LMFDB - Embedded newform 8022.2.a.r.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8022,2,Mod(1,8022)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8022, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("8022.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8022 = 2 \cdot 3 \cdot 7 \cdot 191 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8022.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:	$64.0559925015$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} - 19x^{8} + 28x^{7} + 114x^{6} - 110x^{5} - 282x^{4} + 149x^{3} + 285x^{2} - 49x - 79 $ x^10 - 2x^9 - 19x^8 + 28x^7 + 114x^6 - 110x^5 - 282x^4 + 149x^3 + 285x^2 - 49*x - 79
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$1.48373$ of defining polynomial
Character	$\chi$	$=$	8022.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -0.483732 q^{5} -1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -0.483732 q^{5} -1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} -0.483732 q^{10} -2.89666 q^{11} -1.00000 q^{12} +0.896578 q^{13} +1.00000 q^{14} +0.483732 q^{15} +1.00000 q^{16} -4.05183 q^{17} +1.00000 q^{18} -5.49983 q^{19} -0.483732 q^{20} -1.00000 q^{21} -2.89666 q^{22} +4.14067 q^{23} -1.00000 q^{24} -4.76600 q^{25} +0.896578 q^{26} -1.00000 q^{27} +1.00000 q^{28} -4.47647 q^{29} +0.483732 q^{30} +4.99541 q^{31} +1.00000 q^{32} +2.89666 q^{33} -4.05183 q^{34} -0.483732 q^{35} +1.00000 q^{36} -5.68561 q^{37} -5.49983 q^{38} -0.896578 q^{39} -0.483732 q^{40} +9.36885 q^{41} -1.00000 q^{42} +10.0265 q^{43} -2.89666 q^{44} -0.483732 q^{45} +4.14067 q^{46} +0.591028 q^{47} -1.00000 q^{48} +1.00000 q^{49} -4.76600 q^{50} +4.05183 q^{51} +0.896578 q^{52} +9.53963 q^{53} -1.00000 q^{54} +1.40120 q^{55} +1.00000 q^{56} +5.49983 q^{57} -4.47647 q^{58} +9.44063 q^{59} +0.483732 q^{60} +5.46611 q^{61} +4.99541 q^{62} +1.00000 q^{63} +1.00000 q^{64} -0.433703 q^{65} +2.89666 q^{66} -4.26901 q^{67} -4.05183 q^{68} -4.14067 q^{69} -0.483732 q^{70} -6.49576 q^{71} +1.00000 q^{72} +7.15692 q^{73} -5.68561 q^{74} +4.76600 q^{75} -5.49983 q^{76} -2.89666 q^{77} -0.896578 q^{78} -4.52988 q^{79} -0.483732 q^{80} +1.00000 q^{81} +9.36885 q^{82} +3.92066 q^{83} -1.00000 q^{84} +1.96000 q^{85} +10.0265 q^{86} +4.47647 q^{87} -2.89666 q^{88} -0.197840 q^{89} -0.483732 q^{90} +0.896578 q^{91} +4.14067 q^{92} -4.99541 q^{93} +0.591028 q^{94} +2.66044 q^{95} -1.00000 q^{96} +2.64762 q^{97} +1.00000 q^{98} -2.89666 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 10 q^{2} - 10 q^{3} + 10 q^{4} + 8 q^{5} - 10 q^{6} + 10 q^{7} + 10 q^{8} + 10 q^{9}+O(q^{10}) $ 10 * q + 10 * q^2 - 10 * q^3 + 10 * q^4 + 8 * q^5 - 10 * q^6 + 10 * q^7 + 10 * q^8 + 10 * q^9	\( 10 q + 10 q^{2} - 10 q^{3} + 10 q^{4} + 8 q^{5} - 10 q^{6} + 10 q^{7} + 10 q^{8} + 10 q^{9} + 8 q^{10} + 4 q^{11} - 10 q^{12} + 6 q^{13} + 10 q^{14} - 8 q^{15} + 10 q^{16} + 5 q^{17} + 10 q^{18} + 15 q^{19} + 8 q^{20} - 10 q^{21} + 4 q^{22} + 12 q^{23} - 10 q^{24} - 2 q^{25} + 6 q^{26} - 10 q^{27} + 10 q^{28} + 7 q^{29} - 8 q^{30} + 28 q^{31} + 10 q^{32} - 4 q^{33} + 5 q^{34} + 8 q^{35} + 10 q^{36} - 3 q^{37} + 15 q^{38} - 6 q^{39} + 8 q^{40} + 24 q^{41} - 10 q^{42} + 4 q^{43} + 4 q^{44} + 8 q^{45} + 12 q^{46} + 16 q^{47} - 10 q^{48} + 10 q^{49} - 2 q^{50} - 5 q^{51} + 6 q^{52} + 5 q^{53} - 10 q^{54} - q^{55} + 10 q^{56} - 15 q^{57} + 7 q^{58} + 17 q^{59} - 8 q^{60} + 15 q^{61} + 28 q^{62} + 10 q^{63} + 10 q^{64} + 14 q^{65} - 4 q^{66} + 6 q^{67} + 5 q^{68} - 12 q^{69} + 8 q^{70} + 5 q^{71} + 10 q^{72} + 16 q^{73} - 3 q^{74} + 2 q^{75} + 15 q^{76} + 4 q^{77} - 6 q^{78} - 5 q^{79} + 8 q^{80} + 10 q^{81} + 24 q^{82} + 24 q^{83} - 10 q^{84} - 19 q^{85} + 4 q^{86} - 7 q^{87} + 4 q^{88} + 17 q^{89} + 8 q^{90} + 6 q^{91} + 12 q^{92} - 28 q^{93} + 16 q^{94} + 15 q^{95} - 10 q^{96} + 20 q^{97} + 10 q^{98} + 4 q^{99}+O(q^{100}) \) 10 * q + 10 * q^2 - 10 * q^3 + 10 * q^4 + 8 * q^5 - 10 * q^6 + 10 * q^7 + 10 * q^8 + 10 * q^9 + 8 * q^10 + 4 * q^11 - 10 * q^12 + 6 * q^13 + 10 * q^14 - 8 * q^15 + 10 * q^16 + 5 * q^17 + 10 * q^18 + 15 * q^19 + 8 * q^20 - 10 * q^21 + 4 * q^22 + 12 * q^23 - 10 * q^24 - 2 * q^25 + 6 * q^26 - 10 * q^27 + 10 * q^28 + 7 * q^29 - 8 * q^30 + 28 * q^31 + 10 * q^32 - 4 * q^33 + 5 * q^34 + 8 * q^35 + 10 * q^36 - 3 * q^37 + 15 * q^38 - 6 * q^39 + 8 * q^40 + 24 * q^41 - 10 * q^42 + 4 * q^43 + 4 * q^44 + 8 * q^45 + 12 * q^46 + 16 * q^47 - 10 * q^48 + 10 * q^49 - 2 * q^50 - 5 * q^51 + 6 * q^52 + 5 * q^53 - 10 * q^54 - q^55 + 10 * q^56 - 15 * q^57 + 7 * q^58 + 17 * q^59 - 8 * q^60 + 15 * q^61 + 28 * q^62 + 10 * q^63 + 10 * q^64 + 14 * q^65 - 4 * q^66 + 6 * q^67 + 5 * q^68 - 12 * q^69 + 8 * q^70 + 5 * q^71 + 10 * q^72 + 16 * q^73 - 3 * q^74 + 2 * q^75 + 15 * q^76 + 4 * q^77 - 6 * q^78 - 5 * q^79 + 8 * q^80 + 10 * q^81 + 24 * q^82 + 24 * q^83 - 10 * q^84 - 19 * q^85 + 4 * q^86 - 7 * q^87 + 4 * q^88 + 17 * q^89 + 8 * q^90 + 6 * q^91 + 12 * q^92 - 28 * q^93 + 16 * q^94 + 15 * q^95 - 10 * q^96 + 20 * q^97 + 10 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.00000	0.500000
$5$	−0.483732	−0.216331	−0.108166	−	0.994133i	$-0.534498\pi$
$5$	−0.483732	−0.216331	−0.108166	+	0.994133i	$0.534498\pi$
$6$	−1.00000	−0.408248
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−0.483732	−0.152969
$11$	−2.89666	−0.873375	−0.436687	−	0.899613i	$-0.643848\pi$
$11$	−2.89666	−0.873375	−0.436687	+	0.899613i	$0.643848\pi$
$12$	−1.00000	−0.288675
$13$	0.896578	0.248666	0.124333	−	0.992241i	$-0.460321\pi$
$13$	0.896578	0.248666	0.124333	+	0.992241i	$0.460321\pi$
$14$	1.00000	0.267261
$15$	0.483732	0.124899
$16$	1.00000	0.250000
$17$	−4.05183	−0.982713	−0.491356	−	0.870959i	$-0.663499\pi$
$17$	−4.05183	−0.982713	−0.491356	+	0.870959i	$0.663499\pi$
$18$	1.00000	0.235702
$19$	−5.49983	−1.26175	−0.630873	−	0.775886i	$-0.717303\pi$
$19$	−5.49983	−1.26175	−0.630873	+	0.775886i	$0.717303\pi$
$20$	−0.483732	−0.108166
$21$	−1.00000	−0.218218
$22$	−2.89666	−0.617569
$23$	4.14067	0.863389	0.431695	−	0.902020i	$-0.357916\pi$
$23$	4.14067	0.863389	0.431695	+	0.902020i	$0.357916\pi$
$24$	−1.00000	−0.204124
$25$	−4.76600	−0.953201
$26$	0.896578	0.175833
$27$	−1.00000	−0.192450
$28$	1.00000	0.188982
$29$	−4.47647	−0.831260	−0.415630	−	0.909534i	$-0.636439\pi$
$29$	−4.47647	−0.831260	−0.415630	+	0.909534i	$0.636439\pi$
$30$	0.483732	0.0883169
$31$	4.99541	0.897202	0.448601	−	0.893732i	$-0.351922\pi$
$31$	4.99541	0.897202	0.448601	+	0.893732i	$0.351922\pi$
$32$	1.00000	0.176777
$33$	2.89666	0.504243
$34$	−4.05183	−0.694883
$35$	−0.483732	−0.0817656
$36$	1.00000	0.166667
$37$	−5.68561	−0.934709	−0.467355	−	0.884070i	$-0.654793\pi$
$37$	−5.68561	−0.934709	−0.467355	+	0.884070i	$0.654793\pi$
$38$	−5.49983	−0.892190
$39$	−0.896578	−0.143567
$40$	−0.483732	−0.0764847
$41$	9.36885	1.46317	0.731584	−	0.681751i	$-0.238781\pi$
$41$	9.36885	1.46317	0.731584	+	0.681751i	$0.238781\pi$
$42$	−1.00000	−0.154303
$43$	10.0265	1.52903	0.764514	−	0.644607i	$-0.222979\pi$
$43$	10.0265	1.52903	0.764514	+	0.644607i	$0.222979\pi$
$44$	−2.89666	−0.436687
$45$	−0.483732	−0.0721105
$46$	4.14067	0.610508
$47$	0.591028	0.0862103	0.0431052	−	0.999071i	$-0.486275\pi$
$47$	0.591028	0.0862103	0.0431052	+	0.999071i	$0.486275\pi$
$48$	−1.00000	−0.144338
$49$	1.00000	0.142857
$50$	−4.76600	−0.674015
$51$	4.05183	0.567370
$52$	0.896578	0.124333
$53$	9.53963	1.31037	0.655184	−	0.755469i	$-0.272591\pi$
$53$	9.53963	1.31037	0.655184	+	0.755469i	$0.272591\pi$
$54$	−1.00000	−0.136083
$55$	1.40120	0.188938
$56$	1.00000	0.133631
$57$	5.49983	0.728470
$58$	−4.47647	−0.587790
$59$	9.44063	1.22907	0.614533	−	0.788891i	$-0.289345\pi$
$59$	9.44063	1.22907	0.614533	+	0.788891i	$0.289345\pi$
$60$	0.483732	0.0624495
$61$	5.46611	0.699863	0.349932	−	0.936775i	$-0.386205\pi$
$61$	5.46611	0.699863	0.349932	+	0.936775i	$0.386205\pi$
$62$	4.99541	0.634418
$63$	1.00000	0.125988
$64$	1.00000	0.125000
$65$	−0.433703	−0.0537942
$66$	2.89666	0.356554
$67$	−4.26901	−0.521543	−0.260771	−	0.965401i	$-0.583977\pi$
$67$	−4.26901	−0.521543	−0.260771	+	0.965401i	$0.583977\pi$
$68$	−4.05183	−0.491356
$69$	−4.14067	−0.498478
$70$	−0.483732	−0.0578170
$71$	−6.49576	−0.770905	−0.385452	−	0.922728i	$-0.625955\pi$
$71$	−6.49576	−0.770905	−0.385452	+	0.922728i	$0.625955\pi$
$72$	1.00000	0.117851
$73$	7.15692	0.837654	0.418827	−	0.908066i	$-0.362441\pi$
$73$	7.15692	0.837654	0.418827	+	0.908066i	$0.362441\pi$
$74$	−5.68561	−0.660939
$75$	4.76600	0.550331
$76$	−5.49983	−0.630873
$77$	−2.89666	−0.330105
$78$	−0.896578	−0.101517
$79$	−4.52988	−0.509652	−0.254826	−	0.966987i	$-0.582018\pi$
$79$	−4.52988	−0.509652	−0.254826	+	0.966987i	$0.582018\pi$
$80$	−0.483732	−0.0540828
$81$	1.00000	0.111111
$82$	9.36885	1.03462
$83$	3.92066	0.430348	0.215174	−	0.976576i	$-0.430968\pi$
$83$	3.92066	0.430348	0.215174	+	0.976576i	$0.430968\pi$
$84$	−1.00000	−0.109109
$85$	1.96000	0.212592
$86$	10.0265	1.08119
$87$	4.47647	0.479928
$88$	−2.89666	−0.308785
$89$	−0.197840	−0.0209710	−0.0104855	−	0.999945i	$-0.503338\pi$
$89$	−0.197840	−0.0209710	−0.0104855	+	0.999945i	$0.503338\pi$
$90$	−0.483732	−0.0509898
$91$	0.896578	0.0939869
$92$	4.14067	0.431695
$93$	−4.99541	−0.518000
$94$	0.591028	0.0609599
$95$	2.66044	0.272955
$96$	−1.00000	−0.102062
$97$	2.64762	0.268825	0.134413	−	0.990925i	$-0.457085\pi$
$97$	2.64762	0.268825	0.134413	+	0.990925i	$0.457085\pi$
$98$	1.00000	0.101015
$99$	−2.89666	−0.291125
$100$	−4.76600	−0.476600
$101$	17.4526	1.73660	0.868299	−	0.496041i	$-0.165213\pi$
$101$	17.4526	1.73660	0.868299	+	0.496041i	$0.165213\pi$
$102$	4.05183	0.401191
$103$	13.6303	1.34304	0.671518	−	0.740988i	$-0.265642\pi$
$103$	13.6303	1.34304	0.671518	+	0.740988i	$0.265642\pi$
$104$	0.896578	0.0879167
$105$	0.483732	0.0472074
$106$	9.53963	0.926570
$107$	−16.2715	−1.57303	−0.786515	−	0.617571i	$-0.788117\pi$
$107$	−16.2715	−1.57303	−0.786515	+	0.617571i	$0.788117\pi$
$108$	−1.00000	−0.0962250
$109$	6.56752	0.629054	0.314527	−	0.949249i	$-0.398154\pi$
$109$	6.56752	0.629054	0.314527	+	0.949249i	$0.398154\pi$
$110$	1.40120	0.133600
$111$	5.68561	0.539655
$112$	1.00000	0.0944911
$113$	18.4197	1.73278	0.866392	−	0.499365i	$-0.166433\pi$
$113$	18.4197	1.73278	0.866392	+	0.499365i	$0.166433\pi$
$114$	5.49983	0.515106
$115$	−2.00297	−0.186778
$116$	−4.47647	−0.415630
$117$	0.896578	0.0828887
$118$	9.44063	0.869081
$119$	−4.05183	−0.371431
$120$	0.483732	0.0441585
$121$	−2.60938	−0.237216
$122$	5.46611	0.494878
$123$	−9.36885	−0.844761
$124$	4.99541	0.448601
$125$	4.72412	0.422539
$126$	1.00000	0.0890871
$127$	−3.64964	−0.323853	−0.161927	−	0.986803i	$-0.551771\pi$
$127$	−3.64964	−0.323853	−0.161927	+	0.986803i	$0.551771\pi$
$128$	1.00000	0.0883883
$129$	−10.0265	−0.882785
$130$	−0.433703	−0.0380383
$131$	4.59474	0.401444	0.200722	−	0.979648i	$-0.435671\pi$
$131$	4.59474	0.401444	0.200722	+	0.979648i	$0.435671\pi$
$132$	2.89666	0.252122
$133$	−5.49983	−0.476895
$134$	−4.26901	−0.368787
$135$	0.483732	0.0416330
$136$	−4.05183	−0.347441
$137$	16.6345	1.42118	0.710591	−	0.703606i	$-0.248428\pi$
$137$	16.6345	1.42118	0.710591	+	0.703606i	$0.248428\pi$
$138$	−4.14067	−0.352477
$139$	−17.8329	−1.51257	−0.756284	−	0.654244i	$-0.772987\pi$
$139$	−17.8329	−1.51257	−0.756284	+	0.654244i	$0.772987\pi$
$140$	−0.483732	−0.0408828
$141$	−0.591028	−0.0497736
$142$	−6.49576	−0.545112
$143$	−2.59708	−0.217179
$144$	1.00000	0.0833333
$145$	2.16541	0.179828
$146$	7.15692	0.592311
$147$	−1.00000	−0.0824786
$148$	−5.68561	−0.467355
$149$	−9.42253	−0.771924	−0.385962	−	0.922515i	$-0.626130\pi$
$149$	−9.42253	−0.771924	−0.385962	+	0.922515i	$0.626130\pi$
$150$	4.76600	0.389143
$151$	16.5531	1.34707	0.673535	−	0.739156i	$-0.264775\pi$
$151$	16.5531	1.34707	0.673535	+	0.739156i	$0.264775\pi$
$152$	−5.49983	−0.446095
$153$	−4.05183	−0.327571
$154$	−2.89666	−0.233419
$155$	−2.41644	−0.194093
$156$	−0.896578	−0.0717837
$157$	−8.99174	−0.717619	−0.358809	−	0.933411i	$-0.616817\pi$
$157$	−8.99174	−0.717619	−0.358809	+	0.933411i	$0.616817\pi$
$158$	−4.52988	−0.360378
$159$	−9.53963	−0.756542
$160$	−0.483732	−0.0382423
$161$	4.14067	0.326330
$162$	1.00000	0.0785674
$163$	−18.7933	−1.47200	−0.736002	−	0.676980i	$-0.763288\pi$
$163$	−18.7933	−1.47200	−0.736002	+	0.676980i	$0.763288\pi$
$164$	9.36885	0.731584
$165$	−1.40120	−0.109084
$166$	3.92066	0.304302
$167$	3.42397	0.264954	0.132477	−	0.991186i	$-0.457707\pi$
$167$	3.42397	0.264954	0.132477	+	0.991186i	$0.457707\pi$
$168$	−1.00000	−0.0771517
$169$	−12.1961	−0.938165
$170$	1.96000	0.150325
$171$	−5.49983	−0.420582
$172$	10.0265	0.764514
$173$	0.0751990	0.00571728	0.00285864	−	0.999996i	$-0.499090\pi$
$173$	0.0751990	0.00571728	0.00285864	+	0.999996i	$0.499090\pi$
$174$	4.47647	0.339360
$175$	−4.76600	−0.360276
$176$	−2.89666	−0.218344
$177$	−9.44063	−0.709601
$178$	−0.197840	−0.0148287
$179$	14.4677	1.08137	0.540683	−	0.841226i	$-0.318166\pi$
$179$	14.4677	1.08137	0.540683	+	0.841226i	$0.318166\pi$
$180$	−0.483732	−0.0360552
$181$	9.28103	0.689853	0.344927	−	0.938630i	$-0.387904\pi$
$181$	9.28103	0.689853	0.344927	+	0.938630i	$0.387904\pi$
$182$	0.896578	0.0664588
$183$	−5.46611	−0.404066
$184$	4.14067	0.305254
$185$	2.75031	0.202207
$186$	−4.99541	−0.366281
$187$	11.7368	0.858277
$188$	0.591028	0.0431052
$189$	−1.00000	−0.0727393
$190$	2.66044	0.193009
$191$	1.00000	0.0723575
$191$	1.00000	0.0723575
$192$	−1.00000	−0.0721688
$193$	−5.60145	−0.403201	−0.201601	−	0.979468i	$-0.564614\pi$
$193$	−5.60145	−0.403201	−0.201601	+	0.979468i	$0.564614\pi$
$194$	2.64762	0.190088
$195$	0.433703	0.0310581
$196$	1.00000	0.0714286
$197$	−11.9101	−0.848560	−0.424280	−	0.905531i	$-0.639473\pi$
$197$	−11.9101	−0.848560	−0.424280	+	0.905531i	$0.639473\pi$
$198$	−2.89666	−0.205856
$199$	5.23053	0.370783	0.185391	−	0.982665i	$-0.440645\pi$
$199$	5.23053	0.370783	0.185391	+	0.982665i	$0.440645\pi$
$200$	−4.76600	−0.337007
$201$	4.26901	0.301113
$202$	17.4526	1.22796
$203$	−4.47647	−0.314187
$204$	4.05183	0.283685
$205$	−4.53201	−0.316529
$206$	13.6303	0.949670
$207$	4.14067	0.287796
$208$	0.896578	0.0621665
$209$	15.9311	1.10198
$210$	0.483732	0.0333807
$211$	6.39382	0.440169	0.220084	−	0.975481i	$-0.429367\pi$
$211$	6.39382	0.440169	0.220084	+	0.975481i	$0.429367\pi$
$212$	9.53963	0.655184
$213$	6.49576	0.445082
$214$	−16.2715	−1.11230
$215$	−4.85014	−0.330777
$216$	−1.00000	−0.0680414
$217$	4.99541	0.339110
$218$	6.56752	0.444808
$219$	−7.15692	−0.483620
$220$	1.40120	0.0944692
$221$	−3.63278	−0.244367
$222$	5.68561	0.381593
$223$	−6.57265	−0.440137	−0.220068	−	0.975484i	$-0.570628\pi$
$223$	−6.57265	−0.440137	−0.220068	+	0.975484i	$0.570628\pi$
$224$	1.00000	0.0668153
$225$	−4.76600	−0.317734
$226$	18.4197	1.22526
$227$	14.2674	0.946964	0.473482	−	0.880804i	$-0.342997\pi$
$227$	14.2674	0.946964	0.473482	+	0.880804i	$0.342997\pi$
$228$	5.49983	0.364235
$229$	12.3014	0.812900	0.406450	−	0.913673i	$-0.366767\pi$
$229$	12.3014	0.812900	0.406450	+	0.913673i	$0.366767\pi$
$230$	−2.00297	−0.132072
$231$	2.89666	0.190586
$232$	−4.47647	−0.293895
$233$	−3.95478	−0.259086	−0.129543	−	0.991574i	$-0.541351\pi$
$233$	−3.95478	−0.259086	−0.129543	+	0.991574i	$0.541351\pi$
$234$	0.896578	0.0586111
$235$	−0.285899	−0.0186500
$236$	9.44063	0.614533
$237$	4.52988	0.294248
$238$	−4.05183	−0.262641
$239$	23.1539	1.49770	0.748850	−	0.662739i	$-0.230606\pi$
$239$	23.1539	1.49770	0.748850	+	0.662739i	$0.230606\pi$
$240$	0.483732	0.0312247
$241$	−4.97176	−0.320259	−0.160130	−	0.987096i	$-0.551191\pi$
$241$	−4.97176	−0.320259	−0.160130	+	0.987096i	$0.551191\pi$
$242$	−2.60938	−0.167737
$243$	−1.00000	−0.0641500
$244$	5.46611	0.349932
$245$	−0.483732	−0.0309045
$246$	−9.36885	−0.597336
$247$	−4.93102	−0.313753
$248$	4.99541	0.317209
$249$	−3.92066	−0.248462
$250$	4.72412	0.298780
$251$	14.7480	0.930884	0.465442	−	0.885078i	$-0.345895\pi$
$251$	14.7480	0.930884	0.465442	+	0.885078i	$0.345895\pi$
$252$	1.00000	0.0629941
$253$	−11.9941	−0.754063
$254$	−3.64964	−0.228999
$255$	−1.96000	−0.122740
$256$	1.00000	0.0625000
$257$	−16.2140	−1.01140	−0.505700	−	0.862709i	$-0.668766\pi$
$257$	−16.2140	−1.01140	−0.505700	+	0.862709i	$0.668766\pi$
$258$	−10.0265	−0.624223
$259$	−5.68561	−0.353287
$260$	−0.433703	−0.0268971
$261$	−4.47647	−0.277087
$262$	4.59474	0.283864
$263$	3.12669	0.192800	0.0963999	−	0.995343i	$-0.469267\pi$
$263$	3.12669	0.192800	0.0963999	+	0.995343i	$0.469267\pi$
$264$	2.89666	0.178277
$265$	−4.61462	−0.283474
$266$	−5.49983	−0.337216
$267$	0.197840	0.0121076
$268$	−4.26901	−0.260771
$269$	−9.37107	−0.571364	−0.285682	−	0.958324i	$-0.592220\pi$
$269$	−9.37107	−0.571364	−0.285682	+	0.958324i	$0.592220\pi$
$270$	0.483732	0.0294390
$271$	18.2506	1.10865	0.554323	−	0.832302i	$-0.312977\pi$
$271$	18.2506	1.10865	0.554323	+	0.832302i	$0.312977\pi$
$272$	−4.05183	−0.245678
$273$	−0.896578	−0.0542634
$274$	16.6345	1.00493
$275$	13.8055	0.832502
$276$	−4.14067	−0.249239
$277$	1.42528	0.0856368	0.0428184	−	0.999083i	$-0.486366\pi$
$277$	1.42528	0.0856368	0.0428184	+	0.999083i	$0.486366\pi$
$278$	−17.8329	−1.06955
$279$	4.99541	0.299067
$280$	−0.483732	−0.0289085
$281$	14.0874	0.840386	0.420193	−	0.907435i	$-0.361962\pi$
$281$	14.0874	0.840386	0.420193	+	0.907435i	$0.361962\pi$
$282$	−0.591028	−0.0351952
$283$	30.5712	1.81727	0.908635	−	0.417592i	$-0.137126\pi$
$283$	30.5712	1.81727	0.908635	+	0.417592i	$0.137126\pi$
$284$	−6.49576	−0.385452
$285$	−2.66044	−0.157591
$286$	−2.59708	−0.153568
$287$	9.36885	0.553026
$288$	1.00000	0.0589256
$289$	−0.582680	−0.0342753
$290$	2.16541	0.127157
$291$	−2.64762	−0.155206
$292$	7.15692	0.418827
$293$	10.3750	0.606113	0.303057	−	0.952973i	$-0.401993\pi$
$293$	10.3750	0.606113	0.303057	+	0.952973i	$0.401993\pi$
$294$	−1.00000	−0.0583212
$295$	−4.56673	−0.265885
$296$	−5.68561	−0.330470
$297$	2.89666	0.168081
$298$	−9.42253	−0.545833
$299$	3.71243	0.214696
$300$	4.76600	0.275165
$301$	10.0265	0.577919
$302$	16.5531	0.952522
$303$	−17.4526	−1.00263
$304$	−5.49983	−0.315437
$305$	−2.64413	−0.151402
$306$	−4.05183	−0.231628
$307$	−30.1068	−1.71828	−0.859142	−	0.511736i	$-0.829002\pi$
$307$	−30.1068	−1.71828	−0.859142	+	0.511736i	$0.829002\pi$
$308$	−2.89666	−0.165052
$309$	−13.6303	−0.775403
$310$	−2.41644	−0.137244
$311$	30.3294	1.71982	0.859911	−	0.510445i	$-0.170519\pi$
$311$	30.3294	1.71982	0.859911	+	0.510445i	$0.170519\pi$
$312$	−0.896578	−0.0507587
$313$	−30.6309	−1.73136	−0.865681	−	0.500596i	$-0.833114\pi$
$313$	−30.6309	−1.73136	−0.865681	+	0.500596i	$0.833114\pi$
$314$	−8.99174	−0.507433
$315$	−0.483732	−0.0272552
$316$	−4.52988	−0.254826
$317$	0.403978	0.0226897	0.0113448	−	0.999936i	$-0.496389\pi$
$317$	0.403978	0.0226897	0.0113448	+	0.999936i	$0.496389\pi$
$318$	−9.53963	−0.534956
$319$	12.9668	0.726002
$320$	−0.483732	−0.0270414
$321$	16.2715	0.908189
$322$	4.14067	0.230751
$323$	22.2844	1.23993
$324$	1.00000	0.0555556
$325$	−4.27309	−0.237029
$326$	−18.7933	−1.04086
$327$	−6.56752	−0.363184
$328$	9.36885	0.517308
$329$	0.591028	0.0325844
$330$	−1.40120	−0.0771338
$331$	13.3168	0.731957	0.365978	−	0.930623i	$-0.380734\pi$
$331$	13.3168	0.731957	0.365978	+	0.930623i	$0.380734\pi$
$332$	3.92066	0.215174
$333$	−5.68561	−0.311570
$334$	3.42397	0.187351
$335$	2.06506	0.112826
$336$	−1.00000	−0.0545545
$337$	4.61781	0.251548	0.125774	−	0.992059i	$-0.459859\pi$
$337$	4.61781	0.251548	0.125774	+	0.992059i	$0.459859\pi$
$338$	−12.1961	−0.663383
$339$	−18.4197	−1.00042
$340$	1.96000	0.106296
$341$	−14.4700	−0.783594
$342$	−5.49983	−0.297397
$343$	1.00000	0.0539949
$344$	10.0265	0.540593
$345$	2.00297	0.107836
$346$	0.0751990	0.00404272
$347$	9.78277	0.525167	0.262583	−	0.964909i	$-0.415426\pi$
$347$	9.78277	0.525167	0.262583	+	0.964909i	$0.415426\pi$
$348$	4.47647	0.239964
$349$	−2.68295	−0.143615	−0.0718074	−	0.997419i	$-0.522877\pi$
$349$	−2.68295	−0.143615	−0.0718074	+	0.997419i	$0.522877\pi$
$350$	−4.76600	−0.254754
$351$	−0.896578	−0.0478558
$352$	−2.89666	−0.154392
$353$	35.9570	1.91380	0.956899	−	0.290421i	$-0.0937953\pi$
$353$	35.9570	1.91380	0.956899	+	0.290421i	$0.0937953\pi$
$354$	−9.44063	−0.501764
$355$	3.14220	0.166771
$356$	−0.197840	−0.0104855
$357$	4.05183	0.214446
$358$	14.4677	0.764642
$359$	−22.5760	−1.19152	−0.595759	−	0.803163i	$-0.703149\pi$
$359$	−22.5760	−1.19152	−0.595759	+	0.803163i	$0.703149\pi$
$360$	−0.483732	−0.0254949
$361$	11.2481	0.592005
$362$	9.28103	0.487800
$363$	2.60938	0.136957
$364$	0.896578	0.0469934
$365$	−3.46203	−0.181211
$366$	−5.46611	−0.285718
$367$	23.9094	1.24806	0.624030	−	0.781400i	$-0.285494\pi$
$367$	23.9094	1.24806	0.624030	+	0.781400i	$0.285494\pi$
$368$	4.14067	0.215847
$369$	9.36885	0.487723
$370$	2.75031	0.142982
$371$	9.53963	0.495273
$372$	−4.99541	−0.259000
$373$	4.42954	0.229353	0.114677	−	0.993403i	$-0.463417\pi$
$373$	4.42954	0.229353	0.114677	+	0.993403i	$0.463417\pi$
$374$	11.7368	0.606893
$375$	−4.72412	−0.243953
$376$	0.591028	0.0304800
$377$	−4.01351	−0.206706
$378$	−1.00000	−0.0514344
$379$	−8.01713	−0.411812	−0.205906	−	0.978572i	$-0.566014\pi$
$379$	−8.01713	−0.411812	−0.205906	+	0.978572i	$0.566014\pi$
$380$	2.66044	0.136478
$381$	3.64964	0.186977
$382$	1.00000	0.0511645
$383$	14.6262	0.747365	0.373682	−	0.927557i	$-0.378095\pi$
$383$	14.6262	0.747365	0.373682	+	0.927557i	$0.378095\pi$
$384$	−1.00000	−0.0510310
$385$	1.40120	0.0714120
$386$	−5.60145	−0.285106
$387$	10.0265	0.509676
$388$	2.64762	0.134413
$389$	−3.15453	−0.159941	−0.0799704	−	0.996797i	$-0.525483\pi$
$389$	−3.15453	−0.159941	−0.0799704	+	0.996797i	$0.525483\pi$
$390$	0.433703	0.0219614
$391$	−16.7773	−0.848464
$392$	1.00000	0.0505076
$393$	−4.59474	−0.231774
$394$	−11.9101	−0.600022
$395$	2.19125	0.110254
$396$	−2.89666	−0.145562
$397$	−2.32741	−0.116810	−0.0584048	−	0.998293i	$-0.518601\pi$
$397$	−2.32741	−0.116810	−0.0584048	+	0.998293i	$0.518601\pi$
$398$	5.23053	0.262183
$399$	5.49983	0.275336
$400$	−4.76600	−0.238300
$401$	6.84679	0.341912	0.170956	−	0.985279i	$-0.445314\pi$
$401$	6.84679	0.341912	0.170956	+	0.985279i	$0.445314\pi$
$402$	4.26901	0.212919
$403$	4.47877	0.223104
$404$	17.4526	0.868299
$405$	−0.483732	−0.0240368
$406$	−4.47647	−0.222164
$407$	16.4693	0.816352
$408$	4.05183	0.200595
$409$	−1.68232	−0.0831856	−0.0415928	−	0.999135i	$-0.513243\pi$
$409$	−1.68232	−0.0831856	−0.0415928	+	0.999135i	$0.513243\pi$
$410$	−4.53201	−0.223820
$411$	−16.6345	−0.820520
$412$	13.6303	0.671518
$413$	9.44063	0.464543
$414$	4.14067	0.203503
$415$	−1.89655	−0.0930979
$416$	0.896578	0.0439583
$417$	17.8329	0.873281
$418$	15.9311	0.779216
$419$	−5.35662	−0.261688	−0.130844	−	0.991403i	$-0.541769\pi$
$419$	−5.35662	−0.261688	−0.130844	+	0.991403i	$0.541769\pi$
$420$	0.483732	0.0236037
$421$	3.90985	0.190555	0.0952773	−	0.995451i	$-0.469626\pi$
$421$	3.90985	0.190555	0.0952773	+	0.995451i	$0.469626\pi$
$422$	6.39382	0.311246
$423$	0.591028	0.0287368
$424$	9.53963	0.463285
$425$	19.3110	0.936723
$426$	6.49576	0.314720
$427$	5.46611	0.264523
$428$	−16.2715	−0.786515
$429$	2.59708	0.125388
$430$	−4.85014	−0.233895
$431$	26.8886	1.29518	0.647588	−	0.761990i	$-0.275778\pi$
$431$	26.8886	1.29518	0.647588	+	0.761990i	$0.275778\pi$
$432$	−1.00000	−0.0481125
$433$	−28.7239	−1.38038	−0.690191	−	0.723627i	$-0.742474\pi$
$433$	−28.7239	−1.38038	−0.690191	+	0.723627i	$0.742474\pi$
$434$	4.99541	0.239787
$435$	−2.16541	−0.103824
$436$	6.56752	0.314527
$437$	−22.7730	−1.08938
$438$	−7.15692	−0.341971
$439$	21.6594	1.03375	0.516875	−	0.856061i	$-0.327095\pi$
$439$	21.6594	1.03375	0.516875	+	0.856061i	$0.327095\pi$
$440$	1.40120	0.0667998
$441$	1.00000	0.0476190
$442$	−3.63278	−0.172794
$443$	2.61556	0.124269	0.0621345	−	0.998068i	$-0.480209\pi$
$443$	2.61556	0.124269	0.0621345	+	0.998068i	$0.480209\pi$
$444$	5.68561	0.269827
$445$	0.0957015	0.00453669
$446$	−6.57265	−0.311224
$447$	9.42253	0.445671
$448$	1.00000	0.0472456
$449$	−35.8107	−1.69001	−0.845005	−	0.534759i	$-0.820402\pi$
$449$	−35.8107	−1.69001	−0.845005	+	0.534759i	$0.820402\pi$
$450$	−4.76600	−0.224672
$451$	−27.1384	−1.27790
$452$	18.4197	0.866392
$453$	−16.5531	−0.777731
$454$	14.2674	0.669605
$455$	−0.433703	−0.0203323
$456$	5.49983	0.257553
$457$	34.5634	1.61681	0.808405	−	0.588627i	$-0.200331\pi$
$457$	34.5634	1.61681	0.808405	+	0.588627i	$0.200331\pi$
$458$	12.3014	0.574807
$459$	4.05183	0.189123
$460$	−2.00297	−0.0933891
$461$	−17.5639	−0.818031	−0.409015	−	0.912527i	$-0.634128\pi$
$461$	−17.5639	−0.818031	−0.409015	+	0.912527i	$0.634128\pi$
$462$	2.89666	0.134765
$463$	5.46832	0.254134	0.127067	−	0.991894i	$-0.459444\pi$
$463$	5.46832	0.254134	0.127067	+	0.991894i	$0.459444\pi$
$464$	−4.47647	−0.207815
$465$	2.41644	0.112060
$466$	−3.95478	−0.183202
$467$	−33.6090	−1.55524	−0.777621	−	0.628734i	$-0.783573\pi$
$467$	−33.6090	−1.55524	−0.777621	+	0.628734i	$0.783573\pi$
$468$	0.896578	0.0414443
$469$	−4.26901	−0.197125
$470$	−0.285899	−0.0131875
$471$	8.99174	0.414317
$472$	9.44063	0.434540
$473$	−29.0434	−1.33542
$474$	4.52988	0.208065
$475$	26.2122	1.20270
$476$	−4.05183	−0.185715
$477$	9.53963	0.436789
$478$	23.1539	1.05903
$479$	−19.6510	−0.897877	−0.448938	−	0.893563i	$-0.648198\pi$
$479$	−19.6510	−0.897877	−0.448938	+	0.893563i	$0.648198\pi$
$480$	0.483732	0.0220792
$481$	−5.09760	−0.232430
$482$	−4.97176	−0.226457
$483$	−4.14067	−0.188407
$484$	−2.60938	−0.118608
$485$	−1.28074	−0.0581553
$486$	−1.00000	−0.0453609
$487$	−23.0805	−1.04588	−0.522938	−	0.852370i	$-0.675164\pi$
$487$	−23.0805	−1.04588	−0.522938	+	0.852370i	$0.675164\pi$
$488$	5.46611	0.247439
$489$	18.7933	0.849862
$490$	−0.483732	−0.0218528
$491$	42.6520	1.92486	0.962430	−	0.271531i	$-0.0875299\pi$
$491$	42.6520	1.92486	0.962430	+	0.271531i	$0.0875299\pi$
$492$	−9.36885	−0.422380
$493$	18.1379	0.816890
$494$	−4.93102	−0.221857
$495$	1.40120	0.0629795
$496$	4.99541	0.224300
$497$	−6.49576	−0.291375
$498$	−3.92066	−0.175689
$499$	19.9413	0.892696	0.446348	−	0.894859i	$-0.352724\pi$
$499$	19.9413	0.892696	0.446348	+	0.894859i	$0.352724\pi$
$500$	4.72412	0.211269
$501$	−3.42397	−0.152972
$502$	14.7480	0.658235
$503$	23.7720	1.05994	0.529972	−	0.848015i	$-0.322203\pi$
$503$	23.7720	1.05994	0.529972	+	0.848015i	$0.322203\pi$
$504$	1.00000	0.0445435
$505$	−8.44237	−0.375681
$506$	−11.9941	−0.533203
$507$	12.1961	0.541650
$508$	−3.64964	−0.161927
$509$	32.1025	1.42292	0.711459	−	0.702728i	$-0.248035\pi$
$509$	32.1025	1.42292	0.711459	+	0.702728i	$0.248035\pi$
$510$	−1.96000	−0.0867902
$511$	7.15692	0.316603
$512$	1.00000	0.0441942
$513$	5.49983	0.242823
$514$	−16.2140	−0.715168
$515$	−6.59342	−0.290541
$516$	−10.0265	−0.441393
$517$	−1.71201	−0.0752939
$518$	−5.68561	−0.249812
$519$	−0.0751990	−0.00330087
$520$	−0.433703	−0.0190191
$521$	−28.8787	−1.26520	−0.632599	−	0.774479i	$-0.718012\pi$
$521$	−28.8787	−1.26520	−0.632599	+	0.774479i	$0.718012\pi$
$522$	−4.47647	−0.195930
$523$	14.6844	0.642105	0.321053	−	0.947061i	$-0.395963\pi$
$523$	14.6844	0.642105	0.321053	+	0.947061i	$0.395963\pi$
$524$	4.59474	0.200722
$525$	4.76600	0.208005
$526$	3.12669	0.136330
$527$	−20.2405	−0.881692
$528$	2.89666	0.126061
$529$	−5.85485	−0.254559
$530$	−4.61462	−0.200446
$531$	9.44063	0.409689
$532$	−5.49983	−0.238448
$533$	8.39990	0.363840
$534$	0.197840	0.00856138
$535$	7.87106	0.340296
$536$	−4.26901	−0.184393
$537$	−14.4677	−0.624327
$538$	−9.37107	−0.404015
$539$	−2.89666	−0.124768
$540$	0.483732	0.0208165
$541$	−29.4470	−1.26603	−0.633014	−	0.774141i	$-0.718182\pi$
$541$	−29.4470	−1.26603	−0.633014	+	0.774141i	$0.718182\pi$
$542$	18.2506	0.783931
$543$	−9.28103	−0.398287
$544$	−4.05183	−0.173721
$545$	−3.17691	−0.136084
$546$	−0.896578	−0.0383700
$547$	−12.2607	−0.524230	−0.262115	−	0.965037i	$-0.584420\pi$
$547$	−12.2607	−0.524230	−0.262115	+	0.965037i	$0.584420\pi$
$548$	16.6345	0.710591
$549$	5.46611	0.233288
$550$	13.8055	0.588668
$551$	24.6198	1.04884
$552$	−4.14067	−0.176239
$553$	−4.52988	−0.192630
$554$	1.42528	0.0605543
$555$	−2.75031	−0.116744
$556$	−17.8329	−0.756284
$557$	−22.9471	−0.972298	−0.486149	−	0.873876i	$-0.661599\pi$
$557$	−22.9471	−0.972298	−0.486149	+	0.873876i	$0.661599\pi$
$558$	4.99541	0.211473
$559$	8.98955	0.380217
$560$	−0.483732	−0.0204414
$561$	−11.7368	−0.495526
$562$	14.0874	0.594243
$563$	−16.8720	−0.711070	−0.355535	−	0.934663i	$-0.615701\pi$
$563$	−16.8720	−0.711070	−0.355535	+	0.934663i	$0.615701\pi$
$564$	−0.591028	−0.0248868
$565$	−8.91021	−0.374855
$566$	30.5712	1.28500
$567$	1.00000	0.0419961
$568$	−6.49576	−0.272556
$569$	−24.8067	−1.03995	−0.519976	−	0.854181i	$-0.674059\pi$
$569$	−24.8067	−1.03995	−0.519976	+	0.854181i	$0.674059\pi$
$570$	−2.66044	−0.111434
$571$	−38.0309	−1.59155	−0.795773	−	0.605595i	$-0.792935\pi$
$571$	−38.0309	−1.59155	−0.795773	+	0.605595i	$0.792935\pi$
$572$	−2.59708	−0.108589
$573$	−1.00000	−0.0417756
$574$	9.36885	0.391048
$575$	−19.7344	−0.822983
$576$	1.00000	0.0416667
$577$	23.2471	0.967788	0.483894	−	0.875127i	$-0.339222\pi$
$577$	23.2471	0.967788	0.483894	+	0.875127i	$0.339222\pi$
$578$	−0.582680	−0.0242363
$579$	5.60145	0.232788
$580$	2.16541	0.0899138
$581$	3.92066	0.162656
$582$	−2.64762	−0.109747
$583$	−27.6330	−1.14444
$584$	7.15692	0.296155
$585$	−0.433703	−0.0179314
$586$	10.3750	0.428587
$587$	0.396940	0.0163835	0.00819173	−	0.999966i	$-0.497392\pi$
$587$	0.396940	0.0163835	0.00819173	+	0.999966i	$0.497392\pi$
$588$	−1.00000	−0.0412393
$589$	−27.4739	−1.13204
$590$	−4.56673	−0.188009
$591$	11.9101	0.489916
$592$	−5.68561	−0.233677
$593$	−22.6288	−0.929254	−0.464627	−	0.885507i	$-0.653811\pi$
$593$	−22.6288	−0.929254	−0.464627	+	0.885507i	$0.653811\pi$
$594$	2.89666	0.118851
$595$	1.96000	0.0803521
$596$	−9.42253	−0.385962
$597$	−5.23053	−0.214072
$598$	3.71243	0.151813
$599$	6.36964	0.260256	0.130128	−	0.991497i	$-0.458461\pi$
$599$	6.36964	0.260256	0.130128	+	0.991497i	$0.458461\pi$
$600$	4.76600	0.194571
$601$	30.3024	1.23606	0.618031	−	0.786154i	$-0.287931\pi$
$601$	30.3024	1.23606	0.618031	+	0.786154i	$0.287931\pi$
$602$	10.0265	0.408650
$603$	−4.26901	−0.173848
$604$	16.5531	0.673535
$605$	1.26224	0.0513173
$606$	−17.4526	−0.708963
$607$	18.4126	0.747346	0.373673	−	0.927560i	$-0.378098\pi$
$607$	18.4126	0.747346	0.373673	+	0.927560i	$0.378098\pi$
$608$	−5.49983	−0.223047
$609$	4.47647	0.181396
$610$	−2.64413	−0.107058
$611$	0.529903	0.0214376
$612$	−4.05183	−0.163785
$613$	35.2602	1.42415	0.712074	−	0.702104i	$-0.247756\pi$
$613$	35.2602	1.42415	0.712074	+	0.702104i	$0.247756\pi$
$614$	−30.1068	−1.21501
$615$	4.53201	0.182748
$616$	−2.89666	−0.116710
$617$	−8.01302	−0.322592	−0.161296	−	0.986906i	$-0.551567\pi$
$617$	−8.01302	−0.322592	−0.161296	+	0.986906i	$0.551567\pi$
$618$	−13.6303	−0.548292
$619$	16.4544	0.661357	0.330678	−	0.943743i	$-0.392722\pi$
$619$	16.4544	0.661357	0.330678	+	0.943743i	$0.392722\pi$
$620$	−2.41644	−0.0970464
$621$	−4.14067	−0.166159
$622$	30.3294	1.21610
$623$	−0.197840	−0.00792629
$624$	−0.896578	−0.0358918
$625$	21.5448	0.861792
$626$	−30.6309	−1.22426
$627$	−15.9311	−0.636227
$628$	−8.99174	−0.358809
$629$	23.0371	0.918551
$630$	−0.483732	−0.0192723
$631$	−3.07197	−0.122293	−0.0611465	−	0.998129i	$-0.519476\pi$
$631$	−3.07197	−0.122293	−0.0611465	+	0.998129i	$0.519476\pi$
$632$	−4.52988	−0.180189
$633$	−6.39382	−0.254131
$634$	0.403978	0.0160440
$635$	1.76545	0.0700596
$636$	−9.53963	−0.378271
$637$	0.896578	0.0355237
$638$	12.9668	0.513361
$639$	−6.49576	−0.256968
$640$	−0.483732	−0.0191212
$641$	21.8195	0.861820	0.430910	−	0.902395i	$-0.358193\pi$
$641$	21.8195	0.861820	0.430910	+	0.902395i	$0.358193\pi$
$642$	16.2715	0.642187
$643$	27.9572	1.10252	0.551262	−	0.834332i	$-0.314146\pi$
$643$	27.9572	1.10252	0.551262	+	0.834332i	$0.314146\pi$
$644$	4.14067	0.163165
$645$	4.85014	0.190974
$646$	22.2844	0.876766
$647$	43.3773	1.70534	0.852668	−	0.522453i	$-0.174983\pi$
$647$	43.3773	1.70534	0.852668	+	0.522453i	$0.174983\pi$
$648$	1.00000	0.0392837
$649$	−27.3463	−1.07344
$650$	−4.27309	−0.167605
$651$	−4.99541	−0.195786
$652$	−18.7933	−0.736002
$653$	−2.20873	−0.0864344	−0.0432172	−	0.999066i	$-0.513761\pi$
$653$	−2.20873	−0.0864344	−0.0432172	+	0.999066i	$0.513761\pi$
$654$	−6.56752	−0.256810
$655$	−2.22262	−0.0868450
$656$	9.36885	0.365792
$657$	7.15692	0.279218
$658$	0.591028	0.0230407
$659$	−5.01024	−0.195171	−0.0975857	−	0.995227i	$-0.531112\pi$
$659$	−5.01024	−0.195171	−0.0975857	+	0.995227i	$0.531112\pi$
$660$	−1.40120	−0.0545418
$661$	−24.8861	−0.967956	−0.483978	−	0.875080i	$-0.660809\pi$
$661$	−24.8861	−0.967956	−0.483978	+	0.875080i	$0.660809\pi$
$662$	13.3168	0.517571
$663$	3.63278	0.141085
$664$	3.92066	0.152151
$665$	2.66044	0.103167
$666$	−5.68561	−0.220313
$667$	−18.5356	−0.717701
$668$	3.42397	0.132477
$669$	6.57265	0.254113
$670$	2.06506	0.0797801
$671$	−15.8334	−0.611243
$672$	−1.00000	−0.0385758
$673$	−21.1789	−0.816389	−0.408194	−	0.912895i	$-0.633841\pi$
$673$	−21.1789	−0.816389	−0.408194	+	0.912895i	$0.633841\pi$
$674$	4.61781	0.177871
$675$	4.76600	0.183444
$676$	−12.1961	−0.469083
$677$	17.2335	0.662338	0.331169	−	0.943572i	$-0.392557\pi$
$677$	17.2335	0.662338	0.331169	+	0.943572i	$0.392557\pi$
$678$	−18.4197	−0.707406
$679$	2.64762	0.101606
$680$	1.96000	0.0751625
$681$	−14.2674	−0.546730
$682$	−14.4700	−0.554084
$683$	−7.10940	−0.272034	−0.136017	−	0.990707i	$-0.543430\pi$
$683$	−7.10940	−0.272034	−0.136017	+	0.990707i	$0.543430\pi$
$684$	−5.49983	−0.210291
$685$	−8.04664	−0.307446
$686$	1.00000	0.0381802
$687$	−12.3014	−0.469328
$688$	10.0265	0.382257
$689$	8.55302	0.325844
$690$	2.00297	0.0762519
$691$	−36.8240	−1.40085	−0.700426	−	0.713725i	$-0.747007\pi$
$691$	−36.8240	−1.40085	−0.700426	+	0.713725i	$0.747007\pi$
$692$	0.0751990	0.00285864
$693$	−2.89666	−0.110035
$694$	9.78277	0.371349
$695$	8.62634	0.327216
$696$	4.47647	0.169680
$697$	−37.9610	−1.43787
$698$	−2.68295	−0.101551
$699$	3.95478	0.149583
$700$	−4.76600	−0.180138
$701$	−2.96484	−0.111980	−0.0559902	−	0.998431i	$-0.517832\pi$
$701$	−2.96484	−0.111980	−0.0559902	+	0.998431i	$0.517832\pi$
$702$	−0.896578	−0.0338391
$703$	31.2699	1.17937
$704$	−2.89666	−0.109172
$705$	0.285899	0.0107676
$706$	35.9570	1.35326
$707$	17.4526	0.656372
$708$	−9.44063	−0.354801
$709$	5.28291	0.198404	0.0992019	−	0.995067i	$-0.468371\pi$
$709$	5.28291	0.198404	0.0992019	+	0.995067i	$0.468371\pi$
$710$	3.14220	0.117925
$711$	−4.52988	−0.169884
$712$	−0.197840	−0.00741437
$713$	20.6843	0.774635
$714$	4.05183	0.151636
$715$	1.25629	0.0469825
$716$	14.4677	0.540683
$717$	−23.1539	−0.864698
$718$	−22.5760	−0.842530
$719$	1.05095	0.0391940	0.0195970	−	0.999808i	$-0.493762\pi$
$719$	1.05095	0.0391940	0.0195970	+	0.999808i	$0.493762\pi$
$720$	−0.483732	−0.0180276
$721$	13.6303	0.507620
$722$	11.2481	0.418611
$723$	4.97176	0.184902
$724$	9.28103	0.344927
$725$	21.3349	0.792358
$726$	2.60938	0.0968431
$727$	−45.3248	−1.68100	−0.840501	−	0.541810i	$-0.817739\pi$
$727$	−45.3248	−1.68100	−0.840501	+	0.541810i	$0.817739\pi$
$728$	0.896578	0.0332294
$729$	1.00000	0.0370370
$730$	−3.46203	−0.128135
$731$	−40.6257	−1.50260
$732$	−5.46611	−0.202033
$733$	−10.8313	−0.400064	−0.200032	−	0.979789i	$-0.564105\pi$
$733$	−10.8313	−0.400064	−0.200032	+	0.979789i	$0.564105\pi$
$734$	23.9094	0.882512
$735$	0.483732	0.0178427
$736$	4.14067	0.152627
$737$	12.3659	0.455503
$738$	9.36885	0.344872
$739$	0.715950	0.0263367	0.0131683	−	0.999913i	$-0.495808\pi$
$739$	0.715950	0.0263367	0.0131683	+	0.999913i	$0.495808\pi$
$740$	2.75031	0.101103
$741$	4.93102	0.181146
$742$	9.53963	0.350211
$743$	33.3076	1.22194	0.610969	−	0.791654i	$-0.290780\pi$
$743$	33.3076	1.22194	0.610969	+	0.791654i	$0.290780\pi$
$744$	−4.99541	−0.183141
$745$	4.55798	0.166991
$746$	4.42954	0.162177
$747$	3.92066	0.143449
$748$	11.7368	0.429138
$749$	−16.2715	−0.594549
$750$	−4.72412	−0.172501
$751$	51.9694	1.89639	0.948196	−	0.317686i	$-0.102906\pi$
$751$	51.9694	1.89639	0.948196	+	0.317686i	$0.102906\pi$
$752$	0.591028	0.0215526
$753$	−14.7480	−0.537446
$754$	−4.01351	−0.146163
$755$	−8.00724	−0.291413
$756$	−1.00000	−0.0363696
$757$	20.8712	0.758577	0.379289	−	0.925278i	$-0.376169\pi$
$757$	20.8712	0.758577	0.379289	+	0.925278i	$0.376169\pi$
$758$	−8.01713	−0.291195
$759$	11.9941	0.435358
$760$	2.66044	0.0965043
$761$	−14.3903	−0.521648	−0.260824	−	0.965386i	$-0.583994\pi$
$761$	−14.3903	−0.521648	−0.260824	+	0.965386i	$0.583994\pi$
$762$	3.64964	0.132213
$763$	6.56752	0.237760
$764$	1.00000	0.0361787
$765$	1.96000	0.0708639
$766$	14.6262	0.528467
$767$	8.46426	0.305627
$768$	−1.00000	−0.0360844
$769$	0.662101	0.0238760	0.0119380	−	0.999929i	$-0.496200\pi$
$769$	0.662101	0.0238760	0.0119380	+	0.999929i	$0.496200\pi$
$770$	1.40120	0.0504959
$771$	16.2140	0.583932
$772$	−5.60145	−0.201601
$773$	−25.8823	−0.930923	−0.465462	−	0.885068i	$-0.654112\pi$
$773$	−25.8823	−0.930923	−0.465462	+	0.885068i	$0.654112\pi$
$774$	10.0265	0.360396
$775$	−23.8081	−0.855214
$776$	2.64762	0.0950440
$777$	5.68561	0.203970
$778$	−3.15453	−0.113095
$779$	−51.5271	−1.84615
$780$	0.433703	0.0155291
$781$	18.8160	0.673289
$782$	−16.7773	−0.599955
$783$	4.47647	0.159976
$784$	1.00000	0.0357143
$785$	4.34959	0.155243
$786$	−4.59474	−0.163889
$787$	38.9567	1.38866	0.694329	−	0.719658i	$-0.255701\pi$
$787$	38.9567	1.38866	0.694329	+	0.719658i	$0.255701\pi$
$788$	−11.9101	−0.424280
$789$	−3.12669	−0.111313
$790$	2.19125	0.0779611
$791$	18.4197	0.654931
$792$	−2.89666	−0.102928
$793$	4.90079	0.174032
$794$	−2.32741	−0.0825969
$795$	4.61462	0.163664
$796$	5.23053	0.185391
$797$	−24.5907	−0.871049	−0.435524	−	0.900177i	$-0.643437\pi$
$797$	−24.5907	−0.871049	−0.435524	+	0.900177i	$0.643437\pi$
$798$	5.49983	0.194692
$799$	−2.39475	−0.0847200
$800$	−4.76600	−0.168504
$801$	−0.197840	−0.00699034
$802$	6.84679	0.241768
$803$	−20.7311	−0.731586
$804$	4.26901	0.150556
$805$	−2.00297	−0.0705955
$806$	4.47877	0.157758
$807$	9.37107	0.329877
$808$	17.4526	0.613980
$809$	−21.2621	−0.747536	−0.373768	−	0.927522i	$-0.621934\pi$
$809$	−21.2621	−0.747536	−0.373768	+	0.927522i	$0.621934\pi$
$810$	−0.483732	−0.0169966
$811$	−11.5188	−0.404481	−0.202240	−	0.979336i	$-0.564822\pi$
$811$	−11.5188	−0.404481	−0.202240	+	0.979336i	$0.564822\pi$
$812$	−4.47647	−0.157093
$813$	−18.2506	−0.640077
$814$	16.4693	0.577248
$815$	9.09090	0.318440
$816$	4.05183	0.141842
$817$	−55.1441	−1.92925
$818$	−1.68232	−0.0588211
$819$	0.896578	0.0313290
$820$	−4.53201	−0.158265
$821$	−16.3022	−0.568951	−0.284476	−	0.958683i	$-0.591819\pi$
$821$	−16.3022	−0.568951	−0.284476	+	0.958683i	$0.591819\pi$
$822$	−16.6345	−0.580195
$823$	−28.2546	−0.984895	−0.492448	−	0.870342i	$-0.663898\pi$
$823$	−28.2546	−0.984895	−0.492448	+	0.870342i	$0.663898\pi$
$824$	13.6303	0.474835
$825$	−13.8055	−0.480645
$826$	9.44063	0.328482
$827$	−3.48936	−0.121337	−0.0606685	−	0.998158i	$-0.519323\pi$
$827$	−3.48936	−0.121337	−0.0606685	+	0.998158i	$0.519323\pi$
$828$	4.14067	0.143898
$829$	10.2627	0.356439	0.178220	−	0.983991i	$-0.442966\pi$
$829$	10.2627	0.356439	0.178220	+	0.983991i	$0.442966\pi$
$830$	−1.89655	−0.0658301
$831$	−1.42528	−0.0494424
$832$	0.896578	0.0310832
$833$	−4.05183	−0.140388
$834$	17.8329	0.617503
$835$	−1.65628	−0.0573180
$836$	15.9311	0.550989
$837$	−4.99541	−0.172667
$838$	−5.35662	−0.185042
$839$	32.7506	1.13068	0.565338	−	0.824860i	$-0.308746\pi$
$839$	32.7506	1.13068	0.565338	+	0.824860i	$0.308746\pi$
$840$	0.483732	0.0166903
$841$	−8.96120	−0.309007
$842$	3.90985	0.134742
$843$	−14.0874	−0.485197
$844$	6.39382	0.220084
$845$	5.89966	0.202955
$846$	0.591028	0.0203200
$847$	−2.60938	−0.0896593
$848$	9.53963	0.327592
$849$	−30.5712	−1.04920
$850$	19.3110	0.662363
$851$	−23.5423	−0.807018
$852$	6.49576	0.222541
$853$	−27.0367	−0.925717	−0.462859	−	0.886432i	$-0.653176\pi$
$853$	−27.0367	−0.925717	−0.462859	+	0.886432i	$0.653176\pi$
$854$	5.46611	0.187046
$855$	2.66044	0.0909851
$856$	−16.2715	−0.556150
$857$	−15.0278	−0.513340	−0.256670	−	0.966499i	$-0.582625\pi$
$857$	−15.0278	−0.513340	−0.256670	+	0.966499i	$0.582625\pi$
$858$	2.59708	0.0886628
$859$	−20.8331	−0.710816	−0.355408	−	0.934711i	$-0.615658\pi$
$859$	−20.8331	−0.710816	−0.355408	+	0.934711i	$0.615658\pi$
$860$	−4.85014	−0.165388
$861$	−9.36885	−0.319290
$862$	26.8886	0.915828
$863$	22.5392	0.767243	0.383621	−	0.923491i	$-0.374677\pi$
$863$	22.5392	0.767243	0.383621	+	0.923491i	$0.374677\pi$
$864$	−1.00000	−0.0340207
$865$	−0.0363761	−0.00123683
$866$	−28.7239	−0.976078
$867$	0.582680	0.0197889
$868$	4.99541	0.169555
$869$	13.1215	0.445117
$870$	−2.16541	−0.0734143
$871$	−3.82750	−0.129690
$872$	6.56752	0.222404
$873$	2.64762	0.0896083
$874$	−22.7730	−0.770307
$875$	4.72412	0.159705
$876$	−7.15692	−0.241810
$877$	−8.40045	−0.283663	−0.141832	−	0.989891i	$-0.545299\pi$
$877$	−8.40045	−0.283663	−0.141832	+	0.989891i	$0.545299\pi$
$878$	21.6594	0.730971
$879$	−10.3750	−0.349940
$880$	1.40120	0.0472346
$881$	43.3137	1.45928	0.729638	−	0.683834i	$-0.239689\pi$
$881$	43.3137	1.45928	0.729638	+	0.683834i	$0.239689\pi$
$882$	1.00000	0.0336718
$883$	−38.8363	−1.30695	−0.653473	−	0.756950i	$-0.726689\pi$
$883$	−38.8363	−1.30695	−0.653473	+	0.756950i	$0.726689\pi$
$884$	−3.63278	−0.122184
$885$	4.56673	0.153509
$886$	2.61556	0.0878715
$887$	43.6171	1.46452	0.732260	−	0.681025i	$-0.238466\pi$
$887$	43.6171	1.46452	0.732260	+	0.681025i	$0.238466\pi$
$888$	5.68561	0.190797
$889$	−3.64964	−0.122405
$890$	0.0957015	0.00320792
$891$	−2.89666	−0.0970417
$892$	−6.57265	−0.220068
$893$	−3.25055	−0.108776
$894$	9.42253	0.315137
$895$	−6.99848	−0.233933
$896$	1.00000	0.0334077
$897$	−3.71243	−0.123955
$898$	−35.8107	−1.19502
$899$	−22.3618	−0.745808
$900$	−4.76600	−0.158867
$901$	−38.6529	−1.28772
$902$	−27.1384	−0.903608
$903$	−10.0265	−0.333661
$904$	18.4197	0.612631
$905$	−4.48953	−0.149237
$906$	−16.5531	−0.549939
$907$	−44.7392	−1.48554	−0.742770	−	0.669547i	$-0.766488\pi$
$907$	−44.7392	−1.48554	−0.742770	+	0.669547i	$0.766488\pi$
$908$	14.2674	0.473482
$909$	17.4526	0.578866
$910$	−0.433703	−0.0143771
$911$	−30.1145	−0.997738	−0.498869	−	0.866677i	$-0.666251\pi$
$911$	−30.1145	−0.997738	−0.498869	+	0.866677i	$0.666251\pi$
$912$	5.49983	0.182117
$913$	−11.3568	−0.375856
$914$	34.5634	1.14326
$915$	2.64413	0.0874122
$916$	12.3014	0.406450
$917$	4.59474	0.151732
$918$	4.05183	0.133730
$919$	29.4804	0.972469	0.486235	−	0.873828i	$-0.338370\pi$
$919$	29.4804	0.972469	0.486235	+	0.873828i	$0.338370\pi$
$920$	−2.00297	−0.0660361
$921$	30.1068	0.992052
$922$	−17.5639	−0.578435
$923$	−5.82395	−0.191698
$924$	2.89666	0.0952930
$925$	27.0977	0.890966
$926$	5.46832	0.179700
$927$	13.6303	0.447679
$928$	−4.47647	−0.146947
$929$	21.8603	0.717214	0.358607	−	0.933489i	$-0.383252\pi$
$929$	21.8603	0.717214	0.358607	+	0.933489i	$0.383252\pi$
$930$	2.41644	0.0792381
$931$	−5.49983	−0.180250
$932$	−3.95478	−0.129543
$933$	−30.3294	−0.992939
$934$	−33.6090	−1.09972
$935$	−5.67744	−0.185672
$936$	0.896578	0.0293056
$937$	4.78436	0.156298	0.0781491	−	0.996942i	$-0.475099\pi$
$937$	4.78436	0.156298	0.0781491	+	0.996942i	$0.475099\pi$
$938$	−4.26901	−0.139388
$939$	30.6309	0.999603
$940$	−0.285899	−0.00932500
$941$	15.5288	0.506223	0.253112	−	0.967437i	$-0.418546\pi$
$941$	15.5288	0.506223	0.253112	+	0.967437i	$0.418546\pi$
$942$	8.99174	0.292967
$943$	38.7933	1.26328
$944$	9.44063	0.307266
$945$	0.483732	0.0157358
$946$	−29.0434	−0.944281
$947$	−7.39116	−0.240180	−0.120090	−	0.992763i	$-0.538318\pi$
$947$	−7.39116	−0.240180	−0.120090	+	0.992763i	$0.538318\pi$
$948$	4.52988	0.147124
$949$	6.41673	0.208296
$950$	26.2122	0.850436
$951$	−0.403978	−0.0130999
$952$	−4.05183	−0.131321
$953$	−11.5589	−0.374428	−0.187214	−	0.982319i	$-0.559946\pi$
$953$	−11.5589	−0.374428	−0.187214	+	0.982319i	$0.559946\pi$
$954$	9.53963	0.308857
$955$	−0.483732	−0.0156532
$956$	23.1539	0.748850
$957$	−12.9668	−0.419157
$958$	−19.6510	−0.634895
$959$	16.6345	0.537156
$960$	0.483732	0.0156124
$961$	−6.04589	−0.195029
$962$	−5.09760	−0.164353
$963$	−16.2715	−0.524343
$964$	−4.97176	−0.160130
$965$	2.70960	0.0872250
$966$	−4.14067	−0.133224
$967$	−28.3364	−0.911238	−0.455619	−	0.890175i	$-0.650582\pi$
$967$	−28.3364	−0.911238	−0.455619	+	0.890175i	$0.650582\pi$
$968$	−2.60938	−0.0838686
$969$	−22.2844	−0.715877
$970$	−1.28074	−0.0411220
$971$	40.1365	1.28804	0.644021	−	0.765008i	$-0.277265\pi$
$971$	40.1365	1.28804	0.644021	+	0.765008i	$0.277265\pi$
$972$	−1.00000	−0.0320750
$973$	−17.8329	−0.571697
$974$	−23.0805	−0.739547
$975$	4.27309	0.136849
$976$	5.46611	0.174966
$977$	2.81417	0.0900332	0.0450166	−	0.998986i	$-0.485666\pi$
$977$	2.81417	0.0900332	0.0450166	+	0.998986i	$0.485666\pi$
$978$	18.7933	0.600943
$979$	0.573075	0.0183156
$980$	−0.483732	−0.0154522
$981$	6.56752	0.209685
$982$	42.6520	1.36108
$983$	37.3320	1.19071	0.595354	−	0.803464i	$-0.297012\pi$
$983$	37.3320	1.19071	0.595354	+	0.803464i	$0.297012\pi$
$984$	−9.36885	−0.298668
$985$	5.76129	0.183570
$986$	18.1379	0.577628
$987$	−0.591028	−0.0188126
$988$	−4.93102	−0.156877
$989$	41.5165	1.32015
$990$	1.40120	0.0445332
$991$	2.64031	0.0838721	0.0419360	−	0.999120i	$-0.486647\pi$
$991$	2.64031	0.0838721	0.0419360	+	0.999120i	$0.486647\pi$
$992$	4.99541	0.158604
$993$	−13.3168	−0.422595
$994$	−6.49576	−0.206033
$995$	−2.53017	−0.0802119
$996$	−3.92066	−0.124231
$997$	36.4505	1.15440	0.577200	−	0.816603i	$-0.304145\pi$
$997$	36.4505	1.15440	0.577200	+	0.816603i	$0.304145\pi$
$998$	19.9413	0.631232
$999$	5.68561	0.179885

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8022.2.a.r.1.4	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8022.2.a.r.1.4	✓	10	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:	\( N \)	\(=\)	\( 8022 = 2 \cdot 3 \cdot 7 \cdot 191 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8022.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -0.483732 q^{5} -1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -0.483732 q^{5} -1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} -0.483732 q^{10} -2.89666 q^{11} -1.00000 q^{12} +0.896578 q^{13} +1.00000 q^{14} +0.483732 q^{15} +1.00000 q^{16} -4.05183 q^{17} +1.00000 q^{18} -5.49983 q^{19} -0.483732 q^{20} -1.00000 q^{21} -2.89666 q^{22} +4.14067 q^{23} -1.00000 q^{24} -4.76600 q^{25} +0.896578 q^{26} -1.00000 q^{27} +1.00000 q^{28} -4.47647 q^{29} +0.483732 q^{30} +4.99541 q^{31} +1.00000 q^{32} +2.89666 q^{33} -4.05183 q^{34} -0.483732 q^{35} +1.00000 q^{36} -5.68561 q^{37} -5.49983 q^{38} -0.896578 q^{39} -0.483732 q^{40} +9.36885 q^{41} -1.00000 q^{42} +10.0265 q^{43} -2.89666 q^{44} -0.483732 q^{45} +4.14067 q^{46} +0.591028 q^{47} -1.00000 q^{48} +1.00000 q^{49} -4.76600 q^{50} +4.05183 q^{51} +0.896578 q^{52} +9.53963 q^{53} -1.00000 q^{54} +1.40120 q^{55} +1.00000 q^{56} +5.49983 q^{57} -4.47647 q^{58} +9.44063 q^{59} +0.483732 q^{60} +5.46611 q^{61} +4.99541 q^{62} +1.00000 q^{63} +1.00000 q^{64} -0.433703 q^{65} +2.89666 q^{66} -4.26901 q^{67} -4.05183 q^{68} -4.14067 q^{69} -0.483732 q^{70} -6.49576 q^{71} +1.00000 q^{72} +7.15692 q^{73} -5.68561 q^{74} +4.76600 q^{75} -5.49983 q^{76} -2.89666 q^{77} -0.896578 q^{78} -4.52988 q^{79} -0.483732 q^{80} +1.00000 q^{81} +9.36885 q^{82} +3.92066 q^{83} -1.00000 q^{84} +1.96000 q^{85} +10.0265 q^{86} +4.47647 q^{87} -2.89666 q^{88} -0.197840 q^{89} -0.483732 q^{90} +0.896578 q^{91} +4.14067 q^{92} -4.99541 q^{93} +0.591028 q^{94} +2.66044 q^{95} -1.00000 q^{96} +2.64762 q^{97} +1.00000 q^{98} -2.89666 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 10 q^{2} - 10 q^{3} + 10 q^{4} + 8 q^{5} - 10 q^{6} + 10 q^{7} + 10 q^{8} + 10 q^{9}+O(q^{10}) \) 10 * q + 10 * q^2 - 10 * q^3 + 10 * q^4 + 8 * q^5 - 10 * q^6 + 10 * q^7 + 10 * q^8 + 10 * q^9	\( 10 q + 10 q^{2} - 10 q^{3} + 10 q^{4} + 8 q^{5} - 10 q^{6} + 10 q^{7} + 10 q^{8} + 10 q^{9} + 8 q^{10} + 4 q^{11} - 10 q^{12} + 6 q^{13} + 10 q^{14} - 8 q^{15} + 10 q^{16} + 5 q^{17} + 10 q^{18} + 15 q^{19} + 8 q^{20} - 10 q^{21} + 4 q^{22} + 12 q^{23} - 10 q^{24} - 2 q^{25} + 6 q^{26} - 10 q^{27} + 10 q^{28} + 7 q^{29} - 8 q^{30} + 28 q^{31} + 10 q^{32} - 4 q^{33} + 5 q^{34} + 8 q^{35} + 10 q^{36} - 3 q^{37} + 15 q^{38} - 6 q^{39} + 8 q^{40} + 24 q^{41} - 10 q^{42} + 4 q^{43} + 4 q^{44} + 8 q^{45} + 12 q^{46} + 16 q^{47} - 10 q^{48} + 10 q^{49} - 2 q^{50} - 5 q^{51} + 6 q^{52} + 5 q^{53} - 10 q^{54} - q^{55} + 10 q^{56} - 15 q^{57} + 7 q^{58} + 17 q^{59} - 8 q^{60} + 15 q^{61} + 28 q^{62} + 10 q^{63} + 10 q^{64} + 14 q^{65} - 4 q^{66} + 6 q^{67} + 5 q^{68} - 12 q^{69} + 8 q^{70} + 5 q^{71} + 10 q^{72} + 16 q^{73} - 3 q^{74} + 2 q^{75} + 15 q^{76} + 4 q^{77} - 6 q^{78} - 5 q^{79} + 8 q^{80} + 10 q^{81} + 24 q^{82} + 24 q^{83} - 10 q^{84} - 19 q^{85} + 4 q^{86} - 7 q^{87} + 4 q^{88} + 17 q^{89} + 8 q^{90} + 6 q^{91} + 12 q^{92} - 28 q^{93} + 16 q^{94} + 15 q^{95} - 10 q^{96} + 20 q^{97} + 10 q^{98} + 4 q^{99}+O(q^{100}) \) 10 * q + 10 * q^2 - 10 * q^3 + 10 * q^4 + 8 * q^5 - 10 * q^6 + 10 * q^7 + 10 * q^8 + 10 * q^9 + 8 * q^10 + 4 * q^11 - 10 * q^12 + 6 * q^13 + 10 * q^14 - 8 * q^15 + 10 * q^16 + 5 * q^17 + 10 * q^18 + 15 * q^19 + 8 * q^20 - 10 * q^21 + 4 * q^22 + 12 * q^23 - 10 * q^24 - 2 * q^25 + 6 * q^26 - 10 * q^27 + 10 * q^28 + 7 * q^29 - 8 * q^30 + 28 * q^31 + 10 * q^32 - 4 * q^33 + 5 * q^34 + 8 * q^35 + 10 * q^36 - 3 * q^37 + 15 * q^38 - 6 * q^39 + 8 * q^40 + 24 * q^41 - 10 * q^42 + 4 * q^43 + 4 * q^44 + 8 * q^45 + 12 * q^46 + 16 * q^47 - 10 * q^48 + 10 * q^49 - 2 * q^50 - 5 * q^51 + 6 * q^52 + 5 * q^53 - 10 * q^54 - q^55 + 10 * q^56 - 15 * q^57 + 7 * q^58 + 17 * q^59 - 8 * q^60 + 15 * q^61 + 28 * q^62 + 10 * q^63 + 10 * q^64 + 14 * q^65 - 4 * q^66 + 6 * q^67 + 5 * q^68 - 12 * q^69 + 8 * q^70 + 5 * q^71 + 10 * q^72 + 16 * q^73 - 3 * q^74 + 2 * q^75 + 15 * q^76 + 4 * q^77 - 6 * q^78 - 5 * q^79 + 8 * q^80 + 10 * q^81 + 24 * q^82 + 24 * q^83 - 10 * q^84 - 19 * q^85 + 4 * q^86 - 7 * q^87 + 4 * q^88 + 17 * q^89 + 8 * q^90 + 6 * q^91 + 12 * q^92 - 28 * q^93 + 16 * q^94 + 15 * q^95 - 10 * q^96 + 20 * q^97 + 10 * q^98 + 4 * q^99

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