LMFDB - Embedded newform 8015.2.a.n.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8015,2,Mod(1,8015)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8015, 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("8015.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8015 = 5 \cdot 7 \cdot 229 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8015.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:	$64.0000972201$
Analytic rank:	$0$
Dimension:	$68$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Character	$\chi$	$=$	8015.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.73044 q^{2} +0.281096 q^{3} +5.45528 q^{4} -1.00000 q^{5} -0.767515 q^{6} +1.00000 q^{7} -9.43443 q^{8} -2.92099 q^{9} +O(q^{10})$	\(q-2.73044 q^{2} +0.281096 q^{3} +5.45528 q^{4} -1.00000 q^{5} -0.767515 q^{6} +1.00000 q^{7} -9.43443 q^{8} -2.92099 q^{9} +2.73044 q^{10} -1.40267 q^{11} +1.53346 q^{12} +1.36512 q^{13} -2.73044 q^{14} -0.281096 q^{15} +14.8495 q^{16} -2.30136 q^{17} +7.97556 q^{18} -1.96118 q^{19} -5.45528 q^{20} +0.281096 q^{21} +3.82991 q^{22} +1.58081 q^{23} -2.65198 q^{24} +1.00000 q^{25} -3.72738 q^{26} -1.66436 q^{27} +5.45528 q^{28} -3.96016 q^{29} +0.767515 q^{30} +4.99347 q^{31} -21.6769 q^{32} -0.394286 q^{33} +6.28370 q^{34} -1.00000 q^{35} -15.9348 q^{36} -10.8810 q^{37} +5.35488 q^{38} +0.383730 q^{39} +9.43443 q^{40} +4.96309 q^{41} -0.767515 q^{42} +10.2391 q^{43} -7.65198 q^{44} +2.92099 q^{45} -4.31631 q^{46} +2.77685 q^{47} +4.17415 q^{48} +1.00000 q^{49} -2.73044 q^{50} -0.646902 q^{51} +7.44712 q^{52} +3.12156 q^{53} +4.54444 q^{54} +1.40267 q^{55} -9.43443 q^{56} -0.551280 q^{57} +10.8130 q^{58} -14.9251 q^{59} -1.53346 q^{60} -9.71902 q^{61} -13.6344 q^{62} -2.92099 q^{63} +29.4882 q^{64} -1.36512 q^{65} +1.07657 q^{66} +11.9691 q^{67} -12.5545 q^{68} +0.444360 q^{69} +2.73044 q^{70} +6.85626 q^{71} +27.5578 q^{72} -3.68675 q^{73} +29.7100 q^{74} +0.281096 q^{75} -10.6988 q^{76} -1.40267 q^{77} -1.04775 q^{78} -4.45249 q^{79} -14.8495 q^{80} +8.29511 q^{81} -13.5514 q^{82} +2.14419 q^{83} +1.53346 q^{84} +2.30136 q^{85} -27.9572 q^{86} -1.11319 q^{87} +13.2334 q^{88} -6.47380 q^{89} -7.97556 q^{90} +1.36512 q^{91} +8.62378 q^{92} +1.40364 q^{93} -7.58202 q^{94} +1.96118 q^{95} -6.09328 q^{96} -2.79306 q^{97} -2.73044 q^{98} +4.09719 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q + 9 q^{2} + 83 q^{4} - 68 q^{5} + 5 q^{6} + 68 q^{7} + 30 q^{8} + 86 q^{9}+O(q^{10}) $ 68 * q + 9 * q^2 + 83 * q^4 - 68 * q^5 + 5 * q^6 + 68 * q^7 + 30 * q^8 + 86 * q^9	\( 68 q + 9 q^{2} + 83 q^{4} - 68 q^{5} + 5 q^{6} + 68 q^{7} + 30 q^{8} + 86 q^{9} - 9 q^{10} + 5 q^{11} + 9 q^{12} + 15 q^{13} + 9 q^{14} + 109 q^{16} + 7 q^{17} + 39 q^{18} + 20 q^{19} - 83 q^{20} + 56 q^{22} + 36 q^{23} + q^{24} + 68 q^{25} + q^{26} + 12 q^{27} + 83 q^{28} - 16 q^{29} - 5 q^{30} + 31 q^{31} + 79 q^{32} + 45 q^{33} + 31 q^{34} - 68 q^{35} + 114 q^{36} + 72 q^{37} + 8 q^{38} + 47 q^{39} - 30 q^{40} + 6 q^{41} + 5 q^{42} + 75 q^{43} + 15 q^{44} - 86 q^{45} + 29 q^{46} - 10 q^{47} + 44 q^{48} + 68 q^{49} + 9 q^{50} + 23 q^{51} + 37 q^{52} + 41 q^{53} + 4 q^{54} - 5 q^{55} + 30 q^{56} + 55 q^{57} + 66 q^{58} - 5 q^{59} - 9 q^{60} - 2 q^{61} + 3 q^{62} + 86 q^{63} + 162 q^{64} - 15 q^{65} - 23 q^{66} + 92 q^{67} + 35 q^{68} - 25 q^{69} - 9 q^{70} - 2 q^{71} + 128 q^{72} + 80 q^{73} + 18 q^{74} + 71 q^{76} + 5 q^{77} + 20 q^{78} + 100 q^{79} - 109 q^{80} + 140 q^{81} + 36 q^{82} - 60 q^{83} + 9 q^{84} - 7 q^{85} - 27 q^{86} + 24 q^{87} + 175 q^{88} + 19 q^{89} - 39 q^{90} + 15 q^{91} + 75 q^{92} + 37 q^{93} + 11 q^{94} - 20 q^{95} + 15 q^{96} + 96 q^{97} + 9 q^{98} + 3 q^{99}+O(q^{100}) \) 68 * q + 9 * q^2 + 83 * q^4 - 68 * q^5 + 5 * q^6 + 68 * q^7 + 30 * q^8 + 86 * q^9 - 9 * q^10 + 5 * q^11 + 9 * q^12 + 15 * q^13 + 9 * q^14 + 109 * q^16 + 7 * q^17 + 39 * q^18 + 20 * q^19 - 83 * q^20 + 56 * q^22 + 36 * q^23 + q^24 + 68 * q^25 + q^26 + 12 * q^27 + 83 * q^28 - 16 * q^29 - 5 * q^30 + 31 * q^31 + 79 * q^32 + 45 * q^33 + 31 * q^34 - 68 * q^35 + 114 * q^36 + 72 * q^37 + 8 * q^38 + 47 * q^39 - 30 * q^40 + 6 * q^41 + 5 * q^42 + 75 * q^43 + 15 * q^44 - 86 * q^45 + 29 * q^46 - 10 * q^47 + 44 * q^48 + 68 * q^49 + 9 * q^50 + 23 * q^51 + 37 * q^52 + 41 * q^53 + 4 * q^54 - 5 * q^55 + 30 * q^56 + 55 * q^57 + 66 * q^58 - 5 * q^59 - 9 * q^60 - 2 * q^61 + 3 * q^62 + 86 * q^63 + 162 * q^64 - 15 * q^65 - 23 * q^66 + 92 * q^67 + 35 * q^68 - 25 * q^69 - 9 * q^70 - 2 * q^71 + 128 * q^72 + 80 * q^73 + 18 * q^74 + 71 * q^76 + 5 * q^77 + 20 * q^78 + 100 * q^79 - 109 * q^80 + 140 * q^81 + 36 * q^82 - 60 * q^83 + 9 * q^84 - 7 * q^85 - 27 * q^86 + 24 * q^87 + 175 * q^88 + 19 * q^89 - 39 * q^90 + 15 * q^91 + 75 * q^92 + 37 * q^93 + 11 * q^94 - 20 * q^95 + 15 * q^96 + 96 * q^97 + 9 * q^98 + 3 * 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 $

$2$	−2.73044	−1.93071	−0.965355	−	0.260940i	$-0.915967\pi$
$2$	−2.73044	−1.93071	−0.965355	+	0.260940i	$0.915967\pi$
$3$	0.281096	0.162291	0.0811454	−	0.996702i	$-0.474142\pi$
$3$	0.281096	0.162291	0.0811454	+	0.996702i	$0.474142\pi$
$4$	5.45528	2.72764
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−0.767515	−0.313337
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−9.43443	−3.33557
$9$	−2.92099	−0.973662
$10$	2.73044	0.863440
$11$	−1.40267	−0.422922	−0.211461	−	0.977386i	$-0.567822\pi$
$11$	−1.40267	−0.422922	−0.211461	+	0.977386i	$0.567822\pi$
$12$	1.53346	0.442671
$13$	1.36512	0.378617	0.189308	−	0.981918i	$-0.439375\pi$
$13$	1.36512	0.378617	0.189308	+	0.981918i	$0.439375\pi$
$14$	−2.73044	−0.729740
$15$	−0.281096	−0.0725787
$16$	14.8495	3.71238
$17$	−2.30136	−0.558161	−0.279080	−	0.960268i	$-0.590030\pi$
$17$	−2.30136	−0.558161	−0.279080	+	0.960268i	$0.590030\pi$
$18$	7.97556	1.87986
$19$	−1.96118	−0.449926	−0.224963	−	0.974367i	$-0.572226\pi$
$19$	−1.96118	−0.449926	−0.224963	+	0.974367i	$0.572226\pi$
$20$	−5.45528	−1.21984
$21$	0.281096	0.0613402
$22$	3.82991	0.816540
$23$	1.58081	0.329622	0.164811	−	0.986325i	$-0.447299\pi$
$23$	1.58081	0.329622	0.164811	+	0.986325i	$0.447299\pi$
$24$	−2.65198	−0.541333
$25$	1.00000	0.200000
$26$	−3.72738	−0.730999
$27$	−1.66436	−0.320307
$28$	5.45528	1.03095
$29$	−3.96016	−0.735384	−0.367692	−	0.929948i	$-0.619852\pi$
$29$	−3.96016	−0.735384	−0.367692	+	0.929948i	$0.619852\pi$
$30$	0.767515	0.140128
$31$	4.99347	0.896854	0.448427	−	0.893820i	$-0.351984\pi$
$31$	4.99347	0.896854	0.448427	+	0.893820i	$0.351984\pi$
$32$	−21.6769	−3.83196
$33$	−0.394286	−0.0686363
$34$	6.28370	1.07765
$35$	−1.00000	−0.169031
$36$	−15.9348	−2.65580
$37$	−10.8810	−1.78883	−0.894415	−	0.447238i	$-0.852408\pi$
$37$	−10.8810	−1.78883	−0.894415	+	0.447238i	$0.852408\pi$
$38$	5.35488	0.868676
$39$	0.383730	0.0614460
$40$	9.43443	1.49171
$41$	4.96309	0.775104	0.387552	−	0.921848i	$-0.373321\pi$
$41$	4.96309	0.775104	0.387552	+	0.921848i	$0.373321\pi$
$42$	−0.767515	−0.118430
$43$	10.2391	1.56145	0.780725	−	0.624875i	$-0.214850\pi$
$43$	10.2391	1.56145	0.780725	+	0.624875i	$0.214850\pi$
$44$	−7.65198	−1.15358
$45$	2.92099	0.435435
$46$	−4.31631	−0.636405
$47$	2.77685	0.405046	0.202523	−	0.979278i	$-0.435086\pi$
$47$	2.77685	0.405046	0.202523	+	0.979278i	$0.435086\pi$
$48$	4.17415	0.602486
$49$	1.00000	0.142857
$50$	−2.73044	−0.386142
$51$	−0.646902	−0.0905844
$52$	7.44712	1.03273
$53$	3.12156	0.428779	0.214390	−	0.976748i	$-0.431224\pi$
$53$	3.12156	0.428779	0.214390	+	0.976748i	$0.431224\pi$
$54$	4.54444	0.618420
$55$	1.40267	0.189136
$56$	−9.43443	−1.26073
$57$	−0.551280	−0.0730188
$58$	10.8130	1.41981
$59$	−14.9251	−1.94308	−0.971540	−	0.236877i	$-0.923876\pi$
$59$	−14.9251	−1.94308	−0.971540	+	0.236877i	$0.923876\pi$
$60$	−1.53346	−0.197969
$61$	−9.71902	−1.24439	−0.622197	−	0.782861i	$-0.713760\pi$
$61$	−9.71902	−1.24439	−0.622197	+	0.782861i	$0.713760\pi$
$62$	−13.6344	−1.73156
$63$	−2.92099	−0.368010
$64$	29.4882	3.68603
$65$	−1.36512	−0.169323
$66$	1.07657	0.132517
$67$	11.9691	1.46226	0.731131	−	0.682238i	$-0.238993\pi$
$67$	11.9691	1.46226	0.731131	+	0.682238i	$0.238993\pi$
$68$	−12.5545	−1.52246
$69$	0.444360	0.0534947
$70$	2.73044	0.326350
$71$	6.85626	0.813688	0.406844	−	0.913498i	$-0.366629\pi$
$71$	6.85626	0.813688	0.406844	+	0.913498i	$0.366629\pi$
$72$	27.5578	3.24772
$73$	−3.68675	−0.431502	−0.215751	−	0.976448i	$-0.569220\pi$
$73$	−3.68675	−0.431502	−0.215751	+	0.976448i	$0.569220\pi$
$74$	29.7100	3.45371
$75$	0.281096	0.0324582
$76$	−10.6988	−1.22724
$77$	−1.40267	−0.159849
$78$	−1.04775	−0.118634
$79$	−4.45249	−0.500944	−0.250472	−	0.968124i	$-0.580586\pi$
$79$	−4.45249	−0.500944	−0.250472	+	0.968124i	$0.580586\pi$
$80$	−14.8495	−1.66023
$81$	8.29511	0.921679
$82$	−13.5514	−1.49650
$83$	2.14419	0.235356	0.117678	−	0.993052i	$-0.462455\pi$
$83$	2.14419	0.235356	0.117678	+	0.993052i	$0.462455\pi$
$84$	1.53346	0.167314
$85$	2.30136	0.249617
$86$	−27.9572	−3.01471
$87$	−1.11319	−0.119346
$88$	13.2334	1.41069
$89$	−6.47380	−0.686221	−0.343111	−	0.939295i	$-0.611481\pi$
$89$	−6.47380	−0.686221	−0.343111	+	0.939295i	$0.611481\pi$
$90$	−7.97556	−0.840698
$91$	1.36512	0.143104
$92$	8.62378	0.899091
$93$	1.40364	0.145551
$94$	−7.58202	−0.782026
$95$	1.96118	0.201213
$96$	−6.09328	−0.621893
$97$	−2.79306	−0.283592	−0.141796	−	0.989896i	$-0.545288\pi$
$97$	−2.79306	−0.283592	−0.141796	+	0.989896i	$0.545288\pi$
$98$	−2.73044	−0.275816
$99$	4.09719	0.411783
$100$	5.45528	0.545528
$101$	−16.8746	−1.67909	−0.839544	−	0.543292i	$-0.817178\pi$
$101$	−16.8746	−1.67909	−0.839544	+	0.543292i	$0.817178\pi$
$102$	1.76632	0.174892
$103$	−8.67018	−0.854298	−0.427149	−	0.904181i	$-0.640482\pi$
$103$	−8.67018	−0.854298	−0.427149	+	0.904181i	$0.640482\pi$
$104$	−12.8791	−1.26290
$105$	−0.281096	−0.0274322
$106$	−8.52322	−0.827849
$107$	−18.3809	−1.77695	−0.888475	−	0.458925i	$-0.848235\pi$
$107$	−18.3809	−1.77695	−0.888475	+	0.458925i	$0.848235\pi$
$108$	−9.07958	−0.873683
$109$	−8.30568	−0.795540	−0.397770	−	0.917485i	$-0.630216\pi$
$109$	−8.30568	−0.795540	−0.397770	+	0.917485i	$0.630216\pi$
$110$	−3.82991	−0.365168
$111$	−3.05861	−0.290311
$112$	14.8495	1.40315
$113$	7.35653	0.692044	0.346022	−	0.938226i	$-0.387532\pi$
$113$	7.35653	0.692044	0.346022	+	0.938226i	$0.387532\pi$
$114$	1.50523	0.140978
$115$	−1.58081	−0.147412
$116$	−21.6038	−2.00586
$117$	−3.98750	−0.368645
$118$	40.7520	3.75152
$119$	−2.30136	−0.210965
$120$	2.65198	0.242092
$121$	−9.03251	−0.821137
$122$	26.5372	2.40256
$123$	1.39510	0.125792
$124$	27.2408	2.44629
$125$	−1.00000	−0.0894427
$126$	7.97556	0.710520
$127$	16.2032	1.43780	0.718899	−	0.695115i	$-0.244647\pi$
$127$	16.2032	1.43780	0.718899	+	0.695115i	$0.244647\pi$
$128$	−37.1620	−3.28469
$129$	2.87817	0.253409
$130$	3.72738	0.326913
$131$	−6.23423	−0.544688	−0.272344	−	0.962200i	$-0.587799\pi$
$131$	−6.23423	−0.544688	−0.272344	+	0.962200i	$0.587799\pi$
$132$	−2.15094	−0.187215
$133$	−1.96118	−0.170056
$134$	−32.6809	−2.82320
$135$	1.66436	0.143246
$136$	21.7120	1.86179
$137$	−1.13814	−0.0972381	−0.0486190	−	0.998817i	$-0.515482\pi$
$137$	−1.13814	−0.0972381	−0.0486190	+	0.998817i	$0.515482\pi$
$138$	−1.21330	−0.103283
$139$	14.2666	1.21007	0.605037	−	0.796198i	$-0.293158\pi$
$139$	14.2666	1.21007	0.605037	+	0.796198i	$0.293158\pi$
$140$	−5.45528	−0.461055
$141$	0.780562	0.0657352
$142$	−18.7206	−1.57100
$143$	−1.91482	−0.160125
$144$	−43.3753	−3.61461
$145$	3.96016	0.328874
$146$	10.0664	0.833104
$147$	0.281096	0.0231844
$148$	−59.3591	−4.87929
$149$	9.14486	0.749176	0.374588	−	0.927191i	$-0.377784\pi$
$149$	9.14486	0.749176	0.374588	+	0.927191i	$0.377784\pi$
$150$	−0.767515	−0.0626673
$151$	−4.73992	−0.385729	−0.192865	−	0.981225i	$-0.561778\pi$
$151$	−4.73992	−0.385729	−0.192865	+	0.981225i	$0.561778\pi$
$152$	18.5026	1.50076
$153$	6.72223	0.543460
$154$	3.82991	0.308623
$155$	−4.99347	−0.401085
$156$	2.09336	0.167603
$157$	5.27240	0.420784	0.210392	−	0.977617i	$-0.432526\pi$
$157$	5.27240	0.420784	0.210392	+	0.977617i	$0.432526\pi$
$158$	12.1572	0.967177
$159$	0.877458	0.0695870
$160$	21.6769	1.71371
$161$	1.58081	0.124586
$162$	−22.6493	−1.77949
$163$	20.1090	1.57506	0.787528	−	0.616279i	$-0.211361\pi$
$163$	20.1090	1.57506	0.787528	+	0.616279i	$0.211361\pi$
$164$	27.0750	2.11420
$165$	0.394286	0.0306951
$166$	−5.85458	−0.454404
$167$	16.3594	1.26593	0.632963	−	0.774182i	$-0.281838\pi$
$167$	16.3594	1.26593	0.632963	+	0.774182i	$0.281838\pi$
$168$	−2.65198	−0.204605
$169$	−11.1364	−0.856649
$170$	−6.28370	−0.481938
$171$	5.72858	0.438075
$172$	55.8572	4.25907
$173$	−16.8879	−1.28396	−0.641982	−	0.766720i	$-0.721888\pi$
$173$	−16.8879	−1.28396	−0.641982	+	0.766720i	$0.721888\pi$
$174$	3.03948	0.230423
$175$	1.00000	0.0755929
$176$	−20.8291	−1.57005
$177$	−4.19538	−0.315344
$178$	17.6763	1.32489
$179$	−1.17541	−0.0878546	−0.0439273	−	0.999035i	$-0.513987\pi$
$179$	−1.17541	−0.0878546	−0.0439273	+	0.999035i	$0.513987\pi$
$180$	15.9348	1.18771
$181$	2.95378	0.219553	0.109777	−	0.993956i	$-0.464986\pi$
$181$	2.95378	0.219553	0.109777	+	0.993956i	$0.464986\pi$
$182$	−3.72738	−0.276292
$183$	−2.73198	−0.201954
$184$	−14.9141	−1.09948
$185$	10.8810	0.799989
$186$	−3.83256	−0.281017
$187$	3.22805	0.236058
$188$	15.1485	1.10482
$189$	−1.66436	−0.121065
$190$	−5.35488	−0.388484
$191$	−2.28876	−0.165609	−0.0828043	−	0.996566i	$-0.526388\pi$
$191$	−2.28876	−0.165609	−0.0828043	+	0.996566i	$0.526388\pi$
$192$	8.28902	0.598208
$193$	13.4965	0.971497	0.485749	−	0.874099i	$-0.338547\pi$
$193$	13.4965	0.971497	0.485749	+	0.874099i	$0.338547\pi$
$194$	7.62626	0.547534
$195$	−0.383730	−0.0274795
$196$	5.45528	0.389663
$197$	−20.0846	−1.43097	−0.715485	−	0.698629i	$-0.753794\pi$
$197$	−20.0846	−1.43097	−0.715485	+	0.698629i	$0.753794\pi$
$198$	−11.1871	−0.795033
$199$	−1.60932	−0.114082	−0.0570409	−	0.998372i	$-0.518167\pi$
$199$	−1.60932	−0.114082	−0.0570409	+	0.998372i	$0.518167\pi$
$200$	−9.43443	−0.667115
$201$	3.36447	0.237312
$202$	46.0751	3.24183
$203$	−3.96016	−0.277949
$204$	−3.52903	−0.247082
$205$	−4.96309	−0.346637
$206$	23.6734	1.64940
$207$	−4.61753	−0.320941
$208$	20.2714	1.40557
$209$	2.75090	0.190283
$210$	0.767515	0.0529635
$211$	20.3689	1.40225	0.701125	−	0.713038i	$-0.252681\pi$
$211$	20.3689	1.40225	0.701125	+	0.713038i	$0.252681\pi$
$212$	17.0290	1.16956
$213$	1.92727	0.132054
$214$	50.1879	3.43077
$215$	−10.2391	−0.698302
$216$	15.7023	1.06841
$217$	4.99347	0.338979
$218$	22.6781	1.53596
$219$	−1.03633	−0.0700288
$220$	7.65198	0.515896
$221$	−3.14163	−0.211329
$222$	8.35135	0.560506
$223$	12.6159	0.844826	0.422413	−	0.906404i	$-0.361183\pi$
$223$	12.6159	0.844826	0.422413	+	0.906404i	$0.361183\pi$
$224$	−21.6769	−1.44835
$225$	−2.92099	−0.194732
$226$	−20.0865	−1.33614
$227$	−2.12336	−0.140932	−0.0704661	−	0.997514i	$-0.522449\pi$
$227$	−2.12336	−0.140932	−0.0704661	+	0.997514i	$0.522449\pi$
$228$	−3.00739	−0.199169
$229$	−1.00000	−0.0660819
$229$	−1.00000	−0.0660819
$230$	4.31631	0.284609
$231$	−0.394286	−0.0259421
$232$	37.3619	2.45293
$233$	−3.94855	−0.258678	−0.129339	−	0.991600i	$-0.541286\pi$
$233$	−3.94855	−0.258678	−0.129339	+	0.991600i	$0.541286\pi$
$234$	10.8876	0.711746
$235$	−2.77685	−0.181142
$236$	−81.4205	−5.30002
$237$	−1.25158	−0.0812986
$238$	6.28370	0.407312
$239$	−5.37820	−0.347887	−0.173944	−	0.984756i	$-0.555651\pi$
$239$	−5.37820	−0.347887	−0.173944	+	0.984756i	$0.555651\pi$
$240$	−4.17415	−0.269440
$241$	23.8767	1.53803	0.769017	−	0.639228i	$-0.220746\pi$
$241$	23.8767	1.53803	0.769017	+	0.639228i	$0.220746\pi$
$242$	24.6627	1.58538
$243$	7.32482	0.469887
$244$	−53.0200	−3.39426
$245$	−1.00000	−0.0638877
$246$	−3.80924	−0.242868
$247$	−2.67725	−0.170349
$248$	−47.1105	−2.99152
$249$	0.602724	0.0381961
$250$	2.73044	0.172688
$251$	21.7178	1.37082	0.685409	−	0.728159i	$-0.259624\pi$
$251$	21.7178	1.37082	0.685409	+	0.728159i	$0.259624\pi$
$252$	−15.9348	−1.00380
$253$	−2.21736	−0.139404
$254$	−44.2417	−2.77597
$255$	0.646902	0.0405106
$256$	42.4920	2.65575
$257$	29.2477	1.82442	0.912210	−	0.409723i	$-0.134375\pi$
$257$	29.2477	1.82442	0.912210	+	0.409723i	$0.134375\pi$
$258$	−7.85867	−0.489259
$259$	−10.8810	−0.676114
$260$	−7.44712	−0.461851
$261$	11.5676	0.716015
$262$	17.0222	1.05163
$263$	−18.9087	−1.16596	−0.582982	−	0.812485i	$-0.698114\pi$
$263$	−18.9087	−1.16596	−0.582982	+	0.812485i	$0.698114\pi$
$264$	3.71986	0.228942
$265$	−3.12156	−0.191756
$266$	5.35488	0.328329
$267$	−1.81976	−0.111367
$268$	65.2949	3.98852
$269$	−16.8949	−1.03010	−0.515050	−	0.857160i	$-0.672227\pi$
$269$	−16.8949	−1.03010	−0.515050	+	0.857160i	$0.672227\pi$
$270$	−4.54444	−0.276566
$271$	18.1949	1.10526	0.552631	−	0.833426i	$-0.313624\pi$
$271$	18.1949	1.10526	0.552631	+	0.833426i	$0.313624\pi$
$272$	−34.1741	−2.07211
$273$	0.383730	0.0232244
$274$	3.10763	0.187739
$275$	−1.40267	−0.0845844
$276$	2.42411	0.145914
$277$	1.54904	0.0930728	0.0465364	−	0.998917i	$-0.485182\pi$
$277$	1.54904	0.0930728	0.0465364	+	0.998917i	$0.485182\pi$
$278$	−38.9539	−2.33630
$279$	−14.5859	−0.873232
$280$	9.43443	0.563815
$281$	12.8346	0.765649	0.382825	−	0.923821i	$-0.374951\pi$
$281$	12.8346	0.765649	0.382825	+	0.923821i	$0.374951\pi$
$282$	−2.13128	−0.126916
$283$	−20.9544	−1.24561	−0.622805	−	0.782377i	$-0.714007\pi$
$283$	−20.9544	−1.24561	−0.622805	+	0.782377i	$0.714007\pi$
$284$	37.4028	2.21945
$285$	0.551280	0.0326550
$286$	5.22829	0.309155
$287$	4.96309	0.292962
$288$	63.3178	3.73104
$289$	−11.7038	−0.688457
$290$	−10.8130	−0.634960
$291$	−0.785117	−0.0460244
$292$	−20.1123	−1.17698
$293$	27.3023	1.59502	0.797508	−	0.603308i	$-0.206151\pi$
$293$	27.3023	1.59502	0.797508	+	0.603308i	$0.206151\pi$
$294$	−0.767515	−0.0447624
$295$	14.9251	0.868971
$296$	102.656	5.96677
$297$	2.33456	0.135465
$298$	−24.9695	−1.44644
$299$	2.15800	0.124800
$300$	1.53346	0.0885342
$301$	10.2391	0.590172
$302$	12.9421	0.744731
$303$	−4.74339	−0.272501
$304$	−29.1226	−1.67030
$305$	9.71902	0.556509
$306$	−18.3546	−1.04926
$307$	−4.01812	−0.229326	−0.114663	−	0.993404i	$-0.536579\pi$
$307$	−4.01812	−0.229326	−0.114663	+	0.993404i	$0.536579\pi$
$308$	−7.65198	−0.436012
$309$	−2.43715	−0.138645
$310$	13.6344	0.774379
$311$	28.8454	1.63567	0.817837	−	0.575450i	$-0.195173\pi$
$311$	28.8454	1.63567	0.817837	+	0.575450i	$0.195173\pi$
$312$	−3.62028	−0.204958
$313$	0.985461	0.0557015	0.0278508	−	0.999612i	$-0.491134\pi$
$313$	0.985461	0.0557015	0.0278508	+	0.999612i	$0.491134\pi$
$314$	−14.3960	−0.812411
$315$	2.92099	0.164579
$316$	−24.2896	−1.36639
$317$	18.2239	1.02356	0.511779	−	0.859117i	$-0.328987\pi$
$317$	18.2239	1.02356	0.511779	+	0.859117i	$0.328987\pi$
$318$	−2.39584	−0.134352
$319$	5.55482	0.311010
$320$	−29.4882	−1.64844
$321$	−5.16680	−0.288383
$322$	−4.31631	−0.240538
$323$	4.51337	0.251131
$324$	45.2522	2.51401
$325$	1.36512	0.0757233
$326$	−54.9062	−3.04097
$327$	−2.33469	−0.129109
$328$	−46.8239	−2.58542
$329$	2.77685	0.153093
$330$	−1.07657	−0.0592634
$331$	−4.25206	−0.233714	−0.116857	−	0.993149i	$-0.537282\pi$
$331$	−4.25206	−0.233714	−0.116857	+	0.993149i	$0.537282\pi$
$332$	11.6972	0.641966
$333$	31.7833	1.74172
$334$	−44.6682	−2.44414
$335$	−11.9691	−0.653943
$336$	4.17415	0.227718
$337$	14.3208	0.780103	0.390052	−	0.920793i	$-0.372457\pi$
$337$	14.3208	0.780103	0.390052	+	0.920793i	$0.372457\pi$
$338$	30.4073	1.65394
$339$	2.06789	0.112312
$340$	12.5545	0.680866
$341$	−7.00421	−0.379299
$342$	−15.6415	−0.845797
$343$	1.00000	0.0539949
$344$	−96.6001	−5.20833
$345$	−0.444360	−0.0239235
$346$	46.1114	2.47896
$347$	30.4870	1.63663	0.818315	−	0.574770i	$-0.194909\pi$
$347$	30.4870	1.63663	0.818315	+	0.574770i	$0.194909\pi$
$348$	−6.07274	−0.325533
$349$	−30.5853	−1.63719	−0.818596	−	0.574370i	$-0.805247\pi$
$349$	−30.5853	−1.63719	−0.818596	+	0.574370i	$0.805247\pi$
$350$	−2.73044	−0.145948
$351$	−2.27206	−0.121274
$352$	30.4056	1.62062
$353$	5.12855	0.272965	0.136483	−	0.990642i	$-0.456420\pi$
$353$	5.12855	0.272965	0.136483	+	0.990642i	$0.456420\pi$
$354$	11.4552	0.608838
$355$	−6.85626	−0.363892
$356$	−35.3164	−1.87177
$357$	−0.646902	−0.0342377
$358$	3.20939	0.169622
$359$	−0.100206	−0.00528867	−0.00264434	−	0.999997i	$-0.500842\pi$
$359$	−0.100206	−0.00528867	−0.00264434	+	0.999997i	$0.500842\pi$
$360$	−27.5578	−1.45242
$361$	−15.1538	−0.797567
$362$	−8.06512	−0.423893
$363$	−2.53900	−0.133263
$364$	7.44712	0.390335
$365$	3.68675	0.192973
$366$	7.45949	0.389914
$367$	31.7247	1.65601	0.828007	−	0.560717i	$-0.189474\pi$
$367$	31.7247	1.65601	0.828007	+	0.560717i	$0.189474\pi$
$368$	23.4743	1.22368
$369$	−14.4971	−0.754689
$370$	−29.7100	−1.54455
$371$	3.12156	0.162063
$372$	7.65728	0.397011
$373$	30.5474	1.58168	0.790842	−	0.612021i	$-0.209643\pi$
$373$	30.5474	1.58168	0.790842	+	0.612021i	$0.209643\pi$
$374$	−8.81398	−0.455760
$375$	−0.281096	−0.0145157
$376$	−26.1980	−1.35106
$377$	−5.40611	−0.278429
$378$	4.54444	0.233741
$379$	−11.4082	−0.585998	−0.292999	−	0.956113i	$-0.594653\pi$
$379$	−11.4082	−0.585998	−0.292999	+	0.956113i	$0.594653\pi$
$380$	10.6988	0.548837
$381$	4.55464	0.233341
$382$	6.24930	0.319742
$383$	26.4575	1.35192	0.675959	−	0.736940i	$-0.263730\pi$
$383$	26.4575	1.35192	0.675959	+	0.736940i	$0.263730\pi$
$384$	−10.4461	−0.533074
$385$	1.40267	0.0714869
$386$	−36.8513	−1.87568
$387$	−29.9083	−1.52032
$388$	−15.2369	−0.773537
$389$	−27.0200	−1.36997	−0.684985	−	0.728557i	$-0.740191\pi$
$389$	−27.0200	−1.36997	−0.684985	+	0.728557i	$0.740191\pi$
$390$	1.04775	0.0530549
$391$	−3.63801	−0.183982
$392$	−9.43443	−0.476511
$393$	−1.75242	−0.0883978
$394$	54.8397	2.76279
$395$	4.45249	0.224029
$396$	22.3513	1.12320
$397$	−35.5876	−1.78609	−0.893045	−	0.449967i	$-0.851436\pi$
$397$	−35.5876	−1.78609	−0.893045	+	0.449967i	$0.851436\pi$
$398$	4.39415	0.220259
$399$	−0.551280	−0.0275985
$400$	14.8495	0.742477
$401$	−5.00796	−0.250086	−0.125043	−	0.992151i	$-0.539907\pi$
$401$	−5.00796	−0.250086	−0.125043	+	0.992151i	$0.539907\pi$
$402$	−9.18648	−0.458180
$403$	6.81669	0.339564
$404$	−92.0559	−4.57995
$405$	−8.29511	−0.412187
$406$	10.8130	0.536639
$407$	15.2625	0.756535
$408$	6.10315	0.302151
$409$	−4.50599	−0.222807	−0.111403	−	0.993775i	$-0.535535\pi$
$409$	−4.50599	−0.222807	−0.111403	+	0.993775i	$0.535535\pi$
$410$	13.5514	0.669255
$411$	−0.319927	−0.0157809
$412$	−47.2983	−2.33022
$413$	−14.9251	−0.734415
$414$	12.6079	0.619643
$415$	−2.14419	−0.105254
$416$	−29.5916	−1.45085
$417$	4.01027	0.196384
$418$	−7.51115	−0.367382
$419$	23.9238	1.16876	0.584378	−	0.811482i	$-0.301339\pi$
$419$	23.9238	1.16876	0.584378	+	0.811482i	$0.301339\pi$
$420$	−1.53346	−0.0748251
$421$	−18.2715	−0.890497	−0.445248	−	0.895407i	$-0.646885\pi$
$421$	−18.2715	−0.890497	−0.445248	+	0.895407i	$0.646885\pi$
$422$	−55.6159	−2.70734
$423$	−8.11115	−0.394378
$424$	−29.4501	−1.43023
$425$	−2.30136	−0.111632
$426$	−5.26228	−0.254958
$427$	−9.71902	−0.470336
$428$	−100.273	−4.84688
$429$	−0.538248	−0.0259869
$430$	27.9572	1.34822
$431$	−29.2912	−1.41091	−0.705453	−	0.708756i	$-0.749257\pi$
$431$	−29.2912	−1.41091	−0.705453	+	0.708756i	$0.749257\pi$
$432$	−24.7151	−1.18910
$433$	−30.5928	−1.47019	−0.735097	−	0.677962i	$-0.762863\pi$
$433$	−30.5928	−1.47019	−0.735097	+	0.677962i	$0.762863\pi$
$434$	−13.6344	−0.654470
$435$	1.11319	0.0533732
$436$	−45.3098	−2.16995
$437$	−3.10026	−0.148306
$438$	2.82964	0.135205
$439$	−6.56203	−0.313189	−0.156594	−	0.987663i	$-0.550052\pi$
$439$	−6.56203	−0.313189	−0.156594	+	0.987663i	$0.550052\pi$
$440$	−13.2334	−0.630879
$441$	−2.92099	−0.139095
$442$	8.57802	0.408015
$443$	−16.8766	−0.801834	−0.400917	−	0.916114i	$-0.631308\pi$
$443$	−16.8766	−0.801834	−0.400917	+	0.916114i	$0.631308\pi$
$444$	−16.6856	−0.791863
$445$	6.47380	0.306887
$446$	−34.4470	−1.63111
$447$	2.57058	0.121584
$448$	29.4882	1.39319
$449$	−6.33336	−0.298890	−0.149445	−	0.988770i	$-0.547749\pi$
$449$	−6.33336	−0.298890	−0.149445	+	0.988770i	$0.547749\pi$
$450$	7.97556	0.375972
$451$	−6.96159	−0.327808
$452$	40.1319	1.88765
$453$	−1.33237	−0.0626003
$454$	5.79769	0.272099
$455$	−1.36512	−0.0639979
$456$	5.20101	0.243560
$457$	10.1679	0.475633	0.237817	−	0.971310i	$-0.423568\pi$
$457$	10.1679	0.475633	0.237817	+	0.971310i	$0.423568\pi$
$458$	2.73044	0.127585
$459$	3.83030	0.178783
$460$	−8.62378	−0.402086
$461$	22.2296	1.03534	0.517668	−	0.855582i	$-0.326800\pi$
$461$	22.2296	1.03534	0.517668	+	0.855582i	$0.326800\pi$
$462$	1.07657	0.0500867
$463$	−6.20904	−0.288558	−0.144279	−	0.989537i	$-0.546086\pi$
$463$	−6.20904	−0.288558	−0.144279	+	0.989537i	$0.546086\pi$
$464$	−58.8066	−2.73003
$465$	−1.40364	−0.0650924
$466$	10.7813	0.499433
$467$	−1.97040	−0.0911792	−0.0455896	−	0.998960i	$-0.514517\pi$
$467$	−1.97040	−0.0911792	−0.0455896	+	0.998960i	$0.514517\pi$
$468$	−21.7529	−1.00553
$469$	11.9691	0.552683
$470$	7.58202	0.349733
$471$	1.48205	0.0682893
$472$	140.810	6.48128
$473$	−14.3621	−0.660371
$474$	3.41735	0.156964
$475$	−1.96118	−0.0899851
$476$	−12.5545	−0.575437
$477$	−9.11803	−0.417486
$478$	14.6848	0.671669
$479$	37.3508	1.70660	0.853301	−	0.521418i	$-0.174597\pi$
$479$	37.3508	1.70660	0.853301	+	0.521418i	$0.174597\pi$
$480$	6.09328	0.278119
$481$	−14.8539	−0.677281
$482$	−65.1938	−2.96950
$483$	0.444360	0.0202191
$484$	−49.2749	−2.23977
$485$	2.79306	0.126826
$486$	−19.9999	−0.907216
$487$	18.5549	0.840804	0.420402	−	0.907338i	$-0.361889\pi$
$487$	18.5549	0.840804	0.420402	+	0.907338i	$0.361889\pi$
$488$	91.6934	4.15077
$489$	5.65255	0.255617
$490$	2.73044	0.123349
$491$	−33.9342	−1.53143	−0.765713	−	0.643182i	$-0.777614\pi$
$491$	−33.9342	−1.53143	−0.765713	+	0.643182i	$0.777614\pi$
$492$	7.61068	0.343116
$493$	9.11374	0.410462
$494$	7.31006	0.328895
$495$	−4.09719	−0.184155
$496$	74.1507	3.32947
$497$	6.85626	0.307545
$498$	−1.64570	−0.0737456
$499$	24.1945	1.08310	0.541548	−	0.840670i	$-0.317839\pi$
$499$	24.1945	1.08310	0.541548	+	0.840670i	$0.317839\pi$
$500$	−5.45528	−0.243968
$501$	4.59855	0.205448
$502$	−59.2992	−2.64665
$503$	31.7026	1.41355	0.706774	−	0.707439i	$-0.250150\pi$
$503$	31.7026	1.41355	0.706774	+	0.707439i	$0.250150\pi$
$504$	27.5578	1.22752
$505$	16.8746	0.750911
$506$	6.05437	0.269150
$507$	−3.13041	−0.139026
$508$	88.3928	3.92180
$509$	−7.03583	−0.311858	−0.155929	−	0.987768i	$-0.549837\pi$
$509$	−7.03583	−0.311858	−0.155929	+	0.987768i	$0.549837\pi$
$510$	−1.76632	−0.0782141
$511$	−3.68675	−0.163092
$512$	−41.6976	−1.84279
$513$	3.26412	0.144114
$514$	−79.8589	−3.52243
$515$	8.67018	0.382054
$516$	15.7012	0.691209
$517$	−3.89502	−0.171303
$518$	29.7100	1.30538
$519$	−4.74712	−0.208376
$520$	12.8791	0.564788
$521$	−0.911702	−0.0399424	−0.0199712	−	0.999801i	$-0.506357\pi$
$521$	−0.911702	−0.0399424	−0.0199712	+	0.999801i	$0.506357\pi$
$522$	−31.5845	−1.38242
$523$	9.06008	0.396170	0.198085	−	0.980185i	$-0.436528\pi$
$523$	9.06008	0.396170	0.198085	+	0.980185i	$0.436528\pi$
$524$	−34.0095	−1.48571
$525$	0.281096	0.0122680
$526$	51.6291	2.25114
$527$	−11.4917	−0.500588
$528$	−5.85496	−0.254805
$529$	−20.5010	−0.891349
$530$	8.52322	0.370225
$531$	43.5959	1.89190
$532$	−10.6988	−0.463852
$533$	6.77522	0.293467
$534$	4.96873	0.215018
$535$	18.3809	0.794676
$536$	−112.922	−4.87748
$537$	−0.330404	−0.0142580
$538$	46.1304	1.98882
$539$	−1.40267	−0.0604174
$540$	9.07958	0.390723
$541$	3.14364	0.135155	0.0675777	−	0.997714i	$-0.478473\pi$
$541$	3.14364	0.135155	0.0675777	+	0.997714i	$0.478473\pi$
$542$	−49.6801	−2.13394
$543$	0.830297	0.0356315
$544$	49.8862	2.13885
$545$	8.30568	0.355776
$546$	−1.04775	−0.0448396
$547$	−29.2956	−1.25259	−0.626294	−	0.779587i	$-0.715429\pi$
$547$	−29.2956	−1.25259	−0.626294	+	0.779587i	$0.715429\pi$
$548$	−6.20889	−0.265231
$549$	28.3891	1.21162
$550$	3.82991	0.163308
$551$	7.76660	0.330868
$552$	−4.19228	−0.178435
$553$	−4.45249	−0.189339
$554$	−4.22955	−0.179697
$555$	3.05861	0.129831
$556$	77.8281	3.30065
$557$	15.0947	0.639581	0.319791	−	0.947488i	$-0.396387\pi$
$557$	15.0947	0.639581	0.319791	+	0.947488i	$0.396387\pi$
$558$	39.8257	1.68596
$559$	13.9776	0.591191
$560$	−14.8495	−0.627508
$561$	0.907392	0.0383101
$562$	−35.0441	−1.47825
$563$	−18.7840	−0.791653	−0.395826	−	0.918325i	$-0.629542\pi$
$563$	−18.7840	−0.791653	−0.395826	+	0.918325i	$0.629542\pi$
$564$	4.25819	0.179302
$565$	−7.35653	−0.309491
$566$	57.2147	2.40491
$567$	8.29511	0.348362
$568$	−64.6849	−2.71412
$569$	37.3995	1.56787	0.783934	−	0.620844i	$-0.213210\pi$
$569$	37.3995	1.56787	0.783934	+	0.620844i	$0.213210\pi$
$570$	−1.50523	−0.0630474
$571$	2.57315	0.107683	0.0538415	−	0.998549i	$-0.482853\pi$
$571$	2.57315	0.107683	0.0538415	+	0.998549i	$0.482853\pi$
$572$	−10.4459	−0.436764
$573$	−0.643360	−0.0268767
$574$	−13.5514	−0.565624
$575$	1.58081	0.0659245
$576$	−86.1346	−3.58894
$577$	5.40420	0.224980	0.112490	−	0.993653i	$-0.464117\pi$
$577$	5.40420	0.224980	0.112490	+	0.993653i	$0.464117\pi$
$578$	31.9564	1.32921
$579$	3.79380	0.157665
$580$	21.6038	0.897049
$581$	2.14419	0.0889561
$582$	2.14371	0.0888597
$583$	−4.37853	−0.181340
$584$	34.7824	1.43931
$585$	3.98750	0.164863
$586$	−74.5472	−3.07952
$587$	−31.1741	−1.28669	−0.643346	−	0.765575i	$-0.722454\pi$
$587$	−31.1741	−1.28669	−0.643346	+	0.765575i	$0.722454\pi$
$588$	1.53346	0.0632387
$589$	−9.79310	−0.403518
$590$	−40.7520	−1.67773
$591$	−5.64570	−0.232233
$592$	−161.578	−6.64082
$593$	24.2813	0.997112	0.498556	−	0.866857i	$-0.333864\pi$
$593$	24.2813	0.997112	0.498556	+	0.866857i	$0.333864\pi$
$594$	−6.37437	−0.261544
$595$	2.30136	0.0943464
$596$	49.8878	2.04348
$597$	−0.452374	−0.0185144
$598$	−5.89229	−0.240954
$599$	−0.410708	−0.0167811	−0.00839053	−	0.999965i	$-0.502671\pi$
$599$	−0.410708	−0.0167811	−0.00839053	+	0.999965i	$0.502671\pi$
$600$	−2.65198	−0.108267
$601$	−35.7662	−1.45893	−0.729467	−	0.684016i	$-0.760232\pi$
$601$	−35.7662	−1.45893	−0.729467	+	0.684016i	$0.760232\pi$
$602$	−27.9572	−1.13945
$603$	−34.9616	−1.42375
$604$	−25.8576	−1.05213
$605$	9.03251	0.367224
$606$	12.9515	0.526120
$607$	11.9097	0.483400	0.241700	−	0.970351i	$-0.422295\pi$
$607$	11.9097	0.483400	0.241700	+	0.970351i	$0.422295\pi$
$608$	42.5123	1.72410
$609$	−1.11319	−0.0451086
$610$	−26.5372	−1.07446
$611$	3.79074	0.153357
$612$	36.6716	1.48236
$613$	35.8340	1.44732	0.723661	−	0.690155i	$-0.242458\pi$
$613$	35.8340	1.44732	0.723661	+	0.690155i	$0.242458\pi$
$614$	10.9712	0.442762
$615$	−1.39510	−0.0562560
$616$	13.2334	0.533190
$617$	−8.96448	−0.360896	−0.180448	−	0.983585i	$-0.557755\pi$
$617$	−8.96448	−0.360896	−0.180448	+	0.983585i	$0.557755\pi$
$618$	6.65449	0.267683
$619$	44.3282	1.78170	0.890851	−	0.454296i	$-0.150109\pi$
$619$	44.3282	1.78170	0.890851	+	0.454296i	$0.150109\pi$
$620$	−27.2408	−1.09402
$621$	−2.63105	−0.105580
$622$	−78.7606	−3.15801
$623$	−6.47380	−0.259367
$624$	5.69822	0.228111
$625$	1.00000	0.0400000
$626$	−2.69074	−0.107544
$627$	0.773266	0.0308813
$628$	28.7625	1.14775
$629$	25.0411	0.998455
$630$	−7.97556	−0.317754
$631$	1.21887	0.0485225	0.0242612	−	0.999706i	$-0.492277\pi$
$631$	1.21887	0.0485225	0.0242612	+	0.999706i	$0.492277\pi$
$632$	42.0067	1.67094
$633$	5.72561	0.227572
$634$	−49.7593	−1.97619
$635$	−16.2032	−0.643003
$636$	4.78678	0.189808
$637$	1.36512	0.0540881
$638$	−15.1671	−0.600470
$639$	−20.0270	−0.792257
$640$	37.1620	1.46896
$641$	22.0628	0.871428	0.435714	−	0.900085i	$-0.356496\pi$
$641$	22.0628	0.871428	0.435714	+	0.900085i	$0.356496\pi$
$642$	14.1076	0.556783
$643$	15.0163	0.592186	0.296093	−	0.955159i	$-0.404316\pi$
$643$	15.0163	0.592186	0.296093	+	0.955159i	$0.404316\pi$
$644$	8.62378	0.339825
$645$	−2.87817	−0.113328
$646$	−12.3235	−0.484861
$647$	32.3628	1.27231	0.636156	−	0.771561i	$-0.280524\pi$
$647$	32.3628	1.27231	0.636156	+	0.771561i	$0.280524\pi$
$648$	−78.2596	−3.07433
$649$	20.9350	0.821771
$650$	−3.72738	−0.146200
$651$	1.40364	0.0550132
$652$	109.700	4.29619
$653$	39.6231	1.55057	0.775286	−	0.631611i	$-0.217606\pi$
$653$	39.6231	1.55057	0.775286	+	0.631611i	$0.217606\pi$
$654$	6.37473	0.249272
$655$	6.23423	0.243592
$656$	73.6995	2.87748
$657$	10.7689	0.420137
$658$	−7.58202	−0.295578
$659$	−26.6710	−1.03895	−0.519477	−	0.854484i	$-0.673873\pi$
$659$	−26.6710	−1.03895	−0.519477	+	0.854484i	$0.673873\pi$
$660$	2.15094	0.0837252
$661$	24.1770	0.940375	0.470187	−	0.882567i	$-0.344186\pi$
$661$	24.1770	0.940375	0.470187	+	0.882567i	$0.344186\pi$
$662$	11.6100	0.451234
$663$	−0.883100	−0.0342967
$664$	−20.2292	−0.785047
$665$	1.96118	0.0760513
$666$	−86.7823	−3.36275
$667$	−6.26028	−0.242399
$668$	89.2450	3.45299
$669$	3.54629	0.137107
$670$	32.6809	1.26257
$671$	13.6326	0.526281
$672$	−6.09328	−0.235053
$673$	25.3478	0.977087	0.488544	−	0.872539i	$-0.337528\pi$
$673$	25.3478	0.977087	0.488544	+	0.872539i	$0.337528\pi$
$674$	−39.1020	−1.50615
$675$	−1.66436	−0.0640614
$676$	−60.7524	−2.33663
$677$	−1.53301	−0.0589185	−0.0294593	−	0.999566i	$-0.509379\pi$
$677$	−1.53301	−0.0589185	−0.0294593	+	0.999566i	$0.509379\pi$
$678$	−5.64624	−0.216843
$679$	−2.79306	−0.107188
$680$	−21.7120	−0.832616
$681$	−0.596867	−0.0228720
$682$	19.1245	0.732317
$683$	8.61395	0.329604	0.164802	−	0.986327i	$-0.447302\pi$
$683$	8.61395	0.329604	0.164802	+	0.986327i	$0.447302\pi$
$684$	31.2510	1.19491
$685$	1.13814	0.0434862
$686$	−2.73044	−0.104249
$687$	−0.281096	−0.0107245
$688$	152.046	5.79670
$689$	4.26131	0.162343
$690$	1.21330	0.0461894
$691$	−2.65540	−0.101016	−0.0505080	−	0.998724i	$-0.516084\pi$
$691$	−2.65540	−0.101016	−0.0505080	+	0.998724i	$0.516084\pi$
$692$	−92.1283	−3.50219
$693$	4.09719	0.155639
$694$	−83.2429	−3.15986
$695$	−14.2666	−0.541161
$696$	10.5023	0.398088
$697$	−11.4218	−0.432632
$698$	83.5111	3.16094
$699$	−1.10992	−0.0419811
$700$	5.45528	0.206190
$701$	−10.8720	−0.410629	−0.205314	−	0.978696i	$-0.565822\pi$
$701$	−10.8720	−0.410629	−0.205314	+	0.978696i	$0.565822\pi$
$702$	6.20372	0.234144
$703$	21.3397	0.804841
$704$	−41.3623	−1.55890
$705$	−0.780562	−0.0293977
$706$	−14.0032	−0.527016
$707$	−16.8746	−0.634636
$708$	−22.8870	−0.860145
$709$	23.3231	0.875917	0.437959	−	0.898995i	$-0.355702\pi$
$709$	23.3231	0.875917	0.437959	+	0.898995i	$0.355702\pi$
$710$	18.7206	0.702570
$711$	13.0056	0.487750
$712$	61.0766	2.28894
$713$	7.89374	0.295623
$714$	1.76632	0.0661030
$715$	1.91482	0.0716102
$716$	−6.41221	−0.239636
$717$	−1.51179	−0.0564589
$718$	0.273606	0.0102109
$719$	−14.7563	−0.550317	−0.275158	−	0.961399i	$-0.588730\pi$
$719$	−14.7563	−0.550317	−0.275158	+	0.961399i	$0.588730\pi$
$720$	43.3753	1.61650
$721$	−8.67018	−0.322894
$722$	41.3764	1.53987
$723$	6.71165	0.249609
$724$	16.1137	0.598862
$725$	−3.96016	−0.147077
$726$	6.93258	0.257292
$727$	−8.71767	−0.323320	−0.161660	−	0.986846i	$-0.551685\pi$
$727$	−8.71767	−0.323320	−0.161660	+	0.986846i	$0.551685\pi$
$728$	−12.8791	−0.477333
$729$	−22.8264	−0.845420
$730$	−10.0664	−0.372576
$731$	−23.5638	−0.871540
$732$	−14.9037	−0.550857
$733$	−15.5221	−0.573322	−0.286661	−	0.958032i	$-0.592545\pi$
$733$	−15.5221	−0.573322	−0.286661	+	0.958032i	$0.592545\pi$
$734$	−86.6222	−3.19728
$735$	−0.281096	−0.0103684
$736$	−34.2671	−1.26310
$737$	−16.7888	−0.618422
$738$	39.5834	1.45709
$739$	−1.73305	−0.0637514	−0.0318757	−	0.999492i	$-0.510148\pi$
$739$	−1.73305	−0.0637514	−0.0318757	+	0.999492i	$0.510148\pi$
$740$	59.3591	2.18208
$741$	−0.752564	−0.0276461
$742$	−8.52322	−0.312897
$743$	−16.6605	−0.611213	−0.305607	−	0.952158i	$-0.598859\pi$
$743$	−16.6605	−0.611213	−0.305607	+	0.952158i	$0.598859\pi$
$744$	−13.2426	−0.485497
$745$	−9.14486	−0.335042
$746$	−83.4077	−3.05377
$747$	−6.26316	−0.229157
$748$	17.6099	0.643883
$749$	−18.3809	−0.671624
$750$	0.767515	0.0280257
$751$	38.4305	1.40235	0.701175	−	0.712989i	$-0.252659\pi$
$751$	38.4305	1.40235	0.701175	+	0.712989i	$0.252659\pi$
$752$	41.2350	1.50369
$753$	6.10479	0.222471
$754$	14.7610	0.537565
$755$	4.73992	0.172503
$756$	−9.07958	−0.330221
$757$	−16.5129	−0.600171	−0.300086	−	0.953912i	$-0.597015\pi$
$757$	−16.5129	−0.600171	−0.300086	+	0.953912i	$0.597015\pi$
$758$	31.1493	1.13139
$759$	−0.623292	−0.0226241
$760$	−18.5026	−0.671161
$761$	−4.36943	−0.158392	−0.0791959	−	0.996859i	$-0.525235\pi$
$761$	−4.36943	−0.158392	−0.0791959	+	0.996859i	$0.525235\pi$
$762$	−12.4362	−0.450514
$763$	−8.30568	−0.300686
$764$	−12.4858	−0.451721
$765$	−6.72223	−0.243043
$766$	−72.2406	−2.61016
$767$	−20.3745	−0.735682
$768$	11.9443	0.431003
$769$	53.3469	1.92374	0.961869	−	0.273512i	$-0.0881853\pi$
$769$	53.3469	1.92374	0.961869	+	0.273512i	$0.0881853\pi$
$770$	−3.82991	−0.138020
$771$	8.22140	0.296087
$772$	73.6271	2.64990
$773$	−18.0877	−0.650568	−0.325284	−	0.945616i	$-0.605460\pi$
$773$	−18.0877	−0.650568	−0.325284	+	0.945616i	$0.605460\pi$
$774$	81.6627	2.93530
$775$	4.99347	0.179371
$776$	26.3509	0.945942
$777$	−3.05861	−0.109727
$778$	73.7765	2.64501
$779$	−9.73351	−0.348739
$780$	−2.09336	−0.0749542
$781$	−9.61709	−0.344126
$782$	9.93336	0.355216
$783$	6.59116	0.235549
$784$	14.8495	0.530341
$785$	−5.27240	−0.188180
$786$	4.78487	0.170670
$787$	−8.31858	−0.296525	−0.148263	−	0.988948i	$-0.547368\pi$
$787$	−8.31858	−0.296525	−0.148263	+	0.988948i	$0.547368\pi$
$788$	−109.567	−3.90317
$789$	−5.31517	−0.189225
$790$	−12.1572	−0.432535
$791$	7.35653	0.261568
$792$	−38.6546	−1.37353
$793$	−13.2676	−0.471148
$794$	97.1696	3.44842
$795$	−0.877458	−0.0311202
$796$	−8.77930	−0.311174
$797$	35.2459	1.24847	0.624237	−	0.781235i	$-0.285410\pi$
$797$	35.2459	1.24847	0.624237	+	0.781235i	$0.285410\pi$
$798$	1.50523	0.0532847
$799$	−6.39053	−0.226081
$800$	−21.6769	−0.766393
$801$	18.9099	0.668147
$802$	13.6739	0.482843
$803$	5.17131	0.182491
$804$	18.3541	0.647301
$805$	−1.58081	−0.0557163
$806$	−18.6126	−0.655599
$807$	−4.74908	−0.167176
$808$	159.202	5.60072
$809$	13.1077	0.460844	0.230422	−	0.973091i	$-0.425989\pi$
$809$	13.1077	0.460844	0.230422	+	0.973091i	$0.425989\pi$
$810$	22.6493	0.795814
$811$	−27.6457	−0.970773	−0.485387	−	0.874300i	$-0.661321\pi$
$811$	−27.6457	−0.970773	−0.485387	+	0.874300i	$0.661321\pi$
$812$	−21.6038	−0.758145
$813$	5.11452	0.179374
$814$	−41.6734	−1.46065
$815$	−20.1090	−0.704386
$816$	−9.60619	−0.336284
$817$	−20.0807	−0.702536
$818$	12.3033	0.430175
$819$	−3.98750	−0.139335
$820$	−27.0750	−0.945501
$821$	−19.4903	−0.680216	−0.340108	−	0.940386i	$-0.610464\pi$
$821$	−19.4903	−0.680216	−0.340108	+	0.940386i	$0.610464\pi$
$822$	0.873541	0.0304682
$823$	−6.80926	−0.237356	−0.118678	−	0.992933i	$-0.537866\pi$
$823$	−6.80926	−0.237356	−0.118678	+	0.992933i	$0.537866\pi$
$824$	81.7982	2.84957
$825$	−0.394286	−0.0137273
$826$	40.7520	1.41794
$827$	40.6674	1.41415	0.707073	−	0.707141i	$-0.250015\pi$
$827$	40.6674	1.41415	0.707073	+	0.707141i	$0.250015\pi$
$828$	−25.1899	−0.875411
$829$	−12.6875	−0.440654	−0.220327	−	0.975426i	$-0.570713\pi$
$829$	−12.6875	−0.440654	−0.220327	+	0.975426i	$0.570713\pi$
$830$	5.85458	0.203216
$831$	0.435429	0.0151049
$832$	40.2550	1.39559
$833$	−2.30136	−0.0797372
$834$	−10.9498	−0.379160
$835$	−16.3594	−0.566140
$836$	15.0069	0.519025
$837$	−8.31096	−0.287269
$838$	−65.3225	−2.25653
$839$	2.37977	0.0821589	0.0410795	−	0.999156i	$-0.486920\pi$
$839$	2.37977	0.0821589	0.0410795	+	0.999156i	$0.486920\pi$
$840$	2.65198	0.0915020
$841$	−13.3171	−0.459211
$842$	49.8891	1.71929
$843$	3.60776	0.124258
$844$	111.118	3.82484
$845$	11.1364	0.383105
$846$	22.1470	0.761429
$847$	−9.03251	−0.310361
$848$	46.3537	1.59179
$849$	−5.89020	−0.202151
$850$	6.28370	0.215529
$851$	−17.2009	−0.589638
$852$	10.5138	0.360196
$853$	−11.9763	−0.410062	−0.205031	−	0.978755i	$-0.565730\pi$
$853$	−11.9763	−0.410062	−0.205031	+	0.978755i	$0.565730\pi$
$854$	26.5372	0.908083
$855$	−5.72858	−0.195913
$856$	173.413	5.92715
$857$	3.36860	0.115069	0.0575346	−	0.998344i	$-0.481676\pi$
$857$	3.36860	0.115069	0.0575346	+	0.998344i	$0.481676\pi$
$858$	1.46965	0.0501731
$859$	11.8754	0.405182	0.202591	−	0.979263i	$-0.435064\pi$
$859$	11.8754	0.405182	0.202591	+	0.979263i	$0.435064\pi$
$860$	−55.8572	−1.90472
$861$	1.39510	0.0475450
$862$	79.9777	2.72405
$863$	30.3078	1.03169	0.515845	−	0.856682i	$-0.327478\pi$
$863$	30.3078	1.03169	0.515845	+	0.856682i	$0.327478\pi$
$864$	36.0782	1.22741
$865$	16.8879	0.574206
$866$	83.5316	2.83852
$867$	−3.28988	−0.111730
$868$	27.2408	0.924613
$869$	6.24538	0.211860
$870$	−3.03948	−0.103048
$871$	16.3393	0.553636
$872$	78.3593	2.65358
$873$	8.15848	0.276123
$874$	8.46506	0.286335
$875$	−1.00000	−0.0338062
$876$	−5.65348	−0.191013
$877$	39.9033	1.34744	0.673720	−	0.738987i	$-0.264696\pi$
$877$	39.9033	1.34744	0.673720	+	0.738987i	$0.264696\pi$
$878$	17.9172	0.604677
$879$	7.67456	0.258857
$880$	20.8291	0.702147
$881$	11.7361	0.395398	0.197699	−	0.980263i	$-0.436653\pi$
$881$	11.7361	0.395398	0.197699	+	0.980263i	$0.436653\pi$
$882$	7.97556	0.268551
$883$	48.4286	1.62975	0.814877	−	0.579635i	$-0.196805\pi$
$883$	48.4286	1.62975	0.814877	+	0.579635i	$0.196805\pi$
$884$	−17.1385	−0.576430
$885$	4.19538	0.141026
$886$	46.0806	1.54811
$887$	−48.3124	−1.62217	−0.811086	−	0.584927i	$-0.801123\pi$
$887$	−48.3124	−1.62217	−0.811086	+	0.584927i	$0.801123\pi$
$888$	28.8563	0.968353
$889$	16.2032	0.543436
$890$	−17.6763	−0.592511
$891$	−11.6353	−0.389798
$892$	68.8235	2.30438
$893$	−5.44591	−0.182240
$894$	−7.01882	−0.234744
$895$	1.17541	0.0392898
$896$	−37.1620	−1.24149
$897$	0.606606	0.0202540
$898$	17.2928	0.577070
$899$	−19.7750	−0.659532
$900$	−15.9348	−0.531160
$901$	−7.18382	−0.239328
$902$	19.0082	0.632903
$903$	2.87817	0.0957796
$904$	−69.4046	−2.30836
$905$	−2.95378	−0.0981871
$906$	3.63796	0.120863
$907$	28.9675	0.961849	0.480925	−	0.876762i	$-0.340301\pi$
$907$	28.9675	0.961849	0.480925	+	0.876762i	$0.340301\pi$
$908$	−11.5835	−0.384412
$909$	49.2905	1.63486
$910$	3.72738	0.123561
$911$	53.0628	1.75805	0.879024	−	0.476778i	$-0.158195\pi$
$911$	53.0628	1.75805	0.879024	+	0.476778i	$0.158195\pi$
$912$	−8.18625	−0.271074
$913$	−3.00760	−0.0995371
$914$	−27.7627	−0.918309
$915$	2.73198	0.0903164
$916$	−5.45528	−0.180248
$917$	−6.23423	−0.205873
$918$	−10.4584	−0.345178
$919$	−1.58728	−0.0523595	−0.0261797	−	0.999657i	$-0.508334\pi$
$919$	−1.58728	−0.0523595	−0.0261797	+	0.999657i	$0.508334\pi$
$920$	14.9141	0.491702
$921$	−1.12948	−0.0372175
$922$	−60.6965	−1.99893
$923$	9.35962	0.308076
$924$	−2.15094	−0.0707607
$925$	−10.8810	−0.357766
$926$	16.9534	0.557123
$927$	25.3255	0.831797
$928$	85.8439	2.81797
$929$	27.6202	0.906189	0.453094	−	0.891463i	$-0.350320\pi$
$929$	27.6202	0.906189	0.453094	+	0.891463i	$0.350320\pi$
$930$	3.83256	0.125675
$931$	−1.96118	−0.0642751
$932$	−21.5405	−0.705581
$933$	8.10833	0.265455
$934$	5.38005	0.176041
$935$	−3.22805	−0.105569
$936$	37.6198	1.22964
$937$	31.6202	1.03299	0.516494	−	0.856291i	$-0.327237\pi$
$937$	31.6202	1.03299	0.516494	+	0.856291i	$0.327237\pi$
$938$	−32.6809	−1.06707
$939$	0.277009	0.00903985
$940$	−15.1485	−0.494090
$941$	7.51044	0.244833	0.122417	−	0.992479i	$-0.460936\pi$
$941$	7.51044	0.244833	0.122417	+	0.992479i	$0.460936\pi$
$942$	−4.04665	−0.131847
$943$	7.84571	0.255491
$944$	−221.630	−7.21346
$945$	1.66436	0.0541418
$946$	39.2149	1.27499
$947$	16.3030	0.529778	0.264889	−	0.964279i	$-0.414665\pi$
$947$	16.3030	0.529778	0.264889	+	0.964279i	$0.414665\pi$
$948$	−6.82770	−0.221753
$949$	−5.03286	−0.163374
$950$	5.35488	0.173735
$951$	5.12268	0.166114
$952$	21.7120	0.703689
$953$	29.4131	0.952785	0.476393	−	0.879233i	$-0.341944\pi$
$953$	29.4131	0.952785	0.476393	+	0.879233i	$0.341944\pi$
$954$	24.8962	0.806045
$955$	2.28876	0.0740624
$956$	−29.3396	−0.948911
$957$	1.56144	0.0504741
$958$	−101.984	−3.29495
$959$	−1.13814	−0.0367525
$960$	−8.28902	−0.267527
$961$	−6.06526	−0.195653
$962$	40.5577	1.30763
$963$	53.6904	1.73015
$964$	130.254	4.19521
$965$	−13.4965	−0.434467
$966$	−1.21330	−0.0390372
$967$	−2.22114	−0.0714271	−0.0357136	−	0.999362i	$-0.511370\pi$
$967$	−2.22114	−0.0714271	−0.0357136	+	0.999362i	$0.511370\pi$
$968$	85.2165	2.73896
$969$	1.26869	0.0407562
$970$	−7.62626	−0.244865
$971$	−0.395496	−0.0126921	−0.00634603	−	0.999980i	$-0.502020\pi$
$971$	−0.395496	−0.0126921	−0.00634603	+	0.999980i	$0.502020\pi$
$972$	39.9589	1.28168
$973$	14.2666	0.457365
$974$	−50.6631	−1.62335
$975$	0.383730	0.0122892
$976$	−144.323	−4.61967
$977$	−20.8121	−0.665837	−0.332918	−	0.942956i	$-0.608033\pi$
$977$	−20.8121	−0.665837	−0.332918	+	0.942956i	$0.608033\pi$
$978$	−15.4339	−0.493522
$979$	9.08062	0.290218
$980$	−5.45528	−0.174263
$981$	24.2608	0.774587
$982$	92.6550	2.95674
$983$	−23.4908	−0.749241	−0.374621	−	0.927178i	$-0.622227\pi$
$983$	−23.4908	−0.749241	−0.374621	+	0.927178i	$0.622227\pi$
$984$	−13.1620	−0.419589
$985$	20.0846	0.639949
$986$	−24.8845	−0.792484
$987$	0.780562	0.0248456
$988$	−14.6052	−0.464652
$989$	16.1861	0.514689
$990$	11.1871	0.355550
$991$	33.4429	1.06235	0.531175	−	0.847262i	$-0.321751\pi$
$991$	33.4429	1.06235	0.531175	+	0.847262i	$0.321751\pi$
$992$	−108.243	−3.43671
$993$	−1.19524	−0.0379297
$994$	−18.7206	−0.593780
$995$	1.60932	0.0510189
$996$	3.28803	0.104185
$997$	−53.0704	−1.68076	−0.840379	−	0.542000i	$-0.817667\pi$
$997$	−53.0704	−1.68076	−0.840379	+	0.542000i	$0.817667\pi$
$998$	−66.0616	−2.09114
$999$	18.1100	0.572975

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8015.2.a.n.1.2	✓	68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8015.2.a.n.1.2	✓	68	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:	\( N \)	\(=\)	\( 8015 = 5 \cdot 7 \cdot 229 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8015.a (trivial)

\(f(q)\)	\(=\)	\(q-2.73044 q^{2} +0.281096 q^{3} +5.45528 q^{4} -1.00000 q^{5} -0.767515 q^{6} +1.00000 q^{7} -9.43443 q^{8} -2.92099 q^{9} +O(q^{10})\)	\(q-2.73044 q^{2} +0.281096 q^{3} +5.45528 q^{4} -1.00000 q^{5} -0.767515 q^{6} +1.00000 q^{7} -9.43443 q^{8} -2.92099 q^{9} +2.73044 q^{10} -1.40267 q^{11} +1.53346 q^{12} +1.36512 q^{13} -2.73044 q^{14} -0.281096 q^{15} +14.8495 q^{16} -2.30136 q^{17} +7.97556 q^{18} -1.96118 q^{19} -5.45528 q^{20} +0.281096 q^{21} +3.82991 q^{22} +1.58081 q^{23} -2.65198 q^{24} +1.00000 q^{25} -3.72738 q^{26} -1.66436 q^{27} +5.45528 q^{28} -3.96016 q^{29} +0.767515 q^{30} +4.99347 q^{31} -21.6769 q^{32} -0.394286 q^{33} +6.28370 q^{34} -1.00000 q^{35} -15.9348 q^{36} -10.8810 q^{37} +5.35488 q^{38} +0.383730 q^{39} +9.43443 q^{40} +4.96309 q^{41} -0.767515 q^{42} +10.2391 q^{43} -7.65198 q^{44} +2.92099 q^{45} -4.31631 q^{46} +2.77685 q^{47} +4.17415 q^{48} +1.00000 q^{49} -2.73044 q^{50} -0.646902 q^{51} +7.44712 q^{52} +3.12156 q^{53} +4.54444 q^{54} +1.40267 q^{55} -9.43443 q^{56} -0.551280 q^{57} +10.8130 q^{58} -14.9251 q^{59} -1.53346 q^{60} -9.71902 q^{61} -13.6344 q^{62} -2.92099 q^{63} +29.4882 q^{64} -1.36512 q^{65} +1.07657 q^{66} +11.9691 q^{67} -12.5545 q^{68} +0.444360 q^{69} +2.73044 q^{70} +6.85626 q^{71} +27.5578 q^{72} -3.68675 q^{73} +29.7100 q^{74} +0.281096 q^{75} -10.6988 q^{76} -1.40267 q^{77} -1.04775 q^{78} -4.45249 q^{79} -14.8495 q^{80} +8.29511 q^{81} -13.5514 q^{82} +2.14419 q^{83} +1.53346 q^{84} +2.30136 q^{85} -27.9572 q^{86} -1.11319 q^{87} +13.2334 q^{88} -6.47380 q^{89} -7.97556 q^{90} +1.36512 q^{91} +8.62378 q^{92} +1.40364 q^{93} -7.58202 q^{94} +1.96118 q^{95} -6.09328 q^{96} -2.79306 q^{97} -2.73044 q^{98} +4.09719 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q + 9 q^{2} + 83 q^{4} - 68 q^{5} + 5 q^{6} + 68 q^{7} + 30 q^{8} + 86 q^{9}+O(q^{10}) \) 68 * q + 9 * q^2 + 83 * q^4 - 68 * q^5 + 5 * q^6 + 68 * q^7 + 30 * q^8 + 86 * q^9	\( 68 q + 9 q^{2} + 83 q^{4} - 68 q^{5} + 5 q^{6} + 68 q^{7} + 30 q^{8} + 86 q^{9} - 9 q^{10} + 5 q^{11} + 9 q^{12} + 15 q^{13} + 9 q^{14} + 109 q^{16} + 7 q^{17} + 39 q^{18} + 20 q^{19} - 83 q^{20} + 56 q^{22} + 36 q^{23} + q^{24} + 68 q^{25} + q^{26} + 12 q^{27} + 83 q^{28} - 16 q^{29} - 5 q^{30} + 31 q^{31} + 79 q^{32} + 45 q^{33} + 31 q^{34} - 68 q^{35} + 114 q^{36} + 72 q^{37} + 8 q^{38} + 47 q^{39} - 30 q^{40} + 6 q^{41} + 5 q^{42} + 75 q^{43} + 15 q^{44} - 86 q^{45} + 29 q^{46} - 10 q^{47} + 44 q^{48} + 68 q^{49} + 9 q^{50} + 23 q^{51} + 37 q^{52} + 41 q^{53} + 4 q^{54} - 5 q^{55} + 30 q^{56} + 55 q^{57} + 66 q^{58} - 5 q^{59} - 9 q^{60} - 2 q^{61} + 3 q^{62} + 86 q^{63} + 162 q^{64} - 15 q^{65} - 23 q^{66} + 92 q^{67} + 35 q^{68} - 25 q^{69} - 9 q^{70} - 2 q^{71} + 128 q^{72} + 80 q^{73} + 18 q^{74} + 71 q^{76} + 5 q^{77} + 20 q^{78} + 100 q^{79} - 109 q^{80} + 140 q^{81} + 36 q^{82} - 60 q^{83} + 9 q^{84} - 7 q^{85} - 27 q^{86} + 24 q^{87} + 175 q^{88} + 19 q^{89} - 39 q^{90} + 15 q^{91} + 75 q^{92} + 37 q^{93} + 11 q^{94} - 20 q^{95} + 15 q^{96} + 96 q^{97} + 9 q^{98} + 3 q^{99}+O(q^{100}) \) 68 * q + 9 * q^2 + 83 * q^4 - 68 * q^5 + 5 * q^6 + 68 * q^7 + 30 * q^8 + 86 * q^9 - 9 * q^10 + 5 * q^11 + 9 * q^12 + 15 * q^13 + 9 * q^14 + 109 * q^16 + 7 * q^17 + 39 * q^18 + 20 * q^19 - 83 * q^20 + 56 * q^22 + 36 * q^23 + q^24 + 68 * q^25 + q^26 + 12 * q^27 + 83 * q^28 - 16 * q^29 - 5 * q^30 + 31 * q^31 + 79 * q^32 + 45 * q^33 + 31 * q^34 - 68 * q^35 + 114 * q^36 + 72 * q^37 + 8 * q^38 + 47 * q^39 - 30 * q^40 + 6 * q^41 + 5 * q^42 + 75 * q^43 + 15 * q^44 - 86 * q^45 + 29 * q^46 - 10 * q^47 + 44 * q^48 + 68 * q^49 + 9 * q^50 + 23 * q^51 + 37 * q^52 + 41 * q^53 + 4 * q^54 - 5 * q^55 + 30 * q^56 + 55 * q^57 + 66 * q^58 - 5 * q^59 - 9 * q^60 - 2 * q^61 + 3 * q^62 + 86 * q^63 + 162 * q^64 - 15 * q^65 - 23 * q^66 + 92 * q^67 + 35 * q^68 - 25 * q^69 - 9 * q^70 - 2 * q^71 + 128 * q^72 + 80 * q^73 + 18 * q^74 + 71 * q^76 + 5 * q^77 + 20 * q^78 + 100 * q^79 - 109 * q^80 + 140 * q^81 + 36 * q^82 - 60 * q^83 + 9 * q^84 - 7 * q^85 - 27 * q^86 + 24 * q^87 + 175 * q^88 + 19 * q^89 - 39 * q^90 + 15 * q^91 + 75 * q^92 + 37 * q^93 + 11 * q^94 - 20 * q^95 + 15 * q^96 + 96 * q^97 + 9 * q^98 + 3 * q^99

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