LMFDB - Embedded newform 429.2.a.e.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [429,2,Mod(1,429)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(429, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("429.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 429 = 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	429.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:	$3.42558224671$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.564.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 5x + 3 $ x^3 - x^2 - 5*x + 3
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$2.51414$ of defining polynomial
Character	$\chi$	$=$	429.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.51414 q^{2} -1.00000 q^{3} +4.32088 q^{4} -0.193252 q^{5} +2.51414 q^{6} +3.32088 q^{7} -5.83502 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.51414 q^{2} -1.00000 q^{3} +4.32088 q^{4} -0.193252 q^{5} +2.51414 q^{6} +3.32088 q^{7} -5.83502 q^{8} +1.00000 q^{9} +0.485863 q^{10} +1.00000 q^{11} -4.32088 q^{12} -1.00000 q^{13} -8.34916 q^{14} +0.193252 q^{15} +6.02827 q^{16} +1.51414 q^{17} -2.51414 q^{18} +0.679116 q^{19} -0.835021 q^{20} -3.32088 q^{21} -2.51414 q^{22} -5.70739 q^{23} +5.83502 q^{24} -4.96265 q^{25} +2.51414 q^{26} -1.00000 q^{27} +14.3492 q^{28} +7.12763 q^{29} -0.485863 q^{30} +5.80675 q^{31} -3.48586 q^{32} -1.00000 q^{33} -3.80675 q^{34} -0.641769 q^{35} +4.32088 q^{36} +3.41478 q^{37} -1.70739 q^{38} +1.00000 q^{39} +1.12763 q^{40} +11.3774 q^{41} +8.34916 q^{42} +2.15591 q^{43} +4.32088 q^{44} -0.193252 q^{45} +14.3492 q^{46} -1.61350 q^{47} -6.02827 q^{48} +4.02827 q^{49} +12.4768 q^{50} -1.51414 q^{51} -4.32088 q^{52} +1.02827 q^{53} +2.51414 q^{54} -0.193252 q^{55} -19.3774 q^{56} -0.679116 q^{57} -17.9198 q^{58} +4.38650 q^{59} +0.835021 q^{60} +7.02827 q^{61} -14.5990 q^{62} +3.32088 q^{63} -3.29261 q^{64} +0.193252 q^{65} +2.51414 q^{66} +13.2215 q^{67} +6.54241 q^{68} +5.70739 q^{69} +1.61350 q^{70} +4.64177 q^{71} -5.83502 q^{72} -14.0192 q^{73} -8.58522 q^{74} +4.96265 q^{75} +2.93438 q^{76} +3.32088 q^{77} -2.51414 q^{78} +4.48586 q^{79} -1.16498 q^{80} +1.00000 q^{81} -28.6044 q^{82} +17.6700 q^{83} -14.3492 q^{84} -0.292611 q^{85} -5.42024 q^{86} -7.12763 q^{87} -5.83502 q^{88} -12.4485 q^{89} +0.485863 q^{90} -3.32088 q^{91} -24.6610 q^{92} -5.80675 q^{93} +4.05655 q^{94} -0.131241 q^{95} +3.48586 q^{96} -7.41478 q^{97} -10.1276 q^{98} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - q^{2} - 3 q^{3} + 5 q^{4} - 2 q^{5} + q^{6} + 2 q^{7} - 3 q^{8} + 3 q^{9}+O(q^{10}) $ 3 * q - q^2 - 3 * q^3 + 5 * q^4 - 2 * q^5 + q^6 + 2 * q^7 - 3 * q^8 + 3 * q^9	\( 3 q - q^{2} - 3 q^{3} + 5 q^{4} - 2 q^{5} + q^{6} + 2 q^{7} - 3 q^{8} + 3 q^{9} + 8 q^{10} + 3 q^{11} - 5 q^{12} - 3 q^{13} - 4 q^{14} + 2 q^{15} + 5 q^{16} - 2 q^{17} - q^{18} + 10 q^{19} + 12 q^{20} - 2 q^{21} - q^{22} - 12 q^{23} + 3 q^{24} + 9 q^{25} + q^{26} - 3 q^{27} + 22 q^{28} + 12 q^{29} - 8 q^{30} + 16 q^{31} - 17 q^{32} - 3 q^{33} - 10 q^{34} + 14 q^{35} + 5 q^{36} + 3 q^{39} - 6 q^{40} + 4 q^{42} - 16 q^{43} + 5 q^{44} - 2 q^{45} + 22 q^{46} - 2 q^{47} - 5 q^{48} - q^{49} + 7 q^{50} + 2 q^{51} - 5 q^{52} - 10 q^{53} + q^{54} - 2 q^{55} - 24 q^{56} - 10 q^{57} + 16 q^{59} - 12 q^{60} + 8 q^{61} + 2 q^{62} + 2 q^{63} - 15 q^{64} + 2 q^{65} + q^{66} + 28 q^{67} + 12 q^{69} + 2 q^{70} - 2 q^{71} - 3 q^{72} + 8 q^{73} - 36 q^{74} - 9 q^{75} - 2 q^{76} + 2 q^{77} - q^{78} + 20 q^{79} - 18 q^{80} + 3 q^{81} - 46 q^{82} + 24 q^{83} - 22 q^{84} - 6 q^{85} - 12 q^{86} - 12 q^{87} - 3 q^{88} - 20 q^{89} + 8 q^{90} - 2 q^{91} - 8 q^{92} - 16 q^{93} - 14 q^{94} - 22 q^{95} + 17 q^{96} - 12 q^{97} - 21 q^{98} + 3 q^{99}+O(q^{100}) \) 3 * q - q^2 - 3 * q^3 + 5 * q^4 - 2 * q^5 + q^6 + 2 * q^7 - 3 * q^8 + 3 * q^9 + 8 * q^10 + 3 * q^11 - 5 * q^12 - 3 * q^13 - 4 * q^14 + 2 * q^15 + 5 * q^16 - 2 * q^17 - q^18 + 10 * q^19 + 12 * q^20 - 2 * q^21 - q^22 - 12 * q^23 + 3 * q^24 + 9 * q^25 + q^26 - 3 * q^27 + 22 * q^28 + 12 * q^29 - 8 * q^30 + 16 * q^31 - 17 * q^32 - 3 * q^33 - 10 * q^34 + 14 * q^35 + 5 * q^36 + 3 * q^39 - 6 * q^40 + 4 * q^42 - 16 * q^43 + 5 * q^44 - 2 * q^45 + 22 * q^46 - 2 * q^47 - 5 * q^48 - q^49 + 7 * q^50 + 2 * q^51 - 5 * q^52 - 10 * q^53 + q^54 - 2 * q^55 - 24 * q^56 - 10 * q^57 + 16 * q^59 - 12 * q^60 + 8 * q^61 + 2 * q^62 + 2 * q^63 - 15 * q^64 + 2 * q^65 + q^66 + 28 * q^67 + 12 * q^69 + 2 * q^70 - 2 * q^71 - 3 * q^72 + 8 * q^73 - 36 * q^74 - 9 * q^75 - 2 * q^76 + 2 * q^77 - q^78 + 20 * q^79 - 18 * q^80 + 3 * q^81 - 46 * q^82 + 24 * q^83 - 22 * q^84 - 6 * q^85 - 12 * q^86 - 12 * q^87 - 3 * q^88 - 20 * q^89 + 8 * q^90 - 2 * q^91 - 8 * q^92 - 16 * q^93 - 14 * q^94 - 22 * q^95 + 17 * q^96 - 12 * q^97 - 21 * q^98 + 3 * 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 $

$2$	−2.51414	−1.77776	−0.888882	−	0.458137i	$-0.848517\pi$
$2$	−2.51414	−1.77776	−0.888882	+	0.458137i	$0.848517\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	4.32088	2.16044
$5$	−0.193252	−0.0864251	−0.0432126	−	0.999066i	$-0.513759\pi$
$5$	−0.193252	−0.0864251	−0.0432126	+	0.999066i	$0.513759\pi$
$6$	2.51414	1.02639
$7$	3.32088	1.25518	0.627588	−	0.778545i	$-0.284042\pi$
$7$	3.32088	1.25518	0.627588	+	0.778545i	$0.284042\pi$
$8$	−5.83502	−2.06299
$9$	1.00000	0.333333
$10$	0.485863	0.153643
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−4.32088	−1.24733
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	−8.34916	−2.23141
$15$	0.193252	0.0498976
$16$	6.02827	1.50707
$17$	1.51414	0.367232	0.183616	−	0.982998i	$-0.441220\pi$
$17$	1.51414	0.367232	0.183616	+	0.982998i	$0.441220\pi$
$18$	−2.51414	−0.592588
$19$	0.679116	0.155800	0.0778999	−	0.996961i	$-0.475179\pi$
$19$	0.679116	0.155800	0.0778999	+	0.996961i	$0.475179\pi$
$20$	−0.835021	−0.186716
$21$	−3.32088	−0.724676
$22$	−2.51414	−0.536016
$23$	−5.70739	−1.19007	−0.595036	−	0.803699i	$-0.702862\pi$
$23$	−5.70739	−1.19007	−0.595036	+	0.803699i	$0.702862\pi$
$24$	5.83502	1.19107
$25$	−4.96265	−0.992531
$26$	2.51414	0.493063
$27$	−1.00000	−0.192450
$28$	14.3492	2.71174
$29$	7.12763	1.32357	0.661784	−	0.749695i	$-0.269800\pi$
$29$	7.12763	1.32357	0.661784	+	0.749695i	$0.269800\pi$
$30$	−0.485863	−0.0887061
$31$	5.80675	1.04292	0.521461	−	0.853275i	$-0.325387\pi$
$31$	5.80675	1.04292	0.521461	+	0.853275i	$0.325387\pi$
$32$	−3.48586	−0.616219
$33$	−1.00000	−0.174078
$34$	−3.80675	−0.652852
$35$	−0.641769	−0.108479
$36$	4.32088	0.720147
$37$	3.41478	0.561386	0.280693	−	0.959798i	$-0.409436\pi$
$37$	3.41478	0.561386	0.280693	+	0.959798i	$0.409436\pi$
$38$	−1.70739	−0.276975
$39$	1.00000	0.160128
$40$	1.12763	0.178294
$41$	11.3774	1.77686	0.888428	−	0.459016i	$-0.151798\pi$
$41$	11.3774	1.77686	0.888428	+	0.459016i	$0.151798\pi$
$42$	8.34916	1.28830
$43$	2.15591	0.328773	0.164386	−	0.986396i	$-0.447436\pi$
$43$	2.15591	0.328773	0.164386	+	0.986396i	$0.447436\pi$
$44$	4.32088	0.651398
$45$	−0.193252	−0.0288084
$46$	14.3492	2.11567
$47$	−1.61350	−0.235352	−0.117676	−	0.993052i	$-0.537544\pi$
$47$	−1.61350	−0.235352	−0.117676	+	0.993052i	$0.537544\pi$
$48$	−6.02827	−0.870106
$49$	4.02827	0.575468
$50$	12.4768	1.76448
$51$	−1.51414	−0.212022
$52$	−4.32088	−0.599199
$53$	1.02827	0.141244	0.0706221	−	0.997503i	$-0.477502\pi$
$53$	1.02827	0.141244	0.0706221	+	0.997503i	$0.477502\pi$
$54$	2.51414	0.342131
$55$	−0.193252	−0.0260582
$56$	−19.3774	−2.58942
$57$	−0.679116	−0.0899510
$58$	−17.9198	−2.35299
$59$	4.38650	0.571074	0.285537	−	0.958368i	$-0.407828\pi$
$59$	4.38650	0.571074	0.285537	+	0.958368i	$0.407828\pi$
$60$	0.835021	0.107801
$61$	7.02827	0.899878	0.449939	−	0.893059i	$-0.351446\pi$
$61$	7.02827	0.899878	0.449939	+	0.893059i	$0.351446\pi$
$62$	−14.5990	−1.85407
$63$	3.32088	0.418392
$64$	−3.29261	−0.411576
$65$	0.193252	0.0239700
$66$	2.51414	0.309469
$67$	13.2215	1.61527	0.807633	−	0.589685i	$-0.200748\pi$
$67$	13.2215	1.61527	0.807633	+	0.589685i	$0.200748\pi$
$68$	6.54241	0.793384
$69$	5.70739	0.687089
$70$	1.61350	0.192850
$71$	4.64177	0.550877	0.275438	−	0.961319i	$-0.411177\pi$
$71$	4.64177	0.550877	0.275438	+	0.961319i	$0.411177\pi$
$72$	−5.83502	−0.687664
$73$	−14.0192	−1.64082	−0.820412	−	0.571773i	$-0.806256\pi$
$73$	−14.0192	−1.64082	−0.820412	+	0.571773i	$0.806256\pi$
$74$	−8.58522	−0.998012
$75$	4.96265	0.573038
$76$	2.93438	0.336596
$77$	3.32088	0.378450
$78$	−2.51414	−0.284670
$79$	4.48586	0.504699	0.252350	−	0.967636i	$-0.418797\pi$
$79$	4.48586	0.504699	0.252350	+	0.967636i	$0.418797\pi$
$80$	−1.16498	−0.130249
$81$	1.00000	0.111111
$82$	−28.6044	−3.15883
$83$	17.6700	1.93954	0.969770	−	0.244022i	$-0.0784671\pi$
$83$	17.6700	1.93954	0.969770	+	0.244022i	$0.0784671\pi$
$84$	−14.3492	−1.56562
$85$	−0.292611	−0.0317381
$86$	−5.42024	−0.584480
$87$	−7.12763	−0.764162
$88$	−5.83502	−0.622015
$89$	−12.4485	−1.31954	−0.659770	−	0.751468i	$-0.729346\pi$
$89$	−12.4485	−1.31954	−0.659770	+	0.751468i	$0.729346\pi$
$90$	0.485863	0.0512145
$91$	−3.32088	−0.348123
$92$	−24.6610	−2.57108
$93$	−5.80675	−0.602132
$94$	4.05655	0.418401
$95$	−0.131241	−0.0134650
$96$	3.48586	0.355774
$97$	−7.41478	−0.752857	−0.376428	−	0.926446i	$-0.622848\pi$
$97$	−7.41478	−0.752857	−0.376428	+	0.926446i	$0.622848\pi$
$98$	−10.1276	−1.02305
$99$	1.00000	0.100504
$100$	−21.4431	−2.14431
$101$	−14.2125	−1.41419	−0.707096	−	0.707118i	$-0.749995\pi$
$101$	−14.2125	−1.41419	−0.707096	+	0.707118i	$0.749995\pi$
$102$	3.80675	0.376924
$103$	−6.05655	−0.596769	−0.298385	−	0.954446i	$-0.596448\pi$
$103$	−6.05655	−0.596769	−0.298385	+	0.954446i	$0.596448\pi$
$104$	5.83502	0.572171
$105$	0.641769	0.0626302
$106$	−2.58522	−0.251099
$107$	−3.61350	−0.349330	−0.174665	−	0.984628i	$-0.555884\pi$
$107$	−3.61350	−0.349330	−0.174665	+	0.984628i	$0.555884\pi$
$108$	−4.32088	−0.415777
$109$	7.96265	0.762684	0.381342	−	0.924434i	$-0.375462\pi$
$109$	7.96265	0.762684	0.381342	+	0.924434i	$0.375462\pi$
$110$	0.485863	0.0463252
$111$	−3.41478	−0.324116
$112$	20.0192	1.89164
$113$	−2.38650	−0.224503	−0.112252	−	0.993680i	$-0.535806\pi$
$113$	−2.38650	−0.224503	−0.112252	+	0.993680i	$0.535806\pi$
$114$	1.70739	0.159912
$115$	1.10297	0.102852
$116$	30.7977	2.85949
$117$	−1.00000	−0.0924500
$118$	−11.0283	−1.01523
$119$	5.02827	0.460941
$120$	−1.12763	−0.102938
$121$	1.00000	0.0909091
$122$	−17.6700	−1.59977
$123$	−11.3774	−1.02587
$124$	25.0903	2.25317
$125$	1.92531	0.172205
$126$	−8.34916	−0.743802
$127$	−7.18418	−0.637493	−0.318746	−	0.947840i	$-0.603262\pi$
$127$	−7.18418	−0.637493	−0.318746	+	0.947840i	$0.603262\pi$
$128$	15.2498	1.34790
$129$	−2.15591	−0.189817
$130$	−0.485863	−0.0426130
$131$	15.4148	1.34680	0.673398	−	0.739280i	$-0.264834\pi$
$131$	15.4148	1.34680	0.673398	+	0.739280i	$0.264834\pi$
$132$	−4.32088	−0.376085
$133$	2.25526	0.195556
$134$	−33.2407	−2.87156
$135$	0.193252	0.0166325
$136$	−8.83502	−0.757597
$137$	6.89157	0.588786	0.294393	−	0.955684i	$-0.404882\pi$
$137$	6.89157	0.588786	0.294393	+	0.955684i	$0.404882\pi$
$138$	−14.3492	−1.22148
$139$	8.74113	0.741413	0.370706	−	0.928750i	$-0.379116\pi$
$139$	8.74113	0.741413	0.370706	+	0.928750i	$0.379116\pi$
$140$	−2.77301	−0.234362
$141$	1.61350	0.135881
$142$	−11.6700	−0.979328
$143$	−1.00000	−0.0836242
$144$	6.02827	0.502356
$145$	−1.37743	−0.114390
$146$	35.2462	2.91700
$147$	−4.02827	−0.332246
$148$	14.7549	1.21284
$149$	1.32088	0.108211	0.0541055	−	0.998535i	$-0.482769\pi$
$149$	1.32088	0.108211	0.0541055	+	0.998535i	$0.482769\pi$
$150$	−12.4768	−1.01873
$151$	20.0192	1.62914	0.814570	−	0.580066i	$-0.196973\pi$
$151$	20.0192	1.62914	0.814570	+	0.580066i	$0.196973\pi$
$152$	−3.96265	−0.321414
$153$	1.51414	0.122411
$154$	−8.34916	−0.672794
$155$	−1.12217	−0.0901347
$156$	4.32088	0.345948
$157$	−5.37743	−0.429166	−0.214583	−	0.976706i	$-0.568839\pi$
$157$	−5.37743	−0.429166	−0.214583	+	0.976706i	$0.568839\pi$
$158$	−11.2781	−0.897235
$159$	−1.02827	−0.0815474
$160$	0.673652	0.0532568
$161$	−18.9536	−1.49375
$162$	−2.51414	−0.197529
$163$	−16.3063	−1.27721	−0.638606	−	0.769534i	$-0.720489\pi$
$163$	−16.3063	−1.27721	−0.638606	+	0.769534i	$0.720489\pi$
$164$	49.1606	3.83880
$165$	0.193252	0.0150447
$166$	−44.4249	−3.44804
$167$	15.4148	1.19283	0.596416	−	0.802676i	$-0.296591\pi$
$167$	15.4148	1.19283	0.596416	+	0.802676i	$0.296591\pi$
$168$	19.3774	1.49500
$169$	1.00000	0.0769231
$170$	0.735663	0.0564228
$171$	0.679116	0.0519333
$172$	9.31542	0.710294
$173$	2.48586	0.188997	0.0944983	−	0.995525i	$-0.469875\pi$
$173$	2.48586	0.188997	0.0944983	+	0.995525i	$0.469875\pi$
$174$	17.9198	1.35850
$175$	−16.4804	−1.24580
$176$	6.02827	0.454398
$177$	−4.38650	−0.329710
$178$	31.2973	2.34583
$179$	22.7922	1.70357	0.851785	−	0.523892i	$-0.175520\pi$
$179$	22.7922	1.70357	0.851785	+	0.523892i	$0.175520\pi$
$180$	−0.835021	−0.0622388
$181$	−22.0757	−1.64088	−0.820439	−	0.571734i	$-0.806271\pi$
$181$	−22.0757	−1.64088	−0.820439	+	0.571734i	$0.806271\pi$
$182$	8.34916	0.618881
$183$	−7.02827	−0.519545
$184$	33.3027	2.45511
$185$	−0.659914	−0.0485179
$186$	14.5990	1.07045
$187$	1.51414	0.110725
$188$	−6.97173	−0.508465
$189$	−3.32088	−0.241559
$190$	0.329957	0.0239376
$191$	−7.61350	−0.550893	−0.275447	−	0.961316i	$-0.588826\pi$
$191$	−7.61350	−0.550893	−0.275447	+	0.961316i	$0.588826\pi$
$192$	3.29261	0.237624
$193$	0.735663	0.0529542	0.0264771	−	0.999649i	$-0.491571\pi$
$193$	0.735663	0.0529542	0.0264771	+	0.999649i	$0.491571\pi$
$194$	18.6418	1.33840
$195$	−0.193252	−0.0138391
$196$	17.4057	1.24326
$197$	−4.93438	−0.351560	−0.175780	−	0.984429i	$-0.556245\pi$
$197$	−4.93438	−0.351560	−0.175780	+	0.984429i	$0.556245\pi$
$198$	−2.51414	−0.178672
$199$	23.3401	1.65453	0.827267	−	0.561808i	$-0.189894\pi$
$199$	23.3401	1.65453	0.827267	+	0.561808i	$0.189894\pi$
$200$	28.9572	2.04758
$201$	−13.2215	−0.932575
$202$	35.7321	2.51410
$203$	23.6700	1.66131
$204$	−6.54241	−0.458060
$205$	−2.19872	−0.153565
$206$	15.2270	1.06091
$207$	−5.70739	−0.396691
$208$	−6.02827	−0.417986
$209$	0.679116	0.0469754
$210$	−1.61350	−0.111342
$211$	−23.4394	−1.61364	−0.806819	−	0.590799i	$-0.798813\pi$
$211$	−23.4394	−1.61364	−0.806819	+	0.590799i	$0.798813\pi$
$212$	4.44305	0.305150
$213$	−4.64177	−0.318049
$214$	9.08482	0.621026
$215$	−0.416634	−0.0284142
$216$	5.83502	0.397023
$217$	19.2835	1.30905
$218$	−20.0192	−1.35587
$219$	14.0192	0.947330
$220$	−0.835021	−0.0562971
$221$	−1.51414	−0.101852
$222$	8.58522	0.576202
$223$	9.42024	0.630826	0.315413	−	0.948954i	$-0.397857\pi$
$223$	9.42024	0.630826	0.315413	+	0.948954i	$0.397857\pi$
$224$	−11.5761	−0.773464
$225$	−4.96265	−0.330844
$226$	6.00000	0.399114
$227$	0.480399	0.0318852	0.0159426	−	0.999873i	$-0.494925\pi$
$227$	0.480399	0.0318852	0.0159426	+	0.999873i	$0.494925\pi$
$228$	−2.93438	−0.194334
$229$	−3.61350	−0.238786	−0.119393	−	0.992847i	$-0.538095\pi$
$229$	−3.61350	−0.238786	−0.119393	+	0.992847i	$0.538095\pi$
$230$	−2.77301	−0.182847
$231$	−3.32088	−0.218498
$232$	−41.5899	−2.73051
$233$	−24.5990	−1.61153	−0.805766	−	0.592234i	$-0.798246\pi$
$233$	−24.5990	−1.61153	−0.805766	+	0.592234i	$0.798246\pi$
$234$	2.51414	0.164354
$235$	0.311812	0.0203404
$236$	18.9536	1.23377
$237$	−4.48586	−0.291388
$238$	−12.6418	−0.819444
$239$	−28.3310	−1.83258	−0.916290	−	0.400514i	$-0.868831\pi$
$239$	−28.3310	−1.83258	−0.916290	+	0.400514i	$0.868831\pi$
$240$	1.16498	0.0751990
$241$	−20.3684	−1.31204	−0.656021	−	0.754743i	$-0.727762\pi$
$241$	−20.3684	−1.31204	−0.656021	+	0.754743i	$0.727762\pi$
$242$	−2.51414	−0.161615
$243$	−1.00000	−0.0641500
$244$	30.3684	1.94414
$245$	−0.778474	−0.0497349
$246$	28.6044	1.82375
$247$	−0.679116	−0.0432111
$248$	−33.8825	−2.15154
$249$	−17.6700	−1.11979
$250$	−4.84049	−0.306139
$251$	−15.7266	−0.992654	−0.496327	−	0.868136i	$-0.665318\pi$
$251$	−15.7266	−0.992654	−0.496327	+	0.868136i	$0.665318\pi$
$252$	14.3492	0.903912
$253$	−5.70739	−0.358820
$254$	18.0620	1.13331
$255$	0.292611	0.0183240
$256$	−31.7549	−1.98468
$257$	−3.35823	−0.209481	−0.104740	−	0.994500i	$-0.533401\pi$
$257$	−3.35823	−0.209481	−0.104740	+	0.994500i	$0.533401\pi$
$258$	5.42024	0.337450
$259$	11.3401	0.704639
$260$	0.835021	0.0517858
$261$	7.12763	0.441189
$262$	−38.7549	−2.39428
$263$	−26.4431	−1.63055	−0.815274	−	0.579075i	$-0.803414\pi$
$263$	−26.4431	−1.63055	−0.815274	+	0.579075i	$0.803414\pi$
$264$	5.83502	0.359121
$265$	−0.198716	−0.0122071
$266$	−5.67004	−0.347653
$267$	12.4485	0.761837
$268$	57.1287	3.48969
$269$	2.97173	0.181189	0.0905947	−	0.995888i	$-0.471123\pi$
$269$	2.97173	0.181189	0.0905947	+	0.995888i	$0.471123\pi$
$270$	−0.485863	−0.0295687
$271$	−20.2926	−1.23269	−0.616344	−	0.787477i	$-0.711387\pi$
$271$	−20.2926	−1.23269	−0.616344	+	0.787477i	$0.711387\pi$
$272$	9.12763	0.553444
$273$	3.32088	0.200989
$274$	−17.3263	−1.04672
$275$	−4.96265	−0.299259
$276$	24.6610	1.48442
$277$	19.9819	1.20059	0.600297	−	0.799777i	$-0.295049\pi$
$277$	19.9819	1.20059	0.600297	+	0.799777i	$0.295049\pi$
$278$	−21.9764	−1.31806
$279$	5.80675	0.347641
$280$	3.74474	0.223791
$281$	−25.7458	−1.53587	−0.767933	−	0.640531i	$-0.778714\pi$
$281$	−25.7458	−1.53587	−0.767933	+	0.640531i	$0.778714\pi$
$282$	−4.05655	−0.241564
$283$	21.9006	1.30186	0.650929	−	0.759139i	$-0.274380\pi$
$283$	21.9006	1.30186	0.650929	+	0.759139i	$0.274380\pi$
$284$	20.0565	1.19014
$285$	0.131241	0.00777403
$286$	2.51414	0.148664
$287$	37.7831	2.23027
$288$	−3.48586	−0.205406
$289$	−14.7074	−0.865141
$290$	3.46305	0.203357
$291$	7.41478	0.434662
$292$	−60.5753	−3.54490
$293$	14.8031	0.864809	0.432404	−	0.901680i	$-0.357665\pi$
$293$	14.8031	0.864809	0.432404	+	0.901680i	$0.357665\pi$
$294$	10.1276	0.590655
$295$	−0.847703	−0.0493552
$296$	−19.9253	−1.15813
$297$	−1.00000	−0.0580259
$298$	−3.32088	−0.192374
$299$	5.70739	0.330067
$300$	21.4431	1.23802
$301$	7.15951	0.412668
$302$	−50.3310	−2.89622
$303$	14.2125	0.816484
$304$	4.09389	0.234801
$305$	−1.35823	−0.0777721
$306$	−3.80675	−0.217617
$307$	−32.1323	−1.83389	−0.916944	−	0.399017i	$-0.869351\pi$
$307$	−32.1323	−1.83389	−0.916944	+	0.399017i	$0.869351\pi$
$308$	14.3492	0.817619
$309$	6.05655	0.344545
$310$	2.82128	0.160238
$311$	−2.40571	−0.136415	−0.0682075	−	0.997671i	$-0.521728\pi$
$311$	−2.40571	−0.136415	−0.0682075	+	0.997671i	$0.521728\pi$
$312$	−5.83502	−0.330343
$313$	12.9909	0.734291	0.367145	−	0.930164i	$-0.380335\pi$
$313$	12.9909	0.734291	0.367145	+	0.930164i	$0.380335\pi$
$314$	13.5196	0.762955
$315$	−0.641769	−0.0361596
$316$	19.3829	1.09037
$317$	−24.5616	−1.37952	−0.689759	−	0.724039i	$-0.742283\pi$
$317$	−24.5616	−1.37952	−0.689759	+	0.724039i	$0.742283\pi$
$318$	2.58522	0.144972
$319$	7.12763	0.399071
$320$	0.636305	0.0355705
$321$	3.61350	0.201686
$322$	47.6519	2.65554
$323$	1.02827	0.0572147
$324$	4.32088	0.240049
$325$	4.96265	0.275278
$326$	40.9964	2.27058
$327$	−7.96265	−0.440336
$328$	−66.3876	−3.66564
$329$	−5.35823	−0.295409
$330$	−0.485863	−0.0267459
$331$	7.99454	0.439419	0.219710	−	0.975565i	$-0.429489\pi$
$331$	7.99454	0.439419	0.219710	+	0.975565i	$0.429489\pi$
$332$	76.3502	4.19026
$333$	3.41478	0.187129
$334$	−38.7549	−2.12057
$335$	−2.55509	−0.139600
$336$	−20.0192	−1.09214
$337$	19.0101	1.03555	0.517774	−	0.855518i	$-0.326761\pi$
$337$	19.0101	1.03555	0.517774	+	0.855518i	$0.326761\pi$
$338$	−2.51414	−0.136751
$339$	2.38650	0.129617
$340$	−1.26434	−0.0685683
$341$	5.80675	0.314453
$342$	−1.70739	−0.0923250
$343$	−9.86876	−0.532863
$344$	−12.5798	−0.678255
$345$	−1.10297	−0.0593817
$346$	−6.24980	−0.335991
$347$	14.1131	0.757631	0.378815	−	0.925472i	$-0.376332\pi$
$347$	14.1131	0.757631	0.378815	+	0.925472i	$0.376332\pi$
$348$	−30.7977	−1.65093
$349$	5.80128	0.310536	0.155268	−	0.987872i	$-0.450376\pi$
$349$	5.80128	0.310536	0.155268	+	0.987872i	$0.450376\pi$
$350$	41.4340	2.21474
$351$	1.00000	0.0533761
$352$	−3.48586	−0.185797
$353$	−5.75020	−0.306052	−0.153026	−	0.988222i	$-0.548902\pi$
$353$	−5.75020	−0.306052	−0.153026	+	0.988222i	$0.548902\pi$
$354$	11.0283	0.586146
$355$	−0.897033	−0.0476096
$356$	−53.7886	−2.85079
$357$	−5.02827	−0.266124
$358$	−57.3027	−3.02854
$359$	−30.4623	−1.60774	−0.803868	−	0.594808i	$-0.797228\pi$
$359$	−30.4623	−1.60774	−0.803868	+	0.594808i	$0.797228\pi$
$360$	1.12763	0.0594314
$361$	−18.5388	−0.975726
$362$	55.5015	2.91709
$363$	−1.00000	−0.0524864
$364$	−14.3492	−0.752100
$365$	2.70924	0.141808
$366$	17.6700	0.923628
$367$	19.9144	1.03952	0.519761	−	0.854312i	$-0.326021\pi$
$367$	19.9144	1.03952	0.519761	+	0.854312i	$0.326021\pi$
$368$	−34.4057	−1.79352
$369$	11.3774	0.592285
$370$	1.65911	0.0862533
$371$	3.41478	0.177286
$372$	−25.0903	−1.30087
$373$	−19.0101	−0.984307	−0.492154	−	0.870508i	$-0.663790\pi$
$373$	−19.0101	−0.984307	−0.492154	+	0.870508i	$0.663790\pi$
$374$	−3.80675	−0.196842
$375$	−1.92531	−0.0994224
$376$	9.41478	0.485530
$377$	−7.12763	−0.367092
$378$	8.34916	0.429434
$379$	36.0439	1.85145	0.925725	−	0.378198i	$-0.123456\pi$
$379$	36.0439	1.85145	0.925725	+	0.378198i	$0.123456\pi$
$380$	−0.567076	−0.0290904
$381$	7.18418	0.368057
$382$	19.1414	0.979358
$383$	−18.2553	−0.932800	−0.466400	−	0.884574i	$-0.654449\pi$
$383$	−18.2553	−0.932800	−0.466400	+	0.884574i	$0.654449\pi$
$384$	−15.2498	−0.778213
$385$	−0.641769	−0.0327076
$386$	−1.84956	−0.0941400
$387$	2.15591	0.109591
$388$	−32.0384	−1.62650
$389$	−4.84049	−0.245422	−0.122711	−	0.992442i	$-0.539159\pi$
$389$	−4.84049	−0.245422	−0.122711	+	0.992442i	$0.539159\pi$
$390$	0.485863	0.0246026
$391$	−8.64177	−0.437033
$392$	−23.5051	−1.18719
$393$	−15.4148	−0.777573
$394$	12.4057	0.624990
$395$	−0.866904	−0.0436187
$396$	4.32088	0.217133
$397$	31.1523	1.56349	0.781744	−	0.623599i	$-0.214330\pi$
$397$	31.1523	1.56349	0.781744	+	0.623599i	$0.214330\pi$
$398$	−58.6802	−2.94137
$399$	−2.25526	−0.112904
$400$	−29.9162	−1.49581
$401$	12.2317	0.610820	0.305410	−	0.952221i	$-0.401207\pi$
$401$	12.2317	0.610820	0.305410	+	0.952221i	$0.401207\pi$
$402$	33.2407	1.65790
$403$	−5.80675	−0.289255
$404$	−61.4104	−3.05528
$405$	−0.193252	−0.00960279
$406$	−59.5097	−2.95342
$407$	3.41478	0.169264
$408$	8.83502	0.437399
$409$	−8.73566	−0.431951	−0.215975	−	0.976399i	$-0.569293\pi$
$409$	−8.73566	−0.431951	−0.215975	+	0.976399i	$0.569293\pi$
$410$	5.52787	0.273002
$411$	−6.89157	−0.339936
$412$	−26.1696	−1.28929
$413$	14.5671	0.716799
$414$	14.3492	0.705223
$415$	−3.41478	−0.167625
$416$	3.48586	0.170908
$417$	−8.74113	−0.428055
$418$	−1.70739	−0.0835111
$419$	−16.1504	−0.789001	−0.394500	−	0.918896i	$-0.629082\pi$
$419$	−16.1504	−0.789001	−0.394500	+	0.918896i	$0.629082\pi$
$420$	2.77301	0.135309
$421$	−10.1878	−0.496522	−0.248261	−	0.968693i	$-0.579859\pi$
$421$	−10.1878	−0.496522	−0.248261	+	0.968693i	$0.579859\pi$
$422$	58.9300	2.86867
$423$	−1.61350	−0.0784508
$424$	−6.00000	−0.291386
$425$	−7.51414	−0.364489
$426$	11.6700	0.565415
$427$	23.3401	1.12951
$428$	−15.6135	−0.754707
$429$	1.00000	0.0482805
$430$	1.04748	0.0505137
$431$	−19.5279	−0.940625	−0.470312	−	0.882500i	$-0.655859\pi$
$431$	−19.5279	−0.940625	−0.470312	+	0.882500i	$0.655859\pi$
$432$	−6.02827	−0.290035
$433$	11.3966	0.547687	0.273844	−	0.961774i	$-0.411705\pi$
$433$	11.3966	0.547687	0.273844	+	0.961774i	$0.411705\pi$
$434$	−48.4815	−2.32718
$435$	1.37743	0.0660428
$436$	34.4057	1.64773
$437$	−3.87598	−0.185413
$438$	−35.2462	−1.68413
$439$	13.3829	0.638731	0.319365	−	0.947632i	$-0.396530\pi$
$439$	13.3829	0.638731	0.319365	+	0.947632i	$0.396530\pi$
$440$	1.12763	0.0537577
$441$	4.02827	0.191823
$442$	3.80675	0.181069
$443$	−3.22699	−0.153319	−0.0766595	−	0.997057i	$-0.524425\pi$
$443$	−3.22699	−0.153319	−0.0766595	+	0.997057i	$0.524425\pi$
$444$	−14.7549	−0.700235
$445$	2.40571	0.114041
$446$	−23.6838	−1.12146
$447$	−1.32088	−0.0624757
$448$	−10.9344	−0.516601
$449$	−39.4586	−1.86217	−0.931084	−	0.364804i	$-0.881136\pi$
$449$	−39.4586	−1.86217	−0.931084	+	0.364804i	$0.881136\pi$
$450$	12.4768	0.588162
$451$	11.3774	0.535742
$452$	−10.3118	−0.485027
$453$	−20.0192	−0.940584
$454$	−1.20779	−0.0566843
$455$	0.641769	0.0300866
$456$	3.96265	0.185568
$457$	23.8688	1.11653	0.558267	−	0.829662i	$-0.311467\pi$
$457$	23.8688	1.11653	0.558267	+	0.829662i	$0.311467\pi$
$458$	9.08482	0.424506
$459$	−1.51414	−0.0706739
$460$	4.76579	0.222206
$461$	7.37743	0.343601	0.171801	−	0.985132i	$-0.445042\pi$
$461$	7.37743	0.343601	0.171801	+	0.985132i	$0.445042\pi$
$462$	8.34916	0.388438
$463$	22.0511	1.02480	0.512400	−	0.858747i	$-0.328756\pi$
$463$	22.0511	1.02480	0.512400	+	0.858747i	$0.328756\pi$
$464$	42.9673	1.99471
$465$	1.12217	0.0520393
$466$	61.8452	2.86492
$467$	−6.21792	−0.287731	−0.143865	−	0.989597i	$-0.545953\pi$
$467$	−6.21792	−0.287731	−0.143865	+	0.989597i	$0.545953\pi$
$468$	−4.32088	−0.199733
$469$	43.9072	2.02744
$470$	−0.783938	−0.0361603
$471$	5.37743	0.247779
$472$	−25.5953	−1.17812
$473$	2.15591	0.0991287
$474$	11.2781	0.518019
$475$	−3.37021	−0.154636
$476$	21.7266	0.995837
$477$	1.02827	0.0470814
$478$	71.2280	3.25790
$479$	27.7074	1.26598	0.632991	−	0.774159i	$-0.281827\pi$
$479$	27.7074	1.26598	0.632991	+	0.774159i	$0.281827\pi$
$480$	−0.673652	−0.0307478
$481$	−3.41478	−0.155701
$482$	51.2088	2.33250
$483$	18.9536	0.862418
$484$	4.32088	0.196404
$485$	1.43292	0.0650657
$486$	2.51414	0.114044
$487$	16.7038	0.756921	0.378460	−	0.925618i	$-0.376454\pi$
$487$	16.7038	0.756921	0.378460	+	0.925618i	$0.376454\pi$
$488$	−41.0101	−1.85644
$489$	16.3063	0.737399
$490$	1.95719	0.0884168
$491$	−43.2088	−1.94999	−0.974994	−	0.222231i	$-0.928666\pi$
$491$	−43.2088	−1.94999	−0.974994	+	0.222231i	$0.928666\pi$
$492$	−49.1606	−2.21633
$493$	10.7922	0.486057
$494$	1.70739	0.0768191
$495$	−0.193252	−0.00868605
$496$	35.0047	1.57176
$497$	15.4148	0.691447
$498$	44.4249	1.99073
$499$	−2.59069	−0.115975	−0.0579875	−	0.998317i	$-0.518468\pi$
$499$	−2.59069	−0.115975	−0.0579875	+	0.998317i	$0.518468\pi$
$500$	8.31903	0.372038
$501$	−15.4148	−0.688682
$502$	39.5388	1.76470
$503$	21.2726	0.948499	0.474249	−	0.880391i	$-0.342720\pi$
$503$	21.2726	0.948499	0.474249	+	0.880391i	$0.342720\pi$
$504$	−19.3774	−0.863139
$505$	2.74659	0.122222
$506$	14.3492	0.637898
$507$	−1.00000	−0.0444116
$508$	−31.0420	−1.37727
$509$	−30.1186	−1.33498	−0.667491	−	0.744618i	$-0.732632\pi$
$509$	−30.1186	−1.33498	−0.667491	+	0.744618i	$0.732632\pi$
$510$	−0.735663	−0.0325757
$511$	−46.5561	−2.05952
$512$	49.3365	2.18038
$513$	−0.679116	−0.0299837
$514$	8.44305	0.372407
$515$	1.17044	0.0515759
$516$	−9.31542	−0.410089
$517$	−1.61350	−0.0709614
$518$	−28.5105	−1.25268
$519$	−2.48586	−0.109117
$520$	−1.12763	−0.0494499
$521$	26.6236	1.16640	0.583201	−	0.812328i	$-0.301800\pi$
$521$	26.6236	1.16640	0.583201	+	0.812328i	$0.301800\pi$
$522$	−17.9198	−0.784330
$523$	−41.0986	−1.79711	−0.898557	−	0.438856i	$-0.855384\pi$
$523$	−41.0986	−1.79711	−0.898557	+	0.438856i	$0.855384\pi$
$524$	66.6055	2.90967
$525$	16.4804	0.719264
$526$	66.4815	2.89873
$527$	8.79221	0.382995
$528$	−6.02827	−0.262347
$529$	9.57429	0.416274
$530$	0.499600	0.0217013
$531$	4.38650	0.190358
$532$	9.74474	0.422488
$533$	−11.3774	−0.492811
$534$	−31.2973	−1.35437
$535$	0.698317	0.0301909
$536$	−77.1479	−3.33228
$537$	−22.7922	−0.983556
$538$	−7.47133	−0.322112
$539$	4.02827	0.173510
$540$	0.835021	0.0359336
$541$	−15.3966	−0.661953	−0.330976	−	0.943639i	$-0.607378\pi$
$541$	−15.3966	−0.661953	−0.330976	+	0.943639i	$0.607378\pi$
$542$	51.0184	2.19143
$543$	22.0757	0.947361
$544$	−5.27807	−0.226296
$545$	−1.53880	−0.0659150
$546$	−8.34916	−0.357311
$547$	−41.3648	−1.76863	−0.884315	−	0.466892i	$-0.845374\pi$
$547$	−41.3648	−1.76863	−0.884315	+	0.466892i	$0.845374\pi$
$548$	29.7777	1.27204
$549$	7.02827	0.299959
$550$	12.4768	0.532012
$551$	4.84049	0.206212
$552$	−33.3027	−1.41746
$553$	14.8970	0.633486
$554$	−50.2371	−2.13437
$555$	0.659914	0.0280118
$556$	37.7694	1.60178
$557$	−16.4732	−0.697991	−0.348996	−	0.937124i	$-0.613477\pi$
$557$	−16.4732	−0.697991	−0.348996	+	0.937124i	$0.613477\pi$
$558$	−14.5990	−0.618023
$559$	−2.15591	−0.0911851
$560$	−3.86876	−0.163485
$561$	−1.51414	−0.0639269
$562$	64.7284	2.73040
$563$	37.9819	1.60074	0.800372	−	0.599503i	$-0.204635\pi$
$563$	37.9819	1.60074	0.800372	+	0.599503i	$0.204635\pi$
$564$	6.97173	0.293563
$565$	0.461198	0.0194027
$566$	−55.0612	−2.31440
$567$	3.32088	0.139464
$568$	−27.0848	−1.13645
$569$	−1.62723	−0.0682171	−0.0341086	−	0.999418i	$-0.510859\pi$
$569$	−1.62723	−0.0682171	−0.0341086	+	0.999418i	$0.510859\pi$
$570$	−0.329957	−0.0138204
$571$	−7.51414	−0.314457	−0.157228	−	0.987562i	$-0.550256\pi$
$571$	−7.51414	−0.314457	−0.157228	+	0.987562i	$0.550256\pi$
$572$	−4.32088	−0.180665
$573$	7.61350	0.318058
$574$	−94.9920	−3.96489
$575$	28.3238	1.18118
$576$	−3.29261	−0.137192
$577$	−13.5279	−0.563173	−0.281586	−	0.959536i	$-0.590861\pi$
$577$	−13.5279	−0.563173	−0.281586	+	0.959536i	$0.590861\pi$
$578$	36.9764	1.53802
$579$	−0.735663	−0.0305731
$580$	−5.95173	−0.247132
$581$	58.6802	2.43446
$582$	−18.6418	−0.772726
$583$	1.02827	0.0425868
$584$	81.8023	3.38500
$585$	0.193252	0.00799000
$586$	−37.2171	−1.53742
$587$	16.8970	0.697415	0.348708	−	0.937232i	$-0.386621\pi$
$587$	16.8970	0.697415	0.348708	+	0.937232i	$0.386621\pi$
$588$	−17.4057	−0.717799
$589$	3.94345	0.162487
$590$	2.13124	0.0877418
$591$	4.93438	0.202973
$592$	20.5852	0.846047
$593$	−5.70739	−0.234374	−0.117187	−	0.993110i	$-0.537388\pi$
$593$	−5.70739	−0.234374	−0.117187	+	0.993110i	$0.537388\pi$
$594$	2.51414	0.103156
$595$	−0.971726	−0.0398369
$596$	5.70739	0.233784
$597$	−23.3401	−0.955246
$598$	−14.3492	−0.586781
$599$	−23.6135	−0.964821	−0.482411	−	0.875945i	$-0.660239\pi$
$599$	−23.6135	−0.964821	−0.482411	+	0.875945i	$0.660239\pi$
$600$	−28.9572	−1.18217
$601$	44.5671	1.81793	0.908964	−	0.416874i	$-0.136874\pi$
$601$	44.5671	1.81793	0.908964	+	0.416874i	$0.136874\pi$
$602$	−18.0000	−0.733625
$603$	13.2215	0.538422
$604$	86.5007	3.51966
$605$	−0.193252	−0.00785683
$606$	−35.7321	−1.45152
$607$	22.3255	0.906166	0.453083	−	0.891468i	$-0.350324\pi$
$607$	22.3255	0.906166	0.453083	+	0.891468i	$0.350324\pi$
$608$	−2.36730	−0.0960068
$609$	−23.6700	−0.959159
$610$	3.41478	0.138260
$611$	1.61350	0.0652750
$612$	6.54241	0.264461
$613$	−30.9053	−1.24825	−0.624127	−	0.781323i	$-0.714545\pi$
$613$	−30.9053	−1.24825	−0.624127	+	0.781323i	$0.714545\pi$
$614$	80.7850	3.26022
$615$	2.19872	0.0886608
$616$	−19.3774	−0.780739
$617$	10.8241	0.435762	0.217881	−	0.975975i	$-0.430086\pi$
$617$	10.8241	0.435762	0.217881	+	0.975975i	$0.430086\pi$
$618$	−15.2270	−0.612519
$619$	−5.67551	−0.228118	−0.114059	−	0.993474i	$-0.536385\pi$
$619$	−5.67551	−0.228118	−0.114059	+	0.993474i	$0.536385\pi$
$620$	−4.84876	−0.194731
$621$	5.70739	0.229030
$622$	6.04827	0.242514
$623$	−41.3401	−1.65626
$624$	6.02827	0.241324
$625$	24.4412	0.977648
$626$	−32.6610	−1.30539
$627$	−0.679116	−0.0271213
$628$	−23.2353	−0.927188
$629$	5.17044	0.206159
$630$	1.61350	0.0642832
$631$	−41.4021	−1.64819	−0.824096	−	0.566451i	$-0.808316\pi$
$631$	−41.4021	−1.64819	−0.824096	+	0.566451i	$0.808316\pi$
$632$	−26.1751	−1.04119
$633$	23.4394	0.931634
$634$	61.7513	2.45246
$635$	1.38836	0.0550954
$636$	−4.44305	−0.176178
$637$	−4.02827	−0.159606
$638$	−17.9198	−0.709453
$639$	4.64177	0.183626
$640$	−2.94706	−0.116493
$641$	−33.1523	−1.30944	−0.654719	−	0.755873i	$-0.727213\pi$
$641$	−33.1523	−1.30944	−0.654719	+	0.755873i	$0.727213\pi$
$642$	−9.08482	−0.358549
$643$	−4.44852	−0.175432	−0.0877162	−	0.996146i	$-0.527957\pi$
$643$	−4.44852	−0.175432	−0.0877162	+	0.996146i	$0.527957\pi$
$644$	−81.8962	−3.22716
$645$	0.416634	0.0164050
$646$	−2.58522	−0.101714
$647$	9.55695	0.375722	0.187861	−	0.982196i	$-0.439844\pi$
$647$	9.55695	0.375722	0.187861	+	0.982196i	$0.439844\pi$
$648$	−5.83502	−0.229221
$649$	4.38650	0.172185
$650$	−12.4768	−0.489380
$651$	−19.2835	−0.755781
$652$	−70.4578	−2.75934
$653$	−17.1523	−0.671221	−0.335611	−	0.942001i	$-0.608943\pi$
$653$	−17.1523	−0.671221	−0.335611	+	0.942001i	$0.608943\pi$
$654$	20.0192	0.782813
$655$	−2.97894	−0.116397
$656$	68.5863	2.67784
$657$	−14.0192	−0.546941
$658$	13.4713	0.525167
$659$	31.4823	1.22637	0.613187	−	0.789938i	$-0.289887\pi$
$659$	31.4823	1.22637	0.613187	+	0.789938i	$0.289887\pi$
$660$	0.835021	0.0325032
$661$	19.0848	0.742314	0.371157	−	0.928570i	$-0.378961\pi$
$661$	19.0848	0.742314	0.371157	+	0.928570i	$0.378961\pi$
$662$	−20.0994	−0.781184
$663$	1.51414	0.0588042
$664$	−103.105	−4.00125
$665$	−0.435835	−0.0169010
$666$	−8.58522	−0.332671
$667$	−40.6802	−1.57514
$668$	66.6055	2.57704
$669$	−9.42024	−0.364208
$670$	6.42385	0.248175
$671$	7.02827	0.271324
$672$	11.5761	0.446560
$673$	14.1696	0.546200	0.273100	−	0.961986i	$-0.411951\pi$
$673$	14.1696	0.546200	0.273100	+	0.961986i	$0.411951\pi$
$674$	−47.7941	−1.84096
$675$	4.96265	0.191013
$676$	4.32088	0.166188
$677$	−3.01454	−0.115858	−0.0579290	−	0.998321i	$-0.518450\pi$
$677$	−3.01454	−0.115858	−0.0579290	+	0.998321i	$0.518450\pi$
$678$	−6.00000	−0.230429
$679$	−24.6236	−0.944968
$680$	1.70739	0.0654754
$681$	−0.480399	−0.0184089
$682$	−14.5990	−0.559023
$683$	50.4358	1.92987	0.964937	−	0.262482i	$-0.0845411\pi$
$683$	50.4358	1.92987	0.964937	+	0.262482i	$0.0845411\pi$
$684$	2.93438	0.112199
$685$	−1.33181	−0.0508859
$686$	24.8114	0.947304
$687$	3.61350	0.137863
$688$	12.9964	0.495483
$689$	−1.02827	−0.0391741
$690$	2.77301	0.105567
$691$	−29.7777	−1.13280	−0.566398	−	0.824132i	$-0.691664\pi$
$691$	−29.7777	−1.13280	−0.566398	+	0.824132i	$0.691664\pi$
$692$	10.7411	0.408316
$693$	3.32088	0.126150
$694$	−35.4823	−1.34689
$695$	−1.68924	−0.0640767
$696$	41.5899	1.57646
$697$	17.2270	0.652519
$698$	−14.5852	−0.552059
$699$	24.5990	0.930418
$700$	−71.2099	−2.69148
$701$	8.46772	0.319821	0.159911	−	0.987131i	$-0.448879\pi$
$701$	8.46772	0.319821	0.159911	+	0.987131i	$0.448879\pi$
$702$	−2.51414	−0.0948900
$703$	2.31903	0.0874638
$704$	−3.29261	−0.124095
$705$	−0.311812	−0.0117435
$706$	14.4568	0.544088
$707$	−47.1979	−1.77506
$708$	−18.9536	−0.712319
$709$	−34.3684	−1.29073	−0.645365	−	0.763874i	$-0.723295\pi$
$709$	−34.3684	−1.29073	−0.645365	+	0.763874i	$0.723295\pi$
$710$	2.25526	0.0846386
$711$	4.48586	0.168233
$712$	72.6374	2.72220
$713$	−33.1414	−1.24115
$714$	12.6418	0.473106
$715$	0.193252	0.00722723
$716$	98.4825	3.68046
$717$	28.3310	1.05804
$718$	76.5863	2.85817
$719$	−6.82956	−0.254700	−0.127350	−	0.991858i	$-0.540647\pi$
$719$	−6.82956	−0.254700	−0.127350	+	0.991858i	$0.540647\pi$
$720$	−1.16498	−0.0434162
$721$	−20.1131	−0.749051
$722$	46.6091	1.73461
$723$	20.3684	0.757507
$724$	−95.3868	−3.54502
$725$	−35.3720	−1.31368
$726$	2.51414	0.0933084
$727$	−11.8013	−0.437685	−0.218843	−	0.975760i	$-0.570228\pi$
$727$	−11.8013	−0.437685	−0.218843	+	0.975760i	$0.570228\pi$
$728$	19.3774	0.718175
$729$	1.00000	0.0370370
$730$	−6.81141	−0.252102
$731$	3.26434	0.120736
$732$	−30.3684	−1.12245
$733$	28.9235	1.06831	0.534156	−	0.845386i	$-0.320629\pi$
$733$	28.9235	1.06831	0.534156	+	0.845386i	$0.320629\pi$
$734$	−50.0675	−1.84802
$735$	0.778474	0.0287144
$736$	19.8952	0.733346
$737$	13.2215	0.487021
$738$	−28.6044	−1.05294
$739$	8.01920	0.294991	0.147496	−	0.989063i	$-0.452879\pi$
$739$	8.01920	0.294991	0.147496	+	0.989063i	$0.452879\pi$
$740$	−2.85141	−0.104820
$741$	0.679116	0.0249479
$742$	−8.58522	−0.315173
$743$	−21.1979	−0.777676	−0.388838	−	0.921306i	$-0.627123\pi$
$743$	−21.1979	−0.777676	−0.388838	+	0.921306i	$0.627123\pi$
$744$	33.8825	1.24219
$745$	−0.255264	−0.00935215
$746$	47.7941	1.74987
$747$	17.6700	0.646513
$748$	6.54241	0.239214
$749$	−12.0000	−0.438470
$750$	4.84049	0.176750
$751$	−14.7658	−0.538811	−0.269406	−	0.963027i	$-0.586827\pi$
$751$	−14.7658	−0.538811	−0.269406	+	0.963027i	$0.586827\pi$
$752$	−9.72659	−0.354692
$753$	15.7266	0.573109
$754$	17.9198	0.652602
$755$	−3.86876	−0.140799
$756$	−14.3492	−0.521874
$757$	−47.2846	−1.71859	−0.859294	−	0.511482i	$-0.829097\pi$
$757$	−47.2846	−1.71859	−0.859294	+	0.511482i	$0.829097\pi$
$758$	−90.6192	−3.29144
$759$	5.70739	0.207165
$760$	0.765792	0.0277782
$761$	41.1606	1.49207	0.746035	−	0.665907i	$-0.231955\pi$
$761$	41.1606	1.49207	0.746035	+	0.665907i	$0.231955\pi$
$762$	−18.0620	−0.654318
$763$	26.4431	0.957303
$764$	−32.8970	−1.19017
$765$	−0.292611	−0.0105794
$766$	45.8962	1.65830
$767$	−4.38650	−0.158388
$768$	31.7549	1.14585
$769$	48.9427	1.76492	0.882459	−	0.470390i	$-0.155887\pi$
$769$	48.9427	1.76492	0.882459	+	0.470390i	$0.155887\pi$
$770$	1.61350	0.0581463
$771$	3.35823	0.120944
$772$	3.17872	0.114404
$773$	−26.1076	−0.939026	−0.469513	−	0.882925i	$-0.655571\pi$
$773$	−26.1076	−0.939026	−0.469513	+	0.882925i	$0.655571\pi$
$774$	−5.42024	−0.194827
$775$	−28.8169	−1.03513
$776$	43.2654	1.55314
$777$	−11.3401	−0.406823
$778$	12.1696	0.436303
$779$	7.72659	0.276834
$780$	−0.835021	−0.0298986
$781$	4.64177	0.166096
$782$	21.7266	0.776941
$783$	−7.12763	−0.254721
$784$	24.2835	0.867269
$785$	1.03920	0.0370907
$786$	38.7549	1.38234
$787$	22.8488	0.814470	0.407235	−	0.913323i	$-0.366493\pi$
$787$	22.8488	0.814470	0.407235	+	0.913323i	$0.366493\pi$
$788$	−21.3209	−0.759525
$789$	26.4431	0.941398
$790$	2.17952	0.0775437
$791$	−7.92531	−0.281791
$792$	−5.83502	−0.207338
$793$	−7.02827	−0.249581
$794$	−78.3211	−2.77951
$795$	0.198716	0.00704775
$796$	100.850	3.57453
$797$	−10.3974	−0.368296	−0.184148	−	0.982899i	$-0.558953\pi$
$797$	−10.3974	−0.368296	−0.184148	+	0.982899i	$0.558953\pi$
$798$	5.67004	0.200717
$799$	−2.44305	−0.0864290
$800$	17.2991	0.611617
$801$	−12.4485	−0.439847
$802$	−30.7521	−1.08589
$803$	−14.0192	−0.494727
$804$	−57.1287	−2.01477
$805$	3.66283	0.129098
$806$	14.5990	0.514226
$807$	−2.97173	−0.104610
$808$	82.9300	2.91747
$809$	14.0884	0.495323	0.247661	−	0.968847i	$-0.420338\pi$
$809$	14.0884	0.495323	0.247661	+	0.968847i	$0.420338\pi$
$810$	0.485863	0.0170715
$811$	43.4340	1.52517	0.762587	−	0.646886i	$-0.223929\pi$
$811$	43.4340	1.52517	0.762587	+	0.646886i	$0.223929\pi$
$812$	102.276	3.58917
$813$	20.2926	0.711693
$814$	−8.58522	−0.300912
$815$	3.15124	0.110383
$816$	−9.12763	−0.319531
$817$	1.46411	0.0512227
$818$	21.9627	0.767906
$819$	−3.32088	−0.116041
$820$	−9.50040	−0.331768
$821$	−17.6327	−0.615385	−0.307693	−	0.951486i	$-0.599557\pi$
$821$	−17.6327	−0.615385	−0.307693	+	0.951486i	$0.599557\pi$
$822$	17.3263	0.604326
$823$	−19.6882	−0.686287	−0.343144	−	0.939283i	$-0.611492\pi$
$823$	−19.6882	−0.686287	−0.343144	+	0.939283i	$0.611492\pi$
$824$	35.3401	1.23113
$825$	4.96265	0.172777
$826$	−36.6236	−1.27430
$827$	11.3318	0.394046	0.197023	−	0.980399i	$-0.436873\pi$
$827$	11.3318	0.394046	0.197023	+	0.980399i	$0.436873\pi$
$828$	−24.6610	−0.857028
$829$	−9.22699	−0.320467	−0.160233	−	0.987079i	$-0.551225\pi$
$829$	−9.22699	−0.320467	−0.160233	+	0.987079i	$0.551225\pi$
$830$	8.58522	0.297997
$831$	−19.9819	−0.693163
$832$	3.29261	0.114151
$833$	6.09936	0.211330
$834$	21.9764	0.760980
$835$	−2.97894	−0.103091
$836$	2.93438	0.101488
$837$	−5.80675	−0.200711
$838$	40.6044	1.40266
$839$	28.3009	0.977055	0.488528	−	0.872548i	$-0.337534\pi$
$839$	28.3009	0.977055	0.488528	+	0.872548i	$0.337534\pi$
$840$	−3.74474	−0.129206
$841$	21.8031	0.751832
$842$	25.6135	0.882699
$843$	25.7458	0.886732
$844$	−101.279	−3.48617
$845$	−0.193252	−0.00664809
$846$	4.05655	0.139467
$847$	3.32088	0.114107
$848$	6.19872	0.212865
$849$	−21.9006	−0.751628
$850$	18.8916	0.647975
$851$	−19.4895	−0.668090
$852$	−20.0565	−0.687126
$853$	−13.8122	−0.472921	−0.236461	−	0.971641i	$-0.575987\pi$
$853$	−13.8122	−0.472921	−0.236461	+	0.971641i	$0.575987\pi$
$854$	−58.6802	−2.00799
$855$	−0.131241	−0.00448834
$856$	21.0848	0.720664
$857$	−11.3263	−0.386901	−0.193450	−	0.981110i	$-0.561968\pi$
$857$	−11.3263	−0.386901	−0.193450	+	0.981110i	$0.561968\pi$
$858$	−2.51414	−0.0858312
$859$	35.5388	1.21257	0.606284	−	0.795248i	$-0.292659\pi$
$859$	35.5388	1.21257	0.606284	+	0.795248i	$0.292659\pi$
$860$	−1.80023	−0.0613873
$861$	−37.7831	−1.28765
$862$	49.0957	1.67221
$863$	18.3684	0.625266	0.312633	−	0.949874i	$-0.398789\pi$
$863$	18.3684	0.625266	0.312633	+	0.949874i	$0.398789\pi$
$864$	3.48586	0.118591
$865$	−0.480399	−0.0163341
$866$	−28.6527	−0.973658
$867$	14.7074	0.499489
$868$	83.3219	2.82813
$869$	4.48586	0.152172
$870$	−3.46305	−0.117408
$871$	−13.2215	−0.447994
$872$	−46.4623	−1.57341
$873$	−7.41478	−0.250952
$874$	9.74474	0.329621
$875$	6.39372	0.216147
$876$	60.5753	2.04665
$877$	32.2553	1.08918	0.544591	−	0.838701i	$-0.316685\pi$
$877$	32.2553	1.08918	0.544591	+	0.838701i	$0.316685\pi$
$878$	−33.6464	−1.13551
$879$	−14.8031	−0.499297
$880$	−1.16498	−0.0392714
$881$	−54.6236	−1.84032	−0.920158	−	0.391547i	$-0.871940\pi$
$881$	−54.6236	−1.84032	−0.920158	+	0.391547i	$0.871940\pi$
$882$	−10.1276	−0.341015
$883$	−24.7730	−0.833678	−0.416839	−	0.908980i	$-0.636862\pi$
$883$	−24.7730	−0.833678	−0.416839	+	0.908980i	$0.636862\pi$
$884$	−6.54241	−0.220045
$885$	0.847703	0.0284952
$886$	8.11310	0.272565
$887$	−12.6527	−0.424836	−0.212418	−	0.977179i	$-0.568134\pi$
$887$	−12.6527	−0.424836	−0.212418	+	0.977179i	$0.568134\pi$
$888$	19.9253	0.668650
$889$	−23.8578	−0.800166
$890$	−6.04827	−0.202739
$891$	1.00000	0.0335013
$892$	40.7038	1.36286
$893$	−1.09575	−0.0366679
$894$	3.32088	0.111067
$895$	−4.40465	−0.147231
$896$	50.6428	1.69186
$897$	−5.70739	−0.190564
$898$	99.2044	3.31049
$899$	41.3884	1.38038
$900$	−21.4431	−0.714768
$901$	1.55695	0.0518694
$902$	−28.6044	−0.952423
$903$	−7.15951	−0.238254
$904$	13.9253	0.463149
$905$	4.26619	0.141813
$906$	50.3310	1.67214
$907$	33.4823	1.11176	0.555880	−	0.831263i	$-0.312381\pi$
$907$	33.4823	1.11176	0.555880	+	0.831263i	$0.312381\pi$
$908$	2.07575	0.0688861
$909$	−14.2125	−0.471397
$910$	−1.61350	−0.0534868
$911$	−24.8970	−0.824876	−0.412438	−	0.910986i	$-0.635323\pi$
$911$	−24.8970	−0.824876	−0.412438	+	0.910986i	$0.635323\pi$
$912$	−4.09389	−0.135562
$913$	17.6700	0.584793
$914$	−60.0093	−1.98493
$915$	1.35823	0.0449017
$916$	−15.6135	−0.515884
$917$	51.1907	1.69047
$918$	3.80675	0.125641
$919$	−41.7513	−1.37725	−0.688623	−	0.725119i	$-0.741785\pi$
$919$	−41.7513	−1.37725	−0.688623	+	0.725119i	$0.741785\pi$
$920$	−6.43584	−0.212183
$921$	32.1323	1.05880
$922$	−18.5479	−0.610842
$923$	−4.64177	−0.152786
$924$	−14.3492	−0.472053
$925$	−16.9464	−0.557193
$926$	−55.4394	−1.82185
$927$	−6.05655	−0.198923
$928$	−24.8459	−0.815608
$929$	−1.40931	−0.0462381	−0.0231191	−	0.999733i	$-0.507360\pi$
$929$	−1.40931	−0.0462381	−0.0231191	+	0.999733i	$0.507360\pi$
$930$	−2.82128	−0.0925136
$931$	2.73566	0.0896577
$932$	−106.289	−3.48162
$933$	2.40571	0.0787593
$934$	15.6327	0.511517
$935$	−0.292611	−0.00956939
$936$	5.83502	0.190724
$937$	−37.5844	−1.22783	−0.613915	−	0.789372i	$-0.710406\pi$
$937$	−37.5844	−1.22783	−0.613915	+	0.789372i	$0.710406\pi$
$938$	−110.389	−3.60432
$939$	−12.9909	−0.423943
$940$	1.34730	0.0439442
$941$	−15.3027	−0.498855	−0.249428	−	0.968393i	$-0.580242\pi$
$941$	−15.3027	−0.498855	−0.249428	+	0.968393i	$0.580242\pi$
$942$	−13.5196	−0.440492
$943$	−64.9354	−2.11459
$944$	26.4431	0.860648
$945$	0.641769	0.0208767
$946$	−5.42024	−0.176227
$947$	−13.6882	−0.444806	−0.222403	−	0.974955i	$-0.571390\pi$
$947$	−13.6882	−0.444806	−0.222403	+	0.974955i	$0.571390\pi$
$948$	−19.3829	−0.629527
$949$	14.0192	0.455083
$950$	8.47318	0.274906
$951$	24.5616	0.796465
$952$	−29.3401	−0.950918
$953$	26.9398	0.872667	0.436334	−	0.899785i	$-0.356277\pi$
$953$	26.9398	0.872667	0.436334	+	0.899785i	$0.356277\pi$
$954$	−2.58522	−0.0836996
$955$	1.47133	0.0476110
$956$	−122.415	−3.95919
$957$	−7.12763	−0.230404
$958$	−69.6602	−2.25062
$959$	22.8861	0.739031
$960$	−0.636305	−0.0205367
$961$	2.71832	0.0876877
$962$	8.58522	0.276799
$963$	−3.61350	−0.116443
$964$	−88.0093	−2.83459
$965$	−0.142169	−0.00457657
$966$	−47.6519	−1.53317
$967$	−17.5015	−0.562809	−0.281404	−	0.959589i	$-0.590800\pi$
$967$	−17.5015	−0.562809	−0.281404	+	0.959589i	$0.590800\pi$
$968$	−5.83502	−0.187545
$969$	−1.02827	−0.0330329
$970$	−3.60257	−0.115671
$971$	47.5015	1.52439	0.762197	−	0.647345i	$-0.224121\pi$
$971$	47.5015	1.52439	0.762197	+	0.647345i	$0.224121\pi$
$972$	−4.32088	−0.138592
$973$	29.0283	0.930604
$974$	−41.9956	−1.34563
$975$	−4.96265	−0.158932
$976$	42.3684	1.35618
$977$	21.9945	0.703668	0.351834	−	0.936062i	$-0.385558\pi$
$977$	21.9945	0.703668	0.351834	+	0.936062i	$0.385558\pi$
$978$	−40.9964	−1.31092
$979$	−12.4485	−0.397856
$980$	−3.36369	−0.107449
$981$	7.96265	0.254228
$982$	108.633	3.46662
$983$	−46.6418	−1.48764	−0.743821	−	0.668379i	$-0.766988\pi$
$983$	−46.6418	−1.48764	−0.743821	+	0.668379i	$0.766988\pi$
$984$	66.3876	2.11636
$985$	0.953581	0.0303836
$986$	−27.1331	−0.864094
$987$	5.35823	0.170554
$988$	−2.93438	−0.0933551
$989$	−12.3046	−0.391263
$990$	0.485863	0.0154417
$991$	−8.49960	−0.269999	−0.134999	−	0.990846i	$-0.543103\pi$
$991$	−8.49960	−0.269999	−0.134999	+	0.990846i	$0.543103\pi$
$992$	−20.2415	−0.642669
$993$	−7.99454	−0.253699
$994$	−38.7549	−1.22923
$995$	−4.51053	−0.142993
$996$	−76.3502	−2.41925
$997$	−32.8405	−1.04007	−0.520034	−	0.854145i	$-0.674081\pi$
$997$	−32.8405	−1.04007	−0.520034	+	0.854145i	$0.674081\pi$
$998$	6.51334	0.206176
$999$	−3.41478	−0.108039

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.a.e.1.1	✓	3
3.2	odd	2		1287.2.a.j.1.3		3
4.3	odd	2		6864.2.a.bu.1.2		3
11.10	odd	2		4719.2.a.u.1.3		3
13.12	even	2		5577.2.a.l.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.a.e.1.1	✓	3	1.1	even	1	trivial
1287.2.a.j.1.3		3	3.2	odd	2
4719.2.a.u.1.3		3	11.10	odd	2
5577.2.a.l.1.3		3	13.12	even	2
6864.2.a.bu.1.2		3	4.3	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:	\( N \)	\(=\)	\( 429 = 3 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	429.a (trivial)

\(f(q)\)	\(=\)	\(q-2.51414 q^{2} -1.00000 q^{3} +4.32088 q^{4} -0.193252 q^{5} +2.51414 q^{6} +3.32088 q^{7} -5.83502 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.51414 q^{2} -1.00000 q^{3} +4.32088 q^{4} -0.193252 q^{5} +2.51414 q^{6} +3.32088 q^{7} -5.83502 q^{8} +1.00000 q^{9} +0.485863 q^{10} +1.00000 q^{11} -4.32088 q^{12} -1.00000 q^{13} -8.34916 q^{14} +0.193252 q^{15} +6.02827 q^{16} +1.51414 q^{17} -2.51414 q^{18} +0.679116 q^{19} -0.835021 q^{20} -3.32088 q^{21} -2.51414 q^{22} -5.70739 q^{23} +5.83502 q^{24} -4.96265 q^{25} +2.51414 q^{26} -1.00000 q^{27} +14.3492 q^{28} +7.12763 q^{29} -0.485863 q^{30} +5.80675 q^{31} -3.48586 q^{32} -1.00000 q^{33} -3.80675 q^{34} -0.641769 q^{35} +4.32088 q^{36} +3.41478 q^{37} -1.70739 q^{38} +1.00000 q^{39} +1.12763 q^{40} +11.3774 q^{41} +8.34916 q^{42} +2.15591 q^{43} +4.32088 q^{44} -0.193252 q^{45} +14.3492 q^{46} -1.61350 q^{47} -6.02827 q^{48} +4.02827 q^{49} +12.4768 q^{50} -1.51414 q^{51} -4.32088 q^{52} +1.02827 q^{53} +2.51414 q^{54} -0.193252 q^{55} -19.3774 q^{56} -0.679116 q^{57} -17.9198 q^{58} +4.38650 q^{59} +0.835021 q^{60} +7.02827 q^{61} -14.5990 q^{62} +3.32088 q^{63} -3.29261 q^{64} +0.193252 q^{65} +2.51414 q^{66} +13.2215 q^{67} +6.54241 q^{68} +5.70739 q^{69} +1.61350 q^{70} +4.64177 q^{71} -5.83502 q^{72} -14.0192 q^{73} -8.58522 q^{74} +4.96265 q^{75} +2.93438 q^{76} +3.32088 q^{77} -2.51414 q^{78} +4.48586 q^{79} -1.16498 q^{80} +1.00000 q^{81} -28.6044 q^{82} +17.6700 q^{83} -14.3492 q^{84} -0.292611 q^{85} -5.42024 q^{86} -7.12763 q^{87} -5.83502 q^{88} -12.4485 q^{89} +0.485863 q^{90} -3.32088 q^{91} -24.6610 q^{92} -5.80675 q^{93} +4.05655 q^{94} -0.131241 q^{95} +3.48586 q^{96} -7.41478 q^{97} -10.1276 q^{98} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - q^{2} - 3 q^{3} + 5 q^{4} - 2 q^{5} + q^{6} + 2 q^{7} - 3 q^{8} + 3 q^{9}+O(q^{10}) \) 3 * q - q^2 - 3 * q^3 + 5 * q^4 - 2 * q^5 + q^6 + 2 * q^7 - 3 * q^8 + 3 * q^9	\( 3 q - q^{2} - 3 q^{3} + 5 q^{4} - 2 q^{5} + q^{6} + 2 q^{7} - 3 q^{8} + 3 q^{9} + 8 q^{10} + 3 q^{11} - 5 q^{12} - 3 q^{13} - 4 q^{14} + 2 q^{15} + 5 q^{16} - 2 q^{17} - q^{18} + 10 q^{19} + 12 q^{20} - 2 q^{21} - q^{22} - 12 q^{23} + 3 q^{24} + 9 q^{25} + q^{26} - 3 q^{27} + 22 q^{28} + 12 q^{29} - 8 q^{30} + 16 q^{31} - 17 q^{32} - 3 q^{33} - 10 q^{34} + 14 q^{35} + 5 q^{36} + 3 q^{39} - 6 q^{40} + 4 q^{42} - 16 q^{43} + 5 q^{44} - 2 q^{45} + 22 q^{46} - 2 q^{47} - 5 q^{48} - q^{49} + 7 q^{50} + 2 q^{51} - 5 q^{52} - 10 q^{53} + q^{54} - 2 q^{55} - 24 q^{56} - 10 q^{57} + 16 q^{59} - 12 q^{60} + 8 q^{61} + 2 q^{62} + 2 q^{63} - 15 q^{64} + 2 q^{65} + q^{66} + 28 q^{67} + 12 q^{69} + 2 q^{70} - 2 q^{71} - 3 q^{72} + 8 q^{73} - 36 q^{74} - 9 q^{75} - 2 q^{76} + 2 q^{77} - q^{78} + 20 q^{79} - 18 q^{80} + 3 q^{81} - 46 q^{82} + 24 q^{83} - 22 q^{84} - 6 q^{85} - 12 q^{86} - 12 q^{87} - 3 q^{88} - 20 q^{89} + 8 q^{90} - 2 q^{91} - 8 q^{92} - 16 q^{93} - 14 q^{94} - 22 q^{95} + 17 q^{96} - 12 q^{97} - 21 q^{98} + 3 q^{99}+O(q^{100}) \) 3 * q - q^2 - 3 * q^3 + 5 * q^4 - 2 * q^5 + q^6 + 2 * q^7 - 3 * q^8 + 3 * q^9 + 8 * q^10 + 3 * q^11 - 5 * q^12 - 3 * q^13 - 4 * q^14 + 2 * q^15 + 5 * q^16 - 2 * q^17 - q^18 + 10 * q^19 + 12 * q^20 - 2 * q^21 - q^22 - 12 * q^23 + 3 * q^24 + 9 * q^25 + q^26 - 3 * q^27 + 22 * q^28 + 12 * q^29 - 8 * q^30 + 16 * q^31 - 17 * q^32 - 3 * q^33 - 10 * q^34 + 14 * q^35 + 5 * q^36 + 3 * q^39 - 6 * q^40 + 4 * q^42 - 16 * q^43 + 5 * q^44 - 2 * q^45 + 22 * q^46 - 2 * q^47 - 5 * q^48 - q^49 + 7 * q^50 + 2 * q^51 - 5 * q^52 - 10 * q^53 + q^54 - 2 * q^55 - 24 * q^56 - 10 * q^57 + 16 * q^59 - 12 * q^60 + 8 * q^61 + 2 * q^62 + 2 * q^63 - 15 * q^64 + 2 * q^65 + q^66 + 28 * q^67 + 12 * q^69 + 2 * q^70 - 2 * q^71 - 3 * q^72 + 8 * q^73 - 36 * q^74 - 9 * q^75 - 2 * q^76 + 2 * q^77 - q^78 + 20 * q^79 - 18 * q^80 + 3 * q^81 - 46 * q^82 + 24 * q^83 - 22 * q^84 - 6 * q^85 - 12 * q^86 - 12 * q^87 - 3 * q^88 - 20 * q^89 + 8 * q^90 - 2 * q^91 - 8 * q^92 - 16 * q^93 - 14 * q^94 - 22 * q^95 + 17 * q^96 - 12 * q^97 - 21 * q^98 + 3 * q^99

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