LMFDB - Embedded newform 4029.2.a.j.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4029,2,Mod(1,4029)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4029, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("4029.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4029 = 3 \cdot 17 \cdot 79 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4029.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:	$32.1717269744$
Analytic rank:	$0$
Dimension:	$25$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Character	$\chi$	$=$	4029.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.19187 q^{2} +1.00000 q^{3} -0.579444 q^{4} -1.97485 q^{5} -1.19187 q^{6} +1.20760 q^{7} +3.07436 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.19187 q^{2} +1.00000 q^{3} -0.579444 q^{4} -1.97485 q^{5} -1.19187 q^{6} +1.20760 q^{7} +3.07436 q^{8} +1.00000 q^{9} +2.35376 q^{10} -3.22974 q^{11} -0.579444 q^{12} -3.03451 q^{13} -1.43931 q^{14} -1.97485 q^{15} -2.50536 q^{16} -1.00000 q^{17} -1.19187 q^{18} -7.52481 q^{19} +1.14431 q^{20} +1.20760 q^{21} +3.84943 q^{22} -2.05782 q^{23} +3.07436 q^{24} -1.09998 q^{25} +3.61675 q^{26} +1.00000 q^{27} -0.699739 q^{28} +3.36547 q^{29} +2.35376 q^{30} +5.17898 q^{31} -3.16267 q^{32} -3.22974 q^{33} +1.19187 q^{34} -2.38483 q^{35} -0.579444 q^{36} +7.72570 q^{37} +8.96861 q^{38} -3.03451 q^{39} -6.07139 q^{40} -0.516600 q^{41} -1.43931 q^{42} -8.00167 q^{43} +1.87145 q^{44} -1.97485 q^{45} +2.45265 q^{46} +5.22918 q^{47} -2.50536 q^{48} -5.54169 q^{49} +1.31104 q^{50} -1.00000 q^{51} +1.75833 q^{52} +7.28827 q^{53} -1.19187 q^{54} +6.37824 q^{55} +3.71262 q^{56} -7.52481 q^{57} -4.01121 q^{58} +5.37740 q^{59} +1.14431 q^{60} +5.66411 q^{61} -6.17267 q^{62} +1.20760 q^{63} +8.78020 q^{64} +5.99269 q^{65} +3.84943 q^{66} +2.03108 q^{67} +0.579444 q^{68} -2.05782 q^{69} +2.84241 q^{70} -0.257975 q^{71} +3.07436 q^{72} -5.43805 q^{73} -9.20804 q^{74} -1.09998 q^{75} +4.36021 q^{76} -3.90025 q^{77} +3.61675 q^{78} -1.00000 q^{79} +4.94769 q^{80} +1.00000 q^{81} +0.615720 q^{82} -0.691816 q^{83} -0.699739 q^{84} +1.97485 q^{85} +9.53696 q^{86} +3.36547 q^{87} -9.92939 q^{88} +5.83272 q^{89} +2.35376 q^{90} -3.66449 q^{91} +1.19239 q^{92} +5.17898 q^{93} -6.23250 q^{94} +14.8603 q^{95} -3.16267 q^{96} -10.8506 q^{97} +6.60498 q^{98} -3.22974 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 25 q + 6 q^{2} + 25 q^{3} + 26 q^{4} + 6 q^{5} + 6 q^{6} + 4 q^{7} + 18 q^{8} + 25 q^{9}+O(q^{10}) $ 25 * q + 6 * q^2 + 25 * q^3 + 26 * q^4 + 6 * q^5 + 6 * q^6 + 4 * q^7 + 18 * q^8 + 25 * q^9	\( 25 q + 6 q^{2} + 25 q^{3} + 26 q^{4} + 6 q^{5} + 6 q^{6} + 4 q^{7} + 18 q^{8} + 25 q^{9} + 13 q^{10} + 19 q^{11} + 26 q^{12} + 17 q^{14} + 6 q^{15} + 16 q^{16} - 25 q^{17} + 6 q^{18} + 25 q^{19} + 32 q^{20} + 4 q^{21} - 7 q^{22} + 8 q^{23} + 18 q^{24} + 15 q^{25} + 20 q^{26} + 25 q^{27} + 9 q^{28} + 21 q^{29} + 13 q^{30} + 4 q^{31} + 27 q^{32} + 19 q^{33} - 6 q^{34} + 50 q^{35} + 26 q^{36} - 8 q^{37} + 31 q^{38} + 52 q^{40} + 40 q^{41} + 17 q^{42} + 21 q^{43} + 34 q^{44} + 6 q^{45} + 29 q^{46} + 43 q^{47} + 16 q^{48} + 21 q^{49} + 13 q^{50} - 25 q^{51} + 3 q^{52} + 44 q^{53} + 6 q^{54} + 13 q^{55} + 38 q^{56} + 25 q^{57} - 5 q^{58} + 45 q^{59} + 32 q^{60} + 22 q^{61} + 4 q^{62} + 4 q^{63} + 26 q^{64} + 43 q^{65} - 7 q^{66} + 8 q^{67} - 26 q^{68} + 8 q^{69} + 29 q^{70} + 9 q^{71} + 18 q^{72} - 7 q^{73} + 18 q^{74} + 15 q^{75} + 33 q^{76} + 20 q^{77} + 20 q^{78} - 25 q^{79} + 42 q^{80} + 25 q^{81} - 43 q^{82} + 41 q^{83} + 9 q^{84} - 6 q^{85} - 12 q^{86} + 21 q^{87} - 43 q^{88} + 68 q^{89} + 13 q^{90} + 10 q^{91} + 2 q^{92} + 4 q^{93} - 17 q^{94} + 8 q^{95} + 27 q^{96} + 15 q^{97} + 11 q^{98} + 19 q^{99}+O(q^{100}) \) 25 * q + 6 * q^2 + 25 * q^3 + 26 * q^4 + 6 * q^5 + 6 * q^6 + 4 * q^7 + 18 * q^8 + 25 * q^9 + 13 * q^10 + 19 * q^11 + 26 * q^12 + 17 * q^14 + 6 * q^15 + 16 * q^16 - 25 * q^17 + 6 * q^18 + 25 * q^19 + 32 * q^20 + 4 * q^21 - 7 * q^22 + 8 * q^23 + 18 * q^24 + 15 * q^25 + 20 * q^26 + 25 * q^27 + 9 * q^28 + 21 * q^29 + 13 * q^30 + 4 * q^31 + 27 * q^32 + 19 * q^33 - 6 * q^34 + 50 * q^35 + 26 * q^36 - 8 * q^37 + 31 * q^38 + 52 * q^40 + 40 * q^41 + 17 * q^42 + 21 * q^43 + 34 * q^44 + 6 * q^45 + 29 * q^46 + 43 * q^47 + 16 * q^48 + 21 * q^49 + 13 * q^50 - 25 * q^51 + 3 * q^52 + 44 * q^53 + 6 * q^54 + 13 * q^55 + 38 * q^56 + 25 * q^57 - 5 * q^58 + 45 * q^59 + 32 * q^60 + 22 * q^61 + 4 * q^62 + 4 * q^63 + 26 * q^64 + 43 * q^65 - 7 * q^66 + 8 * q^67 - 26 * q^68 + 8 * q^69 + 29 * q^70 + 9 * q^71 + 18 * q^72 - 7 * q^73 + 18 * q^74 + 15 * q^75 + 33 * q^76 + 20 * q^77 + 20 * q^78 - 25 * q^79 + 42 * q^80 + 25 * q^81 - 43 * q^82 + 41 * q^83 + 9 * q^84 - 6 * q^85 - 12 * q^86 + 21 * q^87 - 43 * q^88 + 68 * q^89 + 13 * q^90 + 10 * q^91 + 2 * q^92 + 4 * q^93 - 17 * q^94 + 8 * q^95 + 27 * q^96 + 15 * q^97 + 11 * q^98 + 19 * 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 $

$2$	−1.19187	−0.842780	−0.421390	−	0.906880i	$-0.638458\pi$
$2$	−1.19187	−0.842780	−0.421390	+	0.906880i	$0.638458\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−0.579444	−0.289722
$5$	−1.97485	−0.883178	−0.441589	−	0.897217i	$-0.645585\pi$
$5$	−1.97485	−0.883178	−0.441589	+	0.897217i	$0.645585\pi$
$6$	−1.19187	−0.486579
$7$	1.20760	0.456432	0.228216	−	0.973611i	$-0.426711\pi$
$7$	1.20760	0.456432	0.228216	+	0.973611i	$0.426711\pi$
$8$	3.07436	1.08695
$9$	1.00000	0.333333
$10$	2.35376	0.744325
$11$	−3.22974	−0.973803	−0.486902	−	0.873457i	$-0.661873\pi$
$11$	−3.22974	−0.973803	−0.486902	+	0.873457i	$0.661873\pi$
$12$	−0.579444	−0.167271
$13$	−3.03451	−0.841622	−0.420811	−	0.907148i	$-0.638255\pi$
$13$	−3.03451	−0.841622	−0.420811	+	0.907148i	$0.638255\pi$
$14$	−1.43931	−0.384671
$15$	−1.97485	−0.509903
$16$	−2.50536	−0.626339
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−1.19187	−0.280927
$19$	−7.52481	−1.72631	−0.863155	−	0.504938i	$-0.831515\pi$
$19$	−7.52481	−1.72631	−0.863155	+	0.504938i	$0.831515\pi$
$20$	1.14431	0.255876
$21$	1.20760	0.263521
$22$	3.84943	0.820702
$23$	−2.05782	−0.429084	−0.214542	−	0.976715i	$-0.568826\pi$
$23$	−2.05782	−0.429084	−0.214542	+	0.976715i	$0.568826\pi$
$24$	3.07436	0.627552
$25$	−1.09998	−0.219997
$26$	3.61675	0.709303
$27$	1.00000	0.192450
$28$	−0.699739	−0.132238
$29$	3.36547	0.624953	0.312476	−	0.949926i	$-0.398842\pi$
$29$	3.36547	0.624953	0.312476	+	0.949926i	$0.398842\pi$
$30$	2.35376	0.429736
$31$	5.17898	0.930172	0.465086	−	0.885266i	$-0.346023\pi$
$31$	5.17898	0.930172	0.465086	+	0.885266i	$0.346023\pi$
$32$	−3.16267	−0.559085
$33$	−3.22974	−0.562225
$34$	1.19187	0.204404
$35$	−2.38483	−0.403110
$36$	−0.579444	−0.0965740
$37$	7.72570	1.27010	0.635049	−	0.772472i	$-0.280980\pi$
$37$	7.72570	1.27010	0.635049	+	0.772472i	$0.280980\pi$
$38$	8.96861	1.45490
$39$	−3.03451	−0.485911
$40$	−6.07139	−0.959972
$41$	−0.516600	−0.0806793	−0.0403397	−	0.999186i	$-0.512844\pi$
$41$	−0.516600	−0.0806793	−0.0403397	+	0.999186i	$0.512844\pi$
$42$	−1.43931	−0.222090
$43$	−8.00167	−1.22024	−0.610122	−	0.792308i	$-0.708879\pi$
$43$	−8.00167	−1.22024	−0.610122	+	0.792308i	$0.708879\pi$
$44$	1.87145	0.282132
$45$	−1.97485	−0.294393
$46$	2.45265	0.361623
$47$	5.22918	0.762754	0.381377	−	0.924420i	$-0.375450\pi$
$47$	5.22918	0.762754	0.381377	+	0.924420i	$0.375450\pi$
$48$	−2.50536	−0.361617
$49$	−5.54169	−0.791670
$50$	1.31104	0.185409
$51$	−1.00000	−0.140028
$52$	1.75833	0.243836
$53$	7.28827	1.00112	0.500561	−	0.865701i	$-0.333127\pi$
$53$	7.28827	1.00112	0.500561	+	0.865701i	$0.333127\pi$
$54$	−1.19187	−0.162193
$55$	6.37824	0.860041
$56$	3.71262	0.496119
$57$	−7.52481	−0.996686
$58$	−4.01121	−0.526697
$59$	5.37740	0.700078	0.350039	−	0.936735i	$-0.386168\pi$
$59$	5.37740	0.700078	0.350039	+	0.936735i	$0.386168\pi$
$60$	1.14431	0.147730
$61$	5.66411	0.725215	0.362608	−	0.931942i	$-0.381887\pi$
$61$	5.66411	0.725215	0.362608	+	0.931942i	$0.381887\pi$
$62$	−6.17267	−0.783930
$63$	1.20760	0.152144
$64$	8.78020	1.09753
$65$	5.99269	0.743302
$66$	3.84943	0.473832
$67$	2.03108	0.248136	0.124068	−	0.992274i	$-0.460406\pi$
$67$	2.03108	0.248136	0.124068	+	0.992274i	$0.460406\pi$
$68$	0.579444	0.0702679
$69$	−2.05782	−0.247732
$70$	2.84241	0.339733
$71$	−0.257975	−0.0306161	−0.0153080	−	0.999883i	$-0.504873\pi$
$71$	−0.257975	−0.0306161	−0.0153080	+	0.999883i	$0.504873\pi$
$72$	3.07436	0.362317
$73$	−5.43805	−0.636476	−0.318238	−	0.948011i	$-0.603091\pi$
$73$	−5.43805	−0.636476	−0.318238	+	0.948011i	$0.603091\pi$
$74$	−9.20804	−1.07041
$75$	−1.09998	−0.127015
$76$	4.36021	0.500150
$77$	−3.90025	−0.444474
$78$	3.61675	0.409516
$79$	−1.00000	−0.112509
$79$	−1.00000	−0.112509
$80$	4.94769	0.553169
$81$	1.00000	0.111111
$82$	0.615720	0.0679949
$83$	−0.691816	−0.0759367	−0.0379684	−	0.999279i	$-0.512089\pi$
$83$	−0.691816	−0.0759367	−0.0379684	+	0.999279i	$0.512089\pi$
$84$	−0.699739	−0.0763478
$85$	1.97485	0.214202
$86$	9.53696	1.02840
$87$	3.36547	0.360816
$88$	−9.92939	−1.05848
$89$	5.83272	0.618267	0.309134	−	0.951019i	$-0.399961\pi$
$89$	5.83272	0.618267	0.309134	+	0.951019i	$0.399961\pi$
$90$	2.35376	0.248108
$91$	−3.66449	−0.384143
$92$	1.19239	0.124315
$93$	5.17898	0.537035
$94$	−6.23250	−0.642834
$95$	14.8603	1.52464
$96$	−3.16267	−0.322788
$97$	−10.8506	−1.10172	−0.550858	−	0.834599i	$-0.685699\pi$
$97$	−10.8506	−1.10172	−0.550858	+	0.834599i	$0.685699\pi$
$98$	6.60498	0.667204
$99$	−3.22974	−0.324601
$100$	0.637379	0.0637379
$101$	−6.26909	−0.623798	−0.311899	−	0.950115i	$-0.600965\pi$
$101$	−6.26909	−0.623798	−0.311899	+	0.950115i	$0.600965\pi$
$102$	1.19187	0.118013
$103$	−3.19646	−0.314956	−0.157478	−	0.987522i	$-0.550336\pi$
$103$	−3.19646	−0.314956	−0.157478	+	0.987522i	$0.550336\pi$
$104$	−9.32920	−0.914803
$105$	−2.38483	−0.232736
$106$	−8.68668	−0.843725
$107$	16.6752	1.61205	0.806024	−	0.591882i	$-0.201615\pi$
$107$	16.6752	1.61205	0.806024	+	0.591882i	$0.201615\pi$
$108$	−0.579444	−0.0557570
$109$	−4.76772	−0.456664	−0.228332	−	0.973583i	$-0.573327\pi$
$109$	−4.76772	−0.456664	−0.228332	+	0.973583i	$0.573327\pi$
$110$	−7.60204	−0.724826
$111$	7.72570	0.733291
$112$	−3.02548	−0.285881
$113$	−10.4145	−0.979717	−0.489858	−	0.871802i	$-0.662952\pi$
$113$	−10.4145	−0.979717	−0.489858	+	0.871802i	$0.662952\pi$
$114$	8.96861	0.839987
$115$	4.06387	0.378958
$116$	−1.95010	−0.181062
$117$	−3.03451	−0.280541
$118$	−6.40917	−0.590012
$119$	−1.20760	−0.110701
$120$	−6.07139	−0.554240
$121$	−0.568784	−0.0517076
$122$	−6.75089	−0.611197
$123$	−0.516600	−0.0465802
$124$	−3.00093	−0.269491
$125$	12.0465	1.07747
$126$	−1.43931	−0.128224
$127$	7.47939	0.663689	0.331844	−	0.943334i	$-0.392329\pi$
$127$	7.47939	0.663689	0.331844	+	0.943334i	$0.392329\pi$
$128$	−4.13954	−0.365887
$129$	−8.00167	−0.704508
$130$	−7.14252	−0.626440
$131$	−3.04975	−0.266458	−0.133229	−	0.991085i	$-0.542535\pi$
$131$	−3.04975	−0.266458	−0.133229	+	0.991085i	$0.542535\pi$
$132$	1.87145	0.162889
$133$	−9.08700	−0.787943
$134$	−2.42079	−0.209124
$135$	−1.97485	−0.169968
$136$	−3.07436	−0.263625
$137$	−1.27059	−0.108554	−0.0542769	−	0.998526i	$-0.517285\pi$
$137$	−1.27059	−0.108554	−0.0542769	+	0.998526i	$0.517285\pi$
$138$	2.45265	0.208783
$139$	5.21341	0.442195	0.221098	−	0.975252i	$-0.429036\pi$
$139$	5.21341	0.442195	0.221098	+	0.975252i	$0.429036\pi$
$140$	1.38188	0.116790
$141$	5.22918	0.440376
$142$	0.307473	0.0258026
$143$	9.80069	0.819574
$144$	−2.50536	−0.208780
$145$	−6.64629	−0.551944
$146$	6.48146	0.536409
$147$	−5.54169	−0.457071
$148$	−4.47661	−0.367975
$149$	2.44211	0.200066	0.100033	−	0.994984i	$-0.468105\pi$
$149$	2.44211	0.200066	0.100033	+	0.994984i	$0.468105\pi$
$150$	1.31104	0.107046
$151$	−6.05638	−0.492861	−0.246431	−	0.969160i	$-0.579258\pi$
$151$	−6.05638	−0.492861	−0.246431	+	0.969160i	$0.579258\pi$
$152$	−23.1340	−1.87642
$153$	−1.00000	−0.0808452
$154$	4.64859	0.374594
$155$	−10.2277	−0.821507
$156$	1.75833	0.140779
$157$	−2.07206	−0.165368	−0.0826841	−	0.996576i	$-0.526349\pi$
$157$	−2.07206	−0.165368	−0.0826841	+	0.996576i	$0.526349\pi$
$158$	1.19187	0.0948202
$159$	7.28827	0.577998
$160$	6.24578	0.493772
$161$	−2.48503	−0.195848
$162$	−1.19187	−0.0936422
$163$	−5.50310	−0.431036	−0.215518	−	0.976500i	$-0.569144\pi$
$163$	−5.50310	−0.431036	−0.215518	+	0.976500i	$0.569144\pi$
$164$	0.299340	0.0233746
$165$	6.37824	0.496545
$166$	0.824556	0.0639979
$167$	19.3282	1.49566	0.747831	−	0.663889i	$-0.231095\pi$
$167$	19.3282	1.49566	0.747831	+	0.663889i	$0.231095\pi$
$168$	3.71262	0.286435
$169$	−3.79173	−0.291672
$170$	−2.35376	−0.180525
$171$	−7.52481	−0.575437
$172$	4.63652	0.353531
$173$	18.7348	1.42438	0.712189	−	0.701988i	$-0.247704\pi$
$173$	18.7348	1.42438	0.712189	+	0.701988i	$0.247704\pi$
$174$	−4.01121	−0.304089
$175$	−1.32835	−0.100414
$176$	8.09165	0.609931
$177$	5.37740	0.404190
$178$	−6.95185	−0.521063
$179$	0.864853	0.0646422	0.0323211	−	0.999478i	$-0.489710\pi$
$179$	0.864853	0.0646422	0.0323211	+	0.999478i	$0.489710\pi$
$180$	1.14431	0.0852920
$181$	18.3484	1.36382	0.681912	−	0.731434i	$-0.261149\pi$
$181$	18.3484	1.36382	0.681912	+	0.731434i	$0.261149\pi$
$182$	4.36760	0.323748
$183$	5.66411	0.418703
$184$	−6.32647	−0.466394
$185$	−15.2571	−1.12172
$186$	−6.17267	−0.452602
$187$	3.22974	0.236182
$188$	−3.03001	−0.220986
$189$	1.20760	0.0878403
$190$	−17.7116	−1.28494
$191$	−3.07720	−0.222659	−0.111329	−	0.993784i	$-0.535511\pi$
$191$	−3.07720	−0.222659	−0.111329	+	0.993784i	$0.535511\pi$
$192$	8.78020	0.633657
$193$	15.5735	1.12101	0.560503	−	0.828152i	$-0.310608\pi$
$193$	15.5735	1.12101	0.560503	+	0.828152i	$0.310608\pi$
$194$	12.9326	0.928503
$195$	5.99269	0.429146
$196$	3.21110	0.229364
$197$	9.28603	0.661602	0.330801	−	0.943700i	$-0.392681\pi$
$197$	9.28603	0.661602	0.330801	+	0.943700i	$0.392681\pi$
$198$	3.84943	0.273567
$199$	18.3045	1.29757	0.648785	−	0.760971i	$-0.275277\pi$
$199$	18.3045	1.29757	0.648785	+	0.760971i	$0.275277\pi$
$200$	−3.38175	−0.239126
$201$	2.03108	0.143262
$202$	7.47194	0.525724
$203$	4.06416	0.285248
$204$	0.579444	0.0405692
$205$	1.02020	0.0712542
$206$	3.80977	0.265439
$207$	−2.05782	−0.143028
$208$	7.60254	0.527141
$209$	24.3032	1.68109
$210$	2.84241	0.196145
$211$	11.7502	0.808917	0.404459	−	0.914556i	$-0.367460\pi$
$211$	11.7502	0.808917	0.404459	+	0.914556i	$0.367460\pi$
$212$	−4.22315	−0.290047
$213$	−0.257975	−0.0176762
$214$	−19.8746	−1.35860
$215$	15.8021	1.07769
$216$	3.07436	0.209184
$217$	6.25416	0.424560
$218$	5.68250	0.384868
$219$	−5.43805	−0.367469
$220$	−3.69583	−0.249173
$221$	3.03451	0.204123
$222$	−9.20804	−0.618003
$223$	3.04271	0.203755	0.101877	−	0.994797i	$-0.467515\pi$
$223$	3.04271	0.203755	0.101877	+	0.994797i	$0.467515\pi$
$224$	−3.81925	−0.255184
$225$	−1.09998	−0.0733323
$226$	12.4128	0.825686
$227$	19.3052	1.28133	0.640666	−	0.767820i	$-0.278658\pi$
$227$	19.3052	1.28133	0.640666	+	0.767820i	$0.278658\pi$
$228$	4.36021	0.288762
$229$	7.39469	0.488655	0.244328	−	0.969693i	$-0.421433\pi$
$229$	7.39469	0.488655	0.244328	+	0.969693i	$0.421433\pi$
$230$	−4.84361	−0.319378
$231$	−3.90025	−0.256617
$232$	10.3467	0.679293
$233$	20.7670	1.36049	0.680246	−	0.732984i	$-0.261873\pi$
$233$	20.7670	1.36049	0.680246	+	0.732984i	$0.261873\pi$
$234$	3.61675	0.236434
$235$	−10.3268	−0.673647
$236$	−3.11590	−0.202828
$237$	−1.00000	−0.0649570
$238$	1.43931	0.0932965
$239$	18.7946	1.21572	0.607859	−	0.794045i	$-0.292028\pi$
$239$	18.7946	1.21572	0.607859	+	0.794045i	$0.292028\pi$
$240$	4.94769	0.319372
$241$	−14.9047	−0.960097	−0.480048	−	0.877242i	$-0.659381\pi$
$241$	−14.9047	−0.960097	−0.480048	+	0.877242i	$0.659381\pi$
$242$	0.677917	0.0435781
$243$	1.00000	0.0641500
$244$	−3.28203	−0.210111
$245$	10.9440	0.699186
$246$	0.615720	0.0392569
$247$	22.8341	1.45290
$248$	15.9221	1.01105
$249$	−0.691816	−0.0438421
$250$	−14.3579	−0.908074
$251$	2.88053	0.181818	0.0909088	−	0.995859i	$-0.471023\pi$
$251$	2.88053	0.181818	0.0909088	+	0.995859i	$0.471023\pi$
$252$	−0.699739	−0.0440794
$253$	6.64621	0.417843
$254$	−8.91447	−0.559344
$255$	1.97485	0.123670
$256$	−12.6266	−0.789163
$257$	−3.32885	−0.207648	−0.103824	−	0.994596i	$-0.533108\pi$
$257$	−3.32885	−0.207648	−0.103824	+	0.994596i	$0.533108\pi$
$258$	9.53696	0.593745
$259$	9.32959	0.579713
$260$	−3.47243	−0.215351
$261$	3.36547	0.208318
$262$	3.63491	0.224565
$263$	12.5731	0.775288	0.387644	−	0.921809i	$-0.373289\pi$
$263$	12.5731	0.775288	0.387644	+	0.921809i	$0.373289\pi$
$264$	−9.92939	−0.611112
$265$	−14.3932	−0.884168
$266$	10.8305	0.664062
$267$	5.83272	0.356957
$268$	−1.17690	−0.0718905
$269$	−5.44753	−0.332142	−0.166071	−	0.986114i	$-0.553108\pi$
$269$	−5.44753	−0.332142	−0.166071	+	0.986114i	$0.553108\pi$
$270$	2.35376	0.143245
$271$	−17.3600	−1.05455	−0.527273	−	0.849696i	$-0.676785\pi$
$271$	−17.3600	−1.05455	−0.527273	+	0.849696i	$0.676785\pi$
$272$	2.50536	0.151910
$273$	−3.66449	−0.221785
$274$	1.51438	0.0914870
$275$	3.55266	0.214234
$276$	1.19239	0.0717733
$277$	−5.23166	−0.314340	−0.157170	−	0.987572i	$-0.550237\pi$
$277$	−5.23166	−0.314340	−0.157170	+	0.987572i	$0.550237\pi$
$278$	−6.21371	−0.372673
$279$	5.17898	0.310057
$280$	−7.33184	−0.438161
$281$	−13.2501	−0.790437	−0.395219	−	0.918587i	$-0.629331\pi$
$281$	−13.2501	−0.790437	−0.395219	+	0.918587i	$0.629331\pi$
$282$	−6.23250	−0.371140
$283$	4.18840	0.248974	0.124487	−	0.992221i	$-0.460271\pi$
$283$	4.18840	0.248974	0.124487	+	0.992221i	$0.460271\pi$
$284$	0.149482	0.00887014
$285$	14.8603	0.880251
$286$	−11.6812	−0.690721
$287$	−0.623848	−0.0368246
$288$	−3.16267	−0.186362
$289$	1.00000	0.0588235
$290$	7.92152	0.465168
$291$	−10.8506	−0.636075
$292$	3.15105	0.184401
$293$	22.3055	1.30310	0.651550	−	0.758606i	$-0.274119\pi$
$293$	22.3055	1.30310	0.651550	+	0.758606i	$0.274119\pi$
$294$	6.60498	0.385210
$295$	−10.6195	−0.618293
$296$	23.7516	1.38053
$297$	−3.22974	−0.187408
$298$	−2.91068	−0.168611
$299$	6.24447	0.361127
$300$	0.637379	0.0367991
$301$	−9.66285	−0.556958
$302$	7.21842	0.415373
$303$	−6.26909	−0.360150
$304$	18.8524	1.08126
$305$	−11.1857	−0.640494
$306$	1.19187	0.0681347
$307$	10.7379	0.612843	0.306422	−	0.951896i	$-0.400868\pi$
$307$	10.7379	0.612843	0.306422	+	0.951896i	$0.400868\pi$
$308$	2.25997	0.128774
$309$	−3.19646	−0.181840
$310$	12.1901	0.692350
$311$	−24.0408	−1.36323	−0.681614	−	0.731712i	$-0.738722\pi$
$311$	−24.0408	−1.36323	−0.681614	+	0.731712i	$0.738722\pi$
$312$	−9.32920	−0.528162
$313$	6.20073	0.350486	0.175243	−	0.984525i	$-0.443929\pi$
$313$	6.20073	0.350486	0.175243	+	0.984525i	$0.443929\pi$
$314$	2.46962	0.139369
$315$	−2.38483	−0.134370
$316$	0.579444	0.0325963
$317$	10.6644	0.598970	0.299485	−	0.954101i	$-0.403185\pi$
$317$	10.6644	0.598970	0.299485	+	0.954101i	$0.403185\pi$
$318$	−8.68668	−0.487125
$319$	−10.8696	−0.608581
$320$	−17.3395	−0.969310
$321$	16.6752	0.930717
$322$	2.96183	0.165056
$323$	7.52481	0.418692
$324$	−0.579444	−0.0321913
$325$	3.33792	0.185154
$326$	6.55899	0.363269
$327$	−4.76772	−0.263655
$328$	−1.58822	−0.0876945
$329$	6.31478	0.348145
$330$	−7.60204	−0.418478
$331$	19.9018	1.09390	0.546950	−	0.837165i	$-0.315789\pi$
$331$	19.9018	1.09390	0.546950	+	0.837165i	$0.315789\pi$
$332$	0.400869	0.0220005
$333$	7.72570	0.423366
$334$	−23.0367	−1.26051
$335$	−4.01108	−0.219148
$336$	−3.02548	−0.165054
$337$	19.2604	1.04918	0.524589	−	0.851355i	$-0.324219\pi$
$337$	19.2604	1.04918	0.524589	+	0.851355i	$0.324219\pi$
$338$	4.51926	0.245815
$339$	−10.4145	−0.565640
$340$	−1.14431	−0.0620590
$341$	−16.7267	−0.905804
$342$	8.96861	0.484967
$343$	−15.1454	−0.817775
$344$	−24.6000	−1.32635
$345$	4.06387	0.218791
$346$	−22.3294	−1.20044
$347$	−15.5144	−0.832854	−0.416427	−	0.909169i	$-0.636718\pi$
$347$	−15.5144	−0.832854	−0.416427	+	0.909169i	$0.636718\pi$
$348$	−1.95010	−0.104536
$349$	23.0328	1.23292	0.616460	−	0.787386i	$-0.288566\pi$
$349$	23.0328	1.23292	0.616460	+	0.787386i	$0.288566\pi$
$350$	1.58322	0.0846265
$351$	−3.03451	−0.161970
$352$	10.2146	0.544439
$353$	25.7559	1.37085	0.685424	−	0.728144i	$-0.259617\pi$
$353$	25.7559	1.37085	0.685424	+	0.728144i	$0.259617\pi$
$354$	−6.40917	−0.340643
$355$	0.509462	0.0270394
$356$	−3.37973	−0.179125
$357$	−1.20760	−0.0639132
$358$	−1.03079	−0.0544791
$359$	13.3888	0.706632	0.353316	−	0.935504i	$-0.385054\pi$
$359$	13.3888	0.706632	0.353316	+	0.935504i	$0.385054\pi$
$360$	−6.07139	−0.319991
$361$	37.6228	1.98015
$362$	−21.8689	−1.14940
$363$	−0.568784	−0.0298534
$364$	2.12337	0.111295
$365$	10.7393	0.562121
$366$	−6.75089	−0.352875
$367$	−21.5428	−1.12452	−0.562262	−	0.826959i	$-0.690069\pi$
$367$	−21.5428	−1.12452	−0.562262	+	0.826959i	$0.690069\pi$
$368$	5.15556	0.268752
$369$	−0.516600	−0.0268931
$370$	18.1845	0.945365
$371$	8.80135	0.456943
$372$	−3.00093	−0.155591
$373$	−31.0851	−1.60953	−0.804764	−	0.593595i	$-0.797708\pi$
$373$	−31.0851	−1.60953	−0.804764	+	0.593595i	$0.797708\pi$
$374$	−3.84943	−0.199049
$375$	12.0465	0.622080
$376$	16.0764	0.829077
$377$	−10.2126	−0.525974
$378$	−1.43931	−0.0740300
$379$	5.13781	0.263912	0.131956	−	0.991256i	$-0.457874\pi$
$379$	5.13781	0.263912	0.131956	+	0.991256i	$0.457874\pi$
$380$	−8.61074	−0.441721
$381$	7.47939	0.383181
$382$	3.66763	0.187652
$383$	−37.1951	−1.90058	−0.950290	−	0.311367i	$-0.899213\pi$
$383$	−37.1951	−1.90058	−0.950290	+	0.311367i	$0.899213\pi$
$384$	−4.13954	−0.211245
$385$	7.70239	0.392550
$386$	−18.5616	−0.944762
$387$	−8.00167	−0.406748
$388$	6.28733	0.319191
$389$	−10.8362	−0.549416	−0.274708	−	0.961528i	$-0.588581\pi$
$389$	−10.8362	−0.549416	−0.274708	+	0.961528i	$0.588581\pi$
$390$	−7.14252	−0.361675
$391$	2.05782	0.104068
$392$	−17.0372	−0.860507
$393$	−3.04975	−0.153839
$394$	−11.0678	−0.557585
$395$	1.97485	0.0993653
$396$	1.87145	0.0940440
$397$	−2.55979	−0.128472	−0.0642360	−	0.997935i	$-0.520461\pi$
$397$	−2.55979	−0.128472	−0.0642360	+	0.997935i	$0.520461\pi$
$398$	−21.8166	−1.09357
$399$	−9.08700	−0.454919
$400$	2.75585	0.137793
$401$	3.36198	0.167889	0.0839447	−	0.996470i	$-0.473248\pi$
$401$	3.36198	0.167889	0.0839447	+	0.996470i	$0.473248\pi$
$402$	−2.42079	−0.120738
$403$	−15.7157	−0.782853
$404$	3.63258	0.180728
$405$	−1.97485	−0.0981309
$406$	−4.84395	−0.240401
$407$	−24.9520	−1.23682
$408$	−3.07436	−0.152204
$409$	−15.9010	−0.786252	−0.393126	−	0.919485i	$-0.628606\pi$
$409$	−15.9010	−0.786252	−0.393126	+	0.919485i	$0.628606\pi$
$410$	−1.21595	−0.0600516
$411$	−1.27059	−0.0626736
$412$	1.85217	0.0912498
$413$	6.49377	0.319538
$414$	2.45265	0.120541
$415$	1.36623	0.0670656
$416$	9.59715	0.470539
$417$	5.21341	0.255302
$418$	−28.9663	−1.41679
$419$	28.4770	1.39119	0.695597	−	0.718432i	$-0.255140\pi$
$419$	28.4770	1.39119	0.695597	+	0.718432i	$0.255140\pi$
$420$	1.38188	0.0674287
$421$	−12.8101	−0.624328	−0.312164	−	0.950028i	$-0.601054\pi$
$421$	−12.8101	−0.624328	−0.312164	+	0.950028i	$0.601054\pi$
$422$	−14.0047	−0.681739
$423$	5.22918	0.254251
$424$	22.4068	1.08817
$425$	1.09998	0.0533571
$426$	0.307473	0.0148971
$427$	6.84001	0.331011
$428$	−9.66232	−0.467046
$429$	9.80069	0.473182
$430$	−18.8340	−0.908257
$431$	8.99801	0.433419	0.216710	−	0.976236i	$-0.430468\pi$
$431$	8.99801	0.433419	0.216710	+	0.976236i	$0.430468\pi$
$432$	−2.50536	−0.120539
$433$	30.5327	1.46731	0.733655	−	0.679523i	$-0.237813\pi$
$433$	30.5327	1.46731	0.733655	+	0.679523i	$0.237813\pi$
$434$	−7.45415	−0.357811
$435$	−6.64629	−0.318665
$436$	2.76262	0.132306
$437$	15.4847	0.740733
$438$	6.48146	0.309696
$439$	0.582729	0.0278121	0.0139061	−	0.999903i	$-0.495573\pi$
$439$	0.582729	0.0278121	0.0139061	+	0.999903i	$0.495573\pi$
$440$	19.6090	0.934823
$441$	−5.54169	−0.263890
$442$	−3.61675	−0.172031
$443$	10.7422	0.510376	0.255188	−	0.966891i	$-0.417863\pi$
$443$	10.7422	0.510376	0.255188	+	0.966891i	$0.417863\pi$
$444$	−4.47661	−0.212450
$445$	−11.5187	−0.546040
$446$	−3.62652	−0.171721
$447$	2.44211	0.115508
$448$	10.6030	0.500945
$449$	−10.4096	−0.491260	−0.245630	−	0.969364i	$-0.578995\pi$
$449$	−10.4096	−0.491260	−0.245630	+	0.969364i	$0.578995\pi$
$450$	1.31104	0.0618030
$451$	1.66848	0.0785658
$452$	6.03464	0.283845
$453$	−6.05638	−0.284553
$454$	−23.0093	−1.07988
$455$	7.23680	0.339267
$456$	−23.1340	−1.08335
$457$	6.92028	0.323717	0.161858	−	0.986814i	$-0.448251\pi$
$457$	6.92028	0.323717	0.161858	+	0.986814i	$0.448251\pi$
$458$	−8.81352	−0.411829
$459$	−1.00000	−0.0466760
$460$	−2.35478	−0.109792
$461$	−15.8022	−0.735981	−0.367990	−	0.929830i	$-0.619954\pi$
$461$	−15.8022	−0.735981	−0.367990	+	0.929830i	$0.619954\pi$
$462$	4.64859	0.216272
$463$	−23.9444	−1.11279	−0.556396	−	0.830917i	$-0.687816\pi$
$463$	−23.9444	−1.11279	−0.556396	+	0.830917i	$0.687816\pi$
$464$	−8.43171	−0.391432
$465$	−10.2277	−0.474297
$466$	−24.7516	−1.14660
$467$	−38.5941	−1.78592	−0.892960	−	0.450136i	$-0.851375\pi$
$467$	−38.5941	−1.78592	−0.892960	+	0.450136i	$0.851375\pi$
$468$	1.75833	0.0812788
$469$	2.45275	0.113257
$470$	12.3082	0.567737
$471$	−2.07206	−0.0954754
$472$	16.5321	0.760951
$473$	25.8433	1.18828
$474$	1.19187	0.0547444
$475$	8.27718	0.379783
$476$	0.699739	0.0320725
$477$	7.28827	0.333707
$478$	−22.4007	−1.02458
$479$	16.7505	0.765348	0.382674	−	0.923883i	$-0.375003\pi$
$479$	16.7505	0.765348	0.382674	+	0.923883i	$0.375003\pi$
$480$	6.24578	0.285079
$481$	−23.4437	−1.06894
$482$	17.7645	0.809150
$483$	−2.48503	−0.113073
$484$	0.329578	0.0149808
$485$	21.4283	0.973010
$486$	−1.19187	−0.0540644
$487$	26.1434	1.18467	0.592335	−	0.805692i	$-0.298206\pi$
$487$	26.1434	1.18467	0.592335	+	0.805692i	$0.298206\pi$
$488$	17.4135	0.788274
$489$	−5.50310	−0.248859
$490$	−13.0438	−0.589260
$491$	20.2725	0.914887	0.457443	−	0.889239i	$-0.348765\pi$
$491$	20.2725	0.914887	0.457443	+	0.889239i	$0.348765\pi$
$492$	0.299340	0.0134953
$493$	−3.36547	−0.151573
$494$	−27.2154	−1.22448
$495$	6.37824	0.286680
$496$	−12.9752	−0.582603
$497$	−0.311532	−0.0139741
$498$	0.824556	0.0369492
$499$	−29.2725	−1.31042	−0.655208	−	0.755448i	$-0.727419\pi$
$499$	−29.2725	−1.31042	−0.655208	+	0.755448i	$0.727419\pi$
$500$	−6.98028	−0.312168
$501$	19.3282	0.863521
$502$	−3.43322	−0.153232
$503$	42.8390	1.91010	0.955049	−	0.296447i	$-0.0958018\pi$
$503$	42.8390	1.91010	0.955049	+	0.296447i	$0.0958018\pi$
$504$	3.71262	0.165373
$505$	12.3805	0.550924
$506$	−7.92142	−0.352150
$507$	−3.79173	−0.168397
$508$	−4.33389	−0.192285
$509$	1.77952	0.0788757	0.0394379	−	0.999222i	$-0.487443\pi$
$509$	1.77952	0.0788757	0.0394379	+	0.999222i	$0.487443\pi$
$510$	−2.35376	−0.104226
$511$	−6.56702	−0.290508
$512$	23.3284	1.03098
$513$	−7.52481	−0.332229
$514$	3.96756	0.175001
$515$	6.31251	0.278163
$516$	4.63652	0.204111
$517$	−16.8889	−0.742772
$518$	−11.1197	−0.488570
$519$	18.7348	0.822365
$520$	18.4237	0.807934
$521$	−37.9675	−1.66339	−0.831693	−	0.555235i	$-0.812628\pi$
$521$	−37.9675	−1.66339	−0.831693	+	0.555235i	$0.812628\pi$
$522$	−4.01121	−0.175566
$523$	−13.1341	−0.574314	−0.287157	−	0.957883i	$-0.592710\pi$
$523$	−13.1341	−0.574314	−0.287157	+	0.957883i	$0.592710\pi$
$524$	1.76716	0.0771986
$525$	−1.32835	−0.0579738
$526$	−14.9855	−0.653397
$527$	−5.17898	−0.225600
$528$	8.09165	0.352144
$529$	−18.7654	−0.815887
$530$	17.1549	0.745159
$531$	5.37740	0.233359
$532$	5.26540	0.228284
$533$	1.56763	0.0679015
$534$	−6.95185	−0.300836
$535$	−32.9309	−1.42373
$536$	6.24429	0.269712
$537$	0.864853	0.0373212
$538$	6.49275	0.279922
$539$	17.8982	0.770931
$540$	1.14431	0.0492433
$541$	−14.0295	−0.603173	−0.301587	−	0.953439i	$-0.597516\pi$
$541$	−14.0295	−0.603173	−0.301587	+	0.953439i	$0.597516\pi$
$542$	20.6909	0.888750
$543$	18.3484	0.787404
$544$	3.16267	0.135598
$545$	9.41550	0.403316
$546$	4.36760	0.186916
$547$	7.37922	0.315513	0.157756	−	0.987478i	$-0.449574\pi$
$547$	7.37922	0.315513	0.157756	+	0.987478i	$0.449574\pi$
$548$	0.736235	0.0314504
$549$	5.66411	0.241738
$550$	−4.23432	−0.180552
$551$	−25.3246	−1.07886
$552$	−6.32647	−0.269273
$553$	−1.20760	−0.0513526
$554$	6.23546	0.264919
$555$	−15.2571	−0.647626
$556$	−3.02088	−0.128114
$557$	5.96331	0.252674	0.126337	−	0.991987i	$-0.459678\pi$
$557$	5.96331	0.252674	0.126337	+	0.991987i	$0.459678\pi$
$558$	−6.17267	−0.261310
$559$	24.2812	1.02698
$560$	5.97486	0.252484
$561$	3.22974	0.136360
$562$	15.7925	0.666165
$563$	29.5631	1.24594	0.622968	−	0.782247i	$-0.285926\pi$
$563$	29.5631	1.24594	0.622968	+	0.782247i	$0.285926\pi$
$564$	−3.03001	−0.127587
$565$	20.5671	0.865264
$566$	−4.99203	−0.209831
$567$	1.20760	0.0507146
$568$	−0.793110	−0.0332782
$569$	15.4328	0.646978	0.323489	−	0.946232i	$-0.395144\pi$
$569$	15.4328	0.646978	0.323489	+	0.946232i	$0.395144\pi$
$570$	−17.7116	−0.741858
$571$	−29.4020	−1.23043	−0.615217	−	0.788358i	$-0.710932\pi$
$571$	−29.4020	−1.23043	−0.615217	+	0.788358i	$0.710932\pi$
$572$	−5.67895	−0.237449
$573$	−3.07720	−0.128552
$574$	0.743546	0.0310350
$575$	2.26356	0.0943972
$576$	8.78020	0.365842
$577$	−26.7349	−1.11299	−0.556494	−	0.830851i	$-0.687854\pi$
$577$	−26.7349	−1.11299	−0.556494	+	0.830851i	$0.687854\pi$
$578$	−1.19187	−0.0495753
$579$	15.5735	0.647214
$580$	3.85115	0.159910
$581$	−0.835441	−0.0346599
$582$	12.9326	0.536072
$583$	−23.5392	−0.974895
$584$	−16.7186	−0.691819
$585$	5.99269	0.247767
$586$	−26.5853	−1.09823
$587$	−42.5242	−1.75516	−0.877582	−	0.479427i	$-0.840844\pi$
$587$	−42.5242	−1.75516	−0.877582	+	0.479427i	$0.840844\pi$
$588$	3.21110	0.132423
$589$	−38.9708	−1.60577
$590$	12.6571	0.521085
$591$	9.28603	0.381976
$592$	−19.3556	−0.795512
$593$	−16.9766	−0.697147	−0.348573	−	0.937281i	$-0.613334\pi$
$593$	−16.9766	−0.697147	−0.348573	+	0.937281i	$0.613334\pi$
$594$	3.84943	0.157944
$595$	2.38483	0.0977686
$596$	−1.41507	−0.0579634
$597$	18.3045	0.749153
$598$	−7.44260	−0.304350
$599$	13.7086	0.560120	0.280060	−	0.959982i	$-0.409646\pi$
$599$	13.7086	0.560120	0.280060	+	0.959982i	$0.409646\pi$
$600$	−3.38175	−0.138059
$601$	6.04952	0.246765	0.123383	−	0.992359i	$-0.460626\pi$
$601$	6.04952	0.246765	0.123383	+	0.992359i	$0.460626\pi$
$602$	11.5169	0.469393
$603$	2.03108	0.0827121
$604$	3.50933	0.142793
$605$	1.12326	0.0456670
$606$	7.47194	0.303527
$607$	−15.8338	−0.642675	−0.321337	−	0.946965i	$-0.604132\pi$
$607$	−15.8338	−0.642675	−0.321337	+	0.946965i	$0.604132\pi$
$608$	23.7985	0.965155
$609$	4.06416	0.164688
$610$	13.3320	0.539795
$611$	−15.8680	−0.641951
$612$	0.579444	0.0234226
$613$	27.2275	1.09971	0.549855	−	0.835260i	$-0.314683\pi$
$613$	27.2275	1.09971	0.549855	+	0.835260i	$0.314683\pi$
$614$	−12.7982	−0.516492
$615$	1.02020	0.0411386
$616$	−11.9908	−0.483122
$617$	1.16815	0.0470280	0.0235140	−	0.999724i	$-0.492515\pi$
$617$	1.16815	0.0470280	0.0235140	+	0.999724i	$0.492515\pi$
$618$	3.80977	0.153251
$619$	16.7676	0.673947	0.336974	−	0.941514i	$-0.390597\pi$
$619$	16.7676	0.673947	0.336974	+	0.941514i	$0.390597\pi$
$620$	5.92637	0.238009
$621$	−2.05782	−0.0825773
$622$	28.6535	1.14890
$623$	7.04362	0.282197
$624$	7.60254	0.304345
$625$	−18.2901	−0.731605
$626$	−7.39046	−0.295382
$627$	24.3032	0.970576
$628$	1.20064	0.0479108
$629$	−7.72570	−0.308044
$630$	2.84241	0.113244
$631$	14.6059	0.581451	0.290725	−	0.956807i	$-0.406103\pi$
$631$	14.6059	0.581451	0.290725	+	0.956807i	$0.406103\pi$
$632$	−3.07436	−0.122292
$633$	11.7502	0.467029
$634$	−12.7105	−0.504800
$635$	−14.7706	−0.586155
$636$	−4.22315	−0.167459
$637$	16.8163	0.666287
$638$	12.9552	0.512900
$639$	−0.257975	−0.0102054
$640$	8.17495	0.323143
$641$	25.6259	1.01216	0.506082	−	0.862485i	$-0.331093\pi$
$641$	25.6259	1.01216	0.506082	+	0.862485i	$0.331093\pi$
$642$	−19.8746	−0.784390
$643$	43.3906	1.71116	0.855578	−	0.517674i	$-0.173202\pi$
$643$	43.3906	1.71116	0.855578	+	0.517674i	$0.173202\pi$
$644$	1.43993	0.0567413
$645$	15.8021	0.622206
$646$	−8.96861	−0.352865
$647$	29.2864	1.15137	0.575684	−	0.817672i	$-0.304736\pi$
$647$	29.2864	1.15137	0.575684	+	0.817672i	$0.304736\pi$
$648$	3.07436	0.120772
$649$	−17.3676	−0.681738
$650$	−3.97837	−0.156044
$651$	6.25416	0.245120
$652$	3.18874	0.124881
$653$	−3.38261	−0.132372	−0.0661859	−	0.997807i	$-0.521083\pi$
$653$	−3.38261	−0.132372	−0.0661859	+	0.997807i	$0.521083\pi$
$654$	5.68250	0.222203
$655$	6.02278	0.235330
$656$	1.29427	0.0505326
$657$	−5.43805	−0.212159
$658$	−7.52640	−0.293410
$659$	20.9583	0.816421	0.408211	−	0.912888i	$-0.366153\pi$
$659$	20.9583	0.816421	0.408211	+	0.912888i	$0.366153\pi$
$660$	−3.69583	−0.143860
$661$	−28.3682	−1.10340	−0.551698	−	0.834044i	$-0.686020\pi$
$661$	−28.3682	−1.10340	−0.551698	+	0.834044i	$0.686020\pi$
$662$	−23.7203	−0.921917
$663$	3.03451	0.117851
$664$	−2.12690	−0.0825395
$665$	17.9454	0.695894
$666$	−9.20804	−0.356804
$667$	−6.92552	−0.268157
$668$	−11.1996	−0.433326
$669$	3.04271	0.117638
$670$	4.78068	0.184694
$671$	−18.2936	−0.706217
$672$	−3.81925	−0.147331
$673$	7.29182	0.281079	0.140540	−	0.990075i	$-0.455116\pi$
$673$	7.29182	0.281079	0.140540	+	0.990075i	$0.455116\pi$
$674$	−22.9559	−0.884227
$675$	−1.09998	−0.0423384
$676$	2.19710	0.0845037
$677$	37.0857	1.42532	0.712660	−	0.701509i	$-0.247490\pi$
$677$	37.0857	1.42532	0.712660	+	0.701509i	$0.247490\pi$
$678$	12.4128	0.476710
$679$	−13.1033	−0.502858
$680$	6.07139	0.232827
$681$	19.3052	0.739777
$682$	19.9361	0.763394
$683$	−34.4405	−1.31783	−0.658914	−	0.752218i	$-0.728984\pi$
$683$	−34.4405	−1.31783	−0.658914	+	0.752218i	$0.728984\pi$
$684$	4.36021	0.166717
$685$	2.50922	0.0958723
$686$	18.0514	0.689204
$687$	7.39469	0.282125
$688$	20.0470	0.764287
$689$	−22.1164	−0.842566
$690$	−4.84361	−0.184393
$691$	−5.83879	−0.222118	−0.111059	−	0.993814i	$-0.535424\pi$
$691$	−5.83879	−0.222118	−0.111059	+	0.993814i	$0.535424\pi$
$692$	−10.8557	−0.412673
$693$	−3.90025	−0.148158
$694$	18.4911	0.701913
$695$	−10.2957	−0.390537
$696$	10.3467	0.392190
$697$	0.516600	0.0195676
$698$	−27.4522	−1.03908
$699$	20.7670	0.785480
$700$	0.769702	0.0290920
$701$	28.1015	1.06138	0.530689	−	0.847567i	$-0.321933\pi$
$701$	28.1015	1.06138	0.530689	+	0.847567i	$0.321933\pi$
$702$	3.61675	0.136505
$703$	−58.1345	−2.19258
$704$	−28.3578	−1.06877
$705$	−10.3268	−0.388931
$706$	−30.6977	−1.15532
$707$	−7.57058	−0.284721
$708$	−3.11590	−0.117103
$709$	30.0641	1.12908	0.564541	−	0.825405i	$-0.309053\pi$
$709$	30.0641	1.12908	0.564541	+	0.825405i	$0.309053\pi$
$710$	−0.607213	−0.0227883
$711$	−1.00000	−0.0375029
$712$	17.9319	0.672026
$713$	−10.6574	−0.399122
$714$	1.43931	0.0538648
$715$	−19.3548	−0.723830
$716$	−0.501134	−0.0187282
$717$	18.7946	0.701895
$718$	−15.9577	−0.595536
$719$	23.7863	0.887079	0.443540	−	0.896255i	$-0.353723\pi$
$719$	23.7863	0.887079	0.443540	+	0.896255i	$0.353723\pi$
$720$	4.94769	0.184390
$721$	−3.86006	−0.143756
$722$	−44.8416	−1.66883
$723$	−14.9047	−0.554312
$724$	−10.6318	−0.395130
$725$	−3.70197	−0.137488
$726$	0.677917	0.0251599
$727$	0.618806	0.0229503	0.0114751	−	0.999934i	$-0.496347\pi$
$727$	0.618806	0.0229503	0.0114751	+	0.999934i	$0.496347\pi$
$728$	−11.2660	−0.417545
$729$	1.00000	0.0370370
$730$	−12.7999	−0.473745
$731$	8.00167	0.295952
$732$	−3.28203	−0.121307
$733$	−4.95936	−0.183178	−0.0915891	−	0.995797i	$-0.529195\pi$
$733$	−4.95936	−0.183178	−0.0915891	+	0.995797i	$0.529195\pi$
$734$	25.6762	0.947726
$735$	10.9440	0.403675
$736$	6.50818	0.239895
$737$	−6.55987	−0.241636
$738$	0.615720	0.0226650
$739$	4.27748	0.157349	0.0786747	−	0.996900i	$-0.474931\pi$
$739$	4.27748	0.157349	0.0786747	+	0.996900i	$0.474931\pi$
$740$	8.84061	0.324987
$741$	22.8341	0.838833
$742$	−10.4901	−0.385103
$743$	−23.3032	−0.854912	−0.427456	−	0.904036i	$-0.640590\pi$
$743$	−23.3032	−0.854912	−0.427456	+	0.904036i	$0.640590\pi$
$744$	15.9221	0.583731
$745$	−4.82279	−0.176694
$746$	37.0495	1.35648
$747$	−0.691816	−0.0253122
$748$	−1.87145	−0.0684271
$749$	20.1370	0.735790
$750$	−14.3579	−0.524277
$751$	−43.3337	−1.58127	−0.790635	−	0.612288i	$-0.790249\pi$
$751$	−43.3337	−1.58127	−0.790635	+	0.612288i	$0.790249\pi$
$752$	−13.1010	−0.477743
$753$	2.88053	0.104972
$754$	12.1721	0.443280
$755$	11.9604	0.435284
$756$	−0.699739	−0.0254493
$757$	32.4587	1.17973	0.589866	−	0.807501i	$-0.299181\pi$
$757$	32.4587	1.17973	0.589866	+	0.807501i	$0.299181\pi$
$758$	−6.12361	−0.222420
$759$	6.64621	0.241242
$760$	45.6861	1.65721
$761$	−24.9242	−0.903500	−0.451750	−	0.892144i	$-0.649200\pi$
$761$	−24.9242	−0.903500	−0.451750	+	0.892144i	$0.649200\pi$
$762$	−8.91447	−0.322937
$763$	−5.75752	−0.208436
$764$	1.78307	0.0645091
$765$	1.97485	0.0714007
$766$	44.3317	1.60177
$767$	−16.3178	−0.589201
$768$	−12.6266	−0.455624
$769$	−11.8348	−0.426774	−0.213387	−	0.976968i	$-0.568450\pi$
$769$	−11.8348	−0.426774	−0.213387	+	0.976968i	$0.568450\pi$
$770$	−9.18025	−0.330833
$771$	−3.32885	−0.119886
$772$	−9.02398	−0.324780
$773$	49.5632	1.78266	0.891332	−	0.453352i	$-0.149772\pi$
$773$	49.5632	1.78266	0.891332	+	0.453352i	$0.149772\pi$
$774$	9.53696	0.342799
$775$	−5.69679	−0.204635
$776$	−33.3588	−1.19751
$777$	9.32959	0.334697
$778$	12.9153	0.463036
$779$	3.88732	0.139278
$780$	−3.47243	−0.124333
$781$	0.833193	0.0298140
$782$	−2.45265	−0.0877066
$783$	3.36547	0.120272
$784$	13.8839	0.495854
$785$	4.09199	0.146050
$786$	3.63491	0.129653
$787$	46.1822	1.64622	0.823109	−	0.567884i	$-0.192238\pi$
$787$	46.1822	1.64622	0.823109	+	0.567884i	$0.192238\pi$
$788$	−5.38073	−0.191681
$789$	12.5731	0.447613
$790$	−2.35376	−0.0837431
$791$	−12.5766	−0.447174
$792$	−9.92939	−0.352826
$793$	−17.1878	−0.610357
$794$	3.05093	0.108274
$795$	−14.3932	−0.510475
$796$	−10.6064	−0.375935
$797$	19.6050	0.694446	0.347223	−	0.937783i	$-0.387125\pi$
$797$	19.6050	0.694446	0.347223	+	0.937783i	$0.387125\pi$
$798$	10.8305	0.383397
$799$	−5.22918	−0.184995
$800$	3.47888	0.122997
$801$	5.83272	0.206089
$802$	−4.00705	−0.141494
$803$	17.5635	0.619802
$804$	−1.17690	−0.0415060
$805$	4.90754	0.172968
$806$	18.7311	0.659773
$807$	−5.44753	−0.191762
$808$	−19.2735	−0.678038
$809$	18.3155	0.643940	0.321970	−	0.946750i	$-0.395655\pi$
$809$	18.3155	0.643940	0.321970	+	0.946750i	$0.395655\pi$
$810$	2.35376	0.0827027
$811$	−6.09419	−0.213996	−0.106998	−	0.994259i	$-0.534124\pi$
$811$	−6.09419	−0.213996	−0.106998	+	0.994259i	$0.534124\pi$
$812$	−2.35495	−0.0826426
$813$	−17.3600	−0.608842
$814$	29.7396	1.04237
$815$	10.8678	0.380682
$816$	2.50536	0.0877051
$817$	60.2111	2.10652
$818$	18.9519	0.662637
$819$	−3.66449	−0.128048
$820$	−0.591151	−0.0206439
$821$	5.49155	0.191656	0.0958282	−	0.995398i	$-0.469450\pi$
$821$	5.49155	0.191656	0.0958282	+	0.995398i	$0.469450\pi$
$822$	1.51438	0.0528200
$823$	−23.0715	−0.804222	−0.402111	−	0.915591i	$-0.631723\pi$
$823$	−23.0715	−0.804222	−0.402111	+	0.915591i	$0.631723\pi$
$824$	−9.82708	−0.342343
$825$	3.55266	0.123688
$826$	−7.73974	−0.269300
$827$	19.3059	0.671333	0.335667	−	0.941981i	$-0.391038\pi$
$827$	19.3059	0.671333	0.335667	+	0.941981i	$0.391038\pi$
$828$	1.19239	0.0414383
$829$	−15.0050	−0.521146	−0.260573	−	0.965454i	$-0.583912\pi$
$829$	−15.0050	−0.521146	−0.260573	+	0.965454i	$0.583912\pi$
$830$	−1.62837	−0.0565216
$831$	−5.23166	−0.181484
$832$	−26.6436	−0.923702
$833$	5.54169	0.192008
$834$	−6.21371	−0.215163
$835$	−38.1703	−1.32094
$836$	−14.0823	−0.487048
$837$	5.17898	0.179012
$838$	−33.9409	−1.17247
$839$	12.5383	0.432872	0.216436	−	0.976297i	$-0.430557\pi$
$839$	12.5383	0.432872	0.216436	+	0.976297i	$0.430557\pi$
$840$	−7.33184	−0.252973
$841$	−17.6736	−0.609434
$842$	15.2680	0.526171
$843$	−13.2501	−0.456359
$844$	−6.80858	−0.234361
$845$	7.48809	0.257598
$846$	−6.23250	−0.214278
$847$	−0.686866	−0.0236010
$848$	−18.2597	−0.627042
$849$	4.18840	0.143745
$850$	−1.31104	−0.0449683
$851$	−15.8981	−0.544979
$852$	0.149482	0.00512118
$853$	42.4006	1.45177	0.725885	−	0.687816i	$-0.241430\pi$
$853$	42.4006	1.45177	0.725885	+	0.687816i	$0.241430\pi$
$854$	−8.15240	−0.278969
$855$	14.8603	0.508213
$856$	51.2655	1.75222
$857$	−7.79955	−0.266428	−0.133214	−	0.991087i	$-0.542530\pi$
$857$	−7.79955	−0.266428	−0.133214	+	0.991087i	$0.542530\pi$
$858$	−11.6812	−0.398788
$859$	49.9784	1.70524	0.852620	−	0.522531i	$-0.175012\pi$
$859$	49.9784	1.70524	0.852620	+	0.522531i	$0.175012\pi$
$860$	−9.15641	−0.312231
$861$	−0.623848	−0.0212607
$862$	−10.7245	−0.365277
$863$	−17.8699	−0.608300	−0.304150	−	0.952624i	$-0.598372\pi$
$863$	−17.8699	−0.608300	−0.304150	+	0.952624i	$0.598372\pi$
$864$	−3.16267	−0.107596
$865$	−36.9983	−1.25798
$866$	−36.3911	−1.23662
$867$	1.00000	0.0339618
$868$	−3.62393	−0.123004
$869$	3.22974	0.109561
$870$	7.92152	0.268565
$871$	−6.16335	−0.208837
$872$	−14.6577	−0.496372
$873$	−10.8506	−0.367238
$874$	−18.4557	−0.624275
$875$	14.5474	0.491793
$876$	3.15105	0.106464
$877$	−39.4529	−1.33223	−0.666114	−	0.745850i	$-0.732044\pi$
$877$	−39.4529	−1.33223	−0.666114	+	0.745850i	$0.732044\pi$
$878$	−0.694537	−0.0234395
$879$	22.3055	0.752345
$880$	−15.9798	−0.538678
$881$	31.1502	1.04948	0.524738	−	0.851264i	$-0.324163\pi$
$881$	31.1502	1.04948	0.524738	+	0.851264i	$0.324163\pi$
$882$	6.60498	0.222401
$883$	17.4395	0.586886	0.293443	−	0.955977i	$-0.405199\pi$
$883$	17.4395	0.586886	0.293443	+	0.955977i	$0.405199\pi$
$884$	−1.75833	−0.0591390
$885$	−10.6195	−0.356972
$886$	−12.8033	−0.430134
$887$	18.9414	0.635989	0.317995	−	0.948093i	$-0.396991\pi$
$887$	18.9414	0.635989	0.317995	+	0.948093i	$0.396991\pi$
$888$	23.7516	0.797052
$889$	9.03215	0.302929
$890$	13.7288	0.460191
$891$	−3.22974	−0.108200
$892$	−1.76308	−0.0590323
$893$	−39.3486	−1.31675
$894$	−2.91068	−0.0973478
$895$	−1.70795	−0.0570905
$896$	−4.99893	−0.167002
$897$	6.24447	0.208497
$898$	12.4069	0.414024
$899$	17.4297	0.581313
$900$	0.637379	0.0212460
$901$	−7.28827	−0.242808
$902$	−1.98862	−0.0662136
$903$	−9.66285	−0.321560
$904$	−32.0181	−1.06490
$905$	−36.2352	−1.20450
$906$	7.21842	0.239816
$907$	−16.3693	−0.543533	−0.271766	−	0.962363i	$-0.587608\pi$
$907$	−16.3693	−0.543533	−0.271766	+	0.962363i	$0.587608\pi$
$908$	−11.1863	−0.371230
$909$	−6.26909	−0.207933
$910$	−8.62534	−0.285927
$911$	−34.4067	−1.13994	−0.569972	−	0.821664i	$-0.693046\pi$
$911$	−34.4067	−1.13994	−0.569972	+	0.821664i	$0.693046\pi$
$912$	18.8524	0.624264
$913$	2.23439	0.0739474
$914$	−8.24807	−0.272822
$915$	−11.1857	−0.369789
$916$	−4.28481	−0.141574
$917$	−3.68289	−0.121620
$918$	1.19187	0.0393376
$919$	5.19822	0.171473	0.0857367	−	0.996318i	$-0.472676\pi$
$919$	5.19822	0.171473	0.0857367	+	0.996318i	$0.472676\pi$
$920$	12.4938	0.411909
$921$	10.7379	0.353825
$922$	18.8342	0.620270
$923$	0.782830	0.0257672
$924$	2.25997	0.0743477
$925$	−8.49815	−0.279417
$926$	28.5387	0.937839
$927$	−3.19646	−0.104985
$928$	−10.6439	−0.349402
$929$	−41.8965	−1.37458	−0.687289	−	0.726384i	$-0.741200\pi$
$929$	−41.8965	−1.37458	−0.687289	+	0.726384i	$0.741200\pi$
$930$	12.1901	0.399728
$931$	41.7002	1.36667
$932$	−12.0333	−0.394164
$933$	−24.0408	−0.787060
$934$	45.9991	1.50514
$935$	−6.37824	−0.208591
$936$	−9.32920	−0.304934
$937$	10.4837	0.342487	0.171243	−	0.985229i	$-0.445222\pi$
$937$	10.4837	0.342487	0.171243	+	0.985229i	$0.445222\pi$
$938$	−2.92336	−0.0954509
$939$	6.20073	0.202353
$940$	5.98381	0.195170
$941$	−33.6061	−1.09553	−0.547763	−	0.836634i	$-0.684520\pi$
$941$	−33.6061	−1.09553	−0.547763	+	0.836634i	$0.684520\pi$
$942$	2.46962	0.0804647
$943$	1.06307	0.0346182
$944$	−13.4723	−0.438486
$945$	−2.38483	−0.0775786
$946$	−30.8019	−1.00146
$947$	−36.7855	−1.19537	−0.597685	−	0.801731i	$-0.703913\pi$
$947$	−36.7855	−1.19537	−0.597685	+	0.801731i	$0.703913\pi$
$948$	0.579444	0.0188195
$949$	16.5018	0.535672
$950$	−9.86533	−0.320073
$951$	10.6644	0.345815
$952$	−3.71262	−0.120327
$953$	−6.83498	−0.221407	−0.110703	−	0.993853i	$-0.535310\pi$
$953$	−6.83498	−0.221407	−0.110703	+	0.993853i	$0.535310\pi$
$954$	−8.68668	−0.281242
$955$	6.07700	0.196647
$956$	−10.8904	−0.352220
$957$	−10.8696	−0.351364
$958$	−19.9644	−0.645020
$959$	−1.53437	−0.0495474
$960$	−17.3395	−0.559631
$961$	−4.17819	−0.134780
$962$	27.9419	0.900883
$963$	16.6752	0.537350
$964$	8.63644	0.278161
$965$	−30.7553	−0.990048
$966$	2.96183	0.0952953
$967$	−5.40539	−0.173826	−0.0869128	−	0.996216i	$-0.527700\pi$
$967$	−5.40539	−0.173826	−0.0869128	+	0.996216i	$0.527700\pi$
$968$	−1.74865	−0.0562037
$969$	7.52481	0.241732
$970$	−25.5398	−0.820034
$971$	−55.6269	−1.78515	−0.892576	−	0.450897i	$-0.851104\pi$
$971$	−55.6269	−1.78515	−0.892576	+	0.450897i	$0.851104\pi$
$972$	−0.579444	−0.0185857
$973$	6.29573	0.201832
$974$	−31.1595	−0.998416
$975$	3.33792	0.106899
$976$	−14.1906	−0.454231
$977$	−26.4231	−0.845349	−0.422674	−	0.906282i	$-0.638909\pi$
$977$	−26.4231	−0.845349	−0.422674	+	0.906282i	$0.638909\pi$
$978$	6.55899	0.209733
$979$	−18.8382	−0.602070
$980$	−6.34142	−0.202569
$981$	−4.76772	−0.152221
$982$	−24.1623	−0.771048
$983$	−27.7471	−0.884994	−0.442497	−	0.896770i	$-0.645907\pi$
$983$	−27.7471	−0.884994	−0.442497	+	0.896770i	$0.645907\pi$
$984$	−1.58822	−0.0506305
$985$	−18.3385	−0.584313
$986$	4.01121	0.127743
$987$	6.31478	0.201002
$988$	−13.2311	−0.420937
$989$	16.4660	0.523587
$990$	−7.60204	−0.241609
$991$	−47.9428	−1.52295	−0.761476	−	0.648193i	$-0.775525\pi$
$991$	−47.9428	−1.52295	−0.761476	+	0.648193i	$0.775525\pi$
$992$	−16.3794	−0.520046
$993$	19.9018	0.631563
$994$	0.371306	0.0117771
$995$	−36.1485	−1.14599
$996$	0.400869	0.0127020
$997$	9.92144	0.314215	0.157108	−	0.987581i	$-0.449783\pi$
$997$	9.92144	0.314215	0.157108	+	0.987581i	$0.449783\pi$
$998$	34.8890	1.10439
$999$	7.72570	0.244430

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4029.2.a.j.1.7	✓	25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4029.2.a.j.1.7	✓	25	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:	\( N \)	\(=\)	\( 4029 = 3 \cdot 17 \cdot 79 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4029.a (trivial)

\(f(q)\)	\(=\)	\(q-1.19187 q^{2} +1.00000 q^{3} -0.579444 q^{4} -1.97485 q^{5} -1.19187 q^{6} +1.20760 q^{7} +3.07436 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.19187 q^{2} +1.00000 q^{3} -0.579444 q^{4} -1.97485 q^{5} -1.19187 q^{6} +1.20760 q^{7} +3.07436 q^{8} +1.00000 q^{9} +2.35376 q^{10} -3.22974 q^{11} -0.579444 q^{12} -3.03451 q^{13} -1.43931 q^{14} -1.97485 q^{15} -2.50536 q^{16} -1.00000 q^{17} -1.19187 q^{18} -7.52481 q^{19} +1.14431 q^{20} +1.20760 q^{21} +3.84943 q^{22} -2.05782 q^{23} +3.07436 q^{24} -1.09998 q^{25} +3.61675 q^{26} +1.00000 q^{27} -0.699739 q^{28} +3.36547 q^{29} +2.35376 q^{30} +5.17898 q^{31} -3.16267 q^{32} -3.22974 q^{33} +1.19187 q^{34} -2.38483 q^{35} -0.579444 q^{36} +7.72570 q^{37} +8.96861 q^{38} -3.03451 q^{39} -6.07139 q^{40} -0.516600 q^{41} -1.43931 q^{42} -8.00167 q^{43} +1.87145 q^{44} -1.97485 q^{45} +2.45265 q^{46} +5.22918 q^{47} -2.50536 q^{48} -5.54169 q^{49} +1.31104 q^{50} -1.00000 q^{51} +1.75833 q^{52} +7.28827 q^{53} -1.19187 q^{54} +6.37824 q^{55} +3.71262 q^{56} -7.52481 q^{57} -4.01121 q^{58} +5.37740 q^{59} +1.14431 q^{60} +5.66411 q^{61} -6.17267 q^{62} +1.20760 q^{63} +8.78020 q^{64} +5.99269 q^{65} +3.84943 q^{66} +2.03108 q^{67} +0.579444 q^{68} -2.05782 q^{69} +2.84241 q^{70} -0.257975 q^{71} +3.07436 q^{72} -5.43805 q^{73} -9.20804 q^{74} -1.09998 q^{75} +4.36021 q^{76} -3.90025 q^{77} +3.61675 q^{78} -1.00000 q^{79} +4.94769 q^{80} +1.00000 q^{81} +0.615720 q^{82} -0.691816 q^{83} -0.699739 q^{84} +1.97485 q^{85} +9.53696 q^{86} +3.36547 q^{87} -9.92939 q^{88} +5.83272 q^{89} +2.35376 q^{90} -3.66449 q^{91} +1.19239 q^{92} +5.17898 q^{93} -6.23250 q^{94} +14.8603 q^{95} -3.16267 q^{96} -10.8506 q^{97} +6.60498 q^{98} -3.22974 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q + 6 q^{2} + 25 q^{3} + 26 q^{4} + 6 q^{5} + 6 q^{6} + 4 q^{7} + 18 q^{8} + 25 q^{9}+O(q^{10}) \) 25 * q + 6 * q^2 + 25 * q^3 + 26 * q^4 + 6 * q^5 + 6 * q^6 + 4 * q^7 + 18 * q^8 + 25 * q^9	\( 25 q + 6 q^{2} + 25 q^{3} + 26 q^{4} + 6 q^{5} + 6 q^{6} + 4 q^{7} + 18 q^{8} + 25 q^{9} + 13 q^{10} + 19 q^{11} + 26 q^{12} + 17 q^{14} + 6 q^{15} + 16 q^{16} - 25 q^{17} + 6 q^{18} + 25 q^{19} + 32 q^{20} + 4 q^{21} - 7 q^{22} + 8 q^{23} + 18 q^{24} + 15 q^{25} + 20 q^{26} + 25 q^{27} + 9 q^{28} + 21 q^{29} + 13 q^{30} + 4 q^{31} + 27 q^{32} + 19 q^{33} - 6 q^{34} + 50 q^{35} + 26 q^{36} - 8 q^{37} + 31 q^{38} + 52 q^{40} + 40 q^{41} + 17 q^{42} + 21 q^{43} + 34 q^{44} + 6 q^{45} + 29 q^{46} + 43 q^{47} + 16 q^{48} + 21 q^{49} + 13 q^{50} - 25 q^{51} + 3 q^{52} + 44 q^{53} + 6 q^{54} + 13 q^{55} + 38 q^{56} + 25 q^{57} - 5 q^{58} + 45 q^{59} + 32 q^{60} + 22 q^{61} + 4 q^{62} + 4 q^{63} + 26 q^{64} + 43 q^{65} - 7 q^{66} + 8 q^{67} - 26 q^{68} + 8 q^{69} + 29 q^{70} + 9 q^{71} + 18 q^{72} - 7 q^{73} + 18 q^{74} + 15 q^{75} + 33 q^{76} + 20 q^{77} + 20 q^{78} - 25 q^{79} + 42 q^{80} + 25 q^{81} - 43 q^{82} + 41 q^{83} + 9 q^{84} - 6 q^{85} - 12 q^{86} + 21 q^{87} - 43 q^{88} + 68 q^{89} + 13 q^{90} + 10 q^{91} + 2 q^{92} + 4 q^{93} - 17 q^{94} + 8 q^{95} + 27 q^{96} + 15 q^{97} + 11 q^{98} + 19 q^{99}+O(q^{100}) \) 25 * q + 6 * q^2 + 25 * q^3 + 26 * q^4 + 6 * q^5 + 6 * q^6 + 4 * q^7 + 18 * q^8 + 25 * q^9 + 13 * q^10 + 19 * q^11 + 26 * q^12 + 17 * q^14 + 6 * q^15 + 16 * q^16 - 25 * q^17 + 6 * q^18 + 25 * q^19 + 32 * q^20 + 4 * q^21 - 7 * q^22 + 8 * q^23 + 18 * q^24 + 15 * q^25 + 20 * q^26 + 25 * q^27 + 9 * q^28 + 21 * q^29 + 13 * q^30 + 4 * q^31 + 27 * q^32 + 19 * q^33 - 6 * q^34 + 50 * q^35 + 26 * q^36 - 8 * q^37 + 31 * q^38 + 52 * q^40 + 40 * q^41 + 17 * q^42 + 21 * q^43 + 34 * q^44 + 6 * q^45 + 29 * q^46 + 43 * q^47 + 16 * q^48 + 21 * q^49 + 13 * q^50 - 25 * q^51 + 3 * q^52 + 44 * q^53 + 6 * q^54 + 13 * q^55 + 38 * q^56 + 25 * q^57 - 5 * q^58 + 45 * q^59 + 32 * q^60 + 22 * q^61 + 4 * q^62 + 4 * q^63 + 26 * q^64 + 43 * q^65 - 7 * q^66 + 8 * q^67 - 26 * q^68 + 8 * q^69 + 29 * q^70 + 9 * q^71 + 18 * q^72 - 7 * q^73 + 18 * q^74 + 15 * q^75 + 33 * q^76 + 20 * q^77 + 20 * q^78 - 25 * q^79 + 42 * q^80 + 25 * q^81 - 43 * q^82 + 41 * q^83 + 9 * q^84 - 6 * q^85 - 12 * q^86 + 21 * q^87 - 43 * q^88 + 68 * q^89 + 13 * q^90 + 10 * q^91 + 2 * q^92 + 4 * q^93 - 17 * q^94 + 8 * q^95 + 27 * q^96 + 15 * q^97 + 11 * q^98 + 19 * q^99

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