LMFDB - Embedded newform 4334.2.a.g.1.9

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:	$26$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
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)

$f(q)$	$=$	$q+1.00000 q^{2} -0.943634 q^{3} +1.00000 q^{4} +2.82946 q^{5} -0.943634 q^{6} +5.06500 q^{7} +1.00000 q^{8} -2.10955 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -0.943634 q^{3} +1.00000 q^{4} +2.82946 q^{5} -0.943634 q^{6} +5.06500 q^{7} +1.00000 q^{8} -2.10955 q^{9} +2.82946 q^{10} +1.00000 q^{11} -0.943634 q^{12} -0.490166 q^{13} +5.06500 q^{14} -2.66998 q^{15} +1.00000 q^{16} -6.15528 q^{17} -2.10955 q^{18} -1.82510 q^{19} +2.82946 q^{20} -4.77951 q^{21} +1.00000 q^{22} +1.13503 q^{23} -0.943634 q^{24} +3.00584 q^{25} -0.490166 q^{26} +4.82155 q^{27} +5.06500 q^{28} +7.76268 q^{29} -2.66998 q^{30} +2.94329 q^{31} +1.00000 q^{32} -0.943634 q^{33} -6.15528 q^{34} +14.3312 q^{35} -2.10955 q^{36} +2.43448 q^{37} -1.82510 q^{38} +0.462538 q^{39} +2.82946 q^{40} +11.2481 q^{41} -4.77951 q^{42} -11.3698 q^{43} +1.00000 q^{44} -5.96890 q^{45} +1.13503 q^{46} -4.93665 q^{47} -0.943634 q^{48} +18.6542 q^{49} +3.00584 q^{50} +5.80834 q^{51} -0.490166 q^{52} +11.5802 q^{53} +4.82155 q^{54} +2.82946 q^{55} +5.06500 q^{56} +1.72223 q^{57} +7.76268 q^{58} +11.4926 q^{59} -2.66998 q^{60} +1.86445 q^{61} +2.94329 q^{62} -10.6849 q^{63} +1.00000 q^{64} -1.38691 q^{65} -0.943634 q^{66} -7.96996 q^{67} -6.15528 q^{68} -1.07105 q^{69} +14.3312 q^{70} -1.19624 q^{71} -2.10955 q^{72} -14.4996 q^{73} +2.43448 q^{74} -2.83642 q^{75} -1.82510 q^{76} +5.06500 q^{77} +0.462538 q^{78} +12.1201 q^{79} +2.82946 q^{80} +1.77888 q^{81} +11.2481 q^{82} +3.31426 q^{83} -4.77951 q^{84} -17.4161 q^{85} -11.3698 q^{86} -7.32513 q^{87} +1.00000 q^{88} +4.58904 q^{89} -5.96890 q^{90} -2.48269 q^{91} +1.13503 q^{92} -2.77739 q^{93} -4.93665 q^{94} -5.16405 q^{95} -0.943634 q^{96} -15.9234 q^{97} +18.6542 q^{98} -2.10955 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 26 q + 26 q^{2} + 12 q^{3} + 26 q^{4} + 13 q^{5} + 12 q^{6} + 13 q^{7} + 26 q^{8} + 38 q^{9}+O(q^{10}) $ 26 * q + 26 * q^2 + 12 * q^3 + 26 * q^4 + 13 * q^5 + 12 * q^6 + 13 * q^7 + 26 * q^8 + 38 * q^9	\( 26 q + 26 q^{2} + 12 q^{3} + 26 q^{4} + 13 q^{5} + 12 q^{6} + 13 q^{7} + 26 q^{8} + 38 q^{9} + 13 q^{10} + 26 q^{11} + 12 q^{12} + 24 q^{13} + 13 q^{14} + 12 q^{15} + 26 q^{16} + q^{17} + 38 q^{18} + 24 q^{19} + 13 q^{20} + 5 q^{21} + 26 q^{22} + 19 q^{23} + 12 q^{24} + 35 q^{25} + 24 q^{26} + 39 q^{27} + 13 q^{28} + 5 q^{29} + 12 q^{30} + 34 q^{31} + 26 q^{32} + 12 q^{33} + q^{34} + 14 q^{35} + 38 q^{36} + 15 q^{37} + 24 q^{38} + 3 q^{39} + 13 q^{40} - 9 q^{41} + 5 q^{42} + 6 q^{43} + 26 q^{44} + 22 q^{45} + 19 q^{46} + 34 q^{47} + 12 q^{48} + 53 q^{49} + 35 q^{50} - 2 q^{51} + 24 q^{52} + 6 q^{53} + 39 q^{54} + 13 q^{55} + 13 q^{56} - 16 q^{57} + 5 q^{58} + 50 q^{59} + 12 q^{60} + 26 q^{61} + 34 q^{62} + 2 q^{63} + 26 q^{64} - 5 q^{65} + 12 q^{66} + 18 q^{67} + q^{68} + 15 q^{69} + 14 q^{70} + 23 q^{71} + 38 q^{72} + 37 q^{73} + 15 q^{74} + 18 q^{75} + 24 q^{76} + 13 q^{77} + 3 q^{78} + 10 q^{79} + 13 q^{80} + 50 q^{81} - 9 q^{82} + 7 q^{83} + 5 q^{84} - 7 q^{85} + 6 q^{86} + 16 q^{87} + 26 q^{88} + 3 q^{89} + 22 q^{90} + 31 q^{91} + 19 q^{92} + 52 q^{93} + 34 q^{94} + 9 q^{95} + 12 q^{96} - 9 q^{97} + 53 q^{98} + 38 q^{99}+O(q^{100}) \) 26 * q + 26 * q^2 + 12 * q^3 + 26 * q^4 + 13 * q^5 + 12 * q^6 + 13 * q^7 + 26 * q^8 + 38 * q^9 + 13 * q^10 + 26 * q^11 + 12 * q^12 + 24 * q^13 + 13 * q^14 + 12 * q^15 + 26 * q^16 + q^17 + 38 * q^18 + 24 * q^19 + 13 * q^20 + 5 * q^21 + 26 * q^22 + 19 * q^23 + 12 * q^24 + 35 * q^25 + 24 * q^26 + 39 * q^27 + 13 * q^28 + 5 * q^29 + 12 * q^30 + 34 * q^31 + 26 * q^32 + 12 * q^33 + q^34 + 14 * q^35 + 38 * q^36 + 15 * q^37 + 24 * q^38 + 3 * q^39 + 13 * q^40 - 9 * q^41 + 5 * q^42 + 6 * q^43 + 26 * q^44 + 22 * q^45 + 19 * q^46 + 34 * q^47 + 12 * q^48 + 53 * q^49 + 35 * q^50 - 2 * q^51 + 24 * q^52 + 6 * q^53 + 39 * q^54 + 13 * q^55 + 13 * q^56 - 16 * q^57 + 5 * q^58 + 50 * q^59 + 12 * q^60 + 26 * q^61 + 34 * q^62 + 2 * q^63 + 26 * q^64 - 5 * q^65 + 12 * q^66 + 18 * q^67 + q^68 + 15 * q^69 + 14 * q^70 + 23 * q^71 + 38 * q^72 + 37 * q^73 + 15 * q^74 + 18 * q^75 + 24 * q^76 + 13 * q^77 + 3 * q^78 + 10 * q^79 + 13 * q^80 + 50 * q^81 - 9 * q^82 + 7 * q^83 + 5 * q^84 - 7 * q^85 + 6 * q^86 + 16 * q^87 + 26 * q^88 + 3 * q^89 + 22 * q^90 + 31 * q^91 + 19 * q^92 + 52 * q^93 + 34 * q^94 + 9 * q^95 + 12 * q^96 - 9 * q^97 + 53 * q^98 + 38 * 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
$3$	−0.943634	−0.544808	−0.272404	−	0.962183i	$-0.587819\pi$
$3$	−0.943634	−0.544808	−0.272404	+	0.962183i	$0.587819\pi$
$4$	1.00000	0.500000
$5$	2.82946	1.26537	0.632686	−	0.774408i	$-0.281952\pi$
$5$	2.82946	1.26537	0.632686	+	0.774408i	$0.281952\pi$
$6$	−0.943634	−0.385237
$7$	5.06500	1.91439	0.957195	−	0.289443i	$-0.0934700\pi$
$7$	5.06500	1.91439	0.957195	+	0.289443i	$0.0934700\pi$
$8$	1.00000	0.353553
$9$	−2.10955	−0.703185
$10$	2.82946	0.894754
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−0.943634	−0.272404
$13$	−0.490166	−0.135948	−0.0679739	−	0.997687i	$-0.521653\pi$
$13$	−0.490166	−0.135948	−0.0679739	+	0.997687i	$0.521653\pi$
$14$	5.06500	1.35368
$15$	−2.66998	−0.689385
$16$	1.00000	0.250000
$17$	−6.15528	−1.49288	−0.746438	−	0.665455i	$-0.768238\pi$
$17$	−6.15528	−1.49288	−0.746438	+	0.665455i	$0.768238\pi$
$18$	−2.10955	−0.497227
$19$	−1.82510	−0.418707	−0.209353	−	0.977840i	$-0.567136\pi$
$19$	−1.82510	−0.418707	−0.209353	+	0.977840i	$0.567136\pi$
$20$	2.82946	0.632686
$21$	−4.77951	−1.04297
$22$	1.00000	0.213201
$23$	1.13503	0.236669	0.118335	−	0.992974i	$-0.462244\pi$
$23$	1.13503	0.236669	0.118335	+	0.992974i	$0.462244\pi$
$24$	−0.943634	−0.192619
$25$	3.00584	0.601169
$26$	−0.490166	−0.0961295
$27$	4.82155	0.927908
$28$	5.06500	0.957195
$29$	7.76268	1.44149	0.720747	−	0.693199i	$-0.243799\pi$
$29$	7.76268	1.44149	0.720747	+	0.693199i	$0.243799\pi$
$30$	−2.66998	−0.487469
$31$	2.94329	0.528630	0.264315	−	0.964436i	$-0.414854\pi$
$31$	2.94329	0.528630	0.264315	+	0.964436i	$0.414854\pi$
$32$	1.00000	0.176777
$33$	−0.943634	−0.164266
$34$	−6.15528	−1.05562
$35$	14.3312	2.42242
$36$	−2.10955	−0.351592
$37$	2.43448	0.400227	0.200113	−	0.979773i	$-0.435869\pi$
$37$	2.43448	0.400227	0.200113	+	0.979773i	$0.435869\pi$
$38$	−1.82510	−0.296070
$39$	0.462538	0.0740653
$40$	2.82946	0.447377
$41$	11.2481	1.75665	0.878326	−	0.478062i	$-0.158661\pi$
$41$	11.2481	1.75665	0.878326	+	0.478062i	$0.158661\pi$
$42$	−4.77951	−0.737494
$43$	−11.3698	−1.73387	−0.866935	−	0.498420i	$-0.833914\pi$
$43$	−11.3698	−1.73387	−0.866935	+	0.498420i	$0.833914\pi$
$44$	1.00000	0.150756
$45$	−5.96890	−0.889791
$46$	1.13503	0.167351
$47$	−4.93665	−0.720084	−0.360042	−	0.932936i	$-0.617238\pi$
$47$	−4.93665	−0.720084	−0.360042	+	0.932936i	$0.617238\pi$
$48$	−0.943634	−0.136202
$49$	18.6542	2.66489
$50$	3.00584	0.425090
$51$	5.80834	0.813330
$52$	−0.490166	−0.0679739
$53$	11.5802	1.59066	0.795331	−	0.606175i	$-0.207297\pi$
$53$	11.5802	1.59066	0.795331	+	0.606175i	$0.207297\pi$
$54$	4.82155	0.656130
$55$	2.82946	0.381524
$56$	5.06500	0.676839
$57$	1.72223	0.228115
$58$	7.76268	1.01929
$59$	11.4926	1.49621	0.748103	−	0.663583i	$-0.230965\pi$
$59$	11.4926	1.49621	0.748103	+	0.663583i	$0.230965\pi$
$60$	−2.66998	−0.344692
$61$	1.86445	0.238719	0.119359	−	0.992851i	$-0.461916\pi$
$61$	1.86445	0.238719	0.119359	+	0.992851i	$0.461916\pi$
$62$	2.94329	0.373798
$63$	−10.6849	−1.34617
$64$	1.00000	0.125000
$65$	−1.38691	−0.172025
$66$	−0.943634	−0.116153
$67$	−7.96996	−0.973686	−0.486843	−	0.873489i	$-0.661852\pi$
$67$	−7.96996	−0.973686	−0.486843	+	0.873489i	$0.661852\pi$
$68$	−6.15528	−0.746438
$69$	−1.07105	−0.128939
$70$	14.3312	1.71291
$71$	−1.19624	−0.141968	−0.0709839	−	0.997477i	$-0.522614\pi$
$71$	−1.19624	−0.141968	−0.0709839	+	0.997477i	$0.522614\pi$
$72$	−2.10955	−0.248613
$73$	−14.4996	−1.69706	−0.848528	−	0.529151i	$-0.822510\pi$
$73$	−14.4996	−1.69706	−0.848528	+	0.529151i	$0.822510\pi$
$74$	2.43448	0.283003
$75$	−2.83642	−0.327521
$76$	−1.82510	−0.209353
$77$	5.06500	0.577211
$78$	0.462538	0.0523721
$79$	12.1201	1.36362	0.681809	−	0.731531i	$-0.261194\pi$
$79$	12.1201	1.36362	0.681809	+	0.731531i	$0.261194\pi$
$80$	2.82946	0.316343
$81$	1.77888	0.197653
$82$	11.2481	1.24214
$83$	3.31426	0.363787	0.181893	−	0.983318i	$-0.441777\pi$
$83$	3.31426	0.363787	0.181893	+	0.983318i	$0.441777\pi$
$84$	−4.77951	−0.521487
$85$	−17.4161	−1.88904
$86$	−11.3698	−1.22603
$87$	−7.32513	−0.785337
$88$	1.00000	0.106600
$89$	4.58904	0.486437	0.243218	−	0.969972i	$-0.421797\pi$
$89$	4.58904	0.486437	0.243218	+	0.969972i	$0.421797\pi$
$90$	−5.96890	−0.629177
$91$	−2.48269	−0.260257
$92$	1.13503	0.118335
$93$	−2.77739	−0.288001
$94$	−4.93665	−0.509176
$95$	−5.16405	−0.529820
$96$	−0.943634	−0.0963093
$97$	−15.9234	−1.61677	−0.808387	−	0.588651i	$-0.799659\pi$
$97$	−15.9234	−1.61677	−0.808387	+	0.588651i	$0.799659\pi$
$98$	18.6542	1.88436
$99$	−2.10955	−0.212018
$100$	3.00584	0.300584
$101$	16.1354	1.60553	0.802765	−	0.596295i	$-0.203361\pi$
$101$	16.1354	1.60553	0.802765	+	0.596295i	$0.203361\pi$
$102$	5.80834	0.575111
$103$	13.6053	1.34057	0.670286	−	0.742103i	$-0.266171\pi$
$103$	13.6053	1.34057	0.670286	+	0.742103i	$0.266171\pi$
$104$	−0.490166	−0.0480648
$105$	−13.5234	−1.31975
$106$	11.5802	1.12477
$107$	−16.6401	−1.60866	−0.804328	−	0.594186i	$-0.797474\pi$
$107$	−16.6401	−1.60866	−0.804328	+	0.594186i	$0.797474\pi$
$108$	4.82155	0.463954
$109$	3.39848	0.325516	0.162758	−	0.986666i	$-0.447961\pi$
$109$	3.39848	0.325516	0.162758	+	0.986666i	$0.447961\pi$
$110$	2.82946	0.269778
$111$	−2.29726	−0.218047
$112$	5.06500	0.478598
$113$	10.2867	0.967689	0.483845	−	0.875154i	$-0.339240\pi$
$113$	10.2867	0.967689	0.483845	+	0.875154i	$0.339240\pi$
$114$	1.72223	0.161301
$115$	3.21151	0.299475
$116$	7.76268	0.720747
$117$	1.03403	0.0955964
$118$	11.4926	1.05798
$119$	−31.1765	−2.85795
$120$	−2.66998	−0.243734
$121$	1.00000	0.0909091
$122$	1.86445	0.168800
$123$	−10.6141	−0.957037
$124$	2.94329	0.264315
$125$	−5.64239	−0.504670
$126$	−10.6849	−0.951886
$127$	14.0276	1.24475	0.622375	−	0.782719i	$-0.286168\pi$
$127$	14.0276	1.24475	0.622375	+	0.782719i	$0.286168\pi$
$128$	1.00000	0.0883883
$129$	10.7289	0.944626
$130$	−1.38691	−0.121640
$131$	−18.9272	−1.65367	−0.826837	−	0.562442i	$-0.809862\pi$
$131$	−18.9272	−1.65367	−0.826837	+	0.562442i	$0.809862\pi$
$132$	−0.943634	−0.0821328
$133$	−9.24414	−0.801568
$134$	−7.96996	−0.688500
$135$	13.6424	1.17415
$136$	−6.15528	−0.527811
$137$	−17.7195	−1.51388	−0.756939	−	0.653486i	$-0.773306\pi$
$137$	−17.7195	−1.51388	−0.756939	+	0.653486i	$0.773306\pi$
$138$	−1.07105	−0.0911738
$139$	−8.98631	−0.762209	−0.381104	−	0.924532i	$-0.624456\pi$
$139$	−8.98631	−0.762209	−0.381104	+	0.924532i	$0.624456\pi$
$140$	14.3312	1.21121
$141$	4.65839	0.392307
$142$	−1.19624	−0.100386
$143$	−0.490166	−0.0409898
$144$	−2.10955	−0.175796
$145$	21.9642	1.82403
$146$	−14.4996	−1.20000
$147$	−17.6028	−1.45185
$148$	2.43448	0.200113
$149$	−17.1097	−1.40168	−0.700841	−	0.713317i	$-0.747192\pi$
$149$	−17.1097	−1.40168	−0.700841	+	0.713317i	$0.747192\pi$
$150$	−2.83642	−0.231593
$151$	2.46706	0.200767	0.100383	−	0.994949i	$-0.467993\pi$
$151$	2.46706	0.200767	0.100383	+	0.994949i	$0.467993\pi$
$152$	−1.82510	−0.148035
$153$	12.9849	1.04977
$154$	5.06500	0.408149
$155$	8.32791	0.668914
$156$	0.462538	0.0370327
$157$	−9.07938	−0.724613	−0.362307	−	0.932059i	$-0.618011\pi$
$157$	−9.07938	−0.724613	−0.362307	+	0.932059i	$0.618011\pi$
$158$	12.1201	0.964223
$159$	−10.9275	−0.866605
$160$	2.82946	0.223688
$161$	5.74891	0.453078
$162$	1.77888	0.139762
$163$	−11.1851	−0.876081	−0.438041	−	0.898955i	$-0.644327\pi$
$163$	−11.1851	−0.876081	−0.438041	+	0.898955i	$0.644327\pi$
$164$	11.2481	0.878326
$165$	−2.66998	−0.207857
$166$	3.31426	0.257236
$167$	−7.97097	−0.616813	−0.308406	−	0.951255i	$-0.599796\pi$
$167$	−7.97097	−0.616813	−0.308406	+	0.951255i	$0.599796\pi$
$168$	−4.77951	−0.368747
$169$	−12.7597	−0.981518
$170$	−17.4161	−1.33576
$171$	3.85015	0.294428
$172$	−11.3698	−0.866935
$173$	−13.9620	−1.06151	−0.530756	−	0.847525i	$-0.678092\pi$
$173$	−13.9620	−1.06151	−0.530756	+	0.847525i	$0.678092\pi$
$174$	−7.32513	−0.555317
$175$	15.2246	1.15087
$176$	1.00000	0.0753778
$177$	−10.8448	−0.815144
$178$	4.58904	0.343963
$179$	4.89426	0.365814	0.182907	−	0.983130i	$-0.441449\pi$
$179$	4.89426	0.365814	0.182907	+	0.983130i	$0.441449\pi$
$180$	−5.96890	−0.444895
$181$	4.54098	0.337528	0.168764	−	0.985656i	$-0.446022\pi$
$181$	4.54098	0.337528	0.168764	+	0.985656i	$0.446022\pi$
$182$	−2.48269	−0.184030
$183$	−1.75936	−0.130056
$184$	1.13503	0.0836753
$185$	6.88827	0.506436
$186$	−2.77739	−0.203648
$187$	−6.15528	−0.450119
$188$	−4.93665	−0.360042
$189$	24.4212	1.77638
$190$	−5.16405	−0.374639
$191$	2.28731	0.165504	0.0827521	−	0.996570i	$-0.473629\pi$
$191$	2.28731	0.165504	0.0827521	+	0.996570i	$0.473629\pi$
$192$	−0.943634	−0.0681009
$193$	−14.0700	−1.01278	−0.506392	−	0.862304i	$-0.669021\pi$
$193$	−14.0700	−1.01278	−0.506392	+	0.862304i	$0.669021\pi$
$194$	−15.9234	−1.14323
$195$	1.30873	0.0937203
$196$	18.6542	1.33245
$197$	1.00000	0.0712470
$197$	1.00000	0.0712470
$198$	−2.10955	−0.149919
$199$	12.1765	0.863172	0.431586	−	0.902072i	$-0.357954\pi$
$199$	12.1765	0.863172	0.431586	+	0.902072i	$0.357954\pi$
$200$	3.00584	0.212545
$201$	7.52073	0.530472
$202$	16.1354	1.13528
$203$	39.3180	2.75958
$204$	5.80834	0.406665
$205$	31.8259	2.22282
$206$	13.6053	0.947928
$207$	−2.39440	−0.166422
$208$	−0.490166	−0.0339869
$209$	−1.82510	−0.126245
$210$	−13.5234	−0.933205
$211$	14.8833	1.02461	0.512304	−	0.858804i	$-0.328792\pi$
$211$	14.8833	1.02461	0.512304	+	0.858804i	$0.328792\pi$
$212$	11.5802	0.795331
$213$	1.12881	0.0773451
$214$	−16.6401	−1.13749
$215$	−32.1703	−2.19399
$216$	4.82155	0.328065
$217$	14.9077	1.01200
$218$	3.39848	0.230174
$219$	13.6824	0.924569
$220$	2.82946	0.190762
$221$	3.01711	0.202953
$222$	−2.29726	−0.154182
$223$	20.9270	1.40137	0.700686	−	0.713469i	$-0.252877\pi$
$223$	20.9270	1.40137	0.700686	+	0.713469i	$0.252877\pi$
$224$	5.06500	0.338420
$225$	−6.34099	−0.422733
$226$	10.2867	0.684260
$227$	18.1905	1.20735	0.603674	−	0.797231i	$-0.293703\pi$
$227$	18.1905	1.20735	0.603674	+	0.797231i	$0.293703\pi$
$228$	1.72223	0.114057
$229$	10.6293	0.702404	0.351202	−	0.936300i	$-0.385773\pi$
$229$	10.6293	0.702404	0.351202	+	0.936300i	$0.385773\pi$
$230$	3.21151	0.211761
$231$	−4.77951	−0.314469
$232$	7.76268	0.509645
$233$	−4.86540	−0.318743	−0.159371	−	0.987219i	$-0.550947\pi$
$233$	−4.86540	−0.318743	−0.159371	+	0.987219i	$0.550947\pi$
$234$	1.03403	0.0675968
$235$	−13.9680	−0.911175
$236$	11.4926	0.748103
$237$	−11.4369	−0.742909
$238$	−31.1765	−2.02087
$239$	−2.33859	−0.151270	−0.0756352	−	0.997136i	$-0.524098\pi$
$239$	−2.33859	−0.151270	−0.0756352	+	0.997136i	$0.524098\pi$
$240$	−2.66998	−0.172346
$241$	27.1790	1.75075	0.875376	−	0.483443i	$-0.160614\pi$
$241$	27.1790	1.75075	0.875376	+	0.483443i	$0.160614\pi$
$242$	1.00000	0.0642824
$243$	−16.1433	−1.03559
$244$	1.86445	0.119359
$245$	52.7814	3.37208
$246$	−10.6141	−0.676728
$247$	0.894603	0.0569222
$248$	2.94329	0.186899
$249$	−3.12745	−0.198194
$250$	−5.64239	−0.356856
$251$	11.7056	0.738848	0.369424	−	0.929261i	$-0.379555\pi$
$251$	11.7056	0.738848	0.369424	+	0.929261i	$0.379555\pi$
$252$	−10.6849	−0.673085
$253$	1.13503	0.0713585
$254$	14.0276	0.880171
$255$	16.4345	1.02917
$256$	1.00000	0.0625000
$257$	−18.1635	−1.13301	−0.566503	−	0.824059i	$-0.691704\pi$
$257$	−18.1635	−1.13301	−0.566503	+	0.824059i	$0.691704\pi$
$258$	10.7289	0.667951
$259$	12.3307	0.766190
$260$	−1.38691	−0.0860123
$261$	−16.3758	−1.01364
$262$	−18.9272	−1.16932
$263$	−10.4604	−0.645014	−0.322507	−	0.946567i	$-0.604526\pi$
$263$	−10.4604	−0.645014	−0.322507	+	0.946567i	$0.604526\pi$
$264$	−0.943634	−0.0580767
$265$	32.7657	2.01278
$266$	−9.24414	−0.566794
$267$	−4.33037	−0.265014
$268$	−7.96996	−0.486843
$269$	−7.27155	−0.443354	−0.221677	−	0.975120i	$-0.571153\pi$
$269$	−7.27155	−0.443354	−0.221677	+	0.975120i	$0.571153\pi$
$270$	13.6424	0.830249
$271$	2.22231	0.134996	0.0674979	−	0.997719i	$-0.478498\pi$
$271$	2.22231	0.134996	0.0674979	+	0.997719i	$0.478498\pi$
$272$	−6.15528	−0.373219
$273$	2.34276	0.141790
$274$	−17.7195	−1.07047
$275$	3.00584	0.181259
$276$	−1.07105	−0.0644696
$277$	−11.5431	−0.693560	−0.346780	−	0.937946i	$-0.612725\pi$
$277$	−11.5431	−0.693560	−0.346780	+	0.937946i	$0.612725\pi$
$278$	−8.98631	−0.538963
$279$	−6.20902	−0.371724
$280$	14.3312	0.856454
$281$	−5.44656	−0.324915	−0.162457	−	0.986716i	$-0.551942\pi$
$281$	−5.44656	−0.324915	−0.162457	+	0.986716i	$0.551942\pi$
$282$	4.65839	0.277403
$283$	1.96581	0.116855	0.0584276	−	0.998292i	$-0.481391\pi$
$283$	1.96581	0.116855	0.0584276	+	0.998292i	$0.481391\pi$
$284$	−1.19624	−0.0709839
$285$	4.87297	0.288650
$286$	−0.490166	−0.0289841
$287$	56.9715	3.36292
$288$	−2.10955	−0.124307
$289$	20.8875	1.22868
$290$	21.9642	1.28978
$291$	15.0259	0.880831
$292$	−14.4996	−0.848528
$293$	−7.21819	−0.421691	−0.210846	−	0.977519i	$-0.567622\pi$
$293$	−7.21819	−0.421691	−0.210846	+	0.977519i	$0.567622\pi$
$294$	−17.6028	−1.02662
$295$	32.5178	1.89326
$296$	2.43448	0.141502
$297$	4.82155	0.279775
$298$	−17.1097	−0.991139
$299$	−0.556352	−0.0321747
$300$	−2.83642	−0.163761
$301$	−57.5878	−3.31931
$302$	2.46706	0.141963
$303$	−15.2259	−0.874705
$304$	−1.82510	−0.104677
$305$	5.27540	0.302068
$306$	12.9849	0.742298
$307$	−9.12524	−0.520805	−0.260402	−	0.965500i	$-0.583855\pi$
$307$	−9.12524	−0.520805	−0.260402	+	0.965500i	$0.583855\pi$
$308$	5.06500	0.288605
$309$	−12.8385	−0.730354
$310$	8.32791	0.472993
$311$	−16.2490	−0.921398	−0.460699	−	0.887556i	$-0.652401\pi$
$311$	−16.2490	−0.921398	−0.460699	+	0.887556i	$0.652401\pi$
$312$	0.462538	0.0261861
$313$	21.9606	1.24128	0.620642	−	0.784094i	$-0.286872\pi$
$313$	21.9606	1.24128	0.620642	+	0.784094i	$0.286872\pi$
$314$	−9.07938	−0.512379
$315$	−30.2325	−1.70341
$316$	12.1201	0.681809
$317$	−10.6717	−0.599380	−0.299690	−	0.954037i	$-0.596883\pi$
$317$	−10.6717	−0.599380	−0.299690	+	0.954037i	$0.596883\pi$
$318$	−10.9275	−0.612782
$319$	7.76268	0.434627
$320$	2.82946	0.158172
$321$	15.7021	0.876408
$322$	5.74891	0.320374
$323$	11.2340	0.625077
$324$	1.77888	0.0988267
$325$	−1.47336	−0.0817275
$326$	−11.1851	−0.619483
$327$	−3.20693	−0.177343
$328$	11.2481	0.621070
$329$	−25.0041	−1.37852
$330$	−2.66998	−0.146977
$331$	−25.6165	−1.40801	−0.704004	−	0.710196i	$-0.748606\pi$
$331$	−25.6165	−1.40801	−0.704004	+	0.710196i	$0.748606\pi$
$332$	3.31426	0.181893
$333$	−5.13568	−0.281433
$334$	−7.97097	−0.436152
$335$	−22.5507	−1.23208
$336$	−4.77951	−0.260744
$337$	−18.2668	−0.995059	−0.497529	−	0.867447i	$-0.665759\pi$
$337$	−18.2668	−0.995059	−0.497529	+	0.867447i	$0.665759\pi$
$338$	−12.7597	−0.694038
$339$	−9.70686	−0.527204
$340$	−17.4161	−0.944522
$341$	2.94329	0.159388
$342$	3.85015	0.208192
$343$	59.0288	3.18725
$344$	−11.3698	−0.613016
$345$	−3.03049	−0.163156
$346$	−13.9620	−0.750602
$347$	−15.5759	−0.836155	−0.418078	−	0.908411i	$-0.637296\pi$
$347$	−15.5759	−0.836155	−0.418078	+	0.908411i	$0.637296\pi$
$348$	−7.32513	−0.392668
$349$	18.9024	1.01182	0.505912	−	0.862585i	$-0.331156\pi$
$349$	18.9024	1.01182	0.505912	+	0.862585i	$0.331156\pi$
$350$	15.2246	0.813789
$351$	−2.36336	−0.126147
$352$	1.00000	0.0533002
$353$	−24.2527	−1.29084	−0.645420	−	0.763828i	$-0.723318\pi$
$353$	−24.2527	−1.29084	−0.645420	+	0.763828i	$0.723318\pi$
$354$	−10.8448	−0.576394
$355$	−3.38472	−0.179642
$356$	4.58904	0.243218
$357$	29.4192	1.55703
$358$	4.89426	0.258670
$359$	4.93024	0.260208	0.130104	−	0.991500i	$-0.458469\pi$
$359$	4.93024	0.260208	0.130104	+	0.991500i	$0.458469\pi$
$360$	−5.96890	−0.314589
$361$	−15.6690	−0.824685
$362$	4.54098	0.238668
$363$	−0.943634	−0.0495280
$364$	−2.48269	−0.130129
$365$	−41.0262	−2.14741
$366$	−1.75936	−0.0919634
$367$	25.4011	1.32593	0.662964	−	0.748651i	$-0.269298\pi$
$367$	25.4011	1.32593	0.662964	+	0.748651i	$0.269298\pi$
$368$	1.13503	0.0591673
$369$	−23.7284	−1.23525
$370$	6.88827	0.358104
$371$	58.6537	3.04515
$372$	−2.77739	−0.144001
$373$	6.82377	0.353322	0.176661	−	0.984272i	$-0.443470\pi$
$373$	6.82377	0.353322	0.176661	+	0.984272i	$0.443470\pi$
$374$	−6.15528	−0.318282
$375$	5.32435	0.274948
$376$	−4.93665	−0.254588
$377$	−3.80501	−0.195968
$378$	24.4212	1.25609
$379$	23.1989	1.19165	0.595823	−	0.803115i	$-0.296826\pi$
$379$	23.1989	1.19165	0.595823	+	0.803115i	$0.296826\pi$
$380$	−5.16405	−0.264910
$381$	−13.2369	−0.678149
$382$	2.28731	0.117029
$383$	−16.6486	−0.850703	−0.425352	−	0.905028i	$-0.639850\pi$
$383$	−16.6486	−0.850703	−0.425352	+	0.905028i	$0.639850\pi$
$384$	−0.943634	−0.0481546
$385$	14.3312	0.730387
$386$	−14.0700	−0.716146
$387$	23.9851	1.21923
$388$	−15.9234	−0.808387
$389$	−10.6314	−0.539034	−0.269517	−	0.962996i	$-0.586864\pi$
$389$	−10.6314	−0.539034	−0.269517	+	0.962996i	$0.586864\pi$
$390$	1.30873	0.0662702
$391$	−6.98641	−0.353318
$392$	18.6542	0.942182
$393$	17.8603	0.900934
$394$	1.00000	0.0503793
$395$	34.2933	1.72548
$396$	−2.10955	−0.106009
$397$	−5.68458	−0.285301	−0.142650	−	0.989773i	$-0.545562\pi$
$397$	−5.68458	−0.285301	−0.142650	+	0.989773i	$0.545562\pi$
$398$	12.1765	0.610355
$399$	8.72309	0.436701
$400$	3.00584	0.150292
$401$	−0.746551	−0.0372810	−0.0186405	−	0.999826i	$-0.505934\pi$
$401$	−0.746551	−0.0372810	−0.0186405	+	0.999826i	$0.505934\pi$
$402$	7.52073	0.375100
$403$	−1.44270	−0.0718660
$404$	16.1354	0.802765
$405$	5.03327	0.250105
$406$	39.3180	1.95132
$407$	2.43448	0.120673
$408$	5.80834	0.287556
$409$	−23.3232	−1.15326	−0.576629	−	0.817006i	$-0.695632\pi$
$409$	−23.3232	−1.15326	−0.576629	+	0.817006i	$0.695632\pi$
$410$	31.8259	1.57177
$411$	16.7207	0.824772
$412$	13.6053	0.670286
$413$	58.2099	2.86432
$414$	−2.39440	−0.117678
$415$	9.37755	0.460326
$416$	−0.490166	−0.0240324
$417$	8.47979	0.415257
$418$	−1.82510	−0.0892686
$419$	−11.1753	−0.545950	−0.272975	−	0.962021i	$-0.588008\pi$
$419$	−11.1753	−0.545950	−0.272975	+	0.962021i	$0.588008\pi$
$420$	−13.5234	−0.659876
$421$	−33.5257	−1.63394	−0.816971	−	0.576679i	$-0.804348\pi$
$421$	−33.5257	−1.63394	−0.816971	+	0.576679i	$0.804348\pi$
$422$	14.8833	0.724508
$423$	10.4141	0.506352
$424$	11.5802	0.562384
$425$	−18.5018	−0.897470
$426$	1.12881	0.0546912
$427$	9.44346	0.457001
$428$	−16.6401	−0.804328
$429$	0.462538	0.0223315
$430$	−32.1703	−1.55139
$431$	−28.9636	−1.39513	−0.697563	−	0.716523i	$-0.745732\pi$
$431$	−28.9636	−1.39513	−0.697563	+	0.716523i	$0.745732\pi$
$432$	4.82155	0.231977
$433$	−40.5590	−1.94914	−0.974569	−	0.224086i	$-0.928060\pi$
$433$	−40.5590	−1.94914	−0.974569	+	0.224086i	$0.928060\pi$
$434$	14.9077	0.715595
$435$	−20.7262	−0.993744
$436$	3.39848	0.162758
$437$	−2.07154	−0.0990951
$438$	13.6824	0.653769
$439$	−7.18835	−0.343081	−0.171541	−	0.985177i	$-0.554874\pi$
$439$	−7.18835	−0.343081	−0.171541	+	0.985177i	$0.554874\pi$
$440$	2.82946	0.134889
$441$	−39.3521	−1.87391
$442$	3.01711	0.143509
$443$	6.81377	0.323732	0.161866	−	0.986813i	$-0.448249\pi$
$443$	6.81377	0.323732	0.161866	+	0.986813i	$0.448249\pi$
$444$	−2.29726	−0.109023
$445$	12.9845	0.615524
$446$	20.9270	0.990920
$447$	16.1453	0.763647
$448$	5.06500	0.239299
$449$	−3.22817	−0.152347	−0.0761733	−	0.997095i	$-0.524270\pi$
$449$	−3.22817	−0.152347	−0.0761733	+	0.997095i	$0.524270\pi$
$450$	−6.34099	−0.298917
$451$	11.2481	0.529651
$452$	10.2867	0.483845
$453$	−2.32800	−0.109379
$454$	18.1905	0.853724
$455$	−7.02468	−0.329322
$456$	1.72223	0.0806507
$457$	24.2471	1.13423	0.567116	−	0.823638i	$-0.308059\pi$
$457$	24.2471	1.13423	0.567116	+	0.823638i	$0.308059\pi$
$458$	10.6293	0.496675
$459$	−29.6780	−1.38525
$460$	3.21151	0.149738
$461$	−3.32357	−0.154794	−0.0773970	−	0.997000i	$-0.524661\pi$
$461$	−3.32357	−0.154794	−0.0773970	+	0.997000i	$0.524661\pi$
$462$	−4.77951	−0.222363
$463$	21.4277	0.995828	0.497914	−	0.867226i	$-0.334100\pi$
$463$	21.4277	0.995828	0.497914	+	0.867226i	$0.334100\pi$
$464$	7.76268	0.360373
$465$	−7.85850	−0.364429
$466$	−4.86540	−0.225385
$467$	4.10197	0.189816	0.0949082	−	0.995486i	$-0.469744\pi$
$467$	4.10197	0.189816	0.0949082	+	0.995486i	$0.469744\pi$
$468$	1.03403	0.0477982
$469$	−40.3679	−1.86402
$470$	−13.9680	−0.644298
$471$	8.56761	0.394775
$472$	11.4926	0.528989
$473$	−11.3698	−0.522782
$474$	−11.4369	−0.525316
$475$	−5.48597	−0.251713
$476$	−31.1765	−1.42897
$477$	−24.4291	−1.11853
$478$	−2.33859	−0.106964
$479$	−34.0565	−1.55608	−0.778041	−	0.628213i	$-0.783787\pi$
$479$	−34.0565	−1.55608	−0.778041	+	0.628213i	$0.783787\pi$
$480$	−2.66998	−0.121867
$481$	−1.19330	−0.0544099
$482$	27.1790	1.23797
$483$	−5.42487	−0.246840
$484$	1.00000	0.0454545
$485$	−45.0546	−2.04582
$486$	−16.1433	−0.732273
$487$	12.2788	0.556404	0.278202	−	0.960523i	$-0.410262\pi$
$487$	12.2788	0.556404	0.278202	+	0.960523i	$0.410262\pi$
$488$	1.86445	0.0843999
$489$	10.5546	0.477296
$490$	52.7814	2.38442
$491$	20.8828	0.942430	0.471215	−	0.882018i	$-0.343816\pi$
$491$	20.8828	0.942430	0.471215	+	0.882018i	$0.343816\pi$
$492$	−10.6141	−0.478519
$493$	−47.7815	−2.15197
$494$	0.894603	0.0402501
$495$	−5.96890	−0.268282
$496$	2.94329	0.132157
$497$	−6.05896	−0.271782
$498$	−3.12745	−0.140144
$499$	28.5263	1.27701	0.638507	−	0.769616i	$-0.279552\pi$
$499$	28.5263	1.27701	0.638507	+	0.769616i	$0.279552\pi$
$500$	−5.64239	−0.252335
$501$	7.52169	0.336044
$502$	11.7056	0.522445
$503$	−7.55199	−0.336726	−0.168363	−	0.985725i	$-0.553848\pi$
$503$	−7.55199	−0.336726	−0.168363	+	0.985725i	$0.553848\pi$
$504$	−10.6849	−0.475943
$505$	45.6544	2.03160
$506$	1.13503	0.0504581
$507$	12.0405	0.534739
$508$	14.0276	0.622375
$509$	−23.6872	−1.04992	−0.524959	−	0.851127i	$-0.675919\pi$
$509$	−23.6872	−1.04992	−0.524959	+	0.851127i	$0.675919\pi$
$510$	16.4345	0.727730
$511$	−73.4407	−3.24883
$512$	1.00000	0.0441942
$513$	−8.79982	−0.388521
$514$	−18.1635	−0.801157
$515$	38.4957	1.69632
$516$	10.7289	0.472313
$517$	−4.93665	−0.217113
$518$	12.3307	0.541778
$519$	13.1750	0.578319
$520$	−1.38691	−0.0608199
$521$	23.3770	1.02416	0.512082	−	0.858936i	$-0.328874\pi$
$521$	23.3770	1.02416	0.512082	+	0.858936i	$0.328874\pi$
$522$	−16.3758	−0.716749
$523$	1.81147	0.0792100	0.0396050	−	0.999215i	$-0.487390\pi$
$523$	1.81147	0.0792100	0.0396050	+	0.999215i	$0.487390\pi$
$524$	−18.9272	−0.826837
$525$	−14.3665	−0.627004
$526$	−10.4604	−0.456094
$527$	−18.1168	−0.789179
$528$	−0.943634	−0.0410664
$529$	−21.7117	−0.943988
$530$	32.7657	1.42325
$531$	−24.2442	−1.05211
$532$	−9.24414	−0.400784
$533$	−5.51342	−0.238813
$534$	−4.33037	−0.187394
$535$	−47.0824	−2.03555
$536$	−7.96996	−0.344250
$537$	−4.61839	−0.199298
$538$	−7.27155	−0.313499
$539$	18.6542	0.803495
$540$	13.6424	0.587075
$541$	−1.44636	−0.0621840	−0.0310920	−	0.999517i	$-0.509898\pi$
$541$	−1.44636	−0.0621840	−0.0310920	+	0.999517i	$0.509898\pi$
$542$	2.22231	0.0954564
$543$	−4.28502	−0.183888
$544$	−6.15528	−0.263906
$545$	9.61588	0.411899
$546$	2.34276	0.100261
$547$	−14.9219	−0.638016	−0.319008	−	0.947752i	$-0.603350\pi$
$547$	−14.9219	−0.638016	−0.319008	+	0.947752i	$0.603350\pi$
$548$	−17.7195	−0.756939
$549$	−3.93317	−0.167863
$550$	3.00584	0.128170
$551$	−14.1677	−0.603563
$552$	−1.07105	−0.0455869
$553$	61.3883	2.61050
$554$	−11.5431	−0.490421
$555$	−6.50001	−0.275910
$556$	−8.98631	−0.381104
$557$	−11.5685	−0.490171	−0.245086	−	0.969501i	$-0.578816\pi$
$557$	−11.5685	−0.490171	−0.245086	+	0.969501i	$0.578816\pi$
$558$	−6.20902	−0.262849
$559$	5.57307	0.235716
$560$	14.3312	0.605605
$561$	5.80834	0.245228
$562$	−5.44656	−0.229749
$563$	21.4413	0.903644	0.451822	−	0.892108i	$-0.350774\pi$
$563$	21.4413	0.903644	0.451822	+	0.892108i	$0.350774\pi$
$564$	4.65839	0.196154
$565$	29.1057	1.22449
$566$	1.96581	0.0826291
$567$	9.01003	0.378386
$568$	−1.19624	−0.0501932
$569$	25.5146	1.06963	0.534813	−	0.844970i	$-0.320382\pi$
$569$	25.5146	1.06963	0.534813	+	0.844970i	$0.320382\pi$
$570$	4.87297	0.204106
$571$	14.6328	0.612364	0.306182	−	0.951973i	$-0.400948\pi$
$571$	14.6328	0.612364	0.306182	+	0.951973i	$0.400948\pi$
$572$	−0.490166	−0.0204949
$573$	−2.15839	−0.0901679
$574$	56.9715	2.37794
$575$	3.41171	0.142278
$576$	−2.10955	−0.0878981
$577$	6.16559	0.256677	0.128338	−	0.991730i	$-0.459036\pi$
$577$	6.16559	0.256677	0.128338	+	0.991730i	$0.459036\pi$
$578$	20.8875	0.868807
$579$	13.2770	0.551772
$580$	21.9642	0.912013
$581$	16.7867	0.696430
$582$	15.0259	0.622842
$583$	11.5802	0.479603
$584$	−14.4996	−0.600000
$585$	2.92575	0.120965
$586$	−7.21819	−0.298181
$587$	−0.325835	−0.0134486	−0.00672432	−	0.999977i	$-0.502140\pi$
$587$	−0.325835	−0.0134486	−0.00672432	+	0.999977i	$0.502140\pi$
$588$	−17.6028	−0.725927
$589$	−5.37179	−0.221341
$590$	32.5178	1.33874
$591$	−0.943634	−0.0388159
$592$	2.43448	0.100057
$593$	16.1459	0.663033	0.331517	−	0.943449i	$-0.392440\pi$
$593$	16.1459	0.663033	0.331517	+	0.943449i	$0.392440\pi$
$594$	4.82155	0.197831
$595$	−88.2127	−3.61637
$596$	−17.1097	−0.700841
$597$	−11.4902	−0.470263
$598$	−0.556352	−0.0227509
$599$	5.29208	0.216229	0.108114	−	0.994138i	$-0.465519\pi$
$599$	5.29208	0.216229	0.108114	+	0.994138i	$0.465519\pi$
$600$	−2.83642	−0.115796
$601$	8.95256	0.365183	0.182591	−	0.983189i	$-0.441552\pi$
$601$	8.95256	0.365183	0.182591	+	0.983189i	$0.441552\pi$
$602$	−57.5878	−2.34710
$603$	16.8131	0.684681
$604$	2.46706	0.100383
$605$	2.82946	0.115034
$606$	−15.2259	−0.618510
$607$	13.0572	0.529974	0.264987	−	0.964252i	$-0.414632\pi$
$607$	13.0572	0.529974	0.264987	+	0.964252i	$0.414632\pi$
$608$	−1.82510	−0.0740176
$609$	−37.1018	−1.50344
$610$	5.27540	0.213595
$611$	2.41978	0.0978938
$612$	12.9849	0.524884
$613$	40.7564	1.64613	0.823067	−	0.567944i	$-0.192261\pi$
$613$	40.7564	1.64613	0.823067	+	0.567944i	$0.192261\pi$
$614$	−9.12524	−0.368265
$615$	−30.0321	−1.21101
$616$	5.06500	0.204075
$617$	−34.9390	−1.40659	−0.703295	−	0.710898i	$-0.748289\pi$
$617$	−34.9390	−1.40659	−0.703295	+	0.710898i	$0.748289\pi$
$618$	−12.8385	−0.516438
$619$	11.5616	0.464701	0.232351	−	0.972632i	$-0.425358\pi$
$619$	11.5616	0.464701	0.232351	+	0.972632i	$0.425358\pi$
$620$	8.32791	0.334457
$621$	5.47259	0.219607
$622$	−16.2490	−0.651527
$623$	23.2435	0.931230
$624$	0.462538	0.0185163
$625$	−30.9941	−1.23976
$626$	21.9606	0.877720
$627$	1.72223	0.0687791
$628$	−9.07938	−0.362307
$629$	−14.9849	−0.597489
$630$	−30.2325	−1.20449
$631$	−40.8073	−1.62451	−0.812256	−	0.583301i	$-0.801761\pi$
$631$	−40.8073	−1.62451	−0.812256	+	0.583301i	$0.801761\pi$
$632$	12.1201	0.482111
$633$	−14.0444	−0.558215
$634$	−10.6717	−0.423826
$635$	39.6906	1.57507
$636$	−10.9275	−0.433303
$637$	−9.14368	−0.362286
$638$	7.76268	0.307327
$639$	2.52354	0.0998295
$640$	2.82946	0.111844
$641$	−8.01673	−0.316642	−0.158321	−	0.987388i	$-0.550608\pi$
$641$	−8.01673	−0.316642	−0.158321	+	0.987388i	$0.550608\pi$
$642$	15.7021	0.619714
$643$	−0.297031	−0.0117138	−0.00585688	−	0.999983i	$-0.501864\pi$
$643$	−0.297031	−0.0117138	−0.00585688	+	0.999983i	$0.501864\pi$
$644$	5.74891	0.226539
$645$	30.3570	1.19530
$646$	11.2340	0.441996
$647$	−2.35924	−0.0927513	−0.0463756	−	0.998924i	$-0.514767\pi$
$647$	−2.35924	−0.0927513	−0.0463756	+	0.998924i	$0.514767\pi$
$648$	1.77888	0.0698810
$649$	11.4926	0.451123
$650$	−1.47336	−0.0577901
$651$	−14.0675	−0.551347
$652$	−11.1851	−0.438041
$653$	−27.3760	−1.07131	−0.535653	−	0.844438i	$-0.679934\pi$
$653$	−27.3760	−1.07131	−0.535653	+	0.844438i	$0.679934\pi$
$654$	−3.20693	−0.125401
$655$	−53.5536	−2.09251
$656$	11.2481	0.439163
$657$	30.5878	1.19334
$658$	−25.0041	−0.974762
$659$	−13.0523	−0.508446	−0.254223	−	0.967146i	$-0.581820\pi$
$659$	−13.0523	−0.508446	−0.254223	+	0.967146i	$0.581820\pi$
$660$	−2.66998	−0.103929
$661$	12.3537	0.480504	0.240252	−	0.970711i	$-0.422770\pi$
$661$	12.3537	0.480504	0.240252	+	0.970711i	$0.422770\pi$
$662$	−25.6165	−0.995612
$663$	−2.84705	−0.110570
$664$	3.31426	0.128618
$665$	−26.1559	−1.01428
$666$	−5.13568	−0.199003
$667$	8.81085	0.341157
$668$	−7.97097	−0.308406
$669$	−19.7474	−0.763479
$670$	−22.5507	−0.871209
$671$	1.86445	0.0719764
$672$	−4.77951	−0.184374
$673$	13.8397	0.533480	0.266740	−	0.963768i	$-0.414053\pi$
$673$	13.8397	0.533480	0.266740	+	0.963768i	$0.414053\pi$
$674$	−18.2668	−0.703613
$675$	14.4928	0.557829
$676$	−12.7597	−0.490759
$677$	−45.0027	−1.72959	−0.864797	−	0.502122i	$-0.832553\pi$
$677$	−45.0027	−1.72959	−0.864797	+	0.502122i	$0.832553\pi$
$678$	−9.70686	−0.372790
$679$	−80.6520	−3.09514
$680$	−17.4161	−0.667878
$681$	−17.1652	−0.657773
$682$	2.94329	0.112704
$683$	−30.4750	−1.16609	−0.583046	−	0.812439i	$-0.698139\pi$
$683$	−30.4750	−1.16609	−0.583046	+	0.812439i	$0.698139\pi$
$684$	3.85015	0.147214
$685$	−50.1366	−1.91562
$686$	59.0288	2.25373
$687$	−10.0302	−0.382675
$688$	−11.3698	−0.433468
$689$	−5.67623	−0.216247
$690$	−3.03049	−0.115369
$691$	35.2204	1.33985	0.669923	−	0.742430i	$-0.266327\pi$
$691$	35.2204	1.33985	0.669923	+	0.742430i	$0.266327\pi$
$692$	−13.9620	−0.530756
$693$	−10.6849	−0.405886
$694$	−15.5759	−0.591251
$695$	−25.4264	−0.964479
$696$	−7.32513	−0.277658
$697$	−69.2350	−2.62246
$698$	18.9024	0.715468
$699$	4.59116	0.173653
$700$	15.2246	0.575436
$701$	−7.48599	−0.282742	−0.141371	−	0.989957i	$-0.545151\pi$
$701$	−7.48599	−0.282742	−0.141371	+	0.989957i	$0.545151\pi$
$702$	−2.36336	−0.0891994
$703$	−4.44318	−0.167578
$704$	1.00000	0.0376889
$705$	13.1807	0.496415
$706$	−24.2527	−0.912762
$707$	81.7258	3.07361
$708$	−10.8448	−0.407572
$709$	51.7469	1.94340	0.971698	−	0.236228i	$-0.0759113\pi$
$709$	51.7469	1.94340	0.971698	+	0.236228i	$0.0759113\pi$
$710$	−3.38472	−0.127026
$711$	−25.5680	−0.958875
$712$	4.58904	0.171981
$713$	3.34071	0.125110
$714$	29.4192	1.10099
$715$	−1.38691	−0.0518674
$716$	4.89426	0.182907
$717$	2.20677	0.0824133
$718$	4.93024	0.183995
$719$	−41.3500	−1.54210	−0.771048	−	0.636777i	$-0.780267\pi$
$719$	−41.3500	−1.54210	−0.771048	+	0.636777i	$0.780267\pi$
$720$	−5.96890	−0.222448
$721$	68.9110	2.56638
$722$	−15.6690	−0.583140
$723$	−25.6470	−0.953823
$724$	4.54098	0.168764
$725$	23.3334	0.866581
$726$	−0.943634	−0.0350216
$727$	−40.0046	−1.48369	−0.741844	−	0.670572i	$-0.766049\pi$
$727$	−40.0046	−1.48369	−0.741844	+	0.670572i	$0.766049\pi$
$728$	−2.48269	−0.0920148
$729$	9.89670	0.366544
$730$	−41.0262	−1.51845
$731$	69.9841	2.58845
$732$	−1.75936	−0.0650279
$733$	−41.5587	−1.53501	−0.767503	−	0.641046i	$-0.778501\pi$
$733$	−41.5587	−1.53501	−0.767503	+	0.641046i	$0.778501\pi$
$734$	25.4011	0.937573
$735$	−49.8064	−1.83714
$736$	1.13503	0.0418376
$737$	−7.96996	−0.293577
$738$	−23.7284	−0.873454
$739$	−48.5015	−1.78416	−0.892079	−	0.451879i	$-0.850754\pi$
$739$	−48.5015	−1.78416	−0.892079	+	0.451879i	$0.850754\pi$
$740$	6.88827	0.253218
$741$	−0.844178	−0.0310117
$742$	58.6537	2.15325
$743$	47.2277	1.73262	0.866309	−	0.499509i	$-0.166486\pi$
$743$	47.2277	1.73262	0.866309	+	0.499509i	$0.166486\pi$
$744$	−2.77739	−0.101824
$745$	−48.4113	−1.77365
$746$	6.82377	0.249836
$747$	−6.99160	−0.255809
$748$	−6.15528	−0.225060
$749$	−84.2820	−3.07960
$750$	5.32435	0.194418
$751$	−1.83671	−0.0670224	−0.0335112	−	0.999438i	$-0.510669\pi$
$751$	−1.83671	−0.0670224	−0.0335112	+	0.999438i	$0.510669\pi$
$752$	−4.93665	−0.180021
$753$	−11.0458	−0.402530
$754$	−3.80501	−0.138570
$755$	6.98045	0.254045
$756$	24.4212	0.888189
$757$	−5.38543	−0.195737	−0.0978684	−	0.995199i	$-0.531202\pi$
$757$	−5.38543	−0.195737	−0.0978684	+	0.995199i	$0.531202\pi$
$758$	23.1989	0.842622
$759$	−1.07105	−0.0388767
$760$	−5.16405	−0.187320
$761$	−1.73321	−0.0628289	−0.0314144	−	0.999506i	$-0.510001\pi$
$761$	−1.73321	−0.0628289	−0.0314144	+	0.999506i	$0.510001\pi$
$762$	−13.2369	−0.479524
$763$	17.2133	0.623164
$764$	2.28731	0.0827521
$765$	36.7403	1.32835
$766$	−16.6486	−0.601538
$767$	−5.63327	−0.203406
$768$	−0.943634	−0.0340505
$769$	−47.9022	−1.72740	−0.863699	−	0.504008i	$-0.831858\pi$
$769$	−47.9022	−1.72740	−0.863699	+	0.504008i	$0.831858\pi$
$770$	14.3312	0.516461
$771$	17.1397	0.617271
$772$	−14.0700	−0.506392
$773$	31.2468	1.12387	0.561934	−	0.827182i	$-0.310057\pi$
$773$	31.2468	1.12387	0.561934	+	0.827182i	$0.310057\pi$
$774$	23.9851	0.862127
$775$	8.84706	0.317796
$776$	−15.9234	−0.571616
$777$	−11.6356	−0.417426
$778$	−10.6314	−0.381154
$779$	−20.5288	−0.735522
$780$	1.30873	0.0468601
$781$	−1.19624	−0.0428049
$782$	−6.98641	−0.249834
$783$	37.4282	1.33757
$784$	18.6542	0.666223
$785$	−25.6897	−0.916906
$786$	17.8603	0.637057
$787$	−14.5713	−0.519411	−0.259705	−	0.965688i	$-0.583625\pi$
$787$	−14.5713	−0.519411	−0.259705	+	0.965688i	$0.583625\pi$
$788$	1.00000	0.0356235
$789$	9.87076	0.351409
$790$	34.2933	1.22010
$791$	52.1020	1.85254
$792$	−2.10955	−0.0749597
$793$	−0.913893	−0.0324533
$794$	−5.68458	−0.201738
$795$	−30.9189	−1.09658
$796$	12.1765	0.431586
$797$	−18.4711	−0.654279	−0.327139	−	0.944976i	$-0.606085\pi$
$797$	−18.4711	−0.654279	−0.327139	+	0.944976i	$0.606085\pi$
$798$	8.72309	0.308794
$799$	30.3865	1.07500
$800$	3.00584	0.106273
$801$	−9.68082	−0.342055
$802$	−0.746551	−0.0263616
$803$	−14.4996	−0.511681
$804$	7.52073	0.265236
$805$	16.2663	0.573312
$806$	−1.44270	−0.0508169
$807$	6.86168	0.241543
$808$	16.1354	0.567641
$809$	−0.0649347	−0.00228298	−0.00114149	−	0.999999i	$-0.500363\pi$
$809$	−0.0649347	−0.00228298	−0.00114149	+	0.999999i	$0.500363\pi$
$810$	5.03327	0.176851
$811$	26.1472	0.918152	0.459076	−	0.888397i	$-0.348181\pi$
$811$	26.1472	0.918152	0.459076	+	0.888397i	$0.348181\pi$
$812$	39.3180	1.37979
$813$	−2.09705	−0.0735467
$814$	2.43448	0.0853286
$815$	−31.6477	−1.10857
$816$	5.80834	0.203333
$817$	20.7509	0.725983
$818$	−23.3232	−0.815476
$819$	5.23738	0.183009
$820$	31.8259	1.11141
$821$	−26.7912	−0.935020	−0.467510	−	0.883988i	$-0.654849\pi$
$821$	−26.7912	−0.935020	−0.467510	+	0.883988i	$0.654849\pi$
$822$	16.7207	0.583202
$823$	9.62229	0.335412	0.167706	−	0.985837i	$-0.446364\pi$
$823$	9.62229	0.335412	0.167706	+	0.985837i	$0.446364\pi$
$824$	13.6053	0.473964
$825$	−2.83642	−0.0987514
$826$	58.2099	2.02538
$827$	−14.0289	−0.487833	−0.243917	−	0.969796i	$-0.578432\pi$
$827$	−14.0289	−0.487833	−0.243917	+	0.969796i	$0.578432\pi$
$828$	−2.39440	−0.0832111
$829$	−40.3735	−1.40223	−0.701115	−	0.713048i	$-0.747314\pi$
$829$	−40.3735	−1.40223	−0.701115	+	0.713048i	$0.747314\pi$
$830$	9.37755	0.325500
$831$	10.8925	0.377857
$832$	−0.490166	−0.0169935
$833$	−114.822	−3.97835
$834$	8.47979	0.293631
$835$	−22.5536	−0.780498
$836$	−1.82510	−0.0631224
$837$	14.1912	0.490520
$838$	−11.1753	−0.386045
$839$	−19.7102	−0.680471	−0.340235	−	0.940340i	$-0.610507\pi$
$839$	−19.7102	−0.680471	−0.340235	+	0.940340i	$0.610507\pi$
$840$	−13.5234	−0.466603
$841$	31.2592	1.07790
$842$	−33.5257	−1.15537
$843$	5.13957	0.177016
$844$	14.8833	0.512304
$845$	−36.1032	−1.24199
$846$	10.4141	0.358045
$847$	5.06500	0.174036
$848$	11.5802	0.397666
$849$	−1.85500	−0.0636636
$850$	−18.5018	−0.634607
$851$	2.76320	0.0947214
$852$	1.12881	0.0386725
$853$	52.1742	1.78641	0.893205	−	0.449650i	$-0.148451\pi$
$853$	52.1742	1.78641	0.893205	+	0.449650i	$0.148451\pi$
$854$	9.44346	0.323149
$855$	10.8938	0.372561
$856$	−16.6401	−0.568746
$857$	24.2213	0.827384	0.413692	−	0.910417i	$-0.364239\pi$
$857$	24.2213	0.827384	0.413692	+	0.910417i	$0.364239\pi$
$858$	0.462538	0.0157908
$859$	26.5822	0.906974	0.453487	−	0.891263i	$-0.350180\pi$
$859$	26.5822	0.906974	0.453487	+	0.891263i	$0.350180\pi$
$860$	−32.1703	−1.09700
$861$	−53.7602	−1.83214
$862$	−28.9636	−0.986503
$863$	−37.2245	−1.26714	−0.633568	−	0.773687i	$-0.718410\pi$
$863$	−37.2245	−1.26714	−0.633568	+	0.773687i	$0.718410\pi$
$864$	4.82155	0.164032
$865$	−39.5049	−1.34321
$866$	−40.5590	−1.37825
$867$	−19.7102	−0.669393
$868$	14.9077	0.506002
$869$	12.1201	0.411146
$870$	−20.7262	−0.702683
$871$	3.90661	0.132370
$872$	3.39848	0.115087
$873$	33.5912	1.13689
$874$	−2.07154	−0.0700708
$875$	−28.5787	−0.966136
$876$	13.6824	0.462284
$877$	10.3039	0.347939	0.173970	−	0.984751i	$-0.444341\pi$
$877$	10.3039	0.347939	0.173970	+	0.984751i	$0.444341\pi$
$878$	−7.18835	−0.242595
$879$	6.81133	0.229741
$880$	2.82946	0.0953811
$881$	2.09765	0.0706715	0.0353357	−	0.999375i	$-0.488750\pi$
$881$	2.09765	0.0706715	0.0353357	+	0.999375i	$0.488750\pi$
$882$	−39.3521	−1.32506
$883$	39.6767	1.33523	0.667613	−	0.744508i	$-0.267316\pi$
$883$	39.6767	1.33523	0.667613	+	0.744508i	$0.267316\pi$
$884$	3.01711	0.101477
$885$	−30.6849	−1.03146
$886$	6.81377	0.228913
$887$	7.08593	0.237922	0.118961	−	0.992899i	$-0.462044\pi$
$887$	7.08593	0.237922	0.118961	+	0.992899i	$0.462044\pi$
$888$	−2.29726	−0.0770911
$889$	71.0499	2.38294
$890$	12.9845	0.435241
$891$	1.77888	0.0595948
$892$	20.9270	0.700686
$893$	9.00988	0.301504
$894$	16.1453	0.539980
$895$	13.8481	0.462891
$896$	5.06500	0.169210
$897$	0.524993	0.0175290
$898$	−3.22817	−0.107725
$899$	22.8478	0.762016
$900$	−6.34099	−0.211366
$901$	−71.2794	−2.37466
$902$	11.2481	0.374520
$903$	54.3418	1.80838
$904$	10.2867	0.342130
$905$	12.8485	0.427099
$906$	−2.32800	−0.0773427
$907$	55.9327	1.85721	0.928607	−	0.371065i	$-0.121007\pi$
$907$	55.9327	1.85721	0.928607	+	0.371065i	$0.121007\pi$
$908$	18.1905	0.603674
$909$	−34.0385	−1.12898
$910$	−7.02468	−0.232866
$911$	46.3072	1.53423	0.767113	−	0.641512i	$-0.221692\pi$
$911$	46.3072	1.53423	0.767113	+	0.641512i	$0.221692\pi$
$912$	1.72223	0.0570287
$913$	3.31426	0.109686
$914$	24.2471	0.802023
$915$	−4.97805	−0.164569
$916$	10.6293	0.351202
$917$	−95.8661	−3.16578
$918$	−29.6780	−0.979521
$919$	11.5248	0.380169	0.190085	−	0.981768i	$-0.439124\pi$
$919$	11.5248	0.380169	0.190085	+	0.981768i	$0.439124\pi$
$920$	3.21151	0.105880
$921$	8.61089	0.283738
$922$	−3.32357	−0.109456
$923$	0.586357	0.0193002
$924$	−4.77951	−0.157234
$925$	7.31768	0.240604
$926$	21.4277	0.704157
$927$	−28.7012	−0.942670
$928$	7.76268	0.254822
$929$	55.3101	1.81467	0.907333	−	0.420414i	$-0.138115\pi$
$929$	55.3101	1.81467	0.907333	+	0.420414i	$0.138115\pi$
$930$	−7.85850	−0.257690
$931$	−34.0459	−1.11581
$932$	−4.86540	−0.159371
$933$	15.3331	0.501985
$934$	4.10197	0.134221
$935$	−17.4161	−0.569568
$936$	1.03403	0.0337984
$937$	−29.1242	−0.951446	−0.475723	−	0.879595i	$-0.657813\pi$
$937$	−29.1242	−0.951446	−0.475723	+	0.879595i	$0.657813\pi$
$938$	−40.3679	−1.31806
$939$	−20.7227	−0.676261
$940$	−13.9680	−0.455587
$941$	31.5537	1.02862	0.514311	−	0.857604i	$-0.328048\pi$
$941$	31.5537	1.02862	0.514311	+	0.857604i	$0.328048\pi$
$942$	8.56761	0.279148
$943$	12.7668	0.415746
$944$	11.4926	0.374051
$945$	69.0987	2.24778
$946$	−11.3698	−0.369663
$947$	−56.8551	−1.84754	−0.923771	−	0.382946i	$-0.874909\pi$
$947$	−56.8551	−1.84754	−0.923771	+	0.382946i	$0.874909\pi$
$948$	−11.4369	−0.371454
$949$	7.10724	0.230711
$950$	−5.48597	−0.177988
$951$	10.0701	0.326547
$952$	−31.1765	−1.01044
$953$	15.5745	0.504508	0.252254	−	0.967661i	$-0.418828\pi$
$953$	15.5745	0.504508	0.252254	+	0.967661i	$0.418828\pi$
$954$	−24.4291	−0.790920
$955$	6.47186	0.209425
$956$	−2.33859	−0.0756352
$957$	−7.32513	−0.236788
$958$	−34.0565	−1.10032
$959$	−89.7492	−2.89815
$960$	−2.66998	−0.0861731
$961$	−22.3371	−0.720551
$962$	−1.19330	−0.0384736
$963$	35.1031	1.13118
$964$	27.1790	0.875376
$965$	−39.8106	−1.28155
$966$	−5.42487	−0.174542
$967$	15.0019	0.482429	0.241215	−	0.970472i	$-0.422454\pi$
$967$	15.0019	0.482429	0.241215	+	0.970472i	$0.422454\pi$
$968$	1.00000	0.0321412
$969$	−10.6008	−0.340547
$970$	−45.0546	−1.44662
$971$	13.2408	0.424919	0.212460	−	0.977170i	$-0.431853\pi$
$971$	13.2408	0.424919	0.212460	+	0.977170i	$0.431853\pi$
$972$	−16.1433	−0.517796
$973$	−45.5157	−1.45917
$974$	12.2788	0.393437
$975$	1.39032	0.0445258
$976$	1.86445	0.0596797
$977$	31.5922	1.01073	0.505363	−	0.862907i	$-0.331359\pi$
$977$	31.5922	1.01073	0.505363	+	0.862907i	$0.331359\pi$
$978$	10.5546	0.337499
$979$	4.58904	0.146666
$980$	52.7814	1.68604
$981$	−7.16929	−0.228898
$982$	20.8828	0.666398
$983$	39.9224	1.27333	0.636663	−	0.771142i	$-0.280314\pi$
$983$	39.9224	1.27333	0.636663	+	0.771142i	$0.280314\pi$
$984$	−10.6141	−0.338364
$985$	2.82946	0.0901541
$986$	−47.7815	−1.52167
$987$	23.5948	0.751029
$988$	0.894603	0.0284611
$989$	−12.9050	−0.410354
$990$	−5.96890	−0.189704
$991$	18.2842	0.580815	0.290408	−	0.956903i	$-0.406209\pi$
$991$	18.2842	0.580815	0.290408	+	0.956903i	$0.406209\pi$
$992$	2.94329	0.0934494
$993$	24.1726	0.767093
$994$	−6.05896	−0.192179
$995$	34.4530	1.09223
$996$	−3.12745	−0.0990969
$997$	35.5064	1.12450	0.562250	−	0.826968i	$-0.309936\pi$
$997$	35.5064	1.12450	0.562250	+	0.826968i	$0.309936\pi$
$998$	28.5263	0.902985
$999$	11.7380	0.371374

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4334.2.a.g.1.9	✓	26

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4334.2.a.g.1.9	✓	26	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -0.943634 q^{3} +1.00000 q^{4} +2.82946 q^{5} -0.943634 q^{6} +5.06500 q^{7} +1.00000 q^{8} -2.10955 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -0.943634 q^{3} +1.00000 q^{4} +2.82946 q^{5} -0.943634 q^{6} +5.06500 q^{7} +1.00000 q^{8} -2.10955 q^{9} +2.82946 q^{10} +1.00000 q^{11} -0.943634 q^{12} -0.490166 q^{13} +5.06500 q^{14} -2.66998 q^{15} +1.00000 q^{16} -6.15528 q^{17} -2.10955 q^{18} -1.82510 q^{19} +2.82946 q^{20} -4.77951 q^{21} +1.00000 q^{22} +1.13503 q^{23} -0.943634 q^{24} +3.00584 q^{25} -0.490166 q^{26} +4.82155 q^{27} +5.06500 q^{28} +7.76268 q^{29} -2.66998 q^{30} +2.94329 q^{31} +1.00000 q^{32} -0.943634 q^{33} -6.15528 q^{34} +14.3312 q^{35} -2.10955 q^{36} +2.43448 q^{37} -1.82510 q^{38} +0.462538 q^{39} +2.82946 q^{40} +11.2481 q^{41} -4.77951 q^{42} -11.3698 q^{43} +1.00000 q^{44} -5.96890 q^{45} +1.13503 q^{46} -4.93665 q^{47} -0.943634 q^{48} +18.6542 q^{49} +3.00584 q^{50} +5.80834 q^{51} -0.490166 q^{52} +11.5802 q^{53} +4.82155 q^{54} +2.82946 q^{55} +5.06500 q^{56} +1.72223 q^{57} +7.76268 q^{58} +11.4926 q^{59} -2.66998 q^{60} +1.86445 q^{61} +2.94329 q^{62} -10.6849 q^{63} +1.00000 q^{64} -1.38691 q^{65} -0.943634 q^{66} -7.96996 q^{67} -6.15528 q^{68} -1.07105 q^{69} +14.3312 q^{70} -1.19624 q^{71} -2.10955 q^{72} -14.4996 q^{73} +2.43448 q^{74} -2.83642 q^{75} -1.82510 q^{76} +5.06500 q^{77} +0.462538 q^{78} +12.1201 q^{79} +2.82946 q^{80} +1.77888 q^{81} +11.2481 q^{82} +3.31426 q^{83} -4.77951 q^{84} -17.4161 q^{85} -11.3698 q^{86} -7.32513 q^{87} +1.00000 q^{88} +4.58904 q^{89} -5.96890 q^{90} -2.48269 q^{91} +1.13503 q^{92} -2.77739 q^{93} -4.93665 q^{94} -5.16405 q^{95} -0.943634 q^{96} -15.9234 q^{97} +18.6542 q^{98} -2.10955 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 26 q + 26 q^{2} + 12 q^{3} + 26 q^{4} + 13 q^{5} + 12 q^{6} + 13 q^{7} + 26 q^{8} + 38 q^{9}+O(q^{10}) \) 26 * q + 26 * q^2 + 12 * q^3 + 26 * q^4 + 13 * q^5 + 12 * q^6 + 13 * q^7 + 26 * q^8 + 38 * q^9	\( 26 q + 26 q^{2} + 12 q^{3} + 26 q^{4} + 13 q^{5} + 12 q^{6} + 13 q^{7} + 26 q^{8} + 38 q^{9} + 13 q^{10} + 26 q^{11} + 12 q^{12} + 24 q^{13} + 13 q^{14} + 12 q^{15} + 26 q^{16} + q^{17} + 38 q^{18} + 24 q^{19} + 13 q^{20} + 5 q^{21} + 26 q^{22} + 19 q^{23} + 12 q^{24} + 35 q^{25} + 24 q^{26} + 39 q^{27} + 13 q^{28} + 5 q^{29} + 12 q^{30} + 34 q^{31} + 26 q^{32} + 12 q^{33} + q^{34} + 14 q^{35} + 38 q^{36} + 15 q^{37} + 24 q^{38} + 3 q^{39} + 13 q^{40} - 9 q^{41} + 5 q^{42} + 6 q^{43} + 26 q^{44} + 22 q^{45} + 19 q^{46} + 34 q^{47} + 12 q^{48} + 53 q^{49} + 35 q^{50} - 2 q^{51} + 24 q^{52} + 6 q^{53} + 39 q^{54} + 13 q^{55} + 13 q^{56} - 16 q^{57} + 5 q^{58} + 50 q^{59} + 12 q^{60} + 26 q^{61} + 34 q^{62} + 2 q^{63} + 26 q^{64} - 5 q^{65} + 12 q^{66} + 18 q^{67} + q^{68} + 15 q^{69} + 14 q^{70} + 23 q^{71} + 38 q^{72} + 37 q^{73} + 15 q^{74} + 18 q^{75} + 24 q^{76} + 13 q^{77} + 3 q^{78} + 10 q^{79} + 13 q^{80} + 50 q^{81} - 9 q^{82} + 7 q^{83} + 5 q^{84} - 7 q^{85} + 6 q^{86} + 16 q^{87} + 26 q^{88} + 3 q^{89} + 22 q^{90} + 31 q^{91} + 19 q^{92} + 52 q^{93} + 34 q^{94} + 9 q^{95} + 12 q^{96} - 9 q^{97} + 53 q^{98} + 38 q^{99}+O(q^{100}) \) 26 * q + 26 * q^2 + 12 * q^3 + 26 * q^4 + 13 * q^5 + 12 * q^6 + 13 * q^7 + 26 * q^8 + 38 * q^9 + 13 * q^10 + 26 * q^11 + 12 * q^12 + 24 * q^13 + 13 * q^14 + 12 * q^15 + 26 * q^16 + q^17 + 38 * q^18 + 24 * q^19 + 13 * q^20 + 5 * q^21 + 26 * q^22 + 19 * q^23 + 12 * q^24 + 35 * q^25 + 24 * q^26 + 39 * q^27 + 13 * q^28 + 5 * q^29 + 12 * q^30 + 34 * q^31 + 26 * q^32 + 12 * q^33 + q^34 + 14 * q^35 + 38 * q^36 + 15 * q^37 + 24 * q^38 + 3 * q^39 + 13 * q^40 - 9 * q^41 + 5 * q^42 + 6 * q^43 + 26 * q^44 + 22 * q^45 + 19 * q^46 + 34 * q^47 + 12 * q^48 + 53 * q^49 + 35 * q^50 - 2 * q^51 + 24 * q^52 + 6 * q^53 + 39 * q^54 + 13 * q^55 + 13 * q^56 - 16 * q^57 + 5 * q^58 + 50 * q^59 + 12 * q^60 + 26 * q^61 + 34 * q^62 + 2 * q^63 + 26 * q^64 - 5 * q^65 + 12 * q^66 + 18 * q^67 + q^68 + 15 * q^69 + 14 * q^70 + 23 * q^71 + 38 * q^72 + 37 * q^73 + 15 * q^74 + 18 * q^75 + 24 * q^76 + 13 * q^77 + 3 * q^78 + 10 * q^79 + 13 * q^80 + 50 * q^81 - 9 * q^82 + 7 * q^83 + 5 * q^84 - 7 * q^85 + 6 * q^86 + 16 * q^87 + 26 * q^88 + 3 * q^89 + 22 * q^90 + 31 * q^91 + 19 * q^92 + 52 * q^93 + 34 * q^94 + 9 * q^95 + 12 * q^96 - 9 * q^97 + 53 * q^98 + 38 * q^99

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