LMFDB - Embedded newform 2005.2.a.d.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2005,2,Mod(1,2005)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2005, 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("2005.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2005 = 5 \cdot 401 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2005.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:	$16.0100056053$
Analytic rank:	$1$
Dimension:	$25$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Character	$\chi$	$=$	2005.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.64150 q^{2} +1.09521 q^{3} +0.694512 q^{4} +1.00000 q^{5} -1.79778 q^{6} -0.515011 q^{7} +2.14295 q^{8} -1.80052 q^{9} +O(q^{10})$	\(q-1.64150 q^{2} +1.09521 q^{3} +0.694512 q^{4} +1.00000 q^{5} -1.79778 q^{6} -0.515011 q^{7} +2.14295 q^{8} -1.80052 q^{9} -1.64150 q^{10} +3.52910 q^{11} +0.760636 q^{12} -1.96733 q^{13} +0.845390 q^{14} +1.09521 q^{15} -4.90668 q^{16} +2.83180 q^{17} +2.95554 q^{18} -5.94068 q^{19} +0.694512 q^{20} -0.564046 q^{21} -5.79301 q^{22} -8.23308 q^{23} +2.34699 q^{24} +1.00000 q^{25} +3.22936 q^{26} -5.25757 q^{27} -0.357681 q^{28} +2.68497 q^{29} -1.79778 q^{30} -5.71720 q^{31} +3.76839 q^{32} +3.86511 q^{33} -4.64839 q^{34} -0.515011 q^{35} -1.25048 q^{36} +3.54000 q^{37} +9.75160 q^{38} -2.15464 q^{39} +2.14295 q^{40} +4.61314 q^{41} +0.925879 q^{42} -2.96853 q^{43} +2.45100 q^{44} -1.80052 q^{45} +13.5146 q^{46} -2.50578 q^{47} -5.37384 q^{48} -6.73476 q^{49} -1.64150 q^{50} +3.10142 q^{51} -1.36633 q^{52} +2.56637 q^{53} +8.63029 q^{54} +3.52910 q^{55} -1.10365 q^{56} -6.50629 q^{57} -4.40737 q^{58} -7.61222 q^{59} +0.760636 q^{60} +0.0740547 q^{61} +9.38477 q^{62} +0.927286 q^{63} +3.62756 q^{64} -1.96733 q^{65} -6.34457 q^{66} -1.96087 q^{67} +1.96672 q^{68} -9.01695 q^{69} +0.845390 q^{70} -2.26874 q^{71} -3.85842 q^{72} -1.86421 q^{73} -5.81090 q^{74} +1.09521 q^{75} -4.12587 q^{76} -1.81753 q^{77} +3.53683 q^{78} -5.21234 q^{79} -4.90668 q^{80} -0.356599 q^{81} -7.57245 q^{82} +2.10479 q^{83} -0.391736 q^{84} +2.83180 q^{85} +4.87283 q^{86} +2.94061 q^{87} +7.56271 q^{88} +4.41157 q^{89} +2.95554 q^{90} +1.01320 q^{91} -5.71797 q^{92} -6.26154 q^{93} +4.11323 q^{94} -5.94068 q^{95} +4.12717 q^{96} -11.1710 q^{97} +11.0551 q^{98} -6.35421 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 25 q - 5 q^{2} - 10 q^{3} + 25 q^{4} + 25 q^{5} + 2 q^{6} - 31 q^{7} - 30 q^{8} + 17 q^{9}+O(q^{10}) $ 25 * q - 5 * q^2 - 10 * q^3 + 25 * q^4 + 25 * q^5 + 2 * q^6 - 31 * q^7 - 30 * q^8 + 17 * q^9	\( 25 q - 5 q^{2} - 10 q^{3} + 25 q^{4} + 25 q^{5} + 2 q^{6} - 31 q^{7} - 30 q^{8} + 17 q^{9} - 5 q^{10} - 30 q^{11} - 29 q^{12} - 18 q^{13} + 6 q^{14} - 10 q^{15} + 21 q^{16} - 18 q^{17} - 30 q^{18} - 17 q^{19} + 25 q^{20} + 6 q^{21} - 2 q^{22} - 44 q^{23} + 11 q^{24} + 25 q^{25} - 14 q^{26} - 25 q^{27} - 50 q^{28} - 9 q^{29} + 2 q^{30} - 13 q^{31} - 45 q^{32} - 21 q^{33} - 21 q^{34} - 31 q^{35} + 5 q^{36} - 28 q^{37} - 32 q^{38} + 9 q^{39} - 30 q^{40} + 28 q^{41} - 67 q^{42} - 61 q^{43} - 49 q^{44} + 17 q^{45} + 18 q^{46} - 53 q^{47} - 44 q^{48} + 28 q^{49} - 5 q^{50} - 30 q^{51} - 3 q^{52} - 36 q^{53} + 17 q^{54} - 30 q^{55} - 3 q^{56} - 13 q^{57} + 2 q^{58} - 39 q^{59} - 29 q^{60} + 10 q^{61} - 30 q^{62} - 44 q^{63} - 4 q^{64} - 18 q^{65} + 33 q^{66} - 10 q^{67} - 18 q^{68} - 6 q^{69} + 6 q^{70} - 7 q^{71} - q^{72} - 26 q^{73} - 3 q^{74} - 10 q^{75} + 12 q^{76} + 29 q^{77} - 5 q^{78} - 6 q^{79} + 21 q^{80} + 13 q^{81} - 30 q^{82} - 35 q^{83} + 117 q^{84} - 18 q^{85} + 14 q^{86} - 104 q^{87} + 53 q^{88} + 7 q^{89} - 30 q^{90} - 25 q^{91} - 31 q^{92} + 2 q^{93} + 68 q^{94} - 17 q^{95} + 92 q^{96} + 6 q^{97} + 15 q^{98} - 36 q^{99}+O(q^{100}) \) 25 * q - 5 * q^2 - 10 * q^3 + 25 * q^4 + 25 * q^5 + 2 * q^6 - 31 * q^7 - 30 * q^8 + 17 * q^9 - 5 * q^10 - 30 * q^11 - 29 * q^12 - 18 * q^13 + 6 * q^14 - 10 * q^15 + 21 * q^16 - 18 * q^17 - 30 * q^18 - 17 * q^19 + 25 * q^20 + 6 * q^21 - 2 * q^22 - 44 * q^23 + 11 * q^24 + 25 * q^25 - 14 * q^26 - 25 * q^27 - 50 * q^28 - 9 * q^29 + 2 * q^30 - 13 * q^31 - 45 * q^32 - 21 * q^33 - 21 * q^34 - 31 * q^35 + 5 * q^36 - 28 * q^37 - 32 * q^38 + 9 * q^39 - 30 * q^40 + 28 * q^41 - 67 * q^42 - 61 * q^43 - 49 * q^44 + 17 * q^45 + 18 * q^46 - 53 * q^47 - 44 * q^48 + 28 * q^49 - 5 * q^50 - 30 * q^51 - 3 * q^52 - 36 * q^53 + 17 * q^54 - 30 * q^55 - 3 * q^56 - 13 * q^57 + 2 * q^58 - 39 * q^59 - 29 * q^60 + 10 * q^61 - 30 * q^62 - 44 * q^63 - 4 * q^64 - 18 * q^65 + 33 * q^66 - 10 * q^67 - 18 * q^68 - 6 * q^69 + 6 * q^70 - 7 * q^71 - q^72 - 26 * q^73 - 3 * q^74 - 10 * q^75 + 12 * q^76 + 29 * q^77 - 5 * q^78 - 6 * q^79 + 21 * q^80 + 13 * q^81 - 30 * q^82 - 35 * q^83 + 117 * q^84 - 18 * q^85 + 14 * q^86 - 104 * q^87 + 53 * q^88 + 7 * q^89 - 30 * q^90 - 25 * q^91 - 31 * q^92 + 2 * q^93 + 68 * q^94 - 17 * q^95 + 92 * q^96 + 6 * q^97 + 15 * q^98 - 36 * 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 $

$2$	−1.64150	−1.16071	−0.580357	−	0.814362i	$-0.697087\pi$
$2$	−1.64150	−1.16071	−0.580357	+	0.814362i	$0.697087\pi$
$3$	1.09521	0.632320	0.316160	−	0.948706i	$-0.397606\pi$
$3$	1.09521	0.632320	0.316160	+	0.948706i	$0.397606\pi$
$4$	0.694512	0.347256
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−1.79778	−0.733942
$7$	−0.515011	−0.194656	−0.0973280	−	0.995252i	$-0.531030\pi$
$7$	−0.515011	−0.194656	−0.0973280	+	0.995252i	$0.531030\pi$
$8$	2.14295	0.757649
$9$	−1.80052	−0.600172
$10$	−1.64150	−0.519087
$11$	3.52910	1.06407	0.532033	−	0.846724i	$-0.321428\pi$
$11$	3.52910	1.06407	0.532033	+	0.846724i	$0.321428\pi$
$12$	0.760636	0.219577
$13$	−1.96733	−0.545639	−0.272819	−	0.962065i	$-0.587956\pi$
$13$	−1.96733	−0.545639	−0.272819	+	0.962065i	$0.587956\pi$
$14$	0.845390	0.225940
$15$	1.09521	0.282782
$16$	−4.90668	−1.22667
$17$	2.83180	0.686813	0.343406	−	0.939187i	$-0.388419\pi$
$17$	2.83180	0.686813	0.343406	+	0.939187i	$0.388419\pi$
$18$	2.95554	0.696627
$19$	−5.94068	−1.36288	−0.681442	−	0.731872i	$-0.738647\pi$
$19$	−5.94068	−1.36288	−0.681442	+	0.731872i	$0.738647\pi$
$20$	0.694512	0.155298
$21$	−0.564046	−0.123085
$22$	−5.79301	−1.23507
$23$	−8.23308	−1.71671	−0.858357	−	0.513052i	$-0.828515\pi$
$23$	−8.23308	−1.71671	−0.858357	+	0.513052i	$0.828515\pi$
$24$	2.34699	0.479076
$25$	1.00000	0.200000
$26$	3.22936	0.633330
$27$	−5.25757	−1.01182
$28$	−0.357681	−0.0675954
$29$	2.68497	0.498586	0.249293	−	0.968428i	$-0.419802\pi$
$29$	2.68497	0.498586	0.249293	+	0.968428i	$0.419802\pi$
$30$	−1.79778	−0.328229
$31$	−5.71720	−1.02684	−0.513420	−	0.858137i	$-0.671622\pi$
$31$	−5.71720	−1.02684	−0.513420	+	0.858137i	$0.671622\pi$
$32$	3.76839	0.666163
$33$	3.86511	0.672829
$34$	−4.64839	−0.797193
$35$	−0.515011	−0.0870528
$36$	−1.25048	−0.208413
$37$	3.54000	0.581972	0.290986	−	0.956727i	$-0.406017\pi$
$37$	3.54000	0.581972	0.290986	+	0.956727i	$0.406017\pi$
$38$	9.75160	1.58192
$39$	−2.15464	−0.345018
$40$	2.14295	0.338831
$41$	4.61314	0.720451	0.360225	−	0.932865i	$-0.382700\pi$
$41$	4.61314	0.720451	0.360225	+	0.932865i	$0.382700\pi$
$42$	0.925879	0.142866
$43$	−2.96853	−0.452696	−0.226348	−	0.974046i	$-0.572679\pi$
$43$	−2.96853	−0.452696	−0.226348	+	0.974046i	$0.572679\pi$
$44$	2.45100	0.369503
$45$	−1.80052	−0.268405
$46$	13.5146	1.99261
$47$	−2.50578	−0.365505	−0.182753	−	0.983159i	$-0.558501\pi$
$47$	−2.50578	−0.365505	−0.182753	+	0.983159i	$0.558501\pi$
$48$	−5.37384	−0.775647
$49$	−6.73476	−0.962109
$50$	−1.64150	−0.232143
$51$	3.10142	0.434285
$52$	−1.36633	−0.189476
$53$	2.56637	0.352518	0.176259	−	0.984344i	$-0.443600\pi$
$53$	2.56637	0.352518	0.176259	+	0.984344i	$0.443600\pi$
$54$	8.63029	1.17443
$55$	3.52910	0.475864
$56$	−1.10365	−0.147481
$57$	−6.50629	−0.861779
$58$	−4.40737	−0.578716
$59$	−7.61222	−0.991027	−0.495513	−	0.868600i	$-0.665020\pi$
$59$	−7.61222	−0.991027	−0.495513	+	0.868600i	$0.665020\pi$
$60$	0.760636	0.0981977
$61$	0.0740547	0.00948173	0.00474087	−	0.999989i	$-0.498491\pi$
$61$	0.0740547	0.00948173	0.00474087	+	0.999989i	$0.498491\pi$
$62$	9.38477	1.19187
$63$	0.927286	0.116827
$64$	3.62756	0.453445
$65$	−1.96733	−0.244017
$66$	−6.34457	−0.780962
$67$	−1.96087	−0.239559	−0.119779	−	0.992801i	$-0.538219\pi$
$67$	−1.96087	−0.239559	−0.119779	+	0.992801i	$0.538219\pi$
$68$	1.96672	0.238500
$69$	−9.01695	−1.08551
$70$	0.845390	0.101043
$71$	−2.26874	−0.269250	−0.134625	−	0.990897i	$-0.542983\pi$
$71$	−2.26874	−0.269250	−0.134625	+	0.990897i	$0.542983\pi$
$72$	−3.85842	−0.454719
$73$	−1.86421	−0.218189	−0.109094	−	0.994031i	$-0.534795\pi$
$73$	−1.86421	−0.218189	−0.109094	+	0.994031i	$0.534795\pi$
$74$	−5.81090	−0.675503
$75$	1.09521	0.126464
$76$	−4.12587	−0.473270
$77$	−1.81753	−0.207127
$78$	3.53683	0.400467
$79$	−5.21234	−0.586434	−0.293217	−	0.956046i	$-0.594726\pi$
$79$	−5.21234	−0.586434	−0.293217	+	0.956046i	$0.594726\pi$
$80$	−4.90668	−0.548583
$81$	−0.356599	−0.0396221
$82$	−7.57245	−0.836237
$83$	2.10479	0.231031	0.115515	−	0.993306i	$-0.463148\pi$
$83$	2.10479	0.231031	0.115515	+	0.993306i	$0.463148\pi$
$84$	−0.391736	−0.0427419
$85$	2.83180	0.307152
$86$	4.87283	0.525451
$87$	2.94061	0.315266
$88$	7.56271	0.806188
$89$	4.41157	0.467626	0.233813	−	0.972282i	$-0.424880\pi$
$89$	4.41157	0.467626	0.233813	+	0.972282i	$0.424880\pi$
$90$	2.95554	0.311541
$91$	1.01320	0.106212
$92$	−5.71797	−0.596139
$93$	−6.26154	−0.649291
$94$	4.11323	0.424247
$95$	−5.94068	−0.609501
$96$	4.12717	0.421228
$97$	−11.1710	−1.13425	−0.567123	−	0.823633i	$-0.691943\pi$
$97$	−11.1710	−1.13425	−0.567123	+	0.823633i	$0.691943\pi$
$98$	11.0551	1.11673
$99$	−6.35421	−0.638622
$100$	0.694512	0.0694512
$101$	10.0982	1.00481	0.502406	−	0.864632i	$-0.332448\pi$
$101$	10.0982	1.00481	0.502406	+	0.864632i	$0.332448\pi$
$102$	−5.09097	−0.504081
$103$	−11.2922	−1.11265	−0.556327	−	0.830964i	$-0.687790\pi$
$103$	−11.2922	−1.11265	−0.556327	+	0.830964i	$0.687790\pi$
$104$	−4.21590	−0.413403
$105$	−0.564046	−0.0550452
$106$	−4.21269	−0.409172
$107$	−0.595935	−0.0576112	−0.0288056	−	0.999585i	$-0.509170\pi$
$107$	−0.595935	−0.0576112	−0.0288056	+	0.999585i	$0.509170\pi$
$108$	−3.65145	−0.351361
$109$	8.69540	0.832868	0.416434	−	0.909166i	$-0.363280\pi$
$109$	8.69540	0.832868	0.416434	+	0.909166i	$0.363280\pi$
$110$	−5.79301	−0.552342
$111$	3.87704	0.367993
$112$	2.52699	0.238779
$113$	−1.56853	−0.147555	−0.0737774	−	0.997275i	$-0.523505\pi$
$113$	−1.56853	−0.147555	−0.0737774	+	0.997275i	$0.523505\pi$
$114$	10.6801	1.00028
$115$	−8.23308	−0.767738
$116$	1.86474	0.173137
$117$	3.54221	0.327477
$118$	12.4954	1.15030
$119$	−1.45841	−0.133692
$120$	2.34699	0.214249
$121$	1.45458	0.132235
$122$	−0.121561	−0.0110056
$123$	5.05235	0.455555
$124$	−3.97067	−0.356576
$125$	1.00000	0.0894427
$126$	−1.52214	−0.135603
$127$	−1.02606	−0.0910483	−0.0455241	−	0.998963i	$-0.514496\pi$
$127$	−1.02606	−0.0910483	−0.0455241	+	0.998963i	$0.514496\pi$
$128$	−13.4914	−1.19248
$129$	−3.25116	−0.286249
$130$	3.22936	0.283234
$131$	8.28623	0.723971	0.361986	−	0.932184i	$-0.382099\pi$
$131$	8.28623	0.723971	0.361986	+	0.932184i	$0.382099\pi$
$132$	2.68436	0.233644
$133$	3.05952	0.265294
$134$	3.21876	0.278059
$135$	−5.25757	−0.452500
$136$	6.06842	0.520363
$137$	−11.6152	−0.992350	−0.496175	−	0.868223i	$-0.665262\pi$
$137$	−11.6152	−0.992350	−0.496175	+	0.868223i	$0.665262\pi$
$138$	14.8013	1.25997
$139$	−4.64359	−0.393864	−0.196932	−	0.980417i	$-0.563098\pi$
$139$	−4.64359	−0.393864	−0.196932	+	0.980417i	$0.563098\pi$
$140$	−0.357681	−0.0302296
$141$	−2.74435	−0.231116
$142$	3.72414	0.312523
$143$	−6.94291	−0.580595
$144$	8.83455	0.736212
$145$	2.68497	0.222975
$146$	3.06009	0.253255
$147$	−7.37598	−0.608361
$148$	2.45857	0.202093
$149$	−18.2502	−1.49512	−0.747558	−	0.664197i	$-0.768774\pi$
$149$	−18.2502	−1.49512	−0.747558	+	0.664197i	$0.768774\pi$
$150$	−1.79778	−0.146788
$151$	23.0175	1.87313	0.936567	−	0.350488i	$-0.113984\pi$
$151$	23.0175	1.87313	0.936567	+	0.350488i	$0.113984\pi$
$152$	−12.7306	−1.03259
$153$	−5.09870	−0.412206
$154$	2.98347	0.240415
$155$	−5.71720	−0.459217
$156$	−1.49642	−0.119810
$157$	0.329063	0.0262621	0.0131310	−	0.999914i	$-0.495820\pi$
$157$	0.329063	0.0262621	0.0131310	+	0.999914i	$0.495820\pi$
$158$	8.55603	0.680681
$159$	2.81071	0.222904
$160$	3.76839	0.297917
$161$	4.24013	0.334169
$162$	0.585356	0.0459899
$163$	0.630882	0.0494145	0.0247073	−	0.999695i	$-0.492135\pi$
$163$	0.630882	0.0494145	0.0247073	+	0.999695i	$0.492135\pi$
$164$	3.20388	0.250181
$165$	3.86511	0.300898
$166$	−3.45500	−0.268160
$167$	−6.14611	−0.475600	−0.237800	−	0.971314i	$-0.576426\pi$
$167$	−6.14611	−0.475600	−0.237800	+	0.971314i	$0.576426\pi$
$168$	−1.20872	−0.0932551
$169$	−9.12962	−0.702278
$170$	−4.64839	−0.356515
$171$	10.6963	0.817965
$172$	−2.06168	−0.157202
$173$	−22.2484	−1.69152	−0.845758	−	0.533566i	$-0.820851\pi$
$173$	−22.2484	−1.69152	−0.845758	+	0.533566i	$0.820851\pi$
$174$	−4.82699	−0.365934
$175$	−0.515011	−0.0389312
$176$	−17.3162	−1.30526
$177$	−8.33698	−0.626646
$178$	−7.24159	−0.542780
$179$	−8.68073	−0.648828	−0.324414	−	0.945915i	$-0.605167\pi$
$179$	−8.68073	−0.648828	−0.324414	+	0.945915i	$0.605167\pi$
$180$	−1.25048	−0.0932052
$181$	13.1545	0.977769	0.488884	−	0.872349i	$-0.337404\pi$
$181$	13.1545	0.977769	0.488884	+	0.872349i	$0.337404\pi$
$182$	−1.66316	−0.123282
$183$	0.0811054	0.00599549
$184$	−17.6431	−1.30067
$185$	3.54000	0.260266
$186$	10.2783	0.753641
$187$	9.99372	0.730813
$188$	−1.74029	−0.126924
$189$	2.70771	0.196957
$190$	9.75160	0.707456
$191$	−6.89791	−0.499115	−0.249558	−	0.968360i	$-0.580285\pi$
$191$	−6.89791	−0.499115	−0.249558	+	0.968360i	$0.580285\pi$
$192$	3.97294	0.286722
$193$	7.87031	0.566517	0.283259	−	0.959044i	$-0.408585\pi$
$193$	7.87031	0.566517	0.283259	+	0.959044i	$0.408585\pi$
$194$	18.3372	1.31653
$195$	−2.15464	−0.154297
$196$	−4.67737	−0.334098
$197$	−18.1596	−1.29382	−0.646908	−	0.762568i	$-0.723938\pi$
$197$	−18.1596	−1.29382	−0.646908	+	0.762568i	$0.723938\pi$
$198$	10.4304	0.741257
$199$	2.96249	0.210005	0.105003	−	0.994472i	$-0.466515\pi$
$199$	2.96249	0.210005	0.105003	+	0.994472i	$0.466515\pi$
$200$	2.14295	0.151530
$201$	−2.14757	−0.151478
$202$	−16.5762	−1.16630
$203$	−1.38279	−0.0970528
$204$	2.15397	0.150808
$205$	4.61314	0.322195
$206$	18.5361	1.29147
$207$	14.8238	1.03032
$208$	9.65305	0.669318
$209$	−20.9653	−1.45020
$210$	0.925879	0.0638917
$211$	5.02338	0.345824	0.172912	−	0.984937i	$-0.444682\pi$
$211$	5.02338	0.345824	0.172912	+	0.984937i	$0.444682\pi$
$212$	1.78237	0.122414
$213$	−2.48475	−0.170252
$214$	0.978226	0.0668701
$215$	−2.96853	−0.202452
$216$	−11.2667	−0.766604
$217$	2.94442	0.199881
$218$	−14.2735	−0.966721
$219$	−2.04170	−0.137965
$220$	2.45100	0.165247
$221$	−5.57108	−0.374752
$222$	−6.36415	−0.427134
$223$	−3.67155	−0.245865	−0.122933	−	0.992415i	$-0.539230\pi$
$223$	−3.67155	−0.245865	−0.122933	+	0.992415i	$0.539230\pi$
$224$	−1.94076	−0.129673
$225$	−1.80052	−0.120034
$226$	2.57474	0.171269
$227$	−26.2276	−1.74079	−0.870393	−	0.492357i	$-0.836135\pi$
$227$	−26.2276	−1.74079	−0.870393	+	0.492357i	$0.836135\pi$
$228$	−4.51869	−0.299258
$229$	−1.37904	−0.0911294	−0.0455647	−	0.998961i	$-0.514509\pi$
$229$	−1.37904	−0.0911294	−0.0455647	+	0.998961i	$0.514509\pi$
$230$	13.5146	0.891124
$231$	−1.99058	−0.130970
$232$	5.75377	0.377753
$233$	−23.1858	−1.51895	−0.759475	−	0.650536i	$-0.774544\pi$
$233$	−23.1858	−1.51895	−0.759475	+	0.650536i	$0.774544\pi$
$234$	−5.81452	−0.380107
$235$	−2.50578	−0.163459
$236$	−5.28678	−0.344140
$237$	−5.70860	−0.370814
$238$	2.39397	0.155178
$239$	0.623585	0.0403363	0.0201682	−	0.999797i	$-0.493580\pi$
$239$	0.623585	0.0403363	0.0201682	+	0.999797i	$0.493580\pi$
$240$	−5.37384	−0.346880
$241$	−3.20609	−0.206523	−0.103261	−	0.994654i	$-0.532928\pi$
$241$	−3.20609	−0.206523	−0.103261	+	0.994654i	$0.532928\pi$
$242$	−2.38769	−0.153486
$243$	15.3822	0.986766
$244$	0.0514319	0.00329259
$245$	−6.73476	−0.430268
$246$	−8.29342	−0.528769
$247$	11.6873	0.743643
$248$	−12.2517	−0.777984
$249$	2.30519	0.146085
$250$	−1.64150	−0.103817
$251$	18.9479	1.19598	0.597991	−	0.801503i	$-0.295966\pi$
$251$	18.9479	1.19598	0.597991	+	0.801503i	$0.295966\pi$
$252$	0.644011	0.0405689
$253$	−29.0554	−1.82670
$254$	1.68428	0.105681
$255$	3.10142	0.194218
$256$	14.8910	0.930686
$257$	−12.1304	−0.756674	−0.378337	−	0.925668i	$-0.623504\pi$
$257$	−12.1304	−0.756674	−0.378337	+	0.925668i	$0.623504\pi$
$258$	5.33677	0.332253
$259$	−1.82314	−0.113284
$260$	−1.36633	−0.0847364
$261$	−4.83433	−0.299237
$262$	−13.6018	−0.840323
$263$	6.92997	0.427320	0.213660	−	0.976908i	$-0.431462\pi$
$263$	6.92997	0.427320	0.213660	+	0.976908i	$0.431462\pi$
$264$	8.28276	0.509768
$265$	2.56637	0.157651
$266$	−5.02219	−0.307930
$267$	4.83160	0.295689
$268$	−1.36185	−0.0831881
$269$	11.4291	0.696844	0.348422	−	0.937338i	$-0.386718\pi$
$269$	11.4291	0.696844	0.348422	+	0.937338i	$0.386718\pi$
$270$	8.63029	0.525223
$271$	−7.62386	−0.463116	−0.231558	−	0.972821i	$-0.574382\pi$
$271$	−7.62386	−0.463116	−0.231558	+	0.972821i	$0.574382\pi$
$272$	−13.8947	−0.842492
$273$	1.10966	0.0671599
$274$	19.0662	1.15183
$275$	3.52910	0.212813
$276$	−6.26238	−0.376951
$277$	9.60178	0.576915	0.288457	−	0.957493i	$-0.406858\pi$
$277$	9.60178	0.576915	0.288457	+	0.957493i	$0.406858\pi$
$278$	7.62244	0.457163
$279$	10.2939	0.616280
$280$	−1.10365	−0.0659555
$281$	12.3658	0.737684	0.368842	−	0.929492i	$-0.379754\pi$
$281$	12.3658	0.737684	0.368842	+	0.929492i	$0.379754\pi$
$282$	4.50485	0.268260
$283$	−14.1594	−0.841688	−0.420844	−	0.907133i	$-0.638266\pi$
$283$	−14.1594	−0.841688	−0.420844	+	0.907133i	$0.638266\pi$
$284$	−1.57567	−0.0934988
$285$	−6.50629	−0.385399
$286$	11.3968	0.673905
$287$	−2.37582	−0.140240
$288$	−6.78504	−0.399812
$289$	−8.98090	−0.528288
$290$	−4.40737	−0.258810
$291$	−12.2346	−0.717206
$292$	−1.29471	−0.0757674
$293$	−17.1831	−1.00385	−0.501925	−	0.864911i	$-0.667374\pi$
$293$	−17.1831	−1.00385	−0.501925	+	0.864911i	$0.667374\pi$
$294$	12.1076	0.706132
$295$	−7.61222	−0.443201
$296$	7.58606	0.440931
$297$	−18.5545	−1.07664
$298$	29.9577	1.73540
$299$	16.1972	0.936706
$300$	0.760636	0.0439154
$301$	1.52883	0.0881201
$302$	−37.7831	−2.17417
$303$	11.0597	0.635362
$304$	29.1490	1.67181
$305$	0.0740547	0.00424036
$306$	8.36950	0.478453
$307$	−11.4819	−0.655309	−0.327655	−	0.944798i	$-0.606258\pi$
$307$	−11.4819	−0.655309	−0.327655	+	0.944798i	$0.606258\pi$
$308$	−1.26230	−0.0719260
$309$	−12.3673	−0.703553
$310$	9.38477	0.533019
$311$	13.9999	0.793864	0.396932	−	0.917848i	$-0.370075\pi$
$311$	13.9999	0.793864	0.396932	+	0.917848i	$0.370075\pi$
$312$	−4.61729	−0.261403
$313$	9.92936	0.561241	0.280620	−	0.959819i	$-0.409460\pi$
$313$	9.92936	0.561241	0.280620	+	0.959819i	$0.409460\pi$
$314$	−0.540156	−0.0304827
$315$	0.927286	0.0522466
$316$	−3.62003	−0.203643
$317$	5.85627	0.328921	0.164461	−	0.986384i	$-0.447412\pi$
$317$	5.85627	0.328921	0.164461	+	0.986384i	$0.447412\pi$
$318$	−4.61377	−0.258728
$319$	9.47554	0.530528
$320$	3.62756	0.202787
$321$	−0.652674	−0.0364287
$322$	−6.96016	−0.387874
$323$	−16.8228	−0.936046
$324$	−0.247662	−0.0137590
$325$	−1.96733	−0.109128
$326$	−1.03559	−0.0573561
$327$	9.52329	0.526639
$328$	9.88574	0.545849
$329$	1.29050	0.0711478
$330$	−6.34457	−0.349257
$331$	−31.1692	−1.71321	−0.856607	−	0.515969i	$-0.827432\pi$
$331$	−31.1692	−1.71321	−0.856607	+	0.515969i	$0.827432\pi$
$332$	1.46180	0.0802267
$333$	−6.37382	−0.349283
$334$	10.0888	0.552035
$335$	−1.96087	−0.107134
$336$	2.76759	0.150984
$337$	−31.2275	−1.70107	−0.850534	−	0.525920i	$-0.823721\pi$
$337$	−31.2275	−1.70107	−0.850534	+	0.525920i	$0.823721\pi$
$338$	14.9862	0.815144
$339$	−1.71787	−0.0933018
$340$	1.96672	0.106660
$341$	−20.1766	−1.09262
$342$	−17.5579	−0.949423
$343$	7.07356	0.381936
$344$	−6.36142	−0.342985
$345$	−9.01695	−0.485456
$346$	36.5207	1.96337
$347$	11.2233	0.602500	0.301250	−	0.953545i	$-0.402596\pi$
$347$	11.2233	0.602500	0.301250	+	0.953545i	$0.402596\pi$
$348$	2.04229	0.109478
$349$	5.83810	0.312507	0.156253	−	0.987717i	$-0.450058\pi$
$349$	5.83810	0.312507	0.156253	+	0.987717i	$0.450058\pi$
$350$	0.845390	0.0451880
$351$	10.3434	0.552088
$352$	13.2990	0.708840
$353$	−2.63614	−0.140307	−0.0701537	−	0.997536i	$-0.522349\pi$
$353$	−2.63614	−0.140307	−0.0701537	+	0.997536i	$0.522349\pi$
$354$	13.6851	0.727356
$355$	−2.26874	−0.120412
$356$	3.06389	0.162386
$357$	−1.59726	−0.0845362
$358$	14.2494	0.753103
$359$	−15.0320	−0.793359	−0.396680	−	0.917957i	$-0.629838\pi$
$359$	−15.0320	−0.793359	−0.396680	+	0.917957i	$0.629838\pi$
$360$	−3.85842	−0.203357
$361$	16.2916	0.857455
$362$	−21.5931	−1.13491
$363$	1.59307	0.0836146
$364$	0.703677	0.0368827
$365$	−1.86421	−0.0975771
$366$	−0.133134	−0.00695904
$367$	12.2398	0.638911	0.319456	−	0.947601i	$-0.396500\pi$
$367$	12.2398	0.638911	0.319456	+	0.947601i	$0.396500\pi$
$368$	40.3970	2.10584
$369$	−8.30602	−0.432394
$370$	−5.81090	−0.302094
$371$	−1.32171	−0.0686197
$372$	−4.34871	−0.225470
$373$	35.2517	1.82526	0.912631	−	0.408785i	$-0.134047\pi$
$373$	35.2517	1.82526	0.912631	+	0.408785i	$0.134047\pi$
$374$	−16.4047	−0.848265
$375$	1.09521	0.0565564
$376$	−5.36977	−0.276925
$377$	−5.28222	−0.272048
$378$	−4.44470	−0.228611
$379$	−0.0548749	−0.00281873	−0.00140937	−	0.999999i	$-0.500449\pi$
$379$	−0.0548749	−0.00281873	−0.00140937	+	0.999999i	$0.500449\pi$
$380$	−4.12587	−0.211653
$381$	−1.12375	−0.0575716
$382$	11.3229	0.579330
$383$	−20.0973	−1.02692	−0.513462	−	0.858113i	$-0.671637\pi$
$383$	−20.0973	−1.02692	−0.513462	+	0.858113i	$0.671637\pi$
$384$	−14.7759	−0.754030
$385$	−1.81753	−0.0926299
$386$	−12.9191	−0.657564
$387$	5.34488	0.271696
$388$	−7.75841	−0.393873
$389$	21.2242	1.07611	0.538054	−	0.842911i	$-0.319160\pi$
$389$	21.2242	1.07611	0.538054	+	0.842911i	$0.319160\pi$
$390$	3.53683	0.179094
$391$	−23.3144	−1.17906
$392$	−14.4323	−0.728941
$393$	9.07516	0.457781
$394$	29.8089	1.50175
$395$	−5.21234	−0.262261
$396$	−4.41307	−0.221765
$397$	33.9145	1.70212	0.851060	−	0.525069i	$-0.175960\pi$
$397$	33.9145	1.70212	0.851060	+	0.525069i	$0.175960\pi$
$398$	−4.86292	−0.243756
$399$	3.35081	0.167750
$400$	−4.90668	−0.245334
$401$	1.00000	0.0499376
$401$	1.00000	0.0499376
$402$	3.52522	0.175822
$403$	11.2476	0.560284
$404$	7.01334	0.348927
$405$	−0.356599	−0.0177195
$406$	2.26985	0.112651
$407$	12.4930	0.619257
$408$	6.64620	0.329036
$409$	−1.72541	−0.0853160	−0.0426580	−	0.999090i	$-0.513583\pi$
$409$	−1.72541	−0.0853160	−0.0426580	+	0.999090i	$0.513583\pi$
$410$	−7.57245	−0.373977
$411$	−12.7210	−0.627482
$412$	−7.84257	−0.386375
$413$	3.92038	0.192909
$414$	−24.3332	−1.19591
$415$	2.10479	0.103320
$416$	−7.41365	−0.363484
$417$	−5.08570	−0.249048
$418$	34.4144	1.68326
$419$	29.4399	1.43823	0.719116	−	0.694890i	$-0.244547\pi$
$419$	29.4399	1.43823	0.719116	+	0.694890i	$0.244547\pi$
$420$	−0.391736	−0.0191148
$421$	2.47431	0.120591	0.0602953	−	0.998181i	$-0.480796\pi$
$421$	2.47431	0.120591	0.0602953	+	0.998181i	$0.480796\pi$
$422$	−8.24586	−0.401402
$423$	4.51169	0.219366
$424$	5.49961	0.267085
$425$	2.83180	0.137363
$426$	4.07871	0.197614
$427$	−0.0381390	−0.00184568
$428$	−0.413884	−0.0200058
$429$	−7.60394	−0.367122
$430$	4.87283	0.234989
$431$	−13.0824	−0.630156	−0.315078	−	0.949066i	$-0.602031\pi$
$431$	−13.0824	−0.630156	−0.315078	+	0.949066i	$0.602031\pi$
$432$	25.7972	1.24117
$433$	14.0334	0.674400	0.337200	−	0.941433i	$-0.390520\pi$
$433$	14.0334	0.674400	0.337200	+	0.941433i	$0.390520\pi$
$434$	−4.83326	−0.232004
$435$	2.94061	0.140991
$436$	6.03906	0.289218
$437$	48.9100	2.33968
$438$	3.35144	0.160138
$439$	2.70264	0.128990	0.0644949	−	0.997918i	$-0.479456\pi$
$439$	2.70264	0.128990	0.0644949	+	0.997918i	$0.479456\pi$
$440$	7.56271	0.360538
$441$	12.1260	0.577431
$442$	9.14492	0.434979
$443$	−29.7422	−1.41309	−0.706547	−	0.707666i	$-0.749748\pi$
$443$	−29.7422	−1.41309	−0.706547	+	0.707666i	$0.749748\pi$
$444$	2.69265	0.127788
$445$	4.41157	0.209129
$446$	6.02683	0.285379
$447$	−19.9878	−0.945391
$448$	−1.86824	−0.0882658
$449$	27.3829	1.29228	0.646140	−	0.763219i	$-0.276382\pi$
$449$	27.3829	1.29228	0.646140	+	0.763219i	$0.276382\pi$
$450$	2.95554	0.139325
$451$	16.2802	0.766607
$452$	−1.08936	−0.0512393
$453$	25.2090	1.18442
$454$	43.0525	2.02055
$455$	1.01320	0.0474994
$456$	−13.9427	−0.652926
$457$	9.59495	0.448833	0.224416	−	0.974493i	$-0.427952\pi$
$457$	9.59495	0.448833	0.224416	+	0.974493i	$0.427952\pi$
$458$	2.26369	0.105775
$459$	−14.8884	−0.694931
$460$	−5.71797	−0.266602
$461$	18.0159	0.839083	0.419542	−	0.907736i	$-0.362191\pi$
$461$	18.0159	0.839083	0.419542	+	0.907736i	$0.362191\pi$
$462$	3.26752	0.152019
$463$	15.7067	0.729952	0.364976	−	0.931017i	$-0.381077\pi$
$463$	15.7067	0.729952	0.364976	+	0.931017i	$0.381077\pi$
$464$	−13.1743	−0.611601
$465$	−6.26154	−0.290372
$466$	38.0594	1.76307
$467$	18.3672	0.849931	0.424965	−	0.905210i	$-0.360286\pi$
$467$	18.3672	0.849931	0.424965	+	0.905210i	$0.360286\pi$
$468$	2.46010	0.113718
$469$	1.00987	0.0466315
$470$	4.11323	0.189729
$471$	0.360393	0.0166060
$472$	−16.3126	−0.750851
$473$	−10.4763	−0.481699
$474$	9.37065	0.430408
$475$	−5.94068	−0.272577
$476$	−1.01288	−0.0464254
$477$	−4.62079	−0.211571
$478$	−1.02361	−0.0468189
$479$	20.0735	0.917183	0.458591	−	0.888647i	$-0.348354\pi$
$479$	20.0735	0.917183	0.458591	+	0.888647i	$0.348354\pi$
$480$	4.12717	0.188379
$481$	−6.96435	−0.317547
$482$	5.26279	0.239713
$483$	4.64383	0.211302
$484$	1.01022	0.0459192
$485$	−11.1710	−0.507250
$486$	−25.2498	−1.14535
$487$	−16.4825	−0.746892	−0.373446	−	0.927652i	$-0.621824\pi$
$487$	−16.4825	−0.746892	−0.373446	+	0.927652i	$0.621824\pi$
$488$	0.158696	0.00718382
$489$	0.690949	0.0312458
$490$	11.0551	0.499418
$491$	−17.4300	−0.786605	−0.393303	−	0.919409i	$-0.628667\pi$
$491$	−17.4300	−0.786605	−0.393303	+	0.919409i	$0.628667\pi$
$492$	3.50892	0.158194
$493$	7.60330	0.342435
$494$	−19.1846	−0.863156
$495$	−6.35421	−0.285600
$496$	28.0525	1.25959
$497$	1.16843	0.0524112
$498$	−3.78395	−0.169563
$499$	15.3146	0.685577	0.342789	−	0.939413i	$-0.388629\pi$
$499$	15.3146	0.685577	0.342789	+	0.939413i	$0.388629\pi$
$500$	0.694512	0.0310595
$501$	−6.73128	−0.300731
$502$	−31.1029	−1.38819
$503$	−1.37379	−0.0612543	−0.0306271	−	0.999531i	$-0.509750\pi$
$503$	−1.37379	−0.0612543	−0.0306271	+	0.999531i	$0.509750\pi$
$504$	1.98713	0.0885139
$505$	10.0982	0.449365
$506$	47.6943	2.12027
$507$	−9.99885	−0.444064
$508$	−0.712612	−0.0316171
$509$	38.7587	1.71795	0.858974	−	0.512019i	$-0.171102\pi$
$509$	38.7587	1.71795	0.858974	+	0.512019i	$0.171102\pi$
$510$	−5.09097	−0.225432
$511$	0.960088	0.0424718
$512$	2.53932	0.112223
$513$	31.2335	1.37899
$514$	19.9120	0.878282
$515$	−11.2922	−0.497594
$516$	−2.25797	−0.0994016
$517$	−8.84316	−0.388922
$518$	2.99268	0.131491
$519$	−24.3667	−1.06958
$520$	−4.21590	−0.184879
$521$	22.7616	0.997202	0.498601	−	0.866832i	$-0.333847\pi$
$521$	22.7616	0.997202	0.498601	+	0.866832i	$0.333847\pi$
$522$	7.93554	0.347329
$523$	9.59605	0.419606	0.209803	−	0.977744i	$-0.432718\pi$
$523$	9.59605	0.419606	0.209803	+	0.977744i	$0.432718\pi$
$524$	5.75488	0.251403
$525$	−0.564046	−0.0246170
$526$	−11.3755	−0.495996
$527$	−16.1900	−0.705247
$528$	−18.9648	−0.825339
$529$	44.7835	1.94711
$530$	−4.21269	−0.182987
$531$	13.7059	0.594786
$532$	2.12487	0.0921248
$533$	−9.07556	−0.393106
$534$	−7.93106	−0.343210
$535$	−0.595935	−0.0257645
$536$	−4.20206	−0.181501
$537$	−9.50722	−0.410267
$538$	−18.7608	−0.808836
$539$	−23.7677	−1.02375
$540$	−3.65145	−0.157133
$541$	23.8040	1.02341	0.511706	−	0.859161i	$-0.329014\pi$
$541$	23.8040	1.02341	0.511706	+	0.859161i	$0.329014\pi$
$542$	12.5145	0.537546
$543$	14.4070	0.618262
$544$	10.6713	0.457529
$545$	8.69540	0.372470
$546$	−1.82151	−0.0779534
$547$	15.5025	0.662839	0.331420	−	0.943483i	$-0.392472\pi$
$547$	15.5025	0.662839	0.331420	+	0.943483i	$0.392472\pi$
$548$	−8.06686	−0.344599
$549$	−0.133337	−0.00569067
$550$	−5.79301	−0.247015
$551$	−15.9505	−0.679516
$552$	−19.3229	−0.822438
$553$	2.68441	0.114153
$554$	−15.7613	−0.669633
$555$	3.87704	0.164571
$556$	−3.22503	−0.136772
$557$	−27.8795	−1.18129	−0.590647	−	0.806930i	$-0.701127\pi$
$557$	−27.8795	−1.18129	−0.590647	+	0.806930i	$0.701127\pi$
$558$	−16.8974	−0.715325
$559$	5.84007	0.247009
$560$	2.52699	0.106785
$561$	10.9452	0.462108
$562$	−20.2985	−0.856240
$563$	−17.3884	−0.732835	−0.366418	−	0.930450i	$-0.619416\pi$
$563$	−17.3884	−0.732835	−0.366418	+	0.930450i	$0.619416\pi$
$564$	−1.90599	−0.0802565
$565$	−1.56853	−0.0659885
$566$	23.2426	0.976959
$567$	0.183652	0.00771268
$568$	−4.86182	−0.203997
$569$	27.5949	1.15684	0.578420	−	0.815739i	$-0.303670\pi$
$569$	27.5949	1.15684	0.578420	+	0.815739i	$0.303670\pi$
$570$	10.6801	0.447338
$571$	−1.37340	−0.0574749	−0.0287375	−	0.999587i	$-0.509149\pi$
$571$	−1.37340	−0.0574749	−0.0287375	+	0.999587i	$0.509149\pi$
$572$	−4.82193	−0.201615
$573$	−7.55466	−0.315600
$574$	3.89990	0.162779
$575$	−8.23308	−0.343343
$576$	−6.53148	−0.272145
$577$	−35.5481	−1.47989	−0.739943	−	0.672670i	$-0.765147\pi$
$577$	−35.5481	−1.47989	−0.739943	+	0.672670i	$0.765147\pi$
$578$	14.7421	0.613191
$579$	8.61964	0.358220
$580$	1.86474	0.0774292
$581$	−1.08399	−0.0449715
$582$	20.0831	0.832470
$583$	9.05698	0.375102
$584$	−3.99491	−0.165311
$585$	3.54221	0.146452
$586$	28.2060	1.16518
$587$	1.75225	0.0723229	0.0361615	−	0.999346i	$-0.488487\pi$
$587$	1.75225	0.0723229	0.0361615	+	0.999346i	$0.488487\pi$
$588$	−5.12270	−0.211257
$589$	33.9641	1.39946
$590$	12.4954	0.514429
$591$	−19.8885	−0.818105
$592$	−17.3696	−0.713888
$593$	33.6290	1.38098	0.690488	−	0.723344i	$-0.257396\pi$
$593$	33.6290	1.38098	0.690488	+	0.723344i	$0.257396\pi$
$594$	30.4572	1.24967
$595$	−1.45841	−0.0597890
$596$	−12.6750	−0.519188
$597$	3.24455	0.132791
$598$	−26.5876	−1.08725
$599$	5.80418	0.237152	0.118576	−	0.992945i	$-0.462167\pi$
$599$	5.80418	0.237152	0.118576	+	0.992945i	$0.462167\pi$
$600$	2.34699	0.0958153
$601$	15.5802	0.635530	0.317765	−	0.948169i	$-0.397068\pi$
$601$	15.5802	0.635530	0.317765	+	0.948169i	$0.397068\pi$
$602$	−2.50956	−0.102282
$603$	3.53058	0.143776
$604$	15.9859	0.650457
$605$	1.45458	0.0591371
$606$	−18.1544	−0.737473
$607$	13.7658	0.558737	0.279368	−	0.960184i	$-0.409875\pi$
$607$	13.7658	0.558737	0.279368	+	0.960184i	$0.409875\pi$
$608$	−22.3868	−0.907903
$609$	−1.51445	−0.0613684
$610$	−0.121561	−0.00492184
$611$	4.92969	0.199434
$612$	−3.54111	−0.143141
$613$	38.6299	1.56025	0.780124	−	0.625624i	$-0.215156\pi$
$613$	38.6299	1.56025	0.780124	+	0.625624i	$0.215156\pi$
$614$	18.8476	0.760626
$615$	5.05235	0.203731
$616$	−3.89488	−0.156929
$617$	−10.5436	−0.424469	−0.212235	−	0.977219i	$-0.568074\pi$
$617$	−10.5436	−0.424469	−0.212235	+	0.977219i	$0.568074\pi$
$618$	20.3009	0.816623
$619$	10.1113	0.406409	0.203205	−	0.979136i	$-0.434864\pi$
$619$	10.1113	0.406409	0.203205	+	0.979136i	$0.434864\pi$
$620$	−3.97067	−0.159466
$621$	43.2860	1.73701
$622$	−22.9809	−0.921448
$623$	−2.27201	−0.0910262
$624$	10.5721	0.423223
$625$	1.00000	0.0400000
$626$	−16.2990	−0.651440
$627$	−22.9614	−0.916989
$628$	0.228538	0.00911966
$629$	10.0246	0.399706
$630$	−1.52214	−0.0606434
$631$	9.34361	0.371963	0.185982	−	0.982553i	$-0.440454\pi$
$631$	9.34361	0.371963	0.185982	+	0.982553i	$0.440454\pi$
$632$	−11.1698	−0.444311
$633$	5.50166	0.218671
$634$	−9.61305	−0.381783
$635$	−1.02606	−0.0407180
$636$	1.95207	0.0774047
$637$	13.2495	0.524964
$638$	−15.5541	−0.615791
$639$	4.08491	0.161596
$640$	−13.4914	−0.533294
$641$	−32.0959	−1.26771	−0.633857	−	0.773450i	$-0.718529\pi$
$641$	−32.0959	−1.26771	−0.633857	+	0.773450i	$0.718529\pi$
$642$	1.07136	0.0422833
$643$	15.1246	0.596456	0.298228	−	0.954495i	$-0.403604\pi$
$643$	15.1246	0.596456	0.298228	+	0.954495i	$0.403604\pi$
$644$	2.94482	0.116042
$645$	−3.25116	−0.128014
$646$	27.6146	1.08648
$647$	−29.6529	−1.16578	−0.582888	−	0.812552i	$-0.698077\pi$
$647$	−29.6529	−1.16578	−0.582888	+	0.812552i	$0.698077\pi$
$648$	−0.764175	−0.0300196
$649$	−26.8643	−1.05452
$650$	3.22936	0.126666
$651$	3.22476	0.126388
$652$	0.438155	0.0171595
$653$	3.19040	0.124850	0.0624250	−	0.998050i	$-0.480117\pi$
$653$	3.19040	0.124850	0.0624250	+	0.998050i	$0.480117\pi$
$654$	−15.6324	−0.611277
$655$	8.28623	0.323770
$656$	−22.6352	−0.883755
$657$	3.35653	0.130951
$658$	−2.11836	−0.0825823
$659$	16.8764	0.657410	0.328705	−	0.944433i	$-0.393388\pi$
$659$	16.8764	0.657410	0.328705	+	0.944433i	$0.393388\pi$
$660$	2.68436	0.104489
$661$	22.8315	0.888043	0.444022	−	0.896016i	$-0.353551\pi$
$661$	22.8315	0.888043	0.444022	+	0.896016i	$0.353551\pi$
$662$	51.1642	1.98855
$663$	−6.10151	−0.236963
$664$	4.51047	0.175040
$665$	3.05952	0.118643
$666$	10.4626	0.405418
$667$	−22.1056	−0.855931
$668$	−4.26854	−0.165155
$669$	−4.02112	−0.155465
$670$	3.21876	0.124352
$671$	0.261347	0.0100892
$672$	−2.12554	−0.0819945
$673$	−29.2219	−1.12642	−0.563210	−	0.826314i	$-0.690434\pi$
$673$	−29.2219	−1.12642	−0.563210	+	0.826314i	$0.690434\pi$
$674$	51.2598	1.97445
$675$	−5.25757	−0.202364
$676$	−6.34063	−0.243870
$677$	−19.5947	−0.753086	−0.376543	−	0.926399i	$-0.622887\pi$
$677$	−19.5947	−0.753086	−0.376543	+	0.926399i	$0.622887\pi$
$678$	2.81988	0.108297
$679$	5.75320	0.220788
$680$	6.06842	0.232713
$681$	−28.7247	−1.10073
$682$	33.1198	1.26822
$683$	33.4281	1.27909	0.639546	−	0.768753i	$-0.279123\pi$
$683$	33.4281	1.27909	0.639546	+	0.768753i	$0.279123\pi$
$684$	7.42869	0.284043
$685$	−11.6152	−0.443792
$686$	−11.6112	−0.443319
$687$	−1.51034	−0.0576229
$688$	14.5656	0.555309
$689$	−5.04889	−0.192347
$690$	14.8013	0.563475
$691$	−7.26266	−0.276285	−0.138142	−	0.990412i	$-0.544113\pi$
$691$	−7.26266	−0.276285	−0.138142	+	0.990412i	$0.544113\pi$
$692$	−15.4518	−0.587389
$693$	3.27249	0.124312
$694$	−18.4231	−0.699330
$695$	−4.64359	−0.176141
$696$	6.30158	0.238861
$697$	13.0635	0.494815
$698$	−9.58323	−0.362731
$699$	−25.3933	−0.960462
$700$	−0.357681	−0.0135191
$701$	3.94077	0.148841	0.0744204	−	0.997227i	$-0.476289\pi$
$701$	3.94077	0.148841	0.0744204	+	0.997227i	$0.476289\pi$
$702$	−16.9786	−0.640817
$703$	−21.0300	−0.793161
$704$	12.8020	0.482495
$705$	−2.74435	−0.103358
$706$	4.32721	0.162857
$707$	−5.20070	−0.195593
$708$	−5.79013	−0.217606
$709$	−25.5871	−0.960945	−0.480473	−	0.877010i	$-0.659535\pi$
$709$	−25.5871	−0.960945	−0.480473	+	0.877010i	$0.659535\pi$
$710$	3.72414	0.139764
$711$	9.38489	0.351961
$712$	9.45380	0.354296
$713$	47.0702	1.76279
$714$	2.62191	0.0981223
$715$	−6.94291	−0.259650
$716$	−6.02887	−0.225309
$717$	0.682956	0.0255055
$718$	24.6750	0.920863
$719$	25.0852	0.935522	0.467761	−	0.883855i	$-0.345061\pi$
$719$	25.0852	0.935522	0.467761	+	0.883855i	$0.345061\pi$
$720$	8.83455	0.329244
$721$	5.81561	0.216585
$722$	−26.7427	−0.995259
$723$	−3.51134	−0.130588
$724$	9.13598	0.339536
$725$	2.68497	0.0997173
$726$	−2.61502	−0.0970525
$727$	−5.12138	−0.189941	−0.0949707	−	0.995480i	$-0.530276\pi$
$727$	−5.12138	−0.189941	−0.0949707	+	0.995480i	$0.530276\pi$
$728$	2.17123	0.0804713
$729$	17.9165	0.663574
$730$	3.06009	0.113259
$731$	−8.40628	−0.310918
$732$	0.0563287	0.00208197
$733$	−32.8917	−1.21488	−0.607441	−	0.794365i	$-0.707804\pi$
$733$	−32.8917	−1.21488	−0.607441	+	0.794365i	$0.707804\pi$
$734$	−20.0916	−0.741593
$735$	−7.37598	−0.272067
$736$	−31.0254	−1.14361
$737$	−6.92012	−0.254906
$738$	13.6343	0.501886
$739$	−38.1964	−1.40508	−0.702538	−	0.711646i	$-0.747950\pi$
$739$	−38.1964	−1.40508	−0.702538	+	0.711646i	$0.747950\pi$
$740$	2.45857	0.0903789
$741$	12.8000	0.470220
$742$	2.16958	0.0796478
$743$	−6.47384	−0.237502	−0.118751	−	0.992924i	$-0.537889\pi$
$743$	−6.47384	−0.237502	−0.118751	+	0.992924i	$0.537889\pi$
$744$	−13.4182	−0.491935
$745$	−18.2502	−0.668636
$746$	−57.8655	−2.11861
$747$	−3.78970	−0.138658
$748$	6.94076	0.253779
$749$	0.306913	0.0112144
$750$	−1.79778	−0.0656458
$751$	−6.16512	−0.224968	−0.112484	−	0.993654i	$-0.535881\pi$
$751$	−6.16512	−0.224968	−0.112484	+	0.993654i	$0.535881\pi$
$752$	12.2950	0.448354
$753$	20.7519	0.756243
$754$	8.67075	0.315770
$755$	23.0175	0.837691
$756$	1.88054	0.0683944
$757$	−13.8265	−0.502531	−0.251266	−	0.967918i	$-0.580847\pi$
$757$	−13.8265	−0.502531	−0.251266	+	0.967918i	$0.580847\pi$
$758$	0.0900769	0.00327174
$759$	−31.8217	−1.15506
$760$	−12.7306	−0.461787
$761$	−26.6096	−0.964598	−0.482299	−	0.876007i	$-0.660198\pi$
$761$	−26.6096	−0.964598	−0.482299	+	0.876007i	$0.660198\pi$
$762$	1.84464	0.0668242
$763$	−4.47823	−0.162123
$764$	−4.79068	−0.173321
$765$	−5.09870	−0.184344
$766$	32.9896	1.19196
$767$	14.9757	0.540743
$768$	16.3087	0.588491
$769$	15.5491	0.560714	0.280357	−	0.959896i	$-0.409547\pi$
$769$	15.5491	0.560714	0.280357	+	0.959896i	$0.409547\pi$
$770$	2.98347	0.107517
$771$	−13.2853	−0.478460
$772$	5.46602	0.196727
$773$	32.0338	1.15218	0.576088	−	0.817388i	$-0.304579\pi$
$773$	32.0338	1.15218	0.576088	+	0.817388i	$0.304579\pi$
$774$	−8.77361	−0.315361
$775$	−5.71720	−0.205368
$776$	−23.9390	−0.859360
$777$	−1.99672	−0.0716320
$778$	−34.8394	−1.24905
$779$	−27.4052	−0.981891
$780$	−1.49642	−0.0535805
$781$	−8.00663	−0.286500
$782$	38.2706	1.36855
$783$	−14.1164	−0.504480
$784$	33.0453	1.18019
$785$	0.329063	0.0117448
$786$	−14.8968	−0.531353
$787$	−36.5337	−1.30229	−0.651144	−	0.758955i	$-0.725710\pi$
$787$	−36.5337	−1.30229	−0.651144	+	0.758955i	$0.725710\pi$
$788$	−12.6120	−0.449285
$789$	7.58977	0.270203
$790$	8.55603	0.304410
$791$	0.807810	0.0287224
$792$	−13.6168	−0.483851
$793$	−0.145690	−0.00517360
$794$	−55.6705	−1.97567
$795$	2.81071	0.0996857
$796$	2.05749	0.0729256
$797$	49.8210	1.76475	0.882376	−	0.470545i	$-0.155943\pi$
$797$	49.8210	1.76475	0.882376	+	0.470545i	$0.155943\pi$
$798$	−5.50035	−0.194710
$799$	−7.09587	−0.251034
$800$	3.76839	0.133233
$801$	−7.94311	−0.280656
$802$	−1.64150	−0.0579633
$803$	−6.57898	−0.232167
$804$	−1.49151	−0.0526015
$805$	4.24013	0.149445
$806$	−18.4629	−0.650329
$807$	12.5173	0.440628
$808$	21.6401	0.761294
$809$	−32.1454	−1.13017	−0.565087	−	0.825032i	$-0.691157\pi$
$809$	−32.1454	−1.13017	−0.565087	+	0.825032i	$0.691157\pi$
$810$	0.585356	0.0205673
$811$	−49.1795	−1.72692	−0.863462	−	0.504413i	$-0.831709\pi$
$811$	−49.1795	−1.72692	−0.863462	+	0.504413i	$0.831709\pi$
$812$	−0.960364	−0.0337022
$813$	−8.34973	−0.292838
$814$	−20.5073	−0.718780
$815$	0.630882	0.0220988
$816$	−15.2176	−0.532724
$817$	17.6351	0.616973
$818$	2.83225	0.0990274
$819$	−1.82428	−0.0637454
$820$	3.20388	0.111884
$821$	−23.1051	−0.806374	−0.403187	−	0.915118i	$-0.632098\pi$
$821$	−23.1051	−0.806374	−0.403187	+	0.915118i	$0.632098\pi$
$822$	20.8815	0.728327
$823$	−14.6282	−0.509907	−0.254953	−	0.966953i	$-0.582060\pi$
$823$	−14.6282	−0.509907	−0.254953	+	0.966953i	$0.582060\pi$
$824$	−24.1987	−0.843001
$825$	3.86511	0.134566
$826$	−6.43529	−0.223912
$827$	6.57703	0.228706	0.114353	−	0.993440i	$-0.463521\pi$
$827$	6.57703	0.228706	0.114353	+	0.993440i	$0.463521\pi$
$828$	10.2953	0.357786
$829$	−40.3379	−1.40099	−0.700496	−	0.713656i	$-0.747038\pi$
$829$	−40.3379	−1.40099	−0.700496	+	0.713656i	$0.747038\pi$
$830$	−3.45500	−0.119925
$831$	10.5160	0.364795
$832$	−7.13661	−0.247417
$833$	−19.0715	−0.660789
$834$	8.34817	0.289073
$835$	−6.14611	−0.212695
$836$	−14.5606	−0.503590
$837$	30.0586	1.03898
$838$	−48.3254	−1.66937
$839$	4.98963	0.172261	0.0861305	−	0.996284i	$-0.472550\pi$
$839$	4.98963	0.172261	0.0861305	+	0.996284i	$0.472550\pi$
$840$	−1.20872	−0.0417049
$841$	−21.7909	−0.751412
$842$	−4.06157	−0.139971
$843$	13.5432	0.466452
$844$	3.48880	0.120089
$845$	−9.12962	−0.314068
$846$	−7.40593	−0.254621
$847$	−0.749126	−0.0257403
$848$	−12.5923	−0.432423
$849$	−15.5075	−0.532216
$850$	−4.64839	−0.159439
$851$	−29.1451	−0.999081
$852$	−1.72569	−0.0591211
$853$	31.6809	1.08473	0.542367	−	0.840142i	$-0.317528\pi$
$853$	31.6809	1.08473	0.542367	+	0.840142i	$0.317528\pi$
$854$	0.0626051	0.00214230
$855$	10.6963	0.365805
$856$	−1.27706	−0.0436491
$857$	31.5331	1.07715	0.538576	−	0.842577i	$-0.318963\pi$
$857$	31.5331	1.07715	0.538576	+	0.842577i	$0.318963\pi$
$858$	12.4819	0.426123
$859$	29.5022	1.00660	0.503302	−	0.864111i	$-0.332118\pi$
$859$	29.5022	1.00660	0.503302	+	0.864111i	$0.332118\pi$
$860$	−2.06168	−0.0703027
$861$	−2.60202	−0.0886766
$862$	21.4747	0.731431
$863$	−56.9843	−1.93977	−0.969884	−	0.243569i	$-0.921682\pi$
$863$	−56.9843	−1.93977	−0.969884	+	0.243569i	$0.921682\pi$
$864$	−19.8126	−0.674037
$865$	−22.2484	−0.756469
$866$	−23.0357	−0.782785
$867$	−9.83597	−0.334047
$868$	2.04494	0.0694097
$869$	−18.3949	−0.624004
$870$	−4.82699	−0.163650
$871$	3.85768	0.130712
$872$	18.6338	0.631022
$873$	20.1136	0.680742
$874$	−80.2857	−2.71570
$875$	−0.515011	−0.0174106
$876$	−1.41798	−0.0479092
$877$	7.51290	0.253692	0.126846	−	0.991922i	$-0.459515\pi$
$877$	7.51290	0.253692	0.126846	+	0.991922i	$0.459515\pi$
$878$	−4.43637	−0.149720
$879$	−18.8191	−0.634754
$880$	−17.3162	−0.583728
$881$	−1.26570	−0.0426426	−0.0213213	−	0.999773i	$-0.506787\pi$
$881$	−1.26570	−0.0426426	−0.0213213	+	0.999773i	$0.506787\pi$
$882$	−19.9049	−0.670232
$883$	8.42558	0.283543	0.141772	−	0.989899i	$-0.454720\pi$
$883$	8.42558	0.283543	0.141772	+	0.989899i	$0.454720\pi$
$884$	−3.86918	−0.130135
$885$	−8.33698	−0.280245
$886$	48.8217	1.64020
$887$	27.0434	0.908029	0.454015	−	0.890994i	$-0.349991\pi$
$887$	27.0434	0.908029	0.454015	+	0.890994i	$0.349991\pi$
$888$	8.30833	0.278809
$889$	0.528434	0.0177231
$890$	−7.24159	−0.242738
$891$	−1.25847	−0.0421605
$892$	−2.54993	−0.0853781
$893$	14.8860	0.498142
$894$	32.8099	1.09733
$895$	−8.68073	−0.290165
$896$	6.94823	0.232124
$897$	17.7393	0.592298
$898$	−44.9490	−1.49997
$899$	−15.3505	−0.511968
$900$	−1.25048	−0.0416826
$901$	7.26744	0.242114
$902$	−26.7240	−0.889811
$903$	1.67439	0.0557201
$904$	−3.36129	−0.111795
$905$	13.1545	0.437271
$906$	−41.3804	−1.37477
$907$	23.5603	0.782306	0.391153	−	0.920326i	$-0.372076\pi$
$907$	23.5603	0.782306	0.391153	+	0.920326i	$0.372076\pi$
$908$	−18.2154	−0.604499
$909$	−18.1820	−0.603059
$910$	−1.66316	−0.0551332
$911$	−22.9959	−0.761887	−0.380944	−	0.924598i	$-0.624401\pi$
$911$	−22.9959	−0.761887	−0.380944	+	0.924598i	$0.624401\pi$
$912$	31.9243	1.05712
$913$	7.42802	0.245832
$914$	−15.7501	−0.520966
$915$	0.0811054	0.00268126
$916$	−0.957758	−0.0316452
$917$	−4.26750	−0.140925
$918$	24.4393	0.806616
$919$	−17.7648	−0.586008	−0.293004	−	0.956111i	$-0.594655\pi$
$919$	−17.7648	−0.586008	−0.293004	+	0.956111i	$0.594655\pi$
$920$	−17.6431	−0.581676
$921$	−12.5751	−0.414365
$922$	−29.5730	−0.973935
$923$	4.46337	0.146913
$924$	−1.38248	−0.0454802
$925$	3.54000	0.116394
$926$	−25.7825	−0.847266
$927$	20.3318	0.667783
$928$	10.1180	0.332140
$929$	−0.306238	−0.0100473	−0.00502367	−	0.999987i	$-0.501599\pi$
$929$	−0.306238	−0.0100473	−0.00502367	+	0.999987i	$0.501599\pi$
$930$	10.2783	0.337039
$931$	40.0090	1.31124
$932$	−16.1028	−0.527464
$933$	15.3329	0.501976
$934$	−30.1496	−0.986526
$935$	9.99372	0.326830
$936$	7.59079	0.248113
$937$	14.3678	0.469374	0.234687	−	0.972071i	$-0.424593\pi$
$937$	14.3678	0.469374	0.234687	+	0.972071i	$0.424593\pi$
$938$	−1.65770	−0.0541258
$939$	10.8747	0.354884
$940$	−1.74029	−0.0567621
$941$	1.44225	0.0470161	0.0235081	−	0.999724i	$-0.492516\pi$
$941$	1.44225	0.0470161	0.0235081	+	0.999724i	$0.492516\pi$
$942$	−0.591584	−0.0192748
$943$	−37.9803	−1.23681
$944$	37.3507	1.21566
$945$	2.70771	0.0880818
$946$	17.1967	0.559114
$947$	44.3027	1.43964	0.719821	−	0.694159i	$-0.244224\pi$
$947$	44.3027	1.43964	0.719821	+	0.694159i	$0.244224\pi$
$948$	−3.96469	−0.128767
$949$	3.66751	0.119052
$950$	9.75160	0.316384
$951$	6.41385	0.207983
$952$	−3.12531	−0.101292
$953$	20.8171	0.674333	0.337167	−	0.941445i	$-0.390531\pi$
$953$	20.8171	0.674333	0.337167	+	0.941445i	$0.390531\pi$
$954$	7.58500	0.245574
$955$	−6.89791	−0.223211
$956$	0.433087	0.0140070
$957$	10.3777	0.335464
$958$	−32.9506	−1.06459
$959$	5.98194	0.193167
$960$	3.97294	0.128226
$961$	1.68641	0.0544004
$962$	11.4320	0.368581
$963$	1.07299	0.0345766
$964$	−2.22667	−0.0717162
$965$	7.87031	0.253354
$966$	−7.62283	−0.245261
$967$	28.8739	0.928521	0.464260	−	0.885699i	$-0.346320\pi$
$967$	28.8739	0.928521	0.464260	+	0.885699i	$0.346320\pi$
$968$	3.11710	0.100187
$969$	−18.4245	−0.591881
$970$	18.3372	0.588772
$971$	−19.1081	−0.613208	−0.306604	−	0.951837i	$-0.599193\pi$
$971$	−19.1081	−0.613208	−0.306604	+	0.951837i	$0.599193\pi$
$972$	10.6831	0.342660
$973$	2.39150	0.0766680
$974$	27.0559	0.866927
$975$	−2.15464	−0.0690036
$976$	−0.363362	−0.0116309
$977$	−30.1689	−0.965187	−0.482594	−	0.875844i	$-0.660305\pi$
$977$	−30.1689	−0.965187	−0.482594	+	0.875844i	$0.660305\pi$
$978$	−1.13419	−0.0362674
$979$	15.5689	0.497584
$980$	−4.67737	−0.149413
$981$	−15.6562	−0.499864
$982$	28.6113	0.913023
$983$	−2.68185	−0.0855378	−0.0427689	−	0.999085i	$-0.513618\pi$
$983$	−2.68185	−0.0855378	−0.0427689	+	0.999085i	$0.513618\pi$
$984$	10.8270	0.345151
$985$	−18.1596	−0.578612
$986$	−12.4808	−0.397469
$987$	1.41337	0.0449882
$988$	8.11694	0.258234
$989$	24.4401	0.777151
$990$	10.4304	0.331500
$991$	6.08643	0.193342	0.0966708	−	0.995316i	$-0.469181\pi$
$991$	6.08643	0.193342	0.0966708	+	0.995316i	$0.469181\pi$
$992$	−21.5446	−0.684042
$993$	−34.1368	−1.08330
$994$	−1.91797	−0.0608344
$995$	2.96249	0.0939173
$996$	1.60098	0.0507289
$997$	56.1991	1.77984	0.889922	−	0.456112i	$-0.150758\pi$
$997$	56.1991	1.77984	0.889922	+	0.456112i	$0.150758\pi$
$998$	−25.1389	−0.795759
$999$	−18.6118	−0.588851

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2005.2.a.d.1.8	✓	25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2005.2.a.d.1.8	✓	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:	\( N \)	\(=\)	\( 2005 = 5 \cdot 401 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2005.a (trivial)

\(f(q)\)	\(=\)	\(q-1.64150 q^{2} +1.09521 q^{3} +0.694512 q^{4} +1.00000 q^{5} -1.79778 q^{6} -0.515011 q^{7} +2.14295 q^{8} -1.80052 q^{9} +O(q^{10})\)	\(q-1.64150 q^{2} +1.09521 q^{3} +0.694512 q^{4} +1.00000 q^{5} -1.79778 q^{6} -0.515011 q^{7} +2.14295 q^{8} -1.80052 q^{9} -1.64150 q^{10} +3.52910 q^{11} +0.760636 q^{12} -1.96733 q^{13} +0.845390 q^{14} +1.09521 q^{15} -4.90668 q^{16} +2.83180 q^{17} +2.95554 q^{18} -5.94068 q^{19} +0.694512 q^{20} -0.564046 q^{21} -5.79301 q^{22} -8.23308 q^{23} +2.34699 q^{24} +1.00000 q^{25} +3.22936 q^{26} -5.25757 q^{27} -0.357681 q^{28} +2.68497 q^{29} -1.79778 q^{30} -5.71720 q^{31} +3.76839 q^{32} +3.86511 q^{33} -4.64839 q^{34} -0.515011 q^{35} -1.25048 q^{36} +3.54000 q^{37} +9.75160 q^{38} -2.15464 q^{39} +2.14295 q^{40} +4.61314 q^{41} +0.925879 q^{42} -2.96853 q^{43} +2.45100 q^{44} -1.80052 q^{45} +13.5146 q^{46} -2.50578 q^{47} -5.37384 q^{48} -6.73476 q^{49} -1.64150 q^{50} +3.10142 q^{51} -1.36633 q^{52} +2.56637 q^{53} +8.63029 q^{54} +3.52910 q^{55} -1.10365 q^{56} -6.50629 q^{57} -4.40737 q^{58} -7.61222 q^{59} +0.760636 q^{60} +0.0740547 q^{61} +9.38477 q^{62} +0.927286 q^{63} +3.62756 q^{64} -1.96733 q^{65} -6.34457 q^{66} -1.96087 q^{67} +1.96672 q^{68} -9.01695 q^{69} +0.845390 q^{70} -2.26874 q^{71} -3.85842 q^{72} -1.86421 q^{73} -5.81090 q^{74} +1.09521 q^{75} -4.12587 q^{76} -1.81753 q^{77} +3.53683 q^{78} -5.21234 q^{79} -4.90668 q^{80} -0.356599 q^{81} -7.57245 q^{82} +2.10479 q^{83} -0.391736 q^{84} +2.83180 q^{85} +4.87283 q^{86} +2.94061 q^{87} +7.56271 q^{88} +4.41157 q^{89} +2.95554 q^{90} +1.01320 q^{91} -5.71797 q^{92} -6.26154 q^{93} +4.11323 q^{94} -5.94068 q^{95} +4.12717 q^{96} -11.1710 q^{97} +11.0551 q^{98} -6.35421 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q - 5 q^{2} - 10 q^{3} + 25 q^{4} + 25 q^{5} + 2 q^{6} - 31 q^{7} - 30 q^{8} + 17 q^{9}+O(q^{10}) \) 25 * q - 5 * q^2 - 10 * q^3 + 25 * q^4 + 25 * q^5 + 2 * q^6 - 31 * q^7 - 30 * q^8 + 17 * q^9	\( 25 q - 5 q^{2} - 10 q^{3} + 25 q^{4} + 25 q^{5} + 2 q^{6} - 31 q^{7} - 30 q^{8} + 17 q^{9} - 5 q^{10} - 30 q^{11} - 29 q^{12} - 18 q^{13} + 6 q^{14} - 10 q^{15} + 21 q^{16} - 18 q^{17} - 30 q^{18} - 17 q^{19} + 25 q^{20} + 6 q^{21} - 2 q^{22} - 44 q^{23} + 11 q^{24} + 25 q^{25} - 14 q^{26} - 25 q^{27} - 50 q^{28} - 9 q^{29} + 2 q^{30} - 13 q^{31} - 45 q^{32} - 21 q^{33} - 21 q^{34} - 31 q^{35} + 5 q^{36} - 28 q^{37} - 32 q^{38} + 9 q^{39} - 30 q^{40} + 28 q^{41} - 67 q^{42} - 61 q^{43} - 49 q^{44} + 17 q^{45} + 18 q^{46} - 53 q^{47} - 44 q^{48} + 28 q^{49} - 5 q^{50} - 30 q^{51} - 3 q^{52} - 36 q^{53} + 17 q^{54} - 30 q^{55} - 3 q^{56} - 13 q^{57} + 2 q^{58} - 39 q^{59} - 29 q^{60} + 10 q^{61} - 30 q^{62} - 44 q^{63} - 4 q^{64} - 18 q^{65} + 33 q^{66} - 10 q^{67} - 18 q^{68} - 6 q^{69} + 6 q^{70} - 7 q^{71} - q^{72} - 26 q^{73} - 3 q^{74} - 10 q^{75} + 12 q^{76} + 29 q^{77} - 5 q^{78} - 6 q^{79} + 21 q^{80} + 13 q^{81} - 30 q^{82} - 35 q^{83} + 117 q^{84} - 18 q^{85} + 14 q^{86} - 104 q^{87} + 53 q^{88} + 7 q^{89} - 30 q^{90} - 25 q^{91} - 31 q^{92} + 2 q^{93} + 68 q^{94} - 17 q^{95} + 92 q^{96} + 6 q^{97} + 15 q^{98} - 36 q^{99}+O(q^{100}) \) 25 * q - 5 * q^2 - 10 * q^3 + 25 * q^4 + 25 * q^5 + 2 * q^6 - 31 * q^7 - 30 * q^8 + 17 * q^9 - 5 * q^10 - 30 * q^11 - 29 * q^12 - 18 * q^13 + 6 * q^14 - 10 * q^15 + 21 * q^16 - 18 * q^17 - 30 * q^18 - 17 * q^19 + 25 * q^20 + 6 * q^21 - 2 * q^22 - 44 * q^23 + 11 * q^24 + 25 * q^25 - 14 * q^26 - 25 * q^27 - 50 * q^28 - 9 * q^29 + 2 * q^30 - 13 * q^31 - 45 * q^32 - 21 * q^33 - 21 * q^34 - 31 * q^35 + 5 * q^36 - 28 * q^37 - 32 * q^38 + 9 * q^39 - 30 * q^40 + 28 * q^41 - 67 * q^42 - 61 * q^43 - 49 * q^44 + 17 * q^45 + 18 * q^46 - 53 * q^47 - 44 * q^48 + 28 * q^49 - 5 * q^50 - 30 * q^51 - 3 * q^52 - 36 * q^53 + 17 * q^54 - 30 * q^55 - 3 * q^56 - 13 * q^57 + 2 * q^58 - 39 * q^59 - 29 * q^60 + 10 * q^61 - 30 * q^62 - 44 * q^63 - 4 * q^64 - 18 * q^65 + 33 * q^66 - 10 * q^67 - 18 * q^68 - 6 * q^69 + 6 * q^70 - 7 * q^71 - q^72 - 26 * q^73 - 3 * q^74 - 10 * q^75 + 12 * q^76 + 29 * q^77 - 5 * q^78 - 6 * q^79 + 21 * q^80 + 13 * q^81 - 30 * q^82 - 35 * q^83 + 117 * q^84 - 18 * q^85 + 14 * q^86 - 104 * q^87 + 53 * q^88 + 7 * q^89 - 30 * q^90 - 25 * q^91 - 31 * q^92 + 2 * q^93 + 68 * q^94 - 17 * q^95 + 92 * q^96 + 6 * q^97 + 15 * q^98 - 36 * q^99

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