LMFDB - Embedded newform 8039.2.a.b.1.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8039,2,Mod(1,8039)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8039, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("8039.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8039 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8039.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:	$64.1917381849$
Analytic rank:	$0$
Dimension:	$391$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
Character	$\chi$	$=$	8039.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.70592 q^{2} +0.720832 q^{3} +5.32200 q^{4} +1.39019 q^{5} -1.95051 q^{6} -3.88734 q^{7} -8.98906 q^{8} -2.48040 q^{9} +O(q^{10})$	\(q-2.70592 q^{2} +0.720832 q^{3} +5.32200 q^{4} +1.39019 q^{5} -1.95051 q^{6} -3.88734 q^{7} -8.98906 q^{8} -2.48040 q^{9} -3.76173 q^{10} +5.55747 q^{11} +3.83627 q^{12} -4.83835 q^{13} +10.5188 q^{14} +1.00209 q^{15} +13.6797 q^{16} -5.62753 q^{17} +6.71177 q^{18} +7.71569 q^{19} +7.39857 q^{20} -2.80212 q^{21} -15.0381 q^{22} -1.10870 q^{23} -6.47961 q^{24} -3.06738 q^{25} +13.0922 q^{26} -3.95045 q^{27} -20.6884 q^{28} +8.15697 q^{29} -2.71158 q^{30} -9.12174 q^{31} -19.0380 q^{32} +4.00600 q^{33} +15.2276 q^{34} -5.40413 q^{35} -13.2007 q^{36} -4.42259 q^{37} -20.8780 q^{38} -3.48764 q^{39} -12.4965 q^{40} +5.93854 q^{41} +7.58231 q^{42} +0.0465999 q^{43} +29.5768 q^{44} -3.44822 q^{45} +3.00006 q^{46} +5.10093 q^{47} +9.86076 q^{48} +8.11142 q^{49} +8.30009 q^{50} -4.05650 q^{51} -25.7497 q^{52} +4.46812 q^{53} +10.6896 q^{54} +7.72592 q^{55} +34.9436 q^{56} +5.56172 q^{57} -22.0721 q^{58} -4.42988 q^{59} +5.33313 q^{60} -3.96578 q^{61} +24.6827 q^{62} +9.64216 q^{63} +24.1559 q^{64} -6.72621 q^{65} -10.8399 q^{66} +1.26306 q^{67} -29.9497 q^{68} -0.799189 q^{69} +14.6231 q^{70} -1.01385 q^{71} +22.2965 q^{72} +16.1255 q^{73} +11.9672 q^{74} -2.21107 q^{75} +41.0629 q^{76} -21.6038 q^{77} +9.43727 q^{78} -11.2849 q^{79} +19.0173 q^{80} +4.59359 q^{81} -16.0692 q^{82} +4.33432 q^{83} -14.9129 q^{84} -7.82331 q^{85} -0.126095 q^{86} +5.87981 q^{87} -49.9564 q^{88} -17.0410 q^{89} +9.33061 q^{90} +18.8083 q^{91} -5.90052 q^{92} -6.57524 q^{93} -13.8027 q^{94} +10.7263 q^{95} -13.7232 q^{96} -5.59497 q^{97} -21.9489 q^{98} -13.7847 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 391 q + 14 q^{2} + 12 q^{3} + 446 q^{4} + 22 q^{5} + 40 q^{6} + 63 q^{7} + 36 q^{8} + 501 q^{9}+O(q^{10}) $ 391 * q + 14 * q^2 + 12 * q^3 + 446 * q^4 + 22 * q^5 + 40 * q^6 + 63 * q^7 + 36 * q^8 + 501 * q^9	\( 391 q + 14 q^{2} + 12 q^{3} + 446 q^{4} + 22 q^{5} + 40 q^{6} + 63 q^{7} + 36 q^{8} + 501 q^{9} + 40 q^{10} + 57 q^{11} + 20 q^{12} + 83 q^{13} + 21 q^{14} + 60 q^{15} + 548 q^{16} + 59 q^{17} + 54 q^{18} + 131 q^{19} + 35 q^{20} + 121 q^{21} + 89 q^{22} + 34 q^{23} + 110 q^{24} + 609 q^{25} + 54 q^{26} + 27 q^{27} + 182 q^{28} + 102 q^{29} + 92 q^{30} + 88 q^{31} + 76 q^{32} + 131 q^{33} + 128 q^{34} + 31 q^{35} + 654 q^{36} + 135 q^{37} + 23 q^{38} + 96 q^{39} + 113 q^{40} + 128 q^{41} + 45 q^{42} + 140 q^{43} + 151 q^{44} + 77 q^{45} + 245 q^{46} + 22 q^{47} + 25 q^{48} + 712 q^{49} + 53 q^{50} + 102 q^{51} + 174 q^{52} + 54 q^{53} + 131 q^{54} + 101 q^{55} + 43 q^{56} + 226 q^{57} + 109 q^{58} + 40 q^{59} + 123 q^{60} + 249 q^{61} + 28 q^{62} + 139 q^{63} + 730 q^{64} + 227 q^{65} + 55 q^{66} + 169 q^{67} + 48 q^{68} + 89 q^{69} + 98 q^{70} + 66 q^{71} + 120 q^{72} + 324 q^{73} + 60 q^{74} + 19 q^{75} + 356 q^{76} + 83 q^{77} - 11 q^{78} + 195 q^{79} + 26 q^{80} + 807 q^{81} + 49 q^{82} + 74 q^{83} + 252 q^{84} + 373 q^{85} + 100 q^{86} + 43 q^{87} + 211 q^{88} + 207 q^{89} + 10 q^{90} + 189 q^{91} + 30 q^{92} + 172 q^{93} + 130 q^{94} + 43 q^{95} + 203 q^{96} + 254 q^{97} + 26 q^{98} + 273 q^{99}+O(q^{100}) \) 391 * q + 14 * q^2 + 12 * q^3 + 446 * q^4 + 22 * q^5 + 40 * q^6 + 63 * q^7 + 36 * q^8 + 501 * q^9 + 40 * q^10 + 57 * q^11 + 20 * q^12 + 83 * q^13 + 21 * q^14 + 60 * q^15 + 548 * q^16 + 59 * q^17 + 54 * q^18 + 131 * q^19 + 35 * q^20 + 121 * q^21 + 89 * q^22 + 34 * q^23 + 110 * q^24 + 609 * q^25 + 54 * q^26 + 27 * q^27 + 182 * q^28 + 102 * q^29 + 92 * q^30 + 88 * q^31 + 76 * q^32 + 131 * q^33 + 128 * q^34 + 31 * q^35 + 654 * q^36 + 135 * q^37 + 23 * q^38 + 96 * q^39 + 113 * q^40 + 128 * q^41 + 45 * q^42 + 140 * q^43 + 151 * q^44 + 77 * q^45 + 245 * q^46 + 22 * q^47 + 25 * q^48 + 712 * q^49 + 53 * q^50 + 102 * q^51 + 174 * q^52 + 54 * q^53 + 131 * q^54 + 101 * q^55 + 43 * q^56 + 226 * q^57 + 109 * q^58 + 40 * q^59 + 123 * q^60 + 249 * q^61 + 28 * q^62 + 139 * q^63 + 730 * q^64 + 227 * q^65 + 55 * q^66 + 169 * q^67 + 48 * q^68 + 89 * q^69 + 98 * q^70 + 66 * q^71 + 120 * q^72 + 324 * q^73 + 60 * q^74 + 19 * q^75 + 356 * q^76 + 83 * q^77 - 11 * q^78 + 195 * q^79 + 26 * q^80 + 807 * q^81 + 49 * q^82 + 74 * q^83 + 252 * q^84 + 373 * q^85 + 100 * q^86 + 43 * q^87 + 211 * q^88 + 207 * q^89 + 10 * q^90 + 189 * q^91 + 30 * q^92 + 172 * q^93 + 130 * q^94 + 43 * q^95 + 203 * q^96 + 254 * q^97 + 26 * q^98 + 273 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.70592	−1.91337	−0.956687	−	0.291119i	$-0.905973\pi$
$2$	−2.70592	−1.91337	−0.956687	+	0.291119i	$0.905973\pi$
$3$	0.720832	0.416173	0.208086	−	0.978110i	$-0.433277\pi$
$3$	0.720832	0.416173	0.208086	+	0.978110i	$0.433277\pi$
$4$	5.32200	2.66100
$5$	1.39019	0.621710	0.310855	−	0.950457i	$-0.399385\pi$
$5$	1.39019	0.621710	0.310855	+	0.950457i	$0.399385\pi$
$6$	−1.95051	−0.796294
$7$	−3.88734	−1.46928	−0.734638	−	0.678459i	$-0.762648\pi$
$7$	−3.88734	−1.46928	−0.734638	+	0.678459i	$0.762648\pi$
$8$	−8.98906	−3.17811
$9$	−2.48040	−0.826800
$10$	−3.76173	−1.18956
$11$	5.55747	1.67564	0.837820	−	0.545947i	$-0.183830\pi$
$11$	5.55747	1.67564	0.837820	+	0.545947i	$0.183830\pi$
$12$	3.83627	1.10744
$13$	−4.83835	−1.34192	−0.670959	−	0.741495i	$-0.734117\pi$
$13$	−4.83835	−1.34192	−0.670959	+	0.741495i	$0.734117\pi$
$14$	10.5188	2.81128
$15$	1.00209	0.258739
$16$	13.6797	3.41992
$17$	−5.62753	−1.36488	−0.682438	−	0.730944i	$-0.739080\pi$
$17$	−5.62753	−1.36488	−0.682438	+	0.730944i	$0.739080\pi$
$18$	6.71177	1.58198
$19$	7.71569	1.77010	0.885051	−	0.465495i	$-0.154124\pi$
$19$	7.71569	1.77010	0.885051	+	0.465495i	$0.154124\pi$
$20$	7.39857	1.65437
$21$	−2.80212	−0.611473
$22$	−15.0381	−3.20612
$23$	−1.10870	−0.231181	−0.115590	−	0.993297i	$-0.536876\pi$
$23$	−1.10870	−0.231181	−0.115590	+	0.993297i	$0.536876\pi$
$24$	−6.47961	−1.32264
$25$	−3.06738	−0.613476
$26$	13.0922	2.56759
$27$	−3.95045	−0.760264
$28$	−20.6884	−3.90975
$29$	8.15697	1.51471	0.757356	−	0.653002i	$-0.226491\pi$
$29$	8.15697	1.51471	0.757356	+	0.653002i	$0.226491\pi$
$30$	−2.71158	−0.495064
$31$	−9.12174	−1.63831	−0.819156	−	0.573571i	$-0.805558\pi$
$31$	−9.12174	−1.63831	−0.819156	+	0.573571i	$0.805558\pi$
$32$	−19.0380	−3.36547
$33$	4.00600	0.697355
$34$	15.2276	2.61152
$35$	−5.40413	−0.913465
$36$	−13.2007	−2.20012
$37$	−4.42259	−0.727069	−0.363534	−	0.931581i	$-0.618430\pi$
$37$	−4.42259	−0.727069	−0.363534	+	0.931581i	$0.618430\pi$
$38$	−20.8780	−3.38687
$39$	−3.48764	−0.558469
$40$	−12.4965	−1.97587
$41$	5.93854	0.927444	0.463722	−	0.885981i	$-0.346514\pi$
$41$	5.93854	0.927444	0.463722	+	0.885981i	$0.346514\pi$
$42$	7.58231	1.16998
$43$	0.0465999	0.00710641	0.00355321	−	0.999994i	$-0.498869\pi$
$43$	0.0465999	0.00710641	0.00355321	+	0.999994i	$0.498869\pi$
$44$	29.5768	4.45888
$45$	−3.44822	−0.514030
$46$	3.00006	0.442335
$47$	5.10093	0.744047	0.372024	−	0.928223i	$-0.378664\pi$
$47$	5.10093	0.744047	0.372024	+	0.928223i	$0.378664\pi$
$48$	9.86076	1.42328
$49$	8.11142	1.15877
$50$	8.30009	1.17381
$51$	−4.05650	−0.568024
$52$	−25.7497	−3.57084
$53$	4.46812	0.613744	0.306872	−	0.951751i	$-0.400718\pi$
$53$	4.46812	0.613744	0.306872	+	0.951751i	$0.400718\pi$
$54$	10.6896	1.45467
$55$	7.72592	1.04176
$56$	34.9436	4.66953
$57$	5.56172	0.736668
$58$	−22.0721	−2.89821
$59$	−4.42988	−0.576721	−0.288361	−	0.957522i	$-0.593110\pi$
$59$	−4.42988	−0.576721	−0.288361	+	0.957522i	$0.593110\pi$
$60$	5.33313	0.688504
$61$	−3.96578	−0.507767	−0.253883	−	0.967235i	$-0.581708\pi$
$61$	−3.96578	−0.507767	−0.253883	+	0.967235i	$0.581708\pi$
$62$	24.6827	3.13470
$63$	9.64216	1.21480
$64$	24.1559	3.01949
$65$	−6.72621	−0.834284
$66$	−10.8399	−1.33430
$67$	1.26306	0.154307	0.0771537	−	0.997019i	$-0.475417\pi$
$67$	1.26306	0.154307	0.0771537	+	0.997019i	$0.475417\pi$
$68$	−29.9497	−3.63193
$69$	−0.799189	−0.0962111
$70$	14.6231	1.74780
$71$	−1.01385	−0.120322	−0.0601611	−	0.998189i	$-0.519161\pi$
$71$	−1.01385	−0.120322	−0.0601611	+	0.998189i	$0.519161\pi$
$72$	22.2965	2.62767
$73$	16.1255	1.88735	0.943674	−	0.330878i	$-0.107345\pi$
$73$	16.1255	1.88735	0.943674	+	0.330878i	$0.107345\pi$
$74$	11.9672	1.39115
$75$	−2.21107	−0.255312
$76$	41.0629	4.71024
$77$	−21.6038	−2.46198
$78$	9.43727	1.06856
$79$	−11.2849	−1.26965	−0.634825	−	0.772656i	$-0.718928\pi$
$79$	−11.2849	−1.26965	−0.634825	+	0.772656i	$0.718928\pi$
$80$	19.0173	2.12620
$81$	4.59359	0.510399
$82$	−16.0692	−1.77455
$83$	4.33432	0.475753	0.237877	−	0.971295i	$-0.423549\pi$
$83$	4.33432	0.475753	0.237877	+	0.971295i	$0.423549\pi$
$84$	−14.9129	−1.62713
$85$	−7.82331	−0.848557
$86$	−0.126095	−0.0135972
$87$	5.87981	0.630382
$88$	−49.9564	−5.32537
$89$	−17.0410	−1.80634	−0.903172	−	0.429279i	$-0.858768\pi$
$89$	−17.0410	−1.80634	−0.903172	+	0.429279i	$0.858768\pi$
$90$	9.33061	0.983532
$91$	18.8083	1.97165
$92$	−5.90052	−0.615172
$93$	−6.57524	−0.681821
$94$	−13.8027	−1.42364
$95$	10.7263	1.10049
$96$	−13.7232	−1.40062
$97$	−5.59497	−0.568083	−0.284042	−	0.958812i	$-0.591675\pi$
$97$	−5.59497	−0.568083	−0.284042	+	0.958812i	$0.591675\pi$
$98$	−21.9489	−2.21717
$99$	−13.7847	−1.38542
$100$	−16.3246	−1.63246
$101$	−12.1184	−1.20582	−0.602912	−	0.797808i	$-0.705993\pi$
$101$	−12.1184	−1.20582	−0.602912	+	0.797808i	$0.705993\pi$
$102$	10.9766	1.08684
$103$	13.2779	1.30831	0.654153	−	0.756362i	$-0.273025\pi$
$103$	13.2779	1.30831	0.654153	+	0.756362i	$0.273025\pi$
$104$	43.4922	4.26477
$105$	−3.89547	−0.380159
$106$	−12.0904	−1.17432
$107$	−12.5811	−1.21626	−0.608132	−	0.793836i	$-0.708081\pi$
$107$	−12.5811	−1.21626	−0.608132	+	0.793836i	$0.708081\pi$
$108$	−21.0243	−2.02306
$109$	−17.9022	−1.71472	−0.857358	−	0.514720i	$-0.827896\pi$
$109$	−17.9022	−1.71472	−0.857358	+	0.514720i	$0.827896\pi$
$110$	−20.9057	−1.99328
$111$	−3.18794	−0.302586
$112$	−53.1776	−5.02481
$113$	−1.88526	−0.177350	−0.0886750	−	0.996061i	$-0.528263\pi$
$113$	−1.88526	−0.177350	−0.0886750	+	0.996061i	$0.528263\pi$
$114$	−15.0496	−1.40952
$115$	−1.54130	−0.143727
$116$	43.4114	4.03065
$117$	12.0011	1.10950
$118$	11.9869	1.10348
$119$	21.8761	2.00538
$120$	−9.00786	−0.822302
$121$	19.8854	1.80777
$122$	10.7311	0.971547
$123$	4.28069	0.385977
$124$	−48.5459	−4.35955
$125$	−11.2152	−1.00311
$126$	−26.0909	−2.32436
$127$	2.98870	0.265204	0.132602	−	0.991169i	$-0.457667\pi$
$127$	2.98870	0.265204	0.132602	+	0.991169i	$0.457667\pi$
$128$	−27.2880	−2.41194
$129$	0.0335907	0.00295749
$130$	18.2006	1.59630
$131$	21.4995	1.87842	0.939208	−	0.343348i	$-0.111561\pi$
$131$	21.4995	1.87842	0.939208	+	0.343348i	$0.111561\pi$
$132$	21.3199	1.85566
$133$	−29.9935	−2.60077
$134$	−3.41774	−0.295248
$135$	−5.49186	−0.472664
$136$	50.5862	4.33773
$137$	−16.0277	−1.36934	−0.684671	−	0.728853i	$-0.740054\pi$
$137$	−16.0277	−1.36934	−0.684671	+	0.728853i	$0.740054\pi$
$138$	2.16254	0.184088
$139$	9.99130	0.847451	0.423726	−	0.905791i	$-0.360722\pi$
$139$	9.99130	0.847451	0.423726	+	0.905791i	$0.360722\pi$
$140$	−28.7608	−2.43073
$141$	3.67691	0.309652
$142$	2.74340	0.230221
$143$	−26.8890	−2.24857
$144$	−33.9311	−2.82759
$145$	11.3397	0.941712
$146$	−43.6343	−3.61120
$147$	5.84697	0.482250
$148$	−23.5370	−1.93473
$149$	−16.0615	−1.31581	−0.657904	−	0.753102i	$-0.728557\pi$
$149$	−16.0615	−1.31581	−0.657904	+	0.753102i	$0.728557\pi$
$150$	5.98297	0.488507
$151$	11.5338	0.938610	0.469305	−	0.883036i	$-0.344505\pi$
$151$	11.5338	0.938610	0.469305	+	0.883036i	$0.344505\pi$
$152$	−69.3569	−5.62558
$153$	13.9585	1.12848
$154$	58.4581	4.71069
$155$	−12.6809	−1.01856
$156$	−18.5612	−1.48609
$157$	15.5974	1.24481	0.622405	−	0.782695i	$-0.286156\pi$
$157$	15.5974	1.24481	0.622405	+	0.782695i	$0.286156\pi$
$158$	30.5360	2.42931
$159$	3.22077	0.255423
$160$	−26.4664	−2.09235
$161$	4.30991	0.339668
$162$	−12.4299	−0.976584
$163$	−3.31779	−0.259870	−0.129935	−	0.991523i	$-0.541477\pi$
$163$	−3.31779	−0.259870	−0.129935	+	0.991523i	$0.541477\pi$
$164$	31.6049	2.46793
$165$	5.56909	0.433553
$166$	−11.7283	−0.910294
$167$	−2.29899	−0.177901	−0.0889507	−	0.996036i	$-0.528351\pi$
$167$	−2.29899	−0.177901	−0.0889507	+	0.996036i	$0.528351\pi$
$168$	25.1884	1.94333
$169$	10.4096	0.800741
$170$	21.1693	1.62361
$171$	−19.1380	−1.46352
$172$	0.248004	0.0189102
$173$	9.21155	0.700341	0.350171	−	0.936686i	$-0.386124\pi$
$173$	9.21155	0.700341	0.350171	+	0.936686i	$0.386124\pi$
$174$	−15.9103	−1.20616
$175$	11.9240	0.901366
$176$	76.0244	5.73055
$177$	−3.19320	−0.240016
$178$	46.1116	3.45621
$179$	20.0302	1.49712	0.748562	−	0.663065i	$-0.230745\pi$
$179$	20.0302	1.49712	0.748562	+	0.663065i	$0.230745\pi$
$180$	−18.3514	−1.36783
$181$	−10.6266	−0.789868	−0.394934	−	0.918709i	$-0.629233\pi$
$181$	−10.6266	−0.789868	−0.394934	+	0.918709i	$0.629233\pi$
$182$	−50.8938	−3.77250
$183$	−2.85866	−0.211319
$184$	9.96621	0.734719
$185$	−6.14822	−0.452026
$186$	17.7921	1.30458
$187$	−31.2748	−2.28704
$188$	27.1472	1.97991
$189$	15.3567	1.11704
$190$	−29.0244	−2.10565
$191$	17.1544	1.24125	0.620624	−	0.784109i	$-0.286880\pi$
$191$	17.1544	1.24125	0.620624	+	0.784109i	$0.286880\pi$
$192$	17.4124	1.25663
$193$	4.59936	0.331070	0.165535	−	0.986204i	$-0.447065\pi$
$193$	4.59936	0.331070	0.165535	+	0.986204i	$0.447065\pi$
$194$	15.1395	1.08696
$195$	−4.84847	−0.347206
$196$	43.1690	3.08350
$197$	8.71436	0.620873	0.310436	−	0.950594i	$-0.399525\pi$
$197$	8.71436	0.620873	0.310436	+	0.950594i	$0.399525\pi$
$198$	37.3004	2.65083
$199$	−9.25044	−0.655746	−0.327873	−	0.944722i	$-0.606332\pi$
$199$	−9.25044	−0.655746	−0.327873	+	0.944722i	$0.606332\pi$
$200$	27.5729	1.94970
$201$	0.910454	0.0642185
$202$	32.7913	2.30719
$203$	−31.7089	−2.22553
$204$	−21.5887	−1.51151
$205$	8.25568	0.576602
$206$	−35.9288	−2.50328
$207$	2.75003	0.191140
$208$	−66.1871	−4.58925
$209$	42.8797	2.96605
$210$	10.5408	0.727386
$211$	18.7508	1.29086	0.645429	−	0.763820i	$-0.276679\pi$
$211$	18.7508	1.29086	0.645429	+	0.763820i	$0.276679\pi$
$212$	23.7793	1.63317
$213$	−0.730818	−0.0500748
$214$	34.0435	2.32717
$215$	0.0647825	0.00441813
$216$	35.5108	2.41621
$217$	35.4593	2.40713
$218$	48.4418	3.28089
$219$	11.6238	0.785462
$220$	41.1173	2.77213
$221$	27.2279	1.83155
$222$	8.62631	0.578960
$223$	2.15280	0.144162	0.0720812	−	0.997399i	$-0.477036\pi$
$223$	2.15280	0.144162	0.0720812	+	0.997399i	$0.477036\pi$
$224$	74.0072	4.94481
$225$	7.60834	0.507222
$226$	5.10135	0.339337
$227$	−0.977918	−0.0649067	−0.0324534	−	0.999473i	$-0.510332\pi$
$227$	−0.977918	−0.0649067	−0.0324534	+	0.999473i	$0.510332\pi$
$228$	29.5995	1.96027
$229$	−15.2891	−1.01033	−0.505166	−	0.863022i	$-0.668569\pi$
$229$	−15.2891	−1.01033	−0.505166	+	0.863022i	$0.668569\pi$
$230$	4.17065	0.275004
$231$	−15.5727	−1.02461
$232$	−73.3236	−4.81393
$233$	−14.1939	−0.929876	−0.464938	−	0.885343i	$-0.653923\pi$
$233$	−14.1939	−0.929876	−0.464938	+	0.885343i	$0.653923\pi$
$234$	−32.4739	−2.12288
$235$	7.09124	0.462582
$236$	−23.5758	−1.53466
$237$	−8.13452	−0.528394
$238$	−59.1950	−3.83704
$239$	4.14688	0.268239	0.134120	−	0.990965i	$-0.457179\pi$
$239$	4.14688	0.268239	0.134120	+	0.990965i	$0.457179\pi$
$240$	13.7083	0.884866
$241$	−1.12921	−0.0727387	−0.0363693	−	0.999338i	$-0.511579\pi$
$241$	−1.12921	−0.0727387	−0.0363693	+	0.999338i	$0.511579\pi$
$242$	−53.8084	−3.45893
$243$	15.1626	0.972678
$244$	−21.1059	−1.35117
$245$	11.2764	0.720422
$246$	−11.5832	−0.738518
$247$	−37.3312	−2.37533
$248$	81.9959	5.20674
$249$	3.12432	0.197995
$250$	30.3473	1.91933
$251$	17.7677	1.12149	0.560745	−	0.827989i	$-0.310515\pi$
$251$	17.7677	1.12149	0.560745	+	0.827989i	$0.310515\pi$
$252$	51.3156	3.23258
$253$	−6.16158	−0.387375
$254$	−8.08717	−0.507434
$255$	−5.63930	−0.353146
$256$	25.5272	1.59545
$257$	12.2845	0.766287	0.383143	−	0.923689i	$-0.374842\pi$
$257$	12.2845	0.766287	0.383143	+	0.923689i	$0.374842\pi$
$258$	−0.0908937	−0.00565879
$259$	17.1921	1.06827
$260$	−35.7969	−2.22003
$261$	−20.2326	−1.25236
$262$	−58.1758	−3.59411
$263$	10.9209	0.673414	0.336707	−	0.941610i	$-0.390687\pi$
$263$	10.9209	0.673414	0.336707	+	0.941610i	$0.390687\pi$
$264$	−36.0102	−2.21627
$265$	6.21152	0.381571
$266$	81.1601	4.97624
$267$	−12.2837	−0.751751
$268$	6.72201	0.410612
$269$	−17.5060	−1.06736	−0.533679	−	0.845687i	$-0.679191\pi$
$269$	−17.5060	−1.06736	−0.533679	+	0.845687i	$0.679191\pi$
$270$	14.8605	0.904383
$271$	9.38812	0.570288	0.285144	−	0.958485i	$-0.407959\pi$
$271$	9.38812	0.570288	0.285144	+	0.958485i	$0.407959\pi$
$272$	−76.9828	−4.66777
$273$	13.5576	0.820546
$274$	43.3697	2.62006
$275$	−17.0469	−1.02796
$276$	−4.25328	−0.256018
$277$	−13.6415	−0.819638	−0.409819	−	0.912167i	$-0.634408\pi$
$277$	−13.6415	−0.819638	−0.409819	+	0.912167i	$0.634408\pi$
$278$	−27.0357	−1.62149
$279$	22.6256	1.35456
$280$	48.5781	2.90309
$281$	1.01210	0.0603768	0.0301884	−	0.999544i	$-0.490389\pi$
$281$	1.01210	0.0603768	0.0301884	+	0.999544i	$0.490389\pi$
$282$	−9.94944	−0.592480
$283$	7.73625	0.459872	0.229936	−	0.973206i	$-0.426148\pi$
$283$	7.73625	0.459872	0.229936	+	0.973206i	$0.426148\pi$
$284$	−5.39573	−0.320177
$285$	7.73183	0.457994
$286$	72.7594	4.30235
$287$	−23.0851	−1.36267
$288$	47.2219	2.78258
$289$	14.6691	0.862886
$290$	−30.6844	−1.80185
$291$	−4.03304	−0.236421
$292$	85.8199	5.02223
$293$	21.0072	1.22725	0.613627	−	0.789596i	$-0.289710\pi$
$293$	21.0072	1.22725	0.613627	+	0.789596i	$0.289710\pi$
$294$	−15.8214	−0.922725
$295$	−6.15836	−0.358554
$296$	39.7549	2.31071
$297$	−21.9545	−1.27393
$298$	43.4611	2.51763
$299$	5.36430	0.310225
$300$	−11.7673	−0.679385
$301$	−0.181150	−0.0104413
$302$	−31.2096	−1.79591
$303$	−8.73531	−0.501831
$304$	105.548	6.05361
$305$	−5.51318	−0.315684
$306$	−37.7706	−2.15920
$307$	23.6175	1.34792	0.673961	−	0.738767i	$-0.264592\pi$
$307$	23.6175	1.34792	0.673961	+	0.738767i	$0.264592\pi$
$308$	−114.975	−6.55132
$309$	9.57111	0.544481
$310$	34.3135	1.94888
$311$	7.77799	0.441050	0.220525	−	0.975381i	$-0.429223\pi$
$311$	7.77799	0.441050	0.220525	+	0.975381i	$0.429223\pi$
$312$	31.3506	1.77488
$313$	18.0984	1.02298	0.511490	−	0.859289i	$-0.329094\pi$
$313$	18.0984	1.02298	0.511490	+	0.859289i	$0.329094\pi$
$314$	−42.2054	−2.38179
$315$	13.4044	0.755253
$316$	−60.0582	−3.37854
$317$	−6.00858	−0.337475	−0.168738	−	0.985661i	$-0.553969\pi$
$317$	−6.00858	−0.337475	−0.168738	+	0.985661i	$0.553969\pi$
$318$	−8.71514	−0.488721
$319$	45.3321	2.53811
$320$	33.5812	1.87725
$321$	−9.06889	−0.506176
$322$	−11.6623	−0.649913
$323$	−43.4203	−2.41597
$324$	24.4471	1.35817
$325$	14.8411	0.823234
$326$	8.97768	0.497228
$327$	−12.9045	−0.713618
$328$	−53.3819	−2.94752
$329$	−19.8291	−1.09321
$330$	−15.0695	−0.829549
$331$	5.52097	0.303460	0.151730	−	0.988422i	$-0.451516\pi$
$331$	5.52097	0.303460	0.151730	+	0.988422i	$0.451516\pi$
$332$	23.0672	1.26598
$333$	10.9698	0.601141
$334$	6.22089	0.340392
$335$	1.75589	0.0959345
$336$	−38.3321	−2.09119
$337$	0.904536	0.0492732	0.0246366	−	0.999696i	$-0.492157\pi$
$337$	0.904536	0.0492732	0.0246366	+	0.999696i	$0.492157\pi$
$338$	−28.1676	−1.53212
$339$	−1.35895	−0.0738082
$340$	−41.6357	−2.25801
$341$	−50.6938	−2.74522
$342$	51.7859	2.80026
$343$	−4.32048	−0.233284
$344$	−0.418889	−0.0225850
$345$	−1.11102	−0.0598154
$346$	−24.9257	−1.34001
$347$	−3.23723	−0.173784	−0.0868918	−	0.996218i	$-0.527693\pi$
$347$	−3.23723	−0.173784	−0.0868918	+	0.996218i	$0.527693\pi$
$348$	31.2923	1.67745
$349$	29.6686	1.58812	0.794062	−	0.607837i	$-0.207963\pi$
$349$	29.6686	1.58812	0.794062	+	0.607837i	$0.207963\pi$
$350$	−32.2653	−1.72465
$351$	19.1137	1.02021
$352$	−105.803	−5.63932
$353$	22.6037	1.20308	0.601538	−	0.798844i	$-0.294555\pi$
$353$	22.6037	1.20308	0.601538	+	0.798844i	$0.294555\pi$
$354$	8.64054	0.459240
$355$	−1.40944	−0.0748056
$356$	−90.6923	−4.80668
$357$	15.7690	0.834584
$358$	−54.2000	−2.86456
$359$	19.5127	1.02984	0.514919	−	0.857239i	$-0.327822\pi$
$359$	19.5127	1.02984	0.514919	+	0.857239i	$0.327822\pi$
$360$	30.9963	1.63365
$361$	40.5319	2.13326
$362$	28.7547	1.51131
$363$	14.3341	0.752343
$364$	100.098	5.24655
$365$	22.4175	1.17338
$366$	7.73532	0.404331
$367$	−7.83813	−0.409147	−0.204574	−	0.978851i	$-0.565581\pi$
$367$	−7.83813	−0.409147	−0.204574	+	0.978851i	$0.565581\pi$
$368$	−15.1667	−0.790620
$369$	−14.7300	−0.766811
$370$	16.6366	0.864895
$371$	−17.3691	−0.901760
$372$	−34.9934	−1.81433
$373$	24.5357	1.27041	0.635205	−	0.772344i	$-0.280916\pi$
$373$	24.5357	1.27041	0.635205	+	0.772344i	$0.280916\pi$
$374$	84.6271	4.37596
$375$	−8.08425	−0.417469
$376$	−45.8526	−2.36467
$377$	−39.4663	−2.03262
$378$	−41.5541	−2.13731
$379$	9.63639	0.494988	0.247494	−	0.968889i	$-0.420393\pi$
$379$	9.63639	0.494988	0.247494	+	0.968889i	$0.420393\pi$
$380$	57.0851	2.92840
$381$	2.15435	0.110371
$382$	−46.4184	−2.37497
$383$	−25.4294	−1.29938	−0.649691	−	0.760199i	$-0.725102\pi$
$383$	−25.4294	−1.29938	−0.649691	+	0.760199i	$0.725102\pi$
$384$	−19.6700	−1.00378
$385$	−30.0333	−1.53064
$386$	−12.4455	−0.633460
$387$	−0.115586	−0.00587558
$388$	−29.7764	−1.51167
$389$	−30.8682	−1.56508	−0.782540	−	0.622601i	$-0.786076\pi$
$389$	−30.8682	−1.56508	−0.782540	+	0.622601i	$0.786076\pi$
$390$	13.1196	0.664335
$391$	6.23926	0.315533
$392$	−72.9141	−3.68272
$393$	15.4975	0.781746
$394$	−23.5804	−1.18796
$395$	−15.6881	−0.789354
$396$	−73.3624	−3.68660
$397$	34.7152	1.74230	0.871152	−	0.491013i	$-0.163373\pi$
$397$	34.7152	1.74230	0.871152	+	0.491013i	$0.163373\pi$
$398$	25.0309	1.25469
$399$	−21.6203	−1.08237
$400$	−41.9608	−2.09804
$401$	17.3085	0.864345	0.432173	−	0.901791i	$-0.357747\pi$
$401$	17.3085	0.864345	0.432173	+	0.901791i	$0.357747\pi$
$402$	−2.46362	−0.122874
$403$	44.1342	2.19848
$404$	−64.4940	−3.20870
$405$	6.38595	0.317320
$406$	85.8018	4.25827
$407$	−24.5784	−1.21830
$408$	36.4642	1.80525
$409$	16.9651	0.838873	0.419436	−	0.907785i	$-0.362228\pi$
$409$	16.9651	0.838873	0.419436	+	0.907785i	$0.362228\pi$
$410$	−22.3392	−1.10325
$411$	−11.5533	−0.569882
$412$	70.6648	3.48140
$413$	17.2205	0.847363
$414$	−7.44136	−0.365723
$415$	6.02551	0.295781
$416$	92.1125	4.51619
$417$	7.20205	0.352686
$418$	−116.029	−5.67517
$419$	−40.2717	−1.96740	−0.983701	−	0.179810i	$-0.942452\pi$
$419$	−40.2717	−1.96740	−0.983701	+	0.179810i	$0.942452\pi$
$420$	−20.7317	−1.01160
$421$	−12.4331	−0.605954	−0.302977	−	0.952998i	$-0.597980\pi$
$421$	−12.4331	−0.605954	−0.302977	+	0.952998i	$0.597980\pi$
$422$	−50.7381	−2.46989
$423$	−12.6524	−0.615178
$424$	−40.1642	−1.95055
$425$	17.2618	0.837319
$426$	1.97753	0.0958119
$427$	15.4164	0.746050
$428$	−66.9568	−3.23648
$429$	−19.3824	−0.935793
$430$	−0.175296	−0.00845353
$431$	21.1805	1.02023	0.510115	−	0.860106i	$-0.329603\pi$
$431$	21.1805	1.02023	0.510115	+	0.860106i	$0.329603\pi$
$432$	−54.0409	−2.60004
$433$	−3.70254	−0.177933	−0.0889664	−	0.996035i	$-0.528356\pi$
$433$	−3.70254	−0.177933	−0.0889664	+	0.996035i	$0.528356\pi$
$434$	−95.9500	−4.60575
$435$	8.17403	0.391915
$436$	−95.2754	−4.56286
$437$	−8.55442	−0.409213
$438$	−31.4530	−1.50288
$439$	31.3256	1.49509	0.747544	−	0.664213i	$-0.231233\pi$
$439$	31.3256	1.49509	0.747544	+	0.664213i	$0.231233\pi$
$440$	−69.4488	−3.31084
$441$	−20.1196	−0.958075
$442$	−73.6766	−3.50444
$443$	11.1848	0.531408	0.265704	−	0.964055i	$-0.414396\pi$
$443$	11.1848	0.531408	0.265704	+	0.964055i	$0.414396\pi$
$444$	−16.9662	−0.805182
$445$	−23.6902	−1.12302
$446$	−5.82532	−0.275837
$447$	−11.5776	−0.547603
$448$	−93.9023	−4.43647
$449$	−29.0666	−1.37174	−0.685869	−	0.727725i	$-0.740578\pi$
$449$	−29.0666	−1.37174	−0.685869	+	0.727725i	$0.740578\pi$
$450$	−20.5875	−0.970506
$451$	33.0032	1.55406
$452$	−10.0333	−0.471929
$453$	8.31396	0.390624
$454$	2.64617	0.124191
$455$	26.1471	1.22579
$456$	−49.9947	−2.34121
$457$	29.0651	1.35961	0.679803	−	0.733395i	$-0.262065\pi$
$457$	29.0651	1.35961	0.679803	+	0.733395i	$0.262065\pi$
$458$	41.3711	1.93314
$459$	22.2313	1.03767
$460$	−8.20282	−0.382459
$461$	2.39308	0.111457	0.0557285	−	0.998446i	$-0.482252\pi$
$461$	2.39308	0.111457	0.0557285	+	0.998446i	$0.482252\pi$
$462$	42.1385	1.96046
$463$	−14.4170	−0.670016	−0.335008	−	0.942215i	$-0.608739\pi$
$463$	−14.4170	−0.670016	−0.335008	+	0.942215i	$0.608739\pi$
$464$	111.585	5.18020
$465$	−9.14081	−0.423895
$466$	38.4077	1.77920
$467$	−2.15382	−0.0996669	−0.0498335	−	0.998758i	$-0.515869\pi$
$467$	−2.15382	−0.0996669	−0.0498335	+	0.998758i	$0.515869\pi$
$468$	63.8696	2.95237
$469$	−4.90995	−0.226720
$470$	−19.1883	−0.885092
$471$	11.2431	0.518056
$472$	39.8205	1.83289
$473$	0.258977	0.0119078
$474$	22.0113	1.01101
$475$	−23.6670	−1.08592
$476$	116.425	5.33632
$477$	−11.0827	−0.507444
$478$	−11.2211	−0.513242
$479$	39.5395	1.80660	0.903302	−	0.429005i	$-0.141136\pi$
$479$	39.5395	1.80660	0.903302	+	0.429005i	$0.141136\pi$
$480$	−19.0778	−0.870779
$481$	21.3980	0.975666
$482$	3.05555	0.139176
$483$	3.10672	0.141361
$484$	105.830	4.81047
$485$	−7.77806	−0.353183
$486$	−41.0287	−1.86110
$487$	9.60303	0.435155	0.217577	−	0.976043i	$-0.430185\pi$
$487$	9.60303	0.435155	0.217577	+	0.976043i	$0.430185\pi$
$488$	35.6487	1.61374
$489$	−2.39157	−0.108151
$490$	−30.5130	−1.37844
$491$	14.2222	0.641838	0.320919	−	0.947107i	$-0.396008\pi$
$491$	14.2222	0.641838	0.320919	+	0.947107i	$0.396008\pi$
$492$	22.7818	1.02708
$493$	−45.9036	−2.06739
$494$	101.015	4.54489
$495$	−19.1634	−0.861329
$496$	−124.782	−5.60290
$497$	3.94119	0.176787
$498$	−8.45415	−0.378839
$499$	−27.6612	−1.23828	−0.619142	−	0.785279i	$-0.712519\pi$
$499$	−27.6612	−1.23828	−0.619142	+	0.785279i	$0.712519\pi$
$500$	−59.6871	−2.66929
$501$	−1.65719	−0.0740377
$502$	−48.0780	−2.14583
$503$	−11.8720	−0.529348	−0.264674	−	0.964338i	$-0.585264\pi$
$503$	−11.8720	−0.529348	−0.264674	+	0.964338i	$0.585264\pi$
$504$	−86.6740	−3.86077
$505$	−16.8468	−0.749673
$506$	16.6727	0.741194
$507$	7.50360	0.333247
$508$	15.9058	0.705708
$509$	−16.6359	−0.737372	−0.368686	−	0.929554i	$-0.620192\pi$
$509$	−16.6359	−0.737372	−0.368686	+	0.929554i	$0.620192\pi$
$510$	15.2595	0.675701
$511$	−62.6853	−2.77304
$512$	−14.4986	−0.640756
$513$	−30.4805	−1.34574
$514$	−33.2409	−1.46619
$515$	18.4587	0.813388
$516$	0.178770	0.00786989
$517$	28.3483	1.24675
$518$	−46.5204	−2.04399
$519$	6.63998	0.291463
$520$	60.4623	2.65145
$521$	8.35176	0.365897	0.182949	−	0.983122i	$-0.441436\pi$
$521$	8.35176	0.365897	0.182949	+	0.983122i	$0.441436\pi$
$522$	54.7477	2.39624
$523$	37.9766	1.66060	0.830301	−	0.557316i	$-0.188169\pi$
$523$	37.9766	1.66060	0.830301	+	0.557316i	$0.188169\pi$
$524$	114.420	4.99847
$525$	8.59517	0.375124
$526$	−29.5512	−1.28849
$527$	51.3328	2.23609
$528$	54.8008	2.38490
$529$	−21.7708	−0.946556
$530$	−16.8079	−0.730088
$531$	10.9879	0.476833
$532$	−159.626	−6.92065
$533$	−28.7327	−1.24455
$534$	33.2387	1.43838
$535$	−17.4901	−0.756164
$536$	−11.3537	−0.490406
$537$	14.4384	0.623062
$538$	47.3698	2.04226
$539$	45.0790	1.94169
$540$	−29.2277	−1.25776
$541$	−18.8628	−0.810975	−0.405487	−	0.914101i	$-0.632898\pi$
$541$	−18.8628	−0.810975	−0.405487	+	0.914101i	$0.632898\pi$
$542$	−25.4035	−1.09117
$543$	−7.65999	−0.328722
$544$	107.137	4.59345
$545$	−24.8874	−1.06606
$546$	−36.6859	−1.57001
$547$	−29.1353	−1.24574	−0.622869	−	0.782326i	$-0.714033\pi$
$547$	−29.1353	−1.24574	−0.622869	+	0.782326i	$0.714033\pi$
$548$	−85.2996	−3.64382
$549$	9.83673	0.419822
$550$	46.1275	1.96688
$551$	62.9367	2.68119
$552$	7.18396	0.305770
$553$	43.8682	1.86547
$554$	36.9128	1.56827
$555$	−4.43183	−0.188121
$556$	53.1737	2.25507
$557$	12.9541	0.548882	0.274441	−	0.961604i	$-0.411507\pi$
$557$	12.9541	0.548882	0.274441	+	0.961604i	$0.411507\pi$
$558$	−61.2230	−2.59177
$559$	−0.225466	−0.00953622
$560$	−73.9268	−3.12398
$561$	−22.5439	−0.951803
$562$	−2.73866	−0.115523
$563$	37.7610	1.59144	0.795719	−	0.605667i	$-0.207093\pi$
$563$	37.7610	1.59144	0.795719	+	0.605667i	$0.207093\pi$
$564$	19.5685	0.823984
$565$	−2.62086	−0.110260
$566$	−20.9337	−0.879908
$567$	−17.8569	−0.749918
$568$	9.11359	0.382398
$569$	−10.9759	−0.460134	−0.230067	−	0.973175i	$-0.573895\pi$
$569$	−10.9759	−0.460134	−0.230067	+	0.973175i	$0.573895\pi$
$570$	−20.9217	−0.876314
$571$	−5.87933	−0.246042	−0.123021	−	0.992404i	$-0.539258\pi$
$571$	−5.87933	−0.246042	−0.123021	+	0.992404i	$0.539258\pi$
$572$	−143.103	−5.98344
$573$	12.3654	0.516573
$574$	62.4665	2.60730
$575$	3.40082	0.141824
$576$	−59.9164	−2.49651
$577$	3.39022	0.141137	0.0705683	−	0.997507i	$-0.477519\pi$
$577$	3.39022	0.141137	0.0705683	+	0.997507i	$0.477519\pi$
$578$	−39.6933	−1.65102
$579$	3.31537	0.137782
$580$	60.3500	2.50590
$581$	−16.8490	−0.699013
$582$	10.9131	0.452361
$583$	24.8314	1.02841
$584$	−144.953	−5.99820
$585$	16.6837	0.689786
$586$	−56.8438	−2.34819
$587$	−36.3095	−1.49865	−0.749326	−	0.662202i	$-0.769622\pi$
$587$	−36.3095	−1.49865	−0.749326	+	0.662202i	$0.769622\pi$
$588$	31.1176	1.28327
$589$	−70.3805	−2.89998
$590$	16.6640	0.686047
$591$	6.28159	0.258390
$592$	−60.4996	−2.48652
$593$	21.1022	0.866564	0.433282	−	0.901258i	$-0.357355\pi$
$593$	21.1022	0.866564	0.433282	+	0.901258i	$0.357355\pi$
$594$	59.4071	2.43750
$595$	30.4119	1.24677
$596$	−85.4792	−3.50137
$597$	−6.66801	−0.272904
$598$	−14.5154	−0.593577
$599$	−26.9845	−1.10256	−0.551279	−	0.834321i	$-0.685860\pi$
$599$	−26.9845	−1.10256	−0.551279	+	0.834321i	$0.685860\pi$
$600$	19.8754	0.811411
$601$	1.28213	0.0522990	0.0261495	−	0.999658i	$-0.491675\pi$
$601$	1.28213	0.0522990	0.0261495	+	0.999658i	$0.491675\pi$
$602$	0.490176	0.0199781
$603$	−3.13290	−0.127581
$604$	61.3831	2.49764
$605$	27.6445	1.12391
$606$	23.6371	0.960190
$607$	−42.2063	−1.71310	−0.856551	−	0.516062i	$-0.827397\pi$
$607$	−42.2063	−1.71310	−0.856551	+	0.516062i	$0.827397\pi$
$608$	−146.891	−5.95723
$609$	−22.8568	−0.926205
$610$	14.9182	0.604021
$611$	−24.6801	−0.998450
$612$	74.2873	3.00288
$613$	−27.6977	−1.11870	−0.559350	−	0.828932i	$-0.688949\pi$
$613$	−27.6977	−1.11870	−0.559350	+	0.828932i	$0.688949\pi$
$614$	−63.9071	−2.57908
$615$	5.95096	0.239966
$616$	194.198	7.82445
$617$	12.0916	0.486789	0.243395	−	0.969927i	$-0.421739\pi$
$617$	12.0916	0.486789	0.243395	+	0.969927i	$0.421739\pi$
$618$	−25.8986	−1.04180
$619$	39.1652	1.57418	0.787092	−	0.616836i	$-0.211586\pi$
$619$	39.1652	1.57418	0.787092	+	0.616836i	$0.211586\pi$
$620$	−67.4878	−2.71038
$621$	4.37988	0.175758
$622$	−21.0466	−0.843893
$623$	66.2442	2.65402
$624$	−47.7098	−1.90992
$625$	−0.254265	−0.0101706
$626$	−48.9727	−1.95734
$627$	30.9091	1.23439
$628$	83.0095	3.31244
$629$	24.8882	0.992358
$630$	−36.2712	−1.44508
$631$	5.00739	0.199341	0.0996705	−	0.995021i	$-0.468221\pi$
$631$	5.00739	0.199341	0.0996705	+	0.995021i	$0.468221\pi$
$632$	101.441	4.03509
$633$	13.5162	0.537220
$634$	16.2587	0.645717
$635$	4.15485	0.164880
$636$	17.1409	0.679682
$637$	−39.2459	−1.55498
$638$	−122.665	−4.85636
$639$	2.51476	0.0994825
$640$	−37.9354	−1.49953
$641$	−43.9610	−1.73635	−0.868177	−	0.496254i	$-0.834708\pi$
$641$	−43.9610	−1.73635	−0.868177	+	0.496254i	$0.834708\pi$
$642$	24.5397	0.968504
$643$	−4.36861	−0.172281	−0.0861405	−	0.996283i	$-0.527453\pi$
$643$	−4.36861	−0.172281	−0.0861405	+	0.996283i	$0.527453\pi$
$644$	22.9373	0.903858
$645$	0.0466973	0.00183870
$646$	117.492	4.62265
$647$	34.6227	1.36116	0.680580	−	0.732674i	$-0.261728\pi$
$647$	34.6227	1.36116	0.680580	+	0.732674i	$0.261728\pi$
$648$	−41.2921	−1.62211
$649$	−24.6189	−0.966377
$650$	−40.1587	−1.57516
$651$	25.5602	1.00178
$652$	−17.6573	−0.691513
$653$	−8.64725	−0.338393	−0.169196	−	0.985582i	$-0.554117\pi$
$653$	−8.64725	−0.338393	−0.169196	+	0.985582i	$0.554117\pi$
$654$	34.9184	1.36542
$655$	29.8883	1.16783
$656$	81.2374	3.17179
$657$	−39.9977	−1.56046
$658$	53.6558	2.09172
$659$	−28.7902	−1.12151	−0.560754	−	0.827982i	$-0.689489\pi$
$659$	−28.7902	−1.12151	−0.560754	+	0.827982i	$0.689489\pi$
$660$	29.6387	1.15368
$661$	−13.4249	−0.522167	−0.261084	−	0.965316i	$-0.584080\pi$
$661$	−13.4249	−0.522167	−0.261084	+	0.965316i	$0.584080\pi$
$662$	−14.9393	−0.580633
$663$	19.6268	0.762241
$664$	−38.9615	−1.51200
$665$	−41.6966	−1.61692
$666$	−29.6834	−1.15021
$667$	−9.04366	−0.350172
$668$	−12.2352	−0.473396
$669$	1.55181	0.0599965
$670$	−4.75129	−0.183559
$671$	−22.0397	−0.850834
$672$	53.3468	2.05790
$673$	21.4295	0.826047	0.413024	−	0.910720i	$-0.364473\pi$
$673$	21.4295	0.826047	0.413024	+	0.910720i	$0.364473\pi$
$674$	−2.44760	−0.0942781
$675$	12.1175	0.466404
$676$	55.4001	2.13077
$677$	2.67449	0.102789	0.0513945	−	0.998678i	$-0.483633\pi$
$677$	2.67449	0.102789	0.0513945	+	0.998678i	$0.483633\pi$
$678$	3.67722	0.141223
$679$	21.7496	0.834672
$680$	70.3243	2.69681
$681$	−0.704915	−0.0270124
$682$	137.173	5.25263
$683$	−3.31371	−0.126796	−0.0633978	−	0.997988i	$-0.520194\pi$
$683$	−3.31371	−0.126796	−0.0633978	+	0.997988i	$0.520194\pi$
$684$	−101.852	−3.89443
$685$	−22.2815	−0.851334
$686$	11.6909	0.446359
$687$	−11.0209	−0.420473
$688$	0.637471	0.0243034
$689$	−21.6183	−0.823593
$690$	3.00634	0.114449
$691$	43.7800	1.66547	0.832734	−	0.553673i	$-0.186774\pi$
$691$	43.7800	1.66547	0.832734	+	0.553673i	$0.186774\pi$
$692$	49.0239	1.86361
$693$	53.5860	2.03556
$694$	8.75968	0.332513
$695$	13.8898	0.526869
$696$	−52.8540	−2.00342
$697$	−33.4193	−1.26585
$698$	−80.2808	−3.03867
$699$	−10.2314	−0.386989
$700$	63.4593	2.39854
$701$	−9.93126	−0.375098	−0.187549	−	0.982255i	$-0.560054\pi$
$701$	−9.93126	−0.375098	−0.187549	+	0.982255i	$0.560054\pi$
$702$	−51.7200	−1.95205
$703$	−34.1233	−1.28698
$704$	134.246	5.05958
$705$	5.11160	0.192514
$706$	−61.1639	−2.30193
$707$	47.1082	1.77169
$708$	−16.9942	−0.638682
$709$	40.4104	1.51764	0.758822	−	0.651298i	$-0.225775\pi$
$709$	40.4104	1.51764	0.758822	+	0.651298i	$0.225775\pi$
$710$	3.81384	0.143131
$711$	27.9911	1.04975
$712$	153.183	5.74077
$713$	10.1133	0.378746
$714$	−42.6697	−1.59687
$715$	−37.3807	−1.39796
$716$	106.600	3.98385
$717$	2.98920	0.111634
$718$	−52.7997	−1.97047
$719$	−5.44650	−0.203120	−0.101560	−	0.994829i	$-0.532383\pi$
$719$	−5.44650	−0.203120	−0.101560	+	0.994829i	$0.532383\pi$
$720$	−47.1706	−1.75794
$721$	−51.6156	−1.92226
$722$	−109.676	−4.08172
$723$	−0.813969	−0.0302718
$724$	−56.5547	−2.10184
$725$	−25.0205	−0.929240
$726$	−38.7868	−1.43951
$727$	32.8393	1.21794	0.608972	−	0.793192i	$-0.291582\pi$
$727$	32.8393	1.21794	0.608972	+	0.793192i	$0.291582\pi$
$728$	−169.069	−6.26612
$729$	−2.85112	−0.105597
$730$	−60.6598	−2.24512
$731$	−0.262242	−0.00969937
$732$	−15.2138	−0.562319
$733$	9.05961	0.334624	0.167312	−	0.985904i	$-0.446491\pi$
$733$	9.05961	0.334624	0.167312	+	0.985904i	$0.446491\pi$
$734$	21.2094	0.782852
$735$	8.12838	0.299820
$736$	21.1075	0.778033
$737$	7.01941	0.258563
$738$	39.8581	1.46720
$739$	20.3031	0.746863	0.373431	−	0.927658i	$-0.378181\pi$
$739$	20.3031	0.746863	0.373431	+	0.927658i	$0.378181\pi$
$740$	−32.7208	−1.20284
$741$	−26.9095	−0.988547
$742$	46.9994	1.72540
$743$	−6.04674	−0.221833	−0.110917	−	0.993830i	$-0.535379\pi$
$743$	−6.04674	−0.221833	−0.110917	+	0.993830i	$0.535379\pi$
$744$	59.1053	2.16690
$745$	−22.3285	−0.818051
$746$	−66.3916	−2.43077
$747$	−10.7508	−0.393353
$748$	−166.444	−6.08581
$749$	48.9072	1.78703
$750$	21.8753	0.798774
$751$	23.9956	0.875612	0.437806	−	0.899070i	$-0.355756\pi$
$751$	23.9956	0.875612	0.437806	+	0.899070i	$0.355756\pi$
$752$	69.7791	2.54458
$753$	12.8076	0.466733
$754$	106.793	3.88916
$755$	16.0342	0.583543
$756$	81.7286	2.97244
$757$	6.64825	0.241635	0.120817	−	0.992675i	$-0.461448\pi$
$757$	6.64825	0.241635	0.120817	+	0.992675i	$0.461448\pi$
$758$	−26.0753	−0.947098
$759$	−4.44147	−0.161215
$760$	−96.4190	−3.49748
$761$	−31.4801	−1.14115	−0.570576	−	0.821244i	$-0.693280\pi$
$761$	−31.4801	−1.14115	−0.570576	+	0.821244i	$0.693280\pi$
$762$	−5.82949	−0.211180
$763$	69.5918	2.51939
$764$	91.2956	3.30296
$765$	19.4050	0.701587
$766$	68.8099	2.48620
$767$	21.4333	0.773912
$768$	18.4008	0.663983
$769$	−37.3613	−1.34728	−0.673642	−	0.739058i	$-0.735271\pi$
$769$	−37.3613	−1.34728	−0.673642	+	0.739058i	$0.735271\pi$
$770$	81.2676	2.92868
$771$	8.85507	0.318908
$772$	24.4778	0.880976
$773$	44.7643	1.61006	0.805030	−	0.593234i	$-0.202149\pi$
$773$	44.7643	1.61006	0.805030	+	0.593234i	$0.202149\pi$
$774$	0.312767	0.0112422
$775$	27.9798	1.00507
$776$	50.2936	1.80543
$777$	12.3926	0.444583
$778$	83.5268	2.99458
$779$	45.8200	1.64167
$780$	−25.8036	−0.923915
$781$	−5.63446	−0.201617
$782$	−16.8829	−0.603732
$783$	−32.2237	−1.15158
$784$	110.962	3.96292
$785$	21.6833	0.773911
$786$	−41.9350	−1.49577
$787$	23.9047	0.852111	0.426055	−	0.904697i	$-0.359903\pi$
$787$	23.9047	0.852111	0.426055	+	0.904697i	$0.359903\pi$
$788$	46.3778	1.65214
$789$	7.87216	0.280256
$790$	42.4508	1.51033
$791$	7.32864	0.260576
$792$	123.912	4.40302
$793$	19.1879	0.681381
$794$	−93.9365	−3.33368
$795$	4.47747	0.158799
$796$	−49.2308	−1.74494
$797$	46.3877	1.64314	0.821569	−	0.570110i	$-0.193099\pi$
$797$	46.3877	1.64314	0.821569	+	0.570110i	$0.193099\pi$
$798$	58.5028	2.07098
$799$	−28.7056	−1.01553
$800$	58.3968	2.06464
$801$	42.2686	1.49349
$802$	−46.8354	−1.65382
$803$	89.6169	3.16251
$804$	4.84544	0.170885
$805$	5.99158	0.211175
$806$	−119.423	−4.20651
$807$	−12.6189	−0.444205
$808$	108.933	3.83224
$809$	−53.0694	−1.86582	−0.932911	−	0.360107i	$-0.882740\pi$
$809$	−53.0694	−1.86582	−0.932911	+	0.360107i	$0.882740\pi$
$810$	−17.2799	−0.607153
$811$	−14.7461	−0.517806	−0.258903	−	0.965903i	$-0.583361\pi$
$811$	−14.7461	−0.517806	−0.258903	+	0.965903i	$0.583361\pi$
$812$	−168.755	−5.92214
$813$	6.76726	0.237338
$814$	66.5071	2.33107
$815$	−4.61235	−0.161564
$816$	−55.4917	−1.94260
$817$	0.359550	0.0125791
$818$	−45.9063	−1.60508
$819$	−46.6522	−1.63016
$820$	43.9367	1.53434
$821$	45.9744	1.60452	0.802259	−	0.596977i	$-0.203632\pi$
$821$	45.9744	1.60452	0.802259	+	0.596977i	$0.203632\pi$
$822$	31.2623	1.09040
$823$	40.7736	1.42128	0.710640	−	0.703556i	$-0.248406\pi$
$823$	40.7736	1.42128	0.710640	+	0.703556i	$0.248406\pi$
$824$	−119.356	−4.15795
$825$	−12.2879	−0.427811
$826$	−46.5972	−1.62132
$827$	30.6757	1.06670	0.533349	−	0.845895i	$-0.320933\pi$
$827$	30.6757	1.06670	0.533349	+	0.845895i	$0.320933\pi$
$828$	14.6357	0.508624
$829$	−0.367392	−0.0127601	−0.00638003	−	0.999980i	$-0.502031\pi$
$829$	−0.367392	−0.0127601	−0.00638003	+	0.999980i	$0.502031\pi$
$830$	−16.3045	−0.565939
$831$	−9.83323	−0.341111
$832$	−116.875	−4.05190
$833$	−45.6472	−1.58158
$834$	−19.4882	−0.674820
$835$	−3.19603	−0.110603
$836$	228.206	7.89266
$837$	36.0350	1.24555
$838$	108.972	3.76438
$839$	−31.6726	−1.09346	−0.546730	−	0.837309i	$-0.684128\pi$
$839$	−31.6726	−1.09346	−0.546730	+	0.837309i	$0.684128\pi$
$840$	35.0166	1.20819
$841$	37.5362	1.29435
$842$	33.6430	1.15942
$843$	0.729554	0.0251272
$844$	99.7917	3.43497
$845$	14.4713	0.497829
$846$	34.2362	1.17707
$847$	−77.3015	−2.65611
$848$	61.1225	2.09896
$849$	5.57654	0.191386
$850$	−46.7090	−1.60210
$851$	4.90334	0.168084
$852$	−3.88941	−0.133249
$853$	14.3406	0.491012	0.245506	−	0.969395i	$-0.421046\pi$
$853$	14.3406	0.491012	0.245506	+	0.969395i	$0.421046\pi$
$854$	−41.7154	−1.42747
$855$	−26.6054	−0.909886
$856$	113.093	3.86543
$857$	4.49557	0.153566	0.0767829	−	0.997048i	$-0.475535\pi$
$857$	4.49557	0.153566	0.0767829	+	0.997048i	$0.475535\pi$
$858$	52.4473	1.79052
$859$	−9.90980	−0.338118	−0.169059	−	0.985606i	$-0.554073\pi$
$859$	−9.90980	−0.338118	−0.169059	+	0.985606i	$0.554073\pi$
$860$	0.344772	0.0117566
$861$	−16.6405	−0.567107
$862$	−57.3127	−1.95208
$863$	−16.0842	−0.547513	−0.273757	−	0.961799i	$-0.588266\pi$
$863$	−16.0842	−0.547513	−0.273757	+	0.961799i	$0.588266\pi$
$864$	75.2086	2.55865
$865$	12.8058	0.435409
$866$	10.0188	0.340452
$867$	10.5739	0.359109
$868$	188.714	6.40539
$869$	−62.7154	−2.12748
$870$	−22.1183	−0.749880
$871$	−6.11113	−0.207068
$872$	160.924	5.44957
$873$	13.8778	0.469692
$874$	23.1476	0.782978
$875$	43.5972	1.47385
$876$	61.8618	2.09011
$877$	8.45157	0.285389	0.142695	−	0.989767i	$-0.454423\pi$
$877$	8.45157	0.285389	0.142695	+	0.989767i	$0.454423\pi$
$878$	−84.7644	−2.86066
$879$	15.1427	0.510749
$880$	105.688	3.56275
$881$	49.6172	1.67165	0.835823	−	0.548999i	$-0.184991\pi$
$881$	49.6172	1.67165	0.835823	+	0.548999i	$0.184991\pi$
$882$	54.4420	1.83316
$883$	19.1119	0.643168	0.321584	−	0.946881i	$-0.395785\pi$
$883$	19.1119	0.643168	0.321584	+	0.946881i	$0.395785\pi$
$884$	144.907	4.87375
$885$	−4.43914	−0.149220
$886$	−30.2653	−1.01678
$887$	−47.3752	−1.59070	−0.795352	−	0.606148i	$-0.792714\pi$
$887$	−47.3752	−1.59070	−0.795352	+	0.606148i	$0.792714\pi$
$888$	28.6566	0.961653
$889$	−11.6181	−0.389658
$890$	64.1038	2.14876
$891$	25.5287	0.855245
$892$	11.4572	0.383616
$893$	39.3572	1.31704
$894$	31.3281	1.04777
$895$	27.8456	0.930777
$896$	106.078	3.54381
$897$	3.86676	0.129107
$898$	78.6519	2.62465
$899$	−74.4058	−2.48157
$900$	40.4916	1.34972
$901$	−25.1445	−0.837684
$902$	−89.3041	−2.97350
$903$	−0.130578	−0.00434538
$904$	16.9467	0.563639
$905$	−14.7729	−0.491069
$906$	−22.4969	−0.747409
$907$	8.03047	0.266647	0.133324	−	0.991073i	$-0.457435\pi$
$907$	8.03047	0.266647	0.133324	+	0.991073i	$0.457435\pi$
$908$	−5.20448	−0.172717
$909$	30.0584	0.996975
$910$	−70.7519	−2.34540
$911$	5.38334	0.178358	0.0891790	−	0.996016i	$-0.471576\pi$
$911$	5.38334	0.178358	0.0891790	+	0.996016i	$0.471576\pi$
$912$	76.0826	2.51935
$913$	24.0878	0.797191
$914$	−78.6477	−2.60144
$915$	−3.97408	−0.131379
$916$	−81.3686	−2.68849
$917$	−83.5757	−2.75991
$918$	−60.1560	−1.98544
$919$	−36.8563	−1.21578	−0.607888	−	0.794023i	$-0.707983\pi$
$919$	−36.8563	−1.21578	−0.607888	+	0.794023i	$0.707983\pi$
$920$	13.8549	0.456782
$921$	17.0243	0.560968
$922$	−6.47549	−0.213259
$923$	4.90538	0.161462
$924$	−82.8779	−2.72648
$925$	13.5658	0.446039
$926$	39.0113	1.28199
$927$	−32.9344	−1.08171
$928$	−155.292	−5.09772
$929$	−1.57006	−0.0515119	−0.0257560	−	0.999668i	$-0.508199\pi$
$929$	−1.57006	−0.0515119	−0.0257560	+	0.999668i	$0.508199\pi$
$930$	24.7343	0.811070
$931$	62.5852	2.05115
$932$	−75.5401	−2.47440
$933$	5.60663	0.183553
$934$	5.82807	0.190700
$935$	−43.4778	−1.42188
$936$	−107.878	−3.52611
$937$	22.5931	0.738084	0.369042	−	0.929413i	$-0.379686\pi$
$937$	22.5931	0.738084	0.369042	+	0.929413i	$0.379686\pi$
$938$	13.2859	0.433801
$939$	13.0459	0.425736
$940$	37.7396	1.23093
$941$	−7.16262	−0.233495	−0.116747	−	0.993162i	$-0.537247\pi$
$941$	−7.16262	−0.233495	−0.116747	+	0.993162i	$0.537247\pi$
$942$	−30.4230	−0.991235
$943$	−6.58408	−0.214407
$944$	−60.5994	−1.97234
$945$	21.3487	0.694475
$946$	−0.700771	−0.0227840
$947$	−3.77128	−0.122550	−0.0612751	−	0.998121i	$-0.519517\pi$
$947$	−3.77128	−0.122550	−0.0612751	+	0.998121i	$0.519517\pi$
$948$	−43.2919	−1.40606
$949$	−78.0208	−2.53266
$950$	64.0409	2.07776
$951$	−4.33118	−0.140448
$952$	−196.646	−6.37333
$953$	21.3369	0.691171	0.345585	−	0.938387i	$-0.387680\pi$
$953$	21.3369	0.691171	0.345585	+	0.938387i	$0.387680\pi$
$954$	29.9890	0.970929
$955$	23.8478	0.771696
$956$	22.0697	0.713785
$957$	32.6768	1.05629
$958$	−106.991	−3.45671
$959$	62.3052	2.01194
$960$	24.2064	0.781259
$961$	52.2061	1.68407
$962$	−57.9013	−1.86681
$963$	31.2063	1.00561
$964$	−6.00964	−0.193558
$965$	6.39397	0.205829
$966$	−8.40654	−0.270476
$967$	27.7357	0.891921	0.445960	−	0.895053i	$-0.352862\pi$
$967$	27.7357	0.891921	0.445960	+	0.895053i	$0.352862\pi$
$968$	−178.752	−5.74529
$969$	−31.2987	−1.00546
$970$	21.0468	0.675772
$971$	4.01676	0.128904	0.0644520	−	0.997921i	$-0.479470\pi$
$971$	4.01676	0.128904	0.0644520	+	0.997921i	$0.479470\pi$
$972$	80.6951	2.58830
$973$	−38.8396	−1.24514
$974$	−25.9850	−0.832614
$975$	10.6979	0.342608
$976$	−54.2507	−1.73652
$977$	36.8959	1.18041	0.590203	−	0.807255i	$-0.299048\pi$
$977$	36.8959	1.18041	0.590203	+	0.807255i	$0.299048\pi$
$978$	6.47140	0.206933
$979$	−94.7049	−3.02678
$980$	60.0129	1.91704
$981$	44.4046	1.41773
$982$	−38.4841	−1.22808
$983$	−56.9417	−1.81616	−0.908079	−	0.418799i	$-0.862451\pi$
$983$	−56.9417	−1.81616	−0.908079	+	0.418799i	$0.862451\pi$
$984$	−38.4794	−1.22668
$985$	12.1146	0.386003
$986$	124.211	3.95570
$987$	−14.2934	−0.454965
$988$	−198.677	−6.32075
$989$	−0.0516654	−0.00164287
$990$	51.8545	1.64805
$991$	43.1429	1.37048	0.685240	−	0.728317i	$-0.259697\pi$
$991$	43.1429	1.37048	0.685240	+	0.728317i	$0.259697\pi$
$992$	173.660	5.51370
$993$	3.97970	0.126292
$994$	−10.6646	−0.338259
$995$	−12.8598	−0.407684
$996$	16.6276	0.526866
$997$	4.85642	0.153804	0.0769022	−	0.997039i	$-0.475497\pi$
$997$	4.85642	0.153804	0.0769022	+	0.997039i	$0.475497\pi$
$998$	74.8489	2.36930
$999$	17.4712	0.552764

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8039.2.a.b.1.13	✓	391

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8039.2.a.b.1.13	✓	391	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:	\( N \)	\(=\)	\( 8039 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8039.a (trivial)

\(f(q)\)	\(=\)	\(q-2.70592 q^{2} +0.720832 q^{3} +5.32200 q^{4} +1.39019 q^{5} -1.95051 q^{6} -3.88734 q^{7} -8.98906 q^{8} -2.48040 q^{9} +O(q^{10})\)	\(q-2.70592 q^{2} +0.720832 q^{3} +5.32200 q^{4} +1.39019 q^{5} -1.95051 q^{6} -3.88734 q^{7} -8.98906 q^{8} -2.48040 q^{9} -3.76173 q^{10} +5.55747 q^{11} +3.83627 q^{12} -4.83835 q^{13} +10.5188 q^{14} +1.00209 q^{15} +13.6797 q^{16} -5.62753 q^{17} +6.71177 q^{18} +7.71569 q^{19} +7.39857 q^{20} -2.80212 q^{21} -15.0381 q^{22} -1.10870 q^{23} -6.47961 q^{24} -3.06738 q^{25} +13.0922 q^{26} -3.95045 q^{27} -20.6884 q^{28} +8.15697 q^{29} -2.71158 q^{30} -9.12174 q^{31} -19.0380 q^{32} +4.00600 q^{33} +15.2276 q^{34} -5.40413 q^{35} -13.2007 q^{36} -4.42259 q^{37} -20.8780 q^{38} -3.48764 q^{39} -12.4965 q^{40} +5.93854 q^{41} +7.58231 q^{42} +0.0465999 q^{43} +29.5768 q^{44} -3.44822 q^{45} +3.00006 q^{46} +5.10093 q^{47} +9.86076 q^{48} +8.11142 q^{49} +8.30009 q^{50} -4.05650 q^{51} -25.7497 q^{52} +4.46812 q^{53} +10.6896 q^{54} +7.72592 q^{55} +34.9436 q^{56} +5.56172 q^{57} -22.0721 q^{58} -4.42988 q^{59} +5.33313 q^{60} -3.96578 q^{61} +24.6827 q^{62} +9.64216 q^{63} +24.1559 q^{64} -6.72621 q^{65} -10.8399 q^{66} +1.26306 q^{67} -29.9497 q^{68} -0.799189 q^{69} +14.6231 q^{70} -1.01385 q^{71} +22.2965 q^{72} +16.1255 q^{73} +11.9672 q^{74} -2.21107 q^{75} +41.0629 q^{76} -21.6038 q^{77} +9.43727 q^{78} -11.2849 q^{79} +19.0173 q^{80} +4.59359 q^{81} -16.0692 q^{82} +4.33432 q^{83} -14.9129 q^{84} -7.82331 q^{85} -0.126095 q^{86} +5.87981 q^{87} -49.9564 q^{88} -17.0410 q^{89} +9.33061 q^{90} +18.8083 q^{91} -5.90052 q^{92} -6.57524 q^{93} -13.8027 q^{94} +10.7263 q^{95} -13.7232 q^{96} -5.59497 q^{97} -21.9489 q^{98} -13.7847 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 391 q + 14 q^{2} + 12 q^{3} + 446 q^{4} + 22 q^{5} + 40 q^{6} + 63 q^{7} + 36 q^{8} + 501 q^{9}+O(q^{10}) \) 391 * q + 14 * q^2 + 12 * q^3 + 446 * q^4 + 22 * q^5 + 40 * q^6 + 63 * q^7 + 36 * q^8 + 501 * q^9	\( 391 q + 14 q^{2} + 12 q^{3} + 446 q^{4} + 22 q^{5} + 40 q^{6} + 63 q^{7} + 36 q^{8} + 501 q^{9} + 40 q^{10} + 57 q^{11} + 20 q^{12} + 83 q^{13} + 21 q^{14} + 60 q^{15} + 548 q^{16} + 59 q^{17} + 54 q^{18} + 131 q^{19} + 35 q^{20} + 121 q^{21} + 89 q^{22} + 34 q^{23} + 110 q^{24} + 609 q^{25} + 54 q^{26} + 27 q^{27} + 182 q^{28} + 102 q^{29} + 92 q^{30} + 88 q^{31} + 76 q^{32} + 131 q^{33} + 128 q^{34} + 31 q^{35} + 654 q^{36} + 135 q^{37} + 23 q^{38} + 96 q^{39} + 113 q^{40} + 128 q^{41} + 45 q^{42} + 140 q^{43} + 151 q^{44} + 77 q^{45} + 245 q^{46} + 22 q^{47} + 25 q^{48} + 712 q^{49} + 53 q^{50} + 102 q^{51} + 174 q^{52} + 54 q^{53} + 131 q^{54} + 101 q^{55} + 43 q^{56} + 226 q^{57} + 109 q^{58} + 40 q^{59} + 123 q^{60} + 249 q^{61} + 28 q^{62} + 139 q^{63} + 730 q^{64} + 227 q^{65} + 55 q^{66} + 169 q^{67} + 48 q^{68} + 89 q^{69} + 98 q^{70} + 66 q^{71} + 120 q^{72} + 324 q^{73} + 60 q^{74} + 19 q^{75} + 356 q^{76} + 83 q^{77} - 11 q^{78} + 195 q^{79} + 26 q^{80} + 807 q^{81} + 49 q^{82} + 74 q^{83} + 252 q^{84} + 373 q^{85} + 100 q^{86} + 43 q^{87} + 211 q^{88} + 207 q^{89} + 10 q^{90} + 189 q^{91} + 30 q^{92} + 172 q^{93} + 130 q^{94} + 43 q^{95} + 203 q^{96} + 254 q^{97} + 26 q^{98} + 273 q^{99}+O(q^{100}) \) 391 * q + 14 * q^2 + 12 * q^3 + 446 * q^4 + 22 * q^5 + 40 * q^6 + 63 * q^7 + 36 * q^8 + 501 * q^9 + 40 * q^10 + 57 * q^11 + 20 * q^12 + 83 * q^13 + 21 * q^14 + 60 * q^15 + 548 * q^16 + 59 * q^17 + 54 * q^18 + 131 * q^19 + 35 * q^20 + 121 * q^21 + 89 * q^22 + 34 * q^23 + 110 * q^24 + 609 * q^25 + 54 * q^26 + 27 * q^27 + 182 * q^28 + 102 * q^29 + 92 * q^30 + 88 * q^31 + 76 * q^32 + 131 * q^33 + 128 * q^34 + 31 * q^35 + 654 * q^36 + 135 * q^37 + 23 * q^38 + 96 * q^39 + 113 * q^40 + 128 * q^41 + 45 * q^42 + 140 * q^43 + 151 * q^44 + 77 * q^45 + 245 * q^46 + 22 * q^47 + 25 * q^48 + 712 * q^49 + 53 * q^50 + 102 * q^51 + 174 * q^52 + 54 * q^53 + 131 * q^54 + 101 * q^55 + 43 * q^56 + 226 * q^57 + 109 * q^58 + 40 * q^59 + 123 * q^60 + 249 * q^61 + 28 * q^62 + 139 * q^63 + 730 * q^64 + 227 * q^65 + 55 * q^66 + 169 * q^67 + 48 * q^68 + 89 * q^69 + 98 * q^70 + 66 * q^71 + 120 * q^72 + 324 * q^73 + 60 * q^74 + 19 * q^75 + 356 * q^76 + 83 * q^77 - 11 * q^78 + 195 * q^79 + 26 * q^80 + 807 * q^81 + 49 * q^82 + 74 * q^83 + 252 * q^84 + 373 * q^85 + 100 * q^86 + 43 * q^87 + 211 * q^88 + 207 * q^89 + 10 * q^90 + 189 * q^91 + 30 * q^92 + 172 * q^93 + 130 * q^94 + 43 * q^95 + 203 * q^96 + 254 * q^97 + 26 * q^98 + 273 * q^99

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