LMFDB - Embedded newform 4010.2.a.l.1.16

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			1.16
Root			$2.89857$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} +2.89857 q^{3} +1.00000 q^{4} -1.00000 q^{5} -2.89857 q^{6} -4.89781 q^{7} -1.00000 q^{8} +5.40172 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +2.89857 q^{3} +1.00000 q^{4} -1.00000 q^{5} -2.89857 q^{6} -4.89781 q^{7} -1.00000 q^{8} +5.40172 q^{9} +1.00000 q^{10} -0.723228 q^{11} +2.89857 q^{12} +5.93703 q^{13} +4.89781 q^{14} -2.89857 q^{15} +1.00000 q^{16} -6.99825 q^{17} -5.40172 q^{18} +5.63026 q^{19} -1.00000 q^{20} -14.1967 q^{21} +0.723228 q^{22} -1.75540 q^{23} -2.89857 q^{24} +1.00000 q^{25} -5.93703 q^{26} +6.96155 q^{27} -4.89781 q^{28} -6.38111 q^{29} +2.89857 q^{30} +0.258193 q^{31} -1.00000 q^{32} -2.09633 q^{33} +6.99825 q^{34} +4.89781 q^{35} +5.40172 q^{36} +8.91838 q^{37} -5.63026 q^{38} +17.2089 q^{39} +1.00000 q^{40} +0.158261 q^{41} +14.1967 q^{42} +7.31409 q^{43} -0.723228 q^{44} -5.40172 q^{45} +1.75540 q^{46} +9.12471 q^{47} +2.89857 q^{48} +16.9886 q^{49} -1.00000 q^{50} -20.2849 q^{51} +5.93703 q^{52} +2.96698 q^{53} -6.96155 q^{54} +0.723228 q^{55} +4.89781 q^{56} +16.3197 q^{57} +6.38111 q^{58} -4.56324 q^{59} -2.89857 q^{60} +12.5819 q^{61} -0.258193 q^{62} -26.4566 q^{63} +1.00000 q^{64} -5.93703 q^{65} +2.09633 q^{66} +9.21549 q^{67} -6.99825 q^{68} -5.08815 q^{69} -4.89781 q^{70} -7.78284 q^{71} -5.40172 q^{72} +0.261257 q^{73} -8.91838 q^{74} +2.89857 q^{75} +5.63026 q^{76} +3.54224 q^{77} -17.2089 q^{78} -4.33300 q^{79} -1.00000 q^{80} +3.97340 q^{81} -0.158261 q^{82} +12.0846 q^{83} -14.1967 q^{84} +6.99825 q^{85} -7.31409 q^{86} -18.4961 q^{87} +0.723228 q^{88} +6.98919 q^{89} +5.40172 q^{90} -29.0785 q^{91} -1.75540 q^{92} +0.748390 q^{93} -9.12471 q^{94} -5.63026 q^{95} -2.89857 q^{96} +16.6118 q^{97} -16.9886 q^{98} -3.90667 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	2.89857	1.67349	0.836746	−	0.547592i	$-0.184455\pi$
$3$	2.89857	1.67349	0.836746	+	0.547592i	$0.184455\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−2.89857	−1.18334
$7$	−4.89781	−1.85120	−0.925599	−	0.378505i	$-0.876438\pi$
$7$	−4.89781	−1.85120	−0.925599	+	0.378505i	$0.876438\pi$
$8$	−1.00000	−0.353553
$9$	5.40172	1.80057
$10$	1.00000	0.316228
$11$	−0.723228	−0.218062	−0.109031	−	0.994038i	$-0.534775\pi$
$11$	−0.723228	−0.218062	−0.109031	+	0.994038i	$0.534775\pi$
$12$	2.89857	0.836746
$13$	5.93703	1.64664	0.823318	−	0.567580i	$-0.192120\pi$
$13$	5.93703	1.64664	0.823318	+	0.567580i	$0.192120\pi$
$14$	4.89781	1.30900
$15$	−2.89857	−0.748408
$16$	1.00000	0.250000
$17$	−6.99825	−1.69732	−0.848662	−	0.528935i	$-0.822591\pi$
$17$	−6.99825	−1.69732	−0.848662	+	0.528935i	$0.822591\pi$
$18$	−5.40172	−1.27320
$19$	5.63026	1.29167	0.645835	−	0.763477i	$-0.276509\pi$
$19$	5.63026	1.29167	0.645835	+	0.763477i	$0.276509\pi$
$20$	−1.00000	−0.223607
$21$	−14.1967	−3.09796
$22$	0.723228	0.154193
$23$	−1.75540	−0.366026	−0.183013	−	0.983110i	$-0.558585\pi$
$23$	−1.75540	−0.366026	−0.183013	+	0.983110i	$0.558585\pi$
$24$	−2.89857	−0.591668
$25$	1.00000	0.200000
$26$	−5.93703	−1.16435
$27$	6.96155	1.33975
$28$	−4.89781	−0.925599
$29$	−6.38111	−1.18494	−0.592471	−	0.805592i	$-0.701847\pi$
$29$	−6.38111	−1.18494	−0.592471	+	0.805592i	$0.701847\pi$
$30$	2.89857	0.529204
$31$	0.258193	0.0463728	0.0231864	−	0.999731i	$-0.492619\pi$
$31$	0.258193	0.0463728	0.0231864	+	0.999731i	$0.492619\pi$
$32$	−1.00000	−0.176777
$33$	−2.09633	−0.364924
$34$	6.99825	1.20019
$35$	4.89781	0.827881
$36$	5.40172	0.900286
$37$	8.91838	1.46617	0.733086	−	0.680136i	$-0.238079\pi$
$37$	8.91838	1.46617	0.733086	+	0.680136i	$0.238079\pi$
$38$	−5.63026	−0.913349
$39$	17.2089	2.75563
$40$	1.00000	0.158114
$41$	0.158261	0.0247162	0.0123581	−	0.999924i	$-0.496066\pi$
$41$	0.158261	0.0247162	0.0123581	+	0.999924i	$0.496066\pi$
$42$	14.1967	2.19059
$43$	7.31409	1.11539	0.557694	−	0.830047i	$-0.311686\pi$
$43$	7.31409	1.11539	0.557694	+	0.830047i	$0.311686\pi$
$44$	−0.723228	−0.109031
$45$	−5.40172	−0.805240
$46$	1.75540	0.258820
$47$	9.12471	1.33098	0.665488	−	0.746409i	$-0.268224\pi$
$47$	9.12471	1.33098	0.665488	+	0.746409i	$0.268224\pi$
$48$	2.89857	0.418373
$49$	16.9886	2.42694
$50$	−1.00000	−0.141421
$51$	−20.2849	−2.84046
$52$	5.93703	0.823318
$53$	2.96698	0.407546	0.203773	−	0.979018i	$-0.434680\pi$
$53$	2.96698	0.407546	0.203773	+	0.979018i	$0.434680\pi$
$54$	−6.96155	−0.947347
$55$	0.723228	0.0975201
$56$	4.89781	0.654498
$57$	16.3197	2.16160
$58$	6.38111	0.837880
$59$	−4.56324	−0.594084	−0.297042	−	0.954864i	$-0.596000\pi$
$59$	−4.56324	−0.594084	−0.297042	+	0.954864i	$0.596000\pi$
$60$	−2.89857	−0.374204
$61$	12.5819	1.61095	0.805473	−	0.592632i	$-0.201911\pi$
$61$	12.5819	1.61095	0.805473	+	0.592632i	$0.201911\pi$
$62$	−0.258193	−0.0327905
$63$	−26.4566	−3.33322
$64$	1.00000	0.125000
$65$	−5.93703	−0.736398
$66$	2.09633	0.258040
$67$	9.21549	1.12585	0.562926	−	0.826507i	$-0.309676\pi$
$67$	9.21549	1.12585	0.562926	+	0.826507i	$0.309676\pi$
$68$	−6.99825	−0.848662
$69$	−5.08815	−0.612541
$70$	−4.89781	−0.585400
$71$	−7.78284	−0.923653	−0.461826	−	0.886970i	$-0.652806\pi$
$71$	−7.78284	−0.923653	−0.461826	+	0.886970i	$0.652806\pi$
$72$	−5.40172	−0.636598
$73$	0.261257	0.0305778	0.0152889	−	0.999883i	$-0.495133\pi$
$73$	0.261257	0.0305778	0.0152889	+	0.999883i	$0.495133\pi$
$74$	−8.91838	−1.03674
$75$	2.89857	0.334698
$76$	5.63026	0.645835
$77$	3.54224	0.403675
$78$	−17.2089	−1.94853
$79$	−4.33300	−0.487501	−0.243750	−	0.969838i	$-0.578378\pi$
$79$	−4.33300	−0.487501	−0.243750	+	0.969838i	$0.578378\pi$
$80$	−1.00000	−0.111803
$81$	3.97340	0.441488
$82$	−0.158261	−0.0174770
$83$	12.0846	1.32645	0.663227	−	0.748418i	$-0.269186\pi$
$83$	12.0846	1.32645	0.663227	+	0.748418i	$0.269186\pi$
$84$	−14.1967	−1.54898
$85$	6.99825	0.759066
$86$	−7.31409	−0.788699
$87$	−18.4961	−1.98299
$88$	0.723228	0.0770964
$89$	6.98919	0.740853	0.370426	−	0.928862i	$-0.379212\pi$
$89$	6.98919	0.740853	0.370426	+	0.928862i	$0.379212\pi$
$90$	5.40172	0.569391
$91$	−29.0785	−3.04825
$92$	−1.75540	−0.183013
$93$	0.748390	0.0776045
$94$	−9.12471	−0.941142
$95$	−5.63026	−0.577652
$96$	−2.89857	−0.295834
$97$	16.6118	1.68667	0.843334	−	0.537389i	$-0.180589\pi$
$97$	16.6118	1.68667	0.843334	+	0.537389i	$0.180589\pi$
$98$	−16.9886	−1.71610
$99$	−3.90667	−0.392636
$100$	1.00000	0.100000
$101$	−2.35755	−0.234585	−0.117292	−	0.993097i	$-0.537422\pi$
$101$	−2.35755	−0.234585	−0.117292	+	0.993097i	$0.537422\pi$
$102$	20.2849	2.00851
$103$	0.813159	0.0801230	0.0400615	−	0.999197i	$-0.487245\pi$
$103$	0.813159	0.0801230	0.0400615	+	0.999197i	$0.487245\pi$
$104$	−5.93703	−0.582174
$105$	14.1967	1.38545
$106$	−2.96698	−0.288179
$107$	14.3876	1.39090	0.695449	−	0.718576i	$-0.255206\pi$
$107$	14.3876	1.39090	0.695449	+	0.718576i	$0.255206\pi$
$108$	6.96155	0.669875
$109$	−18.2956	−1.75241	−0.876203	−	0.481943i	$-0.839931\pi$
$109$	−18.2956	−1.75241	−0.876203	+	0.481943i	$0.839931\pi$
$110$	−0.723228	−0.0689571
$111$	25.8506	2.45363
$112$	−4.89781	−0.462800
$113$	−1.92643	−0.181223	−0.0906115	−	0.995886i	$-0.528882\pi$
$113$	−1.92643	−0.181223	−0.0906115	+	0.995886i	$0.528882\pi$
$114$	−16.3197	−1.52848
$115$	1.75540	0.163692
$116$	−6.38111	−0.592471
$117$	32.0702	2.96489
$118$	4.56324	0.420081
$119$	34.2761	3.14208
$120$	2.89857	0.264602
$121$	−10.4769	−0.952449
$122$	−12.5819	−1.13911
$123$	0.458731	0.0413623
$124$	0.258193	0.0231864
$125$	−1.00000	−0.0894427
$126$	26.4566	2.35694
$127$	−15.5517	−1.37999	−0.689995	−	0.723814i	$-0.742387\pi$
$127$	−15.5517	−1.37999	−0.689995	+	0.723814i	$0.742387\pi$
$128$	−1.00000	−0.0883883
$129$	21.2004	1.86659
$130$	5.93703	0.520712
$131$	14.9136	1.30301	0.651505	−	0.758644i	$-0.274138\pi$
$131$	14.9136	1.30301	0.651505	+	0.758644i	$0.274138\pi$
$132$	−2.09633	−0.182462
$133$	−27.5759	−2.39114
$134$	−9.21549	−0.796097
$135$	−6.96155	−0.599155
$136$	6.99825	0.600095
$137$	0.248336	0.0212168	0.0106084	−	0.999944i	$-0.496623\pi$
$137$	0.248336	0.0212168	0.0106084	+	0.999944i	$0.496623\pi$
$138$	5.08815	0.433132
$139$	−0.399481	−0.0338835	−0.0169418	−	0.999856i	$-0.505393\pi$
$139$	−0.399481	−0.0338835	−0.0169418	+	0.999856i	$0.505393\pi$
$140$	4.89781	0.413941
$141$	26.4486	2.22738
$142$	7.78284	0.653121
$143$	−4.29383	−0.359068
$144$	5.40172	0.450143
$145$	6.38111	0.529922
$146$	−0.261257	−0.0216218
$147$	49.2425	4.06146
$148$	8.91838	0.733086
$149$	−7.06839	−0.579065	−0.289533	−	0.957168i	$-0.593500\pi$
$149$	−7.06839	−0.579065	−0.289533	+	0.957168i	$0.593500\pi$
$150$	−2.89857	−0.236667
$151$	−3.32388	−0.270494	−0.135247	−	0.990812i	$-0.543183\pi$
$151$	−3.32388	−0.270494	−0.135247	+	0.990812i	$0.543183\pi$
$152$	−5.63026	−0.456674
$153$	−37.8025	−3.05615
$154$	−3.54224	−0.285441
$155$	−0.258193	−0.0207385
$156$	17.2089	1.37782
$157$	16.8380	1.34381	0.671907	−	0.740635i	$-0.265475\pi$
$157$	16.8380	1.34381	0.671907	+	0.740635i	$0.265475\pi$
$158$	4.33300	0.344715
$159$	8.60001	0.682025
$160$	1.00000	0.0790569
$161$	8.59762	0.677587
$162$	−3.97340	−0.312179
$163$	2.02298	0.158452	0.0792261	−	0.996857i	$-0.474755\pi$
$163$	2.02298	0.158452	0.0792261	+	0.996857i	$0.474755\pi$
$164$	0.158261	0.0123581
$165$	2.09633	0.163199
$166$	−12.0846	−0.937945
$167$	10.3733	0.802709	0.401354	−	0.915923i	$-0.368540\pi$
$167$	10.3733	0.802709	0.401354	+	0.915923i	$0.368540\pi$
$168$	14.1967	1.09530
$169$	22.2484	1.71141
$170$	−6.99825	−0.536741
$171$	30.4131	2.32575
$172$	7.31409	0.557694
$173$	20.0330	1.52308	0.761542	−	0.648116i	$-0.224443\pi$
$173$	20.0330	1.52308	0.761542	+	0.648116i	$0.224443\pi$
$174$	18.4961	1.40219
$175$	−4.89781	−0.370240
$176$	−0.723228	−0.0545154
$177$	−13.2269	−0.994194
$178$	−6.98919	−0.523862
$179$	10.4350	0.779949	0.389975	−	0.920826i	$-0.372484\pi$
$179$	10.4350	0.779949	0.389975	+	0.920826i	$0.372484\pi$
$180$	−5.40172	−0.402620
$181$	−5.68707	−0.422716	−0.211358	−	0.977409i	$-0.567789\pi$
$181$	−5.68707	−0.422716	−0.211358	+	0.977409i	$0.567789\pi$
$182$	29.0785	2.15544
$183$	36.4695	2.69590
$184$	1.75540	0.129410
$185$	−8.91838	−0.655692
$186$	−0.748390	−0.0548746
$187$	5.06133	0.370121
$188$	9.12471	0.665488
$189$	−34.0964	−2.48014
$190$	5.63026	0.408462
$191$	−13.6015	−0.984171	−0.492085	−	0.870547i	$-0.663765\pi$
$191$	−13.6015	−0.984171	−0.492085	+	0.870547i	$0.663765\pi$
$192$	2.89857	0.209186
$193$	−10.4777	−0.754199	−0.377100	−	0.926173i	$-0.623079\pi$
$193$	−10.4777	−0.754199	−0.377100	+	0.926173i	$0.623079\pi$
$194$	−16.6118	−1.19265
$195$	−17.2089	−1.23236
$196$	16.9886	1.21347
$197$	−11.9722	−0.852985	−0.426492	−	0.904491i	$-0.640251\pi$
$197$	−11.9722	−0.852985	−0.426492	+	0.904491i	$0.640251\pi$
$198$	3.90667	0.277635
$199$	−7.46525	−0.529198	−0.264599	−	0.964359i	$-0.585240\pi$
$199$	−7.46525	−0.529198	−0.264599	+	0.964359i	$0.585240\pi$
$200$	−1.00000	−0.0707107
$201$	26.7118	1.88410
$202$	2.35755	0.165877
$203$	31.2535	2.19356
$204$	−20.2849	−1.42023
$205$	−0.158261	−0.0110534
$206$	−0.813159	−0.0566555
$207$	−9.48217	−0.659057
$208$	5.93703	0.411659
$209$	−4.07196	−0.281663
$210$	−14.1967	−0.979662
$211$	−14.4591	−0.995408	−0.497704	−	0.867347i	$-0.665823\pi$
$211$	−14.4591	−0.995408	−0.497704	+	0.867347i	$0.665823\pi$
$212$	2.96698	0.203773
$213$	−22.5591	−1.54572
$214$	−14.3876	−0.983513
$215$	−7.31409	−0.498817
$216$	−6.96155	−0.473673
$217$	−1.26458	−0.0858453
$218$	18.2956	1.23914
$219$	0.757272	0.0511717
$220$	0.723228	0.0487600
$221$	−41.5488	−2.79488
$222$	−25.8506	−1.73498
$223$	19.1323	1.28119	0.640597	−	0.767877i	$-0.278687\pi$
$223$	19.1323	1.28119	0.640597	+	0.767877i	$0.278687\pi$
$224$	4.89781	0.327249
$225$	5.40172	0.360114
$226$	1.92643	0.128144
$227$	27.0608	1.79609	0.898044	−	0.439906i	$-0.144988\pi$
$227$	27.0608	1.79609	0.898044	+	0.439906i	$0.144988\pi$
$228$	16.3197	1.08080
$229$	22.0577	1.45761	0.728807	−	0.684719i	$-0.240075\pi$
$229$	22.0577	1.45761	0.728807	+	0.684719i	$0.240075\pi$
$230$	−1.75540	−0.115748
$231$	10.2674	0.675547
$232$	6.38111	0.418940
$233$	−1.66338	−0.108972	−0.0544858	−	0.998515i	$-0.517352\pi$
$233$	−1.66338	−0.108972	−0.0544858	+	0.998515i	$0.517352\pi$
$234$	−32.0702	−2.09649
$235$	−9.12471	−0.595230
$236$	−4.56324	−0.297042
$237$	−12.5595	−0.815828
$238$	−34.2761	−2.22179
$239$	10.1373	0.655725	0.327862	−	0.944725i	$-0.393672\pi$
$239$	10.1373	0.655725	0.327862	+	0.944725i	$0.393672\pi$
$240$	−2.89857	−0.187102
$241$	−26.1166	−1.68232	−0.841161	−	0.540785i	$-0.818127\pi$
$241$	−26.1166	−1.68232	−0.841161	+	0.540785i	$0.818127\pi$
$242$	10.4769	0.673483
$243$	−9.36747	−0.600924
$244$	12.5819	0.805473
$245$	−16.9886	−1.08536
$246$	−0.458731	−0.0292476
$247$	33.4270	2.12691
$248$	−0.258193	−0.0163953
$249$	35.0280	2.21981
$250$	1.00000	0.0632456
$251$	7.04319	0.444562	0.222281	−	0.974983i	$-0.428650\pi$
$251$	7.04319	0.444562	0.222281	+	0.974983i	$0.428650\pi$
$252$	−26.4566	−1.66661
$253$	1.26955	0.0798162
$254$	15.5517	0.975800
$255$	20.2849	1.27029
$256$	1.00000	0.0625000
$257$	−16.0094	−0.998642	−0.499321	−	0.866417i	$-0.666417\pi$
$257$	−16.0094	−0.998642	−0.499321	+	0.866417i	$0.666417\pi$
$258$	−21.2004	−1.31988
$259$	−43.6805	−2.71418
$260$	−5.93703	−0.368199
$261$	−34.4689	−2.13357
$262$	−14.9136	−0.921367
$263$	−2.81417	−0.173529	−0.0867647	−	0.996229i	$-0.527653\pi$
$263$	−2.81417	−0.173529	−0.0867647	+	0.996229i	$0.527653\pi$
$264$	2.09633	0.129020
$265$	−2.96698	−0.182260
$266$	27.5759	1.69079
$267$	20.2587	1.23981
$268$	9.21549	0.562926
$269$	6.48393	0.395332	0.197666	−	0.980269i	$-0.436664\pi$
$269$	6.48393	0.395332	0.197666	+	0.980269i	$0.436664\pi$
$270$	6.96155	0.423666
$271$	25.3095	1.53744	0.768720	−	0.639585i	$-0.220894\pi$
$271$	25.3095	1.53744	0.768720	+	0.639585i	$0.220894\pi$
$272$	−6.99825	−0.424331
$273$	−84.2860	−5.10122
$274$	−0.248336	−0.0150025
$275$	−0.723228	−0.0436123
$276$	−5.08815	−0.306271
$277$	−9.66722	−0.580847	−0.290424	−	0.956898i	$-0.593796\pi$
$277$	−9.66722	−0.580847	−0.290424	+	0.956898i	$0.593796\pi$
$278$	0.399481	0.0239593
$279$	1.39468	0.0834976
$280$	−4.89781	−0.292700
$281$	−1.76642	−0.105376	−0.0526880	−	0.998611i	$-0.516779\pi$
$281$	−1.76642	−0.105376	−0.0526880	+	0.998611i	$0.516779\pi$
$282$	−26.4486	−1.57499
$283$	−9.29558	−0.552565	−0.276282	−	0.961077i	$-0.589103\pi$
$283$	−9.29558	−0.552565	−0.276282	+	0.961077i	$0.589103\pi$
$284$	−7.78284	−0.461826
$285$	−16.3197	−0.966696
$286$	4.29383	0.253899
$287$	−0.775132	−0.0457546
$288$	−5.40172	−0.318299
$289$	31.9755	1.88091
$290$	−6.38111	−0.374712
$291$	48.1504	2.82263
$292$	0.261257	0.0152889
$293$	0.445050	0.0260001	0.0130000	−	0.999915i	$-0.495862\pi$
$293$	0.445050	0.0260001	0.0130000	+	0.999915i	$0.495862\pi$
$294$	−49.2425	−2.87188
$295$	4.56324	0.265682
$296$	−8.91838	−0.518370
$297$	−5.03479	−0.292148
$298$	7.06839	0.409461
$299$	−10.4219	−0.602712
$300$	2.89857	0.167349
$301$	−35.8230	−2.06481
$302$	3.32388	0.191268
$303$	−6.83353	−0.392576
$304$	5.63026	0.322917
$305$	−12.5819	−0.720437
$306$	37.8025	2.16103
$307$	13.2442	0.755886	0.377943	−	0.925829i	$-0.376631\pi$
$307$	13.2442	0.755886	0.377943	+	0.925829i	$0.376631\pi$
$308$	3.54224	0.201838
$309$	2.35700	0.134085
$310$	0.258193	0.0146644
$311$	−28.5873	−1.62104	−0.810519	−	0.585713i	$-0.800815\pi$
$311$	−28.5873	−1.62104	−0.810519	+	0.585713i	$0.800815\pi$
$312$	−17.2089	−0.974263
$313$	28.6984	1.62213	0.811064	−	0.584957i	$-0.198889\pi$
$313$	28.6984	1.62213	0.811064	+	0.584957i	$0.198889\pi$
$314$	−16.8380	−0.950221
$315$	26.4566	1.49066
$316$	−4.33300	−0.243750
$317$	−22.7840	−1.27968	−0.639840	−	0.768509i	$-0.720999\pi$
$317$	−22.7840	−1.27968	−0.639840	+	0.768509i	$0.720999\pi$
$318$	−8.60001	−0.482264
$319$	4.61500	0.258390
$320$	−1.00000	−0.0559017
$321$	41.7034	2.32765
$322$	−8.59762	−0.479126
$323$	−39.4019	−2.19238
$324$	3.97340	0.220744
$325$	5.93703	0.329327
$326$	−2.02298	−0.112043
$327$	−53.0312	−2.93263
$328$	−0.158261	−0.00873850
$329$	−44.6911	−2.46390
$330$	−2.09633	−0.115399
$331$	26.5717	1.46051	0.730257	−	0.683173i	$-0.239401\pi$
$331$	26.5717	1.46051	0.730257	+	0.683173i	$0.239401\pi$
$332$	12.0846	0.663227
$333$	48.1746	2.63995
$334$	−10.3733	−0.567601
$335$	−9.21549	−0.503496
$336$	−14.1967	−0.774491
$337$	−3.22487	−0.175670	−0.0878349	−	0.996135i	$-0.527995\pi$
$337$	−3.22487	−0.175670	−0.0878349	+	0.996135i	$0.527995\pi$
$338$	−22.2484	−1.21015
$339$	−5.58389	−0.303275
$340$	6.99825	0.379533
$341$	−0.186732	−0.0101121
$342$	−30.4131	−1.64455
$343$	−48.9220	−2.64154
$344$	−7.31409	−0.394349
$345$	5.08815	0.273937
$346$	−20.0330	−1.07698
$347$	12.4161	0.666531	0.333265	−	0.942833i	$-0.391849\pi$
$347$	12.4161	0.666531	0.333265	+	0.942833i	$0.391849\pi$
$348$	−18.4961	−0.991495
$349$	−28.2704	−1.51328	−0.756641	−	0.653831i	$-0.773161\pi$
$349$	−28.2704	−1.51328	−0.756641	+	0.653831i	$0.773161\pi$
$350$	4.89781	0.261799
$351$	41.3309	2.20608
$352$	0.723228	0.0385482
$353$	20.8438	1.10941	0.554703	−	0.832049i	$-0.312832\pi$
$353$	20.8438	1.10941	0.554703	+	0.832049i	$0.312832\pi$
$354$	13.2269	0.703001
$355$	7.78284	0.413070
$356$	6.98919	0.370426
$357$	99.3517	5.25825
$358$	−10.4350	−0.551507
$359$	16.1993	0.854964	0.427482	−	0.904024i	$-0.359401\pi$
$359$	16.1993	0.854964	0.427482	+	0.904024i	$0.359401\pi$
$360$	5.40172	0.284695
$361$	12.6998	0.668411
$362$	5.68707	0.298906
$363$	−30.3682	−1.59392
$364$	−29.0785	−1.52413
$365$	−0.261257	−0.0136748
$366$	−36.4695	−1.90629
$367$	−15.3554	−0.801545	−0.400773	−	0.916178i	$-0.631258\pi$
$367$	−15.3554	−0.801545	−0.400773	+	0.916178i	$0.631258\pi$
$368$	−1.75540	−0.0915065
$369$	0.854881	0.0445033
$370$	8.91838	0.463645
$371$	−14.5317	−0.754449
$372$	0.748390	0.0388022
$373$	−15.5779	−0.806595	−0.403297	−	0.915069i	$-0.632136\pi$
$373$	−15.5779	−0.806595	−0.403297	+	0.915069i	$0.632136\pi$
$374$	−5.06133	−0.261715
$375$	−2.89857	−0.149682
$376$	−9.12471	−0.470571
$377$	−37.8848	−1.95117
$378$	34.0964	1.75373
$379$	37.9027	1.94693	0.973465	−	0.228837i	$-0.0734924\pi$
$379$	37.9027	1.94693	0.973465	+	0.228837i	$0.0734924\pi$
$380$	−5.63026	−0.288826
$381$	−45.0777	−2.30940
$382$	13.6015	0.695914
$383$	−6.53162	−0.333750	−0.166875	−	0.985978i	$-0.553368\pi$
$383$	−6.53162	−0.333750	−0.166875	+	0.985978i	$0.553368\pi$
$384$	−2.89857	−0.147917
$385$	−3.54224	−0.180529
$386$	10.4777	0.533300
$387$	39.5086	2.00834
$388$	16.6118	0.843334
$389$	15.9126	0.806799	0.403399	−	0.915024i	$-0.367829\pi$
$389$	15.9126	0.806799	0.403399	+	0.915024i	$0.367829\pi$
$390$	17.2089	0.871407
$391$	12.2847	0.621265
$392$	−16.9886	−0.858052
$393$	43.2282	2.18058
$394$	11.9722	0.603151
$395$	4.33300	0.218017
$396$	−3.90667	−0.196318
$397$	−31.7228	−1.59212	−0.796060	−	0.605217i	$-0.793086\pi$
$397$	−31.7228	−1.59212	−0.796060	+	0.605217i	$0.793086\pi$
$398$	7.46525	0.374199
$399$	−79.9308	−4.00155
$400$	1.00000	0.0500000
$401$	1.00000	0.0499376
$401$	1.00000	0.0499376
$402$	−26.7118	−1.33226
$403$	1.53290	0.0763591
$404$	−2.35755	−0.117292
$405$	−3.97340	−0.197440
$406$	−31.2535	−1.55108
$407$	−6.45002	−0.319716
$408$	20.2849	1.00425
$409$	12.5355	0.619841	0.309921	−	0.950762i	$-0.399697\pi$
$409$	12.5355	0.619841	0.309921	+	0.950762i	$0.399697\pi$
$410$	0.158261	0.00781595
$411$	0.719821	0.0355061
$412$	0.813159	0.0400615
$413$	22.3499	1.09977
$414$	9.48217	0.466023
$415$	−12.0846	−0.593208
$416$	−5.93703	−0.291087
$417$	−1.15792	−0.0567037
$418$	4.07196	0.199166
$419$	−16.0369	−0.783455	−0.391727	−	0.920081i	$-0.628122\pi$
$419$	−16.0369	−0.783455	−0.391727	+	0.920081i	$0.628122\pi$
$420$	14.1967	0.692726
$421$	5.36025	0.261242	0.130621	−	0.991432i	$-0.458303\pi$
$421$	5.36025	0.261242	0.130621	+	0.991432i	$0.458303\pi$
$422$	14.4591	0.703860
$423$	49.2891	2.39652
$424$	−2.96698	−0.144089
$425$	−6.99825	−0.339465
$426$	22.5591	1.09299
$427$	−61.6237	−2.98218
$428$	14.3876	0.695449
$429$	−12.4460	−0.600897
$430$	7.31409	0.352717
$431$	−18.4728	−0.889803	−0.444902	−	0.895579i	$-0.646761\pi$
$431$	−18.4728	−0.889803	−0.444902	+	0.895579i	$0.646761\pi$
$432$	6.96155	0.334938
$433$	−8.35003	−0.401277	−0.200638	−	0.979665i	$-0.564302\pi$
$433$	−8.35003	−0.401277	−0.200638	+	0.979665i	$0.564302\pi$
$434$	1.26458	0.0607018
$435$	18.4961	0.886820
$436$	−18.2956	−0.876203
$437$	−9.88335	−0.472785
$438$	−0.757272	−0.0361838
$439$	9.10825	0.434713	0.217357	−	0.976092i	$-0.430257\pi$
$439$	9.10825	0.434713	0.217357	+	0.976092i	$0.430257\pi$
$440$	−0.723228	−0.0344786
$441$	91.7674	4.36987
$442$	41.5488	1.97628
$443$	−30.2049	−1.43508	−0.717538	−	0.696519i	$-0.754731\pi$
$443$	−30.2049	−1.43508	−0.717538	+	0.696519i	$0.754731\pi$
$444$	25.8506	1.22681
$445$	−6.98919	−0.331319
$446$	−19.1323	−0.905941
$447$	−20.4882	−0.969060
$448$	−4.89781	−0.231400
$449$	−4.20296	−0.198350	−0.0991749	−	0.995070i	$-0.531620\pi$
$449$	−4.20296	−0.198350	−0.0991749	+	0.995070i	$0.531620\pi$
$450$	−5.40172	−0.254639
$451$	−0.114459	−0.00538965
$452$	−1.92643	−0.0906115
$453$	−9.63450	−0.452669
$454$	−27.0608	−1.27003
$455$	29.0785	1.36322
$456$	−16.3197	−0.764240
$457$	−7.48558	−0.350161	−0.175080	−	0.984554i	$-0.556019\pi$
$457$	−7.48558	−0.350161	−0.175080	+	0.984554i	$0.556019\pi$
$458$	−22.0577	−1.03069
$459$	−48.7186	−2.27399
$460$	1.75540	0.0818459
$461$	15.5848	0.725855	0.362927	−	0.931817i	$-0.381777\pi$
$461$	15.5848	0.725855	0.362927	+	0.931817i	$0.381777\pi$
$462$	−10.2674	−0.477684
$463$	−9.63084	−0.447583	−0.223792	−	0.974637i	$-0.571843\pi$
$463$	−9.63084	−0.447583	−0.223792	+	0.974637i	$0.571843\pi$
$464$	−6.38111	−0.296235
$465$	−0.748390	−0.0347058
$466$	1.66338	0.0770546
$467$	9.13655	0.422789	0.211395	−	0.977401i	$-0.432199\pi$
$467$	9.13655	0.422789	0.211395	+	0.977401i	$0.432199\pi$
$468$	32.0702	1.48244
$469$	−45.1357	−2.08418
$470$	9.12471	0.420891
$471$	48.8060	2.24886
$472$	4.56324	0.210040
$473$	−5.28976	−0.243223
$474$	12.5595	0.576878
$475$	5.63026	0.258334
$476$	34.2761	1.57104
$477$	16.0268	0.733816
$478$	−10.1373	−0.463668
$479$	13.1942	0.602859	0.301430	−	0.953488i	$-0.402536\pi$
$479$	13.1942	0.602859	0.301430	+	0.953488i	$0.402536\pi$
$480$	2.89857	0.132301
$481$	52.9487	2.41425
$482$	26.1166	1.18958
$483$	24.9208	1.13394
$484$	−10.4769	−0.476225
$485$	−16.6118	−0.754301
$486$	9.36747	0.424917
$487$	9.53652	0.432141	0.216071	−	0.976378i	$-0.430676\pi$
$487$	9.53652	0.432141	0.216071	+	0.976378i	$0.430676\pi$
$488$	−12.5819	−0.569555
$489$	5.86376	0.265168
$490$	16.9886	0.767465
$491$	−25.8252	−1.16547	−0.582737	−	0.812661i	$-0.698018\pi$
$491$	−25.8252	−1.16547	−0.582737	+	0.812661i	$0.698018\pi$
$492$	0.458731	0.0206812
$493$	44.6566	2.01123
$494$	−33.4270	−1.50395
$495$	3.90667	0.175592
$496$	0.258193	0.0115932
$497$	38.1189	1.70986
$498$	−35.0280	−1.56964
$499$	10.9291	0.489253	0.244626	−	0.969617i	$-0.421335\pi$
$499$	10.9291	0.489253	0.244626	+	0.969617i	$0.421335\pi$
$500$	−1.00000	−0.0447214
$501$	30.0677	1.34333
$502$	−7.04319	−0.314353
$503$	31.8967	1.42220	0.711101	−	0.703090i	$-0.248197\pi$
$503$	31.8967	1.42220	0.711101	+	0.703090i	$0.248197\pi$
$504$	26.4566	1.17847
$505$	2.35755	0.104910
$506$	−1.26955	−0.0564386
$507$	64.4884	2.86403
$508$	−15.5517	−0.689995
$509$	−6.04386	−0.267889	−0.133945	−	0.990989i	$-0.542764\pi$
$509$	−6.04386	−0.267889	−0.133945	+	0.990989i	$0.542764\pi$
$510$	−20.2849	−0.898231
$511$	−1.27959	−0.0566056
$512$	−1.00000	−0.0441942
$513$	39.1953	1.73052
$514$	16.0094	0.706146
$515$	−0.813159	−0.0358321
$516$	21.2004	0.933296
$517$	−6.59925	−0.290235
$518$	43.6805	1.91921
$519$	58.0672	2.54887
$520$	5.93703	0.260356
$521$	41.3123	1.80993	0.904963	−	0.425491i	$-0.139899\pi$
$521$	41.3123	1.80993	0.904963	+	0.425491i	$0.139899\pi$
$522$	34.4689	1.50866
$523$	−43.5191	−1.90296	−0.951479	−	0.307713i	$-0.900436\pi$
$523$	−43.5191	−1.90296	−0.951479	+	0.307713i	$0.900436\pi$
$524$	14.9136	0.651505
$525$	−14.1967	−0.619593
$526$	2.81417	0.122704
$527$	−1.80690	−0.0787097
$528$	−2.09633	−0.0912310
$529$	−19.9186	−0.866025
$530$	2.96698	0.128877
$531$	−24.6494	−1.06969
$532$	−27.5759	−1.19557
$533$	0.939600	0.0406986
$534$	−20.2587	−0.876678
$535$	−14.3876	−0.622028
$536$	−9.21549	−0.398049
$537$	30.2466	1.30524
$538$	−6.48393	−0.279542
$539$	−12.2866	−0.529221
$540$	−6.96155	−0.299577
$541$	5.29080	0.227469	0.113735	−	0.993511i	$-0.463719\pi$
$541$	5.29080	0.227469	0.113735	+	0.993511i	$0.463719\pi$
$542$	−25.3095	−1.08713
$543$	−16.4844	−0.707412
$544$	6.99825	0.300047
$545$	18.2956	0.783699
$546$	84.2860	3.60711
$547$	−18.2573	−0.780626	−0.390313	−	0.920682i	$-0.627633\pi$
$547$	−18.2573	−0.780626	−0.390313	+	0.920682i	$0.627633\pi$
$548$	0.248336	0.0106084
$549$	67.9638	2.90063
$550$	0.723228	0.0308386
$551$	−35.9273	−1.53055
$552$	5.08815	0.216566
$553$	21.2222	0.902461
$554$	9.66722	0.410721
$555$	−25.8506	−1.09730
$556$	−0.399481	−0.0169418
$557$	−23.4107	−0.991945	−0.495973	−	0.868338i	$-0.665188\pi$
$557$	−23.4107	−0.991945	−0.495973	+	0.868338i	$0.665188\pi$
$558$	−1.39468	−0.0590417
$559$	43.4240	1.83664
$560$	4.89781	0.206970
$561$	14.6706	0.619394
$562$	1.76642	0.0745120
$563$	−8.54439	−0.360103	−0.180052	−	0.983657i	$-0.557626\pi$
$563$	−8.54439	−0.360103	−0.180052	+	0.983657i	$0.557626\pi$
$564$	26.4486	1.11369
$565$	1.92643	0.0810454
$566$	9.29558	0.390722
$567$	−19.4609	−0.817283
$568$	7.78284	0.326561
$569$	19.1250	0.801761	0.400881	−	0.916130i	$-0.368704\pi$
$569$	19.1250	0.801761	0.400881	+	0.916130i	$0.368704\pi$
$570$	16.3197	0.683557
$571$	−0.0558707	−0.00233812	−0.00116906	−	0.999999i	$-0.500372\pi$
$571$	−0.0558707	−0.00233812	−0.00116906	+	0.999999i	$0.500372\pi$
$572$	−4.29383	−0.179534
$573$	−39.4250	−1.64700
$574$	0.775132	0.0323534
$575$	−1.75540	−0.0732052
$576$	5.40172	0.225072
$577$	31.5021	1.31145	0.655725	−	0.755000i	$-0.272363\pi$
$577$	31.5021	1.31145	0.655725	+	0.755000i	$0.272363\pi$
$578$	−31.9755	−1.33000
$579$	−30.3703	−1.26215
$580$	6.38111	0.264961
$581$	−59.1879	−2.45553
$582$	−48.1504	−1.99590
$583$	−2.14580	−0.0888701
$584$	−0.261257	−0.0108109
$585$	−32.0702	−1.32594
$586$	−0.445050	−0.0183848
$587$	−19.3243	−0.797599	−0.398800	−	0.917038i	$-0.630573\pi$
$587$	−19.3243	−0.797599	−0.398800	+	0.917038i	$0.630573\pi$
$588$	49.2425	2.03073
$589$	1.45369	0.0598984
$590$	−4.56324	−0.187866
$591$	−34.7023	−1.42746
$592$	8.91838	0.366543
$593$	12.1740	0.499925	0.249963	−	0.968255i	$-0.419582\pi$
$593$	12.1740	0.499925	0.249963	+	0.968255i	$0.419582\pi$
$594$	5.03479	0.206580
$595$	−34.2761	−1.40518
$596$	−7.06839	−0.289533
$597$	−21.6386	−0.885607
$598$	10.4219	0.426182
$599$	−17.1563	−0.700989	−0.350495	−	0.936565i	$-0.613987\pi$
$599$	−17.1563	−0.700989	−0.350495	+	0.936565i	$0.613987\pi$
$600$	−2.89857	−0.118334
$601$	3.45428	0.140903	0.0704515	−	0.997515i	$-0.477556\pi$
$601$	3.45428	0.140903	0.0704515	+	0.997515i	$0.477556\pi$
$602$	35.8230	1.46004
$603$	49.7795	2.02718
$604$	−3.32388	−0.135247
$605$	10.4769	0.425948
$606$	6.83353	0.277593
$607$	−28.7943	−1.16872	−0.584361	−	0.811494i	$-0.698655\pi$
$607$	−28.7943	−1.16872	−0.584361	+	0.811494i	$0.698655\pi$
$608$	−5.63026	−0.228337
$609$	90.5904	3.67091
$610$	12.5819	0.509426
$611$	54.1737	2.19163
$612$	−37.8025	−1.52808
$613$	6.71092	0.271052	0.135526	−	0.990774i	$-0.456728\pi$
$613$	6.71092	0.271052	0.135526	+	0.990774i	$0.456728\pi$
$614$	−13.2442	−0.534492
$615$	−0.458731	−0.0184978
$616$	−3.54224	−0.142721
$617$	30.7936	1.23971	0.619853	−	0.784718i	$-0.287192\pi$
$617$	30.7936	1.23971	0.619853	+	0.784718i	$0.287192\pi$
$618$	−2.35700	−0.0948125
$619$	−26.1804	−1.05228	−0.526140	−	0.850398i	$-0.676361\pi$
$619$	−26.1804	−1.05228	−0.526140	+	0.850398i	$0.676361\pi$
$620$	−0.258193	−0.0103693
$621$	−12.2203	−0.490384
$622$	28.5873	1.14625
$623$	−34.2317	−1.37147
$624$	17.2089	0.688908
$625$	1.00000	0.0400000
$626$	−28.6984	−1.14702
$627$	−11.8029	−0.471361
$628$	16.8380	0.671907
$629$	−62.4130	−2.48857
$630$	−26.4566	−1.05406
$631$	−7.91647	−0.315150	−0.157575	−	0.987507i	$-0.550368\pi$
$631$	−7.91647	−0.315150	−0.157575	+	0.987507i	$0.550368\pi$
$632$	4.33300	0.172358
$633$	−41.9108	−1.66581
$634$	22.7840	0.904870
$635$	15.5517	0.617150
$636$	8.60001	0.341012
$637$	100.862	3.99628
$638$	−4.61500	−0.182709
$639$	−42.0407	−1.66310
$640$	1.00000	0.0395285
$641$	−29.6847	−1.17247	−0.586237	−	0.810140i	$-0.699391\pi$
$641$	−29.6847	−1.17247	−0.586237	+	0.810140i	$0.699391\pi$
$642$	−41.7034	−1.64590
$643$	3.36646	0.132760	0.0663801	−	0.997794i	$-0.478855\pi$
$643$	3.36646	0.132760	0.0663801	+	0.997794i	$0.478855\pi$
$644$	8.59762	0.338794
$645$	−21.2004	−0.834765
$646$	39.4019	1.55025
$647$	45.5949	1.79252	0.896261	−	0.443527i	$-0.146273\pi$
$647$	45.5949	1.79252	0.896261	+	0.443527i	$0.146273\pi$
$648$	−3.97340	−0.156090
$649$	3.30027	0.129547
$650$	−5.93703	−0.232870
$651$	−3.66547	−0.143661
$652$	2.02298	0.0792261
$653$	−26.2871	−1.02870	−0.514348	−	0.857582i	$-0.671966\pi$
$653$	−26.2871	−1.02870	−0.514348	+	0.857582i	$0.671966\pi$
$654$	53.0312	2.07369
$655$	−14.9136	−0.582724
$656$	0.158261	0.00617905
$657$	1.41124	0.0550576
$658$	44.6911	1.74224
$659$	8.61373	0.335543	0.167772	−	0.985826i	$-0.446343\pi$
$659$	8.61373	0.335543	0.167772	+	0.985826i	$0.446343\pi$
$660$	2.09633	0.0815995
$661$	−23.0960	−0.898331	−0.449166	−	0.893449i	$-0.648279\pi$
$661$	−23.0960	−0.898331	−0.449166	+	0.893449i	$0.648279\pi$
$662$	−26.5717	−1.03274
$663$	−120.432	−4.67720
$664$	−12.0846	−0.468972
$665$	27.5759	1.06935
$666$	−48.1746	−1.86673
$667$	11.2014	0.433720
$668$	10.3733	0.401354
$669$	55.4564	2.14407
$670$	9.21549	0.356026
$671$	−9.09958	−0.351285
$672$	14.1967	0.547648
$673$	−42.5909	−1.64176	−0.820880	−	0.571101i	$-0.806516\pi$
$673$	−42.5909	−1.64176	−0.820880	+	0.571101i	$0.806516\pi$
$674$	3.22487	0.124217
$675$	6.96155	0.267950
$676$	22.2484	0.855706
$677$	−51.8064	−1.99108	−0.995541	−	0.0943260i	$-0.969930\pi$
$677$	−51.8064	−1.99108	−0.995541	+	0.0943260i	$0.969930\pi$
$678$	5.58389	0.214448
$679$	−81.3613	−3.12236
$680$	−6.99825	−0.268370
$681$	78.4376	3.00574
$682$	0.186732	0.00715035
$683$	18.9565	0.725350	0.362675	−	0.931916i	$-0.381863\pi$
$683$	18.9565	0.725350	0.362675	+	0.931916i	$0.381863\pi$
$684$	30.4131	1.16287
$685$	−0.248336	−0.00948844
$686$	48.9220	1.86785
$687$	63.9359	2.43931
$688$	7.31409	0.278847
$689$	17.6151	0.671080
$690$	−5.08815	−0.193703
$691$	−24.1062	−0.917043	−0.458521	−	0.888683i	$-0.651621\pi$
$691$	−24.1062	−0.917043	−0.458521	+	0.888683i	$0.651621\pi$
$692$	20.0330	0.761542
$693$	19.1342	0.726846
$694$	−12.4161	−0.471308
$695$	0.399481	0.0151532
$696$	18.4961	0.701093
$697$	−1.10755	−0.0419514
$698$	28.2704	1.07005
$699$	−4.82143	−0.182363
$700$	−4.89781	−0.185120
$701$	−20.4041	−0.770653	−0.385327	−	0.922780i	$-0.625911\pi$
$701$	−20.4041	−0.770653	−0.385327	+	0.922780i	$0.625911\pi$
$702$	−41.3309	−1.55994
$703$	50.2128	1.89381
$704$	−0.723228	−0.0272577
$705$	−26.4486	−0.996113
$706$	−20.8438	−0.784468
$707$	11.5468	0.434263
$708$	−13.2269	−0.497097
$709$	−7.02864	−0.263966	−0.131983	−	0.991252i	$-0.542134\pi$
$709$	−7.02864	−0.263966	−0.131983	+	0.991252i	$0.542134\pi$
$710$	−7.78284	−0.292085
$711$	−23.4057	−0.877781
$712$	−6.98919	−0.261931
$713$	−0.453232	−0.0169737
$714$	−99.3517	−3.71814
$715$	4.29383	0.160580
$716$	10.4350	0.389975
$717$	29.3836	1.09735
$718$	−16.1993	−0.604551
$719$	25.4249	0.948187	0.474094	−	0.880474i	$-0.342776\pi$
$719$	25.4249	0.948187	0.474094	+	0.880474i	$0.342776\pi$
$720$	−5.40172	−0.201310
$721$	−3.98270	−0.148324
$722$	−12.6998	−0.472638
$723$	−75.7010	−2.81535
$724$	−5.68707	−0.211358
$725$	−6.38111	−0.236988
$726$	30.3682	1.12707
$727$	33.3469	1.23677	0.618384	−	0.785876i	$-0.287788\pi$
$727$	33.3469	1.23677	0.618384	+	0.785876i	$0.287788\pi$
$728$	29.0785	1.07772
$729$	−39.0725	−1.44713
$730$	0.261257	0.00966955
$731$	−51.1858	−1.89318
$732$	36.4695	1.34795
$733$	4.98176	0.184005	0.0920027	−	0.995759i	$-0.470673\pi$
$733$	4.98176	0.184005	0.0920027	+	0.995759i	$0.470673\pi$
$734$	15.3554	0.566778
$735$	−49.2425	−1.81634
$736$	1.75540	0.0647049
$737$	−6.66491	−0.245505
$738$	−0.854881	−0.0314686
$739$	16.1215	0.593039	0.296520	−	0.955027i	$-0.404174\pi$
$739$	16.1215	0.593039	0.296520	+	0.955027i	$0.404174\pi$
$740$	−8.91838	−0.327846
$741$	96.8906	3.55937
$742$	14.5317	0.533476
$743$	44.2029	1.62165	0.810823	−	0.585291i	$-0.199020\pi$
$743$	44.2029	1.62165	0.810823	+	0.585291i	$0.199020\pi$
$744$	−0.748390	−0.0274373
$745$	7.06839	0.258966
$746$	15.5779	0.570349
$747$	65.2774	2.38838
$748$	5.06133	0.185061
$749$	−70.4675	−2.57483
$750$	2.89857	0.105841
$751$	3.45459	0.126060	0.0630298	−	0.998012i	$-0.479924\pi$
$751$	3.45459	0.126060	0.0630298	+	0.998012i	$0.479924\pi$
$752$	9.12471	0.332744
$753$	20.4152	0.743971
$754$	37.8848	1.37968
$755$	3.32388	0.120968
$756$	−34.0964	−1.24007
$757$	−8.56891	−0.311442	−0.155721	−	0.987801i	$-0.549770\pi$
$757$	−8.56891	−0.311442	−0.155721	+	0.987801i	$0.549770\pi$
$758$	−37.9027	−1.37669
$759$	3.67989	0.133572
$760$	5.63026	0.204231
$761$	14.2865	0.517886	0.258943	−	0.965893i	$-0.416626\pi$
$761$	14.2865	0.517886	0.258943	+	0.965893i	$0.416626\pi$
$762$	45.0777	1.63299
$763$	89.6086	3.24405
$764$	−13.6015	−0.492085
$765$	37.8025	1.36675
$766$	6.53162	0.235997
$767$	−27.0921	−0.978240
$768$	2.89857	0.104593
$769$	−52.2316	−1.88352	−0.941759	−	0.336288i	$-0.890828\pi$
$769$	−52.2316	−1.88352	−0.941759	+	0.336288i	$0.890828\pi$
$770$	3.54224	0.127653
$771$	−46.4045	−1.67122
$772$	−10.4777	−0.377100
$773$	51.8628	1.86538	0.932688	−	0.360684i	$-0.117457\pi$
$773$	51.8628	1.86538	0.932688	+	0.360684i	$0.117457\pi$
$774$	−39.5086	−1.42011
$775$	0.258193	0.00927456
$776$	−16.6118	−0.596327
$777$	−126.611	−4.54215
$778$	−15.9126	−0.570493
$779$	0.891050	0.0319252
$780$	−17.2089	−0.616178
$781$	5.62877	0.201413
$782$	−12.2847	−0.439301
$783$	−44.4224	−1.58753
$784$	16.9886	0.606734
$785$	−16.8380	−0.600972
$786$	−43.2282	−1.54190
$787$	33.1181	1.18053	0.590266	−	0.807208i	$-0.299023\pi$
$787$	33.1181	1.18053	0.590266	+	0.807208i	$0.299023\pi$
$788$	−11.9722	−0.426492
$789$	−8.15708	−0.290400
$790$	−4.33300	−0.154161
$791$	9.43528	0.335480
$792$	3.90667	0.138818
$793$	74.6991	2.65264
$794$	31.7228	1.12580
$795$	−8.60001	−0.305011
$796$	−7.46525	−0.264599
$797$	−22.9894	−0.814325	−0.407162	−	0.913356i	$-0.633482\pi$
$797$	−22.9894	−0.814325	−0.407162	+	0.913356i	$0.633482\pi$
$798$	79.9308	2.82952
$799$	−63.8570	−2.25910
$800$	−1.00000	−0.0353553
$801$	37.7536	1.33396
$802$	−1.00000	−0.0353112
$803$	−0.188948	−0.00666784
$804$	26.7118	0.942051
$805$	−8.59762	−0.303026
$806$	−1.53290	−0.0539941
$807$	18.7941	0.661585
$808$	2.35755	0.0829383
$809$	−20.7351	−0.729007	−0.364504	−	0.931202i	$-0.618761\pi$
$809$	−20.7351	−0.729007	−0.364504	+	0.931202i	$0.618761\pi$
$810$	3.97340	0.139611
$811$	1.07877	0.0378806	0.0189403	−	0.999821i	$-0.493971\pi$
$811$	1.07877	0.0378806	0.0189403	+	0.999821i	$0.493971\pi$
$812$	31.2535	1.09678
$813$	73.3613	2.57289
$814$	6.45002	0.226073
$815$	−2.02298	−0.0708620
$816$	−20.2849	−0.710114
$817$	41.1802	1.44071
$818$	−12.5355	−0.438294
$819$	−157.074	−5.48860
$820$	−0.158261	−0.00552671
$821$	−20.5032	−0.715567	−0.357783	−	0.933805i	$-0.616467\pi$
$821$	−20.5032	−0.715567	−0.357783	+	0.933805i	$0.616467\pi$
$822$	−0.719821	−0.0251066
$823$	−10.8611	−0.378594	−0.189297	−	0.981920i	$-0.560621\pi$
$823$	−10.8611	−0.378594	−0.189297	+	0.981920i	$0.560621\pi$
$824$	−0.813159	−0.0283277
$825$	−2.09633	−0.0729848
$826$	−22.3499	−0.777653
$827$	−33.9104	−1.17918	−0.589590	−	0.807703i	$-0.700711\pi$
$827$	−33.9104	−1.17918	−0.589590	+	0.807703i	$0.700711\pi$
$828$	−9.48217	−0.329528
$829$	−43.2997	−1.50386	−0.751930	−	0.659243i	$-0.770877\pi$
$829$	−43.2997	−1.50386	−0.751930	+	0.659243i	$0.770877\pi$
$830$	12.0846	0.419462
$831$	−28.0211	−0.972043
$832$	5.93703	0.205830
$833$	−118.890	−4.11930
$834$	1.15792	0.0400956
$835$	−10.3733	−0.358982
$836$	−4.07196	−0.140832
$837$	1.79742	0.0621280
$838$	16.0369	0.553986
$839$	−44.0993	−1.52248	−0.761239	−	0.648472i	$-0.775408\pi$
$839$	−44.0993	−1.52248	−0.761239	+	0.648472i	$0.775408\pi$
$840$	−14.1967	−0.489831
$841$	11.7185	0.404087
$842$	−5.36025	−0.184726
$843$	−5.12010	−0.176346
$844$	−14.4591	−0.497704
$845$	−22.2484	−0.765367
$846$	−49.2891	−1.69459
$847$	51.3141	1.76317
$848$	2.96698	0.101887
$849$	−26.9439	−0.924712
$850$	6.99825	0.240038
$851$	−15.6553	−0.536658
$852$	−22.5591	−0.772862
$853$	19.8460	0.679513	0.339757	−	0.940513i	$-0.389655\pi$
$853$	19.8460	0.679513	0.339757	+	0.940513i	$0.389655\pi$
$854$	61.6237	2.10872
$855$	−30.4131	−1.04010
$856$	−14.3876	−0.491756
$857$	3.07591	0.105071	0.0525356	−	0.998619i	$-0.483270\pi$
$857$	3.07591	0.105071	0.0525356	+	0.998619i	$0.483270\pi$
$858$	12.4460	0.424898
$859$	−8.44448	−0.288122	−0.144061	−	0.989569i	$-0.546016\pi$
$859$	−8.44448	−0.288122	−0.144061	+	0.989569i	$0.546016\pi$
$860$	−7.31409	−0.249408
$861$	−2.24678	−0.0765699
$862$	18.4728	0.629186
$863$	30.1685	1.02695	0.513473	−	0.858106i	$-0.328359\pi$
$863$	30.1685	1.02695	0.513473	+	0.858106i	$0.328359\pi$
$864$	−6.96155	−0.236837
$865$	−20.0330	−0.681144
$866$	8.35003	0.283746
$867$	92.6831	3.14768
$868$	−1.26458	−0.0429226
$869$	3.13375	0.106305
$870$	−18.4961	−0.627076
$871$	54.7127	1.85387
$872$	18.2956	0.619569
$873$	89.7320	3.03697
$874$	9.88335	0.334309
$875$	4.89781	0.165576
$876$	0.757272	0.0255858
$877$	−1.69449	−0.0572189	−0.0286094	−	0.999591i	$-0.509108\pi$
$877$	−1.69449	−0.0572189	−0.0286094	+	0.999591i	$0.509108\pi$
$878$	−9.10825	−0.307389
$879$	1.29001	0.0435109
$880$	0.723228	0.0243800
$881$	−38.3913	−1.29344	−0.646718	−	0.762730i	$-0.723859\pi$
$881$	−38.3913	−1.29344	−0.646718	+	0.762730i	$0.723859\pi$
$882$	−91.7674	−3.08997
$883$	4.02726	0.135528	0.0677641	−	0.997701i	$-0.478413\pi$
$883$	4.02726	0.135528	0.0677641	+	0.997701i	$0.478413\pi$
$884$	−41.5488	−1.39744
$885$	13.2269	0.444617
$886$	30.2049	1.01475
$887$	−57.4711	−1.92969	−0.964845	−	0.262821i	$-0.915347\pi$
$887$	−57.4711	−1.92969	−0.964845	+	0.262821i	$0.915347\pi$
$888$	−25.8506	−0.867488
$889$	76.1693	2.55464
$890$	6.98919	0.234278
$891$	−2.87367	−0.0962716
$892$	19.1323	0.640597
$893$	51.3745	1.71918
$894$	20.4882	0.685229
$895$	−10.4350	−0.348804
$896$	4.89781	0.163624
$897$	−30.2085	−1.00863
$898$	4.20296	0.140254
$899$	−1.64756	−0.0549491
$900$	5.40172	0.180057
$901$	−20.7637	−0.691738
$902$	0.114459	0.00381106
$903$	−103.836	−3.45543
$904$	1.92643	0.0640720
$905$	5.68707	0.189044
$906$	9.63450	0.320085
$907$	−21.9659	−0.729365	−0.364682	−	0.931132i	$-0.618822\pi$
$907$	−21.9659	−0.729365	−0.364682	+	0.931132i	$0.618822\pi$
$908$	27.0608	0.898044
$909$	−12.7348	−0.422387
$910$	−29.0785	−0.963942
$911$	58.9675	1.95368	0.976840	−	0.213969i	$-0.0686392\pi$
$911$	58.9675	1.95368	0.976840	+	0.213969i	$0.0686392\pi$
$912$	16.3197	0.540399
$913$	−8.73990	−0.289249
$914$	7.48558	0.247601
$915$	−36.4695	−1.20564
$916$	22.0577	0.728807
$917$	−73.0441	−2.41213
$918$	48.7186	1.60795
$919$	−50.8511	−1.67742	−0.838712	−	0.544575i	$-0.816691\pi$
$919$	−50.8511	−1.67742	−0.838712	+	0.544575i	$0.816691\pi$
$920$	−1.75540	−0.0578738
$921$	38.3893	1.26497
$922$	−15.5848	−0.513257
$923$	−46.2069	−1.52092
$924$	10.2674	0.337773
$925$	8.91838	0.293235
$926$	9.63084	0.316489
$927$	4.39246	0.144267
$928$	6.38111	0.209470
$929$	1.10986	0.0364133	0.0182066	−	0.999834i	$-0.494204\pi$
$929$	1.10986	0.0364133	0.0182066	+	0.999834i	$0.494204\pi$
$930$	0.748390	0.0245407
$931$	95.6499	3.13480
$932$	−1.66338	−0.0544858
$933$	−82.8623	−2.71279
$934$	−9.13655	−0.298957
$935$	−5.06133	−0.165523
$936$	−32.0702	−1.04825
$937$	−12.6525	−0.413338	−0.206669	−	0.978411i	$-0.566262\pi$
$937$	−12.6525	−0.413338	−0.206669	+	0.978411i	$0.566262\pi$
$938$	45.1357	1.47373
$939$	83.1843	2.71462
$940$	−9.12471	−0.297615
$941$	−17.5939	−0.573545	−0.286773	−	0.957999i	$-0.592582\pi$
$941$	−17.5939	−0.573545	−0.286773	+	0.957999i	$0.592582\pi$
$942$	−48.8060	−1.59019
$943$	−0.277811	−0.00904677
$944$	−4.56324	−0.148521
$945$	34.0964	1.10915
$946$	5.28976	0.171985
$947$	−13.8819	−0.451101	−0.225550	−	0.974232i	$-0.572418\pi$
$947$	−13.8819	−0.451101	−0.225550	+	0.974232i	$0.572418\pi$
$948$	−12.5595	−0.407914
$949$	1.55109	0.0503505
$950$	−5.63026	−0.182670
$951$	−66.0412	−2.14153
$952$	−34.2761	−1.11089
$953$	53.1664	1.72223	0.861115	−	0.508411i	$-0.169767\pi$
$953$	53.1664	1.72223	0.861115	+	0.508411i	$0.169767\pi$
$954$	−16.0268	−0.518887
$955$	13.6015	0.440135
$956$	10.1373	0.327862
$957$	13.3769	0.432414
$958$	−13.1942	−0.426286
$959$	−1.21630	−0.0392765
$960$	−2.89857	−0.0935510
$961$	−30.9333	−0.997850
$962$	−52.9487	−1.70713
$963$	77.7175	2.50441
$964$	−26.1166	−0.841161
$965$	10.4777	0.337288
$966$	−24.9208	−0.801814
$967$	−55.6657	−1.79009	−0.895043	−	0.445979i	$-0.852856\pi$
$967$	−55.6657	−1.79009	−0.895043	+	0.445979i	$0.852856\pi$
$968$	10.4769	0.336742
$969$	−114.209	−3.66893
$970$	16.6118	0.533372
$971$	−33.4093	−1.07216	−0.536078	−	0.844168i	$-0.680095\pi$
$971$	−33.4093	−1.07216	−0.536078	+	0.844168i	$0.680095\pi$
$972$	−9.36747	−0.300462
$973$	1.95658	0.0627251
$974$	−9.53652	−0.305570
$975$	17.2089	0.551126
$976$	12.5819	0.402737
$977$	45.3134	1.44970	0.724852	−	0.688905i	$-0.241908\pi$
$977$	45.3134	1.44970	0.724852	+	0.688905i	$0.241908\pi$
$978$	−5.86376	−0.187502
$979$	−5.05478	−0.161551
$980$	−16.9886	−0.542679
$981$	−98.8279	−3.15533
$982$	25.8252	0.824115
$983$	−0.464409	−0.0148123	−0.00740617	−	0.999973i	$-0.502357\pi$
$983$	−0.464409	−0.0148123	−0.00740617	+	0.999973i	$0.502357\pi$
$984$	−0.458731	−0.0146238
$985$	11.9722	0.381466
$986$	−44.6566	−1.42215
$987$	−129.540	−4.12332
$988$	33.4270	1.06346
$989$	−12.8392	−0.408261
$990$	−3.90667	−0.124162
$991$	35.1759	1.11740	0.558699	−	0.829371i	$-0.311301\pi$
$991$	35.1759	1.11740	0.558699	+	0.829371i	$0.311301\pi$
$992$	−0.258193	−0.00819763
$993$	77.0200	2.44416
$994$	−38.1189	−1.20906
$995$	7.46525	0.236664
$996$	35.0280	1.10990
$997$	15.0823	0.477663	0.238831	−	0.971061i	$-0.423236\pi$
$997$	15.0823	0.477663	0.238831	+	0.971061i	$0.423236\pi$
$998$	−10.9291	−0.345954
$999$	62.0857	1.96431

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4010.2.a.l.1.16	✓	17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4010.2.a.l.1.16	✓	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +2.89857 q^{3} +1.00000 q^{4} -1.00000 q^{5} -2.89857 q^{6} -4.89781 q^{7} -1.00000 q^{8} +5.40172 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +2.89857 q^{3} +1.00000 q^{4} -1.00000 q^{5} -2.89857 q^{6} -4.89781 q^{7} -1.00000 q^{8} +5.40172 q^{9} +1.00000 q^{10} -0.723228 q^{11} +2.89857 q^{12} +5.93703 q^{13} +4.89781 q^{14} -2.89857 q^{15} +1.00000 q^{16} -6.99825 q^{17} -5.40172 q^{18} +5.63026 q^{19} -1.00000 q^{20} -14.1967 q^{21} +0.723228 q^{22} -1.75540 q^{23} -2.89857 q^{24} +1.00000 q^{25} -5.93703 q^{26} +6.96155 q^{27} -4.89781 q^{28} -6.38111 q^{29} +2.89857 q^{30} +0.258193 q^{31} -1.00000 q^{32} -2.09633 q^{33} +6.99825 q^{34} +4.89781 q^{35} +5.40172 q^{36} +8.91838 q^{37} -5.63026 q^{38} +17.2089 q^{39} +1.00000 q^{40} +0.158261 q^{41} +14.1967 q^{42} +7.31409 q^{43} -0.723228 q^{44} -5.40172 q^{45} +1.75540 q^{46} +9.12471 q^{47} +2.89857 q^{48} +16.9886 q^{49} -1.00000 q^{50} -20.2849 q^{51} +5.93703 q^{52} +2.96698 q^{53} -6.96155 q^{54} +0.723228 q^{55} +4.89781 q^{56} +16.3197 q^{57} +6.38111 q^{58} -4.56324 q^{59} -2.89857 q^{60} +12.5819 q^{61} -0.258193 q^{62} -26.4566 q^{63} +1.00000 q^{64} -5.93703 q^{65} +2.09633 q^{66} +9.21549 q^{67} -6.99825 q^{68} -5.08815 q^{69} -4.89781 q^{70} -7.78284 q^{71} -5.40172 q^{72} +0.261257 q^{73} -8.91838 q^{74} +2.89857 q^{75} +5.63026 q^{76} +3.54224 q^{77} -17.2089 q^{78} -4.33300 q^{79} -1.00000 q^{80} +3.97340 q^{81} -0.158261 q^{82} +12.0846 q^{83} -14.1967 q^{84} +6.99825 q^{85} -7.31409 q^{86} -18.4961 q^{87} +0.723228 q^{88} +6.98919 q^{89} +5.40172 q^{90} -29.0785 q^{91} -1.75540 q^{92} +0.748390 q^{93} -9.12471 q^{94} -5.63026 q^{95} -2.89857 q^{96} +16.6118 q^{97} -16.9886 q^{98} -3.90667 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q - 17 q^{2} + 3 q^{3} + 17 q^{4} - 17 q^{5} - 3 q^{6} + 4 q^{7} - 17 q^{8} + 6 q^{9}+O(q^{10}) \) 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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