LMFDB - Embedded newform 8029.2.a.h.1.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8029,2,Mod(1,8029)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8029, 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("8029.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8029 = 7 \cdot 31 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8029.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:	$64.1118877829$
Analytic rank:	$0$
Dimension:	$71$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.19
Character	$\chi$	$=$	8029.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.49331 q^{2} -1.98225 q^{3} +0.229971 q^{4} +2.93836 q^{5} +2.96012 q^{6} -1.00000 q^{7} +2.64320 q^{8} +0.929333 q^{9} +O(q^{10})$	\(q-1.49331 q^{2} -1.98225 q^{3} +0.229971 q^{4} +2.93836 q^{5} +2.96012 q^{6} -1.00000 q^{7} +2.64320 q^{8} +0.929333 q^{9} -4.38788 q^{10} +1.21459 q^{11} -0.455861 q^{12} +3.15498 q^{13} +1.49331 q^{14} -5.82459 q^{15} -4.40706 q^{16} +5.27218 q^{17} -1.38778 q^{18} +3.23845 q^{19} +0.675738 q^{20} +1.98225 q^{21} -1.81376 q^{22} +2.67978 q^{23} -5.23949 q^{24} +3.63398 q^{25} -4.71135 q^{26} +4.10459 q^{27} -0.229971 q^{28} +0.921701 q^{29} +8.69790 q^{30} -1.00000 q^{31} +1.29469 q^{32} -2.40763 q^{33} -7.87299 q^{34} -2.93836 q^{35} +0.213719 q^{36} +1.00000 q^{37} -4.83600 q^{38} -6.25397 q^{39} +7.76668 q^{40} +2.07419 q^{41} -2.96012 q^{42} +10.5561 q^{43} +0.279321 q^{44} +2.73072 q^{45} -4.00175 q^{46} +13.3622 q^{47} +8.73590 q^{48} +1.00000 q^{49} -5.42666 q^{50} -10.4508 q^{51} +0.725553 q^{52} -6.06466 q^{53} -6.12942 q^{54} +3.56892 q^{55} -2.64320 q^{56} -6.41943 q^{57} -1.37638 q^{58} +3.90157 q^{59} -1.33948 q^{60} -0.901331 q^{61} +1.49331 q^{62} -0.929333 q^{63} +6.88073 q^{64} +9.27047 q^{65} +3.59534 q^{66} +1.92755 q^{67} +1.21245 q^{68} -5.31201 q^{69} +4.38788 q^{70} +11.8547 q^{71} +2.45641 q^{72} +9.91336 q^{73} -1.49331 q^{74} -7.20348 q^{75} +0.744748 q^{76} -1.21459 q^{77} +9.33910 q^{78} -12.8765 q^{79} -12.9495 q^{80} -10.9243 q^{81} -3.09741 q^{82} +5.11814 q^{83} +0.455861 q^{84} +15.4916 q^{85} -15.7636 q^{86} -1.82705 q^{87} +3.21041 q^{88} -12.2592 q^{89} -4.07780 q^{90} -3.15498 q^{91} +0.616272 q^{92} +1.98225 q^{93} -19.9539 q^{94} +9.51574 q^{95} -2.56641 q^{96} +17.2359 q^{97} -1.49331 q^{98} +1.12876 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 71 q + 6 q^{2} + 8 q^{3} + 78 q^{4} + 5 q^{6} - 71 q^{7} + 18 q^{8} + 87 q^{9}+O(q^{10}) $ 71 * q + 6 * q^2 + 8 * q^3 + 78 * q^4 + 5 * q^6 - 71 * q^7 + 18 * q^8 + 87 * q^9	\( 71 q + 6 q^{2} + 8 q^{3} + 78 q^{4} + 5 q^{6} - 71 q^{7} + 18 q^{8} + 87 q^{9} + 4 q^{10} + 57 q^{11} + 21 q^{12} - 20 q^{13} - 6 q^{14} + 22 q^{15} + 88 q^{16} - 19 q^{17} + q^{18} + 23 q^{19} + 25 q^{20} - 8 q^{21} + 18 q^{22} + 34 q^{23} + 15 q^{24} + 81 q^{25} - 13 q^{26} + 20 q^{27} - 78 q^{28} + 16 q^{29} + 6 q^{30} - 71 q^{31} + 47 q^{32} - 16 q^{33} + 32 q^{34} + 125 q^{36} + 71 q^{37} + 13 q^{38} + 30 q^{39} + 31 q^{40} + 17 q^{41} - 5 q^{42} + 38 q^{43} + 80 q^{44} - q^{45} + 26 q^{46} + 32 q^{47} + 61 q^{48} + 71 q^{49} + 47 q^{50} + 73 q^{51} - 23 q^{52} + 31 q^{53} + 47 q^{54} + 11 q^{55} - 18 q^{56} + 17 q^{57} - 2 q^{58} + 97 q^{59} + 103 q^{60} - q^{61} - 6 q^{62} - 87 q^{63} + 100 q^{64} + 46 q^{65} + 43 q^{66} + 75 q^{67} - 43 q^{68} + 10 q^{69} - 4 q^{70} + 131 q^{71} - 11 q^{72} - 15 q^{73} + 6 q^{74} + 76 q^{75} + 41 q^{76} - 57 q^{77} + 89 q^{78} + 8 q^{79} + 10 q^{80} + 171 q^{81} + 14 q^{82} + 18 q^{83} - 21 q^{84} + 47 q^{85} + 90 q^{86} - 59 q^{87} + 13 q^{88} + 18 q^{89} + 69 q^{90} + 20 q^{91} + 110 q^{92} - 8 q^{93} + 39 q^{94} + 72 q^{95} + 100 q^{96} + 23 q^{97} + 6 q^{98} + 168 q^{99}+O(q^{100}) \) 71 * q + 6 * q^2 + 8 * q^3 + 78 * q^4 + 5 * q^6 - 71 * q^7 + 18 * q^8 + 87 * q^9 + 4 * q^10 + 57 * q^11 + 21 * q^12 - 20 * q^13 - 6 * q^14 + 22 * q^15 + 88 * q^16 - 19 * q^17 + q^18 + 23 * q^19 + 25 * q^20 - 8 * q^21 + 18 * q^22 + 34 * q^23 + 15 * q^24 + 81 * q^25 - 13 * q^26 + 20 * q^27 - 78 * q^28 + 16 * q^29 + 6 * q^30 - 71 * q^31 + 47 * q^32 - 16 * q^33 + 32 * q^34 + 125 * q^36 + 71 * q^37 + 13 * q^38 + 30 * q^39 + 31 * q^40 + 17 * q^41 - 5 * q^42 + 38 * q^43 + 80 * q^44 - q^45 + 26 * q^46 + 32 * q^47 + 61 * q^48 + 71 * q^49 + 47 * q^50 + 73 * q^51 - 23 * q^52 + 31 * q^53 + 47 * q^54 + 11 * q^55 - 18 * q^56 + 17 * q^57 - 2 * q^58 + 97 * q^59 + 103 * q^60 - q^61 - 6 * q^62 - 87 * q^63 + 100 * q^64 + 46 * q^65 + 43 * q^66 + 75 * q^67 - 43 * q^68 + 10 * q^69 - 4 * q^70 + 131 * q^71 - 11 * q^72 - 15 * q^73 + 6 * q^74 + 76 * q^75 + 41 * q^76 - 57 * q^77 + 89 * q^78 + 8 * q^79 + 10 * q^80 + 171 * q^81 + 14 * q^82 + 18 * q^83 - 21 * q^84 + 47 * q^85 + 90 * q^86 - 59 * q^87 + 13 * q^88 + 18 * q^89 + 69 * q^90 + 20 * q^91 + 110 * q^92 - 8 * q^93 + 39 * q^94 + 72 * q^95 + 100 * q^96 + 23 * q^97 + 6 * q^98 + 168 * 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 $

$2$	−1.49331	−1.05593	−0.527964	−	0.849267i	$-0.677045\pi$
$2$	−1.49331	−1.05593	−0.527964	+	0.849267i	$0.677045\pi$
$3$	−1.98225	−1.14446	−0.572228	−	0.820095i	$-0.693921\pi$
$3$	−1.98225	−1.14446	−0.572228	+	0.820095i	$0.693921\pi$
$4$	0.229971	0.114985
$5$	2.93836	1.31408	0.657038	−	0.753857i	$-0.271809\pi$
$5$	2.93836	1.31408	0.657038	+	0.753857i	$0.271809\pi$
$6$	2.96012	1.20846
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	2.64320	0.934512
$9$	0.929333	0.309778
$10$	−4.38788	−1.38757
$11$	1.21459	0.366214	0.183107	−	0.983093i	$-0.441385\pi$
$11$	1.21459	0.366214	0.183107	+	0.983093i	$0.441385\pi$
$12$	−0.455861	−0.131596
$13$	3.15498	0.875033	0.437517	−	0.899210i	$-0.355858\pi$
$13$	3.15498	0.875033	0.437517	+	0.899210i	$0.355858\pi$
$14$	1.49331	0.399104
$15$	−5.82459	−1.50390
$16$	−4.40706	−1.10176
$17$	5.27218	1.27869	0.639345	−	0.768920i	$-0.279205\pi$
$17$	5.27218	1.27869	0.639345	+	0.768920i	$0.279205\pi$
$18$	−1.38778	−0.327103
$19$	3.23845	0.742951	0.371475	−	0.928443i	$-0.378852\pi$
$19$	3.23845	0.742951	0.371475	+	0.928443i	$0.378852\pi$
$20$	0.675738	0.151100
$21$	1.98225	0.432563
$22$	−1.81376	−0.386695
$23$	2.67978	0.558774	0.279387	−	0.960179i	$-0.409869\pi$
$23$	2.67978	0.558774	0.279387	+	0.960179i	$0.409869\pi$
$24$	−5.23949	−1.06951
$25$	3.63398	0.726797
$26$	−4.71135	−0.923973
$27$	4.10459	0.789929
$28$	−0.229971	−0.0434604
$29$	0.921701	0.171156	0.0855778	−	0.996331i	$-0.472726\pi$
$29$	0.921701	0.171156	0.0855778	+	0.996331i	$0.472726\pi$
$30$	8.69790	1.58801
$31$	−1.00000	−0.179605
$31$	−1.00000	−0.179605
$32$	1.29469	0.228872
$33$	−2.40763	−0.419115
$34$	−7.87299	−1.35021
$35$	−2.93836	−0.496674
$36$	0.213719	0.0356199
$37$	1.00000	0.164399
$37$	1.00000	0.164399
$38$	−4.83600	−0.784503
$39$	−6.25397	−1.00144
$40$	7.76668	1.22802
$41$	2.07419	0.323934	0.161967	−	0.986796i	$-0.448216\pi$
$41$	2.07419	0.323934	0.161967	+	0.986796i	$0.448216\pi$
$42$	−2.96012	−0.456756
$43$	10.5561	1.60980	0.804899	−	0.593412i	$-0.202220\pi$
$43$	10.5561	1.60980	0.804899	+	0.593412i	$0.202220\pi$
$44$	0.279321	0.0421092
$45$	2.73072	0.407071
$46$	−4.00175	−0.590025
$47$	13.3622	1.94908	0.974538	−	0.224222i	$-0.0719842\pi$
$47$	13.3622	1.94908	0.974538	+	0.224222i	$0.0719842\pi$
$48$	8.73590	1.26092
$49$	1.00000	0.142857
$50$	−5.42666	−0.767446
$51$	−10.4508	−1.46340
$52$	0.725553	0.100616
$53$	−6.06466	−0.833045	−0.416523	−	0.909125i	$-0.636751\pi$
$53$	−6.06466	−0.833045	−0.416523	+	0.909125i	$0.636751\pi$
$54$	−6.12942	−0.834108
$55$	3.56892	0.481233
$56$	−2.64320	−0.353212
$57$	−6.41943	−0.850274
$58$	−1.37638	−0.180728
$59$	3.90157	0.507941	0.253971	−	0.967212i	$-0.418263\pi$
$59$	3.90157	0.507941	0.253971	+	0.967212i	$0.418263\pi$
$60$	−1.33948	−0.172927
$61$	−0.901331	−0.115404	−0.0577018	−	0.998334i	$-0.518377\pi$
$61$	−0.901331	−0.115404	−0.0577018	+	0.998334i	$0.518377\pi$
$62$	1.49331	0.189650
$63$	−0.929333	−0.117085
$64$	6.88073	0.860092
$65$	9.27047	1.14986
$66$	3.59534	0.442556
$67$	1.92755	0.235487	0.117744	−	0.993044i	$-0.462434\pi$
$67$	1.92755	0.235487	0.117744	+	0.993044i	$0.462434\pi$
$68$	1.21245	0.147031
$69$	−5.31201	−0.639491
$70$	4.38788	0.524453
$71$	11.8547	1.40690	0.703448	−	0.710746i	$-0.251643\pi$
$71$	11.8547	1.40690	0.703448	+	0.710746i	$0.251643\pi$
$72$	2.45641	0.289491
$73$	9.91336	1.16027	0.580135	−	0.814520i	$-0.303000\pi$
$73$	9.91336	1.16027	0.580135	+	0.814520i	$0.303000\pi$
$74$	−1.49331	−0.173594
$75$	−7.20348	−0.831786
$76$	0.744748	0.0854285
$77$	−1.21459	−0.138416
$78$	9.33910	1.05745
$79$	−12.8765	−1.44872	−0.724358	−	0.689424i	$-0.757864\pi$
$79$	−12.8765	−1.44872	−0.724358	+	0.689424i	$0.757864\pi$
$80$	−12.9495	−1.44780
$81$	−10.9243	−1.21382
$82$	−3.09741	−0.342051
$83$	5.11814	0.561789	0.280895	−	0.959739i	$-0.409369\pi$
$83$	5.11814	0.561789	0.280895	+	0.959739i	$0.409369\pi$
$84$	0.455861	0.0497385
$85$	15.4916	1.68030
$86$	−15.7636	−1.69983
$87$	−1.82705	−0.195880
$88$	3.21041	0.342231
$89$	−12.2592	−1.29947	−0.649734	−	0.760161i	$-0.725120\pi$
$89$	−12.2592	−1.29947	−0.649734	+	0.760161i	$0.725120\pi$
$90$	−4.07780	−0.429838
$91$	−3.15498	−0.330731
$92$	0.616272	0.0642508
$93$	1.98225	0.205550
$94$	−19.9539	−2.05809
$95$	9.51574	0.976294
$96$	−2.56641	−0.261933
$97$	17.2359	1.75004	0.875020	−	0.484086i	$-0.160848\pi$
$97$	17.2359	1.75004	0.875020	+	0.484086i	$0.160848\pi$
$98$	−1.49331	−0.150847
$99$	1.12876	0.113445
$100$	0.835710	0.0835710
$101$	−2.56225	−0.254953	−0.127477	−	0.991842i	$-0.540688\pi$
$101$	−2.56225	−0.254953	−0.127477	+	0.991842i	$0.540688\pi$
$102$	15.6063	1.54525
$103$	2.19853	0.216628	0.108314	−	0.994117i	$-0.465455\pi$
$103$	2.19853	0.216628	0.108314	+	0.994117i	$0.465455\pi$
$104$	8.33923	0.817729
$105$	5.82459	0.568421
$106$	9.05641	0.879636
$107$	6.89878	0.666930	0.333465	−	0.942762i	$-0.391782\pi$
$107$	6.89878	0.666930	0.333465	+	0.942762i	$0.391782\pi$
$108$	0.943936	0.0908303
$109$	5.04416	0.483143	0.241571	−	0.970383i	$-0.422337\pi$
$109$	5.04416	0.483143	0.241571	+	0.970383i	$0.422337\pi$
$110$	−5.32950	−0.508147
$111$	−1.98225	−0.188147
$112$	4.40706	0.416428
$113$	−7.40377	−0.696488	−0.348244	−	0.937404i	$-0.613222\pi$
$113$	−7.40377	−0.696488	−0.348244	+	0.937404i	$0.613222\pi$
$114$	9.58619	0.897829
$115$	7.87418	0.734271
$116$	0.211964	0.0196804
$117$	2.93202	0.271066
$118$	−5.82625	−0.536350
$119$	−5.27218	−0.483300
$120$	−15.3955	−1.40541
$121$	−9.52476	−0.865888
$122$	1.34596	0.121858
$123$	−4.11157	−0.370728
$124$	−0.229971	−0.0206520
$125$	−4.01385	−0.359010
$126$	1.38778	0.123633
$127$	4.84658	0.430064	0.215032	−	0.976607i	$-0.431014\pi$
$127$	4.84658	0.430064	0.215032	+	0.976607i	$0.431014\pi$
$128$	−12.8644	−1.13707
$129$	−20.9250	−1.84234
$130$	−13.8437	−1.21417
$131$	9.31159	0.813557	0.406779	−	0.913527i	$-0.366652\pi$
$131$	9.31159	0.813557	0.406779	+	0.913527i	$0.366652\pi$
$132$	−0.553685	−0.0481921
$133$	−3.23845	−0.280809
$134$	−2.87842	−0.248658
$135$	12.0608	1.03803
$136$	13.9354	1.19495
$137$	4.44664	0.379902	0.189951	−	0.981794i	$-0.439167\pi$
$137$	4.44664	0.379902	0.189951	+	0.981794i	$0.439167\pi$
$138$	7.93248	0.675257
$139$	9.93938	0.843047	0.421524	−	0.906817i	$-0.361495\pi$
$139$	9.93938	0.843047	0.421524	+	0.906817i	$0.361495\pi$
$140$	−0.675738	−0.0571103
$141$	−26.4873	−2.23063
$142$	−17.7028	−1.48558
$143$	3.83201	0.320449
$144$	−4.09562	−0.341302
$145$	2.70829	0.224912
$146$	−14.8037	−1.22516
$147$	−1.98225	−0.163494
$148$	0.229971	0.0189035
$149$	−6.93415	−0.568067	−0.284034	−	0.958814i	$-0.591673\pi$
$149$	−6.93415	−0.568067	−0.284034	+	0.958814i	$0.591673\pi$
$150$	10.7570	0.878307
$151$	19.5773	1.59318	0.796588	−	0.604522i	$-0.206636\pi$
$151$	19.5773	1.59318	0.796588	+	0.604522i	$0.206636\pi$
$152$	8.55986	0.694297
$153$	4.89961	0.396110
$154$	1.81376	0.146157
$155$	−2.93836	−0.236015
$156$	−1.43823	−0.115151
$157$	−8.61948	−0.687910	−0.343955	−	0.938986i	$-0.611767\pi$
$157$	−8.61948	−0.687910	−0.343955	+	0.938986i	$0.611767\pi$
$158$	19.2286	1.52974
$159$	12.0217	0.953383
$160$	3.80428	0.300755
$161$	−2.67978	−0.211197
$162$	16.3134	1.28170
$163$	−18.7135	−1.46575	−0.732876	−	0.680362i	$-0.761822\pi$
$163$	−18.7135	−1.46575	−0.732876	+	0.680362i	$0.761822\pi$
$164$	0.477003	0.0372477
$165$	−7.07450	−0.550749
$166$	−7.64297	−0.593209
$167$	−4.43214	−0.342969	−0.171485	−	0.985187i	$-0.554856\pi$
$167$	−4.43214	−0.342969	−0.171485	+	0.985187i	$0.554856\pi$
$168$	5.23949	0.404236
$169$	−3.04612	−0.234317
$170$	−23.1337	−1.77427
$171$	3.00959	0.230149
$172$	2.42761	0.185103
$173$	20.9617	1.59369	0.796843	−	0.604186i	$-0.206502\pi$
$173$	20.9617	1.59369	0.796843	+	0.604186i	$0.206502\pi$
$174$	2.72834	0.206835
$175$	−3.63398	−0.274703
$176$	−5.35278	−0.403481
$177$	−7.73390	−0.581316
$178$	18.3067	1.37215
$179$	−3.72776	−0.278626	−0.139313	−	0.990248i	$-0.544489\pi$
$179$	−3.72776	−0.278626	−0.139313	+	0.990248i	$0.544489\pi$
$180$	0.627985	0.0468073
$181$	7.50498	0.557841	0.278920	−	0.960314i	$-0.410023\pi$
$181$	7.50498	0.557841	0.278920	+	0.960314i	$0.410023\pi$
$182$	4.71135	0.349229
$183$	1.78667	0.132074
$184$	7.08321	0.522181
$185$	2.93836	0.216033
$186$	−2.96012	−0.217046
$187$	6.40355	0.468274
$188$	3.07291	0.224115
$189$	−4.10459	−0.298565
$190$	−14.2099	−1.03090
$191$	−4.49673	−0.325372	−0.162686	−	0.986678i	$-0.552016\pi$
$191$	−4.49673	−0.325372	−0.162686	+	0.986678i	$0.552016\pi$
$192$	−13.6394	−0.984336
$193$	−5.92872	−0.426759	−0.213379	−	0.976969i	$-0.568447\pi$
$193$	−5.92872	−0.426759	−0.213379	+	0.976969i	$0.568447\pi$
$194$	−25.7385	−1.84792
$195$	−18.3764	−1.31596
$196$	0.229971	0.0164265
$197$	−13.8865	−0.989370	−0.494685	−	0.869072i	$-0.664717\pi$
$197$	−13.8865	−0.989370	−0.494685	+	0.869072i	$0.664717\pi$
$198$	−1.68559	−0.119790
$199$	10.3919	0.736661	0.368331	−	0.929695i	$-0.379929\pi$
$199$	10.3919	0.736661	0.368331	+	0.929695i	$0.379929\pi$
$200$	9.60535	0.679201
$201$	−3.82089	−0.269505
$202$	3.82623	0.269212
$203$	−0.921701	−0.0646907
$204$	−2.40338	−0.168270
$205$	6.09473	0.425674
$206$	−3.28309	−0.228743
$207$	2.49041	0.173096
$208$	−13.9042	−0.964080
$209$	3.93340	0.272079
$210$	−8.69790	−0.600212
$211$	−2.85031	−0.196223	−0.0981117	−	0.995175i	$-0.531280\pi$
$211$	−2.85031	−0.196223	−0.0981117	+	0.995175i	$0.531280\pi$
$212$	−1.39469	−0.0957880
$213$	−23.4991	−1.61013
$214$	−10.3020	−0.704231
$215$	31.0178	2.11540
$216$	10.8493	0.738198
$217$	1.00000	0.0678844
$218$	−7.53248	−0.510164
$219$	−19.6508	−1.32788
$220$	0.820747	0.0553347
$221$	16.6336	1.11890
$222$	2.96012	0.198670
$223$	3.59781	0.240927	0.120463	−	0.992718i	$-0.461562\pi$
$223$	3.59781	0.240927	0.120463	+	0.992718i	$0.461562\pi$
$224$	−1.29469	−0.0865054
$225$	3.37718	0.225145
$226$	11.0561	0.735442
$227$	−26.5308	−1.76091	−0.880454	−	0.474131i	$-0.842762\pi$
$227$	−26.5308	−1.76091	−0.880454	+	0.474131i	$0.842762\pi$
$228$	−1.47628	−0.0977691
$229$	26.3980	1.74443	0.872214	−	0.489124i	$-0.162684\pi$
$229$	26.3980	1.74443	0.872214	+	0.489124i	$0.162684\pi$
$230$	−11.7586	−0.775338
$231$	2.40763	0.158411
$232$	2.43624	0.159947
$233$	−25.2604	−1.65487	−0.827433	−	0.561564i	$-0.810200\pi$
$233$	−25.2604	−1.65487	−0.827433	+	0.561564i	$0.810200\pi$
$234$	−4.37841	−0.286226
$235$	39.2630	2.56123
$236$	0.897247	0.0584058
$237$	25.5245	1.65799
$238$	7.87299	0.510330
$239$	−5.21801	−0.337525	−0.168762	−	0.985657i	$-0.553977\pi$
$239$	−5.21801	−0.337525	−0.168762	+	0.985657i	$0.553977\pi$
$240$	25.6693	1.65694
$241$	−12.5174	−0.806319	−0.403160	−	0.915130i	$-0.632088\pi$
$241$	−12.5174	−0.806319	−0.403160	+	0.915130i	$0.632088\pi$
$242$	14.2234	0.914316
$243$	9.34105	0.599229
$244$	−0.207280	−0.0132697
$245$	2.93836	0.187725
$246$	6.13985	0.391463
$247$	10.2172	0.650107
$248$	−2.64320	−0.167843
$249$	−10.1455	−0.642943
$250$	5.99392	0.379089
$251$	−0.236523	−0.0149292	−0.00746461	−	0.999972i	$-0.502376\pi$
$251$	−0.236523	−0.0149292	−0.00746461	+	0.999972i	$0.502376\pi$
$252$	−0.213719	−0.0134631
$253$	3.25485	0.204631
$254$	−7.23744	−0.454117
$255$	−30.7082	−1.92303
$256$	5.44912	0.340570
$257$	−12.6606	−0.789747	−0.394874	−	0.918735i	$-0.629212\pi$
$257$	−12.6606	−0.789747	−0.394874	+	0.918735i	$0.629212\pi$
$258$	31.2474	1.94538
$259$	−1.00000	−0.0621370
$260$	2.13194	0.132217
$261$	0.856567	0.0530202
$262$	−13.9051	−0.859059
$263$	−13.9575	−0.860654	−0.430327	−	0.902673i	$-0.641602\pi$
$263$	−13.9575	−0.860654	−0.430327	+	0.902673i	$0.641602\pi$
$264$	−6.36385	−0.391668
$265$	−17.8202	−1.09469
$266$	4.83600	0.296514
$267$	24.3008	1.48718
$268$	0.443279	0.0270776
$269$	−0.0215549	−0.00131423	−0.000657113	−	1.00000i	$-0.500209\pi$
$269$	−0.0215549	−0.00131423	−0.000657113		1.00000i	$0.500209\pi$
$270$	−18.0105	−1.09608
$271$	−17.3806	−1.05580	−0.527899	−	0.849307i	$-0.677020\pi$
$271$	−17.3806	−1.05580	−0.527899	+	0.849307i	$0.677020\pi$
$272$	−23.2348	−1.40882
$273$	6.25397	0.378507
$274$	−6.64020	−0.401149
$275$	4.41381	0.266163
$276$	−1.22161	−0.0735322
$277$	−28.0292	−1.68411	−0.842054	−	0.539393i	$-0.818654\pi$
$277$	−28.0292	−1.68411	−0.842054	+	0.539393i	$0.818654\pi$
$278$	−14.8426	−0.890198
$279$	−0.929333	−0.0556377
$280$	−7.76668	−0.464148
$281$	−17.4736	−1.04239	−0.521193	−	0.853439i	$-0.674513\pi$
$281$	−17.4736	−1.04239	−0.521193	+	0.853439i	$0.674513\pi$
$282$	39.5537	2.35539
$283$	−0.232178	−0.0138016	−0.00690079	−	0.999976i	$-0.502197\pi$
$283$	−0.232178	−0.0138016	−0.00690079	+	0.999976i	$0.502197\pi$
$284$	2.72624	0.161773
$285$	−18.8626	−1.11732
$286$	−5.72238	−0.338371
$287$	−2.07419	−0.122436
$288$	1.20320	0.0708993
$289$	10.7959	0.635050
$290$	−4.04432	−0.237491
$291$	−34.1659	−2.00284
$292$	2.27978	0.133414
$293$	−16.2269	−0.947983	−0.473992	−	0.880529i	$-0.657187\pi$
$293$	−16.2269	−0.947983	−0.473992	+	0.880529i	$0.657187\pi$
$294$	2.96012	0.172638
$295$	11.4642	0.667473
$296$	2.64320	0.153633
$297$	4.98541	0.289283
$298$	10.3548	0.599839
$299$	8.45466	0.488945
$300$	−1.65659	−0.0956433
$301$	−10.5561	−0.608446
$302$	−29.2349	−1.68228
$303$	5.07902	0.291782
$304$	−14.2720	−0.818556
$305$	−2.64844	−0.151649
$306$	−7.31662	−0.418264
$307$	13.7057	0.782225	0.391113	−	0.920343i	$-0.372090\pi$
$307$	13.7057	0.782225	0.391113	+	0.920343i	$0.372090\pi$
$308$	−0.279321	−0.0159158
$309$	−4.35805	−0.247921
$310$	4.38788	0.249215
$311$	−9.34147	−0.529706	−0.264853	−	0.964289i	$-0.585323\pi$
$311$	−9.34147	−0.529706	−0.264853	+	0.964289i	$0.585323\pi$
$312$	−16.5305	−0.935854
$313$	−13.3298	−0.753447	−0.376723	−	0.926326i	$-0.622949\pi$
$313$	−13.3298	−0.753447	−0.376723	+	0.926326i	$0.622949\pi$
$314$	12.8715	0.726383
$315$	−2.73072	−0.153859
$316$	−2.96121	−0.166581
$317$	−32.7203	−1.83776	−0.918878	−	0.394543i	$-0.870903\pi$
$317$	−32.7203	−1.83776	−0.918878	+	0.394543i	$0.870903\pi$
$318$	−17.9521	−1.00670
$319$	1.11949	0.0626795
$320$	20.2181	1.13023
$321$	−13.6751	−0.763272
$322$	4.00175	0.223009
$323$	17.0737	0.950004
$324$	−2.51228	−0.139571
$325$	11.4651	0.635971
$326$	27.9450	1.54773
$327$	−9.99880	−0.552935
$328$	5.48250	0.302721
$329$	−13.3622	−0.736681
$330$	10.5644	0.581552
$331$	−15.1012	−0.830037	−0.415019	−	0.909813i	$-0.636225\pi$
$331$	−15.1012	−0.830037	−0.415019	+	0.909813i	$0.636225\pi$
$332$	1.17702	0.0645976
$333$	0.929333	0.0509271
$334$	6.61856	0.362151
$335$	5.66383	0.309448
$336$	−8.73590	−0.476583
$337$	19.2353	1.04781	0.523906	−	0.851776i	$-0.324474\pi$
$337$	19.2353	1.04781	0.523906	+	0.851776i	$0.324474\pi$
$338$	4.54880	0.247422
$339$	14.6762	0.797099
$340$	3.56261	0.193210
$341$	−1.21459	−0.0657739
$342$	−4.49425	−0.243021
$343$	−1.00000	−0.0539949
$344$	27.9020	1.50438
$345$	−15.6086	−0.840341
$346$	−31.3023	−1.68282
$347$	16.0458	0.861382	0.430691	−	0.902499i	$-0.358270\pi$
$347$	16.0458	0.861382	0.430691	+	0.902499i	$0.358270\pi$
$348$	−0.420167	−0.0225233
$349$	16.0638	0.859873	0.429937	−	0.902859i	$-0.358536\pi$
$349$	16.0638	0.859873	0.429937	+	0.902859i	$0.358536\pi$
$350$	5.42666	0.290067
$351$	12.9499	0.691214
$352$	1.57253	0.0838159
$353$	−20.1680	−1.07343	−0.536717	−	0.843762i	$-0.680336\pi$
$353$	−20.1680	−1.07343	−0.536717	+	0.843762i	$0.680336\pi$
$354$	11.5491	0.613828
$355$	34.8335	1.84877
$356$	−2.81925	−0.149420
$357$	10.4508	0.553115
$358$	5.56670	0.294209
$359$	−13.1579	−0.694446	−0.347223	−	0.937783i	$-0.612875\pi$
$359$	−13.1579	−0.694446	−0.347223	+	0.937783i	$0.612875\pi$
$360$	7.21783	0.380413
$361$	−8.51246	−0.448024
$362$	−11.2072	−0.589040
$363$	18.8805	0.990969
$364$	−0.725553	−0.0380293
$365$	29.1291	1.52468
$366$	−2.66805	−0.139461
$367$	−28.4580	−1.48549	−0.742747	−	0.669572i	$-0.766478\pi$
$367$	−28.4580	−1.48549	−0.742747	+	0.669572i	$0.766478\pi$
$368$	−11.8100	−0.615637
$369$	1.92761	0.100348
$370$	−4.38788	−0.228115
$371$	6.06466	0.314862
$372$	0.455861	0.0236353
$373$	3.88636	0.201228	0.100614	−	0.994926i	$-0.467919\pi$
$373$	3.88636	0.201228	0.100614	+	0.994926i	$0.467919\pi$
$374$	−9.56248	−0.494464
$375$	7.95647	0.410871
$376$	35.3189	1.82144
$377$	2.90795	0.149767
$378$	6.12942	0.315263
$379$	16.5572	0.850485	0.425243	−	0.905079i	$-0.360189\pi$
$379$	16.5572	0.850485	0.425243	+	0.905079i	$0.360189\pi$
$380$	2.18834	0.112260
$381$	−9.60716	−0.492190
$382$	6.71501	0.343570
$383$	20.3262	1.03862	0.519311	−	0.854585i	$-0.326189\pi$
$383$	20.3262	1.03862	0.519311	+	0.854585i	$0.326189\pi$
$384$	25.5006	1.30132
$385$	−3.56892	−0.181889
$386$	8.85341	0.450627
$387$	9.81017	0.498679
$388$	3.96375	0.201229
$389$	−24.1969	−1.22683	−0.613415	−	0.789761i	$-0.710205\pi$
$389$	−24.1969	−1.22683	−0.613415	+	0.789761i	$0.710205\pi$
$390$	27.4417	1.38956
$391$	14.1283	0.714499
$392$	2.64320	0.133502
$393$	−18.4579	−0.931080
$394$	20.7368	1.04470
$395$	−37.8358	−1.90372
$396$	0.259582	0.0130445
$397$	−19.0219	−0.954683	−0.477342	−	0.878718i	$-0.658400\pi$
$397$	−19.0219	−0.954683	−0.477342	+	0.878718i	$0.658400\pi$
$398$	−15.5183	−0.777862
$399$	6.41943	0.321373
$400$	−16.0152	−0.800758
$401$	21.0329	1.05033	0.525167	−	0.850999i	$-0.324003\pi$
$401$	21.0329	1.05033	0.525167	+	0.850999i	$0.324003\pi$
$402$	5.70576	0.284578
$403$	−3.15498	−0.157161
$404$	−0.589242	−0.0293159
$405$	−32.0997	−1.59505
$406$	1.37638	0.0683088
$407$	1.21459	0.0602051
$408$	−27.6235	−1.36757
$409$	6.70408	0.331495	0.165748	−	0.986168i	$-0.446996\pi$
$409$	6.70408	0.331495	0.165748	+	0.986168i	$0.446996\pi$
$410$	−9.10131	−0.449482
$411$	−8.81437	−0.434781
$412$	0.505598	0.0249090
$413$	−3.90157	−0.191984
$414$	−3.71895	−0.182777
$415$	15.0390	0.738234
$416$	4.08473	0.200270
$417$	−19.7024	−0.964830
$418$	−5.87377	−0.287296
$419$	−16.0530	−0.784242	−0.392121	−	0.919914i	$-0.628259\pi$
$419$	−16.0530	−0.784242	−0.392121	+	0.919914i	$0.628259\pi$
$420$	1.33948	0.0653602
$421$	−14.1071	−0.687538	−0.343769	−	0.939054i	$-0.611704\pi$
$421$	−14.1071	−0.687538	−0.343769	+	0.939054i	$0.611704\pi$
$422$	4.25639	0.207198
$423$	12.4179	0.603780
$424$	−16.0301	−0.778491
$425$	19.1590	0.929348
$426$	35.0914	1.70018
$427$	0.901331	0.0436185
$428$	1.58652	0.0766872
$429$	−7.59603	−0.366740
$430$	−46.3192	−2.23371
$431$	5.18637	0.249819	0.124909	−	0.992168i	$-0.460136\pi$
$431$	5.18637	0.249819	0.124909	+	0.992168i	$0.460136\pi$
$432$	−18.0892	−0.870315
$433$	13.3098	0.639628	0.319814	−	0.947480i	$-0.396380\pi$
$433$	13.3098	0.639628	0.319814	+	0.947480i	$0.396380\pi$
$434$	−1.49331	−0.0716811
$435$	−5.36853	−0.257401
$436$	1.16001	0.0555544
$437$	8.67834	0.415141
$438$	29.3447	1.40214
$439$	0.706604	0.0337244	0.0168622	−	0.999858i	$-0.494632\pi$
$439$	0.706604	0.0337244	0.0168622	+	0.999858i	$0.494632\pi$
$440$	9.43336	0.449718
$441$	0.929333	0.0442539
$442$	−24.8391	−1.18148
$443$	17.2035	0.817362	0.408681	−	0.912677i	$-0.365989\pi$
$443$	17.2035	0.817362	0.408681	+	0.912677i	$0.365989\pi$
$444$	−0.455861	−0.0216342
$445$	−36.0219	−1.70760
$446$	−5.37264	−0.254402
$447$	13.7452	0.650128
$448$	−6.88073	−0.325084
$449$	5.62760	0.265583	0.132791	−	0.991144i	$-0.457606\pi$
$449$	5.62760	0.265583	0.132791	+	0.991144i	$0.457606\pi$
$450$	−5.04317	−0.237737
$451$	2.51930	0.118629
$452$	−1.70265	−0.0800859
$453$	−38.8072	−1.82332
$454$	39.6186	1.85939
$455$	−9.27047	−0.434606
$456$	−16.9678	−0.794591
$457$	22.8948	1.07097	0.535486	−	0.844544i	$-0.320128\pi$
$457$	22.8948	1.07097	0.535486	+	0.844544i	$0.320128\pi$
$458$	−39.4203	−1.84199
$459$	21.6401	1.01007
$460$	1.81083	0.0844305
$461$	22.5813	1.05172	0.525858	−	0.850573i	$-0.323744\pi$
$461$	22.5813	1.05172	0.525858	+	0.850573i	$0.323744\pi$
$462$	−3.59534	−0.167270
$463$	−39.5704	−1.83899	−0.919496	−	0.393099i	$-0.871403\pi$
$463$	−39.5704	−1.83899	−0.919496	+	0.393099i	$0.871403\pi$
$464$	−4.06199	−0.188573
$465$	5.82459	0.270109
$466$	37.7216	1.74742
$467$	18.1518	0.839967	0.419983	−	0.907532i	$-0.362036\pi$
$467$	18.1518	0.839967	0.419983	+	0.907532i	$0.362036\pi$
$468$	0.674280	0.0311686
$469$	−1.92755	−0.0890058
$470$	−58.6318	−2.70448
$471$	17.0860	0.787282
$472$	10.3126	0.474677
$473$	12.8214	0.589530
$474$	−38.1159	−1.75072
$475$	11.7685	0.539974
$476$	−1.21245	−0.0555724
$477$	−5.63609	−0.258059
$478$	7.79209	0.356402
$479$	27.7432	1.26762	0.633809	−	0.773490i	$-0.281491\pi$
$479$	27.7432	1.26762	0.633809	+	0.773490i	$0.281491\pi$
$480$	−7.54105	−0.344200
$481$	3.15498	0.143855
$482$	18.6924	0.851416
$483$	5.31201	0.241705
$484$	−2.19042	−0.0995644
$485$	50.6454	2.29969
$486$	−13.9491	−0.632743
$487$	−34.7599	−1.57512	−0.787560	−	0.616238i	$-0.788656\pi$
$487$	−34.7599	−1.57512	−0.787560	+	0.616238i	$0.788656\pi$
$488$	−2.38240	−0.107846
$489$	37.0948	1.67749
$490$	−4.38788	−0.198224
$491$	−13.9948	−0.631575	−0.315787	−	0.948830i	$-0.602269\pi$
$491$	−13.9948	−0.631575	−0.315787	+	0.948830i	$0.602269\pi$
$492$	−0.945542	−0.0426283
$493$	4.85937	0.218855
$494$	−15.2575	−0.686466
$495$	3.31671	0.149075
$496$	4.40706	0.197883
$497$	−11.8547	−0.531757
$498$	15.1503	0.678902
$499$	−6.88153	−0.308060	−0.154030	−	0.988066i	$-0.549225\pi$
$499$	−6.88153	−0.308060	−0.154030	+	0.988066i	$0.549225\pi$
$500$	−0.923069	−0.0412809
$501$	8.78563	0.392513
$502$	0.353202	0.0157642
$503$	9.15353	0.408136	0.204068	−	0.978957i	$-0.434584\pi$
$503$	9.15353	0.408136	0.204068	+	0.978957i	$0.434584\pi$
$504$	−2.45641	−0.109417
$505$	−7.52881	−0.335028
$506$	−4.86049	−0.216075
$507$	6.03819	0.268165
$508$	1.11457	0.0494511
$509$	22.1694	0.982643	0.491322	−	0.870978i	$-0.336514\pi$
$509$	22.1694	0.982643	0.491322	+	0.870978i	$0.336514\pi$
$510$	45.8569	2.03058
$511$	−9.91336	−0.438541
$512$	17.5917	0.777449
$513$	13.2925	0.586878
$514$	18.9062	0.833917
$515$	6.46008	0.284665
$516$	−4.81213	−0.211842
$517$	16.2296	0.713778
$518$	1.49331	0.0656122
$519$	−41.5514	−1.82390
$520$	24.5037	1.07456
$521$	−17.8876	−0.783670	−0.391835	−	0.920036i	$-0.628160\pi$
$521$	−17.8876	−0.783670	−0.391835	+	0.920036i	$0.628160\pi$
$522$	−1.27912	−0.0559855
$523$	11.1192	0.486209	0.243105	−	0.970000i	$-0.421834\pi$
$523$	11.1192	0.486209	0.243105	+	0.970000i	$0.421834\pi$
$524$	2.14139	0.0935472
$525$	7.20348	0.314386
$526$	20.8428	0.908789
$527$	−5.27218	−0.229660
$528$	10.6106	0.461766
$529$	−15.8188	−0.687772
$530$	26.6110	1.15591
$531$	3.62586	0.157349
$532$	−0.744748	−0.0322889
$533$	6.54403	0.283453
$534$	−36.2886	−1.57036
$535$	20.2711	0.876397
$536$	5.09489	0.220066
$537$	7.38937	0.318875
$538$	0.0321881	0.00138773
$539$	1.21459	0.0523162
$540$	2.77363	0.119358
$541$	36.7381	1.57949	0.789746	−	0.613434i	$-0.210212\pi$
$541$	36.7381	1.57949	0.789746	+	0.613434i	$0.210212\pi$
$542$	25.9547	1.11485
$543$	−14.8768	−0.638423
$544$	6.82585	0.292656
$545$	14.8216	0.634886
$546$	−9.33910	−0.399677
$547$	6.19950	0.265072	0.132536	−	0.991178i	$-0.457688\pi$
$547$	6.19950	0.265072	0.132536	+	0.991178i	$0.457688\pi$
$548$	1.02260	0.0436832
$549$	−0.837636	−0.0357494
$550$	−6.59118	−0.281049
$551$	2.98488	0.127160
$552$	−14.0407	−0.597613
$553$	12.8765	0.547564
$554$	41.8562	1.77830
$555$	−5.82459	−0.247240
$556$	2.28577	0.0969381
$557$	−32.9550	−1.39635	−0.698174	−	0.715928i	$-0.746004\pi$
$557$	−32.9550	−1.39635	−0.698174	+	0.715928i	$0.746004\pi$
$558$	1.38778	0.0587494
$559$	33.3044	1.40863
$560$	12.9495	0.547218
$561$	−12.6935	−0.535919
$562$	26.0934	1.10069
$563$	29.5046	1.24347	0.621736	−	0.783227i	$-0.286428\pi$
$563$	29.5046	1.24347	0.621736	+	0.783227i	$0.286428\pi$
$564$	−6.09130	−0.256490
$565$	−21.7550	−0.915238
$566$	0.346714	0.0145735
$567$	10.9243	0.458779
$568$	31.3344	1.31476
$569$	−9.24549	−0.387591	−0.193796	−	0.981042i	$-0.562080\pi$
$569$	−9.24549	−0.387591	−0.193796	+	0.981042i	$0.562080\pi$
$570$	28.1677	1.17982
$571$	36.4781	1.52656	0.763281	−	0.646067i	$-0.223587\pi$
$571$	36.4781	1.52656	0.763281	+	0.646067i	$0.223587\pi$
$572$	0.881251	0.0368470
$573$	8.91366	0.372374
$574$	3.09741	0.129283
$575$	9.73829	0.406115
$576$	6.39449	0.266437
$577$	24.2132	1.00801	0.504004	−	0.863701i	$-0.331860\pi$
$577$	24.2132	1.00801	0.504004	+	0.863701i	$0.331860\pi$
$578$	−16.1215	−0.670568
$579$	11.7522	0.488406
$580$	0.622828	0.0258615
$581$	−5.11814	−0.212336
$582$	51.0203	2.11486
$583$	−7.36610	−0.305073
$584$	26.2030	1.08429
$585$	8.61535	0.356201
$586$	24.2317	1.00100
$587$	19.6020	0.809062	0.404531	−	0.914524i	$-0.367435\pi$
$587$	19.6020	0.809062	0.404531	+	0.914524i	$0.367435\pi$
$588$	−0.455861	−0.0187994
$589$	−3.23845	−0.133438
$590$	−17.1196	−0.704804
$591$	27.5265	1.13229
$592$	−4.40706	−0.181129
$593$	15.1492	0.622105	0.311052	−	0.950393i	$-0.399319\pi$
$593$	15.1492	0.622105	0.311052	+	0.950393i	$0.399319\pi$
$594$	−7.44475	−0.305462
$595$	−15.4916	−0.635093
$596$	−1.59465	−0.0653195
$597$	−20.5994	−0.843076
$598$	−12.6254	−0.516292
$599$	18.5704	0.758765	0.379382	−	0.925240i	$-0.376137\pi$
$599$	18.5704	0.758765	0.379382	+	0.925240i	$0.376137\pi$
$600$	−19.0402	−0.777315
$601$	24.9153	1.01632	0.508158	−	0.861264i	$-0.330327\pi$
$601$	24.9153	1.01632	0.508158	+	0.861264i	$0.330327\pi$
$602$	15.7636	0.642476
$603$	1.79133	0.0729486
$604$	4.50220	0.183192
$605$	−27.9872	−1.13784
$606$	−7.58455	−0.308101
$607$	24.2535	0.984418	0.492209	−	0.870477i	$-0.336190\pi$
$607$	24.2535	0.984418	0.492209	+	0.870477i	$0.336190\pi$
$608$	4.19280	0.170040
$609$	1.82705	0.0740356
$610$	3.95494	0.160131
$611$	42.1574	1.70551
$612$	1.12677	0.0455468
$613$	33.2379	1.34247	0.671233	−	0.741247i	$-0.265765\pi$
$613$	33.2379	1.34247	0.671233	+	0.741247i	$0.265765\pi$
$614$	−20.4668	−0.825974
$615$	−12.0813	−0.487165
$616$	−3.21041	−0.129351
$617$	41.3704	1.66551	0.832755	−	0.553641i	$-0.186762\pi$
$617$	41.3704	1.66551	0.832755	+	0.553641i	$0.186762\pi$
$618$	6.50791	0.261787
$619$	8.84745	0.355609	0.177805	−	0.984066i	$-0.443101\pi$
$619$	8.84745	0.355609	0.177805	+	0.984066i	$0.443101\pi$
$620$	−0.675738	−0.0271383
$621$	10.9994	0.441391
$622$	13.9497	0.559332
$623$	12.2592	0.491153
$624$	27.5616	1.10335
$625$	−29.9641	−1.19856
$626$	19.9056	0.795586
$627$	−7.79699	−0.311382
$628$	−1.98223	−0.0790996
$629$	5.27218	0.210215
$630$	4.07780	0.162464
$631$	−23.4617	−0.933995	−0.466997	−	0.884259i	$-0.654664\pi$
$631$	−23.4617	−0.933995	−0.466997	+	0.884259i	$0.654664\pi$
$632$	−34.0351	−1.35384
$633$	5.65004	0.224569
$634$	48.8615	1.94054
$635$	14.2410	0.565138
$636$	2.76464	0.109625
$637$	3.15498	0.125005
$638$	−1.67175	−0.0661851
$639$	11.0170	0.435825
$640$	−37.8004	−1.49419
$641$	29.4741	1.16416	0.582078	−	0.813133i	$-0.302240\pi$
$641$	29.4741	1.16416	0.582078	+	0.813133i	$0.302240\pi$
$642$	20.4212	0.805960
$643$	−44.4789	−1.75408	−0.877039	−	0.480420i	$-0.840484\pi$
$643$	−44.4789	−1.75408	−0.877039	+	0.480420i	$0.840484\pi$
$644$	−0.616272	−0.0242845
$645$	−61.4852	−2.42098
$646$	−25.4963	−1.00314
$647$	−28.4043	−1.11669	−0.558345	−	0.829609i	$-0.688563\pi$
$647$	−28.4043	−1.11669	−0.558345	+	0.829609i	$0.688563\pi$
$648$	−28.8752	−1.13433
$649$	4.73882	0.186015
$650$	−17.1210	−0.671540
$651$	−1.98225	−0.0776907
$652$	−4.30355	−0.168540
$653$	−43.3202	−1.69525	−0.847625	−	0.530595i	$-0.821968\pi$
$653$	−43.3202	−1.69525	−0.847625	+	0.530595i	$0.821968\pi$
$654$	14.9313	0.583860
$655$	27.3608	1.06908
$656$	−9.14108	−0.356899
$657$	9.21281	0.359426
$658$	19.9539	0.777883
$659$	0.143597	0.00559376	0.00279688	−	0.999996i	$-0.499110\pi$
$659$	0.143597	0.00559376	0.00279688	+	0.999996i	$0.499110\pi$
$660$	−1.62693	−0.0633281
$661$	−24.2488	−0.943168	−0.471584	−	0.881821i	$-0.656318\pi$
$661$	−24.2488	−0.943168	−0.471584	+	0.881821i	$0.656318\pi$
$662$	22.5508	0.876460
$663$	−32.9720	−1.28053
$664$	13.5283	0.524999
$665$	−9.51574	−0.369004
$666$	−1.38778	−0.0537754
$667$	2.46996	0.0956372
$668$	−1.01926	−0.0394365
$669$	−7.13177	−0.275730
$670$	−8.45785	−0.326755
$671$	−1.09475	−0.0422624
$672$	2.56641	0.0990015
$673$	12.0340	0.463876	0.231938	−	0.972731i	$-0.425493\pi$
$673$	12.0340	0.463876	0.231938	+	0.972731i	$0.425493\pi$
$674$	−28.7242	−1.10641
$675$	14.9160	0.574118
$676$	−0.700519	−0.0269430
$677$	−12.5558	−0.482560	−0.241280	−	0.970456i	$-0.577567\pi$
$677$	−12.5558	−0.482560	−0.241280	+	0.970456i	$0.577567\pi$
$678$	−21.9160	−0.841680
$679$	−17.2359	−0.661453
$680$	40.9473	1.57026
$681$	52.5907	2.01528
$682$	1.81376	0.0694526
$683$	7.99360	0.305867	0.152933	−	0.988237i	$-0.451128\pi$
$683$	7.99360	0.305867	0.152933	+	0.988237i	$0.451128\pi$
$684$	0.692119	0.0264638
$685$	13.0658	0.499220
$686$	1.49331	0.0570148
$687$	−52.3275	−1.99642
$688$	−46.5215	−1.77362
$689$	−19.1339	−0.728942
$690$	23.3085	0.887340
$691$	−19.0860	−0.726065	−0.363033	−	0.931776i	$-0.618259\pi$
$691$	−19.0860	−0.726065	−0.363033	+	0.931776i	$0.618259\pi$
$692$	4.82057	0.183251
$693$	−1.12876	−0.0428781
$694$	−23.9613	−0.909558
$695$	29.2055	1.10783
$696$	−4.82925	−0.183052
$697$	10.9355	0.414212
$698$	−23.9882	−0.907965
$699$	50.0726	1.89392
$700$	−0.835710	−0.0315869
$701$	−46.6057	−1.76027	−0.880136	−	0.474722i	$-0.842549\pi$
$701$	−46.6057	−1.76027	−0.880136	+	0.474722i	$0.842549\pi$
$702$	−19.3382	−0.729872
$703$	3.23845	0.122140
$704$	8.35729	0.314977
$705$	−77.8292	−2.93122
$706$	30.1170	1.13347
$707$	2.56225	0.0963632
$708$	−1.77857	−0.0668428
$709$	26.7264	1.00373	0.501865	−	0.864946i	$-0.332648\pi$
$709$	26.7264	1.00373	0.501865	+	0.864946i	$0.332648\pi$
$710$	−52.0172	−1.95217
$711$	−11.9665	−0.448780
$712$	−32.4034	−1.21437
$713$	−2.67978	−0.100359
$714$	−15.6063	−0.584050
$715$	11.2599	0.421095
$716$	−0.857276	−0.0320379
$717$	10.3434	0.386282
$718$	19.6488	0.733285
$719$	42.3593	1.57973	0.789867	−	0.613278i	$-0.210149\pi$
$719$	42.3593	1.57973	0.789867	+	0.613278i	$0.210149\pi$
$720$	−12.0344	−0.448496
$721$	−2.19853	−0.0818776
$722$	12.7117	0.473082
$723$	24.8128	0.922796
$724$	1.72593	0.0641435
$725$	3.34945	0.124395
$726$	−28.1944	−1.04639
$727$	49.1283	1.82207	0.911033	−	0.412332i	$-0.135286\pi$
$727$	49.1283	1.82207	0.911033	+	0.412332i	$0.135286\pi$
$728$	−8.33923	−0.309073
$729$	14.2567	0.528025
$730$	−43.4987	−1.60996
$731$	55.6539	2.05843
$732$	0.410881	0.0151866
$733$	−17.7192	−0.654472	−0.327236	−	0.944943i	$-0.606117\pi$
$733$	−17.7192	−0.654472	−0.327236	+	0.944943i	$0.606117\pi$
$734$	42.4965	1.56858
$735$	−5.82459	−0.214843
$736$	3.46950	0.127887
$737$	2.34118	0.0862386
$738$	−2.87852	−0.105960
$739$	−46.5865	−1.71371	−0.856855	−	0.515557i	$-0.827585\pi$
$739$	−46.5865	−1.71371	−0.856855	+	0.515557i	$0.827585\pi$
$740$	0.675738	0.0248406
$741$	−20.2531	−0.744018
$742$	−9.05641	−0.332471
$743$	49.3992	1.81228	0.906141	−	0.422975i	$-0.139014\pi$
$743$	49.3992	1.81228	0.906141	+	0.422975i	$0.139014\pi$
$744$	5.23949	0.192089
$745$	−20.3750	−0.746484
$746$	−5.80353	−0.212482
$747$	4.75646	0.174030
$748$	1.47263	0.0538447
$749$	−6.89878	−0.252076
$750$	−11.8815	−0.433850
$751$	47.8659	1.74665	0.873326	−	0.487136i	$-0.161958\pi$
$751$	47.8659	1.74665	0.873326	+	0.487136i	$0.161958\pi$
$752$	−58.8879	−2.14742
$753$	0.468850	0.0170858
$754$	−4.34246	−0.158143
$755$	57.5252	2.09356
$756$	−0.943936	−0.0343306
$757$	29.0157	1.05459	0.527297	−	0.849681i	$-0.323206\pi$
$757$	29.0157	1.05459	0.527297	+	0.849681i	$0.323206\pi$
$758$	−24.7250	−0.898052
$759$	−6.45194	−0.234190
$760$	25.1520	0.912359
$761$	5.02303	0.182085	0.0910423	−	0.995847i	$-0.470980\pi$
$761$	5.02303	0.182085	0.0910423	+	0.995847i	$0.470980\pi$
$762$	14.3464	0.519717
$763$	−5.04416	−0.182611
$764$	−1.03412	−0.0374130
$765$	14.3968	0.520518
$766$	−30.3533	−1.09671
$767$	12.3094	0.444465
$768$	−10.8015	−0.389767
$769$	20.3497	0.733830	0.366915	−	0.930254i	$-0.380414\pi$
$769$	20.3497	0.733830	0.366915	+	0.930254i	$0.380414\pi$
$770$	5.32950	0.192062
$771$	25.0966	0.903830
$772$	−1.36343	−0.0490710
$773$	−18.0859	−0.650506	−0.325253	−	0.945627i	$-0.605450\pi$
$773$	−18.0859	−0.650506	−0.325253	+	0.945627i	$0.605450\pi$
$774$	−14.6496	−0.526570
$775$	−3.63398	−0.130537
$776$	45.5579	1.63543
$777$	1.98225	0.0711130
$778$	36.1334	1.29544
$779$	6.71716	0.240667
$780$	−4.22604	−0.151317
$781$	14.3987	0.515225
$782$	−21.0979	−0.754460
$783$	3.78320	0.135201
$784$	−4.40706	−0.157395
$785$	−25.3272	−0.903966
$786$	27.5634	0.983154
$787$	−37.2313	−1.32715	−0.663577	−	0.748108i	$-0.730962\pi$
$787$	−37.2313	−1.32715	−0.663577	+	0.748108i	$0.730962\pi$
$788$	−3.19348	−0.113763
$789$	27.6672	0.984979
$790$	56.5005	2.01020
$791$	7.40377	0.263248
$792$	2.98354	0.106016
$793$	−2.84368	−0.100982
$794$	28.4056	1.00808
$795$	35.3241	1.25282
$796$	2.38983	0.0847053
$797$	−34.3808	−1.21783	−0.608915	−	0.793235i	$-0.708395\pi$
$797$	−34.3808	−1.21783	−0.608915	+	0.793235i	$0.708395\pi$
$798$	−9.58619	−0.339347
$799$	70.4478	2.49227
$800$	4.70490	0.166343
$801$	−11.3928	−0.402546
$802$	−31.4086	−1.10908
$803$	12.0407	0.424907
$804$	−0.878692	−0.0309891
$805$	−7.87418	−0.277528
$806$	4.71135	0.165950
$807$	0.0427273	0.00150407
$808$	−6.77253	−0.238257
$809$	−3.63871	−0.127930	−0.0639651	−	0.997952i	$-0.520375\pi$
$809$	−3.63871	−0.127930	−0.0639651	+	0.997952i	$0.520375\pi$
$810$	47.9347	1.68426
$811$	−35.1650	−1.23481	−0.617405	−	0.786646i	$-0.711816\pi$
$811$	−35.1650	−1.23481	−0.617405	+	0.786646i	$0.711816\pi$
$812$	−0.211964	−0.00743849
$813$	34.4528	1.20831
$814$	−1.81376	−0.0635723
$815$	−54.9870	−1.92611
$816$	46.0572	1.61233
$817$	34.1855	1.19600
$818$	−10.0113	−0.350035
$819$	−2.93202	−0.102453
$820$	1.40161	0.0489463
$821$	18.8387	0.657476	0.328738	−	0.944421i	$-0.393377\pi$
$821$	18.8387	0.657476	0.328738	+	0.944421i	$0.393377\pi$
$822$	13.1626	0.459097
$823$	16.5874	0.578200	0.289100	−	0.957299i	$-0.406644\pi$
$823$	16.5874	0.578200	0.289100	+	0.957299i	$0.406644\pi$
$824$	5.81116	0.202441
$825$	−8.74930	−0.304612
$826$	5.82625	0.202721
$827$	−19.6166	−0.682136	−0.341068	−	0.940039i	$-0.610789\pi$
$827$	−19.6166	−0.682136	−0.341068	+	0.940039i	$0.610789\pi$
$828$	0.572722	0.0199035
$829$	3.80762	0.132244	0.0661220	−	0.997812i	$-0.478937\pi$
$829$	3.80762	0.132244	0.0661220	+	0.997812i	$0.478937\pi$
$830$	−22.4578	−0.779523
$831$	55.5609	1.92739
$832$	21.7086	0.752609
$833$	5.27218	0.182670
$834$	29.4217	1.01879
$835$	−13.0232	−0.450688
$836$	0.904566	0.0312851
$837$	−4.10459	−0.141875
$838$	23.9721	0.828104
$839$	11.2956	0.389968	0.194984	−	0.980806i	$-0.437535\pi$
$839$	11.2956	0.389968	0.194984	+	0.980806i	$0.437535\pi$
$840$	15.3955	0.531197
$841$	−28.1505	−0.970706
$842$	21.0663	0.725991
$843$	34.6371	1.19296
$844$	−0.655488	−0.0225628
$845$	−8.95061	−0.307910
$846$	−18.5438	−0.637549
$847$	9.52476	0.327275
$848$	26.7273	0.917819
$849$	0.460237	0.0157953
$850$	−28.6103	−0.981326
$851$	2.67978	0.0918618
$852$	−5.40410	−0.185141
$853$	−48.8320	−1.67198	−0.835988	−	0.548748i	$-0.815105\pi$
$853$	−48.8320	−1.67198	−0.835988	+	0.548748i	$0.815105\pi$
$854$	−1.34596	−0.0460580
$855$	8.84328	0.302434
$856$	18.2349	0.623254
$857$	−6.83256	−0.233396	−0.116698	−	0.993167i	$-0.537231\pi$
$857$	−6.83256	−0.233396	−0.116698	+	0.993167i	$0.537231\pi$
$858$	11.3432	0.387251
$859$	27.4462	0.936453	0.468227	−	0.883608i	$-0.344893\pi$
$859$	27.4462	0.936453	0.468227	+	0.883608i	$0.344893\pi$
$860$	7.13319	0.243240
$861$	4.11157	0.140122
$862$	−7.74485	−0.263791
$863$	31.1956	1.06191	0.530955	−	0.847400i	$-0.321833\pi$
$863$	31.1956	1.06191	0.530955	+	0.847400i	$0.321833\pi$
$864$	5.31419	0.180792
$865$	61.5930	2.09423
$866$	−19.8756	−0.675401
$867$	−21.4001	−0.726786
$868$	0.229971	0.00780572
$869$	−15.6397	−0.530540
$870$	8.01687	0.271797
$871$	6.08136	0.206059
$872$	13.3327	0.451503
$873$	16.0179	0.542123
$874$	−12.9594	−0.438360
$875$	4.01385	0.135693
$876$	−4.51911	−0.152687
$877$	−0.864221	−0.0291827	−0.0145913	−	0.999894i	$-0.504645\pi$
$877$	−0.864221	−0.0291827	−0.0145913	+	0.999894i	$0.504645\pi$
$878$	−1.05518	−0.0356106
$879$	32.1658	1.08492
$880$	−15.7284	−0.530205
$881$	−16.5755	−0.558444	−0.279222	−	0.960227i	$-0.590077\pi$
$881$	−16.5755	−0.558444	−0.279222	+	0.960227i	$0.590077\pi$
$882$	−1.38778	−0.0467290
$883$	−49.5740	−1.66830	−0.834150	−	0.551538i	$-0.814041\pi$
$883$	−49.5740	−1.66830	−0.834150	+	0.551538i	$0.814041\pi$
$884$	3.82524	0.128657
$885$	−22.7250	−0.763893
$886$	−25.6901	−0.863075
$887$	18.0574	0.606309	0.303155	−	0.952941i	$-0.401960\pi$
$887$	18.0574	0.606309	0.303155	+	0.952941i	$0.401960\pi$
$888$	−5.23949	−0.175826
$889$	−4.84658	−0.162549
$890$	53.7918	1.80310
$891$	−13.2686	−0.444516
$892$	0.827391	0.0277031
$893$	43.2728	1.44807
$894$	−20.5259	−0.686488
$895$	−10.9535	−0.366136
$896$	12.8644	0.429771
$897$	−16.7593	−0.559576
$898$	−8.40374	−0.280436
$899$	−0.921701	−0.0307405
$900$	0.776653	0.0258884
$901$	−31.9740	−1.06521
$902$	−3.76209	−0.125264
$903$	20.9250	0.696339
$904$	−19.5696	−0.650877
$905$	22.0524	0.733045
$906$	57.9511	1.92530
$907$	8.16795	0.271212	0.135606	−	0.990763i	$-0.456702\pi$
$907$	8.16795	0.271212	0.135606	+	0.990763i	$0.456702\pi$
$908$	−6.10130	−0.202479
$909$	−2.38118	−0.0789787
$910$	13.8437	0.458913
$911$	45.2009	1.49757	0.748786	−	0.662812i	$-0.230637\pi$
$911$	45.2009	1.49757	0.748786	+	0.662812i	$0.230637\pi$
$912$	28.2908	0.936801
$913$	6.21646	0.205735
$914$	−34.1890	−1.13087
$915$	5.24988	0.173556
$916$	6.07077	0.200584
$917$	−9.31159	−0.307496
$918$	−32.3154	−1.06657
$919$	−2.64649	−0.0872997	−0.0436499	−	0.999047i	$-0.513899\pi$
$919$	−2.64649	−0.0872997	−0.0436499	+	0.999047i	$0.513899\pi$
$920$	20.8130	0.686186
$921$	−27.1682	−0.895222
$922$	−33.7208	−1.11054
$923$	37.4014	1.23108
$924$	0.553685	0.0182149
$925$	3.63398	0.119485
$926$	59.0908	1.94184
$927$	2.04317	0.0671064
$928$	1.19332	0.0391727
$929$	36.1808	1.18705	0.593527	−	0.804814i	$-0.297735\pi$
$929$	36.1808	1.18705	0.593527	+	0.804814i	$0.297735\pi$
$930$	−8.69790	−0.285216
$931$	3.23845	0.106136
$932$	−5.80916	−0.190285
$933$	18.5172	0.606225
$934$	−27.1063	−0.886945
$935$	18.8160	0.615348
$936$	7.74992	0.253314
$937$	−16.4423	−0.537146	−0.268573	−	0.963259i	$-0.586552\pi$
$937$	−16.4423	−0.537146	−0.268573	+	0.963259i	$0.586552\pi$
$938$	2.87842	0.0939838
$939$	26.4231	0.862286
$940$	9.02934	0.294505
$941$	−38.5388	−1.25633	−0.628165	−	0.778080i	$-0.716194\pi$
$941$	−38.5388	−1.25633	−0.628165	+	0.778080i	$0.716194\pi$
$942$	−25.5147	−0.831313
$943$	5.55839	0.181006
$944$	−17.1944	−0.559631
$945$	−12.0608	−0.392337
$946$	−19.1463	−0.622501
$947$	1.83248	0.0595476	0.0297738	−	0.999557i	$-0.490521\pi$
$947$	1.83248	0.0595476	0.0297738	+	0.999557i	$0.490521\pi$
$948$	5.86988	0.190645
$949$	31.2764	1.01528
$950$	−17.5740	−0.570174
$951$	64.8600	2.10323
$952$	−13.9354	−0.451650
$953$	42.9592	1.39159	0.695793	−	0.718242i	$-0.255053\pi$
$953$	42.9592	1.39159	0.695793	+	0.718242i	$0.255053\pi$
$954$	8.41642	0.272492
$955$	−13.2130	−0.427564
$956$	−1.19999	−0.0388104
$957$	−2.21912	−0.0717339
$958$	−41.4291	−1.33851
$959$	−4.44664	−0.143589
$960$	−40.0774	−1.29349
$961$	1.00000	0.0322581
$962$	−4.71135	−0.151900
$963$	6.41126	0.206600
$964$	−2.87865	−0.0927150
$965$	−17.4207	−0.560794
$966$	−7.93248	−0.255223
$967$	34.0052	1.09353	0.546767	−	0.837285i	$-0.315858\pi$
$967$	34.0052	1.09353	0.546767	+	0.837285i	$0.315858\pi$
$968$	−25.1759	−0.809183
$969$	−33.8444	−1.08724
$970$	−75.6292	−2.42831
$971$	−5.84639	−0.187620	−0.0938098	−	0.995590i	$-0.529905\pi$
$971$	−5.84639	−0.187620	−0.0938098	+	0.995590i	$0.529905\pi$
$972$	2.14817	0.0689025
$973$	−9.93938	−0.318642
$974$	51.9072	1.66321
$975$	−22.7268	−0.727841
$976$	3.97221	0.127147
$977$	50.8795	1.62778	0.813890	−	0.581019i	$-0.197346\pi$
$977$	50.8795	1.62778	0.813890	+	0.581019i	$0.197346\pi$
$978$	−55.3941	−1.77131
$979$	−14.8899	−0.475883
$980$	0.675738	0.0215857
$981$	4.68770	0.149667
$982$	20.8985	0.666898
$983$	−22.2122	−0.708459	−0.354229	−	0.935159i	$-0.615257\pi$
$983$	−22.2122	−0.708459	−0.354229	+	0.935159i	$0.615257\pi$
$984$	−10.8677	−0.346450
$985$	−40.8035	−1.30011
$986$	−7.25654	−0.231095
$987$	26.4873	0.843099
$988$	2.34966	0.0747528
$989$	28.2882	0.899513
$990$	−4.95287	−0.157413
$991$	−37.3245	−1.18565	−0.592826	−	0.805330i	$-0.701988\pi$
$991$	−37.3245	−1.18565	−0.592826	+	0.805330i	$0.701988\pi$
$992$	−1.29469	−0.0411066
$993$	29.9344	0.949941
$994$	17.7028	0.561497
$995$	30.5352	0.968030
$996$	−2.33316	−0.0739290
$997$	40.9999	1.29848	0.649240	−	0.760584i	$-0.275087\pi$
$997$	40.9999	1.29848	0.649240	+	0.760584i	$0.275087\pi$
$998$	10.2763	0.325289
$999$	4.10459	0.129863

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8029.2.a.h.1.19	✓	71

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8029.2.a.h.1.19	✓	71	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:	\( N \)	\(=\)	\( 8029 = 7 \cdot 31 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8029.a (trivial)

\(f(q)\)	\(=\)	\(q-1.49331 q^{2} -1.98225 q^{3} +0.229971 q^{4} +2.93836 q^{5} +2.96012 q^{6} -1.00000 q^{7} +2.64320 q^{8} +0.929333 q^{9} +O(q^{10})\)	\(q-1.49331 q^{2} -1.98225 q^{3} +0.229971 q^{4} +2.93836 q^{5} +2.96012 q^{6} -1.00000 q^{7} +2.64320 q^{8} +0.929333 q^{9} -4.38788 q^{10} +1.21459 q^{11} -0.455861 q^{12} +3.15498 q^{13} +1.49331 q^{14} -5.82459 q^{15} -4.40706 q^{16} +5.27218 q^{17} -1.38778 q^{18} +3.23845 q^{19} +0.675738 q^{20} +1.98225 q^{21} -1.81376 q^{22} +2.67978 q^{23} -5.23949 q^{24} +3.63398 q^{25} -4.71135 q^{26} +4.10459 q^{27} -0.229971 q^{28} +0.921701 q^{29} +8.69790 q^{30} -1.00000 q^{31} +1.29469 q^{32} -2.40763 q^{33} -7.87299 q^{34} -2.93836 q^{35} +0.213719 q^{36} +1.00000 q^{37} -4.83600 q^{38} -6.25397 q^{39} +7.76668 q^{40} +2.07419 q^{41} -2.96012 q^{42} +10.5561 q^{43} +0.279321 q^{44} +2.73072 q^{45} -4.00175 q^{46} +13.3622 q^{47} +8.73590 q^{48} +1.00000 q^{49} -5.42666 q^{50} -10.4508 q^{51} +0.725553 q^{52} -6.06466 q^{53} -6.12942 q^{54} +3.56892 q^{55} -2.64320 q^{56} -6.41943 q^{57} -1.37638 q^{58} +3.90157 q^{59} -1.33948 q^{60} -0.901331 q^{61} +1.49331 q^{62} -0.929333 q^{63} +6.88073 q^{64} +9.27047 q^{65} +3.59534 q^{66} +1.92755 q^{67} +1.21245 q^{68} -5.31201 q^{69} +4.38788 q^{70} +11.8547 q^{71} +2.45641 q^{72} +9.91336 q^{73} -1.49331 q^{74} -7.20348 q^{75} +0.744748 q^{76} -1.21459 q^{77} +9.33910 q^{78} -12.8765 q^{79} -12.9495 q^{80} -10.9243 q^{81} -3.09741 q^{82} +5.11814 q^{83} +0.455861 q^{84} +15.4916 q^{85} -15.7636 q^{86} -1.82705 q^{87} +3.21041 q^{88} -12.2592 q^{89} -4.07780 q^{90} -3.15498 q^{91} +0.616272 q^{92} +1.98225 q^{93} -19.9539 q^{94} +9.51574 q^{95} -2.56641 q^{96} +17.2359 q^{97} -1.49331 q^{98} +1.12876 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 71 q + 6 q^{2} + 8 q^{3} + 78 q^{4} + 5 q^{6} - 71 q^{7} + 18 q^{8} + 87 q^{9}+O(q^{10}) \) 71 * q + 6 * q^2 + 8 * q^3 + 78 * q^4 + 5 * q^6 - 71 * q^7 + 18 * q^8 + 87 * q^9	\( 71 q + 6 q^{2} + 8 q^{3} + 78 q^{4} + 5 q^{6} - 71 q^{7} + 18 q^{8} + 87 q^{9} + 4 q^{10} + 57 q^{11} + 21 q^{12} - 20 q^{13} - 6 q^{14} + 22 q^{15} + 88 q^{16} - 19 q^{17} + q^{18} + 23 q^{19} + 25 q^{20} - 8 q^{21} + 18 q^{22} + 34 q^{23} + 15 q^{24} + 81 q^{25} - 13 q^{26} + 20 q^{27} - 78 q^{28} + 16 q^{29} + 6 q^{30} - 71 q^{31} + 47 q^{32} - 16 q^{33} + 32 q^{34} + 125 q^{36} + 71 q^{37} + 13 q^{38} + 30 q^{39} + 31 q^{40} + 17 q^{41} - 5 q^{42} + 38 q^{43} + 80 q^{44} - q^{45} + 26 q^{46} + 32 q^{47} + 61 q^{48} + 71 q^{49} + 47 q^{50} + 73 q^{51} - 23 q^{52} + 31 q^{53} + 47 q^{54} + 11 q^{55} - 18 q^{56} + 17 q^{57} - 2 q^{58} + 97 q^{59} + 103 q^{60} - q^{61} - 6 q^{62} - 87 q^{63} + 100 q^{64} + 46 q^{65} + 43 q^{66} + 75 q^{67} - 43 q^{68} + 10 q^{69} - 4 q^{70} + 131 q^{71} - 11 q^{72} - 15 q^{73} + 6 q^{74} + 76 q^{75} + 41 q^{76} - 57 q^{77} + 89 q^{78} + 8 q^{79} + 10 q^{80} + 171 q^{81} + 14 q^{82} + 18 q^{83} - 21 q^{84} + 47 q^{85} + 90 q^{86} - 59 q^{87} + 13 q^{88} + 18 q^{89} + 69 q^{90} + 20 q^{91} + 110 q^{92} - 8 q^{93} + 39 q^{94} + 72 q^{95} + 100 q^{96} + 23 q^{97} + 6 q^{98} + 168 q^{99}+O(q^{100}) \) 71 * q + 6 * q^2 + 8 * q^3 + 78 * q^4 + 5 * q^6 - 71 * q^7 + 18 * q^8 + 87 * q^9 + 4 * q^10 + 57 * q^11 + 21 * q^12 - 20 * q^13 - 6 * q^14 + 22 * q^15 + 88 * q^16 - 19 * q^17 + q^18 + 23 * q^19 + 25 * q^20 - 8 * q^21 + 18 * q^22 + 34 * q^23 + 15 * q^24 + 81 * q^25 - 13 * q^26 + 20 * q^27 - 78 * q^28 + 16 * q^29 + 6 * q^30 - 71 * q^31 + 47 * q^32 - 16 * q^33 + 32 * q^34 + 125 * q^36 + 71 * q^37 + 13 * q^38 + 30 * q^39 + 31 * q^40 + 17 * q^41 - 5 * q^42 + 38 * q^43 + 80 * q^44 - q^45 + 26 * q^46 + 32 * q^47 + 61 * q^48 + 71 * q^49 + 47 * q^50 + 73 * q^51 - 23 * q^52 + 31 * q^53 + 47 * q^54 + 11 * q^55 - 18 * q^56 + 17 * q^57 - 2 * q^58 + 97 * q^59 + 103 * q^60 - q^61 - 6 * q^62 - 87 * q^63 + 100 * q^64 + 46 * q^65 + 43 * q^66 + 75 * q^67 - 43 * q^68 + 10 * q^69 - 4 * q^70 + 131 * q^71 - 11 * q^72 - 15 * q^73 + 6 * q^74 + 76 * q^75 + 41 * q^76 - 57 * q^77 + 89 * q^78 + 8 * q^79 + 10 * q^80 + 171 * q^81 + 14 * q^82 + 18 * q^83 - 21 * q^84 + 47 * q^85 + 90 * q^86 - 59 * q^87 + 13 * q^88 + 18 * q^89 + 69 * q^90 + 20 * q^91 + 110 * q^92 - 8 * q^93 + 39 * q^94 + 72 * q^95 + 100 * q^96 + 23 * q^97 + 6 * q^98 + 168 * q^99

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