LMFDB - Embedded newform 4026.2.a.u.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4026,2,Mod(1,4026)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4026, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4026.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4026 = 2 \cdot 3 \cdot 11 \cdot 61 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4026.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:	$32.1477718538$
Analytic rank:	$0$
Dimension:	$5$
Coefficient field:	5.5.9176805.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - x^{4} - 12x^{3} + 7x^{2} + 30x - 20 $ x^5 - x^4 - 12x^3 + 7x^2 + 30*x - 20
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$3.32361$ of defining polynomial
Character	$\chi$	$=$	4026.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -3.32361 q^{5} -1.00000 q^{6} -3.91566 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -3.32361 q^{5} -1.00000 q^{6} -3.91566 q^{7} -1.00000 q^{8} +1.00000 q^{9} +3.32361 q^{10} -1.00000 q^{11} +1.00000 q^{12} -2.77487 q^{13} +3.91566 q^{14} -3.32361 q^{15} +1.00000 q^{16} +0.807136 q^{17} -1.00000 q^{18} -7.13386 q^{19} -3.32361 q^{20} -3.91566 q^{21} +1.00000 q^{22} -5.96773 q^{23} -1.00000 q^{24} +6.04641 q^{25} +2.77487 q^{26} +1.00000 q^{27} -3.91566 q^{28} -8.37002 q^{29} +3.32361 q^{30} -0.644116 q^{31} -1.00000 q^{32} -1.00000 q^{33} -0.807136 q^{34} +13.0141 q^{35} +1.00000 q^{36} -8.31795 q^{37} +7.13386 q^{38} -2.77487 q^{39} +3.32361 q^{40} +9.01414 q^{41} +3.91566 q^{42} +10.4023 q^{43} -1.00000 q^{44} -3.32361 q^{45} +5.96773 q^{46} -2.49766 q^{47} +1.00000 q^{48} +8.33239 q^{49} -6.04641 q^{50} +0.807136 q^{51} -2.77487 q^{52} +0.130750 q^{53} -1.00000 q^{54} +3.32361 q^{55} +3.91566 q^{56} -7.13386 q^{57} +8.37002 q^{58} -14.3533 q^{59} -3.32361 q^{60} -1.00000 q^{61} +0.644116 q^{62} -3.91566 q^{63} +1.00000 q^{64} +9.22258 q^{65} +1.00000 q^{66} +11.9931 q^{67} +0.807136 q^{68} -5.96773 q^{69} -13.0141 q^{70} -12.0031 q^{71} -1.00000 q^{72} +9.98430 q^{73} +8.31795 q^{74} +6.04641 q^{75} -7.13386 q^{76} +3.91566 q^{77} +2.77487 q^{78} +16.7103 q^{79} -3.32361 q^{80} +1.00000 q^{81} -9.01414 q^{82} +3.25047 q^{83} -3.91566 q^{84} -2.68261 q^{85} -10.4023 q^{86} -8.37002 q^{87} +1.00000 q^{88} -14.1282 q^{89} +3.32361 q^{90} +10.8654 q^{91} -5.96773 q^{92} -0.644116 q^{93} +2.49766 q^{94} +23.7102 q^{95} -1.00000 q^{96} -12.4575 q^{97} -8.33239 q^{98} -1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - 5 q^{2} + 5 q^{3} + 5 q^{4} - q^{5} - 5 q^{6} - 3 q^{7} - 5 q^{8} + 5 q^{9}+O(q^{10}) $ 5 * q - 5 * q^2 + 5 * q^3 + 5 * q^4 - q^5 - 5 * q^6 - 3 * q^7 - 5 * q^8 + 5 * q^9	\( 5 q - 5 q^{2} + 5 q^{3} + 5 q^{4} - q^{5} - 5 q^{6} - 3 q^{7} - 5 q^{8} + 5 q^{9} + q^{10} - 5 q^{11} + 5 q^{12} + 2 q^{13} + 3 q^{14} - q^{15} + 5 q^{16} + 6 q^{17} - 5 q^{18} + 7 q^{19} - q^{20} - 3 q^{21} + 5 q^{22} - 12 q^{23} - 5 q^{24} - 2 q^{26} + 5 q^{27} - 3 q^{28} + 4 q^{29} + q^{30} - q^{31} - 5 q^{32} - 5 q^{33} - 6 q^{34} + 17 q^{35} + 5 q^{36} + 3 q^{37} - 7 q^{38} + 2 q^{39} + q^{40} - 3 q^{41} + 3 q^{42} + 24 q^{43} - 5 q^{44} - q^{45} + 12 q^{46} + 18 q^{47} + 5 q^{48} + 26 q^{49} + 6 q^{51} + 2 q^{52} - 13 q^{53} - 5 q^{54} + q^{55} + 3 q^{56} + 7 q^{57} - 4 q^{58} - 16 q^{59} - q^{60} - 5 q^{61} + q^{62} - 3 q^{63} + 5 q^{64} + 4 q^{65} + 5 q^{66} + 18 q^{67} + 6 q^{68} - 12 q^{69} - 17 q^{70} - 31 q^{71} - 5 q^{72} + 8 q^{73} - 3 q^{74} + 7 q^{76} + 3 q^{77} - 2 q^{78} + 32 q^{79} - q^{80} + 5 q^{81} + 3 q^{82} + 8 q^{83} - 3 q^{84} + 29 q^{85} - 24 q^{86} + 4 q^{87} + 5 q^{88} + q^{89} + q^{90} - 3 q^{91} - 12 q^{92} - q^{93} - 18 q^{94} + 33 q^{95} - 5 q^{96} - 4 q^{97} - 26 q^{98} - 5 q^{99}+O(q^{100}) \) 5 * q - 5 * q^2 + 5 * q^3 + 5 * q^4 - q^5 - 5 * q^6 - 3 * q^7 - 5 * q^8 + 5 * q^9 + q^10 - 5 * q^11 + 5 * q^12 + 2 * q^13 + 3 * q^14 - q^15 + 5 * q^16 + 6 * q^17 - 5 * q^18 + 7 * q^19 - q^20 - 3 * q^21 + 5 * q^22 - 12 * q^23 - 5 * q^24 - 2 * q^26 + 5 * q^27 - 3 * q^28 + 4 * q^29 + q^30 - q^31 - 5 * q^32 - 5 * q^33 - 6 * q^34 + 17 * q^35 + 5 * q^36 + 3 * q^37 - 7 * q^38 + 2 * q^39 + q^40 - 3 * q^41 + 3 * q^42 + 24 * q^43 - 5 * q^44 - q^45 + 12 * q^46 + 18 * q^47 + 5 * q^48 + 26 * q^49 + 6 * q^51 + 2 * q^52 - 13 * q^53 - 5 * q^54 + q^55 + 3 * q^56 + 7 * q^57 - 4 * q^58 - 16 * q^59 - q^60 - 5 * q^61 + q^62 - 3 * q^63 + 5 * q^64 + 4 * q^65 + 5 * q^66 + 18 * q^67 + 6 * q^68 - 12 * q^69 - 17 * q^70 - 31 * q^71 - 5 * q^72 + 8 * q^73 - 3 * q^74 + 7 * q^76 + 3 * q^77 - 2 * q^78 + 32 * q^79 - q^80 + 5 * q^81 + 3 * q^82 + 8 * q^83 - 3 * q^84 + 29 * q^85 - 24 * q^86 + 4 * q^87 + 5 * q^88 + q^89 + q^90 - 3 * q^91 - 12 * q^92 - q^93 - 18 * q^94 + 33 * q^95 - 5 * q^96 - 4 * q^97 - 26 * q^98 - 5 * 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
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	−3.32361	−1.48637	−0.743183	−	0.669089i	$-0.766685\pi$
$5$	−3.32361	−1.48637	−0.743183	+	0.669089i	$0.766685\pi$
$6$	−1.00000	−0.408248
$7$	−3.91566	−1.47998	−0.739990	−	0.672618i	$-0.765170\pi$
$7$	−3.91566	−1.47998	−0.739990	+	0.672618i	$0.765170\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	3.32361	1.05102
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	1.00000	0.288675
$13$	−2.77487	−0.769609	−0.384805	−	0.922998i	$-0.625731\pi$
$13$	−2.77487	−0.769609	−0.384805	+	0.922998i	$0.625731\pi$
$14$	3.91566	1.04650
$15$	−3.32361	−0.858153
$16$	1.00000	0.250000
$17$	0.807136	0.195759	0.0978797	−	0.995198i	$-0.468794\pi$
$17$	0.807136	0.195759	0.0978797	+	0.995198i	$0.468794\pi$
$18$	−1.00000	−0.235702
$19$	−7.13386	−1.63662	−0.818310	−	0.574777i	$-0.805089\pi$
$19$	−7.13386	−1.63662	−0.818310	+	0.574777i	$0.805089\pi$
$20$	−3.32361	−0.743183
$21$	−3.91566	−0.854467
$22$	1.00000	0.213201
$23$	−5.96773	−1.24436	−0.622179	−	0.782875i	$-0.713752\pi$
$23$	−5.96773	−1.24436	−0.622179	+	0.782875i	$0.713752\pi$
$24$	−1.00000	−0.204124
$25$	6.04641	1.20928
$26$	2.77487	0.544196
$27$	1.00000	0.192450
$28$	−3.91566	−0.739990
$29$	−8.37002	−1.55427	−0.777137	−	0.629331i	$-0.783329\pi$
$29$	−8.37002	−1.55427	−0.777137	+	0.629331i	$0.783329\pi$
$30$	3.32361	0.606806
$31$	−0.644116	−0.115687	−0.0578433	−	0.998326i	$-0.518422\pi$
$31$	−0.644116	−0.115687	−0.0578433	+	0.998326i	$0.518422\pi$
$32$	−1.00000	−0.176777
$33$	−1.00000	−0.174078
$34$	−0.807136	−0.138423
$35$	13.0141	2.19979
$36$	1.00000	0.166667
$37$	−8.31795	−1.36746	−0.683732	−	0.729734i	$-0.739644\pi$
$37$	−8.31795	−1.36746	−0.683732	+	0.729734i	$0.739644\pi$
$38$	7.13386	1.15727
$39$	−2.77487	−0.444334
$40$	3.32361	0.525510
$41$	9.01414	1.40777	0.703886	−	0.710313i	$-0.251447\pi$
$41$	9.01414	1.40777	0.703886	+	0.710313i	$0.251447\pi$
$42$	3.91566	0.604199
$43$	10.4023	1.58633	0.793167	−	0.609004i	$-0.208431\pi$
$43$	10.4023	1.58633	0.793167	+	0.609004i	$0.208431\pi$
$44$	−1.00000	−0.150756
$45$	−3.32361	−0.495455
$46$	5.96773	0.879894
$47$	−2.49766	−0.364321	−0.182161	−	0.983269i	$-0.558309\pi$
$47$	−2.49766	−0.364321	−0.182161	+	0.983269i	$0.558309\pi$
$48$	1.00000	0.144338
$49$	8.33239	1.19034
$50$	−6.04641	−0.855091
$51$	0.807136	0.113022
$52$	−2.77487	−0.384805
$53$	0.130750	0.0179599	0.00897997	−	0.999960i	$-0.497142\pi$
$53$	0.130750	0.0179599	0.00897997	+	0.999960i	$0.497142\pi$
$54$	−1.00000	−0.136083
$55$	3.32361	0.448156
$56$	3.91566	0.523252
$57$	−7.13386	−0.944903
$58$	8.37002	1.09904
$59$	−14.3533	−1.86865	−0.934323	−	0.356429i	$-0.883994\pi$
$59$	−14.3533	−1.86865	−0.934323	+	0.356429i	$0.883994\pi$
$60$	−3.32361	−0.429077
$61$	−1.00000	−0.128037
$61$	−1.00000	−0.128037
$62$	0.644116	0.0818028
$63$	−3.91566	−0.493327
$64$	1.00000	0.125000
$65$	9.22258	1.14392
$66$	1.00000	0.123091
$67$	11.9931	1.46519	0.732593	−	0.680667i	$-0.238310\pi$
$67$	11.9931	1.46519	0.732593	+	0.680667i	$0.238310\pi$
$68$	0.807136	0.0978797
$69$	−5.96773	−0.718430
$70$	−13.0141	−1.55549
$71$	−12.0031	−1.42451	−0.712254	−	0.701922i	$-0.752325\pi$
$71$	−12.0031	−1.42451	−0.712254	+	0.701922i	$0.752325\pi$
$72$	−1.00000	−0.117851
$73$	9.98430	1.16857	0.584287	−	0.811547i	$-0.301374\pi$
$73$	9.98430	1.16857	0.584287	+	0.811547i	$0.301374\pi$
$74$	8.31795	0.966942
$75$	6.04641	0.698179
$76$	−7.13386	−0.818310
$77$	3.91566	0.446231
$78$	2.77487	0.314192
$79$	16.7103	1.88006	0.940029	−	0.341094i	$-0.110797\pi$
$79$	16.7103	1.88006	0.940029	+	0.341094i	$0.110797\pi$
$80$	−3.32361	−0.371591
$81$	1.00000	0.111111
$82$	−9.01414	−0.995445
$83$	3.25047	0.356786	0.178393	−	0.983959i	$-0.442910\pi$
$83$	3.25047	0.356786	0.178393	+	0.983959i	$0.442910\pi$
$84$	−3.91566	−0.427233
$85$	−2.68261	−0.290970
$86$	−10.4023	−1.12171
$87$	−8.37002	−0.897361
$88$	1.00000	0.106600
$89$	−14.1282	−1.49759	−0.748793	−	0.662804i	$-0.769366\pi$
$89$	−14.1282	−1.49759	−0.748793	+	0.662804i	$0.769366\pi$
$90$	3.32361	0.350340
$91$	10.8654	1.13901
$92$	−5.96773	−0.622179
$93$	−0.644116	−0.0667917
$94$	2.49766	0.257614
$95$	23.7102	2.43262
$96$	−1.00000	−0.102062
$97$	−12.4575	−1.26487	−0.632433	−	0.774615i	$-0.717943\pi$
$97$	−12.4575	−1.26487	−0.632433	+	0.774615i	$0.717943\pi$
$98$	−8.33239	−0.841698
$99$	−1.00000	−0.100504
$100$	6.04641	0.604641
$101$	−3.04203	−0.302693	−0.151347	−	0.988481i	$-0.548361\pi$
$101$	−3.04203	−0.302693	−0.151347	+	0.988481i	$0.548361\pi$
$102$	−0.807136	−0.0799184
$103$	−12.4252	−1.22429	−0.612146	−	0.790745i	$-0.709694\pi$
$103$	−12.4252	−1.22429	−0.612146	+	0.790745i	$0.709694\pi$
$104$	2.77487	0.272098
$105$	13.0141	1.27005
$106$	−0.130750	−0.0126996
$107$	−0.406685	−0.0393157	−0.0196579	−	0.999807i	$-0.506258\pi$
$107$	−0.406685	−0.0393157	−0.0196579	+	0.999807i	$0.506258\pi$
$108$	1.00000	0.0962250
$109$	−3.50077	−0.335313	−0.167657	−	0.985845i	$-0.553620\pi$
$109$	−3.50077	−0.335313	−0.167657	+	0.985845i	$0.553620\pi$
$110$	−3.32361	−0.316894
$111$	−8.31795	−0.789505
$112$	−3.91566	−0.369995
$113$	−16.9353	−1.59314	−0.796571	−	0.604545i	$-0.793355\pi$
$113$	−16.9353	−1.59314	−0.796571	+	0.604545i	$0.793355\pi$
$114$	7.13386	0.668147
$115$	19.8344	1.84957
$116$	−8.37002	−0.777137
$117$	−2.77487	−0.256536
$118$	14.3533	1.32133
$119$	−3.16047	−0.289720
$120$	3.32361	0.303403
$121$	1.00000	0.0909091
$122$	1.00000	0.0905357
$123$	9.01414	0.812778
$124$	−0.644116	−0.0578433
$125$	−3.47786	−0.311069
$126$	3.91566	0.348835
$127$	0.0833558	0.00739663	0.00369831	−	0.999993i	$-0.498823\pi$
$127$	0.0833558	0.00739663	0.00369831	+	0.999993i	$0.498823\pi$
$128$	−1.00000	−0.0883883
$129$	10.4023	0.915871
$130$	−9.22258	−0.808874
$131$	18.1194	1.58310	0.791551	−	0.611103i	$-0.209274\pi$
$131$	18.1194	1.58310	0.791551	+	0.611103i	$0.209274\pi$
$132$	−1.00000	−0.0870388
$133$	27.9338	2.42217
$134$	−11.9931	−1.03604
$135$	−3.32361	−0.286051
$136$	−0.807136	−0.0692114
$137$	−10.0875	−0.861829	−0.430915	−	0.902393i	$-0.641809\pi$
$137$	−10.0875	−0.861829	−0.430915	+	0.902393i	$0.641809\pi$
$138$	5.96773	0.508007
$139$	−2.57409	−0.218331	−0.109166	−	0.994024i	$-0.534818\pi$
$139$	−2.57409	−0.218331	−0.109166	+	0.994024i	$0.534818\pi$
$140$	13.0141	1.09990
$141$	−2.49766	−0.210341
$142$	12.0031	1.00728
$143$	2.77487	0.232046
$144$	1.00000	0.0833333
$145$	27.8187	2.31022
$146$	−9.98430	−0.826306
$147$	8.33239	0.687244
$148$	−8.31795	−0.683732
$149$	19.3798	1.58765	0.793827	−	0.608144i	$-0.208086\pi$
$149$	19.3798	1.58765	0.793827	+	0.608144i	$0.208086\pi$
$150$	−6.04641	−0.493687
$151$	11.6305	0.946480	0.473240	−	0.880934i	$-0.343084\pi$
$151$	11.6305	0.946480	0.473240	+	0.880934i	$0.343084\pi$
$152$	7.13386	0.578633
$153$	0.807136	0.0652531
$154$	−3.91566	−0.315533
$155$	2.14079	0.171953
$156$	−2.77487	−0.222167
$157$	12.0906	0.964932	0.482466	−	0.875915i	$-0.339741\pi$
$157$	12.0906	0.964932	0.482466	+	0.875915i	$0.339741\pi$
$158$	−16.7103	−1.32940
$159$	0.130750	0.0103692
$160$	3.32361	0.262755
$161$	23.3676	1.84162
$162$	−1.00000	−0.0785674
$163$	23.4030	1.83306	0.916531	−	0.399963i	$-0.130977\pi$
$163$	23.4030	1.83306	0.916531	+	0.399963i	$0.130977\pi$
$164$	9.01414	0.703886
$165$	3.32361	0.258743
$166$	−3.25047	−0.252286
$167$	9.58638	0.741817	0.370908	−	0.928669i	$-0.379046\pi$
$167$	9.58638	0.741817	0.370908	+	0.928669i	$0.379046\pi$
$168$	3.91566	0.302100
$169$	−5.30012	−0.407701
$170$	2.68261	0.205747
$171$	−7.13386	−0.545540
$172$	10.4023	0.793167
$173$	−12.3525	−0.939141	−0.469571	−	0.882895i	$-0.655591\pi$
$173$	−12.3525	−0.939141	−0.469571	+	0.882895i	$0.655591\pi$
$174$	8.37002	0.634530
$175$	−23.6757	−1.78971
$176$	−1.00000	−0.0753778
$177$	−14.3533	−1.07886
$178$	14.1282	1.05895
$179$	−4.78053	−0.357313	−0.178657	−	0.983911i	$-0.557175\pi$
$179$	−4.78053	−0.357313	−0.178657	+	0.983911i	$0.557175\pi$
$180$	−3.32361	−0.247728
$181$	22.0037	1.63552	0.817760	−	0.575559i	$-0.195216\pi$
$181$	22.0037	1.63552	0.817760	+	0.575559i	$0.195216\pi$
$182$	−10.8654	−0.805399
$183$	−1.00000	−0.0739221
$184$	5.96773	0.439947
$185$	27.6457	2.03255
$186$	0.644116	0.0472289
$187$	−0.807136	−0.0590237
$188$	−2.49766	−0.182161
$189$	−3.91566	−0.284822
$190$	−23.7102	−1.72012
$191$	−7.89570	−0.571313	−0.285656	−	0.958332i	$-0.592212\pi$
$191$	−7.89570	−0.571313	−0.285656	+	0.958332i	$0.592212\pi$
$192$	1.00000	0.0721688
$193$	−8.24919	−0.593790	−0.296895	−	0.954910i	$-0.595951\pi$
$193$	−8.24919	−0.593790	−0.296895	+	0.954910i	$0.595951\pi$
$194$	12.4575	0.894395
$195$	9.22258	0.660443
$196$	8.33239	0.595170
$197$	−3.26843	−0.232866	−0.116433	−	0.993199i	$-0.537146\pi$
$197$	−3.26843	−0.232866	−0.116433	+	0.993199i	$0.537146\pi$
$198$	1.00000	0.0710669
$199$	12.1108	0.858510	0.429255	−	0.903183i	$-0.358776\pi$
$199$	12.1108	0.858510	0.429255	+	0.903183i	$0.358776\pi$
$200$	−6.04641	−0.427546
$201$	11.9931	0.845926
$202$	3.04203	0.214036
$203$	32.7742	2.30030
$204$	0.807136	0.0565109
$205$	−29.9595	−2.09246
$206$	12.4252	0.865705
$207$	−5.96773	−0.414786
$208$	−2.77487	−0.192402
$209$	7.13386	0.493460
$210$	−13.0141	−0.898061
$211$	1.11333	0.0766446	0.0383223	−	0.999265i	$-0.487799\pi$
$211$	1.11333	0.0766446	0.0383223	+	0.999265i	$0.487799\pi$
$212$	0.130750	0.00897997
$213$	−12.0031	−0.822440
$214$	0.406685	0.0278004
$215$	−34.5732	−2.35787
$216$	−1.00000	−0.0680414
$217$	2.52214	0.171214
$218$	3.50077	0.237102
$219$	9.98430	0.674676
$220$	3.32361	0.224078
$221$	−2.23970	−0.150658
$222$	8.31795	0.558264
$223$	−23.2289	−1.55552	−0.777762	−	0.628559i	$-0.783645\pi$
$223$	−23.2289	−1.55552	−0.777762	+	0.628559i	$0.783645\pi$
$224$	3.91566	0.261626
$225$	6.04641	0.403094
$226$	16.9353	1.12652
$227$	11.1327	0.738904	0.369452	−	0.929250i	$-0.379545\pi$
$227$	11.1327	0.738904	0.369452	+	0.929250i	$0.379545\pi$
$228$	−7.13386	−0.472452
$229$	13.8435	0.914804	0.457402	−	0.889260i	$-0.348780\pi$
$229$	13.8435	0.914804	0.457402	+	0.889260i	$0.348780\pi$
$230$	−19.8344	−1.30784
$231$	3.91566	0.257631
$232$	8.37002	0.549519
$233$	−23.9928	−1.57182	−0.785909	−	0.618342i	$-0.787805\pi$
$233$	−23.9928	−1.57182	−0.785909	+	0.618342i	$0.787805\pi$
$234$	2.77487	0.181399
$235$	8.30126	0.541515
$236$	−14.3533	−0.934323
$237$	16.7103	1.08545
$238$	3.16047	0.204863
$239$	−18.2856	−1.18279	−0.591397	−	0.806380i	$-0.701423\pi$
$239$	−18.2856	−1.18279	−0.591397	+	0.806380i	$0.701423\pi$
$240$	−3.32361	−0.214538
$241$	−15.7631	−1.01539	−0.507696	−	0.861536i	$-0.669503\pi$
$241$	−15.7631	−1.01539	−0.507696	+	0.861536i	$0.669503\pi$
$242$	−1.00000	−0.0642824
$243$	1.00000	0.0641500
$244$	−1.00000	−0.0640184
$245$	−27.6936	−1.76928
$246$	−9.01414	−0.574721
$247$	19.7955	1.25956
$248$	0.644116	0.0409014
$249$	3.25047	0.205990
$250$	3.47786	0.219959
$251$	13.6086	0.858968	0.429484	−	0.903074i	$-0.358695\pi$
$251$	13.6086	0.858968	0.429484	+	0.903074i	$0.358695\pi$
$252$	−3.91566	−0.246663
$253$	5.96773	0.375188
$254$	−0.0833558	−0.00523021
$255$	−2.68261	−0.167992
$256$	1.00000	0.0625000
$257$	22.9018	1.42857	0.714287	−	0.699852i	$-0.246751\pi$
$257$	22.9018	1.42857	0.714287	+	0.699852i	$0.246751\pi$
$258$	−10.4023	−0.647619
$259$	32.5703	2.02382
$260$	9.22258	0.571960
$261$	−8.37002	−0.518091
$262$	−18.1194	−1.11942
$263$	−19.2813	−1.18894	−0.594468	−	0.804120i	$-0.702637\pi$
$263$	−19.2813	−1.18894	−0.594468	+	0.804120i	$0.702637\pi$
$264$	1.00000	0.0615457
$265$	−0.434564	−0.0266950
$266$	−27.9338	−1.71273
$267$	−14.1282	−0.864632
$268$	11.9931	0.732593
$269$	30.4439	1.85620	0.928099	−	0.372334i	$-0.121443\pi$
$269$	30.4439	1.85620	0.928099	+	0.372334i	$0.121443\pi$
$270$	3.32361	0.202269
$271$	14.8369	0.901275	0.450637	−	0.892707i	$-0.351197\pi$
$271$	14.8369	0.901275	0.450637	+	0.892707i	$0.351197\pi$
$272$	0.807136	0.0489398
$273$	10.8654	0.657606
$274$	10.0875	0.609405
$275$	−6.04641	−0.364612
$276$	−5.96773	−0.359215
$277$	−20.0794	−1.20645	−0.603226	−	0.797570i	$-0.706118\pi$
$277$	−20.0794	−1.20645	−0.603226	+	0.797570i	$0.706118\pi$
$278$	2.57409	0.154383
$279$	−0.644116	−0.0385622
$280$	−13.0141	−0.777744
$281$	9.91566	0.591519	0.295759	−	0.955262i	$-0.404427\pi$
$281$	9.91566	0.591519	0.295759	+	0.955262i	$0.404427\pi$
$282$	2.49766	0.148734
$283$	22.2578	1.32309	0.661544	−	0.749906i	$-0.269901\pi$
$283$	22.2578	1.32309	0.661544	+	0.749906i	$0.269901\pi$
$284$	−12.0031	−0.712254
$285$	23.7102	1.40447
$286$	−2.77487	−0.164081
$287$	−35.2963	−2.08347
$288$	−1.00000	−0.0589256
$289$	−16.3485	−0.961678
$290$	−27.8187	−1.63357
$291$	−12.4575	−0.730270
$292$	9.98430	0.584287
$293$	0.943253	0.0551054	0.0275527	−	0.999620i	$-0.491229\pi$
$293$	0.943253	0.0551054	0.0275527	+	0.999620i	$0.491229\pi$
$294$	−8.33239	−0.485955
$295$	47.7049	2.77749
$296$	8.31795	0.483471
$297$	−1.00000	−0.0580259
$298$	−19.3798	−1.12264
$299$	16.5597	0.957669
$300$	6.04641	0.349090
$301$	−40.7318	−2.34774
$302$	−11.6305	−0.669262
$303$	−3.04203	−0.174760
$304$	−7.13386	−0.409155
$305$	3.32361	0.190310
$306$	−0.807136	−0.0461409
$307$	18.0430	1.02977	0.514884	−	0.857260i	$-0.327835\pi$
$307$	18.0430	1.02977	0.514884	+	0.857260i	$0.327835\pi$
$308$	3.91566	0.223115
$309$	−12.4252	−0.706845
$310$	−2.14079	−0.121589
$311$	15.0514	0.853485	0.426742	−	0.904373i	$-0.359661\pi$
$311$	15.0514	0.853485	0.426742	+	0.904373i	$0.359661\pi$
$312$	2.77487	0.157096
$313$	13.1048	0.740729	0.370364	−	0.928887i	$-0.379233\pi$
$313$	13.1048	0.740729	0.370364	+	0.928887i	$0.379233\pi$
$314$	−12.0906	−0.682310
$315$	13.0141	0.733264
$316$	16.7103	0.940029
$317$	−3.78844	−0.212780	−0.106390	−	0.994324i	$-0.533929\pi$
$317$	−3.78844	−0.212780	−0.106390	+	0.994324i	$0.533929\pi$
$318$	−0.130750	−0.00733211
$319$	8.37002	0.468631
$320$	−3.32361	−0.185796
$321$	−0.406685	−0.0226990
$322$	−23.3676	−1.30223
$323$	−5.75800	−0.320384
$324$	1.00000	0.0555556
$325$	−16.7780	−0.930675
$326$	−23.4030	−1.29617
$327$	−3.50077	−0.193593
$328$	−9.01414	−0.497723
$329$	9.77999	0.539188
$330$	−3.32361	−0.182959
$331$	−33.4307	−1.83752	−0.918760	−	0.394817i	$-0.870808\pi$
$331$	−33.4307	−1.83752	−0.918760	+	0.394817i	$0.870808\pi$
$332$	3.25047	0.178393
$333$	−8.31795	−0.455821
$334$	−9.58638	−0.524544
$335$	−39.8603	−2.17780
$336$	−3.91566	−0.213617
$337$	−6.57265	−0.358035	−0.179017	−	0.983846i	$-0.557292\pi$
$337$	−6.57265	−0.358035	−0.179017	+	0.983846i	$0.557292\pi$
$338$	5.30012	0.288288
$339$	−16.9353	−0.919801
$340$	−2.68261	−0.145485
$341$	0.644116	0.0348808
$342$	7.13386	0.385755
$343$	−5.21717	−0.281701
$344$	−10.4023	−0.560854
$345$	19.8344	1.06785
$346$	12.3525	0.664073
$347$	−13.6625	−0.733442	−0.366721	−	0.930331i	$-0.619520\pi$
$347$	−13.6625	−0.733442	−0.366721	+	0.930331i	$0.619520\pi$
$348$	−8.37002	−0.448680
$349$	15.5871	0.834359	0.417180	−	0.908824i	$-0.363019\pi$
$349$	15.5871	0.834359	0.417180	+	0.908824i	$0.363019\pi$
$350$	23.6757	1.26552
$351$	−2.77487	−0.148111
$352$	1.00000	0.0533002
$353$	−27.3100	−1.45357	−0.726783	−	0.686867i	$-0.758986\pi$
$353$	−27.3100	−1.45357	−0.726783	+	0.686867i	$0.758986\pi$
$354$	14.3533	0.762871
$355$	39.8937	2.11734
$356$	−14.1282	−0.748793
$357$	−3.16047	−0.167270
$358$	4.78053	0.252659
$359$	2.41656	0.127541	0.0637705	−	0.997965i	$-0.479687\pi$
$359$	2.41656	0.127541	0.0637705	+	0.997965i	$0.479687\pi$
$360$	3.32361	0.175170
$361$	31.8920	1.67853
$362$	−22.0037	−1.15649
$363$	1.00000	0.0524864
$364$	10.8654	0.569503
$365$	−33.1839	−1.73693
$366$	1.00000	0.0522708
$367$	−19.6890	−1.02776	−0.513878	−	0.857864i	$-0.671791\pi$
$367$	−19.6890	−1.02776	−0.513878	+	0.857864i	$0.671791\pi$
$368$	−5.96773	−0.311089
$369$	9.01414	0.469257
$370$	−27.6457	−1.43723
$371$	−0.511974	−0.0265804
$372$	−0.644116	−0.0333959
$373$	−3.71020	−0.192107	−0.0960535	−	0.995376i	$-0.530622\pi$
$373$	−3.71020	−0.192107	−0.0960535	+	0.995376i	$0.530622\pi$
$374$	0.807136	0.0417360
$375$	−3.47786	−0.179596
$376$	2.49766	0.128807
$377$	23.2257	1.19618
$378$	3.91566	0.201400
$379$	2.53813	0.130375	0.0651875	−	0.997873i	$-0.479235\pi$
$379$	2.53813	0.130375	0.0651875	+	0.997873i	$0.479235\pi$
$380$	23.7102	1.21631
$381$	0.0833558	0.00427044
$382$	7.89570	0.403979
$383$	−31.5793	−1.61363	−0.806813	−	0.590807i	$-0.798809\pi$
$383$	−31.5793	−1.61363	−0.806813	+	0.590807i	$0.798809\pi$
$384$	−1.00000	−0.0510310
$385$	−13.0141	−0.663262
$386$	8.24919	0.419873
$387$	10.4023	0.528778
$388$	−12.4575	−0.632433
$389$	−4.45252	−0.225752	−0.112876	−	0.993609i	$-0.536006\pi$
$389$	−4.45252	−0.225752	−0.112876	+	0.993609i	$0.536006\pi$
$390$	−9.22258	−0.467004
$391$	−4.81677	−0.243595
$392$	−8.33239	−0.420849
$393$	18.1194	0.914004
$394$	3.26843	0.164661
$395$	−55.5387	−2.79445
$396$	−1.00000	−0.0502519
$397$	−24.1293	−1.21102	−0.605508	−	0.795839i	$-0.707030\pi$
$397$	−24.1293	−1.21102	−0.605508	+	0.795839i	$0.707030\pi$
$398$	−12.1108	−0.607058
$399$	27.9338	1.39844
$400$	6.04641	0.302320
$401$	20.9175	1.04457	0.522285	−	0.852771i	$-0.325080\pi$
$401$	20.9175	1.04457	0.522285	+	0.852771i	$0.325080\pi$
$402$	−11.9931	−0.598160
$403$	1.78734	0.0890335
$404$	−3.04203	−0.151347
$405$	−3.32361	−0.165152
$406$	−32.7742	−1.62655
$407$	8.31795	0.412306
$408$	−0.807136	−0.0399592
$409$	−31.6698	−1.56597	−0.782987	−	0.622039i	$-0.786305\pi$
$409$	−31.6698	−1.56597	−0.782987	+	0.622039i	$0.786305\pi$
$410$	29.9595	1.47960
$411$	−10.0875	−0.497577
$412$	−12.4252	−0.612146
$413$	56.2028	2.76556
$414$	5.96773	0.293298
$415$	−10.8033	−0.530314
$416$	2.77487	0.136049
$417$	−2.57409	−0.126054
$418$	−7.13386	−0.348929
$419$	14.9639	0.731035	0.365517	−	0.930804i	$-0.380892\pi$
$419$	14.9639	0.731035	0.365517	+	0.930804i	$0.380892\pi$
$420$	13.0141	0.635025
$421$	23.1925	1.13033	0.565166	−	0.824977i	$-0.308812\pi$
$421$	23.1925	1.13033	0.565166	+	0.824977i	$0.308812\pi$
$422$	−1.11333	−0.0541959
$423$	−2.49766	−0.121440
$424$	−0.130750	−0.00634980
$425$	4.88028	0.236728
$426$	12.0031	0.581553
$427$	3.91566	0.189492
$428$	−0.406685	−0.0196579
$429$	2.77487	0.133972
$430$	34.5732	1.66727
$431$	31.4330	1.51407	0.757037	−	0.653372i	$-0.226646\pi$
$431$	31.4330	1.51407	0.757037	+	0.653372i	$0.226646\pi$
$432$	1.00000	0.0481125
$433$	−23.8895	−1.14806	−0.574028	−	0.818836i	$-0.694620\pi$
$433$	−23.8895	−1.14806	−0.574028	+	0.818836i	$0.694620\pi$
$434$	−2.52214	−0.121067
$435$	27.8187	1.33381
$436$	−3.50077	−0.167657
$437$	42.5730	2.03654
$438$	−9.98430	−0.477068
$439$	−24.3409	−1.16173	−0.580863	−	0.814001i	$-0.697285\pi$
$439$	−24.3409	−1.16173	−0.580863	+	0.814001i	$0.697285\pi$
$440$	−3.32361	−0.158447
$441$	8.33239	0.396780
$442$	2.23970	0.106531
$443$	−24.7483	−1.17583	−0.587913	−	0.808924i	$-0.700050\pi$
$443$	−24.7483	−1.17583	−0.587913	+	0.808924i	$0.700050\pi$
$444$	−8.31795	−0.394753
$445$	46.9567	2.22596
$446$	23.2289	1.09992
$447$	19.3798	0.916632
$448$	−3.91566	−0.184998
$449$	6.44772	0.304287	0.152143	−	0.988358i	$-0.451382\pi$
$449$	6.44772	0.304287	0.152143	+	0.988358i	$0.451382\pi$
$450$	−6.04641	−0.285030
$451$	−9.01414	−0.424459
$452$	−16.9353	−0.796571
$453$	11.6305	0.546450
$454$	−11.1327	−0.522484
$455$	−36.1125	−1.69298
$456$	7.13386	0.334074
$457$	−8.49877	−0.397556	−0.198778	−	0.980045i	$-0.563697\pi$
$457$	−8.49877	−0.397556	−0.198778	+	0.980045i	$0.563697\pi$
$458$	−13.8435	−0.646864
$459$	0.807136	0.0376739
$460$	19.8344	0.924785
$461$	3.36904	0.156912	0.0784559	−	0.996918i	$-0.475001\pi$
$461$	3.36904	0.156912	0.0784559	+	0.996918i	$0.475001\pi$
$462$	−3.91566	−0.182173
$463$	7.77444	0.361309	0.180655	−	0.983547i	$-0.442178\pi$
$463$	7.77444	0.361309	0.180655	+	0.983547i	$0.442178\pi$
$464$	−8.37002	−0.388569
$465$	2.14079	0.0992769
$466$	23.9928	1.11144
$467$	5.06904	0.234567	0.117284	−	0.993098i	$-0.462581\pi$
$467$	5.06904	0.234567	0.117284	+	0.993098i	$0.462581\pi$
$468$	−2.77487	−0.128268
$469$	−46.9608	−2.16845
$470$	−8.30126	−0.382909
$471$	12.0906	0.557104
$472$	14.3533	0.660666
$473$	−10.4023	−0.478298
$474$	−16.7103	−0.767531
$475$	−43.1343	−1.97914
$476$	−3.16047	−0.144860
$477$	0.130750	0.00598665
$478$	18.2856	0.836362
$479$	2.62190	0.119798	0.0598988	−	0.998204i	$-0.480922\pi$
$479$	2.62190	0.119798	0.0598988	+	0.998204i	$0.480922\pi$
$480$	3.32361	0.151702
$481$	23.0812	1.05241
$482$	15.7631	0.717991
$483$	23.3676	1.06326
$484$	1.00000	0.0454545
$485$	41.4038	1.88005
$486$	−1.00000	−0.0453609
$487$	5.61653	0.254509	0.127255	−	0.991870i	$-0.459383\pi$
$487$	5.61653	0.254509	0.127255	+	0.991870i	$0.459383\pi$
$488$	1.00000	0.0452679
$489$	23.4030	1.05832
$490$	27.6936	1.25107
$491$	−12.3413	−0.556956	−0.278478	−	0.960443i	$-0.589830\pi$
$491$	−12.3413	−0.556956	−0.278478	+	0.960443i	$0.589830\pi$
$492$	9.01414	0.406389
$493$	−6.75575	−0.304264
$494$	−19.7955	−0.890642
$495$	3.32361	0.149385
$496$	−0.644116	−0.0289217
$497$	47.0001	2.10824
$498$	−3.25047	−0.145657
$499$	−22.5628	−1.01005	−0.505024	−	0.863105i	$-0.668516\pi$
$499$	−22.5628	−1.01005	−0.505024	+	0.863105i	$0.668516\pi$
$500$	−3.47786	−0.155535
$501$	9.58638	0.428288
$502$	−13.6086	−0.607382
$503$	4.85240	0.216358	0.108179	−	0.994131i	$-0.465498\pi$
$503$	4.85240	0.216358	0.108179	+	0.994131i	$0.465498\pi$
$504$	3.91566	0.174417
$505$	10.1105	0.449913
$506$	−5.96773	−0.265298
$507$	−5.30012	−0.235386
$508$	0.0833558	0.00369831
$509$	11.4961	0.509556	0.254778	−	0.967000i	$-0.417998\pi$
$509$	11.4961	0.509556	0.254778	+	0.967000i	$0.417998\pi$
$510$	2.68261	0.118788
$511$	−39.0951	−1.72947
$512$	−1.00000	−0.0441942
$513$	−7.13386	−0.314968
$514$	−22.9018	−1.01015
$515$	41.2966	1.81975
$516$	10.4023	0.457935
$517$	2.49766	0.109847
$518$	−32.5703	−1.43106
$519$	−12.3525	−0.542214
$520$	−9.22258	−0.404437
$521$	31.6025	1.38453	0.692265	−	0.721644i	$-0.256613\pi$
$521$	31.6025	1.38453	0.692265	+	0.721644i	$0.256613\pi$
$522$	8.37002	0.366346
$523$	−19.5926	−0.856725	−0.428362	−	0.903607i	$-0.640909\pi$
$523$	−19.5926	−0.856725	−0.428362	+	0.903607i	$0.640909\pi$
$524$	18.1194	0.791551
$525$	−23.6757	−1.03329
$526$	19.2813	0.840704
$527$	−0.519889	−0.0226467
$528$	−1.00000	−0.0435194
$529$	12.6138	0.548426
$530$	0.434564	0.0188762
$531$	−14.3533	−0.622882
$532$	27.9338	1.21108
$533$	−25.0130	−1.08343
$534$	14.1282	0.611387
$535$	1.35166	0.0584376
$536$	−11.9931	−0.518022
$537$	−4.78053	−0.206295
$538$	−30.4439	−1.31253
$539$	−8.33239	−0.358901
$540$	−3.32361	−0.143026
$541$	26.2198	1.12728	0.563638	−	0.826022i	$-0.309401\pi$
$541$	26.2198	1.12728	0.563638	+	0.826022i	$0.309401\pi$
$542$	−14.8369	−0.637298
$543$	22.0037	0.944268
$544$	−0.807136	−0.0346057
$545$	11.6352	0.498398
$546$	−10.8654	−0.464998
$547$	1.24847	0.0533807	0.0266903	−	0.999644i	$-0.491503\pi$
$547$	1.24847	0.0533807	0.0266903	+	0.999644i	$0.491503\pi$
$548$	−10.0875	−0.430915
$549$	−1.00000	−0.0426790
$550$	6.04641	0.257820
$551$	59.7106	2.54376
$552$	5.96773	0.254003
$553$	−65.4319	−2.78245
$554$	20.0794	0.853090
$555$	27.6457	1.17349
$556$	−2.57409	−0.109166
$557$	17.4996	0.741483	0.370741	−	0.928736i	$-0.379104\pi$
$557$	17.4996	0.741483	0.370741	+	0.928736i	$0.379104\pi$
$558$	0.644116	0.0272676
$559$	−28.8650	−1.22086
$560$	13.0141	0.549948
$561$	−0.807136	−0.0340773
$562$	−9.91566	−0.418267
$563$	7.44473	0.313758	0.156879	−	0.987618i	$-0.449857\pi$
$563$	7.44473	0.313758	0.156879	+	0.987618i	$0.449857\pi$
$564$	−2.49766	−0.105171
$565$	56.2865	2.36799
$566$	−22.2578	−0.935565
$567$	−3.91566	−0.164442
$568$	12.0031	0.503639
$569$	17.4883	0.733148	0.366574	−	0.930389i	$-0.380531\pi$
$569$	17.4883	0.733148	0.366574	+	0.930389i	$0.380531\pi$
$570$	−23.7102	−0.993111
$571$	36.6687	1.53454	0.767270	−	0.641325i	$-0.221615\pi$
$571$	36.6687	1.53454	0.767270	+	0.641325i	$0.221615\pi$
$572$	2.77487	0.116023
$573$	−7.89570	−0.329847
$574$	35.2963	1.47324
$575$	−36.0833	−1.50478
$576$	1.00000	0.0416667
$577$	23.6678	0.985301	0.492651	−	0.870227i	$-0.336028\pi$
$577$	23.6678	0.985301	0.492651	+	0.870227i	$0.336028\pi$
$578$	16.3485	0.680009
$579$	−8.24919	−0.342825
$580$	27.8187	1.15511
$581$	−12.7277	−0.528036
$582$	12.4575	0.516379
$583$	−0.130750	−0.00541513
$584$	−9.98430	−0.413153
$585$	9.22258	0.381307
$586$	−0.943253	−0.0389654
$587$	−40.3512	−1.66547	−0.832736	−	0.553670i	$-0.813227\pi$
$587$	−40.3512	−1.66547	−0.832736	+	0.553670i	$0.813227\pi$
$588$	8.33239	0.343622
$589$	4.59503	0.189335
$590$	−47.7049	−1.96398
$591$	−3.26843	−0.134445
$592$	−8.31795	−0.341866
$593$	−20.4508	−0.839816	−0.419908	−	0.907567i	$-0.637938\pi$
$593$	−20.4508	−0.839816	−0.419908	+	0.907567i	$0.637938\pi$
$594$	1.00000	0.0410305
$595$	10.5042	0.430630
$596$	19.3798	0.793827
$597$	12.1108	0.495661
$598$	−16.5597	−0.677175
$599$	8.00213	0.326958	0.163479	−	0.986547i	$-0.447728\pi$
$599$	8.00213	0.326958	0.163479	+	0.986547i	$0.447728\pi$
$600$	−6.04641	−0.246844
$601$	−38.6988	−1.57856	−0.789279	−	0.614035i	$-0.789546\pi$
$601$	−38.6988	−1.57856	−0.789279	+	0.614035i	$0.789546\pi$
$602$	40.7318	1.66011
$603$	11.9931	0.488396
$604$	11.6305	0.473240
$605$	−3.32361	−0.135124
$606$	3.04203	0.123574
$607$	16.4545	0.667867	0.333934	−	0.942597i	$-0.391624\pi$
$607$	16.4545	0.667867	0.333934	+	0.942597i	$0.391624\pi$
$608$	7.13386	0.289316
$609$	32.7742	1.32808
$610$	−3.32361	−0.134569
$611$	6.93068	0.280385
$612$	0.807136	0.0326266
$613$	−22.9397	−0.926527	−0.463263	−	0.886221i	$-0.653322\pi$
$613$	−22.9397	−0.926527	−0.463263	+	0.886221i	$0.653322\pi$
$614$	−18.0430	−0.728156
$615$	−29.9595	−1.20808
$616$	−3.91566	−0.157766
$617$	−47.6198	−1.91710	−0.958550	−	0.284924i	$-0.908032\pi$
$617$	−47.6198	−1.91710	−0.958550	+	0.284924i	$0.908032\pi$
$618$	12.4252	0.499815
$619$	−13.7119	−0.551127	−0.275563	−	0.961283i	$-0.588864\pi$
$619$	−13.7119	−0.551127	−0.275563	+	0.961283i	$0.588864\pi$
$620$	2.14079	0.0859763
$621$	−5.96773	−0.239477
$622$	−15.0514	−0.603505
$623$	55.3212	2.21640
$624$	−2.77487	−0.111084
$625$	−18.6730	−0.746919
$626$	−13.1048	−0.523774
$627$	7.13386	0.284899
$628$	12.0906	0.482466
$629$	−6.71372	−0.267694
$630$	−13.0141	−0.518496
$631$	−29.2950	−1.16622	−0.583108	−	0.812394i	$-0.698164\pi$
$631$	−29.2950	−1.16622	−0.583108	+	0.812394i	$0.698164\pi$
$632$	−16.7103	−0.664701
$633$	1.11333	0.0442508
$634$	3.78844	0.150458
$635$	−0.277042	−0.0109941
$636$	0.130750	0.00518459
$637$	−23.1213	−0.916098
$638$	−8.37002	−0.331372
$639$	−12.0031	−0.474836
$640$	3.32361	0.131377
$641$	35.9524	1.42004	0.710018	−	0.704184i	$-0.248687\pi$
$641$	35.9524	1.42004	0.710018	+	0.704184i	$0.248687\pi$
$642$	0.406685	0.0160506
$643$	−5.34924	−0.210954	−0.105477	−	0.994422i	$-0.533637\pi$
$643$	−5.34924	−0.210954	−0.105477	+	0.994422i	$0.533637\pi$
$644$	23.3676	0.920812
$645$	−34.5732	−1.36132
$646$	5.75800	0.226545
$647$	−18.3927	−0.723091	−0.361546	−	0.932354i	$-0.617751\pi$
$647$	−18.3927	−0.723091	−0.361546	+	0.932354i	$0.617751\pi$
$648$	−1.00000	−0.0392837
$649$	14.3533	0.563418
$650$	16.7780	0.658086
$651$	2.52214	0.0988504
$652$	23.4030	0.916531
$653$	5.98049	0.234035	0.117017	−	0.993130i	$-0.462667\pi$
$653$	5.98049	0.234035	0.117017	+	0.993130i	$0.462667\pi$
$654$	3.50077	0.136891
$655$	−60.2220	−2.35307
$656$	9.01414	0.351943
$657$	9.98430	0.389524
$658$	−9.77999	−0.381264
$659$	−36.7362	−1.43104	−0.715520	−	0.698592i	$-0.753810\pi$
$659$	−36.7362	−1.43104	−0.715520	+	0.698592i	$0.753810\pi$
$660$	3.32361	0.129371
$661$	8.44202	0.328357	0.164178	−	0.986431i	$-0.447503\pi$
$661$	8.44202	0.328357	0.164178	+	0.986431i	$0.447503\pi$
$662$	33.4307	1.29932
$663$	−2.23970	−0.0869826
$664$	−3.25047	−0.126143
$665$	−92.8411	−3.60022
$666$	8.31795	0.322314
$667$	49.9500	1.93407
$668$	9.58638	0.370908
$669$	−23.2289	−0.898083
$670$	39.8603	1.53994
$671$	1.00000	0.0386046
$672$	3.91566	0.151050
$673$	−20.7868	−0.801270	−0.400635	−	0.916238i	$-0.631211\pi$
$673$	−20.7868	−0.801270	−0.400635	+	0.916238i	$0.631211\pi$
$674$	6.57265	0.253169
$675$	6.04641	0.232726
$676$	−5.30012	−0.203851
$677$	−23.0018	−0.884032	−0.442016	−	0.897007i	$-0.645737\pi$
$677$	−23.0018	−0.884032	−0.442016	+	0.897007i	$0.645737\pi$
$678$	16.9353	0.650398
$679$	48.7792	1.87198
$680$	2.68261	0.102873
$681$	11.1327	0.426607
$682$	−0.644116	−0.0246645
$683$	−1.35728	−0.0519349	−0.0259675	−	0.999663i	$-0.508267\pi$
$683$	−1.35728	−0.0519349	−0.0259675	+	0.999663i	$0.508267\pi$
$684$	−7.13386	−0.272770
$685$	33.5268	1.28099
$686$	5.21717	0.199193
$687$	13.8435	0.528163
$688$	10.4023	0.396584
$689$	−0.362815	−0.0138221
$690$	−19.8344	−0.755084
$691$	29.7747	1.13268	0.566342	−	0.824170i	$-0.308358\pi$
$691$	29.7747	1.13268	0.566342	+	0.824170i	$0.308358\pi$
$692$	−12.3525	−0.469571
$693$	3.91566	0.148744
$694$	13.6625	0.518622
$695$	8.55527	0.324520
$696$	8.37002	0.317265
$697$	7.27564	0.275585
$698$	−15.5871	−0.589981
$699$	−23.9928	−0.907490
$700$	−23.6757	−0.894857
$701$	−36.3283	−1.37210	−0.686050	−	0.727554i	$-0.740657\pi$
$701$	−36.3283	−1.37210	−0.686050	+	0.727554i	$0.740657\pi$
$702$	2.77487	0.104731
$703$	59.3391	2.23802
$704$	−1.00000	−0.0376889
$705$	8.30126	0.312644
$706$	27.3100	1.02783
$707$	11.9115	0.447980
$708$	−14.3533	−0.539431
$709$	0.0400134	0.00150274	0.000751368	−	1.00000i	$-0.499761\pi$
$709$	0.0400134	0.00150274	0.000751368		1.00000i	$0.499761\pi$
$710$	−39.8937	−1.49718
$711$	16.7103	0.626686
$712$	14.1282	0.529477
$713$	3.84391	0.143956
$714$	3.16047	0.118278
$715$	−9.22258	−0.344905
$716$	−4.78053	−0.178657
$717$	−18.2856	−0.682887
$718$	−2.41656	−0.0901850
$719$	41.6522	1.55336	0.776682	−	0.629893i	$-0.216901\pi$
$719$	41.6522	1.55336	0.776682	+	0.629893i	$0.216901\pi$
$720$	−3.32361	−0.123864
$721$	48.6529	1.81193
$722$	−31.8920	−1.18690
$723$	−15.7631	−0.586237
$724$	22.0037	0.817760
$725$	−50.6086	−1.87956
$726$	−1.00000	−0.0371135
$727$	−8.83076	−0.327515	−0.163757	−	0.986501i	$-0.552361\pi$
$727$	−8.83076	−0.327515	−0.163757	+	0.986501i	$0.552361\pi$
$728$	−10.8654	−0.402700
$729$	1.00000	0.0370370
$730$	33.1839	1.22819
$731$	8.39607	0.310540
$732$	−1.00000	−0.0369611
$733$	−5.35801	−0.197903	−0.0989513	−	0.995092i	$-0.531549\pi$
$733$	−5.35801	−0.197903	−0.0989513	+	0.995092i	$0.531549\pi$
$734$	19.6890	0.726733
$735$	−27.6936	−1.02150
$736$	5.96773	0.219973
$737$	−11.9931	−0.441770
$738$	−9.01414	−0.331815
$739$	16.4781	0.606158	0.303079	−	0.952965i	$-0.401985\pi$
$739$	16.4781	0.606158	0.303079	+	0.952965i	$0.401985\pi$
$740$	27.6457	1.01627
$741$	19.7955	0.727206
$742$	0.511974	0.0187951
$743$	−30.8241	−1.13083	−0.565413	−	0.824808i	$-0.691283\pi$
$743$	−30.8241	−1.13083	−0.565413	+	0.824808i	$0.691283\pi$
$744$	0.644116	0.0236144
$745$	−64.4109	−2.35983
$746$	3.71020	0.135840
$747$	3.25047	0.118929
$748$	−0.807136	−0.0295118
$749$	1.59244	0.0581865
$750$	3.47786	0.126994
$751$	−0.0567469	−0.00207072	−0.00103536	−	0.999999i	$-0.500330\pi$
$751$	−0.0567469	−0.00207072	−0.00103536	+	0.999999i	$0.500330\pi$
$752$	−2.49766	−0.0910804
$753$	13.6086	0.495925
$754$	−23.2257	−0.845830
$755$	−38.6554	−1.40681
$756$	−3.91566	−0.142411
$757$	51.8773	1.88551	0.942756	−	0.333484i	$-0.108224\pi$
$757$	51.8773	1.88551	0.942756	+	0.333484i	$0.108224\pi$
$758$	−2.53813	−0.0921891
$759$	5.96773	0.216615
$760$	−23.7102	−0.860059
$761$	−10.5467	−0.382319	−0.191160	−	0.981559i	$-0.561225\pi$
$761$	−10.5467	−0.382319	−0.191160	+	0.981559i	$0.561225\pi$
$762$	−0.0833558	−0.00301966
$763$	13.7078	0.496257
$764$	−7.89570	−0.285656
$765$	−2.68261	−0.0969900
$766$	31.5793	1.14101
$767$	39.8286	1.43813
$768$	1.00000	0.0360844
$769$	22.2267	0.801514	0.400757	−	0.916184i	$-0.368747\pi$
$769$	22.2267	0.801514	0.400757	+	0.916184i	$0.368747\pi$
$770$	13.0141	0.468997
$771$	22.9018	0.824788
$772$	−8.24919	−0.296895
$773$	21.0215	0.756090	0.378045	−	0.925787i	$-0.376596\pi$
$773$	21.0215	0.756090	0.378045	+	0.925787i	$0.376596\pi$
$774$	−10.4023	−0.373903
$775$	−3.89459	−0.139898
$776$	12.4575	0.447197
$777$	32.5703	1.16845
$778$	4.45252	0.159631
$779$	−64.3056	−2.30399
$780$	9.22258	0.330221
$781$	12.0031	0.429505
$782$	4.81677	0.172247
$783$	−8.37002	−0.299120
$784$	8.33239	0.297585
$785$	−40.1844	−1.43424
$786$	−18.1194	−0.646299
$787$	−5.60095	−0.199652	−0.0998261	−	0.995005i	$-0.531829\pi$
$787$	−5.60095	−0.199652	−0.0998261	+	0.995005i	$0.531829\pi$
$788$	−3.26843	−0.116433
$789$	−19.2813	−0.686432
$790$	55.5387	1.97598
$791$	66.3130	2.35782
$792$	1.00000	0.0355335
$793$	2.77487	0.0985384
$794$	24.1293	0.856317
$795$	−0.434564	−0.0154124
$796$	12.1108	0.429255
$797$	−6.58795	−0.233357	−0.116679	−	0.993170i	$-0.537225\pi$
$797$	−6.58795	−0.233357	−0.116679	+	0.993170i	$0.537225\pi$
$798$	−27.9338	−0.988845
$799$	−2.01595	−0.0713193
$800$	−6.04641	−0.213773
$801$	−14.1282	−0.499195
$802$	−20.9175	−0.738622
$803$	−9.98430	−0.352338
$804$	11.9931	0.422963
$805$	−77.6649	−2.73733
$806$	−1.78734	−0.0629562
$807$	30.4439	1.07168
$808$	3.04203	0.107018
$809$	−25.7442	−0.905116	−0.452558	−	0.891735i	$-0.649488\pi$
$809$	−25.7442	−0.905116	−0.452558	+	0.891735i	$0.649488\pi$
$810$	3.32361	0.116780
$811$	39.4129	1.38397	0.691987	−	0.721910i	$-0.256736\pi$
$811$	39.4129	1.38397	0.691987	+	0.721910i	$0.256736\pi$
$812$	32.7742	1.15015
$813$	14.8369	0.520351
$814$	−8.31795	−0.291544
$815$	−77.7825	−2.72460
$816$	0.807136	0.0282554
$817$	−74.2085	−2.59623
$818$	31.6698	1.10731
$819$	10.8654	0.379669
$820$	−29.9595	−1.04623
$821$	21.0603	0.735009	0.367505	−	0.930022i	$-0.380212\pi$
$821$	21.0603	0.735009	0.367505	+	0.930022i	$0.380212\pi$
$822$	10.0875	0.351840
$823$	17.3989	0.606487	0.303244	−	0.952913i	$-0.401930\pi$
$823$	17.3989	0.606487	0.303244	+	0.952913i	$0.401930\pi$
$824$	12.4252	0.432853
$825$	−6.04641	−0.210509
$826$	−56.2028	−1.95554
$827$	−15.2596	−0.530630	−0.265315	−	0.964162i	$-0.585476\pi$
$827$	−15.2596	−0.530630	−0.265315	+	0.964162i	$0.585476\pi$
$828$	−5.96773	−0.207393
$829$	−35.3149	−1.22654	−0.613268	−	0.789875i	$-0.710145\pi$
$829$	−35.3149	−1.22654	−0.613268	+	0.789875i	$0.710145\pi$
$830$	10.8033	0.374989
$831$	−20.0794	−0.696545
$832$	−2.77487	−0.0962012
$833$	6.72537	0.233020
$834$	2.57409	0.0891333
$835$	−31.8614	−1.10261
$836$	7.13386	0.246730
$837$	−0.644116	−0.0222639
$838$	−14.9639	−0.516920
$839$	−55.9965	−1.93321	−0.966606	−	0.256266i	$-0.917508\pi$
$839$	−55.9965	−1.93321	−0.966606	+	0.256266i	$0.917508\pi$
$840$	−13.0141	−0.449030
$841$	41.0573	1.41577
$842$	−23.1925	−0.799265
$843$	9.91566	0.341513
$844$	1.11333	0.0383223
$845$	17.6155	0.605993
$846$	2.49766	0.0858714
$847$	−3.91566	−0.134544
$848$	0.130750	0.00448998
$849$	22.2578	0.763886
$850$	−4.88028	−0.167392
$851$	49.6393	1.70161
$852$	−12.0031	−0.411220
$853$	−54.4324	−1.86373	−0.931865	−	0.362805i	$-0.881819\pi$
$853$	−54.4324	−1.86373	−0.931865	+	0.362805i	$0.881819\pi$
$854$	−3.91566	−0.133991
$855$	23.7102	0.810872
$856$	0.406685	0.0139002
$857$	−18.1084	−0.618570	−0.309285	−	0.950969i	$-0.600090\pi$
$857$	−18.1084	−0.618570	−0.309285	+	0.950969i	$0.600090\pi$
$858$	−2.77487	−0.0947324
$859$	17.1123	0.583865	0.291932	−	0.956439i	$-0.405702\pi$
$859$	17.1123	0.583865	0.291932	+	0.956439i	$0.405702\pi$
$860$	−34.5732	−1.17894
$861$	−35.2963	−1.20289
$862$	−31.4330	−1.07061
$863$	22.4227	0.763276	0.381638	−	0.924312i	$-0.375360\pi$
$863$	22.4227	0.763276	0.381638	+	0.924312i	$0.375360\pi$
$864$	−1.00000	−0.0340207
$865$	41.0549	1.39591
$866$	23.8895	0.811798
$867$	−16.3485	−0.555225
$868$	2.52214	0.0856070
$869$	−16.7103	−0.566859
$870$	−27.8187	−0.943143
$871$	−33.2792	−1.12762
$872$	3.50077	0.118551
$873$	−12.4575	−0.421622
$874$	−42.5730	−1.44005
$875$	13.6181	0.460376
$876$	9.98430	0.337338
$877$	−12.6452	−0.426999	−0.213499	−	0.976943i	$-0.568486\pi$
$877$	−12.6452	−0.426999	−0.213499	+	0.976943i	$0.568486\pi$
$878$	24.3409	0.821464
$879$	0.943253	0.0318151
$880$	3.32361	0.112039
$881$	−19.8657	−0.669292	−0.334646	−	0.942344i	$-0.608617\pi$
$881$	−19.8657	−0.669292	−0.334646	+	0.942344i	$0.608617\pi$
$882$	−8.33239	−0.280566
$883$	−37.4856	−1.26149	−0.630746	−	0.775990i	$-0.717251\pi$
$883$	−37.4856	−1.26149	−0.630746	+	0.775990i	$0.717251\pi$
$884$	−2.23970	−0.0753291
$885$	47.7049	1.60358
$886$	24.7483	0.831434
$887$	46.3574	1.55653	0.778265	−	0.627936i	$-0.216100\pi$
$887$	46.3574	1.55653	0.778265	+	0.627936i	$0.216100\pi$
$888$	8.31795	0.279132
$889$	−0.326393	−0.0109469
$890$	−46.9567	−1.57399
$891$	−1.00000	−0.0335013
$892$	−23.2289	−0.777762
$893$	17.8180	0.596256
$894$	−19.3798	−0.648157
$895$	15.8886	0.531098
$896$	3.91566	0.130813
$897$	16.5597	0.552911
$898$	−6.44772	−0.215163
$899$	5.39127	0.179809
$900$	6.04641	0.201547
$901$	0.105533	0.00351583
$902$	9.01414	0.300138
$903$	−40.7318	−1.35547
$904$	16.9353	0.563261
$905$	−73.1317	−2.43098
$906$	−11.6305	−0.386399
$907$	32.1322	1.06693	0.533466	−	0.845822i	$-0.320889\pi$
$907$	32.1322	1.06693	0.533466	+	0.845822i	$0.320889\pi$
$908$	11.1327	0.369452
$909$	−3.04203	−0.100898
$910$	36.1125	1.19712
$911$	18.0275	0.597276	0.298638	−	0.954366i	$-0.403468\pi$
$911$	18.0275	0.597276	0.298638	+	0.954366i	$0.403468\pi$
$912$	−7.13386	−0.236226
$913$	−3.25047	−0.107575
$914$	8.49877	0.281114
$915$	3.32361	0.109875
$916$	13.8435	0.457402
$917$	−70.9495	−2.34296
$918$	−0.807136	−0.0266395
$919$	2.88312	0.0951052	0.0475526	−	0.998869i	$-0.484858\pi$
$919$	2.88312	0.0951052	0.0475526	+	0.998869i	$0.484858\pi$
$920$	−19.8344	−0.653922
$921$	18.0430	0.594537
$922$	−3.36904	−0.110953
$923$	33.3070	1.09631
$924$	3.91566	0.128816
$925$	−50.2937	−1.65365
$926$	−7.77444	−0.255484
$927$	−12.4252	−0.408097
$928$	8.37002	0.274759
$929$	−36.0073	−1.18136	−0.590681	−	0.806905i	$-0.701141\pi$
$929$	−36.0073	−1.18136	−0.590681	+	0.806905i	$0.701141\pi$
$930$	−2.14079	−0.0701994
$931$	−59.4421	−1.94814
$932$	−23.9928	−0.785909
$933$	15.0514	0.492760
$934$	−5.06904	−0.165864
$935$	2.68261	0.0877307
$936$	2.77487	0.0906993
$937$	−47.6008	−1.55505	−0.777525	−	0.628851i	$-0.783525\pi$
$937$	−47.6008	−1.55505	−0.777525	+	0.628851i	$0.783525\pi$
$938$	46.9608	1.53332
$939$	13.1048	0.427660
$940$	8.30126	0.270757
$941$	19.2111	0.626264	0.313132	−	0.949710i	$-0.398622\pi$
$941$	19.2111	0.626264	0.313132	+	0.949710i	$0.398622\pi$
$942$	−12.0906	−0.393932
$943$	−53.7939	−1.75177
$944$	−14.3533	−0.467161
$945$	13.0141	0.423350
$946$	10.4023	0.338208
$947$	−25.5746	−0.831063	−0.415531	−	0.909579i	$-0.636404\pi$
$947$	−25.5746	−0.831063	−0.415531	+	0.909579i	$0.636404\pi$
$948$	16.7103	0.542726
$949$	−27.7051	−0.899345
$950$	43.1343	1.39946
$951$	−3.78844	−0.122849
$952$	3.16047	0.102431
$953$	−24.8695	−0.805603	−0.402801	−	0.915287i	$-0.631963\pi$
$953$	−24.8695	−0.805603	−0.402801	+	0.915287i	$0.631963\pi$
$954$	−0.130750	−0.00423320
$955$	26.2422	0.849179
$956$	−18.2856	−0.591397
$957$	8.37002	0.270564
$958$	−2.62190	−0.0847097
$959$	39.4990	1.27549
$960$	−3.32361	−0.107269
$961$	−30.5851	−0.986617
$962$	−23.0812	−0.744168
$963$	−0.406685	−0.0131052
$964$	−15.7631	−0.507696
$965$	27.4171	0.882589
$966$	−23.3676	−0.751840
$967$	13.5029	0.434223	0.217111	−	0.976147i	$-0.430336\pi$
$967$	13.5029	0.434223	0.217111	+	0.976147i	$0.430336\pi$
$968$	−1.00000	−0.0321412
$969$	−5.75800	−0.184974
$970$	−41.4038	−1.32940
$971$	44.2459	1.41992	0.709959	−	0.704243i	$-0.248713\pi$
$971$	44.2459	1.41992	0.709959	+	0.704243i	$0.248713\pi$
$972$	1.00000	0.0320750
$973$	10.0792	0.323126
$974$	−5.61653	−0.179965
$975$	−16.7780	−0.537325
$976$	−1.00000	−0.0320092
$977$	20.0638	0.641898	0.320949	−	0.947096i	$-0.395998\pi$
$977$	20.0638	0.641898	0.320949	+	0.947096i	$0.395998\pi$
$978$	−23.4030	−0.748345
$979$	14.1282	0.451539
$980$	−27.6936	−0.884641
$981$	−3.50077	−0.111771
$982$	12.3413	0.393828
$983$	−4.55400	−0.145250	−0.0726251	−	0.997359i	$-0.523138\pi$
$983$	−4.55400	−0.145250	−0.0726251	+	0.997359i	$0.523138\pi$
$984$	−9.01414	−0.287360
$985$	10.8630	0.346124
$986$	6.75575	0.215147
$987$	9.77999	0.311301
$988$	19.7955	0.629779
$989$	−62.0781	−1.97397
$990$	−3.32361	−0.105631
$991$	−24.7967	−0.787692	−0.393846	−	0.919176i	$-0.628856\pi$
$991$	−24.7967	−0.787692	−0.393846	+	0.919176i	$0.628856\pi$
$992$	0.644116	0.0204507
$993$	−33.4307	−1.06089
$994$	−47.0001	−1.49075
$995$	−40.2515	−1.27606
$996$	3.25047	0.102995
$997$	−27.5577	−0.872761	−0.436381	−	0.899762i	$-0.643740\pi$
$997$	−27.5577	−0.872761	−0.436381	+	0.899762i	$0.643740\pi$
$998$	22.5628	0.714212
$999$	−8.31795	−0.263168

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4026.2.a.u.1.1	✓	5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4026.2.a.u.1.1	✓	5	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:	\( N \)	\(=\)	\( 4026 = 2 \cdot 3 \cdot 11 \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4026.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -3.32361 q^{5} -1.00000 q^{6} -3.91566 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -3.32361 q^{5} -1.00000 q^{6} -3.91566 q^{7} -1.00000 q^{8} +1.00000 q^{9} +3.32361 q^{10} -1.00000 q^{11} +1.00000 q^{12} -2.77487 q^{13} +3.91566 q^{14} -3.32361 q^{15} +1.00000 q^{16} +0.807136 q^{17} -1.00000 q^{18} -7.13386 q^{19} -3.32361 q^{20} -3.91566 q^{21} +1.00000 q^{22} -5.96773 q^{23} -1.00000 q^{24} +6.04641 q^{25} +2.77487 q^{26} +1.00000 q^{27} -3.91566 q^{28} -8.37002 q^{29} +3.32361 q^{30} -0.644116 q^{31} -1.00000 q^{32} -1.00000 q^{33} -0.807136 q^{34} +13.0141 q^{35} +1.00000 q^{36} -8.31795 q^{37} +7.13386 q^{38} -2.77487 q^{39} +3.32361 q^{40} +9.01414 q^{41} +3.91566 q^{42} +10.4023 q^{43} -1.00000 q^{44} -3.32361 q^{45} +5.96773 q^{46} -2.49766 q^{47} +1.00000 q^{48} +8.33239 q^{49} -6.04641 q^{50} +0.807136 q^{51} -2.77487 q^{52} +0.130750 q^{53} -1.00000 q^{54} +3.32361 q^{55} +3.91566 q^{56} -7.13386 q^{57} +8.37002 q^{58} -14.3533 q^{59} -3.32361 q^{60} -1.00000 q^{61} +0.644116 q^{62} -3.91566 q^{63} +1.00000 q^{64} +9.22258 q^{65} +1.00000 q^{66} +11.9931 q^{67} +0.807136 q^{68} -5.96773 q^{69} -13.0141 q^{70} -12.0031 q^{71} -1.00000 q^{72} +9.98430 q^{73} +8.31795 q^{74} +6.04641 q^{75} -7.13386 q^{76} +3.91566 q^{77} +2.77487 q^{78} +16.7103 q^{79} -3.32361 q^{80} +1.00000 q^{81} -9.01414 q^{82} +3.25047 q^{83} -3.91566 q^{84} -2.68261 q^{85} -10.4023 q^{86} -8.37002 q^{87} +1.00000 q^{88} -14.1282 q^{89} +3.32361 q^{90} +10.8654 q^{91} -5.96773 q^{92} -0.644116 q^{93} +2.49766 q^{94} +23.7102 q^{95} -1.00000 q^{96} -12.4575 q^{97} -8.33239 q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 5 q^{2} + 5 q^{3} + 5 q^{4} - q^{5} - 5 q^{6} - 3 q^{7} - 5 q^{8} + 5 q^{9}+O(q^{10}) \) 5 * q - 5 * q^2 + 5 * q^3 + 5 * q^4 - q^5 - 5 * q^6 - 3 * q^7 - 5 * q^8 + 5 * q^9	\( 5 q - 5 q^{2} + 5 q^{3} + 5 q^{4} - q^{5} - 5 q^{6} - 3 q^{7} - 5 q^{8} + 5 q^{9} + q^{10} - 5 q^{11} + 5 q^{12} + 2 q^{13} + 3 q^{14} - q^{15} + 5 q^{16} + 6 q^{17} - 5 q^{18} + 7 q^{19} - q^{20} - 3 q^{21} + 5 q^{22} - 12 q^{23} - 5 q^{24} - 2 q^{26} + 5 q^{27} - 3 q^{28} + 4 q^{29} + q^{30} - q^{31} - 5 q^{32} - 5 q^{33} - 6 q^{34} + 17 q^{35} + 5 q^{36} + 3 q^{37} - 7 q^{38} + 2 q^{39} + q^{40} - 3 q^{41} + 3 q^{42} + 24 q^{43} - 5 q^{44} - q^{45} + 12 q^{46} + 18 q^{47} + 5 q^{48} + 26 q^{49} + 6 q^{51} + 2 q^{52} - 13 q^{53} - 5 q^{54} + q^{55} + 3 q^{56} + 7 q^{57} - 4 q^{58} - 16 q^{59} - q^{60} - 5 q^{61} + q^{62} - 3 q^{63} + 5 q^{64} + 4 q^{65} + 5 q^{66} + 18 q^{67} + 6 q^{68} - 12 q^{69} - 17 q^{70} - 31 q^{71} - 5 q^{72} + 8 q^{73} - 3 q^{74} + 7 q^{76} + 3 q^{77} - 2 q^{78} + 32 q^{79} - q^{80} + 5 q^{81} + 3 q^{82} + 8 q^{83} - 3 q^{84} + 29 q^{85} - 24 q^{86} + 4 q^{87} + 5 q^{88} + q^{89} + q^{90} - 3 q^{91} - 12 q^{92} - q^{93} - 18 q^{94} + 33 q^{95} - 5 q^{96} - 4 q^{97} - 26 q^{98} - 5 q^{99}+O(q^{100}) \) 5 * q - 5 * q^2 + 5 * q^3 + 5 * q^4 - q^5 - 5 * q^6 - 3 * q^7 - 5 * q^8 + 5 * q^9 + q^10 - 5 * q^11 + 5 * q^12 + 2 * q^13 + 3 * q^14 - q^15 + 5 * q^16 + 6 * q^17 - 5 * q^18 + 7 * q^19 - q^20 - 3 * q^21 + 5 * q^22 - 12 * q^23 - 5 * q^24 - 2 * q^26 + 5 * q^27 - 3 * q^28 + 4 * q^29 + q^30 - q^31 - 5 * q^32 - 5 * q^33 - 6 * q^34 + 17 * q^35 + 5 * q^36 + 3 * q^37 - 7 * q^38 + 2 * q^39 + q^40 - 3 * q^41 + 3 * q^42 + 24 * q^43 - 5 * q^44 - q^45 + 12 * q^46 + 18 * q^47 + 5 * q^48 + 26 * q^49 + 6 * q^51 + 2 * q^52 - 13 * q^53 - 5 * q^54 + q^55 + 3 * q^56 + 7 * q^57 - 4 * q^58 - 16 * q^59 - q^60 - 5 * q^61 + q^62 - 3 * q^63 + 5 * q^64 + 4 * q^65 + 5 * q^66 + 18 * q^67 + 6 * q^68 - 12 * q^69 - 17 * q^70 - 31 * q^71 - 5 * q^72 + 8 * q^73 - 3 * q^74 + 7 * q^76 + 3 * q^77 - 2 * q^78 + 32 * q^79 - q^80 + 5 * q^81 + 3 * q^82 + 8 * q^83 - 3 * q^84 + 29 * q^85 - 24 * q^86 + 4 * q^87 + 5 * q^88 + q^89 + q^90 - 3 * q^91 - 12 * q^92 - q^93 - 18 * q^94 + 33 * q^95 - 5 * q^96 - 4 * q^97 - 26 * q^98 - 5 * q^99

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