LMFDB - Embedded newform 1003.2.a.j.1.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1003,2,Mod(1,1003)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1003, 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("1003.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1003 = 17 \cdot 59 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1003.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:	$8.00899532273$
Analytic rank:	$0$
Dimension:	$22$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
Character	$\chi$	$=$	1003.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.49676 q^{2} -1.13573 q^{3} +0.240278 q^{4} +3.48120 q^{5} -1.69992 q^{6} -1.05586 q^{7} -2.63387 q^{8} -1.71011 q^{9} +O(q^{10})$	\(q+1.49676 q^{2} -1.13573 q^{3} +0.240278 q^{4} +3.48120 q^{5} -1.69992 q^{6} -1.05586 q^{7} -2.63387 q^{8} -1.71011 q^{9} +5.21050 q^{10} +5.79524 q^{11} -0.272892 q^{12} +2.73906 q^{13} -1.58037 q^{14} -3.95371 q^{15} -4.42282 q^{16} -1.00000 q^{17} -2.55961 q^{18} +4.97246 q^{19} +0.836454 q^{20} +1.19918 q^{21} +8.67407 q^{22} +3.90427 q^{23} +2.99138 q^{24} +7.11872 q^{25} +4.09970 q^{26} +5.34943 q^{27} -0.253701 q^{28} +0.0187106 q^{29} -5.91775 q^{30} -5.26507 q^{31} -1.35214 q^{32} -6.58186 q^{33} -1.49676 q^{34} -3.67567 q^{35} -0.410901 q^{36} +10.5170 q^{37} +7.44255 q^{38} -3.11085 q^{39} -9.16903 q^{40} +11.1188 q^{41} +1.79488 q^{42} -12.9195 q^{43} +1.39247 q^{44} -5.95321 q^{45} +5.84373 q^{46} -6.43968 q^{47} +5.02315 q^{48} -5.88515 q^{49} +10.6550 q^{50} +1.13573 q^{51} +0.658136 q^{52} +3.67662 q^{53} +8.00679 q^{54} +20.1744 q^{55} +2.78101 q^{56} -5.64739 q^{57} +0.0280053 q^{58} +1.00000 q^{59} -0.949990 q^{60} -4.10622 q^{61} -7.88052 q^{62} +1.80564 q^{63} +6.82183 q^{64} +9.53520 q^{65} -9.85144 q^{66} +12.3865 q^{67} -0.240278 q^{68} -4.43421 q^{69} -5.50158 q^{70} +0.517663 q^{71} +4.50420 q^{72} +10.8831 q^{73} +15.7414 q^{74} -8.08498 q^{75} +1.19477 q^{76} -6.11899 q^{77} -4.65618 q^{78} -12.1188 q^{79} -15.3967 q^{80} -0.945219 q^{81} +16.6422 q^{82} -13.5730 q^{83} +0.288137 q^{84} -3.48120 q^{85} -19.3374 q^{86} -0.0212503 q^{87} -15.2639 q^{88} -6.25901 q^{89} -8.91051 q^{90} -2.89208 q^{91} +0.938109 q^{92} +5.97972 q^{93} -9.63862 q^{94} +17.3101 q^{95} +1.53567 q^{96} +2.06793 q^{97} -8.80863 q^{98} -9.91048 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q + 5 q^{2} + 7 q^{3} + 25 q^{4} + 19 q^{5} + 5 q^{6} + 3 q^{7} + 21 q^{8} + 31 q^{9}+O(q^{10}) $ 22 * q + 5 * q^2 + 7 * q^3 + 25 * q^4 + 19 * q^5 + 5 * q^6 + 3 * q^7 + 21 * q^8 + 31 * q^9	\( 22 q + 5 q^{2} + 7 q^{3} + 25 q^{4} + 19 q^{5} + 5 q^{6} + 3 q^{7} + 21 q^{8} + 31 q^{9} + 8 q^{11} + 20 q^{12} + 14 q^{13} + 5 q^{14} + 15 q^{15} + 23 q^{16} - 22 q^{17} + 6 q^{18} + 6 q^{19} + 43 q^{20} + 8 q^{21} - 8 q^{22} + 15 q^{23} - 9 q^{24} + 33 q^{25} + 9 q^{26} + 25 q^{27} + 11 q^{28} - q^{29} - 51 q^{30} - 9 q^{31} + 37 q^{32} + 21 q^{33} - 5 q^{34} + 29 q^{35} + 30 q^{36} - 2 q^{37} + 39 q^{38} + 4 q^{39} + 4 q^{40} + 21 q^{41} - 65 q^{42} + q^{43} + 17 q^{44} + 65 q^{45} - 39 q^{46} + 37 q^{47} + 15 q^{48} + 25 q^{49} - 48 q^{50} - 7 q^{51} + 7 q^{52} + 69 q^{53} + 13 q^{54} + 10 q^{55} - 33 q^{56} - 4 q^{57} + 4 q^{58} + 22 q^{59} + 18 q^{60} - 29 q^{61} + 29 q^{62} + 7 q^{63} - 3 q^{64} + 25 q^{65} - 16 q^{66} - 10 q^{67} - 25 q^{68} + 26 q^{69} + 29 q^{70} + 3 q^{71} + 53 q^{72} - 4 q^{73} + 13 q^{74} - 8 q^{75} - 13 q^{76} + 71 q^{77} + 11 q^{78} - 20 q^{79} - 9 q^{80} + 42 q^{81} + 11 q^{82} + 24 q^{83} - 92 q^{84} - 19 q^{85} - 10 q^{86} - 4 q^{87} + 2 q^{88} + 40 q^{89} - 78 q^{90} - 31 q^{91} - 39 q^{92} + 53 q^{93} + 32 q^{94} + 42 q^{95} - 36 q^{96} + 13 q^{97} - 15 q^{98} - 64 q^{99}+O(q^{100}) \) 22 * q + 5 * q^2 + 7 * q^3 + 25 * q^4 + 19 * q^5 + 5 * q^6 + 3 * q^7 + 21 * q^8 + 31 * q^9 + 8 * q^11 + 20 * q^12 + 14 * q^13 + 5 * q^14 + 15 * q^15 + 23 * q^16 - 22 * q^17 + 6 * q^18 + 6 * q^19 + 43 * q^20 + 8 * q^21 - 8 * q^22 + 15 * q^23 - 9 * q^24 + 33 * q^25 + 9 * q^26 + 25 * q^27 + 11 * q^28 - q^29 - 51 * q^30 - 9 * q^31 + 37 * q^32 + 21 * q^33 - 5 * q^34 + 29 * q^35 + 30 * q^36 - 2 * q^37 + 39 * q^38 + 4 * q^39 + 4 * q^40 + 21 * q^41 - 65 * q^42 + q^43 + 17 * q^44 + 65 * q^45 - 39 * q^46 + 37 * q^47 + 15 * q^48 + 25 * q^49 - 48 * q^50 - 7 * q^51 + 7 * q^52 + 69 * q^53 + 13 * q^54 + 10 * q^55 - 33 * q^56 - 4 * q^57 + 4 * q^58 + 22 * q^59 + 18 * q^60 - 29 * q^61 + 29 * q^62 + 7 * q^63 - 3 * q^64 + 25 * q^65 - 16 * q^66 - 10 * q^67 - 25 * q^68 + 26 * q^69 + 29 * q^70 + 3 * q^71 + 53 * q^72 - 4 * q^73 + 13 * q^74 - 8 * q^75 - 13 * q^76 + 71 * q^77 + 11 * q^78 - 20 * q^79 - 9 * q^80 + 42 * q^81 + 11 * q^82 + 24 * q^83 - 92 * q^84 - 19 * q^85 - 10 * q^86 - 4 * q^87 + 2 * q^88 + 40 * q^89 - 78 * q^90 - 31 * q^91 - 39 * q^92 + 53 * q^93 + 32 * q^94 + 42 * q^95 - 36 * q^96 + 13 * q^97 - 15 * q^98 - 64 * 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 $

$2$	1.49676	1.05837	0.529183	−	0.848508i	$-0.322498\pi$
$2$	1.49676	1.05837	0.529183	+	0.848508i	$0.322498\pi$
$3$	−1.13573	−0.655717	−0.327858	−	0.944727i	$-0.606327\pi$
$3$	−1.13573	−0.655717	−0.327858	+	0.944727i	$0.606327\pi$
$4$	0.240278	0.120139
$5$	3.48120	1.55684	0.778419	−	0.627745i	$-0.216022\pi$
$5$	3.48120	1.55684	0.778419	+	0.627745i	$0.216022\pi$
$6$	−1.69992	−0.693989
$7$	−1.05586	−0.399079	−0.199540	−	0.979890i	$-0.563945\pi$
$7$	−1.05586	−0.399079	−0.199540	+	0.979890i	$0.563945\pi$
$8$	−2.63387	−0.931215
$9$	−1.71011	−0.570035
$10$	5.21050	1.64770
$11$	5.79524	1.74733	0.873666	−	0.486526i	$-0.161736\pi$
$11$	5.79524	1.74733	0.873666	+	0.486526i	$0.161736\pi$
$12$	−0.272892	−0.0787771
$13$	2.73906	0.759678	0.379839	−	0.925053i	$-0.375979\pi$
$13$	2.73906	0.759678	0.379839	+	0.925053i	$0.375979\pi$
$14$	−1.58037	−0.422372
$15$	−3.95371	−1.02084
$16$	−4.42282	−1.10571
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−2.55961	−0.603306
$19$	4.97246	1.14076	0.570380	−	0.821381i	$-0.306796\pi$
$19$	4.97246	1.14076	0.570380	+	0.821381i	$0.306796\pi$
$20$	0.836454	0.187037
$21$	1.19918	0.261683
$22$	8.67407	1.84932
$23$	3.90427	0.814096	0.407048	−	0.913407i	$-0.366558\pi$
$23$	3.90427	0.814096	0.407048	+	0.913407i	$0.366558\pi$
$24$	2.99138	0.610614
$25$	7.11872	1.42374
$26$	4.09970	0.804018
$27$	5.34943	1.02950
$28$	−0.253701	−0.0479450
$29$	0.0187106	0.00347448	0.00173724	−	0.999998i	$-0.499447\pi$
$29$	0.0187106	0.00347448	0.00173724	+	0.999998i	$0.499447\pi$
$30$	−5.91775	−1.08043
$31$	−5.26507	−0.945634	−0.472817	−	0.881161i	$-0.656763\pi$
$31$	−5.26507	−0.945634	−0.472817	+	0.881161i	$0.656763\pi$
$32$	−1.35214	−0.239026
$33$	−6.58186	−1.14576
$34$	−1.49676	−0.256692
$35$	−3.67567	−0.621302
$36$	−0.410901	−0.0684835
$37$	10.5170	1.72898	0.864491	−	0.502649i	$-0.167641\pi$
$37$	10.5170	1.72898	0.864491	+	0.502649i	$0.167641\pi$
$38$	7.44255	1.20734
$39$	−3.11085	−0.498134
$40$	−9.16903	−1.44975
$41$	11.1188	1.73647	0.868236	−	0.496152i	$-0.165254\pi$
$41$	11.1188	1.73647	0.868236	+	0.496152i	$0.165254\pi$
$42$	1.79488	0.276956
$43$	−12.9195	−1.97021	−0.985106	−	0.171947i	$-0.944994\pi$
$43$	−12.9195	−1.97021	−0.985106	+	0.171947i	$0.944994\pi$
$44$	1.39247	0.209923
$45$	−5.95321	−0.887453
$46$	5.84373	0.861612
$47$	−6.43968	−0.939324	−0.469662	−	0.882846i	$-0.655624\pi$
$47$	−6.43968	−0.939324	−0.469662	+	0.882846i	$0.655624\pi$
$48$	5.02315	0.725030
$49$	−5.88515	−0.840736
$50$	10.6550	1.50684
$51$	1.13573	0.159035
$52$	0.658136	0.0912670
$53$	3.67662	0.505023	0.252512	−	0.967594i	$-0.418743\pi$
$53$	3.67662	0.505023	0.252512	+	0.967594i	$0.418743\pi$
$54$	8.00679	1.08959
$55$	20.1744	2.72031
$56$	2.78101	0.371629
$57$	−5.64739	−0.748016
$58$	0.0280053	0.00367727
$59$	1.00000	0.130189
$59$	1.00000	0.130189
$60$	−0.949990	−0.122643
$61$	−4.10622	−0.525748	−0.262874	−	0.964830i	$-0.584670\pi$
$61$	−4.10622	−0.525748	−0.262874	+	0.964830i	$0.584670\pi$
$62$	−7.88052	−1.00083
$63$	1.80564	0.227489
$64$	6.82183	0.852728
$65$	9.53520	1.18270
$66$	−9.85144	−1.21263
$67$	12.3865	1.51326	0.756628	−	0.653845i	$-0.226845\pi$
$67$	12.3865	1.51326	0.756628	+	0.653845i	$0.226845\pi$
$68$	−0.240278	−0.0291380
$69$	−4.43421	−0.533816
$70$	−5.50158	−0.657565
$71$	0.517663	0.0614353	0.0307177	−	0.999528i	$-0.490221\pi$
$71$	0.517663	0.0614353	0.0307177	+	0.999528i	$0.490221\pi$
$72$	4.50420	0.530826
$73$	10.8831	1.27378	0.636888	−	0.770957i	$-0.280222\pi$
$73$	10.8831	1.27378	0.636888	+	0.770957i	$0.280222\pi$
$74$	15.7414	1.82990
$75$	−8.08498	−0.933573
$76$	1.19477	0.137050
$77$	−6.11899	−0.697324
$78$	−4.65618	−0.527208
$79$	−12.1188	−1.36347	−0.681734	−	0.731600i	$-0.738774\pi$
$79$	−12.1188	−1.36347	−0.681734	+	0.731600i	$0.738774\pi$
$80$	−15.3967	−1.72140
$81$	−0.945219	−0.105024
$82$	16.6422	1.83782
$83$	−13.5730	−1.48983	−0.744914	−	0.667161i	$-0.767509\pi$
$83$	−13.5730	−1.48983	−0.744914	+	0.667161i	$0.767509\pi$
$84$	0.288137	0.0314383
$85$	−3.48120	−0.377589
$86$	−19.3374	−2.08521
$87$	−0.0212503	−0.00227827
$88$	−15.2639	−1.62714
$89$	−6.25901	−0.663454	−0.331727	−	0.943375i	$-0.607631\pi$
$89$	−6.25901	−0.663454	−0.331727	+	0.943375i	$0.607631\pi$
$90$	−8.91051	−0.939250
$91$	−2.89208	−0.303172
$92$	0.938109	0.0978046
$93$	5.97972	0.620068
$94$	−9.63862	−0.994148
$95$	17.3101	1.77598
$96$	1.53567	0.156734
$97$	2.06793	0.209967	0.104983	−	0.994474i	$-0.466521\pi$
$97$	2.06793	0.209967	0.104983	+	0.994474i	$0.466521\pi$
$98$	−8.80863	−0.889806
$99$	−9.91048	−0.996041
$100$	1.71047	0.171047
$101$	−9.04916	−0.900425	−0.450213	−	0.892921i	$-0.648652\pi$
$101$	−9.04916	−0.900425	−0.450213	+	0.892921i	$0.648652\pi$
$102$	1.69992	0.168317
$103$	8.37584	0.825296	0.412648	−	0.910890i	$-0.364604\pi$
$103$	8.37584	0.825296	0.412648	+	0.910890i	$0.364604\pi$
$104$	−7.21434	−0.707424
$105$	4.17459	0.407398
$106$	5.50301	0.534500
$107$	−17.4398	−1.68597	−0.842983	−	0.537940i	$-0.819203\pi$
$107$	−17.4398	−1.68597	−0.842983	+	0.537940i	$0.819203\pi$
$108$	1.28535	0.123683
$109$	4.42548	0.423884	0.211942	−	0.977282i	$-0.432021\pi$
$109$	4.42548	0.423884	0.211942	+	0.977282i	$0.432021\pi$
$110$	30.1961	2.87909
$111$	−11.9445	−1.13372
$112$	4.66990	0.441264
$113$	−9.99355	−0.940114	−0.470057	−	0.882636i	$-0.655767\pi$
$113$	−9.99355	−0.940114	−0.470057	+	0.882636i	$0.655767\pi$
$114$	−8.45277	−0.791674
$115$	13.5915	1.26742
$116$	0.00449575	0.000417420 0
$117$	−4.68408	−0.433044
$118$	1.49676	0.137788
$119$	1.05586	0.0967909
$120$	10.4136	0.950626
$121$	22.5849	2.05317
$122$	−6.14601	−0.556434
$123$	−12.6281	−1.13863
$124$	−1.26508	−0.113608
$125$	7.37567	0.659700
$126$	2.70260	0.240767
$127$	9.27086	0.822655	0.411328	−	0.911488i	$-0.365065\pi$
$127$	9.27086	0.822655	0.411328	+	0.911488i	$0.365065\pi$
$128$	12.9149	1.14153
$129$	14.6732	1.29190
$130$	14.2719	1.25173
$131$	−9.75599	−0.852385	−0.426192	−	0.904633i	$-0.640145\pi$
$131$	−9.75599	−0.852385	−0.426192	+	0.904633i	$0.640145\pi$
$132$	−1.58148	−0.137650
$133$	−5.25024	−0.455254
$134$	18.5396	1.60158
$135$	18.6224	1.60276
$136$	2.63387	0.225853
$137$	1.46902	0.125507	0.0627535	−	0.998029i	$-0.480012\pi$
$137$	1.46902	0.125507	0.0627535	+	0.998029i	$0.480012\pi$
$138$	−6.63693	−0.564973
$139$	−9.28830	−0.787823	−0.393912	−	0.919148i	$-0.628878\pi$
$139$	−9.28830	−0.787823	−0.393912	+	0.919148i	$0.628878\pi$
$140$	−0.883182	−0.0746425
$141$	7.31377	0.615930
$142$	0.774816	0.0650211
$143$	15.8735	1.32741
$144$	7.56350	0.630291
$145$	0.0651354	0.00540920
$146$	16.2894	1.34812
$147$	6.68397	0.551285
$148$	2.52700	0.207718
$149$	−13.5721	−1.11187	−0.555936	−	0.831225i	$-0.687640\pi$
$149$	−13.5721	−1.11187	−0.555936	+	0.831225i	$0.687640\pi$
$150$	−12.1012	−0.988062
$151$	−1.78096	−0.144932	−0.0724661	−	0.997371i	$-0.523087\pi$
$151$	−1.78096	−0.144932	−0.0724661	+	0.997371i	$0.523087\pi$
$152$	−13.0968	−1.06229
$153$	1.71011	0.138254
$154$	−9.15864	−0.738024
$155$	−18.3287	−1.47220
$156$	−0.747467	−0.0598453
$157$	−6.20438	−0.495164	−0.247582	−	0.968867i	$-0.579636\pi$
$157$	−6.20438	−0.495164	−0.247582	+	0.968867i	$0.579636\pi$
$158$	−18.1388	−1.44305
$159$	−4.17567	−0.331152
$160$	−4.70705	−0.372125
$161$	−4.12238	−0.324889
$162$	−1.41476	−0.111154
$163$	−7.42095	−0.581254	−0.290627	−	0.956836i	$-0.593864\pi$
$163$	−7.42095	−0.581254	−0.290627	+	0.956836i	$0.593864\pi$
$164$	2.67161	0.208618
$165$	−22.9127	−1.78375
$166$	−20.3154	−1.57678
$167$	−5.69527	−0.440713	−0.220357	−	0.975419i	$-0.570722\pi$
$167$	−5.69527	−0.440713	−0.220357	+	0.975419i	$0.570722\pi$
$168$	−3.15849	−0.243683
$169$	−5.49755	−0.422889
$170$	−5.21050	−0.399627
$171$	−8.50343	−0.650274
$172$	−3.10428	−0.236699
$173$	−9.63960	−0.732885	−0.366443	−	0.930441i	$-0.619424\pi$
$173$	−9.63960	−0.732885	−0.366443	+	0.930441i	$0.619424\pi$
$174$	−0.0318066	−0.00241125
$175$	−7.51640	−0.568187
$176$	−25.6313	−1.93203
$177$	−1.13573	−0.0853671
$178$	−9.36821	−0.702177
$179$	−6.72044	−0.502309	−0.251155	−	0.967947i	$-0.580810\pi$
$179$	−6.72044	−0.502309	−0.251155	+	0.967947i	$0.580810\pi$
$180$	−1.43043	−0.106618
$181$	−4.96324	−0.368915	−0.184457	−	0.982840i	$-0.559053\pi$
$181$	−4.96324	−0.368915	−0.184457	+	0.982840i	$0.559053\pi$
$182$	−4.32873	−0.320867
$183$	4.66358	0.344742
$184$	−10.2833	−0.758099
$185$	36.6117	2.69174
$186$	8.95018	0.656259
$187$	−5.79524	−0.423790
$188$	−1.54731	−0.112849
$189$	−5.64827	−0.410852
$190$	25.9090	1.87964
$191$	4.54900	0.329154	0.164577	−	0.986364i	$-0.447374\pi$
$191$	4.54900	0.329154	0.164577	+	0.986364i	$0.447374\pi$
$192$	−7.74779	−0.559148
$193$	−5.82707	−0.419442	−0.209721	−	0.977761i	$-0.567255\pi$
$193$	−5.82707	−0.419442	−0.209721	+	0.977761i	$0.567255\pi$
$194$	3.09519	0.222222
$195$	−10.8295	−0.775514
$196$	−1.41407	−0.101005
$197$	25.0067	1.78166	0.890828	−	0.454340i	$-0.150125\pi$
$197$	25.0067	1.78166	0.890828	+	0.454340i	$0.150125\pi$
$198$	−14.8336	−1.05418
$199$	−18.9860	−1.34588	−0.672942	−	0.739695i	$-0.734970\pi$
$199$	−18.9860	−1.34588	−0.672942	+	0.739695i	$0.734970\pi$
$200$	−18.7498	−1.32581
$201$	−14.0678	−0.992268
$202$	−13.5444	−0.952979
$203$	−0.0197559	−0.00138659
$204$	0.272892	0.0191063
$205$	38.7069	2.70340
$206$	12.5366	0.873466
$207$	−6.67671	−0.464064
$208$	−12.1144	−0.839981
$209$	28.8166	1.99329
$210$	6.24834	0.431176
$211$	7.11802	0.490025	0.245012	−	0.969520i	$-0.421208\pi$
$211$	7.11802	0.490025	0.245012	+	0.969520i	$0.421208\pi$
$212$	0.883412	0.0606730
$213$	−0.587928	−0.0402842
$214$	−26.1031	−1.78437
$215$	−44.9755	−3.06730
$216$	−14.0897	−0.958685
$217$	5.55920	0.377383
$218$	6.62386	0.448624
$219$	−12.3604	−0.835236
$220$	4.84746	0.326816
$221$	−2.73906	−0.184249
$222$	−17.8780	−1.19989
$223$	16.9640	1.13599	0.567995	−	0.823032i	$-0.307719\pi$
$223$	16.9640	1.13599	0.567995	+	0.823032i	$0.307719\pi$
$224$	1.42767	0.0953904
$225$	−12.1738	−0.811584
$226$	−14.9579	−0.994985
$227$	−22.6953	−1.50634	−0.753171	−	0.657824i	$-0.771477\pi$
$227$	−22.6953	−1.50634	−0.753171	+	0.657824i	$0.771477\pi$
$228$	−1.35694	−0.0898658
$229$	−2.71831	−0.179631	−0.0898153	−	0.995958i	$-0.528628\pi$
$229$	−2.71831	−0.179631	−0.0898153	+	0.995958i	$0.528628\pi$
$230$	20.3432	1.34139
$231$	6.94955	0.457247
$232$	−0.0492815	−0.00323549
$233$	19.3842	1.26990	0.634949	−	0.772554i	$-0.281021\pi$
$233$	19.3842	1.26990	0.634949	+	0.772554i	$0.281021\pi$
$234$	−7.01093	−0.458319
$235$	−22.4178	−1.46237
$236$	0.240278	0.0156408
$237$	13.7637	0.894049
$238$	1.58037	0.102440
$239$	−6.41129	−0.414712	−0.207356	−	0.978266i	$-0.566486\pi$
$239$	−6.41129	−0.414712	−0.207356	+	0.978266i	$0.566486\pi$
$240$	17.4866	1.12875
$241$	−25.0811	−1.61562	−0.807808	−	0.589445i	$-0.799346\pi$
$241$	−25.0811	−1.61562	−0.807808	+	0.589445i	$0.799346\pi$
$242$	33.8040	2.17301
$243$	−14.9748	−0.960632
$244$	−0.986634	−0.0631628
$245$	−20.4874	−1.30889
$246$	−18.9011	−1.20509
$247$	13.6199	0.866611
$248$	13.8675	0.880589
$249$	15.4153	0.976905
$250$	11.0396	0.698204
$251$	15.6246	0.986215	0.493108	−	0.869968i	$-0.335861\pi$
$251$	15.6246	0.986215	0.493108	+	0.869968i	$0.335861\pi$
$252$	0.433855	0.0273303
$253$	22.6262	1.42250
$254$	13.8762	0.870671
$255$	3.95371	0.247591
$256$	5.68677	0.355423
$257$	8.10295	0.505448	0.252724	−	0.967538i	$-0.418674\pi$
$257$	8.10295	0.505448	0.252724	+	0.967538i	$0.418674\pi$
$258$	21.9622	1.36730
$259$	−11.1045	−0.690000
$260$	2.29110	0.142088
$261$	−0.0319972	−0.00198058
$262$	−14.6023	−0.902135
$263$	−25.6870	−1.58393	−0.791965	−	0.610566i	$-0.790942\pi$
$263$	−25.6870	−1.58393	−0.791965	+	0.610566i	$0.790942\pi$
$264$	17.3358	1.06694
$265$	12.7990	0.786239
$266$	−7.85833	−0.481825
$267$	7.10858	0.435038
$268$	2.97621	0.181801
$269$	13.0186	0.793757	0.396879	−	0.917871i	$-0.370093\pi$
$269$	13.0186	0.793757	0.396879	+	0.917871i	$0.370093\pi$
$270$	27.8732	1.69631
$271$	−4.23082	−0.257004	−0.128502	−	0.991709i	$-0.541017\pi$
$271$	−4.23082	−0.257004	−0.128502	+	0.991709i	$0.541017\pi$
$272$	4.42282	0.268173
$273$	3.28463	0.198795
$274$	2.19877	0.132832
$275$	41.2547	2.48775
$276$	−1.06544	−0.0641322
$277$	26.3514	1.58330	0.791650	−	0.610975i	$-0.209222\pi$
$277$	26.3514	1.58330	0.791650	+	0.610975i	$0.209222\pi$
$278$	−13.9023	−0.833806
$279$	9.00383	0.539045
$280$	9.68125	0.578565
$281$	−4.31001	−0.257114	−0.128557	−	0.991702i	$-0.541034\pi$
$281$	−4.31001	−0.257114	−0.128557	+	0.991702i	$0.541034\pi$
$282$	10.9469	0.651880
$283$	−2.28062	−0.135569	−0.0677845	−	0.997700i	$-0.521593\pi$
$283$	−2.28062	−0.135569	−0.0677845	+	0.997700i	$0.521593\pi$
$284$	0.124383	0.00738078
$285$	−19.6597	−1.16454
$286$	23.7588	1.40489
$287$	−11.7400	−0.692990
$288$	2.31230	0.136253
$289$	1.00000	0.0588235
$290$	0.0974918	0.00572491
$291$	−2.34862	−0.137679
$292$	2.61498	0.153030
$293$	19.5220	1.14049	0.570245	−	0.821475i	$-0.306848\pi$
$293$	19.5220	1.14049	0.570245	+	0.821475i	$0.306848\pi$
$294$	10.0043	0.583461
$295$	3.48120	0.202683
$296$	−27.7004	−1.61005
$297$	31.0013	1.79888
$298$	−20.3142	−1.17677
$299$	10.6940	0.618451
$300$	−1.94264	−0.112158
$301$	13.6413	0.786271
$302$	−2.66566	−0.153391
$303$	10.2774	0.590424
$304$	−21.9923	−1.26134
$305$	−14.2946	−0.818504
$306$	2.55961	0.146323
$307$	22.1967	1.26683	0.633416	−	0.773811i	$-0.281652\pi$
$307$	22.1967	1.26683	0.633416	+	0.773811i	$0.281652\pi$
$308$	−1.47026	−0.0837758
$309$	−9.51274	−0.541161
$310$	−27.4336	−1.55813
$311$	−20.2862	−1.15033	−0.575163	−	0.818039i	$-0.695061\pi$
$311$	−20.2862	−1.15033	−0.575163	+	0.818039i	$0.695061\pi$
$312$	8.19358	0.463870
$313$	17.9183	1.01280	0.506402	−	0.862298i	$-0.330975\pi$
$313$	17.9183	1.01280	0.506402	+	0.862298i	$0.330975\pi$
$314$	−9.28645	−0.524064
$315$	6.28579	0.354164
$316$	−2.91187	−0.163806
$317$	3.07010	0.172434	0.0862171	−	0.996276i	$-0.472522\pi$
$317$	3.07010	0.172434	0.0862171	+	0.996276i	$0.472522\pi$
$318$	−6.24996	−0.350480
$319$	0.108433	0.00607107
$320$	23.7481	1.32756
$321$	19.8070	1.10552
$322$	−6.17019	−0.343851
$323$	−4.97246	−0.276675
$324$	−0.227115	−0.0126175
$325$	19.4986	1.08159
$326$	−11.1074	−0.615179
$327$	−5.02617	−0.277948
$328$	−29.2856	−1.61703
$329$	6.79943	0.374864
$330$	−34.2948	−1.88787
$331$	20.6602	1.13558	0.567792	−	0.823172i	$-0.307798\pi$
$331$	20.6602	1.13558	0.567792	+	0.823172i	$0.307798\pi$
$332$	−3.26129	−0.178986
$333$	−17.9852	−0.985580
$334$	−8.52443	−0.466436
$335$	43.1200	2.35590
$336$	−5.30377	−0.289344
$337$	−4.72199	−0.257223	−0.128612	−	0.991695i	$-0.541052\pi$
$337$	−4.72199	−0.257223	−0.128612	+	0.991695i	$0.541052\pi$
$338$	−8.22849	−0.447571
$339$	11.3500	0.616449
$340$	−0.836454	−0.0453631
$341$	−30.5124	−1.65234
$342$	−12.7276	−0.688227
$343$	13.6050	0.734599
$344$	34.0285	1.83469
$345$	−15.4364	−0.831066
$346$	−14.4281	−0.775661
$347$	−20.6314	−1.10755	−0.553775	−	0.832666i	$-0.686813\pi$
$347$	−20.6314	−1.10755	−0.553775	+	0.832666i	$0.686813\pi$
$348$	−0.00510598	−0.000273710 0
$349$	2.20936	0.118265	0.0591323	−	0.998250i	$-0.481167\pi$
$349$	2.20936	0.118265	0.0591323	+	0.998250i	$0.481167\pi$
$350$	−11.2502	−0.601349
$351$	14.6524	0.782088
$352$	−7.83596	−0.417658
$353$	31.0774	1.65409	0.827043	−	0.562139i	$-0.190022\pi$
$353$	31.0774	1.65409	0.827043	+	0.562139i	$0.190022\pi$
$354$	−1.69992	−0.0903496
$355$	1.80209	0.0956449
$356$	−1.50390	−0.0797066
$357$	−1.19918	−0.0634674
$358$	−10.0589	−0.531627
$359$	4.21404	0.222408	0.111204	−	0.993798i	$-0.464529\pi$
$359$	4.21404	0.222408	0.111204	+	0.993798i	$0.464529\pi$
$360$	15.6800	0.826409
$361$	5.72533	0.301333
$362$	−7.42876	−0.390447
$363$	−25.6504	−1.34630
$364$	−0.694902	−0.0364228
$365$	37.8863	1.98306
$366$	6.98024	0.364863
$367$	22.7697	1.18857	0.594284	−	0.804255i	$-0.297436\pi$
$367$	22.7697	1.18857	0.594284	+	0.804255i	$0.297436\pi$
$368$	−17.2679	−0.900150
$369$	−19.0144	−0.989850
$370$	54.7987	2.84885
$371$	−3.88202	−0.201544
$372$	1.43680	0.0744944
$373$	−37.8614	−1.96039	−0.980195	−	0.198035i	$-0.936544\pi$
$373$	−37.8614	−1.96039	−0.980195	+	0.198035i	$0.936544\pi$
$374$	−8.67407	−0.448525
$375$	−8.37681	−0.432577
$376$	16.9613	0.874712
$377$	0.0512496	0.00263949
$378$	−8.45409	−0.434831
$379$	−34.5960	−1.77708	−0.888538	−	0.458802i	$-0.848279\pi$
$379$	−34.5960	−1.77708	−0.888538	+	0.458802i	$0.848279\pi$
$380$	4.15923	0.213364
$381$	−10.5292	−0.539429
$382$	6.80874	0.348366
$383$	−1.94458	−0.0993634	−0.0496817	−	0.998765i	$-0.515821\pi$
$383$	−1.94458	−0.0993634	−0.0496817	+	0.998765i	$0.515821\pi$
$384$	−14.6679	−0.748517
$385$	−21.3014	−1.08562
$386$	−8.72170	−0.443923
$387$	22.0938	1.12309
$388$	0.496878	0.0252252
$389$	2.86841	0.145434	0.0727170	−	0.997353i	$-0.476833\pi$
$389$	2.86841	0.145434	0.0727170	+	0.997353i	$0.476833\pi$
$390$	−16.2091	−0.820778
$391$	−3.90427	−0.197447
$392$	15.5007	0.782906
$393$	11.0802	0.558923
$394$	37.4290	1.88564
$395$	−42.1878	−2.12270
$396$	−2.38127	−0.119663
$397$	14.2532	0.715347	0.357674	−	0.933847i	$-0.383570\pi$
$397$	14.2532	0.715347	0.357674	+	0.933847i	$0.383570\pi$
$398$	−28.4174	−1.42444
$399$	5.96288	0.298517
$400$	−31.4848	−1.57424
$401$	15.7829	0.788158	0.394079	−	0.919077i	$-0.371064\pi$
$401$	15.7829	0.788158	0.394079	+	0.919077i	$0.371064\pi$
$402$	−21.0561	−1.05018
$403$	−14.4213	−0.718378
$404$	−2.17431	−0.108176
$405$	−3.29049	−0.163506
$406$	−0.0295698	−0.00146752
$407$	60.9485	3.02110
$408$	−2.99138	−0.148096
$409$	36.0750	1.78379	0.891897	−	0.452239i	$-0.149374\pi$
$409$	36.0750	1.78379	0.891897	+	0.452239i	$0.149374\pi$
$410$	57.9347	2.86119
$411$	−1.66842	−0.0822971
$412$	2.01253	0.0991502
$413$	−1.05586	−0.0519557
$414$	−9.99341	−0.491149
$415$	−47.2502	−2.31942
$416$	−3.70358	−0.181583
$417$	10.5490	0.516589
$418$	43.1314	2.10963
$419$	10.7817	0.526721	0.263361	−	0.964697i	$-0.415169\pi$
$419$	10.7817	0.526721	0.263361	+	0.964697i	$0.415169\pi$
$420$	1.00306	0.0489444
$421$	−25.5523	−1.24534	−0.622672	−	0.782483i	$-0.713953\pi$
$421$	−25.5523	−1.24534	−0.622672	+	0.782483i	$0.713953\pi$
$422$	10.6539	0.518626
$423$	11.0125	0.535448
$424$	−9.68377	−0.470285
$425$	−7.11872	−0.345309
$426$	−0.879985	−0.0426354
$427$	4.33561	0.209815
$428$	−4.19039	−0.202550
$429$	−18.0281	−0.870405
$430$	−67.3173	−3.24633
$431$	25.0314	1.20572	0.602859	−	0.797848i	$-0.294028\pi$
$431$	25.0314	1.20572	0.602859	+	0.797848i	$0.294028\pi$
$432$	−23.6596	−1.13832
$433$	−31.9786	−1.53679	−0.768396	−	0.639974i	$-0.778945\pi$
$433$	−31.9786	−1.53679	−0.768396	+	0.639974i	$0.778945\pi$
$434$	8.32076	0.399409
$435$	−0.0739765	−0.00354690
$436$	1.06334	0.0509250
$437$	19.4138	0.928688
$438$	−18.5004	−0.883985
$439$	−11.7705	−0.561774	−0.280887	−	0.959741i	$-0.590629\pi$
$439$	−11.7705	−0.561774	−0.280887	+	0.959741i	$0.590629\pi$
$440$	−53.1368	−2.53320
$441$	10.0642	0.479249
$442$	−4.09970	−0.195003
$443$	−24.7614	−1.17645	−0.588224	−	0.808698i	$-0.700173\pi$
$443$	−24.7614	−1.17645	−0.588224	+	0.808698i	$0.700173\pi$
$444$	−2.87000	−0.136204
$445$	−21.7888	−1.03289
$446$	25.3909	1.20229
$447$	15.4143	0.729073
$448$	−7.20292	−0.340306
$449$	22.6649	1.06962	0.534812	−	0.844971i	$-0.320382\pi$
$449$	22.6649	1.06962	0.534812	+	0.844971i	$0.320382\pi$
$450$	−18.2212	−0.858953
$451$	64.4364	3.03419
$452$	−2.40123	−0.112944
$453$	2.02269	0.0950345
$454$	−33.9694	−1.59426
$455$	−10.0679	−0.471989
$456$	14.8745	0.696563
$457$	−18.8168	−0.880211	−0.440106	−	0.897946i	$-0.645059\pi$
$457$	−18.8168	−0.880211	−0.440106	+	0.897946i	$0.645059\pi$
$458$	−4.06864	−0.190115
$459$	−5.34943	−0.249690
$460$	3.26574	0.152266
$461$	41.9189	1.95236	0.976180	−	0.216963i	$-0.0696151\pi$
$461$	41.9189	1.95236	0.976180	+	0.216963i	$0.0696151\pi$
$462$	10.4018	0.483935
$463$	−0.720697	−0.0334936	−0.0167468	−	0.999860i	$-0.505331\pi$
$463$	−0.720697	−0.0334936	−0.0167468	+	0.999860i	$0.505331\pi$
$464$	−0.0827538	−0.00384175
$465$	20.8166	0.965346
$466$	29.0134	1.34402
$467$	32.3431	1.49666	0.748329	−	0.663328i	$-0.230856\pi$
$467$	32.3431	1.49666	0.748329	+	0.663328i	$0.230856\pi$
$468$	−1.12548	−0.0520254
$469$	−13.0785	−0.603909
$470$	−33.5539	−1.54773
$471$	7.04653	0.324687
$472$	−2.63387	−0.121234
$473$	−74.8719	−3.44262
$474$	20.6009	0.946232
$475$	35.3975	1.62415
$476$	0.253701	0.0116284
$477$	−6.28742	−0.287881
$478$	−9.59614	−0.438917
$479$	−36.7227	−1.67790	−0.838950	−	0.544208i	$-0.816830\pi$
$479$	−36.7227	−1.67790	−0.838950	+	0.544208i	$0.816830\pi$
$480$	5.34596	0.244009
$481$	28.8066	1.31347
$482$	−37.5403	−1.70991
$483$	4.68193	0.213035
$484$	5.42664	0.246666
$485$	7.19887	0.326884
$486$	−22.4136	−1.01670
$487$	−4.10994	−0.186239	−0.0931197	−	0.995655i	$-0.529684\pi$
$487$	−4.10994	−0.186239	−0.0931197	+	0.995655i	$0.529684\pi$
$488$	10.8153	0.489584
$489$	8.42824	0.381138
$490$	−30.6646	−1.38528
$491$	36.1225	1.63018	0.815092	−	0.579332i	$-0.196687\pi$
$491$	36.1225	1.63018	0.815092	+	0.579332i	$0.196687\pi$
$492$	−3.03424	−0.136794
$493$	−0.0187106	−0.000842685 0
$494$	20.3856	0.917191
$495$	−34.5003	−1.55067
$496$	23.2865	1.04559
$497$	−0.546582	−0.0245176
$498$	23.0729	1.03392
$499$	−9.19782	−0.411751	−0.205875	−	0.978578i	$-0.566004\pi$
$499$	−9.19782	−0.411751	−0.205875	+	0.978578i	$0.566004\pi$
$500$	1.77221	0.0792557
$501$	6.46832	0.288983
$502$	23.3862	1.04378
$503$	16.9835	0.757255	0.378627	−	0.925549i	$-0.376396\pi$
$503$	16.9835	0.757255	0.378627	+	0.925549i	$0.376396\pi$
$504$	−4.75583	−0.211841
$505$	−31.5019	−1.40182
$506$	33.8659	1.50552
$507$	6.24376	0.277295
$508$	2.22758	0.0988330
$509$	6.43115	0.285056	0.142528	−	0.989791i	$-0.454477\pi$
$509$	6.43115	0.285056	0.142528	+	0.989791i	$0.454477\pi$
$510$	5.91775	0.262042
$511$	−11.4911	−0.508337
$512$	−17.3181	−0.765357
$513$	26.5998	1.17441
$514$	12.1281	0.534949
$515$	29.1579	1.28485
$516$	3.52564	0.155208
$517$	−37.3195	−1.64131
$518$	−16.6207	−0.730273
$519$	10.9480	0.480565
$520$	−25.1145	−1.10134
$521$	−15.9577	−0.699121	−0.349560	−	0.936914i	$-0.613669\pi$
$521$	−15.9577	−0.699121	−0.349560	+	0.936914i	$0.613669\pi$
$522$	−0.0478920	−0.00209617
$523$	6.41586	0.280546	0.140273	−	0.990113i	$-0.455202\pi$
$523$	6.41586	0.280546	0.140273	+	0.990113i	$0.455202\pi$
$524$	−2.34415	−0.102405
$525$	8.53664	0.372569
$526$	−38.4472	−1.67638
$527$	5.26507	0.229350
$528$	29.1104	1.26687
$529$	−7.75670	−0.337248
$530$	19.1570	0.832129
$531$	−1.71011	−0.0742123
$532$	−1.26152	−0.0546937
$533$	30.4552	1.31916
$534$	10.6398	0.460429
$535$	−60.7112	−2.62478
$536$	−32.6246	−1.40917
$537$	7.63264	0.329373
$538$	19.4856	0.840086
$539$	−34.1059	−1.46904
$540$	4.47456	0.192554
$541$	−12.2505	−0.526690	−0.263345	−	0.964702i	$-0.584826\pi$
$541$	−12.2505	−0.526690	−0.263345	+	0.964702i	$0.584826\pi$
$542$	−6.33251	−0.272005
$543$	5.63693	0.241904
$544$	1.35214	0.0579724
$545$	15.4059	0.659918
$546$	4.91629	0.210398
$547$	5.68197	0.242943	0.121472	−	0.992595i	$-0.461239\pi$
$547$	5.68197	0.242943	0.121472	+	0.992595i	$0.461239\pi$
$548$	0.352974	0.0150783
$549$	7.02207	0.299695
$550$	61.7482	2.63295
$551$	0.0930379	0.00396355
$552$	11.6792	0.497098
$553$	12.7958	0.544132
$554$	39.4416	1.67571
$555$	−41.5811	−1.76502
$556$	−2.23177	−0.0946483
$557$	32.1406	1.36184	0.680921	−	0.732357i	$-0.261580\pi$
$557$	32.1406	1.36184	0.680921	+	0.732357i	$0.261580\pi$
$558$	13.4765	0.570507
$559$	−35.3874	−1.49673
$560$	16.2568	0.686977
$561$	6.58186	0.277886
$562$	−6.45103	−0.272120
$563$	−43.2858	−1.82428	−0.912140	−	0.409878i	$-0.865571\pi$
$563$	−43.2858	−1.82428	−0.912140	+	0.409878i	$0.865571\pi$
$564$	1.75734	0.0739972
$565$	−34.7895	−1.46361
$566$	−3.41354	−0.143482
$567$	0.998023	0.0419130
$568$	−1.36346	−0.0572095
$569$	−11.8253	−0.495740	−0.247870	−	0.968793i	$-0.579731\pi$
$569$	−11.8253	−0.495740	−0.247870	+	0.968793i	$0.579731\pi$
$570$	−29.4257	−1.23251
$571$	−11.7401	−0.491307	−0.245654	−	0.969358i	$-0.579003\pi$
$571$	−11.7401	−0.491307	−0.245654	+	0.969358i	$0.579003\pi$
$572$	3.81406	0.159474
$573$	−5.16646	−0.215832
$574$	−17.5719	−0.733437
$575$	27.7934	1.15906
$576$	−11.6660	−0.486085
$577$	35.2794	1.46870	0.734350	−	0.678771i	$-0.237487\pi$
$577$	35.2794	1.46870	0.734350	+	0.678771i	$0.237487\pi$
$578$	1.49676	0.0622568
$579$	6.61801	0.275035
$580$	0.0156506	0.000649856 0
$581$	14.3312	0.594559
$582$	−3.51531	−0.145714
$583$	21.3069	0.882443
$584$	−28.6648	−1.18616
$585$	−16.3062	−0.674179
$586$	29.2197	1.20706
$587$	12.9443	0.534268	0.267134	−	0.963659i	$-0.413923\pi$
$587$	12.9443	0.534268	0.267134	+	0.963659i	$0.413923\pi$
$588$	1.60601	0.0662308
$589$	−26.1803	−1.07874
$590$	5.21050	0.214513
$591$	−28.4010	−1.16826
$592$	−46.5147	−1.91174
$593$	24.1293	0.990873	0.495437	−	0.868644i	$-0.335008\pi$
$593$	24.1293	0.990873	0.495437	+	0.868644i	$0.335008\pi$
$594$	46.4013	1.90387
$595$	3.67567	0.150688
$596$	−3.26108	−0.133579
$597$	21.5631	0.882519
$598$	16.0063	0.654548
$599$	−26.5112	−1.08322	−0.541609	−	0.840631i	$-0.682185\pi$
$599$	−26.5112	−1.08322	−0.541609	+	0.840631i	$0.682185\pi$
$600$	21.2948	0.869357
$601$	29.5131	1.20386	0.601932	−	0.798547i	$-0.294398\pi$
$601$	29.5131	1.20386	0.601932	+	0.798547i	$0.294398\pi$
$602$	20.4177	0.832162
$603$	−21.1823	−0.862610
$604$	−0.427925	−0.0174120
$605$	78.6223	3.19645
$606$	15.3828	0.624885
$607$	31.3781	1.27360	0.636799	−	0.771029i	$-0.280258\pi$
$607$	31.3781	1.27360	0.636799	+	0.771029i	$0.280258\pi$
$608$	−6.72344	−0.272672
$609$	0.0224375	0.000909212 0
$610$	−21.3955	−0.866277
$611$	−17.6387	−0.713584
$612$	0.410901	0.0166097
$613$	−3.43759	−0.138843	−0.0694214	−	0.997587i	$-0.522115\pi$
$613$	−3.43759	−0.138843	−0.0694214	+	0.997587i	$0.522115\pi$
$614$	33.2230	1.34077
$615$	−43.9607	−1.77267
$616$	16.1167	0.649359
$617$	−35.6225	−1.43411	−0.717053	−	0.697018i	$-0.754510\pi$
$617$	−35.6225	−1.43411	−0.717053	+	0.697018i	$0.754510\pi$
$618$	−14.2382	−0.572746
$619$	3.21785	0.129336	0.0646682	−	0.997907i	$-0.479401\pi$
$619$	3.21785	0.129336	0.0646682	+	0.997907i	$0.479401\pi$
$620$	−4.40399	−0.176868
$621$	20.8856	0.838111
$622$	−30.3635	−1.21747
$623$	6.60867	0.264771
$624$	13.7587	0.550790
$625$	−9.91744	−0.396697
$626$	26.8193	1.07192
$627$	−32.7280	−1.30703
$628$	−1.49078	−0.0594884
$629$	−10.5170	−0.419340
$630$	9.40829	0.374835
$631$	28.3659	1.12923	0.564614	−	0.825355i	$-0.309025\pi$
$631$	28.3659	1.12923	0.564614	+	0.825355i	$0.309025\pi$
$632$	31.9193	1.26968
$633$	−8.08419	−0.321318
$634$	4.59519	0.182498
$635$	32.2737	1.28074
$636$	−1.00332	−0.0397843
$637$	−16.1198	−0.638689
$638$	0.162297	0.00642541
$639$	−0.885259	−0.0350203
$640$	44.9592	1.77717
$641$	−11.5262	−0.455259	−0.227630	−	0.973748i	$-0.573098\pi$
$641$	−11.5262	−0.455259	−0.227630	+	0.973748i	$0.573098\pi$
$642$	29.6462	1.17004
$643$	−6.14150	−0.242197	−0.121099	−	0.992640i	$-0.538642\pi$
$643$	−6.14150	−0.242197	−0.121099	+	0.992640i	$0.538642\pi$
$644$	−0.990516	−0.0390318
$645$	51.0802	2.01128
$646$	−7.44255	−0.292823
$647$	−33.3818	−1.31237	−0.656186	−	0.754599i	$-0.727831\pi$
$647$	−33.3818	−1.31237	−0.656186	+	0.754599i	$0.727831\pi$
$648$	2.48959	0.0978002
$649$	5.79524	0.227483
$650$	29.1846	1.14472
$651$	−6.31378	−0.247456
$652$	−1.78309	−0.0698312
$653$	−27.7938	−1.08765	−0.543827	−	0.839197i	$-0.683025\pi$
$653$	−27.7938	−1.08765	−0.543827	+	0.839197i	$0.683025\pi$
$654$	−7.52295	−0.294171
$655$	−33.9625	−1.32702
$656$	−49.1767	−1.92003
$657$	−18.6113	−0.726097
$658$	10.1771	0.396744
$659$	−22.0751	−0.859923	−0.429961	−	0.902847i	$-0.641473\pi$
$659$	−22.0751	−0.859923	−0.429961	+	0.902847i	$0.641473\pi$
$660$	−5.50543	−0.214298
$661$	−11.5687	−0.449972	−0.224986	−	0.974362i	$-0.572234\pi$
$661$	−11.5687	−0.449972	−0.224986	+	0.974362i	$0.572234\pi$
$662$	30.9232	1.20186
$663$	3.11085	0.120815
$664$	35.7495	1.38735
$665$	−18.2771	−0.708756
$666$	−26.9194	−1.04311
$667$	0.0730513	0.00282856
$668$	−1.36845	−0.0529468
$669$	−19.2666	−0.744888
$670$	64.5401	2.49340
$671$	−23.7966	−0.918656
$672$	−1.62146	−0.0625491
$673$	−0.895729	−0.0345278	−0.0172639	−	0.999851i	$-0.505496\pi$
$673$	−0.895729	−0.0345278	−0.0172639	+	0.999851i	$0.505496\pi$
$674$	−7.06767	−0.272236
$675$	38.0811	1.46574
$676$	−1.32094	−0.0508054
$677$	−16.6065	−0.638239	−0.319120	−	0.947714i	$-0.603387\pi$
$677$	−16.6065	−0.638239	−0.319120	+	0.947714i	$0.603387\pi$
$678$	16.9882	0.652429
$679$	−2.18346	−0.0837933
$680$	9.16903	0.351616
$681$	25.7759	0.987735
$682$	−45.6696	−1.74878
$683$	−4.97941	−0.190532	−0.0952660	−	0.995452i	$-0.530370\pi$
$683$	−4.97941	−0.190532	−0.0952660	+	0.995452i	$0.530370\pi$
$684$	−2.04319	−0.0781232
$685$	5.11395	0.195394
$686$	20.3633	0.777475
$687$	3.08727	0.117787
$688$	57.1409	2.17847
$689$	10.0705	0.383655
$690$	−23.1045	−0.879572
$691$	−18.5163	−0.704393	−0.352197	−	0.935926i	$-0.614565\pi$
$691$	−18.5163	−0.704393	−0.352197	+	0.935926i	$0.614565\pi$
$692$	−2.31618	−0.0880481
$693$	10.4641	0.397499
$694$	−30.8801	−1.17219
$695$	−32.3344	−1.22651
$696$	0.0559707	0.00212156
$697$	−11.1188	−0.421156
$698$	3.30688	0.125167
$699$	−22.0153	−0.832694
$700$	−1.80603	−0.0682613
$701$	−0.106971	−0.00404024	−0.00202012	−	0.999998i	$-0.500643\pi$
$701$	−0.106971	−0.00404024	−0.00202012	+	0.999998i	$0.500643\pi$
$702$	21.9311	0.827735
$703$	52.2952	1.97235
$704$	39.5342	1.49000
$705$	25.4606	0.958904
$706$	46.5153	1.75063
$707$	9.55469	0.359341
$708$	−0.272892	−0.0102559
$709$	−29.9479	−1.12472	−0.562359	−	0.826893i	$-0.690106\pi$
$709$	−29.9479	−1.12472	−0.562359	+	0.826893i	$0.690106\pi$
$710$	2.69728	0.101227
$711$	20.7244	0.777225
$712$	16.4854	0.617818
$713$	−20.5562	−0.769837
$714$	−1.79488	−0.0671718
$715$	55.2588	2.06656
$716$	−1.61477	−0.0603469
$717$	7.28153	0.271934
$718$	6.30738	0.235390
$719$	9.48484	0.353725	0.176862	−	0.984236i	$-0.443405\pi$
$719$	9.48484	0.353725	0.176862	+	0.984236i	$0.443405\pi$
$720$	26.3300	0.981261
$721$	−8.84375	−0.329359
$722$	8.56942	0.318921
$723$	28.4855	1.05939
$724$	−1.19256	−0.0443211
$725$	0.133196	0.00494677
$726$	−38.3924	−1.42488
$727$	−18.5659	−0.688570	−0.344285	−	0.938865i	$-0.611879\pi$
$727$	−18.5659	−0.688570	−0.344285	+	0.938865i	$0.611879\pi$
$728$	7.61736	0.282318
$729$	19.8430	0.734927
$730$	56.7066	2.09881
$731$	12.9195	0.477847
$732$	1.12055	0.0414169
$733$	−15.6695	−0.578766	−0.289383	−	0.957213i	$-0.593450\pi$
$733$	−15.6695	−0.578766	−0.289383	+	0.957213i	$0.593450\pi$
$734$	34.0807	1.25794
$735$	23.2682	0.858261
$736$	−5.27910	−0.194590
$737$	71.7830	2.64416
$738$	−28.4599	−1.04762
$739$	−28.5254	−1.04932	−0.524662	−	0.851311i	$-0.675808\pi$
$739$	−28.5254	−1.04932	−0.524662	+	0.851311i	$0.675808\pi$
$740$	8.79697	0.323383
$741$	−15.4685	−0.568251
$742$	−5.81043	−0.213308
$743$	11.7106	0.429618	0.214809	−	0.976656i	$-0.431087\pi$
$743$	11.7106	0.429618	0.214809	+	0.976656i	$0.431087\pi$
$744$	−15.7498	−0.577417
$745$	−47.2472	−1.73100
$746$	−56.6693	−2.07481
$747$	23.2112	0.849254
$748$	−1.39247	−0.0509137
$749$	18.4140	0.672834
$750$	−12.5380	−0.457824
$751$	−16.3236	−0.595658	−0.297829	−	0.954619i	$-0.596263\pi$
$751$	−16.3236	−0.595658	−0.297829	+	0.954619i	$0.596263\pi$
$752$	28.4815	1.03862
$753$	−17.7454	−0.646678
$754$	0.0767081	0.00279354
$755$	−6.19986	−0.225636
$756$	−1.35716	−0.0493593
$757$	−39.9794	−1.45307	−0.726537	−	0.687127i	$-0.758872\pi$
$757$	−39.9794	−1.45307	−0.726537	+	0.687127i	$0.758872\pi$
$758$	−51.7818	−1.88080
$759$	−25.6973	−0.932755
$760$	−45.5926	−1.65382
$761$	6.89777	0.250044	0.125022	−	0.992154i	$-0.460100\pi$
$761$	6.89777	0.250044	0.125022	+	0.992154i	$0.460100\pi$
$762$	−15.7597	−0.570913
$763$	−4.67270	−0.169163
$764$	1.09302	0.0395442
$765$	5.95321	0.215239
$766$	−2.91056	−0.105163
$767$	2.73906	0.0989017
$768$	−6.45866	−0.233057
$769$	−16.8633	−0.608105	−0.304053	−	0.952655i	$-0.598340\pi$
$769$	−16.8633	−0.608105	−0.304053	+	0.952655i	$0.598340\pi$
$770$	−31.8830	−1.14898
$771$	−9.20281	−0.331431
$772$	−1.40012	−0.0503913
$773$	−42.5941	−1.53200	−0.766001	−	0.642839i	$-0.777756\pi$
$773$	−42.5941	−1.53200	−0.766001	+	0.642839i	$0.777756\pi$
$774$	33.0690	1.18864
$775$	−37.4805	−1.34634
$776$	−5.44667	−0.195524
$777$	12.6118	0.452445
$778$	4.29331	0.153923
$779$	55.2880	1.98090
$780$	−2.60208	−0.0931694
$781$	2.99999	0.107348
$782$	−5.84373	−0.208972
$783$	0.100091	0.00357697
$784$	26.0290	0.929606
$785$	−21.5987	−0.770889
$786$	16.5844	0.591545
$787$	52.1825	1.86010	0.930052	−	0.367428i	$-0.119762\pi$
$787$	52.1825	1.86010	0.930052	+	0.367428i	$0.119762\pi$
$788$	6.00857	0.214046
$789$	29.1737	1.03861
$790$	−63.1449	−2.24659
$791$	10.5518	0.375180
$792$	26.1030	0.927529
$793$	−11.2472	−0.399399
$794$	21.3335	0.757099
$795$	−14.5363	−0.515550
$796$	−4.56192	−0.161693
$797$	−22.6728	−0.803111	−0.401555	−	0.915835i	$-0.631530\pi$
$797$	−22.6728	−0.803111	−0.401555	+	0.915835i	$0.631530\pi$
$798$	8.92498	0.315941
$799$	6.43968	0.227819
$800$	−9.62548	−0.340312
$801$	10.7036	0.378192
$802$	23.6231	0.834160
$803$	63.0705	2.22571
$804$	−3.38019	−0.119210
$805$	−14.3508	−0.505799
$806$	−21.5852	−0.760307
$807$	−14.7857	−0.520480
$808$	23.8344	0.838490
$809$	6.19707	0.217877	0.108939	−	0.994048i	$-0.465255\pi$
$809$	6.19707	0.217877	0.108939	+	0.994048i	$0.465255\pi$
$810$	−4.92506	−0.173049
$811$	−3.75368	−0.131809	−0.0659047	−	0.997826i	$-0.520993\pi$
$811$	−3.75368	−0.131809	−0.0659047	+	0.997826i	$0.520993\pi$
$812$	−0.00474691	−0.000166584 0
$813$	4.80510	0.168522
$814$	91.2250	3.19743
$815$	−25.8338	−0.904918
$816$	−5.02315	−0.175846
$817$	−64.2419	−2.24754
$818$	53.9955	1.88791
$819$	4.94576	0.172819
$820$	9.30040	0.324784
$821$	−1.41357	−0.0493338	−0.0246669	−	0.999696i	$-0.507853\pi$
$821$	−1.41357	−0.0493338	−0.0246669	+	0.999696i	$0.507853\pi$
$822$	−2.49722	−0.0871005
$823$	−27.1150	−0.945168	−0.472584	−	0.881286i	$-0.656679\pi$
$823$	−27.1150	−0.945168	−0.472584	+	0.881286i	$0.656679\pi$
$824$	−22.0609	−0.768529
$825$	−46.8544	−1.63126
$826$	−1.58037	−0.0549881
$827$	39.0234	1.35698	0.678489	−	0.734611i	$-0.262635\pi$
$827$	39.0234	1.35698	0.678489	+	0.734611i	$0.262635\pi$
$828$	−1.60427	−0.0557521
$829$	−21.5997	−0.750189	−0.375095	−	0.926986i	$-0.622390\pi$
$829$	−21.5997	−0.750189	−0.375095	+	0.926986i	$0.622390\pi$
$830$	−70.7220	−2.45479
$831$	−29.9282	−1.03820
$832$	18.6854	0.647799
$833$	5.88515	0.203908
$834$	15.7893	0.546740
$835$	−19.8263	−0.686119
$836$	6.92399	0.239471
$837$	−28.1651	−0.973529
$838$	16.1376	0.557464
$839$	18.0850	0.624364	0.312182	−	0.950022i	$-0.398940\pi$
$839$	18.0850	0.624364	0.312182	+	0.950022i	$0.398940\pi$
$840$	−10.9953	−0.379375
$841$	−28.9996	−0.999988
$842$	−38.2456	−1.31803
$843$	4.89503	0.168594
$844$	1.71030	0.0588711
$845$	−19.1381	−0.658369
$846$	16.4831	0.566700
$847$	−23.8466	−0.819377
$848$	−16.2611	−0.558407
$849$	2.59019	0.0888949
$850$	−10.6550	−0.365463
$851$	41.0611	1.40756
$852$	−0.141266	−0.00483970
$853$	−29.8900	−1.02342	−0.511708	−	0.859160i	$-0.670987\pi$
$853$	−29.8900	−1.02342	−0.511708	+	0.859160i	$0.670987\pi$
$854$	6.48935	0.222061
$855$	−29.6021	−1.01237
$856$	45.9342	1.57000
$857$	25.5471	0.872673	0.436336	−	0.899784i	$-0.356276\pi$
$857$	25.5471	0.872673	0.436336	+	0.899784i	$0.356276\pi$
$858$	−26.9837	−0.921208
$859$	5.12105	0.174728	0.0873639	−	0.996176i	$-0.472156\pi$
$859$	5.12105	0.174728	0.0873639	+	0.996176i	$0.472156\pi$
$860$	−10.8066	−0.368502
$861$	13.3335	0.454405
$862$	37.4658	1.27609
$863$	−23.5924	−0.803094	−0.401547	−	0.915838i	$-0.631527\pi$
$863$	−23.5924	−0.803094	−0.401547	+	0.915838i	$0.631527\pi$
$864$	−7.23316	−0.246077
$865$	−33.5573	−1.14098
$866$	−47.8641	−1.62649
$867$	−1.13573	−0.0385716
$868$	1.33575	0.0453384
$869$	−70.2313	−2.38243
$870$	−0.110725	−0.00375392
$871$	33.9275	1.14959
$872$	−11.6562	−0.394727
$873$	−3.53638	−0.119688
$874$	29.0577	0.982892
$875$	−7.78771	−0.263273
$876$	−2.96992	−0.100344
$877$	−45.1884	−1.52591	−0.762953	−	0.646454i	$-0.776251\pi$
$877$	−45.1884	−1.52591	−0.762953	+	0.646454i	$0.776251\pi$
$878$	−17.6175	−0.594562
$879$	−22.1719	−0.747838
$880$	−89.2277	−3.00786
$881$	43.8128	1.47609	0.738045	−	0.674751i	$-0.235749\pi$
$881$	43.8128	1.47609	0.738045	+	0.674751i	$0.235749\pi$
$882$	15.0637	0.507221
$883$	−12.5654	−0.422858	−0.211429	−	0.977393i	$-0.567812\pi$
$883$	−12.5654	−0.422858	−0.211429	+	0.977393i	$0.567812\pi$
$884$	−0.658136	−0.0221355
$885$	−3.95371	−0.132903
$886$	−37.0617	−1.24511
$887$	14.4125	0.483924	0.241962	−	0.970286i	$-0.422209\pi$
$887$	14.4125	0.483924	0.241962	+	0.970286i	$0.422209\pi$
$888$	31.4603	1.05574
$889$	−9.78877	−0.328305
$890$	−32.6126	−1.09318
$891$	−5.47777	−0.183512
$892$	4.07606	0.136477
$893$	−32.0210	−1.07154
$894$	23.0715	0.771626
$895$	−23.3952	−0.782014
$896$	−13.6364	−0.455559
$897$	−12.1456	−0.405529
$898$	33.9239	1.13205
$899$	−0.0985128	−0.00328559
$900$	−2.92509	−0.0975029
$901$	−3.67662	−0.122486
$902$	96.4456	3.21129
$903$	−15.4929	−0.515571
$904$	26.3218	0.875449
$905$	−17.2780	−0.574341
$906$	3.02748	0.100581
$907$	43.2520	1.43616	0.718080	−	0.695961i	$-0.245021\pi$
$907$	43.2520	1.43616	0.718080	+	0.695961i	$0.245021\pi$
$908$	−5.45319	−0.180970
$909$	15.4750	0.513274
$910$	−15.0692	−0.499538
$911$	−31.5231	−1.04441	−0.522203	−	0.852821i	$-0.674890\pi$
$911$	−31.5231	−1.04441	−0.522203	+	0.852821i	$0.674890\pi$
$912$	24.9774	0.827085
$913$	−78.6587	−2.60322
$914$	−28.1641	−0.931586
$915$	16.2348	0.536707
$916$	−0.653149	−0.0215806
$917$	10.3010	0.340169
$918$	−8.00679	−0.264264
$919$	14.1709	0.467455	0.233728	−	0.972302i	$-0.424908\pi$
$919$	14.1709	0.467455	0.233728	+	0.972302i	$0.424908\pi$
$920$	−35.7983	−1.18024
$921$	−25.2096	−0.830683
$922$	62.7424	2.06631
$923$	1.41791	0.0466711
$924$	1.66982	0.0549332
$925$	74.8674	2.46163
$926$	−1.07871	−0.0354485
$927$	−14.3236	−0.470448
$928$	−0.0252993	−0.000830492 0
$929$	−26.0007	−0.853055	−0.426527	−	0.904475i	$-0.640263\pi$
$929$	−26.0007	−0.853055	−0.426527	+	0.904475i	$0.640263\pi$
$930$	31.1573	1.02169
$931$	−29.2637	−0.959078
$932$	4.65759	0.152564
$933$	23.0398	0.754288
$934$	48.4097	1.58401
$935$	−20.1744	−0.659773
$936$	12.3373	0.403257
$937$	46.8802	1.53151	0.765755	−	0.643133i	$-0.222366\pi$
$937$	46.8802	1.53151	0.765755	+	0.643133i	$0.222366\pi$
$938$	−19.5753	−0.639157
$939$	−20.3505	−0.664112
$940$	−5.38650	−0.175688
$941$	−41.8125	−1.36305	−0.681525	−	0.731795i	$-0.738683\pi$
$941$	−41.8125	−1.36305	−0.681525	+	0.731795i	$0.738683\pi$
$942$	10.5469	0.343638
$943$	43.4109	1.41365
$944$	−4.42282	−0.143951
$945$	−19.6627	−0.639629
$946$	−112.065	−3.64355
$947$	−11.5707	−0.375996	−0.187998	−	0.982169i	$-0.560200\pi$
$947$	−11.5707	−0.375996	−0.187998	+	0.982169i	$0.560200\pi$
$948$	3.30712	0.107410
$949$	29.8096	0.967660
$950$	52.9815	1.71895
$951$	−3.48682	−0.113068
$952$	−2.78101	−0.0901332
$953$	−4.58120	−0.148399	−0.0741997	−	0.997243i	$-0.523640\pi$
$953$	−4.58120	−0.148399	−0.0741997	+	0.997243i	$0.523640\pi$
$954$	−9.41073	−0.304684
$955$	15.8360	0.512440
$956$	−1.54049	−0.0498231
$957$	−0.123151	−0.00398090
$958$	−54.9648	−1.77583
$959$	−1.55109	−0.0500873
$960$	−26.9716	−0.870503
$961$	−3.27905	−0.105776
$962$	43.1165	1.39013
$963$	29.8239	0.961060
$964$	−6.02644	−0.194098
$965$	−20.2852	−0.653002
$966$	7.00770	0.225469
$967$	−36.8425	−1.18477	−0.592387	−	0.805654i	$-0.701814\pi$
$967$	−36.8425	−1.18477	−0.592387	+	0.805654i	$0.701814\pi$
$968$	−59.4857	−1.91194
$969$	5.64739	0.181420
$970$	10.7750	0.345963
$971$	16.1285	0.517588	0.258794	−	0.965933i	$-0.416675\pi$
$971$	16.1285	0.517588	0.258794	+	0.965933i	$0.416675\pi$
$972$	−3.59811	−0.115409
$973$	9.80719	0.314404
$974$	−6.15158	−0.197109
$975$	−22.1452	−0.709215
$976$	18.1611	0.581322
$977$	−18.0497	−0.577460	−0.288730	−	0.957411i	$-0.593233\pi$
$977$	−18.0497	−0.577460	−0.288730	+	0.957411i	$0.593233\pi$
$978$	12.6150	0.403384
$979$	−36.2725	−1.15927
$980$	−4.92266	−0.157249
$981$	−7.56804	−0.241629
$982$	54.0665	1.72533
$983$	54.8257	1.74867	0.874334	−	0.485324i	$-0.161299\pi$
$983$	54.8257	1.74867	0.874334	+	0.485324i	$0.161299\pi$
$984$	33.2607	1.06031
$985$	87.0533	2.77375
$986$	−0.0280053	−0.000891869 0
$987$	−7.72235	−0.245805
$988$	3.27255	0.104114
$989$	−50.4414	−1.60394
$990$	−51.6386	−1.64118
$991$	−41.7053	−1.32481	−0.662407	−	0.749145i	$-0.730465\pi$
$991$	−41.7053	−1.32481	−0.662407	+	0.749145i	$0.730465\pi$
$992$	7.11909	0.226031
$993$	−23.4645	−0.744622
$994$	−0.818100	−0.0259486
$995$	−66.0941	−2.09532
$996$	3.70396	0.117364
$997$	4.99092	0.158064	0.0790320	−	0.996872i	$-0.474817\pi$
$997$	4.99092	0.158064	0.0790320	+	0.996872i	$0.474817\pi$
$998$	−13.7669	−0.435783
$999$	56.2599	1.77998

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1003.2.a.j.1.15	✓	22
3.2	odd	2		9027.2.a.s.1.8		22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1003.2.a.j.1.15	✓	22	1.1	even	1	trivial
9027.2.a.s.1.8		22	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:	\( N \)	\(=\)	\( 1003 = 17 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1003.a (trivial)

\(f(q)\)	\(=\)	\(q+1.49676 q^{2} -1.13573 q^{3} +0.240278 q^{4} +3.48120 q^{5} -1.69992 q^{6} -1.05586 q^{7} -2.63387 q^{8} -1.71011 q^{9} +O(q^{10})\)	\(q+1.49676 q^{2} -1.13573 q^{3} +0.240278 q^{4} +3.48120 q^{5} -1.69992 q^{6} -1.05586 q^{7} -2.63387 q^{8} -1.71011 q^{9} +5.21050 q^{10} +5.79524 q^{11} -0.272892 q^{12} +2.73906 q^{13} -1.58037 q^{14} -3.95371 q^{15} -4.42282 q^{16} -1.00000 q^{17} -2.55961 q^{18} +4.97246 q^{19} +0.836454 q^{20} +1.19918 q^{21} +8.67407 q^{22} +3.90427 q^{23} +2.99138 q^{24} +7.11872 q^{25} +4.09970 q^{26} +5.34943 q^{27} -0.253701 q^{28} +0.0187106 q^{29} -5.91775 q^{30} -5.26507 q^{31} -1.35214 q^{32} -6.58186 q^{33} -1.49676 q^{34} -3.67567 q^{35} -0.410901 q^{36} +10.5170 q^{37} +7.44255 q^{38} -3.11085 q^{39} -9.16903 q^{40} +11.1188 q^{41} +1.79488 q^{42} -12.9195 q^{43} +1.39247 q^{44} -5.95321 q^{45} +5.84373 q^{46} -6.43968 q^{47} +5.02315 q^{48} -5.88515 q^{49} +10.6550 q^{50} +1.13573 q^{51} +0.658136 q^{52} +3.67662 q^{53} +8.00679 q^{54} +20.1744 q^{55} +2.78101 q^{56} -5.64739 q^{57} +0.0280053 q^{58} +1.00000 q^{59} -0.949990 q^{60} -4.10622 q^{61} -7.88052 q^{62} +1.80564 q^{63} +6.82183 q^{64} +9.53520 q^{65} -9.85144 q^{66} +12.3865 q^{67} -0.240278 q^{68} -4.43421 q^{69} -5.50158 q^{70} +0.517663 q^{71} +4.50420 q^{72} +10.8831 q^{73} +15.7414 q^{74} -8.08498 q^{75} +1.19477 q^{76} -6.11899 q^{77} -4.65618 q^{78} -12.1188 q^{79} -15.3967 q^{80} -0.945219 q^{81} +16.6422 q^{82} -13.5730 q^{83} +0.288137 q^{84} -3.48120 q^{85} -19.3374 q^{86} -0.0212503 q^{87} -15.2639 q^{88} -6.25901 q^{89} -8.91051 q^{90} -2.89208 q^{91} +0.938109 q^{92} +5.97972 q^{93} -9.63862 q^{94} +17.3101 q^{95} +1.53567 q^{96} +2.06793 q^{97} -8.80863 q^{98} -9.91048 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + 5 q^{2} + 7 q^{3} + 25 q^{4} + 19 q^{5} + 5 q^{6} + 3 q^{7} + 21 q^{8} + 31 q^{9}+O(q^{10}) \) 22 * q + 5 * q^2 + 7 * q^3 + 25 * q^4 + 19 * q^5 + 5 * q^6 + 3 * q^7 + 21 * q^8 + 31 * q^9	\( 22 q + 5 q^{2} + 7 q^{3} + 25 q^{4} + 19 q^{5} + 5 q^{6} + 3 q^{7} + 21 q^{8} + 31 q^{9} + 8 q^{11} + 20 q^{12} + 14 q^{13} + 5 q^{14} + 15 q^{15} + 23 q^{16} - 22 q^{17} + 6 q^{18} + 6 q^{19} + 43 q^{20} + 8 q^{21} - 8 q^{22} + 15 q^{23} - 9 q^{24} + 33 q^{25} + 9 q^{26} + 25 q^{27} + 11 q^{28} - q^{29} - 51 q^{30} - 9 q^{31} + 37 q^{32} + 21 q^{33} - 5 q^{34} + 29 q^{35} + 30 q^{36} - 2 q^{37} + 39 q^{38} + 4 q^{39} + 4 q^{40} + 21 q^{41} - 65 q^{42} + q^{43} + 17 q^{44} + 65 q^{45} - 39 q^{46} + 37 q^{47} + 15 q^{48} + 25 q^{49} - 48 q^{50} - 7 q^{51} + 7 q^{52} + 69 q^{53} + 13 q^{54} + 10 q^{55} - 33 q^{56} - 4 q^{57} + 4 q^{58} + 22 q^{59} + 18 q^{60} - 29 q^{61} + 29 q^{62} + 7 q^{63} - 3 q^{64} + 25 q^{65} - 16 q^{66} - 10 q^{67} - 25 q^{68} + 26 q^{69} + 29 q^{70} + 3 q^{71} + 53 q^{72} - 4 q^{73} + 13 q^{74} - 8 q^{75} - 13 q^{76} + 71 q^{77} + 11 q^{78} - 20 q^{79} - 9 q^{80} + 42 q^{81} + 11 q^{82} + 24 q^{83} - 92 q^{84} - 19 q^{85} - 10 q^{86} - 4 q^{87} + 2 q^{88} + 40 q^{89} - 78 q^{90} - 31 q^{91} - 39 q^{92} + 53 q^{93} + 32 q^{94} + 42 q^{95} - 36 q^{96} + 13 q^{97} - 15 q^{98} - 64 q^{99}+O(q^{100}) \) 22 * q + 5 * q^2 + 7 * q^3 + 25 * q^4 + 19 * q^5 + 5 * q^6 + 3 * q^7 + 21 * q^8 + 31 * q^9 + 8 * q^11 + 20 * q^12 + 14 * q^13 + 5 * q^14 + 15 * q^15 + 23 * q^16 - 22 * q^17 + 6 * q^18 + 6 * q^19 + 43 * q^20 + 8 * q^21 - 8 * q^22 + 15 * q^23 - 9 * q^24 + 33 * q^25 + 9 * q^26 + 25 * q^27 + 11 * q^28 - q^29 - 51 * q^30 - 9 * q^31 + 37 * q^32 + 21 * q^33 - 5 * q^34 + 29 * q^35 + 30 * q^36 - 2 * q^37 + 39 * q^38 + 4 * q^39 + 4 * q^40 + 21 * q^41 - 65 * q^42 + q^43 + 17 * q^44 + 65 * q^45 - 39 * q^46 + 37 * q^47 + 15 * q^48 + 25 * q^49 - 48 * q^50 - 7 * q^51 + 7 * q^52 + 69 * q^53 + 13 * q^54 + 10 * q^55 - 33 * q^56 - 4 * q^57 + 4 * q^58 + 22 * q^59 + 18 * q^60 - 29 * q^61 + 29 * q^62 + 7 * q^63 - 3 * q^64 + 25 * q^65 - 16 * q^66 - 10 * q^67 - 25 * q^68 + 26 * q^69 + 29 * q^70 + 3 * q^71 + 53 * q^72 - 4 * q^73 + 13 * q^74 - 8 * q^75 - 13 * q^76 + 71 * q^77 + 11 * q^78 - 20 * q^79 - 9 * q^80 + 42 * q^81 + 11 * q^82 + 24 * q^83 - 92 * q^84 - 19 * q^85 - 10 * q^86 - 4 * q^87 + 2 * q^88 + 40 * q^89 - 78 * q^90 - 31 * q^91 - 39 * q^92 + 53 * q^93 + 32 * q^94 + 42 * q^95 - 36 * q^96 + 13 * q^97 - 15 * q^98 - 64 * q^99

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