$	33.3823	1.11647
$895$	−15.0647	−0.503557
$896$	4.63578	0.154870
$897$	−10.3569	−0.345805
$898$	−6.94912	−0.231895
$899$	1.31965	0.0440129
$900$	18.7124	0.623748
$901$	4.14216	0.137995
$902$	−3.85636	−0.128403
$903$	146.208	4.86551
$904$	−6.28389	−0.208999
$905$	−34.8951	−1.15995
$906$	0.511429	0.0169911
$907$	21.5233	0.714671	0.357335	−	0.933976i	$-0.383685\pi$
$907$	21.5233	0.714671	0.357335	+	0.933976i	$0.383685\pi$
$908$	−12.7222	−0.422200
$909$	−20.3873	−0.676205
$910$	−59.2336	−1.96357
$911$	4.50726	0.149332	0.0746661	−	0.997209i	$-0.476211\pi$
$911$	4.50726	0.149332	0.0746661	+	0.997209i	$0.476211\pi$
$912$	−12.4134	−0.411049
$913$	15.7151	0.520095
$914$	−21.2429	−0.702651
$915$	59.7506	1.97529
$916$	−21.3443	−0.705236
$917$	−4.63578	−0.153087
$918$	−3.22645	−0.106489
$919$	18.5547	0.612064	0.306032	−	0.952021i	$-0.400999\pi$
$919$	18.5547	0.612064	0.306032	+	0.952021i	$0.400999\pi$
$920$	−3.18188	−0.104903
$921$	−52.3510	−1.72502
$922$	−3.90486	−0.128600
$923$	50.1430	1.65048
$924$	15.1185	0.497362
$925$	3.92168	0.128944
$926$	−28.1482	−0.925007
$927$	2.20242	0.0723369
$928$	−2.52740	−0.0829659
$929$	−7.87506	−0.258372	−0.129186	−	0.991620i	$-0.541236\pi$
$929$	−7.87506	−0.258372	−0.129186	+	0.991620i	$0.541236\pi$
$930$	−4.28484	−0.140506
$931$	−69.7440	−2.28577
$932$	−17.6050	−0.576671
$933$	51.1772	1.67547
$934$	−12.7575	−0.417438
$935$	−7.72375	−0.252594
$936$	14.6641	0.479311
$937$	37.0266	1.20961	0.604803	−	0.796375i	$-0.293252\pi$
$937$	37.0266	1.20961	0.604803	+	0.796375i	$0.293252\pi$
$938$	0.471440	0.0153931
$939$	64.8027	2.11476
$940$	−13.4597	−0.439008
$941$	40.8063	1.33025	0.665123	−	0.746734i	$-0.268379\pi$
$941$	40.8063	1.33025	0.665123	+	0.746734i	$0.268379\pi$
$942$	26.5916	0.866400
$943$	−3.04970	−0.0993119
$944$	−12.2789	−0.399643
$945$	−24.7917	−0.806472
$946$	−15.4634	−0.502758
$947$	−28.9980	−0.942310	−0.471155	−	0.882051i	$-0.656163\pi$
$947$	−28.9980	−0.942310	−0.471155	+	0.882051i	$0.656163\pi$
$948$	−21.3688	−0.694025
$949$	−29.8518	−0.969030
$950$	24.6640	0.800206
$951$	32.1441	1.04235
$952$	8.89913	0.288422
$953$	−48.1869	−1.56093	−0.780464	−	0.625201i	$-0.785017\pi$
$953$	−48.1869	−1.56093	−0.780464	+	0.625201i	$0.785017\pi$
$954$	−7.87943	−0.255106
$955$	−1.90402	−0.0616127
$956$	−9.43941	−0.305292
$957$	−8.24251	−0.266443
$958$	−24.6827	−0.797463
$959$	71.8586	2.32044
$960$	8.20633	0.264858
$961$	−30.7274	−0.991206
$962$	3.07325	0.0990854
$963$	28.5757	0.920839
$964$	−14.6685	−0.472442
$965$	54.3468	1.74949
$966$	11.9561	0.384680
$967$	28.8554	0.927927	0.463964	−	0.885854i	$-0.346427\pi$
$967$	28.8554	0.927927	0.463964	+	0.885854i	$0.346427\pi$
$968$	9.40103	0.302161
$969$	−23.8296	−0.765516
$970$	−13.9976	−0.449435
$971$	28.2489	0.906551	0.453275	−	0.891371i	$-0.350255\pi$
$971$	28.2489	0.906551	0.453275	+	0.891371i	$0.350255\pi$
$972$	−22.1165	−0.709386
$973$	76.9460	2.46677
$974$	0.455052	0.0145808
$975$	−53.0720	−1.69966
$976$	7.28104	0.233060
$977$	−10.0988	−0.323089	−0.161545	−	0.986865i	$-0.551648\pi$
$977$	−10.0988	−0.323089	−0.161545	+	0.986865i	$0.551648\pi$
$978$	−41.7569	−1.33524
$979$	−15.2289	−0.486719
$980$	46.1068	1.47283
$981$	25.3487	0.809321
$982$	41.4264	1.32197
$983$	13.4860	0.430138	0.215069	−	0.976599i	$-0.431002\pi$
$983$	13.4860	0.430138	0.215069	+	0.976599i	$0.431002\pi$
$984$	7.86544	0.250741
$985$	−54.9311	−1.75025
$986$	−4.85175	−0.154511
$987$	50.5756	1.60984
$988$	19.3281	0.614907
$989$	−12.2288	−0.388853
$990$	14.6925	0.466959
$991$	−54.2132	−1.72214	−0.861069	−	0.508488i	$-0.830204\pi$
$991$	−54.2132	−1.72214	−0.861069	+	0.508488i	$0.830204\pi$
$992$	−0.522139	−0.0165779
$993$	1.31245	0.0416493
$994$	−57.8856	−1.83602
$995$	9.47165	0.300271
$996$	−32.0526	−1.01563
$997$	30.7947	0.975279	0.487639	−	0.873045i	$-0.337858\pi$
$997$	30.7947	0.975279	0.487639	+	0.873045i	$0.337858\pi$
$998$	−36.2491	−1.14745
$999$	1.28628	0.0406960

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6026.2.a.i.1.23	✓	25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6026.2.a.i.1.23	✓	25	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:	\( N \)	\(=\)	\( 6026 = 2 \cdot 23 \cdot 131 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6026.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +2.57908 q^{3} +1.00000 q^{4} +3.18188 q^{5} -2.57908 q^{6} -4.63578 q^{7} -1.00000 q^{8} +3.65168 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +2.57908 q^{3} +1.00000 q^{4} +3.18188 q^{5} -2.57908 q^{6} -4.63578 q^{7} -1.00000 q^{8} +3.65168 q^{9} -3.18188 q^{10} -1.26450 q^{11} +2.57908 q^{12} -4.01571 q^{13} +4.63578 q^{14} +8.20633 q^{15} +1.00000 q^{16} +1.91966 q^{17} -3.65168 q^{18} -4.81311 q^{19} +3.18188 q^{20} -11.9561 q^{21} +1.26450 q^{22} +1.00000 q^{23} -2.57908 q^{24} +5.12434 q^{25} +4.01571 q^{26} +1.68074 q^{27} -4.63578 q^{28} +2.52740 q^{29} -8.20633 q^{30} +0.522139 q^{31} -1.00000 q^{32} -3.26126 q^{33} -1.91966 q^{34} -14.7505 q^{35} +3.65168 q^{36} +0.765306 q^{37} +4.81311 q^{38} -10.3569 q^{39} -3.18188 q^{40} -3.04970 q^{41} +11.9561 q^{42} -12.2288 q^{43} -1.26450 q^{44} +11.6192 q^{45} -1.00000 q^{46} -4.23012 q^{47} +2.57908 q^{48} +14.4904 q^{49} -5.12434 q^{50} +4.95097 q^{51} -4.01571 q^{52} +2.15776 q^{53} -1.68074 q^{54} -4.02349 q^{55} +4.63578 q^{56} -12.4134 q^{57} -2.52740 q^{58} -12.2789 q^{59} +8.20633 q^{60} +7.28104 q^{61} -0.522139 q^{62} -16.9284 q^{63} +1.00000 q^{64} -12.7775 q^{65} +3.26126 q^{66} +0.101696 q^{67} +1.91966 q^{68} +2.57908 q^{69} +14.7505 q^{70} -12.4867 q^{71} -3.65168 q^{72} +7.43375 q^{73} -0.765306 q^{74} +13.2161 q^{75} -4.81311 q^{76} +5.86196 q^{77} +10.3569 q^{78} -8.28540 q^{79} +3.18188 q^{80} -6.62028 q^{81} +3.04970 q^{82} -12.4279 q^{83} -11.9561 q^{84} +6.10813 q^{85} +12.2288 q^{86} +6.51838 q^{87} +1.26450 q^{88} +12.0434 q^{89} -11.6192 q^{90} +18.6159 q^{91} +1.00000 q^{92} +1.34664 q^{93} +4.23012 q^{94} -15.3147 q^{95} -2.57908 q^{96} +4.39915 q^{97} -14.4904 q^{98} -4.61756 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q - 25 q^{2} - 4 q^{3} + 25 q^{4} - 3 q^{5} + 4 q^{6} - 11 q^{7} - 25 q^{8} + 19 q^{9}+O(q^{10}) \) 25 * q - 25 * q^2 - 4 * q^3 + 25 * q^4 - 3 * q^5 + 4 * q^6 - 11 * q^7 - 25 * q^8 + 19 * q^9	\( 25 q - 25 q^{2} - 4 q^{3} + 25 q^{4} - 3 q^{5} + 4 q^{6} - 11 q^{7} - 25 q^{8} + 19 q^{9} + 3 q^{10} - 12 q^{11} - 4 q^{12} - 6 q^{13} + 11 q^{14} + 25 q^{16} + 8 q^{17} - 19 q^{18} - 23 q^{19} - 3 q^{20} - 16 q^{21} + 12 q^{22} + 25 q^{23} + 4 q^{24} + 4 q^{25} + 6 q^{26} - 13 q^{27} - 11 q^{28} - 7 q^{29} - 7 q^{31} - 25 q^{32} + 3 q^{33} - 8 q^{34} - 18 q^{35} + 19 q^{36} - 7 q^{37} + 23 q^{38} - 2 q^{39} + 3 q^{40} - 10 q^{41} + 16 q^{42} - 26 q^{43} - 12 q^{44} + 20 q^{45} - 25 q^{46} - 2 q^{47} - 4 q^{48} + 2 q^{49} - 4 q^{50} - 28 q^{51} - 6 q^{52} + 47 q^{53} + 13 q^{54} - 38 q^{55} + 11 q^{56} - 4 q^{57} + 7 q^{58} - 19 q^{59} - 26 q^{61} + 7 q^{62} - 15 q^{63} + 25 q^{64} + 13 q^{65} - 3 q^{66} - 34 q^{67} + 8 q^{68} - 4 q^{69} + 18 q^{70} - 10 q^{71} - 19 q^{72} - 22 q^{73} + 7 q^{74} - 8 q^{75} - 23 q^{76} + 28 q^{77} + 2 q^{78} - 21 q^{79} - 3 q^{80} - 27 q^{81} + 10 q^{82} - 16 q^{83} - 16 q^{84} - 42 q^{85} + 26 q^{86} - 17 q^{87} + 12 q^{88} + 27 q^{89} - 20 q^{90} - 26 q^{91} + 25 q^{92} - 27 q^{93} + 2 q^{94} + 4 q^{96} + 4 q^{97} - 2 q^{98} - 2 q^{99}+O(q^{100}) \) 25 * q - 25 * q^2 - 4 * q^3 + 25 * q^4 - 3 * q^5 + 4 * q^6 - 11 * q^7 - 25 * q^8 + 19 * q^9 + 3 * q^10 - 12 * q^11 - 4 * q^12 - 6 * q^13 + 11 * q^14 + 25 * q^16 + 8 * q^17 - 19 * q^18 - 23 * q^19 - 3 * q^20 - 16 * q^21 + 12 * q^22 + 25 * q^23 + 4 * q^24 + 4 * q^25 + 6 * q^26 - 13 * q^27 - 11 * q^28 - 7 * q^29 - 7 * q^31 - 25 * q^32 + 3 * q^33 - 8 * q^34 - 18 * q^35 + 19 * q^36 - 7 * q^37 + 23 * q^38 - 2 * q^39 + 3 * q^40 - 10 * q^41 + 16 * q^42 - 26 * q^43 - 12 * q^44 + 20 * q^45 - 25 * q^46 - 2 * q^47 - 4 * q^48 + 2 * q^49 - 4 * q^50 - 28 * q^51 - 6 * q^52 + 47 * q^53 + 13 * q^54 - 38 * q^55 + 11 * q^56 - 4 * q^57 + 7 * q^58 - 19 * q^59 - 26 * q^61 + 7 * q^62 - 15 * q^63 + 25 * q^64 + 13 * q^65 - 3 * q^66 - 34 * q^67 + 8 * q^68 - 4 * q^69 + 18 * q^70 - 10 * q^71 - 19 * q^72 - 22 * q^73 + 7 * q^74 - 8 * q^75 - 23 * q^76 + 28 * q^77 + 2 * q^78 - 21 * q^79 - 3 * q^80 - 27 * q^81 + 10 * q^82 - 16 * q^83 - 16 * q^84 - 42 * q^85 + 26 * q^86 - 17 * q^87 + 12 * q^88 + 27 * q^89 - 20 * q^90 - 26 * q^91 + 25 * q^92 - 27 * q^93 + 2 * q^94 + 4 * q^96 + 4 * q^97 - 2 * q^98 - 2 * q^99

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