LMFDB - Embedded newform 1502.2.a.h.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1502,2,Mod(1,1502)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1502, 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("1502.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1502 = 2 \cdot 751 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1502.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:	$11.9935303836$
Analytic rank:	$0$
Dimension:	$19$
Coefficient field:	$\mathbb{Q}[x]/(x^{19} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{19} - 6 x^{18} - 23 x^{17} + 190 x^{16} + 128 x^{15} - 2394 x^{14} + 749 x^{13} + 15539 x^{12} + \cdots + 4222 $ x^19 - 6x^18 - 23x^17 + 190x^16 + 128x^15 - 2394x^14 + 749x^13 + 15539x^12 - 11338x^11 - 56744x^10 + 50183x^9 + 120237x^8 - 102992x^7 - 148539x^6 + 99519x^5 + 104388x^4 - 41081x^3 - 35733x^2 + 5542x + 4222
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Root			$0.748702$ of defining polynomial
Character	$\chi$	$=$	1502.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +0.748702 q^{3} +1.00000 q^{4} -1.18128 q^{5} -0.748702 q^{6} -4.67174 q^{7} -1.00000 q^{8} -2.43945 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +0.748702 q^{3} +1.00000 q^{4} -1.18128 q^{5} -0.748702 q^{6} -4.67174 q^{7} -1.00000 q^{8} -2.43945 q^{9} +1.18128 q^{10} +2.23901 q^{11} +0.748702 q^{12} -1.97457 q^{13} +4.67174 q^{14} -0.884430 q^{15} +1.00000 q^{16} +4.90445 q^{17} +2.43945 q^{18} +0.579881 q^{19} -1.18128 q^{20} -3.49774 q^{21} -2.23901 q^{22} -0.198770 q^{23} -0.748702 q^{24} -3.60457 q^{25} +1.97457 q^{26} -4.07252 q^{27} -4.67174 q^{28} +4.80971 q^{29} +0.884430 q^{30} -3.68804 q^{31} -1.00000 q^{32} +1.67635 q^{33} -4.90445 q^{34} +5.51865 q^{35} -2.43945 q^{36} +7.79963 q^{37} -0.579881 q^{38} -1.47836 q^{39} +1.18128 q^{40} +6.02349 q^{41} +3.49774 q^{42} +9.74861 q^{43} +2.23901 q^{44} +2.88168 q^{45} +0.198770 q^{46} +9.27442 q^{47} +0.748702 q^{48} +14.8252 q^{49} +3.60457 q^{50} +3.67197 q^{51} -1.97457 q^{52} -3.45171 q^{53} +4.07252 q^{54} -2.64491 q^{55} +4.67174 q^{56} +0.434158 q^{57} -4.80971 q^{58} -3.38512 q^{59} -0.884430 q^{60} -3.29564 q^{61} +3.68804 q^{62} +11.3965 q^{63} +1.00000 q^{64} +2.33253 q^{65} -1.67635 q^{66} +12.6781 q^{67} +4.90445 q^{68} -0.148819 q^{69} -5.51865 q^{70} -13.8177 q^{71} +2.43945 q^{72} +0.133904 q^{73} -7.79963 q^{74} -2.69875 q^{75} +0.579881 q^{76} -10.4601 q^{77} +1.47836 q^{78} +1.24253 q^{79} -1.18128 q^{80} +4.26923 q^{81} -6.02349 q^{82} +4.98679 q^{83} -3.49774 q^{84} -5.79355 q^{85} -9.74861 q^{86} +3.60103 q^{87} -2.23901 q^{88} -10.4049 q^{89} -2.88168 q^{90} +9.22467 q^{91} -0.198770 q^{92} -2.76124 q^{93} -9.27442 q^{94} -0.685004 q^{95} -0.748702 q^{96} +17.2830 q^{97} -14.8252 q^{98} -5.46195 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 19 q - 19 q^{2} + 6 q^{3} + 19 q^{4} + 2 q^{5} - 6 q^{6} + 13 q^{7} - 19 q^{8} + 25 q^{9}+O(q^{10}) $ 19 * q - 19 * q^2 + 6 * q^3 + 19 * q^4 + 2 * q^5 - 6 * q^6 + 13 * q^7 - 19 * q^8 + 25 * q^9	\( 19 q - 19 q^{2} + 6 q^{3} + 19 q^{4} + 2 q^{5} - 6 q^{6} + 13 q^{7} - 19 q^{8} + 25 q^{9} - 2 q^{10} - 7 q^{11} + 6 q^{12} + 19 q^{13} - 13 q^{14} + 6 q^{15} + 19 q^{16} + 11 q^{17} - 25 q^{18} + 7 q^{19} + 2 q^{20} + 7 q^{21} + 7 q^{22} + 12 q^{23} - 6 q^{24} + 37 q^{25} - 19 q^{26} + 24 q^{27} + 13 q^{28} - 8 q^{29} - 6 q^{30} + 32 q^{31} - 19 q^{32} + 24 q^{33} - 11 q^{34} - 19 q^{35} + 25 q^{36} + 41 q^{37} - 7 q^{38} - 2 q^{39} - 2 q^{40} + 15 q^{41} - 7 q^{42} + 15 q^{43} - 7 q^{44} + 28 q^{45} - 12 q^{46} - 6 q^{47} + 6 q^{48} + 42 q^{49} - 37 q^{50} + 8 q^{51} + 19 q^{52} + 6 q^{53} - 24 q^{54} + 22 q^{55} - 13 q^{56} + 24 q^{57} + 8 q^{58} - 4 q^{59} + 6 q^{60} + 13 q^{61} - 32 q^{62} + 37 q^{63} + 19 q^{64} + 20 q^{65} - 24 q^{66} + 47 q^{67} + 11 q^{68} + 15 q^{69} + 19 q^{70} - 25 q^{72} + 64 q^{73} - 41 q^{74} - 3 q^{75} + 7 q^{76} - 4 q^{77} + 2 q^{78} + 34 q^{79} + 2 q^{80} + 27 q^{81} - 15 q^{82} + 4 q^{83} + 7 q^{84} + 21 q^{85} - 15 q^{86} + 7 q^{88} + 18 q^{89} - 28 q^{90} + 28 q^{91} + 12 q^{92} + 43 q^{93} + 6 q^{94} - 8 q^{95} - 6 q^{96} + 82 q^{97} - 42 q^{98} - 2 q^{99}+O(q^{100}) \) 19 * q - 19 * q^2 + 6 * q^3 + 19 * q^4 + 2 * q^5 - 6 * q^6 + 13 * q^7 - 19 * q^8 + 25 * q^9 - 2 * q^10 - 7 * q^11 + 6 * q^12 + 19 * q^13 - 13 * q^14 + 6 * q^15 + 19 * q^16 + 11 * q^17 - 25 * q^18 + 7 * q^19 + 2 * q^20 + 7 * q^21 + 7 * q^22 + 12 * q^23 - 6 * q^24 + 37 * q^25 - 19 * q^26 + 24 * q^27 + 13 * q^28 - 8 * q^29 - 6 * q^30 + 32 * q^31 - 19 * q^32 + 24 * q^33 - 11 * q^34 - 19 * q^35 + 25 * q^36 + 41 * q^37 - 7 * q^38 - 2 * q^39 - 2 * q^40 + 15 * q^41 - 7 * q^42 + 15 * q^43 - 7 * q^44 + 28 * q^45 - 12 * q^46 - 6 * q^47 + 6 * q^48 + 42 * q^49 - 37 * q^50 + 8 * q^51 + 19 * q^52 + 6 * q^53 - 24 * q^54 + 22 * q^55 - 13 * q^56 + 24 * q^57 + 8 * q^58 - 4 * q^59 + 6 * q^60 + 13 * q^61 - 32 * q^62 + 37 * q^63 + 19 * q^64 + 20 * q^65 - 24 * q^66 + 47 * q^67 + 11 * q^68 + 15 * q^69 + 19 * q^70 - 25 * q^72 + 64 * q^73 - 41 * q^74 - 3 * q^75 + 7 * q^76 - 4 * q^77 + 2 * q^78 + 34 * q^79 + 2 * q^80 + 27 * q^81 - 15 * q^82 + 4 * q^83 + 7 * q^84 + 21 * q^85 - 15 * q^86 + 7 * q^88 + 18 * q^89 - 28 * q^90 + 28 * q^91 + 12 * q^92 + 43 * q^93 + 6 * q^94 - 8 * q^95 - 6 * q^96 + 82 * q^97 - 42 * q^98 - 2 * 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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	0.748702	0.432263	0.216132	−	0.976364i	$-0.430656\pi$
$3$	0.748702	0.432263	0.216132	+	0.976364i	$0.430656\pi$
$4$	1.00000	0.500000
$5$	−1.18128	−0.528286	−0.264143	−	0.964483i	$-0.585089\pi$
$5$	−1.18128	−0.528286	−0.264143	+	0.964483i	$0.585089\pi$
$6$	−0.748702	−0.305656
$7$	−4.67174	−1.76575	−0.882876	−	0.469606i	$-0.844396\pi$
$7$	−4.67174	−1.76575	−0.882876	+	0.469606i	$0.844396\pi$
$8$	−1.00000	−0.353553
$9$	−2.43945	−0.813149
$10$	1.18128	0.373555
$11$	2.23901	0.675088	0.337544	−	0.941310i	$-0.390404\pi$
$11$	2.23901	0.675088	0.337544	+	0.941310i	$0.390404\pi$
$12$	0.748702	0.216132
$13$	−1.97457	−0.547647	−0.273823	−	0.961780i	$-0.588288\pi$
$13$	−1.97457	−0.547647	−0.273823	+	0.961780i	$0.588288\pi$
$14$	4.67174	1.24858
$15$	−0.884430	−0.228359
$16$	1.00000	0.250000
$17$	4.90445	1.18950	0.594752	−	0.803909i	$-0.297250\pi$
$17$	4.90445	1.18950	0.594752	+	0.803909i	$0.297250\pi$
$18$	2.43945	0.574983
$19$	0.579881	0.133034	0.0665169	−	0.997785i	$-0.478811\pi$
$19$	0.579881	0.133034	0.0665169	+	0.997785i	$0.478811\pi$
$20$	−1.18128	−0.264143
$21$	−3.49774	−0.763270
$22$	−2.23901	−0.477360
$23$	−0.198770	−0.0414464	−0.0207232	−	0.999785i	$-0.506597\pi$
$23$	−0.198770	−0.0414464	−0.0207232	+	0.999785i	$0.506597\pi$
$24$	−0.748702	−0.152828
$25$	−3.60457	−0.720913
$26$	1.97457	0.387245
$27$	−4.07252	−0.783757
$28$	−4.67174	−0.882876
$29$	4.80971	0.893140	0.446570	−	0.894749i	$-0.352645\pi$
$29$	4.80971	0.893140	0.446570	+	0.894749i	$0.352645\pi$
$30$	0.884430	0.161474
$31$	−3.68804	−0.662392	−0.331196	−	0.943562i	$-0.607452\pi$
$31$	−3.68804	−0.662392	−0.331196	+	0.943562i	$0.607452\pi$
$32$	−1.00000	−0.176777
$33$	1.67635	0.291816
$34$	−4.90445	−0.841107
$35$	5.51865	0.932823
$36$	−2.43945	−0.406574
$37$	7.79963	1.28225	0.641126	−	0.767436i	$-0.278468\pi$
$37$	7.79963	1.28225	0.641126	+	0.767436i	$0.278468\pi$
$38$	−0.579881	−0.0940691
$39$	−1.47836	−0.236727
$40$	1.18128	0.186777
$41$	6.02349	0.940711	0.470355	−	0.882477i	$-0.344126\pi$
$41$	6.02349	0.940711	0.470355	+	0.882477i	$0.344126\pi$
$42$	3.49774	0.539713
$43$	9.74861	1.48665	0.743324	−	0.668931i	$-0.233248\pi$
$43$	9.74861	1.48665	0.743324	+	0.668931i	$0.233248\pi$
$44$	2.23901	0.337544
$45$	2.88168	0.429575
$46$	0.198770	0.0293070
$47$	9.27442	1.35281	0.676407	−	0.736528i	$-0.263536\pi$
$47$	9.27442	1.35281	0.676407	+	0.736528i	$0.263536\pi$
$48$	0.748702	0.108066
$49$	14.8252	2.11788
$50$	3.60457	0.509763
$51$	3.67197	0.514179
$52$	−1.97457	−0.273823
$53$	−3.45171	−0.474129	−0.237064	−	0.971494i	$-0.576185\pi$
$53$	−3.45171	−0.474129	−0.237064	+	0.971494i	$0.576185\pi$
$54$	4.07252	0.554200
$55$	−2.64491	−0.356640
$56$	4.67174	0.624288
$57$	0.434158	0.0575056
$58$	−4.80971	−0.631545
$59$	−3.38512	−0.440705	−0.220353	−	0.975420i	$-0.570721\pi$
$59$	−3.38512	−0.440705	−0.220353	+	0.975420i	$0.570721\pi$
$60$	−0.884430	−0.114179
$61$	−3.29564	−0.421964	−0.210982	−	0.977490i	$-0.567666\pi$
$61$	−3.29564	−0.421964	−0.210982	+	0.977490i	$0.567666\pi$
$62$	3.68804	0.468382
$63$	11.3965	1.43582
$64$	1.00000	0.125000
$65$	2.33253	0.289314
$66$	−1.67635	−0.206345
$67$	12.6781	1.54887	0.774435	−	0.632653i	$-0.218034\pi$
$67$	12.6781	1.54887	0.774435	+	0.632653i	$0.218034\pi$
$68$	4.90445	0.594752
$69$	−0.148819	−0.0179157
$70$	−5.51865	−0.659605
$71$	−13.8177	−1.63986	−0.819931	−	0.572462i	$-0.805988\pi$
$71$	−13.8177	−1.63986	−0.819931	+	0.572462i	$0.805988\pi$
$72$	2.43945	0.287491
$73$	0.133904	0.0156723	0.00783615	−	0.999969i	$-0.497506\pi$
$73$	0.133904	0.0156723	0.00783615	+	0.999969i	$0.497506\pi$
$74$	−7.79963	−0.906689
$75$	−2.69875	−0.311624
$76$	0.579881	0.0665169
$77$	−10.4601	−1.19204
$78$	1.47836	0.167392
$79$	1.24253	0.139796	0.0698980	−	0.997554i	$-0.477733\pi$
$79$	1.24253	0.139796	0.0698980	+	0.997554i	$0.477733\pi$
$80$	−1.18128	−0.132072
$81$	4.26923	0.474359
$82$	−6.02349	−0.665183
$83$	4.98679	0.547372	0.273686	−	0.961819i	$-0.411757\pi$
$83$	4.98679	0.547372	0.273686	+	0.961819i	$0.411757\pi$
$84$	−3.49774	−0.381635
$85$	−5.79355	−0.628399
$86$	−9.74861	−1.05122
$87$	3.60103	0.386071
$88$	−2.23901	−0.238680
$89$	−10.4049	−1.10292	−0.551460	−	0.834201i	$-0.685929\pi$
$89$	−10.4049	−1.10292	−0.551460	+	0.834201i	$0.685929\pi$
$90$	−2.88168	−0.303756
$91$	9.22467	0.967008
$92$	−0.198770	−0.0207232
$93$	−2.76124	−0.286328
$94$	−9.27442	−0.956583
$95$	−0.685004	−0.0702799
$96$	−0.748702	−0.0764140
$97$	17.2830	1.75482	0.877412	−	0.479737i	$-0.159268\pi$
$97$	17.2830	1.75482	0.877412	+	0.479737i	$0.159268\pi$
$98$	−14.8252	−1.49757
$99$	−5.46195	−0.548947
$100$	−3.60457	−0.360457
$101$	−8.75193	−0.870849	−0.435425	−	0.900225i	$-0.643402\pi$
$101$	−8.75193	−0.870849	−0.435425	+	0.900225i	$0.643402\pi$
$102$	−3.67197	−0.363579
$103$	17.8938	1.76313	0.881564	−	0.472065i	$-0.156491\pi$
$103$	17.8938	1.76313	0.881564	+	0.472065i	$0.156491\pi$
$104$	1.97457	0.193622
$105$	4.13183	0.403225
$106$	3.45171	0.335260
$107$	−0.879267	−0.0850020	−0.0425010	−	0.999096i	$-0.513533\pi$
$107$	−0.879267	−0.0850020	−0.0425010	+	0.999096i	$0.513533\pi$
$108$	−4.07252	−0.391879
$109$	14.1051	1.35103	0.675513	−	0.737348i	$-0.263922\pi$
$109$	14.1051	1.35103	0.675513	+	0.737348i	$0.263922\pi$
$110$	2.64491	0.252183
$111$	5.83960	0.554270
$112$	−4.67174	−0.441438
$113$	−8.64247	−0.813016	−0.406508	−	0.913647i	$-0.633254\pi$
$113$	−8.64247	−0.813016	−0.406508	+	0.913647i	$0.633254\pi$
$114$	−0.434158	−0.0406626
$115$	0.234804	0.0218956
$116$	4.80971	0.446570
$117$	4.81685	0.445318
$118$	3.38512	0.311626
$119$	−22.9123	−2.10037
$120$	0.884430	0.0807370
$121$	−5.98681	−0.544256
$122$	3.29564	0.298373
$123$	4.50979	0.406634
$124$	−3.68804	−0.331196
$125$	10.1644	0.909135
$126$	−11.3965	−1.01528
$127$	−19.0886	−1.69384	−0.846920	−	0.531720i	$-0.821546\pi$
$127$	−19.0886	−1.69384	−0.846920	+	0.531720i	$0.821546\pi$
$128$	−1.00000	−0.0883883
$129$	7.29880	0.642623
$130$	−2.33253	−0.204576
$131$	−1.07067	−0.0935446	−0.0467723	−	0.998906i	$-0.514894\pi$
$131$	−1.07067	−0.0935446	−0.0467723	+	0.998906i	$0.514894\pi$
$132$	1.67635	0.145908
$133$	−2.70905	−0.234905
$134$	−12.6781	−1.09522
$135$	4.81081	0.414048
$136$	−4.90445	−0.420553
$137$	17.5470	1.49914	0.749571	−	0.661924i	$-0.230260\pi$
$137$	17.5470	1.49914	0.749571	+	0.661924i	$0.230260\pi$
$138$	0.148819	0.0126683
$139$	−3.74231	−0.317419	−0.158710	−	0.987325i	$-0.550733\pi$
$139$	−3.74231	−0.317419	−0.158710	+	0.987325i	$0.550733\pi$
$140$	5.51865	0.466411
$141$	6.94377	0.584771
$142$	13.8177	1.15956
$143$	−4.42109	−0.369710
$144$	−2.43945	−0.203287
$145$	−5.68163	−0.471834
$146$	−0.133904	−0.0110820
$147$	11.0996	0.915482
$148$	7.79963	0.641126
$149$	17.8616	1.46328	0.731638	−	0.681694i	$-0.238756\pi$
$149$	17.8616	1.46328	0.731638	+	0.681694i	$0.238756\pi$
$150$	2.69875	0.220352
$151$	−6.03373	−0.491018	−0.245509	−	0.969394i	$-0.578955\pi$
$151$	−6.03373	−0.491018	−0.245509	+	0.969394i	$0.578955\pi$
$152$	−0.579881	−0.0470345
$153$	−11.9641	−0.967244
$154$	10.4601	0.842899
$155$	4.35663	0.349933
$156$	−1.47836	−0.118364
$157$	5.84622	0.466579	0.233290	−	0.972407i	$-0.425051\pi$
$157$	5.84622	0.466579	0.233290	+	0.972407i	$0.425051\pi$
$158$	−1.24253	−0.0988507
$159$	−2.58430	−0.204948
$160$	1.18128	0.0933887
$161$	0.928601	0.0731840
$162$	−4.26923	−0.335423
$163$	16.2750	1.27476	0.637378	−	0.770551i	$-0.280019\pi$
$163$	16.2750	1.27476	0.637378	+	0.770551i	$0.280019\pi$
$164$	6.02349	0.470355
$165$	−1.98025	−0.154162
$166$	−4.98679	−0.387050
$167$	−13.7820	−1.06649	−0.533243	−	0.845962i	$-0.679027\pi$
$167$	−13.7820	−1.06649	−0.533243	+	0.845962i	$0.679027\pi$
$168$	3.49774	0.269857
$169$	−9.10108	−0.700083
$170$	5.79355	0.444345
$171$	−1.41459	−0.108176
$172$	9.74861	0.743324
$173$	10.4947	0.797901	0.398950	−	0.916972i	$-0.369375\pi$
$173$	10.4947	0.797901	0.398950	+	0.916972i	$0.369375\pi$
$174$	−3.60103	−0.272994
$175$	16.8396	1.27295
$176$	2.23901	0.168772
$177$	−2.53445	−0.190501
$178$	10.4049	0.779882
$179$	−14.4061	−1.07676	−0.538381	−	0.842702i	$-0.680964\pi$
$179$	−14.4061	−1.07676	−0.538381	+	0.842702i	$0.680964\pi$
$180$	2.88168	0.214788
$181$	18.1588	1.34974	0.674868	−	0.737938i	$-0.264201\pi$
$181$	18.1588	1.34974	0.674868	+	0.737938i	$0.264201\pi$
$182$	−9.22467	−0.683778
$183$	−2.46745	−0.182399
$184$	0.198770	0.0146535
$185$	−9.21358	−0.677396
$186$	2.76124	0.202464
$187$	10.9811	0.803020
$188$	9.27442	0.676407
$189$	19.0258	1.38392
$190$	0.685004	0.0496954
$191$	−1.97957	−0.143237	−0.0716185	−	0.997432i	$-0.522816\pi$
$191$	−1.97957	−0.143237	−0.0716185	+	0.997432i	$0.522816\pi$
$192$	0.748702	0.0540329
$193$	−23.0331	−1.65796	−0.828979	−	0.559279i	$-0.811078\pi$
$193$	−23.0331	−1.65796	−0.828979	+	0.559279i	$0.811078\pi$
$194$	−17.2830	−1.24085
$195$	1.74637	0.125060
$196$	14.8252	1.05894
$197$	1.04803	0.0746693	0.0373346	−	0.999303i	$-0.488113\pi$
$197$	1.04803	0.0746693	0.0373346	+	0.999303i	$0.488113\pi$
$198$	5.46195	0.388164
$199$	−17.7040	−1.25501	−0.627503	−	0.778614i	$-0.715923\pi$
$199$	−17.7040	−1.25501	−0.627503	+	0.778614i	$0.715923\pi$
$200$	3.60457	0.254881
$201$	9.49208	0.669520
$202$	8.75193	0.615784
$203$	−22.4697	−1.57706
$204$	3.67197	0.257089
$205$	−7.11545	−0.496965
$206$	−17.8938	−1.24672
$207$	0.484888	0.0337021
$208$	−1.97457	−0.136912
$209$	1.29836	0.0898095
$210$	−4.13183	−0.285123
$211$	18.3304	1.26192	0.630959	−	0.775816i	$-0.282662\pi$
$211$	18.3304	1.26192	0.630959	+	0.775816i	$0.282662\pi$
$212$	−3.45171	−0.237064
$213$	−10.3454	−0.708852
$214$	0.879267	0.0601055
$215$	−11.5159	−0.785376
$216$	4.07252	0.277100
$217$	17.2296	1.16962
$218$	−14.1051	−0.955320
$219$	0.100254	0.00677455
$220$	−2.64491	−0.178320
$221$	−9.68417	−0.651428
$222$	−5.83960	−0.391928
$223$	21.6453	1.44948	0.724739	−	0.689023i	$-0.241960\pi$
$223$	21.6453	1.44948	0.724739	+	0.689023i	$0.241960\pi$
$224$	4.67174	0.312144
$225$	8.79315	0.586210
$226$	8.64247	0.574889
$227$	21.4748	1.42533	0.712665	−	0.701504i	$-0.247488\pi$
$227$	21.4748	1.42533	0.712665	+	0.701504i	$0.247488\pi$
$228$	0.434158	0.0287528
$229$	−0.637077	−0.0420992	−0.0210496	−	0.999778i	$-0.506701\pi$
$229$	−0.637077	−0.0420992	−0.0210496	+	0.999778i	$0.506701\pi$
$230$	−0.234804	−0.0154825
$231$	−7.83149	−0.515274
$232$	−4.80971	−0.315773
$233$	0.196347	0.0128631	0.00643156	−	0.999979i	$-0.497953\pi$
$233$	0.196347	0.0128631	0.00643156	+	0.999979i	$0.497953\pi$
$234$	−4.81685	−0.314887
$235$	−10.9557	−0.714673
$236$	−3.38512	−0.220353
$237$	0.930287	0.0604286
$238$	22.9123	1.48519
$239$	6.81785	0.441010	0.220505	−	0.975386i	$-0.429229\pi$
$239$	6.81785	0.441010	0.220505	+	0.975386i	$0.429229\pi$
$240$	−0.884430	−0.0570897
$241$	23.2312	1.49645	0.748226	−	0.663443i	$-0.230906\pi$
$241$	23.2312	1.49645	0.748226	+	0.663443i	$0.230906\pi$
$242$	5.98681	0.384847
$243$	15.4139	0.988805
$244$	−3.29564	−0.210982
$245$	−17.5127	−1.11885
$246$	−4.50979	−0.287534
$247$	−1.14501	−0.0728555
$248$	3.68804	0.234191
$249$	3.73362	0.236609
$250$	−10.1644	−0.642856
$251$	13.4834	0.851062	0.425531	−	0.904944i	$-0.360087\pi$
$251$	13.4834	0.851062	0.425531	+	0.904944i	$0.360087\pi$
$252$	11.3965	0.717909
$253$	−0.445049	−0.0279800
$254$	19.0886	1.19773
$255$	−4.33764	−0.271634
$256$	1.00000	0.0625000
$257$	11.3978	0.710975	0.355487	−	0.934681i	$-0.384315\pi$
$257$	11.3978	0.710975	0.355487	+	0.934681i	$0.384315\pi$
$258$	−7.29880	−0.454403
$259$	−36.4379	−2.26414
$260$	2.33253	0.144657
$261$	−11.7330	−0.726256
$262$	1.07067	0.0661461
$263$	−15.1611	−0.934874	−0.467437	−	0.884026i	$-0.654823\pi$
$263$	−15.1611	−0.934874	−0.467437	+	0.884026i	$0.654823\pi$
$264$	−1.67635	−0.103172
$265$	4.07745	0.250476
$266$	2.70905	0.166103
$267$	−7.79019	−0.476752
$268$	12.6781	0.774435
$269$	−30.3651	−1.85139	−0.925697	−	0.378265i	$-0.876521\pi$
$269$	−30.3651	−1.85139	−0.925697	+	0.378265i	$0.876521\pi$
$270$	−4.81081	−0.292776
$271$	3.93460	0.239010	0.119505	−	0.992834i	$-0.461869\pi$
$271$	3.93460	0.239010	0.119505	+	0.992834i	$0.461869\pi$
$272$	4.90445	0.297376
$273$	6.90653	0.418002
$274$	−17.5470	−1.06005
$275$	−8.07068	−0.486680
$276$	−0.148819	−0.00895787
$277$	−14.5287	−0.872946	−0.436473	−	0.899717i	$-0.643773\pi$
$277$	−14.5287	−0.872946	−0.436473	+	0.899717i	$0.643773\pi$
$278$	3.74231	0.224449
$279$	8.99678	0.538623
$280$	−5.51865	−0.329803
$281$	22.6481	1.35108	0.675538	−	0.737326i	$-0.263912\pi$
$281$	22.6481	1.35108	0.675538	+	0.737326i	$0.263912\pi$
$282$	−6.94377	−0.413496
$283$	−23.8471	−1.41757	−0.708783	−	0.705427i	$-0.750755\pi$
$283$	−23.8471	−1.41757	−0.708783	+	0.705427i	$0.750755\pi$
$284$	−13.8177	−0.819931
$285$	−0.512864	−0.0303794
$286$	4.42109	0.261424
$287$	−28.1402	−1.66106
$288$	2.43945	0.143746
$289$	7.05365	0.414920
$290$	5.68163	0.333637
$291$	12.9398	0.758546
$292$	0.133904	0.00783615
$293$	−6.28338	−0.367079	−0.183539	−	0.983012i	$-0.558756\pi$
$293$	−6.28338	−0.367079	−0.183539	+	0.983012i	$0.558756\pi$
$294$	−11.0996	−0.647343
$295$	3.99879	0.232819
$296$	−7.79963	−0.453344
$297$	−9.11844	−0.529105
$298$	−17.8616	−1.03469
$299$	0.392485	0.0226980
$300$	−2.69875	−0.155812
$301$	−45.5430	−2.62505
$302$	6.03373	0.347202
$303$	−6.55258	−0.376436
$304$	0.579881	0.0332584
$305$	3.89309	0.222918
$306$	11.9641	0.683945
$307$	8.10261	0.462440	0.231220	−	0.972901i	$-0.425728\pi$
$307$	8.10261	0.462440	0.231220	+	0.972901i	$0.425728\pi$
$308$	−10.4601	−0.596019
$309$	13.3971	0.762135
$310$	−4.35663	−0.247440
$311$	−24.1777	−1.37099	−0.685497	−	0.728075i	$-0.740415\pi$
$311$	−24.1777	−1.37099	−0.685497	+	0.728075i	$0.740415\pi$
$312$	1.47836	0.0836958
$313$	29.4644	1.66543	0.832713	−	0.553705i	$-0.186786\pi$
$313$	29.4644	1.66543	0.832713	+	0.553705i	$0.186786\pi$
$314$	−5.84622	−0.329921
$315$	−13.4625	−0.758524
$316$	1.24253	0.0698980
$317$	18.8077	1.05635	0.528173	−	0.849137i	$-0.322877\pi$
$317$	18.8077	1.05635	0.528173	+	0.849137i	$0.322877\pi$
$318$	2.58430	0.144920
$319$	10.7690	0.602948
$320$	−1.18128	−0.0660358
$321$	−0.658309	−0.0367432
$322$	−0.928601	−0.0517489
$323$	2.84400	0.158244
$324$	4.26923	0.237180
$325$	7.11746	0.394806
$326$	−16.2750	−0.901389
$327$	10.5605	0.583999
$328$	−6.02349	−0.332591
$329$	−43.3277	−2.38873
$330$	1.98025	0.109009
$331$	−24.8393	−1.36529	−0.682646	−	0.730749i	$-0.739171\pi$
$331$	−24.8393	−1.36529	−0.682646	+	0.730749i	$0.739171\pi$
$332$	4.98679	0.273686
$333$	−19.0268	−1.04266
$334$	13.7820	0.754120
$335$	−14.9764	−0.818247
$336$	−3.49774	−0.190817
$337$	20.3496	1.10852	0.554258	−	0.832345i	$-0.313002\pi$
$337$	20.3496	1.10852	0.554258	+	0.832345i	$0.313002\pi$
$338$	9.10108	0.495034
$339$	−6.47063	−0.351437
$340$	−5.79355	−0.314199
$341$	−8.25758	−0.447173
$342$	1.41459	0.0764921
$343$	−36.5571	−1.97390
$344$	−9.74861	−0.525610
$345$	0.175798	0.00946464
$346$	−10.4947	−0.564201
$347$	24.0771	1.29253	0.646264	−	0.763114i	$-0.276330\pi$
$347$	24.0771	1.29253	0.646264	+	0.763114i	$0.276330\pi$
$348$	3.60103	0.193036
$349$	−1.66295	−0.0890156	−0.0445078	−	0.999009i	$-0.514172\pi$
$349$	−1.66295	−0.0890156	−0.0445078	+	0.999009i	$0.514172\pi$
$350$	−16.8396	−0.900115
$351$	8.04147	0.429222
$352$	−2.23901	−0.119340
$353$	−29.8055	−1.58638	−0.793192	−	0.608971i	$-0.791582\pi$
$353$	−29.8055	−1.58638	−0.793192	+	0.608971i	$0.791582\pi$
$354$	2.53445	0.134704
$355$	16.3227	0.866317
$356$	−10.4049	−0.551460
$357$	−17.1545	−0.907912
$358$	14.4061	0.761385
$359$	4.17124	0.220150	0.110075	−	0.993923i	$-0.464891\pi$
$359$	4.17124	0.220150	0.110075	+	0.993923i	$0.464891\pi$
$360$	−2.88168	−0.151878
$361$	−18.6637	−0.982302
$362$	−18.1588	−0.954408
$363$	−4.48234	−0.235262
$364$	9.22467	0.483504
$365$	−0.158179	−0.00827946
$366$	2.46745	0.128976
$367$	−8.15584	−0.425731	−0.212866	−	0.977081i	$-0.568280\pi$
$367$	−8.15584	−0.425731	−0.212866	+	0.977081i	$0.568280\pi$
$368$	−0.198770	−0.0103616
$369$	−14.6940	−0.764937
$370$	9.21358	0.478991
$371$	16.1255	0.837194
$372$	−2.76124	−0.143164
$373$	−13.1369	−0.680203	−0.340102	−	0.940389i	$-0.610461\pi$
$373$	−13.1369	−0.680203	−0.340102	+	0.940389i	$0.610461\pi$
$374$	−10.9811	−0.567821
$375$	7.61013	0.392986
$376$	−9.27442	−0.478292
$377$	−9.49709	−0.489125
$378$	−19.0258	−0.978580
$379$	−2.86552	−0.147192	−0.0735959	−	0.997288i	$-0.523447\pi$
$379$	−2.86552	−0.147192	−0.0735959	+	0.997288i	$0.523447\pi$
$380$	−0.685004	−0.0351400
$381$	−14.2917	−0.732185
$382$	1.97957	0.101284
$383$	−13.7337	−0.701760	−0.350880	−	0.936420i	$-0.614118\pi$
$383$	−13.7337	−0.701760	−0.350880	+	0.936420i	$0.614118\pi$
$384$	−0.748702	−0.0382070
$385$	12.3563	0.629738
$386$	23.0331	1.17235
$387$	−23.7812	−1.20887
$388$	17.2830	0.877412
$389$	19.2850	0.977789	0.488895	−	0.872343i	$-0.337400\pi$
$389$	19.2850	0.977789	0.488895	+	0.872343i	$0.337400\pi$
$390$	−1.74637	−0.0884307
$391$	−0.974857	−0.0493006
$392$	−14.8252	−0.748784
$393$	−0.801610	−0.0404359
$394$	−1.04803	−0.0527991
$395$	−1.46779	−0.0738523
$396$	−5.46195	−0.274474
$397$	14.1523	0.710281	0.355141	−	0.934813i	$-0.384433\pi$
$397$	14.1523	0.710281	0.355141	+	0.934813i	$0.384433\pi$
$398$	17.7040	0.887423
$399$	−2.02827	−0.101541
$400$	−3.60457	−0.180228
$401$	3.07992	0.153804	0.0769020	−	0.997039i	$-0.475497\pi$
$401$	3.07992	0.153804	0.0769020	+	0.997039i	$0.475497\pi$
$402$	−9.49208	−0.473422
$403$	7.28229	0.362757
$404$	−8.75193	−0.435425
$405$	−5.04318	−0.250598
$406$	22.4697	1.11515
$407$	17.4635	0.865633
$408$	−3.67197	−0.181790
$409$	−1.31889	−0.0652151	−0.0326075	−	0.999468i	$-0.510381\pi$
$409$	−1.31889	−0.0652151	−0.0326075	+	0.999468i	$0.510381\pi$
$410$	7.11545	0.351407
$411$	13.1375	0.648024
$412$	17.8938	0.881564
$413$	15.8144	0.778176
$414$	−0.484888	−0.0238310
$415$	−5.89082	−0.289169
$416$	1.97457	0.0968112
$417$	−2.80188	−0.137209
$418$	−1.29836	−0.0635049
$419$	−10.5382	−0.514825	−0.257413	−	0.966302i	$-0.582870\pi$
$419$	−10.5382	−0.514825	−0.257413	+	0.966302i	$0.582870\pi$
$420$	4.13183	0.201612
$421$	36.4489	1.77641	0.888206	−	0.459446i	$-0.151952\pi$
$421$	36.4489	1.77641	0.888206	+	0.459446i	$0.151952\pi$
$422$	−18.3304	−0.892311
$423$	−22.6244	−1.10004
$424$	3.45171	0.167630
$425$	−17.6784	−0.857530
$426$	10.3454	0.501234
$427$	15.3964	0.745083
$428$	−0.879267	−0.0425010
$429$	−3.31007	−0.159812
$430$	11.5159	0.555345
$431$	−20.7014	−0.997153	−0.498577	−	0.866846i	$-0.666144\pi$
$431$	−20.7014	−0.997153	−0.498577	+	0.866846i	$0.666144\pi$
$432$	−4.07252	−0.195939
$433$	12.3861	0.595237	0.297619	−	0.954685i	$-0.403808\pi$
$433$	12.3861	0.595237	0.297619	+	0.954685i	$0.403808\pi$
$434$	−17.2296	−0.827046
$435$	−4.25385	−0.203956
$436$	14.1051	0.675513
$437$	−0.115263	−0.00551377
$438$	−0.100254	−0.00479033
$439$	12.6595	0.604206	0.302103	−	0.953275i	$-0.402311\pi$
$439$	12.6595	0.604206	0.302103	+	0.953275i	$0.402311\pi$
$440$	2.64491	0.126091
$441$	−36.1652	−1.72215
$442$	9.68417	0.460629
$443$	7.02786	0.333904	0.166952	−	0.985965i	$-0.446608\pi$
$443$	7.02786	0.333904	0.166952	+	0.985965i	$0.446608\pi$
$444$	5.83960	0.277135
$445$	12.2912	0.582658
$446$	−21.6453	−1.02494
$447$	13.3730	0.632520
$448$	−4.67174	−0.220719
$449$	39.2814	1.85380	0.926902	−	0.375304i	$-0.122462\pi$
$449$	39.2814	1.85380	0.926902	+	0.375304i	$0.122462\pi$
$450$	−8.79315	−0.414513
$451$	13.4867	0.635063
$452$	−8.64247	−0.406508
$453$	−4.51746	−0.212249
$454$	−21.4748	−1.00786
$455$	−10.8970	−0.510857
$456$	−0.434158	−0.0203313
$457$	5.88680	0.275373	0.137687	−	0.990476i	$-0.456033\pi$
$457$	5.88680	0.275373	0.137687	+	0.990476i	$0.456033\pi$
$458$	0.637077	0.0297686
$459$	−19.9735	−0.932283
$460$	0.234804	0.0109478
$461$	28.6973	1.33656	0.668282	−	0.743908i	$-0.267030\pi$
$461$	28.6973	1.33656	0.668282	+	0.743908i	$0.267030\pi$
$462$	7.83149	0.364354
$463$	−2.08278	−0.0967948	−0.0483974	−	0.998828i	$-0.515411\pi$
$463$	−2.08278	−0.0967948	−0.0483974	+	0.998828i	$0.515411\pi$
$464$	4.80971	0.223285
$465$	3.26181	0.151263
$466$	−0.196347	−0.00909560
$467$	11.8640	0.549000	0.274500	−	0.961587i	$-0.411488\pi$
$467$	11.8640	0.549000	0.274500	+	0.961587i	$0.411488\pi$
$468$	4.81685	0.222659
$469$	−59.2286	−2.73492
$470$	10.9557	0.505350
$471$	4.37708	0.201685
$472$	3.38512	0.155813
$473$	21.8273	1.00362
$474$	−0.930287	−0.0427295
$475$	−2.09022	−0.0959058
$476$	−22.9123	−1.05018
$477$	8.42026	0.385537
$478$	−6.81785	−0.311841
$479$	−36.2534	−1.65646	−0.828230	−	0.560389i	$-0.810652\pi$
$479$	−36.2534	−1.65646	−0.828230	+	0.560389i	$0.810652\pi$
$480$	0.884430	0.0403685
$481$	−15.4009	−0.702221
$482$	−23.2312	−1.05815
$483$	0.695245	0.0316348
$484$	−5.98681	−0.272128
$485$	−20.4162	−0.927050
$486$	−15.4139	−0.699191
$487$	2.31853	0.105062	0.0525312	−	0.998619i	$-0.483271\pi$
$487$	2.31853	0.105062	0.0525312	+	0.998619i	$0.483271\pi$
$488$	3.29564	0.149187
$489$	12.1851	0.551030
$490$	17.5127	0.791145
$491$	6.31617	0.285045	0.142522	−	0.989792i	$-0.454479\pi$
$491$	6.31617	0.285045	0.142522	+	0.989792i	$0.454479\pi$
$492$	4.50979	0.203317
$493$	23.5890	1.06239
$494$	1.14501	0.0515166
$495$	6.45212	0.290001
$496$	−3.68804	−0.165598
$497$	64.5528	2.89559
$498$	−3.73362	−0.167308
$499$	19.3075	0.864324	0.432162	−	0.901796i	$-0.357751\pi$
$499$	19.3075	0.864324	0.432162	+	0.901796i	$0.357751\pi$
$500$	10.1644	0.454568
$501$	−10.3186	−0.461003
$502$	−13.4834	−0.601792
$503$	−33.1214	−1.47681	−0.738405	−	0.674358i	$-0.764421\pi$
$503$	−33.1214	−1.47681	−0.738405	+	0.674358i	$0.764421\pi$
$504$	−11.3965	−0.507639
$505$	10.3385	0.460058
$506$	0.445049	0.0197848
$507$	−6.81399	−0.302620
$508$	−19.0886	−0.846920
$509$	−14.1653	−0.627867	−0.313934	−	0.949445i	$-0.601647\pi$
$509$	−14.1653	−0.627867	−0.313934	+	0.949445i	$0.601647\pi$
$510$	4.33764	0.192074
$511$	−0.625566	−0.0276734
$512$	−1.00000	−0.0441942
$513$	−2.36158	−0.104266
$514$	−11.3978	−0.502735
$515$	−21.1377	−0.931436
$516$	7.29880	0.321312
$517$	20.7656	0.913268
$518$	36.4379	1.60099
$519$	7.85744	0.344903
$520$	−2.33253	−0.102288
$521$	6.49924	0.284737	0.142368	−	0.989814i	$-0.454528\pi$
$521$	6.49924	0.284737	0.142368	+	0.989814i	$0.454528\pi$
$522$	11.7330	0.513540
$523$	−4.05101	−0.177138	−0.0885692	−	0.996070i	$-0.528229\pi$
$523$	−4.05101	−0.177138	−0.0885692	+	0.996070i	$0.528229\pi$
$524$	−1.07067	−0.0467723
$525$	12.6078	0.550251
$526$	15.1611	0.661056
$527$	−18.0878	−0.787918
$528$	1.67635	0.0729539
$529$	−22.9605	−0.998282
$530$	−4.07745	−0.177113
$531$	8.25782	0.358359
$532$	−2.70905	−0.117452
$533$	−11.8938	−0.515177
$534$	7.79019	0.337114
$535$	1.03866	0.0449054
$536$	−12.6781	−0.547608
$537$	−10.7859	−0.465444
$538$	30.3651	1.30913
$539$	33.1938	1.42976
$540$	4.81081	0.207024
$541$	−27.4642	−1.18078	−0.590389	−	0.807119i	$-0.701026\pi$
$541$	−27.4642	−1.18078	−0.590389	+	0.807119i	$0.701026\pi$
$542$	−3.93460	−0.169005
$543$	13.5956	0.583441
$544$	−4.90445	−0.210277
$545$	−16.6622	−0.713729
$546$	−6.90653	−0.295572
$547$	−26.6822	−1.14085	−0.570424	−	0.821351i	$-0.693221\pi$
$547$	−26.6822	−1.14085	−0.570424	+	0.821351i	$0.693221\pi$
$548$	17.5470	0.749571
$549$	8.03954	0.343119
$550$	8.07068	0.344135
$551$	2.78906	0.118818
$552$	0.148819	0.00633417
$553$	−5.80480	−0.246845
$554$	14.5287	0.617266
$555$	−6.89822	−0.292813
$556$	−3.74231	−0.158710
$557$	−3.16003	−0.133895	−0.0669474	−	0.997757i	$-0.521326\pi$
$557$	−3.16003	−0.133895	−0.0669474	+	0.997757i	$0.521326\pi$
$558$	−8.99678	−0.380864
$559$	−19.2493	−0.814158
$560$	5.51865	0.233206
$561$	8.22160	0.347116
$562$	−22.6481	−0.955354
$563$	−18.7871	−0.791783	−0.395891	−	0.918297i	$-0.629564\pi$
$563$	−18.7871	−0.791783	−0.395891	+	0.918297i	$0.629564\pi$
$564$	6.94377	0.292386
$565$	10.2092	0.429505
$566$	23.8471	1.00237
$567$	−19.9448	−0.837601
$568$	13.8177	0.579779
$569$	−5.86112	−0.245711	−0.122856	−	0.992425i	$-0.539205\pi$
$569$	−5.86112	−0.245711	−0.122856	+	0.992425i	$0.539205\pi$
$570$	0.512864	0.0214815
$571$	24.9679	1.04487	0.522437	−	0.852678i	$-0.325023\pi$
$571$	24.9679	1.04487	0.522437	+	0.852678i	$0.325023\pi$
$572$	−4.42109	−0.184855
$573$	−1.48211	−0.0619161
$574$	28.1402	1.17455
$575$	0.716479	0.0298793
$576$	−2.43945	−0.101644
$577$	−6.86543	−0.285811	−0.142906	−	0.989736i	$-0.545645\pi$
$577$	−6.86543	−0.285811	−0.142906	+	0.989736i	$0.545645\pi$
$578$	−7.05365	−0.293393
$579$	−17.2449	−0.716674
$580$	−5.68163	−0.235917
$581$	−23.2970	−0.966523
$582$	−12.9398	−0.536373
$583$	−7.72843	−0.320079
$584$	−0.133904	−0.00554099
$585$	−5.69007	−0.235255
$586$	6.28338	0.259564
$587$	2.45485	0.101323	0.0506613	−	0.998716i	$-0.483867\pi$
$587$	2.45485	0.101323	0.0506613	+	0.998716i	$0.483867\pi$
$588$	11.0996	0.457741
$589$	−2.13863	−0.0881205
$590$	−3.99879	−0.164628
$591$	0.784664	0.0322768
$592$	7.79963	0.320563
$593$	−25.5790	−1.05040	−0.525202	−	0.850978i	$-0.676010\pi$
$593$	−25.5790	−1.05040	−0.525202	+	0.850978i	$0.676010\pi$
$594$	9.11844	0.374134
$595$	27.0660	1.10960
$596$	17.8616	0.731638
$597$	−13.2550	−0.542493
$598$	−0.392485	−0.0160499
$599$	−20.8964	−0.853805	−0.426903	−	0.904298i	$-0.640395\pi$
$599$	−20.8964	−0.853805	−0.426903	+	0.904298i	$0.640395\pi$
$600$	2.69875	0.110176
$601$	41.3638	1.68727	0.843633	−	0.536920i	$-0.180412\pi$
$601$	41.3638	1.68727	0.843633	+	0.536920i	$0.180412\pi$
$602$	45.5430	1.85619
$603$	−30.9274	−1.25946
$604$	−6.03373	−0.245509
$605$	7.07213	0.287523
$606$	6.55258	0.266181
$607$	30.2929	1.22955	0.614776	−	0.788702i	$-0.289246\pi$
$607$	30.2929	1.22955	0.614776	+	0.788702i	$0.289246\pi$
$608$	−0.579881	−0.0235173
$609$	−16.8231	−0.681707
$610$	−3.89309	−0.157627
$611$	−18.3130	−0.740864
$612$	−11.9641	−0.483622
$613$	1.22428	0.0494481	0.0247241	−	0.999694i	$-0.492129\pi$
$613$	1.22428	0.0494481	0.0247241	+	0.999694i	$0.492129\pi$
$614$	−8.10261	−0.326995
$615$	−5.32735	−0.214819
$616$	10.4601	0.421449
$617$	31.2037	1.25621	0.628106	−	0.778127i	$-0.283830\pi$
$617$	31.2037	1.25621	0.628106	+	0.778127i	$0.283830\pi$
$618$	−13.3971	−0.538911
$619$	16.3828	0.658482	0.329241	−	0.944246i	$-0.393207\pi$
$619$	16.3828	0.658482	0.329241	+	0.944246i	$0.393207\pi$
$620$	4.35663	0.174966
$621$	0.809495	0.0324839
$622$	24.1777	0.969439
$623$	48.6091	1.94748
$624$	−1.47836	−0.0591819
$625$	6.01574	0.240630
$626$	−29.4644	−1.17763
$627$	0.972085	0.0388214
$628$	5.84622	0.233290
$629$	38.2529	1.52524
$630$	13.4625	0.536357
$631$	5.02221	0.199931	0.0999655	−	0.994991i	$-0.468127\pi$
$631$	5.02221	0.199931	0.0999655	+	0.994991i	$0.468127\pi$
$632$	−1.24253	−0.0494253
$633$	13.7240	0.545480
$634$	−18.8077	−0.746950
$635$	22.5491	0.894833
$636$	−2.58430	−0.102474
$637$	−29.2733	−1.15985
$638$	−10.7690	−0.426349
$639$	33.7076	1.33345
$640$	1.18128	0.0466944
$641$	40.7137	1.60809	0.804047	−	0.594566i	$-0.202676\pi$
$641$	40.7137	1.60809	0.804047	+	0.594566i	$0.202676\pi$
$642$	0.658309	0.0259814
$643$	−8.06759	−0.318155	−0.159077	−	0.987266i	$-0.550852\pi$
$643$	−8.06759	−0.318155	−0.159077	+	0.987266i	$0.550852\pi$
$644$	0.928601	0.0365920
$645$	−8.62195	−0.339489
$646$	−2.84400	−0.111896
$647$	1.14889	0.0451674	0.0225837	−	0.999745i	$-0.492811\pi$
$647$	1.14889	0.0451674	0.0225837	+	0.999745i	$0.492811\pi$
$648$	−4.26923	−0.167711
$649$	−7.57933	−0.297515
$650$	−7.11746	−0.279170
$651$	12.8998	0.505584
$652$	16.2750	0.637378
$653$	32.7700	1.28239	0.641195	−	0.767378i	$-0.278439\pi$
$653$	32.7700	1.28239	0.641195	+	0.767378i	$0.278439\pi$
$654$	−10.5605	−0.412949
$655$	1.26476	0.0494184
$656$	6.02349	0.235178
$657$	−0.326652	−0.0127439
$658$	43.3277	1.68909
$659$	−44.6467	−1.73919	−0.869593	−	0.493769i	$-0.835619\pi$
$659$	−44.6467	−1.73919	−0.869593	+	0.493769i	$0.835619\pi$
$660$	−1.98025	−0.0770811
$661$	29.1491	1.13377	0.566885	−	0.823797i	$-0.308149\pi$
$661$	29.1491	1.13377	0.566885	+	0.823797i	$0.308149\pi$
$662$	24.8393	0.965408
$663$	−7.25056	−0.281588
$664$	−4.98679	−0.193525
$665$	3.20016	0.124097
$666$	19.0268	0.737273
$667$	−0.956025	−0.0370174
$668$	−13.7820	−0.533243
$669$	16.2059	0.626556
$670$	14.9764	0.578588
$671$	−7.37899	−0.284863
$672$	3.49774	0.134928
$673$	−40.3854	−1.55674	−0.778371	−	0.627804i	$-0.783954\pi$
$673$	−40.3854	−1.55674	−0.778371	+	0.627804i	$0.783954\pi$
$674$	−20.3496	−0.783839
$675$	14.6797	0.565021
$676$	−9.10108	−0.350042
$677$	16.4959	0.633990	0.316995	−	0.948427i	$-0.397326\pi$
$677$	16.4959	0.633990	0.316995	+	0.948427i	$0.397326\pi$
$678$	6.47063	0.248503
$679$	−80.7418	−3.09859
$680$	5.79355	0.222173
$681$	16.0782	0.616118
$682$	8.25758	0.316199
$683$	−41.6603	−1.59409	−0.797044	−	0.603921i	$-0.793604\pi$
$683$	−41.6603	−1.59409	−0.797044	+	0.603921i	$0.793604\pi$
$684$	−1.41459	−0.0540881
$685$	−20.7280	−0.791976
$686$	36.5571	1.39576
$687$	−0.476980	−0.0181979
$688$	9.74861	0.371662
$689$	6.81564	0.259655
$690$	−0.175798	−0.00669251
$691$	1.28083	0.0487252	0.0243626	−	0.999703i	$-0.492244\pi$
$691$	1.28083	0.0487252	0.0243626	+	0.999703i	$0.492244\pi$
$692$	10.4947	0.398950
$693$	25.5168	0.969305
$694$	−24.0771	−0.913956
$695$	4.42074	0.167688
$696$	−3.60103	−0.136497
$697$	29.5419	1.11898
$698$	1.66295	0.0629435
$699$	0.147005	0.00556025
$700$	16.8396	0.636477
$701$	−14.8122	−0.559449	−0.279725	−	0.960080i	$-0.590243\pi$
$701$	−14.8122	−0.559449	−0.279725	+	0.960080i	$0.590243\pi$
$702$	−8.04147	−0.303506
$703$	4.52286	0.170583
$704$	2.23901	0.0843860
$705$	−8.20257	−0.308927
$706$	29.8055	1.12174
$707$	40.8867	1.53770
$708$	−2.53445	−0.0952503
$709$	34.1271	1.28167	0.640836	−	0.767678i	$-0.278588\pi$
$709$	34.1271	1.28167	0.640836	+	0.767678i	$0.278588\pi$
$710$	−16.3227	−0.612579
$711$	−3.03109	−0.113675
$712$	10.4049	0.389941
$713$	0.733072	0.0274538
$714$	17.1545	0.641991
$715$	5.22256	0.195313
$716$	−14.4061	−0.538381
$717$	5.10454	0.190632
$718$	−4.17124	−0.155669
$719$	13.6820	0.510252	0.255126	−	0.966908i	$-0.417883\pi$
$719$	13.6820	0.510252	0.255126	+	0.966908i	$0.417883\pi$
$720$	2.88168	0.107394
$721$	−83.5952	−3.11325
$722$	18.6637	0.694592
$723$	17.3932	0.646861
$724$	18.1588	0.674868
$725$	−17.3369	−0.643877
$726$	4.48234	0.166355
$727$	26.1057	0.968206	0.484103	−	0.875011i	$-0.339146\pi$
$727$	26.1057	0.968206	0.484103	+	0.875011i	$0.339146\pi$
$728$	−9.22467	−0.341889
$729$	−1.26725	−0.0469352
$730$	0.158179	0.00585446
$731$	47.8116	1.76837
$732$	−2.46745	−0.0911997
$733$	1.23307	0.0455447	0.0227723	−	0.999741i	$-0.492751\pi$
$733$	1.23307	0.0455447	0.0227723	+	0.999741i	$0.492751\pi$
$734$	8.15584	0.301038
$735$	−13.1118	−0.483637
$736$	0.198770	0.00732675
$737$	28.3863	1.04562
$738$	14.6940	0.540892
$739$	28.7723	1.05841	0.529204	−	0.848495i	$-0.322491\pi$
$739$	28.7723	1.05841	0.529204	+	0.848495i	$0.322491\pi$
$740$	−9.21358	−0.338698
$741$	−0.857274	−0.0314927
$742$	−16.1255	−0.591985
$743$	−23.1409	−0.848958	−0.424479	−	0.905438i	$-0.639543\pi$
$743$	−23.1409	−0.848958	−0.424479	+	0.905438i	$0.639543\pi$
$744$	2.76124	0.101232
$745$	−21.0996	−0.773028
$746$	13.1369	0.480976
$747$	−12.1650	−0.445095
$748$	10.9811	0.401510
$749$	4.10771	0.150092
$750$	−7.61013	−0.277883
$751$	1.00000	0.0364905
$751$	1.00000	0.0364905
$752$	9.27442	0.338203
$753$	10.0950	0.367883
$754$	9.49709	0.345864
$755$	7.12755	0.259398
$756$	19.0258	0.691961
$757$	3.99488	0.145197	0.0725983	−	0.997361i	$-0.476871\pi$
$757$	3.99488	0.145197	0.0725983	+	0.997361i	$0.476871\pi$
$758$	2.86552	0.104080
$759$	−0.333209	−0.0120947
$760$	0.685004	0.0248477
$761$	30.3430	1.09993	0.549966	−	0.835187i	$-0.314641\pi$
$761$	30.3430	1.09993	0.549966	+	0.835187i	$0.314641\pi$
$762$	14.2917	0.517733
$763$	−65.8955	−2.38558
$764$	−1.97957	−0.0716185
$765$	14.1331	0.510982
$766$	13.7337	0.496219
$767$	6.68415	0.241351
$768$	0.748702	0.0270164
$769$	31.6921	1.14285	0.571423	−	0.820656i	$-0.306392\pi$
$769$	31.6921	1.14285	0.571423	+	0.820656i	$0.306392\pi$
$770$	−12.3563	−0.445292
$771$	8.53355	0.307328
$772$	−23.0331	−0.828979
$773$	−12.0188	−0.432288	−0.216144	−	0.976362i	$-0.569348\pi$
$773$	−12.0188	−0.432288	−0.216144	+	0.976362i	$0.569348\pi$
$774$	23.7812	0.854797
$775$	13.2938	0.477527
$776$	−17.2830	−0.620424
$777$	−27.2811	−0.978703
$778$	−19.2850	−0.691401
$779$	3.49290	0.125146
$780$	1.74637	0.0625299
$781$	−30.9381	−1.10705
$782$	0.974857	0.0348608
$783$	−19.5876	−0.700005
$784$	14.8252	0.529470
$785$	−6.90605	−0.246487
$786$	0.801610	0.0285925
$787$	−46.5910	−1.66079	−0.830395	−	0.557175i	$-0.811885\pi$
$787$	−46.5910	−1.66079	−0.830395	+	0.557175i	$0.811885\pi$
$788$	1.04803	0.0373346
$789$	−11.3511	−0.404112
$790$	1.46779	0.0522215
$791$	40.3754	1.43558
$792$	5.46195	0.194082
$793$	6.50747	0.231087
$794$	−14.1523	−0.502245
$795$	3.05279	0.108271
$796$	−17.7040	−0.627503
$797$	31.6148	1.11985	0.559926	−	0.828543i	$-0.310830\pi$
$797$	31.6148	1.11985	0.559926	+	0.828543i	$0.310830\pi$
$798$	2.02827	0.0718001
$799$	45.4860	1.60918
$800$	3.60457	0.127441
$801$	25.3823	0.896838
$802$	−3.07992	−0.108756
$803$	0.299813	0.0105802
$804$	9.49208	0.334760
$805$	−1.09694	−0.0386621
$806$	−7.28229	−0.256508
$807$	−22.7344	−0.800289
$808$	8.75193	0.307892
$809$	−15.1570	−0.532892	−0.266446	−	0.963850i	$-0.585849\pi$
$809$	−15.1570	−0.532892	−0.266446	+	0.963850i	$0.585849\pi$
$810$	5.04318	0.177199
$811$	−41.1963	−1.44660	−0.723298	−	0.690536i	$-0.757375\pi$
$811$	−41.1963	−1.44660	−0.723298	+	0.690536i	$0.757375\pi$
$812$	−22.4697	−0.788532
$813$	2.94584	0.103315
$814$	−17.4635	−0.612095
$815$	−19.2254	−0.673436
$816$	3.67197	0.128545
$817$	5.65303	0.197774
$818$	1.31889	0.0461140
$819$	−22.5031	−0.786321
$820$	−7.11545	−0.248482
$821$	54.1366	1.88938	0.944691	−	0.327963i	$-0.106362\pi$
$821$	54.1366	1.88938	0.944691	+	0.327963i	$0.106362\pi$
$822$	−13.1375	−0.458222
$823$	35.8615	1.25005	0.625026	−	0.780604i	$-0.285088\pi$
$823$	35.8615	1.25005	0.625026	+	0.780604i	$0.285088\pi$
$824$	−17.8938	−0.623360
$825$	−6.04253	−0.210374
$826$	−15.8144	−0.550254
$827$	−30.8235	−1.07184	−0.535919	−	0.844269i	$-0.680035\pi$
$827$	−30.8235	−1.07184	−0.535919	+	0.844269i	$0.680035\pi$
$828$	0.484888	0.0168510
$829$	39.4701	1.37085	0.685427	−	0.728142i	$-0.259616\pi$
$829$	39.4701	1.37085	0.685427	+	0.728142i	$0.259616\pi$
$830$	5.89082	0.204473
$831$	−10.8777	−0.377342
$832$	−1.97457	−0.0684558
$833$	72.7093	2.51923
$834$	2.80188	0.0970211
$835$	16.2805	0.563410
$836$	1.29836	0.0449048
$837$	15.0196	0.519155
$838$	10.5382	0.364036
$839$	37.8803	1.30777	0.653886	−	0.756593i	$-0.273138\pi$
$839$	37.8803	1.30777	0.653886	+	0.756593i	$0.273138\pi$
$840$	−4.13183	−0.142562
$841$	−5.86673	−0.202301
$842$	−36.4489	−1.25611
$843$	16.9567	0.584020
$844$	18.3304	0.630959
$845$	10.7510	0.369844
$846$	22.6244	0.777845
$847$	27.9688	0.961021
$848$	−3.45171	−0.118532
$849$	−17.8544	−0.612761
$850$	17.6784	0.606365
$851$	−1.55033	−0.0531447
$852$	−10.3454	−0.354426
$853$	−44.7950	−1.53375	−0.766875	−	0.641796i	$-0.778190\pi$
$853$	−44.7950	−1.53375	−0.766875	+	0.641796i	$0.778190\pi$
$854$	−15.3964	−0.526854
$855$	1.67103	0.0571480
$856$	0.879267	0.0300527
$857$	25.1587	0.859405	0.429702	−	0.902971i	$-0.358619\pi$
$857$	25.1587	0.859405	0.429702	+	0.902971i	$0.358619\pi$
$858$	3.31007	0.113004
$859$	32.0100	1.09217	0.546084	−	0.837731i	$-0.316118\pi$
$859$	32.0100	1.09217	0.546084	+	0.837731i	$0.316118\pi$
$860$	−11.5159	−0.392688
$861$	−21.0686	−0.718016
$862$	20.7014	0.705094
$863$	−11.6656	−0.397101	−0.198551	−	0.980091i	$-0.563623\pi$
$863$	−11.6656	−0.397101	−0.198551	+	0.980091i	$0.563623\pi$
$864$	4.07252	0.138550
$865$	−12.3973	−0.421520
$866$	−12.3861	−0.420896
$867$	5.28108	0.179355
$868$	17.2296	0.584810
$869$	2.78205	0.0943746
$870$	4.25385	0.144219
$871$	−25.0337	−0.848234
$872$	−14.1051	−0.477660
$873$	−42.1610	−1.42693
$874$	0.115263	0.00389882
$875$	−47.4856	−1.60531
$876$	0.100254	0.00338728
$877$	43.9992	1.48575	0.742874	−	0.669431i	$-0.233462\pi$
$877$	43.9992	1.48575	0.742874	+	0.669431i	$0.233462\pi$
$878$	−12.6595	−0.427238
$879$	−4.70438	−0.158675
$880$	−2.64491	−0.0891600
$881$	−37.6618	−1.26886	−0.634429	−	0.772981i	$-0.718765\pi$
$881$	−37.6618	−1.26886	−0.634429	+	0.772981i	$0.718765\pi$
$882$	36.1652	1.21775
$883$	44.5168	1.49811	0.749054	−	0.662508i	$-0.230508\pi$
$883$	44.5168	1.49811	0.749054	+	0.662508i	$0.230508\pi$
$884$	−9.68417	−0.325714
$885$	2.99390	0.100639
$886$	−7.02786	−0.236106
$887$	25.5948	0.859389	0.429694	−	0.902974i	$-0.358621\pi$
$887$	25.5948	0.859389	0.429694	+	0.902974i	$0.358621\pi$
$888$	−5.83960	−0.195964
$889$	89.1771	2.99090
$890$	−12.2912	−0.412001
$891$	9.55888	0.320234
$892$	21.6453	0.724739
$893$	5.37806	0.179970
$894$	−13.3730	−0.447259
$895$	17.0177	0.568838
$896$	4.67174	0.156072
$897$	0.293854	0.00981150
$898$	−39.2814	−1.31084
$899$	−17.7384	−0.591609
$900$	8.79315	0.293105
$901$	−16.9287	−0.563978
$902$	−13.4867	−0.449057
$903$	−34.0981	−1.13471
$904$	8.64247	0.287444
$905$	−21.4508	−0.713047
$906$	4.51746	0.150083
$907$	−10.8597	−0.360589	−0.180295	−	0.983613i	$-0.557705\pi$
$907$	−10.8597	−0.360589	−0.180295	+	0.983613i	$0.557705\pi$
$908$	21.4748	0.712665
$909$	21.3499	0.708130
$910$	10.8970	0.361231
$911$	26.1694	0.867032	0.433516	−	0.901146i	$-0.357273\pi$
$911$	26.1694	0.867032	0.433516	+	0.901146i	$0.357273\pi$
$912$	0.434158	0.0143764
$913$	11.1655	0.369524
$914$	−5.88680	−0.194718
$915$	2.91476	0.0963591
$916$	−0.637077	−0.0210496
$917$	5.00188	0.165177
$918$	19.9735	0.659223
$919$	−35.1226	−1.15859	−0.579294	−	0.815119i	$-0.696672\pi$
$919$	−35.1226	−1.15859	−0.579294	+	0.815119i	$0.696672\pi$
$920$	−0.234804	−0.00774125
$921$	6.06644	0.199896
$922$	−28.6973	−0.945094
$923$	27.2840	0.898065
$924$	−7.83149	−0.257637
$925$	−28.1143	−0.924392
$926$	2.08278	0.0684442
$927$	−43.6509	−1.43368
$928$	−4.80971	−0.157886
$929$	−11.7632	−0.385939	−0.192969	−	0.981205i	$-0.561812\pi$
$929$	−11.7632	−0.385939	−0.192969	+	0.981205i	$0.561812\pi$
$930$	−3.26181	−0.106959
$931$	8.59683	0.281750
$932$	0.196347	0.00643156
$933$	−18.1019	−0.592630
$934$	−11.8640	−0.388202
$935$	−12.9718	−0.424225
$936$	−4.81685	−0.157444
$937$	47.2861	1.54477	0.772385	−	0.635154i	$-0.219063\pi$
$937$	47.2861	1.54477	0.772385	+	0.635154i	$0.219063\pi$
$938$	59.2286	1.93388
$939$	22.0600	0.719902
$940$	−10.9557	−0.357336
$941$	−17.7522	−0.578705	−0.289352	−	0.957223i	$-0.593440\pi$
$941$	−17.7522	−0.578705	−0.289352	+	0.957223i	$0.593440\pi$
$942$	−4.37708	−0.142613
$943$	−1.19729	−0.0389890
$944$	−3.38512	−0.110176
$945$	−22.4748	−0.731107
$946$	−21.8273	−0.709666
$947$	−33.8938	−1.10140	−0.550700	−	0.834703i	$-0.685639\pi$
$947$	−33.8938	−1.10140	−0.550700	+	0.834703i	$0.685639\pi$
$948$	0.930287	0.0302143
$949$	−0.264403	−0.00858288
$950$	2.09022	0.0678157
$951$	14.0814	0.456620
$952$	22.9123	0.742593
$953$	−1.81508	−0.0587961	−0.0293980	−	0.999568i	$-0.509359\pi$
$953$	−1.81508	−0.0587961	−0.0293980	+	0.999568i	$0.509359\pi$
$954$	−8.42026	−0.272616
$955$	2.33844	0.0756702
$956$	6.81785	0.220505
$957$	8.06277	0.260632
$958$	36.2534	1.17129
$959$	−81.9751	−2.64711
$960$	−0.884430	−0.0285448
$961$	−17.3983	−0.561237
$962$	15.4009	0.496545
$963$	2.14492	0.0691192
$964$	23.2312	0.748226
$965$	27.2086	0.875877
$966$	−0.695245	−0.0223692
$967$	−5.27524	−0.169640	−0.0848202	−	0.996396i	$-0.527032\pi$
$967$	−5.27524	−0.169640	−0.0848202	+	0.996396i	$0.527032\pi$
$968$	5.98681	0.192423
$969$	2.12931	0.0684032
$970$	20.4162	0.655523
$971$	−11.3168	−0.363174	−0.181587	−	0.983375i	$-0.558123\pi$
$971$	−11.3168	−0.363174	−0.181587	+	0.983375i	$0.558123\pi$
$972$	15.4139	0.494403
$973$	17.4831	0.560483
$974$	−2.31853	−0.0742903
$975$	5.32886	0.170660
$976$	−3.29564	−0.105491
$977$	39.5355	1.26485	0.632426	−	0.774621i	$-0.282059\pi$
$977$	39.5355	1.26485	0.632426	+	0.774621i	$0.282059\pi$
$978$	−12.1851	−0.389637
$979$	−23.2968	−0.744569
$980$	−17.5127	−0.559424
$981$	−34.4087	−1.09858
$982$	−6.31617	−0.201557
$983$	13.9442	0.444751	0.222376	−	0.974961i	$-0.428619\pi$
$983$	13.9442	0.444751	0.222376	+	0.974961i	$0.428619\pi$
$984$	−4.50979	−0.143767
$985$	−1.23802	−0.0394468
$986$	−23.5890	−0.751226
$987$	−32.4395	−1.03256
$988$	−1.14501	−0.0364278
$989$	−1.93773	−0.0616162
$990$	−6.45212	−0.205062
$991$	40.1246	1.27460	0.637300	−	0.770616i	$-0.280051\pi$
$991$	40.1246	1.27460	0.637300	+	0.770616i	$0.280051\pi$
$992$	3.68804	0.117095
$993$	−18.5972	−0.590166
$994$	−64.5528	−2.04749
$995$	20.9135	0.663003
$996$	3.73362	0.118304
$997$	−16.5073	−0.522792	−0.261396	−	0.965232i	$-0.584183\pi$
$997$	−16.5073	−0.522792	−0.261396	+	0.965232i	$0.584183\pi$
$998$	−19.3075	−0.611170
$999$	−31.7642	−1.00497

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1502.2.a.h.1.11	✓	19

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1502.2.a.h.1.11	✓	19	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 1502 = 2 \cdot 751 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1502.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +0.748702 q^{3} +1.00000 q^{4} -1.18128 q^{5} -0.748702 q^{6} -4.67174 q^{7} -1.00000 q^{8} -2.43945 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +0.748702 q^{3} +1.00000 q^{4} -1.18128 q^{5} -0.748702 q^{6} -4.67174 q^{7} -1.00000 q^{8} -2.43945 q^{9} +1.18128 q^{10} +2.23901 q^{11} +0.748702 q^{12} -1.97457 q^{13} +4.67174 q^{14} -0.884430 q^{15} +1.00000 q^{16} +4.90445 q^{17} +2.43945 q^{18} +0.579881 q^{19} -1.18128 q^{20} -3.49774 q^{21} -2.23901 q^{22} -0.198770 q^{23} -0.748702 q^{24} -3.60457 q^{25} +1.97457 q^{26} -4.07252 q^{27} -4.67174 q^{28} +4.80971 q^{29} +0.884430 q^{30} -3.68804 q^{31} -1.00000 q^{32} +1.67635 q^{33} -4.90445 q^{34} +5.51865 q^{35} -2.43945 q^{36} +7.79963 q^{37} -0.579881 q^{38} -1.47836 q^{39} +1.18128 q^{40} +6.02349 q^{41} +3.49774 q^{42} +9.74861 q^{43} +2.23901 q^{44} +2.88168 q^{45} +0.198770 q^{46} +9.27442 q^{47} +0.748702 q^{48} +14.8252 q^{49} +3.60457 q^{50} +3.67197 q^{51} -1.97457 q^{52} -3.45171 q^{53} +4.07252 q^{54} -2.64491 q^{55} +4.67174 q^{56} +0.434158 q^{57} -4.80971 q^{58} -3.38512 q^{59} -0.884430 q^{60} -3.29564 q^{61} +3.68804 q^{62} +11.3965 q^{63} +1.00000 q^{64} +2.33253 q^{65} -1.67635 q^{66} +12.6781 q^{67} +4.90445 q^{68} -0.148819 q^{69} -5.51865 q^{70} -13.8177 q^{71} +2.43945 q^{72} +0.133904 q^{73} -7.79963 q^{74} -2.69875 q^{75} +0.579881 q^{76} -10.4601 q^{77} +1.47836 q^{78} +1.24253 q^{79} -1.18128 q^{80} +4.26923 q^{81} -6.02349 q^{82} +4.98679 q^{83} -3.49774 q^{84} -5.79355 q^{85} -9.74861 q^{86} +3.60103 q^{87} -2.23901 q^{88} -10.4049 q^{89} -2.88168 q^{90} +9.22467 q^{91} -0.198770 q^{92} -2.76124 q^{93} -9.27442 q^{94} -0.685004 q^{95} -0.748702 q^{96} +17.2830 q^{97} -14.8252 q^{98} -5.46195 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 19 q - 19 q^{2} + 6 q^{3} + 19 q^{4} + 2 q^{5} - 6 q^{6} + 13 q^{7} - 19 q^{8} + 25 q^{9}+O(q^{10}) \) 19 * q - 19 * q^2 + 6 * q^3 + 19 * q^4 + 2 * q^5 - 6 * q^6 + 13 * q^7 - 19 * q^8 + 25 * q^9	\( 19 q - 19 q^{2} + 6 q^{3} + 19 q^{4} + 2 q^{5} - 6 q^{6} + 13 q^{7} - 19 q^{8} + 25 q^{9} - 2 q^{10} - 7 q^{11} + 6 q^{12} + 19 q^{13} - 13 q^{14} + 6 q^{15} + 19 q^{16} + 11 q^{17} - 25 q^{18} + 7 q^{19} + 2 q^{20} + 7 q^{21} + 7 q^{22} + 12 q^{23} - 6 q^{24} + 37 q^{25} - 19 q^{26} + 24 q^{27} + 13 q^{28} - 8 q^{29} - 6 q^{30} + 32 q^{31} - 19 q^{32} + 24 q^{33} - 11 q^{34} - 19 q^{35} + 25 q^{36} + 41 q^{37} - 7 q^{38} - 2 q^{39} - 2 q^{40} + 15 q^{41} - 7 q^{42} + 15 q^{43} - 7 q^{44} + 28 q^{45} - 12 q^{46} - 6 q^{47} + 6 q^{48} + 42 q^{49} - 37 q^{50} + 8 q^{51} + 19 q^{52} + 6 q^{53} - 24 q^{54} + 22 q^{55} - 13 q^{56} + 24 q^{57} + 8 q^{58} - 4 q^{59} + 6 q^{60} + 13 q^{61} - 32 q^{62} + 37 q^{63} + 19 q^{64} + 20 q^{65} - 24 q^{66} + 47 q^{67} + 11 q^{68} + 15 q^{69} + 19 q^{70} - 25 q^{72} + 64 q^{73} - 41 q^{74} - 3 q^{75} + 7 q^{76} - 4 q^{77} + 2 q^{78} + 34 q^{79} + 2 q^{80} + 27 q^{81} - 15 q^{82} + 4 q^{83} + 7 q^{84} + 21 q^{85} - 15 q^{86} + 7 q^{88} + 18 q^{89} - 28 q^{90} + 28 q^{91} + 12 q^{92} + 43 q^{93} + 6 q^{94} - 8 q^{95} - 6 q^{96} + 82 q^{97} - 42 q^{98} - 2 q^{99}+O(q^{100}) \) 19 * q - 19 * q^2 + 6 * q^3 + 19 * q^4 + 2 * q^5 - 6 * q^6 + 13 * q^7 - 19 * q^8 + 25 * q^9 - 2 * q^10 - 7 * q^11 + 6 * q^12 + 19 * q^13 - 13 * q^14 + 6 * q^15 + 19 * q^16 + 11 * q^17 - 25 * q^18 + 7 * q^19 + 2 * q^20 + 7 * q^21 + 7 * q^22 + 12 * q^23 - 6 * q^24 + 37 * q^25 - 19 * q^26 + 24 * q^27 + 13 * q^28 - 8 * q^29 - 6 * q^30 + 32 * q^31 - 19 * q^32 + 24 * q^33 - 11 * q^34 - 19 * q^35 + 25 * q^36 + 41 * q^37 - 7 * q^38 - 2 * q^39 - 2 * q^40 + 15 * q^41 - 7 * q^42 + 15 * q^43 - 7 * q^44 + 28 * q^45 - 12 * q^46 - 6 * q^47 + 6 * q^48 + 42 * q^49 - 37 * q^50 + 8 * q^51 + 19 * q^52 + 6 * q^53 - 24 * q^54 + 22 * q^55 - 13 * q^56 + 24 * q^57 + 8 * q^58 - 4 * q^59 + 6 * q^60 + 13 * q^61 - 32 * q^62 + 37 * q^63 + 19 * q^64 + 20 * q^65 - 24 * q^66 + 47 * q^67 + 11 * q^68 + 15 * q^69 + 19 * q^70 - 25 * q^72 + 64 * q^73 - 41 * q^74 - 3 * q^75 + 7 * q^76 - 4 * q^77 + 2 * q^78 + 34 * q^79 + 2 * q^80 + 27 * q^81 - 15 * q^82 + 4 * q^83 + 7 * q^84 + 21 * q^85 - 15 * q^86 + 7 * q^88 + 18 * q^89 - 28 * q^90 + 28 * q^91 + 12 * q^92 + 43 * q^93 + 6 * q^94 - 8 * q^95 - 6 * q^96 + 82 * q^97 - 42 * q^98 - 2 * q^99

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