LMFDB - Embedded newform 4026.2.a.bb.1.6

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:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} - 22x^{6} + 42x^{5} + 182x^{4} - 111x^{3} - 538x^{2} - 256x - 32 $ x^8 - 3x^7 - 22x^6 + 42x^5 + 182x^4 - 111x^3 - 538x^2 - 256*x - 32
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			1.6
Root			$2.67396$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +2.72927 q^{5} +1.00000 q^{6} -0.673957 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +2.72927 q^{5} +1.00000 q^{6} -0.673957 q^{7} +1.00000 q^{8} +1.00000 q^{9} +2.72927 q^{10} -1.00000 q^{11} +1.00000 q^{12} +3.59767 q^{13} -0.673957 q^{14} +2.72927 q^{15} +1.00000 q^{16} +4.25138 q^{17} +1.00000 q^{18} +5.82526 q^{19} +2.72927 q^{20} -0.673957 q^{21} -1.00000 q^{22} -2.69468 q^{23} +1.00000 q^{24} +2.44889 q^{25} +3.59767 q^{26} +1.00000 q^{27} -0.673957 q^{28} -7.00036 q^{29} +2.72927 q^{30} +1.96541 q^{31} +1.00000 q^{32} -1.00000 q^{33} +4.25138 q^{34} -1.83941 q^{35} +1.00000 q^{36} +10.3558 q^{37} +5.82526 q^{38} +3.59767 q^{39} +2.72927 q^{40} -3.88057 q^{41} -0.673957 q^{42} -9.14034 q^{43} -1.00000 q^{44} +2.72927 q^{45} -2.69468 q^{46} -10.6370 q^{47} +1.00000 q^{48} -6.54578 q^{49} +2.44889 q^{50} +4.25138 q^{51} +3.59767 q^{52} -3.56328 q^{53} +1.00000 q^{54} -2.72927 q^{55} -0.673957 q^{56} +5.82526 q^{57} -7.00036 q^{58} +3.91975 q^{59} +2.72927 q^{60} +1.00000 q^{61} +1.96541 q^{62} -0.673957 q^{63} +1.00000 q^{64} +9.81900 q^{65} -1.00000 q^{66} +6.94252 q^{67} +4.25138 q^{68} -2.69468 q^{69} -1.83941 q^{70} +0.365213 q^{71} +1.00000 q^{72} -4.95939 q^{73} +10.3558 q^{74} +2.44889 q^{75} +5.82526 q^{76} +0.673957 q^{77} +3.59767 q^{78} -2.75204 q^{79} +2.72927 q^{80} +1.00000 q^{81} -3.88057 q^{82} -0.156532 q^{83} -0.673957 q^{84} +11.6031 q^{85} -9.14034 q^{86} -7.00036 q^{87} -1.00000 q^{88} +16.9930 q^{89} +2.72927 q^{90} -2.42468 q^{91} -2.69468 q^{92} +1.96541 q^{93} -10.6370 q^{94} +15.8987 q^{95} +1.00000 q^{96} -11.2082 q^{97} -6.54578 q^{98} -1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{2} + 8 q^{3} + 8 q^{4} + 5 q^{5} + 8 q^{6} + 13 q^{7} + 8 q^{8} + 8 q^{9}+O(q^{10}) $ 8 * q + 8 * q^2 + 8 * q^3 + 8 * q^4 + 5 * q^5 + 8 * q^6 + 13 * q^7 + 8 * q^8 + 8 * q^9	\( 8 q + 8 q^{2} + 8 q^{3} + 8 q^{4} + 5 q^{5} + 8 q^{6} + 13 q^{7} + 8 q^{8} + 8 q^{9} + 5 q^{10} - 8 q^{11} + 8 q^{12} + 10 q^{13} + 13 q^{14} + 5 q^{15} + 8 q^{16} + 4 q^{17} + 8 q^{18} + 11 q^{19} + 5 q^{20} + 13 q^{21} - 8 q^{22} + 2 q^{23} + 8 q^{24} + 23 q^{25} + 10 q^{26} + 8 q^{27} + 13 q^{28} + 10 q^{29} + 5 q^{30} + 9 q^{31} + 8 q^{32} - 8 q^{33} + 4 q^{34} - 3 q^{35} + 8 q^{36} + 9 q^{37} + 11 q^{38} + 10 q^{39} + 5 q^{40} + 3 q^{41} + 13 q^{42} + 16 q^{43} - 8 q^{44} + 5 q^{45} + 2 q^{46} - 16 q^{47} + 8 q^{48} + 17 q^{49} + 23 q^{50} + 4 q^{51} + 10 q^{52} + 7 q^{53} + 8 q^{54} - 5 q^{55} + 13 q^{56} + 11 q^{57} + 10 q^{58} - 14 q^{59} + 5 q^{60} + 8 q^{61} + 9 q^{62} + 13 q^{63} + 8 q^{64} + 22 q^{65} - 8 q^{66} + 8 q^{67} + 4 q^{68} + 2 q^{69} - 3 q^{70} + 11 q^{71} + 8 q^{72} + 14 q^{73} + 9 q^{74} + 23 q^{75} + 11 q^{76} - 13 q^{77} + 10 q^{78} + 22 q^{79} + 5 q^{80} + 8 q^{81} + 3 q^{82} - 16 q^{83} + 13 q^{84} + 3 q^{85} + 16 q^{86} + 10 q^{87} - 8 q^{88} + q^{89} + 5 q^{90} + 15 q^{91} + 2 q^{92} + 9 q^{93} - 16 q^{94} - 9 q^{95} + 8 q^{96} + 24 q^{97} + 17 q^{98} - 8 q^{99}+O(q^{100}) \) 8 * q + 8 * q^2 + 8 * q^3 + 8 * q^4 + 5 * q^5 + 8 * q^6 + 13 * q^7 + 8 * q^8 + 8 * q^9 + 5 * q^10 - 8 * q^11 + 8 * q^12 + 10 * q^13 + 13 * q^14 + 5 * q^15 + 8 * q^16 + 4 * q^17 + 8 * q^18 + 11 * q^19 + 5 * q^20 + 13 * q^21 - 8 * q^22 + 2 * q^23 + 8 * q^24 + 23 * q^25 + 10 * q^26 + 8 * q^27 + 13 * q^28 + 10 * q^29 + 5 * q^30 + 9 * q^31 + 8 * q^32 - 8 * q^33 + 4 * q^34 - 3 * q^35 + 8 * q^36 + 9 * q^37 + 11 * q^38 + 10 * q^39 + 5 * q^40 + 3 * q^41 + 13 * q^42 + 16 * q^43 - 8 * q^44 + 5 * q^45 + 2 * q^46 - 16 * q^47 + 8 * q^48 + 17 * q^49 + 23 * q^50 + 4 * q^51 + 10 * q^52 + 7 * q^53 + 8 * q^54 - 5 * q^55 + 13 * q^56 + 11 * q^57 + 10 * q^58 - 14 * q^59 + 5 * q^60 + 8 * q^61 + 9 * q^62 + 13 * q^63 + 8 * q^64 + 22 * q^65 - 8 * q^66 + 8 * q^67 + 4 * q^68 + 2 * q^69 - 3 * q^70 + 11 * q^71 + 8 * q^72 + 14 * q^73 + 9 * q^74 + 23 * q^75 + 11 * q^76 - 13 * q^77 + 10 * q^78 + 22 * q^79 + 5 * q^80 + 8 * q^81 + 3 * q^82 - 16 * q^83 + 13 * q^84 + 3 * q^85 + 16 * q^86 + 10 * q^87 - 8 * q^88 + q^89 + 5 * q^90 + 15 * q^91 + 2 * q^92 + 9 * q^93 - 16 * q^94 - 9 * q^95 + 8 * q^96 + 24 * q^97 + 17 * q^98 - 8 * 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
$5$	2.72927	1.22056	0.610282	−	0.792184i	$-0.291056\pi$
$5$	2.72927	1.22056	0.610282	+	0.792184i	$0.291056\pi$
$6$	1.00000	0.408248
$7$	−0.673957	−0.254732	−0.127366	−	0.991856i	$-0.540652\pi$
$7$	−0.673957	−0.254732	−0.127366	+	0.991856i	$0.540652\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	2.72927	0.863069
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	1.00000	0.288675
$13$	3.59767	0.997814	0.498907	−	0.866656i	$-0.333735\pi$
$13$	3.59767	0.997814	0.498907	+	0.866656i	$0.333735\pi$
$14$	−0.673957	−0.180123
$15$	2.72927	0.704693
$16$	1.00000	0.250000
$17$	4.25138	1.03111	0.515556	−	0.856856i	$-0.327586\pi$
$17$	4.25138	1.03111	0.515556	+	0.856856i	$0.327586\pi$
$18$	1.00000	0.235702
$19$	5.82526	1.33641	0.668204	−	0.743978i	$-0.267063\pi$
$19$	5.82526	1.33641	0.668204	+	0.743978i	$0.267063\pi$
$20$	2.72927	0.610282
$21$	−0.673957	−0.147070
$22$	−1.00000	−0.213201
$23$	−2.69468	−0.561879	−0.280940	−	0.959725i	$-0.590646\pi$
$23$	−2.69468	−0.561879	−0.280940	+	0.959725i	$0.590646\pi$
$24$	1.00000	0.204124
$25$	2.44889	0.489778
$26$	3.59767	0.705561
$27$	1.00000	0.192450
$28$	−0.673957	−0.127366
$29$	−7.00036	−1.29993	−0.649967	−	0.759963i	$-0.725217\pi$
$29$	−7.00036	−1.29993	−0.649967	+	0.759963i	$0.725217\pi$
$30$	2.72927	0.498293
$31$	1.96541	0.352999	0.176499	−	0.984301i	$-0.443523\pi$
$31$	1.96541	0.352999	0.176499	+	0.984301i	$0.443523\pi$
$32$	1.00000	0.176777
$33$	−1.00000	−0.174078
$34$	4.25138	0.729106
$35$	−1.83941	−0.310917
$36$	1.00000	0.166667
$37$	10.3558	1.70248	0.851239	−	0.524779i	$-0.175852\pi$
$37$	10.3558	1.70248	0.851239	+	0.524779i	$0.175852\pi$
$38$	5.82526	0.944983
$39$	3.59767	0.576088
$40$	2.72927	0.431535
$41$	−3.88057	−0.606044	−0.303022	−	0.952984i	$-0.597996\pi$
$41$	−3.88057	−0.606044	−0.303022	+	0.952984i	$0.597996\pi$
$42$	−0.673957	−0.103994
$43$	−9.14034	−1.39389	−0.696944	−	0.717125i	$-0.745458\pi$
$43$	−9.14034	−1.39389	−0.696944	+	0.717125i	$0.745458\pi$
$44$	−1.00000	−0.150756
$45$	2.72927	0.406855
$46$	−2.69468	−0.397309
$47$	−10.6370	−1.55156	−0.775779	−	0.631004i	$-0.782643\pi$
$47$	−10.6370	−1.55156	−0.775779	+	0.631004i	$0.782643\pi$
$48$	1.00000	0.144338
$49$	−6.54578	−0.935112
$50$	2.44889	0.346325
$51$	4.25138	0.595312
$52$	3.59767	0.498907
$53$	−3.56328	−0.489454	−0.244727	−	0.969592i	$-0.578698\pi$
$53$	−3.56328	−0.489454	−0.244727	+	0.969592i	$0.578698\pi$
$54$	1.00000	0.136083
$55$	−2.72927	−0.368014
$56$	−0.673957	−0.0900614
$57$	5.82526	0.771575
$58$	−7.00036	−0.919192
$59$	3.91975	0.510307	0.255154	−	0.966900i	$-0.417874\pi$
$59$	3.91975	0.510307	0.255154	+	0.966900i	$0.417874\pi$
$60$	2.72927	0.352347
$61$	1.00000	0.128037
$61$	1.00000	0.128037
$62$	1.96541	0.249608
$63$	−0.673957	−0.0849107
$64$	1.00000	0.125000
$65$	9.81900	1.21790
$66$	−1.00000	−0.123091
$67$	6.94252	0.848164	0.424082	−	0.905624i	$-0.360597\pi$
$67$	6.94252	0.848164	0.424082	+	0.905624i	$0.360597\pi$
$68$	4.25138	0.515556
$69$	−2.69468	−0.324401
$70$	−1.83941	−0.219851
$71$	0.365213	0.0433428	0.0216714	−	0.999765i	$-0.493101\pi$
$71$	0.365213	0.0433428	0.0216714	+	0.999765i	$0.493101\pi$
$72$	1.00000	0.117851
$73$	−4.95939	−0.580453	−0.290226	−	0.956958i	$-0.593731\pi$
$73$	−4.95939	−0.580453	−0.290226	+	0.956958i	$0.593731\pi$
$74$	10.3558	1.20383
$75$	2.44889	0.282773
$76$	5.82526	0.668204
$77$	0.673957	0.0768046
$78$	3.59767	0.407356
$79$	−2.75204	−0.309629	−0.154814	−	0.987944i	$-0.549478\pi$
$79$	−2.75204	−0.309629	−0.154814	+	0.987944i	$0.549478\pi$
$80$	2.72927	0.305141
$81$	1.00000	0.111111
$82$	−3.88057	−0.428538
$83$	−0.156532	−0.0171816	−0.00859082	−	0.999963i	$-0.502735\pi$
$83$	−0.156532	−0.0171816	−0.00859082	+	0.999963i	$0.502735\pi$
$84$	−0.673957	−0.0735348
$85$	11.6031	1.25854
$86$	−9.14034	−0.985628
$87$	−7.00036	−0.750517
$88$	−1.00000	−0.106600
$89$	16.9930	1.80125	0.900626	−	0.434595i	$-0.143109\pi$
$89$	16.9930	1.80125	0.900626	+	0.434595i	$0.143109\pi$
$90$	2.72927	0.287690
$91$	−2.42468	−0.254175
$92$	−2.69468	−0.280940
$93$	1.96541	0.203804
$94$	−10.6370	−1.09712
$95$	15.8987	1.63117
$96$	1.00000	0.102062
$97$	−11.2082	−1.13802	−0.569010	−	0.822330i	$-0.692674\pi$
$97$	−11.2082	−1.13802	−0.569010	+	0.822330i	$0.692674\pi$
$98$	−6.54578	−0.661224
$99$	−1.00000	−0.100504
$100$	2.44889	0.244889
$101$	7.44745	0.741049	0.370524	−	0.928823i	$-0.379178\pi$
$101$	7.44745	0.741049	0.370524	+	0.928823i	$0.379178\pi$
$102$	4.25138	0.420949
$103$	−6.91858	−0.681708	−0.340854	−	0.940116i	$-0.610716\pi$
$103$	−6.91858	−0.681708	−0.340854	+	0.940116i	$0.610716\pi$
$104$	3.59767	0.352781
$105$	−1.83941	−0.179508
$106$	−3.56328	−0.346096
$107$	4.35224	0.420747	0.210374	−	0.977621i	$-0.432532\pi$
$107$	4.35224	0.420747	0.210374	+	0.977621i	$0.432532\pi$
$108$	1.00000	0.0962250
$109$	18.7692	1.79776	0.898879	−	0.438196i	$-0.144382\pi$
$109$	18.7692	1.79776	0.898879	+	0.438196i	$0.144382\pi$
$110$	−2.72927	−0.260225
$111$	10.3558	0.982926
$112$	−0.673957	−0.0636830
$113$	−3.45468	−0.324989	−0.162495	−	0.986709i	$-0.551954\pi$
$113$	−3.45468	−0.324989	−0.162495	+	0.986709i	$0.551954\pi$
$114$	5.82526	0.545586
$115$	−7.35449	−0.685810
$116$	−7.00036	−0.649967
$117$	3.59767	0.332605
$118$	3.91975	0.360842
$119$	−2.86525	−0.262657
$120$	2.72927	0.249147
$121$	1.00000	0.0909091
$122$	1.00000	0.0905357
$123$	−3.88057	−0.349899
$124$	1.96541	0.176499
$125$	−6.96266	−0.622759
$126$	−0.673957	−0.0600409
$127$	−2.79518	−0.248032	−0.124016	−	0.992280i	$-0.539577\pi$
$127$	−2.79518	−0.248032	−0.124016	+	0.992280i	$0.539577\pi$
$128$	1.00000	0.0883883
$129$	−9.14034	−0.804762
$130$	9.81900	0.861183
$131$	1.56261	0.136526	0.0682629	−	0.997667i	$-0.478254\pi$
$131$	1.56261	0.136526	0.0682629	+	0.997667i	$0.478254\pi$
$132$	−1.00000	−0.0870388
$133$	−3.92598	−0.340426
$134$	6.94252	0.599742
$135$	2.72927	0.234898
$136$	4.25138	0.364553
$137$	−11.8420	−1.01173	−0.505867	−	0.862612i	$-0.668827\pi$
$137$	−11.8420	−1.01173	−0.505867	+	0.862612i	$0.668827\pi$
$138$	−2.69468	−0.229386
$139$	18.4081	1.56136	0.780678	−	0.624933i	$-0.214874\pi$
$139$	18.4081	1.56136	0.780678	+	0.624933i	$0.214874\pi$
$140$	−1.83941	−0.155458
$141$	−10.6370	−0.895793
$142$	0.365213	0.0306480
$143$	−3.59767	−0.300852
$144$	1.00000	0.0833333
$145$	−19.1058	−1.58665
$146$	−4.95939	−0.410442
$147$	−6.54578	−0.539887
$148$	10.3558	0.851239
$149$	11.4006	0.933975	0.466988	−	0.884264i	$-0.345339\pi$
$149$	11.4006	0.933975	0.466988	+	0.884264i	$0.345339\pi$
$150$	2.44889	0.199951
$151$	−4.24190	−0.345201	−0.172600	−	0.984992i	$-0.555217\pi$
$151$	−4.24190	−0.345201	−0.172600	+	0.984992i	$0.555217\pi$
$152$	5.82526	0.472491
$153$	4.25138	0.343704
$154$	0.673957	0.0543090
$155$	5.36413	0.430858
$156$	3.59767	0.288044
$157$	21.8267	1.74196	0.870981	−	0.491316i	$-0.163484\pi$
$157$	21.8267	1.74196	0.870981	+	0.491316i	$0.163484\pi$
$158$	−2.75204	−0.218941
$159$	−3.56328	−0.282586
$160$	2.72927	0.215767
$161$	1.81610	0.143129
$162$	1.00000	0.0785674
$163$	1.27864	0.100150	0.0500752	−	0.998745i	$-0.484054\pi$
$163$	1.27864	0.100150	0.0500752	+	0.998745i	$0.484054\pi$
$164$	−3.88057	−0.303022
$165$	−2.72927	−0.212473
$166$	−0.156532	−0.0121493
$167$	13.8118	1.06879	0.534396	−	0.845234i	$-0.320539\pi$
$167$	13.8118	1.06879	0.534396	+	0.845234i	$0.320539\pi$
$168$	−0.673957	−0.0519969
$169$	−0.0567725	−0.00436712
$170$	11.6031	0.889921
$171$	5.82526	0.445469
$172$	−9.14034	−0.696944
$173$	6.63267	0.504273	0.252136	−	0.967692i	$-0.418867\pi$
$173$	6.63267	0.504273	0.252136	+	0.967692i	$0.418867\pi$
$174$	−7.00036	−0.530696
$175$	−1.65045	−0.124762
$176$	−1.00000	−0.0753778
$177$	3.91975	0.294626
$178$	16.9930	1.27368
$179$	−13.7972	−1.03125	−0.515624	−	0.856815i	$-0.672440\pi$
$179$	−13.7972	−1.03125	−0.515624	+	0.856815i	$0.672440\pi$
$180$	2.72927	0.203427
$181$	−10.3165	−0.766819	−0.383409	−	0.923579i	$-0.625250\pi$
$181$	−10.3165	−0.766819	−0.383409	+	0.923579i	$0.625250\pi$
$182$	−2.42468	−0.179729
$183$	1.00000	0.0739221
$184$	−2.69468	−0.198654
$185$	28.2636	2.07798
$186$	1.96541	0.144111
$187$	−4.25138	−0.310892
$188$	−10.6370	−0.775779
$189$	−0.673957	−0.0490232
$190$	15.8987	1.15341
$191$	−3.66910	−0.265486	−0.132743	−	0.991150i	$-0.542379\pi$
$191$	−3.66910	−0.265486	−0.132743	+	0.991150i	$0.542379\pi$
$192$	1.00000	0.0721688
$193$	7.96138	0.573073	0.286536	−	0.958069i	$-0.407496\pi$
$193$	7.96138	0.573073	0.286536	+	0.958069i	$0.407496\pi$
$194$	−11.2082	−0.804702
$195$	9.81900	0.703153
$196$	−6.54578	−0.467556
$197$	−3.60611	−0.256924	−0.128462	−	0.991714i	$-0.541004\pi$
$197$	−3.60611	−0.256924	−0.128462	+	0.991714i	$0.541004\pi$
$198$	−1.00000	−0.0710669
$199$	−16.6285	−1.17877	−0.589383	−	0.807854i	$-0.700629\pi$
$199$	−16.6285	−1.17877	−0.589383	+	0.807854i	$0.700629\pi$
$200$	2.44889	0.173163
$201$	6.94252	0.489688
$202$	7.44745	0.524001
$203$	4.71794	0.331135
$204$	4.25138	0.297656
$205$	−10.5911	−0.739715
$206$	−6.91858	−0.482041
$207$	−2.69468	−0.187293
$208$	3.59767	0.249454
$209$	−5.82526	−0.402942
$210$	−1.83941	−0.126931
$211$	−22.5841	−1.55475	−0.777376	−	0.629036i	$-0.783450\pi$
$211$	−22.5841	−1.55475	−0.777376	+	0.629036i	$0.783450\pi$
$212$	−3.56328	−0.244727
$213$	0.365213	0.0250240
$214$	4.35224	0.297513
$215$	−24.9464	−1.70133
$216$	1.00000	0.0680414
$217$	−1.32460	−0.0899200
$218$	18.7692	1.27121
$219$	−4.95939	−0.335125
$220$	−2.72927	−0.184007
$221$	15.2951	1.02886
$222$	10.3558	0.695033
$223$	−0.596137	−0.0399203	−0.0199601	−	0.999801i	$-0.506354\pi$
$223$	−0.596137	−0.0399203	−0.0199601	+	0.999801i	$0.506354\pi$
$224$	−0.673957	−0.0450307
$225$	2.44889	0.163259
$226$	−3.45468	−0.229802
$227$	−25.8235	−1.71397	−0.856983	−	0.515345i	$-0.827664\pi$
$227$	−25.8235	−1.71397	−0.856983	+	0.515345i	$0.827664\pi$
$228$	5.82526	0.385788
$229$	−24.1601	−1.59654	−0.798271	−	0.602299i	$-0.794252\pi$
$229$	−24.1601	−1.59654	−0.798271	+	0.602299i	$0.794252\pi$
$230$	−7.35449	−0.484941
$231$	0.673957	0.0443431
$232$	−7.00036	−0.459596
$233$	4.62550	0.303027	0.151513	−	0.988455i	$-0.451585\pi$
$233$	4.62550	0.303027	0.151513	+	0.988455i	$0.451585\pi$
$234$	3.59767	0.235187
$235$	−29.0311	−1.89378
$236$	3.91975	0.255154
$237$	−2.75204	−0.178764
$238$	−2.86525	−0.185727
$239$	−24.4212	−1.57967	−0.789837	−	0.613316i	$-0.789835\pi$
$239$	−24.4212	−1.57967	−0.789837	+	0.613316i	$0.789835\pi$
$240$	2.72927	0.176173
$241$	12.0073	0.773457	0.386729	−	0.922194i	$-0.373605\pi$
$241$	12.0073	0.773457	0.386729	+	0.922194i	$0.373605\pi$
$242$	1.00000	0.0642824
$243$	1.00000	0.0641500
$244$	1.00000	0.0640184
$245$	−17.8652	−1.14136
$246$	−3.88057	−0.247416
$247$	20.9574	1.33349
$248$	1.96541	0.124804
$249$	−0.156532	−0.00991983
$250$	−6.96266	−0.440357
$251$	−28.8035	−1.81806	−0.909029	−	0.416732i	$-0.863175\pi$
$251$	−28.8035	−1.81806	−0.909029	+	0.416732i	$0.863175\pi$
$252$	−0.673957	−0.0424553
$253$	2.69468	0.169413
$254$	−2.79518	−0.175385
$255$	11.6031	0.726617
$256$	1.00000	0.0625000
$257$	3.26066	0.203395	0.101697	−	0.994815i	$-0.467573\pi$
$257$	3.26066	0.203395	0.101697	+	0.994815i	$0.467573\pi$
$258$	−9.14034	−0.569053
$259$	−6.97935	−0.433675
$260$	9.81900	0.608948
$261$	−7.00036	−0.433311
$262$	1.56261	0.0965383
$263$	2.24512	0.138440	0.0692199	−	0.997601i	$-0.477949\pi$
$263$	2.24512	0.138440	0.0692199	+	0.997601i	$0.477949\pi$
$264$	−1.00000	−0.0615457
$265$	−9.72513	−0.597410
$266$	−3.92598	−0.240717
$267$	16.9930	1.03995
$268$	6.94252	0.424082
$269$	23.6005	1.43895	0.719474	−	0.694519i	$-0.244383\pi$
$269$	23.6005	1.43895	0.719474	+	0.694519i	$0.244383\pi$
$270$	2.72927	0.166098
$271$	−7.54489	−0.458320	−0.229160	−	0.973389i	$-0.573598\pi$
$271$	−7.54489	−0.458320	−0.229160	+	0.973389i	$0.573598\pi$
$272$	4.25138	0.257778
$273$	−2.42468	−0.146748
$274$	−11.8420	−0.715403
$275$	−2.44889	−0.147674
$276$	−2.69468	−0.162201
$277$	20.2982	1.21960	0.609800	−	0.792556i	$-0.291250\pi$
$277$	20.2982	1.21960	0.609800	+	0.792556i	$0.291250\pi$
$278$	18.4081	1.10405
$279$	1.96541	0.117666
$280$	−1.83941	−0.109926
$281$	4.38450	0.261557	0.130779	−	0.991412i	$-0.458252\pi$
$281$	4.38450	0.261557	0.130779	+	0.991412i	$0.458252\pi$
$282$	−10.6370	−0.633421
$283$	10.5547	0.627409	0.313704	−	0.949521i	$-0.398430\pi$
$283$	10.5547	0.627409	0.313704	+	0.949521i	$0.398430\pi$
$284$	0.365213	0.0216714
$285$	15.8987	0.941757
$286$	−3.59767	−0.212735
$287$	2.61534	0.154379
$288$	1.00000	0.0589256
$289$	1.07423	0.0631903
$290$	−19.1058	−1.12193
$291$	−11.2082	−0.657037
$292$	−4.95939	−0.290226
$293$	−31.7323	−1.85382	−0.926911	−	0.375282i	$-0.877546\pi$
$293$	−31.7323	−1.85382	−0.926911	+	0.375282i	$0.877546\pi$
$294$	−6.54578	−0.381758
$295$	10.6980	0.622863
$296$	10.3558	0.601917
$297$	−1.00000	−0.0580259
$298$	11.4006	0.660420
$299$	−9.69456	−0.560651
$300$	2.44889	0.141387
$301$	6.16020	0.355068
$302$	−4.24190	−0.244094
$303$	7.44745	0.427845
$304$	5.82526	0.334102
$305$	2.72927	0.156277
$306$	4.25138	0.243035
$307$	−0.998640	−0.0569954	−0.0284977	−	0.999594i	$-0.509072\pi$
$307$	−0.998640	−0.0569954	−0.0284977	+	0.999594i	$0.509072\pi$
$308$	0.673957	0.0384023
$309$	−6.91858	−0.393584
$310$	5.36413	0.304662
$311$	3.92585	0.222614	0.111307	−	0.993786i	$-0.464496\pi$
$311$	3.92585	0.222614	0.111307	+	0.993786i	$0.464496\pi$
$312$	3.59767	0.203678
$313$	−20.3307	−1.14916	−0.574578	−	0.818450i	$-0.694834\pi$
$313$	−20.3307	−1.14916	−0.574578	+	0.818450i	$0.694834\pi$
$314$	21.8267	1.23175
$315$	−1.83941	−0.103639
$316$	−2.75204	−0.154814
$317$	−19.7540	−1.10949	−0.554747	−	0.832019i	$-0.687185\pi$
$317$	−19.7540	−1.10949	−0.554747	+	0.832019i	$0.687185\pi$
$318$	−3.56328	−0.199819
$319$	7.00036	0.391945
$320$	2.72927	0.152571
$321$	4.35224	0.242918
$322$	1.81610	0.101207
$323$	24.7654	1.37798
$324$	1.00000	0.0555556
$325$	8.81030	0.488707
$326$	1.27864	0.0708171
$327$	18.7692	1.03794
$328$	−3.88057	−0.214269
$329$	7.16885	0.395232
$330$	−2.72927	−0.150241
$331$	−4.11510	−0.226186	−0.113093	−	0.993584i	$-0.536076\pi$
$331$	−4.11510	−0.226186	−0.113093	+	0.993584i	$0.536076\pi$
$332$	−0.156532	−0.00859082
$333$	10.3558	0.567492
$334$	13.8118	0.755750
$335$	18.9480	1.03524
$336$	−0.673957	−0.0367674
$337$	−11.6712	−0.635769	−0.317884	−	0.948129i	$-0.602972\pi$
$337$	−11.6712	−0.635769	−0.317884	+	0.948129i	$0.602972\pi$
$338$	−0.0567725	−0.00308802
$339$	−3.45468	−0.187633
$340$	11.6031	0.629269
$341$	−1.96541	−0.106433
$342$	5.82526	0.314994
$343$	9.12928	0.492935
$344$	−9.14034	−0.492814
$345$	−7.35449	−0.395953
$346$	6.63267	0.356575
$347$	8.20412	0.440420	0.220210	−	0.975452i	$-0.429326\pi$
$347$	8.20412	0.440420	0.220210	+	0.975452i	$0.429326\pi$
$348$	−7.00036	−0.375259
$349$	−1.81610	−0.0972134	−0.0486067	−	0.998818i	$-0.515478\pi$
$349$	−1.81610	−0.0972134	−0.0486067	+	0.998818i	$0.515478\pi$
$350$	−1.65045	−0.0882201
$351$	3.59767	0.192029
$352$	−1.00000	−0.0533002
$353$	14.3060	0.761432	0.380716	−	0.924692i	$-0.375678\pi$
$353$	14.3060	0.761432	0.380716	+	0.924692i	$0.375678\pi$
$354$	3.91975	0.208332
$355$	0.996762	0.0529026
$356$	16.9930	0.900626
$357$	−2.86525	−0.151645
$358$	−13.7972	−0.729203
$359$	5.14351	0.271464	0.135732	−	0.990746i	$-0.456661\pi$
$359$	5.14351	0.271464	0.135732	+	0.990746i	$0.456661\pi$
$360$	2.72927	0.143845
$361$	14.9337	0.785985
$362$	−10.3165	−0.542223
$363$	1.00000	0.0524864
$364$	−2.42468	−0.127088
$365$	−13.5355	−0.708480
$366$	1.00000	0.0522708
$367$	−31.4881	−1.64367	−0.821834	−	0.569727i	$-0.807049\pi$
$367$	−31.4881	−1.64367	−0.821834	+	0.569727i	$0.807049\pi$
$368$	−2.69468	−0.140470
$369$	−3.88057	−0.202015
$370$	28.2636	1.46936
$371$	2.40150	0.124680
$372$	1.96541	0.101902
$373$	7.12105	0.368714	0.184357	−	0.982859i	$-0.440980\pi$
$373$	7.12105	0.368714	0.184357	+	0.982859i	$0.440980\pi$
$374$	−4.25138	−0.219834
$375$	−6.96266	−0.359550
$376$	−10.6370	−0.548559
$377$	−25.1850	−1.29709
$378$	−0.673957	−0.0346646
$379$	14.0522	0.721815	0.360907	−	0.932602i	$-0.382467\pi$
$379$	14.0522	0.721815	0.360907	+	0.932602i	$0.382467\pi$
$380$	15.8987	0.815586
$381$	−2.79518	−0.143201
$382$	−3.66910	−0.187727
$383$	−18.2433	−0.932187	−0.466094	−	0.884735i	$-0.654339\pi$
$383$	−18.2433	−0.932187	−0.466094	+	0.884735i	$0.654339\pi$
$384$	1.00000	0.0510310
$385$	1.83941	0.0937450
$386$	7.96138	0.405224
$387$	−9.14034	−0.464630
$388$	−11.2082	−0.569010
$389$	38.2158	1.93762	0.968808	−	0.247813i	$-0.0797120\pi$
$389$	38.2158	1.93762	0.968808	+	0.247813i	$0.0797120\pi$
$390$	9.81900	0.497204
$391$	−11.4561	−0.579360
$392$	−6.54578	−0.330612
$393$	1.56261	0.0788232
$394$	−3.60611	−0.181673
$395$	−7.51105	−0.377922
$396$	−1.00000	−0.0502519
$397$	35.0350	1.75836	0.879179	−	0.476491i	$-0.158092\pi$
$397$	35.0350	1.75836	0.879179	+	0.476491i	$0.158092\pi$
$398$	−16.6285	−0.833513
$399$	−3.92598	−0.196545
$400$	2.44889	0.122444
$401$	10.5478	0.526734	0.263367	−	0.964696i	$-0.415167\pi$
$401$	10.5478	0.526734	0.263367	+	0.964696i	$0.415167\pi$
$402$	6.94252	0.346261
$403$	7.07091	0.352227
$404$	7.44745	0.370524
$405$	2.72927	0.135618
$406$	4.71794	0.234148
$407$	−10.3558	−0.513316
$408$	4.25138	0.210475
$409$	−23.1673	−1.14555	−0.572774	−	0.819713i	$-0.694133\pi$
$409$	−23.1673	−1.14555	−0.572774	+	0.819713i	$0.694133\pi$
$410$	−10.5911	−0.523058
$411$	−11.8420	−0.584124
$412$	−6.91858	−0.340854
$413$	−2.64174	−0.129992
$414$	−2.69468	−0.132436
$415$	−0.427218	−0.0209713
$416$	3.59767	0.176390
$417$	18.4081	0.901449
$418$	−5.82526	−0.284923
$419$	−35.4669	−1.73267	−0.866336	−	0.499461i	$-0.833531\pi$
$419$	−35.4669	−1.73267	−0.866336	+	0.499461i	$0.833531\pi$
$420$	−1.83941	−0.0897540
$421$	21.2987	1.03803	0.519017	−	0.854764i	$-0.326298\pi$
$421$	21.2987	1.03803	0.519017	+	0.854764i	$0.326298\pi$
$422$	−22.5841	−1.09938
$423$	−10.6370	−0.517186
$424$	−3.56328	−0.173048
$425$	10.4112	0.505015
$426$	0.365213	0.0176946
$427$	−0.673957	−0.0326151
$428$	4.35224	0.210374
$429$	−3.59767	−0.173697
$430$	−24.9464	−1.20302
$431$	−3.83729	−0.184836	−0.0924179	−	0.995720i	$-0.529460\pi$
$431$	−3.83729	−0.184836	−0.0924179	+	0.995720i	$0.529460\pi$
$432$	1.00000	0.0481125
$433$	−18.4484	−0.886575	−0.443288	−	0.896379i	$-0.646188\pi$
$433$	−18.4484	−0.886575	−0.443288	+	0.896379i	$0.646188\pi$
$434$	−1.32460	−0.0635831
$435$	−19.1058	−0.916055
$436$	18.7692	0.898879
$437$	−15.6972	−0.750900
$438$	−4.95939	−0.236969
$439$	−17.1275	−0.817450	−0.408725	−	0.912658i	$-0.634026\pi$
$439$	−17.1275	−0.817450	−0.408725	+	0.912658i	$0.634026\pi$
$440$	−2.72927	−0.130113
$441$	−6.54578	−0.311704
$442$	15.2951	0.727512
$443$	−5.95809	−0.283077	−0.141539	−	0.989933i	$-0.545205\pi$
$443$	−5.95809	−0.283077	−0.141539	+	0.989933i	$0.545205\pi$
$444$	10.3558	0.491463
$445$	46.3783	2.19854
$446$	−0.596137	−0.0282279
$447$	11.4006	0.539231
$448$	−0.673957	−0.0318415
$449$	−15.5422	−0.733480	−0.366740	−	0.930323i	$-0.619526\pi$
$449$	−15.5422	−0.733480	−0.366740	+	0.930323i	$0.619526\pi$
$450$	2.44889	0.115442
$451$	3.88057	0.182729
$452$	−3.45468	−0.162495
$453$	−4.24190	−0.199302
$454$	−25.8235	−1.21196
$455$	−6.61759	−0.310237
$456$	5.82526	0.272793
$457$	7.16430	0.335132	0.167566	−	0.985861i	$-0.446409\pi$
$457$	7.16430	0.335132	0.167566	+	0.985861i	$0.446409\pi$
$458$	−24.1601	−1.12893
$459$	4.25138	0.198437
$460$	−7.35449	−0.342905
$461$	−19.2505	−0.896583	−0.448292	−	0.893887i	$-0.647967\pi$
$461$	−19.2505	−0.896583	−0.448292	+	0.893887i	$0.647967\pi$
$462$	0.673957	0.0313553
$463$	24.3868	1.13335	0.566674	−	0.823942i	$-0.308230\pi$
$463$	24.3868	1.13335	0.566674	+	0.823942i	$0.308230\pi$
$464$	−7.00036	−0.324983
$465$	5.36413	0.248756
$466$	4.62550	0.214272
$467$	9.41440	0.435647	0.217823	−	0.975988i	$-0.430104\pi$
$467$	9.41440	0.435647	0.217823	+	0.975988i	$0.430104\pi$
$468$	3.59767	0.166302
$469$	−4.67896	−0.216054
$470$	−29.0311	−1.33910
$471$	21.8267	1.00572
$472$	3.91975	0.180421
$473$	9.14034	0.420273
$474$	−2.75204	−0.126405
$475$	14.2654	0.654543
$476$	−2.86525	−0.131328
$477$	−3.56328	−0.163151
$478$	−24.4212	−1.11700
$479$	−21.7380	−0.993236	−0.496618	−	0.867969i	$-0.665425\pi$
$479$	−21.7380	−0.993236	−0.496618	+	0.867969i	$0.665425\pi$
$480$	2.72927	0.124573
$481$	37.2566	1.69876
$482$	12.0073	0.546917
$483$	1.81610	0.0826353
$484$	1.00000	0.0454545
$485$	−30.5902	−1.38903
$486$	1.00000	0.0453609
$487$	17.5946	0.797288	0.398644	−	0.917106i	$-0.369481\pi$
$487$	17.5946	0.797288	0.398644	+	0.917106i	$0.369481\pi$
$488$	1.00000	0.0452679
$489$	1.27864	0.0578219
$490$	−17.8652	−0.807066
$491$	39.4366	1.77975	0.889875	−	0.456205i	$-0.150792\pi$
$491$	39.4366	1.77975	0.889875	+	0.456205i	$0.150792\pi$
$492$	−3.88057	−0.174950
$493$	−29.7612	−1.34038
$494$	20.9574	0.942917
$495$	−2.72927	−0.122671
$496$	1.96541	0.0882496
$497$	−0.246138	−0.0110408
$498$	−0.156532	−0.00701438
$499$	29.9798	1.34208	0.671041	−	0.741420i	$-0.265847\pi$
$499$	29.9798	1.34208	0.671041	+	0.741420i	$0.265847\pi$
$500$	−6.96266	−0.311380
$501$	13.8118	0.617067
$502$	−28.8035	−1.28556
$503$	−26.5171	−1.18234	−0.591170	−	0.806547i	$-0.701334\pi$
$503$	−26.5171	−1.18234	−0.591170	+	0.806547i	$0.701334\pi$
$504$	−0.673957	−0.0300205
$505$	20.3261	0.904498
$506$	2.69468	0.119793
$507$	−0.0567725	−0.00252136
$508$	−2.79518	−0.124016
$509$	1.49678	0.0663434	0.0331717	−	0.999450i	$-0.489439\pi$
$509$	1.49678	0.0663434	0.0331717	+	0.999450i	$0.489439\pi$
$510$	11.6031	0.513796
$511$	3.34242	0.147860
$512$	1.00000	0.0441942
$513$	5.82526	0.257192
$514$	3.26066	0.143822
$515$	−18.8826	−0.832069
$516$	−9.14034	−0.402381
$517$	10.6370	0.467813
$518$	−6.97935	−0.306655
$519$	6.63267	0.291142
$520$	9.81900	0.430591
$521$	−28.0423	−1.22856	−0.614278	−	0.789090i	$-0.710553\pi$
$521$	−28.0423	−1.22856	−0.614278	+	0.789090i	$0.710553\pi$
$522$	−7.00036	−0.306397
$523$	20.9384	0.915570	0.457785	−	0.889063i	$-0.348643\pi$
$523$	20.9384	0.915570	0.457785	+	0.889063i	$0.348643\pi$
$524$	1.56261	0.0682629
$525$	−1.65045	−0.0720314
$526$	2.24512	0.0978917
$527$	8.35572	0.363981
$528$	−1.00000	−0.0435194
$529$	−15.7387	−0.684292
$530$	−9.72513	−0.422433
$531$	3.91975	0.170102
$532$	−3.92598	−0.170213
$533$	−13.9610	−0.604719
$534$	16.9930	0.735358
$535$	11.8784	0.513549
$536$	6.94252	0.299871
$537$	−13.7972	−0.595391
$538$	23.6005	1.01749
$539$	6.54578	0.281947
$540$	2.72927	0.117449
$541$	19.0512	0.819077	0.409539	−	0.912293i	$-0.365690\pi$
$541$	19.0512	0.819077	0.409539	+	0.912293i	$0.365690\pi$
$542$	−7.54489	−0.324081
$543$	−10.3165	−0.442723
$544$	4.25138	0.182276
$545$	51.2260	2.19428
$546$	−2.42468	−0.103767
$547$	−18.5438	−0.792878	−0.396439	−	0.918061i	$-0.629754\pi$
$547$	−18.5438	−0.792878	−0.396439	+	0.918061i	$0.629754\pi$
$548$	−11.8420	−0.505867
$549$	1.00000	0.0426790
$550$	−2.44889	−0.104421
$551$	−40.7789	−1.73724
$552$	−2.69468	−0.114693
$553$	1.85476	0.0788724
$554$	20.2982	0.862387
$555$	28.2636	1.19972
$556$	18.4081	0.780678
$557$	19.5596	0.828768	0.414384	−	0.910102i	$-0.363997\pi$
$557$	19.5596	0.828768	0.414384	+	0.910102i	$0.363997\pi$
$558$	1.96541	0.0832026
$559$	−32.8839	−1.39084
$560$	−1.83941	−0.0777292
$561$	−4.25138	−0.179493
$562$	4.38450	0.184949
$563$	−12.7296	−0.536487	−0.268244	−	0.963351i	$-0.586443\pi$
$563$	−12.7296	−0.536487	−0.268244	+	0.963351i	$0.586443\pi$
$564$	−10.6370	−0.447896
$565$	−9.42874	−0.396670
$566$	10.5547	0.443645
$567$	−0.673957	−0.0283036
$568$	0.365213	0.0153240
$569$	−28.2675	−1.18503	−0.592517	−	0.805558i	$-0.701866\pi$
$569$	−28.2675	−1.18503	−0.592517	+	0.805558i	$0.701866\pi$
$570$	15.8987	0.665923
$571$	16.4863	0.689932	0.344966	−	0.938615i	$-0.387890\pi$
$571$	16.4863	0.689932	0.344966	+	0.938615i	$0.387890\pi$
$572$	−3.59767	−0.150426
$573$	−3.66910	−0.153279
$574$	2.61534	0.109162
$575$	−6.59897	−0.275196
$576$	1.00000	0.0416667
$577$	23.9235	0.995949	0.497975	−	0.867192i	$-0.334077\pi$
$577$	23.9235	0.995949	0.497975	+	0.867192i	$0.334077\pi$
$578$	1.07423	0.0446823
$579$	7.96138	0.330864
$580$	−19.1058	−0.793327
$581$	0.105496	0.00437671
$582$	−11.2082	−0.464595
$583$	3.56328	0.147576
$584$	−4.95939	−0.205221
$585$	9.81900	0.405965
$586$	−31.7323	−1.31085
$587$	19.1867	0.791919	0.395959	−	0.918268i	$-0.370412\pi$
$587$	19.1867	0.791919	0.395959	+	0.918268i	$0.370412\pi$
$588$	−6.54578	−0.269943
$589$	11.4490	0.471750
$590$	10.6980	0.440431
$591$	−3.60611	−0.148335
$592$	10.3558	0.425619
$593$	35.1543	1.44362	0.721808	−	0.692094i	$-0.243311\pi$
$593$	35.1543	1.44362	0.721808	+	0.692094i	$0.243311\pi$
$594$	−1.00000	−0.0410305
$595$	−7.82003	−0.320590
$596$	11.4006	0.466988
$597$	−16.6285	−0.680561
$598$	−9.69456	−0.396440
$599$	−38.0017	−1.55271	−0.776353	−	0.630299i	$-0.782932\pi$
$599$	−38.0017	−1.55271	−0.776353	+	0.630299i	$0.782932\pi$
$600$	2.44889	0.0999755
$601$	−11.9234	−0.486364	−0.243182	−	0.969981i	$-0.578191\pi$
$601$	−11.9234	−0.486364	−0.243182	+	0.969981i	$0.578191\pi$
$602$	6.16020	0.251071
$603$	6.94252	0.282721
$604$	−4.24190	−0.172600
$605$	2.72927	0.110960
$606$	7.44745	0.302532
$607$	2.10367	0.0853854	0.0426927	−	0.999088i	$-0.486406\pi$
$607$	2.10367	0.0853854	0.0426927	+	0.999088i	$0.486406\pi$
$608$	5.82526	0.236246
$609$	4.71794	0.191181
$610$	2.72927	0.110505
$611$	−38.2682	−1.54817
$612$	4.25138	0.171852
$613$	43.7062	1.76528	0.882639	−	0.470052i	$-0.155765\pi$
$613$	43.7062	1.76528	0.882639	+	0.470052i	$0.155765\pi$
$614$	−0.998640	−0.0403018
$615$	−10.5911	−0.427075
$616$	0.673957	0.0271545
$617$	−36.2925	−1.46108	−0.730540	−	0.682870i	$-0.760731\pi$
$617$	−36.2925	−1.46108	−0.730540	+	0.682870i	$0.760731\pi$
$618$	−6.91858	−0.278306
$619$	−11.9174	−0.479002	−0.239501	−	0.970896i	$-0.576984\pi$
$619$	−11.9174	−0.479002	−0.239501	+	0.970896i	$0.576984\pi$
$620$	5.36413	0.215429
$621$	−2.69468	−0.108134
$622$	3.92585	0.157412
$623$	−11.4525	−0.458836
$624$	3.59767	0.144022
$625$	−31.2474	−1.24990
$626$	−20.3307	−0.812576
$627$	−5.82526	−0.232639
$628$	21.8267	0.870981
$629$	44.0263	1.75544
$630$	−1.83941	−0.0732838
$631$	−3.06591	−0.122052	−0.0610260	−	0.998136i	$-0.519437\pi$
$631$	−3.06591	−0.122052	−0.0610260	+	0.998136i	$0.519437\pi$
$632$	−2.75204	−0.109470
$633$	−22.5841	−0.897637
$634$	−19.7540	−0.784530
$635$	−7.62878	−0.302739
$636$	−3.56328	−0.141293
$637$	−23.5496	−0.933068
$638$	7.00036	0.277147
$639$	0.365213	0.0144476
$640$	2.72927	0.107884
$641$	−6.11169	−0.241397	−0.120699	−	0.992689i	$-0.538513\pi$
$641$	−6.11169	−0.241397	−0.120699	+	0.992689i	$0.538513\pi$
$642$	4.35224	0.171769
$643$	1.41675	0.0558711	0.0279356	−	0.999610i	$-0.491107\pi$
$643$	1.41675	0.0558711	0.0279356	+	0.999610i	$0.491107\pi$
$644$	1.81610	0.0715643
$645$	−24.9464	−0.982264
$646$	24.7654	0.974382
$647$	−3.11439	−0.122439	−0.0612197	−	0.998124i	$-0.519499\pi$
$647$	−3.11439	−0.122439	−0.0612197	+	0.998124i	$0.519499\pi$
$648$	1.00000	0.0392837
$649$	−3.91975	−0.153863
$650$	8.81030	0.345568
$651$	−1.32460	−0.0519153
$652$	1.27864	0.0500752
$653$	−39.3794	−1.54103	−0.770517	−	0.637419i	$-0.780002\pi$
$653$	−39.3794	−1.54103	−0.770517	+	0.637419i	$0.780002\pi$
$654$	18.7692	0.733932
$655$	4.26477	0.166639
$656$	−3.88057	−0.151511
$657$	−4.95939	−0.193484
$658$	7.16885	0.279471
$659$	19.6845	0.766800	0.383400	−	0.923582i	$-0.374753\pi$
$659$	19.6845	0.766800	0.383400	+	0.923582i	$0.374753\pi$
$660$	−2.72927	−0.106237
$661$	−44.7958	−1.74236	−0.871178	−	0.490967i	$-0.836643\pi$
$661$	−44.7958	−1.74236	−0.871178	+	0.490967i	$0.836643\pi$
$662$	−4.11510	−0.159938
$663$	15.2951	0.594011
$664$	−0.156532	−0.00607463
$665$	−10.7150	−0.415512
$666$	10.3558	0.401278
$667$	18.8637	0.730406
$668$	13.8118	0.534396
$669$	−0.596137	−0.0230480
$670$	18.9480	0.732024
$671$	−1.00000	−0.0386046
$672$	−0.673957	−0.0259985
$673$	1.26117	0.0486145	0.0243073	−	0.999705i	$-0.492262\pi$
$673$	1.26117	0.0486145	0.0243073	+	0.999705i	$0.492262\pi$
$674$	−11.6712	−0.449556
$675$	2.44889	0.0942578
$676$	−0.0567725	−0.00218356
$677$	−37.5710	−1.44397	−0.721985	−	0.691909i	$-0.756770\pi$
$677$	−37.5710	−1.44397	−0.721985	+	0.691909i	$0.756770\pi$
$678$	−3.45468	−0.132676
$679$	7.55385	0.289890
$680$	11.6031	0.444960
$681$	−25.8235	−0.989559
$682$	−1.96541	−0.0752595
$683$	3.43910	0.131594	0.0657968	−	0.997833i	$-0.479041\pi$
$683$	3.43910	0.131594	0.0657968	+	0.997833i	$0.479041\pi$
$684$	5.82526	0.222735
$685$	−32.3201	−1.23489
$686$	9.12928	0.348558
$687$	−24.1601	−0.921764
$688$	−9.14034	−0.348472
$689$	−12.8195	−0.488384
$690$	−7.35449	−0.279981
$691$	19.0866	0.726087	0.363044	−	0.931772i	$-0.381738\pi$
$691$	19.0866	0.726087	0.363044	+	0.931772i	$0.381738\pi$
$692$	6.63267	0.252136
$693$	0.673957	0.0256015
$694$	8.20412	0.311424
$695$	50.2406	1.90574
$696$	−7.00036	−0.265348
$697$	−16.4978	−0.624898
$698$	−1.81610	−0.0687403
$699$	4.62550	0.174953
$700$	−1.65045	−0.0623810
$701$	19.4078	0.733021	0.366510	−	0.930414i	$-0.380552\pi$
$701$	19.4078	0.733021	0.366510	+	0.930414i	$0.380552\pi$
$702$	3.59767	0.135785
$703$	60.3251	2.27520
$704$	−1.00000	−0.0376889
$705$	−29.0311	−1.09337
$706$	14.3060	0.538414
$707$	−5.01926	−0.188769
$708$	3.91975	0.147313
$709$	−4.02286	−0.151082	−0.0755408	−	0.997143i	$-0.524068\pi$
$709$	−4.02286	−0.151082	−0.0755408	+	0.997143i	$0.524068\pi$
$710$	0.996762	0.0374078
$711$	−2.75204	−0.103210
$712$	16.9930	0.636839
$713$	−5.29615	−0.198343
$714$	−2.86525	−0.107229
$715$	−9.81900	−0.367210
$716$	−13.7972	−0.515624
$717$	−24.4212	−0.912026
$718$	5.14351	0.191954
$719$	−35.7621	−1.33370	−0.666850	−	0.745192i	$-0.732358\pi$
$719$	−35.7621	−1.33370	−0.666850	+	0.745192i	$0.732358\pi$
$720$	2.72927	0.101714
$721$	4.66283	0.173653
$722$	14.9337	0.555775
$723$	12.0073	0.446556
$724$	−10.3165	−0.383409
$725$	−17.1431	−0.636679
$726$	1.00000	0.0371135
$727$	2.06808	0.0767008	0.0383504	−	0.999264i	$-0.487790\pi$
$727$	2.06808	0.0767008	0.0383504	+	0.999264i	$0.487790\pi$
$728$	−2.42468	−0.0898645
$729$	1.00000	0.0370370
$730$	−13.5355	−0.500971
$731$	−38.8591	−1.43725
$732$	1.00000	0.0369611
$733$	5.39491	0.199266	0.0996329	−	0.995024i	$-0.468233\pi$
$733$	5.39491	0.199266	0.0996329	+	0.995024i	$0.468233\pi$
$734$	−31.4881	−1.16225
$735$	−17.8652	−0.658967
$736$	−2.69468	−0.0993272
$737$	−6.94252	−0.255731
$738$	−3.88057	−0.142846
$739$	−2.31206	−0.0850505	−0.0425252	−	0.999095i	$-0.513540\pi$
$739$	−2.31206	−0.0850505	−0.0425252	+	0.999095i	$0.513540\pi$
$740$	28.2636	1.03899
$741$	20.9574	0.769889
$742$	2.40150	0.0881618
$743$	−3.98719	−0.146276	−0.0731380	−	0.997322i	$-0.523301\pi$
$743$	−3.98719	−0.146276	−0.0731380	+	0.997322i	$0.523301\pi$
$744$	1.96541	0.0720555
$745$	31.1153	1.13998
$746$	7.12105	0.260720
$747$	−0.156532	−0.00572722
$748$	−4.25138	−0.155446
$749$	−2.93323	−0.107178
$750$	−6.96266	−0.254240
$751$	−6.45422	−0.235518	−0.117759	−	0.993042i	$-0.537571\pi$
$751$	−6.45422	−0.235518	−0.117759	+	0.993042i	$0.537571\pi$
$752$	−10.6370	−0.387890
$753$	−28.8035	−1.04966
$754$	−25.1850	−0.917183
$755$	−11.5773	−0.421340
$756$	−0.673957	−0.0245116
$757$	−23.2343	−0.844463	−0.422232	−	0.906488i	$-0.638753\pi$
$757$	−23.2343	−0.844463	−0.422232	+	0.906488i	$0.638753\pi$
$758$	14.0522	0.510400
$759$	2.69468	0.0978106
$760$	15.8987	0.576706
$761$	29.5065	1.06961	0.534804	−	0.844976i	$-0.320385\pi$
$761$	29.5065	1.06961	0.534804	+	0.844976i	$0.320385\pi$
$762$	−2.79518	−0.101259
$763$	−12.6496	−0.457947
$764$	−3.66910	−0.132743
$765$	11.6031	0.419513
$766$	−18.2433	−0.659156
$767$	14.1020	0.509192
$768$	1.00000	0.0360844
$769$	33.7110	1.21565	0.607825	−	0.794071i	$-0.292042\pi$
$769$	33.7110	1.21565	0.607825	+	0.794071i	$0.292042\pi$
$770$	1.83941	0.0662877
$771$	3.26066	0.117430
$772$	7.96138	0.286536
$773$	−9.58341	−0.344691	−0.172346	−	0.985037i	$-0.555135\pi$
$773$	−9.58341	−0.344691	−0.172346	+	0.985037i	$0.555135\pi$
$774$	−9.14034	−0.328543
$775$	4.81308	0.172891
$776$	−11.2082	−0.402351
$777$	−6.97935	−0.250383
$778$	38.2158	1.37010
$779$	−22.6054	−0.809921
$780$	9.81900	0.351576
$781$	−0.365213	−0.0130683
$782$	−11.4561	−0.409669
$783$	−7.00036	−0.250172
$784$	−6.54578	−0.233778
$785$	59.5709	2.12618
$786$	1.56261	0.0557364
$787$	−20.2864	−0.723131	−0.361565	−	0.932347i	$-0.617758\pi$
$787$	−20.2864	−0.723131	−0.361565	+	0.932347i	$0.617758\pi$
$788$	−3.60611	−0.128462
$789$	2.24512	0.0799282
$790$	−7.51105	−0.267231
$791$	2.32831	0.0827851
$792$	−1.00000	−0.0355335
$793$	3.59767	0.127757
$794$	35.0350	1.24335
$795$	−9.72513	−0.344915
$796$	−16.6285	−0.589383
$797$	19.8303	0.702426	0.351213	−	0.936296i	$-0.385769\pi$
$797$	19.8303	0.702426	0.351213	+	0.936296i	$0.385769\pi$
$798$	−3.92598	−0.138978
$799$	−45.2217	−1.59983
$800$	2.44889	0.0865813
$801$	16.9930	0.600417
$802$	10.5478	0.372457
$803$	4.95939	0.175013
$804$	6.94252	0.244844
$805$	4.95661	0.174698
$806$	7.07091	0.249062
$807$	23.6005	0.830777
$808$	7.44745	0.262000
$809$	−34.0922	−1.19862	−0.599309	−	0.800518i	$-0.704558\pi$
$809$	−34.0922	−1.19862	−0.599309	+	0.800518i	$0.704558\pi$
$810$	2.72927	0.0958966
$811$	−13.5287	−0.475056	−0.237528	−	0.971381i	$-0.576337\pi$
$811$	−13.5287	−0.475056	−0.237528	+	0.971381i	$0.576337\pi$
$812$	4.71794	0.165567
$813$	−7.54489	−0.264611
$814$	−10.3558	−0.362969
$815$	3.48973	0.122240
$816$	4.25138	0.148828
$817$	−53.2449	−1.86280
$818$	−23.1673	−0.810025
$819$	−2.42468	−0.0847250
$820$	−10.5911	−0.369858
$821$	17.4642	0.609506	0.304753	−	0.952431i	$-0.401426\pi$
$821$	17.4642	0.609506	0.304753	+	0.952431i	$0.401426\pi$
$822$	−11.8420	−0.413038
$823$	50.1561	1.74833	0.874165	−	0.485629i	$-0.161409\pi$
$823$	50.1561	1.74833	0.874165	+	0.485629i	$0.161409\pi$
$824$	−6.91858	−0.241020
$825$	−2.44889	−0.0852594
$826$	−2.64174	−0.0919180
$827$	28.8166	1.00205	0.501025	−	0.865433i	$-0.332956\pi$
$827$	28.8166	1.00205	0.501025	+	0.865433i	$0.332956\pi$
$828$	−2.69468	−0.0936465
$829$	−17.2738	−0.599946	−0.299973	−	0.953948i	$-0.596978\pi$
$829$	−17.2738	−0.599946	−0.299973	+	0.953948i	$0.596978\pi$
$830$	−0.427218	−0.0148290
$831$	20.2982	0.704136
$832$	3.59767	0.124727
$833$	−27.8286	−0.964204
$834$	18.4081	0.637421
$835$	37.6962	1.30453
$836$	−5.82526	−0.201471
$837$	1.96541	0.0679346
$838$	−35.4669	−1.22518
$839$	32.4044	1.11872	0.559362	−	0.828924i	$-0.311046\pi$
$839$	32.4044	1.11872	0.559362	+	0.828924i	$0.311046\pi$
$840$	−1.83941	−0.0634656
$841$	20.0050	0.689828
$842$	21.2987	0.734001
$843$	4.38450	0.151010
$844$	−22.5841	−0.777376
$845$	−0.154947	−0.00533035
$846$	−10.6370	−0.365706
$847$	−0.673957	−0.0231575
$848$	−3.56328	−0.122363
$849$	10.5547	0.362235
$850$	10.4112	0.357100
$851$	−27.9055	−0.956587
$852$	0.365213	0.0125120
$853$	38.8126	1.32892	0.664458	−	0.747325i	$-0.268662\pi$
$853$	38.8126	1.32892	0.664458	+	0.747325i	$0.268662\pi$
$854$	−0.673957	−0.0230623
$855$	15.8987	0.543724
$856$	4.35224	0.148757
$857$	−8.39669	−0.286825	−0.143413	−	0.989663i	$-0.545808\pi$
$857$	−8.39669	−0.286825	−0.143413	+	0.989663i	$0.545808\pi$
$858$	−3.59767	−0.122822
$859$	−21.0504	−0.718231	−0.359115	−	0.933293i	$-0.616922\pi$
$859$	−21.0504	−0.718231	−0.359115	+	0.933293i	$0.616922\pi$
$860$	−24.9464	−0.850666
$861$	2.61534	0.0891306
$862$	−3.83729	−0.130699
$863$	10.7011	0.364270	0.182135	−	0.983273i	$-0.441699\pi$
$863$	10.7011	0.364270	0.182135	+	0.983273i	$0.441699\pi$
$864$	1.00000	0.0340207
$865$	18.1023	0.615498
$866$	−18.4484	−0.626904
$867$	1.07423	0.0364829
$868$	−1.32460	−0.0449600
$869$	2.75204	0.0933566
$870$	−19.1058	−0.647748
$871$	24.9769	0.846310
$872$	18.7692	0.635604
$873$	−11.2082	−0.379340
$874$	−15.6972	−0.530966
$875$	4.69254	0.158637
$876$	−4.95939	−0.167562
$877$	−29.0313	−0.980317	−0.490159	−	0.871633i	$-0.663061\pi$
$877$	−29.0313	−0.980317	−0.490159	+	0.871633i	$0.663061\pi$
$878$	−17.1275	−0.578024
$879$	−31.7323	−1.07030
$880$	−2.72927	−0.0920035
$881$	−26.9938	−0.909445	−0.454723	−	0.890633i	$-0.650262\pi$
$881$	−26.9938	−0.909445	−0.454723	+	0.890633i	$0.650262\pi$
$882$	−6.54578	−0.220408
$883$	−3.19215	−0.107425	−0.0537123	−	0.998556i	$-0.517105\pi$
$883$	−3.19215	−0.107425	−0.0537123	+	0.998556i	$0.517105\pi$
$884$	15.2951	0.514429
$885$	10.6980	0.359610
$886$	−5.95809	−0.200166
$887$	−20.1739	−0.677374	−0.338687	−	0.940899i	$-0.609983\pi$
$887$	−20.1739	−0.677374	−0.338687	+	0.940899i	$0.609983\pi$
$888$	10.3558	0.347517
$889$	1.88383	0.0631817
$890$	46.3783	1.55461
$891$	−1.00000	−0.0335013
$892$	−0.596137	−0.0199601
$893$	−61.9631	−2.07351
$894$	11.4006	0.381294
$895$	−37.6561	−1.25871
$896$	−0.673957	−0.0225153
$897$	−9.69456	−0.323692
$898$	−15.5422	−0.518649
$899$	−13.7586	−0.458875
$900$	2.44889	0.0816296
$901$	−15.1489	−0.504681
$902$	3.88057	0.129209
$903$	6.16020	0.204999
$904$	−3.45468	−0.114901
$905$	−28.1564	−0.935952
$906$	−4.24190	−0.140928
$907$	−25.4686	−0.845670	−0.422835	−	0.906207i	$-0.638965\pi$
$907$	−25.4686	−0.845670	−0.422835	+	0.906207i	$0.638965\pi$
$908$	−25.8235	−0.856983
$909$	7.44745	0.247016
$910$	−6.61759	−0.219371
$911$	−44.0589	−1.45974	−0.729868	−	0.683589i	$-0.760418\pi$
$911$	−44.0589	−1.45974	−0.729868	+	0.683589i	$0.760418\pi$
$912$	5.82526	0.192894
$913$	0.156532	0.00518046
$914$	7.16430	0.236974
$915$	2.72927	0.0902267
$916$	−24.1601	−0.798271
$917$	−1.05313	−0.0347775
$918$	4.25138	0.140316
$919$	−34.8564	−1.14981	−0.574903	−	0.818221i	$-0.694960\pi$
$919$	−34.8564	−1.14981	−0.574903	+	0.818221i	$0.694960\pi$
$920$	−7.35449	−0.242470
$921$	−0.998640	−0.0329063
$922$	−19.2505	−0.633980
$923$	1.31391	0.0432480
$924$	0.673957	0.0221716
$925$	25.3601	0.833836
$926$	24.3868	0.801399
$927$	−6.91858	−0.227236
$928$	−7.00036	−0.229798
$929$	24.6179	0.807687	0.403843	−	0.914828i	$-0.367674\pi$
$929$	24.6179	0.807687	0.403843	+	0.914828i	$0.367674\pi$
$930$	5.36413	0.175897
$931$	−38.1309	−1.24969
$932$	4.62550	0.151513
$933$	3.92585	0.128526
$934$	9.41440	0.308049
$935$	−11.6031	−0.379463
$936$	3.59767	0.117594
$937$	24.8911	0.813157	0.406579	−	0.913616i	$-0.366722\pi$
$937$	24.8911	0.813157	0.406579	+	0.913616i	$0.366722\pi$
$938$	−4.67896	−0.152774
$939$	−20.3307	−0.663466
$940$	−29.0311	−0.946889
$941$	13.5673	0.442282	0.221141	−	0.975242i	$-0.429022\pi$
$941$	13.5673	0.442282	0.221141	+	0.975242i	$0.429022\pi$
$942$	21.8267	0.711153
$943$	10.4569	0.340523
$944$	3.91975	0.127577
$945$	−1.83941	−0.0598360
$946$	9.14034	0.297178
$947$	−37.8393	−1.22961	−0.614806	−	0.788678i	$-0.710766\pi$
$947$	−37.8393	−1.22961	−0.614806	+	0.788678i	$0.710766\pi$
$948$	−2.75204	−0.0893822
$949$	−17.8422	−0.579184
$950$	14.2654	0.462832
$951$	−19.7540	−0.640566
$952$	−2.86525	−0.0928633
$953$	−10.1723	−0.329514	−0.164757	−	0.986334i	$-0.552684\pi$
$953$	−10.1723	−0.329514	−0.164757	+	0.986334i	$0.552684\pi$
$954$	−3.56328	−0.115365
$955$	−10.0139	−0.324043
$956$	−24.4212	−0.789837
$957$	7.00036	0.226289
$958$	−21.7380	−0.702324
$959$	7.98103	0.257721
$960$	2.72927	0.0880867
$961$	−27.1372	−0.875392
$962$	37.2566	1.20120
$963$	4.35224	0.140249
$964$	12.0073	0.386729
$965$	21.7287	0.699473
$966$	1.81610	0.0584320
$967$	−19.8780	−0.639232	−0.319616	−	0.947547i	$-0.603554\pi$
$967$	−19.8780	−0.639232	−0.319616	+	0.947547i	$0.603554\pi$
$968$	1.00000	0.0321412
$969$	24.7654	0.795580
$970$	−30.5902	−0.982191
$971$	33.2038	1.06556	0.532780	−	0.846254i	$-0.321147\pi$
$971$	33.2038	1.06556	0.532780	+	0.846254i	$0.321147\pi$
$972$	1.00000	0.0320750
$973$	−12.4063	−0.397727
$974$	17.5946	0.563768
$975$	8.81030	0.282155
$976$	1.00000	0.0320092
$977$	−32.6561	−1.04476	−0.522381	−	0.852712i	$-0.674956\pi$
$977$	−32.6561	−1.04476	−0.522381	+	0.852712i	$0.674956\pi$
$978$	1.27864	0.0408862
$979$	−16.9930	−0.543098
$980$	−17.8652	−0.570682
$981$	18.7692	0.599253
$982$	39.4366	1.25847
$983$	30.3201	0.967060	0.483530	−	0.875328i	$-0.339354\pi$
$983$	30.3201	0.967060	0.483530	+	0.875328i	$0.339354\pi$
$984$	−3.88057	−0.123708
$985$	−9.84202	−0.313593
$986$	−29.7612	−0.947789
$987$	7.16885	0.228187
$988$	20.9574	0.666743
$989$	24.6303	0.783197
$990$	−2.72927	−0.0867417
$991$	−13.7111	−0.435547	−0.217773	−	0.975999i	$-0.569879\pi$
$991$	−13.7111	−0.435547	−0.217773	+	0.975999i	$0.569879\pi$
$992$	1.96541	0.0624019
$993$	−4.11510	−0.130589
$994$	−0.246138	−0.00780702
$995$	−45.3837	−1.43876
$996$	−0.156532	−0.00495991
$997$	−30.2370	−0.957615	−0.478807	−	0.877920i	$-0.658931\pi$
$997$	−30.2370	−0.957615	−0.478807	+	0.877920i	$0.658931\pi$
$998$	29.9798	0.948995
$999$	10.3558	0.327642

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4026.2.a.bb.1.6	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4026.2.a.bb.1.6	✓	8	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +2.72927 q^{5} +1.00000 q^{6} -0.673957 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +2.72927 q^{5} +1.00000 q^{6} -0.673957 q^{7} +1.00000 q^{8} +1.00000 q^{9} +2.72927 q^{10} -1.00000 q^{11} +1.00000 q^{12} +3.59767 q^{13} -0.673957 q^{14} +2.72927 q^{15} +1.00000 q^{16} +4.25138 q^{17} +1.00000 q^{18} +5.82526 q^{19} +2.72927 q^{20} -0.673957 q^{21} -1.00000 q^{22} -2.69468 q^{23} +1.00000 q^{24} +2.44889 q^{25} +3.59767 q^{26} +1.00000 q^{27} -0.673957 q^{28} -7.00036 q^{29} +2.72927 q^{30} +1.96541 q^{31} +1.00000 q^{32} -1.00000 q^{33} +4.25138 q^{34} -1.83941 q^{35} +1.00000 q^{36} +10.3558 q^{37} +5.82526 q^{38} +3.59767 q^{39} +2.72927 q^{40} -3.88057 q^{41} -0.673957 q^{42} -9.14034 q^{43} -1.00000 q^{44} +2.72927 q^{45} -2.69468 q^{46} -10.6370 q^{47} +1.00000 q^{48} -6.54578 q^{49} +2.44889 q^{50} +4.25138 q^{51} +3.59767 q^{52} -3.56328 q^{53} +1.00000 q^{54} -2.72927 q^{55} -0.673957 q^{56} +5.82526 q^{57} -7.00036 q^{58} +3.91975 q^{59} +2.72927 q^{60} +1.00000 q^{61} +1.96541 q^{62} -0.673957 q^{63} +1.00000 q^{64} +9.81900 q^{65} -1.00000 q^{66} +6.94252 q^{67} +4.25138 q^{68} -2.69468 q^{69} -1.83941 q^{70} +0.365213 q^{71} +1.00000 q^{72} -4.95939 q^{73} +10.3558 q^{74} +2.44889 q^{75} +5.82526 q^{76} +0.673957 q^{77} +3.59767 q^{78} -2.75204 q^{79} +2.72927 q^{80} +1.00000 q^{81} -3.88057 q^{82} -0.156532 q^{83} -0.673957 q^{84} +11.6031 q^{85} -9.14034 q^{86} -7.00036 q^{87} -1.00000 q^{88} +16.9930 q^{89} +2.72927 q^{90} -2.42468 q^{91} -2.69468 q^{92} +1.96541 q^{93} -10.6370 q^{94} +15.8987 q^{95} +1.00000 q^{96} -11.2082 q^{97} -6.54578 q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{2} + 8 q^{3} + 8 q^{4} + 5 q^{5} + 8 q^{6} + 13 q^{7} + 8 q^{8} + 8 q^{9}+O(q^{10}) \) 8 * q + 8 * q^2 + 8 * q^3 + 8 * q^4 + 5 * q^5 + 8 * q^6 + 13 * q^7 + 8 * q^8 + 8 * q^9	\( 8 q + 8 q^{2} + 8 q^{3} + 8 q^{4} + 5 q^{5} + 8 q^{6} + 13 q^{7} + 8 q^{8} + 8 q^{9} + 5 q^{10} - 8 q^{11} + 8 q^{12} + 10 q^{13} + 13 q^{14} + 5 q^{15} + 8 q^{16} + 4 q^{17} + 8 q^{18} + 11 q^{19} + 5 q^{20} + 13 q^{21} - 8 q^{22} + 2 q^{23} + 8 q^{24} + 23 q^{25} + 10 q^{26} + 8 q^{27} + 13 q^{28} + 10 q^{29} + 5 q^{30} + 9 q^{31} + 8 q^{32} - 8 q^{33} + 4 q^{34} - 3 q^{35} + 8 q^{36} + 9 q^{37} + 11 q^{38} + 10 q^{39} + 5 q^{40} + 3 q^{41} + 13 q^{42} + 16 q^{43} - 8 q^{44} + 5 q^{45} + 2 q^{46} - 16 q^{47} + 8 q^{48} + 17 q^{49} + 23 q^{50} + 4 q^{51} + 10 q^{52} + 7 q^{53} + 8 q^{54} - 5 q^{55} + 13 q^{56} + 11 q^{57} + 10 q^{58} - 14 q^{59} + 5 q^{60} + 8 q^{61} + 9 q^{62} + 13 q^{63} + 8 q^{64} + 22 q^{65} - 8 q^{66} + 8 q^{67} + 4 q^{68} + 2 q^{69} - 3 q^{70} + 11 q^{71} + 8 q^{72} + 14 q^{73} + 9 q^{74} + 23 q^{75} + 11 q^{76} - 13 q^{77} + 10 q^{78} + 22 q^{79} + 5 q^{80} + 8 q^{81} + 3 q^{82} - 16 q^{83} + 13 q^{84} + 3 q^{85} + 16 q^{86} + 10 q^{87} - 8 q^{88} + q^{89} + 5 q^{90} + 15 q^{91} + 2 q^{92} + 9 q^{93} - 16 q^{94} - 9 q^{95} + 8 q^{96} + 24 q^{97} + 17 q^{98} - 8 q^{99}+O(q^{100}) \) 8 * q + 8 * q^2 + 8 * q^3 + 8 * q^4 + 5 * q^5 + 8 * q^6 + 13 * q^7 + 8 * q^8 + 8 * q^9 + 5 * q^10 - 8 * q^11 + 8 * q^12 + 10 * q^13 + 13 * q^14 + 5 * q^15 + 8 * q^16 + 4 * q^17 + 8 * q^18 + 11 * q^19 + 5 * q^20 + 13 * q^21 - 8 * q^22 + 2 * q^23 + 8 * q^24 + 23 * q^25 + 10 * q^26 + 8 * q^27 + 13 * q^28 + 10 * q^29 + 5 * q^30 + 9 * q^31 + 8 * q^32 - 8 * q^33 + 4 * q^34 - 3 * q^35 + 8 * q^36 + 9 * q^37 + 11 * q^38 + 10 * q^39 + 5 * q^40 + 3 * q^41 + 13 * q^42 + 16 * q^43 - 8 * q^44 + 5 * q^45 + 2 * q^46 - 16 * q^47 + 8 * q^48 + 17 * q^49 + 23 * q^50 + 4 * q^51 + 10 * q^52 + 7 * q^53 + 8 * q^54 - 5 * q^55 + 13 * q^56 + 11 * q^57 + 10 * q^58 - 14 * q^59 + 5 * q^60 + 8 * q^61 + 9 * q^62 + 13 * q^63 + 8 * q^64 + 22 * q^65 - 8 * q^66 + 8 * q^67 + 4 * q^68 + 2 * q^69 - 3 * q^70 + 11 * q^71 + 8 * q^72 + 14 * q^73 + 9 * q^74 + 23 * q^75 + 11 * q^76 - 13 * q^77 + 10 * q^78 + 22 * q^79 + 5 * q^80 + 8 * q^81 + 3 * q^82 - 16 * q^83 + 13 * q^84 + 3 * q^85 + 16 * q^86 + 10 * q^87 - 8 * q^88 + q^89 + 5 * q^90 + 15 * q^91 + 2 * q^92 + 9 * q^93 - 16 * q^94 - 9 * q^95 + 8 * q^96 + 24 * q^97 + 17 * q^98 - 8 * q^99

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