LMFDB - Embedded newform 8007.2.a.g.1.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8007,2,Mod(1,8007)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8007, 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("8007.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8007 = 3 \cdot 17 \cdot 157 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8007.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:	$63.9362168984$
Analytic rank:	$0$
Dimension:	$56$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.17
Character	$\chi$	$=$	8007.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.26654 q^{2} -1.00000 q^{3} -0.395877 q^{4} +2.14407 q^{5} +1.26654 q^{6} +1.86831 q^{7} +3.03447 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.26654 q^{2} -1.00000 q^{3} -0.395877 q^{4} +2.14407 q^{5} +1.26654 q^{6} +1.86831 q^{7} +3.03447 q^{8} +1.00000 q^{9} -2.71555 q^{10} +2.06649 q^{11} +0.395877 q^{12} +1.96535 q^{13} -2.36629 q^{14} -2.14407 q^{15} -3.05153 q^{16} -1.00000 q^{17} -1.26654 q^{18} +7.43297 q^{19} -0.848787 q^{20} -1.86831 q^{21} -2.61729 q^{22} -0.143684 q^{23} -3.03447 q^{24} -0.402968 q^{25} -2.48920 q^{26} -1.00000 q^{27} -0.739621 q^{28} +3.17069 q^{29} +2.71555 q^{30} +6.33711 q^{31} -2.20407 q^{32} -2.06649 q^{33} +1.26654 q^{34} +4.00579 q^{35} -0.395877 q^{36} +4.70782 q^{37} -9.41416 q^{38} -1.96535 q^{39} +6.50612 q^{40} +10.7426 q^{41} +2.36629 q^{42} +4.86321 q^{43} -0.818074 q^{44} +2.14407 q^{45} +0.181981 q^{46} -2.54897 q^{47} +3.05153 q^{48} -3.50941 q^{49} +0.510375 q^{50} +1.00000 q^{51} -0.778038 q^{52} -1.87787 q^{53} +1.26654 q^{54} +4.43069 q^{55} +5.66934 q^{56} -7.43297 q^{57} -4.01581 q^{58} -1.03911 q^{59} +0.848787 q^{60} -10.6165 q^{61} -8.02620 q^{62} +1.86831 q^{63} +8.89459 q^{64} +4.21385 q^{65} +2.61729 q^{66} -1.17088 q^{67} +0.395877 q^{68} +0.143684 q^{69} -5.07349 q^{70} -5.43264 q^{71} +3.03447 q^{72} -2.52517 q^{73} -5.96264 q^{74} +0.402968 q^{75} -2.94254 q^{76} +3.86084 q^{77} +2.48920 q^{78} +5.70681 q^{79} -6.54269 q^{80} +1.00000 q^{81} -13.6060 q^{82} +11.2506 q^{83} +0.739621 q^{84} -2.14407 q^{85} -6.15945 q^{86} -3.17069 q^{87} +6.27070 q^{88} +11.9176 q^{89} -2.71555 q^{90} +3.67189 q^{91} +0.0568811 q^{92} -6.33711 q^{93} +3.22837 q^{94} +15.9368 q^{95} +2.20407 q^{96} +16.3484 q^{97} +4.44481 q^{98} +2.06649 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + q^{2} - 56 q^{3} + 61 q^{4} + q^{5} - q^{6} + 19 q^{7} + 56 q^{9}+O(q^{10}) $ 56 * q + q^2 - 56 * q^3 + 61 * q^4 + q^5 - q^6 + 19 * q^7 + 56 * q^9	\( 56 q + q^{2} - 56 q^{3} + 61 q^{4} + q^{5} - q^{6} + 19 q^{7} + 56 q^{9} + 8 q^{10} - 7 q^{11} - 61 q^{12} + 8 q^{13} - 8 q^{14} - q^{15} + 71 q^{16} - 56 q^{17} + q^{18} - 2 q^{19} - 4 q^{20} - 19 q^{21} + 47 q^{22} + 16 q^{23} + 85 q^{25} - 11 q^{26} - 56 q^{27} + 52 q^{28} + 17 q^{29} - 8 q^{30} + 23 q^{31} + 11 q^{32} + 7 q^{33} - q^{34} - 41 q^{35} + 61 q^{36} + 58 q^{37} - 22 q^{38} - 8 q^{39} + 38 q^{40} - q^{41} + 8 q^{42} + 27 q^{43} + 2 q^{44} + q^{45} + 46 q^{46} + 5 q^{47} - 71 q^{48} + 59 q^{49} - 4 q^{50} + 56 q^{51} + 25 q^{52} + 15 q^{53} - q^{54} + 9 q^{55} - 36 q^{56} + 2 q^{57} + 89 q^{58} - 61 q^{59} + 4 q^{60} + 47 q^{61} + 8 q^{62} + 19 q^{63} + 88 q^{64} + 39 q^{65} - 47 q^{66} + 20 q^{67} - 61 q^{68} - 16 q^{69} + 36 q^{70} - 2 q^{71} + 93 q^{73} + 48 q^{74} - 85 q^{75} + 38 q^{76} + 26 q^{77} + 11 q^{78} + 72 q^{79} + 42 q^{80} + 56 q^{81} + 33 q^{82} - 11 q^{83} - 52 q^{84} - q^{85} - 4 q^{86} - 17 q^{87} + 130 q^{88} - 6 q^{89} + 8 q^{90} + 37 q^{91} + 132 q^{92} - 23 q^{93} - 32 q^{94} + 12 q^{95} - 11 q^{96} + 100 q^{97} + 42 q^{98} - 7 q^{99}+O(q^{100}) \) 56 * q + q^2 - 56 * q^3 + 61 * q^4 + q^5 - q^6 + 19 * q^7 + 56 * q^9 + 8 * q^10 - 7 * q^11 - 61 * q^12 + 8 * q^13 - 8 * q^14 - q^15 + 71 * q^16 - 56 * q^17 + q^18 - 2 * q^19 - 4 * q^20 - 19 * q^21 + 47 * q^22 + 16 * q^23 + 85 * q^25 - 11 * q^26 - 56 * q^27 + 52 * q^28 + 17 * q^29 - 8 * q^30 + 23 * q^31 + 11 * q^32 + 7 * q^33 - q^34 - 41 * q^35 + 61 * q^36 + 58 * q^37 - 22 * q^38 - 8 * q^39 + 38 * q^40 - q^41 + 8 * q^42 + 27 * q^43 + 2 * q^44 + q^45 + 46 * q^46 + 5 * q^47 - 71 * q^48 + 59 * q^49 - 4 * q^50 + 56 * q^51 + 25 * q^52 + 15 * q^53 - q^54 + 9 * q^55 - 36 * q^56 + 2 * q^57 + 89 * q^58 - 61 * q^59 + 4 * q^60 + 47 * q^61 + 8 * q^62 + 19 * q^63 + 88 * q^64 + 39 * q^65 - 47 * q^66 + 20 * q^67 - 61 * q^68 - 16 * q^69 + 36 * q^70 - 2 * q^71 + 93 * q^73 + 48 * q^74 - 85 * q^75 + 38 * q^76 + 26 * q^77 + 11 * q^78 + 72 * q^79 + 42 * q^80 + 56 * q^81 + 33 * q^82 - 11 * q^83 - 52 * q^84 - q^85 - 4 * q^86 - 17 * q^87 + 130 * q^88 - 6 * q^89 + 8 * q^90 + 37 * q^91 + 132 * q^92 - 23 * q^93 - 32 * q^94 + 12 * q^95 - 11 * q^96 + 100 * q^97 + 42 * q^98 - 7 * 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 $

$2$	−1.26654	−0.895579	−0.447789	−	0.894139i	$-0.647789\pi$
$2$	−1.26654	−0.895579	−0.447789	+	0.894139i	$0.647789\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−0.395877	−0.197938
$5$	2.14407	0.958857	0.479428	−	0.877581i	$-0.340844\pi$
$5$	2.14407	0.958857	0.479428	+	0.877581i	$0.340844\pi$
$6$	1.26654	0.517063
$7$	1.86831	0.706155	0.353078	−	0.935594i	$-0.385135\pi$
$7$	1.86831	0.706155	0.353078	+	0.935594i	$0.385135\pi$
$8$	3.03447	1.07285
$9$	1.00000	0.333333
$10$	−2.71555	−0.858732
$11$	2.06649	0.623069	0.311534	−	0.950235i	$-0.399157\pi$
$11$	2.06649	0.623069	0.311534	+	0.950235i	$0.399157\pi$
$12$	0.395877	0.114280
$13$	1.96535	0.545091	0.272545	−	0.962143i	$-0.412134\pi$
$13$	1.96535	0.545091	0.272545	+	0.962143i	$0.412134\pi$
$14$	−2.36629	−0.632418
$15$	−2.14407	−0.553596
$16$	−3.05153	−0.762882
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−1.26654	−0.298526
$19$	7.43297	1.70524	0.852620	−	0.522531i	$-0.175012\pi$
$19$	7.43297	1.70524	0.852620	+	0.522531i	$0.175012\pi$
$20$	−0.848787	−0.189795
$21$	−1.86831	−0.407699
$22$	−2.61729	−0.558007
$23$	−0.143684	−0.0299602	−0.0149801	−	0.999888i	$-0.504768\pi$
$23$	−0.143684	−0.0299602	−0.0149801	+	0.999888i	$0.504768\pi$
$24$	−3.03447	−0.619409
$25$	−0.402968	−0.0805937
$26$	−2.48920	−0.488172
$27$	−1.00000	−0.192450
$28$	−0.739621	−0.139775
$29$	3.17069	0.588782	0.294391	−	0.955685i	$-0.404883\pi$
$29$	3.17069	0.588782	0.294391	+	0.955685i	$0.404883\pi$
$30$	2.71555	0.495789
$31$	6.33711	1.13818	0.569089	−	0.822276i	$-0.307296\pi$
$31$	6.33711	1.13818	0.569089	+	0.822276i	$0.307296\pi$
$32$	−2.20407	−0.389627
$33$	−2.06649	−0.359729
$34$	1.26654	0.217210
$35$	4.00579	0.677102
$36$	−0.395877	−0.0659795
$37$	4.70782	0.773961	0.386981	−	0.922088i	$-0.373518\pi$
$37$	4.70782	0.773961	0.386981	+	0.922088i	$0.373518\pi$
$38$	−9.41416	−1.52718
$39$	−1.96535	−0.314708
$40$	6.50612	1.02871
$41$	10.7426	1.67772	0.838859	−	0.544349i	$-0.183223\pi$
$41$	10.7426	1.67772	0.838859	+	0.544349i	$0.183223\pi$
$42$	2.36629	0.365127
$43$	4.86321	0.741633	0.370817	−	0.928706i	$-0.379078\pi$
$43$	4.86321	0.741633	0.370817	+	0.928706i	$0.379078\pi$
$44$	−0.818074	−0.123329
$45$	2.14407	0.319619
$46$	0.181981	0.0268317
$47$	−2.54897	−0.371806	−0.185903	−	0.982568i	$-0.559521\pi$
$47$	−2.54897	−0.371806	−0.185903	+	0.982568i	$0.559521\pi$
$48$	3.05153	0.440450
$49$	−3.50941	−0.501345
$50$	0.510375	0.0721780
$51$	1.00000	0.140028
$52$	−0.778038	−0.107894
$53$	−1.87787	−0.257945	−0.128973	−	0.991648i	$-0.541168\pi$
$53$	−1.87787	−0.257945	−0.128973	+	0.991648i	$0.541168\pi$
$54$	1.26654	0.172354
$55$	4.43069	0.597434
$56$	5.66934	0.757598
$57$	−7.43297	−0.984521
$58$	−4.01581	−0.527301
$59$	−1.03911	−0.135280	−0.0676402	−	0.997710i	$-0.521547\pi$
$59$	−1.03911	−0.135280	−0.0676402	+	0.997710i	$0.521547\pi$
$60$	0.848787	0.109578
$61$	−10.6165	−1.35931	−0.679653	−	0.733534i	$-0.737869\pi$
$61$	−10.6165	−1.35931	−0.679653	+	0.733534i	$0.737869\pi$
$62$	−8.02620	−1.01933
$63$	1.86831	0.235385
$64$	8.89459	1.11182
$65$	4.21385	0.522664
$66$	2.61729	0.322166
$67$	−1.17088	−0.143045	−0.0715227	−	0.997439i	$-0.522786\pi$
$67$	−1.17088	−0.143045	−0.0715227	+	0.997439i	$0.522786\pi$
$68$	0.395877	0.0480071
$69$	0.143684	0.0172975
$70$	−5.07349	−0.606398
$71$	−5.43264	−0.644736	−0.322368	−	0.946614i	$-0.604479\pi$
$71$	−5.43264	−0.644736	−0.322368	+	0.946614i	$0.604479\pi$
$72$	3.03447	0.357616
$73$	−2.52517	−0.295549	−0.147775	−	0.989021i	$-0.547211\pi$
$73$	−2.52517	−0.295549	−0.147775	+	0.989021i	$0.547211\pi$
$74$	−5.96264	−0.693143
$75$	0.402968	0.0465308
$76$	−2.94254	−0.337533
$77$	3.86084	0.439983
$78$	2.48920	0.281846
$79$	5.70681	0.642066	0.321033	−	0.947068i	$-0.395970\pi$
$79$	5.70681	0.642066	0.321033	+	0.947068i	$0.395970\pi$
$80$	−6.54269	−0.731495
$81$	1.00000	0.111111
$82$	−13.6060	−1.50253
$83$	11.2506	1.23492	0.617458	−	0.786604i	$-0.288163\pi$
$83$	11.2506	1.23492	0.617458	+	0.786604i	$0.288163\pi$
$84$	0.739621	0.0806993
$85$	−2.14407	−0.232557
$86$	−6.15945	−0.664191
$87$	−3.17069	−0.339934
$88$	6.27070	0.668458
$89$	11.9176	1.26326	0.631631	−	0.775269i	$-0.282386\pi$
$89$	11.9176	1.26326	0.631631	+	0.775269i	$0.282386\pi$
$90$	−2.71555	−0.286244
$91$	3.67189	0.384919
$92$	0.0568811	0.00593027
$93$	−6.33711	−0.657128
$94$	3.22837	0.332981
$95$	15.9368	1.63508
$96$	2.20407	0.224951
$97$	16.3484	1.65993	0.829964	−	0.557817i	$-0.188361\pi$
$97$	16.3484	1.65993	0.829964	+	0.557817i	$0.188361\pi$
$98$	4.44481	0.448994
$99$	2.06649	0.207690
$100$	0.159526	0.0159526
$101$	2.48109	0.246878	0.123439	−	0.992352i	$-0.460608\pi$
$101$	2.48109	0.246878	0.123439	+	0.992352i	$0.460608\pi$
$102$	−1.26654	−0.125406
$103$	9.70428	0.956191	0.478096	−	0.878308i	$-0.341327\pi$
$103$	9.70428	0.956191	0.478096	+	0.878308i	$0.341327\pi$
$104$	5.96381	0.584800
$105$	−4.00579	−0.390925
$106$	2.37839	0.231010
$107$	18.3371	1.77271	0.886356	−	0.463004i	$-0.153228\pi$
$107$	18.3371	1.77271	0.886356	+	0.463004i	$0.153228\pi$
$108$	0.395877	0.0380933
$109$	0.499013	0.0477968	0.0238984	−	0.999714i	$-0.492392\pi$
$109$	0.499013	0.0477968	0.0238984	+	0.999714i	$0.492392\pi$
$110$	−5.61164	−0.535049
$111$	−4.70782	−0.446847
$112$	−5.70120	−0.538713
$113$	11.5253	1.08421	0.542104	−	0.840312i	$-0.317628\pi$
$113$	11.5253	1.08421	0.542104	+	0.840312i	$0.317628\pi$
$114$	9.41416	0.881716
$115$	−0.308068	−0.0287275
$116$	−1.25520	−0.116543
$117$	1.96535	0.181697
$118$	1.31607	0.121154
$119$	−1.86831	−0.171268
$120$	−6.50612	−0.593925
$121$	−6.72964	−0.611785
$122$	13.4462	1.21736
$123$	−10.7426	−0.968630
$124$	−2.50872	−0.225289
$125$	−11.5843	−1.03613
$126$	−2.36629	−0.210806
$127$	18.6071	1.65111	0.825557	−	0.564319i	$-0.190861\pi$
$127$	18.6071	1.65111	0.825557	+	0.564319i	$0.190861\pi$
$128$	−6.85722	−0.606099
$129$	−4.86321	−0.428182
$130$	−5.33701	−0.468087
$131$	−15.0253	−1.31276	−0.656382	−	0.754429i	$-0.727914\pi$
$131$	−15.0253	−1.31276	−0.656382	+	0.754429i	$0.727914\pi$
$132$	0.818074	0.0712042
$133$	13.8871	1.20416
$134$	1.48296	0.128109
$135$	−2.14407	−0.184532
$136$	−3.03447	−0.260204
$137$	−3.85641	−0.329476	−0.164738	−	0.986337i	$-0.552678\pi$
$137$	−3.85641	−0.329476	−0.164738	+	0.986337i	$0.552678\pi$
$138$	−0.181981	−0.0154913
$139$	−3.05177	−0.258848	−0.129424	−	0.991589i	$-0.541313\pi$
$139$	−3.05177	−0.258848	−0.129424	+	0.991589i	$0.541313\pi$
$140$	−1.58580	−0.134024
$141$	2.54897	0.214662
$142$	6.88066	0.577412
$143$	4.06137	0.339629
$144$	−3.05153	−0.254294
$145$	6.79818	0.564558
$146$	3.19823	0.264687
$147$	3.50941	0.289451
$148$	−1.86372	−0.153197
$149$	−10.7831	−0.883387	−0.441693	−	0.897166i	$-0.645622\pi$
$149$	−10.7831	−0.883387	−0.441693	+	0.897166i	$0.645622\pi$
$150$	−0.510375	−0.0416720
$151$	−16.6947	−1.35859	−0.679297	−	0.733863i	$-0.737715\pi$
$151$	−16.6947	−1.35859	−0.679297	+	0.733863i	$0.737715\pi$
$152$	22.5552	1.82946
$153$	−1.00000	−0.0808452
$154$	−4.88991	−0.394040
$155$	13.5872	1.09135
$156$	0.778038	0.0622929
$157$	1.00000	0.0798087
$157$	1.00000	0.0798087
$158$	−7.22790	−0.575021
$159$	1.87787	0.148925
$160$	−4.72567	−0.373597
$161$	−0.268446	−0.0211565
$162$	−1.26654	−0.0995088
$163$	−23.7414	−1.85957	−0.929785	−	0.368104i	$-0.880007\pi$
$163$	−23.7414	−1.85957	−0.929785	+	0.368104i	$0.880007\pi$
$164$	−4.25276	−0.332085
$165$	−4.43069	−0.344929
$166$	−14.2494	−1.10596
$167$	−19.9354	−1.54265	−0.771324	−	0.636443i	$-0.780405\pi$
$167$	−19.9354	−1.54265	−0.771324	+	0.636443i	$0.780405\pi$
$168$	−5.66934	−0.437399
$169$	−9.13739	−0.702876
$170$	2.71555	0.208273
$171$	7.43297	0.568414
$172$	−1.92523	−0.146798
$173$	−3.50000	−0.266100	−0.133050	−	0.991109i	$-0.542477\pi$
$173$	−3.50000	−0.266100	−0.133050	+	0.991109i	$0.542477\pi$
$174$	4.01581	0.304437
$175$	−0.752870	−0.0569117
$176$	−6.30594	−0.475328
$177$	1.03911	0.0781042
$178$	−15.0941	−1.13135
$179$	11.4135	0.853085	0.426542	−	0.904468i	$-0.359732\pi$
$179$	11.4135	0.853085	0.426542	+	0.904468i	$0.359732\pi$
$180$	−0.848787	−0.0632649
$181$	11.4283	0.849457	0.424729	−	0.905321i	$-0.360370\pi$
$181$	11.4283	0.849457	0.424729	+	0.905321i	$0.360370\pi$
$182$	−4.65060	−0.344725
$183$	10.6165	0.784795
$184$	−0.436005	−0.0321427
$185$	10.0939	0.742118
$186$	8.02620	0.588510
$187$	−2.06649	−0.151116
$188$	1.00908	0.0735946
$189$	−1.86831	−0.135900
$190$	−20.1846	−1.46434
$191$	−15.9787	−1.15617	−0.578087	−	0.815975i	$-0.696201\pi$
$191$	−15.9787	−1.15617	−0.578087	+	0.815975i	$0.696201\pi$
$192$	−8.89459	−0.641912
$193$	−18.7190	−1.34742	−0.673711	−	0.738995i	$-0.735301\pi$
$193$	−18.7190	−1.34742	−0.673711	+	0.738995i	$0.735301\pi$
$194$	−20.7059	−1.48660
$195$	−4.21385	−0.301760
$196$	1.38930	0.0992354
$197$	−19.5897	−1.39571	−0.697855	−	0.716239i	$-0.745862\pi$
$197$	−19.5897	−1.39571	−0.697855	+	0.716239i	$0.745862\pi$
$198$	−2.61729	−0.186002
$199$	−19.6553	−1.39333	−0.696663	−	0.717399i	$-0.745333\pi$
$199$	−19.6553	−1.39333	−0.696663	+	0.717399i	$0.745333\pi$
$200$	−1.22280	−0.0864648
$201$	1.17088	0.0825873
$202$	−3.14240	−0.221098
$203$	5.92384	0.415772
$204$	−0.395877	−0.0277169
$205$	23.0329	1.60869
$206$	−12.2909	−0.856345
$207$	−0.143684	−0.00998672
$208$	−5.99733	−0.415840
$209$	15.3601	1.06248
$210$	5.07349	0.350104
$211$	6.42803	0.442524	0.221262	−	0.975214i	$-0.428982\pi$
$211$	6.42803	0.442524	0.221262	+	0.975214i	$0.428982\pi$
$212$	0.743405	0.0510572
$213$	5.43264	0.372239
$214$	−23.2246	−1.58760
$215$	10.4271	0.711120
$216$	−3.03447	−0.206470
$217$	11.8397	0.803731
$218$	−0.632020	−0.0428058
$219$	2.52517	0.170635
$220$	−1.75401	−0.118255
$221$	−1.96535	−0.132204
$222$	5.96264	0.400186
$223$	−12.6969	−0.850250	−0.425125	−	0.905135i	$-0.639770\pi$
$223$	−12.6969	−0.850250	−0.425125	+	0.905135i	$0.639770\pi$
$224$	−4.11788	−0.275137
$225$	−0.402968	−0.0268646
$226$	−14.5972	−0.970993
$227$	−5.45433	−0.362017	−0.181008	−	0.983482i	$-0.557936\pi$
$227$	−5.45433	−0.362017	−0.181008	+	0.983482i	$0.557936\pi$
$228$	2.94254	0.194875
$229$	−16.2163	−1.07161	−0.535803	−	0.844343i	$-0.679991\pi$
$229$	−16.2163	−1.07161	−0.535803	+	0.844343i	$0.679991\pi$
$230$	0.390181	0.0257278
$231$	−3.86084	−0.254025
$232$	9.62138	0.631674
$233$	−11.2241	−0.735314	−0.367657	−	0.929961i	$-0.619840\pi$
$233$	−11.2241	−0.735314	−0.367657	+	0.929961i	$0.619840\pi$
$234$	−2.48920	−0.162724
$235$	−5.46517	−0.356508
$236$	0.411359	0.0267772
$237$	−5.70681	−0.370697
$238$	2.36629	0.153384
$239$	14.3676	0.929364	0.464682	−	0.885478i	$-0.346169\pi$
$239$	14.3676	0.929364	0.464682	+	0.885478i	$0.346169\pi$
$240$	6.54269	0.422329
$241$	26.9683	1.73718	0.868590	−	0.495532i	$-0.165027\pi$
$241$	26.9683	1.73718	0.868590	+	0.495532i	$0.165027\pi$
$242$	8.52335	0.547902
$243$	−1.00000	−0.0641500
$244$	4.20283	0.269059
$245$	−7.52442	−0.480718
$246$	13.6060	0.867485
$247$	14.6084	0.929511
$248$	19.2298	1.22109
$249$	−11.2506	−0.712979
$250$	14.6720	0.927940
$251$	29.2584	1.84677	0.923387	−	0.383870i	$-0.125409\pi$
$251$	29.2584	1.84677	0.923387	+	0.383870i	$0.125409\pi$
$252$	−0.739621	−0.0465918
$253$	−0.296921	−0.0186673
$254$	−23.5666	−1.47870
$255$	2.14407	0.134267
$256$	−9.10424	−0.569015
$257$	−10.2739	−0.640866	−0.320433	−	0.947271i	$-0.603828\pi$
$257$	−10.2739	−0.640866	−0.320433	+	0.947271i	$0.603828\pi$
$258$	6.15945	0.383471
$259$	8.79568	0.546537
$260$	−1.66817	−0.103455
$261$	3.17069	0.196261
$262$	19.0301	1.17568
$263$	−16.1961	−0.998697	−0.499348	−	0.866401i	$-0.666427\pi$
$263$	−16.1961	−0.998697	−0.499348	+	0.866401i	$0.666427\pi$
$264$	−6.27070	−0.385935
$265$	−4.02628	−0.247332
$266$	−17.5886	−1.07842
$267$	−11.9176	−0.729345
$268$	0.463523	0.0283142
$269$	−27.1009	−1.65237	−0.826185	−	0.563398i	$-0.809494\pi$
$269$	−27.1009	−1.65237	−0.826185	+	0.563398i	$0.809494\pi$
$270$	2.71555	0.165263
$271$	−10.0504	−0.610515	−0.305258	−	0.952270i	$-0.598743\pi$
$271$	−10.0504	−0.610515	−0.305258	+	0.952270i	$0.598743\pi$
$272$	3.05153	0.185026
$273$	−3.67189	−0.222233
$274$	4.88430	0.295071
$275$	−0.832728	−0.0502154
$276$	−0.0568811	−0.00342384
$277$	27.8960	1.67611	0.838055	−	0.545586i	$-0.183693\pi$
$277$	27.8960	1.67611	0.838055	+	0.545586i	$0.183693\pi$
$278$	3.86519	0.231819
$279$	6.33711	0.379393
$280$	12.1555	0.726428
$281$	8.68225	0.517940	0.258970	−	0.965885i	$-0.416617\pi$
$281$	8.68225	0.517940	0.258970	+	0.965885i	$0.416617\pi$
$282$	−3.22837	−0.192247
$283$	12.7581	0.758388	0.379194	−	0.925317i	$-0.376201\pi$
$283$	12.7581	0.758388	0.379194	+	0.925317i	$0.376201\pi$
$284$	2.15066	0.127618
$285$	−15.9368	−0.944015
$286$	−5.14389	−0.304165
$287$	20.0706	1.18473
$288$	−2.20407	−0.129876
$289$	1.00000	0.0588235
$290$	−8.61016	−0.505606
$291$	−16.3484	−0.958360
$292$	0.999657	0.0585005
$293$	−25.8240	−1.50865	−0.754327	−	0.656498i	$-0.772037\pi$
$293$	−25.8240	−1.50865	−0.754327	+	0.656498i	$0.772037\pi$
$294$	−4.44481	−0.259227
$295$	−2.22792	−0.129715
$296$	14.2858	0.830343
$297$	−2.06649	−0.119910
$298$	13.6572	0.791142
$299$	−0.282390	−0.0163310
$300$	−0.159526	−0.00921023
$301$	9.08600	0.523708
$302$	21.1445	1.21673
$303$	−2.48109	−0.142535
$304$	−22.6819	−1.30090
$305$	−22.7625	−1.30338
$306$	1.26654	0.0724033
$307$	1.02228	0.0583446	0.0291723	−	0.999574i	$-0.490713\pi$
$307$	1.02228	0.0583446	0.0291723	+	0.999574i	$0.490713\pi$
$308$	−1.52842	−0.0870896
$309$	−9.70428	−0.552057
$310$	−17.2087	−0.977390
$311$	−24.4863	−1.38849	−0.694246	−	0.719738i	$-0.744262\pi$
$311$	−24.4863	−1.38849	−0.694246	+	0.719738i	$0.744262\pi$
$312$	−5.96381	−0.337634
$313$	18.7563	1.06017	0.530084	−	0.847945i	$-0.322160\pi$
$313$	18.7563	1.06017	0.530084	+	0.847945i	$0.322160\pi$
$314$	−1.26654	−0.0714750
$315$	4.00579	0.225701
$316$	−2.25919	−0.127090
$317$	−11.6776	−0.655879	−0.327940	−	0.944699i	$-0.606354\pi$
$317$	−11.6776	−0.655879	−0.327940	+	0.944699i	$0.606354\pi$
$318$	−2.37839	−0.133374
$319$	6.55219	0.366852
$320$	19.0706	1.06608
$321$	−18.3371	−1.02348
$322$	0.339998	0.0189473
$323$	−7.43297	−0.413582
$324$	−0.395877	−0.0219932
$325$	−0.791975	−0.0439309
$326$	30.0694	1.66539
$327$	−0.499013	−0.0275955
$328$	32.5982	1.79994
$329$	−4.76227	−0.262553
$330$	5.61164	0.308911
$331$	−24.7298	−1.35927	−0.679637	−	0.733548i	$-0.737863\pi$
$331$	−24.7298	−1.35927	−0.679637	+	0.733548i	$0.737863\pi$
$332$	−4.45386	−0.244437
$333$	4.70782	0.257987
$334$	25.2490	1.38156
$335$	−2.51044	−0.137160
$336$	5.70120	0.311026
$337$	−6.17756	−0.336513	−0.168257	−	0.985743i	$-0.553814\pi$
$337$	−6.17756	−0.336513	−0.168257	+	0.985743i	$0.553814\pi$
$338$	11.5729	0.629481
$339$	−11.5253	−0.625967
$340$	0.848787	0.0460320
$341$	13.0956	0.709164
$342$	−9.41416	−0.509059
$343$	−19.6349	−1.06018
$344$	14.7573	0.795660
$345$	0.308068	0.0165858
$346$	4.43289	0.238313
$347$	2.24924	0.120745	0.0603727	−	0.998176i	$-0.480771\pi$
$347$	2.24924	0.120745	0.0603727	+	0.998176i	$0.480771\pi$
$348$	1.25520	0.0672859
$349$	−7.17899	−0.384283	−0.192141	−	0.981367i	$-0.561543\pi$
$349$	−7.17899	−0.384283	−0.192141	+	0.981367i	$0.561543\pi$
$350$	0.953540	0.0509689
$351$	−1.96535	−0.104903
$352$	−4.55467	−0.242765
$353$	15.1135	0.804409	0.402205	−	0.915550i	$-0.368244\pi$
$353$	15.1135	0.804409	0.402205	+	0.915550i	$0.368244\pi$
$354$	−1.31607	−0.0699485
$355$	−11.6480	−0.618210
$356$	−4.71790	−0.250048
$357$	1.86831	0.0988815
$358$	−14.4556	−0.764005
$359$	−16.5272	−0.872272	−0.436136	−	0.899881i	$-0.643653\pi$
$359$	−16.5272	−0.872272	−0.436136	+	0.899881i	$0.643653\pi$
$360$	6.50612	0.342903
$361$	36.2491	1.90785
$362$	−14.4744	−0.760756
$363$	6.72964	0.353214
$364$	−1.45362	−0.0761902
$365$	−5.41414	−0.283389
$366$	−13.4462	−0.702846
$367$	3.13201	0.163490	0.0817448	−	0.996653i	$-0.473951\pi$
$367$	3.13201	0.163490	0.0817448	+	0.996653i	$0.473951\pi$
$368$	0.438455	0.0228561
$369$	10.7426	0.559239
$370$	−12.7843	−0.664625
$371$	−3.50844	−0.182149
$372$	2.50872	0.130071
$373$	25.5451	1.32268	0.661338	−	0.750088i	$-0.269989\pi$
$373$	25.5451	1.32268	0.661338	+	0.750088i	$0.269989\pi$
$374$	2.61729	0.135337
$375$	11.5843	0.598213
$376$	−7.73479	−0.398891
$377$	6.23153	0.320940
$378$	2.36629	0.121709
$379$	3.56247	0.182992	0.0914959	−	0.995805i	$-0.470835\pi$
$379$	3.56247	0.182992	0.0914959	+	0.995805i	$0.470835\pi$
$380$	−6.30901	−0.323646
$381$	−18.6071	−0.953271
$382$	20.2376	1.03545
$383$	−11.7966	−0.602780	−0.301390	−	0.953501i	$-0.597451\pi$
$383$	−11.7966	−0.602780	−0.301390	+	0.953501i	$0.597451\pi$
$384$	6.85722	0.349931
$385$	8.27791	0.421881
$386$	23.7083	1.20672
$387$	4.86321	0.247211
$388$	−6.47195	−0.328564
$389$	8.95249	0.453909	0.226955	−	0.973905i	$-0.427123\pi$
$389$	8.95249	0.453909	0.226955	+	0.973905i	$0.427123\pi$
$390$	5.33701	0.270250
$391$	0.143684	0.00726641
$392$	−10.6492	−0.537867
$393$	15.0253	0.757925
$394$	24.8112	1.24997
$395$	12.2358	0.615649
$396$	−0.818074	−0.0411098
$397$	7.17080	0.359892	0.179946	−	0.983676i	$-0.442408\pi$
$397$	7.17080	0.359892	0.179946	+	0.983676i	$0.442408\pi$
$398$	24.8942	1.24783
$399$	−13.8871	−0.695225
$400$	1.22967	0.0614835
$401$	−7.56166	−0.377611	−0.188806	−	0.982014i	$-0.560462\pi$
$401$	−7.56166	−0.377611	−0.188806	+	0.982014i	$0.560462\pi$
$402$	−1.48296	−0.0739635
$403$	12.4547	0.620411
$404$	−0.982206	−0.0488666
$405$	2.14407	0.106540
$406$	−7.50278	−0.372357
$407$	9.72865	0.482231
$408$	3.03447	0.150229
$409$	−12.9599	−0.640826	−0.320413	−	0.947278i	$-0.603822\pi$
$409$	−12.9599	−0.640826	−0.320413	+	0.947278i	$0.603822\pi$
$410$	−29.1721	−1.44071
$411$	3.85641	0.190223
$412$	−3.84170	−0.189267
$413$	−1.94138	−0.0955290
$414$	0.181981	0.00894390
$415$	24.1221	1.18411
$416$	−4.33177	−0.212382
$417$	3.05177	0.149446
$418$	−19.4542	−0.951537
$419$	29.5772	1.44494	0.722469	−	0.691403i	$-0.243007\pi$
$419$	29.5772	1.44494	0.722469	+	0.691403i	$0.243007\pi$
$420$	1.58580	0.0773791
$421$	32.1626	1.56751	0.783756	−	0.621069i	$-0.213301\pi$
$421$	32.1626	1.56751	0.783756	+	0.621069i	$0.213301\pi$
$422$	−8.14135	−0.396315
$423$	−2.54897	−0.123935
$424$	−5.69834	−0.276736
$425$	0.402968	0.0195468
$426$	−6.88066	−0.333369
$427$	−19.8350	−0.959881
$428$	−7.25923	−0.350888
$429$	−4.06137	−0.196085
$430$	−13.2063	−0.636864
$431$	4.39248	0.211578	0.105789	−	0.994389i	$-0.466263\pi$
$431$	4.39248	0.211578	0.105789	+	0.994389i	$0.466263\pi$
$432$	3.05153	0.146817
$433$	23.7553	1.14160	0.570802	−	0.821088i	$-0.306632\pi$
$433$	23.7553	1.14160	0.570802	+	0.821088i	$0.306632\pi$
$434$	−14.9954	−0.719805
$435$	−6.79818	−0.325948
$436$	−0.197548	−0.00946083
$437$	−1.06800	−0.0510893
$438$	−3.19823	−0.152817
$439$	8.22372	0.392497	0.196248	−	0.980554i	$-0.437124\pi$
$439$	8.22372	0.392497	0.196248	+	0.980554i	$0.437124\pi$
$440$	13.4448	0.640956
$441$	−3.50941	−0.167115
$442$	2.48920	0.118399
$443$	−31.1150	−1.47832	−0.739160	−	0.673530i	$-0.764777\pi$
$443$	−31.1150	−1.47832	−0.739160	+	0.673530i	$0.764777\pi$
$444$	1.86372	0.0884481
$445$	25.5521	1.21129
$446$	16.0812	0.761466
$447$	10.7831	0.510023
$448$	16.6179	0.785120
$449$	−29.8440	−1.40842	−0.704212	−	0.709990i	$-0.748700\pi$
$449$	−29.8440	−1.40842	−0.704212	+	0.709990i	$0.748700\pi$
$450$	0.510375	0.0240593
$451$	22.1995	1.04533
$452$	−4.56259	−0.214606
$453$	16.6947	0.784385
$454$	6.90813	0.324215
$455$	7.87279	0.369082
$456$	−22.5552	−1.05624
$457$	22.8934	1.07091	0.535453	−	0.844565i	$-0.320141\pi$
$457$	22.8934	1.07091	0.535453	+	0.844565i	$0.320141\pi$
$458$	20.5387	0.959708
$459$	1.00000	0.0466760
$460$	0.121957	0.00568628
$461$	16.2086	0.754908	0.377454	−	0.926028i	$-0.376800\pi$
$461$	16.2086	0.754908	0.377454	+	0.926028i	$0.376800\pi$
$462$	4.88991	0.227499
$463$	−7.31077	−0.339760	−0.169880	−	0.985465i	$-0.554338\pi$
$463$	−7.31077	−0.339760	−0.169880	+	0.985465i	$0.554338\pi$
$464$	−9.67545	−0.449172
$465$	−13.5872	−0.630091
$466$	14.2157	0.658532
$467$	0.842705	0.0389957	0.0194979	−	0.999810i	$-0.493793\pi$
$467$	0.842705	0.0389957	0.0194979	+	0.999810i	$0.493793\pi$
$468$	−0.778038	−0.0359648
$469$	−2.18756	−0.101012
$470$	6.92186	0.319281
$471$	−1.00000	−0.0460776
$472$	−3.15315	−0.145135
$473$	10.0498	0.462089
$474$	7.22790	0.331988
$475$	−2.99525	−0.137432
$476$	0.739621	0.0339005
$477$	−1.87787	−0.0859817
$478$	−18.1972	−0.832319
$479$	−28.5867	−1.30616	−0.653080	−	0.757289i	$-0.726523\pi$
$479$	−28.5867	−1.30616	−0.653080	+	0.757289i	$0.726523\pi$
$480$	4.72567	0.215696
$481$	9.25253	0.421879
$482$	−34.1564	−1.55578
$483$	0.268446	0.0122147
$484$	2.66411	0.121096
$485$	35.0521	1.59163
$486$	1.26654	0.0574514
$487$	−2.87643	−0.130344	−0.0651718	−	0.997874i	$-0.520760\pi$
$487$	−2.87643	−0.130344	−0.0651718	+	0.997874i	$0.520760\pi$
$488$	−32.2155	−1.45833
$489$	23.7414	1.07362
$490$	9.52998	0.430521
$491$	−32.1372	−1.45033	−0.725166	−	0.688574i	$-0.758237\pi$
$491$	−32.1372	−1.45033	−0.725166	+	0.688574i	$0.758237\pi$
$492$	4.25276	0.191729
$493$	−3.17069	−0.142801
$494$	−18.5021	−0.832451
$495$	4.43069	0.199145
$496$	−19.3379	−0.868296
$497$	−10.1499	−0.455284
$498$	14.2494	0.638529
$499$	−17.1192	−0.766362	−0.383181	−	0.923673i	$-0.625171\pi$
$499$	−17.1192	−0.766362	−0.383181	+	0.923673i	$0.625171\pi$
$500$	4.58597	0.205091
$501$	19.9354	0.890648
$502$	−37.0569	−1.65393
$503$	32.5423	1.45099	0.725494	−	0.688229i	$-0.241611\pi$
$503$	32.5423	1.45099	0.725494	+	0.688229i	$0.241611\pi$
$504$	5.66934	0.252533
$505$	5.31963	0.236720
$506$	0.376062	0.0167180
$507$	9.13739	0.405806
$508$	−7.36612	−0.326819
$509$	7.75016	0.343520	0.171760	−	0.985139i	$-0.445055\pi$
$509$	7.75016	0.343520	0.171760	+	0.985139i	$0.445055\pi$
$510$	−2.71555	−0.120247
$511$	−4.71781	−0.208704
$512$	25.2453	1.11570
$513$	−7.43297	−0.328174
$514$	13.0123	0.573946
$515$	20.8066	0.916850
$516$	1.92523	0.0847537
$517$	−5.26741	−0.231661
$518$	−11.1401	−0.489467
$519$	3.50000	0.153633
$520$	12.7868	0.560739
$521$	−43.1763	−1.89159	−0.945793	−	0.324769i	$-0.894714\pi$
$521$	−43.1763	−1.89159	−0.945793	+	0.324769i	$0.894714\pi$
$522$	−4.01581	−0.175767
$523$	19.1927	0.839240	0.419620	−	0.907700i	$-0.362163\pi$
$523$	19.1927	0.839240	0.419620	+	0.907700i	$0.362163\pi$
$524$	5.94816	0.259846
$525$	0.752870	0.0328580
$526$	20.5131	0.894412
$527$	−6.33711	−0.276049
$528$	6.30594	0.274431
$529$	−22.9794	−0.999102
$530$	5.09944	0.221506
$531$	−1.03911	−0.0450935
$532$	−5.49758	−0.238351
$533$	21.1131	0.914508
$534$	15.0941	0.653186
$535$	39.3160	1.69978
$536$	−3.55300	−0.153466
$537$	−11.4135	−0.492529
$538$	34.3244	1.47983
$539$	−7.25215	−0.312372
$540$	0.848787	0.0365260
$541$	22.2437	0.956332	0.478166	−	0.878269i	$-0.341302\pi$
$541$	22.2437	0.956332	0.478166	+	0.878269i	$0.341302\pi$
$542$	12.7292	0.546765
$543$	−11.4283	−0.490434
$544$	2.20407	0.0944985
$545$	1.06992	0.0458303
$546$	4.65060	0.199027
$547$	19.4981	0.833677	0.416838	−	0.908981i	$-0.363138\pi$
$547$	19.4981	0.833677	0.416838	+	0.908981i	$0.363138\pi$
$548$	1.52666	0.0652159
$549$	−10.6165	−0.453102
$550$	1.05468	0.0449719
$551$	23.5677	1.00402
$552$	0.436005	0.0185576
$553$	10.6621	0.453398
$554$	−35.3314	−1.50109
$555$	−10.0939	−0.428462
$556$	1.20813	0.0512359
$557$	−2.58978	−0.109732	−0.0548662	−	0.998494i	$-0.517473\pi$
$557$	−2.58978	−0.109732	−0.0548662	+	0.998494i	$0.517473\pi$
$558$	−8.02620	−0.339776
$559$	9.55793	0.404257
$560$	−12.2238	−0.516549
$561$	2.06649	0.0872471
$562$	−10.9964	−0.463856
$563$	45.3755	1.91235	0.956175	−	0.292794i	$-0.0945851\pi$
$563$	45.3755	1.91235	0.956175	+	0.292794i	$0.0945851\pi$
$564$	−1.00908	−0.0424899
$565$	24.7110	1.03960
$566$	−16.1586	−0.679197
$567$	1.86831	0.0784617
$568$	−16.4852	−0.691704
$569$	−3.56484	−0.149446	−0.0747230	−	0.997204i	$-0.523807\pi$
$569$	−3.56484	−0.149446	−0.0747230	+	0.997204i	$0.523807\pi$
$570$	20.1846	0.845440
$571$	32.3365	1.35324	0.676620	−	0.736333i	$-0.263444\pi$
$571$	32.3365	1.35324	0.676620	+	0.736333i	$0.263444\pi$
$572$	−1.60780	−0.0672257
$573$	15.9787	0.667518
$574$	−25.4202	−1.06102
$575$	0.0579001	0.00241460
$576$	8.89459	0.370608
$577$	−1.27845	−0.0532226	−0.0266113	−	0.999646i	$-0.508472\pi$
$577$	−1.27845	−0.0532226	−0.0266113	+	0.999646i	$0.508472\pi$
$578$	−1.26654	−0.0526811
$579$	18.7190	0.777935
$580$	−2.69124	−0.111748
$581$	21.0197	0.872042
$582$	20.7059	0.858287
$583$	−3.88059	−0.160718
$584$	−7.66257	−0.317079
$585$	4.21385	0.174221
$586$	32.7071	1.35112
$587$	−16.3877	−0.676393	−0.338196	−	0.941076i	$-0.609817\pi$
$587$	−16.3877	−0.676393	−0.338196	+	0.941076i	$0.609817\pi$
$588$	−1.38930	−0.0572936
$589$	47.1036	1.94087
$590$	2.82175	0.116170
$591$	19.5897	0.805813
$592$	−14.3660	−0.590441
$593$	9.40347	0.386154	0.193077	−	0.981184i	$-0.438153\pi$
$593$	9.40347	0.386154	0.193077	+	0.981184i	$0.438153\pi$
$594$	2.61729	0.107389
$595$	−4.00579	−0.164221
$596$	4.26878	0.174856
$597$	19.6553	0.804437
$598$	0.357658	0.0146257
$599$	17.1879	0.702278	0.351139	−	0.936323i	$-0.385794\pi$
$599$	17.1879	0.702278	0.351139	+	0.936323i	$0.385794\pi$
$600$	1.22280	0.0499205
$601$	33.4315	1.36370	0.681850	−	0.731492i	$-0.261176\pi$
$601$	33.4315	1.36370	0.681850	+	0.731492i	$0.261176\pi$
$602$	−11.5078	−0.469022
$603$	−1.17088	−0.0476818
$604$	6.60904	0.268918
$605$	−14.4288	−0.586614
$606$	3.14240	0.127651
$607$	5.97296	0.242435	0.121217	−	0.992626i	$-0.461320\pi$
$607$	5.97296	0.242435	0.121217	+	0.992626i	$0.461320\pi$
$608$	−16.3828	−0.664409
$609$	−5.92384	−0.240046
$610$	28.8297	1.16728
$611$	−5.00963	−0.202668
$612$	0.395877	0.0160024
$613$	31.4893	1.27184	0.635921	−	0.771754i	$-0.280621\pi$
$613$	31.4893	1.27184	0.635921	+	0.771754i	$0.280621\pi$
$614$	−1.29476	−0.0522522
$615$	−23.0329	−0.928778
$616$	11.7156	0.472036
$617$	44.1714	1.77827	0.889136	−	0.457642i	$-0.151306\pi$
$617$	44.1714	1.77827	0.889136	+	0.457642i	$0.151306\pi$
$618$	12.2909	0.494411
$619$	−37.2575	−1.49751	−0.748754	−	0.662848i	$-0.769347\pi$
$619$	−37.2575	−1.49751	−0.748754	+	0.662848i	$0.769347\pi$
$620$	−5.37886	−0.216020
$621$	0.143684	0.00576584
$622$	31.0129	1.24350
$623$	22.2658	0.892059
$624$	5.99733	0.240085
$625$	−22.8228	−0.912911
$626$	−23.7556	−0.949465
$627$	−15.3601	−0.613425
$628$	−0.395877	−0.0157972
$629$	−4.70782	−0.187713
$630$	−5.07349	−0.202133
$631$	11.8678	0.472450	0.236225	−	0.971698i	$-0.424090\pi$
$631$	11.8678	0.472450	0.236225	+	0.971698i	$0.424090\pi$
$632$	17.3172	0.688840
$633$	−6.42803	−0.255491
$634$	14.7901	0.587392
$635$	39.8949	1.58318
$636$	−0.743405	−0.0294779
$637$	−6.89723	−0.273278
$638$	−8.29861	−0.328545
$639$	−5.43264	−0.214912
$640$	−14.7024	−0.581162
$641$	−22.3729	−0.883676	−0.441838	−	0.897095i	$-0.645673\pi$
$641$	−22.3729	−0.883676	−0.441838	+	0.897095i	$0.645673\pi$
$642$	23.2246	0.916603
$643$	−14.5572	−0.574081	−0.287041	−	0.957918i	$-0.592671\pi$
$643$	−14.5572	−0.574081	−0.287041	+	0.957918i	$0.592671\pi$
$644$	0.106272	0.00418769
$645$	−10.4271	−0.410565
$646$	9.41416	0.370395
$647$	−47.2811	−1.85881	−0.929407	−	0.369058i	$-0.879681\pi$
$647$	−47.2811	−1.85881	−0.929407	+	0.369058i	$0.879681\pi$
$648$	3.03447	0.119205
$649$	−2.14730	−0.0842891
$650$	1.00307	0.0393436
$651$	−11.8397	−0.464034
$652$	9.39867	0.368080
$653$	−33.1949	−1.29902	−0.649509	−	0.760354i	$-0.725025\pi$
$653$	−33.1949	−1.29902	−0.649509	+	0.760354i	$0.725025\pi$
$654$	0.632020	0.0247139
$655$	−32.2152	−1.25875
$656$	−32.7814	−1.27990
$657$	−2.52517	−0.0985163
$658$	6.03161	0.235137
$659$	12.6433	0.492513	0.246256	−	0.969205i	$-0.420799\pi$
$659$	12.6433	0.492513	0.246256	+	0.969205i	$0.420799\pi$
$660$	1.75401	0.0682746
$661$	35.5779	1.38382	0.691910	−	0.721983i	$-0.256769\pi$
$661$	35.5779	1.38382	0.691910	+	0.721983i	$0.256769\pi$
$662$	31.3213	1.21734
$663$	1.96535	0.0763280
$664$	34.1397	1.32488
$665$	29.7749	1.15462
$666$	−5.96264	−0.231048
$667$	−0.455577	−0.0176400
$668$	7.89197	0.305349
$669$	12.6969	0.490892
$670$	3.17958	0.122838
$671$	−21.9389	−0.846941
$672$	4.11788	0.158851
$673$	−14.6582	−0.565032	−0.282516	−	0.959263i	$-0.591169\pi$
$673$	−14.6582	−0.565032	−0.282516	+	0.959263i	$0.591169\pi$
$674$	7.82413	0.301374
$675$	0.402968	0.0155103
$676$	3.61728	0.139126
$677$	−32.8572	−1.26281	−0.631403	−	0.775455i	$-0.717520\pi$
$677$	−32.8572	−1.26281	−0.631403	+	0.775455i	$0.717520\pi$
$678$	14.5972	0.560603
$679$	30.5439	1.17217
$680$	−6.50612	−0.249498
$681$	5.45433	0.209010
$682$	−16.5860	−0.635112
$683$	39.2195	1.50069	0.750346	−	0.661045i	$-0.229887\pi$
$683$	39.2195	1.50069	0.750346	+	0.661045i	$0.229887\pi$
$684$	−2.94254	−0.112511
$685$	−8.26842	−0.315920
$686$	24.8683	0.949477
$687$	16.2163	0.618692
$688$	−14.8402	−0.565779
$689$	−3.69067	−0.140603
$690$	−0.390181	−0.0148539
$691$	−28.3179	−1.07726	−0.538631	−	0.842542i	$-0.681058\pi$
$691$	−28.3179	−1.07726	−0.538631	+	0.842542i	$0.681058\pi$
$692$	1.38557	0.0526714
$693$	3.86084	0.146661
$694$	−2.84875	−0.108137
$695$	−6.54321	−0.248198
$696$	−9.62138	−0.364697
$697$	−10.7426	−0.406906
$698$	9.09248	0.344155
$699$	11.2241	0.424534
$700$	0.298044	0.0112650
$701$	−24.0978	−0.910160	−0.455080	−	0.890450i	$-0.650389\pi$
$701$	−24.0978	−0.910160	−0.455080	+	0.890450i	$0.650389\pi$
$702$	2.48920	0.0939487
$703$	34.9931	1.31979
$704$	18.3805	0.692743
$705$	5.46517	0.205830
$706$	−19.1418	−0.720412
$707$	4.63545	0.174334
$708$	−0.411359	−0.0154598
$709$	−30.9722	−1.16319	−0.581593	−	0.813480i	$-0.697570\pi$
$709$	−30.9722	−1.16319	−0.581593	+	0.813480i	$0.697570\pi$
$710$	14.7526	0.553656
$711$	5.70681	0.214022
$712$	36.1636	1.35529
$713$	−0.910541	−0.0341000
$714$	−2.36629	−0.0885562
$715$	8.70787	0.325656
$716$	−4.51834	−0.168858
$717$	−14.3676	−0.536569
$718$	20.9323	0.781188
$719$	15.0121	0.559855	0.279928	−	0.960021i	$-0.409690\pi$
$719$	15.0121	0.559855	0.279928	+	0.960021i	$0.409690\pi$
$720$	−6.54269	−0.243832
$721$	18.1306	0.675220
$722$	−45.9109	−1.70863
$723$	−26.9683	−1.00296
$724$	−4.52419	−0.168140
$725$	−1.27769	−0.0474521
$726$	−8.52335	−0.316331
$727$	−1.13561	−0.0421175	−0.0210587	−	0.999778i	$-0.506704\pi$
$727$	−1.13561	−0.0421175	−0.0210587	+	0.999778i	$0.506704\pi$
$728$	11.1423	0.412960
$729$	1.00000	0.0370370
$730$	6.85723	0.253797
$731$	−4.86321	−0.179872
$732$	−4.20283	−0.155341
$733$	−24.7906	−0.915663	−0.457832	−	0.889039i	$-0.651374\pi$
$733$	−24.7906	−0.915663	−0.457832	+	0.889039i	$0.651374\pi$
$734$	−3.96682	−0.146418
$735$	7.52442	0.277542
$736$	0.316689	0.0116733
$737$	−2.41960	−0.0891272
$738$	−13.6060	−0.500843
$739$	26.6535	0.980466	0.490233	−	0.871591i	$-0.336912\pi$
$739$	26.6535	0.980466	0.490233	+	0.871591i	$0.336912\pi$
$740$	−3.99594	−0.146894
$741$	−14.6084	−0.536654
$742$	4.44358	0.163129
$743$	−47.1570	−1.73002	−0.865012	−	0.501751i	$-0.832689\pi$
$743$	−47.1570	−1.73002	−0.865012	+	0.501751i	$0.832689\pi$
$744$	−19.2298	−0.704998
$745$	−23.1197	−0.847041
$746$	−32.3539	−1.18456
$747$	11.2506	0.411639
$748$	0.818074	0.0299117
$749$	34.2594	1.25181
$750$	−14.6720	−0.535747
$751$	−24.8402	−0.906430	−0.453215	−	0.891401i	$-0.649723\pi$
$751$	−24.8402	−0.906430	−0.453215	+	0.891401i	$0.649723\pi$
$752$	7.77826	0.283644
$753$	−29.2584	−1.06624
$754$	−7.89248	−0.287427
$755$	−35.7946	−1.30270
$756$	0.739621	0.0268998
$757$	30.7434	1.11739	0.558694	−	0.829374i	$-0.311303\pi$
$757$	30.7434	1.11739	0.558694	+	0.829374i	$0.311303\pi$
$758$	−4.51201	−0.163884
$759$	0.296921	0.0107775
$760$	48.3598	1.75419
$761$	37.7638	1.36894	0.684468	−	0.729043i	$-0.260035\pi$
$761$	37.7638	1.36894	0.684468	+	0.729043i	$0.260035\pi$
$762$	23.5666	0.853729
$763$	0.932312	0.0337520
$764$	6.32558	0.228851
$765$	−2.14407	−0.0775190
$766$	14.9409	0.539837
$767$	−2.04222	−0.0737402
$768$	9.10424	0.328521
$769$	19.4407	0.701048	0.350524	−	0.936554i	$-0.386003\pi$
$769$	19.4407	0.701048	0.350524	+	0.936554i	$0.386003\pi$
$770$	−10.4843	−0.377828
$771$	10.2739	0.370004
$772$	7.41041	0.266707
$773$	29.8191	1.07252	0.536259	−	0.844054i	$-0.319837\pi$
$773$	29.8191	1.07252	0.536259	+	0.844054i	$0.319837\pi$
$774$	−6.15945	−0.221397
$775$	−2.55366	−0.0917300
$776$	49.6088	1.78085
$777$	−8.79568	−0.315543
$778$	−11.3387	−0.406512
$779$	79.8497	2.86091
$780$	1.66817	0.0597300
$781$	−11.2265	−0.401715
$782$	−0.181981	−0.00650764
$783$	−3.17069	−0.113311
$784$	10.7091	0.382467
$785$	2.14407	0.0765251
$786$	−19.0301	−0.678781
$787$	32.1626	1.14647	0.573236	−	0.819390i	$-0.305688\pi$
$787$	32.1626	1.14647	0.573236	+	0.819390i	$0.305688\pi$
$788$	7.75512	0.276265
$789$	16.1961	0.576598
$790$	−15.4971	−0.551363
$791$	21.5328	0.765619
$792$	6.27070	0.222819
$793$	−20.8652	−0.740945
$794$	−9.08211	−0.322312
$795$	4.02628	0.142797
$796$	7.78107	0.275793
$797$	−17.3874	−0.615895	−0.307947	−	0.951403i	$-0.599642\pi$
$797$	−17.3874	−0.615895	−0.307947	+	0.951403i	$0.599642\pi$
$798$	17.5886	0.622629
$799$	2.54897	0.0901761
$800$	0.888169	0.0314015
$801$	11.9176	0.421087
$802$	9.57715	0.338181
$803$	−5.21823	−0.184147
$804$	−0.463523	−0.0163472
$805$	−0.575567	−0.0202861
$806$	−15.7743	−0.555627
$807$	27.1009	0.953997
$808$	7.52880	0.264862
$809$	−27.7927	−0.977139	−0.488570	−	0.872525i	$-0.662481\pi$
$809$	−27.7927	−0.977139	−0.488570	+	0.872525i	$0.662481\pi$
$810$	−2.71555	−0.0954147
$811$	44.3454	1.55718	0.778588	−	0.627535i	$-0.215936\pi$
$811$	44.3454	1.55718	0.778588	+	0.627535i	$0.215936\pi$
$812$	−2.34511	−0.0822972
$813$	10.0504	0.352481
$814$	−12.3217	−0.431876
$815$	−50.9032	−1.78306
$816$	−3.05153	−0.106825
$817$	36.1481	1.26466
$818$	16.4142	0.573910
$819$	3.67189	0.128306
$820$	−9.11821	−0.318422
$821$	−11.1012	−0.387434	−0.193717	−	0.981057i	$-0.562054\pi$
$821$	−11.1012	−0.387434	−0.193717	+	0.981057i	$0.562054\pi$
$822$	−4.88430	−0.170360
$823$	28.5809	0.996268	0.498134	−	0.867100i	$-0.334019\pi$
$823$	28.5809	0.996268	0.498134	+	0.867100i	$0.334019\pi$
$824$	29.4474	1.02585
$825$	0.832728	0.0289919
$826$	2.45883	0.0855538
$827$	1.63625	0.0568979	0.0284489	−	0.999595i	$-0.490943\pi$
$827$	1.63625	0.0568979	0.0284489	+	0.999595i	$0.490943\pi$
$828$	0.0568811	0.00197676
$829$	−33.9320	−1.17851	−0.589253	−	0.807949i	$-0.700578\pi$
$829$	−33.9320	−1.17851	−0.589253	+	0.807949i	$0.700578\pi$
$830$	−30.5516	−1.06046
$831$	−27.8960	−0.967703
$832$	17.4810	0.606045
$833$	3.50941	0.121594
$834$	−3.86519	−0.133841
$835$	−42.7429	−1.47918
$836$	−6.08072	−0.210306
$837$	−6.33711	−0.219043
$838$	−37.4606	−1.29406
$839$	49.2887	1.70163	0.850817	−	0.525462i	$-0.176107\pi$
$839$	49.2887	1.70163	0.850817	+	0.525462i	$0.176107\pi$
$840$	−12.1555	−0.419403
$841$	−18.9467	−0.653335
$842$	−40.7353	−1.40383
$843$	−8.68225	−0.299033
$844$	−2.54471	−0.0875925
$845$	−19.5912	−0.673957
$846$	3.22837	0.110994
$847$	−12.5731	−0.432015
$848$	5.73037	0.196782
$849$	−12.7581	−0.437856
$850$	−0.510375	−0.0175057
$851$	−0.676438	−0.0231880
$852$	−2.15066	−0.0736803
$853$	15.9317	0.545492	0.272746	−	0.962086i	$-0.412068\pi$
$853$	15.9317	0.545492	0.272746	+	0.962086i	$0.412068\pi$
$854$	25.1218	0.859649
$855$	15.9368	0.545027
$856$	55.6434	1.90185
$857$	−3.16192	−0.108009	−0.0540046	−	0.998541i	$-0.517199\pi$
$857$	−3.16192	−0.108009	−0.0540046	+	0.998541i	$0.517199\pi$
$858$	5.14389	0.175610
$859$	18.5510	0.632953	0.316476	−	0.948600i	$-0.397500\pi$
$859$	18.5510	0.632953	0.316476	+	0.948600i	$0.397500\pi$
$860$	−4.12783	−0.140758
$861$	−20.0706	−0.684004
$862$	−5.56325	−0.189485
$863$	−37.9802	−1.29286	−0.646431	−	0.762972i	$-0.723739\pi$
$863$	−37.9802	−1.29286	−0.646431	+	0.762972i	$0.723739\pi$
$864$	2.20407	0.0749838
$865$	−7.50424	−0.255152
$866$	−30.0870	−1.02240
$867$	−1.00000	−0.0339618
$868$	−4.68706	−0.159089
$869$	11.7930	0.400051
$870$	8.61016	0.291912
$871$	−2.30119	−0.0779728
$872$	1.51424	0.0512787
$873$	16.3484	0.553310
$874$	1.35266	0.0457545
$875$	−21.6431	−0.731672
$876$	−0.999657	−0.0337753
$877$	13.2506	0.447440	0.223720	−	0.974653i	$-0.428180\pi$
$877$	13.2506	0.447440	0.223720	+	0.974653i	$0.428180\pi$
$878$	−10.4157	−0.351512
$879$	25.8240	0.871022
$880$	−13.5204	−0.455772
$881$	34.1744	1.15137	0.575683	−	0.817673i	$-0.304736\pi$
$881$	34.1744	1.15137	0.575683	+	0.817673i	$0.304736\pi$
$882$	4.44481	0.149665
$883$	−34.6132	−1.16483	−0.582413	−	0.812893i	$-0.697891\pi$
$883$	−34.6132	−1.16483	−0.582413	+	0.812893i	$0.697891\pi$
$884$	0.778038	0.0261682
$885$	2.22792	0.0748908
$886$	39.4084	1.32395
$887$	−57.3480	−1.92556	−0.962778	−	0.270294i	$-0.912879\pi$
$887$	−57.3480	−1.92556	−0.962778	+	0.270294i	$0.912879\pi$
$888$	−14.2858	−0.479399
$889$	34.7639	1.16594
$890$	−32.3628	−1.08480
$891$	2.06649	0.0692299
$892$	5.02642	0.168297
$893$	−18.9464	−0.634018
$894$	−13.6572	−0.456766
$895$	24.4713	0.817986
$896$	−12.8114	−0.428000
$897$	0.282390	0.00942872
$898$	37.7986	1.26136
$899$	20.0930	0.670140
$900$	0.159526	0.00531753
$901$	1.87787	0.0625609
$902$	−28.1165	−0.936179
$903$	−9.08600	−0.302363
$904$	34.9732	1.16319
$905$	24.5030	0.814508
$906$	−21.1445	−0.702478
$907$	16.0921	0.534329	0.267165	−	0.963651i	$-0.413913\pi$
$907$	16.0921	0.534329	0.267165	+	0.963651i	$0.413913\pi$
$908$	2.15924	0.0716570
$909$	2.48109	0.0822925
$910$	−9.97120	−0.330542
$911$	−30.9876	−1.02666	−0.513332	−	0.858190i	$-0.671589\pi$
$911$	−30.9876	−1.02666	−0.513332	+	0.858190i	$0.671589\pi$
$912$	22.6819	0.751073
$913$	23.2492	0.769438
$914$	−28.9954	−0.959081
$915$	22.7625	0.752506
$916$	6.41968	0.212112
$917$	−28.0719	−0.927015
$918$	−1.26654	−0.0418020
$919$	11.3888	0.375682	0.187841	−	0.982199i	$-0.439851\pi$
$919$	11.3888	0.375682	0.187841	+	0.982199i	$0.439851\pi$
$920$	−0.934825	−0.0308203
$921$	−1.02228	−0.0336853
$922$	−20.5288	−0.676080
$923$	−10.6771	−0.351440
$924$	1.52842	0.0502812
$925$	−1.89710	−0.0623764
$926$	9.25938	0.304282
$927$	9.70428	0.318730
$928$	−6.98841	−0.229406
$929$	11.9679	0.392653	0.196327	−	0.980539i	$-0.437099\pi$
$929$	11.9679	0.392653	0.196327	+	0.980539i	$0.437099\pi$
$930$	17.2087	0.564297
$931$	−26.0854	−0.854913
$932$	4.44335	0.145547
$933$	24.4863	0.801646
$934$	−1.06732	−0.0349238
$935$	−4.43069	−0.144899
$936$	5.96381	0.194933
$937$	28.7727	0.939963	0.469981	−	0.882676i	$-0.344261\pi$
$937$	28.7727	0.939963	0.469981	+	0.882676i	$0.344261\pi$
$938$	2.77064	0.0904645
$939$	−18.7563	−0.612089
$940$	2.16353	0.0705667
$941$	49.0243	1.59815	0.799073	−	0.601234i	$-0.205324\pi$
$941$	49.0243	1.59815	0.799073	+	0.601234i	$0.205324\pi$
$942$	1.26654	0.0412661
$943$	−1.54354	−0.0502647
$944$	3.17087	0.103203
$945$	−4.00579	−0.130308
$946$	−12.7284	−0.413837
$947$	−55.0481	−1.78882	−0.894412	−	0.447244i	$-0.852406\pi$
$947$	−55.0481	−1.78882	−0.894412	+	0.447244i	$0.852406\pi$
$948$	2.25919	0.0733752
$949$	−4.96285	−0.161101
$950$	3.79361	0.123081
$951$	11.6776	0.378672
$952$	−5.66934	−0.183744
$953$	−37.5320	−1.21578	−0.607890	−	0.794021i	$-0.707984\pi$
$953$	−37.5320	−1.21578	−0.607890	+	0.794021i	$0.707984\pi$
$954$	2.37839	0.0770034
$955$	−34.2593	−1.10861
$956$	−5.68781	−0.183957
$957$	−6.55219	−0.211802
$958$	36.2062	1.16977
$959$	−7.20498	−0.232661
$960$	−19.0706	−0.615502
$961$	9.15898	0.295451
$962$	−11.7187	−0.377826
$963$	18.3371	0.590904
$964$	−10.6761	−0.343855
$965$	−40.1348	−1.29198
$966$	−0.339998	−0.0109393
$967$	−8.09967	−0.260468	−0.130234	−	0.991483i	$-0.541573\pi$
$967$	−8.09967	−0.260468	−0.130234	+	0.991483i	$0.541573\pi$
$968$	−20.4209	−0.656353
$969$	7.43297	0.238781
$970$	−44.3949	−1.42543
$971$	6.09430	0.195575	0.0977877	−	0.995207i	$-0.468823\pi$
$971$	6.09430	0.195575	0.0977877	+	0.995207i	$0.468823\pi$
$972$	0.395877	0.0126978
$973$	−5.70166	−0.182787
$974$	3.64311	0.116733
$975$	0.791975	0.0253635
$976$	32.3966	1.03699
$977$	43.9945	1.40751	0.703755	−	0.710443i	$-0.251505\pi$
$977$	43.9945	1.40751	0.703755	+	0.710443i	$0.251505\pi$
$978$	−30.0694	−0.961514
$979$	24.6275	0.787099
$980$	2.97874	0.0951525
$981$	0.499013	0.0159323
$982$	40.7030	1.29889
$983$	−24.7201	−0.788450	−0.394225	−	0.919014i	$-0.628987\pi$
$983$	−24.7201	−0.788450	−0.394225	+	0.919014i	$0.628987\pi$
$984$	−32.5982	−1.03919
$985$	−42.0017	−1.33829
$986$	4.01581	0.127889
$987$	4.76227	0.151585
$988$	−5.78313	−0.183986
$989$	−0.698766	−0.0222195
$990$	−5.61164	−0.178350
$991$	0.935777	0.0297259	0.0148630	−	0.999890i	$-0.495269\pi$
$991$	0.935777	0.0297259	0.0148630	+	0.999890i	$0.495269\pi$
$992$	−13.9674	−0.443466
$993$	24.7298	0.784778
$994$	12.8552	0.407743
$995$	−42.1423	−1.33600
$996$	4.45386	0.141126
$997$	26.3701	0.835151	0.417575	−	0.908642i	$-0.362880\pi$
$997$	26.3701	0.835151	0.417575	+	0.908642i	$0.362880\pi$
$998$	21.6822	0.686338
$999$	−4.70782	−0.148949

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8007.2.a.g.1.17	✓	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8007.2.a.g.1.17	✓	56	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:	\( N \)	\(=\)	\( 8007 = 3 \cdot 17 \cdot 157 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8007.a (trivial)

\(f(q)\)	\(=\)	\(q-1.26654 q^{2} -1.00000 q^{3} -0.395877 q^{4} +2.14407 q^{5} +1.26654 q^{6} +1.86831 q^{7} +3.03447 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.26654 q^{2} -1.00000 q^{3} -0.395877 q^{4} +2.14407 q^{5} +1.26654 q^{6} +1.86831 q^{7} +3.03447 q^{8} +1.00000 q^{9} -2.71555 q^{10} +2.06649 q^{11} +0.395877 q^{12} +1.96535 q^{13} -2.36629 q^{14} -2.14407 q^{15} -3.05153 q^{16} -1.00000 q^{17} -1.26654 q^{18} +7.43297 q^{19} -0.848787 q^{20} -1.86831 q^{21} -2.61729 q^{22} -0.143684 q^{23} -3.03447 q^{24} -0.402968 q^{25} -2.48920 q^{26} -1.00000 q^{27} -0.739621 q^{28} +3.17069 q^{29} +2.71555 q^{30} +6.33711 q^{31} -2.20407 q^{32} -2.06649 q^{33} +1.26654 q^{34} +4.00579 q^{35} -0.395877 q^{36} +4.70782 q^{37} -9.41416 q^{38} -1.96535 q^{39} +6.50612 q^{40} +10.7426 q^{41} +2.36629 q^{42} +4.86321 q^{43} -0.818074 q^{44} +2.14407 q^{45} +0.181981 q^{46} -2.54897 q^{47} +3.05153 q^{48} -3.50941 q^{49} +0.510375 q^{50} +1.00000 q^{51} -0.778038 q^{52} -1.87787 q^{53} +1.26654 q^{54} +4.43069 q^{55} +5.66934 q^{56} -7.43297 q^{57} -4.01581 q^{58} -1.03911 q^{59} +0.848787 q^{60} -10.6165 q^{61} -8.02620 q^{62} +1.86831 q^{63} +8.89459 q^{64} +4.21385 q^{65} +2.61729 q^{66} -1.17088 q^{67} +0.395877 q^{68} +0.143684 q^{69} -5.07349 q^{70} -5.43264 q^{71} +3.03447 q^{72} -2.52517 q^{73} -5.96264 q^{74} +0.402968 q^{75} -2.94254 q^{76} +3.86084 q^{77} +2.48920 q^{78} +5.70681 q^{79} -6.54269 q^{80} +1.00000 q^{81} -13.6060 q^{82} +11.2506 q^{83} +0.739621 q^{84} -2.14407 q^{85} -6.15945 q^{86} -3.17069 q^{87} +6.27070 q^{88} +11.9176 q^{89} -2.71555 q^{90} +3.67189 q^{91} +0.0568811 q^{92} -6.33711 q^{93} +3.22837 q^{94} +15.9368 q^{95} +2.20407 q^{96} +16.3484 q^{97} +4.44481 q^{98} +2.06649 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + q^{2} - 56 q^{3} + 61 q^{4} + q^{5} - q^{6} + 19 q^{7} + 56 q^{9}+O(q^{10}) \) 56 * q + q^2 - 56 * q^3 + 61 * q^4 + q^5 - q^6 + 19 * q^7 + 56 * q^9	\( 56 q + q^{2} - 56 q^{3} + 61 q^{4} + q^{5} - q^{6} + 19 q^{7} + 56 q^{9} + 8 q^{10} - 7 q^{11} - 61 q^{12} + 8 q^{13} - 8 q^{14} - q^{15} + 71 q^{16} - 56 q^{17} + q^{18} - 2 q^{19} - 4 q^{20} - 19 q^{21} + 47 q^{22} + 16 q^{23} + 85 q^{25} - 11 q^{26} - 56 q^{27} + 52 q^{28} + 17 q^{29} - 8 q^{30} + 23 q^{31} + 11 q^{32} + 7 q^{33} - q^{34} - 41 q^{35} + 61 q^{36} + 58 q^{37} - 22 q^{38} - 8 q^{39} + 38 q^{40} - q^{41} + 8 q^{42} + 27 q^{43} + 2 q^{44} + q^{45} + 46 q^{46} + 5 q^{47} - 71 q^{48} + 59 q^{49} - 4 q^{50} + 56 q^{51} + 25 q^{52} + 15 q^{53} - q^{54} + 9 q^{55} - 36 q^{56} + 2 q^{57} + 89 q^{58} - 61 q^{59} + 4 q^{60} + 47 q^{61} + 8 q^{62} + 19 q^{63} + 88 q^{64} + 39 q^{65} - 47 q^{66} + 20 q^{67} - 61 q^{68} - 16 q^{69} + 36 q^{70} - 2 q^{71} + 93 q^{73} + 48 q^{74} - 85 q^{75} + 38 q^{76} + 26 q^{77} + 11 q^{78} + 72 q^{79} + 42 q^{80} + 56 q^{81} + 33 q^{82} - 11 q^{83} - 52 q^{84} - q^{85} - 4 q^{86} - 17 q^{87} + 130 q^{88} - 6 q^{89} + 8 q^{90} + 37 q^{91} + 132 q^{92} - 23 q^{93} - 32 q^{94} + 12 q^{95} - 11 q^{96} + 100 q^{97} + 42 q^{98} - 7 q^{99}+O(q^{100}) \) 56 * q + q^2 - 56 * q^3 + 61 * q^4 + q^5 - q^6 + 19 * q^7 + 56 * q^9 + 8 * q^10 - 7 * q^11 - 61 * q^12 + 8 * q^13 - 8 * q^14 - q^15 + 71 * q^16 - 56 * q^17 + q^18 - 2 * q^19 - 4 * q^20 - 19 * q^21 + 47 * q^22 + 16 * q^23 + 85 * q^25 - 11 * q^26 - 56 * q^27 + 52 * q^28 + 17 * q^29 - 8 * q^30 + 23 * q^31 + 11 * q^32 + 7 * q^33 - q^34 - 41 * q^35 + 61 * q^36 + 58 * q^37 - 22 * q^38 - 8 * q^39 + 38 * q^40 - q^41 + 8 * q^42 + 27 * q^43 + 2 * q^44 + q^45 + 46 * q^46 + 5 * q^47 - 71 * q^48 + 59 * q^49 - 4 * q^50 + 56 * q^51 + 25 * q^52 + 15 * q^53 - q^54 + 9 * q^55 - 36 * q^56 + 2 * q^57 + 89 * q^58 - 61 * q^59 + 4 * q^60 + 47 * q^61 + 8 * q^62 + 19 * q^63 + 88 * q^64 + 39 * q^65 - 47 * q^66 + 20 * q^67 - 61 * q^68 - 16 * q^69 + 36 * q^70 - 2 * q^71 + 93 * q^73 + 48 * q^74 - 85 * q^75 + 38 * q^76 + 26 * q^77 + 11 * q^78 + 72 * q^79 + 42 * q^80 + 56 * q^81 + 33 * q^82 - 11 * q^83 - 52 * q^84 - q^85 - 4 * q^86 - 17 * q^87 + 130 * q^88 - 6 * q^89 + 8 * q^90 + 37 * q^91 + 132 * q^92 - 23 * q^93 - 32 * q^94 + 12 * q^95 - 11 * q^96 + 100 * q^97 + 42 * q^98 - 7 * q^99

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