LMFDB - Embedded newform 4334.2.a.f.1.5

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			1.5
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)

$f(q)$	$=$	$q+1.00000 q^{2} -2.11945 q^{3} +1.00000 q^{4} +2.85950 q^{5} -2.11945 q^{6} +0.696891 q^{7} +1.00000 q^{8} +1.49205 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.11945 q^{3} +1.00000 q^{4} +2.85950 q^{5} -2.11945 q^{6} +0.696891 q^{7} +1.00000 q^{8} +1.49205 q^{9} +2.85950 q^{10} -1.00000 q^{11} -2.11945 q^{12} -3.28300 q^{13} +0.696891 q^{14} -6.06056 q^{15} +1.00000 q^{16} -1.84337 q^{17} +1.49205 q^{18} +3.98902 q^{19} +2.85950 q^{20} -1.47702 q^{21} -1.00000 q^{22} -3.01915 q^{23} -2.11945 q^{24} +3.17676 q^{25} -3.28300 q^{26} +3.19601 q^{27} +0.696891 q^{28} +0.0188547 q^{29} -6.06056 q^{30} +2.31168 q^{31} +1.00000 q^{32} +2.11945 q^{33} -1.84337 q^{34} +1.99276 q^{35} +1.49205 q^{36} +3.68861 q^{37} +3.98902 q^{38} +6.95815 q^{39} +2.85950 q^{40} +5.71570 q^{41} -1.47702 q^{42} +9.47673 q^{43} -1.00000 q^{44} +4.26653 q^{45} -3.01915 q^{46} -0.815428 q^{47} -2.11945 q^{48} -6.51434 q^{49} +3.17676 q^{50} +3.90692 q^{51} -3.28300 q^{52} +1.95048 q^{53} +3.19601 q^{54} -2.85950 q^{55} +0.696891 q^{56} -8.45452 q^{57} +0.0188547 q^{58} +14.7141 q^{59} -6.06056 q^{60} +7.02764 q^{61} +2.31168 q^{62} +1.03980 q^{63} +1.00000 q^{64} -9.38776 q^{65} +2.11945 q^{66} -6.04045 q^{67} -1.84337 q^{68} +6.39892 q^{69} +1.99276 q^{70} +9.69861 q^{71} +1.49205 q^{72} +8.67541 q^{73} +3.68861 q^{74} -6.73298 q^{75} +3.98902 q^{76} -0.696891 q^{77} +6.95815 q^{78} +12.3385 q^{79} +2.85950 q^{80} -11.2499 q^{81} +5.71570 q^{82} -15.0546 q^{83} -1.47702 q^{84} -5.27112 q^{85} +9.47673 q^{86} -0.0399616 q^{87} -1.00000 q^{88} +5.90025 q^{89} +4.26653 q^{90} -2.28789 q^{91} -3.01915 q^{92} -4.89949 q^{93} -0.815428 q^{94} +11.4066 q^{95} -2.11945 q^{96} +12.3474 q^{97} -6.51434 q^{98} -1.49205 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−2.11945	−1.22366	−0.611831	−	0.790988i	$-0.709567\pi$
$3$	−2.11945	−1.22366	−0.611831	+	0.790988i	$0.709567\pi$
$4$	1.00000	0.500000
$5$	2.85950	1.27881	0.639405	−	0.768871i	$-0.279181\pi$
$5$	2.85950	1.27881	0.639405	+	0.768871i	$0.279181\pi$
$6$	−2.11945	−0.865260
$7$	0.696891	0.263400	0.131700	−	0.991290i	$-0.457956\pi$
$7$	0.696891	0.263400	0.131700	+	0.991290i	$0.457956\pi$
$8$	1.00000	0.353553
$9$	1.49205	0.497351
$10$	2.85950	0.904255
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−2.11945	−0.611831
$13$	−3.28300	−0.910542	−0.455271	−	0.890353i	$-0.650458\pi$
$13$	−3.28300	−0.910542	−0.455271	+	0.890353i	$0.650458\pi$
$14$	0.696891	0.186252
$15$	−6.06056	−1.56483
$16$	1.00000	0.250000
$17$	−1.84337	−0.447082	−0.223541	−	0.974695i	$-0.571762\pi$
$17$	−1.84337	−0.447082	−0.223541	+	0.974695i	$0.571762\pi$
$18$	1.49205	0.351680
$19$	3.98902	0.915145	0.457572	−	0.889172i	$-0.348719\pi$
$19$	3.98902	0.915145	0.457572	+	0.889172i	$0.348719\pi$
$20$	2.85950	0.639405
$21$	−1.47702	−0.322313
$22$	−1.00000	−0.213201
$23$	−3.01915	−0.629535	−0.314768	−	0.949169i	$-0.601927\pi$
$23$	−3.01915	−0.629535	−0.314768	+	0.949169i	$0.601927\pi$
$24$	−2.11945	−0.432630
$25$	3.17676	0.635352
$26$	−3.28300	−0.643850
$27$	3.19601	0.615073
$28$	0.696891	0.131700
$29$	0.0188547	0.00350123	0.00175062	−	0.999998i	$-0.499443\pi$
$29$	0.0188547	0.00350123	0.00175062	+	0.999998i	$0.499443\pi$
$30$	−6.06056	−1.10650
$31$	2.31168	0.415190	0.207595	−	0.978215i	$-0.433436\pi$
$31$	2.31168	0.415190	0.207595	+	0.978215i	$0.433436\pi$
$32$	1.00000	0.176777
$33$	2.11945	0.368948
$34$	−1.84337	−0.316135
$35$	1.99276	0.336838
$36$	1.49205	0.248675
$37$	3.68861	0.606404	0.303202	−	0.952926i	$-0.401944\pi$
$37$	3.68861	0.606404	0.303202	+	0.952926i	$0.401944\pi$
$38$	3.98902	0.647105
$39$	6.95815	1.11420
$40$	2.85950	0.452127
$41$	5.71570	0.892642	0.446321	−	0.894873i	$-0.352734\pi$
$41$	5.71570	0.892642	0.446321	+	0.894873i	$0.352734\pi$
$42$	−1.47702	−0.227909
$43$	9.47673	1.44519	0.722594	−	0.691273i	$-0.242950\pi$
$43$	9.47673	1.44519	0.722594	+	0.691273i	$0.242950\pi$
$44$	−1.00000	−0.150756
$45$	4.26653	0.636017
$46$	−3.01915	−0.445149
$47$	−0.815428	−0.118942	−0.0594712	−	0.998230i	$-0.518941\pi$
$47$	−0.815428	−0.118942	−0.0594712	+	0.998230i	$0.518941\pi$
$48$	−2.11945	−0.305916
$49$	−6.51434	−0.930621
$50$	3.17676	0.449262
$51$	3.90692	0.547078
$52$	−3.28300	−0.455271
$53$	1.95048	0.267919	0.133959	−	0.990987i	$-0.457231\pi$
$53$	1.95048	0.267919	0.133959	+	0.990987i	$0.457231\pi$
$54$	3.19601	0.434922
$55$	−2.85950	−0.385575
$56$	0.696891	0.0931259
$57$	−8.45452	−1.11983
$58$	0.0188547	0.00247575
$59$	14.7141	1.91562	0.957808	−	0.287409i	$-0.0927940\pi$
$59$	14.7141	1.91562	0.957808	+	0.287409i	$0.0927940\pi$
$60$	−6.06056	−0.782416
$61$	7.02764	0.899797	0.449899	−	0.893080i	$-0.351460\pi$
$61$	7.02764	0.899797	0.449899	+	0.893080i	$0.351460\pi$
$62$	2.31168	0.293584
$63$	1.03980	0.131002
$64$	1.00000	0.125000
$65$	−9.38776	−1.16441
$66$	2.11945	0.260886
$67$	−6.04045	−0.737959	−0.368979	−	0.929438i	$-0.620293\pi$
$67$	−6.04045	−0.737959	−0.368979	+	0.929438i	$0.620293\pi$
$68$	−1.84337	−0.223541
$69$	6.39892	0.770339
$70$	1.99276	0.238181
$71$	9.69861	1.15101	0.575507	−	0.817797i	$-0.304805\pi$
$71$	9.69861	1.15101	0.575507	+	0.817797i	$0.304805\pi$
$72$	1.49205	0.175840
$73$	8.67541	1.01538	0.507690	−	0.861540i	$-0.330500\pi$
$73$	8.67541	1.01538	0.507690	+	0.861540i	$0.330500\pi$
$74$	3.68861	0.428793
$75$	−6.73298	−0.777457
$76$	3.98902	0.457572
$77$	−0.696891	−0.0794180
$78$	6.95815	0.787856
$79$	12.3385	1.38819	0.694094	−	0.719885i	$-0.255805\pi$
$79$	12.3385	1.38819	0.694094	+	0.719885i	$0.255805\pi$
$80$	2.85950	0.319702
$81$	−11.2499	−1.24999
$82$	5.71570	0.631193
$83$	−15.0546	−1.65246	−0.826230	−	0.563333i	$-0.809519\pi$
$83$	−15.0546	−1.65246	−0.826230	+	0.563333i	$0.809519\pi$
$84$	−1.47702	−0.161156
$85$	−5.27112	−0.571733
$86$	9.47673	1.02190
$87$	−0.0399616	−0.00428433
$88$	−1.00000	−0.106600
$89$	5.90025	0.625425	0.312713	−	0.949848i	$-0.398762\pi$
$89$	5.90025	0.625425	0.312713	+	0.949848i	$0.398762\pi$
$90$	4.26653	0.449732
$91$	−2.28789	−0.239837
$92$	−3.01915	−0.314768
$93$	−4.89949	−0.508053
$94$	−0.815428	−0.0841050
$95$	11.4066	1.17030
$96$	−2.11945	−0.216315
$97$	12.3474	1.25369	0.626845	−	0.779144i	$-0.284346\pi$
$97$	12.3474	1.25369	0.626845	+	0.779144i	$0.284346\pi$
$98$	−6.51434	−0.658048
$99$	−1.49205	−0.149957
$100$	3.17676	0.317676
$101$	−18.6360	−1.85435	−0.927176	−	0.374626i	$-0.877771\pi$
$101$	−18.6360	−1.85435	−0.927176	+	0.374626i	$0.877771\pi$
$102$	3.90692	0.386842
$103$	−11.6671	−1.14959	−0.574797	−	0.818296i	$-0.694919\pi$
$103$	−11.6671	−1.14959	−0.574797	+	0.818296i	$0.694919\pi$
$104$	−3.28300	−0.321925
$105$	−4.22355	−0.412176
$106$	1.95048	0.189447
$107$	1.28478	0.124205	0.0621024	−	0.998070i	$-0.480219\pi$
$107$	1.28478	0.124205	0.0621024	+	0.998070i	$0.480219\pi$
$108$	3.19601	0.307537
$109$	−1.49616	−0.143306	−0.0716529	−	0.997430i	$-0.522827\pi$
$109$	−1.49616	−0.143306	−0.0716529	+	0.997430i	$0.522827\pi$
$110$	−2.85950	−0.272643
$111$	−7.81782	−0.742035
$112$	0.696891	0.0658500
$113$	20.0301	1.88428	0.942139	−	0.335223i	$-0.108812\pi$
$113$	20.0301	1.88428	0.942139	+	0.335223i	$0.108812\pi$
$114$	−8.45452	−0.791838
$115$	−8.63326	−0.805055
$116$	0.0188547	0.00175062
$117$	−4.89842	−0.452859
$118$	14.7141	1.35454
$119$	−1.28463	−0.117761
$120$	−6.06056	−0.553251
$121$	1.00000	0.0909091
$122$	7.02764	0.636253
$123$	−12.1141	−1.09229
$124$	2.31168	0.207595
$125$	−5.21355	−0.466315
$126$	1.03980	0.0926325
$127$	0.673966	0.0598048	0.0299024	−	0.999553i	$-0.490480\pi$
$127$	0.673966	0.0598048	0.0299024	+	0.999553i	$0.490480\pi$
$128$	1.00000	0.0883883
$129$	−20.0854	−1.76842
$130$	−9.38776	−0.823361
$131$	−5.72523	−0.500215	−0.250108	−	0.968218i	$-0.580466\pi$
$131$	−5.72523	−0.500215	−0.250108	+	0.968218i	$0.580466\pi$
$132$	2.11945	0.184474
$133$	2.77991	0.241049
$134$	−6.04045	−0.521816
$135$	9.13901	0.786561
$136$	−1.84337	−0.158067
$137$	−9.98359	−0.852955	−0.426478	−	0.904498i	$-0.640246\pi$
$137$	−9.98359	−0.852955	−0.426478	+	0.904498i	$0.640246\pi$
$138$	6.39892	0.544712
$139$	5.61682	0.476412	0.238206	−	0.971215i	$-0.423441\pi$
$139$	5.61682	0.476412	0.238206	+	0.971215i	$0.423441\pi$
$140$	1.99276	0.168419
$141$	1.72826	0.145545
$142$	9.69861	0.813890
$143$	3.28300	0.274539
$144$	1.49205	0.124338
$145$	0.0539151	0.00447741
$146$	8.67541	0.717982
$147$	13.8068	1.13877
$148$	3.68861	0.303202
$149$	−1.80652	−0.147996	−0.0739979	−	0.997258i	$-0.523576\pi$
$149$	−1.80652	−0.147996	−0.0739979	+	0.997258i	$0.523576\pi$
$150$	−6.73298	−0.549745
$151$	22.3246	1.81675	0.908375	−	0.418157i	$-0.137324\pi$
$151$	22.3246	1.81675	0.908375	+	0.418157i	$0.137324\pi$
$152$	3.98902	0.323553
$153$	−2.75040	−0.222357
$154$	−0.696891	−0.0561570
$155$	6.61026	0.530949
$156$	6.95815	0.557098
$157$	−20.5096	−1.63684	−0.818422	−	0.574617i	$-0.805151\pi$
$157$	−20.5096	−1.63684	−0.818422	+	0.574617i	$0.805151\pi$
$158$	12.3385	0.981597
$159$	−4.13393	−0.327842
$160$	2.85950	0.226064
$161$	−2.10401	−0.165820
$162$	−11.2499	−0.883879
$163$	22.0244	1.72509	0.862543	−	0.505984i	$-0.168870\pi$
$163$	22.0244	1.72509	0.862543	+	0.505984i	$0.168870\pi$
$164$	5.71570	0.446321
$165$	6.06056	0.471814
$166$	−15.0546	−1.16847
$167$	13.3006	1.02923	0.514614	−	0.857422i	$-0.327935\pi$
$167$	13.3006	1.02923	0.514614	+	0.857422i	$0.327935\pi$
$168$	−1.47702	−0.113955
$169$	−2.22188	−0.170914
$170$	−5.27112	−0.404276
$171$	5.95183	0.455148
$172$	9.47673	0.722594
$173$	−12.9457	−0.984245	−0.492123	−	0.870526i	$-0.663779\pi$
$173$	−12.9457	−0.984245	−0.492123	+	0.870526i	$0.663779\pi$
$174$	−0.0399616	−0.00302948
$175$	2.21386	0.167352
$176$	−1.00000	−0.0753778
$177$	−31.1858	−2.34407
$178$	5.90025	0.442242
$179$	−2.71932	−0.203251	−0.101626	−	0.994823i	$-0.532404\pi$
$179$	−2.71932	−0.203251	−0.101626	+	0.994823i	$0.532404\pi$
$180$	4.26653	0.318008
$181$	−1.57227	−0.116866	−0.0584328	−	0.998291i	$-0.518610\pi$
$181$	−1.57227	−0.116866	−0.0584328	+	0.998291i	$0.518610\pi$
$182$	−2.28789	−0.169590
$183$	−14.8947	−1.10105
$184$	−3.01915	−0.222574
$185$	10.5476	0.775475
$186$	−4.89949	−0.359248
$187$	1.84337	0.134800
$188$	−0.815428	−0.0594712
$189$	2.22727	0.162010
$190$	11.4066	0.827524
$191$	−3.37991	−0.244562	−0.122281	−	0.992496i	$-0.539021\pi$
$191$	−3.37991	−0.244562	−0.122281	+	0.992496i	$0.539021\pi$
$192$	−2.11945	−0.152958
$193$	7.05203	0.507616	0.253808	−	0.967255i	$-0.418317\pi$
$193$	7.05203	0.507616	0.253808	+	0.967255i	$0.418317\pi$
$194$	12.3474	0.886493
$195$	19.8969	1.42484
$196$	−6.51434	−0.465310
$197$	−1.00000	−0.0712470
$197$	−1.00000	−0.0712470
$198$	−1.49205	−0.106036
$199$	23.1775	1.64301	0.821505	−	0.570201i	$-0.193135\pi$
$199$	23.1775	1.64301	0.821505	+	0.570201i	$0.193135\pi$
$200$	3.17676	0.224631
$201$	12.8024	0.903013
$202$	−18.6360	−1.31123
$203$	0.0131397	0.000922224 0
$204$	3.90692	0.273539
$205$	16.3441	1.14152
$206$	−11.6671	−0.812885
$207$	−4.50472	−0.313100
$208$	−3.28300	−0.227635
$209$	−3.98902	−0.275927
$210$	−4.22355	−0.291453
$211$	−5.45720	−0.375689	−0.187845	−	0.982199i	$-0.560150\pi$
$211$	−5.45720	−0.375689	−0.187845	+	0.982199i	$0.560150\pi$
$212$	1.95048	0.133959
$213$	−20.5557	−1.40845
$214$	1.28478	0.0878261
$215$	27.0988	1.84812
$216$	3.19601	0.217461
$217$	1.61099	0.109361
$218$	−1.49616	−0.101332
$219$	−18.3871	−1.24248
$220$	−2.85950	−0.192788
$221$	6.05178	0.407087
$222$	−7.81782	−0.524698
$223$	−22.5631	−1.51094	−0.755468	−	0.655185i	$-0.772591\pi$
$223$	−22.5631	−1.51094	−0.755468	+	0.655185i	$0.772591\pi$
$224$	0.696891	0.0465630
$225$	4.73990	0.315993
$226$	20.0301	1.33239
$227$	1.89051	0.125478	0.0627388	−	0.998030i	$-0.480016\pi$
$227$	1.89051	0.125478	0.0627388	+	0.998030i	$0.480016\pi$
$228$	−8.45452	−0.559914
$229$	15.6099	1.03153	0.515766	−	0.856729i	$-0.327507\pi$
$229$	15.6099	1.03153	0.515766	+	0.856729i	$0.327507\pi$
$230$	−8.63326	−0.569260
$231$	1.47702	0.0971809
$232$	0.0188547	0.00123787
$233$	−13.2587	−0.868604	−0.434302	−	0.900767i	$-0.643005\pi$
$233$	−13.2587	−0.868604	−0.434302	+	0.900767i	$0.643005\pi$
$234$	−4.89842	−0.320219
$235$	−2.33172	−0.152105
$236$	14.7141	0.957808
$237$	−26.1507	−1.69867
$238$	−1.28463	−0.0832699
$239$	20.7913	1.34488	0.672438	−	0.740153i	$-0.265247\pi$
$239$	20.7913	1.34488	0.672438	+	0.740153i	$0.265247\pi$
$240$	−6.06056	−0.391208
$241$	4.50420	0.290141	0.145070	−	0.989421i	$-0.453659\pi$
$241$	4.50420	0.290141	0.145070	+	0.989421i	$0.453659\pi$
$242$	1.00000	0.0642824
$243$	14.2556	0.914497
$244$	7.02764	0.449899
$245$	−18.6278	−1.19009
$246$	−12.1141	−0.772368
$247$	−13.0960	−0.833277
$248$	2.31168	0.146792
$249$	31.9075	2.02205
$250$	−5.21355	−0.329734
$251$	17.4989	1.10452	0.552260	−	0.833672i	$-0.313766\pi$
$251$	17.4989	1.10452	0.552260	+	0.833672i	$0.313766\pi$
$252$	1.03980	0.0655011
$253$	3.01915	0.189812
$254$	0.673966	0.0422884
$255$	11.1718	0.699608
$256$	1.00000	0.0625000
$257$	−9.08449	−0.566675	−0.283338	−	0.959020i	$-0.591442\pi$
$257$	−9.08449	−0.566675	−0.283338	+	0.959020i	$0.591442\pi$
$258$	−20.0854	−1.25046
$259$	2.57056	0.159727
$260$	−9.38776	−0.582204
$261$	0.0281322	0.00174134
$262$	−5.72523	−0.353706
$263$	9.15278	0.564384	0.282192	−	0.959358i	$-0.408938\pi$
$263$	9.15278	0.564384	0.282192	+	0.959358i	$0.408938\pi$
$264$	2.11945	0.130443
$265$	5.57740	0.342617
$266$	2.77991	0.170447
$267$	−12.5053	−0.765309
$268$	−6.04045	−0.368979
$269$	21.0704	1.28469	0.642343	−	0.766417i	$-0.277962\pi$
$269$	21.0704	1.28469	0.642343	+	0.766417i	$0.277962\pi$
$270$	9.13901	0.556183
$271$	10.0256	0.609012	0.304506	−	0.952510i	$-0.401509\pi$
$271$	10.0256	0.609012	0.304506	+	0.952510i	$0.401509\pi$
$272$	−1.84337	−0.111771
$273$	4.84907	0.293479
$274$	−9.98359	−0.603131
$275$	−3.17676	−0.191566
$276$	6.39892	0.385169
$277$	−1.19677	−0.0719070	−0.0359535	−	0.999353i	$-0.511447\pi$
$277$	−1.19677	−0.0719070	−0.0359535	+	0.999353i	$0.511447\pi$
$278$	5.61682	0.336874
$279$	3.44915	0.206495
$280$	1.99276	0.119090
$281$	−30.9835	−1.84832	−0.924162	−	0.382002i	$-0.875235\pi$
$281$	−30.9835	−1.84832	−0.924162	+	0.382002i	$0.875235\pi$
$282$	1.72826	0.102916
$283$	9.68164	0.575514	0.287757	−	0.957703i	$-0.407090\pi$
$283$	9.68164	0.575514	0.287757	+	0.957703i	$0.407090\pi$
$284$	9.69861	0.575507
$285$	−24.1757	−1.43205
$286$	3.28300	0.194128
$287$	3.98322	0.235122
$288$	1.49205	0.0879200
$289$	−13.6020	−0.800118
$290$	0.0539151	0.00316601
$291$	−26.1697	−1.53410
$292$	8.67541	0.507690
$293$	27.2111	1.58969	0.794845	−	0.606813i	$-0.207552\pi$
$293$	27.2111	1.58969	0.794845	+	0.606813i	$0.207552\pi$
$294$	13.8068	0.805229
$295$	42.0751	2.44971
$296$	3.68861	0.214396
$297$	−3.19601	−0.185452
$298$	−1.80652	−0.104649
$299$	9.91187	0.573218
$300$	−6.73298	−0.388729
$301$	6.60425	0.380662
$302$	22.3246	1.28464
$303$	39.4980	2.26910
$304$	3.98902	0.228786
$305$	20.0956	1.15067
$306$	−2.75040	−0.157230
$307$	7.72030	0.440621	0.220310	−	0.975430i	$-0.429293\pi$
$307$	7.72030	0.440621	0.220310	+	0.975430i	$0.429293\pi$
$308$	−0.696891	−0.0397090
$309$	24.7278	1.40671
$310$	6.61026	0.375438
$311$	21.9781	1.24627	0.623133	−	0.782116i	$-0.285860\pi$
$311$	21.9781	1.24627	0.623133	+	0.782116i	$0.285860\pi$
$312$	6.95815	0.393928
$313$	−9.34309	−0.528102	−0.264051	−	0.964509i	$-0.585059\pi$
$313$	−9.34309	−0.528102	−0.264051	+	0.964509i	$0.585059\pi$
$314$	−20.5096	−1.15742
$315$	2.97330	0.167527
$316$	12.3385	0.694094
$317$	33.5325	1.88337	0.941687	−	0.336491i	$-0.109240\pi$
$317$	33.5325	1.88337	0.941687	+	0.336491i	$0.109240\pi$
$318$	−4.13393	−0.231819
$319$	−0.0188547	−0.00105566
$320$	2.85950	0.159851
$321$	−2.72303	−0.151985
$322$	−2.10401	−0.117252
$323$	−7.35323	−0.409145
$324$	−11.2499	−0.624996
$325$	−10.4293	−0.578515
$326$	22.0244	1.21982
$327$	3.17102	0.175358
$328$	5.71570	0.315597
$329$	−0.568264	−0.0313294
$330$	6.06056	0.333623
$331$	6.24912	0.343483	0.171741	−	0.985142i	$-0.445061\pi$
$331$	6.24912	0.343483	0.171741	+	0.985142i	$0.445061\pi$
$332$	−15.0546	−0.826230
$333$	5.50361	0.301596
$334$	13.3006	0.727775
$335$	−17.2727	−0.943709
$336$	−1.47702	−0.0805782
$337$	1.69874	0.0925362	0.0462681	−	0.998929i	$-0.485267\pi$
$337$	1.69874	0.0925362	0.0462681	+	0.998929i	$0.485267\pi$
$338$	−2.22188	−0.120854
$339$	−42.4528	−2.30572
$340$	−5.27112	−0.285866
$341$	−2.31168	−0.125185
$342$	5.95183	0.321838
$343$	−9.41802	−0.508525
$344$	9.47673	0.510951
$345$	18.2977	0.985116
$346$	−12.9457	−0.695967
$347$	−5.85178	−0.314140	−0.157070	−	0.987587i	$-0.550205\pi$
$347$	−5.85178	−0.314140	−0.157070	+	0.987587i	$0.550205\pi$
$348$	−0.0399616	−0.00214216
$349$	−33.7148	−1.80471	−0.902356	−	0.430992i	$-0.858164\pi$
$349$	−33.7148	−1.80471	−0.902356	+	0.430992i	$0.858164\pi$
$350$	2.21386	0.118336
$351$	−10.4925	−0.560050
$352$	−1.00000	−0.0533002
$353$	34.5134	1.83696	0.918482	−	0.395462i	$-0.129416\pi$
$353$	34.5134	1.83696	0.918482	+	0.395462i	$0.129416\pi$
$354$	−31.1858	−1.65751
$355$	27.7332	1.47193
$356$	5.90025	0.312713
$357$	2.72269	0.144100
$358$	−2.71932	−0.143720
$359$	−23.4232	−1.23623	−0.618114	−	0.786088i	$-0.712103\pi$
$359$	−23.4232	−1.23623	−0.618114	+	0.786088i	$0.712103\pi$
$360$	4.26653	0.224866
$361$	−3.08769	−0.162510
$362$	−1.57227	−0.0826365
$363$	−2.11945	−0.111242
$364$	−2.28789	−0.119918
$365$	24.8074	1.29848
$366$	−14.8947	−0.778559
$367$	20.7740	1.08439	0.542197	−	0.840251i	$-0.317593\pi$
$367$	20.7740	1.08439	0.542197	+	0.840251i	$0.317593\pi$
$368$	−3.01915	−0.157384
$369$	8.52812	0.443956
$370$	10.5476	0.548344
$371$	1.35927	0.0705697
$372$	−4.89949	−0.254026
$373$	1.78509	0.0924283	0.0462142	−	0.998932i	$-0.485284\pi$
$373$	1.78509	0.0924283	0.0462142	+	0.998932i	$0.485284\pi$
$374$	1.84337	0.0953182
$375$	11.0498	0.570612
$376$	−0.815428	−0.0420525
$377$	−0.0619001	−0.00318802
$378$	2.22727	0.114558
$379$	−25.5578	−1.31282	−0.656409	−	0.754405i	$-0.727925\pi$
$379$	−25.5578	−1.31282	−0.656409	+	0.754405i	$0.727925\pi$
$380$	11.4066	0.585148
$381$	−1.42844	−0.0731810
$382$	−3.37991	−0.172931
$383$	−33.4195	−1.70766	−0.853829	−	0.520553i	$-0.825726\pi$
$383$	−33.4195	−1.70766	−0.853829	+	0.520553i	$0.825726\pi$
$384$	−2.11945	−0.108158
$385$	−1.99276	−0.101561
$386$	7.05203	0.358939
$387$	14.1398	0.718766
$388$	12.3474	0.626845
$389$	26.9646	1.36716	0.683578	−	0.729877i	$-0.260423\pi$
$389$	26.9646	1.36716	0.683578	+	0.729877i	$0.260423\pi$
$390$	19.8969	1.00752
$391$	5.56539	0.281454
$392$	−6.51434	−0.329024
$393$	12.1343	0.612095
$394$	−1.00000	−0.0503793
$395$	35.2819	1.77523
$396$	−1.49205	−0.0749785
$397$	−9.76865	−0.490275	−0.245137	−	0.969488i	$-0.578833\pi$
$397$	−9.76865	−0.490275	−0.245137	+	0.969488i	$0.578833\pi$
$398$	23.1775	1.16178
$399$	−5.89188	−0.294963
$400$	3.17676	0.158838
$401$	−29.1348	−1.45492	−0.727462	−	0.686148i	$-0.759300\pi$
$401$	−29.1348	−1.45492	−0.727462	+	0.686148i	$0.759300\pi$
$402$	12.8024	0.638527
$403$	−7.58926	−0.378048
$404$	−18.6360	−0.927176
$405$	−32.1692	−1.59850
$406$	0.0131397	0.000652111 0
$407$	−3.68861	−0.182838
$408$	3.90692	0.193421
$409$	1.34435	0.0664740	0.0332370	−	0.999447i	$-0.489418\pi$
$409$	1.34435	0.0664740	0.0332370	+	0.999447i	$0.489418\pi$
$410$	16.3441	0.807176
$411$	21.1597	1.04373
$412$	−11.6671	−0.574797
$413$	10.2541	0.504573
$414$	−4.50472	−0.221395
$415$	−43.0488	−2.11318
$416$	−3.28300	−0.160963
$417$	−11.9045	−0.582968
$418$	−3.98902	−0.195110
$419$	−26.8336	−1.31091	−0.655454	−	0.755235i	$-0.727523\pi$
$419$	−26.8336	−1.31091	−0.655454	+	0.755235i	$0.727523\pi$
$420$	−4.22355	−0.206088
$421$	−36.7760	−1.79235	−0.896176	−	0.443699i	$-0.853666\pi$
$421$	−36.7760	−1.79235	−0.896176	+	0.443699i	$0.853666\pi$
$422$	−5.45720	−0.265653
$423$	−1.21666	−0.0591561
$424$	1.95048	0.0947236
$425$	−5.85594	−0.284055
$426$	−20.5557	−0.995926
$427$	4.89750	0.237006
$428$	1.28478	0.0621024
$429$	−6.95815	−0.335943
$430$	27.0988	1.30682
$431$	38.1694	1.83855	0.919277	−	0.393610i	$-0.128774\pi$
$431$	38.1694	1.83855	0.919277	+	0.393610i	$0.128774\pi$
$432$	3.19601	0.153768
$433$	−23.9944	−1.15310	−0.576549	−	0.817063i	$-0.695601\pi$
$433$	−23.9944	−1.15310	−0.576549	+	0.817063i	$0.695601\pi$
$434$	1.61099	0.0773300
$435$	−0.114270	−0.00547884
$436$	−1.49616	−0.0716529
$437$	−12.0434	−0.576116
$438$	−18.3871	−0.878567
$439$	13.9468	0.665646	0.332823	−	0.942989i	$-0.391999\pi$
$439$	13.9468	0.665646	0.332823	+	0.942989i	$0.391999\pi$
$440$	−2.85950	−0.136321
$441$	−9.71974	−0.462845
$442$	6.05178	0.287854
$443$	−7.84346	−0.372654	−0.186327	−	0.982488i	$-0.559658\pi$
$443$	−7.84346	−0.372654	−0.186327	+	0.982488i	$0.559658\pi$
$444$	−7.81782	−0.371017
$445$	16.8718	0.799799
$446$	−22.5631	−1.06839
$447$	3.82882	0.181097
$448$	0.696891	0.0329250
$449$	−41.7427	−1.96996	−0.984980	−	0.172667i	$-0.944762\pi$
$449$	−41.7427	−1.96996	−0.984980	+	0.172667i	$0.944762\pi$
$450$	4.73990	0.223441
$451$	−5.71570	−0.269142
$452$	20.0301	0.942139
$453$	−47.3158	−2.22309
$454$	1.89051	0.0887261
$455$	−6.54224	−0.306705
$456$	−8.45452	−0.395919
$457$	−24.4603	−1.14420	−0.572102	−	0.820182i	$-0.693872\pi$
$457$	−24.4603	−1.14420	−0.572102	+	0.820182i	$0.693872\pi$
$458$	15.6099	0.729403
$459$	−5.89143	−0.274988
$460$	−8.63326	−0.402528
$461$	−5.46962	−0.254745	−0.127373	−	0.991855i	$-0.540654\pi$
$461$	−5.46962	−0.254745	−0.127373	+	0.991855i	$0.540654\pi$
$462$	1.47702	0.0687173
$463$	34.9202	1.62288	0.811439	−	0.584438i	$-0.198685\pi$
$463$	34.9202	1.62288	0.811439	+	0.584438i	$0.198685\pi$
$464$	0.0188547	0.000875308 0
$465$	−14.0101	−0.649703
$466$	−13.2587	−0.614196
$467$	−22.3476	−1.03412	−0.517062	−	0.855948i	$-0.672974\pi$
$467$	−22.3476	−1.03412	−0.517062	+	0.855948i	$0.672974\pi$
$468$	−4.89842	−0.226429
$469$	−4.20954	−0.194378
$470$	−2.33172	−0.107554
$471$	43.4690	2.00295
$472$	14.7141	0.677272
$473$	−9.47673	−0.435741
$474$	−26.1507	−1.20114
$475$	12.6722	0.581439
$476$	−1.28463	−0.0588807
$477$	2.91021	0.133250
$478$	20.7913	0.950971
$479$	26.9630	1.23197	0.615986	−	0.787757i	$-0.288758\pi$
$479$	26.9630	1.23197	0.615986	+	0.787757i	$0.288758\pi$
$480$	−6.06056	−0.276626
$481$	−12.1097	−0.552156
$482$	4.50420	0.205161
$483$	4.45934	0.202907
$484$	1.00000	0.0454545
$485$	35.3075	1.60323
$486$	14.2556	0.646647
$487$	−34.6071	−1.56820	−0.784099	−	0.620636i	$-0.786875\pi$
$487$	−34.6071	−1.56820	−0.784099	+	0.620636i	$0.786875\pi$
$488$	7.02764	0.318126
$489$	−46.6796	−2.11092
$490$	−18.6278	−0.841518
$491$	10.4465	0.471443	0.235722	−	0.971821i	$-0.424255\pi$
$491$	10.4465	0.471443	0.235722	+	0.971821i	$0.424255\pi$
$492$	−12.1141	−0.546146
$493$	−0.0347562	−0.00156534
$494$	−13.0960	−0.589216
$495$	−4.26653	−0.191766
$496$	2.31168	0.103798
$497$	6.75887	0.303177
$498$	31.9075	1.42981
$499$	7.96147	0.356404	0.178202	−	0.983994i	$-0.442972\pi$
$499$	7.96147	0.356404	0.178202	+	0.983994i	$0.442972\pi$
$500$	−5.21355	−0.233157
$501$	−28.1898	−1.25943
$502$	17.4989	0.781013
$503$	0.557963	0.0248783	0.0124392	−	0.999923i	$-0.496040\pi$
$503$	0.557963	0.0248783	0.0124392	+	0.999923i	$0.496040\pi$
$504$	1.03980	0.0463163
$505$	−53.2897	−2.37136
$506$	3.01915	0.134217
$507$	4.70916	0.209141
$508$	0.673966	0.0299024
$509$	5.03770	0.223292	0.111646	−	0.993748i	$-0.464388\pi$
$509$	5.03770	0.223292	0.111646	+	0.993748i	$0.464388\pi$
$510$	11.1718	0.494698
$511$	6.04581	0.267451
$512$	1.00000	0.0441942
$513$	12.7490	0.562881
$514$	−9.08449	−0.400700
$515$	−33.3621	−1.47011
$516$	−20.0854	−0.884212
$517$	0.815428	0.0358625
$518$	2.57056	0.112944
$519$	27.4378	1.20438
$520$	−9.38776	−0.411681
$521$	25.5338	1.11866	0.559329	−	0.828946i	$-0.311059\pi$
$521$	25.5338	1.11866	0.559329	+	0.828946i	$0.311059\pi$
$522$	0.0281322	0.00123131
$523$	20.0017	0.874615	0.437308	−	0.899312i	$-0.355932\pi$
$523$	20.0017	0.874615	0.437308	+	0.899312i	$0.355932\pi$
$524$	−5.72523	−0.250108
$525$	−4.69215	−0.204782
$526$	9.15278	0.399080
$527$	−4.26128	−0.185624
$528$	2.11945	0.0922371
$529$	−13.8848	−0.603685
$530$	5.57740	0.242267
$531$	21.9542	0.952733
$532$	2.77991	0.120524
$533$	−18.7647	−0.812788
$534$	−12.5053	−0.541155
$535$	3.67385	0.158834
$536$	−6.04045	−0.260908
$537$	5.76345	0.248711
$538$	21.0704	0.908410
$539$	6.51434	0.280593
$540$	9.13901	0.393281
$541$	−28.2196	−1.21325	−0.606627	−	0.794987i	$-0.707478\pi$
$541$	−28.2196	−1.21325	−0.606627	+	0.794987i	$0.707478\pi$
$542$	10.0256	0.430637
$543$	3.33233	0.143004
$544$	−1.84337	−0.0790337
$545$	−4.27826	−0.183261
$546$	4.84907	0.207521
$547$	−7.19494	−0.307634	−0.153817	−	0.988099i	$-0.549157\pi$
$547$	−7.19494	−0.307634	−0.153817	+	0.988099i	$0.549157\pi$
$548$	−9.98359	−0.426478
$549$	10.4856	0.447515
$550$	−3.17676	−0.135458
$551$	0.0752119	0.00320413
$552$	6.39892	0.272356
$553$	8.59857	0.365648
$554$	−1.19677	−0.0508459
$555$	−22.3551	−0.948920
$556$	5.61682	0.238206
$557$	−0.270435	−0.0114587	−0.00572935	−	0.999984i	$-0.501824\pi$
$557$	−0.270435	−0.0114587	−0.00572935	+	0.999984i	$0.501824\pi$
$558$	3.44915	0.146014
$559$	−31.1122	−1.31590
$560$	1.99276	0.0842095
$561$	−3.90692	−0.164950
$562$	−30.9835	−1.30696
$563$	7.34403	0.309514	0.154757	−	0.987953i	$-0.450541\pi$
$563$	7.34403	0.309514	0.154757	+	0.987953i	$0.450541\pi$
$564$	1.72826	0.0727727
$565$	57.2763	2.40963
$566$	9.68164	0.406950
$567$	−7.83997	−0.329248
$568$	9.69861	0.406945
$569$	3.61091	0.151377	0.0756885	−	0.997132i	$-0.475885\pi$
$569$	3.61091	0.151377	0.0756885	+	0.997132i	$0.475885\pi$
$570$	−24.1757	−1.01261
$571$	−3.28431	−0.137444	−0.0687221	−	0.997636i	$-0.521892\pi$
$571$	−3.28431	−0.137444	−0.0687221	+	0.997636i	$0.521892\pi$
$572$	3.28300	0.137269
$573$	7.16354	0.299261
$574$	3.98322	0.166256
$575$	−9.59111	−0.399977
$576$	1.49205	0.0621689
$577$	−4.18156	−0.174081	−0.0870403	−	0.996205i	$-0.527741\pi$
$577$	−4.18156	−0.174081	−0.0870403	+	0.996205i	$0.527741\pi$
$578$	−13.6020	−0.565769
$579$	−14.9464	−0.621151
$580$	0.0539151	0.00223870
$581$	−10.4914	−0.435258
$582$	−26.1697	−1.08477
$583$	−1.95048	−0.0807805
$584$	8.67541	0.358991
$585$	−14.0070	−0.579120
$586$	27.2111	1.12408
$587$	−10.3004	−0.425142	−0.212571	−	0.977146i	$-0.568184\pi$
$587$	−10.3004	−0.425142	−0.212571	+	0.977146i	$0.568184\pi$
$588$	13.8068	0.569383
$589$	9.22135	0.379959
$590$	42.0751	1.73220
$591$	2.11945	0.0871824
$592$	3.68861	0.151601
$593$	−20.3651	−0.836295	−0.418147	−	0.908379i	$-0.637320\pi$
$593$	−20.3651	−0.836295	−0.418147	+	0.908379i	$0.637320\pi$
$594$	−3.19601	−0.131134
$595$	−3.67339	−0.150594
$596$	−1.80652	−0.0739979
$597$	−49.1235	−2.01049
$598$	9.91187	0.405326
$599$	−15.1635	−0.619563	−0.309781	−	0.950808i	$-0.600256\pi$
$599$	−15.1635	−0.619563	−0.309781	+	0.950808i	$0.600256\pi$
$600$	−6.73298	−0.274873
$601$	7.72403	0.315070	0.157535	−	0.987513i	$-0.449645\pi$
$601$	7.72403	0.315070	0.157535	+	0.987513i	$0.449645\pi$
$602$	6.60425	0.269169
$603$	−9.01268	−0.367025
$604$	22.3246	0.908375
$605$	2.85950	0.116255
$606$	39.4980	1.60450
$607$	−45.1886	−1.83415	−0.917074	−	0.398718i	$-0.869455\pi$
$607$	−45.1886	−1.83415	−0.917074	+	0.398718i	$0.869455\pi$
$608$	3.98902	0.161776
$609$	−0.0278488	−0.00112849
$610$	20.0956	0.813646
$611$	2.67706	0.108302
$612$	−2.75040	−0.111178
$613$	24.8512	1.00373	0.501865	−	0.864946i	$-0.332647\pi$
$613$	24.8512	1.00373	0.501865	+	0.864946i	$0.332647\pi$
$614$	7.72030	0.311566
$615$	−34.6404	−1.39683
$616$	−0.696891	−0.0280785
$617$	−7.70144	−0.310048	−0.155024	−	0.987911i	$-0.549546\pi$
$617$	−7.70144	−0.310048	−0.155024	+	0.987911i	$0.549546\pi$
$618$	24.7278	0.994697
$619$	−13.5653	−0.545236	−0.272618	−	0.962122i	$-0.587890\pi$
$619$	−13.5653	−0.545236	−0.272618	+	0.962122i	$0.587890\pi$
$620$	6.61026	0.265475
$621$	−9.64923	−0.387210
$622$	21.9781	0.881243
$623$	4.11183	0.164737
$624$	6.95815	0.278549
$625$	−30.7920	−1.23168
$626$	−9.34309	−0.373425
$627$	8.45452	0.337641
$628$	−20.5096	−0.818422
$629$	−6.79947	−0.271113
$630$	2.97330	0.118459
$631$	31.6399	1.25956	0.629781	−	0.776772i	$-0.283144\pi$
$631$	31.6399	1.25956	0.629781	+	0.776772i	$0.283144\pi$
$632$	12.3385	0.490798
$633$	11.5663	0.459717
$634$	33.5325	1.33175
$635$	1.92721	0.0764790
$636$	−4.13393	−0.163921
$637$	21.3866	0.847369
$638$	−0.0188547	−0.000746465 0
$639$	14.4708	0.572458
$640$	2.85950	0.113032
$641$	−29.4236	−1.16216	−0.581081	−	0.813846i	$-0.697370\pi$
$641$	−29.4236	−1.16216	−0.581081	+	0.813846i	$0.697370\pi$
$642$	−2.72303	−0.107469
$643$	17.0190	0.671164	0.335582	−	0.942011i	$-0.391067\pi$
$643$	17.0190	0.671164	0.335582	+	0.942011i	$0.391067\pi$
$644$	−2.10401	−0.0829098
$645$	−57.4344	−2.26148
$646$	−7.35323	−0.289309
$647$	−40.8129	−1.60452	−0.802260	−	0.596975i	$-0.796369\pi$
$647$	−40.8129	−1.60452	−0.802260	+	0.596975i	$0.796369\pi$
$648$	−11.2499	−0.441939
$649$	−14.7141	−0.577580
$650$	−10.4293	−0.409072
$651$	−3.41441	−0.133821
$652$	22.0244	0.862543
$653$	26.5204	1.03782	0.518912	−	0.854828i	$-0.326337\pi$
$653$	26.5204	1.03782	0.518912	+	0.854828i	$0.326337\pi$
$654$	3.17102	0.123997
$655$	−16.3713	−0.639680
$656$	5.71570	0.223160
$657$	12.9442	0.505000
$658$	−0.568264	−0.0221532
$659$	35.7056	1.39089	0.695446	−	0.718578i	$-0.255207\pi$
$659$	35.7056	1.39089	0.695446	+	0.718578i	$0.255207\pi$
$660$	6.06056	0.235907
$661$	20.1312	0.783013	0.391506	−	0.920175i	$-0.371954\pi$
$661$	20.1312	0.783013	0.391506	+	0.920175i	$0.371954\pi$
$662$	6.24912	0.242879
$663$	−12.8264	−0.498137
$664$	−15.0546	−0.584233
$665$	7.94917	0.308256
$666$	5.50361	0.213260
$667$	−0.0569251	−0.00220415
$668$	13.3006	0.514614
$669$	47.8213	1.84888
$670$	−17.2727	−0.667303
$671$	−7.02764	−0.271299
$672$	−1.47702	−0.0569774
$673$	−7.24357	−0.279219	−0.139610	−	0.990207i	$-0.544585\pi$
$673$	−7.24357	−0.279219	−0.139610	+	0.990207i	$0.544585\pi$
$674$	1.69874	0.0654330
$675$	10.1530	0.390788
$676$	−2.22188	−0.0854570
$677$	−49.7032	−1.91025	−0.955125	−	0.296203i	$-0.904280\pi$
$677$	−49.7032	−1.91025	−0.955125	+	0.296203i	$0.904280\pi$
$678$	−42.4528	−1.63039
$679$	8.60480	0.330222
$680$	−5.27112	−0.202138
$681$	−4.00684	−0.153542
$682$	−2.31168	−0.0885189
$683$	−7.71699	−0.295282	−0.147641	−	0.989041i	$-0.547168\pi$
$683$	−7.71699	−0.295282	−0.147641	+	0.989041i	$0.547168\pi$
$684$	5.95183	0.227574
$685$	−28.5481	−1.09077
$686$	−9.41802	−0.359582
$687$	−33.0844	−1.26225
$688$	9.47673	0.361297
$689$	−6.40343	−0.243951
$690$	18.2977	0.696582
$691$	35.6382	1.35574	0.677871	−	0.735180i	$-0.262903\pi$
$691$	35.6382	1.35574	0.677871	+	0.735180i	$0.262903\pi$
$692$	−12.9457	−0.492123
$693$	−1.03980	−0.0394986
$694$	−5.85178	−0.222131
$695$	16.0613	0.609240
$696$	−0.0399616	−0.00151474
$697$	−10.5361	−0.399084
$698$	−33.7148	−1.27612
$699$	28.1010	1.06288
$700$	2.21386	0.0836759
$701$	14.3114	0.540534	0.270267	−	0.962785i	$-0.412888\pi$
$701$	14.3114	0.540534	0.270267	+	0.962785i	$0.412888\pi$
$702$	−10.4925	−0.396015
$703$	14.7140	0.554948
$704$	−1.00000	−0.0376889
$705$	4.94196	0.186125
$706$	34.5134	1.29893
$707$	−12.9873	−0.488436
$708$	−31.1858	−1.17203
$709$	0.644313	0.0241977	0.0120988	−	0.999927i	$-0.496149\pi$
$709$	0.644313	0.0241977	0.0120988	+	0.999927i	$0.496149\pi$
$710$	27.7332	1.04081
$711$	18.4097	0.690416
$712$	5.90025	0.221121
$713$	−6.97930	−0.261377
$714$	2.72269	0.101894
$715$	9.38776	0.351082
$716$	−2.71932	−0.101626
$717$	−44.0660	−1.64568
$718$	−23.4232	−0.874146
$719$	−39.5113	−1.47352	−0.736762	−	0.676152i	$-0.763646\pi$
$719$	−39.5113	−1.47352	−0.736762	+	0.676152i	$0.763646\pi$
$720$	4.26653	0.159004
$721$	−8.13069	−0.302803
$722$	−3.08769	−0.114912
$723$	−9.54640	−0.355035
$724$	−1.57227	−0.0584328
$725$	0.0598970	0.00222452
$726$	−2.11945	−0.0786600
$727$	−47.3220	−1.75508	−0.877538	−	0.479506i	$-0.840816\pi$
$727$	−47.3220	−1.75508	−0.877538	+	0.479506i	$0.840816\pi$
$728$	−2.28789	−0.0847950
$729$	3.53584	0.130957
$730$	24.8074	0.918161
$731$	−17.4691	−0.646118
$732$	−14.8947	−0.550524
$733$	37.9841	1.40297	0.701487	−	0.712682i	$-0.252520\pi$
$733$	37.9841	1.40297	0.701487	+	0.712682i	$0.252520\pi$
$734$	20.7740	0.766783
$735$	39.4806	1.45626
$736$	−3.01915	−0.111287
$737$	6.04045	0.222503
$738$	8.52812	0.313924
$739$	19.3387	0.711387	0.355693	−	0.934603i	$-0.384245\pi$
$739$	19.3387	0.711387	0.355693	+	0.934603i	$0.384245\pi$
$740$	10.5476	0.387738
$741$	27.7562	1.01965
$742$	1.35927	0.0499003
$743$	−52.4985	−1.92598	−0.962992	−	0.269532i	$-0.913131\pi$
$743$	−52.4985	−1.92598	−0.962992	+	0.269532i	$0.913131\pi$
$744$	−4.89949	−0.179624
$745$	−5.16575	−0.189258
$746$	1.78509	0.0653567
$747$	−22.4623	−0.821852
$748$	1.84337	0.0674002
$749$	0.895354	0.0327155
$750$	11.0498	0.403483
$751$	−21.5401	−0.786010	−0.393005	−	0.919536i	$-0.628565\pi$
$751$	−21.5401	−0.786010	−0.393005	+	0.919536i	$0.628565\pi$
$752$	−0.815428	−0.0297356
$753$	−37.0879	−1.35156
$754$	−0.0619001	−0.00225427
$755$	63.8373	2.32328
$756$	2.22727	0.0810051
$757$	−12.0210	−0.436912	−0.218456	−	0.975847i	$-0.570102\pi$
$757$	−12.0210	−0.436912	−0.218456	+	0.975847i	$0.570102\pi$
$758$	−25.5578	−0.928303
$759$	−6.39892	−0.232266
$760$	11.4066	0.413762
$761$	38.3282	1.38940	0.694698	−	0.719302i	$-0.255538\pi$
$761$	38.3282	1.38940	0.694698	+	0.719302i	$0.255538\pi$
$762$	−1.42844	−0.0517467
$763$	−1.04266	−0.0377467
$764$	−3.37991	−0.122281
$765$	−7.86478	−0.284352
$766$	−33.4195	−1.20750
$767$	−48.3065	−1.74425
$768$	−2.11945	−0.0764789
$769$	−33.5753	−1.21076	−0.605378	−	0.795938i	$-0.706978\pi$
$769$	−33.5753	−1.21076	−0.605378	+	0.795938i	$0.706978\pi$
$770$	−1.99276	−0.0718141
$771$	19.2541	0.693419
$772$	7.05203	0.253808
$773$	32.9960	1.18678	0.593391	−	0.804914i	$-0.297789\pi$
$773$	32.9960	1.18678	0.593391	+	0.804914i	$0.297789\pi$
$774$	14.1398	0.508244
$775$	7.34366	0.263792
$776$	12.3474	0.443247
$777$	−5.44816	−0.195452
$778$	26.9646	0.966726
$779$	22.8001	0.816897
$780$	19.8969	0.712422
$781$	−9.69861	−0.347044
$782$	5.56539	0.199018
$783$	0.0602599	0.00215351
$784$	−6.51434	−0.232655
$785$	−58.6473	−2.09321
$786$	12.1343	0.432816
$787$	−36.2961	−1.29382	−0.646909	−	0.762567i	$-0.723939\pi$
$787$	−36.2961	−1.29382	−0.646909	+	0.762567i	$0.723939\pi$
$788$	−1.00000	−0.0356235
$789$	−19.3988	−0.690616
$790$	35.2819	1.25527
$791$	13.9588	0.496318
$792$	−1.49205	−0.0530178
$793$	−23.0718	−0.819303
$794$	−9.76865	−0.346677
$795$	−11.8210	−0.419247
$796$	23.1775	0.821505
$797$	−34.7671	−1.23151	−0.615757	−	0.787936i	$-0.711150\pi$
$797$	−34.7671	−1.23151	−0.615757	+	0.787936i	$0.711150\pi$
$798$	−5.89188	−0.208570
$799$	1.50313	0.0531771
$800$	3.17676	0.112316
$801$	8.80348	0.311056
$802$	−29.1348	−1.02879
$803$	−8.67541	−0.306148
$804$	12.8024	0.451506
$805$	−6.01644	−0.212051
$806$	−7.58926	−0.267320
$807$	−44.6576	−1.57202
$808$	−18.6360	−0.655613
$809$	9.19964	0.323442	0.161721	−	0.986837i	$-0.448296\pi$
$809$	9.19964	0.323442	0.161721	+	0.986837i	$0.448296\pi$
$810$	−32.1692	−1.13031
$811$	34.7624	1.22067	0.610336	−	0.792143i	$-0.291034\pi$
$811$	34.7624	1.22067	0.610336	+	0.792143i	$0.291034\pi$
$812$	0.0131397	0.000461112 0
$813$	−21.2487	−0.745226
$814$	−3.68861	−0.129286
$815$	62.9789	2.20606
$816$	3.90692	0.136769
$817$	37.8029	1.32256
$818$	1.34435	0.0470042
$819$	−3.41366	−0.119283
$820$	16.3441	0.570759
$821$	−7.46949	−0.260687	−0.130344	−	0.991469i	$-0.541608\pi$
$821$	−7.46949	−0.260687	−0.130344	+	0.991469i	$0.541608\pi$
$822$	21.1597	0.738028
$823$	6.53796	0.227899	0.113950	−	0.993487i	$-0.463650\pi$
$823$	6.53796	0.227899	0.113950	+	0.993487i	$0.463650\pi$
$824$	−11.6671	−0.406443
$825$	6.73298	0.234412
$826$	10.2541	0.356787
$827$	9.80026	0.340789	0.170394	−	0.985376i	$-0.445496\pi$
$827$	9.80026	0.340789	0.170394	+	0.985376i	$0.445496\pi$
$828$	−4.50472	−0.156550
$829$	50.2821	1.74637	0.873185	−	0.487390i	$-0.162051\pi$
$829$	50.2821	1.74637	0.873185	+	0.487390i	$0.162051\pi$
$830$	−43.0488	−1.49424
$831$	2.53649	0.0879900
$832$	−3.28300	−0.113818
$833$	12.0083	0.416064
$834$	−11.9045	−0.412221
$835$	38.0330	1.31619
$836$	−3.98902	−0.137963
$837$	7.38817	0.255372
$838$	−26.8336	−0.926953
$839$	2.99053	0.103245	0.0516223	−	0.998667i	$-0.483561\pi$
$839$	2.99053	0.103245	0.0516223	+	0.998667i	$0.483561\pi$
$840$	−4.22355	−0.145726
$841$	−28.9996	−0.999988
$842$	−36.7760	−1.26738
$843$	65.6680	2.26172
$844$	−5.45720	−0.187845
$845$	−6.35348	−0.218566
$846$	−1.21666	−0.0418297
$847$	0.696891	0.0239454
$848$	1.95048	0.0669797
$849$	−20.5197	−0.704235
$850$	−5.85594	−0.200857
$851$	−11.1365	−0.381753
$852$	−20.5557	−0.704226
$853$	37.7965	1.29413	0.647063	−	0.762436i	$-0.275997\pi$
$853$	37.7965	1.29413	0.647063	+	0.762436i	$0.275997\pi$
$854$	4.89750	0.167589
$855$	17.0193	0.582047
$856$	1.28478	0.0439130
$857$	22.1833	0.757766	0.378883	−	0.925445i	$-0.376308\pi$
$857$	22.1833	0.757766	0.378883	+	0.925445i	$0.376308\pi$
$858$	−6.95815	−0.237547
$859$	22.1174	0.754634	0.377317	−	0.926084i	$-0.376847\pi$
$859$	22.1174	0.754634	0.377317	+	0.926084i	$0.376847\pi$
$860$	27.0988	0.924060
$861$	−8.44221	−0.287710
$862$	38.1694	1.30005
$863$	−31.3224	−1.06623	−0.533114	−	0.846044i	$-0.678978\pi$
$863$	−31.3224	−1.06623	−0.533114	+	0.846044i	$0.678978\pi$
$864$	3.19601	0.108731
$865$	−37.0184	−1.25866
$866$	−23.9944	−0.815363
$867$	28.8287	0.979074
$868$	1.61099	0.0546805
$869$	−12.3385	−0.418554
$870$	−0.114270	−0.00387412
$871$	19.8308	0.671942
$872$	−1.49616	−0.0506662
$873$	18.4230	0.623524
$874$	−12.0434	−0.407375
$875$	−3.63328	−0.122827
$876$	−18.3871	−0.621241
$877$	−37.3594	−1.26154	−0.630768	−	0.775971i	$-0.717260\pi$
$877$	−37.3594	−1.26154	−0.630768	+	0.775971i	$0.717260\pi$
$878$	13.9468	0.470683
$879$	−57.6725	−1.94524
$880$	−2.85950	−0.0963939
$881$	13.0153	0.438495	0.219248	−	0.975669i	$-0.429640\pi$
$881$	13.0153	0.438495	0.219248	+	0.975669i	$0.429640\pi$
$882$	−9.71974	−0.327281
$883$	−35.8447	−1.20627	−0.603135	−	0.797639i	$-0.706082\pi$
$883$	−35.8447	−1.20627	−0.603135	+	0.797639i	$0.706082\pi$
$884$	6.05178	0.203543
$885$	−89.1759	−2.99761
$886$	−7.84346	−0.263506
$887$	−32.1716	−1.08022	−0.540109	−	0.841595i	$-0.681617\pi$
$887$	−32.1716	−1.08022	−0.540109	+	0.841595i	$0.681617\pi$
$888$	−7.81782	−0.262349
$889$	0.469681	0.0157526
$890$	16.8718	0.565543
$891$	11.2499	0.376887
$892$	−22.5631	−0.755468
$893$	−3.25276	−0.108850
$894$	3.82882	0.128055
$895$	−7.77590	−0.259920
$896$	0.696891	0.0232815
$897$	−21.0077	−0.701426
$898$	−41.7427	−1.39297
$899$	0.0435861	0.00145368
$900$	4.73990	0.157997
$901$	−3.59545	−0.119782
$902$	−5.71570	−0.190312
$903$	−13.9973	−0.465802
$904$	20.0301	0.666193
$905$	−4.49590	−0.149449
$906$	−47.3158	−1.57196
$907$	−17.8873	−0.593937	−0.296969	−	0.954887i	$-0.595976\pi$
$907$	−17.8873	−0.593937	−0.296969	+	0.954887i	$0.595976\pi$
$908$	1.89051	0.0627388
$909$	−27.8059	−0.922264
$910$	−6.54224	−0.216873
$911$	−39.0023	−1.29220	−0.646102	−	0.763251i	$-0.723602\pi$
$911$	−39.0023	−1.29220	−0.646102	+	0.763251i	$0.723602\pi$
$912$	−8.45452	−0.279957
$913$	15.0546	0.498235
$914$	−24.4603	−0.809075
$915$	−42.5915	−1.40803
$916$	15.6099	0.515766
$917$	−3.98986	−0.131757
$918$	−5.89143	−0.194446
$919$	−19.9488	−0.658051	−0.329026	−	0.944321i	$-0.606720\pi$
$919$	−19.9488	−0.658051	−0.329026	+	0.944321i	$0.606720\pi$
$920$	−8.63326	−0.284630
$921$	−16.3628	−0.539171
$922$	−5.46962	−0.180132
$923$	−31.8406	−1.04805
$924$	1.47702	0.0485905
$925$	11.7178	0.385281
$926$	34.9202	1.14755
$927$	−17.4079	−0.571751
$928$	0.0188547	0.000618936 0
$929$	−20.5262	−0.673442	−0.336721	−	0.941604i	$-0.609318\pi$
$929$	−20.5262	−0.673442	−0.336721	+	0.941604i	$0.609318\pi$
$930$	−14.0101	−0.459409
$931$	−25.9859	−0.851652
$932$	−13.2587	−0.434302
$933$	−46.5815	−1.52501
$934$	−22.3476	−0.731237
$935$	5.27112	0.172384
$936$	−4.89842	−0.160110
$937$	27.4746	0.897557	0.448778	−	0.893643i	$-0.351859\pi$
$937$	27.4746	0.897557	0.448778	+	0.893643i	$0.351859\pi$
$938$	−4.20954	−0.137446
$939$	19.8022	0.646219
$940$	−2.33172	−0.0760523
$941$	−6.38554	−0.208163	−0.104081	−	0.994569i	$-0.533190\pi$
$941$	−6.38554	−0.208163	−0.104081	+	0.994569i	$0.533190\pi$
$942$	43.4690	1.41630
$943$	−17.2565	−0.561950
$944$	14.7141	0.478904
$945$	6.36889	0.207180
$946$	−9.47673	−0.308115
$947$	42.4251	1.37863	0.689316	−	0.724461i	$-0.257911\pi$
$947$	42.4251	1.37863	0.689316	+	0.724461i	$0.257911\pi$
$948$	−26.1507	−0.849337
$949$	−28.4814	−0.924545
$950$	12.6722	0.411140
$951$	−71.0704	−2.30461
$952$	−1.28463	−0.0416349
$953$	−47.2511	−1.53061	−0.765307	−	0.643665i	$-0.777413\pi$
$953$	−47.2511	−1.53061	−0.765307	+	0.643665i	$0.777413\pi$
$954$	2.91021	0.0942217
$955$	−9.66487	−0.312748
$956$	20.7913	0.672438
$957$	0.0399616	0.00129177
$958$	26.9630	0.871135
$959$	−6.95747	−0.224668
$960$	−6.06056	−0.195604
$961$	−25.6561	−0.827617
$962$	−12.1097	−0.390434
$963$	1.91697	0.0617734
$964$	4.50420	0.145070
$965$	20.1653	0.649144
$966$	4.45934	0.143477
$967$	43.5911	1.40180	0.700898	−	0.713261i	$-0.252783\pi$
$967$	43.5911	1.40180	0.700898	+	0.713261i	$0.252783\pi$
$968$	1.00000	0.0321412
$969$	15.5848	0.500655
$970$	35.3075	1.13366
$971$	−31.7587	−1.01919	−0.509593	−	0.860416i	$-0.670204\pi$
$971$	−31.7587	−1.01919	−0.509593	+	0.860416i	$0.670204\pi$
$972$	14.2556	0.457248
$973$	3.91431	0.125487
$974$	−34.6071	−1.10888
$975$	22.1044	0.707907
$976$	7.02764	0.224949
$977$	−24.7845	−0.792925	−0.396463	−	0.918051i	$-0.629762\pi$
$977$	−24.7845	−0.792925	−0.396463	+	0.918051i	$0.629762\pi$
$978$	−46.6796	−1.49265
$979$	−5.90025	−0.188573
$980$	−18.6278	−0.595043
$981$	−2.23234	−0.0712732
$982$	10.4465	0.333361
$983$	−18.4458	−0.588330	−0.294165	−	0.955755i	$-0.595042\pi$
$983$	−18.4458	−0.588330	−0.294165	+	0.955755i	$0.595042\pi$
$984$	−12.1141	−0.386184
$985$	−2.85950	−0.0911114
$986$	−0.0347562	−0.00110686
$987$	1.20441	0.0383367
$988$	−13.0960	−0.416639
$989$	−28.6116	−0.909797
$990$	−4.26653	−0.135599
$991$	−34.4758	−1.09516	−0.547580	−	0.836753i	$-0.684451\pi$
$991$	−34.4758	−1.09516	−0.547580	+	0.836753i	$0.684451\pi$
$992$	2.31168	0.0733960
$993$	−13.2447	−0.420307
$994$	6.75887	0.214378
$995$	66.2762	2.10110
$996$	31.9075	1.01103
$997$	28.7369	0.910106	0.455053	−	0.890464i	$-0.349620\pi$
$997$	28.7369	0.910106	0.455053	+	0.890464i	$0.349620\pi$
$998$	7.96147	0.252016
$999$	11.7889	0.372983

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4334.2.a.f.1.5	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4334.2.a.f.1.5	✓	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.11945 q^{3} +1.00000 q^{4} +2.85950 q^{5} -2.11945 q^{6} +0.696891 q^{7} +1.00000 q^{8} +1.49205 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.11945 q^{3} +1.00000 q^{4} +2.85950 q^{5} -2.11945 q^{6} +0.696891 q^{7} +1.00000 q^{8} +1.49205 q^{9} +2.85950 q^{10} -1.00000 q^{11} -2.11945 q^{12} -3.28300 q^{13} +0.696891 q^{14} -6.06056 q^{15} +1.00000 q^{16} -1.84337 q^{17} +1.49205 q^{18} +3.98902 q^{19} +2.85950 q^{20} -1.47702 q^{21} -1.00000 q^{22} -3.01915 q^{23} -2.11945 q^{24} +3.17676 q^{25} -3.28300 q^{26} +3.19601 q^{27} +0.696891 q^{28} +0.0188547 q^{29} -6.06056 q^{30} +2.31168 q^{31} +1.00000 q^{32} +2.11945 q^{33} -1.84337 q^{34} +1.99276 q^{35} +1.49205 q^{36} +3.68861 q^{37} +3.98902 q^{38} +6.95815 q^{39} +2.85950 q^{40} +5.71570 q^{41} -1.47702 q^{42} +9.47673 q^{43} -1.00000 q^{44} +4.26653 q^{45} -3.01915 q^{46} -0.815428 q^{47} -2.11945 q^{48} -6.51434 q^{49} +3.17676 q^{50} +3.90692 q^{51} -3.28300 q^{52} +1.95048 q^{53} +3.19601 q^{54} -2.85950 q^{55} +0.696891 q^{56} -8.45452 q^{57} +0.0188547 q^{58} +14.7141 q^{59} -6.06056 q^{60} +7.02764 q^{61} +2.31168 q^{62} +1.03980 q^{63} +1.00000 q^{64} -9.38776 q^{65} +2.11945 q^{66} -6.04045 q^{67} -1.84337 q^{68} +6.39892 q^{69} +1.99276 q^{70} +9.69861 q^{71} +1.49205 q^{72} +8.67541 q^{73} +3.68861 q^{74} -6.73298 q^{75} +3.98902 q^{76} -0.696891 q^{77} +6.95815 q^{78} +12.3385 q^{79} +2.85950 q^{80} -11.2499 q^{81} +5.71570 q^{82} -15.0546 q^{83} -1.47702 q^{84} -5.27112 q^{85} +9.47673 q^{86} -0.0399616 q^{87} -1.00000 q^{88} +5.90025 q^{89} +4.26653 q^{90} -2.28789 q^{91} -3.01915 q^{92} -4.89949 q^{93} -0.815428 q^{94} +11.4066 q^{95} -2.11945 q^{96} +12.3474 q^{97} -6.51434 q^{98} -1.49205 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 24 q^{2} + 8 q^{3} + 24 q^{4} + 8 q^{6} + 11 q^{7} + 24 q^{8} + 28 q^{9}+O(q^{10}) \) 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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