LMFDB - Embedded newform 4334.2.a.f.1.17

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			1.17
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)

$f(q)$	$=$	$q+1.00000 q^{2} +1.76169 q^{3} +1.00000 q^{4} -3.63225 q^{5} +1.76169 q^{6} -3.98143 q^{7} +1.00000 q^{8} +0.103544 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.76169 q^{3} +1.00000 q^{4} -3.63225 q^{5} +1.76169 q^{6} -3.98143 q^{7} +1.00000 q^{8} +0.103544 q^{9} -3.63225 q^{10} -1.00000 q^{11} +1.76169 q^{12} +6.84051 q^{13} -3.98143 q^{14} -6.39888 q^{15} +1.00000 q^{16} -7.57893 q^{17} +0.103544 q^{18} +6.99008 q^{19} -3.63225 q^{20} -7.01404 q^{21} -1.00000 q^{22} +7.14079 q^{23} +1.76169 q^{24} +8.19321 q^{25} +6.84051 q^{26} -5.10265 q^{27} -3.98143 q^{28} -0.153131 q^{29} -6.39888 q^{30} -8.94606 q^{31} +1.00000 q^{32} -1.76169 q^{33} -7.57893 q^{34} +14.4616 q^{35} +0.103544 q^{36} +1.14452 q^{37} +6.99008 q^{38} +12.0508 q^{39} -3.63225 q^{40} +2.23866 q^{41} -7.01404 q^{42} +7.86488 q^{43} -1.00000 q^{44} -0.376096 q^{45} +7.14079 q^{46} +7.06435 q^{47} +1.76169 q^{48} +8.85182 q^{49} +8.19321 q^{50} -13.3517 q^{51} +6.84051 q^{52} +5.10851 q^{53} -5.10265 q^{54} +3.63225 q^{55} -3.98143 q^{56} +12.3143 q^{57} -0.153131 q^{58} +0.843210 q^{59} -6.39888 q^{60} +12.5239 q^{61} -8.94606 q^{62} -0.412252 q^{63} +1.00000 q^{64} -24.8464 q^{65} -1.76169 q^{66} +4.34717 q^{67} -7.57893 q^{68} +12.5798 q^{69} +14.4616 q^{70} +9.18784 q^{71} +0.103544 q^{72} +2.33060 q^{73} +1.14452 q^{74} +14.4339 q^{75} +6.99008 q^{76} +3.98143 q^{77} +12.0508 q^{78} -15.8628 q^{79} -3.63225 q^{80} -9.29991 q^{81} +2.23866 q^{82} -7.39948 q^{83} -7.01404 q^{84} +27.5285 q^{85} +7.86488 q^{86} -0.269768 q^{87} -1.00000 q^{88} +3.88596 q^{89} -0.376096 q^{90} -27.2350 q^{91} +7.14079 q^{92} -15.7602 q^{93} +7.06435 q^{94} -25.3897 q^{95} +1.76169 q^{96} +15.5466 q^{97} +8.85182 q^{98} -0.103544 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	1.76169	1.01711	0.508555	−	0.861029i	$-0.330180\pi$
$3$	1.76169	1.01711	0.508555	+	0.861029i	$0.330180\pi$
$4$	1.00000	0.500000
$5$	−3.63225	−1.62439	−0.812195	−	0.583386i	$-0.801727\pi$
$5$	−3.63225	−1.62439	−0.812195	+	0.583386i	$0.801727\pi$
$6$	1.76169	0.719206
$7$	−3.98143	−1.50484	−0.752420	−	0.658683i	$-0.771114\pi$
$7$	−3.98143	−1.50484	−0.752420	+	0.658683i	$0.771114\pi$
$8$	1.00000	0.353553
$9$	0.103544	0.0345145
$10$	−3.63225	−1.14862
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	1.76169	0.508555
$13$	6.84051	1.89722	0.948608	−	0.316453i	$-0.102492\pi$
$13$	6.84051	1.89722	0.948608	+	0.316453i	$0.102492\pi$
$14$	−3.98143	−1.06408
$15$	−6.39888	−1.65218
$16$	1.00000	0.250000
$17$	−7.57893	−1.83816	−0.919080	−	0.394072i	$-0.871066\pi$
$17$	−7.57893	−1.83816	−0.919080	+	0.394072i	$0.871066\pi$
$18$	0.103544	0.0244055
$19$	6.99008	1.60363	0.801817	−	0.597569i	$-0.203867\pi$
$19$	6.99008	1.60363	0.801817	+	0.597569i	$0.203867\pi$
$20$	−3.63225	−0.812195
$21$	−7.01404	−1.53059
$22$	−1.00000	−0.213201
$23$	7.14079	1.48896	0.744479	−	0.667646i	$-0.232698\pi$
$23$	7.14079	1.48896	0.744479	+	0.667646i	$0.232698\pi$
$24$	1.76169	0.359603
$25$	8.19321	1.63864
$26$	6.84051	1.34153
$27$	−5.10265	−0.982006
$28$	−3.98143	−0.752420
$29$	−0.153131	−0.0284356	−0.0142178	−	0.999899i	$-0.504526\pi$
$29$	−0.153131	−0.0284356	−0.0142178	+	0.999899i	$0.504526\pi$
$30$	−6.39888	−1.16827
$31$	−8.94606	−1.60676	−0.803380	−	0.595467i	$-0.796967\pi$
$31$	−8.94606	−1.60676	−0.803380	+	0.595467i	$0.796967\pi$
$32$	1.00000	0.176777
$33$	−1.76169	−0.306670
$34$	−7.57893	−1.29977
$35$	14.4616	2.44445
$36$	0.103544	0.0172573
$37$	1.14452	0.188158	0.0940792	−	0.995565i	$-0.470009\pi$
$37$	1.14452	0.188158	0.0940792	+	0.995565i	$0.470009\pi$
$38$	6.99008	1.13394
$39$	12.0508	1.92968
$40$	−3.63225	−0.574309
$41$	2.23866	0.349620	0.174810	−	0.984602i	$-0.444069\pi$
$41$	2.23866	0.349620	0.174810	+	0.984602i	$0.444069\pi$
$42$	−7.01404	−1.08229
$43$	7.86488	1.19938	0.599692	−	0.800231i	$-0.295290\pi$
$43$	7.86488	1.19938	0.599692	+	0.800231i	$0.295290\pi$
$44$	−1.00000	−0.150756
$45$	−0.376096	−0.0560651
$46$	7.14079	1.05285
$47$	7.06435	1.03044	0.515221	−	0.857058i	$-0.327710\pi$
$47$	7.06435	1.03044	0.515221	+	0.857058i	$0.327710\pi$
$48$	1.76169	0.254278
$49$	8.85182	1.26455
$50$	8.19321	1.15870
$51$	−13.3517	−1.86961
$52$	6.84051	0.948608
$53$	5.10851	0.701708	0.350854	−	0.936430i	$-0.385891\pi$
$53$	5.10851	0.701708	0.350854	+	0.936430i	$0.385891\pi$
$54$	−5.10265	−0.694383
$55$	3.63225	0.489772
$56$	−3.98143	−0.532042
$57$	12.3143	1.63107
$58$	−0.153131	−0.0201070
$59$	0.843210	0.109777	0.0548883	−	0.998493i	$-0.482520\pi$
$59$	0.843210	0.109777	0.0548883	+	0.998493i	$0.482520\pi$
$60$	−6.39888	−0.826092
$61$	12.5239	1.60352	0.801762	−	0.597644i	$-0.203896\pi$
$61$	12.5239	1.60352	0.801762	+	0.597644i	$0.203896\pi$
$62$	−8.94606	−1.13615
$63$	−0.412252	−0.0519389
$64$	1.00000	0.125000
$65$	−24.8464	−3.08182
$66$	−1.76169	−0.216849
$67$	4.34717	0.531092	0.265546	−	0.964098i	$-0.414448\pi$
$67$	4.34717	0.531092	0.265546	+	0.964098i	$0.414448\pi$
$68$	−7.57893	−0.919080
$69$	12.5798	1.51444
$70$	14.4616	1.72849
$71$	9.18784	1.09040	0.545198	−	0.838307i	$-0.316454\pi$
$71$	9.18784	1.09040	0.545198	+	0.838307i	$0.316454\pi$
$72$	0.103544	0.0122027
$73$	2.33060	0.272776	0.136388	−	0.990656i	$-0.456451\pi$
$73$	2.33060	0.272776	0.136388	+	0.990656i	$0.456451\pi$
$74$	1.14452	0.133048
$75$	14.4339	1.66668
$76$	6.99008	0.801817
$77$	3.98143	0.453727
$78$	12.0508	1.36449
$79$	−15.8628	−1.78471	−0.892353	−	0.451337i	$-0.850947\pi$
$79$	−15.8628	−1.78471	−0.892353	+	0.451337i	$0.850947\pi$
$80$	−3.63225	−0.406098
$81$	−9.29991	−1.03332
$82$	2.23866	0.247218
$83$	−7.39948	−0.812199	−0.406099	−	0.913829i	$-0.633111\pi$
$83$	−7.39948	−0.812199	−0.406099	+	0.913829i	$0.633111\pi$
$84$	−7.01404	−0.765295
$85$	27.5285	2.98589
$86$	7.86488	0.848092
$87$	−0.269768	−0.0289222
$88$	−1.00000	−0.106600
$89$	3.88596	0.411911	0.205956	−	0.978561i	$-0.433970\pi$
$89$	3.88596	0.411911	0.205956	+	0.978561i	$0.433970\pi$
$90$	−0.376096	−0.0396440
$91$	−27.2350	−2.85501
$92$	7.14079	0.744479
$93$	−15.7602	−1.63425
$94$	7.06435	0.728632
$95$	−25.3897	−2.60493
$96$	1.76169	0.179801
$97$	15.5466	1.57852	0.789261	−	0.614057i	$-0.210464\pi$
$97$	15.5466	1.57852	0.789261	+	0.614057i	$0.210464\pi$
$98$	8.85182	0.894169
$99$	−0.103544	−0.0104065
$100$	8.19321	0.819321
$101$	9.38522	0.933865	0.466932	−	0.884293i	$-0.345359\pi$
$101$	9.38522	0.933865	0.466932	+	0.884293i	$0.345359\pi$
$102$	−13.3517	−1.32202
$103$	15.7425	1.55115	0.775577	−	0.631253i	$-0.217459\pi$
$103$	15.7425	1.55115	0.775577	+	0.631253i	$0.217459\pi$
$104$	6.84051	0.670767
$105$	25.4767	2.48627
$106$	5.10851	0.496182
$107$	−0.897096	−0.0867256	−0.0433628	−	0.999059i	$-0.513807\pi$
$107$	−0.897096	−0.0867256	−0.0433628	+	0.999059i	$0.513807\pi$
$108$	−5.10265	−0.491003
$109$	−4.54732	−0.435554	−0.217777	−	0.975999i	$-0.569881\pi$
$109$	−4.54732	−0.435554	−0.217777	+	0.975999i	$0.569881\pi$
$110$	3.63225	0.346321
$111$	2.01629	0.191378
$112$	−3.98143	−0.376210
$113$	−13.2528	−1.24671	−0.623357	−	0.781937i	$-0.714232\pi$
$113$	−13.2528	−1.24671	−0.623357	+	0.781937i	$0.714232\pi$
$114$	12.3143	1.15334
$115$	−25.9371	−2.41865
$116$	−0.153131	−0.0142178
$117$	0.708291	0.0654815
$118$	0.843210	0.0776238
$119$	30.1750	2.76614
$120$	−6.39888	−0.584136
$121$	1.00000	0.0909091
$122$	12.5239	1.13386
$123$	3.94382	0.355602
$124$	−8.94606	−0.803380
$125$	−11.5985	−1.03741
$126$	−0.412252	−0.0367263
$127$	19.9289	1.76840	0.884201	−	0.467107i	$-0.154704\pi$
$127$	19.9289	1.76840	0.884201	+	0.467107i	$0.154704\pi$
$128$	1.00000	0.0883883
$129$	13.8555	1.21991
$130$	−24.8464	−2.17918
$131$	7.48370	0.653854	0.326927	−	0.945050i	$-0.393987\pi$
$131$	7.48370	0.653854	0.326927	+	0.945050i	$0.393987\pi$
$132$	−1.76169	−0.153335
$133$	−27.8305	−2.41321
$134$	4.34717	0.375539
$135$	18.5341	1.59516
$136$	−7.57893	−0.649887
$137$	2.96191	0.253053	0.126527	−	0.991963i	$-0.459617\pi$
$137$	2.96191	0.253053	0.126527	+	0.991963i	$0.459617\pi$
$138$	12.5798	1.07087
$139$	−3.78749	−0.321251	−0.160625	−	0.987015i	$-0.551351\pi$
$139$	−3.78749	−0.321251	−0.160625	+	0.987015i	$0.551351\pi$
$140$	14.4616	1.22222
$141$	12.4452	1.04807
$142$	9.18784	0.771027
$143$	−6.84051	−0.572032
$144$	0.103544	0.00862863
$145$	0.556208	0.0461906
$146$	2.33060	0.192881
$147$	15.5941	1.28618
$148$	1.14452	0.0940792
$149$	−5.37240	−0.440124	−0.220062	−	0.975486i	$-0.570626\pi$
$149$	−5.37240	−0.440124	−0.220062	+	0.975486i	$0.570626\pi$
$150$	14.4339	1.17852
$151$	−17.6466	−1.43606	−0.718031	−	0.696011i	$-0.754957\pi$
$151$	−17.6466	−1.43606	−0.718031	+	0.696011i	$0.754957\pi$
$152$	6.99008	0.566970
$153$	−0.784749	−0.0634432
$154$	3.98143	0.320833
$155$	32.4943	2.61000
$156$	12.0508	0.964840
$157$	−7.34152	−0.585917	−0.292959	−	0.956125i	$-0.594640\pi$
$157$	−7.34152	−0.585917	−0.292959	+	0.956125i	$0.594640\pi$
$158$	−15.8628	−1.26198
$159$	8.99960	0.713715
$160$	−3.63225	−0.287154
$161$	−28.4306	−2.24064
$162$	−9.29991	−0.730670
$163$	5.46491	0.428045	0.214023	−	0.976829i	$-0.431343\pi$
$163$	5.46491	0.428045	0.214023	+	0.976829i	$0.431343\pi$
$164$	2.23866	0.174810
$165$	6.39888	0.498152
$166$	−7.39948	−0.574311
$167$	13.8710	1.07337	0.536687	−	0.843782i	$-0.319676\pi$
$167$	13.8710	1.07337	0.536687	+	0.843782i	$0.319676\pi$
$168$	−7.01404	−0.541145
$169$	33.7926	2.59943
$170$	27.5285	2.11134
$171$	0.723778	0.0553487
$172$	7.86488	0.599692
$173$	−23.7606	−1.80649	−0.903244	−	0.429127i	$-0.858821\pi$
$173$	−23.7606	−1.80649	−0.903244	+	0.429127i	$0.858821\pi$
$174$	−0.269768	−0.0204511
$175$	−32.6207	−2.46590
$176$	−1.00000	−0.0753778
$177$	1.48547	0.111655
$178$	3.88596	0.291265
$179$	−1.61495	−0.120707	−0.0603537	−	0.998177i	$-0.519223\pi$
$179$	−1.61495	−0.120707	−0.0603537	+	0.998177i	$0.519223\pi$
$180$	−0.376096	−0.0280325
$181$	−3.59230	−0.267013	−0.133507	−	0.991048i	$-0.542624\pi$
$181$	−3.59230	−0.267013	−0.133507	+	0.991048i	$0.542624\pi$
$182$	−27.2350	−2.01880
$183$	22.0632	1.63096
$184$	7.14079	0.526426
$185$	−4.15719	−0.305643
$186$	−15.7602	−1.15559
$187$	7.57893	0.554226
$188$	7.06435	0.515221
$189$	20.3159	1.47776
$190$	−25.3897	−1.84196
$191$	−21.3060	−1.54165	−0.770825	−	0.637047i	$-0.780156\pi$
$191$	−21.3060	−1.54165	−0.770825	+	0.637047i	$0.780156\pi$
$192$	1.76169	0.127139
$193$	6.08589	0.438072	0.219036	−	0.975717i	$-0.429709\pi$
$193$	6.08589	0.438072	0.219036	+	0.975717i	$0.429709\pi$
$194$	15.5466	1.11618
$195$	−43.7716	−3.13455
$196$	8.85182	0.632273
$197$	−1.00000	−0.0712470
$197$	−1.00000	−0.0712470
$198$	−0.103544	−0.00735852
$199$	3.43264	0.243334	0.121667	−	0.992571i	$-0.461176\pi$
$199$	3.43264	0.243334	0.121667	+	0.992571i	$0.461176\pi$
$200$	8.19321	0.579348
$201$	7.65836	0.540179
$202$	9.38522	0.660342
$203$	0.609679	0.0427911
$204$	−13.3517	−0.934806
$205$	−8.13136	−0.567919
$206$	15.7425	1.09683
$207$	0.739383	0.0513907
$208$	6.84051	0.474304
$209$	−6.99008	−0.483514
$210$	25.4767	1.75806
$211$	4.16030	0.286407	0.143203	−	0.989693i	$-0.454260\pi$
$211$	4.16030	0.286407	0.143203	+	0.989693i	$0.454260\pi$
$212$	5.10851	0.350854
$213$	16.1861	1.10905
$214$	−0.897096	−0.0613242
$215$	−28.5672	−1.94827
$216$	−5.10265	−0.347191
$217$	35.6182	2.41792
$218$	−4.54732	−0.307983
$219$	4.10578	0.277443
$220$	3.63225	0.244886
$221$	−51.8437	−3.48739
$222$	2.01629	0.135325
$223$	20.0594	1.34328	0.671640	−	0.740878i	$-0.265590\pi$
$223$	20.0594	1.34328	0.671640	+	0.740878i	$0.265590\pi$
$224$	−3.98143	−0.266021
$225$	0.848355	0.0565570
$226$	−13.2528	−0.881560
$227$	−5.22716	−0.346939	−0.173469	−	0.984839i	$-0.555498\pi$
$227$	−5.22716	−0.346939	−0.173469	+	0.984839i	$0.555498\pi$
$228$	12.3143	0.815537
$229$	5.63525	0.372388	0.186194	−	0.982513i	$-0.440385\pi$
$229$	5.63525	0.372388	0.186194	+	0.982513i	$0.440385\pi$
$230$	−25.9371	−1.71024
$231$	7.01404	0.461490
$232$	−0.153131	−0.0100535
$233$	−17.5872	−1.15218	−0.576089	−	0.817387i	$-0.695422\pi$
$233$	−17.5872	−1.15218	−0.576089	+	0.817387i	$0.695422\pi$
$234$	0.708291	0.0463024
$235$	−25.6595	−1.67384
$236$	0.843210	0.0548883
$237$	−27.9453	−1.81524
$238$	30.1750	1.95595
$239$	−1.71632	−0.111019	−0.0555096	−	0.998458i	$-0.517678\pi$
$239$	−1.71632	−0.111019	−0.0555096	+	0.998458i	$0.517678\pi$
$240$	−6.39888	−0.413046
$241$	4.48913	0.289170	0.144585	−	0.989492i	$-0.453815\pi$
$241$	4.48913	0.289170	0.144585	+	0.989492i	$0.453815\pi$
$242$	1.00000	0.0642824
$243$	−1.07558	−0.0689986
$244$	12.5239	0.801762
$245$	−32.1520	−2.05411
$246$	3.94382	0.251449
$247$	47.8157	3.04244
$248$	−8.94606	−0.568075
$249$	−13.0356	−0.826096
$250$	−11.5985	−0.733556
$251$	−14.7730	−0.932461	−0.466230	−	0.884663i	$-0.654388\pi$
$251$	−14.7730	−0.932461	−0.466230	+	0.884663i	$0.654388\pi$
$252$	−0.412252	−0.0259694
$253$	−7.14079	−0.448938
$254$	19.9289	1.25045
$255$	48.4967	3.03698
$256$	1.00000	0.0625000
$257$	0.556544	0.0347163	0.0173581	−	0.999849i	$-0.494474\pi$
$257$	0.556544	0.0347163	0.0173581	+	0.999849i	$0.494474\pi$
$258$	13.8555	0.862604
$259$	−4.55684	−0.283148
$260$	−24.8464	−1.54091
$261$	−0.0158557	−0.000981442 0
$262$	7.48370	0.462345
$263$	20.9466	1.29162	0.645810	−	0.763498i	$-0.276520\pi$
$263$	20.9466	1.29162	0.645810	+	0.763498i	$0.276520\pi$
$264$	−1.76169	−0.108424
$265$	−18.5554	−1.13985
$266$	−27.8305	−1.70640
$267$	6.84585	0.418959
$268$	4.34717	0.265546
$269$	3.62371	0.220941	0.110471	−	0.993879i	$-0.464764\pi$
$269$	3.62371	0.220941	0.110471	+	0.993879i	$0.464764\pi$
$270$	18.5341	1.12795
$271$	25.5303	1.55085	0.775426	−	0.631438i	$-0.217535\pi$
$271$	25.5303	1.55085	0.775426	+	0.631438i	$0.217535\pi$
$272$	−7.57893	−0.459540
$273$	−47.9796	−2.90386
$274$	2.96191	0.178936
$275$	−8.19321	−0.494069
$276$	12.5798	0.757218
$277$	11.1565	0.670328	0.335164	−	0.942160i	$-0.391208\pi$
$277$	11.1565	0.670328	0.335164	+	0.942160i	$0.391208\pi$
$278$	−3.78749	−0.227159
$279$	−0.926307	−0.0554566
$280$	14.4616	0.864243
$281$	18.8941	1.12713	0.563564	−	0.826073i	$-0.309430\pi$
$281$	18.8941	1.12713	0.563564	+	0.826073i	$0.309430\pi$
$282$	12.4452	0.741100
$283$	3.16727	0.188275	0.0941374	−	0.995559i	$-0.469991\pi$
$283$	3.16727	0.188275	0.0941374	+	0.995559i	$0.469991\pi$
$284$	9.18784	0.545198
$285$	−44.7287	−2.64950
$286$	−6.84051	−0.404488
$287$	−8.91307	−0.526122
$288$	0.103544	0.00610136
$289$	40.4401	2.37883
$290$	0.556208	0.0326617
$291$	27.3883	1.60553
$292$	2.33060	0.136388
$293$	24.5369	1.43346	0.716729	−	0.697352i	$-0.245638\pi$
$293$	24.5369	1.43346	0.716729	+	0.697352i	$0.245638\pi$
$294$	15.5941	0.909469
$295$	−3.06275	−0.178320
$296$	1.14452	0.0665240
$297$	5.10265	0.296086
$298$	−5.37240	−0.311215
$299$	48.8467	2.82487
$300$	14.4339	0.833341
$301$	−31.3135	−1.80488
$302$	−17.6466	−1.01545
$303$	16.5338	0.949844
$304$	6.99008	0.400909
$305$	−45.4900	−2.60475
$306$	−0.784749	−0.0448611
$307$	−8.98948	−0.513057	−0.256528	−	0.966537i	$-0.582579\pi$
$307$	−8.98948	−0.513057	−0.256528	+	0.966537i	$0.582579\pi$
$308$	3.98143	0.226863
$309$	27.7334	1.57770
$310$	32.4943	1.84555
$311$	−19.9450	−1.13098	−0.565490	−	0.824755i	$-0.691313\pi$
$311$	−19.9450	−1.13098	−0.565490	+	0.824755i	$0.691313\pi$
$312$	12.0508	0.682245
$313$	−25.9954	−1.46935	−0.734673	−	0.678422i	$-0.762664\pi$
$313$	−25.9954	−1.46935	−0.734673	+	0.678422i	$0.762664\pi$
$314$	−7.34152	−0.414306
$315$	1.49740	0.0843690
$316$	−15.8628	−0.892353
$317$	22.1365	1.24331	0.621654	−	0.783292i	$-0.286461\pi$
$317$	22.1365	1.24331	0.621654	+	0.783292i	$0.286461\pi$
$318$	8.99960	0.504672
$319$	0.153131	0.00857366
$320$	−3.63225	−0.203049
$321$	−1.58040	−0.0882095
$322$	−28.4306	−1.58437
$323$	−52.9773	−2.94774
$324$	−9.29991	−0.516662
$325$	56.0458	3.10886
$326$	5.46491	0.302674
$327$	−8.01096	−0.443007
$328$	2.23866	0.123609
$329$	−28.1262	−1.55065
$330$	6.39888	0.352247
$331$	−20.7588	−1.14100	−0.570502	−	0.821296i	$-0.693251\pi$
$331$	−20.7588	−1.14100	−0.570502	+	0.821296i	$0.693251\pi$
$332$	−7.39948	−0.406099
$333$	0.118508	0.00649420
$334$	13.8710	0.758989
$335$	−15.7900	−0.862700
$336$	−7.01404	−0.382647
$337$	−13.9407	−0.759399	−0.379699	−	0.925110i	$-0.623973\pi$
$337$	−13.9407	−0.759399	−0.379699	+	0.925110i	$0.623973\pi$
$338$	33.7926	1.83807
$339$	−23.3472	−1.26805
$340$	27.5285	1.49294
$341$	8.94606	0.484456
$342$	0.723778	0.0391374
$343$	−7.37289	−0.398099
$344$	7.86488	0.424046
$345$	−45.6931	−2.46003
$346$	−23.7606	−1.27738
$347$	−33.1546	−1.77983	−0.889915	−	0.456127i	$-0.849236\pi$
$347$	−33.1546	−1.77983	−0.889915	+	0.456127i	$0.849236\pi$
$348$	−0.269768	−0.0144611
$349$	2.28024	0.122058	0.0610292	−	0.998136i	$-0.480562\pi$
$349$	2.28024	0.122058	0.0610292	+	0.998136i	$0.480562\pi$
$350$	−32.6207	−1.74365
$351$	−34.9047	−1.86308
$352$	−1.00000	−0.0533002
$353$	−13.0470	−0.694422	−0.347211	−	0.937787i	$-0.612871\pi$
$353$	−13.0470	−0.694422	−0.347211	+	0.937787i	$0.612871\pi$
$354$	1.48547	0.0789520
$355$	−33.3725	−1.77123
$356$	3.88596	0.205956
$357$	53.1589	2.81347
$358$	−1.61495	−0.0853530
$359$	−8.52242	−0.449796	−0.224898	−	0.974382i	$-0.572205\pi$
$359$	−8.52242	−0.449796	−0.224898	+	0.974382i	$0.572205\pi$
$360$	−0.376096	−0.0198220
$361$	29.8612	1.57164
$362$	−3.59230	−0.188807
$363$	1.76169	0.0924646
$364$	−27.2350	−1.42750
$365$	−8.46530	−0.443094
$366$	22.0632	1.15326
$367$	−28.2821	−1.47632	−0.738158	−	0.674628i	$-0.764304\pi$
$367$	−28.2821	−1.47632	−0.738158	+	0.674628i	$0.764304\pi$
$368$	7.14079	0.372239
$369$	0.231799	0.0120670
$370$	−4.15719	−0.216122
$371$	−20.3392	−1.05596
$372$	−15.7602	−0.817127
$373$	−8.67615	−0.449234	−0.224617	−	0.974447i	$-0.572113\pi$
$373$	−8.67615	−0.449234	−0.224617	+	0.974447i	$0.572113\pi$
$374$	7.57893	0.391897
$375$	−20.4330	−1.05516
$376$	7.06435	0.364316
$377$	−1.04749	−0.0539485
$378$	20.3159	1.04494
$379$	−31.7838	−1.63262	−0.816311	−	0.577612i	$-0.803985\pi$
$379$	−31.7838	−1.63262	−0.816311	+	0.577612i	$0.803985\pi$
$380$	−25.3897	−1.30246
$381$	35.1085	1.79866
$382$	−21.3060	−1.09011
$383$	−14.4309	−0.737385	−0.368693	−	0.929551i	$-0.620195\pi$
$383$	−14.4309	−0.737385	−0.368693	+	0.929551i	$0.620195\pi$
$384$	1.76169	0.0899007
$385$	−14.4616	−0.737029
$386$	6.08589	0.309764
$387$	0.814358	0.0413962
$388$	15.5466	0.789261
$389$	−2.74621	−0.139239	−0.0696193	−	0.997574i	$-0.522178\pi$
$389$	−2.74621	−0.139239	−0.0696193	+	0.997574i	$0.522178\pi$
$390$	−43.7716	−2.21646
$391$	−54.1195	−2.73694
$392$	8.85182	0.447084
$393$	13.1840	0.665042
$394$	−1.00000	−0.0503793
$395$	57.6177	2.89906
$396$	−0.103544	−0.00520326
$397$	33.4618	1.67940	0.839700	−	0.543050i	$-0.182731\pi$
$397$	33.4618	1.67940	0.839700	+	0.543050i	$0.182731\pi$
$398$	3.43264	0.172063
$399$	−49.0287	−2.45451
$400$	8.19321	0.409661
$401$	−11.0408	−0.551350	−0.275675	−	0.961251i	$-0.588901\pi$
$401$	−11.0408	−0.551350	−0.275675	+	0.961251i	$0.588901\pi$
$402$	7.65836	0.381964
$403$	−61.1956	−3.04837
$404$	9.38522	0.466932
$405$	33.7796	1.67852
$406$	0.609679	0.0302579
$407$	−1.14452	−0.0567319
$408$	−13.3517	−0.661008
$409$	13.5171	0.668379	0.334189	−	0.942506i	$-0.391537\pi$
$409$	13.5171	0.668379	0.334189	+	0.942506i	$0.391537\pi$
$410$	−8.13136	−0.401579
$411$	5.21797	0.257383
$412$	15.7425	0.775577
$413$	−3.35718	−0.165196
$414$	0.739383	0.0363387
$415$	26.8767	1.31933
$416$	6.84051	0.335384
$417$	−6.67237	−0.326748
$418$	−6.99008	−0.341896
$419$	−24.6204	−1.20279	−0.601394	−	0.798953i	$-0.705388\pi$
$419$	−24.6204	−1.20279	−0.601394	+	0.798953i	$0.705388\pi$
$420$	25.4767	1.24314
$421$	−9.55128	−0.465501	−0.232751	−	0.972536i	$-0.574773\pi$
$421$	−9.55128	−0.465501	−0.232751	+	0.972536i	$0.574773\pi$
$422$	4.16030	0.202520
$423$	0.731468	0.0355652
$424$	5.10851	0.248091
$425$	−62.0958	−3.01209
$426$	16.1861	0.784219
$427$	−49.8632	−2.41305
$428$	−0.897096	−0.0433628
$429$	−12.0508	−0.581820
$430$	−28.5672	−1.37763
$431$	34.2351	1.64905	0.824524	−	0.565827i	$-0.191443\pi$
$431$	34.2351	1.64905	0.824524	+	0.565827i	$0.191443\pi$
$432$	−5.10265	−0.245501
$433$	−28.7613	−1.38218	−0.691089	−	0.722770i	$-0.742869\pi$
$433$	−28.7613	−1.38218	−0.691089	+	0.722770i	$0.742869\pi$
$434$	35.6182	1.70973
$435$	0.979865	0.0469809
$436$	−4.54732	−0.217777
$437$	49.9147	2.38774
$438$	4.10578	0.196182
$439$	31.3231	1.49497	0.747485	−	0.664278i	$-0.231261\pi$
$439$	31.3231	1.49497	0.747485	+	0.664278i	$0.231261\pi$
$440$	3.63225	0.173161
$441$	0.916549	0.0436452
$442$	−51.8437	−2.46595
$443$	−2.18930	−0.104017	−0.0520084	−	0.998647i	$-0.516562\pi$
$443$	−2.18930	−0.104017	−0.0520084	+	0.998647i	$0.516562\pi$
$444$	2.01629	0.0956890
$445$	−14.1148	−0.669104
$446$	20.0594	0.949842
$447$	−9.46450	−0.447655
$448$	−3.98143	−0.188105
$449$	9.17220	0.432863	0.216431	−	0.976298i	$-0.430558\pi$
$449$	9.17220	0.432863	0.216431	+	0.976298i	$0.430558\pi$
$450$	0.848355	0.0399918
$451$	−2.23866	−0.105414
$452$	−13.2528	−0.623357
$453$	−31.0879	−1.46063
$454$	−5.22716	−0.245323
$455$	98.9244	4.63765
$456$	12.3143	0.576672
$457$	−27.0393	−1.26484	−0.632421	−	0.774625i	$-0.717939\pi$
$457$	−27.0393	−1.26484	−0.632421	+	0.774625i	$0.717939\pi$
$458$	5.63525	0.263318
$459$	38.6726	1.80508
$460$	−25.9371	−1.20932
$461$	12.1621	0.566446	0.283223	−	0.959054i	$-0.408596\pi$
$461$	12.1621	0.566446	0.283223	+	0.959054i	$0.408596\pi$
$462$	7.01404	0.326323
$463$	−6.84201	−0.317975	−0.158988	−	0.987281i	$-0.550823\pi$
$463$	−6.84201	−0.317975	−0.158988	+	0.987281i	$0.550823\pi$
$464$	−0.153131	−0.00710891
$465$	57.2448	2.65466
$466$	−17.5872	−0.814714
$467$	2.17305	0.100557	0.0502784	−	0.998735i	$-0.483989\pi$
$467$	2.17305	0.100557	0.0502784	+	0.998735i	$0.483989\pi$
$468$	0.708291	0.0327408
$469$	−17.3080	−0.799208
$470$	−25.6595	−1.18358
$471$	−12.9335	−0.595943
$472$	0.843210	0.0388119
$473$	−7.86488	−0.361628
$474$	−27.9453	−1.28357
$475$	57.2712	2.62778
$476$	30.1750	1.38307
$477$	0.528953	0.0242191
$478$	−1.71632	−0.0785024
$479$	−10.2677	−0.469145	−0.234573	−	0.972099i	$-0.575369\pi$
$479$	−10.2677	−0.469145	−0.234573	+	0.972099i	$0.575369\pi$
$480$	−6.39888	−0.292068
$481$	7.82912	0.356977
$482$	4.48913	0.204474
$483$	−50.0858	−2.27898
$484$	1.00000	0.0454545
$485$	−56.4693	−2.56414
$486$	−1.07558	−0.0487894
$487$	15.1781	0.687787	0.343894	−	0.939009i	$-0.388254\pi$
$487$	15.1781	0.687787	0.343894	+	0.939009i	$0.388254\pi$
$488$	12.5239	0.566931
$489$	9.62747	0.435369
$490$	−32.1520	−1.45248
$491$	−19.3087	−0.871389	−0.435695	−	0.900095i	$-0.643497\pi$
$491$	−19.3087	−0.871389	−0.435695	+	0.900095i	$0.643497\pi$
$492$	3.94382	0.177801
$493$	1.16056	0.0522692
$494$	47.8157	2.15133
$495$	0.376096	0.0169043
$496$	−8.94606	−0.401690
$497$	−36.5808	−1.64087
$498$	−13.0356	−0.584138
$499$	24.4353	1.09388	0.546938	−	0.837173i	$-0.315793\pi$
$499$	24.4353	1.09388	0.546938	+	0.837173i	$0.315793\pi$
$500$	−11.5985	−0.518703
$501$	24.4364	1.09174
$502$	−14.7730	−0.659349
$503$	27.6209	1.23156	0.615778	−	0.787920i	$-0.288842\pi$
$503$	27.6209	1.23156	0.615778	+	0.787920i	$0.288842\pi$
$504$	−0.412252	−0.0183632
$505$	−34.0894	−1.51696
$506$	−7.14079	−0.317447
$507$	59.5320	2.64391
$508$	19.9289	0.884201
$509$	10.8574	0.481244	0.240622	−	0.970619i	$-0.422649\pi$
$509$	10.8574	0.481244	0.240622	+	0.970619i	$0.422649\pi$
$510$	48.4967	2.14747
$511$	−9.27911	−0.410484
$512$	1.00000	0.0441942
$513$	−35.6679	−1.57478
$514$	0.556544	0.0245481
$515$	−57.1806	−2.51968
$516$	13.8555	0.609953
$517$	−7.06435	−0.310690
$518$	−4.55684	−0.200216
$519$	−41.8588	−1.83740
$520$	−24.8464	−1.08959
$521$	−3.50607	−0.153604	−0.0768019	−	0.997046i	$-0.524471\pi$
$521$	−3.50607	−0.153604	−0.0768019	+	0.997046i	$0.524471\pi$
$522$	−0.0158557	−0.000693985 0
$523$	−8.29059	−0.362522	−0.181261	−	0.983435i	$-0.558018\pi$
$523$	−8.29059	−0.362522	−0.181261	+	0.983435i	$0.558018\pi$
$524$	7.48370	0.326927
$525$	−57.4676	−2.50809
$526$	20.9466	0.913313
$527$	67.8015	2.95348
$528$	−1.76169	−0.0766676
$529$	27.9909	1.21700
$530$	−18.5554	−0.805994
$531$	0.0873090	0.00378889
$532$	−27.8305	−1.20661
$533$	15.3136	0.663304
$534$	6.84585	0.296249
$535$	3.25847	0.140876
$536$	4.34717	0.187769
$537$	−2.84504	−0.122773
$538$	3.62371	0.156229
$539$	−8.85182	−0.381275
$540$	18.5341	0.797580
$541$	7.04018	0.302681	0.151340	−	0.988482i	$-0.451641\pi$
$541$	7.04018	0.302681	0.151340	+	0.988482i	$0.451641\pi$
$542$	25.5303	1.09662
$543$	−6.32851	−0.271582
$544$	−7.57893	−0.324944
$545$	16.5170	0.707510
$546$	−47.9796	−2.05334
$547$	3.88181	0.165974	0.0829870	−	0.996551i	$-0.473554\pi$
$547$	3.88181	0.165974	0.0829870	+	0.996551i	$0.473554\pi$
$548$	2.96191	0.126527
$549$	1.29677	0.0553449
$550$	−8.19321	−0.349360
$551$	−1.07039	−0.0456004
$552$	12.5798	0.535434
$553$	63.1568	2.68570
$554$	11.1565	0.473993
$555$	−7.32367	−0.310872
$556$	−3.78749	−0.160625
$557$	−4.10229	−0.173820	−0.0869099	−	0.996216i	$-0.527699\pi$
$557$	−4.10229	−0.173820	−0.0869099	+	0.996216i	$0.527699\pi$
$558$	−0.926307	−0.0392137
$559$	53.7998	2.27549
$560$	14.4616	0.611112
$561$	13.3517	0.563709
$562$	18.8941	0.796999
$563$	15.8675	0.668733	0.334367	−	0.942443i	$-0.391478\pi$
$563$	15.8675	0.668733	0.334367	+	0.942443i	$0.391478\pi$
$564$	12.4452	0.524037
$565$	48.1373	2.02515
$566$	3.16727	0.133130
$567$	37.0270	1.55499
$568$	9.18784	0.385513
$569$	27.2722	1.14331	0.571654	−	0.820495i	$-0.306302\pi$
$569$	27.2722	1.14331	0.571654	+	0.820495i	$0.306302\pi$
$570$	−44.7287	−1.87348
$571$	−33.3687	−1.39643	−0.698217	−	0.715886i	$-0.746023\pi$
$571$	−33.3687	−1.39643	−0.698217	+	0.715886i	$0.746023\pi$
$572$	−6.84051	−0.286016
$573$	−37.5346	−1.56803
$574$	−8.91307	−0.372024
$575$	58.5060	2.43987
$576$	0.103544	0.00431432
$577$	36.0100	1.49912	0.749559	−	0.661938i	$-0.230266\pi$
$577$	36.0100	1.49912	0.749559	+	0.661938i	$0.230266\pi$
$578$	40.4401	1.68209
$579$	10.7214	0.445568
$580$	0.556208	0.0230953
$581$	29.4605	1.22223
$582$	27.3883	1.13528
$583$	−5.10851	−0.211573
$584$	2.33060	0.0964407
$585$	−2.57269	−0.106368
$586$	24.5369	1.01361
$587$	7.81981	0.322758	0.161379	−	0.986892i	$-0.448406\pi$
$587$	7.81981	0.322758	0.161379	+	0.986892i	$0.448406\pi$
$588$	15.5941	0.643091
$589$	−62.5337	−2.57666
$590$	−3.06275	−0.126091
$591$	−1.76169	−0.0724661
$592$	1.14452	0.0470396
$593$	10.7263	0.440475	0.220237	−	0.975446i	$-0.429317\pi$
$593$	10.7263	0.440475	0.220237	+	0.975446i	$0.429317\pi$
$594$	5.10265	0.209364
$595$	−109.603	−4.49329
$596$	−5.37240	−0.220062
$597$	6.04725	0.247497
$598$	48.8467	1.99749
$599$	20.1405	0.822918	0.411459	−	0.911428i	$-0.365019\pi$
$599$	20.1405	0.822918	0.411459	+	0.911428i	$0.365019\pi$
$600$	14.4339	0.589261
$601$	−3.29873	−0.134558	−0.0672789	−	0.997734i	$-0.521432\pi$
$601$	−3.29873	−0.134558	−0.0672789	+	0.997734i	$0.521432\pi$
$602$	−31.3135	−1.27624
$603$	0.450122	0.0183304
$604$	−17.6466	−0.718031
$605$	−3.63225	−0.147672
$606$	16.5338	0.671641
$607$	34.1843	1.38750	0.693749	−	0.720217i	$-0.255958\pi$
$607$	34.1843	1.38750	0.693749	+	0.720217i	$0.255958\pi$
$608$	6.99008	0.283485
$609$	1.07406	0.0435233
$610$	−45.4900	−1.84183
$611$	48.3238	1.95497
$612$	−0.784749	−0.0317216
$613$	−4.27639	−0.172722	−0.0863609	−	0.996264i	$-0.527524\pi$
$613$	−4.27639	−0.172722	−0.0863609	+	0.996264i	$0.527524\pi$
$614$	−8.98948	−0.362786
$615$	−14.3249	−0.577636
$616$	3.98143	0.160417
$617$	9.98482	0.401974	0.200987	−	0.979594i	$-0.435585\pi$
$617$	9.98482	0.401974	0.200987	+	0.979594i	$0.435585\pi$
$618$	27.7334	1.11560
$619$	−9.34240	−0.375503	−0.187751	−	0.982217i	$-0.560120\pi$
$619$	−9.34240	−0.375503	−0.187751	+	0.982217i	$0.560120\pi$
$620$	32.4943	1.30500
$621$	−36.4370	−1.46217
$622$	−19.9450	−0.799724
$623$	−15.4717	−0.619861
$624$	12.0508	0.482420
$625$	1.16269	0.0465077
$626$	−25.9954	−1.03898
$627$	−12.3143	−0.491787
$628$	−7.34152	−0.292959
$629$	−8.67425	−0.345865
$630$	1.49740	0.0596579
$631$	12.5951	0.501405	0.250702	−	0.968064i	$-0.419338\pi$
$631$	12.5951	0.501405	0.250702	+	0.968064i	$0.419338\pi$
$632$	−15.8628	−0.630989
$633$	7.32914	0.291307
$634$	22.1365	0.879151
$635$	−72.3866	−2.87257
$636$	8.99960	0.356857
$637$	60.5510	2.39912
$638$	0.153131	0.00606250
$639$	0.951342	0.0376345
$640$	−3.63225	−0.143577
$641$	4.76761	0.188309	0.0941546	−	0.995558i	$-0.469985\pi$
$641$	4.76761	0.188309	0.0941546	+	0.995558i	$0.469985\pi$
$642$	−1.58040	−0.0623735
$643$	33.1398	1.30691	0.653453	−	0.756967i	$-0.273320\pi$
$643$	33.1398	1.30691	0.653453	+	0.756967i	$0.273320\pi$
$644$	−28.4306	−1.12032
$645$	−50.3265	−1.98160
$646$	−52.9773	−2.08436
$647$	−33.1160	−1.30192	−0.650961	−	0.759111i	$-0.725634\pi$
$647$	−33.1160	−1.30192	−0.650961	+	0.759111i	$0.725634\pi$
$648$	−9.29991	−0.365335
$649$	−0.843210	−0.0330989
$650$	56.0458	2.19830
$651$	62.7481	2.45929
$652$	5.46491	0.214023
$653$	42.0765	1.64658	0.823290	−	0.567620i	$-0.192136\pi$
$653$	42.0765	1.64658	0.823290	+	0.567620i	$0.192136\pi$
$654$	−8.01096	−0.313253
$655$	−27.1827	−1.06211
$656$	2.23866	0.0874049
$657$	0.241318	0.00941472
$658$	−28.1262	−1.09648
$659$	−3.46167	−0.134848	−0.0674238	−	0.997724i	$-0.521478\pi$
$659$	−3.46167	−0.134848	−0.0674238	+	0.997724i	$0.521478\pi$
$660$	6.39888	0.249076
$661$	0.466408	0.0181412	0.00907058	−	0.999959i	$-0.497113\pi$
$661$	0.466408	0.0181412	0.00907058	+	0.999959i	$0.497113\pi$
$662$	−20.7588	−0.806812
$663$	−91.3324	−3.54706
$664$	−7.39948	−0.287156
$665$	101.087	3.92000
$666$	0.118508	0.00459209
$667$	−1.09347	−0.0423394
$668$	13.8710	0.536687
$669$	35.3385	1.36626
$670$	−15.7900	−0.610021
$671$	−12.5239	−0.483481
$672$	−7.01404	−0.270573
$673$	−49.3991	−1.90420	−0.952098	−	0.305792i	$-0.901079\pi$
$673$	−49.3991	−1.90420	−0.952098	+	0.305792i	$0.901079\pi$
$674$	−13.9407	−0.536976
$675$	−41.8071	−1.60916
$676$	33.7926	1.29971
$677$	20.1633	0.774940	0.387470	−	0.921882i	$-0.373349\pi$
$677$	20.1633	0.774940	0.387470	+	0.921882i	$0.373349\pi$
$678$	−23.3472	−0.896645
$679$	−61.8979	−2.37543
$680$	27.5285	1.05567
$681$	−9.20863	−0.352875
$682$	8.94606	0.342562
$683$	2.72011	0.104082	0.0520411	−	0.998645i	$-0.483427\pi$
$683$	2.72011	0.104082	0.0520411	+	0.998645i	$0.483427\pi$
$684$	0.723778	0.0276743
$685$	−10.7584	−0.411057
$686$	−7.37289	−0.281498
$687$	9.92756	0.378760
$688$	7.86488	0.299846
$689$	34.9448	1.33129
$690$	−45.6931	−1.73951
$691$	46.7323	1.77778	0.888890	−	0.458121i	$-0.151477\pi$
$691$	46.7323	1.77778	0.888890	+	0.458121i	$0.151477\pi$
$692$	−23.7606	−0.903244
$693$	0.412252	0.0156602
$694$	−33.1546	−1.25853
$695$	13.7571	0.521836
$696$	−0.269768	−0.0102255
$697$	−16.9666	−0.642656
$698$	2.28024	0.0863083
$699$	−30.9832	−1.17189
$700$	−32.6207	−1.23295
$701$	24.4940	0.925125	0.462563	−	0.886587i	$-0.346930\pi$
$701$	24.4940	0.925125	0.462563	+	0.886587i	$0.346930\pi$
$702$	−34.9047	−1.31739
$703$	8.00031	0.301737
$704$	−1.00000	−0.0376889
$705$	−45.2040	−1.70248
$706$	−13.0470	−0.491031
$707$	−37.3667	−1.40532
$708$	1.48547	0.0558275
$709$	−14.3183	−0.537733	−0.268867	−	0.963177i	$-0.586649\pi$
$709$	−14.3183	−0.537733	−0.268867	+	0.963177i	$0.586649\pi$
$710$	−33.3725	−1.25245
$711$	−1.64249	−0.0615983
$712$	3.88596	0.145633
$713$	−63.8819	−2.39240
$714$	53.1589	1.98942
$715$	24.8464	0.929203
$716$	−1.61495	−0.0603537
$717$	−3.02361	−0.112919
$718$	−8.52242	−0.318054
$719$	−3.96591	−0.147903	−0.0739517	−	0.997262i	$-0.523561\pi$
$719$	−3.96591	−0.147903	−0.0739517	+	0.997262i	$0.523561\pi$
$720$	−0.376096	−0.0140163
$721$	−62.6777	−2.33424
$722$	29.8612	1.11132
$723$	7.90844	0.294118
$724$	−3.59230	−0.133507
$725$	−1.25463	−0.0465958
$726$	1.76169	0.0653824
$727$	33.9249	1.25821	0.629103	−	0.777322i	$-0.283423\pi$
$727$	33.9249	1.25821	0.629103	+	0.777322i	$0.283423\pi$
$728$	−27.2350	−1.00940
$729$	26.0049	0.963144
$730$	−8.46530	−0.313315
$731$	−59.6074	−2.20466
$732$	22.0632	0.815481
$733$	15.0000	0.554037	0.277019	−	0.960865i	$-0.410654\pi$
$733$	15.0000	0.554037	0.277019	+	0.960865i	$0.410654\pi$
$734$	−28.2821	−1.04391
$735$	−56.6418	−2.08926
$736$	7.14079	0.263213
$737$	−4.34717	−0.160130
$738$	0.231799	0.00853263
$739$	11.6535	0.428680	0.214340	−	0.976759i	$-0.431240\pi$
$739$	11.6535	0.428680	0.214340	+	0.976759i	$0.431240\pi$
$740$	−4.15719	−0.152821
$741$	84.2364	3.09450
$742$	−20.3392	−0.746675
$743$	−1.08681	−0.0398713	−0.0199356	−	0.999801i	$-0.506346\pi$
$743$	−1.08681	−0.0398713	−0.0199356	+	0.999801i	$0.506346\pi$
$744$	−15.7602	−0.577796
$745$	19.5139	0.714934
$746$	−8.67615	−0.317656
$747$	−0.766169	−0.0280326
$748$	7.57893	0.277113
$749$	3.57173	0.130508
$750$	−20.4330	−0.746108
$751$	−7.90575	−0.288485	−0.144242	−	0.989542i	$-0.546075\pi$
$751$	−7.90575	−0.288485	−0.144242	+	0.989542i	$0.546075\pi$
$752$	7.06435	0.257610
$753$	−26.0253	−0.948416
$754$	−1.04749	−0.0381474
$755$	64.0969	2.33273
$756$	20.3159	0.738881
$757$	−16.0530	−0.583456	−0.291728	−	0.956501i	$-0.594230\pi$
$757$	−16.0530	−0.583456	−0.291728	+	0.956501i	$0.594230\pi$
$758$	−31.7838	−1.15444
$759$	−12.5798	−0.456619
$760$	−25.3897	−0.920981
$761$	−18.5494	−0.672417	−0.336209	−	0.941788i	$-0.609145\pi$
$761$	−18.5494	−0.672417	−0.336209	+	0.941788i	$0.609145\pi$
$762$	35.1085	1.27185
$763$	18.1049	0.655440
$764$	−21.3060	−0.770825
$765$	2.85040	0.103057
$766$	−14.4309	−0.521410
$767$	5.76799	0.208270
$768$	1.76169	0.0635694
$769$	35.4522	1.27844	0.639219	−	0.769024i	$-0.279258\pi$
$769$	35.4522	1.27844	0.639219	+	0.769024i	$0.279258\pi$
$770$	−14.4616	−0.521158
$771$	0.980457	0.0353103
$772$	6.08589	0.219036
$773$	−50.2641	−1.80787	−0.903936	−	0.427667i	$-0.859335\pi$
$773$	−50.2641	−1.80787	−0.903936	+	0.427667i	$0.859335\pi$
$774$	0.814358	0.0292715
$775$	−73.2970	−2.63291
$776$	15.5466	0.558092
$777$	−8.02773	−0.287993
$778$	−2.74621	−0.0984566
$779$	15.6484	0.560662
$780$	−43.7716	−1.56728
$781$	−9.18784	−0.328767
$782$	−54.1195	−1.93531
$783$	0.781372	0.0279240
$784$	8.85182	0.316136
$785$	26.6662	0.951758
$786$	13.1840	0.470256
$787$	52.6968	1.87844	0.939219	−	0.343319i	$-0.111551\pi$
$787$	52.6968	1.87844	0.939219	+	0.343319i	$0.111551\pi$
$788$	−1.00000	−0.0356235
$789$	36.9013	1.31372
$790$	57.6177	2.04994
$791$	52.7650	1.87611
$792$	−0.103544	−0.00367926
$793$	85.6700	3.04223
$794$	33.4618	1.18752
$795$	−32.6888	−1.15935
$796$	3.43264	0.121667
$797$	39.1428	1.38651	0.693255	−	0.720692i	$-0.256176\pi$
$797$	39.1428	1.38651	0.693255	+	0.720692i	$0.256176\pi$
$798$	−49.0287	−1.73560
$799$	−53.5402	−1.89412
$800$	8.19321	0.289674
$801$	0.402366	0.0142169
$802$	−11.0408	−0.389863
$803$	−2.33060	−0.0822449
$804$	7.65836	0.270090
$805$	103.267	3.63968
$806$	−61.1956	−2.15552
$807$	6.38384	0.224722
$808$	9.38522	0.330171
$809$	28.1000	0.987942	0.493971	−	0.869478i	$-0.335545\pi$
$809$	28.1000	0.987942	0.493971	+	0.869478i	$0.335545\pi$
$810$	33.7796	1.18689
$811$	7.51475	0.263879	0.131939	−	0.991258i	$-0.457880\pi$
$811$	7.51475	0.263879	0.131939	+	0.991258i	$0.457880\pi$
$812$	0.609679	0.0213955
$813$	44.9763	1.57739
$814$	−1.14452	−0.0401155
$815$	−19.8499	−0.695312
$816$	−13.3517	−0.467403
$817$	54.9762	1.92337
$818$	13.5171	0.472615
$819$	−2.82001	−0.0985393
$820$	−8.13136	−0.283959
$821$	−27.9666	−0.976041	−0.488021	−	0.872832i	$-0.662281\pi$
$821$	−27.9666	−0.976041	−0.488021	+	0.872832i	$0.662281\pi$
$822$	5.21797	0.181998
$823$	21.4389	0.747313	0.373656	−	0.927567i	$-0.378104\pi$
$823$	21.4389	0.747313	0.373656	+	0.927567i	$0.378104\pi$
$824$	15.7425	0.548416
$825$	−14.4339	−0.502523
$826$	−3.35718	−0.116811
$827$	25.5941	0.889993	0.444997	−	0.895532i	$-0.353205\pi$
$827$	25.5941	0.889993	0.444997	+	0.895532i	$0.353205\pi$
$828$	0.739383	0.0256953
$829$	4.73465	0.164441	0.0822207	−	0.996614i	$-0.473799\pi$
$829$	4.73465	0.164441	0.0822207	+	0.996614i	$0.473799\pi$
$830$	26.8767	0.932905
$831$	19.6542	0.681798
$832$	6.84051	0.237152
$833$	−67.0873	−2.32444
$834$	−6.67237	−0.231045
$835$	−50.3830	−1.74358
$836$	−6.99008	−0.241757
$837$	45.6486	1.57785
$838$	−24.6204	−0.850499
$839$	−8.47594	−0.292622	−0.146311	−	0.989239i	$-0.546740\pi$
$839$	−8.47594	−0.292622	−0.146311	+	0.989239i	$0.546740\pi$
$840$	25.4767	0.879031
$841$	−28.9766	−0.999191
$842$	−9.55128	−0.329159
$843$	33.2855	1.14641
$844$	4.16030	0.143203
$845$	−122.743	−4.22249
$846$	0.731468	0.0251484
$847$	−3.98143	−0.136804
$848$	5.10851	0.175427
$849$	5.57975	0.191496
$850$	−62.0958	−2.12987
$851$	8.17280	0.280160
$852$	16.1861	0.554527
$853$	−12.3160	−0.421691	−0.210845	−	0.977519i	$-0.567622\pi$
$853$	−12.3160	−0.421691	−0.210845	+	0.977519i	$0.567622\pi$
$854$	−49.8632	−1.70628
$855$	−2.62894	−0.0899079
$856$	−0.897096	−0.0306621
$857$	26.8073	0.915720	0.457860	−	0.889024i	$-0.348616\pi$
$857$	26.8073	0.915720	0.457860	+	0.889024i	$0.348616\pi$
$858$	−12.0508	−0.411409
$859$	−7.24556	−0.247215	−0.123608	−	0.992331i	$-0.539446\pi$
$859$	−7.24556	−0.247215	−0.123608	+	0.992331i	$0.539446\pi$
$860$	−28.5672	−0.974133
$861$	−15.7020	−0.535124
$862$	34.2351	1.16605
$863$	−2.29069	−0.0779760	−0.0389880	−	0.999240i	$-0.512413\pi$
$863$	−2.29069	−0.0779760	−0.0389880	+	0.999240i	$0.512413\pi$
$864$	−5.10265	−0.173596
$865$	86.3045	2.93444
$866$	−28.7613	−0.977347
$867$	71.2428	2.41953
$868$	35.6182	1.20896
$869$	15.8628	0.538109
$870$	0.979865	0.0332205
$871$	29.7369	1.00760
$872$	−4.54732	−0.153992
$873$	1.60976	0.0544820
$874$	49.9147	1.68839
$875$	46.1788	1.56113
$876$	4.10578	0.138721
$877$	−3.70766	−0.125199	−0.0625994	−	0.998039i	$-0.519939\pi$
$877$	−3.70766	−0.125199	−0.0625994	+	0.998039i	$0.519939\pi$
$878$	31.3231	1.05710
$879$	43.2263	1.45799
$880$	3.63225	0.122443
$881$	1.95653	0.0659171	0.0329585	−	0.999457i	$-0.489507\pi$
$881$	1.95653	0.0659171	0.0329585	+	0.999457i	$0.489507\pi$
$882$	0.916549	0.0308618
$883$	−52.8017	−1.77692	−0.888460	−	0.458954i	$-0.848224\pi$
$883$	−52.8017	−1.77692	−0.888460	+	0.458954i	$0.848224\pi$
$884$	−51.8437	−1.74369
$885$	−5.39560	−0.181371
$886$	−2.18930	−0.0735509
$887$	24.4046	0.819426	0.409713	−	0.912214i	$-0.365629\pi$
$887$	24.4046	0.819426	0.409713	+	0.912214i	$0.365629\pi$
$888$	2.01629	0.0676623
$889$	−79.3455	−2.66116
$890$	−14.1148	−0.473128
$891$	9.29991	0.311559
$892$	20.0594	0.671640
$893$	49.3804	1.65245
$894$	−9.46450	−0.316540
$895$	5.86591	0.196076
$896$	−3.98143	−0.133010
$897$	86.0525	2.87321
$898$	9.17220	0.306080
$899$	1.36992	0.0456892
$900$	0.848355	0.0282785
$901$	−38.7170	−1.28985
$902$	−2.23866	−0.0745391
$903$	−55.1646	−1.83576
$904$	−13.2528	−0.440780
$905$	13.0481	0.433734
$906$	−31.0879	−1.03282
$907$	−37.3172	−1.23910	−0.619549	−	0.784958i	$-0.712685\pi$
$907$	−37.3172	−1.23910	−0.619549	+	0.784958i	$0.712685\pi$
$908$	−5.22716	−0.173469
$909$	0.971780	0.0322319
$910$	98.9244	3.27931
$911$	54.6866	1.81185	0.905924	−	0.423439i	$-0.139177\pi$
$911$	54.6866	1.81185	0.905924	+	0.423439i	$0.139177\pi$
$912$	12.3143	0.407769
$913$	7.39948	0.244887
$914$	−27.0393	−0.894379
$915$	−80.1391	−2.64932
$916$	5.63525	0.186194
$917$	−29.7959	−0.983947
$918$	38.6726	1.27639
$919$	38.2879	1.26300	0.631501	−	0.775375i	$-0.282439\pi$
$919$	38.2879	1.26300	0.631501	+	0.775375i	$0.282439\pi$
$920$	−25.9371	−0.855121
$921$	−15.8367	−0.521835
$922$	12.1621	0.400538
$923$	62.8495	2.06872
$924$	7.01404	0.230745
$925$	9.37732	0.308324
$926$	−6.84201	−0.224842
$927$	1.63003	0.0535374
$928$	−0.153131	−0.00502676
$929$	9.39484	0.308235	0.154117	−	0.988053i	$-0.450747\pi$
$929$	9.39484	0.308235	0.154117	+	0.988053i	$0.450747\pi$
$930$	57.2448	1.87713
$931$	61.8749	2.02787
$932$	−17.5872	−0.576089
$933$	−35.1369	−1.15033
$934$	2.17305	0.0711044
$935$	−27.5285	−0.900279
$936$	0.708291	0.0231512
$937$	−18.5740	−0.606787	−0.303394	−	0.952865i	$-0.598120\pi$
$937$	−18.5740	−0.606787	−0.303394	+	0.952865i	$0.598120\pi$
$938$	−17.3080	−0.565126
$939$	−45.7957	−1.49449
$940$	−25.6595	−0.836919
$941$	11.9087	0.388214	0.194107	−	0.980980i	$-0.437819\pi$
$941$	11.9087	0.388214	0.194107	+	0.980980i	$0.437819\pi$
$942$	−12.9335	−0.421395
$943$	15.9858	0.520569
$944$	0.843210	0.0274441
$945$	−73.7923	−2.40046
$946$	−7.86488	−0.255709
$947$	−40.8549	−1.32761	−0.663803	−	0.747907i	$-0.731059\pi$
$947$	−40.8549	−1.32761	−0.663803	+	0.747907i	$0.731059\pi$
$948$	−27.9453	−0.907622
$949$	15.9425	0.517514
$950$	57.2712	1.85812
$951$	38.9975	1.26458
$952$	30.1750	0.977977
$953$	42.1843	1.36648	0.683242	−	0.730192i	$-0.260570\pi$
$953$	42.1843	1.36648	0.683242	+	0.730192i	$0.260570\pi$
$954$	0.528953	0.0171255
$955$	77.3887	2.50424
$956$	−1.71632	−0.0555096
$957$	0.269768	0.00872037
$958$	−10.2677	−0.331736
$959$	−11.7927	−0.380805
$960$	−6.39888	−0.206523
$961$	49.0320	1.58168
$962$	7.82912	0.252421
$963$	−0.0928885	−0.00299329
$964$	4.48913	0.144585
$965$	−22.1055	−0.711600
$966$	−50.0858	−1.61148
$967$	−8.30111	−0.266946	−0.133473	−	0.991052i	$-0.542613\pi$
$967$	−8.30111	−0.266946	−0.133473	+	0.991052i	$0.542613\pi$
$968$	1.00000	0.0321412
$969$	−93.3295	−2.99817
$970$	−56.4693	−1.81312
$971$	−49.7251	−1.59576	−0.797878	−	0.602819i	$-0.794044\pi$
$971$	−49.7251	−1.59576	−0.797878	+	0.602819i	$0.794044\pi$
$972$	−1.07558	−0.0344993
$973$	15.0796	0.483431
$974$	15.1781	0.486339
$975$	98.7351	3.16206
$976$	12.5239	0.400881
$977$	−52.0253	−1.66444	−0.832219	−	0.554448i	$-0.812930\pi$
$977$	−52.0253	−1.66444	−0.832219	+	0.554448i	$0.812930\pi$
$978$	9.62747	0.307853
$979$	−3.88596	−0.124196
$980$	−32.1520	−1.02706
$981$	−0.470846	−0.0150330
$982$	−19.3087	−0.616165
$983$	24.7280	0.788701	0.394351	−	0.918960i	$-0.370970\pi$
$983$	24.7280	0.788701	0.394351	+	0.918960i	$0.370970\pi$
$984$	3.94382	0.125724
$985$	3.63225	0.115733
$986$	1.16056	0.0369599
$987$	−49.5497	−1.57718
$988$	47.8157	1.52122
$989$	56.1615	1.78583
$990$	0.376096	0.0119531
$991$	55.3935	1.75963	0.879816	−	0.475314i	$-0.157665\pi$
$991$	55.3935	1.75963	0.879816	+	0.475314i	$0.157665\pi$
$992$	−8.94606	−0.284038
$993$	−36.5704	−1.16053
$994$	−36.5808	−1.16027
$995$	−12.4682	−0.395269
$996$	−13.0356	−0.413048
$997$	−13.1030	−0.414977	−0.207488	−	0.978237i	$-0.566529\pi$
$997$	−13.1030	−0.414977	−0.207488	+	0.978237i	$0.566529\pi$
$998$	24.4353	0.773487
$999$	−5.84010	−0.184773

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4334.2.a.f.1.17	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4334.2.a.f.1.17	✓	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.76169 q^{3} +1.00000 q^{4} -3.63225 q^{5} +1.76169 q^{6} -3.98143 q^{7} +1.00000 q^{8} +0.103544 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.76169 q^{3} +1.00000 q^{4} -3.63225 q^{5} +1.76169 q^{6} -3.98143 q^{7} +1.00000 q^{8} +0.103544 q^{9} -3.63225 q^{10} -1.00000 q^{11} +1.76169 q^{12} +6.84051 q^{13} -3.98143 q^{14} -6.39888 q^{15} +1.00000 q^{16} -7.57893 q^{17} +0.103544 q^{18} +6.99008 q^{19} -3.63225 q^{20} -7.01404 q^{21} -1.00000 q^{22} +7.14079 q^{23} +1.76169 q^{24} +8.19321 q^{25} +6.84051 q^{26} -5.10265 q^{27} -3.98143 q^{28} -0.153131 q^{29} -6.39888 q^{30} -8.94606 q^{31} +1.00000 q^{32} -1.76169 q^{33} -7.57893 q^{34} +14.4616 q^{35} +0.103544 q^{36} +1.14452 q^{37} +6.99008 q^{38} +12.0508 q^{39} -3.63225 q^{40} +2.23866 q^{41} -7.01404 q^{42} +7.86488 q^{43} -1.00000 q^{44} -0.376096 q^{45} +7.14079 q^{46} +7.06435 q^{47} +1.76169 q^{48} +8.85182 q^{49} +8.19321 q^{50} -13.3517 q^{51} +6.84051 q^{52} +5.10851 q^{53} -5.10265 q^{54} +3.63225 q^{55} -3.98143 q^{56} +12.3143 q^{57} -0.153131 q^{58} +0.843210 q^{59} -6.39888 q^{60} +12.5239 q^{61} -8.94606 q^{62} -0.412252 q^{63} +1.00000 q^{64} -24.8464 q^{65} -1.76169 q^{66} +4.34717 q^{67} -7.57893 q^{68} +12.5798 q^{69} +14.4616 q^{70} +9.18784 q^{71} +0.103544 q^{72} +2.33060 q^{73} +1.14452 q^{74} +14.4339 q^{75} +6.99008 q^{76} +3.98143 q^{77} +12.0508 q^{78} -15.8628 q^{79} -3.63225 q^{80} -9.29991 q^{81} +2.23866 q^{82} -7.39948 q^{83} -7.01404 q^{84} +27.5285 q^{85} +7.86488 q^{86} -0.269768 q^{87} -1.00000 q^{88} +3.88596 q^{89} -0.376096 q^{90} -27.2350 q^{91} +7.14079 q^{92} -15.7602 q^{93} +7.06435 q^{94} -25.3897 q^{95} +1.76169 q^{96} +15.5466 q^{97} +8.85182 q^{98} -0.103544 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 24 q^{2} + 8 q^{3} + 24 q^{4} + 8 q^{6} + 11 q^{7} + 24 q^{8} + 28 q^{9}+O(q^{10}) \) 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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