LMFDB - Embedded newform 731.2.a.f.1.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [731,2,Mod(1,731)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(731, 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("731.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 731 = 17 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	731.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:	$5.83706438776$
Analytic rank:	$0$
Dimension:	$21$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.20
Character	$\chi$	$=$	731.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.72856 q^{2} -2.69681 q^{3} +5.44504 q^{4} +0.220730 q^{5} -7.35840 q^{6} +2.22641 q^{7} +9.39999 q^{8} +4.27277 q^{9} +O(q^{10})$	\(q+2.72856 q^{2} -2.69681 q^{3} +5.44504 q^{4} +0.220730 q^{5} -7.35840 q^{6} +2.22641 q^{7} +9.39999 q^{8} +4.27277 q^{9} +0.602275 q^{10} -5.25966 q^{11} -14.6842 q^{12} +5.85386 q^{13} +6.07488 q^{14} -0.595267 q^{15} +14.7584 q^{16} -1.00000 q^{17} +11.6585 q^{18} -1.11481 q^{19} +1.20188 q^{20} -6.00419 q^{21} -14.3513 q^{22} +6.93812 q^{23} -25.3500 q^{24} -4.95128 q^{25} +15.9726 q^{26} -3.43242 q^{27} +12.1229 q^{28} +8.50921 q^{29} -1.62422 q^{30} -6.37447 q^{31} +21.4691 q^{32} +14.1843 q^{33} -2.72856 q^{34} +0.491435 q^{35} +23.2654 q^{36} +3.29440 q^{37} -3.04183 q^{38} -15.7867 q^{39} +2.07486 q^{40} -4.85253 q^{41} -16.3828 q^{42} +1.00000 q^{43} -28.6390 q^{44} +0.943130 q^{45} +18.9311 q^{46} -6.19766 q^{47} -39.8005 q^{48} -2.04312 q^{49} -13.5099 q^{50} +2.69681 q^{51} +31.8745 q^{52} +3.51817 q^{53} -9.36557 q^{54} -1.16097 q^{55} +20.9282 q^{56} +3.00643 q^{57} +23.2179 q^{58} -11.9364 q^{59} -3.24125 q^{60} -5.26179 q^{61} -17.3931 q^{62} +9.51293 q^{63} +29.0629 q^{64} +1.29212 q^{65} +38.7027 q^{66} +3.14898 q^{67} -5.44504 q^{68} -18.7108 q^{69} +1.34091 q^{70} -11.7435 q^{71} +40.1640 q^{72} -1.28447 q^{73} +8.98896 q^{74} +13.3526 q^{75} -6.07019 q^{76} -11.7101 q^{77} -43.0750 q^{78} +0.258933 q^{79} +3.25762 q^{80} -3.56173 q^{81} -13.2404 q^{82} -9.75705 q^{83} -32.6930 q^{84} -0.220730 q^{85} +2.72856 q^{86} -22.9477 q^{87} -49.4408 q^{88} -13.3854 q^{89} +2.57339 q^{90} +13.0331 q^{91} +37.7783 q^{92} +17.1907 q^{93} -16.9107 q^{94} -0.246072 q^{95} -57.8980 q^{96} +1.61738 q^{97} -5.57477 q^{98} -22.4733 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 21 q + 2 q^{2} - q^{3} + 32 q^{4} - 3 q^{5} + q^{6} + 5 q^{7} + 6 q^{8} + 34 q^{9}+O(q^{10}) $ 21 * q + 2 * q^2 - q^3 + 32 * q^4 - 3 * q^5 + q^6 + 5 * q^7 + 6 * q^8 + 34 * q^9	\( 21 q + 2 q^{2} - q^{3} + 32 q^{4} - 3 q^{5} + q^{6} + 5 q^{7} + 6 q^{8} + 34 q^{9} + 12 q^{10} + 2 q^{11} - 5 q^{12} + 26 q^{13} - 3 q^{14} + 5 q^{15} + 62 q^{16} - 21 q^{17} - 10 q^{18} + 16 q^{19} - 27 q^{20} + 36 q^{21} - 14 q^{22} - q^{23} + 15 q^{24} + 40 q^{25} - 3 q^{26} - 16 q^{27} + 25 q^{28} + 15 q^{29} + 38 q^{30} + 18 q^{31} + 14 q^{32} + 14 q^{33} - 2 q^{34} - 5 q^{35} + 73 q^{36} + 12 q^{37} + 19 q^{38} - 11 q^{39} + 41 q^{40} - 45 q^{42} + 21 q^{43} - 34 q^{44} - 18 q^{45} + 28 q^{46} - q^{47} - 36 q^{48} + 40 q^{49} + 24 q^{50} + q^{51} + 23 q^{52} + 39 q^{53} - 83 q^{54} - 2 q^{55} - 10 q^{56} + 3 q^{57} + 19 q^{58} + 4 q^{59} - 35 q^{60} + 50 q^{61} + 5 q^{62} - 37 q^{63} + 120 q^{64} - 8 q^{65} - 37 q^{66} + 16 q^{67} - 32 q^{68} + 33 q^{69} - q^{70} + q^{71} - 54 q^{72} + 15 q^{73} + 52 q^{74} + 11 q^{75} - 15 q^{76} + 13 q^{77} - 100 q^{78} + 56 q^{79} - 100 q^{80} + 97 q^{81} - 11 q^{82} + 61 q^{84} + 3 q^{85} + 2 q^{86} - 8 q^{87} - 56 q^{88} + 5 q^{89} - 69 q^{90} - 4 q^{91} - 27 q^{92} + 17 q^{93} - 47 q^{94} - 9 q^{95} + 81 q^{96} - 28 q^{97} + 18 q^{98} - 19 q^{99}+O(q^{100}) \) 21 * q + 2 * q^2 - q^3 + 32 * q^4 - 3 * q^5 + q^6 + 5 * q^7 + 6 * q^8 + 34 * q^9 + 12 * q^10 + 2 * q^11 - 5 * q^12 + 26 * q^13 - 3 * q^14 + 5 * q^15 + 62 * q^16 - 21 * q^17 - 10 * q^18 + 16 * q^19 - 27 * q^20 + 36 * q^21 - 14 * q^22 - q^23 + 15 * q^24 + 40 * q^25 - 3 * q^26 - 16 * q^27 + 25 * q^28 + 15 * q^29 + 38 * q^30 + 18 * q^31 + 14 * q^32 + 14 * q^33 - 2 * q^34 - 5 * q^35 + 73 * q^36 + 12 * q^37 + 19 * q^38 - 11 * q^39 + 41 * q^40 - 45 * q^42 + 21 * q^43 - 34 * q^44 - 18 * q^45 + 28 * q^46 - q^47 - 36 * q^48 + 40 * q^49 + 24 * q^50 + q^51 + 23 * q^52 + 39 * q^53 - 83 * q^54 - 2 * q^55 - 10 * q^56 + 3 * q^57 + 19 * q^58 + 4 * q^59 - 35 * q^60 + 50 * q^61 + 5 * q^62 - 37 * q^63 + 120 * q^64 - 8 * q^65 - 37 * q^66 + 16 * q^67 - 32 * q^68 + 33 * q^69 - q^70 + q^71 - 54 * q^72 + 15 * q^73 + 52 * q^74 + 11 * q^75 - 15 * q^76 + 13 * q^77 - 100 * q^78 + 56 * q^79 - 100 * q^80 + 97 * q^81 - 11 * q^82 + 61 * q^84 + 3 * q^85 + 2 * q^86 - 8 * q^87 - 56 * q^88 + 5 * q^89 - 69 * q^90 - 4 * q^91 - 27 * q^92 + 17 * q^93 - 47 * q^94 - 9 * q^95 + 81 * q^96 - 28 * q^97 + 18 * q^98 - 19 * 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 $

$2$	2.72856	1.92938	0.964691	−	0.263382i	$-0.0848381\pi$
$2$	2.72856	1.92938	0.964691	+	0.263382i	$0.0848381\pi$
$3$	−2.69681	−1.55700	−0.778501	−	0.627643i	$-0.784020\pi$
$3$	−2.69681	−1.55700	−0.778501	+	0.627643i	$0.784020\pi$
$4$	5.44504	2.72252
$5$	0.220730	0.0987135	0.0493568	−	0.998781i	$-0.484283\pi$
$5$	0.220730	0.0987135	0.0493568	+	0.998781i	$0.484283\pi$
$6$	−7.35840	−3.00405
$7$	2.22641	0.841502	0.420751	−	0.907176i	$-0.361767\pi$
$7$	2.22641	0.841502	0.420751	+	0.907176i	$0.361767\pi$
$8$	9.39999	3.32340
$9$	4.27277	1.42426
$10$	0.602275	0.190456
$11$	−5.25966	−1.58585	−0.792924	−	0.609321i	$-0.791442\pi$
$11$	−5.25966	−1.58585	−0.792924	+	0.609321i	$0.791442\pi$
$12$	−14.6842	−4.23897
$13$	5.85386	1.62357	0.811784	−	0.583958i	$-0.198497\pi$
$13$	5.85386	1.62357	0.811784	+	0.583958i	$0.198497\pi$
$14$	6.07488	1.62358
$15$	−0.595267	−0.153697
$16$	14.7584	3.68959
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	11.6585	2.74794
$19$	−1.11481	−0.255755	−0.127878	−	0.991790i	$-0.540816\pi$
$19$	−1.11481	−0.255755	−0.127878	+	0.991790i	$0.540816\pi$
$20$	1.20188	0.268749
$21$	−6.00419	−1.31022
$22$	−14.3513	−3.05971
$23$	6.93812	1.44670	0.723349	−	0.690483i	$-0.242602\pi$
$23$	6.93812	1.44670	0.723349	+	0.690483i	$0.242602\pi$
$24$	−25.3500	−5.17454
$25$	−4.95128	−0.990256
$26$	15.9726	3.13248
$27$	−3.43242	−0.660570
$28$	12.1229	2.29101
$29$	8.50921	1.58012	0.790060	−	0.613029i	$-0.210049\pi$
$29$	8.50921	1.58012	0.790060	+	0.613029i	$0.210049\pi$
$30$	−1.62422	−0.296541
$31$	−6.37447	−1.14489	−0.572444	−	0.819943i	$-0.694005\pi$
$31$	−6.37447	−1.14489	−0.572444	+	0.819943i	$0.694005\pi$
$32$	21.4691	3.79523
$33$	14.1843	2.46917
$34$	−2.72856	−0.467944
$35$	0.491435	0.0830677
$36$	23.2654	3.87757
$37$	3.29440	0.541595	0.270798	−	0.962636i	$-0.412713\pi$
$37$	3.29440	0.541595	0.270798	+	0.962636i	$0.412713\pi$
$38$	−3.04183	−0.493450
$39$	−15.7867	−2.52790
$40$	2.07486	0.328064
$41$	−4.85253	−0.757837	−0.378919	−	0.925430i	$-0.623704\pi$
$41$	−4.85253	−0.757837	−0.378919	+	0.925430i	$0.623704\pi$
$42$	−16.3828	−2.52792
$43$	1.00000	0.152499
$43$	1.00000	0.152499
$44$	−28.6390	−4.31750
$45$	0.943130	0.140594
$46$	18.9311	2.79123
$47$	−6.19766	−0.904022	−0.452011	−	0.892012i	$-0.649293\pi$
$47$	−6.19766	−0.904022	−0.452011	+	0.892012i	$0.649293\pi$
$48$	−39.8005	−5.74470
$49$	−2.04312	−0.291874
$50$	−13.5099	−1.91058
$51$	2.69681	0.377629
$52$	31.8745	4.42019
$53$	3.51817	0.483257	0.241629	−	0.970369i	$-0.422318\pi$
$53$	3.51817	0.483257	0.241629	+	0.970369i	$0.422318\pi$
$54$	−9.36557	−1.27449
$55$	−1.16097	−0.156545
$56$	20.9282	2.79665
$57$	3.00643	0.398212
$58$	23.2179	3.04866
$59$	−11.9364	−1.55399	−0.776995	−	0.629507i	$-0.783257\pi$
$59$	−11.9364	−1.55399	−0.776995	+	0.629507i	$0.783257\pi$
$60$	−3.24125	−0.418444
$61$	−5.26179	−0.673703	−0.336851	−	0.941558i	$-0.609362\pi$
$61$	−5.26179	−0.673703	−0.336851	+	0.941558i	$0.609362\pi$
$62$	−17.3931	−2.20893
$63$	9.51293	1.19852
$64$	29.0629	3.63287
$65$	1.29212	0.160268
$66$	38.7027	4.76397
$67$	3.14898	0.384709	0.192354	−	0.981326i	$-0.438388\pi$
$67$	3.14898	0.384709	0.192354	+	0.981326i	$0.438388\pi$
$68$	−5.44504	−0.660308
$69$	−18.7108	−2.25251
$70$	1.34091	0.160269
$71$	−11.7435	−1.39370	−0.696848	−	0.717218i	$-0.745415\pi$
$71$	−11.7435	−1.39370	−0.696848	+	0.717218i	$0.745415\pi$
$72$	40.1640	4.73338
$73$	−1.28447	−0.150335	−0.0751677	−	0.997171i	$-0.523949\pi$
$73$	−1.28447	−0.150335	−0.0751677	+	0.997171i	$0.523949\pi$
$74$	8.98896	1.04495
$75$	13.3526	1.54183
$76$	−6.07019	−0.696298
$77$	−11.7101	−1.33449
$78$	−43.0750	−4.87729
$79$	0.258933	0.0291322	0.0145661	−	0.999894i	$-0.495363\pi$
$79$	0.258933	0.0291322	0.0145661	+	0.999894i	$0.495363\pi$
$80$	3.25762	0.364212
$81$	−3.56173	−0.395748
$82$	−13.2404	−1.46216
$83$	−9.75705	−1.07098	−0.535488	−	0.844543i	$-0.679872\pi$
$83$	−9.75705	−1.07098	−0.535488	+	0.844543i	$0.679872\pi$
$84$	−32.6930	−3.56710
$85$	−0.220730	−0.0239415
$86$	2.72856	0.294228
$87$	−22.9477	−2.46025
$88$	−49.4408	−5.27040
$89$	−13.3854	−1.41885	−0.709423	−	0.704783i	$-0.751044\pi$
$89$	−13.3854	−1.41885	−0.709423	+	0.704783i	$0.751044\pi$
$90$	2.57339	0.271259
$91$	13.0331	1.36624
$92$	37.7783	3.93866
$93$	17.1907	1.78260
$94$	−16.9107	−1.74420
$95$	−0.246072	−0.0252465
$96$	−57.8980	−5.90919
$97$	1.61738	0.164220	0.0821100	−	0.996623i	$-0.473834\pi$
$97$	1.61738	0.164220	0.0821100	+	0.996623i	$0.473834\pi$
$98$	−5.57477	−0.563137
$99$	−22.4733	−2.25866
$100$	−26.9599	−2.69599
$101$	2.69250	0.267914	0.133957	−	0.990987i	$-0.457232\pi$
$101$	2.69250	0.267914	0.133957	+	0.990987i	$0.457232\pi$
$102$	7.35840	0.728590
$103$	2.98729	0.294347	0.147173	−	0.989111i	$-0.452982\pi$
$103$	2.98729	0.294347	0.147173	+	0.989111i	$0.452982\pi$
$104$	55.0262	5.39576
$105$	−1.32531	−0.129337
$106$	9.59953	0.932389
$107$	6.43311	0.621913	0.310956	−	0.950424i	$-0.399351\pi$
$107$	6.43311	0.621913	0.310956	+	0.950424i	$0.399351\pi$
$108$	−18.6897	−1.79841
$109$	7.44103	0.712721	0.356361	−	0.934348i	$-0.384017\pi$
$109$	7.44103	0.712721	0.356361	+	0.934348i	$0.384017\pi$
$110$	−3.16776	−0.302035
$111$	−8.88435	−0.843266
$112$	32.8581	3.10480
$113$	−11.3907	−1.07155	−0.535773	−	0.844362i	$-0.679980\pi$
$113$	−11.3907	−1.07155	−0.535773	+	0.844362i	$0.679980\pi$
$114$	8.20323	0.768303
$115$	1.53145	0.142809
$116$	46.3330	4.30191
$117$	25.0122	2.31238
$118$	−32.5692	−2.99824
$119$	−2.22641	−0.204094
$120$	−5.59550	−0.510797
$121$	16.6640	1.51491
$122$	−14.3571	−1.29983
$123$	13.0863	1.17995
$124$	−34.7092	−3.11698
$125$	−2.19655	−0.196465
$126$	25.9566	2.31240
$127$	−19.8062	−1.75752	−0.878760	−	0.477264i	$-0.841628\pi$
$127$	−19.8062	−1.75752	−0.878760	+	0.477264i	$0.841628\pi$
$128$	36.3618	3.21396
$129$	−2.69681	−0.237441
$130$	3.52563	0.309219
$131$	5.40146	0.471928	0.235964	−	0.971762i	$-0.424175\pi$
$131$	5.40146	0.471928	0.235964	+	0.971762i	$0.424175\pi$
$132$	77.2340	6.72236
$133$	−2.48202	−0.215219
$134$	8.59217	0.742250
$135$	−0.757639	−0.0652072
$136$	−9.39999	−0.806043
$137$	13.4053	1.14529	0.572646	−	0.819803i	$-0.305917\pi$
$137$	13.4053	1.14529	0.572646	+	0.819803i	$0.305917\pi$
$138$	−51.0534	−4.34596
$139$	23.3570	1.98112	0.990558	−	0.137095i	$-0.0437764\pi$
$139$	23.3570	1.98112	0.990558	+	0.137095i	$0.0437764\pi$
$140$	2.67588	0.226153
$141$	16.7139	1.40756
$142$	−32.0428	−2.68897
$143$	−30.7893	−2.57473
$144$	63.0591	5.25493
$145$	1.87824	0.155979
$146$	−3.50474	−0.290055
$147$	5.50990	0.454449
$148$	17.9381	1.47450
$149$	−7.40882	−0.606955	−0.303477	−	0.952839i	$-0.598148\pi$
$149$	−7.40882	−0.606955	−0.303477	+	0.952839i	$0.598148\pi$
$150$	36.4335	2.97478
$151$	13.3469	1.08615	0.543076	−	0.839683i	$-0.317259\pi$
$151$	13.3469	1.08615	0.543076	+	0.839683i	$0.317259\pi$
$152$	−10.4792	−0.849976
$153$	−4.27277	−0.345433
$154$	−31.9518	−2.57475
$155$	−1.40704	−0.113016
$156$	−85.9593	−6.88225
$157$	3.83523	0.306085	0.153042	−	0.988220i	$-0.451093\pi$
$157$	3.83523	0.306085	0.153042	+	0.988220i	$0.451093\pi$
$158$	0.706514	0.0562072
$159$	−9.48782	−0.752433
$160$	4.73887	0.374641
$161$	15.4471	1.21740
$162$	−9.71840	−0.763549
$163$	−7.71201	−0.604051	−0.302026	−	0.953300i	$-0.597663\pi$
$163$	−7.71201	−0.604051	−0.302026	+	0.953300i	$0.597663\pi$
$164$	−26.4222	−2.06323
$165$	3.13090	0.243740
$166$	−26.6227	−2.06632
$167$	−14.8330	−1.14781	−0.573906	−	0.818921i	$-0.694573\pi$
$167$	−14.8330	−1.14781	−0.573906	+	0.818921i	$0.694573\pi$
$168$	−56.4393	−4.35439
$169$	21.2676	1.63597
$170$	−0.602275	−0.0461924
$171$	−4.76333	−0.364261
$172$	5.44504	0.415180
$173$	2.10314	0.159899	0.0799495	−	0.996799i	$-0.474524\pi$
$173$	2.10314	0.159899	0.0799495	+	0.996799i	$0.474524\pi$
$174$	−62.6142	−4.74677
$175$	−11.0236	−0.833302
$176$	−77.6240	−5.85113
$177$	32.1902	2.41957
$178$	−36.5228	−2.73750
$179$	7.84623	0.586455	0.293227	−	0.956043i	$-0.405271\pi$
$179$	7.84623	0.586455	0.293227	+	0.956043i	$0.405271\pi$
$180$	5.13538	0.382768
$181$	13.5210	1.00501	0.502503	−	0.864576i	$-0.332413\pi$
$181$	13.5210	1.00501	0.502503	+	0.864576i	$0.332413\pi$
$182$	35.5615	2.63599
$183$	14.1900	1.04896
$184$	65.2182	4.80795
$185$	0.727173	0.0534628
$186$	46.9059	3.43931
$187$	5.25966	0.384624
$188$	−33.7465	−2.46122
$189$	−7.64197	−0.555871
$190$	−0.671423	−0.0487102
$191$	−12.1160	−0.876683	−0.438341	−	0.898809i	$-0.644434\pi$
$191$	−12.1160	−0.876683	−0.438341	+	0.898809i	$0.644434\pi$
$192$	−78.3772	−5.65639
$193$	−0.300400	−0.0216233	−0.0108116	−	0.999942i	$-0.503442\pi$
$193$	−0.300400	−0.0216233	−0.0108116	+	0.999942i	$0.503442\pi$
$194$	4.41312	0.316843
$195$	−3.48461	−0.249538
$196$	−11.1249	−0.794632
$197$	−13.5978	−0.968804	−0.484402	−	0.874846i	$-0.660963\pi$
$197$	−13.5978	−0.968804	−0.484402	+	0.874846i	$0.660963\pi$
$198$	−61.3198	−4.35781
$199$	14.9652	1.06086	0.530428	−	0.847730i	$-0.322031\pi$
$199$	14.9652	1.06086	0.530428	+	0.847730i	$0.322031\pi$
$200$	−46.5420	−3.29101
$201$	−8.49218	−0.598992
$202$	7.34664	0.516908
$203$	18.9450	1.32968
$204$	14.6842	1.02810
$205$	−1.07110	−0.0748088
$206$	8.15100	0.567907
$207$	29.6450	2.06047
$208$	86.3933	5.99030
$209$	5.86353	0.405589
$210$	−3.61618	−0.249540
$211$	−20.4656	−1.40891	−0.704454	−	0.709750i	$-0.748808\pi$
$211$	−20.4656	−1.40891	−0.704454	+	0.709750i	$0.748808\pi$
$212$	19.1566	1.31568
$213$	31.6700	2.16999
$214$	17.5531	1.19991
$215$	0.220730	0.0150537
$216$	−32.2647	−2.19534
$217$	−14.1922	−0.963427
$218$	20.3033	1.37511
$219$	3.46396	0.234073
$220$	−6.32150	−0.426196
$221$	−5.85386	−0.393773
$222$	−24.2415	−1.62698
$223$	−5.13530	−0.343885	−0.171943	−	0.985107i	$-0.555004\pi$
$223$	−5.13530	−0.343885	−0.171943	+	0.985107i	$0.555004\pi$
$224$	47.7989	3.19370
$225$	−21.1557	−1.41038
$226$	−31.0802	−2.06742
$227$	−13.4171	−0.890522	−0.445261	−	0.895401i	$-0.646889\pi$
$227$	−13.4171	−0.890522	−0.445261	+	0.895401i	$0.646889\pi$
$228$	16.3701	1.08414
$229$	22.9059	1.51366	0.756831	−	0.653611i	$-0.226747\pi$
$229$	22.9059	1.51366	0.756831	+	0.653611i	$0.226747\pi$
$230$	4.17866	0.275532
$231$	31.5800	2.07781
$232$	79.9865	5.25137
$233$	7.76339	0.508597	0.254298	−	0.967126i	$-0.418155\pi$
$233$	7.76339	0.508597	0.254298	+	0.967126i	$0.418155\pi$
$234$	68.2473	4.46146
$235$	−1.36801	−0.0892392
$236$	−64.9942	−4.23076
$237$	−0.698292	−0.0453590
$238$	−6.07488	−0.393776
$239$	11.6543	0.753857	0.376928	−	0.926242i	$-0.376980\pi$
$239$	11.6543	0.753857	0.376928	+	0.926242i	$0.376980\pi$
$240$	−8.78516	−0.567080
$241$	7.74866	0.499135	0.249567	−	0.968357i	$-0.419712\pi$
$241$	7.74866	0.499135	0.249567	+	0.968357i	$0.419712\pi$
$242$	45.4688	2.92285
$243$	19.9026	1.27675
$244$	−28.6506	−1.83417
$245$	−0.450978	−0.0288119
$246$	35.7068	2.27658
$247$	−6.52594	−0.415236
$248$	−59.9200	−3.80492
$249$	26.3129	1.66751
$250$	−5.99341	−0.379057
$251$	27.9308	1.76298	0.881489	−	0.472204i	$-0.156541\pi$
$251$	27.9308	1.76298	0.881489	+	0.472204i	$0.156541\pi$
$252$	51.7982	3.26298
$253$	−36.4921	−2.29424
$254$	−54.0425	−3.39093
$255$	0.595267	0.0372771
$256$	41.0895	2.56809
$257$	14.6607	0.914510	0.457255	−	0.889336i	$-0.348833\pi$
$257$	14.6607	0.914510	0.457255	+	0.889336i	$0.348833\pi$
$258$	−7.35840	−0.458114
$259$	7.33466	0.455754
$260$	7.03566	0.436333
$261$	36.3579	2.25050
$262$	14.7382	0.910529
$263$	3.13546	0.193340	0.0966702	−	0.995316i	$-0.469181\pi$
$263$	3.13546	0.193340	0.0966702	+	0.995316i	$0.469181\pi$
$264$	133.332	8.20603
$265$	0.776566	0.0477041
$266$	−6.77234	−0.415239
$267$	36.0978	2.20915
$268$	17.1463	1.04738
$269$	−26.8554	−1.63740	−0.818701	−	0.574220i	$-0.805305\pi$
$269$	−26.8554	−1.63740	−0.818701	+	0.574220i	$0.805305\pi$
$270$	−2.06726	−0.125810
$271$	21.0823	1.28066	0.640329	−	0.768101i	$-0.278798\pi$
$271$	21.0823	1.28066	0.640329	+	0.768101i	$0.278798\pi$
$272$	−14.7584	−0.894857
$273$	−35.1476	−2.12723
$274$	36.5772	2.20971
$275$	26.0420	1.57039
$276$	−101.881	−6.13250
$277$	−9.72743	−0.584465	−0.292232	−	0.956347i	$-0.594398\pi$
$277$	−9.72743	−0.584465	−0.292232	+	0.956347i	$0.594398\pi$
$278$	63.7310	3.82233
$279$	−27.2367	−1.63062
$280$	4.61948	0.276067
$281$	−11.1787	−0.666864	−0.333432	−	0.942774i	$-0.608207\pi$
$281$	−11.1787	−0.666864	−0.333432	+	0.942774i	$0.608207\pi$
$282$	45.6049	2.71573
$283$	9.70463	0.576880	0.288440	−	0.957498i	$-0.406863\pi$
$283$	9.70463	0.576880	0.288440	+	0.957498i	$0.406863\pi$
$284$	−63.9438	−3.79437
$285$	0.663610	0.0393089
$286$	−84.0104	−4.96764
$287$	−10.8037	−0.637722
$288$	91.7325	5.40539
$289$	1.00000	0.0588235
$290$	5.12489	0.300944
$291$	−4.36176	−0.255691
$292$	−6.99397	−0.409291
$293$	15.8788	0.927649	0.463825	−	0.885927i	$-0.346477\pi$
$293$	15.8788	0.927649	0.463825	+	0.885927i	$0.346477\pi$
$294$	15.0341	0.876805
$295$	−2.63473	−0.153400
$296$	30.9673	1.79994
$297$	18.0534	1.04756
$298$	−20.2154	−1.17105
$299$	40.6147	2.34881
$300$	72.7057	4.19766
$301$	2.22641	0.128328
$302$	36.4177	2.09560
$303$	−7.26115	−0.417142
$304$	−16.4528	−0.943632
$305$	−1.16144	−0.0665036
$306$	−11.6585	−0.666473
$307$	8.38192	0.478382	0.239191	−	0.970973i	$-0.423118\pi$
$307$	8.38192	0.478382	0.239191	+	0.970973i	$0.423118\pi$
$308$	−63.7621	−3.63319
$309$	−8.05615	−0.458299
$310$	−3.83919	−0.218051
$311$	−14.0629	−0.797432	−0.398716	−	0.917074i	$-0.630544\pi$
$311$	−14.0629	−0.797432	−0.398716	+	0.917074i	$0.630544\pi$
$312$	−148.395	−8.40121
$313$	−2.31978	−0.131122	−0.0655610	−	0.997849i	$-0.520884\pi$
$313$	−2.31978	−0.131122	−0.0655610	+	0.997849i	$0.520884\pi$
$314$	10.4647	0.590555
$315$	2.09979	0.118310
$316$	1.40990	0.0793130
$317$	10.9765	0.616499	0.308249	−	0.951306i	$-0.400257\pi$
$317$	10.9765	0.616499	0.308249	+	0.951306i	$0.400257\pi$
$318$	−25.8881	−1.45173
$319$	−44.7556	−2.50583
$320$	6.41507	0.358613
$321$	−17.3489	−0.968320
$322$	42.1482	2.34883
$323$	1.11481	0.0620298
$324$	−19.3938	−1.07743
$325$	−28.9841	−1.60775
$326$	−21.0427	−1.16545
$327$	−20.0670	−1.10971
$328$	−45.6137	−2.51860
$329$	−13.7985	−0.760737
$330$	8.54285	0.470269
$331$	−21.6214	−1.18842	−0.594209	−	0.804311i	$-0.702535\pi$
$331$	−21.6214	−1.18842	−0.594209	+	0.804311i	$0.702535\pi$
$332$	−53.1275	−2.91575
$333$	14.0762	0.771371
$334$	−40.4728	−2.21457
$335$	0.695074	0.0379759
$336$	−88.6120	−4.83418
$337$	15.5986	0.849710	0.424855	−	0.905261i	$-0.360325\pi$
$337$	15.5986	0.849710	0.424855	+	0.905261i	$0.360325\pi$
$338$	58.0300	3.15641
$339$	30.7185	1.66840
$340$	−1.20188	−0.0651813
$341$	33.5276	1.81562
$342$	−12.9970	−0.702800
$343$	−20.1336	−1.08711
$344$	9.39999	0.506814
$345$	−4.13003	−0.222353
$346$	5.73855	0.308507
$347$	15.5559	0.835086	0.417543	−	0.908657i	$-0.362891\pi$
$347$	15.5559	0.835086	0.417543	+	0.908657i	$0.362891\pi$
$348$	−124.951	−6.69808
$349$	−7.28419	−0.389914	−0.194957	−	0.980812i	$-0.562457\pi$
$349$	−7.28419	−0.389914	−0.194957	+	0.980812i	$0.562457\pi$
$350$	−30.0784	−1.60776
$351$	−20.0929	−1.07248
$352$	−112.920	−6.01866
$353$	−24.7127	−1.31532	−0.657661	−	0.753314i	$-0.728454\pi$
$353$	−24.7127	−1.31532	−0.657661	+	0.753314i	$0.728454\pi$
$354$	87.8329	4.66827
$355$	−2.59214	−0.137577
$356$	−72.8838	−3.86283
$357$	6.00419	0.317775
$358$	21.4089	1.13150
$359$	−10.8214	−0.571132	−0.285566	−	0.958359i	$-0.592182\pi$
$359$	−10.8214	−0.571132	−0.285566	+	0.958359i	$0.592182\pi$
$360$	8.86541	0.467248
$361$	−17.7572	−0.934589
$362$	36.8927	1.93904
$363$	−44.9397	−2.35872
$364$	70.9655	3.71960
$365$	−0.283520	−0.0148401
$366$	38.7183	2.02384
$367$	22.0453	1.15075	0.575377	−	0.817888i	$-0.304855\pi$
$367$	22.0453	1.15075	0.575377	+	0.817888i	$0.304855\pi$
$368$	102.395	5.33772
$369$	−20.7337	−1.07936
$370$	1.98413	0.103150
$371$	7.83287	0.406662
$372$	93.6041	4.85315
$373$	22.6761	1.17412	0.587061	−	0.809543i	$-0.300285\pi$
$373$	22.6761	1.17412	0.587061	+	0.809543i	$0.300285\pi$
$374$	14.3513	0.742088
$375$	5.92367	0.305897
$376$	−58.2580	−3.00443
$377$	49.8117	2.56543
$378$	−20.8516	−1.07249
$379$	18.5848	0.954637	0.477319	−	0.878730i	$-0.341609\pi$
$379$	18.5848	0.954637	0.477319	+	0.878730i	$0.341609\pi$
$380$	−1.33987	−0.0687341
$381$	53.4136	2.73646
$382$	−33.0592	−1.69146
$383$	−3.85025	−0.196739	−0.0983694	−	0.995150i	$-0.531363\pi$
$383$	−3.85025	−0.196739	−0.0983694	+	0.995150i	$0.531363\pi$
$384$	−98.0609	−5.00415
$385$	−2.58478	−0.131733
$386$	−0.819660	−0.0417196
$387$	4.27277	0.217197
$388$	8.80669	0.447092
$389$	−20.3974	−1.03419	−0.517095	−	0.855928i	$-0.672987\pi$
$389$	−20.3974	−1.03419	−0.517095	+	0.855928i	$0.672987\pi$
$390$	−9.50796	−0.481454
$391$	−6.93812	−0.350876
$392$	−19.2053	−0.970014
$393$	−14.5667	−0.734793
$394$	−37.1024	−1.86919
$395$	0.0571543	0.00287574
$396$	−122.368	−6.14923
$397$	3.38803	0.170041	0.0850203	−	0.996379i	$-0.472904\pi$
$397$	3.38803	0.170041	0.0850203	+	0.996379i	$0.472904\pi$
$398$	40.8335	2.04680
$399$	6.69354	0.335096
$400$	−73.0727	−3.65364
$401$	29.7342	1.48485	0.742427	−	0.669927i	$-0.233675\pi$
$401$	29.7342	1.48485	0.742427	+	0.669927i	$0.233675\pi$
$402$	−23.1714	−1.15569
$403$	−37.3152	−1.85880
$404$	14.6608	0.729400
$405$	−0.786182	−0.0390657
$406$	51.6924	2.56545
$407$	−17.3274	−0.858888
$408$	25.3500	1.25501
$409$	6.74434	0.333486	0.166743	−	0.986000i	$-0.446675\pi$
$409$	6.74434	0.333486	0.166743	+	0.986000i	$0.446675\pi$
$410$	−2.92256	−0.144335
$411$	−36.1515	−1.78322
$412$	16.2659	0.801364
$413$	−26.5753	−1.30769
$414$	80.8881	3.97543
$415$	−2.15368	−0.105720
$416$	125.677	6.16182
$417$	−62.9894	−3.08460
$418$	15.9990	0.782536
$419$	−10.8108	−0.528141	−0.264070	−	0.964503i	$-0.585065\pi$
$419$	−10.8108	−0.528141	−0.264070	+	0.964503i	$0.585065\pi$
$420$	−7.21634	−0.352121
$421$	14.3550	0.699618	0.349809	−	0.936821i	$-0.386246\pi$
$421$	14.3550	0.699618	0.349809	+	0.936821i	$0.386246\pi$
$422$	−55.8415	−2.71832
$423$	−26.4812	−1.28756
$424$	33.0707	1.60606
$425$	4.95128	0.240172
$426$	86.4134	4.18674
$427$	−11.7149	−0.566923
$428$	35.0285	1.69317
$429$	83.0328	4.00886
$430$	0.602275	0.0290443
$431$	−27.7496	−1.33665	−0.668326	−	0.743868i	$-0.732989\pi$
$431$	−27.7496	−1.33665	−0.668326	+	0.743868i	$0.732989\pi$
$432$	−50.6569	−2.43723
$433$	−17.4502	−0.838601	−0.419300	−	0.907848i	$-0.637725\pi$
$433$	−17.4502	−0.838601	−0.419300	+	0.907848i	$0.637725\pi$
$434$	−38.7242	−1.85882
$435$	−5.06525	−0.242860
$436$	40.5167	1.94040
$437$	−7.73469	−0.370000
$438$	9.45162	0.451616
$439$	31.6265	1.50945	0.754725	−	0.656041i	$-0.227770\pi$
$439$	31.6265	1.50945	0.754725	+	0.656041i	$0.227770\pi$
$440$	−10.9131	−0.520260
$441$	−8.72978	−0.415704
$442$	−15.9726	−0.759739
$443$	25.1912	1.19687	0.598435	−	0.801171i	$-0.295789\pi$
$443$	25.1912	1.19687	0.598435	+	0.801171i	$0.295789\pi$
$444$	−48.3756	−2.29581
$445$	−2.95455	−0.140059
$446$	−14.0120	−0.663486
$447$	19.9802	0.945030
$448$	64.7059	3.05707
$449$	−32.4976	−1.53365	−0.766827	−	0.641853i	$-0.778166\pi$
$449$	−32.4976	−1.53365	−0.766827	+	0.641853i	$0.778166\pi$
$450$	−57.7246	−2.72116
$451$	25.5226	1.20181
$452$	−62.0227	−2.91730
$453$	−35.9939	−1.69114
$454$	−36.6093	−1.71816
$455$	2.87679	0.134866
$456$	28.2604	1.32342
$457$	14.9292	0.698358	0.349179	−	0.937056i	$-0.386461\pi$
$457$	14.9292	0.698358	0.349179	+	0.937056i	$0.386461\pi$
$458$	62.5000	2.92043
$459$	3.43242	0.160212
$460$	8.33881	0.388799
$461$	−7.82932	−0.364648	−0.182324	−	0.983239i	$-0.558362\pi$
$461$	−7.82932	−0.364648	−0.182324	+	0.983239i	$0.558362\pi$
$462$	86.1679	4.00889
$463$	7.28534	0.338578	0.169289	−	0.985566i	$-0.445853\pi$
$463$	7.28534	0.338578	0.169289	+	0.985566i	$0.445853\pi$
$464$	125.582	5.83000
$465$	3.79451	0.175966
$466$	21.1829	0.981278
$467$	−36.3849	−1.68369	−0.841847	−	0.539717i	$-0.818531\pi$
$467$	−36.3849	−1.68369	−0.841847	+	0.539717i	$0.818531\pi$
$468$	136.192	6.29549
$469$	7.01090	0.323733
$470$	−3.73270	−0.172177
$471$	−10.3429	−0.476575
$472$	−112.202	−5.16453
$473$	−5.25966	−0.241839
$474$	−1.90533	−0.0875148
$475$	5.51974	0.253263
$476$	−12.1229	−0.555650
$477$	15.0323	0.688283
$478$	31.7996	1.45448
$479$	−36.8200	−1.68235	−0.841174	−	0.540765i	$-0.818135\pi$
$479$	−36.8200	−1.68235	−0.841174	+	0.540765i	$0.818135\pi$
$480$	−12.7798	−0.583317
$481$	19.2849	0.879317
$482$	21.1427	0.963022
$483$	−41.6578	−1.89549
$484$	90.7363	4.12438
$485$	0.357005	0.0162107
$486$	54.3054	2.46334
$487$	−20.3537	−0.922314	−0.461157	−	0.887319i	$-0.652565\pi$
$487$	−20.3537	−0.922314	−0.461157	+	0.887319i	$0.652565\pi$
$488$	−49.4608	−2.23898
$489$	20.7978	0.940510
$490$	−1.23052	−0.0555892
$491$	−26.3742	−1.19025	−0.595127	−	0.803632i	$-0.702898\pi$
$491$	−26.3742	−1.19025	−0.595127	+	0.803632i	$0.702898\pi$
$492$	71.2556	3.21245
$493$	−8.50921	−0.383236
$494$	−17.8064	−0.801149
$495$	−4.96054	−0.222960
$496$	−94.0767	−4.22417
$497$	−26.1458	−1.17280
$498$	71.7963	3.21727
$499$	−34.5087	−1.54482	−0.772412	−	0.635122i	$-0.780950\pi$
$499$	−34.5087	−1.54482	−0.772412	+	0.635122i	$0.780950\pi$
$500$	−11.9603	−0.534880
$501$	40.0018	1.78715
$502$	76.2110	3.40146
$503$	19.3209	0.861476	0.430738	−	0.902477i	$-0.358253\pi$
$503$	19.3209	0.861476	0.430738	+	0.902477i	$0.358253\pi$
$504$	89.4214	3.98315
$505$	0.594315	0.0264467
$506$	−99.5710	−4.42647
$507$	−57.3547	−2.54721
$508$	−107.846	−4.78488
$509$	9.75664	0.432456	0.216228	−	0.976343i	$-0.430625\pi$
$509$	9.75664	0.432456	0.216228	+	0.976343i	$0.430625\pi$
$510$	1.62422	0.0719217
$511$	−2.85974	−0.126508
$512$	39.3915	1.74088
$513$	3.82650	0.168944
$514$	40.0026	1.76444
$515$	0.659386	0.0290560
$516$	−14.6842	−0.646437
$517$	32.5976	1.43364
$518$	20.0131	0.879324
$519$	−5.67177	−0.248963
$520$	12.1459	0.532635
$521$	25.6073	1.12187	0.560937	−	0.827858i	$-0.310441\pi$
$521$	25.6073	1.12187	0.560937	+	0.827858i	$0.310441\pi$
$522$	99.2048	4.34207
$523$	−29.0471	−1.27014	−0.635071	−	0.772454i	$-0.719029\pi$
$523$	−29.0471	−1.27014	−0.635071	+	0.772454i	$0.719029\pi$
$524$	29.4111	1.28483
$525$	29.7284	1.29745
$526$	8.55528	0.373028
$527$	6.37447	0.277676
$528$	209.337	9.11022
$529$	25.1374	1.09293
$530$	2.11891	0.0920394
$531$	−51.0016	−2.21328
$532$	−13.5147	−0.585937
$533$	−28.4060	−1.23040
$534$	98.4949	4.26229
$535$	1.41998	0.0613912
$536$	29.6003	1.27854
$537$	−21.1598	−0.913112
$538$	−73.2765	−3.15918
$539$	10.7461	0.462868
$540$	−4.12538	−0.177528
$541$	−11.4134	−0.490700	−0.245350	−	0.969435i	$-0.578903\pi$
$541$	−11.4134	−0.490700	−0.245350	+	0.969435i	$0.578903\pi$
$542$	57.5243	2.47088
$543$	−36.4634	−1.56480
$544$	−21.4691	−0.920479
$545$	1.64246	0.0703552
$546$	−95.9025	−4.10425
$547$	−5.74538	−0.245655	−0.122827	−	0.992428i	$-0.539196\pi$
$547$	−5.74538	−0.245655	−0.122827	+	0.992428i	$0.539196\pi$
$548$	72.9924	3.11808
$549$	−22.4824	−0.959527
$550$	71.0573	3.02989
$551$	−9.48616	−0.404124
$552$	−175.881	−7.48599
$553$	0.576490	0.0245148
$554$	−26.5419	−1.12766
$555$	−1.96105	−0.0832417
$556$	127.180	5.39363
$557$	25.0584	1.06176	0.530880	−	0.847447i	$-0.321861\pi$
$557$	25.0584	1.06176	0.530880	+	0.847447i	$0.321861\pi$
$558$	−74.3169	−3.14608
$559$	5.85386	0.247592
$560$	7.25277	0.306486
$561$	−14.1843	−0.598861
$562$	−30.5017	−1.28664
$563$	13.7328	0.578769	0.289384	−	0.957213i	$-0.406549\pi$
$563$	13.7328	0.578769	0.289384	+	0.957213i	$0.406549\pi$
$564$	91.0078	3.83212
$565$	−2.51427	−0.105776
$566$	26.4797	1.11302
$567$	−7.92986	−0.333023
$568$	−110.389	−4.63181
$569$	−4.29059	−0.179871	−0.0899355	−	0.995948i	$-0.528666\pi$
$569$	−4.29059	−0.179871	−0.0899355	+	0.995948i	$0.528666\pi$
$570$	1.81070	0.0758419
$571$	−0.817880	−0.0342272	−0.0171136	−	0.999854i	$-0.505448\pi$
$571$	−0.817880	−0.0342272	−0.0171136	+	0.999854i	$0.505448\pi$
$572$	−167.649	−7.00975
$573$	32.6745	1.36500
$574$	−29.4785	−1.23041
$575$	−34.3525	−1.43260
$576$	124.179	5.17414
$577$	−7.01647	−0.292099	−0.146050	−	0.989277i	$-0.546656\pi$
$577$	−7.01647	−0.292099	−0.146050	+	0.989277i	$0.546656\pi$
$578$	2.72856	0.113493
$579$	0.810121	0.0336675
$580$	10.2271	0.424657
$581$	−21.7231	−0.901228
$582$	−11.9013	−0.493326
$583$	−18.5044	−0.766373
$584$	−12.0740	−0.499624
$585$	5.52095	0.228263
$586$	43.3262	1.78979
$587$	10.2874	0.424605	0.212303	−	0.977204i	$-0.431904\pi$
$587$	10.2874	0.424605	0.212303	+	0.977204i	$0.431904\pi$
$588$	30.0016	1.23724
$589$	7.10633	0.292811
$590$	−7.18901	−0.295967
$591$	36.6707	1.50843
$592$	48.6199	1.99826
$593$	19.6651	0.807548	0.403774	−	0.914859i	$-0.367698\pi$
$593$	19.6651	0.807548	0.403774	+	0.914859i	$0.367698\pi$
$594$	49.2597	2.02115
$595$	−0.491435	−0.0201469
$596$	−40.3413	−1.65245
$597$	−40.3583	−1.65176
$598$	110.820	4.53175
$599$	3.09516	0.126465	0.0632323	−	0.997999i	$-0.479859\pi$
$599$	3.09516	0.126465	0.0632323	+	0.997999i	$0.479859\pi$
$600$	125.515	5.12412
$601$	4.06136	0.165666	0.0828332	−	0.996563i	$-0.473603\pi$
$601$	4.06136	0.165666	0.0828332	+	0.996563i	$0.473603\pi$
$602$	6.07488	0.247594
$603$	13.4549	0.547924
$604$	72.6742	2.95707
$605$	3.67825	0.149542
$606$	−19.8125	−0.804827
$607$	18.8182	0.763808	0.381904	−	0.924202i	$-0.375268\pi$
$607$	18.8182	0.763808	0.381904	+	0.924202i	$0.375268\pi$
$608$	−23.9340	−0.970651
$609$	−51.0909	−2.07031
$610$	−3.16905	−0.128311
$611$	−36.2802	−1.46774
$612$	−23.2654	−0.940448
$613$	−28.7307	−1.16042	−0.580212	−	0.814465i	$-0.697030\pi$
$613$	−28.7307	−1.16042	−0.580212	+	0.814465i	$0.697030\pi$
$614$	22.8706	0.922981
$615$	2.88855	0.116478
$616$	−110.075	−4.43506
$617$	31.7841	1.27958	0.639791	−	0.768549i	$-0.279021\pi$
$617$	31.7841	1.27958	0.639791	+	0.768549i	$0.279021\pi$
$618$	−21.9817	−0.884233
$619$	23.4357	0.941959	0.470980	−	0.882144i	$-0.343901\pi$
$619$	23.4357	0.941959	0.470980	+	0.882144i	$0.343901\pi$
$620$	−7.66138	−0.307688
$621$	−23.8146	−0.955645
$622$	−38.3714	−1.53855
$623$	−29.8013	−1.19396
$624$	−232.986	−9.32691
$625$	24.2715	0.970862
$626$	−6.32967	−0.252984
$627$	−15.8128	−0.631503
$628$	20.8830	0.833322
$629$	−3.29440	−0.131356
$630$	5.72940	0.228265
$631$	−17.2342	−0.686083	−0.343041	−	0.939320i	$-0.611457\pi$
$631$	−17.2342	−0.686083	−0.343041	+	0.939320i	$0.611457\pi$
$632$	2.43397	0.0968180
$633$	55.1917	2.19367
$634$	29.9499	1.18946
$635$	−4.37183	−0.173491
$636$	−51.6615	−2.04851
$637$	−11.9601	−0.473877
$638$	−122.118	−4.83471
$639$	−50.1773	−1.98498
$640$	8.02615	0.317262
$641$	13.9898	0.552562	0.276281	−	0.961077i	$-0.410898\pi$
$641$	13.9898	0.552562	0.276281	+	0.961077i	$0.410898\pi$
$642$	−47.3374	−1.86826
$643$	8.22148	0.324224	0.162112	−	0.986772i	$-0.448169\pi$
$643$	8.22148	0.324224	0.162112	+	0.986772i	$0.448169\pi$
$644$	84.1098	3.31439
$645$	−0.595267	−0.0234386
$646$	3.04183	0.119679
$647$	34.0559	1.33887	0.669437	−	0.742869i	$-0.266535\pi$
$647$	34.0559	1.33887	0.669437	+	0.742869i	$0.266535\pi$
$648$	−33.4802	−1.31523
$649$	62.7815	2.46439
$650$	−79.0848	−3.10196
$651$	38.2735	1.50006
$652$	−41.9922	−1.64454
$653$	9.04114	0.353807	0.176904	−	0.984228i	$-0.443392\pi$
$653$	9.04114	0.353807	0.176904	+	0.984228i	$0.443392\pi$
$654$	−54.7541	−2.14105
$655$	1.19227	0.0465856
$656$	−71.6153	−2.79611
$657$	−5.48823	−0.214116
$658$	−37.6501	−1.46775
$659$	44.7449	1.74301	0.871507	−	0.490383i	$-0.163143\pi$
$659$	44.7449	1.74301	0.871507	+	0.490383i	$0.163143\pi$
$660$	17.0479	0.663588
$661$	43.7814	1.70290	0.851449	−	0.524438i	$-0.175725\pi$
$661$	43.7814	1.70290	0.851449	+	0.524438i	$0.175725\pi$
$662$	−58.9952	−2.29291
$663$	15.7867	0.613106
$664$	−91.7162	−3.55928
$665$	−0.547857	−0.0212450
$666$	38.4078	1.48827
$667$	59.0379	2.28596
$668$	−80.7663	−3.12494
$669$	13.8489	0.535430
$670$	1.89655	0.0732701
$671$	27.6752	1.06839
$672$	−128.904	−4.97260
$673$	−16.0740	−0.619607	−0.309804	−	0.950801i	$-0.600263\pi$
$673$	−16.0740	−0.619607	−0.309804	+	0.950801i	$0.600263\pi$
$674$	42.5617	1.63942
$675$	16.9949	0.654133
$676$	115.803	4.45396
$677$	−13.6713	−0.525431	−0.262716	−	0.964873i	$-0.584618\pi$
$677$	−13.6713	−0.525431	−0.262716	+	0.964873i	$0.584618\pi$
$678$	83.8173	3.21898
$679$	3.60094	0.138192
$680$	−2.07486	−0.0795673
$681$	36.1832	1.38655
$682$	91.4819	3.50302
$683$	−17.3027	−0.662069	−0.331034	−	0.943619i	$-0.607398\pi$
$683$	−17.3027	−0.662069	−0.331034	+	0.943619i	$0.607398\pi$
$684$	−25.9365	−0.991708
$685$	2.95896	0.113056
$686$	−54.9359	−2.09746
$687$	−61.7727	−2.35678
$688$	14.7584	0.562657
$689$	20.5948	0.784601
$690$	−11.2690	−0.429005
$691$	17.9241	0.681866	0.340933	−	0.940088i	$-0.389257\pi$
$691$	17.9241	0.681866	0.340933	+	0.940088i	$0.389257\pi$
$692$	11.4517	0.435328
$693$	−50.0348	−1.90066
$694$	42.4453	1.61120
$695$	5.15560	0.195563
$696$	−215.708	−8.17640
$697$	4.85253	0.183803
$698$	−19.8754	−0.752293
$699$	−20.9364	−0.791887
$700$	−60.0237	−2.26868
$701$	36.5628	1.38096	0.690479	−	0.723353i	$-0.257400\pi$
$701$	36.5628	1.38096	0.690479	+	0.723353i	$0.257400\pi$
$702$	−54.8247	−2.06923
$703$	−3.67263	−0.138516
$704$	−152.861	−5.76117
$705$	3.68926	0.138946
$706$	−67.4300	−2.53776
$707$	5.99459	0.225450
$708$	175.277	6.58731
$709$	12.8811	0.483758	0.241879	−	0.970306i	$-0.422236\pi$
$709$	12.8811	0.483758	0.241879	+	0.970306i	$0.422236\pi$
$710$	−7.07282	−0.265438
$711$	1.10636	0.0414918
$712$	−125.822	−4.71539
$713$	−44.2268	−1.65631
$714$	16.3828	0.613110
$715$	−6.79613	−0.254161
$716$	42.7230	1.59663
$717$	−31.4295	−1.17376
$718$	−29.5269	−1.10193
$719$	15.0722	0.562099	0.281049	−	0.959693i	$-0.409318\pi$
$719$	15.0722	0.562099	0.281049	+	0.959693i	$0.409318\pi$
$720$	13.9190	0.518732
$721$	6.65092	0.247693
$722$	−48.4516	−1.80318
$723$	−20.8966	−0.777155
$724$	73.6221	2.73615
$725$	−42.1315	−1.56472
$726$	−122.621	−4.55088
$727$	19.0866	0.707882	0.353941	−	0.935268i	$-0.384841\pi$
$727$	19.0866	0.707882	0.353941	+	0.935268i	$0.384841\pi$
$728$	122.511	4.54055
$729$	−42.9882	−1.59216
$730$	−0.773602	−0.0286323
$731$	−1.00000	−0.0369863
$732$	77.2653	2.85581
$733$	−26.1006	−0.964049	−0.482025	−	0.876158i	$-0.660098\pi$
$733$	−26.1006	−0.964049	−0.482025	+	0.876158i	$0.660098\pi$
$734$	60.1519	2.22025
$735$	1.21620	0.0448602
$736$	148.955	5.49055
$737$	−16.5625	−0.610089
$738$	−56.5733	−2.08249
$739$	30.2633	1.11325	0.556626	−	0.830763i	$-0.312096\pi$
$739$	30.2633	1.11325	0.556626	+	0.830763i	$0.312096\pi$
$740$	3.95948	0.145553
$741$	17.5992	0.646523
$742$	21.3724	0.784607
$743$	40.8536	1.49877	0.749387	−	0.662132i	$-0.230348\pi$
$743$	40.8536	1.49877	0.749387	+	0.662132i	$0.230348\pi$
$744$	161.593	5.92427
$745$	−1.63535	−0.0599146
$746$	61.8730	2.26533
$747$	−41.6896	−1.52534
$748$	28.6390	1.04715
$749$	14.3227	0.523341
$750$	16.1631	0.590192
$751$	22.7482	0.830093	0.415046	−	0.909800i	$-0.363765\pi$
$751$	22.7482	0.830093	0.415046	+	0.909800i	$0.363765\pi$
$752$	−91.4673	−3.33547
$753$	−75.3241	−2.74496
$754$	135.914	4.94970
$755$	2.94606	0.107218
$756$	−41.6108	−1.51337
$757$	−36.4313	−1.32412	−0.662060	−	0.749451i	$-0.730318\pi$
$757$	−36.4313	−1.32412	−0.662060	+	0.749451i	$0.730318\pi$
$758$	50.7097	1.84186
$759$	98.4123	3.57214
$760$	−2.31308	−0.0839042
$761$	23.8136	0.863243	0.431621	−	0.902055i	$-0.357942\pi$
$761$	23.8136	0.863243	0.431621	+	0.902055i	$0.357942\pi$
$762$	145.742	5.27968
$763$	16.5667	0.599757
$764$	−65.9721	−2.38679
$765$	−0.943130	−0.0340989
$766$	−10.5056	−0.379584
$767$	−69.8741	−2.52301
$768$	−110.811	−3.99853
$769$	−44.3298	−1.59857	−0.799286	−	0.600950i	$-0.794789\pi$
$769$	−44.3298	−1.59857	−0.799286	+	0.600950i	$0.794789\pi$
$770$	−7.05273	−0.254163
$771$	−39.5371	−1.42389
$772$	−1.63569	−0.0588698
$773$	−10.9657	−0.394410	−0.197205	−	0.980362i	$-0.563186\pi$
$773$	−10.9657	−0.394410	−0.197205	+	0.980362i	$0.563186\pi$
$774$	11.6585	0.419057
$775$	31.5618	1.13373
$776$	15.2034	0.545769
$777$	−19.7802	−0.709610
$778$	−55.6555	−1.99535
$779$	5.40965	0.193821
$780$	−18.9738	−0.679371
$781$	61.7668	2.21019
$782$	−18.9311	−0.676973
$783$	−29.2072	−1.04378
$784$	−30.1531	−1.07690
$785$	0.846552	0.0302147
$786$	−39.7461	−1.41770
$787$	−31.4964	−1.12272	−0.561362	−	0.827570i	$-0.689723\pi$
$787$	−31.4964	−1.12272	−0.561362	+	0.827570i	$0.689723\pi$
$788$	−74.0406	−2.63759
$789$	−8.45572	−0.301032
$790$	0.155949	0.00554841
$791$	−25.3603	−0.901709
$792$	−211.249	−7.50641
$793$	−30.8017	−1.09380
$794$	9.24445	0.328073
$795$	−2.09425	−0.0742753
$796$	81.4862	2.88820
$797$	−0.294342	−0.0104261	−0.00521307	−	0.999986i	$-0.501659\pi$
$797$	−0.294342	−0.0104261	−0.00521307	+	0.999986i	$0.501659\pi$
$798$	18.2637	0.646528
$799$	6.19766	0.219258
$800$	−106.299	−3.75825
$801$	−57.1926	−2.02080
$802$	81.1315	2.86485
$803$	6.75586	0.238409
$804$	−46.2402	−1.63077
$805$	3.40963	0.120174
$806$	−101.817	−3.58635
$807$	72.4238	2.54944
$808$	25.3095	0.890383
$809$	−43.9882	−1.54654	−0.773272	−	0.634074i	$-0.781381\pi$
$809$	−43.9882	−1.54654	−0.773272	+	0.634074i	$0.781381\pi$
$810$	−2.14514	−0.0753727
$811$	0.321447	0.0112875	0.00564377	−	0.999984i	$-0.498204\pi$
$811$	0.321447	0.0112875	0.00564377	+	0.999984i	$0.498204\pi$
$812$	103.156	3.62007
$813$	−56.8549	−1.99399
$814$	−47.2789	−1.65712
$815$	−1.70227	−0.0596280
$816$	39.8005	1.39329
$817$	−1.11481	−0.0390023
$818$	18.4023	0.643423
$819$	55.6873	1.94587
$820$	−5.83217	−0.203668
$821$	−50.5046	−1.76262	−0.881312	−	0.472535i	$-0.843339\pi$
$821$	−50.5046	−1.76262	−0.881312	+	0.472535i	$0.843339\pi$
$822$	−98.6416	−3.44052
$823$	27.8521	0.970864	0.485432	−	0.874274i	$-0.338662\pi$
$823$	27.8521	0.970864	0.485432	+	0.874274i	$0.338662\pi$
$824$	28.0805	0.978231
$825$	−70.2304	−2.44511
$826$	−72.5123	−2.52303
$827$	20.8215	0.724033	0.362017	−	0.932172i	$-0.382088\pi$
$827$	20.8215	0.724033	0.362017	+	0.932172i	$0.382088\pi$
$828$	161.418	5.60967
$829$	−40.7920	−1.41677	−0.708383	−	0.705829i	$-0.750575\pi$
$829$	−40.7920	−1.41677	−0.708383	+	0.705829i	$0.750575\pi$
$830$	−5.87643	−0.203974
$831$	26.2330	0.910013
$832$	170.130	5.89821
$833$	2.04312	0.0707898
$834$	−171.870	−5.95138
$835$	−3.27409	−0.113305
$836$	31.9271	1.10422
$837$	21.8799	0.756280
$838$	−29.4978	−1.01899
$839$	−33.3916	−1.15281	−0.576403	−	0.817166i	$-0.695544\pi$
$839$	−33.3916	−1.15281	−0.576403	+	0.817166i	$0.695544\pi$
$840$	−12.4579	−0.429837
$841$	43.4067	1.49678
$842$	39.1684	1.34983
$843$	30.1467	1.03831
$844$	−111.436	−3.83578
$845$	4.69441	0.161492
$846$	−72.2555	−2.48420
$847$	37.1009	1.27480
$848$	51.9224	1.78302
$849$	−26.1715	−0.898205
$850$	13.5099	0.463384
$851$	22.8569	0.783525
$852$	172.444	5.90784
$853$	−40.7500	−1.39525	−0.697626	−	0.716462i	$-0.745760\pi$
$853$	−40.7500	−1.39525	−0.697626	+	0.716462i	$0.745760\pi$
$854$	−31.9647	−1.09381
$855$	−1.05141	−0.0359575
$856$	60.4712	2.06686
$857$	−21.5381	−0.735729	−0.367865	−	0.929879i	$-0.619911\pi$
$857$	−21.5381	−0.735729	−0.367865	+	0.929879i	$0.619911\pi$
$858$	226.560	7.73463
$859$	−29.1447	−0.994403	−0.497202	−	0.867635i	$-0.665639\pi$
$859$	−29.1447	−0.994403	−0.497202	+	0.867635i	$0.665639\pi$
$860$	1.20188	0.0409839
$861$	29.1355	0.992935
$862$	−75.7165	−2.57891
$863$	−17.8646	−0.608117	−0.304059	−	0.952653i	$-0.598342\pi$
$863$	−17.8646	−0.608117	−0.304059	+	0.952653i	$0.598342\pi$
$864$	−73.6910	−2.50702
$865$	0.464227	0.0157842
$866$	−47.6138	−1.61798
$867$	−2.69681	−0.0915884
$868$	−77.2768	−2.62295
$869$	−1.36190	−0.0461993
$870$	−13.8208	−0.468570
$871$	18.4336	0.624600
$872$	69.9456	2.36866
$873$	6.91070	0.233892
$874$	−21.1046	−0.713872
$875$	−4.89041	−0.165326
$876$	18.8614	0.637267
$877$	−7.09246	−0.239495	−0.119748	−	0.992804i	$-0.538209\pi$
$877$	−7.09246	−0.239495	−0.119748	+	0.992804i	$0.538209\pi$
$878$	86.2947	2.91231
$879$	−42.8221	−1.44435
$880$	−17.1340	−0.577585
$881$	36.1175	1.21683	0.608415	−	0.793619i	$-0.291806\pi$
$881$	36.1175	1.21683	0.608415	+	0.793619i	$0.291806\pi$
$882$	−23.8197	−0.802052
$883$	43.6798	1.46994	0.734971	−	0.678099i	$-0.237196\pi$
$883$	43.6798	1.46994	0.734971	+	0.678099i	$0.237196\pi$
$884$	−31.8745	−1.07205
$885$	7.10535	0.238844
$886$	68.7357	2.30922
$887$	−36.2779	−1.21809	−0.609047	−	0.793134i	$-0.708448\pi$
$887$	−36.2779	−1.21809	−0.609047	+	0.793134i	$0.708448\pi$
$888$	−83.5128	−2.80251
$889$	−44.0967	−1.47896
$890$	−8.06168	−0.270228
$891$	18.7335	0.627596
$892$	−27.9619	−0.936234
$893$	6.90922	0.231208
$894$	54.5171	1.82332
$895$	1.73190	0.0578910
$896$	80.9562	2.70456
$897$	−109.530	−3.65710
$898$	−88.6715	−2.95901
$899$	−54.2417	−1.80906
$900$	−115.194	−3.83978
$901$	−3.51817	−0.117207
$902$	69.6400	2.31876
$903$	−6.00419	−0.199807
$904$	−107.072	−3.56118
$905$	2.98448	0.0992076
$906$	−98.2116	−3.26286
$907$	30.9431	1.02745	0.513725	−	0.857955i	$-0.328265\pi$
$907$	30.9431	1.02745	0.513725	+	0.857955i	$0.328265\pi$
$908$	−73.0564	−2.42446
$909$	11.5044	0.381578
$910$	7.84949	0.260208
$911$	30.8931	1.02353	0.511767	−	0.859124i	$-0.328991\pi$
$911$	30.8931	1.02353	0.511767	+	0.859124i	$0.328991\pi$
$912$	44.3700	1.46924
$913$	51.3188	1.69840
$914$	40.7352	1.34740
$915$	3.13217	0.103546
$916$	124.723	4.12097
$917$	12.0258	0.397128
$918$	9.36557	0.309110
$919$	−15.8945	−0.524311	−0.262156	−	0.965026i	$-0.584433\pi$
$919$	−15.8945	−0.524311	−0.262156	+	0.965026i	$0.584433\pi$
$920$	14.3956	0.474610
$921$	−22.6044	−0.744841
$922$	−21.3628	−0.703545
$923$	−68.7447	−2.26276
$924$	171.954	5.65688
$925$	−16.3115	−0.536318
$926$	19.8785	0.653247
$927$	12.7640	0.419225
$928$	182.685	5.99693
$929$	48.9639	1.60645	0.803226	−	0.595674i	$-0.203115\pi$
$929$	48.9639	1.60645	0.803226	+	0.595674i	$0.203115\pi$
$930$	10.3536	0.339506
$931$	2.27769	0.0746483
$932$	42.2720	1.38466
$933$	37.9249	1.24160
$934$	−99.2784	−3.24849
$935$	1.16097	0.0379676
$936$	235.114	7.68495
$937$	12.7574	0.416765	0.208382	−	0.978047i	$-0.433180\pi$
$937$	12.7574	0.416765	0.208382	+	0.978047i	$0.433180\pi$
$938$	19.1296	0.624605
$939$	6.25601	0.204157
$940$	−7.44887	−0.242955
$941$	6.60373	0.215275	0.107638	−	0.994190i	$-0.465671\pi$
$941$	6.60373	0.215275	0.107638	+	0.994190i	$0.465671\pi$
$942$	−28.2212	−0.919496
$943$	−33.6674	−1.09636
$944$	−176.162	−5.73358
$945$	−1.68681	−0.0548720
$946$	−14.3513	−0.466601
$947$	28.7413	0.933968	0.466984	−	0.884266i	$-0.345341\pi$
$947$	28.7413	0.933968	0.466984	+	0.884266i	$0.345341\pi$
$948$	−3.80223	−0.123491
$949$	−7.51908	−0.244080
$950$	15.0609	0.488641
$951$	−29.6014	−0.959891
$952$	−20.9282	−0.678287
$953$	−24.8195	−0.803983	−0.401992	−	0.915643i	$-0.631682\pi$
$953$	−24.8195	−0.803983	−0.401992	+	0.915643i	$0.631682\pi$
$954$	41.0166	1.32796
$955$	−2.67437	−0.0865405
$956$	63.4583	2.05239
$957$	120.697	3.90159
$958$	−100.465	−3.24589
$959$	29.8456	0.963766
$960$	−17.3002	−0.558362
$961$	9.63389	0.310771
$962$	52.6201	1.69654
$963$	27.4872	0.885764
$964$	42.1917	1.35890
$965$	−0.0663074	−0.00213451
$966$	−113.666	−3.65713
$967$	34.5932	1.11244	0.556222	−	0.831034i	$-0.312251\pi$
$967$	34.5932	1.11244	0.556222	+	0.831034i	$0.312251\pi$
$968$	156.642	5.03466
$969$	−3.00643	−0.0965805
$970$	0.974108	0.0312767
$971$	−2.62712	−0.0843083	−0.0421541	−	0.999111i	$-0.513422\pi$
$971$	−2.62712	−0.0843083	−0.0421541	+	0.999111i	$0.513422\pi$
$972$	108.370	3.47598
$973$	52.0022	1.66711
$974$	−55.5363	−1.77950
$975$	78.1645	2.50327
$976$	−77.6554	−2.48569
$977$	−16.9832	−0.543342	−0.271671	−	0.962390i	$-0.587576\pi$
$977$	−16.9832	−0.543342	−0.271671	+	0.962390i	$0.587576\pi$
$978$	56.7481	1.81460
$979$	70.4025	2.25007
$980$	−2.45559	−0.0784410
$981$	31.7938	1.01510
$982$	−71.9637	−2.29645
$983$	−11.9114	−0.379916	−0.189958	−	0.981792i	$-0.560835\pi$
$983$	−11.9114	−0.379916	−0.189958	+	0.981792i	$0.560835\pi$
$984$	123.011	3.92146
$985$	−3.00145	−0.0956341
$986$	−23.2179	−0.739408
$987$	37.2119	1.18447
$988$	−35.5340	−1.13049
$989$	6.93812	0.220619
$990$	−13.5351	−0.430175
$991$	−8.77048	−0.278603	−0.139302	−	0.990250i	$-0.544486\pi$
$991$	−8.77048	−0.278603	−0.139302	+	0.990250i	$0.544486\pi$
$992$	−136.854	−4.34512
$993$	58.3087	1.85037
$994$	−71.3403	−2.26278
$995$	3.30328	0.104721
$996$	143.275	4.53983
$997$	19.6834	0.623381	0.311690	−	0.950184i	$-0.399105\pi$
$997$	19.6834	0.623381	0.311690	+	0.950184i	$0.399105\pi$
$998$	−94.1591	−2.98056
$999$	−11.3078	−0.357762

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	731.2.a.f.1.20	✓	21
3.2	odd	2		6579.2.a.u.1.2		21

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
731.2.a.f.1.20	✓	21	1.1	even	1	trivial
6579.2.a.u.1.2		21	3.2	odd	2

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:	\( N \)	\(=\)	\( 731 = 17 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	731.a (trivial)

\(f(q)\)	\(=\)	\(q+2.72856 q^{2} -2.69681 q^{3} +5.44504 q^{4} +0.220730 q^{5} -7.35840 q^{6} +2.22641 q^{7} +9.39999 q^{8} +4.27277 q^{9} +O(q^{10})\)	\(q+2.72856 q^{2} -2.69681 q^{3} +5.44504 q^{4} +0.220730 q^{5} -7.35840 q^{6} +2.22641 q^{7} +9.39999 q^{8} +4.27277 q^{9} +0.602275 q^{10} -5.25966 q^{11} -14.6842 q^{12} +5.85386 q^{13} +6.07488 q^{14} -0.595267 q^{15} +14.7584 q^{16} -1.00000 q^{17} +11.6585 q^{18} -1.11481 q^{19} +1.20188 q^{20} -6.00419 q^{21} -14.3513 q^{22} +6.93812 q^{23} -25.3500 q^{24} -4.95128 q^{25} +15.9726 q^{26} -3.43242 q^{27} +12.1229 q^{28} +8.50921 q^{29} -1.62422 q^{30} -6.37447 q^{31} +21.4691 q^{32} +14.1843 q^{33} -2.72856 q^{34} +0.491435 q^{35} +23.2654 q^{36} +3.29440 q^{37} -3.04183 q^{38} -15.7867 q^{39} +2.07486 q^{40} -4.85253 q^{41} -16.3828 q^{42} +1.00000 q^{43} -28.6390 q^{44} +0.943130 q^{45} +18.9311 q^{46} -6.19766 q^{47} -39.8005 q^{48} -2.04312 q^{49} -13.5099 q^{50} +2.69681 q^{51} +31.8745 q^{52} +3.51817 q^{53} -9.36557 q^{54} -1.16097 q^{55} +20.9282 q^{56} +3.00643 q^{57} +23.2179 q^{58} -11.9364 q^{59} -3.24125 q^{60} -5.26179 q^{61} -17.3931 q^{62} +9.51293 q^{63} +29.0629 q^{64} +1.29212 q^{65} +38.7027 q^{66} +3.14898 q^{67} -5.44504 q^{68} -18.7108 q^{69} +1.34091 q^{70} -11.7435 q^{71} +40.1640 q^{72} -1.28447 q^{73} +8.98896 q^{74} +13.3526 q^{75} -6.07019 q^{76} -11.7101 q^{77} -43.0750 q^{78} +0.258933 q^{79} +3.25762 q^{80} -3.56173 q^{81} -13.2404 q^{82} -9.75705 q^{83} -32.6930 q^{84} -0.220730 q^{85} +2.72856 q^{86} -22.9477 q^{87} -49.4408 q^{88} -13.3854 q^{89} +2.57339 q^{90} +13.0331 q^{91} +37.7783 q^{92} +17.1907 q^{93} -16.9107 q^{94} -0.246072 q^{95} -57.8980 q^{96} +1.61738 q^{97} -5.57477 q^{98} -22.4733 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 21 q + 2 q^{2} - q^{3} + 32 q^{4} - 3 q^{5} + q^{6} + 5 q^{7} + 6 q^{8} + 34 q^{9}+O(q^{10}) \) 21 * q + 2 * q^2 - q^3 + 32 * q^4 - 3 * q^5 + q^6 + 5 * q^7 + 6 * q^8 + 34 * q^9	\( 21 q + 2 q^{2} - q^{3} + 32 q^{4} - 3 q^{5} + q^{6} + 5 q^{7} + 6 q^{8} + 34 q^{9} + 12 q^{10} + 2 q^{11} - 5 q^{12} + 26 q^{13} - 3 q^{14} + 5 q^{15} + 62 q^{16} - 21 q^{17} - 10 q^{18} + 16 q^{19} - 27 q^{20} + 36 q^{21} - 14 q^{22} - q^{23} + 15 q^{24} + 40 q^{25} - 3 q^{26} - 16 q^{27} + 25 q^{28} + 15 q^{29} + 38 q^{30} + 18 q^{31} + 14 q^{32} + 14 q^{33} - 2 q^{34} - 5 q^{35} + 73 q^{36} + 12 q^{37} + 19 q^{38} - 11 q^{39} + 41 q^{40} - 45 q^{42} + 21 q^{43} - 34 q^{44} - 18 q^{45} + 28 q^{46} - q^{47} - 36 q^{48} + 40 q^{49} + 24 q^{50} + q^{51} + 23 q^{52} + 39 q^{53} - 83 q^{54} - 2 q^{55} - 10 q^{56} + 3 q^{57} + 19 q^{58} + 4 q^{59} - 35 q^{60} + 50 q^{61} + 5 q^{62} - 37 q^{63} + 120 q^{64} - 8 q^{65} - 37 q^{66} + 16 q^{67} - 32 q^{68} + 33 q^{69} - q^{70} + q^{71} - 54 q^{72} + 15 q^{73} + 52 q^{74} + 11 q^{75} - 15 q^{76} + 13 q^{77} - 100 q^{78} + 56 q^{79} - 100 q^{80} + 97 q^{81} - 11 q^{82} + 61 q^{84} + 3 q^{85} + 2 q^{86} - 8 q^{87} - 56 q^{88} + 5 q^{89} - 69 q^{90} - 4 q^{91} - 27 q^{92} + 17 q^{93} - 47 q^{94} - 9 q^{95} + 81 q^{96} - 28 q^{97} + 18 q^{98} - 19 q^{99}+O(q^{100}) \) 21 * q + 2 * q^2 - q^3 + 32 * q^4 - 3 * q^5 + q^6 + 5 * q^7 + 6 * q^8 + 34 * q^9 + 12 * q^10 + 2 * q^11 - 5 * q^12 + 26 * q^13 - 3 * q^14 + 5 * q^15 + 62 * q^16 - 21 * q^17 - 10 * q^18 + 16 * q^19 - 27 * q^20 + 36 * q^21 - 14 * q^22 - q^23 + 15 * q^24 + 40 * q^25 - 3 * q^26 - 16 * q^27 + 25 * q^28 + 15 * q^29 + 38 * q^30 + 18 * q^31 + 14 * q^32 + 14 * q^33 - 2 * q^34 - 5 * q^35 + 73 * q^36 + 12 * q^37 + 19 * q^38 - 11 * q^39 + 41 * q^40 - 45 * q^42 + 21 * q^43 - 34 * q^44 - 18 * q^45 + 28 * q^46 - q^47 - 36 * q^48 + 40 * q^49 + 24 * q^50 + q^51 + 23 * q^52 + 39 * q^53 - 83 * q^54 - 2 * q^55 - 10 * q^56 + 3 * q^57 + 19 * q^58 + 4 * q^59 - 35 * q^60 + 50 * q^61 + 5 * q^62 - 37 * q^63 + 120 * q^64 - 8 * q^65 - 37 * q^66 + 16 * q^67 - 32 * q^68 + 33 * q^69 - q^70 + q^71 - 54 * q^72 + 15 * q^73 + 52 * q^74 + 11 * q^75 - 15 * q^76 + 13 * q^77 - 100 * q^78 + 56 * q^79 - 100 * q^80 + 97 * q^81 - 11 * q^82 + 61 * q^84 + 3 * q^85 + 2 * q^86 - 8 * q^87 - 56 * q^88 + 5 * q^89 - 69 * q^90 - 4 * q^91 - 27 * q^92 + 17 * q^93 - 47 * q^94 - 9 * q^95 + 81 * q^96 - 28 * q^97 + 18 * q^98 - 19 * q^99

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