LMFDB - Embedded newform 8026.2.a.b.1.1

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:	$1$
Dimension:	$81$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
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)

$f(q)$	$=$	$q-1.00000 q^{2} -3.26929 q^{3} +1.00000 q^{4} -1.66866 q^{5} +3.26929 q^{6} -1.36572 q^{7} -1.00000 q^{8} +7.68829 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -3.26929 q^{3} +1.00000 q^{4} -1.66866 q^{5} +3.26929 q^{6} -1.36572 q^{7} -1.00000 q^{8} +7.68829 q^{9} +1.66866 q^{10} -2.47020 q^{11} -3.26929 q^{12} -4.48260 q^{13} +1.36572 q^{14} +5.45535 q^{15} +1.00000 q^{16} +5.81792 q^{17} -7.68829 q^{18} -1.65821 q^{19} -1.66866 q^{20} +4.46493 q^{21} +2.47020 q^{22} +1.86242 q^{23} +3.26929 q^{24} -2.21556 q^{25} +4.48260 q^{26} -15.3274 q^{27} -1.36572 q^{28} +0.722005 q^{29} -5.45535 q^{30} -6.88253 q^{31} -1.00000 q^{32} +8.07581 q^{33} -5.81792 q^{34} +2.27892 q^{35} +7.68829 q^{36} -1.76064 q^{37} +1.65821 q^{38} +14.6550 q^{39} +1.66866 q^{40} -1.52448 q^{41} -4.46493 q^{42} +5.84573 q^{43} -2.47020 q^{44} -12.8292 q^{45} -1.86242 q^{46} +1.50351 q^{47} -3.26929 q^{48} -5.13482 q^{49} +2.21556 q^{50} -19.0205 q^{51} -4.48260 q^{52} +11.9036 q^{53} +15.3274 q^{54} +4.12193 q^{55} +1.36572 q^{56} +5.42118 q^{57} -0.722005 q^{58} -4.33407 q^{59} +5.45535 q^{60} -0.735274 q^{61} +6.88253 q^{62} -10.5000 q^{63} +1.00000 q^{64} +7.47996 q^{65} -8.07581 q^{66} -7.66184 q^{67} +5.81792 q^{68} -6.08880 q^{69} -2.27892 q^{70} -8.32609 q^{71} -7.68829 q^{72} -5.17284 q^{73} +1.76064 q^{74} +7.24332 q^{75} -1.65821 q^{76} +3.37359 q^{77} -14.6550 q^{78} +14.9132 q^{79} -1.66866 q^{80} +27.0449 q^{81} +1.52448 q^{82} -2.21733 q^{83} +4.46493 q^{84} -9.70815 q^{85} -5.84573 q^{86} -2.36045 q^{87} +2.47020 q^{88} +1.54388 q^{89} +12.8292 q^{90} +6.12196 q^{91} +1.86242 q^{92} +22.5010 q^{93} -1.50351 q^{94} +2.76700 q^{95} +3.26929 q^{96} +11.7066 q^{97} +5.13482 q^{98} -18.9916 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 81 q - 81 q^{2} - 10 q^{3} + 81 q^{4} - 26 q^{5} + 10 q^{6} + 3 q^{7} - 81 q^{8} + 59 q^{9}+O(q^{10}) $ 81 * q - 81 * q^2 - 10 * q^3 + 81 * q^4 - 26 * q^5 + 10 * q^6 + 3 * q^7 - 81 * q^8 + 59 * q^9	\( 81 q - 81 q^{2} - 10 q^{3} + 81 q^{4} - 26 q^{5} + 10 q^{6} + 3 q^{7} - 81 q^{8} + 59 q^{9} + 26 q^{10} - 41 q^{11} - 10 q^{12} + 33 q^{13} - 3 q^{14} - 7 q^{15} + 81 q^{16} - 9 q^{17} - 59 q^{18} - 32 q^{19} - 26 q^{20} - 23 q^{21} + 41 q^{22} - 28 q^{23} + 10 q^{24} + 81 q^{25} - 33 q^{26} - 37 q^{27} + 3 q^{28} - 35 q^{29} + 7 q^{30} - 29 q^{31} - 81 q^{32} - 7 q^{33} + 9 q^{34} - 67 q^{35} + 59 q^{36} + 13 q^{37} + 32 q^{38} - 42 q^{39} + 26 q^{40} - 66 q^{41} + 23 q^{42} - 22 q^{43} - 41 q^{44} - 65 q^{45} + 28 q^{46} - 71 q^{47} - 10 q^{48} + 64 q^{49} - 81 q^{50} - 43 q^{51} + 33 q^{52} - 37 q^{53} + 37 q^{54} + 12 q^{55} - 3 q^{56} - q^{57} + 35 q^{58} - 162 q^{59} - 7 q^{60} + 19 q^{61} + 29 q^{62} - 16 q^{63} + 81 q^{64} - 45 q^{65} + 7 q^{66} - 43 q^{67} - 9 q^{68} - 21 q^{69} + 67 q^{70} - 99 q^{71} - 59 q^{72} + 53 q^{73} - 13 q^{74} - 61 q^{75} - 32 q^{76} - 31 q^{77} + 42 q^{78} + 4 q^{79} - 26 q^{80} + q^{81} + 66 q^{82} - 112 q^{83} - 23 q^{84} + 17 q^{85} + 22 q^{86} - 15 q^{87} + 41 q^{88} - 111 q^{89} + 65 q^{90} - 49 q^{91} - 28 q^{92} - 19 q^{93} + 71 q^{94} - 53 q^{95} + 10 q^{96} + 50 q^{97} - 64 q^{98} - 97 q^{99}+O(q^{100}) \) 81 * q - 81 * q^2 - 10 * q^3 + 81 * q^4 - 26 * q^5 + 10 * q^6 + 3 * q^7 - 81 * q^8 + 59 * q^9 + 26 * q^10 - 41 * q^11 - 10 * q^12 + 33 * q^13 - 3 * q^14 - 7 * q^15 + 81 * q^16 - 9 * q^17 - 59 * q^18 - 32 * q^19 - 26 * q^20 - 23 * q^21 + 41 * q^22 - 28 * q^23 + 10 * q^24 + 81 * q^25 - 33 * q^26 - 37 * q^27 + 3 * q^28 - 35 * q^29 + 7 * q^30 - 29 * q^31 - 81 * q^32 - 7 * q^33 + 9 * q^34 - 67 * q^35 + 59 * q^36 + 13 * q^37 + 32 * q^38 - 42 * q^39 + 26 * q^40 - 66 * q^41 + 23 * q^42 - 22 * q^43 - 41 * q^44 - 65 * q^45 + 28 * q^46 - 71 * q^47 - 10 * q^48 + 64 * q^49 - 81 * q^50 - 43 * q^51 + 33 * q^52 - 37 * q^53 + 37 * q^54 + 12 * q^55 - 3 * q^56 - q^57 + 35 * q^58 - 162 * q^59 - 7 * q^60 + 19 * q^61 + 29 * q^62 - 16 * q^63 + 81 * q^64 - 45 * q^65 + 7 * q^66 - 43 * q^67 - 9 * q^68 - 21 * q^69 + 67 * q^70 - 99 * q^71 - 59 * q^72 + 53 * q^73 - 13 * q^74 - 61 * q^75 - 32 * q^76 - 31 * q^77 + 42 * q^78 + 4 * q^79 - 26 * q^80 + q^81 + 66 * q^82 - 112 * q^83 - 23 * q^84 + 17 * q^85 + 22 * q^86 - 15 * q^87 + 41 * q^88 - 111 * q^89 + 65 * q^90 - 49 * q^91 - 28 * q^92 - 19 * q^93 + 71 * q^94 - 53 * q^95 + 10 * q^96 + 50 * q^97 - 64 * q^98 - 97 * 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
$3$	−3.26929	−1.88753	−0.943764	−	0.330620i	$-0.892742\pi$
$3$	−3.26929	−1.88753	−0.943764	+	0.330620i	$0.892742\pi$
$4$	1.00000	0.500000
$5$	−1.66866	−0.746249	−0.373125	−	0.927781i	$-0.621714\pi$
$5$	−1.66866	−0.746249	−0.373125	+	0.927781i	$0.621714\pi$
$6$	3.26929	1.33468
$7$	−1.36572	−0.516192	−0.258096	−	0.966119i	$-0.583095\pi$
$7$	−1.36572	−0.516192	−0.258096	+	0.966119i	$0.583095\pi$
$8$	−1.00000	−0.353553
$9$	7.68829	2.56276
$10$	1.66866	0.527678
$11$	−2.47020	−0.744793	−0.372397	−	0.928074i	$-0.621464\pi$
$11$	−2.47020	−0.744793	−0.372397	+	0.928074i	$0.621464\pi$
$12$	−3.26929	−0.943764
$13$	−4.48260	−1.24325	−0.621625	−	0.783315i	$-0.713527\pi$
$13$	−4.48260	−1.24325	−0.621625	+	0.783315i	$0.713527\pi$
$14$	1.36572	0.365003
$15$	5.45535	1.40857
$16$	1.00000	0.250000
$17$	5.81792	1.41105	0.705526	−	0.708684i	$-0.250711\pi$
$17$	5.81792	1.41105	0.705526	+	0.708684i	$0.250711\pi$
$18$	−7.68829	−1.81215
$19$	−1.65821	−0.380420	−0.190210	−	0.981743i	$-0.560917\pi$
$19$	−1.65821	−0.380420	−0.190210	+	0.981743i	$0.560917\pi$
$20$	−1.66866	−0.373125
$21$	4.46493	0.974327
$22$	2.47020	0.526648
$23$	1.86242	0.388341	0.194171	−	0.980968i	$-0.437798\pi$
$23$	1.86242	0.388341	0.194171	+	0.980968i	$0.437798\pi$
$24$	3.26929	0.667342
$25$	−2.21556	−0.443112
$26$	4.48260	0.879111
$27$	−15.3274	−2.94976
$28$	−1.36572	−0.258096
$29$	0.722005	0.134073	0.0670365	−	0.997751i	$-0.478646\pi$
$29$	0.722005	0.134073	0.0670365	+	0.997751i	$0.478646\pi$
$30$	−5.45535	−0.996007
$31$	−6.88253	−1.23614	−0.618069	−	0.786124i	$-0.712085\pi$
$31$	−6.88253	−1.23614	−0.618069	+	0.786124i	$0.712085\pi$
$32$	−1.00000	−0.176777
$33$	8.07581	1.40582
$34$	−5.81792	−0.997765
$35$	2.27892	0.385208
$36$	7.68829	1.28138
$37$	−1.76064	−0.289448	−0.144724	−	0.989472i	$-0.546229\pi$
$37$	−1.76064	−0.289448	−0.144724	+	0.989472i	$0.546229\pi$
$38$	1.65821	0.268997
$39$	14.6550	2.34667
$40$	1.66866	0.263839
$41$	−1.52448	−0.238083	−0.119042	−	0.992889i	$-0.537982\pi$
$41$	−1.52448	−0.238083	−0.119042	+	0.992889i	$0.537982\pi$
$42$	−4.46493	−0.688953
$43$	5.84573	0.891466	0.445733	−	0.895166i	$-0.352943\pi$
$43$	5.84573	0.891466	0.445733	+	0.895166i	$0.352943\pi$
$44$	−2.47020	−0.372397
$45$	−12.8292	−1.91246
$46$	−1.86242	−0.274599
$47$	1.50351	0.219310	0.109655	−	0.993970i	$-0.465025\pi$
$47$	1.50351	0.219310	0.109655	+	0.993970i	$0.465025\pi$
$48$	−3.26929	−0.471882
$49$	−5.13482	−0.733546
$50$	2.21556	0.313328
$51$	−19.0205	−2.66340
$52$	−4.48260	−0.621625
$53$	11.9036	1.63508	0.817540	−	0.575872i	$-0.195337\pi$
$53$	11.9036	1.63508	0.817540	+	0.575872i	$0.195337\pi$
$54$	15.3274	2.08579
$55$	4.12193	0.555801
$56$	1.36572	0.182501
$57$	5.42118	0.718053
$58$	−0.722005	−0.0948040
$59$	−4.33407	−0.564248	−0.282124	−	0.959378i	$-0.591039\pi$
$59$	−4.33407	−0.564248	−0.282124	+	0.959378i	$0.591039\pi$
$60$	5.45535	0.704283
$61$	−0.735274	−0.0941422	−0.0470711	−	0.998892i	$-0.514989\pi$
$61$	−0.735274	−0.0941422	−0.0470711	+	0.998892i	$0.514989\pi$
$62$	6.88253	0.874082
$63$	−10.5000	−1.32288
$64$	1.00000	0.125000
$65$	7.47996	0.927775
$66$	−8.07581	−0.994064
$67$	−7.66184	−0.936043	−0.468021	−	0.883717i	$-0.655033\pi$
$67$	−7.66184	−0.936043	−0.468021	+	0.883717i	$0.655033\pi$
$68$	5.81792	0.705526
$69$	−6.08880	−0.733005
$70$	−2.27892	−0.272383
$71$	−8.32609	−0.988125	−0.494063	−	0.869426i	$-0.664489\pi$
$71$	−8.32609	−0.988125	−0.494063	+	0.869426i	$0.664489\pi$
$72$	−7.68829	−0.906073
$73$	−5.17284	−0.605435	−0.302718	−	0.953080i	$-0.597894\pi$
$73$	−5.17284	−0.605435	−0.302718	+	0.953080i	$0.597894\pi$
$74$	1.76064	0.204671
$75$	7.24332	0.836387
$76$	−1.65821	−0.190210
$77$	3.37359	0.384457
$78$	−14.6550	−1.65935
$79$	14.9132	1.67786	0.838931	−	0.544237i	$-0.183181\pi$
$79$	14.9132	1.67786	0.838931	+	0.544237i	$0.183181\pi$
$80$	−1.66866	−0.186562
$81$	27.0449	3.00499
$82$	1.52448	0.168350
$83$	−2.21733	−0.243383	−0.121692	−	0.992568i	$-0.538832\pi$
$83$	−2.21733	−0.243383	−0.121692	+	0.992568i	$0.538832\pi$
$84$	4.46493	0.487164
$85$	−9.70815	−1.05300
$86$	−5.84573	−0.630361
$87$	−2.36045	−0.253067
$88$	2.47020	0.263324
$89$	1.54388	0.163651	0.0818256	−	0.996647i	$-0.473925\pi$
$89$	1.54388	0.163651	0.0818256	+	0.996647i	$0.473925\pi$
$90$	12.8292	1.35231
$91$	6.12196	0.641756
$92$	1.86242	0.194171
$93$	22.5010	2.33325
$94$	−1.50351	−0.155075
$95$	2.76700	0.283888
$96$	3.26929	0.333671
$97$	11.7066	1.18862	0.594311	−	0.804235i	$-0.297425\pi$
$97$	11.7066	1.18862	0.594311	+	0.804235i	$0.297425\pi$
$98$	5.13482	0.518695
$99$	−18.9916	−1.90873
$100$	−2.21556	−0.221556
$101$	−13.7383	−1.36701	−0.683505	−	0.729946i	$-0.739545\pi$
$101$	−13.7383	−1.36701	−0.683505	+	0.729946i	$0.739545\pi$
$102$	19.0205	1.88331
$103$	8.06265	0.794437	0.397218	−	0.917724i	$-0.369976\pi$
$103$	8.06265	0.794437	0.397218	+	0.917724i	$0.369976\pi$
$104$	4.48260	0.439555
$105$	−7.45046	−0.727091
$106$	−11.9036	−1.15618
$107$	−7.66056	−0.740574	−0.370287	−	0.928917i	$-0.620741\pi$
$107$	−7.66056	−0.740574	−0.370287	+	0.928917i	$0.620741\pi$
$108$	−15.3274	−1.47488
$109$	13.0031	1.24547	0.622736	−	0.782432i	$-0.286021\pi$
$109$	13.0031	1.24547	0.622736	+	0.782432i	$0.286021\pi$
$110$	−4.12193	−0.393011
$111$	5.75606	0.546341
$112$	−1.36572	−0.129048
$113$	13.0881	1.23122	0.615611	−	0.788050i	$-0.288909\pi$
$113$	13.0881	1.23122	0.615611	+	0.788050i	$0.288909\pi$
$114$	−5.42118	−0.507740
$115$	−3.10775	−0.289799
$116$	0.722005	0.0670365
$117$	−34.4635	−3.18616
$118$	4.33407	0.398984
$119$	−7.94563	−0.728374
$120$	−5.45535	−0.498003
$121$	−4.89811	−0.445283
$122$	0.735274	0.0665686
$123$	4.98396	0.449389
$124$	−6.88253	−0.618069
$125$	12.0403	1.07692
$126$	10.5000	0.935416
$127$	16.8834	1.49816	0.749082	−	0.662477i	$-0.230495\pi$
$127$	16.8834	1.49816	0.749082	+	0.662477i	$0.230495\pi$
$128$	−1.00000	−0.0883883
$129$	−19.1114	−1.68267
$130$	−7.47996	−0.656036
$131$	−9.54322	−0.833795	−0.416898	−	0.908953i	$-0.636883\pi$
$131$	−9.54322	−0.833795	−0.416898	+	0.908953i	$0.636883\pi$
$132$	8.07581	0.702909
$133$	2.26465	0.196370
$134$	7.66184	0.661882
$135$	25.5763	2.20125
$136$	−5.81792	−0.498882
$137$	20.2600	1.73092	0.865462	−	0.500974i	$-0.167025\pi$
$137$	20.2600	1.73092	0.865462	+	0.500974i	$0.167025\pi$
$138$	6.08880	0.518313
$139$	−3.80448	−0.322692	−0.161346	−	0.986898i	$-0.551584\pi$
$139$	−3.80448	−0.322692	−0.161346	+	0.986898i	$0.551584\pi$
$140$	2.27892	0.192604
$141$	−4.91542	−0.413953
$142$	8.32609	0.698710
$143$	11.0729	0.925965
$144$	7.68829	0.640691
$145$	−1.20478	−0.100052
$146$	5.17284	0.428107
$147$	16.7872	1.38459
$148$	−1.76064	−0.144724
$149$	3.03242	0.248426	0.124213	−	0.992256i	$-0.460359\pi$
$149$	3.03242	0.248426	0.124213	+	0.992256i	$0.460359\pi$
$150$	−7.24332	−0.591415
$151$	−15.7481	−1.28156	−0.640781	−	0.767724i	$-0.721389\pi$
$151$	−15.7481	−1.28156	−0.640781	+	0.767724i	$0.721389\pi$
$152$	1.65821	0.134499
$153$	44.7298	3.61619
$154$	−3.37359	−0.271852
$155$	11.4846	0.922467
$156$	14.6550	1.17334
$157$	1.34112	0.107033	0.0535165	−	0.998567i	$-0.482957\pi$
$157$	1.34112	0.107033	0.0535165	+	0.998567i	$0.482957\pi$
$158$	−14.9132	−1.18643
$159$	−38.9163	−3.08626
$160$	1.66866	0.131919
$161$	−2.54354	−0.200459
$162$	−27.0449	−2.12485
$163$	0.0974129	0.00762997	0.00381498	−	0.999993i	$-0.498786\pi$
$163$	0.0974129	0.00762997	0.00381498	+	0.999993i	$0.498786\pi$
$164$	−1.52448	−0.119042
$165$	−13.4758	−1.04909
$166$	2.21733	0.172098
$167$	−2.57137	−0.198979	−0.0994895	−	0.995039i	$-0.531721\pi$
$167$	−2.57137	−0.198979	−0.0994895	+	0.995039i	$0.531721\pi$
$168$	−4.46493	−0.344477
$169$	7.09374	0.545672
$170$	9.70815	0.744581
$171$	−12.7488	−0.974925
$172$	5.84573	0.445733
$173$	0.993081	0.0755026	0.0377513	−	0.999287i	$-0.487981\pi$
$173$	0.993081	0.0755026	0.0377513	+	0.999287i	$0.487981\pi$
$174$	2.36045	0.178945
$175$	3.02583	0.228731
$176$	−2.47020	−0.186198
$177$	14.1694	1.06503
$178$	−1.54388	−0.115719
$179$	8.73610	0.652967	0.326483	−	0.945203i	$-0.394136\pi$
$179$	8.73610	0.652967	0.326483	+	0.945203i	$0.394136\pi$
$180$	−12.8292	−0.956230
$181$	6.69399	0.497560	0.248780	−	0.968560i	$-0.419970\pi$
$181$	6.69399	0.497560	0.248780	+	0.968560i	$0.419970\pi$
$182$	−6.12196	−0.453790
$183$	2.40383	0.177696
$184$	−1.86242	−0.137299
$185$	2.93792	0.216000
$186$	−22.5010	−1.64985
$187$	−14.3714	−1.05094
$188$	1.50351	0.109655
$189$	20.9329	1.52264
$190$	−2.76700	−0.200739
$191$	−0.143869	−0.0104100	−0.00520500	−	0.999986i	$-0.501657\pi$
$191$	−0.143869	−0.0104100	−0.00520500	+	0.999986i	$0.501657\pi$
$192$	−3.26929	−0.235941
$193$	6.68854	0.481452	0.240726	−	0.970593i	$-0.422615\pi$
$193$	6.68854	0.481452	0.240726	+	0.970593i	$0.422615\pi$
$194$	−11.7066	−0.840483
$195$	−24.4542	−1.75120
$196$	−5.13482	−0.366773
$197$	16.3505	1.16492	0.582461	−	0.812859i	$-0.302090\pi$
$197$	16.3505	1.16492	0.582461	+	0.812859i	$0.302090\pi$
$198$	18.9916	1.34967
$199$	21.9579	1.55655	0.778275	−	0.627923i	$-0.216095\pi$
$199$	21.9579	1.55655	0.778275	+	0.627923i	$0.216095\pi$
$200$	2.21556	0.156664
$201$	25.0488	1.76681
$202$	13.7383	0.966622
$203$	−0.986055	−0.0692075
$204$	−19.0205	−1.33170
$205$	2.54384	0.177669
$206$	−8.06265	−0.561752
$207$	14.3188	0.995227
$208$	−4.48260	−0.310813
$209$	4.09611	0.283334
$210$	7.45046	0.514131
$211$	21.8203	1.50217	0.751085	−	0.660205i	$-0.229531\pi$
$211$	21.8203	1.50217	0.751085	+	0.660205i	$0.229531\pi$
$212$	11.9036	0.817540
$213$	27.2204	1.86511
$214$	7.66056	0.523665
$215$	−9.75456	−0.665256
$216$	15.3274	1.04290
$217$	9.39958	0.638085
$218$	−13.0031	−0.880682
$219$	16.9115	1.14278
$220$	4.12193	0.277901
$221$	−26.0794	−1.75429
$222$	−5.75606	−0.386322
$223$	1.42229	0.0952434	0.0476217	−	0.998865i	$-0.484836\pi$
$223$	1.42229	0.0952434	0.0476217	+	0.998865i	$0.484836\pi$
$224$	1.36572	0.0912507
$225$	−17.0339	−1.13559
$226$	−13.0881	−0.870605
$227$	7.93675	0.526780	0.263390	−	0.964689i	$-0.415159\pi$
$227$	7.93675	0.526780	0.263390	+	0.964689i	$0.415159\pi$
$228$	5.42118	0.359027
$229$	4.46832	0.295275	0.147638	−	0.989042i	$-0.452833\pi$
$229$	4.46832	0.295275	0.147638	+	0.989042i	$0.452833\pi$
$230$	3.10775	0.204919
$231$	−11.0293	−0.725673
$232$	−0.722005	−0.0474020
$233$	6.84289	0.448293	0.224146	−	0.974555i	$-0.428041\pi$
$233$	6.84289	0.448293	0.224146	+	0.974555i	$0.428041\pi$
$234$	34.4635	2.25295
$235$	−2.50886	−0.163660
$236$	−4.33407	−0.282124
$237$	−48.7555	−3.16701
$238$	7.94563	0.515038
$239$	10.4623	0.676752	0.338376	−	0.941011i	$-0.390122\pi$
$239$	10.4623	0.676752	0.338376	+	0.941011i	$0.390122\pi$
$240$	5.45535	0.352142
$241$	10.0608	0.648072	0.324036	−	0.946045i	$-0.394960\pi$
$241$	10.0608	0.648072	0.324036	+	0.946045i	$0.394960\pi$
$242$	4.89811	0.314863
$243$	−42.4356	−2.72224
$244$	−0.735274	−0.0470711
$245$	8.56829	0.547408
$246$	−4.98396	−0.317766
$247$	7.43310	0.472957
$248$	6.88253	0.437041
$249$	7.24910	0.459393
$250$	−12.0403	−0.761498
$251$	−9.02061	−0.569376	−0.284688	−	0.958620i	$-0.591890\pi$
$251$	−9.02061	−0.569376	−0.284688	+	0.958620i	$0.591890\pi$
$252$	−10.5000	−0.661439
$253$	−4.60055	−0.289234
$254$	−16.8834	−1.05936
$255$	31.7388	1.98756
$256$	1.00000	0.0625000
$257$	−29.2390	−1.82388	−0.911939	−	0.410325i	$-0.865415\pi$
$257$	−29.2390	−1.82388	−0.911939	+	0.410325i	$0.865415\pi$
$258$	19.1114	1.18983
$259$	2.40454	0.149411
$260$	7.47996	0.463887
$261$	5.55099	0.343597
$262$	9.54322	0.589582
$263$	−15.9830	−0.985552	−0.492776	−	0.870156i	$-0.664018\pi$
$263$	−15.9830	−0.985552	−0.492776	+	0.870156i	$0.664018\pi$
$264$	−8.07581	−0.497032
$265$	−19.8630	−1.22018
$266$	−2.26465	−0.138854
$267$	−5.04741	−0.308896
$268$	−7.66184	−0.468021
$269$	5.57090	0.339664	0.169832	−	0.985473i	$-0.445678\pi$
$269$	5.57090	0.339664	0.169832	+	0.985473i	$0.445678\pi$
$270$	−25.5763	−1.55652
$271$	−4.83280	−0.293572	−0.146786	−	0.989168i	$-0.546893\pi$
$271$	−4.83280	−0.293572	−0.146786	+	0.989168i	$0.546893\pi$
$272$	5.81792	0.352763
$273$	−20.0145	−1.21133
$274$	−20.2600	−1.22395
$275$	5.47288	0.330027
$276$	−6.08880	−0.366503
$277$	5.59881	0.336400	0.168200	−	0.985753i	$-0.446205\pi$
$277$	5.59881	0.336400	0.168200	+	0.985753i	$0.446205\pi$
$278$	3.80448	0.228178
$279$	−52.9148	−3.16793
$280$	−2.27892	−0.136192
$281$	13.3974	0.799220	0.399610	−	0.916685i	$-0.369145\pi$
$281$	13.3974	0.799220	0.399610	+	0.916685i	$0.369145\pi$
$282$	4.91542	0.292709
$283$	8.28139	0.492277	0.246139	−	0.969235i	$-0.420838\pi$
$283$	8.28139	0.492277	0.246139	+	0.969235i	$0.420838\pi$
$284$	−8.32609	−0.494063
$285$	−9.04613	−0.535846
$286$	−11.0729	−0.654756
$287$	2.08200	0.122897
$288$	−7.68829	−0.453037
$289$	16.8482	0.991069
$290$	1.20478	0.0707474
$291$	−38.2722	−2.24356
$292$	−5.17284	−0.302718
$293$	−11.8937	−0.694839	−0.347420	−	0.937710i	$-0.612942\pi$
$293$	−11.8937	−0.694839	−0.347420	+	0.937710i	$0.612942\pi$
$294$	−16.7872	−0.979052
$295$	7.23211	0.421070
$296$	1.76064	0.102335
$297$	37.8617	2.19696
$298$	−3.03242	−0.175664
$299$	−8.34849	−0.482806
$300$	7.24332	0.418193
$301$	−7.98361	−0.460168
$302$	15.7481	0.906201
$303$	44.9145	2.58027
$304$	−1.65821	−0.0951049
$305$	1.22693	0.0702536
$306$	−44.7298	−2.55703
$307$	13.8965	0.793116	0.396558	−	0.918010i	$-0.370205\pi$
$307$	13.8965	0.793116	0.396558	+	0.918010i	$0.370205\pi$
$308$	3.37359	0.192228
$309$	−26.3592	−1.49952
$310$	−11.4846	−0.652283
$311$	−16.3562	−0.927473	−0.463736	−	0.885973i	$-0.653492\pi$
$311$	−16.3562	−0.927473	−0.463736	+	0.885973i	$0.653492\pi$
$312$	−14.6550	−0.829673
$313$	6.46571	0.365464	0.182732	−	0.983163i	$-0.441506\pi$
$313$	6.46571	0.365464	0.182732	+	0.983163i	$0.441506\pi$
$314$	−1.34112	−0.0756837
$315$	17.5210	0.987197
$316$	14.9132	0.838931
$317$	−2.63051	−0.147744	−0.0738721	−	0.997268i	$-0.523536\pi$
$317$	−2.63051	−0.147744	−0.0738721	+	0.997268i	$0.523536\pi$
$318$	38.9163	2.18232
$319$	−1.78350	−0.0998567
$320$	−1.66866	−0.0932811
$321$	25.0446	1.39785
$322$	2.54354	0.141746
$323$	−9.64734	−0.536792
$324$	27.0449	1.50249
$325$	9.93148	0.550899
$326$	−0.0974129	−0.00539520
$327$	−42.5110	−2.35087
$328$	1.52448	0.0841751
$329$	−2.05337	−0.113206
$330$	13.4758	0.741819
$331$	14.4302	0.793158	0.396579	−	0.918001i	$-0.370197\pi$
$331$	14.4302	0.793158	0.396579	+	0.918001i	$0.370197\pi$
$332$	−2.21733	−0.121692
$333$	−13.5363	−0.741786
$334$	2.57137	0.140699
$335$	12.7850	0.698521
$336$	4.46493	0.243582
$337$	10.8467	0.590856	0.295428	−	0.955365i	$-0.404538\pi$
$337$	10.8467	0.590856	0.295428	+	0.955365i	$0.404538\pi$
$338$	−7.09374	−0.385848
$339$	−42.7887	−2.32397
$340$	−9.70815	−0.526498
$341$	17.0012	0.920668
$342$	12.7488	0.689376
$343$	16.5727	0.894843
$344$	−5.84573	−0.315181
$345$	10.1602	0.547005
$346$	−0.993081	−0.0533884
$347$	−33.0799	−1.77582	−0.887910	−	0.460017i	$-0.847843\pi$
$347$	−33.0799	−1.77582	−0.887910	+	0.460017i	$0.847843\pi$
$348$	−2.36045	−0.126533
$349$	6.71026	0.359192	0.179596	−	0.983740i	$-0.442521\pi$
$349$	6.71026	0.359192	0.179596	+	0.983740i	$0.442521\pi$
$350$	−3.02583	−0.161737
$351$	68.7066	3.66729
$352$	2.47020	0.131662
$353$	30.9815	1.64898	0.824489	−	0.565878i	$-0.191463\pi$
$353$	30.9815	1.64898	0.824489	+	0.565878i	$0.191463\pi$
$354$	−14.1694	−0.753093
$355$	13.8934	0.737388
$356$	1.54388	0.0818256
$357$	25.9766	1.37483
$358$	−8.73610	−0.461717
$359$	6.40867	0.338237	0.169118	−	0.985596i	$-0.445908\pi$
$359$	6.40867	0.338237	0.169118	+	0.985596i	$0.445908\pi$
$360$	12.8292	0.676156
$361$	−16.2503	−0.855281
$362$	−6.69399	−0.351828
$363$	16.0134	0.840484
$364$	6.12196	0.320878
$365$	8.63173	0.451806
$366$	−2.40383	−0.125650
$367$	−15.9079	−0.830386	−0.415193	−	0.909733i	$-0.636286\pi$
$367$	−15.9079	−0.830386	−0.415193	+	0.909733i	$0.636286\pi$
$368$	1.86242	0.0970853
$369$	−11.7206	−0.610151
$370$	−2.93792	−0.152735
$371$	−16.2569	−0.844016
$372$	22.5010	1.16662
$373$	21.3965	1.10787	0.553934	−	0.832560i	$-0.313126\pi$
$373$	21.3965	1.10787	0.553934	+	0.832560i	$0.313126\pi$
$374$	14.3714	0.743129
$375$	−39.3634	−2.03272
$376$	−1.50351	−0.0775377
$377$	−3.23646	−0.166686
$378$	−20.9329	−1.07667
$379$	−26.8603	−1.37972	−0.689861	−	0.723942i	$-0.742328\pi$
$379$	−26.8603	−1.37972	−0.689861	+	0.723942i	$0.742328\pi$
$380$	2.76700	0.141944
$381$	−55.1970	−2.82783
$382$	0.143869	0.00736098
$383$	−6.05516	−0.309404	−0.154702	−	0.987961i	$-0.549442\pi$
$383$	−6.05516	−0.309404	−0.154702	+	0.987961i	$0.549442\pi$
$384$	3.26929	0.166835
$385$	−5.62939	−0.286900
$386$	−6.68854	−0.340438
$387$	44.9437	2.28462
$388$	11.7066	0.594311
$389$	−20.2788	−1.02818	−0.514088	−	0.857737i	$-0.671870\pi$
$389$	−20.2788	−1.02818	−0.514088	+	0.857737i	$0.671870\pi$
$390$	24.4542	1.23829
$391$	10.8354	0.547970
$392$	5.13482	0.259348
$393$	31.1996	1.57381
$394$	−16.3505	−0.823724
$395$	−24.8851	−1.25210
$396$	−18.9916	−0.954364
$397$	−12.6736	−0.636071	−0.318036	−	0.948079i	$-0.603023\pi$
$397$	−12.6736	−0.636071	−0.318036	+	0.948079i	$0.603023\pi$
$398$	−21.9579	−1.10065
$399$	−7.40379	−0.370653
$400$	−2.21556	−0.110778
$401$	−1.51459	−0.0756352	−0.0378176	−	0.999285i	$-0.512041\pi$
$401$	−1.51459	−0.0756352	−0.0378176	+	0.999285i	$0.512041\pi$
$402$	−25.0488	−1.24932
$403$	30.8516	1.53683
$404$	−13.7383	−0.683505
$405$	−45.1288	−2.24247
$406$	0.986055	0.0489371
$407$	4.34914	0.215579
$408$	19.0205	0.941655
$409$	32.1903	1.59171	0.795854	−	0.605489i	$-0.207022\pi$
$409$	32.1903	1.59171	0.795854	+	0.605489i	$0.207022\pi$
$410$	−2.54384	−0.125631
$411$	−66.2358	−3.26717
$412$	8.06265	0.397218
$413$	5.91911	0.291260
$414$	−14.3188	−0.703732
$415$	3.69998	0.181625
$416$	4.48260	0.219778
$417$	12.4380	0.609090
$418$	−4.09611	−0.200347
$419$	38.4497	1.87839	0.939195	−	0.343385i	$-0.111574\pi$
$419$	38.4497	1.87839	0.939195	+	0.343385i	$0.111574\pi$
$420$	−7.45046	−0.363545
$421$	−23.6302	−1.15166	−0.575832	−	0.817568i	$-0.695322\pi$
$421$	−23.6302	−1.15166	−0.575832	+	0.817568i	$0.695322\pi$
$422$	−21.8203	−1.06219
$423$	11.5594	0.562039
$424$	−11.9036	−0.578088
$425$	−12.8900	−0.625255
$426$	−27.2204	−1.31884
$427$	1.00418	0.0485955
$428$	−7.66056	−0.370287
$429$	−36.2007	−1.74778
$430$	9.75456	0.470407
$431$	−15.9285	−0.767248	−0.383624	−	0.923489i	$-0.625324\pi$
$431$	−15.9285	−0.767248	−0.383624	+	0.923489i	$0.625324\pi$
$432$	−15.3274	−0.737440
$433$	27.3235	1.31308	0.656541	−	0.754290i	$-0.272019\pi$
$433$	27.3235	1.31308	0.656541	+	0.754290i	$0.272019\pi$
$434$	−9.39958	−0.451194
$435$	3.93880	0.188851
$436$	13.0031	0.622736
$437$	−3.08829	−0.147733
$438$	−16.9115	−0.808065
$439$	−20.7917	−0.992335	−0.496168	−	0.868227i	$-0.665260\pi$
$439$	−20.7917	−0.992335	−0.496168	+	0.868227i	$0.665260\pi$
$440$	−4.12193	−0.196505
$441$	−39.4780	−1.87990
$442$	26.0794	1.24047
$443$	−22.9946	−1.09251	−0.546253	−	0.837620i	$-0.683946\pi$
$443$	−22.9946	−1.09251	−0.546253	+	0.837620i	$0.683946\pi$
$444$	5.75606	0.273171
$445$	−2.57622	−0.122125
$446$	−1.42229	−0.0673472
$447$	−9.91388	−0.468911
$448$	−1.36572	−0.0645240
$449$	13.2910	0.627240	0.313620	−	0.949548i	$-0.398458\pi$
$449$	13.2910	0.627240	0.313620	+	0.949548i	$0.398458\pi$
$450$	17.0339	0.802984
$451$	3.76576	0.177323
$452$	13.0881	0.615611
$453$	51.4852	2.41898
$454$	−7.93675	−0.372490
$455$	−10.2155	−0.478910
$456$	−5.42118	−0.253870
$457$	16.1759	0.756677	0.378338	−	0.925667i	$-0.376496\pi$
$457$	16.1759	0.756677	0.378338	+	0.925667i	$0.376496\pi$
$458$	−4.46832	−0.208791
$459$	−89.1735	−4.16226
$460$	−3.10775	−0.144900
$461$	−7.74907	−0.360910	−0.180455	−	0.983583i	$-0.557757\pi$
$461$	−7.74907	−0.360910	−0.180455	+	0.983583i	$0.557757\pi$
$462$	11.0293	0.513128
$463$	4.35584	0.202433	0.101216	−	0.994864i	$-0.467727\pi$
$463$	4.35584	0.202433	0.101216	+	0.994864i	$0.467727\pi$
$464$	0.722005	0.0335183
$465$	−37.5466	−1.74118
$466$	−6.84289	−0.316991
$467$	−12.3000	−0.569177	−0.284589	−	0.958650i	$-0.591857\pi$
$467$	−12.3000	−0.569177	−0.284589	+	0.958650i	$0.591857\pi$
$468$	−34.4635	−1.59308
$469$	10.4639	0.483178
$470$	2.50886	0.115725
$471$	−4.38451	−0.202028
$472$	4.33407	0.199492
$473$	−14.4401	−0.663958
$474$	48.7555	2.23942
$475$	3.67387	0.168569
$476$	−7.94563	−0.364187
$477$	91.5180	4.19032
$478$	−10.4623	−0.478536
$479$	−37.8644	−1.73007	−0.865035	−	0.501712i	$-0.832704\pi$
$479$	−37.8644	−1.73007	−0.865035	+	0.501712i	$0.832704\pi$
$480$	−5.45535	−0.249002
$481$	7.89227	0.359856
$482$	−10.0608	−0.458256
$483$	8.31557	0.378372
$484$	−4.89811	−0.222641
$485$	−19.5343	−0.887008
$486$	42.4356	1.92492
$487$	43.1079	1.95340	0.976702	−	0.214600i	$-0.0688448\pi$
$487$	43.1079	1.95340	0.976702	+	0.214600i	$0.0688448\pi$
$488$	0.735274	0.0332843
$489$	−0.318471	−0.0144018
$490$	−8.56829	−0.387076
$491$	−10.8096	−0.487832	−0.243916	−	0.969796i	$-0.578432\pi$
$491$	−10.8096	−0.487832	−0.243916	+	0.969796i	$0.578432\pi$
$492$	4.98396	0.224694
$493$	4.20057	0.189184
$494$	−7.43310	−0.334431
$495$	31.6906	1.42439
$496$	−6.88253	−0.309035
$497$	11.3711	0.510063
$498$	−7.24910	−0.324840
$499$	−11.2787	−0.504902	−0.252451	−	0.967610i	$-0.581237\pi$
$499$	−11.2787	−0.504902	−0.252451	+	0.967610i	$0.581237\pi$
$500$	12.0403	0.538461
$501$	8.40658	0.375578
$502$	9.02061	0.402609
$503$	14.1787	0.632198	0.316099	−	0.948726i	$-0.397627\pi$
$503$	14.1787	0.632198	0.316099	+	0.948726i	$0.397627\pi$
$504$	10.5000	0.467708
$505$	22.9246	1.02013
$506$	4.60055	0.204519
$507$	−23.1915	−1.02997
$508$	16.8834	0.749082
$509$	5.81771	0.257865	0.128933	−	0.991653i	$-0.458845\pi$
$509$	5.81771	0.257865	0.128933	+	0.991653i	$0.458845\pi$
$510$	−31.7388	−1.40542
$511$	7.06463	0.312521
$512$	−1.00000	−0.0441942
$513$	25.4161	1.12215
$514$	29.2390	1.28968
$515$	−13.4539	−0.592848
$516$	−19.1114	−0.841333
$517$	−3.71398	−0.163340
$518$	−2.40454	−0.105649
$519$	−3.24667	−0.142513
$520$	−7.47996	−0.328018
$521$	−37.8255	−1.65717	−0.828584	−	0.559865i	$-0.810853\pi$
$521$	−37.8255	−1.65717	−0.828584	+	0.559865i	$0.810853\pi$
$522$	−5.55099	−0.242960
$523$	24.4422	1.06878	0.534391	−	0.845237i	$-0.320541\pi$
$523$	24.4422	1.06878	0.534391	+	0.845237i	$0.320541\pi$
$524$	−9.54322	−0.416898
$525$	−9.89232	−0.431736
$526$	15.9830	0.696890
$527$	−40.0420	−1.74426
$528$	8.07581	0.351455
$529$	−19.5314	−0.849191
$530$	19.8630	0.862795
$531$	−33.3216	−1.44603
$532$	2.26465	0.0981849
$533$	6.83362	0.295997
$534$	5.04741	0.218423
$535$	12.7829	0.552653
$536$	7.66184	0.330941
$537$	−28.5609	−1.23249
$538$	−5.57090	−0.240178
$539$	12.6840	0.546340
$540$	25.5763	1.10063
$541$	−32.7214	−1.40680	−0.703402	−	0.710792i	$-0.748337\pi$
$541$	−32.7214	−1.40680	−0.703402	+	0.710792i	$0.748337\pi$
$542$	4.83280	0.207587
$543$	−21.8846	−0.939159
$544$	−5.81792	−0.249441
$545$	−21.6978	−0.929433
$546$	20.0145	0.856542
$547$	−23.3503	−0.998386	−0.499193	−	0.866491i	$-0.666370\pi$
$547$	−23.3503	−0.998386	−0.499193	+	0.866491i	$0.666370\pi$
$548$	20.2600	0.865462
$549$	−5.65300	−0.241264
$550$	−5.47288	−0.233364
$551$	−1.19724	−0.0510040
$552$	6.08880	0.259156
$553$	−20.3672	−0.866100
$554$	−5.59881	−0.237871
$555$	−9.60493	−0.407707
$556$	−3.80448	−0.161346
$557$	−15.3137	−0.648861	−0.324430	−	0.945910i	$-0.605173\pi$
$557$	−15.3137	−0.648861	−0.324430	+	0.945910i	$0.605173\pi$
$558$	52.9148	2.24006
$559$	−26.2041	−1.10832
$560$	2.27892	0.0963020
$561$	46.9844	1.98368
$562$	−13.3974	−0.565134
$563$	−18.2403	−0.768735	−0.384367	−	0.923180i	$-0.625580\pi$
$563$	−18.2403	−0.768735	−0.384367	+	0.923180i	$0.625580\pi$
$564$	−4.91542	−0.206977
$565$	−21.8396	−0.918798
$566$	−8.28139	−0.348093
$567$	−36.9357	−1.55115
$568$	8.32609	0.349355
$569$	−31.6645	−1.32744	−0.663721	−	0.747980i	$-0.731024\pi$
$569$	−31.6645	−1.32744	−0.663721	+	0.747980i	$0.731024\pi$
$570$	9.04613	0.378901
$571$	11.2700	0.471634	0.235817	−	0.971798i	$-0.424223\pi$
$571$	11.2700	0.471634	0.235817	+	0.971798i	$0.424223\pi$
$572$	11.0729	0.462982
$573$	0.470350	0.0196492
$574$	−2.08200	−0.0869011
$575$	−4.12630	−0.172079
$576$	7.68829	0.320345
$577$	−15.9919	−0.665752	−0.332876	−	0.942971i	$-0.608019\pi$
$577$	−15.9919	−0.665752	−0.332876	+	0.942971i	$0.608019\pi$
$578$	−16.8482	−0.700792
$579$	−21.8668	−0.908754
$580$	−1.20478	−0.0500260
$581$	3.02824	0.125633
$582$	38.2722	1.58643
$583$	−29.4042	−1.21780
$584$	5.17284	0.214054
$585$	57.5081	2.37767
$586$	11.8937	0.491325
$587$	−7.78822	−0.321454	−0.160727	−	0.986999i	$-0.551384\pi$
$587$	−7.78822	−0.321454	−0.160727	+	0.986999i	$0.551384\pi$
$588$	16.7872	0.692294
$589$	11.4127	0.470251
$590$	−7.23211	−0.297741
$591$	−53.4545	−2.19882
$592$	−1.76064	−0.0723620
$593$	3.64630	0.149736	0.0748678	−	0.997193i	$-0.476147\pi$
$593$	3.64630	0.149736	0.0748678	+	0.997193i	$0.476147\pi$
$594$	−37.8617	−1.55349
$595$	13.2586	0.543549
$596$	3.03242	0.124213
$597$	−71.7867	−2.93803
$598$	8.34849	0.341395
$599$	−32.5173	−1.32862	−0.664310	−	0.747457i	$-0.731275\pi$
$599$	−32.5173	−1.32862	−0.664310	+	0.747457i	$0.731275\pi$
$600$	−7.24332	−0.295707
$601$	5.72376	0.233477	0.116738	−	0.993163i	$-0.462756\pi$
$601$	5.72376	0.233477	0.116738	+	0.993163i	$0.462756\pi$
$602$	7.98361	0.325388
$603$	−58.9064	−2.39885
$604$	−15.7481	−0.640781
$605$	8.17330	0.332292
$606$	−44.9145	−1.82453
$607$	−8.87069	−0.360050	−0.180025	−	0.983662i	$-0.557618\pi$
$607$	−8.87069	−0.360050	−0.180025	+	0.983662i	$0.557618\pi$
$608$	1.65821	0.0672493
$609$	3.22370	0.130631
$610$	−1.22693	−0.0496768
$611$	−6.73965	−0.272657
$612$	44.7298	1.80810
$613$	−40.9503	−1.65397	−0.826984	−	0.562226i	$-0.809945\pi$
$613$	−40.9503	−1.65397	−0.826984	+	0.562226i	$0.809945\pi$
$614$	−13.8965	−0.560818
$615$	−8.31656	−0.335356
$616$	−3.37359	−0.135926
$617$	6.38180	0.256922	0.128461	−	0.991715i	$-0.458996\pi$
$617$	6.38180	0.256922	0.128461	+	0.991715i	$0.458996\pi$
$618$	26.3592	1.06032
$619$	−15.8492	−0.637032	−0.318516	−	0.947918i	$-0.603184\pi$
$619$	−15.8492	−0.637032	−0.318516	+	0.947918i	$0.603184\pi$
$620$	11.4846	0.461234
$621$	−28.5460	−1.14551
$622$	16.3562	0.655822
$623$	−2.10851	−0.0844755
$624$	14.6550	0.586668
$625$	−9.01349	−0.360539
$626$	−6.46571	−0.258422
$627$	−13.3914	−0.534801
$628$	1.34112	0.0535165
$629$	−10.2433	−0.408426
$630$	−17.5210	−0.698053
$631$	17.7673	0.707306	0.353653	−	0.935377i	$-0.384939\pi$
$631$	17.7673	0.707306	0.353653	+	0.935377i	$0.384939\pi$
$632$	−14.9132	−0.593214
$633$	−71.3369	−2.83539
$634$	2.63051	0.104471
$635$	−28.1728	−1.11800
$636$	−38.9163	−1.54313
$637$	23.0174	0.911981
$638$	1.78350	0.0706094
$639$	−64.0134	−2.53233
$640$	1.66866	0.0659597
$641$	41.2143	1.62787	0.813933	−	0.580959i	$-0.197322\pi$
$641$	41.2143	1.62787	0.813933	+	0.580959i	$0.197322\pi$
$642$	−25.0446	−0.988432
$643$	−16.6183	−0.655360	−0.327680	−	0.944789i	$-0.606267\pi$
$643$	−16.6183	−0.655360	−0.327680	+	0.944789i	$0.606267\pi$
$644$	−2.54354	−0.100229
$645$	31.8905	1.25569
$646$	9.64734	0.379569
$647$	14.0065	0.550652	0.275326	−	0.961351i	$-0.411214\pi$
$647$	14.0065	0.550652	0.275326	+	0.961351i	$0.411214\pi$
$648$	−27.0449	−1.06242
$649$	10.7060	0.420248
$650$	−9.93148	−0.389545
$651$	−30.7300	−1.20440
$652$	0.0974129	0.00381498
$653$	−22.2727	−0.871599	−0.435799	−	0.900044i	$-0.643534\pi$
$653$	−22.2727	−0.871599	−0.435799	+	0.900044i	$0.643534\pi$
$654$	42.5110	1.66231
$655$	15.9244	0.622219
$656$	−1.52448	−0.0595208
$657$	−39.7703	−1.55159
$658$	2.05337	0.0800487
$659$	−48.9389	−1.90639	−0.953195	−	0.302356i	$-0.902227\pi$
$659$	−48.9389	−1.90639	−0.953195	+	0.302356i	$0.902227\pi$
$660$	−13.4758	−0.524545
$661$	−33.8685	−1.31733	−0.658666	−	0.752435i	$-0.728879\pi$
$661$	−33.8685	−1.31733	−0.658666	+	0.752435i	$0.728879\pi$
$662$	−14.4302	−0.560848
$663$	85.2613	3.31128
$664$	2.21733	0.0860490
$665$	−3.77893	−0.146541
$666$	13.5363	0.524522
$667$	1.34468	0.0520661
$668$	−2.57137	−0.0994895
$669$	−4.64987	−0.179775
$670$	−12.7850	−0.493929
$671$	1.81628	0.0701165
$672$	−4.46493	−0.172238
$673$	−11.9786	−0.461741	−0.230870	−	0.972984i	$-0.574157\pi$
$673$	−11.9786	−0.461741	−0.230870	+	0.972984i	$0.574157\pi$
$674$	−10.8467	−0.417798
$675$	33.9588	1.30707
$676$	7.09374	0.272836
$677$	29.7177	1.14214	0.571072	−	0.820900i	$-0.306528\pi$
$677$	29.7177	1.14214	0.571072	+	0.820900i	$0.306528\pi$
$678$	42.7887	1.64329
$679$	−15.9879	−0.613557
$680$	9.70815	0.372291
$681$	−25.9476	−0.994313
$682$	−17.0012	−0.651010
$683$	−10.5606	−0.404091	−0.202046	−	0.979376i	$-0.564759\pi$
$683$	−10.5606	−0.404091	−0.202046	+	0.979376i	$0.564759\pi$
$684$	−12.7488	−0.487463
$685$	−33.8070	−1.29170
$686$	−16.5727	−0.632749
$687$	−14.6083	−0.557340
$688$	5.84573	0.222866
$689$	−53.3590	−2.03281
$690$	−10.1602	−0.386791
$691$	21.5855	0.821153	0.410576	−	0.911826i	$-0.365328\pi$
$691$	21.5855	0.821153	0.410576	+	0.911826i	$0.365328\pi$
$692$	0.993081	0.0377513
$693$	25.9371	0.985271
$694$	33.0799	1.25569
$695$	6.34840	0.240809
$696$	2.36045	0.0894726
$697$	−8.86928	−0.335948
$698$	−6.71026	−0.253987
$699$	−22.3714	−0.846165
$700$	3.02583	0.114366
$701$	−5.82014	−0.219824	−0.109912	−	0.993941i	$-0.535057\pi$
$701$	−5.82014	−0.219824	−0.109912	+	0.993941i	$0.535057\pi$
$702$	−68.7066	−2.59316
$703$	2.91952	0.110112
$704$	−2.47020	−0.0930992
$705$	8.20219	0.308912
$706$	−30.9815	−1.16600
$707$	18.7626	0.705640
$708$	14.1694	0.532517
$709$	9.31063	0.349668	0.174834	−	0.984598i	$-0.444061\pi$
$709$	9.31063	0.349668	0.174834	+	0.984598i	$0.444061\pi$
$710$	−13.8934	−0.521412
$711$	114.657	4.29996
$712$	−1.54388	−0.0578595
$713$	−12.8182	−0.480044
$714$	−25.9766	−0.972150
$715$	−18.4770	−0.691000
$716$	8.73610	0.326483
$717$	−34.2044	−1.27739
$718$	−6.40867	−0.239169
$719$	12.0313	0.448692	0.224346	−	0.974510i	$-0.427975\pi$
$719$	12.0313	0.448692	0.224346	+	0.974510i	$0.427975\pi$
$720$	−12.8292	−0.478115
$721$	−11.0113	−0.410082
$722$	16.2503	0.604775
$723$	−32.8917	−1.22325
$724$	6.69399	0.248780
$725$	−1.59965	−0.0594094
$726$	−16.0134	−0.594312
$727$	−50.7447	−1.88202	−0.941008	−	0.338383i	$-0.890120\pi$
$727$	−50.7447	−1.88202	−0.941008	+	0.338383i	$0.890120\pi$
$728$	−6.12196	−0.226895
$729$	57.5997	2.13332
$730$	−8.63173	−0.319475
$731$	34.0100	1.25791
$732$	2.40383	0.0888481
$733$	−29.4276	−1.08693	−0.543466	−	0.839431i	$-0.682888\pi$
$733$	−29.4276	−1.08693	−0.543466	+	0.839431i	$0.682888\pi$
$734$	15.9079	0.587172
$735$	−28.0123	−1.03325
$736$	−1.86242	−0.0686497
$737$	18.9263	0.697158
$738$	11.7206	0.431442
$739$	−14.2276	−0.523369	−0.261685	−	0.965153i	$-0.584278\pi$
$739$	−14.2276	−0.523369	−0.261685	+	0.965153i	$0.584278\pi$
$740$	2.93792	0.108000
$741$	−24.3010	−0.892720
$742$	16.2569	0.596809
$743$	−44.0338	−1.61544	−0.807722	−	0.589564i	$-0.799300\pi$
$743$	−44.0338	−1.61544	−0.807722	+	0.589564i	$0.799300\pi$
$744$	−22.5010	−0.824927
$745$	−5.06009	−0.185387
$746$	−21.3965	−0.783382
$747$	−17.0475	−0.623734
$748$	−14.3714	−0.525471
$749$	10.4621	0.382278
$750$	39.3634	1.43735
$751$	37.7758	1.37846	0.689230	−	0.724543i	$-0.257949\pi$
$751$	37.7758	1.37846	0.689230	+	0.724543i	$0.257949\pi$
$752$	1.50351	0.0548274
$753$	29.4910	1.07471
$754$	3.23646	0.117865
$755$	26.2783	0.956364
$756$	20.9329	0.761321
$757$	−34.7261	−1.26214	−0.631070	−	0.775726i	$-0.717384\pi$
$757$	−34.7261	−1.26214	−0.631070	+	0.775726i	$0.717384\pi$
$758$	26.8603	0.975611
$759$	15.0406	0.545937
$760$	−2.76700	−0.100370
$761$	25.2423	0.915032	0.457516	−	0.889201i	$-0.348739\pi$
$761$	25.2423	0.915032	0.457516	+	0.889201i	$0.348739\pi$
$762$	55.1970	1.99958
$763$	−17.7586	−0.642903
$764$	−0.143869	−0.00520500
$765$	−74.6391	−2.69858
$766$	6.05516	0.218782
$767$	19.4279	0.701502
$768$	−3.26929	−0.117971
$769$	3.84225	0.138555	0.0692775	−	0.997597i	$-0.477931\pi$
$769$	3.84225	0.138555	0.0692775	+	0.997597i	$0.477931\pi$
$770$	5.62939	0.202869
$771$	95.5909	3.44262
$772$	6.68854	0.240726
$773$	−16.8917	−0.607552	−0.303776	−	0.952744i	$-0.598247\pi$
$773$	−16.8917	−0.607552	−0.303776	+	0.952744i	$0.598247\pi$
$774$	−44.9437	−1.61547
$775$	15.2487	0.547748
$776$	−11.7066	−0.420241
$777$	−7.86115	−0.282017
$778$	20.2788	0.727030
$779$	2.52790	0.0905716
$780$	−24.4542	−0.875600
$781$	20.5671	0.735949
$782$	−10.8354	−0.387473
$783$	−11.0665	−0.395483
$784$	−5.13482	−0.183386
$785$	−2.23788	−0.0798732
$786$	−31.1996	−1.11285
$787$	42.8806	1.52853	0.764264	−	0.644903i	$-0.223102\pi$
$787$	42.8806	1.52853	0.764264	+	0.644903i	$0.223102\pi$
$788$	16.3505	0.582461
$789$	52.2530	1.86026
$790$	24.8851	0.885371
$791$	−17.8746	−0.635547
$792$	18.9916	0.674837
$793$	3.29594	0.117042
$794$	12.6736	0.449770
$795$	64.9381	2.30312
$796$	21.9579	0.778275
$797$	−20.1368	−0.713281	−0.356640	−	0.934242i	$-0.616078\pi$
$797$	−20.1368	−0.713281	−0.356640	+	0.934242i	$0.616078\pi$
$798$	7.40379	0.262091
$799$	8.74731	0.309458
$800$	2.21556	0.0783319
$801$	11.8698	0.419399
$802$	1.51459	0.0534822
$803$	12.7780	0.450924
$804$	25.0488	0.883403
$805$	4.24431	0.149592
$806$	−30.8516	−1.08670
$807$	−18.2129	−0.641125
$808$	13.7383	0.483311
$809$	−3.79078	−0.133277	−0.0666384	−	0.997777i	$-0.521227\pi$
$809$	−3.79078	−0.133277	−0.0666384	+	0.997777i	$0.521227\pi$
$810$	45.1288	1.58567
$811$	−4.16895	−0.146392	−0.0731959	−	0.997318i	$-0.523320\pi$
$811$	−4.16895	−0.146392	−0.0731959	+	0.997318i	$0.523320\pi$
$812$	−0.986055	−0.0346037
$813$	15.7998	0.554125
$814$	−4.34914	−0.152437
$815$	−0.162549	−0.00569386
$816$	−19.0205	−0.665850
$817$	−9.69346	−0.339131
$818$	−32.1903	−1.12551
$819$	47.0674	1.64467
$820$	2.54384	0.0888347
$821$	5.70995	0.199278	0.0996392	−	0.995024i	$-0.468231\pi$
$821$	5.70995	0.199278	0.0996392	+	0.995024i	$0.468231\pi$
$822$	66.2358	2.31024
$823$	−17.8561	−0.622426	−0.311213	−	0.950340i	$-0.600735\pi$
$823$	−17.8561	−0.622426	−0.311213	+	0.950340i	$0.600735\pi$
$824$	−8.06265	−0.280876
$825$	−17.8925	−0.622935
$826$	−5.91911	−0.205952
$827$	−35.1971	−1.22392	−0.611962	−	0.790887i	$-0.709619\pi$
$827$	−35.1971	−1.22392	−0.611962	+	0.790887i	$0.709619\pi$
$828$	14.3188	0.497613
$829$	30.7097	1.06659	0.533296	−	0.845929i	$-0.320953\pi$
$829$	30.7097	1.06659	0.533296	+	0.845929i	$0.320953\pi$
$830$	−3.69998	−0.128428
$831$	−18.3042	−0.634965
$832$	−4.48260	−0.155406
$833$	−29.8740	−1.03507
$834$	−12.4380	−0.430692
$835$	4.29076	0.148488
$836$	4.09611	0.141667
$837$	105.491	3.64631
$838$	−38.4497	−1.32822
$839$	19.9074	0.687281	0.343640	−	0.939101i	$-0.388340\pi$
$839$	19.9074	0.687281	0.343640	+	0.939101i	$0.388340\pi$
$840$	7.45046	0.257065
$841$	−28.4787	−0.982024
$842$	23.6302	0.814349
$843$	−43.8000	−1.50855
$844$	21.8203	0.751085
$845$	−11.8371	−0.407207
$846$	−11.5594	−0.397421
$847$	6.68943	0.229852
$848$	11.9036	0.408770
$849$	−27.0743	−0.929188
$850$	12.8900	0.442122
$851$	−3.27906	−0.112405
$852$	27.2204	0.932557
$853$	−18.8117	−0.644101	−0.322051	−	0.946722i	$-0.604372\pi$
$853$	−18.8117	−0.644101	−0.322051	+	0.946722i	$0.604372\pi$
$854$	−1.00418	−0.0343622
$855$	21.2735	0.727537
$856$	7.66056	0.261832
$857$	42.9068	1.46567	0.732834	−	0.680408i	$-0.238197\pi$
$857$	42.9068	1.46567	0.732834	+	0.680408i	$0.238197\pi$
$858$	36.2007	1.23587
$859$	−12.2051	−0.416434	−0.208217	−	0.978083i	$-0.566766\pi$
$859$	−12.2051	−0.416434	−0.208217	+	0.978083i	$0.566766\pi$
$860$	−9.75456	−0.332628
$861$	−6.80668	−0.231971
$862$	15.9285	0.542526
$863$	44.5428	1.51625	0.758127	−	0.652106i	$-0.226115\pi$
$863$	44.5428	1.51625	0.758127	+	0.652106i	$0.226115\pi$
$864$	15.3274	0.521448
$865$	−1.65712	−0.0563437
$866$	−27.3235	−0.928490
$867$	−55.0817	−1.87067
$868$	9.39958	0.319042
$869$	−36.8385	−1.24966
$870$	−3.93880	−0.133538
$871$	34.3450	1.16374
$872$	−13.0031	−0.440341
$873$	90.0035	3.04616
$874$	3.08829	0.104463
$875$	−16.4437	−0.555898
$876$	16.9115	0.571388
$877$	−3.44974	−0.116489	−0.0582447	−	0.998302i	$-0.518550\pi$
$877$	−3.44974	−0.116489	−0.0582447	+	0.998302i	$0.518550\pi$
$878$	20.7917	0.701687
$879$	38.8841	1.31153
$880$	4.12193	0.138950
$881$	−13.9242	−0.469117	−0.234559	−	0.972102i	$-0.575364\pi$
$881$	−13.9242	−0.469117	−0.234559	+	0.972102i	$0.575364\pi$
$882$	39.4780	1.32929
$883$	8.45867	0.284657	0.142328	−	0.989819i	$-0.454541\pi$
$883$	8.45867	0.284657	0.142328	+	0.989819i	$0.454541\pi$
$884$	−26.0794	−0.877146
$885$	−23.6439	−0.794781
$886$	22.9946	0.772518
$887$	39.7557	1.33486	0.667432	−	0.744671i	$-0.267393\pi$
$887$	39.7557	1.33486	0.667432	+	0.744671i	$0.267393\pi$
$888$	−5.75606	−0.193161
$889$	−23.0580	−0.773341
$890$	2.57622	0.0863551
$891$	−66.8063	−2.23810
$892$	1.42229	0.0476217
$893$	−2.49314	−0.0834298
$894$	9.91388	0.331570
$895$	−14.5776	−0.487276
$896$	1.36572	0.0456254
$897$	27.2937	0.911309
$898$	−13.2910	−0.443526
$899$	−4.96922	−0.165733
$900$	−17.0339	−0.567796
$901$	69.2540	2.30718
$902$	−3.76576	−0.125386
$903$	26.1008	0.868579
$904$	−13.0881	−0.435303
$905$	−11.1700	−0.371304
$906$	−51.4852	−1.71048
$907$	54.7806	1.81896	0.909481	−	0.415746i	$-0.136480\pi$
$907$	54.7806	1.81896	0.909481	+	0.415746i	$0.136480\pi$
$908$	7.93675	0.263390
$909$	−105.624	−3.50332
$910$	10.2155	0.338641
$911$	52.1209	1.72684	0.863422	−	0.504483i	$-0.168317\pi$
$911$	52.1209	1.72684	0.863422	+	0.504483i	$0.168317\pi$
$912$	5.42118	0.179513
$913$	5.47724	0.181270
$914$	−16.1759	−0.535051
$915$	−4.01118	−0.132606
$916$	4.46832	0.147638
$917$	13.0333	0.430399
$918$	89.1735	2.94316
$919$	−51.6274	−1.70303	−0.851515	−	0.524331i	$-0.824316\pi$
$919$	−51.6274	−1.70303	−0.851515	+	0.524331i	$0.824316\pi$
$920$	3.10775	0.102460
$921$	−45.4318	−1.49703
$922$	7.74907	0.255202
$923$	37.3226	1.22849
$924$	−11.0293	−0.362836
$925$	3.90081	0.128258
$926$	−4.35584	−0.143142
$927$	61.9880	2.03595
$928$	−0.722005	−0.0237010
$929$	4.27176	0.140152	0.0700760	−	0.997542i	$-0.477676\pi$
$929$	4.27176	0.140152	0.0700760	+	0.997542i	$0.477676\pi$
$930$	37.5466	1.23120
$931$	8.51462	0.279055
$932$	6.84289	0.224146
$933$	53.4731	1.75063
$934$	12.3000	0.402469
$935$	23.9811	0.784265
$936$	34.4635	1.12648
$937$	11.8825	0.388183	0.194092	−	0.980983i	$-0.437824\pi$
$937$	11.8825	0.388183	0.194092	+	0.980983i	$0.437824\pi$
$938$	−10.4639	−0.341658
$939$	−21.1383	−0.689823
$940$	−2.50886	−0.0818299
$941$	27.8061	0.906453	0.453226	−	0.891395i	$-0.350273\pi$
$941$	27.8061	0.906453	0.453226	+	0.891395i	$0.350273\pi$
$942$	4.38451	0.142855
$943$	−2.83922	−0.0924576
$944$	−4.33407	−0.141062
$945$	−34.9299	−1.13627
$946$	14.4401	0.469489
$947$	46.3284	1.50547	0.752736	−	0.658323i	$-0.228734\pi$
$947$	46.3284	1.50547	0.752736	+	0.658323i	$0.228734\pi$
$948$	−48.7555	−1.58351
$949$	23.1878	0.752708
$950$	−3.67387	−0.119196
$951$	8.59992	0.278872
$952$	7.94563	0.257519
$953$	35.1394	1.13828	0.569139	−	0.822242i	$-0.307277\pi$
$953$	35.1394	1.13828	0.569139	+	0.822242i	$0.307277\pi$
$954$	−91.5180	−2.96300
$955$	0.240069	0.00776845
$956$	10.4623	0.338376
$957$	5.83078	0.188482
$958$	37.8644	1.22334
$959$	−27.6693	−0.893490
$960$	5.45535	0.176071
$961$	16.3692	0.528038
$962$	−7.89227	−0.254457
$963$	−58.8966	−1.89792
$964$	10.0608	0.324036
$965$	−11.1609	−0.359283
$966$	−8.31557	−0.267549
$967$	−31.2537	−1.00505	−0.502526	−	0.864562i	$-0.667596\pi$
$967$	−31.2537	−1.00505	−0.502526	+	0.864562i	$0.667596\pi$
$968$	4.89811	0.157431
$969$	31.5400	1.01321
$970$	19.5343	0.627210
$971$	−39.6882	−1.27366	−0.636828	−	0.771006i	$-0.719754\pi$
$971$	−39.6882	−1.27366	−0.636828	+	0.771006i	$0.719754\pi$
$972$	−42.4356	−1.36112
$973$	5.19584	0.166571
$974$	−43.1079	−1.38127
$975$	−32.4689	−1.03984
$976$	−0.735274	−0.0235356
$977$	−47.9201	−1.53310	−0.766550	−	0.642184i	$-0.778028\pi$
$977$	−47.9201	−1.53310	−0.766550	+	0.642184i	$0.778028\pi$
$978$	0.318471	0.0101836
$979$	−3.81370	−0.121886
$980$	8.56829	0.273704
$981$	99.9717	3.19185
$982$	10.8096	0.344950
$983$	2.90148	0.0925428	0.0462714	−	0.998929i	$-0.485266\pi$
$983$	2.90148	0.0925428	0.0462714	+	0.998929i	$0.485266\pi$
$984$	−4.98396	−0.158883
$985$	−27.2834	−0.869322
$986$	−4.20057	−0.133773
$987$	6.71307	0.213679
$988$	7.43310	0.236479
$989$	10.8872	0.346193
$990$	−31.6906	−1.00719
$991$	27.1166	0.861388	0.430694	−	0.902498i	$-0.358269\pi$
$991$	27.1166	0.861388	0.430694	+	0.902498i	$0.358269\pi$
$992$	6.88253	0.218520
$993$	−47.1767	−1.49711
$994$	−11.3711	−0.360669
$995$	−36.6403	−1.16157
$996$	7.24910	0.229697
$997$	−20.0165	−0.633930	−0.316965	−	0.948437i	$-0.602664\pi$
$997$	−20.0165	−0.633930	−0.316965	+	0.948437i	$0.602664\pi$
$998$	11.2787	0.357020
$999$	26.9861	0.853801

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8026.2.a.b.1.1	✓	81

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8026.2.a.b.1.1	✓	81	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -3.26929 q^{3} +1.00000 q^{4} -1.66866 q^{5} +3.26929 q^{6} -1.36572 q^{7} -1.00000 q^{8} +7.68829 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -3.26929 q^{3} +1.00000 q^{4} -1.66866 q^{5} +3.26929 q^{6} -1.36572 q^{7} -1.00000 q^{8} +7.68829 q^{9} +1.66866 q^{10} -2.47020 q^{11} -3.26929 q^{12} -4.48260 q^{13} +1.36572 q^{14} +5.45535 q^{15} +1.00000 q^{16} +5.81792 q^{17} -7.68829 q^{18} -1.65821 q^{19} -1.66866 q^{20} +4.46493 q^{21} +2.47020 q^{22} +1.86242 q^{23} +3.26929 q^{24} -2.21556 q^{25} +4.48260 q^{26} -15.3274 q^{27} -1.36572 q^{28} +0.722005 q^{29} -5.45535 q^{30} -6.88253 q^{31} -1.00000 q^{32} +8.07581 q^{33} -5.81792 q^{34} +2.27892 q^{35} +7.68829 q^{36} -1.76064 q^{37} +1.65821 q^{38} +14.6550 q^{39} +1.66866 q^{40} -1.52448 q^{41} -4.46493 q^{42} +5.84573 q^{43} -2.47020 q^{44} -12.8292 q^{45} -1.86242 q^{46} +1.50351 q^{47} -3.26929 q^{48} -5.13482 q^{49} +2.21556 q^{50} -19.0205 q^{51} -4.48260 q^{52} +11.9036 q^{53} +15.3274 q^{54} +4.12193 q^{55} +1.36572 q^{56} +5.42118 q^{57} -0.722005 q^{58} -4.33407 q^{59} +5.45535 q^{60} -0.735274 q^{61} +6.88253 q^{62} -10.5000 q^{63} +1.00000 q^{64} +7.47996 q^{65} -8.07581 q^{66} -7.66184 q^{67} +5.81792 q^{68} -6.08880 q^{69} -2.27892 q^{70} -8.32609 q^{71} -7.68829 q^{72} -5.17284 q^{73} +1.76064 q^{74} +7.24332 q^{75} -1.65821 q^{76} +3.37359 q^{77} -14.6550 q^{78} +14.9132 q^{79} -1.66866 q^{80} +27.0449 q^{81} +1.52448 q^{82} -2.21733 q^{83} +4.46493 q^{84} -9.70815 q^{85} -5.84573 q^{86} -2.36045 q^{87} +2.47020 q^{88} +1.54388 q^{89} +12.8292 q^{90} +6.12196 q^{91} +1.86242 q^{92} +22.5010 q^{93} -1.50351 q^{94} +2.76700 q^{95} +3.26929 q^{96} +11.7066 q^{97} +5.13482 q^{98} -18.9916 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 81 q - 81 q^{2} - 10 q^{3} + 81 q^{4} - 26 q^{5} + 10 q^{6} + 3 q^{7} - 81 q^{8} + 59 q^{9}+O(q^{10}) \) 81 * q - 81 * q^2 - 10 * q^3 + 81 * q^4 - 26 * q^5 + 10 * q^6 + 3 * q^7 - 81 * q^8 + 59 * q^9	\( 81 q - 81 q^{2} - 10 q^{3} + 81 q^{4} - 26 q^{5} + 10 q^{6} + 3 q^{7} - 81 q^{8} + 59 q^{9} + 26 q^{10} - 41 q^{11} - 10 q^{12} + 33 q^{13} - 3 q^{14} - 7 q^{15} + 81 q^{16} - 9 q^{17} - 59 q^{18} - 32 q^{19} - 26 q^{20} - 23 q^{21} + 41 q^{22} - 28 q^{23} + 10 q^{24} + 81 q^{25} - 33 q^{26} - 37 q^{27} + 3 q^{28} - 35 q^{29} + 7 q^{30} - 29 q^{31} - 81 q^{32} - 7 q^{33} + 9 q^{34} - 67 q^{35} + 59 q^{36} + 13 q^{37} + 32 q^{38} - 42 q^{39} + 26 q^{40} - 66 q^{41} + 23 q^{42} - 22 q^{43} - 41 q^{44} - 65 q^{45} + 28 q^{46} - 71 q^{47} - 10 q^{48} + 64 q^{49} - 81 q^{50} - 43 q^{51} + 33 q^{52} - 37 q^{53} + 37 q^{54} + 12 q^{55} - 3 q^{56} - q^{57} + 35 q^{58} - 162 q^{59} - 7 q^{60} + 19 q^{61} + 29 q^{62} - 16 q^{63} + 81 q^{64} - 45 q^{65} + 7 q^{66} - 43 q^{67} - 9 q^{68} - 21 q^{69} + 67 q^{70} - 99 q^{71} - 59 q^{72} + 53 q^{73} - 13 q^{74} - 61 q^{75} - 32 q^{76} - 31 q^{77} + 42 q^{78} + 4 q^{79} - 26 q^{80} + q^{81} + 66 q^{82} - 112 q^{83} - 23 q^{84} + 17 q^{85} + 22 q^{86} - 15 q^{87} + 41 q^{88} - 111 q^{89} + 65 q^{90} - 49 q^{91} - 28 q^{92} - 19 q^{93} + 71 q^{94} - 53 q^{95} + 10 q^{96} + 50 q^{97} - 64 q^{98} - 97 q^{99}+O(q^{100}) \) 81 * q - 81 * q^2 - 10 * q^3 + 81 * q^4 - 26 * q^5 + 10 * q^6 + 3 * q^7 - 81 * q^8 + 59 * q^9 + 26 * q^10 - 41 * q^11 - 10 * q^12 + 33 * q^13 - 3 * q^14 - 7 * q^15 + 81 * q^16 - 9 * q^17 - 59 * q^18 - 32 * q^19 - 26 * q^20 - 23 * q^21 + 41 * q^22 - 28 * q^23 + 10 * q^24 + 81 * q^25 - 33 * q^26 - 37 * q^27 + 3 * q^28 - 35 * q^29 + 7 * q^30 - 29 * q^31 - 81 * q^32 - 7 * q^33 + 9 * q^34 - 67 * q^35 + 59 * q^36 + 13 * q^37 + 32 * q^38 - 42 * q^39 + 26 * q^40 - 66 * q^41 + 23 * q^42 - 22 * q^43 - 41 * q^44 - 65 * q^45 + 28 * q^46 - 71 * q^47 - 10 * q^48 + 64 * q^49 - 81 * q^50 - 43 * q^51 + 33 * q^52 - 37 * q^53 + 37 * q^54 + 12 * q^55 - 3 * q^56 - q^57 + 35 * q^58 - 162 * q^59 - 7 * q^60 + 19 * q^61 + 29 * q^62 - 16 * q^63 + 81 * q^64 - 45 * q^65 + 7 * q^66 - 43 * q^67 - 9 * q^68 - 21 * q^69 + 67 * q^70 - 99 * q^71 - 59 * q^72 + 53 * q^73 - 13 * q^74 - 61 * q^75 - 32 * q^76 - 31 * q^77 + 42 * q^78 + 4 * q^79 - 26 * q^80 + q^81 + 66 * q^82 - 112 * q^83 - 23 * q^84 + 17 * q^85 + 22 * q^86 - 15 * q^87 + 41 * q^88 - 111 * q^89 + 65 * q^90 - 49 * q^91 - 28 * q^92 - 19 * q^93 + 71 * q^94 - 53 * q^95 + 10 * q^96 + 50 * q^97 - 64 * q^98 - 97 * q^99

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