LMFDB - Embedded newform 4031.2.a.d.1.4

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:	$98$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
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)

$f(q)$	$=$	$q-2.74332 q^{2} -0.716173 q^{3} +5.52580 q^{4} -3.18087 q^{5} +1.96469 q^{6} +1.27957 q^{7} -9.67240 q^{8} -2.48710 q^{9} +O(q^{10})$	\(q-2.74332 q^{2} -0.716173 q^{3} +5.52580 q^{4} -3.18087 q^{5} +1.96469 q^{6} +1.27957 q^{7} -9.67240 q^{8} -2.48710 q^{9} +8.72614 q^{10} -1.33328 q^{11} -3.95743 q^{12} +1.29623 q^{13} -3.51028 q^{14} +2.27805 q^{15} +15.4829 q^{16} +0.865020 q^{17} +6.82290 q^{18} -4.27030 q^{19} -17.5769 q^{20} -0.916396 q^{21} +3.65762 q^{22} -8.93483 q^{23} +6.92711 q^{24} +5.11793 q^{25} -3.55597 q^{26} +3.92971 q^{27} +7.07067 q^{28} +1.00000 q^{29} -6.24942 q^{30} +4.31561 q^{31} -23.1297 q^{32} +0.954860 q^{33} -2.37303 q^{34} -4.07016 q^{35} -13.7432 q^{36} -3.15238 q^{37} +11.7148 q^{38} -0.928324 q^{39} +30.7666 q^{40} +5.24123 q^{41} +2.51397 q^{42} -10.1511 q^{43} -7.36745 q^{44} +7.91113 q^{45} +24.5111 q^{46} -0.663907 q^{47} -11.0884 q^{48} -5.36269 q^{49} -14.0401 q^{50} -0.619504 q^{51} +7.16270 q^{52} +0.756775 q^{53} -10.7804 q^{54} +4.24100 q^{55} -12.3765 q^{56} +3.05827 q^{57} -2.74332 q^{58} -5.80896 q^{59} +12.5881 q^{60} -3.84721 q^{61} -11.8391 q^{62} -3.18242 q^{63} +32.4863 q^{64} -4.12313 q^{65} -2.61949 q^{66} -12.1987 q^{67} +4.77993 q^{68} +6.39888 q^{69} +11.1657 q^{70} -3.34549 q^{71} +24.0562 q^{72} -1.01719 q^{73} +8.64798 q^{74} -3.66532 q^{75} -23.5968 q^{76} -1.70603 q^{77} +2.54669 q^{78} -5.51870 q^{79} -49.2490 q^{80} +4.64694 q^{81} -14.3784 q^{82} -5.55807 q^{83} -5.06382 q^{84} -2.75152 q^{85} +27.8478 q^{86} -0.716173 q^{87} +12.8960 q^{88} -14.5387 q^{89} -21.7028 q^{90} +1.65862 q^{91} -49.3721 q^{92} -3.09072 q^{93} +1.82131 q^{94} +13.5833 q^{95} +16.5648 q^{96} +12.4514 q^{97} +14.7116 q^{98} +3.31600 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 98 q + 6 q^{2} + 6 q^{3} + 116 q^{4} + q^{5} + 7 q^{6} + 12 q^{7} + 15 q^{8} + 136 q^{9}+O(q^{10}) $ 98 * q + 6 * q^2 + 6 * q^3 + 116 * q^4 + q^5 + 7 * q^6 + 12 * q^7 + 15 * q^8 + 136 * q^9	\( 98 q + 6 q^{2} + 6 q^{3} + 116 q^{4} + q^{5} + 7 q^{6} + 12 q^{7} + 15 q^{8} + 136 q^{9} + 16 q^{10} + 25 q^{11} + 8 q^{12} + 18 q^{13} + 34 q^{14} + 14 q^{15} + 136 q^{16} + 35 q^{17} + 20 q^{18} + 48 q^{19} - 20 q^{20} + 62 q^{21} + 32 q^{22} + q^{23} + 8 q^{24} + 173 q^{25} + 15 q^{26} + 18 q^{27} + 37 q^{28} + 98 q^{29} - 6 q^{30} + 20 q^{31} + 16 q^{32} + 24 q^{33} - 6 q^{34} + 11 q^{35} + 155 q^{36} + 62 q^{37} - 5 q^{38} + 45 q^{39} + 38 q^{40} + 50 q^{41} + 7 q^{42} + 72 q^{43} + 92 q^{44} - 13 q^{45} + 32 q^{46} - 16 q^{47} - 13 q^{48} + 194 q^{49} + 50 q^{50} + 2 q^{51} + 83 q^{52} - 11 q^{53} + 58 q^{54} + 32 q^{55} + 106 q^{56} + 84 q^{57} + 6 q^{58} + 20 q^{59} + 62 q^{60} + 142 q^{61} - 27 q^{62} + 26 q^{63} + 213 q^{64} + 13 q^{65} - 35 q^{66} + 5 q^{67} + 69 q^{68} + 68 q^{69} - 2 q^{70} - 10 q^{71} - 9 q^{72} + 74 q^{73} + 21 q^{74} + 19 q^{75} + 116 q^{76} + 41 q^{77} - 162 q^{78} + 104 q^{79} - 86 q^{80} + 230 q^{81} + 53 q^{82} - 19 q^{83} + 76 q^{84} + 125 q^{85} + 9 q^{86} + 6 q^{87} + 68 q^{88} + 120 q^{89} + 122 q^{90} + 30 q^{91} + 3 q^{92} - 56 q^{93} + 22 q^{94} + 32 q^{95} - 55 q^{96} + 98 q^{97} - 15 q^{98} + 69 q^{99}+O(q^{100}) \) 98 * q + 6 * q^2 + 6 * q^3 + 116 * q^4 + q^5 + 7 * q^6 + 12 * q^7 + 15 * q^8 + 136 * q^9 + 16 * q^10 + 25 * q^11 + 8 * q^12 + 18 * q^13 + 34 * q^14 + 14 * q^15 + 136 * q^16 + 35 * q^17 + 20 * q^18 + 48 * q^19 - 20 * q^20 + 62 * q^21 + 32 * q^22 + q^23 + 8 * q^24 + 173 * q^25 + 15 * q^26 + 18 * q^27 + 37 * q^28 + 98 * q^29 - 6 * q^30 + 20 * q^31 + 16 * q^32 + 24 * q^33 - 6 * q^34 + 11 * q^35 + 155 * q^36 + 62 * q^37 - 5 * q^38 + 45 * q^39 + 38 * q^40 + 50 * q^41 + 7 * q^42 + 72 * q^43 + 92 * q^44 - 13 * q^45 + 32 * q^46 - 16 * q^47 - 13 * q^48 + 194 * q^49 + 50 * q^50 + 2 * q^51 + 83 * q^52 - 11 * q^53 + 58 * q^54 + 32 * q^55 + 106 * q^56 + 84 * q^57 + 6 * q^58 + 20 * q^59 + 62 * q^60 + 142 * q^61 - 27 * q^62 + 26 * q^63 + 213 * q^64 + 13 * q^65 - 35 * q^66 + 5 * q^67 + 69 * q^68 + 68 * q^69 - 2 * q^70 - 10 * q^71 - 9 * q^72 + 74 * q^73 + 21 * q^74 + 19 * q^75 + 116 * q^76 + 41 * q^77 - 162 * q^78 + 104 * q^79 - 86 * q^80 + 230 * q^81 + 53 * q^82 - 19 * q^83 + 76 * q^84 + 125 * q^85 + 9 * q^86 + 6 * q^87 + 68 * q^88 + 120 * q^89 + 122 * q^90 + 30 * q^91 + 3 * q^92 - 56 * q^93 + 22 * q^94 + 32 * q^95 - 55 * q^96 + 98 * q^97 - 15 * q^98 + 69 * 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 $

$2$	−2.74332	−1.93982	−0.969910	−	0.243465i	$-0.921716\pi$
$2$	−2.74332	−1.93982	−0.969910	+	0.243465i	$0.921716\pi$
$3$	−0.716173	−0.413483	−0.206741	−	0.978396i	$-0.566286\pi$
$3$	−0.716173	−0.413483	−0.206741	+	0.978396i	$0.566286\pi$
$4$	5.52580	2.76290
$5$	−3.18087	−1.42253	−0.711264	−	0.702925i	$-0.751877\pi$
$5$	−3.18087	−1.42253	−0.711264	+	0.702925i	$0.751877\pi$
$6$	1.96469	0.802082
$7$	1.27957	0.483633	0.241817	−	0.970322i	$-0.422257\pi$
$7$	1.27957	0.483633	0.241817	+	0.970322i	$0.422257\pi$
$8$	−9.67240	−3.41971
$9$	−2.48710	−0.829032
$10$	8.72614	2.75945
$11$	−1.33328	−0.402000	−0.201000	−	0.979591i	$-0.564419\pi$
$11$	−1.33328	−0.402000	−0.201000	+	0.979591i	$0.564419\pi$
$12$	−3.95743	−1.14241
$13$	1.29623	0.359509	0.179755	−	0.983711i	$-0.442470\pi$
$13$	1.29623	0.359509	0.179755	+	0.983711i	$0.442470\pi$
$14$	−3.51028	−0.938161
$15$	2.27805	0.588191
$16$	15.4829	3.87072
$17$	0.865020	0.209798	0.104899	−	0.994483i	$-0.466548\pi$
$17$	0.865020	0.209798	0.104899	+	0.994483i	$0.466548\pi$
$18$	6.82290	1.60817
$19$	−4.27030	−0.979674	−0.489837	−	0.871814i	$-0.662944\pi$
$19$	−4.27030	−0.979674	−0.489837	+	0.871814i	$0.662944\pi$
$20$	−17.5769	−3.93030
$21$	−0.916396	−0.199974
$22$	3.65762	0.779807
$23$	−8.93483	−1.86304	−0.931520	−	0.363689i	$-0.881517\pi$
$23$	−8.93483	−1.86304	−0.931520	+	0.363689i	$0.881517\pi$
$24$	6.92711	1.41399
$25$	5.11793	1.02359
$26$	−3.55597	−0.697383
$27$	3.92971	0.756273
$28$	7.07067	1.33623
$29$	1.00000	0.185695
$29$	1.00000	0.185695
$30$	−6.24942	−1.14098
$31$	4.31561	0.775106	0.387553	−	0.921847i	$-0.373320\pi$
$31$	4.31561	0.775106	0.387553	+	0.921847i	$0.373320\pi$
$32$	−23.1297	−4.08878
$33$	0.954860	0.166220
$34$	−2.37303	−0.406971
$35$	−4.07016	−0.687982
$36$	−13.7432	−2.29053
$37$	−3.15238	−0.518248	−0.259124	−	0.965844i	$-0.583434\pi$
$37$	−3.15238	−0.518248	−0.259124	+	0.965844i	$0.583434\pi$
$38$	11.7148	1.90039
$39$	−0.928324	−0.148651
$40$	30.7666	4.86463
$41$	5.24123	0.818543	0.409271	−	0.912413i	$-0.365783\pi$
$41$	5.24123	0.818543	0.409271	+	0.912413i	$0.365783\pi$
$42$	2.51397	0.387913
$43$	−10.1511	−1.54803	−0.774017	−	0.633165i	$-0.781756\pi$
$43$	−10.1511	−1.54803	−0.774017	+	0.633165i	$0.781756\pi$
$44$	−7.36745	−1.11068
$45$	7.91113	1.17932
$46$	24.5111	3.61396
$47$	−0.663907	−0.0968409	−0.0484204	−	0.998827i	$-0.515419\pi$
$47$	−0.663907	−0.0968409	−0.0484204	+	0.998827i	$0.515419\pi$
$48$	−11.0884	−1.60047
$49$	−5.36269	−0.766099
$50$	−14.0401	−1.98557
$51$	−0.619504	−0.0867479
$52$	7.16270	0.993288
$53$	0.756775	0.103951	0.0519755	−	0.998648i	$-0.483448\pi$
$53$	0.756775	0.103951	0.0519755	+	0.998648i	$0.483448\pi$
$54$	−10.7804	−1.46703
$55$	4.24100	0.571856
$56$	−12.3765	−1.65388
$57$	3.05827	0.405078
$58$	−2.74332	−0.360215
$59$	−5.80896	−0.756263	−0.378131	−	0.925752i	$-0.623433\pi$
$59$	−5.80896	−0.756263	−0.378131	+	0.925752i	$0.623433\pi$
$60$	12.5881	1.62511
$61$	−3.84721	−0.492585	−0.246292	−	0.969196i	$-0.579212\pi$
$61$	−3.84721	−0.492585	−0.246292	+	0.969196i	$0.579212\pi$
$62$	−11.8391	−1.50357
$63$	−3.18242	−0.400948
$64$	32.4863	4.06079
$65$	−4.12313	−0.511412
$66$	−2.61949	−0.322436
$67$	−12.1987	−1.49031	−0.745156	−	0.666890i	$-0.767625\pi$
$67$	−12.1987	−1.49031	−0.745156	+	0.666890i	$0.767625\pi$
$68$	4.77993	0.579651
$69$	6.39888	0.770335
$70$	11.1657	1.33456
$71$	−3.34549	−0.397037	−0.198519	−	0.980097i	$-0.563613\pi$
$71$	−3.34549	−0.397037	−0.198519	+	0.980097i	$0.563613\pi$
$72$	24.0562	2.83505
$73$	−1.01719	−0.119053	−0.0595264	−	0.998227i	$-0.518959\pi$
$73$	−1.01719	−0.119053	−0.0595264	+	0.998227i	$0.518959\pi$
$74$	8.64798	1.00531
$75$	−3.66532	−0.423235
$76$	−23.5968	−2.70674
$77$	−1.70603	−0.194420
$78$	2.54669	0.288356
$79$	−5.51870	−0.620903	−0.310451	−	0.950589i	$-0.600480\pi$
$79$	−5.51870	−0.620903	−0.310451	+	0.950589i	$0.600480\pi$
$80$	−49.2490	−5.50620
$81$	4.64694	0.516327
$82$	−14.3784	−1.58783
$83$	−5.55807	−0.610077	−0.305039	−	0.952340i	$-0.598669\pi$
$83$	−5.55807	−0.610077	−0.305039	+	0.952340i	$0.598669\pi$
$84$	−5.06382	−0.552508
$85$	−2.75152	−0.298444
$86$	27.8478	3.00291
$87$	−0.716173	−0.0767818
$88$	12.8960	1.37472
$89$	−14.5387	−1.54110	−0.770551	−	0.637379i	$-0.780019\pi$
$89$	−14.5387	−1.54110	−0.770551	+	0.637379i	$0.780019\pi$
$90$	−21.7028	−2.28767
$91$	1.65862	0.173871
$92$	−49.3721	−5.14740
$93$	−3.09072	−0.320493
$94$	1.82131	0.187854
$95$	13.5833	1.39361
$96$	16.5648	1.69064
$97$	12.4514	1.26425	0.632126	−	0.774865i	$-0.282182\pi$
$97$	12.4514	1.26425	0.632126	+	0.774865i	$0.282182\pi$
$98$	14.7116	1.48609
$99$	3.31600	0.333271
$100$	28.2807	2.82807
$101$	11.4867	1.14297	0.571483	−	0.820614i	$-0.306368\pi$
$101$	11.4867	1.14297	0.571483	+	0.820614i	$0.306368\pi$
$102$	1.69950	0.168275
$103$	18.1966	1.79296	0.896481	−	0.443082i	$-0.146115\pi$
$103$	18.1966	1.79296	0.896481	+	0.443082i	$0.146115\pi$
$104$	−12.5376	−1.22942
$105$	2.91494	0.284469
$106$	−2.07608	−0.201646
$107$	−16.3737	−1.58291	−0.791453	−	0.611230i	$-0.790675\pi$
$107$	−16.3737	−1.58291	−0.791453	+	0.611230i	$0.790675\pi$
$108$	21.7148	2.08951
$109$	15.4127	1.47626	0.738132	−	0.674656i	$-0.235708\pi$
$109$	15.4127	1.47626	0.738132	+	0.674656i	$0.235708\pi$
$110$	−11.6344	−1.10930
$111$	2.25765	0.214286
$112$	19.8115	1.87201
$113$	6.46569	0.608241	0.304121	−	0.952634i	$-0.401637\pi$
$113$	6.46569	0.608241	0.304121	+	0.952634i	$0.401637\pi$
$114$	−8.38982	−0.785778
$115$	28.4205	2.65023
$116$	5.52580	0.513058
$117$	−3.22385	−0.298045
$118$	15.9358	1.46701
$119$	1.10686	0.101465
$120$	−22.0342	−2.01144
$121$	−9.22236	−0.838396
$122$	10.5541	0.955526
$123$	−3.75363	−0.338453
$124$	23.8472	2.14154
$125$	−0.375127	−0.0335523
$126$	8.73040	0.777766
$127$	−0.518233	−0.0459857	−0.0229929	−	0.999736i	$-0.507319\pi$
$127$	−0.518233	−0.0459857	−0.0229929	+	0.999736i	$0.507319\pi$
$128$	−42.8610	−3.78841
$129$	7.26997	0.640085
$130$	11.3111	0.992047
$131$	−1.39342	−0.121744	−0.0608720	−	0.998146i	$-0.519388\pi$
$131$	−1.39342	−0.121744	−0.0608720	+	0.998146i	$0.519388\pi$
$132$	5.27637	0.459249
$133$	−5.46416	−0.473803
$134$	33.4650	2.89094
$135$	−12.4999	−1.07582
$136$	−8.36682	−0.717449
$137$	−13.5099	−1.15423	−0.577113	−	0.816665i	$-0.695821\pi$
$137$	−13.5099	−1.15423	−0.577113	+	0.816665i	$0.695821\pi$
$138$	−17.5542	−1.49431
$139$	−1.00000	−0.0848189
$139$	−1.00000	−0.0848189
$140$	−22.4909	−1.90083
$141$	0.475472	0.0400420
$142$	9.17776	0.770180
$143$	−1.72824	−0.144523
$144$	−38.5074	−3.20895
$145$	−3.18087	−0.264157
$146$	2.79047	0.230941
$147$	3.84061	0.316769
$148$	−17.4194	−1.43187
$149$	−7.06190	−0.578533	−0.289267	−	0.957249i	$-0.593411\pi$
$149$	−7.06190	−0.578533	−0.289267	+	0.957249i	$0.593411\pi$
$150$	10.0552	0.821000
$151$	−18.0994	−1.47291	−0.736455	−	0.676487i	$-0.763502\pi$
$151$	−18.0994	−1.47291	−0.736455	+	0.676487i	$0.763502\pi$
$152$	41.3040	3.35020
$153$	−2.15139	−0.173929
$154$	4.68019	0.377140
$155$	−13.7274	−1.10261
$156$	−5.12973	−0.410707
$157$	−2.79102	−0.222747	−0.111374	−	0.993779i	$-0.535525\pi$
$157$	−2.79102	−0.222747	−0.111374	+	0.993779i	$0.535525\pi$
$158$	15.1396	1.20444
$159$	−0.541982	−0.0429819
$160$	73.5724	5.81641
$161$	−11.4328	−0.901029
$162$	−12.7480	−1.00158
$163$	−19.0365	−1.49105	−0.745525	−	0.666477i	$-0.767801\pi$
$163$	−19.0365	−1.49105	−0.745525	+	0.666477i	$0.767801\pi$
$164$	28.9620	2.26155
$165$	−3.03729	−0.236452
$166$	15.2476	1.18344
$167$	−21.3813	−1.65454	−0.827268	−	0.561808i	$-0.810106\pi$
$167$	−21.3813	−1.65454	−0.827268	+	0.561808i	$0.810106\pi$
$168$	8.86374	0.683852
$169$	−11.3198	−0.870753
$170$	7.54829	0.578927
$171$	10.6206	0.812181
$172$	−56.0932	−4.27706
$173$	3.04458	0.231475	0.115738	−	0.993280i	$-0.463077\pi$
$173$	3.04458	0.231475	0.115738	+	0.993280i	$0.463077\pi$
$174$	1.96469	0.148943
$175$	6.54877	0.495040
$176$	−20.6430	−1.55603
$177$	4.16022	0.312701
$178$	39.8844	2.98946
$179$	10.7213	0.801344	0.400672	−	0.916221i	$-0.368777\pi$
$179$	10.7213	0.801344	0.400672	+	0.916221i	$0.368777\pi$
$180$	43.7153	3.25835
$181$	−3.90561	−0.290302	−0.145151	−	0.989410i	$-0.546367\pi$
$181$	−3.90561	−0.290302	−0.145151	+	0.989410i	$0.546367\pi$
$182$	−4.55012	−0.337278
$183$	2.75527	0.203675
$184$	86.4212	6.37106
$185$	10.0273	0.737222
$186$	8.47883	0.621698
$187$	−1.15332	−0.0843388
$188$	−3.66862	−0.267562
$189$	5.02835	0.365759
$190$	−37.2632	−2.70336
$191$	19.9758	1.44540	0.722698	−	0.691164i	$-0.242902\pi$
$191$	19.9758	1.44540	0.722698	+	0.691164i	$0.242902\pi$
$192$	−23.2658	−1.67906
$193$	1.13647	0.0818048	0.0409024	−	0.999163i	$-0.486977\pi$
$193$	1.13647	0.0818048	0.0409024	+	0.999163i	$0.486977\pi$
$194$	−34.1583	−2.45242
$195$	2.95288	0.211460
$196$	−29.6332	−2.11665
$197$	−1.15609	−0.0823681	−0.0411841	−	0.999152i	$-0.513113\pi$
$197$	−1.15609	−0.0823681	−0.0411841	+	0.999152i	$0.513113\pi$
$198$	−9.09685	−0.646485
$199$	−10.0389	−0.711637	−0.355818	−	0.934555i	$-0.615798\pi$
$199$	−10.0389	−0.711637	−0.355818	+	0.934555i	$0.615798\pi$
$200$	−49.5027	−3.50037
$201$	8.73640	0.616218
$202$	−31.5116	−2.21715
$203$	1.27957	0.0898084
$204$	−3.42325	−0.239676
$205$	−16.6717	−1.16440
$206$	−49.9190	−3.47802
$207$	22.2218	1.54452
$208$	20.0693	1.39156
$209$	5.69351	0.393829
$210$	−7.99660	−0.551818
$211$	8.09056	0.556977	0.278489	−	0.960440i	$-0.410167\pi$
$211$	8.09056	0.556977	0.278489	+	0.960440i	$0.410167\pi$
$212$	4.18179	0.287206
$213$	2.39595	0.164168
$214$	44.9183	3.07055
$215$	32.2894	2.20212
$216$	−38.0097	−2.58623
$217$	5.52214	0.374867
$218$	−42.2818	−2.86369
$219$	0.728483	0.0492263
$220$	23.4349	1.57998
$221$	1.12126	0.0754244
$222$	−6.19345	−0.415677
$223$	9.52003	0.637509	0.318754	−	0.947837i	$-0.396736\pi$
$223$	9.52003	0.637509	0.318754	+	0.947837i	$0.396736\pi$
$224$	−29.5961	−1.97747
$225$	−12.7288	−0.848586
$226$	−17.7375	−1.17988
$227$	−22.7345	−1.50894	−0.754470	−	0.656334i	$-0.772106\pi$
$227$	−22.7345	−1.50894	−0.754470	+	0.656334i	$0.772106\pi$
$228$	16.8994	1.11919
$229$	−23.7877	−1.57194	−0.785969	−	0.618266i	$-0.787836\pi$
$229$	−23.7877	−1.57194	−0.785969	+	0.618266i	$0.787836\pi$
$230$	−77.9666	−5.14096
$231$	1.22181	0.0803894
$232$	−9.67240	−0.635024
$233$	−2.44642	−0.160270	−0.0801350	−	0.996784i	$-0.525535\pi$
$233$	−2.44642	−0.160270	−0.0801350	+	0.996784i	$0.525535\pi$
$234$	8.84404	0.578153
$235$	2.11180	0.137759
$236$	−32.0992	−2.08948
$237$	3.95235	0.256732
$238$	−3.03646	−0.196825
$239$	−2.97718	−0.192578	−0.0962888	−	0.995353i	$-0.530697\pi$
$239$	−2.97718	−0.192578	−0.0962888	+	0.995353i	$0.530697\pi$
$240$	35.2708	2.27672
$241$	20.3356	1.30993	0.654966	−	0.755659i	$-0.272683\pi$
$241$	20.3356	1.30993	0.654966	+	0.755659i	$0.272683\pi$
$242$	25.2999	1.62634
$243$	−15.1171	−0.969765
$244$	−21.2589	−1.36096
$245$	17.0580	1.08980
$246$	10.2974	0.656538
$247$	−5.53528	−0.352202
$248$	−41.7423	−2.65064
$249$	3.98054	0.252256
$250$	1.02909	0.0650855
$251$	23.1616	1.46194	0.730972	−	0.682407i	$-0.239067\pi$
$251$	23.1616	1.46194	0.730972	+	0.682407i	$0.239067\pi$
$252$	−17.5854	−1.10778
$253$	11.9126	0.748942
$254$	1.42168	0.0892040
$255$	1.97056	0.123401
$256$	52.6087	3.28804
$257$	−16.7309	−1.04364	−0.521821	−	0.853055i	$-0.674747\pi$
$257$	−16.7309	−1.04364	−0.521821	+	0.853055i	$0.674747\pi$
$258$	−19.9438	−1.24165
$259$	−4.03370	−0.250642
$260$	−22.7836	−1.41298
$261$	−2.48710	−0.153947
$262$	3.82261	0.236161
$263$	14.2192	0.876792	0.438396	−	0.898782i	$-0.355547\pi$
$263$	14.2192	0.876792	0.438396	+	0.898782i	$0.355547\pi$
$264$	−9.23579	−0.568423
$265$	−2.40720	−0.147873
$266$	14.9899	0.919092
$267$	10.4122	0.637219
$268$	−67.4077	−4.11758
$269$	26.0599	1.58890	0.794451	−	0.607328i	$-0.207759\pi$
$269$	26.0599	1.58890	0.794451	+	0.607328i	$0.207759\pi$
$270$	34.2912	2.08690
$271$	−0.0132684	−0.000805999 0	−0.000403000	−	1.00000i	$-0.500128\pi$
$271$	−0.0132684	−0.000805999 0	−0.000403000		1.00000i	$0.500128\pi$
$272$	13.3930	0.812069
$273$	−1.18786	−0.0718925
$274$	37.0619	2.23899
$275$	−6.82365	−0.411481
$276$	35.3589	2.12836
$277$	−10.8163	−0.649891	−0.324946	−	0.945733i	$-0.605346\pi$
$277$	−10.8163	−0.649891	−0.324946	+	0.945733i	$0.605346\pi$
$278$	2.74332	0.164533
$279$	−10.7333	−0.642588
$280$	39.3682	2.35270
$281$	5.66510	0.337952	0.168976	−	0.985620i	$-0.445954\pi$
$281$	5.66510	0.337952	0.168976	+	0.985620i	$0.445954\pi$
$282$	−1.30437	−0.0776743
$283$	17.0973	1.01633	0.508166	−	0.861259i	$-0.330324\pi$
$283$	17.0973	1.01633	0.508166	+	0.861259i	$0.330324\pi$
$284$	−18.4865	−1.09697
$285$	−9.72797	−0.576235
$286$	4.74111	0.280348
$287$	6.70654	0.395875
$288$	57.5257	3.38973
$289$	−16.2517	−0.955985
$290$	8.72614	0.512417
$291$	−8.91738	−0.522746
$292$	−5.62078	−0.328931
$293$	−6.26385	−0.365938	−0.182969	−	0.983119i	$-0.558571\pi$
$293$	−6.26385	−0.365938	−0.182969	+	0.983119i	$0.558571\pi$
$294$	−10.5360	−0.614474
$295$	18.4776	1.07580
$296$	30.4910	1.77226
$297$	−5.23941	−0.304021
$298$	19.3730	1.12225
$299$	−11.5816	−0.669780
$300$	−20.2538	−1.16936
$301$	−12.9891	−0.748681
$302$	49.6525	2.85718
$303$	−8.22644	−0.472596
$304$	−66.1165	−3.79204
$305$	12.2375	0.700716
$306$	5.90194	0.337392
$307$	−7.68682	−0.438710	−0.219355	−	0.975645i	$-0.570395\pi$
$307$	−7.68682	−0.438710	−0.219355	+	0.975645i	$0.570395\pi$
$308$	−9.42719	−0.537164
$309$	−13.0319	−0.741359
$310$	37.6586	2.13886
$311$	24.1269	1.36811	0.684055	−	0.729430i	$-0.260215\pi$
$311$	24.1269	1.36811	0.684055	+	0.729430i	$0.260215\pi$
$312$	8.97911	0.508342
$313$	6.09229	0.344356	0.172178	−	0.985066i	$-0.444920\pi$
$313$	6.09229	0.344356	0.172178	+	0.985066i	$0.444920\pi$
$314$	7.65665	0.432090
$315$	10.1229	0.570359
$316$	−30.4953	−1.71549
$317$	9.85051	0.553260	0.276630	−	0.960977i	$-0.410782\pi$
$317$	9.85051	0.553260	0.276630	+	0.960977i	$0.410782\pi$
$318$	1.48683	0.0833772
$319$	−1.33328	−0.0746495
$320$	−103.335	−5.77658
$321$	11.7264	0.654504
$322$	31.3637	1.74783
$323$	−3.69389	−0.205534
$324$	25.6781	1.42656
$325$	6.63401	0.367989
$326$	52.2231	2.89237
$327$	−11.0381	−0.610410
$328$	−50.6953	−2.79918
$329$	−0.849518	−0.0468355
$330$	8.33225	0.458675
$331$	16.6105	0.912993	0.456497	−	0.889725i	$-0.349104\pi$
$331$	16.6105	0.912993	0.456497	+	0.889725i	$0.349104\pi$
$332$	−30.7128	−1.68558
$333$	7.84027	0.429644
$334$	58.6558	3.20950
$335$	38.8026	2.12001
$336$	−14.1884	−0.774042
$337$	−9.14974	−0.498418	−0.249209	−	0.968450i	$-0.580171\pi$
$337$	−9.14974	−0.498418	−0.249209	+	0.968450i	$0.580171\pi$
$338$	31.0538	1.68910
$339$	−4.63055	−0.251497
$340$	−15.2043	−0.824570
$341$	−5.75392	−0.311592
$342$	−29.1358	−1.57548
$343$	−15.8190	−0.854144
$344$	98.1858	5.29382
$345$	−20.3540	−1.09582
$346$	−8.35225	−0.449020
$347$	−30.7527	−1.65089	−0.825446	−	0.564481i	$-0.809076\pi$
$347$	−30.7527	−1.65089	−0.825446	+	0.564481i	$0.809076\pi$
$348$	−3.95743	−0.212140
$349$	−11.8313	−0.633313	−0.316656	−	0.948540i	$-0.602560\pi$
$349$	−11.8313	−0.633313	−0.316656	+	0.948540i	$0.602560\pi$
$350$	−17.9654	−0.960289
$351$	5.09380	0.271887
$352$	30.8384	1.64369
$353$	31.1542	1.65817	0.829086	−	0.559121i	$-0.188861\pi$
$353$	31.1542	1.65817	0.829086	+	0.559121i	$0.188861\pi$
$354$	−11.4128	−0.606584
$355$	10.6416	0.564796
$356$	−80.3381	−4.25791
$357$	−0.792701	−0.0419542
$358$	−29.4118	−1.55446
$359$	18.8213	0.993350	0.496675	−	0.867936i	$-0.334554\pi$
$359$	18.8213	0.993350	0.496675	+	0.867936i	$0.334554\pi$
$360$	−76.5196	−4.03294
$361$	−0.764545	−0.0402392
$362$	10.7143	0.563133
$363$	6.60480	0.346662
$364$	9.16520	0.480387
$365$	3.23554	0.169356
$366$	−7.55858	−0.395093
$367$	−23.7215	−1.23825	−0.619126	−	0.785292i	$-0.712513\pi$
$367$	−23.7215	−1.23825	−0.619126	+	0.785292i	$0.712513\pi$
$368$	−138.337	−7.21130
$369$	−13.0355	−0.678598
$370$	−27.5081	−1.43008
$371$	0.968349	0.0502742
$372$	−17.0787	−0.885489
$373$	21.0713	1.09103	0.545516	−	0.838101i	$-0.316334\pi$
$373$	21.0713	1.09103	0.545516	+	0.838101i	$0.316334\pi$
$374$	3.16391	0.163602
$375$	0.268655	0.0138733
$376$	6.42158	0.331167
$377$	1.29623	0.0667592
$378$	−13.7944	−0.709506
$379$	26.2517	1.34846	0.674231	−	0.738521i	$-0.264475\pi$
$379$	26.2517	1.34846	0.674231	+	0.738521i	$0.264475\pi$
$380$	75.0584	3.85042
$381$	0.371144	0.0190143
$382$	−54.7999	−2.80381
$383$	7.06588	0.361050	0.180525	−	0.983570i	$-0.442220\pi$
$383$	7.06588	0.361050	0.180525	+	0.983570i	$0.442220\pi$
$384$	30.6959	1.56644
$385$	5.42667	0.276568
$386$	−3.11770	−0.158687
$387$	25.2469	1.28337
$388$	68.8042	3.49300
$389$	−24.7477	−1.25476	−0.627380	−	0.778713i	$-0.715873\pi$
$389$	−24.7477	−1.25476	−0.627380	+	0.778713i	$0.715873\pi$
$390$	−8.10068	−0.410194
$391$	−7.72881	−0.390863
$392$	51.8701	2.61983
$393$	0.997932	0.0503390
$394$	3.17153	0.159779
$395$	17.5543	0.883251
$396$	18.3236	0.920793
$397$	−32.6157	−1.63693	−0.818467	−	0.574553i	$-0.805176\pi$
$397$	−32.6157	−1.63693	−0.818467	+	0.574553i	$0.805176\pi$
$398$	27.5398	1.38045
$399$	3.91328	0.195909
$400$	79.2403	3.96201
$401$	25.6710	1.28195	0.640974	−	0.767562i	$-0.278531\pi$
$401$	25.6710	1.28195	0.640974	+	0.767562i	$0.278531\pi$
$402$	−23.9667	−1.19535
$403$	5.59401	0.278658
$404$	63.4730	3.15790
$405$	−14.7813	−0.734489
$406$	−3.51028	−0.174212
$407$	4.20301	0.208335
$408$	5.99209	0.296652
$409$	23.8655	1.18007	0.590036	−	0.807377i	$-0.299113\pi$
$409$	23.8655	1.18007	0.590036	+	0.807377i	$0.299113\pi$
$410$	45.7357	2.25873
$411$	9.67539	0.477252
$412$	100.551	4.95377
$413$	−7.43299	−0.365754
$414$	−60.9614	−2.99609
$415$	17.6795	0.867852
$416$	−29.9813	−1.46996
$417$	0.716173	0.0350711
$418$	−15.6191	−0.763956
$419$	36.8994	1.80265	0.901327	−	0.433140i	$-0.142594\pi$
$419$	36.8994	1.80265	0.901327	+	0.433140i	$0.142594\pi$
$420$	16.1073	0.785958
$421$	7.97065	0.388466	0.194233	−	0.980955i	$-0.437778\pi$
$421$	7.97065	0.388466	0.194233	+	0.980955i	$0.437778\pi$
$422$	−22.1950	−1.08044
$423$	1.65120	0.0802842
$424$	−7.31983	−0.355482
$425$	4.42711	0.214747
$426$	−6.57286	−0.318456
$427$	−4.92279	−0.238230
$428$	−90.4779	−4.37341
$429$	1.23772	0.0597576
$430$	−88.5803	−4.27172
$431$	17.7724	0.856066	0.428033	−	0.903763i	$-0.359207\pi$
$431$	17.7724	0.856066	0.428033	+	0.903763i	$0.359207\pi$
$432$	60.8432	2.92732
$433$	26.6702	1.28169	0.640844	−	0.767671i	$-0.278584\pi$
$433$	26.6702	1.28169	0.640844	+	0.767671i	$0.278584\pi$
$434$	−15.1490	−0.727174
$435$	2.27805	0.109224
$436$	85.1673	4.07877
$437$	38.1544	1.82517
$438$	−1.99846	−0.0954901
$439$	18.9555	0.904698	0.452349	−	0.891841i	$-0.350586\pi$
$439$	18.9555	0.904698	0.452349	+	0.891841i	$0.350586\pi$
$440$	−41.0206	−1.95558
$441$	13.3375	0.635121
$442$	−3.07598	−0.146310
$443$	−9.97313	−0.473838	−0.236919	−	0.971529i	$-0.576138\pi$
$443$	−9.97313	−0.473838	−0.236919	+	0.971529i	$0.576138\pi$
$444$	12.4753	0.592052
$445$	46.2458	2.19226
$446$	−26.1165	−1.23665
$447$	5.05754	0.239213
$448$	41.5686	1.96393
$449$	9.87725	0.466136	0.233068	−	0.972460i	$-0.425123\pi$
$449$	9.87725	0.466136	0.233068	+	0.972460i	$0.425123\pi$
$450$	34.9191	1.64610
$451$	−6.98804	−0.329054
$452$	35.7281	1.68051
$453$	12.9623	0.609022
$454$	62.3679	2.92707
$455$	−5.27585	−0.247336
$456$	−29.5808	−1.38525
$457$	−13.2792	−0.621176	−0.310588	−	0.950545i	$-0.600526\pi$
$457$	−13.2792	−0.621176	−0.310588	+	0.950545i	$0.600526\pi$
$458$	65.2574	3.04928
$459$	3.39928	0.158665
$460$	157.046	7.32232
$461$	18.2050	0.847893	0.423947	−	0.905687i	$-0.360644\pi$
$461$	18.2050	0.847893	0.423947	+	0.905687i	$0.360644\pi$
$462$	−3.35183	−0.155941
$463$	5.15641	0.239639	0.119819	−	0.992796i	$-0.461768\pi$
$463$	5.15641	0.239639	0.119819	+	0.992796i	$0.461768\pi$
$464$	15.4829	0.718774
$465$	9.83118	0.455910
$466$	6.71130	0.310895
$467$	5.14413	0.238042	0.119021	−	0.992892i	$-0.462024\pi$
$467$	5.14413	0.238042	0.119021	+	0.992892i	$0.462024\pi$
$468$	−17.8143	−0.823468
$469$	−15.6092	−0.720764
$470$	−5.79335	−0.267227
$471$	1.99885	0.0921021
$472$	56.1866	2.58620
$473$	13.5343	0.622309
$474$	−10.8425	−0.498015
$475$	−21.8551	−1.00278
$476$	6.11627	0.280339
$477$	−1.88217	−0.0861787
$478$	8.16735	0.373566
$479$	33.5585	1.53333	0.766663	−	0.642050i	$-0.221916\pi$
$479$	33.5585	1.53333	0.766663	+	0.642050i	$0.221916\pi$
$480$	−52.6906	−2.40498
$481$	−4.08620	−0.186315
$482$	−55.7870	−2.54103
$483$	8.18784	0.372560
$484$	−50.9609	−2.31641
$485$	−39.6064	−1.79843
$486$	41.4711	1.88117
$487$	−4.74154	−0.214860	−0.107430	−	0.994213i	$-0.534262\pi$
$487$	−4.74154	−0.214860	−0.107430	+	0.994213i	$0.534262\pi$
$488$	37.2118	1.68450
$489$	13.6334	0.616524
$490$	−46.7956	−2.11401
$491$	−5.56140	−0.250983	−0.125491	−	0.992095i	$-0.540051\pi$
$491$	−5.56140	−0.250983	−0.125491	+	0.992095i	$0.540051\pi$
$492$	−20.7418	−0.935113
$493$	0.865020	0.0389585
$494$	15.1851	0.683208
$495$	−10.5478	−0.474087
$496$	66.8180	3.00022
$497$	−4.28080	−0.192020
$498$	−10.9199	−0.489332
$499$	31.7172	1.41986	0.709929	−	0.704273i	$-0.248727\pi$
$499$	31.7172	1.41986	0.709929	+	0.704273i	$0.248727\pi$
$500$	−2.07287	−0.0927018
$501$	15.3127	0.684122
$502$	−63.5395	−2.83591
$503$	0.0384871	0.00171605	0.000858027	−	1.00000i	$-0.499727\pi$
$503$	0.0384871	0.00171605	0.000858027		1.00000i	$0.499727\pi$
$504$	30.7816	1.37112
$505$	−36.5376	−1.62590
$506$	−32.6802	−1.45281
$507$	8.10693	0.360041
$508$	−2.86365	−0.127054
$509$	10.9151	0.483803	0.241902	−	0.970301i	$-0.422229\pi$
$509$	10.9151	0.483803	0.241902	+	0.970301i	$0.422229\pi$
$510$	−5.40588	−0.239376
$511$	−1.30157	−0.0575779
$512$	−58.6006	−2.58980
$513$	−16.7810	−0.740901
$514$	45.8981	2.02448
$515$	−57.8809	−2.55054
$516$	40.1724	1.76849
$517$	0.885176	0.0389300
$518$	11.0657	0.486200
$519$	−2.18045	−0.0957109
$520$	39.8806	1.74888
$521$	−19.7651	−0.865923	−0.432962	−	0.901412i	$-0.642531\pi$
$521$	−19.7651	−0.865923	−0.432962	+	0.901412i	$0.642531\pi$
$522$	6.82290	0.298630
$523$	43.4279	1.89897	0.949484	−	0.313815i	$-0.101607\pi$
$523$	43.4279	1.89897	0.949484	+	0.313815i	$0.101607\pi$
$524$	−7.69978	−0.336367
$525$	−4.69005	−0.204691
$526$	−39.0077	−1.70082
$527$	3.73309	0.162616
$528$	14.7840	0.643390
$529$	56.8312	2.47092
$530$	6.60372	0.286847
$531$	14.4475	0.626966
$532$	−30.1939	−1.30907
$533$	6.79384	0.294274
$534$	−28.5641	−1.23609
$535$	52.0827	2.25173
$536$	117.991	5.09643
$537$	−7.67827	−0.331342
$538$	−71.4907	−3.08218
$539$	7.14998	0.307971
$540$	−69.0719	−2.97238
$541$	13.9802	0.601055	0.300527	−	0.953773i	$-0.402837\pi$
$541$	13.9802	0.601055	0.300527	+	0.953773i	$0.402837\pi$
$542$	0.0363995	0.00156349
$543$	2.79709	0.120035
$544$	−20.0076	−0.857819
$545$	−49.0256	−2.10003
$546$	3.25867	0.139458
$547$	−4.69482	−0.200736	−0.100368	−	0.994950i	$-0.532002\pi$
$547$	−4.69482	−0.200736	−0.100368	+	0.994950i	$0.532002\pi$
$548$	−74.6528	−3.18901
$549$	9.56839	0.408369
$550$	18.7194	0.798200
$551$	−4.27030	−0.181921
$552$	−61.8925	−2.63432
$553$	−7.06159	−0.300289
$554$	29.6727	1.26067
$555$	−7.18128	−0.304828
$556$	−5.52580	−0.234346
$557$	−27.1277	−1.14944	−0.574718	−	0.818352i	$-0.694888\pi$
$557$	−27.1277	−1.14944	−0.574718	+	0.818352i	$0.694888\pi$
$558$	29.4449	1.24650
$559$	−13.1582	−0.556532
$560$	−63.0177	−2.66298
$561$	0.825973	0.0348726
$562$	−15.5412	−0.655565
$563$	3.66899	0.154630	0.0773148	−	0.997007i	$-0.475365\pi$
$563$	3.66899	0.154630	0.0773148	+	0.997007i	$0.475365\pi$
$564$	2.62737	0.110632
$565$	−20.5665	−0.865240
$566$	−46.9035	−1.97150
$567$	5.94610	0.249713
$568$	32.3589	1.35775
$569$	2.12495	0.0890825	0.0445413	−	0.999008i	$-0.485817\pi$
$569$	2.12495	0.0890825	0.0445413	+	0.999008i	$0.485817\pi$
$570$	26.6869	1.11779
$571$	−31.3844	−1.31340	−0.656698	−	0.754154i	$-0.728047\pi$
$571$	−31.3844	−1.31340	−0.656698	+	0.754154i	$0.728047\pi$
$572$	−9.54990	−0.399301
$573$	−14.3061	−0.597646
$574$	−18.3982	−0.767925
$575$	−45.7279	−1.90698
$576$	−80.7966	−3.36652
$577$	37.6125	1.56583	0.782914	−	0.622130i	$-0.213732\pi$
$577$	37.6125	1.56583	0.782914	+	0.622130i	$0.213732\pi$
$578$	44.5837	1.85444
$579$	−0.813908	−0.0338249
$580$	−17.5769	−0.729839
$581$	−7.11195	−0.295054
$582$	24.4632	1.01403
$583$	−1.00899	−0.0417883
$584$	9.83865	0.407126
$585$	10.2546	0.423977
$586$	17.1837	0.709854
$587$	−13.6667	−0.564085	−0.282043	−	0.959402i	$-0.591012\pi$
$587$	−13.6667	−0.564085	−0.282043	+	0.959402i	$0.591012\pi$
$588$	21.2225	0.875200
$589$	−18.4289	−0.759351
$590$	−50.6898	−2.08687
$591$	0.827961	0.0340578
$592$	−48.8078	−2.00599
$593$	27.2102	1.11739	0.558694	−	0.829374i	$-0.311303\pi$
$593$	27.2102	1.11739	0.558694	+	0.829374i	$0.311303\pi$
$594$	14.3734	0.589747
$595$	−3.52077	−0.144337
$596$	−39.0227	−1.59843
$597$	7.18957	0.294249
$598$	31.7720	1.29925
$599$	5.24367	0.214251	0.107125	−	0.994246i	$-0.465835\pi$
$599$	5.24367	0.214251	0.107125	+	0.994246i	$0.465835\pi$
$600$	35.4525	1.44734
$601$	6.07453	0.247785	0.123893	−	0.992296i	$-0.460462\pi$
$601$	6.07453	0.247785	0.123893	+	0.992296i	$0.460462\pi$
$602$	35.6333	1.45231
$603$	30.3394	1.23552
$604$	−100.014	−4.06950
$605$	29.3351	1.19264
$606$	22.5677	0.916752
$607$	38.1995	1.55047	0.775235	−	0.631673i	$-0.217632\pi$
$607$	38.1995	1.55047	0.775235	+	0.631673i	$0.217632\pi$
$608$	98.7706	4.00567
$609$	−0.916396	−0.0371342
$610$	−33.5713	−1.35926
$611$	−0.860576	−0.0348152
$612$	−11.8881	−0.480550
$613$	10.7471	0.434071	0.217036	−	0.976164i	$-0.430361\pi$
$613$	10.7471	0.434071	0.217036	+	0.976164i	$0.430361\pi$
$614$	21.0874	0.851018
$615$	11.9398	0.481459
$616$	16.5014	0.664861
$617$	11.9059	0.479313	0.239657	−	0.970858i	$-0.422965\pi$
$617$	11.9059	0.479313	0.239657	+	0.970858i	$0.422965\pi$
$618$	35.7506	1.43810
$619$	−12.1050	−0.486540	−0.243270	−	0.969959i	$-0.578220\pi$
$619$	−12.1050	−0.486540	−0.243270	+	0.969959i	$0.578220\pi$
$620$	−75.8548	−3.04640
$621$	−35.1113	−1.40897
$622$	−66.1878	−2.65389
$623$	−18.6034	−0.745328
$624$	−14.3731	−0.575385
$625$	−24.3964	−0.975857
$626$	−16.7131	−0.667989
$627$	−4.07754	−0.162841
$628$	−15.4226	−0.615429
$629$	−2.72687	−0.108727
$630$	−27.7703	−1.10639
$631$	−9.92371	−0.395057	−0.197528	−	0.980297i	$-0.563291\pi$
$631$	−9.92371	−0.395057	−0.197528	+	0.980297i	$0.563291\pi$
$632$	53.3791	2.12331
$633$	−5.79424	−0.230300
$634$	−27.0231	−1.07322
$635$	1.64843	0.0654160
$636$	−2.99488	−0.118755
$637$	−6.95128	−0.275420
$638$	3.65762	0.144806
$639$	8.32057	0.329156
$640$	136.335	5.38912
$641$	37.1268	1.46642	0.733210	−	0.680002i	$-0.238021\pi$
$641$	37.1268	1.46642	0.733210	+	0.680002i	$0.238021\pi$
$642$	−32.1693	−1.26962
$643$	−29.2596	−1.15389	−0.576944	−	0.816784i	$-0.695755\pi$
$643$	−29.2596	−1.15389	−0.576944	+	0.816784i	$0.695755\pi$
$644$	−63.1752	−2.48945
$645$	−23.1248	−0.910539
$646$	10.1335	0.398698
$647$	−2.82471	−0.111051	−0.0555255	−	0.998457i	$-0.517683\pi$
$647$	−2.82471	−0.111051	−0.0555255	+	0.998457i	$0.517683\pi$
$648$	−44.9470	−1.76569
$649$	7.74499	0.304017
$650$	−18.1992	−0.713832
$651$	−3.95480	−0.155001
$652$	−105.192	−4.11962
$653$	−36.7840	−1.43947	−0.719735	−	0.694249i	$-0.755737\pi$
$653$	−36.7840	−1.43947	−0.719735	+	0.694249i	$0.755737\pi$
$654$	30.2811	1.18408
$655$	4.43230	0.173184
$656$	81.1493	3.16835
$657$	2.52985	0.0986987
$658$	2.33050	0.0908523
$659$	1.42950	0.0556854	0.0278427	−	0.999612i	$-0.491136\pi$
$659$	1.42950	0.0556854	0.0278427	+	0.999612i	$0.491136\pi$
$660$	−16.7834	−0.653294
$661$	−3.52594	−0.137143	−0.0685715	−	0.997646i	$-0.521844\pi$
$661$	−3.52594	−0.137143	−0.0685715	+	0.997646i	$0.521844\pi$
$662$	−45.5678	−1.77104
$663$	−0.803019	−0.0311867
$664$	53.7598	2.08629
$665$	17.3808	0.673998
$666$	−21.5084	−0.833432
$667$	−8.93483	−0.345958
$668$	−118.149	−4.57132
$669$	−6.81799	−0.263599
$670$	−106.448	−4.11244
$671$	5.12942	0.198019
$672$	21.1959	0.817650
$673$	−0.934011	−0.0360035	−0.0180017	−	0.999838i	$-0.505730\pi$
$673$	−0.934011	−0.0360035	−0.0180017	+	0.999838i	$0.505730\pi$
$674$	25.1006	0.966841
$675$	20.1120	0.774111
$676$	−62.5509	−2.40580
$677$	18.8680	0.725156	0.362578	−	0.931953i	$-0.381897\pi$
$677$	18.8680	0.725156	0.362578	+	0.931953i	$0.381897\pi$
$678$	12.7031	0.487859
$679$	15.9325	0.611435
$680$	26.6138	1.02059
$681$	16.2818	0.623921
$682$	15.7848	0.604433
$683$	−14.7452	−0.564211	−0.282105	−	0.959383i	$-0.591033\pi$
$683$	−14.7452	−0.564211	−0.282105	+	0.959383i	$0.591033\pi$
$684$	58.6876	2.24398
$685$	42.9731	1.64192
$686$	43.3965	1.65689
$687$	17.0361	0.649969
$688$	−157.169	−5.99200
$689$	0.980953	0.0373713
$690$	55.8375	2.12570
$691$	−13.9113	−0.529211	−0.264606	−	0.964357i	$-0.585242\pi$
$691$	−13.9113	−0.529211	−0.264606	+	0.964357i	$0.585242\pi$
$692$	16.8237	0.639543
$693$	4.24307	0.161181
$694$	84.3645	3.20243
$695$	3.18087	0.120657
$696$	6.92711	0.262571
$697$	4.53377	0.171729
$698$	32.4569	1.22851
$699$	1.75206	0.0662689
$700$	36.1872	1.36775
$701$	31.3742	1.18499	0.592493	−	0.805575i	$-0.298144\pi$
$701$	31.3742	1.18499	0.592493	+	0.805575i	$0.298144\pi$
$702$	−13.9739	−0.527412
$703$	13.4616	0.507714
$704$	−43.3134	−1.63243
$705$	−1.51242	−0.0569609
$706$	−85.4660	−3.21655
$707$	14.6980	0.552776
$708$	22.9886	0.863963
$709$	20.1437	0.756511	0.378256	−	0.925701i	$-0.376524\pi$
$709$	20.1437	0.756511	0.378256	+	0.925701i	$0.376524\pi$
$710$	−29.1932	−1.09560
$711$	13.7255	0.514748
$712$	140.624	5.27012
$713$	−38.5592	−1.44405
$714$	2.17463	0.0813835
$715$	5.49730	0.205587
$716$	59.2435	2.21403
$717$	2.13217	0.0796275
$718$	−51.6328	−1.92692
$719$	14.0745	0.524891	0.262445	−	0.964947i	$-0.415471\pi$
$719$	14.0745	0.524891	0.262445	+	0.964947i	$0.415471\pi$
$720$	122.487	4.56482
$721$	23.2839	0.867136
$722$	2.09739	0.0780568
$723$	−14.5638	−0.541634
$724$	−21.5816	−0.802075
$725$	5.11793	0.190075
$726$	−18.1191	−0.672462
$727$	−27.2585	−1.01096	−0.505481	−	0.862838i	$-0.668685\pi$
$727$	−27.2585	−1.01096	−0.505481	+	0.862838i	$0.668685\pi$
$728$	−16.0428	−0.594587
$729$	−3.11433	−0.115346
$730$	−8.87613	−0.328520
$731$	−8.78094	−0.324775
$732$	15.2251	0.562734
$733$	−22.7806	−0.841421	−0.420711	−	0.907195i	$-0.638219\pi$
$733$	−22.7806	−0.841421	−0.420711	+	0.907195i	$0.638219\pi$
$734$	65.0756	2.40198
$735$	−12.2165	−0.450612
$736$	206.660	7.61757
$737$	16.2643	0.599105
$738$	35.7604	1.31636
$739$	−36.6995	−1.35001	−0.675007	−	0.737812i	$-0.735859\pi$
$739$	−36.6995	−1.35001	−0.675007	+	0.737812i	$0.735859\pi$
$740$	55.4089	2.03687
$741$	3.96422	0.145629
$742$	−2.65649	−0.0975228
$743$	−39.6535	−1.45475	−0.727374	−	0.686242i	$-0.759259\pi$
$743$	−39.6535	−1.45475	−0.727374	+	0.686242i	$0.759259\pi$
$744$	29.8947	1.09599
$745$	22.4630	0.822980
$746$	−57.8053	−2.11640
$747$	13.8234	0.505774
$748$	−6.37299	−0.233020
$749$	−20.9514	−0.765546
$750$	−0.737008	−0.0269117
$751$	24.2249	0.883980	0.441990	−	0.897020i	$-0.354273\pi$
$751$	24.2249	0.883980	0.441990	+	0.897020i	$0.354273\pi$
$752$	−10.2792	−0.374844
$753$	−16.5877	−0.604489
$754$	−3.55597	−0.129501
$755$	57.5719	2.09526
$756$	27.7857	1.01055
$757$	35.2751	1.28210	0.641048	−	0.767501i	$-0.278500\pi$
$757$	35.2751	1.28210	0.641048	+	0.767501i	$0.278500\pi$
$758$	−72.0169	−2.61577
$759$	−8.53151	−0.309674
$760$	−131.383	−4.76575
$761$	8.83101	0.320124	0.160062	−	0.987107i	$-0.448831\pi$
$761$	8.83101	0.320124	0.160062	+	0.987107i	$0.448831\pi$
$762$	−1.01817	−0.0368843
$763$	19.7216	0.713971
$764$	110.382	3.99349
$765$	6.84329	0.247420
$766$	−19.3840	−0.700372
$767$	−7.52975	−0.271883
$768$	−37.6769	−1.35955
$769$	−7.91886	−0.285561	−0.142781	−	0.989754i	$-0.545604\pi$
$769$	−7.91886	−0.285561	−0.142781	+	0.989754i	$0.545604\pi$
$770$	−14.8871	−0.536493
$771$	11.9822	0.431528
$772$	6.27990	0.226019
$773$	−15.5290	−0.558538	−0.279269	−	0.960213i	$-0.590092\pi$
$773$	−15.5290	−0.558538	−0.279269	+	0.960213i	$0.590092\pi$
$774$	−69.2602	−2.48951
$775$	22.0870	0.793388
$776$	−120.435	−4.32337
$777$	2.88882	0.103636
$778$	67.8909	2.43401
$779$	−22.3816	−0.801905
$780$	16.3170	0.584243
$781$	4.46049	0.159609
$782$	21.2026	0.758203
$783$	3.92971	0.140436
$784$	−83.0298	−2.96535
$785$	8.87786	0.316864
$786$	−2.73765	−0.0976486
$787$	−3.77016	−0.134392	−0.0671959	−	0.997740i	$-0.521405\pi$
$787$	−3.77016	−0.134392	−0.0671959	+	0.997740i	$0.521405\pi$
$788$	−6.38833	−0.227575
$789$	−10.1834	−0.362538
$790$	−48.1570	−1.71335
$791$	8.27333	0.294166
$792$	−32.0737	−1.13969
$793$	−4.98687	−0.177089
$794$	89.4753	3.17536
$795$	1.72397	0.0611430
$796$	−55.4728	−1.96618
$797$	13.6745	0.484376	0.242188	−	0.970229i	$-0.422135\pi$
$797$	13.6745	0.484376	0.242188	+	0.970229i	$0.422135\pi$
$798$	−10.7354	−0.380029
$799$	−0.574293	−0.0203170
$800$	−118.376	−4.18522
$801$	36.1592	1.27762
$802$	−70.4237	−2.48675
$803$	1.35620	0.0478592
$804$	48.2756	1.70255
$805$	36.3662	1.28174
$806$	−15.3462	−0.540546
$807$	−18.6634	−0.656983
$808$	−111.104	−3.90861
$809$	−20.5405	−0.722166	−0.361083	−	0.932534i	$-0.617593\pi$
$809$	−20.5405	−0.722166	−0.361083	+	0.932534i	$0.617593\pi$
$810$	40.5498	1.42478
$811$	39.5381	1.38837	0.694185	−	0.719797i	$-0.255765\pi$
$811$	39.5381	1.38837	0.694185	+	0.719797i	$0.255765\pi$
$812$	7.07067	0.248132
$813$	0.00950249	0.000333267 0
$814$	−11.5302	−0.404133
$815$	60.5525	2.12106
$816$	−9.59170	−0.335777
$817$	43.3484	1.51657
$818$	−65.4707	−2.28913
$819$	−4.12515	−0.144144
$820$	−92.1244	−3.21712
$821$	−9.04213	−0.315573	−0.157786	−	0.987473i	$-0.550436\pi$
$821$	−9.04213	−0.315573	−0.157786	+	0.987473i	$0.550436\pi$
$822$	−26.5427	−0.925783
$823$	47.7339	1.66390	0.831949	−	0.554852i	$-0.187225\pi$
$823$	47.7339	1.66390	0.831949	+	0.554852i	$0.187225\pi$
$824$	−176.004	−6.13141
$825$	4.88691	0.170140
$826$	20.3911	0.709496
$827$	25.4017	0.883304	0.441652	−	0.897186i	$-0.354393\pi$
$827$	25.4017	0.883304	0.441652	+	0.897186i	$0.354393\pi$
$828$	122.793	4.26736
$829$	−49.1286	−1.70631	−0.853153	−	0.521660i	$-0.825313\pi$
$829$	−49.1286	−1.70631	−0.853153	+	0.521660i	$0.825313\pi$
$830$	−48.5005	−1.68348
$831$	7.74637	0.268719
$832$	42.1097	1.45989
$833$	−4.63884	−0.160726
$834$	−1.96469	−0.0680317
$835$	68.0112	2.35362
$836$	31.4612	1.08811
$837$	16.9591	0.586192
$838$	−101.227	−3.49682
$839$	2.82035	0.0973693	0.0486847	−	0.998814i	$-0.484497\pi$
$839$	2.82035	0.0973693	0.0486847	+	0.998814i	$0.484497\pi$
$840$	−28.1944	−0.972799
$841$	1.00000	0.0344828
$842$	−21.8660	−0.753553
$843$	−4.05719	−0.139737
$844$	44.7068	1.53887
$845$	36.0068	1.23867
$846$	−4.52977	−0.155737
$847$	−11.8007	−0.405476
$848$	11.7170	0.402365
$849$	−12.2447	−0.420235
$850$	−12.1450	−0.416570
$851$	28.1660	0.965517
$852$	13.2395	0.453579
$853$	−0.168409	−0.00576620	−0.00288310	−	0.999996i	$-0.500918\pi$
$853$	−0.168409	−0.00576620	−0.00288310	+	0.999996i	$0.500918\pi$
$854$	13.5048	0.462124
$855$	−33.7829	−1.15535
$856$	158.373	5.41308
$857$	34.1231	1.16562	0.582811	−	0.812608i	$-0.301953\pi$
$857$	34.1231	1.16562	0.582811	+	0.812608i	$0.301953\pi$
$858$	−3.39545	−0.115919
$859$	2.46940	0.0842548	0.0421274	−	0.999112i	$-0.486586\pi$
$859$	2.46940	0.0842548	0.0421274	+	0.999112i	$0.486586\pi$
$860$	178.425	6.08424
$861$	−4.80304	−0.163687
$862$	−48.7553	−1.66061
$863$	−49.5990	−1.68837	−0.844184	−	0.536053i	$-0.819915\pi$
$863$	−49.5990	−1.68837	−0.844184	+	0.536053i	$0.819915\pi$
$864$	−90.8928	−3.09224
$865$	−9.68441	−0.329280
$866$	−73.1649	−2.48624
$867$	11.6391	0.395283
$868$	30.5142	1.03572
$869$	7.35799	0.249603
$870$	−6.24942	−0.211875
$871$	−15.8123	−0.535781
$872$	−149.077	−5.04839
$873$	−30.9679	−1.04811
$874$	−104.670	−3.54051
$875$	−0.480002	−0.0162270
$876$	4.02545	0.136007
$877$	−27.5490	−0.930265	−0.465133	−	0.885241i	$-0.653993\pi$
$877$	−27.5490	−0.930265	−0.465133	+	0.885241i	$0.653993\pi$
$878$	−52.0011	−1.75495
$879$	4.48600	0.151309
$880$	65.6628	2.21349
$881$	−24.6953	−0.832006	−0.416003	−	0.909363i	$-0.636569\pi$
$881$	−24.6953	−0.832006	−0.416003	+	0.909363i	$0.636569\pi$
$882$	−36.5891	−1.23202
$883$	−5.64702	−0.190037	−0.0950186	−	0.995475i	$-0.530291\pi$
$883$	−5.64702	−0.190037	−0.0950186	+	0.995475i	$0.530291\pi$
$884$	6.19588	0.208390
$885$	−13.2331	−0.444827
$886$	27.3595	0.919160
$887$	22.2079	0.745668	0.372834	−	0.927898i	$-0.378386\pi$
$887$	22.2079	0.745668	0.372834	+	0.927898i	$0.378386\pi$
$888$	−21.8369	−0.732797
$889$	−0.663117	−0.0222402
$890$	−126.867	−4.25259
$891$	−6.19568	−0.207563
$892$	52.6058	1.76137
$893$	2.83508	0.0948725
$894$	−13.8744	−0.464031
$895$	−34.1029	−1.13993
$896$	−54.8437	−1.83220
$897$	8.29442	0.276942
$898$	−27.0965	−0.904221
$899$	4.31561	0.143934
$900$	−70.3368	−2.34456
$901$	0.654625	0.0218087
$902$	19.1704	0.638305
$903$	9.30246	0.309566
$904$	−62.5387	−2.08001
$905$	12.4232	0.412963
$906$	−35.5597	−1.18139
$907$	39.0495	1.29662	0.648309	−	0.761378i	$-0.275477\pi$
$907$	39.0495	1.29662	0.648309	+	0.761378i	$0.275477\pi$
$908$	−125.626	−4.16905
$909$	−28.5684	−0.947555
$910$	14.4734	0.479787
$911$	−15.8813	−0.526170	−0.263085	−	0.964773i	$-0.584740\pi$
$911$	−15.8813	−0.526170	−0.263085	+	0.964773i	$0.584740\pi$
$912$	47.3508	1.56794
$913$	7.41047	0.245251
$914$	36.4291	1.20497
$915$	−8.76415	−0.289734
$916$	−131.446	−4.34311
$917$	−1.78299	−0.0588794
$918$	−9.32530	−0.307781
$919$	−44.8854	−1.48063	−0.740317	−	0.672258i	$-0.765325\pi$
$919$	−44.8854	−1.48063	−0.740317	+	0.672258i	$0.765325\pi$
$920$	−274.895	−9.06301
$921$	5.50509	0.181399
$922$	−49.9422	−1.64476
$923$	−4.33652	−0.142738
$924$	6.75150	0.222108
$925$	−16.1337	−0.530471
$926$	−14.1457	−0.464856
$927$	−45.2566	−1.48642
$928$	−23.1297	−0.759268
$929$	−39.9092	−1.30938	−0.654689	−	0.755899i	$-0.727200\pi$
$929$	−39.9092	−1.30938	−0.654689	+	0.755899i	$0.727200\pi$
$930$	−26.9701	−0.884383
$931$	22.9003	0.750527
$932$	−13.5184	−0.442810
$933$	−17.2790	−0.565690
$934$	−14.1120	−0.461759
$935$	3.66855	0.119974
$936$	31.1823	1.01923
$937$	20.7902	0.679186	0.339593	−	0.940573i	$-0.389711\pi$
$937$	20.7902	0.679186	0.339593	+	0.940573i	$0.389711\pi$
$938$	42.8209	1.39815
$939$	−4.36313	−0.142385
$940$	11.6694	0.380614
$941$	−22.5553	−0.735281	−0.367641	−	0.929968i	$-0.619834\pi$
$941$	−22.5553	−0.735281	−0.367641	+	0.929968i	$0.619834\pi$
$942$	−5.48348	−0.178662
$943$	−46.8295	−1.52498
$944$	−89.9394	−2.92728
$945$	−15.9945	−0.520302
$946$	−37.1290	−1.20717
$947$	−24.0925	−0.782902	−0.391451	−	0.920199i	$-0.628027\pi$
$947$	−24.0925	−0.782902	−0.391451	+	0.920199i	$0.628027\pi$
$948$	21.8399	0.709326
$949$	−1.31851	−0.0428006
$950$	59.9555	1.94521
$951$	−7.05467	−0.228763
$952$	−10.7060	−0.346982
$953$	−52.2318	−1.69196	−0.845978	−	0.533219i	$-0.820982\pi$
$953$	−52.2318	−1.69196	−0.845978	+	0.533219i	$0.820982\pi$
$954$	5.16340	0.167171
$955$	−63.5404	−2.05612
$956$	−16.4513	−0.532073
$957$	0.954860	0.0308662
$958$	−92.0616	−2.97438
$959$	−17.2869	−0.558222
$960$	74.0055	2.38852
$961$	−12.3755	−0.399211
$962$	11.2098	0.361417
$963$	40.7230	1.31228
$964$	112.370	3.61921
$965$	−3.61496	−0.116370
$966$	−22.4619	−0.722698
$967$	−6.33624	−0.203760	−0.101880	−	0.994797i	$-0.532486\pi$
$967$	−6.33624	−0.203760	−0.101880	+	0.994797i	$0.532486\pi$
$968$	89.2023	2.86707
$969$	2.64547	0.0849846
$970$	108.653	3.48864
$971$	16.0551	0.515233	0.257616	−	0.966247i	$-0.417063\pi$
$971$	16.0551	0.515233	0.257616	+	0.966247i	$0.417063\pi$
$972$	−83.5343	−2.67936
$973$	−1.27957	−0.0410212
$974$	13.0076	0.416789
$975$	−4.75110	−0.152157
$976$	−59.5659	−1.90666
$977$	−24.1771	−0.773496	−0.386748	−	0.922186i	$-0.626402\pi$
$977$	−24.1771	−0.773496	−0.386748	+	0.922186i	$0.626402\pi$
$978$	−37.4008	−1.19594
$979$	19.3842	0.619522
$980$	94.2592	3.01100
$981$	−38.3328	−1.22387
$982$	15.2567	0.486861
$983$	4.96743	0.158436	0.0792182	−	0.996857i	$-0.474758\pi$
$983$	4.96743	0.158436	0.0792182	+	0.996857i	$0.474758\pi$
$984$	36.3066	1.15741
$985$	3.67738	0.117171
$986$	−2.37303	−0.0755725
$987$	0.608402	0.0193656
$988$	−30.5869	−0.973098
$989$	90.6987	2.88405
$990$	28.9359	0.919643
$991$	35.3510	1.12296	0.561481	−	0.827489i	$-0.310232\pi$
$991$	35.3510	1.12296	0.561481	+	0.827489i	$0.310232\pi$
$992$	−99.8185	−3.16924
$993$	−11.8960	−0.377507
$994$	11.7436	0.372485
$995$	31.9323	1.01232
$996$	21.9956	0.696959
$997$	−32.6292	−1.03338	−0.516689	−	0.856173i	$-0.672836\pi$
$997$	−32.6292	−1.03338	−0.516689	+	0.856173i	$0.672836\pi$
$998$	−87.0105	−2.75427
$999$	−12.3879	−0.391937

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4031.2.a.d.1.4	✓	98

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4031.2.a.d.1.4	✓	98	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)

\(f(q)\)	\(=\)	\(q-2.74332 q^{2} -0.716173 q^{3} +5.52580 q^{4} -3.18087 q^{5} +1.96469 q^{6} +1.27957 q^{7} -9.67240 q^{8} -2.48710 q^{9} +O(q^{10})\)	\(q-2.74332 q^{2} -0.716173 q^{3} +5.52580 q^{4} -3.18087 q^{5} +1.96469 q^{6} +1.27957 q^{7} -9.67240 q^{8} -2.48710 q^{9} +8.72614 q^{10} -1.33328 q^{11} -3.95743 q^{12} +1.29623 q^{13} -3.51028 q^{14} +2.27805 q^{15} +15.4829 q^{16} +0.865020 q^{17} +6.82290 q^{18} -4.27030 q^{19} -17.5769 q^{20} -0.916396 q^{21} +3.65762 q^{22} -8.93483 q^{23} +6.92711 q^{24} +5.11793 q^{25} -3.55597 q^{26} +3.92971 q^{27} +7.07067 q^{28} +1.00000 q^{29} -6.24942 q^{30} +4.31561 q^{31} -23.1297 q^{32} +0.954860 q^{33} -2.37303 q^{34} -4.07016 q^{35} -13.7432 q^{36} -3.15238 q^{37} +11.7148 q^{38} -0.928324 q^{39} +30.7666 q^{40} +5.24123 q^{41} +2.51397 q^{42} -10.1511 q^{43} -7.36745 q^{44} +7.91113 q^{45} +24.5111 q^{46} -0.663907 q^{47} -11.0884 q^{48} -5.36269 q^{49} -14.0401 q^{50} -0.619504 q^{51} +7.16270 q^{52} +0.756775 q^{53} -10.7804 q^{54} +4.24100 q^{55} -12.3765 q^{56} +3.05827 q^{57} -2.74332 q^{58} -5.80896 q^{59} +12.5881 q^{60} -3.84721 q^{61} -11.8391 q^{62} -3.18242 q^{63} +32.4863 q^{64} -4.12313 q^{65} -2.61949 q^{66} -12.1987 q^{67} +4.77993 q^{68} +6.39888 q^{69} +11.1657 q^{70} -3.34549 q^{71} +24.0562 q^{72} -1.01719 q^{73} +8.64798 q^{74} -3.66532 q^{75} -23.5968 q^{76} -1.70603 q^{77} +2.54669 q^{78} -5.51870 q^{79} -49.2490 q^{80} +4.64694 q^{81} -14.3784 q^{82} -5.55807 q^{83} -5.06382 q^{84} -2.75152 q^{85} +27.8478 q^{86} -0.716173 q^{87} +12.8960 q^{88} -14.5387 q^{89} -21.7028 q^{90} +1.65862 q^{91} -49.3721 q^{92} -3.09072 q^{93} +1.82131 q^{94} +13.5833 q^{95} +16.5648 q^{96} +12.4514 q^{97} +14.7116 q^{98} +3.31600 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 98 q + 6 q^{2} + 6 q^{3} + 116 q^{4} + q^{5} + 7 q^{6} + 12 q^{7} + 15 q^{8} + 136 q^{9}+O(q^{10}) \) 98 * q + 6 * q^2 + 6 * q^3 + 116 * q^4 + q^5 + 7 * q^6 + 12 * q^7 + 15 * q^8 + 136 * q^9	\( 98 q + 6 q^{2} + 6 q^{3} + 116 q^{4} + q^{5} + 7 q^{6} + 12 q^{7} + 15 q^{8} + 136 q^{9} + 16 q^{10} + 25 q^{11} + 8 q^{12} + 18 q^{13} + 34 q^{14} + 14 q^{15} + 136 q^{16} + 35 q^{17} + 20 q^{18} + 48 q^{19} - 20 q^{20} + 62 q^{21} + 32 q^{22} + q^{23} + 8 q^{24} + 173 q^{25} + 15 q^{26} + 18 q^{27} + 37 q^{28} + 98 q^{29} - 6 q^{30} + 20 q^{31} + 16 q^{32} + 24 q^{33} - 6 q^{34} + 11 q^{35} + 155 q^{36} + 62 q^{37} - 5 q^{38} + 45 q^{39} + 38 q^{40} + 50 q^{41} + 7 q^{42} + 72 q^{43} + 92 q^{44} - 13 q^{45} + 32 q^{46} - 16 q^{47} - 13 q^{48} + 194 q^{49} + 50 q^{50} + 2 q^{51} + 83 q^{52} - 11 q^{53} + 58 q^{54} + 32 q^{55} + 106 q^{56} + 84 q^{57} + 6 q^{58} + 20 q^{59} + 62 q^{60} + 142 q^{61} - 27 q^{62} + 26 q^{63} + 213 q^{64} + 13 q^{65} - 35 q^{66} + 5 q^{67} + 69 q^{68} + 68 q^{69} - 2 q^{70} - 10 q^{71} - 9 q^{72} + 74 q^{73} + 21 q^{74} + 19 q^{75} + 116 q^{76} + 41 q^{77} - 162 q^{78} + 104 q^{79} - 86 q^{80} + 230 q^{81} + 53 q^{82} - 19 q^{83} + 76 q^{84} + 125 q^{85} + 9 q^{86} + 6 q^{87} + 68 q^{88} + 120 q^{89} + 122 q^{90} + 30 q^{91} + 3 q^{92} - 56 q^{93} + 22 q^{94} + 32 q^{95} - 55 q^{96} + 98 q^{97} - 15 q^{98} + 69 q^{99}+O(q^{100}) \) 98 * q + 6 * q^2 + 6 * q^3 + 116 * q^4 + q^5 + 7 * q^6 + 12 * q^7 + 15 * q^8 + 136 * q^9 + 16 * q^10 + 25 * q^11 + 8 * q^12 + 18 * q^13 + 34 * q^14 + 14 * q^15 + 136 * q^16 + 35 * q^17 + 20 * q^18 + 48 * q^19 - 20 * q^20 + 62 * q^21 + 32 * q^22 + q^23 + 8 * q^24 + 173 * q^25 + 15 * q^26 + 18 * q^27 + 37 * q^28 + 98 * q^29 - 6 * q^30 + 20 * q^31 + 16 * q^32 + 24 * q^33 - 6 * q^34 + 11 * q^35 + 155 * q^36 + 62 * q^37 - 5 * q^38 + 45 * q^39 + 38 * q^40 + 50 * q^41 + 7 * q^42 + 72 * q^43 + 92 * q^44 - 13 * q^45 + 32 * q^46 - 16 * q^47 - 13 * q^48 + 194 * q^49 + 50 * q^50 + 2 * q^51 + 83 * q^52 - 11 * q^53 + 58 * q^54 + 32 * q^55 + 106 * q^56 + 84 * q^57 + 6 * q^58 + 20 * q^59 + 62 * q^60 + 142 * q^61 - 27 * q^62 + 26 * q^63 + 213 * q^64 + 13 * q^65 - 35 * q^66 + 5 * q^67 + 69 * q^68 + 68 * q^69 - 2 * q^70 - 10 * q^71 - 9 * q^72 + 74 * q^73 + 21 * q^74 + 19 * q^75 + 116 * q^76 + 41 * q^77 - 162 * q^78 + 104 * q^79 - 86 * q^80 + 230 * q^81 + 53 * q^82 - 19 * q^83 + 76 * q^84 + 125 * q^85 + 9 * q^86 + 6 * q^87 + 68 * q^88 + 120 * q^89 + 122 * q^90 + 30 * q^91 + 3 * q^92 - 56 * q^93 + 22 * q^94 + 32 * q^95 - 55 * q^96 + 98 * q^97 - 15 * q^98 + 69 * q^99

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