LMFDB - Embedded newform 4031.2.a.e.1.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4031, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4031.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

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

Embedding invariants

Embedding label			1.19
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)

$f(q)$	$=$	$q-2.06403 q^{2} +0.822287 q^{3} +2.26023 q^{4} -2.41369 q^{5} -1.69723 q^{6} +3.09601 q^{7} -0.537124 q^{8} -2.32384 q^{9} +O(q^{10})$	\(q-2.06403 q^{2} +0.822287 q^{3} +2.26023 q^{4} -2.41369 q^{5} -1.69723 q^{6} +3.09601 q^{7} -0.537124 q^{8} -2.32384 q^{9} +4.98194 q^{10} +2.32440 q^{11} +1.85856 q^{12} +3.18384 q^{13} -6.39026 q^{14} -1.98475 q^{15} -3.41182 q^{16} +2.44382 q^{17} +4.79649 q^{18} -3.64889 q^{19} -5.45550 q^{20} +2.54581 q^{21} -4.79765 q^{22} -8.37443 q^{23} -0.441671 q^{24} +0.825903 q^{25} -6.57156 q^{26} -4.37773 q^{27} +6.99769 q^{28} -1.00000 q^{29} +4.09658 q^{30} +4.88312 q^{31} +8.11635 q^{32} +1.91133 q^{33} -5.04412 q^{34} -7.47281 q^{35} -5.25242 q^{36} +6.93825 q^{37} +7.53144 q^{38} +2.61803 q^{39} +1.29645 q^{40} +6.75152 q^{41} -5.25463 q^{42} +9.31473 q^{43} +5.25369 q^{44} +5.60904 q^{45} +17.2851 q^{46} +2.29109 q^{47} -2.80550 q^{48} +2.58527 q^{49} -1.70469 q^{50} +2.00952 q^{51} +7.19622 q^{52} +2.08926 q^{53} +9.03578 q^{54} -5.61039 q^{55} -1.66294 q^{56} -3.00044 q^{57} +2.06403 q^{58} -4.96652 q^{59} -4.48599 q^{60} +13.1518 q^{61} -10.0789 q^{62} -7.19464 q^{63} -9.92878 q^{64} -7.68481 q^{65} -3.94504 q^{66} -5.57884 q^{67} +5.52359 q^{68} -6.88619 q^{69} +15.4241 q^{70} -13.4857 q^{71} +1.24819 q^{72} +15.4969 q^{73} -14.3208 q^{74} +0.679130 q^{75} -8.24734 q^{76} +7.19638 q^{77} -5.40371 q^{78} -11.7254 q^{79} +8.23508 q^{80} +3.37178 q^{81} -13.9354 q^{82} -2.10811 q^{83} +5.75411 q^{84} -5.89862 q^{85} -19.2259 q^{86} -0.822287 q^{87} -1.24849 q^{88} +7.36039 q^{89} -11.5772 q^{90} +9.85721 q^{91} -18.9281 q^{92} +4.01532 q^{93} -4.72888 q^{94} +8.80730 q^{95} +6.67397 q^{96} +4.57610 q^{97} -5.33608 q^{98} -5.40155 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 103 q + q^{2} + 2 q^{3} + 127 q^{4} + 9 q^{5} + 19 q^{6} + 18 q^{7} + 149 q^{9}+O(q^{10}) $ 103 * q + q^2 + 2 * q^3 + 127 * q^4 + 9 * q^5 + 19 * q^6 + 18 * q^7 + 149 * q^9	\( 103 q + q^{2} + 2 q^{3} + 127 q^{4} + 9 q^{5} + 19 q^{6} + 18 q^{7} + 149 q^{9} + 20 q^{10} + 9 q^{11} + 36 q^{13} - 10 q^{14} + 16 q^{15} + 179 q^{16} + 21 q^{17} + 7 q^{18} + 42 q^{19} + 24 q^{20} + 28 q^{21} + 32 q^{22} + 25 q^{23} + 68 q^{24} + 194 q^{25} - 5 q^{26} + 14 q^{27} + 59 q^{28} - 103 q^{29} + 84 q^{30} + 34 q^{31} + 11 q^{32} + 42 q^{33} + 54 q^{34} + 35 q^{35} + 214 q^{36} + 34 q^{37} + 9 q^{38} + 23 q^{39} + 46 q^{40} + 16 q^{41} + 13 q^{42} + 68 q^{43} - 6 q^{44} + 25 q^{45} + 60 q^{46} + 6 q^{47} + 5 q^{48} + 257 q^{49} - 51 q^{50} + 68 q^{51} + 37 q^{52} + 35 q^{53} + 30 q^{54} + 66 q^{55} - 54 q^{56} + 78 q^{57} - q^{58} + 10 q^{59} - 24 q^{60} + 70 q^{61} + 29 q^{62} + 26 q^{63} + 276 q^{64} + 95 q^{65} + 77 q^{66} + 71 q^{67} - 21 q^{68} - 20 q^{69} + 48 q^{70} + 32 q^{71} + 32 q^{72} + 94 q^{73} + 35 q^{74} + 7 q^{75} + 134 q^{76} + 17 q^{77} + 58 q^{78} + 110 q^{79} + 78 q^{80} + 267 q^{81} - 71 q^{82} + 35 q^{83} + 96 q^{84} + 71 q^{85} + 33 q^{86} - 2 q^{87} + 100 q^{88} + 22 q^{89} - 134 q^{90} + 108 q^{91} - 11 q^{92} + 78 q^{93} + 90 q^{94} + 12 q^{95} + 177 q^{96} + 44 q^{97} - 18 q^{98} + 83 q^{99}+O(q^{100}) \) 103 * q + q^2 + 2 * q^3 + 127 * q^4 + 9 * q^5 + 19 * q^6 + 18 * q^7 + 149 * q^9 + 20 * q^10 + 9 * q^11 + 36 * q^13 - 10 * q^14 + 16 * q^15 + 179 * q^16 + 21 * q^17 + 7 * q^18 + 42 * q^19 + 24 * q^20 + 28 * q^21 + 32 * q^22 + 25 * q^23 + 68 * q^24 + 194 * q^25 - 5 * q^26 + 14 * q^27 + 59 * q^28 - 103 * q^29 + 84 * q^30 + 34 * q^31 + 11 * q^32 + 42 * q^33 + 54 * q^34 + 35 * q^35 + 214 * q^36 + 34 * q^37 + 9 * q^38 + 23 * q^39 + 46 * q^40 + 16 * q^41 + 13 * q^42 + 68 * q^43 - 6 * q^44 + 25 * q^45 + 60 * q^46 + 6 * q^47 + 5 * q^48 + 257 * q^49 - 51 * q^50 + 68 * q^51 + 37 * q^52 + 35 * q^53 + 30 * q^54 + 66 * q^55 - 54 * q^56 + 78 * q^57 - q^58 + 10 * q^59 - 24 * q^60 + 70 * q^61 + 29 * q^62 + 26 * q^63 + 276 * q^64 + 95 * q^65 + 77 * q^66 + 71 * q^67 - 21 * q^68 - 20 * q^69 + 48 * q^70 + 32 * q^71 + 32 * q^72 + 94 * q^73 + 35 * q^74 + 7 * q^75 + 134 * q^76 + 17 * q^77 + 58 * q^78 + 110 * q^79 + 78 * q^80 + 267 * q^81 - 71 * q^82 + 35 * q^83 + 96 * q^84 + 71 * q^85 + 33 * q^86 - 2 * q^87 + 100 * q^88 + 22 * q^89 - 134 * q^90 + 108 * q^91 - 11 * q^92 + 78 * q^93 + 90 * q^94 + 12 * q^95 + 177 * q^96 + 44 * q^97 - 18 * q^98 + 83 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.06403	−1.45949	−0.729746	−	0.683719i	$-0.760362\pi$
$2$	−2.06403	−1.45949	−0.729746	+	0.683719i	$0.760362\pi$
$3$	0.822287	0.474748	0.237374	−	0.971418i	$-0.423713\pi$
$3$	0.822287	0.474748	0.237374	+	0.971418i	$0.423713\pi$
$4$	2.26023	1.13012
$5$	−2.41369	−1.07944	−0.539718	−	0.841846i	$-0.681469\pi$
$5$	−2.41369	−1.07944	−0.539718	+	0.841846i	$0.681469\pi$
$6$	−1.69723	−0.692890
$7$	3.09601	1.17018	0.585091	−	0.810968i	$-0.301059\pi$
$7$	3.09601	1.17018	0.585091	+	0.810968i	$0.301059\pi$
$8$	−0.537124	−0.189902
$9$	−2.32384	−0.774615
$10$	4.98194	1.57543
$11$	2.32440	0.700834	0.350417	−	0.936594i	$-0.386040\pi$
$11$	2.32440	0.700834	0.350417	+	0.936594i	$0.386040\pi$
$12$	1.85856	0.536520
$13$	3.18384	0.883039	0.441520	−	0.897252i	$-0.354440\pi$
$13$	3.18384	0.883039	0.441520	+	0.897252i	$0.354440\pi$
$14$	−6.39026	−1.70787
$15$	−1.98475	−0.512460
$16$	−3.41182	−0.852955
$17$	2.44382	0.592713	0.296356	−	0.955077i	$-0.404228\pi$
$17$	2.44382	0.592713	0.296356	+	0.955077i	$0.404228\pi$
$18$	4.79649	1.13054
$19$	−3.64889	−0.837114	−0.418557	−	0.908191i	$-0.637464\pi$
$19$	−3.64889	−0.837114	−0.418557	+	0.908191i	$0.637464\pi$
$20$	−5.45550	−1.21989
$21$	2.54581	0.555541
$22$	−4.79765	−1.02286
$23$	−8.37443	−1.74619	−0.873095	−	0.487550i	$-0.837891\pi$
$23$	−8.37443	−1.74619	−0.873095	+	0.487550i	$0.837891\pi$
$24$	−0.441671	−0.0901556
$25$	0.825903	0.165181
$26$	−6.57156	−1.28879
$27$	−4.37773	−0.842494
$28$	6.99769	1.32244
$29$	−1.00000	−0.185695
$29$	−1.00000	−0.185695
$30$	4.09658	0.747930
$31$	4.88312	0.877033	0.438517	−	0.898723i	$-0.355504\pi$
$31$	4.88312	0.877033	0.438517	+	0.898723i	$0.355504\pi$
$32$	8.11635	1.43478
$33$	1.91133	0.332720
$34$	−5.04412	−0.865059
$35$	−7.47281	−1.26313
$36$	−5.25242	−0.875404
$37$	6.93825	1.14064	0.570321	−	0.821422i	$-0.306819\pi$
$37$	6.93825	1.14064	0.570321	+	0.821422i	$0.306819\pi$
$38$	7.53144	1.22176
$39$	2.61803	0.419221
$40$	1.29645	0.204987
$41$	6.75152	1.05441	0.527205	−	0.849738i	$-0.323240\pi$
$41$	6.75152	1.05441	0.527205	+	0.849738i	$0.323240\pi$
$42$	−5.25463	−0.810807
$43$	9.31473	1.42048	0.710241	−	0.703958i	$-0.248586\pi$
$43$	9.31473	1.42048	0.710241	+	0.703958i	$0.248586\pi$
$44$	5.25369	0.792024
$45$	5.60904	0.836146
$46$	17.2851	2.54855
$47$	2.29109	0.334189	0.167095	−	0.985941i	$-0.446561\pi$
$47$	2.29109	0.334189	0.167095	+	0.985941i	$0.446561\pi$
$48$	−2.80550	−0.404938
$49$	2.58527	0.369324
$50$	−1.70469	−0.241080
$51$	2.00952	0.281389
$52$	7.19622	0.997936
$53$	2.08926	0.286982	0.143491	−	0.989652i	$-0.454167\pi$
$53$	2.08926	0.286982	0.143491	+	0.989652i	$0.454167\pi$
$54$	9.03578	1.22961
$55$	−5.61039	−0.756505
$56$	−1.66294	−0.222220
$57$	−3.00044	−0.397418
$58$	2.06403	0.271021
$59$	−4.96652	−0.646586	−0.323293	−	0.946299i	$-0.604790\pi$
$59$	−4.96652	−0.646586	−0.323293	+	0.946299i	$0.604790\pi$
$60$	−4.48599	−0.579138
$61$	13.1518	1.68391	0.841957	−	0.539544i	$-0.181403\pi$
$61$	13.1518	1.68391	0.841957	+	0.539544i	$0.181403\pi$
$62$	−10.0789	−1.28002
$63$	−7.19464	−0.906439
$64$	−9.92878	−1.24110
$65$	−7.68481	−0.953184
$66$	−3.94504	−0.485601
$67$	−5.57884	−0.681564	−0.340782	−	0.940142i	$-0.610692\pi$
$67$	−5.57884	−0.681564	−0.340782	+	0.940142i	$0.610692\pi$
$68$	5.52359	0.669834
$69$	−6.88619	−0.829000
$70$	15.4241	1.84353
$71$	−13.4857	−1.60046	−0.800228	−	0.599696i	$-0.795288\pi$
$71$	−13.4857	−1.60046	−0.800228	+	0.599696i	$0.795288\pi$
$72$	1.24819	0.147101
$73$	15.4969	1.81377	0.906886	−	0.421377i	$-0.138453\pi$
$73$	15.4969	1.81377	0.906886	+	0.421377i	$0.138453\pi$
$74$	−14.3208	−1.66476
$75$	0.679130	0.0784191
$76$	−8.24734	−0.946035
$77$	7.19638	0.820103
$78$	−5.40371	−0.611849
$79$	−11.7254	−1.31921	−0.659606	−	0.751612i	$-0.729277\pi$
$79$	−11.7254	−1.31921	−0.659606	+	0.751612i	$0.729277\pi$
$80$	8.23508	0.920709
$81$	3.37178	0.374642
$82$	−13.9354	−1.53890
$83$	−2.10811	−0.231395	−0.115698	−	0.993284i	$-0.536910\pi$
$83$	−2.10811	−0.231395	−0.115698	+	0.993284i	$0.536910\pi$
$84$	5.75411	0.627825
$85$	−5.89862	−0.639795
$86$	−19.2259	−2.07318
$87$	−0.822287	−0.0881585
$88$	−1.24849	−0.133090
$89$	7.36039	0.780200	0.390100	−	0.920773i	$-0.372440\pi$
$89$	7.36039	0.780200	0.390100	+	0.920773i	$0.372440\pi$
$90$	−11.5772	−1.22035
$91$	9.85721	1.03332
$92$	−18.9281	−1.97340
$93$	4.01532	0.416370
$94$	−4.72888	−0.487746
$95$	8.80730	0.903610
$96$	6.67397	0.681160
$97$	4.57610	0.464633	0.232316	−	0.972640i	$-0.425370\pi$
$97$	4.57610	0.464633	0.232316	+	0.972640i	$0.425370\pi$
$98$	−5.33608	−0.539025
$99$	−5.40155	−0.542877
$100$	1.86673	0.186673
$101$	−8.74385	−0.870046	−0.435023	−	0.900419i	$-0.643260\pi$
$101$	−8.74385	−0.870046	−0.435023	+	0.900419i	$0.643260\pi$
$102$	−4.14771	−0.410685
$103$	−13.2136	−1.30198	−0.650990	−	0.759087i	$-0.725646\pi$
$103$	−13.2136	−1.30198	−0.650990	+	0.759087i	$0.725646\pi$
$104$	−1.71012	−0.167691
$105$	−6.14479	−0.599671
$106$	−4.31230	−0.418847
$107$	2.45905	0.237726	0.118863	−	0.992911i	$-0.462075\pi$
$107$	2.45905	0.237726	0.118863	+	0.992911i	$0.462075\pi$
$108$	−9.89468	−0.952116
$109$	−4.51998	−0.432936	−0.216468	−	0.976290i	$-0.569454\pi$
$109$	−4.51998	−0.432936	−0.216468	+	0.976290i	$0.569454\pi$
$110$	11.5800	1.10411
$111$	5.70524	0.541517
$112$	−10.5630	−0.998112
$113$	5.50514	0.517880	0.258940	−	0.965893i	$-0.416627\pi$
$113$	5.50514	0.517880	0.258940	+	0.965893i	$0.416627\pi$
$114$	6.19300	0.580028
$115$	20.2133	1.88490
$116$	−2.26023	−0.209857
$117$	−7.39875	−0.684015
$118$	10.2511	0.943687
$119$	7.56608	0.693581
$120$	1.06606	0.0973172
$121$	−5.59714	−0.508831
$122$	−27.1457	−2.45766
$123$	5.55169	0.500579
$124$	11.0370	0.991149
$125$	10.0750	0.901134
$126$	14.8500	1.32294
$127$	−18.2608	−1.62039	−0.810193	−	0.586164i	$-0.800638\pi$
$127$	−18.2608	−1.62039	−0.810193	+	0.586164i	$0.800638\pi$
$128$	4.26062	0.376589
$129$	7.65938	0.674371
$130$	15.8617	1.39116
$131$	−17.5788	−1.53587	−0.767933	−	0.640530i	$-0.778715\pi$
$131$	−17.5788	−1.53587	−0.767933	+	0.640530i	$0.778715\pi$
$132$	4.32004	0.376012
$133$	−11.2970	−0.979575
$134$	11.5149	0.994737
$135$	10.5665	0.909418
$136$	−1.31263	−0.112557
$137$	5.15232	0.440192	0.220096	−	0.975478i	$-0.429363\pi$
$137$	5.15232	0.440192	0.220096	+	0.975478i	$0.429363\pi$
$138$	14.2133	1.20992
$139$	1.00000	0.0848189
$139$	1.00000	0.0848189
$140$	−16.8903	−1.42749
$141$	1.88393	0.158656
$142$	27.8349	2.33585
$143$	7.40054	0.618864
$144$	7.92853	0.660711
$145$	2.41369	0.200446
$146$	−31.9860	−2.64718
$147$	2.12583	0.175336
$148$	15.6820	1.28906
$149$	−9.63845	−0.789613	−0.394806	−	0.918764i	$-0.629188\pi$
$149$	−9.63845	−0.789613	−0.394806	+	0.918764i	$0.629188\pi$
$150$	−1.40175	−0.114452
$151$	18.8048	1.53031	0.765154	−	0.643847i	$-0.222663\pi$
$151$	18.8048	1.53031	0.765154	+	0.643847i	$0.222663\pi$
$152$	1.95991	0.158970
$153$	−5.67905	−0.459124
$154$	−14.8536	−1.19693
$155$	−11.7863	−0.946701
$156$	5.91736	0.473768
$157$	23.9948	1.91499	0.957496	−	0.288446i	$-0.0931387\pi$
$157$	23.9948	1.91499	0.957496	+	0.288446i	$0.0931387\pi$
$158$	24.2016	1.92538
$159$	1.71797	0.136244
$160$	−19.5904	−1.54875
$161$	−25.9273	−2.04336
$162$	−6.95946	−0.546787
$163$	14.6753	1.14946	0.574731	−	0.818343i	$-0.305107\pi$
$163$	14.6753	1.14946	0.574731	+	0.818343i	$0.305107\pi$
$164$	15.2600	1.19160
$165$	−4.61336	−0.359149
$166$	4.35121	0.337720
$167$	14.9449	1.15647	0.578237	−	0.815869i	$-0.303741\pi$
$167$	14.9449	1.15647	0.578237	+	0.815869i	$0.303741\pi$
$168$	−1.36742	−0.105498
$169$	−2.86314	−0.220242
$170$	12.1749	0.933775
$171$	8.47946	0.648440
$172$	21.0534	1.60531
$173$	16.4205	1.24843	0.624214	−	0.781253i	$-0.285419\pi$
$173$	16.4205	1.24843	0.624214	+	0.781253i	$0.285419\pi$
$174$	1.69723	0.128667
$175$	2.55700	0.193291
$176$	−7.93045	−0.597780
$177$	−4.08391	−0.306965
$178$	−15.1921	−1.13869
$179$	−17.1696	−1.28332	−0.641658	−	0.766991i	$-0.721753\pi$
$179$	−17.1696	−1.28332	−0.641658	+	0.766991i	$0.721753\pi$
$180$	12.6777	0.944942
$181$	22.8138	1.69574	0.847868	−	0.530208i	$-0.177886\pi$
$181$	22.8138	1.69574	0.847868	+	0.530208i	$0.177886\pi$
$182$	−20.3456	−1.50812
$183$	10.8146	0.799435
$184$	4.49811	0.331605
$185$	−16.7468	−1.23125
$186$	−8.28776	−0.607688
$187$	5.68042	0.415393
$188$	5.17838	0.377672
$189$	−13.5535	−0.985871
$190$	−18.1786	−1.31881
$191$	−7.30874	−0.528842	−0.264421	−	0.964407i	$-0.585181\pi$
$191$	−7.30874	−0.528842	−0.264421	+	0.964407i	$0.585181\pi$
$192$	−8.16431	−0.589208
$193$	20.0498	1.44321	0.721607	−	0.692302i	$-0.243404\pi$
$193$	20.0498	1.44321	0.721607	+	0.692302i	$0.243404\pi$
$194$	−9.44523	−0.678128
$195$	−6.31912	−0.452522
$196$	5.84330	0.417379
$197$	4.35121	0.310011	0.155006	−	0.987914i	$-0.450460\pi$
$197$	4.35121	0.310011	0.155006	+	0.987914i	$0.450460\pi$
$198$	11.1490	0.792324
$199$	−10.7102	−0.759229	−0.379615	−	0.925145i	$-0.623943\pi$
$199$	−10.7102	−0.759229	−0.379615	+	0.925145i	$0.623943\pi$
$200$	−0.443613	−0.0313682
$201$	−4.58741	−0.323571
$202$	18.0476	1.26982
$203$	−3.09601	−0.217297
$204$	4.54198	0.318002
$205$	−16.2961	−1.13817
$206$	27.2734	1.90023
$207$	19.4609	1.35262
$208$	−10.8627	−0.753192
$209$	−8.48151	−0.586678
$210$	12.6831	0.875214
$211$	−23.7142	−1.63255	−0.816277	−	0.577661i	$-0.803966\pi$
$211$	−23.7142	−1.63255	−0.816277	+	0.577661i	$0.803966\pi$
$212$	4.72220	0.324322
$213$	−11.0891	−0.759813
$214$	−5.07556	−0.346958
$215$	−22.4829	−1.53332
$216$	2.35138	0.159991
$217$	15.1182	1.02629
$218$	9.32940	0.631866
$219$	12.7429	0.861084
$220$	−12.6808	−0.854938
$221$	7.78073	0.523388
$222$	−11.7758	−0.790339
$223$	18.3565	1.22924	0.614620	−	0.788824i	$-0.289309\pi$
$223$	18.3565	1.22924	0.614620	+	0.788824i	$0.289309\pi$
$224$	25.1283	1.67896
$225$	−1.91927	−0.127951
$226$	−11.3628	−0.755841
$227$	23.2208	1.54122	0.770610	−	0.637307i	$-0.219952\pi$
$227$	23.2208	1.54122	0.770610	+	0.637307i	$0.219952\pi$
$228$	−6.78168	−0.449128
$229$	14.3468	0.948060	0.474030	−	0.880509i	$-0.342799\pi$
$229$	14.3468	0.948060	0.474030	+	0.880509i	$0.342799\pi$
$230$	−41.7209	−2.75099
$231$	5.91749	0.389342
$232$	0.537124	0.0352639
$233$	15.0621	0.986752	0.493376	−	0.869816i	$-0.335763\pi$
$233$	15.0621	0.986752	0.493376	+	0.869816i	$0.335763\pi$
$234$	15.2713	0.998314
$235$	−5.52997	−0.360736
$236$	−11.2255	−0.730717
$237$	−9.64165	−0.626293
$238$	−15.6166	−1.01228
$239$	13.8449	0.895551	0.447775	−	0.894146i	$-0.352216\pi$
$239$	13.8449	0.895551	0.447775	+	0.894146i	$0.352216\pi$
$240$	6.77160	0.437105
$241$	4.36295	0.281042	0.140521	−	0.990078i	$-0.455122\pi$
$241$	4.36295	0.281042	0.140521	+	0.990078i	$0.455122\pi$
$242$	11.5527	0.742635
$243$	15.9058	1.02035
$244$	29.7261	1.90302
$245$	−6.24004	−0.398661
$246$	−11.4589	−0.730591
$247$	−11.6175	−0.739204
$248$	−2.62284	−0.166551
$249$	−1.73347	−0.109854
$250$	−20.7951	−1.31520
$251$	16.5461	1.04438	0.522189	−	0.852830i	$-0.325116\pi$
$251$	16.5461	1.04438	0.522189	+	0.852830i	$0.325116\pi$
$252$	−16.2615	−1.02438
$253$	−19.4656	−1.22379
$254$	37.6909	2.36494
$255$	−4.85036	−0.303741
$256$	11.0635	0.691469
$257$	5.17431	0.322765	0.161382	−	0.986892i	$-0.448405\pi$
$257$	5.17431	0.322765	0.161382	+	0.986892i	$0.448405\pi$
$258$	−15.8092	−0.984239
$259$	21.4809	1.33476
$260$	−17.3694	−1.07721
$261$	2.32384	0.143842
$262$	36.2832	2.24158
$263$	4.96116	0.305918	0.152959	−	0.988233i	$-0.451120\pi$
$263$	4.96116	0.305918	0.152959	+	0.988233i	$0.451120\pi$
$264$	−1.02662	−0.0631842
$265$	−5.04282	−0.309778
$266$	23.3174	1.42968
$267$	6.05236	0.370398
$268$	−12.6095	−0.770246
$269$	23.6305	1.44078	0.720388	−	0.693571i	$-0.243964\pi$
$269$	23.6305	1.44078	0.720388	+	0.693571i	$0.243964\pi$
$270$	−21.8096	−1.32729
$271$	27.4918	1.67001	0.835003	−	0.550245i	$-0.185466\pi$
$271$	27.4918	1.67001	0.835003	+	0.550245i	$0.185466\pi$
$272$	−8.33786	−0.505557
$273$	8.10545	0.490564
$274$	−10.6346	−0.642457
$275$	1.91973	0.115764
$276$	−15.5644	−0.936865
$277$	−20.4273	−1.22736	−0.613678	−	0.789557i	$-0.710311\pi$
$277$	−20.4273	−1.22736	−0.613678	+	0.789557i	$0.710311\pi$
$278$	−2.06403	−0.123792
$279$	−11.3476	−0.679363
$280$	4.01383	0.239872
$281$	−22.8001	−1.36014	−0.680070	−	0.733147i	$-0.738051\pi$
$281$	−22.8001	−1.36014	−0.680070	+	0.733147i	$0.738051\pi$
$282$	−3.88850	−0.231557
$283$	16.8021	0.998783	0.499392	−	0.866376i	$-0.333557\pi$
$283$	16.8021	0.998783	0.499392	+	0.866376i	$0.333557\pi$
$284$	−30.4807	−1.80870
$285$	7.24213	0.428987
$286$	−15.2750	−0.903227
$287$	20.9028	1.23385
$288$	−18.8611	−1.11140
$289$	−11.0278	−0.648692
$290$	−4.98194	−0.292549
$291$	3.76287	0.220583
$292$	35.0265	2.04977
$293$	−11.3315	−0.661996	−0.330998	−	0.943631i	$-0.607385\pi$
$293$	−11.3315	−0.661996	−0.330998	+	0.943631i	$0.607385\pi$
$294$	−4.38779	−0.255901
$295$	11.9876	0.697948
$296$	−3.72670	−0.216610
$297$	−10.1756	−0.590449
$298$	19.8941	1.15243
$299$	−26.6629	−1.54195
$300$	1.53499	0.0886227
$301$	28.8385	1.66222
$302$	−38.8136	−2.23347
$303$	−7.18996	−0.413052
$304$	12.4494	0.714020
$305$	−31.7444	−1.81768
$306$	11.7217	0.670087
$307$	−3.75012	−0.214031	−0.107015	−	0.994257i	$-0.534129\pi$
$307$	−3.75012	−0.214031	−0.107015	+	0.994257i	$0.534129\pi$
$308$	16.2655	0.926811
$309$	−10.8654	−0.618112
$310$	24.3274	1.38170
$311$	−8.84969	−0.501820	−0.250910	−	0.968010i	$-0.580730\pi$
$311$	−8.84969	−0.501820	−0.250910	+	0.968010i	$0.580730\pi$
$312$	−1.40621	−0.0796110
$313$	16.4491	0.929758	0.464879	−	0.885374i	$-0.346098\pi$
$313$	16.4491	0.929758	0.464879	+	0.885374i	$0.346098\pi$
$314$	−49.5260	−2.79491
$315$	17.3656	0.978443
$316$	−26.5021	−1.49086
$317$	−33.8464	−1.90100	−0.950501	−	0.310722i	$-0.899429\pi$
$317$	−33.8464	−1.90100	−0.950501	+	0.310722i	$0.899429\pi$
$318$	−3.54595	−0.198847
$319$	−2.32440	−0.130142
$320$	23.9650	1.33968
$321$	2.02205	0.112860
$322$	53.5148	2.98226
$323$	−8.91723	−0.496168
$324$	7.62100	0.423389
$325$	2.62955	0.145861
$326$	−30.2904	−1.67763
$327$	−3.71673	−0.205535
$328$	−3.62641	−0.200235
$329$	7.09322	0.391062
$330$	9.52212	0.524175
$331$	22.0124	1.20991	0.604956	−	0.796259i	$-0.293191\pi$
$331$	22.0124	1.20991	0.604956	+	0.796259i	$0.293191\pi$
$332$	−4.76482	−0.261504
$333$	−16.1234	−0.883557
$334$	−30.8468	−1.68786
$335$	13.4656	0.735705
$336$	−8.68584	−0.473851
$337$	34.2661	1.86659	0.933297	−	0.359106i	$-0.116919\pi$
$337$	34.2661	1.86659	0.933297	+	0.359106i	$0.116919\pi$
$338$	5.90962	0.321441
$339$	4.52680	0.245862
$340$	−13.3322	−0.723042
$341$	11.3503	0.614655
$342$	−17.5019	−0.946393
$343$	−13.6680	−0.738005
$344$	−5.00317	−0.269753
$345$	16.6211	0.894852
$346$	−33.8925	−1.82207
$347$	−13.3631	−0.717368	−0.358684	−	0.933459i	$-0.616775\pi$
$347$	−13.3631	−0.717368	−0.358684	+	0.933459i	$0.616775\pi$
$348$	−1.85856	−0.0996292
$349$	−9.86643	−0.528138	−0.264069	−	0.964504i	$-0.585065\pi$
$349$	−9.86643	−0.528138	−0.264069	+	0.964504i	$0.585065\pi$
$350$	−5.27774	−0.282107
$351$	−13.9380	−0.743956
$352$	18.8657	1.00554
$353$	7.20343	0.383400	0.191700	−	0.981454i	$-0.438600\pi$
$353$	7.20343	0.383400	0.191700	+	0.981454i	$0.438600\pi$
$354$	8.42932	0.448013
$355$	32.5502	1.72759
$356$	16.6362	0.881716
$357$	6.22149	0.329276
$358$	35.4386	1.87299
$359$	2.01922	0.106570	0.0532852	−	0.998579i	$-0.483031\pi$
$359$	2.01922	0.106570	0.0532852	+	0.998579i	$0.483031\pi$
$360$	−3.01275	−0.158786
$361$	−5.68557	−0.299241
$362$	−47.0884	−2.47491
$363$	−4.60246	−0.241566
$364$	22.2796	1.16777
$365$	−37.4047	−1.95785
$366$	−22.3216	−1.16677
$367$	−20.1424	−1.05143	−0.525713	−	0.850662i	$-0.676202\pi$
$367$	−20.1424	−1.05143	−0.525713	+	0.850662i	$0.676202\pi$
$368$	28.5720	1.48942
$369$	−15.6895	−0.816761
$370$	34.5659	1.79700
$371$	6.46836	0.335821
$372$	9.07556	0.470546
$373$	0.839405	0.0434627	0.0217314	−	0.999764i	$-0.493082\pi$
$373$	0.839405	0.0434627	0.0217314	+	0.999764i	$0.493082\pi$
$374$	−11.7246	−0.606263
$375$	8.28453	0.427811
$376$	−1.23060	−0.0634633
$377$	−3.18384	−0.163976
$378$	27.9748	1.43887
$379$	12.9819	0.666837	0.333419	−	0.942779i	$-0.391798\pi$
$379$	12.9819	0.666837	0.333419	+	0.942779i	$0.391798\pi$
$380$	19.9065	1.02118
$381$	−15.0156	−0.769274
$382$	15.0855	0.771840
$383$	−10.7559	−0.549599	−0.274799	−	0.961502i	$-0.588611\pi$
$383$	−10.7559	−0.549599	−0.274799	+	0.961502i	$0.588611\pi$
$384$	3.50345	0.178785
$385$	−17.3698	−0.885248
$386$	−41.3834	−2.10636
$387$	−21.6460	−1.10033
$388$	10.3430	0.525089
$389$	16.7535	0.849435	0.424718	−	0.905326i	$-0.360373\pi$
$389$	16.7535	0.849435	0.424718	+	0.905326i	$0.360373\pi$
$390$	13.0429	0.660452
$391$	−20.4656	−1.03499
$392$	−1.38861	−0.0701354
$393$	−14.4548	−0.729149
$394$	−8.98105	−0.452459
$395$	28.3015	1.42400
$396$	−12.2088	−0.613513
$397$	36.5318	1.83348	0.916740	−	0.399485i	$-0.130811\pi$
$397$	36.5318	1.83348	0.916740	+	0.399485i	$0.130811\pi$
$398$	22.1063	1.10809
$399$	−9.28939	−0.465051
$400$	−2.81783	−0.140892
$401$	0.667062	0.0333115	0.0166557	−	0.999861i	$-0.494698\pi$
$401$	0.667062	0.0333115	0.0166557	+	0.999861i	$0.494698\pi$
$402$	9.46857	0.472249
$403$	15.5471	0.774455
$404$	−19.7631	−0.983252
$405$	−8.13843	−0.404402
$406$	6.39026	0.317143
$407$	16.1273	0.799401
$408$	−1.07936	−0.0534364
$409$	−7.97077	−0.394129	−0.197065	−	0.980390i	$-0.563141\pi$
$409$	−7.97077	−0.394129	−0.197065	+	0.980390i	$0.563141\pi$
$410$	33.6356	1.66115
$411$	4.23669	0.208980
$412$	−29.8659	−1.47139
$413$	−15.3764	−0.756623
$414$	−40.1679	−1.97414
$415$	5.08833	0.249776
$416$	25.8412	1.26697
$417$	0.822287	0.0402676
$418$	17.5061	0.856252
$419$	−3.08032	−0.150483	−0.0752417	−	0.997165i	$-0.523973\pi$
$419$	−3.08032	−0.150483	−0.0752417	+	0.997165i	$0.523973\pi$
$420$	−13.8887	−0.677697
$421$	34.4849	1.68069	0.840345	−	0.542053i	$-0.182353\pi$
$421$	34.4849	1.68069	0.840345	+	0.542053i	$0.182353\pi$
$422$	48.9469	2.38270
$423$	−5.32413	−0.258868
$424$	−1.12219	−0.0544984
$425$	2.01836	0.0979046
$426$	22.8883	1.10894
$427$	40.7181	1.97049
$428$	5.55802	0.268657
$429$	6.08537	0.293804
$430$	46.4054	2.23787
$431$	17.2898	0.832820	0.416410	−	0.909177i	$-0.363288\pi$
$431$	17.2898	0.832820	0.416410	+	0.909177i	$0.363288\pi$
$432$	14.9360	0.718610
$433$	−4.34020	−0.208577	−0.104288	−	0.994547i	$-0.533256\pi$
$433$	−4.34020	−0.208577	−0.104288	+	0.994547i	$0.533256\pi$
$434$	−31.2044	−1.49786
$435$	1.98475	0.0951613
$436$	−10.2162	−0.489268
$437$	30.5574	1.46176
$438$	−26.3017	−1.25674
$439$	3.20667	0.153046	0.0765229	−	0.997068i	$-0.475618\pi$
$439$	3.20667	0.153046	0.0765229	+	0.997068i	$0.475618\pi$
$440$	3.01348	0.143662
$441$	−6.00776	−0.286084
$442$	−16.0597	−0.763881
$443$	7.18935	0.341576	0.170788	−	0.985308i	$-0.445369\pi$
$443$	7.18935	0.341576	0.170788	+	0.985308i	$0.445369\pi$
$444$	12.8951	0.611977
$445$	−17.7657	−0.842175
$446$	−37.8883	−1.79406
$447$	−7.92558	−0.374867
$448$	−30.7396	−1.45231
$449$	8.00576	0.377815	0.188907	−	0.981995i	$-0.439505\pi$
$449$	8.00576	0.377815	0.188907	+	0.981995i	$0.439505\pi$
$450$	3.96144	0.186744
$451$	15.6933	0.738967
$452$	12.4429	0.585264
$453$	15.4629	0.726511
$454$	−47.9285	−2.24940
$455$	−23.7922	−1.11540
$456$	1.61161	0.0754705
$457$	−3.60999	−0.168868	−0.0844342	−	0.996429i	$-0.526908\pi$
$457$	−3.60999	−0.168868	−0.0844342	+	0.996429i	$0.526908\pi$
$458$	−29.6122	−1.38369
$459$	−10.6984	−0.499357
$460$	45.6867	2.13015
$461$	36.9051	1.71884	0.859422	−	0.511268i	$-0.170824\pi$
$461$	36.9051	1.71884	0.859422	+	0.511268i	$0.170824\pi$
$462$	−12.2139	−0.568242
$463$	23.2672	1.08132	0.540659	−	0.841242i	$-0.318175\pi$
$463$	23.2672	1.08132	0.540659	+	0.841242i	$0.318175\pi$
$464$	3.41182	0.158390
$465$	−9.69175	−0.449444
$466$	−31.0887	−1.44016
$467$	−4.07371	−0.188509	−0.0942544	−	0.995548i	$-0.530047\pi$
$467$	−4.07371	−0.188509	−0.0942544	+	0.995548i	$0.530047\pi$
$468$	−16.7229	−0.773016
$469$	−17.2722	−0.797554
$470$	11.4140	0.526491
$471$	19.7306	0.909138
$472$	2.66764	0.122788
$473$	21.6512	0.995523
$474$	19.9007	0.914069
$475$	−3.01363	−0.138275
$476$	17.1011	0.783827
$477$	−4.85511	−0.222300
$478$	−28.5763	−1.30705
$479$	−0.387003	−0.0176826	−0.00884130	−	0.999961i	$-0.502814\pi$
$479$	−0.387003	−0.0176826	−0.00884130	+	0.999961i	$0.502814\pi$
$480$	−16.1089	−0.735268
$481$	22.0903	1.00723
$482$	−9.00527	−0.410179
$483$	−21.3197	−0.970080
$484$	−12.6508	−0.575038
$485$	−11.0453	−0.501541
$486$	−32.8300	−1.48920
$487$	8.20371	0.371745	0.185873	−	0.982574i	$-0.440489\pi$
$487$	8.20371	0.371745	0.185873	+	0.982574i	$0.440489\pi$
$488$	−7.06415	−0.319779
$489$	12.0673	0.545704
$490$	12.8796	0.581843
$491$	−25.9235	−1.16991	−0.584955	−	0.811065i	$-0.698888\pi$
$491$	−25.9235	−1.16991	−0.584955	+	0.811065i	$0.698888\pi$
$492$	12.5481	0.565712
$493$	−2.44382	−0.110064
$494$	23.9789	1.07886
$495$	13.0377	0.586000
$496$	−16.6603	−0.748070
$497$	−41.7518	−1.87282
$498$	3.57795	0.160332
$499$	13.7239	0.614368	0.307184	−	0.951650i	$-0.400613\pi$
$499$	13.7239	0.614368	0.307184	+	0.951650i	$0.400613\pi$
$500$	22.7718	1.01838
$501$	12.2890	0.549033
$502$	−34.1516	−1.52426
$503$	4.74127	0.211403	0.105701	−	0.994398i	$-0.466291\pi$
$503$	4.74127	0.211403	0.105701	+	0.994398i	$0.466291\pi$
$504$	3.86442	0.172135
$505$	21.1050	0.939158
$506$	40.1776	1.78611
$507$	−2.35433	−0.104559
$508$	−41.2737	−1.83122
$509$	−0.334660	−0.0148335	−0.00741677	−	0.999972i	$-0.502361\pi$
$509$	−0.334660	−0.0148335	−0.00741677	+	0.999972i	$0.502361\pi$
$510$	10.0113	0.443308
$511$	47.9784	2.12244
$512$	−31.3567	−1.38578
$513$	15.9739	0.705264
$514$	−10.6800	−0.471073
$515$	31.8937	1.40540
$516$	17.3120	0.762117
$517$	5.32541	0.234211
$518$	−44.3372	−1.94807
$519$	13.5024	0.592689
$520$	4.12770	0.181012
$521$	−18.2797	−0.800850	−0.400425	−	0.916330i	$-0.631138\pi$
$521$	−18.2797	−0.800850	−0.400425	+	0.916330i	$0.631138\pi$
$522$	−4.79649	−0.209937
$523$	−20.3788	−0.891102	−0.445551	−	0.895257i	$-0.646992\pi$
$523$	−20.3788	−0.891102	−0.445551	+	0.895257i	$0.646992\pi$
$524$	−39.7321	−1.73571
$525$	2.10259	0.0917646
$526$	−10.2400	−0.446485
$527$	11.9334	0.519829
$528$	−6.52111	−0.283795
$529$	47.1311	2.04918
$530$	10.4085	0.452119
$531$	11.5414	0.500855
$532$	−25.5338	−1.10703
$533$	21.4958	0.931085
$534$	−12.4923	−0.540593
$535$	−5.93539	−0.256609
$536$	2.99653	0.129431
$537$	−14.1183	−0.609252
$538$	−48.7741	−2.10280
$539$	6.00921	0.258835
$540$	23.8827	1.02775
$541$	39.0544	1.67908	0.839540	−	0.543298i	$-0.182825\pi$
$541$	39.0544	1.67908	0.839540	+	0.543298i	$0.182825\pi$
$542$	−56.7439	−2.43736
$543$	18.7595	0.805047
$544$	19.8349	0.850414
$545$	10.9098	0.467326
$546$	−16.7299	−0.715975
$547$	−28.0522	−1.19942	−0.599712	−	0.800216i	$-0.704718\pi$
$547$	−28.0522	−1.19942	−0.599712	+	0.800216i	$0.704718\pi$
$548$	11.6454	0.497468
$549$	−30.5627	−1.30438
$550$	−3.96239	−0.168957
$551$	3.64889	0.155448
$552$	3.69874	0.157429
$553$	−36.3020	−1.54372
$554$	42.1625	1.79132
$555$	−13.7707	−0.584533
$556$	2.26023	0.0958551
$557$	14.4791	0.613499	0.306750	−	0.951790i	$-0.400759\pi$
$557$	14.4791	0.613499	0.306750	+	0.951790i	$0.400759\pi$
$558$	23.4218	0.991524
$559$	29.6566	1.25434
$560$	25.4959	1.07740
$561$	4.67094	0.197207
$562$	47.0602	1.98511
$563$	−32.8847	−1.38593	−0.692963	−	0.720974i	$-0.743695\pi$
$563$	−32.8847	−1.38593	−0.692963	+	0.720974i	$0.743695\pi$
$564$	4.25812	0.179299
$565$	−13.2877	−0.559018
$566$	−34.6802	−1.45772
$567$	10.4391	0.438399
$568$	7.24348	0.303930
$569$	35.3676	1.48269	0.741344	−	0.671125i	$-0.234189\pi$
$569$	35.3676	1.48269	0.741344	+	0.671125i	$0.234189\pi$
$570$	−14.9480	−0.626103
$571$	19.2363	0.805016	0.402508	−	0.915417i	$-0.368139\pi$
$571$	19.2363	0.805016	0.402508	+	0.915417i	$0.368139\pi$
$572$	16.7269	0.699388
$573$	−6.00988	−0.251066
$574$	−43.1440	−1.80079
$575$	−6.91647	−0.288437
$576$	23.0729	0.961372
$577$	−13.3889	−0.557388	−0.278694	−	0.960380i	$-0.589902\pi$
$577$	−13.3889	−0.557388	−0.278694	+	0.960380i	$0.589902\pi$
$578$	22.7617	0.946760
$579$	16.4867	0.685163
$580$	5.45550	0.226527
$581$	−6.52674	−0.270775
$582$	−7.76669	−0.321940
$583$	4.85628	0.201127
$584$	−8.32375	−0.344439
$585$	17.8583	0.738350
$586$	23.3887	0.966178
$587$	8.15824	0.336727	0.168363	−	0.985725i	$-0.446152\pi$
$587$	8.15824	0.336727	0.168363	+	0.985725i	$0.446152\pi$
$588$	4.80487	0.198150
$589$	−17.8180	−0.734177
$590$	−24.7429	−1.01865
$591$	3.57795	0.147177
$592$	−23.6721	−0.972915
$593$	−0.233039	−0.00956976	−0.00478488	−	0.999989i	$-0.501523\pi$
$593$	−0.233039	−0.00956976	−0.00478488	+	0.999989i	$0.501523\pi$
$594$	21.0028	0.861755
$595$	−18.2622	−0.748676
$596$	−21.7851	−0.892353
$597$	−8.80690	−0.360443
$598$	55.0331	2.25047
$599$	−28.8520	−1.17886	−0.589430	−	0.807820i	$-0.700648\pi$
$599$	−28.8520	−1.17886	−0.589430	+	0.807820i	$0.700648\pi$
$600$	−0.364777	−0.0148920
$601$	25.9631	1.05906	0.529529	−	0.848292i	$-0.322369\pi$
$601$	25.9631	1.05906	0.529529	+	0.848292i	$0.322369\pi$
$602$	−59.5236	−2.42600
$603$	12.9644	0.527950
$604$	42.5031	1.72943
$605$	13.5098	0.549250
$606$	14.8403	0.602846
$607$	8.19767	0.332733	0.166367	−	0.986064i	$-0.446797\pi$
$607$	8.19767	0.332733	0.166367	+	0.986064i	$0.446797\pi$
$608$	−29.6157	−1.20108
$609$	−2.54581	−0.103161
$610$	65.5214	2.65288
$611$	7.29446	0.295102
$612$	−12.8360	−0.518863
$613$	−28.7890	−1.16278	−0.581388	−	0.813627i	$-0.697490\pi$
$613$	−28.7890	−1.16278	−0.581388	+	0.813627i	$0.697490\pi$
$614$	7.74038	0.312376
$615$	−13.4001	−0.540342
$616$	−3.86535	−0.155739
$617$	36.2468	1.45924	0.729621	−	0.683852i	$-0.239696\pi$
$617$	36.2468	1.45924	0.729621	+	0.683852i	$0.239696\pi$
$618$	22.4266	0.902129
$619$	35.2183	1.41554	0.707772	−	0.706441i	$-0.249701\pi$
$619$	35.2183	1.41554	0.707772	+	0.706441i	$0.249701\pi$
$620$	−26.6398	−1.06988
$621$	36.6610	1.47116
$622$	18.2660	0.732402
$623$	22.7878	0.912975
$624$	−8.93226	−0.357576
$625$	−28.4474	−1.13790
$626$	−33.9515	−1.35697
$627$	−6.97424	−0.278524
$628$	54.2337	2.16416
$629$	16.9558	0.676073
$630$	−35.8432	−1.42803
$631$	−2.62089	−0.104336	−0.0521681	−	0.998638i	$-0.516613\pi$
$631$	−2.62089	−0.104336	−0.0521681	+	0.998638i	$0.516613\pi$
$632$	6.29800	0.250521
$633$	−19.4999	−0.775051
$634$	69.8600	2.77450
$635$	44.0760	1.74910
$636$	3.88301	0.153971
$637$	8.23109	0.326128
$638$	4.79765	0.189941
$639$	31.3386	1.23974
$640$	−10.2838	−0.406504
$641$	−3.55468	−0.140402	−0.0702008	−	0.997533i	$-0.522364\pi$
$641$	−3.55468	−0.140402	−0.0702008	+	0.997533i	$0.522364\pi$
$642$	−4.17357	−0.164718
$643$	−43.8073	−1.72759	−0.863796	−	0.503842i	$-0.831919\pi$
$643$	−43.8073	−1.72759	−0.863796	+	0.503842i	$0.831919\pi$
$644$	−58.6017	−2.30923
$645$	−18.4874	−0.727940
$646$	18.4054	0.724153
$647$	25.5334	1.00382	0.501910	−	0.864920i	$-0.332631\pi$
$647$	25.5334	1.00382	0.501910	+	0.864920i	$0.332631\pi$
$648$	−1.81107	−0.0711454
$649$	−11.5442	−0.453150
$650$	−5.42747	−0.212883
$651$	12.4315	0.487228
$652$	33.1697	1.29902
$653$	38.6946	1.51424	0.757118	−	0.653278i	$-0.226607\pi$
$653$	38.6946	1.51424	0.757118	+	0.653278i	$0.226607\pi$
$654$	7.67144	0.299977
$655$	42.4298	1.65787
$656$	−23.0350	−0.899364
$657$	−36.0123	−1.40497
$658$	−14.6406	−0.570752
$659$	1.38136	0.0538101	0.0269050	−	0.999638i	$-0.491435\pi$
$659$	1.38136	0.0538101	0.0269050	+	0.999638i	$0.491435\pi$
$660$	−10.4272	−0.405880
$661$	−32.9531	−1.28173	−0.640864	−	0.767655i	$-0.721424\pi$
$661$	−32.9531	−1.28173	−0.640864	+	0.767655i	$0.721424\pi$
$662$	−45.4343	−1.76586
$663$	6.39799	0.248478
$664$	1.13232	0.0439425
$665$	27.2675	1.05739
$666$	33.2792	1.28954
$667$	8.37443	0.324259
$668$	33.7790	1.30695
$669$	15.0943	0.583579
$670$	−27.7935	−1.07375
$671$	30.5701	1.18015
$672$	20.6627	0.797080
$673$	−5.83078	−0.224760	−0.112380	−	0.993665i	$-0.535847\pi$
$673$	−5.83078	−0.224760	−0.112380	+	0.993665i	$0.535847\pi$
$674$	−70.7263	−2.72428
$675$	−3.61558	−0.139164
$676$	−6.47136	−0.248899
$677$	38.5229	1.48055	0.740277	−	0.672302i	$-0.234694\pi$
$677$	38.5229	1.48055	0.740277	+	0.672302i	$0.234694\pi$
$678$	−9.34347	−0.358834
$679$	14.1677	0.543705
$680$	3.16829	0.121498
$681$	19.0942	0.731690
$682$	−23.4275	−0.897084
$683$	16.7833	0.642196	0.321098	−	0.947046i	$-0.395948\pi$
$683$	16.7833	0.642196	0.321098	+	0.947046i	$0.395948\pi$
$684$	19.1655	0.732812
$685$	−12.4361	−0.475159
$686$	28.2113	1.07711
$687$	11.7972	0.450090
$688$	−31.7802	−1.21161
$689$	6.65187	0.253416
$690$	−34.3066	−1.30603
$691$	−25.7120	−0.978130	−0.489065	−	0.872247i	$-0.662662\pi$
$691$	−25.7120	−0.978130	−0.489065	+	0.872247i	$0.662662\pi$
$692$	37.1141	1.41087
$693$	−16.7233	−0.635264
$694$	27.5819	1.04699
$695$	−2.41369	−0.0915565
$696$	0.441671	0.0167415
$697$	16.4995	0.624962
$698$	20.3646	0.770812
$699$	12.3854	0.468458
$700$	5.77942	0.218441
$701$	−34.3692	−1.29811	−0.649054	−	0.760743i	$-0.724835\pi$
$701$	−34.3692	−1.29811	−0.649054	+	0.760743i	$0.724835\pi$
$702$	28.7685	1.08580
$703$	−25.3169	−0.954847
$704$	−23.0785	−0.869804
$705$	−4.54723	−0.171259
$706$	−14.8681	−0.559569
$707$	−27.0710	−1.01811
$708$	−9.23057	−0.346906
$709$	−34.0147	−1.27745	−0.638724	−	0.769436i	$-0.720538\pi$
$709$	−34.0147	−1.27745	−0.638724	+	0.769436i	$0.720538\pi$
$710$	−67.1848	−2.52140
$711$	27.2480	1.02188
$712$	−3.95345	−0.148162
$713$	−40.8933	−1.53147
$714$	−12.8414	−0.480576
$715$	−17.8626	−0.668024
$716$	−38.8073	−1.45030
$717$	11.3845	0.425161
$718$	−4.16774	−0.155539
$719$	34.4109	1.28331	0.641656	−	0.766993i	$-0.278248\pi$
$719$	34.4109	1.28331	0.641656	+	0.766993i	$0.278248\pi$
$720$	−19.1370	−0.713195
$721$	−40.9096	−1.52355
$722$	11.7352	0.436739
$723$	3.58760	0.133424
$724$	51.5644	1.91638
$725$	−0.825903	−0.0306733
$726$	9.49962	0.352564
$727$	10.3835	0.385101	0.192550	−	0.981287i	$-0.438324\pi$
$727$	10.3835	0.385101	0.192550	+	0.981287i	$0.438324\pi$
$728$	−5.29455	−0.196229
$729$	2.96376	0.109769
$730$	77.2044	2.85746
$731$	22.7635	0.841938
$732$	24.4434	0.903454
$733$	−35.0627	−1.29507	−0.647535	−	0.762036i	$-0.724200\pi$
$733$	−35.0627	−1.29507	−0.647535	+	0.762036i	$0.724200\pi$
$734$	41.5747	1.53455
$735$	−5.13110	−0.189264
$736$	−67.9699	−2.50540
$737$	−12.9675	−0.477664
$738$	32.3836	1.19206
$739$	31.2585	1.14986	0.574932	−	0.818201i	$-0.305029\pi$
$739$	31.2585	1.14986	0.574932	+	0.818201i	$0.305029\pi$
$740$	−37.8516	−1.39145
$741$	−9.55293	−0.350936
$742$	−13.3509	−0.490127
$743$	50.8855	1.86681	0.933404	−	0.358827i	$-0.116823\pi$
$743$	50.8855	1.86681	0.933404	+	0.358827i	$0.116823\pi$
$744$	−2.15673	−0.0790695
$745$	23.2642	0.852336
$746$	−1.73256	−0.0634335
$747$	4.89892	0.179242
$748$	12.8391	0.469442
$749$	7.61325	0.278182
$750$	−17.0995	−0.624387
$751$	−0.363055	−0.0132481	−0.00662404	−	0.999978i	$-0.502109\pi$
$751$	−0.363055	−0.0132481	−0.00662404	+	0.999978i	$0.502109\pi$
$752$	−7.81677	−0.285048
$753$	13.6056	0.495816
$754$	6.57156	0.239322
$755$	−45.3889	−1.65187
$756$	−30.6340	−1.11415
$757$	−46.8843	−1.70404	−0.852020	−	0.523509i	$-0.824623\pi$
$757$	−46.8843	−1.70404	−0.852020	+	0.523509i	$0.824623\pi$
$758$	−26.7951	−0.973243
$759$	−16.0063	−0.580992
$760$	−4.73062	−0.171597
$761$	5.88714	0.213409	0.106704	−	0.994291i	$-0.465970\pi$
$761$	5.88714	0.213409	0.106704	+	0.994291i	$0.465970\pi$
$762$	30.9928	1.12275
$763$	−13.9939	−0.506614
$764$	−16.5194	−0.597652
$765$	13.7075	0.495594
$766$	22.2005	0.802135
$767$	−15.8126	−0.570961
$768$	9.09738	0.328273
$769$	−44.3714	−1.60008	−0.800038	−	0.599950i	$-0.795187\pi$
$769$	−44.3714	−1.60008	−0.800038	+	0.599950i	$0.795187\pi$
$770$	35.8519	1.29201
$771$	4.25477	0.153232
$772$	45.3171	1.63100
$773$	−44.0375	−1.58392	−0.791959	−	0.610575i	$-0.790939\pi$
$773$	−44.0375	−1.58392	−0.791959	+	0.610575i	$0.790939\pi$
$774$	44.6780	1.60592
$775$	4.03298	0.144869
$776$	−2.45794	−0.0882348
$777$	17.6635	0.633673
$778$	−34.5797	−1.23974
$779$	−24.6356	−0.882661
$780$	−14.2827	−0.511402
$781$	−31.3462	−1.12165
$782$	42.2416	1.51056
$783$	4.37773	0.156447
$784$	−8.82047	−0.315017
$785$	−57.9160	−2.06711
$786$	29.8352	1.06419
$787$	3.46809	0.123624	0.0618120	−	0.998088i	$-0.480312\pi$
$787$	3.46809	0.123624	0.0618120	+	0.998088i	$0.480312\pi$
$788$	9.83475	0.350348
$789$	4.07950	0.145234
$790$	−58.4152	−2.07832
$791$	17.0439	0.606013
$792$	2.90131	0.103093
$793$	41.8733	1.48696
$794$	−75.4029	−2.67595
$795$	−4.14665	−0.147066
$796$	−24.2076	−0.858017
$797$	4.92539	0.174466	0.0872331	−	0.996188i	$-0.472198\pi$
$797$	4.92539	0.174466	0.0872331	+	0.996188i	$0.472198\pi$
$798$	19.1736	0.678738
$799$	5.59900	0.198078
$800$	6.70332	0.236998
$801$	−17.1044	−0.604354
$802$	−1.37684	−0.0486178
$803$	36.0210	1.27115
$804$	−10.3686	−0.365673
$805$	62.5805	2.20567
$806$	−32.0897	−1.13031
$807$	19.4311	0.684005
$808$	4.69654	0.165224
$809$	−49.7810	−1.75021	−0.875103	−	0.483936i	$-0.839207\pi$
$809$	−49.7810	−1.75021	−0.875103	+	0.483936i	$0.839207\pi$
$810$	16.7980	0.590221
$811$	53.9877	1.89577	0.947883	−	0.318618i	$-0.103219\pi$
$811$	53.9877	1.89577	0.947883	+	0.318618i	$0.103219\pi$
$812$	−6.99769	−0.245571
$813$	22.6061	0.792832
$814$	−33.2873	−1.16672
$815$	−35.4217	−1.24077
$816$	−6.85612	−0.240012
$817$	−33.9885	−1.18911
$818$	16.4519	0.575228
$819$	−22.9066	−0.800422
$820$	−36.8329	−1.28626
$821$	−28.8814	−1.00797	−0.503984	−	0.863713i	$-0.668133\pi$
$821$	−28.8814	−1.00797	−0.503984	+	0.863713i	$0.668133\pi$
$822$	−8.74466	−0.305005
$823$	−35.9698	−1.25383	−0.626914	−	0.779088i	$-0.715682\pi$
$823$	−35.9698	−1.25383	−0.626914	+	0.779088i	$0.715682\pi$
$824$	7.09737	0.247249
$825$	1.57857	0.0549588
$826$	31.7374	1.10428
$827$	−40.5824	−1.41119	−0.705594	−	0.708616i	$-0.749320\pi$
$827$	−40.5824	−1.41119	−0.705594	+	0.708616i	$0.749320\pi$
$828$	43.9861	1.52862
$829$	36.3085	1.26105	0.630523	−	0.776170i	$-0.282840\pi$
$829$	36.3085	1.26105	0.630523	+	0.776170i	$0.282840\pi$
$830$	−10.5025	−0.364547
$831$	−16.7971	−0.582684
$832$	−31.6117	−1.09594
$833$	6.31792	0.218903
$834$	−1.69723	−0.0587702
$835$	−36.0725	−1.24834
$836$	−19.1702	−0.663014
$837$	−21.3770	−0.738896
$838$	6.35788	0.219629
$839$	−4.52537	−0.156233	−0.0781166	−	0.996944i	$-0.524891\pi$
$839$	−4.52537	−0.156233	−0.0781166	+	0.996944i	$0.524891\pi$
$840$	3.30052	0.113879
$841$	1.00000	0.0344828
$842$	−71.1779	−2.45295
$843$	−18.7482	−0.645724
$844$	−53.5996	−1.84497
$845$	6.91074	0.237737
$846$	10.9892	0.377815
$847$	−17.3288	−0.595425
$848$	−7.12817	−0.244782
$849$	13.8162	0.474170
$850$	−4.16595	−0.142891
$851$	−58.1039	−1.99178
$852$	−25.0639	−0.858676
$853$	32.1833	1.10193	0.550967	−	0.834527i	$-0.314259\pi$
$853$	32.1833	1.10193	0.550967	+	0.834527i	$0.314259\pi$
$854$	−84.0434	−2.87591
$855$	−20.4668	−0.699950
$856$	−1.32082	−0.0451446
$857$	−20.4659	−0.699101	−0.349551	−	0.936917i	$-0.613666\pi$
$857$	−20.4659	−0.699101	−0.349551	+	0.936917i	$0.613666\pi$
$858$	−12.5604	−0.428805
$859$	−48.4542	−1.65324	−0.826619	−	0.562763i	$-0.809739\pi$
$859$	−48.4542	−1.65324	−0.826619	+	0.562763i	$0.809739\pi$
$860$	−50.8165	−1.73283
$861$	17.1881	0.585768
$862$	−35.6867	−1.21549
$863$	−10.3032	−0.350725	−0.175363	−	0.984504i	$-0.556110\pi$
$863$	−10.3032	−0.350725	−0.175363	+	0.984504i	$0.556110\pi$
$864$	−35.5312	−1.20880
$865$	−39.6340	−1.34760
$866$	8.95831	0.304416
$867$	−9.06799	−0.307965
$868$	34.1705	1.15982
$869$	−27.2546	−0.924549
$870$	−4.09658	−0.138887
$871$	−17.7622	−0.601848
$872$	2.42779	0.0822155
$873$	−10.6341	−0.359911
$874$	−63.0715	−2.13343
$875$	31.1922	1.05449
$876$	28.8018	0.973124
$877$	−12.9911	−0.438678	−0.219339	−	0.975649i	$-0.570390\pi$
$877$	−12.9911	−0.438678	−0.219339	+	0.975649i	$0.570390\pi$
$878$	−6.61866	−0.223369
$879$	−9.31779	−0.314281
$880$	19.1417	0.645265
$881$	−7.44871	−0.250953	−0.125477	−	0.992097i	$-0.540046\pi$
$881$	−7.44871	−0.250953	−0.125477	+	0.992097i	$0.540046\pi$
$882$	12.4002	0.417537
$883$	15.1864	0.511062	0.255531	−	0.966801i	$-0.417750\pi$
$883$	15.1864	0.511062	0.255531	+	0.966801i	$0.417750\pi$
$884$	17.5862	0.591489
$885$	9.85729	0.331349
$886$	−14.8391	−0.498528
$887$	−17.7306	−0.595335	−0.297667	−	0.954670i	$-0.596209\pi$
$887$	−17.7306	−0.595335	−0.297667	+	0.954670i	$0.596209\pi$
$888$	−3.06442	−0.102835
$889$	−56.5356	−1.89614
$890$	36.6690	1.22915
$891$	7.83738	0.262562
$892$	41.4898	1.38918
$893$	−8.35993	−0.279754
$894$	16.3586	0.547115
$895$	41.4421	1.38526
$896$	13.1909	0.440678
$897$	−21.9245	−0.732039
$898$	−16.5241	−0.551418
$899$	−4.88312	−0.162861
$900$	−4.33799	−0.144600
$901$	5.10576	0.170098
$902$	−32.3914	−1.07852
$903$	23.7135	0.789136
$904$	−2.95694	−0.0983465
$905$	−55.0654	−1.83044
$906$	−31.9159	−1.06034
$907$	33.8466	1.12386	0.561928	−	0.827186i	$-0.310060\pi$
$907$	33.8466	1.12386	0.561928	+	0.827186i	$0.310060\pi$
$908$	52.4844	1.74176
$909$	20.3193	0.673950
$910$	49.1080	1.62791
$911$	47.9762	1.58952	0.794761	−	0.606923i	$-0.207596\pi$
$911$	47.9762	1.58952	0.794761	+	0.606923i	$0.207596\pi$
$912$	10.2370	0.338979
$913$	−4.90011	−0.162170
$914$	7.45115	0.246462
$915$	−26.1030	−0.862938
$916$	32.4270	1.07142
$917$	−54.4241	−1.79724
$918$	22.0818	0.728807
$919$	8.90761	0.293835	0.146917	−	0.989149i	$-0.453065\pi$
$919$	8.90761	0.293835	0.146917	+	0.989149i	$0.453065\pi$
$920$	−10.8571	−0.357946
$921$	−3.08368	−0.101611
$922$	−76.1734	−2.50864
$923$	−42.9363	−1.41326
$924$	13.3749	0.440002
$925$	5.73032	0.188412
$926$	−48.0242	−1.57817
$927$	30.7064	1.00853
$928$	−8.11635	−0.266432
$929$	42.7743	1.40338	0.701690	−	0.712483i	$-0.252429\pi$
$929$	42.7743	1.40338	0.701690	+	0.712483i	$0.252429\pi$
$930$	20.0041	0.655960
$931$	−9.43337	−0.309166
$932$	34.0439	1.11514
$933$	−7.27699	−0.238238
$934$	8.40827	0.275127
$935$	−13.7108	−0.448390
$936$	3.97405	0.129896
$937$	15.3569	0.501687	0.250843	−	0.968028i	$-0.419292\pi$
$937$	15.3569	0.501687	0.250843	+	0.968028i	$0.419292\pi$
$938$	35.6503	1.16402
$939$	13.5259	0.441400
$940$	−12.4990	−0.407673
$941$	1.31032	0.0427152	0.0213576	−	0.999772i	$-0.493201\pi$
$941$	1.31032	0.0427152	0.0213576	+	0.999772i	$0.493201\pi$
$942$	−40.7246	−1.32688
$943$	−56.5401	−1.84120
$944$	16.9449	0.551509
$945$	32.7139	1.06418
$946$	−44.6888	−1.45296
$947$	37.2579	1.21072	0.605360	−	0.795952i	$-0.293029\pi$
$947$	37.2579	1.21072	0.605360	+	0.795952i	$0.293029\pi$
$948$	−21.7924	−0.707783
$949$	49.3396	1.60163
$950$	6.22024	0.201811
$951$	−27.8314	−0.902496
$952$	−4.06392	−0.131713
$953$	−34.9325	−1.13157	−0.565787	−	0.824551i	$-0.691428\pi$
$953$	−34.9325	−1.13157	−0.565787	+	0.824551i	$0.691428\pi$
$954$	10.0211	0.324445
$955$	17.6410	0.570850
$956$	31.2926	1.01208
$957$	−1.91133	−0.0617845
$958$	0.798786	0.0258076
$959$	15.9516	0.515105
$960$	19.7061	0.636012
$961$	−7.15518	−0.230812
$962$	−45.5951	−1.47005
$963$	−5.71445	−0.184146
$964$	9.86127	0.317610
$965$	−48.3940	−1.55786
$966$	44.0046	1.41582
$967$	9.74584	0.313405	0.156702	−	0.987646i	$-0.449914\pi$
$967$	9.74584	0.313405	0.156702	+	0.987646i	$0.449914\pi$
$968$	3.00636	0.0966281
$969$	−7.33252	−0.235555
$970$	22.7979	0.731995
$971$	23.2881	0.747351	0.373676	−	0.927559i	$-0.378097\pi$
$971$	23.2881	0.747351	0.373676	+	0.927559i	$0.378097\pi$
$972$	35.9507	1.15312
$973$	3.09601	0.0992535
$974$	−16.9327	−0.542559
$975$	2.16224	0.0692472
$976$	−44.8715	−1.43630
$977$	52.1884	1.66965	0.834827	−	0.550513i	$-0.185568\pi$
$977$	52.1884	1.66965	0.834827	+	0.550513i	$0.185568\pi$
$978$	−24.9074	−0.796451
$979$	17.1085	0.546791
$980$	−14.1039	−0.450533
$981$	10.5037	0.335359
$982$	53.5069	1.70747
$983$	5.04952	0.161055	0.0805273	−	0.996752i	$-0.474340\pi$
$983$	5.04952	0.161055	0.0805273	+	0.996752i	$0.474340\pi$
$984$	−2.98195	−0.0950610
$985$	−10.5025	−0.334637
$986$	5.04412	0.160637
$987$	5.83267	0.185656
$988$	−26.2582	−0.835386
$989$	−78.0056	−2.48043
$990$	−26.9102	−0.855262
$991$	−53.6989	−1.70580	−0.852901	−	0.522073i	$-0.825159\pi$
$991$	−53.6989	−1.70580	−0.852901	+	0.522073i	$0.825159\pi$
$992$	39.6331	1.25835
$993$	18.1005	0.574403
$994$	86.1770	2.73337
$995$	25.8512	0.819539
$996$	−3.91805	−0.124148
$997$	6.87001	0.217575	0.108788	−	0.994065i	$-0.465303\pi$
$997$	6.87001	0.217575	0.108788	+	0.994065i	$0.465303\pi$
$998$	−28.3267	−0.896665
$999$	−30.3738	−0.960984

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4031.2.a.e.1.19	✓	103

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4031.2.a.e.1.19	✓	103	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q-2.06403 q^{2} +0.822287 q^{3} +2.26023 q^{4} -2.41369 q^{5} -1.69723 q^{6} +3.09601 q^{7} -0.537124 q^{8} -2.32384 q^{9} +O(q^{10})\)	\(q-2.06403 q^{2} +0.822287 q^{3} +2.26023 q^{4} -2.41369 q^{5} -1.69723 q^{6} +3.09601 q^{7} -0.537124 q^{8} -2.32384 q^{9} +4.98194 q^{10} +2.32440 q^{11} +1.85856 q^{12} +3.18384 q^{13} -6.39026 q^{14} -1.98475 q^{15} -3.41182 q^{16} +2.44382 q^{17} +4.79649 q^{18} -3.64889 q^{19} -5.45550 q^{20} +2.54581 q^{21} -4.79765 q^{22} -8.37443 q^{23} -0.441671 q^{24} +0.825903 q^{25} -6.57156 q^{26} -4.37773 q^{27} +6.99769 q^{28} -1.00000 q^{29} +4.09658 q^{30} +4.88312 q^{31} +8.11635 q^{32} +1.91133 q^{33} -5.04412 q^{34} -7.47281 q^{35} -5.25242 q^{36} +6.93825 q^{37} +7.53144 q^{38} +2.61803 q^{39} +1.29645 q^{40} +6.75152 q^{41} -5.25463 q^{42} +9.31473 q^{43} +5.25369 q^{44} +5.60904 q^{45} +17.2851 q^{46} +2.29109 q^{47} -2.80550 q^{48} +2.58527 q^{49} -1.70469 q^{50} +2.00952 q^{51} +7.19622 q^{52} +2.08926 q^{53} +9.03578 q^{54} -5.61039 q^{55} -1.66294 q^{56} -3.00044 q^{57} +2.06403 q^{58} -4.96652 q^{59} -4.48599 q^{60} +13.1518 q^{61} -10.0789 q^{62} -7.19464 q^{63} -9.92878 q^{64} -7.68481 q^{65} -3.94504 q^{66} -5.57884 q^{67} +5.52359 q^{68} -6.88619 q^{69} +15.4241 q^{70} -13.4857 q^{71} +1.24819 q^{72} +15.4969 q^{73} -14.3208 q^{74} +0.679130 q^{75} -8.24734 q^{76} +7.19638 q^{77} -5.40371 q^{78} -11.7254 q^{79} +8.23508 q^{80} +3.37178 q^{81} -13.9354 q^{82} -2.10811 q^{83} +5.75411 q^{84} -5.89862 q^{85} -19.2259 q^{86} -0.822287 q^{87} -1.24849 q^{88} +7.36039 q^{89} -11.5772 q^{90} +9.85721 q^{91} -18.9281 q^{92} +4.01532 q^{93} -4.72888 q^{94} +8.80730 q^{95} +6.67397 q^{96} +4.57610 q^{97} -5.33608 q^{98} -5.40155 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 103 q + q^{2} + 2 q^{3} + 127 q^{4} + 9 q^{5} + 19 q^{6} + 18 q^{7} + 149 q^{9}+O(q^{10}) \) 103 * q + q^2 + 2 * q^3 + 127 * q^4 + 9 * q^5 + 19 * q^6 + 18 * q^7 + 149 * q^9	\( 103 q + q^{2} + 2 q^{3} + 127 q^{4} + 9 q^{5} + 19 q^{6} + 18 q^{7} + 149 q^{9} + 20 q^{10} + 9 q^{11} + 36 q^{13} - 10 q^{14} + 16 q^{15} + 179 q^{16} + 21 q^{17} + 7 q^{18} + 42 q^{19} + 24 q^{20} + 28 q^{21} + 32 q^{22} + 25 q^{23} + 68 q^{24} + 194 q^{25} - 5 q^{26} + 14 q^{27} + 59 q^{28} - 103 q^{29} + 84 q^{30} + 34 q^{31} + 11 q^{32} + 42 q^{33} + 54 q^{34} + 35 q^{35} + 214 q^{36} + 34 q^{37} + 9 q^{38} + 23 q^{39} + 46 q^{40} + 16 q^{41} + 13 q^{42} + 68 q^{43} - 6 q^{44} + 25 q^{45} + 60 q^{46} + 6 q^{47} + 5 q^{48} + 257 q^{49} - 51 q^{50} + 68 q^{51} + 37 q^{52} + 35 q^{53} + 30 q^{54} + 66 q^{55} - 54 q^{56} + 78 q^{57} - q^{58} + 10 q^{59} - 24 q^{60} + 70 q^{61} + 29 q^{62} + 26 q^{63} + 276 q^{64} + 95 q^{65} + 77 q^{66} + 71 q^{67} - 21 q^{68} - 20 q^{69} + 48 q^{70} + 32 q^{71} + 32 q^{72} + 94 q^{73} + 35 q^{74} + 7 q^{75} + 134 q^{76} + 17 q^{77} + 58 q^{78} + 110 q^{79} + 78 q^{80} + 267 q^{81} - 71 q^{82} + 35 q^{83} + 96 q^{84} + 71 q^{85} + 33 q^{86} - 2 q^{87} + 100 q^{88} + 22 q^{89} - 134 q^{90} + 108 q^{91} - 11 q^{92} + 78 q^{93} + 90 q^{94} + 12 q^{95} + 177 q^{96} + 44 q^{97} - 18 q^{98} + 83 q^{99}+O(q^{100}) \) 103 * q + q^2 + 2 * q^3 + 127 * q^4 + 9 * q^5 + 19 * q^6 + 18 * q^7 + 149 * q^9 + 20 * q^10 + 9 * q^11 + 36 * q^13 - 10 * q^14 + 16 * q^15 + 179 * q^16 + 21 * q^17 + 7 * q^18 + 42 * q^19 + 24 * q^20 + 28 * q^21 + 32 * q^22 + 25 * q^23 + 68 * q^24 + 194 * q^25 - 5 * q^26 + 14 * q^27 + 59 * q^28 - 103 * q^29 + 84 * q^30 + 34 * q^31 + 11 * q^32 + 42 * q^33 + 54 * q^34 + 35 * q^35 + 214 * q^36 + 34 * q^37 + 9 * q^38 + 23 * q^39 + 46 * q^40 + 16 * q^41 + 13 * q^42 + 68 * q^43 - 6 * q^44 + 25 * q^45 + 60 * q^46 + 6 * q^47 + 5 * q^48 + 257 * q^49 - 51 * q^50 + 68 * q^51 + 37 * q^52 + 35 * q^53 + 30 * q^54 + 66 * q^55 - 54 * q^56 + 78 * q^57 - q^58 + 10 * q^59 - 24 * q^60 + 70 * q^61 + 29 * q^62 + 26 * q^63 + 276 * q^64 + 95 * q^65 + 77 * q^66 + 71 * q^67 - 21 * q^68 - 20 * q^69 + 48 * q^70 + 32 * q^71 + 32 * q^72 + 94 * q^73 + 35 * q^74 + 7 * q^75 + 134 * q^76 + 17 * q^77 + 58 * q^78 + 110 * q^79 + 78 * q^80 + 267 * q^81 - 71 * q^82 + 35 * q^83 + 96 * q^84 + 71 * q^85 + 33 * q^86 - 2 * q^87 + 100 * q^88 + 22 * q^89 - 134 * q^90 + 108 * q^91 - 11 * q^92 + 78 * q^93 + 90 * q^94 + 12 * q^95 + 177 * q^96 + 44 * q^97 - 18 * q^98 + 83 * q^99

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