LMFDB - Embedded newform 8021.2.a.c.1.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8021,2,Mod(1,8021)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8021, 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("8021.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8021 = 13 \cdot 617 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8021.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:	$64.0480074613$
Analytic rank:	$0$
Dimension:	$169$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.18
Character	$\chi$	$=$	8021.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.41610 q^{2} -2.76712 q^{3} +3.83752 q^{4} +4.12238 q^{5} +6.68562 q^{6} +0.703742 q^{7} -4.43962 q^{8} +4.65694 q^{9} +O(q^{10})$	\(q-2.41610 q^{2} -2.76712 q^{3} +3.83752 q^{4} +4.12238 q^{5} +6.68562 q^{6} +0.703742 q^{7} -4.43962 q^{8} +4.65694 q^{9} -9.96007 q^{10} -1.07959 q^{11} -10.6189 q^{12} -1.00000 q^{13} -1.70031 q^{14} -11.4071 q^{15} +3.05151 q^{16} +2.12420 q^{17} -11.2516 q^{18} +3.46361 q^{19} +15.8197 q^{20} -1.94734 q^{21} +2.60840 q^{22} +8.29891 q^{23} +12.2849 q^{24} +11.9940 q^{25} +2.41610 q^{26} -4.58494 q^{27} +2.70062 q^{28} -2.74674 q^{29} +27.5607 q^{30} -0.917492 q^{31} +1.50650 q^{32} +2.98736 q^{33} -5.13227 q^{34} +2.90109 q^{35} +17.8711 q^{36} -10.2071 q^{37} -8.36841 q^{38} +2.76712 q^{39} -18.3018 q^{40} +6.93891 q^{41} +4.70495 q^{42} +7.51459 q^{43} -4.14295 q^{44} +19.1977 q^{45} -20.0510 q^{46} +0.267183 q^{47} -8.44389 q^{48} -6.50475 q^{49} -28.9787 q^{50} -5.87791 q^{51} -3.83752 q^{52} -12.0524 q^{53} +11.0776 q^{54} -4.45049 q^{55} -3.12435 q^{56} -9.58421 q^{57} +6.63638 q^{58} +10.0844 q^{59} -43.7750 q^{60} +0.286478 q^{61} +2.21675 q^{62} +3.27728 q^{63} -9.74287 q^{64} -4.12238 q^{65} -7.21774 q^{66} +2.60226 q^{67} +8.15166 q^{68} -22.9641 q^{69} -7.00932 q^{70} -7.88597 q^{71} -20.6750 q^{72} -2.36620 q^{73} +24.6612 q^{74} -33.1889 q^{75} +13.2917 q^{76} -0.759754 q^{77} -6.68562 q^{78} +11.0591 q^{79} +12.5795 q^{80} -1.28375 q^{81} -16.7651 q^{82} +1.67529 q^{83} -7.47294 q^{84} +8.75676 q^{85} -18.1560 q^{86} +7.60055 q^{87} +4.79298 q^{88} +11.3848 q^{89} -46.3834 q^{90} -0.703742 q^{91} +31.8472 q^{92} +2.53881 q^{93} -0.645541 q^{94} +14.2783 q^{95} -4.16866 q^{96} +15.4288 q^{97} +15.7161 q^{98} -5.02759 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 169 q + 9 q^{2} + 9 q^{3} + 199 q^{4} + 12 q^{5} + 22 q^{6} + 36 q^{7} + 30 q^{8} + 198 q^{9}+O(q^{10}) $ 169 * q + 9 * q^2 + 9 * q^3 + 199 * q^4 + 12 * q^5 + 22 * q^6 + 36 * q^7 + 30 * q^8 + 198 * q^9	\( 169 q + 9 q^{2} + 9 q^{3} + 199 q^{4} + 12 q^{5} + 22 q^{6} + 36 q^{7} + 30 q^{8} + 198 q^{9} - 3 q^{10} + 59 q^{11} + 11 q^{12} - 169 q^{13} + 30 q^{14} + 50 q^{15} + 267 q^{16} + q^{17} + 53 q^{18} + 107 q^{19} + 48 q^{20} + 36 q^{21} + 14 q^{22} + 12 q^{23} + 78 q^{24} + 217 q^{25} - 9 q^{26} + 39 q^{27} + 99 q^{28} + 30 q^{29} - q^{30} + 106 q^{31} + 74 q^{32} + 16 q^{33} + 56 q^{34} + 46 q^{35} + 271 q^{36} + 73 q^{37} + 2 q^{38} - 9 q^{39} - 16 q^{40} + 52 q^{41} - 2 q^{42} + 64 q^{43} + 124 q^{44} + 84 q^{45} + 105 q^{46} + 55 q^{47} + 26 q^{48} + 257 q^{49} + 60 q^{50} + 117 q^{51} - 199 q^{52} + 7 q^{53} + 78 q^{54} - 4 q^{55} + 63 q^{56} + 51 q^{57} + 84 q^{58} + 98 q^{59} + 94 q^{60} + 32 q^{61} - 25 q^{62} + 128 q^{63} + 380 q^{64} - 12 q^{65} + 16 q^{66} + 170 q^{67} - 10 q^{68} + 55 q^{69} + 70 q^{70} + 124 q^{71} + 173 q^{72} + 81 q^{73} + 54 q^{74} + 120 q^{75} + 212 q^{76} + 20 q^{77} - 22 q^{78} + 92 q^{79} + 66 q^{80} + 265 q^{81} + 21 q^{82} + 62 q^{83} + 98 q^{84} + 139 q^{85} + 51 q^{86} - 33 q^{87} + 31 q^{88} + 58 q^{89} + 16 q^{90} - 36 q^{91} + 40 q^{92} + 37 q^{93} + 55 q^{94} + 23 q^{95} + 164 q^{96} + 78 q^{97} + 69 q^{98} + 307 q^{99}+O(q^{100}) \) 169 * q + 9 * q^2 + 9 * q^3 + 199 * q^4 + 12 * q^5 + 22 * q^6 + 36 * q^7 + 30 * q^8 + 198 * q^9 - 3 * q^10 + 59 * q^11 + 11 * q^12 - 169 * q^13 + 30 * q^14 + 50 * q^15 + 267 * q^16 + q^17 + 53 * q^18 + 107 * q^19 + 48 * q^20 + 36 * q^21 + 14 * q^22 + 12 * q^23 + 78 * q^24 + 217 * q^25 - 9 * q^26 + 39 * q^27 + 99 * q^28 + 30 * q^29 - q^30 + 106 * q^31 + 74 * q^32 + 16 * q^33 + 56 * q^34 + 46 * q^35 + 271 * q^36 + 73 * q^37 + 2 * q^38 - 9 * q^39 - 16 * q^40 + 52 * q^41 - 2 * q^42 + 64 * q^43 + 124 * q^44 + 84 * q^45 + 105 * q^46 + 55 * q^47 + 26 * q^48 + 257 * q^49 + 60 * q^50 + 117 * q^51 - 199 * q^52 + 7 * q^53 + 78 * q^54 - 4 * q^55 + 63 * q^56 + 51 * q^57 + 84 * q^58 + 98 * q^59 + 94 * q^60 + 32 * q^61 - 25 * q^62 + 128 * q^63 + 380 * q^64 - 12 * q^65 + 16 * q^66 + 170 * q^67 - 10 * q^68 + 55 * q^69 + 70 * q^70 + 124 * q^71 + 173 * q^72 + 81 * q^73 + 54 * q^74 + 120 * q^75 + 212 * q^76 + 20 * q^77 - 22 * q^78 + 92 * q^79 + 66 * q^80 + 265 * q^81 + 21 * q^82 + 62 * q^83 + 98 * q^84 + 139 * q^85 + 51 * q^86 - 33 * q^87 + 31 * q^88 + 58 * q^89 + 16 * q^90 - 36 * q^91 + 40 * q^92 + 37 * q^93 + 55 * q^94 + 23 * q^95 + 164 * q^96 + 78 * q^97 + 69 * q^98 + 307 * 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 $

$2$	−2.41610	−1.70844	−0.854219	−	0.519914i	$-0.825964\pi$
$2$	−2.41610	−1.70844	−0.854219	+	0.519914i	$0.825964\pi$
$3$	−2.76712	−1.59760	−0.798798	−	0.601599i	$-0.794530\pi$
$3$	−2.76712	−1.59760	−0.798798	+	0.601599i	$0.794530\pi$
$4$	3.83752	1.91876
$5$	4.12238	1.84359	0.921793	−	0.387683i	$-0.126725\pi$
$5$	4.12238	1.84359	0.921793	+	0.387683i	$0.126725\pi$
$6$	6.68562	2.72939
$7$	0.703742	0.265989	0.132995	−	0.991117i	$-0.457541\pi$
$7$	0.703742	0.265989	0.132995	+	0.991117i	$0.457541\pi$
$8$	−4.43962	−1.56964
$9$	4.65694	1.55231
$10$	−9.96007	−3.14965
$11$	−1.07959	−0.325509	−0.162755	−	0.986667i	$-0.552038\pi$
$11$	−1.07959	−0.325509	−0.162755	+	0.986667i	$0.552038\pi$
$12$	−10.6189	−3.06540
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	−1.70031	−0.454426
$15$	−11.4071	−2.94530
$16$	3.05151	0.762878
$17$	2.12420	0.515194	0.257597	−	0.966252i	$-0.417069\pi$
$17$	2.12420	0.515194	0.257597	+	0.966252i	$0.417069\pi$
$18$	−11.2516	−2.65203
$19$	3.46361	0.794606	0.397303	−	0.917688i	$-0.369946\pi$
$19$	3.46361	0.794606	0.397303	+	0.917688i	$0.369946\pi$
$20$	15.8197	3.53740
$21$	−1.94734	−0.424944
$22$	2.60840	0.556112
$23$	8.29891	1.73044	0.865221	−	0.501390i	$-0.167178\pi$
$23$	8.29891	1.73044	0.865221	+	0.501390i	$0.167178\pi$
$24$	12.2849	2.50765
$25$	11.9940	2.39881
$26$	2.41610	0.473835
$27$	−4.58494	−0.882372
$28$	2.70062	0.510370
$29$	−2.74674	−0.510057	−0.255028	−	0.966934i	$-0.582085\pi$
$29$	−2.74674	−0.510057	−0.255028	+	0.966934i	$0.582085\pi$
$30$	27.5607	5.03187
$31$	−0.917492	−0.164786	−0.0823932	−	0.996600i	$-0.526256\pi$
$31$	−0.917492	−0.164786	−0.0823932	+	0.996600i	$0.526256\pi$
$32$	1.50650	0.266314
$33$	2.98736	0.520032
$34$	−5.13227	−0.880177
$35$	2.90109	0.490374
$36$	17.8711	2.97851
$37$	−10.2071	−1.67803	−0.839016	−	0.544107i	$-0.816868\pi$
$37$	−10.2071	−1.67803	−0.839016	+	0.544107i	$0.816868\pi$
$38$	−8.36841	−1.35753
$39$	2.76712	0.443093
$40$	−18.3018	−2.89377
$41$	6.93891	1.08368	0.541838	−	0.840483i	$-0.317729\pi$
$41$	6.93891	1.08368	0.541838	+	0.840483i	$0.317729\pi$
$42$	4.70495	0.725990
$43$	7.51459	1.14596	0.572982	−	0.819568i	$-0.305786\pi$
$43$	7.51459	1.14596	0.572982	+	0.819568i	$0.305786\pi$
$44$	−4.14295	−0.624574
$45$	19.1977	2.86182
$46$	−20.0510	−2.95635
$47$	0.267183	0.0389727	0.0194864	−	0.999810i	$-0.493797\pi$
$47$	0.267183	0.0389727	0.0194864	+	0.999810i	$0.493797\pi$
$48$	−8.44389	−1.21877
$49$	−6.50475	−0.929250
$50$	−28.9787	−4.09821
$51$	−5.87791	−0.823072
$52$	−3.83752	−0.532168
$53$	−12.0524	−1.65553	−0.827763	−	0.561077i	$-0.810387\pi$
$53$	−12.0524	−1.65553	−0.827763	+	0.561077i	$0.810387\pi$
$54$	11.0776	1.50748
$55$	−4.45049	−0.600104
$56$	−3.12435	−0.417508
$57$	−9.58421	−1.26946
$58$	6.63638	0.871400
$59$	10.0844	1.31288	0.656440	−	0.754378i	$-0.272061\pi$
$59$	10.0844	1.31288	0.656440	+	0.754378i	$0.272061\pi$
$60$	−43.7750	−5.65133
$61$	0.286478	0.0366797	0.0183399	−	0.999832i	$-0.494162\pi$
$61$	0.286478	0.0366797	0.0183399	+	0.999832i	$0.494162\pi$
$62$	2.21675	0.281527
$63$	3.27728	0.412899
$64$	−9.74287	−1.21786
$65$	−4.12238	−0.511319
$66$	−7.21774	−0.888443
$67$	2.60226	0.317917	0.158959	−	0.987285i	$-0.449186\pi$
$67$	2.60226	0.317917	0.158959	+	0.987285i	$0.449186\pi$
$68$	8.15166	0.988533
$69$	−22.9641	−2.76455
$70$	−7.00932	−0.837774
$71$	−7.88597	−0.935892	−0.467946	−	0.883757i	$-0.655006\pi$
$71$	−7.88597	−0.935892	−0.467946	+	0.883757i	$0.655006\pi$
$72$	−20.6750	−2.43658
$73$	−2.36620	−0.276943	−0.138471	−	0.990366i	$-0.544219\pi$
$73$	−2.36620	−0.276943	−0.138471	+	0.990366i	$0.544219\pi$
$74$	24.6612	2.86681
$75$	−33.1889	−3.83232
$76$	13.2917	1.52466
$77$	−0.759754	−0.0865820
$78$	−6.68562	−0.756997
$79$	11.0591	1.24424	0.622121	−	0.782921i	$-0.286271\pi$
$79$	11.0591	1.24424	0.622121	+	0.782921i	$0.286271\pi$
$80$	12.5795	1.40643
$81$	−1.28375	−0.142639
$82$	−16.7651	−1.85139
$83$	1.67529	0.183887	0.0919437	−	0.995764i	$-0.470692\pi$
$83$	1.67529	0.183887	0.0919437	+	0.995764i	$0.470692\pi$
$84$	−7.47294	−0.815364
$85$	8.75676	0.949804
$86$	−18.1560	−1.95781
$87$	7.60055	0.814864
$88$	4.79298	0.510933
$89$	11.3848	1.20679	0.603394	−	0.797443i	$-0.293815\pi$
$89$	11.3848	1.20679	0.603394	+	0.797443i	$0.293815\pi$
$90$	−46.3834	−4.88924
$91$	−0.703742	−0.0737722
$92$	31.8472	3.32030
$93$	2.53881	0.263262
$94$	−0.645541	−0.0665824
$95$	14.2783	1.46492
$96$	−4.16866	−0.425462
$97$	15.4288	1.56655	0.783276	−	0.621674i	$-0.213547\pi$
$97$	15.4288	1.56655	0.783276	+	0.621674i	$0.213547\pi$
$98$	15.7161	1.58757
$99$	−5.02759	−0.505292
$100$	46.0273	4.60273
$101$	17.8353	1.77468	0.887342	−	0.461113i	$-0.152550\pi$
$101$	17.8353	1.77468	0.887342	+	0.461113i	$0.152550\pi$
$102$	14.2016	1.40617
$103$	−3.61032	−0.355735	−0.177868	−	0.984054i	$-0.556920\pi$
$103$	−3.61032	−0.355735	−0.177868	+	0.984054i	$0.556920\pi$
$104$	4.43962	0.435341
$105$	−8.02766	−0.783420
$106$	29.1198	2.82836
$107$	−3.27373	−0.316483	−0.158242	−	0.987400i	$-0.550582\pi$
$107$	−3.27373	−0.316483	−0.158242	+	0.987400i	$0.550582\pi$
$108$	−17.5948	−1.69306
$109$	−1.91009	−0.182953	−0.0914766	−	0.995807i	$-0.529159\pi$
$109$	−1.91009	−0.182953	−0.0914766	+	0.995807i	$0.529159\pi$
$110$	10.7528	1.02524
$111$	28.2441	2.68082
$112$	2.14748	0.202917
$113$	0.203711	0.0191635	0.00958174	−	0.999954i	$-0.496950\pi$
$113$	0.203711	0.0191635	0.00958174	+	0.999954i	$0.496950\pi$
$114$	23.1564	2.16879
$115$	34.2113	3.19022
$116$	−10.5407	−0.978676
$117$	−4.65694	−0.430534
$118$	−24.3649	−2.24297
$119$	1.49489	0.137036
$120$	50.6433	4.62308
$121$	−9.83448	−0.894044
$122$	−0.692158	−0.0626650
$123$	−19.2008	−1.73128
$124$	−3.52089	−0.316185
$125$	28.8321	2.57882
$126$	−7.91823	−0.705412
$127$	−4.07150	−0.361287	−0.180644	−	0.983549i	$-0.557818\pi$
$127$	−4.07150	−0.361287	−0.180644	+	0.983549i	$0.557818\pi$
$128$	20.5267	1.81432
$129$	−20.7938	−1.83079
$130$	9.96007	0.873556
$131$	0.229118	0.0200182	0.0100091	−	0.999950i	$-0.496814\pi$
$131$	0.229118	0.0200182	0.0100091	+	0.999950i	$0.496814\pi$
$132$	11.4640	0.997817
$133$	2.43749	0.211357
$134$	−6.28732	−0.543142
$135$	−18.9009	−1.62673
$136$	−9.43064	−0.808671
$137$	−13.6069	−1.16252	−0.581259	−	0.813719i	$-0.697440\pi$
$137$	−13.6069	−1.16252	−0.581259	+	0.813719i	$0.697440\pi$
$138$	55.4834	4.72306
$139$	11.8712	1.00690	0.503451	−	0.864024i	$-0.332064\pi$
$139$	11.8712	1.00690	0.503451	+	0.864024i	$0.332064\pi$
$140$	11.1330	0.940910
$141$	−0.739328	−0.0622626
$142$	19.0533	1.59891
$143$	1.07959	0.0902800
$144$	14.2107	1.18422
$145$	−11.3231	−0.940333
$146$	5.71697	0.473139
$147$	17.9994	1.48457
$148$	−39.1698	−3.21974
$149$	5.03839	0.412761	0.206380	−	0.978472i	$-0.433832\pi$
$149$	5.03839	0.412761	0.206380	+	0.978472i	$0.433832\pi$
$150$	80.1876	6.54729
$151$	20.1788	1.64213	0.821066	−	0.570834i	$-0.193380\pi$
$151$	20.1788	1.64213	0.821066	+	0.570834i	$0.193380\pi$
$152$	−15.3771	−1.24725
$153$	9.89226	0.799742
$154$	1.83564	0.147920
$155$	−3.78225	−0.303798
$156$	10.6189	0.850189
$157$	9.19732	0.734026	0.367013	−	0.930216i	$-0.380380\pi$
$157$	9.19732	0.734026	0.367013	+	0.930216i	$0.380380\pi$
$158$	−26.7198	−2.12571
$159$	33.3504	2.64486
$160$	6.21036	0.490972
$161$	5.84029	0.460279
$162$	3.10167	0.243690
$163$	−8.87995	−0.695531	−0.347766	−	0.937582i	$-0.613059\pi$
$163$	−8.87995	−0.695531	−0.347766	+	0.937582i	$0.613059\pi$
$164$	26.6282	2.07931
$165$	12.3150	0.958724
$166$	−4.04767	−0.314160
$167$	−4.09089	−0.316562	−0.158281	−	0.987394i	$-0.550595\pi$
$167$	−4.09089	−0.316562	−0.158281	+	0.987394i	$0.550595\pi$
$168$	8.64543	0.667010
$169$	1.00000	0.0769231
$170$	−21.1572	−1.62268
$171$	16.1298	1.23348
$172$	28.8374	2.19883
$173$	−17.1341	−1.30268	−0.651341	−	0.758785i	$-0.725793\pi$
$173$	−17.1341	−1.30268	−0.651341	+	0.758785i	$0.725793\pi$
$174$	−18.3637	−1.39215
$175$	8.44071	0.638057
$176$	−3.29439	−0.248324
$177$	−27.9048	−2.09745
$178$	−27.5068	−2.06172
$179$	−0.216339	−0.0161699	−0.00808496	−	0.999967i	$-0.502574\pi$
$179$	−0.216339	−0.0161699	−0.00808496	+	0.999967i	$0.502574\pi$
$180$	73.6714	5.49114
$181$	1.19973	0.0891750	0.0445875	−	0.999005i	$-0.485803\pi$
$181$	1.19973	0.0891750	0.0445875	+	0.999005i	$0.485803\pi$
$182$	1.70031	0.126035
$183$	−0.792718	−0.0585994
$184$	−36.8440	−2.71618
$185$	−42.0774	−3.09359
$186$	−6.13400	−0.449767
$187$	−2.29327	−0.167700
$188$	1.02532	0.0747792
$189$	−3.22661	−0.234702
$190$	−34.4978	−2.50273
$191$	17.2127	1.24547	0.622733	−	0.782435i	$-0.286022\pi$
$191$	17.2127	1.24547	0.622733	+	0.782435i	$0.286022\pi$
$192$	26.9597	1.94565
$193$	−16.8827	−1.21524	−0.607620	−	0.794228i	$-0.707876\pi$
$193$	−16.8827	−1.21524	−0.607620	+	0.794228i	$0.707876\pi$
$194$	−37.2774	−2.67636
$195$	11.4071	0.816880
$196$	−24.9621	−1.78301
$197$	10.4288	0.743024	0.371512	−	0.928428i	$-0.378839\pi$
$197$	10.4288	0.743024	0.371512	+	0.928428i	$0.378839\pi$
$198$	12.1471	0.863260
$199$	0.198034	0.0140382	0.00701912	−	0.999975i	$-0.497766\pi$
$199$	0.198034	0.0140382	0.00701912	+	0.999975i	$0.497766\pi$
$200$	−53.2490	−3.76527
$201$	−7.20077	−0.507903
$202$	−43.0919	−3.03194
$203$	−1.93300	−0.135670
$204$	−22.5566	−1.57928
$205$	28.6048	1.99785
$206$	8.72288	0.607752
$207$	38.6475	2.68619
$208$	−3.05151	−0.211584
$209$	−3.73928	−0.258652
$210$	19.3956	1.33842
$211$	14.5526	1.00184	0.500922	−	0.865492i	$-0.332994\pi$
$211$	14.5526	1.00184	0.500922	+	0.865492i	$0.332994\pi$
$212$	−46.2514	−3.17656
$213$	21.8214	1.49518
$214$	7.90964	0.540692
$215$	30.9780	2.11268
$216$	20.3554	1.38501
$217$	−0.645678	−0.0438314
$218$	4.61496	0.312564
$219$	6.54755	0.442443
$220$	−17.0788	−1.15146
$221$	−2.12420	−0.142889
$222$	−68.2406	−4.58001
$223$	−9.42786	−0.631336	−0.315668	−	0.948870i	$-0.602229\pi$
$223$	−9.42786	−0.631336	−0.315668	+	0.948870i	$0.602229\pi$
$224$	1.06019	0.0708367
$225$	55.8555	3.72370
$226$	−0.492185	−0.0327396
$227$	−15.5672	−1.03323	−0.516615	−	0.856218i	$-0.672808\pi$
$227$	−15.5672	−1.03323	−0.516615	+	0.856218i	$0.672808\pi$
$228$	−36.7796	−2.43579
$229$	18.0012	1.18956	0.594778	−	0.803890i	$-0.297240\pi$
$229$	18.0012	1.18956	0.594778	+	0.803890i	$0.297240\pi$
$230$	−82.6577	−5.45029
$231$	2.10233	0.138323
$232$	12.1945	0.800607
$233$	−29.8978	−1.95867	−0.979336	−	0.202241i	$-0.935177\pi$
$233$	−29.8978	−1.95867	−0.979336	+	0.202241i	$0.935177\pi$
$234$	11.2516	0.735540
$235$	1.10143	0.0718495
$236$	38.6992	2.51910
$237$	−30.6017	−1.98780
$238$	−3.61179	−0.234118
$239$	10.4410	0.675371	0.337685	−	0.941259i	$-0.390356\pi$
$239$	10.4410	0.675371	0.337685	+	0.941259i	$0.390356\pi$
$240$	−34.8089	−2.24691
$241$	17.6634	1.13780	0.568901	−	0.822406i	$-0.307369\pi$
$241$	17.6634	1.13780	0.568901	+	0.822406i	$0.307369\pi$
$242$	23.7610	1.52742
$243$	17.3071	1.11025
$244$	1.09936	0.0703796
$245$	−26.8151	−1.71315
$246$	46.3909	2.95778
$247$	−3.46361	−0.220384
$248$	4.07332	0.258656
$249$	−4.63574	−0.293778
$250$	−69.6611	−4.40575
$251$	20.4235	1.28912	0.644558	−	0.764555i	$-0.277041\pi$
$251$	20.4235	1.28912	0.644558	+	0.764555i	$0.277041\pi$
$252$	12.5766	0.792253
$253$	−8.95944	−0.563275
$254$	9.83714	0.617237
$255$	−24.2310	−1.51740
$256$	−30.1087	−1.88180
$257$	16.8170	1.04902	0.524508	−	0.851406i	$-0.324249\pi$
$257$	16.8170	1.04902	0.524508	+	0.851406i	$0.324249\pi$
$258$	50.2397	3.12779
$259$	−7.18314	−0.446339
$260$	−15.8197	−0.981097
$261$	−12.7914	−0.791767
$262$	−0.553572	−0.0341998
$263$	−21.8084	−1.34477	−0.672383	−	0.740203i	$-0.734729\pi$
$263$	−21.8084	−1.34477	−0.672383	+	0.740203i	$0.734729\pi$
$264$	−13.2627	−0.816265
$265$	−49.6847	−3.05210
$266$	−5.88920	−0.361090
$267$	−31.5031	−1.92796
$268$	9.98624	0.610007
$269$	11.9318	0.727497	0.363748	−	0.931497i	$-0.381497\pi$
$269$	11.9318	0.727497	0.363748	+	0.931497i	$0.381497\pi$
$270$	45.6663	2.77916
$271$	3.97673	0.241569	0.120785	−	0.992679i	$-0.461459\pi$
$271$	3.97673	0.241569	0.120785	+	0.992679i	$0.461459\pi$
$272$	6.48202	0.393030
$273$	1.94734	0.117858
$274$	32.8756	1.98609
$275$	−12.9487	−0.780834
$276$	−88.1250	−5.30450
$277$	1.26926	0.0762626	0.0381313	−	0.999273i	$-0.487859\pi$
$277$	1.26926	0.0762626	0.0381313	+	0.999273i	$0.487859\pi$
$278$	−28.6819	−1.72023
$279$	−4.27270	−0.255800
$280$	−12.8798	−0.769712
$281$	−15.0320	−0.896733	−0.448366	−	0.893850i	$-0.647994\pi$
$281$	−15.0320	−0.896733	−0.448366	+	0.893850i	$0.647994\pi$
$282$	1.78629	0.106372
$283$	18.0403	1.07238	0.536192	−	0.844096i	$-0.319862\pi$
$283$	18.0403	1.07238	0.536192	+	0.844096i	$0.319862\pi$
$284$	−30.2625	−1.79575
$285$	−39.5098	−2.34036
$286$	−2.60840	−0.154238
$287$	4.88320	0.288246
$288$	7.01567	0.413402
$289$	−12.4878	−0.734575
$290$	27.3577	1.60650
$291$	−42.6932	−2.50272
$292$	−9.08034	−0.531387
$293$	10.5729	0.617677	0.308838	−	0.951115i	$-0.400060\pi$
$293$	10.5729	0.617677	0.308838	+	0.951115i	$0.400060\pi$
$294$	−43.4883	−2.53629
$295$	41.5719	2.42041
$296$	45.3155	2.63391
$297$	4.94986	0.287220
$298$	−12.1732	−0.705176
$299$	−8.29891	−0.479938
$300$	−127.363	−7.35331
$301$	5.28833	0.304814
$302$	−48.7540	−2.80548
$303$	−49.3525	−2.83523
$304$	10.5692	0.606187
$305$	1.18097	0.0676222
$306$	−23.9007	−1.36631
$307$	−14.7394	−0.841221	−0.420611	−	0.907241i	$-0.638184\pi$
$307$	−14.7394	−0.841221	−0.420611	+	0.907241i	$0.638184\pi$
$308$	−2.91557	−0.166130
$309$	9.99018	0.568321
$310$	9.13828	0.519020
$311$	−3.56030	−0.201886	−0.100943	−	0.994892i	$-0.532186\pi$
$311$	−3.56030	−0.201886	−0.100943	+	0.994892i	$0.532186\pi$
$312$	−12.2849	−0.695498
$313$	16.7147	0.944772	0.472386	−	0.881392i	$-0.343393\pi$
$313$	16.7147	0.944772	0.472386	+	0.881392i	$0.343393\pi$
$314$	−22.2216	−1.25404
$315$	13.5102	0.761214
$316$	42.4394	2.38740
$317$	12.6662	0.711407	0.355703	−	0.934599i	$-0.384241\pi$
$317$	12.6662	0.711407	0.355703	+	0.934599i	$0.384241\pi$
$318$	−80.5779	−4.51858
$319$	2.96536	0.166028
$320$	−40.1638	−2.24523
$321$	9.05879	0.505612
$322$	−14.1107	−0.786359
$323$	7.35739	0.409376
$324$	−4.92642	−0.273690
$325$	−11.9940	−0.665309
$326$	21.4548	1.18827
$327$	5.28544	0.292285
$328$	−30.8061	−1.70098
$329$	0.188028	0.0103663
$330$	−29.7543	−1.63792
$331$	−8.85217	−0.486559	−0.243280	−	0.969956i	$-0.578223\pi$
$331$	−8.85217	−0.486559	−0.243280	+	0.969956i	$0.578223\pi$
$332$	6.42897	0.352836
$333$	−47.5337	−2.60483
$334$	9.88397	0.540827
$335$	10.7275	0.586108
$336$	−5.94232	−0.324180
$337$	−19.6176	−1.06864	−0.534318	−	0.845283i	$-0.679432\pi$
$337$	−19.6176	−1.06864	−0.534318	+	0.845283i	$0.679432\pi$
$338$	−2.41610	−0.131418
$339$	−0.563691	−0.0306155
$340$	33.6042	1.82245
$341$	0.990517	0.0536395
$342$	−38.9711	−2.10732
$343$	−9.50386	−0.513160
$344$	−33.3619	−1.79876
$345$	−94.6666	−5.09668
$346$	41.3976	2.22555
$347$	8.53210	0.458027	0.229014	−	0.973423i	$-0.426450\pi$
$347$	8.53210	0.458027	0.229014	+	0.973423i	$0.426450\pi$
$348$	29.1672	1.56353
$349$	−11.2590	−0.602679	−0.301340	−	0.953517i	$-0.597434\pi$
$349$	−11.2590	−0.602679	−0.301340	+	0.953517i	$0.597434\pi$
$350$	−20.3936	−1.09008
$351$	4.58494	0.244726
$352$	−1.62640	−0.0866876
$353$	15.3824	0.818725	0.409362	−	0.912372i	$-0.365751\pi$
$353$	15.3824	0.818725	0.409362	+	0.912372i	$0.365751\pi$
$354$	67.4206	3.58337
$355$	−32.5090	−1.72540
$356$	43.6894	2.31553
$357$	−4.13653	−0.218928
$358$	0.522696	0.0276253
$359$	−33.4363	−1.76470	−0.882350	−	0.470594i	$-0.844040\pi$
$359$	−33.4363	−1.76470	−0.882350	+	0.470594i	$0.844040\pi$
$360$	−85.2304	−4.49204
$361$	−7.00343	−0.368601
$362$	−2.89865	−0.152350
$363$	27.2132	1.42832
$364$	−2.70062	−0.141551
$365$	−9.75438	−0.510568
$366$	1.91528	0.100113
$367$	−10.5696	−0.551728	−0.275864	−	0.961197i	$-0.588964\pi$
$367$	−10.5696	−0.551728	−0.275864	+	0.961197i	$0.588964\pi$
$368$	25.3242	1.32012
$369$	32.3141	1.68220
$370$	101.663	5.28521
$371$	−8.48179	−0.440353
$372$	9.74272	0.505137
$373$	21.5293	1.11474	0.557372	−	0.830263i	$-0.311810\pi$
$373$	21.5293	1.11474	0.557372	+	0.830263i	$0.311810\pi$
$374$	5.54076	0.286506
$375$	−79.7818	−4.11991
$376$	−1.18619	−0.0611732
$377$	2.74674	0.141464
$378$	7.79581	0.400973
$379$	34.5493	1.77468	0.887338	−	0.461119i	$-0.152552\pi$
$379$	34.5493	1.77468	0.887338	+	0.461119i	$0.152552\pi$
$380$	54.7933	2.81084
$381$	11.2663	0.577191
$382$	−41.5875	−2.12780
$383$	−21.7245	−1.11007	−0.555036	−	0.831826i	$-0.687296\pi$
$383$	−21.7245	−1.11007	−0.555036	+	0.831826i	$0.687296\pi$
$384$	−56.7998	−2.89855
$385$	−3.13200	−0.159621
$386$	40.7901	2.07616
$387$	34.9950	1.77889
$388$	59.2081	3.00584
$389$	−15.5774	−0.789804	−0.394902	−	0.918723i	$-0.629221\pi$
$389$	−15.5774	−0.789804	−0.394902	+	0.918723i	$0.629221\pi$
$390$	−27.5607	−1.39559
$391$	17.6285	0.891514
$392$	28.8786	1.45859
$393$	−0.633998	−0.0319809
$394$	−25.1971	−1.26941
$395$	45.5897	2.29387
$396$	−19.2935	−0.969534
$397$	−18.2808	−0.917488	−0.458744	−	0.888569i	$-0.651700\pi$
$397$	−18.2808	−0.917488	−0.458744	+	0.888569i	$0.651700\pi$
$398$	−0.478469	−0.0239835
$399$	−6.74481	−0.337663
$400$	36.5999	1.83000
$401$	−32.5538	−1.62566	−0.812828	−	0.582503i	$-0.802073\pi$
$401$	−32.5538	−1.62566	−0.812828	+	0.582503i	$0.802073\pi$
$402$	17.3978	0.867721
$403$	0.917492	0.0457035
$404$	68.4435	3.40519
$405$	−5.29211	−0.262967
$406$	4.67030	0.231783
$407$	11.0195	0.546215
$408$	26.0957	1.29193
$409$	30.0646	1.48660	0.743301	−	0.668958i	$-0.233259\pi$
$409$	30.0646	1.48660	0.743301	+	0.668958i	$0.233259\pi$
$410$	−69.1120	−3.41320
$411$	37.6520	1.85723
$412$	−13.8547	−0.682571
$413$	7.09683	0.349212
$414$	−93.3761	−4.58918
$415$	6.90620	0.339012
$416$	−1.50650	−0.0738622
$417$	−32.8490	−1.60862
$418$	9.03447	0.441890
$419$	31.9785	1.56225	0.781126	−	0.624373i	$-0.214645\pi$
$419$	31.9785	1.56225	0.781126	+	0.624373i	$0.214645\pi$
$420$	−30.8063	−1.50319
$421$	8.97598	0.437462	0.218731	−	0.975785i	$-0.429808\pi$
$421$	8.97598	0.437462	0.218731	+	0.975785i	$0.429808\pi$
$422$	−35.1605	−1.71159
$423$	1.24426	0.0604978
$424$	53.5082	2.59859
$425$	25.4777	1.23585
$426$	−52.7226	−2.55442
$427$	0.201606	0.00975642
$428$	−12.5630	−0.607255
$429$	−2.98736	−0.144231
$430$	−74.8459	−3.60939
$431$	1.38999	0.0669534	0.0334767	−	0.999439i	$-0.489342\pi$
$431$	1.38999	0.0669534	0.0334767	+	0.999439i	$0.489342\pi$
$432$	−13.9910	−0.673142
$433$	−28.2578	−1.35798	−0.678991	−	0.734147i	$-0.737582\pi$
$433$	−28.2578	−1.35798	−0.678991	+	0.734147i	$0.737582\pi$
$434$	1.56002	0.0748833
$435$	31.3324	1.50227
$436$	−7.33000	−0.351043
$437$	28.7442	1.37502
$438$	−15.8195	−0.755886
$439$	−22.7011	−1.08346	−0.541732	−	0.840552i	$-0.682231\pi$
$439$	−22.7011	−1.08346	−0.541732	+	0.840552i	$0.682231\pi$
$440$	19.7585	0.941949
$441$	−30.2922	−1.44249
$442$	5.13227	0.244117
$443$	27.1772	1.29123	0.645615	−	0.763663i	$-0.276601\pi$
$443$	27.1772	1.29123	0.645615	+	0.763663i	$0.276601\pi$
$444$	108.387	5.14384
$445$	46.9325	2.22482
$446$	22.7786	1.07860
$447$	−13.9418	−0.659425
$448$	−6.85646	−0.323937
$449$	−29.5689	−1.39544	−0.697720	−	0.716370i	$-0.745802\pi$
$449$	−29.5689	−1.39544	−0.697720	+	0.716370i	$0.745802\pi$
$450$	−134.952	−6.36171
$451$	−7.49119	−0.352746
$452$	0.781744	0.0367701
$453$	−55.8372	−2.62346
$454$	37.6118	1.76521
$455$	−2.90109	−0.136005
$456$	42.5502	1.99260
$457$	7.76598	0.363277	0.181639	−	0.983365i	$-0.441860\pi$
$457$	7.76598	0.363277	0.181639	+	0.983365i	$0.441860\pi$
$458$	−43.4927	−2.03228
$459$	−9.73932	−0.454593
$460$	131.286	6.12126
$461$	19.8837	0.926074	0.463037	−	0.886339i	$-0.346760\pi$
$461$	19.8837	0.926074	0.463037	+	0.886339i	$0.346760\pi$
$462$	−5.07943	−0.236316
$463$	−4.11859	−0.191407	−0.0957036	−	0.995410i	$-0.530510\pi$
$463$	−4.11859	−0.191407	−0.0957036	+	0.995410i	$0.530510\pi$
$464$	−8.38170	−0.389111
$465$	10.4659	0.485346
$466$	72.2360	3.34627
$467$	−6.13618	−0.283949	−0.141974	−	0.989870i	$-0.545345\pi$
$467$	−6.13618	−0.283949	−0.141974	+	0.989870i	$0.545345\pi$
$468$	−17.8711	−0.826091
$469$	1.83132	0.0845626
$470$	−2.66117	−0.122750
$471$	−25.4501	−1.17268
$472$	−44.7710	−2.06075
$473$	−8.11269	−0.373022
$474$	73.9367	3.39602
$475$	41.5426	1.90611
$476$	5.73666	0.262939
$477$	−56.1273	−2.56989
$478$	−25.2264	−1.15383
$479$	5.92435	0.270690	0.135345	−	0.990799i	$-0.456786\pi$
$479$	5.92435	0.270690	0.135345	+	0.990799i	$0.456786\pi$
$480$	−17.1848	−0.784375
$481$	10.2071	0.465402
$482$	−42.6766	−1.94386
$483$	−16.1608	−0.735341
$484$	−37.7400	−1.71545
$485$	63.6032	2.88807
$486$	−41.8156	−1.89679
$487$	2.62021	0.118733	0.0593664	−	0.998236i	$-0.481092\pi$
$487$	2.62021	0.118733	0.0593664	+	0.998236i	$0.481092\pi$
$488$	−1.27185	−0.0575741
$489$	24.5719	1.11118
$490$	64.7877	2.92681
$491$	−1.00488	−0.0453496	−0.0226748	−	0.999743i	$-0.507218\pi$
$491$	−1.00488	−0.0453496	−0.0226748	+	0.999743i	$0.507218\pi$
$492$	−73.6833	−3.32190
$493$	−5.83462	−0.262778
$494$	8.36841	0.376512
$495$	−20.7257	−0.931549
$496$	−2.79974	−0.125712
$497$	−5.54969	−0.248937
$498$	11.2004	0.501901
$499$	−16.1125	−0.721295	−0.360647	−	0.932702i	$-0.617444\pi$
$499$	−16.1125	−0.721295	−0.360647	+	0.932702i	$0.617444\pi$
$500$	110.644	4.94814
$501$	11.3200	0.505739
$502$	−49.3450	−2.20238
$503$	42.7848	1.90768	0.953839	−	0.300317i	$-0.0970925\pi$
$503$	42.7848	1.90768	0.953839	+	0.300317i	$0.0970925\pi$
$504$	−14.5499	−0.648103
$505$	73.5241	3.27178
$506$	21.6469	0.962320
$507$	−2.76712	−0.122892
$508$	−15.6245	−0.693223
$509$	−27.1725	−1.20440	−0.602200	−	0.798346i	$-0.705709\pi$
$509$	−27.1725	−1.20440	−0.602200	+	0.798346i	$0.705709\pi$
$510$	58.5444	2.59239
$511$	−1.66519	−0.0736639
$512$	31.6922	1.40061
$513$	−15.8804	−0.701138
$514$	−40.6315	−1.79218
$515$	−14.8831	−0.655829
$516$	−79.7964	−3.51284
$517$	−0.288449	−0.0126860
$518$	17.3552	0.762542
$519$	47.4121	2.08116
$520$	18.3018	0.802588
$521$	−4.94164	−0.216497	−0.108249	−	0.994124i	$-0.534524\pi$
$521$	−4.94164	−0.216497	−0.108249	+	0.994124i	$0.534524\pi$
$522$	30.9052	1.35268
$523$	−4.75766	−0.208038	−0.104019	−	0.994575i	$-0.533170\pi$
$523$	−4.75766	−0.208038	−0.104019	+	0.994575i	$0.533170\pi$
$524$	0.879246	0.0384101
$525$	−23.3564	−1.01936
$526$	52.6913	2.29745
$527$	−1.94894	−0.0848970
$528$	9.11595	0.396721
$529$	45.8719	1.99443
$530$	120.043	5.21433
$531$	46.9625	2.03800
$532$	9.35390	0.405543
$533$	−6.93891	−0.300558
$534$	76.1145	3.29380
$535$	−13.4956	−0.583464
$536$	−11.5531	−0.499017
$537$	0.598635	0.0258330
$538$	−28.8285	−1.24288
$539$	7.02247	0.302479
$540$	−72.5324	−3.12130
$541$	−18.8735	−0.811434	−0.405717	−	0.913999i	$-0.632978\pi$
$541$	−18.8735	−0.811434	−0.405717	+	0.913999i	$0.632978\pi$
$542$	−9.60816	−0.412706
$543$	−3.31978	−0.142466
$544$	3.20010	0.137203
$545$	−7.87411	−0.337290
$546$	−4.70495	−0.201353
$547$	31.4562	1.34497	0.672485	−	0.740111i	$-0.265227\pi$
$547$	31.4562	1.34497	0.672485	+	0.740111i	$0.265227\pi$
$548$	−52.2168	−2.23059
$549$	1.33411	0.0569384
$550$	31.2852	1.33401
$551$	−9.51363	−0.405294
$552$	101.952	4.33935
$553$	7.78273	0.330955
$554$	−3.06666	−0.130290
$555$	116.433	4.94231
$556$	45.5559	1.93200
$557$	−32.3657	−1.37138	−0.685689	−	0.727894i	$-0.740499\pi$
$557$	−32.3657	−1.37138	−0.685689	+	0.727894i	$0.740499\pi$
$558$	10.3233	0.437018
$559$	−7.51459	−0.317833
$560$	8.85272	0.374096
$561$	6.34574	0.267918
$562$	36.3187	1.53201
$563$	−24.6510	−1.03892	−0.519458	−	0.854496i	$-0.673866\pi$
$563$	−24.6510	−1.03892	−0.519458	+	0.854496i	$0.673866\pi$
$564$	−2.83718	−0.119467
$565$	0.839773	0.0353295
$566$	−43.5870	−1.83210
$567$	−0.903429	−0.0379405
$568$	35.0107	1.46902
$569$	3.02955	0.127005	0.0635027	−	0.997982i	$-0.479773\pi$
$569$	3.02955	0.127005	0.0635027	+	0.997982i	$0.479773\pi$
$570$	95.4594	3.99835
$571$	−20.6892	−0.865815	−0.432907	−	0.901438i	$-0.642512\pi$
$571$	−20.6892	−0.865815	−0.432907	+	0.901438i	$0.642512\pi$
$572$	4.14295	0.173226
$573$	−47.6295	−1.98975
$574$	−11.7983	−0.492451
$575$	99.5374	4.15100
$576$	−45.3719	−1.89050
$577$	23.5766	0.981506	0.490753	−	0.871299i	$-0.336722\pi$
$577$	23.5766	0.981506	0.490753	+	0.871299i	$0.336722\pi$
$578$	30.1717	1.25498
$579$	46.7163	1.94146
$580$	−43.4526	−1.80427
$581$	1.17897	0.0489121
$582$	103.151	4.27574
$583$	13.0117	0.538889
$584$	10.5050	0.434701
$585$	−19.1977	−0.793726
$586$	−25.5452	−1.05526
$587$	−27.3287	−1.12797	−0.563987	−	0.825784i	$-0.690733\pi$
$587$	−27.3287	−1.12797	−0.563987	+	0.825784i	$0.690733\pi$
$588$	69.0730	2.84852
$589$	−3.17783	−0.130940
$590$	−100.442	−4.13511
$591$	−28.8578	−1.18705
$592$	−31.1470	−1.28013
$593$	−39.0655	−1.60423	−0.802114	−	0.597171i	$-0.796292\pi$
$593$	−39.0655	−1.60423	−0.802114	+	0.597171i	$0.796292\pi$
$594$	−11.9593	−0.490698
$595$	6.16250	0.252638
$596$	19.3349	0.791988
$597$	−0.547983	−0.0224274
$598$	20.0510	0.819945
$599$	−14.4966	−0.592313	−0.296157	−	0.955139i	$-0.595705\pi$
$599$	−14.4966	−0.592313	−0.296157	+	0.955139i	$0.595705\pi$
$600$	147.346	6.01538
$601$	5.67283	0.231399	0.115700	−	0.993284i	$-0.463089\pi$
$601$	5.67283	0.231399	0.115700	+	0.993284i	$0.463089\pi$
$602$	−12.7771	−0.520757
$603$	12.1186	0.493507
$604$	77.4367	3.15085
$605$	−40.5415	−1.64825
$606$	119.240	4.84381
$607$	−13.8511	−0.562199	−0.281099	−	0.959679i	$-0.590699\pi$
$607$	−13.8511	−0.562199	−0.281099	+	0.959679i	$0.590699\pi$
$608$	5.21792	0.211615
$609$	5.34882	0.216745
$610$	−2.85334	−0.115528
$611$	−0.267183	−0.0108091
$612$	37.9617	1.53451
$613$	−44.7287	−1.80657	−0.903287	−	0.429036i	$-0.858853\pi$
$613$	−44.7287	−1.80657	−0.903287	+	0.429036i	$0.858853\pi$
$614$	35.6118	1.43717
$615$	−79.1529	−3.19175
$616$	3.37302	0.135903
$617$	1.00000	0.0402585
$617$	1.00000	0.0402585
$618$	−24.1372	−0.970942
$619$	23.2128	0.933003	0.466501	−	0.884520i	$-0.345514\pi$
$619$	23.2128	0.933003	0.466501	+	0.884520i	$0.345514\pi$
$620$	−14.5145	−0.582915
$621$	−38.0500	−1.52689
$622$	8.60203	0.344910
$623$	8.01197	0.320993
$624$	8.44389	0.338026
$625$	58.8867	2.35547
$626$	−40.3844	−1.61408
$627$	10.3470	0.413221
$628$	35.2949	1.40842
$629$	−21.6818	−0.864512
$630$	−32.6420	−1.30049
$631$	32.0555	1.27611	0.638056	−	0.769990i	$-0.279739\pi$
$631$	32.0555	1.27611	0.638056	+	0.769990i	$0.279739\pi$
$632$	−49.0980	−1.95301
$633$	−40.2688	−1.60054
$634$	−30.6028	−1.21539
$635$	−16.7843	−0.666064
$636$	127.983	5.07485
$637$	6.50475	0.257727
$638$	−7.16459	−0.283649
$639$	−36.7245	−1.45280
$640$	84.6189	3.34486
$641$	−47.4606	−1.87458	−0.937291	−	0.348547i	$-0.886675\pi$
$641$	−47.4606	−1.87458	−0.937291	+	0.348547i	$0.886675\pi$
$642$	−21.8869	−0.863807
$643$	29.0134	1.14418	0.572089	−	0.820191i	$-0.306133\pi$
$643$	29.0134	1.14418	0.572089	+	0.820191i	$0.306133\pi$
$644$	22.4122	0.883165
$645$	−85.7198	−3.37521
$646$	−17.7762	−0.699394
$647$	17.4293	0.685216	0.342608	−	0.939478i	$-0.388690\pi$
$647$	17.4293	0.685216	0.342608	+	0.939478i	$0.388690\pi$
$648$	5.69937	0.223892
$649$	−10.8871	−0.427355
$650$	28.9787	1.13664
$651$	1.78667	0.0700249
$652$	−34.0770	−1.33456
$653$	4.27854	0.167432	0.0837162	−	0.996490i	$-0.473321\pi$
$653$	4.27854	0.167432	0.0837162	+	0.996490i	$0.473321\pi$
$654$	−12.7701	−0.499351
$655$	0.944514	0.0369052
$656$	21.1742	0.826712
$657$	−11.0192	−0.429902
$658$	−0.454294	−0.0177102
$659$	19.9955	0.778915	0.389457	−	0.921044i	$-0.372663\pi$
$659$	19.9955	0.778915	0.389457	+	0.921044i	$0.372663\pi$
$660$	47.2592	1.83956
$661$	3.58848	0.139576	0.0697878	−	0.997562i	$-0.477768\pi$
$661$	3.58848	0.139576	0.0697878	+	0.997562i	$0.477768\pi$
$662$	21.3877	0.831256
$663$	5.87791	0.228279
$664$	−7.43767	−0.288638
$665$	10.0482	0.389654
$666$	114.846	4.45019
$667$	−22.7949	−0.882624
$668$	−15.6988	−0.607407
$669$	26.0880	1.00862
$670$	−25.9187	−1.00133
$671$	−0.309279	−0.0119396
$672$	−2.93366	−0.113168
$673$	−12.8832	−0.496611	−0.248305	−	0.968682i	$-0.579874\pi$
$673$	−12.8832	−0.496611	−0.248305	+	0.968682i	$0.579874\pi$
$674$	47.3979	1.82570
$675$	−54.9919	−2.11664
$676$	3.83752	0.147597
$677$	4.43982	0.170636	0.0853181	−	0.996354i	$-0.472809\pi$
$677$	4.43982	0.170636	0.0853181	+	0.996354i	$0.472809\pi$
$678$	1.36193	0.0523047
$679$	10.8579	0.416687
$680$	−38.8767	−1.49085
$681$	43.0762	1.65068
$682$	−2.39318	−0.0916398
$683$	−34.2046	−1.30880	−0.654402	−	0.756147i	$-0.727079\pi$
$683$	−34.2046	−1.30880	−0.654402	+	0.756147i	$0.727079\pi$
$684$	61.8984	2.36674
$685$	−56.0929	−2.14320
$686$	22.9622	0.876702
$687$	−49.8115	−1.90043
$688$	22.9309	0.874231
$689$	12.0524	0.459161
$690$	228.724	8.70736
$691$	48.0624	1.82838	0.914190	−	0.405285i	$-0.132828\pi$
$691$	48.0624	1.82838	0.914190	+	0.405285i	$0.132828\pi$
$692$	−65.7524	−2.49953
$693$	−3.53813	−0.134402
$694$	−20.6144	−0.782511
$695$	48.9376	1.85631
$696$	−33.7436	−1.27905
$697$	14.7396	0.558303
$698$	27.2028	1.02964
$699$	82.7308	3.12917
$700$	32.3914	1.22428
$701$	31.6034	1.19364	0.596822	−	0.802374i	$-0.296430\pi$
$701$	31.6034	1.19364	0.596822	+	0.802374i	$0.296430\pi$
$702$	−11.0776	−0.418099
$703$	−35.3533	−1.33337
$704$	10.5183	0.396424
$705$	−3.04779	−0.114786
$706$	−37.1654	−1.39874
$707$	12.5515	0.472047
$708$	−107.085	−4.02451
$709$	1.44172	0.0541449	0.0270724	−	0.999633i	$-0.491382\pi$
$709$	1.44172	0.0541449	0.0270724	+	0.999633i	$0.491382\pi$
$710$	78.5448	2.94773
$711$	51.5013	1.93145
$712$	−50.5442	−1.89423
$713$	−7.61418	−0.285153
$714$	9.99425	0.374026
$715$	4.45049	0.166439
$716$	−0.830205	−0.0310262
$717$	−28.8914	−1.07897
$718$	80.7853	3.01488
$719$	−34.7175	−1.29475	−0.647373	−	0.762173i	$-0.724132\pi$
$719$	−34.7175	−1.29475	−0.647373	+	0.762173i	$0.724132\pi$
$720$	58.5819	2.18322
$721$	−2.54073	−0.0946219
$722$	16.9210	0.629733
$723$	−48.8768	−1.81775
$724$	4.60397	0.171105
$725$	−32.9445	−1.22353
$726$	−65.7496	−2.44020
$727$	−6.64488	−0.246445	−0.123222	−	0.992379i	$-0.539323\pi$
$727$	−6.64488	−0.246445	−0.123222	+	0.992379i	$0.539323\pi$
$728$	3.12435	0.115796
$729$	−44.0395	−1.63109
$730$	23.5675	0.872273
$731$	15.9625	0.590394
$732$	−3.04207	−0.112438
$733$	−16.2633	−0.600698	−0.300349	−	0.953829i	$-0.597103\pi$
$733$	−16.2633	−0.600698	−0.300349	+	0.953829i	$0.597103\pi$
$734$	25.5371	0.942593
$735$	74.2004	2.73692
$736$	12.5023	0.460841
$737$	−2.80938	−0.103485
$738$	−78.0739	−2.87394
$739$	−33.0697	−1.21649	−0.608244	−	0.793750i	$-0.708126\pi$
$739$	−33.0697	−1.21649	−0.608244	+	0.793750i	$0.708126\pi$
$740$	−161.473	−5.93586
$741$	9.58421	0.352085
$742$	20.4928	0.752315
$743$	20.1440	0.739013	0.369506	−	0.929228i	$-0.379527\pi$
$743$	20.1440	0.739013	0.369506	+	0.929228i	$0.379527\pi$
$744$	−11.2713	−0.413227
$745$	20.7701	0.760959
$746$	−52.0168	−1.90447
$747$	7.80174	0.285451
$748$	−8.80046	−0.321777
$749$	−2.30386	−0.0841812
$750$	192.760	7.03861
$751$	−11.5216	−0.420428	−0.210214	−	0.977655i	$-0.567416\pi$
$751$	−11.5216	−0.420428	−0.210214	+	0.977655i	$0.567416\pi$
$752$	0.815313	0.0297314
$753$	−56.5141	−2.05949
$754$	−6.63638	−0.241683
$755$	83.1849	3.02741
$756$	−12.3822	−0.450336
$757$	39.1103	1.42149	0.710743	−	0.703451i	$-0.248359\pi$
$757$	39.1103	1.42149	0.710743	+	0.703451i	$0.248359\pi$
$758$	−83.4743	−3.03192
$759$	24.7918	0.899886
$760$	−63.3903	−2.29941
$761$	−15.9519	−0.578254	−0.289127	−	0.957291i	$-0.593365\pi$
$761$	−15.9519	−0.578254	−0.289127	+	0.957291i	$0.593365\pi$
$762$	−27.2205	−0.986095
$763$	−1.34421	−0.0486636
$764$	66.0539	2.38975
$765$	40.7797	1.47439
$766$	52.4886	1.89649
$767$	−10.0844	−0.364127
$768$	83.3144	3.00635
$769$	3.75814	0.135522	0.0677610	−	0.997702i	$-0.478414\pi$
$769$	3.75814	0.135522	0.0677610	+	0.997702i	$0.478414\pi$
$770$	7.56721	0.272703
$771$	−46.5346	−1.67590
$772$	−64.7875	−2.33175
$773$	13.4127	0.482421	0.241210	−	0.970473i	$-0.422456\pi$
$773$	13.4127	0.482421	0.241210	+	0.970473i	$0.422456\pi$
$774$	−84.5512	−3.03913
$775$	−11.0044	−0.395291
$776$	−68.4978	−2.45893
$777$	19.8766	0.713069
$778$	37.6364	1.34933
$779$	24.0337	0.861095
$780$	43.7750	1.56740
$781$	8.51363	0.304642
$782$	−42.5923	−1.52310
$783$	12.5936	0.450060
$784$	−19.8493	−0.708904
$785$	37.9149	1.35324
$786$	1.53180	0.0546375
$787$	11.7078	0.417338	0.208669	−	0.977986i	$-0.433087\pi$
$787$	11.7078	0.417338	0.208669	+	0.977986i	$0.433087\pi$
$788$	40.0209	1.42568
$789$	60.3465	2.14839
$790$	−110.149	−3.91893
$791$	0.143360	0.00509729
$792$	22.3206	0.793128
$793$	−0.286478	−0.0101731
$794$	44.1682	1.56747
$795$	137.483	4.87603
$796$	0.759959	0.0269360
$797$	−22.0365	−0.780573	−0.390286	−	0.920693i	$-0.627624\pi$
$797$	−22.0365	−0.780573	−0.390286	+	0.920693i	$0.627624\pi$
$798$	16.2961	0.576876
$799$	0.567551	0.0200785
$800$	18.0690	0.638836
$801$	53.0183	1.87331
$802$	78.6530	2.77733
$803$	2.55453	0.0901474
$804$	−27.6331	−0.974544
$805$	24.0759	0.848565
$806$	−2.21675	−0.0780816
$807$	−33.0168	−1.16225
$808$	−79.1822	−2.78562
$809$	−32.8225	−1.15398	−0.576989	−	0.816752i	$-0.695773\pi$
$809$	−32.8225	−1.15398	−0.576989	+	0.816752i	$0.695773\pi$
$810$	12.7862	0.449263
$811$	41.1970	1.44662	0.723311	−	0.690522i	$-0.242619\pi$
$811$	41.1970	1.44662	0.723311	+	0.690522i	$0.242619\pi$
$812$	−7.41791	−0.260317
$813$	−11.0041	−0.385930
$814$	−26.6241	−0.933174
$815$	−36.6065	−1.28227
$816$	−17.9365	−0.627903
$817$	26.0276	0.910590
$818$	−72.6391	−2.53977
$819$	−3.27728	−0.114517
$820$	109.772	3.83339
$821$	−44.5415	−1.55451	−0.777255	−	0.629185i	$-0.783389\pi$
$821$	−44.5415	−1.55451	−0.777255	+	0.629185i	$0.783389\pi$
$822$	−90.9707	−3.17297
$823$	27.5512	0.960374	0.480187	−	0.877166i	$-0.340569\pi$
$823$	27.5512	0.960374	0.480187	+	0.877166i	$0.340569\pi$
$824$	16.0285	0.558378
$825$	35.8305	1.24746
$826$	−17.1466	−0.596607
$827$	9.77729	0.339990	0.169995	−	0.985445i	$-0.445625\pi$
$827$	9.77729	0.339990	0.169995	+	0.985445i	$0.445625\pi$
$828$	148.311	5.15415
$829$	22.8144	0.792376	0.396188	−	0.918169i	$-0.370333\pi$
$829$	22.8144	0.792376	0.396188	+	0.918169i	$0.370333\pi$
$830$	−16.6860	−0.579181
$831$	−3.51220	−0.121837
$832$	9.74287	0.337773
$833$	−13.8174	−0.478744
$834$	79.3663	2.74823
$835$	−16.8642	−0.583610
$836$	−14.3496	−0.496290
$837$	4.20664	0.145403
$838$	−77.2632	−2.66901
$839$	−9.11917	−0.314829	−0.157414	−	0.987533i	$-0.550316\pi$
$839$	−9.11917	−0.314829	−0.157414	+	0.987533i	$0.550316\pi$
$840$	35.6398	1.22969
$841$	−21.4554	−0.739842
$842$	−21.6868	−0.747377
$843$	41.5952	1.43262
$844$	55.8460	1.92230
$845$	4.12238	0.141814
$846$	−3.00624	−0.103357
$847$	−6.92094	−0.237806
$848$	−36.7781	−1.26296
$849$	−49.9196	−1.71324
$850$	−61.5566	−2.11137
$851$	−84.7075	−2.90374
$852$	83.7400	2.86889
$853$	10.7706	0.368777	0.184388	−	0.982853i	$-0.440970\pi$
$853$	10.7706	0.368777	0.184388	+	0.982853i	$0.440970\pi$
$854$	−0.487100	−0.0166682
$855$	66.4932	2.27402
$856$	14.5341	0.496766
$857$	−57.1660	−1.95276	−0.976378	−	0.216072i	$-0.930676\pi$
$857$	−57.1660	−1.95276	−0.976378	+	0.216072i	$0.930676\pi$
$858$	7.21774	0.246410
$859$	34.4443	1.17522	0.587612	−	0.809143i	$-0.300068\pi$
$859$	34.4443	1.17522	0.587612	+	0.809143i	$0.300068\pi$
$860$	118.879	4.05373
$861$	−13.5124	−0.460501
$862$	−3.35834	−0.114386
$863$	9.15487	0.311636	0.155818	−	0.987786i	$-0.450199\pi$
$863$	9.15487	0.311636	0.155818	+	0.987786i	$0.450199\pi$
$864$	−6.90720	−0.234988
$865$	−70.6333	−2.40161
$866$	68.2735	2.32003
$867$	34.5551	1.17355
$868$	−2.47780	−0.0841020
$869$	−11.9393	−0.405012
$870$	−75.7020	−2.56654
$871$	−2.60226	−0.0881744
$872$	8.48007	0.287171
$873$	71.8507	2.43178
$874$	−69.4487	−2.34914
$875$	20.2903	0.685939
$876$	25.1264	0.848941
$877$	39.7123	1.34099	0.670494	−	0.741915i	$-0.266082\pi$
$877$	39.7123	1.34099	0.670494	+	0.741915i	$0.266082\pi$
$878$	54.8480	1.85103
$879$	−29.2565	−0.986798
$880$	−13.5807	−0.457806
$881$	−44.2133	−1.48959	−0.744793	−	0.667296i	$-0.767452\pi$
$881$	−44.2133	−1.48959	−0.744793	+	0.667296i	$0.767452\pi$
$882$	73.1888	2.46440
$883$	39.0232	1.31323	0.656617	−	0.754224i	$-0.271987\pi$
$883$	39.0232	1.31323	0.656617	+	0.754224i	$0.271987\pi$
$884$	−8.15166	−0.274170
$885$	−115.034	−3.86683
$886$	−65.6628	−2.20599
$887$	32.3607	1.08657	0.543283	−	0.839549i	$-0.317181\pi$
$887$	32.3607	1.08657	0.543283	+	0.839549i	$0.317181\pi$
$888$	−125.393	−4.20792
$889$	−2.86529	−0.0960986
$890$	−113.393	−3.80096
$891$	1.38593	0.0464303
$892$	−36.1796	−1.21138
$893$	0.925418	0.0309679
$894$	33.6847	1.12659
$895$	−0.891832	−0.0298106
$896$	14.4455	0.482590
$897$	22.9641	0.766748
$898$	71.4412	2.38402
$899$	2.52011	0.0840504
$900$	214.346	7.14488
$901$	−25.6017	−0.852918
$902$	18.0994	0.602645
$903$	−14.6334	−0.486970
$904$	−0.904398	−0.0300798
$905$	4.94573	0.164402
$906$	134.908	4.48202
$907$	25.2234	0.837529	0.418764	−	0.908095i	$-0.362463\pi$
$907$	25.2234	0.837529	0.418764	+	0.908095i	$0.362463\pi$
$908$	−59.7394	−1.98252
$909$	83.0581	2.75486
$910$	7.00932	0.232357
$911$	6.72956	0.222960	0.111480	−	0.993767i	$-0.464441\pi$
$911$	6.72956	0.222960	0.111480	+	0.993767i	$0.464441\pi$
$912$	−29.2463	−0.968442
$913$	−1.80863	−0.0598571
$914$	−18.7634	−0.620637
$915$	−3.26788	−0.108033
$916$	69.0801	2.28247
$917$	0.161240	0.00532462
$918$	23.5311	0.776643
$919$	−25.0068	−0.824897	−0.412449	−	0.910981i	$-0.635326\pi$
$919$	−25.0068	−0.824897	−0.412449	+	0.910981i	$0.635326\pi$
$920$	−151.885	−5.00750
$921$	40.7856	1.34393
$922$	−48.0408	−1.58214
$923$	7.88597	0.259570
$924$	8.06773	0.265409
$925$	−122.424	−4.02527
$926$	9.95091	0.327007
$927$	−16.8130	−0.552212
$928$	−4.13796	−0.135835
$929$	37.1200	1.21787	0.608935	−	0.793220i	$-0.291597\pi$
$929$	37.1200	1.21787	0.608935	+	0.793220i	$0.291597\pi$
$930$	−25.2867	−0.829184
$931$	−22.5299	−0.738387
$932$	−114.733	−3.75822
$933$	9.85178	0.322533
$934$	14.8256	0.485108
$935$	−9.45373	−0.309170
$936$	20.6750	0.675785
$937$	12.4339	0.406197	0.203098	−	0.979158i	$-0.434899\pi$
$937$	12.4339	0.406197	0.203098	+	0.979158i	$0.434899\pi$
$938$	−4.42465	−0.144470
$939$	−46.2516	−1.50936
$940$	4.22677	0.137862
$941$	57.9489	1.88908	0.944539	−	0.328398i	$-0.106509\pi$
$941$	57.9489	1.88908	0.944539	+	0.328398i	$0.106509\pi$
$942$	61.4898	2.00345
$943$	57.5854	1.87524
$944$	30.7727	1.00157
$945$	−13.3013	−0.432692
$946$	19.6010	0.637285
$947$	9.73332	0.316291	0.158145	−	0.987416i	$-0.449449\pi$
$947$	9.73332	0.316291	0.158145	+	0.987416i	$0.449449\pi$
$948$	−117.435	−3.81410
$949$	2.36620	0.0768101
$950$	−100.371	−3.25646
$951$	−35.0490	−1.13654
$952$	−6.63674	−0.215098
$953$	8.53185	0.276374	0.138187	−	0.990406i	$-0.455873\pi$
$953$	8.53185	0.276374	0.138187	+	0.990406i	$0.455873\pi$
$954$	135.609	4.39050
$955$	70.9572	2.29612
$956$	40.0674	1.29587
$957$	−8.20549	−0.265246
$958$	−14.3138	−0.462458
$959$	−9.57576	−0.309218
$960$	111.138	3.58696
$961$	−30.1582	−0.972845
$962$	−24.6612	−0.795111
$963$	−15.2455	−0.491281
$964$	67.7838	2.18317
$965$	−69.5968	−2.24040
$966$	39.0460	1.25628
$967$	−18.2913	−0.588209	−0.294104	−	0.955773i	$-0.595021\pi$
$967$	−18.2913	−0.588209	−0.294104	+	0.955773i	$0.595021\pi$
$968$	43.6614	1.40333
$969$	−20.3588	−0.654018
$970$	−153.672	−4.93409
$971$	−53.0407	−1.70216	−0.851079	−	0.525038i	$-0.824051\pi$
$971$	−53.0407	−1.70216	−0.851079	+	0.525038i	$0.824051\pi$
$972$	66.4163	2.13030
$973$	8.35426	0.267825
$974$	−6.33067	−0.202848
$975$	33.1889	1.06290
$976$	0.874190	0.0279821
$977$	−2.94119	−0.0940971	−0.0470485	−	0.998893i	$-0.514982\pi$
$977$	−2.94119	−0.0940971	−0.0470485	+	0.998893i	$0.514982\pi$
$978$	−59.3679	−1.89838
$979$	−12.2910	−0.392820
$980$	−102.903	−3.28712
$981$	−8.89516	−0.284001
$982$	2.42788	0.0774769
$983$	−33.7843	−1.07755	−0.538776	−	0.842449i	$-0.681113\pi$
$983$	−33.7843	−1.07755	−0.538776	+	0.842449i	$0.681113\pi$
$984$	85.2441	2.71748
$985$	42.9917	1.36983
$986$	14.0970	0.448940
$987$	−0.520296	−0.0165612
$988$	−13.2917	−0.422864
$989$	62.3629	1.98303
$990$	50.0752	1.59149
$991$	21.1319	0.671276	0.335638	−	0.941991i	$-0.391048\pi$
$991$	21.1319	0.671276	0.335638	+	0.941991i	$0.391048\pi$
$992$	−1.38220	−0.0438849
$993$	24.4950	0.777325
$994$	13.4086	0.425294
$995$	0.816371	0.0258807
$996$	−17.7897	−0.563689
$997$	39.5166	1.25150	0.625751	−	0.780023i	$-0.284793\pi$
$997$	39.5166	1.25150	0.625751	+	0.780023i	$0.284793\pi$
$998$	38.9294	1.23229
$999$	46.7988	1.48065

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8021.2.a.c.1.18	✓	169

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8021.2.a.c.1.18	✓	169	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:	\( N \)	\(=\)	\( 8021 = 13 \cdot 617 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8021.a (trivial)

\(f(q)\)	\(=\)	\(q-2.41610 q^{2} -2.76712 q^{3} +3.83752 q^{4} +4.12238 q^{5} +6.68562 q^{6} +0.703742 q^{7} -4.43962 q^{8} +4.65694 q^{9} +O(q^{10})\)	\(q-2.41610 q^{2} -2.76712 q^{3} +3.83752 q^{4} +4.12238 q^{5} +6.68562 q^{6} +0.703742 q^{7} -4.43962 q^{8} +4.65694 q^{9} -9.96007 q^{10} -1.07959 q^{11} -10.6189 q^{12} -1.00000 q^{13} -1.70031 q^{14} -11.4071 q^{15} +3.05151 q^{16} +2.12420 q^{17} -11.2516 q^{18} +3.46361 q^{19} +15.8197 q^{20} -1.94734 q^{21} +2.60840 q^{22} +8.29891 q^{23} +12.2849 q^{24} +11.9940 q^{25} +2.41610 q^{26} -4.58494 q^{27} +2.70062 q^{28} -2.74674 q^{29} +27.5607 q^{30} -0.917492 q^{31} +1.50650 q^{32} +2.98736 q^{33} -5.13227 q^{34} +2.90109 q^{35} +17.8711 q^{36} -10.2071 q^{37} -8.36841 q^{38} +2.76712 q^{39} -18.3018 q^{40} +6.93891 q^{41} +4.70495 q^{42} +7.51459 q^{43} -4.14295 q^{44} +19.1977 q^{45} -20.0510 q^{46} +0.267183 q^{47} -8.44389 q^{48} -6.50475 q^{49} -28.9787 q^{50} -5.87791 q^{51} -3.83752 q^{52} -12.0524 q^{53} +11.0776 q^{54} -4.45049 q^{55} -3.12435 q^{56} -9.58421 q^{57} +6.63638 q^{58} +10.0844 q^{59} -43.7750 q^{60} +0.286478 q^{61} +2.21675 q^{62} +3.27728 q^{63} -9.74287 q^{64} -4.12238 q^{65} -7.21774 q^{66} +2.60226 q^{67} +8.15166 q^{68} -22.9641 q^{69} -7.00932 q^{70} -7.88597 q^{71} -20.6750 q^{72} -2.36620 q^{73} +24.6612 q^{74} -33.1889 q^{75} +13.2917 q^{76} -0.759754 q^{77} -6.68562 q^{78} +11.0591 q^{79} +12.5795 q^{80} -1.28375 q^{81} -16.7651 q^{82} +1.67529 q^{83} -7.47294 q^{84} +8.75676 q^{85} -18.1560 q^{86} +7.60055 q^{87} +4.79298 q^{88} +11.3848 q^{89} -46.3834 q^{90} -0.703742 q^{91} +31.8472 q^{92} +2.53881 q^{93} -0.645541 q^{94} +14.2783 q^{95} -4.16866 q^{96} +15.4288 q^{97} +15.7161 q^{98} -5.02759 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 169 q + 9 q^{2} + 9 q^{3} + 199 q^{4} + 12 q^{5} + 22 q^{6} + 36 q^{7} + 30 q^{8} + 198 q^{9}+O(q^{10}) \) 169 * q + 9 * q^2 + 9 * q^3 + 199 * q^4 + 12 * q^5 + 22 * q^6 + 36 * q^7 + 30 * q^8 + 198 * q^9	\( 169 q + 9 q^{2} + 9 q^{3} + 199 q^{4} + 12 q^{5} + 22 q^{6} + 36 q^{7} + 30 q^{8} + 198 q^{9} - 3 q^{10} + 59 q^{11} + 11 q^{12} - 169 q^{13} + 30 q^{14} + 50 q^{15} + 267 q^{16} + q^{17} + 53 q^{18} + 107 q^{19} + 48 q^{20} + 36 q^{21} + 14 q^{22} + 12 q^{23} + 78 q^{24} + 217 q^{25} - 9 q^{26} + 39 q^{27} + 99 q^{28} + 30 q^{29} - q^{30} + 106 q^{31} + 74 q^{32} + 16 q^{33} + 56 q^{34} + 46 q^{35} + 271 q^{36} + 73 q^{37} + 2 q^{38} - 9 q^{39} - 16 q^{40} + 52 q^{41} - 2 q^{42} + 64 q^{43} + 124 q^{44} + 84 q^{45} + 105 q^{46} + 55 q^{47} + 26 q^{48} + 257 q^{49} + 60 q^{50} + 117 q^{51} - 199 q^{52} + 7 q^{53} + 78 q^{54} - 4 q^{55} + 63 q^{56} + 51 q^{57} + 84 q^{58} + 98 q^{59} + 94 q^{60} + 32 q^{61} - 25 q^{62} + 128 q^{63} + 380 q^{64} - 12 q^{65} + 16 q^{66} + 170 q^{67} - 10 q^{68} + 55 q^{69} + 70 q^{70} + 124 q^{71} + 173 q^{72} + 81 q^{73} + 54 q^{74} + 120 q^{75} + 212 q^{76} + 20 q^{77} - 22 q^{78} + 92 q^{79} + 66 q^{80} + 265 q^{81} + 21 q^{82} + 62 q^{83} + 98 q^{84} + 139 q^{85} + 51 q^{86} - 33 q^{87} + 31 q^{88} + 58 q^{89} + 16 q^{90} - 36 q^{91} + 40 q^{92} + 37 q^{93} + 55 q^{94} + 23 q^{95} + 164 q^{96} + 78 q^{97} + 69 q^{98} + 307 q^{99}+O(q^{100}) \) 169 * q + 9 * q^2 + 9 * q^3 + 199 * q^4 + 12 * q^5 + 22 * q^6 + 36 * q^7 + 30 * q^8 + 198 * q^9 - 3 * q^10 + 59 * q^11 + 11 * q^12 - 169 * q^13 + 30 * q^14 + 50 * q^15 + 267 * q^16 + q^17 + 53 * q^18 + 107 * q^19 + 48 * q^20 + 36 * q^21 + 14 * q^22 + 12 * q^23 + 78 * q^24 + 217 * q^25 - 9 * q^26 + 39 * q^27 + 99 * q^28 + 30 * q^29 - q^30 + 106 * q^31 + 74 * q^32 + 16 * q^33 + 56 * q^34 + 46 * q^35 + 271 * q^36 + 73 * q^37 + 2 * q^38 - 9 * q^39 - 16 * q^40 + 52 * q^41 - 2 * q^42 + 64 * q^43 + 124 * q^44 + 84 * q^45 + 105 * q^46 + 55 * q^47 + 26 * q^48 + 257 * q^49 + 60 * q^50 + 117 * q^51 - 199 * q^52 + 7 * q^53 + 78 * q^54 - 4 * q^55 + 63 * q^56 + 51 * q^57 + 84 * q^58 + 98 * q^59 + 94 * q^60 + 32 * q^61 - 25 * q^62 + 128 * q^63 + 380 * q^64 - 12 * q^65 + 16 * q^66 + 170 * q^67 - 10 * q^68 + 55 * q^69 + 70 * q^70 + 124 * q^71 + 173 * q^72 + 81 * q^73 + 54 * q^74 + 120 * q^75 + 212 * q^76 + 20 * q^77 - 22 * q^78 + 92 * q^79 + 66 * q^80 + 265 * q^81 + 21 * q^82 + 62 * q^83 + 98 * q^84 + 139 * q^85 + 51 * q^86 - 33 * q^87 + 31 * q^88 + 58 * q^89 + 16 * q^90 - 36 * q^91 + 40 * q^92 + 37 * q^93 + 55 * q^94 + 23 * q^95 + 164 * q^96 + 78 * q^97 + 69 * q^98 + 307 * q^99

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