LMFDB - Embedded newform 4010.2.a.l.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4010,2,Mod(1,4010)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4010, 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("4010.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4010 = 2 \cdot 5 \cdot 401 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4010.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:	$32.0200112105$
Analytic rank:	$0$
Dimension:	$17$
Coefficient field:	$\mathbb{Q}[x]/(x^{17} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{17} - 3 x^{16} - 24 x^{15} + 70 x^{14} + 228 x^{13} - 638 x^{12} - 1075 x^{11} + 2854 x^{10} + \cdots - 2 $ x^17 - 3x^16 - 24x^15 + 70x^14 + 228x^13 - 638x^12 - 1075x^11 + 2854x^10 + 2544x^9 - 6415x^8 - 2573x^7 + 6456x^6 + 485x^5 - 1839x^4 + 67x^3 + 136x^2 - 8x - 2
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-1.71266$ of defining polynomial
Character	$\chi$	$=$	4010.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.71266 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.71266 q^{6} -2.30195 q^{7} -1.00000 q^{8} -0.0668018 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.71266 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.71266 q^{6} -2.30195 q^{7} -1.00000 q^{8} -0.0668018 q^{9} +1.00000 q^{10} -1.96399 q^{11} -1.71266 q^{12} +3.70057 q^{13} +2.30195 q^{14} +1.71266 q^{15} +1.00000 q^{16} -5.25716 q^{17} +0.0668018 q^{18} -7.91478 q^{19} -1.00000 q^{20} +3.94246 q^{21} +1.96399 q^{22} -0.848696 q^{23} +1.71266 q^{24} +1.00000 q^{25} -3.70057 q^{26} +5.25238 q^{27} -2.30195 q^{28} -10.0853 q^{29} -1.71266 q^{30} +2.80357 q^{31} -1.00000 q^{32} +3.36365 q^{33} +5.25716 q^{34} +2.30195 q^{35} -0.0668018 q^{36} +4.22064 q^{37} +7.91478 q^{38} -6.33782 q^{39} +1.00000 q^{40} -5.69055 q^{41} -3.94246 q^{42} -5.08014 q^{43} -1.96399 q^{44} +0.0668018 q^{45} +0.848696 q^{46} -2.64478 q^{47} -1.71266 q^{48} -1.70101 q^{49} -1.00000 q^{50} +9.00372 q^{51} +3.70057 q^{52} -11.2213 q^{53} -5.25238 q^{54} +1.96399 q^{55} +2.30195 q^{56} +13.5553 q^{57} +10.0853 q^{58} -3.24924 q^{59} +1.71266 q^{60} -0.922792 q^{61} -2.80357 q^{62} +0.153775 q^{63} +1.00000 q^{64} -3.70057 q^{65} -3.36365 q^{66} +2.33658 q^{67} -5.25716 q^{68} +1.45353 q^{69} -2.30195 q^{70} +5.21560 q^{71} +0.0668018 q^{72} -14.6348 q^{73} -4.22064 q^{74} -1.71266 q^{75} -7.91478 q^{76} +4.52102 q^{77} +6.33782 q^{78} +5.39554 q^{79} -1.00000 q^{80} -8.79513 q^{81} +5.69055 q^{82} +4.95874 q^{83} +3.94246 q^{84} +5.25716 q^{85} +5.08014 q^{86} +17.2727 q^{87} +1.96399 q^{88} -12.8477 q^{89} -0.0668018 q^{90} -8.51855 q^{91} -0.848696 q^{92} -4.80156 q^{93} +2.64478 q^{94} +7.91478 q^{95} +1.71266 q^{96} -6.19456 q^{97} +1.70101 q^{98} +0.131198 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 17 q - 17 q^{2} + 3 q^{3} + 17 q^{4} - 17 q^{5} - 3 q^{6} + 4 q^{7} - 17 q^{8} + 6 q^{9}+O(q^{10}) $ 17 * q - 17 * q^2 + 3 * q^3 + 17 * q^4 - 17 * q^5 - 3 * q^6 + 4 * q^7 - 17 * q^8 + 6 * q^9	\( 17 q - 17 q^{2} + 3 q^{3} + 17 q^{4} - 17 q^{5} - 3 q^{6} + 4 q^{7} - 17 q^{8} + 6 q^{9} + 17 q^{10} - 8 q^{11} + 3 q^{12} + 14 q^{13} - 4 q^{14} - 3 q^{15} + 17 q^{16} - 8 q^{17} - 6 q^{18} + 7 q^{19} - 17 q^{20} - 11 q^{21} + 8 q^{22} + q^{23} - 3 q^{24} + 17 q^{25} - 14 q^{26} + 15 q^{27} + 4 q^{28} - 18 q^{29} + 3 q^{30} + 8 q^{31} - 17 q^{32} + 3 q^{33} + 8 q^{34} - 4 q^{35} + 6 q^{36} + 49 q^{37} - 7 q^{38} - 12 q^{39} + 17 q^{40} - 23 q^{41} + 11 q^{42} + 35 q^{43} - 8 q^{44} - 6 q^{45} - q^{46} + 11 q^{47} + 3 q^{48} + 27 q^{49} - 17 q^{50} - 16 q^{51} + 14 q^{52} - 3 q^{53} - 15 q^{54} + 8 q^{55} - 4 q^{56} + 9 q^{57} + 18 q^{58} - 6 q^{59} - 3 q^{60} + 6 q^{61} - 8 q^{62} + 10 q^{63} + 17 q^{64} - 14 q^{65} - 3 q^{66} + 55 q^{67} - 8 q^{68} - q^{69} + 4 q^{70} + 5 q^{71} - 6 q^{72} + 62 q^{73} - 49 q^{74} + 3 q^{75} + 7 q^{76} + 2 q^{77} + 12 q^{78} - 3 q^{79} - 17 q^{80} - 15 q^{81} + 23 q^{82} + 7 q^{83} - 11 q^{84} + 8 q^{85} - 35 q^{86} + 10 q^{87} + 8 q^{88} - 18 q^{89} + 6 q^{90} + 18 q^{91} + q^{92} + 33 q^{93} - 11 q^{94} - 7 q^{95} - 3 q^{96} + 63 q^{97} - 27 q^{98} - 11 q^{99}+O(q^{100}) \) 17 * q - 17 * q^2 + 3 * q^3 + 17 * q^4 - 17 * q^5 - 3 * q^6 + 4 * q^7 - 17 * q^8 + 6 * q^9 + 17 * q^10 - 8 * q^11 + 3 * q^12 + 14 * q^13 - 4 * q^14 - 3 * q^15 + 17 * q^16 - 8 * q^17 - 6 * q^18 + 7 * q^19 - 17 * q^20 - 11 * q^21 + 8 * q^22 + q^23 - 3 * q^24 + 17 * q^25 - 14 * q^26 + 15 * q^27 + 4 * q^28 - 18 * q^29 + 3 * q^30 + 8 * q^31 - 17 * q^32 + 3 * q^33 + 8 * q^34 - 4 * q^35 + 6 * q^36 + 49 * q^37 - 7 * q^38 - 12 * q^39 + 17 * q^40 - 23 * q^41 + 11 * q^42 + 35 * q^43 - 8 * q^44 - 6 * q^45 - q^46 + 11 * q^47 + 3 * q^48 + 27 * q^49 - 17 * q^50 - 16 * q^51 + 14 * q^52 - 3 * q^53 - 15 * q^54 + 8 * q^55 - 4 * q^56 + 9 * q^57 + 18 * q^58 - 6 * q^59 - 3 * q^60 + 6 * q^61 - 8 * q^62 + 10 * q^63 + 17 * q^64 - 14 * q^65 - 3 * q^66 + 55 * q^67 - 8 * q^68 - q^69 + 4 * q^70 + 5 * q^71 - 6 * q^72 + 62 * q^73 - 49 * q^74 + 3 * q^75 + 7 * q^76 + 2 * q^77 + 12 * q^78 - 3 * q^79 - 17 * q^80 - 15 * q^81 + 23 * q^82 + 7 * q^83 - 11 * q^84 + 8 * q^85 - 35 * q^86 + 10 * q^87 + 8 * q^88 - 18 * q^89 + 6 * q^90 + 18 * q^91 + q^92 + 33 * q^93 - 11 * q^94 - 7 * q^95 - 3 * q^96 + 63 * q^97 - 27 * q^98 - 11 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−1.71266	−0.988804	−0.494402	−	0.869233i	$-0.664613\pi$
$3$	−1.71266	−0.988804	−0.494402	+	0.869233i	$0.664613\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	1.71266	0.699190
$7$	−2.30195	−0.870057	−0.435028	−	0.900417i	$-0.643262\pi$
$7$	−2.30195	−0.870057	−0.435028	+	0.900417i	$0.643262\pi$
$8$	−1.00000	−0.353553
$9$	−0.0668018	−0.0222673
$10$	1.00000	0.316228
$11$	−1.96399	−0.592167	−0.296083	−	0.955162i	$-0.595681\pi$
$11$	−1.96399	−0.592167	−0.296083	+	0.955162i	$0.595681\pi$
$12$	−1.71266	−0.494402
$13$	3.70057	1.02635	0.513177	−	0.858283i	$-0.328468\pi$
$13$	3.70057	1.02635	0.513177	+	0.858283i	$0.328468\pi$
$14$	2.30195	0.615223
$15$	1.71266	0.442206
$16$	1.00000	0.250000
$17$	−5.25716	−1.27505	−0.637525	−	0.770430i	$-0.720042\pi$
$17$	−5.25716	−1.27505	−0.637525	+	0.770430i	$0.720042\pi$
$18$	0.0668018	0.0157453
$19$	−7.91478	−1.81577	−0.907887	−	0.419214i	$-0.862306\pi$
$19$	−7.91478	−1.81577	−0.907887	+	0.419214i	$0.862306\pi$
$20$	−1.00000	−0.223607
$21$	3.94246	0.860315
$22$	1.96399	0.418725
$23$	−0.848696	−0.176965	−0.0884827	−	0.996078i	$-0.528202\pi$
$23$	−0.848696	−0.176965	−0.0884827	+	0.996078i	$0.528202\pi$
$24$	1.71266	0.349595
$25$	1.00000	0.200000
$26$	−3.70057	−0.725742
$27$	5.25238	1.01082
$28$	−2.30195	−0.435028
$29$	−10.0853	−1.87280	−0.936399	−	0.350936i	$-0.885863\pi$
$29$	−10.0853	−1.87280	−0.936399	+	0.350936i	$0.885863\pi$
$30$	−1.71266	−0.312687
$31$	2.80357	0.503537	0.251768	−	0.967788i	$-0.418988\pi$
$31$	2.80357	0.503537	0.251768	+	0.967788i	$0.418988\pi$
$32$	−1.00000	−0.176777
$33$	3.36365	0.585537
$34$	5.25716	0.901596
$35$	2.30195	0.389101
$36$	−0.0668018	−0.0111336
$37$	4.22064	0.693868	0.346934	−	0.937889i	$-0.387223\pi$
$37$	4.22064	0.693868	0.346934	+	0.937889i	$0.387223\pi$
$38$	7.91478	1.28395
$39$	−6.33782	−1.01486
$40$	1.00000	0.158114
$41$	−5.69055	−0.888714	−0.444357	−	0.895850i	$-0.646568\pi$
$41$	−5.69055	−0.888714	−0.444357	+	0.895850i	$0.646568\pi$
$42$	−3.94246	−0.608335
$43$	−5.08014	−0.774715	−0.387357	−	0.921930i	$-0.626612\pi$
$43$	−5.08014	−0.774715	−0.387357	+	0.921930i	$0.626612\pi$
$44$	−1.96399	−0.296083
$45$	0.0668018	0.00995823
$46$	0.848696	0.125133
$47$	−2.64478	−0.385780	−0.192890	−	0.981220i	$-0.561786\pi$
$47$	−2.64478	−0.385780	−0.192890	+	0.981220i	$0.561786\pi$
$48$	−1.71266	−0.247201
$49$	−1.70101	−0.243001
$50$	−1.00000	−0.141421
$51$	9.00372	1.26077
$52$	3.70057	0.513177
$53$	−11.2213	−1.54137	−0.770685	−	0.637216i	$-0.780086\pi$
$53$	−11.2213	−1.54137	−0.770685	+	0.637216i	$0.780086\pi$
$54$	−5.25238	−0.714759
$55$	1.96399	0.264825
$56$	2.30195	0.307611
$57$	13.5553	1.79544
$58$	10.0853	1.32427
$59$	−3.24924	−0.423015	−0.211508	−	0.977376i	$-0.567837\pi$
$59$	−3.24924	−0.423015	−0.211508	+	0.977376i	$0.567837\pi$
$60$	1.71266	0.221103
$61$	−0.922792	−0.118151	−0.0590757	−	0.998254i	$-0.518815\pi$
$61$	−0.922792	−0.118151	−0.0590757	+	0.998254i	$0.518815\pi$
$62$	−2.80357	−0.356054
$63$	0.153775	0.0193738
$64$	1.00000	0.125000
$65$	−3.70057	−0.459000
$66$	−3.36365	−0.414037
$67$	2.33658	0.285459	0.142729	−	0.989762i	$-0.454412\pi$
$67$	2.33658	0.285459	0.142729	+	0.989762i	$0.454412\pi$
$68$	−5.25716	−0.637525
$69$	1.45353	0.174984
$70$	−2.30195	−0.275136
$71$	5.21560	0.618978	0.309489	−	0.950903i	$-0.399842\pi$
$71$	5.21560	0.618978	0.309489	+	0.950903i	$0.399842\pi$
$72$	0.0668018	0.00787267
$73$	−14.6348	−1.71288	−0.856438	−	0.516250i	$-0.827328\pi$
$73$	−14.6348	−1.71288	−0.856438	+	0.516250i	$0.827328\pi$
$74$	−4.22064	−0.490639
$75$	−1.71266	−0.197761
$76$	−7.91478	−0.907887
$77$	4.52102	0.515218
$78$	6.33782	0.717617
$79$	5.39554	0.607045	0.303523	−	0.952824i	$-0.401837\pi$
$79$	5.39554	0.607045	0.303523	+	0.952824i	$0.401837\pi$
$80$	−1.00000	−0.111803
$81$	−8.79513	−0.977237
$82$	5.69055	0.628416
$83$	4.95874	0.544293	0.272146	−	0.962256i	$-0.412266\pi$
$83$	4.95874	0.544293	0.272146	+	0.962256i	$0.412266\pi$
$84$	3.94246	0.430158
$85$	5.25716	0.570219
$86$	5.08014	0.547806
$87$	17.2727	1.85183
$88$	1.96399	0.209363
$89$	−12.8477	−1.36185	−0.680924	−	0.732354i	$-0.738422\pi$
$89$	−12.8477	−1.36185	−0.680924	+	0.732354i	$0.738422\pi$
$90$	−0.0668018	−0.00704153
$91$	−8.51855	−0.892986
$92$	−0.848696	−0.0884827
$93$	−4.80156	−0.497899
$94$	2.64478	0.272788
$95$	7.91478	0.812039
$96$	1.71266	0.174797
$97$	−6.19456	−0.628962	−0.314481	−	0.949264i	$-0.601831\pi$
$97$	−6.19456	−0.628962	−0.314481	+	0.949264i	$0.601831\pi$
$98$	1.70101	0.171828
$99$	0.131198	0.0131859
$100$	1.00000	0.100000
$101$	−0.591486	−0.0588551	−0.0294275	−	0.999567i	$-0.509368\pi$
$101$	−0.591486	−0.0588551	−0.0294275	+	0.999567i	$0.509368\pi$
$102$	−9.00372	−0.891501
$103$	8.26160	0.814040	0.407020	−	0.913419i	$-0.366568\pi$
$103$	8.26160	0.814040	0.407020	+	0.913419i	$0.366568\pi$
$104$	−3.70057	−0.362871
$105$	−3.94246	−0.384745
$106$	11.2213	1.08991
$107$	10.6847	1.03293	0.516466	−	0.856308i	$-0.327247\pi$
$107$	10.6847	1.03293	0.516466	+	0.856308i	$0.327247\pi$
$108$	5.25238	0.505411
$109$	−14.1604	−1.35632	−0.678162	−	0.734912i	$-0.737223\pi$
$109$	−14.1604	−1.35632	−0.678162	+	0.734912i	$0.737223\pi$
$110$	−1.96399	−0.187260
$111$	−7.22851	−0.686100
$112$	−2.30195	−0.217514
$113$	−8.99833	−0.846492	−0.423246	−	0.906015i	$-0.639109\pi$
$113$	−8.99833	−0.846492	−0.423246	+	0.906015i	$0.639109\pi$
$114$	−13.5553	−1.26957
$115$	0.848696	0.0791413
$116$	−10.0853	−0.936399
$117$	−0.247205	−0.0228541
$118$	3.24924	0.299117
$119$	12.1017	1.10937
$120$	−1.71266	−0.156344
$121$	−7.14273	−0.649339
$122$	0.922792	0.0835457
$123$	9.74596	0.878764
$124$	2.80357	0.251768
$125$	−1.00000	−0.0894427
$126$	−0.153775	−0.0136993
$127$	17.2347	1.52934	0.764668	−	0.644425i	$-0.222903\pi$
$127$	17.2347	1.52934	0.764668	+	0.644425i	$0.222903\pi$
$128$	−1.00000	−0.0883883
$129$	8.70055	0.766041
$130$	3.70057	0.324562
$131$	−13.3843	−1.16940	−0.584698	−	0.811251i	$-0.698787\pi$
$131$	−13.3843	−1.16940	−0.584698	+	0.811251i	$0.698787\pi$
$132$	3.36365	0.292768
$133$	18.2195	1.57983
$134$	−2.33658	−0.201850
$135$	−5.25238	−0.452053
$136$	5.25716	0.450798
$137$	−4.23950	−0.362205	−0.181102	−	0.983464i	$-0.557967\pi$
$137$	−4.23950	−0.362205	−0.181102	+	0.983464i	$0.557967\pi$
$138$	−1.45353	−0.123732
$139$	−6.42501	−0.544962	−0.272481	−	0.962161i	$-0.587844\pi$
$139$	−6.42501	−0.544962	−0.272481	+	0.962161i	$0.587844\pi$
$140$	2.30195	0.194551
$141$	4.52960	0.381461
$142$	−5.21560	−0.437684
$143$	−7.26791	−0.607773
$144$	−0.0668018	−0.00556682
$145$	10.0853	0.837541
$146$	14.6348	1.21119
$147$	2.91325	0.240281
$148$	4.22064	0.346934
$149$	10.3958	0.851658	0.425829	−	0.904804i	$-0.359982\pi$
$149$	10.3958	0.851658	0.425829	+	0.904804i	$0.359982\pi$
$150$	1.71266	0.139838
$151$	−11.1995	−0.911402	−0.455701	−	0.890133i	$-0.650611\pi$
$151$	−11.1995	−0.911402	−0.455701	+	0.890133i	$0.650611\pi$
$152$	7.91478	0.641973
$153$	0.351188	0.0283919
$154$	−4.52102	−0.364314
$155$	−2.80357	−0.225188
$156$	−6.33782	−0.507432
$157$	10.5520	0.842140	0.421070	−	0.907028i	$-0.361655\pi$
$157$	10.5520	0.842140	0.421070	+	0.907028i	$0.361655\pi$
$158$	−5.39554	−0.429246
$159$	19.2183	1.52411
$160$	1.00000	0.0790569
$161$	1.95366	0.153970
$162$	8.79513	0.691011
$163$	2.01688	0.157974	0.0789872	−	0.996876i	$-0.474831\pi$
$163$	2.01688	0.157974	0.0789872	+	0.996876i	$0.474831\pi$
$164$	−5.69055	−0.444357
$165$	−3.36365	−0.261860
$166$	−4.95874	−0.384873
$167$	−13.6053	−1.05281	−0.526404	−	0.850234i	$-0.676460\pi$
$167$	−13.6053	−1.05281	−0.526404	+	0.850234i	$0.676460\pi$
$168$	−3.94246	−0.304167
$169$	0.694244	0.0534034
$170$	−5.25716	−0.403206
$171$	0.528722	0.0404324
$172$	−5.08014	−0.387357
$173$	21.0756	1.60235	0.801175	−	0.598431i	$-0.204209\pi$
$173$	21.0756	1.60235	0.801175	+	0.598431i	$0.204209\pi$
$174$	−17.2727	−1.30944
$175$	−2.30195	−0.174011
$176$	−1.96399	−0.148042
$177$	5.56484	0.418279
$178$	12.8477	0.962972
$179$	−16.1439	−1.20665	−0.603326	−	0.797494i	$-0.706158\pi$
$179$	−16.1439	−1.20665	−0.603326	+	0.797494i	$0.706158\pi$
$180$	0.0668018	0.00497912
$181$	−17.8970	−1.33027	−0.665136	−	0.746723i	$-0.731626\pi$
$181$	−17.8970	−1.33027	−0.665136	+	0.746723i	$0.731626\pi$
$182$	8.51855	0.631437
$183$	1.58043	0.116829
$184$	0.848696	0.0625667
$185$	−4.22064	−0.310307
$186$	4.80156	0.352068
$187$	10.3250	0.755042
$188$	−2.64478	−0.192890
$189$	−12.0907	−0.879472
$190$	−7.91478	−0.574198
$191$	22.1620	1.60358	0.801792	−	0.597604i	$-0.203880\pi$
$191$	22.1620	1.60358	0.801792	+	0.597604i	$0.203880\pi$
$192$	−1.71266	−0.123600
$193$	24.4410	1.75930	0.879652	−	0.475618i	$-0.157776\pi$
$193$	24.4410	1.75930	0.879652	+	0.475618i	$0.157776\pi$
$194$	6.19456	0.444744
$195$	6.33782	0.453861
$196$	−1.70101	−0.121501
$197$	18.8259	1.34129	0.670646	−	0.741778i	$-0.266017\pi$
$197$	18.8259	1.34129	0.670646	+	0.741778i	$0.266017\pi$
$198$	−0.131198	−0.00932387
$199$	−6.41446	−0.454709	−0.227354	−	0.973812i	$-0.573008\pi$
$199$	−6.41446	−0.454709	−0.227354	+	0.973812i	$0.573008\pi$
$200$	−1.00000	−0.0707107
$201$	−4.00176	−0.282263
$202$	0.591486	0.0416168
$203$	23.2160	1.62944
$204$	9.00372	0.630387
$205$	5.69055	0.397445
$206$	−8.26160	−0.575613
$207$	0.0566945	0.00394054
$208$	3.70057	0.256589
$209$	15.5446	1.07524
$210$	3.94246	0.272056
$211$	8.20881	0.565118	0.282559	−	0.959250i	$-0.408817\pi$
$211$	8.20881	0.565118	0.282559	+	0.959250i	$0.408817\pi$
$212$	−11.2213	−0.770685
$213$	−8.93254	−0.612048
$214$	−10.6847	−0.730393
$215$	5.08014	0.346463
$216$	−5.25238	−0.357379
$217$	−6.45370	−0.438105
$218$	14.1604	0.959066
$219$	25.0644	1.69370
$220$	1.96399	0.132412
$221$	−19.4545	−1.30865
$222$	7.22851	0.485146
$223$	5.82498	0.390069	0.195035	−	0.980796i	$-0.437518\pi$
$223$	5.82498	0.390069	0.195035	+	0.980796i	$0.437518\pi$
$224$	2.30195	0.153806
$225$	−0.0668018	−0.00445346
$226$	8.99833	0.598560
$227$	12.3065	0.816809	0.408405	−	0.912801i	$-0.366085\pi$
$227$	12.3065	0.816809	0.408405	+	0.912801i	$0.366085\pi$
$228$	13.5553	0.897722
$229$	3.66644	0.242285	0.121142	−	0.992635i	$-0.461344\pi$
$229$	3.66644	0.242285	0.121142	+	0.992635i	$0.461344\pi$
$230$	−0.848696	−0.0559614
$231$	−7.74297	−0.509450
$232$	10.0853	0.662134
$233$	−11.7405	−0.769148	−0.384574	−	0.923094i	$-0.625652\pi$
$233$	−11.7405	−0.769148	−0.384574	+	0.923094i	$0.625652\pi$
$234$	0.247205	0.0161603
$235$	2.64478	0.172526
$236$	−3.24924	−0.211508
$237$	−9.24071	−0.600249
$238$	−12.1017	−0.784440
$239$	−25.0742	−1.62191	−0.810956	−	0.585106i	$-0.801053\pi$
$239$	−25.0742	−1.62191	−0.810956	+	0.585106i	$0.801053\pi$
$240$	1.71266	0.110552
$241$	17.4670	1.12515	0.562576	−	0.826746i	$-0.309811\pi$
$241$	17.4670	1.12515	0.562576	+	0.826746i	$0.309811\pi$
$242$	7.14273	0.459152
$243$	−0.694095	−0.0445262
$244$	−0.922792	−0.0590757
$245$	1.70101	0.108674
$246$	−9.74596	−0.621380
$247$	−29.2892	−1.86363
$248$	−2.80357	−0.178027
$249$	−8.49263	−0.538199
$250$	1.00000	0.0632456
$251$	12.2966	0.776154	0.388077	−	0.921627i	$-0.373140\pi$
$251$	12.2966	0.776154	0.388077	+	0.921627i	$0.373140\pi$
$252$	0.153775	0.00968690
$253$	1.66683	0.104793
$254$	−17.2347	−1.08140
$255$	−9.00372	−0.563835
$256$	1.00000	0.0625000
$257$	3.54582	0.221182	0.110591	−	0.993866i	$-0.464726\pi$
$257$	3.54582	0.221182	0.110591	+	0.993866i	$0.464726\pi$
$258$	−8.70055	−0.541673
$259$	−9.71571	−0.603705
$260$	−3.70057	−0.229500
$261$	0.673719	0.0417021
$262$	13.3843	0.826888
$263$	14.0579	0.866846	0.433423	−	0.901191i	$-0.357306\pi$
$263$	14.0579	0.866846	0.433423	+	0.901191i	$0.357306\pi$
$264$	−3.36365	−0.207018
$265$	11.2213	0.689322
$266$	−18.2195	−1.11711
$267$	22.0036	1.34660
$268$	2.33658	0.142729
$269$	−1.73695	−0.105903	−0.0529517	−	0.998597i	$-0.516863\pi$
$269$	−1.73695	−0.105903	−0.0529517	+	0.998597i	$0.516863\pi$
$270$	5.25238	0.319650
$271$	−0.533135	−0.0323857	−0.0161928	−	0.999869i	$-0.505155\pi$
$271$	−0.533135	−0.0323857	−0.0161928	+	0.999869i	$0.505155\pi$
$272$	−5.25716	−0.318762
$273$	14.5894	0.882988
$274$	4.23950	0.256117
$275$	−1.96399	−0.118433
$276$	1.45353	0.0874920
$277$	−21.2604	−1.27741	−0.638706	−	0.769451i	$-0.720530\pi$
$277$	−21.2604	−1.27741	−0.638706	+	0.769451i	$0.720530\pi$
$278$	6.42501	0.385346
$279$	−0.187284	−0.0112124
$280$	−2.30195	−0.137568
$281$	−7.39486	−0.441141	−0.220570	−	0.975371i	$-0.570792\pi$
$281$	−7.39486	−0.441141	−0.220570	+	0.975371i	$0.570792\pi$
$282$	−4.52960	−0.269734
$283$	−20.0232	−1.19025	−0.595127	−	0.803631i	$-0.702898\pi$
$283$	−20.0232	−1.19025	−0.595127	+	0.803631i	$0.702898\pi$
$284$	5.21560	0.309489
$285$	−13.5553	−0.802947
$286$	7.26791	0.429760
$287$	13.0994	0.773232
$288$	0.0668018	0.00393634
$289$	10.6378	0.625751
$290$	−10.0853	−0.592231
$291$	10.6092	0.621920
$292$	−14.6348	−0.856438
$293$	−20.2951	−1.18566	−0.592828	−	0.805329i	$-0.701988\pi$
$293$	−20.2951	−1.18566	−0.592828	+	0.805329i	$0.701988\pi$
$294$	−2.91325	−0.169904
$295$	3.24924	0.189178
$296$	−4.22064	−0.245320
$297$	−10.3157	−0.598575
$298$	−10.3958	−0.602213
$299$	−3.14066	−0.181629
$300$	−1.71266	−0.0988804
$301$	11.6943	0.674046
$302$	11.1995	0.644458
$303$	1.01301	0.0581961
$304$	−7.91478	−0.453944
$305$	0.922792	0.0528389
$306$	−0.351188	−0.0200761
$307$	−2.70081	−0.154143	−0.0770717	−	0.997026i	$-0.524557\pi$
$307$	−2.70081	−0.154143	−0.0770717	+	0.997026i	$0.524557\pi$
$308$	4.52102	0.257609
$309$	−14.1493	−0.804925
$310$	2.80357	0.159232
$311$	21.5617	1.22265	0.611325	−	0.791380i	$-0.290637\pi$
$311$	21.5617	1.22265	0.611325	+	0.791380i	$0.290637\pi$
$312$	6.33782	0.358808
$313$	16.8310	0.951346	0.475673	−	0.879622i	$-0.342204\pi$
$313$	16.8310	0.951346	0.475673	+	0.879622i	$0.342204\pi$
$314$	−10.5520	−0.595483
$315$	−0.153775	−0.00866423
$316$	5.39554	0.303523
$317$	20.2733	1.13866	0.569330	−	0.822109i	$-0.307203\pi$
$317$	20.2733	1.13866	0.569330	+	0.822109i	$0.307203\pi$
$318$	−19.2183	−1.07771
$319$	19.8075	1.10901
$320$	−1.00000	−0.0559017
$321$	−18.2993	−1.02137
$322$	−1.95366	−0.108873
$323$	41.6093	2.31520
$324$	−8.79513	−0.488618
$325$	3.70057	0.205271
$326$	−2.01688	−0.111705
$327$	24.2520	1.34114
$328$	5.69055	0.314208
$329$	6.08815	0.335651
$330$	3.36365	0.185163
$331$	13.2236	0.726837	0.363419	−	0.931626i	$-0.381609\pi$
$331$	13.2236	0.726837	0.363419	+	0.931626i	$0.381609\pi$
$332$	4.95874	0.272146
$333$	−0.281946	−0.0154506
$334$	13.6053	0.744448
$335$	−2.33658	−0.127661
$336$	3.94246	0.215079
$337$	−23.9916	−1.30691	−0.653454	−	0.756966i	$-0.726681\pi$
$337$	−23.9916	−1.30691	−0.653454	+	0.756966i	$0.726681\pi$
$338$	−0.694244	−0.0377619
$339$	15.4111	0.837014
$340$	5.25716	0.285110
$341$	−5.50620	−0.298178
$342$	−0.528722	−0.0285900
$343$	20.0293	1.08148
$344$	5.08014	0.273903
$345$	−1.45353	−0.0782552
$346$	−21.0756	−1.13303
$347$	−17.5303	−0.941078	−0.470539	−	0.882379i	$-0.655940\pi$
$347$	−17.5303	−0.941078	−0.470539	+	0.882379i	$0.655940\pi$
$348$	17.2727	0.925915
$349$	29.8649	1.59863	0.799316	−	0.600911i	$-0.205195\pi$
$349$	29.8649	1.59863	0.799316	+	0.600911i	$0.205195\pi$
$350$	2.30195	0.123045
$351$	19.4368	1.03746
$352$	1.96399	0.104681
$353$	−29.7458	−1.58321	−0.791605	−	0.611034i	$-0.790754\pi$
$353$	−29.7458	−1.58321	−0.791605	+	0.611034i	$0.790754\pi$
$354$	−5.56484	−0.295768
$355$	−5.21560	−0.276815
$356$	−12.8477	−0.680924
$357$	−20.7262	−1.09694
$358$	16.1439	0.853232
$359$	5.32584	0.281087	0.140544	−	0.990074i	$-0.455115\pi$
$359$	5.32584	0.281087	0.140544	+	0.990074i	$0.455115\pi$
$360$	−0.0668018	−0.00352077
$361$	43.6437	2.29704
$362$	17.8970	0.940644
$363$	12.2330	0.642069
$364$	−8.51855	−0.446493
$365$	14.6348	0.766021
$366$	−1.58043	−0.0826103
$367$	14.4010	0.751727	0.375863	−	0.926675i	$-0.377346\pi$
$367$	14.4010	0.751727	0.375863	+	0.926675i	$0.377346\pi$
$368$	−0.848696	−0.0442413
$369$	0.380139	0.0197892
$370$	4.22064	0.219420
$371$	25.8310	1.34108
$372$	−4.80156	−0.248949
$373$	15.3222	0.793355	0.396678	−	0.917958i	$-0.370163\pi$
$373$	15.3222	0.793355	0.396678	+	0.917958i	$0.370163\pi$
$374$	−10.3250	−0.533895
$375$	1.71266	0.0884413
$376$	2.64478	0.136394
$377$	−37.3215	−1.92216
$378$	12.0907	0.621881
$379$	11.3282	0.581891	0.290946	−	0.956740i	$-0.406030\pi$
$379$	11.3282	0.581891	0.290946	+	0.956740i	$0.406030\pi$
$380$	7.91478	0.406020
$381$	−29.5172	−1.51221
$382$	−22.1620	−1.13390
$383$	19.7344	1.00838	0.504191	−	0.863592i	$-0.331791\pi$
$383$	19.7344	1.00838	0.504191	+	0.863592i	$0.331791\pi$
$384$	1.71266	0.0873987
$385$	−4.52102	−0.230413
$386$	−24.4410	−1.24402
$387$	0.339363	0.0172508
$388$	−6.19456	−0.314481
$389$	−18.0995	−0.917682	−0.458841	−	0.888518i	$-0.651735\pi$
$389$	−18.0995	−0.917682	−0.458841	+	0.888518i	$0.651735\pi$
$390$	−6.33782	−0.320928
$391$	4.46173	0.225640
$392$	1.70101	0.0859140
$393$	22.9228	1.15630
$394$	−18.8259	−0.948436
$395$	−5.39554	−0.271479
$396$	0.131198	0.00659297
$397$	26.1040	1.31012	0.655062	−	0.755575i	$-0.272643\pi$
$397$	26.1040	1.31012	0.655062	+	0.755575i	$0.272643\pi$
$398$	6.41446	0.321528
$399$	−31.2037	−1.56214
$400$	1.00000	0.0500000
$401$	1.00000	0.0499376
$401$	1.00000	0.0499376
$402$	4.00176	0.199590
$403$	10.3748	0.516807
$404$	−0.591486	−0.0294275
$405$	8.79513	0.437034
$406$	−23.2160	−1.15219
$407$	−8.28931	−0.410886
$408$	−9.00372	−0.445751
$409$	6.42491	0.317692	0.158846	−	0.987303i	$-0.449223\pi$
$409$	6.42491	0.317692	0.158846	+	0.987303i	$0.449223\pi$
$410$	−5.69055	−0.281036
$411$	7.26081	0.358149
$412$	8.26160	0.407020
$413$	7.47960	0.368047
$414$	−0.0566945	−0.00278638
$415$	−4.95874	−0.243415
$416$	−3.70057	−0.181436
$417$	11.0038	0.538861
$418$	−15.5446	−0.760310
$419$	3.67003	0.179293	0.0896463	−	0.995974i	$-0.471426\pi$
$419$	3.67003	0.179293	0.0896463	+	0.995974i	$0.471426\pi$
$420$	−3.94246	−0.192372
$421$	18.0755	0.880944	0.440472	−	0.897766i	$-0.354811\pi$
$421$	18.0755	0.880944	0.440472	+	0.897766i	$0.354811\pi$
$422$	−8.20881	−0.399599
$423$	0.176676	0.00859028
$424$	11.2213	0.544957
$425$	−5.25716	−0.255010
$426$	8.93254	0.432783
$427$	2.12422	0.102798
$428$	10.6847	0.516466
$429$	12.4474	0.600968
$430$	−5.08014	−0.244986
$431$	−20.5628	−0.990476	−0.495238	−	0.868757i	$-0.664919\pi$
$431$	−20.5628	−0.990476	−0.495238	+	0.868757i	$0.664919\pi$
$432$	5.25238	0.252705
$433$	7.37521	0.354430	0.177215	−	0.984172i	$-0.443291\pi$
$433$	7.37521	0.354430	0.177215	+	0.984172i	$0.443291\pi$
$434$	6.45370	0.309787
$435$	−17.2727	−0.828164
$436$	−14.1604	−0.678162
$437$	6.71724	0.321329
$438$	−25.0644	−1.19763
$439$	4.65822	0.222325	0.111162	−	0.993802i	$-0.464543\pi$
$439$	4.65822	0.222325	0.111162	+	0.993802i	$0.464543\pi$
$440$	−1.96399	−0.0936298
$441$	0.113631	0.00541098
$442$	19.4545	0.925357
$443$	−35.5974	−1.69129	−0.845643	−	0.533749i	$-0.820783\pi$
$443$	−35.5974	−1.69129	−0.845643	+	0.533749i	$0.820783\pi$
$444$	−7.22851	−0.343050
$445$	12.8477	0.609037
$446$	−5.82498	−0.275821
$447$	−17.8045	−0.842123
$448$	−2.30195	−0.108757
$449$	24.8061	1.17067	0.585336	−	0.810791i	$-0.300963\pi$
$449$	24.8061	1.17067	0.585336	+	0.810791i	$0.300963\pi$
$450$	0.0668018	0.00314907
$451$	11.1762	0.526267
$452$	−8.99833	−0.423246
$453$	19.1809	0.901197
$454$	−12.3065	−0.577571
$455$	8.51855	0.399356
$456$	−13.5553	−0.634786
$457$	4.85124	0.226931	0.113466	−	0.993542i	$-0.463805\pi$
$457$	4.85124	0.226931	0.113466	+	0.993542i	$0.463805\pi$
$458$	−3.66644	−0.171321
$459$	−27.6126	−1.28885
$460$	0.848696	0.0395707
$461$	−12.3669	−0.575983	−0.287992	−	0.957633i	$-0.592988\pi$
$461$	−12.3669	−0.575983	−0.287992	+	0.957633i	$0.592988\pi$
$462$	7.74297	0.360236
$463$	34.9544	1.62447	0.812235	−	0.583330i	$-0.198251\pi$
$463$	34.9544	1.62447	0.812235	+	0.583330i	$0.198251\pi$
$464$	−10.0853	−0.468200
$465$	4.80156	0.222667
$466$	11.7405	0.543870
$467$	16.7812	0.776543	0.388272	−	0.921545i	$-0.373072\pi$
$467$	16.7812	0.776543	0.388272	+	0.921545i	$0.373072\pi$
$468$	−0.247205	−0.0114271
$469$	−5.37870	−0.248365
$470$	−2.64478	−0.121994
$471$	−18.0719	−0.832711
$472$	3.24924	0.149558
$473$	9.97737	0.458760
$474$	9.24071	0.424440
$475$	−7.91478	−0.363155
$476$	12.1017	0.554683
$477$	0.749607	0.0343221
$478$	25.0742	1.14687
$479$	28.6369	1.30845	0.654227	−	0.756298i	$-0.272994\pi$
$479$	28.6369	1.30845	0.654227	+	0.756298i	$0.272994\pi$
$480$	−1.71266	−0.0781718
$481$	15.6188	0.712155
$482$	−17.4670	−0.795602
$483$	−3.34595	−0.152246
$484$	−7.14273	−0.324669
$485$	6.19456	0.281281
$486$	0.694095	0.0314848
$487$	−23.6341	−1.07096	−0.535481	−	0.844547i	$-0.679870\pi$
$487$	−23.6341	−1.07096	−0.535481	+	0.844547i	$0.679870\pi$
$488$	0.922792	0.0417728
$489$	−3.45423	−0.156206
$490$	−1.70101	−0.0768438
$491$	−0.816709	−0.0368576	−0.0184288	−	0.999830i	$-0.505866\pi$
$491$	−0.816709	−0.0368576	−0.0184288	+	0.999830i	$0.505866\pi$
$492$	9.74596	0.439382
$493$	53.0202	2.38791
$494$	29.2892	1.31778
$495$	−0.131198	−0.00589693
$496$	2.80357	0.125884
$497$	−12.0061	−0.538546
$498$	8.49263	0.380564
$499$	−11.7323	−0.525212	−0.262606	−	0.964903i	$-0.584582\pi$
$499$	−11.7323	−0.525212	−0.262606	+	0.964903i	$0.584582\pi$
$500$	−1.00000	−0.0447214
$501$	23.3012	1.04102
$502$	−12.2966	−0.548823
$503$	29.2709	1.30512	0.652562	−	0.757736i	$-0.273694\pi$
$503$	29.2709	1.30512	0.652562	+	0.757736i	$0.273694\pi$
$504$	−0.153775	−0.00684967
$505$	0.591486	0.0263208
$506$	−1.66683	−0.0740998
$507$	−1.18900	−0.0528055
$508$	17.2347	0.764668
$509$	5.38695	0.238772	0.119386	−	0.992848i	$-0.461907\pi$
$509$	5.38695	0.238772	0.119386	+	0.992848i	$0.461907\pi$
$510$	9.00372	0.398692
$511$	33.6887	1.49030
$512$	−1.00000	−0.0441942
$513$	−41.5715	−1.83542
$514$	−3.54582	−0.156399
$515$	−8.26160	−0.364050
$516$	8.70055	0.383020
$517$	5.19433	0.228446
$518$	9.71571	0.426884
$519$	−36.0953	−1.58441
$520$	3.70057	0.162281
$521$	−9.05537	−0.396723	−0.198362	−	0.980129i	$-0.563562\pi$
$521$	−9.05537	−0.396723	−0.198362	+	0.980129i	$0.563562\pi$
$522$	−0.673719	−0.0294879
$523$	0.477474	0.0208785	0.0104392	−	0.999946i	$-0.496677\pi$
$523$	0.477474	0.0208785	0.0104392	+	0.999946i	$0.496677\pi$
$524$	−13.3843	−0.584698
$525$	3.94246	0.172063
$526$	−14.0579	−0.612953
$527$	−14.7388	−0.642034
$528$	3.36365	0.146384
$529$	−22.2797	−0.968683
$530$	−11.2213	−0.487424
$531$	0.217055	0.00941940
$532$	18.2195	0.789913
$533$	−21.0583	−0.912136
$534$	−22.0036	−0.952191
$535$	−10.6847	−0.461941
$536$	−2.33658	−0.100925
$537$	27.6490	1.19314
$538$	1.73695	0.0748851
$539$	3.34077	0.143897
$540$	−5.25238	−0.226027
$541$	42.0583	1.80823	0.904113	−	0.427294i	$-0.140533\pi$
$541$	42.0583	1.80823	0.904113	+	0.427294i	$0.140533\pi$
$542$	0.533135	0.0229001
$543$	30.6514	1.31538
$544$	5.25716	0.225399
$545$	14.1604	0.606567
$546$	−14.5894	−0.624367
$547$	−21.2973	−0.910607	−0.455304	−	0.890336i	$-0.650469\pi$
$547$	−21.2973	−0.910607	−0.455304	+	0.890336i	$0.650469\pi$
$548$	−4.23950	−0.181102
$549$	0.0616442	0.00263091
$550$	1.96399	0.0837450
$551$	79.8232	3.40058
$552$	−1.45353	−0.0618662
$553$	−12.4203	−0.528164
$554$	21.2604	0.903267
$555$	7.22851	0.306833
$556$	−6.42501	−0.272481
$557$	6.33173	0.268284	0.134142	−	0.990962i	$-0.457172\pi$
$557$	6.33173	0.268284	0.134142	+	0.990962i	$0.457172\pi$
$558$	0.187284	0.00792836
$559$	−18.7994	−0.795132
$560$	2.30195	0.0972753
$561$	−17.6833	−0.746588
$562$	7.39486	0.311934
$563$	−12.5713	−0.529816	−0.264908	−	0.964274i	$-0.585342\pi$
$563$	−12.5713	−0.529816	−0.264908	+	0.964274i	$0.585342\pi$
$564$	4.52960	0.190731
$565$	8.99833	0.378563
$566$	20.0232	0.841637
$567$	20.2460	0.850251
$568$	−5.21560	−0.218842
$569$	−10.7335	−0.449971	−0.224986	−	0.974362i	$-0.572234\pi$
$569$	−10.7335	−0.449971	−0.224986	+	0.974362i	$0.572234\pi$
$570$	13.5553	0.567769
$571$	41.3622	1.73095	0.865477	−	0.500948i	$-0.167015\pi$
$571$	41.3622	1.73095	0.865477	+	0.500948i	$0.167015\pi$
$572$	−7.26791	−0.303886
$573$	−37.9559	−1.58563
$574$	−13.0994	−0.546757
$575$	−0.848696	−0.0353931
$576$	−0.0668018	−0.00278341
$577$	28.5440	1.18830	0.594150	−	0.804354i	$-0.297488\pi$
$577$	28.5440	1.18830	0.594150	+	0.804354i	$0.297488\pi$
$578$	−10.6378	−0.442473
$579$	−41.8591	−1.73961
$580$	10.0853	0.418771
$581$	−11.4148	−0.473566
$582$	−10.6092	−0.439764
$583$	22.0387	0.912748
$584$	14.6348	0.605593
$585$	0.247205	0.0102207
$586$	20.2951	0.838385
$587$	19.8978	0.821270	0.410635	−	0.911800i	$-0.365307\pi$
$587$	19.8978	0.821270	0.410635	+	0.911800i	$0.365307\pi$
$588$	2.91325	0.120140
$589$	−22.1897	−0.914309
$590$	−3.24924	−0.133769
$591$	−32.2424	−1.32627
$592$	4.22064	0.173467
$593$	−32.3490	−1.32841	−0.664207	−	0.747548i	$-0.731231\pi$
$593$	−32.3490	−1.32841	−0.664207	+	0.747548i	$0.731231\pi$
$594$	10.3157	0.423256
$595$	−12.1017	−0.496123
$596$	10.3958	0.425829
$597$	10.9858	0.449618
$598$	3.14066	0.128431
$599$	8.05484	0.329112	0.164556	−	0.986368i	$-0.447381\pi$
$599$	8.05484	0.329112	0.164556	+	0.986368i	$0.447381\pi$
$600$	1.71266	0.0699190
$601$	−36.1324	−1.47387	−0.736936	−	0.675962i	$-0.763728\pi$
$601$	−36.1324	−1.47387	−0.736936	+	0.675962i	$0.763728\pi$
$602$	−11.6943	−0.476622
$603$	−0.156088	−0.00635639
$604$	−11.1995	−0.455701
$605$	7.14273	0.290393
$606$	−1.01301	−0.0411509
$607$	−45.9036	−1.86317	−0.931585	−	0.363524i	$-0.881574\pi$
$607$	−45.9036	−1.86317	−0.931585	+	0.363524i	$0.881574\pi$
$608$	7.91478	0.320987
$609$	−39.7610	−1.61120
$610$	−0.922792	−0.0373628
$611$	−9.78719	−0.395947
$612$	0.351188	0.0141959
$613$	−24.5623	−0.992062	−0.496031	−	0.868305i	$-0.665210\pi$
$613$	−24.5623	−0.992062	−0.496031	+	0.868305i	$0.665210\pi$
$614$	2.70081	0.108996
$615$	−9.74596	−0.392995
$616$	−4.52102	−0.182157
$617$	−20.4384	−0.822821	−0.411410	−	0.911450i	$-0.634964\pi$
$617$	−20.4384	−0.822821	−0.411410	+	0.911450i	$0.634964\pi$
$618$	14.1493	0.569168
$619$	−48.0576	−1.93160	−0.965799	−	0.259293i	$-0.916511\pi$
$619$	−48.0576	−1.93160	−0.965799	+	0.259293i	$0.916511\pi$
$620$	−2.80357	−0.112594
$621$	−4.45768	−0.178880
$622$	−21.5617	−0.864544
$623$	29.5747	1.18489
$624$	−6.33782	−0.253716
$625$	1.00000	0.0400000
$626$	−16.8310	−0.672704
$627$	−26.6226	−1.06320
$628$	10.5520	0.421070
$629$	−22.1886	−0.884716
$630$	0.153775	0.00612653
$631$	−27.0620	−1.07732	−0.538661	−	0.842523i	$-0.681070\pi$
$631$	−27.0620	−1.07732	−0.538661	+	0.842523i	$0.681070\pi$
$632$	−5.39554	−0.214623
$633$	−14.0589	−0.558791
$634$	−20.2733	−0.805154
$635$	−17.2347	−0.683939
$636$	19.2183	0.762056
$637$	−6.29471	−0.249406
$638$	−19.8075	−0.784188
$639$	−0.348412	−0.0137830
$640$	1.00000	0.0395285
$641$	−39.9447	−1.57772	−0.788861	−	0.614572i	$-0.789329\pi$
$641$	−39.9447	−1.57772	−0.788861	+	0.614572i	$0.789329\pi$
$642$	18.2993	0.722215
$643$	8.43230	0.332537	0.166269	−	0.986080i	$-0.446828\pi$
$643$	8.43230	0.332537	0.166269	+	0.986080i	$0.446828\pi$
$644$	1.95366	0.0769849
$645$	−8.70055	−0.342584
$646$	−41.6093	−1.63710
$647$	−11.3557	−0.446439	−0.223219	−	0.974768i	$-0.571657\pi$
$647$	−11.3557	−0.446439	−0.223219	+	0.974768i	$0.571657\pi$
$648$	8.79513	0.345505
$649$	6.38149	0.250496
$650$	−3.70057	−0.145148
$651$	11.0530	0.433200
$652$	2.01688	0.0789872
$653$	29.0567	1.13708	0.568538	−	0.822657i	$-0.307509\pi$
$653$	29.0567	1.13708	0.568538	+	0.822657i	$0.307509\pi$
$654$	−24.2520	−0.948328
$655$	13.3843	0.522970
$656$	−5.69055	−0.222179
$657$	0.977633	0.0381411
$658$	−6.08815	−0.237341
$659$	14.1761	0.552221	0.276111	−	0.961126i	$-0.410954\pi$
$659$	14.1761	0.552221	0.276111	+	0.961126i	$0.410954\pi$
$660$	−3.36365	−0.130930
$661$	−0.364014	−0.0141585	−0.00707926	−	0.999975i	$-0.502253\pi$
$661$	−0.364014	−0.0141585	−0.00707926	+	0.999975i	$0.502253\pi$
$662$	−13.2236	−0.513951
$663$	33.3189	1.29400
$664$	−4.95874	−0.192437
$665$	−18.2195	−0.706520
$666$	0.281946	0.0109252
$667$	8.55938	0.331420
$668$	−13.6053	−0.526404
$669$	−9.97620	−0.385702
$670$	2.33658	0.0902700
$671$	1.81236	0.0699653
$672$	−3.94246	−0.152084
$673$	−22.1876	−0.855271	−0.427635	−	0.903951i	$-0.640653\pi$
$673$	−22.1876	−0.855271	−0.427635	+	0.903951i	$0.640653\pi$
$674$	23.9916	0.924123
$675$	5.25238	0.202164
$676$	0.694244	0.0267017
$677$	16.3642	0.628928	0.314464	−	0.949269i	$-0.398175\pi$
$677$	16.3642	0.628928	0.314464	+	0.949269i	$0.398175\pi$
$678$	−15.4111	−0.591859
$679$	14.2596	0.547233
$680$	−5.25716	−0.201603
$681$	−21.0768	−0.807664
$682$	5.50620	0.210843
$683$	−43.1806	−1.65226	−0.826130	−	0.563480i	$-0.809462\pi$
$683$	−43.1806	−1.65226	−0.826130	+	0.563480i	$0.809462\pi$
$684$	0.528722	0.0202162
$685$	4.23950	0.161983
$686$	−20.0293	−0.764723
$687$	−6.27935	−0.239572
$688$	−5.08014	−0.193679
$689$	−41.5254	−1.58199
$690$	1.45353	0.0553348
$691$	−0.339614	−0.0129195	−0.00645976	−	0.999979i	$-0.502056\pi$
$691$	−0.339614	−0.0129195	−0.00645976	+	0.999979i	$0.502056\pi$
$692$	21.0756	0.801175
$693$	−0.302013	−0.0114725
$694$	17.5303	0.665442
$695$	6.42501	0.243715
$696$	−17.2727	−0.654721
$697$	29.9161	1.13315
$698$	−29.8649	−1.13040
$699$	20.1075	0.760537
$700$	−2.30195	−0.0870057
$701$	14.4616	0.546206	0.273103	−	0.961985i	$-0.411950\pi$
$701$	14.4616	0.546206	0.273103	+	0.961985i	$0.411950\pi$
$702$	−19.4368	−0.733596
$703$	−33.4054	−1.25991
$704$	−1.96399	−0.0740208
$705$	−4.52960	−0.170595
$706$	29.7458	1.11950
$707$	1.36157	0.0512073
$708$	5.56484	0.209140
$709$	−17.2185	−0.646655	−0.323328	−	0.946287i	$-0.604802\pi$
$709$	−17.2185	−0.646655	−0.323328	+	0.946287i	$0.604802\pi$
$710$	5.21560	0.195738
$711$	−0.360432	−0.0135172
$712$	12.8477	0.481486
$713$	−2.37938	−0.0891085
$714$	20.7262	0.775657
$715$	7.26791	0.271804
$716$	−16.1439	−0.603326
$717$	42.9435	1.60375
$718$	−5.32584	−0.198759
$719$	−52.5031	−1.95803	−0.979017	−	0.203779i	$-0.934678\pi$
$719$	−52.5031	−1.95803	−0.979017	+	0.203779i	$0.934678\pi$
$720$	0.0668018	0.00248956
$721$	−19.0178	−0.708261
$722$	−43.6437	−1.62425
$723$	−29.9151	−1.11255
$724$	−17.8970	−0.665136
$725$	−10.0853	−0.374560
$726$	−12.2330	−0.454011
$727$	20.9064	0.775374	0.387687	−	0.921791i	$-0.373274\pi$
$727$	20.9064	0.775374	0.387687	+	0.921791i	$0.373274\pi$
$728$	8.51855	0.315718
$729$	27.5741	1.02126
$730$	−14.6348	−0.541659
$731$	26.7071	0.987799
$732$	1.58043	0.0584143
$733$	−24.2836	−0.896937	−0.448468	−	0.893799i	$-0.648030\pi$
$733$	−24.2836	−0.896937	−0.448468	+	0.893799i	$0.648030\pi$
$734$	−14.4010	−0.531551
$735$	−2.91325	−0.107457
$736$	0.848696	0.0312833
$737$	−4.58903	−0.169039
$738$	−0.380139	−0.0139931
$739$	−46.5545	−1.71253	−0.856267	−	0.516533i	$-0.827222\pi$
$739$	−46.5545	−1.71253	−0.856267	+	0.516533i	$0.827222\pi$
$740$	−4.22064	−0.155154
$741$	50.1624	1.84276
$742$	−25.8310	−0.948287
$743$	−47.0034	−1.72439	−0.862194	−	0.506579i	$-0.830910\pi$
$743$	−47.0034	−1.72439	−0.862194	+	0.506579i	$0.830910\pi$
$744$	4.80156	0.176034
$745$	−10.3958	−0.380873
$746$	−15.3222	−0.560987
$747$	−0.331253	−0.0121199
$748$	10.3250	0.377521
$749$	−24.5957	−0.898709
$750$	−1.71266	−0.0625374
$751$	21.1166	0.770554	0.385277	−	0.922801i	$-0.374106\pi$
$751$	21.1166	0.770554	0.385277	+	0.922801i	$0.374106\pi$
$752$	−2.64478	−0.0964451
$753$	−21.0598	−0.767464
$754$	37.3215	1.35917
$755$	11.1995	0.407591
$756$	−12.0907	−0.439736
$757$	7.39849	0.268903	0.134451	−	0.990920i	$-0.457073\pi$
$757$	7.39849	0.268903	0.134451	+	0.990920i	$0.457073\pi$
$758$	−11.3282	−0.411459
$759$	−2.85472	−0.103620
$760$	−7.91478	−0.287099
$761$	−46.5749	−1.68834	−0.844169	−	0.536077i	$-0.819906\pi$
$761$	−46.5749	−1.68834	−0.844169	+	0.536077i	$0.819906\pi$
$762$	29.5172	1.06930
$763$	32.5967	1.18008
$764$	22.1620	0.801792
$765$	−0.351188	−0.0126972
$766$	−19.7344	−0.713033
$767$	−12.0241	−0.434164
$768$	−1.71266	−0.0618002
$769$	−3.65867	−0.131935	−0.0659675	−	0.997822i	$-0.521013\pi$
$769$	−3.65867	−0.131935	−0.0659675	+	0.997822i	$0.521013\pi$
$770$	4.52102	0.162926
$771$	−6.07277	−0.218706
$772$	24.4410	0.879652
$773$	−36.5623	−1.31505	−0.657527	−	0.753431i	$-0.728397\pi$
$773$	−36.5623	−1.31505	−0.657527	+	0.753431i	$0.728397\pi$
$774$	−0.339363	−0.0121982
$775$	2.80357	0.100707
$776$	6.19456	0.222372
$777$	16.6397	0.596946
$778$	18.0995	0.648899
$779$	45.0394	1.61370
$780$	6.33782	0.226930
$781$	−10.2434	−0.366538
$782$	−4.46173	−0.159551
$783$	−52.9720	−1.89307
$784$	−1.70101	−0.0607504
$785$	−10.5520	−0.376616
$786$	−22.9228	−0.817630
$787$	−33.5159	−1.19471	−0.597356	−	0.801976i	$-0.703782\pi$
$787$	−33.5159	−1.19471	−0.597356	+	0.801976i	$0.703782\pi$
$788$	18.8259	0.670646
$789$	−24.0763	−0.857140
$790$	5.39554	0.191965
$791$	20.7137	0.736496
$792$	−0.131198	−0.00466193
$793$	−3.41486	−0.121265
$794$	−26.1040	−0.926397
$795$	−19.2183	−0.681604
$796$	−6.41446	−0.227354
$797$	−26.9916	−0.956091	−0.478045	−	0.878335i	$-0.658655\pi$
$797$	−26.9916	−0.956091	−0.478045	+	0.878335i	$0.658655\pi$
$798$	31.2037	1.10460
$799$	13.9040	0.491889
$800$	−1.00000	−0.0353553
$801$	0.858247	0.0303247
$802$	−1.00000	−0.0353112
$803$	28.7427	1.01431
$804$	−4.00176	−0.141131
$805$	−1.95366	−0.0688574
$806$	−10.3748	−0.365438
$807$	2.97479	0.104718
$808$	0.591486	0.0208084
$809$	18.1281	0.637351	0.318676	−	0.947864i	$-0.396762\pi$
$809$	18.1281	0.637351	0.318676	+	0.947864i	$0.396762\pi$
$810$	−8.79513	−0.309029
$811$	−9.11489	−0.320067	−0.160034	−	0.987112i	$-0.551160\pi$
$811$	−9.11489	−0.320067	−0.160034	+	0.987112i	$0.551160\pi$
$812$	23.2160	0.814720
$813$	0.913078	0.0320231
$814$	8.28931	0.290540
$815$	−2.01688	−0.0706483
$816$	9.00372	0.315193
$817$	40.2082	1.40671
$818$	−6.42491	−0.224642
$819$	0.569055	0.0198844
$820$	5.69055	0.198723
$821$	17.6093	0.614567	0.307284	−	0.951618i	$-0.400580\pi$
$821$	17.6093	0.614567	0.307284	+	0.951618i	$0.400580\pi$
$822$	−7.26081	−0.253250
$823$	−38.9552	−1.35789	−0.678946	−	0.734188i	$-0.737563\pi$
$823$	−38.9552	−1.35789	−0.678946	+	0.734188i	$0.737563\pi$
$824$	−8.26160	−0.287806
$825$	3.36365	0.117107
$826$	−7.47960	−0.260249
$827$	−9.70933	−0.337627	−0.168813	−	0.985648i	$-0.553993\pi$
$827$	−9.70933	−0.337627	−0.168813	+	0.985648i	$0.553993\pi$
$828$	0.0566945	0.00197027
$829$	8.11870	0.281974	0.140987	−	0.990011i	$-0.454972\pi$
$829$	8.11870	0.281974	0.140987	+	0.990011i	$0.454972\pi$
$830$	4.95874	0.172121
$831$	36.4118	1.26311
$832$	3.70057	0.128294
$833$	8.94249	0.309839
$834$	−11.0038	−0.381032
$835$	13.6053	0.470830
$836$	15.5446	0.537621
$837$	14.7254	0.508986
$838$	−3.67003	−0.126779
$839$	40.2684	1.39022	0.695109	−	0.718904i	$-0.255356\pi$
$839$	40.2684	1.39022	0.695109	+	0.718904i	$0.255356\pi$
$840$	3.94246	0.136028
$841$	72.7139	2.50737
$842$	−18.0755	−0.622921
$843$	12.6649	0.436201
$844$	8.20881	0.282559
$845$	−0.694244	−0.0238827
$846$	−0.176676	−0.00607425
$847$	16.4422	0.564961
$848$	−11.2213	−0.385343
$849$	34.2929	1.17693
$850$	5.25716	0.180319
$851$	−3.58204	−0.122791
$852$	−8.93254	−0.306024
$853$	−39.6854	−1.35880	−0.679401	−	0.733768i	$-0.737760\pi$
$853$	−39.6854	−1.35880	−0.679401	+	0.733768i	$0.737760\pi$
$854$	−2.12422	−0.0726895
$855$	−0.528722	−0.0180819
$856$	−10.6847	−0.365196
$857$	15.8423	0.541164	0.270582	−	0.962697i	$-0.412784\pi$
$857$	15.8423	0.541164	0.270582	+	0.962697i	$0.412784\pi$
$858$	−12.4474	−0.424949
$859$	41.6602	1.42143	0.710715	−	0.703480i	$-0.248372\pi$
$859$	41.6602	1.42143	0.710715	+	0.703480i	$0.248372\pi$
$860$	5.08014	0.173231
$861$	−22.4348	−0.764574
$862$	20.5628	0.700372
$863$	14.7561	0.502304	0.251152	−	0.967948i	$-0.419191\pi$
$863$	14.7561	0.502304	0.251152	+	0.967948i	$0.419191\pi$
$864$	−5.25238	−0.178690
$865$	−21.0756	−0.716592
$866$	−7.37521	−0.250620
$867$	−18.2189	−0.618745
$868$	−6.45370	−0.219053
$869$	−10.5968	−0.359472
$870$	17.2727	0.585600
$871$	8.64669	0.292982
$872$	14.1604	0.479533
$873$	0.413808	0.0140053
$874$	−6.71724	−0.227214
$875$	2.30195	0.0778202
$876$	25.0644	0.846849
$877$	−12.4933	−0.421868	−0.210934	−	0.977500i	$-0.567651\pi$
$877$	−12.4933	−0.421868	−0.210934	+	0.977500i	$0.567651\pi$
$878$	−4.65822	−0.157207
$879$	34.7587	1.17238
$880$	1.96399	0.0662062
$881$	−19.6127	−0.660768	−0.330384	−	0.943847i	$-0.607178\pi$
$881$	−19.6127	−0.660768	−0.330384	+	0.943847i	$0.607178\pi$
$882$	−0.113631	−0.00382614
$883$	1.40308	0.0472174	0.0236087	−	0.999721i	$-0.492484\pi$
$883$	1.40308	0.0472174	0.0236087	+	0.999721i	$0.492484\pi$
$884$	−19.4545	−0.654326
$885$	−5.56484	−0.187060
$886$	35.5974	1.19592
$887$	−35.0034	−1.17530	−0.587650	−	0.809116i	$-0.699947\pi$
$887$	−35.0034	−1.17530	−0.587650	+	0.809116i	$0.699947\pi$
$888$	7.22851	0.242573
$889$	−39.6735	−1.33061
$890$	−12.8477	−0.430654
$891$	17.2736	0.578687
$892$	5.82498	0.195035
$893$	20.9328	0.700490
$894$	17.8045	0.595471
$895$	16.1439	0.539632
$896$	2.30195	0.0769029
$897$	5.37888	0.179596
$898$	−24.8061	−0.827790
$899$	−28.2750	−0.943023
$900$	−0.0668018	−0.00222673
$901$	58.9925	1.96532
$902$	−11.1762	−0.372127
$903$	−20.0283	−0.666499
$904$	8.99833	0.299280
$905$	17.8970	0.594915
$906$	−19.1809	−0.637243
$907$	12.2479	0.406684	0.203342	−	0.979108i	$-0.434820\pi$
$907$	12.2479	0.406684	0.203342	+	0.979108i	$0.434820\pi$
$908$	12.3065	0.408405
$909$	0.0395124	0.00131054
$910$	−8.51855	−0.282387
$911$	−6.83632	−0.226497	−0.113249	−	0.993567i	$-0.536126\pi$
$911$	−6.83632	−0.226497	−0.113249	+	0.993567i	$0.536126\pi$
$912$	13.5553	0.448861
$913$	−9.73895	−0.322312
$914$	−4.85124	−0.160465
$915$	−1.58043	−0.0522473
$916$	3.66644	0.121142
$917$	30.8101	1.01744
$918$	27.6126	0.911353
$919$	−9.23708	−0.304703	−0.152352	−	0.988326i	$-0.548685\pi$
$919$	−9.23708	−0.304703	−0.152352	+	0.988326i	$0.548685\pi$
$920$	−0.848696	−0.0279807
$921$	4.62557	0.152418
$922$	12.3669	0.407282
$923$	19.3007	0.635291
$924$	−7.74297	−0.254725
$925$	4.22064	0.138774
$926$	−34.9544	−1.14867
$927$	−0.551890	−0.0181265
$928$	10.0853	0.331067
$929$	15.5817	0.511218	0.255609	−	0.966780i	$-0.417724\pi$
$929$	15.5817	0.511218	0.255609	+	0.966780i	$0.417724\pi$
$930$	−4.80156	−0.157449
$931$	13.4631	0.441236
$932$	−11.7405	−0.384574
$933$	−36.9278	−1.20896
$934$	−16.7812	−0.549099
$935$	−10.3250	−0.337665
$936$	0.247205	0.00808015
$937$	12.7912	0.417870	0.208935	−	0.977930i	$-0.433000\pi$
$937$	12.7912	0.417870	0.208935	+	0.977930i	$0.433000\pi$
$938$	5.37870	0.175621
$939$	−28.8258	−0.940695
$940$	2.64478	0.0862631
$941$	−14.9520	−0.487423	−0.243711	−	0.969848i	$-0.578365\pi$
$941$	−14.9520	−0.487423	−0.243711	+	0.969848i	$0.578365\pi$
$942$	18.0719	0.588815
$943$	4.82954	0.157272
$944$	−3.24924	−0.105754
$945$	12.0907	0.393312
$946$	−9.97737	−0.324392
$947$	18.7635	0.609733	0.304866	−	0.952395i	$-0.401388\pi$
$947$	18.7635	0.609733	0.304866	+	0.952395i	$0.401388\pi$
$948$	−9.24071	−0.300124
$949$	−54.1572	−1.75802
$950$	7.91478	0.256789
$951$	−34.7212	−1.12591
$952$	−12.1017	−0.392220
$953$	−9.00282	−0.291630	−0.145815	−	0.989312i	$-0.546580\pi$
$953$	−9.00282	−0.291630	−0.145815	+	0.989312i	$0.546580\pi$
$954$	−0.749607	−0.0242694
$955$	−22.1620	−0.717144
$956$	−25.0742	−0.810956
$957$	−33.9235	−1.09659
$958$	−28.6369	−0.925217
$959$	9.75913	0.315139
$960$	1.71266	0.0552758
$961$	−23.1400	−0.746451
$962$	−15.6188	−0.503570
$963$	−0.713759	−0.0230006
$964$	17.4670	0.562576
$965$	−24.4410	−0.786785
$966$	3.34595	0.107654
$967$	−21.5233	−0.692142	−0.346071	−	0.938208i	$-0.612484\pi$
$967$	−21.5233	−0.692142	−0.346071	+	0.938208i	$0.612484\pi$
$968$	7.14273	0.229576
$969$	−71.2625	−2.28928
$970$	−6.19456	−0.198895
$971$	−36.4866	−1.17091	−0.585455	−	0.810705i	$-0.699084\pi$
$971$	−36.4866	−1.17091	−0.585455	+	0.810705i	$0.699084\pi$
$972$	−0.694095	−0.0222631
$973$	14.7901	0.474148
$974$	23.6341	0.757285
$975$	−6.33782	−0.202973
$976$	−0.922792	−0.0295379
$977$	−50.8418	−1.62657	−0.813287	−	0.581863i	$-0.802324\pi$
$977$	−50.8418	−1.62657	−0.813287	+	0.581863i	$0.802324\pi$
$978$	3.45423	0.110454
$979$	25.2327	0.806441
$980$	1.70101	0.0543368
$981$	0.945944	0.0302017
$982$	0.816709	0.0260622
$983$	−30.6989	−0.979142	−0.489571	−	0.871963i	$-0.662847\pi$
$983$	−30.6989	−0.979142	−0.489571	+	0.871963i	$0.662847\pi$
$984$	−9.74596	−0.310690
$985$	−18.8259	−0.599844
$986$	−53.0202	−1.68851
$987$	−10.4269	−0.331893
$988$	−29.2892	−0.931814
$989$	4.31150	0.137098
$990$	0.131198	0.00416976
$991$	41.1977	1.30869	0.654344	−	0.756197i	$-0.272945\pi$
$991$	41.1977	1.30869	0.654344	+	0.756197i	$0.272945\pi$
$992$	−2.80357	−0.0890136
$993$	−22.6476	−0.718699
$994$	12.0061	0.380809
$995$	6.41446	0.203352
$996$	−8.49263	−0.269099
$997$	−23.9431	−0.758287	−0.379143	−	0.925338i	$-0.623781\pi$
$997$	−23.9431	−0.758287	−0.379143	+	0.925338i	$0.623781\pi$
$998$	11.7323	0.371381
$999$	22.1684	0.701377

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4010.2.a.l.1.4	✓	17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4010.2.a.l.1.4	✓	17	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:	\( N \)	\(=\)	\( 4010 = 2 \cdot 5 \cdot 401 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4010.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.71266 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.71266 q^{6} -2.30195 q^{7} -1.00000 q^{8} -0.0668018 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.71266 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.71266 q^{6} -2.30195 q^{7} -1.00000 q^{8} -0.0668018 q^{9} +1.00000 q^{10} -1.96399 q^{11} -1.71266 q^{12} +3.70057 q^{13} +2.30195 q^{14} +1.71266 q^{15} +1.00000 q^{16} -5.25716 q^{17} +0.0668018 q^{18} -7.91478 q^{19} -1.00000 q^{20} +3.94246 q^{21} +1.96399 q^{22} -0.848696 q^{23} +1.71266 q^{24} +1.00000 q^{25} -3.70057 q^{26} +5.25238 q^{27} -2.30195 q^{28} -10.0853 q^{29} -1.71266 q^{30} +2.80357 q^{31} -1.00000 q^{32} +3.36365 q^{33} +5.25716 q^{34} +2.30195 q^{35} -0.0668018 q^{36} +4.22064 q^{37} +7.91478 q^{38} -6.33782 q^{39} +1.00000 q^{40} -5.69055 q^{41} -3.94246 q^{42} -5.08014 q^{43} -1.96399 q^{44} +0.0668018 q^{45} +0.848696 q^{46} -2.64478 q^{47} -1.71266 q^{48} -1.70101 q^{49} -1.00000 q^{50} +9.00372 q^{51} +3.70057 q^{52} -11.2213 q^{53} -5.25238 q^{54} +1.96399 q^{55} +2.30195 q^{56} +13.5553 q^{57} +10.0853 q^{58} -3.24924 q^{59} +1.71266 q^{60} -0.922792 q^{61} -2.80357 q^{62} +0.153775 q^{63} +1.00000 q^{64} -3.70057 q^{65} -3.36365 q^{66} +2.33658 q^{67} -5.25716 q^{68} +1.45353 q^{69} -2.30195 q^{70} +5.21560 q^{71} +0.0668018 q^{72} -14.6348 q^{73} -4.22064 q^{74} -1.71266 q^{75} -7.91478 q^{76} +4.52102 q^{77} +6.33782 q^{78} +5.39554 q^{79} -1.00000 q^{80} -8.79513 q^{81} +5.69055 q^{82} +4.95874 q^{83} +3.94246 q^{84} +5.25716 q^{85} +5.08014 q^{86} +17.2727 q^{87} +1.96399 q^{88} -12.8477 q^{89} -0.0668018 q^{90} -8.51855 q^{91} -0.848696 q^{92} -4.80156 q^{93} +2.64478 q^{94} +7.91478 q^{95} +1.71266 q^{96} -6.19456 q^{97} +1.70101 q^{98} +0.131198 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q - 17 q^{2} + 3 q^{3} + 17 q^{4} - 17 q^{5} - 3 q^{6} + 4 q^{7} - 17 q^{8} + 6 q^{9}+O(q^{10}) \) 17 * q - 17 * q^2 + 3 * q^3 + 17 * q^4 - 17 * q^5 - 3 * q^6 + 4 * q^7 - 17 * q^8 + 6 * q^9	\( 17 q - 17 q^{2} + 3 q^{3} + 17 q^{4} - 17 q^{5} - 3 q^{6} + 4 q^{7} - 17 q^{8} + 6 q^{9} + 17 q^{10} - 8 q^{11} + 3 q^{12} + 14 q^{13} - 4 q^{14} - 3 q^{15} + 17 q^{16} - 8 q^{17} - 6 q^{18} + 7 q^{19} - 17 q^{20} - 11 q^{21} + 8 q^{22} + q^{23} - 3 q^{24} + 17 q^{25} - 14 q^{26} + 15 q^{27} + 4 q^{28} - 18 q^{29} + 3 q^{30} + 8 q^{31} - 17 q^{32} + 3 q^{33} + 8 q^{34} - 4 q^{35} + 6 q^{36} + 49 q^{37} - 7 q^{38} - 12 q^{39} + 17 q^{40} - 23 q^{41} + 11 q^{42} + 35 q^{43} - 8 q^{44} - 6 q^{45} - q^{46} + 11 q^{47} + 3 q^{48} + 27 q^{49} - 17 q^{50} - 16 q^{51} + 14 q^{52} - 3 q^{53} - 15 q^{54} + 8 q^{55} - 4 q^{56} + 9 q^{57} + 18 q^{58} - 6 q^{59} - 3 q^{60} + 6 q^{61} - 8 q^{62} + 10 q^{63} + 17 q^{64} - 14 q^{65} - 3 q^{66} + 55 q^{67} - 8 q^{68} - q^{69} + 4 q^{70} + 5 q^{71} - 6 q^{72} + 62 q^{73} - 49 q^{74} + 3 q^{75} + 7 q^{76} + 2 q^{77} + 12 q^{78} - 3 q^{79} - 17 q^{80} - 15 q^{81} + 23 q^{82} + 7 q^{83} - 11 q^{84} + 8 q^{85} - 35 q^{86} + 10 q^{87} + 8 q^{88} - 18 q^{89} + 6 q^{90} + 18 q^{91} + q^{92} + 33 q^{93} - 11 q^{94} - 7 q^{95} - 3 q^{96} + 63 q^{97} - 27 q^{98} - 11 q^{99}+O(q^{100}) \) 17 * q - 17 * q^2 + 3 * q^3 + 17 * q^4 - 17 * q^5 - 3 * q^6 + 4 * q^7 - 17 * q^8 + 6 * q^9 + 17 * q^10 - 8 * q^11 + 3 * q^12 + 14 * q^13 - 4 * q^14 - 3 * q^15 + 17 * q^16 - 8 * q^17 - 6 * q^18 + 7 * q^19 - 17 * q^20 - 11 * q^21 + 8 * q^22 + q^23 - 3 * q^24 + 17 * q^25 - 14 * q^26 + 15 * q^27 + 4 * q^28 - 18 * q^29 + 3 * q^30 + 8 * q^31 - 17 * q^32 + 3 * q^33 + 8 * q^34 - 4 * q^35 + 6 * q^36 + 49 * q^37 - 7 * q^38 - 12 * q^39 + 17 * q^40 - 23 * q^41 + 11 * q^42 + 35 * q^43 - 8 * q^44 - 6 * q^45 - q^46 + 11 * q^47 + 3 * q^48 + 27 * q^49 - 17 * q^50 - 16 * q^51 + 14 * q^52 - 3 * q^53 - 15 * q^54 + 8 * q^55 - 4 * q^56 + 9 * q^57 + 18 * q^58 - 6 * q^59 - 3 * q^60 + 6 * q^61 - 8 * q^62 + 10 * q^63 + 17 * q^64 - 14 * q^65 - 3 * q^66 + 55 * q^67 - 8 * q^68 - q^69 + 4 * q^70 + 5 * q^71 - 6 * q^72 + 62 * q^73 - 49 * q^74 + 3 * q^75 + 7 * q^76 + 2 * q^77 + 12 * q^78 - 3 * q^79 - 17 * q^80 - 15 * q^81 + 23 * q^82 + 7 * q^83 - 11 * q^84 + 8 * q^85 - 35 * q^86 + 10 * q^87 + 8 * q^88 - 18 * q^89 + 6 * q^90 + 18 * q^91 + q^92 + 33 * q^93 - 11 * q^94 - 7 * q^95 - 3 * q^96 + 63 * q^97 - 27 * q^98 - 11 * q^99

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