LMFDB - Embedded newform 1003.2.a.i.1.17

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:	$18$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 5 x^{17} - 16 x^{16} + 112 x^{15} + 52 x^{14} - 984 x^{13} + 431 x^{12} + 4304 x^{11} + \cdots + 28 $ x^18 - 5x^17 - 16x^16 + 112x^15 + 52x^14 - 984x^13 + 431x^12 + 4304x^11 - 3825x^10 - 9826x^9 + 11533x^8 + 11182x^7 - 15697x^6 - 5604x^5 + 9201x^4 + 1189x^3 - 1952x^2 - 100*x + 28
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.17
Root			$2.58784$ 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)

$f(q)$	$=$	$q+2.58784 q^{2} -0.402595 q^{3} +4.69689 q^{4} +3.31536 q^{5} -1.04185 q^{6} -2.14234 q^{7} +6.97912 q^{8} -2.83792 q^{9} +O(q^{10})$	\(q+2.58784 q^{2} -0.402595 q^{3} +4.69689 q^{4} +3.31536 q^{5} -1.04185 q^{6} -2.14234 q^{7} +6.97912 q^{8} -2.83792 q^{9} +8.57961 q^{10} +0.965417 q^{11} -1.89094 q^{12} +5.15131 q^{13} -5.54403 q^{14} -1.33475 q^{15} +8.66702 q^{16} +1.00000 q^{17} -7.34406 q^{18} -8.60814 q^{19} +15.5719 q^{20} +0.862497 q^{21} +2.49834 q^{22} -2.77397 q^{23} -2.80976 q^{24} +5.99163 q^{25} +13.3307 q^{26} +2.35032 q^{27} -10.0624 q^{28} +4.97584 q^{29} -3.45411 q^{30} -2.77586 q^{31} +8.47059 q^{32} -0.388672 q^{33} +2.58784 q^{34} -7.10265 q^{35} -13.3294 q^{36} +4.56084 q^{37} -22.2764 q^{38} -2.07389 q^{39} +23.1383 q^{40} -0.270261 q^{41} +2.23200 q^{42} -1.39542 q^{43} +4.53446 q^{44} -9.40872 q^{45} -7.17859 q^{46} -6.21573 q^{47} -3.48930 q^{48} -2.41036 q^{49} +15.5053 q^{50} -0.402595 q^{51} +24.1952 q^{52} -7.87170 q^{53} +6.08223 q^{54} +3.20071 q^{55} -14.9517 q^{56} +3.46559 q^{57} +12.8767 q^{58} -1.00000 q^{59} -6.26917 q^{60} +7.61403 q^{61} -7.18346 q^{62} +6.07980 q^{63} +4.58646 q^{64} +17.0785 q^{65} -1.00582 q^{66} -3.15395 q^{67} +4.69689 q^{68} +1.11679 q^{69} -18.3805 q^{70} -7.91550 q^{71} -19.8062 q^{72} -15.5700 q^{73} +11.8027 q^{74} -2.41220 q^{75} -40.4315 q^{76} -2.06826 q^{77} -5.36689 q^{78} +15.2403 q^{79} +28.7343 q^{80} +7.56753 q^{81} -0.699390 q^{82} +8.38648 q^{83} +4.05105 q^{84} +3.31536 q^{85} -3.61112 q^{86} -2.00325 q^{87} +6.73776 q^{88} +13.3526 q^{89} -24.3482 q^{90} -11.0359 q^{91} -13.0291 q^{92} +1.11755 q^{93} -16.0853 q^{94} -28.5391 q^{95} -3.41022 q^{96} +12.0224 q^{97} -6.23762 q^{98} -2.73977 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 5 q^{2} + q^{3} + 21 q^{4} + 21 q^{5} + 5 q^{6} - q^{7} + 9 q^{8} + 17 q^{9}+O(q^{10}) $ 18 * q + 5 * q^2 + q^3 + 21 * q^4 + 21 * q^5 + 5 * q^6 - q^7 + 9 * q^8 + 17 * q^9	\( 18 q + 5 q^{2} + q^{3} + 21 q^{4} + 21 q^{5} + 5 q^{6} - q^{7} + 9 q^{8} + 17 q^{9} + 10 q^{10} + 6 q^{11} + 20 q^{12} + 12 q^{13} + 9 q^{14} - q^{15} + 19 q^{16} + 18 q^{17} + 10 q^{18} - 14 q^{19} + 17 q^{20} - 14 q^{21} - 4 q^{22} + 7 q^{23} - 3 q^{24} + 35 q^{25} + 3 q^{26} + 13 q^{27} + q^{28} + 23 q^{29} + 17 q^{30} - q^{31} + 13 q^{32} + 7 q^{33} + 5 q^{34} + 5 q^{35} - 16 q^{36} + 36 q^{37} - 19 q^{38} + 8 q^{39} - 4 q^{40} + 37 q^{41} + 9 q^{42} - 15 q^{43} - 9 q^{44} + 17 q^{45} + q^{46} + 23 q^{47} + 17 q^{48} + 15 q^{49} + 32 q^{50} + q^{51} - 11 q^{52} + 35 q^{53} - 17 q^{54} - 6 q^{55} + 37 q^{56} - 16 q^{57} + 2 q^{58} - 18 q^{59} - 6 q^{60} + 39 q^{61} - q^{62} + 15 q^{63} + 5 q^{64} + 15 q^{65} - 36 q^{66} + 14 q^{67} + 21 q^{68} + 16 q^{69} - 45 q^{70} + 3 q^{71} - 71 q^{72} + 56 q^{73} - 27 q^{74} + 16 q^{75} - q^{76} + 39 q^{77} - 71 q^{78} - 22 q^{79} + 45 q^{80} - 18 q^{81} + 5 q^{82} + 12 q^{83} + 2 q^{84} + 21 q^{85} + 4 q^{86} + 8 q^{87} - 18 q^{88} + 34 q^{89} + 48 q^{90} + 3 q^{91} + 67 q^{92} - 19 q^{93} - 38 q^{94} - 72 q^{95} + 6 q^{96} + 31 q^{97} + 19 q^{98} + 44 q^{99}+O(q^{100}) \) 18 * q + 5 * q^2 + q^3 + 21 * q^4 + 21 * q^5 + 5 * q^6 - q^7 + 9 * q^8 + 17 * q^9 + 10 * q^10 + 6 * q^11 + 20 * q^12 + 12 * q^13 + 9 * q^14 - q^15 + 19 * q^16 + 18 * q^17 + 10 * q^18 - 14 * q^19 + 17 * q^20 - 14 * q^21 - 4 * q^22 + 7 * q^23 - 3 * q^24 + 35 * q^25 + 3 * q^26 + 13 * q^27 + q^28 + 23 * q^29 + 17 * q^30 - q^31 + 13 * q^32 + 7 * q^33 + 5 * q^34 + 5 * q^35 - 16 * q^36 + 36 * q^37 - 19 * q^38 + 8 * q^39 - 4 * q^40 + 37 * q^41 + 9 * q^42 - 15 * q^43 - 9 * q^44 + 17 * q^45 + q^46 + 23 * q^47 + 17 * q^48 + 15 * q^49 + 32 * q^50 + q^51 - 11 * q^52 + 35 * q^53 - 17 * q^54 - 6 * q^55 + 37 * q^56 - 16 * q^57 + 2 * q^58 - 18 * q^59 - 6 * q^60 + 39 * q^61 - q^62 + 15 * q^63 + 5 * q^64 + 15 * q^65 - 36 * q^66 + 14 * q^67 + 21 * q^68 + 16 * q^69 - 45 * q^70 + 3 * q^71 - 71 * q^72 + 56 * q^73 - 27 * q^74 + 16 * q^75 - q^76 + 39 * q^77 - 71 * q^78 - 22 * q^79 + 45 * q^80 - 18 * q^81 + 5 * q^82 + 12 * q^83 + 2 * q^84 + 21 * q^85 + 4 * q^86 + 8 * q^87 - 18 * q^88 + 34 * q^89 + 48 * q^90 + 3 * q^91 + 67 * q^92 - 19 * q^93 - 38 * q^94 - 72 * q^95 + 6 * q^96 + 31 * q^97 + 19 * q^98 + 44 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	2.58784	1.82988	0.914938	−	0.403594i	$-0.132239\pi$
$2$	2.58784	1.82988	0.914938	+	0.403594i	$0.132239\pi$
$3$	−0.402595	−0.232438	−0.116219	−	0.993224i	$-0.537077\pi$
$3$	−0.402595	−0.232438	−0.116219	+	0.993224i	$0.537077\pi$
$4$	4.69689	2.34845
$5$	3.31536	1.48268	0.741338	−	0.671132i	$-0.234192\pi$
$5$	3.31536	1.48268	0.741338	+	0.671132i	$0.234192\pi$
$6$	−1.04185	−0.425333
$7$	−2.14234	−0.809730	−0.404865	−	0.914376i	$-0.632681\pi$
$7$	−2.14234	−0.809730	−0.404865	+	0.914376i	$0.632681\pi$
$8$	6.97912	2.46749
$9$	−2.83792	−0.945972
$10$	8.57961	2.71311
$11$	0.965417	0.291084	0.145542	−	0.989352i	$-0.453507\pi$
$11$	0.965417	0.291084	0.145542	+	0.989352i	$0.453507\pi$
$12$	−1.89094	−0.545869
$13$	5.15131	1.42872	0.714358	−	0.699780i	$-0.246719\pi$
$13$	5.15131	1.42872	0.714358	+	0.699780i	$0.246719\pi$
$14$	−5.54403	−1.48171
$15$	−1.33475	−0.344630
$16$	8.66702	2.16676
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−7.34406	−1.73101
$19$	−8.60814	−1.97484	−0.987421	−	0.158112i	$-0.949459\pi$
$19$	−8.60814	−1.97484	−0.987421	+	0.158112i	$0.949459\pi$
$20$	15.5719	3.48198
$21$	0.862497	0.188212
$22$	2.49834	0.532648
$23$	−2.77397	−0.578414	−0.289207	−	0.957267i	$-0.593392\pi$
$23$	−2.77397	−0.578414	−0.289207	+	0.957267i	$0.593392\pi$
$24$	−2.80976	−0.573539
$25$	5.99163	1.19833
$26$	13.3307	2.61437
$27$	2.35032	0.452318
$28$	−10.0624	−1.90161
$29$	4.97584	0.923990	0.461995	−	0.886882i	$-0.347134\pi$
$29$	4.97584	0.923990	0.461995	+	0.886882i	$0.347134\pi$
$30$	−3.45411	−0.630631
$31$	−2.77586	−0.498559	−0.249279	−	0.968432i	$-0.580194\pi$
$31$	−2.77586	−0.498559	−0.249279	+	0.968432i	$0.580194\pi$
$32$	8.47059	1.49740
$33$	−0.388672	−0.0676591
$34$	2.58784	0.443810
$35$	−7.10265	−1.20057
$36$	−13.3294	−2.22157
$37$	4.56084	0.749798	0.374899	−	0.927066i	$-0.377677\pi$
$37$	4.56084	0.749798	0.374899	+	0.927066i	$0.377677\pi$
$38$	−22.2764	−3.61372
$39$	−2.07389	−0.332088
$40$	23.1383	3.65849
$41$	−0.270261	−0.0422076	−0.0211038	−	0.999777i	$-0.506718\pi$
$41$	−0.270261	−0.0422076	−0.0211038	+	0.999777i	$0.506718\pi$
$42$	2.23200	0.344405
$43$	−1.39542	−0.212800	−0.106400	−	0.994323i	$-0.533932\pi$
$43$	−1.39542	−0.212800	−0.106400	+	0.994323i	$0.533932\pi$
$44$	4.53446	0.683596
$45$	−9.40872	−1.40257
$46$	−7.17859	−1.05843
$47$	−6.21573	−0.906657	−0.453329	−	0.891343i	$-0.649764\pi$
$47$	−6.21573	−0.906657	−0.453329	+	0.891343i	$0.649764\pi$
$48$	−3.48930	−0.503637
$49$	−2.41036	−0.344337
$50$	15.5053	2.19279
$51$	−0.402595	−0.0563745
$52$	24.1952	3.35526
$53$	−7.87170	−1.08126	−0.540630	−	0.841260i	$-0.681814\pi$
$53$	−7.87170	−1.08126	−0.540630	+	0.841260i	$0.681814\pi$
$54$	6.08223	0.827687
$55$	3.20071	0.431583
$56$	−14.9517	−1.99800
$57$	3.46559	0.459029
$58$	12.8767	1.69079
$59$	−1.00000	−0.130189
$59$	−1.00000	−0.130189
$60$	−6.26917	−0.809346
$61$	7.61403	0.974876	0.487438	−	0.873158i	$-0.337931\pi$
$61$	7.61403	0.974876	0.487438	+	0.873158i	$0.337931\pi$
$62$	−7.18346	−0.912300
$63$	6.07980	0.765982
$64$	4.58646	0.573307
$65$	17.0785	2.11832
$66$	−1.00582	−0.123808
$67$	−3.15395	−0.385316	−0.192658	−	0.981266i	$-0.561711\pi$
$67$	−3.15395	−0.385316	−0.192658	+	0.981266i	$0.561711\pi$
$68$	4.69689	0.569582
$69$	1.11679	0.134445
$70$	−18.3805	−2.19689
$71$	−7.91550	−0.939397	−0.469698	−	0.882827i	$-0.655637\pi$
$71$	−7.91550	−0.939397	−0.469698	+	0.882827i	$0.655637\pi$
$72$	−19.8062	−2.33418
$73$	−15.5700	−1.82233	−0.911165	−	0.412042i	$-0.864816\pi$
$73$	−15.5700	−1.82233	−0.911165	+	0.412042i	$0.864816\pi$
$74$	11.8027	1.37204
$75$	−2.41220	−0.278537
$76$	−40.4315	−4.63781
$77$	−2.06826	−0.235700
$78$	−5.36689	−0.607680
$79$	15.2403	1.71467	0.857335	−	0.514760i	$-0.172119\pi$
$79$	15.2403	1.71467	0.857335	+	0.514760i	$0.172119\pi$
$80$	28.7343	3.21259
$81$	7.56753	0.840836
$82$	−0.699390	−0.0772347
$83$	8.38648	0.920535	0.460268	−	0.887780i	$-0.347753\pi$
$83$	8.38648	0.920535	0.460268	+	0.887780i	$0.347753\pi$
$84$	4.05105	0.442006
$85$	3.31536	0.359602
$86$	−3.61112	−0.389397
$87$	−2.00325	−0.214771
$88$	6.73776	0.718247
$89$	13.3526	1.41538	0.707688	−	0.706525i	$-0.249738\pi$
$89$	13.3526	1.41538	0.707688	+	0.706525i	$0.249738\pi$
$90$	−24.3482	−2.56653
$91$	−11.0359	−1.15687
$92$	−13.0291	−1.35837
$93$	1.11755	0.115884
$94$	−16.0853	−1.65907
$95$	−28.5391	−2.92805
$96$	−3.41022	−0.348054
$97$	12.0224	1.22069	0.610344	−	0.792137i	$-0.291031\pi$
$97$	12.0224	1.22069	0.610344	+	0.792137i	$0.291031\pi$
$98$	−6.23762	−0.630095
$99$	−2.73977	−0.275358
$100$	28.1420	2.81420
$101$	−6.57000	−0.653740	−0.326870	−	0.945069i	$-0.605994\pi$
$101$	−6.57000	−0.653740	−0.326870	+	0.945069i	$0.605994\pi$
$102$	−1.04185	−0.103158
$103$	−9.51738	−0.937776	−0.468888	−	0.883258i	$-0.655345\pi$
$103$	−9.51738	−0.937776	−0.468888	+	0.883258i	$0.655345\pi$
$104$	35.9516	3.52534
$105$	2.85949	0.279057
$106$	−20.3707	−1.97857
$107$	8.44607	0.816512	0.408256	−	0.912867i	$-0.366137\pi$
$107$	8.44607	0.816512	0.408256	+	0.912867i	$0.366137\pi$
$108$	11.0392	1.06225
$109$	−4.10679	−0.393359	−0.196680	−	0.980468i	$-0.563016\pi$
$109$	−4.10679	−0.393359	−0.196680	+	0.980468i	$0.563016\pi$
$110$	8.28290	0.789744
$111$	−1.83617	−0.174282
$112$	−18.5677	−1.75449
$113$	−13.1353	−1.23566	−0.617832	−	0.786310i	$-0.711989\pi$
$113$	−13.1353	−1.23566	−0.617832	+	0.786310i	$0.711989\pi$
$114$	8.96838	0.839966
$115$	−9.19673	−0.857599
$116$	23.3710	2.16994
$117$	−14.6190	−1.35153
$118$	−2.58784	−0.238230
$119$	−2.14234	−0.196388
$120$	−9.31536	−0.850372
$121$	−10.0680	−0.915270
$122$	19.7038	1.78390
$123$	0.108806	0.00981067
$124$	−13.0379	−1.17084
$125$	3.28760	0.294052
$126$	15.7335	1.40165
$127$	8.59505	0.762687	0.381343	−	0.924433i	$-0.375462\pi$
$127$	8.59505	0.762687	0.381343	+	0.924433i	$0.375462\pi$
$128$	−5.07218	−0.448322
$129$	0.561790	0.0494628
$130$	44.1963	3.87627
$131$	8.97100	0.783800	0.391900	−	0.920008i	$-0.371818\pi$
$131$	8.97100	0.783800	0.391900	+	0.920008i	$0.371818\pi$
$132$	−1.82555	−0.158894
$133$	18.4416	1.59909
$134$	−8.16190	−0.705080
$135$	7.79215	0.670641
$136$	6.97912	0.598454
$137$	1.14570	0.0978834	0.0489417	−	0.998802i	$-0.484415\pi$
$137$	1.14570	0.0978834	0.0489417	+	0.998802i	$0.484415\pi$
$138$	2.89006	0.246018
$139$	16.1532	1.37010	0.685048	−	0.728498i	$-0.259781\pi$
$139$	16.1532	1.37010	0.685048	+	0.728498i	$0.259781\pi$
$140$	−33.3604	−2.81947
$141$	2.50242	0.210742
$142$	−20.4840	−1.71898
$143$	4.97316	0.415877
$144$	−24.5963	−2.04969
$145$	16.4967	1.36998
$146$	−40.2926	−3.33464
$147$	0.970399	0.0800372
$148$	21.4218	1.76086
$149$	−21.4023	−1.75334	−0.876672	−	0.481088i	$-0.840242\pi$
$149$	−21.4023	−1.75334	−0.876672	+	0.481088i	$0.840242\pi$
$150$	−6.24237	−0.509687
$151$	18.7485	1.52573	0.762866	−	0.646556i	$-0.223791\pi$
$151$	18.7485	1.52573	0.762866	+	0.646556i	$0.223791\pi$
$152$	−60.0772	−4.87291
$153$	−2.83792	−0.229432
$154$	−5.35230	−0.431301
$155$	−9.20297	−0.739200
$156$	−9.74084	−0.779892
$157$	−10.2510	−0.818121	−0.409061	−	0.912507i	$-0.634144\pi$
$157$	−10.2510	−0.818121	−0.409061	+	0.912507i	$0.634144\pi$
$158$	39.4394	3.13763
$159$	3.16910	0.251326
$160$	28.0831	2.22016
$161$	5.94281	0.468359
$162$	19.5835	1.53863
$163$	−5.49910	−0.430723	−0.215361	−	0.976534i	$-0.569093\pi$
$163$	−5.49910	−0.430723	−0.215361	+	0.976534i	$0.569093\pi$
$164$	−1.26939	−0.0991224
$165$	−1.28859	−0.100316
$166$	21.7028	1.68447
$167$	2.81958	0.218185	0.109093	−	0.994032i	$-0.465205\pi$
$167$	2.81958	0.218185	0.109093	+	0.994032i	$0.465205\pi$
$168$	6.01946	0.464412
$169$	13.5360	1.04123
$170$	8.57961	0.658026
$171$	24.4292	1.86815
$172$	−6.55415	−0.499749
$173$	5.48949	0.417358	0.208679	−	0.977984i	$-0.433084\pi$
$173$	5.48949	0.417358	0.208679	+	0.977984i	$0.433084\pi$
$174$	−5.18407	−0.393004
$175$	−12.8361	−0.970320
$176$	8.36729	0.630708
$177$	0.402595	0.0302609
$178$	34.5544	2.58996
$179$	−10.5643	−0.789613	−0.394806	−	0.918764i	$-0.629188\pi$
$179$	−10.5643	−0.789613	−0.394806	+	0.918764i	$0.629188\pi$
$180$	−44.1918	−3.29386
$181$	2.07095	0.153932	0.0769662	−	0.997034i	$-0.475477\pi$
$181$	2.07095	0.153932	0.0769662	+	0.997034i	$0.475477\pi$
$182$	−28.5590	−2.11694
$183$	−3.06537	−0.226598
$184$	−19.3599	−1.42723
$185$	15.1208	1.11171
$186$	2.89202	0.212053
$187$	0.965417	0.0705983
$188$	−29.1946	−2.12924
$189$	−5.03518	−0.366256
$190$	−73.8545	−5.35797
$191$	12.2735	0.888082	0.444041	−	0.896007i	$-0.353545\pi$
$191$	12.2735	0.888082	0.444041	+	0.896007i	$0.353545\pi$
$192$	−1.84648	−0.133259
$193$	−2.33926	−0.168384	−0.0841919	−	0.996450i	$-0.526831\pi$
$193$	−2.33926	−0.168384	−0.0841919	+	0.996450i	$0.526831\pi$
$194$	31.1119	2.23371
$195$	−6.87570	−0.492379
$196$	−11.3212	−0.808658
$197$	−20.2033	−1.43942	−0.719712	−	0.694272i	$-0.755726\pi$
$197$	−20.2033	−1.43942	−0.719712	+	0.694272i	$0.755726\pi$
$198$	−7.09008	−0.503870
$199$	−0.182579	−0.0129427	−0.00647136	−	0.999979i	$-0.502060\pi$
$199$	−0.182579	−0.0129427	−0.00647136	+	0.999979i	$0.502060\pi$
$200$	41.8163	2.95686
$201$	1.26976	0.0895621
$202$	−17.0021	−1.19626
$203$	−10.6600	−0.748183
$204$	−1.89094	−0.132393
$205$	−0.896012	−0.0625802
$206$	−24.6294	−1.71601
$207$	7.87231	0.547163
$208$	44.6465	3.09568
$209$	−8.31044	−0.574845
$210$	7.39989	0.510641
$211$	13.5496	0.932794	0.466397	−	0.884576i	$-0.345552\pi$
$211$	13.5496	0.932794	0.466397	+	0.884576i	$0.345552\pi$
$212$	−36.9725	−2.53928
$213$	3.18674	0.218352
$214$	21.8570	1.49412
$215$	−4.62633	−0.315513
$216$	16.4031	1.11609
$217$	5.94684	0.403698
$218$	−10.6277	−0.719798
$219$	6.26840	0.423579
$220$	15.0334	1.01355
$221$	5.15131	0.346515
$222$	−4.75171	−0.318914
$223$	−5.44476	−0.364608	−0.182304	−	0.983242i	$-0.558356\pi$
$223$	−5.44476	−0.364608	−0.182304	+	0.983242i	$0.558356\pi$
$224$	−18.1469	−1.21249
$225$	−17.0037	−1.13358
$226$	−33.9920	−2.26111
$227$	−4.58358	−0.304223	−0.152112	−	0.988363i	$-0.548607\pi$
$227$	−4.58358	−0.304223	−0.152112	+	0.988363i	$0.548607\pi$
$228$	16.2775	1.07800
$229$	−4.60282	−0.304163	−0.152082	−	0.988368i	$-0.548598\pi$
$229$	−4.60282	−0.304163	−0.152082	+	0.988368i	$0.548598\pi$
$230$	−23.7996	−1.56930
$231$	0.832669	0.0547856
$232$	34.7270	2.27994
$233$	2.86257	0.187533	0.0937667	−	0.995594i	$-0.470109\pi$
$233$	2.86257	0.187533	0.0937667	+	0.995594i	$0.470109\pi$
$234$	−37.8316	−2.47313
$235$	−20.6074	−1.34428
$236$	−4.69689	−0.305742
$237$	−6.13567	−0.398555
$238$	−5.54403	−0.359366
$239$	−19.0394	−1.23156	−0.615779	−	0.787919i	$-0.711159\pi$
$239$	−19.0394	−1.23156	−0.615779	+	0.787919i	$0.711159\pi$
$240$	−11.5683	−0.746730
$241$	30.3722	1.95644	0.978222	−	0.207559i	$-0.0665519\pi$
$241$	30.3722	1.95644	0.978222	+	0.207559i	$0.0665519\pi$
$242$	−26.0543	−1.67483
$243$	−10.0976	−0.647761
$244$	35.7623	2.28944
$245$	−7.99122	−0.510541
$246$	0.281571	0.0179523
$247$	−44.3432	−2.82149
$248$	−19.3730	−1.23019
$249$	−3.37635	−0.213968
$250$	8.50777	0.538079
$251$	−26.1168	−1.64848	−0.824238	−	0.566244i	$-0.808396\pi$
$251$	−26.1168	−1.64848	−0.824238	+	0.566244i	$0.808396\pi$
$252$	28.5562	1.79887
$253$	−2.67804	−0.168367
$254$	22.2426	1.39562
$255$	−1.33475	−0.0835851
$256$	−22.2989	−1.39368
$257$	25.9291	1.61741	0.808706	−	0.588213i	$-0.200168\pi$
$257$	25.9291	1.61741	0.808706	+	0.588213i	$0.200168\pi$
$258$	1.45382	0.0905108
$259$	−9.77089	−0.607134
$260$	80.2157	4.97477
$261$	−14.1210	−0.874069
$262$	23.2155	1.43426
$263$	−12.7603	−0.786835	−0.393418	−	0.919360i	$-0.628707\pi$
$263$	−12.7603	−0.786835	−0.393418	+	0.919360i	$0.628707\pi$
$264$	−2.71259	−0.166948
$265$	−26.0975	−1.60316
$266$	47.7238	2.92613
$267$	−5.37570	−0.328987
$268$	−14.8138	−0.904894
$269$	11.2935	0.688578	0.344289	−	0.938864i	$-0.388120\pi$
$269$	11.2935	0.688578	0.344289	+	0.938864i	$0.388120\pi$
$270$	20.1648	1.22719
$271$	21.9985	1.33632	0.668158	−	0.744019i	$-0.267083\pi$
$271$	21.9985	1.33632	0.668158	+	0.744019i	$0.267083\pi$
$272$	8.66702	0.525515
$273$	4.44299	0.268902
$274$	2.96487	0.179114
$275$	5.78442	0.348813
$276$	5.24543	0.315738
$277$	−8.90421	−0.535002	−0.267501	−	0.963558i	$-0.586198\pi$
$277$	−8.90421	−0.535002	−0.267501	+	0.963558i	$0.586198\pi$
$278$	41.8018	2.50711
$279$	7.87765	0.471623
$280$	−49.5702	−2.96239
$281$	4.19433	0.250213	0.125107	−	0.992143i	$-0.460073\pi$
$281$	4.19433	0.250213	0.125107	+	0.992143i	$0.460073\pi$
$282$	6.47585	0.385631
$283$	9.42649	0.560347	0.280173	−	0.959949i	$-0.409608\pi$
$283$	9.42649	0.560347	0.280173	+	0.959949i	$0.409608\pi$
$284$	−37.1783	−2.20612
$285$	11.4897	0.680591
$286$	12.8697	0.761003
$287$	0.578991	0.0341768
$288$	−24.0388	−1.41650
$289$	1.00000	0.0588235
$290$	42.6908	2.50689
$291$	−4.84015	−0.283734
$292$	−73.1306	−4.27964
$293$	34.0001	1.98631	0.993154	−	0.116813i	$-0.0372678\pi$
$293$	34.0001	1.98631	0.993154	+	0.116813i	$0.0372678\pi$
$294$	2.51123	0.146458
$295$	−3.31536	−0.193028
$296$	31.8307	1.85012
$297$	2.26903	0.131663
$298$	−55.3856	−3.20840
$299$	−14.2896	−0.826389
$300$	−11.3298	−0.654128
$301$	2.98947	0.172310
$302$	48.5181	2.79190
$303$	2.64505	0.151954
$304$	−74.6069	−4.27900
$305$	25.2433	1.44542
$306$	−7.34406	−0.419832
$307$	9.17152	0.523446	0.261723	−	0.965143i	$-0.415709\pi$
$307$	9.17152	0.523446	0.261723	+	0.965143i	$0.415709\pi$
$308$	−9.71437	−0.553528
$309$	3.83165	0.217975
$310$	−23.8158	−1.35265
$311$	20.8823	1.18413	0.592063	−	0.805892i	$-0.298314\pi$
$311$	20.8823	1.18413	0.592063	+	0.805892i	$0.298314\pi$
$312$	−14.4739	−0.819425
$313$	−14.7747	−0.835114	−0.417557	−	0.908651i	$-0.637114\pi$
$313$	−14.7747	−0.835114	−0.417557	+	0.908651i	$0.637114\pi$
$314$	−26.5280	−1.49706
$315$	20.1567	1.13570
$316$	71.5821	4.02681
$317$	34.7664	1.95268	0.976338	−	0.216249i	$-0.0693822\pi$
$317$	34.7664	1.95268	0.976338	+	0.216249i	$0.0693822\pi$
$318$	8.20112	0.459896
$319$	4.80376	0.268959
$320$	15.2058	0.850028
$321$	−3.40034	−0.189789
$322$	15.3790	0.857039
$323$	−8.60814	−0.478970
$324$	35.5439	1.97466
$325$	30.8647	1.71207
$326$	−14.2308	−0.788169
$327$	1.65337	0.0914317
$328$	−1.88618	−0.104147
$329$	13.3162	0.734148
$330$	−3.33465	−0.183567
$331$	13.5320	0.743788	0.371894	−	0.928275i	$-0.378709\pi$
$331$	13.5320	0.743788	0.371894	+	0.928275i	$0.378709\pi$
$332$	39.3904	2.16183
$333$	−12.9433	−0.709288
$334$	7.29660	0.399252
$335$	−10.4565	−0.571298
$336$	7.47528	0.407810
$337$	29.7615	1.62121	0.810607	−	0.585591i	$-0.199137\pi$
$337$	29.7615	1.62121	0.810607	+	0.585591i	$0.199137\pi$
$338$	35.0290	1.90532
$339$	5.28820	0.287216
$340$	15.5719	0.844505
$341$	−2.67986	−0.145122
$342$	63.2187	3.41848
$343$	20.1602	1.08855
$344$	−9.73881	−0.525082
$345$	3.70255	0.199339
$346$	14.2059	0.763714
$347$	−14.4328	−0.774793	−0.387396	−	0.921913i	$-0.626625\pi$
$347$	−14.4328	−0.774793	−0.387396	+	0.921913i	$0.626625\pi$
$348$	−9.40904	−0.504377
$349$	−19.1576	−1.02548	−0.512741	−	0.858543i	$-0.671370\pi$
$349$	−19.1576	−1.02548	−0.512741	+	0.858543i	$0.671370\pi$
$350$	−33.2178	−1.77557
$351$	12.1072	0.646235
$352$	8.17765	0.435870
$353$	23.9266	1.27349	0.636743	−	0.771076i	$-0.280281\pi$
$353$	23.9266	1.27349	0.636743	+	0.771076i	$0.280281\pi$
$354$	1.04185	0.0553737
$355$	−26.2427	−1.39282
$356$	62.7159	3.32393
$357$	0.862497	0.0456482
$358$	−27.3387	−1.44489
$359$	8.44558	0.445740	0.222870	−	0.974848i	$-0.428457\pi$
$359$	8.44558	0.445740	0.222870	+	0.974848i	$0.428457\pi$
$360$	−65.6646	−3.46083
$361$	55.1001	2.90000
$362$	5.35928	0.281677
$363$	4.05331	0.212744
$364$	−51.8344	−2.71686
$365$	−51.6202	−2.70192
$366$	−7.93267	−0.414647
$367$	12.3351	0.643885	0.321942	−	0.946759i	$-0.395664\pi$
$367$	12.3351	0.643885	0.321942	+	0.946759i	$0.395664\pi$
$368$	−24.0421	−1.25328
$369$	0.766978	0.0399273
$370$	39.1303	2.03429
$371$	16.8639	0.875529
$372$	5.24899	0.272148
$373$	−9.43934	−0.488751	−0.244375	−	0.969681i	$-0.578583\pi$
$373$	−9.43934	−0.488751	−0.244375	+	0.969681i	$0.578583\pi$
$374$	2.49834	0.129186
$375$	−1.32357	−0.0683489
$376$	−43.3803	−2.23717
$377$	25.6321	1.32012
$378$	−13.0302	−0.670203
$379$	−7.50936	−0.385730	−0.192865	−	0.981225i	$-0.561778\pi$
$379$	−7.50936	−0.385730	−0.192865	+	0.981225i	$0.561778\pi$
$380$	−134.045	−6.87637
$381$	−3.46032	−0.177278
$382$	31.7619	1.62508
$383$	4.81291	0.245928	0.122964	−	0.992411i	$-0.460760\pi$
$383$	4.81291	0.245928	0.122964	+	0.992411i	$0.460760\pi$
$384$	2.04203	0.104207
$385$	−6.85701	−0.349466
$386$	−6.05363	−0.308122
$387$	3.96009	0.201303
$388$	56.4678	2.86672
$389$	−31.2176	−1.58280	−0.791399	−	0.611300i	$-0.790647\pi$
$389$	−31.2176	−1.58280	−0.791399	+	0.611300i	$0.790647\pi$
$390$	−17.7932	−0.900993
$391$	−2.77397	−0.140286
$392$	−16.8222	−0.849649
$393$	−3.61168	−0.182185
$394$	−52.2828	−2.63397
$395$	50.5272	2.54230
$396$	−12.8684	−0.646663
$397$	32.8611	1.64925	0.824625	−	0.565679i	$-0.191386\pi$
$397$	32.8611	1.64925	0.824625	+	0.565679i	$0.191386\pi$
$398$	−0.472486	−0.0236836
$399$	−7.42449	−0.371689
$400$	51.9295	2.59648
$401$	28.9567	1.44603	0.723014	−	0.690834i	$-0.242756\pi$
$401$	28.9567	1.44603	0.723014	+	0.690834i	$0.242756\pi$
$402$	3.28594	0.163888
$403$	−14.2993	−0.712299
$404$	−30.8586	−1.53527
$405$	25.0891	1.24669
$406$	−27.5862	−1.36908
$407$	4.40311	0.218254
$408$	−2.80976	−0.139104
$409$	−20.9432	−1.03557	−0.517787	−	0.855510i	$-0.673244\pi$
$409$	−20.9432	−1.03557	−0.517787	+	0.855510i	$0.673244\pi$
$410$	−2.31873	−0.114514
$411$	−0.461251	−0.0227518
$412$	−44.7021	−2.20232
$413$	2.14234	0.105418
$414$	20.3722	1.00124
$415$	27.8042	1.36485
$416$	43.6347	2.13936
$417$	−6.50319	−0.318463
$418$	−21.5061	−1.05190
$419$	5.21459	0.254749	0.127375	−	0.991855i	$-0.459345\pi$
$419$	5.21459	0.254749	0.127375	+	0.991855i	$0.459345\pi$
$420$	13.4307	0.655352
$421$	−26.0833	−1.27122	−0.635611	−	0.772010i	$-0.719252\pi$
$421$	−26.0833	−1.27122	−0.635611	+	0.772010i	$0.719252\pi$
$422$	35.0642	1.70690
$423$	17.6397	0.857673
$424$	−54.9375	−2.66800
$425$	5.99163	0.290637
$426$	8.24676	0.399557
$427$	−16.3119	−0.789386
$428$	39.6703	1.91753
$429$	−2.00217	−0.0966656
$430$	−11.9722	−0.577350
$431$	−29.4188	−1.41705	−0.708527	−	0.705684i	$-0.750640\pi$
$431$	−29.4188	−1.41705	−0.708527	+	0.705684i	$0.750640\pi$
$432$	20.3702	0.980063
$433$	−15.8308	−0.760778	−0.380389	−	0.924827i	$-0.624210\pi$
$433$	−15.8308	−0.760778	−0.380389	+	0.924827i	$0.624210\pi$
$434$	15.3894	0.738717
$435$	−6.64149	−0.318435
$436$	−19.2892	−0.923783
$437$	23.8788	1.14228
$438$	16.2216	0.775097
$439$	27.2865	1.30231	0.651156	−	0.758944i	$-0.274284\pi$
$439$	27.2865	1.30231	0.651156	+	0.758944i	$0.274284\pi$
$440$	22.3381	1.06493
$441$	6.84041	0.325734
$442$	13.3307	0.634079
$443$	−11.9056	−0.565651	−0.282826	−	0.959171i	$-0.591272\pi$
$443$	−11.9056	−0.565651	−0.282826	+	0.959171i	$0.591272\pi$
$444$	−8.62430	−0.409291
$445$	44.2688	2.09854
$446$	−14.0902	−0.667188
$447$	8.61646	0.407544
$448$	−9.82577	−0.464224
$449$	3.74302	0.176644	0.0883219	−	0.996092i	$-0.471850\pi$
$449$	3.74302	0.176644	0.0883219	+	0.996092i	$0.471850\pi$
$450$	−44.0029	−2.07432
$451$	−0.260914	−0.0122860
$452$	−61.6951	−2.90189
$453$	−7.54806	−0.354639
$454$	−11.8616	−0.556691
$455$	−36.5879	−1.71527
$456$	24.1868	1.13265
$457$	−6.90126	−0.322827	−0.161414	−	0.986887i	$-0.551605\pi$
$457$	−6.90126	−0.322827	−0.161414	+	0.986887i	$0.551605\pi$
$458$	−11.9114	−0.556581
$459$	2.35032	0.109703
$460$	−43.1961	−2.01403
$461$	3.99816	0.186213	0.0931065	−	0.995656i	$-0.470320\pi$
$461$	3.99816	0.186213	0.0931065	+	0.995656i	$0.470320\pi$
$462$	2.15481	0.100251
$463$	31.2156	1.45071	0.725355	−	0.688375i	$-0.241675\pi$
$463$	31.2156	1.45071	0.725355	+	0.688375i	$0.241675\pi$
$464$	43.1257	2.00206
$465$	3.70507	0.171818
$466$	7.40787	0.343163
$467$	37.2005	1.72143	0.860717	−	0.509084i	$-0.170016\pi$
$467$	37.2005	1.72143	0.860717	+	0.509084i	$0.170016\pi$
$468$	−68.6639	−3.17399
$469$	6.75684	0.312002
$470$	−53.3286	−2.45986
$471$	4.12701	0.190163
$472$	−6.97912	−0.321240
$473$	−1.34716	−0.0619427
$474$	−15.8781	−0.729306
$475$	−51.5768	−2.36650
$476$	−10.0624	−0.461208
$477$	22.3392	1.02284
$478$	−49.2709	−2.25360
$479$	−35.8156	−1.63646	−0.818229	−	0.574892i	$-0.805044\pi$
$479$	−35.8156	−1.63646	−0.818229	+	0.574892i	$0.805044\pi$
$480$	−11.3061	−0.516051
$481$	23.4943	1.07125
$482$	78.5982	3.58005
$483$	−2.39254	−0.108864
$484$	−47.2882	−2.14946
$485$	39.8585	1.80988
$486$	−26.1309	−1.18532
$487$	−32.2163	−1.45986	−0.729931	−	0.683521i	$-0.760448\pi$
$487$	−32.2163	−1.45986	−0.729931	+	0.683521i	$0.760448\pi$
$488$	53.1392	2.40550
$489$	2.21391	0.100116
$490$	−20.6800	−0.934226
$491$	−0.328679	−0.0148331	−0.00741653	−	0.999972i	$-0.502361\pi$
$491$	−0.328679	−0.0148331	−0.00741653	+	0.999972i	$0.502361\pi$
$492$	0.511048	0.0230398
$493$	4.97584	0.224101
$494$	−114.753	−5.16298
$495$	−9.08334	−0.408266
$496$	−24.0584	−1.08025
$497$	16.9577	0.760658
$498$	−8.73744	−0.391534
$499$	34.3089	1.53588	0.767938	−	0.640524i	$-0.221283\pi$
$499$	34.3089	1.53588	0.767938	+	0.640524i	$0.221283\pi$
$500$	15.4415	0.690565
$501$	−1.13515	−0.0507146
$502$	−67.5859	−3.01651
$503$	−7.19188	−0.320670	−0.160335	−	0.987063i	$-0.551257\pi$
$503$	−7.19188	−0.320670	−0.160335	+	0.987063i	$0.551257\pi$
$504$	42.4316	1.89005
$505$	−21.7819	−0.969284
$506$	−6.93033	−0.308091
$507$	−5.44952	−0.242022
$508$	40.3700	1.79113
$509$	30.8879	1.36908	0.684540	−	0.728975i	$-0.260003\pi$
$509$	30.8879	1.36908	0.684540	+	0.728975i	$0.260003\pi$
$510$	−3.45411	−0.152950
$511$	33.3563	1.47559
$512$	−47.5615	−2.10194
$513$	−20.2318	−0.893258
$514$	67.1002	2.95966
$515$	−31.5536	−1.39042
$516$	2.63867	0.116161
$517$	−6.00077	−0.263914
$518$	−25.2855	−1.11098
$519$	−2.21004	−0.0970101
$520$	119.193	5.22694
$521$	3.07523	0.134728	0.0673642	−	0.997728i	$-0.478541\pi$
$521$	3.07523	0.134728	0.0673642	+	0.997728i	$0.478541\pi$
$522$	−36.5429	−1.59944
$523$	21.7307	0.950217	0.475108	−	0.879927i	$-0.342409\pi$
$523$	21.7307	0.950217	0.475108	+	0.879927i	$0.342409\pi$
$524$	42.1358	1.84071
$525$	5.16776	0.225539
$526$	−33.0216	−1.43981
$527$	−2.77586	−0.120918
$528$	−3.36863	−0.146601
$529$	−15.3051	−0.665438
$530$	−67.5361	−2.93358
$531$	2.83792	0.123155
$532$	86.6182	3.75538
$533$	−1.39220	−0.0603027
$534$	−13.9114	−0.602006
$535$	28.0018	1.21062
$536$	−22.0118	−0.950763
$537$	4.25313	0.183536
$538$	29.2258	1.26001
$539$	−2.32700	−0.100231
$540$	36.5989	1.57496
$541$	−41.6343	−1.79000	−0.894999	−	0.446068i	$-0.852824\pi$
$541$	−41.6343	−1.79000	−0.894999	+	0.446068i	$0.852824\pi$
$542$	56.9286	2.44529
$543$	−0.833753	−0.0357798
$544$	8.47059	0.363174
$545$	−13.6155	−0.583224
$546$	11.4977	0.492057
$547$	15.5466	0.664724	0.332362	−	0.943152i	$-0.392154\pi$
$547$	15.5466	0.664724	0.332362	+	0.943152i	$0.392154\pi$
$548$	5.38121	0.229874
$549$	−21.6080	−0.922206
$550$	14.9691	0.638285
$551$	−42.8327	−1.82474
$552$	7.79419	0.331743
$553$	−32.6500	−1.38842
$554$	−23.0426	−0.978988
$555$	−6.08757	−0.258403
$556$	75.8698	3.21760
$557$	9.05035	0.383475	0.191738	−	0.981446i	$-0.438588\pi$
$557$	9.05035	0.383475	0.191738	+	0.981446i	$0.438588\pi$
$558$	20.3861	0.863011
$559$	−7.18825	−0.304031
$560$	−61.5588	−2.60133
$561$	−0.388672	−0.0164097
$562$	10.8542	0.457859
$563$	−10.2098	−0.430293	−0.215147	−	0.976582i	$-0.569023\pi$
$563$	−10.2098	−0.430293	−0.215147	+	0.976582i	$0.569023\pi$
$564$	11.7536	0.494916
$565$	−43.5483	−1.83209
$566$	24.3942	1.02536
$567$	−16.2122	−0.680850
$568$	−55.2432	−2.31795
$569$	−13.5786	−0.569245	−0.284622	−	0.958640i	$-0.591868\pi$
$569$	−13.5786	−0.569245	−0.284622	+	0.958640i	$0.591868\pi$
$570$	29.7334	1.24540
$571$	−16.5848	−0.694051	−0.347026	−	0.937856i	$-0.612808\pi$
$571$	−16.5848	−0.694051	−0.347026	+	0.937856i	$0.612808\pi$
$572$	23.3584	0.976664
$573$	−4.94126	−0.206424
$574$	1.49833	0.0625393
$575$	−16.6206	−0.693128
$576$	−13.0160	−0.542333
$577$	16.3664	0.681344	0.340672	−	0.940182i	$-0.389345\pi$
$577$	16.3664	0.681344	0.340672	+	0.940182i	$0.389345\pi$
$578$	2.58784	0.107640
$579$	0.941775	0.0391388
$580$	77.4833	3.21732
$581$	−17.9667	−0.745385
$582$	−12.5255	−0.519199
$583$	−7.59947	−0.314738
$584$	−108.665	−4.49658
$585$	−48.4673	−2.00387
$586$	87.9867	3.63470
$587$	38.9245	1.60659	0.803293	−	0.595583i	$-0.203079\pi$
$587$	38.9245	1.60659	0.803293	+	0.595583i	$0.203079\pi$
$588$	4.55786	0.187963
$589$	23.8950	0.984575
$590$	−8.57961	−0.353217
$591$	8.13374	0.334577
$592$	39.5289	1.62463
$593$	14.6525	0.601707	0.300854	−	0.953670i	$-0.402728\pi$
$593$	14.6525	0.601707	0.300854	+	0.953670i	$0.402728\pi$
$594$	5.87189	0.240926
$595$	−7.10265	−0.291180
$596$	−100.524	−4.11764
$597$	0.0735055	0.00300838
$598$	−36.9791	−1.51219
$599$	−7.98971	−0.326451	−0.163225	−	0.986589i	$-0.552190\pi$
$599$	−7.98971	−0.326451	−0.163225	+	0.986589i	$0.552190\pi$
$600$	−16.8350	−0.687286
$601$	−30.1726	−1.23077	−0.615384	−	0.788227i	$-0.710999\pi$
$601$	−30.1726	−1.23077	−0.615384	+	0.788227i	$0.710999\pi$
$602$	7.73627	0.315307
$603$	8.95064	0.364498
$604$	88.0598	3.58310
$605$	−33.3790	−1.35705
$606$	6.84495	0.278057
$607$	−24.5654	−0.997078	−0.498539	−	0.866867i	$-0.666130\pi$
$607$	−24.5654	−0.997078	−0.498539	+	0.866867i	$0.666130\pi$
$608$	−72.9160	−2.95714
$609$	4.29164	0.173906
$610$	65.3254	2.64495
$611$	−32.0192	−1.29536
$612$	−13.3294	−0.538809
$613$	−23.4666	−0.947808	−0.473904	−	0.880576i	$-0.657156\pi$
$613$	−23.4666	−0.947808	−0.473904	+	0.880576i	$0.657156\pi$
$614$	23.7344	0.957842
$615$	0.360730	0.0145460
$616$	−14.4346	−0.581586
$617$	−8.76583	−0.352899	−0.176449	−	0.984310i	$-0.556461\pi$
$617$	−8.76583	−0.352899	−0.176449	+	0.984310i	$0.556461\pi$
$618$	9.91568	0.398867
$619$	−45.9627	−1.84740	−0.923699	−	0.383120i	$-0.874850\pi$
$619$	−45.9627	−1.84740	−0.923699	+	0.383120i	$0.874850\pi$
$620$	−43.2254	−1.73597
$621$	−6.51971	−0.261627
$622$	54.0399	2.16680
$623$	−28.6059	−1.14607
$624$	−17.9745	−0.719554
$625$	−19.0585	−0.762342
$626$	−38.2344	−1.52816
$627$	3.34574	0.133616
$628$	−48.1480	−1.92131
$629$	4.56084	0.181853
$630$	52.1623	2.07820
$631$	27.0450	1.07664	0.538321	−	0.842740i	$-0.319059\pi$
$631$	27.0450	1.07664	0.538321	+	0.842740i	$0.319059\pi$
$632$	106.364	4.23093
$633$	−5.45500	−0.216817
$634$	89.9698	3.57316
$635$	28.4957	1.13082
$636$	14.8849	0.590226
$637$	−12.4165	−0.491961
$638$	12.4313	0.492161
$639$	22.4635	0.888644
$640$	−16.8161	−0.664716
$641$	15.7921	0.623751	0.311875	−	0.950123i	$-0.399043\pi$
$641$	15.7921	0.623751	0.311875	+	0.950123i	$0.399043\pi$
$642$	−8.79953	−0.347290
$643$	29.2236	1.15247	0.576233	−	0.817285i	$-0.304522\pi$
$643$	29.2236	1.15247	0.576233	+	0.817285i	$0.304522\pi$
$644$	27.9127	1.09992
$645$	1.86254	0.0733373
$646$	−22.2764	−0.876455
$647$	27.6051	1.08527	0.542634	−	0.839969i	$-0.317427\pi$
$647$	27.6051	1.08527	0.542634	+	0.839969i	$0.317427\pi$
$648$	52.8147	2.07476
$649$	−0.965417	−0.0378959
$650$	79.8728	3.13287
$651$	−2.39417	−0.0938348
$652$	−25.8287	−1.01153
$653$	3.08482	0.120718	0.0603591	−	0.998177i	$-0.480775\pi$
$653$	3.08482	0.120718	0.0603591	+	0.998177i	$0.480775\pi$
$654$	4.27866	0.167309
$655$	29.7421	1.16212
$656$	−2.34236	−0.0914536
$657$	44.1864	1.72387
$658$	34.4602	1.34340
$659$	−28.9558	−1.12796	−0.563979	−	0.825789i	$-0.690730\pi$
$659$	−28.9558	−1.12796	−0.563979	+	0.825789i	$0.690730\pi$
$660$	−6.05236	−0.235588
$661$	8.57993	0.333721	0.166860	−	0.985981i	$-0.446637\pi$
$661$	8.57993	0.333721	0.166860	+	0.985981i	$0.446637\pi$
$662$	35.0187	1.36104
$663$	−2.07389	−0.0805432
$664$	58.5302	2.27141
$665$	61.1406	2.37093
$666$	−33.4951	−1.29791
$667$	−13.8029	−0.534449
$668$	13.2432	0.512397
$669$	2.19203	0.0847489
$670$	−27.0596	−1.04541
$671$	7.35071	0.283771
$672$	7.30586	0.281830
$673$	18.6574	0.719190	0.359595	−	0.933108i	$-0.382915\pi$
$673$	18.6574	0.719190	0.359595	+	0.933108i	$0.382915\pi$
$674$	77.0179	2.96662
$675$	14.0822	0.542024
$676$	63.5772	2.44528
$677$	−45.2788	−1.74020	−0.870102	−	0.492871i	$-0.835947\pi$
$677$	−45.2788	−1.74020	−0.870102	+	0.492871i	$0.835947\pi$
$678$	13.6850	0.525569
$679$	−25.7561	−0.988427
$680$	23.1383	0.887313
$681$	1.84533	0.0707131
$682$	−6.93503	−0.265556
$683$	21.7972	0.834048	0.417024	−	0.908895i	$-0.363073\pi$
$683$	21.7972	0.834048	0.417024	+	0.908895i	$0.363073\pi$
$684$	114.741	4.38724
$685$	3.79840	0.145129
$686$	52.1714	1.99191
$687$	1.85307	0.0706991
$688$	−12.0942	−0.461085
$689$	−40.5496	−1.54482
$690$	9.58160	0.364765
$691$	−28.4512	−1.08233	−0.541167	−	0.840915i	$-0.682017\pi$
$691$	−28.4512	−1.08233	−0.541167	+	0.840915i	$0.682017\pi$
$692$	25.7836	0.980144
$693$	5.86954	0.222965
$694$	−37.3497	−1.41777
$695$	53.5537	2.03141
$696$	−13.9809	−0.529945
$697$	−0.270261	−0.0102369
$698$	−49.5767	−1.87651
$699$	−1.15246	−0.0435899
$700$	−60.2899	−2.27874
$701$	9.51279	0.359293	0.179646	−	0.983731i	$-0.442505\pi$
$701$	9.51279	0.359293	0.179646	+	0.983731i	$0.442505\pi$
$702$	31.3315	1.18253
$703$	−39.2604	−1.48073
$704$	4.42784	0.166881
$705$	8.29643	0.312462
$706$	61.9182	2.33032
$707$	14.0752	0.529353
$708$	1.89094	0.0710661
$709$	−22.3005	−0.837514	−0.418757	−	0.908098i	$-0.637534\pi$
$709$	−22.3005	−0.837514	−0.418757	+	0.908098i	$0.637534\pi$
$710$	−67.9119	−2.54869
$711$	−43.2507	−1.62203
$712$	93.1895	3.49243
$713$	7.70015	0.288373
$714$	2.23200	0.0835305
$715$	16.4878	0.616610
$716$	−49.6194	−1.85436
$717$	7.66518	0.286261
$718$	21.8558	0.815650
$719$	−40.6074	−1.51440	−0.757201	−	0.653182i	$-0.773434\pi$
$719$	−40.6074	−1.51440	−0.757201	+	0.653182i	$0.773434\pi$
$720$	−81.5456	−3.03903
$721$	20.3895	0.759345
$722$	142.590	5.30665
$723$	−12.2277	−0.454753
$724$	9.72703	0.361502
$725$	29.8134	1.10724
$726$	10.4893	0.389295
$727$	23.3787	0.867068	0.433534	−	0.901137i	$-0.357266\pi$
$727$	23.3787	0.867068	0.433534	+	0.901137i	$0.357266\pi$
$728$	−77.0207	−2.85458
$729$	−18.6373	−0.690272
$730$	−133.585	−4.94418
$731$	−1.39542	−0.0516115
$732$	−14.3977	−0.532154
$733$	−21.1915	−0.782726	−0.391363	−	0.920236i	$-0.627996\pi$
$733$	−21.1915	−0.782726	−0.391363	+	0.920236i	$0.627996\pi$
$734$	31.9211	1.17823
$735$	3.21722	0.118669
$736$	−23.4972	−0.866118
$737$	−3.04487	−0.112159
$738$	1.98481	0.0730619
$739$	−45.6953	−1.68093	−0.840464	−	0.541867i	$-0.817717\pi$
$739$	−45.6953	−1.68093	−0.840464	+	0.541867i	$0.817717\pi$
$740$	71.0210	2.61078
$741$	17.8523	0.655822
$742$	43.6410	1.60211
$743$	−1.12300	−0.0411990	−0.0205995	−	0.999788i	$-0.506557\pi$
$743$	−1.12300	−0.0411990	−0.0205995	+	0.999788i	$0.506557\pi$
$744$	7.79948	0.285943
$745$	−70.9564	−2.59964
$746$	−24.4275	−0.894353
$747$	−23.8001	−0.870801
$748$	4.53446	0.165796
$749$	−18.0944	−0.661154
$750$	−3.42518	−0.125070
$751$	−18.4890	−0.674673	−0.337336	−	0.941384i	$-0.609526\pi$
$751$	−18.4890	−0.674673	−0.337336	+	0.941384i	$0.609526\pi$
$752$	−53.8719	−1.96450
$753$	10.5145	0.383169
$754$	66.3317	2.41566
$755$	62.1581	2.26217
$756$	−23.6497	−0.860132
$757$	−15.9629	−0.580181	−0.290091	−	0.956999i	$-0.593685\pi$
$757$	−15.9629	−0.580181	−0.290091	+	0.956999i	$0.593685\pi$
$758$	−19.4330	−0.705838
$759$	1.07817	0.0391349
$760$	−199.178	−7.22493
$761$	46.9919	1.70346	0.851728	−	0.523985i	$-0.175555\pi$
$761$	46.9919	1.70346	0.851728	+	0.523985i	$0.175555\pi$
$762$	−8.95474	−0.324396
$763$	8.79816	0.318515
$764$	57.6475	2.08561
$765$	−9.40872	−0.340173
$766$	12.4550	0.450018
$767$	−5.15131	−0.186003
$768$	8.97742	0.323945
$769$	−13.5385	−0.488209	−0.244105	−	0.969749i	$-0.578494\pi$
$769$	−13.5385	−0.488209	−0.244105	+	0.969749i	$0.578494\pi$
$770$	−17.7448	−0.639479
$771$	−10.4389	−0.375948
$772$	−10.9873	−0.395440
$773$	20.2653	0.728891	0.364445	−	0.931225i	$-0.381259\pi$
$773$	20.2653	0.728891	0.364445	+	0.931225i	$0.381259\pi$
$774$	10.2481	0.368359
$775$	−16.6319	−0.597435
$776$	83.9056	3.01204
$777$	3.93371	0.141121
$778$	−80.7861	−2.89632
$779$	2.32644	0.0833534
$780$	−32.2944	−1.15633
$781$	−7.64176	−0.273444
$782$	−7.17859	−0.256706
$783$	11.6948	0.417938
$784$	−20.8907	−0.746095
$785$	−33.9859	−1.21301
$786$	−9.34643	−0.333376
$787$	−38.6684	−1.37838	−0.689190	−	0.724581i	$-0.742033\pi$
$787$	−38.6684	−1.37838	−0.689190	+	0.724581i	$0.742033\pi$
$788$	−94.8927	−3.38041
$789$	5.13724	0.182891
$790$	130.756	4.65209
$791$	28.1403	1.00055
$792$	−19.1212	−0.679442
$793$	39.2222	1.39282
$794$	85.0391	3.01792
$795$	10.5067	0.372635
$796$	−0.857556	−0.0303953
$797$	−37.4993	−1.32829	−0.664147	−	0.747602i	$-0.731205\pi$
$797$	−37.4993	−1.32829	−0.664147	+	0.747602i	$0.731205\pi$
$798$	−19.2134	−0.680146
$799$	−6.21573	−0.219897
$800$	50.7526	1.79438
$801$	−37.8936	−1.33891
$802$	74.9351	2.64605
$803$	−15.0315	−0.530451
$804$	5.96394	0.210332
$805$	19.7026	0.694424
$806$	−37.0042	−1.30342
$807$	−4.54671	−0.160052
$808$	−45.8528	−1.61310
$809$	−40.8622	−1.43664	−0.718320	−	0.695713i	$-0.755088\pi$
$809$	−40.8622	−1.43664	−0.718320	+	0.695713i	$0.755088\pi$
$810$	64.9265	2.28128
$811$	−34.4301	−1.20901	−0.604503	−	0.796603i	$-0.706628\pi$
$811$	−34.4301	−1.20901	−0.604503	+	0.796603i	$0.706628\pi$
$812$	−50.0687	−1.75707
$813$	−8.85650	−0.310611
$814$	11.3945	0.399378
$815$	−18.2315	−0.638622
$816$	−3.48930	−0.122150
$817$	12.0120	0.420246
$818$	−54.1975	−1.89497
$819$	31.3189	1.09437
$820$	−4.20847	−0.146966
$821$	−26.1143	−0.911396	−0.455698	−	0.890134i	$-0.650610\pi$
$821$	−26.1143	−0.911396	−0.455698	+	0.890134i	$0.650610\pi$
$822$	−1.19364	−0.0416330
$823$	−5.64588	−0.196803	−0.0984015	−	0.995147i	$-0.531373\pi$
$823$	−5.64588	−0.196803	−0.0984015	+	0.995147i	$0.531373\pi$
$824$	−66.4229	−2.31395
$825$	−2.32878	−0.0810776
$826$	5.54403	0.192902
$827$	26.0967	0.907470	0.453735	−	0.891137i	$-0.350091\pi$
$827$	26.0967	0.907470	0.453735	+	0.891137i	$0.350091\pi$
$828$	36.9754	1.28498
$829$	43.8201	1.52194	0.760968	−	0.648789i	$-0.224724\pi$
$829$	43.8201	1.52194	0.760968	+	0.648789i	$0.224724\pi$
$830$	71.9527	2.49752
$831$	3.58479	0.124355
$832$	23.6263	0.819094
$833$	−2.41036	−0.0835141
$834$	−16.8292	−0.582747
$835$	9.34792	0.323498
$836$	−39.0333	−1.34999
$837$	−6.52414	−0.225507
$838$	13.4945	0.466160
$839$	11.6269	0.401406	0.200703	−	0.979652i	$-0.435677\pi$
$839$	11.6269	0.401406	0.200703	+	0.979652i	$0.435677\pi$
$840$	19.9567	0.688572
$841$	−4.24102	−0.146242
$842$	−67.4993	−2.32618
$843$	−1.68862	−0.0581591
$844$	63.6411	2.19062
$845$	44.8768	1.54381
$846$	45.6487	1.56944
$847$	21.5691	0.741122
$848$	−68.2242	−2.34283
$849$	−3.79506	−0.130246
$850$	15.5053	0.531829
$851$	−12.6517	−0.433693
$852$	14.9678	0.512787
$853$	45.2951	1.55088	0.775438	−	0.631424i	$-0.217529\pi$
$853$	45.2951	1.55088	0.775438	+	0.631424i	$0.217529\pi$
$854$	−42.2124	−1.44448
$855$	80.9916	2.76985
$856$	58.9461	2.01474
$857$	5.06503	0.173018	0.0865090	−	0.996251i	$-0.472429\pi$
$857$	5.06503	0.173018	0.0865090	+	0.996251i	$0.472429\pi$
$858$	−5.18128	−0.176886
$859$	−36.1789	−1.23441	−0.617203	−	0.786804i	$-0.711734\pi$
$859$	−36.1789	−1.23441	−0.617203	+	0.786804i	$0.711734\pi$
$860$	−21.7294	−0.740966
$861$	−0.233099	−0.00794399
$862$	−76.1310	−2.59303
$863$	42.5575	1.44867	0.724337	−	0.689446i	$-0.242146\pi$
$863$	42.5575	1.44867	0.724337	+	0.689446i	$0.242146\pi$
$864$	19.9086	0.677303
$865$	18.1997	0.618807
$866$	−40.9674	−1.39213
$867$	−0.402595	−0.0136728
$868$	27.9317	0.948063
$869$	14.7133	0.499113
$870$	−17.1871	−0.582697
$871$	−16.2470	−0.550507
$872$	−28.6618	−0.970610
$873$	−34.1185	−1.15474
$874$	61.7943	2.09022
$875$	−7.04317	−0.238103
$876$	29.4420	0.994753
$877$	−22.4317	−0.757463	−0.378732	−	0.925507i	$-0.623640\pi$
$877$	−22.4317	−0.757463	−0.378732	+	0.925507i	$0.623640\pi$
$878$	70.6129	2.38307
$879$	−13.6883	−0.461694
$880$	27.7406	0.935135
$881$	0.00418449	0.000140979 0	7.04895e−5	−	1.00000i	$-0.499978\pi$
$881$	0.00418449	0.000140979 0	7.04895e−5		1.00000i	$0.499978\pi$
$882$	17.7019	0.596052
$883$	−28.0202	−0.942956	−0.471478	−	0.881878i	$-0.656279\pi$
$883$	−28.0202	−0.942956	−0.471478	+	0.881878i	$0.656279\pi$
$884$	24.1952	0.813771
$885$	1.33475	0.0448670
$886$	−30.8097	−1.03507
$887$	20.8993	0.701731	0.350865	−	0.936426i	$-0.385887\pi$
$887$	20.8993	0.701731	0.350865	+	0.936426i	$0.385887\pi$
$888$	−12.8149	−0.430038
$889$	−18.4135	−0.617570
$890$	114.560	3.84007
$891$	7.30582	0.244754
$892$	−25.5735	−0.856263
$893$	53.5059	1.79051
$894$	22.2980	0.745756
$895$	−35.0245	−1.17074
$896$	10.8664	0.363020
$897$	5.75292	0.192084
$898$	9.68631	0.323236
$899$	−13.8122	−0.460663
$900$	−79.8648	−2.66216
$901$	−7.87170	−0.262244
$902$	−0.675203	−0.0224818
$903$	−1.20355	−0.0400515
$904$	−91.6728	−3.04899
$905$	6.86595	0.228232
$906$	−19.5331	−0.648945
$907$	−36.6292	−1.21625	−0.608126	−	0.793841i	$-0.708078\pi$
$907$	−36.6292	−1.21625	−0.608126	+	0.793841i	$0.708078\pi$
$908$	−21.5286	−0.714452
$909$	18.6451	0.618420
$910$	−94.6836	−3.13873
$911$	−10.2152	−0.338446	−0.169223	−	0.985578i	$-0.554126\pi$
$911$	−10.2152	−0.338446	−0.169223	+	0.985578i	$0.554126\pi$
$912$	30.0364	0.994603
$913$	8.09645	0.267953
$914$	−17.8593	−0.590734
$915$	−10.1628	−0.335972
$916$	−21.6190	−0.714311
$917$	−19.2190	−0.634666
$918$	6.08223	0.200743
$919$	−31.1936	−1.02898	−0.514491	−	0.857496i	$-0.672019\pi$
$919$	−31.1936	−1.02898	−0.514491	+	0.857496i	$0.672019\pi$
$920$	−64.1850	−2.11612
$921$	−3.69241	−0.121669
$922$	10.3466	0.340747
$923$	−40.7752	−1.34213
$924$	3.91096	0.128661
$925$	27.3269	0.898502
$926$	80.7808	2.65462
$927$	27.0095	0.887110
$928$	42.1483	1.38359
$929$	8.24043	0.270360	0.135180	−	0.990821i	$-0.456839\pi$
$929$	8.24043	0.270360	0.135180	+	0.990821i	$0.456839\pi$
$930$	9.58811	0.314406
$931$	20.7487	0.680012
$932$	13.4452	0.440412
$933$	−8.40709	−0.275236
$934$	96.2688	3.15001
$935$	3.20071	0.104674
$936$	−102.028	−3.33488
$937$	−18.9435	−0.618856	−0.309428	−	0.950923i	$-0.600138\pi$
$937$	−18.9435	−0.618856	−0.309428	+	0.950923i	$0.600138\pi$
$938$	17.4856	0.570925
$939$	5.94821	0.194112
$940$	−96.7907	−3.15697
$941$	17.8226	0.581000	0.290500	−	0.956875i	$-0.406178\pi$
$941$	17.8226	0.581000	0.290500	+	0.956875i	$0.406178\pi$
$942$	10.6800	0.347974
$943$	0.749696	0.0244135
$944$	−8.66702	−0.282088
$945$	−16.6935	−0.543038
$946$	−3.48624	−0.113347
$947$	52.8214	1.71647	0.858233	−	0.513261i	$-0.171563\pi$
$947$	52.8214	1.71647	0.858233	+	0.513261i	$0.171563\pi$
$948$	−28.8186	−0.935984
$949$	−80.2059	−2.60359
$950$	−133.472	−4.33041
$951$	−13.9968	−0.453877
$952$	−14.9517	−0.484586
$953$	−0.321474	−0.0104136	−0.00520678	−	0.999986i	$-0.501657\pi$
$953$	−0.321474	−0.0104136	−0.00520678	+	0.999986i	$0.501657\pi$
$954$	57.8102	1.87168
$955$	40.6912	1.31674
$956$	−89.4262	−2.89225
$957$	−1.93397	−0.0625163
$958$	−92.6850	−2.99452
$959$	−2.45447	−0.0792591
$960$	−6.12176	−0.197579
$961$	−23.2946	−0.751439
$962$	60.7994	1.96025
$963$	−23.9692	−0.772398
$964$	142.655	4.59461
$965$	−7.75550	−0.249659
$966$	−6.19151	−0.199209
$967$	−15.1279	−0.486480	−0.243240	−	0.969966i	$-0.578210\pi$
$967$	−15.1279	−0.486480	−0.243240	+	0.969966i	$0.578210\pi$
$968$	−70.2655	−2.25842
$969$	3.46559	0.111331
$970$	103.147	3.31186
$971$	−54.0785	−1.73546	−0.867732	−	0.497033i	$-0.834423\pi$
$971$	−54.0785	−1.73546	−0.867732	+	0.497033i	$0.834423\pi$
$972$	−47.4273	−1.52123
$973$	−34.6057	−1.10941
$974$	−83.3706	−2.67137
$975$	−12.4260	−0.397950
$976$	65.9909	2.11232
$977$	0.302135	0.00966615	0.00483307	−	0.999988i	$-0.498462\pi$
$977$	0.302135	0.00966615	0.00483307	+	0.999988i	$0.498462\pi$
$978$	5.72923	0.183201
$979$	12.8908	0.411993
$980$	−37.5339	−1.19898
$981$	11.6547	0.372107
$982$	−0.850566	−0.0271427
$983$	4.04823	0.129118	0.0645592	−	0.997914i	$-0.479436\pi$
$983$	4.04823	0.129118	0.0645592	+	0.997914i	$0.479436\pi$
$984$	0.759367	0.0242077
$985$	−66.9812	−2.13420
$986$	12.8767	0.410076
$987$	−5.36105	−0.170644
$988$	−208.275	−6.62612
$989$	3.87086	0.123086
$990$	−23.5062	−0.747076
$991$	35.0716	1.11409	0.557043	−	0.830484i	$-0.311936\pi$
$991$	35.0716	1.11409	0.557043	+	0.830484i	$0.311936\pi$
$992$	−23.5131	−0.746543
$993$	−5.44793	−0.172885
$994$	43.8838	1.39191
$995$	−0.605317	−0.0191898
$996$	−15.8584	−0.502491
$997$	−46.4257	−1.47032	−0.735159	−	0.677895i	$-0.762893\pi$
$997$	−46.4257	−1.47032	−0.735159	+	0.677895i	$0.762893\pi$
$998$	88.7857	2.81046
$999$	10.7194	0.339147

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1003.2.a.i.1.17	✓	18
3.2	odd	2		9027.2.a.q.1.2		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1003.2.a.i.1.17	✓	18	1.1	even	1	trivial
9027.2.a.q.1.2		18	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)

\(f(q)\)	\(=\)	\(q+2.58784 q^{2} -0.402595 q^{3} +4.69689 q^{4} +3.31536 q^{5} -1.04185 q^{6} -2.14234 q^{7} +6.97912 q^{8} -2.83792 q^{9} +O(q^{10})\)	\(q+2.58784 q^{2} -0.402595 q^{3} +4.69689 q^{4} +3.31536 q^{5} -1.04185 q^{6} -2.14234 q^{7} +6.97912 q^{8} -2.83792 q^{9} +8.57961 q^{10} +0.965417 q^{11} -1.89094 q^{12} +5.15131 q^{13} -5.54403 q^{14} -1.33475 q^{15} +8.66702 q^{16} +1.00000 q^{17} -7.34406 q^{18} -8.60814 q^{19} +15.5719 q^{20} +0.862497 q^{21} +2.49834 q^{22} -2.77397 q^{23} -2.80976 q^{24} +5.99163 q^{25} +13.3307 q^{26} +2.35032 q^{27} -10.0624 q^{28} +4.97584 q^{29} -3.45411 q^{30} -2.77586 q^{31} +8.47059 q^{32} -0.388672 q^{33} +2.58784 q^{34} -7.10265 q^{35} -13.3294 q^{36} +4.56084 q^{37} -22.2764 q^{38} -2.07389 q^{39} +23.1383 q^{40} -0.270261 q^{41} +2.23200 q^{42} -1.39542 q^{43} +4.53446 q^{44} -9.40872 q^{45} -7.17859 q^{46} -6.21573 q^{47} -3.48930 q^{48} -2.41036 q^{49} +15.5053 q^{50} -0.402595 q^{51} +24.1952 q^{52} -7.87170 q^{53} +6.08223 q^{54} +3.20071 q^{55} -14.9517 q^{56} +3.46559 q^{57} +12.8767 q^{58} -1.00000 q^{59} -6.26917 q^{60} +7.61403 q^{61} -7.18346 q^{62} +6.07980 q^{63} +4.58646 q^{64} +17.0785 q^{65} -1.00582 q^{66} -3.15395 q^{67} +4.69689 q^{68} +1.11679 q^{69} -18.3805 q^{70} -7.91550 q^{71} -19.8062 q^{72} -15.5700 q^{73} +11.8027 q^{74} -2.41220 q^{75} -40.4315 q^{76} -2.06826 q^{77} -5.36689 q^{78} +15.2403 q^{79} +28.7343 q^{80} +7.56753 q^{81} -0.699390 q^{82} +8.38648 q^{83} +4.05105 q^{84} +3.31536 q^{85} -3.61112 q^{86} -2.00325 q^{87} +6.73776 q^{88} +13.3526 q^{89} -24.3482 q^{90} -11.0359 q^{91} -13.0291 q^{92} +1.11755 q^{93} -16.0853 q^{94} -28.5391 q^{95} -3.41022 q^{96} +12.0224 q^{97} -6.23762 q^{98} -2.73977 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 5 q^{2} + q^{3} + 21 q^{4} + 21 q^{5} + 5 q^{6} - q^{7} + 9 q^{8} + 17 q^{9}+O(q^{10}) \) 18 * q + 5 * q^2 + q^3 + 21 * q^4 + 21 * q^5 + 5 * q^6 - q^7 + 9 * q^8 + 17 * q^9	\( 18 q + 5 q^{2} + q^{3} + 21 q^{4} + 21 q^{5} + 5 q^{6} - q^{7} + 9 q^{8} + 17 q^{9} + 10 q^{10} + 6 q^{11} + 20 q^{12} + 12 q^{13} + 9 q^{14} - q^{15} + 19 q^{16} + 18 q^{17} + 10 q^{18} - 14 q^{19} + 17 q^{20} - 14 q^{21} - 4 q^{22} + 7 q^{23} - 3 q^{24} + 35 q^{25} + 3 q^{26} + 13 q^{27} + q^{28} + 23 q^{29} + 17 q^{30} - q^{31} + 13 q^{32} + 7 q^{33} + 5 q^{34} + 5 q^{35} - 16 q^{36} + 36 q^{37} - 19 q^{38} + 8 q^{39} - 4 q^{40} + 37 q^{41} + 9 q^{42} - 15 q^{43} - 9 q^{44} + 17 q^{45} + q^{46} + 23 q^{47} + 17 q^{48} + 15 q^{49} + 32 q^{50} + q^{51} - 11 q^{52} + 35 q^{53} - 17 q^{54} - 6 q^{55} + 37 q^{56} - 16 q^{57} + 2 q^{58} - 18 q^{59} - 6 q^{60} + 39 q^{61} - q^{62} + 15 q^{63} + 5 q^{64} + 15 q^{65} - 36 q^{66} + 14 q^{67} + 21 q^{68} + 16 q^{69} - 45 q^{70} + 3 q^{71} - 71 q^{72} + 56 q^{73} - 27 q^{74} + 16 q^{75} - q^{76} + 39 q^{77} - 71 q^{78} - 22 q^{79} + 45 q^{80} - 18 q^{81} + 5 q^{82} + 12 q^{83} + 2 q^{84} + 21 q^{85} + 4 q^{86} + 8 q^{87} - 18 q^{88} + 34 q^{89} + 48 q^{90} + 3 q^{91} + 67 q^{92} - 19 q^{93} - 38 q^{94} - 72 q^{95} + 6 q^{96} + 31 q^{97} + 19 q^{98} + 44 q^{99}+O(q^{100}) \) 18 * q + 5 * q^2 + q^3 + 21 * q^4 + 21 * q^5 + 5 * q^6 - q^7 + 9 * q^8 + 17 * q^9 + 10 * q^10 + 6 * q^11 + 20 * q^12 + 12 * q^13 + 9 * q^14 - q^15 + 19 * q^16 + 18 * q^17 + 10 * q^18 - 14 * q^19 + 17 * q^20 - 14 * q^21 - 4 * q^22 + 7 * q^23 - 3 * q^24 + 35 * q^25 + 3 * q^26 + 13 * q^27 + q^28 + 23 * q^29 + 17 * q^30 - q^31 + 13 * q^32 + 7 * q^33 + 5 * q^34 + 5 * q^35 - 16 * q^36 + 36 * q^37 - 19 * q^38 + 8 * q^39 - 4 * q^40 + 37 * q^41 + 9 * q^42 - 15 * q^43 - 9 * q^44 + 17 * q^45 + q^46 + 23 * q^47 + 17 * q^48 + 15 * q^49 + 32 * q^50 + q^51 - 11 * q^52 + 35 * q^53 - 17 * q^54 - 6 * q^55 + 37 * q^56 - 16 * q^57 + 2 * q^58 - 18 * q^59 - 6 * q^60 + 39 * q^61 - q^62 + 15 * q^63 + 5 * q^64 + 15 * q^65 - 36 * q^66 + 14 * q^67 + 21 * q^68 + 16 * q^69 - 45 * q^70 + 3 * q^71 - 71 * q^72 + 56 * q^73 - 27 * q^74 + 16 * q^75 - q^76 + 39 * q^77 - 71 * q^78 - 22 * q^79 + 45 * q^80 - 18 * q^81 + 5 * q^82 + 12 * q^83 + 2 * q^84 + 21 * q^85 + 4 * q^86 + 8 * q^87 - 18 * q^88 + 34 * q^89 + 48 * q^90 + 3 * q^91 + 67 * q^92 - 19 * q^93 - 38 * q^94 - 72 * q^95 + 6 * q^96 + 31 * q^97 + 19 * q^98 + 44 * q^99

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