LMFDB - Embedded newform 2667.2.a.q.1.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2667,2,Mod(1,2667)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2667, 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("2667.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2667 = 3 \cdot 7 \cdot 127 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2667.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:	$21.2961022191$
Analytic rank:	$0$
Dimension:	$19$
Coefficient field:	$\mathbb{Q}[x]/(x^{19} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{19} - 4 x^{18} - 22 x^{17} + 101 x^{16} + 178 x^{15} - 1035 x^{14} - 583 x^{13} + 5572 x^{12} + \cdots + 210 $ x^19 - 4x^18 - 22x^17 + 101x^16 + 178x^15 - 1035x^14 - 583x^13 + 5572x^12 + 21x^11 - 17032x^10 + 4985x^9 + 29792x^8 - 13249x^7 - 28600x^6 + 14000x^5 + 13725x^4 - 5723x^3 - 2913x^2 + 608x + 210
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
Root			$2.26573$ of defining polynomial
Character	$\chi$	$=$	2667.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.26573 q^{2} +1.00000 q^{3} +3.13354 q^{4} -0.263451 q^{5} +2.26573 q^{6} +1.00000 q^{7} +2.56830 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.26573 q^{2} +1.00000 q^{3} +3.13354 q^{4} -0.263451 q^{5} +2.26573 q^{6} +1.00000 q^{7} +2.56830 q^{8} +1.00000 q^{9} -0.596909 q^{10} +2.11462 q^{11} +3.13354 q^{12} +5.02935 q^{13} +2.26573 q^{14} -0.263451 q^{15} -0.448003 q^{16} +0.600740 q^{17} +2.26573 q^{18} -0.662362 q^{19} -0.825534 q^{20} +1.00000 q^{21} +4.79117 q^{22} -0.862531 q^{23} +2.56830 q^{24} -4.93059 q^{25} +11.3952 q^{26} +1.00000 q^{27} +3.13354 q^{28} +7.49718 q^{29} -0.596909 q^{30} -6.27258 q^{31} -6.15165 q^{32} +2.11462 q^{33} +1.36112 q^{34} -0.263451 q^{35} +3.13354 q^{36} +1.88794 q^{37} -1.50074 q^{38} +5.02935 q^{39} -0.676621 q^{40} +9.92148 q^{41} +2.26573 q^{42} -0.837435 q^{43} +6.62626 q^{44} -0.263451 q^{45} -1.95426 q^{46} -6.32880 q^{47} -0.448003 q^{48} +1.00000 q^{49} -11.1714 q^{50} +0.600740 q^{51} +15.7597 q^{52} +2.22979 q^{53} +2.26573 q^{54} -0.557099 q^{55} +2.56830 q^{56} -0.662362 q^{57} +16.9866 q^{58} -8.92253 q^{59} -0.825534 q^{60} +12.6716 q^{61} -14.2120 q^{62} +1.00000 q^{63} -13.0420 q^{64} -1.32499 q^{65} +4.79117 q^{66} -6.63659 q^{67} +1.88244 q^{68} -0.862531 q^{69} -0.596909 q^{70} +3.04160 q^{71} +2.56830 q^{72} +3.58423 q^{73} +4.27757 q^{74} -4.93059 q^{75} -2.07554 q^{76} +2.11462 q^{77} +11.3952 q^{78} -6.24082 q^{79} +0.118027 q^{80} +1.00000 q^{81} +22.4794 q^{82} -15.5940 q^{83} +3.13354 q^{84} -0.158265 q^{85} -1.89740 q^{86} +7.49718 q^{87} +5.43098 q^{88} +10.2988 q^{89} -0.596909 q^{90} +5.02935 q^{91} -2.70278 q^{92} -6.27258 q^{93} -14.3394 q^{94} +0.174500 q^{95} -6.15165 q^{96} +10.8058 q^{97} +2.26573 q^{98} +2.11462 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 19 q + 4 q^{2} + 19 q^{3} + 22 q^{4} + 5 q^{5} + 4 q^{6} + 19 q^{7} + 9 q^{8} + 19 q^{9}+O(q^{10}) $ 19 * q + 4 * q^2 + 19 * q^3 + 22 * q^4 + 5 * q^5 + 4 * q^6 + 19 * q^7 + 9 * q^8 + 19 * q^9	\( 19 q + 4 q^{2} + 19 q^{3} + 22 q^{4} + 5 q^{5} + 4 q^{6} + 19 q^{7} + 9 q^{8} + 19 q^{9} - 9 q^{11} + 22 q^{12} + 24 q^{13} + 4 q^{14} + 5 q^{15} + 20 q^{16} + 17 q^{17} + 4 q^{18} + 23 q^{19} + 5 q^{20} + 19 q^{21} - 3 q^{22} - 17 q^{23} + 9 q^{24} + 38 q^{25} + 28 q^{26} + 19 q^{27} + 22 q^{28} + 2 q^{29} + 16 q^{31} + 17 q^{32} - 9 q^{33} + 29 q^{34} + 5 q^{35} + 22 q^{36} + 56 q^{37} + 2 q^{38} + 24 q^{39} - 13 q^{40} - 7 q^{41} + 4 q^{42} + 19 q^{43} - 29 q^{44} + 5 q^{45} + 10 q^{46} + 25 q^{47} + 20 q^{48} + 19 q^{49} - 9 q^{50} + 17 q^{51} + 16 q^{52} + 18 q^{53} + 4 q^{54} + 10 q^{55} + 9 q^{56} + 23 q^{57} + 31 q^{58} + 11 q^{59} + 5 q^{60} + 26 q^{61} + 26 q^{62} + 19 q^{63} + 45 q^{64} + 27 q^{65} - 3 q^{66} + 24 q^{67} + 14 q^{68} - 17 q^{69} - 32 q^{71} + 9 q^{72} + 51 q^{73} + 38 q^{75} + 12 q^{76} - 9 q^{77} + 28 q^{78} + 30 q^{79} - 30 q^{80} + 19 q^{81} - 52 q^{82} + q^{83} + 22 q^{84} + 44 q^{85} - 24 q^{86} + 2 q^{87} - 30 q^{88} + 5 q^{89} + 24 q^{91} - 88 q^{92} + 16 q^{93} + 7 q^{94} - 24 q^{95} + 17 q^{96} + 5 q^{97} + 4 q^{98} - 9 q^{99}+O(q^{100}) \) 19 * q + 4 * q^2 + 19 * q^3 + 22 * q^4 + 5 * q^5 + 4 * q^6 + 19 * q^7 + 9 * q^8 + 19 * q^9 - 9 * q^11 + 22 * q^12 + 24 * q^13 + 4 * q^14 + 5 * q^15 + 20 * q^16 + 17 * q^17 + 4 * q^18 + 23 * q^19 + 5 * q^20 + 19 * q^21 - 3 * q^22 - 17 * q^23 + 9 * q^24 + 38 * q^25 + 28 * q^26 + 19 * q^27 + 22 * q^28 + 2 * q^29 + 16 * q^31 + 17 * q^32 - 9 * q^33 + 29 * q^34 + 5 * q^35 + 22 * q^36 + 56 * q^37 + 2 * q^38 + 24 * q^39 - 13 * q^40 - 7 * q^41 + 4 * q^42 + 19 * q^43 - 29 * q^44 + 5 * q^45 + 10 * q^46 + 25 * q^47 + 20 * q^48 + 19 * q^49 - 9 * q^50 + 17 * q^51 + 16 * q^52 + 18 * q^53 + 4 * q^54 + 10 * q^55 + 9 * q^56 + 23 * q^57 + 31 * q^58 + 11 * q^59 + 5 * q^60 + 26 * q^61 + 26 * q^62 + 19 * q^63 + 45 * q^64 + 27 * q^65 - 3 * q^66 + 24 * q^67 + 14 * q^68 - 17 * q^69 - 32 * q^71 + 9 * q^72 + 51 * q^73 + 38 * q^75 + 12 * q^76 - 9 * q^77 + 28 * q^78 + 30 * q^79 - 30 * q^80 + 19 * q^81 - 52 * q^82 + q^83 + 22 * q^84 + 44 * q^85 - 24 * q^86 + 2 * q^87 - 30 * q^88 + 5 * q^89 + 24 * q^91 - 88 * q^92 + 16 * q^93 + 7 * q^94 - 24 * q^95 + 17 * q^96 + 5 * q^97 + 4 * q^98 - 9 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	2.26573	1.60211	0.801057	−	0.598588i	$-0.204271\pi$
$2$	2.26573	1.60211	0.801057	+	0.598588i	$0.204271\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	3.13354	1.56677
$5$	−0.263451	−0.117819	−0.0589094	−	0.998263i	$-0.518762\pi$
$5$	−0.263451	−0.117819	−0.0589094	+	0.998263i	$0.518762\pi$
$6$	2.26573	0.924981
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	2.56830	0.908031
$9$	1.00000	0.333333
$10$	−0.596909	−0.188759
$11$	2.11462	0.637583	0.318791	−	0.947825i	$-0.396723\pi$
$11$	2.11462	0.637583	0.318791	+	0.947825i	$0.396723\pi$
$12$	3.13354	0.904575
$13$	5.02935	1.39489	0.697445	−	0.716638i	$-0.254320\pi$
$13$	5.02935	1.39489	0.697445	+	0.716638i	$0.254320\pi$
$14$	2.26573	0.605542
$15$	−0.263451	−0.0680227
$16$	−0.448003	−0.112001
$17$	0.600740	0.145701	0.0728504	−	0.997343i	$-0.476790\pi$
$17$	0.600740	0.145701	0.0728504	+	0.997343i	$0.476790\pi$
$18$	2.26573	0.534038
$19$	−0.662362	−0.151956	−0.0759782	−	0.997109i	$-0.524208\pi$
$19$	−0.662362	−0.151956	−0.0759782	+	0.997109i	$0.524208\pi$
$20$	−0.825534	−0.184595
$21$	1.00000	0.218218
$22$	4.79117	1.02148
$23$	−0.862531	−0.179850	−0.0899251	−	0.995949i	$-0.528663\pi$
$23$	−0.862531	−0.179850	−0.0899251	+	0.995949i	$0.528663\pi$
$24$	2.56830	0.524252
$25$	−4.93059	−0.986119
$26$	11.3952	2.23477
$27$	1.00000	0.192450
$28$	3.13354	0.592184
$29$	7.49718	1.39219	0.696095	−	0.717949i	$-0.254919\pi$
$29$	7.49718	1.39219	0.696095	+	0.717949i	$0.254919\pi$
$30$	−0.596909	−0.108980
$31$	−6.27258	−1.12659	−0.563294	−	0.826256i	$-0.690466\pi$
$31$	−6.27258	−1.12659	−0.563294	+	0.826256i	$0.690466\pi$
$32$	−6.15165	−1.08747
$33$	2.11462	0.368109
$34$	1.36112	0.233429
$35$	−0.263451	−0.0445313
$36$	3.13354	0.522257
$37$	1.88794	0.310376	0.155188	−	0.987885i	$-0.450402\pi$
$37$	1.88794	0.310376	0.155188	+	0.987885i	$0.450402\pi$
$38$	−1.50074	−0.243451
$39$	5.02935	0.805341
$40$	−0.676621	−0.106983
$41$	9.92148	1.54948	0.774738	−	0.632283i	$-0.217882\pi$
$41$	9.92148	1.54948	0.774738	+	0.632283i	$0.217882\pi$
$42$	2.26573	0.349610
$43$	−0.837435	−0.127708	−0.0638538	−	0.997959i	$-0.520339\pi$
$43$	−0.837435	−0.127708	−0.0638538	+	0.997959i	$0.520339\pi$
$44$	6.62626	0.998946
$45$	−0.263451	−0.0392729
$46$	−1.95426	−0.288140
$47$	−6.32880	−0.923150	−0.461575	−	0.887101i	$-0.652716\pi$
$47$	−6.32880	−0.923150	−0.461575	+	0.887101i	$0.652716\pi$
$48$	−0.448003	−0.0646636
$49$	1.00000	0.142857
$50$	−11.1714	−1.57988
$51$	0.600740	0.0841204
$52$	15.7597	2.18547
$53$	2.22979	0.306285	0.153143	−	0.988204i	$-0.451061\pi$
$53$	2.22979	0.306285	0.153143	+	0.988204i	$0.451061\pi$
$54$	2.26573	0.308327
$55$	−0.557099	−0.0751192
$56$	2.56830	0.343204
$57$	−0.662362	−0.0877321
$58$	16.9866	2.23045
$59$	−8.92253	−1.16161	−0.580807	−	0.814041i	$-0.697263\pi$
$59$	−8.92253	−1.16161	−0.580807	+	0.814041i	$0.697263\pi$
$60$	−0.825534	−0.106576
$61$	12.6716	1.62243	0.811215	−	0.584748i	$-0.198806\pi$
$61$	12.6716	1.62243	0.811215	+	0.584748i	$0.198806\pi$
$62$	−14.2120	−1.80492
$63$	1.00000	0.125988
$64$	−13.0420	−1.63025
$65$	−1.32499	−0.164344
$66$	4.79117	0.589752
$67$	−6.63659	−0.810788	−0.405394	−	0.914142i	$-0.632866\pi$
$67$	−6.63659	−0.810788	−0.405394	+	0.914142i	$0.632866\pi$
$68$	1.88244	0.228280
$69$	−0.862531	−0.103837
$70$	−0.596909	−0.0713443
$71$	3.04160	0.360971	0.180486	−	0.983578i	$-0.442233\pi$
$71$	3.04160	0.360971	0.180486	+	0.983578i	$0.442233\pi$
$72$	2.56830	0.302677
$73$	3.58423	0.419502	0.209751	−	0.977755i	$-0.432735\pi$
$73$	3.58423	0.419502	0.209751	+	0.977755i	$0.432735\pi$
$74$	4.27757	0.497257
$75$	−4.93059	−0.569336
$76$	−2.07554	−0.238081
$77$	2.11462	0.240984
$78$	11.3952	1.29025
$79$	−6.24082	−0.702147	−0.351073	−	0.936348i	$-0.614183\pi$
$79$	−6.24082	−0.702147	−0.351073	+	0.936348i	$0.614183\pi$
$80$	0.118027	0.0131958
$81$	1.00000	0.111111
$82$	22.4794	2.48244
$83$	−15.5940	−1.71166	−0.855832	−	0.517254i	$-0.826954\pi$
$83$	−15.5940	−1.71166	−0.855832	+	0.517254i	$0.826954\pi$
$84$	3.13354	0.341897
$85$	−0.158265	−0.0171663
$86$	−1.89740	−0.204602
$87$	7.49718	0.803782
$88$	5.43098	0.578945
$89$	10.2988	1.09167	0.545837	−	0.837891i	$-0.316212\pi$
$89$	10.2988	1.09167	0.545837	+	0.837891i	$0.316212\pi$
$90$	−0.596909	−0.0629197
$91$	5.02935	0.527219
$92$	−2.70278	−0.281784
$93$	−6.27258	−0.650436
$94$	−14.3394	−1.47899
$95$	0.174500	0.0179033
$96$	−6.15165	−0.627851
$97$	10.8058	1.09716	0.548580	−	0.836098i	$-0.315169\pi$
$97$	10.8058	1.09716	0.548580	+	0.836098i	$0.315169\pi$
$98$	2.26573	0.228873
$99$	2.11462	0.212528
$100$	−15.4502	−1.54502
$101$	−11.1783	−1.11229	−0.556143	−	0.831086i	$-0.687719\pi$
$101$	−11.1783	−1.11229	−0.556143	+	0.831086i	$0.687719\pi$
$102$	1.36112	0.134771
$103$	8.91300	0.878224	0.439112	−	0.898432i	$-0.355293\pi$
$103$	8.91300	0.878224	0.439112	+	0.898432i	$0.355293\pi$
$104$	12.9169	1.26660
$105$	−0.263451	−0.0257102
$106$	5.05210	0.490704
$107$	1.40233	0.135568	0.0677840	−	0.997700i	$-0.478407\pi$
$107$	1.40233	0.135568	0.0677840	+	0.997700i	$0.478407\pi$
$108$	3.13354	0.301525
$109$	−7.84506	−0.751421	−0.375710	−	0.926737i	$-0.622601\pi$
$109$	−7.84506	−0.751421	−0.375710	+	0.926737i	$0.622601\pi$
$110$	−1.26224	−0.120350
$111$	1.88794	0.179195
$112$	−0.448003	−0.0423323
$113$	−5.51409	−0.518722	−0.259361	−	0.965780i	$-0.583512\pi$
$113$	−5.51409	−0.518722	−0.259361	+	0.965780i	$0.583512\pi$
$114$	−1.50074	−0.140557
$115$	0.227234	0.0211897
$116$	23.4927	2.18124
$117$	5.02935	0.464964
$118$	−20.2161	−1.86104
$119$	0.600740	0.0550697
$120$	−0.676621	−0.0617667
$121$	−6.52837	−0.593488
$122$	28.7104	2.59932
$123$	9.92148	0.894590
$124$	−19.6554	−1.76511
$125$	2.61622	0.234002
$126$	2.26573	0.201847
$127$	1.00000	0.0887357
$127$	1.00000	0.0887357
$128$	−17.2464	−1.52438
$129$	−0.837435	−0.0737321
$130$	−3.00206	−0.263298
$131$	4.56918	0.399211	0.199606	−	0.979876i	$-0.436034\pi$
$131$	4.56918	0.399211	0.199606	+	0.979876i	$0.436034\pi$
$132$	6.62626	0.576742
$133$	−0.662362	−0.0574341
$134$	−15.0367	−1.29898
$135$	−0.263451	−0.0226742
$136$	1.54288	0.132301
$137$	−11.8489	−1.01232	−0.506158	−	0.862441i	$-0.668935\pi$
$137$	−11.8489	−1.01232	−0.506158	+	0.862441i	$0.668935\pi$
$138$	−1.95426	−0.166358
$139$	15.4594	1.31125	0.655623	−	0.755088i	$-0.272406\pi$
$139$	15.4594	1.31125	0.655623	+	0.755088i	$0.272406\pi$
$140$	−0.825534	−0.0697703
$141$	−6.32880	−0.532981
$142$	6.89144	0.578317
$143$	10.6352	0.889358
$144$	−0.448003	−0.0373336
$145$	−1.97514	−0.164026
$146$	8.12090	0.672090
$147$	1.00000	0.0824786
$148$	5.91594	0.486287
$149$	−19.2171	−1.57433	−0.787163	−	0.616745i	$-0.788451\pi$
$149$	−19.2171	−1.57433	−0.787163	+	0.616745i	$0.788451\pi$
$150$	−11.1714	−0.912141
$151$	−19.4578	−1.58345	−0.791725	−	0.610878i	$-0.790817\pi$
$151$	−19.4578	−1.58345	−0.791725	+	0.610878i	$0.790817\pi$
$152$	−1.70115	−0.137981
$153$	0.600740	0.0485669
$154$	4.79117	0.386083
$155$	1.65252	0.132733
$156$	15.7597	1.26178
$157$	20.3132	1.62117	0.810583	−	0.585623i	$-0.199150\pi$
$157$	20.3132	1.62117	0.810583	+	0.585623i	$0.199150\pi$
$158$	−14.1400	−1.12492
$159$	2.22979	0.176834
$160$	1.62066	0.128124
$161$	−0.862531	−0.0679770
$162$	2.26573	0.178013
$163$	18.2949	1.43297	0.716483	−	0.697605i	$-0.245751\pi$
$163$	18.2949	1.43297	0.716483	+	0.697605i	$0.245751\pi$
$164$	31.0894	2.42767
$165$	−0.557099	−0.0433701
$166$	−35.3318	−2.74228
$167$	0.426687	0.0330181	0.0165090	−	0.999864i	$-0.494745\pi$
$167$	0.426687	0.0330181	0.0165090	+	0.999864i	$0.494745\pi$
$168$	2.56830	0.198149
$169$	12.2944	0.945720
$170$	−0.358587	−0.0275024
$171$	−0.662362	−0.0506521
$172$	−2.62414	−0.200089
$173$	−18.0358	−1.37124	−0.685620	−	0.727960i	$-0.740469\pi$
$173$	−18.0358	−1.37124	−0.685620	+	0.727960i	$0.740469\pi$
$174$	16.9866	1.28775
$175$	−4.93059	−0.372718
$176$	−0.947357	−0.0714097
$177$	−8.92253	−0.670659
$178$	23.3344	1.74899
$179$	−3.90602	−0.291950	−0.145975	−	0.989288i	$-0.546632\pi$
$179$	−3.90602	−0.291950	−0.145975	+	0.989288i	$0.546632\pi$
$180$	−0.825534	−0.0615317
$181$	−19.6214	−1.45845	−0.729223	−	0.684276i	$-0.760118\pi$
$181$	−19.6214	−1.45845	−0.729223	+	0.684276i	$0.760118\pi$
$182$	11.3952	0.844665
$183$	12.6716	0.936711
$184$	−2.21524	−0.163310
$185$	−0.497380	−0.0365681
$186$	−14.2120	−1.04207
$187$	1.27034	0.0928963
$188$	−19.8316	−1.44636
$189$	1.00000	0.0727393
$190$	0.395370	0.0286832
$191$	−18.2968	−1.32391	−0.661957	−	0.749542i	$-0.730274\pi$
$191$	−18.2968	−1.32391	−0.661957	+	0.749542i	$0.730274\pi$
$192$	−13.0420	−0.941225
$193$	−8.29105	−0.596803	−0.298401	−	0.954440i	$-0.596453\pi$
$193$	−8.29105	−0.596803	−0.298401	+	0.954440i	$0.596453\pi$
$194$	24.4830	1.75778
$195$	−1.32499	−0.0948842
$196$	3.13354	0.223824
$197$	−22.0383	−1.57016	−0.785082	−	0.619391i	$-0.787379\pi$
$197$	−22.0383	−1.57016	−0.785082	+	0.619391i	$0.787379\pi$
$198$	4.79117	0.340493
$199$	−7.76159	−0.550204	−0.275102	−	0.961415i	$-0.588712\pi$
$199$	−7.76159	−0.550204	−0.275102	+	0.961415i	$0.588712\pi$
$200$	−12.6632	−0.895427
$201$	−6.63659	−0.468109
$202$	−25.3271	−1.78201
$203$	7.49718	0.526199
$204$	1.88244	0.131797
$205$	−2.61382	−0.182557
$206$	20.1945	1.40702
$207$	−0.862531	−0.0599500
$208$	−2.25316	−0.156229
$209$	−1.40065	−0.0968847
$210$	−0.596909	−0.0411906
$211$	−6.35929	−0.437792	−0.218896	−	0.975748i	$-0.570246\pi$
$211$	−6.35929	−0.437792	−0.218896	+	0.975748i	$0.570246\pi$
$212$	6.98714	0.479878
$213$	3.04160	0.208407
$214$	3.17729	0.217195
$215$	0.220623	0.0150464
$216$	2.56830	0.174751
$217$	−6.27258	−0.425811
$218$	−17.7748	−1.20386
$219$	3.58423	0.242200
$220$	−1.74569	−0.117695
$221$	3.02133	0.203237
$222$	4.27757	0.287092
$223$	−10.9206	−0.731298	−0.365649	−	0.930753i	$-0.619153\pi$
$223$	−10.9206	−0.731298	−0.365649	+	0.930753i	$0.619153\pi$
$224$	−6.15165	−0.411025
$225$	−4.93059	−0.328706
$226$	−12.4934	−0.831051
$227$	1.39196	0.0923874	0.0461937	−	0.998933i	$-0.485291\pi$
$227$	1.39196	0.0923874	0.0461937	+	0.998933i	$0.485291\pi$
$228$	−2.07554	−0.137456
$229$	5.71394	0.377588	0.188794	−	0.982017i	$-0.439542\pi$
$229$	5.71394	0.377588	0.188794	+	0.982017i	$0.439542\pi$
$230$	0.514852	0.0339484
$231$	2.11462	0.139132
$232$	19.2550	1.26415
$233$	14.1302	0.925697	0.462849	−	0.886437i	$-0.346827\pi$
$233$	14.1302	0.925697	0.462849	+	0.886437i	$0.346827\pi$
$234$	11.3952	0.744925
$235$	1.66733	0.108764
$236$	−27.9591	−1.81998
$237$	−6.24082	−0.405385
$238$	1.36112	0.0882280
$239$	−23.6713	−1.53117	−0.765585	−	0.643335i	$-0.777550\pi$
$239$	−23.6713	−1.53117	−0.765585	+	0.643335i	$0.777550\pi$
$240$	0.118027	0.00761859
$241$	18.5876	1.19734	0.598668	−	0.800997i	$-0.295697\pi$
$241$	18.5876	1.19734	0.598668	+	0.800997i	$0.295697\pi$
$242$	−14.7915	−0.950836
$243$	1.00000	0.0641500
$244$	39.7069	2.54198
$245$	−0.263451	−0.0168313
$246$	22.4794	1.43324
$247$	−3.33125	−0.211963
$248$	−16.1099	−1.02298
$249$	−15.5940	−0.988229
$250$	5.92766	0.374898
$251$	−23.4333	−1.47910	−0.739548	−	0.673104i	$-0.764961\pi$
$251$	−23.4333	−1.47910	−0.739548	+	0.673104i	$0.764961\pi$
$252$	3.13354	0.197395
$253$	−1.82393	−0.114669
$254$	2.26573	0.142165
$255$	−0.158265	−0.00991096
$256$	−12.9916	−0.811976
$257$	−7.24896	−0.452178	−0.226089	−	0.974107i	$-0.572594\pi$
$257$	−7.24896	−0.452178	−0.226089	+	0.974107i	$0.572594\pi$
$258$	−1.89740	−0.118127
$259$	1.88794	0.117311
$260$	−4.15190	−0.257490
$261$	7.49718	0.464064
$262$	10.3525	0.639582
$263$	−3.53120	−0.217743	−0.108871	−	0.994056i	$-0.534724\pi$
$263$	−3.53120	−0.217743	−0.108871	+	0.994056i	$0.534724\pi$
$264$	5.43098	0.334254
$265$	−0.587440	−0.0360861
$266$	−1.50074	−0.0920160
$267$	10.2988	0.630279
$268$	−20.7960	−1.27032
$269$	−17.7944	−1.08494	−0.542472	−	0.840074i	$-0.682512\pi$
$269$	−17.7944	−1.08494	−0.542472	+	0.840074i	$0.682512\pi$
$270$	−0.596909	−0.0363267
$271$	12.7007	0.771511	0.385756	−	0.922601i	$-0.373941\pi$
$271$	12.7007	0.771511	0.385756	+	0.922601i	$0.373941\pi$
$272$	−0.269133	−0.0163186
$273$	5.02935	0.304390
$274$	−26.8463	−1.62185
$275$	−10.4263	−0.628732
$276$	−2.70278	−0.162688
$277$	−5.23820	−0.314733	−0.157366	−	0.987540i	$-0.550300\pi$
$277$	−5.23820	−0.314733	−0.157366	+	0.987540i	$0.550300\pi$
$278$	35.0268	2.10077
$279$	−6.27258	−0.375530
$280$	−0.676621	−0.0404358
$281$	17.9732	1.07219	0.536096	−	0.844157i	$-0.319899\pi$
$281$	17.9732	1.07219	0.536096	+	0.844157i	$0.319899\pi$
$282$	−14.3394	−0.853897
$283$	−14.1901	−0.843514	−0.421757	−	0.906709i	$-0.638586\pi$
$283$	−14.1901	−0.843514	−0.421757	+	0.906709i	$0.638586\pi$
$284$	9.53097	0.565559
$285$	0.174500	0.0103365
$286$	24.0965	1.42485
$287$	9.92148	0.585647
$288$	−6.15165	−0.362490
$289$	−16.6391	−0.978771
$290$	−4.47513	−0.262789
$291$	10.8058	0.633446
$292$	11.2313	0.657263
$293$	20.3093	1.18648	0.593241	−	0.805025i	$-0.297848\pi$
$293$	20.3093	1.18648	0.593241	+	0.805025i	$0.297848\pi$
$294$	2.26573	0.132140
$295$	2.35065	0.136860
$296$	4.84880	0.281831
$297$	2.11462	0.122703
$298$	−43.5408	−2.52225
$299$	−4.33797	−0.250871
$300$	−15.4502	−0.892019
$301$	−0.837435	−0.0482690
$302$	−44.0861	−2.53687
$303$	−11.1783	−0.642179
$304$	0.296740	0.0170192
$305$	−3.33834	−0.191153
$306$	1.36112	0.0778098
$307$	−17.4945	−0.998463	−0.499231	−	0.866469i	$-0.666384\pi$
$307$	−17.4945	−0.998463	−0.499231	+	0.866469i	$0.666384\pi$
$308$	6.62626	0.377566
$309$	8.91300	0.507043
$310$	3.74416	0.212654
$311$	9.84459	0.558235	0.279118	−	0.960257i	$-0.409958\pi$
$311$	9.84459	0.558235	0.279118	+	0.960257i	$0.409958\pi$
$312$	12.9169	0.731274
$313$	22.4434	1.26857	0.634287	−	0.773097i	$-0.281294\pi$
$313$	22.4434	1.26857	0.634287	+	0.773097i	$0.281294\pi$
$314$	46.0242	2.59729
$315$	−0.263451	−0.0148438
$316$	−19.5559	−1.10010
$317$	14.8472	0.833905	0.416952	−	0.908928i	$-0.363098\pi$
$317$	14.8472	0.833905	0.416952	+	0.908928i	$0.363098\pi$
$318$	5.05210	0.283308
$319$	15.8537	0.887637
$320$	3.43592	0.192074
$321$	1.40233	0.0782702
$322$	−1.95426	−0.108907
$323$	−0.397908	−0.0221402
$324$	3.13354	0.174086
$325$	−24.7977	−1.37553
$326$	41.4513	2.29577
$327$	−7.84506	−0.433833
$328$	25.4813	1.40697
$329$	−6.32880	−0.348918
$330$	−1.26224	−0.0694839
$331$	27.0357	1.48601	0.743007	−	0.669284i	$-0.233399\pi$
$331$	27.0357	1.48601	0.743007	+	0.669284i	$0.233399\pi$
$332$	−48.8644	−2.68178
$333$	1.88794	0.103459
$334$	0.966759	0.0528987
$335$	1.74841	0.0955261
$336$	−0.448003	−0.0244406
$337$	12.7721	0.695742	0.347871	−	0.937542i	$-0.386905\pi$
$337$	12.7721	0.695742	0.347871	+	0.937542i	$0.386905\pi$
$338$	27.8557	1.51515
$339$	−5.51409	−0.299484
$340$	−0.495931	−0.0268956
$341$	−13.2641	−0.718294
$342$	−1.50074	−0.0811505
$343$	1.00000	0.0539949
$344$	−2.15079	−0.115963
$345$	0.227234	0.0122339
$346$	−40.8644	−2.19688
$347$	−1.00797	−0.0541108	−0.0270554	−	0.999634i	$-0.508613\pi$
$347$	−1.00797	−0.0541108	−0.0270554	+	0.999634i	$0.508613\pi$
$348$	23.4927	1.25934
$349$	21.1658	1.13298	0.566490	−	0.824068i	$-0.308301\pi$
$349$	21.1658	1.13298	0.566490	+	0.824068i	$0.308301\pi$
$350$	−11.1714	−0.597137
$351$	5.02935	0.268447
$352$	−13.0084	−0.693351
$353$	25.1557	1.33890	0.669450	−	0.742857i	$-0.266530\pi$
$353$	25.1557	1.33890	0.669450	+	0.742857i	$0.266530\pi$
$354$	−20.2161	−1.07447
$355$	−0.801311	−0.0425292
$356$	32.2718	1.71040
$357$	0.600740	0.0317945
$358$	−8.84999	−0.467737
$359$	24.8593	1.31202	0.656012	−	0.754750i	$-0.272242\pi$
$359$	24.8593	1.31202	0.656012	+	0.754750i	$0.272242\pi$
$360$	−0.676621	−0.0356610
$361$	−18.5613	−0.976909
$362$	−44.4568	−2.33660
$363$	−6.52837	−0.342651
$364$	15.7597	0.826031
$365$	−0.944267	−0.0494252
$366$	28.7104	1.50072
$367$	17.4263	0.909648	0.454824	−	0.890581i	$-0.349702\pi$
$367$	17.4263	0.909648	0.454824	+	0.890581i	$0.349702\pi$
$368$	0.386416	0.0201433
$369$	9.92148	0.516492
$370$	−1.12693	−0.0585862
$371$	2.22979	0.115765
$372$	−19.6554	−1.01908
$373$	−3.72752	−0.193004	−0.0965018	−	0.995333i	$-0.530765\pi$
$373$	−3.72752	−0.193004	−0.0965018	+	0.995333i	$0.530765\pi$
$374$	2.87825	0.148831
$375$	2.61622	0.135101
$376$	−16.2543	−0.838249
$377$	37.7059	1.94195
$378$	2.26573	0.116537
$379$	−24.7896	−1.27336	−0.636678	−	0.771130i	$-0.719692\pi$
$379$	−24.7896	−1.27336	−0.636678	+	0.771130i	$0.719692\pi$
$380$	0.546803	0.0280504
$381$	1.00000	0.0512316
$382$	−41.4558	−2.12106
$383$	−12.0043	−0.613393	−0.306696	−	0.951807i	$-0.599224\pi$
$383$	−12.0043	−0.613393	−0.306696	+	0.951807i	$0.599224\pi$
$384$	−17.2464	−0.880099
$385$	−0.557099	−0.0283924
$386$	−18.7853	−0.956146
$387$	−0.837435	−0.0425692
$388$	33.8603	1.71900
$389$	−3.92849	−0.199182	−0.0995911	−	0.995028i	$-0.531753\pi$
$389$	−3.92849	−0.199182	−0.0995911	+	0.995028i	$0.531753\pi$
$390$	−3.00206	−0.152015
$391$	−0.518157	−0.0262043
$392$	2.56830	0.129719
$393$	4.56918	0.230485
$394$	−49.9329	−2.51558
$395$	1.64415	0.0827261
$396$	6.62626	0.332982
$397$	−8.49822	−0.426514	−0.213257	−	0.976996i	$-0.568407\pi$
$397$	−8.49822	−0.426514	−0.213257	+	0.976996i	$0.568407\pi$
$398$	−17.5857	−0.881490
$399$	−0.662362	−0.0331596
$400$	2.20892	0.110446
$401$	−22.7863	−1.13790	−0.568948	−	0.822374i	$-0.692649\pi$
$401$	−22.7863	−1.13790	−0.568948	+	0.822374i	$0.692649\pi$
$402$	−15.0367	−0.749964
$403$	−31.5470	−1.57147
$404$	−35.0278	−1.74270
$405$	−0.263451	−0.0130910
$406$	16.9866	0.843031
$407$	3.99228	0.197890
$408$	1.54288	0.0763840
$409$	−0.459834	−0.0227373	−0.0113687	−	0.999935i	$-0.503619\pi$
$409$	−0.459834	−0.0227373	−0.0113687	+	0.999935i	$0.503619\pi$
$410$	−5.92222	−0.292478
$411$	−11.8489	−0.584461
$412$	27.9293	1.37598
$413$	−8.92253	−0.439049
$414$	−1.95426	−0.0960468
$415$	4.10825	0.201666
$416$	−30.9388	−1.51690
$417$	15.4594	0.757048
$418$	−3.17349	−0.155220
$419$	−7.58777	−0.370687	−0.185343	−	0.982674i	$-0.559340\pi$
$419$	−7.58777	−0.370687	−0.185343	+	0.982674i	$0.559340\pi$
$420$	−0.825534	−0.0402819
$421$	−7.86449	−0.383292	−0.191646	−	0.981464i	$-0.561383\pi$
$421$	−7.86449	−0.383292	−0.191646	+	0.981464i	$0.561383\pi$
$422$	−14.4085	−0.701393
$423$	−6.32880	−0.307717
$424$	5.72677	0.278116
$425$	−2.96200	−0.143678
$426$	6.89144	0.333891
$427$	12.6716	0.613221
$428$	4.39425	0.212404
$429$	10.6352	0.513471
$430$	0.499873	0.0241060
$431$	28.4816	1.37191	0.685954	−	0.727645i	$-0.259385\pi$
$431$	28.4816	1.37191	0.685954	+	0.727645i	$0.259385\pi$
$432$	−0.448003	−0.0215545
$433$	3.03914	0.146052	0.0730260	−	0.997330i	$-0.476734\pi$
$433$	3.03914	0.146052	0.0730260	+	0.997330i	$0.476734\pi$
$434$	−14.2120	−0.682197
$435$	−1.97514	−0.0947006
$436$	−24.5828	−1.17730
$437$	0.571308	0.0273294
$438$	8.12090	0.388031
$439$	34.0162	1.62350	0.811752	−	0.584002i	$-0.198514\pi$
$439$	34.0162	1.62350	0.811752	+	0.584002i	$0.198514\pi$
$440$	−1.43080	−0.0682106
$441$	1.00000	0.0476190
$442$	6.84553	0.325609
$443$	−20.9252	−0.994186	−0.497093	−	0.867697i	$-0.665599\pi$
$443$	−20.9252	−0.994186	−0.497093	+	0.867697i	$0.665599\pi$
$444$	5.91594	0.280758
$445$	−2.71324	−0.128620
$446$	−24.7432	−1.17162
$447$	−19.2171	−0.908938
$448$	−13.0420	−0.616176
$449$	2.80824	0.132529	0.0662646	−	0.997802i	$-0.478892\pi$
$449$	2.80824	0.132529	0.0662646	+	0.997802i	$0.478892\pi$
$450$	−11.1714	−0.526625
$451$	20.9802	0.987919
$452$	−17.2786	−0.812718
$453$	−19.4578	−0.914205
$454$	3.15380	0.148015
$455$	−1.32499	−0.0621163
$456$	−1.70115	−0.0796634
$457$	−7.78721	−0.364271	−0.182135	−	0.983273i	$-0.558301\pi$
$457$	−7.78721	−0.364271	−0.182135	+	0.983273i	$0.558301\pi$
$458$	12.9463	0.604939
$459$	0.600740	0.0280401
$460$	0.712048	0.0331994
$461$	−2.68061	−0.124849	−0.0624243	−	0.998050i	$-0.519883\pi$
$461$	−2.68061	−0.124849	−0.0624243	+	0.998050i	$0.519883\pi$
$462$	4.79117	0.222905
$463$	4.95916	0.230472	0.115236	−	0.993338i	$-0.463238\pi$
$463$	4.95916	0.230472	0.115236	+	0.993338i	$0.463238\pi$
$464$	−3.35876	−0.155926
$465$	1.65252	0.0766336
$466$	32.0151	1.48307
$467$	−39.4769	−1.82677	−0.913386	−	0.407095i	$-0.866542\pi$
$467$	−39.4769	−1.82677	−0.913386	+	0.407095i	$0.866542\pi$
$468$	15.7597	0.728491
$469$	−6.63659	−0.306449
$470$	3.77772	0.174253
$471$	20.3132	0.935981
$472$	−22.9157	−1.05478
$473$	−1.77086	−0.0814242
$474$	−14.1400	−0.649473
$475$	3.26584	0.149847
$476$	1.88244	0.0862816
$477$	2.22979	0.102095
$478$	−53.6328	−2.45311
$479$	31.0109	1.41692	0.708462	−	0.705749i	$-0.249390\pi$
$479$	31.0109	1.41692	0.708462	+	0.705749i	$0.249390\pi$
$480$	1.62066	0.0739726
$481$	9.49512	0.432940
$482$	42.1146	1.91827
$483$	−0.862531	−0.0392465
$484$	−20.4569	−0.929860
$485$	−2.84679	−0.129266
$486$	2.26573	0.102776
$487$	39.6366	1.79611	0.898053	−	0.439887i	$-0.144981\pi$
$487$	39.6366	1.79611	0.898053	+	0.439887i	$0.144981\pi$
$488$	32.5444	1.47322
$489$	18.2949	0.827323
$490$	−0.596909	−0.0269656
$491$	16.5621	0.747438	0.373719	−	0.927542i	$-0.378082\pi$
$491$	16.5621	0.747438	0.373719	+	0.927542i	$0.378082\pi$
$492$	31.0894	1.40162
$493$	4.50385	0.202843
$494$	−7.54773	−0.339588
$495$	−0.557099	−0.0250397
$496$	2.81013	0.126179
$497$	3.04160	0.136434
$498$	−35.3318	−1.58326
$499$	39.7879	1.78115	0.890576	−	0.454834i	$-0.150301\pi$
$499$	39.7879	1.78115	0.890576	+	0.454834i	$0.150301\pi$
$500$	8.19804	0.366628
$501$	0.426687	0.0190630
$502$	−53.0935	−2.36968
$503$	18.0707	0.805734	0.402867	−	0.915259i	$-0.368014\pi$
$503$	18.0707	0.805734	0.402867	+	0.915259i	$0.368014\pi$
$504$	2.56830	0.114401
$505$	2.94494	0.131048
$506$	−4.13253	−0.183713
$507$	12.2944	0.546012
$508$	3.13354	0.139028
$509$	23.0487	1.02162	0.510808	−	0.859695i	$-0.329346\pi$
$509$	23.0487	1.02162	0.510808	+	0.859695i	$0.329346\pi$
$510$	−0.358587	−0.0158785
$511$	3.58423	0.158557
$512$	5.05717	0.223497
$513$	−0.662362	−0.0292440
$514$	−16.4242	−0.724441
$515$	−2.34814	−0.103471
$516$	−2.62414	−0.115521
$517$	−13.3830	−0.588585
$518$	4.27757	0.187946
$519$	−18.0358	−0.791685
$520$	−3.40296	−0.149230
$521$	23.3186	1.02161	0.510803	−	0.859698i	$-0.329348\pi$
$521$	23.3186	1.02161	0.510803	+	0.859698i	$0.329348\pi$
$522$	16.9866	0.743483
$523$	5.13133	0.224377	0.112189	−	0.993687i	$-0.464214\pi$
$523$	5.13133	0.224377	0.112189	+	0.993687i	$0.464214\pi$
$524$	14.3177	0.625473
$525$	−4.93059	−0.215189
$526$	−8.00074	−0.348849
$527$	−3.76819	−0.164145
$528$	−0.947357	−0.0412284
$529$	−22.2560	−0.967654
$530$	−1.33098	−0.0578141
$531$	−8.92253	−0.387205
$532$	−2.07554	−0.0899861
$533$	49.8986	2.16135
$534$	23.3344	1.00978
$535$	−0.369444	−0.0159725
$536$	−17.0447	−0.736221
$537$	−3.90602	−0.168557
$538$	−40.3173	−1.73820
$539$	2.11462	0.0910832
$540$	−0.825534	−0.0355253
$541$	31.1702	1.34011	0.670055	−	0.742312i	$-0.266271\pi$
$541$	31.1702	1.34011	0.670055	+	0.742312i	$0.266271\pi$
$542$	28.7763	1.23605
$543$	−19.6214	−0.842034
$544$	−3.69554	−0.158445
$545$	2.06679	0.0885315
$546$	11.3952	0.487668
$547$	−7.59702	−0.324825	−0.162413	−	0.986723i	$-0.551928\pi$
$547$	−7.59702	−0.324825	−0.162413	+	0.986723i	$0.551928\pi$
$548$	−37.1289	−1.58607
$549$	12.6716	0.540810
$550$	−23.6233	−1.00730
$551$	−4.96585	−0.211552
$552$	−2.21524	−0.0942868
$553$	−6.24082	−0.265387
$554$	−11.8684	−0.504238
$555$	−0.497380	−0.0211126
$556$	48.4425	2.05442
$557$	−11.1855	−0.473947	−0.236973	−	0.971516i	$-0.576155\pi$
$557$	−11.1855	−0.473947	−0.236973	+	0.971516i	$0.576155\pi$
$558$	−14.2120	−0.601641
$559$	−4.21176	−0.178138
$560$	0.118027	0.00498754
$561$	1.27034	0.0536337
$562$	40.7225	1.71777
$563$	−28.2073	−1.18879	−0.594397	−	0.804172i	$-0.702609\pi$
$563$	−28.2073	−1.18879	−0.594397	+	0.804172i	$0.702609\pi$
$564$	−19.8316	−0.835059
$565$	1.45269	0.0611152
$566$	−32.1510	−1.35141
$567$	1.00000	0.0419961
$568$	7.81173	0.327773
$569$	24.8095	1.04007	0.520035	−	0.854145i	$-0.325919\pi$
$569$	24.8095	1.04007	0.520035	+	0.854145i	$0.325919\pi$
$570$	0.395370	0.0165602
$571$	−21.0354	−0.880304	−0.440152	−	0.897923i	$-0.645076\pi$
$571$	−21.0354	−0.880304	−0.440152	+	0.897923i	$0.645076\pi$
$572$	33.3258	1.39342
$573$	−18.2968	−0.764362
$574$	22.4794	0.938273
$575$	4.25279	0.177354
$576$	−13.0420	−0.543416
$577$	−13.9122	−0.579171	−0.289585	−	0.957152i	$-0.593517\pi$
$577$	−13.9122	−0.579171	−0.289585	+	0.957152i	$0.593517\pi$
$578$	−37.6998	−1.56810
$579$	−8.29105	−0.344564
$580$	−6.18917	−0.256991
$581$	−15.5940	−0.646948
$582$	24.4830	1.01485
$583$	4.71516	0.195282
$584$	9.20537	0.380921
$585$	−1.32499	−0.0547814
$586$	46.0154	1.90088
$587$	27.0344	1.11583	0.557914	−	0.829899i	$-0.311602\pi$
$587$	27.0344	1.11583	0.557914	+	0.829899i	$0.311602\pi$
$588$	3.13354	0.129225
$589$	4.15472	0.171192
$590$	5.32594	0.219265
$591$	−22.0383	−0.906535
$592$	−0.845803	−0.0347623
$593$	−29.7989	−1.22369	−0.611847	−	0.790976i	$-0.709573\pi$
$593$	−29.7989	−1.22369	−0.611847	+	0.790976i	$0.709573\pi$
$594$	4.79117	0.196584
$595$	−0.158265	−0.00648825
$596$	−60.2176	−2.46661
$597$	−7.76159	−0.317661
$598$	−9.82868	−0.401924
$599$	29.2831	1.19648	0.598238	−	0.801319i	$-0.295868\pi$
$599$	29.2831	1.19648	0.598238	+	0.801319i	$0.295868\pi$
$600$	−12.6632	−0.516975
$601$	−6.01295	−0.245274	−0.122637	−	0.992452i	$-0.539135\pi$
$601$	−6.01295	−0.245274	−0.122637	+	0.992452i	$0.539135\pi$
$602$	−1.89740	−0.0773324
$603$	−6.63659	−0.270263
$604$	−60.9717	−2.48090
$605$	1.71990	0.0699241
$606$	−25.3271	−1.02884
$607$	8.18284	0.332131	0.166066	−	0.986115i	$-0.446894\pi$
$607$	8.18284	0.332131	0.166066	+	0.986115i	$0.446894\pi$
$608$	4.07462	0.165248
$609$	7.49718	0.303801
$610$	−7.56378	−0.306249
$611$	−31.8298	−1.28769
$612$	1.88244	0.0760932
$613$	−33.3302	−1.34619	−0.673097	−	0.739555i	$-0.735036\pi$
$613$	−33.3302	−1.34619	−0.673097	+	0.739555i	$0.735036\pi$
$614$	−39.6378	−1.59965
$615$	−2.61382	−0.105399
$616$	5.43098	0.218821
$617$	−15.3915	−0.619638	−0.309819	−	0.950796i	$-0.600268\pi$
$617$	−15.3915	−0.619638	−0.309819	+	0.950796i	$0.600268\pi$
$618$	20.1945	0.812341
$619$	16.0862	0.646558	0.323279	−	0.946304i	$-0.395215\pi$
$619$	16.0862	0.646558	0.323279	+	0.946304i	$0.395215\pi$
$620$	5.17823	0.207963
$621$	−0.862531	−0.0346122
$622$	22.3052	0.894357
$623$	10.2988	0.412614
$624$	−2.25316	−0.0901987
$625$	23.9637	0.958549
$626$	50.8507	2.03240
$627$	−1.40065	−0.0559364
$628$	63.6521	2.54000
$629$	1.13416	0.0452220
$630$	−0.596909	−0.0237814
$631$	2.67650	0.106550	0.0532749	−	0.998580i	$-0.483034\pi$
$631$	2.67650	0.106550	0.0532749	+	0.998580i	$0.483034\pi$
$632$	−16.0283	−0.637571
$633$	−6.35929	−0.252759
$634$	33.6399	1.33601
$635$	−0.263451	−0.0104547
$636$	6.98714	0.277058
$637$	5.02935	0.199270
$638$	35.9202	1.42210
$639$	3.04160	0.120324
$640$	4.54357	0.179600
$641$	−47.2540	−1.86642	−0.933210	−	0.359333i	$-0.883004\pi$
$641$	−47.2540	−1.86642	−0.933210	+	0.359333i	$0.883004\pi$
$642$	3.17729	0.125398
$643$	14.0330	0.553409	0.276704	−	0.960955i	$-0.410758\pi$
$643$	14.0330	0.553409	0.276704	+	0.960955i	$0.410758\pi$
$644$	−2.70278	−0.106504
$645$	0.220623	0.00868702
$646$	−0.901552	−0.0354711
$647$	−18.8486	−0.741017	−0.370508	−	0.928829i	$-0.620817\pi$
$647$	−18.8486	−0.741017	−0.370508	+	0.928829i	$0.620817\pi$
$648$	2.56830	0.100892
$649$	−18.8678	−0.740625
$650$	−56.1849	−2.20375
$651$	−6.27258	−0.245842
$652$	57.3277	2.24513
$653$	42.9357	1.68020	0.840101	−	0.542429i	$-0.182495\pi$
$653$	42.9357	1.68020	0.840101	+	0.542429i	$0.182495\pi$
$654$	−17.7748	−0.695050
$655$	−1.20376	−0.0470346
$656$	−4.44485	−0.173542
$657$	3.58423	0.139834
$658$	−14.3394	−0.559007
$659$	−6.16411	−0.240120	−0.120060	−	0.992767i	$-0.538309\pi$
$659$	−6.16411	−0.240120	−0.120060	+	0.992767i	$0.538309\pi$
$660$	−1.74569	−0.0679510
$661$	17.9305	0.697416	0.348708	−	0.937231i	$-0.386620\pi$
$661$	17.9305	0.697416	0.348708	+	0.937231i	$0.386620\pi$
$662$	61.2555	2.38076
$663$	3.02133	0.117339
$664$	−40.0501	−1.55424
$665$	0.174500	0.00676682
$666$	4.27757	0.165752
$667$	−6.46655	−0.250386
$668$	1.33704	0.0517317
$669$	−10.9206	−0.422215
$670$	3.96144	0.153044
$671$	26.7956	1.03443
$672$	−6.15165	−0.237305
$673$	27.6482	1.06576	0.532879	−	0.846191i	$-0.321110\pi$
$673$	27.6482	1.06576	0.532879	+	0.846191i	$0.321110\pi$
$674$	28.9382	1.11466
$675$	−4.93059	−0.189779
$676$	38.5249	1.48173
$677$	−44.0086	−1.69139	−0.845694	−	0.533668i	$-0.820813\pi$
$677$	−44.0086	−1.69139	−0.845694	+	0.533668i	$0.820813\pi$
$678$	−12.4934	−0.479808
$679$	10.8058	0.414688
$680$	−0.406473	−0.0155875
$681$	1.39196	0.0533399
$682$	−30.0530	−1.15079
$683$	12.3742	0.473484	0.236742	−	0.971573i	$-0.423920\pi$
$683$	12.3742	0.473484	0.236742	+	0.971573i	$0.423920\pi$
$684$	−2.07554	−0.0793603
$685$	3.12159	0.119270
$686$	2.26573	0.0865060
$687$	5.71394	0.218000
$688$	0.375173	0.0143034
$689$	11.2144	0.427234
$690$	0.514852	0.0196001
$691$	29.0744	1.10604	0.553021	−	0.833168i	$-0.313475\pi$
$691$	29.0744	1.10604	0.553021	+	0.833168i	$0.313475\pi$
$692$	−56.5160	−2.14842
$693$	2.11462	0.0803279
$694$	−2.28380	−0.0866918
$695$	−4.07278	−0.154489
$696$	19.2550	0.729859
$697$	5.96023	0.225760
$698$	47.9561	1.81516
$699$	14.1302	0.534452
$700$	−15.4502	−0.583963
$701$	9.79244	0.369855	0.184928	−	0.982752i	$-0.440795\pi$
$701$	9.79244	0.369855	0.184928	+	0.982752i	$0.440795\pi$
$702$	11.3952	0.430083
$703$	−1.25050	−0.0471635
$704$	−27.5789	−1.03942
$705$	1.66733	0.0627952
$706$	56.9960	2.14507
$707$	−11.1783	−0.420405
$708$	−27.9591	−1.05077
$709$	0.289511	0.0108728	0.00543641	−	0.999985i	$-0.498270\pi$
$709$	0.289511	0.0108728	0.00543641	+	0.999985i	$0.498270\pi$
$710$	−1.81556	−0.0681366
$711$	−6.24082	−0.234049
$712$	26.4505	0.991275
$713$	5.41030	0.202617
$714$	1.36112	0.0509385
$715$	−2.80185	−0.104783
$716$	−12.2397	−0.457418
$717$	−23.6713	−0.884021
$718$	56.3246	2.10201
$719$	−35.0204	−1.30604	−0.653021	−	0.757340i	$-0.726499\pi$
$719$	−35.0204	−1.30604	−0.653021	+	0.757340i	$0.726499\pi$
$720$	0.118027	0.00439860
$721$	8.91300	0.331938
$722$	−42.0549	−1.56512
$723$	18.5876	0.691282
$724$	−61.4844	−2.28505
$725$	−36.9655	−1.37287
$726$	−14.7915	−0.548966
$727$	17.1376	0.635597	0.317798	−	0.948158i	$-0.397057\pi$
$727$	17.1376	0.635597	0.317798	+	0.948158i	$0.397057\pi$
$728$	12.9169	0.478731
$729$	1.00000	0.0370370
$730$	−2.13946	−0.0791848
$731$	−0.503081	−0.0186071
$732$	39.7069	1.46761
$733$	15.9224	0.588106	0.294053	−	0.955789i	$-0.404996\pi$
$733$	15.9224	0.588106	0.294053	+	0.955789i	$0.404996\pi$
$734$	39.4834	1.45736
$735$	−0.263451	−0.00971753
$736$	5.30599	0.195581
$737$	−14.0339	−0.516944
$738$	22.4794	0.827479
$739$	−26.5239	−0.975697	−0.487848	−	0.872928i	$-0.662218\pi$
$739$	−26.5239	−0.975697	−0.487848	+	0.872928i	$0.662218\pi$
$740$	−1.55856	−0.0572938
$741$	−3.33125	−0.122377
$742$	5.05210	0.185469
$743$	−23.2387	−0.852544	−0.426272	−	0.904595i	$-0.640173\pi$
$743$	−23.2387	−0.852544	−0.426272	+	0.904595i	$0.640173\pi$
$744$	−16.1099	−0.590617
$745$	5.06276	0.185485
$746$	−8.44556	−0.309214
$747$	−15.5940	−0.570554
$748$	3.98066	0.145547
$749$	1.40233	0.0512399
$750$	5.92766	0.216448
$751$	−3.26661	−0.119200	−0.0596001	−	0.998222i	$-0.518983\pi$
$751$	−3.26661	−0.119200	−0.0596001	+	0.998222i	$0.518983\pi$
$752$	2.83532	0.103393
$753$	−23.4333	−0.853956
$754$	85.4315	3.11123
$755$	5.12616	0.186560
$756$	3.13354	0.113966
$757$	5.68679	0.206690	0.103345	−	0.994646i	$-0.467045\pi$
$757$	5.68679	0.206690	0.103345	+	0.994646i	$0.467045\pi$
$758$	−56.1666	−2.04006
$759$	−1.82393	−0.0662044
$760$	0.448168	0.0162568
$761$	−41.2816	−1.49646	−0.748229	−	0.663440i	$-0.769096\pi$
$761$	−41.2816	−1.49646	−0.748229	+	0.663440i	$0.769096\pi$
$762$	2.26573	0.0820788
$763$	−7.84506	−0.284010
$764$	−57.3339	−2.07427
$765$	−0.158265	−0.00572210
$766$	−27.1986	−0.982726
$767$	−44.8745	−1.62033
$768$	−12.9916	−0.468795
$769$	−15.3798	−0.554611	−0.277306	−	0.960782i	$-0.589441\pi$
$769$	−15.3798	−0.554611	−0.277306	+	0.960782i	$0.589441\pi$
$770$	−1.26224	−0.0454879
$771$	−7.24896	−0.261065
$772$	−25.9803	−0.935053
$773$	43.4059	1.56120	0.780602	−	0.625029i	$-0.214913\pi$
$773$	43.4059	1.56120	0.780602	+	0.625029i	$0.214913\pi$
$774$	−1.89740	−0.0682008
$775$	30.9276	1.11095
$776$	27.7525	0.996256
$777$	1.88794	0.0677295
$778$	−8.90090	−0.319113
$779$	−6.57162	−0.235453
$780$	−4.15190	−0.148662
$781$	6.43183	0.230149
$782$	−1.17400	−0.0419823
$783$	7.49718	0.267927
$784$	−0.448003	−0.0160001
$785$	−5.35152	−0.191004
$786$	10.3525	0.369263
$787$	3.18555	0.113553	0.0567763	−	0.998387i	$-0.481918\pi$
$787$	3.18555	0.113553	0.0567763	+	0.998387i	$0.481918\pi$
$788$	−69.0580	−2.46009
$789$	−3.53120	−0.125714
$790$	3.72520	0.132537
$791$	−5.51409	−0.196058
$792$	5.43098	0.192982
$793$	63.7299	2.26311
$794$	−19.2547	−0.683324
$795$	−0.587440	−0.0208343
$796$	−24.3212	−0.862044
$797$	44.1424	1.56361	0.781803	−	0.623526i	$-0.214300\pi$
$797$	44.1424	1.56361	0.781803	+	0.623526i	$0.214300\pi$
$798$	−1.50074	−0.0531255
$799$	−3.80196	−0.134504
$800$	30.3313	1.07237
$801$	10.2988	0.363892
$802$	−51.6278	−1.82304
$803$	7.57929	0.267467
$804$	−20.7960	−0.733419
$805$	0.227234	0.00800896
$806$	−71.4771	−2.51767
$807$	−17.7944	−0.626393
$808$	−28.7093	−1.00999
$809$	31.3325	1.10159	0.550797	−	0.834639i	$-0.314324\pi$
$809$	31.3325	1.10159	0.550797	+	0.834639i	$0.314324\pi$
$810$	−0.596909	−0.0209732
$811$	−6.35201	−0.223049	−0.111525	−	0.993762i	$-0.535573\pi$
$811$	−6.35201	−0.223049	−0.111525	+	0.993762i	$0.535573\pi$
$812$	23.4927	0.824433
$813$	12.7007	0.445432
$814$	9.04544	0.317043
$815$	−4.81980	−0.168830
$816$	−0.269133	−0.00942154
$817$	0.554686	0.0194060
$818$	−1.04186	−0.0364278
$819$	5.02935	0.175740
$820$	−8.19052	−0.286025
$821$	19.9589	0.696571	0.348285	−	0.937389i	$-0.386764\pi$
$821$	19.9589	0.696571	0.348285	+	0.937389i	$0.386764\pi$
$822$	−26.8463	−0.936374
$823$	−3.54944	−0.123726	−0.0618629	−	0.998085i	$-0.519704\pi$
$823$	−3.54944	−0.123726	−0.0618629	+	0.998085i	$0.519704\pi$
$824$	22.8913	0.797455
$825$	−10.4263	−0.362999
$826$	−20.2161	−0.703407
$827$	−33.1724	−1.15352	−0.576758	−	0.816915i	$-0.695683\pi$
$827$	−33.1724	−1.15352	−0.576758	+	0.816915i	$0.695683\pi$
$828$	−2.70278	−0.0939280
$829$	17.7237	0.615570	0.307785	−	0.951456i	$-0.400412\pi$
$829$	17.7237	0.615570	0.307785	+	0.951456i	$0.400412\pi$
$830$	9.30819	0.323092
$831$	−5.23820	−0.181711
$832$	−65.5928	−2.27402
$833$	0.600740	0.0208144
$834$	35.0268	1.21288
$835$	−0.112411	−0.00389015
$836$	−4.38898	−0.151796
$837$	−6.27258	−0.216812
$838$	−17.1919	−0.593883
$839$	38.2507	1.32056	0.660280	−	0.751019i	$-0.270438\pi$
$839$	38.2507	1.32056	0.660280	+	0.751019i	$0.270438\pi$
$840$	−0.676621	−0.0233456
$841$	27.2077	0.938196
$842$	−17.8188	−0.614078
$843$	17.9732	0.619030
$844$	−19.9271	−0.685919
$845$	−3.23896	−0.111424
$846$	−14.3394	−0.492997
$847$	−6.52837	−0.224318
$848$	−0.998952	−0.0343041
$849$	−14.1901	−0.487003
$850$	−6.71111	−0.230189
$851$	−1.62841	−0.0558211
$852$	9.53097	0.326526
$853$	29.5909	1.01317	0.506587	−	0.862189i	$-0.330907\pi$
$853$	29.5909	1.01317	0.506587	+	0.862189i	$0.330907\pi$
$854$	28.7104	0.982450
$855$	0.174500	0.00596777
$856$	3.60159	0.123100
$857$	−15.8769	−0.542344	−0.271172	−	0.962531i	$-0.587411\pi$
$857$	−15.8769	−0.542344	−0.271172	+	0.962531i	$0.587411\pi$
$858$	24.0965	0.822640
$859$	42.5121	1.45049	0.725247	−	0.688489i	$-0.241726\pi$
$859$	42.5121	1.45049	0.725247	+	0.688489i	$0.241726\pi$
$860$	0.691331	0.0235742
$861$	9.92148	0.338123
$862$	64.5316	2.19795
$863$	44.1539	1.50302	0.751508	−	0.659724i	$-0.229327\pi$
$863$	44.1539	1.50302	0.751508	+	0.659724i	$0.229327\pi$
$864$	−6.15165	−0.209284
$865$	4.75156	0.161558
$866$	6.88589	0.233992
$867$	−16.6391	−0.565094
$868$	−19.6554	−0.667147
$869$	−13.1970	−0.447677
$870$	−4.47513	−0.151721
$871$	−33.3777	−1.13096
$872$	−20.1485	−0.682313
$873$	10.8058	0.365720
$874$	1.29443	0.0437848
$875$	2.61622	0.0884445
$876$	11.2313	0.379471
$877$	4.55932	0.153957	0.0769786	−	0.997033i	$-0.475473\pi$
$877$	4.55932	0.153957	0.0769786	+	0.997033i	$0.475473\pi$
$878$	77.0716	2.60104
$879$	20.3093	0.685016
$880$	0.249582	0.00841340
$881$	30.1946	1.01728	0.508642	−	0.860978i	$-0.330148\pi$
$881$	30.1946	1.01728	0.508642	+	0.860978i	$0.330148\pi$
$882$	2.26573	0.0762912
$883$	50.7580	1.70814	0.854071	−	0.520156i	$-0.174126\pi$
$883$	50.7580	1.70814	0.854071	+	0.520156i	$0.174126\pi$
$884$	9.46747	0.318425
$885$	2.35065	0.0790162
$886$	−47.4109	−1.59280
$887$	−41.3459	−1.38826	−0.694129	−	0.719851i	$-0.744210\pi$
$887$	−41.3459	−1.38826	−0.694129	+	0.719851i	$0.744210\pi$
$888$	4.84880	0.162715
$889$	1.00000	0.0335389
$890$	−6.14747	−0.206064
$891$	2.11462	0.0708425
$892$	−34.2202	−1.14578
$893$	4.19196	0.140279
$894$	−43.5408	−1.45622
$895$	1.02904	0.0343971
$896$	−17.2464	−0.576160
$897$	−4.33797	−0.144841
$898$	6.36273	0.212327
$899$	−47.0267	−1.56843
$900$	−15.4502	−0.515007
$901$	1.33952	0.0446260
$902$	47.5355	1.58276
$903$	−0.837435	−0.0278681
$904$	−14.1618	−0.471015
$905$	5.16927	0.171832
$906$	−44.0861	−1.46466
$907$	6.47378	0.214958	0.107479	−	0.994207i	$-0.465722\pi$
$907$	6.47378	0.214958	0.107479	+	0.994207i	$0.465722\pi$
$908$	4.36175	0.144750
$909$	−11.1783	−0.370762
$910$	−3.00206	−0.0995175
$911$	−17.7715	−0.588797	−0.294399	−	0.955683i	$-0.595119\pi$
$911$	−17.7715	−0.588797	−0.294399	+	0.955683i	$0.595119\pi$
$912$	0.296740	0.00982605
$913$	−32.9754	−1.09133
$914$	−17.6437	−0.583603
$915$	−3.33834	−0.110362
$916$	17.9049	0.591593
$917$	4.56918	0.150888
$918$	1.36112	0.0449235
$919$	−1.18053	−0.0389421	−0.0194710	−	0.999810i	$-0.506198\pi$
$919$	−1.18053	−0.0389421	−0.0194710	+	0.999810i	$0.506198\pi$
$920$	0.583606	0.0192409
$921$	−17.4945	−0.576463
$922$	−6.07355	−0.200022
$923$	15.2973	0.503515
$924$	6.62626	0.217988
$925$	−9.30867	−0.306067
$926$	11.2361	0.369242
$927$	8.91300	0.292741
$928$	−46.1200	−1.51396
$929$	−29.3261	−0.962159	−0.481080	−	0.876677i	$-0.659755\pi$
$929$	−29.3261	−0.962159	−0.481080	+	0.876677i	$0.659755\pi$
$930$	3.74416	0.122776
$931$	−0.662362	−0.0217081
$932$	44.2774	1.45036
$933$	9.84459	0.322297
$934$	−89.4440	−2.92670
$935$	−0.334672	−0.0109449
$936$	12.9169	0.422201
$937$	24.0660	0.786202	0.393101	−	0.919495i	$-0.371402\pi$
$937$	24.0660	0.786202	0.393101	+	0.919495i	$0.371402\pi$
$938$	−15.0367	−0.490966
$939$	22.4434	0.732412
$940$	5.22464	0.170409
$941$	−33.5049	−1.09223	−0.546115	−	0.837710i	$-0.683894\pi$
$941$	−33.5049	−1.09223	−0.546115	+	0.837710i	$0.683894\pi$
$942$	46.0242	1.49955
$943$	−8.55758	−0.278673
$944$	3.99732	0.130102
$945$	−0.263451	−0.00857006
$946$	−4.01229	−0.130451
$947$	0.188355	0.00612073	0.00306036	−	0.999995i	$-0.499026\pi$
$947$	0.188355	0.00612073	0.00306036	+	0.999995i	$0.499026\pi$
$948$	−19.5559	−0.635145
$949$	18.0263	0.585159
$950$	7.39952	0.240072
$951$	14.8472	0.481455
$952$	1.54288	0.0500050
$953$	−38.4600	−1.24584	−0.622921	−	0.782285i	$-0.714054\pi$
$953$	−38.4600	−1.24584	−0.622921	+	0.782285i	$0.714054\pi$
$954$	5.05210	0.163568
$955$	4.82032	0.155982
$956$	−74.1750	−2.39899
$957$	15.8537	0.512477
$958$	70.2623	2.27007
$959$	−11.8489	−0.382620
$960$	3.43592	0.110894
$961$	8.34528	0.269203
$962$	21.5134	0.693619
$963$	1.40233	0.0451893
$964$	58.2452	1.87595
$965$	2.18428	0.0703146
$966$	−1.95426	−0.0628774
$967$	31.6878	1.01901	0.509505	−	0.860468i	$-0.329829\pi$
$967$	31.6878	1.01901	0.509505	+	0.860468i	$0.329829\pi$
$968$	−16.7668	−0.538906
$969$	−0.397908	−0.0127826
$970$	−6.45006	−0.207099
$971$	−8.21103	−0.263504	−0.131752	−	0.991283i	$-0.542060\pi$
$971$	−8.21103	−0.263504	−0.131752	+	0.991283i	$0.542060\pi$
$972$	3.13354	0.100508
$973$	15.4594	0.495604
$974$	89.8059	2.87757
$975$	−24.7977	−0.794161
$976$	−5.67691	−0.181713
$977$	37.8453	1.21078	0.605389	−	0.795929i	$-0.293017\pi$
$977$	37.8453	1.21078	0.605389	+	0.795929i	$0.293017\pi$
$978$	41.4513	1.32547
$979$	21.7782	0.696033
$980$	−0.825534	−0.0263707
$981$	−7.84506	−0.250474
$982$	37.5253	1.19748
$983$	−54.3534	−1.73360	−0.866802	−	0.498652i	$-0.833829\pi$
$983$	−54.3534	−1.73360	−0.866802	+	0.498652i	$0.833829\pi$
$984$	25.4813	0.812315
$985$	5.80601	0.184995
$986$	10.2045	0.324978
$987$	−6.32880	−0.201448
$988$	−10.4386	−0.332097
$989$	0.722314	0.0229682
$990$	−1.26224	−0.0401165
$991$	11.9772	0.380469	0.190235	−	0.981739i	$-0.439075\pi$
$991$	11.9772	0.380469	0.190235	+	0.981739i	$0.439075\pi$
$992$	38.5868	1.22513
$993$	27.0357	0.857951
$994$	6.89144	0.218583
$995$	2.04480	0.0648244
$996$	−48.8644	−1.54833
$997$	−41.7518	−1.32229	−0.661146	−	0.750258i	$-0.729929\pi$
$997$	−41.7518	−1.32229	−0.661146	+	0.750258i	$0.729929\pi$
$998$	90.1488	2.85361
$999$	1.88794	0.0597318

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2667.2.a.q.1.16	✓	19
3.2	odd	2		8001.2.a.v.1.4		19

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2667.2.a.q.1.16	✓	19	1.1	even	1	trivial
8001.2.a.v.1.4		19	3.2	odd	2

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:	\( N \)	\(=\)	\( 2667 = 3 \cdot 7 \cdot 127 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2667.a (trivial)

\(f(q)\)	\(=\)	\(q+2.26573 q^{2} +1.00000 q^{3} +3.13354 q^{4} -0.263451 q^{5} +2.26573 q^{6} +1.00000 q^{7} +2.56830 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.26573 q^{2} +1.00000 q^{3} +3.13354 q^{4} -0.263451 q^{5} +2.26573 q^{6} +1.00000 q^{7} +2.56830 q^{8} +1.00000 q^{9} -0.596909 q^{10} +2.11462 q^{11} +3.13354 q^{12} +5.02935 q^{13} +2.26573 q^{14} -0.263451 q^{15} -0.448003 q^{16} +0.600740 q^{17} +2.26573 q^{18} -0.662362 q^{19} -0.825534 q^{20} +1.00000 q^{21} +4.79117 q^{22} -0.862531 q^{23} +2.56830 q^{24} -4.93059 q^{25} +11.3952 q^{26} +1.00000 q^{27} +3.13354 q^{28} +7.49718 q^{29} -0.596909 q^{30} -6.27258 q^{31} -6.15165 q^{32} +2.11462 q^{33} +1.36112 q^{34} -0.263451 q^{35} +3.13354 q^{36} +1.88794 q^{37} -1.50074 q^{38} +5.02935 q^{39} -0.676621 q^{40} +9.92148 q^{41} +2.26573 q^{42} -0.837435 q^{43} +6.62626 q^{44} -0.263451 q^{45} -1.95426 q^{46} -6.32880 q^{47} -0.448003 q^{48} +1.00000 q^{49} -11.1714 q^{50} +0.600740 q^{51} +15.7597 q^{52} +2.22979 q^{53} +2.26573 q^{54} -0.557099 q^{55} +2.56830 q^{56} -0.662362 q^{57} +16.9866 q^{58} -8.92253 q^{59} -0.825534 q^{60} +12.6716 q^{61} -14.2120 q^{62} +1.00000 q^{63} -13.0420 q^{64} -1.32499 q^{65} +4.79117 q^{66} -6.63659 q^{67} +1.88244 q^{68} -0.862531 q^{69} -0.596909 q^{70} +3.04160 q^{71} +2.56830 q^{72} +3.58423 q^{73} +4.27757 q^{74} -4.93059 q^{75} -2.07554 q^{76} +2.11462 q^{77} +11.3952 q^{78} -6.24082 q^{79} +0.118027 q^{80} +1.00000 q^{81} +22.4794 q^{82} -15.5940 q^{83} +3.13354 q^{84} -0.158265 q^{85} -1.89740 q^{86} +7.49718 q^{87} +5.43098 q^{88} +10.2988 q^{89} -0.596909 q^{90} +5.02935 q^{91} -2.70278 q^{92} -6.27258 q^{93} -14.3394 q^{94} +0.174500 q^{95} -6.15165 q^{96} +10.8058 q^{97} +2.26573 q^{98} +2.11462 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 19 q + 4 q^{2} + 19 q^{3} + 22 q^{4} + 5 q^{5} + 4 q^{6} + 19 q^{7} + 9 q^{8} + 19 q^{9}+O(q^{10}) \) 19 * q + 4 * q^2 + 19 * q^3 + 22 * q^4 + 5 * q^5 + 4 * q^6 + 19 * q^7 + 9 * q^8 + 19 * q^9	\( 19 q + 4 q^{2} + 19 q^{3} + 22 q^{4} + 5 q^{5} + 4 q^{6} + 19 q^{7} + 9 q^{8} + 19 q^{9} - 9 q^{11} + 22 q^{12} + 24 q^{13} + 4 q^{14} + 5 q^{15} + 20 q^{16} + 17 q^{17} + 4 q^{18} + 23 q^{19} + 5 q^{20} + 19 q^{21} - 3 q^{22} - 17 q^{23} + 9 q^{24} + 38 q^{25} + 28 q^{26} + 19 q^{27} + 22 q^{28} + 2 q^{29} + 16 q^{31} + 17 q^{32} - 9 q^{33} + 29 q^{34} + 5 q^{35} + 22 q^{36} + 56 q^{37} + 2 q^{38} + 24 q^{39} - 13 q^{40} - 7 q^{41} + 4 q^{42} + 19 q^{43} - 29 q^{44} + 5 q^{45} + 10 q^{46} + 25 q^{47} + 20 q^{48} + 19 q^{49} - 9 q^{50} + 17 q^{51} + 16 q^{52} + 18 q^{53} + 4 q^{54} + 10 q^{55} + 9 q^{56} + 23 q^{57} + 31 q^{58} + 11 q^{59} + 5 q^{60} + 26 q^{61} + 26 q^{62} + 19 q^{63} + 45 q^{64} + 27 q^{65} - 3 q^{66} + 24 q^{67} + 14 q^{68} - 17 q^{69} - 32 q^{71} + 9 q^{72} + 51 q^{73} + 38 q^{75} + 12 q^{76} - 9 q^{77} + 28 q^{78} + 30 q^{79} - 30 q^{80} + 19 q^{81} - 52 q^{82} + q^{83} + 22 q^{84} + 44 q^{85} - 24 q^{86} + 2 q^{87} - 30 q^{88} + 5 q^{89} + 24 q^{91} - 88 q^{92} + 16 q^{93} + 7 q^{94} - 24 q^{95} + 17 q^{96} + 5 q^{97} + 4 q^{98} - 9 q^{99}+O(q^{100}) \) 19 * q + 4 * q^2 + 19 * q^3 + 22 * q^4 + 5 * q^5 + 4 * q^6 + 19 * q^7 + 9 * q^8 + 19 * q^9 - 9 * q^11 + 22 * q^12 + 24 * q^13 + 4 * q^14 + 5 * q^15 + 20 * q^16 + 17 * q^17 + 4 * q^18 + 23 * q^19 + 5 * q^20 + 19 * q^21 - 3 * q^22 - 17 * q^23 + 9 * q^24 + 38 * q^25 + 28 * q^26 + 19 * q^27 + 22 * q^28 + 2 * q^29 + 16 * q^31 + 17 * q^32 - 9 * q^33 + 29 * q^34 + 5 * q^35 + 22 * q^36 + 56 * q^37 + 2 * q^38 + 24 * q^39 - 13 * q^40 - 7 * q^41 + 4 * q^42 + 19 * q^43 - 29 * q^44 + 5 * q^45 + 10 * q^46 + 25 * q^47 + 20 * q^48 + 19 * q^49 - 9 * q^50 + 17 * q^51 + 16 * q^52 + 18 * q^53 + 4 * q^54 + 10 * q^55 + 9 * q^56 + 23 * q^57 + 31 * q^58 + 11 * q^59 + 5 * q^60 + 26 * q^61 + 26 * q^62 + 19 * q^63 + 45 * q^64 + 27 * q^65 - 3 * q^66 + 24 * q^67 + 14 * q^68 - 17 * q^69 - 32 * q^71 + 9 * q^72 + 51 * q^73 + 38 * q^75 + 12 * q^76 - 9 * q^77 + 28 * q^78 + 30 * q^79 - 30 * q^80 + 19 * q^81 - 52 * q^82 + q^83 + 22 * q^84 + 44 * q^85 - 24 * q^86 + 2 * q^87 - 30 * q^88 + 5 * q^89 + 24 * q^91 - 88 * q^92 + 16 * q^93 + 7 * q^94 - 24 * q^95 + 17 * q^96 + 5 * q^97 + 4 * q^98 - 9 * q^99

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