LMFDB - Embedded newform 1339.2.a.d.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1339,2,Mod(1,1339)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1339, 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("1339.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1339 = 13 \cdot 103 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1339.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:	$10.6919688306$
Analytic rank:	$1$
Dimension:	$19$
Coefficient field:	$\mathbb{Q}[x]/(x^{19} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{19} - 9 x^{18} + 13 x^{17} + 106 x^{16} - 351 x^{15} - 279 x^{14} + 2337 x^{13} - 1079 x^{12} + \cdots - 63 $ x^19 - 9x^18 + 13x^17 + 106x^16 - 351x^15 - 279x^14 + 2337x^13 - 1079x^12 - 6826x^11 + 7199x^10 + 9364x^9 - 14841x^8 - 5183x^7 + 14037x^6 - 108x^5 - 6099x^4 + 855x^3 + 1062x^2 - 135x - 63
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$1.68626$ of defining polynomial
Character	$\chi$	$=$	1339.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.68626 q^{2} +0.556240 q^{3} +0.843466 q^{4} -0.525039 q^{5} -0.937964 q^{6} +4.12488 q^{7} +1.95021 q^{8} -2.69060 q^{9} +O(q^{10})$	\(q-1.68626 q^{2} +0.556240 q^{3} +0.843466 q^{4} -0.525039 q^{5} -0.937964 q^{6} +4.12488 q^{7} +1.95021 q^{8} -2.69060 q^{9} +0.885350 q^{10} -4.25220 q^{11} +0.469169 q^{12} +1.00000 q^{13} -6.95562 q^{14} -0.292047 q^{15} -4.97550 q^{16} -2.96466 q^{17} +4.53704 q^{18} +5.87698 q^{19} -0.442852 q^{20} +2.29442 q^{21} +7.17030 q^{22} -6.60705 q^{23} +1.08479 q^{24} -4.72433 q^{25} -1.68626 q^{26} -3.16534 q^{27} +3.47920 q^{28} -0.311762 q^{29} +0.492467 q^{30} -2.57946 q^{31} +4.48954 q^{32} -2.36524 q^{33} +4.99918 q^{34} -2.16572 q^{35} -2.26943 q^{36} +3.25141 q^{37} -9.91011 q^{38} +0.556240 q^{39} -1.02394 q^{40} -6.31578 q^{41} -3.86899 q^{42} -0.111555 q^{43} -3.58658 q^{44} +1.41267 q^{45} +11.1412 q^{46} +4.07537 q^{47} -2.76757 q^{48} +10.0147 q^{49} +7.96645 q^{50} -1.64906 q^{51} +0.843466 q^{52} +2.52293 q^{53} +5.33757 q^{54} +2.23257 q^{55} +8.04441 q^{56} +3.26901 q^{57} +0.525712 q^{58} +2.38716 q^{59} -0.246332 q^{60} +6.57976 q^{61} +4.34963 q^{62} -11.0984 q^{63} +2.38047 q^{64} -0.525039 q^{65} +3.98841 q^{66} -14.0349 q^{67} -2.50059 q^{68} -3.67510 q^{69} +3.65197 q^{70} -6.12761 q^{71} -5.24724 q^{72} -13.2366 q^{73} -5.48272 q^{74} -2.62786 q^{75} +4.95703 q^{76} -17.5398 q^{77} -0.937964 q^{78} -3.86122 q^{79} +2.61233 q^{80} +6.31111 q^{81} +10.6500 q^{82} -8.57540 q^{83} +1.93527 q^{84} +1.55656 q^{85} +0.188111 q^{86} -0.173415 q^{87} -8.29270 q^{88} +0.219417 q^{89} -2.38212 q^{90} +4.12488 q^{91} -5.57282 q^{92} -1.43480 q^{93} -6.87212 q^{94} -3.08564 q^{95} +2.49726 q^{96} -4.74942 q^{97} -16.8873 q^{98} +11.4409 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 19 q - 9 q^{2} - 2 q^{3} + 17 q^{4} - 18 q^{5} - 8 q^{6} - 8 q^{7} - 24 q^{8} + 7 q^{9}+O(q^{10}) $ 19 * q - 9 * q^2 - 2 * q^3 + 17 * q^4 - 18 * q^5 - 8 * q^6 - 8 * q^7 - 24 * q^8 + 7 * q^9	\( 19 q - 9 q^{2} - 2 q^{3} + 17 q^{4} - 18 q^{5} - 8 q^{6} - 8 q^{7} - 24 q^{8} + 7 q^{9} - q^{11} + 18 q^{12} + 19 q^{13} - 8 q^{14} - 11 q^{15} + 21 q^{16} - 16 q^{17} - 10 q^{19} - 20 q^{20} - 33 q^{21} + 2 q^{22} - 14 q^{23} - 9 q^{24} + 23 q^{25} - 9 q^{26} + q^{27} + 10 q^{28} - 22 q^{29} + 28 q^{30} - 3 q^{31} - 47 q^{32} - 25 q^{33} - 35 q^{34} - 3 q^{35} - 33 q^{36} - 19 q^{37} - 15 q^{38} - 2 q^{39} + 8 q^{40} - 52 q^{41} - 3 q^{42} - 2 q^{43} - 54 q^{44} - 40 q^{45} + 33 q^{46} - 24 q^{47} - 8 q^{48} + 7 q^{49} - 10 q^{50} - 7 q^{51} + 17 q^{52} - 11 q^{53} - 23 q^{54} - 29 q^{55} - 17 q^{56} - 34 q^{57} + 18 q^{58} - 52 q^{59} - 71 q^{60} - 25 q^{61} - 22 q^{62} - 19 q^{63} + 48 q^{64} - 18 q^{65} + 9 q^{66} - 2 q^{67} + 18 q^{68} - 26 q^{69} - 12 q^{70} - 44 q^{71} - 6 q^{72} - 39 q^{73} - 4 q^{74} + 17 q^{75} - 10 q^{76} - 18 q^{77} - 8 q^{78} + q^{79} - 9 q^{80} - 13 q^{81} + 47 q^{82} - 27 q^{83} - 24 q^{84} - 26 q^{85} - q^{86} + 31 q^{87} + 19 q^{88} - 86 q^{89} + 48 q^{90} - 8 q^{91} - 19 q^{92} + 32 q^{93} + 45 q^{94} + 17 q^{95} - 25 q^{96} - 20 q^{97} + 39 q^{98} + 50 q^{99}+O(q^{100}) \) 19 * q - 9 * q^2 - 2 * q^3 + 17 * q^4 - 18 * q^5 - 8 * q^6 - 8 * q^7 - 24 * q^8 + 7 * q^9 - q^11 + 18 * q^12 + 19 * q^13 - 8 * q^14 - 11 * q^15 + 21 * q^16 - 16 * q^17 - 10 * q^19 - 20 * q^20 - 33 * q^21 + 2 * q^22 - 14 * q^23 - 9 * q^24 + 23 * q^25 - 9 * q^26 + q^27 + 10 * q^28 - 22 * q^29 + 28 * q^30 - 3 * q^31 - 47 * q^32 - 25 * q^33 - 35 * q^34 - 3 * q^35 - 33 * q^36 - 19 * q^37 - 15 * q^38 - 2 * q^39 + 8 * q^40 - 52 * q^41 - 3 * q^42 - 2 * q^43 - 54 * q^44 - 40 * q^45 + 33 * q^46 - 24 * q^47 - 8 * q^48 + 7 * q^49 - 10 * q^50 - 7 * q^51 + 17 * q^52 - 11 * q^53 - 23 * q^54 - 29 * q^55 - 17 * q^56 - 34 * q^57 + 18 * q^58 - 52 * q^59 - 71 * q^60 - 25 * q^61 - 22 * q^62 - 19 * q^63 + 48 * q^64 - 18 * q^65 + 9 * q^66 - 2 * q^67 + 18 * q^68 - 26 * q^69 - 12 * q^70 - 44 * q^71 - 6 * q^72 - 39 * q^73 - 4 * q^74 + 17 * q^75 - 10 * q^76 - 18 * q^77 - 8 * q^78 + q^79 - 9 * q^80 - 13 * q^81 + 47 * q^82 - 27 * q^83 - 24 * q^84 - 26 * q^85 - q^86 + 31 * q^87 + 19 * q^88 - 86 * q^89 + 48 * q^90 - 8 * q^91 - 19 * q^92 + 32 * q^93 + 45 * q^94 + 17 * q^95 - 25 * q^96 - 20 * q^97 + 39 * q^98 + 50 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.68626	−1.19236	−0.596182	−	0.802849i	$-0.703316\pi$
$2$	−1.68626	−1.19236	−0.596182	+	0.802849i	$0.703316\pi$
$3$	0.556240	0.321145	0.160573	−	0.987024i	$-0.448666\pi$
$3$	0.556240	0.321145	0.160573	+	0.987024i	$0.448666\pi$
$4$	0.843466	0.421733
$5$	−0.525039	−0.234804	−0.117402	−	0.993084i	$-0.537457\pi$
$5$	−0.525039	−0.234804	−0.117402	+	0.993084i	$0.537457\pi$
$6$	−0.937964	−0.382922
$7$	4.12488	1.55906	0.779530	−	0.626365i	$-0.215458\pi$
$7$	4.12488	1.55906	0.779530	+	0.626365i	$0.215458\pi$
$8$	1.95021	0.689505
$9$	−2.69060	−0.896866
$10$	0.885350	0.279972
$11$	−4.25220	−1.28209	−0.641043	−	0.767505i	$-0.721498\pi$
$11$	−4.25220	−1.28209	−0.641043	+	0.767505i	$0.721498\pi$
$12$	0.469169	0.135438
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	−6.95562	−1.85897
$15$	−0.292047	−0.0754063
$16$	−4.97550	−1.24387
$17$	−2.96466	−0.719036	−0.359518	−	0.933138i	$-0.617059\pi$
$17$	−2.96466	−0.719036	−0.359518	+	0.933138i	$0.617059\pi$
$18$	4.53704	1.06939
$19$	5.87698	1.34827	0.674136	−	0.738607i	$-0.264516\pi$
$19$	5.87698	1.34827	0.674136	+	0.738607i	$0.264516\pi$
$20$	−0.442852	−0.0990248
$21$	2.29442	0.500685
$22$	7.17030	1.52871
$23$	−6.60705	−1.37766	−0.688832	−	0.724921i	$-0.741876\pi$
$23$	−6.60705	−1.37766	−0.688832	+	0.724921i	$0.741876\pi$
$24$	1.08479	0.221431
$25$	−4.72433	−0.944867
$26$	−1.68626	−0.330702
$27$	−3.16534	−0.609169
$28$	3.47920	0.657507
$29$	−0.311762	−0.0578928	−0.0289464	−	0.999581i	$-0.509215\pi$
$29$	−0.311762	−0.0578928	−0.0289464	+	0.999581i	$0.509215\pi$
$30$	0.492467	0.0899118
$31$	−2.57946	−0.463284	−0.231642	−	0.972801i	$-0.574410\pi$
$31$	−2.57946	−0.463284	−0.231642	+	0.972801i	$0.574410\pi$
$32$	4.48954	0.793646
$33$	−2.36524	−0.411736
$34$	4.99918	0.857353
$35$	−2.16572	−0.366074
$36$	−2.26943	−0.378238
$37$	3.25141	0.534529	0.267265	−	0.963623i	$-0.413880\pi$
$37$	3.25141	0.534529	0.267265	+	0.963623i	$0.413880\pi$
$38$	−9.91011	−1.60763
$39$	0.556240	0.0890696
$40$	−1.02394	−0.161899
$41$	−6.31578	−0.986358	−0.493179	−	0.869928i	$-0.664165\pi$
$41$	−6.31578	−0.986358	−0.493179	+	0.869928i	$0.664165\pi$
$42$	−3.86899	−0.596998
$43$	−0.111555	−0.0170120	−0.00850602	−	0.999964i	$-0.502708\pi$
$43$	−0.111555	−0.0170120	−0.00850602	+	0.999964i	$0.502708\pi$
$44$	−3.58658	−0.540698
$45$	1.41267	0.210588
$46$	11.1412	1.64268
$47$	4.07537	0.594453	0.297227	−	0.954807i	$-0.403938\pi$
$47$	4.07537	0.594453	0.297227	+	0.954807i	$0.403938\pi$
$48$	−2.76757	−0.399464
$49$	10.0147	1.43067
$50$	7.96645	1.12663
$51$	−1.64906	−0.230915
$52$	0.843466	0.116968
$53$	2.52293	0.346551	0.173275	−	0.984873i	$-0.444565\pi$
$53$	2.52293	0.346551	0.173275	+	0.984873i	$0.444565\pi$
$54$	5.33757	0.726352
$55$	2.23257	0.301039
$56$	8.04441	1.07498
$57$	3.26901	0.432991
$58$	0.525712	0.0690293
$59$	2.38716	0.310781	0.155391	−	0.987853i	$-0.450336\pi$
$59$	2.38716	0.310781	0.155391	+	0.987853i	$0.450336\pi$
$60$	−0.246332	−0.0318013
$61$	6.57976	0.842452	0.421226	−	0.906956i	$-0.361600\pi$
$61$	6.57976	0.842452	0.421226	+	0.906956i	$0.361600\pi$
$62$	4.34963	0.552404
$63$	−11.0984	−1.39827
$64$	2.38047	0.297558
$65$	−0.525039	−0.0651230
$66$	3.98841	0.490939
$67$	−14.0349	−1.71463	−0.857317	−	0.514790i	$-0.827870\pi$
$67$	−14.0349	−1.71463	−0.857317	+	0.514790i	$0.827870\pi$
$68$	−2.50059	−0.303241
$69$	−3.67510	−0.442430
$70$	3.65197	0.436494
$71$	−6.12761	−0.727213	−0.363607	−	0.931553i	$-0.618455\pi$
$71$	−6.12761	−0.727213	−0.363607	+	0.931553i	$0.618455\pi$
$72$	−5.24724	−0.618393
$73$	−13.2366	−1.54923	−0.774616	−	0.632432i	$-0.782057\pi$
$73$	−13.2366	−1.54923	−0.774616	+	0.632432i	$0.782057\pi$
$74$	−5.48272	−0.637354
$75$	−2.62786	−0.303439
$76$	4.95703	0.568611
$77$	−17.5398	−1.99885
$78$	−0.937964	−0.106203
$79$	−3.86122	−0.434421	−0.217211	−	0.976125i	$-0.569696\pi$
$79$	−3.86122	−0.434421	−0.217211	+	0.976125i	$0.569696\pi$
$80$	2.61233	0.292067
$81$	6.31111	0.701234
$82$	10.6500	1.17610
$83$	−8.57540	−0.941272	−0.470636	−	0.882327i	$-0.655976\pi$
$83$	−8.57540	−0.941272	−0.470636	+	0.882327i	$0.655976\pi$
$84$	1.93527	0.211155
$85$	1.55656	0.168833
$86$	0.188111	0.0202845
$87$	−0.173415	−0.0185920
$88$	−8.29270	−0.884004
$89$	0.219417	0.0232581	0.0116291	−	0.999932i	$-0.496298\pi$
$89$	0.219417	0.0232581	0.0116291	+	0.999932i	$0.496298\pi$
$90$	−2.38212	−0.251098
$91$	4.12488	0.432405
$92$	−5.57282	−0.581007
$93$	−1.43480	−0.148782
$94$	−6.87212	−0.708805
$95$	−3.08564	−0.316580
$96$	2.49726	0.254876
$97$	−4.74942	−0.482231	−0.241115	−	0.970496i	$-0.577513\pi$
$97$	−4.74942	−0.482231	−0.241115	+	0.970496i	$0.577513\pi$
$98$	−16.8873	−1.70588
$99$	11.4409	1.14986
$100$	−3.98482	−0.398482
$101$	5.27058	0.524442	0.262221	−	0.965008i	$-0.415545\pi$
$101$	5.27058	0.524442	0.262221	+	0.965008i	$0.415545\pi$
$102$	2.78074	0.275335
$103$	1.00000	0.0985329
$103$	1.00000	0.0985329
$104$	1.95021	0.191234
$105$	−1.20466	−0.117563
$106$	−4.25431	−0.413215
$107$	4.67843	0.452281	0.226140	−	0.974095i	$-0.427389\pi$
$107$	4.67843	0.452281	0.226140	+	0.974095i	$0.427389\pi$
$108$	−2.66985	−0.256907
$109$	−5.29571	−0.507237	−0.253619	−	0.967304i	$-0.581621\pi$
$109$	−5.29571	−0.507237	−0.253619	+	0.967304i	$0.581621\pi$
$110$	−3.76468	−0.358949
$111$	1.80857	0.171661
$112$	−20.5234	−1.93927
$113$	3.00950	0.283110	0.141555	−	0.989930i	$-0.454790\pi$
$113$	3.00950	0.283110	0.141555	+	0.989930i	$0.454790\pi$
$114$	−5.51239	−0.516283
$115$	3.46896	0.323482
$116$	−0.262961	−0.0244153
$117$	−2.69060	−0.248746
$118$	−4.02536	−0.370565
$119$	−12.2289	−1.12102
$120$	−0.569555	−0.0519930
$121$	7.08117	0.643743
$122$	−11.0952	−1.00451
$123$	−3.51309	−0.316764
$124$	−2.17569	−0.195382
$125$	5.10565	0.456663
$126$	18.7148	1.66724
$127$	−16.6347	−1.47609	−0.738047	−	0.674749i	$-0.764252\pi$
$127$	−16.6347	−1.47609	−0.738047	+	0.674749i	$0.764252\pi$
$128$	−12.9932	−1.14844
$129$	−0.0620515	−0.00546333
$130$	0.885350	0.0776504
$131$	−19.8897	−1.73777	−0.868886	−	0.495013i	$-0.835163\pi$
$131$	−19.8897	−1.73777	−0.868886	+	0.495013i	$0.835163\pi$
$132$	−1.99500	−0.173642
$133$	24.2419	2.10204
$134$	23.6664	2.04447
$135$	1.66192	0.143036
$136$	−5.78172	−0.495779
$137$	−10.9296	−0.933782	−0.466891	−	0.884315i	$-0.654626\pi$
$137$	−10.9296	−0.933782	−0.466891	+	0.884315i	$0.654626\pi$
$138$	6.19717	0.527538
$139$	−12.7853	−1.08443	−0.542217	−	0.840238i	$-0.682415\pi$
$139$	−12.7853	−1.08443	−0.542217	+	0.840238i	$0.682415\pi$
$140$	−1.82671	−0.154386
$141$	2.26688	0.190906
$142$	10.3327	0.867103
$143$	−4.25220	−0.355587
$144$	13.3871	1.11559
$145$	0.163687	0.0135935
$146$	22.3204	1.84725
$147$	5.57056	0.459452
$148$	2.74246	0.225429
$149$	−15.1002	−1.23706	−0.618530	−	0.785761i	$-0.712272\pi$
$149$	−15.1002	−1.23706	−0.618530	+	0.785761i	$0.712272\pi$
$150$	4.43125	0.361810
$151$	19.7038	1.60347	0.801737	−	0.597677i	$-0.203910\pi$
$151$	19.7038	1.60347	0.801737	+	0.597677i	$0.203910\pi$
$152$	11.4614	0.929640
$153$	7.97671	0.644879
$154$	29.5767	2.38336
$155$	1.35432	0.108781
$156$	0.469169	0.0375636
$157$	−17.3985	−1.38855	−0.694275	−	0.719710i	$-0.744275\pi$
$157$	−17.3985	−1.38855	−0.694275	+	0.719710i	$0.744275\pi$
$158$	6.51101	0.517988
$159$	1.40335	0.111293
$160$	−2.35718	−0.186352
$161$	−27.2533	−2.14786
$162$	−10.6422	−0.836126
$163$	−3.88180	−0.304046	−0.152023	−	0.988377i	$-0.548579\pi$
$163$	−3.88180	−0.304046	−0.152023	+	0.988377i	$0.548579\pi$
$164$	−5.32714	−0.415980
$165$	1.24184	0.0966773
$166$	14.4603	1.12234
$167$	7.53913	0.583396	0.291698	−	0.956511i	$-0.405780\pi$
$167$	7.53913	0.583396	0.291698	+	0.956511i	$0.405780\pi$
$168$	4.47462	0.345225
$169$	1.00000	0.0769231
$170$	−2.62476	−0.201310
$171$	−15.8126	−1.20922
$172$	−0.0940931	−0.00717454
$173$	22.3806	1.70157	0.850783	−	0.525518i	$-0.176128\pi$
$173$	22.3806	1.70157	0.850783	+	0.525518i	$0.176128\pi$
$174$	0.292422	0.0221684
$175$	−19.4873	−1.47310
$176$	21.1568	1.59475
$177$	1.32783	0.0998059
$178$	−0.369993	−0.0277322
$179$	−14.0520	−1.05029	−0.525147	−	0.851011i	$-0.675990\pi$
$179$	−14.0520	−1.05029	−0.525147	+	0.851011i	$0.675990\pi$
$180$	1.19154	0.0888119
$181$	9.28549	0.690185	0.345093	−	0.938569i	$-0.387847\pi$
$181$	9.28549	0.690185	0.345093	+	0.938569i	$0.387847\pi$
$182$	−6.95562	−0.515585
$183$	3.65993	0.270549
$184$	−12.8852	−0.949907
$185$	−1.70712	−0.125510
$186$	2.41944	0.177402
$187$	12.6063	0.921865
$188$	3.43743	0.250701
$189$	−13.0566	−0.949731
$190$	5.20319	0.377479
$191$	−13.4946	−0.976433	−0.488217	−	0.872722i	$-0.662352\pi$
$191$	−13.4946	−0.976433	−0.488217	+	0.872722i	$0.662352\pi$
$192$	1.32411	0.0955595
$193$	−20.1474	−1.45024	−0.725119	−	0.688624i	$-0.758215\pi$
$193$	−20.1474	−1.45024	−0.725119	+	0.688624i	$0.758215\pi$
$194$	8.00875	0.574995
$195$	−0.292047	−0.0209139
$196$	8.44704	0.603360
$197$	2.62051	0.186704	0.0933519	−	0.995633i	$-0.470242\pi$
$197$	2.62051	0.186704	0.0933519	+	0.995633i	$0.470242\pi$
$198$	−19.2924	−1.37105
$199$	9.49735	0.673249	0.336625	−	0.941639i	$-0.390715\pi$
$199$	9.49735	0.673249	0.336625	+	0.941639i	$0.390715\pi$
$200$	−9.21347	−0.651490
$201$	−7.80676	−0.550646
$202$	−8.88756	−0.625326
$203$	−1.28598	−0.0902583
$204$	−1.39093	−0.0973844
$205$	3.31603	0.231601
$206$	−1.68626	−0.117487
$207$	17.7769	1.23558
$208$	−4.97550	−0.344989
$209$	−24.9901	−1.72860
$210$	2.03137	0.140178
$211$	−1.16482	−0.0801895	−0.0400947	−	0.999196i	$-0.512766\pi$
$211$	−1.16482	−0.0801895	−0.0400947	+	0.999196i	$0.512766\pi$
$212$	2.12800	0.146152
$213$	−3.40842	−0.233541
$214$	−7.88904	−0.539284
$215$	0.0585709	0.00399450
$216$	−6.17309	−0.420025
$217$	−10.6400	−0.722288
$218$	8.92994	0.604812
$219$	−7.36275	−0.497528
$220$	1.88309	0.126958
$221$	−2.96466	−0.199425
$222$	−3.04971	−0.204683
$223$	9.48803	0.635366	0.317683	−	0.948197i	$-0.397095\pi$
$223$	9.48803	0.635366	0.317683	+	0.948197i	$0.397095\pi$
$224$	18.5188	1.23734
$225$	12.7113	0.847419
$226$	−5.07480	−0.337571
$227$	−17.0649	−1.13263	−0.566317	−	0.824187i	$-0.691632\pi$
$227$	−17.0649	−1.13263	−0.566317	+	0.824187i	$0.691632\pi$
$228$	2.75730	0.182607
$229$	20.1367	1.33067	0.665334	−	0.746546i	$-0.268289\pi$
$229$	20.1367	1.33067	0.665334	+	0.746546i	$0.268289\pi$
$230$	−5.84955	−0.385708
$231$	−9.75634	−0.641920
$232$	−0.608003	−0.0399174
$233$	−8.11839	−0.531853	−0.265927	−	0.963993i	$-0.585678\pi$
$233$	−8.11839	−0.531853	−0.265927	+	0.963993i	$0.585678\pi$
$234$	4.53704	0.296596
$235$	−2.13972	−0.139580
$236$	2.01349	0.131067
$237$	−2.14776	−0.139512
$238$	20.6211	1.33666
$239$	−4.34712	−0.281192	−0.140596	−	0.990067i	$-0.544902\pi$
$239$	−4.34712	−0.281192	−0.140596	+	0.990067i	$0.544902\pi$
$240$	1.45308	0.0937959
$241$	10.5129	0.677197	0.338598	−	0.940931i	$-0.390047\pi$
$241$	10.5129	0.677197	0.338598	+	0.940931i	$0.390047\pi$
$242$	−11.9407	−0.767576
$243$	13.0065	0.834367
$244$	5.54981	0.355290
$245$	−5.25809	−0.335927
$246$	5.92397	0.377698
$247$	5.87698	0.373943
$248$	−5.03050	−0.319437
$249$	−4.76998	−0.302285
$250$	−8.60944	−0.544509
$251$	11.7224	0.739913	0.369957	−	0.929049i	$-0.379373\pi$
$251$	11.7224	0.739913	0.369957	+	0.929049i	$0.379373\pi$
$252$	−9.36113	−0.589695
$253$	28.0945	1.76628
$254$	28.0505	1.76004
$255$	0.865821	0.0542198
$256$	17.1489	1.07181
$257$	12.2113	0.761717	0.380859	−	0.924633i	$-0.375628\pi$
$257$	12.2113	0.761717	0.380859	+	0.924633i	$0.375628\pi$
$258$	0.104635	0.00651428
$259$	13.4117	0.833363
$260$	−0.442852	−0.0274645
$261$	0.838827	0.0519221
$262$	33.5392	2.07206
$263$	28.7127	1.77050	0.885249	−	0.465117i	$-0.153988\pi$
$263$	28.7127	1.77050	0.885249	+	0.465117i	$0.153988\pi$
$264$	−4.61273	−0.283894
$265$	−1.32463	−0.0813717
$266$	−40.8780	−2.50639
$267$	0.122048	0.00746923
$268$	−11.8379	−0.723117
$269$	2.64531	0.161288	0.0806438	−	0.996743i	$-0.474302\pi$
$269$	2.64531	0.161288	0.0806438	+	0.996743i	$0.474302\pi$
$270$	−2.80243	−0.170551
$271$	6.34496	0.385429	0.192714	−	0.981255i	$-0.438271\pi$
$271$	6.34496	0.385429	0.192714	+	0.981255i	$0.438271\pi$
$272$	14.7507	0.894390
$273$	2.29442	0.138865
$274$	18.4302	1.11341
$275$	20.0888	1.21140
$276$	−3.09982	−0.186588
$277$	−28.3453	−1.70310	−0.851551	−	0.524272i	$-0.824338\pi$
$277$	−28.3453	−1.70310	−0.851551	+	0.524272i	$0.824338\pi$
$278$	21.5593	1.29304
$279$	6.94028	0.415504
$280$	−4.22363	−0.252410
$281$	−2.50999	−0.149733	−0.0748666	−	0.997194i	$-0.523853\pi$
$281$	−2.50999	−0.149733	−0.0748666	+	0.997194i	$0.523853\pi$
$282$	−3.82255	−0.227629
$283$	−17.9667	−1.06801	−0.534003	−	0.845482i	$-0.679313\pi$
$283$	−17.9667	−1.06801	−0.534003	+	0.845482i	$0.679313\pi$
$284$	−5.16843	−0.306690
$285$	−1.71636	−0.101668
$286$	7.17030	0.423989
$287$	−26.0518	−1.53779
$288$	−12.0796	−0.711794
$289$	−8.21079	−0.482988
$290$	−0.276019	−0.0162084
$291$	−2.64182	−0.154866
$292$	−11.1647	−0.653362
$293$	28.7480	1.67948	0.839738	−	0.542991i	$-0.182708\pi$
$293$	28.7480	1.67948	0.839738	+	0.542991i	$0.182708\pi$
$294$	−9.39340	−0.547834
$295$	−1.25335	−0.0729728
$296$	6.34096	0.368561
$297$	13.4596	0.781007
$298$	25.4629	1.47503
$299$	−6.60705	−0.382096
$300$	−2.21651	−0.127970
$301$	−0.460153	−0.0265228
$302$	−33.2257	−1.91193
$303$	2.93171	0.168422
$304$	−29.2409	−1.67708
$305$	−3.45463	−0.197811
$306$	−13.4508	−0.768930
$307$	13.9905	0.798481	0.399240	−	0.916846i	$-0.369274\pi$
$307$	13.9905	0.798481	0.399240	+	0.916846i	$0.369274\pi$
$308$	−14.7942	−0.842980
$309$	0.556240	0.0316434
$310$	−2.28372	−0.129707
$311$	16.5116	0.936285	0.468142	−	0.883653i	$-0.344923\pi$
$311$	16.5116	0.936285	0.468142	+	0.883653i	$0.344923\pi$
$312$	1.08479	0.0614140
$313$	−16.3847	−0.926120	−0.463060	−	0.886327i	$-0.653249\pi$
$313$	−16.3847	−0.926120	−0.463060	+	0.886327i	$0.653249\pi$
$314$	29.3383	1.65566
$315$	5.82709	0.328319
$316$	−3.25681	−0.183210
$317$	22.6238	1.27068	0.635339	−	0.772234i	$-0.280861\pi$
$317$	22.6238	1.27068	0.635339	+	0.772234i	$0.280861\pi$
$318$	−2.36641	−0.132702
$319$	1.32567	0.0742235
$320$	−1.24984	−0.0698680
$321$	2.60233	0.145248
$322$	45.9561	2.56103
$323$	−17.4233	−0.969456
$324$	5.32320	0.295734
$325$	−4.72433	−0.262059
$326$	6.54571	0.362533
$327$	−2.94569	−0.162897
$328$	−12.3171	−0.680099
$329$	16.8104	0.926788
$330$	−2.09407	−0.115275
$331$	32.1834	1.76896	0.884480	−	0.466579i	$-0.154513\pi$
$331$	32.1834	1.76896	0.884480	+	0.466579i	$0.154513\pi$
$332$	−7.23306	−0.396965
$333$	−8.74825	−0.479401
$334$	−12.7129	−0.695620
$335$	7.36885	0.402603
$336$	−11.4159	−0.622789
$337$	15.3810	0.837858	0.418929	−	0.908019i	$-0.362406\pi$
$337$	15.3810	0.837858	0.418929	+	0.908019i	$0.362406\pi$
$338$	−1.68626	−0.0917203
$339$	1.67401	0.0909195
$340$	1.31291	0.0712023
$341$	10.9684	0.593970
$342$	26.6641	1.44183
$343$	12.4352	0.671437
$344$	−0.217557	−0.0117299
$345$	1.92957	0.103885
$346$	−37.7395	−2.02889
$347$	−34.6152	−1.85824	−0.929121	−	0.369777i	$-0.879434\pi$
$347$	−34.6152	−1.85824	−0.929121	+	0.369777i	$0.879434\pi$
$348$	−0.146269	−0.00784086
$349$	−11.6592	−0.624101	−0.312051	−	0.950065i	$-0.601016\pi$
$349$	−11.6592	−0.624101	−0.312051	+	0.950065i	$0.601016\pi$
$350$	32.8607	1.75648
$351$	−3.16534	−0.168953
$352$	−19.0904	−1.01752
$353$	11.9532	0.636205	0.318102	−	0.948056i	$-0.396954\pi$
$353$	11.9532	0.636205	0.318102	+	0.948056i	$0.396954\pi$
$354$	−2.23907	−0.119005
$355$	3.21723	0.170753
$356$	0.185071	0.00980872
$357$	−6.80219	−0.360010
$358$	23.6953	1.25233
$359$	−32.9428	−1.73865	−0.869327	−	0.494237i	$-0.835447\pi$
$359$	−32.9428	−1.73865	−0.869327	+	0.494237i	$0.835447\pi$
$360$	2.75500	0.145201
$361$	15.5389	0.817837
$362$	−15.6577	−0.822952
$363$	3.93883	0.206735
$364$	3.47920	0.182360
$365$	6.94975	0.363766
$366$	−6.17158	−0.322594
$367$	34.8605	1.81970	0.909851	−	0.414936i	$-0.136196\pi$
$367$	34.8605	1.81970	0.909851	+	0.414936i	$0.136196\pi$
$368$	32.8734	1.71364
$369$	16.9932	0.884631
$370$	2.87864	0.149653
$371$	10.4068	0.540293
$372$	−1.21020	−0.0627461
$373$	36.8996	1.91059	0.955295	−	0.295654i	$-0.0955376\pi$
$373$	36.8996	1.91059	0.955295	+	0.295654i	$0.0955376\pi$
$374$	−21.2575	−1.09920
$375$	2.83997	0.146655
$376$	7.94784	0.409879
$377$	−0.311762	−0.0160566
$378$	22.0169	1.13243
$379$	−23.4116	−1.20257	−0.601286	−	0.799034i	$-0.705345\pi$
$379$	−23.4116	−1.20257	−0.601286	+	0.799034i	$0.705345\pi$
$380$	−2.60263	−0.133512
$381$	−9.25290	−0.474040
$382$	22.7553	1.16426
$383$	−5.46492	−0.279244	−0.139622	−	0.990205i	$-0.544589\pi$
$383$	−5.46492	−0.279244	−0.139622	+	0.990205i	$0.544589\pi$
$384$	−7.22732	−0.368817
$385$	9.20908	0.469338
$386$	33.9736	1.72921
$387$	0.300151	0.0152575
$388$	−4.00598	−0.203373
$389$	−31.7544	−1.61001	−0.805007	−	0.593266i	$-0.797838\pi$
$389$	−31.7544	−1.61001	−0.805007	+	0.593266i	$0.797838\pi$
$390$	0.492467	0.0249370
$391$	19.5877	0.990590
$392$	19.5308	0.986453
$393$	−11.0634	−0.558077
$394$	−4.41886	−0.222619
$395$	2.02729	0.102004
$396$	9.65005	0.484933
$397$	26.8588	1.34800	0.674002	−	0.738729i	$-0.264574\pi$
$397$	26.8588	1.34800	0.674002	+	0.738729i	$0.264574\pi$
$398$	−16.0150	−0.802759
$399$	13.4843	0.675059
$400$	23.5059	1.17530
$401$	−6.58869	−0.329024	−0.164512	−	0.986375i	$-0.552605\pi$
$401$	−6.58869	−0.329024	−0.164512	+	0.986375i	$0.552605\pi$
$402$	13.1642	0.656571
$403$	−2.57946	−0.128492
$404$	4.44555	0.221175
$405$	−3.31357	−0.164653
$406$	2.16850	0.107621
$407$	−13.8256	−0.685312
$408$	−3.21603	−0.159217
$409$	18.0538	0.892703	0.446352	−	0.894858i	$-0.352723\pi$
$409$	18.0538	0.892703	0.446352	+	0.894858i	$0.352723\pi$
$410$	−5.59167	−0.276153
$411$	−6.07950	−0.299879
$412$	0.843466	0.0415546
$413$	9.84675	0.484527
$414$	−29.9765	−1.47326
$415$	4.50241	0.221015
$416$	4.48954	0.220118
$417$	−7.11169	−0.348261
$418$	42.1397	2.06112
$419$	25.4212	1.24190	0.620952	−	0.783848i	$-0.286746\pi$
$419$	25.4212	1.24190	0.620952	+	0.783848i	$0.286746\pi$
$420$	−1.01609	−0.0495802
$421$	−22.9555	−1.11878	−0.559392	−	0.828903i	$-0.688965\pi$
$421$	−22.9555	−1.11878	−0.559392	+	0.828903i	$0.688965\pi$
$422$	1.96419	0.0956151
$423$	−10.9652	−0.533145
$424$	4.92025	0.238949
$425$	14.0060	0.679393
$426$	5.74748	0.278466
$427$	27.1408	1.31343
$428$	3.94610	0.190742
$429$	−2.36524	−0.114195
$430$	−0.0987656	−0.00476290
$431$	8.96955	0.432048	0.216024	−	0.976388i	$-0.430691\pi$
$431$	8.96955	0.432048	0.216024	+	0.976388i	$0.430691\pi$
$432$	15.7491	0.757730
$433$	10.4311	0.501286	0.250643	−	0.968080i	$-0.419358\pi$
$433$	10.4311	0.501286	0.250643	+	0.968080i	$0.419358\pi$
$434$	17.9417	0.861231
$435$	0.0910493	0.00436548
$436$	−4.46676	−0.213919
$437$	−38.8295	−1.85747
$438$	12.4155	0.593235
$439$	30.5438	1.45778	0.728889	−	0.684632i	$-0.240037\pi$
$439$	30.5438	1.45778	0.728889	+	0.684632i	$0.240037\pi$
$440$	4.35398	0.207568
$441$	−26.9455	−1.28312
$442$	4.99918	0.237787
$443$	−20.6360	−0.980445	−0.490223	−	0.871597i	$-0.663084\pi$
$443$	−20.6360	−0.980445	−0.490223	+	0.871597i	$0.663084\pi$
$444$	1.52546	0.0723953
$445$	−0.115202	−0.00546111
$446$	−15.9993	−0.757588
$447$	−8.39936	−0.397276
$448$	9.81916	0.463911
$449$	−15.7084	−0.741324	−0.370662	−	0.928768i	$-0.620869\pi$
$449$	−15.7084	−0.741324	−0.370662	+	0.928768i	$0.620869\pi$
$450$	−21.4345	−1.01043
$451$	26.8559	1.26460
$452$	2.53841	0.119397
$453$	10.9600	0.514948
$454$	28.7758	1.35051
$455$	−2.16572	−0.101531
$456$	6.37527	0.298549
$457$	−21.2784	−0.995362	−0.497681	−	0.867360i	$-0.665815\pi$
$457$	−21.2784	−0.995362	−0.497681	+	0.867360i	$0.665815\pi$
$458$	−33.9556	−1.58664
$459$	9.38415	0.438015
$460$	2.92595	0.136423
$461$	11.4219	0.531971	0.265985	−	0.963977i	$-0.414303\pi$
$461$	11.4219	0.531971	0.265985	+	0.963977i	$0.414303\pi$
$462$	16.4517	0.765403
$463$	−28.0802	−1.30500	−0.652499	−	0.757790i	$-0.726279\pi$
$463$	−28.0802	−1.30500	−0.652499	+	0.757790i	$0.726279\pi$
$464$	1.55117	0.0720114
$465$	0.753324	0.0349346
$466$	13.6897	0.634163
$467$	33.4954	1.54998	0.774992	−	0.631972i	$-0.217754\pi$
$467$	33.4954	1.54998	0.774992	+	0.631972i	$0.217754\pi$
$468$	−2.26943	−0.104904
$469$	−57.8922	−2.67322
$470$	3.60813	0.166431
$471$	−9.67772	−0.445926
$472$	4.65547	0.214285
$473$	0.474355	0.0218109
$474$	3.62168	0.166349
$475$	−27.7648	−1.27394
$476$	−10.3146	−0.472771
$477$	−6.78818	−0.310810
$478$	7.33036	0.335283
$479$	9.61829	0.439471	0.219735	−	0.975560i	$-0.429481\pi$
$479$	9.61829	0.439471	0.219735	+	0.975560i	$0.429481\pi$
$480$	−1.31116	−0.0598459
$481$	3.25141	0.148252
$482$	−17.7275	−0.807465
$483$	−15.1594	−0.689776
$484$	5.97273	0.271488
$485$	2.49363	0.113230
$486$	−21.9323	−0.994870
$487$	14.8541	0.673102	0.336551	−	0.941665i	$-0.390740\pi$
$487$	14.8541	0.673102	0.336551	+	0.941665i	$0.390740\pi$
$488$	12.8320	0.580875
$489$	−2.15921	−0.0976428
$490$	8.86650	0.400547
$491$	−13.4838	−0.608514	−0.304257	−	0.952590i	$-0.598408\pi$
$491$	−13.4838	−0.608514	−0.304257	+	0.952590i	$0.598408\pi$
$492$	−2.96317	−0.133590
$493$	0.924269	0.0416270
$494$	−9.91011	−0.445877
$495$	−6.00694	−0.269992
$496$	12.8341	0.576268
$497$	−25.2757	−1.13377
$498$	8.04341	0.360434
$499$	8.45667	0.378573	0.189286	−	0.981922i	$-0.439383\pi$
$499$	8.45667	0.378573	0.189286	+	0.981922i	$0.439383\pi$
$500$	4.30644	0.192590
$501$	4.19357	0.187355
$502$	−19.7670	−0.882246
$503$	28.1136	1.25352	0.626762	−	0.779211i	$-0.284380\pi$
$503$	28.1136	1.25352	0.626762	+	0.779211i	$0.284380\pi$
$504$	−21.6443	−0.964112
$505$	−2.76726	−0.123141
$506$	−47.3745	−2.10605
$507$	0.556240	0.0247035
$508$	−14.0308	−0.622517
$509$	−33.3687	−1.47904	−0.739520	−	0.673135i	$-0.764947\pi$
$509$	−33.3687	−1.47904	−0.739520	+	0.673135i	$0.764947\pi$
$510$	−1.46000	−0.0646498
$511$	−54.5996	−2.41535
$512$	−2.93113	−0.129539
$513$	−18.6026	−0.821326
$514$	−20.5913	−0.908244
$515$	−0.525039	−0.0231360
$516$	−0.0523383	−0.00230407
$517$	−17.3293	−0.762140
$518$	−22.6156	−0.993672
$519$	12.4490	0.546449
$520$	−1.02394	−0.0449026
$521$	9.67029	0.423663	0.211832	−	0.977306i	$-0.432057\pi$
$521$	9.67029	0.423663	0.211832	+	0.977306i	$0.432057\pi$
$522$	−1.41448	−0.0619100
$523$	26.1055	1.14151	0.570757	−	0.821119i	$-0.306650\pi$
$523$	26.1055	1.14151	0.570757	+	0.821119i	$0.306650\pi$
$524$	−16.7763	−0.732876
$525$	−10.8396	−0.473080
$526$	−48.4170	−2.11108
$527$	7.64722	0.333118
$528$	11.7682	0.512147
$529$	20.6531	0.897961
$530$	2.23368	0.0970247
$531$	−6.42288	−0.278729
$532$	20.4472	0.886498
$533$	−6.31578	−0.273567
$534$	−0.205805	−0.00890605
$535$	−2.45636	−0.106198
$536$	−27.3710	−1.18225
$537$	−7.81627	−0.337297
$538$	−4.46068	−0.192314
$539$	−42.5844	−1.83424
$540$	1.40178	0.0603228
$541$	−22.7943	−0.980003	−0.490001	−	0.871722i	$-0.663004\pi$
$541$	−22.7943	−0.980003	−0.490001	+	0.871722i	$0.663004\pi$
$542$	−10.6992	−0.459572
$543$	5.16496	0.221650
$544$	−13.3100	−0.570660
$545$	2.78045	0.119102
$546$	−3.86899	−0.165578
$547$	7.08170	0.302792	0.151396	−	0.988473i	$-0.451623\pi$
$547$	7.08170	0.302792	0.151396	+	0.988473i	$0.451623\pi$
$548$	−9.21877	−0.393806
$549$	−17.7035	−0.755567
$550$	−33.8749	−1.44443
$551$	−1.83222	−0.0780552
$552$	−7.16724	−0.305058
$553$	−15.9271	−0.677289
$554$	47.7974	2.03072
$555$	−0.949567	−0.0403069
$556$	−10.7840	−0.457342
$557$	29.3977	1.24562	0.622811	−	0.782373i	$-0.285991\pi$
$557$	29.3977	1.24562	0.622811	+	0.782373i	$0.285991\pi$
$558$	−11.7031	−0.495432
$559$	−0.111555	−0.00471829
$560$	10.7756	0.455350
$561$	7.01214	0.296053
$562$	4.23248	0.178537
$563$	−3.25189	−0.137051	−0.0685254	−	0.997649i	$-0.521829\pi$
$563$	−3.25189	−0.137051	−0.0685254	+	0.997649i	$0.521829\pi$
$564$	1.91204	0.0805113
$565$	−1.58011	−0.0664755
$566$	30.2964	1.27345
$567$	26.0326	1.09327
$568$	−11.9502	−0.501417
$569$	−0.0820873	−0.00344128	−0.00172064	−	0.999999i	$-0.500548\pi$
$569$	−0.0820873	−0.00344128	−0.00172064	+	0.999999i	$0.500548\pi$
$570$	2.89422	0.121226
$571$	−8.73121	−0.365390	−0.182695	−	0.983170i	$-0.558482\pi$
$571$	−8.73121	−0.365390	−0.182695	+	0.983170i	$0.558482\pi$
$572$	−3.58658	−0.149963
$573$	−7.50622	−0.313577
$574$	43.9301	1.83361
$575$	31.2139	1.30171
$576$	−6.40488	−0.266870
$577$	−28.2838	−1.17747	−0.588735	−	0.808326i	$-0.700374\pi$
$577$	−28.2838	−1.17747	−0.588735	+	0.808326i	$0.700374\pi$
$578$	13.8455	0.575897
$579$	−11.2068	−0.465737
$580$	0.138065	0.00573282
$581$	−35.3725	−1.46750
$582$	4.45478	0.184657
$583$	−10.7280	−0.444308
$584$	−25.8143	−1.06820
$585$	1.41267	0.0584066
$586$	−48.4766	−2.00255
$587$	−1.20071	−0.0495585	−0.0247792	−	0.999693i	$-0.507888\pi$
$587$	−1.20071	−0.0495585	−0.0247792	+	0.999693i	$0.507888\pi$
$588$	4.69858	0.193766
$589$	−15.1594	−0.624633
$590$	2.11347	0.0870102
$591$	1.45763	0.0599590
$592$	−16.1774	−0.664887
$593$	9.43696	0.387530	0.193765	−	0.981048i	$-0.437930\pi$
$593$	9.43696	0.387530	0.193765	+	0.981048i	$0.437930\pi$
$594$	−22.6964	−0.931245
$595$	6.42063	0.263220
$596$	−12.7365	−0.521709
$597$	5.28280	0.216211
$598$	11.1412	0.455597
$599$	−33.8144	−1.38162	−0.690809	−	0.723037i	$-0.742745\pi$
$599$	−33.8144	−1.38162	−0.690809	+	0.723037i	$0.742745\pi$
$600$	−5.12490	−0.209223
$601$	−3.96663	−0.161802	−0.0809011	−	0.996722i	$-0.525780\pi$
$601$	−3.96663	−0.161802	−0.0809011	+	0.996722i	$0.525780\pi$
$602$	0.775937	0.0316248
$603$	37.7622	1.53780
$604$	16.6195	0.676238
$605$	−3.71789	−0.151154
$606$	−4.94361	−0.200821
$607$	33.3507	1.35366	0.676832	−	0.736138i	$-0.263352\pi$
$607$	33.3507	1.35366	0.676832	+	0.736138i	$0.263352\pi$
$608$	26.3850	1.07005
$609$	−0.715315	−0.0289860
$610$	5.82540	0.235863
$611$	4.07537	0.164872
$612$	6.72808	0.271967
$613$	−24.5960	−0.993421	−0.496711	−	0.867916i	$-0.665459\pi$
$613$	−24.5960	−0.993421	−0.496711	+	0.867916i	$0.665459\pi$
$614$	−23.5916	−0.952080
$615$	1.84451	0.0743776
$616$	−34.2064	−1.37822
$617$	−23.7184	−0.954866	−0.477433	−	0.878668i	$-0.658433\pi$
$617$	−23.7184	−0.954866	−0.477433	+	0.878668i	$0.658433\pi$
$618$	−0.937964	−0.0377304
$619$	−19.7988	−0.795783	−0.397891	−	0.917433i	$-0.630258\pi$
$619$	−19.7988	−0.795783	−0.397891	+	0.917433i	$0.630258\pi$
$620$	1.14232	0.0458766
$621$	20.9135	0.839231
$622$	−27.8428	−1.11639
$623$	0.905069	0.0362608
$624$	−2.76757	−0.110791
$625$	20.9410	0.837640
$626$	27.6289	1.10427
$627$	−13.9005	−0.555131
$628$	−14.6750	−0.585597
$629$	−9.63934	−0.384346
$630$	−9.82598	−0.391476
$631$	33.6392	1.33916	0.669579	−	0.742741i	$-0.266475\pi$
$631$	33.6392	1.33916	0.669579	+	0.742741i	$0.266475\pi$
$632$	−7.53021	−0.299536
$633$	−0.647919	−0.0257525
$634$	−38.1495	−1.51511
$635$	8.73388	0.346593
$636$	1.18368	0.0469360
$637$	10.0147	0.396796
$638$	−2.23543	−0.0885015
$639$	16.4869	0.652213
$640$	6.82191	0.269660
$641$	19.7813	0.781313	0.390657	−	0.920537i	$-0.372248\pi$
$641$	19.7813	0.781313	0.390657	+	0.920537i	$0.372248\pi$
$642$	−4.38820	−0.173188
$643$	−32.2431	−1.27154	−0.635772	−	0.771877i	$-0.719318\pi$
$643$	−32.2431	−1.27154	−0.635772	+	0.771877i	$0.719318\pi$
$644$	−22.9872	−0.905824
$645$	0.0325794	0.00128281
$646$	29.3801	1.15594
$647$	−11.7546	−0.462122	−0.231061	−	0.972939i	$-0.574220\pi$
$647$	−11.7546	−0.462122	−0.231061	+	0.972939i	$0.574220\pi$
$648$	12.3080	0.483504
$649$	−10.1507	−0.398448
$650$	7.96645	0.312470
$651$	−5.91837	−0.231959
$652$	−3.27416	−0.128226
$653$	32.2247	1.26105	0.630524	−	0.776170i	$-0.282840\pi$
$653$	32.2247	1.26105	0.630524	+	0.776170i	$0.282840\pi$
$654$	4.96719	0.194232
$655$	10.4429	0.408036
$656$	31.4241	1.22691
$657$	35.6145	1.38945
$658$	−28.3467	−1.10507
$659$	−29.7170	−1.15761	−0.578805	−	0.815466i	$-0.696481\pi$
$659$	−29.7170	−1.15761	−0.578805	+	0.815466i	$0.696481\pi$
$660$	1.04745	0.0407720
$661$	1.05481	0.0410273	0.0205137	−	0.999790i	$-0.493470\pi$
$661$	1.05481	0.0410273	0.0205137	+	0.999790i	$0.493470\pi$
$662$	−54.2695	−2.10924
$663$	−1.64906	−0.0640443
$664$	−16.7239	−0.649012
$665$	−12.7279	−0.493567
$666$	14.7518	0.571621
$667$	2.05983	0.0797569
$668$	6.35900	0.246037
$669$	5.27762	0.204045
$670$	−12.4258	−0.480050
$671$	−27.9784	−1.08010
$672$	10.3009	0.397367
$673$	−6.87294	−0.264932	−0.132466	−	0.991188i	$-0.542290\pi$
$673$	−6.87294	−0.264932	−0.132466	+	0.991188i	$0.542290\pi$
$674$	−25.9364	−0.999032
$675$	14.9541	0.575584
$676$	0.843466	0.0324410
$677$	−13.4344	−0.516324	−0.258162	−	0.966102i	$-0.583117\pi$
$677$	−13.4344	−0.516324	−0.258162	+	0.966102i	$0.583117\pi$
$678$	−2.82280	−0.108409
$679$	−19.5908	−0.751826
$680$	3.03563	0.116411
$681$	−9.49215	−0.363740
$682$	−18.4955	−0.708229
$683$	−15.0224	−0.574817	−0.287409	−	0.957808i	$-0.592794\pi$
$683$	−15.0224	−0.574817	−0.287409	+	0.957808i	$0.592794\pi$
$684$	−13.3374	−0.509967
$685$	5.73848	0.219256
$686$	−20.9689	−0.800597
$687$	11.2008	0.427338
$688$	0.555043	0.0211608
$689$	2.52293	0.0961159
$690$	−3.25375	−0.123868
$691$	14.2899	0.543612	0.271806	−	0.962352i	$-0.412379\pi$
$691$	14.2899	0.543612	0.271806	+	0.962352i	$0.412379\pi$
$692$	18.8773	0.717606
$693$	47.1926	1.79270
$694$	58.3702	2.21570
$695$	6.71277	0.254630
$696$	−0.338196	−0.0128193
$697$	18.7241	0.709227
$698$	19.6604	0.744156
$699$	−4.51577	−0.170802
$700$	−16.4369	−0.621257
$701$	−21.2956	−0.804325	−0.402163	−	0.915568i	$-0.631741\pi$
$701$	−21.2956	−0.804325	−0.402163	+	0.915568i	$0.631741\pi$
$702$	5.33757	0.201454
$703$	19.1085	0.720691
$704$	−10.1222	−0.381495
$705$	−1.19020	−0.0448255
$706$	−20.1562	−0.758588
$707$	21.7405	0.817637
$708$	1.11998	0.0420915
$709$	−11.6067	−0.435898	−0.217949	−	0.975960i	$-0.569937\pi$
$709$	−11.6067	−0.435898	−0.217949	+	0.975960i	$0.569937\pi$
$710$	−5.42508	−0.203600
$711$	10.3890	0.389618
$712$	0.427910	0.0160366
$713$	17.0426	0.638251
$714$	11.4702	0.429263
$715$	2.23257	0.0834933
$716$	−11.8524	−0.442944
$717$	−2.41804	−0.0903033
$718$	55.5500	2.07311
$719$	4.90421	0.182896	0.0914480	−	0.995810i	$-0.470850\pi$
$719$	4.90421	0.182896	0.0914480	+	0.995810i	$0.470850\pi$
$720$	−7.02872	−0.261945
$721$	4.12488	0.153619
$722$	−26.2026	−0.975160
$723$	5.84770	0.217478
$724$	7.83200	0.291074
$725$	1.47287	0.0547010
$726$	−6.64188	−0.246503
$727$	42.1244	1.56231	0.781155	−	0.624338i	$-0.214631\pi$
$727$	42.1244	1.56231	0.781155	+	0.624338i	$0.214631\pi$
$728$	8.04441	0.298146
$729$	−11.6986	−0.433281
$730$	−11.7191	−0.433742
$731$	0.330724	0.0122323
$732$	3.08702	0.114100
$733$	−40.1399	−1.48260	−0.741301	−	0.671173i	$-0.765791\pi$
$733$	−40.1399	−1.48260	−0.741301	+	0.671173i	$0.765791\pi$
$734$	−58.7837	−2.16975
$735$	−2.92476	−0.107881
$736$	−29.6626	−1.09338
$737$	59.6790	2.19831
$738$	−28.6549	−1.05480
$739$	−43.8839	−1.61429	−0.807147	−	0.590350i	$-0.798990\pi$
$739$	−43.8839	−1.61429	−0.807147	+	0.590350i	$0.798990\pi$
$740$	−1.43990	−0.0529316
$741$	3.26901	0.120090
$742$	−17.5485	−0.644227
$743$	47.1176	1.72858	0.864289	−	0.502996i	$-0.167769\pi$
$743$	47.1176	1.72858	0.864289	+	0.502996i	$0.167769\pi$
$744$	−2.79816	−0.102586
$745$	7.92821	0.290467
$746$	−62.2223	−2.27812
$747$	23.0729	0.844195
$748$	10.6330	0.388781
$749$	19.2980	0.705133
$750$	−4.78891	−0.174866
$751$	28.6197	1.04435	0.522175	−	0.852839i	$-0.325121\pi$
$751$	28.6197	1.04435	0.522175	+	0.852839i	$0.325121\pi$
$752$	−20.2770	−0.739425
$753$	6.52048	0.237620
$754$	0.525712	0.0191453
$755$	−10.3453	−0.376503
$756$	−11.0128	−0.400533
$757$	−38.4833	−1.39870	−0.699349	−	0.714780i	$-0.746527\pi$
$757$	−38.4833	−1.39870	−0.699349	+	0.714780i	$0.746527\pi$
$758$	39.4779	1.43390
$759$	15.6273	0.567234
$760$	−6.01766	−0.218284
$761$	−29.0516	−1.05312	−0.526560	−	0.850138i	$-0.676519\pi$
$761$	−29.0516	−1.05312	−0.526560	+	0.850138i	$0.676519\pi$
$762$	15.6028	0.565229
$763$	−21.8442	−0.790814
$764$	−11.3822	−0.411794
$765$	−4.18808	−0.151420
$766$	9.21527	0.332961
$767$	2.38716	0.0861952
$768$	9.53890	0.344205
$769$	−5.60435	−0.202098	−0.101049	−	0.994881i	$-0.532220\pi$
$769$	−5.60435	−0.202098	−0.101049	+	0.994881i	$0.532220\pi$
$770$	−15.5289	−0.559622
$771$	6.79238	0.244622
$772$	−16.9936	−0.611613
$773$	−3.56168	−0.128105	−0.0640523	−	0.997947i	$-0.520402\pi$
$773$	−3.56168	−0.128105	−0.0640523	+	0.997947i	$0.520402\pi$
$774$	−0.506131	−0.0181925
$775$	12.1862	0.437742
$776$	−9.26239	−0.332500
$777$	7.46012	0.267630
$778$	53.5462	1.91972
$779$	−37.1177	−1.32988
$780$	−0.246332	−0.00882010
$781$	26.0558	0.932350
$782$	−33.0298	−1.18114
$783$	0.986833	0.0352665
$784$	−49.8280	−1.77957
$785$	9.13487	0.326038
$786$	18.6558	0.665431
$787$	−1.84572	−0.0657928	−0.0328964	−	0.999459i	$-0.510473\pi$
$787$	−1.84572	−0.0657928	−0.0328964	+	0.999459i	$0.510473\pi$
$788$	2.21031	0.0787391
$789$	15.9711	0.568587
$790$	−3.41853	−0.121626
$791$	12.4139	0.441386
$792$	22.3123	0.792833
$793$	6.57976	0.233654
$794$	−45.2909	−1.60731
$795$	−0.736814	−0.0261321
$796$	8.01069	0.283932
$797$	−31.2677	−1.10756	−0.553780	−	0.832663i	$-0.686815\pi$
$797$	−31.2677	−1.10756	−0.553780	+	0.832663i	$0.686815\pi$
$798$	−22.7380	−0.804916
$799$	−12.0821	−0.427433
$800$	−21.2101	−0.749890
$801$	−0.590362	−0.0208594
$802$	11.1102	0.392316
$803$	56.2848	1.98625
$804$	−6.58473	−0.232226
$805$	14.3090	0.504327
$806$	4.34963	0.153209
$807$	1.47143	0.0517967
$808$	10.2788	0.361606
$809$	48.1698	1.69356	0.846779	−	0.531944i	$-0.178538\pi$
$809$	48.1698	1.69356	0.846779	+	0.531944i	$0.178538\pi$
$810$	5.58754	0.196326
$811$	2.01245	0.0706667	0.0353333	−	0.999376i	$-0.488751\pi$
$811$	2.01245	0.0706667	0.0353333	+	0.999376i	$0.488751\pi$
$812$	−1.08468	−0.0380649
$813$	3.52932	0.123779
$814$	23.3136	0.817142
$815$	2.03809	0.0713913
$816$	8.20490	0.287229
$817$	−0.655609	−0.0229368
$818$	−30.4434	−1.06443
$819$	−11.0984	−0.387810
$820$	2.79695	0.0976739
$821$	9.52777	0.332522	0.166261	−	0.986082i	$-0.446831\pi$
$821$	9.52777	0.332522	0.166261	+	0.986082i	$0.446831\pi$
$822$	10.2516	0.357566
$823$	27.7226	0.966348	0.483174	−	0.875524i	$-0.339484\pi$
$823$	27.7226	0.966348	0.483174	+	0.875524i	$0.339484\pi$
$824$	1.95021	0.0679389
$825$	11.1742	0.389035
$826$	−16.6042	−0.577733
$827$	−2.61454	−0.0909164	−0.0454582	−	0.998966i	$-0.514475\pi$
$827$	−2.61454	−0.0909164	−0.0454582	+	0.998966i	$0.514475\pi$
$828$	14.9942	0.521085
$829$	−56.4536	−1.96071	−0.980357	−	0.197232i	$-0.936805\pi$
$829$	−56.4536	−1.96071	−0.980357	+	0.197232i	$0.936805\pi$
$830$	−7.59223	−0.263530
$831$	−15.7668	−0.546943
$832$	2.38047	0.0825279
$833$	−29.6901	−1.02870
$834$	11.9921	0.415254
$835$	−3.95834	−0.136984
$836$	−21.0783	−0.729007
$837$	8.16485	0.282219
$838$	−42.8666	−1.48080
$839$	21.8968	0.755960	0.377980	−	0.925814i	$-0.376619\pi$
$839$	21.8968	0.755960	0.377980	+	0.925814i	$0.376619\pi$
$840$	−2.34935	−0.0810602
$841$	−28.9028	−0.996648
$842$	38.7089	1.33400
$843$	−1.39615	−0.0480861
$844$	−0.982486	−0.0338185
$845$	−0.525039	−0.0180619
$846$	18.4901	0.635703
$847$	29.2090	1.00363
$848$	−12.5528	−0.431066
$849$	−9.99377	−0.342985
$850$	−23.6178	−0.810084
$851$	−21.4823	−0.736402
$852$	−2.87489	−0.0984920
$853$	−23.4125	−0.801628	−0.400814	−	0.916159i	$-0.631273\pi$
$853$	−23.4125	−0.801628	−0.400814	+	0.916159i	$0.631273\pi$
$854$	−45.7663	−1.56609
$855$	8.30222	0.283930
$856$	9.12394	0.311850
$857$	4.67967	0.159854	0.0799272	−	0.996801i	$-0.474531\pi$
$857$	4.67967	0.159854	0.0799272	+	0.996801i	$0.474531\pi$
$858$	3.98841	0.136162
$859$	46.6212	1.59070	0.795348	−	0.606153i	$-0.207288\pi$
$859$	46.6212	1.59070	0.795348	+	0.606153i	$0.207288\pi$
$860$	0.0494025	0.00168461
$861$	−14.4911	−0.493854
$862$	−15.1250	−0.515159
$863$	50.7278	1.72680	0.863398	−	0.504524i	$-0.168332\pi$
$863$	50.7278	1.72680	0.863398	+	0.504524i	$0.168332\pi$
$864$	−14.2109	−0.483465
$865$	−11.7507	−0.399535
$866$	−17.5895	−0.597715
$867$	−4.56717	−0.155109
$868$	−8.97445	−0.304613
$869$	16.4187	0.556965
$870$	−0.153533	−0.00520525
$871$	−14.0349	−0.475554
$872$	−10.3278	−0.349743
$873$	12.7788	0.432496
$874$	65.4766	2.21478
$875$	21.0602	0.711965
$876$	−6.21023	−0.209824
$877$	18.4910	0.624398	0.312199	−	0.950017i	$-0.398934\pi$
$877$	18.4910	0.624398	0.312199	+	0.950017i	$0.398934\pi$
$878$	−51.5048	−1.73820
$879$	15.9908	0.539356
$880$	−11.1081	−0.374455
$881$	20.2081	0.680829	0.340415	−	0.940275i	$-0.389433\pi$
$881$	20.2081	0.680829	0.340415	+	0.940275i	$0.389433\pi$
$882$	45.4370	1.52994
$883$	53.2547	1.79216	0.896082	−	0.443889i	$-0.146402\pi$
$883$	53.2547	1.79216	0.896082	+	0.443889i	$0.146402\pi$
$884$	−2.50059	−0.0841039
$885$	−0.697163	−0.0234349
$886$	34.7976	1.16905
$887$	−19.8155	−0.665341	−0.332670	−	0.943043i	$-0.607950\pi$
$887$	−19.8155	−0.665341	−0.332670	+	0.943043i	$0.607950\pi$
$888$	3.52709	0.118361
$889$	−68.6164	−2.30132
$890$	0.194261	0.00651163
$891$	−26.8361	−0.899042
$892$	8.00283	0.267955
$893$	23.9509	0.801485
$894$	14.1635	0.473698
$895$	7.37783	0.246614
$896$	−53.5953	−1.79049
$897$	−3.67510	−0.122708
$898$	26.4884	0.883929
$899$	0.804178	0.0268208
$900$	10.7215	0.357384
$901$	−7.47963	−0.249182
$902$	−45.2860	−1.50786
$903$	−0.255955	−0.00851766
$904$	5.86918	0.195206
$905$	−4.87524	−0.162059
$906$	−18.4815	−0.614006
$907$	−9.28785	−0.308398	−0.154199	−	0.988040i	$-0.549280\pi$
$907$	−9.28785	−0.308398	−0.154199	+	0.988040i	$0.549280\pi$
$908$	−14.3936	−0.477669
$909$	−14.1810	−0.470354
$910$	3.65197	0.121062
$911$	30.2258	1.00143	0.500713	−	0.865613i	$-0.333071\pi$
$911$	30.2258	1.00143	0.500713	+	0.865613i	$0.333071\pi$
$912$	−16.2650	−0.538586
$913$	36.4643	1.20679
$914$	35.8809	1.18683
$915$	−1.92160	−0.0635262
$916$	16.9846	0.561187
$917$	−82.0427	−2.70929
$918$	−15.8241	−0.522273
$919$	−2.83835	−0.0936284	−0.0468142	−	0.998904i	$-0.514907\pi$
$919$	−2.83835	−0.0936284	−0.0468142	+	0.998904i	$0.514907\pi$
$920$	6.76521	0.223042
$921$	7.78208	0.256428
$922$	−19.2603	−0.634303
$923$	−6.12761	−0.201693
$924$	−8.22914	−0.270719
$925$	−15.3608	−0.505059
$926$	47.3504	1.55603
$927$	−2.69060	−0.0883708
$928$	−1.39967	−0.0459464
$929$	−1.99736	−0.0655312	−0.0327656	−	0.999463i	$-0.510431\pi$
$929$	−1.99736	−0.0655312	−0.0327656	+	0.999463i	$0.510431\pi$
$930$	−1.27030	−0.0416547
$931$	58.8560	1.92893
$932$	−6.84758	−0.224300
$933$	9.18439	0.300683
$934$	−56.4819	−1.84814
$935$	−6.61880	−0.216458
$936$	−5.24724	−0.171511
$937$	−7.14386	−0.233380	−0.116690	−	0.993168i	$-0.537228\pi$
$937$	−7.14386	−0.233380	−0.116690	+	0.993168i	$0.537228\pi$
$938$	97.6213	3.18745
$939$	−9.11385	−0.297419
$940$	−1.80479	−0.0588656
$941$	29.5981	0.964870	0.482435	−	0.875932i	$-0.339752\pi$
$941$	29.5981	0.964870	0.482435	+	0.875932i	$0.339752\pi$
$942$	16.3191	0.531706
$943$	41.7286	1.35887
$944$	−11.8773	−0.386573
$945$	6.85524	0.223001
$946$	−0.799885	−0.0260065
$947$	−3.53904	−0.115003	−0.0575016	−	0.998345i	$-0.518313\pi$
$947$	−3.53904	−0.115003	−0.0575016	+	0.998345i	$0.518313\pi$
$948$	−1.81157	−0.0588369
$949$	−13.2366	−0.429680
$950$	46.8187	1.51900
$951$	12.5842	0.408072
$952$	−23.8489	−0.772949
$953$	48.2988	1.56455	0.782276	−	0.622931i	$-0.214058\pi$
$953$	48.2988	1.56455	0.782276	+	0.622931i	$0.214058\pi$
$954$	11.4466	0.370598
$955$	7.08517	0.229271
$956$	−3.66665	−0.118588
$957$	0.737393	0.0238365
$958$	−16.2189	−0.524009
$959$	−45.0835	−1.45582
$960$	−0.695209	−0.0224378
$961$	−24.3464	−0.785368
$962$	−5.48272	−0.176770
$963$	−12.5878	−0.405635
$964$	8.86729	0.285596
$965$	10.5781	0.340522
$966$	25.5626	0.822464
$967$	−12.4347	−0.399871	−0.199936	−	0.979809i	$-0.564073\pi$
$967$	−12.4347	−0.399871	−0.199936	+	0.979809i	$0.564073\pi$
$968$	13.8098	0.443864
$969$	−9.69151	−0.311336
$970$	−4.20490	−0.135011
$971$	33.3182	1.06923	0.534616	−	0.845095i	$-0.320456\pi$
$971$	33.3182	1.06923	0.534616	+	0.845095i	$0.320456\pi$
$972$	10.9705	0.351880
$973$	−52.7378	−1.69070
$974$	−25.0478	−0.802583
$975$	−2.62786	−0.0841590
$976$	−32.7376	−1.04790
$977$	−3.78300	−0.121029	−0.0605144	−	0.998167i	$-0.519274\pi$
$977$	−3.78300	−0.121029	−0.0605144	+	0.998167i	$0.519274\pi$
$978$	3.64098	0.116426
$979$	−0.933003	−0.0298189
$980$	−4.43502	−0.141672
$981$	14.2486	0.454924
$982$	22.7371	0.725570
$983$	2.44610	0.0780183	0.0390092	−	0.999239i	$-0.487580\pi$
$983$	2.44610	0.0780183	0.0390092	+	0.999239i	$0.487580\pi$
$984$	−6.85127	−0.218411
$985$	−1.37587	−0.0438389
$986$	−1.55856	−0.0496346
$987$	9.35062	0.297634
$988$	4.95703	0.157704
$989$	0.737052	0.0234369
$990$	10.1292	0.321929
$991$	−17.8500	−0.567025	−0.283512	−	0.958969i	$-0.591500\pi$
$991$	−17.8500	−0.567025	−0.283512	+	0.958969i	$0.591500\pi$
$992$	−11.5806	−0.367684
$993$	17.9017	0.568093
$994$	42.6213	1.35187
$995$	−4.98648	−0.158082
$996$	−4.02331	−0.127484
$997$	−58.4222	−1.85025	−0.925125	−	0.379662i	$-0.876040\pi$
$997$	−58.4222	−1.85025	−0.925125	+	0.379662i	$0.876040\pi$
$998$	−14.2601	−0.451397
$999$	−10.2918	−0.325619

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1339.2.a.d.1.6	✓	19

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1339.2.a.d.1.6	✓	19	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1339 = 13 \cdot 103 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1339.a (trivial)

\(f(q)\)	\(=\)	\(q-1.68626 q^{2} +0.556240 q^{3} +0.843466 q^{4} -0.525039 q^{5} -0.937964 q^{6} +4.12488 q^{7} +1.95021 q^{8} -2.69060 q^{9} +O(q^{10})\)	\(q-1.68626 q^{2} +0.556240 q^{3} +0.843466 q^{4} -0.525039 q^{5} -0.937964 q^{6} +4.12488 q^{7} +1.95021 q^{8} -2.69060 q^{9} +0.885350 q^{10} -4.25220 q^{11} +0.469169 q^{12} +1.00000 q^{13} -6.95562 q^{14} -0.292047 q^{15} -4.97550 q^{16} -2.96466 q^{17} +4.53704 q^{18} +5.87698 q^{19} -0.442852 q^{20} +2.29442 q^{21} +7.17030 q^{22} -6.60705 q^{23} +1.08479 q^{24} -4.72433 q^{25} -1.68626 q^{26} -3.16534 q^{27} +3.47920 q^{28} -0.311762 q^{29} +0.492467 q^{30} -2.57946 q^{31} +4.48954 q^{32} -2.36524 q^{33} +4.99918 q^{34} -2.16572 q^{35} -2.26943 q^{36} +3.25141 q^{37} -9.91011 q^{38} +0.556240 q^{39} -1.02394 q^{40} -6.31578 q^{41} -3.86899 q^{42} -0.111555 q^{43} -3.58658 q^{44} +1.41267 q^{45} +11.1412 q^{46} +4.07537 q^{47} -2.76757 q^{48} +10.0147 q^{49} +7.96645 q^{50} -1.64906 q^{51} +0.843466 q^{52} +2.52293 q^{53} +5.33757 q^{54} +2.23257 q^{55} +8.04441 q^{56} +3.26901 q^{57} +0.525712 q^{58} +2.38716 q^{59} -0.246332 q^{60} +6.57976 q^{61} +4.34963 q^{62} -11.0984 q^{63} +2.38047 q^{64} -0.525039 q^{65} +3.98841 q^{66} -14.0349 q^{67} -2.50059 q^{68} -3.67510 q^{69} +3.65197 q^{70} -6.12761 q^{71} -5.24724 q^{72} -13.2366 q^{73} -5.48272 q^{74} -2.62786 q^{75} +4.95703 q^{76} -17.5398 q^{77} -0.937964 q^{78} -3.86122 q^{79} +2.61233 q^{80} +6.31111 q^{81} +10.6500 q^{82} -8.57540 q^{83} +1.93527 q^{84} +1.55656 q^{85} +0.188111 q^{86} -0.173415 q^{87} -8.29270 q^{88} +0.219417 q^{89} -2.38212 q^{90} +4.12488 q^{91} -5.57282 q^{92} -1.43480 q^{93} -6.87212 q^{94} -3.08564 q^{95} +2.49726 q^{96} -4.74942 q^{97} -16.8873 q^{98} +11.4409 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 19 q - 9 q^{2} - 2 q^{3} + 17 q^{4} - 18 q^{5} - 8 q^{6} - 8 q^{7} - 24 q^{8} + 7 q^{9}+O(q^{10}) \) 19 * q - 9 * q^2 - 2 * q^3 + 17 * q^4 - 18 * q^5 - 8 * q^6 - 8 * q^7 - 24 * q^8 + 7 * q^9	\( 19 q - 9 q^{2} - 2 q^{3} + 17 q^{4} - 18 q^{5} - 8 q^{6} - 8 q^{7} - 24 q^{8} + 7 q^{9} - q^{11} + 18 q^{12} + 19 q^{13} - 8 q^{14} - 11 q^{15} + 21 q^{16} - 16 q^{17} - 10 q^{19} - 20 q^{20} - 33 q^{21} + 2 q^{22} - 14 q^{23} - 9 q^{24} + 23 q^{25} - 9 q^{26} + q^{27} + 10 q^{28} - 22 q^{29} + 28 q^{30} - 3 q^{31} - 47 q^{32} - 25 q^{33} - 35 q^{34} - 3 q^{35} - 33 q^{36} - 19 q^{37} - 15 q^{38} - 2 q^{39} + 8 q^{40} - 52 q^{41} - 3 q^{42} - 2 q^{43} - 54 q^{44} - 40 q^{45} + 33 q^{46} - 24 q^{47} - 8 q^{48} + 7 q^{49} - 10 q^{50} - 7 q^{51} + 17 q^{52} - 11 q^{53} - 23 q^{54} - 29 q^{55} - 17 q^{56} - 34 q^{57} + 18 q^{58} - 52 q^{59} - 71 q^{60} - 25 q^{61} - 22 q^{62} - 19 q^{63} + 48 q^{64} - 18 q^{65} + 9 q^{66} - 2 q^{67} + 18 q^{68} - 26 q^{69} - 12 q^{70} - 44 q^{71} - 6 q^{72} - 39 q^{73} - 4 q^{74} + 17 q^{75} - 10 q^{76} - 18 q^{77} - 8 q^{78} + q^{79} - 9 q^{80} - 13 q^{81} + 47 q^{82} - 27 q^{83} - 24 q^{84} - 26 q^{85} - q^{86} + 31 q^{87} + 19 q^{88} - 86 q^{89} + 48 q^{90} - 8 q^{91} - 19 q^{92} + 32 q^{93} + 45 q^{94} + 17 q^{95} - 25 q^{96} - 20 q^{97} + 39 q^{98} + 50 q^{99}+O(q^{100}) \) 19 * q - 9 * q^2 - 2 * q^3 + 17 * q^4 - 18 * q^5 - 8 * q^6 - 8 * q^7 - 24 * q^8 + 7 * q^9 - q^11 + 18 * q^12 + 19 * q^13 - 8 * q^14 - 11 * q^15 + 21 * q^16 - 16 * q^17 - 10 * q^19 - 20 * q^20 - 33 * q^21 + 2 * q^22 - 14 * q^23 - 9 * q^24 + 23 * q^25 - 9 * q^26 + q^27 + 10 * q^28 - 22 * q^29 + 28 * q^30 - 3 * q^31 - 47 * q^32 - 25 * q^33 - 35 * q^34 - 3 * q^35 - 33 * q^36 - 19 * q^37 - 15 * q^38 - 2 * q^39 + 8 * q^40 - 52 * q^41 - 3 * q^42 - 2 * q^43 - 54 * q^44 - 40 * q^45 + 33 * q^46 - 24 * q^47 - 8 * q^48 + 7 * q^49 - 10 * q^50 - 7 * q^51 + 17 * q^52 - 11 * q^53 - 23 * q^54 - 29 * q^55 - 17 * q^56 - 34 * q^57 + 18 * q^58 - 52 * q^59 - 71 * q^60 - 25 * q^61 - 22 * q^62 - 19 * q^63 + 48 * q^64 - 18 * q^65 + 9 * q^66 - 2 * q^67 + 18 * q^68 - 26 * q^69 - 12 * q^70 - 44 * q^71 - 6 * q^72 - 39 * q^73 - 4 * q^74 + 17 * q^75 - 10 * q^76 - 18 * q^77 - 8 * q^78 + q^79 - 9 * q^80 - 13 * q^81 + 47 * q^82 - 27 * q^83 - 24 * q^84 - 26 * q^85 - q^86 + 31 * q^87 + 19 * q^88 - 86 * q^89 + 48 * q^90 - 8 * q^91 - 19 * q^92 + 32 * q^93 + 45 * q^94 + 17 * q^95 - 25 * q^96 - 20 * q^97 + 39 * q^98 + 50 * q^99

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