LMFDB - Embedded newform 8029.2.a.d.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:	$1$
Dimension:	$66$
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)

$f(q)$	$=$	$q-1.30686 q^{2} +2.83406 q^{3} -0.292114 q^{4} -4.20735 q^{5} -3.70372 q^{6} +1.00000 q^{7} +2.99547 q^{8} +5.03190 q^{9} +O(q^{10})$	\(q-1.30686 q^{2} +2.83406 q^{3} -0.292114 q^{4} -4.20735 q^{5} -3.70372 q^{6} +1.00000 q^{7} +2.99547 q^{8} +5.03190 q^{9} +5.49842 q^{10} +1.61240 q^{11} -0.827869 q^{12} -1.96490 q^{13} -1.30686 q^{14} -11.9239 q^{15} -3.33044 q^{16} -3.84933 q^{17} -6.57599 q^{18} -0.404170 q^{19} +1.22903 q^{20} +2.83406 q^{21} -2.10719 q^{22} -2.37324 q^{23} +8.48935 q^{24} +12.7018 q^{25} +2.56786 q^{26} +5.75851 q^{27} -0.292114 q^{28} +8.50432 q^{29} +15.5828 q^{30} +1.00000 q^{31} -1.63853 q^{32} +4.56965 q^{33} +5.03053 q^{34} -4.20735 q^{35} -1.46989 q^{36} -1.00000 q^{37} +0.528194 q^{38} -5.56865 q^{39} -12.6030 q^{40} -8.36514 q^{41} -3.70372 q^{42} -1.59295 q^{43} -0.471006 q^{44} -21.1709 q^{45} +3.10149 q^{46} +2.29922 q^{47} -9.43867 q^{48} +1.00000 q^{49} -16.5994 q^{50} -10.9092 q^{51} +0.573976 q^{52} +0.319947 q^{53} -7.52558 q^{54} -6.78394 q^{55} +2.99547 q^{56} -1.14544 q^{57} -11.1140 q^{58} +7.48092 q^{59} +3.48313 q^{60} -9.02007 q^{61} -1.30686 q^{62} +5.03190 q^{63} +8.80221 q^{64} +8.26703 q^{65} -5.97189 q^{66} -0.0718931 q^{67} +1.12444 q^{68} -6.72589 q^{69} +5.49842 q^{70} +8.26090 q^{71} +15.0729 q^{72} +3.79151 q^{73} +1.30686 q^{74} +35.9976 q^{75} +0.118064 q^{76} +1.61240 q^{77} +7.27746 q^{78} +8.21193 q^{79} +14.0123 q^{80} +1.22428 q^{81} +10.9321 q^{82} -17.2309 q^{83} -0.827869 q^{84} +16.1954 q^{85} +2.08176 q^{86} +24.1017 q^{87} +4.82991 q^{88} -10.4705 q^{89} +27.6675 q^{90} -1.96490 q^{91} +0.693256 q^{92} +2.83406 q^{93} -3.00477 q^{94} +1.70048 q^{95} -4.64368 q^{96} -4.74112 q^{97} -1.30686 q^{98} +8.11344 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 66 q - 5 q^{2} - 12 q^{3} + 63 q^{4} - 26 q^{5} - 19 q^{6} + 66 q^{7} - 15 q^{8} + 66 q^{9}+O(q^{10}) $ 66 * q - 5 * q^2 - 12 * q^3 + 63 * q^4 - 26 * q^5 - 19 * q^6 + 66 * q^7 - 15 * q^8 + 66 * q^9	\( 66 q - 5 q^{2} - 12 q^{3} + 63 q^{4} - 26 q^{5} - 19 q^{6} + 66 q^{7} - 15 q^{8} + 66 q^{9} - 6 q^{10} - 57 q^{11} - 29 q^{12} - 28 q^{13} - 5 q^{14} - 24 q^{15} + 69 q^{16} - 47 q^{17} + 8 q^{18} - 27 q^{19} - 77 q^{20} - 12 q^{21} - 12 q^{22} - 46 q^{23} - 57 q^{24} + 72 q^{25} - 21 q^{26} - 36 q^{27} + 63 q^{28} - 62 q^{29} + 2 q^{30} + 66 q^{31} - 40 q^{32} + 4 q^{33} - 46 q^{34} - 26 q^{35} + 62 q^{36} - 66 q^{37} - 31 q^{38} - 8 q^{39} - 37 q^{40} - 33 q^{41} - 19 q^{42} - 22 q^{43} - 84 q^{44} - 77 q^{45} - 14 q^{46} - 20 q^{47} - 43 q^{48} + 66 q^{49} - 10 q^{50} - 39 q^{51} - 41 q^{52} - 47 q^{53} - 65 q^{54} - 15 q^{55} - 15 q^{56} + 5 q^{57} + 24 q^{58} - 125 q^{59} - 77 q^{60} - 57 q^{61} - 5 q^{62} + 66 q^{63} + 81 q^{64} - 40 q^{65} + 33 q^{66} - 25 q^{67} - 107 q^{68} - 72 q^{69} - 6 q^{70} - 57 q^{71} + 38 q^{72} + 5 q^{73} + 5 q^{74} - 60 q^{75} - 33 q^{76} - 57 q^{77} - 19 q^{78} - 4 q^{79} - 132 q^{80} + 58 q^{81} + 8 q^{82} - 84 q^{83} - 29 q^{84} - 33 q^{85} - 60 q^{86} - 31 q^{87} + 21 q^{88} - 132 q^{89} - 61 q^{90} - 28 q^{91} - 100 q^{92} - 12 q^{93} - 35 q^{94} + 4 q^{95} - 198 q^{96} - 39 q^{97} - 5 q^{98} - 174 q^{99}+O(q^{100}) \) 66 * q - 5 * q^2 - 12 * q^3 + 63 * q^4 - 26 * q^5 - 19 * q^6 + 66 * q^7 - 15 * q^8 + 66 * q^9 - 6 * q^10 - 57 * q^11 - 29 * q^12 - 28 * q^13 - 5 * q^14 - 24 * q^15 + 69 * q^16 - 47 * q^17 + 8 * q^18 - 27 * q^19 - 77 * q^20 - 12 * q^21 - 12 * q^22 - 46 * q^23 - 57 * q^24 + 72 * q^25 - 21 * q^26 - 36 * q^27 + 63 * q^28 - 62 * q^29 + 2 * q^30 + 66 * q^31 - 40 * q^32 + 4 * q^33 - 46 * q^34 - 26 * q^35 + 62 * q^36 - 66 * q^37 - 31 * q^38 - 8 * q^39 - 37 * q^40 - 33 * q^41 - 19 * q^42 - 22 * q^43 - 84 * q^44 - 77 * q^45 - 14 * q^46 - 20 * q^47 - 43 * q^48 + 66 * q^49 - 10 * q^50 - 39 * q^51 - 41 * q^52 - 47 * q^53 - 65 * q^54 - 15 * q^55 - 15 * q^56 + 5 * q^57 + 24 * q^58 - 125 * q^59 - 77 * q^60 - 57 * q^61 - 5 * q^62 + 66 * q^63 + 81 * q^64 - 40 * q^65 + 33 * q^66 - 25 * q^67 - 107 * q^68 - 72 * q^69 - 6 * q^70 - 57 * q^71 + 38 * q^72 + 5 * q^73 + 5 * q^74 - 60 * q^75 - 33 * q^76 - 57 * q^77 - 19 * q^78 - 4 * q^79 - 132 * q^80 + 58 * q^81 + 8 * q^82 - 84 * q^83 - 29 * q^84 - 33 * q^85 - 60 * q^86 - 31 * q^87 + 21 * q^88 - 132 * q^89 - 61 * q^90 - 28 * q^91 - 100 * q^92 - 12 * q^93 - 35 * q^94 + 4 * q^95 - 198 * q^96 - 39 * q^97 - 5 * q^98 - 174 * 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 $

$2$	−1.30686	−0.924090	−0.462045	−	0.886856i	$-0.652884\pi$
$2$	−1.30686	−0.924090	−0.462045	+	0.886856i	$0.652884\pi$
$3$	2.83406	1.63625	0.818123	−	0.575044i	$-0.195015\pi$
$3$	2.83406	1.63625	0.818123	+	0.575044i	$0.195015\pi$
$4$	−0.292114	−0.146057
$5$	−4.20735	−1.88158	−0.940791	−	0.338987i	$-0.889916\pi$
$5$	−4.20735	−1.88158	−0.940791	+	0.338987i	$0.889916\pi$
$6$	−3.70372	−1.51204
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	2.99547	1.05906
$9$	5.03190	1.67730
$10$	5.49842	1.73875
$11$	1.61240	0.486158	0.243079	−	0.970007i	$-0.421843\pi$
$11$	1.61240	0.486158	0.243079	+	0.970007i	$0.421843\pi$
$12$	−0.827869	−0.238985
$13$	−1.96490	−0.544966	−0.272483	−	0.962161i	$-0.587845\pi$
$13$	−1.96490	−0.544966	−0.272483	+	0.962161i	$0.587845\pi$
$14$	−1.30686	−0.349273
$15$	−11.9239	−3.07873
$16$	−3.33044	−0.832610
$17$	−3.84933	−0.933599	−0.466799	−	0.884363i	$-0.654593\pi$
$17$	−3.84933	−0.933599	−0.466799	+	0.884363i	$0.654593\pi$
$18$	−6.57599	−1.54998
$19$	−0.404170	−0.0927230	−0.0463615	−	0.998925i	$-0.514763\pi$
$19$	−0.404170	−0.0927230	−0.0463615	+	0.998925i	$0.514763\pi$
$20$	1.22903	0.274819
$21$	2.83406	0.618443
$22$	−2.10719	−0.449254
$23$	−2.37324	−0.494854	−0.247427	−	0.968907i	$-0.579585\pi$
$23$	−2.37324	−0.494854	−0.247427	+	0.968907i	$0.579585\pi$
$24$	8.48935	1.73288
$25$	12.7018	2.54035
$26$	2.56786	0.503598
$27$	5.75851	1.10823
$28$	−0.292114	−0.0552044
$29$	8.50432	1.57921	0.789606	−	0.613614i	$-0.210285\pi$
$29$	8.50432	1.57921	0.789606	+	0.613614i	$0.210285\pi$
$30$	15.5828	2.84502
$31$	1.00000	0.179605
$31$	1.00000	0.179605
$32$	−1.63853	−0.289653
$33$	4.56965	0.795474
$34$	5.03053	0.862729
$35$	−4.20735	−0.711171
$36$	−1.46989	−0.244981
$37$	−1.00000	−0.164399
$37$	−1.00000	−0.164399
$38$	0.528194	0.0856844
$39$	−5.56865	−0.891698
$40$	−12.6030	−1.99271
$41$	−8.36514	−1.30642	−0.653208	−	0.757179i	$-0.726577\pi$
$41$	−8.36514	−1.30642	−0.653208	+	0.757179i	$0.726577\pi$
$42$	−3.70372	−0.571497
$43$	−1.59295	−0.242922	−0.121461	−	0.992596i	$-0.538758\pi$
$43$	−1.59295	−0.242922	−0.121461	+	0.992596i	$0.538758\pi$
$44$	−0.471006	−0.0710068
$45$	−21.1709	−3.15598
$46$	3.10149	0.457290
$47$	2.29922	0.335376	0.167688	−	0.985840i	$-0.446370\pi$
$47$	2.29922	0.335376	0.167688	+	0.985840i	$0.446370\pi$
$48$	−9.43867	−1.36235
$49$	1.00000	0.142857
$50$	−16.5994	−2.34752
$51$	−10.9092	−1.52760
$52$	0.573976	0.0795962
$53$	0.319947	0.0439482	0.0219741	−	0.999759i	$-0.493005\pi$
$53$	0.319947	0.0439482	0.0219741	+	0.999759i	$0.493005\pi$
$54$	−7.52558	−1.02410
$55$	−6.78394	−0.914746
$56$	2.99547	0.400287
$57$	−1.14544	−0.151718
$58$	−11.1140	−1.45933
$59$	7.48092	0.973933	0.486967	−	0.873421i	$-0.338103\pi$
$59$	7.48092	0.973933	0.486967	+	0.873421i	$0.338103\pi$
$60$	3.48313	0.449671
$61$	−9.02007	−1.15490	−0.577451	−	0.816426i	$-0.695952\pi$
$61$	−9.02007	−1.15490	−0.577451	+	0.816426i	$0.695952\pi$
$62$	−1.30686	−0.165972
$63$	5.03190	0.633959
$64$	8.80221	1.10028
$65$	8.26703	1.02540
$66$	−5.97189	−0.735089
$67$	−0.0718931	−0.00878314	−0.00439157	−	0.999990i	$-0.501398\pi$
$67$	−0.0718931	−0.00878314	−0.00439157	+	0.999990i	$0.501398\pi$
$68$	1.12444	0.136359
$69$	−6.72589	−0.809702
$70$	5.49842	0.657187
$71$	8.26090	0.980388	0.490194	−	0.871613i	$-0.336926\pi$
$71$	8.26090	0.980388	0.490194	+	0.871613i	$0.336926\pi$
$72$	15.0729	1.77636
$73$	3.79151	0.443763	0.221881	−	0.975074i	$-0.428780\pi$
$73$	3.79151	0.443763	0.221881	+	0.975074i	$0.428780\pi$
$74$	1.30686	0.151920
$75$	35.9976	4.15664
$76$	0.118064	0.0135429
$77$	1.61240	0.183750
$78$	7.27746	0.824010
$79$	8.21193	0.923914	0.461957	−	0.886902i	$-0.347147\pi$
$79$	8.21193	0.923914	0.461957	+	0.886902i	$0.347147\pi$
$80$	14.0123	1.56662
$81$	1.22428	0.136032
$82$	10.9321	1.20725
$83$	−17.2309	−1.89133	−0.945667	−	0.325136i	$-0.894590\pi$
$83$	−17.2309	−1.89133	−0.945667	+	0.325136i	$0.894590\pi$
$84$	−0.827869	−0.0903279
$85$	16.1954	1.75664
$86$	2.08176	0.224482
$87$	24.1017	2.58398
$88$	4.82991	0.514871
$89$	−10.4705	−1.10987	−0.554937	−	0.831892i	$-0.687258\pi$
$89$	−10.4705	−1.10987	−0.554937	+	0.831892i	$0.687258\pi$
$90$	27.6675	2.91641
$91$	−1.96490	−0.205978
$92$	0.693256	0.0722769
$93$	2.83406	0.293878
$94$	−3.00477	−0.309918
$95$	1.70048	0.174466
$96$	−4.64368	−0.473944
$97$	−4.74112	−0.481388	−0.240694	−	0.970601i	$-0.577375\pi$
$97$	−4.74112	−0.481388	−0.240694	+	0.970601i	$0.577375\pi$
$98$	−1.30686	−0.132013
$99$	8.11344	0.815432
$100$	−3.71037	−0.371037
$101$	6.80938	0.677558	0.338779	−	0.940866i	$-0.389986\pi$
$101$	6.80938	0.677558	0.338779	+	0.940866i	$0.389986\pi$
$102$	14.2568	1.41164
$103$	0.0828209	0.00816059	0.00408029	−	0.999992i	$-0.498701\pi$
$103$	0.0828209	0.00816059	0.00408029	+	0.999992i	$0.498701\pi$
$104$	−5.88582	−0.577152
$105$	−11.9239	−1.16365
$106$	−0.418127	−0.0406121
$107$	−2.00747	−0.194069	−0.0970346	−	0.995281i	$-0.530936\pi$
$107$	−2.00747	−0.194069	−0.0970346	+	0.995281i	$0.530936\pi$
$108$	−1.68214	−0.161864
$109$	1.19085	0.114062	0.0570312	−	0.998372i	$-0.481837\pi$
$109$	1.19085	0.114062	0.0570312	+	0.998372i	$0.481837\pi$
$110$	8.86567	0.845308
$111$	−2.83406	−0.268997
$112$	−3.33044	−0.314697
$113$	−5.41795	−0.509678	−0.254839	−	0.966983i	$-0.582022\pi$
$113$	−5.41795	−0.509678	−0.254839	+	0.966983i	$0.582022\pi$
$114$	1.49693	0.140201
$115$	9.98502	0.931108
$116$	−2.48423	−0.230655
$117$	−9.88719	−0.914071
$118$	−9.77653	−0.900002
$119$	−3.84933	−0.352867
$120$	−35.7177	−3.26056
$121$	−8.40016	−0.763650
$122$	11.7880	1.06723
$123$	−23.7073	−2.13762
$124$	−0.292114	−0.0262326
$125$	−32.4040	−2.89830
$126$	−6.57599	−0.585836
$127$	4.51536	0.400673	0.200337	−	0.979727i	$-0.435796\pi$
$127$	4.51536	0.400673	0.200337	+	0.979727i	$0.435796\pi$
$128$	−8.22621	−0.727101
$129$	−4.51450	−0.397480
$130$	−10.8039	−0.947561
$131$	−6.04421	−0.528085	−0.264043	−	0.964511i	$-0.585056\pi$
$131$	−6.04421	−0.528085	−0.264043	+	0.964511i	$0.585056\pi$
$132$	−1.33486	−0.116185
$133$	−0.404170	−0.0350460
$134$	0.0939543	0.00811641
$135$	−24.2281	−2.08522
$136$	−11.5306	−0.988737
$137$	5.61438	0.479669	0.239834	−	0.970814i	$-0.422907\pi$
$137$	5.61438	0.479669	0.239834	+	0.970814i	$0.422907\pi$
$138$	8.78980	0.748238
$139$	6.32437	0.536426	0.268213	−	0.963360i	$-0.413567\pi$
$139$	6.32437	0.536426	0.268213	+	0.963360i	$0.413567\pi$
$140$	1.22903	0.103872
$141$	6.51614	0.548758
$142$	−10.7958	−0.905967
$143$	−3.16822	−0.264940
$144$	−16.7584	−1.39654
$145$	−35.7806	−2.97142
$146$	−4.95498	−0.410077
$147$	2.83406	0.233749
$148$	0.292114	0.0240116
$149$	16.2022	1.32733	0.663667	−	0.748028i	$-0.268999\pi$
$149$	16.2022	1.32733	0.663667	+	0.748028i	$0.268999\pi$
$150$	−47.0438	−3.84111
$151$	−3.74739	−0.304958	−0.152479	−	0.988307i	$-0.548726\pi$
$151$	−3.74739	−0.304958	−0.152479	+	0.988307i	$0.548726\pi$
$152$	−1.21068	−0.0981993
$153$	−19.3694	−1.56592
$154$	−2.10719	−0.169802
$155$	−4.20735	−0.337942
$156$	1.62668	0.130239
$157$	−3.29503	−0.262972	−0.131486	−	0.991318i	$-0.541975\pi$
$157$	−3.29503	−0.262972	−0.131486	+	0.991318i	$0.541975\pi$
$158$	−10.7319	−0.853780
$159$	0.906750	0.0719100
$160$	6.89385	0.545007
$161$	−2.37324	−0.187037
$162$	−1.59997	−0.125705
$163$	−0.752566	−0.0589455	−0.0294727	−	0.999566i	$-0.509383\pi$
$163$	−0.752566	−0.0589455	−0.0294727	+	0.999566i	$0.509383\pi$
$164$	2.44358	0.190811
$165$	−19.2261	−1.49675
$166$	22.5184	1.74776
$167$	−1.41047	−0.109146	−0.0545728	−	0.998510i	$-0.517380\pi$
$167$	−1.41047	−0.109146	−0.0545728	+	0.998510i	$0.517380\pi$
$168$	8.48935	0.654968
$169$	−9.13915	−0.703012
$170$	−21.1652	−1.62330
$171$	−2.03374	−0.155524
$172$	0.465322	0.0354805
$173$	−5.74566	−0.436835	−0.218417	−	0.975855i	$-0.570089\pi$
$173$	−5.74566	−0.436835	−0.218417	+	0.975855i	$0.570089\pi$
$174$	−31.4976	−2.38783
$175$	12.7018	0.960163
$176$	−5.37001	−0.404780
$177$	21.2014	1.59359
$178$	13.6835	1.02562
$179$	−18.6443	−1.39354	−0.696771	−	0.717294i	$-0.745380\pi$
$179$	−18.6443	−1.39354	−0.696771	+	0.717294i	$0.745380\pi$
$180$	6.18433	0.460953
$181$	20.4153	1.51745	0.758727	−	0.651409i	$-0.225822\pi$
$181$	20.4153	1.51745	0.758727	+	0.651409i	$0.225822\pi$
$182$	2.56786	0.190342
$183$	−25.5634	−1.88970
$184$	−7.10897	−0.524080
$185$	4.20735	0.309330
$186$	−3.70372	−0.271570
$187$	−6.20667	−0.453876
$188$	−0.671636	−0.0489841
$189$	5.75851	0.418870
$190$	−2.22230	−0.161222
$191$	−20.5458	−1.48664	−0.743319	−	0.668937i	$-0.766750\pi$
$191$	−20.5458	−1.48664	−0.743319	+	0.668937i	$0.766750\pi$
$192$	24.9460	1.80032
$193$	12.2795	0.883895	0.441947	−	0.897041i	$-0.354288\pi$
$193$	12.2795	0.883895	0.441947	+	0.897041i	$0.354288\pi$
$194$	6.19598	0.444846
$195$	23.4293	1.67780
$196$	−0.292114	−0.0208653
$197$	−11.4282	−0.814227	−0.407113	−	0.913378i	$-0.633465\pi$
$197$	−11.4282	−0.814227	−0.407113	+	0.913378i	$0.633465\pi$
$198$	−10.6031	−0.753533
$199$	−10.2309	−0.725252	−0.362626	−	0.931935i	$-0.618120\pi$
$199$	−10.2309	−0.725252	−0.362626	+	0.931935i	$0.618120\pi$
$200$	38.0478	2.69039
$201$	−0.203749	−0.0143714
$202$	−8.89891	−0.626125
$203$	8.50432	0.596886
$204$	3.18674	0.223116
$205$	35.1950	2.45813
$206$	−0.108235	−0.00754112
$207$	−11.9419	−0.830017
$208$	6.54399	0.453744
$209$	−0.651685	−0.0450780
$210$	15.5828	1.07532
$211$	10.9163	0.751512	0.375756	−	0.926719i	$-0.377383\pi$
$211$	10.9163	0.751512	0.375756	+	0.926719i	$0.377383\pi$
$212$	−0.0934612	−0.00641894
$213$	23.4119	1.60416
$214$	2.62348	0.179337
$215$	6.70207	0.457078
$216$	17.2495	1.17368
$217$	1.00000	0.0678844
$218$	−1.55627	−0.105404
$219$	10.7454	0.726105
$220$	1.98169	0.133605
$221$	7.56355	0.508780
$222$	3.70372	0.248578
$223$	−16.0268	−1.07323	−0.536617	−	0.843826i	$-0.680298\pi$
$223$	−16.0268	−1.07323	−0.536617	+	0.843826i	$0.680298\pi$
$224$	−1.63853	−0.109479
$225$	63.9139	4.26093
$226$	7.08051	0.470988
$227$	−18.6847	−1.24015	−0.620073	−	0.784544i	$-0.712897\pi$
$227$	−18.6847	−1.24015	−0.620073	+	0.784544i	$0.712897\pi$
$228$	0.334600	0.0221594
$229$	20.1408	1.33094	0.665470	−	0.746424i	$-0.268231\pi$
$229$	20.1408	1.33094	0.665470	+	0.746424i	$0.268231\pi$
$230$	−13.0490	−0.860428
$231$	4.56965	0.300661
$232$	25.4745	1.67248
$233$	9.90175	0.648685	0.324342	−	0.945940i	$-0.394857\pi$
$233$	9.90175	0.648685	0.324342	+	0.945940i	$0.394857\pi$
$234$	12.9212	0.844684
$235$	−9.67363	−0.631038
$236$	−2.18528	−0.142250
$237$	23.2731	1.51175
$238$	5.03053	0.326081
$239$	−18.9203	−1.22385	−0.611927	−	0.790914i	$-0.709605\pi$
$239$	−18.9203	−1.22385	−0.611927	+	0.790914i	$0.709605\pi$
$240$	39.7117	2.56338
$241$	14.9212	0.961156	0.480578	−	0.876952i	$-0.340427\pi$
$241$	14.9212	0.961156	0.480578	+	0.876952i	$0.340427\pi$
$242$	10.9778	0.705682
$243$	−13.8058	−0.885645
$244$	2.63489	0.168682
$245$	−4.20735	−0.268797
$246$	30.9822	1.97535
$247$	0.794155	0.0505309
$248$	2.99547	0.190213
$249$	−48.8333	−3.09469
$250$	42.3475	2.67829
$251$	−28.8761	−1.82264	−0.911320	−	0.411699i	$-0.864936\pi$
$251$	−28.8761	−1.82264	−0.911320	+	0.411699i	$0.864936\pi$
$252$	−1.46989	−0.0925943
$253$	−3.82661	−0.240577
$254$	−5.90094	−0.370258
$255$	45.8989	2.87430
$256$	−6.85390	−0.428369
$257$	−9.95179	−0.620775	−0.310388	−	0.950610i	$-0.600459\pi$
$257$	−9.95179	−0.620775	−0.310388	+	0.950610i	$0.600459\pi$
$258$	5.89983	0.367307
$259$	−1.00000	−0.0621370
$260$	−2.41492	−0.149767
$261$	42.7928	2.64881
$262$	7.89895	0.487999
$263$	7.90869	0.487671	0.243835	−	0.969817i	$-0.421594\pi$
$263$	7.90869	0.487671	0.243835	+	0.969817i	$0.421594\pi$
$264$	13.6883	0.842454
$265$	−1.34613	−0.0826921
$266$	0.528194	0.0323857
$267$	−29.6741	−1.81603
$268$	0.0210010	0.00128284
$269$	14.9688	0.912663	0.456331	−	0.889810i	$-0.349163\pi$
$269$	14.9688	0.912663	0.456331	+	0.889810i	$0.349163\pi$
$270$	31.6627	1.92693
$271$	−26.7195	−1.62309	−0.811546	−	0.584288i	$-0.801374\pi$
$271$	−26.7195	−1.62309	−0.811546	+	0.584288i	$0.801374\pi$
$272$	12.8200	0.777324
$273$	−5.56865	−0.337030
$274$	−7.33721	−0.443257
$275$	20.4804	1.23501
$276$	1.96473	0.118263
$277$	22.9800	1.38074	0.690368	−	0.723458i	$-0.257449\pi$
$277$	22.9800	1.38074	0.690368	+	0.723458i	$0.257449\pi$
$278$	−8.26507	−0.495706
$279$	5.03190	0.301252
$280$	−12.6030	−0.753173
$281$	−32.7671	−1.95472	−0.977361	−	0.211578i	$-0.932140\pi$
$281$	−32.7671	−1.95472	−0.977361	+	0.211578i	$0.932140\pi$
$282$	−8.51569	−0.507102
$283$	19.5737	1.16354	0.581769	−	0.813354i	$-0.302361\pi$
$283$	19.5737	1.16354	0.581769	+	0.813354i	$0.302361\pi$
$284$	−2.41313	−0.143193
$285$	4.81927	0.285469
$286$	4.14042	0.244828
$287$	−8.36514	−0.493779
$288$	−8.24489	−0.485835
$289$	−2.18269	−0.128394
$290$	46.7603	2.74586
$291$	−13.4366	−0.787668
$292$	−1.10755	−0.0648147
$293$	−26.1174	−1.52579	−0.762896	−	0.646521i	$-0.776223\pi$
$293$	−26.1174	−1.52579	−0.762896	+	0.646521i	$0.776223\pi$
$294$	−3.70372	−0.216005
$295$	−31.4748	−1.83254
$296$	−2.99547	−0.174108
$297$	9.28505	0.538773
$298$	−21.1740	−1.22658
$299$	4.66318	0.269679
$300$	−10.5154	−0.607107
$301$	−1.59295	−0.0918159
$302$	4.89731	0.281809
$303$	19.2982	1.10865
$304$	1.34606	0.0772021
$305$	37.9506	2.17304
$306$	25.3131	1.44705
$307$	13.8206	0.788783	0.394392	−	0.918942i	$-0.370955\pi$
$307$	13.8206	0.788783	0.394392	+	0.918942i	$0.370955\pi$
$308$	−0.471006	−0.0268381
$309$	0.234719	0.0133527
$310$	5.49842	0.312289
$311$	4.30475	0.244100	0.122050	−	0.992524i	$-0.461053\pi$
$311$	4.30475	0.244100	0.122050	+	0.992524i	$0.461053\pi$
$312$	−16.6808	−0.944362
$313$	−4.86040	−0.274726	−0.137363	−	0.990521i	$-0.543863\pi$
$313$	−4.86040	−0.274726	−0.137363	+	0.990521i	$0.543863\pi$
$314$	4.30615	0.243010
$315$	−21.1709	−1.19285
$316$	−2.39882	−0.134944
$317$	18.8191	1.05698	0.528492	−	0.848938i	$-0.322757\pi$
$317$	18.8191	1.05698	0.528492	+	0.848938i	$0.322757\pi$
$318$	−1.18500	−0.0664513
$319$	13.7124	0.767746
$320$	−37.0339	−2.07026
$321$	−5.68928	−0.317545
$322$	3.10149	0.172839
$323$	1.55578	0.0865661
$324$	−0.357631	−0.0198684
$325$	−24.9577	−1.38441
$326$	0.983499	0.0544710
$327$	3.37493	0.186634
$328$	−25.0576	−1.38357
$329$	2.29922	0.126760
$330$	25.1258	1.38313
$331$	−23.6758	−1.30134	−0.650669	−	0.759361i	$-0.725511\pi$
$331$	−23.6758	−1.30134	−0.650669	+	0.759361i	$0.725511\pi$
$332$	5.03338	0.276243
$333$	−5.03190	−0.275746
$334$	1.84329	0.100860
$335$	0.302479	0.0165262
$336$	−9.43867	−0.514922
$337$	−9.82756	−0.535342	−0.267671	−	0.963510i	$-0.586254\pi$
$337$	−9.82756	−0.535342	−0.267671	+	0.963510i	$0.586254\pi$
$338$	11.9436	0.649646
$339$	−15.3548	−0.833958
$340$	−4.73092	−0.256570
$341$	1.61240	0.0873165
$342$	2.65782	0.143718
$343$	1.00000	0.0539949
$344$	−4.77163	−0.257269
$345$	28.2982	1.52352
$346$	7.50878	0.403675
$347$	−3.58325	−0.192359	−0.0961795	−	0.995364i	$-0.530662\pi$
$347$	−3.58325	−0.192359	−0.0961795	+	0.995364i	$0.530662\pi$
$348$	−7.04046	−0.377408
$349$	−22.0357	−1.17954	−0.589771	−	0.807570i	$-0.700782\pi$
$349$	−22.0357	−1.17954	−0.589771	+	0.807570i	$0.700782\pi$
$350$	−16.5994	−0.887277
$351$	−11.3149	−0.603946
$352$	−2.64197	−0.140817
$353$	13.7125	0.729841	0.364921	−	0.931039i	$-0.381096\pi$
$353$	13.7125	0.729841	0.364921	+	0.931039i	$0.381096\pi$
$354$	−27.7073	−1.47262
$355$	−34.7565	−1.84468
$356$	3.05859	0.162105
$357$	−10.9092	−0.577377
$358$	24.3655	1.28776
$359$	−11.6107	−0.612791	−0.306395	−	0.951904i	$-0.599123\pi$
$359$	−11.6107	−0.612791	−0.306395	+	0.951904i	$0.599123\pi$
$360$	−63.4170	−3.34237
$361$	−18.8366	−0.991402
$362$	−26.6799	−1.40226
$363$	−23.8065	−1.24952
$364$	0.573976	0.0300845
$365$	−15.9522	−0.834976
$366$	33.4078	1.74626
$367$	−0.638755	−0.0333427	−0.0166714	−	0.999861i	$-0.505307\pi$
$367$	−0.638755	−0.0333427	−0.0166714	+	0.999861i	$0.505307\pi$
$368$	7.90392	0.412020
$369$	−42.0925	−2.19125
$370$	−5.49842	−0.285849
$371$	0.319947	0.0166108
$372$	−0.827869	−0.0429230
$373$	6.92244	0.358431	0.179215	−	0.983810i	$-0.442644\pi$
$373$	6.92244	0.358431	0.179215	+	0.983810i	$0.442644\pi$
$374$	8.11125	0.419423
$375$	−91.8348	−4.74233
$376$	6.88727	0.355184
$377$	−16.7102	−0.860617
$378$	−7.52558	−0.387074
$379$	−10.8228	−0.555928	−0.277964	−	0.960592i	$-0.589660\pi$
$379$	−10.8228	−0.555928	−0.277964	+	0.960592i	$0.589660\pi$
$380$	−0.496736	−0.0254820
$381$	12.7968	0.655599
$382$	26.8504	1.37379
$383$	29.2735	1.49580	0.747902	−	0.663809i	$-0.231061\pi$
$383$	29.2735	1.49580	0.747902	+	0.663809i	$0.231061\pi$
$384$	−23.3136	−1.18972
$385$	−6.78394	−0.345742
$386$	−16.0475	−0.816799
$387$	−8.01554	−0.407453
$388$	1.38495	0.0703101
$389$	−15.8961	−0.805964	−0.402982	−	0.915208i	$-0.632026\pi$
$389$	−15.8961	−0.805964	−0.402982	+	0.915208i	$0.632026\pi$
$390$	−30.6188	−1.55044
$391$	9.13536	0.461995
$392$	2.99547	0.151294
$393$	−17.1297	−0.864077
$394$	14.9351	0.752419
$395$	−34.5504	−1.73842
$396$	−2.37005	−0.119100
$397$	5.65600	0.283867	0.141933	−	0.989876i	$-0.454668\pi$
$397$	5.65600	0.283867	0.141933	+	0.989876i	$0.454668\pi$
$398$	13.3704	0.670198
$399$	−1.14544	−0.0573439
$400$	−42.3025	−2.11512
$401$	26.5321	1.32495	0.662476	−	0.749083i	$-0.269506\pi$
$401$	26.5321	1.32495	0.662476	+	0.749083i	$0.269506\pi$
$402$	0.266272	0.0132804
$403$	−1.96490	−0.0978788
$404$	−1.98912	−0.0989622
$405$	−5.15098	−0.255954
$406$	−11.1140	−0.551577
$407$	−1.61240	−0.0799239
$408$	−32.6783	−1.61782
$409$	−9.33178	−0.461427	−0.230713	−	0.973022i	$-0.574106\pi$
$409$	−9.33178	−0.461427	−0.230713	+	0.973022i	$0.574106\pi$
$410$	−45.9950	−2.27153
$411$	15.9115	0.784856
$412$	−0.0241932	−0.00119191
$413$	7.48092	0.368112
$414$	15.6064	0.767011
$415$	72.4963	3.55870
$416$	3.21955	0.157851
$417$	17.9236	0.877724
$418$	0.851662	0.0416562
$419$	−32.7038	−1.59769	−0.798843	−	0.601539i	$-0.794554\pi$
$419$	−32.7038	−1.59769	−0.798843	+	0.601539i	$0.794554\pi$
$420$	3.48313	0.169959
$421$	−19.4105	−0.946007	−0.473004	−	0.881060i	$-0.656830\pi$
$421$	−19.4105	−0.946007	−0.473004	+	0.881060i	$0.656830\pi$
$422$	−14.2661	−0.694465
$423$	11.5695	0.562526
$424$	0.958395	0.0465438
$425$	−48.8932	−2.37167
$426$	−30.5961	−1.48238
$427$	−9.02007	−0.436512
$428$	0.586410	0.0283452
$429$	−8.97892	−0.433506
$430$	−8.75868	−0.422381
$431$	−21.6679	−1.04370	−0.521852	−	0.853036i	$-0.674759\pi$
$431$	−21.6679	−1.04370	−0.521852	+	0.853036i	$0.674759\pi$
$432$	−19.1784	−0.922720
$433$	0.234935	0.0112903	0.00564513	−	0.999984i	$-0.498203\pi$
$433$	0.234935	0.0112903	0.00564513	+	0.999984i	$0.498203\pi$
$434$	−1.30686	−0.0627313
$435$	−101.404	−4.86197
$436$	−0.347863	−0.0166596
$437$	0.959191	0.0458843
$438$	−14.0427	−0.670986
$439$	−29.8434	−1.42435	−0.712174	−	0.702003i	$-0.752289\pi$
$439$	−29.8434	−1.42435	−0.712174	+	0.702003i	$0.752289\pi$
$440$	−20.3211	−0.968771
$441$	5.03190	0.239614
$442$	−9.88451	−0.470158
$443$	−20.3131	−0.965103	−0.482552	−	0.875868i	$-0.660290\pi$
$443$	−20.3131	−0.965103	−0.482552	+	0.875868i	$0.660290\pi$
$444$	0.827869	0.0392889
$445$	44.0532	2.08832
$446$	20.9448	0.991765
$447$	45.9179	2.17184
$448$	8.80221	0.415865
$449$	−8.57555	−0.404705	−0.202353	−	0.979313i	$-0.564859\pi$
$449$	−8.57555	−0.404705	−0.202353	+	0.979313i	$0.564859\pi$
$450$	−83.5266	−3.93748
$451$	−13.4880	−0.635124
$452$	1.58266	0.0744421
$453$	−10.6203	−0.498986
$454$	24.4183	1.14601
$455$	8.26703	0.387564
$456$	−3.43114	−0.160678
$457$	10.1275	0.473743	0.236872	−	0.971541i	$-0.423878\pi$
$457$	10.1275	0.473743	0.236872	+	0.971541i	$0.423878\pi$
$458$	−26.3212	−1.22991
$459$	−22.1664	−1.03464
$460$	−2.91677	−0.135995
$461$	−21.4927	−1.00102	−0.500508	−	0.865732i	$-0.666853\pi$
$461$	−21.4927	−1.00102	−0.500508	+	0.865732i	$0.666853\pi$
$462$	−5.97189	−0.277838
$463$	33.7516	1.56857	0.784285	−	0.620401i	$-0.213030\pi$
$463$	33.7516	1.56857	0.784285	+	0.620401i	$0.213030\pi$
$464$	−28.3231	−1.31487
$465$	−11.9239	−0.552956
$466$	−12.9402	−0.599443
$467$	−4.78840	−0.221581	−0.110790	−	0.993844i	$-0.535338\pi$
$467$	−4.78840	−0.221581	−0.110790	+	0.993844i	$0.535338\pi$
$468$	2.88819	0.133507
$469$	−0.0718931	−0.00331971
$470$	12.6421	0.583136
$471$	−9.33832	−0.430287
$472$	22.4089	1.03145
$473$	−2.56847	−0.118098
$474$	−30.4147	−1.39699
$475$	−5.13367	−0.235549
$476$	1.12444	0.0515388
$477$	1.60994	0.0737142
$478$	24.7262	1.13095
$479$	−23.2098	−1.06048	−0.530240	−	0.847847i	$-0.677898\pi$
$479$	−23.2098	−1.06048	−0.530240	+	0.847847i	$0.677898\pi$
$480$	19.5376	0.891764
$481$	1.96490	0.0895919
$482$	−19.4999	−0.888195
$483$	−6.72589	−0.306039
$484$	2.45381	0.111537
$485$	19.9475	0.905771
$486$	18.0423	0.818416
$487$	5.82478	0.263946	0.131973	−	0.991253i	$-0.457869\pi$
$487$	5.82478	0.263946	0.131973	+	0.991253i	$0.457869\pi$
$488$	−27.0194	−1.22311
$489$	−2.13282	−0.0964493
$490$	5.49842	0.248393
$491$	23.9840	1.08238	0.541190	−	0.840900i	$-0.317974\pi$
$491$	23.9840	1.08238	0.541190	+	0.840900i	$0.317974\pi$
$492$	6.92524	0.312214
$493$	−32.7359	−1.47435
$494$	−1.03785	−0.0466951
$495$	−34.1361	−1.53430
$496$	−3.33044	−0.149541
$497$	8.26090	0.370552
$498$	63.8184	2.85977
$499$	−43.6860	−1.95565	−0.977826	−	0.209418i	$-0.932843\pi$
$499$	−43.6860	−1.95565	−0.977826	+	0.209418i	$0.932843\pi$
$500$	9.46567	0.423317
$501$	−3.99736	−0.178589
$502$	37.7370	1.68428
$503$	20.0480	0.893897	0.446948	−	0.894560i	$-0.352511\pi$
$503$	20.0480	0.893897	0.446948	+	0.894560i	$0.352511\pi$
$504$	15.0729	0.671401
$505$	−28.6494	−1.27488
$506$	5.00085	0.222315
$507$	−25.9009	−1.15030
$508$	−1.31900	−0.0585212
$509$	−37.0481	−1.64213	−0.821064	−	0.570837i	$-0.806619\pi$
$509$	−37.0481	−1.64213	−0.821064	+	0.570837i	$0.806619\pi$
$510$	−59.9834	−2.65611
$511$	3.79151	0.167727
$512$	25.4095	1.12295
$513$	−2.32742	−0.102758
$514$	13.0056	0.573653
$515$	−0.348456	−0.0153548
$516$	1.31875	0.0580548
$517$	3.70728	0.163046
$518$	1.30686	0.0574202
$519$	−16.2836	−0.714769
$520$	24.7637	1.08596
$521$	−39.9158	−1.74874	−0.874371	−	0.485259i	$-0.838725\pi$
$521$	−39.9158	−1.74874	−0.874371	+	0.485259i	$0.838725\pi$
$522$	−55.9243	−2.44774
$523$	−6.73392	−0.294454	−0.147227	−	0.989103i	$-0.547035\pi$
$523$	−6.73392	−0.294454	−0.147227	+	0.989103i	$0.547035\pi$
$524$	1.76560	0.0771306
$525$	35.9976	1.57106
$526$	−10.3356	−0.450652
$527$	−3.84933	−0.167679
$528$	−15.2189	−0.662319
$529$	−17.3678	−0.755120
$530$	1.75920	0.0764150
$531$	37.6432	1.63358
$532$	0.118064	0.00511872
$533$	16.4367	0.711952
$534$	38.7800	1.67817
$535$	8.44611	0.365157
$536$	−0.215354	−0.00930187
$537$	−52.8391	−2.28018
$538$	−19.5621	−0.843383
$539$	1.61240	0.0694511
$540$	7.07736	0.304561
$541$	15.0535	0.647199	0.323599	−	0.946194i	$-0.395107\pi$
$541$	15.0535	0.647199	0.323599	+	0.946194i	$0.395107\pi$
$542$	34.9186	1.49988
$543$	57.8580	2.48293
$544$	6.30722	0.270420
$545$	−5.01031	−0.214618
$546$	7.27746	0.311446
$547$	−22.3704	−0.956489	−0.478244	−	0.878227i	$-0.658727\pi$
$547$	−22.3704	−0.956489	−0.478244	+	0.878227i	$0.658727\pi$
$548$	−1.64004	−0.0700590
$549$	−45.3880	−1.93711
$550$	−26.7650	−1.14126
$551$	−3.43719	−0.146429
$552$	−20.1472	−0.857523
$553$	8.21193	0.349207
$554$	−30.0317	−1.27592
$555$	11.9239	0.506140
$556$	−1.84744	−0.0783488
$557$	−29.6795	−1.25756	−0.628780	−	0.777584i	$-0.716445\pi$
$557$	−29.6795	−1.25756	−0.628780	+	0.777584i	$0.716445\pi$
$558$	−6.57599	−0.278384
$559$	3.12998	0.132384
$560$	14.0123	0.592128
$561$	−17.5901	−0.742653
$562$	42.8221	1.80634
$563$	17.0109	0.716923	0.358461	−	0.933545i	$-0.383301\pi$
$563$	17.0109	0.716923	0.358461	+	0.933545i	$0.383301\pi$
$564$	−1.90346	−0.0801500
$565$	22.7952	0.959001
$566$	−25.5802	−1.07521
$567$	1.22428	0.0514151
$568$	24.7453	1.03829
$569$	7.78701	0.326448	0.163224	−	0.986589i	$-0.447811\pi$
$569$	7.78701	0.326448	0.163224	+	0.986589i	$0.447811\pi$
$570$	−6.29812	−0.263799
$571$	40.2891	1.68605	0.843024	−	0.537876i	$-0.180773\pi$
$571$	40.2891	1.68605	0.843024	+	0.537876i	$0.180773\pi$
$572$	0.925481	0.0386963
$573$	−58.2279	−2.43251
$574$	10.9321	0.456296
$575$	−30.1443	−1.25710
$576$	44.2918	1.84549
$577$	−47.5943	−1.98138	−0.990689	−	0.136147i	$-0.956528\pi$
$577$	−47.5943	−1.98138	−0.990689	+	0.136147i	$0.956528\pi$
$578$	2.85248	0.118647
$579$	34.8007	1.44627
$580$	10.4520	0.433997
$581$	−17.2309	−0.714857
$582$	17.5598	0.727877
$583$	0.515884	0.0213657
$584$	11.3574	0.469971
$585$	41.5988	1.71990
$586$	34.1318	1.40997
$587$	18.0585	0.745356	0.372678	−	0.927961i	$-0.378440\pi$
$587$	18.0585	0.745356	0.372678	+	0.927961i	$0.378440\pi$
$588$	−0.827869	−0.0341408
$589$	−0.404170	−0.0166535
$590$	41.1332	1.69343
$591$	−32.3882	−1.33227
$592$	3.33044	0.136880
$593$	−23.6887	−0.972780	−0.486390	−	0.873742i	$-0.661687\pi$
$593$	−23.6887	−0.972780	−0.486390	+	0.873742i	$0.661687\pi$
$594$	−12.1343	−0.497875
$595$	16.1954	0.663949
$596$	−4.73288	−0.193866
$597$	−28.9951	−1.18669
$598$	−6.09413	−0.249207
$599$	14.8610	0.607204	0.303602	−	0.952799i	$-0.401811\pi$
$599$	14.8610	0.607204	0.303602	+	0.952799i	$0.401811\pi$
$600$	107.830	4.40213
$601$	11.1934	0.456586	0.228293	−	0.973592i	$-0.426686\pi$
$601$	11.1934	0.456586	0.228293	+	0.973592i	$0.426686\pi$
$602$	2.08176	0.0848461
$603$	−0.361758	−0.0147319
$604$	1.09466	0.0445413
$605$	35.3424	1.43687
$606$	−25.2200	−1.02449
$607$	7.32076	0.297141	0.148570	−	0.988902i	$-0.452533\pi$
$607$	7.32076	0.297141	0.148570	+	0.988902i	$0.452533\pi$
$608$	0.662244	0.0268575
$609$	24.1017	0.976652
$610$	−49.5961	−2.00809
$611$	−4.51775	−0.182769
$612$	5.65808	0.228714
$613$	−31.2403	−1.26178	−0.630892	−	0.775871i	$-0.717311\pi$
$613$	−31.2403	−1.26178	−0.630892	+	0.775871i	$0.717311\pi$
$614$	−18.0616	−0.728907
$615$	99.7448	4.02210
$616$	4.82991	0.194603
$617$	16.3654	0.658847	0.329424	−	0.944182i	$-0.393146\pi$
$617$	16.3654	0.658847	0.329424	+	0.944182i	$0.393146\pi$
$618$	−0.306746	−0.0123391
$619$	21.2330	0.853428	0.426714	−	0.904387i	$-0.359671\pi$
$619$	21.2330	0.853428	0.426714	+	0.904387i	$0.359671\pi$
$620$	1.22903	0.0493589
$621$	−13.6663	−0.548410
$622$	−5.62571	−0.225570
$623$	−10.4705	−0.419493
$624$	18.5461	0.742437
$625$	72.8260	2.91304
$626$	6.35187	0.253872
$627$	−1.84692	−0.0737587
$628$	0.962526	0.0384090
$629$	3.84933	0.153483
$630$	27.6675	1.10230
$631$	−21.4747	−0.854896	−0.427448	−	0.904040i	$-0.640587\pi$
$631$	−21.4747	−0.854896	−0.427448	+	0.904040i	$0.640587\pi$
$632$	24.5986	0.978481
$633$	30.9376	1.22966
$634$	−24.5939	−0.976750
$635$	−18.9977	−0.753899
$636$	−0.264875	−0.0105030
$637$	−1.96490	−0.0778523
$638$	−17.9202	−0.709467
$639$	41.5680	1.64440
$640$	34.6105	1.36810
$641$	−0.668724	−0.0264130	−0.0132065	−	0.999913i	$-0.504204\pi$
$641$	−0.668724	−0.0264130	−0.0132065	+	0.999913i	$0.504204\pi$
$642$	7.43510	0.293440
$643$	−13.0113	−0.513116	−0.256558	−	0.966529i	$-0.582588\pi$
$643$	−13.0113	−0.513116	−0.256558	+	0.966529i	$0.582588\pi$
$644$	0.693256	0.0273181
$645$	18.9941	0.747891
$646$	−2.03319	−0.0799949
$647$	−26.5798	−1.04496	−0.522480	−	0.852652i	$-0.674993\pi$
$647$	−26.5798	−1.04496	−0.522480	+	0.852652i	$0.674993\pi$
$648$	3.66731	0.144066
$649$	12.0623	0.473485
$650$	32.6163	1.27932
$651$	2.83406	0.111076
$652$	0.219835	0.00860941
$653$	−4.33419	−0.169610	−0.0848050	−	0.996398i	$-0.527027\pi$
$653$	−4.33419	−0.169610	−0.0848050	+	0.996398i	$0.527027\pi$
$654$	−4.41057	−0.172467
$655$	25.4301	0.993636
$656$	27.8596	1.08773
$657$	19.0785	0.744322
$658$	−3.00477	−0.117138
$659$	0.212323	0.00827095	0.00413547	−	0.999991i	$-0.498684\pi$
$659$	0.212323	0.00827095	0.00413547	+	0.999991i	$0.498684\pi$
$660$	5.61622	0.218611
$661$	−20.6938	−0.804894	−0.402447	−	0.915443i	$-0.631840\pi$
$661$	−20.6938	−0.804894	−0.402447	+	0.915443i	$0.631840\pi$
$662$	30.9409	1.20255
$663$	21.4356	0.832488
$664$	−51.6147	−2.00304
$665$	1.70048	0.0659419
$666$	6.57599	0.254814
$667$	−20.1827	−0.781479
$668$	0.412019	0.0159415
$669$	−45.4209	−1.75607
$670$	−0.395298	−0.0152717
$671$	−14.5440	−0.561464
$672$	−4.64368	−0.179134
$673$	34.4101	1.32641	0.663205	−	0.748438i	$-0.269196\pi$
$673$	34.4101	1.32641	0.663205	+	0.748438i	$0.269196\pi$
$674$	12.8433	0.494704
$675$	73.1433	2.81529
$676$	2.66968	0.102680
$677$	−11.7250	−0.450628	−0.225314	−	0.974286i	$-0.572341\pi$
$677$	−11.7250	−0.450628	−0.225314	+	0.974286i	$0.572341\pi$
$678$	20.0666	0.770653
$679$	−4.74112	−0.181947
$680$	48.5130	1.86039
$681$	−52.9536	−2.02918
$682$	−2.10719	−0.0806884
$683$	−0.108015	−0.00413309	−0.00206654	−	0.999998i	$-0.500658\pi$
$683$	−0.108015	−0.00413309	−0.00206654	+	0.999998i	$0.500658\pi$
$684$	0.594085	0.0227154
$685$	−23.6216	−0.902536
$686$	−1.30686	−0.0498962
$687$	57.0802	2.17774
$688$	5.30521	0.202259
$689$	−0.628666	−0.0239503
$690$	−36.9818	−1.40787
$691$	21.9446	0.834810	0.417405	−	0.908721i	$-0.362940\pi$
$691$	21.9446	0.834810	0.417405	+	0.908721i	$0.362940\pi$
$692$	1.67839	0.0638028
$693$	8.11344	0.308204
$694$	4.68281	0.177757
$695$	−26.6088	−1.00933
$696$	72.1962	2.73659
$697$	32.2001	1.21967
$698$	28.7976	1.09000
$699$	28.0621	1.06141
$700$	−3.71037	−0.140239
$701$	−22.4640	−0.848454	−0.424227	−	0.905556i	$-0.639454\pi$
$701$	−22.4640	−0.848454	−0.424227	+	0.905556i	$0.639454\pi$
$702$	14.7870	0.558100
$703$	0.404170	0.0152436
$704$	14.1927	0.534908
$705$	−27.4157	−1.03253
$706$	−17.9203	−0.674439
$707$	6.80938	0.256093
$708$	−6.19323	−0.232756
$709$	30.7626	1.15531	0.577657	−	0.816279i	$-0.303967\pi$
$709$	30.7626	1.15531	0.577657	+	0.816279i	$0.303967\pi$
$710$	45.4219	1.70465
$711$	41.3216	1.54968
$712$	−31.3642	−1.17542
$713$	−2.37324	−0.0888784
$714$	14.2568	0.533549
$715$	13.3298	0.498506
$716$	5.44627	0.203537
$717$	−53.6213	−2.00252
$718$	15.1736	0.566274
$719$	−11.4906	−0.428526	−0.214263	−	0.976776i	$-0.568735\pi$
$719$	−11.4906	−0.428526	−0.214263	+	0.976776i	$0.568735\pi$
$720$	70.5085	2.62770
$721$	0.0828209	0.00308441
$722$	24.6169	0.916145
$723$	42.2874	1.57269
$724$	−5.96359	−0.221635
$725$	108.020	4.01175
$726$	31.1118	1.15467
$727$	−16.8376	−0.624470	−0.312235	−	0.950005i	$-0.601078\pi$
$727$	−16.8376	−0.624470	−0.312235	+	0.950005i	$0.601078\pi$
$728$	−5.88582	−0.218143
$729$	−42.7994	−1.58516
$730$	20.8473	0.771593
$731$	6.13177	0.226792
$732$	7.46744	0.276004
$733$	−8.50930	−0.314298	−0.157149	−	0.987575i	$-0.550230\pi$
$733$	−8.50930	−0.314298	−0.157149	+	0.987575i	$0.550230\pi$
$734$	0.834764	0.0308117
$735$	−11.9239	−0.439819
$736$	3.88861	0.143336
$737$	−0.115921	−0.00426999
$738$	55.0090	2.02491
$739$	−46.7400	−1.71936	−0.859679	−	0.510835i	$-0.829336\pi$
$739$	−46.7400	−1.71936	−0.859679	+	0.510835i	$0.829336\pi$
$740$	−1.22903	−0.0451799
$741$	2.25068	0.0826809
$742$	−0.418127	−0.0153499
$743$	−2.01368	−0.0738747	−0.0369374	−	0.999318i	$-0.511760\pi$
$743$	−2.01368	−0.0738747	−0.0369374	+	0.999318i	$0.511760\pi$
$744$	8.48935	0.311235
$745$	−68.1681	−2.49749
$746$	−9.04667	−0.331222
$747$	−86.7040	−3.17233
$748$	1.81306	0.0662919
$749$	−2.00747	−0.0733513
$750$	120.015	4.38234
$751$	18.8114	0.686439	0.343219	−	0.939255i	$-0.388483\pi$
$751$	18.8114	0.686439	0.343219	+	0.939255i	$0.388483\pi$
$752$	−7.65743	−0.279238
$753$	−81.8365	−2.98229
$754$	21.8379	0.795288
$755$	15.7666	0.573804
$756$	−1.68214	−0.0611790
$757$	32.8154	1.19270	0.596348	−	0.802726i	$-0.296618\pi$
$757$	32.8154	1.19270	0.596348	+	0.802726i	$0.296618\pi$
$758$	14.1438	0.513728
$759$	−10.8448	−0.393643
$760$	5.09376	0.184770
$761$	−6.28972	−0.228002	−0.114001	−	0.993481i	$-0.536367\pi$
$761$	−6.28972	−0.228002	−0.114001	+	0.993481i	$0.536367\pi$
$762$	−16.7236	−0.605833
$763$	1.19085	0.0431116
$764$	6.00171	0.217134
$765$	81.4938	2.94641
$766$	−38.2563	−1.38226
$767$	−14.6993	−0.530761
$768$	−19.4244	−0.700917
$769$	−18.0809	−0.652014	−0.326007	−	0.945367i	$-0.605703\pi$
$769$	−18.0809	−0.652014	−0.326007	+	0.945367i	$0.605703\pi$
$770$	8.86567	0.319496
$771$	−28.2040	−1.01574
$772$	−3.58701	−0.129099
$773$	−5.97060	−0.214748	−0.107374	−	0.994219i	$-0.534244\pi$
$773$	−5.97060	−0.214748	−0.107374	+	0.994219i	$0.534244\pi$
$774$	10.4752	0.376523
$775$	12.7018	0.456261
$776$	−14.2019	−0.509819
$777$	−2.83406	−0.101671
$778$	20.7740	0.744783
$779$	3.38094	0.121135
$780$	−6.84402	−0.245055
$781$	13.3199	0.476623
$782$	−11.9386	−0.426925
$783$	48.9722	1.75012
$784$	−3.33044	−0.118944
$785$	13.8633	0.494804
$786$	22.3861	0.798485
$787$	14.9337	0.532330	0.266165	−	0.963927i	$-0.414243\pi$
$787$	14.9337	0.532330	0.266165	+	0.963927i	$0.414243\pi$
$788$	3.33834	0.118924
$789$	22.4137	0.797949
$790$	45.1526	1.60646
$791$	−5.41795	−0.192640
$792$	24.3036	0.863592
$793$	17.7236	0.629382
$794$	−7.39161	−0.262318
$795$	−3.81501	−0.135305
$796$	2.98860	0.105928
$797$	−43.5616	−1.54303	−0.771516	−	0.636210i	$-0.780501\pi$
$797$	−43.5616	−1.54303	−0.771516	+	0.636210i	$0.780501\pi$
$798$	1.49693	0.0529909
$799$	−8.85046	−0.313107
$800$	−20.8122	−0.735821
$801$	−52.6866	−1.86159
$802$	−34.6738	−1.22438
$803$	6.11344	0.215739
$804$	0.0595181	0.00209904
$805$	9.98502	0.351926
$806$	2.56786	0.0904489
$807$	42.4224	1.49334
$808$	20.3973	0.717575
$809$	−17.5470	−0.616921	−0.308461	−	0.951237i	$-0.599814\pi$
$809$	−17.5470	−0.616921	−0.308461	+	0.951237i	$0.599814\pi$
$810$	6.73162	0.236525
$811$	−48.4696	−1.70200	−0.850998	−	0.525168i	$-0.824002\pi$
$811$	−48.4696	−1.70200	−0.850998	+	0.525168i	$0.824002\pi$
$812$	−2.48423	−0.0871795
$813$	−75.7246	−2.65578
$814$	2.10719	0.0738569
$815$	3.16630	0.110911
$816$	36.3325	1.27189
$817$	0.643821	0.0225245
$818$	12.1953	0.426400
$819$	−9.88719	−0.345486
$820$	−10.2810	−0.359027
$821$	36.1575	1.26190	0.630952	−	0.775821i	$-0.282664\pi$
$821$	36.1575	1.26190	0.630952	+	0.775821i	$0.282664\pi$
$822$	−20.7941	−0.725278
$823$	41.9606	1.46265	0.731327	−	0.682028i	$-0.238902\pi$
$823$	41.9606	1.46265	0.731327	+	0.682028i	$0.238902\pi$
$824$	0.248088	0.00864255
$825$	58.0426	2.02078
$826$	−9.77653	−0.340169
$827$	−26.8535	−0.933787	−0.466893	−	0.884314i	$-0.654627\pi$
$827$	−26.8535	−0.933787	−0.466893	+	0.884314i	$0.654627\pi$
$828$	3.48839	0.121230
$829$	31.7872	1.10401	0.552007	−	0.833839i	$-0.313862\pi$
$829$	31.7872	1.10401	0.552007	+	0.833839i	$0.313862\pi$
$830$	−94.7425	−3.28856
$831$	65.1268	2.25922
$832$	−17.2955	−0.599613
$833$	−3.84933	−0.133371
$834$	−23.4237	−0.811096
$835$	5.93434	0.205366
$836$	0.190367	0.00658397
$837$	5.75851	0.199043
$838$	42.7394	1.47641
$839$	28.6722	0.989876	0.494938	−	0.868928i	$-0.335191\pi$
$839$	28.6722	0.989876	0.494938	+	0.868928i	$0.335191\pi$
$840$	−35.7177	−1.23238
$841$	43.3234	1.49391
$842$	25.3668	0.874196
$843$	−92.8640	−3.19840
$844$	−3.18882	−0.109764
$845$	38.4516	1.32277
$846$	−15.1197	−0.519825
$847$	−8.40016	−0.288633
$848$	−1.06557	−0.0365917
$849$	55.4731	1.90383
$850$	63.8966	2.19164
$851$	2.37324	0.0813535
$852$	−6.83894	−0.234298
$853$	−39.3353	−1.34682	−0.673408	−	0.739271i	$-0.735170\pi$
$853$	−39.3353	−1.34682	−0.673408	+	0.739271i	$0.735170\pi$
$854$	11.7880	0.403376
$855$	8.55666	0.292632
$856$	−6.01332	−0.205531
$857$	18.1128	0.618722	0.309361	−	0.950945i	$-0.399885\pi$
$857$	18.1128	0.618722	0.309361	+	0.950945i	$0.399885\pi$
$858$	11.7342	0.400599
$859$	11.9701	0.408414	0.204207	−	0.978928i	$-0.434538\pi$
$859$	11.9701	0.408414	0.204207	+	0.978928i	$0.434538\pi$
$860$	−1.95777	−0.0667595
$861$	−23.7073	−0.807943
$862$	28.3169	0.964477
$863$	−52.2789	−1.77960	−0.889798	−	0.456355i	$-0.849155\pi$
$863$	−52.2789	−1.77960	−0.889798	+	0.456355i	$0.849155\pi$
$864$	−9.43547	−0.321001
$865$	24.1740	0.821941
$866$	−0.307028	−0.0104332
$867$	−6.18588	−0.210084
$868$	−0.292114	−0.00991500
$869$	13.2409	0.449168
$870$	132.521	4.49290
$871$	0.141263	0.00478651
$872$	3.56715	0.120799
$873$	−23.8568	−0.807431
$874$	−1.25353	−0.0424013
$875$	−32.4040	−1.09545
$876$	−3.13887	−0.106053
$877$	27.6034	0.932101	0.466050	−	0.884758i	$-0.345677\pi$
$877$	27.6034	0.932101	0.466050	+	0.884758i	$0.345677\pi$
$878$	39.0012	1.31623
$879$	−74.0182	−2.49657
$880$	22.5935	0.761627
$881$	−6.11206	−0.205920	−0.102960	−	0.994685i	$-0.532831\pi$
$881$	−6.11206	−0.205920	−0.102960	+	0.994685i	$0.532831\pi$
$882$	−6.57599	−0.221425
$883$	−44.5051	−1.49772	−0.748858	−	0.662731i	$-0.769397\pi$
$883$	−44.5051	−1.49772	−0.748858	+	0.662731i	$0.769397\pi$
$884$	−2.20942	−0.0743109
$885$	−89.2016	−2.99848
$886$	26.5464	0.891842
$887$	34.4230	1.15581	0.577906	−	0.816104i	$-0.303870\pi$
$887$	34.4230	1.15581	0.577906	+	0.816104i	$0.303870\pi$
$888$	−8.48935	−0.284884
$889$	4.51536	0.151440
$890$	−57.5714	−1.92980
$891$	1.97404	0.0661328
$892$	4.68166	0.156754
$893$	−0.929278	−0.0310971
$894$	−60.0083	−2.00698
$895$	78.4431	2.62206
$896$	−8.22621	−0.274818
$897$	13.2157	0.441260
$898$	11.2071	0.373984
$899$	8.50432	0.283635
$900$	−18.6702	−0.622339
$901$	−1.23158	−0.0410299
$902$	17.6269	0.586912
$903$	−4.51450	−0.150233
$904$	−16.2293	−0.539780
$905$	−85.8940	−2.85521
$906$	13.8793	0.461108
$907$	9.25279	0.307234	0.153617	−	0.988130i	$-0.450908\pi$
$907$	9.25279	0.307234	0.153617	+	0.988130i	$0.450908\pi$
$908$	5.45807	0.181132
$909$	34.2641	1.13647
$910$	−10.8039	−0.358144
$911$	47.9986	1.59027	0.795133	−	0.606435i	$-0.207401\pi$
$911$	47.9986	1.59027	0.795133	+	0.606435i	$0.207401\pi$
$912$	3.81483	0.126322
$913$	−27.7831	−0.919487
$914$	−13.2352	−0.437782
$915$	107.554	3.55563
$916$	−5.88341	−0.194393
$917$	−6.04421	−0.199598
$918$	28.9684	0.956099
$919$	11.9796	0.395170	0.197585	−	0.980286i	$-0.436690\pi$
$919$	11.9796	0.395170	0.197585	+	0.980286i	$0.436690\pi$
$920$	29.9099	0.986100
$921$	39.1684	1.29064
$922$	28.0880	0.925029
$923$	−16.2319	−0.534278
$924$	−1.33486	−0.0439136
$925$	−12.7018	−0.417631
$926$	−44.1087	−1.44950
$927$	0.416746	0.0136877
$928$	−13.9345	−0.457424
$929$	5.71244	0.187419	0.0937095	−	0.995600i	$-0.470127\pi$
$929$	5.71244	0.187419	0.0937095	+	0.995600i	$0.470127\pi$
$930$	15.5828	0.510982
$931$	−0.404170	−0.0132461
$932$	−2.89244	−0.0947451
$933$	12.1999	0.399407
$934$	6.25778	0.204761
$935$	26.1136	0.854006
$936$	−29.6168	−0.968056
$937$	31.7723	1.03796	0.518978	−	0.854788i	$-0.326313\pi$
$937$	31.7723	1.03796	0.518978	+	0.854788i	$0.326313\pi$
$938$	0.0939543	0.00306772
$939$	−13.7747	−0.449520
$940$	2.82581	0.0921676
$941$	52.8932	1.72427	0.862135	−	0.506679i	$-0.169127\pi$
$941$	52.8932	1.72427	0.862135	+	0.506679i	$0.169127\pi$
$942$	12.2039	0.397624
$943$	19.8524	0.646484
$944$	−24.9148	−0.810907
$945$	−24.2281	−0.788139
$946$	3.35663	0.109134
$947$	13.8043	0.448580	0.224290	−	0.974522i	$-0.427994\pi$
$947$	13.8043	0.448580	0.224290	+	0.974522i	$0.427994\pi$
$948$	−6.79841	−0.220802
$949$	−7.44995	−0.241836
$950$	6.70900	0.217669
$951$	53.3344	1.72949
$952$	−11.5306	−0.373708
$953$	−27.6143	−0.894515	−0.447257	−	0.894405i	$-0.647599\pi$
$953$	−27.6143	−0.894515	−0.447257	+	0.894405i	$0.647599\pi$
$954$	−2.10397	−0.0681186
$955$	86.4431	2.79723
$956$	5.52689	0.178753
$957$	38.8617	1.25622
$958$	30.3319	0.979980
$959$	5.61438	0.181298
$960$	−104.956	−3.38745
$961$	1.00000	0.0322581
$962$	−2.56786	−0.0827910
$963$	−10.1014	−0.325512
$964$	−4.35868	−0.140384
$965$	−51.6639	−1.66312
$966$	8.78980	0.282807
$967$	12.4011	0.398792	0.199396	−	0.979919i	$-0.436102\pi$
$967$	12.4011	0.398792	0.199396	+	0.979919i	$0.436102\pi$
$968$	−25.1625	−0.808752
$969$	4.40918	0.141643
$970$	−26.0687	−0.837014
$971$	−37.4951	−1.20327	−0.601637	−	0.798769i	$-0.705485\pi$
$971$	−37.4951	−1.20327	−0.601637	+	0.798769i	$0.705485\pi$
$972$	4.03288	0.129355
$973$	6.32437	0.202750
$974$	−7.61218	−0.243910
$975$	−70.7317	−2.26523
$976$	30.0408	0.961583
$977$	46.0826	1.47431	0.737157	−	0.675721i	$-0.236168\pi$
$977$	46.0826	1.47431	0.737157	+	0.675721i	$0.236168\pi$
$978$	2.78729	0.0891278
$979$	−16.8827	−0.539574
$980$	1.22903	0.0392598
$981$	5.99222	0.191317
$982$	−31.3437	−1.00022
$983$	−57.5504	−1.83557	−0.917786	−	0.397075i	$-0.870025\pi$
$983$	−57.5504	−1.83557	−0.917786	+	0.397075i	$0.870025\pi$
$984$	−71.0146	−2.26386
$985$	48.0825	1.53203
$986$	42.7812	1.36243
$987$	6.51614	0.207411
$988$	−0.231984	−0.00738040
$989$	3.78044	0.120211
$990$	44.6111	1.41783
$991$	−1.80960	−0.0574838	−0.0287419	−	0.999587i	$-0.509150\pi$
$991$	−1.80960	−0.0574838	−0.0287419	+	0.999587i	$0.509150\pi$
$992$	−1.63853	−0.0520233
$993$	−67.0986	−2.12931
$994$	−10.7958	−0.342423
$995$	43.0451	1.36462
$996$	14.2649	0.452001
$997$	3.98255	0.126129	0.0630643	−	0.998009i	$-0.479913\pi$
$997$	3.98255	0.126129	0.0630643	+	0.998009i	$0.479913\pi$
$998$	57.0915	1.80720
$999$	−5.75851	−0.182191

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8029.2.a.d.1.19	✓	66

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8029.2.a.d.1.19	✓	66	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)

\(f(q)\)	\(=\)	\(q-1.30686 q^{2} +2.83406 q^{3} -0.292114 q^{4} -4.20735 q^{5} -3.70372 q^{6} +1.00000 q^{7} +2.99547 q^{8} +5.03190 q^{9} +O(q^{10})\)	\(q-1.30686 q^{2} +2.83406 q^{3} -0.292114 q^{4} -4.20735 q^{5} -3.70372 q^{6} +1.00000 q^{7} +2.99547 q^{8} +5.03190 q^{9} +5.49842 q^{10} +1.61240 q^{11} -0.827869 q^{12} -1.96490 q^{13} -1.30686 q^{14} -11.9239 q^{15} -3.33044 q^{16} -3.84933 q^{17} -6.57599 q^{18} -0.404170 q^{19} +1.22903 q^{20} +2.83406 q^{21} -2.10719 q^{22} -2.37324 q^{23} +8.48935 q^{24} +12.7018 q^{25} +2.56786 q^{26} +5.75851 q^{27} -0.292114 q^{28} +8.50432 q^{29} +15.5828 q^{30} +1.00000 q^{31} -1.63853 q^{32} +4.56965 q^{33} +5.03053 q^{34} -4.20735 q^{35} -1.46989 q^{36} -1.00000 q^{37} +0.528194 q^{38} -5.56865 q^{39} -12.6030 q^{40} -8.36514 q^{41} -3.70372 q^{42} -1.59295 q^{43} -0.471006 q^{44} -21.1709 q^{45} +3.10149 q^{46} +2.29922 q^{47} -9.43867 q^{48} +1.00000 q^{49} -16.5994 q^{50} -10.9092 q^{51} +0.573976 q^{52} +0.319947 q^{53} -7.52558 q^{54} -6.78394 q^{55} +2.99547 q^{56} -1.14544 q^{57} -11.1140 q^{58} +7.48092 q^{59} +3.48313 q^{60} -9.02007 q^{61} -1.30686 q^{62} +5.03190 q^{63} +8.80221 q^{64} +8.26703 q^{65} -5.97189 q^{66} -0.0718931 q^{67} +1.12444 q^{68} -6.72589 q^{69} +5.49842 q^{70} +8.26090 q^{71} +15.0729 q^{72} +3.79151 q^{73} +1.30686 q^{74} +35.9976 q^{75} +0.118064 q^{76} +1.61240 q^{77} +7.27746 q^{78} +8.21193 q^{79} +14.0123 q^{80} +1.22428 q^{81} +10.9321 q^{82} -17.2309 q^{83} -0.827869 q^{84} +16.1954 q^{85} +2.08176 q^{86} +24.1017 q^{87} +4.82991 q^{88} -10.4705 q^{89} +27.6675 q^{90} -1.96490 q^{91} +0.693256 q^{92} +2.83406 q^{93} -3.00477 q^{94} +1.70048 q^{95} -4.64368 q^{96} -4.74112 q^{97} -1.30686 q^{98} +8.11344 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 66 q - 5 q^{2} - 12 q^{3} + 63 q^{4} - 26 q^{5} - 19 q^{6} + 66 q^{7} - 15 q^{8} + 66 q^{9}+O(q^{10}) \) 66 * q - 5 * q^2 - 12 * q^3 + 63 * q^4 - 26 * q^5 - 19 * q^6 + 66 * q^7 - 15 * q^8 + 66 * q^9	\( 66 q - 5 q^{2} - 12 q^{3} + 63 q^{4} - 26 q^{5} - 19 q^{6} + 66 q^{7} - 15 q^{8} + 66 q^{9} - 6 q^{10} - 57 q^{11} - 29 q^{12} - 28 q^{13} - 5 q^{14} - 24 q^{15} + 69 q^{16} - 47 q^{17} + 8 q^{18} - 27 q^{19} - 77 q^{20} - 12 q^{21} - 12 q^{22} - 46 q^{23} - 57 q^{24} + 72 q^{25} - 21 q^{26} - 36 q^{27} + 63 q^{28} - 62 q^{29} + 2 q^{30} + 66 q^{31} - 40 q^{32} + 4 q^{33} - 46 q^{34} - 26 q^{35} + 62 q^{36} - 66 q^{37} - 31 q^{38} - 8 q^{39} - 37 q^{40} - 33 q^{41} - 19 q^{42} - 22 q^{43} - 84 q^{44} - 77 q^{45} - 14 q^{46} - 20 q^{47} - 43 q^{48} + 66 q^{49} - 10 q^{50} - 39 q^{51} - 41 q^{52} - 47 q^{53} - 65 q^{54} - 15 q^{55} - 15 q^{56} + 5 q^{57} + 24 q^{58} - 125 q^{59} - 77 q^{60} - 57 q^{61} - 5 q^{62} + 66 q^{63} + 81 q^{64} - 40 q^{65} + 33 q^{66} - 25 q^{67} - 107 q^{68} - 72 q^{69} - 6 q^{70} - 57 q^{71} + 38 q^{72} + 5 q^{73} + 5 q^{74} - 60 q^{75} - 33 q^{76} - 57 q^{77} - 19 q^{78} - 4 q^{79} - 132 q^{80} + 58 q^{81} + 8 q^{82} - 84 q^{83} - 29 q^{84} - 33 q^{85} - 60 q^{86} - 31 q^{87} + 21 q^{88} - 132 q^{89} - 61 q^{90} - 28 q^{91} - 100 q^{92} - 12 q^{93} - 35 q^{94} + 4 q^{95} - 198 q^{96} - 39 q^{97} - 5 q^{98} - 174 q^{99}+O(q^{100}) \) 66 * q - 5 * q^2 - 12 * q^3 + 63 * q^4 - 26 * q^5 - 19 * q^6 + 66 * q^7 - 15 * q^8 + 66 * q^9 - 6 * q^10 - 57 * q^11 - 29 * q^12 - 28 * q^13 - 5 * q^14 - 24 * q^15 + 69 * q^16 - 47 * q^17 + 8 * q^18 - 27 * q^19 - 77 * q^20 - 12 * q^21 - 12 * q^22 - 46 * q^23 - 57 * q^24 + 72 * q^25 - 21 * q^26 - 36 * q^27 + 63 * q^28 - 62 * q^29 + 2 * q^30 + 66 * q^31 - 40 * q^32 + 4 * q^33 - 46 * q^34 - 26 * q^35 + 62 * q^36 - 66 * q^37 - 31 * q^38 - 8 * q^39 - 37 * q^40 - 33 * q^41 - 19 * q^42 - 22 * q^43 - 84 * q^44 - 77 * q^45 - 14 * q^46 - 20 * q^47 - 43 * q^48 + 66 * q^49 - 10 * q^50 - 39 * q^51 - 41 * q^52 - 47 * q^53 - 65 * q^54 - 15 * q^55 - 15 * q^56 + 5 * q^57 + 24 * q^58 - 125 * q^59 - 77 * q^60 - 57 * q^61 - 5 * q^62 + 66 * q^63 + 81 * q^64 - 40 * q^65 + 33 * q^66 - 25 * q^67 - 107 * q^68 - 72 * q^69 - 6 * q^70 - 57 * q^71 + 38 * q^72 + 5 * q^73 + 5 * q^74 - 60 * q^75 - 33 * q^76 - 57 * q^77 - 19 * q^78 - 4 * q^79 - 132 * q^80 + 58 * q^81 + 8 * q^82 - 84 * q^83 - 29 * q^84 - 33 * q^85 - 60 * q^86 - 31 * q^87 + 21 * q^88 - 132 * q^89 - 61 * q^90 - 28 * q^91 - 100 * q^92 - 12 * q^93 - 35 * q^94 + 4 * q^95 - 198 * q^96 - 39 * q^97 - 5 * q^98 - 174 * q^99

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