LMFDB - Embedded newform 1003.2.a.h.1.3

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			1.3
Root			$2.33579$ 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)

$f(q)$	$=$	$q-2.33579 q^{2} +2.58736 q^{3} +3.45592 q^{4} -4.30332 q^{5} -6.04353 q^{6} +1.79793 q^{7} -3.40073 q^{8} +3.69442 q^{9} +O(q^{10})$	\(q-2.33579 q^{2} +2.58736 q^{3} +3.45592 q^{4} -4.30332 q^{5} -6.04353 q^{6} +1.79793 q^{7} -3.40073 q^{8} +3.69442 q^{9} +10.0517 q^{10} -4.87519 q^{11} +8.94170 q^{12} +2.64784 q^{13} -4.19959 q^{14} -11.1342 q^{15} +1.03155 q^{16} +1.00000 q^{17} -8.62938 q^{18} -3.80200 q^{19} -14.8719 q^{20} +4.65189 q^{21} +11.3874 q^{22} +7.68178 q^{23} -8.79889 q^{24} +13.5186 q^{25} -6.18479 q^{26} +1.79670 q^{27} +6.21350 q^{28} -8.84846 q^{29} +26.0072 q^{30} -5.05465 q^{31} +4.39198 q^{32} -12.6139 q^{33} -2.33579 q^{34} -7.73707 q^{35} +12.7676 q^{36} -12.1221 q^{37} +8.88067 q^{38} +6.85090 q^{39} +14.6344 q^{40} -5.93352 q^{41} -10.8658 q^{42} +4.61501 q^{43} -16.8483 q^{44} -15.8983 q^{45} -17.9430 q^{46} -6.07450 q^{47} +2.66898 q^{48} -3.76745 q^{49} -31.5765 q^{50} +2.58736 q^{51} +9.15071 q^{52} +5.69605 q^{53} -4.19672 q^{54} +20.9795 q^{55} -6.11427 q^{56} -9.83712 q^{57} +20.6682 q^{58} +1.00000 q^{59} -38.4790 q^{60} -8.74129 q^{61} +11.8066 q^{62} +6.64230 q^{63} -12.3218 q^{64} -11.3945 q^{65} +29.4633 q^{66} -1.12524 q^{67} +3.45592 q^{68} +19.8755 q^{69} +18.0722 q^{70} -3.32894 q^{71} -12.5637 q^{72} +0.691263 q^{73} +28.3147 q^{74} +34.9773 q^{75} -13.1394 q^{76} -8.76525 q^{77} -16.0023 q^{78} -11.7657 q^{79} -4.43907 q^{80} -6.43454 q^{81} +13.8595 q^{82} +4.80577 q^{83} +16.0765 q^{84} -4.30332 q^{85} -10.7797 q^{86} -22.8941 q^{87} +16.5792 q^{88} +7.29040 q^{89} +37.1350 q^{90} +4.76062 q^{91} +26.5476 q^{92} -13.0782 q^{93} +14.1888 q^{94} +16.3612 q^{95} +11.3636 q^{96} -0.107234 q^{97} +8.79998 q^{98} -18.0110 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.33579	−1.65165	−0.825827	−	0.563924i	$-0.809291\pi$
$2$	−2.33579	−1.65165	−0.825827	+	0.563924i	$0.809291\pi$
$3$	2.58736	1.49381	0.746906	−	0.664930i	$-0.231539\pi$
$3$	2.58736	1.49381	0.746906	+	0.664930i	$0.231539\pi$
$4$	3.45592	1.72796
$5$	−4.30332	−1.92450	−0.962252	−	0.272161i	$-0.912262\pi$
$5$	−4.30332	−1.92450	−0.962252	+	0.272161i	$0.912262\pi$
$6$	−6.04353	−2.46726
$7$	1.79793	0.679553	0.339777	−	0.940506i	$-0.389648\pi$
$7$	1.79793	0.679553	0.339777	+	0.940506i	$0.389648\pi$
$8$	−3.40073	−1.20234
$9$	3.69442	1.23147
$10$	10.0517	3.17861
$11$	−4.87519	−1.46993	−0.734963	−	0.678108i	$-0.762800\pi$
$11$	−4.87519	−1.46993	−0.734963	+	0.678108i	$0.762800\pi$
$12$	8.94170	2.58125
$13$	2.64784	0.734378	0.367189	−	0.930146i	$-0.380320\pi$
$13$	2.64784	0.734378	0.367189	+	0.930146i	$0.380320\pi$
$14$	−4.19959	−1.12239
$15$	−11.1342	−2.87484
$16$	1.03155	0.257886
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−8.62938	−2.03397
$19$	−3.80200	−0.872238	−0.436119	−	0.899889i	$-0.643647\pi$
$19$	−3.80200	−0.872238	−0.436119	+	0.899889i	$0.643647\pi$
$20$	−14.8719	−3.32547
$21$	4.65189	1.01512
$22$	11.3874	2.42781
$23$	7.68178	1.60176	0.800881	−	0.598824i	$-0.204365\pi$
$23$	7.68178	1.60176	0.800881	+	0.598824i	$0.204365\pi$
$24$	−8.79889	−1.79607
$25$	13.5186	2.70371
$26$	−6.18479	−1.21294
$27$	1.79670	0.345775
$28$	6.21350	1.17424
$29$	−8.84846	−1.64312	−0.821559	−	0.570123i	$-0.806896\pi$
$29$	−8.84846	−1.64312	−0.821559	+	0.570123i	$0.806896\pi$
$30$	26.0072	4.74825
$31$	−5.05465	−0.907842	−0.453921	−	0.891042i	$-0.649975\pi$
$31$	−5.05465	−0.907842	−0.453921	+	0.891042i	$0.649975\pi$
$32$	4.39198	0.776399
$33$	−12.6139	−2.19579
$34$	−2.33579	−0.400585
$35$	−7.73707	−1.30780
$36$	12.7676	2.12793
$37$	−12.1221	−1.99286	−0.996432	−	0.0844007i	$-0.973102\pi$
$37$	−12.1221	−1.99286	−0.996432	+	0.0844007i	$0.973102\pi$
$38$	8.88067	1.44063
$39$	6.85090	1.09702
$40$	14.6344	2.31390
$41$	−5.93352	−0.926660	−0.463330	−	0.886186i	$-0.653345\pi$
$41$	−5.93352	−0.926660	−0.463330	+	0.886186i	$0.653345\pi$
$42$	−10.8658	−1.67663
$43$	4.61501	0.703783	0.351891	−	0.936041i	$-0.385539\pi$
$43$	4.61501	0.703783	0.351891	+	0.936041i	$0.385539\pi$
$44$	−16.8483	−2.53997
$45$	−15.8983	−2.36997
$46$	−17.9430	−2.64556
$47$	−6.07450	−0.886057	−0.443028	−	0.896508i	$-0.646096\pi$
$47$	−6.07450	−0.886057	−0.443028	+	0.896508i	$0.646096\pi$
$48$	2.66898	0.385233
$49$	−3.76745	−0.538207
$50$	−31.5765	−4.46560
$51$	2.58736	0.362302
$52$	9.15071	1.26898
$53$	5.69605	0.782413	0.391206	−	0.920303i	$-0.372058\pi$
$53$	5.69605	0.782413	0.391206	+	0.920303i	$0.372058\pi$
$54$	−4.19672	−0.571101
$55$	20.9795	2.82888
$56$	−6.11427	−0.817053
$57$	−9.83712	−1.30296
$58$	20.6682	2.71386
$59$	1.00000	0.130189
$59$	1.00000	0.130189
$60$	−38.4790	−4.96762
$61$	−8.74129	−1.11921	−0.559604	−	0.828760i	$-0.689047\pi$
$61$	−8.74129	−1.11921	−0.559604	+	0.828760i	$0.689047\pi$
$62$	11.8066	1.49944
$63$	6.64230	0.836851
$64$	−12.3218	−1.54023
$65$	−11.3945	−1.41331
$66$	29.4633	3.62669
$67$	−1.12524	−0.137470	−0.0687348	−	0.997635i	$-0.521896\pi$
$67$	−1.12524	−0.137470	−0.0687348	+	0.997635i	$0.521896\pi$
$68$	3.45592	0.419092
$69$	19.8755	2.39273
$70$	18.0722	2.16004
$71$	−3.32894	−0.395073	−0.197536	−	0.980296i	$-0.563294\pi$
$71$	−3.32894	−0.395073	−0.197536	+	0.980296i	$0.563294\pi$
$72$	−12.5637	−1.48065
$73$	0.691263	0.0809062	0.0404531	−	0.999181i	$-0.487120\pi$
$73$	0.691263	0.0809062	0.0404531	+	0.999181i	$0.487120\pi$
$74$	28.3147	3.29152
$75$	34.9773	4.03884
$76$	−13.1394	−1.50719
$77$	−8.76525	−0.998893
$78$	−16.0023	−1.81190
$79$	−11.7657	−1.32374	−0.661870	−	0.749618i	$-0.730237\pi$
$79$	−11.7657	−1.32374	−0.661870	+	0.749618i	$0.730237\pi$
$80$	−4.43907	−0.496303
$81$	−6.43454	−0.714949
$82$	13.8595	1.53052
$83$	4.80577	0.527502	0.263751	−	0.964591i	$-0.415040\pi$
$83$	4.80577	0.527502	0.263751	+	0.964591i	$0.415040\pi$
$84$	16.0765	1.75409
$85$	−4.30332	−0.466761
$86$	−10.7797	−1.16241
$87$	−22.8941	−2.45451
$88$	16.5792	1.76735
$89$	7.29040	0.772781	0.386391	−	0.922335i	$-0.373722\pi$
$89$	7.29040	0.772781	0.386391	+	0.922335i	$0.373722\pi$
$90$	37.1350	3.91437
$91$	4.76062	0.499049
$92$	26.5476	2.76778
$93$	−13.0782	−1.35614
$94$	14.1888	1.46346
$95$	16.3612	1.67862
$96$	11.3636	1.15979
$97$	−0.107234	−0.0108880	−0.00544400	−	0.999985i	$-0.501733\pi$
$97$	−0.107234	−0.0108880	−0.00544400	+	0.999985i	$0.501733\pi$
$98$	8.79998	0.888932
$99$	−18.0110	−1.81017
$100$	46.7191	4.67191
$101$	−4.93862	−0.491411	−0.245706	−	0.969344i	$-0.579020\pi$
$101$	−4.93862	−0.491411	−0.245706	+	0.969344i	$0.579020\pi$
$102$	−6.04353	−0.598398
$103$	3.53105	0.347925	0.173962	−	0.984752i	$-0.444343\pi$
$103$	3.53105	0.347925	0.173962	+	0.984752i	$0.444343\pi$
$104$	−9.00457	−0.882970
$105$	−20.0186	−1.95361
$106$	−13.3048	−1.29227
$107$	−8.27733	−0.800200	−0.400100	−	0.916471i	$-0.631025\pi$
$107$	−8.27733	−0.800200	−0.400100	+	0.916471i	$0.631025\pi$
$108$	6.20925	0.597486
$109$	17.3289	1.65981	0.829903	−	0.557908i	$-0.188396\pi$
$109$	17.3289	1.65981	0.829903	+	0.557908i	$0.188396\pi$
$110$	−49.0037	−4.67232
$111$	−31.3642	−2.97696
$112$	1.85465	0.175248
$113$	−1.67473	−0.157546	−0.0787729	−	0.996893i	$-0.525100\pi$
$113$	−1.67473	−0.157546	−0.0787729	+	0.996893i	$0.525100\pi$
$114$	22.9775	2.15204
$115$	−33.0572	−3.08260
$116$	−30.5796	−2.83924
$117$	9.78221	0.904365
$118$	−2.33579	−0.215027
$119$	1.79793	0.164816
$120$	37.8644	3.45654
$121$	12.7675	1.16068
$122$	20.4178	1.84854
$123$	−15.3521	−1.38425
$124$	−17.4685	−1.56871
$125$	−36.6581	−3.27880
$126$	−15.5150	−1.38219
$127$	−13.5156	−1.19931	−0.599656	−	0.800258i	$-0.704696\pi$
$127$	−13.5156	−1.19931	−0.599656	+	0.800258i	$0.704696\pi$
$128$	19.9973	1.76753
$129$	11.9407	1.05132
$130$	26.6151	2.33430
$131$	−7.46696	−0.652391	−0.326196	−	0.945302i	$-0.605767\pi$
$131$	−7.46696	−0.652391	−0.326196	+	0.945302i	$0.605767\pi$
$132$	−43.5925	−3.79424
$133$	−6.83572	−0.592732
$134$	2.62832	0.227052
$135$	−7.73178	−0.665446
$136$	−3.40073	−0.291610
$137$	6.00579	0.513109	0.256555	−	0.966530i	$-0.417413\pi$
$137$	6.00579	0.513109	0.256555	+	0.966530i	$0.417413\pi$
$138$	−46.4250	−3.95196
$139$	−18.6683	−1.58342	−0.791711	−	0.610895i	$-0.790810\pi$
$139$	−18.6683	−1.58342	−0.791711	+	0.610895i	$0.790810\pi$
$140$	−26.7387	−2.25983
$141$	−15.7169	−1.32360
$142$	7.77572	0.652524
$143$	−12.9087	−1.07948
$144$	3.81096	0.317580
$145$	38.0778	3.16219
$146$	−1.61465	−0.133629
$147$	−9.74774	−0.803980
$148$	−41.8931	−3.44359
$149$	6.84141	0.560470	0.280235	−	0.959931i	$-0.409588\pi$
$149$	6.84141	0.560470	0.280235	+	0.959931i	$0.409588\pi$
$150$	−81.6998	−6.67076
$151$	−7.83536	−0.637633	−0.318816	−	0.947816i	$-0.603285\pi$
$151$	−7.83536	−0.637633	−0.318816	+	0.947816i	$0.603285\pi$
$152$	12.9295	1.04872
$153$	3.69442	0.298676
$154$	20.4738	1.64982
$155$	21.7518	1.74714
$156$	23.6762	1.89561
$157$	−11.6750	−0.931769	−0.465884	−	0.884846i	$-0.654264\pi$
$157$	−11.6750	−0.931769	−0.465884	+	0.884846i	$0.654264\pi$
$158$	27.4821	2.18636
$159$	14.7377	1.16878
$160$	−18.9001	−1.49418
$161$	13.8113	1.08848
$162$	15.0297	1.18085
$163$	7.27447	0.569781	0.284890	−	0.958560i	$-0.408043\pi$
$163$	7.27447	0.569781	0.284890	+	0.958560i	$0.408043\pi$
$164$	−20.5058	−1.60123
$165$	54.2815	4.22581
$166$	−11.2253	−0.871250
$167$	11.6132	0.898654	0.449327	−	0.893367i	$-0.351664\pi$
$167$	11.6132	0.898654	0.449327	+	0.893367i	$0.351664\pi$
$168$	−15.8198	−1.22052
$169$	−5.98896	−0.460689
$170$	10.0517	0.770927
$171$	−14.0462	−1.07414
$172$	15.9491	1.21611
$173$	2.57679	0.195910	0.0979548	−	0.995191i	$-0.468770\pi$
$173$	2.57679	0.195910	0.0979548	+	0.995191i	$0.468770\pi$
$174$	53.4759	4.05400
$175$	24.3054	1.83732
$176$	−5.02898	−0.379074
$177$	2.58736	0.194478
$178$	−17.0289	−1.27637
$179$	−5.07070	−0.379002	−0.189501	−	0.981881i	$-0.560687\pi$
$179$	−5.07070	−0.379002	−0.189501	+	0.981881i	$0.560687\pi$
$180$	−54.9431	−4.09522
$181$	−18.5238	−1.37687	−0.688433	−	0.725300i	$-0.741701\pi$
$181$	−18.5238	−1.37687	−0.688433	+	0.725300i	$0.741701\pi$
$182$	−11.1198	−0.824256
$183$	−22.6168	−1.67188
$184$	−26.1236	−1.92586
$185$	52.1653	3.83527
$186$	30.5479	2.23988
$187$	−4.87519	−0.356509
$188$	−20.9930	−1.53107
$189$	3.23034	0.234973
$190$	−38.2164	−2.77251
$191$	17.7791	1.28645	0.643224	−	0.765678i	$-0.277597\pi$
$191$	17.7791	1.28645	0.643224	+	0.765678i	$0.277597\pi$
$192$	−31.8810	−2.30081
$193$	20.5091	1.47628	0.738139	−	0.674649i	$-0.235705\pi$
$193$	20.5091	1.47628	0.738139	+	0.674649i	$0.235705\pi$
$194$	0.250477	0.0179832
$195$	−29.4816	−2.11122
$196$	−13.0200	−0.930000
$197$	−7.02648	−0.500616	−0.250308	−	0.968166i	$-0.580532\pi$
$197$	−7.02648	−0.500616	−0.250308	+	0.968166i	$0.580532\pi$
$198$	42.0699	2.98978
$199$	4.10577	0.291050	0.145525	−	0.989355i	$-0.453513\pi$
$199$	4.10577	0.291050	0.145525	+	0.989355i	$0.453513\pi$
$200$	−45.9729	−3.25078
$201$	−2.91139	−0.205354
$202$	11.5356	0.811641
$203$	−15.9089	−1.11659
$204$	8.94170	0.626044
$205$	25.5338	1.78336
$206$	−8.24779	−0.574651
$207$	28.3797	1.97252
$208$	2.73136	0.189386
$209$	18.5355	1.28212
$210$	46.7592	3.22669
$211$	13.4871	0.928492	0.464246	−	0.885706i	$-0.346325\pi$
$211$	13.4871	0.928492	0.464246	+	0.885706i	$0.346325\pi$
$212$	19.6851	1.35198
$213$	−8.61316	−0.590164
$214$	19.3341	1.32165
$215$	−19.8599	−1.35443
$216$	−6.11009	−0.415739
$217$	−9.08790	−0.616927
$218$	−40.4767	−2.74142
$219$	1.78854	0.120859
$220$	72.5035	4.88818
$221$	2.64784	0.178113
$222$	73.2603	4.91691
$223$	−7.93676	−0.531485	−0.265742	−	0.964044i	$-0.585617\pi$
$223$	−7.93676	−0.531485	−0.265742	+	0.964044i	$0.585617\pi$
$224$	7.89647	0.527605
$225$	49.9432	3.32955
$226$	3.91183	0.260211
$227$	6.21840	0.412730	0.206365	−	0.978475i	$-0.433837\pi$
$227$	6.21840	0.412730	0.206365	+	0.978475i	$0.433837\pi$
$228$	−33.9963	−2.25146
$229$	23.6989	1.56607	0.783035	−	0.621978i	$-0.213671\pi$
$229$	23.6989	1.56607	0.783035	+	0.621978i	$0.213671\pi$
$230$	77.2146	5.09138
$231$	−22.6788	−1.49216
$232$	30.0912	1.97558
$233$	−14.2724	−0.935013	−0.467506	−	0.883990i	$-0.654848\pi$
$233$	−14.2724	−0.935013	−0.467506	+	0.883990i	$0.654848\pi$
$234$	−22.8492	−1.49370
$235$	26.1405	1.70522
$236$	3.45592	0.224961
$237$	−30.4420	−1.97742
$238$	−4.19959	−0.272219
$239$	−12.1706	−0.787249	−0.393624	−	0.919271i	$-0.628779\pi$
$239$	−12.1706	−0.787249	−0.393624	+	0.919271i	$0.628779\pi$
$240$	−11.4855	−0.741383
$241$	12.1923	0.785375	0.392688	−	0.919672i	$-0.371545\pi$
$241$	12.1923	0.785375	0.392688	+	0.919672i	$0.371545\pi$
$242$	−29.8222	−1.91704
$243$	−22.0386	−1.41377
$244$	−30.2092	−1.93395
$245$	16.2125	1.03578
$246$	35.8594	2.28631
$247$	−10.0671	−0.640552
$248$	17.1895	1.09153
$249$	12.4342	0.787988
$250$	85.6257	5.41544
$251$	17.5438	1.10736	0.553678	−	0.832731i	$-0.313224\pi$
$251$	17.5438	1.10736	0.553678	+	0.832731i	$0.313224\pi$
$252$	22.9553	1.44605
$253$	−37.4501	−2.35447
$254$	31.5695	1.98085
$255$	−11.1342	−0.697252
$256$	−22.0658	−1.37911
$257$	−7.29743	−0.455201	−0.227600	−	0.973755i	$-0.573088\pi$
$257$	−7.29743	−0.455201	−0.227600	+	0.973755i	$0.573088\pi$
$258$	−27.8909	−1.73641
$259$	−21.7947	−1.35426
$260$	−39.3784	−2.44215
$261$	−32.6899	−2.02345
$262$	17.4413	1.07752
$263$	8.74956	0.539521	0.269761	−	0.962927i	$-0.413055\pi$
$263$	8.74956	0.539521	0.269761	+	0.962927i	$0.413055\pi$
$264$	42.8963	2.64008
$265$	−24.5119	−1.50576
$266$	15.9668	0.978988
$267$	18.8629	1.15439
$268$	−3.88873	−0.237542
$269$	−20.5929	−1.25557	−0.627787	−	0.778386i	$-0.716039\pi$
$269$	−20.5929	−1.25557	−0.627787	+	0.778386i	$0.716039\pi$
$270$	18.0598	1.09909
$271$	−7.96146	−0.483624	−0.241812	−	0.970323i	$-0.577742\pi$
$271$	−7.96146	−0.483624	−0.241812	+	0.970323i	$0.577742\pi$
$272$	1.03155	0.0625466
$273$	12.3174	0.745485
$274$	−14.0283	−0.847479
$275$	−65.9056	−3.97426
$276$	68.6882	4.13454
$277$	2.92941	0.176011	0.0880055	−	0.996120i	$-0.471951\pi$
$277$	2.92941	0.176011	0.0880055	+	0.996120i	$0.471951\pi$
$278$	43.6052	2.61527
$279$	−18.6740	−1.11798
$280$	26.3116	1.57242
$281$	18.7893	1.12087	0.560436	−	0.828197i	$-0.310633\pi$
$281$	18.7893	1.12087	0.560436	+	0.828197i	$0.310633\pi$
$282$	36.7114	2.18613
$283$	12.5305	0.744860	0.372430	−	0.928060i	$-0.378525\pi$
$283$	12.5305	0.744860	0.372430	+	0.928060i	$0.378525\pi$
$284$	−11.5046	−0.682670
$285$	42.3323	2.50755
$286$	30.1520	1.78293
$287$	−10.6680	−0.629715
$288$	16.2258	0.956114
$289$	1.00000	0.0588235
$290$	−88.9417	−5.22284
$291$	−0.277454	−0.0162646
$292$	2.38895	0.139803
$293$	1.55832	0.0910381	0.0455190	−	0.998963i	$-0.485506\pi$
$293$	1.55832	0.0910381	0.0455190	+	0.998963i	$0.485506\pi$
$294$	22.7687	1.32790
$295$	−4.30332	−0.250549
$296$	41.2240	2.39610
$297$	−8.75926	−0.508264
$298$	−15.9801	−0.925702
$299$	20.3401	1.17630
$300$	120.879	6.97895
$301$	8.29746	0.478258
$302$	18.3018	1.05315
$303$	−12.7780	−0.734076
$304$	−3.92193	−0.224938
$305$	37.6166	2.15392
$306$	−8.62938	−0.493309
$307$	24.9664	1.42491	0.712454	−	0.701718i	$-0.247583\pi$
$307$	24.9664	1.42491	0.712454	+	0.701718i	$0.247583\pi$
$308$	−30.2920	−1.72605
$309$	9.13609	0.519734
$310$	−50.8076	−2.88568
$311$	−27.2448	−1.54491	−0.772457	−	0.635067i	$-0.780972\pi$
$311$	−27.2448	−1.54491	−0.772457	+	0.635067i	$0.780972\pi$
$312$	−23.2980	−1.31899
$313$	16.2413	0.918014	0.459007	−	0.888433i	$-0.348205\pi$
$313$	16.2413	0.918014	0.459007	+	0.888433i	$0.348205\pi$
$314$	27.2704	1.53896
$315$	−28.5839	−1.61052
$316$	−40.6612	−2.28737
$317$	10.7060	0.601309	0.300655	−	0.953733i	$-0.402795\pi$
$317$	10.7060	0.601309	0.300655	+	0.953733i	$0.402795\pi$
$318$	−34.4242	−1.93041
$319$	43.1379	2.41526
$320$	53.0248	2.96418
$321$	−21.4164	−1.19535
$322$	−32.2603	−1.79780
$323$	−3.80200	−0.211549
$324$	−22.2373	−1.23540
$325$	35.7949	1.98555
$326$	−16.9917	−0.941081
$327$	44.8360	2.47944
$328$	20.1783	1.11416
$329$	−10.9215	−0.602123
$330$	−126.790	−6.97957
$331$	1.07324	0.0589906	0.0294953	−	0.999565i	$-0.490610\pi$
$331$	1.07324	0.0589906	0.0294953	+	0.999565i	$0.490610\pi$
$332$	16.6084	0.911502
$333$	−44.7841	−2.45416
$334$	−27.1259	−1.48427
$335$	4.84225	0.264561
$336$	4.79863	0.261787
$337$	30.7884	1.67715	0.838574	−	0.544787i	$-0.183390\pi$
$337$	30.7884	1.67715	0.838574	+	0.544787i	$0.183390\pi$
$338$	13.9890	0.760899
$339$	−4.33313	−0.235344
$340$	−14.8719	−0.806544
$341$	24.6424	1.33446
$342$	32.8089	1.77410
$343$	−19.3591	−1.04529
$344$	−15.6944	−0.846185
$345$	−85.5307	−4.60482
$346$	−6.01884	−0.323575
$347$	25.0861	1.34669	0.673347	−	0.739326i	$-0.264856\pi$
$347$	25.0861	1.34669	0.673347	+	0.739326i	$0.264856\pi$
$348$	−79.1203	−4.24129
$349$	11.8433	0.633958	0.316979	−	0.948433i	$-0.397332\pi$
$349$	11.8433	0.633958	0.316979	+	0.948433i	$0.397332\pi$
$350$	−56.7724	−3.03461
$351$	4.75737	0.253930
$352$	−21.4117	−1.14125
$353$	12.9742	0.690548	0.345274	−	0.938502i	$-0.387786\pi$
$353$	12.9742	0.690548	0.345274	+	0.938502i	$0.387786\pi$
$354$	−6.04353	−0.321210
$355$	14.3255	0.760319
$356$	25.1950	1.33533
$357$	4.65189	0.246204
$358$	11.8441	0.625980
$359$	12.9723	0.684650	0.342325	−	0.939582i	$-0.388786\pi$
$359$	12.9723	0.684650	0.342325	+	0.939582i	$0.388786\pi$
$360$	54.0656	2.84951
$361$	−4.54482	−0.239201
$362$	43.2678	2.27411
$363$	33.0340	1.73384
$364$	16.4523	0.862337
$365$	−2.97473	−0.155704
$366$	52.8282	2.76137
$367$	5.89395	0.307662	0.153831	−	0.988097i	$-0.450839\pi$
$367$	5.89395	0.307662	0.153831	+	0.988097i	$0.450839\pi$
$368$	7.92410	0.413072
$369$	−21.9209	−1.14116
$370$	−121.847	−6.33454
$371$	10.2411	0.531691
$372$	−45.1972	−2.34336
$373$	6.48987	0.336033	0.168016	−	0.985784i	$-0.446264\pi$
$373$	6.48987	0.336033	0.168016	+	0.985784i	$0.446264\pi$
$374$	11.3874	0.588830
$375$	−94.8476	−4.89791
$376$	20.6577	1.06534
$377$	−23.4293	−1.20667
$378$	−7.54540	−0.388094
$379$	−19.1226	−0.982261	−0.491131	−	0.871086i	$-0.663416\pi$
$379$	−19.1226	−0.982261	−0.491131	+	0.871086i	$0.663416\pi$
$380$	56.5430	2.90060
$381$	−34.9696	−1.79155
$382$	−41.5282	−2.12477
$383$	6.79300	0.347106	0.173553	−	0.984825i	$-0.444475\pi$
$383$	6.79300	0.347106	0.173553	+	0.984825i	$0.444475\pi$
$384$	51.7401	2.64035
$385$	37.7197	1.92237
$386$	−47.9050	−2.43830
$387$	17.0498	0.866688
$388$	−0.370593	−0.0188140
$389$	−16.0210	−0.812295	−0.406147	−	0.913808i	$-0.633128\pi$
$389$	−16.0210	−0.812295	−0.406147	+	0.913808i	$0.633128\pi$
$390$	68.8629	3.48701
$391$	7.68178	0.388484
$392$	12.8121	0.647107
$393$	−19.3197	−0.974550
$394$	16.4124	0.826844
$395$	50.6314	2.54754
$396$	−62.2445	−3.12790
$397$	−19.9833	−1.00294	−0.501468	−	0.865176i	$-0.667206\pi$
$397$	−19.9833	−1.00294	−0.501468	+	0.865176i	$0.667206\pi$
$398$	−9.59021	−0.480714
$399$	−17.6865	−0.885430
$400$	13.9450	0.697250
$401$	21.1518	1.05627	0.528134	−	0.849161i	$-0.322892\pi$
$401$	21.1518	1.05627	0.528134	+	0.849161i	$0.322892\pi$
$402$	6.80040	0.339173
$403$	−13.3839	−0.666699
$404$	−17.0675	−0.849139
$405$	27.6899	1.37592
$406$	37.1599	1.84421
$407$	59.0976	2.92936
$408$	−8.79889	−0.435610
$409$	27.3026	1.35002	0.675012	−	0.737806i	$-0.264138\pi$
$409$	27.3026	1.35002	0.675012	+	0.737806i	$0.264138\pi$
$410$	−59.6417	−2.94549
$411$	15.5391	0.766488
$412$	12.2030	0.601200
$413$	1.79793	0.0884703
$414$	−66.2890	−3.25793
$415$	−20.6808	−1.01518
$416$	11.6292	0.570170
$417$	−48.3015	−2.36533
$418$	−43.2950	−2.11763
$419$	13.6923	0.668914	0.334457	−	0.942411i	$-0.391447\pi$
$419$	13.6923	0.668914	0.334457	+	0.942411i	$0.391447\pi$
$420$	−69.1825	−3.37576
$421$	−5.79775	−0.282565	−0.141282	−	0.989969i	$-0.545123\pi$
$421$	−5.79775	−0.282565	−0.141282	+	0.989969i	$0.545123\pi$
$422$	−31.5031	−1.53355
$423$	−22.4417	−1.09115
$424$	−19.3707	−0.940725
$425$	13.5186	0.655747
$426$	20.1186	0.974747
$427$	−15.7162	−0.760561
$428$	−28.6058	−1.38271
$429$	−33.3994	−1.61254
$430$	46.3885	2.23705
$431$	−19.8548	−0.956371	−0.478185	−	0.878259i	$-0.658705\pi$
$431$	−19.8548	−0.956371	−0.478185	+	0.878259i	$0.658705\pi$
$432$	1.85338	0.0891707
$433$	−5.36399	−0.257777	−0.128888	−	0.991659i	$-0.541141\pi$
$433$	−5.36399	−0.257777	−0.128888	+	0.991659i	$0.541141\pi$
$434$	21.2274	1.01895
$435$	98.5208	4.72371
$436$	59.8872	2.86808
$437$	−29.2061	−1.39712
$438$	−4.17767	−0.199617
$439$	33.0244	1.57617	0.788084	−	0.615568i	$-0.211073\pi$
$439$	33.0244	1.57617	0.788084	+	0.615568i	$0.211073\pi$
$440$	−71.3455	−3.40127
$441$	−13.9185	−0.662787
$442$	−6.18479	−0.294181
$443$	−4.79711	−0.227918	−0.113959	−	0.993485i	$-0.536353\pi$
$443$	−4.79711	−0.227918	−0.113959	+	0.993485i	$0.536353\pi$
$444$	−108.392	−5.14407
$445$	−31.3729	−1.48722
$446$	18.5386	0.877829
$447$	17.7012	0.837236
$448$	−22.1538	−1.04667
$449$	0.474013	0.0223701	0.0111850	−	0.999937i	$-0.496440\pi$
$449$	0.474013	0.0223701	0.0111850	+	0.999937i	$0.496440\pi$
$450$	−116.657	−5.49926
$451$	28.9270	1.36212
$452$	−5.78775	−0.272233
$453$	−20.2729	−0.952503
$454$	−14.5249	−0.681687
$455$	−20.4865	−0.960421
$456$	33.4534	1.56660
$457$	12.4827	0.583915	0.291957	−	0.956431i	$-0.405693\pi$
$457$	12.4827	0.583915	0.291957	+	0.956431i	$0.405693\pi$
$458$	−55.3558	−2.58661
$459$	1.79670	0.0838628
$460$	−114.243	−5.32660
$461$	−31.1061	−1.44876	−0.724378	−	0.689403i	$-0.757873\pi$
$461$	−31.1061	−1.44876	−0.724378	+	0.689403i	$0.757873\pi$
$462$	52.9730	2.46453
$463$	11.4961	0.534270	0.267135	−	0.963659i	$-0.413923\pi$
$463$	11.4961	0.534270	0.267135	+	0.963659i	$0.413923\pi$
$464$	−9.12759	−0.423738
$465$	56.2796	2.60990
$466$	33.3372	1.54432
$467$	−34.2036	−1.58275	−0.791377	−	0.611328i	$-0.790635\pi$
$467$	−34.2036	−1.58275	−0.791377	+	0.611328i	$0.790635\pi$
$468$	33.8065	1.56271
$469$	−2.02310	−0.0934179
$470$	−61.0588	−2.81643
$471$	−30.2075	−1.39189
$472$	−3.40073	−0.156531
$473$	−22.4991	−1.03451
$474$	71.1061	3.26601
$475$	−51.3975	−2.35828
$476$	6.21350	0.284795
$477$	21.0436	0.963519
$478$	28.4279	1.30026
$479$	−21.8060	−0.996342	−0.498171	−	0.867079i	$-0.665995\pi$
$479$	−21.8060	−0.996342	−0.498171	+	0.867079i	$0.665995\pi$
$480$	−48.9013	−2.23203
$481$	−32.0974	−1.46351
$482$	−28.4787	−1.29717
$483$	35.7348	1.62599
$484$	44.1234	2.00561
$485$	0.461464	0.0209540
$486$	51.4775	2.33507
$487$	1.82794	0.0828320	0.0414160	−	0.999142i	$-0.486813\pi$
$487$	1.82794	0.0828320	0.0414160	+	0.999142i	$0.486813\pi$
$488$	29.7267	1.34567
$489$	18.8217	0.851145
$490$	−37.8691	−1.71075
$491$	−0.165610	−0.00747386	−0.00373693	−	0.999993i	$-0.501190\pi$
$491$	−0.165610	−0.00747386	−0.00373693	+	0.999993i	$0.501190\pi$
$492$	−53.0557	−2.39194
$493$	−8.84846	−0.398515
$494$	23.5146	1.05797
$495$	77.5070	3.48368
$496$	−5.21410	−0.234120
$497$	−5.98521	−0.268473
$498$	−29.0438	−1.30148
$499$	−20.0454	−0.897354	−0.448677	−	0.893694i	$-0.648105\pi$
$499$	−20.0454	−0.897354	−0.448677	+	0.893694i	$0.648105\pi$
$500$	−126.687	−5.66564
$501$	30.0474	1.34242
$502$	−40.9787	−1.82897
$503$	−4.97108	−0.221649	−0.110825	−	0.993840i	$-0.535349\pi$
$503$	−4.97108	−0.221649	−0.110825	+	0.993840i	$0.535349\pi$
$504$	−22.5886	−1.00618
$505$	21.2525	0.945723
$506$	87.4757	3.88877
$507$	−15.4956	−0.688183
$508$	−46.7087	−2.07236
$509$	−16.0731	−0.712426	−0.356213	−	0.934405i	$-0.615932\pi$
$509$	−16.0731	−0.712426	−0.356213	+	0.934405i	$0.615932\pi$
$510$	26.0072	1.15162
$511$	1.24284	0.0549801
$512$	11.5465	0.510289
$513$	−6.83105	−0.301598
$514$	17.0453	0.751834
$515$	−15.1952	−0.669582
$516$	41.2660	1.81664
$517$	29.6143	1.30244
$518$	50.9079	2.23676
$519$	6.66707	0.292652
$520$	38.7495	1.69928
$521$	24.9001	1.09089	0.545447	−	0.838146i	$-0.316360\pi$
$521$	24.9001	1.09089	0.545447	+	0.838146i	$0.316360\pi$
$522$	76.3568	3.34205
$523$	−5.60564	−0.245118	−0.122559	−	0.992461i	$-0.539110\pi$
$523$	−5.60564	−0.245118	−0.122559	+	0.992461i	$0.539110\pi$
$524$	−25.8052	−1.12731
$525$	62.8868	2.74461
$526$	−20.4372	−0.891102
$527$	−5.05465	−0.220184
$528$	−13.0118	−0.566264
$529$	36.0097	1.56564
$530$	57.2547	2.48699
$531$	3.69442	0.160324
$532$	−23.6237	−1.02422
$533$	−15.7110	−0.680518
$534$	−44.0597	−1.90665
$535$	35.6200	1.53999
$536$	3.82662	0.165285
$537$	−13.1197	−0.566158
$538$	48.1008	2.07377
$539$	18.3670	0.791124
$540$	−26.7204	−1.14986
$541$	32.2926	1.38837	0.694184	−	0.719798i	$-0.255766\pi$
$541$	32.2926	1.38837	0.694184	+	0.719798i	$0.255766\pi$
$542$	18.5963	0.798780
$543$	−47.9278	−2.05678
$544$	4.39198	0.188305
$545$	−74.5717	−3.19430
$546$	−28.7709	−1.23128
$547$	12.7341	0.544473	0.272236	−	0.962230i	$-0.412237\pi$
$547$	12.7341	0.544473	0.272236	+	0.962230i	$0.412237\pi$
$548$	20.7555	0.886632
$549$	−32.2939	−1.37827
$550$	153.942	6.56409
$551$	33.6418	1.43319
$552$	−67.5911	−2.87687
$553$	−21.1538	−0.899552
$554$	−6.84248	−0.290709
$555$	134.970	5.72917
$556$	−64.5161	−2.73609
$557$	−34.8501	−1.47665	−0.738323	−	0.674448i	$-0.764382\pi$
$557$	−34.8501	−1.47665	−0.738323	+	0.674448i	$0.764382\pi$
$558$	43.6185	1.84652
$559$	12.2198	0.516842
$560$	−7.98113	−0.337264
$561$	−12.6139	−0.532557
$562$	−43.8878	−1.85129
$563$	31.5585	1.33003	0.665015	−	0.746830i	$-0.268425\pi$
$563$	31.5585	1.33003	0.665015	+	0.746830i	$0.268425\pi$
$564$	−54.3163	−2.28713
$565$	7.20692	0.303197
$566$	−29.2686	−1.23025
$567$	−11.5689	−0.485846
$568$	11.3208	0.475011
$569$	−41.6350	−1.74543	−0.872716	−	0.488229i	$-0.837643\pi$
$569$	−41.6350	−1.74543	−0.872716	+	0.488229i	$0.837643\pi$
$570$	−98.8794	−4.14160
$571$	−4.53007	−0.189577	−0.0947887	−	0.995497i	$-0.530218\pi$
$571$	−4.53007	−0.189577	−0.0947887	+	0.995497i	$0.530218\pi$
$572$	−44.6115	−1.86530
$573$	46.0008	1.92171
$574$	24.9183	1.04007
$575$	103.847	4.33070
$576$	−45.5220	−1.89675
$577$	−23.1810	−0.965039	−0.482519	−	0.875885i	$-0.660278\pi$
$577$	−23.1810	−0.965039	−0.482519	+	0.875885i	$0.660278\pi$
$578$	−2.33579	−0.0971561
$579$	53.0643	2.20528
$580$	131.594	5.46413
$581$	8.64043	0.358466
$582$	0.648074	0.0268635
$583$	−27.7693	−1.15009
$584$	−2.35080	−0.0972766
$585$	−42.0960	−1.74045
$586$	−3.63991	−0.150363
$587$	−26.1180	−1.07801	−0.539003	−	0.842304i	$-0.681199\pi$
$587$	−26.1180	−1.07801	−0.539003	+	0.842304i	$0.681199\pi$
$588$	−33.6874	−1.38925
$589$	19.2178	0.791854
$590$	10.0517	0.413820
$591$	−18.1800	−0.747826
$592$	−12.5045	−0.513932
$593$	−14.2587	−0.585536	−0.292768	−	0.956183i	$-0.594576\pi$
$593$	−14.2587	−0.585536	−0.292768	+	0.956183i	$0.594576\pi$
$594$	20.4598	0.839476
$595$	−7.73707	−0.317189
$596$	23.6434	0.968469
$597$	10.6231	0.434774
$598$	−47.5102	−1.94284
$599$	−24.0166	−0.981291	−0.490645	−	0.871359i	$-0.663239\pi$
$599$	−24.0166	−0.981291	−0.490645	+	0.871359i	$0.663239\pi$
$600$	−118.948	−4.85605
$601$	−19.7065	−0.803844	−0.401922	−	0.915674i	$-0.631658\pi$
$601$	−19.7065	−0.803844	−0.401922	+	0.915674i	$0.631658\pi$
$602$	−19.3811	−0.789916
$603$	−4.15709	−0.169290
$604$	−27.0784	−1.10180
$605$	−54.9425	−2.23373
$606$	29.8467	1.21244
$607$	7.25634	0.294526	0.147263	−	0.989097i	$-0.452954\pi$
$607$	7.25634	0.294526	0.147263	+	0.989097i	$0.452954\pi$
$608$	−16.6983	−0.677205
$609$	−41.1620	−1.66797
$610$	−87.8644	−3.55753
$611$	−16.0843	−0.650700
$612$	12.7676	0.516100
$613$	40.0050	1.61579	0.807893	−	0.589329i	$-0.200608\pi$
$613$	40.0050	1.61579	0.807893	+	0.589329i	$0.200608\pi$
$614$	−58.3163	−2.35346
$615$	66.0651	2.66400
$616$	29.8082	1.20101
$617$	28.7829	1.15876	0.579378	−	0.815059i	$-0.303295\pi$
$617$	28.7829	1.15876	0.579378	+	0.815059i	$0.303295\pi$
$618$	−21.3400	−0.858420
$619$	−30.0343	−1.20718	−0.603590	−	0.797295i	$-0.706264\pi$
$619$	−30.0343	−1.20718	−0.603590	+	0.797295i	$0.706264\pi$
$620$	75.1724	3.01900
$621$	13.8019	0.553849
$622$	63.6383	2.55166
$623$	13.1076	0.525146
$624$	7.06701	0.282907
$625$	90.1587	3.60635
$626$	−37.9363	−1.51624
$627$	47.9578	1.91525
$628$	−40.3480	−1.61006
$629$	−12.1221	−0.483340
$630$	66.7661	2.66003
$631$	−45.8270	−1.82434	−0.912171	−	0.409810i	$-0.865595\pi$
$631$	−45.8270	−1.82434	−0.912171	+	0.409810i	$0.865595\pi$
$632$	40.0118	1.59158
$633$	34.8960	1.38699
$634$	−25.0070	−0.993155
$635$	58.1618	2.30808
$636$	50.9324	2.01960
$637$	−9.97559	−0.395247
$638$	−100.761	−3.98918
$639$	−12.2985	−0.486521
$640$	−86.0547	−3.40161
$641$	48.1308	1.90105	0.950527	−	0.310643i	$-0.100544\pi$
$641$	48.1308	1.90105	0.950527	+	0.310643i	$0.100544\pi$
$642$	50.0243	1.97430
$643$	−8.33498	−0.328700	−0.164350	−	0.986402i	$-0.552553\pi$
$643$	−8.33498	−0.328700	−0.164350	+	0.986402i	$0.552553\pi$
$644$	47.7307	1.88085
$645$	−51.3846	−2.02327
$646$	8.88067	0.349405
$647$	6.86310	0.269816	0.134908	−	0.990858i	$-0.456926\pi$
$647$	6.86310	0.269816	0.134908	+	0.990858i	$0.456926\pi$
$648$	21.8821	0.859610
$649$	−4.87519	−0.191368
$650$	−83.6095	−3.27944
$651$	−23.5136	−0.921572
$652$	25.1400	0.984559
$653$	−9.80364	−0.383646	−0.191823	−	0.981430i	$-0.561440\pi$
$653$	−9.80364	−0.383646	−0.191823	+	0.981430i	$0.561440\pi$
$654$	−104.728	−4.09517
$655$	32.1327	1.25553
$656$	−6.12069	−0.238973
$657$	2.55381	0.0996337
$658$	25.5104	0.994498
$659$	−19.1507	−0.746005	−0.373003	−	0.927830i	$-0.621672\pi$
$659$	−19.1507	−0.746005	−0.373003	+	0.927830i	$0.621672\pi$
$660$	187.592	7.30202
$661$	−30.1570	−1.17297	−0.586486	−	0.809960i	$-0.699489\pi$
$661$	−30.1570	−1.17297	−0.586486	+	0.809960i	$0.699489\pi$
$662$	−2.50686	−0.0974321
$663$	6.85090	0.266067
$664$	−16.3431	−0.634236
$665$	29.4163	1.14072
$666$	104.606	4.05342
$667$	−67.9719	−2.63188
$668$	40.1342	1.55284
$669$	−20.5352	−0.793938
$670$	−11.3105	−0.436962
$671$	42.6154	1.64515
$672$	20.4310	0.788142
$673$	−24.1203	−0.929770	−0.464885	−	0.885371i	$-0.653904\pi$
$673$	−24.1203	−0.929770	−0.464885	+	0.885371i	$0.653904\pi$
$674$	−71.9152	−2.77007
$675$	24.2888	0.934877
$676$	−20.6974	−0.796053
$677$	−8.29674	−0.318870	−0.159435	−	0.987208i	$-0.550967\pi$
$677$	−8.29674	−0.318870	−0.159435	+	0.987208i	$0.550967\pi$
$678$	10.1213	0.388706
$679$	−0.192800	−0.00739898
$680$	14.6344	0.561204
$681$	16.0892	0.616540
$682$	−57.5594	−2.20406
$683$	−30.2706	−1.15827	−0.579136	−	0.815231i	$-0.696610\pi$
$683$	−30.2706	−1.15827	−0.579136	+	0.815231i	$0.696610\pi$
$684$	−48.5424	−1.85606
$685$	−25.8448	−0.987480
$686$	45.2188	1.72646
$687$	61.3176	2.33941
$688$	4.76059	0.181496
$689$	15.0822	0.574586
$690$	199.782	7.60556
$691$	−11.5090	−0.437823	−0.218911	−	0.975745i	$-0.570251\pi$
$691$	−11.5090	−0.437823	−0.218911	+	0.975745i	$0.570251\pi$
$692$	8.90518	0.338524
$693$	−32.3825	−1.23011
$694$	−58.5960	−2.22427
$695$	80.3356	3.04730
$696$	77.8567	2.95115
$697$	−5.93352	−0.224748
$698$	−27.6635	−1.04708
$699$	−36.9277	−1.39673
$700$	83.9976	3.17481
$701$	−5.62857	−0.212588	−0.106294	−	0.994335i	$-0.533898\pi$
$701$	−5.62857	−0.212588	−0.106294	+	0.994335i	$0.533898\pi$
$702$	−11.1122	−0.419404
$703$	46.0882	1.73825
$704$	60.0713	2.26402
$705$	67.6348	2.54727
$706$	−30.3051	−1.14055
$707$	−8.87929	−0.333940
$708$	8.94170	0.336050
$709$	−4.33852	−0.162937	−0.0814683	−	0.996676i	$-0.525961\pi$
$709$	−4.33852	−0.162937	−0.0814683	+	0.996676i	$0.525961\pi$
$710$	−33.4614	−1.25578
$711$	−43.4672	−1.63015
$712$	−24.7927	−0.929144
$713$	−38.8287	−1.45415
$714$	−10.8658	−0.406644
$715$	55.5503	2.07746
$716$	−17.5239	−0.654901
$717$	−31.4896	−1.17600
$718$	−30.3005	−1.13080
$719$	−2.17231	−0.0810135	−0.0405068	−	0.999179i	$-0.512897\pi$
$719$	−2.17231	−0.0810135	−0.0405068	+	0.999179i	$0.512897\pi$
$720$	−16.3998	−0.611183
$721$	6.34858	0.236433
$722$	10.6158	0.395078
$723$	31.5458	1.17320
$724$	−64.0169	−2.37917
$725$	−119.619	−4.44252
$726$	−77.1606	−2.86370
$727$	−4.10989	−0.152427	−0.0762136	−	0.997092i	$-0.524283\pi$
$727$	−4.10989	−0.152427	−0.0762136	+	0.997092i	$0.524283\pi$
$728$	−16.1896	−0.600026
$729$	−37.7180	−1.39696
$730$	6.94834	0.257170
$731$	4.61501	0.170692
$732$	−78.1620	−2.88895
$733$	6.85039	0.253025	0.126512	−	0.991965i	$-0.459622\pi$
$733$	6.85039	0.253025	0.126512	+	0.991965i	$0.459622\pi$
$734$	−13.7670	−0.508151
$735$	41.9476	1.54726
$736$	33.7382	1.24361
$737$	5.48574	0.202070
$738$	51.2026	1.88479
$739$	−25.2036	−0.927131	−0.463565	−	0.886063i	$-0.653430\pi$
$739$	−25.2036	−0.927131	−0.463565	+	0.886063i	$0.653430\pi$
$740$	180.279	6.62720
$741$	−26.0471	−0.956864
$742$	−23.9211	−0.878170
$743$	−2.18138	−0.0800270	−0.0400135	−	0.999199i	$-0.512740\pi$
$743$	−2.18138	−0.0800270	−0.0400135	+	0.999199i	$0.512740\pi$
$744$	44.4753	1.63054
$745$	−29.4408	−1.07863
$746$	−15.1590	−0.555010
$747$	17.7545	0.649604
$748$	−16.8483	−0.616034
$749$	−14.8821	−0.543779
$750$	221.544	8.08965
$751$	−21.4283	−0.781931	−0.390966	−	0.920405i	$-0.627859\pi$
$751$	−21.4283	−0.781931	−0.390966	+	0.920405i	$0.627859\pi$
$752$	−6.26612	−0.228502
$753$	45.3921	1.65418
$754$	54.7259	1.99300
$755$	33.7181	1.22713
$756$	11.1638	0.406024
$757$	−15.3277	−0.557094	−0.278547	−	0.960423i	$-0.589853\pi$
$757$	−15.3277	−0.557094	−0.278547	+	0.960423i	$0.589853\pi$
$758$	44.6664	1.62236
$759$	−96.8969	−3.51713
$760$	−55.6400	−2.01827
$761$	35.4019	1.28332	0.641659	−	0.766990i	$-0.278246\pi$
$761$	35.4019	1.28332	0.641659	+	0.766990i	$0.278246\pi$
$762$	81.6817	2.95901
$763$	31.1561	1.12793
$764$	61.4430	2.22293
$765$	−15.8983	−0.574803
$766$	−15.8670	−0.573299
$767$	2.64784	0.0956078
$768$	−57.0921	−2.06013
$769$	5.71763	0.206183	0.103092	−	0.994672i	$-0.467127\pi$
$769$	5.71763	0.206183	0.103092	+	0.994672i	$0.467127\pi$
$770$	−88.1053	−3.17509
$771$	−18.8810	−0.679984
$772$	70.8778	2.55095
$773$	−50.7187	−1.82423	−0.912113	−	0.409939i	$-0.865550\pi$
$773$	−50.7187	−1.82423	−0.912113	+	0.409939i	$0.865550\pi$
$774$	−39.8247	−1.43147
$775$	−68.3316	−2.45454
$776$	0.364675	0.0130911
$777$	−56.3907	−2.02300
$778$	37.4216	1.34163
$779$	22.5592	0.808268
$780$	−101.886	−3.64811
$781$	16.2292	0.580728
$782$	−17.9430	−0.641641
$783$	−15.8980	−0.568150
$784$	−3.88629	−0.138796
$785$	50.2414	1.79319
$786$	45.1268	1.60962
$787$	25.1845	0.897732	0.448866	−	0.893599i	$-0.351828\pi$
$787$	25.1845	0.897732	0.448866	+	0.893599i	$0.351828\pi$
$788$	−24.2830	−0.865044
$789$	22.6382	0.805943
$790$	−118.264	−4.20766
$791$	−3.01105	−0.107061
$792$	61.2504	2.17644
$793$	−23.1455	−0.821921
$794$	46.6769	1.65650
$795$	−63.4211	−2.24931
$796$	14.1892	0.502923
$797$	−12.5468	−0.444429	−0.222215	−	0.974998i	$-0.571329\pi$
$797$	−12.5468	−0.444429	−0.222215	+	0.974998i	$0.571329\pi$
$798$	41.3119	1.46242
$799$	−6.07450	−0.214900
$800$	59.3732	2.09916
$801$	26.9338	0.951658
$802$	−49.4061	−1.74459
$803$	−3.37004	−0.118926
$804$	−10.0615	−0.354843
$805$	−59.4344	−2.09479
$806$	31.2620	1.10116
$807$	−53.2813	−1.87559
$808$	16.7949	0.590843
$809$	−26.5238	−0.932529	−0.466264	−	0.884645i	$-0.654400\pi$
$809$	−26.5238	−0.932529	−0.466264	+	0.884645i	$0.654400\pi$
$810$	−64.6778	−2.27255
$811$	7.99132	0.280613	0.140307	−	0.990108i	$-0.455191\pi$
$811$	7.99132	0.280613	0.140307	+	0.990108i	$0.455191\pi$
$812$	−54.9799	−1.92942
$813$	−20.5991	−0.722443
$814$	−138.040	−4.83829
$815$	−31.3044	−1.09655
$816$	2.66898	0.0934328
$817$	−17.5463	−0.613866
$818$	−63.7731	−2.22977
$819$	17.5877	0.614565
$820$	88.2429	3.08157
$821$	18.7554	0.654568	0.327284	−	0.944926i	$-0.393867\pi$
$821$	18.7554	0.654568	0.327284	+	0.944926i	$0.393867\pi$
$822$	−36.2961	−1.26597
$823$	−4.13837	−0.144255	−0.0721273	−	0.997395i	$-0.522979\pi$
$823$	−4.13837	−0.144255	−0.0721273	+	0.997395i	$0.522979\pi$
$824$	−12.0081	−0.418323
$825$	−170.521	−5.93679
$826$	−4.19959	−0.146122
$827$	41.5615	1.44524	0.722618	−	0.691248i	$-0.242939\pi$
$827$	41.5615	1.44524	0.722618	+	0.691248i	$0.242939\pi$
$828$	98.0779	3.40844
$829$	−23.8029	−0.826710	−0.413355	−	0.910570i	$-0.635643\pi$
$829$	−23.8029	−0.826710	−0.413355	+	0.910570i	$0.635643\pi$
$830$	48.3059	1.67672
$831$	7.57942	0.262927
$832$	−32.6262	−1.13111
$833$	−3.76745	−0.130534
$834$	112.822	3.90671
$835$	−49.9752	−1.72946
$836$	64.0571	2.21546
$837$	−9.08169	−0.313909
$838$	−31.9824	−1.10481
$839$	16.7512	0.578315	0.289157	−	0.957282i	$-0.406625\pi$
$839$	16.7512	0.578315	0.289157	+	0.957282i	$0.406625\pi$
$840$	68.0776	2.34890
$841$	49.2953	1.69984
$842$	13.5423	0.466699
$843$	48.6145	1.67437
$844$	46.6104	1.60440
$845$	25.7724	0.886598
$846$	52.4192	1.80221
$847$	22.9550	0.788744
$848$	5.87573	0.201773
$849$	32.4208	1.11268
$850$	−31.5765	−1.08307
$851$	−93.1194	−3.19209
$852$	−29.7664	−1.01978
$853$	32.6233	1.11700	0.558501	−	0.829504i	$-0.311377\pi$
$853$	32.6233	1.11700	0.558501	+	0.829504i	$0.311377\pi$
$854$	36.7098	1.25618
$855$	60.4451	2.06718
$856$	28.1489	0.962111
$857$	−39.4332	−1.34701	−0.673506	−	0.739182i	$-0.735212\pi$
$857$	−39.4332	−1.34701	−0.673506	+	0.739182i	$0.735212\pi$
$858$	78.0141	2.66336
$859$	5.83834	0.199201	0.0996007	−	0.995027i	$-0.468243\pi$
$859$	5.83834	0.199201	0.0996007	+	0.995027i	$0.468243\pi$
$860$	−68.6341	−2.34040
$861$	−27.6020	−0.940675
$862$	46.3766	1.57959
$863$	−23.1213	−0.787057	−0.393528	−	0.919312i	$-0.628746\pi$
$863$	−23.1213	−0.787057	−0.393528	+	0.919312i	$0.628746\pi$
$864$	7.89107	0.268460
$865$	−11.0887	−0.377029
$866$	12.5292	0.425758
$867$	2.58736	0.0878712
$868$	−31.4071	−1.06603
$869$	57.3598	1.94580
$870$	−230.124	−7.80193
$871$	−2.97944	−0.100955
$872$	−58.9308	−1.99565
$873$	−0.396168	−0.0134083
$874$	68.2193	2.30755
$875$	−65.9087	−2.22812
$876$	6.18107	0.208839
$877$	41.4363	1.39920	0.699601	−	0.714533i	$-0.253361\pi$
$877$	41.4363	1.39920	0.699601	+	0.714533i	$0.253361\pi$
$878$	−77.1381	−2.60328
$879$	4.03193	0.135994
$880$	21.6413	0.729528
$881$	7.65696	0.257969	0.128985	−	0.991647i	$-0.458828\pi$
$881$	7.65696	0.257969	0.128985	+	0.991647i	$0.458828\pi$
$882$	32.5108	1.09469
$883$	8.06643	0.271457	0.135728	−	0.990746i	$-0.456663\pi$
$883$	8.06643	0.271457	0.135728	+	0.990746i	$0.456663\pi$
$884$	9.15071	0.307772
$885$	−11.1342	−0.374273
$886$	11.2051	0.376441
$887$	3.34001	0.112147	0.0560733	−	0.998427i	$-0.482142\pi$
$887$	3.34001	0.112147	0.0560733	+	0.998427i	$0.482142\pi$
$888$	106.661	3.57932
$889$	−24.3000	−0.814997
$890$	73.2806	2.45637
$891$	31.3696	1.05092
$892$	−27.4288	−0.918385
$893$	23.0952	0.772852
$894$	−41.3462	−1.38282
$895$	21.8209	0.729391
$896$	35.9537	1.20113
$897$	52.6271	1.75717
$898$	−1.10720	−0.0369476
$899$	44.7259	1.49169
$900$	172.600	5.75332
$901$	5.69605	0.189763
$902$	−67.5675	−2.24975
$903$	21.4685	0.714427
$904$	5.69531	0.189423
$905$	79.7140	2.64978
$906$	47.3532	1.57321
$907$	−5.09956	−0.169328	−0.0846641	−	0.996410i	$-0.526982\pi$
$907$	−5.09956	−0.169328	−0.0846641	+	0.996410i	$0.526982\pi$
$908$	21.4903	0.713181
$909$	−18.2453	−0.605159
$910$	47.8522	1.58628
$911$	−4.75695	−0.157605	−0.0788024	−	0.996890i	$-0.525110\pi$
$911$	−4.75695	−0.157605	−0.0788024	+	0.996890i	$0.525110\pi$
$912$	−10.1474	−0.336015
$913$	−23.4290	−0.775388
$914$	−29.1569	−0.964425
$915$	97.3275	3.21755
$916$	81.9016	2.70611
$917$	−13.4251	−0.443335
$918$	−4.19672	−0.138512
$919$	6.29068	0.207511	0.103755	−	0.994603i	$-0.466914\pi$
$919$	6.29068	0.207511	0.103755	+	0.994603i	$0.466914\pi$
$920$	112.418	3.70632
$921$	64.5970	2.12854
$922$	72.6574	2.39284
$923$	−8.81450	−0.290133
$924$	−78.3762	−2.57839
$925$	−163.874	−5.38813
$926$	−26.8525	−0.882429
$927$	13.0452	0.428459
$928$	−38.8623	−1.27572
$929$	−5.76287	−0.189074	−0.0945368	−	0.995521i	$-0.530137\pi$
$929$	−5.76287	−0.189074	−0.0945368	+	0.995521i	$0.530137\pi$
$930$	−131.457	−4.31066
$931$	14.3238	0.469445
$932$	−49.3241	−1.61567
$933$	−70.4921	−2.30781
$934$	79.8925	2.61416
$935$	20.9795	0.686103
$936$	−33.2666	−1.08735
$937$	−1.78227	−0.0582243	−0.0291121	−	0.999576i	$-0.509268\pi$
$937$	−1.78227	−0.0582243	−0.0291121	+	0.999576i	$0.509268\pi$
$938$	4.72553	0.154294
$939$	42.0221	1.37134
$940$	90.3395	2.94655
$941$	44.8208	1.46112	0.730559	−	0.682850i	$-0.239260\pi$
$941$	44.8208	1.46112	0.730559	+	0.682850i	$0.239260\pi$
$942$	70.5583	2.29891
$943$	−45.5800	−1.48429
$944$	1.03155	0.0335739
$945$	−13.9012	−0.452206
$946$	52.5531	1.70865
$947$	−36.6354	−1.19049	−0.595246	−	0.803544i	$-0.702945\pi$
$947$	−36.6354	−1.19049	−0.595246	+	0.803544i	$0.702945\pi$
$948$	−105.205	−3.41690
$949$	1.83035	0.0594157
$950$	120.054	3.89506
$951$	27.7003	0.898243
$952$	−6.11427	−0.198164
$953$	−1.23085	−0.0398713	−0.0199356	−	0.999801i	$-0.506346\pi$
$953$	−1.23085	−0.0398713	−0.0199356	+	0.999801i	$0.506346\pi$
$954$	−49.1534	−1.59140
$955$	−76.5090	−2.47577
$956$	−42.0605	−1.36033
$957$	111.613	3.60794
$958$	50.9343	1.64561
$959$	10.7980	0.348685
$960$	137.194	4.42792
$961$	−5.45053	−0.175823
$962$	74.9728	2.41722
$963$	−30.5799	−0.985424
$964$	42.1356	1.35710
$965$	−88.2572	−2.84110
$966$	−83.4689	−2.68557
$967$	53.7008	1.72690	0.863450	−	0.504434i	$-0.168299\pi$
$967$	53.7008	1.72690	0.863450	+	0.504434i	$0.168299\pi$
$968$	−43.4187	−1.39553
$969$	−9.83712	−0.316014
$970$	−1.07788	−0.0346087
$971$	54.1820	1.73878	0.869391	−	0.494125i	$-0.164511\pi$
$971$	54.1820	1.73878	0.869391	+	0.494125i	$0.164511\pi$
$972$	−76.1635	−2.44295
$973$	−33.5642	−1.07602
$974$	−4.26969	−0.136810
$975$	92.6143	2.96603
$976$	−9.01703	−0.288628
$977$	23.8591	0.763321	0.381660	−	0.924303i	$-0.375352\pi$
$977$	23.8591	0.763321	0.381660	+	0.924303i	$0.375352\pi$
$978$	−43.9635	−1.40580
$979$	−35.5421	−1.13593
$980$	56.0293	1.78979
$981$	64.0201	2.04400
$982$	0.386830	0.0123442
$983$	9.91780	0.316329	0.158164	−	0.987413i	$-0.449442\pi$
$983$	9.91780	0.316329	0.158164	+	0.987413i	$0.449442\pi$
$984$	52.2084	1.66434
$985$	30.2372	0.963437
$986$	20.6682	0.658208
$987$	−28.2579	−0.899458
$988$	−34.7910	−1.10685
$989$	35.4515	1.12729
$990$	−181.040	−5.75383
$991$	8.45656	0.268632	0.134316	−	0.990939i	$-0.457116\pi$
$991$	8.45656	0.268632	0.134316	+	0.990939i	$0.457116\pi$
$992$	−22.1999	−0.704848
$993$	2.77685	0.0881208
$994$	13.9802	0.443425
$995$	−17.6684	−0.560127
$996$	42.9717	1.36161
$997$	31.8868	1.00987	0.504933	−	0.863159i	$-0.331517\pi$
$997$	31.8868	1.00987	0.504933	+	0.863159i	$0.331517\pi$
$998$	46.8218	1.48212
$999$	−21.7798	−0.689083

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1003.2.a.h.1.3	✓	16
3.2	odd	2		9027.2.a.n.1.14		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1003.2.a.h.1.3	✓	16	1.1	even	1	trivial
9027.2.a.n.1.14		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)

\(f(q)\)	\(=\)	\(q-2.33579 q^{2} +2.58736 q^{3} +3.45592 q^{4} -4.30332 q^{5} -6.04353 q^{6} +1.79793 q^{7} -3.40073 q^{8} +3.69442 q^{9} +O(q^{10})\)	\(q-2.33579 q^{2} +2.58736 q^{3} +3.45592 q^{4} -4.30332 q^{5} -6.04353 q^{6} +1.79793 q^{7} -3.40073 q^{8} +3.69442 q^{9} +10.0517 q^{10} -4.87519 q^{11} +8.94170 q^{12} +2.64784 q^{13} -4.19959 q^{14} -11.1342 q^{15} +1.03155 q^{16} +1.00000 q^{17} -8.62938 q^{18} -3.80200 q^{19} -14.8719 q^{20} +4.65189 q^{21} +11.3874 q^{22} +7.68178 q^{23} -8.79889 q^{24} +13.5186 q^{25} -6.18479 q^{26} +1.79670 q^{27} +6.21350 q^{28} -8.84846 q^{29} +26.0072 q^{30} -5.05465 q^{31} +4.39198 q^{32} -12.6139 q^{33} -2.33579 q^{34} -7.73707 q^{35} +12.7676 q^{36} -12.1221 q^{37} +8.88067 q^{38} +6.85090 q^{39} +14.6344 q^{40} -5.93352 q^{41} -10.8658 q^{42} +4.61501 q^{43} -16.8483 q^{44} -15.8983 q^{45} -17.9430 q^{46} -6.07450 q^{47} +2.66898 q^{48} -3.76745 q^{49} -31.5765 q^{50} +2.58736 q^{51} +9.15071 q^{52} +5.69605 q^{53} -4.19672 q^{54} +20.9795 q^{55} -6.11427 q^{56} -9.83712 q^{57} +20.6682 q^{58} +1.00000 q^{59} -38.4790 q^{60} -8.74129 q^{61} +11.8066 q^{62} +6.64230 q^{63} -12.3218 q^{64} -11.3945 q^{65} +29.4633 q^{66} -1.12524 q^{67} +3.45592 q^{68} +19.8755 q^{69} +18.0722 q^{70} -3.32894 q^{71} -12.5637 q^{72} +0.691263 q^{73} +28.3147 q^{74} +34.9773 q^{75} -13.1394 q^{76} -8.76525 q^{77} -16.0023 q^{78} -11.7657 q^{79} -4.43907 q^{80} -6.43454 q^{81} +13.8595 q^{82} +4.80577 q^{83} +16.0765 q^{84} -4.30332 q^{85} -10.7797 q^{86} -22.8941 q^{87} +16.5792 q^{88} +7.29040 q^{89} +37.1350 q^{90} +4.76062 q^{91} +26.5476 q^{92} -13.0782 q^{93} +14.1888 q^{94} +16.3612 q^{95} +11.3636 q^{96} -0.107234 q^{97} +8.79998 q^{98} -18.0110 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 6 q^{2} - 7 q^{3} + 14 q^{4} - 21 q^{5} - 5 q^{6} - 11 q^{7} - 12 q^{8} + 17 q^{9}+O(q^{10}) \) 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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