LMFDB - Embedded newform 803.2.a.f.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [803,2,Mod(1,803)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(803, 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("803.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 803 = 11 \cdot 73 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	803.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:	$6.41198728231$
Analytic rank:	$0$
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} - 7 x^{18} - 6 x^{17} + 141 x^{16} - 155 x^{15} - 1063 x^{14} + 2102 x^{13} + 3638 x^{12} + \cdots - 512 $ x^19 - 7x^18 - 6x^17 + 141x^16 - 155x^15 - 1063x^14 + 2102x^13 + 3638x^12 - 10680x^11 - 4833x^10 + 27461x^9 - 2771x^8 - 37520x^7 + 14985x^6 + 25749x^5 - 15182x^4 - 7256x^3 + 5536x^2 + 384x - 512
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Root			$0.693824$ of defining polynomial
Character	$\chi$	$=$	803.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.693824 q^{2} +2.06808 q^{3} -1.51861 q^{4} +3.85866 q^{5} +1.43488 q^{6} +0.209786 q^{7} -2.44129 q^{8} +1.27695 q^{9} +O(q^{10})$	\(q+0.693824 q^{2} +2.06808 q^{3} -1.51861 q^{4} +3.85866 q^{5} +1.43488 q^{6} +0.209786 q^{7} -2.44129 q^{8} +1.27695 q^{9} +2.67723 q^{10} +1.00000 q^{11} -3.14060 q^{12} +4.67425 q^{13} +0.145555 q^{14} +7.98001 q^{15} +1.34339 q^{16} -6.55675 q^{17} +0.885978 q^{18} +4.78125 q^{19} -5.85979 q^{20} +0.433855 q^{21} +0.693824 q^{22} -8.51049 q^{23} -5.04879 q^{24} +9.88925 q^{25} +3.24311 q^{26} -3.56340 q^{27} -0.318583 q^{28} +7.36952 q^{29} +5.53672 q^{30} -3.01166 q^{31} +5.81466 q^{32} +2.06808 q^{33} -4.54923 q^{34} +0.809494 q^{35} -1.93919 q^{36} +2.95988 q^{37} +3.31735 q^{38} +9.66672 q^{39} -9.42012 q^{40} -2.21434 q^{41} +0.301019 q^{42} +3.93317 q^{43} -1.51861 q^{44} +4.92731 q^{45} -5.90478 q^{46} -5.26514 q^{47} +2.77823 q^{48} -6.95599 q^{49} +6.86140 q^{50} -13.5599 q^{51} -7.09836 q^{52} +0.548853 q^{53} -2.47237 q^{54} +3.85866 q^{55} -0.512151 q^{56} +9.88800 q^{57} +5.11315 q^{58} -10.3071 q^{59} -12.1185 q^{60} -8.54353 q^{61} -2.08956 q^{62} +0.267887 q^{63} +1.34758 q^{64} +18.0363 q^{65} +1.43488 q^{66} +12.7328 q^{67} +9.95714 q^{68} -17.6004 q^{69} +0.561647 q^{70} -14.2310 q^{71} -3.11741 q^{72} -1.00000 q^{73} +2.05363 q^{74} +20.4517 q^{75} -7.26085 q^{76} +0.209786 q^{77} +6.70700 q^{78} +12.7119 q^{79} +5.18368 q^{80} -11.2002 q^{81} -1.53636 q^{82} +6.22067 q^{83} -0.658856 q^{84} -25.3003 q^{85} +2.72893 q^{86} +15.2407 q^{87} -2.44129 q^{88} +11.1522 q^{89} +3.41869 q^{90} +0.980595 q^{91} +12.9241 q^{92} -6.22836 q^{93} -3.65308 q^{94} +18.4492 q^{95} +12.0252 q^{96} -10.5540 q^{97} -4.82623 q^{98} +1.27695 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 19 q + 7 q^{2} + 3 q^{3} + 23 q^{4} + 2 q^{5} + 16 q^{7} + 18 q^{8} + 22 q^{9}+O(q^{10}) $ 19 * q + 7 * q^2 + 3 * q^3 + 23 * q^4 + 2 * q^5 + 16 * q^7 + 18 * q^8 + 22 * q^9	\( 19 q + 7 q^{2} + 3 q^{3} + 23 q^{4} + 2 q^{5} + 16 q^{7} + 18 q^{8} + 22 q^{9} + 8 q^{10} + 19 q^{11} - 5 q^{12} + 30 q^{13} - 9 q^{14} - 11 q^{15} + 31 q^{16} + 9 q^{17} + 3 q^{18} - q^{19} - 9 q^{20} + 13 q^{21} + 7 q^{22} - 2 q^{23} - 19 q^{24} + 39 q^{25} - 3 q^{26} - 9 q^{27} + 49 q^{28} + 18 q^{29} - 17 q^{30} + 5 q^{31} + 38 q^{32} + 3 q^{33} + 26 q^{34} - 14 q^{35} + 19 q^{36} + 36 q^{37} + 9 q^{38} + 27 q^{39} + 7 q^{40} + 9 q^{41} + 25 q^{42} + 33 q^{43} + 23 q^{44} + 8 q^{45} - 47 q^{46} - 28 q^{47} - 49 q^{48} + 33 q^{49} + 27 q^{50} + 2 q^{51} + 18 q^{52} + 27 q^{53} + 7 q^{54} + 2 q^{55} - 28 q^{56} - 6 q^{57} + 16 q^{58} - 28 q^{59} + 4 q^{61} + 5 q^{62} + 26 q^{63} + 80 q^{64} + 12 q^{65} + 21 q^{67} - 23 q^{68} - 34 q^{69} - 74 q^{70} - 7 q^{71} + 54 q^{72} - 19 q^{73} + 4 q^{74} - 25 q^{75} - 23 q^{76} + 16 q^{77} - 28 q^{78} + 25 q^{79} - 49 q^{80} - 9 q^{81} - 10 q^{82} + 15 q^{83} + 37 q^{84} + 23 q^{85} - 29 q^{86} + q^{87} + 18 q^{88} - 21 q^{89} - 94 q^{90} + 4 q^{91} - 74 q^{92} + 22 q^{93} + 69 q^{94} + 23 q^{95} - 116 q^{96} + 18 q^{97} - 4 q^{98} + 22 q^{99}+O(q^{100}) \) 19 * q + 7 * q^2 + 3 * q^3 + 23 * q^4 + 2 * q^5 + 16 * q^7 + 18 * q^8 + 22 * q^9 + 8 * q^10 + 19 * q^11 - 5 * q^12 + 30 * q^13 - 9 * q^14 - 11 * q^15 + 31 * q^16 + 9 * q^17 + 3 * q^18 - q^19 - 9 * q^20 + 13 * q^21 + 7 * q^22 - 2 * q^23 - 19 * q^24 + 39 * q^25 - 3 * q^26 - 9 * q^27 + 49 * q^28 + 18 * q^29 - 17 * q^30 + 5 * q^31 + 38 * q^32 + 3 * q^33 + 26 * q^34 - 14 * q^35 + 19 * q^36 + 36 * q^37 + 9 * q^38 + 27 * q^39 + 7 * q^40 + 9 * q^41 + 25 * q^42 + 33 * q^43 + 23 * q^44 + 8 * q^45 - 47 * q^46 - 28 * q^47 - 49 * q^48 + 33 * q^49 + 27 * q^50 + 2 * q^51 + 18 * q^52 + 27 * q^53 + 7 * q^54 + 2 * q^55 - 28 * q^56 - 6 * q^57 + 16 * q^58 - 28 * q^59 + 4 * q^61 + 5 * q^62 + 26 * q^63 + 80 * q^64 + 12 * q^65 + 21 * q^67 - 23 * q^68 - 34 * q^69 - 74 * q^70 - 7 * q^71 + 54 * q^72 - 19 * q^73 + 4 * q^74 - 25 * q^75 - 23 * q^76 + 16 * q^77 - 28 * q^78 + 25 * q^79 - 49 * q^80 - 9 * q^81 - 10 * q^82 + 15 * q^83 + 37 * q^84 + 23 * q^85 - 29 * q^86 + q^87 + 18 * q^88 - 21 * q^89 - 94 * q^90 + 4 * q^91 - 74 * q^92 + 22 * q^93 + 69 * q^94 + 23 * q^95 - 116 * q^96 + 18 * q^97 - 4 * q^98 + 22 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	0.693824	0.490608	0.245304	−	0.969446i	$-0.421112\pi$
$2$	0.693824	0.490608	0.245304	+	0.969446i	$0.421112\pi$
$3$	2.06808	1.19401	0.597003	−	0.802239i	$-0.296358\pi$
$3$	2.06808	1.19401	0.597003	+	0.802239i	$0.296358\pi$
$4$	−1.51861	−0.759304
$5$	3.85866	1.72564	0.862822	−	0.505507i	$-0.168695\pi$
$5$	3.85866	1.72564	0.862822	+	0.505507i	$0.168695\pi$
$6$	1.43488	0.585788
$7$	0.209786	0.0792918	0.0396459	−	0.999214i	$-0.487377\pi$
$7$	0.209786	0.0792918	0.0396459	+	0.999214i	$0.487377\pi$
$8$	−2.44129	−0.863128
$9$	1.27695	0.425650
$10$	2.67723	0.846614
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−3.14060	−0.906614
$13$	4.67425	1.29640	0.648202	−	0.761468i	$-0.275521\pi$
$13$	4.67425	1.29640	0.648202	+	0.761468i	$0.275521\pi$
$14$	0.145555	0.0389012
$15$	7.98001	2.06043
$16$	1.34339	0.335847
$17$	−6.55675	−1.59025	−0.795123	−	0.606448i	$-0.792594\pi$
$17$	−6.55675	−1.59025	−0.795123	+	0.606448i	$0.792594\pi$
$18$	0.885978	0.208827
$19$	4.78125	1.09689	0.548447	−	0.836185i	$-0.315219\pi$
$19$	4.78125	1.09689	0.548447	+	0.836185i	$0.315219\pi$
$20$	−5.85979	−1.31029
$21$	0.433855	0.0946749
$22$	0.693824	0.147924
$23$	−8.51049	−1.77456	−0.887280	−	0.461232i	$-0.847408\pi$
$23$	−8.51049	−1.77456	−0.887280	+	0.461232i	$0.847408\pi$
$24$	−5.04879	−1.03058
$25$	9.88925	1.97785
$26$	3.24311	0.636026
$27$	−3.56340	−0.685777
$28$	−0.318583	−0.0602066
$29$	7.36952	1.36849	0.684243	−	0.729254i	$-0.260133\pi$
$29$	7.36952	1.36849	0.684243	+	0.729254i	$0.260133\pi$
$30$	5.53672	1.01086
$31$	−3.01166	−0.540911	−0.270455	−	0.962732i	$-0.587174\pi$
$31$	−3.01166	−0.540911	−0.270455	+	0.962732i	$0.587174\pi$
$32$	5.81466	1.02790
$33$	2.06808	0.360006
$34$	−4.54923	−0.780187
$35$	0.809494	0.136830
$36$	−1.93919	−0.323198
$37$	2.95988	0.486601	0.243300	−	0.969951i	$-0.421770\pi$
$37$	2.95988	0.486601	0.243300	+	0.969951i	$0.421770\pi$
$38$	3.31735	0.538145
$39$	9.66672	1.54791
$40$	−9.42012	−1.48945
$41$	−2.21434	−0.345822	−0.172911	−	0.984937i	$-0.555317\pi$
$41$	−2.21434	−0.345822	−0.172911	+	0.984937i	$0.555317\pi$
$42$	0.301019	0.0464482
$43$	3.93317	0.599802	0.299901	−	0.953970i	$-0.403046\pi$
$43$	3.93317	0.599802	0.299901	+	0.953970i	$0.403046\pi$
$44$	−1.51861	−0.228939
$45$	4.92731	0.734521
$46$	−5.90478	−0.870612
$47$	−5.26514	−0.767999	−0.384000	−	0.923333i	$-0.625454\pi$
$47$	−5.26514	−0.767999	−0.384000	+	0.923333i	$0.625454\pi$
$48$	2.77823	0.401003
$49$	−6.95599	−0.993713
$50$	6.86140	0.970348
$51$	−13.5599	−1.89876
$52$	−7.09836	−0.984365
$53$	0.548853	0.0753908	0.0376954	−	0.999289i	$-0.487998\pi$
$53$	0.548853	0.0753908	0.0376954	+	0.999289i	$0.487998\pi$
$54$	−2.47237	−0.336448
$55$	3.85866	0.520301
$56$	−0.512151	−0.0684390
$57$	9.88800	1.30970
$58$	5.11315	0.671389
$59$	−10.3071	−1.34188	−0.670938	−	0.741513i	$-0.734108\pi$
$59$	−10.3071	−1.34188	−0.670938	+	0.741513i	$0.734108\pi$
$60$	−12.1185	−1.56449
$61$	−8.54353	−1.09389	−0.546944	−	0.837170i	$-0.684209\pi$
$61$	−8.54353	−1.09389	−0.546944	+	0.837170i	$0.684209\pi$
$62$	−2.08956	−0.265375
$63$	0.267887	0.0337506
$64$	1.34758	0.168447
$65$	18.0363	2.23713
$66$	1.43488	0.176622
$67$	12.7328	1.55556	0.777779	−	0.628538i	$-0.216347\pi$
$67$	12.7328	1.55556	0.777779	+	0.628538i	$0.216347\pi$
$68$	9.95714	1.20748
$69$	−17.6004	−2.11883
$70$	0.561647	0.0671296
$71$	−14.2310	−1.68891	−0.844454	−	0.535628i	$-0.820075\pi$
$71$	−14.2310	−1.68891	−0.844454	+	0.535628i	$0.820075\pi$
$72$	−3.11741	−0.367390
$73$	−1.00000	−0.117041
$73$	−1.00000	−0.117041
$74$	2.05363	0.238730
$75$	20.4517	2.36156
$76$	−7.26085	−0.832876
$77$	0.209786	0.0239074
$78$	6.70700	0.759418
$79$	12.7119	1.43020	0.715099	−	0.699023i	$-0.246382\pi$
$79$	12.7119	1.43020	0.715099	+	0.699023i	$0.246382\pi$
$80$	5.18368	0.579553
$81$	−11.2002	−1.24447
$82$	−1.53636	−0.169663
$83$	6.22067	0.682808	0.341404	−	0.939917i	$-0.389098\pi$
$83$	6.22067	0.682808	0.341404	+	0.939917i	$0.389098\pi$
$84$	−0.658856	−0.0718870
$85$	−25.3003	−2.74420
$86$	2.72893	0.294268
$87$	15.2407	1.63398
$88$	−2.44129	−0.260243
$89$	11.1522	1.18213	0.591064	−	0.806625i	$-0.298708\pi$
$89$	11.1522	1.18213	0.591064	+	0.806625i	$0.298708\pi$
$90$	3.41869	0.360361
$91$	0.980595	0.102794
$92$	12.9241	1.34743
$93$	−6.22836	−0.645851
$94$	−3.65308	−0.376786
$95$	18.4492	1.89285
$96$	12.0252	1.22732
$97$	−10.5540	−1.07159	−0.535796	−	0.844347i	$-0.679989\pi$
$97$	−10.5540	−1.07159	−0.535796	+	0.844347i	$0.679989\pi$
$98$	−4.82623	−0.487523
$99$	1.27695	0.128338
$100$	−15.0179	−1.50179
$101$	−1.36066	−0.135391	−0.0676953	−	0.997706i	$-0.521565\pi$
$101$	−1.36066	−0.135391	−0.0676953	+	0.997706i	$0.521565\pi$
$102$	−9.40817	−0.931548
$103$	−18.8007	−1.85249	−0.926243	−	0.376926i	$-0.876981\pi$
$103$	−18.8007	−1.85249	−0.926243	+	0.376926i	$0.876981\pi$
$104$	−11.4112	−1.11896
$105$	1.67410	0.163375
$106$	0.380807	0.0369873
$107$	4.50483	0.435499	0.217749	−	0.976005i	$-0.430128\pi$
$107$	4.50483	0.435499	0.217749	+	0.976005i	$0.430128\pi$
$108$	5.41141	0.520714
$109$	2.64160	0.253019	0.126510	−	0.991965i	$-0.459623\pi$
$109$	2.64160	0.253019	0.126510	+	0.991965i	$0.459623\pi$
$110$	2.67723	0.255264
$111$	6.12126	0.581004
$112$	0.281825	0.0266299
$113$	6.34177	0.596583	0.298292	−	0.954475i	$-0.403583\pi$
$113$	6.34177	0.596583	0.298292	+	0.954475i	$0.403583\pi$
$114$	6.86053	0.642548
$115$	−32.8391	−3.06226
$116$	−11.1914	−1.03910
$117$	5.96878	0.551814
$118$	−7.15134	−0.658335
$119$	−1.37552	−0.126094
$120$	−19.4816	−1.77841
$121$	1.00000	0.0909091
$122$	−5.92771	−0.536669
$123$	−4.57943	−0.412913
$124$	4.57354	0.410716
$125$	18.8659	1.68742
$126$	0.185866	0.0165583
$127$	1.89135	0.167830	0.0839151	−	0.996473i	$-0.473258\pi$
$127$	1.89135	0.167830	0.0839151	+	0.996473i	$0.473258\pi$
$128$	−10.6943	−0.945256
$129$	8.13410	0.716167
$130$	12.5140	1.09755
$131$	−16.3971	−1.43262	−0.716309	−	0.697784i	$-0.754170\pi$
$131$	−16.3971	−1.43262	−0.716309	+	0.697784i	$0.754170\pi$
$132$	−3.14060	−0.273354
$133$	1.00304	0.0869747
$134$	8.83431	0.763168
$135$	−13.7500	−1.18341
$136$	16.0070	1.37259
$137$	7.74936	0.662073	0.331036	−	0.943618i	$-0.392602\pi$
$137$	7.74936	0.662073	0.331036	+	0.943618i	$0.392602\pi$
$138$	−12.2116	−1.03952
$139$	−8.15464	−0.691668	−0.345834	−	0.938296i	$-0.612404\pi$
$139$	−8.15464	−0.691668	−0.345834	+	0.938296i	$0.612404\pi$
$140$	−1.22930	−0.103895
$141$	−10.8887	−0.916996
$142$	−9.87381	−0.828591
$143$	4.67425	0.390881
$144$	1.71544	0.142953
$145$	28.4365	2.36152
$146$	−0.693824	−0.0574213
$147$	−14.3855	−1.18650
$148$	−4.49489	−0.369478
$149$	11.2474	0.921425	0.460713	−	0.887549i	$-0.347594\pi$
$149$	11.2474	0.921425	0.460713	+	0.887549i	$0.347594\pi$
$150$	14.1899	1.15860
$151$	−3.88226	−0.315933	−0.157967	−	0.987444i	$-0.550494\pi$
$151$	−3.88226	−0.315933	−0.157967	+	0.987444i	$0.550494\pi$
$152$	−11.6724	−0.946760
$153$	−8.37265	−0.676888
$154$	0.145555	0.0117291
$155$	−11.6210	−0.933420
$156$	−14.6800	−1.17534
$157$	6.00515	0.479264	0.239632	−	0.970864i	$-0.422973\pi$
$157$	6.00515	0.479264	0.239632	+	0.970864i	$0.422973\pi$
$158$	8.81980	0.701666
$159$	1.13507	0.0900170
$160$	22.4368	1.77379
$161$	−1.78539	−0.140708
$162$	−7.77100	−0.610547
$163$	5.99758	0.469767	0.234883	−	0.972024i	$-0.424529\pi$
$163$	5.99758	0.469767	0.234883	+	0.972024i	$0.424529\pi$
$164$	3.36271	0.262584
$165$	7.98001	0.621243
$166$	4.31605	0.334991
$167$	−15.8378	−1.22556	−0.612781	−	0.790253i	$-0.709949\pi$
$167$	−15.8378	−1.22556	−0.612781	+	0.790253i	$0.709949\pi$
$168$	−1.05917	−0.0817166
$169$	8.84863	0.680664
$170$	−17.5539	−1.34633
$171$	6.10542	0.466893
$172$	−5.97294	−0.455432
$173$	−19.7485	−1.50145	−0.750724	−	0.660616i	$-0.770295\pi$
$173$	−19.7485	−1.50145	−0.750724	+	0.660616i	$0.770295\pi$
$174$	10.5744	0.801643
$175$	2.07463	0.156827
$176$	1.34339	0.101262
$177$	−21.3160	−1.60221
$178$	7.73765	0.579961
$179$	−16.8188	−1.25710	−0.628549	−	0.777770i	$-0.716351\pi$
$179$	−16.8188	−1.25710	−0.628549	+	0.777770i	$0.716351\pi$
$180$	−7.48266	−0.557724
$181$	−5.29312	−0.393435	−0.196717	−	0.980460i	$-0.563028\pi$
$181$	−5.29312	−0.393435	−0.196717	+	0.980460i	$0.563028\pi$
$182$	0.680360	0.0504316
$183$	−17.6687	−1.30611
$184$	20.7766	1.53167
$185$	11.4212	0.839700
$186$	−4.32138	−0.316859
$187$	−6.55675	−0.479477
$188$	7.99568	0.583145
$189$	−0.747554	−0.0543765
$190$	12.8005	0.928646
$191$	2.91728	0.211087	0.105543	−	0.994415i	$-0.466342\pi$
$191$	2.91728	0.211087	0.105543	+	0.994415i	$0.466342\pi$
$192$	2.78690	0.201127
$193$	−0.946694	−0.0681445	−0.0340723	−	0.999419i	$-0.510848\pi$
$193$	−0.946694	−0.0681445	−0.0340723	+	0.999419i	$0.510848\pi$
$194$	−7.32259	−0.525732
$195$	37.3006	2.67115
$196$	10.5634	0.754530
$197$	−10.4766	−0.746430	−0.373215	−	0.927745i	$-0.621745\pi$
$197$	−10.4766	−0.746430	−0.373215	+	0.927745i	$0.621745\pi$
$198$	0.885978	0.0629637
$199$	−13.0826	−0.927402	−0.463701	−	0.885992i	$-0.653479\pi$
$199$	−13.0826	−0.927402	−0.463701	+	0.885992i	$0.653479\pi$
$200$	−24.1426	−1.70714
$201$	26.3324	1.85734
$202$	−0.944058	−0.0664237
$203$	1.54603	0.108510
$204$	20.5922	1.44174
$205$	−8.54438	−0.596765
$206$	−13.0444	−0.908844
$207$	−10.8675	−0.755341
$208$	6.27933	0.435393
$209$	4.78125	0.330726
$210$	1.16153	0.0801531
$211$	14.9508	1.02926	0.514628	−	0.857413i	$-0.327930\pi$
$211$	14.9508	1.02926	0.514628	+	0.857413i	$0.327930\pi$
$212$	−0.833493	−0.0572445
$213$	−29.4308	−2.01657
$214$	3.12556	0.213659
$215$	15.1767	1.03505
$216$	8.69932	0.591914
$217$	−0.631806	−0.0428898
$218$	1.83281	0.124133
$219$	−2.06808	−0.139748
$220$	−5.85979	−0.395067
$221$	−30.6479	−2.06160
$222$	4.24708	0.285045
$223$	11.6634	0.781040	0.390520	−	0.920594i	$-0.372295\pi$
$223$	11.6634	0.781040	0.390520	+	0.920594i	$0.372295\pi$
$224$	1.21984	0.0815038
$225$	12.6281	0.841872
$226$	4.40007	0.292688
$227$	16.5313	1.09722	0.548611	−	0.836078i	$-0.315157\pi$
$227$	16.5313	1.09722	0.548611	+	0.836078i	$0.315157\pi$
$228$	−15.0160	−0.994459
$229$	17.8678	1.18074	0.590368	−	0.807134i	$-0.298982\pi$
$229$	17.8678	1.18074	0.590368	+	0.807134i	$0.298982\pi$
$230$	−22.7845	−1.50237
$231$	0.433855	0.0285456
$232$	−17.9912	−1.18118
$233$	14.7040	0.963290	0.481645	−	0.876366i	$-0.340039\pi$
$233$	14.7040	0.963290	0.481645	+	0.876366i	$0.340039\pi$
$234$	4.14129	0.270724
$235$	−20.3164	−1.32529
$236$	15.6525	1.01889
$237$	26.2892	1.70766
$238$	−0.954368	−0.0618625
$239$	−1.80977	−0.117064	−0.0585322	−	0.998286i	$-0.518642\pi$
$239$	−1.80977	−0.117064	−0.0585322	+	0.998286i	$0.518642\pi$
$240$	10.7202	0.691989
$241$	−14.4056	−0.927947	−0.463974	−	0.885849i	$-0.653577\pi$
$241$	−14.4056	−0.927947	−0.463974	+	0.885849i	$0.653577\pi$
$242$	0.693824	0.0446007
$243$	−12.4728	−0.800130
$244$	12.9743	0.830593
$245$	−26.8408	−1.71480
$246$	−3.17732	−0.202578
$247$	22.3488	1.42202
$248$	7.35236	0.466875
$249$	12.8648	0.815276
$250$	13.0896	0.827862
$251$	7.57633	0.478214	0.239107	−	0.970993i	$-0.423145\pi$
$251$	7.57633	0.478214	0.239107	+	0.970993i	$0.423145\pi$
$252$	−0.406815	−0.0256269
$253$	−8.51049	−0.535050
$254$	1.31226	0.0823388
$255$	−52.3230	−3.27659
$256$	−10.1151	−0.632197
$257$	11.8965	0.742086	0.371043	−	0.928616i	$-0.379000\pi$
$257$	11.8965	0.742086	0.371043	+	0.928616i	$0.379000\pi$
$258$	5.64363	0.351357
$259$	0.620942	0.0385835
$260$	−27.3901	−1.69866
$261$	9.41051	0.582496
$262$	−11.3767	−0.702853
$263$	−0.193000	−0.0119009	−0.00595044	−	0.999982i	$-0.501894\pi$
$263$	−0.193000	−0.0119009	−0.00595044	+	0.999982i	$0.501894\pi$
$264$	−5.04879	−0.310732
$265$	2.11784	0.130098
$266$	0.695934	0.0426705
$267$	23.0636	1.41147
$268$	−19.3361	−1.18114
$269$	−25.0102	−1.52490	−0.762449	−	0.647049i	$-0.776003\pi$
$269$	−25.0102	−1.52490	−0.762449	+	0.647049i	$0.776003\pi$
$270$	−9.54005	−0.580589
$271$	31.1643	1.89310	0.946548	−	0.322564i	$-0.104545\pi$
$271$	31.1643	1.89310	0.946548	+	0.322564i	$0.104545\pi$
$272$	−8.80826	−0.534079
$273$	2.02795	0.122737
$274$	5.37669	0.324818
$275$	9.88925	0.596344
$276$	26.7281	1.60884
$277$	21.8462	1.31261	0.656305	−	0.754495i	$-0.272118\pi$
$277$	21.8462	1.31261	0.656305	+	0.754495i	$0.272118\pi$
$278$	−5.65789	−0.339338
$279$	−3.84574	−0.230239
$280$	−1.97621	−0.118101
$281$	−18.4881	−1.10291	−0.551453	−	0.834206i	$-0.685926\pi$
$281$	−18.4881	−1.10291	−0.551453	+	0.834206i	$0.685926\pi$
$282$	−7.55485	−0.449885
$283$	−21.1077	−1.25472	−0.627360	−	0.778729i	$-0.715865\pi$
$283$	−21.1077	−1.25472	−0.627360	+	0.778729i	$0.715865\pi$
$284$	21.6113	1.28240
$285$	38.1544	2.26007
$286$	3.24311	0.191769
$287$	−0.464538	−0.0274208
$288$	7.42503	0.437524
$289$	25.9910	1.52888
$290$	19.7299	1.15858
$291$	−21.8264	−1.27949
$292$	1.51861	0.0888698
$293$	20.5541	1.20078	0.600392	−	0.799706i	$-0.295011\pi$
$293$	20.5541	1.20078	0.600392	+	0.799706i	$0.295011\pi$
$294$	−9.98103	−0.582105
$295$	−39.7718	−2.31560
$296$	−7.22593	−0.419999
$297$	−3.56340	−0.206770
$298$	7.80374	0.452058
$299$	−39.7802	−2.30055
$300$	−31.0582	−1.79315
$301$	0.825125	0.0475594
$302$	−2.69360	−0.154999
$303$	−2.81395	−0.161657
$304$	6.42307	0.368389
$305$	−32.9666	−1.88766
$306$	−5.80914	−0.332087
$307$	22.5131	1.28489	0.642444	−	0.766332i	$-0.277920\pi$
$307$	22.5131	1.28489	0.642444	+	0.766332i	$0.277920\pi$
$308$	−0.318583	−0.0181530
$309$	−38.8813	−2.21188
$310$	−8.06292	−0.457943
$311$	−3.26296	−0.185026	−0.0925129	−	0.995711i	$-0.529490\pi$
$311$	−3.26296	−0.185026	−0.0925129	+	0.995711i	$0.529490\pi$
$312$	−23.5993	−1.33605
$313$	−13.4796	−0.761911	−0.380955	−	0.924593i	$-0.624405\pi$
$313$	−13.4796	−0.761911	−0.380955	+	0.924593i	$0.624405\pi$
$314$	4.16652	0.235130
$315$	1.03368	0.0582415
$316$	−19.3044	−1.08596
$317$	19.4117	1.09027	0.545133	−	0.838349i	$-0.316479\pi$
$317$	19.4117	1.09027	0.545133	+	0.838349i	$0.316479\pi$
$318$	0.787540	0.0441630
$319$	7.36952	0.412614
$320$	5.19984	0.290680
$321$	9.31635	0.519988
$322$	−1.23874	−0.0690324
$323$	−31.3495	−1.74433
$324$	17.0088	0.944933
$325$	46.2248	2.56409
$326$	4.16127	0.230471
$327$	5.46304	0.302107
$328$	5.40586	0.298488
$329$	−1.10455	−0.0608961
$330$	5.53672	0.304787
$331$	−11.5023	−0.632221	−0.316111	−	0.948722i	$-0.602377\pi$
$331$	−11.5023	−0.632221	−0.316111	+	0.948722i	$0.602377\pi$
$332$	−9.44677	−0.518459
$333$	3.77961	0.207122
$334$	−10.9886	−0.601270
$335$	49.1315	2.68434
$336$	0.582835	0.0317963
$337$	−6.61605	−0.360399	−0.180200	−	0.983630i	$-0.557674\pi$
$337$	−6.61605	−0.360399	−0.180200	+	0.983630i	$0.557674\pi$
$338$	6.13939	0.333939
$339$	13.1153	0.712324
$340$	38.4212	2.08368
$341$	−3.01166	−0.163091
$342$	4.23608	0.229061
$343$	−2.92778	−0.158085
$344$	−9.60202	−0.517706
$345$	−67.9138	−3.65636
$346$	−13.7020	−0.736622
$347$	−9.20316	−0.494052	−0.247026	−	0.969009i	$-0.579453\pi$
$347$	−9.20316	−0.494052	−0.247026	+	0.969009i	$0.579453\pi$
$348$	−23.1447	−1.24069
$349$	31.4785	1.68501	0.842503	−	0.538691i	$-0.181081\pi$
$349$	31.4785	1.68501	0.842503	+	0.538691i	$0.181081\pi$
$350$	1.43943	0.0769407
$351$	−16.6562	−0.889045
$352$	5.81466	0.309923
$353$	26.4125	1.40580	0.702899	−	0.711290i	$-0.251889\pi$
$353$	26.4125	1.40580	0.702899	+	0.711290i	$0.251889\pi$
$354$	−14.7895	−0.786055
$355$	−54.9126	−2.91446
$356$	−16.9358	−0.897595
$357$	−2.84468	−0.150556
$358$	−11.6693	−0.616742
$359$	12.3413	0.651348	0.325674	−	0.945482i	$-0.394409\pi$
$359$	12.3413	0.651348	0.325674	+	0.945482i	$0.394409\pi$
$360$	−12.0290	−0.633985
$361$	3.86036	0.203177
$362$	−3.67250	−0.193022
$363$	2.06808	0.108546
$364$	−1.48914	−0.0780521
$365$	−3.85866	−0.201971
$366$	−12.2590	−0.640786
$367$	−8.44319	−0.440731	−0.220365	−	0.975417i	$-0.570725\pi$
$367$	−8.44319	−0.440731	−0.220365	+	0.975417i	$0.570725\pi$
$368$	−11.4329	−0.595980
$369$	−2.82760	−0.147199
$370$	7.92427	0.411963
$371$	0.115142	0.00597787
$372$	9.45844	0.490397
$373$	−0.713674	−0.0369526	−0.0184763	−	0.999829i	$-0.505882\pi$
$373$	−0.713674	−0.0369526	−0.0184763	+	0.999829i	$0.505882\pi$
$374$	−4.54923	−0.235235
$375$	39.0163	2.01479
$376$	12.8538	0.662882
$377$	34.4470	1.77411
$378$	−0.518671	−0.0266775
$379$	34.3319	1.76351	0.881755	−	0.471708i	$-0.156362\pi$
$379$	34.3319	1.76351	0.881755	+	0.471708i	$0.156362\pi$
$380$	−28.0171	−1.43725
$381$	3.91146	0.200390
$382$	2.02408	0.103561
$383$	28.1545	1.43863	0.719314	−	0.694685i	$-0.244456\pi$
$383$	28.1545	1.43863	0.719314	+	0.694685i	$0.244456\pi$
$384$	−22.1168	−1.12864
$385$	0.809494	0.0412557
$386$	−0.656839	−0.0334322
$387$	5.02246	0.255306
$388$	16.0273	0.813665
$389$	26.1952	1.32815	0.664074	−	0.747667i	$-0.268826\pi$
$389$	26.1952	1.32815	0.664074	+	0.747667i	$0.268826\pi$
$390$	25.8800	1.31049
$391$	55.8012	2.82199
$392$	16.9816	0.857701
$393$	−33.9104	−1.71055
$394$	−7.26894	−0.366204
$395$	49.0508	2.46801
$396$	−1.93919	−0.0974478
$397$	18.5745	0.932229	0.466115	−	0.884724i	$-0.345653\pi$
$397$	18.5745	0.932229	0.466115	+	0.884724i	$0.345653\pi$
$398$	−9.07703	−0.454990
$399$	2.07437	0.103848
$400$	13.2851	0.664255
$401$	32.6633	1.63113	0.815564	−	0.578667i	$-0.196427\pi$
$401$	32.6633	1.63113	0.815564	+	0.578667i	$0.196427\pi$
$402$	18.2700	0.911227
$403$	−14.0773	−0.701239
$404$	2.06631	0.102803
$405$	−43.2179	−2.14752
$406$	1.07267	0.0532357
$407$	2.95988	0.146716
$408$	33.1037	1.63888
$409$	9.49820	0.469656	0.234828	−	0.972037i	$-0.424547\pi$
$409$	9.49820	0.469656	0.234828	+	0.972037i	$0.424547\pi$
$410$	−5.92830	−0.292778
$411$	16.0263	0.790519
$412$	28.5509	1.40660
$413$	−2.16230	−0.106400
$414$	−7.54011	−0.370576
$415$	24.0035	1.17828
$416$	27.1792	1.33257
$417$	−16.8644	−0.825855
$418$	3.31735	0.162257
$419$	10.8222	0.528698	0.264349	−	0.964427i	$-0.414843\pi$
$419$	10.8222	0.528698	0.264349	+	0.964427i	$0.414843\pi$
$420$	−2.54230	−0.124052
$421$	27.0246	1.31710	0.658548	−	0.752538i	$-0.271171\pi$
$421$	27.0246	1.31710	0.658548	+	0.752538i	$0.271171\pi$
$422$	10.3732	0.504961
$423$	−6.72332	−0.326899
$424$	−1.33991	−0.0650719
$425$	−64.8414	−3.14527
$426$	−20.4198	−0.989343
$427$	−1.79232	−0.0867363
$428$	−6.84108	−0.330676
$429$	9.66672	0.466714
$430$	10.5300	0.507801
$431$	25.0601	1.20710	0.603551	−	0.797325i	$-0.293752\pi$
$431$	25.0601	1.20710	0.603551	+	0.797325i	$0.293752\pi$
$432$	−4.78703	−0.230316
$433$	14.3250	0.688417	0.344209	−	0.938893i	$-0.388147\pi$
$433$	14.3250	0.688417	0.344209	+	0.938893i	$0.388147\pi$
$434$	−0.438362	−0.0210421
$435$	58.8088	2.81967
$436$	−4.01156	−0.192119
$437$	−40.6908	−1.94650
$438$	−1.43488	−0.0685613
$439$	−25.7749	−1.23017	−0.615084	−	0.788462i	$-0.710878\pi$
$439$	−25.7749	−1.23017	−0.615084	+	0.788462i	$0.710878\pi$
$440$	−9.42012	−0.449087
$441$	−8.88245	−0.422974
$442$	−21.2643	−1.01144
$443$	22.5763	1.07263	0.536316	−	0.844017i	$-0.319815\pi$
$443$	22.5763	1.07263	0.536316	+	0.844017i	$0.319815\pi$
$444$	−9.29579	−0.441159
$445$	43.0324	2.03993
$446$	8.09236	0.383184
$447$	23.2606	1.10019
$448$	0.282704	0.0133565
$449$	20.7029	0.977029	0.488514	−	0.872556i	$-0.337539\pi$
$449$	20.7029	0.977029	0.488514	+	0.872556i	$0.337539\pi$
$450$	8.76166	0.413029
$451$	−2.21434	−0.104269
$452$	−9.63066	−0.452988
$453$	−8.02881	−0.377226
$454$	11.4698	0.538305
$455$	3.78378	0.177386
$456$	−24.1395	−1.13044
$457$	−6.09160	−0.284953	−0.142476	−	0.989798i	$-0.545507\pi$
$457$	−6.09160	−0.284953	−0.142476	+	0.989798i	$0.545507\pi$
$458$	12.3971	0.579279
$459$	23.3644	1.09056
$460$	49.8697	2.32519
$461$	−37.4019	−1.74198	−0.870990	−	0.491300i	$-0.836522\pi$
$461$	−37.4019	−1.74198	−0.870990	+	0.491300i	$0.836522\pi$
$462$	0.301019	0.0140047
$463$	1.65007	0.0766852	0.0383426	−	0.999265i	$-0.487792\pi$
$463$	1.65007	0.0766852	0.0383426	+	0.999265i	$0.487792\pi$
$464$	9.90012	0.459602
$465$	−24.0331	−1.11451
$466$	10.2020	0.472597
$467$	−16.9000	−0.782037	−0.391019	−	0.920383i	$-0.627877\pi$
$467$	−16.9000	−0.782037	−0.391019	+	0.920383i	$0.627877\pi$
$468$	−9.06424	−0.418995
$469$	2.67117	0.123343
$470$	−14.0960	−0.650199
$471$	12.4191	0.572243
$472$	25.1628	1.15821
$473$	3.93317	0.180847
$474$	18.2400	0.837793
$475$	47.2830	2.16949
$476$	2.08887	0.0957434
$477$	0.700858	0.0320901
$478$	−1.25566	−0.0574327
$479$	−3.52242	−0.160943	−0.0804716	−	0.996757i	$-0.525643\pi$
$479$	−3.52242	−0.160943	−0.0804716	+	0.996757i	$0.525643\pi$
$480$	46.4011	2.11791
$481$	13.8352	0.630831
$482$	−9.99496	−0.455258
$483$	−3.69232	−0.168006
$484$	−1.51861	−0.0690277
$485$	−40.7242	−1.84919
$486$	−8.65392	−0.392550
$487$	−15.1857	−0.688130	−0.344065	−	0.938946i	$-0.611804\pi$
$487$	−15.1857	−0.688130	−0.344065	+	0.938946i	$0.611804\pi$
$488$	20.8573	0.944165
$489$	12.4035	0.560904
$490$	−18.6228	−0.841292
$491$	−33.2082	−1.49867	−0.749333	−	0.662194i	$-0.769626\pi$
$491$	−33.2082	−1.49867	−0.749333	+	0.662194i	$0.769626\pi$
$492$	6.95436	0.313527
$493$	−48.3201	−2.17623
$494$	15.5061	0.697653
$495$	4.92731	0.221466
$496$	−4.04583	−0.181663
$497$	−2.98547	−0.133917
$498$	8.92594	0.399981
$499$	−16.6501	−0.745359	−0.372679	−	0.927960i	$-0.621561\pi$
$499$	−16.6501	−0.745359	−0.372679	+	0.927960i	$0.621561\pi$
$500$	−28.6500	−1.28127
$501$	−32.7537	−1.46333
$502$	5.25664	0.234615
$503$	−19.5733	−0.872733	−0.436366	−	0.899769i	$-0.643735\pi$
$503$	−19.5733	−0.872733	−0.436366	+	0.899769i	$0.643735\pi$
$504$	−0.653990	−0.0291311
$505$	−5.25032	−0.233636
$506$	−5.90478	−0.262500
$507$	18.2997	0.812716
$508$	−2.87222	−0.127434
$509$	0.985980	0.0437028	0.0218514	−	0.999761i	$-0.493044\pi$
$509$	0.985980	0.0437028	0.0218514	+	0.999761i	$0.493044\pi$
$510$	−36.3029	−1.60752
$511$	−0.209786	−0.00928041
$512$	14.3706	0.635095
$513$	−17.0375	−0.752225
$514$	8.25411	0.364073
$515$	−72.5454	−3.19673
$516$	−12.3525	−0.543789
$517$	−5.26514	−0.231561
$518$	0.430824	0.0189293
$519$	−40.8414	−1.79274
$520$	−44.0320	−1.93093
$521$	−34.1004	−1.49396	−0.746982	−	0.664844i	$-0.768498\pi$
$521$	−34.1004	−1.49396	−0.746982	+	0.664844i	$0.768498\pi$
$522$	6.52923	0.285777
$523$	27.5300	1.20380	0.601902	−	0.798570i	$-0.294410\pi$
$523$	27.5300	1.20380	0.601902	+	0.798570i	$0.294410\pi$
$524$	24.9007	1.08779
$525$	4.29050	0.187253
$526$	−0.133908	−0.00583866
$527$	19.7467	0.860182
$528$	2.77823	0.120907
$529$	49.4284	2.14906
$530$	1.46941	0.0638269
$531$	−13.1617	−0.571169
$532$	−1.52323	−0.0660403
$533$	−10.3504	−0.448325
$534$	16.0021	0.692477
$535$	17.3826	0.751516
$536$	−31.0845	−1.34264
$537$	−34.7827	−1.50098
$538$	−17.3527	−0.748126
$539$	−6.95599	−0.299616
$540$	20.8808	0.898567
$541$	29.9810	1.28898	0.644492	−	0.764611i	$-0.277069\pi$
$541$	29.9810	1.28898	0.644492	+	0.764611i	$0.277069\pi$
$542$	21.6225	0.928767
$543$	−10.9466	−0.469763
$544$	−38.1253	−1.63461
$545$	10.1930	0.436622
$546$	1.40704	0.0602157
$547$	−2.27385	−0.0972227	−0.0486113	−	0.998818i	$-0.515480\pi$
$547$	−2.27385	−0.0972227	−0.0486113	+	0.998818i	$0.515480\pi$
$548$	−11.7682	−0.502715
$549$	−10.9097	−0.465613
$550$	6.86140	0.292571
$551$	35.2355	1.50108
$552$	42.9677	1.82883
$553$	2.66678	0.113403
$554$	15.1574	0.643977
$555$	23.6198	1.00261
$556$	12.3837	0.525186
$557$	19.7371	0.836289	0.418144	−	0.908381i	$-0.362681\pi$
$557$	19.7371	0.836289	0.418144	+	0.908381i	$0.362681\pi$
$558$	−2.66827	−0.112957
$559$	18.3846	0.777586
$560$	1.08746	0.0459538
$561$	−13.5599	−0.572499
$562$	−12.8275	−0.541094
$563$	38.2015	1.61000	0.805000	−	0.593274i	$-0.202165\pi$
$563$	38.2015	1.61000	0.805000	+	0.593274i	$0.202165\pi$
$564$	16.5357	0.696279
$565$	24.4707	1.02949
$566$	−14.6450	−0.615576
$567$	−2.34966	−0.0986765
$568$	34.7421	1.45774
$569$	42.3394	1.77496	0.887480	−	0.460846i	$-0.152454\pi$
$569$	42.3394	1.77496	0.887480	+	0.460846i	$0.152454\pi$
$570$	26.4725	1.10881
$571$	−31.3683	−1.31272	−0.656362	−	0.754446i	$-0.727906\pi$
$571$	−31.3683	−1.31272	−0.656362	+	0.754446i	$0.727906\pi$
$572$	−7.09836	−0.296797
$573$	6.03316	0.252039
$574$	−0.322308	−0.0134529
$575$	−84.1623	−3.50981
$576$	1.72079	0.0716995
$577$	−3.37361	−0.140445	−0.0702226	−	0.997531i	$-0.522371\pi$
$577$	−3.37361	−0.140445	−0.0702226	+	0.997531i	$0.522371\pi$
$578$	18.0332	0.750082
$579$	−1.95784	−0.0813650
$580$	−43.1839	−1.79311
$581$	1.30501	0.0541411
$582$	−15.1437	−0.627727
$583$	0.548853	0.0227312
$584$	2.44129	0.101021
$585$	23.0315	0.952235
$586$	14.2609	0.589114
$587$	−6.68301	−0.275837	−0.137919	−	0.990444i	$-0.544041\pi$
$587$	−6.68301	−0.275837	−0.137919	+	0.990444i	$0.544041\pi$
$588$	21.8460	0.900914
$589$	−14.3995	−0.593322
$590$	−27.5946	−1.13605
$591$	−21.6665	−0.891241
$592$	3.97626	0.163423
$593$	2.25998	0.0928061	0.0464031	−	0.998923i	$-0.485224\pi$
$593$	2.25998	0.0928061	0.0464031	+	0.998923i	$0.485224\pi$
$594$	−2.47237	−0.101443
$595$	−5.30766	−0.217593
$596$	−17.0804	−0.699642
$597$	−27.0559	−1.10732
$598$	−27.6004	−1.12867
$599$	−32.6957	−1.33591	−0.667956	−	0.744201i	$-0.732830\pi$
$599$	−32.6957	−1.33591	−0.667956	+	0.744201i	$0.732830\pi$
$600$	−49.9287	−2.03833
$601$	16.9253	0.690396	0.345198	−	0.938530i	$-0.387812\pi$
$601$	16.9253	0.690396	0.345198	+	0.938530i	$0.387812\pi$
$602$	0.572492	0.0233330
$603$	16.2591	0.662123
$604$	5.89563	0.239890
$605$	3.85866	0.156877
$606$	−1.95239	−0.0793103
$607$	−9.95911	−0.404228	−0.202114	−	0.979362i	$-0.564781\pi$
$607$	−9.95911	−0.404228	−0.202114	+	0.979362i	$0.564781\pi$
$608$	27.8014	1.12749
$609$	3.19730	0.129561
$610$	−22.8730	−0.926101
$611$	−24.6106	−0.995637
$612$	12.7148	0.513964
$613$	26.3564	1.06453	0.532263	−	0.846579i	$-0.321342\pi$
$613$	26.3564	1.06453	0.532263	+	0.846579i	$0.321342\pi$
$614$	15.6201	0.630376
$615$	−17.6705	−0.712541
$616$	−0.512151	−0.0206351
$617$	13.2562	0.533673	0.266837	−	0.963742i	$-0.414022\pi$
$617$	13.2562	0.533673	0.266837	+	0.963742i	$0.414022\pi$
$618$	−26.9768	−1.08517
$619$	−42.3767	−1.70326	−0.851632	−	0.524140i	$-0.824387\pi$
$619$	−42.3767	−1.70326	−0.851632	+	0.524140i	$0.824387\pi$
$620$	17.6477	0.708750
$621$	30.3263	1.21695
$622$	−2.26392	−0.0907750
$623$	2.33958	0.0937331
$624$	12.9862	0.519862
$625$	23.3510	0.934040
$626$	−9.35245	−0.373799
$627$	9.88800	0.394889
$628$	−9.11948	−0.363907
$629$	−19.4072	−0.773815
$630$	0.717194	0.0285737
$631$	32.5817	1.29706	0.648528	−	0.761191i	$-0.275385\pi$
$631$	32.5817	1.29706	0.648528	+	0.761191i	$0.275385\pi$
$632$	−31.0334	−1.23444
$633$	30.9195	1.22894
$634$	13.4683	0.534893
$635$	7.29808	0.289615
$636$	−1.72373	−0.0683503
$637$	−32.5140	−1.28825
$638$	5.11315	0.202432
$639$	−18.1723	−0.718884
$640$	−41.2658	−1.63118
$641$	−36.6074	−1.44590	−0.722952	−	0.690898i	$-0.757215\pi$
$641$	−36.6074	−1.44590	−0.722952	+	0.690898i	$0.757215\pi$
$642$	6.46390	0.255110
$643$	−1.78640	−0.0704489	−0.0352245	−	0.999379i	$-0.511215\pi$
$643$	−1.78640	−0.0704489	−0.0352245	+	0.999379i	$0.511215\pi$
$644$	2.71130	0.106840
$645$	31.3867	1.23585
$646$	−21.7510	−0.855783
$647$	−1.96729	−0.0773421	−0.0386711	−	0.999252i	$-0.512312\pi$
$647$	−1.96729	−0.0773421	−0.0386711	+	0.999252i	$0.512312\pi$
$648$	27.3431	1.07414
$649$	−10.3071	−0.404591
$650$	32.0719	1.25796
$651$	−1.30663	−0.0512107
$652$	−9.10798	−0.356696
$653$	3.72263	0.145678	0.0728388	−	0.997344i	$-0.476794\pi$
$653$	3.72263	0.145678	0.0728388	+	0.997344i	$0.476794\pi$
$654$	3.79039	0.148216
$655$	−63.2706	−2.47219
$656$	−2.97472	−0.116143
$657$	−1.27695	−0.0498186
$658$	−0.766366	−0.0298761
$659$	−13.9764	−0.544443	−0.272221	−	0.962235i	$-0.587758\pi$
$659$	−13.9764	−0.544443	−0.272221	+	0.962235i	$0.587758\pi$
$660$	−12.1185	−0.471712
$661$	−35.1142	−1.36578	−0.682891	−	0.730520i	$-0.739278\pi$
$661$	−35.1142	−1.36578	−0.682891	+	0.730520i	$0.739278\pi$
$662$	−7.98054	−0.310173
$663$	−63.3823	−2.46157
$664$	−15.1865	−0.589350
$665$	3.87040	0.150087
$666$	2.62239	0.101615
$667$	−62.7182	−2.42846
$668$	24.0514	0.930575
$669$	24.1209	0.932567
$670$	34.0886	1.31696
$671$	−8.54353	−0.329819
$672$	2.52272	0.0973161
$673$	−34.4646	−1.32851	−0.664257	−	0.747505i	$-0.731252\pi$
$673$	−34.4646	−1.32851	−0.664257	+	0.747505i	$0.731252\pi$
$674$	−4.59037	−0.176815
$675$	−35.2394	−1.35636
$676$	−13.4376	−0.516831
$677$	−19.2328	−0.739177	−0.369589	−	0.929195i	$-0.620501\pi$
$677$	−19.2328	−0.739177	−0.369589	+	0.929195i	$0.620501\pi$
$678$	9.09969	0.349472
$679$	−2.21408	−0.0849686
$680$	61.7654	2.36860
$681$	34.1880	1.31009
$682$	−2.08956	−0.0800136
$683$	−20.9325	−0.800962	−0.400481	−	0.916305i	$-0.631157\pi$
$683$	−20.9325	−0.800962	−0.400481	+	0.916305i	$0.631157\pi$
$684$	−9.27174	−0.354514
$685$	29.9021	1.14250
$686$	−2.03136	−0.0775578
$687$	36.9520	1.40981
$688$	5.28377	0.201442
$689$	2.56548	0.0977369
$690$	−47.1202	−1.79384
$691$	−4.14074	−0.157521	−0.0787606	−	0.996894i	$-0.525096\pi$
$691$	−4.14074	−0.157521	−0.0787606	+	0.996894i	$0.525096\pi$
$692$	29.9902	1.14006
$693$	0.267887	0.0101762
$694$	−6.38537	−0.242385
$695$	−31.4660	−1.19357
$696$	−37.2072	−1.41033
$697$	14.5189	0.549942
$698$	21.8405	0.826677
$699$	30.4090	1.15017
$700$	−3.15055	−0.119080
$701$	35.8340	1.35343	0.676716	−	0.736245i	$-0.263403\pi$
$701$	35.8340	1.35343	0.676716	+	0.736245i	$0.263403\pi$
$702$	−11.5565	−0.436172
$703$	14.1519	0.533750
$704$	1.34758	0.0507887
$705$	−42.0159	−1.58241
$706$	18.3256	0.689695
$707$	−0.285448	−0.0107354
$708$	32.3706	1.21656
$709$	−31.0931	−1.16773	−0.583863	−	0.811852i	$-0.698459\pi$
$709$	−31.0931	−1.16773	−0.583863	+	0.811852i	$0.698459\pi$
$710$	−38.0997	−1.42985
$711$	16.2324	0.608764
$712$	−27.2257	−1.02033
$713$	25.6307	0.959878
$714$	−1.97371	−0.0738641
$715$	18.0363	0.674521
$716$	25.5412	0.954520
$717$	−3.74275	−0.139776
$718$	8.56268	0.319556
$719$	7.55307	0.281682	0.140841	−	0.990032i	$-0.455019\pi$
$719$	7.55307	0.281682	0.140841	+	0.990032i	$0.455019\pi$
$720$	6.61929	0.246686
$721$	−3.94413	−0.146887
$722$	2.67841	0.0996800
$723$	−29.7919	−1.10797
$724$	8.03818	0.298737
$725$	72.8790	2.70666
$726$	1.43488	0.0532535
$727$	12.1680	0.451287	0.225644	−	0.974210i	$-0.427551\pi$
$727$	12.1680	0.451287	0.225644	+	0.974210i	$0.427551\pi$
$728$	−2.39392	−0.0887246
$729$	7.80605	0.289113
$730$	−2.67723	−0.0990887
$731$	−25.7888	−0.953834
$732$	26.8318	0.991733
$733$	33.1751	1.22535	0.612675	−	0.790335i	$-0.290094\pi$
$733$	33.1751	1.22535	0.612675	+	0.790335i	$0.290094\pi$
$734$	−5.85809	−0.216226
$735$	−55.5089	−2.04748
$736$	−49.4856	−1.82406
$737$	12.7328	0.469018
$738$	−1.96186	−0.0722169
$739$	10.4640	0.384925	0.192463	−	0.981304i	$-0.438353\pi$
$739$	10.4640	0.384925	0.192463	+	0.981304i	$0.438353\pi$
$740$	−17.3443	−0.637588
$741$	46.2190	1.69790
$742$	0.0798882	0.00293279
$743$	27.6703	1.01513	0.507563	−	0.861615i	$-0.330547\pi$
$743$	27.6703	1.01513	0.507563	+	0.861615i	$0.330547\pi$
$744$	15.2053	0.557452
$745$	43.4000	1.59005
$746$	−0.495164	−0.0181292
$747$	7.94349	0.290637
$748$	9.95714	0.364069
$749$	0.945053	0.0345315
$750$	27.0704	0.988472
$751$	−0.693349	−0.0253007	−0.0126503	−	0.999920i	$-0.504027\pi$
$751$	−0.693349	−0.0253007	−0.0126503	+	0.999920i	$0.504027\pi$
$752$	−7.07312	−0.257930
$753$	15.6685	0.570990
$754$	23.9001	0.870392
$755$	−14.9803	−0.545189
$756$	1.13524	0.0412883
$757$	−19.2843	−0.700900	−0.350450	−	0.936581i	$-0.613971\pi$
$757$	−19.2843	−0.700900	−0.350450	+	0.936581i	$0.613971\pi$
$758$	23.8203	0.865191
$759$	−17.6004	−0.638853
$760$	−45.0400	−1.63377
$761$	12.5794	0.456002	0.228001	−	0.973661i	$-0.426781\pi$
$761$	12.5794	0.456002	0.228001	+	0.973661i	$0.426781\pi$
$762$	2.71387	0.0983130
$763$	0.554172	0.0200624
$764$	−4.43020	−0.160279
$765$	−32.3072	−1.16807
$766$	19.5343	0.705802
$767$	−48.1782	−1.73961
$768$	−20.9189	−0.754847
$769$	−14.0807	−0.507764	−0.253882	−	0.967235i	$-0.581707\pi$
$769$	−14.0807	−0.507764	−0.253882	+	0.967235i	$0.581707\pi$
$770$	0.561647	0.0202403
$771$	24.6030	0.886055
$772$	1.43766	0.0517424
$773$	−24.4794	−0.880464	−0.440232	−	0.897884i	$-0.645104\pi$
$773$	−24.4794	−0.880464	−0.440232	+	0.897884i	$0.645104\pi$
$774$	3.48470	0.125255
$775$	−29.7831	−1.06984
$776$	25.7653	0.924922
$777$	1.28416	0.0460689
$778$	18.1748	0.651600
$779$	−10.5873	−0.379330
$780$	−56.6450	−2.02822
$781$	−14.2310	−0.509225
$782$	38.7162	1.38449
$783$	−26.2606	−0.938476
$784$	−9.34459	−0.333735
$785$	23.1718	0.827039
$786$	−23.5278	−0.839211
$787$	−17.0656	−0.608323	−0.304162	−	0.952620i	$-0.598376\pi$
$787$	−17.0656	−0.608323	−0.304162	+	0.952620i	$0.598376\pi$
$788$	15.9099	0.566767
$789$	−0.399139	−0.0142097
$790$	34.0326	1.21083
$791$	1.33042	0.0473042
$792$	−3.11741	−0.110772
$793$	−39.9346	−1.41812
$794$	12.8875	0.457359
$795$	4.37985	0.155337
$796$	19.8674	0.704180
$797$	−48.2553	−1.70929	−0.854645	−	0.519214i	$-0.826225\pi$
$797$	−48.2553	−1.70929	−0.854645	+	0.519214i	$0.826225\pi$
$798$	1.43925	0.0509488
$799$	34.5222	1.22131
$800$	57.5027	2.03303
$801$	14.2408	0.503173
$802$	22.6626	0.800244
$803$	−1.00000	−0.0352892
$804$	−39.9886	−1.41029
$805$	−6.88919	−0.242812
$806$	−9.76715	−0.344033
$807$	−51.7230	−1.82074
$808$	3.32177	0.116859
$809$	−16.3890	−0.576206	−0.288103	−	0.957599i	$-0.593024\pi$
$809$	−16.3890	−0.576206	−0.288103	+	0.957599i	$0.593024\pi$
$810$	−29.9856	−1.05359
$811$	−45.4994	−1.59770	−0.798849	−	0.601531i	$-0.794558\pi$
$811$	−45.4994	−1.59770	−0.798849	+	0.601531i	$0.794558\pi$
$812$	−2.34781	−0.0823919
$813$	64.4502	2.26037
$814$	2.05363	0.0719798
$815$	23.1426	0.810651
$816$	−18.2162	−0.637694
$817$	18.8055	0.657920
$818$	6.59008	0.230417
$819$	1.25217	0.0437544
$820$	12.9756	0.453126
$821$	21.8529	0.762673	0.381336	−	0.924436i	$-0.375464\pi$
$821$	21.8529	0.762673	0.381336	+	0.924436i	$0.375464\pi$
$822$	11.1194	0.387834
$823$	39.7351	1.38508	0.692539	−	0.721380i	$-0.256492\pi$
$823$	39.7351	1.38508	0.692539	+	0.721380i	$0.256492\pi$
$824$	45.8980	1.59893
$825$	20.4517	0.712038
$826$	−1.50026	−0.0522005
$827$	−50.8707	−1.76895	−0.884474	−	0.466590i	$-0.845482\pi$
$827$	−50.8707	−1.76895	−0.884474	+	0.466590i	$0.845482\pi$
$828$	16.5034	0.573534
$829$	−3.61200	−0.125450	−0.0627251	−	0.998031i	$-0.519979\pi$
$829$	−3.61200	−0.125450	−0.0627251	+	0.998031i	$0.519979\pi$
$830$	16.6542	0.578075
$831$	45.1797	1.56726
$832$	6.29892	0.218376
$833$	45.6087	1.58025
$834$	−11.7010	−0.405171
$835$	−61.1125	−2.11489
$836$	−7.26085	−0.251122
$837$	10.7318	0.370944
$838$	7.50869	0.259384
$839$	50.5868	1.74645	0.873226	−	0.487316i	$-0.162024\pi$
$839$	50.5868	1.74645	0.873226	+	0.487316i	$0.162024\pi$
$840$	−4.08697	−0.141014
$841$	25.3098	0.872752
$842$	18.7503	0.646178
$843$	−38.2348	−1.31688
$844$	−22.7044	−0.781519
$845$	34.1438	1.17458
$846$	−4.66480	−0.160379
$847$	0.209786	0.00720835
$848$	0.737323	0.0253198
$849$	−43.6523	−1.49814
$850$	−44.9885	−1.54309
$851$	−25.1900	−0.863502
$852$	44.6939	1.53119
$853$	−6.30024	−0.215716	−0.107858	−	0.994166i	$-0.534399\pi$
$853$	−6.30024	−0.215716	−0.107858	+	0.994166i	$0.534399\pi$
$854$	−1.24355	−0.0425535
$855$	23.5587	0.805691
$856$	−10.9976	−0.375891
$857$	11.0127	0.376187	0.188093	−	0.982151i	$-0.439769\pi$
$857$	11.0127	0.376187	0.188093	+	0.982151i	$0.439769\pi$
$858$	6.70700	0.228973
$859$	18.5007	0.631236	0.315618	−	0.948886i	$-0.397788\pi$
$859$	18.5007	0.631236	0.315618	+	0.948886i	$0.397788\pi$
$860$	−23.0475	−0.785914
$861$	−0.960702	−0.0327406
$862$	17.3873	0.592213
$863$	−35.7389	−1.21657	−0.608283	−	0.793720i	$-0.708141\pi$
$863$	−35.7389	−1.21657	−0.608283	+	0.793720i	$0.708141\pi$
$864$	−20.7200	−0.704909
$865$	−76.2026	−2.59097
$866$	9.93905	0.337743
$867$	53.7515	1.82550
$868$	0.959466	0.0325664
$869$	12.7119	0.431221
$870$	40.8030	1.38335
$871$	59.5162	2.01663
$872$	−6.44893	−0.218388
$873$	−13.4769	−0.456123
$874$	−28.2322	−0.954970
$875$	3.95782	0.133799
$876$	3.14060	0.106111
$877$	46.3754	1.56599	0.782993	−	0.622031i	$-0.213692\pi$
$877$	46.3754	1.56599	0.782993	+	0.622031i	$0.213692\pi$
$878$	−17.8832	−0.603529
$879$	42.5075	1.43374
$880$	5.18368	0.174742
$881$	−25.7913	−0.868933	−0.434466	−	0.900688i	$-0.643063\pi$
$881$	−25.7913	−0.868933	−0.434466	+	0.900688i	$0.643063\pi$
$882$	−6.16286	−0.207514
$883$	−12.0949	−0.407027	−0.203514	−	0.979072i	$-0.565236\pi$
$883$	−12.0949	−0.407027	−0.203514	+	0.979072i	$0.565236\pi$
$884$	46.5422	1.56538
$885$	−82.2511	−2.76484
$886$	15.6640	0.526242
$887$	−10.5746	−0.355059	−0.177530	−	0.984115i	$-0.556811\pi$
$887$	−10.5746	−0.355059	−0.177530	+	0.984115i	$0.556811\pi$
$888$	−14.9438	−0.501481
$889$	0.396780	0.0133076
$890$	29.8569	1.00081
$891$	−11.2002	−0.375222
$892$	−17.7122	−0.593047
$893$	−25.1739	−0.842414
$894$	16.1387	0.539760
$895$	−64.8982	−2.16931
$896$	−2.24353	−0.0749510
$897$	−82.2685	−2.74687
$898$	14.3641	0.479338
$899$	−22.1945	−0.740229
$900$	−19.1771	−0.639237
$901$	−3.59869	−0.119890
$902$	−1.53636	−0.0511552
$903$	1.70642	0.0567862
$904$	−15.4821	−0.514928
$905$	−20.4244	−0.678929
$906$	−5.57058	−0.185070
$907$	28.6796	0.952289	0.476145	−	0.879367i	$-0.342034\pi$
$907$	28.6796	0.952289	0.476145	+	0.879367i	$0.342034\pi$
$908$	−25.1046	−0.833125
$909$	−1.73749	−0.0576290
$910$	2.62528	0.0870271
$911$	−5.48913	−0.181863	−0.0909314	−	0.995857i	$-0.528984\pi$
$911$	−5.48913	−0.181863	−0.0909314	+	0.995857i	$0.528984\pi$
$912$	13.2834	0.439858
$913$	6.22067	0.205874
$914$	−4.22649	−0.139800
$915$	−68.1775	−2.25388
$916$	−27.1342	−0.896539
$917$	−3.43988	−0.113595
$918$	16.2108	0.535035
$919$	53.5809	1.76747	0.883735	−	0.467987i	$-0.155021\pi$
$919$	53.5809	1.76747	0.883735	+	0.467987i	$0.155021\pi$
$920$	80.1699	2.64312
$921$	46.5588	1.53416
$922$	−25.9503	−0.854629
$923$	−66.5193	−2.18951
$924$	−0.658856	−0.0216748
$925$	29.2710	0.962423
$926$	1.14486	0.0376223
$927$	−24.0075	−0.788511
$928$	42.8513	1.40666
$929$	23.0466	0.756133	0.378066	−	0.925778i	$-0.376589\pi$
$929$	23.0466	0.756133	0.378066	+	0.925778i	$0.376589\pi$
$930$	−16.6747	−0.546787
$931$	−33.2583	−1.09000
$932$	−22.3296	−0.731430
$933$	−6.74807	−0.220922
$934$	−11.7256	−0.383673
$935$	−25.3003	−0.827408
$936$	−14.5716	−0.476286
$937$	28.9897	0.947053	0.473526	−	0.880780i	$-0.342981\pi$
$937$	28.9897	0.947053	0.473526	+	0.880780i	$0.342981\pi$
$938$	1.85332	0.0605130
$939$	−27.8768	−0.909726
$940$	30.8526	1.00630
$941$	3.10832	0.101328	0.0506641	−	0.998716i	$-0.483866\pi$
$941$	3.10832	0.101328	0.0506641	+	0.998716i	$0.483866\pi$
$942$	8.61669	0.280747
$943$	18.8451	0.613681
$944$	−13.8465	−0.450665
$945$	−2.88456	−0.0938346
$946$	2.72893	0.0887250
$947$	−12.7381	−0.413934	−0.206967	−	0.978348i	$-0.566359\pi$
$947$	−12.7381	−0.413934	−0.206967	+	0.978348i	$0.566359\pi$
$948$	−39.9229	−1.29664
$949$	−4.67425	−0.151733
$950$	32.8061	1.06437
$951$	40.1448	1.30179
$952$	3.35805	0.108835
$953$	23.5700	0.763506	0.381753	−	0.924264i	$-0.375320\pi$
$953$	23.5700	0.763506	0.381753	+	0.924264i	$0.375320\pi$
$954$	0.486272	0.0157436
$955$	11.2568	0.364261
$956$	2.74834	0.0888876
$957$	15.2407	0.492663
$958$	−2.44394	−0.0789600
$959$	1.62571	0.0524970
$960$	10.7537	0.347074
$961$	−21.9299	−0.707415
$962$	9.59920	0.309491
$963$	5.75244	0.185370
$964$	21.8765	0.704594
$965$	−3.65297	−0.117593
$966$	−2.56182	−0.0824251
$967$	10.0378	0.322794	0.161397	−	0.986890i	$-0.448400\pi$
$967$	10.0378	0.322794	0.161397	+	0.986890i	$0.448400\pi$
$968$	−2.44129	−0.0784662
$969$	−64.8332	−2.08274
$970$	−28.2554	−0.907226
$971$	−47.5603	−1.52628	−0.763141	−	0.646233i	$-0.776344\pi$
$971$	−47.5603	−1.52628	−0.763141	+	0.646233i	$0.776344\pi$
$972$	18.9413	0.607542
$973$	−1.71073	−0.0548436
$974$	−10.5362	−0.337602
$975$	95.5966	3.06154
$976$	−11.4773	−0.367379
$977$	2.50696	0.0802047	0.0401024	−	0.999196i	$-0.487232\pi$
$977$	2.50696	0.0802047	0.0401024	+	0.999196i	$0.487232\pi$
$978$	8.60582	0.275184
$979$	11.1522	0.356425
$980$	40.7607	1.30205
$981$	3.37319	0.107698
$982$	−23.0406	−0.735257
$983$	−57.3915	−1.83051	−0.915253	−	0.402880i	$-0.868009\pi$
$983$	−57.3915	−1.83051	−0.915253	+	0.402880i	$0.868009\pi$
$984$	11.1797	0.356397
$985$	−40.4258	−1.28807
$986$	−33.5257	−1.06767
$987$	−2.28431	−0.0727103
$988$	−33.9390	−1.07974
$989$	−33.4732	−1.06438
$990$	3.41869	0.108653
$991$	−51.5558	−1.63773	−0.818863	−	0.573989i	$-0.805395\pi$
$991$	−51.5558	−1.63773	−0.818863	+	0.573989i	$0.805395\pi$
$992$	−17.5118	−0.556001
$993$	−23.7876	−0.754876
$994$	−2.07139	−0.0657005
$995$	−50.4813	−1.60037
$996$	−19.5367	−0.619043
$997$	8.90577	0.282048	0.141024	−	0.990006i	$-0.454960\pi$
$997$	8.90577	0.282048	0.141024	+	0.990006i	$0.454960\pi$
$998$	−11.5522	−0.365679
$999$	−10.5472	−0.333700

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	803.2.a.f.1.11	✓	19
3.2	odd	2		7227.2.a.ba.1.9		19
11.10	odd	2		8833.2.a.k.1.9		19

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
803.2.a.f.1.11	✓	19	1.1	even	1	trivial
7227.2.a.ba.1.9		19	3.2	odd	2
8833.2.a.k.1.9		19	11.10	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:	\( N \)	\(=\)	\( 803 = 11 \cdot 73 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	803.a (trivial)

\(f(q)\)	\(=\)	\(q+0.693824 q^{2} +2.06808 q^{3} -1.51861 q^{4} +3.85866 q^{5} +1.43488 q^{6} +0.209786 q^{7} -2.44129 q^{8} +1.27695 q^{9} +O(q^{10})\)	\(q+0.693824 q^{2} +2.06808 q^{3} -1.51861 q^{4} +3.85866 q^{5} +1.43488 q^{6} +0.209786 q^{7} -2.44129 q^{8} +1.27695 q^{9} +2.67723 q^{10} +1.00000 q^{11} -3.14060 q^{12} +4.67425 q^{13} +0.145555 q^{14} +7.98001 q^{15} +1.34339 q^{16} -6.55675 q^{17} +0.885978 q^{18} +4.78125 q^{19} -5.85979 q^{20} +0.433855 q^{21} +0.693824 q^{22} -8.51049 q^{23} -5.04879 q^{24} +9.88925 q^{25} +3.24311 q^{26} -3.56340 q^{27} -0.318583 q^{28} +7.36952 q^{29} +5.53672 q^{30} -3.01166 q^{31} +5.81466 q^{32} +2.06808 q^{33} -4.54923 q^{34} +0.809494 q^{35} -1.93919 q^{36} +2.95988 q^{37} +3.31735 q^{38} +9.66672 q^{39} -9.42012 q^{40} -2.21434 q^{41} +0.301019 q^{42} +3.93317 q^{43} -1.51861 q^{44} +4.92731 q^{45} -5.90478 q^{46} -5.26514 q^{47} +2.77823 q^{48} -6.95599 q^{49} +6.86140 q^{50} -13.5599 q^{51} -7.09836 q^{52} +0.548853 q^{53} -2.47237 q^{54} +3.85866 q^{55} -0.512151 q^{56} +9.88800 q^{57} +5.11315 q^{58} -10.3071 q^{59} -12.1185 q^{60} -8.54353 q^{61} -2.08956 q^{62} +0.267887 q^{63} +1.34758 q^{64} +18.0363 q^{65} +1.43488 q^{66} +12.7328 q^{67} +9.95714 q^{68} -17.6004 q^{69} +0.561647 q^{70} -14.2310 q^{71} -3.11741 q^{72} -1.00000 q^{73} +2.05363 q^{74} +20.4517 q^{75} -7.26085 q^{76} +0.209786 q^{77} +6.70700 q^{78} +12.7119 q^{79} +5.18368 q^{80} -11.2002 q^{81} -1.53636 q^{82} +6.22067 q^{83} -0.658856 q^{84} -25.3003 q^{85} +2.72893 q^{86} +15.2407 q^{87} -2.44129 q^{88} +11.1522 q^{89} +3.41869 q^{90} +0.980595 q^{91} +12.9241 q^{92} -6.22836 q^{93} -3.65308 q^{94} +18.4492 q^{95} +12.0252 q^{96} -10.5540 q^{97} -4.82623 q^{98} +1.27695 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 19 q + 7 q^{2} + 3 q^{3} + 23 q^{4} + 2 q^{5} + 16 q^{7} + 18 q^{8} + 22 q^{9}+O(q^{10}) \) 19 * q + 7 * q^2 + 3 * q^3 + 23 * q^4 + 2 * q^5 + 16 * q^7 + 18 * q^8 + 22 * q^9	\( 19 q + 7 q^{2} + 3 q^{3} + 23 q^{4} + 2 q^{5} + 16 q^{7} + 18 q^{8} + 22 q^{9} + 8 q^{10} + 19 q^{11} - 5 q^{12} + 30 q^{13} - 9 q^{14} - 11 q^{15} + 31 q^{16} + 9 q^{17} + 3 q^{18} - q^{19} - 9 q^{20} + 13 q^{21} + 7 q^{22} - 2 q^{23} - 19 q^{24} + 39 q^{25} - 3 q^{26} - 9 q^{27} + 49 q^{28} + 18 q^{29} - 17 q^{30} + 5 q^{31} + 38 q^{32} + 3 q^{33} + 26 q^{34} - 14 q^{35} + 19 q^{36} + 36 q^{37} + 9 q^{38} + 27 q^{39} + 7 q^{40} + 9 q^{41} + 25 q^{42} + 33 q^{43} + 23 q^{44} + 8 q^{45} - 47 q^{46} - 28 q^{47} - 49 q^{48} + 33 q^{49} + 27 q^{50} + 2 q^{51} + 18 q^{52} + 27 q^{53} + 7 q^{54} + 2 q^{55} - 28 q^{56} - 6 q^{57} + 16 q^{58} - 28 q^{59} + 4 q^{61} + 5 q^{62} + 26 q^{63} + 80 q^{64} + 12 q^{65} + 21 q^{67} - 23 q^{68} - 34 q^{69} - 74 q^{70} - 7 q^{71} + 54 q^{72} - 19 q^{73} + 4 q^{74} - 25 q^{75} - 23 q^{76} + 16 q^{77} - 28 q^{78} + 25 q^{79} - 49 q^{80} - 9 q^{81} - 10 q^{82} + 15 q^{83} + 37 q^{84} + 23 q^{85} - 29 q^{86} + q^{87} + 18 q^{88} - 21 q^{89} - 94 q^{90} + 4 q^{91} - 74 q^{92} + 22 q^{93} + 69 q^{94} + 23 q^{95} - 116 q^{96} + 18 q^{97} - 4 q^{98} + 22 q^{99}+O(q^{100}) \) 19 * q + 7 * q^2 + 3 * q^3 + 23 * q^4 + 2 * q^5 + 16 * q^7 + 18 * q^8 + 22 * q^9 + 8 * q^10 + 19 * q^11 - 5 * q^12 + 30 * q^13 - 9 * q^14 - 11 * q^15 + 31 * q^16 + 9 * q^17 + 3 * q^18 - q^19 - 9 * q^20 + 13 * q^21 + 7 * q^22 - 2 * q^23 - 19 * q^24 + 39 * q^25 - 3 * q^26 - 9 * q^27 + 49 * q^28 + 18 * q^29 - 17 * q^30 + 5 * q^31 + 38 * q^32 + 3 * q^33 + 26 * q^34 - 14 * q^35 + 19 * q^36 + 36 * q^37 + 9 * q^38 + 27 * q^39 + 7 * q^40 + 9 * q^41 + 25 * q^42 + 33 * q^43 + 23 * q^44 + 8 * q^45 - 47 * q^46 - 28 * q^47 - 49 * q^48 + 33 * q^49 + 27 * q^50 + 2 * q^51 + 18 * q^52 + 27 * q^53 + 7 * q^54 + 2 * q^55 - 28 * q^56 - 6 * q^57 + 16 * q^58 - 28 * q^59 + 4 * q^61 + 5 * q^62 + 26 * q^63 + 80 * q^64 + 12 * q^65 + 21 * q^67 - 23 * q^68 - 34 * q^69 - 74 * q^70 - 7 * q^71 + 54 * q^72 - 19 * q^73 + 4 * q^74 - 25 * q^75 - 23 * q^76 + 16 * q^77 - 28 * q^78 + 25 * q^79 - 49 * q^80 - 9 * q^81 - 10 * q^82 + 15 * q^83 + 37 * q^84 + 23 * q^85 - 29 * q^86 + q^87 + 18 * q^88 - 21 * q^89 - 94 * q^90 + 4 * q^91 - 74 * q^92 + 22 * q^93 + 69 * q^94 + 23 * q^95 - 116 * q^96 + 18 * q^97 - 4 * q^98 + 22 * q^99

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