LMFDB - Embedded newform 6010.2.a.f.1.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6010,2,Mod(1,6010)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6010, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("6010.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6010 = 2 \cdot 5 \cdot 601 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6010.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:	$47.9900916148$
Analytic rank:	$1$
Dimension:	$22$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
Character	$\chi$	$=$	6010.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +0.530792 q^{3} +1.00000 q^{4} -1.00000 q^{5} +0.530792 q^{6} -3.74336 q^{7} +1.00000 q^{8} -2.71826 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +0.530792 q^{3} +1.00000 q^{4} -1.00000 q^{5} +0.530792 q^{6} -3.74336 q^{7} +1.00000 q^{8} -2.71826 q^{9} -1.00000 q^{10} +0.679203 q^{11} +0.530792 q^{12} +2.07855 q^{13} -3.74336 q^{14} -0.530792 q^{15} +1.00000 q^{16} +2.66492 q^{17} -2.71826 q^{18} +6.55799 q^{19} -1.00000 q^{20} -1.98694 q^{21} +0.679203 q^{22} -0.336559 q^{23} +0.530792 q^{24} +1.00000 q^{25} +2.07855 q^{26} -3.03520 q^{27} -3.74336 q^{28} -1.80029 q^{29} -0.530792 q^{30} +4.24726 q^{31} +1.00000 q^{32} +0.360515 q^{33} +2.66492 q^{34} +3.74336 q^{35} -2.71826 q^{36} -3.93997 q^{37} +6.55799 q^{38} +1.10328 q^{39} -1.00000 q^{40} -10.7131 q^{41} -1.98694 q^{42} -4.18584 q^{43} +0.679203 q^{44} +2.71826 q^{45} -0.336559 q^{46} -7.33024 q^{47} +0.530792 q^{48} +7.01274 q^{49} +1.00000 q^{50} +1.41452 q^{51} +2.07855 q^{52} -9.56781 q^{53} -3.03520 q^{54} -0.679203 q^{55} -3.74336 q^{56} +3.48093 q^{57} -1.80029 q^{58} -2.86104 q^{59} -0.530792 q^{60} +8.54335 q^{61} +4.24726 q^{62} +10.1754 q^{63} +1.00000 q^{64} -2.07855 q^{65} +0.360515 q^{66} -1.35946 q^{67} +2.66492 q^{68} -0.178643 q^{69} +3.74336 q^{70} -13.1541 q^{71} -2.71826 q^{72} -1.86964 q^{73} -3.93997 q^{74} +0.530792 q^{75} +6.55799 q^{76} -2.54250 q^{77} +1.10328 q^{78} +1.06862 q^{79} -1.00000 q^{80} +6.54372 q^{81} -10.7131 q^{82} -6.44237 q^{83} -1.98694 q^{84} -2.66492 q^{85} -4.18584 q^{86} -0.955577 q^{87} +0.679203 q^{88} -4.36392 q^{89} +2.71826 q^{90} -7.78078 q^{91} -0.336559 q^{92} +2.25441 q^{93} -7.33024 q^{94} -6.55799 q^{95} +0.530792 q^{96} +7.15483 q^{97} +7.01274 q^{98} -1.84625 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q + 22 q^{2} - 6 q^{3} + 22 q^{4} - 22 q^{5} - 6 q^{6} - 12 q^{7} + 22 q^{8} + 12 q^{9}+O(q^{10}) $ 22 * q + 22 * q^2 - 6 * q^3 + 22 * q^4 - 22 * q^5 - 6 * q^6 - 12 * q^7 + 22 * q^8 + 12 * q^9	\( 22 q + 22 q^{2} - 6 q^{3} + 22 q^{4} - 22 q^{5} - 6 q^{6} - 12 q^{7} + 22 q^{8} + 12 q^{9} - 22 q^{10} - 4 q^{11} - 6 q^{12} - 20 q^{13} - 12 q^{14} + 6 q^{15} + 22 q^{16} - 23 q^{17} + 12 q^{18} + q^{19} - 22 q^{20} - 8 q^{21} - 4 q^{22} - 17 q^{23} - 6 q^{24} + 22 q^{25} - 20 q^{26} - 21 q^{27} - 12 q^{28} - 13 q^{29} + 6 q^{30} - 13 q^{31} + 22 q^{32} - 21 q^{33} - 23 q^{34} + 12 q^{35} + 12 q^{36} - 16 q^{37} + q^{38} - 4 q^{39} - 22 q^{40} - 31 q^{41} - 8 q^{42} - 9 q^{43} - 4 q^{44} - 12 q^{45} - 17 q^{46} - 41 q^{47} - 6 q^{48} - 6 q^{49} + 22 q^{50} - 7 q^{51} - 20 q^{52} - 15 q^{53} - 21 q^{54} + 4 q^{55} - 12 q^{56} - 26 q^{57} - 13 q^{58} - 32 q^{59} + 6 q^{60} - 22 q^{61} - 13 q^{62} - 55 q^{63} + 22 q^{64} + 20 q^{65} - 21 q^{66} - 19 q^{67} - 23 q^{68} - 37 q^{69} + 12 q^{70} - 36 q^{71} + 12 q^{72} - 47 q^{73} - 16 q^{74} - 6 q^{75} + q^{76} - 26 q^{77} - 4 q^{78} - 10 q^{79} - 22 q^{80} - 18 q^{81} - 31 q^{82} - 48 q^{83} - 8 q^{84} + 23 q^{85} - 9 q^{86} - 50 q^{87} - 4 q^{88} - 42 q^{89} - 12 q^{90} + 25 q^{91} - 17 q^{92} - 48 q^{93} - 41 q^{94} - q^{95} - 6 q^{96} - 67 q^{97} - 6 q^{98} - 3 q^{99}+O(q^{100}) \) 22 * q + 22 * q^2 - 6 * q^3 + 22 * q^4 - 22 * q^5 - 6 * q^6 - 12 * q^7 + 22 * q^8 + 12 * q^9 - 22 * q^10 - 4 * q^11 - 6 * q^12 - 20 * q^13 - 12 * q^14 + 6 * q^15 + 22 * q^16 - 23 * q^17 + 12 * q^18 + q^19 - 22 * q^20 - 8 * q^21 - 4 * q^22 - 17 * q^23 - 6 * q^24 + 22 * q^25 - 20 * q^26 - 21 * q^27 - 12 * q^28 - 13 * q^29 + 6 * q^30 - 13 * q^31 + 22 * q^32 - 21 * q^33 - 23 * q^34 + 12 * q^35 + 12 * q^36 - 16 * q^37 + q^38 - 4 * q^39 - 22 * q^40 - 31 * q^41 - 8 * q^42 - 9 * q^43 - 4 * q^44 - 12 * q^45 - 17 * q^46 - 41 * q^47 - 6 * q^48 - 6 * q^49 + 22 * q^50 - 7 * q^51 - 20 * q^52 - 15 * q^53 - 21 * q^54 + 4 * q^55 - 12 * q^56 - 26 * q^57 - 13 * q^58 - 32 * q^59 + 6 * q^60 - 22 * q^61 - 13 * q^62 - 55 * q^63 + 22 * q^64 + 20 * q^65 - 21 * q^66 - 19 * q^67 - 23 * q^68 - 37 * q^69 + 12 * q^70 - 36 * q^71 + 12 * q^72 - 47 * q^73 - 16 * q^74 - 6 * q^75 + q^76 - 26 * q^77 - 4 * q^78 - 10 * q^79 - 22 * q^80 - 18 * q^81 - 31 * q^82 - 48 * q^83 - 8 * q^84 + 23 * q^85 - 9 * q^86 - 50 * q^87 - 4 * q^88 - 42 * q^89 - 12 * q^90 + 25 * q^91 - 17 * q^92 - 48 * q^93 - 41 * q^94 - q^95 - 6 * q^96 - 67 * q^97 - 6 * q^98 - 3 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	0.530792	0.306453	0.153226	−	0.988191i	$-0.451034\pi$
$3$	0.530792	0.306453	0.153226	+	0.988191i	$0.451034\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	0.530792	0.216695
$7$	−3.74336	−1.41486	−0.707428	−	0.706785i	$-0.750145\pi$
$7$	−3.74336	−1.41486	−0.707428	+	0.706785i	$0.750145\pi$
$8$	1.00000	0.353553
$9$	−2.71826	−0.906087
$10$	−1.00000	−0.316228
$11$	0.679203	0.204787	0.102394	−	0.994744i	$-0.467350\pi$
$11$	0.679203	0.204787	0.102394	+	0.994744i	$0.467350\pi$
$12$	0.530792	0.153226
$13$	2.07855	0.576487	0.288244	−	0.957557i	$-0.406929\pi$
$13$	2.07855	0.576487	0.288244	+	0.957557i	$0.406929\pi$
$14$	−3.74336	−1.00045
$15$	−0.530792	−0.137050
$16$	1.00000	0.250000
$17$	2.66492	0.646337	0.323169	−	0.946341i	$-0.395252\pi$
$17$	2.66492	0.646337	0.323169	+	0.946341i	$0.395252\pi$
$18$	−2.71826	−0.640700
$19$	6.55799	1.50451	0.752253	−	0.658874i	$-0.228967\pi$
$19$	6.55799	1.50451	0.752253	+	0.658874i	$0.228967\pi$
$20$	−1.00000	−0.223607
$21$	−1.98694	−0.433587
$22$	0.679203	0.144806
$23$	−0.336559	−0.0701774	−0.0350887	−	0.999384i	$-0.511171\pi$
$23$	−0.336559	−0.0701774	−0.0350887	+	0.999384i	$0.511171\pi$
$24$	0.530792	0.108347
$25$	1.00000	0.200000
$26$	2.07855	0.407638
$27$	−3.03520	−0.584125
$28$	−3.74336	−0.707428
$29$	−1.80029	−0.334305	−0.167152	−	0.985931i	$-0.553457\pi$
$29$	−1.80029	−0.334305	−0.167152	+	0.985931i	$0.553457\pi$
$30$	−0.530792	−0.0969089
$31$	4.24726	0.762830	0.381415	−	0.924404i	$-0.375437\pi$
$31$	4.24726	0.762830	0.381415	+	0.924404i	$0.375437\pi$
$32$	1.00000	0.176777
$33$	0.360515	0.0627576
$34$	2.66492	0.457030
$35$	3.74336	0.632743
$36$	−2.71826	−0.453043
$37$	−3.93997	−0.647727	−0.323864	−	0.946104i	$-0.604982\pi$
$37$	−3.93997	−0.647727	−0.323864	+	0.946104i	$0.604982\pi$
$38$	6.55799	1.06385
$39$	1.10328	0.176666
$40$	−1.00000	−0.158114
$41$	−10.7131	−1.67310	−0.836552	−	0.547887i	$-0.815432\pi$
$41$	−10.7131	−1.67310	−0.836552	+	0.547887i	$0.815432\pi$
$42$	−1.98694	−0.306592
$43$	−4.18584	−0.638334	−0.319167	−	0.947698i	$-0.603403\pi$
$43$	−4.18584	−0.638334	−0.319167	+	0.947698i	$0.603403\pi$
$44$	0.679203	0.102394
$45$	2.71826	0.405214
$46$	−0.336559	−0.0496229
$47$	−7.33024	−1.06923	−0.534613	−	0.845097i	$-0.679543\pi$
$47$	−7.33024	−1.06923	−0.534613	+	0.845097i	$0.679543\pi$
$48$	0.530792	0.0766132
$49$	7.01274	1.00182
$50$	1.00000	0.141421
$51$	1.41452	0.198072
$52$	2.07855	0.288244
$53$	−9.56781	−1.31424	−0.657120	−	0.753786i	$-0.728225\pi$
$53$	−9.56781	−1.31424	−0.657120	+	0.753786i	$0.728225\pi$
$54$	−3.03520	−0.413039
$55$	−0.679203	−0.0915837
$56$	−3.74336	−0.500227
$57$	3.48093	0.461060
$58$	−1.80029	−0.236389
$59$	−2.86104	−0.372476	−0.186238	−	0.982505i	$-0.559629\pi$
$59$	−2.86104	−0.372476	−0.186238	+	0.982505i	$0.559629\pi$
$60$	−0.530792	−0.0685249
$61$	8.54335	1.09386	0.546932	−	0.837177i	$-0.315796\pi$
$61$	8.54335	1.09386	0.546932	+	0.837177i	$0.315796\pi$
$62$	4.24726	0.539402
$63$	10.1754	1.28198
$64$	1.00000	0.125000
$65$	−2.07855	−0.257813
$66$	0.360515	0.0443763
$67$	−1.35946	−0.166085	−0.0830424	−	0.996546i	$-0.526464\pi$
$67$	−1.35946	−0.166085	−0.0830424	+	0.996546i	$0.526464\pi$
$68$	2.66492	0.323169
$69$	−0.178643	−0.0215061
$70$	3.74336	0.447417
$71$	−13.1541	−1.56110	−0.780552	−	0.625091i	$-0.785062\pi$
$71$	−13.1541	−1.56110	−0.780552	+	0.625091i	$0.785062\pi$
$72$	−2.71826	−0.320350
$73$	−1.86964	−0.218825	−0.109412	−	0.993996i	$-0.534897\pi$
$73$	−1.86964	−0.218825	−0.109412	+	0.993996i	$0.534897\pi$
$74$	−3.93997	−0.458012
$75$	0.530792	0.0612905
$76$	6.55799	0.752253
$77$	−2.54250	−0.289745
$78$	1.10328	0.124922
$79$	1.06862	0.120229	0.0601144	−	0.998191i	$-0.480853\pi$
$79$	1.06862	0.120229	0.0601144	+	0.998191i	$0.480853\pi$
$80$	−1.00000	−0.111803
$81$	6.54372	0.727080
$82$	−10.7131	−1.18306
$83$	−6.44237	−0.707142	−0.353571	−	0.935408i	$-0.615033\pi$
$83$	−6.44237	−0.707142	−0.353571	+	0.935408i	$0.615033\pi$
$84$	−1.98694	−0.216793
$85$	−2.66492	−0.289051
$86$	−4.18584	−0.451370
$87$	−0.955577	−0.102449
$88$	0.679203	0.0724032
$89$	−4.36392	−0.462574	−0.231287	−	0.972886i	$-0.574294\pi$
$89$	−4.36392	−0.462574	−0.231287	+	0.972886i	$0.574294\pi$
$90$	2.71826	0.286530
$91$	−7.78078	−0.815647
$92$	−0.336559	−0.0350887
$93$	2.25441	0.233771
$94$	−7.33024	−0.756057
$95$	−6.55799	−0.672836
$96$	0.530792	0.0541737
$97$	7.15483	0.726463	0.363232	−	0.931699i	$-0.381673\pi$
$97$	7.15483	0.726463	0.363232	+	0.931699i	$0.381673\pi$
$98$	7.01274	0.708393
$99$	−1.84625	−0.185555
$100$	1.00000	0.100000
$101$	4.43968	0.441764	0.220882	−	0.975301i	$-0.429106\pi$
$101$	4.43968	0.441764	0.220882	+	0.975301i	$0.429106\pi$
$102$	1.41452	0.140058
$103$	−5.66409	−0.558100	−0.279050	−	0.960277i	$-0.590019\pi$
$103$	−5.66409	−0.558100	−0.279050	+	0.960277i	$0.590019\pi$
$104$	2.07855	0.203819
$105$	1.98694	0.193906
$106$	−9.56781	−0.929308
$107$	−0.869938	−0.0841001	−0.0420500	−	0.999116i	$-0.513389\pi$
$107$	−0.869938	−0.0841001	−0.0420500	+	0.999116i	$0.513389\pi$
$108$	−3.03520	−0.292063
$109$	10.2435	0.981146	0.490573	−	0.871400i	$-0.336787\pi$
$109$	10.2435	0.981146	0.490573	+	0.871400i	$0.336787\pi$
$110$	−0.679203	−0.0647594
$111$	−2.09130	−0.198498
$112$	−3.74336	−0.353714
$113$	−9.45936	−0.889861	−0.444931	−	0.895565i	$-0.646772\pi$
$113$	−9.45936	−0.889861	−0.444931	+	0.895565i	$0.646772\pi$
$114$	3.48093	0.326019
$115$	0.336559	0.0313843
$116$	−1.80029	−0.167152
$117$	−5.65005	−0.522348
$118$	−2.86104	−0.263380
$119$	−9.97574	−0.914475
$120$	−0.530792	−0.0484544
$121$	−10.5387	−0.958062
$122$	8.54335	0.773478
$123$	−5.68642	−0.512727
$124$	4.24726	0.381415
$125$	−1.00000	−0.0894427
$126$	10.1754	0.906499
$127$	−13.6168	−1.20829	−0.604146	−	0.796874i	$-0.706486\pi$
$127$	−13.6168	−1.20829	−0.604146	+	0.796874i	$0.706486\pi$
$128$	1.00000	0.0883883
$129$	−2.22181	−0.195619
$130$	−2.07855	−0.182301
$131$	−17.9395	−1.56738	−0.783691	−	0.621151i	$-0.786665\pi$
$131$	−17.9395	−1.56738	−0.783691	+	0.621151i	$0.786665\pi$
$132$	0.360515	0.0313788
$133$	−24.5489	−2.12866
$134$	−1.35946	−0.117440
$135$	3.03520	0.261229
$136$	2.66492	0.228515
$137$	−1.15530	−0.0987044	−0.0493522	−	0.998781i	$-0.515716\pi$
$137$	−1.15530	−0.0987044	−0.0493522	+	0.998781i	$0.515716\pi$
$138$	−0.178643	−0.0152071
$139$	17.4452	1.47968	0.739840	−	0.672783i	$-0.234901\pi$
$139$	17.4452	1.47968	0.739840	+	0.672783i	$0.234901\pi$
$140$	3.74336	0.316372
$141$	−3.89083	−0.327667
$142$	−13.1541	−1.10387
$143$	1.41176	0.118057
$144$	−2.71826	−0.226522
$145$	1.80029	0.149506
$146$	−1.86964	−0.154733
$147$	3.72230	0.307010
$148$	−3.93997	−0.323864
$149$	−11.0099	−0.901970	−0.450985	−	0.892532i	$-0.648927\pi$
$149$	−11.0099	−0.901970	−0.450985	+	0.892532i	$0.648927\pi$
$150$	0.530792	0.0433390
$151$	−5.37962	−0.437787	−0.218894	−	0.975749i	$-0.570245\pi$
$151$	−5.37962	−0.437787	−0.218894	+	0.975749i	$0.570245\pi$
$152$	6.55799	0.531923
$153$	−7.24394	−0.585638
$154$	−2.54250	−0.204880
$155$	−4.24726	−0.341148
$156$	1.10328	0.0883330
$157$	−1.24490	−0.0993539	−0.0496770	−	0.998765i	$-0.515819\pi$
$157$	−1.24490	−0.0993539	−0.0496770	+	0.998765i	$0.515819\pi$
$158$	1.06862	0.0850147
$159$	−5.07851	−0.402752
$160$	−1.00000	−0.0790569
$161$	1.25986	0.0992910
$162$	6.54372	0.514123
$163$	−18.5020	−1.44919	−0.724595	−	0.689175i	$-0.757973\pi$
$163$	−18.5020	−1.44919	−0.724595	+	0.689175i	$0.757973\pi$
$164$	−10.7131	−0.836552
$165$	−0.360515	−0.0280661
$166$	−6.44237	−0.500025
$167$	8.40377	0.650303	0.325152	−	0.945662i	$-0.394585\pi$
$167$	8.40377	0.650303	0.325152	+	0.945662i	$0.394585\pi$
$168$	−1.98694	−0.153296
$169$	−8.67961	−0.667662
$170$	−2.66492	−0.204390
$171$	−17.8263	−1.36321
$172$	−4.18584	−0.319167
$173$	21.0459	1.60009	0.800046	−	0.599939i	$-0.204809\pi$
$173$	21.0459	1.60009	0.800046	+	0.599939i	$0.204809\pi$
$174$	−0.955577	−0.0724421
$175$	−3.74336	−0.282971
$176$	0.679203	0.0511968
$177$	−1.51862	−0.114146
$178$	−4.36392	−0.327090
$179$	10.2836	0.768634	0.384317	−	0.923201i	$-0.374437\pi$
$179$	10.2836	0.768634	0.384317	+	0.923201i	$0.374437\pi$
$180$	2.71826	0.202607
$181$	−22.1454	−1.64605	−0.823027	−	0.568002i	$-0.807717\pi$
$181$	−22.1454	−1.64605	−0.823027	+	0.568002i	$0.807717\pi$
$182$	−7.78078	−0.576749
$183$	4.53474	0.335217
$184$	−0.336559	−0.0248115
$185$	3.93997	0.289672
$186$	2.25441	0.165301
$187$	1.81002	0.132362
$188$	−7.33024	−0.534613
$189$	11.3619	0.826454
$190$	−6.55799	−0.475767
$191$	−12.5100	−0.905190	−0.452595	−	0.891716i	$-0.649502\pi$
$191$	−12.5100	−0.905190	−0.452595	+	0.891716i	$0.649502\pi$
$192$	0.530792	0.0383066
$193$	11.6646	0.839634	0.419817	−	0.907609i	$-0.362094\pi$
$193$	11.6646	0.839634	0.419817	+	0.907609i	$0.362094\pi$
$194$	7.15483	0.513687
$195$	−1.10328	−0.0790075
$196$	7.01274	0.500910
$197$	−19.9924	−1.42440	−0.712201	−	0.701976i	$-0.752302\pi$
$197$	−19.9924	−1.42440	−0.712201	+	0.701976i	$0.752302\pi$
$198$	−1.84625	−0.131207
$199$	13.0480	0.924946	0.462473	−	0.886633i	$-0.346962\pi$
$199$	13.0480	0.924946	0.462473	+	0.886633i	$0.346962\pi$
$200$	1.00000	0.0707107
$201$	−0.721592	−0.0508971
$202$	4.43968	0.312374
$203$	6.73912	0.472993
$204$	1.41452	0.0990359
$205$	10.7131	0.748235
$206$	−5.66409	−0.394636
$207$	0.914855	0.0635868
$208$	2.07855	0.144122
$209$	4.45420	0.308104
$210$	1.98694	0.137112
$211$	−15.4720	−1.06514	−0.532570	−	0.846386i	$-0.678774\pi$
$211$	−15.4720	−1.06514	−0.532570	+	0.846386i	$0.678774\pi$
$212$	−9.56781	−0.657120
$213$	−6.98208	−0.478404
$214$	−0.869938	−0.0594677
$215$	4.18584	0.285472
$216$	−3.03520	−0.206520
$217$	−15.8990	−1.07930
$218$	10.2435	0.693775
$219$	−0.992390	−0.0670595
$220$	−0.679203	−0.0457918
$221$	5.53918	0.372605
$222$	−2.09130	−0.140359
$223$	6.35358	0.425467	0.212733	−	0.977110i	$-0.431763\pi$
$223$	6.35358	0.425467	0.212733	+	0.977110i	$0.431763\pi$
$224$	−3.74336	−0.250114
$225$	−2.71826	−0.181217
$226$	−9.45936	−0.629227
$227$	7.46136	0.495228	0.247614	−	0.968859i	$-0.420354\pi$
$227$	7.46136	0.495228	0.247614	+	0.968859i	$0.420354\pi$
$228$	3.48093	0.230530
$229$	−22.6192	−1.49472	−0.747359	−	0.664420i	$-0.768678\pi$
$229$	−22.6192	−1.49472	−0.747359	+	0.664420i	$0.768678\pi$
$230$	0.336559	0.0221920
$231$	−1.34954	−0.0887930
$232$	−1.80029	−0.118195
$233$	5.53334	0.362501	0.181251	−	0.983437i	$-0.441985\pi$
$233$	5.53334	0.362501	0.181251	+	0.983437i	$0.441985\pi$
$234$	−5.65005	−0.369355
$235$	7.33024	0.478172
$236$	−2.86104	−0.186238
$237$	0.567213	0.0368445
$238$	−9.97574	−0.646631
$239$	10.3778	0.671287	0.335643	−	0.941989i	$-0.391046\pi$
$239$	10.3778	0.671287	0.335643	+	0.941989i	$0.391046\pi$
$240$	−0.530792	−0.0342625
$241$	11.1697	0.719505	0.359753	−	0.933048i	$-0.382861\pi$
$241$	11.1697	0.719505	0.359753	+	0.933048i	$0.382861\pi$
$242$	−10.5387	−0.677452
$243$	12.5790	0.806941
$244$	8.54335	0.546932
$245$	−7.01274	−0.448027
$246$	−5.68642	−0.362553
$247$	13.6311	0.867329
$248$	4.24726	0.269701
$249$	−3.41956	−0.216706
$250$	−1.00000	−0.0632456
$251$	−6.97747	−0.440414	−0.220207	−	0.975453i	$-0.570673\pi$
$251$	−6.97747	−0.440414	−0.220207	+	0.975453i	$0.570673\pi$
$252$	10.1754	0.640991
$253$	−0.228592	−0.0143714
$254$	−13.6168	−0.854392
$255$	−1.41452	−0.0885804
$256$	1.00000	0.0625000
$257$	−0.849844	−0.0530118	−0.0265059	−	0.999649i	$-0.508438\pi$
$257$	−0.849844	−0.0530118	−0.0265059	+	0.999649i	$0.508438\pi$
$258$	−2.22181	−0.138324
$259$	14.7487	0.916441
$260$	−2.07855	−0.128906
$261$	4.89364	0.302909
$262$	−17.9395	−1.10831
$263$	−19.6021	−1.20872	−0.604360	−	0.796711i	$-0.706571\pi$
$263$	−19.6021	−1.20872	−0.604360	+	0.796711i	$0.706571\pi$
$264$	0.360515	0.0221882
$265$	9.56781	0.587746
$266$	−24.5489	−1.50519
$267$	−2.31633	−0.141757
$268$	−1.35946	−0.0830424
$269$	15.3183	0.933973	0.466986	−	0.884264i	$-0.345340\pi$
$269$	15.3183	0.933973	0.466986	+	0.884264i	$0.345340\pi$
$270$	3.03520	0.184717
$271$	−10.3638	−0.629557	−0.314779	−	0.949165i	$-0.601930\pi$
$271$	−10.3638	−0.629557	−0.314779	+	0.949165i	$0.601930\pi$
$272$	2.66492	0.161584
$273$	−4.12997	−0.249957
$274$	−1.15530	−0.0697945
$275$	0.679203	0.0409575
$276$	−0.178643	−0.0107530
$277$	−24.0300	−1.44382	−0.721911	−	0.691985i	$-0.756736\pi$
$277$	−24.0300	−1.44382	−0.721911	+	0.691985i	$0.756736\pi$
$278$	17.4452	1.04629
$279$	−11.5452	−0.691190
$280$	3.74336	0.223708
$281$	13.6583	0.814785	0.407393	−	0.913253i	$-0.366438\pi$
$281$	13.6583	0.814785	0.407393	+	0.913253i	$0.366438\pi$
$282$	−3.89083	−0.231696
$283$	−11.5568	−0.686981	−0.343490	−	0.939156i	$-0.611609\pi$
$283$	−11.5568	−0.686981	−0.343490	+	0.939156i	$0.611609\pi$
$284$	−13.1541	−0.780552
$285$	−3.48093	−0.206192
$286$	1.41176	0.0834791
$287$	40.1030	2.36720
$288$	−2.71826	−0.160175
$289$	−9.89821	−0.582248
$290$	1.80029	0.105716
$291$	3.79772	0.222627
$292$	−1.86964	−0.109412
$293$	−11.3998	−0.665986	−0.332993	−	0.942929i	$-0.608059\pi$
$293$	−11.3998	−0.665986	−0.332993	+	0.942929i	$0.608059\pi$
$294$	3.72230	0.217089
$295$	2.86104	0.166576
$296$	−3.93997	−0.229006
$297$	−2.06152	−0.119621
$298$	−11.0099	−0.637789
$299$	−0.699556	−0.0404564
$300$	0.530792	0.0306453
$301$	15.6691	0.903151
$302$	−5.37962	−0.309562
$303$	2.35654	0.135380
$304$	6.55799	0.376127
$305$	−8.54335	−0.489191
$306$	−7.24394	−0.414108
$307$	19.9057	1.13608	0.568039	−	0.823002i	$-0.307702\pi$
$307$	19.9057	1.13608	0.568039	+	0.823002i	$0.307702\pi$
$308$	−2.54250	−0.144872
$309$	−3.00645	−0.171031
$310$	−4.24726	−0.241228
$311$	1.70729	0.0968116	0.0484058	−	0.998828i	$-0.484586\pi$
$311$	1.70729	0.0968116	0.0484058	+	0.998828i	$0.484586\pi$
$312$	1.10328	0.0624609
$313$	−22.5685	−1.27565	−0.637823	−	0.770183i	$-0.720165\pi$
$313$	−22.5685	−1.27565	−0.637823	+	0.770183i	$0.720165\pi$
$314$	−1.24490	−0.0702538
$315$	−10.1754	−0.573320
$316$	1.06862	0.0601144
$317$	−20.4222	−1.14703	−0.573513	−	0.819196i	$-0.694420\pi$
$317$	−20.4222	−1.14703	−0.573513	+	0.819196i	$0.694420\pi$
$318$	−5.07851	−0.284789
$319$	−1.22276	−0.0684613
$320$	−1.00000	−0.0559017
$321$	−0.461756	−0.0257727
$322$	1.25986	0.0702093
$323$	17.4765	0.972419
$324$	6.54372	0.363540
$325$	2.07855	0.115297
$326$	−18.5020	−1.02473
$327$	5.43715	0.300675
$328$	−10.7131	−0.591532
$329$	27.4397	1.51280
$330$	−0.360515	−0.0198457
$331$	29.4779	1.62025	0.810125	−	0.586257i	$-0.199399\pi$
$331$	29.4779	1.62025	0.810125	+	0.586257i	$0.199399\pi$
$332$	−6.44237	−0.353571
$333$	10.7099	0.586897
$334$	8.40377	0.459834
$335$	1.35946	0.0742754
$336$	−1.98694	−0.108397
$337$	14.5475	0.792455	0.396228	−	0.918152i	$-0.370319\pi$
$337$	14.5475	0.792455	0.396228	+	0.918152i	$0.370319\pi$
$338$	−8.67961	−0.472109
$339$	−5.02095	−0.272700
$340$	−2.66492	−0.144525
$341$	2.88475	0.156218
$342$	−17.8263	−0.963937
$343$	−0.0476729	−0.00257409
$344$	−4.18584	−0.225685
$345$	0.178643	0.00961780
$346$	21.0459	1.13144
$347$	32.0519	1.72064	0.860319	−	0.509756i	$-0.170264\pi$
$347$	32.0519	1.72064	0.860319	+	0.509756i	$0.170264\pi$
$348$	−0.955577	−0.0512243
$349$	−15.3894	−0.823777	−0.411888	−	0.911234i	$-0.635131\pi$
$349$	−15.3894	−0.823777	−0.411888	+	0.911234i	$0.635131\pi$
$350$	−3.74336	−0.200091
$351$	−6.30884	−0.336741
$352$	0.679203	0.0362016
$353$	23.6376	1.25810	0.629051	−	0.777364i	$-0.283444\pi$
$353$	23.6376	1.25810	0.629051	+	0.777364i	$0.283444\pi$
$354$	−1.51862	−0.0807135
$355$	13.1541	0.698147
$356$	−4.36392	−0.231287
$357$	−5.29504	−0.280243
$358$	10.2836	0.543506
$359$	2.71864	0.143484	0.0717421	−	0.997423i	$-0.477144\pi$
$359$	2.71864	0.143484	0.0717421	+	0.997423i	$0.477144\pi$
$360$	2.71826	0.143265
$361$	24.0072	1.26354
$362$	−22.1454	−1.16394
$363$	−5.59385	−0.293601
$364$	−7.78078	−0.407823
$365$	1.86964	0.0978615
$366$	4.53474	0.237035
$367$	0.979270	0.0511175	0.0255587	−	0.999673i	$-0.491864\pi$
$367$	0.979270	0.0511175	0.0255587	+	0.999673i	$0.491864\pi$
$368$	−0.336559	−0.0175444
$369$	29.1210	1.51598
$370$	3.93997	0.204829
$371$	35.8157	1.85946
$372$	2.25441	0.116886
$373$	10.9989	0.569500	0.284750	−	0.958602i	$-0.408089\pi$
$373$	10.9989	0.569500	0.284750	+	0.958602i	$0.408089\pi$
$374$	1.81002	0.0935938
$375$	−0.530792	−0.0274100
$376$	−7.33024	−0.378028
$377$	−3.74199	−0.192722
$378$	11.3619	0.584391
$379$	29.2466	1.50230	0.751149	−	0.660133i	$-0.229500\pi$
$379$	29.2466	1.50230	0.751149	+	0.660133i	$0.229500\pi$
$380$	−6.55799	−0.336418
$381$	−7.22766	−0.370284
$382$	−12.5100	−0.640066
$383$	−4.41468	−0.225580	−0.112790	−	0.993619i	$-0.535979\pi$
$383$	−4.41468	−0.225580	−0.112790	+	0.993619i	$0.535979\pi$
$384$	0.530792	0.0270868
$385$	2.54250	0.129578
$386$	11.6646	0.593711
$387$	11.3782	0.578386
$388$	7.15483	0.363232
$389$	−8.37960	−0.424863	−0.212431	−	0.977176i	$-0.568138\pi$
$389$	−8.37960	−0.424863	−0.212431	+	0.977176i	$0.568138\pi$
$390$	−1.10328	−0.0558667
$391$	−0.896902	−0.0453583
$392$	7.01274	0.354197
$393$	−9.52214	−0.480328
$394$	−19.9924	−1.00720
$395$	−1.06862	−0.0537680
$396$	−1.84625	−0.0927775
$397$	−3.26976	−0.164105	−0.0820523	−	0.996628i	$-0.526147\pi$
$397$	−3.26976	−0.164105	−0.0820523	+	0.996628i	$0.526147\pi$
$398$	13.0480	0.654035
$399$	−13.0304	−0.652334
$400$	1.00000	0.0500000
$401$	−31.5764	−1.57685	−0.788426	−	0.615129i	$-0.789104\pi$
$401$	−31.5764	−1.57685	−0.788426	+	0.615129i	$0.789104\pi$
$402$	−0.721592	−0.0359897
$403$	8.82816	0.439762
$404$	4.43968	0.220882
$405$	−6.54372	−0.325160
$406$	6.73912	0.334457
$407$	−2.67604	−0.132646
$408$	1.41452	0.0700290
$409$	32.5353	1.60877	0.804384	−	0.594110i	$-0.202496\pi$
$409$	32.5353	1.60877	0.804384	+	0.594110i	$0.202496\pi$
$410$	10.7131	0.529082
$411$	−0.613226	−0.0302482
$412$	−5.66409	−0.279050
$413$	10.7099	0.527000
$414$	0.914855	0.0449627
$415$	6.44237	0.316243
$416$	2.07855	0.101910
$417$	9.25975	0.453452
$418$	4.45420	0.217862
$419$	−15.6741	−0.765729	−0.382864	−	0.923805i	$-0.625062\pi$
$419$	−15.6741	−0.765729	−0.382864	+	0.923805i	$0.625062\pi$
$420$	1.98694	0.0969529
$421$	21.2708	1.03668	0.518338	−	0.855176i	$-0.326551\pi$
$421$	21.2708	1.03668	0.518338	+	0.855176i	$0.326551\pi$
$422$	−15.4720	−0.753167
$423$	19.9255	0.968811
$424$	−9.56781	−0.464654
$425$	2.66492	0.129267
$426$	−6.98208	−0.338283
$427$	−31.9808	−1.54766
$428$	−0.869938	−0.0420500
$429$	0.749350	0.0361790
$430$	4.18584	0.201859
$431$	10.8213	0.521245	0.260622	−	0.965441i	$-0.416072\pi$
$431$	10.8213	0.521245	0.260622	+	0.965441i	$0.416072\pi$
$432$	−3.03520	−0.146031
$433$	−36.7685	−1.76698	−0.883490	−	0.468449i	$-0.844813\pi$
$433$	−36.7685	−1.76698	−0.883490	+	0.468449i	$0.844813\pi$
$434$	−15.8990	−0.763177
$435$	0.955577	0.0458164
$436$	10.2435	0.490573
$437$	−2.20715	−0.105582
$438$	−0.992390	−0.0474182
$439$	22.7649	1.08651	0.543256	−	0.839567i	$-0.317191\pi$
$439$	22.7649	1.08651	0.543256	+	0.839567i	$0.317191\pi$
$440$	−0.679203	−0.0323797
$441$	−19.0624	−0.907735
$442$	5.53918	0.263472
$443$	−16.3934	−0.778873	−0.389436	−	0.921053i	$-0.627330\pi$
$443$	−16.3934	−0.778873	−0.389436	+	0.921053i	$0.627330\pi$
$444$	−2.09130	−0.0992489
$445$	4.36392	0.206870
$446$	6.35358	0.300851
$447$	−5.84399	−0.276411
$448$	−3.74336	−0.176857
$449$	20.5608	0.970323	0.485161	−	0.874425i	$-0.338761\pi$
$449$	20.5608	0.970323	0.485161	+	0.874425i	$0.338761\pi$
$450$	−2.71826	−0.128140
$451$	−7.27636	−0.342630
$452$	−9.45936	−0.444931
$453$	−2.85546	−0.134161
$454$	7.46136	0.350179
$455$	7.78078	0.364768
$456$	3.48093	0.163009
$457$	−3.70945	−0.173521	−0.0867605	−	0.996229i	$-0.527651\pi$
$457$	−3.70945	−0.173521	−0.0867605	+	0.996229i	$0.527651\pi$
$458$	−22.6192	−1.05693
$459$	−8.08857	−0.377542
$460$	0.336559	0.0156921
$461$	−8.27972	−0.385625	−0.192812	−	0.981236i	$-0.561761\pi$
$461$	−8.27972	−0.385625	−0.192812	+	0.981236i	$0.561761\pi$
$462$	−1.34954	−0.0627862
$463$	17.7489	0.824862	0.412431	−	0.910989i	$-0.364680\pi$
$463$	17.7489	0.824862	0.412431	+	0.910989i	$0.364680\pi$
$464$	−1.80029	−0.0835762
$465$	−2.25441	−0.104546
$466$	5.53334	0.256327
$467$	−17.0009	−0.786707	−0.393354	−	0.919387i	$-0.628685\pi$
$467$	−17.0009	−0.786707	−0.393354	+	0.919387i	$0.628685\pi$
$468$	−5.65005	−0.261174
$469$	5.08896	0.234986
$470$	7.33024	0.338119
$471$	−0.660783	−0.0304473
$472$	−2.86104	−0.131690
$473$	−2.84303	−0.130723
$474$	0.567213	0.0260530
$475$	6.55799	0.300901
$476$	−9.97574	−0.457237
$477$	26.0078	1.19082
$478$	10.3778	0.474671
$479$	−34.3633	−1.57010	−0.785049	−	0.619434i	$-0.787362\pi$
$479$	−34.3633	−1.57010	−0.785049	+	0.619434i	$0.787362\pi$
$480$	−0.530792	−0.0242272
$481$	−8.18944	−0.373407
$482$	11.1697	0.508767
$483$	0.668724	0.0304280
$484$	−10.5387	−0.479031
$485$	−7.15483	−0.324884
$486$	12.5790	0.570593
$487$	−2.88615	−0.130784	−0.0653920	−	0.997860i	$-0.520830\pi$
$487$	−2.88615	−0.130784	−0.0653920	+	0.997860i	$0.520830\pi$
$488$	8.54335	0.386739
$489$	−9.82071	−0.444108
$490$	−7.01274	−0.316803
$491$	−2.10442	−0.0949714	−0.0474857	−	0.998872i	$-0.515121\pi$
$491$	−2.10442	−0.0949714	−0.0474857	+	0.998872i	$0.515121\pi$
$492$	−5.68642	−0.256364
$493$	−4.79761	−0.216074
$494$	13.6311	0.613294
$495$	1.84625	0.0829827
$496$	4.24726	0.190708
$497$	49.2405	2.20874
$498$	−3.41956	−0.153234
$499$	−1.59998	−0.0716248	−0.0358124	−	0.999359i	$-0.511402\pi$
$499$	−1.59998	−0.0716248	−0.0358124	+	0.999359i	$0.511402\pi$
$500$	−1.00000	−0.0447214
$501$	4.46065	0.199287
$502$	−6.97747	−0.311420
$503$	25.2630	1.12642	0.563211	−	0.826313i	$-0.309566\pi$
$503$	25.2630	1.12642	0.563211	+	0.826313i	$0.309566\pi$
$504$	10.1754	0.453249
$505$	−4.43968	−0.197563
$506$	−0.228592	−0.0101621
$507$	−4.60706	−0.204607
$508$	−13.6168	−0.604146
$509$	34.8919	1.54656	0.773279	−	0.634066i	$-0.218615\pi$
$509$	34.8919	1.54656	0.773279	+	0.634066i	$0.218615\pi$
$510$	−1.41452	−0.0626358
$511$	6.99873	0.309606
$512$	1.00000	0.0441942
$513$	−19.9048	−0.878820
$514$	−0.849844	−0.0374850
$515$	5.66409	0.249590
$516$	−2.22181	−0.0978096
$517$	−4.97872	−0.218964
$518$	14.7487	0.648022
$519$	11.1710	0.490352
$520$	−2.07855	−0.0911506
$521$	39.1313	1.71437	0.857187	−	0.515005i	$-0.172210\pi$
$521$	39.1313	1.71437	0.857187	+	0.515005i	$0.172210\pi$
$522$	4.89364	0.214189
$523$	11.8321	0.517381	0.258691	−	0.965960i	$-0.416709\pi$
$523$	11.8321	0.517381	0.258691	+	0.965960i	$0.416709\pi$
$524$	−17.9395	−0.783691
$525$	−1.98694	−0.0867173
$526$	−19.6021	−0.854694
$527$	11.3186	0.493046
$528$	0.360515	0.0156894
$529$	−22.8867	−0.995075
$530$	9.56781	0.415599
$531$	7.77705	0.337495
$532$	−24.5489	−1.06433
$533$	−22.2678	−0.964523
$534$	−2.31633	−0.100237
$535$	0.869938	0.0376107
$536$	−1.35946	−0.0587199
$537$	5.45846	0.235550
$538$	15.3183	0.660419
$539$	4.76307	0.205160
$540$	3.03520	0.130614
$541$	−17.8239	−0.766307	−0.383154	−	0.923685i	$-0.625162\pi$
$541$	−17.8239	−0.766307	−0.383154	+	0.923685i	$0.625162\pi$
$542$	−10.3638	−0.445164
$543$	−11.7546	−0.504438
$544$	2.66492	0.114257
$545$	−10.2435	−0.438782
$546$	−4.12997	−0.176746
$547$	6.94122	0.296785	0.148393	−	0.988929i	$-0.452590\pi$
$547$	6.94122	0.296785	0.148393	+	0.988929i	$0.452590\pi$
$548$	−1.15530	−0.0493522
$549$	−23.2230	−0.991135
$550$	0.679203	0.0289613
$551$	−11.8063	−0.502963
$552$	−0.178643	−0.00760354
$553$	−4.00022	−0.170107
$554$	−24.0300	−1.02094
$555$	2.09130	0.0887709
$556$	17.4452	0.739840
$557$	−11.9785	−0.507545	−0.253772	−	0.967264i	$-0.581671\pi$
$557$	−11.9785	−0.507545	−0.253772	+	0.967264i	$0.581671\pi$
$558$	−11.5452	−0.488745
$559$	−8.70049	−0.367992
$560$	3.74336	0.158186
$561$	0.960743	0.0405626
$562$	13.6583	0.576140
$563$	9.94140	0.418980	0.209490	−	0.977811i	$-0.432820\pi$
$563$	9.94140	0.418980	0.209490	+	0.977811i	$0.432820\pi$
$564$	−3.89083	−0.163834
$565$	9.45936	0.397958
$566$	−11.5568	−0.485769
$567$	−24.4955	−1.02871
$568$	−13.1541	−0.551933
$569$	32.4240	1.35928	0.679642	−	0.733544i	$-0.262135\pi$
$569$	32.4240	1.35928	0.679642	+	0.733544i	$0.262135\pi$
$570$	−3.48093	−0.145800
$571$	−4.79109	−0.200501	−0.100250	−	0.994962i	$-0.531964\pi$
$571$	−4.79109	−0.200501	−0.100250	+	0.994962i	$0.531964\pi$
$572$	1.41176	0.0590286
$573$	−6.64019	−0.277398
$574$	40.1030	1.67387
$575$	−0.336559	−0.0140355
$576$	−2.71826	−0.113261
$577$	32.6799	1.36048	0.680241	−	0.732988i	$-0.261875\pi$
$577$	32.6799	1.36048	0.680241	+	0.732988i	$0.261875\pi$
$578$	−9.89821	−0.411711
$579$	6.19146	0.257308
$580$	1.80029	0.0747528
$581$	24.1161	1.00050
$582$	3.79772	0.157421
$583$	−6.49848	−0.269140
$584$	−1.86964	−0.0773663
$585$	5.65005	0.233601
$586$	−11.3998	−0.470923
$587$	−3.15296	−0.130137	−0.0650683	−	0.997881i	$-0.520727\pi$
$587$	−3.15296	−0.130137	−0.0650683	+	0.997881i	$0.520727\pi$
$588$	3.72230	0.153505
$589$	27.8535	1.14768
$590$	2.86104	0.117787
$591$	−10.6118	−0.436512
$592$	−3.93997	−0.161932
$593$	−24.2053	−0.993992	−0.496996	−	0.867753i	$-0.665564\pi$
$593$	−24.2053	−0.993992	−0.496996	+	0.867753i	$0.665564\pi$
$594$	−2.06152	−0.0845851
$595$	9.97574	0.408966
$596$	−11.0099	−0.450985
$597$	6.92575	0.283452
$598$	−0.699556	−0.0286070
$599$	−9.61755	−0.392962	−0.196481	−	0.980508i	$-0.562951\pi$
$599$	−9.61755	−0.392962	−0.196481	+	0.980508i	$0.562951\pi$
$600$	0.530792	0.0216695
$601$	1.00000	0.0407909
$601$	1.00000	0.0407909
$602$	15.6691	0.638624
$603$	3.69537	0.150487
$604$	−5.37962	−0.218894
$605$	10.5387	0.428458
$606$	2.35654	0.0957280
$607$	32.4562	1.31736	0.658678	−	0.752425i	$-0.271116\pi$
$607$	32.4562	1.31736	0.658678	+	0.752425i	$0.271116\pi$
$608$	6.55799	0.265962
$609$	3.57707	0.144950
$610$	−8.54335	−0.345910
$611$	−15.2363	−0.616395
$612$	−7.24394	−0.292819
$613$	−22.5667	−0.911462	−0.455731	−	0.890118i	$-0.650622\pi$
$613$	−22.5667	−0.911462	−0.455731	+	0.890118i	$0.650622\pi$
$614$	19.9057	0.803328
$615$	5.68642	0.229299
$616$	−2.54250	−0.102440
$617$	−4.14499	−0.166871	−0.0834355	−	0.996513i	$-0.526589\pi$
$617$	−4.14499	−0.166871	−0.0834355	+	0.996513i	$0.526589\pi$
$618$	−3.00645	−0.120937
$619$	−0.428047	−0.0172047	−0.00860233	−	0.999963i	$-0.502738\pi$
$619$	−0.428047	−0.0172047	−0.00860233	+	0.999963i	$0.502738\pi$
$620$	−4.24726	−0.170574
$621$	1.02153	0.0409924
$622$	1.70729	0.0684562
$623$	16.3357	0.654477
$624$	1.10328	0.0441665
$625$	1.00000	0.0400000
$626$	−22.5685	−0.902018
$627$	2.36425	0.0944192
$628$	−1.24490	−0.0496770
$629$	−10.4997	−0.418650
$630$	−10.1754	−0.405399
$631$	−22.6326	−0.900990	−0.450495	−	0.892779i	$-0.648753\pi$
$631$	−22.6326	−0.900990	−0.450495	+	0.892779i	$0.648753\pi$
$632$	1.06862	0.0425073
$633$	−8.21243	−0.326415
$634$	−20.4222	−0.811070
$635$	13.6168	0.540365
$636$	−5.07851	−0.201376
$637$	14.5764	0.577536
$638$	−1.22276	−0.0484095
$639$	35.7562	1.41449
$640$	−1.00000	−0.0395285
$641$	23.3233	0.921216	0.460608	−	0.887604i	$-0.347631\pi$
$641$	23.3233	0.921216	0.460608	+	0.887604i	$0.347631\pi$
$642$	−0.461756	−0.0182240
$643$	−23.0552	−0.909210	−0.454605	−	0.890693i	$-0.650219\pi$
$643$	−23.0552	−0.909210	−0.454605	+	0.890693i	$0.650219\pi$
$644$	1.25986	0.0496455
$645$	2.22181	0.0874836
$646$	17.4765	0.687604
$647$	11.3779	0.447310	0.223655	−	0.974668i	$-0.428201\pi$
$647$	11.3779	0.447310	0.223655	+	0.974668i	$0.428201\pi$
$648$	6.54372	0.257062
$649$	−1.94323	−0.0762783
$650$	2.07855	0.0815276
$651$	−8.43907	−0.330753
$652$	−18.5020	−0.724595
$653$	−14.6814	−0.574527	−0.287264	−	0.957852i	$-0.592746\pi$
$653$	−14.6814	−0.574527	−0.287264	+	0.957852i	$0.592746\pi$
$654$	5.43715	0.212609
$655$	17.9395	0.700955
$656$	−10.7131	−0.418276
$657$	5.08217	0.198274
$658$	27.4397	1.06971
$659$	10.4518	0.407145	0.203572	−	0.979060i	$-0.434745\pi$
$659$	10.4518	0.407145	0.203572	+	0.979060i	$0.434745\pi$
$660$	−0.360515	−0.0140330
$661$	35.2205	1.36992	0.684959	−	0.728581i	$-0.259820\pi$
$661$	35.2205	1.36992	0.684959	+	0.728581i	$0.259820\pi$
$662$	29.4779	1.14569
$663$	2.94015	0.114186
$664$	−6.44237	−0.250012
$665$	24.5489	0.951966
$666$	10.7099	0.414999
$667$	0.605902	0.0234606
$668$	8.40377	0.325152
$669$	3.37243	0.130386
$670$	1.35946	0.0525206
$671$	5.80266	0.224009
$672$	−1.98694	−0.0766480
$673$	−30.1817	−1.16342	−0.581710	−	0.813397i	$-0.697616\pi$
$673$	−30.1817	−1.16342	−0.581710	+	0.813397i	$0.697616\pi$
$674$	14.5475	0.560351
$675$	−3.03520	−0.116825
$676$	−8.67961	−0.333831
$677$	−46.3036	−1.77959	−0.889797	−	0.456357i	$-0.849154\pi$
$677$	−46.3036	−1.77959	−0.889797	+	0.456357i	$0.849154\pi$
$678$	−5.02095	−0.192828
$679$	−26.7831	−1.02784
$680$	−2.66492	−0.102195
$681$	3.96043	0.151764
$682$	2.88475	0.110463
$683$	−24.0090	−0.918677	−0.459339	−	0.888261i	$-0.651914\pi$
$683$	−24.0090	−0.918677	−0.459339	+	0.888261i	$0.651914\pi$
$684$	−17.8263	−0.681606
$685$	1.15530	0.0441419
$686$	−0.0476729	−0.00182016
$687$	−12.0061	−0.458060
$688$	−4.18584	−0.159584
$689$	−19.8872	−0.757642
$690$	0.178643	0.00680081
$691$	32.0764	1.22024	0.610122	−	0.792308i	$-0.291121\pi$
$691$	32.0764	1.22024	0.610122	+	0.792308i	$0.291121\pi$
$692$	21.0459	0.800046
$693$	6.91117	0.262534
$694$	32.0519	1.21668
$695$	−17.4452	−0.661733
$696$	−0.955577	−0.0362210
$697$	−28.5495	−1.08139
$698$	−15.3894	−0.582498
$699$	2.93705	0.111090
$700$	−3.74336	−0.141486
$701$	46.6528	1.76205	0.881025	−	0.473069i	$-0.156854\pi$
$701$	46.6528	1.76205	0.881025	+	0.473069i	$0.156854\pi$
$702$	−6.30884	−0.238112
$703$	−25.8383	−0.974509
$704$	0.679203	0.0255984
$705$	3.89083	0.146537
$706$	23.6376	0.889612
$707$	−16.6193	−0.625033
$708$	−1.51862	−0.0570731
$709$	−27.7974	−1.04395	−0.521977	−	0.852960i	$-0.674805\pi$
$709$	−27.7974	−1.04395	−0.521977	+	0.852960i	$0.674805\pi$
$710$	13.1541	0.493664
$711$	−2.90478	−0.108938
$712$	−4.36392	−0.163545
$713$	−1.42945	−0.0535335
$714$	−5.29504	−0.198162
$715$	−1.41176	−0.0527968
$716$	10.2836	0.384317
$717$	5.50847	0.205718
$718$	2.71864	0.101459
$719$	8.83452	0.329472	0.164736	−	0.986338i	$-0.447323\pi$
$719$	8.83452	0.329472	0.164736	+	0.986338i	$0.447323\pi$
$720$	2.71826	0.101304
$721$	21.2027	0.789631
$722$	24.0072	0.893457
$723$	5.92880	0.220494
$724$	−22.1454	−0.823027
$725$	−1.80029	−0.0668609
$726$	−5.59385	−0.207607
$727$	49.1171	1.82165	0.910826	−	0.412790i	$-0.135446\pi$
$727$	49.1171	1.82165	0.910826	+	0.412790i	$0.135446\pi$
$728$	−7.78078	−0.288375
$729$	−12.9543	−0.479791
$730$	1.86964	0.0691985
$731$	−11.1549	−0.412579
$732$	4.53474	0.167609
$733$	−47.0990	−1.73964	−0.869821	−	0.493368i	$-0.835765\pi$
$733$	−47.0990	−1.73964	−0.869821	+	0.493368i	$0.835765\pi$
$734$	0.979270	0.0361455
$735$	−3.72230	−0.137299
$736$	−0.336559	−0.0124057
$737$	−0.923351	−0.0340121
$738$	29.1210	1.07196
$739$	49.3804	1.81649	0.908243	−	0.418442i	$-0.137424\pi$
$739$	49.3804	1.81649	0.908243	+	0.418442i	$0.137424\pi$
$740$	3.93997	0.144836
$741$	7.23530	0.265795
$742$	35.8157	1.31484
$743$	1.39981	0.0513541	0.0256770	−	0.999670i	$-0.491826\pi$
$743$	1.39981	0.0513541	0.0256770	+	0.999670i	$0.491826\pi$
$744$	2.25441	0.0826507
$745$	11.0099	0.403373
$746$	10.9989	0.402697
$747$	17.5120	0.640732
$748$	1.81002	0.0661808
$749$	3.25649	0.118990
$750$	−0.530792	−0.0193818
$751$	−49.1414	−1.79320	−0.896598	−	0.442845i	$-0.853969\pi$
$751$	−49.1414	−1.79320	−0.896598	+	0.442845i	$0.853969\pi$
$752$	−7.33024	−0.267306
$753$	−3.70358	−0.134966
$754$	−3.74199	−0.136275
$755$	5.37962	0.195784
$756$	11.3619	0.413227
$757$	−26.1512	−0.950483	−0.475241	−	0.879855i	$-0.657639\pi$
$757$	−26.1512	−0.950483	−0.475241	+	0.879855i	$0.657639\pi$
$758$	29.2466	1.06228
$759$	−0.121335	−0.00440417
$760$	−6.55799	−0.237883
$761$	8.41218	0.304941	0.152471	−	0.988308i	$-0.451277\pi$
$761$	8.41218	0.304941	0.152471	+	0.988308i	$0.451277\pi$
$762$	−7.22766	−0.261831
$763$	−38.3450	−1.38818
$764$	−12.5100	−0.452595
$765$	7.24394	0.261905
$766$	−4.41468	−0.159509
$767$	−5.94683	−0.214728
$768$	0.530792	0.0191533
$769$	38.2614	1.37974	0.689870	−	0.723933i	$-0.257668\pi$
$769$	38.2614	1.37974	0.689870	+	0.723933i	$0.257668\pi$
$770$	2.54250	0.0916253
$771$	−0.451090	−0.0162456
$772$	11.6646	0.419817
$773$	−34.9563	−1.25729	−0.628646	−	0.777692i	$-0.716390\pi$
$773$	−34.9563	−1.25729	−0.628646	+	0.777692i	$0.716390\pi$
$774$	11.3782	0.408981
$775$	4.24726	0.152566
$776$	7.15483	0.256843
$777$	7.82850	0.280846
$778$	−8.37960	−0.300423
$779$	−70.2564	−2.51720
$780$	−1.10328	−0.0395037
$781$	−8.93429	−0.319694
$782$	−0.896902	−0.0320732
$783$	5.46424	0.195276
$784$	7.01274	0.250455
$785$	1.24490	0.0444324
$786$	−9.52214	−0.339643
$787$	34.5417	1.23128	0.615639	−	0.788028i	$-0.288898\pi$
$787$	34.5417	1.23128	0.615639	+	0.788028i	$0.288898\pi$
$788$	−19.9924	−0.712201
$789$	−10.4047	−0.370415
$790$	−1.06862	−0.0380197
$791$	35.4098	1.25903
$792$	−1.84625	−0.0656036
$793$	17.7578	0.630598
$794$	−3.26976	−0.116040
$795$	5.07851	0.180116
$796$	13.0480	0.462473
$797$	−50.2403	−1.77960	−0.889801	−	0.456348i	$-0.849157\pi$
$797$	−50.2403	−1.77960	−0.889801	+	0.456348i	$0.849157\pi$
$798$	−13.0304	−0.461270
$799$	−19.5345	−0.691081
$800$	1.00000	0.0353553
$801$	11.8623	0.419133
$802$	−31.5764	−1.11500
$803$	−1.26986	−0.0448125
$804$	−0.721592	−0.0254486
$805$	−1.25986	−0.0444043
$806$	8.82816	0.310959
$807$	8.13082	0.286219
$808$	4.43968	0.156187
$809$	0.457562	0.0160870	0.00804352	−	0.999968i	$-0.497440\pi$
$809$	0.457562	0.0160870	0.00804352	+	0.999968i	$0.497440\pi$
$810$	−6.54372	−0.229923
$811$	−23.8227	−0.836527	−0.418264	−	0.908326i	$-0.637361\pi$
$811$	−23.8227	−0.836527	−0.418264	+	0.908326i	$0.637361\pi$
$812$	6.73912	0.236497
$813$	−5.50103	−0.192930
$814$	−2.67604	−0.0937951
$815$	18.5020	0.648097
$816$	1.41452	0.0495180
$817$	−27.4507	−0.960378
$818$	32.5353	1.13757
$819$	21.1502	0.739047
$820$	10.7131	0.374117
$821$	−13.5056	−0.471348	−0.235674	−	0.971832i	$-0.575730\pi$
$821$	−13.5056	−0.471348	−0.235674	+	0.971832i	$0.575730\pi$
$822$	−0.613226	−0.0213887
$823$	−39.9536	−1.39270	−0.696348	−	0.717705i	$-0.745193\pi$
$823$	−39.9536	−1.39270	−0.696348	+	0.717705i	$0.745193\pi$
$824$	−5.66409	−0.197318
$825$	0.360515	0.0125515
$826$	10.7099	0.372645
$827$	40.0394	1.39231	0.696153	−	0.717893i	$-0.254893\pi$
$827$	40.0394	1.39231	0.696153	+	0.717893i	$0.254893\pi$
$828$	0.914855	0.0317934
$829$	−16.6772	−0.579225	−0.289612	−	0.957144i	$-0.593526\pi$
$829$	−16.6772	−0.579225	−0.289612	+	0.957144i	$0.593526\pi$
$830$	6.44237	0.223618
$831$	−12.7549	−0.442463
$832$	2.07855	0.0720609
$833$	18.6884	0.647513
$834$	9.25975	0.320639
$835$	−8.40377	−0.290825
$836$	4.45420	0.154052
$837$	−12.8913	−0.445589
$838$	−15.6741	−0.541452
$839$	−28.2064	−0.973792	−0.486896	−	0.873460i	$-0.661871\pi$
$839$	−28.2064	−0.973792	−0.486896	+	0.873460i	$0.661871\pi$
$840$	1.98694	0.0685561
$841$	−25.7590	−0.888240
$842$	21.2708	0.733041
$843$	7.24970	0.249693
$844$	−15.4720	−0.532570
$845$	8.67961	0.298588
$846$	19.9255	0.685053
$847$	39.4501	1.35552
$848$	−9.56781	−0.328560
$849$	−6.13426	−0.210527
$850$	2.66492	0.0914059
$851$	1.32603	0.0454558
$852$	−6.98208	−0.239202
$853$	−18.5488	−0.635100	−0.317550	−	0.948242i	$-0.602860\pi$
$853$	−18.5488	−0.635100	−0.317550	+	0.948242i	$0.602860\pi$
$854$	−31.9808	−1.09436
$855$	17.8263	0.609647
$856$	−0.869938	−0.0297339
$857$	23.0501	0.787376	0.393688	−	0.919244i	$-0.371199\pi$
$857$	23.0501	0.787376	0.393688	+	0.919244i	$0.371199\pi$
$858$	0.749350	0.0255824
$859$	−19.2585	−0.657092	−0.328546	−	0.944488i	$-0.606559\pi$
$859$	−19.2585	−0.657092	−0.328546	+	0.944488i	$0.606559\pi$
$860$	4.18584	0.142736
$861$	21.2863	0.725436
$862$	10.8213	0.368576
$863$	20.6270	0.702151	0.351075	−	0.936347i	$-0.385816\pi$
$863$	20.6270	0.702151	0.351075	+	0.936347i	$0.385816\pi$
$864$	−3.03520	−0.103260
$865$	−21.0459	−0.715583
$866$	−36.7685	−1.24944
$867$	−5.25389	−0.178431
$868$	−15.8990	−0.539648
$869$	0.725808	0.0246213
$870$	0.955577	0.0323971
$871$	−2.82572	−0.0957458
$872$	10.2435	0.346888
$873$	−19.4487	−0.658239
$874$	−2.20715	−0.0746580
$875$	3.74336	0.126549
$876$	−0.992390	−0.0335297
$877$	1.08930	0.0367829	0.0183915	−	0.999831i	$-0.494145\pi$
$877$	1.08930	0.0367829	0.0183915	+	0.999831i	$0.494145\pi$
$878$	22.7649	0.768280
$879$	−6.05094	−0.204093
$880$	−0.679203	−0.0228959
$881$	35.9118	1.20990	0.604950	−	0.796263i	$-0.293193\pi$
$881$	35.9118	1.20990	0.604950	+	0.796263i	$0.293193\pi$
$882$	−19.0624	−0.641866
$883$	−7.05315	−0.237357	−0.118679	−	0.992933i	$-0.537866\pi$
$883$	−7.05315	−0.237357	−0.118679	+	0.992933i	$0.537866\pi$
$884$	5.53918	0.186303
$885$	1.51862	0.0510477
$886$	−16.3934	−0.550746
$887$	15.7403	0.528508	0.264254	−	0.964453i	$-0.414874\pi$
$887$	15.7403	0.528508	0.264254	+	0.964453i	$0.414874\pi$
$888$	−2.09130	−0.0701796
$889$	50.9724	1.70956
$890$	4.36392	0.146279
$891$	4.44451	0.148897
$892$	6.35358	0.212733
$893$	−48.0717	−1.60866
$894$	−5.84399	−0.195452
$895$	−10.2836	−0.343744
$896$	−3.74336	−0.125057
$897$	−0.371319	−0.0123980
$898$	20.5608	0.686122
$899$	−7.64628	−0.255018
$900$	−2.71826	−0.0906087
$901$	−25.4974	−0.849442
$902$	−7.27636	−0.242276
$903$	8.31702	0.276773
$904$	−9.45936	−0.314613
$905$	22.1454	0.736138
$906$	−2.85546	−0.0948662
$907$	12.3836	0.411192	0.205596	−	0.978637i	$-0.434087\pi$
$907$	12.3836	0.411192	0.205596	+	0.978637i	$0.434087\pi$
$908$	7.46136	0.247614
$909$	−12.0682	−0.400277
$910$	7.78078	0.257930
$911$	−15.4774	−0.512791	−0.256395	−	0.966572i	$-0.582535\pi$
$911$	−15.4774	−0.512791	−0.256395	+	0.966572i	$0.582535\pi$
$912$	3.48093	0.115265
$913$	−4.37567	−0.144814
$914$	−3.70945	−0.122698
$915$	−4.53474	−0.149914
$916$	−22.6192	−0.747359
$917$	67.1540	2.21762
$918$	−8.08857	−0.266963
$919$	−8.85630	−0.292142	−0.146071	−	0.989274i	$-0.546663\pi$
$919$	−8.85630	−0.292142	−0.146071	+	0.989274i	$0.546663\pi$
$920$	0.336559	0.0110960
$921$	10.5658	0.348154
$922$	−8.27972	−0.272678
$923$	−27.3415	−0.899956
$924$	−1.34954	−0.0443965
$925$	−3.93997	−0.129545
$926$	17.7489	0.583265
$927$	15.3965	0.505687
$928$	−1.80029	−0.0590973
$929$	−39.3131	−1.28982	−0.644911	−	0.764258i	$-0.723105\pi$
$929$	−39.3131	−1.28982	−0.644911	+	0.764258i	$0.723105\pi$
$930$	−2.25441	−0.0739250
$931$	45.9894	1.50724
$932$	5.53334	0.181251
$933$	0.906216	0.0296682
$934$	−17.0009	−0.556286
$935$	−1.81002	−0.0591939
$936$	−5.65005	−0.184678
$937$	53.1814	1.73736	0.868680	−	0.495375i	$-0.164969\pi$
$937$	53.1814	1.73736	0.868680	+	0.495375i	$0.164969\pi$
$938$	5.08896	0.166160
$939$	−11.9792	−0.390925
$940$	7.33024	0.239086
$941$	−3.98421	−0.129882	−0.0649408	−	0.997889i	$-0.520686\pi$
$941$	−3.98421	−0.129882	−0.0649408	+	0.997889i	$0.520686\pi$
$942$	−0.660783	−0.0215295
$943$	3.60559	0.117414
$944$	−2.86104	−0.0931189
$945$	−11.3619	−0.369601
$946$	−2.84303	−0.0924349
$947$	−44.7738	−1.45495	−0.727477	−	0.686132i	$-0.759307\pi$
$947$	−44.7738	−1.45495	−0.727477	+	0.686132i	$0.759307\pi$
$948$	0.567213	0.0184222
$949$	−3.88615	−0.126150
$950$	6.55799	0.212769
$951$	−10.8399	−0.351509
$952$	−9.97574	−0.323316
$953$	−4.95914	−0.160642	−0.0803211	−	0.996769i	$-0.525595\pi$
$953$	−4.95914	−0.160642	−0.0803211	+	0.996769i	$0.525595\pi$
$954$	26.0078	0.842033
$955$	12.5100	0.404813
$956$	10.3778	0.335643
$957$	−0.649030	−0.0209802
$958$	−34.3633	−1.11023
$959$	4.32472	0.139653
$960$	−0.530792	−0.0171312
$961$	−12.9608	−0.418090
$962$	−8.18944	−0.264038
$963$	2.36472	0.0762020
$964$	11.1697	0.359753
$965$	−11.6646	−0.375496
$966$	0.668724	0.0215158
$967$	−9.00272	−0.289508	−0.144754	−	0.989468i	$-0.546239\pi$
$967$	−9.00272	−0.289508	−0.144754	+	0.989468i	$0.546239\pi$
$968$	−10.5387	−0.338726
$969$	9.27638	0.298000
$970$	−7.15483	−0.229728
$971$	−36.0659	−1.15741	−0.578704	−	0.815537i	$-0.696441\pi$
$971$	−36.0659	−1.15741	−0.578704	+	0.815537i	$0.696441\pi$
$972$	12.5790	0.403471
$973$	−65.3035	−2.09353
$974$	−2.88615	−0.0924783
$975$	1.10328	0.0353332
$976$	8.54335	0.273466
$977$	−18.1035	−0.579182	−0.289591	−	0.957151i	$-0.593519\pi$
$977$	−18.1035	−0.579182	−0.289591	+	0.957151i	$0.593519\pi$
$978$	−9.82071	−0.314032
$979$	−2.96398	−0.0947294
$980$	−7.01274	−0.224014
$981$	−27.8444	−0.889003
$982$	−2.10442	−0.0671549
$983$	27.2859	0.870286	0.435143	−	0.900361i	$-0.356698\pi$
$983$	27.2859	0.870286	0.435143	+	0.900361i	$0.356698\pi$
$984$	−5.68642	−0.181276
$985$	19.9924	0.637012
$986$	−4.79761	−0.152787
$987$	14.5648	0.463602
$988$	13.6311	0.433664
$989$	1.40878	0.0447966
$990$	1.84625	0.0586777
$991$	4.13903	0.131481	0.0657403	−	0.997837i	$-0.479059\pi$
$991$	4.13903	0.131481	0.0657403	+	0.997837i	$0.479059\pi$
$992$	4.24726	0.134851
$993$	15.6466	0.496530
$994$	49.2405	1.56181
$995$	−13.0480	−0.413648
$996$	−3.41956	−0.108353
$997$	28.9096	0.915576	0.457788	−	0.889062i	$-0.348642\pi$
$997$	28.9096	0.915576	0.457788	+	0.889062i	$0.348642\pi$
$998$	−1.59998	−0.0506464
$999$	11.9586	0.378354

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6010.2.a.f.1.14	✓	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6010.2.a.f.1.14	✓	22	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:	\( N \)	\(=\)	\( 6010 = 2 \cdot 5 \cdot 601 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6010.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +0.530792 q^{3} +1.00000 q^{4} -1.00000 q^{5} +0.530792 q^{6} -3.74336 q^{7} +1.00000 q^{8} -2.71826 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +0.530792 q^{3} +1.00000 q^{4} -1.00000 q^{5} +0.530792 q^{6} -3.74336 q^{7} +1.00000 q^{8} -2.71826 q^{9} -1.00000 q^{10} +0.679203 q^{11} +0.530792 q^{12} +2.07855 q^{13} -3.74336 q^{14} -0.530792 q^{15} +1.00000 q^{16} +2.66492 q^{17} -2.71826 q^{18} +6.55799 q^{19} -1.00000 q^{20} -1.98694 q^{21} +0.679203 q^{22} -0.336559 q^{23} +0.530792 q^{24} +1.00000 q^{25} +2.07855 q^{26} -3.03520 q^{27} -3.74336 q^{28} -1.80029 q^{29} -0.530792 q^{30} +4.24726 q^{31} +1.00000 q^{32} +0.360515 q^{33} +2.66492 q^{34} +3.74336 q^{35} -2.71826 q^{36} -3.93997 q^{37} +6.55799 q^{38} +1.10328 q^{39} -1.00000 q^{40} -10.7131 q^{41} -1.98694 q^{42} -4.18584 q^{43} +0.679203 q^{44} +2.71826 q^{45} -0.336559 q^{46} -7.33024 q^{47} +0.530792 q^{48} +7.01274 q^{49} +1.00000 q^{50} +1.41452 q^{51} +2.07855 q^{52} -9.56781 q^{53} -3.03520 q^{54} -0.679203 q^{55} -3.74336 q^{56} +3.48093 q^{57} -1.80029 q^{58} -2.86104 q^{59} -0.530792 q^{60} +8.54335 q^{61} +4.24726 q^{62} +10.1754 q^{63} +1.00000 q^{64} -2.07855 q^{65} +0.360515 q^{66} -1.35946 q^{67} +2.66492 q^{68} -0.178643 q^{69} +3.74336 q^{70} -13.1541 q^{71} -2.71826 q^{72} -1.86964 q^{73} -3.93997 q^{74} +0.530792 q^{75} +6.55799 q^{76} -2.54250 q^{77} +1.10328 q^{78} +1.06862 q^{79} -1.00000 q^{80} +6.54372 q^{81} -10.7131 q^{82} -6.44237 q^{83} -1.98694 q^{84} -2.66492 q^{85} -4.18584 q^{86} -0.955577 q^{87} +0.679203 q^{88} -4.36392 q^{89} +2.71826 q^{90} -7.78078 q^{91} -0.336559 q^{92} +2.25441 q^{93} -7.33024 q^{94} -6.55799 q^{95} +0.530792 q^{96} +7.15483 q^{97} +7.01274 q^{98} -1.84625 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + 22 q^{2} - 6 q^{3} + 22 q^{4} - 22 q^{5} - 6 q^{6} - 12 q^{7} + 22 q^{8} + 12 q^{9}+O(q^{10}) \) 22 * q + 22 * q^2 - 6 * q^3 + 22 * q^4 - 22 * q^5 - 6 * q^6 - 12 * q^7 + 22 * q^8 + 12 * q^9	\( 22 q + 22 q^{2} - 6 q^{3} + 22 q^{4} - 22 q^{5} - 6 q^{6} - 12 q^{7} + 22 q^{8} + 12 q^{9} - 22 q^{10} - 4 q^{11} - 6 q^{12} - 20 q^{13} - 12 q^{14} + 6 q^{15} + 22 q^{16} - 23 q^{17} + 12 q^{18} + q^{19} - 22 q^{20} - 8 q^{21} - 4 q^{22} - 17 q^{23} - 6 q^{24} + 22 q^{25} - 20 q^{26} - 21 q^{27} - 12 q^{28} - 13 q^{29} + 6 q^{30} - 13 q^{31} + 22 q^{32} - 21 q^{33} - 23 q^{34} + 12 q^{35} + 12 q^{36} - 16 q^{37} + q^{38} - 4 q^{39} - 22 q^{40} - 31 q^{41} - 8 q^{42} - 9 q^{43} - 4 q^{44} - 12 q^{45} - 17 q^{46} - 41 q^{47} - 6 q^{48} - 6 q^{49} + 22 q^{50} - 7 q^{51} - 20 q^{52} - 15 q^{53} - 21 q^{54} + 4 q^{55} - 12 q^{56} - 26 q^{57} - 13 q^{58} - 32 q^{59} + 6 q^{60} - 22 q^{61} - 13 q^{62} - 55 q^{63} + 22 q^{64} + 20 q^{65} - 21 q^{66} - 19 q^{67} - 23 q^{68} - 37 q^{69} + 12 q^{70} - 36 q^{71} + 12 q^{72} - 47 q^{73} - 16 q^{74} - 6 q^{75} + q^{76} - 26 q^{77} - 4 q^{78} - 10 q^{79} - 22 q^{80} - 18 q^{81} - 31 q^{82} - 48 q^{83} - 8 q^{84} + 23 q^{85} - 9 q^{86} - 50 q^{87} - 4 q^{88} - 42 q^{89} - 12 q^{90} + 25 q^{91} - 17 q^{92} - 48 q^{93} - 41 q^{94} - q^{95} - 6 q^{96} - 67 q^{97} - 6 q^{98} - 3 q^{99}+O(q^{100}) \) 22 * q + 22 * q^2 - 6 * q^3 + 22 * q^4 - 22 * q^5 - 6 * q^6 - 12 * q^7 + 22 * q^8 + 12 * q^9 - 22 * q^10 - 4 * q^11 - 6 * q^12 - 20 * q^13 - 12 * q^14 + 6 * q^15 + 22 * q^16 - 23 * q^17 + 12 * q^18 + q^19 - 22 * q^20 - 8 * q^21 - 4 * q^22 - 17 * q^23 - 6 * q^24 + 22 * q^25 - 20 * q^26 - 21 * q^27 - 12 * q^28 - 13 * q^29 + 6 * q^30 - 13 * q^31 + 22 * q^32 - 21 * q^33 - 23 * q^34 + 12 * q^35 + 12 * q^36 - 16 * q^37 + q^38 - 4 * q^39 - 22 * q^40 - 31 * q^41 - 8 * q^42 - 9 * q^43 - 4 * q^44 - 12 * q^45 - 17 * q^46 - 41 * q^47 - 6 * q^48 - 6 * q^49 + 22 * q^50 - 7 * q^51 - 20 * q^52 - 15 * q^53 - 21 * q^54 + 4 * q^55 - 12 * q^56 - 26 * q^57 - 13 * q^58 - 32 * q^59 + 6 * q^60 - 22 * q^61 - 13 * q^62 - 55 * q^63 + 22 * q^64 + 20 * q^65 - 21 * q^66 - 19 * q^67 - 23 * q^68 - 37 * q^69 + 12 * q^70 - 36 * q^71 + 12 * q^72 - 47 * q^73 - 16 * q^74 - 6 * q^75 + q^76 - 26 * q^77 - 4 * q^78 - 10 * q^79 - 22 * q^80 - 18 * q^81 - 31 * q^82 - 48 * q^83 - 8 * q^84 + 23 * q^85 - 9 * q^86 - 50 * q^87 - 4 * q^88 - 42 * q^89 - 12 * q^90 + 25 * q^91 - 17 * q^92 - 48 * q^93 - 41 * q^94 - q^95 - 6 * q^96 - 67 * q^97 - 6 * q^98 - 3 * q^99

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