LMFDB - Embedded newform 6041.2.a.c.1.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6041,2,Mod(1,6041)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6041, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6041.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6041 = 7 \cdot 863 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6041.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:	$48.2376278611$
Analytic rank:	$1$
Dimension:	$83$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
Character	$\chi$	$=$	6041.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.14754 q^{2} -2.08287 q^{3} +2.61192 q^{4} -2.63815 q^{5} +4.47305 q^{6} +1.00000 q^{7} -1.31412 q^{8} +1.33837 q^{9} +O(q^{10})$	\(q-2.14754 q^{2} -2.08287 q^{3} +2.61192 q^{4} -2.63815 q^{5} +4.47305 q^{6} +1.00000 q^{7} -1.31412 q^{8} +1.33837 q^{9} +5.66553 q^{10} +4.69465 q^{11} -5.44030 q^{12} +4.54623 q^{13} -2.14754 q^{14} +5.49494 q^{15} -2.40171 q^{16} +1.39418 q^{17} -2.87420 q^{18} -3.25219 q^{19} -6.89064 q^{20} -2.08287 q^{21} -10.0819 q^{22} -1.96232 q^{23} +2.73715 q^{24} +1.95984 q^{25} -9.76320 q^{26} +3.46097 q^{27} +2.61192 q^{28} +7.04705 q^{29} -11.8006 q^{30} +7.19599 q^{31} +7.78602 q^{32} -9.77836 q^{33} -2.99406 q^{34} -2.63815 q^{35} +3.49571 q^{36} -7.49766 q^{37} +6.98421 q^{38} -9.46923 q^{39} +3.46685 q^{40} -9.56471 q^{41} +4.47305 q^{42} -9.99183 q^{43} +12.2620 q^{44} -3.53082 q^{45} +4.21416 q^{46} +10.2386 q^{47} +5.00247 q^{48} +1.00000 q^{49} -4.20883 q^{50} -2.90391 q^{51} +11.8744 q^{52} -5.72110 q^{53} -7.43257 q^{54} -12.3852 q^{55} -1.31412 q^{56} +6.77391 q^{57} -15.1338 q^{58} -3.44152 q^{59} +14.3523 q^{60} -5.23388 q^{61} -15.4537 q^{62} +1.33837 q^{63} -11.9173 q^{64} -11.9936 q^{65} +20.9994 q^{66} +0.747135 q^{67} +3.64149 q^{68} +4.08727 q^{69} +5.66553 q^{70} -6.05545 q^{71} -1.75878 q^{72} +3.95519 q^{73} +16.1015 q^{74} -4.08210 q^{75} -8.49447 q^{76} +4.69465 q^{77} +20.3355 q^{78} -7.60348 q^{79} +6.33609 q^{80} -11.2239 q^{81} +20.5406 q^{82} +2.43143 q^{83} -5.44030 q^{84} -3.67807 q^{85} +21.4578 q^{86} -14.6781 q^{87} -6.16933 q^{88} -6.99970 q^{89} +7.58256 q^{90} +4.54623 q^{91} -5.12542 q^{92} -14.9884 q^{93} -21.9877 q^{94} +8.57978 q^{95} -16.2173 q^{96} -8.59701 q^{97} -2.14754 q^{98} +6.28316 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 83 q - 8 q^{2} - 12 q^{3} + 48 q^{4} - 11 q^{5} - 8 q^{6} + 83 q^{7} - 18 q^{8} + 39 q^{9}+O(q^{10}) $ 83 * q - 8 * q^2 - 12 * q^3 + 48 * q^4 - 11 * q^5 - 8 * q^6 + 83 * q^7 - 18 * q^8 + 39 * q^9	\( 83 q - 8 q^{2} - 12 q^{3} + 48 q^{4} - 11 q^{5} - 8 q^{6} + 83 q^{7} - 18 q^{8} + 39 q^{9} - 20 q^{10} - 26 q^{11} - 14 q^{12} - 22 q^{13} - 8 q^{14} - 37 q^{15} - 10 q^{16} - 9 q^{17} - 27 q^{18} - 42 q^{19} - 22 q^{20} - 12 q^{21} - 44 q^{22} - 46 q^{23} - 24 q^{24} - 20 q^{25} - 9 q^{26} - 39 q^{27} + 48 q^{28} - 36 q^{29} - 11 q^{30} - 107 q^{31} - 19 q^{32} - 25 q^{33} - 24 q^{34} - 11 q^{35} - 32 q^{36} - 75 q^{37} - 16 q^{38} - 78 q^{39} - 34 q^{40} - 17 q^{41} - 8 q^{42} - 87 q^{43} - 32 q^{44} - 17 q^{45} - 56 q^{46} - 39 q^{47} - 16 q^{48} + 83 q^{49} - 26 q^{50} - 71 q^{51} - 53 q^{52} - 28 q^{53} - 25 q^{54} - 94 q^{55} - 18 q^{56} - 79 q^{57} - 69 q^{58} - 26 q^{59} - 43 q^{60} - 56 q^{61} - 6 q^{62} + 39 q^{63} - 108 q^{64} - 26 q^{65} + 10 q^{66} - 123 q^{67} - 11 q^{68} + 2 q^{69} - 20 q^{70} - 96 q^{71} - 11 q^{72} - 53 q^{73} - 26 q^{74} - 27 q^{75} - 65 q^{76} - 26 q^{77} - 43 q^{78} - 160 q^{79} + 12 q^{80} - 53 q^{81} - 20 q^{82} - 2 q^{83} - 14 q^{84} - 110 q^{85} + 24 q^{86} - 52 q^{87} - 79 q^{88} - 5 q^{89} - 4 q^{90} - 22 q^{91} - 51 q^{92} - 30 q^{93} - 9 q^{94} - 76 q^{95} - 3 q^{96} - 44 q^{97} - 8 q^{98} - 82 q^{99}+O(q^{100}) \) 83 * q - 8 * q^2 - 12 * q^3 + 48 * q^4 - 11 * q^5 - 8 * q^6 + 83 * q^7 - 18 * q^8 + 39 * q^9 - 20 * q^10 - 26 * q^11 - 14 * q^12 - 22 * q^13 - 8 * q^14 - 37 * q^15 - 10 * q^16 - 9 * q^17 - 27 * q^18 - 42 * q^19 - 22 * q^20 - 12 * q^21 - 44 * q^22 - 46 * q^23 - 24 * q^24 - 20 * q^25 - 9 * q^26 - 39 * q^27 + 48 * q^28 - 36 * q^29 - 11 * q^30 - 107 * q^31 - 19 * q^32 - 25 * q^33 - 24 * q^34 - 11 * q^35 - 32 * q^36 - 75 * q^37 - 16 * q^38 - 78 * q^39 - 34 * q^40 - 17 * q^41 - 8 * q^42 - 87 * q^43 - 32 * q^44 - 17 * q^45 - 56 * q^46 - 39 * q^47 - 16 * q^48 + 83 * q^49 - 26 * q^50 - 71 * q^51 - 53 * q^52 - 28 * q^53 - 25 * q^54 - 94 * q^55 - 18 * q^56 - 79 * q^57 - 69 * q^58 - 26 * q^59 - 43 * q^60 - 56 * q^61 - 6 * q^62 + 39 * q^63 - 108 * q^64 - 26 * q^65 + 10 * q^66 - 123 * q^67 - 11 * q^68 + 2 * q^69 - 20 * q^70 - 96 * q^71 - 11 * q^72 - 53 * q^73 - 26 * q^74 - 27 * q^75 - 65 * q^76 - 26 * q^77 - 43 * q^78 - 160 * q^79 + 12 * q^80 - 53 * q^81 - 20 * q^82 - 2 * q^83 - 14 * q^84 - 110 * q^85 + 24 * q^86 - 52 * q^87 - 79 * q^88 - 5 * q^89 - 4 * q^90 - 22 * q^91 - 51 * q^92 - 30 * q^93 - 9 * q^94 - 76 * q^95 - 3 * q^96 - 44 * q^97 - 8 * q^98 - 82 * 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 $

$2$	−2.14754	−1.51854	−0.759269	−	0.650776i	$-0.774443\pi$
$2$	−2.14754	−1.51854	−0.759269	+	0.650776i	$0.774443\pi$
$3$	−2.08287	−1.20255	−0.601274	−	0.799043i	$-0.705340\pi$
$3$	−2.08287	−1.20255	−0.601274	+	0.799043i	$0.705340\pi$
$4$	2.61192	1.30596
$5$	−2.63815	−1.17982	−0.589909	−	0.807470i	$-0.700836\pi$
$5$	−2.63815	−1.17982	−0.589909	+	0.807470i	$0.700836\pi$
$6$	4.47305	1.82612
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−1.31412	−0.464612
$9$	1.33837	0.446123
$10$	5.66553	1.79160
$11$	4.69465	1.41549	0.707745	−	0.706468i	$-0.249713\pi$
$11$	4.69465	1.41549	0.707745	+	0.706468i	$0.249713\pi$
$12$	−5.44030	−1.57048
$13$	4.54623	1.26090	0.630448	−	0.776231i	$-0.282871\pi$
$13$	4.54623	1.26090	0.630448	+	0.776231i	$0.282871\pi$
$14$	−2.14754	−0.573954
$15$	5.49494	1.41879
$16$	−2.40171	−0.600429
$17$	1.39418	0.338139	0.169070	−	0.985604i	$-0.445924\pi$
$17$	1.39418	0.338139	0.169070	+	0.985604i	$0.445924\pi$
$18$	−2.87420	−0.677455
$19$	−3.25219	−0.746104	−0.373052	−	0.927810i	$-0.621689\pi$
$19$	−3.25219	−0.746104	−0.373052	+	0.927810i	$0.621689\pi$
$20$	−6.89064	−1.54079
$21$	−2.08287	−0.454521
$22$	−10.0819	−2.14947
$23$	−1.96232	−0.409172	−0.204586	−	0.978849i	$-0.565585\pi$
$23$	−1.96232	−0.409172	−0.204586	+	0.978849i	$0.565585\pi$
$24$	2.73715	0.558718
$25$	1.95984	0.391968
$26$	−9.76320	−1.91472
$27$	3.46097	0.666064
$28$	2.61192	0.493606
$29$	7.04705	1.30861	0.654303	−	0.756233i	$-0.272962\pi$
$29$	7.04705	1.30861	0.654303	+	0.756233i	$0.272962\pi$
$30$	−11.8006	−2.15448
$31$	7.19599	1.29244	0.646219	−	0.763152i	$-0.276349\pi$
$31$	7.19599	1.29244	0.646219	+	0.763152i	$0.276349\pi$
$32$	7.78602	1.37639
$33$	−9.77836	−1.70219
$34$	−2.99406	−0.513477
$35$	−2.63815	−0.445929
$36$	3.49571	0.582618
$37$	−7.49766	−1.23261	−0.616304	−	0.787508i	$-0.711371\pi$
$37$	−7.49766	−1.23261	−0.616304	+	0.787508i	$0.711371\pi$
$38$	6.98421	1.13299
$39$	−9.46923	−1.51629
$40$	3.46685	0.548157
$41$	−9.56471	−1.49376	−0.746879	−	0.664960i	$-0.768448\pi$
$41$	−9.56471	−1.49376	−0.746879	+	0.664960i	$0.768448\pi$
$42$	4.47305	0.690207
$43$	−9.99183	−1.52374	−0.761870	−	0.647730i	$-0.775719\pi$
$43$	−9.99183	−1.52374	−0.761870	+	0.647730i	$0.775719\pi$
$44$	12.2620	1.84857
$45$	−3.53082	−0.526343
$46$	4.21416	0.621343
$47$	10.2386	1.49345	0.746725	−	0.665133i	$-0.231625\pi$
$47$	10.2386	1.49345	0.746725	+	0.665133i	$0.231625\pi$
$48$	5.00247	0.722044
$49$	1.00000	0.142857
$50$	−4.20883	−0.595219
$51$	−2.90391	−0.406629
$52$	11.8744	1.64668
$53$	−5.72110	−0.785854	−0.392927	−	0.919570i	$-0.628537\pi$
$53$	−5.72110	−0.785854	−0.392927	+	0.919570i	$0.628537\pi$
$54$	−7.43257	−1.01144
$55$	−12.3852	−1.67002
$56$	−1.31412	−0.175607
$57$	6.77391	0.897227
$58$	−15.1338	−1.98717
$59$	−3.44152	−0.448048	−0.224024	−	0.974584i	$-0.571919\pi$
$59$	−3.44152	−0.448048	−0.224024	+	0.974584i	$0.571919\pi$
$60$	14.3523	1.85288
$61$	−5.23388	−0.670130	−0.335065	−	0.942195i	$-0.608758\pi$
$61$	−5.23388	−0.670130	−0.335065	+	0.942195i	$0.608758\pi$
$62$	−15.4537	−1.96262
$63$	1.33837	0.168619
$64$	−11.9173	−1.48967
$65$	−11.9936	−1.48763
$66$	20.9994	2.58485
$67$	0.747135	0.0912771	0.0456385	−	0.998958i	$-0.485468\pi$
$67$	0.747135	0.0912771	0.0456385	+	0.998958i	$0.485468\pi$
$68$	3.64149	0.441596
$69$	4.08727	0.492049
$70$	5.66553	0.677160
$71$	−6.05545	−0.718650	−0.359325	−	0.933212i	$-0.616993\pi$
$71$	−6.05545	−0.718650	−0.359325	+	0.933212i	$0.616993\pi$
$72$	−1.75878	−0.207274
$73$	3.95519	0.462920	0.231460	−	0.972844i	$-0.425650\pi$
$73$	3.95519	0.462920	0.231460	+	0.972844i	$0.425650\pi$
$74$	16.1015	1.87176
$75$	−4.08210	−0.471361
$76$	−8.49447	−0.974383
$77$	4.69465	0.535005
$78$	20.3355	2.30254
$79$	−7.60348	−0.855459	−0.427729	−	0.903907i	$-0.640686\pi$
$79$	−7.60348	−0.855459	−0.427729	+	0.903907i	$0.640686\pi$
$80$	6.33609	0.708396
$81$	−11.2239	−1.24710
$82$	20.5406	2.26833
$83$	2.43143	0.266884	0.133442	−	0.991057i	$-0.457397\pi$
$83$	2.43143	0.266884	0.133442	+	0.991057i	$0.457397\pi$
$84$	−5.44030	−0.593586
$85$	−3.67807	−0.398942
$86$	21.4578	2.31386
$87$	−14.6781	−1.57366
$88$	−6.16933	−0.657653
$89$	−6.99970	−0.741966	−0.370983	−	0.928640i	$-0.620979\pi$
$89$	−6.99970	−0.741966	−0.370983	+	0.928640i	$0.620979\pi$
$90$	7.58256	0.799272
$91$	4.54623	0.476574
$92$	−5.12542	−0.534362
$93$	−14.9884	−1.55422
$94$	−21.9877	−2.26786
$95$	8.57978	0.880267
$96$	−16.2173	−1.65517
$97$	−8.59701	−0.872894	−0.436447	−	0.899730i	$-0.643763\pi$
$97$	−8.59701	−0.872894	−0.436447	+	0.899730i	$0.643763\pi$
$98$	−2.14754	−0.216934
$99$	6.28316	0.631482
$100$	5.11895	0.511895
$101$	−10.2693	−1.02184	−0.510918	−	0.859629i	$-0.670694\pi$
$101$	−10.2693	−1.02184	−0.510918	+	0.859629i	$0.670694\pi$
$102$	6.23626	0.617481
$103$	−6.44833	−0.635372	−0.317686	−	0.948196i	$-0.602906\pi$
$103$	−6.44833	−0.635372	−0.317686	+	0.948196i	$0.602906\pi$
$104$	−5.97430	−0.585828
$105$	5.49494	0.536251
$106$	12.2863	1.19335
$107$	−2.06556	−0.199685	−0.0998425	−	0.995003i	$-0.531834\pi$
$107$	−2.06556	−0.199685	−0.0998425	+	0.995003i	$0.531834\pi$
$108$	9.03978	0.869853
$109$	18.1289	1.73644	0.868219	−	0.496182i	$-0.165265\pi$
$109$	18.1289	1.73644	0.868219	+	0.496182i	$0.165265\pi$
$110$	26.5977	2.53599
$111$	15.6167	1.48227
$112$	−2.40171	−0.226941
$113$	4.73345	0.445286	0.222643	−	0.974900i	$-0.428532\pi$
$113$	4.73345	0.445286	0.222643	+	0.974900i	$0.428532\pi$
$114$	−14.5472	−1.36247
$115$	5.17689	0.482748
$116$	18.4063	1.70899
$117$	6.08453	0.562515
$118$	7.39081	0.680379
$119$	1.39418	0.127805
$120$	−7.22102	−0.659186
$121$	11.0397	1.00361
$122$	11.2400	1.01762
$123$	19.9221	1.79632
$124$	18.7954	1.68787
$125$	8.02040	0.717366
$126$	−2.87420	−0.256054
$127$	12.1168	1.07519	0.537596	−	0.843203i	$-0.319333\pi$
$127$	12.1168	1.07519	0.537596	+	0.843203i	$0.319333\pi$
$128$	10.0209	0.885731
$129$	20.8117	1.83237
$130$	25.7568	2.25902
$131$	20.3921	1.78167	0.890833	−	0.454330i	$-0.150121\pi$
$131$	20.3921	1.78167	0.890833	+	0.454330i	$0.150121\pi$
$132$	−25.5403	−2.22300
$133$	−3.25219	−0.282001
$134$	−1.60450	−0.138608
$135$	−9.13057	−0.785834
$136$	−1.83213	−0.157103
$137$	−3.78818	−0.323646	−0.161823	−	0.986820i	$-0.551737\pi$
$137$	−3.78818	−0.323646	−0.161823	+	0.986820i	$0.551737\pi$
$138$	−8.77756	−0.747195
$139$	−18.6928	−1.58550	−0.792752	−	0.609545i	$-0.791352\pi$
$139$	−18.6928	−1.58550	−0.792752	+	0.609545i	$0.791352\pi$
$140$	−6.89064	−0.582365
$141$	−21.3257	−1.79595
$142$	13.0043	1.09130
$143$	21.3429	1.78479
$144$	−3.21438	−0.267865
$145$	−18.5912	−1.54391
$146$	−8.49393	−0.702962
$147$	−2.08287	−0.171793
$148$	−19.5833	−1.60974
$149$	−4.62874	−0.379201	−0.189601	−	0.981861i	$-0.560719\pi$
$149$	−4.62874	−0.379201	−0.189601	+	0.981861i	$0.560719\pi$
$150$	8.76647	0.715780
$151$	11.5057	0.936321	0.468161	−	0.883643i	$-0.344917\pi$
$151$	11.5057	0.936321	0.468161	+	0.883643i	$0.344917\pi$
$152$	4.27378	0.346649
$153$	1.86593	0.150852
$154$	−10.0819	−0.812425
$155$	−18.9841	−1.52484
$156$	−24.7329	−1.98021
$157$	0.681186	0.0543646	0.0271823	−	0.999630i	$-0.491347\pi$
$157$	0.681186	0.0543646	0.0271823	+	0.999630i	$0.491347\pi$
$158$	16.3288	1.29905
$159$	11.9163	0.945027
$160$	−20.5407	−1.62388
$161$	−1.96232	−0.154652
$162$	24.1037	1.89377
$163$	−8.99341	−0.704419	−0.352209	−	0.935921i	$-0.614569\pi$
$163$	−8.99341	−0.704419	−0.352209	+	0.935921i	$0.614569\pi$
$164$	−24.9823	−1.95079
$165$	25.7968	2.00828
$166$	−5.22158	−0.405273
$167$	9.81048	0.759158	0.379579	−	0.925159i	$-0.376069\pi$
$167$	9.81048	0.759158	0.379579	+	0.925159i	$0.376069\pi$
$168$	2.73715	0.211176
$169$	7.66820	0.589861
$170$	7.89879	0.605809
$171$	−4.35263	−0.332854
$172$	−26.0979	−1.98994
$173$	18.8215	1.43097	0.715487	−	0.698626i	$-0.246205\pi$
$173$	18.8215	1.43097	0.715487	+	0.698626i	$0.246205\pi$
$174$	31.5218	2.38967
$175$	1.95984	0.148150
$176$	−11.2752	−0.849900
$177$	7.16827	0.538800
$178$	15.0321	1.12670
$179$	−7.89718	−0.590263	−0.295131	−	0.955457i	$-0.595363\pi$
$179$	−7.89718	−0.590263	−0.295131	+	0.955457i	$0.595363\pi$
$180$	−9.22221	−0.687383
$181$	20.5731	1.52919	0.764593	−	0.644514i	$-0.222940\pi$
$181$	20.5731	1.52919	0.764593	+	0.644514i	$0.222940\pi$
$182$	−9.76320	−0.723696
$183$	10.9015	0.805864
$184$	2.57873	0.190106
$185$	19.7800	1.45425
$186$	32.1881	2.36014
$187$	6.54520	0.478632
$188$	26.7424	1.95039
$189$	3.46097	0.251749
$190$	−18.4254	−1.33672
$191$	12.3739	0.895344	0.447672	−	0.894198i	$-0.352253\pi$
$191$	12.3739	0.895344	0.447672	+	0.894198i	$0.352253\pi$
$192$	24.8223	1.79140
$193$	−19.2130	−1.38298	−0.691489	−	0.722387i	$-0.743045\pi$
$193$	−19.2130	−1.38298	−0.691489	+	0.722387i	$0.743045\pi$
$194$	18.4624	1.32552
$195$	24.9812	1.78894
$196$	2.61192	0.186566
$197$	4.11801	0.293396	0.146698	−	0.989181i	$-0.453135\pi$
$197$	4.11801	0.293396	0.146698	+	0.989181i	$0.453135\pi$
$198$	−13.4933	−0.958930
$199$	−16.0226	−1.13581	−0.567905	−	0.823094i	$-0.692246\pi$
$199$	−16.0226	−1.13581	−0.567905	+	0.823094i	$0.692246\pi$
$200$	−2.57547	−0.182113
$201$	−1.55619	−0.109765
$202$	22.0538	1.55170
$203$	7.04705	0.494606
$204$	−7.58478	−0.531041
$205$	25.2332	1.76236
$206$	13.8480	0.964838
$207$	−2.62631	−0.182541
$208$	−10.9187	−0.757079
$209$	−15.2679	−1.05610
$210$	−11.8006	−0.814318
$211$	−12.9305	−0.890174	−0.445087	−	0.895487i	$-0.646827\pi$
$211$	−12.9305	−0.890174	−0.445087	+	0.895487i	$0.646827\pi$
$212$	−14.9431	−1.02629
$213$	12.6128	0.864211
$214$	4.43586	0.303229
$215$	26.3600	1.79773
$216$	−4.54814	−0.309461
$217$	7.19599	0.488496
$218$	−38.9326	−2.63685
$219$	−8.23817	−0.556684
$220$	−32.3491	−2.18098
$221$	6.33827	0.426359
$222$	−33.5374	−2.25089
$223$	−26.2338	−1.75674	−0.878372	−	0.477977i	$-0.841370\pi$
$223$	−26.2338	−1.75674	−0.878372	+	0.477977i	$0.841370\pi$
$224$	7.78602	0.520225
$225$	2.62299	0.174866
$226$	−10.1653	−0.676184
$227$	8.29704	0.550694	0.275347	−	0.961345i	$-0.411207\pi$
$227$	8.29704	0.550694	0.275347	+	0.961345i	$0.411207\pi$
$228$	17.6929	1.17174
$229$	7.05365	0.466118	0.233059	−	0.972463i	$-0.425126\pi$
$229$	7.05365	0.466118	0.233059	+	0.972463i	$0.425126\pi$
$230$	−11.1176	−0.733071
$231$	−9.77836	−0.643369
$232$	−9.26068	−0.607994
$233$	10.6842	0.699943	0.349972	−	0.936760i	$-0.386191\pi$
$233$	10.6842	0.699943	0.349972	+	0.936760i	$0.386191\pi$
$234$	−13.0668	−0.854200
$235$	−27.0109	−1.76200
$236$	−8.98899	−0.585133
$237$	15.8371	1.02873
$238$	−2.99406	−0.194076
$239$	5.80335	0.375387	0.187694	−	0.982228i	$-0.439899\pi$
$239$	5.80335	0.375387	0.187694	+	0.982228i	$0.439899\pi$
$240$	−13.1973	−0.851880
$241$	−25.3978	−1.63602	−0.818008	−	0.575207i	$-0.804921\pi$
$241$	−25.3978	−1.63602	−0.818008	+	0.575207i	$0.804921\pi$
$242$	−23.7082	−1.52402
$243$	12.9950	0.833631
$244$	−13.6705	−0.875163
$245$	−2.63815	−0.168545
$246$	−42.7835	−2.72777
$247$	−14.7852	−0.940761
$248$	−9.45641	−0.600482
$249$	−5.06436	−0.320941
$250$	−17.2241	−1.08935
$251$	18.6915	1.17980	0.589898	−	0.807478i	$-0.299168\pi$
$251$	18.6915	1.17980	0.589898	+	0.807478i	$0.299168\pi$
$252$	3.49571	0.220209
$253$	−9.21239	−0.579178
$254$	−26.0213	−1.63272
$255$	7.66095	0.479747
$256$	2.31440	0.144650
$257$	15.6401	0.975601	0.487800	−	0.872955i	$-0.337799\pi$
$257$	15.6401	0.975601	0.487800	+	0.872955i	$0.337799\pi$
$258$	−44.6940	−2.78253
$259$	−7.49766	−0.465882
$260$	−31.3264	−1.94278
$261$	9.43155	0.583798
$262$	−43.7928	−2.70553
$263$	11.0842	0.683482	0.341741	−	0.939794i	$-0.388983\pi$
$263$	11.0842	0.683482	0.341741	+	0.939794i	$0.388983\pi$
$264$	12.8500	0.790860
$265$	15.0931	0.927163
$266$	6.98421	0.428229
$267$	14.5795	0.892250
$268$	1.95146	0.119204
$269$	−13.9427	−0.850103	−0.425052	−	0.905169i	$-0.639744\pi$
$269$	−13.9427	−0.850103	−0.425052	+	0.905169i	$0.639744\pi$
$270$	19.6082	1.19332
$271$	−4.27816	−0.259880	−0.129940	−	0.991522i	$-0.541478\pi$
$271$	−4.27816	−0.259880	−0.129940	+	0.991522i	$0.541478\pi$
$272$	−3.34843	−0.203028
$273$	−9.46923	−0.573104
$274$	8.13526	0.491469
$275$	9.20076	0.554827
$276$	10.6756	0.642596
$277$	−19.2273	−1.15526	−0.577628	−	0.816300i	$-0.696021\pi$
$277$	−19.2273	−1.15526	−0.577628	+	0.816300i	$0.696021\pi$
$278$	40.1435	2.40765
$279$	9.63089	0.576586
$280$	3.46685	0.207184
$281$	−19.7030	−1.17538	−0.587692	−	0.809085i	$-0.699963\pi$
$281$	−19.7030	−1.17538	−0.587692	+	0.809085i	$0.699963\pi$
$282$	45.7977	2.72721
$283$	−9.27207	−0.551168	−0.275584	−	0.961277i	$-0.588871\pi$
$283$	−9.27207	−0.551168	−0.275584	+	0.961277i	$0.588871\pi$
$284$	−15.8164	−0.938528
$285$	−17.8706	−1.05856
$286$	−45.8348	−2.71027
$287$	−9.56471	−0.564587
$288$	10.4206	0.614037
$289$	−15.0563	−0.885662
$290$	39.9253	2.34449
$291$	17.9065	1.04970
$292$	10.3306	0.604555
$293$	17.5051	1.02266	0.511330	−	0.859385i	$-0.329153\pi$
$293$	17.5051	1.02266	0.511330	+	0.859385i	$0.329153\pi$
$294$	4.47305	0.260874
$295$	9.07926	0.528615
$296$	9.85283	0.572684
$297$	16.2480	0.942807
$298$	9.94040	0.575832
$299$	−8.92115	−0.515924
$300$	−10.6621	−0.615578
$301$	−9.99183	−0.575920
$302$	−24.7089	−1.42184
$303$	21.3897	1.22881
$304$	7.81084	0.447982
$305$	13.8078	0.790631
$306$	−4.00716	−0.229074
$307$	−9.87874	−0.563809	−0.281905	−	0.959442i	$-0.590966\pi$
$307$	−9.87874	−0.563809	−0.281905	+	0.959442i	$0.590966\pi$
$308$	12.2620	0.698695
$309$	13.4311	0.764066
$310$	40.7691	2.31553
$311$	−24.6652	−1.39864	−0.699319	−	0.714810i	$-0.746513\pi$
$311$	−24.6652	−1.39864	−0.699319	+	0.714810i	$0.746513\pi$
$312$	12.4437	0.704486
$313$	7.23625	0.409017	0.204509	−	0.978865i	$-0.434440\pi$
$313$	7.23625	0.409017	0.204509	+	0.978865i	$0.434440\pi$
$314$	−1.46287	−0.0825547
$315$	−3.53082	−0.198939
$316$	−19.8597	−1.11719
$317$	−22.0678	−1.23945	−0.619725	−	0.784819i	$-0.712756\pi$
$317$	−22.0678	−1.23945	−0.619725	+	0.784819i	$0.712756\pi$
$318$	−25.5908	−1.43506
$319$	33.0834	1.85232
$320$	31.4397	1.75753
$321$	4.30230	0.240131
$322$	4.21416	0.234846
$323$	−4.53415	−0.252287
$324$	−29.3159	−1.62866
$325$	8.90989	0.494231
$326$	19.3137	1.06969
$327$	−37.7603	−2.08815
$328$	12.5692	0.694017
$329$	10.2386	0.564471
$330$	−55.3996	−3.04965
$331$	−22.4696	−1.23504	−0.617520	−	0.786555i	$-0.711863\pi$
$331$	−22.4696	−1.23504	−0.617520	+	0.786555i	$0.711863\pi$
$332$	6.35069	0.348540
$333$	−10.0346	−0.549894
$334$	−21.0684	−1.15281
$335$	−1.97106	−0.107690
$336$	5.00247	0.272907
$337$	28.9473	1.57686	0.788431	−	0.615124i	$-0.210894\pi$
$337$	28.9473	1.57686	0.788431	+	0.615124i	$0.210894\pi$
$338$	−16.4677	−0.895727
$339$	−9.85919	−0.535478
$340$	−9.60681	−0.521003
$341$	33.7826	1.82943
$342$	9.34745	0.505452
$343$	1.00000	0.0539949
$344$	13.1305	0.707948
$345$	−10.7828	−0.580528
$346$	−40.4199	−2.17299
$347$	17.5506	0.942165	0.471082	−	0.882089i	$-0.343863\pi$
$347$	17.5506	0.942165	0.471082	+	0.882089i	$0.343863\pi$
$348$	−38.3381	−2.05514
$349$	−17.8733	−0.956734	−0.478367	−	0.878160i	$-0.658771\pi$
$349$	−17.8733	−0.956734	−0.478367	+	0.878160i	$0.658771\pi$
$350$	−4.20883	−0.224972
$351$	15.7344	0.839838
$352$	36.5526	1.94826
$353$	17.0197	0.905868	0.452934	−	0.891544i	$-0.350377\pi$
$353$	17.0197	0.905868	0.452934	+	0.891544i	$0.350377\pi$
$354$	−15.3941	−0.818188
$355$	15.9752	0.847876
$356$	−18.2826	−0.968978
$357$	−2.90391	−0.153691
$358$	16.9595	0.896337
$359$	−3.05537	−0.161256	−0.0806280	−	0.996744i	$-0.525693\pi$
$359$	−3.05537	−0.161256	−0.0806280	+	0.996744i	$0.525693\pi$
$360$	4.63992	0.244545
$361$	−8.42323	−0.443328
$362$	−44.1815	−2.32213
$363$	−22.9943	−1.20689
$364$	11.8744	0.622387
$365$	−10.4344	−0.546161
$366$	−23.4114	−1.22374
$367$	24.5325	1.28058	0.640292	−	0.768132i	$-0.278813\pi$
$367$	24.5325	1.28058	0.640292	+	0.768132i	$0.278813\pi$
$368$	4.71293	0.245678
$369$	−12.8011	−0.666399
$370$	−42.4782	−2.20834
$371$	−5.72110	−0.297025
$372$	−39.1484	−2.02975
$373$	−10.9627	−0.567628	−0.283814	−	0.958879i	$-0.591600\pi$
$373$	−10.9627	−0.567628	−0.283814	+	0.958879i	$0.591600\pi$
$374$	−14.0561	−0.726821
$375$	−16.7055	−0.862668
$376$	−13.4547	−0.693875
$377$	32.0375	1.65002
$378$	−7.43257	−0.382290
$379$	8.50610	0.436929	0.218464	−	0.975845i	$-0.429895\pi$
$379$	8.50610	0.436929	0.218464	+	0.975845i	$0.429895\pi$
$380$	22.4097	1.14959
$381$	−25.2378	−1.29297
$382$	−26.5734	−1.35961
$383$	7.61213	0.388962	0.194481	−	0.980906i	$-0.437698\pi$
$383$	7.61213	0.388962	0.194481	+	0.980906i	$0.437698\pi$
$384$	−20.8723	−1.06513
$385$	−12.3852	−0.631207
$386$	41.2605	2.10011
$387$	−13.3728	−0.679775
$388$	−22.4547	−1.13996
$389$	−37.4409	−1.89833	−0.949165	−	0.314780i	$-0.898069\pi$
$389$	−37.4409	−1.89833	−0.949165	+	0.314780i	$0.898069\pi$
$390$	−53.6482	−2.71658
$391$	−2.73583	−0.138357
$392$	−1.31412	−0.0663731
$393$	−42.4742	−2.14254
$394$	−8.84359	−0.445534
$395$	20.0591	1.00928
$396$	16.4111	0.824690
$397$	20.8192	1.04488	0.522442	−	0.852675i	$-0.325021\pi$
$397$	20.8192	1.04488	0.522442	+	0.852675i	$0.325021\pi$
$398$	34.4091	1.72477
$399$	6.77391	0.339120
$400$	−4.70698	−0.235349
$401$	−25.7746	−1.28712	−0.643562	−	0.765394i	$-0.722544\pi$
$401$	−25.7746	−1.28712	−0.643562	+	0.765394i	$0.722544\pi$
$402$	3.34197	0.166683
$403$	32.7146	1.62963
$404$	−26.8227	−1.33448
$405$	29.6103	1.47135
$406$	−15.1338	−0.751079
$407$	−35.1989	−1.74474
$408$	3.81609	0.188925
$409$	9.21644	0.455723	0.227862	−	0.973694i	$-0.426827\pi$
$409$	9.21644	0.455723	0.227862	+	0.973694i	$0.426827\pi$
$410$	−54.1892	−2.67621
$411$	7.89030	0.389200
$412$	−16.8425	−0.829771
$413$	−3.44152	−0.169346
$414$	5.64009	0.277195
$415$	−6.41447	−0.314874
$416$	35.3970	1.73548
$417$	38.9348	1.90664
$418$	32.7884	1.60373
$419$	39.4813	1.92879	0.964393	−	0.264474i	$-0.0851984\pi$
$419$	39.4813	1.92879	0.964393	+	0.264474i	$0.0851984\pi$
$420$	14.3523	0.700322
$421$	−3.17646	−0.154811	−0.0774055	−	0.997000i	$-0.524664\pi$
$421$	−3.17646	−0.154811	−0.0774055	+	0.997000i	$0.524664\pi$
$422$	27.7688	1.35176
$423$	13.7030	0.666262
$424$	7.51822	0.365117
$425$	2.73238	0.132540
$426$	−27.0864	−1.31234
$427$	−5.23388	−0.253285
$428$	−5.39507	−0.260781
$429$	−44.4547	−2.14629
$430$	−56.6090	−2.72993
$431$	−9.30724	−0.448314	−0.224157	−	0.974553i	$-0.571963\pi$
$431$	−9.30724	−0.448314	−0.224157	+	0.974553i	$0.571963\pi$
$432$	−8.31226	−0.399924
$433$	35.5458	1.70822	0.854111	−	0.520091i	$-0.174102\pi$
$433$	35.5458	1.70822	0.854111	+	0.520091i	$0.174102\pi$
$434$	−15.4537	−0.741800
$435$	38.7231	1.85663
$436$	47.3513	2.26772
$437$	6.38184	0.305285
$438$	17.6918	0.845346
$439$	3.13501	0.149626	0.0748129	−	0.997198i	$-0.476164\pi$
$439$	3.13501	0.149626	0.0748129	+	0.997198i	$0.476164\pi$
$440$	16.2756	0.775910
$441$	1.33837	0.0637318
$442$	−13.6117	−0.647442
$443$	22.9625	1.09098	0.545491	−	0.838116i	$-0.316343\pi$
$443$	22.9625	1.09098	0.545491	+	0.838116i	$0.316343\pi$
$444$	40.7895	1.93579
$445$	18.4663	0.875384
$446$	56.3381	2.66768
$447$	9.64109	0.456008
$448$	−11.9173	−0.563041
$449$	20.2347	0.954935	0.477468	−	0.878649i	$-0.341555\pi$
$449$	20.2347	0.954935	0.477468	+	0.878649i	$0.341555\pi$
$450$	−5.63297	−0.265541
$451$	−44.9029	−2.11440
$452$	12.3634	0.581525
$453$	−23.9649	−1.12597
$454$	−17.8182	−0.836250
$455$	−11.9936	−0.562270
$456$	−8.90174	−0.416862
$457$	−25.6123	−1.19809	−0.599046	−	0.800715i	$-0.704453\pi$
$457$	−25.6123	−1.19809	−0.599046	+	0.800715i	$0.704453\pi$
$458$	−15.1480	−0.707819
$459$	4.82523	0.225222
$460$	13.5216	0.630449
$461$	−3.89756	−0.181528	−0.0907638	−	0.995872i	$-0.528931\pi$
$461$	−3.89756	−0.181528	−0.0907638	+	0.995872i	$0.528931\pi$
$462$	20.9994	0.976981
$463$	−10.7308	−0.498703	−0.249352	−	0.968413i	$-0.580217\pi$
$463$	−10.7308	−0.498703	−0.249352	+	0.968413i	$0.580217\pi$
$464$	−16.9250	−0.785724
$465$	39.5415	1.83369
$466$	−22.9447	−1.06289
$467$	−31.5588	−1.46037	−0.730183	−	0.683252i	$-0.760565\pi$
$467$	−31.5588	−1.46037	−0.730183	+	0.683252i	$0.760565\pi$
$468$	15.8923	0.734622
$469$	0.747135	0.0344995
$470$	58.0070	2.67566
$471$	−1.41883	−0.0653760
$472$	4.52258	0.208169
$473$	−46.9081	−2.15684
$474$	−34.0108	−1.56217
$475$	−6.37378	−0.292449
$476$	3.64149	0.166908
$477$	−7.65694	−0.350587
$478$	−12.4629	−0.570040
$479$	37.5291	1.71475	0.857373	−	0.514695i	$-0.172095\pi$
$479$	37.5291	1.71475	0.857373	+	0.514695i	$0.172095\pi$
$480$	42.7837	1.95280
$481$	−34.0861	−1.55419
$482$	54.5427	2.48435
$483$	4.08727	0.185977
$484$	28.8348	1.31067
$485$	22.6802	1.02986
$486$	−27.9073	−1.26590
$487$	−14.9243	−0.676285	−0.338143	−	0.941095i	$-0.609799\pi$
$487$	−14.9243	−0.676285	−0.338143	+	0.941095i	$0.609799\pi$
$488$	6.87796	0.311350
$489$	18.7322	0.847097
$490$	5.66553	0.255943
$491$	−35.2243	−1.58965	−0.794825	−	0.606839i	$-0.792437\pi$
$491$	−35.2243	−1.58965	−0.794825	+	0.606839i	$0.792437\pi$
$492$	52.0349	2.34592
$493$	9.82488	0.442490
$494$	31.7518	1.42858
$495$	−16.5759	−0.745033
$496$	−17.2827	−0.776017
$497$	−6.05545	−0.271624
$498$	10.8759	0.487361
$499$	18.8435	0.843552	0.421776	−	0.906700i	$-0.361407\pi$
$499$	18.8435	0.843552	0.421776	+	0.906700i	$0.361407\pi$
$500$	20.9486	0.936852
$501$	−20.4340	−0.912924
$502$	−40.1407	−1.79157
$503$	5.92751	0.264295	0.132147	−	0.991230i	$-0.457813\pi$
$503$	5.92751	0.264295	0.132147	+	0.991230i	$0.457813\pi$
$504$	−1.75878	−0.0783422
$505$	27.0920	1.20558
$506$	19.7840	0.879505
$507$	−15.9719	−0.709337
$508$	31.6481	1.40416
$509$	−41.0476	−1.81940	−0.909701	−	0.415263i	$-0.863690\pi$
$509$	−41.0476	−1.81940	−0.909701	+	0.415263i	$0.863690\pi$
$510$	−16.4522	−0.728515
$511$	3.95519	0.174967
$512$	−25.0121	−1.10539
$513$	−11.2558	−0.496954
$514$	−33.5876	−1.48149
$515$	17.0117	0.749623
$516$	54.3586	2.39300
$517$	48.0665	2.11396
$518$	16.1015	0.707460
$519$	−39.2029	−1.72082
$520$	15.7611	0.691170
$521$	−17.1149	−0.749819	−0.374909	−	0.927061i	$-0.622326\pi$
$521$	−17.1149	−0.749819	−0.374909	+	0.927061i	$0.622326\pi$
$522$	−20.2546	−0.886521
$523$	27.1377	1.18665	0.593325	−	0.804963i	$-0.297815\pi$
$523$	27.1377	1.18665	0.593325	+	0.804963i	$0.297815\pi$
$524$	53.2626	2.32679
$525$	−4.08210	−0.178158
$526$	−23.8038	−1.03789
$527$	10.0325	0.437024
$528$	23.4848	1.02205
$529$	−19.1493	−0.832578
$530$	−32.4131	−1.40793
$531$	−4.60603	−0.199885
$532$	−8.49447	−0.368282
$533$	−43.4834	−1.88347
$534$	−31.3100	−1.35492
$535$	5.44925	0.235592
$536$	−0.981826	−0.0424084
$537$	16.4488	0.709820
$538$	29.9425	1.29091
$539$	4.69465	0.202213
$540$	−23.8483	−1.02627
$541$	8.85795	0.380833	0.190417	−	0.981703i	$-0.439016\pi$
$541$	8.85795	0.380833	0.190417	+	0.981703i	$0.439016\pi$
$542$	9.18752	0.394638
$543$	−42.8512	−1.83892
$544$	10.8551	0.465410
$545$	−47.8269	−2.04868
$546$	20.3355	0.870280
$547$	−14.7344	−0.629998	−0.314999	−	0.949092i	$-0.602004\pi$
$547$	−14.7344	−0.629998	−0.314999	+	0.949092i	$0.602004\pi$
$548$	−9.89442	−0.422669
$549$	−7.00486	−0.298960
$550$	−19.7590	−0.842526
$551$	−22.9184	−0.976356
$552$	−5.37116	−0.228612
$553$	−7.60348	−0.323333
$554$	41.2913	1.75430
$555$	−41.1992	−1.74881
$556$	−48.8241	−2.07060
$557$	31.3341	1.32767	0.663834	−	0.747880i	$-0.268928\pi$
$557$	31.3341	1.32767	0.663834	+	0.747880i	$0.268928\pi$
$558$	−20.6827	−0.875568
$559$	−45.4252	−1.92128
$560$	6.33609	0.267748
$561$	−13.6328	−0.575578
$562$	42.3130	1.78487
$563$	−34.9656	−1.47363	−0.736813	−	0.676097i	$-0.763670\pi$
$563$	−34.9656	−1.47363	−0.736813	+	0.676097i	$0.763670\pi$
$564$	−55.7010	−2.34543
$565$	−12.4876	−0.525356
$566$	19.9121	0.836969
$567$	−11.2239	−0.471358
$568$	7.95760	0.333893
$569$	−4.14279	−0.173675	−0.0868374	−	0.996222i	$-0.527676\pi$
$569$	−4.14279	−0.173675	−0.0868374	+	0.996222i	$0.527676\pi$
$570$	38.3778	1.60747
$571$	−19.4878	−0.815538	−0.407769	−	0.913085i	$-0.633693\pi$
$571$	−19.4878	−0.815538	−0.407769	+	0.913085i	$0.633693\pi$
$572$	55.7460	2.33086
$573$	−25.7733	−1.07669
$574$	20.5406	0.857347
$575$	−3.84583	−0.160382
$576$	−15.9498	−0.664574
$577$	0.391365	0.0162927	0.00814636	−	0.999967i	$-0.497407\pi$
$577$	0.391365	0.0162927	0.00814636	+	0.999967i	$0.497407\pi$
$578$	32.3339	1.34491
$579$	40.0182	1.66310
$580$	−48.5587	−2.01629
$581$	2.43143	0.100873
$582$	−38.4549	−1.59401
$583$	−26.8585	−1.11237
$584$	−5.19760	−0.215078
$585$	−16.0519	−0.663665
$586$	−37.5929	−1.55295
$587$	10.9592	0.452333	0.226166	−	0.974089i	$-0.427381\pi$
$587$	10.9592	0.452333	0.226166	+	0.974089i	$0.427381\pi$
$588$	−5.44030	−0.224354
$589$	−23.4028	−0.964294
$590$	−19.4981	−0.802722
$591$	−8.57731	−0.352823
$592$	18.0072	0.740093
$593$	−25.8627	−1.06205	−0.531026	−	0.847355i	$-0.678194\pi$
$593$	−25.8627	−1.06205	−0.531026	+	0.847355i	$0.678194\pi$
$594$	−34.8933	−1.43169
$595$	−3.67807	−0.150786
$596$	−12.0899	−0.495221
$597$	33.3730	1.36587
$598$	19.1585	0.783450
$599$	29.4357	1.20271	0.601356	−	0.798981i	$-0.294627\pi$
$599$	29.4357	1.20271	0.601356	+	0.798981i	$0.294627\pi$
$600$	5.36438	0.219000
$601$	−30.4396	−1.24166	−0.620830	−	0.783946i	$-0.713204\pi$
$601$	−30.4396	−1.24166	−0.620830	+	0.783946i	$0.713204\pi$
$602$	21.4578	0.874556
$603$	0.999942	0.0407208
$604$	30.0520	1.22280
$605$	−29.1244	−1.18408
$606$	−45.9352	−1.86599
$607$	45.6918	1.85457	0.927287	−	0.374350i	$-0.122134\pi$
$607$	45.6918	1.85457	0.927287	+	0.374350i	$0.122134\pi$
$608$	−25.3216	−1.02693
$609$	−14.6781	−0.594788
$610$	−29.6527	−1.20060
$611$	46.5469	1.88309
$612$	4.87366	0.197006
$613$	18.2191	0.735863	0.367931	−	0.929853i	$-0.380066\pi$
$613$	18.2191	0.735863	0.367931	+	0.929853i	$0.380066\pi$
$614$	21.2150	0.856166
$615$	−52.5575	−2.11932
$616$	−6.16933	−0.248570
$617$	−10.4796	−0.421895	−0.210947	−	0.977497i	$-0.567655\pi$
$617$	−10.4796	−0.421895	−0.210947	+	0.977497i	$0.567655\pi$
$618$	−28.8437	−1.16026
$619$	−11.5049	−0.462419	−0.231210	−	0.972904i	$-0.574268\pi$
$619$	−11.5049	−0.462419	−0.231210	+	0.972904i	$0.574268\pi$
$620$	−49.5850	−1.99138
$621$	−6.79153	−0.272535
$622$	52.9695	2.12388
$623$	−6.99970	−0.280437
$624$	22.7424	0.910424
$625$	−30.9582	−1.23833
$626$	−15.5401	−0.621108
$627$	31.8011	1.27001
$628$	1.77920	0.0709979
$629$	−10.4531	−0.416793
$630$	7.58256	0.302097
$631$	−28.8874	−1.14999	−0.574996	−	0.818157i	$-0.694996\pi$
$631$	−28.8874	−1.14999	−0.574996	+	0.818157i	$0.694996\pi$
$632$	9.99190	0.397456
$633$	26.9327	1.07048
$634$	47.3914	1.88215
$635$	−31.9659	−1.26853
$636$	31.1245	1.23417
$637$	4.54623	0.180128
$638$	−71.0479	−2.81281
$639$	−8.10443	−0.320606
$640$	−26.4367	−1.04500
$641$	0.921278	0.0363883	0.0181942	−	0.999834i	$-0.494208\pi$
$641$	0.921278	0.0363883	0.0181942	+	0.999834i	$0.494208\pi$
$642$	−9.23935	−0.364648
$643$	−4.44945	−0.175469	−0.0877345	−	0.996144i	$-0.527963\pi$
$643$	−4.44945	−0.175469	−0.0877345	+	0.996144i	$0.527963\pi$
$644$	−5.12542	−0.201970
$645$	−54.9045	−2.16186
$646$	9.73727	0.383108
$647$	−14.0256	−0.551403	−0.275702	−	0.961243i	$-0.588910\pi$
$647$	−14.0256	−0.551403	−0.275702	+	0.961243i	$0.588910\pi$
$648$	14.7495	0.579416
$649$	−16.1567	−0.634208
$650$	−19.1343	−0.750510
$651$	−14.9884	−0.587440
$652$	−23.4901	−0.919942
$653$	−5.86078	−0.229350	−0.114675	−	0.993403i	$-0.536583\pi$
$653$	−5.86078	−0.229350	−0.114675	+	0.993403i	$0.536583\pi$
$654$	81.0917	3.17094
$655$	−53.7975	−2.10204
$656$	22.9717	0.896894
$657$	5.29350	0.206519
$658$	−21.9877	−0.857171
$659$	−29.1898	−1.13707	−0.568537	−	0.822658i	$-0.692490\pi$
$659$	−29.1898	−1.13707	−0.568537	+	0.822658i	$0.692490\pi$
$660$	67.3792	2.62273
$661$	−29.4563	−1.14572	−0.572859	−	0.819654i	$-0.694166\pi$
$661$	−29.4563	−1.14572	−0.572859	+	0.819654i	$0.694166\pi$
$662$	48.2543	1.87546
$663$	−13.2018	−0.512717
$664$	−3.19519	−0.123997
$665$	8.57978	0.332710
$666$	21.5497	0.835036
$667$	−13.8286	−0.535444
$668$	25.6242	0.991430
$669$	54.6417	2.11257
$670$	4.23292	0.163532
$671$	−24.5712	−0.948562
$672$	−16.2173	−0.625596
$673$	−41.2328	−1.58941	−0.794703	−	0.606998i	$-0.792374\pi$
$673$	−41.2328	−1.58941	−0.794703	+	0.606998i	$0.792374\pi$
$674$	−62.1655	−2.39452
$675$	6.78295	0.261076
$676$	20.0287	0.770335
$677$	22.8297	0.877418	0.438709	−	0.898629i	$-0.355436\pi$
$677$	22.8297	0.877418	0.438709	+	0.898629i	$0.355436\pi$
$678$	21.1730	0.813144
$679$	−8.59701	−0.329923
$680$	4.83342	0.185353
$681$	−17.2817	−0.662236
$682$	−72.5495	−2.77806
$683$	−36.3498	−1.39089	−0.695443	−	0.718581i	$-0.744792\pi$
$683$	−36.3498	−1.39089	−0.695443	+	0.718581i	$0.744792\pi$
$684$	−11.3687	−0.434694
$685$	9.99379	0.381843
$686$	−2.14754	−0.0819934
$687$	−14.6919	−0.560530
$688$	23.9975	0.914897
$689$	−26.0094	−0.990880
$690$	23.1565	0.881554
$691$	−34.0476	−1.29523	−0.647615	−	0.761968i	$-0.724234\pi$
$691$	−34.0476	−1.29523	−0.647615	+	0.761968i	$0.724234\pi$
$692$	49.1603	1.86879
$693$	6.28316	0.238678
$694$	−37.6906	−1.43071
$695$	49.3144	1.87060
$696$	19.2888	0.731142
$697$	−13.3350	−0.505098
$698$	38.3835	1.45284
$699$	−22.2538	−0.841715
$700$	5.11895	0.193478
$701$	35.3892	1.33663	0.668316	−	0.743877i	$-0.267015\pi$
$701$	35.3892	1.33663	0.668316	+	0.743877i	$0.267015\pi$
$702$	−33.7902	−1.27533
$703$	24.3838	0.919654
$704$	−55.9477	−2.10861
$705$	56.2604	2.11889
$706$	−36.5505	−1.37560
$707$	−10.2693	−0.386218
$708$	18.7229	0.703651
$709$	23.9846	0.900759	0.450380	−	0.892837i	$-0.351289\pi$
$709$	23.9846	0.900759	0.450380	+	0.892837i	$0.351289\pi$
$710$	−34.3073	−1.28753
$711$	−10.1763	−0.381640
$712$	9.19845	0.344726
$713$	−14.1208	−0.528829
$714$	6.23626	0.233386
$715$	−56.3059	−2.10572
$716$	−20.6268	−0.770859
$717$	−12.0877	−0.451422
$718$	6.56151	0.244874
$719$	−4.44245	−0.165675	−0.0828377	−	0.996563i	$-0.526398\pi$
$719$	−4.44245	−0.165675	−0.0828377	+	0.996563i	$0.526398\pi$
$720$	8.48001	0.316031
$721$	−6.44833	−0.240148
$722$	18.0892	0.673211
$723$	52.9004	1.96739
$724$	53.7353	1.99706
$725$	13.8111	0.512932
$726$	49.3812	1.83271
$727$	−21.8722	−0.811194	−0.405597	−	0.914052i	$-0.632936\pi$
$727$	−21.8722	−0.811194	−0.405597	+	0.914052i	$0.632936\pi$
$728$	−5.97430	−0.221422
$729$	6.60464	0.244616
$730$	22.4083	0.829367
$731$	−13.9304	−0.515236
$732$	28.4739	1.05243
$733$	−37.4849	−1.38454	−0.692269	−	0.721640i	$-0.743389\pi$
$733$	−37.4849	−1.38454	−0.692269	+	0.721640i	$0.743389\pi$
$734$	−52.6844	−1.94462
$735$	5.49494	0.202684
$736$	−15.2786	−0.563178
$737$	3.50753	0.129202
$738$	27.4909	1.01195
$739$	−39.8637	−1.46641	−0.733204	−	0.680009i	$-0.761976\pi$
$739$	−39.8637	−1.46641	−0.733204	+	0.680009i	$0.761976\pi$
$740$	51.6637	1.89919
$741$	30.7958	1.13131
$742$	12.2863	0.451044
$743$	−51.2485	−1.88012	−0.940062	−	0.341004i	$-0.889233\pi$
$743$	−51.2485	−1.88012	−0.940062	+	0.341004i	$0.889233\pi$
$744$	19.6965	0.722109
$745$	12.2113	0.447388
$746$	23.5429	0.861966
$747$	3.25414	0.119063
$748$	17.0955	0.625074
$749$	−2.06556	−0.0754738
$750$	35.8757	1.30999
$751$	−23.7452	−0.866473	−0.433237	−	0.901280i	$-0.642629\pi$
$751$	−23.7452	−0.866473	−0.433237	+	0.901280i	$0.642629\pi$
$752$	−24.5901	−0.896710
$753$	−38.9320	−1.41876
$754$	−68.8018	−2.50561
$755$	−30.3538	−1.10469
$756$	9.03978	0.328774
$757$	−26.4481	−0.961272	−0.480636	−	0.876920i	$-0.659594\pi$
$757$	−26.4481	−0.961272	−0.480636	+	0.876920i	$0.659594\pi$
$758$	−18.2672	−0.663493
$759$	19.1883	0.696490
$760$	−11.2749	−0.408983
$761$	21.0528	0.763164	0.381582	−	0.924335i	$-0.375379\pi$
$761$	21.0528	0.763164	0.381582	+	0.924335i	$0.375379\pi$
$762$	54.1991	1.96342
$763$	18.1289	0.656312
$764$	32.3196	1.16928
$765$	−4.92261	−0.177977
$766$	−16.3473	−0.590653
$767$	−15.6460	−0.564943
$768$	−4.82061	−0.173949
$769$	19.2962	0.695840	0.347920	−	0.937524i	$-0.386888\pi$
$769$	19.2962	0.695840	0.347920	+	0.937524i	$0.386888\pi$
$770$	26.5977	0.958513
$771$	−32.5763	−1.17321
$772$	−50.1827	−1.80611
$773$	31.6357	1.13786	0.568928	−	0.822387i	$-0.307358\pi$
$773$	31.6357	1.13786	0.568928	+	0.822387i	$0.307358\pi$
$774$	28.7185	1.03226
$775$	14.1030	0.506595
$776$	11.2975	0.405557
$777$	15.6167	0.560246
$778$	80.4058	2.88269
$779$	31.1063	1.11450
$780$	65.2490	2.33629
$781$	−28.4282	−1.01724
$782$	5.87530	0.210100
$783$	24.3897	0.871615
$784$	−2.40171	−0.0857755
$785$	−1.79707	−0.0641402
$786$	91.2150	3.25353
$787$	24.9936	0.890926	0.445463	−	0.895300i	$-0.353039\pi$
$787$	24.9936	0.890926	0.445463	+	0.895300i	$0.353039\pi$
$788$	10.7559	0.383164
$789$	−23.0870	−0.821921
$790$	−43.0778	−1.53264
$791$	4.73345	0.168302
$792$	−8.25684	−0.293394
$793$	−23.7944	−0.844965
$794$	−44.7100	−1.58670
$795$	−31.4371	−1.11496
$796$	−41.8496	−1.48332
$797$	20.1138	0.712469	0.356234	−	0.934397i	$-0.384060\pi$
$797$	20.1138	0.712469	0.356234	+	0.934397i	$0.384060\pi$
$798$	−14.5472	−0.514967
$799$	14.2745	0.504994
$800$	15.2594	0.539500
$801$	−9.36817	−0.331008
$802$	55.3520	1.95455
$803$	18.5682	0.655258
$804$	−4.06464	−0.143349
$805$	5.17689	0.182462
$806$	−70.2559	−2.47466
$807$	29.0410	1.02229
$808$	13.4951	0.474757
$809$	−15.0901	−0.530539	−0.265270	−	0.964174i	$-0.585461\pi$
$809$	−15.0901	−0.530539	−0.265270	+	0.964174i	$0.585461\pi$
$810$	−63.5892	−2.23430
$811$	−12.6921	−0.445679	−0.222839	−	0.974855i	$-0.571533\pi$
$811$	−12.6921	−0.445679	−0.222839	+	0.974855i	$0.571533\pi$
$812$	18.4063	0.645936
$813$	8.91088	0.312518
$814$	75.5909	2.64946
$815$	23.7260	0.831085
$816$	6.97436	0.244151
$817$	32.4954	1.13687
$818$	−19.7926	−0.692034
$819$	6.08453	0.212611
$820$	65.9070	2.30157
$821$	38.0119	1.32662	0.663312	−	0.748343i	$-0.269150\pi$
$821$	38.0119	1.32662	0.663312	+	0.748343i	$0.269150\pi$
$822$	−16.9447	−0.591015
$823$	−20.0363	−0.698421	−0.349211	−	0.937044i	$-0.613550\pi$
$823$	−20.0363	−0.698421	−0.349211	+	0.937044i	$0.613550\pi$
$824$	8.47388	0.295202
$825$	−19.1640	−0.667206
$826$	7.39081	0.257159
$827$	−41.5846	−1.44604	−0.723020	−	0.690827i	$-0.757246\pi$
$827$	−41.5846	−1.44604	−0.723020	+	0.690827i	$0.757246\pi$
$828$	−6.85970	−0.238391
$829$	34.1828	1.18722	0.593609	−	0.804754i	$-0.297703\pi$
$829$	34.1828	1.18722	0.593609	+	0.804754i	$0.297703\pi$
$830$	13.7753	0.478148
$831$	40.0480	1.38925
$832$	−54.1789	−1.87832
$833$	1.39418	0.0483056
$834$	−83.6139	−2.89531
$835$	−25.8815	−0.895667
$836$	−39.8785	−1.37923
$837$	24.9051	0.860847
$838$	−84.7875	−2.92894
$839$	17.8997	0.617966	0.308983	−	0.951068i	$-0.400011\pi$
$839$	17.8997	0.617966	0.308983	+	0.951068i	$0.400011\pi$
$840$	−7.22102	−0.249149
$841$	20.6610	0.712447
$842$	6.82156	0.235086
$843$	41.0389	1.41346
$844$	−33.7735	−1.16253
$845$	−20.2299	−0.695928
$846$	−29.4277	−1.01174
$847$	11.0397	0.379329
$848$	13.7404	0.471849
$849$	19.3126	0.662806
$850$	−5.86788	−0.201267
$851$	14.7128	0.504348
$852$	32.9435	1.12863
$853$	48.9544	1.67617	0.838084	−	0.545541i	$-0.183676\pi$
$853$	48.9544	1.67617	0.838084	+	0.545541i	$0.183676\pi$
$854$	11.2400	0.384624
$855$	11.4829	0.392707
$856$	2.71439	0.0927760
$857$	51.2184	1.74959	0.874794	−	0.484495i	$-0.160997\pi$
$857$	51.2184	1.74959	0.874794	+	0.484495i	$0.160997\pi$
$858$	95.4681	3.25923
$859$	3.81546	0.130182	0.0650909	−	0.997879i	$-0.479266\pi$
$859$	3.81546	0.130182	0.0650909	+	0.997879i	$0.479266\pi$
$860$	68.8501	2.34777
$861$	19.9221	0.678943
$862$	19.9877	0.680782
$863$	1.00000	0.0340404
$863$	1.00000	0.0340404
$864$	26.9472	0.916762
$865$	−49.6540	−1.68829
$866$	−76.3360	−2.59400
$867$	31.3603	1.06505
$868$	18.7954	0.637956
$869$	−35.6957	−1.21089
$870$	−83.1594	−2.81937
$871$	3.39665	0.115091
$872$	−23.8236	−0.806770
$873$	−11.5060	−0.389418
$874$	−13.7053	−0.463587
$875$	8.02040	0.271139
$876$	−21.5174	−0.727007
$877$	21.7816	0.735513	0.367756	−	0.929922i	$-0.380126\pi$
$877$	21.7816	0.735513	0.367756	+	0.929922i	$0.380126\pi$
$878$	−6.73255	−0.227213
$879$	−36.4609	−1.22980
$880$	29.7457	1.00273
$881$	1.99752	0.0672981	0.0336491	−	0.999434i	$-0.489287\pi$
$881$	1.99752	0.0672981	0.0336491	+	0.999434i	$0.489287\pi$
$882$	−2.87420	−0.0967792
$883$	27.4087	0.922376	0.461188	−	0.887302i	$-0.347423\pi$
$883$	27.4087	0.922376	0.461188	+	0.887302i	$0.347423\pi$
$884$	16.5551	0.556807
$885$	−18.9110	−0.635685
$886$	−49.3129	−1.65670
$887$	−7.43296	−0.249574	−0.124787	−	0.992184i	$-0.539825\pi$
$887$	−7.43296	−0.249574	−0.124787	+	0.992184i	$0.539825\pi$
$888$	−20.5222	−0.688681
$889$	12.1168	0.406384
$890$	−39.6570	−1.32931
$891$	−52.6921	−1.76525
$892$	−68.5205	−2.29424
$893$	−33.2979	−1.11427
$894$	−20.7046	−0.692465
$895$	20.8339	0.696402
$896$	10.0209	0.334775
$897$	18.5816	0.620423
$898$	−43.4548	−1.45011
$899$	50.7105	1.69129
$900$	6.85104	0.228368
$901$	−7.97626	−0.265728
$902$	96.4308	3.21079
$903$	20.8117	0.692571
$904$	−6.22033	−0.206885
$905$	−54.2749	−1.80416
$906$	51.4656	1.70983
$907$	48.4739	1.60955	0.804775	−	0.593580i	$-0.202286\pi$
$907$	48.4739	1.60955	0.804775	+	0.593580i	$0.202286\pi$
$908$	21.6712	0.719184
$909$	−13.7441	−0.455864
$910$	25.7568	0.853829
$911$	9.75089	0.323061	0.161531	−	0.986868i	$-0.448357\pi$
$911$	9.75089	0.323061	0.161531	+	0.986868i	$0.448357\pi$
$912$	−16.2690	−0.538721
$913$	11.4147	0.377771
$914$	55.0033	1.81935
$915$	−28.7599	−0.950772
$916$	18.4236	0.608732
$917$	20.3921	0.673407
$918$	−10.3624	−0.342009
$919$	−0.157887	−0.00520821	−0.00260411	−	0.999997i	$-0.500829\pi$
$919$	−0.157887	−0.00520821	−0.00260411	+	0.999997i	$0.500829\pi$
$920$	−6.80307	−0.224290
$921$	20.5762	0.678008
$922$	8.37017	0.275657
$923$	−27.5295	−0.906144
$924$	−25.5403	−0.840214
$925$	−14.6942	−0.483143
$926$	23.0448	0.757300
$927$	−8.63023	−0.283454
$928$	54.8685	1.80115
$929$	13.4345	0.440771	0.220385	−	0.975413i	$-0.429269\pi$
$929$	13.4345	0.440771	0.220385	+	0.975413i	$0.429269\pi$
$930$	−84.9170	−2.78454
$931$	−3.25219	−0.106586
$932$	27.9062	0.914098
$933$	51.3746	1.68193
$934$	67.7736	2.21762
$935$	−17.2672	−0.564698
$936$	−7.99581	−0.261351
$937$	34.8941	1.13994	0.569969	−	0.821666i	$-0.306955\pi$
$937$	34.8941	1.13994	0.569969	+	0.821666i	$0.306955\pi$
$938$	−1.60450	−0.0523888
$939$	−15.0722	−0.491863
$940$	−70.5504	−2.30110
$941$	12.4305	0.405221	0.202611	−	0.979259i	$-0.435057\pi$
$941$	12.4305	0.405221	0.202611	+	0.979259i	$0.435057\pi$
$942$	3.04698	0.0992760
$943$	18.7690	0.611203
$944$	8.26556	0.269021
$945$	−9.13057	−0.297017
$946$	100.737	3.27524
$947$	−4.82169	−0.156684	−0.0783420	−	0.996927i	$-0.524963\pi$
$947$	−4.82169	−0.156684	−0.0783420	+	0.996927i	$0.524963\pi$
$948$	41.3652	1.34348
$949$	17.9812	0.583695
$950$	13.6879	0.444095
$951$	45.9644	1.49050
$952$	−1.83213	−0.0593795
$953$	−40.5985	−1.31512	−0.657558	−	0.753404i	$-0.728410\pi$
$953$	−40.5985	−1.31512	−0.657558	+	0.753404i	$0.728410\pi$
$954$	16.4436	0.532380
$955$	−32.6442	−1.05634
$956$	15.1579	0.490241
$957$	−68.9086	−2.22750
$958$	−80.5951	−2.60391
$959$	−3.78818	−0.122327
$960$	−65.4850	−2.11352
$961$	20.7823	0.670397
$962$	73.2012	2.36010
$963$	−2.76448	−0.0890840
$964$	−66.3370	−2.13657
$965$	50.6867	1.63166
$966$	−8.77756	−0.282413
$967$	43.5103	1.39920	0.699599	−	0.714536i	$-0.253362\pi$
$967$	43.5103	1.39920	0.699599	+	0.714536i	$0.253362\pi$
$968$	−14.5075	−0.466289
$969$	9.44408	0.303387
$970$	−48.7066	−1.56388
$971$	−53.4409	−1.71500	−0.857500	−	0.514484i	$-0.827984\pi$
$971$	−53.4409	−1.71500	−0.857500	+	0.514484i	$0.827984\pi$
$972$	33.9419	1.08869
$973$	−18.6928	−0.599264
$974$	32.0505	1.02697
$975$	−18.5582	−0.594337
$976$	12.5703	0.402365
$977$	−4.39925	−0.140744	−0.0703722	−	0.997521i	$-0.522419\pi$
$977$	−4.39925	−0.140744	−0.0703722	+	0.997521i	$0.522419\pi$
$978$	−40.2280	−1.28635
$979$	−32.8611	−1.05025
$980$	−6.89064	−0.220113
$981$	24.2632	0.774664
$982$	75.6455	2.41395
$983$	−12.1225	−0.386647	−0.193324	−	0.981135i	$-0.561927\pi$
$983$	−12.1225	−0.386647	−0.193324	+	0.981135i	$0.561927\pi$
$984$	−26.1801	−0.834590
$985$	−10.8639	−0.346154
$986$	−21.0993	−0.671939
$987$	−21.3257	−0.678804
$988$	−38.6178	−1.22860
$989$	19.6072	0.623472
$990$	35.5975	1.13136
$991$	−33.8492	−1.07526	−0.537628	−	0.843182i	$-0.680680\pi$
$991$	−33.8492	−1.07526	−0.537628	+	0.843182i	$0.680680\pi$
$992$	56.0281	1.77889
$993$	46.8013	1.48520
$994$	13.0043	0.412472
$995$	42.2699	1.34005
$996$	−13.2277	−0.419136
$997$	−12.8607	−0.407303	−0.203652	−	0.979043i	$-0.565281\pi$
$997$	−12.8607	−0.407303	−0.203652	+	0.979043i	$0.565281\pi$
$998$	−40.4672	−1.28097
$999$	−25.9492	−0.820996

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6041.2.a.c.1.13	✓	83

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6041.2.a.c.1.13	✓	83	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:	\( N \)	\(=\)	\( 6041 = 7 \cdot 863 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6041.a (trivial)

\(f(q)\)	\(=\)	\(q-2.14754 q^{2} -2.08287 q^{3} +2.61192 q^{4} -2.63815 q^{5} +4.47305 q^{6} +1.00000 q^{7} -1.31412 q^{8} +1.33837 q^{9} +O(q^{10})\)	\(q-2.14754 q^{2} -2.08287 q^{3} +2.61192 q^{4} -2.63815 q^{5} +4.47305 q^{6} +1.00000 q^{7} -1.31412 q^{8} +1.33837 q^{9} +5.66553 q^{10} +4.69465 q^{11} -5.44030 q^{12} +4.54623 q^{13} -2.14754 q^{14} +5.49494 q^{15} -2.40171 q^{16} +1.39418 q^{17} -2.87420 q^{18} -3.25219 q^{19} -6.89064 q^{20} -2.08287 q^{21} -10.0819 q^{22} -1.96232 q^{23} +2.73715 q^{24} +1.95984 q^{25} -9.76320 q^{26} +3.46097 q^{27} +2.61192 q^{28} +7.04705 q^{29} -11.8006 q^{30} +7.19599 q^{31} +7.78602 q^{32} -9.77836 q^{33} -2.99406 q^{34} -2.63815 q^{35} +3.49571 q^{36} -7.49766 q^{37} +6.98421 q^{38} -9.46923 q^{39} +3.46685 q^{40} -9.56471 q^{41} +4.47305 q^{42} -9.99183 q^{43} +12.2620 q^{44} -3.53082 q^{45} +4.21416 q^{46} +10.2386 q^{47} +5.00247 q^{48} +1.00000 q^{49} -4.20883 q^{50} -2.90391 q^{51} +11.8744 q^{52} -5.72110 q^{53} -7.43257 q^{54} -12.3852 q^{55} -1.31412 q^{56} +6.77391 q^{57} -15.1338 q^{58} -3.44152 q^{59} +14.3523 q^{60} -5.23388 q^{61} -15.4537 q^{62} +1.33837 q^{63} -11.9173 q^{64} -11.9936 q^{65} +20.9994 q^{66} +0.747135 q^{67} +3.64149 q^{68} +4.08727 q^{69} +5.66553 q^{70} -6.05545 q^{71} -1.75878 q^{72} +3.95519 q^{73} +16.1015 q^{74} -4.08210 q^{75} -8.49447 q^{76} +4.69465 q^{77} +20.3355 q^{78} -7.60348 q^{79} +6.33609 q^{80} -11.2239 q^{81} +20.5406 q^{82} +2.43143 q^{83} -5.44030 q^{84} -3.67807 q^{85} +21.4578 q^{86} -14.6781 q^{87} -6.16933 q^{88} -6.99970 q^{89} +7.58256 q^{90} +4.54623 q^{91} -5.12542 q^{92} -14.9884 q^{93} -21.9877 q^{94} +8.57978 q^{95} -16.2173 q^{96} -8.59701 q^{97} -2.14754 q^{98} +6.28316 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 83 q - 8 q^{2} - 12 q^{3} + 48 q^{4} - 11 q^{5} - 8 q^{6} + 83 q^{7} - 18 q^{8} + 39 q^{9}+O(q^{10}) \) 83 * q - 8 * q^2 - 12 * q^3 + 48 * q^4 - 11 * q^5 - 8 * q^6 + 83 * q^7 - 18 * q^8 + 39 * q^9	\( 83 q - 8 q^{2} - 12 q^{3} + 48 q^{4} - 11 q^{5} - 8 q^{6} + 83 q^{7} - 18 q^{8} + 39 q^{9} - 20 q^{10} - 26 q^{11} - 14 q^{12} - 22 q^{13} - 8 q^{14} - 37 q^{15} - 10 q^{16} - 9 q^{17} - 27 q^{18} - 42 q^{19} - 22 q^{20} - 12 q^{21} - 44 q^{22} - 46 q^{23} - 24 q^{24} - 20 q^{25} - 9 q^{26} - 39 q^{27} + 48 q^{28} - 36 q^{29} - 11 q^{30} - 107 q^{31} - 19 q^{32} - 25 q^{33} - 24 q^{34} - 11 q^{35} - 32 q^{36} - 75 q^{37} - 16 q^{38} - 78 q^{39} - 34 q^{40} - 17 q^{41} - 8 q^{42} - 87 q^{43} - 32 q^{44} - 17 q^{45} - 56 q^{46} - 39 q^{47} - 16 q^{48} + 83 q^{49} - 26 q^{50} - 71 q^{51} - 53 q^{52} - 28 q^{53} - 25 q^{54} - 94 q^{55} - 18 q^{56} - 79 q^{57} - 69 q^{58} - 26 q^{59} - 43 q^{60} - 56 q^{61} - 6 q^{62} + 39 q^{63} - 108 q^{64} - 26 q^{65} + 10 q^{66} - 123 q^{67} - 11 q^{68} + 2 q^{69} - 20 q^{70} - 96 q^{71} - 11 q^{72} - 53 q^{73} - 26 q^{74} - 27 q^{75} - 65 q^{76} - 26 q^{77} - 43 q^{78} - 160 q^{79} + 12 q^{80} - 53 q^{81} - 20 q^{82} - 2 q^{83} - 14 q^{84} - 110 q^{85} + 24 q^{86} - 52 q^{87} - 79 q^{88} - 5 q^{89} - 4 q^{90} - 22 q^{91} - 51 q^{92} - 30 q^{93} - 9 q^{94} - 76 q^{95} - 3 q^{96} - 44 q^{97} - 8 q^{98} - 82 q^{99}+O(q^{100}) \) 83 * q - 8 * q^2 - 12 * q^3 + 48 * q^4 - 11 * q^5 - 8 * q^6 + 83 * q^7 - 18 * q^8 + 39 * q^9 - 20 * q^10 - 26 * q^11 - 14 * q^12 - 22 * q^13 - 8 * q^14 - 37 * q^15 - 10 * q^16 - 9 * q^17 - 27 * q^18 - 42 * q^19 - 22 * q^20 - 12 * q^21 - 44 * q^22 - 46 * q^23 - 24 * q^24 - 20 * q^25 - 9 * q^26 - 39 * q^27 + 48 * q^28 - 36 * q^29 - 11 * q^30 - 107 * q^31 - 19 * q^32 - 25 * q^33 - 24 * q^34 - 11 * q^35 - 32 * q^36 - 75 * q^37 - 16 * q^38 - 78 * q^39 - 34 * q^40 - 17 * q^41 - 8 * q^42 - 87 * q^43 - 32 * q^44 - 17 * q^45 - 56 * q^46 - 39 * q^47 - 16 * q^48 + 83 * q^49 - 26 * q^50 - 71 * q^51 - 53 * q^52 - 28 * q^53 - 25 * q^54 - 94 * q^55 - 18 * q^56 - 79 * q^57 - 69 * q^58 - 26 * q^59 - 43 * q^60 - 56 * q^61 - 6 * q^62 + 39 * q^63 - 108 * q^64 - 26 * q^65 + 10 * q^66 - 123 * q^67 - 11 * q^68 + 2 * q^69 - 20 * q^70 - 96 * q^71 - 11 * q^72 - 53 * q^73 - 26 * q^74 - 27 * q^75 - 65 * q^76 - 26 * q^77 - 43 * q^78 - 160 * q^79 + 12 * q^80 - 53 * q^81 - 20 * q^82 - 2 * q^83 - 14 * q^84 - 110 * q^85 + 24 * q^86 - 52 * q^87 - 79 * q^88 - 5 * q^89 - 4 * q^90 - 22 * q^91 - 51 * q^92 - 30 * q^93 - 9 * q^94 - 76 * q^95 - 3 * q^96 - 44 * q^97 - 8 * q^98 - 82 * q^99

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