LMFDB - Embedded newform 4011.2.a.m.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4011,2,Mod(1,4011)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4011, 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("4011.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4011 = 3 \cdot 7 \cdot 191 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4011.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:	$32.0279962507$
Analytic rank:	$0$
Dimension:	$29$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Character	$\chi$	$=$	4011.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.96996 q^{2} +1.00000 q^{3} +1.88076 q^{4} +4.31773 q^{5} -1.96996 q^{6} -1.00000 q^{7} +0.234907 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.96996 q^{2} +1.00000 q^{3} +1.88076 q^{4} +4.31773 q^{5} -1.96996 q^{6} -1.00000 q^{7} +0.234907 q^{8} +1.00000 q^{9} -8.50578 q^{10} -2.03173 q^{11} +1.88076 q^{12} +3.99082 q^{13} +1.96996 q^{14} +4.31773 q^{15} -4.22427 q^{16} +5.63951 q^{17} -1.96996 q^{18} +6.75323 q^{19} +8.12060 q^{20} -1.00000 q^{21} +4.00243 q^{22} +1.90141 q^{23} +0.234907 q^{24} +13.6428 q^{25} -7.86176 q^{26} +1.00000 q^{27} -1.88076 q^{28} -3.06480 q^{29} -8.50578 q^{30} -8.64381 q^{31} +7.85184 q^{32} -2.03173 q^{33} -11.1096 q^{34} -4.31773 q^{35} +1.88076 q^{36} +9.40368 q^{37} -13.3036 q^{38} +3.99082 q^{39} +1.01427 q^{40} -0.254069 q^{41} +1.96996 q^{42} +6.07132 q^{43} -3.82118 q^{44} +4.31773 q^{45} -3.74570 q^{46} -9.20116 q^{47} -4.22427 q^{48} +1.00000 q^{49} -26.8758 q^{50} +5.63951 q^{51} +7.50575 q^{52} +9.42931 q^{53} -1.96996 q^{54} -8.77246 q^{55} -0.234907 q^{56} +6.75323 q^{57} +6.03755 q^{58} -9.48049 q^{59} +8.12060 q^{60} -12.2989 q^{61} +17.0280 q^{62} -1.00000 q^{63} -7.01930 q^{64} +17.2313 q^{65} +4.00243 q^{66} -4.51641 q^{67} +10.6065 q^{68} +1.90141 q^{69} +8.50578 q^{70} -7.37828 q^{71} +0.234907 q^{72} -14.8580 q^{73} -18.5249 q^{74} +13.6428 q^{75} +12.7012 q^{76} +2.03173 q^{77} -7.86176 q^{78} -2.06572 q^{79} -18.2393 q^{80} +1.00000 q^{81} +0.500507 q^{82} +11.2656 q^{83} -1.88076 q^{84} +24.3499 q^{85} -11.9603 q^{86} -3.06480 q^{87} -0.477268 q^{88} +12.6317 q^{89} -8.50578 q^{90} -3.99082 q^{91} +3.57608 q^{92} -8.64381 q^{93} +18.1260 q^{94} +29.1586 q^{95} +7.85184 q^{96} +14.3984 q^{97} -1.96996 q^{98} -2.03173 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 29 q + 6 q^{2} + 29 q^{3} + 40 q^{4} + 22 q^{5} + 6 q^{6} - 29 q^{7} + 15 q^{8} + 29 q^{9}+O(q^{10}) $ 29 * q + 6 * q^2 + 29 * q^3 + 40 * q^4 + 22 * q^5 + 6 * q^6 - 29 * q^7 + 15 * q^8 + 29 * q^9	\( 29 q + 6 q^{2} + 29 q^{3} + 40 q^{4} + 22 q^{5} + 6 q^{6} - 29 q^{7} + 15 q^{8} + 29 q^{9} + 11 q^{11} + 40 q^{12} + 13 q^{13} - 6 q^{14} + 22 q^{15} + 58 q^{16} + 17 q^{17} + 6 q^{18} + 3 q^{19} + 52 q^{20} - 29 q^{21} + 17 q^{22} + 36 q^{23} + 15 q^{24} + 57 q^{25} + 25 q^{26} + 29 q^{27} - 40 q^{28} + 20 q^{29} + 6 q^{31} + 46 q^{32} + 11 q^{33} + 18 q^{34} - 22 q^{35} + 40 q^{36} + 22 q^{37} + 8 q^{38} + 13 q^{39} + 6 q^{40} + 26 q^{41} - 6 q^{42} + 21 q^{43} + 22 q^{44} + 22 q^{45} + 28 q^{46} + 41 q^{47} + 58 q^{48} + 29 q^{49} + 18 q^{50} + 17 q^{51} + 2 q^{52} + 37 q^{53} + 6 q^{54} + 7 q^{55} - 15 q^{56} + 3 q^{57} + 9 q^{58} + 27 q^{59} + 52 q^{60} + 20 q^{61} - 12 q^{62} - 29 q^{63} + 59 q^{64} + 3 q^{65} + 17 q^{66} + 30 q^{67} + 33 q^{68} + 36 q^{69} + 68 q^{71} + 15 q^{72} + q^{73} + 21 q^{74} + 57 q^{75} + 11 q^{76} - 11 q^{77} + 25 q^{78} + 34 q^{79} + 110 q^{80} + 29 q^{81} - 49 q^{82} + 13 q^{83} - 40 q^{84} + 27 q^{85} + 35 q^{86} + 20 q^{87} + 17 q^{88} + 61 q^{89} - 13 q^{91} + 86 q^{92} + 6 q^{93} - 19 q^{94} + 25 q^{95} + 46 q^{96} - 3 q^{97} + 6 q^{98} + 11 q^{99}+O(q^{100}) \) 29 * q + 6 * q^2 + 29 * q^3 + 40 * q^4 + 22 * q^5 + 6 * q^6 - 29 * q^7 + 15 * q^8 + 29 * q^9 + 11 * q^11 + 40 * q^12 + 13 * q^13 - 6 * q^14 + 22 * q^15 + 58 * q^16 + 17 * q^17 + 6 * q^18 + 3 * q^19 + 52 * q^20 - 29 * q^21 + 17 * q^22 + 36 * q^23 + 15 * q^24 + 57 * q^25 + 25 * q^26 + 29 * q^27 - 40 * q^28 + 20 * q^29 + 6 * q^31 + 46 * q^32 + 11 * q^33 + 18 * q^34 - 22 * q^35 + 40 * q^36 + 22 * q^37 + 8 * q^38 + 13 * q^39 + 6 * q^40 + 26 * q^41 - 6 * q^42 + 21 * q^43 + 22 * q^44 + 22 * q^45 + 28 * q^46 + 41 * q^47 + 58 * q^48 + 29 * q^49 + 18 * q^50 + 17 * q^51 + 2 * q^52 + 37 * q^53 + 6 * q^54 + 7 * q^55 - 15 * q^56 + 3 * q^57 + 9 * q^58 + 27 * q^59 + 52 * q^60 + 20 * q^61 - 12 * q^62 - 29 * q^63 + 59 * q^64 + 3 * q^65 + 17 * q^66 + 30 * q^67 + 33 * q^68 + 36 * q^69 + 68 * q^71 + 15 * q^72 + q^73 + 21 * q^74 + 57 * q^75 + 11 * q^76 - 11 * q^77 + 25 * q^78 + 34 * q^79 + 110 * q^80 + 29 * q^81 - 49 * q^82 + 13 * q^83 - 40 * q^84 + 27 * q^85 + 35 * q^86 + 20 * q^87 + 17 * q^88 + 61 * q^89 - 13 * q^91 + 86 * q^92 + 6 * q^93 - 19 * q^94 + 25 * q^95 + 46 * q^96 - 3 * q^97 + 6 * q^98 + 11 * 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 $

$2$	−1.96996	−1.39297	−0.696487	−	0.717569i	$-0.745255\pi$
$2$	−1.96996	−1.39297	−0.696487	+	0.717569i	$0.745255\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.88076	0.940378
$5$	4.31773	1.93095	0.965474	−	0.260498i	$-0.0838867\pi$
$5$	4.31773	1.93095	0.965474	+	0.260498i	$0.0838867\pi$
$6$	−1.96996	−0.804234
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	0.234907	0.0830523
$9$	1.00000	0.333333
$10$	−8.50578	−2.68976
$11$	−2.03173	−0.612589	−0.306294	−	0.951937i	$-0.599089\pi$
$11$	−2.03173	−0.612589	−0.306294	+	0.951937i	$0.599089\pi$
$12$	1.88076	0.542927
$13$	3.99082	1.10685	0.553426	−	0.832898i	$-0.313320\pi$
$13$	3.99082	1.10685	0.553426	+	0.832898i	$0.313320\pi$
$14$	1.96996	0.526495
$15$	4.31773	1.11483
$16$	−4.22427	−1.05607
$17$	5.63951	1.36778	0.683891	−	0.729584i	$-0.260286\pi$
$17$	5.63951	1.36778	0.683891	+	0.729584i	$0.260286\pi$
$18$	−1.96996	−0.464325
$19$	6.75323	1.54930	0.774648	−	0.632392i	$-0.217927\pi$
$19$	6.75323	1.54930	0.774648	+	0.632392i	$0.217927\pi$
$20$	8.12060	1.81582
$21$	−1.00000	−0.218218
$22$	4.00243	0.853321
$23$	1.90141	0.396470	0.198235	−	0.980154i	$-0.436479\pi$
$23$	1.90141	0.396470	0.198235	+	0.980154i	$0.436479\pi$
$24$	0.234907	0.0479503
$25$	13.6428	2.72856
$26$	−7.86176	−1.54182
$27$	1.00000	0.192450
$28$	−1.88076	−0.355429
$29$	−3.06480	−0.569119	−0.284560	−	0.958658i	$-0.591847\pi$
$29$	−3.06480	−0.569119	−0.284560	+	0.958658i	$0.591847\pi$
$30$	−8.50578	−1.55293
$31$	−8.64381	−1.55247	−0.776237	−	0.630441i	$-0.782874\pi$
$31$	−8.64381	−1.55247	−0.776237	+	0.630441i	$0.782874\pi$
$32$	7.85184	1.38802
$33$	−2.03173	−0.353678
$34$	−11.1096	−1.90529
$35$	−4.31773	−0.729830
$36$	1.88076	0.313459
$37$	9.40368	1.54596	0.772978	−	0.634433i	$-0.218767\pi$
$37$	9.40368	1.54596	0.772978	+	0.634433i	$0.218767\pi$
$38$	−13.3036	−2.15813
$39$	3.99082	0.639042
$40$	1.01427	0.160370
$41$	−0.254069	−0.0396790	−0.0198395	−	0.999803i	$-0.506316\pi$
$41$	−0.254069	−0.0396790	−0.0198395	+	0.999803i	$0.506316\pi$
$42$	1.96996	0.303972
$43$	6.07132	0.925868	0.462934	−	0.886393i	$-0.346797\pi$
$43$	6.07132	0.925868	0.462934	+	0.886393i	$0.346797\pi$
$44$	−3.82118	−0.576065
$45$	4.31773	0.643650
$46$	−3.74570	−0.552273
$47$	−9.20116	−1.34213	−0.671064	−	0.741400i	$-0.734162\pi$
$47$	−9.20116	−1.34213	−0.671064	+	0.741400i	$0.734162\pi$
$48$	−4.22427	−0.609721
$49$	1.00000	0.142857
$50$	−26.8758	−3.80082
$51$	5.63951	0.789690
$52$	7.50575	1.04086
$53$	9.42931	1.29522	0.647608	−	0.761974i	$-0.275770\pi$
$53$	9.42931	1.29522	0.647608	+	0.761974i	$0.275770\pi$
$54$	−1.96996	−0.268078
$55$	−8.77246	−1.18288
$56$	−0.234907	−0.0313908
$57$	6.75323	0.894487
$58$	6.03755	0.792769
$59$	−9.48049	−1.23425	−0.617127	−	0.786863i	$-0.711704\pi$
$59$	−9.48049	−1.23425	−0.617127	+	0.786863i	$0.711704\pi$
$60$	8.12060	1.04836
$61$	−12.2989	−1.57471	−0.787355	−	0.616499i	$-0.788550\pi$
$61$	−12.2989	−1.57471	−0.787355	+	0.616499i	$0.788550\pi$
$62$	17.0280	2.16256
$63$	−1.00000	−0.125988
$64$	−7.01930	−0.877413
$65$	17.2313	2.13728
$66$	4.00243	0.492665
$67$	−4.51641	−0.551768	−0.275884	−	0.961191i	$-0.588971\pi$
$67$	−4.51641	−0.551768	−0.275884	+	0.961191i	$0.588971\pi$
$68$	10.6065	1.28623
$69$	1.90141	0.228902
$70$	8.50578	1.01663
$71$	−7.37828	−0.875641	−0.437820	−	0.899063i	$-0.644249\pi$
$71$	−7.37828	−0.875641	−0.437820	+	0.899063i	$0.644249\pi$
$72$	0.234907	0.0276841
$73$	−14.8580	−1.73900	−0.869501	−	0.493932i	$-0.835559\pi$
$73$	−14.8580	−1.73900	−0.869501	+	0.493932i	$0.835559\pi$
$74$	−18.5249	−2.15348
$75$	13.6428	1.57534
$76$	12.7012	1.45692
$77$	2.03173	0.231537
$78$	−7.86176	−0.890169
$79$	−2.06572	−0.232412	−0.116206	−	0.993225i	$-0.537073\pi$
$79$	−2.06572	−0.232412	−0.116206	+	0.993225i	$0.537073\pi$
$80$	−18.2393	−2.03921
$81$	1.00000	0.111111
$82$	0.500507	0.0552718
$83$	11.2656	1.23656	0.618280	−	0.785958i	$-0.287830\pi$
$83$	11.2656	1.23656	0.618280	+	0.785958i	$0.287830\pi$
$84$	−1.88076	−0.205207
$85$	24.3499	2.64112
$86$	−11.9603	−1.28971
$87$	−3.06480	−0.328581
$88$	−0.477268	−0.0508769
$89$	12.6317	1.33896	0.669479	−	0.742831i	$-0.266518\pi$
$89$	12.6317	1.33896	0.669479	+	0.742831i	$0.266518\pi$
$90$	−8.50578	−0.896587
$91$	−3.99082	−0.418351
$92$	3.57608	0.372832
$93$	−8.64381	−0.896321
$94$	18.1260	1.86955
$95$	29.1586	2.99161
$96$	7.85184	0.801375
$97$	14.3984	1.46193	0.730967	−	0.682413i	$-0.239069\pi$
$97$	14.3984	1.46193	0.730967	+	0.682413i	$0.239069\pi$
$98$	−1.96996	−0.198996
$99$	−2.03173	−0.204196
$100$	25.6588	2.56588
$101$	−6.00166	−0.597188	−0.298594	−	0.954380i	$-0.596518\pi$
$101$	−6.00166	−0.597188	−0.298594	+	0.954380i	$0.596518\pi$
$102$	−11.1096	−1.10002
$103$	−1.77356	−0.174754	−0.0873770	−	0.996175i	$-0.527848\pi$
$103$	−1.77356	−0.174754	−0.0873770	+	0.996175i	$0.527848\pi$
$104$	0.937472	0.0919267
$105$	−4.31773	−0.421368
$106$	−18.5754	−1.80420
$107$	6.59494	0.637557	0.318778	−	0.947829i	$-0.396727\pi$
$107$	6.59494	0.637557	0.318778	+	0.947829i	$0.396727\pi$
$108$	1.88076	0.180976
$109$	11.9976	1.14916	0.574581	−	0.818448i	$-0.305165\pi$
$109$	11.9976	1.14916	0.574581	+	0.818448i	$0.305165\pi$
$110$	17.2814	1.64772
$111$	9.40368	0.892558
$112$	4.22427	0.399156
$113$	9.06317	0.852592	0.426296	−	0.904584i	$-0.359818\pi$
$113$	9.06317	0.852592	0.426296	+	0.904584i	$0.359818\pi$
$114$	−13.3036	−1.24600
$115$	8.20976	0.765564
$116$	−5.76414	−0.535187
$117$	3.99082	0.368951
$118$	18.6762	1.71928
$119$	−5.63951	−0.516973
$120$	1.01427	0.0925895
$121$	−6.87208	−0.624735
$122$	24.2283	2.19353
$123$	−0.254069	−0.0229087
$124$	−16.2569	−1.45991
$125$	37.3174	3.33777
$126$	1.96996	0.175498
$127$	1.24401	0.110388	0.0551939	−	0.998476i	$-0.482422\pi$
$127$	1.24401	0.110388	0.0551939	+	0.998476i	$0.482422\pi$
$128$	−1.87592	−0.165809
$129$	6.07132	0.534550
$130$	−33.9450	−2.97717
$131$	−13.9676	−1.22036	−0.610178	−	0.792264i	$-0.708902\pi$
$131$	−13.9676	−1.22036	−0.610178	+	0.792264i	$0.708902\pi$
$132$	−3.82118	−0.332591
$133$	−6.75323	−0.585579
$134$	8.89717	0.768598
$135$	4.31773	0.371611
$136$	1.32476	0.113598
$137$	−17.6888	−1.51125	−0.755627	−	0.655002i	$-0.772668\pi$
$137$	−17.6888	−1.51125	−0.755627	+	0.655002i	$0.772668\pi$
$138$	−3.74570	−0.318855
$139$	−17.4143	−1.47706	−0.738529	−	0.674222i	$-0.764479\pi$
$139$	−17.4143	−1.47706	−0.738529	+	0.674222i	$0.764479\pi$
$140$	−8.12060	−0.686316
$141$	−9.20116	−0.774878
$142$	14.5349	1.21974
$143$	−8.10825	−0.678046
$144$	−4.22427	−0.352022
$145$	−13.2330	−1.09894
$146$	29.2698	2.42238
$147$	1.00000	0.0824786
$148$	17.6860	1.45378
$149$	7.77691	0.637110	0.318555	−	0.947904i	$-0.396803\pi$
$149$	7.77691	0.637110	0.318555	+	0.947904i	$0.396803\pi$
$150$	−26.8758	−2.19440
$151$	−1.62501	−0.132241	−0.0661207	−	0.997812i	$-0.521062\pi$
$151$	−1.62501	−0.132241	−0.0661207	+	0.997812i	$0.521062\pi$
$152$	1.58638	0.128673
$153$	5.63951	0.455928
$154$	−4.00243	−0.322525
$155$	−37.3217	−2.99775
$156$	7.50575	0.600941
$157$	−21.3535	−1.70419	−0.852097	−	0.523383i	$-0.824670\pi$
$157$	−21.3535	−1.70419	−0.852097	+	0.523383i	$0.824670\pi$
$158$	4.06940	0.323744
$159$	9.42931	0.747793
$160$	33.9022	2.68020
$161$	−1.90141	−0.149852
$162$	−1.96996	−0.154775
$163$	−11.3602	−0.889796	−0.444898	−	0.895581i	$-0.646760\pi$
$163$	−11.3602	−0.889796	−0.444898	+	0.895581i	$0.646760\pi$
$164$	−0.477842	−0.0373132
$165$	−8.77246	−0.682935
$166$	−22.1928	−1.72250
$167$	3.00614	0.232622	0.116311	−	0.993213i	$-0.462893\pi$
$167$	3.00614	0.232622	0.116311	+	0.993213i	$0.462893\pi$
$168$	−0.234907	−0.0181235
$169$	2.92661	0.225123
$170$	−47.9684	−3.67901
$171$	6.75323	0.516432
$172$	11.4187	0.870666
$173$	15.5153	1.17961	0.589804	−	0.807547i	$-0.299205\pi$
$173$	15.5153	1.17961	0.589804	+	0.807547i	$0.299205\pi$
$174$	6.03755	0.457705
$175$	−13.6428	−1.03130
$176$	8.58256	0.646935
$177$	−9.48049	−0.712597
$178$	−24.8840	−1.86513
$179$	18.6552	1.39435	0.697177	−	0.716899i	$-0.254439\pi$
$179$	18.6552	1.39435	0.697177	+	0.716899i	$0.254439\pi$
$180$	8.12060	0.605274
$181$	−20.1390	−1.49692	−0.748460	−	0.663180i	$-0.769206\pi$
$181$	−20.1390	−1.49692	−0.748460	+	0.663180i	$0.769206\pi$
$182$	7.86176	0.582752
$183$	−12.2989	−0.909160
$184$	0.446654	0.0329278
$185$	40.6026	2.98516
$186$	17.0280	1.24855
$187$	−11.4580	−0.837888
$188$	−17.3051	−1.26211
$189$	−1.00000	−0.0727393
$190$	−57.4414	−4.16724
$191$	−1.00000	−0.0723575
$191$	−1.00000	−0.0723575
$192$	−7.01930	−0.506574
$193$	−18.7409	−1.34900	−0.674498	−	0.738276i	$-0.735640\pi$
$193$	−18.7409	−1.34900	−0.674498	+	0.738276i	$0.735640\pi$
$194$	−28.3643	−2.03644
$195$	17.2313	1.23396
$196$	1.88076	0.134340
$197$	7.05384	0.502565	0.251283	−	0.967914i	$-0.419148\pi$
$197$	7.05384	0.502565	0.251283	+	0.967914i	$0.419148\pi$
$198$	4.00243	0.284440
$199$	5.02835	0.356450	0.178225	−	0.983990i	$-0.442965\pi$
$199$	5.02835	0.356450	0.178225	+	0.983990i	$0.442965\pi$
$200$	3.20480	0.226613
$201$	−4.51641	−0.318563
$202$	11.8231	0.831867
$203$	3.06480	0.215107
$204$	10.6065	0.742607
$205$	−1.09700	−0.0766181
$206$	3.49384	0.243428
$207$	1.90141	0.132157
$208$	−16.8583	−1.16891
$209$	−13.7207	−0.949082
$210$	8.50578	0.586954
$211$	−14.3182	−0.985708	−0.492854	−	0.870112i	$-0.664046\pi$
$211$	−14.3182	−0.985708	−0.492854	+	0.870112i	$0.664046\pi$
$212$	17.7342	1.21799
$213$	−7.37828	−0.505551
$214$	−12.9918	−0.888100
$215$	26.2143	1.78780
$216$	0.234907	0.0159834
$217$	8.64381	0.586780
$218$	−23.6348	−1.60075
$219$	−14.8580	−1.00401
$220$	−16.4988	−1.11235
$221$	22.5063	1.51393
$222$	−18.5249	−1.24331
$223$	8.11266	0.543264	0.271632	−	0.962401i	$-0.412437\pi$
$223$	8.11266	0.543264	0.271632	+	0.962401i	$0.412437\pi$
$224$	−7.85184	−0.524623
$225$	13.6428	0.909521
$226$	−17.8541	−1.18764
$227$	2.65493	0.176214	0.0881070	−	0.996111i	$-0.471918\pi$
$227$	2.65493	0.176214	0.0881070	+	0.996111i	$0.471918\pi$
$228$	12.7012	0.841155
$229$	16.6635	1.10115	0.550576	−	0.834785i	$-0.314408\pi$
$229$	16.6635	1.10115	0.550576	+	0.834785i	$0.314408\pi$
$230$	−16.1729	−1.06641
$231$	2.03173	0.133678
$232$	−0.719945	−0.0472667
$233$	−27.0594	−1.77272	−0.886359	−	0.462998i	$-0.846774\pi$
$233$	−27.0594	−1.77272	−0.886359	+	0.462998i	$0.846774\pi$
$234$	−7.86176	−0.513939
$235$	−39.7282	−2.59158
$236$	−17.8305	−1.16067
$237$	−2.06572	−0.134183
$238$	11.1096	0.720131
$239$	2.29171	0.148238	0.0741192	−	0.997249i	$-0.476385\pi$
$239$	2.29171	0.148238	0.0741192	+	0.997249i	$0.476385\pi$
$240$	−18.2393	−1.17734
$241$	−11.6718	−0.751845	−0.375922	−	0.926651i	$-0.622674\pi$
$241$	−11.6718	−0.751845	−0.375922	+	0.926651i	$0.622674\pi$
$242$	13.5378	0.870240
$243$	1.00000	0.0641500
$244$	−23.1312	−1.48082
$245$	4.31773	0.275850
$246$	0.500507	0.0319112
$247$	26.9509	1.71484
$248$	−2.03050	−0.128937
$249$	11.2656	0.713928
$250$	−73.5138	−4.64942
$251$	−18.0396	−1.13865	−0.569326	−	0.822112i	$-0.692796\pi$
$251$	−18.0396	−1.13865	−0.569326	+	0.822112i	$0.692796\pi$
$252$	−1.88076	−0.118476
$253$	−3.86314	−0.242873
$254$	−2.45065	−0.153767
$255$	24.3499	1.52485
$256$	17.7341	1.10838
$257$	24.0669	1.50125	0.750626	−	0.660728i	$-0.229752\pi$
$257$	24.0669	1.50125	0.750626	+	0.660728i	$0.229752\pi$
$258$	−11.9603	−0.744615
$259$	−9.40368	−0.584316
$260$	32.4078	2.00985
$261$	−3.06480	−0.189706
$262$	27.5157	1.69993
$263$	21.6860	1.33722	0.668609	−	0.743614i	$-0.266890\pi$
$263$	21.6860	1.33722	0.668609	+	0.743614i	$0.266890\pi$
$264$	−0.477268	−0.0293738
$265$	40.7133	2.50100
$266$	13.3036	0.815697
$267$	12.6317	0.773047
$268$	−8.49427	−0.518870
$269$	−11.2227	−0.684262	−0.342131	−	0.939652i	$-0.611149\pi$
$269$	−11.2227	−0.684262	−0.342131	+	0.939652i	$0.611149\pi$
$270$	−8.50578	−0.517645
$271$	24.1824	1.46897	0.734487	−	0.678622i	$-0.237423\pi$
$271$	24.1824	1.46897	0.734487	+	0.678622i	$0.237423\pi$
$272$	−23.8228	−1.44447
$273$	−3.99082	−0.241535
$274$	34.8462	2.10514
$275$	−27.7185	−1.67149
$276$	3.57608	0.215255
$277$	3.67676	0.220915	0.110458	−	0.993881i	$-0.464768\pi$
$277$	3.67676	0.220915	0.110458	+	0.993881i	$0.464768\pi$
$278$	34.3055	2.05750
$279$	−8.64381	−0.517491
$280$	−1.01427	−0.0606141
$281$	−27.2474	−1.62545	−0.812723	−	0.582650i	$-0.802016\pi$
$281$	−27.2474	−1.62545	−0.812723	+	0.582650i	$0.802016\pi$
$282$	18.1260	1.07938
$283$	1.27990	0.0760824	0.0380412	−	0.999276i	$-0.487888\pi$
$283$	1.27990	0.0760824	0.0380412	+	0.999276i	$0.487888\pi$
$284$	−13.8767	−0.823433
$285$	29.1586	1.72721
$286$	15.9730	0.944500
$287$	0.254069	0.0149972
$288$	7.85184	0.462674
$289$	14.8041	0.870829
$290$	26.0685	1.53080
$291$	14.3984	0.844048
$292$	−27.9443	−1.63532
$293$	2.98781	0.174550	0.0872748	−	0.996184i	$-0.472184\pi$
$293$	2.98781	0.174550	0.0872748	+	0.996184i	$0.472184\pi$
$294$	−1.96996	−0.114891
$295$	−40.9342	−2.38328
$296$	2.20899	0.128395
$297$	−2.03173	−0.117893
$298$	−15.3202	−0.887477
$299$	7.58816	0.438835
$300$	25.6588	1.48141
$301$	−6.07132	−0.349945
$302$	3.20121	0.184209
$303$	−6.00166	−0.344787
$304$	−28.5275	−1.63616
$305$	−53.1033	−3.04069
$306$	−11.1096	−0.635095
$307$	−9.31227	−0.531479	−0.265740	−	0.964045i	$-0.585616\pi$
$307$	−9.31227	−0.531479	−0.265740	+	0.964045i	$0.585616\pi$
$308$	3.82118	0.217732
$309$	−1.77356	−0.100894
$310$	73.5223	4.17579
$311$	16.1077	0.913381	0.456691	−	0.889626i	$-0.349035\pi$
$311$	16.1077	0.913381	0.456691	+	0.889626i	$0.349035\pi$
$312$	0.937472	0.0530739
$313$	−5.91733	−0.334467	−0.167234	−	0.985917i	$-0.553483\pi$
$313$	−5.91733	−0.334467	−0.167234	+	0.985917i	$0.553483\pi$
$314$	42.0656	2.37390
$315$	−4.31773	−0.243277
$316$	−3.88512	−0.218555
$317$	8.06759	0.453121	0.226561	−	0.973997i	$-0.427252\pi$
$317$	8.06759	0.453121	0.226561	+	0.973997i	$0.427252\pi$
$318$	−18.5754	−1.04166
$319$	6.22684	0.348636
$320$	−30.3075	−1.69424
$321$	6.59494	0.368094
$322$	3.74570	0.208740
$323$	38.0849	2.11910
$324$	1.88076	0.104486
$325$	54.4460	3.02012
$326$	22.3791	1.23946
$327$	11.9976	0.663469
$328$	−0.0596828	−0.00329543
$329$	9.20116	0.507277
$330$	17.2814	0.951311
$331$	34.8362	1.91477	0.957384	−	0.288818i	$-0.0932621\pi$
$331$	34.8362	1.91477	0.957384	+	0.288818i	$0.0932621\pi$
$332$	21.1878	1.16283
$333$	9.40368	0.515318
$334$	−5.92199	−0.324037
$335$	−19.5007	−1.06544
$336$	4.22427	0.230453
$337$	15.0955	0.822306	0.411153	−	0.911566i	$-0.365126\pi$
$337$	15.0955	0.822306	0.411153	+	0.911566i	$0.365126\pi$
$338$	−5.76530	−0.313591
$339$	9.06317	0.492244
$340$	45.7962	2.48365
$341$	17.5619	0.951028
$342$	−13.3036	−0.719377
$343$	−1.00000	−0.0539949
$344$	1.42620	0.0768955
$345$	8.20976	0.441999
$346$	−30.5646	−1.64316
$347$	−9.84603	−0.528563	−0.264281	−	0.964446i	$-0.585135\pi$
$347$	−9.84603	−0.528563	−0.264281	+	0.964446i	$0.585135\pi$
$348$	−5.76414	−0.308990
$349$	−33.6001	−1.79857	−0.899285	−	0.437363i	$-0.855913\pi$
$349$	−33.6001	−1.79857	−0.899285	+	0.437363i	$0.855913\pi$
$350$	26.8758	1.43657
$351$	3.99082	0.213014
$352$	−15.9528	−0.850287
$353$	0.930152	0.0495070	0.0247535	−	0.999694i	$-0.492120\pi$
$353$	0.930152	0.0495070	0.0247535	+	0.999694i	$0.492120\pi$
$354$	18.6762	0.992630
$355$	−31.8574	−1.69082
$356$	23.7571	1.25913
$357$	−5.63951	−0.298475
$358$	−36.7500	−1.94230
$359$	14.8128	0.781788	0.390894	−	0.920436i	$-0.372166\pi$
$359$	14.8128	0.781788	0.390894	+	0.920436i	$0.372166\pi$
$360$	1.01427	0.0534566
$361$	26.6061	1.40032
$362$	39.6731	2.08517
$363$	−6.87208	−0.360691
$364$	−7.50575	−0.393408
$365$	−64.1530	−3.35792
$366$	24.2283	1.26644
$367$	−29.4040	−1.53488	−0.767438	−	0.641123i	$-0.778469\pi$
$367$	−29.4040	−1.53488	−0.767438	+	0.641123i	$0.778469\pi$
$368$	−8.03205	−0.418700
$369$	−0.254069	−0.0132263
$370$	−79.9856	−4.15825
$371$	−9.42931	−0.489546
$372$	−16.2569	−0.842881
$373$	−24.5867	−1.27305	−0.636525	−	0.771256i	$-0.719629\pi$
$373$	−24.5867	−1.27305	−0.636525	+	0.771256i	$0.719629\pi$
$374$	22.5717	1.16716
$375$	37.3174	1.92706
$376$	−2.16142	−0.111467
$377$	−12.2311	−0.629931
$378$	1.96996	0.101324
$379$	−14.1213	−0.725365	−0.362682	−	0.931913i	$-0.618139\pi$
$379$	−14.1213	−0.725365	−0.362682	+	0.931913i	$0.618139\pi$
$380$	54.8403	2.81325
$381$	1.24401	0.0637324
$382$	1.96996	0.100792
$383$	8.46756	0.432672	0.216336	−	0.976319i	$-0.430589\pi$
$383$	8.46756	0.432672	0.216336	+	0.976319i	$0.430589\pi$
$384$	−1.87592	−0.0957301
$385$	8.77246	0.447086
$386$	36.9188	1.87912
$387$	6.07132	0.308623
$388$	27.0798	1.37477
$389$	22.7924	1.15562	0.577810	−	0.816171i	$-0.303907\pi$
$389$	22.7924	1.15562	0.577810	+	0.816171i	$0.303907\pi$
$390$	−33.9450	−1.71887
$391$	10.7230	0.542285
$392$	0.234907	0.0118646
$393$	−13.9676	−0.704573
$394$	−13.8958	−0.700061
$395$	−8.91923	−0.448775
$396$	−3.82118	−0.192022
$397$	−1.34760	−0.0676340	−0.0338170	−	0.999428i	$-0.510766\pi$
$397$	−1.34760	−0.0676340	−0.0338170	+	0.999428i	$0.510766\pi$
$398$	−9.90566	−0.496526
$399$	−6.75323	−0.338084
$400$	−57.6309	−2.88155
$401$	−0.724977	−0.0362036	−0.0181018	−	0.999836i	$-0.505762\pi$
$401$	−0.724977	−0.0362036	−0.0181018	+	0.999836i	$0.505762\pi$
$402$	8.89717	0.443750
$403$	−34.4958	−1.71836
$404$	−11.2877	−0.561582
$405$	4.31773	0.214550
$406$	−6.03755	−0.299638
$407$	−19.1057	−0.947035
$408$	1.32476	0.0655856
$409$	−7.98194	−0.394681	−0.197341	−	0.980335i	$-0.563231\pi$
$409$	−7.98194	−0.394681	−0.197341	+	0.980335i	$0.563231\pi$
$410$	2.16106	0.106727
$411$	−17.6888	−0.872523
$412$	−3.33563	−0.164335
$413$	9.48049	0.466504
$414$	−3.74570	−0.184091
$415$	48.6418	2.38773
$416$	31.3352	1.53634
$417$	−17.4143	−0.852780
$418$	27.0293	1.32205
$419$	24.8924	1.21608	0.608038	−	0.793908i	$-0.291957\pi$
$419$	24.8924	1.21608	0.608038	+	0.793908i	$0.291957\pi$
$420$	−8.12060	−0.396245
$421$	19.5369	0.952171	0.476085	−	0.879399i	$-0.342055\pi$
$421$	19.5369	0.952171	0.476085	+	0.879399i	$0.342055\pi$
$422$	28.2064	1.37307
$423$	−9.20116	−0.447376
$424$	2.21502	0.107571
$425$	76.9388	3.73208
$426$	14.5349	0.704220
$427$	12.2989	0.595185
$428$	12.4035	0.599544
$429$	−8.10825	−0.391470
$430$	−51.6413	−2.49036
$431$	17.5740	0.846508	0.423254	−	0.906011i	$-0.360888\pi$
$431$	17.5740	0.846508	0.423254	+	0.906011i	$0.360888\pi$
$432$	−4.22427	−0.203240
$433$	8.04117	0.386434	0.193217	−	0.981156i	$-0.438108\pi$
$433$	8.04117	0.386434	0.193217	+	0.981156i	$0.438108\pi$
$434$	−17.0280	−0.817370
$435$	−13.2330	−0.634474
$436$	22.5646	1.08065
$437$	12.8406	0.614250
$438$	29.2698	1.39856
$439$	−11.6400	−0.555548	−0.277774	−	0.960646i	$-0.589597\pi$
$439$	−11.6400	−0.555548	−0.277774	+	0.960646i	$0.589597\pi$
$440$	−2.06071	−0.0982407
$441$	1.00000	0.0476190
$442$	−44.3365	−2.10887
$443$	−6.14055	−0.291746	−0.145873	−	0.989303i	$-0.546599\pi$
$443$	−6.14055	−0.291746	−0.145873	+	0.989303i	$0.546599\pi$
$444$	17.6860	0.839341
$445$	54.5403	2.58546
$446$	−15.9817	−0.756753
$447$	7.77691	0.367835
$448$	7.01930	0.331631
$449$	−36.5126	−1.72313	−0.861567	−	0.507643i	$-0.830517\pi$
$449$	−36.5126	−1.72313	−0.861567	+	0.507643i	$0.830517\pi$
$450$	−26.8758	−1.26694
$451$	0.516200	0.0243069
$452$	17.0456	0.801758
$453$	−1.62501	−0.0763497
$454$	−5.23012	−0.245462
$455$	−17.2313	−0.807815
$456$	1.58638	0.0742892
$457$	31.2379	1.46125	0.730624	−	0.682780i	$-0.239229\pi$
$457$	31.2379	1.46125	0.730624	+	0.682780i	$0.239229\pi$
$458$	−32.8264	−1.53388
$459$	5.63951	0.263230
$460$	15.4406	0.719920
$461$	2.43312	0.113322	0.0566610	−	0.998393i	$-0.481955\pi$
$461$	2.43312	0.113322	0.0566610	+	0.998393i	$0.481955\pi$
$462$	−4.00243	−0.186210
$463$	12.8854	0.598834	0.299417	−	0.954122i	$-0.403208\pi$
$463$	12.8854	0.598834	0.299417	+	0.954122i	$0.403208\pi$
$464$	12.9465	0.601028
$465$	−37.3217	−1.73075
$466$	53.3060	2.46935
$467$	11.4202	0.528464	0.264232	−	0.964459i	$-0.414882\pi$
$467$	11.4202	0.528464	0.264232	+	0.964459i	$0.414882\pi$
$468$	7.50575	0.346953
$469$	4.51641	0.208549
$470$	78.2630	3.61000
$471$	−21.3535	−0.983917
$472$	−2.22704	−0.102508
$473$	−12.3353	−0.567176
$474$	4.06940	0.186914
$475$	92.1330	4.22735
$476$	−10.6065	−0.486150
$477$	9.42931	0.431739
$478$	−4.51459	−0.206492
$479$	−18.1292	−0.828345	−0.414172	−	0.910198i	$-0.635929\pi$
$479$	−18.1292	−0.828345	−0.414172	+	0.910198i	$0.635929\pi$
$480$	33.9022	1.54741
$481$	37.5283	1.71114
$482$	22.9929	1.04730
$483$	−1.90141	−0.0865170
$484$	−12.9247	−0.587487
$485$	62.1683	2.82292
$486$	−1.96996	−0.0893594
$487$	4.11146	0.186308	0.0931539	−	0.995652i	$-0.470305\pi$
$487$	4.11146	0.186308	0.0931539	+	0.995652i	$0.470305\pi$
$488$	−2.88910	−0.130783
$489$	−11.3602	−0.513724
$490$	−8.50578	−0.384252
$491$	38.7322	1.74796	0.873980	−	0.485963i	$-0.161531\pi$
$491$	38.7322	1.74796	0.873980	+	0.485963i	$0.161531\pi$
$492$	−0.477842	−0.0215428
$493$	−17.2840	−0.778432
$494$	−53.0922	−2.38873
$495$	−8.77246	−0.394293
$496$	36.5138	1.63952
$497$	7.37828	0.330961
$498$	−22.1928	−0.994484
$499$	29.7102	1.33001	0.665006	−	0.746838i	$-0.268429\pi$
$499$	29.7102	1.33001	0.665006	+	0.746838i	$0.268429\pi$
$500$	70.1848	3.13876
$501$	3.00614	0.134304
$502$	35.5374	1.58611
$503$	−3.64907	−0.162704	−0.0813521	−	0.996685i	$-0.525924\pi$
$503$	−3.64907	−0.162704	−0.0813521	+	0.996685i	$0.525924\pi$
$504$	−0.234907	−0.0104636
$505$	−25.9136	−1.15314
$506$	7.61024	0.338316
$507$	2.92661	0.129975
$508$	2.33967	0.103806
$509$	17.0921	0.757592	0.378796	−	0.925480i	$-0.376338\pi$
$509$	17.0921	0.757592	0.378796	+	0.925480i	$0.376338\pi$
$510$	−47.9684	−2.12408
$511$	14.8580	0.657281
$512$	−31.1837	−1.37814
$513$	6.75323	0.298162
$514$	−47.4109	−2.09121
$515$	−7.65775	−0.337441
$516$	11.4187	0.502679
$517$	18.6943	0.822172
$518$	18.5249	0.813937
$519$	15.5153	0.681047
$520$	4.04775	0.177506
$521$	11.7405	0.514361	0.257181	−	0.966363i	$-0.417206\pi$
$521$	11.7405	0.514361	0.257181	+	0.966363i	$0.417206\pi$
$522$	6.03755	0.264256
$523$	−7.43517	−0.325117	−0.162559	−	0.986699i	$-0.551975\pi$
$523$	−7.43517	−0.325117	−0.162559	+	0.986699i	$0.551975\pi$
$524$	−26.2697	−1.14760
$525$	−13.6428	−0.595421
$526$	−42.7207	−1.86271
$527$	−48.7469	−2.12345
$528$	8.58256	0.373508
$529$	−19.3847	−0.842811
$530$	−80.2036	−3.48382
$531$	−9.48049	−0.411418
$532$	−12.7012	−0.550666
$533$	−1.01394	−0.0439188
$534$	−24.8840	−1.07684
$535$	28.4752	1.23109
$536$	−1.06094	−0.0458256
$537$	18.6552	0.805031
$538$	22.1084	0.953159
$539$	−2.03173	−0.0875127
$540$	8.12060	0.349455
$541$	6.76988	0.291060	0.145530	−	0.989354i	$-0.453511\pi$
$541$	6.76988	0.291060	0.145530	+	0.989354i	$0.453511\pi$
$542$	−47.6384	−2.04624
$543$	−20.1390	−0.864247
$544$	44.2806	1.89851
$545$	51.8025	2.21897
$546$	7.86176	0.336452
$547$	−23.8248	−1.01868	−0.509338	−	0.860566i	$-0.670110\pi$
$547$	−23.8248	−1.01868	−0.509338	+	0.860566i	$0.670110\pi$
$548$	−33.2683	−1.42115
$549$	−12.2989	−0.524904
$550$	54.6044	2.32834
$551$	−20.6973	−0.881735
$552$	0.446654	0.0190109
$553$	2.06572	0.0878434
$554$	−7.24308	−0.307729
$555$	40.6026	1.72348
$556$	−32.7520	−1.38899
$557$	44.6853	1.89338	0.946689	−	0.322150i	$-0.104405\pi$
$557$	44.6853	1.89338	0.946689	+	0.322150i	$0.104405\pi$
$558$	17.0280	0.720852
$559$	24.2295	1.02480
$560$	18.2393	0.770750
$561$	−11.4580	−0.483755
$562$	53.6764	2.26420
$563$	23.7624	1.00146	0.500732	−	0.865602i	$-0.333064\pi$
$563$	23.7624	1.00146	0.500732	+	0.865602i	$0.333064\pi$
$564$	−17.3051	−0.728678
$565$	39.1324	1.64631
$566$	−2.52136	−0.105981
$567$	−1.00000	−0.0419961
$568$	−1.73321	−0.0727240
$569$	−4.68805	−0.196533	−0.0982666	−	0.995160i	$-0.531330\pi$
$569$	−4.68805	−0.196533	−0.0982666	+	0.995160i	$0.531330\pi$
$570$	−57.4414	−2.40596
$571$	−13.2475	−0.554389	−0.277194	−	0.960814i	$-0.589405\pi$
$571$	−13.2475	−0.554389	−0.277194	+	0.960814i	$0.589405\pi$
$572$	−15.2496	−0.637619
$573$	−1.00000	−0.0417756
$574$	−0.500507	−0.0208908
$575$	25.9405	1.08179
$576$	−7.01930	−0.292471
$577$	−9.06529	−0.377393	−0.188696	−	0.982035i	$-0.560426\pi$
$577$	−9.06529	−0.377393	−0.188696	+	0.982035i	$0.560426\pi$
$578$	−29.1635	−1.21304
$579$	−18.7409	−0.778843
$580$	−24.8880	−1.03342
$581$	−11.2656	−0.467376
$582$	−28.3643	−1.17574
$583$	−19.1578	−0.793435
$584$	−3.49026	−0.144428
$585$	17.2313	0.712425
$586$	−5.88587	−0.243143
$587$	−22.7328	−0.938285	−0.469142	−	0.883122i	$-0.655437\pi$
$587$	−22.7328	−0.938285	−0.469142	+	0.883122i	$0.655437\pi$
$588$	1.88076	0.0775610
$589$	−58.3736	−2.40524
$590$	80.6389	3.31985
$591$	7.05384	0.290156
$592$	−39.7237	−1.63263
$593$	−17.2490	−0.708332	−0.354166	−	0.935183i	$-0.615235\pi$
$593$	−17.2490	−0.708332	−0.354166	+	0.935183i	$0.615235\pi$
$594$	4.00243	0.164222
$595$	−24.3499	−0.998249
$596$	14.6265	0.599124
$597$	5.02835	0.205796
$598$	−14.9484	−0.611285
$599$	−20.1504	−0.823322	−0.411661	−	0.911337i	$-0.635051\pi$
$599$	−20.1504	−0.823322	−0.411661	+	0.911337i	$0.635051\pi$
$600$	3.20480	0.130835
$601$	−47.8519	−1.95192	−0.975961	−	0.217947i	$-0.930064\pi$
$601$	−47.8519	−1.95192	−0.975961	+	0.217947i	$0.930064\pi$
$602$	11.9603	0.487465
$603$	−4.51641	−0.183923
$604$	−3.05625	−0.124357
$605$	−29.6718	−1.20633
$606$	11.8231	0.480279
$607$	18.7703	0.761864	0.380932	−	0.924603i	$-0.375603\pi$
$607$	18.7703	0.761864	0.380932	+	0.924603i	$0.375603\pi$
$608$	53.0253	2.15046
$609$	3.06480	0.124192
$610$	104.612	4.23560
$611$	−36.7201	−1.48554
$612$	10.6065	0.428744
$613$	−19.2516	−0.777564	−0.388782	−	0.921330i	$-0.627104\pi$
$613$	−19.2516	−0.777564	−0.388782	+	0.921330i	$0.627104\pi$
$614$	18.3448	0.740337
$615$	−1.09700	−0.0442355
$616$	0.477268	0.0192297
$617$	38.5024	1.55005	0.775024	−	0.631931i	$-0.217738\pi$
$617$	38.5024	1.55005	0.775024	+	0.631931i	$0.217738\pi$
$618$	3.49384	0.140543
$619$	28.2234	1.13440	0.567198	−	0.823582i	$-0.308028\pi$
$619$	28.2234	1.13440	0.567198	+	0.823582i	$0.308028\pi$
$620$	−70.1929	−2.81902
$621$	1.90141	0.0763008
$622$	−31.7315	−1.27232
$623$	−12.6317	−0.506078
$624$	−16.8583	−0.674871
$625$	92.9123	3.71649
$626$	11.6569	0.465905
$627$	−13.7207	−0.547953
$628$	−40.1607	−1.60259
$629$	53.0322	2.11453
$630$	8.50578	0.338878
$631$	3.17024	0.126205	0.0631027	−	0.998007i	$-0.479900\pi$
$631$	3.17024	0.126205	0.0631027	+	0.998007i	$0.479900\pi$
$632$	−0.485253	−0.0193023
$633$	−14.3182	−0.569099
$634$	−15.8929	−0.631186
$635$	5.37129	0.213153
$636$	17.7342	0.703208
$637$	3.99082	0.158122
$638$	−12.2666	−0.485641
$639$	−7.37828	−0.291880
$640$	−8.09972	−0.320169
$641$	−19.9275	−0.787089	−0.393545	−	0.919305i	$-0.628751\pi$
$641$	−19.9275	−0.787089	−0.393545	+	0.919305i	$0.628751\pi$
$642$	−12.9918	−0.512745
$643$	11.6226	0.458352	0.229176	−	0.973385i	$-0.426397\pi$
$643$	11.6226	0.458352	0.229176	+	0.973385i	$0.426397\pi$
$644$	−3.57608	−0.140917
$645$	26.2143	1.03219
$646$	−75.0259	−2.95185
$647$	18.4209	0.724199	0.362100	−	0.932139i	$-0.382060\pi$
$647$	18.4209	0.724199	0.362100	+	0.932139i	$0.382060\pi$
$648$	0.234907	0.00922803
$649$	19.2618	0.756091
$650$	−107.257	−4.20695
$651$	8.64381	0.338778
$652$	−21.3657	−0.836744
$653$	28.2146	1.10412	0.552062	−	0.833803i	$-0.313841\pi$
$653$	28.2146	1.10412	0.552062	+	0.833803i	$0.313841\pi$
$654$	−23.6348	−0.924195
$655$	−60.3084	−2.35645
$656$	1.07326	0.0419037
$657$	−14.8580	−0.579667
$658$	−18.1260	−0.706623
$659$	−41.2015	−1.60498	−0.802492	−	0.596663i	$-0.796493\pi$
$659$	−41.2015	−1.60498	−0.802492	+	0.596663i	$0.796493\pi$
$660$	−16.4988	−0.642217
$661$	10.8469	0.421895	0.210948	−	0.977497i	$-0.432345\pi$
$661$	10.8469	0.421895	0.210948	+	0.977497i	$0.432345\pi$
$662$	−68.6259	−2.66722
$663$	22.5063	0.874070
$664$	2.64637	0.102699
$665$	−29.1586	−1.13072
$666$	−18.5249	−0.717825
$667$	−5.82743	−0.225639
$668$	5.65382	0.218753
$669$	8.11266	0.313654
$670$	38.4156	1.48412
$671$	24.9880	0.964650
$672$	−7.85184	−0.302891
$673$	33.5255	1.29231	0.646157	−	0.763204i	$-0.276375\pi$
$673$	33.5255	1.29231	0.646157	+	0.763204i	$0.276375\pi$
$674$	−29.7377	−1.14545
$675$	13.6428	0.525112
$676$	5.50423	0.211701
$677$	−18.2346	−0.700811	−0.350406	−	0.936598i	$-0.613956\pi$
$677$	−18.2346	−0.700811	−0.350406	+	0.936598i	$0.613956\pi$
$678$	−17.8541	−0.685683
$679$	−14.3984	−0.552559
$680$	5.71997	0.219351
$681$	2.65493	0.101737
$682$	−34.5962	−1.32476
$683$	−19.6428	−0.751611	−0.375806	−	0.926699i	$-0.622634\pi$
$683$	−19.6428	−0.751611	−0.375806	+	0.926699i	$0.622634\pi$
$684$	12.7012	0.485641
$685$	−76.3754	−2.91815
$686$	1.96996	0.0752135
$687$	16.6635	0.635750
$688$	−25.6469	−0.977779
$689$	37.6306	1.43361
$690$	−16.1729	−0.615693
$691$	14.9540	0.568876	0.284438	−	0.958694i	$-0.408193\pi$
$691$	14.9540	0.568876	0.284438	+	0.958694i	$0.408193\pi$
$692$	29.1805	1.10928
$693$	2.03173	0.0771789
$694$	19.3963	0.736274
$695$	−75.1901	−2.85212
$696$	−0.719945	−0.0272894
$697$	−1.43283	−0.0542722
$698$	66.1909	2.50536
$699$	−27.0594	−1.02348
$700$	−25.6588	−0.969811
$701$	−3.38531	−0.127861	−0.0639307	−	0.997954i	$-0.520364\pi$
$701$	−3.38531	−0.127861	−0.0639307	+	0.997954i	$0.520364\pi$
$702$	−7.86176	−0.296723
$703$	63.5052	2.39514
$704$	14.2613	0.537493
$705$	−39.7282	−1.49625
$706$	−1.83237	−0.0689620
$707$	6.00166	0.225716
$708$	−17.8305	−0.670111
$709$	−11.3668	−0.426889	−0.213445	−	0.976955i	$-0.568468\pi$
$709$	−11.3668	−0.426889	−0.213445	+	0.976955i	$0.568468\pi$
$710$	62.7580	2.35526
$711$	−2.06572	−0.0774706
$712$	2.96728	0.111203
$713$	−16.4354	−0.615510
$714$	11.1096	0.415768
$715$	−35.0092	−1.30927
$716$	35.0859	1.31122
$717$	2.29171	0.0855855
$718$	−29.1806	−1.08901
$719$	4.80498	0.179196	0.0895978	−	0.995978i	$-0.471442\pi$
$719$	4.80498	0.179196	0.0895978	+	0.995978i	$0.471442\pi$
$720$	−18.2393	−0.679737
$721$	1.77356	0.0660508
$722$	−52.4130	−1.95061
$723$	−11.6718	−0.434078
$724$	−37.8765	−1.40767
$725$	−41.8125	−1.55288
$726$	13.5378	0.502433
$727$	−26.4565	−0.981218	−0.490609	−	0.871380i	$-0.663226\pi$
$727$	−26.4565	−0.981218	−0.490609	+	0.871380i	$0.663226\pi$
$728$	−0.937472	−0.0347450
$729$	1.00000	0.0370370
$730$	126.379	4.67750
$731$	34.2393	1.26639
$732$	−23.1312	−0.854953
$733$	12.1234	0.447787	0.223894	−	0.974614i	$-0.428123\pi$
$733$	12.1234	0.447787	0.223894	+	0.974614i	$0.428123\pi$
$734$	57.9248	2.13804
$735$	4.31773	0.159262
$736$	14.9295	0.550310
$737$	9.17612	0.338007
$738$	0.500507	0.0184239
$739$	−39.5605	−1.45526	−0.727629	−	0.685971i	$-0.759378\pi$
$739$	−39.5605	−1.45526	−0.727629	+	0.685971i	$0.759378\pi$
$740$	76.3635	2.80718
$741$	26.9509	0.990065
$742$	18.5754	0.681924
$743$	−29.7457	−1.09127	−0.545633	−	0.838025i	$-0.683711\pi$
$743$	−29.7457	−1.09127	−0.545633	+	0.838025i	$0.683711\pi$
$744$	−2.03050	−0.0744416
$745$	33.5786	1.23023
$746$	48.4349	1.77333
$747$	11.2656	0.412187
$748$	−21.5496	−0.787932
$749$	−6.59494	−0.240974
$750$	−73.5138	−2.68435
$751$	−25.7586	−0.939944	−0.469972	−	0.882681i	$-0.655736\pi$
$751$	−25.7586	−0.939944	−0.469972	+	0.882681i	$0.655736\pi$
$752$	38.8682	1.41738
$753$	−18.0396	−0.657401
$754$	24.0947	0.877478
$755$	−7.01636	−0.255352
$756$	−1.88076	−0.0684024
$757$	−38.5734	−1.40197	−0.700987	−	0.713174i	$-0.747257\pi$
$757$	−38.5734	−1.40197	−0.700987	+	0.713174i	$0.747257\pi$
$758$	27.8185	1.01041
$759$	−3.86314	−0.140223
$760$	6.84958	0.248460
$761$	14.4207	0.522749	0.261375	−	0.965237i	$-0.415824\pi$
$761$	14.4207	0.522749	0.261375	+	0.965237i	$0.415824\pi$
$762$	−2.45065	−0.0887776
$763$	−11.9976	−0.434342
$764$	−1.88076	−0.0680433
$765$	24.3499	0.880373
$766$	−16.6808	−0.602701
$767$	−37.8349	−1.36614
$768$	17.7341	0.639924
$769$	14.5634	0.525168	0.262584	−	0.964909i	$-0.415425\pi$
$769$	14.5634	0.525168	0.262584	+	0.964909i	$0.415425\pi$
$770$	−17.2814	−0.622779
$771$	24.0669	0.866748
$772$	−35.2470	−1.26857
$773$	2.19339	0.0788909	0.0394455	−	0.999222i	$-0.487441\pi$
$773$	2.19339	0.0788909	0.0394455	+	0.999222i	$0.487441\pi$
$774$	−11.9603	−0.429903
$775$	−117.926	−4.23602
$776$	3.38229	0.121417
$777$	−9.40368	−0.337355
$778$	−44.9002	−1.60975
$779$	−1.71579	−0.0614745
$780$	32.4078	1.16039
$781$	14.9906	0.536408
$782$	−21.1239	−0.755390
$783$	−3.06480	−0.109527
$784$	−4.22427	−0.150867
$785$	−92.1987	−3.29071
$786$	27.5157	0.981452
$787$	−4.08148	−0.145489	−0.0727445	−	0.997351i	$-0.523176\pi$
$787$	−4.08148	−0.145489	−0.0727445	+	0.997351i	$0.523176\pi$
$788$	13.2665	0.472601
$789$	21.6860	0.772043
$790$	17.5706	0.625133
$791$	−9.06317	−0.322249
$792$	−0.477268	−0.0169590
$793$	−49.0826	−1.74297
$794$	2.65472	0.0942125
$795$	40.7133	1.44395
$796$	9.45709	0.335198
$797$	−12.3707	−0.438193	−0.219097	−	0.975703i	$-0.570311\pi$
$797$	−12.3707	−0.438193	−0.219097	+	0.975703i	$0.570311\pi$
$798$	13.3036	0.470943
$799$	−51.8901	−1.83574
$800$	107.121	3.78731
$801$	12.6317	0.446319
$802$	1.42818	0.0504307
$803$	30.1875	1.06529
$804$	−8.49427	−0.299570
$805$	−8.20976	−0.289356
$806$	67.9556	2.39363
$807$	−11.2227	−0.395059
$808$	−1.40984	−0.0495978
$809$	8.92394	0.313749	0.156875	−	0.987619i	$-0.449858\pi$
$809$	8.92394	0.313749	0.156875	+	0.987619i	$0.449858\pi$
$810$	−8.50578	−0.298862
$811$	−53.4465	−1.87676	−0.938381	−	0.345603i	$-0.887674\pi$
$811$	−53.4465	−1.87676	−0.938381	+	0.345603i	$0.887674\pi$
$812$	5.76414	0.202282
$813$	24.1824	0.848113
$814$	37.6375	1.31920
$815$	−49.0501	−1.71815
$816$	−23.8228	−0.833966
$817$	41.0010	1.43444
$818$	15.7241	0.549781
$819$	−3.99082	−0.139450
$820$	−2.06320	−0.0720499
$821$	11.6100	0.405191	0.202595	−	0.979263i	$-0.435062\pi$
$821$	11.6100	0.405191	0.202595	+	0.979263i	$0.435062\pi$
$822$	34.8462	1.21540
$823$	43.8496	1.52850	0.764251	−	0.644919i	$-0.223109\pi$
$823$	43.8496	1.52850	0.764251	+	0.644919i	$0.223109\pi$
$824$	−0.416622	−0.0145137
$825$	−27.7185	−0.965034
$826$	−18.6762	−0.649829
$827$	−11.0204	−0.383216	−0.191608	−	0.981472i	$-0.561370\pi$
$827$	−11.0204	−0.383216	−0.191608	+	0.981472i	$0.561370\pi$
$828$	3.57608	0.124277
$829$	15.9591	0.554284	0.277142	−	0.960829i	$-0.410613\pi$
$829$	15.9591	0.554284	0.277142	+	0.960829i	$0.410613\pi$
$830$	−95.8227	−3.32605
$831$	3.67676	0.127545
$832$	−28.0127	−0.971167
$833$	5.63951	0.195398
$834$	34.3055	1.18790
$835$	12.9797	0.449182
$836$	−25.8053	−0.892495
$837$	−8.64381	−0.298774
$838$	−49.0372	−1.69396
$839$	−12.7871	−0.441461	−0.220730	−	0.975335i	$-0.570844\pi$
$839$	−12.7871	−0.441461	−0.220730	+	0.975335i	$0.570844\pi$
$840$	−1.01427	−0.0349956
$841$	−19.6070	−0.676103
$842$	−38.4870	−1.32635
$843$	−27.2474	−0.938451
$844$	−26.9291	−0.926938
$845$	12.6363	0.434702
$846$	18.1260	0.623183
$847$	6.87208	0.236128
$848$	−39.8320	−1.36784
$849$	1.27990	0.0439262
$850$	−151.567	−5.19869
$851$	17.8802	0.612926
$852$	−13.8767	−0.475409
$853$	−58.3550	−1.99804	−0.999018	−	0.0443052i	$-0.985893\pi$
$853$	−58.3550	−1.99804	−0.999018	+	0.0443052i	$0.985893\pi$
$854$	−24.2283	−0.829077
$855$	29.1586	0.997204
$856$	1.54920	0.0529506
$857$	−7.91645	−0.270421	−0.135210	−	0.990817i	$-0.543171\pi$
$857$	−7.91645	−0.270421	−0.135210	+	0.990817i	$0.543171\pi$
$858$	15.9730	0.545308
$859$	41.0713	1.40133	0.700667	−	0.713488i	$-0.252886\pi$
$859$	41.0713	1.40133	0.700667	+	0.713488i	$0.252886\pi$
$860$	49.3028	1.68121
$861$	0.254069	0.00865866
$862$	−34.6201	−1.17916
$863$	16.7867	0.571424	0.285712	−	0.958315i	$-0.407770\pi$
$863$	16.7867	0.571424	0.285712	+	0.958315i	$0.407770\pi$
$864$	7.85184	0.267125
$865$	66.9910	2.27776
$866$	−15.8408	−0.538292
$867$	14.8041	0.502774
$868$	16.2569	0.551795
$869$	4.19698	0.142373
$870$	26.0685	0.883805
$871$	−18.0242	−0.610726
$872$	2.81833	0.0954406
$873$	14.3984	0.487311
$874$	−25.2956	−0.855635
$875$	−37.3174	−1.26156
$876$	−27.9443	−0.944152
$877$	5.31579	0.179502	0.0897508	−	0.995964i	$-0.471393\pi$
$877$	5.31579	0.179502	0.0897508	+	0.995964i	$0.471393\pi$
$878$	22.9304	0.773865
$879$	2.98781	0.100776
$880$	37.0572	1.24920
$881$	23.5225	0.792493	0.396246	−	0.918144i	$-0.370313\pi$
$881$	23.5225	0.792493	0.396246	+	0.918144i	$0.370313\pi$
$882$	−1.96996	−0.0663321
$883$	32.7230	1.10122	0.550608	−	0.834764i	$-0.314396\pi$
$883$	32.7230	1.10122	0.550608	+	0.834764i	$0.314396\pi$
$884$	42.3288	1.42367
$885$	−40.9342	−1.37599
$886$	12.0967	0.406395
$887$	−27.9337	−0.937922	−0.468961	−	0.883219i	$-0.655372\pi$
$887$	−27.9337	−0.937922	−0.468961	+	0.883219i	$0.655372\pi$
$888$	2.20899	0.0741290
$889$	−1.24401	−0.0417226
$890$	−107.442	−3.60148
$891$	−2.03173	−0.0680654
$892$	15.2579	0.510874
$893$	−62.1376	−2.07935
$894$	−15.3202	−0.512385
$895$	80.5481	2.69243
$896$	1.87592	0.0626701
$897$	7.58816	0.253361
$898$	71.9284	2.40028
$899$	26.4916	0.883543
$900$	25.6588	0.855293
$901$	53.1767	1.77157
$902$	−1.01689	−0.0338589
$903$	−6.07132	−0.202041
$904$	2.12901	0.0708097
$905$	−86.9548	−2.89048
$906$	3.20121	0.106353
$907$	20.1519	0.669133	0.334567	−	0.942372i	$-0.391410\pi$
$907$	20.1519	0.669133	0.334567	+	0.942372i	$0.391410\pi$
$908$	4.99328	0.165708
$909$	−6.00166	−0.199063
$910$	33.9450	1.12526
$911$	23.1470	0.766896	0.383448	−	0.923563i	$-0.374737\pi$
$911$	23.1470	0.766896	0.383448	+	0.923563i	$0.374737\pi$
$912$	−28.5275	−0.944638
$913$	−22.8886	−0.757503
$914$	−61.5375	−2.03548
$915$	−53.1033	−1.75554
$916$	31.3399	1.03550
$917$	13.9676	0.461251
$918$	−11.1096	−0.366673
$919$	31.7896	1.04864	0.524322	−	0.851520i	$-0.324319\pi$
$919$	31.7896	1.04864	0.524322	+	0.851520i	$0.324319\pi$
$920$	1.92853	0.0635819
$921$	−9.31227	−0.306850
$922$	−4.79317	−0.157855
$923$	−29.4453	−0.969205
$924$	3.82118	0.125708
$925$	128.293	4.21824
$926$	−25.3837	−0.834160
$927$	−1.77356	−0.0582513
$928$	−24.0643	−0.789951
$929$	11.5842	0.380065	0.190033	−	0.981778i	$-0.439141\pi$
$929$	11.5842	0.380065	0.190033	+	0.981778i	$0.439141\pi$
$930$	73.5223	2.41089
$931$	6.75323	0.221328
$932$	−50.8921	−1.66702
$933$	16.1077	0.527341
$934$	−22.4974	−0.736136
$935$	−49.4724	−1.61792
$936$	0.937472	0.0306422
$937$	−33.1570	−1.08319	−0.541596	−	0.840639i	$-0.682180\pi$
$937$	−33.1570	−1.08319	−0.541596	+	0.840639i	$0.682180\pi$
$938$	−8.89717	−0.290503
$939$	−5.91733	−0.193105
$940$	−74.7190	−2.43706
$941$	−3.08534	−0.100579	−0.0502896	−	0.998735i	$-0.516014\pi$
$941$	−3.08534	−0.100579	−0.0502896	+	0.998735i	$0.516014\pi$
$942$	42.0656	1.37057
$943$	−0.483089	−0.0157315
$944$	40.0481	1.30346
$945$	−4.31773	−0.140456
$946$	24.3000	0.790062
$947$	−3.54330	−0.115142	−0.0575709	−	0.998341i	$-0.518336\pi$
$947$	−3.54330	−0.115142	−0.0575709	+	0.998341i	$0.518336\pi$
$948$	−3.88512	−0.126183
$949$	−59.2957	−1.92482
$950$	−181.499	−5.88860
$951$	8.06759	0.261610
$952$	−1.32476	−0.0429358
$953$	50.1071	1.62313	0.811564	−	0.584264i	$-0.198617\pi$
$953$	50.1071	1.62313	0.811564	+	0.584264i	$0.198617\pi$
$954$	−18.5754	−0.601401
$955$	−4.31773	−0.139719
$956$	4.31015	0.139400
$957$	6.22684	0.201285
$958$	35.7139	1.15386
$959$	17.6888	0.571200
$960$	−30.3075	−0.978169
$961$	43.7155	1.41018
$962$	−73.9294	−2.38358
$963$	6.59494	0.212519
$964$	−21.9517	−0.707018
$965$	−80.9180	−2.60484
$966$	3.74570	0.120516
$967$	49.8795	1.60402	0.802008	−	0.597313i	$-0.203765\pi$
$967$	49.8795	1.60402	0.802008	+	0.597313i	$0.203765\pi$
$968$	−1.61430	−0.0518857
$969$	38.0849	1.22346
$970$	−122.469	−3.93225
$971$	9.52212	0.305579	0.152790	−	0.988259i	$-0.451174\pi$
$971$	9.52212	0.305579	0.152790	+	0.988259i	$0.451174\pi$
$972$	1.88076	0.0603253
$973$	17.4143	0.558276
$974$	−8.09942	−0.259522
$975$	54.4460	1.74367
$976$	51.9538	1.66300
$977$	−39.1694	−1.25314	−0.626570	−	0.779365i	$-0.715542\pi$
$977$	−39.1694	−1.25314	−0.626570	+	0.779365i	$0.715542\pi$
$978$	22.3791	0.715604
$979$	−25.6642	−0.820230
$980$	8.12060	0.259403
$981$	11.9976	0.383054
$982$	−76.3010	−2.43486
$983$	49.0025	1.56294	0.781469	−	0.623945i	$-0.214471\pi$
$983$	49.0025	1.56294	0.781469	+	0.623945i	$0.214471\pi$
$984$	−0.0596828	−0.00190262
$985$	30.4566	0.970428
$986$	34.0488	1.08434
$987$	9.20116	0.292876
$988$	50.6880	1.61260
$989$	11.5440	0.367079
$990$	17.2814	0.549239
$991$	−55.4228	−1.76056	−0.880282	−	0.474450i	$-0.842647\pi$
$991$	−55.4228	−1.76056	−0.880282	+	0.474450i	$0.842647\pi$
$992$	−67.8698	−2.15487
$993$	34.8362	1.10549
$994$	−14.5349	−0.461020
$995$	21.7111	0.688287
$996$	21.1878	0.671362
$997$	−41.5444	−1.31573	−0.657863	−	0.753138i	$-0.728539\pi$
$997$	−41.5444	−1.31573	−0.657863	+	0.753138i	$0.728539\pi$
$998$	−58.5281	−1.85267
$999$	9.40368	0.297519

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4011.2.a.m.1.7	✓	29

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4011.2.a.m.1.7	✓	29	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:	\( N \)	\(=\)	\( 4011 = 3 \cdot 7 \cdot 191 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4011.a (trivial)

\(f(q)\)	\(=\)	\(q-1.96996 q^{2} +1.00000 q^{3} +1.88076 q^{4} +4.31773 q^{5} -1.96996 q^{6} -1.00000 q^{7} +0.234907 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.96996 q^{2} +1.00000 q^{3} +1.88076 q^{4} +4.31773 q^{5} -1.96996 q^{6} -1.00000 q^{7} +0.234907 q^{8} +1.00000 q^{9} -8.50578 q^{10} -2.03173 q^{11} +1.88076 q^{12} +3.99082 q^{13} +1.96996 q^{14} +4.31773 q^{15} -4.22427 q^{16} +5.63951 q^{17} -1.96996 q^{18} +6.75323 q^{19} +8.12060 q^{20} -1.00000 q^{21} +4.00243 q^{22} +1.90141 q^{23} +0.234907 q^{24} +13.6428 q^{25} -7.86176 q^{26} +1.00000 q^{27} -1.88076 q^{28} -3.06480 q^{29} -8.50578 q^{30} -8.64381 q^{31} +7.85184 q^{32} -2.03173 q^{33} -11.1096 q^{34} -4.31773 q^{35} +1.88076 q^{36} +9.40368 q^{37} -13.3036 q^{38} +3.99082 q^{39} +1.01427 q^{40} -0.254069 q^{41} +1.96996 q^{42} +6.07132 q^{43} -3.82118 q^{44} +4.31773 q^{45} -3.74570 q^{46} -9.20116 q^{47} -4.22427 q^{48} +1.00000 q^{49} -26.8758 q^{50} +5.63951 q^{51} +7.50575 q^{52} +9.42931 q^{53} -1.96996 q^{54} -8.77246 q^{55} -0.234907 q^{56} +6.75323 q^{57} +6.03755 q^{58} -9.48049 q^{59} +8.12060 q^{60} -12.2989 q^{61} +17.0280 q^{62} -1.00000 q^{63} -7.01930 q^{64} +17.2313 q^{65} +4.00243 q^{66} -4.51641 q^{67} +10.6065 q^{68} +1.90141 q^{69} +8.50578 q^{70} -7.37828 q^{71} +0.234907 q^{72} -14.8580 q^{73} -18.5249 q^{74} +13.6428 q^{75} +12.7012 q^{76} +2.03173 q^{77} -7.86176 q^{78} -2.06572 q^{79} -18.2393 q^{80} +1.00000 q^{81} +0.500507 q^{82} +11.2656 q^{83} -1.88076 q^{84} +24.3499 q^{85} -11.9603 q^{86} -3.06480 q^{87} -0.477268 q^{88} +12.6317 q^{89} -8.50578 q^{90} -3.99082 q^{91} +3.57608 q^{92} -8.64381 q^{93} +18.1260 q^{94} +29.1586 q^{95} +7.85184 q^{96} +14.3984 q^{97} -1.96996 q^{98} -2.03173 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 29 q + 6 q^{2} + 29 q^{3} + 40 q^{4} + 22 q^{5} + 6 q^{6} - 29 q^{7} + 15 q^{8} + 29 q^{9}+O(q^{10}) \) 29 * q + 6 * q^2 + 29 * q^3 + 40 * q^4 + 22 * q^5 + 6 * q^6 - 29 * q^7 + 15 * q^8 + 29 * q^9	\( 29 q + 6 q^{2} + 29 q^{3} + 40 q^{4} + 22 q^{5} + 6 q^{6} - 29 q^{7} + 15 q^{8} + 29 q^{9} + 11 q^{11} + 40 q^{12} + 13 q^{13} - 6 q^{14} + 22 q^{15} + 58 q^{16} + 17 q^{17} + 6 q^{18} + 3 q^{19} + 52 q^{20} - 29 q^{21} + 17 q^{22} + 36 q^{23} + 15 q^{24} + 57 q^{25} + 25 q^{26} + 29 q^{27} - 40 q^{28} + 20 q^{29} + 6 q^{31} + 46 q^{32} + 11 q^{33} + 18 q^{34} - 22 q^{35} + 40 q^{36} + 22 q^{37} + 8 q^{38} + 13 q^{39} + 6 q^{40} + 26 q^{41} - 6 q^{42} + 21 q^{43} + 22 q^{44} + 22 q^{45} + 28 q^{46} + 41 q^{47} + 58 q^{48} + 29 q^{49} + 18 q^{50} + 17 q^{51} + 2 q^{52} + 37 q^{53} + 6 q^{54} + 7 q^{55} - 15 q^{56} + 3 q^{57} + 9 q^{58} + 27 q^{59} + 52 q^{60} + 20 q^{61} - 12 q^{62} - 29 q^{63} + 59 q^{64} + 3 q^{65} + 17 q^{66} + 30 q^{67} + 33 q^{68} + 36 q^{69} + 68 q^{71} + 15 q^{72} + q^{73} + 21 q^{74} + 57 q^{75} + 11 q^{76} - 11 q^{77} + 25 q^{78} + 34 q^{79} + 110 q^{80} + 29 q^{81} - 49 q^{82} + 13 q^{83} - 40 q^{84} + 27 q^{85} + 35 q^{86} + 20 q^{87} + 17 q^{88} + 61 q^{89} - 13 q^{91} + 86 q^{92} + 6 q^{93} - 19 q^{94} + 25 q^{95} + 46 q^{96} - 3 q^{97} + 6 q^{98} + 11 q^{99}+O(q^{100}) \) 29 * q + 6 * q^2 + 29 * q^3 + 40 * q^4 + 22 * q^5 + 6 * q^6 - 29 * q^7 + 15 * q^8 + 29 * q^9 + 11 * q^11 + 40 * q^12 + 13 * q^13 - 6 * q^14 + 22 * q^15 + 58 * q^16 + 17 * q^17 + 6 * q^18 + 3 * q^19 + 52 * q^20 - 29 * q^21 + 17 * q^22 + 36 * q^23 + 15 * q^24 + 57 * q^25 + 25 * q^26 + 29 * q^27 - 40 * q^28 + 20 * q^29 + 6 * q^31 + 46 * q^32 + 11 * q^33 + 18 * q^34 - 22 * q^35 + 40 * q^36 + 22 * q^37 + 8 * q^38 + 13 * q^39 + 6 * q^40 + 26 * q^41 - 6 * q^42 + 21 * q^43 + 22 * q^44 + 22 * q^45 + 28 * q^46 + 41 * q^47 + 58 * q^48 + 29 * q^49 + 18 * q^50 + 17 * q^51 + 2 * q^52 + 37 * q^53 + 6 * q^54 + 7 * q^55 - 15 * q^56 + 3 * q^57 + 9 * q^58 + 27 * q^59 + 52 * q^60 + 20 * q^61 - 12 * q^62 - 29 * q^63 + 59 * q^64 + 3 * q^65 + 17 * q^66 + 30 * q^67 + 33 * q^68 + 36 * q^69 + 68 * q^71 + 15 * q^72 + q^73 + 21 * q^74 + 57 * q^75 + 11 * q^76 - 11 * q^77 + 25 * q^78 + 34 * q^79 + 110 * q^80 + 29 * q^81 - 49 * q^82 + 13 * q^83 - 40 * q^84 + 27 * q^85 + 35 * q^86 + 20 * q^87 + 17 * q^88 + 61 * q^89 - 13 * q^91 + 86 * q^92 + 6 * q^93 - 19 * q^94 + 25 * q^95 + 46 * q^96 - 3 * q^97 + 6 * q^98 + 11 * q^99

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