LMFDB - Embedded newform 4010.2.a.l.1.7

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			1.7
Root			$-0.291319$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} -0.291319 q^{3} +1.00000 q^{4} -1.00000 q^{5} +0.291319 q^{6} -2.64183 q^{7} -1.00000 q^{8} -2.91513 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -0.291319 q^{3} +1.00000 q^{4} -1.00000 q^{5} +0.291319 q^{6} -2.64183 q^{7} -1.00000 q^{8} -2.91513 q^{9} +1.00000 q^{10} -5.86070 q^{11} -0.291319 q^{12} -3.17844 q^{13} +2.64183 q^{14} +0.291319 q^{15} +1.00000 q^{16} -1.44133 q^{17} +2.91513 q^{18} +5.31478 q^{19} -1.00000 q^{20} +0.769615 q^{21} +5.86070 q^{22} -2.52729 q^{23} +0.291319 q^{24} +1.00000 q^{25} +3.17844 q^{26} +1.72319 q^{27} -2.64183 q^{28} -6.93836 q^{29} -0.291319 q^{30} -9.71386 q^{31} -1.00000 q^{32} +1.70733 q^{33} +1.44133 q^{34} +2.64183 q^{35} -2.91513 q^{36} +1.02797 q^{37} -5.31478 q^{38} +0.925941 q^{39} +1.00000 q^{40} -7.99719 q^{41} -0.769615 q^{42} +3.90260 q^{43} -5.86070 q^{44} +2.91513 q^{45} +2.52729 q^{46} -8.48780 q^{47} -0.291319 q^{48} -0.0207335 q^{49} -1.00000 q^{50} +0.419887 q^{51} -3.17844 q^{52} -12.9594 q^{53} -1.72319 q^{54} +5.86070 q^{55} +2.64183 q^{56} -1.54830 q^{57} +6.93836 q^{58} +1.76796 q^{59} +0.291319 q^{60} -0.583256 q^{61} +9.71386 q^{62} +7.70129 q^{63} +1.00000 q^{64} +3.17844 q^{65} -1.70733 q^{66} -7.98448 q^{67} -1.44133 q^{68} +0.736247 q^{69} -2.64183 q^{70} -12.4265 q^{71} +2.91513 q^{72} +14.8220 q^{73} -1.02797 q^{74} -0.291319 q^{75} +5.31478 q^{76} +15.4830 q^{77} -0.925941 q^{78} -7.49812 q^{79} -1.00000 q^{80} +8.24340 q^{81} +7.99719 q^{82} +11.3267 q^{83} +0.769615 q^{84} +1.44133 q^{85} -3.90260 q^{86} +2.02128 q^{87} +5.86070 q^{88} +6.82450 q^{89} -2.91513 q^{90} +8.39691 q^{91} -2.52729 q^{92} +2.82983 q^{93} +8.48780 q^{94} -5.31478 q^{95} +0.291319 q^{96} +4.90077 q^{97} +0.0207335 q^{98} +17.0847 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−0.291319	−0.168193	−0.0840966	−	0.996458i	$-0.526800\pi$
$3$	−0.291319	−0.168193	−0.0840966	+	0.996458i	$0.526800\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	0.291319	0.118931
$7$	−2.64183	−0.998518	−0.499259	−	0.866453i	$-0.666394\pi$
$7$	−2.64183	−0.998518	−0.499259	+	0.866453i	$0.666394\pi$
$8$	−1.00000	−0.353553
$9$	−2.91513	−0.971711
$10$	1.00000	0.316228
$11$	−5.86070	−1.76707	−0.883533	−	0.468369i	$-0.844842\pi$
$11$	−5.86070	−1.76707	−0.883533	+	0.468369i	$0.844842\pi$
$12$	−0.291319	−0.0840966
$13$	−3.17844	−0.881542	−0.440771	−	0.897620i	$-0.645295\pi$
$13$	−3.17844	−0.881542	−0.440771	+	0.897620i	$0.645295\pi$
$14$	2.64183	0.706059
$15$	0.291319	0.0752183
$16$	1.00000	0.250000
$17$	−1.44133	−0.349574	−0.174787	−	0.984606i	$-0.555924\pi$
$17$	−1.44133	−0.349574	−0.174787	+	0.984606i	$0.555924\pi$
$18$	2.91513	0.687103
$19$	5.31478	1.21929	0.609647	−	0.792673i	$-0.291311\pi$
$19$	5.31478	1.21929	0.609647	+	0.792673i	$0.291311\pi$
$20$	−1.00000	−0.223607
$21$	0.769615	0.167944
$22$	5.86070	1.24950
$23$	−2.52729	−0.526976	−0.263488	−	0.964663i	$-0.584873\pi$
$23$	−2.52729	−0.526976	−0.263488	+	0.964663i	$0.584873\pi$
$24$	0.291319	0.0594653
$25$	1.00000	0.200000
$26$	3.17844	0.623344
$27$	1.72319	0.331628
$28$	−2.64183	−0.499259
$29$	−6.93836	−1.28842	−0.644211	−	0.764848i	$-0.722814\pi$
$29$	−6.93836	−1.28842	−0.644211	+	0.764848i	$0.722814\pi$
$30$	−0.291319	−0.0531873
$31$	−9.71386	−1.74466	−0.872331	−	0.488916i	$-0.837392\pi$
$31$	−9.71386	−1.74466	−0.872331	+	0.488916i	$0.837392\pi$
$32$	−1.00000	−0.176777
$33$	1.70733	0.297208
$34$	1.44133	0.247186
$35$	2.64183	0.446551
$36$	−2.91513	−0.485856
$37$	1.02797	0.168997	0.0844983	−	0.996424i	$-0.473071\pi$
$37$	1.02797	0.168997	0.0844983	+	0.996424i	$0.473071\pi$
$38$	−5.31478	−0.862171
$39$	0.925941	0.148269
$40$	1.00000	0.158114
$41$	−7.99719	−1.24895	−0.624475	−	0.781045i	$-0.714687\pi$
$41$	−7.99719	−1.24895	−0.624475	+	0.781045i	$0.714687\pi$
$42$	−0.769615	−0.118754
$43$	3.90260	0.595141	0.297570	−	0.954700i	$-0.403824\pi$
$43$	3.90260	0.595141	0.297570	+	0.954700i	$0.403824\pi$
$44$	−5.86070	−0.883533
$45$	2.91513	0.434562
$46$	2.52729	0.372628
$47$	−8.48780	−1.23807	−0.619036	−	0.785362i	$-0.712477\pi$
$47$	−8.48780	−1.23807	−0.619036	+	0.785362i	$0.712477\pi$
$48$	−0.291319	−0.0420483
$49$	−0.0207335	−0.00296193
$50$	−1.00000	−0.141421
$51$	0.419887	0.0587960
$52$	−3.17844	−0.440771
$53$	−12.9594	−1.78011	−0.890054	−	0.455855i	$-0.849334\pi$
$53$	−12.9594	−1.78011	−0.890054	+	0.455855i	$0.849334\pi$
$54$	−1.72319	−0.234497
$55$	5.86070	0.790256
$56$	2.64183	0.353029
$57$	−1.54830	−0.205077
$58$	6.93836	0.911052
$59$	1.76796	0.230169	0.115084	−	0.993356i	$-0.463286\pi$
$59$	1.76796	0.230169	0.115084	+	0.993356i	$0.463286\pi$
$60$	0.291319	0.0376091
$61$	−0.583256	−0.0746783	−0.0373392	−	0.999303i	$-0.511888\pi$
$61$	−0.583256	−0.0746783	−0.0373392	+	0.999303i	$0.511888\pi$
$62$	9.71386	1.23366
$63$	7.70129	0.970271
$64$	1.00000	0.125000
$65$	3.17844	0.394237
$66$	−1.70733	−0.210158
$67$	−7.98448	−0.975460	−0.487730	−	0.872995i	$-0.662175\pi$
$67$	−7.98448	−0.975460	−0.487730	+	0.872995i	$0.662175\pi$
$68$	−1.44133	−0.174787
$69$	0.736247	0.0886337
$70$	−2.64183	−0.315759
$71$	−12.4265	−1.47475	−0.737377	−	0.675482i	$-0.763936\pi$
$71$	−12.4265	−1.47475	−0.737377	+	0.675482i	$0.763936\pi$
$72$	2.91513	0.343552
$73$	14.8220	1.73478	0.867391	−	0.497628i	$-0.165795\pi$
$73$	14.8220	1.73478	0.867391	+	0.497628i	$0.165795\pi$
$74$	−1.02797	−0.119499
$75$	−0.291319	−0.0336386
$76$	5.31478	0.609647
$77$	15.4830	1.76445
$78$	−0.925941	−0.104842
$79$	−7.49812	−0.843604	−0.421802	−	0.906688i	$-0.638602\pi$
$79$	−7.49812	−0.843604	−0.421802	+	0.906688i	$0.638602\pi$
$80$	−1.00000	−0.111803
$81$	8.24340	0.915933
$82$	7.99719	0.883141
$83$	11.3267	1.24326	0.621631	−	0.783310i	$-0.286470\pi$
$83$	11.3267	1.24326	0.621631	+	0.783310i	$0.286470\pi$
$84$	0.769615	0.0839719
$85$	1.44133	0.156334
$86$	−3.90260	−0.420828
$87$	2.02128	0.216704
$88$	5.86070	0.624752
$89$	6.82450	0.723395	0.361698	−	0.932295i	$-0.382197\pi$
$89$	6.82450	0.723395	0.361698	+	0.932295i	$0.382197\pi$
$90$	−2.91513	−0.307282
$91$	8.39691	0.880235
$92$	−2.52729	−0.263488
$93$	2.82983	0.293440
$94$	8.48780	0.875449
$95$	−5.31478	−0.545285
$96$	0.291319	0.0297326
$97$	4.90077	0.497598	0.248799	−	0.968555i	$-0.419964\pi$
$97$	4.90077	0.497598	0.248799	+	0.968555i	$0.419964\pi$
$98$	0.0207335	0.00209440
$99$	17.0847	1.71708
$100$	1.00000	0.100000
$101$	−6.02484	−0.599494	−0.299747	−	0.954019i	$-0.596902\pi$
$101$	−6.02484	−0.599494	−0.299747	+	0.954019i	$0.596902\pi$
$102$	−0.419887	−0.0415751
$103$	−13.3479	−1.31521	−0.657603	−	0.753365i	$-0.728429\pi$
$103$	−13.3479	−1.31521	−0.657603	+	0.753365i	$0.728429\pi$
$104$	3.17844	0.311672
$105$	−0.769615	−0.0751068
$106$	12.9594	1.25873
$107$	10.6689	1.03140	0.515702	−	0.856768i	$-0.327531\pi$
$107$	10.6689	1.03140	0.515702	+	0.856768i	$0.327531\pi$
$108$	1.72319	0.165814
$109$	−6.67042	−0.638910	−0.319455	−	0.947601i	$-0.603500\pi$
$109$	−6.67042	−0.638910	−0.319455	+	0.947601i	$0.603500\pi$
$110$	−5.86070	−0.558795
$111$	−0.299466	−0.0284241
$112$	−2.64183	−0.249629
$113$	10.4076	0.979061	0.489531	−	0.871986i	$-0.337168\pi$
$113$	10.4076	0.979061	0.489531	+	0.871986i	$0.337168\pi$
$114$	1.54830	0.145011
$115$	2.52729	0.235671
$116$	−6.93836	−0.644211
$117$	9.26559	0.856604
$118$	−1.76796	−0.162754
$119$	3.80775	0.349056
$120$	−0.291319	−0.0265937
$121$	23.3477	2.12252
$122$	0.583256	0.0528055
$123$	2.32973	0.210065
$124$	−9.71386	−0.872331
$125$	−1.00000	−0.0894427
$126$	−7.70129	−0.686085
$127$	10.8117	0.959381	0.479690	−	0.877438i	$-0.340749\pi$
$127$	10.8117	0.959381	0.479690	+	0.877438i	$0.340749\pi$
$128$	−1.00000	−0.0883883
$129$	−1.13690	−0.100099
$130$	−3.17844	−0.278768
$131$	−0.438178	−0.0382837	−0.0191419	−	0.999817i	$-0.506093\pi$
$131$	−0.438178	−0.0382837	−0.0191419	+	0.999817i	$0.506093\pi$
$132$	1.70733	0.148604
$133$	−14.0407	−1.21749
$134$	7.98448	0.689754
$135$	−1.72319	−0.148309
$136$	1.44133	0.123593
$137$	6.63070	0.566499	0.283249	−	0.959046i	$-0.408588\pi$
$137$	6.63070	0.566499	0.283249	+	0.959046i	$0.408588\pi$
$138$	−0.736247	−0.0626735
$139$	−18.2650	−1.54922	−0.774610	−	0.632439i	$-0.782054\pi$
$139$	−18.2650	−1.54922	−0.774610	+	0.632439i	$0.782054\pi$
$140$	2.64183	0.223275
$141$	2.47266	0.208235
$142$	12.4265	1.04281
$143$	18.6279	1.55774
$144$	−2.91513	−0.242928
$145$	6.93836	0.576200
$146$	−14.8220	−1.22668
$147$	0.00604006	0.000498176 0
$148$	1.02797	0.0844983
$149$	−7.63873	−0.625789	−0.312894	−	0.949788i	$-0.601299\pi$
$149$	−7.63873	−0.625789	−0.312894	+	0.949788i	$0.601299\pi$
$150$	0.291319	0.0237861
$151$	21.3107	1.73424	0.867122	−	0.498096i	$-0.165967\pi$
$151$	21.3107	1.73424	0.867122	+	0.498096i	$0.165967\pi$
$152$	−5.31478	−0.431086
$153$	4.20167	0.339685
$154$	−15.4830	−1.24765
$155$	9.71386	0.780236
$156$	0.925941	0.0741346
$157$	−17.4769	−1.39481	−0.697403	−	0.716679i	$-0.745661\pi$
$157$	−17.4769	−1.39481	−0.697403	+	0.716679i	$0.745661\pi$
$158$	7.49812	0.596518
$159$	3.77532	0.299402
$160$	1.00000	0.0790569
$161$	6.67666	0.526195
$162$	−8.24340	−0.647663
$163$	−7.75602	−0.607498	−0.303749	−	0.952752i	$-0.598238\pi$
$163$	−7.75602	−0.607498	−0.303749	+	0.952752i	$0.598238\pi$
$164$	−7.99719	−0.624475
$165$	−1.70733	−0.132916
$166$	−11.3267	−0.879119
$167$	23.0018	1.77994	0.889968	−	0.456024i	$-0.150727\pi$
$167$	23.0018	1.77994	0.889968	+	0.456024i	$0.150727\pi$
$168$	−0.769615	−0.0593771
$169$	−2.89749	−0.222884
$170$	−1.44133	−0.110545
$171$	−15.4933	−1.18480
$172$	3.90260	0.297570
$173$	−15.0460	−1.14393	−0.571963	−	0.820279i	$-0.693818\pi$
$173$	−15.0460	−1.14393	−0.571963	+	0.820279i	$0.693818\pi$
$174$	−2.02128	−0.153233
$175$	−2.64183	−0.199704
$176$	−5.86070	−0.441767
$177$	−0.515040	−0.0387128
$178$	−6.82450	−0.511518
$179$	4.17768	0.312255	0.156127	−	0.987737i	$-0.450099\pi$
$179$	4.17768	0.312255	0.156127	+	0.987737i	$0.450099\pi$
$180$	2.91513	0.217281
$181$	−10.0201	−0.744787	−0.372394	−	0.928075i	$-0.621463\pi$
$181$	−10.0201	−0.744787	−0.372394	+	0.928075i	$0.621463\pi$
$182$	−8.39691	−0.622420
$183$	0.169914	0.0125604
$184$	2.52729	0.186314
$185$	−1.02797	−0.0755776
$186$	−2.82983	−0.207493
$187$	8.44721	0.617721
$188$	−8.48780	−0.619036
$189$	−4.55238	−0.331137
$190$	5.31478	0.385575
$191$	12.8378	0.928908	0.464454	−	0.885597i	$-0.346251\pi$
$191$	12.8378	0.928908	0.464454	+	0.885597i	$0.346251\pi$
$192$	−0.291319	−0.0210241
$193$	−16.4089	−1.18114	−0.590570	−	0.806986i	$-0.701097\pi$
$193$	−16.4089	−1.18114	−0.590570	+	0.806986i	$0.701097\pi$
$194$	−4.90077	−0.351855
$195$	−0.925941	−0.0663080
$196$	−0.0207335	−0.00148096
$197$	−10.5077	−0.748642	−0.374321	−	0.927299i	$-0.622124\pi$
$197$	−10.5077	−0.748642	−0.374321	+	0.927299i	$0.622124\pi$
$198$	−17.0847	−1.21416
$199$	17.2786	1.22485	0.612423	−	0.790530i	$-0.290195\pi$
$199$	17.2786	1.22485	0.612423	+	0.790530i	$0.290195\pi$
$200$	−1.00000	−0.0707107
$201$	2.32603	0.164066
$202$	6.02484	0.423906
$203$	18.3300	1.28651
$204$	0.419887	0.0293980
$205$	7.99719	0.558548
$206$	13.3479	0.929990
$207$	7.36738	0.512068
$208$	−3.17844	−0.220385
$209$	−31.1483	−2.15457
$210$	0.769615	0.0531085
$211$	−8.02908	−0.552745	−0.276372	−	0.961051i	$-0.589132\pi$
$211$	−8.02908	−0.552745	−0.276372	+	0.961051i	$0.589132\pi$
$212$	−12.9594	−0.890054
$213$	3.62007	0.248043
$214$	−10.6689	−0.729313
$215$	−3.90260	−0.266155
$216$	−1.72319	−0.117248
$217$	25.6624	1.74208
$218$	6.67042	0.451778
$219$	−4.31793	−0.291778
$220$	5.86070	0.395128
$221$	4.58119	0.308164
$222$	0.299466	0.0200989
$223$	18.6434	1.24846	0.624228	−	0.781242i	$-0.285413\pi$
$223$	18.6434	1.24846	0.624228	+	0.781242i	$0.285413\pi$
$224$	2.64183	0.176515
$225$	−2.91513	−0.194342
$226$	−10.4076	−0.692301
$227$	−19.4931	−1.29380	−0.646901	−	0.762574i	$-0.723935\pi$
$227$	−19.4931	−1.29380	−0.646901	+	0.762574i	$0.723935\pi$
$228$	−1.54830	−0.102538
$229$	−0.179136	−0.0118376	−0.00591882	−	0.999982i	$-0.501884\pi$
$229$	−0.179136	−0.0118376	−0.00591882	+	0.999982i	$0.501884\pi$
$230$	−2.52729	−0.166644
$231$	−4.51048	−0.296768
$232$	6.93836	0.455526
$233$	−18.0076	−1.17972	−0.589860	−	0.807506i	$-0.700817\pi$
$233$	−18.0076	−1.17972	−0.589860	+	0.807506i	$0.700817\pi$
$234$	−9.26559	−0.605710
$235$	8.48780	0.553683
$236$	1.76796	0.115084
$237$	2.18434	0.141888
$238$	−3.80775	−0.246820
$239$	−18.1195	−1.17206	−0.586028	−	0.810291i	$-0.699309\pi$
$239$	−18.1195	−1.17206	−0.586028	+	0.810291i	$0.699309\pi$
$240$	0.291319	0.0188046
$241$	18.1236	1.16744	0.583721	−	0.811954i	$-0.301596\pi$
$241$	18.1236	1.16744	0.583721	+	0.811954i	$0.301596\pi$
$242$	−23.3477	−1.50085
$243$	−7.57103	−0.485682
$244$	−0.583256	−0.0373392
$245$	0.0207335	0.00132461
$246$	−2.32973	−0.148538
$247$	−16.8927	−1.07486
$248$	9.71386	0.616831
$249$	−3.29967	−0.209108
$250$	1.00000	0.0632456
$251$	24.6858	1.55815	0.779077	−	0.626929i	$-0.215688\pi$
$251$	24.6858	1.55815	0.779077	+	0.626929i	$0.215688\pi$
$252$	7.70129	0.485135
$253$	14.8117	0.931201
$254$	−10.8117	−0.678385
$255$	−0.419887	−0.0262944
$256$	1.00000	0.0625000
$257$	23.1320	1.44294	0.721468	−	0.692448i	$-0.243468\pi$
$257$	23.1320	1.44294	0.721468	+	0.692448i	$0.243468\pi$
$258$	1.13690	0.0707804
$259$	−2.71571	−0.168746
$260$	3.17844	0.197119
$261$	20.2263	1.25197
$262$	0.438178	0.0270707
$263$	−1.40791	−0.0868156	−0.0434078	−	0.999057i	$-0.513821\pi$
$263$	−1.40791	−0.0868156	−0.0434078	+	0.999057i	$0.513821\pi$
$264$	−1.70733	−0.105079
$265$	12.9594	0.796089
$266$	14.0407	0.860893
$267$	−1.98811	−0.121670
$268$	−7.98448	−0.487730
$269$	−19.8126	−1.20799	−0.603997	−	0.796987i	$-0.706426\pi$
$269$	−19.8126	−1.20799	−0.603997	+	0.796987i	$0.706426\pi$
$270$	1.72319	0.104870
$271$	−16.8190	−1.02168	−0.510840	−	0.859676i	$-0.670666\pi$
$271$	−16.8190	−1.02168	−0.510840	+	0.859676i	$0.670666\pi$
$272$	−1.44133	−0.0873936
$273$	−2.44618	−0.148050
$274$	−6.63070	−0.400575
$275$	−5.86070	−0.353413
$276$	0.736247	0.0443169
$277$	20.2880	1.21899	0.609494	−	0.792791i	$-0.291373\pi$
$277$	20.2880	1.21899	0.609494	+	0.792791i	$0.291373\pi$
$278$	18.2650	1.09546
$279$	28.3172	1.69531
$280$	−2.64183	−0.157880
$281$	−18.3031	−1.09187	−0.545936	−	0.837827i	$-0.683826\pi$
$281$	−18.3031	−1.09187	−0.545936	+	0.837827i	$0.683826\pi$
$282$	−2.47266	−0.147245
$283$	26.3710	1.56760	0.783798	−	0.621016i	$-0.213280\pi$
$283$	26.3710	1.56760	0.783798	+	0.621016i	$0.213280\pi$
$284$	−12.4265	−0.737377
$285$	1.54830	0.0917132
$286$	−18.6279	−1.10149
$287$	21.1272	1.24710
$288$	2.91513	0.171776
$289$	−14.9226	−0.877798
$290$	−6.93836	−0.407435
$291$	−1.42769	−0.0836926
$292$	14.8220	0.867391
$293$	31.8360	1.85988	0.929940	−	0.367711i	$-0.119858\pi$
$293$	31.8360	1.85988	0.929940	+	0.367711i	$0.119858\pi$
$294$	−0.00604006	−0.000352263 0
$295$	−1.76796	−0.102935
$296$	−1.02797	−0.0597493
$297$	−10.0991	−0.586009
$298$	7.63873	0.442499
$299$	8.03284	0.464551
$300$	−0.291319	−0.0168193
$301$	−10.3100	−0.594258
$302$	−21.3107	−1.22630
$303$	1.75515	0.100831
$304$	5.31478	0.304824
$305$	0.583256	0.0333972
$306$	−4.20167	−0.240194
$307$	33.1191	1.89021	0.945104	−	0.326769i	$-0.105960\pi$
$307$	33.1191	1.89021	0.945104	+	0.326769i	$0.105960\pi$
$308$	15.4830	0.882224
$309$	3.88849	0.221208
$310$	−9.71386	−0.551710
$311$	−21.1543	−1.19955	−0.599776	−	0.800168i	$-0.704744\pi$
$311$	−21.1543	−1.19955	−0.599776	+	0.800168i	$0.704744\pi$
$312$	−0.925941	−0.0524211
$313$	−15.3188	−0.865871	−0.432935	−	0.901425i	$-0.642522\pi$
$313$	−15.3188	−0.865871	−0.432935	+	0.901425i	$0.642522\pi$
$314$	17.4769	0.986277
$315$	−7.70129	−0.433918
$316$	−7.49812	−0.421802
$317$	2.26036	0.126955	0.0634773	−	0.997983i	$-0.479781\pi$
$317$	2.26036	0.126955	0.0634773	+	0.997983i	$0.479781\pi$
$318$	−3.77532	−0.211709
$319$	40.6636	2.27673
$320$	−1.00000	−0.0559017
$321$	−3.10806	−0.173475
$322$	−6.67666	−0.372076
$323$	−7.66036	−0.426234
$324$	8.24340	0.457967
$325$	−3.17844	−0.176308
$326$	7.75602	0.429566
$327$	1.94322	0.107460
$328$	7.99719	0.441571
$329$	22.4233	1.23624
$330$	1.70733	0.0939855
$331$	−10.9264	−0.600569	−0.300285	−	0.953850i	$-0.597082\pi$
$331$	−10.9264	−0.600569	−0.300285	+	0.953850i	$0.597082\pi$
$332$	11.3267	0.621631
$333$	−2.99666	−0.164216
$334$	−23.0018	−1.25860
$335$	7.98448	0.436239
$336$	0.769615	0.0419860
$337$	10.2066	0.555989	0.277995	−	0.960583i	$-0.410330\pi$
$337$	10.2066	0.555989	0.277995	+	0.960583i	$0.410330\pi$
$338$	2.89749	0.157603
$339$	−3.03192	−0.164671
$340$	1.44133	0.0781672
$341$	56.9300	3.08293
$342$	15.4933	0.837781
$343$	18.5476	1.00148
$344$	−3.90260	−0.210414
$345$	−0.736247	−0.0396382
$346$	15.0460	0.808878
$347$	−33.1742	−1.78088	−0.890441	−	0.455099i	$-0.849604\pi$
$347$	−33.1742	−1.78088	−0.890441	+	0.455099i	$0.849604\pi$
$348$	2.02128	0.108352
$349$	13.7339	0.735161	0.367581	−	0.929992i	$-0.380186\pi$
$349$	13.7339	0.735161	0.367581	+	0.929992i	$0.380186\pi$
$350$	2.64183	0.141212
$351$	−5.47707	−0.292344
$352$	5.86070	0.312376
$353$	−22.7810	−1.21251	−0.606256	−	0.795270i	$-0.707329\pi$
$353$	−22.7810	−1.21251	−0.606256	+	0.795270i	$0.707329\pi$
$354$	0.515040	0.0273741
$355$	12.4265	0.659530
$356$	6.82450	0.361698
$357$	−1.10927	−0.0587089
$358$	−4.17768	−0.220797
$359$	−12.6387	−0.667045	−0.333522	−	0.942742i	$-0.608237\pi$
$359$	−12.6387	−0.667045	−0.333522	+	0.942742i	$0.608237\pi$
$360$	−2.91513	−0.153641
$361$	9.24689	0.486679
$362$	10.0201	0.526644
$363$	−6.80164	−0.356994
$364$	8.39691	0.440118
$365$	−14.8220	−0.775818
$366$	−0.169914	−0.00888153
$367$	−13.3943	−0.699178	−0.349589	−	0.936903i	$-0.613679\pi$
$367$	−13.3943	−0.699178	−0.349589	+	0.936903i	$0.613679\pi$
$368$	−2.52729	−0.131744
$369$	23.3129	1.21362
$370$	1.02797	0.0534414
$371$	34.2365	1.77747
$372$	2.82983	0.146720
$373$	−5.69672	−0.294965	−0.147482	−	0.989065i	$-0.547117\pi$
$373$	−5.69672	−0.294965	−0.147482	+	0.989065i	$0.547117\pi$
$374$	−8.44721	−0.436795
$375$	0.291319	0.0150437
$376$	8.48780	0.437725
$377$	22.0532	1.13580
$378$	4.55238	0.234149
$379$	−25.6507	−1.31759	−0.658794	−	0.752323i	$-0.728933\pi$
$379$	−25.6507	−1.31759	−0.658794	+	0.752323i	$0.728933\pi$
$380$	−5.31478	−0.272642
$381$	−3.14965	−0.161361
$382$	−12.8378	−0.656837
$383$	−18.8795	−0.964697	−0.482349	−	0.875979i	$-0.660216\pi$
$383$	−18.8795	−0.964697	−0.482349	+	0.875979i	$0.660216\pi$
$384$	0.291319	0.0148663
$385$	−15.4830	−0.789085
$386$	16.4089	0.835192
$387$	−11.3766	−0.578305
$388$	4.90077	0.248799
$389$	−16.6212	−0.842730	−0.421365	−	0.906891i	$-0.638449\pi$
$389$	−16.6212	−0.842730	−0.421365	+	0.906891i	$0.638449\pi$
$390$	0.925941	0.0468869
$391$	3.64266	0.184217
$392$	0.0207335	0.00104720
$393$	0.127649	0.00643906
$394$	10.5077	0.529370
$395$	7.49812	0.377271
$396$	17.0847	0.858539
$397$	−7.09134	−0.355904	−0.177952	−	0.984039i	$-0.556947\pi$
$397$	−7.09134	−0.355904	−0.177952	+	0.984039i	$0.556947\pi$
$398$	−17.2786	−0.866097
$399$	4.09034	0.204773
$400$	1.00000	0.0500000
$401$	1.00000	0.0499376
$401$	1.00000	0.0499376
$402$	−2.32603	−0.116012
$403$	30.8750	1.53799
$404$	−6.02484	−0.299747
$405$	−8.24340	−0.409618
$406$	−18.3300	−0.909702
$407$	−6.02460	−0.298628
$408$	−0.419887	−0.0207875
$409$	−37.6908	−1.86369	−0.931844	−	0.362859i	$-0.881801\pi$
$409$	−37.6908	−1.86369	−0.931844	+	0.362859i	$0.881801\pi$
$410$	−7.99719	−0.394953
$411$	−1.93165	−0.0952812
$412$	−13.3479	−0.657603
$413$	−4.67065	−0.229827
$414$	−7.36738	−0.362087
$415$	−11.3267	−0.556004
$416$	3.17844	0.155836
$417$	5.32095	0.260568
$418$	31.1483	1.52351
$419$	−33.6780	−1.64528	−0.822639	−	0.568565i	$-0.807499\pi$
$419$	−33.6780	−1.64528	−0.822639	+	0.568565i	$0.807499\pi$
$420$	−0.769615	−0.0375534
$421$	−10.0102	−0.487869	−0.243935	−	0.969792i	$-0.578438\pi$
$421$	−10.0102	−0.487869	−0.243935	+	0.969792i	$0.578438\pi$
$422$	8.02908	0.390850
$423$	24.7431	1.20305
$424$	12.9594	0.629363
$425$	−1.44133	−0.0699149
$426$	−3.62007	−0.175393
$427$	1.54086	0.0745676
$428$	10.6689	0.515702
$429$	−5.42666	−0.262002
$430$	3.90260	0.188200
$431$	−13.4049	−0.645691	−0.322845	−	0.946452i	$-0.604639\pi$
$431$	−13.4049	−0.645691	−0.322845	+	0.946452i	$0.604639\pi$
$432$	1.72319	0.0829071
$433$	−5.18861	−0.249349	−0.124674	−	0.992198i	$-0.539789\pi$
$433$	−5.18861	−0.249349	−0.124674	+	0.992198i	$0.539789\pi$
$434$	−25.6624	−1.23183
$435$	−2.02128	−0.0969128
$436$	−6.67042	−0.319455
$437$	−13.4320	−0.642539
$438$	4.31793	0.206318
$439$	34.5514	1.64905	0.824523	−	0.565828i	$-0.191443\pi$
$439$	34.5514	1.64905	0.824523	+	0.565828i	$0.191443\pi$
$440$	−5.86070	−0.279398
$441$	0.0604409	0.00287814
$442$	−4.58119	−0.217905
$443$	40.2110	1.91048	0.955242	−	0.295826i	$-0.0955947\pi$
$443$	40.2110	1.91048	0.955242	+	0.295826i	$0.0955947\pi$
$444$	−0.299466	−0.0142120
$445$	−6.82450	−0.323512
$446$	−18.6434	−0.882792
$447$	2.22531	0.105253
$448$	−2.64183	−0.124815
$449$	−28.8003	−1.35917	−0.679584	−	0.733597i	$-0.737840\pi$
$449$	−28.8003	−1.35917	−0.679584	+	0.733597i	$0.737840\pi$
$450$	2.91513	0.137421
$451$	46.8691	2.20698
$452$	10.4076	0.489531
$453$	−6.20823	−0.291688
$454$	19.4931	0.914856
$455$	−8.39691	−0.393653
$456$	1.54830	0.0725056
$457$	−15.3473	−0.717916	−0.358958	−	0.933354i	$-0.616868\pi$
$457$	−15.3473	−0.717916	−0.358958	+	0.933354i	$0.616868\pi$
$458$	0.179136	0.00837047
$459$	−2.48369	−0.115929
$460$	2.52729	0.117835
$461$	4.26461	0.198623	0.0993114	−	0.995056i	$-0.468336\pi$
$461$	4.26461	0.198623	0.0993114	+	0.995056i	$0.468336\pi$
$462$	4.51048	0.209847
$463$	−35.6331	−1.65601	−0.828006	−	0.560719i	$-0.810525\pi$
$463$	−35.6331	−1.65601	−0.828006	+	0.560719i	$0.810525\pi$
$464$	−6.93836	−0.322105
$465$	−2.82983	−0.131230
$466$	18.0076	0.834188
$467$	−15.0520	−0.696521	−0.348261	−	0.937398i	$-0.613228\pi$
$467$	−15.0520	−0.696521	−0.348261	+	0.937398i	$0.613228\pi$
$468$	9.26559	0.428302
$469$	21.0937	0.974014
$470$	−8.48780	−0.391513
$471$	5.09135	0.234597
$472$	−1.76796	−0.0813769
$473$	−22.8719	−1.05165
$474$	−2.18434	−0.100330
$475$	5.31478	0.243859
$476$	3.80775	0.174528
$477$	37.7783	1.72975
$478$	18.1195	0.828769
$479$	−15.8804	−0.725594	−0.362797	−	0.931868i	$-0.618178\pi$
$479$	−15.8804	−0.725594	−0.362797	+	0.931868i	$0.618178\pi$
$480$	−0.291319	−0.0132968
$481$	−3.26733	−0.148978
$482$	−18.1236	−0.825506
$483$	−1.94504	−0.0885023
$484$	23.3477	1.06126
$485$	−4.90077	−0.222533
$486$	7.57103	0.343429
$487$	32.9320	1.49229	0.746146	−	0.665782i	$-0.231902\pi$
$487$	32.9320	1.49229	0.746146	+	0.665782i	$0.231902\pi$
$488$	0.583256	0.0264028
$489$	2.25948	0.102177
$490$	−0.0207335	−0.000936644 0
$491$	33.8389	1.52713	0.763564	−	0.645733i	$-0.223448\pi$
$491$	33.8389	1.52713	0.763564	+	0.645733i	$0.223448\pi$
$492$	2.32973	0.105032
$493$	10.0005	0.450399
$494$	16.8927	0.760040
$495$	−17.0847	−0.767900
$496$	−9.71386	−0.436165
$497$	32.8287	1.47257
$498$	3.29967	0.147862
$499$	15.0904	0.675539	0.337769	−	0.941229i	$-0.390328\pi$
$499$	15.0904	0.675539	0.337769	+	0.941229i	$0.390328\pi$
$500$	−1.00000	−0.0447214
$501$	−6.70087	−0.299373
$502$	−24.6858	−1.10178
$503$	−19.9312	−0.888689	−0.444345	−	0.895856i	$-0.646563\pi$
$503$	−19.9312	−0.888689	−0.444345	+	0.895856i	$0.646563\pi$
$504$	−7.70129	−0.343043
$505$	6.02484	0.268102
$506$	−14.8117	−0.658459
$507$	0.844095	0.0374876
$508$	10.8117	0.479690
$509$	23.0931	1.02358	0.511792	−	0.859110i	$-0.328982\pi$
$509$	23.0931	1.02358	0.511792	+	0.859110i	$0.328982\pi$
$510$	0.419887	0.0185929
$511$	−39.1572	−1.73221
$512$	−1.00000	−0.0441942
$513$	9.15838	0.404352
$514$	−23.1320	−1.02031
$515$	13.3479	0.588178
$516$	−1.13690	−0.0500493
$517$	49.7444	2.18776
$518$	2.71571	0.119322
$519$	4.38319	0.192401
$520$	−3.17844	−0.139384
$521$	−6.18679	−0.271048	−0.135524	−	0.990774i	$-0.543272\pi$
$521$	−6.18679	−0.271048	−0.135524	+	0.990774i	$0.543272\pi$
$522$	−20.2263	−0.885279
$523$	4.57858	0.200207	0.100104	−	0.994977i	$-0.468083\pi$
$523$	4.57858	0.200207	0.100104	+	0.994977i	$0.468083\pi$
$524$	−0.438178	−0.0191419
$525$	0.769615	0.0335888
$526$	1.40791	0.0613879
$527$	14.0009	0.609889
$528$	1.70733	0.0743021
$529$	−16.6128	−0.722297
$530$	−12.9594	−0.562920
$531$	−5.15383	−0.223657
$532$	−14.0407	−0.608744
$533$	25.4186	1.10100
$534$	1.98811	0.0860338
$535$	−10.6689	−0.461258
$536$	7.98448	0.344877
$537$	−1.21704	−0.0525191
$538$	19.8126	0.854181
$539$	0.121513	0.00523392
$540$	−1.72319	−0.0741543
$541$	27.3390	1.17539	0.587697	−	0.809081i	$-0.300035\pi$
$541$	27.3390	1.17539	0.587697	+	0.809081i	$0.300035\pi$
$542$	16.8190	0.722437
$543$	2.91904	0.125268
$544$	1.44133	0.0617966
$545$	6.67042	0.285729
$546$	2.44618	0.104687
$547$	−27.2922	−1.16693	−0.583465	−	0.812138i	$-0.698304\pi$
$547$	−27.2922	−1.16693	−0.583465	+	0.812138i	$0.698304\pi$
$548$	6.63070	0.283249
$549$	1.70027	0.0725657
$550$	5.86070	0.249901
$551$	−36.8759	−1.57097
$552$	−0.736247	−0.0313367
$553$	19.8088	0.842354
$554$	−20.2880	−0.861955
$555$	0.299466	0.0127116
$556$	−18.2650	−0.774610
$557$	−6.97633	−0.295597	−0.147798	−	0.989018i	$-0.547219\pi$
$557$	−6.97633	−0.295597	−0.147798	+	0.989018i	$0.547219\pi$
$558$	−28.3172	−1.19876
$559$	−12.4042	−0.524641
$560$	2.64183	0.111638
$561$	−2.46083	−0.103896
$562$	18.3031	0.772070
$563$	22.1935	0.935343	0.467672	−	0.883902i	$-0.345093\pi$
$563$	22.1935	0.935343	0.467672	+	0.883902i	$0.345093\pi$
$564$	2.47266	0.104118
$565$	−10.4076	−0.437849
$566$	−26.3710	−1.10846
$567$	−21.7777	−0.914576
$568$	12.4265	0.521404
$569$	−38.9664	−1.63356	−0.816779	−	0.576951i	$-0.804242\pi$
$569$	−38.9664	−1.63356	−0.816779	+	0.576951i	$0.804242\pi$
$570$	−1.54830	−0.0648510
$571$	5.26331	0.220263	0.110131	−	0.993917i	$-0.464873\pi$
$571$	5.26331	0.220263	0.110131	+	0.993917i	$0.464873\pi$
$572$	18.6279	0.778871
$573$	−3.73989	−0.156236
$574$	−21.1272	−0.881833
$575$	−2.52729	−0.105395
$576$	−2.91513	−0.121464
$577$	8.72704	0.363312	0.181656	−	0.983362i	$-0.441854\pi$
$577$	8.72704	0.363312	0.181656	+	0.983362i	$0.441854\pi$
$578$	14.9226	0.620697
$579$	4.78023	0.198660
$580$	6.93836	0.288100
$581$	−29.9231	−1.24142
$582$	1.42769	0.0591796
$583$	75.9510	3.14557
$584$	−14.8220	−0.613338
$585$	−9.26559	−0.383085
$586$	−31.8360	−1.31513
$587$	28.0967	1.15968	0.579838	−	0.814732i	$-0.303116\pi$
$587$	28.0967	1.15968	0.579838	+	0.814732i	$0.303116\pi$
$588$	0.00604006	0.000249088 0
$589$	−51.6271	−2.12726
$590$	1.76796	0.0727857
$591$	3.06109	0.125916
$592$	1.02797	0.0422492
$593$	−0.626869	−0.0257424	−0.0128712	−	0.999917i	$-0.504097\pi$
$593$	−0.626869	−0.0257424	−0.0128712	+	0.999917i	$0.504097\pi$
$594$	10.0991	0.414371
$595$	−3.80775	−0.156103
$596$	−7.63873	−0.312894
$597$	−5.03358	−0.206011
$598$	−8.03284	−0.328487
$599$	−18.0258	−0.736514	−0.368257	−	0.929724i	$-0.620045\pi$
$599$	−18.0258	−0.736514	−0.368257	+	0.929724i	$0.620045\pi$
$600$	0.291319	0.0118931
$601$	−6.02010	−0.245565	−0.122783	−	0.992434i	$-0.539182\pi$
$601$	−6.02010	−0.245565	−0.122783	+	0.992434i	$0.539182\pi$
$602$	10.3100	0.420204
$603$	23.2758	0.947865
$604$	21.3107	0.867122
$605$	−23.3477	−0.949221
$606$	−1.75515	−0.0712981
$607$	−7.31550	−0.296927	−0.148464	−	0.988918i	$-0.547433\pi$
$607$	−7.31550	−0.296927	−0.148464	+	0.988918i	$0.547433\pi$
$608$	−5.31478	−0.215543
$609$	−5.33987	−0.216383
$610$	−0.583256	−0.0236154
$611$	26.9780	1.09141
$612$	4.20167	0.169843
$613$	20.9070	0.844427	0.422214	−	0.906496i	$-0.361253\pi$
$613$	20.9070	0.844427	0.422214	+	0.906496i	$0.361253\pi$
$614$	−33.1191	−1.33658
$615$	−2.32973	−0.0939439
$616$	−15.4830	−0.623826
$617$	4.50219	0.181251	0.0906256	−	0.995885i	$-0.471113\pi$
$617$	4.50219	0.181251	0.0906256	+	0.995885i	$0.471113\pi$
$618$	−3.88849	−0.156418
$619$	−23.5611	−0.947002	−0.473501	−	0.880793i	$-0.657010\pi$
$619$	−23.5611	−0.947002	−0.473501	+	0.880793i	$0.657010\pi$
$620$	9.71386	0.390118
$621$	−4.35500	−0.174760
$622$	21.1543	0.848212
$623$	−18.0292	−0.722323
$624$	0.925941	0.0370673
$625$	1.00000	0.0400000
$626$	15.3188	0.612263
$627$	9.07410	0.362384
$628$	−17.4769	−0.697403
$629$	−1.48164	−0.0590769
$630$	7.70129	0.306827
$631$	42.6323	1.69717	0.848583	−	0.529063i	$-0.177456\pi$
$631$	42.6323	1.69717	0.848583	+	0.529063i	$0.177456\pi$
$632$	7.49812	0.298259
$633$	2.33902	0.0929679
$634$	−2.26036	−0.0897705
$635$	−10.8117	−0.429048
$636$	3.77532	0.149701
$637$	0.0659002	0.00261106
$638$	−40.6636	−1.60989
$639$	36.2249	1.43303
$640$	1.00000	0.0395285
$641$	−28.3208	−1.11860	−0.559302	−	0.828964i	$-0.688931\pi$
$641$	−28.3208	−1.11860	−0.559302	+	0.828964i	$0.688931\pi$
$642$	3.10806	0.122665
$643$	−41.7469	−1.64634	−0.823168	−	0.567797i	$-0.807796\pi$
$643$	−41.7469	−1.64634	−0.823168	+	0.567797i	$0.807796\pi$
$644$	6.67666	0.263097
$645$	1.13690	0.0447654
$646$	7.66036	0.301393
$647$	48.0797	1.89021	0.945105	−	0.326767i	$-0.105959\pi$
$647$	48.0797	1.89021	0.945105	+	0.326767i	$0.105959\pi$
$648$	−8.24340	−0.323831
$649$	−10.3615	−0.406723
$650$	3.17844	0.124669
$651$	−7.47594	−0.293005
$652$	−7.75602	−0.303749
$653$	−36.3806	−1.42368	−0.711842	−	0.702340i	$-0.752139\pi$
$653$	−36.3806	−1.42368	−0.711842	+	0.702340i	$0.752139\pi$
$654$	−1.94322	−0.0759859
$655$	0.438178	0.0171210
$656$	−7.99719	−0.312238
$657$	−43.2080	−1.68571
$658$	−22.4233	−0.874152
$659$	−12.4433	−0.484723	−0.242361	−	0.970186i	$-0.577922\pi$
$659$	−12.4433	−0.484723	−0.242361	+	0.970186i	$0.577922\pi$
$660$	−1.70733	−0.0664578
$661$	−21.2445	−0.826314	−0.413157	−	0.910660i	$-0.635574\pi$
$661$	−21.2445	−0.826314	−0.413157	+	0.910660i	$0.635574\pi$
$662$	10.9264	0.424666
$663$	−1.33459	−0.0518311
$664$	−11.3267	−0.439560
$665$	14.0407	0.544477
$666$	2.99666	0.116118
$667$	17.5352	0.678967
$668$	23.0018	0.889968
$669$	−5.43119	−0.209982
$670$	−7.98448	−0.308468
$671$	3.41829	0.131961
$672$	−0.769615	−0.0296886
$673$	−13.3130	−0.513180	−0.256590	−	0.966520i	$-0.582599\pi$
$673$	−13.3130	−0.513180	−0.256590	+	0.966520i	$0.582599\pi$
$674$	−10.2066	−0.393144
$675$	1.72319	0.0663257
$676$	−2.89749	−0.111442
$677$	24.0216	0.923225	0.461612	−	0.887082i	$-0.347271\pi$
$677$	24.0216	0.923225	0.461612	+	0.887082i	$0.347271\pi$
$678$	3.03192	0.116440
$679$	−12.9470	−0.496860
$680$	−1.44133	−0.0552726
$681$	5.67871	0.217609
$682$	−56.9300	−2.17996
$683$	50.5633	1.93475	0.967376	−	0.253347i	$-0.0815313\pi$
$683$	50.5633	1.93475	0.967376	+	0.253347i	$0.0815313\pi$
$684$	−15.4933	−0.592401
$685$	−6.63070	−0.253346
$686$	−18.5476	−0.708150
$687$	0.0521857	0.00199101
$688$	3.90260	0.148785
$689$	41.1907	1.56924
$690$	0.736247	0.0280284
$691$	36.1805	1.37637	0.688185	−	0.725536i	$-0.258408\pi$
$691$	36.1805	1.37637	0.688185	+	0.725536i	$0.258408\pi$
$692$	−15.0460	−0.571963
$693$	−45.1349	−1.71453
$694$	33.1742	1.25927
$695$	18.2650	0.692832
$696$	−2.02128	−0.0766163
$697$	11.5266	0.436601
$698$	−13.7339	−0.519837
$699$	5.24597	0.198421
$700$	−2.64183	−0.0998518
$701$	−40.4507	−1.52780	−0.763901	−	0.645333i	$-0.776719\pi$
$701$	−40.4507	−1.52780	−0.763901	+	0.645333i	$0.776719\pi$
$702$	5.47707	0.206719
$703$	5.46342	0.206057
$704$	−5.86070	−0.220883
$705$	−2.47266	−0.0931256
$706$	22.7810	0.857376
$707$	15.9166	0.598605
$708$	−0.515040	−0.0193564
$709$	0.195081	0.00732641	0.00366321	−	0.999993i	$-0.498834\pi$
$709$	0.195081	0.00732641	0.00366321	+	0.999993i	$0.498834\pi$
$710$	−12.4265	−0.466358
$711$	21.8580	0.819740
$712$	−6.82450	−0.255759
$713$	24.5497	0.919394
$714$	1.10927	0.0415134
$715$	−18.6279	−0.696644
$716$	4.17768	0.156127
$717$	5.27857	0.197132
$718$	12.6387	0.471672
$719$	40.5564	1.51250	0.756250	−	0.654283i	$-0.227029\pi$
$719$	40.5564	1.51250	0.756250	+	0.654283i	$0.227029\pi$
$720$	2.91513	0.108641
$721$	35.2628	1.31326
$722$	−9.24689	−0.344134
$723$	−5.27974	−0.196356
$724$	−10.0201	−0.372394
$725$	−6.93836	−0.257684
$726$	6.80164	0.252433
$727$	−10.2805	−0.381284	−0.190642	−	0.981660i	$-0.561057\pi$
$727$	−10.2805	−0.381284	−0.190642	+	0.981660i	$0.561057\pi$
$728$	−8.39691	−0.311210
$729$	−22.5246	−0.834245
$730$	14.8220	0.548586
$731$	−5.62494	−0.208046
$732$	0.169914	0.00628019
$733$	−33.8238	−1.24931	−0.624654	−	0.780901i	$-0.714760\pi$
$733$	−33.8238	−1.24931	−0.624654	+	0.780901i	$0.714760\pi$
$734$	13.3943	0.494393
$735$	−0.00604006	−0.000222791 0
$736$	2.52729	0.0931570
$737$	46.7946	1.72370
$738$	−23.3129	−0.858158
$739$	−8.88439	−0.326818	−0.163409	−	0.986558i	$-0.552249\pi$
$739$	−8.88439	−0.326818	−0.163409	+	0.986558i	$0.552249\pi$
$740$	−1.02797	−0.0377888
$741$	4.92117	0.180784
$742$	−34.2365	−1.25686
$743$	21.5465	0.790465	0.395233	−	0.918581i	$-0.370664\pi$
$743$	21.5465	0.790465	0.395233	+	0.918581i	$0.370664\pi$
$744$	−2.82983	−0.103747
$745$	7.63873	0.279861
$746$	5.69672	0.208572
$747$	−33.0187	−1.20809
$748$	8.44721	0.308860
$749$	−28.1855	−1.02988
$750$	−0.291319	−0.0106375
$751$	−48.7387	−1.77850	−0.889251	−	0.457420i	$-0.848774\pi$
$751$	−48.7387	−1.77850	−0.889251	+	0.457420i	$0.848774\pi$
$752$	−8.48780	−0.309518
$753$	−7.19144	−0.262071
$754$	−22.0532	−0.803130
$755$	−21.3107	−0.775578
$756$	−4.55238	−0.165568
$757$	−23.5843	−0.857187	−0.428593	−	0.903498i	$-0.640991\pi$
$757$	−23.5843	−0.857187	−0.428593	+	0.903498i	$0.640991\pi$
$758$	25.6507	0.931676
$759$	−4.31492	−0.156622
$760$	5.31478	0.192787
$761$	−31.1015	−1.12743	−0.563715	−	0.825970i	$-0.690628\pi$
$761$	−31.1015	−1.12743	−0.563715	+	0.825970i	$0.690628\pi$
$762$	3.14965	0.114100
$763$	17.6221	0.637963
$764$	12.8378	0.464454
$765$	−4.20167	−0.151912
$766$	18.8795	0.682144
$767$	−5.61936	−0.202903
$768$	−0.291319	−0.0105121
$769$	48.8544	1.76173	0.880867	−	0.473364i	$-0.156961\pi$
$769$	48.8544	1.76173	0.880867	+	0.473364i	$0.156961\pi$
$770$	15.4830	0.557967
$771$	−6.73879	−0.242692
$772$	−16.4089	−0.590570
$773$	−18.3509	−0.660037	−0.330019	−	0.943974i	$-0.607055\pi$
$773$	−18.3509	−0.660037	−0.330019	+	0.943974i	$0.607055\pi$
$774$	11.3766	0.408923
$775$	−9.71386	−0.348932
$776$	−4.90077	−0.175927
$777$	0.791139	0.0283819
$778$	16.6212	0.595900
$779$	−42.5033	−1.52284
$780$	−0.925941	−0.0331540
$781$	72.8279	2.60599
$782$	−3.64266	−0.130261
$783$	−11.9561	−0.427277
$784$	−0.0207335	−0.000740482 0
$785$	17.4769	0.623776
$786$	−0.127649	−0.00455311
$787$	−46.0636	−1.64199	−0.820995	−	0.570935i	$-0.806581\pi$
$787$	−46.0636	−1.64199	−0.820995	+	0.570935i	$0.806581\pi$
$788$	−10.5077	−0.374321
$789$	0.410152	0.0146018
$790$	−7.49812	−0.266771
$791$	−27.4950	−0.977610
$792$	−17.0847	−0.607079
$793$	1.85385	0.0658320
$794$	7.09134	0.251662
$795$	−3.77532	−0.133897
$796$	17.2786	0.612423
$797$	21.8059	0.772404	0.386202	−	0.922414i	$-0.373787\pi$
$797$	21.8059	0.772404	0.386202	+	0.922414i	$0.373787\pi$
$798$	−4.09034	−0.144796
$799$	12.2337	0.432798
$800$	−1.00000	−0.0353553
$801$	−19.8943	−0.702931
$802$	−1.00000	−0.0353112
$803$	−86.8671	−3.06547
$804$	2.32603	0.0820328
$805$	−6.67666	−0.235321
$806$	−30.8750	−1.08752
$807$	5.77178	0.203176
$808$	6.02484	0.211953
$809$	−32.8945	−1.15651	−0.578255	−	0.815856i	$-0.696266\pi$
$809$	−32.8945	−1.15651	−0.578255	+	0.815856i	$0.696266\pi$
$810$	8.24340	0.289644
$811$	33.2735	1.16839	0.584195	−	0.811613i	$-0.301410\pi$
$811$	33.2735	1.16839	0.584195	+	0.811613i	$0.301410\pi$
$812$	18.3300	0.643256
$813$	4.89969	0.171840
$814$	6.02460	0.211162
$815$	7.75602	0.271681
$816$	0.419887	0.0146990
$817$	20.7414	0.725651
$818$	37.6908	1.31783
$819$	−24.4781	−0.855334
$820$	7.99719	0.279274
$821$	−7.90063	−0.275734	−0.137867	−	0.990451i	$-0.544025\pi$
$821$	−7.90063	−0.275734	−0.137867	+	0.990451i	$0.544025\pi$
$822$	1.93165	0.0673740
$823$	−21.8251	−0.760777	−0.380388	−	0.924827i	$-0.624210\pi$
$823$	−21.8251	−0.760777	−0.380388	+	0.924827i	$0.624210\pi$
$824$	13.3479	0.464995
$825$	1.70733	0.0594417
$826$	4.67065	0.162513
$827$	−20.3536	−0.707763	−0.353882	−	0.935290i	$-0.615138\pi$
$827$	−20.3536	−0.707763	−0.353882	+	0.935290i	$0.615138\pi$
$828$	7.36738	0.256034
$829$	−13.1067	−0.455215	−0.227608	−	0.973753i	$-0.573090\pi$
$829$	−13.1067	−0.455215	−0.227608	+	0.973753i	$0.573090\pi$
$830$	11.3267	0.393154
$831$	−5.91028	−0.205025
$832$	−3.17844	−0.110193
$833$	0.0298838	0.00103541
$834$	−5.32095	−0.184249
$835$	−23.0018	−0.796011
$836$	−31.1483	−1.07729
$837$	−16.7388	−0.578579
$838$	33.6780	1.16339
$839$	−18.7635	−0.647789	−0.323895	−	0.946093i	$-0.604992\pi$
$839$	−18.7635	−0.647789	−0.323895	+	0.946093i	$0.604992\pi$
$840$	0.769615	0.0265543
$841$	19.1409	0.660031
$842$	10.0102	0.344976
$843$	5.33205	0.183645
$844$	−8.02908	−0.276372
$845$	2.89749	0.0996768
$846$	−24.7431	−0.850684
$847$	−61.6808	−2.11938
$848$	−12.9594	−0.445027
$849$	−7.68239	−0.263659
$850$	1.44133	0.0494373
$851$	−2.59797	−0.0890571
$852$	3.62007	0.124022
$853$	−28.1258	−0.963010	−0.481505	−	0.876443i	$-0.659910\pi$
$853$	−28.1258	−0.963010	−0.481505	+	0.876443i	$0.659910\pi$
$854$	−1.54086	−0.0527273
$855$	15.4933	0.529859
$856$	−10.6689	−0.364656
$857$	−28.2116	−0.963689	−0.481844	−	0.876257i	$-0.660033\pi$
$857$	−28.2116	−0.963689	−0.481844	+	0.876257i	$0.660033\pi$
$858$	5.42666	0.185263
$859$	39.5432	1.34920	0.674598	−	0.738185i	$-0.264317\pi$
$859$	39.5432	1.34920	0.674598	+	0.738185i	$0.264317\pi$
$860$	−3.90260	−0.133077
$861$	−6.15476	−0.209754
$862$	13.4049	0.456572
$863$	−7.40684	−0.252132	−0.126066	−	0.992022i	$-0.540235\pi$
$863$	−7.40684	−0.252132	−0.126066	+	0.992022i	$0.540235\pi$
$864$	−1.72319	−0.0586241
$865$	15.0460	0.511579
$866$	5.18861	0.176316
$867$	4.34723	0.147640
$868$	25.6624	0.871038
$869$	43.9442	1.49070
$870$	2.02128	0.0685277
$871$	25.3782	0.859909
$872$	6.67042	0.225889
$873$	−14.2864	−0.483521
$874$	13.4320	0.454343
$875$	2.64183	0.0893102
$876$	−4.31793	−0.145889
$877$	34.6822	1.17114	0.585568	−	0.810624i	$-0.300872\pi$
$877$	34.6822	1.17114	0.585568	+	0.810624i	$0.300872\pi$
$878$	−34.5514	−1.16605
$879$	−9.27444	−0.312819
$880$	5.86070	0.197564
$881$	−8.24298	−0.277713	−0.138856	−	0.990313i	$-0.544343\pi$
$881$	−8.24298	−0.277713	−0.138856	+	0.990313i	$0.544343\pi$
$882$	−0.0604409	−0.00203515
$883$	−9.18474	−0.309091	−0.154546	−	0.987986i	$-0.549391\pi$
$883$	−9.18474	−0.309091	−0.154546	+	0.987986i	$0.549391\pi$
$884$	4.58119	0.154082
$885$	0.515040	0.0173129
$886$	−40.2110	−1.35092
$887$	−29.3383	−0.985084	−0.492542	−	0.870289i	$-0.663932\pi$
$887$	−29.3383	−0.985084	−0.492542	+	0.870289i	$0.663932\pi$
$888$	0.299466	0.0100494
$889$	−28.5626	−0.957959
$890$	6.82450	0.228758
$891$	−48.3121	−1.61851
$892$	18.6434	0.624228
$893$	−45.1108	−1.50957
$894$	−2.22531	−0.0744254
$895$	−4.17768	−0.139645
$896$	2.64183	0.0882574
$897$	−2.34012	−0.0781343
$898$	28.8003	0.961078
$899$	67.3983	2.24786
$900$	−2.91513	−0.0971711
$901$	18.6788	0.622280
$902$	−46.8691	−1.56057
$903$	3.00350	0.0999502
$904$	−10.4076	−0.346150
$905$	10.0201	0.333079
$906$	6.20823	0.206255
$907$	36.6274	1.21619	0.608097	−	0.793863i	$-0.291933\pi$
$907$	36.6274	1.21619	0.608097	+	0.793863i	$0.291933\pi$
$908$	−19.4931	−0.646901
$909$	17.5632	0.582535
$910$	8.39691	0.278355
$911$	17.2688	0.572139	0.286070	−	0.958209i	$-0.407651\pi$
$911$	17.2688	0.572139	0.286070	+	0.958209i	$0.407651\pi$
$912$	−1.54830	−0.0512692
$913$	−66.3821	−2.19693
$914$	15.3473	0.507643
$915$	−0.169914	−0.00561717
$916$	−0.179136	−0.00591882
$917$	1.15759	0.0382270
$918$	2.48369	0.0819740
$919$	−32.8914	−1.08499	−0.542493	−	0.840060i	$-0.682519\pi$
$919$	−32.8914	−1.08499	−0.542493	+	0.840060i	$0.682519\pi$
$920$	−2.52729	−0.0833222
$921$	−9.64823	−0.317920
$922$	−4.26461	−0.140448
$923$	39.4969	1.30006
$924$	−4.51048	−0.148384
$925$	1.02797	0.0337993
$926$	35.6331	1.17098
$927$	38.9108	1.27800
$928$	6.93836	0.227763
$929$	44.7944	1.46966	0.734828	−	0.678253i	$-0.237263\pi$
$929$	44.7944	1.46966	0.734828	+	0.678253i	$0.237263\pi$
$930$	2.82983	0.0927939
$931$	−0.110194	−0.00361146
$932$	−18.0076	−0.589860
$933$	6.16266	0.201757
$934$	15.0520	0.492515
$935$	−8.44721	−0.276253
$936$	−9.26559	−0.302855
$937$	−40.0864	−1.30957	−0.654783	−	0.755817i	$-0.727240\pi$
$937$	−40.0864	−1.30957	−0.654783	+	0.755817i	$0.727240\pi$
$938$	−21.0937	−0.688732
$939$	4.46266	0.145634
$940$	8.48780	0.276841
$941$	36.3112	1.18371	0.591855	−	0.806044i	$-0.298396\pi$
$941$	36.3112	1.18371	0.591855	+	0.806044i	$0.298396\pi$
$942$	−5.09135	−0.165885
$943$	20.2112	0.658167
$944$	1.76796	0.0575421
$945$	4.55238	0.148089
$946$	22.8719	0.743631
$947$	56.2481	1.82782	0.913909	−	0.405918i	$-0.133048\pi$
$947$	56.2481	1.82782	0.913909	+	0.405918i	$0.133048\pi$
$948$	2.18434	0.0709442
$949$	−47.1108	−1.52928
$950$	−5.31478	−0.172434
$951$	−0.658487	−0.0213529
$952$	−3.80775	−0.123410
$953$	−29.1679	−0.944842	−0.472421	−	0.881373i	$-0.656620\pi$
$953$	−29.1679	−0.944842	−0.472421	+	0.881373i	$0.656620\pi$
$954$	−37.7783	−1.22312
$955$	−12.8378	−0.415420
$956$	−18.1195	−0.586028
$957$	−11.8461	−0.382930
$958$	15.8804	0.513073
$959$	−17.5172	−0.565659
$960$	0.291319	0.00940228
$961$	63.3592	2.04384
$962$	3.26733	0.105343
$963$	−31.1013	−1.00223
$964$	18.1236	0.583721
$965$	16.4089	0.528222
$966$	1.94504	0.0625806
$967$	−35.1477	−1.13027	−0.565137	−	0.824997i	$-0.691177\pi$
$967$	−35.1477	−1.13027	−0.565137	+	0.824997i	$0.691177\pi$
$968$	−23.3477	−0.750425
$969$	2.23161	0.0716896
$970$	4.90077	0.157354
$971$	−51.8076	−1.66258	−0.831292	−	0.555836i	$-0.812398\pi$
$971$	−51.8076	−1.66258	−0.831292	+	0.555836i	$0.812398\pi$
$972$	−7.57103	−0.242841
$973$	48.2531	1.54692
$974$	−32.9320	−1.05521
$975$	0.925941	0.0296539
$976$	−0.583256	−0.0186696
$977$	3.12480	0.0999712	0.0499856	−	0.998750i	$-0.484082\pi$
$977$	3.12480	0.0999712	0.0499856	+	0.998750i	$0.484082\pi$
$978$	−2.25948	−0.0722501
$979$	−39.9963	−1.27829
$980$	0.0207335	0.000662307 0
$981$	19.4452	0.620836
$982$	−33.8389	−1.07984
$983$	−32.4573	−1.03523	−0.517614	−	0.855614i	$-0.673180\pi$
$983$	−32.4573	−1.03523	−0.517614	+	0.855614i	$0.673180\pi$
$984$	−2.32973	−0.0742692
$985$	10.5077	0.334803
$986$	−10.0005	−0.318480
$987$	−6.53234	−0.207927
$988$	−16.8927	−0.537429
$989$	−9.86298	−0.313625
$990$	17.0847	0.542988
$991$	−25.8493	−0.821130	−0.410565	−	0.911831i	$-0.634669\pi$
$991$	−25.8493	−0.821130	−0.410565	+	0.911831i	$0.634669\pi$
$992$	9.71386	0.308416
$993$	3.18307	0.101012
$994$	−32.8287	−1.04126
$995$	−17.2786	−0.547768
$996$	−3.29967	−0.104554
$997$	−43.2791	−1.37066	−0.685332	−	0.728231i	$-0.740343\pi$
$997$	−43.2791	−1.37066	−0.685332	+	0.728231i	$0.740343\pi$
$998$	−15.0904	−0.477678
$999$	1.77138	0.0560441

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4010.2.a.l.1.7	✓	17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4010.2.a.l.1.7	✓	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -0.291319 q^{3} +1.00000 q^{4} -1.00000 q^{5} +0.291319 q^{6} -2.64183 q^{7} -1.00000 q^{8} -2.91513 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -0.291319 q^{3} +1.00000 q^{4} -1.00000 q^{5} +0.291319 q^{6} -2.64183 q^{7} -1.00000 q^{8} -2.91513 q^{9} +1.00000 q^{10} -5.86070 q^{11} -0.291319 q^{12} -3.17844 q^{13} +2.64183 q^{14} +0.291319 q^{15} +1.00000 q^{16} -1.44133 q^{17} +2.91513 q^{18} +5.31478 q^{19} -1.00000 q^{20} +0.769615 q^{21} +5.86070 q^{22} -2.52729 q^{23} +0.291319 q^{24} +1.00000 q^{25} +3.17844 q^{26} +1.72319 q^{27} -2.64183 q^{28} -6.93836 q^{29} -0.291319 q^{30} -9.71386 q^{31} -1.00000 q^{32} +1.70733 q^{33} +1.44133 q^{34} +2.64183 q^{35} -2.91513 q^{36} +1.02797 q^{37} -5.31478 q^{38} +0.925941 q^{39} +1.00000 q^{40} -7.99719 q^{41} -0.769615 q^{42} +3.90260 q^{43} -5.86070 q^{44} +2.91513 q^{45} +2.52729 q^{46} -8.48780 q^{47} -0.291319 q^{48} -0.0207335 q^{49} -1.00000 q^{50} +0.419887 q^{51} -3.17844 q^{52} -12.9594 q^{53} -1.72319 q^{54} +5.86070 q^{55} +2.64183 q^{56} -1.54830 q^{57} +6.93836 q^{58} +1.76796 q^{59} +0.291319 q^{60} -0.583256 q^{61} +9.71386 q^{62} +7.70129 q^{63} +1.00000 q^{64} +3.17844 q^{65} -1.70733 q^{66} -7.98448 q^{67} -1.44133 q^{68} +0.736247 q^{69} -2.64183 q^{70} -12.4265 q^{71} +2.91513 q^{72} +14.8220 q^{73} -1.02797 q^{74} -0.291319 q^{75} +5.31478 q^{76} +15.4830 q^{77} -0.925941 q^{78} -7.49812 q^{79} -1.00000 q^{80} +8.24340 q^{81} +7.99719 q^{82} +11.3267 q^{83} +0.769615 q^{84} +1.44133 q^{85} -3.90260 q^{86} +2.02128 q^{87} +5.86070 q^{88} +6.82450 q^{89} -2.91513 q^{90} +8.39691 q^{91} -2.52729 q^{92} +2.82983 q^{93} +8.48780 q^{94} -5.31478 q^{95} +0.291319 q^{96} +4.90077 q^{97} +0.0207335 q^{98} +17.0847 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q - 17 q^{2} + 3 q^{3} + 17 q^{4} - 17 q^{5} - 3 q^{6} + 4 q^{7} - 17 q^{8} + 6 q^{9}+O(q^{10}) \) 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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