LMFDB - Embedded newform 2023.2.a.m.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2023,2,Mod(1,2023)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2023, 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("2023.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2023 = 7 \cdot 17^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2023.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:	$16.1537363289$
Analytic rank:	$1$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 16x^{8} + 88x^{6} - 2x^{5} - 192x^{4} + 16x^{3} + 136x^{2} - 40x - 7 $ x^10 - 16x^8 + 88x^6 - 2x^5 - 192x^4 + 16x^3 + 136x^2 - 40*x - 7
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 119)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-1.57229$ of defining polynomial
Character	$\chi$	$=$	2023.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.57229 q^{2} -2.03431 q^{3} +0.472100 q^{4} -3.39483 q^{5} +3.19853 q^{6} -1.00000 q^{7} +2.40230 q^{8} +1.13841 q^{9} +O(q^{10})$	\(q-1.57229 q^{2} -2.03431 q^{3} +0.472100 q^{4} -3.39483 q^{5} +3.19853 q^{6} -1.00000 q^{7} +2.40230 q^{8} +1.13841 q^{9} +5.33766 q^{10} -4.67063 q^{11} -0.960397 q^{12} -3.63777 q^{13} +1.57229 q^{14} +6.90613 q^{15} -4.72132 q^{16} -1.78992 q^{18} +6.19754 q^{19} -1.60270 q^{20} +2.03431 q^{21} +7.34359 q^{22} +0.672091 q^{23} -4.88703 q^{24} +6.52485 q^{25} +5.71963 q^{26} +3.78704 q^{27} -0.472100 q^{28} +5.59267 q^{29} -10.8584 q^{30} -7.65857 q^{31} +2.61868 q^{32} +9.50150 q^{33} +3.39483 q^{35} +0.537445 q^{36} -1.36854 q^{37} -9.74433 q^{38} +7.40035 q^{39} -8.15541 q^{40} -0.696033 q^{41} -3.19853 q^{42} +6.64216 q^{43} -2.20500 q^{44} -3.86472 q^{45} -1.05672 q^{46} -4.32592 q^{47} +9.60463 q^{48} +1.00000 q^{49} -10.2590 q^{50} -1.71739 q^{52} +4.07940 q^{53} -5.95433 q^{54} +15.8560 q^{55} -2.40230 q^{56} -12.6077 q^{57} -8.79330 q^{58} -2.73239 q^{59} +3.26038 q^{60} +12.0980 q^{61} +12.0415 q^{62} -1.13841 q^{63} +5.32531 q^{64} +12.3496 q^{65} -14.9391 q^{66} +12.5590 q^{67} -1.36724 q^{69} -5.33766 q^{70} +4.30572 q^{71} +2.73482 q^{72} +1.65114 q^{73} +2.15174 q^{74} -13.2736 q^{75} +2.92586 q^{76} +4.67063 q^{77} -11.6355 q^{78} +10.0047 q^{79} +16.0281 q^{80} -11.1193 q^{81} +1.09437 q^{82} -4.69160 q^{83} +0.960397 q^{84} -10.4434 q^{86} -11.3772 q^{87} -11.2203 q^{88} +2.04706 q^{89} +6.07647 q^{90} +3.63777 q^{91} +0.317294 q^{92} +15.5799 q^{93} +6.80161 q^{94} -21.0396 q^{95} -5.32721 q^{96} +4.23013 q^{97} -1.57229 q^{98} -5.31711 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 4 q^{3} + 12 q^{4} - 8 q^{5} - 14 q^{6} - 10 q^{7} + 10 q^{9}+O(q^{10}) $ 10 * q - 4 * q^3 + 12 * q^4 - 8 * q^5 - 14 * q^6 - 10 * q^7 + 10 * q^9	$ 10 q - 4 q^{3} + 12 q^{4} - 8 q^{5} - 14 q^{6} - 10 q^{7} + 10 q^{9} - 4 q^{10} - 8 q^{11} + 16 q^{12} + 12 q^{15} + 8 q^{16} - 4 q^{18} - 8 q^{19} - 30 q^{20} + 4 q^{21} - 8 q^{22} - 12 q^{23} - 32 q^{24} + 10 q^{25} - 16 q^{27} - 12 q^{28} - 8 q^{29} + 18 q^{30} + 16 q^{31} + 10 q^{32} - 8 q^{33} + 8 q^{35} + 18 q^{36} - 20 q^{37} - 24 q^{38} + 8 q^{39} - 6 q^{40} - 36 q^{41} + 14 q^{42} + 12 q^{43} - 24 q^{44} - 40 q^{45} + 56 q^{46} - 20 q^{47} + 18 q^{48} + 10 q^{49} - 14 q^{50} + 12 q^{53} - 46 q^{54} + 20 q^{55} - 28 q^{57} - 24 q^{58} - 4 q^{59} - 18 q^{60} - 8 q^{61} - 4 q^{62} - 10 q^{63} - 16 q^{64} - 12 q^{65} - 60 q^{66} - 44 q^{69} + 4 q^{70} - 36 q^{71} - 54 q^{72} + 20 q^{73} + 36 q^{74} - 36 q^{75} - 44 q^{76} + 8 q^{77} - 24 q^{78} - 4 q^{80} - 2 q^{81} - 6 q^{82} - 4 q^{83} - 16 q^{84} + 22 q^{86} - 24 q^{87} - 60 q^{88} - 24 q^{89} + 18 q^{90} - 32 q^{92} + 8 q^{93} - 56 q^{94} - 16 q^{95} - 4 q^{96} - 28 q^{97} + 60 q^{99}+O(q^{100}) $ 10 * q - 4 * q^3 + 12 * q^4 - 8 * q^5 - 14 * q^6 - 10 * q^7 + 10 * q^9 - 4 * q^10 - 8 * q^11 + 16 * q^12 + 12 * q^15 + 8 * q^16 - 4 * q^18 - 8 * q^19 - 30 * q^20 + 4 * q^21 - 8 * q^22 - 12 * q^23 - 32 * q^24 + 10 * q^25 - 16 * q^27 - 12 * q^28 - 8 * q^29 + 18 * q^30 + 16 * q^31 + 10 * q^32 - 8 * q^33 + 8 * q^35 + 18 * q^36 - 20 * q^37 - 24 * q^38 + 8 * q^39 - 6 * q^40 - 36 * q^41 + 14 * q^42 + 12 * q^43 - 24 * q^44 - 40 * q^45 + 56 * q^46 - 20 * q^47 + 18 * q^48 + 10 * q^49 - 14 * q^50 + 12 * q^53 - 46 * q^54 + 20 * q^55 - 28 * q^57 - 24 * q^58 - 4 * q^59 - 18 * q^60 - 8 * q^61 - 4 * q^62 - 10 * q^63 - 16 * q^64 - 12 * q^65 - 60 * q^66 - 44 * q^69 + 4 * q^70 - 36 * q^71 - 54 * q^72 + 20 * q^73 + 36 * q^74 - 36 * q^75 - 44 * q^76 + 8 * q^77 - 24 * q^78 - 4 * q^80 - 2 * q^81 - 6 * q^82 - 4 * q^83 - 16 * q^84 + 22 * q^86 - 24 * q^87 - 60 * q^88 - 24 * q^89 + 18 * q^90 - 32 * q^92 + 8 * q^93 - 56 * q^94 - 16 * q^95 - 4 * q^96 - 28 * q^97 + 60 * 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 $

$2$	−1.57229	−1.11178	−0.555889	−	0.831257i	$-0.687622\pi$
$2$	−1.57229	−1.11178	−0.555889	+	0.831257i	$0.687622\pi$
$3$	−2.03431	−1.17451	−0.587255	−	0.809402i	$-0.699791\pi$
$3$	−2.03431	−1.17451	−0.587255	+	0.809402i	$0.699791\pi$
$4$	0.472100	0.236050
$5$	−3.39483	−1.51821	−0.759106	−	0.650967i	$-0.774364\pi$
$5$	−3.39483	−1.51821	−0.759106	+	0.650967i	$0.774364\pi$
$6$	3.19853	1.30579
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	2.40230	0.849343
$9$	1.13841	0.379471
$10$	5.33766	1.68792
$11$	−4.67063	−1.40825	−0.704123	−	0.710078i	$-0.748660\pi$
$11$	−4.67063	−1.40825	−0.704123	+	0.710078i	$0.748660\pi$
$12$	−0.960397	−0.277243
$13$	−3.63777	−1.00894	−0.504468	−	0.863430i	$-0.668311\pi$
$13$	−3.63777	−1.00894	−0.504468	+	0.863430i	$0.668311\pi$
$14$	1.57229	0.420213
$15$	6.90613	1.78315
$16$	−4.72132	−1.18033
$17$	0	0
$17$	0	0
$18$	−1.78992	−0.421888
$19$	6.19754	1.42181	0.710906	−	0.703287i	$-0.248285\pi$
$19$	6.19754	1.42181	0.710906	+	0.703287i	$0.248285\pi$
$20$	−1.60270	−0.358374
$21$	2.03431	0.443923
$22$	7.34359	1.56566
$23$	0.672091	0.140141	0.0700704	−	0.997542i	$-0.477678\pi$
$23$	0.672091	0.140141	0.0700704	+	0.997542i	$0.477678\pi$
$24$	−4.88703	−0.997561
$25$	6.52485	1.30497
$26$	5.71963	1.12171
$27$	3.78704	0.728816
$28$	−0.472100	−0.0892185
$29$	5.59267	1.03853	0.519266	−	0.854613i	$-0.326205\pi$
$29$	5.59267	1.03853	0.519266	+	0.854613i	$0.326205\pi$
$30$	−10.8584	−1.98247
$31$	−7.65857	−1.37552	−0.687760	−	0.725938i	$-0.741406\pi$
$31$	−7.65857	−1.37552	−0.687760	+	0.725938i	$0.741406\pi$
$32$	2.61868	0.462922
$33$	9.50150	1.65400
$34$	0	0
$35$	3.39483	0.573831
$36$	0.537445	0.0895742
$37$	−1.36854	−0.224986	−0.112493	−	0.993653i	$-0.535884\pi$
$37$	−1.36854	−0.224986	−0.112493	+	0.993653i	$0.535884\pi$
$38$	−9.74433	−1.58074
$39$	7.40035	1.18500
$40$	−8.15541	−1.28948
$41$	−0.696033	−0.108702	−0.0543510	−	0.998522i	$-0.517309\pi$
$41$	−0.696033	−0.108702	−0.0543510	+	0.998522i	$0.517309\pi$
$42$	−3.19853	−0.493543
$43$	6.64216	1.01292	0.506460	−	0.862264i	$-0.330954\pi$
$43$	6.64216	1.01292	0.506460	+	0.862264i	$0.330954\pi$
$44$	−2.20500	−0.332417
$45$	−3.86472	−0.576118
$46$	−1.05672	−0.155805
$47$	−4.32592	−0.631000	−0.315500	−	0.948926i	$-0.602172\pi$
$47$	−4.32592	−0.631000	−0.315500	+	0.948926i	$0.602172\pi$
$48$	9.60463	1.38631
$49$	1.00000	0.142857
$50$	−10.2590	−1.45084
$51$	0	0
$52$	−1.71739	−0.238159
$53$	4.07940	0.560349	0.280175	−	0.959949i	$-0.409608\pi$
$53$	4.07940	0.560349	0.280175	+	0.959949i	$0.409608\pi$
$54$	−5.95433	−0.810282
$55$	15.8560	2.13802
$56$	−2.40230	−0.321021
$57$	−12.6077	−1.66993
$58$	−8.79330	−1.15462
$59$	−2.73239	−0.355727	−0.177864	−	0.984055i	$-0.556919\pi$
$59$	−2.73239	−0.355727	−0.177864	+	0.984055i	$0.556919\pi$
$60$	3.26038	0.420914
$61$	12.0980	1.54898	0.774492	−	0.632583i	$-0.218005\pi$
$61$	12.0980	1.54898	0.774492	+	0.632583i	$0.218005\pi$
$62$	12.0415	1.52927
$63$	−1.13841	−0.143427
$64$	5.32531	0.665664
$65$	12.3496	1.53178
$66$	−14.9391	−1.83888
$67$	12.5590	1.53433	0.767165	−	0.641450i	$-0.221667\pi$
$67$	12.5590	1.53433	0.767165	+	0.641450i	$0.221667\pi$
$68$	0	0
$69$	−1.36724	−0.164597
$70$	−5.33766	−0.637972
$71$	4.30572	0.510996	0.255498	−	0.966810i	$-0.417761\pi$
$71$	4.30572	0.510996	0.255498	+	0.966810i	$0.417761\pi$
$72$	2.73482	0.322301
$73$	1.65114	0.193251	0.0966255	−	0.995321i	$-0.469195\pi$
$73$	1.65114	0.193251	0.0966255	+	0.995321i	$0.469195\pi$
$74$	2.15174	0.250135
$75$	−13.2736	−1.53270
$76$	2.92586	0.335619
$77$	4.67063	0.532267
$78$	−11.6355	−1.31746
$79$	10.0047	1.12562	0.562811	−	0.826586i	$-0.309720\pi$
$79$	10.0047	1.12562	0.562811	+	0.826586i	$0.309720\pi$
$80$	16.0281	1.79199
$81$	−11.1193	−1.23547
$82$	1.09437	0.120853
$83$	−4.69160	−0.514970	−0.257485	−	0.966282i	$-0.582894\pi$
$83$	−4.69160	−0.514970	−0.257485	+	0.966282i	$0.582894\pi$
$84$	0.960397	0.104788
$85$	0	0
$86$	−10.4434	−1.12614
$87$	−11.3772	−1.21977
$88$	−11.2203	−1.19608
$89$	2.04706	0.216988	0.108494	−	0.994097i	$-0.465397\pi$
$89$	2.04706	0.216988	0.108494	+	0.994097i	$0.465397\pi$
$90$	6.07647	0.640516
$91$	3.63777	0.381342
$92$	0.317294	0.0330802
$93$	15.5799	1.61556
$94$	6.80161	0.701532
$95$	−21.0396	−2.15861
$96$	−5.32721	−0.543706
$97$	4.23013	0.429505	0.214753	−	0.976668i	$-0.431105\pi$
$97$	4.23013	0.429505	0.214753	+	0.976668i	$0.431105\pi$
$98$	−1.57229	−0.158825
$99$	−5.31711	−0.534389
$100$	3.08038	0.308038
$101$	−5.38529	−0.535856	−0.267928	−	0.963439i	$-0.586339\pi$
$101$	−5.38529	−0.535856	−0.267928	+	0.963439i	$0.586339\pi$
$102$	0	0
$103$	−3.96255	−0.390442	−0.195221	−	0.980759i	$-0.562542\pi$
$103$	−3.96255	−0.390442	−0.195221	+	0.980759i	$0.562542\pi$
$104$	−8.73903	−0.856932
$105$	−6.90613	−0.673969
$106$	−6.41401	−0.622984
$107$	−11.3798	−1.10013	−0.550063	−	0.835123i	$-0.685396\pi$
$107$	−11.3798	−1.10013	−0.550063	+	0.835123i	$0.685396\pi$
$108$	1.78786	0.172037
$109$	4.40579	0.421998	0.210999	−	0.977486i	$-0.432328\pi$
$109$	4.40579	0.421998	0.210999	+	0.977486i	$0.432328\pi$
$110$	−24.9302	−2.37700
$111$	2.78403	0.264248
$112$	4.72132	0.446123
$113$	−11.5971	−1.09097	−0.545484	−	0.838121i	$-0.683654\pi$
$113$	−11.5971	−1.09097	−0.545484	+	0.838121i	$0.683654\pi$
$114$	19.8230	1.85659
$115$	−2.28163	−0.212764
$116$	2.64030	0.245145
$117$	−4.14129	−0.382862
$118$	4.29612	0.395490
$119$	0	0
$120$	16.5906	1.51451
$121$	10.8148	0.983159
$122$	−19.0215	−1.72213
$123$	1.41595	0.127672
$124$	−3.61561	−0.324691
$125$	−5.17661	−0.463010
$126$	1.78992	0.159459
$127$	5.12889	0.455115	0.227558	−	0.973765i	$-0.426926\pi$
$127$	5.12889	0.455115	0.227558	+	0.973765i	$0.426926\pi$
$128$	−13.6103	−1.20299
$129$	−13.5122	−1.18968
$130$	−19.4172	−1.70300
$131$	−8.35345	−0.729844	−0.364922	−	0.931038i	$-0.618904\pi$
$131$	−8.35345	−0.729844	−0.364922	+	0.931038i	$0.618904\pi$
$132$	4.48566	0.390426
$133$	−6.19754	−0.537395
$134$	−19.7465	−1.70583
$135$	−12.8564	−1.10650
$136$	0	0
$137$	−20.1939	−1.72528	−0.862639	−	0.505821i	$-0.831190\pi$
$137$	−20.1939	−1.72528	−0.862639	+	0.505821i	$0.831190\pi$
$138$	2.14970	0.182995
$139$	7.80511	0.662021	0.331011	−	0.943627i	$-0.392610\pi$
$139$	7.80511	0.662021	0.331011	+	0.943627i	$0.392610\pi$
$140$	1.60270	0.135453
$141$	8.80026	0.741116
$142$	−6.76985	−0.568113
$143$	16.9907	1.42083
$144$	−5.37482	−0.447902
$145$	−18.9861	−1.57671
$146$	−2.59607	−0.214852
$147$	−2.03431	−0.167787
$148$	−0.646087	−0.0531080
$149$	−0.670580	−0.0549361	−0.0274680	−	0.999623i	$-0.508744\pi$
$149$	−0.670580	−0.0549361	−0.0274680	+	0.999623i	$0.508744\pi$
$150$	20.8699	1.70402
$151$	−11.4237	−0.929644	−0.464822	−	0.885404i	$-0.653882\pi$
$151$	−11.4237	−0.929644	−0.464822	+	0.885404i	$0.653882\pi$
$152$	14.8884	1.20761
$153$	0	0
$154$	−7.34359	−0.591763
$155$	25.9995	2.08833
$156$	3.49370	0.279720
$157$	−23.3832	−1.86618	−0.933090	−	0.359642i	$-0.882899\pi$
$157$	−23.3832	−1.86618	−0.933090	+	0.359642i	$0.882899\pi$
$158$	−15.7304	−1.25144
$159$	−8.29877	−0.658135
$160$	−8.88998	−0.702815
$161$	−0.672091	−0.0529682
$162$	17.4827	1.37357
$163$	−12.0770	−0.945946	−0.472973	−	0.881077i	$-0.656819\pi$
$163$	−12.0770	−0.945946	−0.472973	+	0.881077i	$0.656819\pi$
$164$	−0.328597	−0.0256591
$165$	−32.2559	−2.51112
$166$	7.37656	0.572532
$167$	−24.5341	−1.89850	−0.949251	−	0.314519i	$-0.898157\pi$
$167$	−24.5341	−1.89850	−0.949251	+	0.314519i	$0.898157\pi$
$168$	4.88703	0.377043
$169$	0.233365	0.0179511
$170$	0	0
$171$	7.05537	0.539537
$172$	3.13576	0.239100
$173$	3.56524	0.271060	0.135530	−	0.990773i	$-0.456726\pi$
$173$	3.56524	0.271060	0.135530	+	0.990773i	$0.456726\pi$
$174$	17.8883	1.35611
$175$	−6.52485	−0.493232
$176$	22.0515	1.66220
$177$	5.55853	0.417805
$178$	−3.21857	−0.241242
$179$	3.96115	0.296071	0.148035	−	0.988982i	$-0.452705\pi$
$179$	3.96115	0.296071	0.148035	+	0.988982i	$0.452705\pi$
$180$	−1.82453	−0.135993
$181$	−1.92711	−0.143241	−0.0716204	−	0.997432i	$-0.522817\pi$
$181$	−1.92711	−0.143241	−0.0716204	+	0.997432i	$0.522817\pi$
$182$	−5.71963	−0.423967
$183$	−24.6110	−1.81930
$184$	1.61457	0.119028
$185$	4.64595	0.341577
$186$	−24.4961	−1.79614
$187$	0	0
$188$	−2.04227	−0.148948
$189$	−3.78704	−0.275467
$190$	33.0803	2.39990
$191$	25.1726	1.82143	0.910714	−	0.413038i	$-0.135532\pi$
$191$	25.1726	1.82143	0.910714	+	0.413038i	$0.135532\pi$
$192$	−10.8333	−0.781828
$193$	11.2467	0.809557	0.404778	−	0.914415i	$-0.367349\pi$
$193$	11.2467	0.809557	0.404778	+	0.914415i	$0.367349\pi$
$194$	−6.65100	−0.477514
$195$	−25.1229	−1.79909
$196$	0.472100	0.0337214
$197$	22.6324	1.61249	0.806244	−	0.591583i	$-0.201497\pi$
$197$	22.6324	1.61249	0.806244	+	0.591583i	$0.201497\pi$
$198$	8.36004	0.594122
$199$	5.24945	0.372124	0.186062	−	0.982538i	$-0.440428\pi$
$199$	5.24945	0.372124	0.186062	+	0.982538i	$0.440428\pi$
$200$	15.6747	1.10837
$201$	−25.5490	−1.80208
$202$	8.46724	0.595753
$203$	−5.59267	−0.392528
$204$	0	0
$205$	2.36291	0.165033
$206$	6.23029	0.434085
$207$	0.765119	0.0531794
$208$	17.1751	1.19088
$209$	−28.9464	−2.00226
$210$	10.8584	0.749304
$211$	9.72721	0.669649	0.334824	−	0.942281i	$-0.391323\pi$
$211$	9.72721	0.669649	0.334824	+	0.942281i	$0.391323\pi$
$212$	1.92589	0.132270
$213$	−8.75918	−0.600169
$214$	17.8924	1.22310
$215$	−22.5490	−1.53783
$216$	9.09762	0.619015
$217$	7.65857	0.519898
$218$	−6.92718	−0.469168
$219$	−3.35892	−0.226975
$220$	7.48560	0.504679
$221$	0	0
$222$	−4.37731	−0.293786
$223$	17.5438	1.17482	0.587411	−	0.809289i	$-0.300147\pi$
$223$	17.5438	1.17482	0.587411	+	0.809289i	$0.300147\pi$
$224$	−2.61868	−0.174968
$225$	7.42798	0.495199
$226$	18.2341	1.21291
$227$	−8.34361	−0.553785	−0.276892	−	0.960901i	$-0.589305\pi$
$227$	−8.34361	−0.553785	−0.276892	+	0.960901i	$0.589305\pi$
$228$	−5.95210	−0.394187
$229$	15.3443	1.01398	0.506990	−	0.861952i	$-0.330758\pi$
$229$	15.3443	1.01398	0.506990	+	0.861952i	$0.330758\pi$
$230$	3.58739	0.236546
$231$	−9.50150	−0.625153
$232$	13.4353	0.882070
$233$	−24.4774	−1.60357	−0.801784	−	0.597613i	$-0.796116\pi$
$233$	−24.4774	−1.60357	−0.801784	+	0.597613i	$0.796116\pi$
$234$	6.51131	0.425658
$235$	14.6858	0.957993
$236$	−1.28996	−0.0839694
$237$	−20.3527	−1.32205
$238$	0	0
$239$	14.5771	0.942916	0.471458	−	0.881889i	$-0.343728\pi$
$239$	14.5771	0.942916	0.471458	+	0.881889i	$0.343728\pi$
$240$	−32.6061	−2.10471
$241$	−15.2154	−0.980108	−0.490054	−	0.871692i	$-0.663023\pi$
$241$	−15.2154	−0.980108	−0.490054	+	0.871692i	$0.663023\pi$
$242$	−17.0039	−1.09305
$243$	11.2589	0.722258
$244$	5.71144	0.365638
$245$	−3.39483	−0.216888
$246$	−2.22628	−0.141942
$247$	−22.5452	−1.43452
$248$	−18.3982	−1.16829
$249$	9.54417	0.604837
$250$	8.13914	0.514764
$251$	−1.54033	−0.0972246	−0.0486123	−	0.998818i	$-0.515480\pi$
$251$	−1.54033	−0.0972246	−0.0486123	+	0.998818i	$0.515480\pi$
$252$	−0.537445	−0.0338559
$253$	−3.13909	−0.197353
$254$	−8.06411	−0.505987
$255$	0	0
$256$	10.7487	0.671797
$257$	4.02923	0.251337	0.125668	−	0.992072i	$-0.459893\pi$
$257$	4.02923	0.251337	0.125668	+	0.992072i	$0.459893\pi$
$258$	21.2451	1.32266
$259$	1.36854	0.0850368
$260$	5.83024	0.361576
$261$	6.36677	0.394093
$262$	13.1341	0.811424
$263$	17.9741	1.10833	0.554164	−	0.832407i	$-0.313038\pi$
$263$	17.9741	1.10833	0.554164	+	0.832407i	$0.313038\pi$
$264$	22.8255	1.40481
$265$	−13.8489	−0.850729
$266$	9.74433	0.597463
$267$	−4.16435	−0.254854
$268$	5.92912	0.362178
$269$	18.0317	1.09941	0.549705	−	0.835359i	$-0.314740\pi$
$269$	18.0317	1.09941	0.549705	+	0.835359i	$0.314740\pi$
$270$	20.2139	1.23018
$271$	16.7080	1.01494	0.507469	−	0.861670i	$-0.330581\pi$
$271$	16.7080	1.01494	0.507469	+	0.861670i	$0.330581\pi$
$272$	0	0
$273$	−7.40035	−0.447889
$274$	31.7506	1.91812
$275$	−30.4751	−1.83772
$276$	−0.645475	−0.0388530
$277$	1.04360	0.0627036	0.0313518	−	0.999508i	$-0.490019\pi$
$277$	1.04360	0.0627036	0.0313518	+	0.999508i	$0.490019\pi$
$278$	−12.2719	−0.736020
$279$	−8.71863	−0.521971
$280$	8.15541	0.487379
$281$	−3.53036	−0.210604	−0.105302	−	0.994440i	$-0.533581\pi$
$281$	−3.53036	−0.210604	−0.105302	+	0.994440i	$0.533581\pi$
$282$	−13.8366	−0.823956
$283$	−1.82347	−0.108394	−0.0541971	−	0.998530i	$-0.517260\pi$
$283$	−1.82347	−0.108394	−0.0541971	+	0.998530i	$0.517260\pi$
$284$	2.03273	0.120620
$285$	42.8010	2.53531
$286$	−26.7143	−1.57965
$287$	0.696033	0.0410855
$288$	2.98115	0.175666
$289$	0	0
$290$	29.8517	1.75295
$291$	−8.60540	−0.504458
$292$	0.779501	0.0456169
$293$	−14.9585	−0.873883	−0.436942	−	0.899490i	$-0.643938\pi$
$293$	−14.9585	−0.873883	−0.436942	+	0.899490i	$0.643938\pi$
$294$	3.19853	0.186542
$295$	9.27600	0.540070
$296$	−3.28764	−0.191090
$297$	−17.6879	−1.02635
$298$	1.05435	0.0610767
$299$	−2.44491	−0.141393
$300$	−6.26645	−0.361794
$301$	−6.64216	−0.382848
$302$	17.9613	1.03356
$303$	10.9553	0.629368
$304$	−29.2606	−1.67821
$305$	−41.0705	−2.35169
$306$	0	0
$307$	−7.16409	−0.408876	−0.204438	−	0.978879i	$-0.565537\pi$
$307$	−7.16409	−0.408876	−0.204438	+	0.978879i	$0.565537\pi$
$308$	2.20500	0.125642
$309$	8.06106	0.458578
$310$	−40.8788	−2.32176
$311$	6.29448	0.356927	0.178464	−	0.983947i	$-0.442887\pi$
$311$	6.29448	0.356927	0.178464	+	0.983947i	$0.442887\pi$
$312$	17.7779	1.00647
$313$	−31.3719	−1.77325	−0.886623	−	0.462493i	$-0.846955\pi$
$313$	−31.3719	−1.77325	−0.886623	+	0.462493i	$0.846955\pi$
$314$	36.7652	2.07478
$315$	3.86472	0.217752
$316$	4.72324	0.265703
$317$	16.5655	0.930411	0.465205	−	0.885203i	$-0.345980\pi$
$317$	16.5655	0.930411	0.465205	+	0.885203i	$0.345980\pi$
$318$	13.0481	0.731700
$319$	−26.1213	−1.46251
$320$	−18.0785	−1.01062
$321$	23.1500	1.29211
$322$	1.05672	0.0588889
$323$	0	0
$324$	−5.24940	−0.291633
$325$	−23.7359	−1.31663
$326$	18.9886	1.05168
$327$	−8.96274	−0.495640
$328$	−1.67208	−0.0923253
$329$	4.32592	0.238496
$330$	50.7157	2.79181
$331$	4.73294	0.260146	0.130073	−	0.991504i	$-0.458479\pi$
$331$	4.73294	0.260146	0.130073	+	0.991504i	$0.458479\pi$
$332$	−2.21490	−0.121559
$333$	−1.55796	−0.0853759
$334$	38.5747	2.11071
$335$	−42.6357	−2.32944
$336$	−9.60463	−0.523975
$337$	24.1156	1.31366	0.656830	−	0.754039i	$-0.271897\pi$
$337$	24.1156	1.31366	0.656830	+	0.754039i	$0.271897\pi$
$338$	−0.366917	−0.0199577
$339$	23.5922	1.28135
$340$	0	0
$341$	35.7703	1.93707
$342$	−11.0931	−0.599846
$343$	−1.00000	−0.0539949
$344$	15.9565	0.860316
$345$	4.64155	0.249893
$346$	−5.60560	−0.301359
$347$	22.9061	1.22967	0.614833	−	0.788657i	$-0.289223\pi$
$347$	22.9061	1.22967	0.614833	+	0.788657i	$0.289223\pi$
$348$	−5.37118	−0.287925
$349$	−10.1897	−0.545442	−0.272721	−	0.962093i	$-0.587924\pi$
$349$	−10.1897	−0.545442	−0.272721	+	0.962093i	$0.587924\pi$
$350$	10.2590	0.548365
$351$	−13.7764	−0.735329
$352$	−12.2309	−0.651909
$353$	16.7999	0.894167	0.447084	−	0.894492i	$-0.352463\pi$
$353$	16.7999	0.894167	0.447084	+	0.894492i	$0.352463\pi$
$354$	−8.73963	−0.464506
$355$	−14.6172	−0.775800
$356$	0.966416	0.0512199
$357$	0	0
$358$	−6.22809	−0.329165
$359$	−28.2418	−1.49055	−0.745273	−	0.666759i	$-0.767681\pi$
$359$	−28.2418	−1.49055	−0.745273	+	0.666759i	$0.767681\pi$
$360$	−9.28423	−0.489322
$361$	19.4095	1.02155
$362$	3.02998	0.159252
$363$	−22.0006	−1.15473
$364$	1.71739	0.0900157
$365$	−5.60532	−0.293396
$366$	38.6956	2.02265
$367$	18.8125	0.982004	0.491002	−	0.871158i	$-0.336631\pi$
$367$	18.8125	0.982004	0.491002	+	0.871158i	$0.336631\pi$
$368$	−3.17316	−0.165412
$369$	−0.792374	−0.0412493
$370$	−7.30479	−0.379758
$371$	−4.07940	−0.211792
$372$	7.35527	0.381353
$373$	30.9655	1.60333	0.801666	−	0.597772i	$-0.203947\pi$
$373$	30.9655	1.60333	0.801666	+	0.597772i	$0.203947\pi$
$374$	0	0
$375$	10.5308	0.543809
$376$	−10.3922	−0.535936
$377$	−20.3448	−1.04781
$378$	5.95433	0.306258
$379$	12.4504	0.639533	0.319766	−	0.947496i	$-0.396396\pi$
$379$	12.4504	0.639533	0.319766	+	0.947496i	$0.396396\pi$
$380$	−9.93278	−0.509541
$381$	−10.4338	−0.534537
$382$	−39.5787	−2.02502
$383$	−29.8457	−1.52505	−0.762523	−	0.646961i	$-0.776040\pi$
$383$	−29.8457	−1.52505	−0.762523	+	0.646961i	$0.776040\pi$
$384$	27.6876	1.41293
$385$	−15.8560	−0.808095
$386$	−17.6831	−0.900047
$387$	7.56153	0.384374
$388$	1.99705	0.101385
$389$	20.9404	1.06172	0.530861	−	0.847459i	$-0.321869\pi$
$389$	20.9404	1.06172	0.530861	+	0.847459i	$0.321869\pi$
$390$	39.5005	2.00019
$391$	0	0
$392$	2.40230	0.121335
$393$	16.9935	0.857208
$394$	−35.5847	−1.79273
$395$	−33.9644	−1.70893
$396$	−2.51021	−0.126143
$397$	−28.3607	−1.42338	−0.711692	−	0.702492i	$-0.752071\pi$
$397$	−28.3607	−1.42338	−0.711692	+	0.702492i	$0.752071\pi$
$398$	−8.25367	−0.413719
$399$	12.6077	0.631175
$400$	−30.8059	−1.54030
$401$	−3.26883	−0.163237	−0.0816187	−	0.996664i	$-0.526009\pi$
$401$	−3.26883	−0.163237	−0.0816187	+	0.996664i	$0.526009\pi$
$402$	40.1704	2.00352
$403$	27.8601	1.38781
$404$	−2.54239	−0.126489
$405$	37.7480	1.87571
$406$	8.79330	0.436404
$407$	6.39193	0.316836
$408$	0	0
$409$	−34.3864	−1.70030	−0.850149	−	0.526542i	$-0.823488\pi$
$409$	−34.3864	−1.70030	−0.850149	+	0.526542i	$0.823488\pi$
$410$	−3.71518	−0.183480
$411$	41.0805	2.02635
$412$	−1.87072	−0.0921638
$413$	2.73239	0.134452
$414$	−1.20299	−0.0591237
$415$	15.9272	0.781834
$416$	−9.52617	−0.467059
$417$	−15.8780	−0.777550
$418$	45.5121	2.22607
$419$	−17.5177	−0.855797	−0.427899	−	0.903827i	$-0.640746\pi$
$419$	−17.5177	−0.855797	−0.427899	+	0.903827i	$0.640746\pi$
$420$	−3.26038	−0.159090
$421$	13.1028	0.638593	0.319296	−	0.947655i	$-0.396553\pi$
$421$	13.1028	0.638593	0.319296	+	0.947655i	$0.396553\pi$
$422$	−15.2940	−0.744500
$423$	−4.92469	−0.239447
$424$	9.79997	0.475929
$425$	0	0
$426$	13.7720	0.667254
$427$	−12.0980	−0.585461
$428$	−5.37240	−0.259685
$429$	−34.5643	−1.66878
$430$	35.4536	1.70972
$431$	26.2828	1.26600	0.633000	−	0.774152i	$-0.281823\pi$
$431$	26.2828	1.26600	0.633000	+	0.774152i	$0.281823\pi$
$432$	−17.8798	−0.860244
$433$	0.783681	0.0376613	0.0188307	−	0.999823i	$-0.494006\pi$
$433$	0.783681	0.0376613	0.0188307	+	0.999823i	$0.494006\pi$
$434$	−12.0415	−0.578011
$435$	38.6237	1.85186
$436$	2.07997	0.0996126
$437$	4.16531	0.199254
$438$	5.28120	0.252346
$439$	25.1540	1.20054	0.600268	−	0.799799i	$-0.295060\pi$
$439$	25.1540	1.20054	0.600268	+	0.799799i	$0.295060\pi$
$440$	38.0909	1.81591
$441$	1.13841	0.0542102
$442$	0	0
$443$	−12.1317	−0.576395	−0.288197	−	0.957571i	$-0.593056\pi$
$443$	−12.1317	−0.576395	−0.288197	+	0.957571i	$0.593056\pi$
$444$	1.31434	0.0623758
$445$	−6.94941	−0.329434
$446$	−27.5840	−1.30614
$447$	1.36417	0.0645229
$448$	−5.32531	−0.251597
$449$	−37.0044	−1.74635	−0.873174	−	0.487409i	$-0.837942\pi$
$449$	−37.0044	−1.74635	−0.873174	+	0.487409i	$0.837942\pi$
$450$	−11.6790	−0.550551
$451$	3.25091	0.153079
$452$	−5.47501	−0.257523
$453$	23.2393	1.09188
$454$	13.1186	0.615685
$455$	−12.3496	−0.578958
$456$	−30.2876	−1.41834
$457$	−12.7879	−0.598192	−0.299096	−	0.954223i	$-0.596685\pi$
$457$	−12.7879	−0.598192	−0.299096	+	0.954223i	$0.596685\pi$
$458$	−24.1257	−1.12732
$459$	0	0
$460$	−1.07716	−0.0502228
$461$	4.58089	0.213353	0.106677	−	0.994294i	$-0.465979\pi$
$461$	4.58089	0.213353	0.106677	+	0.994294i	$0.465979\pi$
$462$	14.9391	0.695031
$463$	1.53844	0.0714973	0.0357486	−	0.999361i	$-0.488618\pi$
$463$	1.53844	0.0714973	0.0357486	+	0.999361i	$0.488618\pi$
$464$	−26.4048	−1.22581
$465$	−52.8911	−2.45277
$466$	38.4856	1.78281
$467$	−11.0027	−0.509143	−0.254572	−	0.967054i	$-0.581934\pi$
$467$	−11.0027	−0.509143	−0.254572	+	0.967054i	$0.581934\pi$
$468$	−1.95510	−0.0903746
$469$	−12.5590	−0.579922
$470$	−23.0903	−1.06508
$471$	47.5686	2.19185
$472$	−6.56404	−0.302134
$473$	−31.0230	−1.42644
$474$	32.0004	1.46983
$475$	40.4380	1.85542
$476$	0	0
$477$	4.64405	0.212637
$478$	−22.9195	−1.04831
$479$	23.2619	1.06286	0.531432	−	0.847101i	$-0.321654\pi$
$479$	23.2619	1.06286	0.531432	+	0.847101i	$0.321654\pi$
$480$	18.0850	0.825462
$481$	4.97843	0.226997
$482$	23.9230	1.08966
$483$	1.36724	0.0622117
$484$	5.10564	0.232075
$485$	−14.3606	−0.652080
$486$	−17.7022	−0.802990
$487$	22.0360	0.998547	0.499273	−	0.866444i	$-0.333600\pi$
$487$	22.0360	0.998547	0.499273	+	0.866444i	$0.333600\pi$
$488$	29.0630	1.31562
$489$	24.5684	1.11102
$490$	5.33766	0.241131
$491$	19.2671	0.869512	0.434756	−	0.900548i	$-0.356835\pi$
$491$	19.2671	0.869512	0.434756	+	0.900548i	$0.356835\pi$
$492$	0.668468	0.0301369
$493$	0	0
$494$	35.4476	1.59486
$495$	18.0507	0.811317
$496$	36.1586	1.62357
$497$	−4.30572	−0.193138
$498$	−15.0062	−0.672444
$499$	42.3615	1.89636	0.948180	−	0.317733i	$-0.102922\pi$
$499$	42.3615	1.89636	0.948180	+	0.317733i	$0.102922\pi$
$500$	−2.44388	−0.109293
$501$	49.9099	2.22981
$502$	2.42184	0.108092
$503$	11.1668	0.497904	0.248952	−	0.968516i	$-0.419914\pi$
$503$	11.1668	0.497904	0.248952	+	0.968516i	$0.419914\pi$
$504$	−2.73482	−0.121818
$505$	18.2821	0.813543
$506$	4.93556	0.219412
$507$	−0.474736	−0.0210838
$508$	2.42135	0.107430
$509$	−33.7960	−1.49798	−0.748991	−	0.662580i	$-0.769462\pi$
$509$	−33.7960	−1.49798	−0.748991	+	0.662580i	$0.769462\pi$
$510$	0	0
$511$	−1.65114	−0.0730420
$512$	10.3205	0.456104
$513$	23.4703	1.03624
$514$	−6.33513	−0.279430
$515$	13.4522	0.592774
$516$	−6.37911	−0.280825
$517$	20.2048	0.888604
$518$	−2.15174	−0.0945420
$519$	−7.25281	−0.318363
$520$	29.6675	1.30101
$521$	14.8212	0.649329	0.324664	−	0.945829i	$-0.394749\pi$
$521$	14.8212	0.649329	0.324664	+	0.945829i	$0.394749\pi$
$522$	−10.0104	−0.438144
$523$	2.75940	0.120660	0.0603300	−	0.998178i	$-0.480785\pi$
$523$	2.75940	0.120660	0.0603300	+	0.998178i	$0.480785\pi$
$524$	−3.94366	−0.172280
$525$	13.2736	0.579306
$526$	−28.2605	−1.23221
$527$	0	0
$528$	−44.8596	−1.95226
$529$	−22.5483	−0.980361
$530$	21.7745	0.945822
$531$	−3.11059	−0.134988
$532$	−2.92586	−0.126852
$533$	2.53201	0.109673
$534$	6.54757	0.283341
$535$	38.6325	1.67023
$536$	30.1706	1.30317
$537$	−8.05821	−0.347738
$538$	−28.3510	−1.22230
$539$	−4.67063	−0.201178
$540$	−6.06948	−0.261189
$541$	11.1546	0.479574	0.239787	−	0.970825i	$-0.422922\pi$
$541$	11.1546	0.479574	0.239787	+	0.970825i	$0.422922\pi$
$542$	−26.2698	−1.12839
$543$	3.92034	0.168238
$544$	0	0
$545$	−14.9569	−0.640683
$546$	11.6355	0.497954
$547$	7.31331	0.312694	0.156347	−	0.987702i	$-0.450028\pi$
$547$	7.31331	0.312694	0.156347	+	0.987702i	$0.450028\pi$
$548$	−9.53351	−0.407252
$549$	13.7725	0.587795
$550$	47.9158	2.04314
$551$	34.6608	1.47660
$552$	−3.28453	−0.139799
$553$	−10.0047	−0.425445
$554$	−1.64084	−0.0697125
$555$	−9.45130	−0.401185
$556$	3.68479	0.156270
$557$	−15.3543	−0.650583	−0.325291	−	0.945614i	$-0.605462\pi$
$557$	−15.3543	−0.650583	−0.325291	+	0.945614i	$0.605462\pi$
$558$	13.7082	0.580315
$559$	−24.1626	−1.02197
$560$	−16.0281	−0.677310
$561$	0	0
$562$	5.55076	0.234145
$563$	6.62599	0.279252	0.139626	−	0.990204i	$-0.455410\pi$
$563$	6.62599	0.279252	0.139626	+	0.990204i	$0.455410\pi$
$564$	4.15460	0.174940
$565$	39.3703	1.65632
$566$	2.86703	0.120510
$567$	11.1193	0.466965
$568$	10.3437	0.434010
$569$	−36.9677	−1.54977	−0.774883	−	0.632105i	$-0.782191\pi$
$569$	−36.9677	−1.54977	−0.774883	+	0.632105i	$0.782191\pi$
$570$	−67.2956	−2.81870
$571$	36.5860	1.53108	0.765539	−	0.643390i	$-0.222472\pi$
$571$	36.5860	1.53108	0.765539	+	0.643390i	$0.222472\pi$
$572$	8.02129	0.335387
$573$	−51.2089	−2.13928
$574$	−1.09437	−0.0456780
$575$	4.38530	0.182880
$576$	6.06241	0.252600
$577$	6.70916	0.279306	0.139653	−	0.990200i	$-0.455401\pi$
$577$	6.70916	0.279306	0.139653	+	0.990200i	$0.455401\pi$
$578$	0	0
$579$	−22.8793	−0.950832
$580$	−8.96335	−0.372183
$581$	4.69160	0.194640
$582$	13.5302	0.560845
$583$	−19.0534	−0.789110
$584$	3.96653	0.164136
$585$	14.0590	0.581266
$586$	23.5191	0.971564
$587$	−0.653601	−0.0269770	−0.0134885	−	0.999909i	$-0.504294\pi$
$587$	−0.653601	−0.0269770	−0.0134885	+	0.999909i	$0.504294\pi$
$588$	−0.960397	−0.0396061
$589$	−47.4643	−1.95573
$590$	−14.5846	−0.600437
$591$	−46.0412	−1.89388
$592$	6.46131	0.265558
$593$	−27.7090	−1.13787	−0.568937	−	0.822381i	$-0.692645\pi$
$593$	−27.7090	−1.13787	−0.568937	+	0.822381i	$0.692645\pi$
$594$	27.8105	1.14108
$595$	0	0
$596$	−0.316581	−0.0129677
$597$	−10.6790	−0.437063
$598$	3.84412	0.157198
$599$	7.54536	0.308295	0.154148	−	0.988048i	$-0.450737\pi$
$599$	7.54536	0.308295	0.154148	+	0.988048i	$0.450737\pi$
$600$	−31.8871	−1.30179
$601$	18.2058	0.742631	0.371315	−	0.928507i	$-0.378907\pi$
$601$	18.2058	0.742631	0.371315	+	0.928507i	$0.378907\pi$
$602$	10.4434	0.425641
$603$	14.2974	0.582234
$604$	−5.39311	−0.219442
$605$	−36.7142	−1.49265
$606$	−17.2250	−0.699717
$607$	12.2293	0.496372	0.248186	−	0.968712i	$-0.420166\pi$
$607$	12.2293	0.496372	0.248186	+	0.968712i	$0.420166\pi$
$608$	16.2294	0.658189
$609$	11.3772	0.461028
$610$	64.5748	2.61456
$611$	15.7367	0.636639
$612$	0	0
$613$	−39.4099	−1.59175	−0.795876	−	0.605460i	$-0.792989\pi$
$613$	−39.4099	−1.59175	−0.795876	+	0.605460i	$0.792989\pi$
$614$	11.2640	0.454580
$615$	−4.80689	−0.193833
$616$	11.2203	0.452077
$617$	−14.7279	−0.592923	−0.296461	−	0.955045i	$-0.595807\pi$
$617$	−14.7279	−0.592923	−0.296461	+	0.955045i	$0.595807\pi$
$618$	−12.6743	−0.509836
$619$	−36.9936	−1.48690	−0.743449	−	0.668792i	$-0.766812\pi$
$619$	−36.9936	−1.48690	−0.743449	+	0.668792i	$0.766812\pi$
$620$	12.2744	0.492951
$621$	2.54524	0.102137
$622$	−9.89676	−0.396824
$623$	−2.04706	−0.0820136
$624$	−34.9394	−1.39870
$625$	−15.0506	−0.602023
$626$	49.3258	1.97146
$627$	58.8859	2.35168
$628$	−11.0392	−0.440512
$629$	0	0
$630$	−6.07647	−0.242092
$631$	−31.7794	−1.26512	−0.632559	−	0.774512i	$-0.717996\pi$
$631$	−31.7794	−1.26512	−0.632559	+	0.774512i	$0.717996\pi$
$632$	24.0344	0.956039
$633$	−19.7881	−0.786508
$634$	−26.0458	−1.03441
$635$	−17.4117	−0.690962
$636$	−3.91785	−0.155353
$637$	−3.63777	−0.144134
$638$	41.0702	1.62599
$639$	4.90170	0.193908
$640$	46.2046	1.82640
$641$	18.9527	0.748587	0.374294	−	0.927310i	$-0.377885\pi$
$641$	18.9527	0.748587	0.374294	+	0.927310i	$0.377885\pi$
$642$	−36.3986	−1.43654
$643$	−26.9549	−1.06300	−0.531498	−	0.847059i	$-0.678371\pi$
$643$	−26.9549	−1.06300	−0.531498	+	0.847059i	$0.678371\pi$
$644$	−0.317294	−0.0125031
$645$	45.8716	1.80619
$646$	0	0
$647$	0.816139	0.0320858	0.0160429	−	0.999871i	$-0.494893\pi$
$647$	0.816139	0.0320858	0.0160429	+	0.999871i	$0.494893\pi$
$648$	−26.7118	−1.04934
$649$	12.7620	0.500952
$650$	37.3198	1.46380
$651$	−15.5799	−0.610625
$652$	−5.70156	−0.223290
$653$	−26.5153	−1.03762	−0.518812	−	0.854888i	$-0.673626\pi$
$653$	−26.5153	−1.03762	−0.518812	+	0.854888i	$0.673626\pi$
$654$	14.0920	0.551042
$655$	28.3585	1.10806
$656$	3.28619	0.128304
$657$	1.87968	0.0733332
$658$	−6.80161	−0.265154
$659$	15.6995	0.611566	0.305783	−	0.952101i	$-0.401082\pi$
$659$	15.6995	0.611566	0.305783	+	0.952101i	$0.401082\pi$
$660$	−15.2280	−0.592750
$661$	15.5120	0.603348	0.301674	−	0.953411i	$-0.402455\pi$
$661$	15.5120	0.603348	0.301674	+	0.953411i	$0.402455\pi$
$662$	−7.44156	−0.289224
$663$	0	0
$664$	−11.2707	−0.437386
$665$	21.0396	0.815880
$666$	2.44957	0.0949190
$667$	3.75878	0.145541
$668$	−11.5825	−0.448141
$669$	−35.6896	−1.37984
$670$	67.0358	2.58982
$671$	−56.5050	−2.18135
$672$	5.32721	0.205502
$673$	−36.3666	−1.40183	−0.700915	−	0.713245i	$-0.747225\pi$
$673$	−36.3666	−1.40183	−0.700915	+	0.713245i	$0.747225\pi$
$674$	−37.9167	−1.46050
$675$	24.7099	0.951084
$676$	0.110171	0.00423736
$677$	−28.6632	−1.10161	−0.550807	−	0.834632i	$-0.685680\pi$
$677$	−28.6632	−1.10161	−0.550807	+	0.834632i	$0.685680\pi$
$678$	−37.0938	−1.42458
$679$	−4.23013	−0.162338
$680$	0	0
$681$	16.9735	0.650425
$682$	−56.2414	−2.15359
$683$	19.7800	0.756860	0.378430	−	0.925630i	$-0.376464\pi$
$683$	19.7800	0.756860	0.378430	+	0.925630i	$0.376464\pi$
$684$	3.33084	0.127358
$685$	68.5546	2.61934
$686$	1.57229	0.0600304
$687$	−31.2150	−1.19093
$688$	−31.3598	−1.19558
$689$	−14.8399	−0.565356
$690$	−7.29787	−0.277825
$691$	37.6955	1.43400	0.717002	−	0.697071i	$-0.245514\pi$
$691$	37.6955	1.43400	0.717002	+	0.697071i	$0.245514\pi$
$692$	1.68315	0.0639838
$693$	5.31711	0.201980
$694$	−36.0151	−1.36712
$695$	−26.4970	−1.00509
$696$	−27.3315	−1.03600
$697$	0	0
$698$	16.0212	0.606410
$699$	49.7946	1.88341
$700$	−3.08038	−0.116427
$701$	−12.4612	−0.470652	−0.235326	−	0.971916i	$-0.575616\pi$
$701$	−12.4612	−0.470652	−0.235326	+	0.971916i	$0.575616\pi$
$702$	21.6605	0.817522
$703$	−8.48157	−0.319888
$704$	−24.8725	−0.937419
$705$	−29.8754	−1.12517
$706$	−26.4143	−0.994116
$707$	5.38529	0.202535
$708$	2.62418	0.0986228
$709$	14.4389	0.542265	0.271133	−	0.962542i	$-0.412602\pi$
$709$	14.4389	0.542265	0.271133	+	0.962542i	$0.412602\pi$
$710$	22.9825	0.862517
$711$	11.3895	0.427141
$712$	4.91766	0.184297
$713$	−5.14726	−0.192766
$714$	0	0
$715$	−57.6804	−2.15712
$716$	1.87006	0.0698874
$717$	−29.6544	−1.10746
$718$	44.4044	1.65716
$719$	9.25058	0.344989	0.172494	−	0.985011i	$-0.444817\pi$
$719$	9.25058	0.344989	0.172494	+	0.985011i	$0.444817\pi$
$720$	18.2466	0.680010
$721$	3.96255	0.147573
$722$	−30.5173	−1.13574
$723$	30.9528	1.15115
$724$	−0.909788	−0.0338120
$725$	36.4913	1.35525
$726$	34.5913	1.28380
$727$	−33.0618	−1.22619	−0.613096	−	0.790008i	$-0.710076\pi$
$727$	−33.0618	−1.22619	−0.613096	+	0.790008i	$0.710076\pi$
$728$	8.73903	0.323890
$729$	10.4537	0.387175
$730$	8.81320	0.326191
$731$	0	0
$732$	−11.6188	−0.429445
$733$	−1.81758	−0.0671338	−0.0335669	−	0.999436i	$-0.510687\pi$
$733$	−1.81758	−0.0671338	−0.0335669	+	0.999436i	$0.510687\pi$
$734$	−29.5787	−1.09177
$735$	6.90613	0.254736
$736$	1.76000	0.0648743
$737$	−58.6585	−2.16072
$738$	1.24584	0.0458601
$739$	−30.1602	−1.10946	−0.554730	−	0.832031i	$-0.687178\pi$
$739$	−30.1602	−1.10946	−0.554730	+	0.832031i	$0.687178\pi$
$740$	2.19335	0.0806292
$741$	45.8639	1.68485
$742$	6.41401	0.235466
$743$	−39.6582	−1.45492	−0.727458	−	0.686152i	$-0.759299\pi$
$743$	−39.6582	−1.45492	−0.727458	+	0.686152i	$0.759299\pi$
$744$	37.4277	1.37216
$745$	2.27650	0.0834046
$746$	−48.6867	−1.78255
$747$	−5.34098	−0.195416
$748$	0	0
$749$	11.3798	0.415809
$750$	−16.5575	−0.604595
$751$	−41.8308	−1.52643	−0.763214	−	0.646145i	$-0.776380\pi$
$751$	−41.8308	−1.52643	−0.763214	+	0.646145i	$0.776380\pi$
$752$	20.4241	0.744789
$753$	3.13350	0.114191
$754$	31.9880	1.16493
$755$	38.7813	1.41140
$756$	−1.78786	−0.0650239
$757$	29.9024	1.08682	0.543411	−	0.839467i	$-0.317133\pi$
$757$	29.9024	1.08682	0.543411	+	0.839467i	$0.317133\pi$
$758$	−19.5756	−0.711019
$759$	6.38588	0.231793
$760$	−50.5434	−1.83340
$761$	29.8807	1.08318	0.541588	−	0.840644i	$-0.317823\pi$
$761$	29.8807	1.08318	0.541588	+	0.840644i	$0.317823\pi$
$762$	16.4049	0.594287
$763$	−4.40579	−0.159500
$764$	11.8840	0.429948
$765$	0	0
$766$	46.9262	1.69551
$767$	9.93981	0.358906
$768$	−21.8663	−0.789031
$769$	−35.8821	−1.29394	−0.646971	−	0.762514i	$-0.723965\pi$
$769$	−35.8821	−1.29394	−0.646971	+	0.762514i	$0.723965\pi$
$770$	24.9302	0.898422
$771$	−8.19670	−0.295197
$772$	5.30957	0.191096
$773$	13.1964	0.474642	0.237321	−	0.971431i	$-0.423731\pi$
$773$	13.1964	0.474642	0.237321	+	0.971431i	$0.423731\pi$
$774$	−11.8889	−0.427338
$775$	−49.9710	−1.79501
$776$	10.1621	0.364797
$777$	−2.78403	−0.0998765
$778$	−32.9245	−1.18040
$779$	−4.31369	−0.154554
$780$	−11.8605	−0.424675
$781$	−20.1104	−0.719608
$782$	0	0
$783$	21.1797	0.756899
$784$	−4.72132	−0.168619
$785$	79.3818	2.83326
$786$	−26.7187	−0.953025
$787$	−28.6967	−1.02293	−0.511463	−	0.859305i	$-0.670896\pi$
$787$	−28.6967	−1.02293	−0.511463	+	0.859305i	$0.670896\pi$
$788$	10.6847	0.380628
$789$	−36.5648	−1.30174
$790$	53.4019	1.89995
$791$	11.5971	0.412347
$792$	−12.7733	−0.453880
$793$	−44.0096	−1.56283
$794$	44.5913	1.58249
$795$	28.1729	0.999189
$796$	2.47826	0.0878398
$797$	−10.8120	−0.382980	−0.191490	−	0.981495i	$-0.561332\pi$
$797$	−10.8120	−0.382980	−0.191490	+	0.981495i	$0.561332\pi$
$798$	−19.8230	−0.701726
$799$	0	0
$800$	17.0865	0.604100
$801$	2.33040	0.0823406
$802$	5.13955	0.181484
$803$	−7.71184	−0.272145
$804$	−12.0617	−0.425382
$805$	2.28163	0.0804170
$806$	−43.8042	−1.54294
$807$	−36.6820	−1.29127
$808$	−12.9371	−0.455125
$809$	−50.9884	−1.79266	−0.896329	−	0.443390i	$-0.853776\pi$
$809$	−50.9884	−1.79266	−0.896329	+	0.443390i	$0.853776\pi$
$810$	−59.3508	−2.08537
$811$	−15.3571	−0.539261	−0.269631	−	0.962964i	$-0.586902\pi$
$811$	−15.3571	−0.539261	−0.269631	+	0.962964i	$0.586902\pi$
$812$	−2.64030	−0.0926562
$813$	−33.9892	−1.19205
$814$	−10.0500	−0.352251
$815$	40.9994	1.43615
$816$	0	0
$817$	41.1650	1.44018
$818$	54.0654	1.89035
$819$	4.14129	0.144708
$820$	1.11553	0.0389560
$821$	−13.9352	−0.486341	−0.243170	−	0.969984i	$-0.578187\pi$
$821$	−13.9352	−0.486341	−0.243170	+	0.969984i	$0.578187\pi$
$822$	−64.5906	−2.25286
$823$	−12.2744	−0.427860	−0.213930	−	0.976849i	$-0.568627\pi$
$823$	−12.2744	−0.427860	−0.213930	+	0.976849i	$0.568627\pi$
$824$	−9.51926	−0.331619
$825$	61.9959	2.15842
$826$	−4.29612	−0.149481
$827$	16.7624	0.582885	0.291443	−	0.956588i	$-0.405865\pi$
$827$	16.7624	0.582885	0.291443	+	0.956588i	$0.405865\pi$
$828$	0.361212	0.0125530
$829$	43.4266	1.50827	0.754134	−	0.656721i	$-0.228057\pi$
$829$	43.4266	1.50827	0.754134	+	0.656721i	$0.228057\pi$
$830$	−25.0422	−0.869226
$831$	−2.12300	−0.0736459
$832$	−19.3722	−0.671612
$833$	0	0
$834$	24.9649	0.864463
$835$	83.2889	2.88233
$836$	−13.6656	−0.472634
$837$	−29.0033	−1.00250
$838$	27.5430	0.951456
$839$	5.94274	0.205166	0.102583	−	0.994724i	$-0.467289\pi$
$839$	5.94274	0.205166	0.102583	+	0.994724i	$0.467289\pi$
$840$	−16.5906	−0.572431
$841$	2.27792	0.0785488
$842$	−20.6015	−0.709973
$843$	7.18185	0.247356
$844$	4.59221	0.158070
$845$	−0.792233	−0.0272536
$846$	7.74305	0.266211
$847$	−10.8148	−0.371599
$848$	−19.2602	−0.661397
$849$	3.70950	0.127310
$850$	0	0
$851$	−0.919783	−0.0315297
$852$	−4.13521	−0.141670
$853$	−12.9874	−0.444680	−0.222340	−	0.974969i	$-0.571370\pi$
$853$	−12.9874	−0.444680	−0.222340	+	0.974969i	$0.571370\pi$
$854$	19.0215	0.650903
$855$	−23.9517	−0.819132
$856$	−27.3377	−0.934385
$857$	28.7933	0.983562	0.491781	−	0.870719i	$-0.336346\pi$
$857$	28.7933	0.983562	0.491781	+	0.870719i	$0.336346\pi$
$858$	54.3451	1.85531
$859$	8.24733	0.281395	0.140698	−	0.990053i	$-0.455065\pi$
$859$	8.24733	0.281395	0.140698	+	0.990053i	$0.455065\pi$
$860$	−10.6454	−0.363004
$861$	−1.41595	−0.0482553
$862$	−41.3243	−1.40751
$863$	35.6828	1.21466	0.607329	−	0.794450i	$-0.292241\pi$
$863$	35.6828	1.21466	0.607329	+	0.794450i	$0.292241\pi$
$864$	9.91706	0.337385
$865$	−12.1034	−0.411527
$866$	−1.23218	−0.0418710
$867$	0	0
$868$	3.61561	0.122722
$869$	−46.7284	−1.58515
$870$	−60.7277	−2.05886
$871$	−45.6869	−1.54804
$872$	10.5840	0.358421
$873$	4.81565	0.162985
$874$	−6.54908	−0.221526
$875$	5.17661	0.175001
$876$	−1.58575	−0.0535774
$877$	14.0735	0.475229	0.237615	−	0.971359i	$-0.423634\pi$
$877$	14.0735	0.475229	0.237615	+	0.971359i	$0.423634\pi$
$878$	−39.5495	−1.33473
$879$	30.4302	1.02638
$880$	−74.8611	−2.52357
$881$	14.7720	0.497682	0.248841	−	0.968544i	$-0.419950\pi$
$881$	14.7720	0.497682	0.248841	+	0.968544i	$0.419950\pi$
$882$	−1.78992	−0.0602697
$883$	4.72305	0.158943	0.0794717	−	0.996837i	$-0.474677\pi$
$883$	4.72305	0.158943	0.0794717	+	0.996837i	$0.474677\pi$
$884$	0	0
$885$	−18.8703	−0.634317
$886$	19.0746	0.640823
$887$	−45.1201	−1.51498	−0.757492	−	0.652844i	$-0.773576\pi$
$887$	−45.1201	−1.51498	−0.757492	+	0.652844i	$0.773576\pi$
$888$	6.68809	0.224437
$889$	−5.12889	−0.172017
$890$	10.9265	0.366257
$891$	51.9339	1.73985
$892$	8.28245	0.277317
$893$	−26.8101	−0.897164
$894$	−2.14487	−0.0717351
$895$	−13.4474	−0.449498
$896$	13.6103	0.454688
$897$	4.97371	0.166067
$898$	58.1818	1.94155
$899$	−42.8318	−1.42852
$900$	3.50675	0.116892
$901$	0	0
$902$	−5.11138	−0.170190
$903$	13.5122	0.449658
$904$	−27.8599	−0.926605
$905$	6.54220	0.217470
$906$	−36.5389	−1.21392
$907$	33.8698	1.12463	0.562314	−	0.826924i	$-0.309911\pi$
$907$	33.8698	1.12463	0.562314	+	0.826924i	$0.309911\pi$
$908$	−3.93902	−0.130721
$909$	−6.13069	−0.203342
$910$	19.4172	0.643673
$911$	−10.1357	−0.335812	−0.167906	−	0.985803i	$-0.553700\pi$
$911$	−10.1357	−0.335812	−0.167906	+	0.985803i	$0.553700\pi$
$912$	59.5250	1.97107
$913$	21.9127	0.725205
$914$	20.1063	0.665057
$915$	83.5501	2.76208
$916$	7.24404	0.239350
$917$	8.35345	0.275855
$918$	0	0
$919$	−7.90071	−0.260620	−0.130310	−	0.991473i	$-0.541597\pi$
$919$	−7.90071	−0.260620	−0.130310	+	0.991473i	$0.541597\pi$
$920$	−5.48118	−0.180709
$921$	14.5740	0.480229
$922$	−7.20249	−0.237201
$923$	−15.6632	−0.515562
$924$	−4.48566	−0.147567
$925$	−8.92951	−0.293600
$926$	−2.41887	−0.0794891
$927$	−4.51103	−0.148162
$928$	14.6454	0.480760
$929$	−9.15950	−0.300513	−0.150257	−	0.988647i	$-0.548010\pi$
$929$	−9.15950	−0.300513	−0.150257	+	0.988647i	$0.548010\pi$
$930$	83.1602	2.72693
$931$	6.19754	0.203116
$932$	−11.5558	−0.378522
$933$	−12.8049	−0.419214
$934$	17.2994	0.566054
$935$	0	0
$936$	−9.94863	−0.325181
$937$	−53.4400	−1.74581	−0.872905	−	0.487891i	$-0.837766\pi$
$937$	−53.4400	−1.74581	−0.872905	+	0.487891i	$0.837766\pi$
$938$	19.7465	0.644745
$939$	63.8202	2.08269
$940$	6.93314	0.226134
$941$	50.1457	1.63470	0.817351	−	0.576140i	$-0.195442\pi$
$941$	50.1457	1.63470	0.817351	+	0.576140i	$0.195442\pi$
$942$	−74.7917	−2.43685
$943$	−0.467798	−0.0152336
$944$	12.9005	0.419876
$945$	12.8564	0.418217
$946$	48.7772	1.58589
$947$	14.6734	0.476823	0.238411	−	0.971164i	$-0.423373\pi$
$947$	14.6734	0.476823	0.238411	+	0.971164i	$0.423373\pi$
$948$	−9.60853	−0.312070
$949$	−6.00645	−0.194978
$950$	−63.5803	−2.06282
$951$	−33.6993	−1.09278
$952$	0	0
$953$	−4.66197	−0.151016	−0.0755080	−	0.997145i	$-0.524058\pi$
$953$	−4.66197	−0.151016	−0.0755080	+	0.997145i	$0.524058\pi$
$954$	−7.30180	−0.236405
$955$	−85.4567	−2.76532
$956$	6.88186	0.222575
$957$	53.1387	1.71773
$958$	−36.5745	−1.18167
$959$	20.1939	0.652093
$960$	36.7773	1.18698
$961$	27.6537	0.892056
$962$	−7.82753	−0.252370
$963$	−12.9549	−0.417467
$964$	−7.18317	−0.231354
$965$	−38.1807	−1.22908
$966$	−2.14970	−0.0691655
$967$	−15.2606	−0.490748	−0.245374	−	0.969428i	$-0.578911\pi$
$967$	−15.2606	−0.490748	−0.245374	+	0.969428i	$0.578911\pi$
$968$	25.9803	0.835039
$969$	0	0
$970$	22.5790	0.724968
$971$	18.5971	0.596810	0.298405	−	0.954439i	$-0.403545\pi$
$971$	18.5971	0.596810	0.298405	+	0.954439i	$0.403545\pi$
$972$	5.31532	0.170489
$973$	−7.80511	−0.250220
$974$	−34.6470	−1.11016
$975$	48.2862	1.54640
$976$	−57.1183	−1.82831
$977$	21.7450	0.695683	0.347842	−	0.937553i	$-0.386915\pi$
$977$	21.7450	0.695683	0.347842	+	0.937553i	$0.386915\pi$
$978$	−38.6287	−1.23521
$979$	−9.56104	−0.305572
$980$	−1.60270	−0.0511963
$981$	5.01561	0.160136
$982$	−30.2935	−0.966704
$983$	−3.57168	−0.113919	−0.0569595	−	0.998376i	$-0.518141\pi$
$983$	−3.57168	−0.113919	−0.0569595	+	0.998376i	$0.518141\pi$
$984$	3.40153	0.108437
$985$	−76.8329	−2.44810
$986$	0	0
$987$	−8.80026	−0.280115
$988$	−10.6436	−0.338618
$989$	4.46414	0.141951
$990$	−28.3809	−0.902004
$991$	0.424339	0.0134796	0.00673979	−	0.999977i	$-0.497855\pi$
$991$	0.424339	0.0134796	0.00673979	+	0.999977i	$0.497855\pi$
$992$	−20.0554	−0.636759
$993$	−9.62826	−0.305544
$994$	6.76985	0.214727
$995$	−17.8210	−0.564963
$996$	4.50580	0.142772
$997$	−37.4388	−1.18570	−0.592850	−	0.805313i	$-0.701997\pi$
$997$	−37.4388	−1.18570	−0.592850	+	0.805313i	$0.701997\pi$
$998$	−66.6046	−2.10833
$999$	−5.18271	−0.163974

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2023.2.a.m.1.3		10
17.2	even	8		119.2.g.a.106.3	yes	20
17.9	even	8		119.2.g.a.64.8	✓	20
17.16	even	2		2023.2.a.n.1.3		10
51.2	odd	8		1071.2.n.c.820.8		20
51.26	odd	8		1071.2.n.c.64.3		20
119.2	even	24		833.2.o.g.361.3		40
119.9	even	24		833.2.o.g.557.8		40
119.19	odd	24		833.2.o.f.361.3		40
119.26	odd	24		833.2.o.f.557.8		40
119.53	even	24		833.2.o.g.667.8		40
119.60	even	24		833.2.o.g.30.3		40
119.87	odd	24		833.2.o.f.667.8		40
119.94	odd	24		833.2.o.f.30.3		40
119.104	odd	8		833.2.g.h.344.3		20
119.111	odd	8		833.2.g.h.540.8		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
119.2.g.a.64.8	✓	20	17.9	even	8
119.2.g.a.106.3	yes	20	17.2	even	8
833.2.g.h.344.3		20	119.104	odd	8
833.2.g.h.540.8		20	119.111	odd	8
833.2.o.f.30.3		40	119.94	odd	24
833.2.o.f.361.3		40	119.19	odd	24
833.2.o.f.557.8		40	119.26	odd	24
833.2.o.f.667.8		40	119.87	odd	24
833.2.o.g.30.3		40	119.60	even	24
833.2.o.g.361.3		40	119.2	even	24
833.2.o.g.557.8		40	119.9	even	24
833.2.o.g.667.8		40	119.53	even	24
1071.2.n.c.64.3		20	51.26	odd	8
1071.2.n.c.820.8		20	51.2	odd	8
2023.2.a.m.1.3		10	1.1	even	1	trivial
2023.2.a.n.1.3		10	17.16	even	2

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:	\( N \)	\(=\)	\( 2023 = 7 \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2023.a (trivial)

\(f(q)\)	\(=\)	\(q-1.57229 q^{2} -2.03431 q^{3} +0.472100 q^{4} -3.39483 q^{5} +3.19853 q^{6} -1.00000 q^{7} +2.40230 q^{8} +1.13841 q^{9} +O(q^{10})\)	\(q-1.57229 q^{2} -2.03431 q^{3} +0.472100 q^{4} -3.39483 q^{5} +3.19853 q^{6} -1.00000 q^{7} +2.40230 q^{8} +1.13841 q^{9} +5.33766 q^{10} -4.67063 q^{11} -0.960397 q^{12} -3.63777 q^{13} +1.57229 q^{14} +6.90613 q^{15} -4.72132 q^{16} -1.78992 q^{18} +6.19754 q^{19} -1.60270 q^{20} +2.03431 q^{21} +7.34359 q^{22} +0.672091 q^{23} -4.88703 q^{24} +6.52485 q^{25} +5.71963 q^{26} +3.78704 q^{27} -0.472100 q^{28} +5.59267 q^{29} -10.8584 q^{30} -7.65857 q^{31} +2.61868 q^{32} +9.50150 q^{33} +3.39483 q^{35} +0.537445 q^{36} -1.36854 q^{37} -9.74433 q^{38} +7.40035 q^{39} -8.15541 q^{40} -0.696033 q^{41} -3.19853 q^{42} +6.64216 q^{43} -2.20500 q^{44} -3.86472 q^{45} -1.05672 q^{46} -4.32592 q^{47} +9.60463 q^{48} +1.00000 q^{49} -10.2590 q^{50} -1.71739 q^{52} +4.07940 q^{53} -5.95433 q^{54} +15.8560 q^{55} -2.40230 q^{56} -12.6077 q^{57} -8.79330 q^{58} -2.73239 q^{59} +3.26038 q^{60} +12.0980 q^{61} +12.0415 q^{62} -1.13841 q^{63} +5.32531 q^{64} +12.3496 q^{65} -14.9391 q^{66} +12.5590 q^{67} -1.36724 q^{69} -5.33766 q^{70} +4.30572 q^{71} +2.73482 q^{72} +1.65114 q^{73} +2.15174 q^{74} -13.2736 q^{75} +2.92586 q^{76} +4.67063 q^{77} -11.6355 q^{78} +10.0047 q^{79} +16.0281 q^{80} -11.1193 q^{81} +1.09437 q^{82} -4.69160 q^{83} +0.960397 q^{84} -10.4434 q^{86} -11.3772 q^{87} -11.2203 q^{88} +2.04706 q^{89} +6.07647 q^{90} +3.63777 q^{91} +0.317294 q^{92} +15.5799 q^{93} +6.80161 q^{94} -21.0396 q^{95} -5.32721 q^{96} +4.23013 q^{97} -1.57229 q^{98} -5.31711 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 4 q^{3} + 12 q^{4} - 8 q^{5} - 14 q^{6} - 10 q^{7} + 10 q^{9}+O(q^{10}) \) 10 * q - 4 * q^3 + 12 * q^4 - 8 * q^5 - 14 * q^6 - 10 * q^7 + 10 * q^9	\( 10 q - 4 q^{3} + 12 q^{4} - 8 q^{5} - 14 q^{6} - 10 q^{7} + 10 q^{9} - 4 q^{10} - 8 q^{11} + 16 q^{12} + 12 q^{15} + 8 q^{16} - 4 q^{18} - 8 q^{19} - 30 q^{20} + 4 q^{21} - 8 q^{22} - 12 q^{23} - 32 q^{24} + 10 q^{25} - 16 q^{27} - 12 q^{28} - 8 q^{29} + 18 q^{30} + 16 q^{31} + 10 q^{32} - 8 q^{33} + 8 q^{35} + 18 q^{36} - 20 q^{37} - 24 q^{38} + 8 q^{39} - 6 q^{40} - 36 q^{41} + 14 q^{42} + 12 q^{43} - 24 q^{44} - 40 q^{45} + 56 q^{46} - 20 q^{47} + 18 q^{48} + 10 q^{49} - 14 q^{50} + 12 q^{53} - 46 q^{54} + 20 q^{55} - 28 q^{57} - 24 q^{58} - 4 q^{59} - 18 q^{60} - 8 q^{61} - 4 q^{62} - 10 q^{63} - 16 q^{64} - 12 q^{65} - 60 q^{66} - 44 q^{69} + 4 q^{70} - 36 q^{71} - 54 q^{72} + 20 q^{73} + 36 q^{74} - 36 q^{75} - 44 q^{76} + 8 q^{77} - 24 q^{78} - 4 q^{80} - 2 q^{81} - 6 q^{82} - 4 q^{83} - 16 q^{84} + 22 q^{86} - 24 q^{87} - 60 q^{88} - 24 q^{89} + 18 q^{90} - 32 q^{92} + 8 q^{93} - 56 q^{94} - 16 q^{95} - 4 q^{96} - 28 q^{97} + 60 q^{99}+O(q^{100}) \) 10 * q - 4 * q^3 + 12 * q^4 - 8 * q^5 - 14 * q^6 - 10 * q^7 + 10 * q^9 - 4 * q^10 - 8 * q^11 + 16 * q^12 + 12 * q^15 + 8 * q^16 - 4 * q^18 - 8 * q^19 - 30 * q^20 + 4 * q^21 - 8 * q^22 - 12 * q^23 - 32 * q^24 + 10 * q^25 - 16 * q^27 - 12 * q^28 - 8 * q^29 + 18 * q^30 + 16 * q^31 + 10 * q^32 - 8 * q^33 + 8 * q^35 + 18 * q^36 - 20 * q^37 - 24 * q^38 + 8 * q^39 - 6 * q^40 - 36 * q^41 + 14 * q^42 + 12 * q^43 - 24 * q^44 - 40 * q^45 + 56 * q^46 - 20 * q^47 + 18 * q^48 + 10 * q^49 - 14 * q^50 + 12 * q^53 - 46 * q^54 + 20 * q^55 - 28 * q^57 - 24 * q^58 - 4 * q^59 - 18 * q^60 - 8 * q^61 - 4 * q^62 - 10 * q^63 - 16 * q^64 - 12 * q^65 - 60 * q^66 - 44 * q^69 + 4 * q^70 - 36 * q^71 - 54 * q^72 + 20 * q^73 + 36 * q^74 - 36 * q^75 - 44 * q^76 + 8 * q^77 - 24 * q^78 - 4 * q^80 - 2 * q^81 - 6 * q^82 - 4 * q^83 - 16 * q^84 + 22 * q^86 - 24 * q^87 - 60 * q^88 - 24 * q^89 + 18 * q^90 - 32 * q^92 + 8 * q^93 - 56 * q^94 - 16 * q^95 - 4 * q^96 - 28 * q^97 + 60 * q^99

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