LMFDB - Embedded newform 1003.2.a.h.1.12

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:	$1$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 6 x^{15} - 5 x^{14} + 90 x^{13} - 82 x^{12} - 456 x^{11} + 723 x^{10} + 951 x^{9} - 2105 x^{8} + \cdots - 1 $ x^16 - 6x^15 - 5x^14 + 90x^13 - 82x^12 - 456x^11 + 723x^10 + 951x^9 - 2105x^8 - 695x^7 + 2641x^6 - 151x^5 - 1323x^4 + 301x^3 + 179x^2 - 50*x - 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
Root			$-0.896165$ 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)

$f(q)$	$=$	$q+0.896165 q^{2} +1.99385 q^{3} -1.19689 q^{4} -0.516029 q^{5} +1.78681 q^{6} -1.20609 q^{7} -2.86494 q^{8} +0.975426 q^{9} +O(q^{10})$	\(q+0.896165 q^{2} +1.99385 q^{3} -1.19689 q^{4} -0.516029 q^{5} +1.78681 q^{6} -1.20609 q^{7} -2.86494 q^{8} +0.975426 q^{9} -0.462447 q^{10} -5.42223 q^{11} -2.38641 q^{12} -5.20462 q^{13} -1.08086 q^{14} -1.02888 q^{15} -0.173678 q^{16} +1.00000 q^{17} +0.874142 q^{18} -6.18063 q^{19} +0.617629 q^{20} -2.40477 q^{21} -4.85921 q^{22} +7.51988 q^{23} -5.71225 q^{24} -4.73371 q^{25} -4.66420 q^{26} -4.03669 q^{27} +1.44356 q^{28} +8.09638 q^{29} -0.922048 q^{30} +3.29641 q^{31} +5.57423 q^{32} -10.8111 q^{33} +0.896165 q^{34} +0.622380 q^{35} -1.16748 q^{36} -0.264962 q^{37} -5.53886 q^{38} -10.3772 q^{39} +1.47839 q^{40} +8.12197 q^{41} -2.15507 q^{42} +9.88755 q^{43} +6.48981 q^{44} -0.503348 q^{45} +6.73905 q^{46} -8.20206 q^{47} -0.346287 q^{48} -5.54534 q^{49} -4.24219 q^{50} +1.99385 q^{51} +6.22935 q^{52} -3.00377 q^{53} -3.61754 q^{54} +2.79803 q^{55} +3.45539 q^{56} -12.3232 q^{57} +7.25569 q^{58} +1.00000 q^{59} +1.23146 q^{60} -1.61013 q^{61} +2.95413 q^{62} -1.17646 q^{63} +5.34279 q^{64} +2.68573 q^{65} -9.68853 q^{66} +10.9403 q^{67} -1.19689 q^{68} +14.9935 q^{69} +0.557755 q^{70} -6.67456 q^{71} -2.79453 q^{72} -10.0334 q^{73} -0.237450 q^{74} -9.43830 q^{75} +7.39752 q^{76} +6.53973 q^{77} -9.29969 q^{78} -7.33271 q^{79} +0.0896228 q^{80} -10.9748 q^{81} +7.27862 q^{82} -14.9364 q^{83} +2.87824 q^{84} -0.516029 q^{85} +8.86087 q^{86} +16.1429 q^{87} +15.5344 q^{88} -14.7686 q^{89} -0.451082 q^{90} +6.27726 q^{91} -9.00047 q^{92} +6.57254 q^{93} -7.35040 q^{94} +3.18938 q^{95} +11.1142 q^{96} +0.769891 q^{97} -4.96953 q^{98} -5.28899 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 6 q^{2} - 7 q^{3} + 14 q^{4} - 21 q^{5} - 5 q^{6} - 11 q^{7} - 12 q^{8} + 17 q^{9}+O(q^{10}) $ 16 * q - 6 * q^2 - 7 * q^3 + 14 * q^4 - 21 * q^5 - 5 * q^6 - 11 * q^7 - 12 * q^8 + 17 * q^9	\( 16 q - 6 q^{2} - 7 q^{3} + 14 q^{4} - 21 q^{5} - 5 q^{6} - 11 q^{7} - 12 q^{8} + 17 q^{9} + 12 q^{10} - 7 q^{11} - 4 q^{12} - 16 q^{13} + 11 q^{14} + 7 q^{15} + 22 q^{16} + 16 q^{17} + 11 q^{18} + q^{19} - 43 q^{20} - 8 q^{21} - 18 q^{22} - 8 q^{23} - 39 q^{24} + 23 q^{25} - 49 q^{26} - 7 q^{27} - 15 q^{28} - 39 q^{29} + q^{30} - 3 q^{31} - 15 q^{33} - 6 q^{34} + 9 q^{35} - 17 q^{36} - 28 q^{37} - 27 q^{38} - 4 q^{39} + 26 q^{40} - 31 q^{41} - 45 q^{42} + 5 q^{43} - 19 q^{44} - 79 q^{45} - 39 q^{46} - 47 q^{47} - 31 q^{48} + 35 q^{49} - 13 q^{50} - 7 q^{51} + 9 q^{52} - 36 q^{53} + 9 q^{54} + 32 q^{55} + 3 q^{56} + 6 q^{57} + 22 q^{58} + 16 q^{59} + 6 q^{60} - 22 q^{61} + q^{62} - 19 q^{63} + 32 q^{64} - 19 q^{65} + 48 q^{66} + 4 q^{67} + 14 q^{68} + 14 q^{69} - 11 q^{70} - 5 q^{71} + 40 q^{72} - 35 q^{73} + 31 q^{74} - 12 q^{75} + q^{76} - 79 q^{77} + 31 q^{78} - 48 q^{79} - 127 q^{80} - 28 q^{81} - 7 q^{82} - 42 q^{83} + 28 q^{84} - 21 q^{85} + 58 q^{86} - 16 q^{87} - 2 q^{88} + 20 q^{89} - 14 q^{90} + 49 q^{91} - 21 q^{92} - 55 q^{93} - 22 q^{95} + 24 q^{96} - 2 q^{97} - 78 q^{98} - 35 q^{99}+O(q^{100}) \) 16 * q - 6 * q^2 - 7 * q^3 + 14 * q^4 - 21 * q^5 - 5 * q^6 - 11 * q^7 - 12 * q^8 + 17 * q^9 + 12 * q^10 - 7 * q^11 - 4 * q^12 - 16 * q^13 + 11 * q^14 + 7 * q^15 + 22 * q^16 + 16 * q^17 + 11 * q^18 + q^19 - 43 * q^20 - 8 * q^21 - 18 * q^22 - 8 * q^23 - 39 * q^24 + 23 * q^25 - 49 * q^26 - 7 * q^27 - 15 * q^28 - 39 * q^29 + q^30 - 3 * q^31 - 15 * q^33 - 6 * q^34 + 9 * q^35 - 17 * q^36 - 28 * q^37 - 27 * q^38 - 4 * q^39 + 26 * q^40 - 31 * q^41 - 45 * q^42 + 5 * q^43 - 19 * q^44 - 79 * q^45 - 39 * q^46 - 47 * q^47 - 31 * q^48 + 35 * q^49 - 13 * q^50 - 7 * q^51 + 9 * q^52 - 36 * q^53 + 9 * q^54 + 32 * q^55 + 3 * q^56 + 6 * q^57 + 22 * q^58 + 16 * q^59 + 6 * q^60 - 22 * q^61 + q^62 - 19 * q^63 + 32 * q^64 - 19 * q^65 + 48 * q^66 + 4 * q^67 + 14 * q^68 + 14 * q^69 - 11 * q^70 - 5 * q^71 + 40 * q^72 - 35 * q^73 + 31 * q^74 - 12 * q^75 + q^76 - 79 * q^77 + 31 * q^78 - 48 * q^79 - 127 * q^80 - 28 * q^81 - 7 * q^82 - 42 * q^83 + 28 * q^84 - 21 * q^85 + 58 * q^86 - 16 * q^87 - 2 * q^88 + 20 * q^89 - 14 * q^90 + 49 * q^91 - 21 * q^92 - 55 * q^93 - 22 * q^95 + 24 * q^96 - 2 * q^97 - 78 * q^98 - 35 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	0.896165	0.633684	0.316842	−	0.948478i	$-0.397378\pi$
$2$	0.896165	0.633684	0.316842	+	0.948478i	$0.397378\pi$
$3$	1.99385	1.15115	0.575574	−	0.817750i	$-0.304779\pi$
$3$	1.99385	1.15115	0.575574	+	0.817750i	$0.304779\pi$
$4$	−1.19689	−0.598445
$5$	−0.516029	−0.230775	−0.115388	−	0.993321i	$-0.536811\pi$
$5$	−0.516029	−0.230775	−0.115388	+	0.993321i	$0.536811\pi$
$6$	1.78681	0.729464
$7$	−1.20609	−0.455861	−0.227930	−	0.973677i	$-0.573196\pi$
$7$	−1.20609	−0.455861	−0.227930	+	0.973677i	$0.573196\pi$
$8$	−2.86494	−1.01291
$9$	0.975426	0.325142
$10$	−0.462447	−0.146239
$11$	−5.42223	−1.63487	−0.817433	−	0.576024i	$-0.804603\pi$
$11$	−5.42223	−1.63487	−0.817433	+	0.576024i	$0.804603\pi$
$12$	−2.38641	−0.688898
$13$	−5.20462	−1.44350	−0.721751	−	0.692153i	$-0.756662\pi$
$13$	−5.20462	−1.44350	−0.721751	+	0.692153i	$0.756662\pi$
$14$	−1.08086	−0.288872
$15$	−1.02888	−0.265656
$16$	−0.173678	−0.0434195
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	0.874142	0.206037
$19$	−6.18063	−1.41793	−0.708966	−	0.705242i	$-0.750838\pi$
$19$	−6.18063	−1.41793	−0.708966	+	0.705242i	$0.750838\pi$
$20$	0.617629	0.138106
$21$	−2.40477	−0.524763
$22$	−4.85921	−1.03599
$23$	7.51988	1.56800	0.784002	−	0.620758i	$-0.213175\pi$
$23$	7.51988	1.56800	0.784002	+	0.620758i	$0.213175\pi$
$24$	−5.71225	−1.16601
$25$	−4.73371	−0.946743
$26$	−4.66420	−0.914724
$27$	−4.03669	−0.776862
$28$	1.44356	0.272807
$29$	8.09638	1.50346	0.751730	−	0.659471i	$-0.229220\pi$
$29$	8.09638	1.50346	0.751730	+	0.659471i	$0.229220\pi$
$30$	−0.922048	−0.168342
$31$	3.29641	0.592053	0.296026	−	0.955180i	$-0.404338\pi$
$31$	3.29641	0.592053	0.296026	+	0.955180i	$0.404338\pi$
$32$	5.57423	0.985395
$33$	−10.8111	−1.88197
$34$	0.896165	0.153691
$35$	0.622380	0.105201
$36$	−1.16748	−0.194579
$37$	−0.264962	−0.0435595	−0.0217798	−	0.999763i	$-0.506933\pi$
$37$	−0.264962	−0.0435595	−0.0217798	+	0.999763i	$0.506933\pi$
$38$	−5.53886	−0.898521
$39$	−10.3772	−1.66168
$40$	1.47839	0.233754
$41$	8.12197	1.26844	0.634219	−	0.773153i	$-0.281322\pi$
$41$	8.12197	1.26844	0.634219	+	0.773153i	$0.281322\pi$
$42$	−2.15507	−0.332534
$43$	9.88755	1.50784	0.753919	−	0.656968i	$-0.228161\pi$
$43$	9.88755	1.50784	0.753919	+	0.656968i	$0.228161\pi$
$44$	6.48981	0.978376
$45$	−0.503348	−0.0750347
$46$	6.73905	0.993619
$47$	−8.20206	−1.19639	−0.598197	−	0.801349i	$-0.704116\pi$
$47$	−8.20206	−1.19639	−0.598197	+	0.801349i	$0.704116\pi$
$48$	−0.346287	−0.0499822
$49$	−5.54534	−0.792191
$50$	−4.24219	−0.599936
$51$	1.99385	0.279194
$52$	6.22935	0.863856
$53$	−3.00377	−0.412599	−0.206300	−	0.978489i	$-0.566142\pi$
$53$	−3.00377	−0.412599	−0.206300	+	0.978489i	$0.566142\pi$
$54$	−3.61754	−0.492285
$55$	2.79803	0.377286
$56$	3.45539	0.461745
$57$	−12.3232	−1.63225
$58$	7.25569	0.952719
$59$	1.00000	0.130189
$59$	1.00000	0.130189
$60$	1.23146	0.158981
$61$	−1.61013	−0.206156	−0.103078	−	0.994673i	$-0.532869\pi$
$61$	−1.61013	−0.206156	−0.103078	+	0.994673i	$0.532869\pi$
$62$	2.95413	0.375174
$63$	−1.17646	−0.148219
$64$	5.34279	0.667848
$65$	2.68573	0.333124
$66$	−9.68853	−1.19258
$67$	10.9403	1.33657	0.668287	−	0.743904i	$-0.267028\pi$
$67$	10.9403	1.33657	0.668287	+	0.743904i	$0.267028\pi$
$68$	−1.19689	−0.145144
$69$	14.9935	1.80500
$70$	0.557755	0.0666644
$71$	−6.67456	−0.792124	−0.396062	−	0.918224i	$-0.629623\pi$
$71$	−6.67456	−0.792124	−0.396062	+	0.918224i	$0.629623\pi$
$72$	−2.79453	−0.329339
$73$	−10.0334	−1.17432	−0.587162	−	0.809469i	$-0.699755\pi$
$73$	−10.0334	−1.17432	−0.587162	+	0.809469i	$0.699755\pi$
$74$	−0.237450	−0.0276030
$75$	−9.43830	−1.08984
$76$	7.39752	0.848554
$77$	6.53973	0.745271
$78$	−9.29969	−1.05298
$79$	−7.33271	−0.824995	−0.412497	−	0.910959i	$-0.635343\pi$
$79$	−7.33271	−0.824995	−0.412497	+	0.910959i	$0.635343\pi$
$80$	0.0896228	0.0100201
$81$	−10.9748	−1.21942
$82$	7.27862	0.803789
$83$	−14.9364	−1.63948	−0.819739	−	0.572737i	$-0.805881\pi$
$83$	−14.9364	−1.63948	−0.819739	+	0.572737i	$0.805881\pi$
$84$	2.87824	0.314042
$85$	−0.516029	−0.0559712
$86$	8.86087	0.955493
$87$	16.1429	1.73071
$88$	15.5344	1.65597
$89$	−14.7686	−1.56546	−0.782732	−	0.622358i	$-0.786175\pi$
$89$	−14.7686	−1.56546	−0.782732	+	0.622358i	$0.786175\pi$
$90$	−0.451082	−0.0475483
$91$	6.27726	0.658036
$92$	−9.00047	−0.938364
$93$	6.57254	0.681541
$94$	−7.35040	−0.758136
$95$	3.18938	0.327224
$96$	11.1142	1.13434
$97$	0.769891	0.0781706	0.0390853	−	0.999236i	$-0.487556\pi$
$97$	0.769891	0.0781706	0.0390853	+	0.999236i	$0.487556\pi$
$98$	−4.96953	−0.501999
$99$	−5.28899	−0.531563
$100$	5.66573	0.566573
$101$	−12.3331	−1.22719	−0.613596	−	0.789620i	$-0.710278\pi$
$101$	−12.3331	−1.22719	−0.613596	+	0.789620i	$0.710278\pi$
$102$	1.78681	0.176921
$103$	−6.64916	−0.655161	−0.327580	−	0.944823i	$-0.606233\pi$
$103$	−6.64916	−0.655161	−0.327580	+	0.944823i	$0.606233\pi$
$104$	14.9109	1.46214
$105$	1.24093	0.121102
$106$	−2.69187	−0.261458
$107$	3.72318	0.359933	0.179967	−	0.983673i	$-0.442401\pi$
$107$	3.72318	0.359933	0.179967	+	0.983673i	$0.442401\pi$
$108$	4.83147	0.464909
$109$	−5.78745	−0.554337	−0.277168	−	0.960821i	$-0.589396\pi$
$109$	−5.78745	−0.554337	−0.277168	+	0.960821i	$0.589396\pi$
$110$	2.50749	0.239080
$111$	−0.528294	−0.0501435
$112$	0.209472	0.0197932
$113$	9.78344	0.920349	0.460174	−	0.887829i	$-0.347787\pi$
$113$	9.78344	0.920349	0.460174	+	0.887829i	$0.347787\pi$
$114$	−11.0436	−1.03433
$115$	−3.88048	−0.361856
$116$	−9.69047	−0.899738
$117$	−5.07672	−0.469343
$118$	0.896165	0.0824986
$119$	−1.20609	−0.110563
$120$	2.94769	0.269086
$121$	18.4006	1.67278
$122$	−1.44294	−0.130638
$123$	16.1940	1.46016
$124$	−3.94544	−0.354311
$125$	5.02288	0.449260
$126$	−1.05430	−0.0939243
$127$	6.00487	0.532846	0.266423	−	0.963856i	$-0.414158\pi$
$127$	6.00487	0.532846	0.266423	+	0.963856i	$0.414158\pi$
$128$	−6.36045	−0.562190
$129$	19.7143	1.73574
$130$	2.40686	0.211096
$131$	0.734356	0.0641610	0.0320805	−	0.999485i	$-0.489787\pi$
$131$	0.734356	0.0641610	0.0320805	+	0.999485i	$0.489787\pi$
$132$	12.9397	1.12626
$133$	7.45442	0.646380
$134$	9.80433	0.846965
$135$	2.08305	0.179280
$136$	−2.86494	−0.245666
$137$	5.55730	0.474792	0.237396	−	0.971413i	$-0.423706\pi$
$137$	5.55730	0.474792	0.237396	+	0.971413i	$0.423706\pi$
$138$	13.4366	1.14380
$139$	−2.46537	−0.209110	−0.104555	−	0.994519i	$-0.533342\pi$
$139$	−2.46537	−0.209110	−0.104555	+	0.994519i	$0.533342\pi$
$140$	−0.744919	−0.0629572
$141$	−16.3537	−1.37723
$142$	−5.98150	−0.501956
$143$	28.2207	2.35993
$144$	−0.169410	−0.0141175
$145$	−4.17797	−0.346961
$146$	−8.99161	−0.744151
$147$	−11.0566	−0.911929
$148$	0.317131	0.0260680
$149$	−5.01078	−0.410499	−0.205249	−	0.978710i	$-0.565801\pi$
$149$	−5.01078	−0.410499	−0.205249	+	0.978710i	$0.565801\pi$
$150$	−8.45827	−0.690615
$151$	15.5267	1.26355	0.631773	−	0.775153i	$-0.282327\pi$
$151$	15.5267	1.26355	0.631773	+	0.775153i	$0.282327\pi$
$152$	17.7071	1.43624
$153$	0.975426	0.0788585
$154$	5.86067	0.472266
$155$	−1.70104	−0.136631
$156$	12.4204	0.994426
$157$	−23.9127	−1.90844	−0.954219	−	0.299108i	$-0.903311\pi$
$157$	−23.9127	−1.90844	−0.954219	+	0.299108i	$0.903311\pi$
$158$	−6.57132	−0.522786
$159$	−5.98906	−0.474963
$160$	−2.87647	−0.227405
$161$	−9.06969	−0.714792
$162$	−9.83525	−0.772730
$163$	−11.6858	−0.915299	−0.457649	−	0.889133i	$-0.651309\pi$
$163$	−11.6858	−0.915299	−0.457649	+	0.889133i	$0.651309\pi$
$164$	−9.72110	−0.759090
$165$	5.57884	0.434312
$166$	−13.3854	−1.03891
$167$	−24.2595	−1.87726	−0.938628	−	0.344931i	$-0.887902\pi$
$167$	−24.2595	−1.87726	−0.938628	+	0.344931i	$0.887902\pi$
$168$	6.88951	0.531537
$169$	14.0881	1.08370
$170$	−0.462447	−0.0354680
$171$	−6.02874	−0.461029
$172$	−11.8343	−0.902357
$173$	2.51265	0.191033	0.0955167	−	0.995428i	$-0.469550\pi$
$173$	2.51265	0.191033	0.0955167	+	0.995428i	$0.469550\pi$
$174$	14.4667	1.09672
$175$	5.70931	0.431583
$176$	0.941722	0.0709850
$177$	1.99385	0.149867
$178$	−13.2351	−0.992010
$179$	5.58086	0.417133	0.208567	−	0.978008i	$-0.433120\pi$
$179$	5.58086	0.417133	0.208567	+	0.978008i	$0.433120\pi$
$180$	0.602452	0.0449041
$181$	1.65969	0.123364	0.0616820	−	0.998096i	$-0.480354\pi$
$181$	1.65969	0.123364	0.0616820	+	0.998096i	$0.480354\pi$
$182$	5.62546	0.416987
$183$	−3.21036	−0.237316
$184$	−21.5440	−1.58825
$185$	0.136728	0.0100525
$186$	5.89008	0.431881
$187$	−5.42223	−0.396513
$188$	9.81696	0.715976
$189$	4.86863	0.354141
$190$	2.85821	0.207356
$191$	2.58606	0.187121	0.0935604	−	0.995614i	$-0.470175\pi$
$191$	2.58606	0.187121	0.0935604	+	0.995614i	$0.470175\pi$
$192$	10.6527	0.768792
$193$	−5.46085	−0.393081	−0.196540	−	0.980496i	$-0.562971\pi$
$193$	−5.46085	−0.393081	−0.196540	+	0.980496i	$0.562971\pi$
$194$	0.689949	0.0495355
$195$	5.35494	0.383475
$196$	6.63715	0.474082
$197$	−3.94861	−0.281327	−0.140663	−	0.990057i	$-0.544924\pi$
$197$	−3.94861	−0.281327	−0.140663	+	0.990057i	$0.544924\pi$
$198$	−4.73980	−0.336843
$199$	1.90311	0.134908	0.0674541	−	0.997722i	$-0.478512\pi$
$199$	1.90311	0.134908	0.0674541	+	0.997722i	$0.478512\pi$
$200$	13.5618	0.958964
$201$	21.8133	1.53859
$202$	−11.0525	−0.777652
$203$	−9.76500	−0.685369
$204$	−2.38641	−0.167082
$205$	−4.19117	−0.292724
$206$	−5.95874	−0.415165
$207$	7.33509	0.509824
$208$	0.903927	0.0626761
$209$	33.5128	2.31813
$210$	1.11208	0.0767406
$211$	−12.8679	−0.885866	−0.442933	−	0.896555i	$-0.646062\pi$
$211$	−12.8679	−0.885866	−0.442933	+	0.896555i	$0.646062\pi$
$212$	3.59518	0.246918
$213$	−13.3080	−0.911852
$214$	3.33658	0.228084
$215$	−5.10226	−0.347971
$216$	11.5649	0.786890
$217$	−3.97578	−0.269894
$218$	−5.18651	−0.351274
$219$	−20.0051	−1.35182
$220$	−3.34893	−0.225785
$221$	−5.20462	−0.350101
$222$	−0.473439	−0.0317751
$223$	9.48069	0.634874	0.317437	−	0.948279i	$-0.397178\pi$
$223$	9.48069	0.634874	0.317437	+	0.948279i	$0.397178\pi$
$224$	−6.72305	−0.449203
$225$	−4.61739	−0.307826
$226$	8.76757	0.583210
$227$	24.4489	1.62273	0.811365	−	0.584540i	$-0.198725\pi$
$227$	24.4489	1.62273	0.811365	+	0.584540i	$0.198725\pi$
$228$	14.7495	0.976812
$229$	−0.120799	−0.00798264	−0.00399132	−	0.999992i	$-0.501270\pi$
$229$	−0.120799	−0.00798264	−0.00399132	+	0.999992i	$0.501270\pi$
$230$	−3.47755	−0.229303
$231$	13.0392	0.857917
$232$	−23.1956	−1.52287
$233$	20.3658	1.33421	0.667104	−	0.744964i	$-0.267534\pi$
$233$	20.3658	1.33421	0.667104	+	0.744964i	$0.267534\pi$
$234$	−4.54958	−0.297415
$235$	4.23250	0.276098
$236$	−1.19689	−0.0779108
$237$	−14.6203	−0.949691
$238$	−1.08086	−0.0700617
$239$	−14.4564	−0.935105	−0.467553	−	0.883965i	$-0.654864\pi$
$239$	−14.4564	−0.935105	−0.467553	+	0.883965i	$0.654864\pi$
$240$	0.178694	0.0115347
$241$	5.17249	0.333190	0.166595	−	0.986025i	$-0.446723\pi$
$241$	5.17249	0.333190	0.166595	+	0.986025i	$0.446723\pi$
$242$	16.4900	1.06002
$243$	−9.77204	−0.626877
$244$	1.92715	0.123373
$245$	2.86155	0.182818
$246$	14.5125	0.925281
$247$	32.1678	2.04679
$248$	−9.44402	−0.599696
$249$	−29.7808	−1.88728
$250$	4.50132	0.284689
$251$	−28.8228	−1.81928	−0.909639	−	0.415399i	$-0.863642\pi$
$251$	−28.8228	−1.81928	−0.909639	+	0.415399i	$0.863642\pi$
$252$	1.40809	0.0887011
$253$	−40.7746	−2.56348
$254$	5.38136	0.337656
$255$	−1.02888	−0.0644311
$256$	−16.3856	−1.02410
$257$	−17.8164	−1.11135	−0.555677	−	0.831398i	$-0.687541\pi$
$257$	−17.8164	−1.11135	−0.555677	+	0.831398i	$0.687541\pi$
$258$	17.6672	1.09991
$259$	0.319570	0.0198571
$260$	−3.21453	−0.199356
$261$	7.89742	0.488838
$262$	0.658104	0.0406578
$263$	−4.96522	−0.306168	−0.153084	−	0.988213i	$-0.548921\pi$
$263$	−4.96522	−0.306168	−0.153084	+	0.988213i	$0.548921\pi$
$264$	30.9732	1.90627
$265$	1.55003	0.0952177
$266$	6.68039	0.409601
$267$	−29.4463	−1.80208
$268$	−13.0944	−0.799865
$269$	16.8759	1.02894	0.514472	−	0.857507i	$-0.327988\pi$
$269$	16.8759	1.02894	0.514472	+	0.857507i	$0.327988\pi$
$270$	1.86676	0.113607
$271$	28.9756	1.76014	0.880071	−	0.474842i	$-0.157495\pi$
$271$	28.9756	1.76014	0.880071	+	0.474842i	$0.157495\pi$
$272$	−0.173678	−0.0105308
$273$	12.5159	0.757497
$274$	4.98025	0.300868
$275$	25.6673	1.54780
$276$	−17.9456	−1.08020
$277$	3.85415	0.231573	0.115787	−	0.993274i	$-0.463061\pi$
$277$	3.85415	0.231573	0.115787	+	0.993274i	$0.463061\pi$
$278$	−2.20938	−0.132510
$279$	3.21540	0.192501
$280$	−1.78308	−0.106559
$281$	22.0109	1.31306	0.656531	−	0.754299i	$-0.272023\pi$
$281$	22.0109	1.31306	0.656531	+	0.754299i	$0.272023\pi$
$282$	−14.6556	−0.872727
$283$	28.0513	1.66748	0.833738	−	0.552160i	$-0.186196\pi$
$283$	28.0513	1.66748	0.833738	+	0.552160i	$0.186196\pi$
$284$	7.98870	0.474042
$285$	6.35914	0.376683
$286$	25.2904	1.49545
$287$	−9.79587	−0.578232
$288$	5.43725	0.320393
$289$	1.00000	0.0588235
$290$	−3.74415	−0.219864
$291$	1.53505	0.0899859
$292$	12.0089	0.702768
$293$	−17.4115	−1.01719	−0.508595	−	0.861006i	$-0.669835\pi$
$293$	−17.4115	−1.01719	−0.508595	+	0.861006i	$0.669835\pi$
$294$	−9.90849	−0.577875
$295$	−0.516029	−0.0300444
$296$	0.759101	0.0441218
$297$	21.8879	1.27006
$298$	−4.49048	−0.260127
$299$	−39.1381	−2.26342
$300$	11.2966	0.652210
$301$	−11.9253	−0.687364
$302$	13.9145	0.800689
$303$	−24.5904	−1.41268
$304$	1.07344	0.0615659
$305$	0.830874	0.0475757
$306$	0.874142	0.0499714
$307$	5.29798	0.302372	0.151186	−	0.988505i	$-0.451691\pi$
$307$	5.29798	0.302372	0.151186	+	0.988505i	$0.451691\pi$
$308$	−7.82733	−0.446003
$309$	−13.2574	−0.754187
$310$	−1.52441	−0.0865809
$311$	−0.766700	−0.0434756	−0.0217378	−	0.999764i	$-0.506920\pi$
$311$	−0.766700	−0.0434756	−0.0217378	+	0.999764i	$0.506920\pi$
$312$	29.7301	1.68313
$313$	20.6632	1.16795	0.583977	−	0.811770i	$-0.301496\pi$
$313$	20.6632	1.16795	0.583977	+	0.811770i	$0.301496\pi$
$314$	−21.4297	−1.20935
$315$	0.607085	0.0342054
$316$	8.77644	0.493714
$317$	−18.9097	−1.06207	−0.531037	−	0.847348i	$-0.678198\pi$
$317$	−18.9097	−1.06207	−0.531037	+	0.847348i	$0.678198\pi$
$318$	−5.36718	−0.300976
$319$	−43.9005	−2.45796
$320$	−2.75703	−0.154123
$321$	7.42345	0.414337
$322$	−8.12793	−0.452952
$323$	−6.18063	−0.343899
$324$	13.1356	0.729758
$325$	24.6372	1.36662
$326$	−10.4724	−0.580010
$327$	−11.5393	−0.638124
$328$	−23.2689	−1.28481
$329$	9.89247	0.545389
$330$	4.99956	0.275217
$331$	4.79821	0.263733	0.131867	−	0.991267i	$-0.457903\pi$
$331$	4.79821	0.263733	0.131867	+	0.991267i	$0.457903\pi$
$332$	17.8772	0.981137
$333$	−0.258451	−0.0141630
$334$	−21.7405	−1.18959
$335$	−5.64552	−0.308448
$336$	0.417655	0.0227850
$337$	0.694807	0.0378486	0.0189243	−	0.999821i	$-0.493976\pi$
$337$	0.694807	0.0378486	0.0189243	+	0.999821i	$0.493976\pi$
$338$	12.6252	0.686722
$339$	19.5067	1.05946
$340$	0.617629	0.0334957
$341$	−17.8739	−0.967927
$342$	−5.40274	−0.292147
$343$	15.1309	0.816990
$344$	−28.3272	−1.52730
$345$	−7.73708	−0.416550
$346$	2.25175	0.121055
$347$	−15.9424	−0.855834	−0.427917	−	0.903818i	$-0.640752\pi$
$347$	−15.9424	−0.855834	−0.427917	+	0.903818i	$0.640752\pi$
$348$	−19.3213	−1.03573
$349$	17.6591	0.945267	0.472634	−	0.881259i	$-0.343303\pi$
$349$	17.6591	0.945267	0.472634	+	0.881259i	$0.343303\pi$
$350$	5.11648	0.273487
$351$	21.0094	1.12140
$352$	−30.2248	−1.61099
$353$	27.9126	1.48564	0.742818	−	0.669493i	$-0.233489\pi$
$353$	27.9126	1.48564	0.742818	+	0.669493i	$0.233489\pi$
$354$	1.78681	0.0949681
$355$	3.44426	0.182803
$356$	17.6763	0.936844
$357$	−2.40477	−0.127274
$358$	5.00137	0.264331
$359$	−14.3545	−0.757604	−0.378802	−	0.925478i	$-0.623664\pi$
$359$	−14.3545	−0.757604	−0.378802	+	0.925478i	$0.623664\pi$
$360$	1.44206	0.0760033
$361$	19.2001	1.01053
$362$	1.48736	0.0781738
$363$	36.6880	1.92562
$364$	−7.51319	−0.393798
$365$	5.17754	0.271005
$366$	−2.87701	−0.150384
$367$	28.3202	1.47830	0.739151	−	0.673540i	$-0.235227\pi$
$367$	28.3202	1.47830	0.739151	+	0.673540i	$0.235227\pi$
$368$	−1.30604	−0.0680819
$369$	7.92238	0.412423
$370$	0.122531	0.00637008
$371$	3.62283	0.188088
$372$	−7.86660	−0.407864
$373$	24.8273	1.28551	0.642756	−	0.766071i	$-0.277791\pi$
$373$	24.8273	1.28551	0.642756	+	0.766071i	$0.277791\pi$
$374$	−4.85921	−0.251264
$375$	10.0148	0.517165
$376$	23.4984	1.21184
$377$	−42.1386	−2.17025
$378$	4.36309	0.224413
$379$	5.88915	0.302505	0.151253	−	0.988495i	$-0.451669\pi$
$379$	5.88915	0.302505	0.151253	+	0.988495i	$0.451669\pi$
$380$	−3.81734	−0.195825
$381$	11.9728	0.613385
$382$	2.31754	0.118575
$383$	19.1958	0.980858	0.490429	−	0.871481i	$-0.336840\pi$
$383$	19.1958	0.980858	0.490429	+	0.871481i	$0.336840\pi$
$384$	−12.6818	−0.647164
$385$	−3.37469	−0.171990
$386$	−4.89382	−0.249089
$387$	9.64457	0.490261
$388$	−0.921475	−0.0467808
$389$	−10.7157	−0.543306	−0.271653	−	0.962395i	$-0.587570\pi$
$389$	−10.7157	−0.543306	−0.271653	+	0.962395i	$0.587570\pi$
$390$	4.79891	0.243002
$391$	7.51988	0.380297
$392$	15.8870	0.802417
$393$	1.46419	0.0738588
$394$	−3.53860	−0.178272
$395$	3.78389	0.190388
$396$	6.33033	0.318111
$397$	−15.0380	−0.754736	−0.377368	−	0.926063i	$-0.623171\pi$
$397$	−15.0380	−0.754736	−0.377368	+	0.926063i	$0.623171\pi$
$398$	1.70550	0.0854892
$399$	14.8630	0.744079
$400$	0.822142	0.0411071
$401$	19.7178	0.984658	0.492329	−	0.870409i	$-0.336146\pi$
$401$	19.7178	0.984658	0.492329	+	0.870409i	$0.336146\pi$
$402$	19.5483	0.974982
$403$	−17.1566	−0.854629
$404$	14.7614	0.734407
$405$	5.66333	0.281413
$406$	−8.75105	−0.434307
$407$	1.43669	0.0712140
$408$	−5.71225	−0.282798
$409$	−30.8885	−1.52734	−0.763669	−	0.645608i	$-0.776604\pi$
$409$	−30.8885	−1.52734	−0.763669	+	0.645608i	$0.776604\pi$
$410$	−3.75598	−0.185495
$411$	11.0804	0.546556
$412$	7.95830	0.392078
$413$	−1.20609	−0.0593480
$414$	6.57344	0.323067
$415$	7.70759	0.378351
$416$	−29.0118	−1.42242
$417$	−4.91557	−0.240717
$418$	30.0330	1.46896
$419$	−2.38503	−0.116516	−0.0582582	−	0.998302i	$-0.518555\pi$
$419$	−2.38503	−0.116516	−0.0582582	+	0.998302i	$0.518555\pi$
$420$	−1.48526	−0.0724730
$421$	−18.2996	−0.891869	−0.445935	−	0.895065i	$-0.647129\pi$
$421$	−18.2996	−0.891869	−0.445935	+	0.895065i	$0.647129\pi$
$422$	−11.5318	−0.561359
$423$	−8.00050	−0.388998
$424$	8.60561	0.417926
$425$	−4.73371	−0.229619
$426$	−11.9262	−0.577826
$427$	1.94197	0.0939785
$428$	−4.45623	−0.215400
$429$	56.2677	2.71663
$430$	−4.57247	−0.220504
$431$	0.931209	0.0448548	0.0224274	−	0.999748i	$-0.492861\pi$
$431$	0.931209	0.0448548	0.0224274	+	0.999748i	$0.492861\pi$
$432$	0.701084	0.0337309
$433$	25.7506	1.23750	0.618748	−	0.785589i	$-0.287640\pi$
$433$	25.7506	1.23750	0.618748	+	0.785589i	$0.287640\pi$
$434$	−3.56296	−0.171027
$435$	−8.33023	−0.399404
$436$	6.92693	0.331740
$437$	−46.4776	−2.22332
$438$	−17.9279	−0.856628
$439$	−38.0390	−1.81550	−0.907752	−	0.419508i	$-0.862203\pi$
$439$	−38.0390	−1.81550	−0.907752	+	0.419508i	$0.862203\pi$
$440$	−8.01618	−0.382157
$441$	−5.40906	−0.257574
$442$	−4.66420	−0.221853
$443$	−29.9203	−1.42156	−0.710778	−	0.703416i	$-0.751657\pi$
$443$	−29.9203	−1.42156	−0.710778	+	0.703416i	$0.751657\pi$
$444$	0.632310	0.0300081
$445$	7.62101	0.361270
$446$	8.49626	0.402309
$447$	−9.99072	−0.472545
$448$	−6.44390	−0.304446
$449$	−24.6563	−1.16360	−0.581800	−	0.813332i	$-0.697651\pi$
$449$	−24.6563	−1.16360	−0.581800	+	0.813332i	$0.697651\pi$
$450$	−4.13794	−0.195064
$451$	−44.0392	−2.07373
$452$	−11.7097	−0.550778
$453$	30.9579	1.45453
$454$	21.9102	1.02830
$455$	−3.23925	−0.151858
$456$	35.3053	1.65332
$457$	2.98540	0.139651	0.0698255	−	0.997559i	$-0.477756\pi$
$457$	2.98540	0.139651	0.0698255	+	0.997559i	$0.477756\pi$
$458$	−0.108256	−0.00505847
$459$	−4.03669	−0.188417
$460$	4.64450	0.216551
$461$	14.1611	0.659550	0.329775	−	0.944060i	$-0.393027\pi$
$461$	14.1611	0.659550	0.329775	+	0.944060i	$0.393027\pi$
$462$	11.6853	0.543648
$463$	−0.940142	−0.0436921	−0.0218460	−	0.999761i	$-0.506954\pi$
$463$	−0.940142	−0.0436921	−0.0218460	+	0.999761i	$0.506954\pi$
$464$	−1.40616	−0.0652795
$465$	−3.39162	−0.157283
$466$	18.2511	0.845467
$467$	7.76755	0.359439	0.179720	−	0.983718i	$-0.442481\pi$
$467$	7.76755	0.359439	0.179720	+	0.983718i	$0.442481\pi$
$468$	6.07627	0.280876
$469$	−13.1951	−0.609292
$470$	3.79302	0.174959
$471$	−47.6782	−2.19690
$472$	−2.86494	−0.131869
$473$	−53.6126	−2.46511
$474$	−13.1022	−0.601804
$475$	29.2573	1.34242
$476$	1.44356	0.0661655
$477$	−2.92995	−0.134153
$478$	−12.9553	−0.592561
$479$	−12.9393	−0.591211	−0.295605	−	0.955310i	$-0.595521\pi$
$479$	−12.9393	−0.591211	−0.295605	+	0.955310i	$0.595521\pi$
$480$	−5.73523	−0.261776
$481$	1.37903	0.0628783
$482$	4.63540	0.211137
$483$	−18.0836	−0.822831
$484$	−22.0235	−1.00107
$485$	−0.397286	−0.0180398
$486$	−8.75736	−0.397242
$487$	−3.96280	−0.179571	−0.0897857	−	0.995961i	$-0.528618\pi$
$487$	−3.96280	−0.179571	−0.0897857	+	0.995961i	$0.528618\pi$
$488$	4.61293	0.208817
$489$	−23.2996	−1.05364
$490$	2.56442	0.115849
$491$	25.4974	1.15068	0.575341	−	0.817914i	$-0.304869\pi$
$491$	25.4974	1.15068	0.575341	+	0.817914i	$0.304869\pi$
$492$	−19.3824	−0.873825
$493$	8.09638	0.364643
$494$	28.8276	1.29702
$495$	2.72927	0.122672
$496$	−0.572514	−0.0257066
$497$	8.05015	0.361098
$498$	−26.6885	−1.19594
$499$	−36.1984	−1.62046	−0.810232	−	0.586109i	$-0.800659\pi$
$499$	−36.1984	−1.62046	−0.810232	+	0.586109i	$0.800659\pi$
$500$	−6.01183	−0.268857
$501$	−48.3697	−2.16100
$502$	−25.8300	−1.15285
$503$	−19.8464	−0.884907	−0.442453	−	0.896792i	$-0.645892\pi$
$503$	−19.8464	−0.884907	−0.442453	+	0.896792i	$0.645892\pi$
$504$	3.37047	0.150133
$505$	6.36425	0.283206
$506$	−36.5407	−1.62443
$507$	28.0894	1.24750
$508$	−7.18717	−0.318879
$509$	−41.1034	−1.82188	−0.910938	−	0.412543i	$-0.864641\pi$
$509$	−41.1034	−1.82188	−0.910938	+	0.412543i	$0.864641\pi$
$510$	−0.922048	−0.0408290
$511$	12.1013	0.535329
$512$	−1.96327	−0.0867653
$513$	24.9493	1.10154
$514$	−15.9664	−0.704247
$515$	3.43116	0.151195
$516$	−23.5958	−1.03875
$517$	44.4735	1.95594
$518$	0.286387	0.0125831
$519$	5.00984	0.219908
$520$	−7.69446	−0.337425
$521$	−27.2229	−1.19266	−0.596328	−	0.802741i	$-0.703374\pi$
$521$	−27.2229	−1.19266	−0.596328	+	0.802741i	$0.703374\pi$
$522$	7.07739	0.309769
$523$	17.3323	0.757886	0.378943	−	0.925420i	$-0.376288\pi$
$523$	17.3323	0.757886	0.378943	+	0.925420i	$0.376288\pi$
$524$	−0.878943	−0.0383968
$525$	11.3835	0.496816
$526$	−4.44965	−0.194014
$527$	3.29641	0.143594
$528$	1.87765	0.0817142
$529$	33.5486	1.45864
$530$	1.38908	0.0603379
$531$	0.975426	0.0423299
$532$	−8.92211	−0.386823
$533$	−42.2718	−1.83099
$534$	−26.3887	−1.14195
$535$	−1.92127	−0.0830637
$536$	−31.3434	−1.35383
$537$	11.1274	0.480182
$538$	15.1236	0.652026
$539$	30.0681	1.29513
$540$	−2.49318	−0.107289
$541$	0.0199932	0.000859573 0	0.000429786	−	1.00000i	$-0.499863\pi$
$541$	0.0199932	0.000859573 0	0.000429786		1.00000i	$0.499863\pi$
$542$	25.9669	1.11537
$543$	3.30917	0.142010
$544$	5.57423	0.238993
$545$	2.98649	0.127927
$546$	11.2163	0.480014
$547$	12.9453	0.553500	0.276750	−	0.960942i	$-0.410743\pi$
$547$	12.9453	0.553500	0.276750	+	0.960942i	$0.410743\pi$
$548$	−6.65147	−0.284137
$549$	−1.57056	−0.0670300
$550$	23.0021	0.980814
$551$	−50.0407	−2.13181
$552$	−42.9554	−1.82831
$553$	8.84394	0.376083
$554$	3.45395	0.146744
$555$	0.272615	0.0115719
$556$	2.95078	0.125141
$557$	−6.69450	−0.283655	−0.141827	−	0.989891i	$-0.545298\pi$
$557$	−6.69450	−0.283655	−0.141827	+	0.989891i	$0.545298\pi$
$558$	2.88153	0.121985
$559$	−51.4610	−2.17657
$560$	−0.108094	−0.00456779
$561$	−10.8111	−0.456445
$562$	19.7254	0.832067
$563$	16.5658	0.698165	0.349083	−	0.937092i	$-0.386493\pi$
$563$	16.5658	0.698165	0.349083	+	0.937092i	$0.386493\pi$
$564$	19.5735	0.824194
$565$	−5.04854	−0.212394
$566$	25.1386	1.05665
$567$	13.2367	0.555888
$568$	19.1222	0.802349
$569$	−37.4048	−1.56809	−0.784044	−	0.620705i	$-0.786847\pi$
$569$	−37.4048	−1.56809	−0.784044	+	0.620705i	$0.786847\pi$
$570$	5.69883	0.238698
$571$	33.8831	1.41796	0.708982	−	0.705227i	$-0.249155\pi$
$571$	33.8831	1.41796	0.708982	+	0.705227i	$0.249155\pi$
$572$	−33.7770	−1.41229
$573$	5.15621	0.215404
$574$	−8.77871	−0.366416
$575$	−35.5970	−1.48450
$576$	5.21149	0.217145
$577$	1.06500	0.0443366	0.0221683	−	0.999754i	$-0.492943\pi$
$577$	1.06500	0.0443366	0.0221683	+	0.999754i	$0.492943\pi$
$578$	0.896165	0.0372755
$579$	−10.8881	−0.452494
$580$	5.00056	0.207637
$581$	18.0147	0.747374
$582$	1.37565	0.0570227
$583$	16.2871	0.674544
$584$	28.7452	1.18948
$585$	2.61973	0.108313
$586$	−15.6035	−0.644577
$587$	39.8474	1.64468	0.822340	−	0.568997i	$-0.192668\pi$
$587$	39.8474	1.64468	0.822340	+	0.568997i	$0.192668\pi$
$588$	13.2335	0.545739
$589$	−20.3739	−0.839491
$590$	−0.462447	−0.0190386
$591$	−7.87292	−0.323849
$592$	0.0460181	0.00189133
$593$	35.2898	1.44918	0.724590	−	0.689180i	$-0.242029\pi$
$593$	35.2898	1.44918	0.724590	+	0.689180i	$0.242029\pi$
$594$	19.6151	0.804819
$595$	0.622380	0.0255151
$596$	5.99734	0.245661
$597$	3.79452	0.155299
$598$	−35.0742	−1.43429
$599$	−11.2298	−0.458838	−0.229419	−	0.973328i	$-0.573683\pi$
$599$	−11.2298	−0.458838	−0.229419	+	0.973328i	$0.573683\pi$
$600$	27.0402	1.10391
$601$	−20.9918	−0.856275	−0.428137	−	0.903714i	$-0.640830\pi$
$601$	−20.9918	−0.856275	−0.428137	+	0.903714i	$0.640830\pi$
$602$	−10.6871	−0.435572
$603$	10.6715	0.434576
$604$	−18.5838	−0.756162
$605$	−9.49525	−0.386037
$606$	−22.0370	−0.895193
$607$	−27.7995	−1.12835	−0.564174	−	0.825656i	$-0.690805\pi$
$607$	−27.7995	−1.12835	−0.564174	+	0.825656i	$0.690805\pi$
$608$	−34.4523	−1.39722
$609$	−19.4699	−0.788961
$610$	0.744600	0.0301480
$611$	42.6886	1.72700
$612$	−1.16748	−0.0471924
$613$	−48.6276	−1.96405	−0.982024	−	0.188754i	$-0.939555\pi$
$613$	−48.6276	−1.96405	−0.982024	+	0.188754i	$0.939555\pi$
$614$	4.74786	0.191608
$615$	−8.35656	−0.336969
$616$	−18.7359	−0.754892
$617$	−47.5477	−1.91420	−0.957098	−	0.289764i	$-0.906423\pi$
$617$	−47.5477	−1.91420	−0.957098	+	0.289764i	$0.906423\pi$
$618$	−11.8808	−0.477916
$619$	−40.3267	−1.62087	−0.810433	−	0.585831i	$-0.800768\pi$
$619$	−40.3267	−1.62087	−0.810433	+	0.585831i	$0.800768\pi$
$620$	2.03596	0.0817661
$621$	−30.3554	−1.21812
$622$	−0.687090	−0.0275498
$623$	17.8123	0.713634
$624$	1.80229	0.0721495
$625$	21.0766	0.843065
$626$	18.5176	0.740114
$627$	66.8194	2.66851
$628$	28.6208	1.14209
$629$	−0.264962	−0.0105647
$630$	0.544048	0.0216754
$631$	38.3737	1.52763	0.763816	−	0.645434i	$-0.223323\pi$
$631$	38.3737	1.52763	0.763816	+	0.645434i	$0.223323\pi$
$632$	21.0078	0.835644
$633$	−25.6567	−1.01976
$634$	−16.9462	−0.673020
$635$	−3.09869	−0.122968
$636$	7.16824	0.284239
$637$	28.8614	1.14353
$638$	−39.3421	−1.55757
$639$	−6.51053	−0.257553
$640$	3.28218	0.129739
$641$	3.75978	0.148502	0.0742511	−	0.997240i	$-0.476343\pi$
$641$	3.75978	0.148502	0.0742511	+	0.997240i	$0.476343\pi$
$642$	6.65263	0.262558
$643$	−9.73333	−0.383845	−0.191923	−	0.981410i	$-0.561472\pi$
$643$	−9.73333	−0.383845	−0.191923	+	0.981410i	$0.561472\pi$
$644$	10.8554	0.427763
$645$	−10.1731	−0.400567
$646$	−5.53886	−0.217923
$647$	25.4600	1.00094	0.500468	−	0.865755i	$-0.333161\pi$
$647$	25.4600	1.00094	0.500468	+	0.865755i	$0.333161\pi$
$648$	31.4422	1.23517
$649$	−5.42223	−0.212841
$650$	22.0790	0.866008
$651$	−7.92710	−0.310688
$652$	13.9866	0.547756
$653$	−40.6813	−1.59198	−0.795992	−	0.605307i	$-0.793050\pi$
$653$	−40.6813	−1.59198	−0.795992	+	0.605307i	$0.793050\pi$
$654$	−10.3411	−0.404369
$655$	−0.378949	−0.0148068
$656$	−1.41061	−0.0550749
$657$	−9.78687	−0.381822
$658$	8.86528	0.345604
$659$	13.7946	0.537361	0.268681	−	0.963229i	$-0.413412\pi$
$659$	13.7946	0.537361	0.268681	+	0.963229i	$0.413412\pi$
$660$	−6.67726	−0.259912
$661$	−36.3775	−1.41492	−0.707460	−	0.706753i	$-0.750159\pi$
$661$	−36.3775	−1.41492	−0.707460	+	0.706753i	$0.750159\pi$
$662$	4.29998	0.167124
$663$	−10.3772	−0.403018
$664$	42.7917	1.66064
$665$	−3.84670	−0.149168
$666$	−0.231615	−0.00897488
$667$	60.8839	2.35743
$668$	29.0359	1.12343
$669$	18.9030	0.730834
$670$	−5.05932	−0.195459
$671$	8.73051	0.337038
$672$	−13.4047	−0.517099
$673$	20.5933	0.793813	0.396907	−	0.917859i	$-0.370084\pi$
$673$	20.5933	0.793813	0.396907	+	0.917859i	$0.370084\pi$
$674$	0.622661	0.0239840
$675$	19.1085	0.735488
$676$	−16.8619	−0.648533
$677$	−18.8668	−0.725112	−0.362556	−	0.931962i	$-0.618096\pi$
$677$	−18.8668	−0.725112	−0.362556	+	0.931962i	$0.618096\pi$
$678$	17.4812	0.671361
$679$	−0.928562	−0.0356349
$680$	1.47839	0.0566937
$681$	48.7474	1.86800
$682$	−16.0180	−0.613360
$683$	13.6788	0.523403	0.261701	−	0.965149i	$-0.415716\pi$
$683$	13.6788	0.523403	0.261701	+	0.965149i	$0.415716\pi$
$684$	7.21574	0.275901
$685$	−2.86773	−0.109570
$686$	13.5597	0.517713
$687$	−0.240855	−0.00918920
$688$	−1.71725	−0.0654695
$689$	15.6335	0.595588
$690$	−6.93369	−0.263961
$691$	38.9094	1.48018	0.740092	−	0.672505i	$-0.234782\pi$
$691$	38.9094	1.48018	0.740092	+	0.672505i	$0.234782\pi$
$692$	−3.00737	−0.114323
$693$	6.37902	0.242319
$694$	−14.2870	−0.542328
$695$	1.27220	0.0482574
$696$	−46.2486	−1.75305
$697$	8.12197	0.307642
$698$	15.8254	0.599001
$699$	40.6063	1.53587
$700$	−6.83341	−0.258279
$701$	39.4549	1.49019	0.745095	−	0.666958i	$-0.232404\pi$
$701$	39.4549	1.49019	0.745095	+	0.666958i	$0.232404\pi$
$702$	18.8279	0.710614
$703$	1.63763	0.0617645
$704$	−28.9698	−1.09184
$705$	8.43896	0.317830
$706$	25.0143	0.941424
$707$	14.8749	0.559429
$708$	−2.38641	−0.0896869
$709$	−34.6885	−1.30276	−0.651378	−	0.758754i	$-0.725809\pi$
$709$	−34.6885	−1.30276	−0.651378	+	0.758754i	$0.725809\pi$
$710$	3.08663	0.115839
$711$	−7.15251	−0.268240
$712$	42.3110	1.58567
$713$	24.7886	0.928341
$714$	−2.15507	−0.0806514
$715$	−14.5627	−0.544613
$716$	−6.67967	−0.249631
$717$	−28.8238	−1.07644
$718$	−12.8640	−0.480082
$719$	−27.2163	−1.01500	−0.507499	−	0.861652i	$-0.669430\pi$
$719$	−27.2163	−1.01500	−0.507499	+	0.861652i	$0.669430\pi$
$720$	0.0874204	0.00325797
$721$	8.01951	0.298662
$722$	17.2065	0.640359
$723$	10.3132	0.383551
$724$	−1.98647	−0.0738265
$725$	−38.3260	−1.42339
$726$	32.8785	1.22024
$727$	27.3164	1.01311	0.506555	−	0.862207i	$-0.330919\pi$
$727$	27.3164	1.01311	0.506555	+	0.862207i	$0.330919\pi$
$728$	−17.9840	−0.666530
$729$	13.4405	0.497797
$730$	4.63993	0.171731
$731$	9.88755	0.365704
$732$	3.84244	0.142021
$733$	−16.1551	−0.596703	−0.298351	−	0.954456i	$-0.596437\pi$
$733$	−16.1551	−0.596703	−0.298351	+	0.954456i	$0.596437\pi$
$734$	25.3796	0.936776
$735$	5.70550	0.210451
$736$	41.9176	1.54510
$737$	−59.3210	−2.18512
$738$	7.09975	0.261346
$739$	−13.1514	−0.483780	−0.241890	−	0.970304i	$-0.577767\pi$
$739$	−13.1514	−0.483780	−0.241890	+	0.970304i	$0.577767\pi$
$740$	−0.163649	−0.00601584
$741$	64.1377	2.35616
$742$	3.24665	0.119188
$743$	9.88944	0.362808	0.181404	−	0.983409i	$-0.441936\pi$
$743$	9.88944	0.362808	0.181404	+	0.983409i	$0.441936\pi$
$744$	−18.8299	−0.690338
$745$	2.58571	0.0947329
$746$	22.2494	0.814608
$747$	−14.5693	−0.533063
$748$	6.48981	0.237291
$749$	−4.49051	−0.164080
$750$	8.97495	0.327719
$751$	10.8917	0.397443	0.198721	−	0.980056i	$-0.436321\pi$
$751$	10.8917	0.397443	0.198721	+	0.980056i	$0.436321\pi$
$752$	1.42452	0.0519468
$753$	−57.4682	−2.09426
$754$	−37.7631	−1.37525
$755$	−8.01223	−0.291595
$756$	−5.82721	−0.211934
$757$	−7.95075	−0.288975	−0.144487	−	0.989507i	$-0.546153\pi$
$757$	−7.95075	−0.288975	−0.144487	+	0.989507i	$0.546153\pi$
$758$	5.27765	0.191693
$759$	−81.2982	−2.95094
$760$	−9.13738	−0.331448
$761$	4.64784	0.168484	0.0842420	−	0.996445i	$-0.473153\pi$
$761$	4.64784	0.168484	0.0842420	+	0.996445i	$0.473153\pi$
$762$	10.7296	0.388692
$763$	6.98021	0.252701
$764$	−3.09523	−0.111981
$765$	−0.503348	−0.0181986
$766$	17.2026	0.621554
$767$	−5.20462	−0.187928
$768$	−32.6703	−1.17889
$769$	−24.1961	−0.872533	−0.436267	−	0.899817i	$-0.643700\pi$
$769$	−24.1961	−0.872533	−0.436267	+	0.899817i	$0.643700\pi$
$770$	−3.02428	−0.108987
$771$	−35.5231	−1.27933
$772$	6.53603	0.235237
$773$	−38.0608	−1.36895	−0.684475	−	0.729036i	$-0.739969\pi$
$773$	−38.0608	−1.36895	−0.684475	+	0.729036i	$0.739969\pi$
$774$	8.64312	0.310671
$775$	−15.6043	−0.560522
$776$	−2.20569	−0.0791797
$777$	0.637173	0.0228584
$778$	−9.60301	−0.344285
$779$	−50.1989	−1.79856
$780$	−6.40927	−0.229489
$781$	36.1910	1.29502
$782$	6.73905	0.240988
$783$	−32.6826	−1.16798
$784$	0.963102	0.0343965
$785$	12.3396	0.440420
$786$	1.31216	0.0468031
$787$	−5.55855	−0.198141	−0.0990705	−	0.995080i	$-0.531587\pi$
$787$	−5.55855	−0.198141	−0.0990705	+	0.995080i	$0.531587\pi$
$788$	4.72605	0.168359
$789$	−9.89988	−0.352445
$790$	3.39099	0.120646
$791$	−11.7998	−0.419551
$792$	15.1526	0.538425
$793$	8.38012	0.297587
$794$	−13.4765	−0.478264
$795$	3.09053	0.109610
$796$	−2.27782	−0.0807351
$797$	−47.6111	−1.68647	−0.843236	−	0.537544i	$-0.819352\pi$
$797$	−47.6111	−1.68647	−0.843236	+	0.537544i	$0.819352\pi$
$798$	13.3197	0.471511
$799$	−8.20206	−0.290168
$800$	−26.3868	−0.932915
$801$	−14.4056	−0.508998
$802$	17.6703	0.623962
$803$	54.4036	1.91986
$804$	−26.1081	−0.920763
$805$	4.68022	0.164956
$806$	−15.3751	−0.541565
$807$	33.6481	1.18447
$808$	35.3337	1.24303
$809$	40.8231	1.43526	0.717632	−	0.696422i	$-0.245226\pi$
$809$	40.8231	1.43526	0.717632	+	0.696422i	$0.245226\pi$
$810$	5.07527	0.178327
$811$	−10.4628	−0.367397	−0.183699	−	0.982983i	$-0.558807\pi$
$811$	−10.4628	−0.367397	−0.183699	+	0.982983i	$0.558807\pi$
$812$	11.6876	0.410155
$813$	57.7729	2.02618
$814$	1.28751	0.0451271
$815$	6.03019	0.211228
$816$	−0.346287	−0.0121225
$817$	−61.1113	−2.13801
$818$	−27.6812	−0.967850
$819$	6.12300	0.213955
$820$	5.01637	0.175179
$821$	−19.1038	−0.666727	−0.333363	−	0.942798i	$-0.608184\pi$
$821$	−19.1038	−0.666727	−0.333363	+	0.942798i	$0.608184\pi$
$822$	9.92986	0.346344
$823$	40.7061	1.41892	0.709462	−	0.704744i	$-0.248938\pi$
$823$	40.7061	1.41892	0.709462	+	0.704744i	$0.248938\pi$
$824$	19.0494	0.663618
$825$	51.1767	1.78174
$826$	−1.08086	−0.0376079
$827$	31.0258	1.07887	0.539437	−	0.842026i	$-0.318637\pi$
$827$	31.0258	1.07887	0.539437	+	0.842026i	$0.318637\pi$
$828$	−8.77929	−0.305101
$829$	−9.38578	−0.325982	−0.162991	−	0.986628i	$-0.552114\pi$
$829$	−9.38578	−0.325982	−0.162991	+	0.986628i	$0.552114\pi$
$830$	6.90727	0.239755
$831$	7.68458	0.266575
$832$	−27.8072	−0.964040
$833$	−5.54534	−0.192135
$834$	−4.40516	−0.152538
$835$	12.5186	0.433224
$836$	−40.1111	−1.38727
$837$	−13.3066	−0.459943
$838$	−2.13738	−0.0738346
$839$	3.45641	0.119328	0.0596642	−	0.998219i	$-0.480997\pi$
$839$	3.45641	0.119328	0.0596642	+	0.998219i	$0.480997\pi$
$840$	−3.55519	−0.122666
$841$	36.5514	1.26039
$842$	−16.3995	−0.565163
$843$	43.8864	1.51153
$844$	15.4015	0.530141
$845$	−7.26985	−0.250090
$846$	−7.16977	−0.246502
$847$	−22.1929	−0.762557
$848$	0.521688	0.0179148
$849$	55.9300	1.91951
$850$	−4.24219	−0.145506
$851$	−1.99249	−0.0683015
$852$	15.9283	0.545693
$853$	20.4180	0.699097	0.349549	−	0.936918i	$-0.386335\pi$
$853$	20.4180	0.699097	0.349549	+	0.936918i	$0.386335\pi$
$854$	1.74033	0.0595527
$855$	3.11100	0.106394
$856$	−10.6667	−0.364580
$857$	40.5835	1.38631	0.693153	−	0.720790i	$-0.256221\pi$
$857$	40.5835	1.38631	0.693153	+	0.720790i	$0.256221\pi$
$858$	50.4251	1.72148
$859$	−44.3596	−1.51353	−0.756765	−	0.653687i	$-0.773221\pi$
$859$	−44.3596	−1.51353	−0.756765	+	0.653687i	$0.773221\pi$
$860$	6.10684	0.208242
$861$	−19.5315	−0.665630
$862$	0.834517	0.0284238
$863$	−23.3703	−0.795533	−0.397766	−	0.917487i	$-0.630215\pi$
$863$	−23.3703	−0.795533	−0.397766	+	0.917487i	$0.630215\pi$
$864$	−22.5015	−0.765515
$865$	−1.29660	−0.0440858
$866$	23.0768	0.784182
$867$	1.99385	0.0677146
$868$	4.75857	0.161516
$869$	39.7597	1.34875
$870$	−7.46525	−0.253096
$871$	−56.9402	−1.92935
$872$	16.5807	0.561493
$873$	0.750972	0.0254165
$874$	−41.6516	−1.40889
$875$	−6.05807	−0.204800
$876$	23.9439	0.808990
$877$	−17.0716	−0.576467	−0.288233	−	0.957560i	$-0.593068\pi$
$877$	−17.0716	−0.576467	−0.288233	+	0.957560i	$0.593068\pi$
$878$	−34.0892	−1.15046
$879$	−34.7158	−1.17094
$880$	−0.485956	−0.0163816
$881$	8.22548	0.277123	0.138562	−	0.990354i	$-0.455752\pi$
$881$	8.22548	0.277123	0.138562	+	0.990354i	$0.455752\pi$
$882$	−4.84741	−0.163221
$883$	−15.9937	−0.538230	−0.269115	−	0.963108i	$-0.586731\pi$
$883$	−15.9937	−0.538230	−0.269115	+	0.963108i	$0.586731\pi$
$884$	6.22935	0.209516
$885$	−1.02888	−0.0345855
$886$	−26.8135	−0.900818
$887$	−6.90382	−0.231808	−0.115904	−	0.993260i	$-0.536976\pi$
$887$	−6.90382	−0.231808	−0.115904	+	0.993260i	$0.536976\pi$
$888$	1.51353	0.0507908
$889$	−7.24245	−0.242904
$890$	6.82968	0.228931
$891$	59.5081	1.99359
$892$	−11.3473	−0.379937
$893$	50.6939	1.69641
$894$	−8.95333	−0.299444
$895$	−2.87989	−0.0962639
$896$	7.67131	0.256280
$897$	−78.0354	−2.60553
$898$	−22.0961	−0.737355
$899$	26.6890	0.890128
$900$	5.52650	0.184217
$901$	−3.00377	−0.100070
$902$	−39.4664	−1.31409
$903$	−23.7773	−0.791258
$904$	−28.0290	−0.932229
$905$	−0.856449	−0.0284693
$906$	27.7434	0.921712
$907$	0.268999	0.00893198	0.00446599	−	0.999990i	$-0.498578\pi$
$907$	0.268999	0.00893198	0.00446599	+	0.999990i	$0.498578\pi$
$908$	−29.2626	−0.971114
$909$	−12.0301	−0.399012
$910$	−2.90290	−0.0962302
$911$	37.6338	1.24686	0.623432	−	0.781877i	$-0.285738\pi$
$911$	37.6338	1.24686	0.623432	+	0.781877i	$0.285738\pi$
$912$	2.14027	0.0708715
$913$	80.9884	2.68032
$914$	2.67541	0.0884946
$915$	1.65664	0.0547667
$916$	0.144583	0.00477717
$917$	−0.885703	−0.0292485
$918$	−3.61754	−0.119397
$919$	37.0429	1.22193	0.610965	−	0.791657i	$-0.290781\pi$
$919$	37.0429	1.22193	0.610965	+	0.791657i	$0.290781\pi$
$920$	11.1173	0.366527
$921$	10.5634	0.348075
$922$	12.6907	0.417946
$923$	34.7385	1.14343
$924$	−15.6065	−0.513416
$925$	1.25426	0.0412397
$926$	−0.842522	−0.0276870
$927$	−6.48576	−0.213020
$928$	45.1311	1.48150
$929$	26.9930	0.885612	0.442806	−	0.896617i	$-0.353983\pi$
$929$	26.9930	0.885612	0.442806	+	0.896617i	$0.353983\pi$
$930$	−3.03945	−0.0996675
$931$	34.2736	1.12327
$932$	−24.3756	−0.798450
$933$	−1.52868	−0.0500468
$934$	6.96100	0.227771
$935$	2.79803	0.0915054
$936$	14.5445	0.475401
$937$	−10.7654	−0.351689	−0.175844	−	0.984418i	$-0.556266\pi$
$937$	−10.7654	−0.351689	−0.175844	+	0.984418i	$0.556266\pi$
$938$	−11.8250	−0.386098
$939$	41.1993	1.34449
$940$	−5.06584	−0.165229
$941$	−0.519990	−0.0169512	−0.00847559	−	0.999964i	$-0.502698\pi$
$941$	−0.519990	−0.0169512	−0.00847559	+	0.999964i	$0.502698\pi$
$942$	−42.7275	−1.39214
$943$	61.0763	1.98892
$944$	−0.173678	−0.00565273
$945$	−2.51235	−0.0817269
$946$	−48.0457	−1.56210
$947$	−20.7772	−0.675167	−0.337584	−	0.941296i	$-0.609610\pi$
$947$	−20.7772	−0.675167	−0.337584	+	0.941296i	$0.609610\pi$
$948$	17.4989	0.568337
$949$	52.2202	1.69514
$950$	26.2194	0.850669
$951$	−37.7030	−1.22260
$952$	3.45539	0.111990
$953$	10.6711	0.345669	0.172835	−	0.984951i	$-0.444707\pi$
$953$	10.6711	0.345669	0.172835	+	0.984951i	$0.444707\pi$
$954$	−2.62572	−0.0850108
$955$	−1.33448	−0.0431828
$956$	17.3027	0.559609
$957$	−87.5308	−2.82947
$958$	−11.5957	−0.374641
$959$	−6.70262	−0.216439
$960$	−5.49710	−0.177418
$961$	−20.1337	−0.649473
$962$	1.23584	0.0398449
$963$	3.63168	0.117029
$964$	−6.19090	−0.199395
$965$	2.81796	0.0907132
$966$	−16.2059	−0.521415
$967$	55.5798	1.78733	0.893663	−	0.448738i	$-0.148126\pi$
$967$	55.5798	1.78733	0.893663	+	0.448738i	$0.148126\pi$
$968$	−52.7167	−1.69438
$969$	−12.3232	−0.395879
$970$	−0.356034	−0.0114316
$971$	41.8119	1.34181	0.670904	−	0.741544i	$-0.265906\pi$
$971$	41.8119	1.34181	0.670904	+	0.741544i	$0.265906\pi$
$972$	11.6960	0.375151
$973$	2.97347	0.0953251
$974$	−3.55132	−0.113792
$975$	49.1228	1.57319
$976$	0.279644	0.00895119
$977$	−36.9480	−1.18207	−0.591035	−	0.806646i	$-0.701281\pi$
$977$	−36.9480	−1.18207	−0.591035	+	0.806646i	$0.701281\pi$
$978$	−20.8803	−0.667678
$979$	80.0786	2.55932
$980$	−3.42496	−0.109406
$981$	−5.64522	−0.180238
$982$	22.8499	0.729169
$983$	−46.4146	−1.48040	−0.740199	−	0.672388i	$-0.765269\pi$
$983$	−46.4146	−1.48040	−0.740199	+	0.672388i	$0.765269\pi$
$984$	−46.3947	−1.47901
$985$	2.03760	0.0649232
$986$	7.25569	0.231068
$987$	19.7241	0.627824
$988$	−38.5013	−1.22489
$989$	74.3532	2.36430
$990$	2.44587	0.0777350
$991$	−11.2104	−0.356110	−0.178055	−	0.984021i	$-0.556981\pi$
$991$	−11.2104	−0.356110	−0.178055	+	0.984021i	$0.556981\pi$
$992$	18.3750	0.583406
$993$	9.56689	0.303596
$994$	7.21426	0.228822
$995$	−0.982062	−0.0311335
$996$	35.6443	1.12943
$997$	−39.6724	−1.25644	−0.628218	−	0.778037i	$-0.716216\pi$
$997$	−39.6724	−1.25644	−0.628218	+	0.778037i	$0.716216\pi$
$998$	−32.4397	−1.02686
$999$	1.06957	0.0338397

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1003.2.a.h.1.12	✓	16
3.2	odd	2		9027.2.a.n.1.5		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1003.2.a.h.1.12	✓	16	1.1	even	1	trivial
9027.2.a.n.1.5		16	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)

\(f(q)\)	\(=\)	\(q+0.896165 q^{2} +1.99385 q^{3} -1.19689 q^{4} -0.516029 q^{5} +1.78681 q^{6} -1.20609 q^{7} -2.86494 q^{8} +0.975426 q^{9} +O(q^{10})\)	\(q+0.896165 q^{2} +1.99385 q^{3} -1.19689 q^{4} -0.516029 q^{5} +1.78681 q^{6} -1.20609 q^{7} -2.86494 q^{8} +0.975426 q^{9} -0.462447 q^{10} -5.42223 q^{11} -2.38641 q^{12} -5.20462 q^{13} -1.08086 q^{14} -1.02888 q^{15} -0.173678 q^{16} +1.00000 q^{17} +0.874142 q^{18} -6.18063 q^{19} +0.617629 q^{20} -2.40477 q^{21} -4.85921 q^{22} +7.51988 q^{23} -5.71225 q^{24} -4.73371 q^{25} -4.66420 q^{26} -4.03669 q^{27} +1.44356 q^{28} +8.09638 q^{29} -0.922048 q^{30} +3.29641 q^{31} +5.57423 q^{32} -10.8111 q^{33} +0.896165 q^{34} +0.622380 q^{35} -1.16748 q^{36} -0.264962 q^{37} -5.53886 q^{38} -10.3772 q^{39} +1.47839 q^{40} +8.12197 q^{41} -2.15507 q^{42} +9.88755 q^{43} +6.48981 q^{44} -0.503348 q^{45} +6.73905 q^{46} -8.20206 q^{47} -0.346287 q^{48} -5.54534 q^{49} -4.24219 q^{50} +1.99385 q^{51} +6.22935 q^{52} -3.00377 q^{53} -3.61754 q^{54} +2.79803 q^{55} +3.45539 q^{56} -12.3232 q^{57} +7.25569 q^{58} +1.00000 q^{59} +1.23146 q^{60} -1.61013 q^{61} +2.95413 q^{62} -1.17646 q^{63} +5.34279 q^{64} +2.68573 q^{65} -9.68853 q^{66} +10.9403 q^{67} -1.19689 q^{68} +14.9935 q^{69} +0.557755 q^{70} -6.67456 q^{71} -2.79453 q^{72} -10.0334 q^{73} -0.237450 q^{74} -9.43830 q^{75} +7.39752 q^{76} +6.53973 q^{77} -9.29969 q^{78} -7.33271 q^{79} +0.0896228 q^{80} -10.9748 q^{81} +7.27862 q^{82} -14.9364 q^{83} +2.87824 q^{84} -0.516029 q^{85} +8.86087 q^{86} +16.1429 q^{87} +15.5344 q^{88} -14.7686 q^{89} -0.451082 q^{90} +6.27726 q^{91} -9.00047 q^{92} +6.57254 q^{93} -7.35040 q^{94} +3.18938 q^{95} +11.1142 q^{96} +0.769891 q^{97} -4.96953 q^{98} -5.28899 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 6 q^{2} - 7 q^{3} + 14 q^{4} - 21 q^{5} - 5 q^{6} - 11 q^{7} - 12 q^{8} + 17 q^{9}+O(q^{10}) \) 16 * q - 6 * q^2 - 7 * q^3 + 14 * q^4 - 21 * q^5 - 5 * q^6 - 11 * q^7 - 12 * q^8 + 17 * q^9	\( 16 q - 6 q^{2} - 7 q^{3} + 14 q^{4} - 21 q^{5} - 5 q^{6} - 11 q^{7} - 12 q^{8} + 17 q^{9} + 12 q^{10} - 7 q^{11} - 4 q^{12} - 16 q^{13} + 11 q^{14} + 7 q^{15} + 22 q^{16} + 16 q^{17} + 11 q^{18} + q^{19} - 43 q^{20} - 8 q^{21} - 18 q^{22} - 8 q^{23} - 39 q^{24} + 23 q^{25} - 49 q^{26} - 7 q^{27} - 15 q^{28} - 39 q^{29} + q^{30} - 3 q^{31} - 15 q^{33} - 6 q^{34} + 9 q^{35} - 17 q^{36} - 28 q^{37} - 27 q^{38} - 4 q^{39} + 26 q^{40} - 31 q^{41} - 45 q^{42} + 5 q^{43} - 19 q^{44} - 79 q^{45} - 39 q^{46} - 47 q^{47} - 31 q^{48} + 35 q^{49} - 13 q^{50} - 7 q^{51} + 9 q^{52} - 36 q^{53} + 9 q^{54} + 32 q^{55} + 3 q^{56} + 6 q^{57} + 22 q^{58} + 16 q^{59} + 6 q^{60} - 22 q^{61} + q^{62} - 19 q^{63} + 32 q^{64} - 19 q^{65} + 48 q^{66} + 4 q^{67} + 14 q^{68} + 14 q^{69} - 11 q^{70} - 5 q^{71} + 40 q^{72} - 35 q^{73} + 31 q^{74} - 12 q^{75} + q^{76} - 79 q^{77} + 31 q^{78} - 48 q^{79} - 127 q^{80} - 28 q^{81} - 7 q^{82} - 42 q^{83} + 28 q^{84} - 21 q^{85} + 58 q^{86} - 16 q^{87} - 2 q^{88} + 20 q^{89} - 14 q^{90} + 49 q^{91} - 21 q^{92} - 55 q^{93} - 22 q^{95} + 24 q^{96} - 2 q^{97} - 78 q^{98} - 35 q^{99}+O(q^{100}) \) 16 * q - 6 * q^2 - 7 * q^3 + 14 * q^4 - 21 * q^5 - 5 * q^6 - 11 * q^7 - 12 * q^8 + 17 * q^9 + 12 * q^10 - 7 * q^11 - 4 * q^12 - 16 * q^13 + 11 * q^14 + 7 * q^15 + 22 * q^16 + 16 * q^17 + 11 * q^18 + q^19 - 43 * q^20 - 8 * q^21 - 18 * q^22 - 8 * q^23 - 39 * q^24 + 23 * q^25 - 49 * q^26 - 7 * q^27 - 15 * q^28 - 39 * q^29 + q^30 - 3 * q^31 - 15 * q^33 - 6 * q^34 + 9 * q^35 - 17 * q^36 - 28 * q^37 - 27 * q^38 - 4 * q^39 + 26 * q^40 - 31 * q^41 - 45 * q^42 + 5 * q^43 - 19 * q^44 - 79 * q^45 - 39 * q^46 - 47 * q^47 - 31 * q^48 + 35 * q^49 - 13 * q^50 - 7 * q^51 + 9 * q^52 - 36 * q^53 + 9 * q^54 + 32 * q^55 + 3 * q^56 + 6 * q^57 + 22 * q^58 + 16 * q^59 + 6 * q^60 - 22 * q^61 + q^62 - 19 * q^63 + 32 * q^64 - 19 * q^65 + 48 * q^66 + 4 * q^67 + 14 * q^68 + 14 * q^69 - 11 * q^70 - 5 * q^71 + 40 * q^72 - 35 * q^73 + 31 * q^74 - 12 * q^75 + q^76 - 79 * q^77 + 31 * q^78 - 48 * q^79 - 127 * q^80 - 28 * q^81 - 7 * q^82 - 42 * q^83 + 28 * q^84 - 21 * q^85 + 58 * q^86 - 16 * q^87 - 2 * q^88 + 20 * q^89 - 14 * q^90 + 49 * q^91 - 21 * q^92 - 55 * q^93 - 22 * q^95 + 24 * q^96 - 2 * q^97 - 78 * q^98 - 35 * q^99

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