LMFDB - Embedded newform 4029.2.a.g.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4029,2,Mod(1,4029)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4029, 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("4029.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4029 = 3 \cdot 17 \cdot 79 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4029.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:	$32.1717269744$
Analytic rank:	$1$
Dimension:	$22$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Character	$\chi$	$=$	4029.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.32697 q^{2} -1.00000 q^{3} -0.239163 q^{4} -0.116261 q^{5} +1.32697 q^{6} +0.614865 q^{7} +2.97129 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.32697 q^{2} -1.00000 q^{3} -0.239163 q^{4} -0.116261 q^{5} +1.32697 q^{6} +0.614865 q^{7} +2.97129 q^{8} +1.00000 q^{9} +0.154274 q^{10} +3.02336 q^{11} +0.239163 q^{12} -2.02543 q^{13} -0.815905 q^{14} +0.116261 q^{15} -3.46447 q^{16} -1.00000 q^{17} -1.32697 q^{18} +5.38000 q^{19} +0.0278053 q^{20} -0.614865 q^{21} -4.01190 q^{22} -2.04160 q^{23} -2.97129 q^{24} -4.98648 q^{25} +2.68767 q^{26} -1.00000 q^{27} -0.147053 q^{28} -4.05053 q^{29} -0.154274 q^{30} -5.32172 q^{31} -1.34535 q^{32} -3.02336 q^{33} +1.32697 q^{34} -0.0714847 q^{35} -0.239163 q^{36} +9.56880 q^{37} -7.13907 q^{38} +2.02543 q^{39} -0.345445 q^{40} -4.42595 q^{41} +0.815905 q^{42} +7.89454 q^{43} -0.723077 q^{44} -0.116261 q^{45} +2.70913 q^{46} -7.42983 q^{47} +3.46447 q^{48} -6.62194 q^{49} +6.61689 q^{50} +1.00000 q^{51} +0.484408 q^{52} -2.50456 q^{53} +1.32697 q^{54} -0.351499 q^{55} +1.82694 q^{56} -5.38000 q^{57} +5.37491 q^{58} -1.56807 q^{59} -0.0278053 q^{60} -1.24120 q^{61} +7.06174 q^{62} +0.614865 q^{63} +8.71418 q^{64} +0.235478 q^{65} +4.01190 q^{66} -10.5018 q^{67} +0.239163 q^{68} +2.04160 q^{69} +0.0948577 q^{70} +16.5916 q^{71} +2.97129 q^{72} -3.06638 q^{73} -12.6975 q^{74} +4.98648 q^{75} -1.28670 q^{76} +1.85896 q^{77} -2.68767 q^{78} -1.00000 q^{79} +0.402783 q^{80} +1.00000 q^{81} +5.87308 q^{82} +9.42124 q^{83} +0.147053 q^{84} +0.116261 q^{85} -10.4758 q^{86} +4.05053 q^{87} +8.98330 q^{88} -0.0471276 q^{89} +0.154274 q^{90} -1.24537 q^{91} +0.488275 q^{92} +5.32172 q^{93} +9.85913 q^{94} -0.625482 q^{95} +1.34535 q^{96} -4.81385 q^{97} +8.78709 q^{98} +3.02336 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q + 2 q^{2} - 22 q^{3} + 16 q^{4} + 5 q^{5} - 2 q^{6} - 4 q^{7} + 6 q^{8} + 22 q^{9}+O(q^{10}) $ 22 * q + 2 * q^2 - 22 * q^3 + 16 * q^4 + 5 * q^5 - 2 * q^6 - 4 * q^7 + 6 * q^8 + 22 * q^9	\( 22 q + 2 q^{2} - 22 q^{3} + 16 q^{4} + 5 q^{5} - 2 q^{6} - 4 q^{7} + 6 q^{8} + 22 q^{9} - 5 q^{10} - 2 q^{11} - 16 q^{12} - 11 q^{13} - 7 q^{14} - 5 q^{15} - 22 q^{17} + 2 q^{18} - 36 q^{19} + 4 q^{21} - 9 q^{22} + 21 q^{23} - 6 q^{24} + 9 q^{25} - 16 q^{26} - 22 q^{27} - 17 q^{28} - q^{29} + 5 q^{30} - 12 q^{31} - 11 q^{32} + 2 q^{33} - 2 q^{34} - 14 q^{35} + 16 q^{36} - 6 q^{37} + q^{38} + 11 q^{39} - 24 q^{40} - 17 q^{41} + 7 q^{42} - 36 q^{43} + 16 q^{44} + 5 q^{45} - 23 q^{46} - 17 q^{47} - 6 q^{49} - 33 q^{50} + 22 q^{51} - 57 q^{52} - 2 q^{53} - 2 q^{54} - 24 q^{55} - 64 q^{56} + 36 q^{57} - 7 q^{58} - 59 q^{59} - 30 q^{61} - 4 q^{62} - 4 q^{63} - 22 q^{64} + 36 q^{65} + 9 q^{66} - 16 q^{67} - 16 q^{68} - 21 q^{69} - 39 q^{70} - 11 q^{71} + 6 q^{72} - 19 q^{73} - 28 q^{74} - 9 q^{75} - 77 q^{76} + 2 q^{77} + 16 q^{78} - 22 q^{79} - 2 q^{80} + 22 q^{81} + 33 q^{82} - 23 q^{83} + 17 q^{84} - 5 q^{85} + 6 q^{86} + q^{87} - 23 q^{88} + 12 q^{89} - 5 q^{90} - 24 q^{91} + 66 q^{92} + 12 q^{93} - 61 q^{94} - 11 q^{95} + 11 q^{96} - 9 q^{97} + 17 q^{98} - 2 q^{99}+O(q^{100}) \) 22 * q + 2 * q^2 - 22 * q^3 + 16 * q^4 + 5 * q^5 - 2 * q^6 - 4 * q^7 + 6 * q^8 + 22 * q^9 - 5 * q^10 - 2 * q^11 - 16 * q^12 - 11 * q^13 - 7 * q^14 - 5 * q^15 - 22 * q^17 + 2 * q^18 - 36 * q^19 + 4 * q^21 - 9 * q^22 + 21 * q^23 - 6 * q^24 + 9 * q^25 - 16 * q^26 - 22 * q^27 - 17 * q^28 - q^29 + 5 * q^30 - 12 * q^31 - 11 * q^32 + 2 * q^33 - 2 * q^34 - 14 * q^35 + 16 * q^36 - 6 * q^37 + q^38 + 11 * q^39 - 24 * q^40 - 17 * q^41 + 7 * q^42 - 36 * q^43 + 16 * q^44 + 5 * q^45 - 23 * q^46 - 17 * q^47 - 6 * q^49 - 33 * q^50 + 22 * q^51 - 57 * q^52 - 2 * q^53 - 2 * q^54 - 24 * q^55 - 64 * q^56 + 36 * q^57 - 7 * q^58 - 59 * q^59 - 30 * q^61 - 4 * q^62 - 4 * q^63 - 22 * q^64 + 36 * q^65 + 9 * q^66 - 16 * q^67 - 16 * q^68 - 21 * q^69 - 39 * q^70 - 11 * q^71 + 6 * q^72 - 19 * q^73 - 28 * q^74 - 9 * q^75 - 77 * q^76 + 2 * q^77 + 16 * q^78 - 22 * q^79 - 2 * q^80 + 22 * q^81 + 33 * q^82 - 23 * q^83 + 17 * q^84 - 5 * q^85 + 6 * q^86 + q^87 - 23 * q^88 + 12 * q^89 - 5 * q^90 - 24 * q^91 + 66 * q^92 + 12 * q^93 - 61 * q^94 - 11 * q^95 + 11 * q^96 - 9 * q^97 + 17 * q^98 - 2 * 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 $

$2$	−1.32697	−0.938306	−0.469153	−	0.883117i	$-0.655441\pi$
$2$	−1.32697	−0.938306	−0.469153	+	0.883117i	$0.655441\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−0.239163	−0.119582
$5$	−0.116261	−0.0519934	−0.0259967	−	0.999662i	$-0.508276\pi$
$5$	−0.116261	−0.0519934	−0.0259967	+	0.999662i	$0.508276\pi$
$6$	1.32697	0.541731
$7$	0.614865	0.232397	0.116199	−	0.993226i	$-0.462929\pi$
$7$	0.614865	0.232397	0.116199	+	0.993226i	$0.462929\pi$
$8$	2.97129	1.05051
$9$	1.00000	0.333333
$10$	0.154274	0.0487857
$11$	3.02336	0.911579	0.455789	−	0.890088i	$-0.349357\pi$
$11$	3.02336	0.911579	0.455789	+	0.890088i	$0.349357\pi$
$12$	0.239163	0.0690404
$13$	−2.02543	−0.561753	−0.280876	−	0.959744i	$-0.590625\pi$
$13$	−2.02543	−0.561753	−0.280876	+	0.959744i	$0.590625\pi$
$14$	−0.815905	−0.218060
$15$	0.116261	0.0300184
$16$	−3.46447	−0.866119
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−1.32697	−0.312769
$19$	5.38000	1.23426	0.617128	−	0.786863i	$-0.288296\pi$
$19$	5.38000	1.23426	0.617128	+	0.786863i	$0.288296\pi$
$20$	0.0278053	0.00621745
$21$	−0.614865	−0.134175
$22$	−4.01190	−0.855340
$23$	−2.04160	−0.425703	−0.212851	−	0.977085i	$-0.568275\pi$
$23$	−2.04160	−0.425703	−0.212851	+	0.977085i	$0.568275\pi$
$24$	−2.97129	−0.606512
$25$	−4.98648	−0.997297
$26$	2.68767	0.527096
$27$	−1.00000	−0.192450
$28$	−0.147053	−0.0277904
$29$	−4.05053	−0.752164	−0.376082	−	0.926586i	$-0.622729\pi$
$29$	−4.05053	−0.752164	−0.376082	+	0.926586i	$0.622729\pi$
$30$	−0.154274	−0.0281665
$31$	−5.32172	−0.955809	−0.477904	−	0.878412i	$-0.658603\pi$
$31$	−5.32172	−0.955809	−0.477904	+	0.878412i	$0.658603\pi$
$32$	−1.34535	−0.237826
$33$	−3.02336	−0.526300
$34$	1.32697	0.227573
$35$	−0.0714847	−0.0120831
$36$	−0.239163	−0.0398605
$37$	9.56880	1.57310	0.786551	−	0.617526i	$-0.211865\pi$
$37$	9.56880	1.57310	0.786551	+	0.617526i	$0.211865\pi$
$38$	−7.13907	−1.15811
$39$	2.02543	0.324328
$40$	−0.345445	−0.0546196
$41$	−4.42595	−0.691217	−0.345609	−	0.938379i	$-0.612328\pi$
$41$	−4.42595	−0.691217	−0.345609	+	0.938379i	$0.612328\pi$
$42$	0.815905	0.125897
$43$	7.89454	1.20391	0.601953	−	0.798531i	$-0.294389\pi$
$43$	7.89454	1.20391	0.601953	+	0.798531i	$0.294389\pi$
$44$	−0.723077	−0.109008
$45$	−0.116261	−0.0173311
$46$	2.70913	0.399440
$47$	−7.42983	−1.08375	−0.541876	−	0.840458i	$-0.682286\pi$
$47$	−7.42983	−1.08375	−0.541876	+	0.840458i	$0.682286\pi$
$48$	3.46447	0.500054
$49$	−6.62194	−0.945992
$50$	6.61689	0.935770
$51$	1.00000	0.140028
$52$	0.484408	0.0671753
$53$	−2.50456	−0.344028	−0.172014	−	0.985094i	$-0.555027\pi$
$53$	−2.50456	−0.344028	−0.172014	+	0.985094i	$0.555027\pi$
$54$	1.32697	0.180577
$55$	−0.351499	−0.0473961
$56$	1.82694	0.244136
$57$	−5.38000	−0.712598
$58$	5.37491	0.705760
$59$	−1.56807	−0.204146	−0.102073	−	0.994777i	$-0.532548\pi$
$59$	−1.56807	−0.204146	−0.102073	+	0.994777i	$0.532548\pi$
$60$	−0.0278053	−0.00358965
$61$	−1.24120	−0.158920	−0.0794598	−	0.996838i	$-0.525320\pi$
$61$	−1.24120	−0.158920	−0.0794598	+	0.996838i	$0.525320\pi$
$62$	7.06174	0.896841
$63$	0.614865	0.0774657
$64$	8.71418	1.08927
$65$	0.235478	0.0292074
$66$	4.01190	0.493831
$67$	−10.5018	−1.28300	−0.641499	−	0.767124i	$-0.721687\pi$
$67$	−10.5018	−1.28300	−0.641499	+	0.767124i	$0.721687\pi$
$68$	0.239163	0.0290028
$69$	2.04160	0.245780
$70$	0.0948577	0.0113377
$71$	16.5916	1.96907	0.984533	−	0.175201i	$-0.0560575\pi$
$71$	16.5916	1.96907	0.984533	+	0.175201i	$0.0560575\pi$
$72$	2.97129	0.350170
$73$	−3.06638	−0.358892	−0.179446	−	0.983768i	$-0.557431\pi$
$73$	−3.06638	−0.358892	−0.179446	+	0.983768i	$0.557431\pi$
$74$	−12.6975	−1.47605
$75$	4.98648	0.575790
$76$	−1.28670	−0.147594
$77$	1.85896	0.211848
$78$	−2.68767	−0.304319
$79$	−1.00000	−0.112509
$79$	−1.00000	−0.112509
$80$	0.402783	0.0450325
$81$	1.00000	0.111111
$82$	5.87308	0.648574
$83$	9.42124	1.03412	0.517058	−	0.855950i	$-0.327027\pi$
$83$	9.42124	1.03412	0.517058	+	0.855950i	$0.327027\pi$
$84$	0.147053	0.0160448
$85$	0.116261	0.0126103
$86$	−10.4758	−1.12963
$87$	4.05053	0.434262
$88$	8.98330	0.957623
$89$	−0.0471276	−0.00499551	−0.00249776	−	0.999997i	$-0.500795\pi$
$89$	−0.0471276	−0.00499551	−0.00249776	+	0.999997i	$0.500795\pi$
$90$	0.154274	0.0162619
$91$	−1.24537	−0.130550
$92$	0.488275	0.0509062
$93$	5.32172	0.551837
$94$	9.85913	1.01689
$95$	−0.625482	−0.0641731
$96$	1.34535	0.137309
$97$	−4.81385	−0.488772	−0.244386	−	0.969678i	$-0.578586\pi$
$97$	−4.81385	−0.488772	−0.244386	+	0.969678i	$0.578586\pi$
$98$	8.78709	0.887630
$99$	3.02336	0.303860
$100$	1.19258	0.119258
$101$	11.8301	1.17714	0.588569	−	0.808447i	$-0.299691\pi$
$101$	11.8301	1.17714	0.588569	+	0.808447i	$0.299691\pi$
$102$	−1.32697	−0.131389
$103$	7.73322	0.761977	0.380988	−	0.924580i	$-0.375584\pi$
$103$	7.73322	0.761977	0.380988	+	0.924580i	$0.375584\pi$
$104$	−6.01814	−0.590127
$105$	0.0714847	0.00697619
$106$	3.32347	0.322804
$107$	7.20506	0.696539	0.348269	−	0.937394i	$-0.386769\pi$
$107$	7.20506	0.696539	0.348269	+	0.937394i	$0.386769\pi$
$108$	0.239163	0.0230135
$109$	−11.1522	−1.06818	−0.534092	−	0.845426i	$-0.679347\pi$
$109$	−11.1522	−1.06818	−0.534092	+	0.845426i	$0.679347\pi$
$110$	0.466427	0.0444720
$111$	−9.56880	−0.908230
$112$	−2.13019	−0.201284
$113$	−7.15446	−0.673035	−0.336517	−	0.941677i	$-0.609249\pi$
$113$	−7.15446	−0.673035	−0.336517	+	0.941677i	$0.609249\pi$
$114$	7.13907	0.668635
$115$	0.237358	0.0221337
$116$	0.968737	0.0899449
$117$	−2.02543	−0.187251
$118$	2.08078	0.191551
$119$	−0.614865	−0.0563646
$120$	0.345445	0.0315346
$121$	−1.85927	−0.169025
$122$	1.64703	0.149115
$123$	4.42595	0.399075
$124$	1.27276	0.114297
$125$	1.16104	0.103846
$126$	−0.815905	−0.0726866
$127$	−4.36688	−0.387498	−0.193749	−	0.981051i	$-0.562065\pi$
$127$	−4.36688	−0.387498	−0.193749	+	0.981051i	$0.562065\pi$
$128$	−8.87272	−0.784245
$129$	−7.89454	−0.695076
$130$	−0.312471	−0.0274055
$131$	−6.57575	−0.574526	−0.287263	−	0.957852i	$-0.592745\pi$
$131$	−6.57575	−0.574526	−0.287263	+	0.957852i	$0.592745\pi$
$132$	0.723077	0.0629358
$133$	3.30797	0.286838
$134$	13.9355	1.20384
$135$	0.116261	0.0100061
$136$	−2.97129	−0.254786
$137$	5.33173	0.455521	0.227760	−	0.973717i	$-0.426860\pi$
$137$	5.33173	0.455521	0.227760	+	0.973717i	$0.426860\pi$
$138$	−2.70913	−0.230617
$139$	−16.7511	−1.42081	−0.710406	−	0.703792i	$-0.751488\pi$
$139$	−16.7511	−1.42081	−0.710406	+	0.703792i	$0.751488\pi$
$140$	0.0170965	0.00144492
$141$	7.42983	0.625705
$142$	−22.0165	−1.84759
$143$	−6.12361	−0.512082
$144$	−3.46447	−0.288706
$145$	0.470918	0.0391076
$146$	4.06898	0.336751
$147$	6.62194	0.546168
$148$	−2.28850	−0.188114
$149$	20.7911	1.70328	0.851638	−	0.524130i	$-0.175609\pi$
$149$	20.7911	1.70328	0.851638	+	0.524130i	$0.175609\pi$
$150$	−6.61689	−0.540267
$151$	−13.8576	−1.12771	−0.563857	−	0.825872i	$-0.690683\pi$
$151$	−13.8576	−1.12771	−0.563857	+	0.825872i	$0.690683\pi$
$152$	15.9855	1.29660
$153$	−1.00000	−0.0808452
$154$	−2.46678	−0.198779
$155$	0.618707	0.0496958
$156$	−0.484408	−0.0387837
$157$	3.86928	0.308802	0.154401	−	0.988008i	$-0.450655\pi$
$157$	3.86928	0.308802	0.154401	+	0.988008i	$0.450655\pi$
$158$	1.32697	0.105568
$159$	2.50456	0.198625
$160$	0.156411	0.0123654
$161$	−1.25531	−0.0989322
$162$	−1.32697	−0.104256
$163$	13.4352	1.05233	0.526163	−	0.850384i	$-0.323630\pi$
$163$	13.4352	1.05233	0.526163	+	0.850384i	$0.323630\pi$
$164$	1.05852	0.0826568
$165$	0.351499	0.0273641
$166$	−12.5017	−0.970317
$167$	13.8094	1.06860	0.534301	−	0.845294i	$-0.320575\pi$
$167$	13.8094	1.06860	0.534301	+	0.845294i	$0.320575\pi$
$168$	−1.82694	−0.140952
$169$	−8.89764	−0.684434
$170$	−0.154274	−0.0118323
$171$	5.38000	0.411419
$172$	−1.88808	−0.143965
$173$	−12.8299	−0.975437	−0.487718	−	0.873001i	$-0.662171\pi$
$173$	−12.8299	−0.975437	−0.487718	+	0.873001i	$0.662171\pi$
$174$	−5.37491	−0.407471
$175$	−3.06602	−0.231769
$176$	−10.4744	−0.789535
$177$	1.56807	0.117864
$178$	0.0625367	0.00468732
$179$	20.1144	1.50342	0.751711	−	0.659492i	$-0.229229\pi$
$179$	20.1144	1.50342	0.751711	+	0.659492i	$0.229229\pi$
$180$	0.0278053	0.00207248
$181$	−20.8970	−1.55326	−0.776632	−	0.629954i	$-0.783074\pi$
$181$	−20.8970	−1.55326	−0.776632	+	0.629954i	$0.783074\pi$
$182$	1.65256	0.122496
$183$	1.24120	0.0917523
$184$	−6.06619	−0.447205
$185$	−1.11248	−0.0817909
$186$	−7.06174	−0.517792
$187$	−3.02336	−0.221090
$188$	1.77694	0.129597
$189$	−0.614865	−0.0447249
$190$	0.829994	0.0602141
$191$	−14.7186	−1.06500	−0.532499	−	0.846430i	$-0.678747\pi$
$191$	−14.7186	−1.06500	−0.532499	+	0.846430i	$0.678747\pi$
$192$	−8.71418	−0.628892
$193$	−0.0695823	−0.00500865	−0.00250432	−	0.999997i	$-0.500797\pi$
$193$	−0.0695823	−0.00500865	−0.00250432	+	0.999997i	$0.500797\pi$
$194$	6.38781	0.458618
$195$	−0.235478	−0.0168629
$196$	1.58372	0.113123
$197$	7.30690	0.520595	0.260298	−	0.965528i	$-0.416179\pi$
$197$	7.30690	0.520595	0.260298	+	0.965528i	$0.416179\pi$
$198$	−4.01190	−0.285113
$199$	−21.0021	−1.48880	−0.744399	−	0.667735i	$-0.767264\pi$
$199$	−21.0021	−1.48880	−0.744399	+	0.667735i	$0.767264\pi$
$200$	−14.8163	−1.04767
$201$	10.5018	0.740739
$202$	−15.6981	−1.10452
$203$	−2.49053	−0.174801
$204$	−0.239163	−0.0167448
$205$	0.514565	0.0359387
$206$	−10.2617	−0.714968
$207$	−2.04160	−0.141901
$208$	7.01705	0.486545
$209$	16.2657	1.12512
$210$	−0.0948577	−0.00654581
$211$	6.73000	0.463312	0.231656	−	0.972798i	$-0.425586\pi$
$211$	6.73000	0.463312	0.231656	+	0.972798i	$0.425586\pi$
$212$	0.598999	0.0411394
$213$	−16.5916	−1.13684
$214$	−9.56086	−0.653567
$215$	−0.917826	−0.0625952
$216$	−2.97129	−0.202171
$217$	−3.27214	−0.222127
$218$	14.7986	1.00228
$219$	3.06638	0.207207
$220$	0.0840655	0.00566769
$221$	2.02543	0.136245
$222$	12.6975	0.852198
$223$	10.0872	0.675490	0.337745	−	0.941238i	$-0.390336\pi$
$223$	10.0872	0.675490	0.337745	+	0.941238i	$0.390336\pi$
$224$	−0.827206	−0.0552700
$225$	−4.98648	−0.332432
$226$	9.49372	0.631513
$227$	−4.37018	−0.290059	−0.145030	−	0.989427i	$-0.546328\pi$
$227$	−4.37018	−0.290059	−0.145030	+	0.989427i	$0.546328\pi$
$228$	1.28670	0.0852135
$229$	−27.6443	−1.82679	−0.913394	−	0.407076i	$-0.866548\pi$
$229$	−27.6443	−1.82679	−0.913394	+	0.407076i	$0.866548\pi$
$230$	−0.314966	−0.0207682
$231$	−1.85896	−0.122311
$232$	−12.0353	−0.790156
$233$	17.7714	1.16425	0.582123	−	0.813101i	$-0.302222\pi$
$233$	17.7714	1.16425	0.582123	+	0.813101i	$0.302222\pi$
$234$	2.68767	0.175699
$235$	0.863798	0.0563480
$236$	0.375025	0.0244121
$237$	1.00000	0.0649570
$238$	0.815905	0.0528873
$239$	−10.3394	−0.668803	−0.334401	−	0.942431i	$-0.608534\pi$
$239$	−10.3394	−0.668803	−0.334401	+	0.942431i	$0.608534\pi$
$240$	−0.402783	−0.0259995
$241$	9.83101	0.633271	0.316636	−	0.948547i	$-0.397447\pi$
$241$	9.83101	0.633271	0.316636	+	0.948547i	$0.397447\pi$
$242$	2.46719	0.158597
$243$	−1.00000	−0.0641500
$244$	0.296850	0.0190038
$245$	0.769872	0.0491853
$246$	−5.87308	−0.374454
$247$	−10.8968	−0.693347
$248$	−15.8124	−1.00409
$249$	−9.42124	−0.597047
$250$	−1.54066	−0.0974396
$251$	−10.8721	−0.686238	−0.343119	−	0.939292i	$-0.611483\pi$
$251$	−10.8721	−0.686238	−0.343119	+	0.939292i	$0.611483\pi$
$252$	−0.147053	−0.00926347
$253$	−6.17250	−0.388062
$254$	5.79470	0.363592
$255$	−0.116261	−0.00728053
$256$	−5.65456	−0.353410
$257$	−14.3167	−0.893048	−0.446524	−	0.894772i	$-0.647338\pi$
$257$	−14.3167	−0.893048	−0.446524	+	0.894772i	$0.647338\pi$
$258$	10.4758	0.652194
$259$	5.88352	0.365584
$260$	−0.0563176	−0.00349267
$261$	−4.05053	−0.250721
$262$	8.72579	0.539081
$263$	−28.9465	−1.78492	−0.892460	−	0.451127i	$-0.851022\pi$
$263$	−28.9465	−1.78492	−0.892460	+	0.451127i	$0.851022\pi$
$264$	−8.98330	−0.552884
$265$	0.291183	0.0178872
$266$	−4.38956	−0.269141
$267$	0.0471276	0.00288416
$268$	2.51164	0.153423
$269$	0.935961	0.0570665	0.0285333	−	0.999593i	$-0.490916\pi$
$269$	0.935961	0.0570665	0.0285333	+	0.999593i	$0.490916\pi$
$270$	−0.154274	−0.00938882
$271$	−6.58129	−0.399785	−0.199892	−	0.979818i	$-0.564059\pi$
$271$	−6.58129	−0.399785	−0.199892	+	0.979818i	$0.564059\pi$
$272$	3.46447	0.210065
$273$	1.24537	0.0753730
$274$	−7.07503	−0.427418
$275$	−15.0760	−0.909114
$276$	−0.488275	−0.0293907
$277$	7.33594	0.440774	0.220387	−	0.975412i	$-0.429268\pi$
$277$	7.33594	0.440774	0.220387	+	0.975412i	$0.429268\pi$
$278$	22.2282	1.33316
$279$	−5.32172	−0.318603
$280$	−0.212402	−0.0126934
$281$	−22.4171	−1.33729	−0.668645	−	0.743581i	$-0.733126\pi$
$281$	−22.4171	−1.33729	−0.668645	+	0.743581i	$0.733126\pi$
$282$	−9.85913	−0.587102
$283$	−1.65344	−0.0982868	−0.0491434	−	0.998792i	$-0.515649\pi$
$283$	−1.65344	−0.0982868	−0.0491434	+	0.998792i	$0.515649\pi$
$284$	−3.96811	−0.235464
$285$	0.625482	0.0370504
$286$	8.12582	0.480490
$287$	−2.72136	−0.160637
$288$	−1.34535	−0.0792752
$289$	1.00000	0.0588235
$290$	−0.624891	−0.0366949
$291$	4.81385	0.282193
$292$	0.733364	0.0429169
$293$	−4.88078	−0.285138	−0.142569	−	0.989785i	$-0.545536\pi$
$293$	−4.88078	−0.285138	−0.142569	+	0.989785i	$0.545536\pi$
$294$	−8.78709	−0.512473
$295$	0.182306	0.0106142
$296$	28.4317	1.65256
$297$	−3.02336	−0.175433
$298$	−27.5891	−1.59820
$299$	4.13512	0.239140
$300$	−1.19258	−0.0688538
$301$	4.85408	0.279785
$302$	18.3885	1.05814
$303$	−11.8301	−0.679621
$304$	−18.6389	−1.06901
$305$	0.144303	0.00826277
$306$	1.32697	0.0758576
$307$	−12.1425	−0.693009	−0.346505	−	0.938048i	$-0.612632\pi$
$307$	−12.1425	−0.693009	−0.346505	+	0.938048i	$0.612632\pi$
$308$	−0.444595	−0.0253331
$309$	−7.73322	−0.439928
$310$	−0.821003	−0.0466298
$311$	−12.1116	−0.686787	−0.343394	−	0.939192i	$-0.611576\pi$
$311$	−12.1116	−0.686787	−0.343394	+	0.939192i	$0.611576\pi$
$312$	6.01814	0.340710
$313$	−32.7805	−1.85287	−0.926433	−	0.376460i	$-0.877141\pi$
$313$	−32.7805	−1.85287	−0.926433	+	0.376460i	$0.877141\pi$
$314$	−5.13440	−0.289751
$315$	−0.0714847	−0.00402771
$316$	0.239163	0.0134540
$317$	−11.9247	−0.669760	−0.334880	−	0.942261i	$-0.608696\pi$
$317$	−11.9247	−0.669760	−0.334880	+	0.942261i	$0.608696\pi$
$318$	−3.32347	−0.186371
$319$	−12.2462	−0.685657
$320$	−1.01312	−0.0566350
$321$	−7.20506	−0.402147
$322$	1.66575	0.0928287
$323$	−5.38000	−0.299351
$324$	−0.239163	−0.0132868
$325$	10.0998	0.560234
$326$	−17.8280	−0.987403
$327$	11.1522	0.616717
$328$	−13.1508	−0.726131
$329$	−4.56834	−0.251861
$330$	−0.466427	−0.0256759
$331$	0.168736	0.00927458	0.00463729	−	0.999989i	$-0.498524\pi$
$331$	0.168736	0.00927458	0.00463729	+	0.999989i	$0.498524\pi$
$332$	−2.25321	−0.123661
$333$	9.56880	0.524367
$334$	−18.3246	−1.00268
$335$	1.22095	0.0667074
$336$	2.13019	0.116211
$337$	3.28094	0.178724	0.0893621	−	0.995999i	$-0.471517\pi$
$337$	3.28094	0.178724	0.0893621	+	0.995999i	$0.471517\pi$
$338$	11.8069	0.642208
$339$	7.15446	0.388577
$340$	−0.0278053	−0.00150795
$341$	−16.0895	−0.871295
$342$	−7.13907	−0.386037
$343$	−8.37566	−0.452243
$344$	23.4570	1.26472
$345$	−0.237358	−0.0127789
$346$	17.0248	0.915258
$347$	−2.62645	−0.140995	−0.0704977	−	0.997512i	$-0.522459\pi$
$347$	−2.62645	−0.140995	−0.0704977	+	0.997512i	$0.522459\pi$
$348$	−0.968737	−0.0519297
$349$	4.50469	0.241131	0.120565	−	0.992705i	$-0.461529\pi$
$349$	4.50469	0.241131	0.120565	+	0.992705i	$0.461529\pi$
$350$	4.06850	0.217470
$351$	2.02543	0.108109
$352$	−4.06747	−0.216797
$353$	−11.9524	−0.636164	−0.318082	−	0.948063i	$-0.603039\pi$
$353$	−11.9524	−0.636164	−0.318082	+	0.948063i	$0.603039\pi$
$354$	−2.08078	−0.110592
$355$	−1.92896	−0.102378
$356$	0.0112712	0.000597371 0
$357$	0.614865	0.0325421
$358$	−26.6911	−1.41067
$359$	25.6191	1.35212	0.676061	−	0.736845i	$-0.263685\pi$
$359$	25.6191	1.35212	0.676061	+	0.736845i	$0.263685\pi$
$360$	−0.345445	−0.0182065
$361$	9.94435	0.523387
$362$	27.7296	1.45744
$363$	1.85927	0.0975864
$364$	0.297845	0.0156113
$365$	0.356500	0.0186600
$366$	−1.64703	−0.0860917
$367$	−0.729349	−0.0380717	−0.0190358	−	0.999819i	$-0.506060\pi$
$367$	−0.729349	−0.0380717	−0.0190358	+	0.999819i	$0.506060\pi$
$368$	7.07307	0.368709
$369$	−4.42595	−0.230406
$370$	1.47622	0.0767449
$371$	−1.53997	−0.0799512
$372$	−1.27276	−0.0659894
$373$	4.24154	0.219618	0.109809	−	0.993953i	$-0.464976\pi$
$373$	4.24154	0.219618	0.109809	+	0.993953i	$0.464976\pi$
$374$	4.01190	0.207450
$375$	−1.16104	−0.0599557
$376$	−22.0762	−1.13849
$377$	8.20406	0.422531
$378$	0.815905	0.0419656
$379$	−35.5402	−1.82558	−0.912790	−	0.408429i	$-0.866077\pi$
$379$	−35.5402	−1.82558	−0.912790	+	0.408429i	$0.866077\pi$
$380$	0.149592	0.00767392
$381$	4.36688	0.223722
$382$	19.5310	0.999295
$383$	2.02632	0.103540	0.0517700	−	0.998659i	$-0.483514\pi$
$383$	2.02632	0.103540	0.0517700	+	0.998659i	$0.483514\pi$
$384$	8.87272	0.452784
$385$	−0.216124	−0.0110147
$386$	0.0923334	0.00469964
$387$	7.89454	0.401302
$388$	1.15130	0.0584481
$389$	−3.41239	−0.173015	−0.0865075	−	0.996251i	$-0.527571\pi$
$389$	−3.41239	−0.173015	−0.0865075	+	0.996251i	$0.527571\pi$
$390$	0.312471	0.0158226
$391$	2.04160	0.103248
$392$	−19.6757	−0.993774
$393$	6.57575	0.331702
$394$	−9.69600	−0.488478
$395$	0.116261	0.00584972
$396$	−0.723077	−0.0363360
$397$	9.76003	0.489842	0.244921	−	0.969543i	$-0.421238\pi$
$397$	9.76003	0.489842	0.244921	+	0.969543i	$0.421238\pi$
$398$	27.8690	1.39695
$399$	−3.30797	−0.165606
$400$	17.2755	0.863777
$401$	14.4855	0.723369	0.361684	−	0.932301i	$-0.382202\pi$
$401$	14.4855	0.723369	0.361684	+	0.932301i	$0.382202\pi$
$402$	−13.9355	−0.695040
$403$	10.7788	0.536928
$404$	−2.82932	−0.140764
$405$	−0.116261	−0.00577705
$406$	3.30485	0.164017
$407$	28.9300	1.43401
$408$	2.97129	0.147101
$409$	−12.6085	−0.623448	−0.311724	−	0.950173i	$-0.600906\pi$
$409$	−12.6085	−0.623448	−0.311724	+	0.950173i	$0.600906\pi$
$410$	−0.682809	−0.0337215
$411$	−5.33173	−0.262995
$412$	−1.84950	−0.0911184
$413$	−0.964154	−0.0474429
$414$	2.70913	0.133147
$415$	−1.09532	−0.0537672
$416$	2.72490	0.133599
$417$	16.7511	0.820306
$418$	−21.5840	−1.05571
$419$	20.8614	1.01914	0.509572	−	0.860428i	$-0.329804\pi$
$419$	20.8614	1.01914	0.509572	+	0.860428i	$0.329804\pi$
$420$	−0.0170965	−0.000834224 0
$421$	−6.58388	−0.320879	−0.160439	−	0.987046i	$-0.551291\pi$
$421$	−6.58388	−0.320879	−0.160439	+	0.987046i	$0.551291\pi$
$422$	−8.93048	−0.434729
$423$	−7.42983	−0.361251
$424$	−7.44179	−0.361405
$425$	4.98648	0.241880
$426$	22.0165	1.06670
$427$	−0.763172	−0.0369325
$428$	−1.72318	−0.0832932
$429$	6.12361	0.295651
$430$	1.21792	0.0587335
$431$	−29.4295	−1.41757	−0.708785	−	0.705425i	$-0.750756\pi$
$431$	−29.4295	−1.41757	−0.708785	+	0.705425i	$0.750756\pi$
$432$	3.46447	0.166685
$433$	8.45315	0.406232	0.203116	−	0.979155i	$-0.434893\pi$
$433$	8.45315	0.406232	0.203116	+	0.979155i	$0.434893\pi$
$434$	4.34202	0.208423
$435$	−0.470918	−0.0225788
$436$	2.66719	0.127735
$437$	−10.9838	−0.525426
$438$	−4.06898	−0.194423
$439$	24.1972	1.15487	0.577435	−	0.816437i	$-0.304054\pi$
$439$	24.1972	1.15487	0.577435	+	0.816437i	$0.304054\pi$
$440$	−1.04441	−0.0497901
$441$	−6.62194	−0.315331
$442$	−2.68767	−0.127840
$443$	11.5916	0.550732	0.275366	−	0.961340i	$-0.411201\pi$
$443$	11.5916	0.550732	0.275366	+	0.961340i	$0.411201\pi$
$444$	2.28850	0.108608
$445$	0.00547909	0.000259734 0
$446$	−13.3854	−0.633816
$447$	−20.7911	−0.983387
$448$	5.35804	0.253144
$449$	−19.9755	−0.942700	−0.471350	−	0.881946i	$-0.656233\pi$
$449$	−19.9755	−0.942700	−0.471350	+	0.881946i	$0.656233\pi$
$450$	6.61689	0.311923
$451$	−13.3813	−0.630099
$452$	1.71108	0.0804825
$453$	13.8576	0.651086
$454$	5.79908	0.272164
$455$	0.144787	0.00678773
$456$	−15.9855	−0.748591
$457$	−18.5543	−0.867934	−0.433967	−	0.900929i	$-0.642887\pi$
$457$	−18.5543	−0.867934	−0.433967	+	0.900929i	$0.642887\pi$
$458$	36.6831	1.71409
$459$	1.00000	0.0466760
$460$	−0.0567673	−0.00264679
$461$	36.4545	1.69786	0.848928	−	0.528508i	$-0.177248\pi$
$461$	36.4545	1.69786	0.848928	+	0.528508i	$0.177248\pi$
$462$	2.46678	0.114765
$463$	−1.79385	−0.0833672	−0.0416836	−	0.999131i	$-0.513272\pi$
$463$	−1.79385	−0.0833672	−0.0416836	+	0.999131i	$0.513272\pi$
$464$	14.0330	0.651464
$465$	−0.618707	−0.0286919
$466$	−23.5821	−1.09242
$467$	−9.92274	−0.459169	−0.229585	−	0.973289i	$-0.573737\pi$
$467$	−9.92274	−0.459169	−0.229585	+	0.973289i	$0.573737\pi$
$468$	0.484408	0.0223918
$469$	−6.45718	−0.298165
$470$	−1.14623	−0.0528716
$471$	−3.86928	−0.178287
$472$	−4.65921	−0.214457
$473$	23.8681	1.09746
$474$	−1.32697	−0.0609495
$475$	−26.8273	−1.23092
$476$	0.147053	0.00674016
$477$	−2.50456	−0.114676
$478$	13.7201	0.627542
$479$	12.2694	0.560603	0.280302	−	0.959912i	$-0.409566\pi$
$479$	12.2694	0.560603	0.280302	+	0.959912i	$0.409566\pi$
$480$	−0.156411	−0.00713915
$481$	−19.3809	−0.883694
$482$	−13.0454	−0.594202
$483$	1.25531	0.0571185
$484$	0.444669	0.0202122
$485$	0.559662	0.0254129
$486$	1.32697	0.0601924
$487$	9.27288	0.420194	0.210097	−	0.977681i	$-0.432622\pi$
$487$	9.27288	0.420194	0.210097	+	0.977681i	$0.432622\pi$
$488$	−3.68797	−0.166947
$489$	−13.4352	−0.607560
$490$	−1.02159	−0.0461509
$491$	−0.0295420	−0.00133321	−0.000666605	−	1.00000i	$-0.500212\pi$
$491$	−0.0295420	−0.00133321	−0.000666605		1.00000i	$0.500212\pi$
$492$	−1.05852	−0.0477219
$493$	4.05053	0.182427
$494$	14.4597	0.650571
$495$	−0.351499	−0.0157987
$496$	18.4370	0.827844
$497$	10.2016	0.457605
$498$	12.5017	0.560213
$499$	−12.4078	−0.555449	−0.277724	−	0.960661i	$-0.589580\pi$
$499$	−12.4078	−0.555449	−0.277724	+	0.960661i	$0.589580\pi$
$500$	−0.277677	−0.0124181
$501$	−13.8094	−0.616958
$502$	14.4268	0.643902
$503$	18.1969	0.811358	0.405679	−	0.914016i	$-0.367035\pi$
$503$	18.1969	0.811358	0.405679	+	0.914016i	$0.367035\pi$
$504$	1.82694	0.0813786
$505$	−1.37538	−0.0612034
$506$	8.19069	0.364121
$507$	8.89764	0.395158
$508$	1.04440	0.0463376
$509$	23.3230	1.03377	0.516886	−	0.856054i	$-0.327091\pi$
$509$	23.3230	1.03377	0.516886	+	0.856054i	$0.327091\pi$
$510$	0.154274	0.00683137
$511$	−1.88541	−0.0834056
$512$	25.2488	1.11585
$513$	−5.38000	−0.237533
$514$	18.9977	0.837953
$515$	−0.899070	−0.0396178
$516$	1.88808	0.0831182
$517$	−22.4631	−0.987925
$518$	−7.80723	−0.343030
$519$	12.8299	0.563169
$520$	0.699674	0.0306827
$521$	−31.8721	−1.39634	−0.698171	−	0.715931i	$-0.746003\pi$
$521$	−31.8721	−1.39634	−0.698171	+	0.715931i	$0.746003\pi$
$522$	5.37491	0.235253
$523$	−37.2462	−1.62866	−0.814331	−	0.580401i	$-0.802896\pi$
$523$	−37.2462	−1.62866	−0.814331	+	0.580401i	$0.802896\pi$
$524$	1.57268	0.0687026
$525$	3.06602	0.133812
$526$	38.4110	1.67480
$527$	5.32172	0.231818
$528$	10.4744	0.455838
$529$	−18.8319	−0.818777
$530$	−0.386389	−0.0167837
$531$	−1.56807	−0.0680486
$532$	−0.791145	−0.0343005
$533$	8.96445	0.388293
$534$	−0.0625367	−0.00270623
$535$	−0.837665	−0.0362154
$536$	−31.2039	−1.34780
$537$	−20.1144	−0.868002
$538$	−1.24199	−0.0535459
$539$	−20.0205	−0.862346
$540$	−0.0278053	−0.00119655
$541$	15.7163	0.675696	0.337848	−	0.941201i	$-0.390301\pi$
$541$	15.7163	0.675696	0.337848	+	0.941201i	$0.390301\pi$
$542$	8.73314	0.375121
$543$	20.8970	0.896778
$544$	1.34535	0.0576812
$545$	1.29656	0.0555386
$546$	−1.65256	−0.0707229
$547$	−0.551319	−0.0235727	−0.0117863	−	0.999931i	$-0.503752\pi$
$547$	−0.551319	−0.0235727	−0.0117863	+	0.999931i	$0.503752\pi$
$548$	−1.27515	−0.0544719
$549$	−1.24120	−0.0529732
$550$	20.0053	0.853028
$551$	−21.7918	−0.928363
$552$	6.06619	0.258194
$553$	−0.614865	−0.0261467
$554$	−9.73454	−0.413581
$555$	1.11248	0.0472220
$556$	4.00625	0.169903
$557$	−34.2518	−1.45130	−0.725648	−	0.688067i	$-0.758460\pi$
$557$	−34.2518	−1.45130	−0.725648	+	0.688067i	$0.758460\pi$
$558$	7.06174	0.298947
$559$	−15.9898	−0.676298
$560$	0.247657	0.0104654
$561$	3.02336	0.127647
$562$	29.7467	1.25479
$563$	1.38568	0.0583993	0.0291997	−	0.999574i	$-0.490704\pi$
$563$	1.38568	0.0583993	0.0291997	+	0.999574i	$0.490704\pi$
$564$	−1.77694	−0.0748227
$565$	0.831783	0.0349934
$566$	2.19406	0.0922231
$567$	0.614865	0.0258219
$568$	49.2986	2.06852
$569$	−21.2880	−0.892439	−0.446219	−	0.894924i	$-0.647230\pi$
$569$	−21.2880	−0.892439	−0.446219	+	0.894924i	$0.647230\pi$
$570$	−0.829994	−0.0347646
$571$	1.19788	0.0501298	0.0250649	−	0.999686i	$-0.492021\pi$
$571$	1.19788	0.0501298	0.0250649	+	0.999686i	$0.492021\pi$
$572$	1.46454	0.0612355
$573$	14.7186	0.614877
$574$	3.61115	0.150727
$575$	10.1804	0.424552
$576$	8.71418	0.363091
$577$	11.4645	0.477273	0.238636	−	0.971109i	$-0.423300\pi$
$577$	11.4645	0.477273	0.238636	+	0.971109i	$0.423300\pi$
$578$	−1.32697	−0.0551945
$579$	0.0695823	0.00289174
$580$	−0.112626	−0.00467654
$581$	5.79279	0.240326
$582$	−6.38781	−0.264783
$583$	−7.57221	−0.313609
$584$	−9.11111	−0.377020
$585$	0.235478	0.00973582
$586$	6.47662	0.267547
$587$	−33.3423	−1.37618	−0.688091	−	0.725624i	$-0.741551\pi$
$587$	−33.3423	−1.37618	−0.688091	+	0.725624i	$0.741551\pi$
$588$	−1.58372	−0.0653117
$589$	−28.6308	−1.17971
$590$	−0.241913	−0.00995941
$591$	−7.30690	−0.300566
$592$	−33.1509	−1.36249
$593$	−7.23563	−0.297132	−0.148566	−	0.988903i	$-0.547466\pi$
$593$	−7.23563	−0.297132	−0.148566	+	0.988903i	$0.547466\pi$
$594$	4.01190	0.164610
$595$	0.0714847	0.00293059
$596$	−4.97247	−0.203680
$597$	21.0021	0.859558
$598$	−5.48715	−0.224386
$599$	−8.76396	−0.358086	−0.179043	−	0.983841i	$-0.557300\pi$
$599$	−8.76396	−0.358086	−0.179043	+	0.983841i	$0.557300\pi$
$600$	14.8163	0.604873
$601$	1.25354	0.0511329	0.0255664	−	0.999673i	$-0.491861\pi$
$601$	1.25354	0.0511329	0.0255664	+	0.999673i	$0.491861\pi$
$602$	−6.44120	−0.262524
$603$	−10.5018	−0.427666
$604$	3.31422	0.134854
$605$	0.216160	0.00878816
$606$	15.6981	0.637693
$607$	−38.9220	−1.57980	−0.789898	−	0.613239i	$-0.789866\pi$
$607$	−38.9220	−1.57980	−0.789898	+	0.613239i	$0.789866\pi$
$608$	−7.23795	−0.293538
$609$	2.49053	0.100921
$610$	−0.191485	−0.00775301
$611$	15.0486	0.608801
$612$	0.239163	0.00966759
$613$	21.4771	0.867451	0.433726	−	0.901045i	$-0.357199\pi$
$613$	21.4771	0.867451	0.433726	+	0.901045i	$0.357199\pi$
$614$	16.1127	0.650255
$615$	−0.514565	−0.0207492
$616$	5.52352	0.222549
$617$	−31.1612	−1.25450	−0.627251	−	0.778817i	$-0.715820\pi$
$617$	−31.1612	−1.25450	−0.627251	+	0.778817i	$0.715820\pi$
$618$	10.2617	0.412787
$619$	−14.3522	−0.576863	−0.288431	−	0.957501i	$-0.593134\pi$
$619$	−14.3522	−0.576863	−0.288431	+	0.957501i	$0.593134\pi$
$620$	−0.147972	−0.00594269
$621$	2.04160	0.0819266
$622$	16.0717	0.644417
$623$	−0.0289771	−0.00116094
$624$	−7.01705	−0.280907
$625$	24.7974	0.991897
$626$	43.4986	1.73856
$627$	−16.2657	−0.649589
$628$	−0.925388	−0.0369270
$629$	−9.56880	−0.381533
$630$	0.0948577	0.00377922
$631$	−34.2764	−1.36452	−0.682261	−	0.731109i	$-0.739003\pi$
$631$	−34.2764	−1.36452	−0.682261	+	0.731109i	$0.739003\pi$
$632$	−2.97129	−0.118192
$633$	−6.73000	−0.267494
$634$	15.8237	0.628440
$635$	0.507697	0.0201473
$636$	−0.598999	−0.0237519
$637$	13.4123	0.531414
$638$	16.2503	0.643356
$639$	16.5916	0.656355
$640$	1.03155	0.0407756
$641$	7.56572	0.298828	0.149414	−	0.988775i	$-0.452261\pi$
$641$	7.56572	0.298828	0.149414	+	0.988775i	$0.452261\pi$
$642$	9.56086	0.377337
$643$	16.8826	0.665785	0.332892	−	0.942965i	$-0.391975\pi$
$643$	16.8826	0.665785	0.332892	+	0.942965i	$0.391975\pi$
$644$	0.300223	0.0118305
$645$	0.917826	0.0361394
$646$	7.13907	0.280883
$647$	−9.48028	−0.372708	−0.186354	−	0.982483i	$-0.559667\pi$
$647$	−9.48028	−0.372708	−0.186354	+	0.982483i	$0.559667\pi$
$648$	2.97129	0.116723
$649$	−4.74086	−0.186095
$650$	−13.4020	−0.525671
$651$	3.27214	0.128245
$652$	−3.21320	−0.125839
$653$	40.3892	1.58055	0.790276	−	0.612751i	$-0.209937\pi$
$653$	40.3892	1.58055	0.790276	+	0.612751i	$0.209937\pi$
$654$	−14.7986	−0.578669
$655$	0.764501	0.0298715
$656$	15.3336	0.598676
$657$	−3.06638	−0.119631
$658$	6.06203	0.236323
$659$	−18.3317	−0.714100	−0.357050	−	0.934085i	$-0.616218\pi$
$659$	−18.3317	−0.714100	−0.357050	+	0.934085i	$0.616218\pi$
$660$	−0.0840655	−0.00327224
$661$	16.5876	0.645184	0.322592	−	0.946538i	$-0.395446\pi$
$661$	16.5876	0.645184	0.322592	+	0.946538i	$0.395446\pi$
$662$	−0.223907	−0.00870239
$663$	−2.02543	−0.0786611
$664$	27.9933	1.08635
$665$	−0.384587	−0.0149137
$666$	−12.6975	−0.492017
$667$	8.26956	0.320199
$668$	−3.30269	−0.127785
$669$	−10.0872	−0.389994
$670$	−1.62015	−0.0625920
$671$	−3.75260	−0.144868
$672$	0.827206	0.0319102
$673$	−4.28619	−0.165221	−0.0826103	−	0.996582i	$-0.526326\pi$
$673$	−4.28619	−0.165221	−0.0826103	+	0.996582i	$0.526326\pi$
$674$	−4.35369	−0.167698
$675$	4.98648	0.191930
$676$	2.12799	0.0818456
$677$	−45.8667	−1.76280	−0.881399	−	0.472372i	$-0.843398\pi$
$677$	−45.8667	−1.76280	−0.881399	+	0.472372i	$0.843398\pi$
$678$	−9.49372	−0.364604
$679$	−2.95987	−0.113589
$680$	0.345445	0.0132472
$681$	4.37018	0.167466
$682$	21.3502	0.817541
$683$	−24.3967	−0.933513	−0.466756	−	0.884386i	$-0.654578\pi$
$683$	−24.3967	−0.933513	−0.466756	+	0.884386i	$0.654578\pi$
$684$	−1.28670	−0.0491980
$685$	−0.619872	−0.0236841
$686$	11.1142	0.424342
$687$	27.6443	1.05470
$688$	−27.3504	−1.04273
$689$	5.07282	0.193259
$690$	0.314966	0.0119905
$691$	−43.7265	−1.66344	−0.831718	−	0.555198i	$-0.812642\pi$
$691$	−43.7265	−1.66344	−0.831718	+	0.555198i	$0.812642\pi$
$692$	3.06843	0.116644
$693$	1.85896	0.0706161
$694$	3.48521	0.132297
$695$	1.94750	0.0738728
$696$	12.0353	0.456197
$697$	4.42595	0.167645
$698$	−5.97757	−0.226254
$699$	−17.7714	−0.672178
$700$	0.733278	0.0277153
$701$	36.6728	1.38511	0.692556	−	0.721364i	$-0.256484\pi$
$701$	36.6728	1.38511	0.692556	+	0.721364i	$0.256484\pi$
$702$	−2.68767	−0.101440
$703$	51.4801	1.94161
$704$	26.3461	0.992957
$705$	−0.863798	−0.0325325
$706$	15.8605	0.596917
$707$	7.27391	0.273564
$708$	−0.375025	−0.0140943
$709$	−28.8304	−1.08275	−0.541375	−	0.840781i	$-0.682096\pi$
$709$	−28.8304	−1.08275	−0.541375	+	0.840781i	$0.682096\pi$
$710$	2.55966	0.0960623
$711$	−1.00000	−0.0375029
$712$	−0.140030	−0.00524784
$713$	10.8648	0.406891
$714$	−0.815905	−0.0305345
$715$	0.711936	0.0266249
$716$	−4.81063	−0.179782
$717$	10.3394	0.386133
$718$	−33.9956	−1.26871
$719$	−30.9568	−1.15449	−0.577247	−	0.816570i	$-0.695873\pi$
$719$	−30.9568	−1.15449	−0.577247	+	0.816570i	$0.695873\pi$
$720$	0.402783	0.0150108
$721$	4.75489	0.177081
$722$	−13.1958	−0.491097
$723$	−9.83101	−0.365619
$724$	4.99780	0.185742
$725$	20.1979	0.750131
$726$	−2.46719	−0.0915659
$727$	−13.0502	−0.484006	−0.242003	−	0.970276i	$-0.577804\pi$
$727$	−13.0502	−0.484006	−0.242003	+	0.970276i	$0.577804\pi$
$728$	−3.70035	−0.137144
$729$	1.00000	0.0370370
$730$	−0.473063	−0.0175088
$731$	−7.89454	−0.291990
$732$	−0.296850	−0.0109719
$733$	48.6379	1.79648	0.898241	−	0.439503i	$-0.144845\pi$
$733$	48.6379	1.79648	0.898241	+	0.439503i	$0.144845\pi$
$734$	0.967821	0.0357229
$735$	−0.769872	−0.0283972
$736$	2.74666	0.101243
$737$	−31.7507	−1.16955
$738$	5.87308	0.216191
$739$	1.70544	0.0627355	0.0313678	−	0.999508i	$-0.490014\pi$
$739$	1.70544	0.0627355	0.0313678	+	0.999508i	$0.490014\pi$
$740$	0.266063	0.00978068
$741$	10.8968	0.400304
$742$	2.04349	0.0750187
$743$	5.91190	0.216887	0.108443	−	0.994103i	$-0.465413\pi$
$743$	5.91190	0.216887	0.108443	+	0.994103i	$0.465413\pi$
$744$	15.8124	0.579710
$745$	−2.41719	−0.0885592
$746$	−5.62837	−0.206069
$747$	9.42124	0.344705
$748$	0.723077	0.0264383
$749$	4.43014	0.161874
$750$	1.54066	0.0562568
$751$	−4.42252	−0.161380	−0.0806900	−	0.996739i	$-0.525712\pi$
$751$	−4.42252	−0.161380	−0.0806900	+	0.996739i	$0.525712\pi$
$752$	25.7405	0.938658
$753$	10.8721	0.396200
$754$	−10.8865	−0.396463
$755$	1.61109	0.0586337
$756$	0.147053	0.00534827
$757$	−30.3412	−1.10277	−0.551384	−	0.834252i	$-0.685900\pi$
$757$	−30.3412	−1.10277	−0.551384	+	0.834252i	$0.685900\pi$
$758$	47.1607	1.71295
$759$	6.17250	0.224048
$760$	−1.85849	−0.0674146
$761$	−17.2699	−0.626032	−0.313016	−	0.949748i	$-0.601339\pi$
$761$	−17.2699	−0.626032	−0.313016	+	0.949748i	$0.601339\pi$
$762$	−5.79470	−0.209920
$763$	−6.85709	−0.248243
$764$	3.52014	0.127354
$765$	0.116261	0.00420342
$766$	−2.68886	−0.0971523
$767$	3.17602	0.114680
$768$	5.65456	0.204041
$769$	19.9115	0.718026	0.359013	−	0.933333i	$-0.383113\pi$
$769$	19.9115	0.718026	0.359013	+	0.933333i	$0.383113\pi$
$770$	0.286789	0.0103352
$771$	14.3167	0.515602
$772$	0.0166415	0.000598942 0
$773$	39.9252	1.43601	0.718005	−	0.696038i	$-0.245055\pi$
$773$	39.9252	1.43601	0.718005	+	0.696038i	$0.245055\pi$
$774$	−10.4758	−0.376544
$775$	26.5367	0.953225
$776$	−14.3034	−0.513460
$777$	−5.88352	−0.211070
$778$	4.52812	0.162341
$779$	−23.8116	−0.853139
$780$	0.0563176	0.00201649
$781$	50.1626	1.79496
$782$	−2.70913	−0.0968784
$783$	4.05053	0.144754
$784$	22.9415	0.819341
$785$	−0.449845	−0.0160557
$786$	−8.72579	−0.311238
$787$	−6.31356	−0.225054	−0.112527	−	0.993649i	$-0.535894\pi$
$787$	−6.31356	−0.225054	−0.112527	+	0.993649i	$0.535894\pi$
$788$	−1.74754	−0.0622535
$789$	28.9465	1.03052
$790$	−0.154274	−0.00548882
$791$	−4.39903	−0.156411
$792$	8.98330	0.319208
$793$	2.51397	0.0892735
$794$	−12.9512	−0.459621
$795$	−0.291183	−0.0103272
$796$	5.02292	0.178033
$797$	35.6688	1.26345	0.631726	−	0.775191i	$-0.282347\pi$
$797$	35.6688	1.26345	0.631726	+	0.775191i	$0.282347\pi$
$798$	4.38956	0.155389
$799$	7.42983	0.262849
$800$	6.70854	0.237183
$801$	−0.0471276	−0.00166517
$802$	−19.2217	−0.678742
$803$	−9.27078	−0.327159
$804$	−2.51164	−0.0885787
$805$	0.145943	0.00514382
$806$	−14.3030	−0.503803
$807$	−0.935961	−0.0329474
$808$	35.1507	1.23660
$809$	54.2373	1.90688	0.953440	−	0.301582i	$-0.0975147\pi$
$809$	54.2373	1.90688	0.953440	+	0.301582i	$0.0975147\pi$
$810$	0.154274	0.00542064
$811$	−46.2375	−1.62362	−0.811809	−	0.583924i	$-0.801517\pi$
$811$	−46.2375	−1.62362	−0.811809	+	0.583924i	$0.801517\pi$
$812$	0.595643	0.0209030
$813$	6.58129	0.230816
$814$	−38.3891	−1.34554
$815$	−1.56199	−0.0547140
$816$	−3.46447	−0.121281
$817$	42.4726	1.48593
$818$	16.7310	0.584985
$819$	−1.24537	−0.0435166
$820$	−0.123065	−0.00429761
$821$	24.5475	0.856714	0.428357	−	0.903610i	$-0.359093\pi$
$821$	24.5475	0.856714	0.428357	+	0.903610i	$0.359093\pi$
$822$	7.07503	0.246770
$823$	−1.98955	−0.0693512	−0.0346756	−	0.999399i	$-0.511040\pi$
$823$	−1.98955	−0.0693512	−0.0346756	+	0.999399i	$0.511040\pi$
$824$	22.9777	0.800465
$825$	15.0760	0.524877
$826$	1.27940	0.0445160
$827$	−19.1731	−0.666714	−0.333357	−	0.942801i	$-0.608181\pi$
$827$	−19.1731	−0.666714	−0.333357	+	0.942801i	$0.608181\pi$
$828$	0.488275	0.0169687
$829$	−27.0560	−0.939695	−0.469848	−	0.882748i	$-0.655691\pi$
$829$	−27.0560	−0.939695	−0.469848	+	0.882748i	$0.655691\pi$
$830$	1.45345	0.0504501
$831$	−7.33594	−0.254481
$832$	−17.6499	−0.611902
$833$	6.62194	0.229437
$834$	−22.2282	−0.769698
$835$	−1.60549	−0.0555603
$836$	−3.89015	−0.134544
$837$	5.32172	0.183946
$838$	−27.6823	−0.956269
$839$	−1.19530	−0.0412665	−0.0206332	−	0.999787i	$-0.506568\pi$
$839$	−1.19530	−0.0412665	−0.0206332	+	0.999787i	$0.506568\pi$
$840$	0.212402	0.00732856
$841$	−12.5932	−0.434249
$842$	8.73658	0.301083
$843$	22.4171	0.772085
$844$	−1.60957	−0.0554036
$845$	1.03445	0.0355860
$846$	9.85913	0.338964
$847$	−1.14320	−0.0392808
$848$	8.67700	0.297969
$849$	1.65344	0.0567459
$850$	−6.61689	−0.226957
$851$	−19.5357	−0.669674
$852$	3.96811	0.135945
$853$	3.81966	0.130783	0.0653913	−	0.997860i	$-0.479170\pi$
$853$	3.81966	0.130783	0.0653913	+	0.997860i	$0.479170\pi$
$854$	1.01270	0.0346540
$855$	−0.625482	−0.0213910
$856$	21.4083	0.731721
$857$	39.7339	1.35728	0.678642	−	0.734470i	$-0.262569\pi$
$857$	39.7339	1.35728	0.678642	+	0.734470i	$0.262569\pi$
$858$	−8.12582	−0.277411
$859$	29.9669	1.02246	0.511229	−	0.859445i	$-0.329191\pi$
$859$	29.9669	1.02246	0.511229	+	0.859445i	$0.329191\pi$
$860$	0.219510	0.00748523
$861$	2.72136	0.0927438
$862$	39.0519	1.33011
$863$	1.05168	0.0357996	0.0178998	−	0.999840i	$-0.494302\pi$
$863$	1.05168	0.0357996	0.0178998	+	0.999840i	$0.494302\pi$
$864$	1.34535	0.0457696
$865$	1.49161	0.0507163
$866$	−11.2170	−0.381170
$867$	−1.00000	−0.0339618
$868$	0.782575	0.0265623
$869$	−3.02336	−0.102561
$870$	0.624891	0.0211858
$871$	21.2706	0.720728
$872$	−33.1364	−1.12214
$873$	−4.81385	−0.162924
$874$	14.5751	0.493011
$875$	0.713881	0.0241336
$876$	−0.733364	−0.0247781
$877$	7.58828	0.256238	0.128119	−	0.991759i	$-0.459106\pi$
$877$	7.58828	0.256238	0.128119	+	0.991759i	$0.459106\pi$
$878$	−32.1088	−1.08362
$879$	4.88078	0.164625
$880$	1.21776	0.0410506
$881$	2.79897	0.0942997	0.0471498	−	0.998888i	$-0.484986\pi$
$881$	2.79897	0.0942997	0.0471498	+	0.998888i	$0.484986\pi$
$882$	8.78709	0.295877
$883$	42.1154	1.41730	0.708648	−	0.705562i	$-0.249306\pi$
$883$	42.1154	1.41730	0.708648	+	0.705562i	$0.249306\pi$
$884$	−0.484408	−0.0162924
$885$	−0.182306	−0.00612813
$886$	−15.3816	−0.516755
$887$	6.23617	0.209390	0.104695	−	0.994504i	$-0.466613\pi$
$887$	6.23617	0.209390	0.104695	+	0.994504i	$0.466613\pi$
$888$	−28.4317	−0.954105
$889$	−2.68504	−0.0900535
$890$	−0.00727056	−0.000243710 0
$891$	3.02336	0.101287
$892$	−2.41249	−0.0807761
$893$	−39.9725	−1.33763
$894$	27.5891	0.922718
$895$	−2.33852	−0.0781681
$896$	−5.45553	−0.182256
$897$	−4.13512	−0.138067
$898$	26.5067	0.884542
$899$	21.5558	0.718925
$900$	1.19258	0.0397527
$901$	2.50456	0.0834391
$902$	17.7565	0.591226
$903$	−4.85408	−0.161534
$904$	−21.2580	−0.707030
$905$	2.42951	0.0807595
$906$	−18.3885	−0.610918
$907$	13.7035	0.455017	0.227509	−	0.973776i	$-0.426942\pi$
$907$	13.7035	0.455017	0.227509	+	0.973776i	$0.426942\pi$
$908$	1.04519	0.0346857
$909$	11.8301	0.392379
$910$	−0.192128	−0.00636897
$911$	40.8517	1.35348	0.676739	−	0.736223i	$-0.263393\pi$
$911$	40.8517	1.35348	0.676739	+	0.736223i	$0.263393\pi$
$912$	18.6389	0.617194
$913$	28.4838	0.942678
$914$	24.6209	0.814388
$915$	−0.144303	−0.00477051
$916$	6.61150	0.218450
$917$	−4.04320	−0.133518
$918$	−1.32697	−0.0437964
$919$	13.6246	0.449436	0.224718	−	0.974424i	$-0.427854\pi$
$919$	13.6246	0.449436	0.224718	+	0.974424i	$0.427854\pi$
$920$	0.705260	0.0232517
$921$	12.1425	0.400109
$922$	−48.3739	−1.59311
$923$	−33.6052	−1.10613
$924$	0.444595	0.0146261
$925$	−47.7147	−1.56885
$926$	2.38037	0.0782239
$927$	7.73322	0.253992
$928$	5.44936	0.178884
$929$	−30.1046	−0.987701	−0.493851	−	0.869547i	$-0.664411\pi$
$929$	−30.1046	−0.987701	−0.493851	+	0.869547i	$0.664411\pi$
$930$	0.821003	0.0269217
$931$	−35.6260	−1.16760
$932$	−4.25027	−0.139222
$933$	12.1116	0.396517
$934$	13.1671	0.430842
$935$	0.351499	0.0114952
$936$	−6.01814	−0.196709
$937$	−13.0766	−0.427192	−0.213596	−	0.976922i	$-0.568518\pi$
$937$	−13.0766	−0.427192	−0.213596	+	0.976922i	$0.568518\pi$
$938$	8.56846	0.279770
$939$	32.7805	1.06975
$940$	−0.206589	−0.00673817
$941$	41.6844	1.35887	0.679436	−	0.733735i	$-0.262224\pi$
$941$	41.6844	1.35887	0.679436	+	0.733735i	$0.262224\pi$
$942$	5.13440	0.167288
$943$	9.03602	0.294253
$944$	5.43255	0.176815
$945$	0.0714847	0.00232540
$946$	−31.6721	−1.02975
$947$	−2.24976	−0.0731073	−0.0365537	−	0.999332i	$-0.511638\pi$
$947$	−2.24976	−0.0731073	−0.0365537	+	0.999332i	$0.511638\pi$
$948$	−0.239163	−0.00776765
$949$	6.21073	0.201609
$950$	35.5988	1.15498
$951$	11.9247	0.386686
$952$	−1.82694	−0.0592116
$953$	38.8431	1.25825	0.629126	−	0.777303i	$-0.283413\pi$
$953$	38.8431	1.25825	0.629126	+	0.777303i	$0.283413\pi$
$954$	3.32347	0.107601
$955$	1.71119	0.0553729
$956$	2.47281	0.0799764
$957$	12.2462	0.395864
$958$	−16.2811	−0.526017
$959$	3.27830	0.105862
$960$	1.01312	0.0326982
$961$	−2.67931	−0.0864294
$962$	25.7178	0.829176
$963$	7.20506	0.232180
$964$	−2.35121	−0.0757275
$965$	0.00808970	0.000260417 0
$966$	−1.66575	−0.0535947
$967$	−2.78793	−0.0896537	−0.0448269	−	0.998995i	$-0.514274\pi$
$967$	−2.78793	−0.0896537	−0.0448269	+	0.998995i	$0.514274\pi$
$968$	−5.52443	−0.177562
$969$	5.38000	0.172830
$970$	−0.742652	−0.0238451
$971$	−14.4566	−0.463933	−0.231967	−	0.972724i	$-0.574516\pi$
$971$	−14.4566	−0.463933	−0.231967	+	0.972724i	$0.574516\pi$
$972$	0.239163	0.00767116
$973$	−10.2997	−0.330193
$974$	−12.3048	−0.394271
$975$	−10.0998	−0.323451
$976$	4.30011	0.137643
$977$	7.70104	0.246378	0.123189	−	0.992383i	$-0.460688\pi$
$977$	7.70104	0.246378	0.123189	+	0.992383i	$0.460688\pi$
$978$	17.8280	0.570078
$979$	−0.142484	−0.00455380
$980$	−0.184125	−0.00588166
$981$	−11.1522	−0.356062
$982$	0.0392012	0.00125096
$983$	17.1694	0.547619	0.273809	−	0.961784i	$-0.411716\pi$
$983$	17.1694	0.547619	0.273809	+	0.961784i	$0.411716\pi$
$984$	13.1508	0.419232
$985$	−0.849506	−0.0270675
$986$	−5.37491	−0.171172
$987$	4.56834	0.145412
$988$	2.60611	0.0829114
$989$	−16.1175	−0.512507
$990$	0.466427	0.0148240
$991$	6.66232	0.211636	0.105818	−	0.994386i	$-0.466254\pi$
$991$	6.66232	0.211636	0.105818	+	0.994386i	$0.466254\pi$
$992$	7.15955	0.227316
$993$	−0.168736	−0.00535468
$994$	−13.5372	−0.429374
$995$	2.44172	0.0774077
$996$	2.25321	0.0713958
$997$	22.6173	0.716299	0.358149	−	0.933664i	$-0.383408\pi$
$997$	22.6173	0.716299	0.358149	+	0.933664i	$0.383408\pi$
$998$	16.4647	0.521181
$999$	−9.56880	−0.302743

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4029.2.a.g.1.6	✓	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4029.2.a.g.1.6	✓	22	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:	\( N \)	\(=\)	\( 4029 = 3 \cdot 17 \cdot 79 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4029.a (trivial)

\(f(q)\)	\(=\)	\(q-1.32697 q^{2} -1.00000 q^{3} -0.239163 q^{4} -0.116261 q^{5} +1.32697 q^{6} +0.614865 q^{7} +2.97129 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.32697 q^{2} -1.00000 q^{3} -0.239163 q^{4} -0.116261 q^{5} +1.32697 q^{6} +0.614865 q^{7} +2.97129 q^{8} +1.00000 q^{9} +0.154274 q^{10} +3.02336 q^{11} +0.239163 q^{12} -2.02543 q^{13} -0.815905 q^{14} +0.116261 q^{15} -3.46447 q^{16} -1.00000 q^{17} -1.32697 q^{18} +5.38000 q^{19} +0.0278053 q^{20} -0.614865 q^{21} -4.01190 q^{22} -2.04160 q^{23} -2.97129 q^{24} -4.98648 q^{25} +2.68767 q^{26} -1.00000 q^{27} -0.147053 q^{28} -4.05053 q^{29} -0.154274 q^{30} -5.32172 q^{31} -1.34535 q^{32} -3.02336 q^{33} +1.32697 q^{34} -0.0714847 q^{35} -0.239163 q^{36} +9.56880 q^{37} -7.13907 q^{38} +2.02543 q^{39} -0.345445 q^{40} -4.42595 q^{41} +0.815905 q^{42} +7.89454 q^{43} -0.723077 q^{44} -0.116261 q^{45} +2.70913 q^{46} -7.42983 q^{47} +3.46447 q^{48} -6.62194 q^{49} +6.61689 q^{50} +1.00000 q^{51} +0.484408 q^{52} -2.50456 q^{53} +1.32697 q^{54} -0.351499 q^{55} +1.82694 q^{56} -5.38000 q^{57} +5.37491 q^{58} -1.56807 q^{59} -0.0278053 q^{60} -1.24120 q^{61} +7.06174 q^{62} +0.614865 q^{63} +8.71418 q^{64} +0.235478 q^{65} +4.01190 q^{66} -10.5018 q^{67} +0.239163 q^{68} +2.04160 q^{69} +0.0948577 q^{70} +16.5916 q^{71} +2.97129 q^{72} -3.06638 q^{73} -12.6975 q^{74} +4.98648 q^{75} -1.28670 q^{76} +1.85896 q^{77} -2.68767 q^{78} -1.00000 q^{79} +0.402783 q^{80} +1.00000 q^{81} +5.87308 q^{82} +9.42124 q^{83} +0.147053 q^{84} +0.116261 q^{85} -10.4758 q^{86} +4.05053 q^{87} +8.98330 q^{88} -0.0471276 q^{89} +0.154274 q^{90} -1.24537 q^{91} +0.488275 q^{92} +5.32172 q^{93} +9.85913 q^{94} -0.625482 q^{95} +1.34535 q^{96} -4.81385 q^{97} +8.78709 q^{98} +3.02336 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + 2 q^{2} - 22 q^{3} + 16 q^{4} + 5 q^{5} - 2 q^{6} - 4 q^{7} + 6 q^{8} + 22 q^{9}+O(q^{10}) \) 22 * q + 2 * q^2 - 22 * q^3 + 16 * q^4 + 5 * q^5 - 2 * q^6 - 4 * q^7 + 6 * q^8 + 22 * q^9	\( 22 q + 2 q^{2} - 22 q^{3} + 16 q^{4} + 5 q^{5} - 2 q^{6} - 4 q^{7} + 6 q^{8} + 22 q^{9} - 5 q^{10} - 2 q^{11} - 16 q^{12} - 11 q^{13} - 7 q^{14} - 5 q^{15} - 22 q^{17} + 2 q^{18} - 36 q^{19} + 4 q^{21} - 9 q^{22} + 21 q^{23} - 6 q^{24} + 9 q^{25} - 16 q^{26} - 22 q^{27} - 17 q^{28} - q^{29} + 5 q^{30} - 12 q^{31} - 11 q^{32} + 2 q^{33} - 2 q^{34} - 14 q^{35} + 16 q^{36} - 6 q^{37} + q^{38} + 11 q^{39} - 24 q^{40} - 17 q^{41} + 7 q^{42} - 36 q^{43} + 16 q^{44} + 5 q^{45} - 23 q^{46} - 17 q^{47} - 6 q^{49} - 33 q^{50} + 22 q^{51} - 57 q^{52} - 2 q^{53} - 2 q^{54} - 24 q^{55} - 64 q^{56} + 36 q^{57} - 7 q^{58} - 59 q^{59} - 30 q^{61} - 4 q^{62} - 4 q^{63} - 22 q^{64} + 36 q^{65} + 9 q^{66} - 16 q^{67} - 16 q^{68} - 21 q^{69} - 39 q^{70} - 11 q^{71} + 6 q^{72} - 19 q^{73} - 28 q^{74} - 9 q^{75} - 77 q^{76} + 2 q^{77} + 16 q^{78} - 22 q^{79} - 2 q^{80} + 22 q^{81} + 33 q^{82} - 23 q^{83} + 17 q^{84} - 5 q^{85} + 6 q^{86} + q^{87} - 23 q^{88} + 12 q^{89} - 5 q^{90} - 24 q^{91} + 66 q^{92} + 12 q^{93} - 61 q^{94} - 11 q^{95} + 11 q^{96} - 9 q^{97} + 17 q^{98} - 2 q^{99}+O(q^{100}) \) 22 * q + 2 * q^2 - 22 * q^3 + 16 * q^4 + 5 * q^5 - 2 * q^6 - 4 * q^7 + 6 * q^8 + 22 * q^9 - 5 * q^10 - 2 * q^11 - 16 * q^12 - 11 * q^13 - 7 * q^14 - 5 * q^15 - 22 * q^17 + 2 * q^18 - 36 * q^19 + 4 * q^21 - 9 * q^22 + 21 * q^23 - 6 * q^24 + 9 * q^25 - 16 * q^26 - 22 * q^27 - 17 * q^28 - q^29 + 5 * q^30 - 12 * q^31 - 11 * q^32 + 2 * q^33 - 2 * q^34 - 14 * q^35 + 16 * q^36 - 6 * q^37 + q^38 + 11 * q^39 - 24 * q^40 - 17 * q^41 + 7 * q^42 - 36 * q^43 + 16 * q^44 + 5 * q^45 - 23 * q^46 - 17 * q^47 - 6 * q^49 - 33 * q^50 + 22 * q^51 - 57 * q^52 - 2 * q^53 - 2 * q^54 - 24 * q^55 - 64 * q^56 + 36 * q^57 - 7 * q^58 - 59 * q^59 - 30 * q^61 - 4 * q^62 - 4 * q^63 - 22 * q^64 + 36 * q^65 + 9 * q^66 - 16 * q^67 - 16 * q^68 - 21 * q^69 - 39 * q^70 - 11 * q^71 + 6 * q^72 - 19 * q^73 - 28 * q^74 - 9 * q^75 - 77 * q^76 + 2 * q^77 + 16 * q^78 - 22 * q^79 - 2 * q^80 + 22 * q^81 + 33 * q^82 - 23 * q^83 + 17 * q^84 - 5 * q^85 + 6 * q^86 + q^87 - 23 * q^88 + 12 * q^89 - 5 * q^90 - 24 * q^91 + 66 * q^92 + 12 * q^93 - 61 * q^94 - 11 * q^95 + 11 * q^96 - 9 * q^97 + 17 * q^98 - 2 * q^99

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