LMFDB - Embedded newform 1003.2.a.g.1.4

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:	$1$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 3x^{9} - 10x^{8} + 34x^{7} + 28x^{6} - 129x^{5} - 3x^{4} + 178x^{3} - 56x^{2} - 56x + 15 $ x^10 - 3x^9 - 10x^8 + 34x^7 + 28x^6 - 129x^5 - 3x^4 + 178x^3 - 56x^2 - 56*x + 15
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$2.40612$ of defining polynomial
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)

$f(q)$	$=$	$q-1.85341 q^{2} +1.40612 q^{3} +1.43512 q^{4} -4.08879 q^{5} -2.60611 q^{6} +1.71195 q^{7} +1.04695 q^{8} -1.02283 q^{9} +O(q^{10})$	\(q-1.85341 q^{2} +1.40612 q^{3} +1.43512 q^{4} -4.08879 q^{5} -2.60611 q^{6} +1.71195 q^{7} +1.04695 q^{8} -1.02283 q^{9} +7.57819 q^{10} +5.46364 q^{11} +2.01795 q^{12} -5.16830 q^{13} -3.17294 q^{14} -5.74932 q^{15} -4.81067 q^{16} -1.00000 q^{17} +1.89573 q^{18} +6.66287 q^{19} -5.86790 q^{20} +2.40720 q^{21} -10.1264 q^{22} -6.04349 q^{23} +1.47214 q^{24} +11.7182 q^{25} +9.57897 q^{26} -5.65658 q^{27} +2.45685 q^{28} -1.29232 q^{29} +10.6558 q^{30} +7.77684 q^{31} +6.82223 q^{32} +7.68252 q^{33} +1.85341 q^{34} -6.99979 q^{35} -1.46789 q^{36} -2.94870 q^{37} -12.3490 q^{38} -7.26724 q^{39} -4.28076 q^{40} -8.37108 q^{41} -4.46153 q^{42} -4.55240 q^{43} +7.84098 q^{44} +4.18214 q^{45} +11.2011 q^{46} -3.75306 q^{47} -6.76437 q^{48} -4.06923 q^{49} -21.7186 q^{50} -1.40612 q^{51} -7.41714 q^{52} -9.86414 q^{53} +10.4839 q^{54} -22.3397 q^{55} +1.79233 q^{56} +9.36878 q^{57} +2.39520 q^{58} -1.00000 q^{59} -8.25096 q^{60} +3.09075 q^{61} -14.4137 q^{62} -1.75104 q^{63} -3.02303 q^{64} +21.1321 q^{65} -14.2388 q^{66} +6.99881 q^{67} -1.43512 q^{68} -8.49786 q^{69} +12.9735 q^{70} -9.77171 q^{71} -1.07086 q^{72} -8.11872 q^{73} +5.46515 q^{74} +16.4771 q^{75} +9.56202 q^{76} +9.35347 q^{77} +13.4692 q^{78} -3.50389 q^{79} +19.6698 q^{80} -4.88532 q^{81} +15.5150 q^{82} -6.36095 q^{83} +3.45463 q^{84} +4.08879 q^{85} +8.43745 q^{86} -1.81716 q^{87} +5.72017 q^{88} -5.97929 q^{89} -7.75122 q^{90} -8.84787 q^{91} -8.67314 q^{92} +10.9352 q^{93} +6.95594 q^{94} -27.2430 q^{95} +9.59286 q^{96} +6.81606 q^{97} +7.54194 q^{98} -5.58839 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - q^{2} - 7 q^{3} + 15 q^{4} - 12 q^{5} + 5 q^{6} - 9 q^{7} - 12 q^{8} + 3 q^{9}+O(q^{10}) $ 10 * q - q^2 - 7 * q^3 + 15 * q^4 - 12 * q^5 + 5 * q^6 - 9 * q^7 - 12 * q^8 + 3 * q^9	\( 10 q - q^{2} - 7 q^{3} + 15 q^{4} - 12 q^{5} + 5 q^{6} - 9 q^{7} - 12 q^{8} + 3 q^{9} + 4 q^{10} + 12 q^{11} - 24 q^{12} - 11 q^{13} - 12 q^{14} + 9 q^{15} - 3 q^{16} - 10 q^{17} - 22 q^{18} - 5 q^{19} - 36 q^{20} - 10 q^{21} + 6 q^{22} - 7 q^{23} + 35 q^{24} + 2 q^{25} + q^{26} - 31 q^{27} - 4 q^{28} + 10 q^{29} - 9 q^{30} + 13 q^{31} - 15 q^{32} - 9 q^{33} + q^{34} - 8 q^{35} + 40 q^{36} + 12 q^{37} - 50 q^{38} + 24 q^{39} + 5 q^{40} - 29 q^{41} - 17 q^{42} - 18 q^{43} - 6 q^{44} - 14 q^{45} + 11 q^{46} - 18 q^{47} - 43 q^{48} - 9 q^{49} - 31 q^{50} + 7 q^{51} - 68 q^{52} + 19 q^{54} - 27 q^{55} - 7 q^{56} + 20 q^{57} + 23 q^{58} - 10 q^{59} + 38 q^{60} + 8 q^{61} - 46 q^{62} + 39 q^{63} - 20 q^{64} + 58 q^{65} - 34 q^{66} - 6 q^{67} - 15 q^{68} + 6 q^{69} + 73 q^{70} + 8 q^{71} - 70 q^{72} - 41 q^{73} - 10 q^{74} + 10 q^{75} + 12 q^{76} - 22 q^{77} - 43 q^{78} + 3 q^{79} - 15 q^{80} + 26 q^{81} + 8 q^{82} - 22 q^{84} + 12 q^{85} - 29 q^{86} - 28 q^{87} + 33 q^{88} - 45 q^{89} + 56 q^{90} - 14 q^{91} + 36 q^{92} - 19 q^{93} + 15 q^{94} - 17 q^{95} + 90 q^{96} - 5 q^{97} + 30 q^{98} + 14 q^{99}+O(q^{100}) \) 10 * q - q^2 - 7 * q^3 + 15 * q^4 - 12 * q^5 + 5 * q^6 - 9 * q^7 - 12 * q^8 + 3 * q^9 + 4 * q^10 + 12 * q^11 - 24 * q^12 - 11 * q^13 - 12 * q^14 + 9 * q^15 - 3 * q^16 - 10 * q^17 - 22 * q^18 - 5 * q^19 - 36 * q^20 - 10 * q^21 + 6 * q^22 - 7 * q^23 + 35 * q^24 + 2 * q^25 + q^26 - 31 * q^27 - 4 * q^28 + 10 * q^29 - 9 * q^30 + 13 * q^31 - 15 * q^32 - 9 * q^33 + q^34 - 8 * q^35 + 40 * q^36 + 12 * q^37 - 50 * q^38 + 24 * q^39 + 5 * q^40 - 29 * q^41 - 17 * q^42 - 18 * q^43 - 6 * q^44 - 14 * q^45 + 11 * q^46 - 18 * q^47 - 43 * q^48 - 9 * q^49 - 31 * q^50 + 7 * q^51 - 68 * q^52 + 19 * q^54 - 27 * q^55 - 7 * q^56 + 20 * q^57 + 23 * q^58 - 10 * q^59 + 38 * q^60 + 8 * q^61 - 46 * q^62 + 39 * q^63 - 20 * q^64 + 58 * q^65 - 34 * q^66 - 6 * q^67 - 15 * q^68 + 6 * q^69 + 73 * q^70 + 8 * q^71 - 70 * q^72 - 41 * q^73 - 10 * q^74 + 10 * q^75 + 12 * q^76 - 22 * q^77 - 43 * q^78 + 3 * q^79 - 15 * q^80 + 26 * q^81 + 8 * q^82 - 22 * q^84 + 12 * q^85 - 29 * q^86 - 28 * q^87 + 33 * q^88 - 45 * q^89 + 56 * q^90 - 14 * q^91 + 36 * q^92 - 19 * q^93 + 15 * q^94 - 17 * q^95 + 90 * q^96 - 5 * q^97 + 30 * q^98 + 14 * 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 $

$2$	−1.85341	−1.31056	−0.655279	−	0.755387i	$-0.727449\pi$
$2$	−1.85341	−1.31056	−0.655279	+	0.755387i	$0.727449\pi$
$3$	1.40612	0.811823	0.405911	−	0.913912i	$-0.366954\pi$
$3$	1.40612	0.811823	0.405911	+	0.913912i	$0.366954\pi$
$4$	1.43512	0.717560
$5$	−4.08879	−1.82856	−0.914280	−	0.405082i	$-0.867243\pi$
$5$	−4.08879	−1.82856	−0.914280	+	0.405082i	$0.867243\pi$
$6$	−2.60611	−1.06394
$7$	1.71195	0.647056	0.323528	−	0.946219i	$-0.395131\pi$
$7$	1.71195	0.647056	0.323528	+	0.946219i	$0.395131\pi$
$8$	1.04695	0.370153
$9$	−1.02283	−0.340944
$10$	7.57819	2.39643
$11$	5.46364	1.64735	0.823675	−	0.567063i	$-0.191920\pi$
$11$	5.46364	1.64735	0.823675	+	0.567063i	$0.191920\pi$
$12$	2.01795	0.582532
$13$	−5.16830	−1.43343	−0.716715	−	0.697367i	$-0.754355\pi$
$13$	−5.16830	−1.43343	−0.716715	+	0.697367i	$0.754355\pi$
$14$	−3.17294	−0.848004
$15$	−5.74932	−1.48447
$16$	−4.81067	−1.20267
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	1.89573	0.446827
$19$	6.66287	1.52857	0.764283	−	0.644881i	$-0.223093\pi$
$19$	6.66287	1.52857	0.764283	+	0.644881i	$0.223093\pi$
$20$	−5.86790	−1.31210
$21$	2.40720	0.525295
$22$	−10.1264	−2.15895
$23$	−6.04349	−1.26015	−0.630077	−	0.776532i	$-0.716977\pi$
$23$	−6.04349	−1.26015	−0.630077	+	0.776532i	$0.716977\pi$
$24$	1.47214	0.300499
$25$	11.7182	2.34363
$26$	9.57897	1.87859
$27$	−5.65658	−1.08861
$28$	2.45685	0.464302
$29$	−1.29232	−0.239979	−0.119989	−	0.992775i	$-0.538286\pi$
$29$	−1.29232	−0.239979	−0.119989	+	0.992775i	$0.538286\pi$
$30$	10.6558	1.94548
$31$	7.77684	1.39676	0.698381	−	0.715726i	$-0.253904\pi$
$31$	7.77684	1.39676	0.698381	+	0.715726i	$0.253904\pi$
$32$	6.82223	1.20601
$33$	7.68252	1.33736
$34$	1.85341	0.317857
$35$	−6.99979	−1.18318
$36$	−1.46789	−0.244648
$37$	−2.94870	−0.484764	−0.242382	−	0.970181i	$-0.577929\pi$
$37$	−2.94870	−0.484764	−0.242382	+	0.970181i	$0.577929\pi$
$38$	−12.3490	−2.00327
$39$	−7.26724	−1.16369
$40$	−4.28076	−0.676848
$41$	−8.37108	−1.30734	−0.653671	−	0.756779i	$-0.726772\pi$
$41$	−8.37108	−1.30734	−0.653671	+	0.756779i	$0.726772\pi$
$42$	−4.46153	−0.688429
$43$	−4.55240	−0.694234	−0.347117	−	0.937822i	$-0.612839\pi$
$43$	−4.55240	−0.694234	−0.347117	+	0.937822i	$0.612839\pi$
$44$	7.84098	1.18207
$45$	4.18214	0.623437
$46$	11.2011	1.65151
$47$	−3.75306	−0.547440	−0.273720	−	0.961809i	$-0.588254\pi$
$47$	−3.75306	−0.547440	−0.273720	+	0.961809i	$0.588254\pi$
$48$	−6.76437	−0.976353
$49$	−4.06923	−0.581319
$50$	−21.7186	−3.07147
$51$	−1.40612	−0.196896
$52$	−7.41714	−1.02857
$53$	−9.86414	−1.35494	−0.677472	−	0.735549i	$-0.736924\pi$
$53$	−9.86414	−1.35494	−0.677472	+	0.735549i	$0.736924\pi$
$54$	10.4839	1.42668
$55$	−22.3397	−3.01228
$56$	1.79233	0.239510
$57$	9.36878	1.24092
$58$	2.39520	0.314506
$59$	−1.00000	−0.130189
$59$	−1.00000	−0.130189
$60$	−8.25096	−1.06519
$61$	3.09075	0.395730	0.197865	−	0.980229i	$-0.436599\pi$
$61$	3.09075	0.395730	0.197865	+	0.980229i	$0.436599\pi$
$62$	−14.4137	−1.83054
$63$	−1.75104	−0.220610
$64$	−3.02303	−0.377879
$65$	21.1321	2.62111
$66$	−14.2388	−1.75268
$67$	6.99881	0.855041	0.427520	−	0.904006i	$-0.359387\pi$
$67$	6.99881	0.855041	0.427520	+	0.904006i	$0.359387\pi$
$68$	−1.43512	−0.174034
$69$	−8.49786	−1.02302
$70$	12.9735	1.55063
$71$	−9.77171	−1.15969	−0.579844	−	0.814727i	$-0.696887\pi$
$71$	−9.77171	−1.15969	−0.579844	+	0.814727i	$0.696887\pi$
$72$	−1.07086	−0.126202
$73$	−8.11872	−0.950224	−0.475112	−	0.879925i	$-0.657592\pi$
$73$	−8.11872	−0.950224	−0.475112	+	0.879925i	$0.657592\pi$
$74$	5.46515	0.635311
$75$	16.4771	1.90262
$76$	9.56202	1.09684
$77$	9.35347	1.06593
$78$	13.4692	1.52508
$79$	−3.50389	−0.394219	−0.197109	−	0.980381i	$-0.563155\pi$
$79$	−3.50389	−0.394219	−0.197109	+	0.980381i	$0.563155\pi$
$80$	19.6698	2.19915
$81$	−4.88532	−0.542813
$82$	15.5150	1.71335
$83$	−6.36095	−0.698205	−0.349102	−	0.937085i	$-0.613513\pi$
$83$	−6.36095	−0.698205	−0.349102	+	0.937085i	$0.613513\pi$
$84$	3.45463	0.376931
$85$	4.08879	0.443491
$86$	8.43745	0.909833
$87$	−1.81716	−0.194820
$88$	5.72017	0.609772
$89$	−5.97929	−0.633804	−0.316902	−	0.948458i	$-0.602643\pi$
$89$	−5.97929	−0.633804	−0.316902	+	0.948458i	$0.602643\pi$
$90$	−7.75122	−0.817050
$91$	−8.84787	−0.927509
$92$	−8.67314	−0.904237
$93$	10.9352	1.13392
$94$	6.95594	0.717451
$95$	−27.2430	−2.79508
$96$	9.59286	0.979067
$97$	6.81606	0.692066	0.346033	−	0.938222i	$-0.387529\pi$
$97$	6.81606	0.692066	0.346033	+	0.938222i	$0.387529\pi$
$98$	7.54194	0.761851
$99$	−5.58839	−0.561654
$100$	16.8170	1.68170
$101$	−12.8081	−1.27445	−0.637225	−	0.770678i	$-0.719918\pi$
$101$	−12.8081	−1.27445	−0.637225	+	0.770678i	$0.719918\pi$
$102$	2.60611	0.258043
$103$	−11.3542	−1.11876	−0.559382	−	0.828910i	$-0.688961\pi$
$103$	−11.3542	−1.11876	−0.559382	+	0.828910i	$0.688961\pi$
$104$	−5.41096	−0.530589
$105$	−9.84253	−0.960533
$106$	18.2823	1.77573
$107$	−18.1489	−1.75452	−0.877261	−	0.480013i	$-0.840632\pi$
$107$	−18.1489	−1.75452	−0.877261	+	0.480013i	$0.840632\pi$
$108$	−8.11787	−0.781142
$109$	0.200397	0.0191945	0.00959726	−	0.999954i	$-0.496945\pi$
$109$	0.200397	0.0191945	0.00959726	+	0.999954i	$0.496945\pi$
$110$	41.4045	3.94776
$111$	−4.14622	−0.393542
$112$	−8.23562	−0.778193
$113$	16.5677	1.55856	0.779281	−	0.626674i	$-0.215584\pi$
$113$	16.5677	1.55856	0.779281	+	0.626674i	$0.215584\pi$
$114$	−17.3642	−1.62630
$115$	24.7105	2.30427
$116$	−1.85464	−0.172199
$117$	5.28631	0.488719
$118$	1.85341	0.170620
$119$	−1.71195	−0.156934
$120$	−6.01926	−0.549480
$121$	18.8514	1.71376
$122$	−5.72842	−0.518627
$123$	−11.7707	−1.06133
$124$	11.1607	1.00226
$125$	−27.4692	−2.45692
$126$	3.24539	0.289122
$127$	−0.297171	−0.0263696	−0.0131848	−	0.999913i	$-0.504197\pi$
$127$	−0.297171	−0.0263696	−0.0131848	+	0.999913i	$0.504197\pi$
$128$	−8.04154	−0.710779
$129$	−6.40121	−0.563595
$130$	−39.1664	−3.43512
$131$	−7.67851	−0.670874	−0.335437	−	0.942063i	$-0.608884\pi$
$131$	−7.67851	−0.670874	−0.335437	+	0.942063i	$0.608884\pi$
$132$	11.0253	0.959633
$133$	11.4065	0.989068
$134$	−12.9717	−1.12058
$135$	23.1285	1.99059
$136$	−1.04695	−0.0897754
$137$	0.881599	0.0753201	0.0376600	−	0.999291i	$-0.488010\pi$
$137$	0.881599	0.0753201	0.0376600	+	0.999291i	$0.488010\pi$
$138$	15.7500	1.34073
$139$	13.5252	1.14720	0.573598	−	0.819137i	$-0.305547\pi$
$139$	13.5252	1.14720	0.573598	+	0.819137i	$0.305547\pi$
$140$	−10.0455	−0.849004
$141$	−5.27724	−0.444424
$142$	18.1110	1.51984
$143$	−28.2377	−2.36136
$144$	4.92051	0.410042
$145$	5.28404	0.438815
$146$	15.0473	1.24532
$147$	−5.72182	−0.471928
$148$	−4.23174	−0.347847
$149$	1.53029	0.125366	0.0626831	−	0.998033i	$-0.480034\pi$
$149$	1.53029	0.125366	0.0626831	+	0.998033i	$0.480034\pi$
$150$	−30.5388	−2.49349
$151$	−11.2764	−0.917663	−0.458831	−	0.888523i	$-0.651732\pi$
$151$	−11.2764	−0.917663	−0.458831	+	0.888523i	$0.651732\pi$
$152$	6.97570	0.565804
$153$	1.02283	0.0826911
$154$	−17.3358	−1.39696
$155$	−31.7978	−2.55406
$156$	−10.4294	−0.835018
$157$	5.03548	0.401875	0.200938	−	0.979604i	$-0.435601\pi$
$157$	5.03548	0.401875	0.200938	+	0.979604i	$0.435601\pi$
$158$	6.49414	0.516646
$159$	−13.8701	−1.09997
$160$	−27.8946	−2.20526
$161$	−10.3461	−0.815391
$162$	9.05448	0.711387
$163$	−23.1844	−1.81594	−0.907972	−	0.419031i	$-0.862370\pi$
$163$	−23.1844	−1.81594	−0.907972	+	0.419031i	$0.862370\pi$
$164$	−12.0135	−0.938097
$165$	−31.4122	−2.44544
$166$	11.7894	0.915037
$167$	4.12008	0.318822	0.159411	−	0.987212i	$-0.449041\pi$
$167$	4.12008	0.318822	0.159411	+	0.987212i	$0.449041\pi$
$168$	2.52022	0.194440
$169$	13.7114	1.05472
$170$	−7.57819	−0.581221
$171$	−6.81500	−0.521156
$172$	−6.53324	−0.498155
$173$	2.80143	0.212988	0.106494	−	0.994313i	$-0.466037\pi$
$173$	2.80143	0.212988	0.106494	+	0.994313i	$0.466037\pi$
$174$	3.36794	0.255323
$175$	20.0609	1.51646
$176$	−26.2838	−1.98121
$177$	−1.40612	−0.105690
$178$	11.0821	0.830636
$179$	20.4415	1.52787	0.763935	−	0.645293i	$-0.223265\pi$
$179$	20.4415	1.52787	0.763935	+	0.645293i	$0.223265\pi$
$180$	6.00188	0.447354
$181$	−17.4705	−1.29857	−0.649286	−	0.760545i	$-0.724932\pi$
$181$	−17.4705	−1.29857	−0.649286	+	0.760545i	$0.724932\pi$
$182$	16.3987	1.21555
$183$	4.34596	0.321263
$184$	−6.32724	−0.466450
$185$	12.0566	0.886420
$186$	−20.2673	−1.48607
$187$	−5.46364	−0.399541
$188$	−5.38609	−0.392821
$189$	−9.68377	−0.704391
$190$	50.4925	3.66311
$191$	14.5867	1.05546	0.527728	−	0.849414i	$-0.323044\pi$
$191$	14.5867	1.05546	0.527728	+	0.849414i	$0.323044\pi$
$192$	−4.25074	−0.306771
$193$	1.05388	0.0758600	0.0379300	−	0.999280i	$-0.487924\pi$
$193$	1.05388	0.0758600	0.0379300	+	0.999280i	$0.487924\pi$
$194$	−12.6329	−0.906992
$195$	29.7142	2.12788
$196$	−5.83984	−0.417131
$197$	8.64737	0.616099	0.308050	−	0.951370i	$-0.400324\pi$
$197$	8.64737	0.616099	0.308050	+	0.951370i	$0.400324\pi$
$198$	10.3576	0.736080
$199$	3.34163	0.236882	0.118441	−	0.992961i	$-0.462210\pi$
$199$	3.34163	0.236882	0.118441	+	0.992961i	$0.462210\pi$
$200$	12.2684	0.867504
$201$	9.84115	0.694142
$202$	23.7386	1.67024
$203$	−2.21239	−0.155280
$204$	−2.01795	−0.141285
$205$	34.2275	2.39055
$206$	21.0440	1.46620
$207$	6.18148	0.429642
$208$	24.8630	1.72394
$209$	36.4035	2.51808
$210$	18.2422	1.25883
$211$	−18.4993	−1.27354	−0.636771	−	0.771053i	$-0.719730\pi$
$211$	−18.4993	−1.27354	−0.636771	+	0.771053i	$0.719730\pi$
$212$	−14.1562	−0.972254
$213$	−13.7402	−0.941461
$214$	33.6373	2.29940
$215$	18.6138	1.26945
$216$	−5.92216	−0.402952
$217$	13.3136	0.903783
$218$	−0.371417	−0.0251555
$219$	−11.4159	−0.771413
$220$	−32.0601	−2.16149
$221$	5.16830	0.347658
$222$	7.68464	0.515760
$223$	21.4033	1.43327	0.716637	−	0.697447i	$-0.245681\pi$
$223$	21.4033	1.43327	0.716637	+	0.697447i	$0.245681\pi$
$224$	11.6793	0.780357
$225$	−11.9857	−0.799048
$226$	−30.7068	−2.04259
$227$	10.6509	0.706925	0.353463	−	0.935449i	$-0.385004\pi$
$227$	10.6509	0.706925	0.353463	+	0.935449i	$0.385004\pi$
$228$	13.4453	0.890438
$229$	−13.6940	−0.904924	−0.452462	−	0.891784i	$-0.649454\pi$
$229$	−13.6940	−0.904924	−0.452462	+	0.891784i	$0.649454\pi$
$230$	−45.7987	−3.01988
$231$	13.1521	0.865344
$232$	−1.35300	−0.0888289
$233$	−7.99943	−0.524060	−0.262030	−	0.965060i	$-0.584392\pi$
$233$	−7.99943	−0.524060	−0.262030	+	0.965060i	$0.584392\pi$
$234$	−9.79768	−0.640495
$235$	15.3454	1.00103
$236$	−1.43512	−0.0934184
$237$	−4.92689	−0.320036
$238$	3.17294	0.205671
$239$	6.34342	0.410322	0.205161	−	0.978728i	$-0.434228\pi$
$239$	6.34342	0.410322	0.205161	+	0.978728i	$0.434228\pi$
$240$	27.6581	1.78532
$241$	−17.8053	−1.14694	−0.573469	−	0.819227i	$-0.694403\pi$
$241$	−17.8053	−1.14694	−0.573469	+	0.819227i	$0.694403\pi$
$242$	−34.9393	−2.24598
$243$	10.1004	0.647941
$244$	4.43560	0.283960
$245$	16.6382	1.06298
$246$	21.8159	1.39093
$247$	−34.4357	−2.19109
$248$	8.14198	0.517016
$249$	−8.94424	−0.566818
$250$	50.9116	3.21993
$251$	11.7813	0.743626	0.371813	−	0.928308i	$-0.378736\pi$
$251$	11.7813	0.743626	0.371813	+	0.928308i	$0.378736\pi$
$252$	−2.51295	−0.158301
$253$	−33.0195	−2.07592
$254$	0.550779	0.0345589
$255$	5.74932	0.360036
$256$	20.9503	1.30940
$257$	4.53891	0.283129	0.141565	−	0.989929i	$-0.454787\pi$
$257$	4.53891	0.283129	0.141565	+	0.989929i	$0.454787\pi$
$258$	11.8640	0.738623
$259$	−5.04803	−0.313669
$260$	30.3271	1.88081
$261$	1.32183	0.0818193
$262$	14.2314	0.879219
$263$	1.16646	0.0719270	0.0359635	−	0.999353i	$-0.488550\pi$
$263$	1.16646	0.0719270	0.0359635	+	0.999353i	$0.488550\pi$
$264$	8.04323	0.495027
$265$	40.3324	2.47760
$266$	−21.1409	−1.29623
$267$	−8.40759	−0.514536
$268$	10.0441	0.613543
$269$	12.3017	0.750048	0.375024	−	0.927015i	$-0.377634\pi$
$269$	12.3017	0.750048	0.375024	+	0.927015i	$0.377634\pi$
$270$	−42.8666	−2.60878
$271$	−7.08031	−0.430098	−0.215049	−	0.976603i	$-0.568991\pi$
$271$	−7.08031	−0.430098	−0.215049	+	0.976603i	$0.568991\pi$
$272$	4.81067	0.291690
$273$	−12.4411	−0.752973
$274$	−1.63396	−0.0987112
$275$	64.0239	3.86078
$276$	−12.1955	−0.734080
$277$	31.5449	1.89535	0.947676	−	0.319234i	$-0.103426\pi$
$277$	31.5449	1.89535	0.947676	+	0.319234i	$0.103426\pi$
$278$	−25.0678	−1.50347
$279$	−7.95440	−0.476218
$280$	−7.32845	−0.437958
$281$	2.46223	0.146884	0.0734422	−	0.997299i	$-0.476602\pi$
$281$	2.46223	0.146884	0.0734422	+	0.997299i	$0.476602\pi$
$282$	9.78088	0.582443
$283$	−30.8995	−1.83679	−0.918393	−	0.395670i	$-0.870512\pi$
$283$	−30.8995	−1.83679	−0.918393	+	0.395670i	$0.870512\pi$
$284$	−14.0236	−0.832147
$285$	−38.3069	−2.26911
$286$	52.3361	3.09470
$287$	−14.3309	−0.845924
$288$	−6.97800	−0.411182
$289$	1.00000	0.0588235
$290$	−9.79348	−0.575093
$291$	9.58418	0.561834
$292$	−11.6513	−0.681843
$293$	4.90062	0.286297	0.143149	−	0.989701i	$-0.454277\pi$
$293$	4.90062	0.286297	0.143149	+	0.989701i	$0.454277\pi$
$294$	10.6049	0.618488
$295$	4.08879	0.238058
$296$	−3.08715	−0.179437
$297$	−30.9055	−1.79332
$298$	−2.83625	−0.164300
$299$	31.2346	1.80634
$300$	23.6467	1.36524
$301$	−7.79347	−0.449208
$302$	20.8998	1.20265
$303$	−18.0097	−1.03463
$304$	−32.0529	−1.83836
$305$	−12.6374	−0.723617
$306$	−1.89573	−0.108371
$307$	−1.02329	−0.0584020	−0.0292010	−	0.999574i	$-0.509296\pi$
$307$	−1.02329	−0.0584020	−0.0292010	+	0.999574i	$0.509296\pi$
$308$	13.4234	0.764867
$309$	−15.9654	−0.908238
$310$	58.9344	3.34725
$311$	17.6331	0.999881	0.499941	−	0.866060i	$-0.333355\pi$
$311$	17.6331	0.999881	0.499941	+	0.866060i	$0.333355\pi$
$312$	−7.60845	−0.430744
$313$	7.93781	0.448672	0.224336	−	0.974512i	$-0.427979\pi$
$313$	7.93781	0.448672	0.224336	+	0.974512i	$0.427979\pi$
$314$	−9.33280	−0.526681
$315$	7.15962	0.403399
$316$	−5.02851	−0.282876
$317$	−19.1984	−1.07829	−0.539144	−	0.842214i	$-0.681252\pi$
$317$	−19.1984	−1.07829	−0.539144	+	0.842214i	$0.681252\pi$
$318$	25.7070	1.44158
$319$	−7.06079	−0.395329
$320$	12.3605	0.690975
$321$	−25.5195	−1.42436
$322$	19.1756	1.06862
$323$	−6.66287	−0.370732
$324$	−7.01102	−0.389501
$325$	−60.5631	−3.35943
$326$	42.9702	2.37990
$327$	0.281781	0.0155825
$328$	−8.76411	−0.483917
$329$	−6.42504	−0.354224
$330$	58.2196	3.20488
$331$	21.6509	1.19004	0.595019	−	0.803711i	$-0.297144\pi$
$331$	21.6509	1.19004	0.595019	+	0.803711i	$0.297144\pi$
$332$	−9.12873	−0.501004
$333$	3.01603	0.165277
$334$	−7.63619	−0.417834
$335$	−28.6166	−1.56349
$336$	−11.5803	−0.631755
$337$	10.3669	0.564723	0.282361	−	0.959308i	$-0.408882\pi$
$337$	10.3669	0.564723	0.282361	+	0.959308i	$0.408882\pi$
$338$	−25.4127	−1.38227
$339$	23.2962	1.26528
$340$	5.86790	0.318232
$341$	42.4899	2.30095
$342$	12.6310	0.683004
$343$	−18.9500	−1.02320
$344$	−4.76614	−0.256973
$345$	34.7459	1.87066
$346$	−5.19218	−0.279133
$347$	21.9071	1.17603	0.588016	−	0.808849i	$-0.299909\pi$
$347$	21.9071	1.17603	0.588016	+	0.808849i	$0.299909\pi$
$348$	−2.60784	−0.139795
$349$	35.3808	1.89389	0.946946	−	0.321393i	$-0.104151\pi$
$349$	35.3808	1.89389	0.946946	+	0.321393i	$0.104151\pi$
$350$	−37.1811	−1.98741
$351$	29.2349	1.56044
$352$	37.2742	1.98672
$353$	−24.7999	−1.31996	−0.659982	−	0.751282i	$-0.729436\pi$
$353$	−24.7999	−1.31996	−0.659982	+	0.751282i	$0.729436\pi$
$354$	2.60611	0.138513
$355$	39.9544	2.12056
$356$	−8.58100	−0.454792
$357$	−2.40720	−0.127403
$358$	−37.8865	−2.00236
$359$	3.66093	0.193216	0.0966082	−	0.995322i	$-0.469201\pi$
$359$	3.66093	0.193216	0.0966082	+	0.995322i	$0.469201\pi$
$360$	4.37850	0.230767
$361$	25.3938	1.33652
$362$	32.3799	1.70185
$363$	26.5072	1.39127
$364$	−12.6978	−0.665544
$365$	33.1957	1.73754
$366$	−8.05484	−0.421033
$367$	−10.1511	−0.529886	−0.264943	−	0.964264i	$-0.585353\pi$
$367$	−10.1511	−0.529886	−0.264943	+	0.964264i	$0.585353\pi$
$368$	29.0732	1.51555
$369$	8.56221	0.445731
$370$	−22.3458	−1.16170
$371$	−16.8869	−0.876724
$372$	15.6933	0.813658
$373$	−17.3632	−0.899033	−0.449517	−	0.893272i	$-0.648404\pi$
$373$	−17.3632	−0.899033	−0.449517	+	0.893272i	$0.648404\pi$
$374$	10.1264	0.523621
$375$	−38.6249	−1.99458
$376$	−3.92927	−0.202637
$377$	6.67912	0.343992
$378$	17.9480	0.923144
$379$	14.7123	0.755721	0.377860	−	0.925863i	$-0.376660\pi$
$379$	14.7123	0.755721	0.377860	+	0.925863i	$0.376660\pi$
$380$	−39.0970	−2.00564
$381$	−0.417857	−0.0214075
$382$	−27.0351	−1.38323
$383$	8.08413	0.413080	0.206540	−	0.978438i	$-0.433780\pi$
$383$	8.08413	0.413080	0.206540	+	0.978438i	$0.433780\pi$
$384$	−11.3074	−0.577026
$385$	−38.2443	−1.94911
$386$	−1.95327	−0.0994188
$387$	4.65634	0.236695
$388$	9.78186	0.496599
$389$	−18.5273	−0.939373	−0.469687	−	0.882833i	$-0.655633\pi$
$389$	−18.5273	−0.939373	−0.469687	+	0.882833i	$0.655633\pi$
$390$	−55.0725	−2.78871
$391$	6.04349	0.305632
$392$	−4.26029	−0.215177
$393$	−10.7969	−0.544631
$394$	−16.0271	−0.807433
$395$	14.3267	0.720853
$396$	−8.02001	−0.403021
$397$	−30.2298	−1.51719	−0.758596	−	0.651561i	$-0.774114\pi$
$397$	−30.2298	−1.51719	−0.758596	+	0.651561i	$0.774114\pi$
$398$	−6.19340	−0.310447
$399$	16.0389	0.802948
$400$	−56.3723	−2.81861
$401$	−1.82078	−0.0909253	−0.0454626	−	0.998966i	$-0.514476\pi$
$401$	−1.82078	−0.0909253	−0.0454626	+	0.998966i	$0.514476\pi$
$402$	−18.2397	−0.909712
$403$	−40.1931	−2.00216
$404$	−18.3811	−0.914495
$405$	19.9750	0.992566
$406$	4.10047	0.203503
$407$	−16.1106	−0.798575
$408$	−1.47214	−0.0728817
$409$	−23.9101	−1.18228	−0.591138	−	0.806570i	$-0.701321\pi$
$409$	−23.9101	−1.18228	−0.591138	+	0.806570i	$0.701321\pi$
$410$	−63.4376	−3.13296
$411$	1.23963	0.0611465
$412$	−16.2947	−0.802781
$413$	−1.71195	−0.0842395
$414$	−11.4568	−0.563071
$415$	26.0086	1.27671
$416$	−35.2594	−1.72873
$417$	19.0181	0.931320
$418$	−67.4705	−3.30009
$419$	−9.36572	−0.457546	−0.228773	−	0.973480i	$-0.573471\pi$
$419$	−9.36572	−0.457546	−0.228773	+	0.973480i	$0.573471\pi$
$420$	−14.1252	−0.689240
$421$	0.214747	0.0104661	0.00523306	−	0.999986i	$-0.498334\pi$
$421$	0.214747	0.0104661	0.00523306	+	0.999986i	$0.498334\pi$
$422$	34.2867	1.66905
$423$	3.83875	0.186646
$424$	−10.3273	−0.501537
$425$	−11.7182	−0.568415
$426$	25.4662	1.23384
$427$	5.29121	0.256060
$428$	−26.0459	−1.25898
$429$	−39.7056	−1.91700
$430$	−34.4989	−1.66369
$431$	27.4077	1.32018	0.660091	−	0.751186i	$-0.270518\pi$
$431$	27.4077	1.32018	0.660091	+	0.751186i	$0.270518\pi$
$432$	27.2119	1.30923
$433$	2.20612	0.106019	0.0530096	−	0.998594i	$-0.483119\pi$
$433$	2.20612	0.106019	0.0530096	+	0.998594i	$0.483119\pi$
$434$	−24.6754	−1.18446
$435$	7.42998	0.356240
$436$	0.287593	0.0137732
$437$	−40.2670	−1.92623
$438$	21.1583	1.01098
$439$	−18.7152	−0.893229	−0.446615	−	0.894726i	$-0.647371\pi$
$439$	−18.7152	−0.893229	−0.446615	+	0.894726i	$0.647371\pi$
$440$	−23.3885	−1.11500
$441$	4.16214	0.198197
$442$	−9.57897	−0.455625
$443$	10.0621	0.478065	0.239032	−	0.971012i	$-0.423170\pi$
$443$	10.0621	0.478065	0.239032	+	0.971012i	$0.423170\pi$
$444$	−5.95033	−0.282390
$445$	24.4480	1.15895
$446$	−39.6691	−1.87839
$447$	2.15177	0.101775
$448$	−5.17528	−0.244509
$449$	11.3450	0.535403	0.267702	−	0.963502i	$-0.413736\pi$
$449$	11.3450	0.535403	0.267702	+	0.963502i	$0.413736\pi$
$450$	22.2144	1.04720
$451$	−45.7365	−2.15365
$452$	23.7767	1.11836
$453$	−15.8560	−0.744979
$454$	−19.7405	−0.926466
$455$	36.1771	1.69601
$456$	9.80866	0.459332
$457$	11.7918	0.551599	0.275799	−	0.961215i	$-0.411057\pi$
$457$	11.7918	0.551599	0.275799	+	0.961215i	$0.411057\pi$
$458$	25.3805	1.18595
$459$	5.65658	0.264026
$460$	35.4626	1.65345
$461$	−1.50005	−0.0698643	−0.0349321	−	0.999390i	$-0.511122\pi$
$461$	−1.50005	−0.0698643	−0.0349321	+	0.999390i	$0.511122\pi$
$462$	−24.3762	−1.13408
$463$	−15.4138	−0.716342	−0.358171	−	0.933656i	$-0.616600\pi$
$463$	−15.4138	−0.716342	−0.358171	+	0.933656i	$0.616600\pi$
$464$	6.21695	0.288614
$465$	−44.7115	−2.07345
$466$	14.8262	0.686811
$467$	−24.0612	−1.11342	−0.556709	−	0.830708i	$-0.687936\pi$
$467$	−24.0612	−1.11342	−0.556709	+	0.830708i	$0.687936\pi$
$468$	7.58649	0.350686
$469$	11.9816	0.553259
$470$	−28.4414	−1.31190
$471$	7.08048	0.326251
$472$	−1.04695	−0.0481899
$473$	−24.8727	−1.14365
$474$	9.13153	0.419425
$475$	78.0766	3.58240
$476$	−2.45685	−0.112610
$477$	10.0894	0.461960
$478$	−11.7569	−0.537750
$479$	−11.0684	−0.505730	−0.252865	−	0.967502i	$-0.581373\pi$
$479$	−11.0684	−0.505730	−0.252865	+	0.967502i	$0.581373\pi$
$480$	−39.2232	−1.79028
$481$	15.2398	0.694875
$482$	33.0004	1.50313
$483$	−14.5479	−0.661952
$484$	27.0540	1.22973
$485$	−27.8694	−1.26548
$486$	−18.7202	−0.849164
$487$	8.24098	0.373434	0.186717	−	0.982414i	$-0.440215\pi$
$487$	8.24098	0.373434	0.186717	+	0.982414i	$0.440215\pi$
$488$	3.23587	0.146481
$489$	−32.6000	−1.47422
$490$	−30.8374	−1.39309
$491$	−9.05163	−0.408494	−0.204247	−	0.978919i	$-0.565475\pi$
$491$	−9.05163	−0.408494	−0.204247	+	0.978919i	$0.565475\pi$
$492$	−16.8924	−0.761568
$493$	1.29232	0.0582034
$494$	63.8234	2.87155
$495$	22.8497	1.02702
$496$	−37.4118	−1.67984
$497$	−16.7287	−0.750383
$498$	16.5773	0.742848
$499$	3.93088	0.175970	0.0879851	−	0.996122i	$-0.471957\pi$
$499$	3.93088	0.175970	0.0879851	+	0.996122i	$0.471957\pi$
$500$	−39.4216	−1.76299
$501$	5.79332	0.258827
$502$	−21.8355	−0.974564
$503$	−20.8948	−0.931651	−0.465825	−	0.884877i	$-0.654243\pi$
$503$	−20.8948	−0.931651	−0.465825	+	0.884877i	$0.654243\pi$
$504$	−1.83325	−0.0816595
$505$	52.3695	2.33041
$506$	61.1985	2.72061
$507$	19.2798	0.856245
$508$	−0.426476	−0.0189218
$509$	−29.2464	−1.29632	−0.648162	−	0.761502i	$-0.724462\pi$
$509$	−29.2464	−1.29632	−0.648162	+	0.761502i	$0.724462\pi$
$510$	−10.6558	−0.471848
$511$	−13.8988	−0.614848
$512$	−22.7464	−1.00526
$513$	−37.6890	−1.66401
$514$	−8.41245	−0.371057
$515$	46.4250	2.04573
$516$	−9.18650	−0.404413
$517$	−20.5053	−0.901824
$518$	9.35606	0.411081
$519$	3.93913	0.172909
$520$	22.1243	0.970214
$521$	37.0838	1.62467	0.812335	−	0.583190i	$-0.198196\pi$
$521$	37.0838	1.62467	0.812335	+	0.583190i	$0.198196\pi$
$522$	−2.44989	−0.107229
$523$	−31.1771	−1.36328	−0.681641	−	0.731687i	$-0.738733\pi$
$523$	−31.1771	−1.36328	−0.681641	+	0.731687i	$0.738733\pi$
$524$	−11.0196	−0.481393
$525$	28.2080	1.23110
$526$	−2.16193	−0.0942645
$527$	−7.77684	−0.338764
$528$	−36.9581	−1.60839
$529$	13.5238	0.587990
$530$	−74.7523	−3.24703
$531$	1.02283	0.0443871
$532$	16.3697	0.709716
$533$	43.2643	1.87398
$534$	15.5827	0.674329
$535$	74.2071	3.20825
$536$	7.32742	0.316496
$537$	28.7432	1.24036
$538$	−22.8001	−0.982981
$539$	−22.2328	−0.957635
$540$	33.1922	1.42837
$541$	−16.0444	−0.689802	−0.344901	−	0.938639i	$-0.612087\pi$
$541$	−16.0444	−0.689802	−0.344901	+	0.938639i	$0.612087\pi$
$542$	13.1227	0.563669
$543$	−24.5656	−1.05421
$544$	−6.82223	−0.292501
$545$	−0.819379	−0.0350984
$546$	23.0585	0.986814
$547$	42.1258	1.80117	0.900585	−	0.434680i	$-0.143138\pi$
$547$	42.1258	1.80117	0.900585	+	0.434680i	$0.143138\pi$
$548$	1.26520	0.0540467
$549$	−3.16132	−0.134922
$550$	−118.662	−5.05978
$551$	−8.61058	−0.366823
$552$	−8.89685	−0.378675
$553$	−5.99849	−0.255082
$554$	−58.4656	−2.48397
$555$	16.9530	0.719616
$556$	19.4104	0.823183
$557$	6.44579	0.273117	0.136558	−	0.990632i	$-0.456396\pi$
$557$	6.44579	0.273117	0.136558	+	0.990632i	$0.456396\pi$
$558$	14.7428	0.624111
$559$	23.5282	0.995135
$560$	33.6737	1.42297
$561$	−7.68252	−0.324356
$562$	−4.56352	−0.192500
$563$	13.7738	0.580498	0.290249	−	0.956951i	$-0.406262\pi$
$563$	13.7738	0.580498	0.290249	+	0.956951i	$0.406262\pi$
$564$	−7.57348	−0.318901
$565$	−67.7420	−2.84993
$566$	57.2694	2.40721
$567$	−8.36341	−0.351230
$568$	−10.2305	−0.429263
$569$	14.3406	0.601188	0.300594	−	0.953752i	$-0.402815\pi$
$569$	14.3406	0.601188	0.300594	+	0.953752i	$0.402815\pi$
$570$	70.9983	2.97379
$571$	−5.22712	−0.218748	−0.109374	−	0.994001i	$-0.534885\pi$
$571$	−5.22712	−0.218748	−0.109374	+	0.994001i	$0.534885\pi$
$572$	−40.5246	−1.69442
$573$	20.5106	0.856843
$574$	26.5609	1.10863
$575$	−70.8187	−2.95334
$576$	3.09206	0.128836
$577$	38.8483	1.61728	0.808638	−	0.588306i	$-0.200205\pi$
$577$	38.8483	1.61728	0.808638	+	0.588306i	$0.200205\pi$
$578$	−1.85341	−0.0770916
$579$	1.48188	0.0615848
$580$	7.58323	0.314877
$581$	−10.8896	−0.451777
$582$	−17.7634	−0.736316
$583$	−53.8941	−2.23207
$584$	−8.49990	−0.351729
$585$	−21.6146	−0.893653
$586$	−9.08284	−0.375209
$587$	−14.9073	−0.615289	−0.307645	−	0.951501i	$-0.599541\pi$
$587$	−14.9073	−0.615289	−0.307645	+	0.951501i	$0.599541\pi$
$588$	−8.21150	−0.338637
$589$	51.8160	2.13504
$590$	−7.57819	−0.311989
$591$	12.1592	0.500163
$592$	14.1852	0.583010
$593$	31.5793	1.29681	0.648403	−	0.761297i	$-0.275437\pi$
$593$	31.5793	1.29681	0.648403	+	0.761297i	$0.275437\pi$
$594$	57.2805	2.35025
$595$	6.99979	0.286964
$596$	2.19615	0.0899579
$597$	4.69872	0.192306
$598$	−57.8904	−2.36732
$599$	−14.9483	−0.610770	−0.305385	−	0.952229i	$-0.598785\pi$
$599$	−14.9483	−0.610770	−0.305385	+	0.952229i	$0.598785\pi$
$600$	17.2508	0.704259
$601$	−13.9673	−0.569738	−0.284869	−	0.958566i	$-0.591950\pi$
$601$	−13.9673	−0.569738	−0.284869	+	0.958566i	$0.591950\pi$
$602$	14.4445	0.588713
$603$	−7.15861	−0.291521
$604$	−16.1830	−0.658478
$605$	−77.0792	−3.13371
$606$	33.3792	1.35594
$607$	−1.52926	−0.0620708	−0.0310354	−	0.999518i	$-0.509880\pi$
$607$	−1.52926	−0.0620708	−0.0310354	+	0.999518i	$0.509880\pi$
$608$	45.4556	1.84347
$609$	−3.11089	−0.126059
$610$	23.4223	0.948341
$611$	19.3969	0.784716
$612$	1.46789	0.0593359
$613$	−30.1137	−1.21628	−0.608140	−	0.793830i	$-0.708084\pi$
$613$	−30.1137	−1.21628	−0.608140	+	0.793830i	$0.708084\pi$
$614$	1.89657	0.0765392
$615$	48.1280	1.94071
$616$	9.79263	0.394556
$617$	−8.10749	−0.326395	−0.163198	−	0.986593i	$-0.552181\pi$
$617$	−8.10749	−0.326395	−0.163198	+	0.986593i	$0.552181\pi$
$618$	29.5903	1.19030
$619$	−40.6181	−1.63258	−0.816291	−	0.577642i	$-0.803973\pi$
$619$	−40.6181	−1.63258	−0.816291	+	0.577642i	$0.803973\pi$
$620$	−45.6337	−1.83269
$621$	34.1855	1.37182
$622$	−32.6813	−1.31040
$623$	−10.2362	−0.410106
$624$	34.9603	1.39953
$625$	53.7247	2.14899
$626$	−14.7120	−0.588010
$627$	51.1876	2.04424
$628$	7.22653	0.288370
$629$	2.94870	0.117572
$630$	−13.2697	−0.528677
$631$	−9.41591	−0.374842	−0.187421	−	0.982280i	$-0.560013\pi$
$631$	−9.41591	−0.374842	−0.187421	+	0.982280i	$0.560013\pi$
$632$	−3.66841	−0.145921
$633$	−26.0121	−1.03389
$634$	35.5824	1.41316
$635$	1.21507	0.0482185
$636$	−19.9053	−0.789298
$637$	21.0310	0.833279
$638$	13.0865	0.518101
$639$	9.99482	0.395389
$640$	32.8802	1.29970
$641$	44.6435	1.76331	0.881656	−	0.471893i	$-0.156429\pi$
$641$	44.6435	1.76331	0.881656	+	0.471893i	$0.156429\pi$
$642$	47.2981	1.86671
$643$	−7.36542	−0.290464	−0.145232	−	0.989398i	$-0.546393\pi$
$643$	−7.36542	−0.290464	−0.145232	+	0.989398i	$0.546393\pi$
$644$	−14.8480	−0.585092
$645$	26.1732	1.03057
$646$	12.3490	0.485865
$647$	18.8841	0.742410	0.371205	−	0.928551i	$-0.378945\pi$
$647$	18.8841	0.742410	0.371205	+	0.928551i	$0.378945\pi$
$648$	−5.11469	−0.200924
$649$	−5.46364	−0.214467
$650$	112.248	4.40273
$651$	18.7204	0.733711
$652$	−33.2724	−1.30305
$653$	−44.4740	−1.74040	−0.870200	−	0.492698i	$-0.836011\pi$
$653$	−44.4740	−1.74040	−0.870200	+	0.492698i	$0.836011\pi$
$654$	−0.522256	−0.0204218
$655$	31.3958	1.22673
$656$	40.2705	1.57230
$657$	8.30409	0.323973
$658$	11.9082	0.464231
$659$	−40.1586	−1.56436	−0.782178	−	0.623056i	$-0.785891\pi$
$659$	−40.1586	−1.56436	−0.782178	+	0.623056i	$0.785891\pi$
$660$	−45.0803	−1.75475
$661$	4.40806	0.171454	0.0857268	−	0.996319i	$-0.472679\pi$
$661$	4.40806	0.171454	0.0857268	+	0.996319i	$0.472679\pi$
$662$	−40.1279	−1.55961
$663$	7.26724	0.282236
$664$	−6.65961	−0.258443
$665$	−46.6387	−1.80857
$666$	−5.58993	−0.216605
$667$	7.81015	0.302410
$668$	5.91282	0.228774
$669$	30.0956	1.16356
$670$	53.0383	2.04905
$671$	16.8868	0.651906
$672$	16.4225	0.633511
$673$	7.85198	0.302671	0.151336	−	0.988482i	$-0.451643\pi$
$673$	7.85198	0.302671	0.151336	+	0.988482i	$0.451643\pi$
$674$	−19.2142	−0.740102
$675$	−66.2847	−2.55130
$676$	19.6774	0.756825
$677$	7.52575	0.289238	0.144619	−	0.989487i	$-0.453804\pi$
$677$	7.52575	0.289238	0.144619	+	0.989487i	$0.453804\pi$
$678$	−43.1774	−1.65822
$679$	11.6687	0.447805
$680$	4.28076	0.164160
$681$	14.9764	0.573898
$682$	−78.7510	−3.01553
$683$	−48.2583	−1.84655	−0.923276	−	0.384138i	$-0.874499\pi$
$683$	−48.2583	−1.84655	−0.923276	+	0.384138i	$0.874499\pi$
$684$	−9.78034	−0.373961
$685$	−3.60467	−0.137727
$686$	35.1220	1.34096
$687$	−19.2554	−0.734638
$688$	21.9001	0.834933
$689$	50.9809	1.94222
$690$	−64.3984	−2.45160
$691$	−46.7915	−1.78003	−0.890017	−	0.455928i	$-0.849308\pi$
$691$	−46.7915	−1.78003	−0.890017	+	0.455928i	$0.849308\pi$
$692$	4.02038	0.152832
$693$	−9.56703	−0.363422
$694$	−40.6027	−1.54126
$695$	−55.3018	−2.09772
$696$	−1.90248	−0.0721133
$697$	8.37108	0.317077
$698$	−65.5751	−2.48205
$699$	−11.2481	−0.425444
$700$	28.7898	1.08815
$701$	−12.8904	−0.486864	−0.243432	−	0.969918i	$-0.578273\pi$
$701$	−12.8904	−0.486864	−0.243432	+	0.969918i	$0.578273\pi$
$702$	−54.1842	−2.04505
$703$	−19.6468	−0.740994
$704$	−16.5168	−0.622499
$705$	21.5775	0.812656
$706$	45.9643	1.72989
$707$	−21.9268	−0.824641
$708$	−2.01795	−0.0758392
$709$	45.8266	1.72105	0.860527	−	0.509405i	$-0.170135\pi$
$709$	45.8266	1.72105	0.860527	+	0.509405i	$0.170135\pi$
$710$	−74.0519	−2.77912
$711$	3.58390	0.134407
$712$	−6.26003	−0.234605
$713$	−46.9993	−1.76014
$714$	4.46153	0.166968
$715$	115.458	4.31789
$716$	29.3360	1.09634
$717$	8.91959	0.333108
$718$	−6.78520	−0.253221
$719$	39.3979	1.46929	0.734647	−	0.678449i	$-0.237348\pi$
$719$	39.3979	1.46929	0.734647	+	0.678449i	$0.237348\pi$
$720$	−20.1189	−0.749788
$721$	−19.4378	−0.723903
$722$	−47.0650	−1.75158
$723$	−25.0363	−0.931110
$724$	−25.0723	−0.931803
$725$	−15.1437	−0.562422
$726$	−49.1287	−1.82334
$727$	−18.0661	−0.670036	−0.335018	−	0.942212i	$-0.608742\pi$
$727$	−18.0661	−0.670036	−0.335018	+	0.942212i	$0.608742\pi$
$728$	−9.26329	−0.343321
$729$	28.8583	1.06883
$730$	−61.5252	−2.27715
$731$	4.55240	0.168376
$732$	6.23698	0.230525
$733$	25.9493	0.958458	0.479229	−	0.877690i	$-0.340916\pi$
$733$	25.9493	0.958458	0.479229	+	0.877690i	$0.340916\pi$
$734$	18.8142	0.694446
$735$	23.3953	0.862948
$736$	−41.2301	−1.51976
$737$	38.2390	1.40855
$738$	−15.8693	−0.584156
$739$	22.5934	0.831112	0.415556	−	0.909568i	$-0.363587\pi$
$739$	22.5934	0.831112	0.415556	+	0.909568i	$0.363587\pi$
$740$	17.3027	0.636060
$741$	−48.4207	−1.77878
$742$	31.2983	1.14900
$743$	38.0076	1.39436	0.697181	−	0.716895i	$-0.254437\pi$
$743$	38.0076	1.39436	0.697181	+	0.716895i	$0.254437\pi$
$744$	11.4486	0.419725
$745$	−6.25703	−0.229240
$746$	32.1811	1.17823
$747$	6.50618	0.238049
$748$	−7.84098	−0.286695
$749$	−31.0700	−1.13527
$750$	71.5877	2.61401
$751$	43.7030	1.59474	0.797372	−	0.603488i	$-0.206223\pi$
$751$	43.7030	1.59474	0.797372	+	0.603488i	$0.206223\pi$
$752$	18.0547	0.658388
$753$	16.5658	0.603692
$754$	−12.3791	−0.450822
$755$	46.1069	1.67800
$756$	−13.8974	−0.505443
$757$	9.04898	0.328891	0.164445	−	0.986386i	$-0.447417\pi$
$757$	9.04898	0.328891	0.164445	+	0.986386i	$0.447417\pi$
$758$	−27.2679	−0.990415
$759$	−46.4292	−1.68527
$760$	−28.5221	−1.03461
$761$	−50.5389	−1.83203	−0.916017	−	0.401140i	$-0.868614\pi$
$761$	−50.5389	−1.83203	−0.916017	+	0.401140i	$0.868614\pi$
$762$	0.774460	0.0280557
$763$	0.343069	0.0124199
$764$	20.9337	0.757353
$765$	−4.18214	−0.151206
$766$	−14.9832	−0.541365
$767$	5.16830	0.186617
$768$	29.4586	1.06300
$769$	−44.5545	−1.60668	−0.803338	−	0.595524i	$-0.796945\pi$
$769$	−44.5545	−1.60668	−0.803338	+	0.595524i	$0.796945\pi$
$770$	70.8824	2.55442
$771$	6.38224	0.229851
$772$	1.51245	0.0544341
$773$	−36.1676	−1.30086	−0.650428	−	0.759568i	$-0.725411\pi$
$773$	−36.1676	−1.30086	−0.650428	+	0.759568i	$0.725411\pi$
$774$	−8.63010	−0.310202
$775$	91.1304	3.27350
$776$	7.13608	0.256170
$777$	−7.09812	−0.254644
$778$	34.3387	1.23110
$779$	−55.7754	−1.99836
$780$	42.6435	1.52688
$781$	−53.3891	−1.91041
$782$	−11.2011	−0.400549
$783$	7.31013	0.261243
$784$	19.5757	0.699133
$785$	−20.5890	−0.734853
$786$	20.0110	0.713770
$787$	−19.0635	−0.679542	−0.339771	−	0.940508i	$-0.610350\pi$
$787$	−19.0635	−0.679542	−0.339771	+	0.940508i	$0.610350\pi$
$788$	12.4100	0.442088
$789$	1.64018	0.0583920
$790$	−26.5532	−0.944719
$791$	28.3631	1.00848
$792$	−5.85077	−0.207898
$793$	−15.9739	−0.567251
$794$	56.0282	1.98837
$795$	56.7120	2.01137
$796$	4.79564	0.169977
$797$	−55.5655	−1.96823	−0.984115	−	0.177534i	$-0.943188\pi$
$797$	−55.5655	−1.96823	−0.984115	+	0.177534i	$0.943188\pi$
$798$	−29.7266	−1.05231
$799$	3.75306	0.132774
$800$	79.9441	2.82645
$801$	6.11581	0.216092
$802$	3.37464	0.119163
$803$	−44.3577	−1.56535
$804$	14.1232	0.498088
$805$	42.3032	1.49099
$806$	74.4941	2.62394
$807$	17.2976	0.608906
$808$	−13.4094	−0.471742
$809$	13.5573	0.476649	0.238325	−	0.971186i	$-0.423402\pi$
$809$	13.5573	0.476649	0.238325	+	0.971186i	$0.423402\pi$
$810$	−37.0218	−1.30082
$811$	40.5868	1.42519	0.712597	−	0.701573i	$-0.247519\pi$
$811$	40.5868	1.42519	0.712597	+	0.701573i	$0.247519\pi$
$812$	−3.17505	−0.111422
$813$	−9.95575	−0.349164
$814$	29.8596	1.04658
$815$	94.7961	3.32056
$816$	6.76437	0.236800
$817$	−30.3320	−1.06118
$818$	44.3151	1.54944
$819$	9.04989	0.316229
$820$	49.1206	1.71537
$821$	28.8396	1.00651	0.503255	−	0.864138i	$-0.332136\pi$
$821$	28.8396	1.00651	0.503255	+	0.864138i	$0.332136\pi$
$822$	−2.29754	−0.0801360
$823$	−42.7506	−1.49019	−0.745097	−	0.666957i	$-0.767597\pi$
$823$	−42.7506	−1.49019	−0.745097	+	0.666957i	$0.767597\pi$
$824$	−11.8873	−0.414114
$825$	90.0251	3.13427
$826$	3.17294	0.110401
$827$	25.4241	0.884082	0.442041	−	0.896995i	$-0.354255\pi$
$827$	25.4241	0.884082	0.442041	+	0.896995i	$0.354255\pi$
$828$	8.87117	0.308294
$829$	−3.95399	−0.137328	−0.0686638	−	0.997640i	$-0.521874\pi$
$829$	−3.95399	−0.137328	−0.0686638	+	0.997640i	$0.521874\pi$
$830$	−48.2045	−1.67320
$831$	44.3559	1.53869
$832$	15.6240	0.541663
$833$	4.06923	0.140990
$834$	−35.2483	−1.22055
$835$	−16.8461	−0.582985
$836$	52.2434	1.80688
$837$	−43.9903	−1.52053
$838$	17.3585	0.599640
$839$	35.5580	1.22760	0.613799	−	0.789463i	$-0.289641\pi$
$839$	35.5580	1.22760	0.613799	+	0.789463i	$0.289641\pi$
$840$	−10.3047	−0.355545
$841$	−27.3299	−0.942410
$842$	−0.398014	−0.0137165
$843$	3.46219	0.119244
$844$	−26.5487	−0.913843
$845$	−56.0628	−1.92862
$846$	−7.11477	−0.244611
$847$	32.2726	1.10890
$848$	47.4531	1.62955
$849$	−43.4484	−1.49114
$850$	21.7186	0.744940
$851$	17.8205	0.610877
$852$	−19.7188	−0.675555
$853$	8.01232	0.274337	0.137168	−	0.990548i	$-0.456200\pi$
$853$	8.01232	0.274337	0.137168	+	0.990548i	$0.456200\pi$
$854$	−9.80677	−0.335581
$855$	27.8651	0.952965
$856$	−19.0010	−0.649442
$857$	−38.6681	−1.32088	−0.660439	−	0.750880i	$-0.729630\pi$
$857$	−38.6681	−1.32088	−0.660439	+	0.750880i	$0.729630\pi$
$858$	73.5907	2.51234
$859$	−16.1689	−0.551676	−0.275838	−	0.961204i	$-0.588955\pi$
$859$	−16.1689	−0.551676	−0.275838	+	0.961204i	$0.588955\pi$
$860$	26.7130	0.910906
$861$	−20.1509	−0.686740
$862$	−50.7976	−1.73017
$863$	−5.15520	−0.175485	−0.0877425	−	0.996143i	$-0.527965\pi$
$863$	−5.15520	−0.175485	−0.0877425	+	0.996143i	$0.527965\pi$
$864$	−38.5905	−1.31287
$865$	−11.4544	−0.389462
$866$	−4.08884	−0.138944
$867$	1.40612	0.0477543
$868$	19.1066	0.648519
$869$	−19.1440	−0.649416
$870$	−13.7708	−0.466873
$871$	−36.1720	−1.22564
$872$	0.209806	0.00710492
$873$	−6.97168	−0.235956
$874$	74.6311	2.52443
$875$	−47.0258	−1.58976
$876$	−16.3832	−0.553535
$877$	39.1136	1.32077	0.660386	−	0.750926i	$-0.270393\pi$
$877$	39.1136	1.32077	0.660386	+	0.750926i	$0.270393\pi$
$878$	34.6870	1.17063
$879$	6.89084	0.232422
$880$	107.469	3.62277
$881$	−35.1825	−1.18533	−0.592665	−	0.805449i	$-0.701924\pi$
$881$	−35.1825	−1.18533	−0.592665	+	0.805449i	$0.701924\pi$
$882$	−7.71415	−0.259749
$883$	7.83422	0.263642	0.131821	−	0.991274i	$-0.457918\pi$
$883$	7.83422	0.263642	0.131821	+	0.991274i	$0.457918\pi$
$884$	7.41714	0.249465
$885$	5.74932	0.193261
$886$	−18.6492	−0.626531
$887$	−40.8155	−1.37045	−0.685225	−	0.728331i	$-0.740296\pi$
$887$	−40.8155	−1.37045	−0.685225	+	0.728331i	$0.740296\pi$
$888$	−4.34090	−0.145671
$889$	−0.508741	−0.0170626
$890$	−45.3122	−1.51887
$891$	−26.6916	−0.894203
$892$	30.7164	1.02846
$893$	−25.0061	−0.836798
$894$	−3.98811	−0.133382
$895$	−83.5810	−2.79380
$896$	−13.7667	−0.459914
$897$	43.9195	1.46643
$898$	−21.0269	−0.701677
$899$	−10.0502	−0.335193
$900$	−17.2010	−0.573366
$901$	9.86414	0.328622
$902$	84.7685	2.82248
$903$	−10.9585	−0.364677
$904$	17.3456	0.576907
$905$	71.4331	2.37452
$906$	29.3876	0.976338
$907$	−23.6932	−0.786719	−0.393359	−	0.919385i	$-0.628687\pi$
$907$	−23.6932	−0.786719	−0.393359	+	0.919385i	$0.628687\pi$
$908$	15.2853	0.507261
$909$	13.1005	0.434516
$910$	−67.0508	−2.22271
$911$	9.95401	0.329791	0.164895	−	0.986311i	$-0.447271\pi$
$911$	9.95401	0.329791	0.164895	+	0.986311i	$0.447271\pi$
$912$	−45.0701	−1.49242
$913$	−34.7539	−1.15019
$914$	−21.8551	−0.722902
$915$	−17.7697	−0.587448
$916$	−19.6525	−0.649338
$917$	−13.1452	−0.434093
$918$	−10.4839	−0.346022
$919$	0.378106	0.0124726	0.00623629	−	0.999981i	$-0.498015\pi$
$919$	0.378106	0.0124726	0.00623629	+	0.999981i	$0.498015\pi$
$920$	25.8707	0.852933
$921$	−1.43886	−0.0474121
$922$	2.78020	0.0915611
$923$	50.5032	1.66233
$924$	18.8748	0.620936
$925$	−34.5534	−1.13611
$926$	28.5681	0.938807
$927$	11.6135	0.381436
$928$	−8.81653	−0.289417
$929$	43.8153	1.43753	0.718766	−	0.695252i	$-0.244707\pi$
$929$	43.8153	1.43753	0.718766	+	0.695252i	$0.244707\pi$
$930$	82.8687	2.71737
$931$	−27.1127	−0.888584
$932$	−11.4802	−0.376045
$933$	24.7942	0.811726
$934$	44.5951	1.45920
$935$	22.3397	0.730585
$936$	5.53451	0.180901
$937$	−58.2818	−1.90398	−0.951991	−	0.306125i	$-0.900967\pi$
$937$	−58.2818	−1.90398	−0.951991	+	0.306125i	$0.900967\pi$
$938$	−22.2068	−0.725078
$939$	11.1615	0.364242
$940$	22.0226	0.718297
$941$	−11.0106	−0.358934	−0.179467	−	0.983764i	$-0.557437\pi$
$941$	−11.0106	−0.358934	−0.179467	+	0.983764i	$0.557437\pi$
$942$	−13.1230	−0.427571
$943$	50.5905	1.64745
$944$	4.81067	0.156574
$945$	39.5949	1.28802
$946$	46.0992	1.49881
$947$	−15.1996	−0.493921	−0.246961	−	0.969026i	$-0.579432\pi$
$947$	−15.1996	−0.493921	−0.246961	+	0.969026i	$0.579432\pi$
$948$	−7.07068	−0.229645
$949$	41.9600	1.36208
$950$	−144.708	−4.69494
$951$	−26.9952	−0.875378
$952$	−1.79233	−0.0580897
$953$	−13.9921	−0.453250	−0.226625	−	0.973982i	$-0.572769\pi$
$953$	−13.9921	−0.453250	−0.226625	+	0.973982i	$0.572769\pi$
$954$	−18.6997	−0.605425
$955$	−59.6418	−1.92996
$956$	9.10357	0.294431
$957$	−9.92831	−0.320937
$958$	20.5143	0.662788
$959$	1.50925	0.0487363
$960$	17.3804	0.560949
$961$	29.4792	0.950943
$962$	−28.2455	−0.910673
$963$	18.5633	0.598194
$964$	−25.5527	−0.822997
$965$	−4.30909	−0.138715
$966$	26.9632	0.867527
$967$	57.1658	1.83833	0.919164	−	0.393876i	$-0.128866\pi$
$967$	57.1658	1.83833	0.919164	+	0.393876i	$0.128866\pi$
$968$	19.7365	0.634354
$969$	−9.36878	−0.300968
$970$	51.6534	1.65849
$971$	−6.09862	−0.195714	−0.0978569	−	0.995200i	$-0.531199\pi$
$971$	−6.09862	−0.195714	−0.0978569	+	0.995200i	$0.531199\pi$
$972$	14.4953	0.464937
$973$	23.1545	0.742300
$974$	−15.2739	−0.489407
$975$	−85.1588	−2.72726
$976$	−14.8686	−0.475932
$977$	18.1655	0.581167	0.290584	−	0.956850i	$-0.406151\pi$
$977$	18.1655	0.581167	0.290584	+	0.956850i	$0.406151\pi$
$978$	60.4211	1.93205
$979$	−32.6687	−1.04410
$980$	23.8778	0.762750
$981$	−0.204972	−0.00654426
$982$	16.7764	0.535355
$983$	26.7933	0.854574	0.427287	−	0.904116i	$-0.359469\pi$
$983$	26.7933	0.854574	0.427287	+	0.904116i	$0.359469\pi$
$984$	−12.3234	−0.392855
$985$	−35.3572	−1.12657
$986$	−2.39520	−0.0762788
$987$	−9.03436	−0.287567
$988$	−49.4194	−1.57224
$989$	27.5124	0.874842
$990$	−42.3499	−1.34597
$991$	−3.46950	−0.110212	−0.0551061	−	0.998481i	$-0.517550\pi$
$991$	−3.46950	−0.110212	−0.0551061	+	0.998481i	$0.517550\pi$
$992$	53.0554	1.68451
$993$	30.4437	0.966100
$994$	31.0050	0.983420
$995$	−13.6632	−0.433153
$996$	−12.8361	−0.406726
$997$	54.1061	1.71356	0.856779	−	0.515684i	$-0.172462\pi$
$997$	54.1061	1.71356	0.856779	+	0.515684i	$0.172462\pi$
$998$	−7.28551	−0.230619
$999$	16.6796	0.527718

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1003.2.a.g.1.4	✓	10
3.2	odd	2		9027.2.a.j.1.7		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1003.2.a.g.1.4	✓	10	1.1	even	1	trivial
9027.2.a.j.1.7		10	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)

\(f(q)\)	\(=\)	\(q-1.85341 q^{2} +1.40612 q^{3} +1.43512 q^{4} -4.08879 q^{5} -2.60611 q^{6} +1.71195 q^{7} +1.04695 q^{8} -1.02283 q^{9} +O(q^{10})\)	\(q-1.85341 q^{2} +1.40612 q^{3} +1.43512 q^{4} -4.08879 q^{5} -2.60611 q^{6} +1.71195 q^{7} +1.04695 q^{8} -1.02283 q^{9} +7.57819 q^{10} +5.46364 q^{11} +2.01795 q^{12} -5.16830 q^{13} -3.17294 q^{14} -5.74932 q^{15} -4.81067 q^{16} -1.00000 q^{17} +1.89573 q^{18} +6.66287 q^{19} -5.86790 q^{20} +2.40720 q^{21} -10.1264 q^{22} -6.04349 q^{23} +1.47214 q^{24} +11.7182 q^{25} +9.57897 q^{26} -5.65658 q^{27} +2.45685 q^{28} -1.29232 q^{29} +10.6558 q^{30} +7.77684 q^{31} +6.82223 q^{32} +7.68252 q^{33} +1.85341 q^{34} -6.99979 q^{35} -1.46789 q^{36} -2.94870 q^{37} -12.3490 q^{38} -7.26724 q^{39} -4.28076 q^{40} -8.37108 q^{41} -4.46153 q^{42} -4.55240 q^{43} +7.84098 q^{44} +4.18214 q^{45} +11.2011 q^{46} -3.75306 q^{47} -6.76437 q^{48} -4.06923 q^{49} -21.7186 q^{50} -1.40612 q^{51} -7.41714 q^{52} -9.86414 q^{53} +10.4839 q^{54} -22.3397 q^{55} +1.79233 q^{56} +9.36878 q^{57} +2.39520 q^{58} -1.00000 q^{59} -8.25096 q^{60} +3.09075 q^{61} -14.4137 q^{62} -1.75104 q^{63} -3.02303 q^{64} +21.1321 q^{65} -14.2388 q^{66} +6.99881 q^{67} -1.43512 q^{68} -8.49786 q^{69} +12.9735 q^{70} -9.77171 q^{71} -1.07086 q^{72} -8.11872 q^{73} +5.46515 q^{74} +16.4771 q^{75} +9.56202 q^{76} +9.35347 q^{77} +13.4692 q^{78} -3.50389 q^{79} +19.6698 q^{80} -4.88532 q^{81} +15.5150 q^{82} -6.36095 q^{83} +3.45463 q^{84} +4.08879 q^{85} +8.43745 q^{86} -1.81716 q^{87} +5.72017 q^{88} -5.97929 q^{89} -7.75122 q^{90} -8.84787 q^{91} -8.67314 q^{92} +10.9352 q^{93} +6.95594 q^{94} -27.2430 q^{95} +9.59286 q^{96} +6.81606 q^{97} +7.54194 q^{98} -5.58839 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - q^{2} - 7 q^{3} + 15 q^{4} - 12 q^{5} + 5 q^{6} - 9 q^{7} - 12 q^{8} + 3 q^{9}+O(q^{10}) \) 10 * q - q^2 - 7 * q^3 + 15 * q^4 - 12 * q^5 + 5 * q^6 - 9 * q^7 - 12 * q^8 + 3 * q^9	\( 10 q - q^{2} - 7 q^{3} + 15 q^{4} - 12 q^{5} + 5 q^{6} - 9 q^{7} - 12 q^{8} + 3 q^{9} + 4 q^{10} + 12 q^{11} - 24 q^{12} - 11 q^{13} - 12 q^{14} + 9 q^{15} - 3 q^{16} - 10 q^{17} - 22 q^{18} - 5 q^{19} - 36 q^{20} - 10 q^{21} + 6 q^{22} - 7 q^{23} + 35 q^{24} + 2 q^{25} + q^{26} - 31 q^{27} - 4 q^{28} + 10 q^{29} - 9 q^{30} + 13 q^{31} - 15 q^{32} - 9 q^{33} + q^{34} - 8 q^{35} + 40 q^{36} + 12 q^{37} - 50 q^{38} + 24 q^{39} + 5 q^{40} - 29 q^{41} - 17 q^{42} - 18 q^{43} - 6 q^{44} - 14 q^{45} + 11 q^{46} - 18 q^{47} - 43 q^{48} - 9 q^{49} - 31 q^{50} + 7 q^{51} - 68 q^{52} + 19 q^{54} - 27 q^{55} - 7 q^{56} + 20 q^{57} + 23 q^{58} - 10 q^{59} + 38 q^{60} + 8 q^{61} - 46 q^{62} + 39 q^{63} - 20 q^{64} + 58 q^{65} - 34 q^{66} - 6 q^{67} - 15 q^{68} + 6 q^{69} + 73 q^{70} + 8 q^{71} - 70 q^{72} - 41 q^{73} - 10 q^{74} + 10 q^{75} + 12 q^{76} - 22 q^{77} - 43 q^{78} + 3 q^{79} - 15 q^{80} + 26 q^{81} + 8 q^{82} - 22 q^{84} + 12 q^{85} - 29 q^{86} - 28 q^{87} + 33 q^{88} - 45 q^{89} + 56 q^{90} - 14 q^{91} + 36 q^{92} - 19 q^{93} + 15 q^{94} - 17 q^{95} + 90 q^{96} - 5 q^{97} + 30 q^{98} + 14 q^{99}+O(q^{100}) \) 10 * q - q^2 - 7 * q^3 + 15 * q^4 - 12 * q^5 + 5 * q^6 - 9 * q^7 - 12 * q^8 + 3 * q^9 + 4 * q^10 + 12 * q^11 - 24 * q^12 - 11 * q^13 - 12 * q^14 + 9 * q^15 - 3 * q^16 - 10 * q^17 - 22 * q^18 - 5 * q^19 - 36 * q^20 - 10 * q^21 + 6 * q^22 - 7 * q^23 + 35 * q^24 + 2 * q^25 + q^26 - 31 * q^27 - 4 * q^28 + 10 * q^29 - 9 * q^30 + 13 * q^31 - 15 * q^32 - 9 * q^33 + q^34 - 8 * q^35 + 40 * q^36 + 12 * q^37 - 50 * q^38 + 24 * q^39 + 5 * q^40 - 29 * q^41 - 17 * q^42 - 18 * q^43 - 6 * q^44 - 14 * q^45 + 11 * q^46 - 18 * q^47 - 43 * q^48 - 9 * q^49 - 31 * q^50 + 7 * q^51 - 68 * q^52 + 19 * q^54 - 27 * q^55 - 7 * q^56 + 20 * q^57 + 23 * q^58 - 10 * q^59 + 38 * q^60 + 8 * q^61 - 46 * q^62 + 39 * q^63 - 20 * q^64 + 58 * q^65 - 34 * q^66 - 6 * q^67 - 15 * q^68 + 6 * q^69 + 73 * q^70 + 8 * q^71 - 70 * q^72 - 41 * q^73 - 10 * q^74 + 10 * q^75 + 12 * q^76 - 22 * q^77 - 43 * q^78 + 3 * q^79 - 15 * q^80 + 26 * q^81 + 8 * q^82 - 22 * q^84 + 12 * q^85 - 29 * q^86 - 28 * q^87 + 33 * q^88 - 45 * q^89 + 56 * q^90 - 14 * q^91 + 36 * q^92 - 19 * q^93 + 15 * q^94 - 17 * q^95 + 90 * q^96 - 5 * q^97 + 30 * q^98 + 14 * q^99

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