LMFDB - Embedded newform 4334.2.a.f.1.19

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			1.19
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)

$f(q)$	$=$	$q+1.00000 q^{2} +2.48464 q^{3} +1.00000 q^{4} +3.25684 q^{5} +2.48464 q^{6} +4.41893 q^{7} +1.00000 q^{8} +3.17343 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +2.48464 q^{3} +1.00000 q^{4} +3.25684 q^{5} +2.48464 q^{6} +4.41893 q^{7} +1.00000 q^{8} +3.17343 q^{9} +3.25684 q^{10} -1.00000 q^{11} +2.48464 q^{12} -2.96940 q^{13} +4.41893 q^{14} +8.09207 q^{15} +1.00000 q^{16} -6.19810 q^{17} +3.17343 q^{18} +0.0372713 q^{19} +3.25684 q^{20} +10.9794 q^{21} -1.00000 q^{22} -6.66485 q^{23} +2.48464 q^{24} +5.60699 q^{25} -2.96940 q^{26} +0.430913 q^{27} +4.41893 q^{28} +5.72125 q^{29} +8.09207 q^{30} -2.84231 q^{31} +1.00000 q^{32} -2.48464 q^{33} -6.19810 q^{34} +14.3917 q^{35} +3.17343 q^{36} -4.47442 q^{37} +0.0372713 q^{38} -7.37790 q^{39} +3.25684 q^{40} -8.29655 q^{41} +10.9794 q^{42} +7.60491 q^{43} -1.00000 q^{44} +10.3353 q^{45} -6.66485 q^{46} +8.80620 q^{47} +2.48464 q^{48} +12.5269 q^{49} +5.60699 q^{50} -15.4000 q^{51} -2.96940 q^{52} +11.3827 q^{53} +0.430913 q^{54} -3.25684 q^{55} +4.41893 q^{56} +0.0926058 q^{57} +5.72125 q^{58} -3.94745 q^{59} +8.09207 q^{60} +5.21285 q^{61} -2.84231 q^{62} +14.0232 q^{63} +1.00000 q^{64} -9.67087 q^{65} -2.48464 q^{66} -2.85496 q^{67} -6.19810 q^{68} -16.5597 q^{69} +14.3917 q^{70} -7.66988 q^{71} +3.17343 q^{72} +5.80848 q^{73} -4.47442 q^{74} +13.9313 q^{75} +0.0372713 q^{76} -4.41893 q^{77} -7.37790 q^{78} -0.538144 q^{79} +3.25684 q^{80} -8.44963 q^{81} -8.29655 q^{82} +15.6816 q^{83} +10.9794 q^{84} -20.1862 q^{85} +7.60491 q^{86} +14.2152 q^{87} -1.00000 q^{88} -13.7240 q^{89} +10.3353 q^{90} -13.1216 q^{91} -6.66485 q^{92} -7.06212 q^{93} +8.80620 q^{94} +0.121387 q^{95} +2.48464 q^{96} +6.43924 q^{97} +12.5269 q^{98} -3.17343 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	2.48464	1.43451	0.717253	−	0.696812i	$-0.245399\pi$
$3$	2.48464	1.43451	0.717253	+	0.696812i	$0.245399\pi$
$4$	1.00000	0.500000
$5$	3.25684	1.45650	0.728251	−	0.685311i	$-0.240334\pi$
$5$	3.25684	1.45650	0.728251	+	0.685311i	$0.240334\pi$
$6$	2.48464	1.01435
$7$	4.41893	1.67020	0.835099	−	0.550099i	$-0.185410\pi$
$7$	4.41893	1.67020	0.835099	+	0.550099i	$0.185410\pi$
$8$	1.00000	0.353553
$9$	3.17343	1.05781
$10$	3.25684	1.02990
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	2.48464	0.717253
$13$	−2.96940	−0.823564	−0.411782	−	0.911282i	$-0.635094\pi$
$13$	−2.96940	−0.823564	−0.411782	+	0.911282i	$0.635094\pi$
$14$	4.41893	1.18101
$15$	8.09207	2.08936
$16$	1.00000	0.250000
$17$	−6.19810	−1.50326	−0.751630	−	0.659585i	$-0.770732\pi$
$17$	−6.19810	−1.50326	−0.751630	+	0.659585i	$0.770732\pi$
$18$	3.17343	0.747985
$19$	0.0372713	0.00855063	0.00427532	−	0.999991i	$-0.498639\pi$
$19$	0.0372713	0.00855063	0.00427532	+	0.999991i	$0.498639\pi$
$20$	3.25684	0.728251
$21$	10.9794	2.39591
$22$	−1.00000	−0.213201
$23$	−6.66485	−1.38972	−0.694858	−	0.719147i	$-0.744533\pi$
$23$	−6.66485	−1.38972	−0.694858	+	0.719147i	$0.744533\pi$
$24$	2.48464	0.507175
$25$	5.60699	1.12140
$26$	−2.96940	−0.582348
$27$	0.430913	0.0829293
$28$	4.41893	0.835099
$29$	5.72125	1.06241	0.531204	−	0.847244i	$-0.321740\pi$
$29$	5.72125	1.06241	0.531204	+	0.847244i	$0.321740\pi$
$30$	8.09207	1.47740
$31$	−2.84231	−0.510494	−0.255247	−	0.966876i	$-0.582157\pi$
$31$	−2.84231	−0.510494	−0.255247	+	0.966876i	$0.582157\pi$
$32$	1.00000	0.176777
$33$	−2.48464	−0.432520
$34$	−6.19810	−1.06296
$35$	14.3917	2.43265
$36$	3.17343	0.528905
$37$	−4.47442	−0.735591	−0.367795	−	0.929907i	$-0.619887\pi$
$37$	−4.47442	−0.735591	−0.367795	+	0.929907i	$0.619887\pi$
$38$	0.0372713	0.00604621
$39$	−7.37790	−1.18141
$40$	3.25684	0.514951
$41$	−8.29655	−1.29570	−0.647852	−	0.761766i	$-0.724332\pi$
$41$	−8.29655	−1.29570	−0.647852	+	0.761766i	$0.724332\pi$
$42$	10.9794	1.69417
$43$	7.60491	1.15974	0.579869	−	0.814710i	$-0.303104\pi$
$43$	7.60491	1.15974	0.579869	+	0.814710i	$0.303104\pi$
$44$	−1.00000	−0.150756
$45$	10.3353	1.54070
$46$	−6.66485	−0.982678
$47$	8.80620	1.28452	0.642258	−	0.766489i	$-0.277998\pi$
$47$	8.80620	1.28452	0.642258	+	0.766489i	$0.277998\pi$
$48$	2.48464	0.358627
$49$	12.5269	1.78956
$50$	5.60699	0.792948
$51$	−15.4000	−2.15644
$52$	−2.96940	−0.411782
$53$	11.3827	1.56354	0.781768	−	0.623570i	$-0.214318\pi$
$53$	11.3827	1.56354	0.781768	+	0.623570i	$0.214318\pi$
$54$	0.430913	0.0586399
$55$	−3.25684	−0.439152
$56$	4.41893	0.590504
$57$	0.0926058	0.0122659
$58$	5.72125	0.751236
$59$	−3.94745	−0.513914	−0.256957	−	0.966423i	$-0.582720\pi$
$59$	−3.94745	−0.513914	−0.256957	+	0.966423i	$0.582720\pi$
$60$	8.09207	1.04468
$61$	5.21285	0.667437	0.333718	−	0.942673i	$-0.391697\pi$
$61$	5.21285	0.667437	0.333718	+	0.942673i	$0.391697\pi$
$62$	−2.84231	−0.360974
$63$	14.0232	1.76675
$64$	1.00000	0.125000
$65$	−9.67087	−1.19952
$66$	−2.48464	−0.305838
$67$	−2.85496	−0.348789	−0.174395	−	0.984676i	$-0.555797\pi$
$67$	−2.85496	−0.348789	−0.174395	+	0.984676i	$0.555797\pi$
$68$	−6.19810	−0.751630
$69$	−16.5597	−1.99356
$70$	14.3917	1.72014
$71$	−7.66988	−0.910248	−0.455124	−	0.890428i	$-0.650405\pi$
$71$	−7.66988	−0.910248	−0.455124	+	0.890428i	$0.650405\pi$
$72$	3.17343	0.373992
$73$	5.80848	0.679831	0.339916	−	0.940456i	$-0.389602\pi$
$73$	5.80848	0.679831	0.339916	+	0.940456i	$0.389602\pi$
$74$	−4.47442	−0.520141
$75$	13.9313	1.60865
$76$	0.0372713	0.00427532
$77$	−4.41893	−0.503584
$78$	−7.37790	−0.835382
$79$	−0.538144	−0.0605459	−0.0302730	−	0.999542i	$-0.509638\pi$
$79$	−0.538144	−0.0605459	−0.0302730	+	0.999542i	$0.509638\pi$
$80$	3.25684	0.364125
$81$	−8.44963	−0.938848
$82$	−8.29655	−0.916201
$83$	15.6816	1.72128	0.860638	−	0.509217i	$-0.170065\pi$
$83$	15.6816	1.72128	0.860638	+	0.509217i	$0.170065\pi$
$84$	10.9794	1.19796
$85$	−20.1862	−2.18950
$86$	7.60491	0.820058
$87$	14.2152	1.52403
$88$	−1.00000	−0.106600
$89$	−13.7240	−1.45474	−0.727372	−	0.686244i	$-0.759258\pi$
$89$	−13.7240	−1.45474	−0.727372	+	0.686244i	$0.759258\pi$
$90$	10.3353	1.08944
$91$	−13.1216	−1.37552
$92$	−6.66485	−0.694858
$93$	−7.06212	−0.732308
$94$	8.80620	0.908290
$95$	0.121387	0.0124540
$96$	2.48464	0.253587
$97$	6.43924	0.653805	0.326903	−	0.945058i	$-0.393995\pi$
$97$	6.43924	0.653805	0.326903	+	0.945058i	$0.393995\pi$
$98$	12.5269	1.26541
$99$	−3.17343	−0.318942
$100$	5.60699	0.560699
$101$	−17.1044	−1.70195	−0.850975	−	0.525206i	$-0.823988\pi$
$101$	−17.1044	−1.70195	−0.850975	+	0.525206i	$0.823988\pi$
$102$	−15.4000	−1.52483
$103$	−11.1501	−1.09865	−0.549324	−	0.835609i	$-0.685115\pi$
$103$	−11.1501	−1.09865	−0.549324	+	0.835609i	$0.685115\pi$
$104$	−2.96940	−0.291174
$105$	35.7583	3.48965
$106$	11.3827	1.10559
$107$	9.08681	0.878455	0.439228	−	0.898376i	$-0.355252\pi$
$107$	9.08681	0.878455	0.439228	+	0.898376i	$0.355252\pi$
$108$	0.430913	0.0414647
$109$	15.3056	1.46601	0.733005	−	0.680223i	$-0.238117\pi$
$109$	15.3056	1.46601	0.733005	+	0.680223i	$0.238117\pi$
$110$	−3.25684	−0.310527
$111$	−11.1173	−1.05521
$112$	4.41893	0.417550
$113$	5.85506	0.550798	0.275399	−	0.961330i	$-0.411190\pi$
$113$	5.85506	0.550798	0.275399	+	0.961330i	$0.411190\pi$
$114$	0.0926058	0.00867333
$115$	−21.7063	−2.02413
$116$	5.72125	0.531204
$117$	−9.42320	−0.871175
$118$	−3.94745	−0.363392
$119$	−27.3890	−2.51074
$120$	8.09207	0.738701
$121$	1.00000	0.0909091
$122$	5.21285	0.471949
$123$	−20.6139	−1.85870
$124$	−2.84231	−0.255247
$125$	1.97687	0.176816
$126$	14.0232	1.24928
$127$	7.34558	0.651815	0.325907	−	0.945402i	$-0.394330\pi$
$127$	7.34558	0.651815	0.325907	+	0.945402i	$0.394330\pi$
$128$	1.00000	0.0883883
$129$	18.8954	1.66365
$130$	−9.67087	−0.848191
$131$	−0.941419	−0.0822521	−0.0411261	−	0.999154i	$-0.513095\pi$
$131$	−0.941419	−0.0822521	−0.0411261	+	0.999154i	$0.513095\pi$
$132$	−2.48464	−0.216260
$133$	0.164699	0.0142813
$134$	−2.85496	−0.246631
$135$	1.40341	0.120787
$136$	−6.19810	−0.531482
$137$	0.855617	0.0731003	0.0365501	−	0.999332i	$-0.488363\pi$
$137$	0.855617	0.0731003	0.0365501	+	0.999332i	$0.488363\pi$
$138$	−16.5597	−1.40966
$139$	−1.24766	−0.105825	−0.0529125	−	0.998599i	$-0.516850\pi$
$139$	−1.24766	−0.105825	−0.0529125	+	0.998599i	$0.516850\pi$
$140$	14.3917	1.21632
$141$	21.8802	1.84265
$142$	−7.66988	−0.643642
$143$	2.96940	0.248314
$144$	3.17343	0.264453
$145$	18.6332	1.54740
$146$	5.80848	0.480713
$147$	31.1249	2.56714
$148$	−4.47442	−0.367795
$149$	−8.88439	−0.727838	−0.363919	−	0.931431i	$-0.618561\pi$
$149$	−8.88439	−0.727838	−0.363919	+	0.931431i	$0.618561\pi$
$150$	13.9313	1.13749
$151$	−16.4895	−1.34190	−0.670948	−	0.741504i	$-0.734113\pi$
$151$	−16.4895	−1.34190	−0.670948	+	0.741504i	$0.734113\pi$
$152$	0.0372713	0.00302310
$153$	−19.6692	−1.59016
$154$	−4.41893	−0.356088
$155$	−9.25695	−0.743536
$156$	−7.37790	−0.590704
$157$	−20.1501	−1.60815	−0.804076	−	0.594526i	$-0.797340\pi$
$157$	−20.1501	−1.60815	−0.804076	+	0.594526i	$0.797340\pi$
$158$	−0.538144	−0.0428124
$159$	28.2819	2.24290
$160$	3.25684	0.257476
$161$	−29.4515	−2.32110
$162$	−8.44963	−0.663866
$163$	−15.8316	−1.24003	−0.620013	−	0.784591i	$-0.712873\pi$
$163$	−15.8316	−1.24003	−0.620013	+	0.784591i	$0.712873\pi$
$164$	−8.29655	−0.647852
$165$	−8.09207	−0.629966
$166$	15.6816	1.21713
$167$	4.54755	0.351900	0.175950	−	0.984399i	$-0.443700\pi$
$167$	4.54755	0.351900	0.175950	+	0.984399i	$0.443700\pi$
$168$	10.9794	0.847083
$169$	−4.18264	−0.321742
$170$	−20.1862	−1.54821
$171$	0.118278	0.00904495
$172$	7.60491	0.579869
$173$	−1.73194	−0.131677	−0.0658386	−	0.997830i	$-0.520972\pi$
$173$	−1.73194	−0.131677	−0.0658386	+	0.997830i	$0.520972\pi$
$174$	14.2152	1.07765
$175$	24.7769	1.87296
$176$	−1.00000	−0.0753778
$177$	−9.80799	−0.737214
$178$	−13.7240	−1.02866
$179$	−26.4178	−1.97456	−0.987278	−	0.159002i	$-0.949172\pi$
$179$	−26.4178	−1.97456	−0.987278	+	0.159002i	$0.949172\pi$
$180$	10.3353	0.770351
$181$	−7.62676	−0.566892	−0.283446	−	0.958988i	$-0.591478\pi$
$181$	−7.62676	−0.566892	−0.283446	+	0.958988i	$0.591478\pi$
$182$	−13.1216	−0.972637
$183$	12.9520	0.957443
$184$	−6.66485	−0.491339
$185$	−14.5725	−1.07139
$186$	−7.06212	−0.517820
$187$	6.19810	0.453250
$188$	8.80620	0.642258
$189$	1.90418	0.138508
$190$	0.121387	0.00880632
$191$	6.60592	0.477987	0.238994	−	0.971021i	$-0.423182\pi$
$191$	6.60592	0.477987	0.238994	+	0.971021i	$0.423182\pi$
$192$	2.48464	0.179313
$193$	20.4169	1.46964	0.734822	−	0.678260i	$-0.237266\pi$
$193$	20.4169	1.46964	0.734822	+	0.678260i	$0.237266\pi$
$194$	6.43924	0.462310
$195$	−24.0286	−1.72072
$196$	12.5269	0.894781
$197$	−1.00000	−0.0712470
$197$	−1.00000	−0.0712470
$198$	−3.17343	−0.225526
$199$	−12.3826	−0.877777	−0.438889	−	0.898541i	$-0.644628\pi$
$199$	−12.3826	−0.877777	−0.438889	+	0.898541i	$0.644628\pi$
$200$	5.60699	0.396474
$201$	−7.09355	−0.500341
$202$	−17.1044	−1.20346
$203$	25.2818	1.77443
$204$	−15.4000	−1.07822
$205$	−27.0205	−1.88719
$206$	−11.1501	−0.776862
$207$	−21.1504	−1.47006
$208$	−2.96940	−0.205891
$209$	−0.0372713	−0.00257811
$210$	35.7583	2.46755
$211$	−3.10938	−0.214059	−0.107029	−	0.994256i	$-0.534134\pi$
$211$	−3.10938	−0.214059	−0.107029	+	0.994256i	$0.534134\pi$
$212$	11.3827	0.781768
$213$	−19.0569	−1.30576
$214$	9.08681	0.621162
$215$	24.7679	1.68916
$216$	0.430913	0.0293199
$217$	−12.5600	−0.852627
$218$	15.3056	1.03663
$219$	14.4320	0.975222
$220$	−3.25684	−0.219576
$221$	18.4047	1.23803
$222$	−11.1173	−0.746146
$223$	10.4245	0.698079	0.349040	−	0.937108i	$-0.386508\pi$
$223$	10.4245	0.698079	0.349040	+	0.937108i	$0.386508\pi$
$224$	4.41893	0.295252
$225$	17.7934	1.18623
$226$	5.85506	0.389473
$227$	−8.35871	−0.554787	−0.277393	−	0.960756i	$-0.589471\pi$
$227$	−8.35871	−0.554787	−0.277393	+	0.960756i	$0.589471\pi$
$228$	0.0926058	0.00613297
$229$	27.5073	1.81774	0.908868	−	0.417084i	$-0.136948\pi$
$229$	27.5073	1.81774	0.908868	+	0.417084i	$0.136948\pi$
$230$	−21.7063	−1.43127
$231$	−10.9794	−0.722394
$232$	5.72125	0.375618
$233$	−18.7321	−1.22718	−0.613590	−	0.789625i	$-0.710275\pi$
$233$	−18.7321	−1.22718	−0.613590	+	0.789625i	$0.710275\pi$
$234$	−9.42320	−0.616014
$235$	28.6804	1.87090
$236$	−3.94745	−0.256957
$237$	−1.33709	−0.0868535
$238$	−27.3890	−1.77536
$239$	−20.1764	−1.30510	−0.652552	−	0.757744i	$-0.726302\pi$
$239$	−20.1764	−1.30510	−0.652552	+	0.757744i	$0.726302\pi$
$240$	8.09207	0.522341
$241$	26.5023	1.70716	0.853580	−	0.520961i	$-0.174426\pi$
$241$	26.5023	1.70716	0.853580	+	0.520961i	$0.174426\pi$
$242$	1.00000	0.0642824
$243$	−22.2870	−1.42971
$244$	5.21285	0.333718
$245$	40.7982	2.60650
$246$	−20.6139	−1.31430
$247$	−0.110674	−0.00704200
$248$	−2.84231	−0.180487
$249$	38.9630	2.46918
$250$	1.97687	0.125028
$251$	−22.7303	−1.43472	−0.717361	−	0.696701i	$-0.754650\pi$
$251$	−22.7303	−1.43472	−0.717361	+	0.696701i	$0.754650\pi$
$252$	14.0232	0.883377
$253$	6.66485	0.419015
$254$	7.34558	0.460902
$255$	−50.1554	−3.14085
$256$	1.00000	0.0625000
$257$	18.2090	1.13585	0.567924	−	0.823081i	$-0.307747\pi$
$257$	18.2090	1.13585	0.567924	+	0.823081i	$0.307747\pi$
$258$	18.8954	1.17638
$259$	−19.7722	−1.22858
$260$	−9.67087	−0.599762
$261$	18.1560	1.12383
$262$	−0.941419	−0.0581611
$263$	14.3245	0.883289	0.441644	−	0.897190i	$-0.354395\pi$
$263$	14.3245	0.883289	0.441644	+	0.897190i	$0.354395\pi$
$264$	−2.48464	−0.152919
$265$	37.0716	2.27729
$266$	0.164699	0.0100984
$267$	−34.0992	−2.08684
$268$	−2.85496	−0.174395
$269$	−2.62869	−0.160274	−0.0801369	−	0.996784i	$-0.525536\pi$
$269$	−2.62869	−0.160274	−0.0801369	+	0.996784i	$0.525536\pi$
$270$	1.40341	0.0854091
$271$	17.8713	1.08560	0.542802	−	0.839861i	$-0.317364\pi$
$271$	17.8713	1.08560	0.542802	+	0.839861i	$0.317364\pi$
$272$	−6.19810	−0.375815
$273$	−32.6024	−1.97319
$274$	0.855617	0.0516897
$275$	−5.60699	−0.338114
$276$	−16.5597	−0.996779
$277$	−15.1517	−0.910380	−0.455190	−	0.890394i	$-0.650429\pi$
$277$	−15.1517	−0.910380	−0.455190	+	0.890394i	$0.650429\pi$
$278$	−1.24766	−0.0748296
$279$	−9.01988	−0.540006
$280$	14.3917	0.860071
$281$	−5.49350	−0.327715	−0.163857	−	0.986484i	$-0.552394\pi$
$281$	−5.49350	−0.327715	−0.163857	+	0.986484i	$0.552394\pi$
$282$	21.8802	1.30295
$283$	−4.04257	−0.240306	−0.120153	−	0.992755i	$-0.538339\pi$
$283$	−4.04257	−0.240306	−0.120153	+	0.992755i	$0.538339\pi$
$284$	−7.66988	−0.455124
$285$	0.301602	0.0178654
$286$	2.96940	0.175585
$287$	−36.6619	−2.16408
$288$	3.17343	0.186996
$289$	21.4164	1.25979
$290$	18.6332	1.09418
$291$	15.9992	0.937888
$292$	5.80848	0.339916
$293$	−6.54070	−0.382112	−0.191056	−	0.981579i	$-0.561191\pi$
$293$	−6.54070	−0.382112	−0.191056	+	0.981579i	$0.561191\pi$
$294$	31.1249	1.81524
$295$	−12.8562	−0.748517
$296$	−4.47442	−0.260071
$297$	−0.430913	−0.0250041
$298$	−8.88439	−0.514659
$299$	19.7906	1.14452
$300$	13.9313	0.804327
$301$	33.6055	1.93699
$302$	−16.4895	−0.948864
$303$	−42.4982	−2.44146
$304$	0.0372713	0.00213766
$305$	16.9774	0.972123
$306$	−19.6692	−1.12442
$307$	−14.0915	−0.804242	−0.402121	−	0.915587i	$-0.631727\pi$
$307$	−14.0915	−0.804242	−0.402121	+	0.915587i	$0.631727\pi$
$308$	−4.41893	−0.251792
$309$	−27.7039	−1.57602
$310$	−9.25695	−0.525759
$311$	19.6609	1.11487	0.557435	−	0.830221i	$-0.311786\pi$
$311$	19.6609	1.11487	0.557435	+	0.830221i	$0.311786\pi$
$312$	−7.37790	−0.417691
$313$	27.6887	1.56506	0.782530	−	0.622613i	$-0.213929\pi$
$313$	27.6887	1.56506	0.782530	+	0.622613i	$0.213929\pi$
$314$	−20.1501	−1.13714
$315$	45.6712	2.57328
$316$	−0.538144	−0.0302730
$317$	−14.1444	−0.794431	−0.397216	−	0.917725i	$-0.630023\pi$
$317$	−14.1444	−0.794431	−0.397216	+	0.917725i	$0.630023\pi$
$318$	28.2819	1.58597
$319$	−5.72125	−0.320328
$320$	3.25684	0.182063
$321$	22.5774	1.26015
$322$	−29.4515	−1.64127
$323$	−0.231011	−0.0128538
$324$	−8.44963	−0.469424
$325$	−16.6494	−0.923543
$326$	−15.8316	−0.876831
$327$	38.0289	2.10300
$328$	−8.29655	−0.458100
$329$	38.9140	2.14540
$330$	−8.09207	−0.445454
$331$	−12.3319	−0.677821	−0.338911	−	0.940819i	$-0.610058\pi$
$331$	−12.3319	−0.677821	−0.338911	+	0.940819i	$0.610058\pi$
$332$	15.6816	0.860638
$333$	−14.1993	−0.778115
$334$	4.54755	0.248831
$335$	−9.29815	−0.508012
$336$	10.9794	0.598978
$337$	32.0585	1.74634	0.873168	−	0.487420i	$-0.162062\pi$
$337$	32.0585	1.74634	0.873168	+	0.487420i	$0.162062\pi$
$338$	−4.18264	−0.227506
$339$	14.5477	0.790124
$340$	−20.1862	−1.09475
$341$	2.84231	0.153920
$342$	0.118278	0.00639574
$343$	24.4232	1.31873
$344$	7.60491	0.410029
$345$	−53.9324	−2.90362
$346$	−1.73194	−0.0931099
$347$	0.608987	0.0326921	0.0163461	−	0.999866i	$-0.494797\pi$
$347$	0.608987	0.0326921	0.0163461	+	0.999866i	$0.494797\pi$
$348$	14.2152	0.762016
$349$	2.01009	0.107597	0.0537987	−	0.998552i	$-0.482867\pi$
$349$	2.01009	0.107597	0.0537987	+	0.998552i	$0.482867\pi$
$350$	24.7769	1.32438
$351$	−1.27956	−0.0682976
$352$	−1.00000	−0.0533002
$353$	29.1141	1.54959	0.774794	−	0.632214i	$-0.217854\pi$
$353$	29.1141	1.54959	0.774794	+	0.632214i	$0.217854\pi$
$354$	−9.80799	−0.521289
$355$	−24.9796	−1.32578
$356$	−13.7240	−0.727372
$357$	−68.0517	−3.60168
$358$	−26.4178	−1.39622
$359$	−24.7773	−1.30769	−0.653847	−	0.756626i	$-0.726846\pi$
$359$	−24.7773	−1.30769	−0.653847	+	0.756626i	$0.726846\pi$
$360$	10.3353	0.544721
$361$	−18.9986	−0.999927
$362$	−7.62676	−0.400853
$363$	2.48464	0.130410
$364$	−13.1216	−0.687758
$365$	18.9173	0.990175
$366$	12.9520	0.677014
$367$	30.6929	1.60216	0.801079	−	0.598559i	$-0.204260\pi$
$367$	30.6929	1.60216	0.801079	+	0.598559i	$0.204260\pi$
$368$	−6.66485	−0.347429
$369$	−26.3285	−1.37061
$370$	−14.5725	−0.757587
$371$	50.2994	2.61141
$372$	−7.06212	−0.366154
$373$	−14.7790	−0.765229	−0.382615	−	0.923908i	$-0.624976\pi$
$373$	−14.7790	−0.765229	−0.382615	+	0.923908i	$0.624976\pi$
$374$	6.19810	0.320496
$375$	4.91180	0.253644
$376$	8.80620	0.454145
$377$	−16.9887	−0.874962
$378$	1.90418	0.0979402
$379$	7.50622	0.385569	0.192784	−	0.981241i	$-0.438248\pi$
$379$	7.50622	0.385569	0.192784	+	0.981241i	$0.438248\pi$
$380$	0.121387	0.00622701
$381$	18.2511	0.935033
$382$	6.60592	0.337988
$383$	−5.08868	−0.260019	−0.130010	−	0.991513i	$-0.541501\pi$
$383$	−5.08868	−0.260019	−0.130010	+	0.991513i	$0.541501\pi$
$384$	2.48464	0.126794
$385$	−14.3917	−0.733471
$386$	20.4169	1.03920
$387$	24.1336	1.22678
$388$	6.43924	0.326903
$389$	−29.5488	−1.49819	−0.749093	−	0.662465i	$-0.769510\pi$
$389$	−29.5488	−1.49819	−0.749093	+	0.662465i	$0.769510\pi$
$390$	−24.0286	−1.21674
$391$	41.3094	2.08910
$392$	12.5269	0.632706
$393$	−2.33909	−0.117991
$394$	−1.00000	−0.0503793
$395$	−1.75265	−0.0881852
$396$	−3.17343	−0.159471
$397$	−11.9505	−0.599777	−0.299889	−	0.953974i	$-0.596950\pi$
$397$	−11.9505	−0.599777	−0.299889	+	0.953974i	$0.596950\pi$
$398$	−12.3826	−0.620682
$399$	0.409219	0.0204866
$400$	5.60699	0.280349
$401$	16.2631	0.812141	0.406071	−	0.913842i	$-0.366899\pi$
$401$	16.2631	0.812141	0.406071	+	0.913842i	$0.366899\pi$
$402$	−7.09355	−0.353794
$403$	8.43997	0.420425
$404$	−17.1044	−0.850975
$405$	−27.5191	−1.36743
$406$	25.2818	1.25471
$407$	4.47442	0.221789
$408$	−15.4000	−0.762415
$409$	−14.3751	−0.710801	−0.355401	−	0.934714i	$-0.615656\pi$
$409$	−14.3751	−0.710801	−0.355401	+	0.934714i	$0.615656\pi$
$410$	−27.0205	−1.33445
$411$	2.12590	0.104863
$412$	−11.1501	−0.549324
$413$	−17.4435	−0.858339
$414$	−21.1504	−1.03949
$415$	51.0723	2.50704
$416$	−2.96940	−0.145587
$417$	−3.09998	−0.151807
$418$	−0.0372713	−0.00182300
$419$	10.3742	0.506814	0.253407	−	0.967360i	$-0.418449\pi$
$419$	10.3742	0.506814	0.253407	+	0.967360i	$0.418449\pi$
$420$	35.7583	1.74482
$421$	4.77552	0.232744	0.116372	−	0.993206i	$-0.462873\pi$
$421$	4.77552	0.232744	0.116372	+	0.993206i	$0.462873\pi$
$422$	−3.10938	−0.151362
$423$	27.9459	1.35877
$424$	11.3827	0.552793
$425$	−34.7527	−1.68575
$426$	−19.0569	−0.923310
$427$	23.0352	1.11475
$428$	9.08681	0.439228
$429$	7.37790	0.356208
$430$	24.7679	1.19442
$431$	29.6793	1.42960	0.714800	−	0.699329i	$-0.246518\pi$
$431$	29.6793	1.42960	0.714800	+	0.699329i	$0.246518\pi$
$432$	0.430913	0.0207323
$433$	11.9644	0.574974	0.287487	−	0.957784i	$-0.407180\pi$
$433$	11.9644	0.574974	0.287487	+	0.957784i	$0.407180\pi$
$434$	−12.5600	−0.602898
$435$	46.2967	2.21976
$436$	15.3056	0.733005
$437$	−0.248408	−0.0118830
$438$	14.4320	0.689586
$439$	−8.52076	−0.406674	−0.203337	−	0.979109i	$-0.565179\pi$
$439$	−8.52076	−0.406674	−0.203337	+	0.979109i	$0.565179\pi$
$440$	−3.25684	−0.155264
$441$	39.7534	1.89302
$442$	18.4047	0.875420
$443$	3.88586	0.184623	0.0923114	−	0.995730i	$-0.470574\pi$
$443$	3.88586	0.184623	0.0923114	+	0.995730i	$0.470574\pi$
$444$	−11.1173	−0.527605
$445$	−44.6969	−2.11884
$446$	10.4245	0.493617
$447$	−22.0745	−1.04409
$448$	4.41893	0.208775
$449$	39.0723	1.84394	0.921968	−	0.387267i	$-0.126581\pi$
$449$	39.0723	1.84394	0.921968	+	0.387267i	$0.126581\pi$
$450$	17.7934	0.838789
$451$	8.29655	0.390669
$452$	5.85506	0.275399
$453$	−40.9704	−1.92496
$454$	−8.35871	−0.392294
$455$	−42.7349	−2.00344
$456$	0.0926058	0.00433666
$457$	31.7115	1.48340	0.741701	−	0.670731i	$-0.234019\pi$
$457$	31.7115	1.48340	0.741701	+	0.670731i	$0.234019\pi$
$458$	27.5073	1.28533
$459$	−2.67084	−0.124664
$460$	−21.7063	−1.01206
$461$	−0.688364	−0.0320603	−0.0160302	−	0.999872i	$-0.505103\pi$
$461$	−0.688364	−0.0320603	−0.0160302	+	0.999872i	$0.505103\pi$
$462$	−10.9794	−0.510810
$463$	−36.5758	−1.69982	−0.849911	−	0.526926i	$-0.823344\pi$
$463$	−36.5758	−1.69982	−0.849911	+	0.526926i	$0.823344\pi$
$464$	5.72125	0.265602
$465$	−23.0002	−1.06661
$466$	−18.7321	−0.867747
$467$	25.4702	1.17862	0.589311	−	0.807907i	$-0.299399\pi$
$467$	25.4702	1.17862	0.589311	+	0.807907i	$0.299399\pi$
$468$	−9.42320	−0.435587
$469$	−12.6159	−0.582547
$470$	28.6804	1.32293
$471$	−50.0657	−2.30691
$472$	−3.94745	−0.181696
$473$	−7.60491	−0.349674
$474$	−1.33709	−0.0614147
$475$	0.208980	0.00958866
$476$	−27.3890	−1.25537
$477$	36.1222	1.65392
$478$	−20.1764	−0.922848
$479$	27.0596	1.23639	0.618193	−	0.786026i	$-0.287865\pi$
$479$	27.0596	1.23639	0.618193	+	0.786026i	$0.287865\pi$
$480$	8.09207	0.369351
$481$	13.2864	0.605806
$482$	26.5023	1.20714
$483$	−73.1763	−3.32964
$484$	1.00000	0.0454545
$485$	20.9715	0.952269
$486$	−22.2870	−1.01096
$487$	−34.5291	−1.56466	−0.782332	−	0.622861i	$-0.785970\pi$
$487$	−34.5291	−1.56466	−0.782332	+	0.622861i	$0.785970\pi$
$488$	5.21285	0.235975
$489$	−39.3358	−1.77883
$490$	40.7982	1.84308
$491$	19.9404	0.899896	0.449948	−	0.893055i	$-0.351443\pi$
$491$	19.9404	0.899896	0.449948	+	0.893055i	$0.351443\pi$
$492$	−20.6139	−0.929348
$493$	−35.4608	−1.59708
$494$	−0.110674	−0.00497944
$495$	−10.3353	−0.464539
$496$	−2.84231	−0.127624
$497$	−33.8927	−1.52029
$498$	38.9630	1.74598
$499$	22.3359	0.999890	0.499945	−	0.866057i	$-0.333353\pi$
$499$	22.3359	0.999890	0.499945	+	0.866057i	$0.333353\pi$
$500$	1.97687	0.0884082
$501$	11.2990	0.504803
$502$	−22.7303	−1.01450
$503$	35.0700	1.56369	0.781846	−	0.623471i	$-0.214278\pi$
$503$	35.0700	1.56369	0.781846	+	0.623471i	$0.214278\pi$
$504$	14.0232	0.624642
$505$	−55.7062	−2.47889
$506$	6.66485	0.296289
$507$	−10.3924	−0.461541
$508$	7.34558	0.325907
$509$	16.3168	0.723230	0.361615	−	0.932328i	$-0.382226\pi$
$509$	16.3168	0.723230	0.361615	+	0.932328i	$0.382226\pi$
$510$	−50.1554	−2.22092
$511$	25.6673	1.13545
$512$	1.00000	0.0441942
$513$	0.0160607	0.000709098 0
$514$	18.2090	0.803166
$515$	−36.3139	−1.60018
$516$	18.8954	0.831826
$517$	−8.80620	−0.387296
$518$	−19.7722	−0.868739
$519$	−4.30325	−0.188892
$520$	−9.67087	−0.424095
$521$	−39.4061	−1.72641	−0.863207	−	0.504851i	$-0.831548\pi$
$521$	−39.4061	−1.72641	−0.863207	+	0.504851i	$0.831548\pi$
$522$	18.1560	0.794666
$523$	−6.10894	−0.267125	−0.133563	−	0.991040i	$-0.542642\pi$
$523$	−6.10894	−0.267125	−0.133563	+	0.991040i	$0.542642\pi$
$524$	−0.941419	−0.0411261
$525$	61.5616	2.68677
$526$	14.3245	0.624580
$527$	17.6169	0.767406
$528$	−2.48464	−0.108130
$529$	21.4202	0.931313
$530$	37.0716	1.61029
$531$	−12.5270	−0.543624
$532$	0.164699	0.00714063
$533$	24.6358	1.06710
$534$	−34.0992	−1.47562
$535$	29.5943	1.27947
$536$	−2.85496	−0.123316
$537$	−65.6386	−2.83252
$538$	−2.62869	−0.113331
$539$	−12.5269	−0.539573
$540$	1.40341	0.0603934
$541$	31.9164	1.37219	0.686097	−	0.727510i	$-0.259322\pi$
$541$	31.9164	1.37219	0.686097	+	0.727510i	$0.259322\pi$
$542$	17.8713	0.767638
$543$	−18.9497	−0.813211
$544$	−6.19810	−0.265741
$545$	49.8478	2.13525
$546$	−32.6024	−1.39525
$547$	15.5837	0.666312	0.333156	−	0.942872i	$-0.391886\pi$
$547$	15.5837	0.666312	0.333156	+	0.942872i	$0.391886\pi$
$548$	0.855617	0.0365501
$549$	16.5426	0.706022
$550$	−5.60699	−0.239083
$551$	0.213238	0.00908426
$552$	−16.5597	−0.704829
$553$	−2.37802	−0.101124
$554$	−15.1517	−0.643736
$555$	−36.2073	−1.53692
$556$	−1.24766	−0.0529125
$557$	−32.9131	−1.39457	−0.697287	−	0.716792i	$-0.745610\pi$
$557$	−32.9131	−1.39457	−0.697287	+	0.716792i	$0.745610\pi$
$558$	−9.01988	−0.381842
$559$	−22.5820	−0.955118
$560$	14.3917	0.608162
$561$	15.4000	0.650190
$562$	−5.49350	−0.231729
$563$	31.6718	1.33481	0.667403	−	0.744697i	$-0.267406\pi$
$563$	31.6718	1.33481	0.667403	+	0.744697i	$0.267406\pi$
$564$	21.8802	0.921324
$565$	19.0690	0.802238
$566$	−4.04257	−0.169922
$567$	−37.3383	−1.56806
$568$	−7.66988	−0.321821
$569$	−1.72640	−0.0723744	−0.0361872	−	0.999345i	$-0.511521\pi$
$569$	−1.72640	−0.0723744	−0.0361872	+	0.999345i	$0.511521\pi$
$570$	0.301602	0.0126327
$571$	10.6350	0.445061	0.222531	−	0.974926i	$-0.428568\pi$
$571$	10.6350	0.445061	0.222531	+	0.974926i	$0.428568\pi$
$572$	2.96940	0.124157
$573$	16.4133	0.685676
$574$	−36.6619	−1.53024
$575$	−37.3697	−1.55843
$576$	3.17343	0.132226
$577$	−46.7181	−1.94490	−0.972451	−	0.233109i	$-0.925110\pi$
$577$	−46.7181	−1.94490	−0.972451	+	0.233109i	$0.925110\pi$
$578$	21.4164	0.890805
$579$	50.7288	2.10821
$580$	18.6332	0.773700
$581$	69.2958	2.87487
$582$	15.9992	0.663187
$583$	−11.3827	−0.471424
$584$	5.80848	0.240357
$585$	−30.6898	−1.26887
$586$	−6.54070	−0.270194
$587$	43.0583	1.77721	0.888603	−	0.458678i	$-0.151677\pi$
$587$	43.0583	1.77721	0.888603	+	0.458678i	$0.151677\pi$
$588$	31.1249	1.28357
$589$	−0.105937	−0.00436505
$590$	−12.8562	−0.529282
$591$	−2.48464	−0.102204
$592$	−4.47442	−0.183898
$593$	−20.6114	−0.846408	−0.423204	−	0.906034i	$-0.639095\pi$
$593$	−20.6114	−0.846408	−0.423204	+	0.906034i	$0.639095\pi$
$594$	−0.430913	−0.0176806
$595$	−89.2014	−3.65690
$596$	−8.88439	−0.363919
$597$	−30.7662	−1.25918
$598$	19.7906	0.809299
$599$	−6.89464	−0.281707	−0.140854	−	0.990030i	$-0.544985\pi$
$599$	−6.89464	−0.281707	−0.140854	+	0.990030i	$0.544985\pi$
$600$	13.9313	0.568745
$601$	−1.33933	−0.0546323	−0.0273162	−	0.999627i	$-0.508696\pi$
$601$	−1.33933	−0.0546323	−0.0273162	+	0.999627i	$0.508696\pi$
$602$	33.6055	1.36966
$603$	−9.06003	−0.368953
$604$	−16.4895	−0.670948
$605$	3.25684	0.132409
$606$	−42.4982	−1.72637
$607$	0.876338	0.0355695	0.0177847	−	0.999842i	$-0.494339\pi$
$607$	0.876338	0.0355695	0.0177847	+	0.999842i	$0.494339\pi$
$608$	0.0372713	0.00151155
$609$	62.8161	2.54544
$610$	16.9774	0.687395
$611$	−26.1492	−1.05788
$612$	−19.6692	−0.795082
$613$	−20.3056	−0.820137	−0.410069	−	0.912055i	$-0.634495\pi$
$613$	−20.3056	−0.820137	−0.410069	+	0.912055i	$0.634495\pi$
$614$	−14.0915	−0.568685
$615$	−67.1362	−2.70719
$616$	−4.41893	−0.178044
$617$	−19.9614	−0.803615	−0.401807	−	0.915724i	$-0.631618\pi$
$617$	−19.9614	−0.803615	−0.401807	+	0.915724i	$0.631618\pi$
$618$	−27.7039	−1.11441
$619$	32.3130	1.29877	0.649384	−	0.760461i	$-0.275027\pi$
$619$	32.3130	1.29877	0.649384	+	0.760461i	$0.275027\pi$
$620$	−9.25695	−0.371768
$621$	−2.87197	−0.115248
$622$	19.6609	0.788331
$623$	−60.6455	−2.42971
$624$	−7.37790	−0.295352
$625$	−21.5966	−0.863865
$626$	27.6887	1.10666
$627$	−0.0926058	−0.00369832
$628$	−20.1501	−0.804076
$629$	27.7329	1.10578
$630$	45.6712	1.81958
$631$	−32.0652	−1.27650	−0.638248	−	0.769831i	$-0.720341\pi$
$631$	−32.0652	−1.27650	−0.638248	+	0.769831i	$0.720341\pi$
$632$	−0.538144	−0.0214062
$633$	−7.72569	−0.307069
$634$	−14.1444	−0.561748
$635$	23.9233	0.949369
$636$	28.2819	1.12145
$637$	−37.1975	−1.47382
$638$	−5.72125	−0.226506
$639$	−24.3398	−0.962870
$640$	3.25684	0.128738
$641$	−30.2921	−1.19646	−0.598232	−	0.801323i	$-0.704130\pi$
$641$	−30.2921	−1.19646	−0.598232	+	0.801323i	$0.704130\pi$
$642$	22.5774	0.891061
$643$	10.9326	0.431141	0.215570	−	0.976488i	$-0.430839\pi$
$643$	10.9326	0.431141	0.215570	+	0.976488i	$0.430839\pi$
$644$	−29.4515	−1.16055
$645$	61.5394	2.42311
$646$	−0.231011	−0.00908902
$647$	1.27374	0.0500758	0.0250379	−	0.999687i	$-0.492029\pi$
$647$	1.27374	0.0500758	0.0250379	+	0.999687i	$0.492029\pi$
$648$	−8.44963	−0.331933
$649$	3.94745	0.154951
$650$	−16.6494	−0.653044
$651$	−31.2070	−1.22310
$652$	−15.8316	−0.620013
$653$	−7.77798	−0.304376	−0.152188	−	0.988352i	$-0.548632\pi$
$653$	−7.77798	−0.304376	−0.152188	+	0.988352i	$0.548632\pi$
$654$	38.0289	1.48705
$655$	−3.06605	−0.119800
$656$	−8.29655	−0.323926
$657$	18.4328	0.719132
$658$	38.9140	1.51702
$659$	−40.6773	−1.58456	−0.792281	−	0.610156i	$-0.791107\pi$
$659$	−40.6773	−1.58456	−0.792281	+	0.610156i	$0.791107\pi$
$660$	−8.09207	−0.314983
$661$	−14.5440	−0.565697	−0.282849	−	0.959165i	$-0.591279\pi$
$661$	−14.5440	−0.565697	−0.282849	+	0.959165i	$0.591279\pi$
$662$	−12.3319	−0.479292
$663$	45.7289	1.77596
$664$	15.6816	0.608563
$665$	0.536399	0.0208007
$666$	−14.1993	−0.550211
$667$	−38.1312	−1.47645
$668$	4.54755	0.175950
$669$	25.9012	1.00140
$670$	−9.29815	−0.359219
$671$	−5.21285	−0.201240
$672$	10.9794	0.423541
$673$	40.2775	1.55258	0.776292	−	0.630374i	$-0.217098\pi$
$673$	40.2775	1.55258	0.776292	+	0.630374i	$0.217098\pi$
$674$	32.0585	1.23485
$675$	2.41613	0.0929968
$676$	−4.18264	−0.160871
$677$	12.7119	0.488557	0.244279	−	0.969705i	$-0.421449\pi$
$677$	12.7119	0.488557	0.244279	+	0.969705i	$0.421449\pi$
$678$	14.5477	0.558702
$679$	28.4545	1.09198
$680$	−20.1862	−0.774105
$681$	−20.7684	−0.795846
$682$	2.84231	0.108838
$683$	12.2012	0.466864	0.233432	−	0.972373i	$-0.425004\pi$
$683$	12.2012	0.466864	0.233432	+	0.972373i	$0.425004\pi$
$684$	0.118278	0.00452247
$685$	2.78660	0.106471
$686$	24.4232	0.932481
$687$	68.3458	2.60755
$688$	7.60491	0.289934
$689$	−33.7999	−1.28767
$690$	−53.9324	−2.05317
$691$	38.6126	1.46889	0.734445	−	0.678668i	$-0.237442\pi$
$691$	38.6126	1.46889	0.734445	+	0.678668i	$0.237442\pi$
$692$	−1.73194	−0.0658386
$693$	−14.0232	−0.532696
$694$	0.608987	0.0231168
$695$	−4.06342	−0.154134
$696$	14.2152	0.538827
$697$	51.4228	1.94778
$698$	2.01009	0.0760829
$699$	−46.5425	−1.76040
$700$	24.7769	0.936479
$701$	27.4551	1.03697	0.518483	−	0.855088i	$-0.326497\pi$
$701$	27.4551	1.03697	0.518483	+	0.855088i	$0.326497\pi$
$702$	−1.27956	−0.0482937
$703$	−0.166768	−0.00628976
$704$	−1.00000	−0.0376889
$705$	71.2603	2.68382
$706$	29.1141	1.09572
$707$	−75.5831	−2.84259
$708$	−9.80799	−0.368607
$709$	−36.2980	−1.36320	−0.681600	−	0.731725i	$-0.738715\pi$
$709$	−36.2980	−1.36320	−0.681600	+	0.731725i	$0.738715\pi$
$710$	−24.9796	−0.937466
$711$	−1.70776	−0.0640461
$712$	−13.7240	−0.514329
$713$	18.9436	0.709443
$714$	−68.0517	−2.54677
$715$	9.67087	0.361670
$716$	−26.4178	−0.987278
$717$	−50.1311	−1.87218
$718$	−24.7773	−0.924680
$719$	−7.44830	−0.277775	−0.138887	−	0.990308i	$-0.544353\pi$
$719$	−7.44830	−0.277775	−0.138887	+	0.990308i	$0.544353\pi$
$720$	10.3353	0.385176
$721$	−49.2714	−1.83496
$722$	−18.9986	−0.707055
$723$	65.8486	2.44893
$724$	−7.62676	−0.283446
$725$	32.0790	1.19138
$726$	2.48464	0.0922136
$727$	40.8131	1.51367	0.756836	−	0.653604i	$-0.226744\pi$
$727$	40.8131	1.51367	0.756836	+	0.653604i	$0.226744\pi$
$728$	−13.1216	−0.486318
$729$	−30.0263	−1.11209
$730$	18.9173	0.700160
$731$	−47.1359	−1.74339
$732$	12.9520	0.478721
$733$	6.38717	0.235915	0.117958	−	0.993019i	$-0.462365\pi$
$733$	6.38717	0.235915	0.117958	+	0.993019i	$0.462365\pi$
$734$	30.6929	1.13290
$735$	101.369	3.73904
$736$	−6.66485	−0.245670
$737$	2.85496	0.105164
$738$	−26.3285	−0.969167
$739$	−25.9294	−0.953829	−0.476915	−	0.878950i	$-0.658245\pi$
$739$	−25.9294	−0.953829	−0.476915	+	0.878950i	$0.658245\pi$
$740$	−14.5725	−0.535695
$741$	−0.274984	−0.0101018
$742$	50.2994	1.84655
$743$	−1.95036	−0.0715519	−0.0357759	−	0.999360i	$-0.511390\pi$
$743$	−1.95036	−0.0715519	−0.0357759	+	0.999360i	$0.511390\pi$
$744$	−7.06212	−0.258910
$745$	−28.9350	−1.06010
$746$	−14.7790	−0.541099
$747$	49.7644	1.82078
$748$	6.19810	0.226625
$749$	40.1540	1.46719
$750$	4.91180	0.179354
$751$	20.7596	0.757528	0.378764	−	0.925493i	$-0.376349\pi$
$751$	20.7596	0.757528	0.378764	+	0.925493i	$0.376349\pi$
$752$	8.80620	0.321129
$753$	−56.4766	−2.05812
$754$	−16.9887	−0.618692
$755$	−53.7036	−1.95447
$756$	1.90418	0.0692542
$757$	47.3194	1.71985	0.859927	−	0.510417i	$-0.170509\pi$
$757$	47.3194	1.71985	0.859927	+	0.510417i	$0.170509\pi$
$758$	7.50622	0.272638
$759$	16.5597	0.601080
$760$	0.121387	0.00440316
$761$	18.1717	0.658724	0.329362	−	0.944204i	$-0.393166\pi$
$761$	18.1717	0.658724	0.329362	+	0.944204i	$0.393166\pi$
$762$	18.2511	0.661168
$763$	67.6343	2.44853
$764$	6.60592	0.238994
$765$	−64.0595	−2.31608
$766$	−5.08868	−0.183862
$767$	11.7216	0.423241
$768$	2.48464	0.0896567
$769$	42.7339	1.54102	0.770511	−	0.637426i	$-0.220001\pi$
$769$	42.7339	1.54102	0.770511	+	0.637426i	$0.220001\pi$
$770$	−14.3917	−0.518642
$771$	45.2429	1.62938
$772$	20.4169	0.734822
$773$	14.7373	0.530065	0.265032	−	0.964240i	$-0.414617\pi$
$773$	14.7373	0.530065	0.265032	+	0.964240i	$0.414617\pi$
$774$	24.1336	0.867466
$775$	−15.9368	−0.572467
$776$	6.43924	0.231155
$777$	−49.1267	−1.76241
$778$	−29.5488	−1.05938
$779$	−0.309224	−0.0110791
$780$	−24.0286	−0.860362
$781$	7.66988	0.274450
$782$	41.3094	1.47722
$783$	2.46536	0.0881048
$784$	12.5269	0.447391
$785$	−65.6256	−2.34228
$786$	−2.33909	−0.0834324
$787$	39.1861	1.39683	0.698417	−	0.715691i	$-0.253888\pi$
$787$	39.1861	1.39683	0.698417	+	0.715691i	$0.253888\pi$
$788$	−1.00000	−0.0356235
$789$	35.5913	1.26708
$790$	−1.75265	−0.0623564
$791$	25.8731	0.919942
$792$	−3.17343	−0.112763
$793$	−15.4791	−0.549677
$794$	−11.9505	−0.424106
$795$	92.1096	3.26679
$796$	−12.3826	−0.438889
$797$	13.1987	0.467524	0.233762	−	0.972294i	$-0.424896\pi$
$797$	13.1987	0.467524	0.233762	+	0.972294i	$0.424896\pi$
$798$	0.409219	0.0144862
$799$	−54.5817	−1.93096
$800$	5.60699	0.198237
$801$	−43.5522	−1.53884
$802$	16.2631	0.574271
$803$	−5.80848	−0.204977
$804$	−7.09355	−0.250170
$805$	−95.9187	−3.38069
$806$	8.43997	0.297285
$807$	−6.53133	−0.229914
$808$	−17.1044	−0.601730
$809$	5.39358	0.189628	0.0948140	−	0.995495i	$-0.469774\pi$
$809$	5.39358	0.189628	0.0948140	+	0.995495i	$0.469774\pi$
$810$	−27.5191	−0.966921
$811$	−44.6432	−1.56764	−0.783818	−	0.620991i	$-0.786730\pi$
$811$	−44.6432	−1.56764	−0.783818	+	0.620991i	$0.786730\pi$
$812$	25.2818	0.887217
$813$	44.4037	1.55731
$814$	4.47442	0.156828
$815$	−51.5610	−1.80610
$816$	−15.4000	−0.539109
$817$	0.283445	0.00991649
$818$	−14.3751	−0.502612
$819$	−41.6404	−1.45504
$820$	−27.0205	−0.943597
$821$	−18.8031	−0.656234	−0.328117	−	0.944637i	$-0.606414\pi$
$821$	−18.8031	−0.656234	−0.328117	+	0.944637i	$0.606414\pi$
$822$	2.12590	0.0741492
$823$	−10.2047	−0.355713	−0.177856	−	0.984056i	$-0.556916\pi$
$823$	−10.2047	−0.355713	−0.177856	+	0.984056i	$0.556916\pi$
$824$	−11.1501	−0.388431
$825$	−13.9313	−0.485027
$826$	−17.4435	−0.606937
$827$	−29.5993	−1.02927	−0.514634	−	0.857410i	$-0.672072\pi$
$827$	−29.5993	−1.02927	−0.514634	+	0.857410i	$0.672072\pi$
$828$	−21.1504	−0.735028
$829$	26.3976	0.916828	0.458414	−	0.888739i	$-0.348418\pi$
$829$	26.3976	0.916828	0.458414	+	0.888739i	$0.348418\pi$
$830$	51.0723	1.77275
$831$	−37.6466	−1.30595
$832$	−2.96940	−0.102946
$833$	−77.6432	−2.69018
$834$	−3.09998	−0.107344
$835$	14.8106	0.512543
$836$	−0.0372713	−0.00128906
$837$	−1.22479	−0.0423350
$838$	10.3742	0.358372
$839$	45.5568	1.57279	0.786397	−	0.617721i	$-0.211944\pi$
$839$	45.5568	1.57279	0.786397	+	0.617721i	$0.211944\pi$
$840$	35.7583	1.23378
$841$	3.73265	0.128712
$842$	4.77552	0.164575
$843$	−13.6494	−0.470109
$844$	−3.10938	−0.107029
$845$	−13.6222	−0.468617
$846$	27.9459	0.960799
$847$	4.41893	0.151836
$848$	11.3827	0.390884
$849$	−10.0443	−0.344721
$850$	−34.7527	−1.19201
$851$	29.8213	1.02226
$852$	−19.0569	−0.652878
$853$	19.8826	0.680767	0.340384	−	0.940287i	$-0.389443\pi$
$853$	19.8826	0.680767	0.340384	+	0.940287i	$0.389443\pi$
$854$	23.0352	0.788249
$855$	0.385212	0.0131740
$856$	9.08681	0.310581
$857$	−16.1508	−0.551700	−0.275850	−	0.961201i	$-0.588959\pi$
$857$	−16.1508	−0.551700	−0.275850	+	0.961201i	$0.588959\pi$
$858$	7.37790	0.251877
$859$	−35.5645	−1.21344	−0.606722	−	0.794914i	$-0.707516\pi$
$859$	−35.5645	−1.21344	−0.606722	+	0.794914i	$0.707516\pi$
$860$	24.7679	0.844580
$861$	−91.0915	−3.10439
$862$	29.6793	1.01088
$863$	13.2475	0.450951	0.225475	−	0.974249i	$-0.427607\pi$
$863$	13.2475	0.450951	0.225475	+	0.974249i	$0.427607\pi$
$864$	0.430913	0.0146600
$865$	−5.64066	−0.191788
$866$	11.9644	0.406568
$867$	53.2121	1.80718
$868$	−12.5600	−0.426314
$869$	0.538144	0.0182553
$870$	46.2967	1.56960
$871$	8.47754	0.287250
$872$	15.3056	0.518313
$873$	20.4345	0.691602
$874$	−0.248408	−0.00840252
$875$	8.73563	0.295318
$876$	14.4320	0.487611
$877$	−26.8328	−0.906079	−0.453039	−	0.891490i	$-0.649660\pi$
$877$	−26.8328	−0.906079	−0.453039	+	0.891490i	$0.649660\pi$
$878$	−8.52076	−0.287562
$879$	−16.2513	−0.548142
$880$	−3.25684	−0.109788
$881$	−20.5391	−0.691980	−0.345990	−	0.938238i	$-0.612457\pi$
$881$	−20.5391	−0.691980	−0.345990	+	0.938238i	$0.612457\pi$
$882$	39.7534	1.33857
$883$	9.29780	0.312896	0.156448	−	0.987686i	$-0.449996\pi$
$883$	9.29780	0.312896	0.156448	+	0.987686i	$0.449996\pi$
$884$	18.4047	0.619016
$885$	−31.9430	−1.07375
$886$	3.88586	0.130548
$887$	16.4525	0.552422	0.276211	−	0.961097i	$-0.410921\pi$
$887$	16.4525	0.552422	0.276211	+	0.961097i	$0.410921\pi$
$888$	−11.1173	−0.373073
$889$	32.4596	1.08866
$890$	−44.6969	−1.49824
$891$	8.44963	0.283073
$892$	10.4245	0.349040
$893$	0.328219	0.0109834
$894$	−22.0745	−0.738282
$895$	−86.0384	−2.87595
$896$	4.41893	0.147626
$897$	49.1726	1.64182
$898$	39.0723	1.30386
$899$	−16.2616	−0.542354
$900$	17.7934	0.593113
$901$	−70.5511	−2.35040
$902$	8.29655	0.276245
$903$	83.4976	2.77863
$904$	5.85506	0.194737
$905$	−24.8391	−0.825680
$906$	−40.9704	−1.36115
$907$	−7.59470	−0.252178	−0.126089	−	0.992019i	$-0.540242\pi$
$907$	−7.59470	−0.252178	−0.126089	+	0.992019i	$0.540242\pi$
$908$	−8.35871	−0.277393
$909$	−54.2796	−1.80034
$910$	−42.7349	−1.41665
$911$	−14.4467	−0.478639	−0.239320	−	0.970941i	$-0.576924\pi$
$911$	−14.4467	−0.478639	−0.239320	+	0.970941i	$0.576924\pi$
$912$	0.0926058	0.00306649
$913$	−15.6816	−0.518984
$914$	31.7115	1.04892
$915$	42.1827	1.39452
$916$	27.5073	0.908868
$917$	−4.16006	−0.137377
$918$	−2.67084	−0.0881510
$919$	13.8140	0.455683	0.227841	−	0.973698i	$-0.426833\pi$
$919$	13.8140	0.455683	0.227841	+	0.973698i	$0.426833\pi$
$920$	−21.7063	−0.715636
$921$	−35.0122	−1.15369
$922$	−0.688364	−0.0226701
$923$	22.7750	0.749648
$924$	−10.9794	−0.361197
$925$	−25.0880	−0.824890
$926$	−36.5758	−1.20196
$927$	−35.3840	−1.16216
$928$	5.72125	0.187809
$929$	16.9630	0.556539	0.278270	−	0.960503i	$-0.410239\pi$
$929$	16.9630	0.556539	0.278270	+	0.960503i	$0.410239\pi$
$930$	−23.0002	−0.754206
$931$	0.466896	0.0153019
$932$	−18.7321	−0.613590
$933$	48.8503	1.59929
$934$	25.4702	0.833411
$935$	20.1862	0.660159
$936$	−9.42320	−0.308007
$937$	28.1184	0.918589	0.459295	−	0.888284i	$-0.348102\pi$
$937$	28.1184	0.918589	0.459295	+	0.888284i	$0.348102\pi$
$938$	−12.6159	−0.411923
$939$	68.7965	2.24509
$940$	28.6804	0.935450
$941$	25.5015	0.831325	0.415663	−	0.909519i	$-0.363550\pi$
$941$	25.5015	0.831325	0.415663	+	0.909519i	$0.363550\pi$
$942$	−50.0657	−1.63123
$943$	55.2953	1.80066
$944$	−3.94745	−0.128479
$945$	6.20159	0.201738
$946$	−7.60491	−0.247257
$947$	10.1588	0.330117	0.165059	−	0.986284i	$-0.447219\pi$
$947$	10.1588	0.330117	0.165059	+	0.986284i	$0.447219\pi$
$948$	−1.33709	−0.0434268
$949$	−17.2477	−0.559885
$950$	0.208980	0.00678021
$951$	−35.1438	−1.13962
$952$	−27.3890	−0.887681
$953$	−0.889768	−0.0288224	−0.0144112	−	0.999896i	$-0.504587\pi$
$953$	−0.889768	−0.0288224	−0.0144112	+	0.999896i	$0.504587\pi$
$954$	36.1222	1.16950
$955$	21.5144	0.696190
$956$	−20.1764	−0.652552
$957$	−14.2152	−0.459513
$958$	27.0596	0.874257
$959$	3.78091	0.122092
$960$	8.09207	0.261170
$961$	−22.9213	−0.739395
$962$	13.2864	0.428370
$963$	28.8364	0.929239
$964$	26.5023	0.853580
$965$	66.4947	2.14054
$966$	−73.1763	−2.35441
$967$	37.7090	1.21264	0.606321	−	0.795220i	$-0.292645\pi$
$967$	37.7090	1.21264	0.606321	+	0.795220i	$0.292645\pi$
$968$	1.00000	0.0321412
$969$	−0.573980	−0.0184389
$970$	20.9715	0.673356
$971$	−35.2964	−1.13271	−0.566357	−	0.824160i	$-0.691648\pi$
$971$	−35.2964	−1.13271	−0.566357	+	0.824160i	$0.691648\pi$
$972$	−22.2870	−0.714856
$973$	−5.51332	−0.176749
$974$	−34.5291	−1.10639
$975$	−41.3678	−1.32483
$976$	5.21285	0.166859
$977$	20.7194	0.662871	0.331436	−	0.943478i	$-0.392467\pi$
$977$	20.7194	0.662871	0.331436	+	0.943478i	$0.392467\pi$
$978$	−39.3358	−1.25782
$979$	13.7240	0.438622
$980$	40.7982	1.30325
$981$	48.5712	1.55076
$982$	19.9404	0.636322
$983$	−41.9395	−1.33766	−0.668831	−	0.743415i	$-0.733205\pi$
$983$	−41.9395	−1.33766	−0.668831	+	0.743415i	$0.733205\pi$
$984$	−20.6139	−0.657148
$985$	−3.25684	−0.103771
$986$	−35.4608	−1.12930
$987$	96.6872	3.07759
$988$	−0.110674	−0.00352100
$989$	−50.6855	−1.61171
$990$	−10.3353	−0.328479
$991$	49.5446	1.57384	0.786919	−	0.617057i	$-0.211675\pi$
$991$	49.5446	1.57384	0.786919	+	0.617057i	$0.211675\pi$
$992$	−2.84231	−0.0902435
$993$	−30.6403	−0.972339
$994$	−33.8927	−1.07501
$995$	−40.3280	−1.27848
$996$	38.9630	1.23459
$997$	21.7738	0.689582	0.344791	−	0.938679i	$-0.387950\pi$
$997$	21.7738	0.689582	0.344791	+	0.938679i	$0.387950\pi$
$998$	22.3359	0.707029
$999$	−1.92809	−0.0610020

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4334.2.a.f.1.19	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4334.2.a.f.1.19	✓	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +2.48464 q^{3} +1.00000 q^{4} +3.25684 q^{5} +2.48464 q^{6} +4.41893 q^{7} +1.00000 q^{8} +3.17343 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +2.48464 q^{3} +1.00000 q^{4} +3.25684 q^{5} +2.48464 q^{6} +4.41893 q^{7} +1.00000 q^{8} +3.17343 q^{9} +3.25684 q^{10} -1.00000 q^{11} +2.48464 q^{12} -2.96940 q^{13} +4.41893 q^{14} +8.09207 q^{15} +1.00000 q^{16} -6.19810 q^{17} +3.17343 q^{18} +0.0372713 q^{19} +3.25684 q^{20} +10.9794 q^{21} -1.00000 q^{22} -6.66485 q^{23} +2.48464 q^{24} +5.60699 q^{25} -2.96940 q^{26} +0.430913 q^{27} +4.41893 q^{28} +5.72125 q^{29} +8.09207 q^{30} -2.84231 q^{31} +1.00000 q^{32} -2.48464 q^{33} -6.19810 q^{34} +14.3917 q^{35} +3.17343 q^{36} -4.47442 q^{37} +0.0372713 q^{38} -7.37790 q^{39} +3.25684 q^{40} -8.29655 q^{41} +10.9794 q^{42} +7.60491 q^{43} -1.00000 q^{44} +10.3353 q^{45} -6.66485 q^{46} +8.80620 q^{47} +2.48464 q^{48} +12.5269 q^{49} +5.60699 q^{50} -15.4000 q^{51} -2.96940 q^{52} +11.3827 q^{53} +0.430913 q^{54} -3.25684 q^{55} +4.41893 q^{56} +0.0926058 q^{57} +5.72125 q^{58} -3.94745 q^{59} +8.09207 q^{60} +5.21285 q^{61} -2.84231 q^{62} +14.0232 q^{63} +1.00000 q^{64} -9.67087 q^{65} -2.48464 q^{66} -2.85496 q^{67} -6.19810 q^{68} -16.5597 q^{69} +14.3917 q^{70} -7.66988 q^{71} +3.17343 q^{72} +5.80848 q^{73} -4.47442 q^{74} +13.9313 q^{75} +0.0372713 q^{76} -4.41893 q^{77} -7.37790 q^{78} -0.538144 q^{79} +3.25684 q^{80} -8.44963 q^{81} -8.29655 q^{82} +15.6816 q^{83} +10.9794 q^{84} -20.1862 q^{85} +7.60491 q^{86} +14.2152 q^{87} -1.00000 q^{88} -13.7240 q^{89} +10.3353 q^{90} -13.1216 q^{91} -6.66485 q^{92} -7.06212 q^{93} +8.80620 q^{94} +0.121387 q^{95} +2.48464 q^{96} +6.43924 q^{97} +12.5269 q^{98} -3.17343 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 24 q^{2} + 8 q^{3} + 24 q^{4} + 8 q^{6} + 11 q^{7} + 24 q^{8} + 28 q^{9}+O(q^{10}) \) 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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