LMFDB - Embedded newform 503.2.a.e.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [503,2,Mod(1,503)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(503, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("503.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 503 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	503.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:	$4.01647522167$
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} - 2x^{9} - 9x^{8} + 14x^{7} + 27x^{6} - 27x^{5} - 34x^{4} + 14x^{3} + 17x^{2} + x - 1 $ x^10 - 2x^9 - 9x^8 + 14x^7 + 27x^6 - 27x^5 - 34x^4 + 14x^3 + 17x^2 + x - 1
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			1.3
Root			$-0.489003$ of defining polynomial
Character	$\chi$	$=$	503.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.62786 q^{2} -1.48900 q^{3} +0.649933 q^{4} -1.79865 q^{5} +2.42389 q^{6} +0.552233 q^{7} +2.19772 q^{8} -0.782869 q^{9} +O(q^{10})$	\(q-1.62786 q^{2} -1.48900 q^{3} +0.649933 q^{4} -1.79865 q^{5} +2.42389 q^{6} +0.552233 q^{7} +2.19772 q^{8} -0.782869 q^{9} +2.92795 q^{10} +4.33718 q^{11} -0.967753 q^{12} +2.54873 q^{13} -0.898958 q^{14} +2.67819 q^{15} -4.87745 q^{16} +2.52304 q^{17} +1.27440 q^{18} -5.11893 q^{19} -1.16900 q^{20} -0.822276 q^{21} -7.06033 q^{22} -3.78409 q^{23} -3.27241 q^{24} -1.76486 q^{25} -4.14898 q^{26} +5.63270 q^{27} +0.358914 q^{28} +0.907287 q^{29} -4.35973 q^{30} +0.380820 q^{31} +3.54438 q^{32} -6.45807 q^{33} -4.10717 q^{34} -0.993273 q^{35} -0.508813 q^{36} -5.43266 q^{37} +8.33291 q^{38} -3.79507 q^{39} -3.95293 q^{40} +5.72459 q^{41} +1.33855 q^{42} -9.21553 q^{43} +2.81888 q^{44} +1.40811 q^{45} +6.15997 q^{46} -8.81077 q^{47} +7.26254 q^{48} -6.69504 q^{49} +2.87295 q^{50} -3.75682 q^{51} +1.65651 q^{52} -6.46357 q^{53} -9.16926 q^{54} -7.80106 q^{55} +1.21365 q^{56} +7.62210 q^{57} -1.47694 q^{58} +3.40568 q^{59} +1.74065 q^{60} -1.06109 q^{61} -0.619922 q^{62} -0.432326 q^{63} +3.98515 q^{64} -4.58427 q^{65} +10.5129 q^{66} -0.253929 q^{67} +1.63981 q^{68} +5.63451 q^{69} +1.61691 q^{70} +11.7311 q^{71} -1.72053 q^{72} -16.1271 q^{73} +8.84362 q^{74} +2.62789 q^{75} -3.32696 q^{76} +2.39513 q^{77} +6.17785 q^{78} +7.76447 q^{79} +8.77283 q^{80} -6.03851 q^{81} -9.31884 q^{82} -16.3846 q^{83} -0.534425 q^{84} -4.53807 q^{85} +15.0016 q^{86} -1.35095 q^{87} +9.53191 q^{88} -3.09992 q^{89} -2.29220 q^{90} +1.40749 q^{91} -2.45940 q^{92} -0.567042 q^{93} +14.3427 q^{94} +9.20715 q^{95} -5.27759 q^{96} -4.28605 q^{97} +10.8986 q^{98} -3.39544 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 4 q^{2} - 8 q^{3} + 4 q^{4} - q^{5} - 2 q^{6} - 5 q^{7} - 3 q^{8} - 2 q^{9}+O(q^{10}) $ 10 * q - 4 * q^2 - 8 * q^3 + 4 * q^4 - q^5 - 2 * q^6 - 5 * q^7 - 3 * q^8 - 2 * q^9	\( 10 q - 4 q^{2} - 8 q^{3} + 4 q^{4} - q^{5} - 2 q^{6} - 5 q^{7} - 3 q^{8} - 2 q^{9} - 4 q^{10} - 3 q^{11} - 7 q^{12} - 18 q^{13} + q^{14} - 2 q^{15} - 4 q^{16} - 11 q^{17} - q^{18} - 3 q^{20} + q^{21} - 18 q^{22} - 2 q^{23} + 10 q^{24} - 27 q^{25} + 11 q^{26} - 2 q^{27} - 22 q^{28} - 9 q^{29} + 12 q^{30} - 22 q^{31} - 10 q^{32} - 10 q^{33} - 10 q^{34} - 6 q^{35} + 2 q^{36} - 35 q^{37} + 2 q^{38} + 8 q^{39} - 19 q^{40} - 4 q^{41} + 4 q^{42} - 20 q^{43} + 9 q^{44} + 2 q^{45} - q^{46} + 7 q^{47} - 27 q^{49} + 16 q^{50} + 9 q^{51} - 7 q^{52} - 24 q^{53} + 17 q^{54} - 11 q^{55} + 12 q^{56} - 23 q^{57} + 2 q^{58} + 17 q^{59} - 4 q^{61} + 8 q^{62} + 10 q^{63} + 3 q^{64} - 16 q^{65} + 46 q^{66} - 6 q^{67} + 28 q^{68} - 2 q^{69} + 26 q^{70} - q^{71} - q^{72} - 31 q^{73} + 11 q^{74} + 30 q^{75} + 20 q^{76} + 3 q^{77} + 11 q^{78} - 10 q^{79} + 24 q^{80} - 6 q^{81} - 9 q^{82} + 22 q^{83} + 22 q^{84} - 6 q^{85} + 38 q^{86} + 25 q^{87} - 3 q^{88} + q^{89} + 2 q^{90} + 10 q^{91} + 27 q^{92} - 6 q^{93} + 33 q^{94} + 39 q^{95} + 46 q^{96} - 57 q^{97} + 40 q^{98} + 35 q^{99}+O(q^{100}) \) 10 * q - 4 * q^2 - 8 * q^3 + 4 * q^4 - q^5 - 2 * q^6 - 5 * q^7 - 3 * q^8 - 2 * q^9 - 4 * q^10 - 3 * q^11 - 7 * q^12 - 18 * q^13 + q^14 - 2 * q^15 - 4 * q^16 - 11 * q^17 - q^18 - 3 * q^20 + q^21 - 18 * q^22 - 2 * q^23 + 10 * q^24 - 27 * q^25 + 11 * q^26 - 2 * q^27 - 22 * q^28 - 9 * q^29 + 12 * q^30 - 22 * q^31 - 10 * q^32 - 10 * q^33 - 10 * q^34 - 6 * q^35 + 2 * q^36 - 35 * q^37 + 2 * q^38 + 8 * q^39 - 19 * q^40 - 4 * q^41 + 4 * q^42 - 20 * q^43 + 9 * q^44 + 2 * q^45 - q^46 + 7 * q^47 - 27 * q^49 + 16 * q^50 + 9 * q^51 - 7 * q^52 - 24 * q^53 + 17 * q^54 - 11 * q^55 + 12 * q^56 - 23 * q^57 + 2 * q^58 + 17 * q^59 - 4 * q^61 + 8 * q^62 + 10 * q^63 + 3 * q^64 - 16 * q^65 + 46 * q^66 - 6 * q^67 + 28 * q^68 - 2 * q^69 + 26 * q^70 - q^71 - q^72 - 31 * q^73 + 11 * q^74 + 30 * q^75 + 20 * q^76 + 3 * q^77 + 11 * q^78 - 10 * q^79 + 24 * q^80 - 6 * q^81 - 9 * q^82 + 22 * q^83 + 22 * q^84 - 6 * q^85 + 38 * q^86 + 25 * q^87 - 3 * q^88 + q^89 + 2 * q^90 + 10 * q^91 + 27 * q^92 - 6 * q^93 + 33 * q^94 + 39 * q^95 + 46 * q^96 - 57 * q^97 + 40 * q^98 + 35 * 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 $

$2$	−1.62786	−1.15107	−0.575536	−	0.817776i	$-0.695207\pi$
$2$	−1.62786	−1.15107	−0.575536	+	0.817776i	$0.695207\pi$
$3$	−1.48900	−0.859676	−0.429838	−	0.902906i	$-0.641429\pi$
$3$	−1.48900	−0.859676	−0.429838	+	0.902906i	$0.641429\pi$
$4$	0.649933	0.324967
$5$	−1.79865	−0.804380	−0.402190	−	0.915556i	$-0.631751\pi$
$5$	−1.79865	−0.804380	−0.402190	+	0.915556i	$0.631751\pi$
$6$	2.42389	0.989549
$7$	0.552233	0.208724	0.104362	−	0.994539i	$-0.466720\pi$
$7$	0.552233	0.208724	0.104362	+	0.994539i	$0.466720\pi$
$8$	2.19772	0.777012
$9$	−0.782869	−0.260956
$10$	2.92795	0.925900
$11$	4.33718	1.30771	0.653854	−	0.756620i	$-0.273151\pi$
$11$	4.33718	1.30771	0.653854	+	0.756620i	$0.273151\pi$
$12$	−0.967753	−0.279366
$13$	2.54873	0.706891	0.353445	−	0.935455i	$-0.385010\pi$
$13$	2.54873	0.706891	0.353445	+	0.935455i	$0.385010\pi$
$14$	−0.898958	−0.240257
$15$	2.67819	0.691507
$16$	−4.87745	−1.21936
$17$	2.52304	0.611928	0.305964	−	0.952043i	$-0.401021\pi$
$17$	2.52304	0.611928	0.305964	+	0.952043i	$0.401021\pi$
$18$	1.27440	0.300380
$19$	−5.11893	−1.17436	−0.587181	−	0.809455i	$-0.699762\pi$
$19$	−5.11893	−1.17436	−0.587181	+	0.809455i	$0.699762\pi$
$20$	−1.16900	−0.261397
$21$	−0.822276	−0.179435
$22$	−7.06033	−1.50527
$23$	−3.78409	−0.789036	−0.394518	−	0.918888i	$-0.629088\pi$
$23$	−3.78409	−0.789036	−0.394518	+	0.918888i	$0.629088\pi$
$24$	−3.27241	−0.667979
$25$	−1.76486	−0.352972
$26$	−4.14898	−0.813682
$27$	5.63270	1.08401
$28$	0.358914	0.0678284
$29$	0.907287	0.168479	0.0842395	−	0.996446i	$-0.473154\pi$
$29$	0.907287	0.168479	0.0842395	+	0.996446i	$0.473154\pi$
$30$	−4.35973	−0.795974
$31$	0.380820	0.0683972	0.0341986	−	0.999415i	$-0.489112\pi$
$31$	0.380820	0.0683972	0.0341986	+	0.999415i	$0.489112\pi$
$32$	3.54438	0.626563
$33$	−6.45807	−1.12421
$34$	−4.10717	−0.704373
$35$	−0.993273	−0.167894
$36$	−0.508813	−0.0848021
$37$	−5.43266	−0.893124	−0.446562	−	0.894753i	$-0.647352\pi$
$37$	−5.43266	−0.893124	−0.446562	+	0.894753i	$0.647352\pi$
$38$	8.33291	1.35178
$39$	−3.79507	−0.607697
$40$	−3.95293	−0.625013
$41$	5.72459	0.894031	0.447015	−	0.894526i	$-0.352487\pi$
$41$	5.72459	0.894031	0.447015	+	0.894526i	$0.352487\pi$
$42$	1.33855	0.206543
$43$	−9.21553	−1.40536	−0.702678	−	0.711508i	$-0.748012\pi$
$43$	−9.21553	−1.40536	−0.702678	+	0.711508i	$0.748012\pi$
$44$	2.81888	0.424962
$45$	1.40811	0.209908
$46$	6.15997	0.908238
$47$	−8.81077	−1.28518	−0.642592	−	0.766209i	$-0.722141\pi$
$47$	−8.81077	−1.28518	−0.642592	+	0.766209i	$0.722141\pi$
$48$	7.26254	1.04826
$49$	−6.69504	−0.956434
$50$	2.87295	0.406297
$51$	−3.75682	−0.526060
$52$	1.65651	0.229716
$53$	−6.46357	−0.887840	−0.443920	−	0.896066i	$-0.646413\pi$
$53$	−6.46357	−0.887840	−0.443920	+	0.896066i	$0.646413\pi$
$54$	−9.16926	−1.24778
$55$	−7.80106	−1.05190
$56$	1.21365	0.162181
$57$	7.62210	1.00957
$58$	−1.47694	−0.193932
$59$	3.40568	0.443381	0.221691	−	0.975117i	$-0.428843\pi$
$59$	3.40568	0.443381	0.221691	+	0.975117i	$0.428843\pi$
$60$	1.74065	0.224717
$61$	−1.06109	−0.135859	−0.0679294	−	0.997690i	$-0.521639\pi$
$61$	−1.06109	−0.135859	−0.0679294	+	0.997690i	$0.521639\pi$
$62$	−0.619922	−0.0787301
$63$	−0.432326	−0.0544679
$64$	3.98515	0.498144
$65$	−4.58427	−0.568609
$66$	10.5129	1.29404
$67$	−0.253929	−0.0310223	−0.0155112	−	0.999880i	$-0.504938\pi$
$67$	−0.253929	−0.0310223	−0.0155112	+	0.999880i	$0.504938\pi$
$68$	1.63981	0.198856
$69$	5.63451	0.678316
$70$	1.61691	0.193258
$71$	11.7311	1.39222	0.696112	−	0.717933i	$-0.254912\pi$
$71$	11.7311	1.39222	0.696112	+	0.717933i	$0.254912\pi$
$72$	−1.72053	−0.202766
$73$	−16.1271	−1.88753	−0.943765	−	0.330617i	$-0.892743\pi$
$73$	−16.1271	−1.88753	−0.943765	+	0.330617i	$0.892743\pi$
$74$	8.84362	1.02805
$75$	2.62789	0.303442
$76$	−3.32696	−0.381629
$77$	2.39513	0.272951
$78$	6.17785	0.699504
$79$	7.76447	0.873571	0.436785	−	0.899566i	$-0.356117\pi$
$79$	7.76447	0.873571	0.436785	+	0.899566i	$0.356117\pi$
$80$	8.77283	0.980832
$81$	−6.03851	−0.670945
$82$	−9.31884	−1.02909
$83$	−16.3846	−1.79844	−0.899222	−	0.437492i	$-0.855867\pi$
$83$	−16.3846	−1.79844	−0.899222	+	0.437492i	$0.855867\pi$
$84$	−0.534425	−0.0583105
$85$	−4.53807	−0.492223
$86$	15.0016	1.61767
$87$	−1.35095	−0.144837
$88$	9.53191	1.01611
$89$	−3.09992	−0.328590	−0.164295	−	0.986411i	$-0.552535\pi$
$89$	−3.09992	−0.328590	−0.164295	+	0.986411i	$0.552535\pi$
$90$	−2.29220	−0.241619
$91$	1.40749	0.147545
$92$	−2.45940	−0.256410
$93$	−0.567042	−0.0587995
$94$	14.3427	1.47934
$95$	9.20715	0.944634
$96$	−5.27759	−0.538641
$97$	−4.28605	−0.435183	−0.217591	−	0.976040i	$-0.569820\pi$
$97$	−4.28605	−0.435183	−0.217591	+	0.976040i	$0.569820\pi$
$98$	10.8986	1.10092
$99$	−3.39544	−0.341255
$100$	−1.14704	−0.114704
$101$	−3.73446	−0.371592	−0.185796	−	0.982588i	$-0.559486\pi$
$101$	−3.73446	−0.371592	−0.185796	+	0.982588i	$0.559486\pi$
$102$	6.11559	0.605533
$103$	2.83220	0.279065	0.139533	−	0.990217i	$-0.455440\pi$
$103$	2.83220	0.279065	0.139533	+	0.990217i	$0.455440\pi$
$104$	5.60140	0.549263
$105$	1.47899	0.144334
$106$	10.5218	1.02197
$107$	10.0994	0.976343	0.488172	−	0.872748i	$-0.337664\pi$
$107$	10.0994	0.976343	0.488172	+	0.872748i	$0.337664\pi$
$108$	3.66088	0.352269
$109$	−6.86764	−0.657800	−0.328900	−	0.944365i	$-0.606678\pi$
$109$	−6.86764	−0.657800	−0.328900	+	0.944365i	$0.606678\pi$
$110$	12.6991	1.21081
$111$	8.08925	0.767798
$112$	−2.69349	−0.254511
$113$	2.80558	0.263927	0.131963	−	0.991255i	$-0.457872\pi$
$113$	2.80558	0.263927	0.131963	+	0.991255i	$0.457872\pi$
$114$	−12.4077	−1.16209
$115$	6.80624	0.634685
$116$	0.589676	0.0547501
$117$	−1.99532	−0.184468
$118$	−5.54397	−0.510364
$119$	1.39331	0.127724
$120$	5.88593	0.537309
$121$	7.81112	0.710102
$122$	1.72731	0.156383
$123$	−8.52393	−0.768577
$124$	0.247507	0.0222268
$125$	12.1676	1.08830
$126$	0.703767	0.0626965
$127$	−14.9147	−1.32347	−0.661734	−	0.749739i	$-0.730179\pi$
$127$	−14.9147	−1.32347	−0.661734	+	0.749739i	$0.730179\pi$
$128$	−13.5760	−1.19996
$129$	13.7220	1.20815
$130$	7.46256	0.654510
$131$	13.5207	1.18131	0.590654	−	0.806925i	$-0.298870\pi$
$131$	13.5207	1.18131	0.590654	+	0.806925i	$0.298870\pi$
$132$	−4.19732	−0.365330
$133$	−2.82684	−0.245118
$134$	0.413361	0.0357090
$135$	−10.1313	−0.871960
$136$	5.54495	0.475476
$137$	−12.4479	−1.06350	−0.531750	−	0.846901i	$-0.678465\pi$
$137$	−12.4479	−1.06350	−0.531750	+	0.846901i	$0.678465\pi$
$138$	−9.17221	−0.780790
$139$	2.15443	0.182736	0.0913681	−	0.995817i	$-0.470876\pi$
$139$	2.15443	0.182736	0.0913681	+	0.995817i	$0.470876\pi$
$140$	−0.645561	−0.0545599
$141$	13.1193	1.10484
$142$	−19.0966	−1.60255
$143$	11.0543	0.924407
$144$	3.81841	0.318201
$145$	−1.63189	−0.135521
$146$	26.2526	2.17268
$147$	9.96894	0.822224
$148$	−3.53087	−0.290236
$149$	−8.59253	−0.703927	−0.351964	−	0.936014i	$-0.614486\pi$
$149$	−8.59253	−0.703927	−0.351964	+	0.936014i	$0.614486\pi$
$150$	−4.27783	−0.349284
$151$	0.527862	0.0429568	0.0214784	−	0.999769i	$-0.493163\pi$
$151$	0.527862	0.0429568	0.0214784	+	0.999769i	$0.493163\pi$
$152$	−11.2500	−0.912494
$153$	−1.97521	−0.159687
$154$	−3.89894	−0.314186
$155$	−0.684961	−0.0550174
$156$	−2.46654	−0.197481
$157$	11.1711	0.891554	0.445777	−	0.895144i	$-0.352927\pi$
$157$	11.1711	0.891554	0.445777	+	0.895144i	$0.352927\pi$
$158$	−12.6395	−1.00554
$159$	9.62428	0.763255
$160$	−6.37509	−0.503995
$161$	−2.08970	−0.164691
$162$	9.82985	0.772306
$163$	20.0109	1.56738	0.783689	−	0.621153i	$-0.213336\pi$
$163$	20.0109	1.56738	0.783689	+	0.621153i	$0.213336\pi$
$164$	3.72060	0.290530
$165$	11.6158	0.904289
$166$	26.6719	2.07014
$167$	−11.9520	−0.924877	−0.462439	−	0.886651i	$-0.653025\pi$
$167$	−11.9520	−0.924877	−0.462439	+	0.886651i	$0.653025\pi$
$168$	−1.80713	−0.139423
$169$	−6.50397	−0.500305
$170$	7.38735	0.566584
$171$	4.00745	0.306457
$172$	−5.98948	−0.456694
$173$	3.14561	0.239156	0.119578	−	0.992825i	$-0.461846\pi$
$173$	3.14561	0.239156	0.119578	+	0.992825i	$0.461846\pi$
$174$	2.19917	0.166718
$175$	−0.974615	−0.0736739
$176$	−21.1544	−1.59457
$177$	−5.07106	−0.381164
$178$	5.04623	0.378231
$179$	−6.02096	−0.450028	−0.225014	−	0.974356i	$-0.572243\pi$
$179$	−6.02096	−0.450028	−0.225014	+	0.974356i	$0.572243\pi$
$180$	0.915176	0.0682132
$181$	−23.0475	−1.71311	−0.856553	−	0.516059i	$-0.827398\pi$
$181$	−23.0475	−1.71311	−0.856553	+	0.516059i	$0.827398\pi$
$182$	−2.29120	−0.169835
$183$	1.57997	0.116795
$184$	−8.31637	−0.613091
$185$	9.77145	0.718412
$186$	0.923065	0.0676824
$187$	10.9429	0.800224
$188$	−5.72641	−0.417642
$189$	3.11056	0.226260
$190$	−14.9880	−1.08734
$191$	−17.9774	−1.30080	−0.650398	−	0.759594i	$-0.725398\pi$
$191$	−17.9774	−1.30080	−0.650398	+	0.759594i	$0.725398\pi$
$192$	−5.93391	−0.428243
$193$	−10.4429	−0.751697	−0.375848	−	0.926681i	$-0.622649\pi$
$193$	−10.4429	−0.751697	−0.375848	+	0.926681i	$0.622649\pi$
$194$	6.97710	0.500927
$195$	6.82600	0.488820
$196$	−4.35133	−0.310809
$197$	−4.36026	−0.310656	−0.155328	−	0.987863i	$-0.549643\pi$
$197$	−4.36026	−0.310656	−0.155328	+	0.987863i	$0.549643\pi$
$198$	5.52731	0.392809
$199$	14.0205	0.993888	0.496944	−	0.867783i	$-0.334455\pi$
$199$	14.0205	0.993888	0.496944	+	0.867783i	$0.334455\pi$
$200$	−3.87868	−0.274264
$201$	0.378101	0.0266692
$202$	6.07918	0.427729
$203$	0.501034	0.0351657
$204$	−2.44168	−0.170952
$205$	−10.2965	−0.719141
$206$	−4.61043	−0.321224
$207$	2.96244	0.205904
$208$	−12.4313	−0.861957
$209$	−22.2017	−1.53572
$210$	−2.40758	−0.166139
$211$	−11.0580	−0.761265	−0.380633	−	0.924726i	$-0.624294\pi$
$211$	−11.0580	−0.761265	−0.380633	+	0.924726i	$0.624294\pi$
$212$	−4.20089	−0.288518
$213$	−17.4676	−1.19686
$214$	−16.4404	−1.12384
$215$	16.5755	1.13044
$216$	12.3791	0.842292
$217$	0.210301	0.0142762
$218$	11.1796	0.757175
$219$	24.0133	1.62267
$220$	−5.07017	−0.341831
$221$	6.43056	0.432566
$222$	−13.1682	−0.883791
$223$	−15.5502	−1.04132	−0.520658	−	0.853765i	$-0.674313\pi$
$223$	−15.5502	−1.04132	−0.520658	+	0.853765i	$0.674313\pi$
$224$	1.95732	0.130779
$225$	1.38166	0.0921104
$226$	−4.56710	−0.303799
$227$	1.27577	0.0846759	0.0423379	−	0.999103i	$-0.486519\pi$
$227$	1.27577	0.0846759	0.0423379	+	0.999103i	$0.486519\pi$
$228$	4.95386	0.328077
$229$	−15.5232	−1.02580	−0.512901	−	0.858448i	$-0.671429\pi$
$229$	−15.5232	−1.02580	−0.512901	+	0.858448i	$0.671429\pi$
$230$	−11.0796	−0.730568
$231$	−3.56636	−0.234649
$232$	1.99397	0.130910
$233$	−27.8010	−1.82130	−0.910651	−	0.413177i	$-0.864419\pi$
$233$	−27.8010	−1.82130	−0.910651	+	0.413177i	$0.864419\pi$
$234$	3.24811	0.212336
$235$	15.8475	1.03378
$236$	2.21346	0.144084
$237$	−11.5613	−0.750988
$238$	−2.26811	−0.147020
$239$	1.20369	0.0778601	0.0389301	−	0.999242i	$-0.487605\pi$
$239$	1.20369	0.0778601	0.0389301	+	0.999242i	$0.487605\pi$
$240$	−13.0628	−0.843198
$241$	−25.6025	−1.64920	−0.824602	−	0.565713i	$-0.808601\pi$
$241$	−25.6025	−1.64920	−0.824602	+	0.565713i	$0.808601\pi$
$242$	−12.7154	−0.817379
$243$	−7.90676	−0.507219
$244$	−0.689638	−0.0441496
$245$	12.0420	0.769337
$246$	13.8758	0.884688
$247$	−13.0468	−0.830146
$248$	0.836936	0.0531455
$249$	24.3967	1.54608
$250$	−19.8072	−1.25272
$251$	13.2638	0.837205	0.418603	−	0.908170i	$-0.362520\pi$
$251$	13.2638	0.837205	0.418603	+	0.908170i	$0.362520\pi$
$252$	−0.280983	−0.0177003
$253$	−16.4123	−1.03183
$254$	24.2791	1.52341
$255$	6.75720	0.423152
$256$	14.1296	0.883099
$257$	−16.1006	−1.00433	−0.502163	−	0.864773i	$-0.667462\pi$
$257$	−16.1006	−1.00433	−0.502163	+	0.864773i	$0.667462\pi$
$258$	−22.3374	−1.39067
$259$	−3.00009	−0.186417
$260$	−2.97947	−0.184779
$261$	−0.710288	−0.0439657
$262$	−22.0098	−1.35977
$263$	6.77336	0.417663	0.208832	−	0.977952i	$-0.433034\pi$
$263$	6.77336	0.417663	0.208832	+	0.977952i	$0.433034\pi$
$264$	−14.1930	−0.873522
$265$	11.6257	0.714161
$266$	4.60170	0.282148
$267$	4.61579	0.282481
$268$	−0.165037	−0.0100812
$269$	23.4853	1.43192	0.715962	−	0.698139i	$-0.245988\pi$
$269$	23.4853	1.43192	0.715962	+	0.698139i	$0.245988\pi$
$270$	16.4923	1.00369
$271$	17.5886	1.06843	0.534216	−	0.845348i	$-0.320607\pi$
$271$	17.5886	1.06843	0.534216	+	0.845348i	$0.320607\pi$
$272$	−12.3060	−0.746163
$273$	−2.09576	−0.126841
$274$	20.2635	1.22417
$275$	−7.65452	−0.461585
$276$	3.66206	0.220430
$277$	−11.3448	−0.681645	−0.340823	−	0.940128i	$-0.610706\pi$
$277$	−11.3448	−0.681645	−0.340823	+	0.940128i	$0.610706\pi$
$278$	−3.50711	−0.210343
$279$	−0.298132	−0.0178487
$280$	−2.18294	−0.130455
$281$	−9.36752	−0.558820	−0.279410	−	0.960172i	$-0.590139\pi$
$281$	−9.36752	−0.558820	−0.279410	+	0.960172i	$0.590139\pi$
$282$	−21.3564	−1.27175
$283$	26.8789	1.59778	0.798892	−	0.601474i	$-0.205420\pi$
$283$	26.8789	1.59778	0.798892	+	0.601474i	$0.205420\pi$
$284$	7.62443	0.452426
$285$	−13.7095	−0.812080
$286$	−17.9949	−1.06406
$287$	3.16131	0.186606
$288$	−2.77478	−0.163506
$289$	−10.6342	−0.625544
$290$	2.65649	0.155995
$291$	6.38195	0.374117
$292$	−10.4815	−0.613384
$293$	17.2365	1.00697	0.503485	−	0.864004i	$-0.332051\pi$
$293$	17.2365	1.00697	0.503485	+	0.864004i	$0.332051\pi$
$294$	−16.2280	−0.946439
$295$	−6.12561	−0.356647
$296$	−11.9395	−0.693968
$297$	24.4301	1.41758
$298$	13.9874	0.810271
$299$	−9.64462	−0.557763
$300$	1.70795	0.0986086
$301$	−5.08912	−0.293332
$302$	−0.859286	−0.0494464
$303$	5.56062	0.319449
$304$	24.9673	1.43197
$305$	1.90853	0.109282
$306$	3.21538	0.183811
$307$	29.0001	1.65512	0.827561	−	0.561376i	$-0.189728\pi$
$307$	29.0001	1.65512	0.827561	+	0.561376i	$0.189728\pi$
$308$	1.55668	0.0886998
$309$	−4.21716	−0.239906
$310$	1.11502	0.0633290
$311$	27.2312	1.54414	0.772071	−	0.635536i	$-0.219221\pi$
$311$	27.2312	1.54414	0.772071	+	0.635536i	$0.219221\pi$
$312$	−8.34051	−0.472188
$313$	5.53059	0.312607	0.156304	−	0.987709i	$-0.450042\pi$
$313$	5.53059	0.312607	0.156304	+	0.987709i	$0.450042\pi$
$314$	−18.1851	−1.02624
$315$	0.777603	0.0438129
$316$	5.04639	0.283881
$317$	31.2030	1.75253	0.876267	−	0.481826i	$-0.160026\pi$
$317$	31.2030	1.75253	0.876267	+	0.481826i	$0.160026\pi$
$318$	−15.6670	−0.878562
$319$	3.93507	0.220322
$320$	−7.16789	−0.400697
$321$	−15.0380	−0.839339
$322$	3.40173	0.189571
$323$	−12.9153	−0.718626
$324$	−3.92463	−0.218035
$325$	−4.49816	−0.249513
$326$	−32.5751	−1.80417
$327$	10.2259	0.565495
$328$	12.5811	0.694673
$329$	−4.86560	−0.268249
$330$	−18.9089	−1.04090
$331$	16.8025	0.923551	0.461775	−	0.886997i	$-0.347213\pi$
$331$	16.8025	0.923551	0.461775	+	0.886997i	$0.347213\pi$
$332$	−10.6489	−0.584434
$333$	4.25307	0.233067
$334$	19.4563	1.06460
$335$	0.456729	0.0249538
$336$	4.01061	0.218797
$337$	7.57943	0.412878	0.206439	−	0.978459i	$-0.433813\pi$
$337$	7.57943	0.412878	0.206439	+	0.978459i	$0.433813\pi$
$338$	10.5876	0.575887
$339$	−4.17752	−0.226892
$340$	−2.94944	−0.159956
$341$	1.65168	0.0894437
$342$	−6.52358	−0.352755
$343$	−7.56285	−0.408355
$344$	−20.2532	−1.09198
$345$	−10.1345	−0.545624
$346$	−5.12062	−0.275286
$347$	−28.0855	−1.50771	−0.753853	−	0.657043i	$-0.771807\pi$
$347$	−28.0855	−1.50771	−0.753853	+	0.657043i	$0.771807\pi$
$348$	−0.878030	−0.0470673
$349$	11.6230	0.622164	0.311082	−	0.950383i	$-0.399309\pi$
$349$	11.6230	0.622164	0.311082	+	0.950383i	$0.399309\pi$
$350$	1.58654	0.0848040
$351$	14.3563	0.766280
$352$	15.3726	0.819362
$353$	−6.16556	−0.328160	−0.164080	−	0.986447i	$-0.552465\pi$
$353$	−6.16556	−0.328160	−0.164080	+	0.986447i	$0.552465\pi$
$354$	8.25499	0.438748
$355$	−21.1001	−1.11988
$356$	−2.01474	−0.106781
$357$	−2.07464	−0.109802
$358$	9.80129	0.518014
$359$	−10.3896	−0.548344	−0.274172	−	0.961681i	$-0.588404\pi$
$359$	−10.3896	−0.548344	−0.274172	+	0.961681i	$0.588404\pi$
$360$	3.09463	0.163101
$361$	7.20342	0.379127
$362$	37.5181	1.97191
$363$	−11.6308	−0.610458
$364$	0.914776	0.0479473
$365$	29.0069	1.51829
$366$	−2.57197	−0.134439
$367$	0.571294	0.0298213	0.0149107	−	0.999889i	$-0.495254\pi$
$367$	0.571294	0.0298213	0.0149107	+	0.999889i	$0.495254\pi$
$368$	18.4567	0.962122
$369$	−4.48161	−0.233303
$370$	−15.9066	−0.826943
$371$	−3.56940	−0.185314
$372$	−0.368539	−0.0191079
$373$	2.95332	0.152917	0.0764586	−	0.997073i	$-0.475639\pi$
$373$	2.95332	0.152917	0.0764586	+	0.997073i	$0.475639\pi$
$374$	−17.8135	−0.921115
$375$	−18.1176	−0.935590
$376$	−19.3636	−0.998603
$377$	2.31243	0.119096
$378$	−5.06357	−0.260442
$379$	−26.2705	−1.34942	−0.674711	−	0.738082i	$-0.735732\pi$
$379$	−26.2705	−1.34942	−0.674711	+	0.738082i	$0.735732\pi$
$380$	5.98404	0.306975
$381$	22.2081	1.13775
$382$	29.2646	1.49731
$383$	3.44503	0.176033	0.0880164	−	0.996119i	$-0.471947\pi$
$383$	3.44503	0.176033	0.0880164	+	0.996119i	$0.471947\pi$
$384$	20.2148	1.03158
$385$	−4.30800	−0.219556
$386$	16.9996	0.865257
$387$	7.21456	0.366736
$388$	−2.78565	−0.141420
$389$	−7.95150	−0.403157	−0.201578	−	0.979472i	$-0.564607\pi$
$389$	−7.95150	−0.403157	−0.201578	+	0.979472i	$0.564607\pi$
$390$	−11.1118	−0.562667
$391$	−9.54742	−0.482834
$392$	−14.7138	−0.743161
$393$	−20.1323	−1.01554
$394$	7.09790	0.357587
$395$	−13.9656	−0.702683
$396$	−2.20681	−0.110896
$397$	21.7255	1.09037	0.545186	−	0.838315i	$-0.316459\pi$
$397$	21.7255	1.09037	0.545186	+	0.838315i	$0.316459\pi$
$398$	−22.8235	−1.14404
$399$	4.20917	0.210722
$400$	8.60803	0.430402
$401$	14.1072	0.704481	0.352241	−	0.935909i	$-0.385420\pi$
$401$	14.1072	0.704481	0.352241	+	0.935909i	$0.385420\pi$
$402$	−0.615496	−0.0306981
$403$	0.970607	0.0483494
$404$	−2.42715	−0.120755
$405$	10.8612	0.539695
$406$	−0.815614	−0.0404782
$407$	−23.5624	−1.16795
$408$	−8.25645	−0.408755
$409$	−10.2905	−0.508834	−0.254417	−	0.967095i	$-0.581884\pi$
$409$	−10.2905	−0.508834	−0.254417	+	0.967095i	$0.581884\pi$
$410$	16.7613	0.827783
$411$	18.5350	0.914266
$412$	1.84074	0.0906869
$413$	1.88072	0.0925444
$414$	−4.82245	−0.237010
$415$	29.4702	1.44663
$416$	9.03366	0.442912
$417$	−3.20795	−0.157094
$418$	36.1413	1.76773
$419$	19.0965	0.932925	0.466463	−	0.884541i	$-0.345528\pi$
$419$	19.0965	0.932925	0.466463	+	0.884541i	$0.345528\pi$
$420$	0.961242	0.0469038
$421$	26.3025	1.28191	0.640953	−	0.767580i	$-0.278539\pi$
$421$	26.3025	1.28191	0.640953	+	0.767580i	$0.278539\pi$
$422$	18.0009	0.876271
$423$	6.89768	0.335377
$424$	−14.2051	−0.689862
$425$	−4.45283	−0.215994
$426$	28.4349	1.37767
$427$	−0.585969	−0.0283570
$428$	6.56392	0.317279
$429$	−16.4599	−0.794691
$430$	−26.9826	−1.30122
$431$	−16.5246	−0.795963	−0.397982	−	0.917393i	$-0.630289\pi$
$431$	−16.5246	−0.795963	−0.397982	+	0.917393i	$0.630289\pi$
$432$	−27.4733	−1.32181
$433$	4.52467	0.217442	0.108721	−	0.994072i	$-0.465325\pi$
$433$	4.52467	0.217442	0.108721	+	0.994072i	$0.465325\pi$
$434$	−0.342341	−0.0164329
$435$	2.42989	0.116504
$436$	−4.46351	−0.213763
$437$	19.3705	0.926615
$438$	−39.0902	−1.86780
$439$	−9.06783	−0.432784	−0.216392	−	0.976307i	$-0.569429\pi$
$439$	−9.06783	−0.432784	−0.216392	+	0.976307i	$0.569429\pi$
$440$	−17.1446	−0.817335
$441$	5.24134	0.249588
$442$	−10.4681	−0.497915
$443$	−12.6542	−0.601219	−0.300609	−	0.953747i	$-0.597190\pi$
$443$	−12.6542	−0.601219	−0.300609	+	0.953747i	$0.597190\pi$
$444$	5.25748	0.249509
$445$	5.57566	0.264312
$446$	25.3135	1.19863
$447$	12.7943	0.605150
$448$	2.20073	0.103975
$449$	34.8336	1.64390	0.821950	−	0.569560i	$-0.192886\pi$
$449$	34.8336	1.64390	0.821950	+	0.569560i	$0.192886\pi$
$450$	−2.24915	−0.106026
$451$	24.8286	1.16913
$452$	1.82344	0.0857674
$453$	−0.785988	−0.0369290
$454$	−2.07678	−0.0974680
$455$	−2.53158	−0.118683
$456$	16.7513	0.784449
$457$	−14.3718	−0.672283	−0.336141	−	0.941812i	$-0.609122\pi$
$457$	−14.3718	−0.672283	−0.336141	+	0.941812i	$0.609122\pi$
$458$	25.2696	1.18077
$459$	14.2116	0.663339
$460$	4.42360	0.206252
$461$	−20.9323	−0.974914	−0.487457	−	0.873147i	$-0.662075\pi$
$461$	−20.9323	−0.974914	−0.487457	+	0.873147i	$0.662075\pi$
$462$	5.80554	0.270098
$463$	19.4204	0.902541	0.451271	−	0.892387i	$-0.350971\pi$
$463$	19.4204	0.902541	0.451271	+	0.892387i	$0.350971\pi$
$464$	−4.42525	−0.205437
$465$	1.01991	0.0472971
$466$	45.2561	2.09645
$467$	22.0847	1.02196	0.510980	−	0.859593i	$-0.329283\pi$
$467$	22.0847	1.02196	0.510980	+	0.859593i	$0.329283\pi$
$468$	−1.29683	−0.0599459
$469$	−0.140228	−0.00647512
$470$	−25.7975	−1.18995
$471$	−16.6339	−0.766448
$472$	7.48473	0.344512
$473$	−39.9694	−1.83780
$474$	18.8202	0.864442
$475$	9.03420	0.414518
$476$	0.905557	0.0415061
$477$	5.06013	0.231688
$478$	−1.95944	−0.0896226
$479$	25.4118	1.16109	0.580547	−	0.814227i	$-0.302839\pi$
$479$	25.4118	1.16109	0.580547	+	0.814227i	$0.302839\pi$
$480$	9.49252	0.433272
$481$	−13.8464	−0.631342
$482$	41.6774	1.89835
$483$	3.11156	0.141581
$484$	5.07671	0.230760
$485$	7.70911	0.350053
$486$	12.8711	0.583845
$487$	−36.7671	−1.66608	−0.833039	−	0.553214i	$-0.813401\pi$
$487$	−36.7671	−1.66608	−0.833039	+	0.553214i	$0.813401\pi$
$488$	−2.33198	−0.105564
$489$	−29.7964	−1.34744
$490$	−19.6027	−0.885562
$491$	−12.6572	−0.571212	−0.285606	−	0.958347i	$-0.592195\pi$
$491$	−12.6572	−0.571212	−0.285606	+	0.958347i	$0.592195\pi$
$492$	−5.53999	−0.249762
$493$	2.28913	0.103097
$494$	21.2383	0.955558
$495$	6.10721	0.274499
$496$	−1.85743	−0.0834011
$497$	6.47829	0.290591
$498$	−39.7145	−1.77965
$499$	2.39500	0.107215	0.0536074	−	0.998562i	$-0.482928\pi$
$499$	2.39500	0.107215	0.0536074	+	0.998562i	$0.482928\pi$
$500$	7.90814	0.353663
$501$	17.7966	0.795095
$502$	−21.5917	−0.963683
$503$	−1.00000	−0.0445878
$503$	−1.00000	−0.0445878
$504$	−0.950132	−0.0423222
$505$	6.71697	0.298901
$506$	26.7169	1.18771
$507$	9.68443	0.430101
$508$	−9.69357	−0.430083
$509$	6.46329	0.286480	0.143240	−	0.989688i	$-0.454248\pi$
$509$	6.46329	0.286480	0.143240	+	0.989688i	$0.454248\pi$
$510$	−10.9998	−0.487079
$511$	−8.90589	−0.393973
$512$	4.15104	0.183452
$513$	−28.8334	−1.27303
$514$	26.2095	1.15605
$515$	−5.09414	−0.224475
$516$	8.91836	0.392609
$517$	−38.2139	−1.68065
$518$	4.88374	0.214579
$519$	−4.68382	−0.205597
$520$	−10.0750	−0.441816
$521$	34.3036	1.50287	0.751434	−	0.659808i	$-0.229363\pi$
$521$	34.3036	1.50287	0.751434	+	0.659808i	$0.229363\pi$
$522$	1.15625	0.0506077
$523$	30.3662	1.32782	0.663910	−	0.747812i	$-0.268896\pi$
$523$	30.3662	1.32782	0.663910	+	0.747812i	$0.268896\pi$
$524$	8.78754	0.383885
$525$	1.45120	0.0633357
$526$	−11.0261	−0.480761
$527$	0.960825	0.0418542
$528$	31.4990	1.37082
$529$	−8.68070	−0.377422
$530$	−18.9250	−0.822051
$531$	−2.66620	−0.115703
$532$	−1.83726	−0.0796552
$533$	14.5904	0.631982
$534$	−7.51386	−0.325157
$535$	−18.1652	−0.785351
$536$	−0.558065	−0.0241047
$537$	8.96523	0.386878
$538$	−38.2308	−1.64825
$539$	−29.0376	−1.25074
$540$	−6.58464	−0.283358
$541$	39.1371	1.68263	0.841317	−	0.540542i	$-0.181781\pi$
$541$	39.1371	1.68263	0.841317	+	0.540542i	$0.181781\pi$
$542$	−28.6318	−1.22984
$543$	34.3178	1.47272
$544$	8.94262	0.383412
$545$	12.3525	0.529121
$546$	3.41161	0.146003
$547$	24.0487	1.02825	0.514125	−	0.857715i	$-0.328117\pi$
$547$	24.0487	1.02825	0.514125	+	0.857715i	$0.328117\pi$
$548$	−8.09034	−0.345602
$549$	0.830696	0.0354532
$550$	12.4605	0.531318
$551$	−4.64434	−0.197855
$552$	12.3831	0.527060
$553$	4.28779	0.182335
$554$	18.4678	0.784623
$555$	−14.5497	−0.617602
$556$	1.40023	0.0593832
$557$	−17.2987	−0.732971	−0.366486	−	0.930424i	$-0.619439\pi$
$557$	−17.2987	−0.732971	−0.366486	+	0.930424i	$0.619439\pi$
$558$	0.485318	0.0205451
$559$	−23.4879	−0.993433
$560$	4.84464	0.204723
$561$	−16.2940	−0.687934
$562$	15.2490	0.643242
$563$	5.63944	0.237674	0.118837	−	0.992914i	$-0.462083\pi$
$563$	5.63944	0.237674	0.118837	+	0.992914i	$0.462083\pi$
$564$	8.52665	0.359037
$565$	−5.04626	−0.212298
$566$	−43.7551	−1.83917
$567$	−3.33466	−0.140043
$568$	25.7817	1.08177
$569$	−12.0350	−0.504535	−0.252268	−	0.967658i	$-0.581176\pi$
$569$	−12.0350	−0.504535	−0.252268	+	0.967658i	$0.581176\pi$
$570$	22.3171	0.934762
$571$	29.9404	1.25297	0.626484	−	0.779434i	$-0.284493\pi$
$571$	29.9404	1.25297	0.626484	+	0.779434i	$0.284493\pi$
$572$	7.18456	0.300402
$573$	26.7683	1.11826
$574$	−5.14617	−0.214797
$575$	6.67839	0.278508
$576$	−3.11985	−0.129994
$577$	17.6080	0.733032	0.366516	−	0.930412i	$-0.380551\pi$
$577$	17.6080	0.733032	0.366516	+	0.930412i	$0.380551\pi$
$578$	17.3111	0.720046
$579$	15.5495	0.646216
$580$	−1.06062	−0.0440399
$581$	−9.04811	−0.375379
$582$	−10.3889	−0.430635
$583$	−28.0337	−1.16104
$584$	−35.4428	−1.46663
$585$	3.58889	0.148382
$586$	−28.0587	−1.15909
$587$	−21.2268	−0.876125	−0.438062	−	0.898945i	$-0.644335\pi$
$587$	−21.2268	−0.876125	−0.438062	+	0.898945i	$0.644335\pi$
$588$	6.47914	0.267195
$589$	−1.94939	−0.0803231
$590$	9.97165	0.410526
$591$	6.49244	0.267063
$592$	26.4976	1.08904
$593$	1.78783	0.0734175	0.0367087	−	0.999326i	$-0.488313\pi$
$593$	1.78783	0.0734175	0.0367087	+	0.999326i	$0.488313\pi$
$594$	−39.7687	−1.63173
$595$	−2.50607	−0.102739
$596$	−5.58457	−0.228753
$597$	−20.8766	−0.854422
$598$	15.7001	0.642025
$599$	−4.15199	−0.169646	−0.0848228	−	0.996396i	$-0.527032\pi$
$599$	−4.15199	−0.169646	−0.0848228	+	0.996396i	$0.527032\pi$
$600$	5.77536	0.235778
$601$	−4.87221	−0.198742	−0.0993708	−	0.995050i	$-0.531683\pi$
$601$	−4.87221	−0.198742	−0.0993708	+	0.995050i	$0.531683\pi$
$602$	8.28438	0.337646
$603$	0.198793	0.00809548
$604$	0.343075	0.0139595
$605$	−14.0495	−0.571192
$606$	−9.05191	−0.367709
$607$	−22.0579	−0.895303	−0.447652	−	0.894208i	$-0.647739\pi$
$607$	−22.0579	−0.895303	−0.447652	+	0.894208i	$0.647739\pi$
$608$	−18.1434	−0.735812
$609$	−0.746041	−0.0302311
$610$	−3.10682	−0.125792
$611$	−22.4563	−0.908484
$612$	−1.28376	−0.0518928
$613$	−19.0369	−0.768895	−0.384447	−	0.923147i	$-0.625608\pi$
$613$	−19.0369	−0.768895	−0.384447	+	0.923147i	$0.625608\pi$
$614$	−47.2081	−1.90516
$615$	15.3316	0.618228
$616$	5.26383	0.212086
$617$	−22.0697	−0.888494	−0.444247	−	0.895904i	$-0.646529\pi$
$617$	−22.0697	−0.888494	−0.444247	+	0.895904i	$0.646529\pi$
$618$	6.86495	0.276149
$619$	−5.69372	−0.228850	−0.114425	−	0.993432i	$-0.536503\pi$
$619$	−5.69372	−0.228850	−0.114425	+	0.993432i	$0.536503\pi$
$620$	−0.445179	−0.0178788
$621$	−21.3146	−0.855327
$622$	−44.3287	−1.77742
$623$	−1.71187	−0.0685848
$624$	18.5103	0.741004
$625$	−13.0609	−0.522438
$626$	−9.00303	−0.359833
$627$	33.0584	1.32023
$628$	7.26050	0.289725
$629$	−13.7069	−0.546528
$630$	−1.26583	−0.0504318
$631$	37.6327	1.49813	0.749067	−	0.662494i	$-0.230502\pi$
$631$	37.6327	1.49813	0.749067	+	0.662494i	$0.230502\pi$
$632$	17.0641	0.678775
$633$	16.4654	0.654442
$634$	−50.7941	−2.01729
$635$	26.8263	1.06457
$636$	6.25514	0.248032
$637$	−17.0639	−0.676095
$638$	−6.40575	−0.253606
$639$	−9.18391	−0.363310
$640$	24.4185	0.965226
$641$	6.63550	0.262086	0.131043	−	0.991377i	$-0.458167\pi$
$641$	6.63550	0.262086	0.131043	+	0.991377i	$0.458167\pi$
$642$	24.4798	0.966140
$643$	−29.4970	−1.16325	−0.581625	−	0.813457i	$-0.697583\pi$
$643$	−29.4970	−1.16325	−0.581625	+	0.813457i	$0.697583\pi$
$644$	−1.35816	−0.0535191
$645$	−24.6810	−0.971813
$646$	21.0243	0.827190
$647$	−45.6726	−1.79558	−0.897788	−	0.440427i	$-0.854827\pi$
$647$	−45.6726	−1.79558	−0.897788	+	0.440427i	$0.854827\pi$
$648$	−13.2710	−0.521333
$649$	14.7710	0.579813
$650$	7.32238	0.287207
$651$	−0.313139	−0.0122729
$652$	13.0058	0.509346
$653$	−31.6691	−1.23931	−0.619655	−	0.784875i	$-0.712727\pi$
$653$	−31.6691	−1.23931	−0.619655	+	0.784875i	$0.712727\pi$
$654$	−16.6464	−0.650926
$655$	−24.3190	−0.950220
$656$	−27.9214	−1.09015
$657$	12.6254	0.492563
$658$	7.92052	0.308774
$659$	9.73186	0.379099	0.189550	−	0.981871i	$-0.439297\pi$
$659$	9.73186	0.379099	0.189550	+	0.981871i	$0.439297\pi$
$660$	7.54950	0.293864
$661$	−14.5544	−0.566100	−0.283050	−	0.959105i	$-0.591346\pi$
$661$	−14.5544	−0.566100	−0.283050	+	0.959105i	$0.591346\pi$
$662$	−27.3522	−1.06307
$663$	−9.57513	−0.371867
$664$	−36.0088	−1.39741
$665$	5.08449	0.197168
$666$	−6.92340	−0.268276
$667$	−3.43325	−0.132936
$668$	−7.76803	−0.300554
$669$	23.1542	0.895195
$670$	−0.743491	−0.0287236
$671$	−4.60214	−0.177664
$672$	−2.91446	−0.112428
$673$	−46.1914	−1.78055	−0.890273	−	0.455427i	$-0.849486\pi$
$673$	−46.1914	−1.78055	−0.890273	+	0.455427i	$0.849486\pi$
$674$	−12.3383	−0.475252
$675$	−9.94095	−0.382627
$676$	−4.22715	−0.162583
$677$	−10.6087	−0.407725	−0.203863	−	0.978999i	$-0.565350\pi$
$677$	−10.6087	−0.407725	−0.203863	+	0.978999i	$0.565350\pi$
$678$	6.80042	0.261169
$679$	−2.36690	−0.0908333
$680$	−9.97342	−0.382463
$681$	−1.89963	−0.0727939
$682$	−2.68871	−0.102956
$683$	−35.9985	−1.37745	−0.688723	−	0.725025i	$-0.741828\pi$
$683$	−35.9985	−1.37745	−0.688723	+	0.725025i	$0.741828\pi$
$684$	2.60458	0.0995885
$685$	22.3895	0.855458
$686$	12.3113	0.470046
$687$	23.1141	0.881858
$688$	44.9483	1.71364
$689$	−16.4739	−0.627606
$690$	16.4976	0.628052
$691$	24.7115	0.940070	0.470035	−	0.882648i	$-0.344241\pi$
$691$	24.7115	0.940070	0.470035	+	0.882648i	$0.344241\pi$
$692$	2.04444	0.0777178
$693$	−1.87508	−0.0712282
$694$	45.7192	1.73548
$695$	−3.87506	−0.146989
$696$	−2.96902	−0.112540
$697$	14.4434	0.547083
$698$	−18.9206	−0.716155
$699$	41.3957	1.56573
$700$	−0.633434	−0.0239416
$701$	28.8712	1.09045	0.545225	−	0.838290i	$-0.316444\pi$
$701$	28.8712	1.09045	0.545225	+	0.838290i	$0.316444\pi$
$702$	−23.3700	−0.882043
$703$	27.8094	1.04885
$704$	17.2843	0.651428
$705$	−23.5970	−0.888713
$706$	10.0367	0.377735
$707$	−2.06229	−0.0775603
$708$	−3.29585	−0.123866
$709$	−31.6656	−1.18923	−0.594614	−	0.804012i	$-0.702695\pi$
$709$	−31.6656	−1.18923	−0.594614	+	0.804012i	$0.702695\pi$
$710$	34.3481	1.28906
$711$	−6.07856	−0.227964
$712$	−6.81275	−0.255319
$713$	−1.44105	−0.0539679
$714$	3.37723	0.126389
$715$	−19.8828	−0.743575
$716$	−3.91322	−0.146244
$717$	−1.79230	−0.0669345
$718$	16.9129	0.631183
$719$	30.1524	1.12449	0.562247	−	0.826969i	$-0.309937\pi$
$719$	30.1524	1.12449	0.562247	+	0.826969i	$0.309937\pi$
$720$	−6.86798	−0.255954
$721$	1.56403	0.0582477
$722$	−11.7262	−0.436403
$723$	38.1222	1.41778
$724$	−14.9793	−0.556702
$725$	−1.60124	−0.0594685
$726$	18.9333	0.702681
$727$	15.1905	0.563384	0.281692	−	0.959505i	$-0.409104\pi$
$727$	15.1905	0.563384	0.281692	+	0.959505i	$0.409104\pi$
$728$	3.09328	0.114644
$729$	29.8887	1.10699
$730$	−47.2193	−1.74766
$731$	−23.2512	−0.859977
$732$	1.02687	0.0379543
$733$	39.8270	1.47104	0.735522	−	0.677501i	$-0.236937\pi$
$733$	39.8270	1.47104	0.735522	+	0.677501i	$0.236937\pi$
$734$	−0.929988	−0.0343265
$735$	−17.9306	−0.661381
$736$	−13.4122	−0.494381
$737$	−1.10134	−0.0405682
$738$	7.29544	0.268549
$739$	−26.4367	−0.972489	−0.486245	−	0.873823i	$-0.661634\pi$
$739$	−26.4367	−0.972489	−0.486245	+	0.873823i	$0.661634\pi$
$740$	6.35079	0.233460
$741$	19.4267	0.713657
$742$	5.81048	0.213310
$743$	−26.5745	−0.974923	−0.487462	−	0.873144i	$-0.662077\pi$
$743$	−26.5745	−0.974923	−0.487462	+	0.873144i	$0.662077\pi$
$744$	−1.24620	−0.0456879
$745$	15.4549	0.566225
$746$	−4.80760	−0.176019
$747$	12.8270	0.469316
$748$	7.11215	0.260046
$749$	5.57720	0.203787
$750$	29.4930	1.07693
$751$	−30.1977	−1.10193	−0.550964	−	0.834529i	$-0.685740\pi$
$751$	−30.1977	−1.10193	−0.550964	+	0.834529i	$0.685740\pi$
$752$	42.9741	1.56711
$753$	−19.7499	−0.719725
$754$	−3.76432	−0.137088
$755$	−0.949439	−0.0345536
$756$	2.02166	0.0735270
$757$	31.3606	1.13982	0.569911	−	0.821706i	$-0.306978\pi$
$757$	31.3606	1.13982	0.569911	+	0.821706i	$0.306978\pi$
$758$	42.7647	1.55328
$759$	24.4379	0.887040
$760$	20.2348	0.733992
$761$	40.3426	1.46242	0.731210	−	0.682153i	$-0.238956\pi$
$761$	40.3426	1.46242	0.731210	+	0.682153i	$0.238956\pi$
$762$	−36.1517	−1.30964
$763$	−3.79253	−0.137299
$764$	−11.6841	−0.422715
$765$	3.55272	0.128449
$766$	−5.60803	−0.202626
$767$	8.68015	0.313422
$768$	−21.0390	−0.759180
$769$	−20.4304	−0.736739	−0.368369	−	0.929680i	$-0.620084\pi$
$769$	−20.4304	−0.736739	−0.368369	+	0.929680i	$0.620084\pi$
$770$	7.01283	0.252725
$771$	23.9738	0.863395
$772$	−6.78719	−0.244276
$773$	45.6859	1.64321	0.821605	−	0.570058i	$-0.193079\pi$
$773$	45.6859	1.64321	0.821605	+	0.570058i	$0.193079\pi$
$774$	−11.7443	−0.422140
$775$	−0.672094	−0.0241423
$776$	−9.41956	−0.338142
$777$	4.46715	0.160258
$778$	12.9439	0.464063
$779$	−29.3038	−1.04992
$780$	4.43644	0.158850
$781$	50.8798	1.82062
$782$	15.5419	0.555776
$783$	5.11048	0.182634
$784$	32.6547	1.16624
$785$	−20.0930	−0.717149
$786$	32.7727	1.16896
$787$	15.1038	0.538392	0.269196	−	0.963085i	$-0.413242\pi$
$787$	15.1038	0.538392	0.269196	+	0.963085i	$0.413242\pi$
$788$	−2.83388	−0.100953
$789$	−10.0856	−0.359055
$790$	22.7340	0.808839
$791$	1.54933	0.0550880
$792$	−7.46224	−0.265159
$793$	−2.70444	−0.0960373
$794$	−35.3661	−1.25510
$795$	−17.3107	−0.613947
$796$	9.11240	0.322980
$797$	13.0697	0.462954	0.231477	−	0.972840i	$-0.425644\pi$
$797$	13.0697	0.462954	0.231477	+	0.972840i	$0.425644\pi$
$798$	−6.85195	−0.242556
$799$	−22.2300	−0.786440
$800$	−6.25533	−0.221159
$801$	2.42683	0.0857478
$802$	−22.9646	−0.810909
$803$	−69.9460	−2.46834
$804$	0.245740	0.00866659
$805$	3.75863	0.132474
$806$	−1.58001	−0.0556536
$807$	−34.9697	−1.23099
$808$	−8.20729	−0.288732
$809$	−19.0282	−0.668996	−0.334498	−	0.942396i	$-0.608567\pi$
$809$	−19.0282	−0.668996	−0.334498	+	0.942396i	$0.608567\pi$
$810$	−17.6805	−0.621228
$811$	21.0749	0.740042	0.370021	−	0.929023i	$-0.379351\pi$
$811$	21.0749	0.740042	0.370021	+	0.929023i	$0.379351\pi$
$812$	0.325638	0.0114277
$813$	−26.1895	−0.918506
$814$	38.3564	1.34439
$815$	−35.9927	−1.26077
$816$	18.3237	0.641459
$817$	47.1736	1.65040
$818$	16.7516	0.585705
$819$	−1.10188	−0.0385029
$820$	−6.69206	−0.233697
$821$	10.5704	0.368909	0.184454	−	0.982841i	$-0.440948\pi$
$821$	10.5704	0.368909	0.184454	+	0.982841i	$0.440948\pi$
$822$	−30.1725	−1.05239
$823$	40.5293	1.41276	0.706381	−	0.707832i	$-0.250327\pi$
$823$	40.5293	1.41276	0.706381	+	0.707832i	$0.250327\pi$
$824$	6.22439	0.216837
$825$	11.3976	0.396814
$826$	−3.06156	−0.106525
$827$	−47.1057	−1.63803	−0.819013	−	0.573775i	$-0.805478\pi$
$827$	−47.1057	−1.63803	−0.819013	+	0.573775i	$0.805478\pi$
$828$	1.92539	0.0669120
$829$	−9.69487	−0.336717	−0.168358	−	0.985726i	$-0.553847\pi$
$829$	−9.69487	−0.336717	−0.168358	+	0.985726i	$0.553847\pi$
$830$	−47.9733	−1.66518
$831$	16.8925	0.585994
$832$	10.1571	0.352134
$833$	−16.8919	−0.585269
$834$	5.22210	0.180827
$835$	21.4975	0.743953
$836$	−14.4296	−0.499059
$837$	2.14504	0.0741436
$838$	−31.0865	−1.07386
$839$	29.2517	1.00988	0.504940	−	0.863154i	$-0.331515\pi$
$839$	29.2517	1.00988	0.504940	+	0.863154i	$0.331515\pi$
$840$	3.25040	0.112149
$841$	−28.1768	−0.971615
$842$	−42.8168	−1.47557
$843$	13.9483	0.480404
$844$	−7.18697	−0.247386
$845$	11.6984	0.402436
$846$	−11.2285	−0.386043
$847$	4.31356	0.148216
$848$	31.5258	1.08260
$849$	−40.0228	−1.37358
$850$	7.24858	0.248624
$851$	20.5577	0.704708
$852$	−11.3528	−0.388940
$853$	−31.0610	−1.06351	−0.531754	−	0.846899i	$-0.678467\pi$
$853$	−31.0610	−1.06351	−0.531754	+	0.846899i	$0.678467\pi$
$854$	0.953876	0.0326410
$855$	−7.20800	−0.246508
$856$	22.1956	0.758630
$857$	−27.3567	−0.934486	−0.467243	−	0.884129i	$-0.654753\pi$
$857$	−27.3567	−0.934486	−0.467243	+	0.884129i	$0.654753\pi$
$858$	26.7944	0.914747
$859$	−37.0124	−1.26285	−0.631424	−	0.775438i	$-0.717529\pi$
$859$	−37.0124	−1.26285	−0.631424	+	0.775438i	$0.717529\pi$
$860$	10.7730	0.367355
$861$	−4.70719	−0.160421
$862$	26.8998	0.916211
$863$	−37.6253	−1.28078	−0.640389	−	0.768051i	$-0.721227\pi$
$863$	−37.6253	−1.28078	−0.640389	+	0.768051i	$0.721227\pi$
$864$	19.9644	0.679203
$865$	−5.65785	−0.192373
$866$	−7.36554	−0.250291
$867$	15.8344	0.537765
$868$	0.136682	0.00463928
$869$	33.6759	1.14238
$870$	−3.95553	−0.134105
$871$	−0.647196	−0.0219294
$872$	−15.0932	−0.511119
$873$	3.35542	0.113564
$874$	−31.5324	−1.06660
$875$	6.71935	0.227156
$876$	15.6070	0.527312
$877$	35.6727	1.20458	0.602291	−	0.798277i	$-0.294255\pi$
$877$	35.6727	1.20458	0.602291	+	0.798277i	$0.294255\pi$
$878$	14.7612	0.498165
$879$	−25.6653	−0.865668
$880$	38.0493	1.28264
$881$	−30.3930	−1.02397	−0.511984	−	0.858995i	$-0.671089\pi$
$881$	−30.3930	−1.02397	−0.511984	+	0.858995i	$0.671089\pi$
$882$	−8.53218	−0.287293
$883$	23.6017	0.794260	0.397130	−	0.917762i	$-0.370006\pi$
$883$	23.6017	0.794260	0.397130	+	0.917762i	$0.370006\pi$
$884$	4.17944	0.140570
$885$	9.12106	0.306601
$886$	20.5993	0.692046
$887$	−18.1804	−0.610437	−0.305219	−	0.952282i	$-0.598730\pi$
$887$	−18.1804	−0.610437	−0.305219	+	0.952282i	$0.598730\pi$
$888$	17.7779	0.596588
$889$	−8.23639	−0.276240
$890$	−9.07640	−0.304242
$891$	−26.1901	−0.877401
$892$	−10.1066	−0.338393
$893$	45.1017	1.50927
$894$	−20.8273	−0.696571
$895$	10.8296	0.361993
$896$	−7.49713	−0.250461
$897$	14.3609	0.479495
$898$	−56.7043	−1.89225
$899$	0.345513	0.0115235
$900$	0.897985	0.0299328
$901$	−16.3079	−0.543294
$902$	−40.4175	−1.34576
$903$	7.57771	0.252170
$904$	6.16589	0.205074
$905$	41.4543	1.37799
$906$	1.27948	0.0425079
$907$	−26.8615	−0.891921	−0.445961	−	0.895053i	$-0.647138\pi$
$907$	−26.8615	−0.891921	−0.445961	+	0.895053i	$0.647138\pi$
$908$	0.829166	0.0275168
$909$	2.92359	0.0969694
$910$	4.12107	0.136612
$911$	42.7019	1.41478	0.707388	−	0.706825i	$-0.249873\pi$
$911$	42.7019	1.41478	0.707388	+	0.706825i	$0.249873\pi$
$912$	−37.1764	−1.23103
$913$	−71.0630	−2.35184
$914$	23.3952	0.773846
$915$	−2.84181	−0.0939473
$916$	−10.0891	−0.333352
$917$	7.46656	0.246568
$918$	−23.1345	−0.763551
$919$	−7.59767	−0.250624	−0.125312	−	0.992117i	$-0.539993\pi$
$919$	−7.59767	−0.250624	−0.125312	+	0.992117i	$0.539993\pi$
$920$	14.9582	0.493158
$921$	−43.1812	−1.42287
$922$	34.0749	1.12220
$923$	29.8994	0.984151
$924$	−2.31790	−0.0762532
$925$	9.58790	0.315248
$926$	−31.6137	−1.03889
$927$	−2.21724	−0.0728239
$928$	3.21577	0.105563
$929$	−34.5765	−1.13442	−0.567210	−	0.823574i	$-0.691977\pi$
$929$	−34.5765	−1.13442	−0.567210	+	0.823574i	$0.691977\pi$
$930$	−1.66027	−0.0544424
$931$	34.2714	1.12320
$932$	−18.0688	−0.591862
$933$	−40.5474	−1.32746
$934$	−35.9509	−1.17635
$935$	−19.6824	−0.643684
$936$	−4.38517	−0.143334
$937$	40.4353	1.32096	0.660482	−	0.750842i	$-0.270352\pi$
$937$	40.4353	1.32096	0.660482	+	0.750842i	$0.270352\pi$
$938$	0.228271	0.00745333
$939$	−8.23506	−0.268741
$940$	10.2998	0.335943
$941$	−22.3193	−0.727587	−0.363794	−	0.931480i	$-0.618519\pi$
$941$	−22.3193	−0.727587	−0.363794	+	0.931480i	$0.618519\pi$
$942$	27.0776	0.882237
$943$	−21.6623	−0.705423
$944$	−16.6110	−0.540643
$945$	−5.59481	−0.181999
$946$	65.0647	2.11543
$947$	−40.0277	−1.30073	−0.650363	−	0.759623i	$-0.725383\pi$
$947$	−40.0277	−1.30073	−0.650363	+	0.759623i	$0.725383\pi$
$948$	−7.51409	−0.244046
$949$	−41.1036	−1.33428
$950$	−14.7064	−0.477140
$951$	−46.4613	−1.50661
$952$	3.06210	0.0992433
$953$	−6.33099	−0.205081	−0.102540	−	0.994729i	$-0.532697\pi$
$953$	−6.33099	−0.205081	−0.102540	+	0.994729i	$0.532697\pi$
$954$	−8.23720	−0.266689
$955$	32.3349	1.04633
$956$	0.782317	0.0253019
$957$	−5.85933	−0.189405
$958$	−41.3669	−1.33650
$959$	−6.87416	−0.221978
$960$	10.6730	0.344470
$961$	−30.8550	−0.995322
$962$	22.5400	0.726720
$963$	−7.90649	−0.254783
$964$	−16.6399	−0.535936
$965$	18.7831	0.604650
$966$	−5.06519	−0.162970
$967$	−12.8388	−0.412867	−0.206433	−	0.978461i	$-0.566186\pi$
$967$	−12.8388	−0.412867	−0.206433	+	0.978461i	$0.566186\pi$
$968$	17.1667	0.551758
$969$	19.2309	0.617785
$970$	−12.5494	−0.402936
$971$	22.1505	0.710842	0.355421	−	0.934706i	$-0.384338\pi$
$971$	22.1505	0.710842	0.355421	+	0.934706i	$0.384338\pi$
$972$	−5.13886	−0.164829
$973$	1.18975	0.0381415
$974$	59.8518	1.91778
$975$	6.69778	0.214500
$976$	5.17542	0.165661
$977$	41.0297	1.31266	0.656328	−	0.754475i	$-0.272109\pi$
$977$	41.0297	1.31266	0.656328	+	0.754475i	$0.272109\pi$
$978$	48.5044	1.55100
$979$	−13.4449	−0.429701
$980$	7.82651	0.250009
$981$	5.37646	0.171657
$982$	20.6042	0.657506
$983$	43.9691	1.40240	0.701199	−	0.712966i	$-0.252649\pi$
$983$	43.9691	1.40240	0.701199	+	0.712966i	$0.252649\pi$
$984$	−18.7332	−0.597194
$985$	7.84258	0.249885
$986$	−3.72638	−0.118672
$987$	7.24489	0.230607
$988$	−8.47953	−0.269770
$989$	34.8724	1.10888
$990$	−9.94170	−0.315968
$991$	20.6965	0.657446	0.328723	−	0.944426i	$-0.393382\pi$
$991$	20.6965	0.657446	0.328723	+	0.944426i	$0.393382\pi$
$992$	1.34977	0.0428552
$993$	−25.0190	−0.793955
$994$	−10.5458	−0.334491
$995$	−25.2180	−0.799464
$996$	15.8562	0.502424
$997$	52.9018	1.67542	0.837709	−	0.546117i	$-0.183895\pi$
$997$	52.9018	1.67542	0.837709	+	0.546117i	$0.183895\pi$
$998$	−3.89873	−0.123412
$999$	−30.6006	−0.968160

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	503.2.a.e.1.3	✓	10
3.2	odd	2		4527.2.a.k.1.8		10
4.3	odd	2		8048.2.a.p.1.6		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
503.2.a.e.1.3	✓	10	1.1	even	1	trivial
4527.2.a.k.1.8		10	3.2	odd	2
8048.2.a.p.1.6		10	4.3	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:	\( N \)	\(=\)	\( 503 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	503.a (trivial)

\(f(q)\)	\(=\)	\(q-1.62786 q^{2} -1.48900 q^{3} +0.649933 q^{4} -1.79865 q^{5} +2.42389 q^{6} +0.552233 q^{7} +2.19772 q^{8} -0.782869 q^{9} +O(q^{10})\)	\(q-1.62786 q^{2} -1.48900 q^{3} +0.649933 q^{4} -1.79865 q^{5} +2.42389 q^{6} +0.552233 q^{7} +2.19772 q^{8} -0.782869 q^{9} +2.92795 q^{10} +4.33718 q^{11} -0.967753 q^{12} +2.54873 q^{13} -0.898958 q^{14} +2.67819 q^{15} -4.87745 q^{16} +2.52304 q^{17} +1.27440 q^{18} -5.11893 q^{19} -1.16900 q^{20} -0.822276 q^{21} -7.06033 q^{22} -3.78409 q^{23} -3.27241 q^{24} -1.76486 q^{25} -4.14898 q^{26} +5.63270 q^{27} +0.358914 q^{28} +0.907287 q^{29} -4.35973 q^{30} +0.380820 q^{31} +3.54438 q^{32} -6.45807 q^{33} -4.10717 q^{34} -0.993273 q^{35} -0.508813 q^{36} -5.43266 q^{37} +8.33291 q^{38} -3.79507 q^{39} -3.95293 q^{40} +5.72459 q^{41} +1.33855 q^{42} -9.21553 q^{43} +2.81888 q^{44} +1.40811 q^{45} +6.15997 q^{46} -8.81077 q^{47} +7.26254 q^{48} -6.69504 q^{49} +2.87295 q^{50} -3.75682 q^{51} +1.65651 q^{52} -6.46357 q^{53} -9.16926 q^{54} -7.80106 q^{55} +1.21365 q^{56} +7.62210 q^{57} -1.47694 q^{58} +3.40568 q^{59} +1.74065 q^{60} -1.06109 q^{61} -0.619922 q^{62} -0.432326 q^{63} +3.98515 q^{64} -4.58427 q^{65} +10.5129 q^{66} -0.253929 q^{67} +1.63981 q^{68} +5.63451 q^{69} +1.61691 q^{70} +11.7311 q^{71} -1.72053 q^{72} -16.1271 q^{73} +8.84362 q^{74} +2.62789 q^{75} -3.32696 q^{76} +2.39513 q^{77} +6.17785 q^{78} +7.76447 q^{79} +8.77283 q^{80} -6.03851 q^{81} -9.31884 q^{82} -16.3846 q^{83} -0.534425 q^{84} -4.53807 q^{85} +15.0016 q^{86} -1.35095 q^{87} +9.53191 q^{88} -3.09992 q^{89} -2.29220 q^{90} +1.40749 q^{91} -2.45940 q^{92} -0.567042 q^{93} +14.3427 q^{94} +9.20715 q^{95} -5.27759 q^{96} -4.28605 q^{97} +10.8986 q^{98} -3.39544 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 4 q^{2} - 8 q^{3} + 4 q^{4} - q^{5} - 2 q^{6} - 5 q^{7} - 3 q^{8} - 2 q^{9}+O(q^{10}) \) 10 * q - 4 * q^2 - 8 * q^3 + 4 * q^4 - q^5 - 2 * q^6 - 5 * q^7 - 3 * q^8 - 2 * q^9	\( 10 q - 4 q^{2} - 8 q^{3} + 4 q^{4} - q^{5} - 2 q^{6} - 5 q^{7} - 3 q^{8} - 2 q^{9} - 4 q^{10} - 3 q^{11} - 7 q^{12} - 18 q^{13} + q^{14} - 2 q^{15} - 4 q^{16} - 11 q^{17} - q^{18} - 3 q^{20} + q^{21} - 18 q^{22} - 2 q^{23} + 10 q^{24} - 27 q^{25} + 11 q^{26} - 2 q^{27} - 22 q^{28} - 9 q^{29} + 12 q^{30} - 22 q^{31} - 10 q^{32} - 10 q^{33} - 10 q^{34} - 6 q^{35} + 2 q^{36} - 35 q^{37} + 2 q^{38} + 8 q^{39} - 19 q^{40} - 4 q^{41} + 4 q^{42} - 20 q^{43} + 9 q^{44} + 2 q^{45} - q^{46} + 7 q^{47} - 27 q^{49} + 16 q^{50} + 9 q^{51} - 7 q^{52} - 24 q^{53} + 17 q^{54} - 11 q^{55} + 12 q^{56} - 23 q^{57} + 2 q^{58} + 17 q^{59} - 4 q^{61} + 8 q^{62} + 10 q^{63} + 3 q^{64} - 16 q^{65} + 46 q^{66} - 6 q^{67} + 28 q^{68} - 2 q^{69} + 26 q^{70} - q^{71} - q^{72} - 31 q^{73} + 11 q^{74} + 30 q^{75} + 20 q^{76} + 3 q^{77} + 11 q^{78} - 10 q^{79} + 24 q^{80} - 6 q^{81} - 9 q^{82} + 22 q^{83} + 22 q^{84} - 6 q^{85} + 38 q^{86} + 25 q^{87} - 3 q^{88} + q^{89} + 2 q^{90} + 10 q^{91} + 27 q^{92} - 6 q^{93} + 33 q^{94} + 39 q^{95} + 46 q^{96} - 57 q^{97} + 40 q^{98} + 35 q^{99}+O(q^{100}) \) 10 * q - 4 * q^2 - 8 * q^3 + 4 * q^4 - q^5 - 2 * q^6 - 5 * q^7 - 3 * q^8 - 2 * q^9 - 4 * q^10 - 3 * q^11 - 7 * q^12 - 18 * q^13 + q^14 - 2 * q^15 - 4 * q^16 - 11 * q^17 - q^18 - 3 * q^20 + q^21 - 18 * q^22 - 2 * q^23 + 10 * q^24 - 27 * q^25 + 11 * q^26 - 2 * q^27 - 22 * q^28 - 9 * q^29 + 12 * q^30 - 22 * q^31 - 10 * q^32 - 10 * q^33 - 10 * q^34 - 6 * q^35 + 2 * q^36 - 35 * q^37 + 2 * q^38 + 8 * q^39 - 19 * q^40 - 4 * q^41 + 4 * q^42 - 20 * q^43 + 9 * q^44 + 2 * q^45 - q^46 + 7 * q^47 - 27 * q^49 + 16 * q^50 + 9 * q^51 - 7 * q^52 - 24 * q^53 + 17 * q^54 - 11 * q^55 + 12 * q^56 - 23 * q^57 + 2 * q^58 + 17 * q^59 - 4 * q^61 + 8 * q^62 + 10 * q^63 + 3 * q^64 - 16 * q^65 + 46 * q^66 - 6 * q^67 + 28 * q^68 - 2 * q^69 + 26 * q^70 - q^71 - q^72 - 31 * q^73 + 11 * q^74 + 30 * q^75 + 20 * q^76 + 3 * q^77 + 11 * q^78 - 10 * q^79 + 24 * q^80 - 6 * q^81 - 9 * q^82 + 22 * q^83 + 22 * q^84 - 6 * q^85 + 38 * q^86 + 25 * q^87 - 3 * q^88 + q^89 + 2 * q^90 + 10 * q^91 + 27 * q^92 - 6 * q^93 + 33 * q^94 + 39 * q^95 + 46 * q^96 - 57 * q^97 + 40 * q^98 + 35 * q^99

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