LMFDB - Embedded newform 4334.2.a.f.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4334,2,Mod(1,4334)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4334, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("4334.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4334 = 2 \cdot 11 \cdot 197 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4334.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:	$34.6071642360$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Character	$\chi$	$=$	4334.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -0.533021 q^{3} +1.00000 q^{4} -1.76896 q^{5} -0.533021 q^{6} -1.67093 q^{7} +1.00000 q^{8} -2.71589 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -0.533021 q^{3} +1.00000 q^{4} -1.76896 q^{5} -0.533021 q^{6} -1.67093 q^{7} +1.00000 q^{8} -2.71589 q^{9} -1.76896 q^{10} -1.00000 q^{11} -0.533021 q^{12} +0.722697 q^{13} -1.67093 q^{14} +0.942894 q^{15} +1.00000 q^{16} +2.58663 q^{17} -2.71589 q^{18} -6.87052 q^{19} -1.76896 q^{20} +0.890641 q^{21} -1.00000 q^{22} +1.81618 q^{23} -0.533021 q^{24} -1.87077 q^{25} +0.722697 q^{26} +3.04669 q^{27} -1.67093 q^{28} +5.34637 q^{29} +0.942894 q^{30} -3.89658 q^{31} +1.00000 q^{32} +0.533021 q^{33} +2.58663 q^{34} +2.95581 q^{35} -2.71589 q^{36} +7.00847 q^{37} -6.87052 q^{38} -0.385213 q^{39} -1.76896 q^{40} -4.36456 q^{41} +0.890641 q^{42} +10.7070 q^{43} -1.00000 q^{44} +4.80430 q^{45} +1.81618 q^{46} +3.79134 q^{47} -0.533021 q^{48} -4.20799 q^{49} -1.87077 q^{50} -1.37873 q^{51} +0.722697 q^{52} -8.69006 q^{53} +3.04669 q^{54} +1.76896 q^{55} -1.67093 q^{56} +3.66213 q^{57} +5.34637 q^{58} +11.1363 q^{59} +0.942894 q^{60} +2.11094 q^{61} -3.89658 q^{62} +4.53806 q^{63} +1.00000 q^{64} -1.27842 q^{65} +0.533021 q^{66} -2.77863 q^{67} +2.58663 q^{68} -0.968064 q^{69} +2.95581 q^{70} -0.488720 q^{71} -2.71589 q^{72} +5.80703 q^{73} +7.00847 q^{74} +0.997162 q^{75} -6.87052 q^{76} +1.67093 q^{77} -0.385213 q^{78} +6.21817 q^{79} -1.76896 q^{80} +6.52371 q^{81} -4.36456 q^{82} +10.8971 q^{83} +0.890641 q^{84} -4.57565 q^{85} +10.7070 q^{86} -2.84973 q^{87} -1.00000 q^{88} +5.27440 q^{89} +4.80430 q^{90} -1.20758 q^{91} +1.81618 q^{92} +2.07696 q^{93} +3.79134 q^{94} +12.1537 q^{95} -0.533021 q^{96} +17.0282 q^{97} -4.20799 q^{98} +2.71589 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 24 q^{2} + 8 q^{3} + 24 q^{4} + 8 q^{6} + 11 q^{7} + 24 q^{8} + 28 q^{9}+O(q^{10}) $ 24 * q + 24 * q^2 + 8 * q^3 + 24 * q^4 + 8 * q^6 + 11 * q^7 + 24 * q^8 + 28 * q^9	\( 24 q + 24 q^{2} + 8 q^{3} + 24 q^{4} + 8 q^{6} + 11 q^{7} + 24 q^{8} + 28 q^{9} - 24 q^{11} + 8 q^{12} + 9 q^{13} + 11 q^{14} + 6 q^{15} + 24 q^{16} - q^{17} + 28 q^{18} + 35 q^{19} + 21 q^{21} - 24 q^{22} + 13 q^{23} + 8 q^{24} + 38 q^{25} + 9 q^{26} + 23 q^{27} + 11 q^{28} + 15 q^{29} + 6 q^{30} + 31 q^{31} + 24 q^{32} - 8 q^{33} - q^{34} + 28 q^{35} + 28 q^{36} + 13 q^{37} + 35 q^{38} + 31 q^{39} + 16 q^{41} + 21 q^{42} + 35 q^{43} - 24 q^{44} + 13 q^{45} + 13 q^{46} + 46 q^{47} + 8 q^{48} + 55 q^{49} + 38 q^{50} + 18 q^{51} + 9 q^{52} + 6 q^{53} + 23 q^{54} + 11 q^{56} + 18 q^{57} + 15 q^{58} + 13 q^{59} + 6 q^{60} + 60 q^{61} + 31 q^{62} + 52 q^{63} + 24 q^{64} - 9 q^{65} - 8 q^{66} + 28 q^{67} - q^{68} + 21 q^{69} + 28 q^{70} + 10 q^{71} + 28 q^{72} + 3 q^{73} + 13 q^{74} + 48 q^{75} + 35 q^{76} - 11 q^{77} + 31 q^{78} + 47 q^{79} + 16 q^{81} + 16 q^{82} + 66 q^{83} + 21 q^{84} + 37 q^{85} + 35 q^{86} + 34 q^{87} - 24 q^{88} - 5 q^{89} + 13 q^{90} + q^{91} + 13 q^{92} - 16 q^{93} + 46 q^{94} + 9 q^{95} + 8 q^{96} + 24 q^{97} + 55 q^{98} - 28 q^{99}+O(q^{100}) \) 24 * q + 24 * q^2 + 8 * q^3 + 24 * q^4 + 8 * q^6 + 11 * q^7 + 24 * q^8 + 28 * q^9 - 24 * q^11 + 8 * q^12 + 9 * q^13 + 11 * q^14 + 6 * q^15 + 24 * q^16 - q^17 + 28 * q^18 + 35 * q^19 + 21 * q^21 - 24 * q^22 + 13 * q^23 + 8 * q^24 + 38 * q^25 + 9 * q^26 + 23 * q^27 + 11 * q^28 + 15 * q^29 + 6 * q^30 + 31 * q^31 + 24 * q^32 - 8 * q^33 - q^34 + 28 * q^35 + 28 * q^36 + 13 * q^37 + 35 * q^38 + 31 * q^39 + 16 * q^41 + 21 * q^42 + 35 * q^43 - 24 * q^44 + 13 * q^45 + 13 * q^46 + 46 * q^47 + 8 * q^48 + 55 * q^49 + 38 * q^50 + 18 * q^51 + 9 * q^52 + 6 * q^53 + 23 * q^54 + 11 * q^56 + 18 * q^57 + 15 * q^58 + 13 * q^59 + 6 * q^60 + 60 * q^61 + 31 * q^62 + 52 * q^63 + 24 * q^64 - 9 * q^65 - 8 * q^66 + 28 * q^67 - q^68 + 21 * q^69 + 28 * q^70 + 10 * q^71 + 28 * q^72 + 3 * q^73 + 13 * q^74 + 48 * q^75 + 35 * q^76 - 11 * q^77 + 31 * q^78 + 47 * q^79 + 16 * q^81 + 16 * q^82 + 66 * q^83 + 21 * q^84 + 37 * q^85 + 35 * q^86 + 34 * q^87 - 24 * q^88 - 5 * q^89 + 13 * q^90 + q^91 + 13 * q^92 - 16 * q^93 + 46 * q^94 + 9 * q^95 + 8 * q^96 + 24 * q^97 + 55 * q^98 - 28 * 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
$3$	−0.533021	−0.307740	−0.153870	−	0.988091i	$-0.549174\pi$
$3$	−0.533021	−0.307740	−0.153870	+	0.988091i	$0.549174\pi$
$4$	1.00000	0.500000
$5$	−1.76896	−0.791104	−0.395552	−	0.918444i	$-0.629447\pi$
$5$	−1.76896	−0.791104	−0.395552	+	0.918444i	$0.629447\pi$
$6$	−0.533021	−0.217605
$7$	−1.67093	−0.631552	−0.315776	−	0.948834i	$-0.602265\pi$
$7$	−1.67093	−0.631552	−0.315776	+	0.948834i	$0.602265\pi$
$8$	1.00000	0.353553
$9$	−2.71589	−0.905296
$10$	−1.76896	−0.559395
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−0.533021	−0.153870
$13$	0.722697	0.200440	0.100220	−	0.994965i	$-0.468045\pi$
$13$	0.722697	0.200440	0.100220	+	0.994965i	$0.468045\pi$
$14$	−1.67093	−0.446575
$15$	0.942894	0.243454
$16$	1.00000	0.250000
$17$	2.58663	0.627350	0.313675	−	0.949530i	$-0.398440\pi$
$17$	2.58663	0.627350	0.313675	+	0.949530i	$0.398440\pi$
$18$	−2.71589	−0.640141
$19$	−6.87052	−1.57620	−0.788102	−	0.615544i	$-0.788936\pi$
$19$	−6.87052	−1.57620	−0.788102	+	0.615544i	$0.788936\pi$
$20$	−1.76896	−0.395552
$21$	0.890641	0.194354
$22$	−1.00000	−0.213201
$23$	1.81618	0.378700	0.189350	−	0.981910i	$-0.439362\pi$
$23$	1.81618	0.378700	0.189350	+	0.981910i	$0.439362\pi$
$24$	−0.533021	−0.108803
$25$	−1.87077	−0.374155
$26$	0.722697	0.141733
$27$	3.04669	0.586336
$28$	−1.67093	−0.315776
$29$	5.34637	0.992795	0.496398	−	0.868095i	$-0.334656\pi$
$29$	5.34637	0.992795	0.496398	+	0.868095i	$0.334656\pi$
$30$	0.942894	0.172148
$31$	−3.89658	−0.699847	−0.349923	−	0.936778i	$-0.613792\pi$
$31$	−3.89658	−0.699847	−0.349923	+	0.936778i	$0.613792\pi$
$32$	1.00000	0.176777
$33$	0.533021	0.0927871
$34$	2.58663	0.443603
$35$	2.95581	0.499624
$36$	−2.71589	−0.452648
$37$	7.00847	1.15219	0.576093	−	0.817384i	$-0.304577\pi$
$37$	7.00847	1.15219	0.576093	+	0.817384i	$0.304577\pi$
$38$	−6.87052	−1.11454
$39$	−0.385213	−0.0616834
$40$	−1.76896	−0.279697
$41$	−4.36456	−0.681629	−0.340815	−	0.940131i	$-0.610703\pi$
$41$	−4.36456	−0.681629	−0.340815	+	0.940131i	$0.610703\pi$
$42$	0.890641	0.137429
$43$	10.7070	1.63280	0.816401	−	0.577485i	$-0.195966\pi$
$43$	10.7070	1.63280	0.816401	+	0.577485i	$0.195966\pi$
$44$	−1.00000	−0.150756
$45$	4.80430	0.716183
$46$	1.81618	0.267781
$47$	3.79134	0.553024	0.276512	−	0.961010i	$-0.410821\pi$
$47$	3.79134	0.553024	0.276512	+	0.961010i	$0.410821\pi$
$48$	−0.533021	−0.0769350
$49$	−4.20799	−0.601142
$50$	−1.87077	−0.264567
$51$	−1.37873	−0.193061
$52$	0.722697	0.100220
$53$	−8.69006	−1.19367	−0.596836	−	0.802363i	$-0.703576\pi$
$53$	−8.69006	−1.19367	−0.596836	+	0.802363i	$0.703576\pi$
$54$	3.04669	0.414602
$55$	1.76896	0.238527
$56$	−1.67093	−0.223287
$57$	3.66213	0.485061
$58$	5.34637	0.702012
$59$	11.1363	1.44982	0.724910	−	0.688843i	$-0.241881\pi$
$59$	11.1363	1.44982	0.724910	+	0.688843i	$0.241881\pi$
$60$	0.942894	0.121727
$61$	2.11094	0.270278	0.135139	−	0.990827i	$-0.456852\pi$
$61$	2.11094	0.270278	0.135139	+	0.990827i	$0.456852\pi$
$62$	−3.89658	−0.494867
$63$	4.53806	0.571742
$64$	1.00000	0.125000
$65$	−1.27842	−0.158569
$66$	0.533021	0.0656104
$67$	−2.77863	−0.339464	−0.169732	−	0.985490i	$-0.554290\pi$
$67$	−2.77863	−0.339464	−0.169732	+	0.985490i	$0.554290\pi$
$68$	2.58663	0.313675
$69$	−0.968064	−0.116541
$70$	2.95581	0.353287
$71$	−0.488720	−0.0580004	−0.0290002	−	0.999579i	$-0.509232\pi$
$71$	−0.488720	−0.0580004	−0.0290002	+	0.999579i	$0.509232\pi$
$72$	−2.71589	−0.320071
$73$	5.80703	0.679661	0.339831	−	0.940487i	$-0.389630\pi$
$73$	5.80703	0.679661	0.339831	+	0.940487i	$0.389630\pi$
$74$	7.00847	0.814719
$75$	0.997162	0.115142
$76$	−6.87052	−0.788102
$77$	1.67093	0.190420
$78$	−0.385213	−0.0436168
$79$	6.21817	0.699599	0.349800	−	0.936825i	$-0.386250\pi$
$79$	6.21817	0.699599	0.349800	+	0.936825i	$0.386250\pi$
$80$	−1.76896	−0.197776
$81$	6.52371	0.724857
$82$	−4.36456	−0.481985
$83$	10.8971	1.19611	0.598057	−	0.801453i	$-0.295939\pi$
$83$	10.8971	1.19611	0.598057	+	0.801453i	$0.295939\pi$
$84$	0.890641	0.0971769
$85$	−4.57565	−0.496299
$86$	10.7070	1.15457
$87$	−2.84973	−0.305523
$88$	−1.00000	−0.106600
$89$	5.27440	0.559085	0.279542	−	0.960133i	$-0.409817\pi$
$89$	5.27440	0.559085	0.279542	+	0.960133i	$0.409817\pi$
$90$	4.80430	0.506418
$91$	−1.20758	−0.126588
$92$	1.81618	0.189350
$93$	2.07696	0.215371
$94$	3.79134	0.391047
$95$	12.1537	1.24694
$96$	−0.533021	−0.0544013
$97$	17.0282	1.72895	0.864477	−	0.502672i	$-0.167650\pi$
$97$	17.0282	1.72895	0.864477	+	0.502672i	$0.167650\pi$
$98$	−4.20799	−0.425071
$99$	2.71589	0.272957
$100$	−1.87077	−0.187077
$101$	−11.8912	−1.18321	−0.591607	−	0.806227i	$-0.701506\pi$
$101$	−11.8912	−1.18321	−0.591607	+	0.806227i	$0.701506\pi$
$102$	−1.37873	−0.136515
$103$	13.2828	1.30879	0.654397	−	0.756151i	$-0.272922\pi$
$103$	13.2828	1.30879	0.654397	+	0.756151i	$0.272922\pi$
$104$	0.722697	0.0708663
$105$	−1.57551	−0.153754
$106$	−8.69006	−0.844053
$107$	−14.4839	−1.40021	−0.700105	−	0.714040i	$-0.746864\pi$
$107$	−14.4839	−1.40021	−0.700105	+	0.714040i	$0.746864\pi$
$108$	3.04669	0.293168
$109$	−15.4554	−1.48036	−0.740182	−	0.672407i	$-0.765261\pi$
$109$	−15.4554	−1.48036	−0.740182	+	0.672407i	$0.765261\pi$
$110$	1.76896	0.168664
$111$	−3.73567	−0.354574
$112$	−1.67093	−0.157888
$113$	2.27266	0.213794	0.106897	−	0.994270i	$-0.465908\pi$
$113$	2.27266	0.213794	0.106897	+	0.994270i	$0.465908\pi$
$114$	3.66213	0.342990
$115$	−3.21276	−0.299591
$116$	5.34637	0.496398
$117$	−1.96276	−0.181458
$118$	11.1363	1.02518
$119$	−4.32208	−0.396204
$120$	0.942894	0.0860741
$121$	1.00000	0.0909091
$122$	2.11094	0.191115
$123$	2.32640	0.209765
$124$	−3.89658	−0.349923
$125$	12.1541	1.08710
$126$	4.53806	0.404283
$127$	3.96184	0.351557	0.175778	−	0.984430i	$-0.443756\pi$
$127$	3.96184	0.351557	0.175778	+	0.984430i	$0.443756\pi$
$128$	1.00000	0.0883883
$129$	−5.70706	−0.502479
$130$	−1.27842	−0.112125
$131$	14.2677	1.24657	0.623286	−	0.781994i	$-0.285797\pi$
$131$	14.2677	1.24657	0.623286	+	0.781994i	$0.285797\pi$
$132$	0.533021	0.0463935
$133$	11.4802	0.995456
$134$	−2.77863	−0.240037
$135$	−5.38948	−0.463852
$136$	2.58663	0.221802
$137$	13.8481	1.18312	0.591562	−	0.806259i	$-0.298511\pi$
$137$	13.8481	1.18312	0.591562	+	0.806259i	$0.298511\pi$
$138$	−0.968064	−0.0824071
$139$	−6.46482	−0.548339	−0.274169	−	0.961681i	$-0.588403\pi$
$139$	−6.46482	−0.548339	−0.274169	+	0.961681i	$0.588403\pi$
$140$	2.95581	0.249812
$141$	−2.02087	−0.170188
$142$	−0.488720	−0.0410125
$143$	−0.722697	−0.0604350
$144$	−2.71589	−0.226324
$145$	−9.45752	−0.785404
$146$	5.80703	0.480593
$147$	2.24295	0.184995
$148$	7.00847	0.576093
$149$	2.84076	0.232724	0.116362	−	0.993207i	$-0.462877\pi$
$149$	2.84076	0.232724	0.116362	+	0.993207i	$0.462877\pi$
$150$	0.997162	0.0814179
$151$	6.30961	0.513469	0.256734	−	0.966482i	$-0.417353\pi$
$151$	6.30961	0.513469	0.256734	+	0.966482i	$0.417353\pi$
$152$	−6.87052	−0.557272
$153$	−7.02500	−0.567938
$154$	1.67093	0.134647
$155$	6.89291	0.553652
$156$	−0.385213	−0.0308417
$157$	−2.60890	−0.208213	−0.104106	−	0.994566i	$-0.533198\pi$
$157$	−2.60890	−0.208213	−0.104106	+	0.994566i	$0.533198\pi$
$158$	6.21817	0.494691
$159$	4.63199	0.367340
$160$	−1.76896	−0.139849
$161$	−3.03471	−0.239169
$162$	6.52371	0.512551
$163$	−12.9145	−1.01154	−0.505771	−	0.862668i	$-0.668792\pi$
$163$	−12.9145	−1.01154	−0.505771	+	0.862668i	$0.668792\pi$
$164$	−4.36456	−0.340815
$165$	−0.942894	−0.0734042
$166$	10.8971	0.845781
$167$	14.6250	1.13172	0.565859	−	0.824502i	$-0.308545\pi$
$167$	14.6250	1.13172	0.565859	+	0.824502i	$0.308545\pi$
$168$	0.890641	0.0687145
$169$	−12.4777	−0.959824
$170$	−4.57565	−0.350936
$171$	18.6596	1.42693
$172$	10.7070	0.816401
$173$	20.7730	1.57934	0.789671	−	0.613531i	$-0.210251\pi$
$173$	20.7730	1.57934	0.789671	+	0.613531i	$0.210251\pi$
$174$	−2.84973	−0.216037
$175$	3.12593	0.236298
$176$	−1.00000	−0.0753778
$177$	−5.93587	−0.446168
$178$	5.27440	0.395333
$179$	6.58005	0.491816	0.245908	−	0.969293i	$-0.420914\pi$
$179$	6.58005	0.491816	0.245908	+	0.969293i	$0.420914\pi$
$180$	4.80430	0.358092
$181$	−13.2322	−0.983545	−0.491773	−	0.870724i	$-0.663651\pi$
$181$	−13.2322	−0.983545	−0.491773	+	0.870724i	$0.663651\pi$
$182$	−1.20758	−0.0895115
$183$	−1.12518	−0.0831753
$184$	1.81618	0.133891
$185$	−12.3977	−0.911499
$186$	2.07696	0.152290
$187$	−2.58663	−0.189153
$188$	3.79134	0.276512
$189$	−5.09081	−0.370302
$190$	12.1537	0.881721
$191$	−4.33190	−0.313445	−0.156723	−	0.987643i	$-0.550093\pi$
$191$	−4.33190	−0.313445	−0.156723	+	0.987643i	$0.550093\pi$
$192$	−0.533021	−0.0384675
$193$	−9.19096	−0.661580	−0.330790	−	0.943704i	$-0.607315\pi$
$193$	−9.19096	−0.661580	−0.330790	+	0.943704i	$0.607315\pi$
$194$	17.0282	1.22256
$195$	0.681427	0.0487980
$196$	−4.20799	−0.300571
$197$	−1.00000	−0.0712470
$197$	−1.00000	−0.0712470
$198$	2.71589	0.193010
$199$	7.43309	0.526917	0.263459	−	0.964671i	$-0.415137\pi$
$199$	7.43309	0.526917	0.263459	+	0.964671i	$0.415137\pi$
$200$	−1.87077	−0.132284
$201$	1.48107	0.104467
$202$	−11.8912	−0.836658
$203$	−8.93341	−0.627002
$204$	−1.37873	−0.0965303
$205$	7.72073	0.539239
$206$	13.2828	0.925457
$207$	−4.93255	−0.342836
$208$	0.722697	0.0501100
$209$	6.87052	0.475244
$210$	−1.57551	−0.108721
$211$	15.6043	1.07424	0.537122	−	0.843505i	$-0.319512\pi$
$211$	15.6043	1.07424	0.537122	+	0.843505i	$0.319512\pi$
$212$	−8.69006	−0.596836
$213$	0.260498	0.0178490
$214$	−14.4839	−0.990098
$215$	−18.9403	−1.29172
$216$	3.04669	0.207301
$217$	6.51092	0.441990
$218$	−15.4554	−1.04678
$219$	−3.09527	−0.209159
$220$	1.76896	0.119263
$221$	1.86935	0.125746
$222$	−3.73567	−0.250721
$223$	23.3595	1.56427	0.782135	−	0.623110i	$-0.214131\pi$
$223$	23.3595	1.56427	0.782135	+	0.623110i	$0.214131\pi$
$224$	−1.67093	−0.111644
$225$	5.08081	0.338721
$226$	2.27266	0.151175
$227$	5.80846	0.385521	0.192760	−	0.981246i	$-0.438256\pi$
$227$	5.80846	0.385521	0.192760	+	0.981246i	$0.438256\pi$
$228$	3.66213	0.242531
$229$	1.68935	0.111636	0.0558178	−	0.998441i	$-0.482223\pi$
$229$	1.68935	0.111636	0.0558178	+	0.998441i	$0.482223\pi$
$230$	−3.21276	−0.211843
$231$	−0.890641	−0.0585999
$232$	5.34637	0.351006
$233$	17.7056	1.15993	0.579965	−	0.814641i	$-0.303066\pi$
$233$	17.7056	1.15993	0.579965	+	0.814641i	$0.303066\pi$
$234$	−1.96276	−0.128310
$235$	−6.70674	−0.437500
$236$	11.1363	0.724910
$237$	−3.31442	−0.215295
$238$	−4.32208	−0.280159
$239$	−9.18343	−0.594027	−0.297013	−	0.954873i	$-0.595991\pi$
$239$	−9.18343	−0.594027	−0.297013	+	0.954873i	$0.595991\pi$
$240$	0.942894	0.0608636
$241$	22.7784	1.46729	0.733644	−	0.679535i	$-0.237818\pi$
$241$	22.7784	1.46729	0.733644	+	0.679535i	$0.237818\pi$
$242$	1.00000	0.0642824
$243$	−12.6173	−0.809403
$244$	2.11094	0.135139
$245$	7.44378	0.475565
$246$	2.32640	0.148326
$247$	−4.96530	−0.315935
$248$	−3.89658	−0.247433
$249$	−5.80840	−0.368092
$250$	12.1541	0.768695
$251$	23.6863	1.49507	0.747534	−	0.664223i	$-0.231238\pi$
$251$	23.6863	1.49507	0.747534	+	0.664223i	$0.231238\pi$
$252$	4.53806	0.285871
$253$	−1.81618	−0.114182
$254$	3.96184	0.248588
$255$	2.43892	0.152731
$256$	1.00000	0.0625000
$257$	−3.88349	−0.242245	−0.121123	−	0.992638i	$-0.538649\pi$
$257$	−3.88349	−0.242245	−0.121123	+	0.992638i	$0.538649\pi$
$258$	−5.70706	−0.355306
$259$	−11.7107	−0.727666
$260$	−1.27842	−0.0792845
$261$	−14.5201	−0.898774
$262$	14.2677	0.881460
$263$	−5.45200	−0.336185	−0.168092	−	0.985771i	$-0.553761\pi$
$263$	−5.45200	−0.336185	−0.168092	+	0.985771i	$0.553761\pi$
$264$	0.533021	0.0328052
$265$	15.3724	0.944318
$266$	11.4802	0.703894
$267$	−2.81136	−0.172053
$268$	−2.77863	−0.169732
$269$	−26.6701	−1.62611	−0.813053	−	0.582190i	$-0.802196\pi$
$269$	−26.6701	−1.62611	−0.813053	+	0.582190i	$0.802196\pi$
$270$	−5.38948	−0.327993
$271$	−24.1783	−1.46873	−0.734363	−	0.678757i	$-0.762519\pi$
$271$	−24.1783	−1.46873	−0.734363	+	0.678757i	$0.762519\pi$
$272$	2.58663	0.156838
$273$	0.643664	0.0389563
$274$	13.8481	0.836595
$275$	1.87077	0.112812
$276$	−0.968064	−0.0582706
$277$	16.0546	0.964626	0.482313	−	0.875999i	$-0.339797\pi$
$277$	16.0546	0.964626	0.482313	+	0.875999i	$0.339797\pi$
$278$	−6.46482	−0.387734
$279$	10.5827	0.633569
$280$	2.95581	0.176644
$281$	−13.2201	−0.788645	−0.394323	−	0.918972i	$-0.629021\pi$
$281$	−13.2201	−0.788645	−0.394323	+	0.918972i	$0.629021\pi$
$282$	−2.02087	−0.120341
$283$	−29.2409	−1.73819	−0.869097	−	0.494642i	$-0.835299\pi$
$283$	−29.2409	−1.73819	−0.869097	+	0.494642i	$0.835299\pi$
$284$	−0.488720	−0.0290002
$285$	−6.47817	−0.383734
$286$	−0.722697	−0.0427340
$287$	7.29287	0.430485
$288$	−2.71589	−0.160035
$289$	−10.3093	−0.606432
$290$	−9.45752	−0.555365
$291$	−9.07640	−0.532068
$292$	5.80703	0.339831
$293$	4.97229	0.290485	0.145242	−	0.989396i	$-0.453604\pi$
$293$	4.97229	0.290485	0.145242	+	0.989396i	$0.453604\pi$
$294$	2.24295	0.130811
$295$	−19.6997	−1.14696
$296$	7.00847	0.407359
$297$	−3.04669	−0.176787
$298$	2.84076	0.164561
$299$	1.31255	0.0759067
$300$	0.997162	0.0575712
$301$	−17.8907	−1.03120
$302$	6.30961	0.363077
$303$	6.33824	0.364122
$304$	−6.87052	−0.394051
$305$	−3.73417	−0.213818
$306$	−7.02500	−0.401592
$307$	−18.4936	−1.05549	−0.527744	−	0.849403i	$-0.676962\pi$
$307$	−18.4936	−1.05549	−0.527744	+	0.849403i	$0.676962\pi$
$308$	1.67093	0.0952101
$309$	−7.08002	−0.402768
$310$	6.89291	0.391491
$311$	−32.3269	−1.83309	−0.916546	−	0.399929i	$-0.869035\pi$
$311$	−32.3269	−1.83309	−0.916546	+	0.399929i	$0.869035\pi$
$312$	−0.385213	−0.0218084
$313$	28.3296	1.60129	0.800643	−	0.599142i	$-0.204491\pi$
$313$	28.3296	1.60129	0.800643	+	0.599142i	$0.204491\pi$
$314$	−2.60890	−0.147229
$315$	−8.02766	−0.452307
$316$	6.21817	0.349800
$317$	5.39821	0.303193	0.151597	−	0.988442i	$-0.451559\pi$
$317$	5.39821	0.303193	0.151597	+	0.988442i	$0.451559\pi$
$318$	4.63199	0.259749
$319$	−5.34637	−0.299339
$320$	−1.76896	−0.0988880
$321$	7.72022	0.430901
$322$	−3.03471	−0.169118
$323$	−17.7715	−0.988832
$324$	6.52371	0.362429
$325$	−1.35200	−0.0749956
$326$	−12.9145	−0.715268
$327$	8.23808	0.455567
$328$	−4.36456	−0.240992
$329$	−6.33507	−0.349264
$330$	−0.942894	−0.0519046
$331$	0.358618	0.0197114	0.00985571	−	0.999951i	$-0.496863\pi$
$331$	0.358618	0.0197114	0.00985571	+	0.999951i	$0.496863\pi$
$332$	10.8971	0.598057
$333$	−19.0342	−1.04307
$334$	14.6250	0.800246
$335$	4.91529	0.268551
$336$	0.890641	0.0485885
$337$	11.5542	0.629397	0.314698	−	0.949192i	$-0.398097\pi$
$337$	11.5542	0.629397	0.314698	+	0.949192i	$0.398097\pi$
$338$	−12.4777	−0.678698
$339$	−1.21138	−0.0657930
$340$	−4.57565	−0.248150
$341$	3.89658	0.211012
$342$	18.6596	1.00899
$343$	18.7278	1.01120
$344$	10.7070	0.577283
$345$	1.71247	0.0921962
$346$	20.7730	1.11676
$347$	15.0160	0.806098	0.403049	−	0.915178i	$-0.367950\pi$
$347$	15.0160	0.806098	0.403049	+	0.915178i	$0.367950\pi$
$348$	−2.84973	−0.152761
$349$	7.24100	0.387602	0.193801	−	0.981041i	$-0.437918\pi$
$349$	7.24100	0.387602	0.193801	+	0.981041i	$0.437918\pi$
$350$	3.12593	0.167088
$351$	2.20183	0.117525
$352$	−1.00000	−0.0533002
$353$	−28.0903	−1.49510	−0.747548	−	0.664208i	$-0.768769\pi$
$353$	−28.0903	−1.49510	−0.747548	+	0.664208i	$0.768769\pi$
$354$	−5.93587	−0.315488
$355$	0.864527	0.0458843
$356$	5.27440	0.279542
$357$	2.30376	0.121928
$358$	6.58005	0.347767
$359$	−27.7999	−1.46723	−0.733613	−	0.679568i	$-0.762167\pi$
$359$	−27.7999	−1.46723	−0.733613	+	0.679568i	$0.762167\pi$
$360$	4.80430	0.253209
$361$	28.2040	1.48442
$362$	−13.2322	−0.695471
$363$	−0.533021	−0.0279764
$364$	−1.20758	−0.0632942
$365$	−10.2724	−0.537683
$366$	−1.12518	−0.0588138
$367$	7.07544	0.369335	0.184667	−	0.982801i	$-0.440879\pi$
$367$	7.07544	0.369335	0.184667	+	0.982801i	$0.440879\pi$
$368$	1.81618	0.0946750
$369$	11.8536	0.617076
$370$	−12.3977	−0.644527
$371$	14.5205	0.753866
$372$	2.07696	0.107685
$373$	−18.9348	−0.980406	−0.490203	−	0.871608i	$-0.663077\pi$
$373$	−18.9348	−0.980406	−0.490203	+	0.871608i	$0.663077\pi$
$374$	−2.58663	−0.133751
$375$	−6.47841	−0.334544
$376$	3.79134	0.195524
$377$	3.86380	0.198996
$378$	−5.09081	−0.261843
$379$	5.04858	0.259328	0.129664	−	0.991558i	$-0.458610\pi$
$379$	5.04858	0.259328	0.129664	+	0.991558i	$0.458610\pi$
$380$	12.1537	0.623471
$381$	−2.11175	−0.108188
$382$	−4.33190	−0.221639
$383$	6.41893	0.327992	0.163996	−	0.986461i	$-0.447562\pi$
$383$	6.41893	0.327992	0.163996	+	0.986461i	$0.447562\pi$
$384$	−0.533021	−0.0272006
$385$	−2.95581	−0.150642
$386$	−9.19096	−0.467808
$387$	−29.0790	−1.47817
$388$	17.0282	0.864477
$389$	−13.6464	−0.691902	−0.345951	−	0.938253i	$-0.612444\pi$
$389$	−13.6464	−0.691902	−0.345951	+	0.938253i	$0.612444\pi$
$390$	0.681427	0.0345054
$391$	4.69779	0.237578
$392$	−4.20799	−0.212536
$393$	−7.60497	−0.383620
$394$	−1.00000	−0.0503793
$395$	−10.9997	−0.553456
$396$	2.71589	0.136479
$397$	36.9795	1.85595	0.927974	−	0.372646i	$-0.121549\pi$
$397$	36.9795	1.85595	0.927974	+	0.372646i	$0.121549\pi$
$398$	7.43309	0.372587
$399$	−6.11917	−0.306342
$400$	−1.87077	−0.0935387
$401$	2.05910	0.102827	0.0514133	−	0.998677i	$-0.483627\pi$
$401$	2.05910	0.102827	0.0514133	+	0.998677i	$0.483627\pi$
$402$	1.48107	0.0738691
$403$	−2.81605	−0.140277
$404$	−11.8912	−0.591607
$405$	−11.5402	−0.573437
$406$	−8.93341	−0.443357
$407$	−7.00847	−0.347397
$408$	−1.37873	−0.0682573
$409$	−8.63508	−0.426977	−0.213489	−	0.976946i	$-0.568483\pi$
$409$	−8.63508	−0.426977	−0.213489	+	0.976946i	$0.568483\pi$
$410$	7.72073	0.381300
$411$	−7.38134	−0.364095
$412$	13.2828	0.654397
$413$	−18.6080	−0.915638
$414$	−4.93255	−0.242422
$415$	−19.2766	−0.946251
$416$	0.722697	0.0354331
$417$	3.44589	0.168746
$418$	6.87052	0.336048
$419$	28.5561	1.39506	0.697529	−	0.716557i	$-0.254283\pi$
$419$	28.5561	1.39506	0.697529	+	0.716557i	$0.254283\pi$
$420$	−1.57551	−0.0768771
$421$	−4.15589	−0.202546	−0.101273	−	0.994859i	$-0.532292\pi$
$421$	−4.15589	−0.202546	−0.101273	+	0.994859i	$0.532292\pi$
$422$	15.6043	0.759605
$423$	−10.2969	−0.500651
$424$	−8.69006	−0.422027
$425$	−4.83900	−0.234726
$426$	0.260498	0.0126212
$427$	−3.52723	−0.170695
$428$	−14.4839	−0.700105
$429$	0.385213	0.0185982
$430$	−18.9403	−0.913382
$431$	41.3657	1.99251	0.996257	−	0.0864355i	$-0.0275476\pi$
$431$	41.3657	1.99251	0.996257	+	0.0864355i	$0.0275476\pi$
$432$	3.04669	0.146584
$433$	16.8923	0.811791	0.405895	−	0.913920i	$-0.366960\pi$
$433$	16.8923	0.811791	0.405895	+	0.913920i	$0.366960\pi$
$434$	6.51092	0.312534
$435$	5.04106	0.241700
$436$	−15.4554	−0.740182
$437$	−12.4781	−0.596909
$438$	−3.09527	−0.147898
$439$	−32.0222	−1.52834	−0.764168	−	0.645017i	$-0.776850\pi$
$439$	−32.0222	−1.52834	−0.764168	+	0.645017i	$0.776850\pi$
$440$	1.76896	0.0843320
$441$	11.4284	0.544211
$442$	1.86935	0.0889159
$443$	−0.483757	−0.0229840	−0.0114920	−	0.999934i	$-0.503658\pi$
$443$	−0.483757	−0.0229840	−0.0114920	+	0.999934i	$0.503658\pi$
$444$	−3.73567	−0.177287
$445$	−9.33021	−0.442294
$446$	23.3595	1.10611
$447$	−1.51419	−0.0716186
$448$	−1.67093	−0.0789440
$449$	−30.9802	−1.46205	−0.731023	−	0.682352i	$-0.760957\pi$
$449$	−30.9802	−1.46205	−0.731023	+	0.682352i	$0.760957\pi$
$450$	5.08081	0.239512
$451$	4.36456	0.205519
$452$	2.27266	0.106897
$453$	−3.36315	−0.158015
$454$	5.80846	0.272604
$455$	2.13616	0.100145
$456$	3.66213	0.171495
$457$	26.7574	1.25166	0.625829	−	0.779960i	$-0.284761\pi$
$457$	26.7574	1.25166	0.625829	+	0.779960i	$0.284761\pi$
$458$	1.68935	0.0789383
$459$	7.88066	0.367838
$460$	−3.21276	−0.149796
$461$	−21.1498	−0.985047	−0.492523	−	0.870299i	$-0.663925\pi$
$461$	−21.1498	−0.985047	−0.492523	+	0.870299i	$0.663925\pi$
$462$	−0.890641	−0.0414364
$463$	35.1465	1.63339	0.816697	−	0.577067i	$-0.195803\pi$
$463$	35.1465	1.63339	0.816697	+	0.577067i	$0.195803\pi$
$464$	5.34637	0.248199
$465$	−3.67407	−0.170381
$466$	17.7056	0.820195
$467$	6.75697	0.312675	0.156338	−	0.987704i	$-0.450031\pi$
$467$	6.75697	0.312675	0.156338	+	0.987704i	$0.450031\pi$
$468$	−1.96276	−0.0907288
$469$	4.64290	0.214389
$470$	−6.70674	−0.309359
$471$	1.39060	0.0640754
$472$	11.1363	0.512589
$473$	−10.7070	−0.492309
$474$	−3.31442	−0.152236
$475$	12.8532	0.589744
$476$	−4.32208	−0.198102
$477$	23.6012	1.08063
$478$	−9.18343	−0.420040
$479$	−10.8763	−0.496949	−0.248474	−	0.968638i	$-0.579929\pi$
$479$	−10.8763	−0.496949	−0.248474	+	0.968638i	$0.579929\pi$
$480$	0.942894	0.0430370
$481$	5.06500	0.230944
$482$	22.7784	1.03753
$483$	1.61757	0.0736019
$484$	1.00000	0.0454545
$485$	−30.1223	−1.36778
$486$	−12.6173	−0.572335
$487$	12.7646	0.578421	0.289211	−	0.957265i	$-0.406607\pi$
$487$	12.7646	0.578421	0.289211	+	0.957265i	$0.406607\pi$
$488$	2.11094	0.0955577
$489$	6.88370	0.311292
$490$	7.44378	0.336276
$491$	5.17892	0.233721	0.116861	−	0.993148i	$-0.462717\pi$
$491$	5.17892	0.233721	0.116861	+	0.993148i	$0.462717\pi$
$492$	2.32640	0.104882
$493$	13.8291	0.622830
$494$	−4.96530	−0.223399
$495$	−4.80430	−0.215937
$496$	−3.89658	−0.174962
$497$	0.816617	0.0366303
$498$	−5.80840	−0.260281
$499$	37.7912	1.69177	0.845883	−	0.533369i	$-0.179074\pi$
$499$	37.7912	1.69177	0.845883	+	0.533369i	$0.179074\pi$
$500$	12.1541	0.543550
$501$	−7.79545	−0.348275
$502$	23.6863	1.05717
$503$	−20.1829	−0.899911	−0.449956	−	0.893051i	$-0.648560\pi$
$503$	−20.1829	−0.899911	−0.449956	+	0.893051i	$0.648560\pi$
$504$	4.53806	0.202141
$505$	21.0350	0.936045
$506$	−1.81618	−0.0807391
$507$	6.65088	0.295376
$508$	3.96184	0.175778
$509$	13.6008	0.602843	0.301421	−	0.953491i	$-0.402539\pi$
$509$	13.6008	0.602843	0.301421	+	0.953491i	$0.402539\pi$
$510$	2.43892	0.107997
$511$	−9.70314	−0.429242
$512$	1.00000	0.0441942
$513$	−20.9323	−0.924185
$514$	−3.88349	−0.171293
$515$	−23.4968	−1.03539
$516$	−5.70706	−0.251239
$517$	−3.79134	−0.166743
$518$	−11.7107	−0.514537
$519$	−11.0724	−0.486026
$520$	−1.27842	−0.0560626
$521$	−28.1874	−1.23491	−0.617455	−	0.786606i	$-0.711836\pi$
$521$	−28.1874	−1.23491	−0.617455	+	0.786606i	$0.711836\pi$
$522$	−14.5201	−0.635529
$523$	31.5482	1.37951	0.689753	−	0.724044i	$-0.257719\pi$
$523$	31.5482	1.37951	0.689753	+	0.724044i	$0.257719\pi$
$524$	14.2677	0.623286
$525$	−1.66619	−0.0727184
$526$	−5.45200	−0.237718
$527$	−10.0790	−0.439049
$528$	0.533021	0.0231968
$529$	−19.7015	−0.856586
$530$	15.3724	0.667734
$531$	−30.2449	−1.31252
$532$	11.4802	0.497728
$533$	−3.15425	−0.136626
$534$	−2.81136	−0.121660
$535$	25.6215	1.10771
$536$	−2.77863	−0.120019
$537$	−3.50731	−0.151351
$538$	−26.6701	−1.14983
$539$	4.20799	0.181251
$540$	−5.38948	−0.231926
$541$	28.6806	1.23307	0.616537	−	0.787326i	$-0.288535\pi$
$541$	28.6806	1.23307	0.616537	+	0.787326i	$0.288535\pi$
$542$	−24.1783	−1.03855
$543$	7.05307	0.302676
$544$	2.58663	0.110901
$545$	27.3401	1.17112
$546$	0.643664	0.0275463
$547$	−36.7768	−1.57246	−0.786231	−	0.617932i	$-0.787971\pi$
$547$	−36.7768	−1.57246	−0.786231	+	0.617932i	$0.787971\pi$
$548$	13.8481	0.591562
$549$	−5.73307	−0.244682
$550$	1.87077	0.0797700
$551$	−36.7323	−1.56485
$552$	−0.968064	−0.0412035
$553$	−10.3901	−0.441834
$554$	16.0546	0.682093
$555$	6.60825	0.280505
$556$	−6.46482	−0.274169
$557$	12.9746	0.549750	0.274875	−	0.961480i	$-0.411363\pi$
$557$	12.9746	0.549750	0.274875	+	0.961480i	$0.411363\pi$
$558$	10.5827	0.448001
$559$	7.73792	0.327279
$560$	2.95581	0.124906
$561$	1.37873	0.0582100
$562$	−13.2201	−0.557656
$563$	1.29134	0.0544234	0.0272117	−	0.999630i	$-0.491337\pi$
$563$	1.29134	0.0544234	0.0272117	+	0.999630i	$0.491337\pi$
$564$	−2.02087	−0.0850939
$565$	−4.02025	−0.169133
$566$	−29.2409	−1.22909
$567$	−10.9007	−0.457785
$568$	−0.488720	−0.0205062
$569$	−4.70503	−0.197245	−0.0986225	−	0.995125i	$-0.531444\pi$
$569$	−4.70503	−0.197245	−0.0986225	+	0.995125i	$0.531444\pi$
$570$	−6.47817	−0.271341
$571$	−14.0394	−0.587529	−0.293764	−	0.955878i	$-0.594908\pi$
$571$	−14.0394	−0.587529	−0.293764	+	0.955878i	$0.594908\pi$
$572$	−0.722697	−0.0302175
$573$	2.30899	0.0964596
$574$	7.29287	0.304399
$575$	−3.39766	−0.141692
$576$	−2.71589	−0.113162
$577$	−25.0610	−1.04330	−0.521652	−	0.853159i	$-0.674684\pi$
$577$	−25.0610	−1.04330	−0.521652	+	0.853159i	$0.674684\pi$
$578$	−10.3093	−0.428812
$579$	4.89898	0.203595
$580$	−9.45752	−0.392702
$581$	−18.2083	−0.755409
$582$	−9.07640	−0.376229
$583$	8.69006	0.359906
$584$	5.80703	0.240297
$585$	3.47206	0.143552
$586$	4.97229	0.205404
$587$	13.3493	0.550986	0.275493	−	0.961303i	$-0.411159\pi$
$587$	13.3493	0.550986	0.275493	+	0.961303i	$0.411159\pi$
$588$	2.24295	0.0924976
$589$	26.7715	1.10310
$590$	−19.6997	−0.811022
$591$	0.533021	0.0219256
$592$	7.00847	0.288047
$593$	−5.04672	−0.207244	−0.103622	−	0.994617i	$-0.533043\pi$
$593$	−5.04672	−0.207244	−0.103622	+	0.994617i	$0.533043\pi$
$594$	−3.04669	−0.125007
$595$	7.64560	0.313439
$596$	2.84076	0.116362
$597$	−3.96199	−0.162154
$598$	1.31255	0.0536741
$599$	−7.29282	−0.297977	−0.148988	−	0.988839i	$-0.547602\pi$
$599$	−7.29282	−0.297977	−0.148988	+	0.988839i	$0.547602\pi$
$600$	0.997162	0.0407090
$601$	−0.0119987	−0.000489436 0	−0.000244718	−	1.00000i	$-0.500078\pi$
$601$	−0.0119987	−0.000489436 0	−0.000244718		1.00000i	$0.500078\pi$
$602$	−17.8907	−0.729169
$603$	7.54645	0.307315
$604$	6.30961	0.256734
$605$	−1.76896	−0.0719185
$606$	6.33824	0.257473
$607$	24.8080	1.00693	0.503463	−	0.864017i	$-0.332059\pi$
$607$	24.8080	1.00693	0.503463	+	0.864017i	$0.332059\pi$
$608$	−6.87052	−0.278636
$609$	4.76169	0.192954
$610$	−3.73417	−0.151192
$611$	2.73999	0.110848
$612$	−7.02500	−0.283969
$613$	−0.909580	−0.0367376	−0.0183688	−	0.999831i	$-0.505847\pi$
$613$	−0.909580	−0.0367376	−0.0183688	+	0.999831i	$0.505847\pi$
$614$	−18.4936	−0.746343
$615$	−4.11532	−0.165946
$616$	1.67093	0.0673237
$617$	−42.5839	−1.71436	−0.857182	−	0.515014i	$-0.827787\pi$
$617$	−42.5839	−1.71436	−0.857182	+	0.515014i	$0.827787\pi$
$618$	−7.08002	−0.284800
$619$	−32.5987	−1.31025	−0.655127	−	0.755519i	$-0.727385\pi$
$619$	−32.5987	−1.31025	−0.655127	+	0.755519i	$0.727385\pi$
$620$	6.89291	0.276826
$621$	5.53334	0.222045
$622$	−32.3269	−1.29619
$623$	−8.81315	−0.353091
$624$	−0.385213	−0.0154209
$625$	−12.1463	−0.485854
$626$	28.3296	1.13228
$627$	−3.66213	−0.146251
$628$	−2.60890	−0.104106
$629$	18.1283	0.722824
$630$	−8.02766	−0.319830
$631$	−42.0234	−1.67292	−0.836462	−	0.548024i	$-0.815380\pi$
$631$	−42.0234	−1.67292	−0.836462	+	0.548024i	$0.815380\pi$
$632$	6.21817	0.247346
$633$	−8.31741	−0.330588
$634$	5.39821	0.214390
$635$	−7.00835	−0.278118
$636$	4.63199	0.183670
$637$	−3.04110	−0.120493
$638$	−5.34637	−0.211665
$639$	1.32731	0.0525075
$640$	−1.76896	−0.0699244
$641$	1.94995	0.0770183	0.0385092	−	0.999258i	$-0.487739\pi$
$641$	1.94995	0.0770183	0.0385092	+	0.999258i	$0.487739\pi$
$642$	7.72022	0.304693
$643$	48.2028	1.90093	0.950467	−	0.310825i	$-0.100605\pi$
$643$	48.2028	1.90093	0.950467	+	0.310825i	$0.100605\pi$
$644$	−3.03471	−0.119584
$645$	10.0956	0.397513
$646$	−17.7715	−0.699210
$647$	36.5038	1.43511	0.717555	−	0.696501i	$-0.245261\pi$
$647$	36.5038	1.43511	0.717555	+	0.696501i	$0.245261\pi$
$648$	6.52371	0.256276
$649$	−11.1363	−0.437137
$650$	−1.35200	−0.0530299
$651$	−3.47046	−0.136018
$652$	−12.9145	−0.505771
$653$	−39.7289	−1.55471	−0.777356	−	0.629061i	$-0.783440\pi$
$653$	−39.7289	−1.55471	−0.777356	+	0.629061i	$0.783440\pi$
$654$	8.23808	0.322135
$655$	−25.2390	−0.986168
$656$	−4.36456	−0.170407
$657$	−15.7712	−0.615295
$658$	−6.33507	−0.246967
$659$	28.8117	1.12235	0.561173	−	0.827698i	$-0.310350\pi$
$659$	28.8117	1.12235	0.561173	+	0.827698i	$0.310350\pi$
$660$	−0.942894	−0.0367021
$661$	23.8849	0.929016	0.464508	−	0.885569i	$-0.346231\pi$
$661$	23.8849	0.929016	0.464508	+	0.885569i	$0.346231\pi$
$662$	0.358618	0.0139381
$663$	−0.996403	−0.0386971
$664$	10.8971	0.422890
$665$	−20.3080	−0.787509
$666$	−19.0342	−0.737562
$667$	9.70997	0.375972
$668$	14.6250	0.565859
$669$	−12.4511	−0.481388
$670$	4.91529	0.189894
$671$	−2.11094	−0.0814919
$672$	0.890641	0.0343572
$673$	−48.8278	−1.88217	−0.941087	−	0.338164i	$-0.890194\pi$
$673$	−48.8278	−1.88217	−0.941087	+	0.338164i	$0.890194\pi$
$674$	11.5542	0.445051
$675$	−5.69967	−0.219380
$676$	−12.4777	−0.479912
$677$	−12.4684	−0.479201	−0.239601	−	0.970872i	$-0.577017\pi$
$677$	−12.4684	−0.479201	−0.239601	+	0.970872i	$0.577017\pi$
$678$	−1.21138	−0.0465227
$679$	−28.4530	−1.09193
$680$	−4.57565	−0.175468
$681$	−3.09603	−0.118640
$682$	3.89658	0.149208
$683$	2.01005	0.0769126	0.0384563	−	0.999260i	$-0.487756\pi$
$683$	2.01005	0.0769126	0.0384563	+	0.999260i	$0.487756\pi$
$684$	18.6596	0.713466
$685$	−24.4968	−0.935974
$686$	18.7278	0.715030
$687$	−0.900462	−0.0343548
$688$	10.7070	0.408201
$689$	−6.28028	−0.239260
$690$	1.71247	0.0651925
$691$	37.8089	1.43832	0.719160	−	0.694845i	$-0.244527\pi$
$691$	37.8089	1.43832	0.719160	+	0.694845i	$0.244527\pi$
$692$	20.7730	0.789671
$693$	−4.53806	−0.172387
$694$	15.0160	0.569998
$695$	11.4360	0.433793
$696$	−2.84973	−0.108019
$697$	−11.2895	−0.427620
$698$	7.24100	0.274076
$699$	−9.43745	−0.356957
$700$	3.12593	0.118149
$701$	32.1738	1.21519	0.607594	−	0.794248i	$-0.292135\pi$
$701$	32.1738	1.21519	0.607594	+	0.794248i	$0.292135\pi$
$702$	2.20183	0.0831028
$703$	−48.1518	−1.81608
$704$	−1.00000	−0.0376889
$705$	3.57484	0.134636
$706$	−28.0903	−1.05719
$707$	19.8693	0.747261
$708$	−5.93587	−0.223084
$709$	−18.1524	−0.681728	−0.340864	−	0.940113i	$-0.610720\pi$
$709$	−18.1524	−0.681728	−0.340864	+	0.940113i	$0.610720\pi$
$710$	0.864527	0.0324451
$711$	−16.8879	−0.633345
$712$	5.27440	0.197666
$713$	−7.07690	−0.265032
$714$	2.30376	0.0862161
$715$	1.27842	0.0478103
$716$	6.58005	0.245908
$717$	4.89496	0.182806
$718$	−27.7999	−1.03748
$719$	22.4938	0.838876	0.419438	−	0.907784i	$-0.362227\pi$
$719$	22.4938	0.838876	0.419438	+	0.907784i	$0.362227\pi$
$720$	4.80430	0.179046
$721$	−22.1947	−0.826572
$722$	28.2040	1.04964
$723$	−12.1414	−0.451543
$724$	−13.2322	−0.491773
$725$	−10.0018	−0.371459
$726$	−0.533021	−0.0197823
$727$	−4.45069	−0.165067	−0.0825335	−	0.996588i	$-0.526301\pi$
$727$	−4.45069	−0.165067	−0.0825335	+	0.996588i	$0.526301\pi$
$728$	−1.20758	−0.0447558
$729$	−12.8458	−0.475771
$730$	−10.2724	−0.380199
$731$	27.6951	1.02434
$732$	−1.12518	−0.0415877
$733$	14.3915	0.531564	0.265782	−	0.964033i	$-0.414370\pi$
$733$	14.3915	0.531564	0.265782	+	0.964033i	$0.414370\pi$
$734$	7.07544	0.261159
$735$	−3.96769	−0.146350
$736$	1.81618	0.0669454
$737$	2.77863	0.102352
$738$	11.8536	0.436339
$739$	8.29983	0.305314	0.152657	−	0.988279i	$-0.451217\pi$
$739$	8.29983	0.305314	0.152657	+	0.988279i	$0.451217\pi$
$740$	−12.3977	−0.455749
$741$	2.64661	0.0972257
$742$	14.5205	0.533064
$743$	2.08004	0.0763092	0.0381546	−	0.999272i	$-0.487852\pi$
$743$	2.08004	0.0763092	0.0381546	+	0.999272i	$0.487852\pi$
$744$	2.07696	0.0761451
$745$	−5.02520	−0.184109
$746$	−18.9348	−0.693252
$747$	−29.5954	−1.08284
$748$	−2.58663	−0.0945766
$749$	24.2016	0.884306
$750$	−6.47841	−0.236558
$751$	24.9299	0.909705	0.454852	−	0.890567i	$-0.349692\pi$
$751$	24.9299	0.909705	0.454852	+	0.890567i	$0.349692\pi$
$752$	3.79134	0.138256
$753$	−12.6253	−0.460092
$754$	3.86380	0.140711
$755$	−11.1615	−0.406207
$756$	−5.09081	−0.185151
$757$	29.8720	1.08572	0.542858	−	0.839824i	$-0.317342\pi$
$757$	29.8720	1.08572	0.542858	+	0.839824i	$0.317342\pi$
$758$	5.04858	0.183373
$759$	0.968064	0.0351385
$760$	12.1537	0.440860
$761$	3.31137	0.120037	0.0600186	−	0.998197i	$-0.480884\pi$
$761$	3.31137	0.120037	0.0600186	+	0.998197i	$0.480884\pi$
$762$	−2.11175	−0.0765005
$763$	25.8250	0.934927
$764$	−4.33190	−0.156723
$765$	12.4270	0.449298
$766$	6.41893	0.231926
$767$	8.04816	0.290602
$768$	−0.533021	−0.0192337
$769$	−0.630093	−0.0227217	−0.0113609	−	0.999935i	$-0.503616\pi$
$769$	−0.630093	−0.0227217	−0.0113609	+	0.999935i	$0.503616\pi$
$770$	−2.95581	−0.106520
$771$	2.06998	0.0745486
$772$	−9.19096	−0.330790
$773$	−36.1471	−1.30012	−0.650061	−	0.759882i	$-0.725257\pi$
$773$	−36.1471	−1.30012	−0.650061	+	0.759882i	$0.725257\pi$
$774$	−29.0790	−1.04522
$775$	7.28962	0.261851
$776$	17.0282	0.611278
$777$	6.24204	0.223932
$778$	−13.6464	−0.489249
$779$	29.9868	1.07439
$780$	0.681427	0.0243990
$781$	0.488720	0.0174878
$782$	4.69779	0.167993
$783$	16.2887	0.582111
$784$	−4.20799	−0.150285
$785$	4.61504	0.164718
$786$	−7.60497	−0.271260
$787$	−18.4380	−0.657243	−0.328622	−	0.944462i	$-0.606584\pi$
$787$	−18.4380	−0.657243	−0.328622	+	0.944462i	$0.606584\pi$
$788$	−1.00000	−0.0356235
$789$	2.90603	0.103457
$790$	−10.9997	−0.391352
$791$	−3.79746	−0.135022
$792$	2.71589	0.0965049
$793$	1.52557	0.0541745
$794$	36.9795	1.31235
$795$	−8.19381	−0.290604
$796$	7.43309	0.263459
$797$	3.52734	0.124945	0.0624724	−	0.998047i	$-0.480101\pi$
$797$	3.52734	0.124945	0.0624724	+	0.998047i	$0.480101\pi$
$798$	−6.11917	−0.216616
$799$	9.80681	0.346940
$800$	−1.87077	−0.0661418
$801$	−14.3247	−0.506137
$802$	2.05910	0.0727094
$803$	−5.80703	−0.204926
$804$	1.48107	0.0522333
$805$	5.36829	0.189208
$806$	−2.81605	−0.0991911
$807$	14.2157	0.500418
$808$	−11.8912	−0.418329
$809$	−41.5712	−1.46157	−0.730783	−	0.682610i	$-0.760845\pi$
$809$	−41.5712	−1.46157	−0.730783	+	0.682610i	$0.760845\pi$
$810$	−11.5402	−0.405481
$811$	48.4719	1.70208	0.851040	−	0.525101i	$-0.175972\pi$
$811$	48.4719	1.70208	0.851040	+	0.525101i	$0.175972\pi$
$812$	−8.93341	−0.313501
$813$	12.8875	0.451986
$814$	−7.00847	−0.245647
$815$	22.8453	0.800235
$816$	−1.37873	−0.0482652
$817$	−73.5626	−2.57363
$818$	−8.63508	−0.301918
$819$	3.27964	0.114600
$820$	7.72073	0.269620
$821$	53.1281	1.85418	0.927092	−	0.374834i	$-0.122300\pi$
$821$	53.1281	1.85418	0.927092	+	0.374834i	$0.122300\pi$
$822$	−7.38134	−0.257454
$823$	50.7200	1.76799	0.883993	−	0.467499i	$-0.154845\pi$
$823$	50.7200	1.76799	0.883993	+	0.467499i	$0.154845\pi$
$824$	13.2828	0.462729
$825$	−0.997162	−0.0347167
$826$	−18.6080	−0.647454
$827$	−8.19799	−0.285072	−0.142536	−	0.989790i	$-0.545526\pi$
$827$	−8.19799	−0.285072	−0.142536	+	0.989790i	$0.545526\pi$
$828$	−4.93255	−0.171418
$829$	37.9962	1.31966	0.659831	−	0.751414i	$-0.270628\pi$
$829$	37.9962	1.31966	0.659831	+	0.751414i	$0.270628\pi$
$830$	−19.2766	−0.669101
$831$	−8.55743	−0.296854
$832$	0.722697	0.0250550
$833$	−10.8845	−0.377126
$834$	3.44589	0.119321
$835$	−25.8711	−0.895307
$836$	6.87052	0.237622
$837$	−11.8717	−0.410345
$838$	28.5561	0.986455
$839$	19.5421	0.674667	0.337334	−	0.941385i	$-0.390475\pi$
$839$	19.5421	0.674667	0.337334	+	0.941385i	$0.390475\pi$
$840$	−1.57551	−0.0543603
$841$	−0.416373	−0.0143577
$842$	−4.15589	−0.143222
$843$	7.04659	0.242698
$844$	15.6043	0.537122
$845$	22.0726	0.759320
$846$	−10.2969	−0.354014
$847$	−1.67093	−0.0574139
$848$	−8.69006	−0.298418
$849$	15.5860	0.534911
$850$	−4.83900	−0.165976
$851$	12.7287	0.436333
$852$	0.260498	0.00892451
$853$	−56.5480	−1.93617	−0.968083	−	0.250631i	$-0.919362\pi$
$853$	−56.5480	−1.93617	−0.968083	+	0.250631i	$0.919362\pi$
$854$	−3.52723	−0.120699
$855$	−33.0080	−1.12885
$856$	−14.4839	−0.495049
$857$	−3.78637	−0.129340	−0.0646700	−	0.997907i	$-0.520599\pi$
$857$	−3.78637	−0.129340	−0.0646700	+	0.997907i	$0.520599\pi$
$858$	0.385213	0.0131509
$859$	44.2576	1.51005	0.755025	−	0.655697i	$-0.227625\pi$
$859$	44.2576	1.51005	0.755025	+	0.655697i	$0.227625\pi$
$860$	−18.9403	−0.645858
$861$	−3.88725	−0.132477
$862$	41.3657	1.40892
$863$	13.8868	0.472711	0.236355	−	0.971667i	$-0.424047\pi$
$863$	13.8868	0.472711	0.236355	+	0.971667i	$0.424047\pi$
$864$	3.04669	0.103650
$865$	−36.7466	−1.24942
$866$	16.8923	0.574023
$867$	5.49510	0.186623
$868$	6.51092	0.220995
$869$	−6.21817	−0.210937
$870$	5.04106	0.170908
$871$	−2.00811	−0.0680422
$872$	−15.4554	−0.523388
$873$	−46.2468	−1.56522
$874$	−12.4781	−0.422078
$875$	−20.3087	−0.686560
$876$	−3.09527	−0.104579
$877$	32.3026	1.09078	0.545391	−	0.838182i	$-0.316381\pi$
$877$	32.3026	1.09078	0.545391	+	0.838182i	$0.316381\pi$
$878$	−32.0222	−1.08070
$879$	−2.65034	−0.0893937
$880$	1.76896	0.0596317
$881$	−33.2382	−1.11982	−0.559912	−	0.828552i	$-0.689165\pi$
$881$	−33.2382	−1.11982	−0.559912	+	0.828552i	$0.689165\pi$
$882$	11.4284	0.384815
$883$	25.9656	0.873813	0.436906	−	0.899507i	$-0.356074\pi$
$883$	25.9656	0.873813	0.436906	+	0.899507i	$0.356074\pi$
$884$	1.86935	0.0628730
$885$	10.5003	0.352965
$886$	−0.483757	−0.0162521
$887$	−25.4802	−0.855542	−0.427771	−	0.903887i	$-0.640701\pi$
$887$	−25.4802	−0.855542	−0.427771	+	0.903887i	$0.640701\pi$
$888$	−3.73567	−0.125361
$889$	−6.61997	−0.222027
$890$	−9.33021	−0.312749
$891$	−6.52371	−0.218553
$892$	23.3595	0.782135
$893$	−26.0485	−0.871680
$894$	−1.51419	−0.0506420
$895$	−11.6399	−0.389078
$896$	−1.67093	−0.0558219
$897$	−0.699617	−0.0233595
$898$	−30.9802	−1.03382
$899$	−20.8326	−0.694805
$900$	5.08081	0.169360
$901$	−22.4780	−0.748850
$902$	4.36456	0.145324
$903$	9.53610	0.317342
$904$	2.27266	0.0755876
$905$	23.4073	0.778086
$906$	−3.36315	−0.111733
$907$	−44.9988	−1.49416	−0.747081	−	0.664733i	$-0.768545\pi$
$907$	−44.9988	−1.49416	−0.747081	+	0.664733i	$0.768545\pi$
$908$	5.80846	0.192760
$909$	32.2950	1.07116
$910$	2.13616	0.0708129
$911$	−14.2287	−0.471419	−0.235709	−	0.971824i	$-0.575741\pi$
$911$	−14.2287	−0.471419	−0.235709	+	0.971824i	$0.575741\pi$
$912$	3.66213	0.121265
$913$	−10.8971	−0.360642
$914$	26.7574	0.885056
$915$	1.99039	0.0658003
$916$	1.68935	0.0558178
$917$	−23.8403	−0.787276
$918$	7.88066	0.260101
$919$	−22.3401	−0.736933	−0.368466	−	0.929641i	$-0.620117\pi$
$919$	−22.3401	−0.736933	−0.368466	+	0.929641i	$0.620117\pi$
$920$	−3.21276	−0.105921
$921$	9.85751	0.324816
$922$	−21.1498	−0.696533
$923$	−0.353196	−0.0116256
$924$	−0.890641	−0.0293000
$925$	−13.1113	−0.431096
$926$	35.1465	1.15498
$927$	−36.0746	−1.18485
$928$	5.34637	0.175503
$929$	25.3511	0.831744	0.415872	−	0.909423i	$-0.363476\pi$
$929$	25.3511	0.831744	0.415872	+	0.909423i	$0.363476\pi$
$930$	−3.67407	−0.120477
$931$	28.9111	0.947522
$932$	17.7056	0.579965
$933$	17.2309	0.564116
$934$	6.75697	0.221095
$935$	4.57565	0.149640
$936$	−1.96276	−0.0641550
$937$	−15.0208	−0.490709	−0.245354	−	0.969433i	$-0.578904\pi$
$937$	−15.0208	−0.490709	−0.245354	+	0.969433i	$0.578904\pi$
$938$	4.64290	0.151596
$939$	−15.1003	−0.492780
$940$	−6.70674	−0.218750
$941$	−3.66239	−0.119390	−0.0596952	−	0.998217i	$-0.519013\pi$
$941$	−3.66239	−0.119390	−0.0596952	+	0.998217i	$0.519013\pi$
$942$	1.39060	0.0453082
$943$	−7.92683	−0.258133
$944$	11.1363	0.362455
$945$	9.00544	0.292947
$946$	−10.7070	−0.348115
$947$	−33.5666	−1.09077	−0.545383	−	0.838187i	$-0.683616\pi$
$947$	−33.5666	−1.09077	−0.545383	+	0.838187i	$0.683616\pi$
$948$	−3.31442	−0.107647
$949$	4.19672	0.136231
$950$	12.8532	0.417012
$951$	−2.87736	−0.0933047
$952$	−4.32208	−0.140079
$953$	33.9566	1.09996	0.549981	−	0.835177i	$-0.314635\pi$
$953$	33.9566	1.09996	0.549981	+	0.835177i	$0.314635\pi$
$954$	23.6012	0.764118
$955$	7.66296	0.247968
$956$	−9.18343	−0.297013
$957$	2.84973	0.0921186
$958$	−10.8763	−0.351396
$959$	−23.1392	−0.747205
$960$	0.942894	0.0304318
$961$	−15.8166	−0.510214
$962$	5.06500	0.163302
$963$	39.3366	1.26761
$964$	22.7784	0.733644
$965$	16.2585	0.523378
$966$	1.61757	0.0520444
$967$	−3.74081	−0.120296	−0.0601482	−	0.998189i	$-0.519157\pi$
$967$	−3.74081	−0.120296	−0.0601482	+	0.998189i	$0.519157\pi$
$968$	1.00000	0.0321412
$969$	9.47258	0.304303
$970$	−30.1223	−0.967168
$971$	−10.7700	−0.345624	−0.172812	−	0.984955i	$-0.555285\pi$
$971$	−10.7700	−0.345624	−0.172812	+	0.984955i	$0.555285\pi$
$972$	−12.6173	−0.404702
$973$	10.8023	0.346305
$974$	12.7646	0.409006
$975$	0.720646	0.0230791
$976$	2.11094	0.0675695
$977$	−29.0125	−0.928191	−0.464096	−	0.885785i	$-0.653621\pi$
$977$	−29.0125	−0.928191	−0.464096	+	0.885785i	$0.653621\pi$
$978$	6.88370	0.220117
$979$	−5.27440	−0.168570
$980$	7.44378	0.237783
$981$	41.9753	1.34017
$982$	5.17892	0.165266
$983$	−15.2337	−0.485878	−0.242939	−	0.970042i	$-0.578112\pi$
$983$	−15.2337	−0.485878	−0.242939	+	0.970042i	$0.578112\pi$
$984$	2.32640	0.0741630
$985$	1.76896	0.0563638
$986$	13.8291	0.440407
$987$	3.37673	0.107482
$988$	−4.96530	−0.157967
$989$	19.4459	0.618343
$990$	−4.80430	−0.152691
$991$	20.7709	0.659810	0.329905	−	0.944014i	$-0.392983\pi$
$991$	20.7709	0.659810	0.329905	+	0.944014i	$0.392983\pi$
$992$	−3.89658	−0.123717
$993$	−0.191151	−0.00606599
$994$	0.816617	0.0259015
$995$	−13.1488	−0.416846
$996$	−5.80840	−0.184046
$997$	59.6685	1.88972	0.944860	−	0.327475i	$-0.106198\pi$
$997$	59.6685	1.88972	0.944860	+	0.327475i	$0.106198\pi$
$998$	37.7912	1.19626
$999$	21.3526	0.675568

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4334.2.a.f.1.8	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4334.2.a.f.1.8	✓	24	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:	\( N \)	\(=\)	\( 4334 = 2 \cdot 11 \cdot 197 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4334.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -0.533021 q^{3} +1.00000 q^{4} -1.76896 q^{5} -0.533021 q^{6} -1.67093 q^{7} +1.00000 q^{8} -2.71589 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -0.533021 q^{3} +1.00000 q^{4} -1.76896 q^{5} -0.533021 q^{6} -1.67093 q^{7} +1.00000 q^{8} -2.71589 q^{9} -1.76896 q^{10} -1.00000 q^{11} -0.533021 q^{12} +0.722697 q^{13} -1.67093 q^{14} +0.942894 q^{15} +1.00000 q^{16} +2.58663 q^{17} -2.71589 q^{18} -6.87052 q^{19} -1.76896 q^{20} +0.890641 q^{21} -1.00000 q^{22} +1.81618 q^{23} -0.533021 q^{24} -1.87077 q^{25} +0.722697 q^{26} +3.04669 q^{27} -1.67093 q^{28} +5.34637 q^{29} +0.942894 q^{30} -3.89658 q^{31} +1.00000 q^{32} +0.533021 q^{33} +2.58663 q^{34} +2.95581 q^{35} -2.71589 q^{36} +7.00847 q^{37} -6.87052 q^{38} -0.385213 q^{39} -1.76896 q^{40} -4.36456 q^{41} +0.890641 q^{42} +10.7070 q^{43} -1.00000 q^{44} +4.80430 q^{45} +1.81618 q^{46} +3.79134 q^{47} -0.533021 q^{48} -4.20799 q^{49} -1.87077 q^{50} -1.37873 q^{51} +0.722697 q^{52} -8.69006 q^{53} +3.04669 q^{54} +1.76896 q^{55} -1.67093 q^{56} +3.66213 q^{57} +5.34637 q^{58} +11.1363 q^{59} +0.942894 q^{60} +2.11094 q^{61} -3.89658 q^{62} +4.53806 q^{63} +1.00000 q^{64} -1.27842 q^{65} +0.533021 q^{66} -2.77863 q^{67} +2.58663 q^{68} -0.968064 q^{69} +2.95581 q^{70} -0.488720 q^{71} -2.71589 q^{72} +5.80703 q^{73} +7.00847 q^{74} +0.997162 q^{75} -6.87052 q^{76} +1.67093 q^{77} -0.385213 q^{78} +6.21817 q^{79} -1.76896 q^{80} +6.52371 q^{81} -4.36456 q^{82} +10.8971 q^{83} +0.890641 q^{84} -4.57565 q^{85} +10.7070 q^{86} -2.84973 q^{87} -1.00000 q^{88} +5.27440 q^{89} +4.80430 q^{90} -1.20758 q^{91} +1.81618 q^{92} +2.07696 q^{93} +3.79134 q^{94} +12.1537 q^{95} -0.533021 q^{96} +17.0282 q^{97} -4.20799 q^{98} +2.71589 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 24 q^{2} + 8 q^{3} + 24 q^{4} + 8 q^{6} + 11 q^{7} + 24 q^{8} + 28 q^{9}+O(q^{10}) \) 24 * q + 24 * q^2 + 8 * q^3 + 24 * q^4 + 8 * q^6 + 11 * q^7 + 24 * q^8 + 28 * q^9	\( 24 q + 24 q^{2} + 8 q^{3} + 24 q^{4} + 8 q^{6} + 11 q^{7} + 24 q^{8} + 28 q^{9} - 24 q^{11} + 8 q^{12} + 9 q^{13} + 11 q^{14} + 6 q^{15} + 24 q^{16} - q^{17} + 28 q^{18} + 35 q^{19} + 21 q^{21} - 24 q^{22} + 13 q^{23} + 8 q^{24} + 38 q^{25} + 9 q^{26} + 23 q^{27} + 11 q^{28} + 15 q^{29} + 6 q^{30} + 31 q^{31} + 24 q^{32} - 8 q^{33} - q^{34} + 28 q^{35} + 28 q^{36} + 13 q^{37} + 35 q^{38} + 31 q^{39} + 16 q^{41} + 21 q^{42} + 35 q^{43} - 24 q^{44} + 13 q^{45} + 13 q^{46} + 46 q^{47} + 8 q^{48} + 55 q^{49} + 38 q^{50} + 18 q^{51} + 9 q^{52} + 6 q^{53} + 23 q^{54} + 11 q^{56} + 18 q^{57} + 15 q^{58} + 13 q^{59} + 6 q^{60} + 60 q^{61} + 31 q^{62} + 52 q^{63} + 24 q^{64} - 9 q^{65} - 8 q^{66} + 28 q^{67} - q^{68} + 21 q^{69} + 28 q^{70} + 10 q^{71} + 28 q^{72} + 3 q^{73} + 13 q^{74} + 48 q^{75} + 35 q^{76} - 11 q^{77} + 31 q^{78} + 47 q^{79} + 16 q^{81} + 16 q^{82} + 66 q^{83} + 21 q^{84} + 37 q^{85} + 35 q^{86} + 34 q^{87} - 24 q^{88} - 5 q^{89} + 13 q^{90} + q^{91} + 13 q^{92} - 16 q^{93} + 46 q^{94} + 9 q^{95} + 8 q^{96} + 24 q^{97} + 55 q^{98} - 28 q^{99}+O(q^{100}) \) 24 * q + 24 * q^2 + 8 * q^3 + 24 * q^4 + 8 * q^6 + 11 * q^7 + 24 * q^8 + 28 * q^9 - 24 * q^11 + 8 * q^12 + 9 * q^13 + 11 * q^14 + 6 * q^15 + 24 * q^16 - q^17 + 28 * q^18 + 35 * q^19 + 21 * q^21 - 24 * q^22 + 13 * q^23 + 8 * q^24 + 38 * q^25 + 9 * q^26 + 23 * q^27 + 11 * q^28 + 15 * q^29 + 6 * q^30 + 31 * q^31 + 24 * q^32 - 8 * q^33 - q^34 + 28 * q^35 + 28 * q^36 + 13 * q^37 + 35 * q^38 + 31 * q^39 + 16 * q^41 + 21 * q^42 + 35 * q^43 - 24 * q^44 + 13 * q^45 + 13 * q^46 + 46 * q^47 + 8 * q^48 + 55 * q^49 + 38 * q^50 + 18 * q^51 + 9 * q^52 + 6 * q^53 + 23 * q^54 + 11 * q^56 + 18 * q^57 + 15 * q^58 + 13 * q^59 + 6 * q^60 + 60 * q^61 + 31 * q^62 + 52 * q^63 + 24 * q^64 - 9 * q^65 - 8 * q^66 + 28 * q^67 - q^68 + 21 * q^69 + 28 * q^70 + 10 * q^71 + 28 * q^72 + 3 * q^73 + 13 * q^74 + 48 * q^75 + 35 * q^76 - 11 * q^77 + 31 * q^78 + 47 * q^79 + 16 * q^81 + 16 * q^82 + 66 * q^83 + 21 * q^84 + 37 * q^85 + 35 * q^86 + 34 * q^87 - 24 * q^88 - 5 * q^89 + 13 * q^90 + q^91 + 13 * q^92 - 16 * q^93 + 46 * q^94 + 9 * q^95 + 8 * q^96 + 24 * q^97 + 55 * q^98 - 28 * q^99

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