LMFDB - Embedded newform 6026.2.a.h.1.11

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:	$24$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
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)

$f(q)$	$=$	$q-1.00000 q^{2} -0.672761 q^{3} +1.00000 q^{4} -2.38352 q^{5} +0.672761 q^{6} -0.506434 q^{7} -1.00000 q^{8} -2.54739 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -0.672761 q^{3} +1.00000 q^{4} -2.38352 q^{5} +0.672761 q^{6} -0.506434 q^{7} -1.00000 q^{8} -2.54739 q^{9} +2.38352 q^{10} +1.82292 q^{11} -0.672761 q^{12} +1.61132 q^{13} +0.506434 q^{14} +1.60354 q^{15} +1.00000 q^{16} -5.88597 q^{17} +2.54739 q^{18} -3.78727 q^{19} -2.38352 q^{20} +0.340709 q^{21} -1.82292 q^{22} -1.00000 q^{23} +0.672761 q^{24} +0.681154 q^{25} -1.61132 q^{26} +3.73207 q^{27} -0.506434 q^{28} +9.57271 q^{29} -1.60354 q^{30} +4.60370 q^{31} -1.00000 q^{32} -1.22639 q^{33} +5.88597 q^{34} +1.20709 q^{35} -2.54739 q^{36} +8.91792 q^{37} +3.78727 q^{38} -1.08403 q^{39} +2.38352 q^{40} +11.6782 q^{41} -0.340709 q^{42} -6.39686 q^{43} +1.82292 q^{44} +6.07175 q^{45} +1.00000 q^{46} -1.18292 q^{47} -0.672761 q^{48} -6.74352 q^{49} -0.681154 q^{50} +3.95985 q^{51} +1.61132 q^{52} +2.70654 q^{53} -3.73207 q^{54} -4.34495 q^{55} +0.506434 q^{56} +2.54793 q^{57} -9.57271 q^{58} +8.49714 q^{59} +1.60354 q^{60} -9.41813 q^{61} -4.60370 q^{62} +1.29009 q^{63} +1.00000 q^{64} -3.84060 q^{65} +1.22639 q^{66} +9.70644 q^{67} -5.88597 q^{68} +0.672761 q^{69} -1.20709 q^{70} -7.20117 q^{71} +2.54739 q^{72} +0.843850 q^{73} -8.91792 q^{74} -0.458254 q^{75} -3.78727 q^{76} -0.923187 q^{77} +1.08403 q^{78} -13.7873 q^{79} -2.38352 q^{80} +5.13139 q^{81} -11.6782 q^{82} +3.54948 q^{83} +0.340709 q^{84} +14.0293 q^{85} +6.39686 q^{86} -6.44014 q^{87} -1.82292 q^{88} -8.85251 q^{89} -6.07175 q^{90} -0.816026 q^{91} -1.00000 q^{92} -3.09719 q^{93} +1.18292 q^{94} +9.02703 q^{95} +0.672761 q^{96} +16.5081 q^{97} +6.74352 q^{98} -4.64368 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 24 q^{2} - q^{3} + 24 q^{4} - q^{5} + q^{6} - 7 q^{7} - 24 q^{8} + 27 q^{9}+O(q^{10}) $ 24 * q - 24 * q^2 - q^3 + 24 * q^4 - q^5 + q^6 - 7 * q^7 - 24 * q^8 + 27 * q^9	\( 24 q - 24 q^{2} - q^{3} + 24 q^{4} - q^{5} + q^{6} - 7 q^{7} - 24 q^{8} + 27 q^{9} + q^{10} - 4 q^{11} - q^{12} - 5 q^{13} + 7 q^{14} - 6 q^{15} + 24 q^{16} + 5 q^{17} - 27 q^{18} - 20 q^{19} - q^{20} + 4 q^{22} - 24 q^{23} + q^{24} + q^{25} + 5 q^{26} - q^{27} - 7 q^{28} - 6 q^{29} + 6 q^{30} - 23 q^{31} - 24 q^{32} - 6 q^{33} - 5 q^{34} + 5 q^{35} + 27 q^{36} - 6 q^{37} + 20 q^{38} - 39 q^{39} + q^{40} - q^{41} - 44 q^{43} - 4 q^{44} - 13 q^{45} + 24 q^{46} + 32 q^{47} - q^{48} - 13 q^{49} - q^{50} - 44 q^{51} - 5 q^{52} + 21 q^{53} + q^{54} - 13 q^{55} + 7 q^{56} + 10 q^{57} + 6 q^{58} - 24 q^{59} - 6 q^{60} - 40 q^{61} + 23 q^{62} - 54 q^{63} + 24 q^{64} - 29 q^{65} + 6 q^{66} - 17 q^{67} + 5 q^{68} + q^{69} - 5 q^{70} + 4 q^{71} - 27 q^{72} - 16 q^{73} + 6 q^{74} - 36 q^{75} - 20 q^{76} + 24 q^{77} + 39 q^{78} - 53 q^{79} - q^{80} + 24 q^{81} + q^{82} - 9 q^{83} - 37 q^{85} + 44 q^{86} + 7 q^{87} + 4 q^{88} - 46 q^{89} + 13 q^{90} - 44 q^{91} - 24 q^{92} + 23 q^{93} - 32 q^{94} + 28 q^{95} + q^{96} - 20 q^{97} + 13 q^{98} - 78 q^{99}+O(q^{100}) \) 24 * q - 24 * q^2 - q^3 + 24 * q^4 - q^5 + q^6 - 7 * q^7 - 24 * q^8 + 27 * q^9 + q^10 - 4 * q^11 - q^12 - 5 * q^13 + 7 * q^14 - 6 * q^15 + 24 * q^16 + 5 * q^17 - 27 * q^18 - 20 * q^19 - q^20 + 4 * q^22 - 24 * q^23 + q^24 + q^25 + 5 * q^26 - q^27 - 7 * q^28 - 6 * q^29 + 6 * q^30 - 23 * q^31 - 24 * q^32 - 6 * q^33 - 5 * q^34 + 5 * q^35 + 27 * q^36 - 6 * q^37 + 20 * q^38 - 39 * q^39 + q^40 - q^41 - 44 * q^43 - 4 * q^44 - 13 * q^45 + 24 * q^46 + 32 * q^47 - q^48 - 13 * q^49 - q^50 - 44 * q^51 - 5 * q^52 + 21 * q^53 + q^54 - 13 * q^55 + 7 * q^56 + 10 * q^57 + 6 * q^58 - 24 * q^59 - 6 * q^60 - 40 * q^61 + 23 * q^62 - 54 * q^63 + 24 * q^64 - 29 * q^65 + 6 * q^66 - 17 * q^67 + 5 * q^68 + q^69 - 5 * q^70 + 4 * q^71 - 27 * q^72 - 16 * q^73 + 6 * q^74 - 36 * q^75 - 20 * q^76 + 24 * q^77 + 39 * q^78 - 53 * q^79 - q^80 + 24 * q^81 + q^82 - 9 * q^83 - 37 * q^85 + 44 * q^86 + 7 * q^87 + 4 * q^88 - 46 * q^89 + 13 * q^90 - 44 * q^91 - 24 * q^92 + 23 * q^93 - 32 * q^94 + 28 * q^95 + q^96 - 20 * q^97 + 13 * q^98 - 78 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−0.672761	−0.388419	−0.194209	−	0.980960i	$-0.562214\pi$
$3$	−0.672761	−0.388419	−0.194209	+	0.980960i	$0.562214\pi$
$4$	1.00000	0.500000
$5$	−2.38352	−1.06594	−0.532971	−	0.846134i	$-0.678924\pi$
$5$	−2.38352	−1.06594	−0.532971	+	0.846134i	$0.678924\pi$
$6$	0.672761	0.274654
$7$	−0.506434	−0.191414	−0.0957071	−	0.995410i	$-0.530511\pi$
$7$	−0.506434	−0.191414	−0.0957071	+	0.995410i	$0.530511\pi$
$8$	−1.00000	−0.353553
$9$	−2.54739	−0.849131
$10$	2.38352	0.753734
$11$	1.82292	0.549630	0.274815	−	0.961497i	$-0.411383\pi$
$11$	1.82292	0.549630	0.274815	+	0.961497i	$0.411383\pi$
$12$	−0.672761	−0.194209
$13$	1.61132	0.446899	0.223449	−	0.974716i	$-0.428268\pi$
$13$	1.61132	0.446899	0.223449	+	0.974716i	$0.428268\pi$
$14$	0.506434	0.135350
$15$	1.60354	0.414032
$16$	1.00000	0.250000
$17$	−5.88597	−1.42756	−0.713779	−	0.700371i	$-0.753018\pi$
$17$	−5.88597	−1.42756	−0.713779	+	0.700371i	$0.753018\pi$
$18$	2.54739	0.600426
$19$	−3.78727	−0.868860	−0.434430	−	0.900706i	$-0.643050\pi$
$19$	−3.78727	−0.868860	−0.434430	+	0.900706i	$0.643050\pi$
$20$	−2.38352	−0.532971
$21$	0.340709	0.0743488
$22$	−1.82292	−0.388647
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	0.672761	0.137327
$25$	0.681154	0.136231
$26$	−1.61132	−0.316005
$27$	3.73207	0.718237
$28$	−0.506434	−0.0957071
$29$	9.57271	1.77761	0.888803	−	0.458289i	$-0.151537\pi$
$29$	9.57271	1.77761	0.888803	+	0.458289i	$0.151537\pi$
$30$	−1.60354	−0.292765
$31$	4.60370	0.826849	0.413424	−	0.910538i	$-0.364333\pi$
$31$	4.60370	0.826849	0.413424	+	0.910538i	$0.364333\pi$
$32$	−1.00000	−0.176777
$33$	−1.22639	−0.213486
$34$	5.88597	1.00944
$35$	1.20709	0.204036
$36$	−2.54739	−0.424565
$37$	8.91792	1.46610	0.733048	−	0.680177i	$-0.238097\pi$
$37$	8.91792	1.46610	0.733048	+	0.680177i	$0.238097\pi$
$38$	3.78727	0.614377
$39$	−1.08403	−0.173584
$40$	2.38352	0.376867
$41$	11.6782	1.82383	0.911917	−	0.410375i	$-0.134602\pi$
$41$	11.6782	1.82383	0.911917	+	0.410375i	$0.134602\pi$
$42$	−0.340709	−0.0525726
$43$	−6.39686	−0.975511	−0.487756	−	0.872980i	$-0.662184\pi$
$43$	−6.39686	−0.975511	−0.487756	+	0.872980i	$0.662184\pi$
$44$	1.82292	0.274815
$45$	6.07175	0.905124
$46$	1.00000	0.147442
$47$	−1.18292	−0.172546	−0.0862732	−	0.996272i	$-0.527496\pi$
$47$	−1.18292	−0.172546	−0.0862732	+	0.996272i	$0.527496\pi$
$48$	−0.672761	−0.0971047
$49$	−6.74352	−0.963361
$50$	−0.681154	−0.0963297
$51$	3.95985	0.554490
$52$	1.61132	0.223449
$53$	2.70654	0.371772	0.185886	−	0.982571i	$-0.440484\pi$
$53$	2.70654	0.371772	0.185886	+	0.982571i	$0.440484\pi$
$54$	−3.73207	−0.507870
$55$	−4.34495	−0.585873
$56$	0.506434	0.0676751
$57$	2.54793	0.337481
$58$	−9.57271	−1.25696
$59$	8.49714	1.10623	0.553117	−	0.833104i	$-0.313438\pi$
$59$	8.49714	1.10623	0.553117	+	0.833104i	$0.313438\pi$
$60$	1.60354	0.207016
$61$	−9.41813	−1.20587	−0.602934	−	0.797791i	$-0.706002\pi$
$61$	−9.41813	−1.20587	−0.602934	+	0.797791i	$0.706002\pi$
$62$	−4.60370	−0.584670
$63$	1.29009	0.162536
$64$	1.00000	0.125000
$65$	−3.84060	−0.476368
$66$	1.22639	0.150958
$67$	9.70644	1.18583	0.592915	−	0.805265i	$-0.297977\pi$
$67$	9.70644	1.18583	0.592915	+	0.805265i	$0.297977\pi$
$68$	−5.88597	−0.713779
$69$	0.672761	0.0809909
$70$	−1.20709	−0.144275
$71$	−7.20117	−0.854621	−0.427311	−	0.904105i	$-0.640539\pi$
$71$	−7.20117	−0.854621	−0.427311	+	0.904105i	$0.640539\pi$
$72$	2.54739	0.300213
$73$	0.843850	0.0987651	0.0493826	−	0.998780i	$-0.484275\pi$
$73$	0.843850	0.0987651	0.0493826	+	0.998780i	$0.484275\pi$
$74$	−8.91792	−1.03669
$75$	−0.458254	−0.0529146
$76$	−3.78727	−0.434430
$77$	−0.923187	−0.105207
$78$	1.08403	0.122742
$79$	−13.7873	−1.55119	−0.775596	−	0.631229i	$-0.782551\pi$
$79$	−13.7873	−1.55119	−0.775596	+	0.631229i	$0.782551\pi$
$80$	−2.38352	−0.266485
$81$	5.13139	0.570154
$82$	−11.6782	−1.28964
$83$	3.54948	0.389606	0.194803	−	0.980842i	$-0.437593\pi$
$83$	3.54948	0.389606	0.194803	+	0.980842i	$0.437593\pi$
$84$	0.340709	0.0371744
$85$	14.0293	1.52169
$86$	6.39686	0.689791
$87$	−6.44014	−0.690456
$88$	−1.82292	−0.194323
$89$	−8.85251	−0.938364	−0.469182	−	0.883101i	$-0.655451\pi$
$89$	−8.85251	−0.938364	−0.469182	+	0.883101i	$0.655451\pi$
$90$	−6.07175	−0.640019
$91$	−0.816026	−0.0855427
$92$	−1.00000	−0.104257
$93$	−3.09719	−0.321164
$94$	1.18292	0.122009
$95$	9.02703	0.926153
$96$	0.672761	0.0686634
$97$	16.5081	1.67614	0.838071	−	0.545561i	$-0.183683\pi$
$97$	16.5081	1.67614	0.838071	+	0.545561i	$0.183683\pi$
$98$	6.74352	0.681199
$99$	−4.64368	−0.466707
$100$	0.681154	0.0681154
$101$	−3.84068	−0.382162	−0.191081	−	0.981574i	$-0.561199\pi$
$101$	−3.84068	−0.382162	−0.191081	+	0.981574i	$0.561199\pi$
$102$	−3.95985	−0.392084
$103$	−7.33545	−0.722783	−0.361392	−	0.932414i	$-0.617698\pi$
$103$	−7.33545	−0.722783	−0.361392	+	0.932414i	$0.617698\pi$
$104$	−1.61132	−0.158003
$105$	−0.812086	−0.0792515
$106$	−2.70654	−0.262883
$107$	12.2690	1.18609	0.593044	−	0.805170i	$-0.297926\pi$
$107$	12.2690	1.18609	0.593044	+	0.805170i	$0.297926\pi$
$108$	3.73207	0.359119
$109$	−17.9443	−1.71876	−0.859378	−	0.511340i	$-0.829149\pi$
$109$	−17.9443	−1.71876	−0.859378	+	0.511340i	$0.829149\pi$
$110$	4.34495	0.414275
$111$	−5.99963	−0.569459
$112$	−0.506434	−0.0478535
$113$	−5.84266	−0.549631	−0.274816	−	0.961497i	$-0.588617\pi$
$113$	−5.84266	−0.549631	−0.274816	+	0.961497i	$0.588617\pi$
$114$	−2.54793	−0.238635
$115$	2.38352	0.222264
$116$	9.57271	0.888803
$117$	−4.10466	−0.379476
$118$	−8.49714	−0.782225
$119$	2.98086	0.273255
$120$	−1.60354	−0.146382
$121$	−7.67698	−0.697907
$122$	9.41813	0.852678
$123$	−7.85666	−0.708411
$124$	4.60370	0.413424
$125$	10.2940	0.920727
$126$	−1.29009	−0.114930
$127$	12.9448	1.14866	0.574331	−	0.818623i	$-0.305262\pi$
$127$	12.9448	1.14866	0.574331	+	0.818623i	$0.305262\pi$
$128$	−1.00000	−0.0883883
$129$	4.30356	0.378907
$130$	3.84060	0.336843
$131$	−1.00000	−0.0873704
$131$	−1.00000	−0.0873704
$132$	−1.22639	−0.106743
$133$	1.91800	0.166312
$134$	−9.70644	−0.838508
$135$	−8.89545	−0.765599
$136$	5.88597	0.504718
$137$	11.9182	1.01824	0.509119	−	0.860696i	$-0.329971\pi$
$137$	11.9182	1.01824	0.509119	+	0.860696i	$0.329971\pi$
$138$	−0.672761	−0.0572692
$139$	8.66538	0.734988	0.367494	−	0.930026i	$-0.380216\pi$
$139$	8.66538	0.734988	0.367494	+	0.930026i	$0.380216\pi$
$140$	1.20709	0.102018
$141$	0.795822	0.0670203
$142$	7.20117	0.604308
$143$	2.93729	0.245629
$144$	−2.54739	−0.212283
$145$	−22.8167	−1.89482
$146$	−0.843850	−0.0698375
$147$	4.53678	0.374187
$148$	8.91792	0.733048
$149$	3.82877	0.313665	0.156833	−	0.987625i	$-0.449872\pi$
$149$	3.82877	0.313665	0.156833	+	0.987625i	$0.449872\pi$
$150$	0.458254	0.0374163
$151$	18.7863	1.52881	0.764404	−	0.644738i	$-0.223033\pi$
$151$	18.7863	1.52881	0.764404	+	0.644738i	$0.223033\pi$
$152$	3.78727	0.307188
$153$	14.9939	1.21218
$154$	0.923187	0.0743925
$155$	−10.9730	−0.881372
$156$	−1.08403	−0.0867919
$157$	−24.5004	−1.95534	−0.977672	−	0.210137i	$-0.932609\pi$
$157$	−24.5004	−1.95534	−0.977672	+	0.210137i	$0.932609\pi$
$158$	13.7873	1.09686
$159$	−1.82086	−0.144403
$160$	2.38352	0.188434
$161$	0.506434	0.0399126
$162$	−5.13139	−0.403160
$163$	4.13777	0.324095	0.162047	−	0.986783i	$-0.448190\pi$
$163$	4.13777	0.324095	0.162047	+	0.986783i	$0.448190\pi$
$164$	11.6782	0.911917
$165$	2.92311	0.227564
$166$	−3.54948	−0.275493
$167$	16.2307	1.25597	0.627983	−	0.778227i	$-0.283881\pi$
$167$	16.2307	1.25597	0.627983	+	0.778227i	$0.283881\pi$
$168$	−0.340709	−0.0262863
$169$	−10.4037	−0.800281
$170$	−14.0293	−1.07600
$171$	9.64767	0.737775
$172$	−6.39686	−0.487756
$173$	7.54592	0.573706	0.286853	−	0.957975i	$-0.407391\pi$
$173$	7.54592	0.573706	0.286853	+	0.957975i	$0.407391\pi$
$174$	6.44014	0.488226
$175$	−0.344960	−0.0260765
$176$	1.82292	0.137407
$177$	−5.71655	−0.429682
$178$	8.85251	0.663524
$179$	12.1313	0.906740	0.453370	−	0.891323i	$-0.350222\pi$
$179$	12.1313	0.906740	0.453370	+	0.891323i	$0.350222\pi$
$180$	6.07175	0.452562
$181$	8.61582	0.640409	0.320204	−	0.947348i	$-0.396248\pi$
$181$	8.61582	0.640409	0.320204	+	0.947348i	$0.396248\pi$
$182$	0.816026	0.0604879
$183$	6.33615	0.468382
$184$	1.00000	0.0737210
$185$	−21.2560	−1.56277
$186$	3.09719	0.227097
$187$	−10.7296	−0.784628
$188$	−1.18292	−0.0862732
$189$	−1.89005	−0.137481
$190$	−9.02703	−0.654889
$191$	−21.5763	−1.56121	−0.780605	−	0.625025i	$-0.785089\pi$
$191$	−21.5763	−1.56121	−0.780605	+	0.625025i	$0.785089\pi$
$192$	−0.672761	−0.0485524
$193$	−15.6581	−1.12710	−0.563549	−	0.826083i	$-0.690564\pi$
$193$	−15.6581	−1.12710	−0.563549	+	0.826083i	$0.690564\pi$
$194$	−16.5081	−1.18521
$195$	2.58381	0.185030
$196$	−6.74352	−0.481680
$197$	1.27537	0.0908664	0.0454332	−	0.998967i	$-0.485533\pi$
$197$	1.27537	0.0908664	0.0454332	+	0.998967i	$0.485533\pi$
$198$	4.64368	0.330012
$199$	−9.18160	−0.650866	−0.325433	−	0.945565i	$-0.605510\pi$
$199$	−9.18160	−0.650866	−0.325433	+	0.945565i	$0.605510\pi$
$200$	−0.681154	−0.0481649
$201$	−6.53011	−0.460599
$202$	3.84068	0.270229
$203$	−4.84795	−0.340259
$204$	3.95985	0.277245
$205$	−27.8353	−1.94410
$206$	7.33545	0.511085
$207$	2.54739	0.177056
$208$	1.61132	0.111725
$209$	−6.90387	−0.477551
$210$	0.812086	0.0560393
$211$	−12.3775	−0.852104	−0.426052	−	0.904699i	$-0.640096\pi$
$211$	−12.3775	−0.852104	−0.426052	+	0.904699i	$0.640096\pi$
$212$	2.70654	0.185886
$213$	4.84466	0.331951
$214$	−12.2690	−0.838690
$215$	15.2470	1.03984
$216$	−3.73207	−0.253935
$217$	−2.33147	−0.158271
$218$	17.9443	1.21534
$219$	−0.567709	−0.0383622
$220$	−4.34495	−0.292936
$221$	−9.48416	−0.637974
$222$	5.99963	0.402669
$223$	1.12783	0.0755250	0.0377625	−	0.999287i	$-0.487977\pi$
$223$	1.12783	0.0755250	0.0377625	+	0.999287i	$0.487977\pi$
$224$	0.506434	0.0338376
$225$	−1.73517	−0.115678
$226$	5.84266	0.388648
$227$	−17.4568	−1.15865	−0.579323	−	0.815098i	$-0.696683\pi$
$227$	−17.4568	−1.15865	−0.579323	+	0.815098i	$0.696683\pi$
$228$	2.54793	0.168741
$229$	21.0847	1.39332	0.696659	−	0.717402i	$-0.254669\pi$
$229$	21.0847	1.39332	0.696659	+	0.717402i	$0.254669\pi$
$230$	−2.38352	−0.157164
$231$	0.621084	0.0408643
$232$	−9.57271	−0.628479
$233$	−11.8051	−0.773380	−0.386690	−	0.922210i	$-0.626382\pi$
$233$	−11.8051	−0.773380	−0.386690	+	0.922210i	$0.626382\pi$
$234$	4.10466	0.268330
$235$	2.81951	0.183924
$236$	8.49714	0.553117
$237$	9.27556	0.602512
$238$	−2.98086	−0.193220
$239$	4.00218	0.258879	0.129440	−	0.991587i	$-0.458682\pi$
$239$	4.00218	0.258879	0.129440	+	0.991587i	$0.458682\pi$
$240$	1.60354	0.103508
$241$	−24.3560	−1.56891	−0.784455	−	0.620186i	$-0.787057\pi$
$241$	−24.3560	−1.56891	−0.784455	+	0.620186i	$0.787057\pi$
$242$	7.67698	0.493495
$243$	−14.6484	−0.939696
$244$	−9.41813	−0.602934
$245$	16.0733	1.02689
$246$	7.85666	0.500922
$247$	−6.10249	−0.388292
$248$	−4.60370	−0.292335
$249$	−2.38795	−0.151330
$250$	−10.2940	−0.651052
$251$	24.9801	1.57673	0.788364	−	0.615209i	$-0.210929\pi$
$251$	24.9801	1.57673	0.788364	+	0.615209i	$0.210929\pi$
$252$	1.29009	0.0812678
$253$	−1.82292	−0.114606
$254$	−12.9448	−0.812226
$255$	−9.43837	−0.591054
$256$	1.00000	0.0625000
$257$	15.1813	0.946983	0.473491	−	0.880798i	$-0.342994\pi$
$257$	15.1813	0.946983	0.473491	+	0.880798i	$0.342994\pi$
$258$	−4.30356	−0.267928
$259$	−4.51634	−0.280632
$260$	−3.84060	−0.238184
$261$	−24.3854	−1.50942
$262$	1.00000	0.0617802
$263$	−22.7905	−1.40532	−0.702660	−	0.711526i	$-0.748004\pi$
$263$	−22.7905	−1.40532	−0.702660	+	0.711526i	$0.748004\pi$
$264$	1.22639	0.0754789
$265$	−6.45109	−0.396287
$266$	−1.91800	−0.117600
$267$	5.95562	0.364478
$268$	9.70644	0.592915
$269$	−31.5945	−1.92635	−0.963176	−	0.268870i	$-0.913350\pi$
$269$	−31.5945	−1.92635	−0.963176	+	0.268870i	$0.913350\pi$
$270$	8.89545	0.541360
$271$	−31.6981	−1.92552	−0.962761	−	0.270353i	$-0.912860\pi$
$271$	−31.6981	−1.92552	−0.962761	+	0.270353i	$0.912860\pi$
$272$	−5.88597	−0.356889
$273$	0.548990	0.0332264
$274$	−11.9182	−0.720003
$275$	1.24169	0.0748765
$276$	0.672761	0.0404955
$277$	−6.76294	−0.406346	−0.203173	−	0.979143i	$-0.565125\pi$
$277$	−6.76294	−0.406346	−0.203173	+	0.979143i	$0.565125\pi$
$278$	−8.66538	−0.519715
$279$	−11.7274	−0.702103
$280$	−1.20709	−0.0721377
$281$	−9.61368	−0.573504	−0.286752	−	0.958005i	$-0.592576\pi$
$281$	−9.61368	−0.573504	−0.286752	+	0.958005i	$0.592576\pi$
$282$	−0.795822	−0.0473905
$283$	1.57030	0.0933446	0.0466723	−	0.998910i	$-0.485138\pi$
$283$	1.57030	0.0933446	0.0466723	+	0.998910i	$0.485138\pi$
$284$	−7.20117	−0.427311
$285$	−6.07303	−0.359735
$286$	−2.93729	−0.173686
$287$	−5.91426	−0.349107
$288$	2.54739	0.150107
$289$	17.6446	1.03792
$290$	22.8167	1.33984
$291$	−11.1060	−0.651045
$292$	0.843850	0.0493826
$293$	12.8511	0.750771	0.375385	−	0.926869i	$-0.377510\pi$
$293$	12.8511	0.750771	0.375385	+	0.926869i	$0.377510\pi$
$294$	−4.53678	−0.264590
$295$	−20.2531	−1.17918
$296$	−8.91792	−0.518343
$297$	6.80325	0.394764
$298$	−3.82877	−0.221795
$299$	−1.61132	−0.0931848
$300$	−0.458254	−0.0264573
$301$	3.23959	0.186727
$302$	−18.7863	−1.08103
$303$	2.58386	0.148439
$304$	−3.78727	−0.217215
$305$	22.4483	1.28538
$306$	−14.9939	−0.857143
$307$	19.7982	1.12994	0.564972	−	0.825110i	$-0.308887\pi$
$307$	19.7982	1.12994	0.564972	+	0.825110i	$0.308887\pi$
$308$	−0.923187	−0.0526034
$309$	4.93500	0.280743
$310$	10.9730	0.623224
$311$	5.47894	0.310682	0.155341	−	0.987861i	$-0.450352\pi$
$311$	5.47894	0.310682	0.155341	+	0.987861i	$0.450352\pi$
$312$	1.08403	0.0613712
$313$	0.110383	0.00623924	0.00311962	−	0.999995i	$-0.499007\pi$
$313$	0.110383	0.00623924	0.00311962	+	0.999995i	$0.499007\pi$
$314$	24.5004	1.38264
$315$	−3.07494	−0.173253
$316$	−13.7873	−0.775596
$317$	1.84352	0.103542	0.0517711	−	0.998659i	$-0.483513\pi$
$317$	1.84352	0.103542	0.0517711	+	0.998659i	$0.483513\pi$
$318$	1.82086	0.102109
$319$	17.4502	0.977025
$320$	−2.38352	−0.133243
$321$	−8.25409	−0.460699
$322$	−0.506434	−0.0282225
$323$	22.2918	1.24035
$324$	5.13139	0.285077
$325$	1.09755	0.0608814
$326$	−4.13777	−0.229170
$327$	12.0723	0.667597
$328$	−11.6782	−0.644822
$329$	0.599071	0.0330278
$330$	−2.92311	−0.160912
$331$	−27.4908	−1.51103	−0.755515	−	0.655132i	$-0.772613\pi$
$331$	−27.4908	−1.51103	−0.755515	+	0.655132i	$0.772613\pi$
$332$	3.54948	0.194803
$333$	−22.7174	−1.24491
$334$	−16.2307	−0.888102
$335$	−23.1355	−1.26403
$336$	0.340709	0.0185872
$337$	−28.4809	−1.55145	−0.775726	−	0.631070i	$-0.782616\pi$
$337$	−28.4809	−1.55145	−0.775726	+	0.631070i	$0.782616\pi$
$338$	10.4037	0.565884
$339$	3.93072	0.213487
$340$	14.0293	0.760846
$341$	8.39215	0.454461
$342$	−9.64767	−0.521686
$343$	6.96019	0.375815
$344$	6.39686	0.344895
$345$	−1.60354	−0.0863316
$346$	−7.54592	−0.405671
$347$	2.15208	0.115530	0.0577649	−	0.998330i	$-0.481603\pi$
$347$	2.15208	0.115530	0.0577649	+	0.998330i	$0.481603\pi$
$348$	−6.44014	−0.345228
$349$	3.84808	0.205983	0.102992	−	0.994682i	$-0.467159\pi$
$349$	3.84808	0.205983	0.102992	+	0.994682i	$0.467159\pi$
$350$	0.344960	0.0184389
$351$	6.01355	0.320979
$352$	−1.82292	−0.0971617
$353$	−2.14133	−0.113971	−0.0569857	−	0.998375i	$-0.518149\pi$
$353$	−2.14133	−0.113971	−0.0569857	+	0.998375i	$0.518149\pi$
$354$	5.71655	0.303831
$355$	17.1641	0.910976
$356$	−8.85251	−0.469182
$357$	−2.00540	−0.106137
$358$	−12.1313	−0.641162
$359$	7.16507	0.378158	0.189079	−	0.981962i	$-0.439450\pi$
$359$	7.16507	0.378158	0.189079	+	0.981962i	$0.439450\pi$
$360$	−6.07175	−0.320010
$361$	−4.65658	−0.245083
$362$	−8.61582	−0.452837
$363$	5.16477	0.271080
$364$	−0.816026	−0.0427714
$365$	−2.01133	−0.105278
$366$	−6.33615	−0.331196
$367$	−20.6045	−1.07555	−0.537774	−	0.843089i	$-0.680734\pi$
$367$	−20.6045	−1.07555	−0.537774	+	0.843089i	$0.680734\pi$
$368$	−1.00000	−0.0521286
$369$	−29.7490	−1.54867
$370$	21.2560	1.10505
$371$	−1.37069	−0.0711624
$372$	−3.09719	−0.160582
$373$	−32.3418	−1.67459	−0.837296	−	0.546749i	$-0.815865\pi$
$373$	−32.3418	−1.67459	−0.837296	+	0.546749i	$0.815865\pi$
$374$	10.7296	0.554816
$375$	−6.92543	−0.357628
$376$	1.18292	0.0610044
$377$	15.4247	0.794410
$378$	1.89005	0.0972136
$379$	13.4038	0.688508	0.344254	−	0.938877i	$-0.388132\pi$
$379$	13.4038	0.688508	0.344254	+	0.938877i	$0.388132\pi$
$380$	9.02703	0.463077
$381$	−8.70873	−0.446162
$382$	21.5763	1.10394
$383$	5.03055	0.257049	0.128525	−	0.991706i	$-0.458976\pi$
$383$	5.03055	0.257049	0.128525	+	0.991706i	$0.458976\pi$
$384$	0.672761	0.0343317
$385$	2.20043	0.112144
$386$	15.6581	0.796979
$387$	16.2953	0.828337
$388$	16.5081	0.838071
$389$	10.8135	0.548264	0.274132	−	0.961692i	$-0.411609\pi$
$389$	10.8135	0.548264	0.274132	+	0.961692i	$0.411609\pi$
$390$	−2.58381	−0.130836
$391$	5.88597	0.297666
$392$	6.74352	0.340599
$393$	0.672761	0.0339363
$394$	−1.27537	−0.0642523
$395$	32.8623	1.65348
$396$	−4.64368	−0.233354
$397$	32.4228	1.62725	0.813627	−	0.581387i	$-0.197490\pi$
$397$	32.4228	1.62725	0.813627	+	0.581387i	$0.197490\pi$
$398$	9.18160	0.460232
$399$	−1.29036	−0.0645987
$400$	0.681154	0.0340577
$401$	−14.2130	−0.709763	−0.354881	−	0.934911i	$-0.615479\pi$
$401$	−14.2130	−0.709763	−0.354881	+	0.934911i	$0.615479\pi$
$402$	6.53011	0.325692
$403$	7.41802	0.369518
$404$	−3.84068	−0.191081
$405$	−12.2307	−0.607751
$406$	4.84795	0.240599
$407$	16.2566	0.805810
$408$	−3.95985	−0.196042
$409$	20.0218	0.990014	0.495007	−	0.868889i	$-0.335165\pi$
$409$	20.0218	0.990014	0.495007	+	0.868889i	$0.335165\pi$
$410$	27.8353	1.37469
$411$	−8.01808	−0.395503
$412$	−7.33545	−0.361392
$413$	−4.30324	−0.211749
$414$	−2.54739	−0.125198
$415$	−8.46024	−0.415297
$416$	−1.61132	−0.0790013
$417$	−5.82973	−0.285483
$418$	6.90387	0.337680
$419$	−37.3997	−1.82709	−0.913547	−	0.406733i	$-0.866668\pi$
$419$	−37.3997	−1.82709	−0.913547	+	0.406733i	$0.866668\pi$
$420$	−0.812086	−0.0396258
$421$	−28.0323	−1.36621	−0.683106	−	0.730319i	$-0.739371\pi$
$421$	−28.0323	−1.36621	−0.683106	+	0.730319i	$0.739371\pi$
$422$	12.3775	0.602528
$423$	3.01336	0.146515
$424$	−2.70654	−0.131441
$425$	−4.00925	−0.194477
$426$	−4.84466	−0.234725
$427$	4.76966	0.230820
$428$	12.2690	0.593044
$429$	−1.97610	−0.0954069
$430$	−15.2470	−0.735276
$431$	−30.4709	−1.46773	−0.733867	−	0.679294i	$-0.762286\pi$
$431$	−30.4709	−1.46773	−0.733867	+	0.679294i	$0.762286\pi$
$432$	3.73207	0.179559
$433$	8.97319	0.431224	0.215612	−	0.976479i	$-0.430825\pi$
$433$	8.97319	0.431224	0.215612	+	0.976479i	$0.430825\pi$
$434$	2.33147	0.111914
$435$	15.3502	0.735986
$436$	−17.9443	−0.859378
$437$	3.78727	0.181170
$438$	0.567709	0.0271262
$439$	−25.1764	−1.20160	−0.600802	−	0.799398i	$-0.705152\pi$
$439$	−25.1764	−1.20160	−0.600802	+	0.799398i	$0.705152\pi$
$440$	4.34495	0.207137
$441$	17.1784	0.818019
$442$	9.48416	0.451115
$443$	−2.46405	−0.117071	−0.0585353	−	0.998285i	$-0.518643\pi$
$443$	−2.46405	−0.117071	−0.0585353	+	0.998285i	$0.518643\pi$
$444$	−5.99963	−0.284730
$445$	21.1001	1.00024
$446$	−1.12783	−0.0534042
$447$	−2.57585	−0.121833
$448$	−0.506434	−0.0239268
$449$	21.0293	0.992432	0.496216	−	0.868199i	$-0.334722\pi$
$449$	21.0293	0.992432	0.496216	+	0.868199i	$0.334722\pi$
$450$	1.73517	0.0817965
$451$	21.2884	1.00243
$452$	−5.84266	−0.274816
$453$	−12.6387	−0.593818
$454$	17.4568	0.819286
$455$	1.94501	0.0911835
$456$	−2.54793	−0.119318
$457$	−1.97969	−0.0926061	−0.0463030	−	0.998927i	$-0.514744\pi$
$457$	−1.97969	−0.0926061	−0.0463030	+	0.998927i	$0.514744\pi$
$458$	−21.0847	−0.985225
$459$	−21.9668	−1.02532
$460$	2.38352	0.111132
$461$	6.49877	0.302678	0.151339	−	0.988482i	$-0.451641\pi$
$461$	6.49877	0.302678	0.151339	+	0.988482i	$0.451641\pi$
$462$	−0.621084	−0.0288954
$463$	−27.2991	−1.26869	−0.634347	−	0.773048i	$-0.718731\pi$
$463$	−27.2991	−1.26869	−0.634347	+	0.773048i	$0.718731\pi$
$464$	9.57271	0.444402
$465$	7.38221	0.342342
$466$	11.8051	0.546862
$467$	9.73770	0.450607	0.225303	−	0.974289i	$-0.427663\pi$
$467$	9.73770	0.450607	0.225303	+	0.974289i	$0.427663\pi$
$468$	−4.10466	−0.189738
$469$	−4.91567	−0.226985
$470$	−2.81951	−0.130054
$471$	16.4829	0.759492
$472$	−8.49714	−0.391113
$473$	−11.6609	−0.536170
$474$	−9.27556	−0.426041
$475$	−2.57972	−0.118365
$476$	2.98086	0.136627
$477$	−6.89462	−0.315683
$478$	−4.00218	−0.183055
$479$	7.05123	0.322179	0.161090	−	0.986940i	$-0.448499\pi$
$479$	7.05123	0.322179	0.161090	+	0.986940i	$0.448499\pi$
$480$	−1.60354	−0.0731911
$481$	14.3696	0.655197
$482$	24.3560	1.10939
$483$	−0.340709	−0.0155028
$484$	−7.67698	−0.348954
$485$	−39.3473	−1.78667
$486$	14.6484	0.664465
$487$	10.7401	0.486680	0.243340	−	0.969941i	$-0.421757\pi$
$487$	10.7401	0.486680	0.243340	+	0.969941i	$0.421757\pi$
$488$	9.41813	0.426339
$489$	−2.78373	−0.125885
$490$	−16.0733	−0.726118
$491$	−24.6316	−1.11161	−0.555805	−	0.831313i	$-0.687590\pi$
$491$	−24.6316	−1.11161	−0.555805	+	0.831313i	$0.687590\pi$
$492$	−7.85666	−0.354206
$493$	−56.3446	−2.53764
$494$	6.10249	0.274564
$495$	11.0683	0.497483
$496$	4.60370	0.206712
$497$	3.64692	0.163587
$498$	2.38795	0.107007
$499$	−2.20103	−0.0985316	−0.0492658	−	0.998786i	$-0.515688\pi$
$499$	−2.20103	−0.0985316	−0.0492658	+	0.998786i	$0.515688\pi$
$500$	10.2940	0.460364
$501$	−10.9194	−0.487841
$502$	−24.9801	−1.11491
$503$	−3.44258	−0.153497	−0.0767486	−	0.997050i	$-0.524454\pi$
$503$	−3.44258	−0.153497	−0.0767486	+	0.997050i	$0.524454\pi$
$504$	−1.29009	−0.0574650
$505$	9.15433	0.407362
$506$	1.82292	0.0810385
$507$	6.99918	0.310844
$508$	12.9448	0.574331
$509$	17.9197	0.794279	0.397139	−	0.917758i	$-0.370003\pi$
$509$	17.9197	0.794279	0.397139	+	0.917758i	$0.370003\pi$
$510$	9.43837	0.417938
$511$	−0.427354	−0.0189050
$512$	−1.00000	−0.0441942
$513$	−14.1344	−0.624047
$514$	−15.1813	−0.669618
$515$	17.4842	0.770444
$516$	4.30356	0.189453
$517$	−2.15636	−0.0948366
$518$	4.51634	0.198436
$519$	−5.07660	−0.222838
$520$	3.84060	0.168421
$521$	−2.62225	−0.114883	−0.0574415	−	0.998349i	$-0.518294\pi$
$521$	−2.62225	−0.114883	−0.0574415	+	0.998349i	$0.518294\pi$
$522$	24.3854	1.06732
$523$	−1.92644	−0.0842373	−0.0421186	−	0.999113i	$-0.513411\pi$
$523$	−1.92644	−0.0842373	−0.0421186	+	0.999113i	$0.513411\pi$
$524$	−1.00000	−0.0436852
$525$	0.232075	0.0101286
$526$	22.7905	0.993711
$527$	−27.0972	−1.18037
$528$	−1.22639	−0.0533716
$529$	1.00000	0.0434783
$530$	6.45109	0.280217
$531$	−21.6456	−0.939337
$532$	1.91800	0.0831560
$533$	18.8173	0.815069
$534$	−5.95562	−0.257725
$535$	−29.2433	−1.26430
$536$	−9.70644	−0.419254
$537$	−8.16150	−0.352195
$538$	31.5945	1.36214
$539$	−12.2929	−0.529492
$540$	−8.89545	−0.382799
$541$	−11.7766	−0.506317	−0.253158	−	0.967425i	$-0.581469\pi$
$541$	−11.7766	−0.506317	−0.253158	+	0.967425i	$0.581469\pi$
$542$	31.6981	1.36155
$543$	−5.79639	−0.248747
$544$	5.88597	0.252359
$545$	42.7707	1.83209
$546$	−0.548990	−0.0234946
$547$	21.3311	0.912052	0.456026	−	0.889966i	$-0.349272\pi$
$547$	21.3311	0.912052	0.456026	+	0.889966i	$0.349272\pi$
$548$	11.9182	0.509119
$549$	23.9917	1.02394
$550$	−1.24169	−0.0529457
$551$	−36.2544	−1.54449
$552$	−0.672761	−0.0286346
$553$	6.98236	0.296920
$554$	6.76294	0.287330
$555$	14.3002	0.607010
$556$	8.66538	0.367494
$557$	−45.8374	−1.94219	−0.971096	−	0.238689i	$-0.923282\pi$
$557$	−45.8374	−1.94219	−0.971096	+	0.238689i	$0.923282\pi$
$558$	11.7274	0.496462
$559$	−10.3074	−0.435955
$560$	1.20709	0.0510091
$561$	7.21847	0.304764
$562$	9.61368	0.405529
$563$	−17.0173	−0.717196	−0.358598	−	0.933492i	$-0.616745\pi$
$563$	−17.0173	−0.717196	−0.358598	+	0.933492i	$0.616745\pi$
$564$	0.795822	0.0335101
$565$	13.9261	0.585875
$566$	−1.57030	−0.0660046
$567$	−2.59871	−0.109136
$568$	7.20117	0.302154
$569$	28.3751	1.18954	0.594772	−	0.803894i	$-0.297242\pi$
$569$	28.3751	1.18954	0.594772	+	0.803894i	$0.297242\pi$
$570$	6.07303	0.254371
$571$	−21.4665	−0.898345	−0.449172	−	0.893445i	$-0.648281\pi$
$571$	−21.4665	−0.898345	−0.449172	+	0.893445i	$0.648281\pi$
$572$	2.93729	0.122814
$573$	14.5157	0.606403
$574$	5.91426	0.246856
$575$	−0.681154	−0.0284061
$576$	−2.54739	−0.106141
$577$	6.69544	0.278735	0.139367	−	0.990241i	$-0.455493\pi$
$577$	6.69544	0.278735	0.139367	+	0.990241i	$0.455493\pi$
$578$	−17.6446	−0.733920
$579$	10.5342	0.437786
$580$	−22.8167	−0.947412
$581$	−1.79758	−0.0745761
$582$	11.1060	0.460358
$583$	4.93380	0.204337
$584$	−0.843850	−0.0349188
$585$	9.78352	0.404499
$586$	−12.8511	−0.530875
$587$	−11.2909	−0.466026	−0.233013	−	0.972474i	$-0.574858\pi$
$587$	−11.2909	−0.466026	−0.233013	+	0.972474i	$0.574858\pi$
$588$	4.53678	0.187094
$589$	−17.4355	−0.718416
$590$	20.2531	0.833806
$591$	−0.858020	−0.0352942
$592$	8.91792	0.366524
$593$	−20.7622	−0.852602	−0.426301	−	0.904581i	$-0.640184\pi$
$593$	−20.7622	−0.852602	−0.426301	+	0.904581i	$0.640184\pi$
$594$	−6.80325	−0.279141
$595$	−7.10492	−0.291273
$596$	3.82877	0.156833
$597$	6.17702	0.252809
$598$	1.61132	0.0658916
$599$	−29.4352	−1.20269	−0.601345	−	0.798990i	$-0.705368\pi$
$599$	−29.4352	−1.20269	−0.601345	+	0.798990i	$0.705368\pi$
$600$	0.458254	0.0187081
$601$	−25.0299	−1.02099	−0.510495	−	0.859881i	$-0.670538\pi$
$601$	−25.0299	−1.02099	−0.510495	+	0.859881i	$0.670538\pi$
$602$	−3.23959	−0.132036
$603$	−24.7261	−1.00692
$604$	18.7863	0.764404
$605$	18.2982	0.743928
$606$	−2.58386	−0.104962
$607$	−3.98260	−0.161649	−0.0808245	−	0.996728i	$-0.525755\pi$
$607$	−3.98260	−0.161649	−0.0808245	+	0.996728i	$0.525755\pi$
$608$	3.78727	0.153594
$609$	3.26151	0.132163
$610$	−22.4483	−0.908904
$611$	−1.90606	−0.0771108
$612$	14.9939	0.606091
$613$	8.61945	0.348136	0.174068	−	0.984734i	$-0.444309\pi$
$613$	8.61945	0.348136	0.174068	+	0.984734i	$0.444309\pi$
$614$	−19.7982	−0.798991
$615$	18.7265	0.755125
$616$	0.923187	0.0371962
$617$	4.45564	0.179377	0.0896886	−	0.995970i	$-0.471413\pi$
$617$	4.45564	0.179377	0.0896886	+	0.995970i	$0.471413\pi$
$618$	−4.93500	−0.198515
$619$	22.3404	0.897936	0.448968	−	0.893548i	$-0.351792\pi$
$619$	22.3404	0.897936	0.448968	+	0.893548i	$0.351792\pi$
$620$	−10.9730	−0.440686
$621$	−3.73207	−0.149763
$622$	−5.47894	−0.219685
$623$	4.48321	0.179616
$624$	−1.08403	−0.0433960
$625$	−27.9418	−1.11767
$626$	−0.110383	−0.00441181
$627$	4.64466	0.185490
$628$	−24.5004	−0.977672
$629$	−52.4906	−2.09294
$630$	3.07494	0.122509
$631$	−23.3547	−0.929736	−0.464868	−	0.885380i	$-0.653898\pi$
$631$	−23.3547	−0.929736	−0.464868	+	0.885380i	$0.653898\pi$
$632$	13.7873	0.548429
$633$	8.32712	0.330973
$634$	−1.84352	−0.0732154
$635$	−30.8541	−1.22441
$636$	−1.82086	−0.0722016
$637$	−10.8660	−0.430525
$638$	−17.4502	−0.690861
$639$	18.3442	0.725685
$640$	2.38352	0.0942168
$641$	38.1623	1.50732	0.753660	−	0.657265i	$-0.228287\pi$
$641$	38.1623	1.50732	0.753660	+	0.657265i	$0.228287\pi$
$642$	8.25409	0.325763
$643$	−38.7678	−1.52885	−0.764426	−	0.644712i	$-0.776977\pi$
$643$	−38.7678	−1.52885	−0.764426	+	0.644712i	$0.776977\pi$
$644$	0.506434	0.0199563
$645$	−10.2576	−0.403893
$646$	−22.2918	−0.877058
$647$	−10.6725	−0.419581	−0.209791	−	0.977746i	$-0.567278\pi$
$647$	−10.6725	−0.419581	−0.209791	+	0.977746i	$0.567278\pi$
$648$	−5.13139	−0.201580
$649$	15.4896	0.608019
$650$	−1.09755	−0.0430496
$651$	1.56852	0.0614753
$652$	4.13777	0.162047
$653$	37.2012	1.45580	0.727898	−	0.685685i	$-0.240497\pi$
$653$	37.2012	1.45580	0.727898	+	0.685685i	$0.240497\pi$
$654$	−12.0723	−0.472063
$655$	2.38352	0.0931317
$656$	11.6782	0.455958
$657$	−2.14962	−0.0838645
$658$	−0.599071	−0.0233542
$659$	−33.8271	−1.31772	−0.658858	−	0.752267i	$-0.728960\pi$
$659$	−33.8271	−1.31772	−0.658858	+	0.752267i	$0.728960\pi$
$660$	2.92311	0.113782
$661$	−5.57946	−0.217016	−0.108508	−	0.994096i	$-0.534607\pi$
$661$	−5.57946	−0.217016	−0.108508	+	0.994096i	$0.534607\pi$
$662$	27.4908	1.06846
$663$	6.38057	0.247801
$664$	−3.54948	−0.137746
$665$	−4.57159	−0.177279
$666$	22.7174	0.880283
$667$	−9.57271	−0.370657
$668$	16.2307	0.627983
$669$	−0.758759	−0.0293353
$670$	23.1355	0.893801
$671$	−17.1685	−0.662781
$672$	−0.340709	−0.0131431
$673$	19.3252	0.744933	0.372467	−	0.928046i	$-0.378512\pi$
$673$	19.3252	0.744933	0.372467	+	0.928046i	$0.378512\pi$
$674$	28.4809	1.09704
$675$	2.54211	0.0978460
$676$	−10.4037	−0.400141
$677$	−37.3926	−1.43711	−0.718556	−	0.695469i	$-0.755197\pi$
$677$	−37.3926	−1.43711	−0.718556	+	0.695469i	$0.755197\pi$
$678$	−3.93072	−0.150958
$679$	−8.36026	−0.320837
$680$	−14.0293	−0.537999
$681$	11.7442	0.450040
$682$	−8.39215	−0.321352
$683$	−46.9554	−1.79670	−0.898349	−	0.439283i	$-0.855232\pi$
$683$	−46.9554	−1.79670	−0.898349	+	0.439283i	$0.855232\pi$
$684$	9.64767	0.368888
$685$	−28.4071	−1.08538
$686$	−6.96019	−0.265741
$687$	−14.1850	−0.541191
$688$	−6.39686	−0.243878
$689$	4.36110	0.166144
$690$	1.60354	0.0610456
$691$	24.3915	0.927896	0.463948	−	0.885862i	$-0.346432\pi$
$691$	24.3915	0.927896	0.463948	+	0.885862i	$0.346432\pi$
$692$	7.54592	0.286853
$693$	2.35172	0.0893344
$694$	−2.15208	−0.0816918
$695$	−20.6541	−0.783454
$696$	6.44014	0.244113
$697$	−68.7377	−2.60363
$698$	−3.84808	−0.145652
$699$	7.94203	0.300395
$700$	−0.344960	−0.0130383
$701$	−18.8202	−0.710830	−0.355415	−	0.934709i	$-0.615660\pi$
$701$	−18.8202	−0.710830	−0.355415	+	0.934709i	$0.615660\pi$
$702$	−6.01355	−0.226967
$703$	−33.7746	−1.27383
$704$	1.82292	0.0687037
$705$	−1.89685	−0.0714397
$706$	2.14133	0.0805900
$707$	1.94505	0.0731512
$708$	−5.71655	−0.214841
$709$	34.8272	1.30796	0.653982	−	0.756510i	$-0.273097\pi$
$709$	34.8272	1.30796	0.653982	+	0.756510i	$0.273097\pi$
$710$	−17.1641	−0.644157
$711$	35.1217	1.31717
$712$	8.85251	0.331762
$713$	−4.60370	−0.172410
$714$	2.00540	0.0750504
$715$	−7.00109	−0.261826
$716$	12.1313	0.453370
$717$	−2.69251	−0.100554
$718$	−7.16507	−0.267398
$719$	−48.2471	−1.79931	−0.899656	−	0.436599i	$-0.856183\pi$
$719$	−48.2471	−1.79931	−0.899656	+	0.436599i	$0.856183\pi$
$720$	6.07175	0.226281
$721$	3.71492	0.138351
$722$	4.65658	0.173300
$723$	16.3858	0.609394
$724$	8.61582	0.320204
$725$	6.52049	0.242165
$726$	−5.16477	−0.191683
$727$	13.0458	0.483843	0.241922	−	0.970296i	$-0.422222\pi$
$727$	13.0458	0.483843	0.241922	+	0.970296i	$0.422222\pi$
$728$	0.816026	0.0302439
$729$	−5.53928	−0.205158
$730$	2.01133	0.0744427
$731$	37.6517	1.39260
$732$	6.33615	0.234191
$733$	22.1887	0.819559	0.409780	−	0.912185i	$-0.365606\pi$
$733$	22.1887	0.819559	0.409780	+	0.912185i	$0.365606\pi$
$734$	20.6045	0.760527
$735$	−10.8135	−0.398862
$736$	1.00000	0.0368605
$737$	17.6940	0.651767
$738$	29.7490	1.09508
$739$	34.2684	1.26059	0.630293	−	0.776358i	$-0.282935\pi$
$739$	34.2684	1.26059	0.630293	+	0.776358i	$0.282935\pi$
$740$	−21.2560	−0.781386
$741$	4.10552	0.150820
$742$	1.37069	0.0503194
$743$	−7.69305	−0.282231	−0.141115	−	0.989993i	$-0.545069\pi$
$743$	−7.69305	−0.282231	−0.141115	+	0.989993i	$0.545069\pi$
$744$	3.09719	0.113548
$745$	−9.12594	−0.334349
$746$	32.3418	1.18412
$747$	−9.04191	−0.330826
$748$	−10.7296	−0.392314
$749$	−6.21343	−0.227034
$750$	6.92543	0.252881
$751$	−0.0799624	−0.00291787	−0.00145893	−	0.999999i	$-0.500464\pi$
$751$	−0.0799624	−0.00291787	−0.00145893	+	0.999999i	$0.500464\pi$
$752$	−1.18292	−0.0431366
$753$	−16.8056	−0.612431
$754$	−15.4247	−0.561733
$755$	−44.7775	−1.62962
$756$	−1.89005	−0.0687404
$757$	13.9771	0.508006	0.254003	−	0.967203i	$-0.418253\pi$
$757$	13.9771	0.508006	0.254003	+	0.967203i	$0.418253\pi$
$758$	−13.4038	−0.486848
$759$	1.22639	0.0445150
$760$	−9.02703	−0.327445
$761$	−23.1755	−0.840113	−0.420056	−	0.907498i	$-0.637990\pi$
$761$	−23.1755	−0.840113	−0.420056	+	0.907498i	$0.637990\pi$
$762$	8.70873	0.315484
$763$	9.08763	0.328994
$764$	−21.5763	−0.780605
$765$	−35.7382	−1.29212
$766$	−5.03055	−0.181761
$767$	13.6916	0.494374
$768$	−0.672761	−0.0242762
$769$	48.1369	1.73586	0.867930	−	0.496686i	$-0.165450\pi$
$769$	48.1369	1.73586	0.867930	+	0.496686i	$0.165450\pi$
$770$	−2.20043	−0.0792980
$771$	−10.2134	−0.367826
$772$	−15.6581	−0.563549
$773$	−12.2053	−0.438995	−0.219498	−	0.975613i	$-0.570442\pi$
$773$	−12.2053	−0.438995	−0.219498	+	0.975613i	$0.570442\pi$
$774$	−16.2953	−0.585722
$775$	3.13583	0.112642
$776$	−16.5081	−0.592606
$777$	3.03842	0.109003
$778$	−10.8135	−0.387681
$779$	−44.2286	−1.58466
$780$	2.58381	0.0925151
$781$	−13.1271	−0.469725
$782$	−5.88597	−0.210482
$783$	35.7260	1.27674
$784$	−6.74352	−0.240840
$785$	58.3971	2.08428
$786$	−0.672761	−0.0239966
$787$	4.55518	0.162375	0.0811873	−	0.996699i	$-0.474129\pi$
$787$	4.55518	0.162375	0.0811873	+	0.996699i	$0.474129\pi$
$788$	1.27537	0.0454332
$789$	15.3325	0.545852
$790$	−32.8623	−1.16919
$791$	2.95892	0.105207
$792$	4.64368	0.165006
$793$	−15.1756	−0.538901
$794$	−32.4228	−1.15064
$795$	4.34004	0.153925
$796$	−9.18160	−0.325433
$797$	39.4654	1.39794	0.698968	−	0.715153i	$-0.253643\pi$
$797$	39.4654	1.39794	0.698968	+	0.715153i	$0.253643\pi$
$798$	1.29036	0.0456782
$799$	6.96262	0.246320
$800$	−0.681154	−0.0240824
$801$	22.5508	0.796794
$802$	14.2130	0.501878
$803$	1.53827	0.0542843
$804$	−6.53011	−0.230299
$805$	−1.20709	−0.0425445
$806$	−7.41802	−0.261289
$807$	21.2556	0.748232
$808$	3.84068	0.135115
$809$	47.6537	1.67541	0.837707	−	0.546121i	$-0.183896\pi$
$809$	47.6537	1.67541	0.837707	+	0.546121i	$0.183896\pi$
$810$	12.2307	0.429745
$811$	−56.7207	−1.99173	−0.995867	−	0.0908286i	$-0.971048\pi$
$811$	−56.7207	−1.99173	−0.995867	+	0.0908286i	$0.971048\pi$
$812$	−4.84795	−0.170130
$813$	21.3253	0.747909
$814$	−16.2566	−0.569794
$815$	−9.86244	−0.345466
$816$	3.95985	0.138623
$817$	24.2266	0.847582
$818$	−20.0218	−0.700046
$819$	2.07874	0.0726370
$820$	−27.8353	−0.972050
$821$	−7.87088	−0.274696	−0.137348	−	0.990523i	$-0.543858\pi$
$821$	−7.87088	−0.274696	−0.137348	+	0.990523i	$0.543858\pi$
$822$	8.01808	0.279663
$823$	−43.7404	−1.52469	−0.762347	−	0.647169i	$-0.775953\pi$
$823$	−43.7404	−1.52469	−0.762347	+	0.647169i	$0.775953\pi$
$824$	7.33545	0.255542
$825$	−0.835358	−0.0290834
$826$	4.30324	0.149729
$827$	−22.6754	−0.788499	−0.394250	−	0.919003i	$-0.628995\pi$
$827$	−22.6754	−0.788499	−0.394250	+	0.919003i	$0.628995\pi$
$828$	2.54739	0.0885280
$829$	18.9462	0.658030	0.329015	−	0.944325i	$-0.393283\pi$
$829$	18.9462	0.658030	0.329015	+	0.944325i	$0.393283\pi$
$830$	8.46024	0.293659
$831$	4.54984	0.157832
$832$	1.61132	0.0558623
$833$	39.6922	1.37525
$834$	5.82973	0.201867
$835$	−38.6861	−1.33879
$836$	−6.90387	−0.238775
$837$	17.1813	0.593874
$838$	37.3997	1.29195
$839$	43.6875	1.50826	0.754130	−	0.656725i	$-0.228059\pi$
$839$	43.6875	1.50826	0.754130	+	0.656725i	$0.228059\pi$
$840$	0.812086	0.0280196
$841$	62.6367	2.15989
$842$	28.0323	0.966058
$843$	6.46771	0.222760
$844$	−12.3775	−0.426052
$845$	24.7973	0.853053
$846$	−3.01336	−0.103601
$847$	3.88788	0.133589
$848$	2.70654	0.0929430
$849$	−1.05644	−0.0362568
$850$	4.00925	0.137516
$851$	−8.91792	−0.305702
$852$	4.84466	0.165975
$853$	3.03424	0.103890	0.0519452	−	0.998650i	$-0.483458\pi$
$853$	3.03424	0.103890	0.0519452	+	0.998650i	$0.483458\pi$
$854$	−4.76966	−0.163215
$855$	−22.9954	−0.786425
$856$	−12.2690	−0.419345
$857$	10.7632	0.367664	0.183832	−	0.982958i	$-0.441150\pi$
$857$	10.7632	0.367664	0.183832	+	0.982958i	$0.441150\pi$
$858$	1.97610	0.0674628
$859$	−3.14654	−0.107359	−0.0536793	−	0.998558i	$-0.517095\pi$
$859$	−3.14654	−0.107359	−0.0536793	+	0.998558i	$0.517095\pi$
$860$	15.2470	0.519919
$861$	3.97888	0.135600
$862$	30.4709	1.03784
$863$	12.4796	0.424812	0.212406	−	0.977182i	$-0.431870\pi$
$863$	12.4796	0.424812	0.212406	+	0.977182i	$0.431870\pi$
$864$	−3.73207	−0.126968
$865$	−17.9858	−0.611537
$866$	−8.97319	−0.304921
$867$	−11.8706	−0.403147
$868$	−2.33147	−0.0791353
$869$	−25.1331	−0.852581
$870$	−15.3502	−0.520420
$871$	15.6401	0.529946
$872$	17.9443	0.607672
$873$	−42.0526	−1.42326
$874$	−3.78727	−0.128106
$875$	−5.21326	−0.176240
$876$	−0.567709	−0.0191811
$877$	29.8172	1.00685	0.503427	−	0.864038i	$-0.332072\pi$
$877$	29.8172	1.00685	0.503427	+	0.864038i	$0.332072\pi$
$878$	25.1764	0.849663
$879$	−8.64574	−0.291613
$880$	−4.34495	−0.146468
$881$	4.56774	0.153891	0.0769456	−	0.997035i	$-0.475483\pi$
$881$	4.56774	0.153891	0.0769456	+	0.997035i	$0.475483\pi$
$882$	−17.1784	−0.578427
$883$	10.7647	0.362260	0.181130	−	0.983459i	$-0.442024\pi$
$883$	10.7647	0.362260	0.181130	+	0.983459i	$0.442024\pi$
$884$	−9.48416	−0.318987
$885$	13.6255	0.458016
$886$	2.46405	0.0827814
$887$	8.26673	0.277570	0.138785	−	0.990323i	$-0.455680\pi$
$887$	8.26673	0.277570	0.138785	+	0.990323i	$0.455680\pi$
$888$	5.99963	0.201334
$889$	−6.55567	−0.219870
$890$	−21.1001	−0.707277
$891$	9.35408	0.313374
$892$	1.12783	0.0377625
$893$	4.48003	0.149919
$894$	2.57585	0.0861493
$895$	−28.9153	−0.966531
$896$	0.506434	0.0169188
$897$	1.08403	0.0361947
$898$	−21.0293	−0.701756
$899$	44.0699	1.46981
$900$	−1.73517	−0.0578389
$901$	−15.9306	−0.530726
$902$	−21.2884	−0.708827
$903$	−2.17947	−0.0725281
$904$	5.84266	0.194324
$905$	−20.5360	−0.682638
$906$	12.6387	0.419892
$907$	−28.7898	−0.955949	−0.477975	−	0.878374i	$-0.658629\pi$
$907$	−28.7898	−0.955949	−0.477975	+	0.878374i	$0.658629\pi$
$908$	−17.4568	−0.579323
$909$	9.78372	0.324506
$910$	−1.94501	−0.0644765
$911$	4.02025	0.133197	0.0665985	−	0.997780i	$-0.478785\pi$
$911$	4.02025	0.133197	0.0665985	+	0.997780i	$0.478785\pi$
$912$	2.54793	0.0843704
$913$	6.47040	0.214139
$914$	1.97969	0.0654824
$915$	−15.1023	−0.499268
$916$	21.0847	0.696659
$917$	0.506434	0.0167239
$918$	21.9668	0.725014
$919$	14.8215	0.488915	0.244458	−	0.969660i	$-0.421390\pi$
$919$	14.8215	0.488915	0.244458	+	0.969660i	$0.421390\pi$
$920$	−2.38352	−0.0785822
$921$	−13.3195	−0.438891
$922$	−6.49877	−0.214026
$923$	−11.6034	−0.381929
$924$	0.621084	0.0204322
$925$	6.07447	0.199727
$926$	27.2991	0.897103
$927$	18.6863	0.613737
$928$	−9.57271	−0.314239
$929$	−19.4765	−0.639004	−0.319502	−	0.947586i	$-0.603516\pi$
$929$	−19.4765	−0.639004	−0.319502	+	0.947586i	$0.603516\pi$
$930$	−7.38221	−0.242072
$931$	25.5396	0.837025
$932$	−11.8051	−0.386690
$933$	−3.68602	−0.120675
$934$	−9.73770	−0.318627
$935$	25.5742	0.836367
$936$	4.10466	0.134165
$937$	−33.9966	−1.11062	−0.555310	−	0.831643i	$-0.687400\pi$
$937$	−33.9966	−1.11062	−0.555310	+	0.831643i	$0.687400\pi$
$938$	4.91567	0.160502
$939$	−0.0742616	−0.00242344
$940$	2.81951	0.0919622
$941$	44.1517	1.43931	0.719653	−	0.694334i	$-0.244301\pi$
$941$	44.1517	1.43931	0.719653	+	0.694334i	$0.244301\pi$
$942$	−16.4829	−0.537042
$943$	−11.6782	−0.380296
$944$	8.49714	0.276558
$945$	4.50496	0.146546
$946$	11.6609	0.379129
$947$	−6.86659	−0.223134	−0.111567	−	0.993757i	$-0.535587\pi$
$947$	−6.86659	−0.223134	−0.111567	+	0.993757i	$0.535587\pi$
$948$	9.27556	0.301256
$949$	1.35971	0.0441380
$950$	2.57972	0.0836970
$951$	−1.24025	−0.0402178
$952$	−2.98086	−0.0966101
$953$	−26.9441	−0.872805	−0.436403	−	0.899751i	$-0.643748\pi$
$953$	−26.9441	−0.872805	−0.436403	+	0.899751i	$0.643748\pi$
$954$	6.89462	0.223222
$955$	51.4276	1.66416
$956$	4.00218	0.129440
$957$	−11.7398	−0.379495
$958$	−7.05123	−0.227815
$959$	−6.03577	−0.194905
$960$	1.60354	0.0517540
$961$	−9.80595	−0.316321
$962$	−14.3696	−0.463294
$963$	−31.2539	−1.00714
$964$	−24.3560	−0.784455
$965$	37.3215	1.20142
$966$	0.340709	0.0109621
$967$	9.65533	0.310495	0.155247	−	0.987876i	$-0.450383\pi$
$967$	9.65533	0.310495	0.155247	+	0.987876i	$0.450383\pi$
$968$	7.67698	0.246747
$969$	−14.9970	−0.481774
$970$	39.3473	1.26337
$971$	33.3561	1.07045	0.535224	−	0.844710i	$-0.320227\pi$
$971$	33.3561	1.07045	0.535224	+	0.844710i	$0.320227\pi$
$972$	−14.6484	−0.469848
$973$	−4.38844	−0.140687
$974$	−10.7401	−0.344135
$975$	−0.738392	−0.0236475
$976$	−9.41813	−0.301467
$977$	33.4629	1.07057	0.535287	−	0.844671i	$-0.320204\pi$
$977$	33.4629	1.07057	0.535287	+	0.844671i	$0.320204\pi$
$978$	2.78373	0.0890138
$979$	−16.1374	−0.515753
$980$	16.0733	0.513443
$981$	45.7113	1.45945
$982$	24.6316	0.786026
$983$	−0.234127	−0.00746750	−0.00373375	−	0.999993i	$-0.501188\pi$
$983$	−0.234127	−0.00746750	−0.00373375	+	0.999993i	$0.501188\pi$
$984$	7.85666	0.250461
$985$	−3.03987	−0.0968583
$986$	56.3446	1.79438
$987$	−0.403031	−0.0128286
$988$	−6.10249	−0.194146
$989$	6.39686	0.203408
$990$	−11.0683	−0.351773
$991$	29.2613	0.929517	0.464758	−	0.885438i	$-0.346141\pi$
$991$	29.2613	0.929517	0.464758	+	0.885438i	$0.346141\pi$
$992$	−4.60370	−0.146168
$993$	18.4947	0.586912
$994$	−3.64692	−0.115673
$995$	21.8845	0.693785
$996$	−2.38795	−0.0756651
$997$	32.2678	1.02193	0.510966	−	0.859601i	$-0.329288\pi$
$997$	32.2678	1.02193	0.510966	+	0.859601i	$0.329288\pi$
$998$	2.20103	0.0696724
$999$	33.2823	1.05300

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6026.2.a.h.1.11	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6026.2.a.h.1.11	✓	24	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -0.672761 q^{3} +1.00000 q^{4} -2.38352 q^{5} +0.672761 q^{6} -0.506434 q^{7} -1.00000 q^{8} -2.54739 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -0.672761 q^{3} +1.00000 q^{4} -2.38352 q^{5} +0.672761 q^{6} -0.506434 q^{7} -1.00000 q^{8} -2.54739 q^{9} +2.38352 q^{10} +1.82292 q^{11} -0.672761 q^{12} +1.61132 q^{13} +0.506434 q^{14} +1.60354 q^{15} +1.00000 q^{16} -5.88597 q^{17} +2.54739 q^{18} -3.78727 q^{19} -2.38352 q^{20} +0.340709 q^{21} -1.82292 q^{22} -1.00000 q^{23} +0.672761 q^{24} +0.681154 q^{25} -1.61132 q^{26} +3.73207 q^{27} -0.506434 q^{28} +9.57271 q^{29} -1.60354 q^{30} +4.60370 q^{31} -1.00000 q^{32} -1.22639 q^{33} +5.88597 q^{34} +1.20709 q^{35} -2.54739 q^{36} +8.91792 q^{37} +3.78727 q^{38} -1.08403 q^{39} +2.38352 q^{40} +11.6782 q^{41} -0.340709 q^{42} -6.39686 q^{43} +1.82292 q^{44} +6.07175 q^{45} +1.00000 q^{46} -1.18292 q^{47} -0.672761 q^{48} -6.74352 q^{49} -0.681154 q^{50} +3.95985 q^{51} +1.61132 q^{52} +2.70654 q^{53} -3.73207 q^{54} -4.34495 q^{55} +0.506434 q^{56} +2.54793 q^{57} -9.57271 q^{58} +8.49714 q^{59} +1.60354 q^{60} -9.41813 q^{61} -4.60370 q^{62} +1.29009 q^{63} +1.00000 q^{64} -3.84060 q^{65} +1.22639 q^{66} +9.70644 q^{67} -5.88597 q^{68} +0.672761 q^{69} -1.20709 q^{70} -7.20117 q^{71} +2.54739 q^{72} +0.843850 q^{73} -8.91792 q^{74} -0.458254 q^{75} -3.78727 q^{76} -0.923187 q^{77} +1.08403 q^{78} -13.7873 q^{79} -2.38352 q^{80} +5.13139 q^{81} -11.6782 q^{82} +3.54948 q^{83} +0.340709 q^{84} +14.0293 q^{85} +6.39686 q^{86} -6.44014 q^{87} -1.82292 q^{88} -8.85251 q^{89} -6.07175 q^{90} -0.816026 q^{91} -1.00000 q^{92} -3.09719 q^{93} +1.18292 q^{94} +9.02703 q^{95} +0.672761 q^{96} +16.5081 q^{97} +6.74352 q^{98} -4.64368 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 24 q^{2} - q^{3} + 24 q^{4} - q^{5} + q^{6} - 7 q^{7} - 24 q^{8} + 27 q^{9}+O(q^{10}) \) 24 * q - 24 * q^2 - q^3 + 24 * q^4 - q^5 + q^6 - 7 * q^7 - 24 * q^8 + 27 * q^9	\( 24 q - 24 q^{2} - q^{3} + 24 q^{4} - q^{5} + q^{6} - 7 q^{7} - 24 q^{8} + 27 q^{9} + q^{10} - 4 q^{11} - q^{12} - 5 q^{13} + 7 q^{14} - 6 q^{15} + 24 q^{16} + 5 q^{17} - 27 q^{18} - 20 q^{19} - q^{20} + 4 q^{22} - 24 q^{23} + q^{24} + q^{25} + 5 q^{26} - q^{27} - 7 q^{28} - 6 q^{29} + 6 q^{30} - 23 q^{31} - 24 q^{32} - 6 q^{33} - 5 q^{34} + 5 q^{35} + 27 q^{36} - 6 q^{37} + 20 q^{38} - 39 q^{39} + q^{40} - q^{41} - 44 q^{43} - 4 q^{44} - 13 q^{45} + 24 q^{46} + 32 q^{47} - q^{48} - 13 q^{49} - q^{50} - 44 q^{51} - 5 q^{52} + 21 q^{53} + q^{54} - 13 q^{55} + 7 q^{56} + 10 q^{57} + 6 q^{58} - 24 q^{59} - 6 q^{60} - 40 q^{61} + 23 q^{62} - 54 q^{63} + 24 q^{64} - 29 q^{65} + 6 q^{66} - 17 q^{67} + 5 q^{68} + q^{69} - 5 q^{70} + 4 q^{71} - 27 q^{72} - 16 q^{73} + 6 q^{74} - 36 q^{75} - 20 q^{76} + 24 q^{77} + 39 q^{78} - 53 q^{79} - q^{80} + 24 q^{81} + q^{82} - 9 q^{83} - 37 q^{85} + 44 q^{86} + 7 q^{87} + 4 q^{88} - 46 q^{89} + 13 q^{90} - 44 q^{91} - 24 q^{92} + 23 q^{93} - 32 q^{94} + 28 q^{95} + q^{96} - 20 q^{97} + 13 q^{98} - 78 q^{99}+O(q^{100}) \) 24 * q - 24 * q^2 - q^3 + 24 * q^4 - q^5 + q^6 - 7 * q^7 - 24 * q^8 + 27 * q^9 + q^10 - 4 * q^11 - q^12 - 5 * q^13 + 7 * q^14 - 6 * q^15 + 24 * q^16 + 5 * q^17 - 27 * q^18 - 20 * q^19 - q^20 + 4 * q^22 - 24 * q^23 + q^24 + q^25 + 5 * q^26 - q^27 - 7 * q^28 - 6 * q^29 + 6 * q^30 - 23 * q^31 - 24 * q^32 - 6 * q^33 - 5 * q^34 + 5 * q^35 + 27 * q^36 - 6 * q^37 + 20 * q^38 - 39 * q^39 + q^40 - q^41 - 44 * q^43 - 4 * q^44 - 13 * q^45 + 24 * q^46 + 32 * q^47 - q^48 - 13 * q^49 - q^50 - 44 * q^51 - 5 * q^52 + 21 * q^53 + q^54 - 13 * q^55 + 7 * q^56 + 10 * q^57 + 6 * q^58 - 24 * q^59 - 6 * q^60 - 40 * q^61 + 23 * q^62 - 54 * q^63 + 24 * q^64 - 29 * q^65 + 6 * q^66 - 17 * q^67 + 5 * q^68 + q^69 - 5 * q^70 + 4 * q^71 - 27 * q^72 - 16 * q^73 + 6 * q^74 - 36 * q^75 - 20 * q^76 + 24 * q^77 + 39 * q^78 - 53 * q^79 - q^80 + 24 * q^81 + q^82 - 9 * q^83 - 37 * q^85 + 44 * q^86 + 7 * q^87 + 4 * q^88 - 46 * q^89 + 13 * q^90 - 44 * q^91 - 24 * q^92 + 23 * q^93 - 32 * q^94 + 28 * q^95 + q^96 - 20 * q^97 + 13 * q^98 - 78 * q^99

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