LMFDB - Embedded newform 4031.2.a.d.1.10

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			1.10
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)

$f(q)$	$=$	$q-2.44621 q^{2} +0.244458 q^{3} +3.98396 q^{4} -3.48270 q^{5} -0.597997 q^{6} +1.44143 q^{7} -4.85320 q^{8} -2.94024 q^{9} +O(q^{10})$	\(q-2.44621 q^{2} +0.244458 q^{3} +3.98396 q^{4} -3.48270 q^{5} -0.597997 q^{6} +1.44143 q^{7} -4.85320 q^{8} -2.94024 q^{9} +8.51943 q^{10} -1.26461 q^{11} +0.973912 q^{12} +5.55217 q^{13} -3.52604 q^{14} -0.851374 q^{15} +3.90404 q^{16} +2.09611 q^{17} +7.19246 q^{18} +7.90030 q^{19} -13.8750 q^{20} +0.352368 q^{21} +3.09350 q^{22} +5.58541 q^{23} -1.18640 q^{24} +7.12920 q^{25} -13.5818 q^{26} -1.45214 q^{27} +5.74259 q^{28} +1.00000 q^{29} +2.08264 q^{30} +2.97662 q^{31} +0.156287 q^{32} -0.309143 q^{33} -5.12753 q^{34} -5.02005 q^{35} -11.7138 q^{36} -4.68336 q^{37} -19.3258 q^{38} +1.35727 q^{39} +16.9022 q^{40} +3.19259 q^{41} -0.861968 q^{42} +5.78276 q^{43} -5.03815 q^{44} +10.2400 q^{45} -13.6631 q^{46} -8.41340 q^{47} +0.954373 q^{48} -4.92229 q^{49} -17.4396 q^{50} +0.512411 q^{51} +22.1196 q^{52} -11.4301 q^{53} +3.55224 q^{54} +4.40425 q^{55} -6.99553 q^{56} +1.93129 q^{57} -2.44621 q^{58} +3.72968 q^{59} -3.39184 q^{60} -12.4360 q^{61} -7.28145 q^{62} -4.23814 q^{63} -8.19039 q^{64} -19.3365 q^{65} +0.756231 q^{66} +16.0008 q^{67} +8.35082 q^{68} +1.36540 q^{69} +12.2801 q^{70} -10.8519 q^{71} +14.2696 q^{72} +2.87718 q^{73} +11.4565 q^{74} +1.74279 q^{75} +31.4745 q^{76} -1.82284 q^{77} -3.32018 q^{78} -13.9457 q^{79} -13.5966 q^{80} +8.46573 q^{81} -7.80976 q^{82} -1.98994 q^{83} +1.40382 q^{84} -7.30012 q^{85} -14.1459 q^{86} +0.244458 q^{87} +6.13739 q^{88} +10.1404 q^{89} -25.0492 q^{90} +8.00304 q^{91} +22.2521 q^{92} +0.727658 q^{93} +20.5810 q^{94} -27.5144 q^{95} +0.0382055 q^{96} -7.41083 q^{97} +12.0410 q^{98} +3.71825 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.44621	−1.72973	−0.864867	−	0.502001i	$-0.832598\pi$
$2$	−2.44621	−1.72973	−0.864867	+	0.502001i	$0.832598\pi$
$3$	0.244458	0.141138	0.0705689	−	0.997507i	$-0.477519\pi$
$3$	0.244458	0.141138	0.0705689	+	0.997507i	$0.477519\pi$
$4$	3.98396	1.99198
$5$	−3.48270	−1.55751	−0.778756	−	0.627328i	$-0.784149\pi$
$5$	−3.48270	−1.55751	−0.778756	+	0.627328i	$0.784149\pi$
$6$	−0.597997	−0.244131
$7$	1.44143	0.544808	0.272404	−	0.962183i	$-0.412181\pi$
$7$	1.44143	0.544808	0.272404	+	0.962183i	$0.412181\pi$
$8$	−4.85320	−1.71587
$9$	−2.94024	−0.980080
$10$	8.51943	2.69408
$11$	−1.26461	−0.381293	−0.190647	−	0.981659i	$-0.561058\pi$
$11$	−1.26461	−0.381293	−0.190647	+	0.981659i	$0.561058\pi$
$12$	0.973912	0.281144
$13$	5.55217	1.53989	0.769947	−	0.638107i	$-0.220282\pi$
$13$	5.55217	1.53989	0.769947	+	0.638107i	$0.220282\pi$
$14$	−3.52604	−0.942373
$15$	−0.851374	−0.219824
$16$	3.90404	0.976009
$17$	2.09611	0.508381	0.254191	−	0.967154i	$-0.418191\pi$
$17$	2.09611	0.508381	0.254191	+	0.967154i	$0.418191\pi$
$18$	7.19246	1.69528
$19$	7.90030	1.81245	0.906227	−	0.422792i	$-0.138950\pi$
$19$	7.90030	1.81245	0.906227	+	0.422792i	$0.138950\pi$
$20$	−13.8750	−3.10253
$21$	0.352368	0.0768930
$22$	3.09350	0.659536
$23$	5.58541	1.16464	0.582319	−	0.812960i	$-0.302145\pi$
$23$	5.58541	1.16464	0.582319	+	0.812960i	$0.302145\pi$
$24$	−1.18640	−0.242174
$25$	7.12920	1.42584
$26$	−13.5818	−2.66361
$27$	−1.45214	−0.279464
$28$	5.74259	1.08525
$29$	1.00000	0.185695
$29$	1.00000	0.185695
$30$	2.08264	0.380237
$31$	2.97662	0.534616	0.267308	−	0.963611i	$-0.413866\pi$
$31$	2.97662	0.534616	0.267308	+	0.963611i	$0.413866\pi$
$32$	0.156287	0.0276278
$33$	−0.309143	−0.0538149
$34$	−5.12753	−0.879365
$35$	−5.02005	−0.848544
$36$	−11.7138	−1.95230
$37$	−4.68336	−0.769940	−0.384970	−	0.922929i	$-0.625788\pi$
$37$	−4.68336	−0.769940	−0.384970	+	0.922929i	$0.625788\pi$
$38$	−19.3258	−3.13506
$39$	1.35727	0.217337
$40$	16.9022	2.67248
$41$	3.19259	0.498599	0.249299	−	0.968426i	$-0.419800\pi$
$41$	3.19259	0.498599	0.249299	+	0.968426i	$0.419800\pi$
$42$	−0.861968	−0.133005
$43$	5.78276	0.881863	0.440932	−	0.897541i	$-0.354648\pi$
$43$	5.78276	0.881863	0.440932	+	0.897541i	$0.354648\pi$
$44$	−5.03815	−0.759529
$45$	10.2400	1.52649
$46$	−13.6631	−2.01452
$47$	−8.41340	−1.22722	−0.613610	−	0.789609i	$-0.710283\pi$
$47$	−8.41340	−1.22722	−0.613610	+	0.789609i	$0.710283\pi$
$48$	0.954373	0.137752
$49$	−4.92229	−0.703184
$50$	−17.4396	−2.46633
$51$	0.512411	0.0717518
$52$	22.1196	3.06744
$53$	−11.4301	−1.57004	−0.785021	−	0.619469i	$-0.787348\pi$
$53$	−11.4301	−1.57004	−0.785021	+	0.619469i	$0.787348\pi$
$54$	3.55224	0.483399
$55$	4.40425	0.593869
$56$	−6.99553	−0.934817
$57$	1.93129	0.255806
$58$	−2.44621	−0.321204
$59$	3.72968	0.485563	0.242782	−	0.970081i	$-0.421940\pi$
$59$	3.72968	0.485563	0.242782	+	0.970081i	$0.421940\pi$
$60$	−3.39184	−0.437885
$61$	−12.4360	−1.59226	−0.796131	−	0.605124i	$-0.793124\pi$
$61$	−12.4360	−1.59226	−0.796131	+	0.605124i	$0.793124\pi$
$62$	−7.28145	−0.924745
$63$	−4.23814	−0.533955
$64$	−8.19039	−1.02380
$65$	−19.3365	−2.39840
$66$	0.756231	0.0930856
$67$	16.0008	1.95480	0.977402	−	0.211389i	$-0.0677987\pi$
$67$	16.0008	1.95480	0.977402	+	0.211389i	$0.0677987\pi$
$68$	8.35082	1.01269
$69$	1.36540	0.164375
$70$	12.2801	1.46776
$71$	−10.8519	−1.28788	−0.643941	−	0.765075i	$-0.722702\pi$
$71$	−10.8519	−1.28788	−0.643941	+	0.765075i	$0.722702\pi$
$72$	14.2696	1.68169
$73$	2.87718	0.336749	0.168374	−	0.985723i	$-0.446148\pi$
$73$	2.87718	0.336749	0.168374	+	0.985723i	$0.446148\pi$
$74$	11.4565	1.33179
$75$	1.74279	0.201240
$76$	31.4745	3.61037
$77$	−1.82284	−0.207732
$78$	−3.32018	−0.375936
$79$	−13.9457	−1.56901	−0.784505	−	0.620122i	$-0.787083\pi$
$79$	−13.9457	−1.56901	−0.784505	+	0.620122i	$0.787083\pi$
$80$	−13.5966	−1.52015
$81$	8.46573	0.940637
$82$	−7.80976	−0.862443
$83$	−1.98994	−0.218424	−0.109212	−	0.994018i	$-0.534833\pi$
$83$	−1.98994	−0.218424	−0.109212	+	0.994018i	$0.534833\pi$
$84$	1.40382	0.153169
$85$	−7.30012	−0.791809
$86$	−14.1459	−1.52539
$87$	0.244458	0.0262086
$88$	6.13739	0.654248
$89$	10.1404	1.07488	0.537438	−	0.843303i	$-0.319392\pi$
$89$	10.1404	1.07488	0.537438	+	0.843303i	$0.319392\pi$
$90$	−25.0492	−2.64041
$91$	8.00304	0.838947
$92$	22.2521	2.31994
$93$	0.727658	0.0754546
$94$	20.5810	2.12277
$95$	−27.5144	−2.82292
$96$	0.0382055	0.00389934
$97$	−7.41083	−0.752456	−0.376228	−	0.926527i	$-0.622779\pi$
$97$	−7.41083	−0.752456	−0.376228	+	0.926527i	$0.622779\pi$
$98$	12.0410	1.21632
$99$	3.71825	0.373698
$100$	28.4025	2.84025
$101$	6.92430	0.688994	0.344497	−	0.938788i	$-0.388050\pi$
$101$	6.92430	0.688994	0.344497	+	0.938788i	$0.388050\pi$
$102$	−1.25347	−0.124112
$103$	8.11446	0.799541	0.399771	−	0.916615i	$-0.369090\pi$
$103$	8.11446	0.799541	0.399771	+	0.916615i	$0.369090\pi$
$104$	−26.9458	−2.64225
$105$	−1.22719	−0.119762
$106$	27.9604	2.71576
$107$	19.6389	1.89857	0.949284	−	0.314421i	$-0.101810\pi$
$107$	19.6389	1.89857	0.949284	+	0.314421i	$0.101810\pi$
$108$	−5.78527	−0.556688
$109$	−18.4344	−1.76570	−0.882848	−	0.469659i	$-0.844377\pi$
$109$	−18.4344	−1.76570	−0.882848	+	0.469659i	$0.844377\pi$
$110$	−10.7737	−1.02724
$111$	−1.14489	−0.108668
$112$	5.62738	0.531737
$113$	−5.26412	−0.495207	−0.247604	−	0.968861i	$-0.579643\pi$
$113$	−5.26412	−0.495207	−0.247604	+	0.968861i	$0.579643\pi$
$114$	−4.72435	−0.442476
$115$	−19.4523	−1.81394
$116$	3.98396	0.369902
$117$	−16.3247	−1.50922
$118$	−9.12360	−0.839895
$119$	3.02139	0.276970
$120$	4.13189	0.377188
$121$	−9.40077	−0.854615
$122$	30.4210	2.75419
$123$	0.780454	0.0703711
$124$	11.8587	1.06495
$125$	−7.41538	−0.663252
$126$	10.3674	0.923601
$127$	12.9976	1.15335	0.576673	−	0.816975i	$-0.304351\pi$
$127$	12.9976	1.15335	0.576673	+	0.816975i	$0.304351\pi$
$128$	19.7229	1.74327
$129$	1.41364	0.124464
$130$	47.3013	4.14860
$131$	−6.00815	−0.524934	−0.262467	−	0.964941i	$-0.584536\pi$
$131$	−6.00815	−0.524934	−0.262467	+	0.964941i	$0.584536\pi$
$132$	−1.23162	−0.107198
$133$	11.3877	0.987439
$134$	−39.1413	−3.38129
$135$	5.05737	0.435269
$136$	−10.1728	−0.872313
$137$	14.5787	1.24554	0.622772	−	0.782403i	$-0.286006\pi$
$137$	14.5787	1.24554	0.622772	+	0.782403i	$0.286006\pi$
$138$	−3.34006	−0.284324
$139$	−1.00000	−0.0848189
$139$	−1.00000	−0.0848189
$140$	−19.9997	−1.69028
$141$	−2.05672	−0.173207
$142$	26.5460	2.22769
$143$	−7.02131	−0.587152
$144$	−11.4788	−0.956567
$145$	−3.48270	−0.289223
$146$	−7.03820	−0.582486
$147$	−1.20329	−0.0992460
$148$	−18.6583	−1.53371
$149$	22.1374	1.81356	0.906782	−	0.421600i	$-0.138531\pi$
$149$	22.1374	1.81356	0.906782	+	0.421600i	$0.138531\pi$
$150$	−4.26324	−0.348092
$151$	9.03490	0.735250	0.367625	−	0.929974i	$-0.380171\pi$
$151$	9.03490	0.735250	0.367625	+	0.929974i	$0.380171\pi$
$152$	−38.3417	−3.10993
$153$	−6.16307	−0.498254
$154$	4.45905	0.359321
$155$	−10.3667	−0.832671
$156$	5.40732	0.432932
$157$	3.29056	0.262615	0.131307	−	0.991342i	$-0.458082\pi$
$157$	3.29056	0.262615	0.131307	+	0.991342i	$0.458082\pi$
$158$	34.1141	2.71397
$159$	−2.79418	−0.221593
$160$	−0.544300	−0.0430307
$161$	8.05095	0.634504
$162$	−20.7090	−1.62705
$163$	−4.68419	−0.366894	−0.183447	−	0.983030i	$-0.558726\pi$
$163$	−4.68419	−0.366894	−0.183447	+	0.983030i	$0.558726\pi$
$164$	12.7192	0.993199
$165$	1.07665	0.0838174
$166$	4.86782	0.377816
$167$	17.0384	1.31847	0.659236	−	0.751936i	$-0.270880\pi$
$167$	17.0384	1.31847	0.659236	+	0.751936i	$0.270880\pi$
$168$	−1.71011	−0.131938
$169$	17.8266	1.37128
$170$	17.8577	1.36962
$171$	−23.2288	−1.77635
$172$	23.0383	1.75666
$173$	−0.0494551	−0.00376000	−0.00188000	−	0.999998i	$-0.500598\pi$
$173$	−0.0494551	−0.00376000	−0.00188000	+	0.999998i	$0.500598\pi$
$174$	−0.597997	−0.0453340
$175$	10.2762	0.776809
$176$	−4.93707	−0.372146
$177$	0.911750	0.0685313
$178$	−24.8055	−1.85925
$179$	4.38395	0.327672	0.163836	−	0.986488i	$-0.447613\pi$
$179$	4.38395	0.327672	0.163836	+	0.986488i	$0.447613\pi$
$180$	40.7957	3.04073
$181$	19.7270	1.46629	0.733147	−	0.680070i	$-0.238051\pi$
$181$	19.7270	1.46629	0.733147	+	0.680070i	$0.238051\pi$
$182$	−19.5772	−1.45116
$183$	−3.04007	−0.224729
$184$	−27.1071	−1.99836
$185$	16.3108	1.19919
$186$	−1.78001	−0.130516
$187$	−2.65075	−0.193842
$188$	−33.5187	−2.44460
$189$	−2.09315	−0.152254
$190$	67.3061	4.88290
$191$	−1.83840	−0.133022	−0.0665108	−	0.997786i	$-0.521187\pi$
$191$	−1.83840	−0.133022	−0.0665108	+	0.997786i	$0.521187\pi$
$192$	−2.00221	−0.144497
$193$	−12.0468	−0.867148	−0.433574	−	0.901118i	$-0.642748\pi$
$193$	−12.0468	−0.867148	−0.433574	+	0.901118i	$0.642748\pi$
$194$	18.1285	1.30155
$195$	−4.72697	−0.338506
$196$	−19.6102	−1.40073
$197$	−16.6686	−1.18759	−0.593795	−	0.804616i	$-0.702371\pi$
$197$	−16.6686	−1.18759	−0.593795	+	0.804616i	$0.702371\pi$
$198$	−9.09563	−0.646398
$199$	−6.04251	−0.428342	−0.214171	−	0.976796i	$-0.568705\pi$
$199$	−6.04251	−0.428342	−0.214171	+	0.976796i	$0.568705\pi$
$200$	−34.5994	−2.44655
$201$	3.91151	0.275897
$202$	−16.9383	−1.19178
$203$	1.44143	0.101168
$204$	2.04143	0.142928
$205$	−11.1188	−0.776573
$206$	−19.8497	−1.38299
$207$	−16.4224	−1.14144
$208$	21.6759	1.50295
$209$	−9.99078	−0.691077
$210$	3.00198	0.207156
$211$	24.0161	1.65334	0.826669	−	0.562689i	$-0.190233\pi$
$211$	24.0161	1.65334	0.826669	+	0.562689i	$0.190233\pi$
$212$	−45.5370	−3.12750
$213$	−2.65283	−0.181769
$214$	−48.0410	−3.28402
$215$	−20.1396	−1.37351
$216$	7.04752	0.479523
$217$	4.29057	0.291263
$218$	45.0945	3.05418
$219$	0.703350	0.0475280
$220$	17.5464	1.18298
$221$	11.6380	0.782854
$222$	2.80064	0.187966
$223$	−6.62950	−0.443944	−0.221972	−	0.975053i	$-0.571249\pi$
$223$	−6.62950	−0.443944	−0.221972	+	0.975053i	$0.571249\pi$
$224$	0.225276	0.0150519
$225$	−20.9616	−1.39744
$226$	12.8772	0.856577
$227$	−13.5260	−0.897750	−0.448875	−	0.893595i	$-0.648175\pi$
$227$	−13.5260	−0.897750	−0.448875	+	0.893595i	$0.648175\pi$
$228$	7.69420	0.509561
$229$	7.61349	0.503113	0.251557	−	0.967843i	$-0.419058\pi$
$229$	7.61349	0.503113	0.251557	+	0.967843i	$0.419058\pi$
$230$	47.5845	3.13763
$231$	−0.445607	−0.0293188
$232$	−4.85320	−0.318628
$233$	−25.4727	−1.66877	−0.834385	−	0.551182i	$-0.814177\pi$
$233$	−25.4727	−1.66877	−0.834385	+	0.551182i	$0.814177\pi$
$234$	39.9337	2.61055
$235$	29.3014	1.91141
$236$	14.8589	0.967233
$237$	−3.40913	−0.221447
$238$	−7.39096	−0.479085
$239$	1.73366	0.112141	0.0560707	−	0.998427i	$-0.482143\pi$
$239$	1.73366	0.112141	0.0560707	+	0.998427i	$0.482143\pi$
$240$	−3.32380	−0.214550
$241$	18.9083	1.21799	0.608996	−	0.793173i	$-0.291573\pi$
$241$	18.9083	1.21799	0.608996	+	0.793173i	$0.291573\pi$
$242$	22.9963	1.47826
$243$	6.42593	0.412224
$244$	−49.5444	−3.17176
$245$	17.1429	1.09522
$246$	−1.90916	−0.121723
$247$	43.8638	2.79099
$248$	−14.4461	−0.917330
$249$	−0.486457	−0.0308279
$250$	18.1396	1.14725
$251$	2.94933	0.186160	0.0930799	−	0.995659i	$-0.470329\pi$
$251$	2.94933	0.186160	0.0930799	+	0.995659i	$0.470329\pi$
$252$	−16.8846	−1.06363
$253$	−7.06335	−0.444069
$254$	−31.7948	−1.99498
$255$	−1.78457	−0.111754
$256$	−31.8656	−1.99160
$257$	16.4862	1.02838	0.514190	−	0.857676i	$-0.328093\pi$
$257$	16.4862	1.02838	0.514190	+	0.857676i	$0.328093\pi$
$258$	−3.45807	−0.215290
$259$	−6.75072	−0.419469
$260$	−77.0361	−4.77758
$261$	−2.94024	−0.181996
$262$	14.6972	0.907997
$263$	7.68912	0.474132	0.237066	−	0.971494i	$-0.423814\pi$
$263$	7.68912	0.474132	0.237066	+	0.971494i	$0.423814\pi$
$264$	1.50033	0.0923392
$265$	39.8076	2.44536
$266$	−27.8568	−1.70801
$267$	2.47889	0.151706
$268$	63.7464	3.89393
$269$	16.5227	1.00740	0.503702	−	0.863877i	$-0.331971\pi$
$269$	16.5227	1.00740	0.503702	+	0.863877i	$0.331971\pi$
$270$	−12.3714	−0.752899
$271$	11.0450	0.670938	0.335469	−	0.942051i	$-0.391105\pi$
$271$	11.0450	0.670938	0.335469	+	0.942051i	$0.391105\pi$
$272$	8.18329	0.496185
$273$	1.95641	0.118407
$274$	−35.6627	−2.15446
$275$	−9.01564	−0.543664
$276$	5.43970	0.327431
$277$	−29.0381	−1.74473	−0.872366	−	0.488853i	$-0.837415\pi$
$277$	−29.0381	−1.74473	−0.872366	+	0.488853i	$0.837415\pi$
$278$	2.44621	0.146714
$279$	−8.75197	−0.523967
$280$	24.3633	1.45599
$281$	−26.4023	−1.57503	−0.787514	−	0.616297i	$-0.788632\pi$
$281$	−26.4023	−1.57503	−0.787514	+	0.616297i	$0.788632\pi$
$282$	5.03119	0.299603
$283$	−3.45536	−0.205400	−0.102700	−	0.994712i	$-0.532748\pi$
$283$	−3.45536	−0.205400	−0.102700	+	0.994712i	$0.532748\pi$
$284$	−43.2335	−2.56544
$285$	−6.72611	−0.398420
$286$	17.1756	1.01562
$287$	4.60188	0.271640
$288$	−0.459520	−0.0270775
$289$	−12.6063	−0.741549
$290$	8.51943	0.500278
$291$	−1.81164	−0.106200
$292$	11.4626	0.670797
$293$	−11.9346	−0.697230	−0.348615	−	0.937266i	$-0.613348\pi$
$293$	−11.9346	−0.697230	−0.348615	+	0.937266i	$0.613348\pi$
$294$	2.94351	0.171669
$295$	−12.9894	−0.756270
$296$	22.7293	1.32111
$297$	1.83639	0.106558
$298$	−54.1527	−3.13698
$299$	31.0111	1.79342
$300$	6.94321	0.400867
$301$	8.33542	0.480446
$302$	−22.1013	−1.27179
$303$	1.69270	0.0972431
$304$	30.8431	1.76897
$305$	43.3108	2.47997
$306$	15.0762	0.861848
$307$	1.60380	0.0915337	0.0457668	−	0.998952i	$-0.485427\pi$
$307$	1.60380	0.0915337	0.0457668	+	0.998952i	$0.485427\pi$
$308$	−7.26212	−0.413798
$309$	1.98364	0.112846
$310$	25.3591	1.44030
$311$	15.8214	0.897151	0.448575	−	0.893745i	$-0.351932\pi$
$311$	15.8214	0.897151	0.448575	+	0.893745i	$0.351932\pi$
$312$	−6.58711	−0.372922
$313$	18.4055	1.04034	0.520171	−	0.854062i	$-0.325868\pi$
$313$	18.4055	1.04034	0.520171	+	0.854062i	$0.325868\pi$
$314$	−8.04941	−0.454254
$315$	14.7602	0.831641
$316$	−55.5590	−3.12544
$317$	−5.43118	−0.305046	−0.152523	−	0.988300i	$-0.548740\pi$
$317$	−5.43118	−0.305046	−0.152523	+	0.988300i	$0.548740\pi$
$318$	6.83515	0.383296
$319$	−1.26461	−0.0708044
$320$	28.5247	1.59458
$321$	4.80089	0.267960
$322$	−19.6944	−1.09752
$323$	16.5599	0.921417
$324$	33.7272	1.87373
$325$	39.5826	2.19564
$326$	11.4585	0.634629
$327$	−4.50644	−0.249207
$328$	−15.4943	−0.855528
$329$	−12.1273	−0.668599
$330$	−2.63373	−0.144982
$331$	4.78449	0.262979	0.131490	−	0.991318i	$-0.458024\pi$
$331$	4.78449	0.262979	0.131490	+	0.991318i	$0.458024\pi$
$332$	−7.92785	−0.435097
$333$	13.7702	0.754603
$334$	−41.6796	−2.28061
$335$	−55.7259	−3.04463
$336$	1.37566	0.0750483
$337$	−33.6012	−1.83037	−0.915186	−	0.403032i	$-0.867956\pi$
$337$	−33.6012	−1.83037	−0.915186	+	0.403032i	$0.867956\pi$
$338$	−43.6077	−2.37194
$339$	−1.28686	−0.0698925
$340$	−29.0834	−1.57727
$341$	−3.76425	−0.203846
$342$	56.8226	3.07261
$343$	−17.1851	−0.927908
$344$	−28.0649	−1.51316
$345$	−4.75527	−0.256015
$346$	0.120978	0.00650381
$347$	26.8760	1.44278	0.721390	−	0.692529i	$-0.243504\pi$
$347$	26.8760	1.44278	0.721390	+	0.692529i	$0.243504\pi$
$348$	0.973912	0.0522071
$349$	−12.3433	−0.660719	−0.330360	−	0.943855i	$-0.607170\pi$
$349$	−12.3433	−0.660719	−0.330360	+	0.943855i	$0.607170\pi$
$350$	−25.1378	−1.34367
$351$	−8.06252	−0.430346
$352$	−0.197641	−0.0105343
$353$	−11.5167	−0.612974	−0.306487	−	0.951875i	$-0.599154\pi$
$353$	−11.5167	−0.612974	−0.306487	+	0.951875i	$0.599154\pi$
$354$	−2.23034	−0.118541
$355$	37.7939	2.00589
$356$	40.3988	2.14113
$357$	0.738602	0.0390910
$358$	−10.7241	−0.566786
$359$	−12.9844	−0.685288	−0.342644	−	0.939465i	$-0.611322\pi$
$359$	−12.9844	−0.685288	−0.342644	+	0.939465i	$0.611322\pi$
$360$	−49.6966	−2.61924
$361$	43.4148	2.28499
$362$	−48.2564	−2.53630
$363$	−2.29809	−0.120619
$364$	31.8838	1.67117
$365$	−10.0204	−0.524490
$366$	7.43667	0.388721
$367$	35.8191	1.86974	0.934870	−	0.354989i	$-0.115515\pi$
$367$	35.8191	1.86974	0.934870	+	0.354989i	$0.115515\pi$
$368$	21.8057	1.13670
$369$	−9.38698	−0.488667
$370$	−39.8996	−2.07428
$371$	−16.4756	−0.855371
$372$	2.89896	0.150304
$373$	2.04114	0.105686	0.0528430	−	0.998603i	$-0.483172\pi$
$373$	2.04114	0.105686	0.0528430	+	0.998603i	$0.483172\pi$
$374$	6.48431	0.335296
$375$	−1.81275	−0.0936099
$376$	40.8319	2.10575
$377$	5.55217	0.285951
$378$	5.12030	0.263360
$379$	−12.5931	−0.646863	−0.323431	−	0.946252i	$-0.604836\pi$
$379$	−12.5931	−0.646863	−0.323431	+	0.946252i	$0.604836\pi$
$380$	−109.616	−5.62320
$381$	3.17736	0.162781
$382$	4.49711	0.230092
$383$	−17.2238	−0.880095	−0.440048	−	0.897974i	$-0.645038\pi$
$383$	−17.2238	−0.880095	−0.440048	+	0.897974i	$0.645038\pi$
$384$	4.82141	0.246042
$385$	6.34840	0.323544
$386$	29.4691	1.49994
$387$	−17.0027	−0.864296
$388$	−29.5245	−1.49888
$389$	20.8108	1.05515	0.527576	−	0.849508i	$-0.323101\pi$
$389$	20.8108	1.05515	0.527576	+	0.849508i	$0.323101\pi$
$390$	11.5632	0.585525
$391$	11.7076	0.592080
$392$	23.8889	1.20657
$393$	−1.46874	−0.0740881
$394$	40.7750	2.05422
$395$	48.5686	2.44375
$396$	14.8134	0.744400
$397$	−30.5348	−1.53250	−0.766250	−	0.642542i	$-0.777880\pi$
$397$	−30.5348	−1.53250	−0.766250	+	0.642542i	$0.777880\pi$
$398$	14.7813	0.740918
$399$	2.78381	0.139365
$400$	27.8327	1.39163
$401$	−33.2919	−1.66252	−0.831258	−	0.555887i	$-0.812379\pi$
$401$	−33.2919	−1.66252	−0.831258	+	0.555887i	$0.812379\pi$
$402$	−9.56840	−0.477228
$403$	16.5267	0.823253
$404$	27.5862	1.37246
$405$	−29.4836	−1.46505
$406$	−3.52604	−0.174994
$407$	5.92262	0.293573
$408$	−2.48683	−0.123116
$409$	12.0799	0.597313	0.298657	−	0.954361i	$-0.403461\pi$
$409$	12.0799	0.597313	0.298657	+	0.954361i	$0.403461\pi$
$410$	27.1990	1.34326
$411$	3.56388	0.175793
$412$	32.3277	1.59267
$413$	5.37606	0.264539
$414$	40.1728	1.97439
$415$	6.93037	0.340198
$416$	0.867730	0.0425440
$417$	−0.244458	−0.0119712
$418$	24.4396	1.19538
$419$	28.0736	1.37149	0.685743	−	0.727844i	$-0.259477\pi$
$419$	28.0736	1.37149	0.685743	+	0.727844i	$0.259477\pi$
$420$	−4.88909	−0.238563
$421$	−11.1578	−0.543798	−0.271899	−	0.962326i	$-0.587652\pi$
$421$	−11.1578	−0.543798	−0.271899	+	0.962326i	$0.587652\pi$
$422$	−58.7486	−2.85984
$423$	24.7374	1.20277
$424$	55.4725	2.69398
$425$	14.9436	0.724871
$426$	6.48939	0.314412
$427$	−17.9255	−0.867477
$428$	78.2408	3.78191
$429$	−1.71642	−0.0828694
$430$	49.2659	2.37581
$431$	18.8029	0.905704	0.452852	−	0.891586i	$-0.350407\pi$
$431$	18.8029	0.905704	0.452852	+	0.891586i	$0.350407\pi$
$432$	−5.66921	−0.272760
$433$	15.3585	0.738081	0.369040	−	0.929413i	$-0.379686\pi$
$433$	15.3585	0.738081	0.369040	+	0.929413i	$0.379686\pi$
$434$	−10.4957	−0.503808
$435$	−0.851374	−0.0408203
$436$	−73.4420	−3.51723
$437$	44.1264	2.11085
$438$	−1.72054	−0.0822108
$439$	34.4724	1.64528	0.822639	−	0.568564i	$-0.192501\pi$
$439$	34.4724	1.64528	0.822639	+	0.568564i	$0.192501\pi$
$440$	−21.3747	−1.01900
$441$	14.4727	0.689177
$442$	−28.4689	−1.35413
$443$	39.3679	1.87043	0.935213	−	0.354085i	$-0.115208\pi$
$443$	39.3679	1.87043	0.935213	+	0.354085i	$0.115208\pi$
$444$	−4.56118	−0.216464
$445$	−35.3158	−1.67413
$446$	16.2172	0.767906
$447$	5.41166	0.255963
$448$	−11.8058	−0.557773
$449$	7.27982	0.343556	0.171778	−	0.985136i	$-0.445049\pi$
$449$	7.27982	0.343556	0.171778	+	0.985136i	$0.445049\pi$
$450$	51.2765	2.41720
$451$	−4.03737	−0.190112
$452$	−20.9721	−0.986443
$453$	2.20865	0.103772
$454$	33.0874	1.55287
$455$	−27.8722	−1.30667
$456$	−9.37294	−0.438928
$457$	14.3109	0.669436	0.334718	−	0.942318i	$-0.391359\pi$
$457$	14.3109	0.669436	0.334718	+	0.942318i	$0.391359\pi$
$458$	−18.6242	−0.870253
$459$	−3.04384	−0.142074
$460$	−77.4973	−3.61333
$461$	−0.829869	−0.0386508	−0.0193254	−	0.999813i	$-0.506152\pi$
$461$	−0.829869	−0.0386508	−0.0193254	+	0.999813i	$0.506152\pi$
$462$	1.09005	0.0507137
$463$	22.2082	1.03210	0.516052	−	0.856557i	$-0.327401\pi$
$463$	22.2082	1.03210	0.516052	+	0.856557i	$0.327401\pi$
$464$	3.90404	0.181240
$465$	−2.53422	−0.117521
$466$	62.3116	2.88653
$467$	−2.12443	−0.0983069	−0.0491535	−	0.998791i	$-0.515652\pi$
$467$	−2.12443	−0.0983069	−0.0491535	+	0.998791i	$0.515652\pi$
$468$	−65.0371	−3.00634
$469$	23.0639	1.06499
$470$	−71.6774	−3.30623
$471$	0.804403	0.0370649
$472$	−18.1009	−0.833161
$473$	−7.31292	−0.336249
$474$	8.33946	0.383044
$475$	56.3229	2.58427
$476$	12.0371	0.551719
$477$	33.6072	1.53877
$478$	−4.24091	−0.193975
$479$	41.5112	1.89669	0.948347	−	0.317235i	$-0.102754\pi$
$479$	41.5112	1.89669	0.948347	+	0.317235i	$0.102754\pi$
$480$	−0.133058	−0.00607326
$481$	−26.0028	−1.18563
$482$	−46.2538	−2.10680
$483$	1.96812	0.0895526
$484$	−37.4523	−1.70238
$485$	25.8097	1.17196
$486$	−15.7192	−0.713038
$487$	26.5314	1.20225	0.601126	−	0.799154i	$-0.294719\pi$
$487$	26.5314	1.20225	0.601126	+	0.799154i	$0.294719\pi$
$488$	60.3542	2.73211
$489$	−1.14509	−0.0517826
$490$	−41.9351	−1.89444
$491$	13.3146	0.600879	0.300440	−	0.953801i	$-0.402867\pi$
$491$	13.3146	0.600879	0.300440	+	0.953801i	$0.402867\pi$
$492$	3.10930	0.140178
$493$	2.09611	0.0944040
$494$	−107.300	−4.82767
$495$	−12.9495	−0.582039
$496$	11.6208	0.521791
$497$	−15.6422	−0.701648
$498$	1.18998	0.0533242
$499$	−28.9031	−1.29388	−0.646939	−	0.762542i	$-0.723951\pi$
$499$	−28.9031	−1.29388	−0.646939	+	0.762542i	$0.723951\pi$
$500$	−29.5426	−1.32119
$501$	4.16518	0.186086
$502$	−7.21468	−0.322007
$503$	2.29404	0.102286	0.0511431	−	0.998691i	$-0.483714\pi$
$503$	2.29404	0.102286	0.0511431	+	0.998691i	$0.483714\pi$
$504$	20.5685	0.916195
$505$	−24.1153	−1.07312
$506$	17.2785	0.768121
$507$	4.35785	0.193539
$508$	51.7818	2.29745
$509$	−23.4098	−1.03762	−0.518811	−	0.854889i	$-0.673625\pi$
$509$	−23.4098	−1.03762	−0.518811	+	0.854889i	$0.673625\pi$
$510$	4.36545	0.193305
$511$	4.14724	0.183463
$512$	38.5043	1.70167
$513$	−11.4723	−0.506516
$514$	−40.3288	−1.77883
$515$	−28.2602	−1.24529
$516$	5.63190	0.247931
$517$	10.6396	0.467931
$518$	16.5137	0.725571
$519$	−0.0120897	−0.000530679 0
$520$	93.8441	4.11534
$521$	30.3040	1.32764	0.663820	−	0.747892i	$-0.268934\pi$
$521$	30.3040	1.32764	0.663820	+	0.747892i	$0.268934\pi$
$522$	7.19246	0.314805
$523$	13.1804	0.576337	0.288168	−	0.957580i	$-0.406954\pi$
$523$	13.1804	0.576337	0.288168	+	0.957580i	$0.406954\pi$
$524$	−23.9362	−1.04566
$525$	2.51210	0.109637
$526$	−18.8092	−0.820122
$527$	6.23932	0.271789
$528$	−1.20691	−0.0525239
$529$	8.19681	0.356383
$530$	−97.3778	−4.22982
$531$	−10.9662	−0.475891
$532$	45.3682	1.96696
$533$	17.7258	0.767789
$534$	−6.06390	−0.262411
$535$	−68.3965	−2.95704
$536$	−77.6549	−3.35418
$537$	1.07169	0.0462469
$538$	−40.4180	−1.74254
$539$	6.22476	0.268120
$540$	20.1484	0.867047
$541$	−35.2207	−1.51426	−0.757128	−	0.653267i	$-0.773398\pi$
$541$	−35.2207	−1.51426	−0.757128	+	0.653267i	$0.773398\pi$
$542$	−27.0185	−1.16054
$543$	4.82242	0.206950
$544$	0.327594	0.0140455
$545$	64.2015	2.75009
$546$	−4.78579	−0.204813
$547$	27.8485	1.19071	0.595357	−	0.803461i	$-0.297011\pi$
$547$	27.8485	1.19071	0.595357	+	0.803461i	$0.297011\pi$
$548$	58.0811	2.48110
$549$	36.5647	1.56054
$550$	22.0542	0.940394
$551$	7.90030	0.336564
$552$	−6.62655	−0.282045
$553$	−20.1017	−0.854809
$554$	71.0335	3.01792
$555$	3.98729	0.169251
$556$	−3.98396	−0.168958
$557$	20.3260	0.861242	0.430621	−	0.902533i	$-0.358295\pi$
$557$	20.3260	0.861242	0.430621	+	0.902533i	$0.358295\pi$
$558$	21.4092	0.906324
$559$	32.1069	1.35798
$560$	−19.5985	−0.828187
$561$	−0.647998	−0.0273585
$562$	64.5856	2.72438
$563$	−2.33896	−0.0985753	−0.0492877	−	0.998785i	$-0.515695\pi$
$563$	−2.33896	−0.0985753	−0.0492877	+	0.998785i	$0.515695\pi$
$564$	−8.19391	−0.345026
$565$	18.3334	0.771290
$566$	8.45254	0.355287
$567$	12.2027	0.512466
$568$	52.6664	2.20983
$569$	15.3106	0.641856	0.320928	−	0.947104i	$-0.396005\pi$
$569$	15.3106	0.641856	0.320928	+	0.947104i	$0.396005\pi$
$570$	16.4535	0.689162
$571$	−39.4348	−1.65030	−0.825148	−	0.564917i	$-0.808908\pi$
$571$	−39.4348	−1.65030	−0.825148	+	0.564917i	$0.808908\pi$
$572$	−27.9727	−1.16960
$573$	−0.449410	−0.0187744
$574$	−11.2572	−0.469866
$575$	39.8195	1.66059
$576$	24.0817	1.00340
$577$	−12.7678	−0.531532	−0.265766	−	0.964038i	$-0.585625\pi$
$577$	−12.7678	−0.531532	−0.265766	+	0.964038i	$0.585625\pi$
$578$	30.8378	1.28268
$579$	−2.94494	−0.122387
$580$	−13.8750	−0.576126
$581$	−2.86835	−0.118999
$582$	4.43165	0.183698
$583$	14.4546	0.598647
$584$	−13.9635	−0.577815
$585$	56.8541	2.35063
$586$	29.1947	1.20602
$587$	−20.6718	−0.853217	−0.426608	−	0.904436i	$-0.640292\pi$
$587$	−20.6718	−0.853217	−0.426608	+	0.904436i	$0.640292\pi$
$588$	−4.79388	−0.197696
$589$	23.5162	0.968967
$590$	31.7748	1.30815
$591$	−4.07478	−0.167614
$592$	−18.2840	−0.751469
$593$	−11.5423	−0.473986	−0.236993	−	0.971511i	$-0.576162\pi$
$593$	−11.5423	−0.473986	−0.236993	+	0.971511i	$0.576162\pi$
$594$	−4.49219	−0.184317
$595$	−10.5226	−0.431384
$596$	88.1945	3.61259
$597$	−1.47714	−0.0604553
$598$	−75.8599	−3.10214
$599$	37.4167	1.52880	0.764402	−	0.644740i	$-0.223034\pi$
$599$	37.4167	1.52880	0.764402	+	0.644740i	$0.223034\pi$
$600$	−8.45811	−0.345301
$601$	35.0037	1.42783	0.713915	−	0.700232i	$-0.246920\pi$
$601$	35.0037	1.42783	0.713915	+	0.700232i	$0.246920\pi$
$602$	−20.3902	−0.831044
$603$	−47.0461	−1.91586
$604$	35.9947	1.46460
$605$	32.7401	1.33107
$606$	−4.14071	−0.168205
$607$	18.1968	0.738584	0.369292	−	0.929313i	$-0.379600\pi$
$607$	18.1968	0.738584	0.369292	+	0.929313i	$0.379600\pi$
$608$	1.23471	0.0500742
$609$	0.352368	0.0142787
$610$	−105.947	−4.28968
$611$	−46.7126	−1.88979
$612$	−24.5534	−0.992513
$613$	−3.03810	−0.122708	−0.0613538	−	0.998116i	$-0.519542\pi$
$613$	−3.03810	−0.122708	−0.0613538	+	0.998116i	$0.519542\pi$
$614$	−3.92324	−0.158329
$615$	−2.71809	−0.109604
$616$	8.84659	0.356439
$617$	0.791925	0.0318817	0.0159409	−	0.999873i	$-0.494926\pi$
$617$	0.791925	0.0318817	0.0159409	+	0.999873i	$0.494926\pi$
$618$	−4.85242	−0.195193
$619$	12.5329	0.503738	0.251869	−	0.967761i	$-0.418955\pi$
$619$	12.5329	0.503738	0.251869	+	0.967761i	$0.418955\pi$
$620$	−41.3004	−1.65867
$621$	−8.11079	−0.325475
$622$	−38.7026	−1.55183
$623$	14.6166	0.585601
$624$	5.29884	0.212123
$625$	−9.82047	−0.392819
$626$	−45.0238	−1.79951
$627$	−2.44233	−0.0975371
$628$	13.1095	0.523124
$629$	−9.81684	−0.391423
$630$	−36.1065	−1.43852
$631$	−26.4794	−1.05413	−0.527065	−	0.849825i	$-0.676708\pi$
$631$	−26.4794	−1.05413	−0.527065	+	0.849825i	$0.676708\pi$
$632$	67.6811	2.69221
$633$	5.87093	0.233349
$634$	13.2858	0.527648
$635$	−45.2666	−1.79635
$636$	−11.1319	−0.441408
$637$	−27.3294	−1.08283
$638$	3.09350	0.122473
$639$	31.9072	1.26223
$640$	−68.6888	−2.71516
$641$	2.39145	0.0944567	0.0472284	−	0.998884i	$-0.484961\pi$
$641$	2.39145	0.0944567	0.0472284	+	0.998884i	$0.484961\pi$
$642$	−11.7440	−0.463499
$643$	10.0173	0.395042	0.197521	−	0.980299i	$-0.436711\pi$
$643$	10.0173	0.395042	0.197521	+	0.980299i	$0.436711\pi$
$644$	32.0747	1.26392
$645$	−4.92329	−0.193855
$646$	−40.5091	−1.59381
$647$	28.8036	1.13239	0.566193	−	0.824273i	$-0.308416\pi$
$647$	28.8036	1.13239	0.566193	+	0.824273i	$0.308416\pi$
$648$	−41.0859	−1.61401
$649$	−4.71658	−0.185142
$650$	−96.8274	−3.79788
$651$	1.04887	0.0411083
$652$	−18.6616	−0.730846
$653$	−50.5898	−1.97973	−0.989866	−	0.142003i	$-0.954646\pi$
$653$	−50.5898	−1.97973	−0.989866	+	0.142003i	$0.954646\pi$
$654$	11.0237	0.431061
$655$	20.9246	0.817591
$656$	12.4640	0.486637
$657$	−8.45960	−0.330041
$658$	29.6660	1.15650
$659$	19.6990	0.767363	0.383682	−	0.923465i	$-0.374656\pi$
$659$	19.6990	0.767363	0.383682	+	0.923465i	$0.374656\pi$
$660$	4.28935	0.166963
$661$	34.3554	1.33627	0.668135	−	0.744040i	$-0.267093\pi$
$661$	34.3554	1.33627	0.668135	+	0.744040i	$0.267093\pi$
$662$	−11.7039	−0.454885
$663$	2.84499	0.110490
$664$	9.65758	0.374787
$665$	−39.6599	−1.53795
$666$	−33.6849	−1.30526
$667$	5.58541	0.216268
$668$	67.8804	2.62637
$669$	−1.62064	−0.0626574
$670$	136.317	5.26640
$671$	15.7266	0.607119
$672$	0.0550704	0.00212439
$673$	10.4436	0.402572	0.201286	−	0.979532i	$-0.435488\pi$
$673$	10.4436	0.402572	0.201286	+	0.979532i	$0.435488\pi$
$674$	82.1956	3.16606
$675$	−10.3526	−0.398472
$676$	71.0205	2.73156
$677$	−42.7493	−1.64299	−0.821495	−	0.570215i	$-0.806860\pi$
$677$	−42.7493	−1.64299	−0.821495	+	0.570215i	$0.806860\pi$
$678$	3.14793	0.120895
$679$	−10.6822	−0.409944
$680$	35.4289	1.35864
$681$	−3.30653	−0.126706
$682$	9.20817	0.352599
$683$	−11.6692	−0.446510	−0.223255	−	0.974760i	$-0.571668\pi$
$683$	−11.6692	−0.446510	−0.223255	+	0.974760i	$0.571668\pi$
$684$	−92.5426	−3.53846
$685$	−50.7733	−1.93995
$686$	42.0384	1.60503
$687$	1.86118	0.0710083
$688$	22.5761	0.860707
$689$	−63.4618	−2.41770
$690$	11.6324	0.442838
$691$	27.3582	1.04076	0.520378	−	0.853936i	$-0.325791\pi$
$691$	27.3582	1.04076	0.520378	+	0.853936i	$0.325791\pi$
$692$	−0.197027	−0.00748986
$693$	5.35958	0.203594
$694$	−65.7445	−2.49563
$695$	3.48270	0.132106
$696$	−1.18640	−0.0449705
$697$	6.69202	0.253478
$698$	30.1942	1.14287
$699$	−6.22700	−0.235527
$700$	40.9401	1.54739
$701$	29.3253	1.10760	0.553801	−	0.832649i	$-0.313177\pi$
$701$	29.3253	1.10760	0.553801	+	0.832649i	$0.313177\pi$
$702$	19.7227	0.744384
$703$	−37.0000	−1.39548
$704$	10.3576	0.390368
$705$	7.16295	0.269772
$706$	28.1724	1.06028
$707$	9.98086	0.375369
$708$	3.63238	0.136513
$709$	−0.337844	−0.0126880	−0.00634400	−	0.999980i	$-0.502019\pi$
$709$	−0.337844	−0.0126880	−0.00634400	+	0.999980i	$0.502019\pi$
$710$	−92.4519	−3.46966
$711$	41.0036	1.53776
$712$	−49.2132	−1.84434
$713$	16.6256	0.622635
$714$	−1.80678	−0.0676170
$715$	24.4531	0.914495
$716$	17.4655	0.652717
$717$	0.423808	0.0158274
$718$	31.7625	1.18537
$719$	21.1583	0.789073	0.394537	−	0.918880i	$-0.370905\pi$
$719$	21.1583	0.789073	0.394537	+	0.918880i	$0.370905\pi$
$720$	39.9773	1.48986
$721$	11.6964	0.435596
$722$	−106.202	−3.95242
$723$	4.62229	0.171905
$724$	78.5916	2.92083
$725$	7.12920	0.264772
$726$	5.62163	0.208638
$727$	−34.9724	−1.29705	−0.648527	−	0.761192i	$-0.724615\pi$
$727$	−34.9724	−1.29705	−0.648527	+	0.761192i	$0.724615\pi$
$728$	−38.8404	−1.43952
$729$	−23.8263	−0.882457
$730$	24.5119	0.907228
$731$	12.1213	0.448323
$732$	−12.1115	−0.447655
$733$	5.11407	0.188892	0.0944462	−	0.995530i	$-0.469892\pi$
$733$	5.11407	0.188892	0.0944462	+	0.995530i	$0.469892\pi$
$734$	−87.6211	−3.23416
$735$	4.19071	0.154577
$736$	0.872925	0.0321765
$737$	−20.2347	−0.745354
$738$	22.9626	0.845263
$739$	−2.06963	−0.0761325	−0.0380663	−	0.999275i	$-0.512120\pi$
$739$	−2.06963	−0.0761325	−0.0380663	+	0.999275i	$0.512120\pi$
$740$	64.9814	2.38877
$741$	10.7229	0.393914
$742$	40.3029	1.47957
$743$	−36.0523	−1.32263	−0.661315	−	0.750109i	$-0.730001\pi$
$743$	−36.0523	−1.32263	−0.661315	+	0.750109i	$0.730001\pi$
$744$	−3.53147	−0.129470
$745$	−77.0978	−2.82465
$746$	−4.99306	−0.182809
$747$	5.85090	0.214073
$748$	−10.5605	−0.386130
$749$	28.3081	1.03435
$750$	4.43437	0.161920
$751$	54.2893	1.98105	0.990523	−	0.137348i	$-0.0438577\pi$
$751$	54.2893	1.98105	0.990523	+	0.137348i	$0.0438577\pi$
$752$	−32.8462	−1.19778
$753$	0.720986	0.0262742
$754$	−13.5818	−0.494620
$755$	−31.4659	−1.14516
$756$	−8.33904	−0.303288
$757$	−13.2431	−0.481330	−0.240665	−	0.970608i	$-0.577366\pi$
$757$	−13.2431	−0.481330	−0.240665	+	0.970608i	$0.577366\pi$
$758$	30.8053	1.11890
$759$	−1.72669	−0.0626750
$760$	133.533	4.84374
$761$	31.7739	1.15180	0.575901	−	0.817520i	$-0.304651\pi$
$761$	31.7739	1.15180	0.575901	+	0.817520i	$0.304651\pi$
$762$	−7.77249	−0.281568
$763$	−26.5718	−0.961965
$764$	−7.32410	−0.264977
$765$	21.4641	0.776037
$766$	42.1331	1.52233
$767$	20.7078	0.747716
$768$	−7.78979	−0.281090
$769$	−20.2528	−0.730335	−0.365167	−	0.930942i	$-0.618988\pi$
$769$	−20.2528	−0.730335	−0.365167	+	0.930942i	$0.618988\pi$
$770$	−15.5295	−0.559646
$771$	4.03018	0.145143
$772$	−47.9940	−1.72734
$773$	−24.8087	−0.892307	−0.446153	−	0.894956i	$-0.647206\pi$
$773$	−24.8087	−0.892307	−0.446153	+	0.894956i	$0.647206\pi$
$774$	41.5923	1.49500
$775$	21.2209	0.762278
$776$	35.9662	1.29111
$777$	−1.65027	−0.0592030
$778$	−50.9078	−1.82513
$779$	25.2224	0.903687
$780$	−18.8321	−0.674297
$781$	13.7234	0.491061
$782$	−28.6394	−1.02414
$783$	−1.45214	−0.0518952
$784$	−19.2168	−0.686315
$785$	−11.4600	−0.409026
$786$	3.59285	0.128153
$787$	−29.8317	−1.06338	−0.531692	−	0.846938i	$-0.678444\pi$
$787$	−29.8317	−1.06338	−0.531692	+	0.846938i	$0.678444\pi$
$788$	−66.4072	−2.36566
$789$	1.87967	0.0669179
$790$	−118.809	−4.22704
$791$	−7.58784	−0.269793
$792$	−18.0454	−0.641215
$793$	−69.0466	−2.45192
$794$	74.6948	2.65082
$795$	9.73128	0.345133
$796$	−24.0731	−0.853249
$797$	−15.4586	−0.547572	−0.273786	−	0.961791i	$-0.588276\pi$
$797$	−15.4586	−0.547572	−0.273786	+	0.961791i	$0.588276\pi$
$798$	−6.80980	−0.241064
$799$	−17.6354	−0.623896
$800$	1.11420	0.0393929
$801$	−29.8151	−1.05346
$802$	81.4390	2.87571
$803$	−3.63850	−0.128400
$804$	15.5833	0.549582
$805$	−28.0391	−0.988247
$806$	−40.4278	−1.42401
$807$	4.03909	0.142183
$808$	−33.6050	−1.18222
$809$	−7.04711	−0.247763	−0.123882	−	0.992297i	$-0.539534\pi$
$809$	−7.04711	−0.247763	−0.123882	+	0.992297i	$0.539534\pi$
$810$	72.1232	2.53415
$811$	−20.6263	−0.724287	−0.362144	−	0.932122i	$-0.617955\pi$
$811$	−20.6263	−0.724287	−0.362144	+	0.932122i	$0.617955\pi$
$812$	5.74259	0.201525
$813$	2.70005	0.0946948
$814$	−14.4880	−0.507804
$815$	16.3136	0.571442
$816$	2.00047	0.0700305
$817$	45.6856	1.59834
$818$	−29.5501	−1.03319
$819$	−23.5309	−0.822235
$820$	−44.2970	−1.54692
$821$	19.4838	0.679989	0.339995	−	0.940427i	$-0.389575\pi$
$821$	19.4838	0.679989	0.339995	+	0.940427i	$0.389575\pi$
$822$	−8.71802	−0.304076
$823$	−3.61715	−0.126086	−0.0630430	−	0.998011i	$-0.520081\pi$
$823$	−3.61715	−0.126086	−0.0630430	+	0.998011i	$0.520081\pi$
$824$	−39.3811	−1.37191
$825$	−2.20395	−0.0767315
$826$	−13.1510	−0.457581
$827$	3.20729	0.111528	0.0557642	−	0.998444i	$-0.482240\pi$
$827$	3.20729	0.111528	0.0557642	+	0.998444i	$0.482240\pi$
$828$	−65.4264	−2.27373
$829$	56.6728	1.96833	0.984163	−	0.177265i	$-0.0567251\pi$
$829$	56.6728	1.96833	0.984163	+	0.177265i	$0.0567251\pi$
$830$	−16.9532	−0.588453
$831$	−7.09860	−0.246248
$832$	−45.4744	−1.57654
$833$	−10.3177	−0.357486
$834$	0.597997	0.0207069
$835$	−59.3397	−2.05353
$836$	−39.8029	−1.37661
$837$	−4.32246	−0.149406
$838$	−68.6741	−2.37231
$839$	−19.7915	−0.683277	−0.341639	−	0.939831i	$-0.610982\pi$
$839$	−19.7915	−0.683277	−0.341639	+	0.939831i	$0.610982\pi$
$840$	5.95581	0.205495
$841$	1.00000	0.0344828
$842$	27.2944	0.940626
$843$	−6.45425	−0.222296
$844$	95.6793	3.29342
$845$	−62.0847	−2.13578
$846$	−60.5130	−2.08048
$847$	−13.5505	−0.465601
$848$	−44.6235	−1.53238
$849$	−0.844689	−0.0289897
$850$	−36.5552	−1.25383
$851$	−26.1585	−0.896702
$852$	−10.5688	−0.362081
$853$	−19.7045	−0.674671	−0.337335	−	0.941385i	$-0.609526\pi$
$853$	−19.7045	−0.674671	−0.337335	+	0.941385i	$0.609526\pi$
$854$	43.8497	1.50051
$855$	80.8989	2.76668
$856$	−95.3117	−3.25769
$857$	18.4851	0.631438	0.315719	−	0.948853i	$-0.397754\pi$
$857$	18.4851	0.631438	0.315719	+	0.948853i	$0.397754\pi$
$858$	4.19872	0.143342
$859$	4.83979	0.165132	0.0825658	−	0.996586i	$-0.473689\pi$
$859$	4.83979	0.165132	0.0825658	+	0.996586i	$0.473689\pi$
$860$	−80.2356	−2.73601
$861$	1.12497	0.0383387
$862$	−45.9959	−1.56663
$863$	−17.5200	−0.596389	−0.298194	−	0.954505i	$-0.596384\pi$
$863$	−17.5200	−0.596389	−0.298194	+	0.954505i	$0.596384\pi$
$864$	−0.226950	−0.00772100
$865$	0.172237	0.00585625
$866$	−37.5701	−1.27668
$867$	−3.08172	−0.104661
$868$	17.0935	0.580191
$869$	17.6358	0.598253
$870$	2.08264	0.0706082
$871$	88.8389	3.01019
$872$	89.4658	3.02970
$873$	21.7896	0.737467
$874$	−107.943	−3.65122
$875$	−10.6887	−0.361345
$876$	2.80212	0.0946748
$877$	8.18346	0.276336	0.138168	−	0.990409i	$-0.455879\pi$
$877$	8.18346	0.276336	0.138168	+	0.990409i	$0.455879\pi$
$878$	−84.3269	−2.84590
$879$	−2.91752	−0.0984055
$880$	17.1943	0.579621
$881$	39.8202	1.34158	0.670788	−	0.741649i	$-0.265956\pi$
$881$	39.8202	1.34158	0.670788	+	0.741649i	$0.265956\pi$
$882$	−35.4034	−1.19209
$883$	−34.7578	−1.16969	−0.584846	−	0.811144i	$-0.698845\pi$
$883$	−34.7578	−1.16969	−0.584846	+	0.811144i	$0.698845\pi$
$884$	46.3652	1.55943
$885$	−3.17535	−0.106738
$886$	−96.3024	−3.23534
$887$	0.554449	0.0186166	0.00930828	−	0.999957i	$-0.497037\pi$
$887$	0.554449	0.0186166	0.00930828	+	0.999957i	$0.497037\pi$
$888$	5.55636	0.186459
$889$	18.7350	0.628352
$890$	86.3901	2.89580
$891$	−10.7058	−0.358659
$892$	−26.4117	−0.884329
$893$	−66.4684	−2.22428
$894$	−13.2381	−0.442747
$895$	−15.2680	−0.510353
$896$	28.4290	0.949748
$897$	7.58092	0.253120
$898$	−17.8080	−0.594261
$899$	2.97662	0.0992758
$900$	−83.5101	−2.78367
$901$	−23.9587	−0.798180
$902$	9.87627	0.328844
$903$	2.03766	0.0678091
$904$	25.5478	0.849708
$905$	−68.7032	−2.28377
$906$	−5.40284	−0.179497
$907$	−15.6597	−0.519972	−0.259986	−	0.965612i	$-0.583718\pi$
$907$	−15.6597	−0.519972	−0.259986	+	0.965612i	$0.583718\pi$
$908$	−53.8869	−1.78830
$909$	−20.3591	−0.675269
$910$	68.1814	2.26019
$911$	−11.8172	−0.391523	−0.195761	−	0.980652i	$-0.562718\pi$
$911$	−11.8172	−0.391523	−0.195761	+	0.980652i	$0.562718\pi$
$912$	7.53984	0.249669
$913$	2.51649	0.0832837
$914$	−35.0075	−1.15795
$915$	10.5877	0.350017
$916$	30.3319	1.00219
$917$	−8.66030	−0.285988
$918$	7.44589	0.245751
$919$	−11.4205	−0.376728	−0.188364	−	0.982099i	$-0.560318\pi$
$919$	−11.4205	−0.376728	−0.188364	+	0.982099i	$0.560318\pi$
$920$	94.4059	3.11247
$921$	0.392062	0.0129189
$922$	2.03004	0.0668557
$923$	−60.2515	−1.98320
$924$	−1.77528	−0.0584025
$925$	−33.3887	−1.09781
$926$	−54.3261	−1.78527
$927$	−23.8585	−0.783615
$928$	0.156287	0.00513036
$929$	22.1256	0.725917	0.362959	−	0.931805i	$-0.381767\pi$
$929$	22.1256	0.725917	0.362959	+	0.931805i	$0.381767\pi$
$930$	6.19923	0.203281
$931$	−38.8876	−1.27449
$932$	−101.482	−3.32416
$933$	3.86767	0.126622
$934$	5.19681	0.170045
$935$	9.23179	0.301912
$936$	79.2271	2.58962
$937$	22.6824	0.741003	0.370501	−	0.928832i	$-0.379186\pi$
$937$	22.6824	0.741003	0.370501	+	0.928832i	$0.379186\pi$
$938$	−56.4193	−1.84215
$939$	4.49938	0.146832
$940$	116.736	3.80749
$941$	−45.4556	−1.48181	−0.740905	−	0.671610i	$-0.765603\pi$
$941$	−45.4556	−1.48181	−0.740905	+	0.671610i	$0.765603\pi$
$942$	−1.96774	−0.0641125
$943$	17.8319	0.580687
$944$	14.5608	0.473914
$945$	7.28982	0.237138
$946$	17.8890	0.581621
$947$	49.7800	1.61763	0.808816	−	0.588062i	$-0.200109\pi$
$947$	49.7800	1.61763	0.808816	+	0.588062i	$0.200109\pi$
$948$	−13.5819	−0.441118
$949$	15.9746	0.518557
$950$	−137.778	−4.47010
$951$	−1.32770	−0.0430535
$952$	−14.6634	−0.475243
$953$	−7.24169	−0.234581	−0.117291	−	0.993098i	$-0.537421\pi$
$953$	−7.24169	−0.234581	−0.117291	+	0.993098i	$0.537421\pi$
$954$	−82.2104	−2.66166
$955$	6.40258	0.207183
$956$	6.90685	0.223383
$957$	−0.309143	−0.00999318
$958$	−101.545	−3.28078
$959$	21.0141	0.678582
$960$	6.97308	0.225055
$961$	−22.1397	−0.714185
$962$	63.6085	2.05082
$963$	−57.7432	−1.86075
$964$	75.3300	2.42622
$965$	41.9554	1.35059
$966$	−4.81444	−0.154902
$967$	31.2590	1.00522	0.502611	−	0.864513i	$-0.332373\pi$
$967$	31.2590	1.00522	0.502611	+	0.864513i	$0.332373\pi$
$968$	45.6238	1.46640
$969$	4.04820	0.130047
$970$	−63.1360	−2.02718
$971$	24.0402	0.771486	0.385743	−	0.922606i	$-0.373945\pi$
$971$	24.0402	0.771486	0.385743	+	0.922606i	$0.373945\pi$
$972$	25.6007	0.821142
$973$	−1.44143	−0.0462100
$974$	−64.9015	−2.07958
$975$	9.67627	0.309889
$976$	−48.5505	−1.55406
$977$	−12.6006	−0.403128	−0.201564	−	0.979475i	$-0.564602\pi$
$977$	−12.6006	−0.403128	−0.201564	+	0.979475i	$0.564602\pi$
$978$	2.80113	0.0895702
$979$	−12.8236	−0.409843
$980$	68.2966	2.18165
$981$	54.2016	1.73052
$982$	−32.5703	−1.03936
$983$	25.1312	0.801562	0.400781	−	0.916174i	$-0.368739\pi$
$983$	25.1312	0.801562	0.400781	+	0.916174i	$0.368739\pi$
$984$	−3.78770	−0.120747
$985$	58.0519	1.84969
$986$	−5.12753	−0.163294
$987$	−2.96461	−0.0943647
$988$	174.752	5.55960
$989$	32.2991	1.02705
$990$	31.6774	1.00677
$991$	−26.3085	−0.835719	−0.417859	−	0.908512i	$-0.637219\pi$
$991$	−26.3085	−0.835719	−0.417859	+	0.908512i	$0.637219\pi$
$992$	0.465206	0.0147703
$993$	1.16961	0.0371164
$994$	38.2642	1.21367
$995$	21.0442	0.667147
$996$	−1.93803	−0.0614087
$997$	15.2066	0.481598	0.240799	−	0.970575i	$-0.422590\pi$
$997$	15.2066	0.481598	0.240799	+	0.970575i	$0.422590\pi$
$998$	70.7031	2.23807
$999$	6.80090	0.215171

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4031.2.a.d.1.10	✓	98

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4031.2.a.d.1.10	✓	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)

\(f(q)\)	\(=\)	\(q-2.44621 q^{2} +0.244458 q^{3} +3.98396 q^{4} -3.48270 q^{5} -0.597997 q^{6} +1.44143 q^{7} -4.85320 q^{8} -2.94024 q^{9} +O(q^{10})\)	\(q-2.44621 q^{2} +0.244458 q^{3} +3.98396 q^{4} -3.48270 q^{5} -0.597997 q^{6} +1.44143 q^{7} -4.85320 q^{8} -2.94024 q^{9} +8.51943 q^{10} -1.26461 q^{11} +0.973912 q^{12} +5.55217 q^{13} -3.52604 q^{14} -0.851374 q^{15} +3.90404 q^{16} +2.09611 q^{17} +7.19246 q^{18} +7.90030 q^{19} -13.8750 q^{20} +0.352368 q^{21} +3.09350 q^{22} +5.58541 q^{23} -1.18640 q^{24} +7.12920 q^{25} -13.5818 q^{26} -1.45214 q^{27} +5.74259 q^{28} +1.00000 q^{29} +2.08264 q^{30} +2.97662 q^{31} +0.156287 q^{32} -0.309143 q^{33} -5.12753 q^{34} -5.02005 q^{35} -11.7138 q^{36} -4.68336 q^{37} -19.3258 q^{38} +1.35727 q^{39} +16.9022 q^{40} +3.19259 q^{41} -0.861968 q^{42} +5.78276 q^{43} -5.03815 q^{44} +10.2400 q^{45} -13.6631 q^{46} -8.41340 q^{47} +0.954373 q^{48} -4.92229 q^{49} -17.4396 q^{50} +0.512411 q^{51} +22.1196 q^{52} -11.4301 q^{53} +3.55224 q^{54} +4.40425 q^{55} -6.99553 q^{56} +1.93129 q^{57} -2.44621 q^{58} +3.72968 q^{59} -3.39184 q^{60} -12.4360 q^{61} -7.28145 q^{62} -4.23814 q^{63} -8.19039 q^{64} -19.3365 q^{65} +0.756231 q^{66} +16.0008 q^{67} +8.35082 q^{68} +1.36540 q^{69} +12.2801 q^{70} -10.8519 q^{71} +14.2696 q^{72} +2.87718 q^{73} +11.4565 q^{74} +1.74279 q^{75} +31.4745 q^{76} -1.82284 q^{77} -3.32018 q^{78} -13.9457 q^{79} -13.5966 q^{80} +8.46573 q^{81} -7.80976 q^{82} -1.98994 q^{83} +1.40382 q^{84} -7.30012 q^{85} -14.1459 q^{86} +0.244458 q^{87} +6.13739 q^{88} +10.1404 q^{89} -25.0492 q^{90} +8.00304 q^{91} +22.2521 q^{92} +0.727658 q^{93} +20.5810 q^{94} -27.5144 q^{95} +0.0382055 q^{96} -7.41083 q^{97} +12.0410 q^{98} +3.71825 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 98 q + 6 q^{2} + 6 q^{3} + 116 q^{4} + q^{5} + 7 q^{6} + 12 q^{7} + 15 q^{8} + 136 q^{9}+O(q^{10}) \) 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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