LMFDB - Embedded newform 8041.2.a.h.1.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8041,2,Mod(1,8041)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8041, 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("8041.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8041 = 11 \cdot 17 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8041.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:	$64.2077082653$
Analytic rank:	$1$
Dimension:	$74$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
Character	$\chi$	$=$	8041.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.14896 q^{2} -2.65732 q^{3} +2.61805 q^{4} +2.21050 q^{5} +5.71048 q^{6} +0.288836 q^{7} -1.32816 q^{8} +4.06133 q^{9} +O(q^{10})$	\(q-2.14896 q^{2} -2.65732 q^{3} +2.61805 q^{4} +2.21050 q^{5} +5.71048 q^{6} +0.288836 q^{7} -1.32816 q^{8} +4.06133 q^{9} -4.75028 q^{10} -1.00000 q^{11} -6.95698 q^{12} +5.15530 q^{13} -0.620698 q^{14} -5.87399 q^{15} -2.38192 q^{16} -1.00000 q^{17} -8.72765 q^{18} -4.16046 q^{19} +5.78719 q^{20} -0.767529 q^{21} +2.14896 q^{22} -6.85642 q^{23} +3.52934 q^{24} -0.113695 q^{25} -11.0786 q^{26} -2.82029 q^{27} +0.756186 q^{28} +8.86798 q^{29} +12.6230 q^{30} +3.29505 q^{31} +7.77499 q^{32} +2.65732 q^{33} +2.14896 q^{34} +0.638472 q^{35} +10.6328 q^{36} +0.889189 q^{37} +8.94068 q^{38} -13.6993 q^{39} -2.93590 q^{40} +10.5329 q^{41} +1.64939 q^{42} -1.00000 q^{43} -2.61805 q^{44} +8.97757 q^{45} +14.7342 q^{46} +3.18786 q^{47} +6.32953 q^{48} -6.91657 q^{49} +0.244327 q^{50} +2.65732 q^{51} +13.4968 q^{52} -8.40587 q^{53} +6.06071 q^{54} -2.21050 q^{55} -0.383620 q^{56} +11.0557 q^{57} -19.0570 q^{58} -5.12485 q^{59} -15.3784 q^{60} +0.213499 q^{61} -7.08094 q^{62} +1.17306 q^{63} -11.9443 q^{64} +11.3958 q^{65} -5.71048 q^{66} +4.34441 q^{67} -2.61805 q^{68} +18.2197 q^{69} -1.37205 q^{70} -3.09998 q^{71} -5.39410 q^{72} +3.79854 q^{73} -1.91084 q^{74} +0.302124 q^{75} -10.8923 q^{76} -0.288836 q^{77} +29.4392 q^{78} -11.5000 q^{79} -5.26524 q^{80} -4.68958 q^{81} -22.6347 q^{82} -8.17575 q^{83} -2.00943 q^{84} -2.21050 q^{85} +2.14896 q^{86} -23.5650 q^{87} +1.32816 q^{88} -16.2242 q^{89} -19.2925 q^{90} +1.48904 q^{91} -17.9504 q^{92} -8.75599 q^{93} -6.85060 q^{94} -9.19670 q^{95} -20.6606 q^{96} -0.0290401 q^{97} +14.8635 q^{98} -4.06133 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 74 q - 7 q^{2} - 3 q^{3} + 79 q^{4} - 6 q^{5} - 12 q^{6} - 16 q^{7} - 21 q^{8} + 75 q^{9}+O(q^{10}) $ 74 * q - 7 * q^2 - 3 * q^3 + 79 * q^4 - 6 * q^5 - 12 * q^6 - 16 * q^7 - 21 * q^8 + 75 * q^9	\( 74 q - 7 q^{2} - 3 q^{3} + 79 q^{4} - 6 q^{5} - 12 q^{6} - 16 q^{7} - 21 q^{8} + 75 q^{9} - 9 q^{10} - 74 q^{11} - 3 q^{12} + 4 q^{13} - 5 q^{14} - 17 q^{15} + 85 q^{16} - 74 q^{17} - 23 q^{18} - 21 q^{20} - 22 q^{21} + 7 q^{22} - 23 q^{23} - 51 q^{24} + 90 q^{25} - 46 q^{26} - 27 q^{27} - 61 q^{28} - 63 q^{29} - 22 q^{30} - 31 q^{31} - 69 q^{32} + 3 q^{33} + 7 q^{34} - 20 q^{35} + 51 q^{36} + 8 q^{37} - 2 q^{38} - 77 q^{39} - 37 q^{40} - 64 q^{41} + 13 q^{42} - 74 q^{43} - 79 q^{44} - 12 q^{45} - 53 q^{46} - 32 q^{47} + 2 q^{48} + 78 q^{49} - 104 q^{50} + 3 q^{51} + 13 q^{52} + 25 q^{53} - 110 q^{54} + 6 q^{55} - 29 q^{56} - 29 q^{57} - 14 q^{58} - 61 q^{59} - 82 q^{60} - 36 q^{61} - 63 q^{62} - 104 q^{63} + 107 q^{64} - 65 q^{65} + 12 q^{66} + 33 q^{67} - 79 q^{68} - 34 q^{69} - 3 q^{70} - 168 q^{71} - 67 q^{72} - 47 q^{73} - 54 q^{74} - 53 q^{75} - 4 q^{76} + 16 q^{77} - 3 q^{78} - 79 q^{79} - 59 q^{80} + 70 q^{81} - 18 q^{82} - 36 q^{83} - 118 q^{84} + 6 q^{85} + 7 q^{86} - 24 q^{87} + 21 q^{88} - 24 q^{89} + 25 q^{90} - 14 q^{91} - 18 q^{92} - 13 q^{93} + 9 q^{94} - 155 q^{95} - 50 q^{96} + q^{97} - 60 q^{98} - 75 q^{99}+O(q^{100}) \) 74 * q - 7 * q^2 - 3 * q^3 + 79 * q^4 - 6 * q^5 - 12 * q^6 - 16 * q^7 - 21 * q^8 + 75 * q^9 - 9 * q^10 - 74 * q^11 - 3 * q^12 + 4 * q^13 - 5 * q^14 - 17 * q^15 + 85 * q^16 - 74 * q^17 - 23 * q^18 - 21 * q^20 - 22 * q^21 + 7 * q^22 - 23 * q^23 - 51 * q^24 + 90 * q^25 - 46 * q^26 - 27 * q^27 - 61 * q^28 - 63 * q^29 - 22 * q^30 - 31 * q^31 - 69 * q^32 + 3 * q^33 + 7 * q^34 - 20 * q^35 + 51 * q^36 + 8 * q^37 - 2 * q^38 - 77 * q^39 - 37 * q^40 - 64 * q^41 + 13 * q^42 - 74 * q^43 - 79 * q^44 - 12 * q^45 - 53 * q^46 - 32 * q^47 + 2 * q^48 + 78 * q^49 - 104 * q^50 + 3 * q^51 + 13 * q^52 + 25 * q^53 - 110 * q^54 + 6 * q^55 - 29 * q^56 - 29 * q^57 - 14 * q^58 - 61 * q^59 - 82 * q^60 - 36 * q^61 - 63 * q^62 - 104 * q^63 + 107 * q^64 - 65 * q^65 + 12 * q^66 + 33 * q^67 - 79 * q^68 - 34 * q^69 - 3 * q^70 - 168 * q^71 - 67 * q^72 - 47 * q^73 - 54 * q^74 - 53 * q^75 - 4 * q^76 + 16 * q^77 - 3 * q^78 - 79 * q^79 - 59 * q^80 + 70 * q^81 - 18 * q^82 - 36 * q^83 - 118 * q^84 + 6 * q^85 + 7 * q^86 - 24 * q^87 + 21 * q^88 - 24 * q^89 + 25 * q^90 - 14 * q^91 - 18 * q^92 - 13 * q^93 + 9 * q^94 - 155 * q^95 - 50 * q^96 + q^97 - 60 * q^98 - 75 * 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 $

$2$	−2.14896	−1.51955	−0.759774	−	0.650188i	$-0.774690\pi$
$2$	−2.14896	−1.51955	−0.759774	+	0.650188i	$0.774690\pi$
$3$	−2.65732	−1.53420	−0.767101	−	0.641526i	$-0.778302\pi$
$3$	−2.65732	−1.53420	−0.767101	+	0.641526i	$0.778302\pi$
$4$	2.61805	1.30902
$5$	2.21050	0.988565	0.494283	−	0.869301i	$-0.335431\pi$
$5$	2.21050	0.988565	0.494283	+	0.869301i	$0.335431\pi$
$6$	5.71048	2.33129
$7$	0.288836	0.109170	0.0545849	−	0.998509i	$-0.482616\pi$
$7$	0.288836	0.109170	0.0545849	+	0.998509i	$0.482616\pi$
$8$	−1.32816	−0.469576
$9$	4.06133	1.35378
$10$	−4.75028	−1.50217
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−6.95698	−2.00831
$13$	5.15530	1.42982	0.714912	−	0.699215i	$-0.246467\pi$
$13$	5.15530	1.42982	0.714912	+	0.699215i	$0.246467\pi$
$14$	−0.620698	−0.165889
$15$	−5.87399	−1.51666
$16$	−2.38192	−0.595481
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−8.72765	−2.05713
$19$	−4.16046	−0.954475	−0.477238	−	0.878774i	$-0.658362\pi$
$19$	−4.16046	−0.954475	−0.477238	+	0.878774i	$0.658362\pi$
$20$	5.78719	1.29405
$21$	−0.767529	−0.167488
$22$	2.14896	0.458161
$23$	−6.85642	−1.42966	−0.714831	−	0.699297i	$-0.753496\pi$
$23$	−6.85642	−1.42966	−0.714831	+	0.699297i	$0.753496\pi$
$24$	3.52934	0.720424
$25$	−0.113695	−0.0227390
$26$	−11.0786	−2.17268
$27$	−2.82029	−0.542766
$28$	0.756186	0.142906
$29$	8.86798	1.64674	0.823371	−	0.567503i	$-0.192091\pi$
$29$	8.86798	1.64674	0.823371	+	0.567503i	$0.192091\pi$
$30$	12.6230	2.30463
$31$	3.29505	0.591808	0.295904	−	0.955218i	$-0.404379\pi$
$31$	3.29505	0.591808	0.295904	+	0.955218i	$0.404379\pi$
$32$	7.77499	1.37444
$33$	2.65732	0.462579
$34$	2.14896	0.368544
$35$	0.638472	0.107921
$36$	10.6328	1.77213
$37$	0.889189	0.146182	0.0730909	−	0.997325i	$-0.476714\pi$
$37$	0.889189	0.146182	0.0730909	+	0.997325i	$0.476714\pi$
$38$	8.94068	1.45037
$39$	−13.6993	−2.19364
$40$	−2.93590	−0.464206
$41$	10.5329	1.64496	0.822478	−	0.568796i	$-0.192591\pi$
$41$	10.5329	1.64496	0.822478	+	0.568796i	$0.192591\pi$
$42$	1.64939	0.254507
$43$	−1.00000	−0.152499
$43$	−1.00000	−0.152499
$44$	−2.61805	−0.394685
$45$	8.97757	1.33830
$46$	14.7342	2.17244
$47$	3.18786	0.464997	0.232499	−	0.972597i	$-0.425310\pi$
$47$	3.18786	0.464997	0.232499	+	0.972597i	$0.425310\pi$
$48$	6.32953	0.913589
$49$	−6.91657	−0.988082
$50$	0.244327	0.0345530
$51$	2.65732	0.372099
$52$	13.4968	1.87167
$53$	−8.40587	−1.15464	−0.577318	−	0.816520i	$-0.695901\pi$
$53$	−8.40587	−1.15464	−0.577318	+	0.816520i	$0.695901\pi$
$54$	6.06071	0.824758
$55$	−2.21050	−0.298064
$56$	−0.383620	−0.0512634
$57$	11.0557	1.46436
$58$	−19.0570	−2.50230
$59$	−5.12485	−0.667199	−0.333599	−	0.942715i	$-0.608263\pi$
$59$	−5.12485	−0.667199	−0.333599	+	0.942715i	$0.608263\pi$
$60$	−15.3784	−1.98534
$61$	0.213499	0.0273357	0.0136679	−	0.999907i	$-0.495649\pi$
$61$	0.213499	0.0273357	0.0136679	+	0.999907i	$0.495649\pi$
$62$	−7.08094	−0.899281
$63$	1.17306	0.147792
$64$	−11.9443	−1.49304
$65$	11.3958	1.41347
$66$	−5.71048	−0.702911
$67$	4.34441	0.530754	0.265377	−	0.964145i	$-0.414504\pi$
$67$	4.34441	0.530754	0.265377	+	0.964145i	$0.414504\pi$
$68$	−2.61805	−0.317485
$69$	18.2197	2.19339
$70$	−1.37205	−0.163992
$71$	−3.09998	−0.367900	−0.183950	−	0.982936i	$-0.558888\pi$
$71$	−3.09998	−0.367900	−0.183950	+	0.982936i	$0.558888\pi$
$72$	−5.39410	−0.635701
$73$	3.79854	0.444585	0.222293	−	0.974980i	$-0.428646\pi$
$73$	3.79854	0.444585	0.222293	+	0.974980i	$0.428646\pi$
$74$	−1.91084	−0.222130
$75$	0.302124	0.0348862
$76$	−10.8923	−1.24943
$77$	−0.288836	−0.0329159
$78$	29.4392	3.33334
$79$	−11.5000	−1.29385	−0.646925	−	0.762554i	$-0.723945\pi$
$79$	−11.5000	−1.29385	−0.646925	+	0.762554i	$0.723945\pi$
$80$	−5.26524	−0.588672
$81$	−4.68958	−0.521065
$82$	−22.6347	−2.49959
$83$	−8.17575	−0.897405	−0.448703	−	0.893681i	$-0.648114\pi$
$83$	−8.17575	−0.897405	−0.448703	+	0.893681i	$0.648114\pi$
$84$	−2.00943	−0.219246
$85$	−2.21050	−0.239762
$86$	2.14896	0.231729
$87$	−23.5650	−2.52644
$88$	1.32816	0.141582
$89$	−16.2242	−1.71976	−0.859879	−	0.510498i	$-0.829461\pi$
$89$	−16.2242	−1.71976	−0.859879	+	0.510498i	$0.829461\pi$
$90$	−19.2925	−2.03360
$91$	1.48904	0.156093
$92$	−17.9504	−1.87146
$93$	−8.75599	−0.907954
$94$	−6.85060	−0.706585
$95$	−9.19670	−0.943561
$96$	−20.6606	−2.10866
$97$	−0.0290401	−0.00294858	−0.00147429	−	0.999999i	$-0.500469\pi$
$97$	−0.0290401	−0.00294858	−0.00147429	+	0.999999i	$0.500469\pi$
$98$	14.8635	1.50144
$99$	−4.06133	−0.408179
$100$	−0.297659	−0.0297659
$101$	−5.64790	−0.561987	−0.280994	−	0.959710i	$-0.590664\pi$
$101$	−5.64790	−0.561987	−0.280994	+	0.959710i	$0.590664\pi$
$102$	−5.71048	−0.565422
$103$	7.11054	0.700622	0.350311	−	0.936633i	$-0.386076\pi$
$103$	7.11054	0.700622	0.350311	+	0.936633i	$0.386076\pi$
$104$	−6.84707	−0.671410
$105$	−1.69662	−0.165573
$106$	18.0639	1.75452
$107$	13.4983	1.30493	0.652463	−	0.757821i	$-0.273736\pi$
$107$	13.4983	1.30493	0.652463	+	0.757821i	$0.273736\pi$
$108$	−7.38366	−0.710493
$109$	16.3740	1.56835	0.784173	−	0.620542i	$-0.213087\pi$
$109$	16.3740	1.56835	0.784173	+	0.620542i	$0.213087\pi$
$110$	4.75028	0.452922
$111$	−2.36286	−0.224272
$112$	−0.687986	−0.0650085
$113$	4.92935	0.463714	0.231857	−	0.972750i	$-0.425520\pi$
$113$	4.92935	0.463714	0.231857	+	0.972750i	$0.425520\pi$
$114$	−23.7582	−2.22516
$115$	−15.1561	−1.41331
$116$	23.2168	2.15562
$117$	20.9374	1.93566
$118$	11.0131	1.01384
$119$	−0.288836	−0.0264776
$120$	7.80161	0.712186
$121$	1.00000	0.0909091
$122$	−0.458801	−0.0415379
$123$	−27.9892	−2.52370
$124$	8.62659	0.774691
$125$	−11.3038	−1.01104
$126$	−2.52086	−0.224576
$127$	1.48823	0.132059	0.0660293	−	0.997818i	$-0.478967\pi$
$127$	1.48823	0.132059	0.0660293	+	0.997818i	$0.478967\pi$
$128$	10.1179	0.894309
$129$	2.65732	0.233964
$130$	−24.4891	−2.14784
$131$	−9.66730	−0.844636	−0.422318	−	0.906448i	$-0.638783\pi$
$131$	−9.66730	−0.844636	−0.422318	+	0.906448i	$0.638783\pi$
$132$	6.95698	0.605527
$133$	−1.20169	−0.104200
$134$	−9.33598	−0.806506
$135$	−6.23425	−0.536559
$136$	1.32816	0.113889
$137$	−7.58916	−0.648386	−0.324193	−	0.945991i	$-0.605093\pi$
$137$	−7.58916	−0.648386	−0.324193	+	0.945991i	$0.605093\pi$
$138$	−39.1534	−3.33296
$139$	−17.6480	−1.49688	−0.748441	−	0.663201i	$-0.769197\pi$
$139$	−17.6480	−1.49688	−0.748441	+	0.663201i	$0.769197\pi$
$140$	1.67155	0.141272
$141$	−8.47116	−0.713400
$142$	6.66175	0.559042
$143$	−5.15530	−0.431108
$144$	−9.67379	−0.806149
$145$	19.6027	1.62791
$146$	−8.16292	−0.675568
$147$	18.3795	1.51592
$148$	2.32794	0.191355
$149$	−2.09497	−0.171627	−0.0858135	−	0.996311i	$-0.527349\pi$
$149$	−2.09497	−0.171627	−0.0858135	+	0.996311i	$0.527349\pi$
$150$	−0.649253	−0.0530113
$151$	−12.7914	−1.04095	−0.520474	−	0.853877i	$-0.674245\pi$
$151$	−12.7914	−1.04095	−0.520474	+	0.853877i	$0.674245\pi$
$152$	5.52576	0.448198
$153$	−4.06133	−0.328339
$154$	0.620698	0.0500173
$155$	7.28370	0.585041
$156$	−35.8653	−2.87152
$157$	−4.67998	−0.373503	−0.186751	−	0.982407i	$-0.559796\pi$
$157$	−4.67998	−0.373503	−0.186751	+	0.982407i	$0.559796\pi$
$158$	24.7131	1.96607
$159$	22.3371	1.77144
$160$	17.1866	1.35872
$161$	−1.98038	−0.156076
$162$	10.0777	0.791783
$163$	−18.5627	−1.45395	−0.726973	−	0.686666i	$-0.759074\pi$
$163$	−18.5627	−1.45395	−0.726973	+	0.686666i	$0.759074\pi$
$164$	27.5755	2.15329
$165$	5.87399	0.457290
$166$	17.5694	1.36365
$167$	8.32835	0.644467	0.322233	−	0.946660i	$-0.395566\pi$
$167$	8.32835	0.644467	0.322233	+	0.946660i	$0.395566\pi$
$168$	1.01940	0.0786485
$169$	13.5771	1.04439
$170$	4.75028	0.364330
$171$	−16.8970	−1.29215
$172$	−2.61805	−0.199624
$173$	−10.6878	−0.812580	−0.406290	−	0.913744i	$-0.633178\pi$
$173$	−10.6878	−0.812580	−0.406290	+	0.913744i	$0.633178\pi$
$174$	50.6404	3.83904
$175$	−0.0328392	−0.00248241
$176$	2.38192	0.179544
$177$	13.6184	1.02362
$178$	34.8651	2.61325
$179$	−1.91060	−0.142805	−0.0714025	−	0.997448i	$-0.522747\pi$
$179$	−1.91060	−0.142805	−0.0714025	+	0.997448i	$0.522747\pi$
$180$	23.5037	1.75186
$181$	18.0094	1.33863	0.669313	−	0.742981i	$-0.266589\pi$
$181$	18.0094	1.33863	0.669313	+	0.742981i	$0.266589\pi$
$182$	−3.19989	−0.237191
$183$	−0.567334	−0.0419385
$184$	9.10642	0.671334
$185$	1.96555	0.144510
$186$	18.8163	1.37968
$187$	1.00000	0.0731272
$188$	8.34597	0.608692
$189$	−0.814602	−0.0592536
$190$	19.7634	1.43379
$191$	−5.02033	−0.363258	−0.181629	−	0.983367i	$-0.558137\pi$
$191$	−5.02033	−0.363258	−0.181629	+	0.983367i	$0.558137\pi$
$192$	31.7399	2.29063
$193$	−12.7415	−0.917154	−0.458577	−	0.888655i	$-0.651641\pi$
$193$	−12.7415	−0.917154	−0.458577	+	0.888655i	$0.651641\pi$
$194$	0.0624062	0.00448051
$195$	−30.2822	−2.16855
$196$	−18.1079	−1.29342
$197$	1.63125	0.116222	0.0581108	−	0.998310i	$-0.481492\pi$
$197$	1.63125	0.116222	0.0581108	+	0.998310i	$0.481492\pi$
$198$	8.72765	0.620247
$199$	14.7571	1.04610	0.523052	−	0.852301i	$-0.324793\pi$
$199$	14.7571	1.04610	0.523052	+	0.852301i	$0.324793\pi$
$200$	0.151005	0.0106777
$201$	−11.5445	−0.814284
$202$	12.1371	0.853966
$203$	2.56139	0.179774
$204$	6.95698	0.487086
$205$	23.2829	1.62615
$206$	−15.2803	−1.06463
$207$	−27.8462	−1.93544
$208$	−12.2795	−0.851433
$209$	4.16046	0.287785
$210$	3.64598	0.251596
$211$	14.7070	1.01247	0.506235	−	0.862396i	$-0.331037\pi$
$211$	14.7070	1.01247	0.506235	+	0.862396i	$0.331037\pi$
$212$	−22.0070	−1.51144
$213$	8.23763	0.564433
$214$	−29.0073	−1.98290
$215$	−2.21050	−0.150755
$216$	3.74580	0.254869
$217$	0.951729	0.0646076
$218$	−35.1872	−2.38318
$219$	−10.0939	−0.682083
$220$	−5.78719	−0.390172
$221$	−5.15530	−0.346783
$222$	5.07770	0.340793
$223$	4.76228	0.318906	0.159453	−	0.987206i	$-0.449027\pi$
$223$	4.76228	0.318906	0.159453	+	0.987206i	$0.449027\pi$
$224$	2.24570	0.150047
$225$	−0.461753	−0.0307835
$226$	−10.5930	−0.704636
$227$	−15.2723	−1.01365	−0.506827	−	0.862048i	$-0.669182\pi$
$227$	−15.2723	−1.01365	−0.506827	+	0.862048i	$0.669182\pi$
$228$	28.9442	1.91688
$229$	−19.3504	−1.27871	−0.639356	−	0.768911i	$-0.720799\pi$
$229$	−19.3504	−1.27871	−0.639356	+	0.768911i	$0.720799\pi$
$230$	32.5699	2.14760
$231$	0.767529	0.0504997
$232$	−11.7781	−0.773270
$233$	10.7051	0.701317	0.350658	−	0.936503i	$-0.385958\pi$
$233$	10.7051	0.701317	0.350658	+	0.936503i	$0.385958\pi$
$234$	−44.9937	−2.94133
$235$	7.04676	0.459680
$236$	−13.4171	−0.873379
$237$	30.5591	1.98503
$238$	0.620698	0.0402339
$239$	1.00935	0.0652892	0.0326446	−	0.999467i	$-0.489607\pi$
$239$	1.00935	0.0652892	0.0326446	+	0.999467i	$0.489607\pi$
$240$	13.9914	0.903142
$241$	−3.93423	−0.253426	−0.126713	−	0.991939i	$-0.540443\pi$
$241$	−3.93423	−0.253426	−0.126713	+	0.991939i	$0.540443\pi$
$242$	−2.14896	−0.138141
$243$	20.9226	1.34218
$244$	0.558950	0.0357831
$245$	−15.2891	−0.976783
$246$	60.1477	3.83488
$247$	−21.4484	−1.36473
$248$	−4.37635	−0.277899
$249$	21.7256	1.37680
$250$	24.2915	1.53633
$251$	−25.2827	−1.59583	−0.797915	−	0.602771i	$-0.794063\pi$
$251$	−25.2827	−1.59583	−0.797915	+	0.602771i	$0.794063\pi$
$252$	3.07112	0.193463
$253$	6.85642	0.431059
$254$	−3.19814	−0.200669
$255$	5.87399	0.367844
$256$	2.14555	0.134097
$257$	29.3672	1.83188	0.915938	−	0.401320i	$-0.131448\pi$
$257$	29.3672	1.83188	0.915938	+	0.401320i	$0.131448\pi$
$258$	−5.71048	−0.355519
$259$	0.256830	0.0159586
$260$	29.8347	1.85027
$261$	36.0158	2.22932
$262$	20.7747	1.28346
$263$	−4.40476	−0.271609	−0.135805	−	0.990736i	$-0.543362\pi$
$263$	−4.40476	−0.271609	−0.135805	+	0.990736i	$0.543362\pi$
$264$	−3.52934	−0.217216
$265$	−18.5812	−1.14143
$266$	2.58239	0.158337
$267$	43.1127	2.63846
$268$	11.3739	0.694770
$269$	10.1253	0.617350	0.308675	−	0.951168i	$-0.400114\pi$
$269$	10.1253	0.617350	0.308675	+	0.951168i	$0.400114\pi$
$270$	13.3972	0.815327
$271$	28.1445	1.70966	0.854830	−	0.518909i	$-0.173662\pi$
$271$	28.1445	1.70966	0.854830	+	0.518909i	$0.173662\pi$
$272$	2.38192	0.144425
$273$	−3.95684	−0.239479
$274$	16.3088	0.985253
$275$	0.113695	0.00685607
$276$	47.7000	2.87120
$277$	4.56792	0.274460	0.137230	−	0.990539i	$-0.456180\pi$
$277$	4.56792	0.274460	0.137230	+	0.990539i	$0.456180\pi$
$278$	37.9249	2.27458
$279$	13.3823	0.801177
$280$	−0.847993	−0.0506773
$281$	−4.69408	−0.280025	−0.140013	−	0.990150i	$-0.544714\pi$
$281$	−4.69408	−0.280025	−0.140013	+	0.990150i	$0.544714\pi$
$282$	18.2042	1.08404
$283$	−12.0728	−0.717656	−0.358828	−	0.933404i	$-0.616824\pi$
$283$	−12.0728	−0.717656	−0.358828	+	0.933404i	$0.616824\pi$
$284$	−8.11590	−0.481590
$285$	24.4385	1.44761
$286$	11.0786	0.655089
$287$	3.04227	0.179580
$288$	31.5768	1.86068
$289$	1.00000	0.0588235
$290$	−42.1254	−2.47369
$291$	0.0771689	0.00452372
$292$	9.94475	0.581972
$293$	−11.2786	−0.658902	−0.329451	−	0.944173i	$-0.606864\pi$
$293$	−11.2786	−0.658902	−0.329451	+	0.944173i	$0.606864\pi$
$294$	−39.4969	−2.30351
$295$	−11.3285	−0.659570
$296$	−1.18099	−0.0686434
$297$	2.82029	0.163650
$298$	4.50202	0.260795
$299$	−35.3469	−2.04416
$300$	0.790974	0.0456669
$301$	−0.288836	−0.0166482
$302$	27.4882	1.58177
$303$	15.0083	0.862202
$304$	9.90991	0.568372
$305$	0.471939	0.0270232
$306$	8.72765	0.498927
$307$	5.22397	0.298148	0.149074	−	0.988826i	$-0.452371\pi$
$307$	5.22397	0.298148	0.149074	+	0.988826i	$0.452371\pi$
$308$	−0.756186	−0.0430877
$309$	−18.8950	−1.07490
$310$	−15.6524	−0.888998
$311$	5.58177	0.316513	0.158256	−	0.987398i	$-0.449413\pi$
$311$	5.58177	0.316513	0.158256	+	0.987398i	$0.449413\pi$
$312$	18.1948	1.03008
$313$	6.61311	0.373795	0.186897	−	0.982379i	$-0.440157\pi$
$313$	6.61311	0.373795	0.186897	+	0.982379i	$0.440157\pi$
$314$	10.0571	0.567555
$315$	2.59304	0.146102
$316$	−30.1075	−1.69368
$317$	−6.14552	−0.345167	−0.172583	−	0.984995i	$-0.555211\pi$
$317$	−6.14552	−0.345167	−0.172583	+	0.984995i	$0.555211\pi$
$318$	−48.0015	−2.69179
$319$	−8.86798	−0.496511
$320$	−26.4029	−1.47597
$321$	−35.8691	−2.00202
$322$	4.25577	0.237165
$323$	4.16046	0.231494
$324$	−12.2775	−0.682086
$325$	−0.586132	−0.0325128
$326$	39.8907	2.20934
$327$	−43.5109	−2.40616
$328$	−13.9893	−0.772432
$329$	0.920769	0.0507636
$330$	−12.6230	−0.694874
$331$	16.4298	0.903064	0.451532	−	0.892255i	$-0.350878\pi$
$331$	16.4298	0.903064	0.451532	+	0.892255i	$0.350878\pi$
$332$	−21.4045	−1.17472
$333$	3.61129	0.197898
$334$	−17.8973	−0.979298
$335$	9.60331	0.524685
$336$	1.82820	0.0997363
$337$	2.62757	0.143133	0.0715664	−	0.997436i	$-0.477200\pi$
$337$	2.62757	0.143133	0.0715664	+	0.997436i	$0.477200\pi$
$338$	−29.1768	−1.58701
$339$	−13.0988	−0.711432
$340$	−5.78719	−0.313854
$341$	−3.29505	−0.178437
$342$	36.3111	1.96348
$343$	−4.01961	−0.217038
$344$	1.32816	0.0716096
$345$	40.2746	2.16831
$346$	22.9677	1.23475
$347$	−19.1727	−1.02924	−0.514622	−	0.857417i	$-0.672068\pi$
$347$	−19.1727	−1.02924	−0.514622	+	0.857417i	$0.672068\pi$
$348$	−61.6943	−3.30716
$349$	−21.7834	−1.16604	−0.583020	−	0.812458i	$-0.698129\pi$
$349$	−21.7834	−1.16604	−0.583020	+	0.812458i	$0.698129\pi$
$350$	0.0705703	0.00377214
$351$	−14.5395	−0.776059
$352$	−7.77499	−0.414408
$353$	26.5110	1.41104	0.705518	−	0.708692i	$-0.250714\pi$
$353$	26.5110	1.41104	0.705518	+	0.708692i	$0.250714\pi$
$354$	−29.2654	−1.55544
$355$	−6.85251	−0.363693
$356$	−42.4756	−2.25120
$357$	0.767529	0.0406219
$358$	4.10581	0.216999
$359$	33.8518	1.78663	0.893314	−	0.449434i	$-0.148374\pi$
$359$	33.8518	1.78663	0.893314	+	0.449434i	$0.148374\pi$
$360$	−11.9236	−0.628431
$361$	−1.69056	−0.0889767
$362$	−38.7015	−2.03410
$363$	−2.65732	−0.139473
$364$	3.89837	0.204330
$365$	8.39666	0.439501
$366$	1.21918	0.0637276
$367$	−15.5549	−0.811957	−0.405978	−	0.913883i	$-0.633069\pi$
$367$	−15.5549	−0.811957	−0.405978	+	0.913883i	$0.633069\pi$
$368$	16.3315	0.851337
$369$	42.7774	2.22690
$370$	−4.22390	−0.219590
$371$	−2.42792	−0.126051
$372$	−22.9236	−1.18853
$373$	−14.6079	−0.756370	−0.378185	−	0.925730i	$-0.623452\pi$
$373$	−14.6079	−0.756370	−0.378185	+	0.925730i	$0.623452\pi$
$374$	−2.14896	−0.111120
$375$	30.0378	1.55115
$376$	−4.23399	−0.218351
$377$	45.7171	2.35455
$378$	1.75055	0.0900386
$379$	13.2089	0.678498	0.339249	−	0.940697i	$-0.389827\pi$
$379$	13.2089	0.678498	0.339249	+	0.940697i	$0.389827\pi$
$380$	−24.0774	−1.23514
$381$	−3.95469	−0.202605
$382$	10.7885	0.551988
$383$	−10.3153	−0.527088	−0.263544	−	0.964647i	$-0.584891\pi$
$383$	−10.3153	−0.527088	−0.263544	+	0.964647i	$0.584891\pi$
$384$	−26.8866	−1.37205
$385$	−0.638472	−0.0325395
$386$	27.3810	1.39366
$387$	−4.06133	−0.206449
$388$	−0.0760285	−0.00385976
$389$	−29.8894	−1.51545	−0.757725	−	0.652574i	$-0.773689\pi$
$389$	−29.8894	−1.51545	−0.757725	+	0.652574i	$0.773689\pi$
$390$	65.0754	3.29522
$391$	6.85642	0.346744
$392$	9.18632	0.463979
$393$	25.6891	1.29584
$394$	−3.50549	−0.176604
$395$	−25.4207	−1.27905
$396$	−10.6328	−0.534316
$397$	24.0258	1.20582	0.602910	−	0.797809i	$-0.294008\pi$
$397$	24.0258	1.20582	0.602910	+	0.797809i	$0.294008\pi$
$398$	−31.7125	−1.58961
$399$	3.19327	0.159864
$400$	0.270813	0.0135407
$401$	−5.87866	−0.293566	−0.146783	−	0.989169i	$-0.546892\pi$
$401$	−5.87866	−0.293566	−0.146783	+	0.989169i	$0.546892\pi$
$402$	24.8087	1.23734
$403$	16.9870	0.846181
$404$	−14.7865	−0.735654
$405$	−10.3663	−0.515106
$406$	−5.50434	−0.273176
$407$	−0.889189	−0.0440755
$408$	−3.52934	−0.174728
$409$	−13.5584	−0.670420	−0.335210	−	0.942143i	$-0.608807\pi$
$409$	−13.5584	−0.670420	−0.335210	+	0.942143i	$0.608807\pi$
$410$	−50.0341	−2.47101
$411$	20.1668	0.994755
$412$	18.6157	0.917131
$413$	−1.48024	−0.0728379
$414$	59.8405	2.94100
$415$	−18.0725	−0.887143
$416$	40.0824	1.96520
$417$	46.8963	2.29652
$418$	−8.94068	−0.437303
$419$	−24.2909	−1.18669	−0.593345	−	0.804948i	$-0.702193\pi$
$419$	−24.2909	−1.18669	−0.593345	+	0.804948i	$0.702193\pi$
$420$	−4.44183	−0.216739
$421$	−9.04004	−0.440585	−0.220292	−	0.975434i	$-0.570701\pi$
$421$	−9.04004	−0.440585	−0.220292	+	0.975434i	$0.570701\pi$
$422$	−31.6047	−1.53849
$423$	12.9470	0.629503
$424$	11.1643	0.542188
$425$	0.113695	0.00551502
$426$	−17.7024	−0.857683
$427$	0.0616662	0.00298424
$428$	35.3391	1.70818
$429$	13.6993	0.661407
$430$	4.75028	0.229079
$431$	−6.36096	−0.306397	−0.153198	−	0.988195i	$-0.548957\pi$
$431$	−6.36096	−0.306397	−0.153198	+	0.988195i	$0.548957\pi$
$432$	6.71773	0.323207
$433$	39.5705	1.90164	0.950818	−	0.309749i	$-0.100245\pi$
$433$	39.5705	1.90164	0.950818	+	0.309749i	$0.100245\pi$
$434$	−2.04523	−0.0981743
$435$	−52.0905	−2.49755
$436$	42.8679	2.05300
$437$	28.5259	1.36458
$438$	21.6915	1.03646
$439$	−17.3948	−0.830207	−0.415104	−	0.909774i	$-0.636255\pi$
$439$	−17.3948	−0.830207	−0.415104	+	0.909774i	$0.636255\pi$
$440$	2.93590	0.139963
$441$	−28.0905	−1.33764
$442$	11.0786	0.526953
$443$	17.7604	0.843821	0.421910	−	0.906638i	$-0.361360\pi$
$443$	17.7604	0.843821	0.421910	+	0.906638i	$0.361360\pi$
$444$	−6.18607	−0.293578
$445$	−35.8635	−1.70009
$446$	−10.2340	−0.484592
$447$	5.56701	0.263311
$448$	−3.44995	−0.162995
$449$	−19.2185	−0.906977	−0.453488	−	0.891262i	$-0.649821\pi$
$449$	−19.2185	−0.906977	−0.453488	+	0.891262i	$0.649821\pi$
$450$	0.992291	0.0467770
$451$	−10.5329	−0.495973
$452$	12.9053	0.607013
$453$	33.9908	1.59703
$454$	32.8195	1.54030
$455$	3.29151	0.154309
$456$	−14.6837	−0.687627
$457$	31.0831	1.45401	0.727003	−	0.686635i	$-0.240913\pi$
$457$	31.0831	1.45401	0.727003	+	0.686635i	$0.240913\pi$
$458$	41.5833	1.94306
$459$	2.82029	0.131640
$460$	−39.6794	−1.85006
$461$	−8.06174	−0.375473	−0.187736	−	0.982219i	$-0.560115\pi$
$461$	−8.06174	−0.375473	−0.187736	+	0.982219i	$0.560115\pi$
$462$	−1.64939	−0.0767366
$463$	4.59607	0.213597	0.106799	−	0.994281i	$-0.465940\pi$
$463$	4.59607	0.213597	0.106799	+	0.994281i	$0.465940\pi$
$464$	−21.1229	−0.980604
$465$	−19.3551	−0.897572
$466$	−23.0050	−1.06568
$467$	22.7127	1.05102	0.525510	−	0.850788i	$-0.323875\pi$
$467$	22.7127	1.05102	0.525510	+	0.850788i	$0.323875\pi$
$468$	54.8150	2.53383
$469$	1.25482	0.0579423
$470$	−15.1432	−0.698506
$471$	12.4362	0.573029
$472$	6.80662	0.313300
$473$	1.00000	0.0459800
$474$	−65.6704	−3.01634
$475$	0.473024	0.0217038
$476$	−0.756186	−0.0346597
$477$	−34.1390	−1.56312
$478$	−2.16905	−0.0992100
$479$	−19.2682	−0.880387	−0.440194	−	0.897903i	$-0.645090\pi$
$479$	−19.2682	−0.880387	−0.440194	+	0.897903i	$0.645090\pi$
$480$	−45.6703	−2.08455
$481$	4.58404	0.209014
$482$	8.45451	0.385092
$483$	5.26250	0.239452
$484$	2.61805	0.119002
$485$	−0.0641932	−0.00291486
$486$	−44.9619	−2.03951
$487$	23.1297	1.04811	0.524053	−	0.851686i	$-0.324419\pi$
$487$	23.1297	1.04811	0.524053	+	0.851686i	$0.324419\pi$
$488$	−0.283561	−0.0128362
$489$	49.3271	2.23065
$490$	32.8557	1.48427
$491$	−20.2483	−0.913791	−0.456896	−	0.889520i	$-0.651039\pi$
$491$	−20.2483	−0.913791	−0.456896	+	0.889520i	$0.651039\pi$
$492$	−73.2769	−3.30358
$493$	−8.86798	−0.399394
$494$	46.0919	2.07377
$495$	−8.97757	−0.403512
$496$	−7.84856	−0.352411
$497$	−0.895387	−0.0401636
$498$	−46.6874	−2.09211
$499$	−10.2974	−0.460973	−0.230487	−	0.973075i	$-0.574032\pi$
$499$	−10.2974	−0.460973	−0.230487	+	0.973075i	$0.574032\pi$
$500$	−29.5939	−1.32348
$501$	−22.1311	−0.988743
$502$	54.3316	2.42494
$503$	−1.39672	−0.0622767	−0.0311384	−	0.999515i	$-0.509913\pi$
$503$	−1.39672	−0.0622767	−0.0311384	+	0.999515i	$0.509913\pi$
$504$	−1.55801	−0.0693993
$505$	−12.4847	−0.555561
$506$	−14.7342	−0.655015
$507$	−36.0787	−1.60231
$508$	3.89624	0.172868
$509$	34.7156	1.53874	0.769371	−	0.638803i	$-0.220570\pi$
$509$	34.7156	1.53874	0.769371	+	0.638803i	$0.220570\pi$
$510$	−12.6230	−0.558956
$511$	1.09715	0.0485352
$512$	−24.8466	−1.09808
$513$	11.7337	0.518056
$514$	−63.1091	−2.78362
$515$	15.7178	0.692611
$516$	6.95698	0.306264
$517$	−3.18786	−0.140202
$518$	−0.551918	−0.0242499
$519$	28.4009	1.24666
$520$	−15.1354	−0.663733
$521$	−43.4512	−1.90363	−0.951815	−	0.306673i	$-0.900784\pi$
$521$	−43.4512	−1.90363	−0.951815	+	0.306673i	$0.900784\pi$
$522$	−77.3966	−3.38756
$523$	30.8436	1.34870	0.674349	−	0.738413i	$-0.264424\pi$
$523$	30.8436	1.34870	0.674349	+	0.738413i	$0.264424\pi$
$524$	−25.3094	−1.10565
$525$	0.0872642	0.00380852
$526$	9.46568	0.412723
$527$	−3.29505	−0.143535
$528$	−6.32953	−0.275457
$529$	24.0105	1.04393
$530$	39.9303	1.73446
$531$	−20.8137	−0.903239
$532$	−3.14608	−0.136400
$533$	54.3001	2.35200
$534$	−92.6477	−4.00926
$535$	29.8379	1.29000
$536$	−5.77007	−0.249229
$537$	5.07707	0.219092
$538$	−21.7589	−0.938092
$539$	6.91657	0.297918
$540$	−16.3216	−0.702368
$541$	−6.24085	−0.268315	−0.134158	−	0.990960i	$-0.542833\pi$
$541$	−6.24085	−0.268315	−0.134158	+	0.990960i	$0.542833\pi$
$542$	−60.4816	−2.59791
$543$	−47.8566	−2.05372
$544$	−7.77499	−0.333350
$545$	36.1947	1.55041
$546$	8.50311	0.363900
$547$	28.9096	1.23608	0.618042	−	0.786145i	$-0.287926\pi$
$547$	28.9096	1.23608	0.618042	+	0.786145i	$0.287926\pi$
$548$	−19.8688	−0.848752
$549$	0.867090	0.0370065
$550$	−0.244327	−0.0104181
$551$	−36.8949	−1.57177
$552$	−24.1986	−1.02996
$553$	−3.32161	−0.141249
$554$	−9.81630	−0.417055
$555$	−5.22309	−0.221708
$556$	−46.2032	−1.95945
$557$	39.9799	1.69400	0.847001	−	0.531591i	$-0.178406\pi$
$557$	39.9799	1.69400	0.847001	+	0.531591i	$0.178406\pi$
$558$	−28.7581	−1.21743
$559$	−5.15530	−0.218046
$560$	−1.52079	−0.0642652
$561$	−2.65732	−0.112192
$562$	10.0874	0.425512
$563$	−3.10547	−0.130880	−0.0654401	−	0.997857i	$-0.520845\pi$
$563$	−3.10547	−0.130880	−0.0654401	+	0.997857i	$0.520845\pi$
$564$	−22.1779	−0.933857
$565$	10.8963	0.458412
$566$	25.9441	1.09051
$567$	−1.35452	−0.0568845
$568$	4.11727	0.172757
$569$	−19.7982	−0.829985	−0.414993	−	0.909825i	$-0.636216\pi$
$569$	−19.7982	−0.829985	−0.414993	+	0.909825i	$0.636216\pi$
$570$	−52.5175	−2.19972
$571$	−20.4182	−0.854475	−0.427238	−	0.904139i	$-0.640513\pi$
$571$	−20.4182	−0.854475	−0.427238	+	0.904139i	$0.640513\pi$
$572$	−13.4968	−0.564330
$573$	13.3406	0.557312
$574$	−6.53773	−0.272880
$575$	0.779541	0.0325091
$576$	−48.5099	−2.02124
$577$	0.747230	0.0311076	0.0155538	−	0.999879i	$-0.495049\pi$
$577$	0.747230	0.0311076	0.0155538	+	0.999879i	$0.495049\pi$
$578$	−2.14896	−0.0893851
$579$	33.8582	1.40710
$580$	51.3207	2.13097
$581$	−2.36145	−0.0979695
$582$	−0.165833	−0.00687400
$583$	8.40587	0.348136
$584$	−5.04506	−0.208766
$585$	46.2821	1.91353
$586$	24.2373	1.00123
$587$	−36.9537	−1.52524	−0.762620	−	0.646846i	$-0.776088\pi$
$587$	−36.9537	−1.52524	−0.762620	+	0.646846i	$0.776088\pi$
$588$	48.1185	1.98437
$589$	−13.7089	−0.564867
$590$	24.3445	1.00225
$591$	−4.33474	−0.178308
$592$	−2.11798	−0.0870485
$593$	5.16889	0.212261	0.106130	−	0.994352i	$-0.466154\pi$
$593$	5.16889	0.212261	0.106130	+	0.994352i	$0.466154\pi$
$594$	−6.06071	−0.248674
$595$	−0.638472	−0.0261748
$596$	−5.48474	−0.224664
$597$	−39.2143	−1.60494
$598$	75.9592	3.10620
$599$	−0.650584	−0.0265822	−0.0132911	−	0.999912i	$-0.504231\pi$
$599$	−0.650584	−0.0265822	−0.0132911	+	0.999912i	$0.504231\pi$
$600$	−0.401269	−0.0163817
$601$	−21.9847	−0.896774	−0.448387	−	0.893840i	$-0.648001\pi$
$601$	−21.9847	−0.896774	−0.448387	+	0.893840i	$0.648001\pi$
$602$	0.620698	0.0252978
$603$	17.6441	0.718523
$604$	−33.4885	−1.36263
$605$	2.21050	0.0898696
$606$	−32.2522	−1.31016
$607$	−14.3703	−0.583274	−0.291637	−	0.956529i	$-0.594200\pi$
$607$	−14.3703	−0.583274	−0.291637	+	0.956529i	$0.594200\pi$
$608$	−32.3476	−1.31187
$609$	−6.80643	−0.275810
$610$	−1.01418	−0.0410630
$611$	16.4344	0.664864
$612$	−10.6328	−0.429804
$613$	−1.51934	−0.0613654	−0.0306827	−	0.999529i	$-0.509768\pi$
$613$	−1.51934	−0.0613654	−0.0306827	+	0.999529i	$0.509768\pi$
$614$	−11.2261	−0.453050
$615$	−61.8700	−2.49484
$616$	0.383620	0.0154565
$617$	−19.0688	−0.767679	−0.383840	−	0.923400i	$-0.625398\pi$
$617$	−19.0688	−0.767679	−0.383840	+	0.923400i	$0.625398\pi$
$618$	40.6046	1.63336
$619$	35.2846	1.41821	0.709104	−	0.705103i	$-0.249099\pi$
$619$	35.2846	1.41821	0.709104	+	0.705103i	$0.249099\pi$
$620$	19.0691	0.765833
$621$	19.3371	0.775971
$622$	−11.9950	−0.480956
$623$	−4.68612	−0.187746
$624$	32.6306	1.30627
$625$	−24.4186	−0.976744
$626$	−14.2113	−0.567999
$627$	−11.0557	−0.441521
$628$	−12.2524	−0.488924
$629$	−0.889189	−0.0354543
$630$	−5.57236	−0.222008
$631$	35.5276	1.41433	0.707166	−	0.707047i	$-0.249973\pi$
$631$	35.5276	1.41433	0.707166	+	0.707047i	$0.249973\pi$
$632$	15.2738	0.607560
$633$	−39.0811	−1.55333
$634$	13.2065	0.524497
$635$	3.28972	0.130549
$636$	58.4795	2.31886
$637$	−35.6570	−1.41278
$638$	19.0570	0.754472
$639$	−12.5901	−0.498055
$640$	22.3657	0.884082
$641$	−29.2515	−1.15536	−0.577682	−	0.816262i	$-0.696043\pi$
$641$	−29.2515	−1.15536	−0.577682	+	0.816262i	$0.696043\pi$
$642$	77.0815	3.04216
$643$	11.5746	0.456457	0.228229	−	0.973608i	$-0.426707\pi$
$643$	11.5746	0.456457	0.228229	+	0.973608i	$0.426707\pi$
$644$	−5.18473	−0.204307
$645$	5.87399	0.231288
$646$	−8.94068	−0.351766
$647$	−38.1931	−1.50153	−0.750763	−	0.660572i	$-0.770314\pi$
$647$	−38.1931	−1.50153	−0.750763	+	0.660572i	$0.770314\pi$
$648$	6.22852	0.244679
$649$	5.12485	0.201168
$650$	1.25958	0.0494047
$651$	−2.52905	−0.0991211
$652$	−48.5981	−1.90325
$653$	−25.7749	−1.00865	−0.504324	−	0.863514i	$-0.668258\pi$
$653$	−25.7749	−1.00865	−0.504324	+	0.863514i	$0.668258\pi$
$654$	93.5035	3.65627
$655$	−21.3695	−0.834977
$656$	−25.0885	−0.979541
$657$	15.4271	0.601869
$658$	−1.97870	−0.0771378
$659$	32.0884	1.24999	0.624993	−	0.780630i	$-0.285102\pi$
$659$	32.0884	1.24999	0.624993	+	0.780630i	$0.285102\pi$
$660$	15.3784	0.598603
$661$	19.6161	0.762979	0.381489	−	0.924373i	$-0.375411\pi$
$661$	19.6161	0.762979	0.381489	+	0.924373i	$0.375411\pi$
$662$	−35.3071	−1.37225
$663$	13.6993	0.532035
$664$	10.8587	0.421399
$665$	−2.65634	−0.103008
$666$	−7.76054	−0.300715
$667$	−60.8026	−2.35428
$668$	21.8040	0.843622
$669$	−12.6549	−0.489266
$670$	−20.6372	−0.797284
$671$	−0.213499	−0.00824203
$672$	−5.96753	−0.230202
$673$	−8.06608	−0.310925	−0.155462	−	0.987842i	$-0.549687\pi$
$673$	−8.06608	−0.310925	−0.155462	+	0.987842i	$0.549687\pi$
$674$	−5.64655	−0.217497
$675$	0.320653	0.0123419
$676$	35.5456	1.36714
$677$	5.86520	0.225418	0.112709	−	0.993628i	$-0.464047\pi$
$677$	5.86520	0.225418	0.112709	+	0.993628i	$0.464047\pi$
$678$	28.1489	1.08105
$679$	−0.00838784	−0.000321896 0
$680$	2.93590	0.112586
$681$	40.5832	1.55515
$682$	7.08094	0.271143
$683$	3.84892	0.147275	0.0736375	−	0.997285i	$-0.476539\pi$
$683$	3.84892	0.147275	0.0736375	+	0.997285i	$0.476539\pi$
$684$	−44.2372	−1.69145
$685$	−16.7758	−0.640972
$686$	8.63799	0.329800
$687$	51.4202	1.96180
$688$	2.38192	0.0908100
$689$	−43.3348	−1.65092
$690$	−86.5486	−3.29485
$691$	−18.3734	−0.698957	−0.349479	−	0.936944i	$-0.613641\pi$
$691$	−18.3734	−0.698957	−0.349479	+	0.936944i	$0.613641\pi$
$692$	−27.9812	−1.06369
$693$	−1.17306	−0.0445608
$694$	41.2015	1.56399
$695$	−39.0108	−1.47977
$696$	31.2981	1.18635
$697$	−10.5329	−0.398961
$698$	46.8118	1.77185
$699$	−28.4469	−1.07596
$700$	−0.0859746	−0.00324953
$701$	−41.4702	−1.56631	−0.783155	−	0.621827i	$-0.786391\pi$
$701$	−41.4702	−1.56631	−0.783155	+	0.621827i	$0.786391\pi$
$702$	31.2448	1.17926
$703$	−3.69944	−0.139527
$704$	11.9443	0.450169
$705$	−18.7255	−0.705242
$706$	−56.9711	−2.14414
$707$	−1.63132	−0.0613520
$708$	35.6535	1.33994
$709$	−46.0824	−1.73066	−0.865331	−	0.501201i	$-0.832892\pi$
$709$	−46.0824	−1.73066	−0.865331	+	0.501201i	$0.832892\pi$
$710$	14.7258	0.552649
$711$	−46.7053	−1.75158
$712$	21.5483	0.807556
$713$	−22.5922	−0.846086
$714$	−1.64939	−0.0617269
$715$	−11.3958	−0.426178
$716$	−5.00204	−0.186935
$717$	−2.68215	−0.100167
$718$	−72.7462	−2.71486
$719$	25.4145	0.947802	0.473901	−	0.880578i	$-0.342845\pi$
$719$	25.4145	0.947802	0.473901	+	0.880578i	$0.342845\pi$
$720$	−21.3839	−0.796931
$721$	2.05378	0.0764868
$722$	3.63295	0.135204
$723$	10.4545	0.388806
$724$	47.1494	1.75229
$725$	−1.00824	−0.0374453
$726$	5.71048	0.211936
$727$	−15.3495	−0.569280	−0.284640	−	0.958635i	$-0.591874\pi$
$727$	−15.3495	−0.569280	−0.284640	+	0.958635i	$0.591874\pi$
$728$	−1.97768	−0.0732977
$729$	−41.5292	−1.53812
$730$	−18.0441	−0.667843
$731$	1.00000	0.0369863
$732$	−1.48531	−0.0548985
$733$	12.0617	0.445507	0.222754	−	0.974875i	$-0.428495\pi$
$733$	12.0617	0.445507	0.222754	+	0.974875i	$0.428495\pi$
$734$	33.4268	1.23381
$735$	40.6279	1.49858
$736$	−53.3086	−1.96498
$737$	−4.34441	−0.160028
$738$	−91.9272	−3.38389
$739$	−1.42930	−0.0525776	−0.0262888	−	0.999654i	$-0.508369\pi$
$739$	−1.42930	−0.0525776	−0.0262888	+	0.999654i	$0.508369\pi$
$740$	5.14591	0.189167
$741$	56.9953	2.09377
$742$	5.21751	0.191541
$743$	−12.2189	−0.448267	−0.224133	−	0.974558i	$-0.571955\pi$
$743$	−12.2189	−0.448267	−0.224133	+	0.974558i	$0.571955\pi$
$744$	11.6294	0.426353
$745$	−4.63094	−0.169664
$746$	31.3919	1.14934
$747$	−33.2044	−1.21489
$748$	2.61805	0.0957253
$749$	3.89878	0.142458
$750$	−64.5502	−2.35704
$751$	−43.7964	−1.59815	−0.799076	−	0.601229i	$-0.794678\pi$
$751$	−43.7964	−1.59815	−0.799076	+	0.601229i	$0.794678\pi$
$752$	−7.59325	−0.276897
$753$	67.1841	2.44832
$754$	−98.2444	−3.57785
$755$	−28.2754	−1.02905
$756$	−2.13267	−0.0775643
$757$	12.1639	0.442103	0.221052	−	0.975262i	$-0.429051\pi$
$757$	12.1639	0.442103	0.221052	+	0.975262i	$0.429051\pi$
$758$	−28.3856	−1.03101
$759$	−18.2197	−0.661332
$760$	12.2147	0.443073
$761$	0.00253787	9.19978e−5 0	4.59989e−5	−	1.00000i	$-0.499985\pi$
$761$	0.00253787	9.19978e−5 0	4.59989e−5		1.00000i	$0.499985\pi$
$762$	8.49848	0.307867
$763$	4.72941	0.171216
$764$	−13.1435	−0.475514
$765$	−8.97757	−0.324585
$766$	22.1673	0.800935
$767$	−26.4202	−0.953977
$768$	−5.70140	−0.205732
$769$	−8.67157	−0.312705	−0.156352	−	0.987701i	$-0.549974\pi$
$769$	−8.67157	−0.312705	−0.156352	+	0.987701i	$0.549974\pi$
$770$	1.37205	0.0494453
$771$	−78.0380	−2.81047
$772$	−33.3579	−1.20058
$773$	24.6984	0.888340	0.444170	−	0.895942i	$-0.353499\pi$
$773$	24.6984	0.888340	0.444170	+	0.895942i	$0.353499\pi$
$774$	8.72765	0.313709
$775$	−0.374631	−0.0134571
$776$	0.0385700	0.00138458
$777$	−0.682478	−0.0244838
$778$	64.2311	2.30280
$779$	−43.8216	−1.57007
$780$	−79.2802	−2.83869
$781$	3.09998	0.110926
$782$	−14.7342	−0.526894
$783$	−25.0103	−0.893795
$784$	16.4748	0.588384
$785$	−10.3451	−0.369232
$786$	−55.2049	−1.96909
$787$	−33.2722	−1.18603	−0.593013	−	0.805193i	$-0.702062\pi$
$787$	−33.2722	−1.18603	−0.593013	+	0.805193i	$0.702062\pi$
$788$	4.27068	0.152137
$789$	11.7048	0.416704
$790$	54.6282	1.94358
$791$	1.42377	0.0506236
$792$	5.39410	0.191671
$793$	1.10065	0.0390853
$794$	−51.6306	−1.83230
$795$	49.3761	1.75119
$796$	38.6348	1.36938
$797$	−14.8004	−0.524256	−0.262128	−	0.965033i	$-0.584424\pi$
$797$	−14.8004	−0.524256	−0.262128	+	0.965033i	$0.584424\pi$
$798$	−6.86223	−0.242920
$799$	−3.18786	−0.112778
$800$	−0.883978	−0.0312533
$801$	−65.8917	−2.32817
$802$	12.6330	0.446088
$803$	−3.79854	−0.134047
$804$	−30.2240	−1.06592
$805$	−4.37763	−0.154291
$806$	−36.5044	−1.28581
$807$	−26.9061	−0.947140
$808$	7.50132	0.263895
$809$	−9.16133	−0.322095	−0.161048	−	0.986947i	$-0.551487\pi$
$809$	−9.16133	−0.322095	−0.161048	+	0.986947i	$0.551487\pi$
$810$	22.2768	0.782729
$811$	−35.6649	−1.25236	−0.626182	−	0.779677i	$-0.715383\pi$
$811$	−35.6649	−1.25236	−0.626182	+	0.779677i	$0.715383\pi$
$812$	6.70584	0.235329
$813$	−74.7890	−2.62296
$814$	1.91084	0.0669748
$815$	−41.0329	−1.43732
$816$	−6.32953	−0.221578
$817$	4.16046	0.145556
$818$	29.1365	1.01874
$819$	6.04747	0.211316
$820$	60.9557	2.12866
$821$	−35.1155	−1.22554	−0.612770	−	0.790261i	$-0.709945\pi$
$821$	−35.1155	−1.22554	−0.612770	+	0.790261i	$0.709945\pi$
$822$	−43.3377	−1.51158
$823$	−34.9379	−1.21786	−0.608930	−	0.793224i	$-0.708401\pi$
$823$	−34.9379	−1.21786	−0.608930	+	0.793224i	$0.708401\pi$
$824$	−9.44393	−0.328995
$825$	−0.302124	−0.0105186
$826$	3.18099	0.110681
$827$	34.2521	1.19106	0.595531	−	0.803332i	$-0.296942\pi$
$827$	34.2521	1.19106	0.595531	+	0.803332i	$0.296942\pi$
$828$	−72.9026	−2.53354
$829$	−26.9208	−0.934999	−0.467499	−	0.883993i	$-0.654845\pi$
$829$	−26.9208	−0.934999	−0.467499	+	0.883993i	$0.654845\pi$
$830$	38.8371	1.34806
$831$	−12.1384	−0.421077
$832$	−61.5766	−2.13478
$833$	6.91657	0.239645
$834$	−100.778	−3.48967
$835$	18.4098	0.637097
$836$	10.8923	0.376717
$837$	−9.29300	−0.321213
$838$	52.2004	1.80323
$839$	−33.1336	−1.14390	−0.571949	−	0.820289i	$-0.693813\pi$
$839$	−33.1336	−1.14390	−0.571949	+	0.820289i	$0.693813\pi$
$840$	2.25338	0.0777492
$841$	49.6410	1.71176
$842$	19.4267	0.669489
$843$	12.4737	0.429616
$844$	38.5035	1.32535
$845$	30.0122	1.03245
$846$	−27.8226	−0.956559
$847$	0.288836	0.00992452
$848$	20.0222	0.687564
$849$	32.0814	1.10103
$850$	−0.244327	−0.00838033
$851$	−6.09665	−0.208991
$852$	21.5665	0.738856
$853$	6.80510	0.233002	0.116501	−	0.993191i	$-0.462832\pi$
$853$	6.80510	0.233002	0.116501	+	0.993191i	$0.462832\pi$
$854$	−0.132518	−0.00453469
$855$	−37.3508	−1.27737
$856$	−17.9278	−0.612761
$857$	−19.4899	−0.665763	−0.332882	−	0.942969i	$-0.608021\pi$
$857$	−19.4899	−0.665763	−0.332882	+	0.942969i	$0.608021\pi$
$858$	−29.4392	−1.00504
$859$	−24.8256	−0.847038	−0.423519	−	0.905887i	$-0.639205\pi$
$859$	−24.8256	−0.847038	−0.423519	+	0.905887i	$0.639205\pi$
$860$	−5.78719	−0.197342
$861$	−8.08428	−0.275511
$862$	13.6695	0.465584
$863$	55.0583	1.87421	0.937103	−	0.349054i	$-0.113497\pi$
$863$	55.0583	1.87421	0.937103	+	0.349054i	$0.113497\pi$
$864$	−21.9278	−0.745997
$865$	−23.6254	−0.803288
$866$	−85.0356	−2.88963
$867$	−2.65732	−0.0902472
$868$	2.49167	0.0845728
$869$	11.5000	0.390110
$870$	111.941	3.79514
$871$	22.3967	0.758885
$872$	−21.7473	−0.736457
$873$	−0.117942	−0.00399172
$874$	−61.3011	−2.07354
$875$	−3.26495	−0.110375
$876$	−26.4263	−0.892863
$877$	−7.48418	−0.252723	−0.126361	−	0.991984i	$-0.540330\pi$
$877$	−7.48418	−0.252723	−0.126361	+	0.991984i	$0.540330\pi$
$878$	37.3807	1.26154
$879$	29.9708	1.01089
$880$	5.26524	0.177491
$881$	18.9188	0.637392	0.318696	−	0.947857i	$-0.396755\pi$
$881$	18.9188	0.637392	0.318696	+	0.947857i	$0.396755\pi$
$882$	60.3655	2.03261
$883$	47.5395	1.59983	0.799916	−	0.600112i	$-0.204877\pi$
$883$	47.5395	1.59983	0.799916	+	0.600112i	$0.204877\pi$
$884$	−13.4968	−0.453947
$885$	30.1034	1.01191
$886$	−38.1664	−1.28223
$887$	−36.3434	−1.22029	−0.610145	−	0.792289i	$-0.708889\pi$
$887$	−36.3434	−1.22029	−0.610145	+	0.792289i	$0.708889\pi$
$888$	3.13825	0.105313
$889$	0.429853	0.0144168
$890$	77.0694	2.58337
$891$	4.68958	0.157107
$892$	12.4679	0.417455
$893$	−13.2630	−0.443829
$894$	−11.9633	−0.400113
$895$	−4.22338	−0.141172
$896$	2.92243	0.0976315
$897$	93.9279	3.13616
$898$	41.2998	1.37819
$899$	29.2204	0.974556
$900$	−1.20889	−0.0402964
$901$	8.40587	0.280040
$902$	22.6347	0.753655
$903$	0.767529	0.0255418
$904$	−6.54697	−0.217749
$905$	39.8097	1.32332
$906$	−73.0450	−2.42676
$907$	11.6248	0.385994	0.192997	−	0.981199i	$-0.438179\pi$
$907$	11.6248	0.385994	0.192997	+	0.981199i	$0.438179\pi$
$908$	−39.9835	−1.32690
$909$	−22.9380	−0.760805
$910$	−7.07334	−0.234479
$911$	6.48991	0.215020	0.107510	−	0.994204i	$-0.465712\pi$
$911$	6.48991	0.215020	0.107510	+	0.994204i	$0.465712\pi$
$912$	−26.3338	−0.871998
$913$	8.17575	0.270578
$914$	−66.7964	−2.20943
$915$	−1.25409	−0.0414590
$916$	−50.6603	−1.67386
$917$	−2.79226	−0.0922087
$918$	−6.06071	−0.200033
$919$	4.80938	0.158647	0.0793233	−	0.996849i	$-0.474724\pi$
$919$	4.80938	0.158647	0.0793233	+	0.996849i	$0.474724\pi$
$920$	20.1297	0.663658
$921$	−13.8818	−0.457419
$922$	17.3244	0.570548
$923$	−15.9813	−0.526032
$924$	2.00943	0.0661053
$925$	−0.101096	−0.00332403
$926$	−9.87679	−0.324571
$927$	28.8783	0.948486
$928$	68.9484	2.26334
$929$	−25.4919	−0.836363	−0.418182	−	0.908363i	$-0.637332\pi$
$929$	−25.4919	−0.836363	−0.418182	+	0.908363i	$0.637332\pi$
$930$	41.5934	1.36390
$931$	28.7761	0.943100
$932$	28.0265	0.918040
$933$	−14.8325	−0.485595
$934$	−48.8088	−1.59707
$935$	2.21050	0.0722910
$936$	−27.8082	−0.908939
$937$	−10.3349	−0.337627	−0.168814	−	0.985648i	$-0.553994\pi$
$937$	−10.3349	−0.337627	−0.168814	+	0.985648i	$0.553994\pi$
$938$	−2.69657	−0.0880461
$939$	−17.5731	−0.573477
$940$	18.4488	0.601732
$941$	−6.24132	−0.203461	−0.101731	−	0.994812i	$-0.532438\pi$
$941$	−6.24132	−0.203461	−0.101731	+	0.994812i	$0.532438\pi$
$942$	−26.7249	−0.870744
$943$	−72.2177	−2.35173
$944$	12.2070	0.397304
$945$	−1.80068	−0.0585760
$946$	−2.14896	−0.0698688
$947$	6.52435	0.212013	0.106006	−	0.994365i	$-0.466194\pi$
$947$	6.52435	0.212013	0.106006	+	0.994365i	$0.466194\pi$
$948$	80.0052	2.59845
$949$	19.5826	0.635678
$950$	−1.01651	−0.0329800
$951$	16.3306	0.529556
$952$	0.383620	0.0124332
$953$	−16.7222	−0.541684	−0.270842	−	0.962624i	$-0.587302\pi$
$953$	−16.7222	−0.541684	−0.270842	+	0.962624i	$0.587302\pi$
$954$	73.3636	2.37523
$955$	−11.0974	−0.359105
$956$	2.64251	0.0854650
$957$	23.5650	0.761749
$958$	41.4067	1.33779
$959$	−2.19202	−0.0707841
$960$	70.1609	2.26443
$961$	−20.1426	−0.649763
$962$	−9.85093	−0.317607
$963$	54.8209	1.76658
$964$	−10.3000	−0.331740
$965$	−28.1651	−0.906666
$966$	−11.3089	−0.363859
$967$	20.1211	0.647051	0.323526	−	0.946219i	$-0.395132\pi$
$967$	20.1211	0.647051	0.323526	+	0.946219i	$0.395132\pi$
$968$	−1.32816	−0.0426887
$969$	−11.0557	−0.355159
$970$	0.137949	0.00442927
$971$	−59.3205	−1.90369	−0.951843	−	0.306585i	$-0.900814\pi$
$971$	−59.3205	−1.90369	−0.951843	+	0.306585i	$0.900814\pi$
$972$	54.7763	1.75695
$973$	−5.09737	−0.163414
$974$	−49.7048	−1.59265
$975$	1.55754	0.0498812
$976$	−0.508538	−0.0162779
$977$	−2.27615	−0.0728204	−0.0364102	−	0.999337i	$-0.511592\pi$
$977$	−2.27615	−0.0728204	−0.0364102	+	0.999337i	$0.511592\pi$
$978$	−106.002	−3.38957
$979$	16.2242	0.518526
$980$	−40.0275	−1.27863
$981$	66.5003	2.12319
$982$	43.5128	1.38855
$983$	−30.7368	−0.980351	−0.490175	−	0.871624i	$-0.663067\pi$
$983$	−30.7368	−0.980351	−0.490175	+	0.871624i	$0.663067\pi$
$984$	37.1741	1.18507
$985$	3.60587	0.114893
$986$	19.0570	0.606897
$987$	−2.44678	−0.0778817
$988$	−56.1530	−1.78646
$989$	6.85642	0.218021
$990$	19.2925	0.613155
$991$	47.7734	1.51757	0.758786	−	0.651340i	$-0.225793\pi$
$991$	47.7734	1.51757	0.758786	+	0.651340i	$0.225793\pi$
$992$	25.6190	0.813404
$993$	−43.6592	−1.38548
$994$	1.92415	0.0610304
$995$	32.6206	1.03414
$996$	56.8785	1.80226
$997$	8.95345	0.283559	0.141779	−	0.989898i	$-0.454718\pi$
$997$	8.95345	0.283559	0.141779	+	0.989898i	$0.454718\pi$
$998$	22.1287	0.700471
$999$	−2.50777	−0.0793424

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8041.2.a.h.1.13	✓	74

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8041.2.a.h.1.13	✓	74	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:	\( N \)	\(=\)	\( 8041 = 11 \cdot 17 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8041.a (trivial)

\(f(q)\)	\(=\)	\(q-2.14896 q^{2} -2.65732 q^{3} +2.61805 q^{4} +2.21050 q^{5} +5.71048 q^{6} +0.288836 q^{7} -1.32816 q^{8} +4.06133 q^{9} +O(q^{10})\)	\(q-2.14896 q^{2} -2.65732 q^{3} +2.61805 q^{4} +2.21050 q^{5} +5.71048 q^{6} +0.288836 q^{7} -1.32816 q^{8} +4.06133 q^{9} -4.75028 q^{10} -1.00000 q^{11} -6.95698 q^{12} +5.15530 q^{13} -0.620698 q^{14} -5.87399 q^{15} -2.38192 q^{16} -1.00000 q^{17} -8.72765 q^{18} -4.16046 q^{19} +5.78719 q^{20} -0.767529 q^{21} +2.14896 q^{22} -6.85642 q^{23} +3.52934 q^{24} -0.113695 q^{25} -11.0786 q^{26} -2.82029 q^{27} +0.756186 q^{28} +8.86798 q^{29} +12.6230 q^{30} +3.29505 q^{31} +7.77499 q^{32} +2.65732 q^{33} +2.14896 q^{34} +0.638472 q^{35} +10.6328 q^{36} +0.889189 q^{37} +8.94068 q^{38} -13.6993 q^{39} -2.93590 q^{40} +10.5329 q^{41} +1.64939 q^{42} -1.00000 q^{43} -2.61805 q^{44} +8.97757 q^{45} +14.7342 q^{46} +3.18786 q^{47} +6.32953 q^{48} -6.91657 q^{49} +0.244327 q^{50} +2.65732 q^{51} +13.4968 q^{52} -8.40587 q^{53} +6.06071 q^{54} -2.21050 q^{55} -0.383620 q^{56} +11.0557 q^{57} -19.0570 q^{58} -5.12485 q^{59} -15.3784 q^{60} +0.213499 q^{61} -7.08094 q^{62} +1.17306 q^{63} -11.9443 q^{64} +11.3958 q^{65} -5.71048 q^{66} +4.34441 q^{67} -2.61805 q^{68} +18.2197 q^{69} -1.37205 q^{70} -3.09998 q^{71} -5.39410 q^{72} +3.79854 q^{73} -1.91084 q^{74} +0.302124 q^{75} -10.8923 q^{76} -0.288836 q^{77} +29.4392 q^{78} -11.5000 q^{79} -5.26524 q^{80} -4.68958 q^{81} -22.6347 q^{82} -8.17575 q^{83} -2.00943 q^{84} -2.21050 q^{85} +2.14896 q^{86} -23.5650 q^{87} +1.32816 q^{88} -16.2242 q^{89} -19.2925 q^{90} +1.48904 q^{91} -17.9504 q^{92} -8.75599 q^{93} -6.85060 q^{94} -9.19670 q^{95} -20.6606 q^{96} -0.0290401 q^{97} +14.8635 q^{98} -4.06133 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 74 q - 7 q^{2} - 3 q^{3} + 79 q^{4} - 6 q^{5} - 12 q^{6} - 16 q^{7} - 21 q^{8} + 75 q^{9}+O(q^{10}) \) 74 * q - 7 * q^2 - 3 * q^3 + 79 * q^4 - 6 * q^5 - 12 * q^6 - 16 * q^7 - 21 * q^8 + 75 * q^9	\( 74 q - 7 q^{2} - 3 q^{3} + 79 q^{4} - 6 q^{5} - 12 q^{6} - 16 q^{7} - 21 q^{8} + 75 q^{9} - 9 q^{10} - 74 q^{11} - 3 q^{12} + 4 q^{13} - 5 q^{14} - 17 q^{15} + 85 q^{16} - 74 q^{17} - 23 q^{18} - 21 q^{20} - 22 q^{21} + 7 q^{22} - 23 q^{23} - 51 q^{24} + 90 q^{25} - 46 q^{26} - 27 q^{27} - 61 q^{28} - 63 q^{29} - 22 q^{30} - 31 q^{31} - 69 q^{32} + 3 q^{33} + 7 q^{34} - 20 q^{35} + 51 q^{36} + 8 q^{37} - 2 q^{38} - 77 q^{39} - 37 q^{40} - 64 q^{41} + 13 q^{42} - 74 q^{43} - 79 q^{44} - 12 q^{45} - 53 q^{46} - 32 q^{47} + 2 q^{48} + 78 q^{49} - 104 q^{50} + 3 q^{51} + 13 q^{52} + 25 q^{53} - 110 q^{54} + 6 q^{55} - 29 q^{56} - 29 q^{57} - 14 q^{58} - 61 q^{59} - 82 q^{60} - 36 q^{61} - 63 q^{62} - 104 q^{63} + 107 q^{64} - 65 q^{65} + 12 q^{66} + 33 q^{67} - 79 q^{68} - 34 q^{69} - 3 q^{70} - 168 q^{71} - 67 q^{72} - 47 q^{73} - 54 q^{74} - 53 q^{75} - 4 q^{76} + 16 q^{77} - 3 q^{78} - 79 q^{79} - 59 q^{80} + 70 q^{81} - 18 q^{82} - 36 q^{83} - 118 q^{84} + 6 q^{85} + 7 q^{86} - 24 q^{87} + 21 q^{88} - 24 q^{89} + 25 q^{90} - 14 q^{91} - 18 q^{92} - 13 q^{93} + 9 q^{94} - 155 q^{95} - 50 q^{96} + q^{97} - 60 q^{98} - 75 q^{99}+O(q^{100}) \) 74 * q - 7 * q^2 - 3 * q^3 + 79 * q^4 - 6 * q^5 - 12 * q^6 - 16 * q^7 - 21 * q^8 + 75 * q^9 - 9 * q^10 - 74 * q^11 - 3 * q^12 + 4 * q^13 - 5 * q^14 - 17 * q^15 + 85 * q^16 - 74 * q^17 - 23 * q^18 - 21 * q^20 - 22 * q^21 + 7 * q^22 - 23 * q^23 - 51 * q^24 + 90 * q^25 - 46 * q^26 - 27 * q^27 - 61 * q^28 - 63 * q^29 - 22 * q^30 - 31 * q^31 - 69 * q^32 + 3 * q^33 + 7 * q^34 - 20 * q^35 + 51 * q^36 + 8 * q^37 - 2 * q^38 - 77 * q^39 - 37 * q^40 - 64 * q^41 + 13 * q^42 - 74 * q^43 - 79 * q^44 - 12 * q^45 - 53 * q^46 - 32 * q^47 + 2 * q^48 + 78 * q^49 - 104 * q^50 + 3 * q^51 + 13 * q^52 + 25 * q^53 - 110 * q^54 + 6 * q^55 - 29 * q^56 - 29 * q^57 - 14 * q^58 - 61 * q^59 - 82 * q^60 - 36 * q^61 - 63 * q^62 - 104 * q^63 + 107 * q^64 - 65 * q^65 + 12 * q^66 + 33 * q^67 - 79 * q^68 - 34 * q^69 - 3 * q^70 - 168 * q^71 - 67 * q^72 - 47 * q^73 - 54 * q^74 - 53 * q^75 - 4 * q^76 + 16 * q^77 - 3 * q^78 - 79 * q^79 - 59 * q^80 + 70 * q^81 - 18 * q^82 - 36 * q^83 - 118 * q^84 + 6 * q^85 + 7 * q^86 - 24 * q^87 + 21 * q^88 - 24 * q^89 + 25 * q^90 - 14 * q^91 - 18 * q^92 - 13 * q^93 + 9 * q^94 - 155 * q^95 - 50 * q^96 + q^97 - 60 * q^98 - 75 * q^99

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