LMFDB - Embedded newform 8043.2.a.r.1.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8043,2,Mod(1,8043)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8043, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("8043.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8043 = 3 \cdot 7 \cdot 383 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8043.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:	$64.2236783457$
Analytic rank:	$1$
Dimension:	$46$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.19
Character	$\chi$	$=$	8043.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.522616 q^{2} -1.00000 q^{3} -1.72687 q^{4} -3.91798 q^{5} +0.522616 q^{6} -1.00000 q^{7} +1.94772 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.522616 q^{2} -1.00000 q^{3} -1.72687 q^{4} -3.91798 q^{5} +0.522616 q^{6} -1.00000 q^{7} +1.94772 q^{8} +1.00000 q^{9} +2.04760 q^{10} +5.06020 q^{11} +1.72687 q^{12} -2.90745 q^{13} +0.522616 q^{14} +3.91798 q^{15} +2.43583 q^{16} -3.73170 q^{17} -0.522616 q^{18} -2.13519 q^{19} +6.76585 q^{20} +1.00000 q^{21} -2.64454 q^{22} -6.84734 q^{23} -1.94772 q^{24} +10.3506 q^{25} +1.51948 q^{26} -1.00000 q^{27} +1.72687 q^{28} -1.32068 q^{29} -2.04760 q^{30} -3.43709 q^{31} -5.16845 q^{32} -5.06020 q^{33} +1.95025 q^{34} +3.91798 q^{35} -1.72687 q^{36} -1.67340 q^{37} +1.11588 q^{38} +2.90745 q^{39} -7.63114 q^{40} -1.31501 q^{41} -0.522616 q^{42} +1.56836 q^{43} -8.73832 q^{44} -3.91798 q^{45} +3.57853 q^{46} -4.61729 q^{47} -2.43583 q^{48} +1.00000 q^{49} -5.40937 q^{50} +3.73170 q^{51} +5.02080 q^{52} +9.18603 q^{53} +0.522616 q^{54} -19.8258 q^{55} -1.94772 q^{56} +2.13519 q^{57} +0.690207 q^{58} +4.42834 q^{59} -6.76585 q^{60} -3.23345 q^{61} +1.79628 q^{62} -1.00000 q^{63} -2.17055 q^{64} +11.3913 q^{65} +2.64454 q^{66} +12.4145 q^{67} +6.44417 q^{68} +6.84734 q^{69} -2.04760 q^{70} +14.8285 q^{71} +1.94772 q^{72} -3.50179 q^{73} +0.874545 q^{74} -10.3506 q^{75} +3.68720 q^{76} -5.06020 q^{77} -1.51948 q^{78} -0.125892 q^{79} -9.54354 q^{80} +1.00000 q^{81} +0.687245 q^{82} +10.2768 q^{83} -1.72687 q^{84} +14.6207 q^{85} -0.819651 q^{86} +1.32068 q^{87} +9.85587 q^{88} +6.62296 q^{89} +2.04760 q^{90} +2.90745 q^{91} +11.8245 q^{92} +3.43709 q^{93} +2.41307 q^{94} +8.36562 q^{95} +5.16845 q^{96} +12.6670 q^{97} -0.522616 q^{98} +5.06020 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 46 q + 3 q^{2} - 46 q^{3} + 45 q^{4} - 9 q^{5} - 3 q^{6} - 46 q^{7} + 6 q^{8} + 46 q^{9}+O(q^{10}) $ 46 * q + 3 * q^2 - 46 * q^3 + 45 * q^4 - 9 * q^5 - 3 * q^6 - 46 * q^7 + 6 * q^8 + 46 * q^9	\( 46 q + 3 q^{2} - 46 q^{3} + 45 q^{4} - 9 q^{5} - 3 q^{6} - 46 q^{7} + 6 q^{8} + 46 q^{9} - 10 q^{10} + 31 q^{11} - 45 q^{12} - 32 q^{13} - 3 q^{14} + 9 q^{15} + 43 q^{16} - 36 q^{17} + 3 q^{18} - 13 q^{19} - 19 q^{20} + 46 q^{21} - 13 q^{22} + 24 q^{23} - 6 q^{24} + 35 q^{25} - 11 q^{26} - 46 q^{27} - 45 q^{28} + 11 q^{29} + 10 q^{30} - 23 q^{31} + 5 q^{32} - 31 q^{33} - 35 q^{34} + 9 q^{35} + 45 q^{36} - 37 q^{37} - 32 q^{38} + 32 q^{39} - 28 q^{40} - 27 q^{41} + 3 q^{42} - 7 q^{43} + 46 q^{44} - 9 q^{45} + 16 q^{46} - 18 q^{47} - 43 q^{48} + 46 q^{49} + 10 q^{50} + 36 q^{51} - 62 q^{52} - 62 q^{53} - 3 q^{54} - 28 q^{55} - 6 q^{56} + 13 q^{57} - 36 q^{58} - 3 q^{59} + 19 q^{60} - 31 q^{61} - 41 q^{62} - 46 q^{63} + 42 q^{64} + 2 q^{65} + 13 q^{66} - 9 q^{67} - 70 q^{68} - 24 q^{69} + 10 q^{70} + 77 q^{71} + 6 q^{72} - 38 q^{73} + 14 q^{74} - 35 q^{75} - 41 q^{76} - 31 q^{77} + 11 q^{78} + 8 q^{79} - 59 q^{80} + 46 q^{81} - 53 q^{82} - 38 q^{83} + 45 q^{84} - 26 q^{85} + 37 q^{86} - 11 q^{87} - 26 q^{88} - 39 q^{89} - 10 q^{90} + 32 q^{91} + 2 q^{92} + 23 q^{93} - 55 q^{94} + 35 q^{95} - 5 q^{96} - 61 q^{97} + 3 q^{98} + 31 q^{99}+O(q^{100}) \) 46 * q + 3 * q^2 - 46 * q^3 + 45 * q^4 - 9 * q^5 - 3 * q^6 - 46 * q^7 + 6 * q^8 + 46 * q^9 - 10 * q^10 + 31 * q^11 - 45 * q^12 - 32 * q^13 - 3 * q^14 + 9 * q^15 + 43 * q^16 - 36 * q^17 + 3 * q^18 - 13 * q^19 - 19 * q^20 + 46 * q^21 - 13 * q^22 + 24 * q^23 - 6 * q^24 + 35 * q^25 - 11 * q^26 - 46 * q^27 - 45 * q^28 + 11 * q^29 + 10 * q^30 - 23 * q^31 + 5 * q^32 - 31 * q^33 - 35 * q^34 + 9 * q^35 + 45 * q^36 - 37 * q^37 - 32 * q^38 + 32 * q^39 - 28 * q^40 - 27 * q^41 + 3 * q^42 - 7 * q^43 + 46 * q^44 - 9 * q^45 + 16 * q^46 - 18 * q^47 - 43 * q^48 + 46 * q^49 + 10 * q^50 + 36 * q^51 - 62 * q^52 - 62 * q^53 - 3 * q^54 - 28 * q^55 - 6 * q^56 + 13 * q^57 - 36 * q^58 - 3 * q^59 + 19 * q^60 - 31 * q^61 - 41 * q^62 - 46 * q^63 + 42 * q^64 + 2 * q^65 + 13 * q^66 - 9 * q^67 - 70 * q^68 - 24 * q^69 + 10 * q^70 + 77 * q^71 + 6 * q^72 - 38 * q^73 + 14 * q^74 - 35 * q^75 - 41 * q^76 - 31 * q^77 + 11 * q^78 + 8 * q^79 - 59 * q^80 + 46 * q^81 - 53 * q^82 - 38 * q^83 + 45 * q^84 - 26 * q^85 + 37 * q^86 - 11 * q^87 - 26 * q^88 - 39 * q^89 - 10 * q^90 + 32 * q^91 + 2 * q^92 + 23 * q^93 - 55 * q^94 + 35 * q^95 - 5 * q^96 - 61 * q^97 + 3 * q^98 + 31 * 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 $

$2$	−0.522616	−0.369545	−0.184773	−	0.982781i	$-0.559155\pi$
$2$	−0.522616	−0.369545	−0.184773	+	0.982781i	$0.559155\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.72687	−0.863436
$5$	−3.91798	−1.75217	−0.876087	−	0.482154i	$-0.839855\pi$
$5$	−3.91798	−1.75217	−0.876087	+	0.482154i	$0.839855\pi$
$6$	0.522616	0.213357
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	1.94772	0.688624
$9$	1.00000	0.333333
$10$	2.04760	0.647508
$11$	5.06020	1.52571	0.762854	−	0.646571i	$-0.223798\pi$
$11$	5.06020	1.52571	0.762854	+	0.646571i	$0.223798\pi$
$12$	1.72687	0.498505
$13$	−2.90745	−0.806383	−0.403191	−	0.915116i	$-0.632099\pi$
$13$	−2.90745	−0.806383	−0.403191	+	0.915116i	$0.632099\pi$
$14$	0.522616	0.139675
$15$	3.91798	1.01162
$16$	2.43583	0.608958
$17$	−3.73170	−0.905070	−0.452535	−	0.891747i	$-0.649480\pi$
$17$	−3.73170	−0.905070	−0.452535	+	0.891747i	$0.649480\pi$
$18$	−0.522616	−0.123182
$19$	−2.13519	−0.489846	−0.244923	−	0.969543i	$-0.578763\pi$
$19$	−2.13519	−0.489846	−0.244923	+	0.969543i	$0.578763\pi$
$20$	6.76585	1.51289
$21$	1.00000	0.218218
$22$	−2.64454	−0.563818
$23$	−6.84734	−1.42777	−0.713885	−	0.700263i	$-0.753066\pi$
$23$	−6.84734	−1.42777	−0.713885	+	0.700263i	$0.753066\pi$
$24$	−1.94772	−0.397577
$25$	10.3506	2.07011
$26$	1.51948	0.297995
$27$	−1.00000	−0.192450
$28$	1.72687	0.326348
$29$	−1.32068	−0.245244	−0.122622	−	0.992453i	$-0.539130\pi$
$29$	−1.32068	−0.245244	−0.122622	+	0.992453i	$0.539130\pi$
$30$	−2.04760	−0.373839
$31$	−3.43709	−0.617319	−0.308660	−	0.951173i	$-0.599880\pi$
$31$	−3.43709	−0.617319	−0.308660	+	0.951173i	$0.599880\pi$
$32$	−5.16845	−0.913662
$33$	−5.06020	−0.880868
$34$	1.95025	0.334465
$35$	3.91798	0.662259
$36$	−1.72687	−0.287812
$37$	−1.67340	−0.275105	−0.137553	−	0.990494i	$-0.543924\pi$
$37$	−1.67340	−0.275105	−0.137553	+	0.990494i	$0.543924\pi$
$38$	1.11588	0.181020
$39$	2.90745	0.465565
$40$	−7.63114	−1.20659
$41$	−1.31501	−0.205370	−0.102685	−	0.994714i	$-0.532743\pi$
$41$	−1.31501	−0.205370	−0.102685	+	0.994714i	$0.532743\pi$
$42$	−0.522616	−0.0806414
$43$	1.56836	0.239173	0.119586	−	0.992824i	$-0.461843\pi$
$43$	1.56836	0.239173	0.119586	+	0.992824i	$0.461843\pi$
$44$	−8.73832	−1.31735
$45$	−3.91798	−0.584058
$46$	3.57853	0.527626
$47$	−4.61729	−0.673501	−0.336751	−	0.941594i	$-0.609328\pi$
$47$	−4.61729	−0.673501	−0.336751	+	0.941594i	$0.609328\pi$
$48$	−2.43583	−0.351582
$49$	1.00000	0.142857
$50$	−5.40937	−0.765000
$51$	3.73170	0.522543
$52$	5.02080	0.696260
$53$	9.18603	1.26180	0.630899	−	0.775865i	$-0.282686\pi$
$53$	9.18603	1.26180	0.630899	+	0.775865i	$0.282686\pi$
$54$	0.522616	0.0711191
$55$	−19.8258	−2.67330
$56$	−1.94772	−0.260276
$57$	2.13519	0.282813
$58$	0.690207	0.0906287
$59$	4.42834	0.576521	0.288260	−	0.957552i	$-0.406923\pi$
$59$	4.42834	0.576521	0.288260	+	0.957552i	$0.406923\pi$
$60$	−6.76585	−0.873467
$61$	−3.23345	−0.414001	−0.207000	−	0.978341i	$-0.566370\pi$
$61$	−3.23345	−0.414001	−0.207000	+	0.978341i	$0.566370\pi$
$62$	1.79628	0.228127
$63$	−1.00000	−0.125988
$64$	−2.17055	−0.271318
$65$	11.3913	1.41292
$66$	2.64454	0.325521
$67$	12.4145	1.51667	0.758335	−	0.651865i	$-0.226013\pi$
$67$	12.4145	1.51667	0.758335	+	0.651865i	$0.226013\pi$
$68$	6.44417	0.781471
$69$	6.84734	0.824323
$70$	−2.04760	−0.244735
$71$	14.8285	1.75982	0.879909	−	0.475143i	$-0.157604\pi$
$71$	14.8285	1.75982	0.879909	+	0.475143i	$0.157604\pi$
$72$	1.94772	0.229541
$73$	−3.50179	−0.409853	−0.204927	−	0.978777i	$-0.565696\pi$
$73$	−3.50179	−0.409853	−0.204927	+	0.978777i	$0.565696\pi$
$74$	0.874545	0.101664
$75$	−10.3506	−1.19518
$76$	3.68720	0.422951
$77$	−5.06020	−0.576663
$78$	−1.51948	−0.172048
$79$	−0.125892	−0.0141639	−0.00708196	−	0.999975i	$-0.502254\pi$
$79$	−0.125892	−0.0141639	−0.00708196	+	0.999975i	$0.502254\pi$
$80$	−9.54354	−1.06700
$81$	1.00000	0.111111
$82$	0.687245	0.0758935
$83$	10.2768	1.12802	0.564011	−	0.825768i	$-0.309258\pi$
$83$	10.2768	1.12802	0.564011	+	0.825768i	$0.309258\pi$
$84$	−1.72687	−0.188417
$85$	14.6207	1.58584
$86$	−0.819651	−0.0883852
$87$	1.32068	0.141591
$88$	9.85587	1.05064
$89$	6.62296	0.702032	0.351016	−	0.936369i	$-0.385836\pi$
$89$	6.62296	0.702032	0.351016	+	0.936369i	$0.385836\pi$
$90$	2.04760	0.215836
$91$	2.90745	0.304784
$92$	11.8245	1.23279
$93$	3.43709	0.356409
$94$	2.41307	0.248889
$95$	8.36562	0.858295
$96$	5.16845	0.527503
$97$	12.6670	1.28614	0.643071	−	0.765806i	$-0.277660\pi$
$97$	12.6670	1.28614	0.643071	+	0.765806i	$0.277660\pi$
$98$	−0.522616	−0.0527922
$99$	5.06020	0.508569
$100$	−17.8741	−1.78741
$101$	−7.90921	−0.786996	−0.393498	−	0.919325i	$-0.628735\pi$
$101$	−7.90921	−0.786996	−0.393498	+	0.919325i	$0.628735\pi$
$102$	−1.95025	−0.193103
$103$	−1.75102	−0.172533	−0.0862667	−	0.996272i	$-0.527494\pi$
$103$	−1.75102	−0.172533	−0.0862667	+	0.996272i	$0.527494\pi$
$104$	−5.66292	−0.555295
$105$	−3.91798	−0.382356
$106$	−4.80077	−0.466292
$107$	0.345104	0.0333625	0.0166812	−	0.999861i	$-0.494690\pi$
$107$	0.345104	0.0333625	0.0166812	+	0.999861i	$0.494690\pi$
$108$	1.72687	0.166168
$109$	−5.35166	−0.512596	−0.256298	−	0.966598i	$-0.582503\pi$
$109$	−5.35166	−0.512596	−0.256298	+	0.966598i	$0.582503\pi$
$110$	10.3613	0.987908
$111$	1.67340	0.158832
$112$	−2.43583	−0.230165
$113$	3.31368	0.311725	0.155862	−	0.987779i	$-0.450184\pi$
$113$	3.31368	0.311725	0.155862	+	0.987779i	$0.450184\pi$
$114$	−1.11588	−0.104512
$115$	26.8277	2.50170
$116$	2.28064	0.211752
$117$	−2.90745	−0.268794
$118$	−2.31432	−0.213051
$119$	3.73170	0.342084
$120$	7.63114	0.696625
$121$	14.6056	1.32778
$122$	1.68985	0.152992
$123$	1.31501	0.118570
$124$	5.93541	0.533016
$125$	−20.9634	−1.87502
$126$	0.522616	0.0465584
$127$	1.43398	0.127246	0.0636228	−	0.997974i	$-0.479735\pi$
$127$	1.43398	0.127246	0.0636228	+	0.997974i	$0.479735\pi$
$128$	11.4713	1.01393
$129$	−1.56836	−0.138087
$130$	−5.95330	−0.522139
$131$	12.8065	1.11891	0.559456	−	0.828860i	$-0.311010\pi$
$131$	12.8065	1.11891	0.559456	+	0.828860i	$0.311010\pi$
$132$	8.73832	0.760573
$133$	2.13519	0.185144
$134$	−6.48801	−0.560478
$135$	3.91798	0.337206
$136$	−7.26832	−0.623254
$137$	3.93807	0.336452	0.168226	−	0.985748i	$-0.446196\pi$
$137$	3.93807	0.336452	0.168226	+	0.985748i	$0.446196\pi$
$138$	−3.57853	−0.304625
$139$	10.1300	0.859211	0.429606	−	0.903017i	$-0.358653\pi$
$139$	10.1300	0.859211	0.429606	+	0.903017i	$0.358653\pi$
$140$	−6.76585	−0.571819
$141$	4.61729	0.388846
$142$	−7.74961	−0.650333
$143$	−14.7123	−1.23030
$144$	2.43583	0.202986
$145$	5.17439	0.429709
$146$	1.83009	0.151459
$147$	−1.00000	−0.0824786
$148$	2.88975	0.237536
$149$	−2.73317	−0.223910	−0.111955	−	0.993713i	$-0.535711\pi$
$149$	−2.73317	−0.223910	−0.111955	+	0.993713i	$0.535711\pi$
$150$	5.40937	0.441673
$151$	−7.66598	−0.623849	−0.311924	−	0.950107i	$-0.600974\pi$
$151$	−7.66598	−0.623849	−0.311924	+	0.950107i	$0.600974\pi$
$152$	−4.15876	−0.337320
$153$	−3.73170	−0.301690
$154$	2.64454	0.213103
$155$	13.4664	1.08165
$156$	−5.02080	−0.401986
$157$	0.625999	0.0499601	0.0249801	−	0.999688i	$-0.492048\pi$
$157$	0.625999	0.0499601	0.0249801	+	0.999688i	$0.492048\pi$
$158$	0.0657931	0.00523422
$159$	−9.18603	−0.728499
$160$	20.2499	1.60089
$161$	6.84734	0.539646
$162$	−0.522616	−0.0410606
$163$	−10.7251	−0.840057	−0.420028	−	0.907511i	$-0.637980\pi$
$163$	−10.7251	−0.840057	−0.420028	+	0.907511i	$0.637980\pi$
$164$	2.27085	0.177324
$165$	19.8258	1.54343
$166$	−5.37080	−0.416855
$167$	−17.9301	−1.38748	−0.693738	−	0.720228i	$-0.744037\pi$
$167$	−17.9301	−1.38748	−0.693738	+	0.720228i	$0.744037\pi$
$168$	1.94772	0.150270
$169$	−4.54671	−0.349747
$170$	−7.64103	−0.586040
$171$	−2.13519	−0.163282
$172$	−2.70836	−0.206510
$173$	−6.83836	−0.519911	−0.259955	−	0.965621i	$-0.583708\pi$
$173$	−6.83836	−0.519911	−0.259955	+	0.965621i	$0.583708\pi$
$174$	−0.690207	−0.0523245
$175$	−10.3506	−0.782429
$176$	12.3258	0.929092
$177$	−4.42834	−0.332854
$178$	−3.46127	−0.259433
$179$	−1.66792	−0.124666	−0.0623331	−	0.998055i	$-0.519854\pi$
$179$	−1.66792	−0.124666	−0.0623331	+	0.998055i	$0.519854\pi$
$180$	6.76585	0.504297
$181$	16.1304	1.19897	0.599483	−	0.800387i	$-0.295373\pi$
$181$	16.1304	1.19897	0.599483	+	0.800387i	$0.295373\pi$
$182$	−1.51948	−0.112632
$183$	3.23345	0.239023
$184$	−13.3367	−0.983197
$185$	6.55634	0.482032
$186$	−1.79628	−0.131709
$187$	−18.8832	−1.38087
$188$	7.97347	0.581525
$189$	1.00000	0.0727393
$190$	−4.37201	−0.317179
$191$	6.02003	0.435594	0.217797	−	0.975994i	$-0.430113\pi$
$191$	6.02003	0.435594	0.217797	+	0.975994i	$0.430113\pi$
$192$	2.17055	0.156646
$193$	23.8946	1.71997	0.859986	−	0.510318i	$-0.170472\pi$
$193$	23.8946	1.71997	0.859986	+	0.510318i	$0.170472\pi$
$194$	−6.62000	−0.475288
$195$	−11.3913	−0.815751
$196$	−1.72687	−0.123348
$197$	−26.3934	−1.88045	−0.940227	−	0.340549i	$-0.889387\pi$
$197$	−26.3934	−1.88045	−0.940227	+	0.340549i	$0.889387\pi$
$198$	−2.64454	−0.187939
$199$	1.79317	0.127114	0.0635572	−	0.997978i	$-0.479755\pi$
$199$	1.79317	0.127114	0.0635572	+	0.997978i	$0.479755\pi$
$200$	20.1600	1.42553
$201$	−12.4145	−0.875650
$202$	4.13348	0.290831
$203$	1.32068	0.0926934
$204$	−6.44417	−0.451182
$205$	5.15217	0.359843
$206$	0.915113	0.0637590
$207$	−6.84734	−0.475923
$208$	−7.08207	−0.491053
$209$	−10.8045	−0.747362
$210$	2.04760	0.141298
$211$	−8.79540	−0.605500	−0.302750	−	0.953070i	$-0.597905\pi$
$211$	−8.79540	−0.605500	−0.302750	+	0.953070i	$0.597905\pi$
$212$	−15.8631	−1.08948
$213$	−14.8285	−1.01603
$214$	−0.180357	−0.0123290
$215$	−6.14481	−0.419072
$216$	−1.94772	−0.132526
$217$	3.43709	0.233325
$218$	2.79687	0.189428
$219$	3.50179	0.236629
$220$	34.2366	2.30823
$221$	10.8498	0.729833
$222$	−0.874545	−0.0586956
$223$	−17.5896	−1.17789	−0.588945	−	0.808173i	$-0.700456\pi$
$223$	−17.5896	−1.17789	−0.588945	+	0.808173i	$0.700456\pi$
$224$	5.16845	0.345332
$225$	10.3506	0.690037
$226$	−1.73178	−0.115196
$227$	19.3501	1.28431	0.642156	−	0.766574i	$-0.278040\pi$
$227$	19.3501	1.28431	0.642156	+	0.766574i	$0.278040\pi$
$228$	−3.68720	−0.244191
$229$	23.5690	1.55748	0.778741	−	0.627345i	$-0.215859\pi$
$229$	23.5690	1.55748	0.778741	+	0.627345i	$0.215859\pi$
$230$	−14.0206	−0.924492
$231$	5.06020	0.332937
$232$	−2.57231	−0.168881
$233$	20.6141	1.35048	0.675239	−	0.737599i	$-0.264041\pi$
$233$	20.6141	1.35048	0.675239	+	0.737599i	$0.264041\pi$
$234$	1.51948	0.0993317
$235$	18.0905	1.18009
$236$	−7.64718	−0.497789
$237$	0.125892	0.00817755
$238$	−1.95025	−0.126416
$239$	−11.6304	−0.752310	−0.376155	−	0.926557i	$-0.622754\pi$
$239$	−11.6304	−0.752310	−0.376155	+	0.926557i	$0.622754\pi$
$240$	9.54354	0.616033
$241$	25.4063	1.63656	0.818280	−	0.574819i	$-0.194928\pi$
$241$	25.4063	1.63656	0.818280	+	0.574819i	$0.194928\pi$
$242$	−7.63314	−0.490677
$243$	−1.00000	−0.0641500
$244$	5.58375	0.357463
$245$	−3.91798	−0.250310
$246$	−0.687245	−0.0438171
$247$	6.20796	0.395003
$248$	−6.69450	−0.425101
$249$	−10.2768	−0.651263
$250$	10.9558	0.692906
$251$	−8.92987	−0.563648	−0.281824	−	0.959466i	$-0.590939\pi$
$251$	−8.92987	−0.563648	−0.281824	+	0.959466i	$0.590939\pi$
$252$	1.72687	0.108783
$253$	−34.6489	−2.17836
$254$	−0.749424	−0.0470230
$255$	−14.6207	−0.915585
$256$	−1.65398	−0.103374
$257$	12.6448	0.788764	0.394382	−	0.918947i	$-0.370959\pi$
$257$	12.6448	0.788764	0.394382	+	0.918947i	$0.370959\pi$
$258$	0.819651	0.0510292
$259$	1.67340	0.103980
$260$	−19.6714	−1.21997
$261$	−1.32068	−0.0817479
$262$	−6.69290	−0.413489
$263$	10.2109	0.629633	0.314817	−	0.949153i	$-0.398057\pi$
$263$	10.2109	0.629633	0.314817	+	0.949153i	$0.398057\pi$
$264$	−9.85587	−0.606587
$265$	−35.9907	−2.21089
$266$	−1.11588	−0.0684193
$267$	−6.62296	−0.405319
$268$	−21.4382	−1.30955
$269$	−10.3988	−0.634026	−0.317013	−	0.948421i	$-0.602680\pi$
$269$	−10.3988	−0.634026	−0.317013	+	0.948421i	$0.602680\pi$
$270$	−2.04760	−0.124613
$271$	−22.3788	−1.35942	−0.679708	−	0.733483i	$-0.737893\pi$
$271$	−22.3788	−1.35942	−0.679708	+	0.733483i	$0.737893\pi$
$272$	−9.08980	−0.551150
$273$	−2.90745	−0.175967
$274$	−2.05810	−0.124334
$275$	52.3759	3.15839
$276$	−11.8245	−0.711750
$277$	−12.8518	−0.772191	−0.386096	−	0.922459i	$-0.626177\pi$
$277$	−12.8518	−0.772191	−0.386096	+	0.922459i	$0.626177\pi$
$278$	−5.29408	−0.317518
$279$	−3.43709	−0.205773
$280$	7.63114	0.456048
$281$	2.16812	0.129339	0.0646696	−	0.997907i	$-0.479401\pi$
$281$	2.16812	0.129339	0.0646696	+	0.997907i	$0.479401\pi$
$282$	−2.41307	−0.143696
$283$	5.46827	0.325055	0.162528	−	0.986704i	$-0.448035\pi$
$283$	5.46827	0.325055	0.162528	+	0.986704i	$0.448035\pi$
$284$	−25.6069	−1.51949
$285$	−8.36562	−0.495537
$286$	7.68889	0.454653
$287$	1.31501	0.0776225
$288$	−5.16845	−0.304554
$289$	−3.07441	−0.180847
$290$	−2.70422	−0.158797
$291$	−12.6670	−0.742555
$292$	6.04714	0.353882
$293$	−2.84688	−0.166316	−0.0831582	−	0.996536i	$-0.526501\pi$
$293$	−2.84688	−0.166316	−0.0831582	+	0.996536i	$0.526501\pi$
$294$	0.522616	0.0304796
$295$	−17.3501	−1.01016
$296$	−3.25932	−0.189444
$297$	−5.06020	−0.293623
$298$	1.42840	0.0827449
$299$	19.9083	1.15133
$300$	17.8741	1.03196
$301$	−1.56836	−0.0903988
$302$	4.00637	0.230540
$303$	7.90921	0.454372
$304$	−5.20096	−0.298296
$305$	12.6686	0.725401
$306$	1.95025	0.111488
$307$	−5.06325	−0.288975	−0.144487	−	0.989507i	$-0.546153\pi$
$307$	−5.06325	−0.288975	−0.144487	+	0.989507i	$0.546153\pi$
$308$	8.73832	0.497912
$309$	1.75102	0.0996123
$310$	−7.03778	−0.399719
$311$	26.6242	1.50972	0.754859	−	0.655887i	$-0.227705\pi$
$311$	26.6242	1.50972	0.754859	+	0.655887i	$0.227705\pi$
$312$	5.66292	0.320600
$313$	−23.7295	−1.34127	−0.670634	−	0.741788i	$-0.733978\pi$
$313$	−23.7295	−1.34127	−0.670634	+	0.741788i	$0.733978\pi$
$314$	−0.327157	−0.0184625
$315$	3.91798	0.220753
$316$	0.217399	0.0122296
$317$	18.2125	1.02292	0.511459	−	0.859307i	$-0.329105\pi$
$317$	18.2125	1.02292	0.511459	+	0.859307i	$0.329105\pi$
$318$	4.80077	0.269214
$319$	−6.68289	−0.374170
$320$	8.50416	0.475397
$321$	−0.345104	−0.0192618
$322$	−3.57853	−0.199424
$323$	7.96789	0.443345
$324$	−1.72687	−0.0959373
$325$	−30.0938	−1.66930
$326$	5.60512	0.310439
$327$	5.35166	0.295948
$328$	−2.56127	−0.141423
$329$	4.61729	0.254560
$330$	−10.3613	−0.570369
$331$	−1.16774	−0.0641846	−0.0320923	−	0.999485i	$-0.510217\pi$
$331$	−1.16774	−0.0641846	−0.0320923	+	0.999485i	$0.510217\pi$
$332$	−17.7467	−0.973974
$333$	−1.67340	−0.0917017
$334$	9.37058	0.512735
$335$	−48.6397	−2.65747
$336$	2.43583	0.132886
$337$	4.65545	0.253599	0.126799	−	0.991928i	$-0.459530\pi$
$337$	4.65545	0.253599	0.126799	+	0.991928i	$0.459530\pi$
$338$	2.37618	0.129247
$339$	−3.31368	−0.179974
$340$	−25.2481	−1.36927
$341$	−17.3923	−0.941849
$342$	1.11588	0.0603401
$343$	−1.00000	−0.0539949
$344$	3.05473	0.164700
$345$	−26.8277	−1.44436
$346$	3.57384	0.192131
$347$	−11.5940	−0.622399	−0.311199	−	0.950345i	$-0.600731\pi$
$347$	−11.5940	−0.622399	−0.311199	+	0.950345i	$0.600731\pi$
$348$	−2.28064	−0.122255
$349$	−12.2280	−0.654549	−0.327275	−	0.944929i	$-0.606130\pi$
$349$	−12.2280	−0.654549	−0.327275	+	0.944929i	$0.606130\pi$
$350$	5.40937	0.289143
$351$	2.90745	0.155188
$352$	−26.1534	−1.39398
$353$	8.96621	0.477223	0.238611	−	0.971115i	$-0.423308\pi$
$353$	8.96621	0.477223	0.238611	+	0.971115i	$0.423308\pi$
$354$	2.31432	0.123005
$355$	−58.0977	−3.08351
$356$	−11.4370	−0.606160
$357$	−3.73170	−0.197503
$358$	0.871682	0.0460698
$359$	−1.08402	−0.0572122	−0.0286061	−	0.999591i	$-0.509107\pi$
$359$	−1.08402	−0.0572122	−0.0286061	+	0.999591i	$0.509107\pi$
$360$	−7.63114	−0.402196
$361$	−14.4410	−0.760051
$362$	−8.43003	−0.443073
$363$	−14.6056	−0.766597
$364$	−5.02080	−0.263162
$365$	13.7199	0.718134
$366$	−1.68985	−0.0883300
$367$	−2.25177	−0.117542	−0.0587708	−	0.998272i	$-0.518718\pi$
$367$	−2.25177	−0.117542	−0.0587708	+	0.998272i	$0.518718\pi$
$368$	−16.6790	−0.869452
$369$	−1.31501	−0.0684566
$370$	−3.42645	−0.178133
$371$	−9.18603	−0.476915
$372$	−5.93541	−0.307737
$373$	16.6581	0.862526	0.431263	−	0.902226i	$-0.358068\pi$
$373$	16.6581	0.862526	0.431263	+	0.902226i	$0.358068\pi$
$374$	9.86864	0.510295
$375$	20.9634	1.08254
$376$	−8.99321	−0.463789
$377$	3.83981	0.197760
$378$	−0.522616	−0.0268805
$379$	−0.771933	−0.0396515	−0.0198258	−	0.999803i	$-0.506311\pi$
$379$	−0.771933	−0.0396515	−0.0198258	+	0.999803i	$0.506311\pi$
$380$	−14.4464	−0.741083
$381$	−1.43398	−0.0734653
$382$	−3.14616	−0.160972
$383$	−1.00000	−0.0510976
$383$	−1.00000	−0.0510976
$384$	−11.4713	−0.585391
$385$	19.8258	1.01041
$386$	−12.4877	−0.635608
$387$	1.56836	0.0797243
$388$	−21.8743	−1.11050
$389$	1.09289	0.0554116	0.0277058	−	0.999616i	$-0.491180\pi$
$389$	1.09289	0.0554116	0.0277058	+	0.999616i	$0.491180\pi$
$390$	5.95330	0.301457
$391$	25.5522	1.29223
$392$	1.94772	0.0983749
$393$	−12.8065	−0.646004
$394$	13.7936	0.694913
$395$	0.493241	0.0248177
$396$	−8.73832	−0.439117
$397$	−32.4635	−1.62930	−0.814648	−	0.579955i	$-0.803070\pi$
$397$	−32.4635	−1.62930	−0.814648	+	0.579955i	$0.803070\pi$
$398$	−0.937140	−0.0469746
$399$	−2.13519	−0.106893
$400$	25.2122	1.26061
$401$	−5.49953	−0.274634	−0.137317	−	0.990527i	$-0.543848\pi$
$401$	−5.49953	−0.274634	−0.137317	+	0.990527i	$0.543848\pi$
$402$	6.48801	0.323592
$403$	9.99317	0.497795
$404$	13.6582	0.679521
$405$	−3.91798	−0.194686
$406$	−0.690207	−0.0342544
$407$	−8.46773	−0.419730
$408$	7.26832	0.359836
$409$	−6.93784	−0.343054	−0.171527	−	0.985179i	$-0.554870\pi$
$409$	−6.93784	−0.343054	−0.171527	+	0.985179i	$0.554870\pi$
$410$	−2.69261	−0.132979
$411$	−3.93807	−0.194251
$412$	3.02379	0.148972
$413$	−4.42834	−0.217904
$414$	3.57853	0.175875
$415$	−40.2641	−1.97649
$416$	15.0270	0.736761
$417$	−10.1300	−0.496066
$418$	5.64660	0.276184
$419$	6.72677	0.328624	0.164312	−	0.986408i	$-0.447460\pi$
$419$	6.72677	0.328624	0.164312	+	0.986408i	$0.447460\pi$
$420$	6.76585	0.330140
$421$	−1.50420	−0.0733103	−0.0366551	−	0.999328i	$-0.511670\pi$
$421$	−1.50420	−0.0733103	−0.0366551	+	0.999328i	$0.511670\pi$
$422$	4.59662	0.223760
$423$	−4.61729	−0.224500
$424$	17.8918	0.868905
$425$	−38.6252	−1.87360
$426$	7.74961	0.375470
$427$	3.23345	0.156478
$428$	−0.595951	−0.0288064
$429$	14.7123	0.710317
$430$	3.21138	0.154866
$431$	26.0726	1.25587	0.627936	−	0.778265i	$-0.283900\pi$
$431$	26.0726	1.25587	0.627936	+	0.778265i	$0.283900\pi$
$432$	−2.43583	−0.117194
$433$	−28.3791	−1.36381	−0.681905	−	0.731440i	$-0.738848\pi$
$433$	−28.3791	−1.36381	−0.681905	+	0.731440i	$0.738848\pi$
$434$	−1.79628	−0.0862241
$435$	−5.17439	−0.248093
$436$	9.24164	0.442594
$437$	14.6204	0.699387
$438$	−1.83009	−0.0874451
$439$	−34.0986	−1.62744	−0.813718	−	0.581260i	$-0.802560\pi$
$439$	−34.0986	−1.62744	−0.813718	+	0.581260i	$0.802560\pi$
$440$	−38.6151	−1.84090
$441$	1.00000	0.0476190
$442$	−5.67026	−0.269707
$443$	22.6748	1.07731	0.538657	−	0.842525i	$-0.318932\pi$
$443$	22.6748	1.07731	0.538657	+	0.842525i	$0.318932\pi$
$444$	−2.88975	−0.137141
$445$	−25.9486	−1.23008
$446$	9.19263	0.435284
$447$	2.73317	0.129275
$448$	2.17055	0.102549
$449$	22.2061	1.04797	0.523984	−	0.851728i	$-0.324445\pi$
$449$	22.2061	1.04797	0.523984	+	0.851728i	$0.324445\pi$
$450$	−5.40937	−0.255000
$451$	−6.65421	−0.313334
$452$	−5.72230	−0.269154
$453$	7.66598	0.360179
$454$	−10.1127	−0.474611
$455$	−11.3913	−0.534034
$456$	4.15876	0.194752
$457$	−17.5286	−0.819955	−0.409977	−	0.912096i	$-0.634463\pi$
$457$	−17.5286	−0.819955	−0.409977	+	0.912096i	$0.634463\pi$
$458$	−12.3175	−0.575560
$459$	3.73170	0.174181
$460$	−46.3281	−2.16006
$461$	20.7277	0.965383	0.482692	−	0.875790i	$-0.339659\pi$
$461$	20.7277	0.965383	0.482692	+	0.875790i	$0.339659\pi$
$462$	−2.64454	−0.123035
$463$	1.15629	0.0537375	0.0268687	−	0.999639i	$-0.491446\pi$
$463$	1.15629	0.0537375	0.0268687	+	0.999639i	$0.491446\pi$
$464$	−3.21695	−0.149343
$465$	−13.4664	−0.624491
$466$	−10.7733	−0.499063
$467$	−20.4617	−0.946853	−0.473427	−	0.880833i	$-0.656983\pi$
$467$	−20.4617	−0.946853	−0.473427	+	0.880833i	$0.656983\pi$
$468$	5.02080	0.232087
$469$	−12.4145	−0.573247
$470$	−9.45436	−0.436097
$471$	−0.625999	−0.0288445
$472$	8.62518	0.397006
$473$	7.93622	0.364908
$474$	−0.0657931	−0.00302198
$475$	−22.1004	−1.01404
$476$	−6.44417	−0.295368
$477$	9.18603	0.420599
$478$	6.07825	0.278013
$479$	−18.8831	−0.862791	−0.431396	−	0.902163i	$-0.641979\pi$
$479$	−18.8831	−0.862791	−0.431396	+	0.902163i	$0.641979\pi$
$480$	−20.2499	−0.924277
$481$	4.86533	0.221840
$482$	−13.2777	−0.604784
$483$	−6.84734	−0.311565
$484$	−25.2221	−1.14646
$485$	−49.6292	−2.25354
$486$	0.522616	0.0237064
$487$	−2.09905	−0.0951168	−0.0475584	−	0.998868i	$-0.515144\pi$
$487$	−2.09905	−0.0951168	−0.0475584	+	0.998868i	$0.515144\pi$
$488$	−6.29787	−0.285091
$489$	10.7251	0.485007
$490$	2.04760	0.0925011
$491$	24.3268	1.09785	0.548926	−	0.835871i	$-0.315037\pi$
$491$	24.3268	1.09785	0.548926	+	0.835871i	$0.315037\pi$
$492$	−2.27085	−0.102378
$493$	4.92837	0.221963
$494$	−3.24438	−0.145972
$495$	−19.8258	−0.891102
$496$	−8.37217	−0.375921
$497$	−14.8285	−0.665148
$498$	5.37080	0.240671
$499$	−34.4363	−1.54158	−0.770790	−	0.637089i	$-0.780138\pi$
$499$	−34.4363	−1.54158	−0.770790	+	0.637089i	$0.780138\pi$
$500$	36.2011	1.61896
$501$	17.9301	0.801059
$502$	4.66689	0.208294
$503$	−24.9099	−1.11068	−0.555339	−	0.831624i	$-0.687412\pi$
$503$	−24.9099	−1.11068	−0.555339	+	0.831624i	$0.687412\pi$
$504$	−1.94772	−0.0867585
$505$	30.9881	1.37895
$506$	18.1081	0.805003
$507$	4.54671	0.201926
$508$	−2.47631	−0.109868
$509$	15.0563	0.667361	0.333680	−	0.942686i	$-0.391709\pi$
$509$	15.0563	0.667361	0.333680	+	0.942686i	$0.391709\pi$
$510$	7.64103	0.338350
$511$	3.50179	0.154910
$512$	−22.0781	−0.975725
$513$	2.13519	0.0942709
$514$	−6.60840	−0.291484
$515$	6.86047	0.302309
$516$	2.70836	0.119229
$517$	−23.3644	−1.02757
$518$	−0.874545	−0.0384253
$519$	6.83836	0.300170
$520$	22.1872	0.972973
$521$	41.2062	1.80528	0.902639	−	0.430399i	$-0.141627\pi$
$521$	41.2062	1.80528	0.902639	+	0.430399i	$0.141627\pi$
$522$	0.690207	0.0302096
$523$	−41.9818	−1.83574	−0.917868	−	0.396886i	$-0.870091\pi$
$523$	−41.9818	−1.83574	−0.917868	+	0.396886i	$0.870091\pi$
$524$	−22.1152	−0.966109
$525$	10.3506	0.451735
$526$	−5.33640	−0.232678
$527$	12.8262	0.558717
$528$	−12.3258	−0.536412
$529$	23.8861	1.03853
$530$	18.8093	0.817024
$531$	4.42834	0.192174
$532$	−3.68720	−0.159860
$533$	3.82333	0.165607
$534$	3.46127	0.149784
$535$	−1.35211	−0.0584569
$536$	24.1800	1.04442
$537$	1.66792	0.0719760
$538$	5.43458	0.234302
$539$	5.06020	0.217958
$540$	−6.76585	−0.291156
$541$	37.5773	1.61557	0.807787	−	0.589474i	$-0.200665\pi$
$541$	37.5773	1.61557	0.807787	+	0.589474i	$0.200665\pi$
$542$	11.6955	0.502366
$543$	−16.1304	−0.692224
$544$	19.2871	0.826929
$545$	20.9677	0.898158
$546$	1.51948	0.0650279
$547$	−12.9353	−0.553074	−0.276537	−	0.961003i	$-0.589187\pi$
$547$	−12.9353	−0.553074	−0.276537	+	0.961003i	$0.589187\pi$
$548$	−6.80055	−0.290505
$549$	−3.23345	−0.138000
$550$	−27.3725	−1.16717
$551$	2.81990	0.120132
$552$	13.3367	0.567649
$553$	0.125892	0.00535346
$554$	6.71657	0.285360
$555$	−6.55634	−0.278301
$556$	−17.4931	−0.741874
$557$	8.66380	0.367097	0.183549	−	0.983011i	$-0.441242\pi$
$557$	8.66380	0.367097	0.183549	+	0.983011i	$0.441242\pi$
$558$	1.79628	0.0760425
$559$	−4.55994	−0.192865
$560$	9.54354	0.403288
$561$	18.8832	0.797247
$562$	−1.13309	−0.0477967
$563$	16.5552	0.697721	0.348860	−	0.937175i	$-0.386569\pi$
$563$	16.5552	0.697721	0.348860	+	0.937175i	$0.386569\pi$
$564$	−7.97347	−0.335744
$565$	−12.9829	−0.546195
$566$	−2.85781	−0.120123
$567$	−1.00000	−0.0419961
$568$	28.8818	1.21185
$569$	−8.19472	−0.343541	−0.171770	−	0.985137i	$-0.554949\pi$
$569$	−8.19472	−0.343541	−0.171770	+	0.985137i	$0.554949\pi$
$570$	4.37201	0.183123
$571$	−22.4994	−0.941571	−0.470785	−	0.882248i	$-0.656029\pi$
$571$	−22.4994	−0.941571	−0.470785	+	0.882248i	$0.656029\pi$
$572$	25.4063	1.06229
$573$	−6.02003	−0.251490
$574$	−0.687245	−0.0286850
$575$	−70.8738	−2.95564
$576$	−2.17055	−0.0904395
$577$	−14.8600	−0.618631	−0.309315	−	0.950960i	$-0.600100\pi$
$577$	−14.8600	−0.618631	−0.309315	+	0.950960i	$0.600100\pi$
$578$	1.60673	0.0668314
$579$	−23.8946	−0.993026
$580$	−8.93550	−0.371027
$581$	−10.2768	−0.426352
$582$	6.62000	0.274408
$583$	46.4831	1.92514
$584$	−6.82051	−0.282235
$585$	11.3913	0.470974
$586$	1.48783	0.0614615
$587$	−37.6154	−1.55255	−0.776277	−	0.630391i	$-0.782894\pi$
$587$	−37.6154	−1.55255	−0.776277	+	0.630391i	$0.782894\pi$
$588$	1.72687	0.0712150
$589$	7.33883	0.302391
$590$	9.06747	0.373302
$591$	26.3934	1.08568
$592$	−4.07612	−0.167527
$593$	−18.4269	−0.756702	−0.378351	−	0.925662i	$-0.623509\pi$
$593$	−18.4269	−0.756702	−0.378351	+	0.925662i	$0.623509\pi$
$594$	2.64454	0.108507
$595$	−14.6207	−0.599391
$596$	4.71984	0.193332
$597$	−1.79317	−0.0733896
$598$	−10.4044	−0.425468
$599$	8.62074	0.352234	0.176117	−	0.984369i	$-0.443646\pi$
$599$	8.62074	0.352234	0.176117	+	0.984369i	$0.443646\pi$
$600$	−20.1600	−0.823030
$601$	41.0430	1.67418	0.837090	−	0.547065i	$-0.184255\pi$
$601$	41.0430	1.67418	0.837090	+	0.547065i	$0.184255\pi$
$602$	0.819651	0.0334065
$603$	12.4145	0.505557
$604$	13.2382	0.538653
$605$	−57.2246	−2.32651
$606$	−4.13348	−0.167911
$607$	−24.4106	−0.990795	−0.495398	−	0.868666i	$-0.664978\pi$
$607$	−24.4106	−0.990795	−0.495398	+	0.868666i	$0.664978\pi$
$608$	11.0356	0.447554
$609$	−1.32068	−0.0535165
$610$	−6.62081	−0.268069
$611$	13.4246	0.543100
$612$	6.44417	0.260490
$613$	−29.8616	−1.20610	−0.603049	−	0.797704i	$-0.706048\pi$
$613$	−29.8616	−1.20610	−0.603049	+	0.797704i	$0.706048\pi$
$614$	2.64614	0.106789
$615$	−5.15217	−0.207756
$616$	−9.85587	−0.397104
$617$	−29.5284	−1.18877	−0.594384	−	0.804181i	$-0.702604\pi$
$617$	−29.5284	−1.18877	−0.594384	+	0.804181i	$0.702604\pi$
$618$	−0.915113	−0.0368113
$619$	42.2400	1.69777	0.848885	−	0.528578i	$-0.177275\pi$
$619$	42.2400	1.69777	0.848885	+	0.528578i	$0.177275\pi$
$620$	−23.2548	−0.933936
$621$	6.84734	0.274774
$622$	−13.9142	−0.557909
$623$	−6.62296	−0.265343
$624$	7.08207	0.283510
$625$	30.3813	1.21525
$626$	12.4014	0.495660
$627$	10.8045	0.431489
$628$	−1.08102	−0.0431374
$629$	6.24462	0.248989
$630$	−2.04760	−0.0815783
$631$	−6.54216	−0.260439	−0.130220	−	0.991485i	$-0.541568\pi$
$631$	−6.54216	−0.260439	−0.130220	+	0.991485i	$0.541568\pi$
$632$	−0.245202	−0.00975363
$633$	8.79540	0.349586
$634$	−9.51817	−0.378015
$635$	−5.61832	−0.222956
$636$	15.8631	0.629013
$637$	−2.90745	−0.115198
$638$	3.49259	0.138273
$639$	14.8285	0.586606
$640$	−44.9442	−1.77658
$641$	−9.14187	−0.361082	−0.180541	−	0.983567i	$-0.557785\pi$
$641$	−9.14187	−0.361082	−0.180541	+	0.983567i	$0.557785\pi$
$642$	0.180357	0.00711812
$643$	−23.8218	−0.939439	−0.469720	−	0.882816i	$-0.655645\pi$
$643$	−23.8218	−0.939439	−0.469720	+	0.882816i	$0.655645\pi$
$644$	−11.8245	−0.465950
$645$	6.14481	0.241952
$646$	−4.16415	−0.163836
$647$	26.6368	1.04720	0.523601	−	0.851964i	$-0.324588\pi$
$647$	26.6368	1.04720	0.523601	+	0.851964i	$0.324588\pi$
$648$	1.94772	0.0765138
$649$	22.4083	0.879602
$650$	15.7275	0.616883
$651$	−3.43709	−0.134710
$652$	18.5209	0.725335
$653$	27.3670	1.07095	0.535477	−	0.844550i	$-0.320132\pi$
$653$	27.3670	1.07095	0.535477	+	0.844550i	$0.320132\pi$
$654$	−2.79687	−0.109366
$655$	−50.1757	−1.96053
$656$	−3.20314	−0.125062
$657$	−3.50179	−0.136618
$658$	−2.41307	−0.0940713
$659$	14.1905	0.552785	0.276392	−	0.961045i	$-0.410861\pi$
$659$	14.1905	0.552785	0.276392	+	0.961045i	$0.410861\pi$
$660$	−34.2366	−1.33266
$661$	49.5470	1.92716	0.963578	−	0.267426i	$-0.0861732\pi$
$661$	49.5470	1.92716	0.963578	+	0.267426i	$0.0861732\pi$
$662$	0.610278	0.0237191
$663$	−10.8498	−0.421369
$664$	20.0163	0.776783
$665$	−8.36562	−0.324405
$666$	0.874545	0.0338879
$667$	9.04313	0.350151
$668$	30.9630	1.19800
$669$	17.5896	0.680055
$670$	25.4199	0.982056
$671$	−16.3619	−0.631644
$672$	−5.16845	−0.199377
$673$	−29.7227	−1.14573	−0.572863	−	0.819651i	$-0.694167\pi$
$673$	−29.7227	−1.14573	−0.572863	+	0.819651i	$0.694167\pi$
$674$	−2.43302	−0.0937163
$675$	−10.3506	−0.398393
$676$	7.85159	0.301984
$677$	50.6074	1.94500	0.972501	−	0.232900i	$-0.0748215\pi$
$677$	50.6074	1.94500	0.972501	+	0.232900i	$0.0748215\pi$
$678$	1.73178	0.0665087
$679$	−12.6670	−0.486116
$680$	28.4771	1.09205
$681$	−19.3501	−0.741498
$682$	9.08952	0.348056
$683$	−42.2097	−1.61511	−0.807555	−	0.589793i	$-0.799210\pi$
$683$	−42.2097	−1.61511	−0.807555	+	0.589793i	$0.799210\pi$
$684$	3.68720	0.140984
$685$	−15.4293	−0.589522
$686$	0.522616	0.0199536
$687$	−23.5690	−0.899213
$688$	3.82027	0.145646
$689$	−26.7080	−1.01749
$690$	14.0206	0.533756
$691$	17.9858	0.684212	0.342106	−	0.939661i	$-0.388860\pi$
$691$	17.9858	0.684212	0.342106	+	0.939661i	$0.388860\pi$
$692$	11.8090	0.448910
$693$	−5.06020	−0.192221
$694$	6.05922	0.230005
$695$	−39.6889	−1.50549
$696$	2.57231	0.0975033
$697$	4.90722	0.185874
$698$	6.39055	0.241886
$699$	−20.6141	−0.779699
$700$	17.8741	0.675577
$701$	8.18440	0.309120	0.154560	−	0.987983i	$-0.450604\pi$
$701$	8.18440	0.309120	0.154560	+	0.987983i	$0.450604\pi$
$702$	−1.51948	−0.0573492
$703$	3.57302	0.134759
$704$	−10.9834	−0.413953
$705$	−18.0905	−0.681326
$706$	−4.68588	−0.176356
$707$	7.90921	0.297457
$708$	7.64718	0.287399
$709$	28.4666	1.06909	0.534543	−	0.845141i	$-0.320484\pi$
$709$	28.4666	1.06909	0.534543	+	0.845141i	$0.320484\pi$
$710$	30.3628	1.13950
$711$	−0.125892	−0.00472131
$712$	12.8997	0.483437
$713$	23.5349	0.881389
$714$	1.95025	0.0729862
$715$	57.6425	2.15571
$716$	2.88028	0.107641
$717$	11.6304	0.434346
$718$	0.566525	0.0211425
$719$	−3.70021	−0.137994	−0.0689972	−	0.997617i	$-0.521980\pi$
$719$	−3.70021	−0.137994	−0.0689972	+	0.997617i	$0.521980\pi$
$720$	−9.54354	−0.355667
$721$	1.75102	0.0652115
$722$	7.54708	0.280873
$723$	−25.4063	−0.944869
$724$	−27.8552	−1.03523
$725$	−13.6697	−0.507682
$726$	7.63314	0.283292
$727$	−16.1585	−0.599284	−0.299642	−	0.954052i	$-0.596867\pi$
$727$	−16.1585	−0.599284	−0.299642	+	0.954052i	$0.596867\pi$
$728$	5.66292	0.209882
$729$	1.00000	0.0370370
$730$	−7.17025	−0.265383
$731$	−5.85266	−0.216468
$732$	−5.58375	−0.206381
$733$	−53.8123	−1.98760	−0.993801	−	0.111172i	$-0.964539\pi$
$733$	−53.8123	−1.98760	−0.993801	+	0.111172i	$0.964539\pi$
$734$	1.17681	0.0434370
$735$	3.91798	0.144517
$736$	35.3902	1.30450
$737$	62.8198	2.31400
$738$	0.687245	0.0252978
$739$	−31.2298	−1.14881	−0.574403	−	0.818573i	$-0.694766\pi$
$739$	−31.2298	−1.14881	−0.574403	+	0.818573i	$0.694766\pi$
$740$	−11.3220	−0.416204
$741$	−6.20796	−0.228055
$742$	4.80077	0.176242
$743$	24.6070	0.902742	0.451371	−	0.892336i	$-0.350935\pi$
$743$	24.6070	0.902742	0.451371	+	0.892336i	$0.350935\pi$
$744$	6.69450	0.245432
$745$	10.7085	0.392329
$746$	−8.70581	−0.318742
$747$	10.2768	0.376007
$748$	32.6088	1.19230
$749$	−0.345104	−0.0126098
$750$	−10.9558	−0.400049
$751$	33.4013	1.21883	0.609416	−	0.792851i	$-0.291404\pi$
$751$	33.4013	1.21883	0.609416	+	0.792851i	$0.291404\pi$
$752$	−11.2470	−0.410134
$753$	8.92987	0.325422
$754$	−2.00675	−0.0730814
$755$	30.0351	1.09309
$756$	−1.72687	−0.0628057
$757$	−34.7787	−1.26405	−0.632027	−	0.774946i	$-0.717777\pi$
$757$	−34.7787	−1.26405	−0.632027	+	0.774946i	$0.717777\pi$
$758$	0.403424	0.0146530
$759$	34.6489	1.25768
$760$	16.2939	0.591043
$761$	52.8082	1.91430	0.957148	−	0.289598i	$-0.0935216\pi$
$761$	52.8082	1.91430	0.957148	+	0.289598i	$0.0935216\pi$
$762$	0.749424	0.0271488
$763$	5.35166	0.193743
$764$	−10.3958	−0.376108
$765$	14.6207	0.528613
$766$	0.522616	0.0188829
$767$	−12.8752	−0.464896
$768$	1.65398	0.0596827
$769$	23.5633	0.849715	0.424858	−	0.905260i	$-0.360324\pi$
$769$	23.5633	0.849715	0.424858	+	0.905260i	$0.360324\pi$
$770$	−10.3613	−0.373394
$771$	−12.6448	−0.455393
$772$	−41.2629	−1.48509
$773$	27.6555	0.994700	0.497350	−	0.867550i	$-0.334307\pi$
$773$	27.6555	0.994700	0.497350	+	0.867550i	$0.334307\pi$
$774$	−0.819651	−0.0294617
$775$	−35.5758	−1.27792
$776$	24.6719	0.885669
$777$	−1.67340	−0.0600329
$778$	−0.571161	−0.0204771
$779$	2.80779	0.100600
$780$	19.6714	0.704349
$781$	75.0351	2.68497
$782$	−13.3540	−0.477539
$783$	1.32068	0.0471972
$784$	2.43583	0.0869940
$785$	−2.45265	−0.0875388
$786$	6.69290	0.238728
$787$	−38.0197	−1.35526	−0.677629	−	0.735404i	$-0.736992\pi$
$787$	−38.0197	−1.35526	−0.677629	+	0.735404i	$0.736992\pi$
$788$	45.5781	1.62365
$789$	−10.2109	−0.363519
$790$	−0.257776	−0.00917125
$791$	−3.31368	−0.117821
$792$	9.85587	0.350213
$793$	9.40111	0.333843
$794$	16.9660	0.602099
$795$	35.9907	1.27646
$796$	−3.09658	−0.109755
$797$	29.4370	1.04271	0.521355	−	0.853340i	$-0.325427\pi$
$797$	29.4370	1.04271	0.521355	+	0.853340i	$0.325427\pi$
$798$	1.11588	0.0395019
$799$	17.2304	0.609566
$800$	−53.4964	−1.89138
$801$	6.62296	0.234011
$802$	2.87415	0.101490
$803$	−17.7197	−0.625316
$804$	21.4382	0.756068
$805$	−26.8277	−0.945554
$806$	−5.22259	−0.183958
$807$	10.3988	0.366055
$808$	−15.4050	−0.541945
$809$	−22.6246	−0.795437	−0.397719	−	0.917507i	$-0.630198\pi$
$809$	−22.6246	−0.795437	−0.397719	+	0.917507i	$0.630198\pi$
$810$	2.04760	0.0719453
$811$	23.7364	0.833496	0.416748	−	0.909022i	$-0.363170\pi$
$811$	23.7364	0.833496	0.416748	+	0.909022i	$0.363170\pi$
$812$	−2.28064	−0.0800348
$813$	22.3788	0.784859
$814$	4.42538	0.155109
$815$	42.0208	1.47192
$816$	9.08980	0.318207
$817$	−3.34875	−0.117158
$818$	3.62583	0.126774
$819$	2.90745	0.101595
$820$	−8.89715	−0.310702
$821$	−28.6197	−0.998833	−0.499416	−	0.866362i	$-0.666452\pi$
$821$	−28.6197	−0.998833	−0.499416	+	0.866362i	$0.666452\pi$
$822$	2.05810	0.0717845
$823$	−14.0684	−0.490393	−0.245196	−	0.969473i	$-0.578852\pi$
$823$	−14.0684	−0.490393	−0.245196	+	0.969473i	$0.578852\pi$
$824$	−3.41051	−0.118811
$825$	−52.3759	−1.82349
$826$	2.31432	0.0805256
$827$	−46.6589	−1.62249	−0.811244	−	0.584707i	$-0.801209\pi$
$827$	−46.6589	−1.62249	−0.811244	+	0.584707i	$0.801209\pi$
$828$	11.8245	0.410929
$829$	−4.35424	−0.151229	−0.0756145	−	0.997137i	$-0.524092\pi$
$829$	−4.35424	−0.151229	−0.0756145	+	0.997137i	$0.524092\pi$
$830$	21.0427	0.730402
$831$	12.8518	0.445825
$832$	6.31077	0.218786
$833$	−3.73170	−0.129296
$834$	5.29408	0.183319
$835$	70.2499	2.43110
$836$	18.6580	0.645299
$837$	3.43709	0.118803
$838$	−3.51552	−0.121442
$839$	33.5739	1.15910	0.579550	−	0.814937i	$-0.303228\pi$
$839$	33.5739	1.15910	0.579550	+	0.814937i	$0.303228\pi$
$840$	−7.63114	−0.263299
$841$	−27.2558	−0.939856
$842$	0.786120	0.0270915
$843$	−2.16812	−0.0746740
$844$	15.1885	0.522811
$845$	17.8139	0.612817
$846$	2.41307	0.0829631
$847$	−14.6056	−0.501855
$848$	22.3756	0.768382
$849$	−5.46827	−0.187671
$850$	20.1862	0.692379
$851$	11.4583	0.392787
$852$	25.6069	0.877278
$853$	26.8405	0.919001	0.459501	−	0.888177i	$-0.348028\pi$
$853$	26.8405	0.919001	0.459501	+	0.888177i	$0.348028\pi$
$854$	−1.68985	−0.0578256
$855$	8.36562	0.286098
$856$	0.672168	0.0229742
$857$	20.4189	0.697497	0.348749	−	0.937216i	$-0.386607\pi$
$857$	20.4189	0.697497	0.348749	+	0.937216i	$0.386607\pi$
$858$	−7.68889	−0.262494
$859$	−39.5525	−1.34951	−0.674757	−	0.738040i	$-0.735752\pi$
$859$	−39.5525	−1.34951	−0.674757	+	0.738040i	$0.735752\pi$
$860$	10.6113	0.361842
$861$	−1.31501	−0.0448154
$862$	−13.6260	−0.464102
$863$	−44.7918	−1.52473	−0.762366	−	0.647146i	$-0.775962\pi$
$863$	−44.7918	−1.52473	−0.762366	+	0.647146i	$0.775962\pi$
$864$	5.16845	0.175834
$865$	26.7925	0.910973
$866$	14.8314	0.503990
$867$	3.07441	0.104412
$868$	−5.93541	−0.201461
$869$	−0.637038	−0.0216100
$870$	2.70422	0.0916816
$871$	−36.0945	−1.22302
$872$	−10.4236	−0.352986
$873$	12.6670	0.428714
$874$	−7.64084	−0.258455
$875$	20.9634	0.708691
$876$	−6.04714	−0.204314
$877$	−31.8008	−1.07384	−0.536918	−	0.843635i	$-0.680411\pi$
$877$	−31.8008	−1.07384	−0.536918	+	0.843635i	$0.680411\pi$
$878$	17.8205	0.601411
$879$	2.84688	0.0960229
$880$	−48.2922	−1.62793
$881$	−17.8583	−0.601660	−0.300830	−	0.953678i	$-0.597264\pi$
$881$	−17.8583	−0.601660	−0.300830	+	0.953678i	$0.597264\pi$
$882$	−0.522616	−0.0175974
$883$	−22.7842	−0.766748	−0.383374	−	0.923593i	$-0.625238\pi$
$883$	−22.7842	−0.766748	−0.383374	+	0.923593i	$0.625238\pi$
$884$	−18.7361	−0.630164
$885$	17.3501	0.583219
$886$	−11.8502	−0.398116
$887$	41.2205	1.38405	0.692025	−	0.721873i	$-0.256719\pi$
$887$	41.2205	1.38405	0.692025	+	0.721873i	$0.256719\pi$
$888$	3.25932	0.109376
$889$	−1.43398	−0.0480943
$890$	13.5612	0.454571
$891$	5.06020	0.169523
$892$	30.3751	1.01703
$893$	9.85879	0.329912
$894$	−1.42840	−0.0477728
$895$	6.53487	0.218437
$896$	−11.4713	−0.383228
$897$	−19.9083	−0.664720
$898$	−11.6052	−0.387272
$899$	4.53928	0.151394
$900$	−17.8741	−0.595803
$901$	−34.2795	−1.14202
$902$	3.47760	0.115791
$903$	1.56836	0.0521918
$904$	6.45413	0.214661
$905$	−63.1987	−2.10080
$906$	−4.00637	−0.133103
$907$	38.6119	1.28209	0.641044	−	0.767504i	$-0.278502\pi$
$907$	38.6119	1.28209	0.641044	+	0.767504i	$0.278502\pi$
$908$	−33.4152	−1.10892
$909$	−7.90921	−0.262332
$910$	5.95330	0.197350
$911$	−11.1993	−0.371049	−0.185525	−	0.982640i	$-0.559398\pi$
$911$	−11.1993	−0.371049	−0.185525	+	0.982640i	$0.559398\pi$
$912$	5.20096	0.172221
$913$	52.0025	1.72103
$914$	9.16075	0.303011
$915$	−12.6686	−0.418811
$916$	−40.7006	−1.34479
$917$	−12.8065	−0.422909
$918$	−1.95025	−0.0643678
$919$	−22.7675	−0.751031	−0.375515	−	0.926816i	$-0.622534\pi$
$919$	−22.7675	−0.751031	−0.375515	+	0.926816i	$0.622534\pi$
$920$	52.2530	1.72273
$921$	5.06325	0.166840
$922$	−10.8326	−0.356753
$923$	−43.1131	−1.41909
$924$	−8.73832	−0.287470
$925$	−17.3206	−0.569498
$926$	−0.604297	−0.0198584
$927$	−1.75102	−0.0575112
$928$	6.82586	0.224070
$929$	−22.9593	−0.753270	−0.376635	−	0.926362i	$-0.622919\pi$
$929$	−22.9593	−0.753270	−0.376635	+	0.926362i	$0.622919\pi$
$930$	7.03778	0.230778
$931$	−2.13519	−0.0699780
$932$	−35.5980	−1.16605
$933$	−26.6242	−0.871636
$934$	10.6936	0.349905
$935$	73.9838	2.41953
$936$	−5.66292	−0.185098
$937$	6.64022	0.216927	0.108463	−	0.994100i	$-0.465407\pi$
$937$	6.64022	0.216927	0.108463	+	0.994100i	$0.465407\pi$
$938$	6.48801	0.211841
$939$	23.7295	0.774382
$940$	−31.2399	−1.01893
$941$	−35.8841	−1.16979	−0.584893	−	0.811110i	$-0.698864\pi$
$941$	−35.8841	−1.16979	−0.584893	+	0.811110i	$0.698864\pi$
$942$	0.327157	0.0106594
$943$	9.00431	0.293221
$944$	10.7867	0.351077
$945$	−3.91798	−0.127452
$946$	−4.14760	−0.134850
$947$	−41.9778	−1.36409	−0.682047	−	0.731309i	$-0.738910\pi$
$947$	−41.9778	−1.36409	−0.682047	+	0.731309i	$0.738910\pi$
$948$	−0.217399	−0.00706079
$949$	10.1813	0.330498
$950$	11.5500	0.374732
$951$	−18.2125	−0.590582
$952$	7.26832	0.235568
$953$	−24.4005	−0.790410	−0.395205	−	0.918593i	$-0.629326\pi$
$953$	−24.4005	−0.790410	−0.395205	+	0.918593i	$0.629326\pi$
$954$	−4.80077	−0.155431
$955$	−23.5863	−0.763236
$956$	20.0843	0.649571
$957$	6.68289	0.216027
$958$	9.86862	0.318841
$959$	−3.93807	−0.127167
$960$	−8.50416	−0.274471
$961$	−19.1864	−0.618917
$962$	−2.54270	−0.0819800
$963$	0.345104	0.0111208
$964$	−43.8734	−1.41307
$965$	−93.6186	−3.01369
$966$	3.57853	0.115137
$967$	−7.46183	−0.239956	−0.119978	−	0.992777i	$-0.538282\pi$
$967$	−7.46183	−0.239956	−0.119978	+	0.992777i	$0.538282\pi$
$968$	28.4477	0.914345
$969$	−7.96789	−0.255965
$970$	25.9370	0.832787
$971$	−1.31480	−0.0421940	−0.0210970	−	0.999777i	$-0.506716\pi$
$971$	−1.31480	−0.0421940	−0.0210970	+	0.999777i	$0.506716\pi$
$972$	1.72687	0.0553895
$973$	−10.1300	−0.324751
$974$	1.09700	0.0351500
$975$	30.0938	0.963772
$976$	−7.87614	−0.252109
$977$	−53.1797	−1.70137	−0.850685	−	0.525675i	$-0.823813\pi$
$977$	−53.1797	−1.70137	−0.850685	+	0.525675i	$0.823813\pi$
$978$	−5.60512	−0.179232
$979$	33.5135	1.07110
$980$	6.76585	0.216127
$981$	−5.35166	−0.170865
$982$	−12.7136	−0.405707
$983$	−2.88831	−0.0921228	−0.0460614	−	0.998939i	$-0.514667\pi$
$983$	−2.88831	−0.0921228	−0.0460614	+	0.998939i	$0.514667\pi$
$984$	2.56127	0.0816504
$985$	103.409	3.29488
$986$	−2.57565	−0.0820253
$987$	−4.61729	−0.146970
$988$	−10.7204	−0.341060
$989$	−10.7391	−0.341484
$990$	10.3613	0.329303
$991$	28.2291	0.896727	0.448363	−	0.893851i	$-0.352007\pi$
$991$	28.2291	0.896727	0.448363	+	0.893851i	$0.352007\pi$
$992$	17.7644	0.564021
$993$	1.16774	0.0370570
$994$	7.74961	0.245803
$995$	−7.02560	−0.222727
$996$	17.7467	0.562324
$997$	−1.70466	−0.0539871	−0.0269935	−	0.999636i	$-0.508593\pi$
$997$	−1.70466	−0.0539871	−0.0269935	+	0.999636i	$0.508593\pi$
$998$	17.9970	0.569684
$999$	1.67340	0.0529440

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8043.2.a.r.1.19	✓	46

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8043.2.a.r.1.19	✓	46	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:	\( N \)	\(=\)	\( 8043 = 3 \cdot 7 \cdot 383 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8043.a (trivial)

\(f(q)\)	\(=\)	\(q-0.522616 q^{2} -1.00000 q^{3} -1.72687 q^{4} -3.91798 q^{5} +0.522616 q^{6} -1.00000 q^{7} +1.94772 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.522616 q^{2} -1.00000 q^{3} -1.72687 q^{4} -3.91798 q^{5} +0.522616 q^{6} -1.00000 q^{7} +1.94772 q^{8} +1.00000 q^{9} +2.04760 q^{10} +5.06020 q^{11} +1.72687 q^{12} -2.90745 q^{13} +0.522616 q^{14} +3.91798 q^{15} +2.43583 q^{16} -3.73170 q^{17} -0.522616 q^{18} -2.13519 q^{19} +6.76585 q^{20} +1.00000 q^{21} -2.64454 q^{22} -6.84734 q^{23} -1.94772 q^{24} +10.3506 q^{25} +1.51948 q^{26} -1.00000 q^{27} +1.72687 q^{28} -1.32068 q^{29} -2.04760 q^{30} -3.43709 q^{31} -5.16845 q^{32} -5.06020 q^{33} +1.95025 q^{34} +3.91798 q^{35} -1.72687 q^{36} -1.67340 q^{37} +1.11588 q^{38} +2.90745 q^{39} -7.63114 q^{40} -1.31501 q^{41} -0.522616 q^{42} +1.56836 q^{43} -8.73832 q^{44} -3.91798 q^{45} +3.57853 q^{46} -4.61729 q^{47} -2.43583 q^{48} +1.00000 q^{49} -5.40937 q^{50} +3.73170 q^{51} +5.02080 q^{52} +9.18603 q^{53} +0.522616 q^{54} -19.8258 q^{55} -1.94772 q^{56} +2.13519 q^{57} +0.690207 q^{58} +4.42834 q^{59} -6.76585 q^{60} -3.23345 q^{61} +1.79628 q^{62} -1.00000 q^{63} -2.17055 q^{64} +11.3913 q^{65} +2.64454 q^{66} +12.4145 q^{67} +6.44417 q^{68} +6.84734 q^{69} -2.04760 q^{70} +14.8285 q^{71} +1.94772 q^{72} -3.50179 q^{73} +0.874545 q^{74} -10.3506 q^{75} +3.68720 q^{76} -5.06020 q^{77} -1.51948 q^{78} -0.125892 q^{79} -9.54354 q^{80} +1.00000 q^{81} +0.687245 q^{82} +10.2768 q^{83} -1.72687 q^{84} +14.6207 q^{85} -0.819651 q^{86} +1.32068 q^{87} +9.85587 q^{88} +6.62296 q^{89} +2.04760 q^{90} +2.90745 q^{91} +11.8245 q^{92} +3.43709 q^{93} +2.41307 q^{94} +8.36562 q^{95} +5.16845 q^{96} +12.6670 q^{97} -0.522616 q^{98} +5.06020 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 46 q + 3 q^{2} - 46 q^{3} + 45 q^{4} - 9 q^{5} - 3 q^{6} - 46 q^{7} + 6 q^{8} + 46 q^{9}+O(q^{10}) \) 46 * q + 3 * q^2 - 46 * q^3 + 45 * q^4 - 9 * q^5 - 3 * q^6 - 46 * q^7 + 6 * q^8 + 46 * q^9	\( 46 q + 3 q^{2} - 46 q^{3} + 45 q^{4} - 9 q^{5} - 3 q^{6} - 46 q^{7} + 6 q^{8} + 46 q^{9} - 10 q^{10} + 31 q^{11} - 45 q^{12} - 32 q^{13} - 3 q^{14} + 9 q^{15} + 43 q^{16} - 36 q^{17} + 3 q^{18} - 13 q^{19} - 19 q^{20} + 46 q^{21} - 13 q^{22} + 24 q^{23} - 6 q^{24} + 35 q^{25} - 11 q^{26} - 46 q^{27} - 45 q^{28} + 11 q^{29} + 10 q^{30} - 23 q^{31} + 5 q^{32} - 31 q^{33} - 35 q^{34} + 9 q^{35} + 45 q^{36} - 37 q^{37} - 32 q^{38} + 32 q^{39} - 28 q^{40} - 27 q^{41} + 3 q^{42} - 7 q^{43} + 46 q^{44} - 9 q^{45} + 16 q^{46} - 18 q^{47} - 43 q^{48} + 46 q^{49} + 10 q^{50} + 36 q^{51} - 62 q^{52} - 62 q^{53} - 3 q^{54} - 28 q^{55} - 6 q^{56} + 13 q^{57} - 36 q^{58} - 3 q^{59} + 19 q^{60} - 31 q^{61} - 41 q^{62} - 46 q^{63} + 42 q^{64} + 2 q^{65} + 13 q^{66} - 9 q^{67} - 70 q^{68} - 24 q^{69} + 10 q^{70} + 77 q^{71} + 6 q^{72} - 38 q^{73} + 14 q^{74} - 35 q^{75} - 41 q^{76} - 31 q^{77} + 11 q^{78} + 8 q^{79} - 59 q^{80} + 46 q^{81} - 53 q^{82} - 38 q^{83} + 45 q^{84} - 26 q^{85} + 37 q^{86} - 11 q^{87} - 26 q^{88} - 39 q^{89} - 10 q^{90} + 32 q^{91} + 2 q^{92} + 23 q^{93} - 55 q^{94} + 35 q^{95} - 5 q^{96} - 61 q^{97} + 3 q^{98} + 31 q^{99}+O(q^{100}) \) 46 * q + 3 * q^2 - 46 * q^3 + 45 * q^4 - 9 * q^5 - 3 * q^6 - 46 * q^7 + 6 * q^8 + 46 * q^9 - 10 * q^10 + 31 * q^11 - 45 * q^12 - 32 * q^13 - 3 * q^14 + 9 * q^15 + 43 * q^16 - 36 * q^17 + 3 * q^18 - 13 * q^19 - 19 * q^20 + 46 * q^21 - 13 * q^22 + 24 * q^23 - 6 * q^24 + 35 * q^25 - 11 * q^26 - 46 * q^27 - 45 * q^28 + 11 * q^29 + 10 * q^30 - 23 * q^31 + 5 * q^32 - 31 * q^33 - 35 * q^34 + 9 * q^35 + 45 * q^36 - 37 * q^37 - 32 * q^38 + 32 * q^39 - 28 * q^40 - 27 * q^41 + 3 * q^42 - 7 * q^43 + 46 * q^44 - 9 * q^45 + 16 * q^46 - 18 * q^47 - 43 * q^48 + 46 * q^49 + 10 * q^50 + 36 * q^51 - 62 * q^52 - 62 * q^53 - 3 * q^54 - 28 * q^55 - 6 * q^56 + 13 * q^57 - 36 * q^58 - 3 * q^59 + 19 * q^60 - 31 * q^61 - 41 * q^62 - 46 * q^63 + 42 * q^64 + 2 * q^65 + 13 * q^66 - 9 * q^67 - 70 * q^68 - 24 * q^69 + 10 * q^70 + 77 * q^71 + 6 * q^72 - 38 * q^73 + 14 * q^74 - 35 * q^75 - 41 * q^76 - 31 * q^77 + 11 * q^78 + 8 * q^79 - 59 * q^80 + 46 * q^81 - 53 * q^82 - 38 * q^83 + 45 * q^84 - 26 * q^85 + 37 * q^86 - 11 * q^87 - 26 * q^88 - 39 * q^89 - 10 * q^90 + 32 * q^91 + 2 * q^92 + 23 * q^93 - 55 * q^94 + 35 * q^95 - 5 * q^96 - 61 * q^97 + 3 * q^98 + 31 * q^99

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