LMFDB - Embedded newform 8026.2.a.c.1.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8026,2,Mod(1,8026)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8026, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8026.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8026 = 2 \cdot 4013 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8026.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:	$64.0879326623$
Analytic rank:	$0$
Dimension:	$86$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.20
Character	$\chi$	$=$	8026.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.77113 q^{3} +1.00000 q^{4} -2.88416 q^{5} +1.77113 q^{6} -2.34784 q^{7} -1.00000 q^{8} +0.136917 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.77113 q^{3} +1.00000 q^{4} -2.88416 q^{5} +1.77113 q^{6} -2.34784 q^{7} -1.00000 q^{8} +0.136917 q^{9} +2.88416 q^{10} -1.52146 q^{11} -1.77113 q^{12} +5.80761 q^{13} +2.34784 q^{14} +5.10823 q^{15} +1.00000 q^{16} +4.96718 q^{17} -0.136917 q^{18} +1.05435 q^{19} -2.88416 q^{20} +4.15834 q^{21} +1.52146 q^{22} +6.81108 q^{23} +1.77113 q^{24} +3.31837 q^{25} -5.80761 q^{26} +5.07091 q^{27} -2.34784 q^{28} +7.25956 q^{29} -5.10823 q^{30} +4.96242 q^{31} -1.00000 q^{32} +2.69470 q^{33} -4.96718 q^{34} +6.77155 q^{35} +0.136917 q^{36} +5.58796 q^{37} -1.05435 q^{38} -10.2861 q^{39} +2.88416 q^{40} -1.03560 q^{41} -4.15834 q^{42} -7.17683 q^{43} -1.52146 q^{44} -0.394889 q^{45} -6.81108 q^{46} +6.21800 q^{47} -1.77113 q^{48} -1.48765 q^{49} -3.31837 q^{50} -8.79754 q^{51} +5.80761 q^{52} -3.64768 q^{53} -5.07091 q^{54} +4.38812 q^{55} +2.34784 q^{56} -1.86739 q^{57} -7.25956 q^{58} +3.05294 q^{59} +5.10823 q^{60} -9.14586 q^{61} -4.96242 q^{62} -0.321458 q^{63} +1.00000 q^{64} -16.7501 q^{65} -2.69470 q^{66} +2.45198 q^{67} +4.96718 q^{68} -12.0633 q^{69} -6.77155 q^{70} -2.98139 q^{71} -0.136917 q^{72} -0.456785 q^{73} -5.58796 q^{74} -5.87729 q^{75} +1.05435 q^{76} +3.57214 q^{77} +10.2861 q^{78} +8.22600 q^{79} -2.88416 q^{80} -9.39200 q^{81} +1.03560 q^{82} -3.16041 q^{83} +4.15834 q^{84} -14.3261 q^{85} +7.17683 q^{86} -12.8577 q^{87} +1.52146 q^{88} -7.21512 q^{89} +0.394889 q^{90} -13.6353 q^{91} +6.81108 q^{92} -8.78911 q^{93} -6.21800 q^{94} -3.04090 q^{95} +1.77113 q^{96} -4.40675 q^{97} +1.48765 q^{98} -0.208313 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 86 q - 86 q^{2} + 11 q^{3} + 86 q^{4} + 25 q^{5} - 11 q^{6} - 3 q^{7} - 86 q^{8} + 105 q^{9}+O(q^{10}) $ 86 * q - 86 * q^2 + 11 * q^3 + 86 * q^4 + 25 * q^5 - 11 * q^6 - 3 * q^7 - 86 * q^8 + 105 * q^9	\( 86 q - 86 q^{2} + 11 q^{3} + 86 q^{4} + 25 q^{5} - 11 q^{6} - 3 q^{7} - 86 q^{8} + 105 q^{9} - 25 q^{10} + 44 q^{11} + 11 q^{12} - 36 q^{13} + 3 q^{14} + 19 q^{15} + 86 q^{16} + 21 q^{17} - 105 q^{18} + 35 q^{19} + 25 q^{20} + 23 q^{21} - 44 q^{22} + 38 q^{23} - 11 q^{24} + 85 q^{25} + 36 q^{26} + 47 q^{27} - 3 q^{28} + 30 q^{29} - 19 q^{30} + 23 q^{31} - 86 q^{32} + 5 q^{33} - 21 q^{34} + 59 q^{35} + 105 q^{36} - 20 q^{37} - 35 q^{38} + 4 q^{39} - 25 q^{40} + 64 q^{41} - 23 q^{42} + 23 q^{43} + 44 q^{44} + 60 q^{45} - 38 q^{46} + 77 q^{47} + 11 q^{48} + 109 q^{49} - 85 q^{50} + 47 q^{51} - 36 q^{52} + 22 q^{53} - 47 q^{54} + 6 q^{55} + 3 q^{56} - 9 q^{57} - 30 q^{58} + 145 q^{59} + 19 q^{60} - 24 q^{61} - 23 q^{62} + 6 q^{63} + 86 q^{64} + 37 q^{65} - 5 q^{66} + 44 q^{67} + 21 q^{68} + 25 q^{69} - 59 q^{70} + 107 q^{71} - 105 q^{72} - 55 q^{73} + 20 q^{74} + 86 q^{75} + 35 q^{76} + 25 q^{77} - 4 q^{78} + 2 q^{79} + 25 q^{80} + 170 q^{81} - 64 q^{82} + 109 q^{83} + 23 q^{84} - 13 q^{85} - 23 q^{86} + 3 q^{87} - 44 q^{88} + 121 q^{89} - 60 q^{90} + 81 q^{91} + 38 q^{92} + 27 q^{93} - 77 q^{94} + 49 q^{95} - 11 q^{96} - 56 q^{97} - 109 q^{98} + 158 q^{99}+O(q^{100}) \) 86 * q - 86 * q^2 + 11 * q^3 + 86 * q^4 + 25 * q^5 - 11 * q^6 - 3 * q^7 - 86 * q^8 + 105 * q^9 - 25 * q^10 + 44 * q^11 + 11 * q^12 - 36 * q^13 + 3 * q^14 + 19 * q^15 + 86 * q^16 + 21 * q^17 - 105 * q^18 + 35 * q^19 + 25 * q^20 + 23 * q^21 - 44 * q^22 + 38 * q^23 - 11 * q^24 + 85 * q^25 + 36 * q^26 + 47 * q^27 - 3 * q^28 + 30 * q^29 - 19 * q^30 + 23 * q^31 - 86 * q^32 + 5 * q^33 - 21 * q^34 + 59 * q^35 + 105 * q^36 - 20 * q^37 - 35 * q^38 + 4 * q^39 - 25 * q^40 + 64 * q^41 - 23 * q^42 + 23 * q^43 + 44 * q^44 + 60 * q^45 - 38 * q^46 + 77 * q^47 + 11 * q^48 + 109 * q^49 - 85 * q^50 + 47 * q^51 - 36 * q^52 + 22 * q^53 - 47 * q^54 + 6 * q^55 + 3 * q^56 - 9 * q^57 - 30 * q^58 + 145 * q^59 + 19 * q^60 - 24 * q^61 - 23 * q^62 + 6 * q^63 + 86 * q^64 + 37 * q^65 - 5 * q^66 + 44 * q^67 + 21 * q^68 + 25 * q^69 - 59 * q^70 + 107 * q^71 - 105 * q^72 - 55 * q^73 + 20 * q^74 + 86 * q^75 + 35 * q^76 + 25 * q^77 - 4 * q^78 + 2 * q^79 + 25 * q^80 + 170 * q^81 - 64 * q^82 + 109 * q^83 + 23 * q^84 - 13 * q^85 - 23 * q^86 + 3 * q^87 - 44 * q^88 + 121 * q^89 - 60 * q^90 + 81 * q^91 + 38 * q^92 + 27 * q^93 - 77 * q^94 + 49 * q^95 - 11 * q^96 - 56 * q^97 - 109 * q^98 + 158 * 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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−1.77113	−1.02256	−0.511282	−	0.859413i	$-0.670829\pi$
$3$	−1.77113	−1.02256	−0.511282	+	0.859413i	$0.670829\pi$
$4$	1.00000	0.500000
$5$	−2.88416	−1.28984	−0.644918	−	0.764252i	$-0.723108\pi$
$5$	−2.88416	−1.28984	−0.644918	+	0.764252i	$0.723108\pi$
$6$	1.77113	0.723063
$7$	−2.34784	−0.887400	−0.443700	−	0.896175i	$-0.646334\pi$
$7$	−2.34784	−0.887400	−0.443700	+	0.896175i	$0.646334\pi$
$8$	−1.00000	−0.353553
$9$	0.136917	0.0456389
$10$	2.88416	0.912051
$11$	−1.52146	−0.458736	−0.229368	−	0.973340i	$-0.573666\pi$
$11$	−1.52146	−0.458736	−0.229368	+	0.973340i	$0.573666\pi$
$12$	−1.77113	−0.511282
$13$	5.80761	1.61074	0.805370	−	0.592772i	$-0.201967\pi$
$13$	5.80761	1.61074	0.805370	+	0.592772i	$0.201967\pi$
$14$	2.34784	0.627487
$15$	5.10823	1.31894
$16$	1.00000	0.250000
$17$	4.96718	1.20472	0.602359	−	0.798225i	$-0.294228\pi$
$17$	4.96718	1.20472	0.602359	+	0.798225i	$0.294228\pi$
$18$	−0.136917	−0.0322716
$19$	1.05435	0.241884	0.120942	−	0.992660i	$-0.461409\pi$
$19$	1.05435	0.241884	0.120942	+	0.992660i	$0.461409\pi$
$20$	−2.88416	−0.644918
$21$	4.15834	0.907424
$22$	1.52146	0.324376
$23$	6.81108	1.42021	0.710104	−	0.704097i	$-0.248648\pi$
$23$	6.81108	1.42021	0.710104	+	0.704097i	$0.248648\pi$
$24$	1.77113	0.361531
$25$	3.31837	0.663675
$26$	−5.80761	−1.13897
$27$	5.07091	0.975896
$28$	−2.34784	−0.443700
$29$	7.25956	1.34807	0.674034	−	0.738701i	$-0.264560\pi$
$29$	7.25956	1.34807	0.674034	+	0.738701i	$0.264560\pi$
$30$	−5.10823	−0.932632
$31$	4.96242	0.891276	0.445638	−	0.895213i	$-0.352977\pi$
$31$	4.96242	0.891276	0.445638	+	0.895213i	$0.352977\pi$
$32$	−1.00000	−0.176777
$33$	2.69470	0.469088
$34$	−4.96718	−0.851864
$35$	6.77155	1.14460
$36$	0.136917	0.0228194
$37$	5.58796	0.918655	0.459327	−	0.888267i	$-0.348091\pi$
$37$	5.58796	0.918655	0.459327	+	0.888267i	$0.348091\pi$
$38$	−1.05435	−0.171038
$39$	−10.2861	−1.64709
$40$	2.88416	0.456026
$41$	−1.03560	−0.161733	−0.0808667	−	0.996725i	$-0.525769\pi$
$41$	−1.03560	−0.161733	−0.0808667	+	0.996725i	$0.525769\pi$
$42$	−4.15834	−0.641646
$43$	−7.17683	−1.09446	−0.547228	−	0.836983i	$-0.684317\pi$
$43$	−7.17683	−1.09446	−0.547228	+	0.836983i	$0.684317\pi$
$44$	−1.52146	−0.229368
$45$	−0.394889	−0.0588666
$46$	−6.81108	−1.00424
$47$	6.21800	0.906988	0.453494	−	0.891259i	$-0.350177\pi$
$47$	6.21800	0.906988	0.453494	+	0.891259i	$0.350177\pi$
$48$	−1.77113	−0.255641
$49$	−1.48765	−0.212521
$50$	−3.31837	−0.469289
$51$	−8.79754	−1.23190
$52$	5.80761	0.805370
$53$	−3.64768	−0.501047	−0.250524	−	0.968110i	$-0.580603\pi$
$53$	−3.64768	−0.501047	−0.250524	+	0.968110i	$0.580603\pi$
$54$	−5.07091	−0.690063
$55$	4.38812	0.591694
$56$	2.34784	0.313743
$57$	−1.86739	−0.247342
$58$	−7.25956	−0.953227
$59$	3.05294	0.397458	0.198729	−	0.980054i	$-0.436319\pi$
$59$	3.05294	0.397458	0.198729	+	0.980054i	$0.436319\pi$
$60$	5.10823	0.659470
$61$	−9.14586	−1.17101	−0.585504	−	0.810670i	$-0.699103\pi$
$61$	−9.14586	−1.17101	−0.585504	+	0.810670i	$0.699103\pi$
$62$	−4.96242	−0.630228
$63$	−0.321458	−0.0404999
$64$	1.00000	0.125000
$65$	−16.7501	−2.07759
$66$	−2.69470	−0.331695
$67$	2.45198	0.299557	0.149778	−	0.988720i	$-0.452144\pi$
$67$	2.45198	0.299557	0.149778	+	0.988720i	$0.452144\pi$
$68$	4.96718	0.602359
$69$	−12.0633	−1.45226
$70$	−6.77155	−0.809354
$71$	−2.98139	−0.353826	−0.176913	−	0.984227i	$-0.556611\pi$
$71$	−2.98139	−0.353826	−0.176913	+	0.984227i	$0.556611\pi$
$72$	−0.136917	−0.0161358
$73$	−0.456785	−0.0534626	−0.0267313	−	0.999643i	$-0.508510\pi$
$73$	−0.456785	−0.0534626	−0.0267313	+	0.999643i	$0.508510\pi$
$74$	−5.58796	−0.649587
$75$	−5.87729	−0.678651
$76$	1.05435	0.120942
$77$	3.57214	0.407083
$78$	10.2861	1.16467
$79$	8.22600	0.925497	0.462749	−	0.886490i	$-0.346863\pi$
$79$	8.22600	0.925497	0.462749	+	0.886490i	$0.346863\pi$
$80$	−2.88416	−0.322459
$81$	−9.39200	−1.04356
$82$	1.03560	0.114363
$83$	−3.16041	−0.346900	−0.173450	−	0.984843i	$-0.555491\pi$
$83$	−3.16041	−0.346900	−0.173450	+	0.984843i	$0.555491\pi$
$84$	4.15834	0.453712
$85$	−14.3261	−1.55389
$86$	7.17683	0.773898
$87$	−12.8577	−1.37849
$88$	1.52146	0.162188
$89$	−7.21512	−0.764801	−0.382401	−	0.923997i	$-0.624903\pi$
$89$	−7.21512	−0.764801	−0.382401	+	0.923997i	$0.624903\pi$
$90$	0.394889	0.0416250
$91$	−13.6353	−1.42937
$92$	6.81108	0.710104
$93$	−8.78911	−0.911388
$94$	−6.21800	−0.641337
$95$	−3.04090	−0.311990
$96$	1.77113	0.180766
$97$	−4.40675	−0.447437	−0.223719	−	0.974654i	$-0.571820\pi$
$97$	−4.40675	−0.447437	−0.223719	+	0.974654i	$0.571820\pi$
$98$	1.48765	0.150275
$99$	−0.208313	−0.0209362
$100$	3.31837	0.331837
$101$	4.19383	0.417301	0.208651	−	0.977990i	$-0.433093\pi$
$101$	4.19383	0.417301	0.208651	+	0.977990i	$0.433093\pi$
$102$	8.79754	0.871086
$103$	2.02392	0.199423	0.0997113	−	0.995016i	$-0.468208\pi$
$103$	2.02392	0.199423	0.0997113	+	0.995016i	$0.468208\pi$
$104$	−5.80761	−0.569483
$105$	−11.9933	−1.17043
$106$	3.64768	0.354294
$107$	9.91911	0.958916	0.479458	−	0.877565i	$-0.340833\pi$
$107$	9.91911	0.958916	0.479458	+	0.877565i	$0.340833\pi$
$108$	5.07091	0.487948
$109$	−2.61394	−0.250370	−0.125185	−	0.992133i	$-0.539952\pi$
$109$	−2.61394	−0.250370	−0.125185	+	0.992133i	$0.539952\pi$
$110$	−4.38812	−0.418391
$111$	−9.89702	−0.939384
$112$	−2.34784	−0.221850
$113$	−4.78067	−0.449728	−0.224864	−	0.974390i	$-0.572194\pi$
$113$	−4.78067	−0.449728	−0.224864	+	0.974390i	$0.572194\pi$
$114$	1.86739	0.174897
$115$	−19.6442	−1.83183
$116$	7.25956	0.674034
$117$	0.795158	0.0735124
$118$	−3.05294	−0.281045
$119$	−11.6621	−1.06907
$120$	−5.10823	−0.466316
$121$	−8.68517	−0.789561
$122$	9.14586	0.828027
$123$	1.83419	0.165383
$124$	4.96242	0.445638
$125$	4.85008	0.433804
$126$	0.321458	0.0286378
$127$	3.27560	0.290663	0.145331	−	0.989383i	$-0.453575\pi$
$127$	3.27560	0.290663	0.145331	+	0.989383i	$0.453575\pi$
$128$	−1.00000	−0.0883883
$129$	12.7111	1.11915
$130$	16.7501	1.46908
$131$	11.4854	1.00349	0.501744	−	0.865016i	$-0.332692\pi$
$131$	11.4854	1.00349	0.501744	+	0.865016i	$0.332692\pi$
$132$	2.69470	0.234544
$133$	−2.47544	−0.214648
$134$	−2.45198	−0.211819
$135$	−14.6253	−1.25875
$136$	−4.96718	−0.425932
$137$	20.3701	1.74034	0.870168	−	0.492755i	$-0.164010\pi$
$137$	20.3701	1.74034	0.870168	+	0.492755i	$0.164010\pi$
$138$	12.0633	1.02690
$139$	−5.40670	−0.458591	−0.229295	−	0.973357i	$-0.573642\pi$
$139$	−5.40670	−0.458591	−0.229295	+	0.973357i	$0.573642\pi$
$140$	6.77155	0.572300
$141$	−11.0129	−0.927454
$142$	2.98139	0.250193
$143$	−8.83602	−0.738905
$144$	0.136917	0.0114097
$145$	−20.9377	−1.73878
$146$	0.456785	0.0378038
$147$	2.63482	0.217316
$148$	5.58796	0.459327
$149$	16.3338	1.33812	0.669060	−	0.743208i	$-0.266697\pi$
$149$	16.3338	1.33812	0.669060	+	0.743208i	$0.266697\pi$
$150$	5.87729	0.479878
$151$	−13.8018	−1.12317	−0.561586	−	0.827419i	$-0.689808\pi$
$151$	−13.8018	−1.12317	−0.561586	+	0.827419i	$0.689808\pi$
$152$	−1.05435	−0.0855188
$153$	0.680089	0.0549820
$154$	−3.57214	−0.287851
$155$	−14.3124	−1.14960
$156$	−10.2861	−0.823543
$157$	−9.28303	−0.740866	−0.370433	−	0.928859i	$-0.620791\pi$
$157$	−9.28303	−0.740866	−0.370433	+	0.928859i	$0.620791\pi$
$158$	−8.22600	−0.654425
$159$	6.46053	0.512353
$160$	2.88416	0.228013
$161$	−15.9913	−1.26029
$162$	9.39200	0.737906
$163$	20.6300	1.61587	0.807933	−	0.589274i	$-0.200586\pi$
$163$	20.6300	1.61587	0.807933	+	0.589274i	$0.200586\pi$
$164$	−1.03560	−0.0808667
$165$	−7.77195	−0.605046
$166$	3.16041	0.245295
$167$	10.1290	0.783803	0.391902	−	0.920007i	$-0.371817\pi$
$167$	10.1290	0.783803	0.391902	+	0.920007i	$0.371817\pi$
$168$	−4.15834	−0.320823
$169$	20.7283	1.59448
$170$	14.3261	1.09876
$171$	0.144358	0.0110393
$172$	−7.17683	−0.547228
$173$	−21.2182	−1.61319	−0.806594	−	0.591106i	$-0.798691\pi$
$173$	−21.2182	−1.61319	−0.806594	+	0.591106i	$0.798691\pi$
$174$	12.8577	0.974737
$175$	−7.79101	−0.588945
$176$	−1.52146	−0.114684
$177$	−5.40716	−0.406427
$178$	7.21512	0.540796
$179$	11.5608	0.864091	0.432046	−	0.901852i	$-0.357792\pi$
$179$	11.5608	0.864091	0.432046	+	0.901852i	$0.357792\pi$
$180$	−0.394889	−0.0294333
$181$	12.1403	0.902382	0.451191	−	0.892427i	$-0.350999\pi$
$181$	12.1403	0.902382	0.451191	+	0.892427i	$0.350999\pi$
$182$	13.6353	1.01072
$183$	16.1985	1.19743
$184$	−6.81108	−0.502119
$185$	−16.1166	−1.18491
$186$	8.78911	0.644449
$187$	−7.55735	−0.552648
$188$	6.21800	0.453494
$189$	−11.9057	−0.866011
$190$	3.04090	0.220610
$191$	6.98966	0.505754	0.252877	−	0.967498i	$-0.418623\pi$
$191$	6.98966	0.505754	0.252877	+	0.967498i	$0.418623\pi$
$192$	−1.77113	−0.127821
$193$	8.21604	0.591403	0.295702	−	0.955280i	$-0.404447\pi$
$193$	8.21604	0.591403	0.295702	+	0.955280i	$0.404447\pi$
$194$	4.40675	0.316386
$195$	29.6666	2.12447
$196$	−1.48765	−0.106260
$197$	2.47401	0.176266	0.0881329	−	0.996109i	$-0.471910\pi$
$197$	2.47401	0.176266	0.0881329	+	0.996109i	$0.471910\pi$
$198$	0.208313	0.0148041
$199$	8.67889	0.615230	0.307615	−	0.951511i	$-0.400469\pi$
$199$	8.67889	0.615230	0.307615	+	0.951511i	$0.400469\pi$
$200$	−3.31837	−0.234644
$201$	−4.34278	−0.306316
$202$	−4.19383	−0.295077
$203$	−17.0443	−1.19628
$204$	−8.79754	−0.615951
$205$	2.98683	0.208610
$206$	−2.02392	−0.141013
$207$	0.932550	0.0648167
$208$	5.80761	0.402685
$209$	−1.60414	−0.110961
$210$	11.9933	0.827617
$211$	16.2561	1.11911	0.559557	−	0.828792i	$-0.310971\pi$
$211$	16.2561	1.11911	0.559557	+	0.828792i	$0.310971\pi$
$212$	−3.64768	−0.250524
$213$	5.28044	0.361810
$214$	−9.91911	−0.678056
$215$	20.6991	1.41167
$216$	−5.07091	−0.345031
$217$	−11.6510	−0.790919
$218$	2.61394	0.177038
$219$	0.809027	0.0546690
$220$	4.38812	0.295847
$221$	28.8474	1.94049
$222$	9.89702	0.664245
$223$	14.4036	0.964536	0.482268	−	0.876024i	$-0.339813\pi$
$223$	14.4036	0.964536	0.482268	+	0.876024i	$0.339813\pi$
$224$	2.34784	0.156872
$225$	0.454341	0.0302894
$226$	4.78067	0.318006
$227$	−15.7901	−1.04802	−0.524012	−	0.851711i	$-0.675565\pi$
$227$	−15.7901	−1.04802	−0.524012	+	0.851711i	$0.675565\pi$
$228$	−1.86739	−0.123671
$229$	−23.9139	−1.58027	−0.790136	−	0.612931i	$-0.789990\pi$
$229$	−23.9139	−1.58027	−0.790136	+	0.612931i	$0.789990\pi$
$230$	19.6442	1.29530
$231$	−6.32673	−0.416269
$232$	−7.25956	−0.476614
$233$	−16.2537	−1.06482	−0.532409	−	0.846487i	$-0.678713\pi$
$233$	−16.2537	−1.06482	−0.532409	+	0.846487i	$0.678713\pi$
$234$	−0.795158	−0.0519811
$235$	−17.9337	−1.16987
$236$	3.05294	0.198729
$237$	−14.5693	−0.946381
$238$	11.6621	0.755944
$239$	8.61903	0.557519	0.278759	−	0.960361i	$-0.410077\pi$
$239$	8.61903	0.557519	0.278759	+	0.960361i	$0.410077\pi$
$240$	5.10823	0.329735
$241$	−12.0780	−0.778011	−0.389006	−	0.921235i	$-0.627181\pi$
$241$	−12.0780	−0.778011	−0.389006	+	0.921235i	$0.627181\pi$
$242$	8.68517	0.558304
$243$	1.42178	0.0912075
$244$	−9.14586	−0.585504
$245$	4.29061	0.274117
$246$	−1.83419	−0.116943
$247$	6.12323	0.389612
$248$	−4.96242	−0.315114
$249$	5.59751	0.354727
$250$	−4.85008	−0.306746
$251$	13.9375	0.879728	0.439864	−	0.898064i	$-0.355027\pi$
$251$	13.9375	0.879728	0.439864	+	0.898064i	$0.355027\pi$
$252$	−0.321458	−0.0202500
$253$	−10.3628	−0.651501
$254$	−3.27560	−0.205530
$255$	25.3735	1.58895
$256$	1.00000	0.0625000
$257$	5.76125	0.359377	0.179689	−	0.983724i	$-0.442491\pi$
$257$	5.76125	0.359377	0.179689	+	0.983724i	$0.442491\pi$
$258$	−12.7111	−0.791361
$259$	−13.1196	−0.815214
$260$	−16.7501	−1.03879
$261$	0.993955	0.0615243
$262$	−11.4854	−0.709573
$263$	8.48893	0.523450	0.261725	−	0.965143i	$-0.415709\pi$
$263$	8.48893	0.523450	0.261725	+	0.965143i	$0.415709\pi$
$264$	−2.69470	−0.165848
$265$	10.5205	0.646269
$266$	2.47544	0.151779
$267$	12.7789	0.782059
$268$	2.45198	0.149778
$269$	25.0944	1.53003	0.765017	−	0.644010i	$-0.222731\pi$
$269$	25.0944	1.53003	0.765017	+	0.644010i	$0.222731\pi$
$270$	14.6253	0.890067
$271$	10.6858	0.649119	0.324559	−	0.945865i	$-0.394784\pi$
$271$	10.6858	0.649119	0.324559	+	0.945865i	$0.394784\pi$
$272$	4.96718	0.301179
$273$	24.1500	1.46162
$274$	−20.3701	−1.23060
$275$	−5.04876	−0.304452
$276$	−12.0633	−0.726128
$277$	−20.8626	−1.25351	−0.626755	−	0.779216i	$-0.715617\pi$
$277$	−20.8626	−1.25351	−0.626755	+	0.779216i	$0.715617\pi$
$278$	5.40670	0.324273
$279$	0.679437	0.0406768
$280$	−6.77155	−0.404677
$281$	−23.9725	−1.43008	−0.715040	−	0.699084i	$-0.753591\pi$
$281$	−23.9725	−1.43008	−0.715040	+	0.699084i	$0.753591\pi$
$282$	11.0129	0.655809
$283$	−8.31525	−0.494290	−0.247145	−	0.968978i	$-0.579492\pi$
$283$	−8.31525	−0.494290	−0.247145	+	0.968978i	$0.579492\pi$
$284$	−2.98139	−0.176913
$285$	5.38585	0.319030
$286$	8.83602	0.522485
$287$	2.43142	0.143522
$288$	−0.136917	−0.00806789
$289$	7.67286	0.451345
$290$	20.9377	1.22951
$291$	7.80494	0.457534
$292$	−0.456785	−0.0267313
$293$	14.5178	0.848138	0.424069	−	0.905630i	$-0.360601\pi$
$293$	14.5178	0.848138	0.424069	+	0.905630i	$0.360601\pi$
$294$	−2.63482	−0.153666
$295$	−8.80515	−0.512656
$296$	−5.58796	−0.324793
$297$	−7.71516	−0.447679
$298$	−16.3338	−0.946194
$299$	39.5561	2.28759
$300$	−5.87729	−0.339325
$301$	16.8501	0.971221
$302$	13.8018	0.794202
$303$	−7.42783	−0.426718
$304$	1.05435	0.0604709
$305$	26.3781	1.51041
$306$	−0.680089	−0.0388781
$307$	15.4305	0.880664	0.440332	−	0.897835i	$-0.354861\pi$
$307$	15.4305	0.880664	0.440332	+	0.897835i	$0.354861\pi$
$308$	3.57214	0.203541
$309$	−3.58463	−0.203923
$310$	14.3124	0.812890
$311$	5.45693	0.309434	0.154717	−	0.987959i	$-0.450553\pi$
$311$	5.45693	0.309434	0.154717	+	0.987959i	$0.450553\pi$
$312$	10.2861	0.582333
$313$	−8.83420	−0.499338	−0.249669	−	0.968331i	$-0.580322\pi$
$313$	−8.83420	−0.499338	−0.249669	+	0.968331i	$0.580322\pi$
$314$	9.28303	0.523872
$315$	0.927137	0.0522383
$316$	8.22600	0.462749
$317$	4.05847	0.227946	0.113973	−	0.993484i	$-0.463642\pi$
$317$	4.05847	0.227946	0.113973	+	0.993484i	$0.463642\pi$
$318$	−6.46053	−0.362289
$319$	−11.0451	−0.618407
$320$	−2.88416	−0.161229
$321$	−17.5681	−0.980554
$322$	15.9913	0.891162
$323$	5.23713	0.291402
$324$	−9.39200	−0.521778
$325$	19.2718	1.06901
$326$	−20.6300	−1.14259
$327$	4.62964	0.256020
$328$	1.03560	0.0571814
$329$	−14.5989	−0.804861
$330$	7.77195	0.427832
$331$	10.0363	0.551646	0.275823	−	0.961209i	$-0.411050\pi$
$331$	10.0363	0.551646	0.275823	+	0.961209i	$0.411050\pi$
$332$	−3.16041	−0.173450
$333$	0.765084	0.0419264
$334$	−10.1290	−0.554233
$335$	−7.07190	−0.386379
$336$	4.15834	0.226856
$337$	−31.2419	−1.70185	−0.850926	−	0.525286i	$-0.823959\pi$
$337$	−31.2419	−1.70185	−0.850926	+	0.525286i	$0.823959\pi$
$338$	−20.7283	−1.12747
$339$	8.46721	0.459876
$340$	−14.3261	−0.776944
$341$	−7.55010	−0.408861
$342$	−0.144358	−0.00780596
$343$	19.9276	1.07599
$344$	7.17683	0.386949
$345$	34.7926	1.87317
$346$	21.2182	1.14070
$347$	−34.1317	−1.83228	−0.916142	−	0.400854i	$-0.868714\pi$
$347$	−34.1317	−1.83228	−0.916142	+	0.400854i	$0.868714\pi$
$348$	−12.8577	−0.689243
$349$	−3.56334	−0.190741	−0.0953706	−	0.995442i	$-0.530404\pi$
$349$	−3.56334	−0.190741	−0.0953706	+	0.995442i	$0.530404\pi$
$350$	7.79101	0.416447
$351$	29.4498	1.57192
$352$	1.52146	0.0810939
$353$	9.80476	0.521855	0.260927	−	0.965358i	$-0.415972\pi$
$353$	9.80476	0.521855	0.260927	+	0.965358i	$0.415972\pi$
$354$	5.40716	0.287387
$355$	8.59880	0.456377
$356$	−7.21512	−0.382401
$357$	20.6552	1.09319
$358$	−11.5608	−0.611005
$359$	15.1721	0.800752	0.400376	−	0.916351i	$-0.368880\pi$
$359$	15.1721	0.800752	0.400376	+	0.916351i	$0.368880\pi$
$360$	0.394889	0.0208125
$361$	−17.8884	−0.941492
$362$	−12.1403	−0.638081
$363$	15.3826	0.807377
$364$	−13.6353	−0.714686
$365$	1.31744	0.0689580
$366$	−16.1985	−0.846711
$367$	−5.88777	−0.307339	−0.153670	−	0.988122i	$-0.549109\pi$
$367$	−5.88777	−0.307339	−0.153670	+	0.988122i	$0.549109\pi$
$368$	6.81108	0.355052
$369$	−0.141791	−0.00738133
$370$	16.1166	0.837860
$371$	8.56417	0.444630
$372$	−8.78911	−0.455694
$373$	9.81999	0.508460	0.254230	−	0.967144i	$-0.418178\pi$
$373$	9.81999	0.508460	0.254230	+	0.967144i	$0.418178\pi$
$374$	7.55735	0.390781
$375$	−8.59014	−0.443593
$376$	−6.21800	−0.320669
$377$	42.1607	2.17139
$378$	11.9057	0.612362
$379$	12.8395	0.659523	0.329761	−	0.944064i	$-0.393032\pi$
$379$	12.8395	0.659523	0.329761	+	0.944064i	$0.393032\pi$
$380$	−3.04090	−0.155995
$381$	−5.80154	−0.297222
$382$	−6.98966	−0.357622
$383$	−27.7289	−1.41688	−0.708439	−	0.705772i	$-0.750600\pi$
$383$	−27.7289	−1.41688	−0.708439	+	0.705772i	$0.750600\pi$
$384$	1.77113	0.0903828
$385$	−10.3026	−0.525070
$386$	−8.21604	−0.418185
$387$	−0.982628	−0.0499498
$388$	−4.40675	−0.223719
$389$	1.32245	0.0670510	0.0335255	−	0.999438i	$-0.489327\pi$
$389$	1.32245	0.0670510	0.0335255	+	0.999438i	$0.489327\pi$
$390$	−29.6666	−1.50223
$391$	33.8318	1.71095
$392$	1.48765	0.0751374
$393$	−20.3422	−1.02613
$394$	−2.47401	−0.124639
$395$	−23.7251	−1.19374
$396$	−0.208313	−0.0104681
$397$	−14.6659	−0.736062	−0.368031	−	0.929814i	$-0.619968\pi$
$397$	−14.6659	−0.736062	−0.368031	+	0.929814i	$0.619968\pi$
$398$	−8.67889	−0.435033
$399$	4.38433	0.219491
$400$	3.31837	0.165919
$401$	19.7146	0.984498	0.492249	−	0.870454i	$-0.336175\pi$
$401$	19.7146	0.984498	0.492249	+	0.870454i	$0.336175\pi$
$402$	4.34278	0.216598
$403$	28.8198	1.43561
$404$	4.19383	0.208651
$405$	27.0880	1.34602
$406$	17.0443	0.845894
$407$	−8.50183	−0.421420
$408$	8.79754	0.435543
$409$	8.61892	0.426178	0.213089	−	0.977033i	$-0.431648\pi$
$409$	8.61892	0.426178	0.213089	+	0.977033i	$0.431648\pi$
$410$	−2.98683	−0.147509
$411$	−36.0782	−1.77961
$412$	2.02392	0.0997113
$413$	−7.16780	−0.352705
$414$	−0.932550	−0.0458323
$415$	9.11512	0.447443
$416$	−5.80761	−0.284741
$417$	9.57600	0.468939
$418$	1.60414	0.0784612
$419$	−2.61729	−0.127863	−0.0639314	−	0.997954i	$-0.520364\pi$
$419$	−2.61729	−0.127863	−0.0639314	+	0.997954i	$0.520364\pi$
$420$	−11.9933	−0.585214
$421$	20.7303	1.01033	0.505166	−	0.863022i	$-0.331431\pi$
$421$	20.7303	1.01033	0.505166	+	0.863022i	$0.331431\pi$
$422$	−16.2561	−0.791333
$423$	0.851347	0.0413939
$424$	3.64768	0.177147
$425$	16.4830	0.799541
$426$	−5.28044	−0.255838
$427$	21.4730	1.03915
$428$	9.91911	0.479458
$429$	15.6498	0.755578
$430$	−20.6991	−0.998200
$431$	16.9470	0.816307	0.408154	−	0.912913i	$-0.366173\pi$
$431$	16.9470	0.816307	0.408154	+	0.912913i	$0.366173\pi$
$432$	5.07091	0.243974
$433$	−10.9414	−0.525810	−0.262905	−	0.964822i	$-0.584681\pi$
$433$	−10.9414	−0.525810	−0.262905	+	0.964822i	$0.584681\pi$
$434$	11.6510	0.559264
$435$	37.0835	1.77802
$436$	−2.61394	−0.125185
$437$	7.18124	0.343525
$438$	−0.809027	−0.0386568
$439$	−20.2536	−0.966653	−0.483327	−	0.875440i	$-0.660572\pi$
$439$	−20.2536	−0.966653	−0.483327	+	0.875440i	$0.660572\pi$
$440$	−4.38812	−0.209196
$441$	−0.203683	−0.00969921
$442$	−28.8474	−1.37213
$443$	−36.5646	−1.73724	−0.868618	−	0.495483i	$-0.834991\pi$
$443$	−36.5646	−1.73724	−0.868618	+	0.495483i	$0.834991\pi$
$444$	−9.89702	−0.469692
$445$	20.8096	0.986467
$446$	−14.4036	−0.682030
$447$	−28.9294	−1.36831
$448$	−2.34784	−0.110925
$449$	6.26587	0.295705	0.147852	−	0.989009i	$-0.452764\pi$
$449$	6.26587	0.295705	0.147852	+	0.989009i	$0.452764\pi$
$450$	−0.454341	−0.0214178
$451$	1.57562	0.0741930
$452$	−4.78067	−0.224864
$453$	24.4448	1.14852
$454$	15.7901	0.741065
$455$	39.3265	1.84365
$456$	1.86739	0.0874485
$457$	−30.3431	−1.41939	−0.709695	−	0.704509i	$-0.751167\pi$
$457$	−30.3431	−1.41939	−0.709695	+	0.704509i	$0.751167\pi$
$458$	23.9139	1.11742
$459$	25.1881	1.17568
$460$	−19.6442	−0.915917
$461$	−4.29219	−0.199907	−0.0999536	−	0.994992i	$-0.531869\pi$
$461$	−4.29219	−0.199907	−0.0999536	+	0.994992i	$0.531869\pi$
$462$	6.32673	0.294346
$463$	−34.8940	−1.62166	−0.810830	−	0.585281i	$-0.800984\pi$
$463$	−34.8940	−1.62166	−0.810830	+	0.585281i	$0.800984\pi$
$464$	7.25956	0.337017
$465$	25.3492	1.17554
$466$	16.2537	0.752940
$467$	−6.83449	−0.316263	−0.158131	−	0.987418i	$-0.550547\pi$
$467$	−6.83449	−0.316263	−0.158131	+	0.987418i	$0.550547\pi$
$468$	0.795158	0.0367562
$469$	−5.75686	−0.265827
$470$	17.9337	0.827220
$471$	16.4415	0.757584
$472$	−3.05294	−0.140523
$473$	10.9192	0.502067
$474$	14.5693	0.669192
$475$	3.49872	0.160532
$476$	−11.6621	−0.534533
$477$	−0.499428	−0.0228672
$478$	−8.61903	−0.394225
$479$	−14.5476	−0.664698	−0.332349	−	0.943156i	$-0.607841\pi$
$479$	−14.5476	−0.664698	−0.332349	+	0.943156i	$0.607841\pi$
$480$	−5.10823	−0.233158
$481$	32.4527	1.47971
$482$	12.0780	0.550137
$483$	28.3228	1.28873
$484$	−8.68517	−0.394780
$485$	12.7098	0.577120
$486$	−1.42178	−0.0644934
$487$	−22.4709	−1.01826	−0.509128	−	0.860691i	$-0.670032\pi$
$487$	−22.4709	−1.01826	−0.509128	+	0.860691i	$0.670032\pi$
$488$	9.14586	0.414014
$489$	−36.5385	−1.65233
$490$	−4.29061	−0.193830
$491$	−19.3497	−0.873240	−0.436620	−	0.899646i	$-0.643825\pi$
$491$	−19.3497	−0.873240	−0.436620	+	0.899646i	$0.643825\pi$
$492$	1.83419	0.0826915
$493$	36.0595	1.62404
$494$	−6.12323	−0.275497
$495$	0.600807	0.0270043
$496$	4.96242	0.222819
$497$	6.99982	0.313985
$498$	−5.59751	−0.250830
$499$	−24.2643	−1.08622	−0.543109	−	0.839662i	$-0.682753\pi$
$499$	−24.2643	−1.08622	−0.543109	+	0.839662i	$0.682753\pi$
$500$	4.85008	0.216902
$501$	−17.9398	−0.801490
$502$	−13.9375	−0.622062
$503$	18.6064	0.829619	0.414810	−	0.909908i	$-0.363848\pi$
$503$	18.6064	0.829619	0.414810	+	0.909908i	$0.363848\pi$
$504$	0.321458	0.0143189
$505$	−12.0957	−0.538250
$506$	10.3628	0.460681
$507$	−36.7126	−1.63046
$508$	3.27560	0.145331
$509$	11.0525	0.489895	0.244947	−	0.969536i	$-0.421229\pi$
$509$	11.0525	0.489895	0.244947	+	0.969536i	$0.421229\pi$
$510$	−25.3735	−1.12356
$511$	1.07246	0.0474427
$512$	−1.00000	−0.0441942
$513$	5.34649	0.236053
$514$	−5.76125	−0.254118
$515$	−5.83731	−0.257222
$516$	12.7111	0.559576
$517$	−9.46041	−0.416068
$518$	13.1196	0.576444
$519$	37.5802	1.64959
$520$	16.7501	0.734539
$521$	−7.59056	−0.332548	−0.166274	−	0.986080i	$-0.553174\pi$
$521$	−7.59056	−0.332548	−0.166274	+	0.986080i	$0.553174\pi$
$522$	−0.993955	−0.0435042
$523$	−24.2870	−1.06200	−0.530998	−	0.847373i	$-0.678183\pi$
$523$	−24.2870	−1.06200	−0.530998	+	0.847373i	$0.678183\pi$
$524$	11.4854	0.501744
$525$	13.7989	0.602235
$526$	−8.48893	−0.370135
$527$	24.6492	1.07374
$528$	2.69470	0.117272
$529$	23.3908	1.01699
$530$	−10.5205	−0.456981
$531$	0.417998	0.0181395
$532$	−2.47544	−0.107324
$533$	−6.01435	−0.260511
$534$	−12.7789	−0.552999
$535$	−28.6083	−1.23684
$536$	−2.45198	−0.105909
$537$	−20.4756	−0.883589
$538$	−25.0944	−1.08190
$539$	2.26339	0.0974910
$540$	−14.6253	−0.629373
$541$	−12.2350	−0.526026	−0.263013	−	0.964792i	$-0.584716\pi$
$541$	−12.2350	−0.526026	−0.263013	+	0.964792i	$0.584716\pi$
$542$	−10.6858	−0.458996
$543$	−21.5021	−0.922744
$544$	−4.96718	−0.212966
$545$	7.53902	0.322936
$546$	−24.1500	−1.03352
$547$	−25.9473	−1.10943	−0.554713	−	0.832042i	$-0.687172\pi$
$547$	−25.9473	−1.10943	−0.554713	+	0.832042i	$0.687172\pi$
$548$	20.3701	0.870168
$549$	−1.25222	−0.0534435
$550$	5.04876	0.215280
$551$	7.65410	0.326075
$552$	12.0633	0.513450
$553$	−19.3133	−0.821286
$554$	20.8626	0.886365
$555$	28.5446	1.21165
$556$	−5.40670	−0.229295
$557$	12.1509	0.514848	0.257424	−	0.966298i	$-0.417126\pi$
$557$	12.1509	0.514848	0.257424	+	0.966298i	$0.417126\pi$
$558$	−0.679437	−0.0287629
$559$	−41.6802	−1.76289
$560$	6.77155	0.286150
$561$	13.3851	0.565118
$562$	23.9725	1.01122
$563$	1.61566	0.0680919	0.0340459	−	0.999420i	$-0.489161\pi$
$563$	1.61566	0.0680919	0.0340459	+	0.999420i	$0.489161\pi$
$564$	−11.0129	−0.463727
$565$	13.7882	0.580075
$566$	8.31525	0.349516
$567$	22.0509	0.926052
$568$	2.98139	0.125096
$569$	−4.90195	−0.205500	−0.102750	−	0.994707i	$-0.532764\pi$
$569$	−4.90195	−0.205500	−0.102750	+	0.994707i	$0.532764\pi$
$570$	−5.38585	−0.225588
$571$	−12.0471	−0.504157	−0.252078	−	0.967707i	$-0.581114\pi$
$571$	−12.0471	−0.504157	−0.252078	+	0.967707i	$0.581114\pi$
$572$	−8.83602	−0.369453
$573$	−12.3796	−0.517166
$574$	−2.43142	−0.101486
$575$	22.6017	0.942556
$576$	0.136917	0.00570486
$577$	−37.4114	−1.55746	−0.778729	−	0.627361i	$-0.784135\pi$
$577$	−37.4114	−1.55746	−0.778729	+	0.627361i	$0.784135\pi$
$578$	−7.67286	−0.319149
$579$	−14.5517	−0.604748
$580$	−20.9377	−0.869392
$581$	7.42013	0.307839
$582$	−7.80494	−0.323525
$583$	5.54979	0.229849
$584$	0.456785	0.0189019
$585$	−2.29336	−0.0948188
$586$	−14.5178	−0.599724
$587$	40.9719	1.69109	0.845546	−	0.533903i	$-0.179275\pi$
$587$	40.9719	1.69109	0.845546	+	0.533903i	$0.179275\pi$
$588$	2.63482	0.108658
$589$	5.23211	0.215585
$590$	8.80515	0.362502
$591$	−4.38180	−0.180243
$592$	5.58796	0.229664
$593$	−28.2439	−1.15984	−0.579918	−	0.814675i	$-0.696916\pi$
$593$	−28.2439	−1.15984	−0.579918	+	0.814675i	$0.696916\pi$
$594$	7.71516	0.316557
$595$	33.6355	1.37892
$596$	16.3338	0.669060
$597$	−15.3715	−0.629113
$598$	−39.5561	−1.61757
$599$	−19.3115	−0.789045	−0.394522	−	0.918886i	$-0.629090\pi$
$599$	−19.3115	−0.789045	−0.394522	+	0.918886i	$0.629090\pi$
$600$	5.87729	0.239939
$601$	27.7007	1.12994	0.564968	−	0.825113i	$-0.308889\pi$
$601$	27.7007	1.12994	0.564968	+	0.825113i	$0.308889\pi$
$602$	−16.8501	−0.686757
$603$	0.335717	0.0136714
$604$	−13.8018	−0.561586
$605$	25.0494	1.01840
$606$	7.42783	0.301735
$607$	−17.6388	−0.715935	−0.357968	−	0.933734i	$-0.616530\pi$
$607$	−17.6388	−0.715935	−0.357968	+	0.933734i	$0.616530\pi$
$608$	−1.05435	−0.0427594
$609$	30.1877	1.22327
$610$	−26.3781	−1.06802
$611$	36.1117	1.46092
$612$	0.680089	0.0274910
$613$	35.9689	1.45277	0.726385	−	0.687288i	$-0.241199\pi$
$613$	35.9689	1.45277	0.726385	+	0.687288i	$0.241199\pi$
$614$	−15.4305	−0.622723
$615$	−5.29008	−0.213317
$616$	−3.57214	−0.143926
$617$	29.4110	1.18404	0.592022	−	0.805922i	$-0.298330\pi$
$617$	29.4110	1.18404	0.592022	+	0.805922i	$0.298330\pi$
$618$	3.58463	0.144195
$619$	11.3628	0.456710	0.228355	−	0.973578i	$-0.426665\pi$
$619$	11.3628	0.456710	0.228355	+	0.973578i	$0.426665\pi$
$620$	−14.3124	−0.574800
$621$	34.5383	1.38598
$622$	−5.45693	−0.218803
$623$	16.9399	0.678685
$624$	−10.2861	−0.411772
$625$	−30.5803	−1.22321
$626$	8.83420	0.353086
$627$	2.84115	0.113465
$628$	−9.28303	−0.370433
$629$	27.7564	1.10672
$630$	−0.927137	−0.0369380
$631$	35.4192	1.41002	0.705009	−	0.709199i	$-0.250943\pi$
$631$	35.4192	1.41002	0.705009	+	0.709199i	$0.250943\pi$
$632$	−8.22600	−0.327213
$633$	−28.7917	−1.14437
$634$	−4.05847	−0.161182
$635$	−9.44737	−0.374907
$636$	6.46053	0.256177
$637$	−8.63966	−0.342316
$638$	11.0451	0.437280
$639$	−0.408202	−0.0161482
$640$	2.88416	0.114006
$641$	11.5312	0.455454	0.227727	−	0.973725i	$-0.426871\pi$
$641$	11.5312	0.455454	0.227727	+	0.973725i	$0.426871\pi$
$642$	17.5681	0.693356
$643$	5.89123	0.232327	0.116164	−	0.993230i	$-0.462940\pi$
$643$	5.89123	0.232327	0.116164	+	0.993230i	$0.462940\pi$
$644$	−15.9913	−0.630147
$645$	−36.6609	−1.44352
$646$	−5.23713	−0.206052
$647$	28.6755	1.12735	0.563675	−	0.825997i	$-0.309387\pi$
$647$	28.6755	1.12735	0.563675	+	0.825997i	$0.309387\pi$
$648$	9.39200	0.368953
$649$	−4.64491	−0.182329
$650$	−19.2718	−0.755903
$651$	20.6354	0.808766
$652$	20.6300	0.807933
$653$	22.3629	0.875127	0.437563	−	0.899188i	$-0.355842\pi$
$653$	22.3629	0.875127	0.437563	+	0.899188i	$0.355842\pi$
$654$	−4.62964	−0.181033
$655$	−33.1258	−1.29433
$656$	−1.03560	−0.0404334
$657$	−0.0625414	−0.00243997
$658$	14.5989	0.569123
$659$	−35.4827	−1.38221	−0.691105	−	0.722754i	$-0.742876\pi$
$659$	−35.4827	−1.38221	−0.691105	+	0.722754i	$0.742876\pi$
$660$	−7.77195	−0.302523
$661$	21.3109	0.828899	0.414449	−	0.910072i	$-0.363974\pi$
$661$	21.3109	0.828899	0.414449	+	0.910072i	$0.363974\pi$
$662$	−10.0363	−0.390072
$663$	−51.0926	−1.98427
$664$	3.16041	0.122648
$665$	7.13956	0.276860
$666$	−0.765084	−0.0296464
$667$	49.4455	1.91454
$668$	10.1290	0.391902
$669$	−25.5107	−0.986300
$670$	7.07190	0.273211
$671$	13.9150	0.537184
$672$	−4.15834	−0.160411
$673$	−6.86512	−0.264631	−0.132316	−	0.991208i	$-0.542241\pi$
$673$	−6.86512	−0.264631	−0.132316	+	0.991208i	$0.542241\pi$
$674$	31.2419	1.20339
$675$	16.8272	0.647678
$676$	20.7283	0.797242
$677$	−26.5685	−1.02111	−0.510555	−	0.859845i	$-0.670560\pi$
$677$	−26.5685	−1.02111	−0.510555	+	0.859845i	$0.670560\pi$
$678$	−8.46721	−0.325181
$679$	10.3463	0.397056
$680$	14.3261	0.549382
$681$	27.9663	1.07167
$682$	7.55010	0.289108
$683$	−21.5816	−0.825798	−0.412899	−	0.910777i	$-0.635484\pi$
$683$	−21.5816	−0.825798	−0.412899	+	0.910777i	$0.635484\pi$
$684$	0.144358	0.00551965
$685$	−58.7506	−2.24475
$686$	−19.9276	−0.760841
$687$	42.3547	1.61593
$688$	−7.17683	−0.273614
$689$	−21.1843	−0.807057
$690$	−34.7926	−1.32453
$691$	8.71724	0.331620	0.165810	−	0.986158i	$-0.446976\pi$
$691$	8.71724	0.331620	0.165810	+	0.986158i	$0.446976\pi$
$692$	−21.2182	−0.806594
$693$	0.489085	0.0185788
$694$	34.1317	1.29562
$695$	15.5938	0.591506
$696$	12.8577	0.487368
$697$	−5.14401	−0.194843
$698$	3.56334	0.134874
$699$	28.7876	1.08885
$700$	−7.79101	−0.294473
$701$	36.4201	1.37557	0.687784	−	0.725915i	$-0.258584\pi$
$701$	36.4201	1.37557	0.687784	+	0.725915i	$0.258584\pi$
$702$	−29.4498	−1.11151
$703$	5.89164	0.222208
$704$	−1.52146	−0.0573421
$705$	31.7630	1.19626
$706$	−9.80476	−0.369007
$707$	−9.84643	−0.370313
$708$	−5.40716	−0.203213
$709$	−11.8397	−0.444650	−0.222325	−	0.974973i	$-0.571365\pi$
$709$	−11.8397	−0.444650	−0.222325	+	0.974973i	$0.571365\pi$
$710$	−8.59880	−0.322707
$711$	1.12628	0.0422386
$712$	7.21512	0.270398
$713$	33.7994	1.26580
$714$	−20.6552	−0.773002
$715$	25.4845	0.953066
$716$	11.5608	0.432046
$717$	−15.2655	−0.570099
$718$	−15.1721	−0.566217
$719$	−9.51972	−0.355026	−0.177513	−	0.984118i	$-0.556805\pi$
$719$	−9.51972	−0.355026	−0.177513	+	0.984118i	$0.556805\pi$
$720$	−0.394889	−0.0147167
$721$	−4.75184	−0.176968
$722$	17.8884	0.665736
$723$	21.3917	0.795567
$724$	12.1403	0.451191
$725$	24.0899	0.894678
$726$	−15.3826	−0.570902
$727$	0.160684	0.00595945	0.00297972	−	0.999996i	$-0.499052\pi$
$727$	0.160684	0.00595945	0.00297972	+	0.999996i	$0.499052\pi$
$728$	13.6353	0.505359
$729$	25.6578	0.950290
$730$	−1.31744	−0.0487606
$731$	−35.6486	−1.31851
$732$	16.1985	0.598715
$733$	−29.5501	−1.09146	−0.545729	−	0.837962i	$-0.683747\pi$
$733$	−29.5501	−1.09146	−0.545729	+	0.837962i	$0.683747\pi$
$734$	5.88777	0.217322
$735$	−7.59924	−0.280302
$736$	−6.81108	−0.251060
$737$	−3.73058	−0.137418
$738$	0.141791	0.00521939
$739$	32.6112	1.19962	0.599811	−	0.800142i	$-0.295242\pi$
$739$	32.6112	1.19962	0.599811	+	0.800142i	$0.295242\pi$
$740$	−16.1166	−0.592456
$741$	−10.8451	−0.398403
$742$	−8.56417	−0.314401
$743$	29.6526	1.08785	0.543924	−	0.839134i	$-0.316938\pi$
$743$	29.6526	1.08785	0.543924	+	0.839134i	$0.316938\pi$
$744$	8.78911	0.322224
$745$	−47.1094	−1.72595
$746$	−9.81999	−0.359535
$747$	−0.432712	−0.0158321
$748$	−7.55735	−0.276324
$749$	−23.2885	−0.850942
$750$	8.59014	0.313667
$751$	30.8493	1.12571	0.562854	−	0.826556i	$-0.309703\pi$
$751$	30.8493	1.12571	0.562854	+	0.826556i	$0.309703\pi$
$752$	6.21800	0.226747
$753$	−24.6852	−0.899579
$754$	−42.1607	−1.53540
$755$	39.8065	1.44871
$756$	−11.9057	−0.433005
$757$	1.37662	0.0500340	0.0250170	−	0.999687i	$-0.492036\pi$
$757$	1.37662	0.0500340	0.0250170	+	0.999687i	$0.492036\pi$
$758$	−12.8395	−0.466353
$759$	18.3538	0.666202
$760$	3.04090	0.110305
$761$	−21.7238	−0.787488	−0.393744	−	0.919220i	$-0.628820\pi$
$761$	−21.7238	−0.787488	−0.393744	+	0.919220i	$0.628820\pi$
$762$	5.80154	0.210167
$763$	6.13711	0.222178
$764$	6.98966	0.252877
$765$	−1.96149	−0.0709177
$766$	27.7289	1.00188
$767$	17.7302	0.640202
$768$	−1.77113	−0.0639103
$769$	−6.37557	−0.229909	−0.114954	−	0.993371i	$-0.536672\pi$
$769$	−6.37557	−0.229909	−0.114954	+	0.993371i	$0.536672\pi$
$770$	10.3026	0.371280
$771$	−10.2040	−0.367486
$772$	8.21604	0.295702
$773$	6.75982	0.243134	0.121567	−	0.992583i	$-0.461208\pi$
$773$	6.75982	0.243134	0.121567	+	0.992583i	$0.461208\pi$
$774$	0.982628	0.0353198
$775$	16.4672	0.591518
$776$	4.40675	0.158193
$777$	23.2366	0.833610
$778$	−1.32245	−0.0474122
$779$	−1.09188	−0.0391207
$780$	29.6666	1.06223
$781$	4.53605	0.162313
$782$	−33.8318	−1.20982
$783$	36.8126	1.31557
$784$	−1.48765	−0.0531302
$785$	26.7737	0.955596
$786$	20.3422	0.725584
$787$	36.9807	1.31822	0.659110	−	0.752047i	$-0.270933\pi$
$787$	36.9807	1.31822	0.659110	+	0.752047i	$0.270933\pi$
$788$	2.47401	0.0881329
$789$	−15.0350	−0.535261
$790$	23.7251	0.844101
$791$	11.2243	0.399089
$792$	0.208313	0.00740207
$793$	−53.1155	−1.88619
$794$	14.6659	0.520474
$795$	−18.6332	−0.660851
$796$	8.67889	0.307615
$797$	31.1648	1.10391	0.551957	−	0.833873i	$-0.313881\pi$
$797$	31.1648	1.10391	0.551957	+	0.833873i	$0.313881\pi$
$798$	−4.38433	−0.155204
$799$	30.8859	1.09266
$800$	−3.31837	−0.117322
$801$	−0.987870	−0.0349047
$802$	−19.7146	−0.696145
$803$	0.694978	0.0245252
$804$	−4.34278	−0.153158
$805$	46.1215	1.62557
$806$	−28.8198	−1.01513
$807$	−44.4456	−1.56456
$808$	−4.19383	−0.147538
$809$	19.0896	0.671156	0.335578	−	0.942013i	$-0.391068\pi$
$809$	19.0896	0.671156	0.335578	+	0.942013i	$0.391068\pi$
$810$	−27.0880	−0.951776
$811$	17.7471	0.623184	0.311592	−	0.950216i	$-0.399138\pi$
$811$	17.7471	0.623184	0.311592	+	0.950216i	$0.399138\pi$
$812$	−17.0443	−0.598138
$813$	−18.9261	−0.663766
$814$	8.50183	0.297989
$815$	−59.5002	−2.08420
$816$	−8.79754	−0.307976
$817$	−7.56687	−0.264731
$818$	−8.61892	−0.301353
$819$	−1.86690	−0.0652349
$820$	2.98683	0.104305
$821$	−11.5210	−0.402085	−0.201042	−	0.979583i	$-0.564433\pi$
$821$	−11.5210	−0.402085	−0.201042	+	0.979583i	$0.564433\pi$
$822$	36.0782	1.25837
$823$	1.94883	0.0679320	0.0339660	−	0.999423i	$-0.489186\pi$
$823$	1.94883	0.0679320	0.0339660	+	0.999423i	$0.489186\pi$
$824$	−2.02392	−0.0705066
$825$	8.94203	0.311322
$826$	7.16780	0.249400
$827$	17.9002	0.622451	0.311225	−	0.950336i	$-0.399261\pi$
$827$	17.9002	0.622451	0.311225	+	0.950336i	$0.399261\pi$
$828$	0.932550	0.0324084
$829$	56.0475	1.94661	0.973305	−	0.229517i	$-0.0737148\pi$
$829$	56.0475	1.94661	0.973305	+	0.229517i	$0.0737148\pi$
$830$	−9.11512	−0.316390
$831$	36.9504	1.28180
$832$	5.80761	0.201343
$833$	−7.38940	−0.256027
$834$	−9.57600	−0.331590
$835$	−29.2136	−1.01098
$836$	−1.60414	−0.0554804
$837$	25.1639	0.869793
$838$	2.61729	0.0904127
$839$	49.4140	1.70596	0.852980	−	0.521944i	$-0.174793\pi$
$839$	49.4140	1.70596	0.852980	+	0.521944i	$0.174793\pi$
$840$	11.9933	0.413809
$841$	23.7013	0.817285
$842$	−20.7303	−0.714412
$843$	42.4585	1.46235
$844$	16.2561	0.559557
$845$	−59.7837	−2.05662
$846$	−0.851347	−0.0292699
$847$	20.3914	0.700657
$848$	−3.64768	−0.125262
$849$	14.7274	0.505444
$850$	−16.4830	−0.565361
$851$	38.0600	1.30468
$852$	5.28044	0.180905
$853$	−10.5706	−0.361931	−0.180966	−	0.983489i	$-0.557922\pi$
$853$	−10.5706	−0.361931	−0.180966	+	0.983489i	$0.557922\pi$
$854$	−21.4730	−0.734792
$855$	−0.416350	−0.0142389
$856$	−9.91911	−0.339028
$857$	23.2634	0.794664	0.397332	−	0.917675i	$-0.369936\pi$
$857$	23.2634	0.794664	0.397332	+	0.917675i	$0.369936\pi$
$858$	−15.6498	−0.534275
$859$	−11.4583	−0.390953	−0.195476	−	0.980708i	$-0.562625\pi$
$859$	−11.4583	−0.390953	−0.195476	+	0.980708i	$0.562625\pi$
$860$	20.6991	0.705834
$861$	−4.30638	−0.146761
$862$	−16.9470	−0.577216
$863$	43.4052	1.47753	0.738765	−	0.673963i	$-0.235409\pi$
$863$	43.4052	1.47753	0.738765	+	0.673963i	$0.235409\pi$
$864$	−5.07091	−0.172516
$865$	61.1966	2.08075
$866$	10.9414	0.371804
$867$	−13.5897	−0.461529
$868$	−11.6510	−0.395459
$869$	−12.5155	−0.424559
$870$	−37.0835	−1.25725
$871$	14.2401	0.482508
$872$	2.61394	0.0885192
$873$	−0.603357	−0.0204205
$874$	−7.18124	−0.242909
$875$	−11.3872	−0.384958
$876$	0.809027	0.0273345
$877$	34.0541	1.14992	0.574962	−	0.818180i	$-0.305017\pi$
$877$	34.0541	1.14992	0.574962	+	0.818180i	$0.305017\pi$
$878$	20.2536	0.683527
$879$	−25.7130	−0.867277
$880$	4.38812	0.147924
$881$	22.7038	0.764909	0.382454	−	0.923974i	$-0.375079\pi$
$881$	22.7038	0.764909	0.382454	+	0.923974i	$0.375079\pi$
$882$	0.203683	0.00685837
$883$	14.1103	0.474850	0.237425	−	0.971406i	$-0.423697\pi$
$883$	14.1103	0.474850	0.237425	+	0.971406i	$0.423697\pi$
$884$	28.8474	0.970244
$885$	15.5951	0.524224
$886$	36.5646	1.22841
$887$	−19.0591	−0.639942	−0.319971	−	0.947427i	$-0.603673\pi$
$887$	−19.0591	−0.639942	−0.319971	+	0.947427i	$0.603673\pi$
$888$	9.89702	0.332122
$889$	−7.69060	−0.257934
$890$	−20.8096	−0.697538
$891$	14.2895	0.478717
$892$	14.4036	0.482268
$893$	6.55592	0.219386
$894$	28.9294	0.967545
$895$	−33.3431	−1.11454
$896$	2.34784	0.0784358
$897$	−70.0591	−2.33921
$898$	−6.26587	−0.209095
$899$	36.0250	1.20150
$900$	0.454341	0.0151447
$901$	−18.1187	−0.603621
$902$	−1.57562	−0.0524624
$903$	−29.8437	−0.993137
$904$	4.78067	0.159003
$905$	−35.0146	−1.16392
$906$	−24.4448	−0.812123
$907$	−16.4878	−0.547467	−0.273734	−	0.961806i	$-0.588259\pi$
$907$	−16.4878	−0.547467	−0.273734	+	0.961806i	$0.588259\pi$
$908$	−15.7901	−0.524012
$909$	0.574204	0.0190452
$910$	−39.3265	−1.30366
$911$	−35.8994	−1.18940	−0.594700	−	0.803948i	$-0.702729\pi$
$911$	−35.8994	−1.18940	−0.594700	+	0.803948i	$0.702729\pi$
$912$	−1.86739	−0.0618354
$913$	4.80842	0.159136
$914$	30.3431	1.00366
$915$	−46.7192	−1.54449
$916$	−23.9139	−0.790136
$917$	−26.9660	−0.890495
$918$	−25.1881	−0.831331
$919$	−32.7188	−1.07929	−0.539647	−	0.841891i	$-0.681442\pi$
$919$	−32.7188	−1.07929	−0.539647	+	0.841891i	$0.681442\pi$
$920$	19.6442	0.647651
$921$	−27.3295	−0.900536
$922$	4.29219	0.141356
$923$	−17.3147	−0.569921
$924$	−6.32673	−0.208134
$925$	18.5429	0.609688
$926$	34.8940	1.14669
$927$	0.277108	0.00910143
$928$	−7.25956	−0.238307
$929$	−23.8955	−0.783985	−0.391993	−	0.919968i	$-0.628214\pi$
$929$	−23.8955	−0.783985	−0.391993	+	0.919968i	$0.628214\pi$
$930$	−25.3492	−0.831232
$931$	−1.56849	−0.0514053
$932$	−16.2537	−0.532409
$933$	−9.66495	−0.316416
$934$	6.83449	0.223631
$935$	21.7966	0.712825
$936$	−0.795158	−0.0259905
$937$	−39.2277	−1.28151	−0.640756	−	0.767744i	$-0.721379\pi$
$937$	−39.2277	−1.28151	−0.640756	+	0.767744i	$0.721379\pi$
$938$	5.75686	0.187968
$939$	15.6465	0.510606
$940$	−17.9337	−0.584933
$941$	−11.4340	−0.372736	−0.186368	−	0.982480i	$-0.559672\pi$
$941$	−11.4340	−0.372736	−0.186368	+	0.982480i	$0.559672\pi$
$942$	−16.4415	−0.535693
$943$	−7.05355	−0.229695
$944$	3.05294	0.0993646
$945$	34.3379	1.11701
$946$	−10.9192	−0.355015
$947$	−1.87273	−0.0608555	−0.0304278	−	0.999537i	$-0.509687\pi$
$947$	−1.87273	−0.0608555	−0.0304278	+	0.999537i	$0.509687\pi$
$948$	−14.5693	−0.473190
$949$	−2.65283	−0.0861144
$950$	−3.49872	−0.113513
$951$	−7.18810	−0.233090
$952$	11.6621	0.377972
$953$	11.1465	0.361072	0.180536	−	0.983568i	$-0.442217\pi$
$953$	11.1465	0.361072	0.180536	+	0.983568i	$0.442217\pi$
$954$	0.499428	0.0161696
$955$	−20.1593	−0.652339
$956$	8.61903	0.278759
$957$	19.5624	0.632362
$958$	14.5476	0.470013
$959$	−47.8258	−1.54437
$960$	5.10823	0.164868
$961$	−6.37442	−0.205626
$962$	−32.4527	−1.04632
$963$	1.35809	0.0437639
$964$	−12.0780	−0.389006
$965$	−23.6964	−0.762813
$966$	−28.3228	−0.911271
$967$	21.1359	0.679684	0.339842	−	0.940483i	$-0.389626\pi$
$967$	21.1359	0.679684	0.339842	+	0.940483i	$0.389626\pi$
$968$	8.68517	0.279152
$969$	−9.27566	−0.297977
$970$	−12.7098	−0.408086
$971$	−40.7160	−1.30664	−0.653319	−	0.757082i	$-0.726624\pi$
$971$	−40.7160	−1.30664	−0.653319	+	0.757082i	$0.726624\pi$
$972$	1.42178	0.0456038
$973$	12.6941	0.406954
$974$	22.4709	0.720016
$975$	−34.1330	−1.09313
$976$	−9.14586	−0.292752
$977$	33.1453	1.06041	0.530206	−	0.847869i	$-0.322115\pi$
$977$	33.1453	1.06041	0.530206	+	0.847869i	$0.322115\pi$
$978$	36.5385	1.16837
$979$	10.9775	0.350842
$980$	4.29061	0.137058
$981$	−0.357892	−0.0114266
$982$	19.3497	0.617474
$983$	58.5409	1.86716	0.933582	−	0.358363i	$-0.116665\pi$
$983$	58.5409	1.86716	0.933582	+	0.358363i	$0.116665\pi$
$984$	−1.83419	−0.0584717
$985$	−7.13543	−0.227354
$986$	−36.0595	−1.14837
$987$	25.8565	0.823023
$988$	6.12323	0.194806
$989$	−48.8820	−1.55436
$990$	−0.600807	−0.0190949
$991$	−19.1011	−0.606766	−0.303383	−	0.952869i	$-0.598116\pi$
$991$	−19.1011	−0.606766	−0.303383	+	0.952869i	$0.598116\pi$
$992$	−4.96242	−0.157557
$993$	−17.7757	−0.564093
$994$	−6.99982	−0.222021
$995$	−25.0313	−0.793546
$996$	5.59751	0.177364
$997$	−25.5594	−0.809474	−0.404737	−	0.914433i	$-0.632637\pi$
$997$	−25.5594	−0.809474	−0.404737	+	0.914433i	$0.632637\pi$
$998$	24.2643	0.768072
$999$	28.3360	0.896511

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8026.2.a.c.1.20	✓	86

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8026.2.a.c.1.20	✓	86	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:	\( N \)	\(=\)	\( 8026 = 2 \cdot 4013 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8026.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.77113 q^{3} +1.00000 q^{4} -2.88416 q^{5} +1.77113 q^{6} -2.34784 q^{7} -1.00000 q^{8} +0.136917 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.77113 q^{3} +1.00000 q^{4} -2.88416 q^{5} +1.77113 q^{6} -2.34784 q^{7} -1.00000 q^{8} +0.136917 q^{9} +2.88416 q^{10} -1.52146 q^{11} -1.77113 q^{12} +5.80761 q^{13} +2.34784 q^{14} +5.10823 q^{15} +1.00000 q^{16} +4.96718 q^{17} -0.136917 q^{18} +1.05435 q^{19} -2.88416 q^{20} +4.15834 q^{21} +1.52146 q^{22} +6.81108 q^{23} +1.77113 q^{24} +3.31837 q^{25} -5.80761 q^{26} +5.07091 q^{27} -2.34784 q^{28} +7.25956 q^{29} -5.10823 q^{30} +4.96242 q^{31} -1.00000 q^{32} +2.69470 q^{33} -4.96718 q^{34} +6.77155 q^{35} +0.136917 q^{36} +5.58796 q^{37} -1.05435 q^{38} -10.2861 q^{39} +2.88416 q^{40} -1.03560 q^{41} -4.15834 q^{42} -7.17683 q^{43} -1.52146 q^{44} -0.394889 q^{45} -6.81108 q^{46} +6.21800 q^{47} -1.77113 q^{48} -1.48765 q^{49} -3.31837 q^{50} -8.79754 q^{51} +5.80761 q^{52} -3.64768 q^{53} -5.07091 q^{54} +4.38812 q^{55} +2.34784 q^{56} -1.86739 q^{57} -7.25956 q^{58} +3.05294 q^{59} +5.10823 q^{60} -9.14586 q^{61} -4.96242 q^{62} -0.321458 q^{63} +1.00000 q^{64} -16.7501 q^{65} -2.69470 q^{66} +2.45198 q^{67} +4.96718 q^{68} -12.0633 q^{69} -6.77155 q^{70} -2.98139 q^{71} -0.136917 q^{72} -0.456785 q^{73} -5.58796 q^{74} -5.87729 q^{75} +1.05435 q^{76} +3.57214 q^{77} +10.2861 q^{78} +8.22600 q^{79} -2.88416 q^{80} -9.39200 q^{81} +1.03560 q^{82} -3.16041 q^{83} +4.15834 q^{84} -14.3261 q^{85} +7.17683 q^{86} -12.8577 q^{87} +1.52146 q^{88} -7.21512 q^{89} +0.394889 q^{90} -13.6353 q^{91} +6.81108 q^{92} -8.78911 q^{93} -6.21800 q^{94} -3.04090 q^{95} +1.77113 q^{96} -4.40675 q^{97} +1.48765 q^{98} -0.208313 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 86 q - 86 q^{2} + 11 q^{3} + 86 q^{4} + 25 q^{5} - 11 q^{6} - 3 q^{7} - 86 q^{8} + 105 q^{9}+O(q^{10}) \) 86 * q - 86 * q^2 + 11 * q^3 + 86 * q^4 + 25 * q^5 - 11 * q^6 - 3 * q^7 - 86 * q^8 + 105 * q^9	\( 86 q - 86 q^{2} + 11 q^{3} + 86 q^{4} + 25 q^{5} - 11 q^{6} - 3 q^{7} - 86 q^{8} + 105 q^{9} - 25 q^{10} + 44 q^{11} + 11 q^{12} - 36 q^{13} + 3 q^{14} + 19 q^{15} + 86 q^{16} + 21 q^{17} - 105 q^{18} + 35 q^{19} + 25 q^{20} + 23 q^{21} - 44 q^{22} + 38 q^{23} - 11 q^{24} + 85 q^{25} + 36 q^{26} + 47 q^{27} - 3 q^{28} + 30 q^{29} - 19 q^{30} + 23 q^{31} - 86 q^{32} + 5 q^{33} - 21 q^{34} + 59 q^{35} + 105 q^{36} - 20 q^{37} - 35 q^{38} + 4 q^{39} - 25 q^{40} + 64 q^{41} - 23 q^{42} + 23 q^{43} + 44 q^{44} + 60 q^{45} - 38 q^{46} + 77 q^{47} + 11 q^{48} + 109 q^{49} - 85 q^{50} + 47 q^{51} - 36 q^{52} + 22 q^{53} - 47 q^{54} + 6 q^{55} + 3 q^{56} - 9 q^{57} - 30 q^{58} + 145 q^{59} + 19 q^{60} - 24 q^{61} - 23 q^{62} + 6 q^{63} + 86 q^{64} + 37 q^{65} - 5 q^{66} + 44 q^{67} + 21 q^{68} + 25 q^{69} - 59 q^{70} + 107 q^{71} - 105 q^{72} - 55 q^{73} + 20 q^{74} + 86 q^{75} + 35 q^{76} + 25 q^{77} - 4 q^{78} + 2 q^{79} + 25 q^{80} + 170 q^{81} - 64 q^{82} + 109 q^{83} + 23 q^{84} - 13 q^{85} - 23 q^{86} + 3 q^{87} - 44 q^{88} + 121 q^{89} - 60 q^{90} + 81 q^{91} + 38 q^{92} + 27 q^{93} - 77 q^{94} + 49 q^{95} - 11 q^{96} - 56 q^{97} - 109 q^{98} + 158 q^{99}+O(q^{100}) \) 86 * q - 86 * q^2 + 11 * q^3 + 86 * q^4 + 25 * q^5 - 11 * q^6 - 3 * q^7 - 86 * q^8 + 105 * q^9 - 25 * q^10 + 44 * q^11 + 11 * q^12 - 36 * q^13 + 3 * q^14 + 19 * q^15 + 86 * q^16 + 21 * q^17 - 105 * q^18 + 35 * q^19 + 25 * q^20 + 23 * q^21 - 44 * q^22 + 38 * q^23 - 11 * q^24 + 85 * q^25 + 36 * q^26 + 47 * q^27 - 3 * q^28 + 30 * q^29 - 19 * q^30 + 23 * q^31 - 86 * q^32 + 5 * q^33 - 21 * q^34 + 59 * q^35 + 105 * q^36 - 20 * q^37 - 35 * q^38 + 4 * q^39 - 25 * q^40 + 64 * q^41 - 23 * q^42 + 23 * q^43 + 44 * q^44 + 60 * q^45 - 38 * q^46 + 77 * q^47 + 11 * q^48 + 109 * q^49 - 85 * q^50 + 47 * q^51 - 36 * q^52 + 22 * q^53 - 47 * q^54 + 6 * q^55 + 3 * q^56 - 9 * q^57 - 30 * q^58 + 145 * q^59 + 19 * q^60 - 24 * q^61 - 23 * q^62 + 6 * q^63 + 86 * q^64 + 37 * q^65 - 5 * q^66 + 44 * q^67 + 21 * q^68 + 25 * q^69 - 59 * q^70 + 107 * q^71 - 105 * q^72 - 55 * q^73 + 20 * q^74 + 86 * q^75 + 35 * q^76 + 25 * q^77 - 4 * q^78 + 2 * q^79 + 25 * q^80 + 170 * q^81 - 64 * q^82 + 109 * q^83 + 23 * q^84 - 13 * q^85 - 23 * q^86 + 3 * q^87 - 44 * q^88 + 121 * q^89 - 60 * q^90 + 81 * q^91 + 38 * q^92 + 27 * q^93 - 77 * q^94 + 49 * q^95 - 11 * q^96 - 56 * q^97 - 109 * q^98 + 158 * q^99

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