LMFDB - Embedded newform 1003.2.a.i.1.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1003, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1003.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1003 = 17 \cdot 59 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1003.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$8.00899532273$
Analytic rank:	$0$
Dimension:	$18$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 5 x^{17} - 16 x^{16} + 112 x^{15} + 52 x^{14} - 984 x^{13} + 431 x^{12} + 4304 x^{11} + \cdots + 28 $ x^18 - 5x^17 - 16x^16 + 112x^15 + 52x^14 - 984x^13 + 431x^12 + 4304x^11 - 3825x^10 - 9826x^9 + 11533x^8 + 11182x^7 - 15697x^6 - 5604x^5 + 9201x^4 + 1189x^3 - 1952x^2 - 100*x + 28
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
Root			$1.79692$ of defining polynomial
Character	$\chi$	$=$	1003.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.79692 q^{2} +1.63689 q^{3} +1.22893 q^{4} +2.71894 q^{5} +2.94136 q^{6} +4.07184 q^{7} -1.38555 q^{8} -0.320597 q^{9} +O(q^{10})$	\(q+1.79692 q^{2} +1.63689 q^{3} +1.22893 q^{4} +2.71894 q^{5} +2.94136 q^{6} +4.07184 q^{7} -1.38555 q^{8} -0.320597 q^{9} +4.88573 q^{10} -2.21196 q^{11} +2.01162 q^{12} +1.69044 q^{13} +7.31679 q^{14} +4.45061 q^{15} -4.94759 q^{16} +1.00000 q^{17} -0.576087 q^{18} -5.88800 q^{19} +3.34139 q^{20} +6.66515 q^{21} -3.97471 q^{22} -4.49183 q^{23} -2.26799 q^{24} +2.39265 q^{25} +3.03759 q^{26} -5.43545 q^{27} +5.00402 q^{28} -8.25473 q^{29} +7.99740 q^{30} +1.95954 q^{31} -6.11933 q^{32} -3.62072 q^{33} +1.79692 q^{34} +11.0711 q^{35} -0.393991 q^{36} +7.31104 q^{37} -10.5803 q^{38} +2.76706 q^{39} -3.76724 q^{40} +9.05015 q^{41} +11.9768 q^{42} -6.88915 q^{43} -2.71834 q^{44} -0.871684 q^{45} -8.07147 q^{46} +5.32653 q^{47} -8.09865 q^{48} +9.57992 q^{49} +4.29941 q^{50} +1.63689 q^{51} +2.07743 q^{52} +9.80472 q^{53} -9.76708 q^{54} -6.01418 q^{55} -5.64175 q^{56} -9.63800 q^{57} -14.8331 q^{58} -1.00000 q^{59} +5.46949 q^{60} -11.8739 q^{61} +3.52114 q^{62} -1.30542 q^{63} -1.10079 q^{64} +4.59621 q^{65} -6.50616 q^{66} +15.4130 q^{67} +1.22893 q^{68} -7.35262 q^{69} +19.8939 q^{70} +3.50861 q^{71} +0.444203 q^{72} -2.52127 q^{73} +13.1374 q^{74} +3.91651 q^{75} -7.23595 q^{76} -9.00674 q^{77} +4.97219 q^{78} -15.7994 q^{79} -13.4522 q^{80} -7.93543 q^{81} +16.2624 q^{82} -1.53014 q^{83} +8.19101 q^{84} +2.71894 q^{85} -12.3793 q^{86} -13.5121 q^{87} +3.06478 q^{88} +3.86827 q^{89} -1.56635 q^{90} +6.88320 q^{91} -5.52015 q^{92} +3.20754 q^{93} +9.57136 q^{94} -16.0091 q^{95} -10.0167 q^{96} -5.90996 q^{97} +17.2144 q^{98} +0.709146 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 5 q^{2} + q^{3} + 21 q^{4} + 21 q^{5} + 5 q^{6} - q^{7} + 9 q^{8} + 17 q^{9}+O(q^{10}) $ 18 * q + 5 * q^2 + q^3 + 21 * q^4 + 21 * q^5 + 5 * q^6 - q^7 + 9 * q^8 + 17 * q^9	\( 18 q + 5 q^{2} + q^{3} + 21 q^{4} + 21 q^{5} + 5 q^{6} - q^{7} + 9 q^{8} + 17 q^{9} + 10 q^{10} + 6 q^{11} + 20 q^{12} + 12 q^{13} + 9 q^{14} - q^{15} + 19 q^{16} + 18 q^{17} + 10 q^{18} - 14 q^{19} + 17 q^{20} - 14 q^{21} - 4 q^{22} + 7 q^{23} - 3 q^{24} + 35 q^{25} + 3 q^{26} + 13 q^{27} + q^{28} + 23 q^{29} + 17 q^{30} - q^{31} + 13 q^{32} + 7 q^{33} + 5 q^{34} + 5 q^{35} - 16 q^{36} + 36 q^{37} - 19 q^{38} + 8 q^{39} - 4 q^{40} + 37 q^{41} + 9 q^{42} - 15 q^{43} - 9 q^{44} + 17 q^{45} + q^{46} + 23 q^{47} + 17 q^{48} + 15 q^{49} + 32 q^{50} + q^{51} - 11 q^{52} + 35 q^{53} - 17 q^{54} - 6 q^{55} + 37 q^{56} - 16 q^{57} + 2 q^{58} - 18 q^{59} - 6 q^{60} + 39 q^{61} - q^{62} + 15 q^{63} + 5 q^{64} + 15 q^{65} - 36 q^{66} + 14 q^{67} + 21 q^{68} + 16 q^{69} - 45 q^{70} + 3 q^{71} - 71 q^{72} + 56 q^{73} - 27 q^{74} + 16 q^{75} - q^{76} + 39 q^{77} - 71 q^{78} - 22 q^{79} + 45 q^{80} - 18 q^{81} + 5 q^{82} + 12 q^{83} + 2 q^{84} + 21 q^{85} + 4 q^{86} + 8 q^{87} - 18 q^{88} + 34 q^{89} + 48 q^{90} + 3 q^{91} + 67 q^{92} - 19 q^{93} - 38 q^{94} - 72 q^{95} + 6 q^{96} + 31 q^{97} + 19 q^{98} + 44 q^{99}+O(q^{100}) \) 18 * q + 5 * q^2 + q^3 + 21 * q^4 + 21 * q^5 + 5 * q^6 - q^7 + 9 * q^8 + 17 * q^9 + 10 * q^10 + 6 * q^11 + 20 * q^12 + 12 * q^13 + 9 * q^14 - q^15 + 19 * q^16 + 18 * q^17 + 10 * q^18 - 14 * q^19 + 17 * q^20 - 14 * q^21 - 4 * q^22 + 7 * q^23 - 3 * q^24 + 35 * q^25 + 3 * q^26 + 13 * q^27 + q^28 + 23 * q^29 + 17 * q^30 - q^31 + 13 * q^32 + 7 * q^33 + 5 * q^34 + 5 * q^35 - 16 * q^36 + 36 * q^37 - 19 * q^38 + 8 * q^39 - 4 * q^40 + 37 * q^41 + 9 * q^42 - 15 * q^43 - 9 * q^44 + 17 * q^45 + q^46 + 23 * q^47 + 17 * q^48 + 15 * q^49 + 32 * q^50 + q^51 - 11 * q^52 + 35 * q^53 - 17 * q^54 - 6 * q^55 + 37 * q^56 - 16 * q^57 + 2 * q^58 - 18 * q^59 - 6 * q^60 + 39 * q^61 - q^62 + 15 * q^63 + 5 * q^64 + 15 * q^65 - 36 * q^66 + 14 * q^67 + 21 * q^68 + 16 * q^69 - 45 * q^70 + 3 * q^71 - 71 * q^72 + 56 * q^73 - 27 * q^74 + 16 * q^75 - q^76 + 39 * q^77 - 71 * q^78 - 22 * q^79 + 45 * q^80 - 18 * q^81 + 5 * q^82 + 12 * q^83 + 2 * q^84 + 21 * q^85 + 4 * q^86 + 8 * q^87 - 18 * q^88 + 34 * q^89 + 48 * q^90 + 3 * q^91 + 67 * q^92 - 19 * q^93 - 38 * q^94 - 72 * q^95 + 6 * q^96 + 31 * q^97 + 19 * q^98 + 44 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.79692	1.27062	0.635308	−	0.772259i	$-0.280873\pi$
$2$	1.79692	1.27062	0.635308	+	0.772259i	$0.280873\pi$
$3$	1.63689	0.945058	0.472529	−	0.881315i	$-0.343341\pi$
$3$	1.63689	0.945058	0.472529	+	0.881315i	$0.343341\pi$
$4$	1.22893	0.614465
$5$	2.71894	1.21595	0.607974	−	0.793957i	$-0.291982\pi$
$5$	2.71894	1.21595	0.607974	+	0.793957i	$0.291982\pi$
$6$	2.94136	1.20081
$7$	4.07184	1.53901	0.769506	−	0.638639i	$-0.220502\pi$
$7$	4.07184	1.53901	0.769506	+	0.638639i	$0.220502\pi$
$8$	−1.38555	−0.489866
$9$	−0.320597	−0.106866
$10$	4.88573	1.54500
$11$	−2.21196	−0.666930	−0.333465	−	0.942763i	$-0.608218\pi$
$11$	−2.21196	−0.666930	−0.333465	+	0.942763i	$0.608218\pi$
$12$	2.01162	0.580705
$13$	1.69044	0.468843	0.234422	−	0.972135i	$-0.424680\pi$
$13$	1.69044	0.468843	0.234422	+	0.972135i	$0.424680\pi$
$14$	7.31679	1.95549
$15$	4.45061	1.14914
$16$	−4.94759	−1.23690
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−0.576087	−0.135785
$19$	−5.88800	−1.35080	−0.675400	−	0.737452i	$-0.736029\pi$
$19$	−5.88800	−1.35080	−0.675400	+	0.737452i	$0.736029\pi$
$20$	3.34139	0.747158
$21$	6.66515	1.45446
$22$	−3.97471	−0.847412
$23$	−4.49183	−0.936611	−0.468306	−	0.883567i	$-0.655135\pi$
$23$	−4.49183	−0.936611	−0.468306	+	0.883567i	$0.655135\pi$
$24$	−2.26799	−0.462952
$25$	2.39265	0.478531
$26$	3.03759	0.595720
$27$	−5.43545	−1.04605
$28$	5.00402	0.945670
$29$	−8.25473	−1.53286	−0.766432	−	0.642325i	$-0.777970\pi$
$29$	−8.25473	−1.53286	−0.766432	+	0.642325i	$0.777970\pi$
$30$	7.99740	1.46012
$31$	1.95954	0.351943	0.175972	−	0.984395i	$-0.443693\pi$
$31$	1.95954	0.351943	0.175972	+	0.984395i	$0.443693\pi$
$32$	−6.11933	−1.08176
$33$	−3.62072	−0.630287
$34$	1.79692	0.308170
$35$	11.0711	1.87136
$36$	−0.393991	−0.0656652
$37$	7.31104	1.20193	0.600964	−	0.799276i	$-0.294783\pi$
$37$	7.31104	1.20193	0.600964	+	0.799276i	$0.294783\pi$
$38$	−10.5803	−1.71635
$39$	2.76706	0.443084
$40$	−3.76724	−0.595652
$41$	9.05015	1.41340	0.706698	−	0.707515i	$-0.250184\pi$
$41$	9.05015	1.41340	0.706698	+	0.707515i	$0.250184\pi$
$42$	11.9768	1.84806
$43$	−6.88915	−1.05059	−0.525293	−	0.850922i	$-0.676044\pi$
$43$	−6.88915	−1.05059	−0.525293	+	0.850922i	$0.676044\pi$
$44$	−2.71834	−0.409805
$45$	−0.871684	−0.129943
$46$	−8.07147	−1.19007
$47$	5.32653	0.776954	0.388477	−	0.921458i	$-0.373001\pi$
$47$	5.32653	0.776954	0.388477	+	0.921458i	$0.373001\pi$
$48$	−8.09865	−1.16894
$49$	9.57992	1.36856
$50$	4.29941	0.608029
$51$	1.63689	0.229210
$52$	2.07743	0.288088
$53$	9.80472	1.34678	0.673391	−	0.739286i	$-0.264837\pi$
$53$	9.80472	1.34678	0.673391	+	0.739286i	$0.264837\pi$
$54$	−9.76708	−1.32913
$55$	−6.01418	−0.810952
$56$	−5.64175	−0.753911
$57$	−9.63800	−1.27658
$58$	−14.8331	−1.94768
$59$	−1.00000	−0.130189
$59$	−1.00000	−0.130189
$60$	5.46949	0.706108
$61$	−11.8739	−1.52030	−0.760148	−	0.649749i	$-0.774874\pi$
$61$	−11.8739	−1.52030	−0.760148	+	0.649749i	$0.774874\pi$
$62$	3.52114	0.447185
$63$	−1.30542	−0.164467
$64$	−1.10079	−0.137599
$65$	4.59621	0.570089
$66$	−6.50616	−0.800853
$67$	15.4130	1.88299	0.941496	−	0.337025i	$-0.109421\pi$
$67$	15.4130	1.88299	0.941496	+	0.337025i	$0.109421\pi$
$68$	1.22893	0.149030
$69$	−7.35262	−0.885152
$70$	19.8939	2.37778
$71$	3.50861	0.416395	0.208198	−	0.978087i	$-0.433240\pi$
$71$	3.50861	0.416395	0.208198	+	0.978087i	$0.433240\pi$
$72$	0.444203	0.0523499
$73$	−2.52127	−0.295092	−0.147546	−	0.989055i	$-0.547137\pi$
$73$	−2.52127	−0.295092	−0.147546	+	0.989055i	$0.547137\pi$
$74$	13.1374	1.52719
$75$	3.91651	0.452239
$76$	−7.23595	−0.830020
$77$	−9.00674	−1.02641
$78$	4.97219	0.562990
$79$	−15.7994	−1.77757	−0.888784	−	0.458327i	$-0.848449\pi$
$79$	−15.7994	−1.77757	−0.888784	+	0.458327i	$0.848449\pi$
$80$	−13.4522	−1.50400
$81$	−7.93543	−0.881714
$82$	16.2624	1.79588
$83$	−1.53014	−0.167954	−0.0839772	−	0.996468i	$-0.526762\pi$
$83$	−1.53014	−0.167954	−0.0839772	+	0.996468i	$0.526762\pi$
$84$	8.19101	0.893713
$85$	2.71894	0.294911
$86$	−12.3793	−1.33489
$87$	−13.5121	−1.44865
$88$	3.06478	0.326706
$89$	3.86827	0.410035	0.205018	−	0.978758i	$-0.434275\pi$
$89$	3.86827	0.410035	0.205018	+	0.978758i	$0.434275\pi$
$90$	−1.56635	−0.165108
$91$	6.88320	0.721556
$92$	−5.52015	−0.575515
$93$	3.20754	0.332607
$94$	9.57136	0.987210
$95$	−16.0091	−1.64250
$96$	−10.0167	−1.02232
$97$	−5.90996	−0.600065	−0.300033	−	0.953929i	$-0.596998\pi$
$97$	−5.90996	−0.600065	−0.300033	+	0.953929i	$0.596998\pi$
$98$	17.2144	1.73891
$99$	0.709146	0.0712718
$100$	2.94041	0.294041
$101$	15.8813	1.58025	0.790127	−	0.612944i	$-0.210015\pi$
$101$	15.8813	1.58025	0.790127	+	0.612944i	$0.210015\pi$
$102$	2.94136	0.291238
$103$	−0.778749	−0.0767325	−0.0383662	−	0.999264i	$-0.512215\pi$
$103$	−0.778749	−0.0767325	−0.0383662	+	0.999264i	$0.512215\pi$
$104$	−2.34219	−0.229671
$105$	18.1222	1.76854
$106$	17.6183	1.71124
$107$	9.55941	0.924143	0.462071	−	0.886843i	$-0.347106\pi$
$107$	9.55941	0.924143	0.462071	+	0.886843i	$0.347106\pi$
$108$	−6.67979	−0.642763
$109$	9.16662	0.878003	0.439002	−	0.898486i	$-0.355332\pi$
$109$	9.16662	0.878003	0.439002	+	0.898486i	$0.355332\pi$
$110$	−10.8070	−1.03041
$111$	11.9674	1.13589
$112$	−20.1458	−1.90360
$113$	19.7016	1.85337	0.926683	−	0.375843i	$-0.122647\pi$
$113$	19.7016	1.85337	0.926683	+	0.375843i	$0.122647\pi$
$114$	−17.3187	−1.62205
$115$	−12.2130	−1.13887
$116$	−10.1445	−0.941892
$117$	−0.541949	−0.0501032
$118$	−1.79692	−0.165420
$119$	4.07184	0.373265
$120$	−6.16655	−0.562926
$121$	−6.10725	−0.555205
$122$	−21.3365	−1.93171
$123$	14.8141	1.33574
$124$	2.40814	0.216257
$125$	−7.08923	−0.634080
$126$	−2.34574	−0.208975
$127$	6.89517	0.611848	0.305924	−	0.952056i	$-0.401035\pi$
$127$	6.89517	0.611848	0.305924	+	0.952056i	$0.401035\pi$
$128$	10.2606	0.906921
$129$	−11.2768	−0.992864
$130$	8.25903	0.724365
$131$	16.3318	1.42691	0.713456	−	0.700700i	$-0.247129\pi$
$131$	16.3318	1.42691	0.713456	+	0.700700i	$0.247129\pi$
$132$	−4.44962	−0.387290
$133$	−23.9750	−2.07890
$134$	27.6959	2.39256
$135$	−14.7787	−1.27195
$136$	−1.38555	−0.118810
$137$	−18.8176	−1.60770	−0.803848	−	0.594835i	$-0.797217\pi$
$137$	−18.8176	−1.60770	−0.803848	+	0.594835i	$0.797217\pi$
$138$	−13.2121	−1.12469
$139$	−19.6328	−1.66523	−0.832614	−	0.553853i	$-0.813157\pi$
$139$	−19.6328	−1.66523	−0.832614	+	0.553853i	$0.813157\pi$
$140$	13.6056	1.14989
$141$	8.71893	0.734266
$142$	6.30470	0.529079
$143$	−3.73918	−0.312686
$144$	1.58618	0.132182
$145$	−22.4441	−1.86388
$146$	−4.53052	−0.374949
$147$	15.6813	1.29337
$148$	8.98477	0.738543
$149$	7.90887	0.647920	0.323960	−	0.946071i	$-0.394986\pi$
$149$	7.90887	0.647920	0.323960	+	0.946071i	$0.394986\pi$
$150$	7.03766	0.574622
$151$	4.76970	0.388153	0.194076	−	0.980986i	$-0.437829\pi$
$151$	4.76970	0.388153	0.194076	+	0.980986i	$0.437829\pi$
$152$	8.15813	0.661712
$153$	−0.320597	−0.0259187
$154$	−16.1844	−1.30418
$155$	5.32787	0.427945
$156$	3.40052	0.272260
$157$	1.32617	0.105840	0.0529201	−	0.998599i	$-0.483147\pi$
$157$	1.32617	0.105840	0.0529201	+	0.998599i	$0.483147\pi$
$158$	−28.3902	−2.25861
$159$	16.0492	1.27279
$160$	−16.6381	−1.31536
$161$	−18.2900	−1.44146
$162$	−14.2593	−1.12032
$163$	6.88862	0.539558	0.269779	−	0.962922i	$-0.413049\pi$
$163$	6.88862	0.539558	0.269779	+	0.962922i	$0.413049\pi$
$164$	11.1220	0.868483
$165$	−9.84454	−0.766397
$166$	−2.74954	−0.213405
$167$	−16.2866	−1.26030	−0.630149	−	0.776474i	$-0.717006\pi$
$167$	−16.2866	−1.26030	−0.630149	+	0.776474i	$0.717006\pi$
$168$	−9.23492	−0.712489
$169$	−10.1424	−0.780186
$170$	4.88573	0.374718
$171$	1.88767	0.144354
$172$	−8.46629	−0.645548
$173$	−11.3310	−0.861482	−0.430741	−	0.902476i	$-0.641748\pi$
$173$	−11.3310	−0.861482	−0.430741	+	0.902476i	$0.641748\pi$
$174$	−24.2801	−1.84067
$175$	9.74251	0.736465
$176$	10.9439	0.824924
$177$	−1.63689	−0.123036
$178$	6.95097	0.520998
$179$	10.4261	0.779285	0.389642	−	0.920966i	$-0.372599\pi$
$179$	10.4261	0.779285	0.389642	+	0.920966i	$0.372599\pi$
$180$	−1.07124	−0.0798455
$181$	−3.48572	−0.259091	−0.129546	−	0.991573i	$-0.541352\pi$
$181$	−3.48572	−0.259091	−0.129546	+	0.991573i	$0.541352\pi$
$182$	12.3686	0.916820
$183$	−19.4362	−1.43677
$184$	6.22366	0.458814
$185$	19.8783	1.46148
$186$	5.76371	0.422616
$187$	−2.21196	−0.161754
$188$	6.54593	0.477411
$189$	−22.1323	−1.60989
$190$	−28.7672	−2.08699
$191$	−9.89110	−0.715695	−0.357848	−	0.933780i	$-0.616489\pi$
$191$	−9.89110	−0.715695	−0.357848	+	0.933780i	$0.616489\pi$
$192$	−1.80187	−0.130039
$193$	7.22444	0.520026	0.260013	−	0.965605i	$-0.416273\pi$
$193$	7.22444	0.520026	0.260013	+	0.965605i	$0.416273\pi$
$194$	−10.6197	−0.762453
$195$	7.52348	0.538767
$196$	11.7731	0.840933
$197$	−20.4993	−1.46051	−0.730256	−	0.683173i	$-0.760599\pi$
$197$	−20.4993	−1.46051	−0.730256	+	0.683173i	$0.760599\pi$
$198$	1.27428	0.0905591
$199$	10.1887	0.722258	0.361129	−	0.932516i	$-0.382391\pi$
$199$	10.1887	0.722258	0.361129	+	0.932516i	$0.382391\pi$
$200$	−3.31514	−0.234416
$201$	25.2293	1.77954
$202$	28.5376	2.00790
$203$	−33.6120	−2.35910
$204$	2.01162	0.140842
$205$	24.6069	1.71862
$206$	−1.39935	−0.0974975
$207$	1.44007	0.100091
$208$	−8.36360	−0.579911
$209$	13.0240	0.900889
$210$	32.5642	2.24714
$211$	9.01710	0.620763	0.310382	−	0.950612i	$-0.399543\pi$
$211$	9.01710	0.620763	0.310382	+	0.950612i	$0.399543\pi$
$212$	12.0493	0.827551
$213$	5.74320	0.393518
$214$	17.1775	1.17423
$215$	−18.7312	−1.27746
$216$	7.53109	0.512426
$217$	7.97893	0.541645
$218$	16.4717	1.11561
$219$	−4.12703	−0.278879
$220$	−7.39101	−0.498302
$221$	1.69044	0.113711
$222$	21.5044	1.44328
$223$	−22.1217	−1.48138	−0.740690	−	0.671847i	$-0.765501\pi$
$223$	−22.1217	−1.48138	−0.740690	+	0.671847i	$0.765501\pi$
$224$	−24.9170	−1.66484
$225$	−0.767077	−0.0511384
$226$	35.4022	2.35492
$227$	−2.25011	−0.149345	−0.0746726	−	0.997208i	$-0.523791\pi$
$227$	−2.25011	−0.149345	−0.0746726	+	0.997208i	$0.523791\pi$
$228$	−11.8444	−0.784417
$229$	−13.0055	−0.859427	−0.429713	−	0.902965i	$-0.641385\pi$
$229$	−13.0055	−0.859427	−0.429713	+	0.902965i	$0.641385\pi$
$230$	−21.9459	−1.44707
$231$	−14.7430	−0.970020
$232$	11.4374	0.750899
$233$	−4.98394	−0.326509	−0.163254	−	0.986584i	$-0.552199\pi$
$233$	−4.98394	−0.326509	−0.163254	+	0.986584i	$0.552199\pi$
$234$	−0.973840	−0.0636619
$235$	14.4825	0.944736
$236$	−1.22893	−0.0799966
$237$	−25.8618	−1.67990
$238$	7.31679	0.474277
$239$	−30.2052	−1.95381	−0.976906	−	0.213671i	$-0.931458\pi$
$239$	−30.2052	−1.95381	−0.976906	+	0.213671i	$0.931458\pi$
$240$	−22.0198	−1.42137
$241$	7.34996	0.473453	0.236726	−	0.971576i	$-0.423925\pi$
$241$	7.34996	0.473453	0.236726	+	0.971576i	$0.423925\pi$
$242$	−10.9743	−0.705452
$243$	3.31693	0.212781
$244$	−14.5922	−0.934170
$245$	26.0473	1.66410
$246$	26.6198	1.69721
$247$	−9.95330	−0.633314
$248$	−2.71504	−0.172405
$249$	−2.50466	−0.158727
$250$	−12.7388	−0.805672
$251$	28.9206	1.82545	0.912726	−	0.408573i	$-0.133973\pi$
$251$	28.9206	1.82545	0.912726	+	0.408573i	$0.133973\pi$
$252$	−1.60427	−0.101060
$253$	9.93573	0.624654
$254$	12.3901	0.777423
$255$	4.45061	0.278708
$256$	20.6391	1.28995
$257$	15.9744	0.996455	0.498227	−	0.867046i	$-0.333984\pi$
$257$	15.9744	0.996455	0.498227	+	0.867046i	$0.333984\pi$
$258$	−20.2635	−1.26155
$259$	29.7694	1.84978
$260$	5.64842	0.350300
$261$	2.64644	0.163810
$262$	29.3469	1.81306
$263$	−14.7177	−0.907534	−0.453767	−	0.891120i	$-0.649920\pi$
$263$	−14.7177	−0.907534	−0.453767	+	0.891120i	$0.649920\pi$
$264$	5.01670	0.308757
$265$	26.6585	1.63762
$266$	−43.0813	−2.64148
$267$	6.33192	0.387507
$268$	18.9415	1.15703
$269$	8.21931	0.501140	0.250570	−	0.968098i	$-0.419382\pi$
$269$	8.21931	0.501140	0.250570	+	0.968098i	$0.419382\pi$
$270$	−26.5561	−1.61615
$271$	23.1822	1.40822	0.704110	−	0.710091i	$-0.251346\pi$
$271$	23.1822	1.40822	0.704110	+	0.710091i	$0.251346\pi$
$272$	−4.94759	−0.299992
$273$	11.2670	0.681912
$274$	−33.8137	−2.04276
$275$	−5.29244	−0.319146
$276$	−9.03586	−0.543895
$277$	7.28991	0.438008	0.219004	−	0.975724i	$-0.429719\pi$
$277$	7.28991	0.438008	0.219004	+	0.975724i	$0.429719\pi$
$278$	−35.2785	−2.11587
$279$	−0.628221	−0.0376106
$280$	−15.3396	−0.916717
$281$	−2.80868	−0.167552	−0.0837760	−	0.996485i	$-0.526698\pi$
$281$	−2.80868	−0.167552	−0.0837760	+	0.996485i	$0.526698\pi$
$282$	15.6672	0.932971
$283$	−10.7942	−0.641651	−0.320826	−	0.947138i	$-0.603960\pi$
$283$	−10.7942	−0.641651	−0.320826	+	0.947138i	$0.603960\pi$
$284$	4.31184	0.255861
$285$	−26.2052	−1.55226
$286$	−6.71901	−0.397303
$287$	36.8508	2.17523
$288$	1.96184	0.115602
$289$	1.00000	0.0588235
$290$	−40.3304	−2.36828
$291$	−9.67394	−0.567096
$292$	−3.09846	−0.181324
$293$	−6.88039	−0.401957	−0.200978	−	0.979596i	$-0.564412\pi$
$293$	−6.88039	−0.401957	−0.200978	+	0.979596i	$0.564412\pi$
$294$	28.1780	1.64337
$295$	−2.71894	−0.158303
$296$	−10.1298	−0.588784
$297$	12.0230	0.697643
$298$	14.2116	0.823258
$299$	−7.59316	−0.439124
$300$	4.81312	0.277885
$301$	−28.0515	−1.61686
$302$	8.57079	0.493193
$303$	25.9960	1.49343
$304$	29.1314	1.67080
$305$	−32.2845	−1.84860
$306$	−0.576087	−0.0329327
$307$	−21.1569	−1.20749	−0.603743	−	0.797179i	$-0.706325\pi$
$307$	−21.1569	−1.20749	−0.603743	+	0.797179i	$0.706325\pi$
$308$	−11.0687	−0.630695
$309$	−1.27473	−0.0725166
$310$	9.57377	0.543754
$311$	−24.8386	−1.40847	−0.704233	−	0.709969i	$-0.748709\pi$
$311$	−24.8386	−1.40847	−0.704233	+	0.709969i	$0.748709\pi$
$312$	−3.83390	−0.217052
$313$	−6.51101	−0.368024	−0.184012	−	0.982924i	$-0.558909\pi$
$313$	−6.51101	−0.368024	−0.184012	+	0.982924i	$0.558909\pi$
$314$	2.38303	0.134482
$315$	−3.54936	−0.199984
$316$	−19.4163	−1.09225
$317$	21.6848	1.21794	0.608969	−	0.793194i	$-0.291583\pi$
$317$	21.6848	1.21794	0.608969	+	0.793194i	$0.291583\pi$
$318$	28.8392	1.61722
$319$	18.2591	1.02231
$320$	−2.99298	−0.167313
$321$	15.6477	0.873368
$322$	−32.8658	−1.83154
$323$	−5.88800	−0.327617
$324$	−9.75209	−0.541783
$325$	4.04463	0.224356
$326$	12.3783	0.685571
$327$	15.0047	0.829764
$328$	−12.5395	−0.692375
$329$	21.6888	1.19574
$330$	−17.6899	−0.973796
$331$	−17.7448	−0.975345	−0.487672	−	0.873027i	$-0.662154\pi$
$331$	−17.7448	−0.975345	−0.487672	+	0.873027i	$0.662154\pi$
$332$	−1.88043	−0.103202
$333$	−2.34390	−0.128445
$334$	−29.2658	−1.60136
$335$	41.9069	2.28962
$336$	−32.9765	−1.79901
$337$	23.2905	1.26871	0.634357	−	0.773040i	$-0.281265\pi$
$337$	23.2905	1.26871	0.634357	+	0.773040i	$0.281265\pi$
$338$	−18.2251	−0.991317
$339$	32.2493	1.75154
$340$	3.34139	0.181213
$341$	−4.33441	−0.234721
$342$	3.39200	0.183419
$343$	10.5050	0.567218
$344$	9.54527	0.514647
$345$	−19.9914	−1.07630
$346$	−20.3610	−1.09461
$347$	28.6547	1.53827	0.769133	−	0.639089i	$-0.220688\pi$
$347$	28.6547	1.53827	0.769133	+	0.639089i	$0.220688\pi$
$348$	−16.6054	−0.890143
$349$	−2.86402	−0.153307	−0.0766537	−	0.997058i	$-0.524424\pi$
$349$	−2.86402	−0.153307	−0.0766537	+	0.997058i	$0.524424\pi$
$350$	17.5065	0.935764
$351$	−9.18829	−0.490435
$352$	13.5357	0.721455
$353$	−5.48885	−0.292142	−0.146071	−	0.989274i	$-0.546663\pi$
$353$	−5.48885	−0.292142	−0.146071	+	0.989274i	$0.546663\pi$
$354$	−2.94136	−0.156332
$355$	9.53971	0.506315
$356$	4.75383	0.251953
$357$	6.66515	0.352757
$358$	18.7349	0.990172
$359$	4.98810	0.263262	0.131631	−	0.991299i	$-0.457979\pi$
$359$	4.98810	0.263262	0.131631	+	0.991299i	$0.457979\pi$
$360$	1.20776	0.0636547
$361$	15.6686	0.824661
$362$	−6.26357	−0.329206
$363$	−9.99689	−0.524701
$364$	8.45898	0.443371
$365$	−6.85518	−0.358817
$366$	−34.9254	−1.82558
$367$	−24.6799	−1.28828	−0.644141	−	0.764907i	$-0.722785\pi$
$367$	−24.6799	−1.28828	−0.644141	+	0.764907i	$0.722785\pi$
$368$	22.2237	1.15849
$369$	−2.90145	−0.151043
$370$	35.7198	1.85698
$371$	39.9233	2.07271
$372$	3.94185	0.204375
$373$	32.9321	1.70516	0.852579	−	0.522598i	$-0.175037\pi$
$373$	32.9321	1.70516	0.852579	+	0.522598i	$0.175037\pi$
$374$	−3.97471	−0.205528
$375$	−11.6043	−0.599242
$376$	−7.38018	−0.380604
$377$	−13.9541	−0.718673
$378$	−39.7700	−2.04555
$379$	20.6093	1.05863	0.529315	−	0.848425i	$-0.322449\pi$
$379$	20.6093	1.05863	0.529315	+	0.848425i	$0.322449\pi$
$380$	−19.6741	−1.00926
$381$	11.2866	0.578231
$382$	−17.7735	−0.909374
$383$	−18.6698	−0.953984	−0.476992	−	0.878908i	$-0.658273\pi$
$383$	−18.6698	−0.953984	−0.476992	+	0.878908i	$0.658273\pi$
$384$	16.7955	0.857093
$385$	−24.4888	−1.24807
$386$	12.9818	0.660754
$387$	2.20864	0.112271
$388$	−7.26293	−0.368719
$389$	7.41646	0.376029	0.188015	−	0.982166i	$-0.439795\pi$
$389$	7.41646	0.376029	0.188015	+	0.982166i	$0.439795\pi$
$390$	13.5191	0.684567
$391$	−4.49183	−0.227162
$392$	−13.2735	−0.670412
$393$	26.7333	1.34852
$394$	−36.8356	−1.85575
$395$	−42.9576	−2.16143
$396$	0.871491	0.0437941
$397$	19.8724	0.997369	0.498684	−	0.866784i	$-0.333817\pi$
$397$	19.8724	0.997369	0.498684	+	0.866784i	$0.333817\pi$
$398$	18.3083	0.917713
$399$	−39.2444	−1.96468
$400$	−11.8379	−0.591893
$401$	20.7556	1.03648	0.518242	−	0.855234i	$-0.326587\pi$
$401$	20.7556	1.03648	0.518242	+	0.855234i	$0.326587\pi$
$402$	45.3351	2.26111
$403$	3.31248	0.165006
$404$	19.5171	0.971011
$405$	−21.5760	−1.07212
$406$	−60.3981	−2.99751
$407$	−16.1717	−0.801602
$408$	−2.26799	−0.112282
$409$	8.25625	0.408245	0.204123	−	0.978945i	$-0.434566\pi$
$409$	8.25625	0.408245	0.204123	+	0.978945i	$0.434566\pi$
$410$	44.2166	2.18370
$411$	−30.8023	−1.51936
$412$	−0.957029	−0.0471494
$413$	−4.07184	−0.200362
$414$	2.58769	0.127178
$415$	−4.16036	−0.204224
$416$	−10.3444	−0.507174
$417$	−32.1366	−1.57374
$418$	23.4031	1.14468
$419$	11.0088	0.537817	0.268909	−	0.963166i	$-0.413337\pi$
$419$	11.0088	0.537817	0.268909	+	0.963166i	$0.413337\pi$
$420$	22.2709	1.08671
$421$	3.47340	0.169283	0.0846417	−	0.996411i	$-0.473025\pi$
$421$	3.47340	0.169283	0.0846417	+	0.996411i	$0.473025\pi$
$422$	16.2030	0.788752
$423$	−1.70767	−0.0830296
$424$	−13.5849	−0.659743
$425$	2.39265	0.116061
$426$	10.3201	0.500010
$427$	−48.3487	−2.33976
$428$	11.7479	0.567854
$429$	−6.12061	−0.295506
$430$	−33.6585	−1.62316
$431$	20.5822	0.991409	0.495705	−	0.868491i	$-0.334910\pi$
$431$	20.5822	0.991409	0.495705	+	0.868491i	$0.334910\pi$
$432$	26.8924	1.29386
$433$	−5.75567	−0.276600	−0.138300	−	0.990390i	$-0.544164\pi$
$433$	−5.75567	−0.276600	−0.138300	+	0.990390i	$0.544164\pi$
$434$	14.3375	0.688223
$435$	−36.7385	−1.76148
$436$	11.2651	0.539503
$437$	26.4479	1.26517
$438$	−7.41596	−0.354348
$439$	−8.97531	−0.428368	−0.214184	−	0.976793i	$-0.568709\pi$
$439$	−8.97531	−0.428368	−0.214184	+	0.976793i	$0.568709\pi$
$440$	8.33296	0.397258
$441$	−3.07129	−0.146252
$442$	3.03759	0.144483
$443$	−1.43305	−0.0680862	−0.0340431	−	0.999420i	$-0.510838\pi$
$443$	−1.43305	−0.0680862	−0.0340431	+	0.999420i	$0.510838\pi$
$444$	14.7071	0.697966
$445$	10.5176	0.498582
$446$	−39.7510	−1.88227
$447$	12.9459	0.612322
$448$	−4.48224	−0.211766
$449$	14.8442	0.700539	0.350269	−	0.936649i	$-0.386090\pi$
$449$	14.8442	0.700539	0.350269	+	0.936649i	$0.386090\pi$
$450$	−1.37838	−0.0649773
$451$	−20.0185	−0.942636
$452$	24.2119	1.13883
$453$	7.80747	0.366827
$454$	−4.04328	−0.189760
$455$	18.7150	0.877375
$456$	13.3539	0.625356
$457$	−36.9423	−1.72809	−0.864044	−	0.503417i	$-0.832076\pi$
$457$	−36.9423	−1.72809	−0.864044	+	0.503417i	$0.832076\pi$
$458$	−23.3699	−1.09200
$459$	−5.43545	−0.253705
$460$	−15.0090	−0.699797
$461$	7.80164	0.363359	0.181679	−	0.983358i	$-0.441847\pi$
$461$	7.80164	0.363359	0.181679	+	0.983358i	$0.441847\pi$
$462$	−26.4921	−1.23252
$463$	39.6938	1.84473	0.922363	−	0.386325i	$-0.126256\pi$
$463$	39.6938	1.84473	0.922363	+	0.386325i	$0.126256\pi$
$464$	40.8410	1.89600
$465$	8.72113	0.404433
$466$	−8.95575	−0.414867
$467$	−21.2439	−0.983049	−0.491524	−	0.870864i	$-0.663560\pi$
$467$	−21.2439	−0.983049	−0.491524	+	0.870864i	$0.663560\pi$
$468$	−0.666018	−0.0307867
$469$	62.7591	2.89795
$470$	26.0240	1.20040
$471$	2.17080	0.100025
$472$	1.38555	0.0637752
$473$	15.2385	0.700667
$474$	−46.4716	−2.13451
$475$	−14.0879	−0.646399
$476$	5.00402	0.229359
$477$	−3.14336	−0.143925
$478$	−54.2764	−2.48254
$479$	35.9548	1.64282	0.821409	−	0.570340i	$-0.193189\pi$
$479$	35.9548	1.64282	0.821409	+	0.570340i	$0.193189\pi$
$480$	−27.2348	−1.24309
$481$	12.3589	0.563516
$482$	13.2073	0.601577
$483$	−29.9387	−1.36226
$484$	−7.50539	−0.341154
$485$	−16.0688	−0.729648
$486$	5.96026	0.270363
$487$	−26.0057	−1.17843	−0.589215	−	0.807977i	$-0.700563\pi$
$487$	−26.0057	−1.17843	−0.589215	+	0.807977i	$0.700563\pi$
$488$	16.4519	0.744742
$489$	11.2759	0.509914
$490$	46.8049	2.11443
$491$	6.99992	0.315902	0.157951	−	0.987447i	$-0.449511\pi$
$491$	6.99992	0.315902	0.157951	+	0.987447i	$0.449511\pi$
$492$	18.2055	0.820767
$493$	−8.25473	−0.371774
$494$	−17.8853	−0.804698
$495$	1.92813	0.0866629
$496$	−9.69499	−0.435318
$497$	14.2865	0.640838
$498$	−4.50069	−0.201681
$499$	−14.7888	−0.662038	−0.331019	−	0.943624i	$-0.607392\pi$
$499$	−14.7888	−0.662038	−0.331019	+	0.943624i	$0.607392\pi$
$500$	−8.71217	−0.389620
$501$	−26.6594	−1.19105
$502$	51.9681	2.31945
$503$	−25.6476	−1.14357	−0.571785	−	0.820403i	$-0.693749\pi$
$503$	−25.6476	−1.14357	−0.571785	+	0.820403i	$0.693749\pi$
$504$	1.80873	0.0805671
$505$	43.1805	1.92151
$506$	17.8537	0.793695
$507$	−16.6020	−0.737321
$508$	8.47369	0.375959
$509$	28.1015	1.24558	0.622788	−	0.782390i	$-0.286000\pi$
$509$	28.1015	1.24558	0.622788	+	0.782390i	$0.286000\pi$
$510$	7.99740	0.354131
$511$	−10.2662	−0.454150
$512$	16.5657	0.732106
$513$	32.0039	1.41301
$514$	28.7047	1.26611
$515$	−2.11738	−0.0933027
$516$	−13.8584	−0.610081
$517$	−11.7820	−0.518174
$518$	53.4934	2.35036
$519$	−18.5476	−0.814150
$520$	−6.36828	−0.279268
$521$	12.9461	0.567179	0.283590	−	0.958946i	$-0.408475\pi$
$521$	12.9461	0.567179	0.283590	+	0.958946i	$0.408475\pi$
$522$	4.75544	0.208140
$523$	28.6300	1.25190	0.625951	−	0.779862i	$-0.284711\pi$
$523$	28.6300	1.25190	0.625951	+	0.779862i	$0.284711\pi$
$524$	20.0706	0.876789
$525$	15.9474	0.696002
$526$	−26.4466	−1.15313
$527$	1.95954	0.0853588
$528$	17.9139	0.779601
$529$	−2.82347	−0.122760
$530$	47.9032	2.08078
$531$	0.320597	0.0139127
$532$	−29.4636	−1.27741
$533$	15.2987	0.662661
$534$	11.3780	0.492373
$535$	25.9915	1.12371
$536$	−21.3554	−0.922415
$537$	17.0664	0.736469
$538$	14.7695	0.636757
$539$	−21.1904	−0.912733
$540$	−18.1620	−0.781566
$541$	−21.1858	−0.910850	−0.455425	−	0.890274i	$-0.650513\pi$
$541$	−21.1858	−0.910850	−0.455425	+	0.890274i	$0.650513\pi$
$542$	41.6567	1.78931
$543$	−5.70573	−0.244856
$544$	−6.11933	−0.262364
$545$	24.9235	1.06761
$546$	20.2460	0.866448
$547$	9.03211	0.386185	0.193093	−	0.981181i	$-0.438148\pi$
$547$	9.03211	0.386185	0.193093	+	0.981181i	$0.438148\pi$
$548$	−23.1255	−0.987873
$549$	3.80673	0.162467
$550$	−9.51011	−0.405512
$551$	48.6038	2.07059
$552$	10.1874	0.433606
$553$	−64.3325	−2.73570
$554$	13.0994	0.556540
$555$	32.5386	1.38119
$556$	−24.1273	−1.02323
$557$	2.72819	0.115597	0.0577985	−	0.998328i	$-0.481592\pi$
$557$	2.72819	0.115597	0.0577985	+	0.998328i	$0.481592\pi$
$558$	−1.12886	−0.0477887
$559$	−11.6457	−0.492560
$560$	−54.7753	−2.31468
$561$	−3.62072	−0.152867
$562$	−5.04699	−0.212894
$563$	7.07448	0.298154	0.149077	−	0.988826i	$-0.452370\pi$
$563$	7.07448	0.298154	0.149077	+	0.988826i	$0.452370\pi$
$564$	10.7150	0.451181
$565$	53.5674	2.25360
$566$	−19.3964	−0.815292
$567$	−32.3118	−1.35697
$568$	−4.86136	−0.203978
$569$	17.9916	0.754247	0.377123	−	0.926163i	$-0.376913\pi$
$569$	17.9916	0.754247	0.377123	+	0.926163i	$0.376913\pi$
$570$	−47.0887	−1.97233
$571$	−38.8353	−1.62520	−0.812602	−	0.582818i	$-0.801950\pi$
$571$	−38.8353	−1.62520	−0.812602	+	0.582818i	$0.801950\pi$
$572$	−4.59519	−0.192134
$573$	−16.1906	−0.676373
$574$	66.2181	2.76389
$575$	−10.7474	−0.448197
$576$	0.352909	0.0147046
$577$	6.54940	0.272655	0.136328	−	0.990664i	$-0.456470\pi$
$577$	6.54940	0.272655	0.136328	+	0.990664i	$0.456470\pi$
$578$	1.79692	0.0747421
$579$	11.8256	0.491455
$580$	−27.5823	−1.14529
$581$	−6.23048	−0.258484
$582$	−17.3833	−0.720562
$583$	−21.6876	−0.898209
$584$	3.49335	0.144556
$585$	−1.47353	−0.0609229
$586$	−12.3635	−0.510732
$587$	−5.48596	−0.226430	−0.113215	−	0.993571i	$-0.536115\pi$
$587$	−5.48596	−0.226430	−0.113215	+	0.993571i	$0.536115\pi$
$588$	19.2712	0.794730
$589$	−11.5378	−0.475405
$590$	−4.88573	−0.201142
$591$	−33.5550	−1.38027
$592$	−36.1721	−1.48666
$593$	−8.10542	−0.332850	−0.166425	−	0.986054i	$-0.553222\pi$
$593$	−8.10542	−0.332850	−0.166425	+	0.986054i	$0.553222\pi$
$594$	21.6043	0.886437
$595$	11.0711	0.453871
$596$	9.71946	0.398124
$597$	16.6778	0.682576
$598$	−13.6443	−0.557958
$599$	−22.2244	−0.908066	−0.454033	−	0.890985i	$-0.650015\pi$
$599$	−22.2244	−0.908066	−0.454033	+	0.890985i	$0.650015\pi$
$600$	−5.42652	−0.221537
$601$	−4.00039	−0.163179	−0.0815896	−	0.996666i	$-0.526000\pi$
$601$	−4.00039	−0.163179	−0.0815896	+	0.996666i	$0.526000\pi$
$602$	−50.4065	−2.05441
$603$	−4.94134	−0.201227
$604$	5.86164	0.238507
$605$	−16.6053	−0.675100
$606$	46.7128	1.89758
$607$	−31.7289	−1.28783	−0.643917	−	0.765095i	$-0.722692\pi$
$607$	−31.7289	−1.28783	−0.643917	+	0.765095i	$0.722692\pi$
$608$	36.0306	1.46124
$609$	−55.0190	−2.22948
$610$	−58.0127	−2.34886
$611$	9.00417	0.364270
$612$	−0.393991	−0.0159261
$613$	−3.45888	−0.139703	−0.0698514	−	0.997557i	$-0.522253\pi$
$613$	−3.45888	−0.139703	−0.0698514	+	0.997557i	$0.522253\pi$
$614$	−38.0172	−1.53425
$615$	40.2787	1.62419
$616$	12.4793	0.502805
$617$	8.18688	0.329591	0.164796	−	0.986328i	$-0.447304\pi$
$617$	8.18688	0.329591	0.164796	+	0.986328i	$0.447304\pi$
$618$	−2.29058	−0.0921408
$619$	15.1888	0.610490	0.305245	−	0.952274i	$-0.401262\pi$
$619$	15.1888	0.610490	0.305245	+	0.952274i	$0.401262\pi$
$620$	6.54759	0.262957
$621$	24.4151	0.979744
$622$	−44.6330	−1.78962
$623$	15.7510	0.631050
$624$	−13.6903	−0.548050
$625$	−31.2385	−1.24954
$626$	−11.6998	−0.467617
$627$	21.3188	0.851392
$628$	1.62977	0.0650351
$629$	7.31104	0.291510
$630$	−6.37793	−0.254103
$631$	13.0722	0.520395	0.260197	−	0.965555i	$-0.416212\pi$
$631$	13.0722	0.520395	0.260197	+	0.965555i	$0.416212\pi$
$632$	21.8908	0.870770
$633$	14.7600	0.586657
$634$	38.9659	1.54753
$635$	18.7476	0.743975
$636$	19.7234	0.782084
$637$	16.1943	0.641640
$638$	32.8102	1.29897
$639$	−1.12485	−0.0444983
$640$	27.8981	1.10277
$641$	−6.83410	−0.269931	−0.134965	−	0.990850i	$-0.543092\pi$
$641$	−6.83410	−0.269931	−0.134965	+	0.990850i	$0.543092\pi$
$642$	28.1177	1.10972
$643$	−14.2456	−0.561793	−0.280896	−	0.959738i	$-0.590632\pi$
$643$	−14.2456	−0.561793	−0.280896	+	0.959738i	$0.590632\pi$
$644$	−22.4772	−0.885725
$645$	−30.6609	−1.20727
$646$	−10.5803	−0.416276
$647$	1.79230	0.0704625	0.0352312	−	0.999379i	$-0.488783\pi$
$647$	1.79230	0.0704625	0.0352312	+	0.999379i	$0.488783\pi$
$648$	10.9949	0.431922
$649$	2.21196	0.0868269
$650$	7.26789	0.285070
$651$	13.0606	0.511886
$652$	8.46563	0.331540
$653$	−35.3346	−1.38275	−0.691375	−	0.722496i	$-0.742995\pi$
$653$	−35.3346	−1.38275	−0.691375	+	0.722496i	$0.742995\pi$
$654$	26.9624	1.05431
$655$	44.4051	1.73505
$656$	−44.7764	−1.74823
$657$	0.808310	0.0315352
$658$	38.9731	1.51933
$659$	32.7099	1.27420	0.637099	−	0.770782i	$-0.280134\pi$
$659$	32.7099	1.27420	0.637099	+	0.770782i	$0.280134\pi$
$660$	−12.0983	−0.470924
$661$	−28.0095	−1.08944	−0.544721	−	0.838617i	$-0.683364\pi$
$661$	−28.0095	−1.08944	−0.544721	+	0.838617i	$0.683364\pi$
$662$	−31.8861	−1.23929
$663$	2.76706	0.107464
$664$	2.12008	0.0822752
$665$	−65.1867	−2.52783
$666$	−4.21180	−0.163204
$667$	37.0788	1.43570
$668$	−20.0152	−0.774410
$669$	−36.2108	−1.39999
$670$	75.3035	2.90923
$671$	26.2645	1.01393
$672$	−40.7863	−1.57337
$673$	−19.0433	−0.734065	−0.367033	−	0.930208i	$-0.619626\pi$
$673$	−19.0433	−0.734065	−0.367033	+	0.930208i	$0.619626\pi$
$674$	41.8512	1.61205
$675$	−13.0051	−0.500568
$676$	−12.4643	−0.479397
$677$	32.1601	1.23601	0.618006	−	0.786173i	$-0.287941\pi$
$677$	32.1601	1.23601	0.618006	+	0.786173i	$0.287941\pi$
$678$	57.9494	2.22553
$679$	−24.0644	−0.923508
$680$	−3.76724	−0.144467
$681$	−3.68318	−0.141140
$682$	−7.78860	−0.298241
$683$	−26.9291	−1.03041	−0.515207	−	0.857066i	$-0.672285\pi$
$683$	−26.9291	−1.03041	−0.515207	+	0.857066i	$0.672285\pi$
$684$	2.31982	0.0887005
$685$	−51.1640	−1.95487
$686$	18.8767	0.720717
$687$	−21.2885	−0.812208
$688$	34.0847	1.29947
$689$	16.5743	0.631430
$690$	−35.9229	−1.36756
$691$	8.13546	0.309487	0.154744	−	0.987955i	$-0.450545\pi$
$691$	8.13546	0.309487	0.154744	+	0.987955i	$0.450545\pi$
$692$	−13.9250	−0.529351
$693$	2.88753	0.109688
$694$	51.4903	1.95455
$695$	−53.3804	−2.02483
$696$	18.7217	0.709643
$697$	9.05015	0.342799
$698$	−5.14642	−0.194795
$699$	−8.15815	−0.308570
$700$	11.9729	0.452532
$701$	−11.9583	−0.451660	−0.225830	−	0.974167i	$-0.572509\pi$
$701$	−11.9583	−0.451660	−0.225830	+	0.974167i	$0.572509\pi$
$702$	−16.5106	−0.623154
$703$	−43.0474	−1.62356
$704$	2.43490	0.0917686
$705$	23.7063	0.892830
$706$	−9.86304	−0.371200
$707$	64.6664	2.43203
$708$	−2.01162	−0.0756014
$709$	41.0897	1.54316	0.771579	−	0.636134i	$-0.219467\pi$
$709$	41.0897	1.54316	0.771579	+	0.636134i	$0.219467\pi$
$710$	17.1421	0.643333
$711$	5.06522	0.189961
$712$	−5.35968	−0.200863
$713$	−8.80191	−0.329634
$714$	11.9768	0.448219
$715$	−10.1666	−0.380209
$716$	12.8130	0.478844
$717$	−49.4425	−1.84646
$718$	8.96324	0.334505
$719$	34.5244	1.28754	0.643771	−	0.765218i	$-0.277369\pi$
$719$	34.5244	1.28754	0.643771	+	0.765218i	$0.277369\pi$
$720$	4.31274	0.160726
$721$	−3.17095	−0.118092
$722$	28.1552	1.04783
$723$	12.0311	0.447440
$724$	−4.28371	−0.159203
$725$	−19.7507	−0.733523
$726$	−17.9636	−0.666693
$727$	21.1467	0.784289	0.392144	−	0.919904i	$-0.371733\pi$
$727$	21.1467	0.784289	0.392144	+	0.919904i	$0.371733\pi$
$728$	−9.53703	−0.353466
$729$	29.2357	1.08280
$730$	−12.3182	−0.455918
$731$	−6.88915	−0.254804
$732$	−23.8858	−0.882845
$733$	26.5523	0.980732	0.490366	−	0.871517i	$-0.336863\pi$
$733$	26.5523	0.980732	0.490366	+	0.871517i	$0.336863\pi$
$734$	−44.3479	−1.63691
$735$	42.6364	1.57267
$736$	27.4870	1.01318
$737$	−34.0928	−1.25582
$738$	−5.21368	−0.191918
$739$	−48.5380	−1.78550	−0.892750	−	0.450551i	$-0.851227\pi$
$739$	−48.5380	−1.78550	−0.892750	+	0.450551i	$0.851227\pi$
$740$	24.4291	0.898031
$741$	−16.2924	−0.598518
$742$	71.7391	2.63362
$743$	−5.99229	−0.219836	−0.109918	−	0.993941i	$-0.535059\pi$
$743$	−5.99229	−0.219836	−0.109918	+	0.993941i	$0.535059\pi$
$744$	−4.44422	−0.162933
$745$	21.5038	0.787837
$746$	59.1764	2.16660
$747$	0.490557	0.0179485
$748$	−2.71834	−0.0993924
$749$	38.9244	1.42227
$750$	−20.8520	−0.761407
$751$	−43.5091	−1.58767	−0.793834	−	0.608135i	$-0.791918\pi$
$751$	−43.5091	−1.58767	−0.793834	+	0.608135i	$0.791918\pi$
$752$	−26.3535	−0.961012
$753$	47.3398	1.72516
$754$	−25.0745	−0.913158
$755$	12.9686	0.471974
$756$	−27.1991	−0.989220
$757$	32.0804	1.16598	0.582990	−	0.812479i	$-0.301882\pi$
$757$	32.0804	1.16598	0.582990	+	0.812479i	$0.301882\pi$
$758$	37.0334	1.34511
$759$	16.2637	0.590334
$760$	22.1815	0.804607
$761$	−17.5216	−0.635159	−0.317579	−	0.948232i	$-0.602870\pi$
$761$	−17.5216	−0.635159	−0.317579	+	0.948232i	$0.602870\pi$
$762$	20.2812	0.734710
$763$	37.3251	1.35126
$764$	−12.1555	−0.439770
$765$	−0.871684	−0.0315158
$766$	−33.5483	−1.21215
$767$	−1.69044	−0.0610382
$768$	33.7840	1.21907
$769$	−20.8963	−0.753538	−0.376769	−	0.926307i	$-0.622965\pi$
$769$	−20.8963	−0.753538	−0.376769	+	0.926307i	$0.622965\pi$
$770$	−44.0045	−1.58581
$771$	26.1483	0.941708
$772$	8.87833	0.319538
$773$	−44.6535	−1.60608	−0.803038	−	0.595928i	$-0.796784\pi$
$773$	−44.6535	−1.60608	−0.803038	+	0.595928i	$0.796784\pi$
$774$	3.96875	0.142654
$775$	4.68849	0.168416
$776$	8.18855	0.293952
$777$	48.7292	1.74815
$778$	13.3268	0.477789
$779$	−53.2873	−1.90922
$780$	9.24583	0.331054
$781$	−7.76089	−0.277706
$782$	−8.07147	−0.288635
$783$	44.8681	1.60346
$784$	−47.3975	−1.69277
$785$	3.60579	0.128696
$786$	48.0376	1.71345
$787$	−50.4646	−1.79887	−0.899434	−	0.437057i	$-0.856021\pi$
$787$	−50.4646	−1.79887	−0.899434	+	0.437057i	$0.856021\pi$
$788$	−25.1922	−0.897435
$789$	−24.0913	−0.857672
$790$	−77.1914	−2.74635
$791$	80.2217	2.85235
$792$	−0.982558	−0.0349137
$793$	−20.0721	−0.712781
$794$	35.7092	1.26727
$795$	43.6370	1.54764
$796$	12.5212	0.443803
$797$	23.1203	0.818964	0.409482	−	0.912318i	$-0.365709\pi$
$797$	23.1203	0.818964	0.409482	+	0.912318i	$0.365709\pi$
$798$	−70.5192	−2.49635
$799$	5.32653	0.188439
$800$	−14.6414	−0.517653
$801$	−1.24015	−0.0438187
$802$	37.2962	1.31697
$803$	5.57693	0.196806
$804$	31.0050	1.09346
$805$	−49.7296	−1.75274
$806$	5.95227	0.209660
$807$	13.4541	0.473606
$808$	−22.0044	−0.774113
$809$	−10.4107	−0.366019	−0.183010	−	0.983111i	$-0.558584\pi$
$809$	−10.4107	−0.366019	−0.183010	+	0.983111i	$0.558584\pi$
$810$	−38.7704	−1.36225
$811$	−20.0461	−0.703915	−0.351958	−	0.936016i	$-0.614484\pi$
$811$	−20.0461	−0.703915	−0.351958	+	0.936016i	$0.614484\pi$
$812$	−41.3068	−1.44958
$813$	37.9467	1.33085
$814$	−29.0593	−1.01853
$815$	18.7298	0.656075
$816$	−8.09865	−0.283510
$817$	40.5633	1.41913
$818$	14.8358	0.518723
$819$	−2.20673	−0.0771095
$820$	30.2401	1.05603
$821$	28.6165	0.998722	0.499361	−	0.866394i	$-0.333568\pi$
$821$	28.6165	0.998722	0.499361	+	0.866394i	$0.333568\pi$
$822$	−55.3493	−1.93053
$823$	−8.48673	−0.295829	−0.147914	−	0.989000i	$-0.547256\pi$
$823$	−8.48673	−0.295829	−0.147914	+	0.989000i	$0.547256\pi$
$824$	1.07900	0.0375887
$825$	−8.66314	−0.301612
$826$	−7.31679	−0.254584
$827$	27.3880	0.952372	0.476186	−	0.879344i	$-0.342019\pi$
$827$	27.3880	0.952372	0.476186	+	0.879344i	$0.342019\pi$
$828$	1.76974	0.0615028
$829$	35.3449	1.22758	0.613789	−	0.789470i	$-0.289645\pi$
$829$	35.3449	1.22758	0.613789	+	0.789470i	$0.289645\pi$
$830$	−7.47584	−0.259490
$831$	11.9328	0.413943
$832$	−1.86082	−0.0645122
$833$	9.57992	0.331924
$834$	−57.7470	−1.99962
$835$	−44.2825	−1.53246
$836$	16.0056	0.553565
$837$	−10.6510	−0.368151
$838$	19.7820	0.683360
$839$	5.68193	0.196162	0.0980811	−	0.995178i	$-0.468730\pi$
$839$	5.68193	0.196162	0.0980811	+	0.995178i	$0.468730\pi$
$840$	−25.1092	−0.866350
$841$	39.1405	1.34967
$842$	6.24144	0.215094
$843$	−4.59750	−0.158346
$844$	11.0814	0.381437
$845$	−27.5767	−0.948666
$846$	−3.06855	−0.105499
$847$	−24.8678	−0.854467
$848$	−48.5098	−1.66583
$849$	−17.6690	−0.606398
$850$	4.29941	0.147469
$851$	−32.8400	−1.12574
$852$	7.05800	0.241803
$853$	17.4774	0.598415	0.299208	−	0.954188i	$-0.403278\pi$
$853$	17.4774	0.598415	0.299208	+	0.954188i	$0.403278\pi$
$854$	−86.8788	−2.97293
$855$	5.13248	0.175527
$856$	−13.2451	−0.452707
$857$	−57.8381	−1.97571	−0.987856	−	0.155372i	$-0.950342\pi$
$857$	−57.8381	−1.97571	−0.987856	+	0.155372i	$0.950342\pi$
$858$	−10.9983	−0.375475
$859$	−27.0792	−0.923930	−0.461965	−	0.886898i	$-0.652855\pi$
$859$	−27.0792	−0.923930	−0.461965	+	0.886898i	$0.652855\pi$
$860$	−23.0194	−0.784954
$861$	60.3207	2.05572
$862$	36.9846	1.25970
$863$	−51.0309	−1.73711	−0.868556	−	0.495591i	$-0.834951\pi$
$863$	−51.0309	−1.73711	−0.868556	+	0.495591i	$0.834951\pi$
$864$	33.2613	1.13157
$865$	−30.8084	−1.04752
$866$	−10.3425	−0.351452
$867$	1.63689	0.0555916
$868$	9.80555	0.332822
$869$	34.9475	1.18551
$870$	−66.0163	−2.23816
$871$	26.0546	0.882828
$872$	−12.7008	−0.430104
$873$	1.89471	0.0641263
$874$	47.5248	1.60755
$875$	−28.8662	−0.975857
$876$	−5.07184	−0.171362
$877$	−1.70516	−0.0575792	−0.0287896	−	0.999585i	$-0.509165\pi$
$877$	−1.70516	−0.0575792	−0.0287896	+	0.999585i	$0.509165\pi$
$878$	−16.1279	−0.544291
$879$	−11.2624	−0.379872
$880$	29.7557	1.00306
$881$	13.1344	0.442509	0.221255	−	0.975216i	$-0.428985\pi$
$881$	13.1344	0.442509	0.221255	+	0.975216i	$0.428985\pi$
$882$	−5.51887	−0.185830
$883$	−39.0606	−1.31449	−0.657246	−	0.753676i	$-0.728279\pi$
$883$	−39.0606	−1.31449	−0.657246	+	0.753676i	$0.728279\pi$
$884$	2.07743	0.0698716
$885$	−4.45061	−0.149606
$886$	−2.57508	−0.0865114
$887$	41.2251	1.38420	0.692102	−	0.721800i	$-0.256685\pi$
$887$	41.2251	1.38420	0.692102	+	0.721800i	$0.256685\pi$
$888$	−16.5814	−0.556435
$889$	28.0761	0.941641
$890$	18.8993	0.633506
$891$	17.5528	0.588041
$892$	−27.1861	−0.910257
$893$	−31.3626	−1.04951
$894$	23.2629	0.778026
$895$	28.3480	0.947570
$896$	41.7797	1.39576
$897$	−12.4292	−0.414997
$898$	26.6738	0.890116
$899$	−16.1754	−0.539481
$900$	−0.942684	−0.0314228
$901$	9.80472	0.326643
$902$	−35.9718	−1.19773
$903$	−45.9172	−1.52803
$904$	−27.2975	−0.907902
$905$	−9.47747	−0.315042
$906$	14.0294	0.466096
$907$	−41.1672	−1.36694	−0.683468	−	0.729981i	$-0.739529\pi$
$907$	−41.1672	−1.36694	−0.683468	+	0.729981i	$0.739529\pi$
$908$	−2.76523	−0.0917674
$909$	−5.09151	−0.168875
$910$	33.6295	1.11481
$911$	25.1465	0.833141	0.416570	−	0.909103i	$-0.363232\pi$
$911$	25.1465	0.833141	0.416570	+	0.909103i	$0.363232\pi$
$912$	47.6849	1.57900
$913$	3.38459	0.112014
$914$	−66.3824	−2.19574
$915$	−52.8461	−1.74704
$916$	−15.9828	−0.528088
$917$	66.5004	2.19604
$918$	−9.76708	−0.322362
$919$	13.4086	0.442308	0.221154	−	0.975239i	$-0.429018\pi$
$919$	13.4086	0.442308	0.221154	+	0.975239i	$0.429018\pi$
$920$	16.9218	0.557895
$921$	−34.6314	−1.14114
$922$	14.0189	0.461689
$923$	5.93109	0.195224
$924$	−18.1182	−0.596044
$925$	17.4928	0.575160
$926$	71.3266	2.34394
$927$	0.249664	0.00820006
$928$	50.5134	1.65818
$929$	−9.63501	−0.316114	−0.158057	−	0.987430i	$-0.550523\pi$
$929$	−9.63501	−0.316114	−0.158057	+	0.987430i	$0.550523\pi$
$930$	15.6712	0.513879
$931$	−56.4066	−1.84865
$932$	−6.12492	−0.200628
$933$	−40.6579	−1.33108
$934$	−38.1736	−1.24908
$935$	−6.01418	−0.196685
$936$	0.750898	0.0245439
$937$	7.44238	0.243132	0.121566	−	0.992583i	$-0.461208\pi$
$937$	7.44238	0.243132	0.121566	+	0.992583i	$0.461208\pi$
$938$	112.773	3.68218
$939$	−10.6578	−0.347804
$940$	17.7980	0.580508
$941$	−25.9644	−0.846416	−0.423208	−	0.906033i	$-0.639096\pi$
$941$	−25.9644	−0.846416	−0.423208	+	0.906033i	$0.639096\pi$
$942$	3.90075	0.127093
$943$	−40.6517	−1.32380
$944$	4.94759	0.161030
$945$	−60.1764	−1.95754
$946$	27.3824	0.890278
$947$	15.9321	0.517722	0.258861	−	0.965915i	$-0.416653\pi$
$947$	15.9321	0.517722	0.258861	+	0.965915i	$0.416653\pi$
$948$	−31.7824	−1.03224
$949$	−4.26205	−0.138352
$950$	−25.3149	−0.821325
$951$	35.4955	1.15102
$952$	−5.64175	−0.182850
$953$	−6.02315	−0.195109	−0.0975545	−	0.995230i	$-0.531102\pi$
$953$	−6.02315	−0.195109	−0.0975545	+	0.995230i	$0.531102\pi$
$954$	−5.64838	−0.182873
$955$	−26.8934	−0.870248
$956$	−37.1201	−1.20055
$957$	29.8881	0.966145
$958$	64.6080	2.08739
$959$	−76.6223	−2.47426
$960$	−4.89918	−0.158120
$961$	−27.1602	−0.876136
$962$	22.2079	0.716013
$963$	−3.06471	−0.0987590
$964$	9.03260	0.290920
$965$	19.6428	0.632325
$966$	−53.7976	−1.73091
$967$	25.0930	0.806937	0.403469	−	0.914994i	$-0.367804\pi$
$967$	25.0930	0.806937	0.403469	+	0.914994i	$0.367804\pi$
$968$	8.46191	0.271976
$969$	−9.63800	−0.309617
$970$	−28.8745	−0.927103
$971$	40.4530	1.29820	0.649099	−	0.760704i	$-0.275146\pi$
$971$	40.4530	1.29820	0.649099	+	0.760704i	$0.275146\pi$
$972$	4.07628	0.130747
$973$	−79.9415	−2.56281
$974$	−46.7302	−1.49733
$975$	6.62061	0.212029
$976$	58.7472	1.88045
$977$	−28.9656	−0.926691	−0.463346	−	0.886178i	$-0.653351\pi$
$977$	−28.9656	−0.926691	−0.463346	+	0.886178i	$0.653351\pi$
$978$	20.2619	0.647904
$979$	−8.55643	−0.273465
$980$	32.0103	1.02253
$981$	−2.93879	−0.0938283
$982$	12.5783	0.401390
$983$	2.03060	0.0647661	0.0323830	−	0.999476i	$-0.489690\pi$
$983$	2.03060	0.0647661	0.0323830	+	0.999476i	$0.489690\pi$
$984$	−20.5257	−0.654335
$985$	−55.7364	−1.77591
$986$	−14.8331	−0.472382
$987$	35.5021	1.13005
$988$	−12.2319	−0.389149
$989$	30.9449	0.983990
$990$	3.46469	0.110115
$991$	−48.8086	−1.55046	−0.775228	−	0.631681i	$-0.782365\pi$
$991$	−48.8086	−1.55046	−0.775228	+	0.631681i	$0.782365\pi$
$992$	−11.9911	−0.380717
$993$	−29.0463	−0.921757
$994$	25.6718	0.814259
$995$	27.7025	0.878229
$996$	−3.07806	−0.0975320
$997$	−12.7087	−0.402488	−0.201244	−	0.979541i	$-0.564498\pi$
$997$	−12.7087	−0.402488	−0.201244	+	0.979541i	$0.564498\pi$
$998$	−26.5743	−0.841196
$999$	−39.7388	−1.25728

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1003.2.a.i.1.14	✓	18
3.2	odd	2		9027.2.a.q.1.5		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1003.2.a.i.1.14	✓	18	1.1	even	1	trivial
9027.2.a.q.1.5		18	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1003 = 17 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1003.a (trivial)

\(f(q)\)	\(=\)	\(q+1.79692 q^{2} +1.63689 q^{3} +1.22893 q^{4} +2.71894 q^{5} +2.94136 q^{6} +4.07184 q^{7} -1.38555 q^{8} -0.320597 q^{9} +O(q^{10})\)	\(q+1.79692 q^{2} +1.63689 q^{3} +1.22893 q^{4} +2.71894 q^{5} +2.94136 q^{6} +4.07184 q^{7} -1.38555 q^{8} -0.320597 q^{9} +4.88573 q^{10} -2.21196 q^{11} +2.01162 q^{12} +1.69044 q^{13} +7.31679 q^{14} +4.45061 q^{15} -4.94759 q^{16} +1.00000 q^{17} -0.576087 q^{18} -5.88800 q^{19} +3.34139 q^{20} +6.66515 q^{21} -3.97471 q^{22} -4.49183 q^{23} -2.26799 q^{24} +2.39265 q^{25} +3.03759 q^{26} -5.43545 q^{27} +5.00402 q^{28} -8.25473 q^{29} +7.99740 q^{30} +1.95954 q^{31} -6.11933 q^{32} -3.62072 q^{33} +1.79692 q^{34} +11.0711 q^{35} -0.393991 q^{36} +7.31104 q^{37} -10.5803 q^{38} +2.76706 q^{39} -3.76724 q^{40} +9.05015 q^{41} +11.9768 q^{42} -6.88915 q^{43} -2.71834 q^{44} -0.871684 q^{45} -8.07147 q^{46} +5.32653 q^{47} -8.09865 q^{48} +9.57992 q^{49} +4.29941 q^{50} +1.63689 q^{51} +2.07743 q^{52} +9.80472 q^{53} -9.76708 q^{54} -6.01418 q^{55} -5.64175 q^{56} -9.63800 q^{57} -14.8331 q^{58} -1.00000 q^{59} +5.46949 q^{60} -11.8739 q^{61} +3.52114 q^{62} -1.30542 q^{63} -1.10079 q^{64} +4.59621 q^{65} -6.50616 q^{66} +15.4130 q^{67} +1.22893 q^{68} -7.35262 q^{69} +19.8939 q^{70} +3.50861 q^{71} +0.444203 q^{72} -2.52127 q^{73} +13.1374 q^{74} +3.91651 q^{75} -7.23595 q^{76} -9.00674 q^{77} +4.97219 q^{78} -15.7994 q^{79} -13.4522 q^{80} -7.93543 q^{81} +16.2624 q^{82} -1.53014 q^{83} +8.19101 q^{84} +2.71894 q^{85} -12.3793 q^{86} -13.5121 q^{87} +3.06478 q^{88} +3.86827 q^{89} -1.56635 q^{90} +6.88320 q^{91} -5.52015 q^{92} +3.20754 q^{93} +9.57136 q^{94} -16.0091 q^{95} -10.0167 q^{96} -5.90996 q^{97} +17.2144 q^{98} +0.709146 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 5 q^{2} + q^{3} + 21 q^{4} + 21 q^{5} + 5 q^{6} - q^{7} + 9 q^{8} + 17 q^{9}+O(q^{10}) \) 18 * q + 5 * q^2 + q^3 + 21 * q^4 + 21 * q^5 + 5 * q^6 - q^7 + 9 * q^8 + 17 * q^9	\( 18 q + 5 q^{2} + q^{3} + 21 q^{4} + 21 q^{5} + 5 q^{6} - q^{7} + 9 q^{8} + 17 q^{9} + 10 q^{10} + 6 q^{11} + 20 q^{12} + 12 q^{13} + 9 q^{14} - q^{15} + 19 q^{16} + 18 q^{17} + 10 q^{18} - 14 q^{19} + 17 q^{20} - 14 q^{21} - 4 q^{22} + 7 q^{23} - 3 q^{24} + 35 q^{25} + 3 q^{26} + 13 q^{27} + q^{28} + 23 q^{29} + 17 q^{30} - q^{31} + 13 q^{32} + 7 q^{33} + 5 q^{34} + 5 q^{35} - 16 q^{36} + 36 q^{37} - 19 q^{38} + 8 q^{39} - 4 q^{40} + 37 q^{41} + 9 q^{42} - 15 q^{43} - 9 q^{44} + 17 q^{45} + q^{46} + 23 q^{47} + 17 q^{48} + 15 q^{49} + 32 q^{50} + q^{51} - 11 q^{52} + 35 q^{53} - 17 q^{54} - 6 q^{55} + 37 q^{56} - 16 q^{57} + 2 q^{58} - 18 q^{59} - 6 q^{60} + 39 q^{61} - q^{62} + 15 q^{63} + 5 q^{64} + 15 q^{65} - 36 q^{66} + 14 q^{67} + 21 q^{68} + 16 q^{69} - 45 q^{70} + 3 q^{71} - 71 q^{72} + 56 q^{73} - 27 q^{74} + 16 q^{75} - q^{76} + 39 q^{77} - 71 q^{78} - 22 q^{79} + 45 q^{80} - 18 q^{81} + 5 q^{82} + 12 q^{83} + 2 q^{84} + 21 q^{85} + 4 q^{86} + 8 q^{87} - 18 q^{88} + 34 q^{89} + 48 q^{90} + 3 q^{91} + 67 q^{92} - 19 q^{93} - 38 q^{94} - 72 q^{95} + 6 q^{96} + 31 q^{97} + 19 q^{98} + 44 q^{99}+O(q^{100}) \) 18 * q + 5 * q^2 + q^3 + 21 * q^4 + 21 * q^5 + 5 * q^6 - q^7 + 9 * q^8 + 17 * q^9 + 10 * q^10 + 6 * q^11 + 20 * q^12 + 12 * q^13 + 9 * q^14 - q^15 + 19 * q^16 + 18 * q^17 + 10 * q^18 - 14 * q^19 + 17 * q^20 - 14 * q^21 - 4 * q^22 + 7 * q^23 - 3 * q^24 + 35 * q^25 + 3 * q^26 + 13 * q^27 + q^28 + 23 * q^29 + 17 * q^30 - q^31 + 13 * q^32 + 7 * q^33 + 5 * q^34 + 5 * q^35 - 16 * q^36 + 36 * q^37 - 19 * q^38 + 8 * q^39 - 4 * q^40 + 37 * q^41 + 9 * q^42 - 15 * q^43 - 9 * q^44 + 17 * q^45 + q^46 + 23 * q^47 + 17 * q^48 + 15 * q^49 + 32 * q^50 + q^51 - 11 * q^52 + 35 * q^53 - 17 * q^54 - 6 * q^55 + 37 * q^56 - 16 * q^57 + 2 * q^58 - 18 * q^59 - 6 * q^60 + 39 * q^61 - q^62 + 15 * q^63 + 5 * q^64 + 15 * q^65 - 36 * q^66 + 14 * q^67 + 21 * q^68 + 16 * q^69 - 45 * q^70 + 3 * q^71 - 71 * q^72 + 56 * q^73 - 27 * q^74 + 16 * q^75 - q^76 + 39 * q^77 - 71 * q^78 - 22 * q^79 + 45 * q^80 - 18 * q^81 + 5 * q^82 + 12 * q^83 + 2 * q^84 + 21 * q^85 + 4 * q^86 + 8 * q^87 - 18 * q^88 + 34 * q^89 + 48 * q^90 + 3 * q^91 + 67 * q^92 - 19 * q^93 - 38 * q^94 - 72 * q^95 + 6 * q^96 + 31 * q^97 + 19 * q^98 + 44 * q^99

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