LMFDB - Embedded newform 8029.2.a.d.1.9

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			1.9
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)

$f(q)$	$=$	$q-2.28651 q^{2} +1.33514 q^{3} +3.22812 q^{4} -2.86692 q^{5} -3.05281 q^{6} +1.00000 q^{7} -2.80810 q^{8} -1.21739 q^{9} +O(q^{10})$	\(q-2.28651 q^{2} +1.33514 q^{3} +3.22812 q^{4} -2.86692 q^{5} -3.05281 q^{6} +1.00000 q^{7} -2.80810 q^{8} -1.21739 q^{9} +6.55524 q^{10} +2.63304 q^{11} +4.31000 q^{12} +7.12642 q^{13} -2.28651 q^{14} -3.82775 q^{15} -0.0354884 q^{16} -0.298405 q^{17} +2.78358 q^{18} +3.78206 q^{19} -9.25476 q^{20} +1.33514 q^{21} -6.02047 q^{22} -7.69362 q^{23} -3.74922 q^{24} +3.21923 q^{25} -16.2946 q^{26} -5.63082 q^{27} +3.22812 q^{28} -0.884286 q^{29} +8.75217 q^{30} +1.00000 q^{31} +5.69735 q^{32} +3.51548 q^{33} +0.682306 q^{34} -2.86692 q^{35} -3.92989 q^{36} -1.00000 q^{37} -8.64770 q^{38} +9.51479 q^{39} +8.05060 q^{40} -2.89845 q^{41} -3.05281 q^{42} -1.43256 q^{43} +8.49977 q^{44} +3.49017 q^{45} +17.5915 q^{46} -1.07883 q^{47} -0.0473820 q^{48} +1.00000 q^{49} -7.36079 q^{50} -0.398413 q^{51} +23.0049 q^{52} -3.25344 q^{53} +12.8749 q^{54} -7.54872 q^{55} -2.80810 q^{56} +5.04958 q^{57} +2.02193 q^{58} -5.59080 q^{59} -12.3564 q^{60} +2.22825 q^{61} -2.28651 q^{62} -1.21739 q^{63} -12.9561 q^{64} -20.4309 q^{65} -8.03818 q^{66} +2.06783 q^{67} -0.963287 q^{68} -10.2721 q^{69} +6.55524 q^{70} -6.23189 q^{71} +3.41857 q^{72} +10.4047 q^{73} +2.28651 q^{74} +4.29813 q^{75} +12.2089 q^{76} +2.63304 q^{77} -21.7556 q^{78} -15.7632 q^{79} +0.101742 q^{80} -3.86577 q^{81} +6.62733 q^{82} -0.692919 q^{83} +4.31000 q^{84} +0.855504 q^{85} +3.27556 q^{86} -1.18065 q^{87} -7.39385 q^{88} +3.04996 q^{89} -7.98030 q^{90} +7.12642 q^{91} -24.8359 q^{92} +1.33514 q^{93} +2.46676 q^{94} -10.8429 q^{95} +7.60677 q^{96} -13.7361 q^{97} -2.28651 q^{98} -3.20545 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.28651	−1.61681	−0.808403	−	0.588630i	$-0.799668\pi$
$2$	−2.28651	−1.61681	−0.808403	+	0.588630i	$0.799668\pi$
$3$	1.33514	0.770845	0.385423	−	0.922740i	$-0.374056\pi$
$3$	1.33514	0.770845	0.385423	+	0.922740i	$0.374056\pi$
$4$	3.22812	1.61406
$5$	−2.86692	−1.28213	−0.641063	−	0.767488i	$-0.721506\pi$
$5$	−2.86692	−1.28213	−0.641063	+	0.767488i	$0.721506\pi$
$6$	−3.05281	−1.24631
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−2.80810	−0.992814
$9$	−1.21739	−0.405798
$10$	6.55524	2.07295
$11$	2.63304	0.793891	0.396946	−	0.917842i	$-0.370070\pi$
$11$	2.63304	0.793891	0.396946	+	0.917842i	$0.370070\pi$
$12$	4.31000	1.24419
$13$	7.12642	1.97651	0.988257	−	0.152803i	$-0.0488301\pi$
$13$	7.12642	1.97651	0.988257	+	0.152803i	$0.0488301\pi$
$14$	−2.28651	−0.611095
$15$	−3.82775	−0.988320
$16$	−0.0354884	−0.00887209
$17$	−0.298405	−0.0723739	−0.0361869	−	0.999345i	$-0.511521\pi$
$17$	−0.298405	−0.0723739	−0.0361869	+	0.999345i	$0.511521\pi$
$18$	2.78358	0.656096
$19$	3.78206	0.867663	0.433832	−	0.900994i	$-0.357161\pi$
$19$	3.78206	0.867663	0.433832	+	0.900994i	$0.357161\pi$
$20$	−9.25476	−2.06943
$21$	1.33514	0.291352
$22$	−6.02047	−1.28357
$23$	−7.69362	−1.60423	−0.802115	−	0.597170i	$-0.796292\pi$
$23$	−7.69362	−1.60423	−0.802115	+	0.597170i	$0.796292\pi$
$24$	−3.74922	−0.765306
$25$	3.21923	0.643846
$26$	−16.2946	−3.19564
$27$	−5.63082	−1.08365
$28$	3.22812	0.610057
$29$	−0.884286	−0.164208	−0.0821039	−	0.996624i	$-0.526164\pi$
$29$	−0.884286	−0.164208	−0.0821039	+	0.996624i	$0.526164\pi$
$30$	8.75217	1.59792
$31$	1.00000	0.179605
$31$	1.00000	0.179605
$32$	5.69735	1.00716
$33$	3.51548	0.611967
$34$	0.682306	0.117014
$35$	−2.86692	−0.484598
$36$	−3.92989	−0.654982
$37$	−1.00000	−0.164399
$37$	−1.00000	−0.164399
$38$	−8.64770	−1.40284
$39$	9.51479	1.52359
$40$	8.05060	1.27291
$41$	−2.89845	−0.452662	−0.226331	−	0.974050i	$-0.572673\pi$
$41$	−2.89845	−0.452662	−0.226331	+	0.974050i	$0.572673\pi$
$42$	−3.05281	−0.471059
$43$	−1.43256	−0.218463	−0.109232	−	0.994016i	$-0.534839\pi$
$43$	−1.43256	−0.218463	−0.109232	+	0.994016i	$0.534839\pi$
$44$	8.49977	1.28139
$45$	3.49017	0.520284
$46$	17.5915	2.59373
$47$	−1.07883	−0.157364	−0.0786821	−	0.996900i	$-0.525071\pi$
$47$	−1.07883	−0.157364	−0.0786821	+	0.996900i	$0.525071\pi$
$48$	−0.0473820	−0.00683901
$49$	1.00000	0.142857
$50$	−7.36079	−1.04097
$51$	−0.398413	−0.0557890
$52$	23.0049	3.19021
$53$	−3.25344	−0.446894	−0.223447	−	0.974716i	$-0.571731\pi$
$53$	−3.25344	−0.446894	−0.223447	+	0.974716i	$0.571731\pi$
$54$	12.8749	1.75205
$55$	−7.54872	−1.01787
$56$	−2.80810	−0.375248
$57$	5.04958	0.668834
$58$	2.02193	0.265492
$59$	−5.59080	−0.727860	−0.363930	−	0.931426i	$-0.618565\pi$
$59$	−5.59080	−0.727860	−0.363930	+	0.931426i	$0.618565\pi$
$60$	−12.3564	−1.59521
$61$	2.22825	0.285298	0.142649	−	0.989773i	$-0.454438\pi$
$61$	2.22825	0.285298	0.142649	+	0.989773i	$0.454438\pi$
$62$	−2.28651	−0.290387
$63$	−1.21739	−0.153377
$64$	−12.9561	−1.61951
$65$	−20.4309	−2.53414
$66$	−8.03818	−0.989432
$67$	2.06783	0.252625	0.126313	−	0.991990i	$-0.459686\pi$
$67$	2.06783	0.252625	0.126313	+	0.991990i	$0.459686\pi$
$68$	−0.963287	−0.116816
$69$	−10.2721	−1.23661
$70$	6.55524	0.783500
$71$	−6.23189	−0.739589	−0.369794	−	0.929114i	$-0.620572\pi$
$71$	−6.23189	−0.739589	−0.369794	+	0.929114i	$0.620572\pi$
$72$	3.41857	0.402882
$73$	10.4047	1.21778	0.608890	−	0.793255i	$-0.291615\pi$
$73$	10.4047	1.21778	0.608890	+	0.793255i	$0.291615\pi$
$74$	2.28651	0.265801
$75$	4.29813	0.496305
$76$	12.2089	1.40046
$77$	2.63304	0.300063
$78$	−21.7556	−2.46334
$79$	−15.7632	−1.77349	−0.886747	−	0.462254i	$-0.847041\pi$
$79$	−15.7632	−1.77349	−0.886747	+	0.462254i	$0.847041\pi$
$80$	0.101742	0.0113751
$81$	−3.86577	−0.429530
$82$	6.62733	0.731866
$83$	−0.692919	−0.0760577	−0.0380289	−	0.999277i	$-0.512108\pi$
$83$	−0.692919	−0.0760577	−0.0380289	+	0.999277i	$0.512108\pi$
$84$	4.31000	0.470259
$85$	0.855504	0.0927924
$86$	3.27556	0.353212
$87$	−1.18065	−0.126579
$88$	−7.39385	−0.788187
$89$	3.04996	0.323295	0.161648	−	0.986849i	$-0.448319\pi$
$89$	3.04996	0.323295	0.161648	+	0.986849i	$0.448319\pi$
$90$	−7.98030	−0.841198
$91$	7.12642	0.747052
$92$	−24.8359	−2.58932
$93$	1.33514	0.138448
$94$	2.46676	0.254427
$95$	−10.8429	−1.11245
$96$	7.60677	0.776363
$97$	−13.7361	−1.39469	−0.697346	−	0.716734i	$-0.745636\pi$
$97$	−13.7361	−1.39469	−0.697346	+	0.716734i	$0.745636\pi$
$98$	−2.28651	−0.230972
$99$	−3.20545	−0.322160
$100$	10.3921	1.03921
$101$	−5.34926	−0.532271	−0.266135	−	0.963936i	$-0.585747\pi$
$101$	−5.34926	−0.532271	−0.266135	+	0.963936i	$0.585747\pi$
$102$	0.910975	0.0902000
$103$	−15.7748	−1.55434	−0.777171	−	0.629289i	$-0.783346\pi$
$103$	−15.7748	−1.55434	−0.777171	+	0.629289i	$0.783346\pi$
$104$	−20.0117	−1.96231
$105$	−3.82775	−0.373550
$106$	7.43901	0.722541
$107$	−13.1078	−1.26718	−0.633589	−	0.773670i	$-0.718419\pi$
$107$	−13.1078	−1.26718	−0.633589	+	0.773670i	$0.718419\pi$
$108$	−18.1770	−1.74908
$109$	12.3774	1.18554	0.592772	−	0.805370i	$-0.298033\pi$
$109$	12.3774	1.18554	0.592772	+	0.805370i	$0.298033\pi$
$110$	17.2602	1.64570
$111$	−1.33514	−0.126726
$112$	−0.0354884	−0.00335334
$113$	2.75650	0.259309	0.129655	−	0.991559i	$-0.458613\pi$
$113$	2.75650	0.259309	0.129655	+	0.991559i	$0.458613\pi$
$114$	−11.5459	−1.08137
$115$	22.0570	2.05682
$116$	−2.85458	−0.265041
$117$	−8.67566	−0.802065
$118$	12.7834	1.17681
$119$	−0.298405	−0.0273548
$120$	10.7487	0.981218
$121$	−4.06710	−0.369736
$122$	−5.09490	−0.461271
$123$	−3.86984	−0.348932
$124$	3.22812	0.289894
$125$	5.10533	0.456634
$126$	2.78358	0.247981
$127$	11.8826	1.05441	0.527205	−	0.849738i	$-0.323240\pi$
$127$	11.8826	1.05441	0.527205	+	0.849738i	$0.323240\pi$
$128$	18.2294	1.61127
$129$	−1.91267	−0.168401
$130$	46.7154	4.09721
$131$	−6.90522	−0.603312	−0.301656	−	0.953417i	$-0.597539\pi$
$131$	−6.90522	−0.603312	−0.301656	+	0.953417i	$0.597539\pi$
$132$	11.3484	0.987751
$133$	3.78206	0.327946
$134$	−4.72810	−0.408446
$135$	16.1431	1.38938
$136$	0.837952	0.0718538
$137$	18.3649	1.56902	0.784509	−	0.620118i	$-0.212915\pi$
$137$	18.3649	1.56902	0.784509	+	0.620118i	$0.212915\pi$
$138$	23.4872	1.99936
$139$	−2.63758	−0.223717	−0.111858	−	0.993724i	$-0.535680\pi$
$139$	−2.63758	−0.223717	−0.111858	+	0.993724i	$0.535680\pi$
$140$	−9.25476	−0.782170
$141$	−1.44040	−0.121303
$142$	14.2493	1.19577
$143$	18.7642	1.56914
$144$	0.0432033	0.00360028
$145$	2.53518	0.210535
$146$	−23.7905	−1.96891
$147$	1.33514	0.110121
$148$	−3.22812	−0.265350
$149$	12.6880	1.03944	0.519722	−	0.854335i	$-0.326035\pi$
$149$	12.6880	1.03944	0.519722	+	0.854335i	$0.326035\pi$
$150$	−9.82771	−0.802429
$151$	−8.82382	−0.718072	−0.359036	−	0.933324i	$-0.616895\pi$
$151$	−8.82382	−0.718072	−0.359036	+	0.933324i	$0.616895\pi$
$152$	−10.6204	−0.861428
$153$	0.363277	0.0293692
$154$	−6.02047	−0.485143
$155$	−2.86692	−0.230277
$156$	30.7149	2.45916
$157$	7.86261	0.627505	0.313752	−	0.949505i	$-0.398414\pi$
$157$	7.86261	0.627505	0.313752	+	0.949505i	$0.398414\pi$
$158$	36.0426	2.86740
$159$	−4.34380	−0.344486
$160$	−16.3338	−1.29130
$161$	−7.69362	−0.606342
$162$	8.83911	0.694466
$163$	−5.83433	−0.456980	−0.228490	−	0.973546i	$-0.573379\pi$
$163$	−5.83433	−0.456980	−0.228490	+	0.973546i	$0.573379\pi$
$164$	−9.35654	−0.730623
$165$	−10.0786	−0.784619
$166$	1.58436	0.122971
$167$	14.3242	1.10844	0.554219	−	0.832371i	$-0.313017\pi$
$167$	14.3242	1.10844	0.554219	+	0.832371i	$0.313017\pi$
$168$	−3.74922	−0.289258
$169$	37.7859	2.90660
$170$	−1.95612	−0.150027
$171$	−4.60425	−0.352096
$172$	−4.62447	−0.352612
$173$	−7.84220	−0.596232	−0.298116	−	0.954530i	$-0.596358\pi$
$173$	−7.84220	−0.596232	−0.298116	+	0.954530i	$0.596358\pi$
$174$	2.69956	0.204653
$175$	3.21923	0.243351
$176$	−0.0934423	−0.00704348
$177$	−7.46451	−0.561067
$178$	−6.97376	−0.522706
$179$	−16.1162	−1.20458	−0.602290	−	0.798278i	$-0.705745\pi$
$179$	−16.1162	−1.20458	−0.602290	+	0.798278i	$0.705745\pi$
$180$	11.2667	0.839769
$181$	12.7554	0.948098	0.474049	−	0.880498i	$-0.342792\pi$
$181$	12.7554	0.948098	0.474049	+	0.880498i	$0.342792\pi$
$182$	−16.2946	−1.20784
$183$	2.97503	0.219920
$184$	21.6045	1.59270
$185$	2.86692	0.210780
$186$	−3.05281	−0.223843
$187$	−0.785713	−0.0574570
$188$	−3.48261	−0.253995
$189$	−5.63082	−0.409582
$190$	24.7923	1.79862
$191$	0.997967	0.0722104	0.0361052	−	0.999348i	$-0.488505\pi$
$191$	0.997967	0.0722104	0.0361052	+	0.999348i	$0.488505\pi$
$192$	−17.2982	−1.24839
$193$	−20.9923	−1.51106	−0.755531	−	0.655113i	$-0.772621\pi$
$193$	−20.9923	−1.51106	−0.755531	+	0.655113i	$0.772621\pi$
$194$	31.4078	2.25495
$195$	−27.2781	−1.95343
$196$	3.22812	0.230580
$197$	−5.13501	−0.365855	−0.182927	−	0.983126i	$-0.558557\pi$
$197$	−5.13501	−0.365855	−0.182927	+	0.983126i	$0.558557\pi$
$198$	7.32928	0.520869
$199$	−12.0415	−0.853600	−0.426800	−	0.904346i	$-0.640359\pi$
$199$	−12.0415	−0.853600	−0.426800	+	0.904346i	$0.640359\pi$
$200$	−9.03993	−0.639219
$201$	2.76084	0.194735
$202$	12.2311	0.860579
$203$	−0.884286	−0.0620647
$204$	−1.28613	−0.0900468
$205$	8.30962	0.580369
$206$	36.0693	2.51307
$207$	9.36616	0.650993
$208$	−0.252905	−0.0175358
$209$	9.95830	0.688830
$210$	8.75217	0.603957
$211$	3.47788	0.239427	0.119714	−	0.992808i	$-0.461802\pi$
$211$	3.47788	0.239427	0.119714	+	0.992808i	$0.461802\pi$
$212$	−10.5025	−0.721313
$213$	−8.32046	−0.570108
$214$	29.9711	2.04878
$215$	4.10703	0.280097
$216$	15.8119	1.07587
$217$	1.00000	0.0678844
$218$	−28.3011	−1.91679
$219$	13.8918	0.938719
$220$	−24.3681	−1.64290
$221$	−2.12656	−0.143048
$222$	3.05281	0.204891
$223$	−1.49267	−0.0999563	−0.0499782	−	0.998750i	$-0.515915\pi$
$223$	−1.49267	−0.0999563	−0.0499782	+	0.998750i	$0.515915\pi$
$224$	5.69735	0.380670
$225$	−3.91907	−0.261271
$226$	−6.30275	−0.419253
$227$	−7.99990	−0.530972	−0.265486	−	0.964115i	$-0.585532\pi$
$227$	−7.99990	−0.530972	−0.265486	+	0.964115i	$0.585532\pi$
$228$	16.3007	1.07954
$229$	15.2743	1.00935	0.504677	−	0.863308i	$-0.331611\pi$
$229$	15.2743	1.00935	0.504677	+	0.863308i	$0.331611\pi$
$230$	−50.4335	−3.32548
$231$	3.51548	0.231302
$232$	2.48317	0.163028
$233$	11.1797	0.732406	0.366203	−	0.930535i	$-0.380658\pi$
$233$	11.1797	0.732406	0.366203	+	0.930535i	$0.380658\pi$
$234$	19.8370	1.29678
$235$	3.09293	0.201761
$236$	−18.0478	−1.17481
$237$	−21.0461	−1.36709
$238$	0.682306	0.0442273
$239$	−17.6757	−1.14335	−0.571673	−	0.820481i	$-0.693706\pi$
$239$	−17.6757	−1.14335	−0.571673	+	0.820481i	$0.693706\pi$
$240$	0.135841	0.00876847
$241$	−4.11874	−0.265312	−0.132656	−	0.991162i	$-0.542350\pi$
$241$	−4.11874	−0.265312	−0.132656	+	0.991162i	$0.542350\pi$
$242$	9.29945	0.597792
$243$	11.7311	0.752551
$244$	7.19304	0.460487
$245$	−2.86692	−0.183161
$246$	8.84843	0.564155
$247$	26.9525	1.71495
$248$	−2.80810	−0.178315
$249$	−0.925146	−0.0586287
$250$	−11.6734	−0.738289
$251$	22.6271	1.42821	0.714104	−	0.700040i	$-0.246834\pi$
$251$	22.6271	1.42821	0.714104	+	0.700040i	$0.246834\pi$
$252$	−3.92989	−0.247560
$253$	−20.2576	−1.27358
$254$	−27.1697	−1.70478
$255$	1.14222	0.0715286
$256$	−15.7696	−0.985601
$257$	10.4581	0.652356	0.326178	−	0.945308i	$-0.394239\pi$
$257$	10.4581	0.652356	0.326178	+	0.945308i	$0.394239\pi$
$258$	4.37334	0.272272
$259$	−1.00000	−0.0621370
$260$	−65.9533	−4.09025
$261$	1.07652	0.0666352
$262$	15.7888	0.975438
$263$	−9.11148	−0.561838	−0.280919	−	0.959731i	$-0.590639\pi$
$263$	−9.11148	−0.561838	−0.280919	+	0.959731i	$0.590639\pi$
$264$	−9.87184	−0.607570
$265$	9.32735	0.572974
$266$	−8.64770	−0.530224
$267$	4.07213	0.249211
$268$	6.67519	0.407752
$269$	20.2200	1.23284	0.616418	−	0.787419i	$-0.288583\pi$
$269$	20.2200	1.23284	0.616418	+	0.787419i	$0.288583\pi$
$270$	−36.9114	−2.24635
$271$	23.8747	1.45029	0.725143	−	0.688598i	$-0.241773\pi$
$271$	23.8747	1.45029	0.725143	+	0.688598i	$0.241773\pi$
$272$	0.0105899	0.000642108 0
$273$	9.51479	0.575861
$274$	−41.9914	−2.53680
$275$	8.47636	0.511144
$276$	−33.1595	−1.99597
$277$	−2.10430	−0.126435	−0.0632175	−	0.998000i	$-0.520136\pi$
$277$	−2.10430	−0.126435	−0.0632175	+	0.998000i	$0.520136\pi$
$278$	6.03085	0.361706
$279$	−1.21739	−0.0728835
$280$	8.05060	0.481116
$281$	−7.81814	−0.466391	−0.233196	−	0.972430i	$-0.574918\pi$
$281$	−7.81814	−0.466391	−0.233196	+	0.972430i	$0.574918\pi$
$282$	3.29348	0.196124
$283$	−26.5432	−1.57783	−0.788914	−	0.614503i	$-0.789356\pi$
$283$	−26.5432	−1.57783	−0.788914	+	0.614503i	$0.789356\pi$
$284$	−20.1173	−1.19374
$285$	−14.4768	−0.857529
$286$	−42.9044	−2.53699
$287$	−2.89845	−0.171090
$288$	−6.93592	−0.408703
$289$	−16.9110	−0.994762
$290$	−5.79671	−0.340394
$291$	−18.3397	−1.07509
$292$	33.5876	1.96557
$293$	−10.9907	−0.642082	−0.321041	−	0.947065i	$-0.604033\pi$
$293$	−10.9907	−0.642082	−0.321041	+	0.947065i	$0.604033\pi$
$294$	−3.05281	−0.178044
$295$	16.0284	0.933208
$296$	2.80810	0.163218
$297$	−14.8262	−0.860302
$298$	−29.0113	−1.68058
$299$	−54.8279	−3.17078
$300$	13.8749	0.801066
$301$	−1.43256	−0.0825713
$302$	20.1757	1.16098
$303$	−7.14202	−0.410298
$304$	−0.134219	−0.00769799
$305$	−6.38820	−0.365787
$306$	−0.830635	−0.0474842
$307$	−7.85048	−0.448051	−0.224025	−	0.974583i	$-0.571920\pi$
$307$	−7.85048	−0.448051	−0.224025	+	0.974583i	$0.571920\pi$
$308$	8.49977	0.484319
$309$	−21.0617	−1.19816
$310$	6.55524	0.372312
$311$	1.39796	0.0792713	0.0396356	−	0.999214i	$-0.487380\pi$
$311$	1.39796	0.0792713	0.0396356	+	0.999214i	$0.487380\pi$
$312$	−26.7185	−1.51264
$313$	−20.3438	−1.14990	−0.574949	−	0.818189i	$-0.694978\pi$
$313$	−20.3438	−1.14990	−0.574949	+	0.818189i	$0.694978\pi$
$314$	−17.9779	−1.01455
$315$	3.49017	0.196649
$316$	−50.8854	−2.86253
$317$	−10.9889	−0.617198	−0.308599	−	0.951192i	$-0.599860\pi$
$317$	−10.9889	−0.617198	−0.308599	+	0.951192i	$0.599860\pi$
$318$	9.93214	0.556967
$319$	−2.32836	−0.130363
$320$	37.1440	2.07641
$321$	−17.5008	−0.976798
$322$	17.5915	0.980337
$323$	−1.12858	−0.0627961
$324$	−12.4792	−0.693287
$325$	22.9416	1.27257
$326$	13.3402	0.738847
$327$	16.5257	0.913871
$328$	8.13915	0.449409
$329$	−1.07883	−0.0594781
$330$	23.0448	1.26858
$331$	0.357356	0.0196421	0.00982104	−	0.999952i	$-0.496874\pi$
$331$	0.357356	0.0196421	0.00982104	+	0.999952i	$0.496874\pi$
$332$	−2.23682	−0.122762
$333$	1.21739	0.0667128
$334$	−32.7524	−1.79213
$335$	−5.92829	−0.323897
$336$	−0.0473820	−0.00258490
$337$	−27.9529	−1.52269	−0.761346	−	0.648345i	$-0.775461\pi$
$337$	−27.9529	−1.52269	−0.761346	+	0.648345i	$0.775461\pi$
$338$	−86.3977	−4.69941
$339$	3.68032	0.199887
$340$	2.76167	0.149772
$341$	2.63304	0.142587
$342$	10.5277	0.569270
$343$	1.00000	0.0539949
$344$	4.02277	0.216893
$345$	29.4492	1.58549
$346$	17.9313	0.963991
$347$	−6.98913	−0.375196	−0.187598	−	0.982246i	$-0.560070\pi$
$347$	−6.98913	−0.375196	−0.187598	+	0.982246i	$0.560070\pi$
$348$	−3.81127	−0.204306
$349$	21.3189	1.14118	0.570588	−	0.821236i	$-0.306715\pi$
$349$	21.3189	1.14118	0.570588	+	0.821236i	$0.306715\pi$
$350$	−7.36079	−0.393451
$351$	−40.1276	−2.14185
$352$	15.0013	0.799575
$353$	28.6554	1.52517	0.762586	−	0.646887i	$-0.223929\pi$
$353$	28.6554	1.52517	0.762586	+	0.646887i	$0.223929\pi$
$354$	17.0677	0.907136
$355$	17.8663	0.948246
$356$	9.84564	0.521818
$357$	−0.398413	−0.0210863
$358$	36.8498	1.94757
$359$	−30.0257	−1.58469	−0.792347	−	0.610071i	$-0.791141\pi$
$359$	−30.0257	−1.58469	−0.792347	+	0.610071i	$0.791141\pi$
$360$	−9.80076	−0.516545
$361$	−4.69606	−0.247161
$362$	−29.1652	−1.53289
$363$	−5.43016	−0.285009
$364$	23.0049	1.20579
$365$	−29.8295	−1.56135
$366$	−6.80242	−0.355568
$367$	−7.62639	−0.398094	−0.199047	−	0.979990i	$-0.563785\pi$
$367$	−7.62639	−0.398094	−0.199047	+	0.979990i	$0.563785\pi$
$368$	0.273034	0.0142329
$369$	3.52856	0.183689
$370$	−6.55524	−0.340790
$371$	−3.25344	−0.168910
$372$	4.31000	0.223463
$373$	18.9105	0.979151	0.489575	−	0.871961i	$-0.337152\pi$
$373$	18.9105	0.979151	0.489575	+	0.871961i	$0.337152\pi$
$374$	1.79654	0.0928968
$375$	6.81634	0.351994
$376$	3.02948	0.156233
$377$	−6.30180	−0.324559
$378$	12.8749	0.662214
$379$	−10.9188	−0.560862	−0.280431	−	0.959874i	$-0.590477\pi$
$379$	−10.9188	−0.560862	−0.280431	+	0.959874i	$0.590477\pi$
$380$	−35.0020	−1.79556
$381$	15.8650	0.812787
$382$	−2.28186	−0.116750
$383$	−16.0288	−0.819035	−0.409518	−	0.912302i	$-0.634303\pi$
$383$	−16.0288	−0.819035	−0.409518	+	0.912302i	$0.634303\pi$
$384$	24.3389	1.24204
$385$	−7.54872	−0.384718
$386$	47.9991	2.44309
$387$	1.74399	0.0886519
$388$	−44.3419	−2.25112
$389$	13.7603	0.697675	0.348838	−	0.937183i	$-0.386576\pi$
$389$	13.7603	0.697675	0.348838	+	0.937183i	$0.386576\pi$
$390$	62.3717	3.15831
$391$	2.29581	0.116104
$392$	−2.80810	−0.141831
$393$	−9.21945	−0.465060
$394$	11.7412	0.591516
$395$	45.1917	2.27384
$396$	−10.3476	−0.519985
$397$	29.6521	1.48819	0.744097	−	0.668072i	$-0.232880\pi$
$397$	29.6521	1.48819	0.744097	+	0.668072i	$0.232880\pi$
$398$	27.5330	1.38010
$399$	5.04958	0.252795
$400$	−0.114245	−0.00571226
$401$	−30.1234	−1.50429	−0.752146	−	0.658996i	$-0.770981\pi$
$401$	−30.1234	−1.50429	−0.752146	+	0.658996i	$0.770981\pi$
$402$	−6.31269	−0.314848
$403$	7.12642	0.354992
$404$	−17.2680	−0.859117
$405$	11.0829	0.550711
$406$	2.02193	0.100347
$407$	−2.63304	−0.130515
$408$	1.11879	0.0553881
$409$	27.2671	1.34827	0.674135	−	0.738608i	$-0.264517\pi$
$409$	27.2671	1.34827	0.674135	+	0.738608i	$0.264517\pi$
$410$	−19.0000	−0.938344
$411$	24.5197	1.20947
$412$	−50.9231	−2.50880
$413$	−5.59080	−0.275105
$414$	−21.4158	−1.05253
$415$	1.98654	0.0975156
$416$	40.6017	1.99066
$417$	−3.52154	−0.172451
$418$	−22.7697	−1.11370
$419$	32.5429	1.58982	0.794912	−	0.606725i	$-0.207517\pi$
$419$	32.5429	1.58982	0.794912	+	0.606725i	$0.207517\pi$
$420$	−12.3564	−0.602932
$421$	−27.4306	−1.33688	−0.668442	−	0.743764i	$-0.733039\pi$
$421$	−27.4306	−1.33688	−0.668442	+	0.743764i	$0.733039\pi$
$422$	−7.95220	−0.387107
$423$	1.31337	0.0638581
$424$	9.13599	0.443683
$425$	−0.960635	−0.0465976
$426$	19.0248	0.921754
$427$	2.22825	0.107832
$428$	−42.3135	−2.04530
$429$	25.0528	1.20956
$430$	−9.39076	−0.452863
$431$	−31.8692	−1.53509	−0.767543	−	0.640997i	$-0.778521\pi$
$431$	−31.8692	−1.53509	−0.767543	+	0.640997i	$0.778521\pi$
$432$	0.199829	0.00961426
$433$	−14.2681	−0.685684	−0.342842	−	0.939393i	$-0.611389\pi$
$433$	−14.2681	−0.685684	−0.342842	+	0.939393i	$0.611389\pi$
$434$	−2.28651	−0.109756
$435$	3.38483	0.162290
$436$	39.9559	1.91354
$437$	−29.0977	−1.39193
$438$	−31.7636	−1.51773
$439$	−28.1738	−1.34466	−0.672332	−	0.740250i	$-0.734707\pi$
$439$	−28.1738	−1.34466	−0.672332	+	0.740250i	$0.734707\pi$
$440$	21.1976	1.01055
$441$	−1.21739	−0.0579711
$442$	4.86240	0.231281
$443$	−4.76585	−0.226433	−0.113216	−	0.993570i	$-0.536115\pi$
$443$	−4.76585	−0.226433	−0.113216	+	0.993570i	$0.536115\pi$
$444$	−4.31000	−0.204543
$445$	−8.74400	−0.414505
$446$	3.41299	0.161610
$447$	16.9403	0.801251
$448$	−12.9561	−0.612116
$449$	−32.6467	−1.54069	−0.770346	−	0.637626i	$-0.779916\pi$
$449$	−32.6467	−1.54069	−0.770346	+	0.637626i	$0.779916\pi$
$450$	8.96099	0.422425
$451$	−7.63174	−0.359364
$452$	8.89830	0.418541
$453$	−11.7811	−0.553523
$454$	18.2918	0.858478
$455$	−20.4309	−0.957814
$456$	−14.1797	−0.664028
$457$	26.2109	1.22610	0.613048	−	0.790046i	$-0.289943\pi$
$457$	26.2109	1.22610	0.613048	+	0.790046i	$0.289943\pi$
$458$	−34.9248	−1.63193
$459$	1.68027	0.0784281
$460$	71.2026	3.31984
$461$	32.7266	1.52423	0.762115	−	0.647442i	$-0.224161\pi$
$461$	32.7266	1.52423	0.762115	+	0.647442i	$0.224161\pi$
$462$	−8.03818	−0.373970
$463$	−23.8191	−1.10697	−0.553483	−	0.832860i	$-0.686702\pi$
$463$	−23.8191	−1.10697	−0.553483	+	0.832860i	$0.686702\pi$
$464$	0.0313819	0.00145687
$465$	−3.82775	−0.177508
$466$	−25.5624	−1.18416
$467$	−11.7628	−0.544320	−0.272160	−	0.962252i	$-0.587738\pi$
$467$	−11.7628	−0.544320	−0.272160	+	0.962252i	$0.587738\pi$
$468$	−28.0061	−1.29458
$469$	2.06783	0.0954833
$470$	−7.07201	−0.326208
$471$	10.4977	0.483709
$472$	15.6995	0.722630
$473$	−3.77198	−0.173436
$474$	48.1220	2.21032
$475$	12.1753	0.558641
$476$	−0.963287	−0.0441522
$477$	3.96072	0.181349
$478$	40.4157	1.84857
$479$	−24.0412	−1.09847	−0.549236	−	0.835667i	$-0.685081\pi$
$479$	−24.0412	−1.09847	−0.549236	+	0.835667i	$0.685081\pi$
$480$	−21.8080	−0.995395
$481$	−7.12642	−0.324937
$482$	9.41754	0.428957
$483$	−10.2721	−0.467396
$484$	−13.1291	−0.596776
$485$	39.3804	1.78817
$486$	−26.8233	−1.21673
$487$	−18.4701	−0.836958	−0.418479	−	0.908226i	$-0.637437\pi$
$487$	−18.4701	−0.836958	−0.418479	+	0.908226i	$0.637437\pi$
$488$	−6.25714	−0.283248
$489$	−7.78966	−0.352261
$490$	6.55524	0.296135
$491$	−8.40496	−0.379310	−0.189655	−	0.981851i	$-0.560737\pi$
$491$	−8.40496	−0.379310	−0.189655	+	0.981851i	$0.560737\pi$
$492$	−12.4923	−0.563197
$493$	0.263876	0.0118844
$494$	−61.6271	−2.77274
$495$	9.18976	0.413049
$496$	−0.0354884	−0.00159347
$497$	−6.23189	−0.279538
$498$	2.11535	0.0947912
$499$	−19.3375	−0.865668	−0.432834	−	0.901474i	$-0.642486\pi$
$499$	−19.3375	−0.865668	−0.432834	+	0.901474i	$0.642486\pi$
$500$	16.4806	0.737035
$501$	19.1248	0.854434
$502$	−51.7370	−2.30913
$503$	−27.6133	−1.23122	−0.615608	−	0.788052i	$-0.711090\pi$
$503$	−27.6133	−1.23122	−0.615608	+	0.788052i	$0.711090\pi$
$504$	3.41857	0.152275
$505$	15.3359	0.682438
$506$	46.3192	2.05914
$507$	50.4495	2.24054
$508$	38.3584	1.70188
$509$	5.52103	0.244716	0.122358	−	0.992486i	$-0.460954\pi$
$509$	5.52103	0.244716	0.122358	+	0.992486i	$0.460954\pi$
$510$	−2.61169	−0.115648
$511$	10.4047	0.460277
$512$	−0.401500	−0.0177439
$513$	−21.2961	−0.940245
$514$	−23.9124	−1.05473
$515$	45.2252	1.99286
$516$	−6.17433	−0.271810
$517$	−2.84061	−0.124930
$518$	2.28651	0.100463
$519$	−10.4705	−0.459602
$520$	57.3720	2.51593
$521$	10.9334	0.479000	0.239500	−	0.970896i	$-0.423016\pi$
$521$	10.9334	0.479000	0.239500	+	0.970896i	$0.423016\pi$
$522$	−2.46148	−0.107736
$523$	12.8878	0.563544	0.281772	−	0.959481i	$-0.409078\pi$
$523$	12.8878	0.563544	0.281772	+	0.959481i	$0.409078\pi$
$524$	−22.2909	−0.973781
$525$	4.29813	0.187586
$526$	20.8335	0.908383
$527$	−0.298405	−0.0129987
$528$	−0.124759	−0.00542943
$529$	36.1917	1.57355
$530$	−21.3270	−0.926388
$531$	6.80620	0.295364
$532$	12.2089	0.529324
$533$	−20.6556	−0.894692
$534$	−9.31097	−0.402925
$535$	37.5790	1.62468
$536$	−5.80667	−0.250810
$537$	−21.5174	−0.928544
$538$	−46.2333	−1.99326
$539$	2.63304	0.113413
$540$	52.1119	2.24254
$541$	34.6059	1.48783	0.743913	−	0.668277i	$-0.232968\pi$
$541$	34.6059	1.48783	0.743913	+	0.668277i	$0.232968\pi$
$542$	−54.5898	−2.34483
$543$	17.0302	0.730837
$544$	−1.70012	−0.0728920
$545$	−35.4852	−1.52002
$546$	−21.7556	−0.931055
$547$	16.7153	0.714695	0.357348	−	0.933971i	$-0.383681\pi$
$547$	16.7153	0.714695	0.357348	+	0.933971i	$0.383681\pi$
$548$	59.2840	2.53249
$549$	−2.71265	−0.115773
$550$	−19.3813	−0.826420
$551$	−3.34442	−0.142477
$552$	28.8450	1.22773
$553$	−15.7632	−0.670318
$554$	4.81149	0.204421
$555$	3.82775	0.162479
$556$	−8.51442	−0.361092
$557$	17.3183	0.733799	0.366899	−	0.930261i	$-0.380419\pi$
$557$	17.3183	0.733799	0.366899	+	0.930261i	$0.380419\pi$
$558$	2.78358	0.117838
$559$	−10.2090	−0.431795
$560$	0.101742	0.00429940
$561$	−1.04904	−0.0442904
$562$	17.8762	0.754064
$563$	3.34749	0.141080	0.0705399	−	0.997509i	$-0.477528\pi$
$563$	3.34749	0.141080	0.0705399	+	0.997509i	$0.477528\pi$
$564$	−4.64978	−0.195791
$565$	−7.90265	−0.332467
$566$	60.6912	2.55104
$567$	−3.86577	−0.162347
$568$	17.4998	0.734274
$569$	−39.5345	−1.65737	−0.828685	−	0.559715i	$-0.810911\pi$
$569$	−39.5345	−1.65737	−0.828685	+	0.559715i	$0.810911\pi$
$570$	33.1012	1.38646
$571$	−15.6032	−0.652975	−0.326487	−	0.945202i	$-0.605865\pi$
$571$	−15.6032	−0.652975	−0.326487	+	0.945202i	$0.605865\pi$
$572$	60.5729	2.53268
$573$	1.33243	0.0556630
$574$	6.62733	0.276619
$575$	−24.7675	−1.03288
$576$	15.7726	0.657193
$577$	−8.39259	−0.349388	−0.174694	−	0.984623i	$-0.555894\pi$
$577$	−8.39259	−0.349388	−0.174694	+	0.984623i	$0.555894\pi$
$578$	38.6670	1.60834
$579$	−28.0278	−1.16479
$580$	8.18386	0.339816
$581$	−0.692919	−0.0287471
$582$	41.9339	1.73821
$583$	−8.56643	−0.354785
$584$	−29.2175	−1.20903
$585$	24.8724	1.02835
$586$	25.1303	1.03812
$587$	4.75156	0.196118	0.0980589	−	0.995181i	$-0.468737\pi$
$587$	4.75156	0.196118	0.0980589	+	0.995181i	$0.468737\pi$
$588$	4.31000	0.177741
$589$	3.78206	0.155837
$590$	−36.6490	−1.50882
$591$	−6.85598	−0.282017
$592$	0.0354884	0.00145856
$593$	5.04052	0.206989	0.103495	−	0.994630i	$-0.466998\pi$
$593$	5.04052	0.206989	0.103495	+	0.994630i	$0.466998\pi$
$594$	33.9002	1.39094
$595$	0.855504	0.0350722
$596$	40.9585	1.67773
$597$	−16.0771	−0.657993
$598$	125.365	5.12654
$599$	28.7546	1.17488	0.587441	−	0.809267i	$-0.300135\pi$
$599$	28.7546	1.17488	0.587441	+	0.809267i	$0.300135\pi$
$600$	−12.0696	−0.492739
$601$	−35.3966	−1.44386	−0.721928	−	0.691968i	$-0.756744\pi$
$601$	−35.3966	−1.44386	−0.721928	+	0.691968i	$0.756744\pi$
$602$	3.27556	0.133502
$603$	−2.51736	−0.102515
$604$	−28.4843	−1.15901
$605$	11.6600	0.474048
$606$	16.3303	0.663373
$607$	−26.9387	−1.09341	−0.546705	−	0.837325i	$-0.684118\pi$
$607$	−26.9387	−1.09341	−0.546705	+	0.837325i	$0.684118\pi$
$608$	21.5477	0.873874
$609$	−1.18065	−0.0478423
$610$	14.6067	0.591407
$611$	−7.68823	−0.311032
$612$	1.17270	0.0474036
$613$	−11.6888	−0.472106	−0.236053	−	0.971740i	$-0.575854\pi$
$613$	−11.6888	−0.472106	−0.236053	+	0.971740i	$0.575854\pi$
$614$	17.9502	0.724410
$615$	11.0945	0.447375
$616$	−7.39385	−0.297907
$617$	−1.12941	−0.0454683	−0.0227342	−	0.999742i	$-0.507237\pi$
$617$	−1.12941	−0.0454683	−0.0227342	+	0.999742i	$0.507237\pi$
$618$	48.1577	1.93719
$619$	−12.8604	−0.516904	−0.258452	−	0.966024i	$-0.583212\pi$
$619$	−12.8604	−0.516904	−0.258452	+	0.966024i	$0.583212\pi$
$620$	−9.25476	−0.371680
$621$	43.3214	1.73843
$622$	−3.19646	−0.128166
$623$	3.04996	0.122194
$624$	−0.337664	−0.0135174
$625$	−30.7327	−1.22931
$626$	46.5162	1.85916
$627$	13.2958	0.530981
$628$	25.3815	1.01283
$629$	0.298405	0.0118982
$630$	−7.98030	−0.317943
$631$	23.1397	0.921178	0.460589	−	0.887613i	$-0.347638\pi$
$631$	23.1397	0.921178	0.460589	+	0.887613i	$0.347638\pi$
$632$	44.2646	1.76075
$633$	4.64346	0.184561
$634$	25.1262	0.997889
$635$	−34.0665	−1.35189
$636$	−14.0223	−0.556021
$637$	7.12642	0.282359
$638$	5.32382	0.210772
$639$	7.58666	0.300124
$640$	−52.2623	−2.06585
$641$	−39.4620	−1.55866	−0.779328	−	0.626616i	$-0.784439\pi$
$641$	−39.4620	−1.55866	−0.779328	+	0.626616i	$0.784439\pi$
$642$	40.0157	1.57929
$643$	12.7441	0.502578	0.251289	−	0.967912i	$-0.419146\pi$
$643$	12.7441	0.502578	0.251289	+	0.967912i	$0.419146\pi$
$644$	−24.8359	−0.978672
$645$	5.48347	0.215912
$646$	2.58052	0.101529
$647$	2.99359	0.117690	0.0588451	−	0.998267i	$-0.481258\pi$
$647$	2.99359	0.117690	0.0588451	+	0.998267i	$0.481258\pi$
$648$	10.8555	0.426443
$649$	−14.7208	−0.577842
$650$	−52.4561	−2.05750
$651$	1.33514	0.0523284
$652$	−18.8339	−0.737593
$653$	44.3147	1.73417	0.867083	−	0.498163i	$-0.165992\pi$
$653$	44.3147	1.73417	0.867083	+	0.498163i	$0.165992\pi$
$654$	−37.7861	−1.47755
$655$	19.7967	0.773521
$656$	0.102861	0.00401606
$657$	−12.6666	−0.494172
$658$	2.46676	0.0961645
$659$	−26.5418	−1.03392	−0.516961	−	0.856009i	$-0.672937\pi$
$659$	−26.5418	−1.03392	−0.516961	+	0.856009i	$0.672937\pi$
$660$	−32.5350	−1.26642
$661$	−32.0880	−1.24808	−0.624039	−	0.781393i	$-0.714509\pi$
$661$	−32.0880	−1.24808	−0.624039	+	0.781393i	$0.714509\pi$
$662$	−0.817098	−0.0317574
$663$	−2.83926	−0.110268
$664$	1.94579	0.0755112
$665$	−10.8429	−0.420468
$666$	−2.78358	−0.107862
$667$	6.80336	0.263427
$668$	46.2402	1.78909
$669$	−1.99292	−0.0770508
$670$	13.5551	0.523679
$671$	5.86706	0.226495
$672$	7.60677	0.293438
$673$	−29.6549	−1.14311	−0.571555	−	0.820564i	$-0.693660\pi$
$673$	−29.6549	−1.14311	−0.571555	+	0.820564i	$0.693660\pi$
$674$	63.9146	2.46190
$675$	−18.1269	−0.697705
$676$	121.977	4.69143
$677$	40.4140	1.55324	0.776619	−	0.629971i	$-0.216933\pi$
$677$	40.4140	1.55324	0.776619	+	0.629971i	$0.216933\pi$
$678$	−8.41507	−0.323179
$679$	−13.7361	−0.527144
$680$	−2.40234	−0.0921256
$681$	−10.6810	−0.409297
$682$	−6.02047	−0.230536
$683$	−43.7010	−1.67217	−0.836086	−	0.548598i	$-0.815162\pi$
$683$	−43.7010	−1.67217	−0.836086	+	0.548598i	$0.815162\pi$
$684$	−14.8631	−0.568304
$685$	−52.6506	−2.01168
$686$	−2.28651	−0.0872993
$687$	20.3934	0.778056
$688$	0.0508392	0.00193823
$689$	−23.1854	−0.883292
$690$	−67.3359	−2.56343
$691$	11.5990	0.441246	0.220623	−	0.975359i	$-0.429191\pi$
$691$	11.5990	0.441246	0.220623	+	0.975359i	$0.429191\pi$
$692$	−25.3156	−0.962353
$693$	−3.20545	−0.121765
$694$	15.9807	0.606619
$695$	7.56173	0.286833
$696$	3.31538	0.125669
$697$	0.864912	0.0327609
$698$	−48.7459	−1.84506
$699$	14.9265	0.564571
$700$	10.3921	0.392783
$701$	−5.41956	−0.204694	−0.102347	−	0.994749i	$-0.532635\pi$
$701$	−5.41956	−0.204694	−0.102347	+	0.994749i	$0.532635\pi$
$702$	91.7521	3.46296
$703$	−3.78206	−0.142643
$704$	−34.1138	−1.28571
$705$	4.12951	0.155526
$706$	−65.5208	−2.46591
$707$	−5.34926	−0.201180
$708$	−24.0963	−0.905596
$709$	−2.67723	−0.100546	−0.0502728	−	0.998736i	$-0.516009\pi$
$709$	−2.67723	−0.100546	−0.0502728	+	0.998736i	$0.516009\pi$
$710$	−40.8515	−1.53313
$711$	19.1900	0.719681
$712$	−8.56461	−0.320972
$713$	−7.69362	−0.288128
$714$	0.910975	0.0340924
$715$	−53.7953	−2.01183
$716$	−52.0249	−1.94426
$717$	−23.5996	−0.881343
$718$	68.6539	2.56214
$719$	−13.4578	−0.501891	−0.250946	−	0.968001i	$-0.580742\pi$
$719$	−13.4578	−0.501891	−0.250946	+	0.968001i	$0.580742\pi$
$720$	−0.123860	−0.00461601
$721$	−15.7748	−0.587486
$722$	10.7376	0.399611
$723$	−5.49911	−0.204514
$724$	41.1758	1.53029
$725$	−2.84672	−0.105725
$726$	12.4161	0.460805
$727$	27.0524	1.00332	0.501658	−	0.865066i	$-0.332723\pi$
$727$	27.0524	1.00332	0.501658	+	0.865066i	$0.332723\pi$
$728$	−20.0117	−0.741684
$729$	27.2600	1.00963
$730$	68.2053	2.52439
$731$	0.427483	0.0158110
$732$	9.60374	0.354964
$733$	23.0148	0.850072	0.425036	−	0.905176i	$-0.360261\pi$
$733$	23.0148	0.850072	0.425036	+	0.905176i	$0.360261\pi$
$734$	17.4378	0.643641
$735$	−3.82775	−0.141189
$736$	−43.8332	−1.61571
$737$	5.44467	0.200557
$738$	−8.06807	−0.296990
$739$	38.0404	1.39934	0.699669	−	0.714467i	$-0.253331\pi$
$739$	38.0404	1.39934	0.699669	+	0.714467i	$0.253331\pi$
$740$	9.25476	0.340212
$741$	35.9855	1.32196
$742$	7.43901	0.273095
$743$	−13.8242	−0.507162	−0.253581	−	0.967314i	$-0.581608\pi$
$743$	−13.8242	−0.507162	−0.253581	+	0.967314i	$0.581608\pi$
$744$	−3.74922	−0.137453
$745$	−36.3756	−1.33270
$746$	−43.2391	−1.58310
$747$	0.843555	0.0308641
$748$	−2.53637	−0.0927390
$749$	−13.1078	−0.478948
$750$	−15.5856	−0.569106
$751$	41.0014	1.49616	0.748082	−	0.663607i	$-0.230975\pi$
$751$	41.0014	1.49616	0.748082	+	0.663607i	$0.230975\pi$
$752$	0.0382861	0.00139615
$753$	30.2104	1.10093
$754$	14.4091	0.524749
$755$	25.2972	0.920659
$756$	−18.1770	−0.661090
$757$	−37.2460	−1.35373	−0.676864	−	0.736109i	$-0.736661\pi$
$757$	−37.2460	−1.35373	−0.676864	+	0.736109i	$0.736661\pi$
$758$	24.9660	0.906805
$759$	−27.0468	−0.981736
$760$	30.4478	1.10446
$761$	15.9417	0.577887	0.288943	−	0.957346i	$-0.406696\pi$
$761$	15.9417	0.577887	0.288943	+	0.957346i	$0.406696\pi$
$762$	−36.2754	−1.31412
$763$	12.3774	0.448094
$764$	3.22156	0.116552
$765$	−1.04148	−0.0376550
$766$	36.6501	1.32422
$767$	−39.8424	−1.43862
$768$	−21.0547	−0.759746
$769$	−12.6442	−0.455961	−0.227980	−	0.973666i	$-0.573212\pi$
$769$	−12.6442	−0.455961	−0.227980	+	0.973666i	$0.573212\pi$
$770$	17.2602	0.622014
$771$	13.9630	0.502865
$772$	−67.7658	−2.43894
$773$	−40.5226	−1.45750	−0.728748	−	0.684782i	$-0.759897\pi$
$773$	−40.5226	−1.45750	−0.728748	+	0.684782i	$0.759897\pi$
$774$	−3.98764	−0.143333
$775$	3.21923	0.115638
$776$	38.5725	1.38467
$777$	−1.33514	−0.0478980
$778$	−31.4630	−1.12800
$779$	−10.9621	−0.392758
$780$	−88.0570	−3.15295
$781$	−16.4088	−0.587153
$782$	−5.24940	−0.187718
$783$	4.97926	0.177944
$784$	−0.0354884	−0.00126744
$785$	−22.5415	−0.804540
$786$	21.0804	0.751911
$787$	−17.4458	−0.621875	−0.310937	−	0.950430i	$-0.600643\pi$
$787$	−17.4458	−0.621875	−0.310937	+	0.950430i	$0.600643\pi$
$788$	−16.5764	−0.590511
$789$	−12.1651	−0.433090
$790$	−103.331	−3.67636
$791$	2.75650	0.0980097
$792$	9.00122	0.319845
$793$	15.8794	0.563895
$794$	−67.7996	−2.40612
$795$	12.4533	0.441674
$796$	−38.8714	−1.37776
$797$	37.6245	1.33273	0.666365	−	0.745626i	$-0.267849\pi$
$797$	37.6245	1.33273	0.666365	+	0.745626i	$0.267849\pi$
$798$	−11.5459	−0.408721
$799$	0.321930	0.0113891
$800$	18.3411	0.648455
$801$	−3.71301	−0.131193
$802$	68.8775	2.43215
$803$	27.3960	0.966785
$804$	8.91233	0.314314
$805$	22.0570	0.777406
$806$	−16.2946	−0.573953
$807$	26.9966	0.950326
$808$	15.0213	0.528446
$809$	−2.35923	−0.0829462	−0.0414731	−	0.999140i	$-0.513205\pi$
$809$	−2.35923	−0.0829462	−0.0414731	+	0.999140i	$0.513205\pi$
$810$	−25.3410	−0.890393
$811$	7.64520	0.268459	0.134230	−	0.990950i	$-0.457144\pi$
$811$	7.64520	0.268459	0.134230	+	0.990950i	$0.457144\pi$
$812$	−2.85458	−0.100176
$813$	31.8762	1.11795
$814$	6.02047	0.211017
$815$	16.7266	0.585906
$816$	0.0141390	0.000494966 0
$817$	−5.41802	−0.189552
$818$	−62.3464	−2.17989
$819$	−8.67566	−0.303152
$820$	26.8245	0.936750
$821$	11.4870	0.400901	0.200450	−	0.979704i	$-0.435759\pi$
$821$	11.4870	0.400901	0.200450	+	0.979704i	$0.435759\pi$
$822$	−56.0646	−1.95548
$823$	−22.9035	−0.798367	−0.399184	−	0.916871i	$-0.630706\pi$
$823$	−22.9035	−0.798367	−0.399184	+	0.916871i	$0.630706\pi$
$824$	44.2974	1.54317
$825$	11.3172	0.394013
$826$	12.7834	0.444791
$827$	17.6794	0.614772	0.307386	−	0.951585i	$-0.400546\pi$
$827$	17.6794	0.614772	0.307386	+	0.951585i	$0.400546\pi$
$828$	30.2351	1.05074
$829$	−37.1531	−1.29038	−0.645190	−	0.764022i	$-0.723222\pi$
$829$	−37.1531	−1.29038	−0.645190	+	0.764022i	$0.723222\pi$
$830$	−4.54225	−0.157664
$831$	−2.80954	−0.0974617
$832$	−92.3303	−3.20098
$833$	−0.298405	−0.0103391
$834$	8.05204	0.278819
$835$	−41.0663	−1.42116
$836$	32.1466	1.11181
$837$	−5.63082	−0.194630
$838$	−74.4096	−2.57044
$839$	−10.3135	−0.356063	−0.178032	−	0.984025i	$-0.556973\pi$
$839$	−10.3135	−0.356063	−0.178032	+	0.984025i	$0.556973\pi$
$840$	10.7487	0.370866
$841$	−28.2180	−0.973036
$842$	62.7202	2.16148
$843$	−10.4383	−0.359515
$844$	11.2270	0.386449
$845$	−108.329	−3.72663
$846$	−3.00302	−0.103246
$847$	−4.06710	−0.139747
$848$	0.115459	0.00396489
$849$	−35.4389	−1.21626
$850$	2.19650	0.0753393
$851$	7.69362	0.263734
$852$	−26.8594	−0.920188
$853$	−30.0572	−1.02914	−0.514569	−	0.857449i	$-0.672048\pi$
$853$	−30.0572	−1.02914	−0.514569	+	0.857449i	$0.672048\pi$
$854$	−5.09490	−0.174344
$855$	13.2000	0.451431
$856$	36.8080	1.25807
$857$	−25.5562	−0.872984	−0.436492	−	0.899708i	$-0.643779\pi$
$857$	−25.5562	−0.872984	−0.436492	+	0.899708i	$0.643779\pi$
$858$	−57.2835	−1.95563
$859$	49.0720	1.67431	0.837157	−	0.546963i	$-0.184216\pi$
$859$	49.0720	1.67431	0.837157	+	0.546963i	$0.184216\pi$
$860$	13.2580	0.452093
$861$	−3.86984	−0.131884
$862$	72.8692	2.48194
$863$	−40.7899	−1.38851	−0.694253	−	0.719731i	$-0.744265\pi$
$863$	−40.7899	−1.38851	−0.694253	+	0.719731i	$0.744265\pi$
$864$	−32.0808	−1.09141
$865$	22.4830	0.764444
$866$	32.6242	1.10862
$867$	−22.5785	−0.766807
$868$	3.22812	0.109569
$869$	−41.5051	−1.40796
$870$	−7.73943	−0.262391
$871$	14.7362	0.499317
$872$	−34.7571	−1.17703
$873$	16.7223	0.565964
$874$	66.5321	2.25048
$875$	5.10533	0.172592
$876$	44.8443	1.51515
$877$	−13.9339	−0.470515	−0.235258	−	0.971933i	$-0.575593\pi$
$877$	−13.9339	−0.470515	−0.235258	+	0.971933i	$0.575593\pi$
$878$	64.4197	2.17406
$879$	−14.6741	−0.494946
$880$	0.267892	0.00903062
$881$	−14.8148	−0.499122	−0.249561	−	0.968359i	$-0.580286\pi$
$881$	−14.8148	−0.499122	−0.249561	+	0.968359i	$0.580286\pi$
$882$	2.78358	0.0937280
$883$	−21.5374	−0.724792	−0.362396	−	0.932024i	$-0.618041\pi$
$883$	−21.5374	−0.724792	−0.362396	+	0.932024i	$0.618041\pi$
$884$	−6.86479	−0.230888
$885$	21.4002	0.719358
$886$	10.8972	0.366097
$887$	−15.9010	−0.533902	−0.266951	−	0.963710i	$-0.586016\pi$
$887$	−15.9010	−0.533902	−0.266951	+	0.963710i	$0.586016\pi$
$888$	3.74922	0.125816
$889$	11.8826	0.398529
$890$	19.9932	0.670174
$891$	−10.1787	−0.341000
$892$	−4.81850	−0.161335
$893$	−4.08021	−0.136539
$894$	−38.7342	−1.29547
$895$	46.2038	1.54442
$896$	18.2294	0.609002
$897$	−73.2031	−2.44418
$898$	74.6469	2.49100
$899$	−0.884286	−0.0294926
$900$	−12.6512	−0.421707
$901$	0.970842	0.0323435
$902$	17.4500	0.581022
$903$	−1.91267	−0.0636497
$904$	−7.74052	−0.257446
$905$	−36.5686	−1.21558
$906$	26.9375	0.894938
$907$	0.218590	0.00725815	0.00362907	−	0.999993i	$-0.498845\pi$
$907$	0.218590	0.00725815	0.00362907	+	0.999993i	$0.498845\pi$
$908$	−25.8246	−0.857020
$909$	6.51215	0.215994
$910$	46.7154	1.54860
$911$	−9.66079	−0.320076	−0.160038	−	0.987111i	$-0.551162\pi$
$911$	−9.66079	−0.320076	−0.160038	+	0.987111i	$0.551162\pi$
$912$	−0.179201	−0.00593395
$913$	−1.82448	−0.0603816
$914$	−59.9315	−1.98236
$915$	−8.52916	−0.281965
$916$	49.3073	1.62916
$917$	−6.90522	−0.228030
$918$	−3.84194	−0.126803
$919$	−52.5219	−1.73254	−0.866269	−	0.499578i	$-0.833488\pi$
$919$	−52.5219	−1.73254	−0.866269	+	0.499578i	$0.833488\pi$
$920$	−61.9383	−2.04204
$921$	−10.4815	−0.345378
$922$	−74.8296	−2.46438
$923$	−44.4110	−1.46181
$924$	11.3484	0.373335
$925$	−3.21923	−0.105848
$926$	54.4625	1.78975
$927$	19.2042	0.630749
$928$	−5.03809	−0.165383
$929$	20.9546	0.687498	0.343749	−	0.939062i	$-0.388303\pi$
$929$	20.9546	0.687498	0.343749	+	0.939062i	$0.388303\pi$
$930$	8.75217	0.286995
$931$	3.78206	0.123952
$932$	36.0893	1.18215
$933$	1.86648	0.0611059
$934$	26.8958	0.880059
$935$	2.25258	0.0736671
$936$	24.3621	0.796302
$937$	26.4227	0.863192	0.431596	−	0.902067i	$-0.357951\pi$
$937$	26.4227	0.863192	0.431596	+	0.902067i	$0.357951\pi$
$938$	−4.72810	−0.154378
$939$	−27.1618	−0.886393
$940$	9.98435	0.325654
$941$	−31.8518	−1.03834	−0.519170	−	0.854671i	$-0.673759\pi$
$941$	−31.8518	−1.03834	−0.519170	+	0.854671i	$0.673759\pi$
$942$	−24.0031	−0.782063
$943$	22.2996	0.726174
$944$	0.198408	0.00645764
$945$	16.1431	0.525136
$946$	8.62467	0.280412
$947$	−12.4928	−0.405960	−0.202980	−	0.979183i	$-0.565063\pi$
$947$	−12.4928	−0.405960	−0.202980	+	0.979183i	$0.565063\pi$
$948$	−67.9392	−2.20656
$949$	74.1483	2.40696
$950$	−27.8389	−0.903214
$951$	−14.6717	−0.475764
$952$	0.837952	0.0271582
$953$	38.2755	1.23987	0.619933	−	0.784655i	$-0.287160\pi$
$953$	38.2755	1.23987	0.619933	+	0.784655i	$0.287160\pi$
$954$	−9.05621	−0.293206
$955$	−2.86109	−0.0925828
$956$	−57.0593	−1.84543
$957$	−3.10870	−0.100490
$958$	54.9705	1.77602
$959$	18.3649	0.593033
$960$	49.5925	1.60059
$961$	1.00000	0.0322581
$962$	16.2946	0.525359
$963$	15.9574	0.514218
$964$	−13.2958	−0.428229
$965$	60.1834	1.93737
$966$	23.4872	0.755688
$967$	−7.74696	−0.249125	−0.124563	−	0.992212i	$-0.539753\pi$
$967$	−7.74696	−0.249125	−0.124563	+	0.992212i	$0.539753\pi$
$968$	11.4208	0.367079
$969$	−1.50682	−0.0484061
$970$	−90.0436	−2.89112
$971$	25.8768	0.830425	0.415212	−	0.909725i	$-0.363707\pi$
$971$	25.8768	0.830425	0.415212	+	0.909725i	$0.363707\pi$
$972$	37.8694	1.21466
$973$	−2.63758	−0.0845569
$974$	42.2319	1.35320
$975$	30.6303	0.980954
$976$	−0.0790768	−0.00253119
$977$	9.55586	0.305719	0.152859	−	0.988248i	$-0.451152\pi$
$977$	9.55586	0.305719	0.152859	+	0.988248i	$0.451152\pi$
$978$	17.8111	0.569537
$979$	8.03067	0.256661
$980$	−9.25476	−0.295632
$981$	−15.0682	−0.481092
$982$	19.2180	0.613271
$983$	−2.10126	−0.0670197	−0.0335099	−	0.999438i	$-0.510669\pi$
$983$	−2.10126	−0.0670197	−0.0335099	+	0.999438i	$0.510669\pi$
$984$	10.8669	0.346425
$985$	14.7217	0.469071
$986$	−0.603354	−0.0192147
$987$	−1.44040	−0.0458484
$988$	87.0059	2.76803
$989$	11.0216	0.350465
$990$	−21.0125	−0.667820
$991$	18.9077	0.600623	0.300312	−	0.953841i	$-0.402909\pi$
$991$	18.9077	0.600623	0.300312	+	0.953841i	$0.402909\pi$
$992$	5.69735	0.180891
$993$	0.477122	0.0151410
$994$	14.2493	0.451959
$995$	34.5220	1.09442
$996$	−2.98648	−0.0946302
$997$	−33.0373	−1.04630	−0.523152	−	0.852240i	$-0.675244\pi$
$997$	−33.0373	−1.04630	−0.523152	+	0.852240i	$0.675244\pi$
$998$	44.2155	1.39962
$999$	5.63082	0.178151

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8029.2.a.d.1.9	✓	66

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8029.2.a.d.1.9	✓	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)

\(f(q)\)	\(=\)	\(q-2.28651 q^{2} +1.33514 q^{3} +3.22812 q^{4} -2.86692 q^{5} -3.05281 q^{6} +1.00000 q^{7} -2.80810 q^{8} -1.21739 q^{9} +O(q^{10})\)	\(q-2.28651 q^{2} +1.33514 q^{3} +3.22812 q^{4} -2.86692 q^{5} -3.05281 q^{6} +1.00000 q^{7} -2.80810 q^{8} -1.21739 q^{9} +6.55524 q^{10} +2.63304 q^{11} +4.31000 q^{12} +7.12642 q^{13} -2.28651 q^{14} -3.82775 q^{15} -0.0354884 q^{16} -0.298405 q^{17} +2.78358 q^{18} +3.78206 q^{19} -9.25476 q^{20} +1.33514 q^{21} -6.02047 q^{22} -7.69362 q^{23} -3.74922 q^{24} +3.21923 q^{25} -16.2946 q^{26} -5.63082 q^{27} +3.22812 q^{28} -0.884286 q^{29} +8.75217 q^{30} +1.00000 q^{31} +5.69735 q^{32} +3.51548 q^{33} +0.682306 q^{34} -2.86692 q^{35} -3.92989 q^{36} -1.00000 q^{37} -8.64770 q^{38} +9.51479 q^{39} +8.05060 q^{40} -2.89845 q^{41} -3.05281 q^{42} -1.43256 q^{43} +8.49977 q^{44} +3.49017 q^{45} +17.5915 q^{46} -1.07883 q^{47} -0.0473820 q^{48} +1.00000 q^{49} -7.36079 q^{50} -0.398413 q^{51} +23.0049 q^{52} -3.25344 q^{53} +12.8749 q^{54} -7.54872 q^{55} -2.80810 q^{56} +5.04958 q^{57} +2.02193 q^{58} -5.59080 q^{59} -12.3564 q^{60} +2.22825 q^{61} -2.28651 q^{62} -1.21739 q^{63} -12.9561 q^{64} -20.4309 q^{65} -8.03818 q^{66} +2.06783 q^{67} -0.963287 q^{68} -10.2721 q^{69} +6.55524 q^{70} -6.23189 q^{71} +3.41857 q^{72} +10.4047 q^{73} +2.28651 q^{74} +4.29813 q^{75} +12.2089 q^{76} +2.63304 q^{77} -21.7556 q^{78} -15.7632 q^{79} +0.101742 q^{80} -3.86577 q^{81} +6.62733 q^{82} -0.692919 q^{83} +4.31000 q^{84} +0.855504 q^{85} +3.27556 q^{86} -1.18065 q^{87} -7.39385 q^{88} +3.04996 q^{89} -7.98030 q^{90} +7.12642 q^{91} -24.8359 q^{92} +1.33514 q^{93} +2.46676 q^{94} -10.8429 q^{95} +7.60677 q^{96} -13.7361 q^{97} -2.28651 q^{98} -3.20545 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 66 q - 5 q^{2} - 12 q^{3} + 63 q^{4} - 26 q^{5} - 19 q^{6} + 66 q^{7} - 15 q^{8} + 66 q^{9}+O(q^{10}) \) 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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