LMFDB - Embedded newform 6043.2.a.c.1.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6043,2,Mod(1,6043)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6043, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6043.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6043 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6043.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:	$48.2535979415$
Analytic rank:	$0$
Dimension:	$259$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
Character	$\chi$	$=$	6043.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.52420 q^{2} -2.07136 q^{3} +4.37157 q^{4} -1.62373 q^{5} +5.22852 q^{6} +0.688788 q^{7} -5.98631 q^{8} +1.29054 q^{9} +O(q^{10})$	\(q-2.52420 q^{2} -2.07136 q^{3} +4.37157 q^{4} -1.62373 q^{5} +5.22852 q^{6} +0.688788 q^{7} -5.98631 q^{8} +1.29054 q^{9} +4.09861 q^{10} +2.09195 q^{11} -9.05510 q^{12} -4.48255 q^{13} -1.73864 q^{14} +3.36333 q^{15} +6.36747 q^{16} +5.61737 q^{17} -3.25757 q^{18} +5.89460 q^{19} -7.09824 q^{20} -1.42673 q^{21} -5.28050 q^{22} +6.65297 q^{23} +12.3998 q^{24} -2.36351 q^{25} +11.3148 q^{26} +3.54091 q^{27} +3.01108 q^{28} -3.30090 q^{29} -8.48970 q^{30} +3.19087 q^{31} -4.10015 q^{32} -4.33319 q^{33} -14.1793 q^{34} -1.11840 q^{35} +5.64167 q^{36} +9.00368 q^{37} -14.8791 q^{38} +9.28498 q^{39} +9.72013 q^{40} +2.16057 q^{41} +3.60134 q^{42} +6.94751 q^{43} +9.14511 q^{44} -2.09548 q^{45} -16.7934 q^{46} -0.852802 q^{47} -13.1893 q^{48} -6.52557 q^{49} +5.96596 q^{50} -11.6356 q^{51} -19.5958 q^{52} +10.0050 q^{53} -8.93797 q^{54} -3.39676 q^{55} -4.12330 q^{56} -12.2098 q^{57} +8.33213 q^{58} +0.480979 q^{59} +14.7030 q^{60} +1.56106 q^{61} -8.05437 q^{62} +0.888907 q^{63} -2.38537 q^{64} +7.27844 q^{65} +10.9378 q^{66} -1.13929 q^{67} +24.5567 q^{68} -13.7807 q^{69} +2.82307 q^{70} +6.51436 q^{71} -7.72555 q^{72} -1.97652 q^{73} -22.7271 q^{74} +4.89568 q^{75} +25.7687 q^{76} +1.44091 q^{77} -23.4371 q^{78} +7.77639 q^{79} -10.3390 q^{80} -11.2061 q^{81} -5.45370 q^{82} +16.5602 q^{83} -6.23704 q^{84} -9.12108 q^{85} -17.5369 q^{86} +6.83737 q^{87} -12.5231 q^{88} -11.6107 q^{89} +5.28941 q^{90} -3.08753 q^{91} +29.0839 q^{92} -6.60944 q^{93} +2.15264 q^{94} -9.57123 q^{95} +8.49288 q^{96} +3.05657 q^{97} +16.4718 q^{98} +2.69974 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 259 q + 39 q^{2} + 25 q^{3} + 271 q^{4} + 83 q^{5} + 18 q^{6} + 26 q^{7} + 111 q^{8} + 286 q^{9}+O(q^{10}) $ 259 * q + 39 * q^2 + 25 * q^3 + 271 * q^4 + 83 * q^5 + 18 * q^6 + 26 * q^7 + 111 * q^8 + 286 * q^9	\( 259 q + 39 q^{2} + 25 q^{3} + 271 q^{4} + 83 q^{5} + 18 q^{6} + 26 q^{7} + 111 q^{8} + 286 q^{9} + 36 q^{10} + 35 q^{11} + 58 q^{12} + 109 q^{13} + 31 q^{14} + 30 q^{15} + 287 q^{16} + 124 q^{17} + 97 q^{18} + 42 q^{19} + 149 q^{20} + 99 q^{21} + 22 q^{22} + 63 q^{23} + 53 q^{24} + 308 q^{25} + 86 q^{26} + 82 q^{27} + 52 q^{28} + 131 q^{29} + 6 q^{30} + 29 q^{31} + 251 q^{32} + 147 q^{33} + 24 q^{34} + 79 q^{35} + 315 q^{36} + 108 q^{37} + 124 q^{38} + 48 q^{39} + 87 q^{40} + 190 q^{41} + 28 q^{42} + 36 q^{43} + 70 q^{44} + 211 q^{45} + 19 q^{46} + 186 q^{47} + 103 q^{48} + 297 q^{49} + 161 q^{50} + 20 q^{51} + 173 q^{52} + 213 q^{53} + 56 q^{54} + 35 q^{55} + 99 q^{56} + 80 q^{57} + 32 q^{58} + 135 q^{59} + 23 q^{60} + 83 q^{61} + 172 q^{62} + 85 q^{63} + 297 q^{64} + 177 q^{65} + 41 q^{66} + 30 q^{67} + 271 q^{68} + 168 q^{69} + 24 q^{70} + 63 q^{71} + 241 q^{72} + 152 q^{73} + 32 q^{74} + 36 q^{75} + 92 q^{76} + 396 q^{77} + 21 q^{78} - 2 q^{79} + 242 q^{80} + 343 q^{81} + 40 q^{82} + 236 q^{83} + 92 q^{84} + 124 q^{85} + 55 q^{86} + 113 q^{87} + 7 q^{88} + 214 q^{89} + 100 q^{90} + 2 q^{91} + 176 q^{92} + 228 q^{93} + 51 q^{94} + 96 q^{95} + 48 q^{96} + 135 q^{97} + 261 q^{98} + 26 q^{99}+O(q^{100}) \) 259 * q + 39 * q^2 + 25 * q^3 + 271 * q^4 + 83 * q^5 + 18 * q^6 + 26 * q^7 + 111 * q^8 + 286 * q^9 + 36 * q^10 + 35 * q^11 + 58 * q^12 + 109 * q^13 + 31 * q^14 + 30 * q^15 + 287 * q^16 + 124 * q^17 + 97 * q^18 + 42 * q^19 + 149 * q^20 + 99 * q^21 + 22 * q^22 + 63 * q^23 + 53 * q^24 + 308 * q^25 + 86 * q^26 + 82 * q^27 + 52 * q^28 + 131 * q^29 + 6 * q^30 + 29 * q^31 + 251 * q^32 + 147 * q^33 + 24 * q^34 + 79 * q^35 + 315 * q^36 + 108 * q^37 + 124 * q^38 + 48 * q^39 + 87 * q^40 + 190 * q^41 + 28 * q^42 + 36 * q^43 + 70 * q^44 + 211 * q^45 + 19 * q^46 + 186 * q^47 + 103 * q^48 + 297 * q^49 + 161 * q^50 + 20 * q^51 + 173 * q^52 + 213 * q^53 + 56 * q^54 + 35 * q^55 + 99 * q^56 + 80 * q^57 + 32 * q^58 + 135 * q^59 + 23 * q^60 + 83 * q^61 + 172 * q^62 + 85 * q^63 + 297 * q^64 + 177 * q^65 + 41 * q^66 + 30 * q^67 + 271 * q^68 + 168 * q^69 + 24 * q^70 + 63 * q^71 + 241 * q^72 + 152 * q^73 + 32 * q^74 + 36 * q^75 + 92 * q^76 + 396 * q^77 + 21 * q^78 - 2 * q^79 + 242 * q^80 + 343 * q^81 + 40 * q^82 + 236 * q^83 + 92 * q^84 + 124 * q^85 + 55 * q^86 + 113 * q^87 + 7 * q^88 + 214 * q^89 + 100 * q^90 + 2 * q^91 + 176 * q^92 + 228 * q^93 + 51 * q^94 + 96 * q^95 + 48 * q^96 + 135 * q^97 + 261 * q^98 + 26 * 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 $

$2$	−2.52420	−1.78488	−0.892438	−	0.451170i	$-0.851007\pi$
$2$	−2.52420	−1.78488	−0.892438	+	0.451170i	$0.851007\pi$
$3$	−2.07136	−1.19590	−0.597950	−	0.801533i	$-0.704018\pi$
$3$	−2.07136	−1.19590	−0.597950	+	0.801533i	$0.704018\pi$
$4$	4.37157	2.18578
$5$	−1.62373	−0.726153	−0.363077	−	0.931759i	$-0.618274\pi$
$5$	−1.62373	−0.726153	−0.363077	+	0.931759i	$0.618274\pi$
$6$	5.22852	2.13454
$7$	0.688788	0.260337	0.130169	−	0.991492i	$-0.458448\pi$
$7$	0.688788	0.260337	0.130169	+	0.991492i	$0.458448\pi$
$8$	−5.98631	−2.11648
$9$	1.29054	0.430179
$10$	4.09861	1.29609
$11$	2.09195	0.630747	0.315374	−	0.948968i	$-0.397870\pi$
$11$	2.09195	0.630747	0.315374	+	0.948968i	$0.397870\pi$
$12$	−9.05510	−2.61398
$13$	−4.48255	−1.24324	−0.621618	−	0.783321i	$-0.713524\pi$
$13$	−4.48255	−1.24324	−0.621618	+	0.783321i	$0.713524\pi$
$14$	−1.73864	−0.464670
$15$	3.36333	0.868407
$16$	6.36747	1.59187
$17$	5.61737	1.36241	0.681206	−	0.732092i	$-0.261456\pi$
$17$	5.61737	1.36241	0.681206	+	0.732092i	$0.261456\pi$
$18$	−3.25757	−0.767817
$19$	5.89460	1.35231	0.676157	−	0.736757i	$-0.263644\pi$
$19$	5.89460	1.35231	0.676157	+	0.736757i	$0.263644\pi$
$20$	−7.09824	−1.58721
$21$	−1.42673	−0.311338
$22$	−5.28050	−1.12581
$23$	6.65297	1.38724	0.693620	−	0.720341i	$-0.256015\pi$
$23$	6.65297	1.38724	0.693620	+	0.720341i	$0.256015\pi$
$24$	12.3998	2.53110
$25$	−2.36351	−0.472702
$26$	11.3148	2.21902
$27$	3.54091	0.681449
$28$	3.01108	0.569041
$29$	−3.30090	−0.612963	−0.306481	−	0.951877i	$-0.599152\pi$
$29$	−3.30090	−0.612963	−0.306481	+	0.951877i	$0.599152\pi$
$30$	−8.48970	−1.55000
$31$	3.19087	0.573096	0.286548	−	0.958066i	$-0.407492\pi$
$31$	3.19087	0.573096	0.286548	+	0.958066i	$0.407492\pi$
$32$	−4.10015	−0.724810
$33$	−4.33319	−0.754311
$34$	−14.1793	−2.43174
$35$	−1.11840	−0.189045
$36$	5.64167	0.940279
$37$	9.00368	1.48020	0.740098	−	0.672499i	$-0.234779\pi$
$37$	9.00368	1.48020	0.740098	+	0.672499i	$0.234779\pi$
$38$	−14.8791	−2.41371
$39$	9.28498	1.48679
$40$	9.72013	1.53689
$41$	2.16057	0.337424	0.168712	−	0.985665i	$-0.446039\pi$
$41$	2.16057	0.337424	0.168712	+	0.985665i	$0.446039\pi$
$42$	3.60134	0.555700
$43$	6.94751	1.05949	0.529743	−	0.848158i	$-0.322288\pi$
$43$	6.94751	1.05949	0.529743	+	0.848158i	$0.322288\pi$
$44$	9.14511	1.37868
$45$	−2.09548	−0.312376
$46$	−16.7934	−2.47605
$47$	−0.852802	−0.124394	−0.0621969	−	0.998064i	$-0.519811\pi$
$47$	−0.852802	−0.124394	−0.0621969	+	0.998064i	$0.519811\pi$
$48$	−13.1893	−1.90372
$49$	−6.52557	−0.932224
$50$	5.96596	0.843714
$51$	−11.6356	−1.62931
$52$	−19.5958	−2.71745
$53$	10.0050	1.37429	0.687147	−	0.726519i	$-0.258863\pi$
$53$	10.0050	1.37429	0.687147	+	0.726519i	$0.258863\pi$
$54$	−8.93797	−1.21630
$55$	−3.39676	−0.458019
$56$	−4.12330	−0.550999
$57$	−12.2098	−1.61723
$58$	8.33213	1.09406
$59$	0.480979	0.0626182	0.0313091	−	0.999510i	$-0.490032\pi$
$59$	0.480979	0.0626182	0.0313091	+	0.999510i	$0.490032\pi$
$60$	14.7030	1.89815
$61$	1.56106	0.199874	0.0999369	−	0.994994i	$-0.468136\pi$
$61$	1.56106	0.199874	0.0999369	+	0.994994i	$0.468136\pi$
$62$	−8.05437	−1.02291
$63$	0.888907	0.111992
$64$	−2.38537	−0.298172
$65$	7.27844	0.902780
$66$	10.9378	1.34635
$67$	−1.13929	−0.139186	−0.0695930	−	0.997575i	$-0.522170\pi$
$67$	−1.13929	−0.139186	−0.0695930	+	0.997575i	$0.522170\pi$
$68$	24.5567	2.97794
$69$	−13.7807	−1.65900
$70$	2.82307	0.337422
$71$	6.51436	0.773112	0.386556	−	0.922266i	$-0.373665\pi$
$71$	6.51436	0.773112	0.386556	+	0.922266i	$0.373665\pi$
$72$	−7.72555	−0.910465
$73$	−1.97652	−0.231334	−0.115667	−	0.993288i	$-0.536901\pi$
$73$	−1.97652	−0.231334	−0.115667	+	0.993288i	$0.536901\pi$
$74$	−22.7271	−2.64197
$75$	4.89568	0.565304
$76$	25.7687	2.95587
$77$	1.44091	0.164207
$78$	−23.4371	−2.65373
$79$	7.77639	0.874912	0.437456	−	0.899240i	$-0.355880\pi$
$79$	7.77639	0.874912	0.437456	+	0.899240i	$0.355880\pi$
$80$	−10.3390	−1.15594
$81$	−11.2061	−1.24513
$82$	−5.45370	−0.602260
$83$	16.5602	1.81772	0.908859	−	0.417104i	$-0.136955\pi$
$83$	16.5602	1.81772	0.908859	+	0.417104i	$0.136955\pi$
$84$	−6.23704	−0.680517
$85$	−9.12108	−0.989320
$86$	−17.5369	−1.89105
$87$	6.83737	0.733043
$88$	−12.5231	−1.33496
$89$	−11.6107	−1.23073	−0.615363	−	0.788244i	$-0.710991\pi$
$89$	−11.6107	−1.23073	−0.615363	+	0.788244i	$0.710991\pi$
$90$	5.28941	0.557552
$91$	−3.08753	−0.323661
$92$	29.0839	3.03221
$93$	−6.60944	−0.685367
$94$	2.15264	0.222028
$95$	−9.57123	−0.981987
$96$	8.49288	0.866801
$97$	3.05657	0.310348	0.155174	−	0.987887i	$-0.450406\pi$
$97$	3.05657	0.310348	0.155174	+	0.987887i	$0.450406\pi$
$98$	16.4718	1.66391
$99$	2.69974	0.271334
$100$	−10.3322	−1.03322
$101$	−0.496871	−0.0494405	−0.0247203	−	0.999694i	$-0.507870\pi$
$101$	−0.496871	−0.0494405	−0.0247203	+	0.999694i	$0.507870\pi$
$102$	29.3705	2.90812
$103$	16.5147	1.62724	0.813621	−	0.581395i	$-0.197493\pi$
$103$	16.5147	1.62724	0.813621	+	0.581395i	$0.197493\pi$
$104$	26.8339	2.63128
$105$	2.31662	0.226079
$106$	−25.2546	−2.45294
$107$	4.35250	0.420772	0.210386	−	0.977618i	$-0.432528\pi$
$107$	4.35250	0.420772	0.210386	+	0.977618i	$0.432528\pi$
$108$	15.4794	1.48950
$109$	0.672082	0.0643738	0.0321869	−	0.999482i	$-0.489753\pi$
$109$	0.672082	0.0643738	0.0321869	+	0.999482i	$0.489753\pi$
$110$	8.57409	0.817508
$111$	−18.6499	−1.77017
$112$	4.38584	0.414423
$113$	13.3391	1.25484	0.627418	−	0.778682i	$-0.284112\pi$
$113$	13.3391	1.25484	0.627418	+	0.778682i	$0.284112\pi$
$114$	30.8201	2.88656
$115$	−10.8026	−1.00735
$116$	−14.4301	−1.33980
$117$	−5.78490	−0.534814
$118$	−1.21409	−0.111766
$119$	3.86918	0.354687
$120$	−20.1339	−1.83797
$121$	−6.62374	−0.602158
$122$	−3.94043	−0.356750
$123$	−4.47532	−0.403526
$124$	13.9491	1.25267
$125$	11.9563	1.06941
$126$	−2.24378	−0.199891
$127$	−3.54946	−0.314963	−0.157482	−	0.987522i	$-0.550338\pi$
$127$	−3.54946	−0.314963	−0.157482	+	0.987522i	$0.550338\pi$
$128$	14.2214	1.25701
$129$	−14.3908	−1.26704
$130$	−18.3722	−1.61135
$131$	0.171634	0.0149957	0.00749787	−	0.999972i	$-0.497613\pi$
$131$	0.171634	0.0149957	0.00749787	+	0.999972i	$0.497613\pi$
$132$	−18.9428	−1.64876
$133$	4.06013	0.352058
$134$	2.87578	0.248430
$135$	−5.74948	−0.494837
$136$	−33.6273	−2.88352
$137$	−4.02905	−0.344225	−0.172112	−	0.985077i	$-0.555059\pi$
$137$	−4.02905	−0.344225	−0.172112	+	0.985077i	$0.555059\pi$
$138$	34.7852	2.96111
$139$	0.424771	0.0360286	0.0180143	−	0.999838i	$-0.494266\pi$
$139$	0.424771	0.0360286	0.0180143	+	0.999838i	$0.494266\pi$
$140$	−4.88918	−0.413211
$141$	1.76646	0.148763
$142$	−16.4435	−1.37991
$143$	−9.37728	−0.784168
$144$	8.21746	0.684788
$145$	5.35977	0.445105
$146$	4.98913	0.412903
$147$	13.5168	1.11485
$148$	39.3602	3.23539
$149$	−3.50478	−0.287122	−0.143561	−	0.989641i	$-0.545855\pi$
$149$	−3.50478	−0.287122	−0.143561	+	0.989641i	$0.545855\pi$
$150$	−12.3577	−1.00900
$151$	−11.8839	−0.967101	−0.483551	−	0.875316i	$-0.660653\pi$
$151$	−11.8839	−0.967101	−0.483551	+	0.875316i	$0.660653\pi$
$152$	−35.2869	−2.86214
$153$	7.24942	0.586081
$154$	−3.63715	−0.293090
$155$	−5.18110	−0.416156
$156$	40.5899	3.24980
$157$	−5.18353	−0.413690	−0.206845	−	0.978374i	$-0.566320\pi$
$157$	−5.18353	−0.413690	−0.206845	+	0.978374i	$0.566320\pi$
$158$	−19.6291	−1.56161
$159$	−20.7240	−1.64352
$160$	6.65752	0.526323
$161$	4.58249	0.361150
$162$	28.2865	2.22239
$163$	−13.8207	−1.08252	−0.541260	−	0.840855i	$-0.682052\pi$
$163$	−13.8207	−1.08252	−0.541260	+	0.840855i	$0.682052\pi$
$164$	9.44507	0.737536
$165$	7.03592	0.547746
$166$	−41.8012	−3.24440
$167$	23.0276	1.78193	0.890964	−	0.454073i	$-0.150029\pi$
$167$	23.0276	1.78193	0.890964	+	0.454073i	$0.150029\pi$
$168$	8.54084	0.658940
$169$	7.09326	0.545635
$170$	23.0234	1.76581
$171$	7.60720	0.581737
$172$	30.3715	2.31581
$173$	3.12579	0.237649	0.118825	−	0.992915i	$-0.462087\pi$
$173$	3.12579	0.237649	0.118825	+	0.992915i	$0.462087\pi$
$174$	−17.2589	−1.30839
$175$	−1.62796	−0.123062
$176$	13.3205	1.00407
$177$	−0.996282	−0.0748851
$178$	29.3076	2.19669
$179$	7.09578	0.530363	0.265182	−	0.964198i	$-0.414568\pi$
$179$	7.09578	0.530363	0.265182	+	0.964198i	$0.414568\pi$
$180$	−9.16054	−0.682786
$181$	−18.0689	−1.34305	−0.671524	−	0.740983i	$-0.734360\pi$
$181$	−18.0689	−1.34305	−0.671524	+	0.740983i	$0.734360\pi$
$182$	7.79353	0.577695
$183$	−3.23353	−0.239029
$184$	−39.8267	−2.93606
$185$	−14.6195	−1.07485
$186$	16.6835	1.22329
$187$	11.7513	0.859338
$188$	−3.72808	−0.271898
$189$	2.43894	0.177407
$190$	24.1597	1.75273
$191$	12.5840	0.910545	0.455272	−	0.890352i	$-0.349542\pi$
$191$	12.5840	0.910545	0.455272	+	0.890352i	$0.349542\pi$
$192$	4.94097	0.356584
$193$	−14.3178	−1.03062	−0.515309	−	0.857004i	$-0.672323\pi$
$193$	−14.3178	−1.03062	−0.515309	+	0.857004i	$0.672323\pi$
$194$	−7.71540	−0.553933
$195$	−15.0763	−1.07963
$196$	−28.5270	−2.03764
$197$	−21.9980	−1.56729	−0.783647	−	0.621206i	$-0.786643\pi$
$197$	−21.9980	−1.56729	−0.783647	+	0.621206i	$0.786643\pi$
$198$	−6.81468	−0.484298
$199$	5.89430	0.417836	0.208918	−	0.977933i	$-0.433006\pi$
$199$	5.89430	0.417836	0.208918	+	0.977933i	$0.433006\pi$
$200$	14.1487	1.00046
$201$	2.35987	0.166453
$202$	1.25420	0.0882452
$203$	−2.27362	−0.159577
$204$	−50.8658	−3.56132
$205$	−3.50818	−0.245022
$206$	−41.6864	−2.90443
$207$	8.58590	0.596762
$208$	−28.5425	−1.97907
$209$	12.3312	0.852969
$210$	−5.84760	−0.403523
$211$	−13.0520	−0.898534	−0.449267	−	0.893397i	$-0.648315\pi$
$211$	−13.0520	−0.898534	−0.449267	+	0.893397i	$0.648315\pi$
$212$	43.7376	3.00391
$213$	−13.4936	−0.924565
$214$	−10.9866	−0.751026
$215$	−11.2809	−0.769349
$216$	−21.1970	−1.44227
$217$	2.19783	0.149198
$218$	−1.69647	−0.114899
$219$	4.09409	0.276653
$220$	−14.8492	−1.00113
$221$	−25.1801	−1.69380
$222$	47.0760	3.15953
$223$	16.3424	1.09437	0.547183	−	0.837013i	$-0.315700\pi$
$223$	16.3424	1.09437	0.547183	+	0.837013i	$0.315700\pi$
$224$	−2.82413	−0.188695
$225$	−3.05020	−0.203346
$226$	−33.6705	−2.23973
$227$	15.5276	1.03060	0.515302	−	0.857008i	$-0.327680\pi$
$227$	15.5276	1.03060	0.515302	+	0.857008i	$0.327680\pi$
$228$	−53.3762	−3.53492
$229$	−27.0451	−1.78719	−0.893596	−	0.448872i	$-0.851826\pi$
$229$	−27.0451	−1.78719	−0.893596	+	0.448872i	$0.851826\pi$
$230$	27.2679	1.79799
$231$	−2.98465	−0.196376
$232$	19.7602	1.29732
$233$	−7.40687	−0.485240	−0.242620	−	0.970121i	$-0.578007\pi$
$233$	−7.40687	−0.485240	−0.242620	+	0.970121i	$0.578007\pi$
$234$	14.6022	0.954577
$235$	1.38472	0.0903290
$236$	2.10263	0.136870
$237$	−16.1077	−1.04631
$238$	−9.76656	−0.633072
$239$	−13.4465	−0.869781	−0.434890	−	0.900483i	$-0.643213\pi$
$239$	−13.4465	−0.869781	−0.434890	+	0.900483i	$0.643213\pi$
$240$	21.4159	1.38239
$241$	−4.46948	−0.287905	−0.143952	−	0.989585i	$-0.545981\pi$
$241$	−4.46948	−0.287905	−0.143952	+	0.989585i	$0.545981\pi$
$242$	16.7196	1.07478
$243$	12.5892	0.807597
$244$	6.82430	0.436881
$245$	10.5958	0.676938
$246$	11.2966	0.720244
$247$	−26.4228	−1.68125
$248$	−19.1015	−1.21295
$249$	−34.3021	−2.17381
$250$	−30.1801	−1.90876
$251$	13.6837	0.863707	0.431853	−	0.901944i	$-0.357860\pi$
$251$	13.6837	0.863707	0.431853	+	0.901944i	$0.357860\pi$
$252$	3.88592	0.244790
$253$	13.9177	0.874998
$254$	8.95953	0.562171
$255$	18.8930	1.18313
$256$	−31.1270	−1.94544
$257$	−21.8454	−1.36268	−0.681341	−	0.731966i	$-0.738603\pi$
$257$	−21.8454	−1.36268	−0.681341	+	0.731966i	$0.738603\pi$
$258$	36.3252	2.26151
$259$	6.20163	0.385351
$260$	31.8182	1.97328
$261$	−4.25994	−0.263684
$262$	−0.433238	−0.0267655
$263$	−15.5863	−0.961091	−0.480545	−	0.876970i	$-0.659561\pi$
$263$	−15.5863	−0.961091	−0.480545	+	0.876970i	$0.659561\pi$
$264$	25.9398	1.59648
$265$	−16.2454	−0.997947
$266$	−10.2486	−0.628380
$267$	24.0499	1.47183
$268$	−4.98047	−0.304230
$269$	22.1090	1.34801	0.674005	−	0.738727i	$-0.264573\pi$
$269$	22.1090	1.34801	0.674005	+	0.738727i	$0.264573\pi$
$270$	14.5128	0.883222
$271$	19.1852	1.16542	0.582710	−	0.812680i	$-0.301992\pi$
$271$	19.1852	1.16542	0.582710	+	0.812680i	$0.301992\pi$
$272$	35.7685	2.16878
$273$	6.39538	0.387066
$274$	10.1701	0.614399
$275$	−4.94435	−0.298155
$276$	−60.2433	−3.62622
$277$	22.7089	1.36445	0.682224	−	0.731144i	$-0.261013\pi$
$277$	22.7089	1.36445	0.682224	+	0.731144i	$0.261013\pi$
$278$	−1.07221	−0.0643067
$279$	4.11793	0.246534
$280$	6.69511	0.400109
$281$	20.6902	1.23428	0.617138	−	0.786855i	$-0.288292\pi$
$281$	20.6902	1.23428	0.617138	+	0.786855i	$0.288292\pi$
$282$	−4.45889	−0.265523
$283$	−23.4113	−1.39166	−0.695828	−	0.718209i	$-0.744962\pi$
$283$	−23.4113	−1.39166	−0.695828	+	0.718209i	$0.744962\pi$
$284$	28.4780	1.68986
$285$	19.8255	1.17436
$286$	23.6701	1.39964
$287$	1.48817	0.0878441
$288$	−5.29139	−0.311798
$289$	14.5548	0.856167
$290$	−13.5291	−0.794457
$291$	−6.33127	−0.371146
$292$	−8.64050	−0.505647
$293$	−25.2693	−1.47625	−0.738124	−	0.674665i	$-0.764288\pi$
$293$	−25.2693	−1.47625	−0.738124	+	0.674665i	$0.764288\pi$
$294$	−34.1191	−1.98987
$295$	−0.780979	−0.0454704
$296$	−53.8988	−3.13280
$297$	7.40743	0.429822
$298$	8.84674	0.512478
$299$	−29.8223	−1.72467
$300$	21.4018	1.23563
$301$	4.78536	0.275824
$302$	29.9974	1.72616
$303$	1.02920	0.0591260
$304$	37.5337	2.15271
$305$	−2.53474	−0.145139
$306$	−18.2990	−1.04608
$307$	−27.8547	−1.58975	−0.794875	−	0.606774i	$-0.792463\pi$
$307$	−27.8547	−1.58975	−0.794875	+	0.606774i	$0.792463\pi$
$308$	6.29905	0.358921
$309$	−34.2079	−1.94602
$310$	13.0781	0.742787
$311$	−29.0968	−1.64993	−0.824963	−	0.565186i	$-0.808804\pi$
$311$	−29.0968	−1.64993	−0.824963	+	0.565186i	$0.808804\pi$
$312$	−55.5827	−3.14675
$313$	−7.39086	−0.417756	−0.208878	−	0.977942i	$-0.566981\pi$
$313$	−7.39086	−0.417756	−0.208878	+	0.977942i	$0.566981\pi$
$314$	13.0842	0.738386
$315$	−1.44334	−0.0813231
$316$	33.9950	1.91237
$317$	12.0602	0.677369	0.338685	−	0.940900i	$-0.390018\pi$
$317$	12.0602	0.677369	0.338685	+	0.940900i	$0.390018\pi$
$318$	52.3114	2.93348
$319$	−6.90534	−0.386625
$320$	3.87320	0.216518
$321$	−9.01560	−0.503202
$322$	−11.5671	−0.644609
$323$	33.1122	1.84241
$324$	−48.9883	−2.72157
$325$	10.5945	0.587680
$326$	34.8861	1.93216
$327$	−1.39212	−0.0769846
$328$	−12.9338	−0.714151
$329$	−0.587400	−0.0323844
$330$	−17.7600	−0.977658
$331$	−12.7449	−0.700525	−0.350262	−	0.936652i	$-0.613908\pi$
$331$	−12.7449	−0.700525	−0.350262	+	0.936652i	$0.613908\pi$
$332$	72.3940	3.97314
$333$	11.6196	0.636750
$334$	−58.1262	−3.18052
$335$	1.84989	0.101070
$336$	−9.08466	−0.495609
$337$	−16.6467	−0.906804	−0.453402	−	0.891306i	$-0.649790\pi$
$337$	−16.6467	−0.906804	−0.453402	+	0.891306i	$0.649790\pi$
$338$	−17.9048	−0.973892
$339$	−27.6301	−1.50066
$340$	−39.8734	−2.16244
$341$	6.67514	0.361479
$342$	−19.2021	−1.03833
$343$	−9.31625	−0.503030
$344$	−41.5899	−2.24238
$345$	22.3761	1.20469
$346$	−7.89010	−0.424175
$347$	33.8128	1.81516	0.907582	−	0.419874i	$-0.137926\pi$
$347$	33.8128	1.81516	0.907582	+	0.419874i	$0.137926\pi$
$348$	29.8900	1.60227
$349$	−5.99679	−0.321001	−0.160501	−	0.987036i	$-0.551311\pi$
$349$	−5.99679	−0.321001	−0.160501	+	0.987036i	$0.551311\pi$
$350$	4.10928	0.219650
$351$	−15.8723	−0.847202
$352$	−8.57731	−0.457172
$353$	12.2642	0.652756	0.326378	−	0.945239i	$-0.394172\pi$
$353$	12.2642	0.652756	0.326378	+	0.945239i	$0.394172\pi$
$354$	2.51481	0.133661
$355$	−10.5775	−0.561398
$356$	−50.7568	−2.69010
$357$	−8.01446	−0.424170
$358$	−17.9111	−0.946633
$359$	−1.62838	−0.0859427	−0.0429713	−	0.999076i	$-0.513682\pi$
$359$	−1.62838	−0.0859427	−0.0429713	+	0.999076i	$0.513682\pi$
$360$	12.5442	0.661137
$361$	15.7463	0.828754
$362$	45.6093	2.39717
$363$	13.7201	0.720121
$364$	−13.4973	−0.707453
$365$	3.20933	0.167984
$366$	8.16206	0.426638
$367$	−37.2740	−1.94569	−0.972843	−	0.231464i	$-0.925648\pi$
$367$	−37.2740	−1.94569	−0.972843	+	0.231464i	$0.925648\pi$
$368$	42.3626	2.20830
$369$	2.78829	0.145153
$370$	36.9026	1.91847
$371$	6.89133	0.357780
$372$	−28.8936	−1.49806
$373$	−13.6188	−0.705154	−0.352577	−	0.935783i	$-0.614695\pi$
$373$	−13.6188	−0.705154	−0.352577	+	0.935783i	$0.614695\pi$
$374$	−29.6625	−1.53381
$375$	−24.7659	−1.27890
$376$	5.10513	0.263277
$377$	14.7965	0.762057
$378$	−6.15636	−0.316649
$379$	26.5360	1.36306	0.681531	−	0.731789i	$-0.261314\pi$
$379$	26.5360	1.36306	0.681531	+	0.731789i	$0.261314\pi$
$380$	−41.8413	−2.14641
$381$	7.35221	0.376665
$382$	−31.7644	−1.62521
$383$	−20.5615	−1.05064	−0.525322	−	0.850904i	$-0.676055\pi$
$383$	−20.5615	−1.05064	−0.525322	+	0.850904i	$0.676055\pi$
$384$	−29.4577	−1.50326
$385$	−2.33965	−0.119240
$386$	36.1410	1.83953
$387$	8.96602	0.455769
$388$	13.3620	0.678354
$389$	−8.25424	−0.418507	−0.209253	−	0.977861i	$-0.567103\pi$
$389$	−8.25424	−0.418507	−0.209253	+	0.977861i	$0.567103\pi$
$390$	38.0555	1.92701
$391$	37.3722	1.88999
$392$	39.0641	1.97303
$393$	−0.355516	−0.0179334
$394$	55.5274	2.79743
$395$	−12.6267	−0.635320
$396$	11.8021	0.593078
$397$	25.1977	1.26464	0.632318	−	0.774709i	$-0.282104\pi$
$397$	25.1977	1.26464	0.632318	+	0.774709i	$0.282104\pi$
$398$	−14.8784	−0.745786
$399$	−8.41000	−0.421027
$400$	−15.0496	−0.752479
$401$	−26.4193	−1.31932	−0.659659	−	0.751565i	$-0.729299\pi$
$401$	−26.4193	−1.31932	−0.659659	+	0.751565i	$0.729299\pi$
$402$	−5.95678	−0.297097
$403$	−14.3032	−0.712494
$404$	−2.17211	−0.108066
$405$	18.1957	0.904151
$406$	5.73907	0.284825
$407$	18.8353	0.933630
$408$	69.6543	3.44840
$409$	27.7135	1.37034	0.685172	−	0.728382i	$-0.259727\pi$
$409$	27.7135	1.37034	0.685172	+	0.728382i	$0.259727\pi$
$410$	8.85532	0.437333
$411$	8.34562	0.411659
$412$	72.1952	3.55680
$413$	0.331293	0.0163019
$414$	−21.6725	−1.06515
$415$	−26.8892	−1.31994
$416$	18.3791	0.901110
$417$	−0.879855	−0.0430867
$418$	−31.1264	−1.52244
$419$	16.2752	0.795097	0.397548	−	0.917581i	$-0.369861\pi$
$419$	16.2752	0.795097	0.397548	+	0.917581i	$0.369861\pi$
$420$	10.1273	0.494160
$421$	9.12951	0.444945	0.222473	−	0.974939i	$-0.428587\pi$
$421$	9.12951	0.444945	0.222473	+	0.974939i	$0.428587\pi$
$422$	32.9457	1.60377
$423$	−1.10057	−0.0535116
$424$	−59.8930	−2.90866
$425$	−13.2767	−0.644014
$426$	34.0605	1.65023
$427$	1.07524	0.0520346
$428$	19.0273	0.919717
$429$	19.4237	0.937787
$430$	28.4751	1.37319
$431$	−3.14663	−0.151568	−0.0757840	−	0.997124i	$-0.524146\pi$
$431$	−3.14663	−0.151568	−0.0757840	+	0.997124i	$0.524146\pi$
$432$	22.5467	1.08478
$433$	−14.3577	−0.689987	−0.344993	−	0.938605i	$-0.612119\pi$
$433$	−14.3577	−0.689987	−0.344993	+	0.938605i	$0.612119\pi$
$434$	−5.54776	−0.266301
$435$	−11.1020	−0.532301
$436$	2.93805	0.140707
$437$	39.2166	1.87598
$438$	−10.3343	−0.493792
$439$	25.5655	1.22017	0.610087	−	0.792334i	$-0.291134\pi$
$439$	25.5655	1.22017	0.610087	+	0.792334i	$0.291134\pi$
$440$	20.3340	0.969388
$441$	−8.42149	−0.401023
$442$	63.5596	3.02322
$443$	23.9462	1.13772	0.568859	−	0.822435i	$-0.307385\pi$
$443$	23.9462	1.13772	0.568859	+	0.822435i	$0.307385\pi$
$444$	−81.5292	−3.86921
$445$	18.8525	0.893696
$446$	−41.2514	−1.95331
$447$	7.25966	0.343370
$448$	−1.64302	−0.0776253
$449$	36.9754	1.74498	0.872489	−	0.488634i	$-0.162504\pi$
$449$	36.9754	1.74498	0.872489	+	0.488634i	$0.162504\pi$
$450$	7.69929	0.362948
$451$	4.51981	0.212829
$452$	58.3128	2.74280
$453$	24.6159	1.15656
$454$	−39.1948	−1.83950
$455$	5.01330	0.235027
$456$	73.0919	3.42284
$457$	19.4683	0.910691	0.455345	−	0.890315i	$-0.349516\pi$
$457$	19.4683	0.910691	0.455345	+	0.890315i	$0.349516\pi$
$458$	68.2672	3.18992
$459$	19.8906	0.928415
$460$	−47.2243	−2.20185
$461$	−3.32823	−0.155011	−0.0775055	−	0.996992i	$-0.524696\pi$
$461$	−3.32823	−0.155011	−0.0775055	+	0.996992i	$0.524696\pi$
$462$	7.53384	0.350506
$463$	4.57456	0.212598	0.106299	−	0.994334i	$-0.466100\pi$
$463$	4.57456	0.212598	0.106299	+	0.994334i	$0.466100\pi$
$464$	−21.0184	−0.975756
$465$	10.7319	0.497681
$466$	18.6964	0.866094
$467$	18.3399	0.848671	0.424335	−	0.905505i	$-0.360508\pi$
$467$	18.3399	0.848671	0.424335	+	0.905505i	$0.360508\pi$
$468$	−25.2891	−1.16899
$469$	−0.784727	−0.0362353
$470$	−3.49530	−0.161226
$471$	10.7370	0.494733
$472$	−2.87929	−0.132530
$473$	14.5339	0.668268
$474$	40.6590	1.86753
$475$	−13.9319	−0.639241
$476$	16.9144	0.775269
$477$	12.9118	0.591192
$478$	33.9416	1.55245
$479$	18.8036	0.859159	0.429579	−	0.903029i	$-0.358662\pi$
$479$	18.8036	0.859159	0.429579	+	0.903029i	$0.358662\pi$
$480$	−13.7901	−0.629430
$481$	−40.3595	−1.84023
$482$	11.2819	0.513874
$483$	−9.49198	−0.431900
$484$	−28.9561	−1.31619
$485$	−4.96304	−0.225360
$486$	−31.7776	−1.44146
$487$	−16.5401	−0.749503	−0.374752	−	0.927125i	$-0.622272\pi$
$487$	−16.5401	−0.749503	−0.374752	+	0.927125i	$0.622272\pi$
$488$	−9.34501	−0.423029
$489$	28.6276	1.29459
$490$	−26.7458	−1.20825
$491$	12.9076	0.582513	0.291257	−	0.956645i	$-0.405927\pi$
$491$	12.9076	0.582513	0.291257	+	0.956645i	$0.405927\pi$
$492$	−19.5642	−0.882020
$493$	−18.5424	−0.835108
$494$	66.6965	3.00082
$495$	−4.38365	−0.197030
$496$	20.3178	0.912294
$497$	4.48701	0.201270
$498$	86.5854	3.87998
$499$	4.10677	0.183844	0.0919221	−	0.995766i	$-0.470699\pi$
$499$	4.10677	0.183844	0.0919221	+	0.995766i	$0.470699\pi$
$500$	52.2679	2.33749
$501$	−47.6985	−2.13101
$502$	−34.5403	−1.54161
$503$	17.0676	0.761005	0.380503	−	0.924780i	$-0.375751\pi$
$503$	17.0676	0.761005	0.380503	+	0.924780i	$0.375751\pi$
$504$	−5.32127	−0.237028
$505$	0.806783	0.0359014
$506$	−35.1310	−1.56176
$507$	−14.6927	−0.652526
$508$	−15.5167	−0.688442
$509$	15.8543	0.702729	0.351365	−	0.936239i	$-0.385718\pi$
$509$	15.8543	0.702729	0.351365	+	0.936239i	$0.385718\pi$
$510$	−47.6898	−2.11174
$511$	−1.36141	−0.0602250
$512$	50.1277	2.21535
$513$	20.8723	0.921534
$514$	55.1422	2.43222
$515$	−26.8154	−1.18163
$516$	−62.9104	−2.76948
$517$	−1.78402	−0.0784611
$518$	−15.6541	−0.687803
$519$	−6.47464	−0.284205
$520$	−43.5710	−1.91071
$521$	1.98542	0.0869826	0.0434913	−	0.999054i	$-0.486152\pi$
$521$	1.98542	0.0869826	0.0434913	+	0.999054i	$0.486152\pi$
$522$	10.7529	0.470643
$523$	0.196445	0.00858995	0.00429498	−	0.999991i	$-0.498633\pi$
$523$	0.196445	0.00858995	0.00429498	+	0.999991i	$0.498633\pi$
$524$	0.750310	0.0327774
$525$	3.37209	0.147170
$526$	39.3428	1.71543
$527$	17.9243	0.780794
$528$	−27.5915	−1.20076
$529$	21.2620	0.924434
$530$	41.0066	1.78121
$531$	0.620722	0.0269370
$532$	17.7491	0.769523
$533$	−9.68486	−0.419498
$534$	−60.7065	−2.62703
$535$	−7.06727	−0.305545
$536$	6.82011	0.294584
$537$	−14.6979	−0.634262
$538$	−55.8075	−2.40603
$539$	−13.6512	−0.587998
$540$	−25.1343	−1.08161
$541$	−29.3091	−1.26010	−0.630048	−	0.776556i	$-0.716965\pi$
$541$	−29.3091	−1.26010	−0.630048	+	0.776556i	$0.716965\pi$
$542$	−48.4273	−2.08013
$543$	37.4271	1.60615
$544$	−23.0320	−0.987490
$545$	−1.09128	−0.0467452
$546$	−16.1432	−0.690866
$547$	5.34934	0.228721	0.114361	−	0.993439i	$-0.463518\pi$
$547$	5.34934	0.228721	0.114361	+	0.993439i	$0.463518\pi$
$548$	−17.6133	−0.752401
$549$	2.01461	0.0859815
$550$	12.4805	0.532170
$551$	−19.4575	−0.828918
$552$	82.4955	3.51124
$553$	5.35628	0.227772
$554$	−57.3218	−2.43537
$555$	30.2823	1.28541
$556$	1.85692	0.0787508
$557$	6.67068	0.282646	0.141323	−	0.989964i	$-0.454864\pi$
$557$	6.67068	0.282646	0.141323	+	0.989964i	$0.454864\pi$
$558$	−10.3945	−0.440033
$559$	−31.1426	−1.31719
$560$	−7.12141	−0.300935
$561$	−24.3411	−1.02768
$562$	−52.2262	−2.20303
$563$	−5.30501	−0.223579	−0.111790	−	0.993732i	$-0.535658\pi$
$563$	−5.30501	−0.223579	−0.111790	+	0.993732i	$0.535658\pi$
$564$	7.72220	0.325163
$565$	−21.6591	−0.911204
$566$	59.0946	2.48393
$567$	−7.71865	−0.324153
$568$	−38.9969	−1.63627
$569$	−1.42531	−0.0597521	−0.0298760	−	0.999554i	$-0.509511\pi$
$569$	−1.42531	−0.0597521	−0.0298760	+	0.999554i	$0.509511\pi$
$570$	−50.0434	−2.09609
$571$	22.2837	0.932543	0.466272	−	0.884642i	$-0.345597\pi$
$571$	22.2837	0.932543	0.466272	+	0.884642i	$0.345597\pi$
$572$	−40.9934	−1.71402
$573$	−26.0660	−1.08892
$574$	−3.75644	−0.156791
$575$	−15.7243	−0.655751
$576$	−3.07841	−0.128267
$577$	−15.9398	−0.663582	−0.331791	−	0.943353i	$-0.607653\pi$
$577$	−15.9398	−0.663582	−0.331791	+	0.943353i	$0.607653\pi$
$578$	−36.7393	−1.52815
$579$	29.6574	1.23252
$580$	23.4306	0.972903
$581$	11.4065	0.473220
$582$	15.9814	0.662449
$583$	20.9300	0.866832
$584$	11.8321	0.489614
$585$	9.39310	0.388357
$586$	63.7847	2.63492
$587$	−16.8990	−0.697495	−0.348748	−	0.937217i	$-0.613393\pi$
$587$	−16.8990	−0.697495	−0.348748	+	0.937217i	$0.613393\pi$
$588$	59.0897	2.43682
$589$	18.8089	0.775007
$590$	1.97135	0.0811590
$591$	45.5659	1.87433
$592$	57.3307	2.35628
$593$	13.1854	0.541459	0.270730	−	0.962655i	$-0.412735\pi$
$593$	13.1854	0.541459	0.270730	+	0.962655i	$0.412735\pi$
$594$	−18.6978	−0.767180
$595$	−6.28249	−0.257557
$596$	−15.3214	−0.627588
$597$	−12.2092	−0.499691
$598$	75.2773	3.07832
$599$	−1.11554	−0.0455798	−0.0227899	−	0.999740i	$-0.507255\pi$
$599$	−1.11554	−0.0455798	−0.0227899	+	0.999740i	$0.507255\pi$
$600$	−29.3070	−1.19645
$601$	1.17284	0.0478413	0.0239206	−	0.999714i	$-0.492385\pi$
$601$	1.17284	0.0478413	0.0239206	+	0.999714i	$0.492385\pi$
$602$	−12.0792	−0.492311
$603$	−1.47029	−0.0598749
$604$	−51.9514	−2.11387
$605$	10.7551	0.437259
$606$	−2.59790	−0.105533
$607$	11.6594	0.473240	0.236620	−	0.971602i	$-0.423960\pi$
$607$	11.6594	0.473240	0.236620	+	0.971602i	$0.423960\pi$
$608$	−24.1687	−0.980171
$609$	4.70950	0.190838
$610$	6.39819	0.259055
$611$	3.82273	0.154651
$612$	31.6914	1.28105
$613$	−45.3192	−1.83043	−0.915213	−	0.402970i	$-0.867978\pi$
$613$	−45.3192	−1.83043	−0.915213	+	0.402970i	$0.867978\pi$
$614$	70.3106	2.83751
$615$	7.26670	0.293022
$616$	−8.62574	−0.347541
$617$	−30.5786	−1.23105	−0.615524	−	0.788118i	$-0.711055\pi$
$617$	−30.5786	−1.23105	−0.615524	+	0.788118i	$0.711055\pi$
$618$	86.3475	3.47341
$619$	39.2501	1.57759	0.788796	−	0.614655i	$-0.210705\pi$
$619$	39.2501	1.57759	0.788796	+	0.614655i	$0.210705\pi$
$620$	−22.6495	−0.909627
$621$	23.5576	0.945334
$622$	73.4460	2.94492
$623$	−7.99728	−0.320404
$624$	59.1219	2.36677
$625$	−7.59629	−0.303851
$626$	18.6560	0.745643
$627$	−25.5424	−1.02007
$628$	−22.6601	−0.904238
$629$	50.5770	2.01664
$630$	3.64328	0.145152
$631$	−10.0891	−0.401642	−0.200821	−	0.979628i	$-0.564361\pi$
$631$	−10.0891	−0.401642	−0.200821	+	0.979628i	$0.564361\pi$
$632$	−46.5518	−1.85173
$633$	27.0353	1.07456
$634$	−30.4423	−1.20902
$635$	5.76335	0.228712
$636$	−90.5963	−3.59238
$637$	29.2512	1.15897
$638$	17.4304	0.690077
$639$	8.40702	0.332577
$640$	−23.0918	−0.912782
$641$	8.33297	0.329132	0.164566	−	0.986366i	$-0.447378\pi$
$641$	8.33297	0.329132	0.164566	+	0.986366i	$0.447378\pi$
$642$	22.7571	0.898153
$643$	4.36176	0.172011	0.0860055	−	0.996295i	$-0.472590\pi$
$643$	4.36176	0.172011	0.0860055	+	0.996295i	$0.472590\pi$
$644$	20.0327	0.789397
$645$	23.3668	0.920065
$646$	−83.5816	−3.28847
$647$	9.63376	0.378742	0.189371	−	0.981906i	$-0.439355\pi$
$647$	9.63376	0.378742	0.189371	+	0.981906i	$0.439355\pi$
$648$	67.0833	2.63528
$649$	1.00619	0.0394962
$650$	−26.7427	−1.04894
$651$	−4.55250	−0.178427
$652$	−60.4181	−2.36615
$653$	−11.8282	−0.462872	−0.231436	−	0.972850i	$-0.574342\pi$
$653$	−11.8282	−0.462872	−0.231436	+	0.972850i	$0.574342\pi$
$654$	3.51400	0.137408
$655$	−0.278687	−0.0108892
$656$	13.7574	0.537135
$657$	−2.55078	−0.0995152
$658$	1.48271	0.0578021
$659$	−2.86190	−0.111484	−0.0557419	−	0.998445i	$-0.517752\pi$
$659$	−2.86190	−0.111484	−0.0557419	+	0.998445i	$0.517752\pi$
$660$	30.7580	1.19725
$661$	−2.89709	−0.112684	−0.0563419	−	0.998412i	$-0.517944\pi$
$661$	−2.89709	−0.112684	−0.0563419	+	0.998412i	$0.517944\pi$
$662$	32.1707	1.25035
$663$	52.1572	2.02562
$664$	−99.1344	−3.84716
$665$	−6.59255	−0.255648
$666$	−29.3301	−1.13652
$667$	−21.9608	−0.850326
$668$	100.667	3.89491
$669$	−33.8510	−1.30875
$670$	−4.66949	−0.180398
$671$	3.26567	0.126070
$672$	5.84980	0.225661
$673$	43.7221	1.68536	0.842681	−	0.538413i	$-0.180976\pi$
$673$	43.7221	1.68536	0.842681	+	0.538413i	$0.180976\pi$
$674$	42.0196	1.61853
$675$	−8.36898	−0.322122
$676$	31.0087	1.19264
$677$	−30.0260	−1.15399	−0.576997	−	0.816746i	$-0.695776\pi$
$677$	−30.0260	−1.15399	−0.576997	+	0.816746i	$0.695776\pi$
$678$	69.7438	2.67849
$679$	2.10533	0.0807952
$680$	54.6016	2.09387
$681$	−32.1633	−1.23250
$682$	−16.8494	−0.645196
$683$	7.90073	0.302313	0.151156	−	0.988510i	$-0.451700\pi$
$683$	7.90073	0.302313	0.151156	+	0.988510i	$0.451700\pi$
$684$	33.2554	1.27155
$685$	6.54208	0.249960
$686$	23.5161	0.897847
$687$	56.0202	2.13730
$688$	44.2381	1.68656
$689$	−44.8479	−1.70857
$690$	−56.4817	−2.15022
$691$	24.1033	0.916931	0.458466	−	0.888712i	$-0.348399\pi$
$691$	24.1033	0.916931	0.458466	+	0.888712i	$0.348399\pi$
$692$	13.6646	0.519450
$693$	1.85955	0.0706385
$694$	−85.3501	−3.23985
$695$	−0.689713	−0.0261623
$696$	−40.9306	−1.55147
$697$	12.1367	0.459711
$698$	15.1371	0.572947
$699$	15.3423	0.580299
$700$	−7.11672	−0.268987
$701$	−42.2891	−1.59724	−0.798618	−	0.601838i	$-0.794435\pi$
$701$	−42.2891	−1.59724	−0.798618	+	0.601838i	$0.794435\pi$
$702$	40.0649	1.51215
$703$	53.0731	2.00169
$704$	−4.99009	−0.188071
$705$	−2.86825	−0.108025
$706$	−30.9572	−1.16509
$707$	−0.342239	−0.0128712
$708$	−4.35531	−0.163683
$709$	16.7600	0.629435	0.314718	−	0.949185i	$-0.398090\pi$
$709$	16.7600	0.629435	0.314718	+	0.949185i	$0.398090\pi$
$710$	26.6998	1.00203
$711$	10.0357	0.376369
$712$	69.5049	2.60481
$713$	21.2287	0.795022
$714$	20.2301	0.757092
$715$	15.2262	0.569426
$716$	31.0197	1.15926
$717$	27.8525	1.04017
$718$	4.11035	0.153397
$719$	−1.50368	−0.0560777	−0.0280389	−	0.999607i	$-0.508926\pi$
$719$	−1.50368	−0.0560777	−0.0280389	+	0.999607i	$0.508926\pi$
$720$	−13.3429	−0.497261
$721$	11.3751	0.423632
$722$	−39.7468	−1.47922
$723$	9.25791	0.344305
$724$	−78.9892	−2.93561
$725$	7.80172	0.289748
$726$	−34.6324	−1.28533
$727$	−11.2221	−0.416206	−0.208103	−	0.978107i	$-0.566729\pi$
$727$	−11.2221	−0.416206	−0.208103	+	0.978107i	$0.566729\pi$
$728$	18.4829	0.685021
$729$	7.54162	0.279319
$730$	−8.10099	−0.299831
$731$	39.0267	1.44346
$732$	−14.1356	−0.522466
$733$	39.2750	1.45065	0.725327	−	0.688405i	$-0.241689\pi$
$733$	39.2750	1.45065	0.725327	+	0.688405i	$0.241689\pi$
$734$	94.0869	3.47281
$735$	−21.9476	−0.809550
$736$	−27.2781	−1.00549
$737$	−2.38333	−0.0877912
$738$	−7.03820	−0.259080
$739$	3.19304	0.117458	0.0587289	−	0.998274i	$-0.481295\pi$
$739$	3.19304	0.117458	0.0587289	+	0.998274i	$0.481295\pi$
$740$	−63.9103	−2.34939
$741$	54.7313	2.01060
$742$	−17.3951	−0.638593
$743$	−31.2082	−1.14492	−0.572458	−	0.819934i	$-0.694010\pi$
$743$	−31.2082	−1.14492	−0.572458	+	0.819934i	$0.694010\pi$
$744$	39.5661	1.45056
$745$	5.69080	0.208495
$746$	34.3765	1.25861
$747$	21.3715	0.781944
$748$	51.3715	1.87833
$749$	2.99795	0.109543
$750$	62.5140	2.28269
$751$	−20.5658	−0.750456	−0.375228	−	0.926932i	$-0.622436\pi$
$751$	−20.5658	−0.750456	−0.375228	+	0.926932i	$0.622436\pi$
$752$	−5.43019	−0.198019
$753$	−28.3439	−1.03291
$754$	−37.3492	−1.36018
$755$	19.2963	0.702264
$756$	10.6620	0.387773
$757$	41.5545	1.51032	0.755162	−	0.655538i	$-0.227558\pi$
$757$	41.5545	1.51032	0.755162	+	0.655538i	$0.227558\pi$
$758$	−66.9820	−2.43290
$759$	−28.8286	−1.04641
$760$	57.2963	2.07835
$761$	7.44436	0.269858	0.134929	−	0.990855i	$-0.456919\pi$
$761$	7.44436	0.269858	0.134929	+	0.990855i	$0.456919\pi$
$762$	−18.5584	−0.672300
$763$	0.462922	0.0167589
$764$	55.0117	1.99025
$765$	−11.7711	−0.425585
$766$	51.9013	1.87527
$767$	−2.15601	−0.0778492
$768$	64.4752	2.32655
$769$	14.3588	0.517793	0.258897	−	0.965905i	$-0.416641\pi$
$769$	14.3588	0.517793	0.258897	+	0.965905i	$0.416641\pi$
$770$	5.90573	0.212828
$771$	45.2498	1.62963
$772$	−62.5913	−2.25271
$773$	−14.7312	−0.529844	−0.264922	−	0.964270i	$-0.585346\pi$
$773$	−14.7312	−0.529844	−0.264922	+	0.964270i	$0.585346\pi$
$774$	−22.6320	−0.813491
$775$	−7.54164	−0.270904
$776$	−18.2976	−0.656845
$777$	−12.8458	−0.460841
$778$	20.8353	0.746982
$779$	12.7357	0.456304
$780$	−65.9070	−2.35985
$781$	13.6277	0.487638
$782$	−94.3347	−3.37340
$783$	−11.6882	−0.417703
$784$	−41.5514	−1.48398
$785$	8.41663	0.300403
$786$	0.897392	0.0320089
$787$	46.4281	1.65498	0.827492	−	0.561478i	$-0.189767\pi$
$787$	46.4281	1.65498	0.827492	+	0.561478i	$0.189767\pi$
$788$	−96.1659	−3.42577
$789$	32.2848	1.14937
$790$	31.8724	1.13397
$791$	9.18781	0.326681
$792$	−16.1615	−0.574273
$793$	−6.99755	−0.248490
$794$	−63.6040	−2.25722
$795$	33.6501	1.19345
$796$	25.7674	0.913300
$797$	50.7996	1.79941	0.899706	−	0.436495i	$-0.143781\pi$
$797$	50.7996	1.79941	0.899706	+	0.436495i	$0.143781\pi$
$798$	21.2285	0.751480
$799$	−4.79050	−0.169476
$800$	9.69073	0.342619
$801$	−14.9840	−0.529433
$802$	66.6875	2.35482
$803$	−4.13479	−0.145914
$804$	10.3163	0.363829
$805$	−7.44071	−0.262251
$806$	36.1041	1.27171
$807$	−45.7957	−1.61209
$808$	2.97442	0.104640
$809$	21.0852	0.741315	0.370657	−	0.928770i	$-0.379132\pi$
$809$	21.0852	0.741315	0.370657	+	0.928770i	$0.379132\pi$
$810$	−45.9295	−1.61380
$811$	−18.4030	−0.646215	−0.323108	−	0.946362i	$-0.604728\pi$
$811$	−18.4030	−0.646215	−0.323108	+	0.946362i	$0.604728\pi$
$812$	−9.93930	−0.348801
$813$	−39.7396	−1.39373
$814$	−47.5439	−1.66641
$815$	22.4410	0.786075
$816$	−74.0894	−2.59365
$817$	40.9528	1.43276
$818$	−69.9543	−2.44589
$819$	−3.98457	−0.139232
$820$	−15.3362	−0.535564
$821$	−13.9096	−0.485447	−0.242723	−	0.970096i	$-0.578041\pi$
$821$	−13.9096	−0.485447	−0.242723	+	0.970096i	$0.578041\pi$
$822$	−21.0660	−0.734760
$823$	13.8770	0.483720	0.241860	−	0.970311i	$-0.422242\pi$
$823$	13.8770	0.483720	0.241860	+	0.970311i	$0.422242\pi$
$824$	−98.8621	−3.44402
$825$	10.2415	0.356564
$826$	−0.836248	−0.0290968
$827$	0.248566	0.00864348	0.00432174	−	0.999991i	$-0.498624\pi$
$827$	0.248566	0.00864348	0.00432174	+	0.999991i	$0.498624\pi$
$828$	37.5339	1.30439
$829$	54.3703	1.88836	0.944179	−	0.329432i	$-0.106857\pi$
$829$	54.3703	1.88836	0.944179	+	0.329432i	$0.106857\pi$
$830$	67.8738	2.35593
$831$	−47.0384	−1.63174
$832$	10.6926	0.370698
$833$	−36.6565	−1.27007
$834$	2.22093	0.0769044
$835$	−37.3905	−1.29395
$836$	53.9068	1.86441
$837$	11.2986	0.390536
$838$	−41.0819	−1.41915
$839$	−22.4326	−0.774458	−0.387229	−	0.921983i	$-0.626568\pi$
$839$	−22.4326	−0.774458	−0.387229	+	0.921983i	$0.626568\pi$
$840$	−13.8680	−0.478491
$841$	−18.1040	−0.624277
$842$	−23.0447	−0.794172
$843$	−42.8569	−1.47607
$844$	−57.0576	−1.96400
$845$	−11.5175	−0.396215
$846$	2.77806	0.0955117
$847$	−4.56235	−0.156764
$848$	63.7066	2.18769
$849$	48.4932	1.66428
$850$	33.5130	1.14949
$851$	59.9012	2.05339
$852$	−58.9881	−2.02090
$853$	43.1163	1.47627	0.738137	−	0.674651i	$-0.235706\pi$
$853$	43.1163	1.47627	0.738137	+	0.674651i	$0.235706\pi$
$854$	−2.71412	−0.0928754
$855$	−12.3520	−0.422430
$856$	−26.0554	−0.890555
$857$	19.2837	0.658717	0.329359	−	0.944205i	$-0.393167\pi$
$857$	19.2837	0.658717	0.329359	+	0.944205i	$0.393167\pi$
$858$	−49.0293	−1.67383
$859$	−42.2019	−1.43991	−0.719955	−	0.694021i	$-0.755837\pi$
$859$	−42.2019	−1.43991	−0.719955	+	0.694021i	$0.755837\pi$
$860$	−49.3151	−1.68163
$861$	−3.08255	−0.105053
$862$	7.94272	0.270530
$863$	10.8416	0.369051	0.184526	−	0.982828i	$-0.440925\pi$
$863$	10.8416	0.369051	0.184526	+	0.982828i	$0.440925\pi$
$864$	−14.5183	−0.493922
$865$	−5.07543	−0.172570
$866$	36.2416	1.23154
$867$	−30.1483	−1.02389
$868$	9.60797	0.326116
$869$	16.2678	0.551849
$870$	28.0237	0.950092
$871$	5.10691	0.173041
$872$	−4.02329	−0.136246
$873$	3.94462	0.133505
$874$	−98.9904	−3.34840
$875$	8.23538	0.278407
$876$	17.8976	0.604704
$877$	36.6629	1.23802	0.619010	−	0.785383i	$-0.287534\pi$
$877$	36.6629	1.23802	0.619010	+	0.785383i	$0.287534\pi$
$878$	−64.5323	−2.17786
$879$	52.3418	1.76545
$880$	−21.6288	−0.729106
$881$	−10.8467	−0.365435	−0.182717	−	0.983165i	$-0.558489\pi$
$881$	−10.8467	−0.365435	−0.182717	+	0.983165i	$0.558489\pi$
$882$	21.2575	0.715777
$883$	−39.2528	−1.32096	−0.660481	−	0.750842i	$-0.729648\pi$
$883$	−39.2528	−1.32096	−0.660481	+	0.750842i	$0.729648\pi$
$884$	−110.077	−3.70228
$885$	1.61769	0.0543781
$886$	−60.4449	−2.03069
$887$	21.5717	0.724307	0.362153	−	0.932118i	$-0.382042\pi$
$887$	21.5717	0.724307	0.362153	+	0.932118i	$0.382042\pi$
$888$	111.644	3.74652
$889$	−2.44482	−0.0819967
$890$	−47.5875	−1.59514
$891$	−23.4427	−0.785359
$892$	71.4418	2.39205
$893$	−5.02692	−0.168220
$894$	−18.3248	−0.612873
$895$	−11.5216	−0.385125
$896$	9.79556	0.327247
$897$	61.7727	2.06253
$898$	−93.3332	−3.11457
$899$	−10.5327	−0.351287
$900$	−13.3341	−0.444471
$901$	56.2018	1.87235
$902$	−11.4089	−0.379874
$903$	−9.91222	−0.329858
$904$	−79.8519	−2.65584
$905$	29.3389	0.975258
$906$	−62.1354	−2.06431
$907$	33.8923	1.12538	0.562688	−	0.826670i	$-0.309767\pi$
$907$	33.8923	1.12538	0.562688	+	0.826670i	$0.309767\pi$
$908$	67.8801	2.25268
$909$	−0.641231	−0.0212683
$910$	−12.6546	−0.419495
$911$	−2.59335	−0.0859215	−0.0429607	−	0.999077i	$-0.513679\pi$
$911$	−2.59335	−0.0859215	−0.0429607	+	0.999077i	$0.513679\pi$
$912$	−77.7459	−2.57442
$913$	34.6431	1.14652
$914$	−49.1419	−1.62547
$915$	5.25037	0.173572
$916$	−118.230	−3.90642
$917$	0.118219	0.00390395
$918$	−50.2079	−1.65711
$919$	−27.5326	−0.908216	−0.454108	−	0.890947i	$-0.650042\pi$
$919$	−27.5326	−0.908216	−0.454108	+	0.890947i	$0.650042\pi$
$920$	64.6677	2.13203
$921$	57.6970	1.90118
$922$	8.40110	0.276675
$923$	−29.2009	−0.961160
$924$	−13.0476	−0.429234
$925$	−21.2803	−0.699691
$926$	−11.5471	−0.379461
$927$	21.3128	0.700006
$928$	13.5342	0.444282
$929$	6.35068	0.208359	0.104180	−	0.994559i	$-0.466778\pi$
$929$	6.35068	0.208359	0.104180	+	0.994559i	$0.466778\pi$
$930$	−27.0895	−0.888299
$931$	−38.4656	−1.26066
$932$	−32.3796	−1.06063
$933$	60.2699	1.97315
$934$	−46.2936	−1.51477
$935$	−19.0809	−0.624011
$936$	34.6302	1.13192
$937$	−41.7164	−1.36281	−0.681407	−	0.731905i	$-0.738632\pi$
$937$	−41.7164	−1.36281	−0.681407	+	0.731905i	$0.738632\pi$
$938$	1.98080	0.0646756
$939$	15.3091	0.499595
$940$	6.05339	0.197440
$941$	2.08806	0.0680689	0.0340344	−	0.999421i	$-0.489164\pi$
$941$	2.08806	0.0680689	0.0340344	+	0.999421i	$0.489164\pi$
$942$	−27.1022	−0.883037
$943$	14.3742	0.468088
$944$	3.06262	0.0996799
$945$	−3.96017	−0.128824
$946$	−36.6863	−1.19278
$947$	7.53538	0.244867	0.122433	−	0.992477i	$-0.460930\pi$
$947$	7.53538	0.244867	0.122433	+	0.992477i	$0.460930\pi$
$948$	−70.4160	−2.28700
$949$	8.85986	0.287603
$950$	35.1670	1.14097
$951$	−24.9811	−0.810066
$952$	−23.1621	−0.750687
$953$	59.4725	1.92650	0.963252	−	0.268599i	$-0.0865608\pi$
$953$	59.4725	1.92650	0.963252	+	0.268599i	$0.0865608\pi$
$954$	−32.5920	−1.05520
$955$	−20.4330	−0.661195
$956$	−58.7822	−1.90115
$957$	14.3034	0.462365
$958$	−47.4640	−1.53349
$959$	−2.77516	−0.0896146
$960$	−8.02279	−0.258934
$961$	−20.8184	−0.671560
$962$	101.875	3.28459
$963$	5.61706	0.181007
$964$	−19.5386	−0.629297
$965$	23.2482	0.748387
$966$	23.9596	0.770889
$967$	−30.9105	−0.994013	−0.497007	−	0.867747i	$-0.665568\pi$
$967$	−30.9105	−0.994013	−0.497007	+	0.867747i	$0.665568\pi$
$968$	39.6517	1.27445
$969$	−68.5872	−2.20334
$970$	12.5277	0.402240
$971$	29.2378	0.938286	0.469143	−	0.883122i	$-0.344563\pi$
$971$	29.2378	0.938286	0.469143	+	0.883122i	$0.344563\pi$
$972$	55.0345	1.76523
$973$	0.292578	0.00937961
$974$	41.7505	1.33777
$975$	−21.9451	−0.702807
$976$	9.94003	0.318173
$977$	−39.5008	−1.26374	−0.631871	−	0.775074i	$-0.717713\pi$
$977$	−39.5008	−1.26374	−0.631871	+	0.775074i	$0.717713\pi$
$978$	−72.2618	−2.31068
$979$	−24.2889	−0.776277
$980$	46.3200	1.47964
$981$	0.867347	0.0276922
$982$	−32.5814	−1.03971
$983$	19.6440	0.626546	0.313273	−	0.949663i	$-0.398575\pi$
$983$	19.6440	0.626546	0.313273	+	0.949663i	$0.398575\pi$
$984$	26.7906	0.854054
$985$	35.7188	1.13810
$986$	46.8047	1.49056
$987$	1.21672	0.0387285
$988$	−115.509	−3.67484
$989$	46.2216	1.46976
$990$	11.0652	0.351675
$991$	10.4506	0.331976	0.165988	−	0.986128i	$-0.446919\pi$
$991$	10.4506	0.331976	0.165988	+	0.986128i	$0.446919\pi$
$992$	−13.0830	−0.415386
$993$	26.3994	0.837758
$994$	−11.3261	−0.359242
$995$	−9.57075	−0.303413
$996$	−149.954	−4.75148
$997$	18.3579	0.581402	0.290701	−	0.956814i	$-0.406112\pi$
$997$	18.3579	0.581402	0.290701	+	0.956814i	$0.406112\pi$
$998$	−10.3663	−0.328139
$999$	31.8813	1.00868

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6043.2.a.c.1.12	✓	259

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6043.2.a.c.1.12	✓	259	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:	\( N \)	\(=\)	\( 6043 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6043.a (trivial)

\(f(q)\)	\(=\)	\(q-2.52420 q^{2} -2.07136 q^{3} +4.37157 q^{4} -1.62373 q^{5} +5.22852 q^{6} +0.688788 q^{7} -5.98631 q^{8} +1.29054 q^{9} +O(q^{10})\)	\(q-2.52420 q^{2} -2.07136 q^{3} +4.37157 q^{4} -1.62373 q^{5} +5.22852 q^{6} +0.688788 q^{7} -5.98631 q^{8} +1.29054 q^{9} +4.09861 q^{10} +2.09195 q^{11} -9.05510 q^{12} -4.48255 q^{13} -1.73864 q^{14} +3.36333 q^{15} +6.36747 q^{16} +5.61737 q^{17} -3.25757 q^{18} +5.89460 q^{19} -7.09824 q^{20} -1.42673 q^{21} -5.28050 q^{22} +6.65297 q^{23} +12.3998 q^{24} -2.36351 q^{25} +11.3148 q^{26} +3.54091 q^{27} +3.01108 q^{28} -3.30090 q^{29} -8.48970 q^{30} +3.19087 q^{31} -4.10015 q^{32} -4.33319 q^{33} -14.1793 q^{34} -1.11840 q^{35} +5.64167 q^{36} +9.00368 q^{37} -14.8791 q^{38} +9.28498 q^{39} +9.72013 q^{40} +2.16057 q^{41} +3.60134 q^{42} +6.94751 q^{43} +9.14511 q^{44} -2.09548 q^{45} -16.7934 q^{46} -0.852802 q^{47} -13.1893 q^{48} -6.52557 q^{49} +5.96596 q^{50} -11.6356 q^{51} -19.5958 q^{52} +10.0050 q^{53} -8.93797 q^{54} -3.39676 q^{55} -4.12330 q^{56} -12.2098 q^{57} +8.33213 q^{58} +0.480979 q^{59} +14.7030 q^{60} +1.56106 q^{61} -8.05437 q^{62} +0.888907 q^{63} -2.38537 q^{64} +7.27844 q^{65} +10.9378 q^{66} -1.13929 q^{67} +24.5567 q^{68} -13.7807 q^{69} +2.82307 q^{70} +6.51436 q^{71} -7.72555 q^{72} -1.97652 q^{73} -22.7271 q^{74} +4.89568 q^{75} +25.7687 q^{76} +1.44091 q^{77} -23.4371 q^{78} +7.77639 q^{79} -10.3390 q^{80} -11.2061 q^{81} -5.45370 q^{82} +16.5602 q^{83} -6.23704 q^{84} -9.12108 q^{85} -17.5369 q^{86} +6.83737 q^{87} -12.5231 q^{88} -11.6107 q^{89} +5.28941 q^{90} -3.08753 q^{91} +29.0839 q^{92} -6.60944 q^{93} +2.15264 q^{94} -9.57123 q^{95} +8.49288 q^{96} +3.05657 q^{97} +16.4718 q^{98} +2.69974 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 259 q + 39 q^{2} + 25 q^{3} + 271 q^{4} + 83 q^{5} + 18 q^{6} + 26 q^{7} + 111 q^{8} + 286 q^{9}+O(q^{10}) \) 259 * q + 39 * q^2 + 25 * q^3 + 271 * q^4 + 83 * q^5 + 18 * q^6 + 26 * q^7 + 111 * q^8 + 286 * q^9	\( 259 q + 39 q^{2} + 25 q^{3} + 271 q^{4} + 83 q^{5} + 18 q^{6} + 26 q^{7} + 111 q^{8} + 286 q^{9} + 36 q^{10} + 35 q^{11} + 58 q^{12} + 109 q^{13} + 31 q^{14} + 30 q^{15} + 287 q^{16} + 124 q^{17} + 97 q^{18} + 42 q^{19} + 149 q^{20} + 99 q^{21} + 22 q^{22} + 63 q^{23} + 53 q^{24} + 308 q^{25} + 86 q^{26} + 82 q^{27} + 52 q^{28} + 131 q^{29} + 6 q^{30} + 29 q^{31} + 251 q^{32} + 147 q^{33} + 24 q^{34} + 79 q^{35} + 315 q^{36} + 108 q^{37} + 124 q^{38} + 48 q^{39} + 87 q^{40} + 190 q^{41} + 28 q^{42} + 36 q^{43} + 70 q^{44} + 211 q^{45} + 19 q^{46} + 186 q^{47} + 103 q^{48} + 297 q^{49} + 161 q^{50} + 20 q^{51} + 173 q^{52} + 213 q^{53} + 56 q^{54} + 35 q^{55} + 99 q^{56} + 80 q^{57} + 32 q^{58} + 135 q^{59} + 23 q^{60} + 83 q^{61} + 172 q^{62} + 85 q^{63} + 297 q^{64} + 177 q^{65} + 41 q^{66} + 30 q^{67} + 271 q^{68} + 168 q^{69} + 24 q^{70} + 63 q^{71} + 241 q^{72} + 152 q^{73} + 32 q^{74} + 36 q^{75} + 92 q^{76} + 396 q^{77} + 21 q^{78} - 2 q^{79} + 242 q^{80} + 343 q^{81} + 40 q^{82} + 236 q^{83} + 92 q^{84} + 124 q^{85} + 55 q^{86} + 113 q^{87} + 7 q^{88} + 214 q^{89} + 100 q^{90} + 2 q^{91} + 176 q^{92} + 228 q^{93} + 51 q^{94} + 96 q^{95} + 48 q^{96} + 135 q^{97} + 261 q^{98} + 26 q^{99}+O(q^{100}) \) 259 * q + 39 * q^2 + 25 * q^3 + 271 * q^4 + 83 * q^5 + 18 * q^6 + 26 * q^7 + 111 * q^8 + 286 * q^9 + 36 * q^10 + 35 * q^11 + 58 * q^12 + 109 * q^13 + 31 * q^14 + 30 * q^15 + 287 * q^16 + 124 * q^17 + 97 * q^18 + 42 * q^19 + 149 * q^20 + 99 * q^21 + 22 * q^22 + 63 * q^23 + 53 * q^24 + 308 * q^25 + 86 * q^26 + 82 * q^27 + 52 * q^28 + 131 * q^29 + 6 * q^30 + 29 * q^31 + 251 * q^32 + 147 * q^33 + 24 * q^34 + 79 * q^35 + 315 * q^36 + 108 * q^37 + 124 * q^38 + 48 * q^39 + 87 * q^40 + 190 * q^41 + 28 * q^42 + 36 * q^43 + 70 * q^44 + 211 * q^45 + 19 * q^46 + 186 * q^47 + 103 * q^48 + 297 * q^49 + 161 * q^50 + 20 * q^51 + 173 * q^52 + 213 * q^53 + 56 * q^54 + 35 * q^55 + 99 * q^56 + 80 * q^57 + 32 * q^58 + 135 * q^59 + 23 * q^60 + 83 * q^61 + 172 * q^62 + 85 * q^63 + 297 * q^64 + 177 * q^65 + 41 * q^66 + 30 * q^67 + 271 * q^68 + 168 * q^69 + 24 * q^70 + 63 * q^71 + 241 * q^72 + 152 * q^73 + 32 * q^74 + 36 * q^75 + 92 * q^76 + 396 * q^77 + 21 * q^78 - 2 * q^79 + 242 * q^80 + 343 * q^81 + 40 * q^82 + 236 * q^83 + 92 * q^84 + 124 * q^85 + 55 * q^86 + 113 * q^87 + 7 * q^88 + 214 * q^89 + 100 * q^90 + 2 * q^91 + 176 * q^92 + 228 * q^93 + 51 * q^94 + 96 * q^95 + 48 * q^96 + 135 * q^97 + 261 * q^98 + 26 * q^99

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