LMFDB - Embedded newform 8045.2.a.d.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8045,2,Mod(1,8045)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8045, 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("8045.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8045 = 5 \cdot 1609 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8045.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:	$64.2396484261$
Analytic rank:	$0$
Dimension:	$141$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Character	$\chi$	$=$	8045.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.61030 q^{2} -1.72585 q^{3} +4.81367 q^{4} -1.00000 q^{5} +4.50499 q^{6} -4.19514 q^{7} -7.34453 q^{8} -0.0214352 q^{9} +O(q^{10})$	\(q-2.61030 q^{2} -1.72585 q^{3} +4.81367 q^{4} -1.00000 q^{5} +4.50499 q^{6} -4.19514 q^{7} -7.34453 q^{8} -0.0214352 q^{9} +2.61030 q^{10} +4.69195 q^{11} -8.30768 q^{12} -4.64310 q^{13} +10.9506 q^{14} +1.72585 q^{15} +9.54409 q^{16} +2.75148 q^{17} +0.0559522 q^{18} +1.97602 q^{19} -4.81367 q^{20} +7.24019 q^{21} -12.2474 q^{22} +6.28027 q^{23} +12.6756 q^{24} +1.00000 q^{25} +12.1199 q^{26} +5.21455 q^{27} -20.1940 q^{28} +5.78704 q^{29} -4.50499 q^{30} +0.563492 q^{31} -10.2239 q^{32} -8.09761 q^{33} -7.18218 q^{34} +4.19514 q^{35} -0.103182 q^{36} +3.07774 q^{37} -5.15802 q^{38} +8.01330 q^{39} +7.34453 q^{40} +2.05240 q^{41} -18.8991 q^{42} +8.28943 q^{43} +22.5855 q^{44} +0.0214352 q^{45} -16.3934 q^{46} +10.9691 q^{47} -16.4717 q^{48} +10.5992 q^{49} -2.61030 q^{50} -4.74864 q^{51} -22.3503 q^{52} +2.49644 q^{53} -13.6115 q^{54} -4.69195 q^{55} +30.8113 q^{56} -3.41032 q^{57} -15.1059 q^{58} +0.383242 q^{59} +8.30768 q^{60} +13.2015 q^{61} -1.47088 q^{62} +0.0899235 q^{63} +7.59925 q^{64} +4.64310 q^{65} +21.1372 q^{66} -9.48234 q^{67} +13.2447 q^{68} -10.8388 q^{69} -10.9506 q^{70} -14.2815 q^{71} +0.157431 q^{72} -1.25350 q^{73} -8.03382 q^{74} -1.72585 q^{75} +9.51193 q^{76} -19.6834 q^{77} -20.9171 q^{78} +2.00630 q^{79} -9.54409 q^{80} -8.93524 q^{81} -5.35738 q^{82} -4.01890 q^{83} +34.8519 q^{84} -2.75148 q^{85} -21.6379 q^{86} -9.98758 q^{87} -34.4601 q^{88} +18.6630 q^{89} -0.0559522 q^{90} +19.4784 q^{91} +30.2312 q^{92} -0.972503 q^{93} -28.6328 q^{94} -1.97602 q^{95} +17.6449 q^{96} +13.6803 q^{97} -27.6671 q^{98} -0.100573 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 141 q - 8 q^{2} + 11 q^{3} + 158 q^{4} - 141 q^{5} + 23 q^{6} + 29 q^{7} - 21 q^{8} + 160 q^{9}+O(q^{10}) $ 141 * q - 8 * q^2 + 11 * q^3 + 158 * q^4 - 141 * q^5 + 23 * q^6 + 29 * q^7 - 21 * q^8 + 160 * q^9	\( 141 q - 8 q^{2} + 11 q^{3} + 158 q^{4} - 141 q^{5} + 23 q^{6} + 29 q^{7} - 21 q^{8} + 160 q^{9} + 8 q^{10} + 32 q^{11} + 17 q^{12} + 35 q^{13} + 18 q^{14} - 11 q^{15} + 188 q^{16} - 13 q^{17} - 16 q^{18} + 152 q^{19} - 158 q^{20} + 40 q^{21} + 14 q^{22} - 77 q^{23} + 69 q^{24} + 141 q^{25} + 27 q^{26} + 38 q^{27} + 67 q^{28} + 22 q^{29} - 23 q^{30} + 86 q^{31} - 65 q^{32} + 51 q^{33} + 79 q^{34} - 29 q^{35} + 191 q^{36} + 45 q^{37} - 9 q^{38} + 55 q^{39} + 21 q^{40} + 36 q^{41} + 6 q^{42} + 132 q^{43} + 74 q^{44} - 160 q^{45} + 72 q^{46} - 16 q^{47} + 22 q^{48} + 212 q^{49} - 8 q^{50} + 82 q^{51} + 106 q^{52} - 28 q^{53} + 86 q^{54} - 32 q^{55} + 27 q^{56} + 10 q^{57} + 23 q^{58} + 71 q^{59} - 17 q^{60} + 116 q^{61} - 36 q^{62} + 45 q^{63} + 237 q^{64} - 35 q^{65} + 69 q^{66} + 99 q^{67} - 7 q^{68} + 45 q^{69} - 18 q^{70} + 34 q^{71} - 53 q^{72} + 125 q^{73} + 50 q^{74} + 11 q^{75} + 271 q^{76} - 31 q^{77} + 2 q^{78} + 101 q^{79} - 188 q^{80} + 221 q^{81} + 67 q^{82} + 67 q^{83} + 141 q^{84} + 13 q^{85} + 48 q^{86} - 21 q^{87} + 71 q^{88} + 79 q^{89} + 16 q^{90} + 228 q^{91} - 198 q^{92} - 12 q^{93} + 114 q^{94} - 152 q^{95} + 129 q^{96} + 98 q^{97} - 31 q^{98} + 195 q^{99}+O(q^{100}) \) 141 * q - 8 * q^2 + 11 * q^3 + 158 * q^4 - 141 * q^5 + 23 * q^6 + 29 * q^7 - 21 * q^8 + 160 * q^9 + 8 * q^10 + 32 * q^11 + 17 * q^12 + 35 * q^13 + 18 * q^14 - 11 * q^15 + 188 * q^16 - 13 * q^17 - 16 * q^18 + 152 * q^19 - 158 * q^20 + 40 * q^21 + 14 * q^22 - 77 * q^23 + 69 * q^24 + 141 * q^25 + 27 * q^26 + 38 * q^27 + 67 * q^28 + 22 * q^29 - 23 * q^30 + 86 * q^31 - 65 * q^32 + 51 * q^33 + 79 * q^34 - 29 * q^35 + 191 * q^36 + 45 * q^37 - 9 * q^38 + 55 * q^39 + 21 * q^40 + 36 * q^41 + 6 * q^42 + 132 * q^43 + 74 * q^44 - 160 * q^45 + 72 * q^46 - 16 * q^47 + 22 * q^48 + 212 * q^49 - 8 * q^50 + 82 * q^51 + 106 * q^52 - 28 * q^53 + 86 * q^54 - 32 * q^55 + 27 * q^56 + 10 * q^57 + 23 * q^58 + 71 * q^59 - 17 * q^60 + 116 * q^61 - 36 * q^62 + 45 * q^63 + 237 * q^64 - 35 * q^65 + 69 * q^66 + 99 * q^67 - 7 * q^68 + 45 * q^69 - 18 * q^70 + 34 * q^71 - 53 * q^72 + 125 * q^73 + 50 * q^74 + 11 * q^75 + 271 * q^76 - 31 * q^77 + 2 * q^78 + 101 * q^79 - 188 * q^80 + 221 * q^81 + 67 * q^82 + 67 * q^83 + 141 * q^84 + 13 * q^85 + 48 * q^86 - 21 * q^87 + 71 * q^88 + 79 * q^89 + 16 * q^90 + 228 * q^91 - 198 * q^92 - 12 * q^93 + 114 * q^94 - 152 * q^95 + 129 * q^96 + 98 * q^97 - 31 * q^98 + 195 * 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 $

$2$	−2.61030	−1.84576	−0.922881	−	0.385086i	$-0.874172\pi$
$2$	−2.61030	−1.84576	−0.922881	+	0.385086i	$0.874172\pi$
$3$	−1.72585	−0.996421	−0.498211	−	0.867056i	$-0.666009\pi$
$3$	−1.72585	−0.996421	−0.498211	+	0.867056i	$0.666009\pi$
$4$	4.81367	2.40684
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	4.50499	1.83916
$7$	−4.19514	−1.58561	−0.792807	−	0.609473i	$-0.791381\pi$
$7$	−4.19514	−1.58561	−0.792807	+	0.609473i	$0.791381\pi$
$8$	−7.34453	−2.59668
$9$	−0.0214352	−0.00714505
$10$	2.61030	0.825450
$11$	4.69195	1.41468	0.707338	−	0.706876i	$-0.249896\pi$
$11$	4.69195	1.41468	0.707338	+	0.706876i	$0.249896\pi$
$12$	−8.30768	−2.39822
$13$	−4.64310	−1.28776	−0.643882	−	0.765125i	$-0.722677\pi$
$13$	−4.64310	−1.28776	−0.643882	+	0.765125i	$0.722677\pi$
$14$	10.9506	2.92666
$15$	1.72585	0.445613
$16$	9.54409	2.38602
$17$	2.75148	0.667331	0.333666	−	0.942691i	$-0.391714\pi$
$17$	2.75148	0.667331	0.333666	+	0.942691i	$0.391714\pi$
$18$	0.0559522	0.0131881
$19$	1.97602	0.453331	0.226665	−	0.973973i	$-0.427218\pi$
$19$	1.97602	0.453331	0.226665	+	0.973973i	$0.427218\pi$
$20$	−4.81367	−1.07637
$21$	7.24019	1.57994
$22$	−12.2474	−2.61115
$23$	6.28027	1.30953	0.654764	−	0.755834i	$-0.272768\pi$
$23$	6.28027	1.30953	0.654764	+	0.755834i	$0.272768\pi$
$24$	12.6756	2.58739
$25$	1.00000	0.200000
$26$	12.1199	2.37690
$27$	5.21455	1.00354
$28$	−20.1940	−3.81631
$29$	5.78704	1.07463	0.537314	−	0.843383i	$-0.319439\pi$
$29$	5.78704	1.07463	0.537314	+	0.843383i	$0.319439\pi$
$30$	−4.50499	−0.822495
$31$	0.563492	0.101206	0.0506030	−	0.998719i	$-0.483886\pi$
$31$	0.563492	0.101206	0.0506030	+	0.998719i	$0.483886\pi$
$32$	−10.2239	−1.80735
$33$	−8.09761	−1.40961
$34$	−7.18218	−1.23173
$35$	4.19514	0.709108
$36$	−0.103182	−0.0171970
$37$	3.07774	0.505977	0.252988	−	0.967469i	$-0.418587\pi$
$37$	3.07774	0.505977	0.252988	+	0.967469i	$0.418587\pi$
$38$	−5.15802	−0.836741
$39$	8.01330	1.28315
$40$	7.34453	1.16127
$41$	2.05240	0.320531	0.160265	−	0.987074i	$-0.448765\pi$
$41$	2.05240	0.320531	0.160265	+	0.987074i	$0.448765\pi$
$42$	−18.8991	−2.91619
$43$	8.28943	1.26413	0.632063	−	0.774917i	$-0.282208\pi$
$43$	8.28943	1.26413	0.632063	+	0.774917i	$0.282208\pi$
$44$	22.5855	3.40489
$45$	0.0214352	0.00319537
$46$	−16.3934	−2.41708
$47$	10.9691	1.60001	0.800007	−	0.599991i	$-0.204829\pi$
$47$	10.9691	1.60001	0.800007	+	0.599991i	$0.204829\pi$
$48$	−16.4717	−2.37748
$49$	10.5992	1.51417
$50$	−2.61030	−0.369152
$51$	−4.74864	−0.664943
$52$	−22.3503	−3.09944
$53$	2.49644	0.342912	0.171456	−	0.985192i	$-0.445153\pi$
$53$	2.49644	0.342912	0.171456	+	0.985192i	$0.445153\pi$
$54$	−13.6115	−1.85230
$55$	−4.69195	−0.632662
$56$	30.8113	4.11734
$57$	−3.41032	−0.451708
$58$	−15.1059	−1.98351
$59$	0.383242	0.0498939	0.0249469	−	0.999689i	$-0.492058\pi$
$59$	0.383242	0.0498939	0.0249469	+	0.999689i	$0.492058\pi$
$60$	8.30768	1.07252
$61$	13.2015	1.69028	0.845139	−	0.534546i	$-0.179517\pi$
$61$	13.2015	1.69028	0.845139	+	0.534546i	$0.179517\pi$
$62$	−1.47088	−0.186802
$63$	0.0899235	0.0113293
$64$	7.59925	0.949906
$65$	4.64310	0.575905
$66$	21.1372	2.60181
$67$	−9.48234	−1.15845	−0.579226	−	0.815167i	$-0.696645\pi$
$67$	−9.48234	−1.15845	−0.579226	+	0.815167i	$0.696645\pi$
$68$	13.2447	1.60616
$69$	−10.8388	−1.30484
$70$	−10.9506	−1.30884
$71$	−14.2815	−1.69490	−0.847451	−	0.530873i	$-0.821864\pi$
$71$	−14.2815	−1.69490	−0.847451	+	0.530873i	$0.821864\pi$
$72$	0.157431	0.0185534
$73$	−1.25350	−0.146711	−0.0733555	−	0.997306i	$-0.523371\pi$
$73$	−1.25350	−0.146711	−0.0733555	+	0.997306i	$0.523371\pi$
$74$	−8.03382	−0.933912
$75$	−1.72585	−0.199284
$76$	9.51193	1.09109
$77$	−19.6834	−2.24313
$78$	−20.9171	−2.36840
$79$	2.00630	0.225726	0.112863	−	0.993611i	$-0.463998\pi$
$79$	2.00630	0.225726	0.112863	+	0.993611i	$0.463998\pi$
$80$	−9.54409	−1.06706
$81$	−8.93524	−0.992804
$82$	−5.35738	−0.591624
$83$	−4.01890	−0.441132	−0.220566	−	0.975372i	$-0.570790\pi$
$83$	−4.01890	−0.441132	−0.220566	+	0.975372i	$0.570790\pi$
$84$	34.8519	3.80265
$85$	−2.75148	−0.298440
$86$	−21.6379	−2.33327
$87$	−9.98758	−1.07078
$88$	−34.4601	−3.67346
$89$	18.6630	1.97828	0.989139	−	0.146983i	$-0.0469563\pi$
$89$	18.6630	1.97828	0.989139	+	0.146983i	$0.0469563\pi$
$90$	−0.0559522	−0.00589788
$91$	19.4784	2.04190
$92$	30.2312	3.15182
$93$	−0.972503	−0.100844
$94$	−28.6328	−2.95324
$95$	−1.97602	−0.202736
$96$	17.6449	1.80088
$97$	13.6803	1.38902	0.694512	−	0.719481i	$-0.255620\pi$
$97$	13.6803	1.38902	0.694512	+	0.719481i	$0.255620\pi$
$98$	−27.6671	−2.79480
$99$	−0.100573	−0.0101079
$100$	4.81367	0.481367
$101$	0.148960	0.0148221	0.00741105	−	0.999973i	$-0.497641\pi$
$101$	0.148960	0.0148221	0.00741105	+	0.999973i	$0.497641\pi$
$102$	12.3954	1.22733
$103$	2.73196	0.269188	0.134594	−	0.990901i	$-0.457027\pi$
$103$	2.73196	0.269188	0.134594	+	0.990901i	$0.457027\pi$
$104$	34.1014	3.34391
$105$	−7.24019	−0.706570
$106$	−6.51645	−0.632934
$107$	−6.71623	−0.649282	−0.324641	−	0.945837i	$-0.605244\pi$
$107$	−6.71623	−0.649282	−0.324641	+	0.945837i	$0.605244\pi$
$108$	25.1011	2.41536
$109$	−11.4697	−1.09860	−0.549300	−	0.835625i	$-0.685106\pi$
$109$	−11.4697	−1.09860	−0.549300	+	0.835625i	$0.685106\pi$
$110$	12.2474	1.16774
$111$	−5.31172	−0.504166
$112$	−40.0388	−3.78331
$113$	−15.6176	−1.46918	−0.734590	−	0.678512i	$-0.762625\pi$
$113$	−15.6176	−1.46918	−0.734590	+	0.678512i	$0.762625\pi$
$114$	8.90197	0.833746
$115$	−6.28027	−0.585639
$116$	27.8569	2.58645
$117$	0.0995256	0.00920114
$118$	−1.00038	−0.0920922
$119$	−11.5428	−1.05813
$120$	−12.6756	−1.15712
$121$	11.0144	1.00131
$122$	−34.4599	−3.11985
$123$	−3.54214	−0.319384
$124$	2.71246	0.243586
$125$	−1.00000	−0.0894427
$126$	−0.234727	−0.0209112
$127$	0.280925	0.0249281	0.0124640	−	0.999922i	$-0.496032\pi$
$127$	0.280925	0.0249281	0.0124640	+	0.999922i	$0.496032\pi$
$128$	0.611454	0.0540454
$129$	−14.3063	−1.25960
$130$	−12.1199	−1.06298
$131$	−7.03057	−0.614264	−0.307132	−	0.951667i	$-0.599369\pi$
$131$	−7.03057	−0.614264	−0.307132	+	0.951667i	$0.599369\pi$
$132$	−38.9792	−3.39271
$133$	−8.28969	−0.718808
$134$	24.7518	2.13823
$135$	−5.21455	−0.448797
$136$	−20.2083	−1.73285
$137$	−3.57659	−0.305569	−0.152784	−	0.988260i	$-0.548824\pi$
$137$	−3.57659	−0.305569	−0.152784	+	0.988260i	$0.548824\pi$
$138$	28.2926	2.40843
$139$	−13.2857	−1.12688	−0.563440	−	0.826157i	$-0.690523\pi$
$139$	−13.2857	−1.12688	−0.563440	+	0.826157i	$0.690523\pi$
$140$	20.1940	1.70671
$141$	−18.9311	−1.59429
$142$	37.2790	3.12839
$143$	−21.7852	−1.82177
$144$	−0.204579	−0.0170483
$145$	−5.78704	−0.480588
$146$	3.27201	0.270794
$147$	−18.2926	−1.50875
$148$	14.8152	1.21780
$149$	23.6360	1.93633	0.968167	−	0.250306i	$-0.0805311\pi$
$149$	23.6360	1.93633	0.968167	+	0.250306i	$0.0805311\pi$
$150$	4.50499	0.367831
$151$	7.64025	0.621755	0.310878	−	0.950450i	$-0.399377\pi$
$151$	7.64025	0.621755	0.310878	+	0.950450i	$0.399377\pi$
$152$	−14.5130	−1.17716
$153$	−0.0589784	−0.00476812
$154$	51.3795	4.14028
$155$	−0.563492	−0.0452607
$156$	38.5734	3.08834
$157$	4.57688	0.365275	0.182637	−	0.983180i	$-0.441537\pi$
$157$	4.57688	0.365275	0.182637	+	0.983180i	$0.441537\pi$
$158$	−5.23705	−0.416637
$159$	−4.30848	−0.341685
$160$	10.2239	0.808269
$161$	−26.3466	−2.07640
$162$	23.3237	1.83248
$163$	11.6237	0.910437	0.455219	−	0.890380i	$-0.349561\pi$
$163$	11.6237	0.910437	0.455219	+	0.890380i	$0.349561\pi$
$164$	9.87958	0.771465
$165$	8.09761	0.630398
$166$	10.4905	0.814224
$167$	1.47644	0.114251	0.0571253	−	0.998367i	$-0.481807\pi$
$167$	1.47644	0.114251	0.0571253	+	0.998367i	$0.481807\pi$
$168$	−53.1758	−4.10260
$169$	8.55836	0.658335
$170$	7.18218	0.550848
$171$	−0.0423564	−0.00323907
$172$	39.9026	3.04254
$173$	−7.50318	−0.570456	−0.285228	−	0.958460i	$-0.592069\pi$
$173$	−7.50318	−0.570456	−0.285228	+	0.958460i	$0.592069\pi$
$174$	26.0706	1.97641
$175$	−4.19514	−0.317123
$176$	44.7804	3.37545
$177$	−0.661419	−0.0497153
$178$	−48.7161	−3.65143
$179$	−0.301754	−0.0225542	−0.0112771	−	0.999936i	$-0.503590\pi$
$179$	−0.301754	−0.0225542	−0.0112771	+	0.999936i	$0.503590\pi$
$180$	0.103182	0.00769072
$181$	−6.58748	−0.489644	−0.244822	−	0.969568i	$-0.578729\pi$
$181$	−6.58748	−0.489644	−0.244822	+	0.969568i	$0.578729\pi$
$182$	−50.8446	−3.76885
$183$	−22.7838	−1.68423
$184$	−46.1257	−3.40043
$185$	−3.07774	−0.226280
$186$	2.53853	0.186134
$187$	12.9098	0.944057
$188$	52.8018	3.85097
$189$	−21.8758	−1.59123
$190$	5.15802	0.374202
$191$	−24.1960	−1.75076	−0.875379	−	0.483436i	$-0.839388\pi$
$191$	−24.1960	−1.75076	−0.875379	+	0.483436i	$0.839388\pi$
$192$	−13.1152	−0.946506
$193$	15.2222	1.09572	0.547861	−	0.836570i	$-0.315442\pi$
$193$	15.2222	1.09572	0.547861	+	0.836570i	$0.315442\pi$
$194$	−35.7097	−2.56381
$195$	−8.01330	−0.573844
$196$	51.0210	3.64436
$197$	16.5306	1.17775	0.588877	−	0.808223i	$-0.299570\pi$
$197$	16.5306	1.17775	0.588877	+	0.808223i	$0.299570\pi$
$198$	0.262525	0.0186568
$199$	12.4236	0.880686	0.440343	−	0.897830i	$-0.354857\pi$
$199$	12.4236	0.880686	0.440343	+	0.897830i	$0.354857\pi$
$200$	−7.34453	−0.519337
$201$	16.3651	1.15431
$202$	−0.388831	−0.0273580
$203$	−24.2775	−1.70394
$204$	−22.8584	−1.60041
$205$	−2.05240	−0.143346
$206$	−7.13124	−0.496857
$207$	−0.134619	−0.00935665
$208$	−44.3141	−3.07263
$209$	9.27140	0.641316
$210$	18.8991	1.30416
$211$	20.5951	1.41783	0.708914	−	0.705295i	$-0.249185\pi$
$211$	20.5951	1.41783	0.708914	+	0.705295i	$0.249185\pi$
$212$	12.0170	0.825333
$213$	24.6478	1.68884
$214$	17.5314	1.19842
$215$	−8.28943	−0.565334
$216$	−38.2984	−2.60588
$217$	−2.36393	−0.160474
$218$	29.9394	2.02775
$219$	2.16335	0.146186
$220$	−22.5855	−1.52271
$221$	−12.7754	−0.859365
$222$	13.8652	0.930570
$223$	11.7907	0.789567	0.394783	−	0.918774i	$-0.370820\pi$
$223$	11.7907	0.789567	0.394783	+	0.918774i	$0.370820\pi$
$224$	42.8906	2.86575
$225$	−0.0214352	−0.00142901
$226$	40.7666	2.71175
$227$	23.8792	1.58492	0.792458	−	0.609927i	$-0.208801\pi$
$227$	23.8792	1.58492	0.792458	+	0.609927i	$0.208801\pi$
$228$	−16.4162	−1.08719
$229$	18.2728	1.20750	0.603751	−	0.797173i	$-0.293672\pi$
$229$	18.2728	1.20750	0.603751	+	0.797173i	$0.293672\pi$
$230$	16.3934	1.08095
$231$	33.9706	2.23510
$232$	−42.5031	−2.79047
$233$	18.0850	1.18479	0.592394	−	0.805648i	$-0.298183\pi$
$233$	18.0850	1.18479	0.592394	+	0.805648i	$0.298183\pi$
$234$	−0.259792	−0.0169831
$235$	−10.9691	−0.715548
$236$	1.84480	0.120086
$237$	−3.46258	−0.224919
$238$	30.1303	1.95305
$239$	9.39962	0.608011	0.304005	−	0.952670i	$-0.401676\pi$
$239$	9.39962	0.608011	0.304005	+	0.952670i	$0.401676\pi$
$240$	16.4717	1.06324
$241$	9.03047	0.581704	0.290852	−	0.956768i	$-0.406061\pi$
$241$	9.03047	0.581704	0.290852	+	0.956768i	$0.406061\pi$
$242$	−28.7508	−1.84817
$243$	−0.222756	−0.0142898
$244$	63.5477	4.06822
$245$	−10.5992	−0.677158
$246$	9.24604	0.589506
$247$	−9.17487	−0.583783
$248$	−4.13858	−0.262800
$249$	6.93603	0.439553
$250$	2.61030	0.165090
$251$	2.72810	0.172196	0.0860982	−	0.996287i	$-0.472560\pi$
$251$	2.72810	0.172196	0.0860982	+	0.996287i	$0.472560\pi$
$252$	0.432862	0.0272678
$253$	29.4667	1.85256
$254$	−0.733299	−0.0460113
$255$	4.74864	0.297371
$256$	−16.7946	−1.04966
$257$	−18.4249	−1.14931	−0.574657	−	0.818394i	$-0.694865\pi$
$257$	−18.4249	−1.14931	−0.574657	+	0.818394i	$0.694865\pi$
$258$	37.3438	2.32492
$259$	−12.9115	−0.802284
$260$	22.3503	1.38611
$261$	−0.124046	−0.00767827
$262$	18.3519	1.13378
$263$	−30.2702	−1.86654	−0.933269	−	0.359179i	$-0.883057\pi$
$263$	−30.2702	−1.86654	−0.933269	+	0.359179i	$0.883057\pi$
$264$	59.4731	3.66032
$265$	−2.49644	−0.153355
$266$	21.6386	1.32675
$267$	−32.2096	−1.97120
$268$	−45.6449	−2.78820
$269$	−18.2634	−1.11354	−0.556769	−	0.830667i	$-0.687959\pi$
$269$	−18.2634	−1.11354	−0.556769	+	0.830667i	$0.687959\pi$
$270$	13.6115	0.828372
$271$	−14.5443	−0.883501	−0.441750	−	0.897138i	$-0.645642\pi$
$271$	−14.5443	−0.883501	−0.441750	+	0.897138i	$0.645642\pi$
$272$	26.2603	1.59227
$273$	−33.6169	−2.03459
$274$	9.33598	0.564007
$275$	4.69195	0.282935
$276$	−52.1745	−3.14054
$277$	2.13918	0.128531	0.0642655	−	0.997933i	$-0.479530\pi$
$277$	2.13918	0.128531	0.0642655	+	0.997933i	$0.479530\pi$
$278$	34.6797	2.07995
$279$	−0.0120785	−0.000723123 0
$280$	−30.8113	−1.84133
$281$	21.6430	1.29112	0.645558	−	0.763712i	$-0.276625\pi$
$281$	21.6430	1.29112	0.645558	+	0.763712i	$0.276625\pi$
$282$	49.4159	2.94267
$283$	9.19962	0.546861	0.273430	−	0.961892i	$-0.411842\pi$
$283$	9.19962	0.546861	0.273430	+	0.961892i	$0.411842\pi$
$284$	−68.7465	−4.07935
$285$	3.41032	0.202010
$286$	56.8659	3.36255
$287$	−8.61010	−0.508238
$288$	0.219151	0.0129136
$289$	−9.42937	−0.554669
$290$	15.1059	0.887051
$291$	−23.6102	−1.38405
$292$	−6.03393	−0.353109
$293$	−11.8196	−0.690509	−0.345255	−	0.938509i	$-0.612207\pi$
$293$	−11.8196	−0.690509	−0.345255	+	0.938509i	$0.612207\pi$
$294$	47.7493	2.78480
$295$	−0.383242	−0.0223132
$296$	−22.6045	−1.31386
$297$	24.4664	1.41968
$298$	−61.6970	−3.57401
$299$	−29.1599	−1.68636
$300$	−8.30768	−0.479644
$301$	−34.7753	−2.00441
$302$	−19.9434	−1.14761
$303$	−0.257083	−0.0147690
$304$	18.8593	1.08166
$305$	−13.2015	−0.755916
$306$	0.153951	0.00880081
$307$	16.5726	0.945847	0.472923	−	0.881104i	$-0.343199\pi$
$307$	16.5726	0.945847	0.472923	+	0.881104i	$0.343199\pi$
$308$	−94.7493	−5.39884
$309$	−4.71496	−0.268225
$310$	1.47088	0.0835405
$311$	−7.80672	−0.442678	−0.221339	−	0.975197i	$-0.571043\pi$
$311$	−7.80672	−0.442678	−0.221339	+	0.975197i	$0.571043\pi$
$312$	−58.8539	−3.33195
$313$	2.44081	0.137963	0.0689814	−	0.997618i	$-0.478025\pi$
$313$	2.44081	0.137963	0.0689814	+	0.997618i	$0.478025\pi$
$314$	−11.9470	−0.674210
$315$	−0.0899235	−0.00506661
$316$	9.65767	0.543286
$317$	−15.8024	−0.887552	−0.443776	−	0.896138i	$-0.646361\pi$
$317$	−15.8024	−0.887552	−0.443776	+	0.896138i	$0.646361\pi$
$318$	11.2464	0.630668
$319$	27.1525	1.52025
$320$	−7.59925	−0.424811
$321$	11.5912	0.646959
$322$	68.7726	3.83255
$323$	5.43698	0.302522
$324$	−43.0113	−2.38952
$325$	−4.64310	−0.257553
$326$	−30.3413	−1.68045
$327$	19.7950	1.09467
$328$	−15.0739	−0.832317
$329$	−46.0171	−2.53700
$330$	−21.1372	−1.16356
$331$	−8.39470	−0.461415	−0.230707	−	0.973023i	$-0.574104\pi$
$331$	−8.39470	−0.461415	−0.230707	+	0.973023i	$0.574104\pi$
$332$	−19.3457	−1.06173
$333$	−0.0659718	−0.00361523
$334$	−3.85396	−0.210879
$335$	9.48234	0.518075
$336$	69.1010	3.76977
$337$	2.85541	0.155544	0.0777719	−	0.996971i	$-0.475219\pi$
$337$	2.85541	0.155544	0.0777719	+	0.996971i	$0.475219\pi$
$338$	−22.3399	−1.21513
$339$	26.9536	1.46392
$340$	−13.2447	−0.718295
$341$	2.64387	0.143174
$342$	0.110563	0.00597856
$343$	−15.0991	−0.815276
$344$	−60.8819	−3.28253
$345$	10.8388	0.583543
$346$	19.5856	1.05293
$347$	23.3546	1.25374	0.626871	−	0.779123i	$-0.284335\pi$
$347$	23.3546	1.25374	0.626871	+	0.779123i	$0.284335\pi$
$348$	−48.0769	−2.57719
$349$	−19.3737	−1.03705	−0.518525	−	0.855062i	$-0.673519\pi$
$349$	−19.3737	−1.03705	−0.518525	+	0.855062i	$0.673519\pi$
$350$	10.9506	0.585333
$351$	−24.2117	−1.29232
$352$	−47.9700	−2.55681
$353$	−8.18257	−0.435514	−0.217757	−	0.976003i	$-0.569874\pi$
$353$	−8.18257	−0.435514	−0.217757	+	0.976003i	$0.569874\pi$
$354$	1.72650	0.0917626
$355$	14.2815	0.757984
$356$	89.8377	4.76139
$357$	19.9212	1.05434
$358$	0.787670	0.0416296
$359$	−1.08038	−0.0570202	−0.0285101	−	0.999594i	$-0.509076\pi$
$359$	−1.08038	−0.0570202	−0.0285101	+	0.999594i	$0.509076\pi$
$360$	−0.157431	−0.00829735
$361$	−15.0953	−0.794491
$362$	17.1953	0.903765
$363$	−19.0092	−0.997723
$364$	93.7628	4.91451
$365$	1.25350	0.0656112
$366$	59.4727	3.10869
$367$	−23.5609	−1.22987	−0.614933	−	0.788579i	$-0.710817\pi$
$367$	−23.5609	−1.22987	−0.614933	+	0.788579i	$0.710817\pi$
$368$	59.9395	3.12456
$369$	−0.0439935	−0.00229021
$370$	8.03382	0.417658
$371$	−10.4729	−0.543726
$372$	−4.68131	−0.242715
$373$	−15.6551	−0.810589	−0.405295	−	0.914186i	$-0.632831\pi$
$373$	−15.6551	−0.810589	−0.405295	+	0.914186i	$0.632831\pi$
$374$	−33.6984	−1.74250
$375$	1.72585	0.0891226
$376$	−80.5632	−4.15473
$377$	−26.8698	−1.38387
$378$	57.1023	2.93703
$379$	−12.7194	−0.653349	−0.326675	−	0.945137i	$-0.605928\pi$
$379$	−12.7194	−0.653349	−0.326675	+	0.945137i	$0.605928\pi$
$380$	−9.51193	−0.487952
$381$	−0.484835	−0.0248389
$382$	63.1588	3.23148
$383$	29.7973	1.52257	0.761284	−	0.648418i	$-0.224569\pi$
$383$	29.7973	1.52257	0.761284	+	0.648418i	$0.224569\pi$
$384$	−1.05528	−0.0538519
$385$	19.6834	1.00316
$386$	−39.7346	−2.02244
$387$	−0.177685	−0.00903224
$388$	65.8525	3.34315
$389$	31.4557	1.59487	0.797434	−	0.603406i	$-0.206190\pi$
$389$	31.4557	1.59487	0.797434	+	0.603406i	$0.206190\pi$
$390$	20.9171	1.05918
$391$	17.2800	0.873889
$392$	−77.8461	−3.93182
$393$	12.1337	0.612065
$394$	−43.1497	−2.17385
$395$	−2.00630	−0.100948
$396$	−0.484124	−0.0243281
$397$	−14.4570	−0.725577	−0.362789	−	0.931871i	$-0.618175\pi$
$397$	−14.4570	−0.725577	−0.362789	+	0.931871i	$0.618175\pi$
$398$	−32.4294	−1.62554
$399$	14.3068	0.716235
$400$	9.54409	0.477205
$401$	−38.9166	−1.94340	−0.971702	−	0.236209i	$-0.924095\pi$
$401$	−38.9166	−1.94340	−0.971702	+	0.236209i	$0.924095\pi$
$402$	−42.7179	−2.13057
$403$	−2.61635	−0.130329
$404$	0.717045	0.0356743
$405$	8.93524	0.443995
$406$	63.3715	3.14507
$407$	14.4406	0.715793
$408$	34.8765	1.72665
$409$	32.9159	1.62759	0.813793	−	0.581155i	$-0.197399\pi$
$409$	32.9159	1.62759	0.813793	+	0.581155i	$0.197399\pi$
$410$	5.35738	0.264582
$411$	6.17266	0.304475
$412$	13.1508	0.647891
$413$	−1.60775	−0.0791124
$414$	0.351395	0.0172701
$415$	4.01890	0.197280
$416$	47.4705	2.32743
$417$	22.9292	1.12285
$418$	−24.2011	−1.18372
$419$	11.3451	0.554247	0.277123	−	0.960834i	$-0.410619\pi$
$419$	11.3451	0.554247	0.277123	+	0.960834i	$0.410619\pi$
$420$	−34.8519	−1.70060
$421$	−29.0995	−1.41822	−0.709111	−	0.705097i	$-0.750903\pi$
$421$	−29.0995	−1.41822	−0.709111	+	0.705097i	$0.750903\pi$
$422$	−53.7595	−2.61697
$423$	−0.235125	−0.0114322
$424$	−18.3351	−0.890434
$425$	2.75148	0.133466
$426$	−64.3381	−3.11719
$427$	−55.3821	−2.68013
$428$	−32.3297	−1.56272
$429$	37.5980	1.81525
$430$	21.6379	1.04347
$431$	8.66209	0.417238	0.208619	−	0.977997i	$-0.433103\pi$
$431$	8.66209	0.417238	0.208619	+	0.977997i	$0.433103\pi$
$432$	49.7681	2.39447
$433$	−9.36339	−0.449976	−0.224988	−	0.974362i	$-0.572234\pi$
$433$	−9.36339	−0.449976	−0.224988	+	0.974362i	$0.572234\pi$
$434$	6.17056	0.296196
$435$	9.98758	0.478868
$436$	−55.2115	−2.64415
$437$	12.4100	0.593649
$438$	−5.64701	−0.269824
$439$	−15.1761	−0.724316	−0.362158	−	0.932117i	$-0.617960\pi$
$439$	−15.1761	−0.724316	−0.362158	+	0.932117i	$0.617960\pi$
$440$	34.4601	1.64282
$441$	−0.227195	−0.0108188
$442$	33.3476	1.58618
$443$	1.36489	0.0648479	0.0324240	−	0.999474i	$-0.489677\pi$
$443$	1.36489	0.0648479	0.0324240	+	0.999474i	$0.489677\pi$
$444$	−25.5689	−1.21344
$445$	−18.6630	−0.884713
$446$	−30.7774	−1.45735
$447$	−40.7922	−1.92940
$448$	−31.8799	−1.50618
$449$	18.9836	0.895891	0.447945	−	0.894061i	$-0.352156\pi$
$449$	18.9836	0.895891	0.447945	+	0.894061i	$0.352156\pi$
$450$	0.0559522	0.00263761
$451$	9.62975	0.453447
$452$	−75.1779	−3.53607
$453$	−13.1859	−0.619530
$454$	−62.3318	−2.92538
$455$	−19.4784	−0.913164
$456$	25.0472	1.17294
$457$	12.9304	0.604858	0.302429	−	0.953172i	$-0.402203\pi$
$457$	12.9304	0.604858	0.302429	+	0.953172i	$0.402203\pi$
$458$	−47.6976	−2.22876
$459$	14.3477	0.669694
$460$	−30.2312	−1.40954
$461$	−25.0271	−1.16563	−0.582815	−	0.812605i	$-0.698049\pi$
$461$	−25.0271	−1.16563	−0.582815	+	0.812605i	$0.698049\pi$
$462$	−88.6735	−4.12546
$463$	27.8816	1.29577	0.647884	−	0.761739i	$-0.275654\pi$
$463$	27.8816	1.29577	0.647884	+	0.761739i	$0.275654\pi$
$464$	55.2321	2.56408
$465$	0.972503	0.0450987
$466$	−47.2073	−2.18684
$467$	15.8843	0.735040	0.367520	−	0.930016i	$-0.380207\pi$
$467$	15.8843	0.735040	0.367520	+	0.930016i	$0.380207\pi$
$468$	0.479083	0.0221456
$469$	39.7797	1.83686
$470$	28.6328	1.32073
$471$	−7.89902	−0.363968
$472$	−2.81473	−0.129559
$473$	38.8936	1.78833
$474$	9.03837	0.415146
$475$	1.97602	0.0906662
$476$	−55.5634	−2.54674
$477$	−0.0535115	−0.00245012
$478$	−24.5358	−1.12224
$479$	40.5362	1.85215	0.926074	−	0.377342i	$-0.123162\pi$
$479$	40.5362	1.85215	0.926074	+	0.377342i	$0.123162\pi$
$480$	−17.6449	−0.805377
$481$	−14.2902	−0.651579
$482$	−23.5722	−1.07369
$483$	45.4704	2.06897
$484$	53.0196	2.40998
$485$	−13.6803	−0.621191
$486$	0.581461	0.0263756
$487$	13.7753	0.624219	0.312110	−	0.950046i	$-0.398964\pi$
$487$	13.7753	0.624219	0.312110	+	0.950046i	$0.398964\pi$
$488$	−96.9588	−4.38912
$489$	−20.0608	−0.907179
$490$	27.6671	1.24987
$491$	−25.9343	−1.17040	−0.585200	−	0.810889i	$-0.698984\pi$
$491$	−25.9343	−1.17040	−0.585200	+	0.810889i	$0.698984\pi$
$492$	−17.0507	−0.768704
$493$	15.9229	0.717132
$494$	23.9492	1.07752
$495$	0.100573	0.00452040
$496$	5.37801	0.241480
$497$	59.9129	2.68746
$498$	−18.1051	−0.811310
$499$	−4.49403	−0.201180	−0.100590	−	0.994928i	$-0.532073\pi$
$499$	−4.49403	−0.201180	−0.100590	+	0.994928i	$0.532073\pi$
$500$	−4.81367	−0.215274
$501$	−2.54812	−0.113842
$502$	−7.12117	−0.317833
$503$	−27.2509	−1.21506	−0.607529	−	0.794298i	$-0.707839\pi$
$503$	−27.2509	−1.21506	−0.607529	+	0.794298i	$0.707839\pi$
$504$	−0.660446	−0.0294186
$505$	−0.148960	−0.00662864
$506$	−76.9170	−3.41938
$507$	−14.7705	−0.655979
$508$	1.35228	0.0599978
$509$	−40.7196	−1.80486	−0.902432	−	0.430832i	$-0.858220\pi$
$509$	−40.7196	−1.80486	−0.902432	+	0.430832i	$0.858220\pi$
$510$	−12.3954	−0.548877
$511$	5.25861	0.232627
$512$	42.6160	1.88338
$513$	10.3041	0.454936
$514$	48.0946	2.12136
$515$	−2.73196	−0.120385
$516$	−68.8659	−3.03165
$517$	51.4666	2.26350
$518$	33.7030	1.48082
$519$	12.9494	0.568415
$520$	−34.1014	−1.49544
$521$	−33.7266	−1.47759	−0.738795	−	0.673931i	$-0.764605\pi$
$521$	−33.7266	−1.47759	−0.738795	+	0.673931i	$0.764605\pi$
$522$	0.323798	0.0141723
$523$	25.7259	1.12491	0.562456	−	0.826827i	$-0.309856\pi$
$523$	25.7259	1.12491	0.562456	+	0.826827i	$0.309856\pi$
$524$	−33.8429	−1.47843
$525$	7.24019	0.315988
$526$	79.0142	3.44518
$527$	1.55043	0.0675380
$528$	−77.2843	−3.36337
$529$	16.4418	0.714863
$530$	6.51645	0.283056
$531$	−0.00821486	−0.000356495 0
$532$	−39.9039	−1.73005
$533$	−9.52949	−0.412768
$534$	84.0769	3.63836
$535$	6.71623	0.290368
$536$	69.6433	3.00813
$537$	0.520783	0.0224735
$538$	47.6729	2.05533
$539$	49.7309	2.14206
$540$	−25.1011	−1.08018
$541$	−2.51847	−0.108278	−0.0541388	−	0.998533i	$-0.517241\pi$
$541$	−2.51847	−0.108278	−0.0541388	+	0.998533i	$0.517241\pi$
$542$	37.9649	1.63073
$543$	11.3690	0.487891
$544$	−28.1308	−1.20610
$545$	11.4697	0.491309
$546$	87.7503	3.75536
$547$	−17.1481	−0.733201	−0.366600	−	0.930379i	$-0.619478\pi$
$547$	−17.1481	−0.733201	−0.366600	+	0.930379i	$0.619478\pi$
$548$	−17.2165	−0.735454
$549$	−0.282976	−0.0120771
$550$	−12.2474	−0.522231
$551$	11.4353	0.487162
$552$	79.6061	3.38826
$553$	−8.41671	−0.357915
$554$	−5.58391	−0.237237
$555$	5.31172	0.225470
$556$	−63.9531	−2.71222
$557$	−27.1016	−1.14833	−0.574166	−	0.818739i	$-0.694674\pi$
$557$	−27.1016	−1.14833	−0.574166	+	0.818739i	$0.694674\pi$
$558$	0.0315286	0.00133471
$559$	−38.4886	−1.62789
$560$	40.0388	1.69195
$561$	−22.2804	−0.940678
$562$	−56.4948	−2.38309
$563$	16.1864	0.682174	0.341087	−	0.940032i	$-0.389205\pi$
$563$	16.1864	0.682174	0.341087	+	0.940032i	$0.389205\pi$
$564$	−91.1282	−3.83719
$565$	15.6176	0.657037
$566$	−24.0138	−1.00937
$567$	37.4846	1.57420
$568$	104.891	4.40113
$569$	−2.92315	−0.122545	−0.0612724	−	0.998121i	$-0.519516\pi$
$569$	−2.92315	−0.122545	−0.0612724	+	0.998121i	$0.519516\pi$
$570$	−8.90197	−0.372863
$571$	44.1240	1.84653	0.923265	−	0.384164i	$-0.125510\pi$
$571$	44.1240	1.84653	0.923265	+	0.384164i	$0.125510\pi$
$572$	−104.867	−4.38470
$573$	41.7587	1.74449
$574$	22.4750	0.938087
$575$	6.28027	0.261906
$576$	−0.162891	−0.00678713
$577$	19.0835	0.794456	0.397228	−	0.917720i	$-0.369972\pi$
$577$	19.0835	0.794456	0.397228	+	0.917720i	$0.369972\pi$
$578$	24.6135	1.02379
$579$	−26.2713	−1.09180
$580$	−27.8569	−1.15670
$581$	16.8599	0.699465
$582$	61.6297	2.55463
$583$	11.7131	0.485109
$584$	9.20636	0.380962
$585$	−0.0995256	−0.00411488
$586$	30.8528	1.27452
$587$	−17.6959	−0.730387	−0.365193	−	0.930932i	$-0.618997\pi$
$587$	−17.6959	−0.730387	−0.365193	+	0.930932i	$0.618997\pi$
$588$	−88.0548	−3.63132
$589$	1.11347	0.0458798
$590$	1.00038	0.0411849
$591$	−28.5293	−1.17354
$592$	29.3742	1.20727
$593$	3.91690	0.160848	0.0804238	−	0.996761i	$-0.474373\pi$
$593$	3.91690	0.160848	0.0804238	+	0.996761i	$0.474373\pi$
$594$	−63.8647	−2.62040
$595$	11.5428	0.473210
$596$	113.776	4.66044
$597$	−21.4413	−0.877534
$598$	76.1162	3.11262
$599$	−14.9550	−0.611043	−0.305521	−	0.952185i	$-0.598831\pi$
$599$	−14.9550	−0.611043	−0.305521	+	0.952185i	$0.598831\pi$
$600$	12.6756	0.517478
$601$	−28.1392	−1.14782	−0.573912	−	0.818917i	$-0.694575\pi$
$601$	−28.1392	−1.14782	−0.573912	+	0.818917i	$0.694575\pi$
$602$	90.7740	3.69967
$603$	0.203255	0.00827720
$604$	36.7777	1.49646
$605$	−11.0144	−0.447798
$606$	0.671064	0.0272601
$607$	−37.5357	−1.52353	−0.761764	−	0.647854i	$-0.775667\pi$
$607$	−37.5357	−1.52353	−0.761764	+	0.647854i	$0.775667\pi$
$608$	−20.2026	−0.819325
$609$	41.8993	1.69785
$610$	34.4599	1.39524
$611$	−50.9308	−2.06044
$612$	−0.283902	−0.0114761
$613$	27.7215	1.11966	0.559831	−	0.828607i	$-0.310866\pi$
$613$	27.7215	1.11966	0.559831	+	0.828607i	$0.310866\pi$
$614$	−43.2594	−1.74581
$615$	3.54214	0.142833
$616$	144.565	5.82470
$617$	−5.20000	−0.209344	−0.104672	−	0.994507i	$-0.533379\pi$
$617$	−5.20000	−0.209344	−0.104672	+	0.994507i	$0.533379\pi$
$618$	12.3075	0.495079
$619$	9.53975	0.383435	0.191717	−	0.981450i	$-0.438594\pi$
$619$	9.53975	0.383435	0.191717	+	0.981450i	$0.438594\pi$
$620$	−2.71246	−0.108935
$621$	32.7488	1.31416
$622$	20.3779	0.817079
$623$	−78.2940	−3.13678
$624$	76.4797	3.06164
$625$	1.00000	0.0400000
$626$	−6.37125	−0.254646
$627$	−16.0011	−0.639021
$628$	22.0316	0.879156
$629$	8.46832	0.337654
$630$	0.234727	0.00935176
$631$	40.0155	1.59299	0.796497	−	0.604643i	$-0.206684\pi$
$631$	40.0155	1.59299	0.796497	+	0.604643i	$0.206684\pi$
$632$	−14.7353	−0.586140
$633$	−35.5442	−1.41275
$634$	41.2491	1.63821
$635$	−0.280925	−0.0111482
$636$	−20.7396	−0.822379
$637$	−49.2131	−1.94989
$638$	−70.8762	−2.80602
$639$	0.306126	0.0121102
$640$	−0.611454	−0.0241698
$641$	14.2425	0.562547	0.281273	−	0.959628i	$-0.409243\pi$
$641$	14.2425	0.562547	0.281273	+	0.959628i	$0.409243\pi$
$642$	−30.2566	−1.19413
$643$	−4.52576	−0.178478	−0.0892392	−	0.996010i	$-0.528444\pi$
$643$	−4.52576	−0.178478	−0.0892392	+	0.996010i	$0.528444\pi$
$644$	−126.824	−4.99757
$645$	14.3063	0.563311
$646$	−14.1922	−0.558383
$647$	−12.3237	−0.484496	−0.242248	−	0.970214i	$-0.577885\pi$
$647$	−12.3237	−0.484496	−0.242248	+	0.970214i	$0.577885\pi$
$648$	65.6251	2.57800
$649$	1.79815	0.0705837
$650$	12.1199	0.475381
$651$	4.07979	0.159899
$652$	55.9526	2.19127
$653$	−7.27896	−0.284848	−0.142424	−	0.989806i	$-0.545490\pi$
$653$	−7.27896	−0.284848	−0.142424	+	0.989806i	$0.545490\pi$
$654$	−51.6710	−2.02050
$655$	7.03057	0.274707
$656$	19.5883	0.764794
$657$	0.0268690	0.00104826
$658$	120.118	4.68270
$659$	23.2949	0.907441	0.453720	−	0.891144i	$-0.350097\pi$
$659$	23.2949	0.907441	0.453720	+	0.891144i	$0.350097\pi$
$660$	38.9792	1.51726
$661$	−34.3008	−1.33415	−0.667073	−	0.744992i	$-0.732453\pi$
$661$	−34.3008	−1.33415	−0.667073	+	0.744992i	$0.732453\pi$
$662$	21.9127	0.851661
$663$	22.0484	0.856289
$664$	29.5170	1.14548
$665$	8.28969	0.321461
$666$	0.172206	0.00667285
$667$	36.3442	1.40725
$668$	7.10711	0.274983
$669$	−20.3491	−0.786741
$670$	−24.7518	−0.956244
$671$	61.9407	2.39120
$672$	−74.0229	−2.85550
$673$	26.2837	1.01316	0.506582	−	0.862192i	$-0.330909\pi$
$673$	26.2837	1.01316	0.506582	+	0.862192i	$0.330909\pi$
$674$	−7.45347	−0.287097
$675$	5.21455	0.200708
$676$	41.1971	1.58450
$677$	−16.4163	−0.630930	−0.315465	−	0.948937i	$-0.602161\pi$
$677$	−16.4163	−0.630930	−0.315465	+	0.948937i	$0.602161\pi$
$678$	−70.3571	−2.70205
$679$	−57.3908	−2.20246
$680$	20.2083	0.774953
$681$	−41.2119	−1.57924
$682$	−6.90130	−0.264265
$683$	8.02756	0.307166	0.153583	−	0.988136i	$-0.450919\pi$
$683$	8.02756	0.307166	0.153583	+	0.988136i	$0.450919\pi$
$684$	−0.203890	−0.00779592
$685$	3.57659	0.136654
$686$	39.4133	1.50481
$687$	−31.5362	−1.20318
$688$	79.1150	3.01623
$689$	−11.5912	−0.441589
$690$	−28.2926	−1.07708
$691$	21.4190	0.814818	0.407409	−	0.913246i	$-0.366432\pi$
$691$	21.4190	0.814818	0.407409	+	0.913246i	$0.366432\pi$
$692$	−36.1178	−1.37299
$693$	0.421916	0.0160273
$694$	−60.9626	−2.31411
$695$	13.2857	0.503956
$696$	73.3541	2.78048
$697$	5.64713	0.213900
$698$	50.5712	1.91415
$699$	−31.2121	−1.18055
$700$	−20.1940	−0.763262
$701$	−15.2238	−0.574994	−0.287497	−	0.957782i	$-0.592823\pi$
$701$	−15.2238	−0.574994	−0.287497	+	0.957782i	$0.592823\pi$
$702$	63.1997	2.38532
$703$	6.08168	0.229375
$704$	35.6553	1.34381
$705$	18.9311	0.712987
$706$	21.3590	0.803856
$707$	−0.624909	−0.0235021
$708$	−3.18386	−0.119657
$709$	−8.90640	−0.334487	−0.167243	−	0.985916i	$-0.553487\pi$
$709$	−8.90640	−0.334487	−0.167243	+	0.985916i	$0.553487\pi$
$710$	−37.2790	−1.39906
$711$	−0.0430054	−0.00161283
$712$	−137.071	−5.13696
$713$	3.53888	0.132532
$714$	−52.0004	−1.94606
$715$	21.7852	0.814719
$716$	−1.45255	−0.0542842
$717$	−16.2223	−0.605835
$718$	2.82011	0.105246
$719$	46.6604	1.74014	0.870070	−	0.492928i	$-0.164073\pi$
$719$	46.6604	1.74014	0.870070	+	0.492928i	$0.164073\pi$
$720$	0.204579	0.00762421
$721$	−11.4609	−0.426828
$722$	39.4034	1.46644
$723$	−15.5853	−0.579622
$724$	−31.7100	−1.17849
$725$	5.78704	0.214925
$726$	49.6197	1.84156
$727$	35.7654	1.32647	0.663233	−	0.748413i	$-0.269184\pi$
$727$	35.7654	1.32647	0.663233	+	0.748413i	$0.269184\pi$
$728$	−143.060	−5.30216
$729$	27.1901	1.00704
$730$	−3.27201	−0.121103
$731$	22.8082	0.843590
$732$	−109.674	−4.05366
$733$	23.9999	0.886457	0.443229	−	0.896409i	$-0.353833\pi$
$733$	23.9999	0.886457	0.443229	+	0.896409i	$0.353833\pi$
$734$	61.5009	2.27004
$735$	18.2926	0.674734
$736$	−64.2088	−2.36677
$737$	−44.4906	−1.63883
$738$	0.114836	0.00422718
$739$	14.7101	0.541119	0.270559	−	0.962703i	$-0.412791\pi$
$739$	14.7101	0.541119	0.270559	+	0.962703i	$0.412791\pi$
$740$	−14.8152	−0.544618
$741$	15.8345	0.581694
$742$	27.3374	1.00359
$743$	−12.4820	−0.457919	−0.228960	−	0.973436i	$-0.573532\pi$
$743$	−12.4820	−0.457919	−0.228960	+	0.973436i	$0.573532\pi$
$744$	7.14258	0.261860
$745$	−23.6360	−0.865955
$746$	40.8645	1.49615
$747$	0.0861458	0.00315191
$748$	62.1435	2.27219
$749$	28.1755	1.02951
$750$	−4.50499	−0.164499
$751$	−21.6542	−0.790172	−0.395086	−	0.918644i	$-0.629285\pi$
$751$	−21.6542	−0.790172	−0.395086	+	0.918644i	$0.629285\pi$
$752$	104.690	3.81767
$753$	−4.70830	−0.171580
$754$	70.1383	2.55429
$755$	−7.64025	−0.278057
$756$	−105.303	−3.82982
$757$	40.3599	1.46691	0.733453	−	0.679740i	$-0.237907\pi$
$757$	40.3599	1.46691	0.733453	+	0.679740i	$0.237907\pi$
$758$	33.2013	1.20593
$759$	−50.8552	−1.84593
$760$	14.5130	0.526440
$761$	12.4123	0.449944	0.224972	−	0.974365i	$-0.427771\pi$
$761$	12.4123	0.449944	0.224972	+	0.974365i	$0.427771\pi$
$762$	1.26557	0.0458466
$763$	48.1171	1.74196
$764$	−116.471	−4.21379
$765$	0.0589784	0.00213237
$766$	−77.7798	−2.81030
$767$	−1.77943	−0.0642515
$768$	28.9849	1.04590
$769$	30.0724	1.08444	0.542220	−	0.840236i	$-0.317584\pi$
$769$	30.0724	1.08444	0.542220	+	0.840236i	$0.317584\pi$
$770$	−51.3795	−1.85159
$771$	31.7987	1.14520
$772$	73.2749	2.63722
$773$	15.2751	0.549406	0.274703	−	0.961529i	$-0.411421\pi$
$773$	15.2751	0.549406	0.274703	+	0.961529i	$0.411421\pi$
$774$	0.463812	0.0166714
$775$	0.563492	0.0202412
$776$	−100.475	−3.60686
$777$	22.2834	0.799412
$778$	−82.1089	−2.94375
$779$	4.05559	0.145307
$780$	−38.5734	−1.38115
$781$	−67.0081	−2.39774
$782$	−45.1061	−1.61299
$783$	30.1768	1.07843
$784$	101.160	3.61285
$785$	−4.57688	−0.163356
$786$	−31.6727	−1.12973
$787$	−34.4395	−1.22763	−0.613817	−	0.789448i	$-0.710367\pi$
$787$	−34.4395	−1.22763	−0.613817	+	0.789448i	$0.710367\pi$
$788$	79.5726	2.83466
$789$	52.2418	1.85986
$790$	5.23705	0.186326
$791$	65.5180	2.32955
$792$	0.738659	0.0262471
$793$	−61.2959	−2.17668
$794$	37.7372	1.33924
$795$	4.30848	0.152806
$796$	59.8032	2.11967
$797$	−45.8959	−1.62572	−0.812858	−	0.582463i	$-0.802089\pi$
$797$	−45.8959	−1.62572	−0.812858	+	0.582463i	$0.802089\pi$
$798$	−37.3450	−1.32200
$799$	30.1813	1.06774
$800$	−10.2239	−0.361469
$801$	−0.400045	−0.0141349
$802$	101.584	3.58706
$803$	−5.88135	−0.207548
$804$	78.7763	2.77822
$805$	26.3466	0.928597
$806$	6.82945	0.240557
$807$	31.5199	1.10955
$808$	−1.09404	−0.0384883
$809$	11.2512	0.395572	0.197786	−	0.980245i	$-0.436625\pi$
$809$	11.2512	0.395572	0.197786	+	0.980245i	$0.436625\pi$
$810$	−23.3237	−0.819510
$811$	13.3500	0.468782	0.234391	−	0.972142i	$-0.424690\pi$
$811$	13.3500	0.468782	0.234391	+	0.972142i	$0.424690\pi$
$812$	−116.864	−4.10111
$813$	25.1012	0.880339
$814$	−37.6943	−1.32118
$815$	−11.6237	−0.407160
$816$	−45.3215	−1.58657
$817$	16.3801	0.573067
$818$	−85.9204	−3.00414
$819$	−0.417524	−0.0145895
$820$	−9.87958	−0.345010
$821$	−32.7781	−1.14396	−0.571982	−	0.820266i	$-0.693825\pi$
$821$	−32.7781	−1.14396	−0.571982	+	0.820266i	$0.693825\pi$
$822$	−16.1125	−0.561988
$823$	19.2178	0.669889	0.334944	−	0.942238i	$-0.391282\pi$
$823$	19.2178	0.669889	0.334944	+	0.942238i	$0.391282\pi$
$824$	−20.0650	−0.698996
$825$	−8.09761	−0.281922
$826$	4.19672	0.146023
$827$	−4.05149	−0.140884	−0.0704421	−	0.997516i	$-0.522441\pi$
$827$	−4.05149	−0.140884	−0.0704421	+	0.997516i	$0.522441\pi$
$828$	−0.648010	−0.0225199
$829$	−25.5300	−0.886694	−0.443347	−	0.896350i	$-0.646209\pi$
$829$	−25.5300	−0.886694	−0.443347	+	0.896350i	$0.646209\pi$
$830$	−10.4905	−0.364132
$831$	−3.69191	−0.128071
$832$	−35.2841	−1.22325
$833$	29.1634	1.01045
$834$	−59.8521	−2.07251
$835$	−1.47644	−0.0510944
$836$	44.6295	1.54354
$837$	2.93835	0.101564
$838$	−29.6143	−1.02301
$839$	39.6085	1.36744	0.683719	−	0.729745i	$-0.260361\pi$
$839$	39.6085	1.36744	0.683719	+	0.729745i	$0.260361\pi$
$840$	53.1758	1.83474
$841$	4.48987	0.154823
$842$	75.9584	2.61770
$843$	−37.3527	−1.28649
$844$	99.1382	3.41248
$845$	−8.55836	−0.294416
$846$	0.613748	0.0211011
$847$	−46.2068	−1.58769
$848$	23.8262	0.818195
$849$	−15.8772	−0.544904
$850$	−7.18218	−0.246347
$851$	19.3290	0.662591
$852$	118.646	4.06475
$853$	39.9322	1.36725	0.683626	−	0.729833i	$-0.260402\pi$
$853$	39.9322	1.36725	0.683626	+	0.729833i	$0.260402\pi$
$854$	144.564	4.94688
$855$	0.0423564	0.00144856
$856$	49.3275	1.68598
$857$	−13.8481	−0.473042	−0.236521	−	0.971626i	$-0.576007\pi$
$857$	−13.8481	−0.473042	−0.236521	+	0.971626i	$0.576007\pi$
$858$	−98.1421	−3.35051
$859$	−0.242739	−0.00828214	−0.00414107	−	0.999991i	$-0.501318\pi$
$859$	−0.242739	−0.00828214	−0.00414107	+	0.999991i	$0.501318\pi$
$860$	−39.9026	−1.36067
$861$	14.8598	0.506419
$862$	−22.6107	−0.770122
$863$	25.6130	0.871876	0.435938	−	0.899977i	$-0.356417\pi$
$863$	25.6130	0.871876	0.435938	+	0.899977i	$0.356417\pi$
$864$	−53.3130	−1.81374
$865$	7.50318	0.255116
$866$	24.4413	0.830548
$867$	16.2737	0.552684
$868$	−11.3792	−0.386234
$869$	9.41346	0.319330
$870$	−26.0706	−0.883876
$871$	44.0274	1.49181
$872$	84.2397	2.85272
$873$	−0.293240	−0.00992466
$874$	−32.3938	−1.09573
$875$	4.19514	0.141822
$876$	10.4137	0.351846
$877$	6.47065	0.218498	0.109249	−	0.994014i	$-0.465155\pi$
$877$	6.47065	0.218498	0.109249	+	0.994014i	$0.465155\pi$
$878$	39.6142	1.33692
$879$	20.3989	0.688038
$880$	−44.7804	−1.50955
$881$	−26.4520	−0.891192	−0.445596	−	0.895234i	$-0.647008\pi$
$881$	−26.4520	−0.891192	−0.445596	+	0.895234i	$0.647008\pi$
$882$	0.593049	0.0199690
$883$	−43.1229	−1.45120	−0.725601	−	0.688116i	$-0.758438\pi$
$883$	−43.1229	−1.45120	−0.725601	+	0.688116i	$0.758438\pi$
$884$	−61.4965	−2.06835
$885$	0.661419	0.0222334
$886$	−3.56278	−0.119694
$887$	−10.9346	−0.367146	−0.183573	−	0.983006i	$-0.558766\pi$
$887$	−10.9346	−0.367146	−0.183573	+	0.983006i	$0.558766\pi$
$888$	39.0121	1.30916
$889$	−1.17852	−0.0395263
$890$	48.7161	1.63297
$891$	−41.9237	−1.40450
$892$	56.7568	1.90036
$893$	21.6753	0.725336
$894$	106.480	3.56122
$895$	0.301754	0.0100865
$896$	−2.56513	−0.0856951
$897$	50.3257	1.68033
$898$	−49.5529	−1.65360
$899$	3.26095	0.108759
$900$	−0.103182	−0.00343939
$901$	6.86889	0.228836
$902$	−25.1365	−0.836955
$903$	60.0170	1.99724
$904$	114.704	3.81499
$905$	6.58748	0.218975
$906$	34.4193	1.14350
$907$	5.00137	0.166068	0.0830339	−	0.996547i	$-0.473539\pi$
$907$	5.00137	0.166068	0.0830339	+	0.996547i	$0.473539\pi$
$908$	114.946	3.81463
$909$	−0.00319299	−0.000105905 0
$910$	50.8446	1.68548
$911$	48.8095	1.61713	0.808566	−	0.588406i	$-0.200244\pi$
$911$	48.8095	1.61713	0.808566	+	0.588406i	$0.200244\pi$
$912$	−32.5484	−1.07779
$913$	−18.8565	−0.624059
$914$	−33.7522	−1.11642
$915$	22.7838	0.753210
$916$	87.9594	2.90626
$917$	29.4942	0.973985
$918$	−37.4519	−1.23610
$919$	29.1616	0.961952	0.480976	−	0.876734i	$-0.340282\pi$
$919$	29.1616	0.961952	0.480976	+	0.876734i	$0.340282\pi$
$920$	46.1257	1.52072
$921$	−28.6018	−0.942461
$922$	65.3284	2.15148
$923$	66.3104	2.18263
$924$	163.523	5.37952
$925$	3.07774	0.101195
$926$	−72.7794	−2.39168
$927$	−0.0585600	−0.00192336
$928$	−59.1661	−1.94222
$929$	−10.3692	−0.340203	−0.170102	−	0.985427i	$-0.554410\pi$
$929$	−10.3692	−0.340203	−0.170102	+	0.985427i	$0.554410\pi$
$930$	−2.53853	−0.0832415
$931$	20.9443	0.686420
$932$	87.0553	2.85159
$933$	13.4732	0.441094
$934$	−41.4629	−1.35671
$935$	−12.9098	−0.422195
$936$	−0.730968	−0.0238924
$937$	−44.3939	−1.45028	−0.725142	−	0.688599i	$-0.758226\pi$
$937$	−44.3939	−1.45028	−0.725142	+	0.688599i	$0.758226\pi$
$938$	−103.837	−3.39040
$939$	−4.21248	−0.137469
$940$	−52.8018	−1.72221
$941$	55.2942	1.80254	0.901269	−	0.433260i	$-0.142637\pi$
$941$	55.2942	1.80254	0.901269	+	0.433260i	$0.142637\pi$
$942$	20.6188	0.671797
$943$	12.8896	0.419744
$944$	3.65770	0.119048
$945$	21.8758	0.711619
$946$	−101.524	−3.30083
$947$	16.0956	0.523038	0.261519	−	0.965198i	$-0.415777\pi$
$947$	16.0956	0.523038	0.261519	+	0.965198i	$0.415777\pi$
$948$	−16.6677	−0.541342
$949$	5.82012	0.188929
$950$	−5.15802	−0.167348
$951$	27.2726	0.884376
$952$	84.7767	2.74763
$953$	19.2073	0.622186	0.311093	−	0.950380i	$-0.399305\pi$
$953$	19.2073	0.622186	0.311093	+	0.950380i	$0.399305\pi$
$954$	0.139681	0.00452234
$955$	24.1960	0.782963
$956$	45.2467	1.46338
$957$	−46.8612	−1.51481
$958$	−105.812	−3.41862
$959$	15.0043	0.484514
$960$	13.1152	0.423290
$961$	−30.6825	−0.989757
$962$	37.3018	1.20266
$963$	0.143963	0.00463916
$964$	43.4697	1.40007
$965$	−15.2222	−0.490021
$966$	−118.691	−3.81883
$967$	30.2037	0.971284	0.485642	−	0.874158i	$-0.338586\pi$
$967$	30.2037	0.971284	0.485642	+	0.874158i	$0.338586\pi$
$968$	−80.8954	−2.60008
$969$	−9.38343	−0.301439
$970$	35.7097	1.14657
$971$	−4.36043	−0.139933	−0.0699664	−	0.997549i	$-0.522289\pi$
$971$	−4.36043	−0.139933	−0.0699664	+	0.997549i	$0.522289\pi$
$972$	−1.07228	−0.0343933
$973$	55.7355	1.78680
$974$	−35.9577	−1.15216
$975$	8.01330	0.256631
$976$	125.996	4.03304
$977$	59.3455	1.89863	0.949315	−	0.314327i	$-0.101779\pi$
$977$	59.3455	1.89863	0.949315	+	0.314327i	$0.101779\pi$
$978$	52.3646	1.67444
$979$	87.5660	2.79862
$980$	−51.0210	−1.62981
$981$	0.245855	0.00784955
$982$	67.6965	2.16028
$983$	58.4663	1.86478	0.932392	−	0.361449i	$-0.117718\pi$
$983$	58.4663	1.86478	0.932392	+	0.361449i	$0.117718\pi$
$984$	26.0153	0.829338
$985$	−16.5306	−0.526707
$986$	−41.5636	−1.32365
$987$	79.4187	2.52792
$988$	−44.1648	−1.40507
$989$	52.0599	1.65541
$990$	−0.262525	−0.00834359
$991$	−58.0217	−1.84312	−0.921560	−	0.388236i	$-0.873084\pi$
$991$	−58.0217	−1.84312	−0.921560	+	0.388236i	$0.873084\pi$
$992$	−5.76107	−0.182914
$993$	14.4880	0.459763
$994$	−156.391	−4.96041
$995$	−12.4236	−0.393855
$996$	33.3878	1.05793
$997$	−7.26754	−0.230165	−0.115083	−	0.993356i	$-0.536713\pi$
$997$	−7.26754	−0.230165	−0.115083	+	0.993356i	$0.536713\pi$
$998$	11.7308	0.371331
$999$	16.0490	0.507768

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8045.2.a.d.1.9	✓	141

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8045.2.a.d.1.9	✓	141	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:	\( N \)	\(=\)	\( 8045 = 5 \cdot 1609 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8045.a (trivial)

\(f(q)\)	\(=\)	\(q-2.61030 q^{2} -1.72585 q^{3} +4.81367 q^{4} -1.00000 q^{5} +4.50499 q^{6} -4.19514 q^{7} -7.34453 q^{8} -0.0214352 q^{9} +O(q^{10})\)	\(q-2.61030 q^{2} -1.72585 q^{3} +4.81367 q^{4} -1.00000 q^{5} +4.50499 q^{6} -4.19514 q^{7} -7.34453 q^{8} -0.0214352 q^{9} +2.61030 q^{10} +4.69195 q^{11} -8.30768 q^{12} -4.64310 q^{13} +10.9506 q^{14} +1.72585 q^{15} +9.54409 q^{16} +2.75148 q^{17} +0.0559522 q^{18} +1.97602 q^{19} -4.81367 q^{20} +7.24019 q^{21} -12.2474 q^{22} +6.28027 q^{23} +12.6756 q^{24} +1.00000 q^{25} +12.1199 q^{26} +5.21455 q^{27} -20.1940 q^{28} +5.78704 q^{29} -4.50499 q^{30} +0.563492 q^{31} -10.2239 q^{32} -8.09761 q^{33} -7.18218 q^{34} +4.19514 q^{35} -0.103182 q^{36} +3.07774 q^{37} -5.15802 q^{38} +8.01330 q^{39} +7.34453 q^{40} +2.05240 q^{41} -18.8991 q^{42} +8.28943 q^{43} +22.5855 q^{44} +0.0214352 q^{45} -16.3934 q^{46} +10.9691 q^{47} -16.4717 q^{48} +10.5992 q^{49} -2.61030 q^{50} -4.74864 q^{51} -22.3503 q^{52} +2.49644 q^{53} -13.6115 q^{54} -4.69195 q^{55} +30.8113 q^{56} -3.41032 q^{57} -15.1059 q^{58} +0.383242 q^{59} +8.30768 q^{60} +13.2015 q^{61} -1.47088 q^{62} +0.0899235 q^{63} +7.59925 q^{64} +4.64310 q^{65} +21.1372 q^{66} -9.48234 q^{67} +13.2447 q^{68} -10.8388 q^{69} -10.9506 q^{70} -14.2815 q^{71} +0.157431 q^{72} -1.25350 q^{73} -8.03382 q^{74} -1.72585 q^{75} +9.51193 q^{76} -19.6834 q^{77} -20.9171 q^{78} +2.00630 q^{79} -9.54409 q^{80} -8.93524 q^{81} -5.35738 q^{82} -4.01890 q^{83} +34.8519 q^{84} -2.75148 q^{85} -21.6379 q^{86} -9.98758 q^{87} -34.4601 q^{88} +18.6630 q^{89} -0.0559522 q^{90} +19.4784 q^{91} +30.2312 q^{92} -0.972503 q^{93} -28.6328 q^{94} -1.97602 q^{95} +17.6449 q^{96} +13.6803 q^{97} -27.6671 q^{98} -0.100573 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 141 q - 8 q^{2} + 11 q^{3} + 158 q^{4} - 141 q^{5} + 23 q^{6} + 29 q^{7} - 21 q^{8} + 160 q^{9}+O(q^{10}) \) 141 * q - 8 * q^2 + 11 * q^3 + 158 * q^4 - 141 * q^5 + 23 * q^6 + 29 * q^7 - 21 * q^8 + 160 * q^9	\( 141 q - 8 q^{2} + 11 q^{3} + 158 q^{4} - 141 q^{5} + 23 q^{6} + 29 q^{7} - 21 q^{8} + 160 q^{9} + 8 q^{10} + 32 q^{11} + 17 q^{12} + 35 q^{13} + 18 q^{14} - 11 q^{15} + 188 q^{16} - 13 q^{17} - 16 q^{18} + 152 q^{19} - 158 q^{20} + 40 q^{21} + 14 q^{22} - 77 q^{23} + 69 q^{24} + 141 q^{25} + 27 q^{26} + 38 q^{27} + 67 q^{28} + 22 q^{29} - 23 q^{30} + 86 q^{31} - 65 q^{32} + 51 q^{33} + 79 q^{34} - 29 q^{35} + 191 q^{36} + 45 q^{37} - 9 q^{38} + 55 q^{39} + 21 q^{40} + 36 q^{41} + 6 q^{42} + 132 q^{43} + 74 q^{44} - 160 q^{45} + 72 q^{46} - 16 q^{47} + 22 q^{48} + 212 q^{49} - 8 q^{50} + 82 q^{51} + 106 q^{52} - 28 q^{53} + 86 q^{54} - 32 q^{55} + 27 q^{56} + 10 q^{57} + 23 q^{58} + 71 q^{59} - 17 q^{60} + 116 q^{61} - 36 q^{62} + 45 q^{63} + 237 q^{64} - 35 q^{65} + 69 q^{66} + 99 q^{67} - 7 q^{68} + 45 q^{69} - 18 q^{70} + 34 q^{71} - 53 q^{72} + 125 q^{73} + 50 q^{74} + 11 q^{75} + 271 q^{76} - 31 q^{77} + 2 q^{78} + 101 q^{79} - 188 q^{80} + 221 q^{81} + 67 q^{82} + 67 q^{83} + 141 q^{84} + 13 q^{85} + 48 q^{86} - 21 q^{87} + 71 q^{88} + 79 q^{89} + 16 q^{90} + 228 q^{91} - 198 q^{92} - 12 q^{93} + 114 q^{94} - 152 q^{95} + 129 q^{96} + 98 q^{97} - 31 q^{98} + 195 q^{99}+O(q^{100}) \) 141 * q - 8 * q^2 + 11 * q^3 + 158 * q^4 - 141 * q^5 + 23 * q^6 + 29 * q^7 - 21 * q^8 + 160 * q^9 + 8 * q^10 + 32 * q^11 + 17 * q^12 + 35 * q^13 + 18 * q^14 - 11 * q^15 + 188 * q^16 - 13 * q^17 - 16 * q^18 + 152 * q^19 - 158 * q^20 + 40 * q^21 + 14 * q^22 - 77 * q^23 + 69 * q^24 + 141 * q^25 + 27 * q^26 + 38 * q^27 + 67 * q^28 + 22 * q^29 - 23 * q^30 + 86 * q^31 - 65 * q^32 + 51 * q^33 + 79 * q^34 - 29 * q^35 + 191 * q^36 + 45 * q^37 - 9 * q^38 + 55 * q^39 + 21 * q^40 + 36 * q^41 + 6 * q^42 + 132 * q^43 + 74 * q^44 - 160 * q^45 + 72 * q^46 - 16 * q^47 + 22 * q^48 + 212 * q^49 - 8 * q^50 + 82 * q^51 + 106 * q^52 - 28 * q^53 + 86 * q^54 - 32 * q^55 + 27 * q^56 + 10 * q^57 + 23 * q^58 + 71 * q^59 - 17 * q^60 + 116 * q^61 - 36 * q^62 + 45 * q^63 + 237 * q^64 - 35 * q^65 + 69 * q^66 + 99 * q^67 - 7 * q^68 + 45 * q^69 - 18 * q^70 + 34 * q^71 - 53 * q^72 + 125 * q^73 + 50 * q^74 + 11 * q^75 + 271 * q^76 - 31 * q^77 + 2 * q^78 + 101 * q^79 - 188 * q^80 + 221 * q^81 + 67 * q^82 + 67 * q^83 + 141 * q^84 + 13 * q^85 + 48 * q^86 - 21 * q^87 + 71 * q^88 + 79 * q^89 + 16 * q^90 + 228 * q^91 - 198 * q^92 - 12 * q^93 + 114 * q^94 - 152 * q^95 + 129 * q^96 + 98 * q^97 - 31 * q^98 + 195 * q^99

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