LMFDB - Embedded newform 4031.2.a.e.1.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4031,2,Mod(1,4031)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4031, 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("4031.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4031 = 29 \cdot 139 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4031.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$32.1876970548$
Analytic rank:	$0$
Dimension:	$103$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
Character	$\chi$	$=$	4031.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.35149 q^{2} +2.74768 q^{3} +3.52949 q^{4} +4.05795 q^{5} -6.46113 q^{6} +3.42169 q^{7} -3.59657 q^{8} +4.54974 q^{9} +O(q^{10})$	\(q-2.35149 q^{2} +2.74768 q^{3} +3.52949 q^{4} +4.05795 q^{5} -6.46113 q^{6} +3.42169 q^{7} -3.59657 q^{8} +4.54974 q^{9} -9.54222 q^{10} -2.15653 q^{11} +9.69790 q^{12} +3.81063 q^{13} -8.04605 q^{14} +11.1500 q^{15} +1.39830 q^{16} -3.73844 q^{17} -10.6987 q^{18} +4.00370 q^{19} +14.3225 q^{20} +9.40170 q^{21} +5.07106 q^{22} +8.78040 q^{23} -9.88221 q^{24} +11.4670 q^{25} -8.96064 q^{26} +4.25819 q^{27} +12.0768 q^{28} -1.00000 q^{29} -26.2190 q^{30} -5.29878 q^{31} +3.90504 q^{32} -5.92546 q^{33} +8.79088 q^{34} +13.8850 q^{35} +16.0583 q^{36} -9.27455 q^{37} -9.41465 q^{38} +10.4704 q^{39} -14.5947 q^{40} -9.17699 q^{41} -22.1080 q^{42} +2.44117 q^{43} -7.61146 q^{44} +18.4626 q^{45} -20.6470 q^{46} +0.736224 q^{47} +3.84209 q^{48} +4.70795 q^{49} -26.9645 q^{50} -10.2720 q^{51} +13.4496 q^{52} -6.36197 q^{53} -10.0131 q^{54} -8.75111 q^{55} -12.3063 q^{56} +11.0009 q^{57} +2.35149 q^{58} -13.2290 q^{59} +39.3536 q^{60} +6.37035 q^{61} +12.4600 q^{62} +15.5678 q^{63} -11.9793 q^{64} +15.4634 q^{65} +13.9336 q^{66} +4.86386 q^{67} -13.1948 q^{68} +24.1257 q^{69} -32.6505 q^{70} -4.29456 q^{71} -16.3634 q^{72} +11.6780 q^{73} +21.8090 q^{74} +31.5076 q^{75} +14.1310 q^{76} -7.37898 q^{77} -24.6210 q^{78} -6.45489 q^{79} +5.67424 q^{80} -1.94907 q^{81} +21.5796 q^{82} -4.42769 q^{83} +33.1832 q^{84} -15.1704 q^{85} -5.74038 q^{86} -2.74768 q^{87} +7.75612 q^{88} -2.11858 q^{89} -43.4146 q^{90} +13.0388 q^{91} +30.9903 q^{92} -14.5593 q^{93} -1.73122 q^{94} +16.2468 q^{95} +10.7298 q^{96} -17.1199 q^{97} -11.0707 q^{98} -9.81167 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 103 q + q^{2} + 2 q^{3} + 127 q^{4} + 9 q^{5} + 19 q^{6} + 18 q^{7} + 149 q^{9}+O(q^{10}) $ 103 * q + q^2 + 2 * q^3 + 127 * q^4 + 9 * q^5 + 19 * q^6 + 18 * q^7 + 149 * q^9	\( 103 q + q^{2} + 2 q^{3} + 127 q^{4} + 9 q^{5} + 19 q^{6} + 18 q^{7} + 149 q^{9} + 20 q^{10} + 9 q^{11} + 36 q^{13} - 10 q^{14} + 16 q^{15} + 179 q^{16} + 21 q^{17} + 7 q^{18} + 42 q^{19} + 24 q^{20} + 28 q^{21} + 32 q^{22} + 25 q^{23} + 68 q^{24} + 194 q^{25} - 5 q^{26} + 14 q^{27} + 59 q^{28} - 103 q^{29} + 84 q^{30} + 34 q^{31} + 11 q^{32} + 42 q^{33} + 54 q^{34} + 35 q^{35} + 214 q^{36} + 34 q^{37} + 9 q^{38} + 23 q^{39} + 46 q^{40} + 16 q^{41} + 13 q^{42} + 68 q^{43} - 6 q^{44} + 25 q^{45} + 60 q^{46} + 6 q^{47} + 5 q^{48} + 257 q^{49} - 51 q^{50} + 68 q^{51} + 37 q^{52} + 35 q^{53} + 30 q^{54} + 66 q^{55} - 54 q^{56} + 78 q^{57} - q^{58} + 10 q^{59} - 24 q^{60} + 70 q^{61} + 29 q^{62} + 26 q^{63} + 276 q^{64} + 95 q^{65} + 77 q^{66} + 71 q^{67} - 21 q^{68} - 20 q^{69} + 48 q^{70} + 32 q^{71} + 32 q^{72} + 94 q^{73} + 35 q^{74} + 7 q^{75} + 134 q^{76} + 17 q^{77} + 58 q^{78} + 110 q^{79} + 78 q^{80} + 267 q^{81} - 71 q^{82} + 35 q^{83} + 96 q^{84} + 71 q^{85} + 33 q^{86} - 2 q^{87} + 100 q^{88} + 22 q^{89} - 134 q^{90} + 108 q^{91} - 11 q^{92} + 78 q^{93} + 90 q^{94} + 12 q^{95} + 177 q^{96} + 44 q^{97} - 18 q^{98} + 83 q^{99}+O(q^{100}) \) 103 * q + q^2 + 2 * q^3 + 127 * q^4 + 9 * q^5 + 19 * q^6 + 18 * q^7 + 149 * q^9 + 20 * q^10 + 9 * q^11 + 36 * q^13 - 10 * q^14 + 16 * q^15 + 179 * q^16 + 21 * q^17 + 7 * q^18 + 42 * q^19 + 24 * q^20 + 28 * q^21 + 32 * q^22 + 25 * q^23 + 68 * q^24 + 194 * q^25 - 5 * q^26 + 14 * q^27 + 59 * q^28 - 103 * q^29 + 84 * q^30 + 34 * q^31 + 11 * q^32 + 42 * q^33 + 54 * q^34 + 35 * q^35 + 214 * q^36 + 34 * q^37 + 9 * q^38 + 23 * q^39 + 46 * q^40 + 16 * q^41 + 13 * q^42 + 68 * q^43 - 6 * q^44 + 25 * q^45 + 60 * q^46 + 6 * q^47 + 5 * q^48 + 257 * q^49 - 51 * q^50 + 68 * q^51 + 37 * q^52 + 35 * q^53 + 30 * q^54 + 66 * q^55 - 54 * q^56 + 78 * q^57 - q^58 + 10 * q^59 - 24 * q^60 + 70 * q^61 + 29 * q^62 + 26 * q^63 + 276 * q^64 + 95 * q^65 + 77 * q^66 + 71 * q^67 - 21 * q^68 - 20 * q^69 + 48 * q^70 + 32 * q^71 + 32 * q^72 + 94 * q^73 + 35 * q^74 + 7 * q^75 + 134 * q^76 + 17 * q^77 + 58 * q^78 + 110 * q^79 + 78 * q^80 + 267 * q^81 - 71 * q^82 + 35 * q^83 + 96 * q^84 + 71 * q^85 + 33 * q^86 - 2 * q^87 + 100 * q^88 + 22 * q^89 - 134 * q^90 + 108 * q^91 - 11 * q^92 + 78 * q^93 + 90 * q^94 + 12 * q^95 + 177 * q^96 + 44 * q^97 - 18 * q^98 + 83 * 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 $

$2$	−2.35149	−1.66275	−0.831376	−	0.555711i	$-0.812446\pi$
$2$	−2.35149	−1.66275	−0.831376	+	0.555711i	$0.812446\pi$
$3$	2.74768	1.58637	0.793187	−	0.608979i	$-0.208420\pi$
$3$	2.74768	1.58637	0.793187	+	0.608979i	$0.208420\pi$
$4$	3.52949	1.76474
$5$	4.05795	1.81477	0.907386	−	0.420298i	$-0.138075\pi$
$5$	4.05795	1.81477	0.907386	+	0.420298i	$0.138075\pi$
$6$	−6.46113	−2.63775
$7$	3.42169	1.29328	0.646638	−	0.762797i	$-0.276174\pi$
$7$	3.42169	1.29328	0.646638	+	0.762797i	$0.276174\pi$
$8$	−3.59657	−1.27158
$9$	4.54974	1.51658
$10$	−9.54222	−3.01752
$11$	−2.15653	−0.650219	−0.325110	−	0.945676i	$-0.605401\pi$
$11$	−2.15653	−0.650219	−0.325110	+	0.945676i	$0.605401\pi$
$12$	9.69790	2.79954
$13$	3.81063	1.05688	0.528439	−	0.848971i	$-0.322778\pi$
$13$	3.81063	1.05688	0.528439	+	0.848971i	$0.322778\pi$
$14$	−8.04605	−2.15040
$15$	11.1500	2.87891
$16$	1.39830	0.349575
$17$	−3.73844	−0.906704	−0.453352	−	0.891332i	$-0.649772\pi$
$17$	−3.73844	−0.906704	−0.453352	+	0.891332i	$0.649772\pi$
$18$	−10.6987	−2.52170
$19$	4.00370	0.918512	0.459256	−	0.888304i	$-0.348116\pi$
$19$	4.00370	0.918512	0.459256	+	0.888304i	$0.348116\pi$
$20$	14.3225	3.20261
$21$	9.40170	2.05162
$22$	5.07106	1.08115
$23$	8.78040	1.83084	0.915420	−	0.402499i	$-0.131858\pi$
$23$	8.78040	1.83084	0.915420	+	0.402499i	$0.131858\pi$
$24$	−9.88221	−2.01720
$25$	11.4670	2.29340
$26$	−8.96064	−1.75733
$27$	4.25819	0.819490
$28$	12.0768	2.28230
$29$	−1.00000	−0.185695
$29$	−1.00000	−0.185695
$30$	−26.2190	−4.78691
$31$	−5.29878	−0.951689	−0.475844	−	0.879529i	$-0.657857\pi$
$31$	−5.29878	−0.951689	−0.475844	+	0.879529i	$0.657857\pi$
$32$	3.90504	0.690321
$33$	−5.92546	−1.03149
$34$	8.79088	1.50762
$35$	13.8850	2.34700
$36$	16.0583	2.67638
$37$	−9.27455	−1.52473	−0.762364	−	0.647149i	$-0.775961\pi$
$37$	−9.27455	−1.52473	−0.762364	+	0.647149i	$0.775961\pi$
$38$	−9.41465	−1.52726
$39$	10.4704	1.67660
$40$	−14.5947	−2.30762
$41$	−9.17699	−1.43320	−0.716602	−	0.697482i	$-0.754304\pi$
$41$	−9.17699	−1.43320	−0.716602	+	0.697482i	$0.754304\pi$
$42$	−22.1080	−3.41133
$43$	2.44117	0.372275	0.186138	−	0.982524i	$-0.440403\pi$
$43$	2.44117	0.372275	0.186138	+	0.982524i	$0.440403\pi$
$44$	−7.61146	−1.14747
$45$	18.4626	2.75225
$46$	−20.6470	−3.04423
$47$	0.736224	0.107389	0.0536947	−	0.998557i	$-0.482900\pi$
$47$	0.736224	0.107389	0.0536947	+	0.998557i	$0.482900\pi$
$48$	3.84209	0.554557
$49$	4.70795	0.672564
$50$	−26.9645	−3.81335
$51$	−10.2720	−1.43837
$52$	13.4496	1.86512
$53$	−6.36197	−0.873884	−0.436942	−	0.899490i	$-0.643939\pi$
$53$	−6.36197	−0.873884	−0.436942	+	0.899490i	$0.643939\pi$
$54$	−10.0131	−1.36261
$55$	−8.75111	−1.18000
$56$	−12.3063	−1.64450
$57$	11.0009	1.45710
$58$	2.35149	0.308765
$59$	−13.2290	−1.72227	−0.861137	−	0.508373i	$-0.830247\pi$
$59$	−13.2290	−1.72227	−0.861137	+	0.508373i	$0.830247\pi$
$60$	39.3536	5.08053
$61$	6.37035	0.815640	0.407820	−	0.913062i	$-0.366289\pi$
$61$	6.37035	0.815640	0.407820	+	0.913062i	$0.366289\pi$
$62$	12.4600	1.58242
$63$	15.5678	1.96136
$64$	−11.9793	−1.49741
$65$	15.4634	1.91799
$66$	13.9336	1.71511
$67$	4.86386	0.594214	0.297107	−	0.954844i	$-0.403978\pi$
$67$	4.86386	0.594214	0.297107	+	0.954844i	$0.403978\pi$
$68$	−13.1948	−1.60010
$69$	24.1257	2.90440
$70$	−32.6505	−3.90248
$71$	−4.29456	−0.509671	−0.254836	−	0.966984i	$-0.582021\pi$
$71$	−4.29456	−0.509671	−0.254836	+	0.966984i	$0.582021\pi$
$72$	−16.3634	−1.92845
$73$	11.6780	1.36680	0.683401	−	0.730043i	$-0.260500\pi$
$73$	11.6780	1.36680	0.683401	+	0.730043i	$0.260500\pi$
$74$	21.8090	2.53524
$75$	31.5076	3.63819
$76$	14.1310	1.62094
$77$	−7.37898	−0.840913
$78$	−24.6210	−2.78777
$79$	−6.45489	−0.726232	−0.363116	−	0.931744i	$-0.618287\pi$
$79$	−6.45489	−0.726232	−0.363116	+	0.931744i	$0.618287\pi$
$80$	5.67424	0.634400
$81$	−1.94907	−0.216564
$82$	21.5796	2.38306
$83$	−4.42769	−0.486002	−0.243001	−	0.970026i	$-0.578132\pi$
$83$	−4.42769	−0.486002	−0.243001	+	0.970026i	$0.578132\pi$
$84$	33.1832	3.62058
$85$	−15.1704	−1.64546
$86$	−5.74038	−0.619001
$87$	−2.74768	−0.294582
$88$	7.75612	0.826805
$89$	−2.11858	−0.224569	−0.112285	−	0.993676i	$-0.535817\pi$
$89$	−2.11858	−0.224569	−0.112285	+	0.993676i	$0.535817\pi$
$90$	−43.4146	−4.57631
$91$	13.0388	1.36684
$92$	30.9903	3.23096
$93$	−14.5593	−1.50973
$94$	−1.73122	−0.178562
$95$	16.2468	1.66689
$96$	10.7298	1.09511
$97$	−17.1199	−1.73826	−0.869130	−	0.494584i	$-0.835320\pi$
$97$	−17.1199	−1.73826	−0.869130	+	0.494584i	$0.835320\pi$
$98$	−11.0707	−1.11831
$99$	−9.81167	−0.986110
$100$	40.4726	4.04726
$101$	−8.85573	−0.881178	−0.440589	−	0.897709i	$-0.645230\pi$
$101$	−8.85573	−0.881178	−0.440589	+	0.897709i	$0.645230\pi$
$102$	24.1545	2.39165
$103$	−1.52724	−0.150484	−0.0752419	−	0.997165i	$-0.523973\pi$
$103$	−1.52724	−0.150484	−0.0752419	+	0.997165i	$0.523973\pi$
$104$	−13.7052	−1.34390
$105$	38.1517	3.72322
$106$	14.9601	1.45305
$107$	5.82004	0.562645	0.281322	−	0.959613i	$-0.409227\pi$
$107$	5.82004	0.562645	0.281322	+	0.959613i	$0.409227\pi$
$108$	15.0292	1.44619
$109$	5.94718	0.569636	0.284818	−	0.958582i	$-0.408067\pi$
$109$	5.94718	0.569636	0.284818	+	0.958582i	$0.408067\pi$
$110$	20.5781	1.96205
$111$	−25.4835	−2.41879
$112$	4.78455	0.452098
$113$	1.21782	0.114563	0.0572813	−	0.998358i	$-0.481757\pi$
$113$	1.21782	0.114563	0.0572813	+	0.998358i	$0.481757\pi$
$114$	−25.8684	−2.42280
$115$	35.6305	3.32256
$116$	−3.52949	−0.327705
$117$	17.3374	1.60284
$118$	31.1079	2.86371
$119$	−12.7918	−1.17262
$120$	−40.1016	−3.66075
$121$	−6.34936	−0.577215
$122$	−14.9798	−1.35621
$123$	−25.2154	−2.27360
$124$	−18.7020	−1.67949
$125$	26.2427	2.34722
$126$	−36.6075	−3.26125
$127$	17.3406	1.53873	0.769363	−	0.638812i	$-0.220574\pi$
$127$	17.3406	1.53873	0.769363	+	0.638812i	$0.220574\pi$
$128$	20.3590	1.79950
$129$	6.70756	0.590568
$130$	−36.3619	−3.18915
$131$	1.30229	0.113782	0.0568908	−	0.998380i	$-0.481881\pi$
$131$	1.30229	0.113782	0.0568908	+	0.998380i	$0.481881\pi$
$132$	−20.9138	−1.82032
$133$	13.6994	1.18789
$134$	−11.4373	−0.988031
$135$	17.2796	1.48719
$136$	13.4455	1.15295
$137$	−13.1747	−1.12559	−0.562794	−	0.826597i	$-0.690274\pi$
$137$	−13.1747	−1.12559	−0.562794	+	0.826597i	$0.690274\pi$
$138$	−56.7313	−4.82929
$139$	1.00000	0.0848189
$139$	1.00000	0.0848189
$140$	49.0071	4.14186
$141$	2.02291	0.170360
$142$	10.0986	0.847456
$143$	−8.21775	−0.687202
$144$	6.36191	0.530159
$145$	−4.05795	−0.336995
$146$	−27.4606	−2.27265
$147$	12.9359	1.06694
$148$	−32.7344	−2.69075
$149$	0.907574	0.0743513	0.0371757	−	0.999309i	$-0.488164\pi$
$149$	0.907574	0.0743513	0.0371757	+	0.999309i	$0.488164\pi$
$150$	−74.0897	−6.04940
$151$	−20.5805	−1.67482	−0.837410	−	0.546575i	$-0.815931\pi$
$151$	−20.5805	−1.67482	−0.837410	+	0.546575i	$0.815931\pi$
$152$	−14.3996	−1.16796
$153$	−17.0089	−1.37509
$154$	17.3516	1.39823
$155$	−21.5022	−1.72710
$156$	36.9551	2.95877
$157$	3.45409	0.275667	0.137833	−	0.990455i	$-0.455986\pi$
$157$	3.45409	0.275667	0.137833	+	0.990455i	$0.455986\pi$
$158$	15.1786	1.20754
$159$	−17.4807	−1.38631
$160$	15.8465	1.25278
$161$	30.0438	2.36778
$162$	4.58322	0.360091
$163$	13.2592	1.03854	0.519272	−	0.854609i	$-0.326203\pi$
$163$	13.2592	1.03854	0.519272	+	0.854609i	$0.326203\pi$
$164$	−32.3900	−2.52924
$165$	−24.0453	−1.87192
$166$	10.4116	0.808100
$167$	22.2516	1.72188	0.860941	−	0.508705i	$-0.169876\pi$
$167$	22.2516	1.72188	0.860941	+	0.508705i	$0.169876\pi$
$168$	−33.8138	−2.60879
$169$	1.52088	0.116991
$170$	35.6730	2.73599
$171$	18.2158	1.39300
$172$	8.61609	0.656970
$173$	11.1791	0.849928	0.424964	−	0.905210i	$-0.360287\pi$
$173$	11.1791	0.849928	0.424964	+	0.905210i	$0.360287\pi$
$174$	6.46113	0.489817
$175$	39.2365	2.96600
$176$	−3.01549	−0.227301
$177$	−36.3491	−2.73217
$178$	4.98182	0.373403
$179$	−1.11460	−0.0833092	−0.0416546	−	0.999132i	$-0.513263\pi$
$179$	−1.11460	−0.0833092	−0.0416546	+	0.999132i	$0.513263\pi$
$180$	65.1637	4.85701
$181$	−1.72445	−0.128177	−0.0640886	−	0.997944i	$-0.520414\pi$
$181$	−1.72445	−0.128177	−0.0640886	+	0.997944i	$0.520414\pi$
$182$	−30.6605	−2.27271
$183$	17.5037	1.29391
$184$	−31.5793	−2.32806
$185$	−37.6357	−2.76703
$186$	34.2361	2.51031
$187$	8.06207	0.589557
$188$	2.59849	0.189515
$189$	14.5702	1.05983
$190$	−38.2042	−2.77162
$191$	4.85617	0.351380	0.175690	−	0.984446i	$-0.443784\pi$
$191$	4.85617	0.351380	0.175690	+	0.984446i	$0.443784\pi$
$192$	−32.9152	−2.37545
$193$	−10.3820	−0.747314	−0.373657	−	0.927567i	$-0.621896\pi$
$193$	−10.3820	−0.747314	−0.373657	+	0.927567i	$0.621896\pi$
$194$	40.2571	2.89029
$195$	42.4883	3.04265
$196$	16.6166	1.18690
$197$	−18.6408	−1.32810	−0.664050	−	0.747688i	$-0.731164\pi$
$197$	−18.6408	−1.32810	−0.664050	+	0.747688i	$0.731164\pi$
$198$	23.0720	1.63966
$199$	0.699314	0.0495731	0.0247865	−	0.999693i	$-0.492109\pi$
$199$	0.699314	0.0495731	0.0247865	+	0.999693i	$0.492109\pi$
$200$	−41.2418	−2.91623
$201$	13.3643	0.942646
$202$	20.8241	1.46518
$203$	−3.42169	−0.240155
$204$	−36.2550	−2.53836
$205$	−37.2398	−2.60094
$206$	3.59129	0.250217
$207$	39.9486	2.77662
$208$	5.32841	0.369459
$209$	−8.63412	−0.597234
$210$	−89.7131	−6.19079
$211$	−25.4076	−1.74913	−0.874565	−	0.484907i	$-0.838853\pi$
$211$	−25.4076	−1.74913	−0.874565	+	0.484907i	$0.838853\pi$
$212$	−22.4545	−1.54218
$213$	−11.8001	−0.808529
$214$	−13.6857	−0.935538
$215$	9.90617	0.675595
$216$	−15.3149	−1.04205
$217$	−18.1308	−1.23080
$218$	−13.9847	−0.947164
$219$	32.0873	2.16826
$220$	−30.8869	−2.08240
$221$	−14.2458	−0.958276
$222$	59.9241	4.02184
$223$	3.53881	0.236976	0.118488	−	0.992955i	$-0.462195\pi$
$223$	3.53881	0.236976	0.118488	+	0.992955i	$0.462195\pi$
$224$	13.3618	0.892776
$225$	52.1718	3.47812
$226$	−2.86368	−0.190489
$227$	−16.4704	−1.09318	−0.546588	−	0.837402i	$-0.684074\pi$
$227$	−16.4704	−1.09318	−0.546588	+	0.837402i	$0.684074\pi$
$228$	38.8275	2.57141
$229$	19.1681	1.26666	0.633331	−	0.773881i	$-0.281687\pi$
$229$	19.1681	1.26666	0.633331	+	0.773881i	$0.281687\pi$
$230$	−83.7846	−5.52459
$231$	−20.2751	−1.33400
$232$	3.59657	0.236126
$233$	4.67342	0.306166	0.153083	−	0.988213i	$-0.451080\pi$
$233$	4.67342	0.306166	0.153083	+	0.988213i	$0.451080\pi$
$234$	−40.7686	−2.66513
$235$	2.98756	0.194887
$236$	−46.6917	−3.03937
$237$	−17.7360	−1.15207
$238$	30.0797	1.94977
$239$	−2.22852	−0.144151	−0.0720754	−	0.997399i	$-0.522962\pi$
$239$	−2.22852	−0.144151	−0.0720754	+	0.997399i	$0.522962\pi$
$240$	15.5910	1.00640
$241$	−21.0598	−1.35658	−0.678292	−	0.734793i	$-0.737279\pi$
$241$	−21.0598	−1.35658	−0.678292	+	0.734793i	$0.737279\pi$
$242$	14.9304	0.959765
$243$	−18.1300	−1.16304
$244$	22.4841	1.43940
$245$	19.1046	1.22055
$246$	59.2937	3.78043
$247$	15.2566	0.970755
$248$	19.0574	1.21015
$249$	−12.1659	−0.770980
$250$	−61.7094	−3.90285
$251$	−21.2018	−1.33824	−0.669121	−	0.743153i	$-0.733329\pi$
$251$	−21.2018	−1.33824	−0.669121	+	0.743153i	$0.733329\pi$
$252$	54.9463	3.46129
$253$	−18.9352	−1.19045
$254$	−40.7761	−2.55852
$255$	−41.6834	−2.61032
$256$	−23.9153	−1.49471
$257$	8.21849	0.512655	0.256328	−	0.966590i	$-0.417487\pi$
$257$	8.21849	0.512655	0.256328	+	0.966590i	$0.417487\pi$
$258$	−15.7727	−0.981967
$259$	−31.7346	−1.97189
$260$	54.5777	3.38476
$261$	−4.54974	−0.281622
$262$	−3.06231	−0.189190
$263$	15.3118	0.944169	0.472084	−	0.881553i	$-0.343502\pi$
$263$	15.3118	0.944169	0.472084	+	0.881553i	$0.343502\pi$
$264$	21.3113	1.31162
$265$	−25.8166	−1.58590
$266$	−32.2140	−1.97517
$267$	−5.82119	−0.356251
$268$	17.1669	1.04864
$269$	−7.09114	−0.432354	−0.216177	−	0.976354i	$-0.569359\pi$
$269$	−7.09114	−0.432354	−0.216177	+	0.976354i	$0.569359\pi$
$270$	−40.6326	−2.47282
$271$	18.8809	1.14693	0.573466	−	0.819229i	$-0.305599\pi$
$271$	18.8809	1.14693	0.573466	+	0.819229i	$0.305599\pi$
$272$	−5.22746	−0.316962
$273$	35.8264	2.16831
$274$	30.9801	1.87157
$275$	−24.7289	−1.49121
$276$	85.1515	5.12552
$277$	2.82036	0.169459	0.0847294	−	0.996404i	$-0.472997\pi$
$277$	2.82036	0.169459	0.0847294	+	0.996404i	$0.472997\pi$
$278$	−2.35149	−0.141033
$279$	−24.1081	−1.44331
$280$	−49.9385	−2.98440
$281$	−19.2887	−1.15067	−0.575333	−	0.817919i	$-0.695128\pi$
$281$	−19.2887	−1.15067	−0.575333	+	0.817919i	$0.695128\pi$
$282$	−4.75684	−0.283266
$283$	−20.1984	−1.20067	−0.600336	−	0.799748i	$-0.704967\pi$
$283$	−20.1984	−1.20067	−0.600336	+	0.799748i	$0.704967\pi$
$284$	−15.1576	−0.899439
$285$	44.6411	2.64431
$286$	19.3239	1.14265
$287$	−31.4008	−1.85353
$288$	17.7669	1.04693
$289$	−3.02409	−0.177888
$290$	9.54222	0.560339
$291$	−47.0399	−2.75753
$292$	41.2172	2.41205
$293$	18.8836	1.10319	0.551597	−	0.834111i	$-0.314019\pi$
$293$	18.8836	1.10319	0.551597	+	0.834111i	$0.314019\pi$
$294$	−30.4186	−1.77405
$295$	−53.6828	−3.12553
$296$	33.3565	1.93881
$297$	−9.18294	−0.532848
$298$	−2.13415	−0.123628
$299$	33.4588	1.93498
$300$	111.206	6.42046
$301$	8.35293	0.481455
$302$	48.3949	2.78481
$303$	−24.3327	−1.39788
$304$	5.59838	0.321089
$305$	25.8506	1.48020
$306$	39.9962	2.28643
$307$	25.8936	1.47782	0.738912	−	0.673802i	$-0.235340\pi$
$307$	25.8936	1.47782	0.738912	+	0.673802i	$0.235340\pi$
$308$	−26.0440	−1.48400
$309$	−4.19637	−0.238723
$310$	50.5621	2.87174
$311$	−21.4666	−1.21726	−0.608630	−	0.793454i	$-0.708281\pi$
$311$	−21.4666	−1.21726	−0.608630	+	0.793454i	$0.708281\pi$
$312$	−37.6574	−2.13193
$313$	25.7363	1.45470	0.727350	−	0.686267i	$-0.240752\pi$
$313$	25.7363	1.45470	0.727350	+	0.686267i	$0.240752\pi$
$314$	−8.12225	−0.458365
$315$	63.1734	3.55942
$316$	−22.7824	−1.28161
$317$	−16.5278	−0.928295	−0.464148	−	0.885758i	$-0.653639\pi$
$317$	−16.5278	−0.928295	−0.464148	+	0.885758i	$0.653639\pi$
$318$	41.1055	2.30508
$319$	2.15653	0.120743
$320$	−48.6113	−2.71745
$321$	15.9916	0.892565
$322$	−70.6476	−3.93703
$323$	−14.9676	−0.832819
$324$	−6.87922	−0.382179
$325$	43.6964	2.42384
$326$	−31.1789	−1.72684
$327$	16.3409	0.903656
$328$	33.0056	1.82243
$329$	2.51913	0.138884
$330$	56.5421	3.11254
$331$	−30.8512	−1.69573	−0.847867	−	0.530210i	$-0.822113\pi$
$331$	−30.8512	−1.69573	−0.847867	+	0.530210i	$0.822113\pi$
$332$	−15.6275	−0.857668
$333$	−42.1968	−2.31237
$334$	−52.3244	−2.86306
$335$	19.7373	1.07836
$336$	13.1464	0.717196
$337$	18.1054	0.986263	0.493131	−	0.869955i	$-0.335852\pi$
$337$	18.1054	0.986263	0.493131	+	0.869955i	$0.335852\pi$
$338$	−3.57633	−0.194527
$339$	3.34617	0.181739
$340$	−53.5437	−2.90382
$341$	11.4270	0.618806
$342$	−42.8342	−2.31621
$343$	−7.84269	−0.423466
$344$	−8.77984	−0.473377
$345$	97.9011	5.27082
$346$	−26.2874	−1.41322
$347$	13.6711	0.733905	0.366952	−	0.930240i	$-0.380401\pi$
$347$	13.6711	0.733905	0.366952	+	0.930240i	$0.380401\pi$
$348$	−9.69790	−0.519862
$349$	33.3721	1.78637	0.893185	−	0.449690i	$-0.148465\pi$
$349$	33.3721	1.78637	0.893185	+	0.449690i	$0.148465\pi$
$350$	−92.2640	−4.93172
$351$	16.2264	0.866101
$352$	−8.42136	−0.448860
$353$	8.00028	0.425812	0.212906	−	0.977073i	$-0.431707\pi$
$353$	8.00028	0.425812	0.212906	+	0.977073i	$0.431707\pi$
$354$	85.4745	4.54292
$355$	−17.4271	−0.924937
$356$	−7.47751	−0.396307
$357$	−35.1477	−1.86021
$358$	2.62097	0.138522
$359$	34.6837	1.83054	0.915269	−	0.402844i	$-0.131978\pi$
$359$	34.6837	1.83054	0.915269	+	0.402844i	$0.131978\pi$
$360$	−66.4021	−3.49970
$361$	−2.97038	−0.156336
$362$	4.05502	0.213127
$363$	−17.4460	−0.915678
$364$	46.0202	2.41211
$365$	47.3886	2.48043
$366$	−41.1597	−2.15145
$367$	−3.41454	−0.178238	−0.0891188	−	0.996021i	$-0.528405\pi$
$367$	−3.41454	−0.178238	−0.0891188	+	0.996021i	$0.528405\pi$
$368$	12.2777	0.640017
$369$	−41.7529	−2.17357
$370$	88.4998	4.60089
$371$	−21.7687	−1.13017
$372$	−51.3870	−2.66429
$373$	10.8469	0.561632	0.280816	−	0.959762i	$-0.409395\pi$
$373$	10.8469	0.561632	0.280816	+	0.959762i	$0.409395\pi$
$374$	−18.9578	−0.980286
$375$	72.1066	3.72357
$376$	−2.64788	−0.136554
$377$	−3.81063	−0.196257
$378$	−34.2616	−1.76223
$379$	31.6926	1.62794	0.813971	−	0.580906i	$-0.197301\pi$
$379$	31.6926	1.62794	0.813971	+	0.580906i	$0.197301\pi$
$380$	57.3430	2.94163
$381$	47.6463	2.44099
$382$	−11.4192	−0.584258
$383$	−15.8506	−0.809927	−0.404964	−	0.914333i	$-0.632716\pi$
$383$	−15.8506	−0.809927	−0.404964	+	0.914333i	$0.632716\pi$
$384$	55.9399	2.85467
$385$	−29.9436	−1.52607
$386$	24.4132	1.24260
$387$	11.1067	0.564586
$388$	−60.4243	−3.06758
$389$	−10.7861	−0.546875	−0.273438	−	0.961890i	$-0.588161\pi$
$389$	−10.7861	−0.546875	−0.273438	+	0.961890i	$0.588161\pi$
$390$	−99.9107	−5.05918
$391$	−32.8250	−1.66003
$392$	−16.9324	−0.855217
$393$	3.57827	0.180500
$394$	43.8335	2.20830
$395$	−26.1936	−1.31794
$396$	−34.6302	−1.74023
$397$	20.1425	1.01092	0.505462	−	0.862849i	$-0.331322\pi$
$397$	20.1425	1.01092	0.505462	+	0.862849i	$0.331322\pi$
$398$	−1.64443	−0.0824277
$399$	37.6416	1.88444
$400$	16.0343	0.801716
$401$	−12.7641	−0.637407	−0.318703	−	0.947855i	$-0.603247\pi$
$401$	−12.7641	−0.637407	−0.318703	+	0.947855i	$0.603247\pi$
$402$	−31.4260	−1.56739
$403$	−20.1917	−1.00582
$404$	−31.2562	−1.55505
$405$	−7.90925	−0.393014
$406$	8.04605	0.399319
$407$	20.0009	0.991407
$408$	36.9440	1.82900
$409$	9.02446	0.446231	0.223115	−	0.974792i	$-0.428377\pi$
$409$	9.02446	0.446231	0.223115	+	0.974792i	$0.428377\pi$
$410$	87.5688	4.32472
$411$	−36.1998	−1.78560
$412$	−5.39038	−0.265565
$413$	−45.2656	−2.22738
$414$	−93.9385	−4.61683
$415$	−17.9674	−0.881983
$416$	14.8807	0.729585
$417$	2.74768	0.134554
$418$	20.3030	0.993052
$419$	13.2341	0.646527	0.323263	−	0.946309i	$-0.395220\pi$
$419$	13.2341	0.646527	0.323263	+	0.946309i	$0.395220\pi$
$420$	134.656	6.57053
$421$	21.5094	1.04830	0.524151	−	0.851625i	$-0.324383\pi$
$421$	21.5094	1.04830	0.524151	+	0.851625i	$0.324383\pi$
$422$	59.7456	2.90837
$423$	3.34963	0.162865
$424$	22.8813	1.11121
$425$	−42.8686	−2.07943
$426$	27.7477	1.34438
$427$	21.7974	1.05485
$428$	20.5418	0.992923
$429$	−22.5797	−1.09016
$430$	−23.2942	−1.12335
$431$	−37.0272	−1.78354	−0.891768	−	0.452492i	$-0.850535\pi$
$431$	−37.0272	−1.78354	−0.891768	+	0.452492i	$0.850535\pi$
$432$	5.95424	0.286474
$433$	−7.43105	−0.357113	−0.178557	−	0.983930i	$-0.557143\pi$
$433$	−7.43105	−0.357113	−0.178557	+	0.983930i	$0.557143\pi$
$434$	42.6342	2.04651
$435$	−11.1500	−0.534599
$436$	20.9905	1.00526
$437$	35.1541	1.68165
$438$	−75.4528	−3.60527
$439$	−11.8103	−0.563673	−0.281837	−	0.959462i	$-0.590944\pi$
$439$	−11.8103	−0.563673	−0.281837	+	0.959462i	$0.590944\pi$
$440$	31.4740	1.50046
$441$	21.4199	1.02000
$442$	33.4988	1.59337
$443$	−26.6037	−1.26398	−0.631990	−	0.774977i	$-0.717762\pi$
$443$	−26.6037	−1.26398	−0.631990	+	0.774977i	$0.717762\pi$
$444$	−89.9437	−4.26854
$445$	−8.59711	−0.407542
$446$	−8.32145	−0.394032
$447$	2.49372	0.117949
$448$	−40.9893	−1.93656
$449$	−0.0793778	−0.00374607	−0.00187304	−	0.999998i	$-0.500596\pi$
$449$	−0.0793778	−0.00374607	−0.00187304	+	0.999998i	$0.500596\pi$
$450$	−122.681	−5.78325
$451$	19.7905	0.931897
$452$	4.29827	0.202174
$453$	−56.5487	−2.65689
$454$	38.7298	1.81768
$455$	52.9108	2.48049
$456$	−39.5654	−1.85282
$457$	19.3294	0.904193	0.452096	−	0.891969i	$-0.350676\pi$
$457$	19.3294	0.904193	0.452096	+	0.891969i	$0.350676\pi$
$458$	−45.0735	−2.10614
$459$	−15.9190	−0.743035
$460$	125.757	5.86346
$461$	30.5776	1.42414	0.712071	−	0.702107i	$-0.247757\pi$
$461$	30.5776	1.42414	0.712071	+	0.702107i	$0.247757\pi$
$462$	47.6766	2.21812
$463$	−9.70996	−0.451260	−0.225630	−	0.974213i	$-0.572444\pi$
$463$	−9.70996	−0.451260	−0.225630	+	0.974213i	$0.572444\pi$
$464$	−1.39830	−0.0649145
$465$	−59.0812	−2.73982
$466$	−10.9895	−0.509078
$467$	−4.05649	−0.187712	−0.0938560	−	0.995586i	$-0.529919\pi$
$467$	−4.05649	−0.187712	−0.0938560	+	0.995586i	$0.529919\pi$
$468$	61.1920	2.82860
$469$	16.6426	0.768484
$470$	−7.02522	−0.324049
$471$	9.49074	0.437310
$472$	47.5791	2.19001
$473$	−5.26447	−0.242061
$474$	41.7059	1.91561
$475$	45.9104	2.10651
$476$	−45.1484	−2.06937
$477$	−28.9453	−1.32532
$478$	5.24033	0.239687
$479$	−31.4512	−1.43704	−0.718521	−	0.695505i	$-0.755181\pi$
$479$	−31.4512	−1.43704	−0.718521	+	0.695505i	$0.755181\pi$
$480$	43.5411	1.98737
$481$	−35.3419	−1.61145
$482$	49.5219	2.25566
$483$	82.5507	3.75619
$484$	−22.4100	−1.01864
$485$	−69.4716	−3.15454
$486$	42.6325	1.93385
$487$	29.0785	1.31767	0.658836	−	0.752287i	$-0.271049\pi$
$487$	29.0785	1.31767	0.658836	+	0.752287i	$0.271049\pi$
$488$	−22.9114	−1.03715
$489$	36.4322	1.64752
$490$	−44.9243	−2.02947
$491$	12.2598	0.553279	0.276639	−	0.960974i	$-0.410779\pi$
$491$	12.2598	0.553279	0.276639	+	0.960974i	$0.410779\pi$
$492$	−88.9975	−4.01232
$493$	3.73844	0.168371
$494$	−35.8757	−1.61412
$495$	−39.8153	−1.78957
$496$	−7.40929	−0.332687
$497$	−14.6947	−0.659146
$498$	28.6079	1.28195
$499$	0.0528517	0.00236597	0.00118298	−	0.999999i	$-0.499623\pi$
$499$	0.0528517	0.00236597	0.00118298	+	0.999999i	$0.499623\pi$
$500$	92.6234	4.14224
$501$	61.1403	2.73155
$502$	49.8556	2.22517
$503$	38.5038	1.71680	0.858400	−	0.512980i	$-0.171459\pi$
$503$	38.5038	1.71680	0.858400	+	0.512980i	$0.171459\pi$
$504$	−55.9906	−2.49402
$505$	−35.9362	−1.59914
$506$	44.5259	1.97942
$507$	4.17890	0.185591
$508$	61.2033	2.71546
$509$	−21.8959	−0.970519	−0.485259	−	0.874370i	$-0.661275\pi$
$509$	−21.8959	−0.970519	−0.485259	+	0.874370i	$0.661275\pi$
$510$	98.0180	4.34031
$511$	39.9583	1.76765
$512$	15.5186	0.685832
$513$	17.0485	0.752711
$514$	−19.3257	−0.852419
$515$	−6.19748	−0.273094
$516$	23.6742	1.04220
$517$	−1.58769	−0.0698266
$518$	74.6235	3.27877
$519$	30.7165	1.34830
$520$	−55.6150	−2.43888
$521$	15.3052	0.670533	0.335267	−	0.942123i	$-0.391174\pi$
$521$	15.3052	0.670533	0.335267	+	0.942123i	$0.391174\pi$
$522$	10.6987	0.468267
$523$	−0.952420	−0.0416464	−0.0208232	−	0.999783i	$-0.506629\pi$
$523$	−0.952420	−0.0416464	−0.0208232	+	0.999783i	$0.506629\pi$
$524$	4.59641	0.200795
$525$	107.809	4.70518
$526$	−36.0056	−1.56992
$527$	19.8092	0.862900
$528$	−8.28559	−0.360584
$529$	54.0955	2.35198
$530$	60.7074	2.63696
$531$	−60.1887	−2.61197
$532$	48.3519	2.09632
$533$	−34.9701	−1.51472
$534$	13.6884	0.592357
$535$	23.6175	1.02107
$536$	−17.4932	−0.755590
$537$	−3.06257	−0.132159
$538$	16.6747	0.718898
$539$	−10.1528	−0.437314
$540$	60.9880	2.62450
$541$	46.3749	1.99381	0.996906	−	0.0786058i	$-0.0250469\pi$
$541$	46.3749	1.99381	0.996906	+	0.0786058i	$0.0250469\pi$
$542$	−44.3981	−1.90706
$543$	−4.73823	−0.203337
$544$	−14.5988	−0.625917
$545$	24.1334	1.03376
$546$	−84.2452	−3.60536
$547$	13.3092	0.569060	0.284530	−	0.958667i	$-0.408162\pi$
$547$	13.3092	0.569060	0.284530	+	0.958667i	$0.408162\pi$
$548$	−46.4998	−1.98638
$549$	28.9835	1.23698
$550$	58.1498	2.47951
$551$	−4.00370	−0.170563
$552$	−86.7698	−3.69317
$553$	−22.0866	−0.939218
$554$	−6.63203	−0.281768
$555$	−103.411	−4.38955
$556$	3.52949	0.149684
$557$	−30.1021	−1.27547	−0.637733	−	0.770258i	$-0.720128\pi$
$557$	−30.1021	−1.27547	−0.637733	+	0.770258i	$0.720128\pi$
$558$	56.6898	2.39987
$559$	9.30240	0.393450
$560$	19.4155	0.820454
$561$	22.1520	0.935257
$562$	45.3571	1.91327
$563$	27.4241	1.15579	0.577894	−	0.816112i	$-0.303875\pi$
$563$	27.4241	1.15579	0.577894	+	0.816112i	$0.303875\pi$
$564$	7.13983	0.300641
$565$	4.94185	0.207905
$566$	47.4963	1.99642
$567$	−6.66912	−0.280077
$568$	15.4457	0.648087
$569$	−33.0224	−1.38437	−0.692185	−	0.721720i	$-0.743352\pi$
$569$	−33.0224	−1.38437	−0.692185	+	0.721720i	$0.743352\pi$
$570$	−104.973	−4.39683
$571$	8.23825	0.344760	0.172380	−	0.985031i	$-0.444854\pi$
$571$	8.23825	0.344760	0.172380	+	0.985031i	$0.444854\pi$
$572$	−29.0044	−1.21274
$573$	13.3432	0.557420
$574$	73.8385	3.08196
$575$	100.685	4.19885
$576$	−54.5026	−2.27094
$577$	39.5899	1.64815	0.824075	−	0.566480i	$-0.191695\pi$
$577$	39.5899	1.64815	0.824075	+	0.566480i	$0.191695\pi$
$578$	7.11110	0.295783
$579$	−28.5265	−1.18552
$580$	−14.3225	−0.594709
$581$	−15.1502	−0.628535
$582$	110.614	4.58508
$583$	13.7198	0.568217
$584$	−42.0005	−1.73800
$585$	70.3543	2.90879
$586$	−44.4046	−1.83434
$587$	−23.8564	−0.984657	−0.492329	−	0.870409i	$-0.663854\pi$
$587$	−23.8564	−0.984657	−0.492329	+	0.870409i	$0.663854\pi$
$588$	45.6572	1.88287
$589$	−21.2147	−0.874137
$590$	126.234	5.19699
$591$	−51.2189	−2.10686
$592$	−12.9686	−0.533007
$593$	10.6101	0.435705	0.217853	−	0.975982i	$-0.430095\pi$
$593$	10.6101	0.435705	0.217853	+	0.975982i	$0.430095\pi$
$594$	21.5936	0.885994
$595$	−51.9084	−2.12804
$596$	3.20327	0.131211
$597$	1.92149	0.0786414
$598$	−78.6780	−3.21738
$599$	9.42553	0.385117	0.192558	−	0.981286i	$-0.438322\pi$
$599$	9.42553	0.385117	0.192558	+	0.981286i	$0.438322\pi$
$600$	−113.319	−4.62624
$601$	−34.6343	−1.41276	−0.706381	−	0.707832i	$-0.749673\pi$
$601$	−34.6343	−1.41276	−0.706381	+	0.707832i	$0.749673\pi$
$602$	−19.6418	−0.800540
$603$	22.1293	0.901174
$604$	−72.6387	−2.95563
$605$	−25.7654	−1.04751
$606$	57.2180	2.32432
$607$	38.4033	1.55874	0.779372	−	0.626562i	$-0.215538\pi$
$607$	38.4033	1.55874	0.779372	+	0.626562i	$0.215538\pi$
$608$	15.6346	0.634068
$609$	−9.40170	−0.380976
$610$	−60.7873	−2.46121
$611$	2.80548	0.113497
$612$	−60.0328	−2.42668
$613$	37.2623	1.50501	0.752505	−	0.658586i	$-0.228845\pi$
$613$	37.2623	1.50501	0.752505	+	0.658586i	$0.228845\pi$
$614$	−60.8883	−2.45725
$615$	−102.323	−4.12606
$616$	26.5390	1.06929
$617$	−1.34481	−0.0541399	−0.0270700	−	0.999634i	$-0.508618\pi$
$617$	−1.34481	−0.0541399	−0.0270700	+	0.999634i	$0.508618\pi$
$618$	9.86771	0.396938
$619$	−3.40791	−0.136975	−0.0684876	−	0.997652i	$-0.521817\pi$
$619$	−3.40791	−0.136975	−0.0684876	+	0.997652i	$0.521817\pi$
$620$	−75.8917	−3.04789
$621$	37.3887	1.50036
$622$	50.4785	2.02400
$623$	−7.24913	−0.290430
$624$	14.6408	0.586099
$625$	49.1569	1.96628
$626$	−60.5185	−2.41880
$627$	−23.7238	−0.947437
$628$	12.1912	0.486481
$629$	34.6723	1.38248
$630$	−148.551	−5.91843
$631$	21.9535	0.873954	0.436977	−	0.899473i	$-0.356049\pi$
$631$	21.9535	0.873954	0.436977	+	0.899473i	$0.356049\pi$
$632$	23.2154	0.923460
$633$	−69.8119	−2.77477
$634$	38.8649	1.54352
$635$	70.3672	2.79244
$636$	−61.6978	−2.44648
$637$	17.9402	0.710818
$638$	−5.07106	−0.200765
$639$	−19.5392	−0.772957
$640$	82.6158	3.26568
$641$	30.5828	1.20795	0.603973	−	0.797004i	$-0.293583\pi$
$641$	30.5828	1.20795	0.603973	+	0.797004i	$0.293583\pi$
$642$	−37.6040	−1.48411
$643$	7.80554	0.307820	0.153910	−	0.988085i	$-0.450813\pi$
$643$	7.80554	0.307820	0.153910	+	0.988085i	$0.450813\pi$
$644$	106.039	4.17853
$645$	27.2190	1.07175
$646$	35.1961	1.38477
$647$	−8.13477	−0.319811	−0.159905	−	0.987132i	$-0.551119\pi$
$647$	−8.13477	−0.319811	−0.159905	+	0.987132i	$0.551119\pi$
$648$	7.00997	0.275378
$649$	28.5289	1.11986
$650$	−102.752	−4.03025
$651$	−49.8175	−1.95250
$652$	46.7983	1.83276
$653$	24.6841	0.965963	0.482981	−	0.875631i	$-0.339554\pi$
$653$	24.6841	0.965963	0.482981	+	0.875631i	$0.339554\pi$
$654$	−38.4255	−1.50256
$655$	5.28463	0.206488
$656$	−12.8322	−0.501013
$657$	53.1317	2.07287
$658$	−5.92370	−0.230930
$659$	27.9387	1.08834	0.544169	−	0.838975i	$-0.316845\pi$
$659$	27.9387	1.08834	0.544169	+	0.838975i	$0.316845\pi$
$660$	−84.8674	−3.30346
$661$	−18.2726	−0.710722	−0.355361	−	0.934729i	$-0.615642\pi$
$661$	−18.2726	−0.710722	−0.355361	+	0.934729i	$0.615642\pi$
$662$	72.5461	2.81958
$663$	−39.1429	−1.52018
$664$	15.9245	0.617989
$665$	55.5916	2.15575
$666$	99.2252	3.84490
$667$	−8.78040	−0.339979
$668$	78.5368	3.03868
$669$	9.72350	0.375932
$670$	−46.4120	−1.79305
$671$	−13.7379	−0.530345
$672$	36.7141	1.41628
$673$	−0.506178	−0.0195117	−0.00975586	−	0.999952i	$-0.503105\pi$
$673$	−0.506178	−0.0195117	−0.00975586	+	0.999952i	$0.503105\pi$
$674$	−42.5745	−1.63991
$675$	48.8287	1.87942
$676$	5.36793	0.206459
$677$	1.13890	0.0437714	0.0218857	−	0.999760i	$-0.493033\pi$
$677$	1.13890	0.0437714	0.0218857	+	0.999760i	$0.493033\pi$
$678$	−7.86848	−0.302187
$679$	−58.5788	−2.24805
$680$	54.5614	2.09233
$681$	−45.2553	−1.73419
$682$	−26.8704	−1.02892
$683$	24.5238	0.938376	0.469188	−	0.883098i	$-0.344547\pi$
$683$	24.5238	0.938376	0.469188	+	0.883098i	$0.344547\pi$
$684$	64.2924	2.45828
$685$	−53.4622	−2.04269
$686$	18.4420	0.704118
$687$	52.6677	2.00940
$688$	3.41350	0.130138
$689$	−24.2431	−0.923589
$690$	−230.213	−8.76406
$691$	−49.2780	−1.87462	−0.937312	−	0.348491i	$-0.886694\pi$
$691$	−49.2780	−1.87462	−0.937312	+	0.348491i	$0.886694\pi$
$692$	39.4563	1.49990
$693$	−33.5725	−1.27531
$694$	−32.1475	−1.22030
$695$	4.05795	0.153927
$696$	9.88221	0.374584
$697$	34.3076	1.29949
$698$	−78.4741	−2.97029
$699$	12.8411	0.485693
$700$	138.485	5.23422
$701$	−3.45323	−0.130427	−0.0652133	−	0.997871i	$-0.520773\pi$
$701$	−3.45323	−0.130427	−0.0652133	+	0.997871i	$0.520773\pi$
$702$	−38.1561	−1.44011
$703$	−37.1325	−1.40048
$704$	25.8337	0.973644
$705$	8.20887	0.309164
$706$	−18.8126	−0.708020
$707$	−30.3016	−1.13961
$708$	−128.294	−4.82158
$709$	37.2628	1.39943	0.699717	−	0.714421i	$-0.253310\pi$
$709$	37.2628	1.39943	0.699717	+	0.714421i	$0.253310\pi$
$710$	40.9797	1.53794
$711$	−29.3681	−1.10139
$712$	7.61962	0.285557
$713$	−46.5254	−1.74239
$714$	82.6492	3.09307
$715$	−33.3472	−1.24712
$716$	−3.93397	−0.147019
$717$	−6.12325	−0.228677
$718$	−81.5583	−3.04373
$719$	13.5464	0.505196	0.252598	−	0.967571i	$-0.418715\pi$
$719$	13.5464	0.505196	0.252598	+	0.967571i	$0.418715\pi$
$720$	25.8163	0.962119
$721$	−5.22575	−0.194617
$722$	6.98481	0.259948
$723$	−57.8657	−2.15205
$724$	−6.08642	−0.226200
$725$	−11.4670	−0.425873
$726$	41.0241	1.52255
$727$	−3.46014	−0.128330	−0.0641648	−	0.997939i	$-0.520438\pi$
$727$	−3.46014	−0.128330	−0.0641648	+	0.997939i	$0.520438\pi$
$728$	−46.8948	−1.73804
$729$	−43.9682	−1.62845
$730$	−111.434	−4.12434
$731$	−9.12617	−0.337544
$732$	61.7790	2.28342
$733$	−15.3524	−0.567054	−0.283527	−	0.958964i	$-0.591505\pi$
$733$	−15.3524	−0.567054	−0.283527	+	0.958964i	$0.591505\pi$
$734$	8.02925	0.296365
$735$	52.4934	1.93625
$736$	34.2879	1.26387
$737$	−10.4891	−0.386370
$738$	98.1814	3.61411
$739$	−51.9110	−1.90958	−0.954788	−	0.297287i	$-0.903918\pi$
$739$	−51.9110	−1.90958	−0.954788	+	0.297287i	$0.903918\pi$
$740$	−132.835	−4.88310
$741$	41.9203	1.53998
$742$	51.1888	1.87920
$743$	18.5140	0.679212	0.339606	−	0.940568i	$-0.389706\pi$
$743$	18.5140	0.679212	0.339606	+	0.940568i	$0.389706\pi$
$744$	52.3636	1.91974
$745$	3.68289	0.134931
$746$	−25.5064	−0.933854
$747$	−20.1448	−0.737061
$748$	28.4549	1.04042
$749$	19.9144	0.727655
$750$	−169.558	−6.19137
$751$	−36.4184	−1.32893	−0.664464	−	0.747321i	$-0.731340\pi$
$751$	−36.4184	−1.32893	−0.664464	+	0.747321i	$0.731340\pi$
$752$	1.02946	0.0375407
$753$	−58.2556	−2.12295
$754$	8.96064	0.326327
$755$	−83.5149	−3.03942
$756$	51.4254	1.87032
$757$	−21.2326	−0.771714	−0.385857	−	0.922559i	$-0.626094\pi$
$757$	−21.2326	−0.771714	−0.385857	+	0.922559i	$0.626094\pi$
$758$	−74.5248	−2.70686
$759$	−52.0280	−1.88850
$760$	−58.4328	−2.11958
$761$	−13.4606	−0.487947	−0.243974	−	0.969782i	$-0.578451\pi$
$761$	−13.4606	−0.487947	−0.243974	+	0.969782i	$0.578451\pi$
$762$	−112.040	−4.05877
$763$	20.3494	0.736697
$764$	17.1398	0.620095
$765$	−69.0214	−2.49548
$766$	37.2724	1.34671
$767$	−50.4109	−1.82023
$768$	−65.7117	−2.37116
$769$	39.1131	1.41045	0.705227	−	0.708982i	$-0.250845\pi$
$769$	39.1131	1.41045	0.705227	+	0.708982i	$0.250845\pi$
$770$	70.4119	2.53747
$771$	22.5818	0.813263
$772$	−36.6432	−1.31882
$773$	37.2161	1.33857	0.669284	−	0.743006i	$-0.266601\pi$
$773$	37.2161	1.33857	0.669284	+	0.743006i	$0.266601\pi$
$774$	−26.1173	−0.938766
$775$	−60.7610	−2.18260
$776$	61.5727	2.21033
$777$	−87.1966	−3.12816
$778$	25.3633	0.909317
$779$	−36.7419	−1.31642
$780$	149.962	5.36950
$781$	9.26137	0.331398
$782$	77.1875	2.76022
$783$	−4.25819	−0.152175
$784$	6.58313	0.235112
$785$	14.0165	0.500272
$786$	−8.41426	−0.300127
$787$	−46.4330	−1.65516	−0.827578	−	0.561351i	$-0.810282\pi$
$787$	−46.4330	−1.65516	−0.827578	+	0.561351i	$0.810282\pi$
$788$	−65.7924	−2.34376
$789$	42.0720	1.49780
$790$	61.5940	2.19142
$791$	4.16699	0.148161
$792$	35.2883	1.25392
$793$	24.2750	0.862032
$794$	−47.3648	−1.68092
$795$	−70.9357	−2.51583
$796$	2.46822	0.0874837
$797$	42.7398	1.51392	0.756960	−	0.653461i	$-0.226684\pi$
$797$	42.7398	1.51392	0.756960	+	0.653461i	$0.226684\pi$
$798$	−88.5137	−3.13335
$799$	−2.75233	−0.0973704
$800$	44.7791	1.58318
$801$	−9.63901	−0.340578
$802$	30.0145	1.05985
$803$	−25.1839	−0.888721
$804$	47.1692	1.66353
$805$	121.916	4.29699
$806$	47.4804	1.67243
$807$	−19.4842	−0.685876
$808$	31.8502	1.12049
$809$	−51.8556	−1.82314	−0.911572	−	0.411140i	$-0.865131\pi$
$809$	−51.8556	−1.82314	−0.911572	+	0.411140i	$0.865131\pi$
$810$	18.5985	0.653484
$811$	52.0653	1.82826	0.914130	−	0.405422i	$-0.132875\pi$
$811$	52.0653	1.82826	0.914130	+	0.405422i	$0.132875\pi$
$812$	−12.0768	−0.423813
$813$	51.8786	1.81946
$814$	−47.0318	−1.64846
$815$	53.8054	1.88472
$816$	−14.3634	−0.502819
$817$	9.77372	0.341939
$818$	−21.2209	−0.741971
$819$	59.3231	2.07292
$820$	−131.437	−4.58999
$821$	17.6319	0.615356	0.307678	−	0.951490i	$-0.400448\pi$
$821$	17.6319	0.615356	0.307678	+	0.951490i	$0.400448\pi$
$822$	85.1233	2.96902
$823$	47.9156	1.67023	0.835117	−	0.550073i	$-0.185400\pi$
$823$	47.9156	1.67023	0.835117	+	0.550073i	$0.185400\pi$
$824$	5.49283	0.191352
$825$	−67.9472	−2.36562
$826$	106.441	3.70357
$827$	−38.3717	−1.33432	−0.667158	−	0.744917i	$-0.732489\pi$
$827$	−38.3717	−1.33432	−0.667158	+	0.744917i	$0.732489\pi$
$828$	140.998	4.90002
$829$	22.8887	0.794959	0.397480	−	0.917611i	$-0.369885\pi$
$829$	22.8887	0.794959	0.397480	+	0.917611i	$0.369885\pi$
$830$	42.2500	1.46652
$831$	7.74944	0.268825
$832$	−45.6485	−1.58258
$833$	−17.6004	−0.609816
$834$	−6.46113	−0.223731
$835$	90.2960	3.12482
$836$	−30.4740	−1.05397
$837$	−22.5632	−0.779899
$838$	−31.1197	−1.07501
$839$	30.8486	1.06501	0.532505	−	0.846427i	$-0.321251\pi$
$839$	30.8486	1.06501	0.532505	+	0.846427i	$0.321251\pi$
$840$	−137.215	−4.73437
$841$	1.00000	0.0344828
$842$	−50.5790	−1.74307
$843$	−52.9991	−1.82539
$844$	−89.6758	−3.08677
$845$	6.17167	0.212312
$846$	−7.87661	−0.270803
$847$	−21.7255	−0.746498
$848$	−8.89596	−0.305489
$849$	−55.4988	−1.90471
$850$	100.805	3.45758
$851$	−81.4343	−2.79153
$852$	−41.6482	−1.42685
$853$	0.228235	0.00781463	0.00390732	−	0.999992i	$-0.498756\pi$
$853$	0.228235	0.00781463	0.00390732	+	0.999992i	$0.498756\pi$
$854$	−51.2562	−1.75395
$855$	73.9189	2.52797
$856$	−20.9322	−0.715447
$857$	−15.6262	−0.533782	−0.266891	−	0.963727i	$-0.585996\pi$
$857$	−15.6262	−0.533782	−0.266891	+	0.963727i	$0.585996\pi$
$858$	53.0959	1.81267
$859$	−24.5485	−0.837582	−0.418791	−	0.908083i	$-0.637546\pi$
$859$	−24.5485	−0.837582	−0.418791	+	0.908083i	$0.637546\pi$
$860$	34.9637	1.19225
$861$	−86.2793	−2.94039
$862$	87.0689	2.96558
$863$	0.455471	0.0155044	0.00775220	−	0.999970i	$-0.497532\pi$
$863$	0.455471	0.0155044	0.00775220	+	0.999970i	$0.497532\pi$
$864$	16.6284	0.565711
$865$	45.3641	1.54243
$866$	17.4740	0.593791
$867$	−8.30923	−0.282196
$868$	−63.9923	−2.17204
$869$	13.9202	0.472210
$870$	26.2190	0.888906
$871$	18.5343	0.628012
$872$	−21.3894	−0.724337
$873$	−77.8910	−2.63621
$874$	−82.6644	−2.79616
$875$	89.7945	3.03561
$876$	113.252	3.82642
$877$	28.4324	0.960094	0.480047	−	0.877243i	$-0.340620\pi$
$877$	28.4324	0.960094	0.480047	+	0.877243i	$0.340620\pi$
$878$	27.7717	0.937249
$879$	51.8861	1.75008
$880$	−12.2367	−0.412499
$881$	−23.9525	−0.806979	−0.403490	−	0.914984i	$-0.632203\pi$
$881$	−23.9525	−0.806979	−0.403490	+	0.914984i	$0.632203\pi$
$882$	−50.3687	−1.69600
$883$	−27.7495	−0.933844	−0.466922	−	0.884299i	$-0.654637\pi$
$883$	−27.7495	−0.933844	−0.466922	+	0.884299i	$0.654637\pi$
$884$	−50.2803	−1.69111
$885$	−147.503	−4.95826
$886$	62.5582	2.10168
$887$	22.0519	0.740431	0.370216	−	0.928946i	$-0.379284\pi$
$887$	22.0519	0.740431	0.370216	+	0.928946i	$0.379284\pi$
$888$	91.6531	3.07568
$889$	59.3340	1.99000
$890$	20.2160	0.677642
$891$	4.20324	0.140814
$892$	12.4902	0.418202
$893$	2.94762	0.0986384
$894$	−5.86395	−0.196120
$895$	−4.52300	−0.151187
$896$	69.6621	2.32725
$897$	91.9342	3.06959
$898$	0.186656	0.00622878
$899$	5.29878	0.176724
$900$	184.140	6.13799
$901$	23.7838	0.792355
$902$	−46.5370	−1.54951
$903$	22.9512	0.763767
$904$	−4.37996	−0.145675
$905$	−6.99773	−0.232613
$906$	132.974	4.41775
$907$	−24.2395	−0.804859	−0.402429	−	0.915451i	$-0.631834\pi$
$907$	−24.2395	−0.804859	−0.402429	+	0.915451i	$0.631834\pi$
$908$	−58.1319	−1.92918
$909$	−40.2913	−1.33638
$910$	−124.419	−4.12445
$911$	48.9790	1.62275	0.811373	−	0.584529i	$-0.198721\pi$
$911$	48.9790	1.62275	0.811373	+	0.584529i	$0.198721\pi$
$912$	15.3826	0.509367
$913$	9.54846	0.316008
$914$	−45.4529	−1.50345
$915$	71.0292	2.34815
$916$	67.6535	2.23533
$917$	4.45603	0.147151
$918$	37.4333	1.23548
$919$	28.8192	0.950659	0.475330	−	0.879808i	$-0.342329\pi$
$919$	28.8192	0.950659	0.475330	+	0.879808i	$0.342329\pi$
$920$	−128.147	−4.22489
$921$	71.1472	2.34438
$922$	−71.9029	−2.36800
$923$	−16.3650	−0.538660
$924$	−71.5606	−2.35417
$925$	−106.351	−3.49681
$926$	22.8328	0.750334
$927$	−6.94856	−0.228221
$928$	−3.90504	−0.128189
$929$	5.90747	0.193818	0.0969089	−	0.995293i	$-0.469104\pi$
$929$	5.90747	0.193818	0.0969089	+	0.995293i	$0.469104\pi$
$930$	138.929	4.55565
$931$	18.8492	0.617758
$932$	16.4948	0.540304
$933$	−58.9834	−1.93103
$934$	9.53878	0.312119
$935$	32.7155	1.06991
$936$	−62.3550	−2.03814
$937$	28.9109	0.944476	0.472238	−	0.881471i	$-0.343446\pi$
$937$	28.9109	0.944476	0.472238	+	0.881471i	$0.343446\pi$
$938$	−39.1348	−1.27780
$939$	70.7150	2.30770
$940$	10.5446	0.343926
$941$	10.3181	0.336361	0.168180	−	0.985756i	$-0.446211\pi$
$941$	10.3181	0.336361	0.168180	+	0.985756i	$0.446211\pi$
$942$	−22.3173	−0.727138
$943$	−80.5776	−2.62397
$944$	−18.4982	−0.602065
$945$	59.1252	1.92334
$946$	12.3793	0.402487
$947$	−59.4214	−1.93094	−0.965468	−	0.260520i	$-0.916106\pi$
$947$	−59.4214	−1.93094	−0.965468	+	0.260520i	$0.916106\pi$
$948$	−62.5988	−2.03312
$949$	44.5003	1.44454
$950$	−107.958	−3.50261
$951$	−45.4132	−1.47262
$952$	46.0064	1.49108
$953$	−16.2397	−0.526055	−0.263027	−	0.964788i	$-0.584721\pi$
$953$	−16.2397	−0.526055	−0.263027	+	0.964788i	$0.584721\pi$
$954$	68.0646	2.20367
$955$	19.7061	0.637675
$956$	−7.86552	−0.254389
$957$	5.92546	0.191543
$958$	73.9571	2.38945
$959$	−45.0796	−1.45570
$960$	−133.568	−4.31090
$961$	−2.92294	−0.0942885
$962$	83.1059	2.67944
$963$	26.4797	0.853296
$964$	−74.3304	−2.39402
$965$	−42.1298	−1.35620
$966$	−194.117	−6.24561
$967$	−7.02834	−0.226016	−0.113008	−	0.993594i	$-0.536049\pi$
$967$	−7.02834	−0.226016	−0.113008	+	0.993594i	$0.536049\pi$
$968$	22.8359	0.733974
$969$	−41.1261	−1.32116
$970$	163.362	5.24522
$971$	52.5570	1.68663	0.843317	−	0.537417i	$-0.180600\pi$
$971$	52.5570	1.68663	0.843317	+	0.537417i	$0.180600\pi$
$972$	−63.9896	−2.05247
$973$	3.42169	0.109694
$974$	−68.3776	−2.19096
$975$	120.064	3.84512
$976$	8.90768	0.285128
$977$	−27.7582	−0.888065	−0.444032	−	0.896011i	$-0.646453\pi$
$977$	−27.7582	−0.888065	−0.444032	+	0.896011i	$0.646453\pi$
$978$	−85.6697	−2.73941
$979$	4.56880	0.146019
$980$	67.4295	2.15396
$981$	27.0581	0.863900
$982$	−28.8288	−0.919965
$983$	−7.81662	−0.249311	−0.124656	−	0.992200i	$-0.539783\pi$
$983$	−7.81662	−0.249311	−0.124656	+	0.992200i	$0.539783\pi$
$984$	90.6889	2.89106
$985$	−75.6434	−2.41020
$986$	−8.79088	−0.279959
$987$	6.92176	0.220322
$988$	53.8480	1.71313
$989$	21.4345	0.681577
$990$	93.6252	2.97560
$991$	28.5945	0.908335	0.454168	−	0.890916i	$-0.349937\pi$
$991$	28.5945	0.908335	0.454168	+	0.890916i	$0.349937\pi$
$992$	−20.6920	−0.656971
$993$	−84.7691	−2.69007
$994$	34.5543	1.09600
$995$	2.83778	0.0899638
$996$	−42.9393	−1.36058
$997$	−50.5100	−1.59967	−0.799834	−	0.600221i	$-0.795079\pi$
$997$	−50.5100	−1.59967	−0.799834	+	0.600221i	$0.795079\pi$
$998$	−0.124280	−0.00393402
$999$	−39.4929	−1.24950

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4031.2.a.e.1.13	✓	103

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4031.2.a.e.1.13	✓	103	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:	\( N \)	\(=\)	\( 4031 = 29 \cdot 139 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4031.a (trivial)

\(f(q)\)	\(=\)	\(q-2.35149 q^{2} +2.74768 q^{3} +3.52949 q^{4} +4.05795 q^{5} -6.46113 q^{6} +3.42169 q^{7} -3.59657 q^{8} +4.54974 q^{9} +O(q^{10})\)	\(q-2.35149 q^{2} +2.74768 q^{3} +3.52949 q^{4} +4.05795 q^{5} -6.46113 q^{6} +3.42169 q^{7} -3.59657 q^{8} +4.54974 q^{9} -9.54222 q^{10} -2.15653 q^{11} +9.69790 q^{12} +3.81063 q^{13} -8.04605 q^{14} +11.1500 q^{15} +1.39830 q^{16} -3.73844 q^{17} -10.6987 q^{18} +4.00370 q^{19} +14.3225 q^{20} +9.40170 q^{21} +5.07106 q^{22} +8.78040 q^{23} -9.88221 q^{24} +11.4670 q^{25} -8.96064 q^{26} +4.25819 q^{27} +12.0768 q^{28} -1.00000 q^{29} -26.2190 q^{30} -5.29878 q^{31} +3.90504 q^{32} -5.92546 q^{33} +8.79088 q^{34} +13.8850 q^{35} +16.0583 q^{36} -9.27455 q^{37} -9.41465 q^{38} +10.4704 q^{39} -14.5947 q^{40} -9.17699 q^{41} -22.1080 q^{42} +2.44117 q^{43} -7.61146 q^{44} +18.4626 q^{45} -20.6470 q^{46} +0.736224 q^{47} +3.84209 q^{48} +4.70795 q^{49} -26.9645 q^{50} -10.2720 q^{51} +13.4496 q^{52} -6.36197 q^{53} -10.0131 q^{54} -8.75111 q^{55} -12.3063 q^{56} +11.0009 q^{57} +2.35149 q^{58} -13.2290 q^{59} +39.3536 q^{60} +6.37035 q^{61} +12.4600 q^{62} +15.5678 q^{63} -11.9793 q^{64} +15.4634 q^{65} +13.9336 q^{66} +4.86386 q^{67} -13.1948 q^{68} +24.1257 q^{69} -32.6505 q^{70} -4.29456 q^{71} -16.3634 q^{72} +11.6780 q^{73} +21.8090 q^{74} +31.5076 q^{75} +14.1310 q^{76} -7.37898 q^{77} -24.6210 q^{78} -6.45489 q^{79} +5.67424 q^{80} -1.94907 q^{81} +21.5796 q^{82} -4.42769 q^{83} +33.1832 q^{84} -15.1704 q^{85} -5.74038 q^{86} -2.74768 q^{87} +7.75612 q^{88} -2.11858 q^{89} -43.4146 q^{90} +13.0388 q^{91} +30.9903 q^{92} -14.5593 q^{93} -1.73122 q^{94} +16.2468 q^{95} +10.7298 q^{96} -17.1199 q^{97} -11.0707 q^{98} -9.81167 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 103 q + q^{2} + 2 q^{3} + 127 q^{4} + 9 q^{5} + 19 q^{6} + 18 q^{7} + 149 q^{9}+O(q^{10}) \) 103 * q + q^2 + 2 * q^3 + 127 * q^4 + 9 * q^5 + 19 * q^6 + 18 * q^7 + 149 * q^9	\( 103 q + q^{2} + 2 q^{3} + 127 q^{4} + 9 q^{5} + 19 q^{6} + 18 q^{7} + 149 q^{9} + 20 q^{10} + 9 q^{11} + 36 q^{13} - 10 q^{14} + 16 q^{15} + 179 q^{16} + 21 q^{17} + 7 q^{18} + 42 q^{19} + 24 q^{20} + 28 q^{21} + 32 q^{22} + 25 q^{23} + 68 q^{24} + 194 q^{25} - 5 q^{26} + 14 q^{27} + 59 q^{28} - 103 q^{29} + 84 q^{30} + 34 q^{31} + 11 q^{32} + 42 q^{33} + 54 q^{34} + 35 q^{35} + 214 q^{36} + 34 q^{37} + 9 q^{38} + 23 q^{39} + 46 q^{40} + 16 q^{41} + 13 q^{42} + 68 q^{43} - 6 q^{44} + 25 q^{45} + 60 q^{46} + 6 q^{47} + 5 q^{48} + 257 q^{49} - 51 q^{50} + 68 q^{51} + 37 q^{52} + 35 q^{53} + 30 q^{54} + 66 q^{55} - 54 q^{56} + 78 q^{57} - q^{58} + 10 q^{59} - 24 q^{60} + 70 q^{61} + 29 q^{62} + 26 q^{63} + 276 q^{64} + 95 q^{65} + 77 q^{66} + 71 q^{67} - 21 q^{68} - 20 q^{69} + 48 q^{70} + 32 q^{71} + 32 q^{72} + 94 q^{73} + 35 q^{74} + 7 q^{75} + 134 q^{76} + 17 q^{77} + 58 q^{78} + 110 q^{79} + 78 q^{80} + 267 q^{81} - 71 q^{82} + 35 q^{83} + 96 q^{84} + 71 q^{85} + 33 q^{86} - 2 q^{87} + 100 q^{88} + 22 q^{89} - 134 q^{90} + 108 q^{91} - 11 q^{92} + 78 q^{93} + 90 q^{94} + 12 q^{95} + 177 q^{96} + 44 q^{97} - 18 q^{98} + 83 q^{99}+O(q^{100}) \) 103 * q + q^2 + 2 * q^3 + 127 * q^4 + 9 * q^5 + 19 * q^6 + 18 * q^7 + 149 * q^9 + 20 * q^10 + 9 * q^11 + 36 * q^13 - 10 * q^14 + 16 * q^15 + 179 * q^16 + 21 * q^17 + 7 * q^18 + 42 * q^19 + 24 * q^20 + 28 * q^21 + 32 * q^22 + 25 * q^23 + 68 * q^24 + 194 * q^25 - 5 * q^26 + 14 * q^27 + 59 * q^28 - 103 * q^29 + 84 * q^30 + 34 * q^31 + 11 * q^32 + 42 * q^33 + 54 * q^34 + 35 * q^35 + 214 * q^36 + 34 * q^37 + 9 * q^38 + 23 * q^39 + 46 * q^40 + 16 * q^41 + 13 * q^42 + 68 * q^43 - 6 * q^44 + 25 * q^45 + 60 * q^46 + 6 * q^47 + 5 * q^48 + 257 * q^49 - 51 * q^50 + 68 * q^51 + 37 * q^52 + 35 * q^53 + 30 * q^54 + 66 * q^55 - 54 * q^56 + 78 * q^57 - q^58 + 10 * q^59 - 24 * q^60 + 70 * q^61 + 29 * q^62 + 26 * q^63 + 276 * q^64 + 95 * q^65 + 77 * q^66 + 71 * q^67 - 21 * q^68 - 20 * q^69 + 48 * q^70 + 32 * q^71 + 32 * q^72 + 94 * q^73 + 35 * q^74 + 7 * q^75 + 134 * q^76 + 17 * q^77 + 58 * q^78 + 110 * q^79 + 78 * q^80 + 267 * q^81 - 71 * q^82 + 35 * q^83 + 96 * q^84 + 71 * q^85 + 33 * q^86 - 2 * q^87 + 100 * q^88 + 22 * q^89 - 134 * q^90 + 108 * q^91 - 11 * q^92 + 78 * q^93 + 90 * q^94 + 12 * q^95 + 177 * q^96 + 44 * q^97 - 18 * q^98 + 83 * q^99

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