LMFDB - Embedded newform 1003.2.a.i.1.2

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			1.2
Root			$-2.46111$ of defining polynomial
Character	$\chi$	$=$	1003.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.46111 q^{2} +2.84715 q^{3} +4.05705 q^{4} -0.414665 q^{5} -7.00714 q^{6} -0.439244 q^{7} -5.06262 q^{8} +5.10626 q^{9} +O(q^{10})$	\(q-2.46111 q^{2} +2.84715 q^{3} +4.05705 q^{4} -0.414665 q^{5} -7.00714 q^{6} -0.439244 q^{7} -5.06262 q^{8} +5.10626 q^{9} +1.02054 q^{10} +4.90924 q^{11} +11.5510 q^{12} -0.372782 q^{13} +1.08103 q^{14} -1.18061 q^{15} +4.34556 q^{16} +1.00000 q^{17} -12.5671 q^{18} -1.13847 q^{19} -1.68232 q^{20} -1.25059 q^{21} -12.0822 q^{22} +2.97744 q^{23} -14.4140 q^{24} -4.82805 q^{25} +0.917456 q^{26} +5.99685 q^{27} -1.78204 q^{28} +5.04031 q^{29} +2.90562 q^{30} +0.227163 q^{31} -0.569638 q^{32} +13.9774 q^{33} -2.46111 q^{34} +0.182139 q^{35} +20.7164 q^{36} +11.6156 q^{37} +2.80190 q^{38} -1.06137 q^{39} +2.09929 q^{40} -3.23522 q^{41} +3.07785 q^{42} -4.66150 q^{43} +19.9171 q^{44} -2.11739 q^{45} -7.32780 q^{46} +7.42089 q^{47} +12.3725 q^{48} -6.80706 q^{49} +11.8824 q^{50} +2.84715 q^{51} -1.51239 q^{52} +1.45997 q^{53} -14.7589 q^{54} -2.03569 q^{55} +2.22373 q^{56} -3.24140 q^{57} -12.4047 q^{58} -1.00000 q^{59} -4.78981 q^{60} -5.65168 q^{61} -0.559073 q^{62} -2.24290 q^{63} -7.28917 q^{64} +0.154580 q^{65} -34.3998 q^{66} +6.82127 q^{67} +4.05705 q^{68} +8.47722 q^{69} -0.448264 q^{70} +6.93924 q^{71} -25.8511 q^{72} -1.80317 q^{73} -28.5873 q^{74} -13.7462 q^{75} -4.61883 q^{76} -2.15636 q^{77} +2.61213 q^{78} -6.29048 q^{79} -1.80195 q^{80} +1.75514 q^{81} +7.96223 q^{82} +2.38111 q^{83} -5.07372 q^{84} -0.414665 q^{85} +11.4725 q^{86} +14.3505 q^{87} -24.8536 q^{88} +2.94587 q^{89} +5.21112 q^{90} +0.163742 q^{91} +12.0796 q^{92} +0.646767 q^{93} -18.2636 q^{94} +0.472084 q^{95} -1.62184 q^{96} +7.33401 q^{97} +16.7529 q^{98} +25.0679 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 5 q^{2} + q^{3} + 21 q^{4} + 21 q^{5} + 5 q^{6} - q^{7} + 9 q^{8} + 17 q^{9}+O(q^{10}) $ 18 * q + 5 * q^2 + q^3 + 21 * q^4 + 21 * q^5 + 5 * q^6 - q^7 + 9 * q^8 + 17 * q^9	\( 18 q + 5 q^{2} + q^{3} + 21 q^{4} + 21 q^{5} + 5 q^{6} - q^{7} + 9 q^{8} + 17 q^{9} + 10 q^{10} + 6 q^{11} + 20 q^{12} + 12 q^{13} + 9 q^{14} - q^{15} + 19 q^{16} + 18 q^{17} + 10 q^{18} - 14 q^{19} + 17 q^{20} - 14 q^{21} - 4 q^{22} + 7 q^{23} - 3 q^{24} + 35 q^{25} + 3 q^{26} + 13 q^{27} + q^{28} + 23 q^{29} + 17 q^{30} - q^{31} + 13 q^{32} + 7 q^{33} + 5 q^{34} + 5 q^{35} - 16 q^{36} + 36 q^{37} - 19 q^{38} + 8 q^{39} - 4 q^{40} + 37 q^{41} + 9 q^{42} - 15 q^{43} - 9 q^{44} + 17 q^{45} + q^{46} + 23 q^{47} + 17 q^{48} + 15 q^{49} + 32 q^{50} + q^{51} - 11 q^{52} + 35 q^{53} - 17 q^{54} - 6 q^{55} + 37 q^{56} - 16 q^{57} + 2 q^{58} - 18 q^{59} - 6 q^{60} + 39 q^{61} - q^{62} + 15 q^{63} + 5 q^{64} + 15 q^{65} - 36 q^{66} + 14 q^{67} + 21 q^{68} + 16 q^{69} - 45 q^{70} + 3 q^{71} - 71 q^{72} + 56 q^{73} - 27 q^{74} + 16 q^{75} - q^{76} + 39 q^{77} - 71 q^{78} - 22 q^{79} + 45 q^{80} - 18 q^{81} + 5 q^{82} + 12 q^{83} + 2 q^{84} + 21 q^{85} + 4 q^{86} + 8 q^{87} - 18 q^{88} + 34 q^{89} + 48 q^{90} + 3 q^{91} + 67 q^{92} - 19 q^{93} - 38 q^{94} - 72 q^{95} + 6 q^{96} + 31 q^{97} + 19 q^{98} + 44 q^{99}+O(q^{100}) \) 18 * q + 5 * q^2 + q^3 + 21 * q^4 + 21 * q^5 + 5 * q^6 - q^7 + 9 * q^8 + 17 * q^9 + 10 * q^10 + 6 * q^11 + 20 * q^12 + 12 * q^13 + 9 * q^14 - q^15 + 19 * q^16 + 18 * q^17 + 10 * q^18 - 14 * q^19 + 17 * q^20 - 14 * q^21 - 4 * q^22 + 7 * q^23 - 3 * q^24 + 35 * q^25 + 3 * q^26 + 13 * q^27 + q^28 + 23 * q^29 + 17 * q^30 - q^31 + 13 * q^32 + 7 * q^33 + 5 * q^34 + 5 * q^35 - 16 * q^36 + 36 * q^37 - 19 * q^38 + 8 * q^39 - 4 * q^40 + 37 * q^41 + 9 * q^42 - 15 * q^43 - 9 * q^44 + 17 * q^45 + q^46 + 23 * q^47 + 17 * q^48 + 15 * q^49 + 32 * q^50 + q^51 - 11 * q^52 + 35 * q^53 - 17 * q^54 - 6 * q^55 + 37 * q^56 - 16 * q^57 + 2 * q^58 - 18 * q^59 - 6 * q^60 + 39 * q^61 - q^62 + 15 * q^63 + 5 * q^64 + 15 * q^65 - 36 * q^66 + 14 * q^67 + 21 * q^68 + 16 * q^69 - 45 * q^70 + 3 * q^71 - 71 * q^72 + 56 * q^73 - 27 * q^74 + 16 * q^75 - q^76 + 39 * q^77 - 71 * q^78 - 22 * q^79 + 45 * q^80 - 18 * q^81 + 5 * q^82 + 12 * q^83 + 2 * q^84 + 21 * q^85 + 4 * q^86 + 8 * q^87 - 18 * q^88 + 34 * q^89 + 48 * q^90 + 3 * q^91 + 67 * q^92 - 19 * q^93 - 38 * q^94 - 72 * q^95 + 6 * q^96 + 31 * q^97 + 19 * q^98 + 44 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.46111	−1.74027	−0.870133	−	0.492817i	$-0.835967\pi$
$2$	−2.46111	−1.74027	−0.870133	+	0.492817i	$0.835967\pi$
$3$	2.84715	1.64380	0.821901	−	0.569630i	$-0.192913\pi$
$3$	2.84715	1.64380	0.821901	+	0.569630i	$0.192913\pi$
$4$	4.05705	2.02853
$5$	−0.414665	−0.185444	−0.0927220	−	0.995692i	$-0.529557\pi$
$5$	−0.414665	−0.185444	−0.0927220	+	0.995692i	$0.529557\pi$
$6$	−7.00714	−2.86065
$7$	−0.439244	−0.166019	−0.0830093	−	0.996549i	$-0.526453\pi$
$7$	−0.439244	−0.166019	−0.0830093	+	0.996549i	$0.526453\pi$
$8$	−5.06262	−1.78991
$9$	5.10626	1.70209
$10$	1.02054	0.322722
$11$	4.90924	1.48019	0.740096	−	0.672501i	$-0.234780\pi$
$11$	4.90924	1.48019	0.740096	+	0.672501i	$0.234780\pi$
$12$	11.5510	3.33450
$13$	−0.372782	−0.103391	−0.0516955	−	0.998663i	$-0.516463\pi$
$13$	−0.372782	−0.103391	−0.0516955	+	0.998663i	$0.516463\pi$
$14$	1.08103	0.288917
$15$	−1.18061	−0.304833
$16$	4.34556	1.08639
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−12.5671	−2.96209
$19$	−1.13847	−0.261183	−0.130592	−	0.991436i	$-0.541688\pi$
$19$	−1.13847	−0.261183	−0.130592	+	0.991436i	$0.541688\pi$
$20$	−1.68232	−0.376178
$21$	−1.25059	−0.272902
$22$	−12.0822	−2.57593
$23$	2.97744	0.620840	0.310420	−	0.950600i	$-0.399530\pi$
$23$	2.97744	0.620840	0.310420	+	0.950600i	$0.399530\pi$
$24$	−14.4140	−2.94225
$25$	−4.82805	−0.965611
$26$	0.917456	0.179928
$27$	5.99685	1.15409
$28$	−1.78204	−0.336773
$29$	5.04031	0.935962	0.467981	−	0.883739i	$-0.344982\pi$
$29$	5.04031	0.935962	0.467981	+	0.883739i	$0.344982\pi$
$30$	2.90562	0.530491
$31$	0.227163	0.0407997	0.0203998	−	0.999792i	$-0.493506\pi$
$31$	0.227163	0.0407997	0.0203998	+	0.999792i	$0.493506\pi$
$32$	−0.569638	−0.100699
$33$	13.9774	2.43315
$34$	−2.46111	−0.422076
$35$	0.182139	0.0307872
$36$	20.7164	3.45273
$37$	11.6156	1.90960	0.954798	−	0.297255i	$-0.0960713\pi$
$37$	11.6156	1.90960	0.954798	+	0.297255i	$0.0960713\pi$
$38$	2.80190	0.454528
$39$	−1.06137	−0.169955
$40$	2.09929	0.331927
$41$	−3.23522	−0.505257	−0.252628	−	0.967563i	$-0.581295\pi$
$41$	−3.23522	−0.505257	−0.252628	+	0.967563i	$0.581295\pi$
$42$	3.07785	0.474922
$43$	−4.66150	−0.710872	−0.355436	−	0.934701i	$-0.615668\pi$
$43$	−4.66150	−0.710872	−0.355436	+	0.934701i	$0.615668\pi$
$44$	19.9171	3.00261
$45$	−2.11739	−0.315642
$46$	−7.32780	−1.08043
$47$	7.42089	1.08245	0.541224	−	0.840879i	$-0.317961\pi$
$47$	7.42089	1.08245	0.541224	+	0.840879i	$0.317961\pi$
$48$	12.3725	1.78581
$49$	−6.80706	−0.972438
$50$	11.8824	1.68042
$51$	2.84715	0.398681
$52$	−1.51239	−0.209731
$53$	1.45997	0.200543	0.100271	−	0.994960i	$-0.468029\pi$
$53$	1.45997	0.200543	0.100271	+	0.994960i	$0.468029\pi$
$54$	−14.7589	−2.00843
$55$	−2.03569	−0.274493
$56$	2.22373	0.297158
$57$	−3.24140	−0.429334
$58$	−12.4047	−1.62882
$59$	−1.00000	−0.130189
$59$	−1.00000	−0.130189
$60$	−4.78981	−0.618362
$61$	−5.65168	−0.723623	−0.361811	−	0.932251i	$-0.617842\pi$
$61$	−5.65168	−0.723623	−0.361811	+	0.932251i	$0.617842\pi$
$62$	−0.559073	−0.0710023
$63$	−2.24290	−0.282578
$64$	−7.28917	−0.911147
$65$	0.154580	0.0191732
$66$	−34.3998	−4.23432
$67$	6.82127	0.833351	0.416676	−	0.909055i	$-0.363195\pi$
$67$	6.82127	0.833351	0.416676	+	0.909055i	$0.363195\pi$
$68$	4.05705	0.491990
$69$	8.47722	1.02054
$70$	−0.448264	−0.0535778
$71$	6.93924	0.823537	0.411768	−	0.911289i	$-0.364911\pi$
$71$	6.93924	0.823537	0.411768	+	0.911289i	$0.364911\pi$
$72$	−25.8511	−3.04658
$73$	−1.80317	−0.211045	−0.105523	−	0.994417i	$-0.533652\pi$
$73$	−1.80317	−0.211045	−0.105523	+	0.994417i	$0.533652\pi$
$74$	−28.5873	−3.32320
$75$	−13.7462	−1.58727
$76$	−4.61883	−0.529817
$77$	−2.15636	−0.245740
$78$	2.61213	0.295766
$79$	−6.29048	−0.707734	−0.353867	−	0.935296i	$-0.615134\pi$
$79$	−6.29048	−0.707734	−0.353867	+	0.935296i	$0.615134\pi$
$80$	−1.80195	−0.201464
$81$	1.75514	0.195015
$82$	7.96223	0.879281
$83$	2.38111	0.261361	0.130680	−	0.991425i	$-0.458284\pi$
$83$	2.38111	0.261361	0.130680	+	0.991425i	$0.458284\pi$
$84$	−5.07372	−0.553588
$85$	−0.414665	−0.0449768
$86$	11.4725	1.23711
$87$	14.3505	1.53854
$88$	−24.8536	−2.64941
$89$	2.94587	0.312262	0.156131	−	0.987736i	$-0.450098\pi$
$89$	2.94587	0.312262	0.156131	+	0.987736i	$0.450098\pi$
$90$	5.21112	0.549301
$91$	0.163742	0.0171648
$92$	12.0796	1.25939
$93$	0.646767	0.0670666
$94$	−18.2636	−1.88375
$95$	0.472084	0.0484348
$96$	−1.62184	−0.165529
$97$	7.33401	0.744656	0.372328	−	0.928101i	$-0.378560\pi$
$97$	7.33401	0.744656	0.372328	+	0.928101i	$0.378560\pi$
$98$	16.7529	1.69230
$99$	25.0679	2.51942
$100$	−19.5877	−1.95877
$101$	3.18475	0.316895	0.158447	−	0.987367i	$-0.449351\pi$
$101$	3.18475	0.316895	0.158447	+	0.987367i	$0.449351\pi$
$102$	−7.00714	−0.693810
$103$	12.5911	1.24064	0.620321	−	0.784348i	$-0.287002\pi$
$103$	12.5911	1.24064	0.620321	+	0.784348i	$0.287002\pi$
$104$	1.88725	0.185060
$105$	0.518578	0.0506080
$106$	−3.59315	−0.348998
$107$	−9.10169	−0.879894	−0.439947	−	0.898024i	$-0.645003\pi$
$107$	−9.10169	−0.879894	−0.439947	+	0.898024i	$0.645003\pi$
$108$	24.3295	2.34111
$109$	−14.8467	−1.42206	−0.711030	−	0.703162i	$-0.751771\pi$
$109$	−14.8467	−1.42206	−0.711030	+	0.703162i	$0.751771\pi$
$110$	5.01006	0.477690
$111$	33.0714	3.13900
$112$	−1.90876	−0.180361
$113$	−8.66928	−0.815538	−0.407769	−	0.913085i	$-0.633693\pi$
$113$	−8.66928	−0.815538	−0.407769	+	0.913085i	$0.633693\pi$
$114$	7.97743	0.747154
$115$	−1.23464	−0.115131
$116$	20.4488	1.89862
$117$	−1.90352	−0.175981
$118$	2.46111	0.226563
$119$	−0.439244	−0.0402654
$120$	5.97700	0.545623
$121$	13.1007	1.19097
$122$	13.9094	1.25930
$123$	−9.21116	−0.830542
$124$	0.921612	0.0827632
$125$	4.07535	0.364511
$126$	5.52001	0.491761
$127$	12.1211	1.07558	0.537788	−	0.843080i	$-0.319260\pi$
$127$	12.1211	1.07558	0.537788	+	0.843080i	$0.319260\pi$
$128$	19.0787	1.68634
$129$	−13.2720	−1.16853
$130$	−0.380437	−0.0333665
$131$	−18.5888	−1.62411	−0.812056	−	0.583580i	$-0.801651\pi$
$131$	−18.5888	−1.62411	−0.812056	+	0.583580i	$0.801651\pi$
$132$	56.7068	4.93570
$133$	0.500067	0.0433613
$134$	−16.7879	−1.45025
$135$	−2.48668	−0.214020
$136$	−5.06262	−0.434116
$137$	10.4264	0.890784	0.445392	−	0.895336i	$-0.353064\pi$
$137$	10.4264	0.890784	0.445392	+	0.895336i	$0.353064\pi$
$138$	−20.8634	−1.77601
$139$	2.49442	0.211574	0.105787	−	0.994389i	$-0.466264\pi$
$139$	2.49442	0.211574	0.105787	+	0.994389i	$0.466264\pi$
$140$	0.738948	0.0624525
$141$	21.1284	1.77933
$142$	−17.0782	−1.43317
$143$	−1.83008	−0.153039
$144$	22.1896	1.84913
$145$	−2.09004	−0.173568
$146$	4.43780	0.367275
$147$	−19.3807	−1.59850
$148$	47.1251	3.87366
$149$	20.3450	1.66672	0.833362	−	0.552728i	$-0.186413\pi$
$149$	20.3450	1.66672	0.833362	+	0.552728i	$0.186413\pi$
$150$	33.8309	2.76228
$151$	−4.16391	−0.338854	−0.169427	−	0.985543i	$-0.554192\pi$
$151$	−4.16391	−0.338854	−0.169427	+	0.985543i	$0.554192\pi$
$152$	5.76365	0.467494
$153$	5.10626	0.412817
$154$	5.30702	0.427652
$155$	−0.0941966	−0.00756605
$156$	−4.30601	−0.344757
$157$	−10.8608	−0.866787	−0.433393	−	0.901205i	$-0.642684\pi$
$157$	−10.8608	−0.866787	−0.433393	+	0.901205i	$0.642684\pi$
$158$	15.4816	1.23165
$159$	4.15676	0.329653
$160$	0.236209	0.0186740
$161$	−1.30782	−0.103071
$162$	−4.31958	−0.339378
$163$	1.38529	0.108504	0.0542520	−	0.998527i	$-0.482723\pi$
$163$	1.38529	0.108504	0.0542520	+	0.998527i	$0.482723\pi$
$164$	−13.1255	−1.02493
$165$	−5.79592	−0.451212
$166$	−5.86017	−0.454837
$167$	9.55539	0.739419	0.369709	−	0.929147i	$-0.379457\pi$
$167$	9.55539	0.739419	0.369709	+	0.929147i	$0.379457\pi$
$168$	6.33128	0.488469
$169$	−12.8610	−0.989310
$170$	1.02054	0.0782715
$171$	−5.81333	−0.444557
$172$	−18.9119	−1.44202
$173$	19.9782	1.51891	0.759456	−	0.650558i	$-0.225465\pi$
$173$	19.9782	1.51891	0.759456	+	0.650558i	$0.225465\pi$
$174$	−35.3182	−2.67746
$175$	2.12069	0.160309
$176$	21.3334	1.60807
$177$	−2.84715	−0.214005
$178$	−7.25010	−0.543418
$179$	−5.32071	−0.397689	−0.198844	−	0.980031i	$-0.563719\pi$
$179$	−5.32071	−0.397689	−0.198844	+	0.980031i	$0.563719\pi$
$180$	−8.59036	−0.640288
$181$	9.90999	0.736604	0.368302	−	0.929706i	$-0.379939\pi$
$181$	9.90999	0.736604	0.368302	+	0.929706i	$0.379939\pi$
$182$	−0.402987	−0.0298714
$183$	−16.0912	−1.18949
$184$	−15.0737	−1.11125
$185$	−4.81659	−0.354123
$186$	−1.59176	−0.116714
$187$	4.90924	0.358999
$188$	30.1069	2.19577
$189$	−2.63408	−0.191601
$190$	−1.16185	−0.0842895
$191$	13.7274	0.993276	0.496638	−	0.867958i	$-0.334568\pi$
$191$	13.7274	0.993276	0.496638	+	0.867958i	$0.334568\pi$
$192$	−20.7534	−1.49775
$193$	−13.6741	−0.984282	−0.492141	−	0.870515i	$-0.663786\pi$
$193$	−13.6741	−0.984282	−0.492141	+	0.870515i	$0.663786\pi$
$194$	−18.0498	−1.29590
$195$	0.440111	0.0315170
$196$	−27.6166	−1.97261
$197$	−24.1485	−1.72051	−0.860256	−	0.509862i	$-0.829696\pi$
$197$	−24.1485	−1.72051	−0.860256	+	0.509862i	$0.829696\pi$
$198$	−61.6948	−4.38446
$199$	−22.8277	−1.61822	−0.809108	−	0.587660i	$-0.800049\pi$
$199$	−22.8277	−1.61822	−0.809108	+	0.587660i	$0.800049\pi$
$200$	24.4426	1.72835
$201$	19.4212	1.36986
$202$	−7.83802	−0.551481
$203$	−2.21393	−0.155387
$204$	11.5510	0.808734
$205$	1.34153	0.0936968
$206$	−30.9881	−2.15905
$207$	15.2036	1.05672
$208$	−1.61994	−0.112323
$209$	−5.58903	−0.386601
$210$	−1.27628	−0.0880714
$211$	20.4674	1.40903	0.704517	−	0.709687i	$-0.251163\pi$
$211$	20.4674	1.40903	0.704517	+	0.709687i	$0.251163\pi$
$212$	5.92319	0.406806
$213$	19.7571	1.35373
$214$	22.4002	1.53125
$215$	1.93296	0.131827
$216$	−30.3598	−2.06572
$217$	−0.0997800	−0.00677351
$218$	36.5394	2.47476
$219$	−5.13390	−0.346917
$220$	−8.25891	−0.556816
$221$	−0.372782	−0.0250760
$222$	−81.3923	−5.46269
$223$	12.7463	0.853555	0.426778	−	0.904357i	$-0.359649\pi$
$223$	12.7463	0.853555	0.426778	+	0.904357i	$0.359649\pi$
$224$	0.250210	0.0167179
$225$	−24.6533	−1.64355
$226$	21.3360	1.41925
$227$	−16.0792	−1.06721	−0.533606	−	0.845733i	$-0.679163\pi$
$227$	−16.0792	−1.06721	−0.533606	+	0.845733i	$0.679163\pi$
$228$	−13.1505	−0.870914
$229$	−24.7993	−1.63879	−0.819393	−	0.573232i	$-0.805689\pi$
$229$	−24.7993	−1.63879	−0.819393	+	0.573232i	$0.805689\pi$
$230$	3.03859	0.200358
$231$	−6.13947	−0.403947
$232$	−25.5172	−1.67529
$233$	−19.0819	−1.25010	−0.625050	−	0.780585i	$-0.714921\pi$
$233$	−19.0819	−1.25010	−0.625050	+	0.780585i	$0.714921\pi$
$234$	4.68477	0.306253
$235$	−3.07718	−0.200733
$236$	−4.05705	−0.264091
$237$	−17.9099	−1.16338
$238$	1.08103	0.0700726
$239$	−14.7630	−0.954939	−0.477469	−	0.878648i	$-0.658446\pi$
$239$	−14.7630	−0.954939	−0.477469	+	0.878648i	$0.658446\pi$
$240$	−5.13043	−0.331168
$241$	10.4380	0.672372	0.336186	−	0.941796i	$-0.390863\pi$
$241$	10.4380	0.672372	0.336186	+	0.941796i	$0.390863\pi$
$242$	−32.2422	−2.07261
$243$	−12.9934	−0.833528
$244$	−22.9291	−1.46789
$245$	2.82265	0.180333
$246$	22.6697	1.44536
$247$	0.424401	0.0270040
$248$	−1.15004	−0.0730276
$249$	6.77938	0.429626
$250$	−10.0299	−0.634345
$251$	3.54105	0.223509	0.111754	−	0.993736i	$-0.464353\pi$
$251$	3.54105	0.223509	0.111754	+	0.993736i	$0.464353\pi$
$252$	−9.09954	−0.573217
$253$	14.6170	0.918962
$254$	−29.8314	−1.87179
$255$	−1.18061	−0.0739329
$256$	−32.3764	−2.02353
$257$	−21.7241	−1.35511	−0.677557	−	0.735470i	$-0.736961\pi$
$257$	−21.7241	−1.35511	−0.677557	+	0.735470i	$0.736961\pi$
$258$	32.6638	2.03356
$259$	−5.10209	−0.317029
$260$	0.627137	0.0388934
$261$	25.7371	1.59309
$262$	45.7490	2.82639
$263$	−7.47385	−0.460857	−0.230429	−	0.973089i	$-0.574013\pi$
$263$	−7.47385	−0.460857	−0.230429	+	0.973089i	$0.574013\pi$
$264$	−70.7621	−4.35510
$265$	−0.605400	−0.0371894
$266$	−1.23072	−0.0754601
$267$	8.38734	0.513297
$268$	27.6742	1.69047
$269$	−4.12462	−0.251482	−0.125741	−	0.992063i	$-0.540131\pi$
$269$	−4.12462	−0.251482	−0.125741	+	0.992063i	$0.540131\pi$
$270$	6.12000	0.372451
$271$	6.50464	0.395129	0.197564	−	0.980290i	$-0.436697\pi$
$271$	6.50464	0.395129	0.197564	+	0.980290i	$0.436697\pi$
$272$	4.34556	0.263488
$273$	0.466198	0.0282156
$274$	−25.6604	−1.55020
$275$	−23.7021	−1.42929
$276$	34.3925	2.07019
$277$	−4.16095	−0.250007	−0.125004	−	0.992156i	$-0.539894\pi$
$277$	−4.16095	−0.250007	−0.125004	+	0.992156i	$0.539894\pi$
$278$	−6.13903	−0.368195
$279$	1.15995	0.0694446
$280$	−0.922102	−0.0551061
$281$	4.14049	0.247001	0.123501	−	0.992345i	$-0.460588\pi$
$281$	4.14049	0.247001	0.123501	+	0.992345i	$0.460588\pi$
$282$	−51.9992	−3.09651
$283$	24.4500	1.45340	0.726701	−	0.686954i	$-0.241053\pi$
$283$	24.4500	1.45340	0.726701	+	0.686954i	$0.241053\pi$
$284$	28.1529	1.67056
$285$	1.34409	0.0796173
$286$	4.50402	0.266328
$287$	1.42105	0.0838820
$288$	−2.90872	−0.171398
$289$	1.00000	0.0588235
$290$	5.14382	0.302055
$291$	20.8810	1.22407
$292$	−7.31556	−0.428111
$293$	−14.0484	−0.820715	−0.410357	−	0.911925i	$-0.634596\pi$
$293$	−14.0484	−0.820715	−0.410357	+	0.911925i	$0.634596\pi$
$294$	47.6981	2.78181
$295$	0.414665	0.0241427
$296$	−58.8055	−3.41800
$297$	29.4400	1.70828
$298$	−50.0711	−2.90054
$299$	−1.10994	−0.0641892
$300$	−55.7690	−3.21982
$301$	2.04754	0.118018
$302$	10.2478	0.589696
$303$	9.06747	0.520913
$304$	−4.94729	−0.283746
$305$	2.34355	0.134191
$306$	−12.5671	−0.718411
$307$	−11.3082	−0.645394	−0.322697	−	0.946502i	$-0.604590\pi$
$307$	−11.3082	−0.645394	−0.322697	+	0.946502i	$0.604590\pi$
$308$	−8.74845	−0.498489
$309$	35.8489	2.03937
$310$	0.231828	0.0131669
$311$	−7.58019	−0.429833	−0.214917	−	0.976632i	$-0.568948\pi$
$311$	−7.58019	−0.429833	−0.214917	+	0.976632i	$0.568948\pi$
$312$	5.37329	0.304203
$313$	−6.83988	−0.386613	−0.193306	−	0.981138i	$-0.561921\pi$
$313$	−6.83988	−0.386613	−0.193306	+	0.981138i	$0.561921\pi$
$314$	26.7296	1.50844
$315$	0.930051	0.0524024
$316$	−25.5208	−1.43566
$317$	3.05818	0.171764	0.0858822	−	0.996305i	$-0.472629\pi$
$317$	3.05818	0.171764	0.0858822	+	0.996305i	$0.472629\pi$
$318$	−10.2302	−0.573683
$319$	24.7441	1.38540
$320$	3.02257	0.168967
$321$	−25.9139	−1.44637
$322$	3.21869	0.179371
$323$	−1.13847	−0.0633462
$324$	7.12067	0.395593
$325$	1.79981	0.0998355
$326$	−3.40934	−0.188826
$327$	−42.2709	−2.33759
$328$	16.3787	0.904363
$329$	−3.25958	−0.179706
$330$	14.2644	0.785229
$331$	−17.7239	−0.974196	−0.487098	−	0.873347i	$-0.661945\pi$
$331$	−17.7239	−0.974196	−0.487098	+	0.873347i	$0.661945\pi$
$332$	9.66029	0.530177
$333$	59.3124	3.25030
$334$	−23.5169	−1.28678
$335$	−2.82855	−0.154540
$336$	−5.43453	−0.296478
$337$	−31.2111	−1.70018	−0.850088	−	0.526641i	$-0.823451\pi$
$337$	−31.2111	−1.70018	−0.850088	+	0.526641i	$0.823451\pi$
$338$	31.6524	1.72166
$339$	−24.6828	−1.34058
$340$	−1.68232	−0.0912365
$341$	1.11520	0.0603914
$342$	14.3072	0.773647
$343$	6.06467	0.327461
$344$	23.5994	1.27240
$345$	−3.51521	−0.189253
$346$	−49.1684	−2.64331
$347$	−20.2060	−1.08472	−0.542358	−	0.840147i	$-0.682468\pi$
$347$	−20.2060	−1.08472	−0.542358	+	0.840147i	$0.682468\pi$
$348$	58.2208	3.12096
$349$	−3.10908	−0.166425	−0.0832126	−	0.996532i	$-0.526518\pi$
$349$	−3.10908	−0.166425	−0.0832126	+	0.996532i	$0.526518\pi$
$350$	−5.21925	−0.278981
$351$	−2.23552	−0.119323
$352$	−2.79649	−0.149053
$353$	16.3570	0.870594	0.435297	−	0.900287i	$-0.356643\pi$
$353$	16.3570	0.870594	0.435297	+	0.900287i	$0.356643\pi$
$354$	7.00714	0.372425
$355$	−2.87746	−0.152720
$356$	11.9515	0.633431
$357$	−1.25059	−0.0661884
$358$	13.0948	0.692084
$359$	13.5636	0.715858	0.357929	−	0.933749i	$-0.383483\pi$
$359$	13.5636	0.715858	0.357929	+	0.933749i	$0.383483\pi$
$360$	10.7195	0.564970
$361$	−17.7039	−0.931783
$362$	−24.3895	−1.28189
$363$	37.2996	1.95772
$364$	0.664310	0.0348193
$365$	0.747713	0.0391371
$366$	39.6021	2.07003
$367$	29.1210	1.52010	0.760051	−	0.649864i	$-0.225174\pi$
$367$	29.1210	1.52010	0.760051	+	0.649864i	$0.225174\pi$
$368$	12.9386	0.674473
$369$	−16.5199	−0.859991
$370$	11.8542	0.616268
$371$	−0.641285	−0.0332938
$372$	2.62397	0.136046
$373$	−1.86573	−0.0966037	−0.0483019	−	0.998833i	$-0.515381\pi$
$373$	−1.86573	−0.0966037	−0.0483019	+	0.998833i	$0.515381\pi$
$374$	−12.0822	−0.624755
$375$	11.6031	0.599184
$376$	−37.5691	−1.93748
$377$	−1.87894	−0.0967701
$378$	6.48275	0.333437
$379$	−14.8753	−0.764095	−0.382047	−	0.924143i	$-0.624781\pi$
$379$	−14.8753	−0.764095	−0.382047	+	0.924143i	$0.624781\pi$
$380$	1.91527	0.0982513
$381$	34.5107	1.76803
$382$	−33.7845	−1.72857
$383$	−14.7282	−0.752574	−0.376287	−	0.926503i	$-0.622799\pi$
$383$	−14.7282	−0.752574	−0.376287	+	0.926503i	$0.622799\pi$
$384$	54.3200	2.77200
$385$	0.894166	0.0455709
$386$	33.6534	1.71291
$387$	−23.8028	−1.20997
$388$	29.7545	1.51055
$389$	−19.4758	−0.987460	−0.493730	−	0.869615i	$-0.664367\pi$
$389$	−19.4758	−0.987460	−0.493730	+	0.869615i	$0.664367\pi$
$390$	−1.08316	−0.0548480
$391$	2.97744	0.150576
$392$	34.4616	1.74057
$393$	−52.9251	−2.66972
$394$	59.4322	2.99415
$395$	2.60844	0.131245
$396$	101.702	5.11070
$397$	−9.08387	−0.455907	−0.227953	−	0.973672i	$-0.573203\pi$
$397$	−9.08387	−0.455907	−0.227953	+	0.973672i	$0.573203\pi$
$398$	56.1815	2.81613
$399$	1.42376	0.0712774
$400$	−20.9806	−1.04903
$401$	15.9954	0.798770	0.399385	−	0.916783i	$-0.369224\pi$
$401$	15.9954	0.798770	0.399385	+	0.916783i	$0.369224\pi$
$402$	−47.7976	−2.38393
$403$	−0.0846822	−0.00421832
$404$	12.9207	0.642829
$405$	−0.727794	−0.0361644
$406$	5.44871	0.270415
$407$	57.0239	2.82657
$408$	−14.4140	−0.713602
$409$	−8.87172	−0.438678	−0.219339	−	0.975649i	$-0.570390\pi$
$409$	−8.87172	−0.438678	−0.219339	+	0.975649i	$0.570390\pi$
$410$	−3.30166	−0.163057
$411$	29.6854	1.46427
$412$	51.0829	2.51667
$413$	0.439244	0.0216138
$414$	−37.4177	−1.83898
$415$	−0.987364	−0.0484678
$416$	0.212351	0.0104113
$417$	7.10198	0.347786
$418$	13.7552	0.672789
$419$	1.99544	0.0974836	0.0487418	−	0.998811i	$-0.484479\pi$
$419$	1.99544	0.0974836	0.0487418	+	0.998811i	$0.484479\pi$
$420$	2.10390	0.102660
$421$	−38.7803	−1.89004	−0.945018	−	0.327019i	$-0.893956\pi$
$421$	−38.7803	−1.89004	−0.945018	+	0.327019i	$0.893956\pi$
$422$	−50.3725	−2.45210
$423$	37.8930	1.84242
$424$	−7.39129	−0.358953
$425$	−4.82805	−0.234195
$426$	−48.6243	−2.35585
$427$	2.48246	0.120135
$428$	−36.9260	−1.78489
$429$	−5.21050	−0.251565
$430$	−4.75723	−0.229414
$431$	−27.9986	−1.34865	−0.674324	−	0.738436i	$-0.735565\pi$
$431$	−27.9986	−1.34865	−0.674324	+	0.738436i	$0.735565\pi$
$432$	26.0596	1.25380
$433$	38.0831	1.83016	0.915080	−	0.403273i	$-0.132128\pi$
$433$	38.0831	1.83016	0.915080	+	0.403273i	$0.132128\pi$
$434$	0.245569	0.0117877
$435$	−5.95066	−0.285312
$436$	−60.2340	−2.88468
$437$	−3.38973	−0.162153
$438$	12.6351	0.603728
$439$	−27.4585	−1.31052	−0.655261	−	0.755403i	$-0.727441\pi$
$439$	−27.4585	−1.31052	−0.655261	+	0.755403i	$0.727441\pi$
$440$	10.3059	0.491317
$441$	−34.7587	−1.65517
$442$	0.917456	0.0436389
$443$	−7.33361	−0.348430	−0.174215	−	0.984708i	$-0.555739\pi$
$443$	−7.33361	−0.348430	−0.174215	+	0.984708i	$0.555739\pi$
$444$	134.172	6.36754
$445$	−1.22155	−0.0579070
$446$	−31.3700	−1.48541
$447$	57.9251	2.73976
$448$	3.20173	0.151267
$449$	−22.8690	−1.07925	−0.539627	−	0.841904i	$-0.681435\pi$
$449$	−22.8690	−1.07925	−0.539627	+	0.841904i	$0.681435\pi$
$450$	60.6744	2.86022
$451$	−15.8825	−0.747877
$452$	−35.1717	−1.65434
$453$	−11.8553	−0.557010
$454$	39.5725	1.85723
$455$	−0.0678982	−0.00318312
$456$	16.4100	0.768467
$457$	−39.0640	−1.82734	−0.913668	−	0.406461i	$-0.866763\pi$
$457$	−39.0640	−1.82734	−0.913668	+	0.406461i	$0.866763\pi$
$458$	61.0338	2.85192
$459$	5.99685	0.279909
$460$	−5.00900	−0.233546
$461$	−2.74592	−0.127890	−0.0639451	−	0.997953i	$-0.520368\pi$
$461$	−2.74592	−0.127890	−0.0639451	+	0.997953i	$0.520368\pi$
$462$	15.1099	0.702976
$463$	−3.84225	−0.178565	−0.0892823	−	0.996006i	$-0.528457\pi$
$463$	−3.84225	−0.178565	−0.0892823	+	0.996006i	$0.528457\pi$
$464$	21.9029	1.01682
$465$	−0.268192	−0.0124371
$466$	46.9627	2.17551
$467$	−2.87405	−0.132995	−0.0664976	−	0.997787i	$-0.521182\pi$
$467$	−2.87405	−0.132995	−0.0664976	+	0.997787i	$0.521182\pi$
$468$	−7.72268	−0.356981
$469$	−2.99620	−0.138352
$470$	7.57328	0.349329
$471$	−30.9223	−1.42483
$472$	5.06262	0.233026
$473$	−22.8844	−1.05223
$474$	44.0783	2.02458
$475$	5.49660	0.252201
$476$	−1.78204	−0.0816795
$477$	7.45501	0.341341
$478$	36.3333	1.66185
$479$	19.9229	0.910299	0.455150	−	0.890415i	$-0.349586\pi$
$479$	19.9229	0.910299	0.455150	+	0.890415i	$0.349586\pi$
$480$	0.672522	0.0306963
$481$	−4.33009	−0.197435
$482$	−25.6891	−1.17011
$483$	−3.72357	−0.169428
$484$	53.1501	2.41591
$485$	−3.04116	−0.138092
$486$	31.9782	1.45056
$487$	−11.4691	−0.519715	−0.259858	−	0.965647i	$-0.583676\pi$
$487$	−11.4691	−0.519715	−0.259858	+	0.965647i	$0.583676\pi$
$488$	28.6123	1.29522
$489$	3.94412	0.178359
$490$	−6.94685	−0.313827
$491$	−10.2995	−0.464810	−0.232405	−	0.972619i	$-0.574659\pi$
$491$	−10.2995	−0.464810	−0.232405	+	0.972619i	$0.574659\pi$
$492$	−37.3701	−1.68478
$493$	5.04031	0.227004
$494$	−1.04450	−0.0469941
$495$	−10.3948	−0.467211
$496$	0.987150	0.0443243
$497$	−3.04802	−0.136722
$498$	−16.6848	−0.747663
$499$	28.6714	1.28351	0.641754	−	0.766911i	$-0.278207\pi$
$499$	28.6714	1.28351	0.641754	+	0.766911i	$0.278207\pi$
$500$	16.5339	0.739419
$501$	27.2056	1.21546
$502$	−8.71490	−0.388965
$503$	−27.2884	−1.21673	−0.608365	−	0.793658i	$-0.708174\pi$
$503$	−27.2884	−1.21673	−0.608365	+	0.793658i	$0.708174\pi$
$504$	11.3549	0.505789
$505$	−1.32061	−0.0587663
$506$	−35.9740	−1.59924
$507$	−36.6173	−1.62623
$508$	49.1760	2.18183
$509$	−24.8152	−1.09992	−0.549958	−	0.835192i	$-0.685356\pi$
$509$	−24.8152	−1.09992	−0.549958	+	0.835192i	$0.685356\pi$
$510$	2.90562	0.128663
$511$	0.792033	0.0350375
$512$	41.5244	1.83514
$513$	−6.82724	−0.301430
$514$	53.4654	2.35826
$515$	−5.22111	−0.230070
$516$	−53.8451	−2.37040
$517$	36.4309	1.60223
$518$	12.5568	0.551714
$519$	56.8809	2.49679
$520$	−0.782578	−0.0343183
$521$	22.0076	0.964168	0.482084	−	0.876125i	$-0.339880\pi$
$521$	22.0076	0.964168	0.482084	+	0.876125i	$0.339880\pi$
$522$	−63.3419	−2.77240
$523$	−33.0076	−1.44332	−0.721661	−	0.692247i	$-0.756621\pi$
$523$	−33.0076	−1.44332	−0.721661	+	0.692247i	$0.756621\pi$
$524$	−75.4157	−3.29455
$525$	6.03793	0.263517
$526$	18.3939	0.802014
$527$	0.227163	0.00989538
$528$	60.7394	2.64334
$529$	−14.1348	−0.614558
$530$	1.48996	0.0647195
$531$	−5.10626	−0.221593
$532$	2.02880	0.0879594
$533$	1.20603	0.0522390
$534$	−20.6421	−0.893273
$535$	3.77416	0.163171
$536$	−34.5335	−1.49162
$537$	−15.1489	−0.653722
$538$	10.1511	0.437646
$539$	−33.4175	−1.43940
$540$	−10.0886	−0.434144
$541$	−32.4326	−1.39439	−0.697194	−	0.716882i	$-0.745568\pi$
$541$	−32.4326	−1.39439	−0.697194	+	0.716882i	$0.745568\pi$
$542$	−16.0086	−0.687629
$543$	28.2152	1.21083
$544$	−0.569638	−0.0244230
$545$	6.15643	0.263712
$546$	−1.14736	−0.0491027
$547$	−29.1411	−1.24598	−0.622992	−	0.782228i	$-0.714083\pi$
$547$	−29.1411	−1.24598	−0.622992	+	0.782228i	$0.714083\pi$
$548$	42.3003	1.80698
$549$	−28.8589	−1.23167
$550$	58.3334	2.48734
$551$	−5.73825	−0.244457
$552$	−42.9170	−1.82667
$553$	2.76306	0.117497
$554$	10.2405	0.435079
$555$	−13.7136	−0.582108
$556$	10.1200	0.429183
$557$	23.6670	1.00280	0.501402	−	0.865214i	$-0.332818\pi$
$557$	23.6670	1.00280	0.501402	+	0.865214i	$0.332818\pi$
$558$	−2.85477	−0.120852
$559$	1.73772	0.0734978
$560$	0.791496	0.0334468
$561$	13.9774	0.590124
$562$	−10.1902	−0.429848
$563$	17.8097	0.750590	0.375295	−	0.926905i	$-0.377541\pi$
$563$	17.8097	0.750590	0.375295	+	0.926905i	$0.377541\pi$
$564$	85.7189	3.60942
$565$	3.59485	0.151237
$566$	−60.1741	−2.52930
$567$	−0.770933	−0.0323761
$568$	−35.1308	−1.47405
$569$	−2.79767	−0.117284	−0.0586421	−	0.998279i	$-0.518677\pi$
$569$	−2.79767	−0.117284	−0.0586421	+	0.998279i	$0.518677\pi$
$570$	−3.30796	−0.138555
$571$	−32.8002	−1.37264	−0.686322	−	0.727298i	$-0.740776\pi$
$571$	−32.8002	−1.37264	−0.686322	+	0.727298i	$0.740776\pi$
$572$	−7.42471	−0.310443
$573$	39.0838	1.63275
$574$	−3.49736	−0.145977
$575$	−14.3752	−0.599489
$576$	−37.2204	−1.55085
$577$	36.2977	1.51109	0.755547	−	0.655094i	$-0.227371\pi$
$577$	36.2977	1.51109	0.755547	+	0.655094i	$0.227371\pi$
$578$	−2.46111	−0.102369
$579$	−38.9322	−1.61797
$580$	−8.47940	−0.352088
$581$	−1.04589	−0.0433908
$582$	−51.3905	−2.13020
$583$	7.16737	0.296842
$584$	9.12878	0.377752
$585$	0.789324	0.0326345
$586$	34.5745	1.42826
$587$	44.5900	1.84043	0.920213	−	0.391419i	$-0.128016\pi$
$587$	44.5900	1.84043	0.920213	+	0.391419i	$0.128016\pi$
$588$	−78.6286	−3.24259
$589$	−0.258618	−0.0106562
$590$	−1.02054	−0.0420148
$591$	−68.7545	−2.82818
$592$	50.4763	2.07456
$593$	26.4638	1.08674	0.543368	−	0.839494i	$-0.317149\pi$
$593$	26.4638	1.08674	0.543368	+	0.839494i	$0.317149\pi$
$594$	−72.4550	−2.97286
$595$	0.182139	0.00746698
$596$	82.5405	3.38099
$597$	−64.9940	−2.66003
$598$	2.73167	0.111706
$599$	−22.8572	−0.933920	−0.466960	−	0.884279i	$-0.654651\pi$
$599$	−22.8572	−0.933920	−0.466960	+	0.884279i	$0.654651\pi$
$600$	69.5918	2.84107
$601$	35.2866	1.43937	0.719686	−	0.694300i	$-0.244286\pi$
$601$	35.2866	1.43937	0.719686	+	0.694300i	$0.244286\pi$
$602$	−5.03921	−0.205383
$603$	34.8312	1.41844
$604$	−16.8932	−0.687374
$605$	−5.43240	−0.220858
$606$	−22.3160	−0.906527
$607$	−22.0108	−0.893391	−0.446696	−	0.894686i	$-0.647399\pi$
$607$	−22.0108	−0.893391	−0.446696	+	0.894686i	$0.647399\pi$
$608$	0.648516	0.0263008
$609$	−6.30338	−0.255426
$610$	−5.76774	−0.233529
$611$	−2.76637	−0.111915
$612$	20.7164	0.837410
$613$	40.0601	1.61801	0.809006	−	0.587800i	$-0.200006\pi$
$613$	40.0601	1.61801	0.809006	+	0.587800i	$0.200006\pi$
$614$	27.8308	1.12316
$615$	3.81955	0.154019
$616$	10.9168	0.439851
$617$	20.3672	0.819952	0.409976	−	0.912096i	$-0.365537\pi$
$617$	20.3672	0.819952	0.409976	+	0.912096i	$0.365537\pi$
$618$	−88.2279	−3.54905
$619$	−9.06177	−0.364223	−0.182112	−	0.983278i	$-0.558293\pi$
$619$	−9.06177	−0.364223	−0.182112	+	0.983278i	$0.558293\pi$
$620$	−0.382160	−0.0153479
$621$	17.8553	0.716507
$622$	18.6557	0.748024
$623$	−1.29396	−0.0518413
$624$	−4.61222	−0.184637
$625$	22.4504	0.898014
$626$	16.8337	0.672809
$627$	−15.9128	−0.635496
$628$	−44.0628	−1.75830
$629$	11.6156	0.463145
$630$	−2.28896	−0.0911942
$631$	9.51913	0.378951	0.189475	−	0.981885i	$-0.439321\pi$
$631$	9.51913	0.378951	0.189475	+	0.981885i	$0.439321\pi$
$632$	31.8463	1.26678
$633$	58.2738	2.31618
$634$	−7.52651	−0.298916
$635$	−5.02621	−0.199459
$636$	16.8642	0.668709
$637$	2.53755	0.100541
$638$	−60.8979	−2.41097
$639$	35.4336	1.40173
$640$	−7.91128	−0.312721
$641$	8.38478	0.331179	0.165589	−	0.986195i	$-0.447047\pi$
$641$	8.38478	0.331179	0.165589	+	0.986195i	$0.447047\pi$
$642$	63.7769	2.51707
$643$	−4.07693	−0.160779	−0.0803893	−	0.996764i	$-0.525616\pi$
$643$	−4.07693	−0.160779	−0.0803893	+	0.996764i	$0.525616\pi$
$644$	−5.30591	−0.209082
$645$	5.50343	0.216697
$646$	2.80190	0.110239
$647$	16.8543	0.662610	0.331305	−	0.943524i	$-0.392511\pi$
$647$	16.8543	0.662610	0.331305	+	0.943524i	$0.392511\pi$
$648$	−8.88559	−0.349059
$649$	−4.90924	−0.192705
$650$	−4.42953	−0.173740
$651$	−0.284089	−0.0111343
$652$	5.62018	0.220103
$653$	4.93861	0.193263	0.0966314	−	0.995320i	$-0.469193\pi$
$653$	4.93861	0.193263	0.0966314	+	0.995320i	$0.469193\pi$
$654$	104.033	4.06802
$655$	7.70813	0.301182
$656$	−14.0588	−0.548905
$657$	−9.20747	−0.359218
$658$	8.02218	0.312737
$659$	12.4396	0.484579	0.242289	−	0.970204i	$-0.422102\pi$
$659$	12.4396	0.484579	0.242289	+	0.970204i	$0.422102\pi$
$660$	−23.5144	−0.915295
$661$	31.7053	1.23319	0.616597	−	0.787279i	$-0.288511\pi$
$661$	31.7053	1.23319	0.616597	+	0.787279i	$0.288511\pi$
$662$	43.6205	1.69536
$663$	−1.06137	−0.0412200
$664$	−12.0547	−0.467812
$665$	−0.207360	−0.00804108
$666$	−145.974	−5.65639
$667$	15.0072	0.581082
$668$	38.7667	1.49993
$669$	36.2906	1.40308
$670$	6.96135	0.268941
$671$	−27.7455	−1.07110
$672$	0.712385	0.0274809
$673$	40.5291	1.56228	0.781140	−	0.624356i	$-0.214638\pi$
$673$	40.5291	1.56228	0.781140	+	0.624356i	$0.214638\pi$
$674$	76.8138	2.95876
$675$	−28.9531	−1.11441
$676$	−52.1779	−2.00684
$677$	−20.5147	−0.788443	−0.394222	−	0.919015i	$-0.628986\pi$
$677$	−20.5147	−0.788443	−0.394222	+	0.919015i	$0.628986\pi$
$678$	60.7469	2.33297
$679$	−3.22142	−0.123627
$680$	2.09929	0.0805042
$681$	−45.7798	−1.75428
$682$	−2.74462	−0.105097
$683$	−47.4022	−1.81380	−0.906898	−	0.421350i	$-0.861556\pi$
$683$	−47.4022	−1.81380	−0.906898	+	0.421350i	$0.861556\pi$
$684$	−23.5850	−0.901794
$685$	−4.32345	−0.165191
$686$	−14.9258	−0.569870
$687$	−70.6074	−2.69384
$688$	−20.2568	−0.772284
$689$	−0.544251	−0.0207343
$690$	8.65131	0.329350
$691$	23.4876	0.893512	0.446756	−	0.894656i	$-0.352579\pi$
$691$	23.4876	0.893512	0.446756	+	0.894656i	$0.352579\pi$
$692$	81.0525	3.08115
$693$	−11.0109	−0.418270
$694$	49.7292	1.88769
$695$	−1.03435	−0.0392351
$696$	−72.6512	−2.75384
$697$	−3.23522	−0.122543
$698$	7.65178	0.289624
$699$	−54.3291	−2.05492
$700$	8.60376	0.325192
$701$	10.7253	0.405091	0.202545	−	0.979273i	$-0.435079\pi$
$701$	10.7253	0.405091	0.202545	+	0.979273i	$0.435079\pi$
$702$	5.50184	0.207654
$703$	−13.2240	−0.498754
$704$	−35.7843	−1.34867
$705$	−8.76120	−0.329966
$706$	−40.2563	−1.51506
$707$	−1.39888	−0.0526105
$708$	−11.5510	−0.434114
$709$	38.3033	1.43851	0.719256	−	0.694745i	$-0.244483\pi$
$709$	38.3033	1.43851	0.719256	+	0.694745i	$0.244483\pi$
$710$	7.08175	0.265773
$711$	−32.1209	−1.20463
$712$	−14.9138	−0.558919
$713$	0.676365	0.0253301
$714$	3.07785	0.115185
$715$	0.758869	0.0283801
$716$	−21.5864	−0.806721
$717$	−42.0325	−1.56973
$718$	−33.3814	−1.24578
$719$	45.2033	1.68580	0.842899	−	0.538072i	$-0.180847\pi$
$719$	45.2033	1.68580	0.842899	+	0.538072i	$0.180847\pi$
$720$	−9.20124	−0.342910
$721$	−5.53058	−0.205970
$722$	43.5712	1.62155
$723$	29.7186	1.10525
$724$	40.2053	1.49422
$725$	−24.3349	−0.903775
$726$	−91.7983	−3.40696
$727$	47.5534	1.76366	0.881829	−	0.471569i	$-0.156312\pi$
$727$	47.5534	1.76366	0.881829	+	0.471569i	$0.156312\pi$
$728$	−0.828965	−0.0307235
$729$	−42.2596	−1.56517
$730$	−1.84020	−0.0681089
$731$	−4.66150	−0.172412
$732$	−65.2827	−2.41292
$733$	−12.6151	−0.465951	−0.232975	−	0.972483i	$-0.574846\pi$
$733$	−12.6151	−0.465951	−0.232975	+	0.972483i	$0.574846\pi$
$734$	−71.6698	−2.64538
$735$	8.03652	0.296431
$736$	−1.69606	−0.0625177
$737$	33.4873	1.23352
$738$	40.6572	1.49661
$739$	−3.44790	−0.126833	−0.0634165	−	0.997987i	$-0.520200\pi$
$739$	−3.44790	−0.126833	−0.0634165	+	0.997987i	$0.520200\pi$
$740$	−19.5412	−0.718347
$741$	1.20833	0.0443892
$742$	1.57827	0.0579401
$743$	−30.2974	−1.11150	−0.555751	−	0.831349i	$-0.687569\pi$
$743$	−30.2974	−1.11150	−0.555751	+	0.831349i	$0.687569\pi$
$744$	−3.27434	−0.120043
$745$	−8.43634	−0.309084
$746$	4.59176	0.168116
$747$	12.1586	0.444859
$748$	19.9171	0.728239
$749$	3.99787	0.146079
$750$	−28.5566	−1.04274
$751$	−45.6320	−1.66513	−0.832567	−	0.553924i	$-0.813130\pi$
$751$	−45.6320	−1.66513	−0.832567	+	0.553924i	$0.813130\pi$
$752$	32.2479	1.17596
$753$	10.0819	0.367405
$754$	4.62426	0.168406
$755$	1.72663	0.0628385
$756$	−10.6866	−0.388668
$757$	39.7419	1.44444	0.722222	−	0.691661i	$-0.243121\pi$
$757$	39.7419	1.44444	0.722222	+	0.691661i	$0.243121\pi$
$758$	36.6098	1.32973
$759$	41.6168	1.51059
$760$	−2.38998	−0.0866938
$761$	30.0509	1.08934	0.544672	−	0.838649i	$-0.316654\pi$
$761$	30.0509	1.08934	0.544672	+	0.838649i	$0.316654\pi$
$762$	−84.9344	−3.07685
$763$	6.52134	0.236088
$764$	55.6926	2.01489
$765$	−2.11739	−0.0765544
$766$	36.2476	1.30968
$767$	0.372782	0.0134604
$768$	−92.1805	−3.32628
$769$	−52.0456	−1.87681	−0.938406	−	0.345536i	$-0.887697\pi$
$769$	−52.0456	−1.87681	−0.938406	+	0.345536i	$0.887697\pi$
$770$	−2.20064	−0.0793055
$771$	−61.8519	−2.22754
$772$	−55.4764	−1.99664
$773$	0.659575	0.0237233	0.0118616	−	0.999930i	$-0.496224\pi$
$773$	0.659575	0.0237233	0.0118616	+	0.999930i	$0.496224\pi$
$774$	58.5814	2.10566
$775$	−1.09676	−0.0393966
$776$	−37.1293	−1.33287
$777$	−14.5264	−0.521132
$778$	47.9319	1.71844
$779$	3.68321	0.131965
$780$	1.78555	0.0639331
$781$	34.0664	1.21899
$782$	−7.32780	−0.262042
$783$	30.2260	1.08019
$784$	−29.5805	−1.05645
$785$	4.50360	0.160740
$786$	130.254	4.64602
$787$	−26.0887	−0.929963	−0.464981	−	0.885320i	$-0.653939\pi$
$787$	−26.0887	−0.929963	−0.464981	+	0.885320i	$0.653939\pi$
$788$	−97.9718	−3.49010
$789$	−21.2792	−0.757558
$790$	−6.41966	−0.228401
$791$	3.80793	0.135394
$792$	−126.909	−4.50952
$793$	2.10684	0.0748161
$794$	22.3564	0.793399
$795$	−1.72367	−0.0611321
$796$	−92.6133	−3.28259
$797$	49.9440	1.76911	0.884554	−	0.466438i	$-0.154463\pi$
$797$	49.9440	1.76911	0.884554	+	0.466438i	$0.154463\pi$
$798$	−3.50404	−0.124042
$799$	7.42089	0.262532
$800$	2.75024	0.0972357
$801$	15.0424	0.531497
$802$	−39.3663	−1.39007
$803$	−8.85221	−0.312388
$804$	78.7927	2.77881
$805$	0.542309	0.0191139
$806$	0.208412	0.00734100
$807$	−11.7434	−0.413387
$808$	−16.1232	−0.567213
$809$	−42.5204	−1.49494	−0.747468	−	0.664297i	$-0.768731\pi$
$809$	−42.5204	−1.49494	−0.747468	+	0.664297i	$0.768731\pi$
$810$	1.79118	0.0629356
$811$	54.5386	1.91511	0.957555	−	0.288249i	$-0.0930731\pi$
$811$	54.5386	1.91511	0.957555	+	0.288249i	$0.0930731\pi$
$812$	−8.98201	−0.315207
$813$	18.5197	0.649514
$814$	−140.342	−4.91898
$815$	−0.574430	−0.0201214
$816$	12.3725	0.433122
$817$	5.30698	0.185668
$818$	21.8343	0.763417
$819$	0.836111	0.0292161
$820$	5.44267	0.190066
$821$	40.5488	1.41516	0.707582	−	0.706631i	$-0.249786\pi$
$821$	40.5488	1.41516	0.707582	+	0.706631i	$0.249786\pi$
$822$	−73.0590	−2.54823
$823$	−3.02659	−0.105500	−0.0527502	−	0.998608i	$-0.516799\pi$
$823$	−3.02659	−0.105500	−0.0527502	+	0.998608i	$0.516799\pi$
$824$	−63.7442	−2.22063
$825$	−67.4834	−2.34947
$826$	−1.08103	−0.0376137
$827$	7.60079	0.264305	0.132153	−	0.991229i	$-0.457811\pi$
$827$	7.60079	0.264305	0.132153	+	0.991229i	$0.457811\pi$
$828$	61.6818	2.14359
$829$	−39.9171	−1.38638	−0.693188	−	0.720756i	$-0.743795\pi$
$829$	−39.9171	−1.38638	−0.693188	+	0.720756i	$0.743795\pi$
$830$	2.43001	0.0843468
$831$	−11.8468	−0.410962
$832$	2.71727	0.0942044
$833$	−6.80706	−0.235851
$834$	−17.4787	−0.605240
$835$	−3.96229	−0.137121
$836$	−22.6750	−0.784231
$837$	1.36226	0.0470867
$838$	−4.91099	−0.169647
$839$	−52.9006	−1.82633	−0.913165	−	0.407589i	$-0.866370\pi$
$839$	−52.9006	−1.82633	−0.913165	+	0.407589i	$0.866370\pi$
$840$	−2.62536	−0.0905836
$841$	−3.59528	−0.123975
$842$	95.4425	3.28916
$843$	11.7886	0.406021
$844$	83.0373	2.85826
$845$	5.33302	0.183462
$846$	−93.2587	−3.20630
$847$	−5.75440	−0.197723
$848$	6.34440	0.217867
$849$	69.6128	2.38911
$850$	11.8824	0.407561
$851$	34.5848	1.18555
$852$	80.1554	2.74608
$853$	20.0639	0.686975	0.343487	−	0.939157i	$-0.388392\pi$
$853$	20.0639	0.686975	0.343487	+	0.939157i	$0.388392\pi$
$854$	−6.10961	−0.209067
$855$	2.41059	0.0824403
$856$	46.0784	1.57493
$857$	42.2226	1.44229	0.721147	−	0.692782i	$-0.243615\pi$
$857$	42.2226	1.44229	0.721147	+	0.692782i	$0.243615\pi$
$858$	12.8236	0.437791
$859$	−32.5422	−1.11032	−0.555162	−	0.831742i	$-0.687344\pi$
$859$	−32.5422	−1.11032	−0.555162	+	0.831742i	$0.687344\pi$
$860$	7.84213	0.267414
$861$	4.04595	0.137886
$862$	68.9077	2.34700
$863$	−48.2028	−1.64084	−0.820422	−	0.571759i	$-0.806261\pi$
$863$	−48.2028	−1.64084	−0.820422	+	0.571759i	$0.806261\pi$
$864$	−3.41603	−0.116216
$865$	−8.28426	−0.281673
$866$	−93.7267	−3.18496
$867$	2.84715	0.0966943
$868$	−0.404812	−0.0137402
$869$	−30.8815	−1.04758
$870$	14.6452	0.496519
$871$	−2.54285	−0.0861610
$872$	75.1634	2.54535
$873$	37.4494	1.26747
$874$	8.34249	0.282189
$875$	−1.79007	−0.0605156
$876$	−20.8285	−0.703730
$877$	30.1658	1.01863	0.509313	−	0.860582i	$-0.329900\pi$
$877$	30.1658	1.01863	0.509313	+	0.860582i	$0.329900\pi$
$878$	67.5783	2.28066
$879$	−39.9978	−1.34909
$880$	−8.84622	−0.298206
$881$	44.0873	1.48534	0.742669	−	0.669659i	$-0.233560\pi$
$881$	44.0873	1.48534	0.742669	+	0.669659i	$0.233560\pi$
$882$	85.5448	2.88044
$883$	−8.32945	−0.280308	−0.140154	−	0.990130i	$-0.544760\pi$
$883$	−8.32945	−0.280308	−0.140154	+	0.990130i	$0.544760\pi$
$884$	−1.51239	−0.0508673
$885$	1.18061	0.0396859
$886$	18.0488	0.606362
$887$	23.7301	0.796778	0.398389	−	0.917216i	$-0.369569\pi$
$887$	23.7301	0.796778	0.398389	+	0.917216i	$0.369569\pi$
$888$	−167.428	−5.61852
$889$	−5.32413	−0.178566
$890$	3.00637	0.100774
$891$	8.61639	0.288660
$892$	51.7124	1.73146
$893$	−8.44846	−0.282717
$894$	−142.560	−4.76792
$895$	2.20631	0.0737490
$896$	−8.38021	−0.279963
$897$	−3.16015	−0.105514
$898$	56.2831	1.87819
$899$	1.14497	0.0381870
$900$	−100.020	−3.33399
$901$	1.45997	0.0486388
$902$	39.0885	1.30151
$903$	5.82964	0.193998
$904$	43.8893	1.45974
$905$	−4.10933	−0.136599
$906$	29.1771	0.969345
$907$	1.34729	0.0447359	0.0223679	−	0.999750i	$-0.492879\pi$
$907$	1.34729	0.0447359	0.0223679	+	0.999750i	$0.492879\pi$
$908$	−65.2339	−2.16486
$909$	16.2622	0.539383
$910$	0.167105	0.00553947
$911$	−38.5728	−1.27797	−0.638986	−	0.769218i	$-0.720646\pi$
$911$	−38.5728	−1.27797	−0.638986	+	0.769218i	$0.720646\pi$
$912$	−14.0857	−0.466423
$913$	11.6895	0.386865
$914$	96.1407	3.18005
$915$	6.67245	0.220584
$916$	−100.612	−3.32432
$917$	8.16502	0.269633
$918$	−14.7589	−0.487116
$919$	−1.97678	−0.0652079	−0.0326040	−	0.999468i	$-0.510380\pi$
$919$	−1.97678	−0.0652079	−0.0326040	+	0.999468i	$0.510380\pi$
$920$	6.25052	0.206074
$921$	−32.1962	−1.06090
$922$	6.75800	0.222563
$923$	−2.58682	−0.0851463
$924$	−24.9081	−0.819418
$925$	−56.0808	−1.84393
$926$	9.45620	0.310750
$927$	64.2937	2.11168
$928$	−2.87115	−0.0942501
$929$	40.7689	1.33758	0.668791	−	0.743450i	$-0.266812\pi$
$929$	40.7689	1.33758	0.668791	+	0.743450i	$0.266812\pi$
$930$	0.660049	0.0216439
$931$	7.74964	0.253984
$932$	−77.4164	−2.53586
$933$	−21.5819	−0.706561
$934$	7.07335	0.231447
$935$	−2.03569	−0.0665743
$936$	9.63681	0.314989
$937$	8.87970	0.290087	0.145044	−	0.989425i	$-0.453668\pi$
$937$	8.87970	0.290087	0.145044	+	0.989425i	$0.453668\pi$
$938$	7.37398	0.240769
$939$	−19.4742	−0.635516
$940$	−12.4843	−0.407193
$941$	−23.8029	−0.775953	−0.387976	−	0.921669i	$-0.626826\pi$
$941$	−23.8029	−0.775953	−0.387976	+	0.921669i	$0.626826\pi$
$942$	76.1032	2.47958
$943$	−9.63268	−0.313683
$944$	−4.34556	−0.141436
$945$	1.09226	0.0355313
$946$	56.3211	1.83116
$947$	−5.76904	−0.187469	−0.0937343	−	0.995597i	$-0.529880\pi$
$947$	−5.76904	−0.187469	−0.0937343	+	0.995597i	$0.529880\pi$
$948$	−72.6615	−2.35994
$949$	0.672190	0.0218202
$950$	−13.5277	−0.438897
$951$	8.70709	0.282347
$952$	2.22373	0.0720714
$953$	14.6045	0.473085	0.236542	−	0.971621i	$-0.423986\pi$
$953$	14.6045	0.473085	0.236542	+	0.971621i	$0.423986\pi$
$954$	−18.3476	−0.594025
$955$	−5.69226	−0.184197
$956$	−59.8942	−1.93712
$957$	70.4502	2.27733
$958$	−49.0323	−1.58416
$959$	−4.57972	−0.147887
$960$	8.60570	0.277748
$961$	−30.9484	−0.998335
$962$	10.6568	0.343590
$963$	−46.4756	−1.49766
$964$	42.3476	1.36392
$965$	5.67017	0.182529
$966$	9.16411	0.294850
$967$	−12.3588	−0.397433	−0.198717	−	0.980057i	$-0.563677\pi$
$967$	−12.3588	−0.397433	−0.198717	+	0.980057i	$0.563677\pi$
$968$	−66.3238	−2.13173
$969$	−3.24140	−0.104129
$970$	7.48462	0.240317
$971$	58.7545	1.88552	0.942761	−	0.333470i	$-0.108220\pi$
$971$	58.7545	1.88552	0.942761	+	0.333470i	$0.108220\pi$
$972$	−52.7149	−1.69083
$973$	−1.09566	−0.0351252
$974$	28.2267	0.904442
$975$	5.12433	0.164110
$976$	−24.5597	−0.786136
$977$	−40.4003	−1.29252	−0.646261	−	0.763117i	$-0.723668\pi$
$977$	−40.4003	−1.29252	−0.646261	+	0.763117i	$0.723668\pi$
$978$	−9.70690	−0.310392
$979$	14.4620	0.462207
$980$	11.4516	0.365809
$981$	−75.8114	−2.42047
$982$	25.3482	0.808893
$983$	−16.7890	−0.535487	−0.267744	−	0.963490i	$-0.586278\pi$
$983$	−16.7890	−0.535487	−0.267744	+	0.963490i	$0.586278\pi$
$984$	46.6326	1.48659
$985$	10.0136	0.319059
$986$	−12.4047	−0.395048
$987$	−9.28051	−0.295402
$988$	1.72182	0.0547783
$989$	−13.8793	−0.441338
$990$	25.5827	0.813071
$991$	37.9861	1.20667	0.603334	−	0.797489i	$-0.293839\pi$
$991$	37.9861	1.20667	0.603334	+	0.797489i	$0.293839\pi$
$992$	−0.129401	−0.00410847
$993$	−50.4627	−1.60139
$994$	7.50151	0.237933
$995$	9.46587	0.300088
$996$	27.5043	0.871507
$997$	20.7881	0.658365	0.329183	−	0.944266i	$-0.393227\pi$
$997$	20.7881	0.658365	0.329183	+	0.944266i	$0.393227\pi$
$998$	−70.5634	−2.23364
$999$	69.6571	2.20385

Twists

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

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-2.46111 q^{2} +2.84715 q^{3} +4.05705 q^{4} -0.414665 q^{5} -7.00714 q^{6} -0.439244 q^{7} -5.06262 q^{8} +5.10626 q^{9} +O(q^{10})\)	\(q-2.46111 q^{2} +2.84715 q^{3} +4.05705 q^{4} -0.414665 q^{5} -7.00714 q^{6} -0.439244 q^{7} -5.06262 q^{8} +5.10626 q^{9} +1.02054 q^{10} +4.90924 q^{11} +11.5510 q^{12} -0.372782 q^{13} +1.08103 q^{14} -1.18061 q^{15} +4.34556 q^{16} +1.00000 q^{17} -12.5671 q^{18} -1.13847 q^{19} -1.68232 q^{20} -1.25059 q^{21} -12.0822 q^{22} +2.97744 q^{23} -14.4140 q^{24} -4.82805 q^{25} +0.917456 q^{26} +5.99685 q^{27} -1.78204 q^{28} +5.04031 q^{29} +2.90562 q^{30} +0.227163 q^{31} -0.569638 q^{32} +13.9774 q^{33} -2.46111 q^{34} +0.182139 q^{35} +20.7164 q^{36} +11.6156 q^{37} +2.80190 q^{38} -1.06137 q^{39} +2.09929 q^{40} -3.23522 q^{41} +3.07785 q^{42} -4.66150 q^{43} +19.9171 q^{44} -2.11739 q^{45} -7.32780 q^{46} +7.42089 q^{47} +12.3725 q^{48} -6.80706 q^{49} +11.8824 q^{50} +2.84715 q^{51} -1.51239 q^{52} +1.45997 q^{53} -14.7589 q^{54} -2.03569 q^{55} +2.22373 q^{56} -3.24140 q^{57} -12.4047 q^{58} -1.00000 q^{59} -4.78981 q^{60} -5.65168 q^{61} -0.559073 q^{62} -2.24290 q^{63} -7.28917 q^{64} +0.154580 q^{65} -34.3998 q^{66} +6.82127 q^{67} +4.05705 q^{68} +8.47722 q^{69} -0.448264 q^{70} +6.93924 q^{71} -25.8511 q^{72} -1.80317 q^{73} -28.5873 q^{74} -13.7462 q^{75} -4.61883 q^{76} -2.15636 q^{77} +2.61213 q^{78} -6.29048 q^{79} -1.80195 q^{80} +1.75514 q^{81} +7.96223 q^{82} +2.38111 q^{83} -5.07372 q^{84} -0.414665 q^{85} +11.4725 q^{86} +14.3505 q^{87} -24.8536 q^{88} +2.94587 q^{89} +5.21112 q^{90} +0.163742 q^{91} +12.0796 q^{92} +0.646767 q^{93} -18.2636 q^{94} +0.472084 q^{95} -1.62184 q^{96} +7.33401 q^{97} +16.7529 q^{98} +25.0679 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 5 q^{2} + q^{3} + 21 q^{4} + 21 q^{5} + 5 q^{6} - q^{7} + 9 q^{8} + 17 q^{9}+O(q^{10}) \) 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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