LMFDB - Embedded newform 8041.2.a.f.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8041,2,Mod(1,8041)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8041, 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("8041.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8041 = 11 \cdot 17 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8041.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:	$64.2077082653$
Analytic rank:	$0$
Dimension:	$66$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	8041.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.69318 q^{2} -2.72821 q^{3} +5.25323 q^{4} +0.571799 q^{5} +7.34757 q^{6} +0.634478 q^{7} -8.76155 q^{8} +4.44313 q^{9} +O(q^{10})$	\(q-2.69318 q^{2} -2.72821 q^{3} +5.25323 q^{4} +0.571799 q^{5} +7.34757 q^{6} +0.634478 q^{7} -8.76155 q^{8} +4.44313 q^{9} -1.53996 q^{10} -1.00000 q^{11} -14.3319 q^{12} -2.83881 q^{13} -1.70877 q^{14} -1.55999 q^{15} +13.0900 q^{16} +1.00000 q^{17} -11.9662 q^{18} -2.49012 q^{19} +3.00379 q^{20} -1.73099 q^{21} +2.69318 q^{22} +1.33564 q^{23} +23.9034 q^{24} -4.67305 q^{25} +7.64544 q^{26} -3.93718 q^{27} +3.33306 q^{28} +5.52657 q^{29} +4.20133 q^{30} +6.72024 q^{31} -17.7306 q^{32} +2.72821 q^{33} -2.69318 q^{34} +0.362794 q^{35} +23.3408 q^{36} -3.75694 q^{37} +6.70634 q^{38} +7.74488 q^{39} -5.00984 q^{40} -1.22976 q^{41} +4.66187 q^{42} -1.00000 q^{43} -5.25323 q^{44} +2.54058 q^{45} -3.59714 q^{46} -12.2325 q^{47} -35.7123 q^{48} -6.59744 q^{49} +12.5854 q^{50} -2.72821 q^{51} -14.9129 q^{52} -1.54189 q^{53} +10.6035 q^{54} -0.571799 q^{55} -5.55901 q^{56} +6.79356 q^{57} -14.8841 q^{58} -1.52524 q^{59} -8.19498 q^{60} -8.50086 q^{61} -18.0988 q^{62} +2.81907 q^{63} +21.5719 q^{64} -1.62323 q^{65} -7.34757 q^{66} -4.37172 q^{67} +5.25323 q^{68} -3.64392 q^{69} -0.977070 q^{70} +12.4681 q^{71} -38.9287 q^{72} +12.5933 q^{73} +10.1181 q^{74} +12.7491 q^{75} -13.0812 q^{76} -0.634478 q^{77} -20.8584 q^{78} -4.82690 q^{79} +7.48484 q^{80} -2.58796 q^{81} +3.31198 q^{82} +2.01465 q^{83} -9.09330 q^{84} +0.571799 q^{85} +2.69318 q^{86} -15.0777 q^{87} +8.76155 q^{88} +7.32848 q^{89} -6.84224 q^{90} -1.80117 q^{91} +7.01645 q^{92} -18.3342 q^{93} +32.9443 q^{94} -1.42384 q^{95} +48.3729 q^{96} -0.697040 q^{97} +17.7681 q^{98} -4.44313 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 66 q + 12 q^{2} + 66 q^{4} + 6 q^{5} + 7 q^{6} + 13 q^{7} + 30 q^{8} + 58 q^{9}+O(q^{10}) $ 66 * q + 12 * q^2 + 66 * q^4 + 6 * q^5 + 7 * q^6 + 13 * q^7 + 30 * q^8 + 58 * q^9	\( 66 q + 12 q^{2} + 66 q^{4} + 6 q^{5} + 7 q^{6} + 13 q^{7} + 30 q^{8} + 58 q^{9} + 7 q^{10} - 66 q^{11} + 12 q^{12} + 12 q^{13} + 13 q^{14} + 35 q^{15} + 58 q^{16} + 66 q^{17} + 37 q^{18} + 24 q^{19} + 17 q^{20} + 16 q^{21} - 12 q^{22} + 25 q^{23} + 22 q^{24} + 56 q^{25} + 36 q^{26} + 17 q^{28} + 29 q^{29} + 28 q^{30} + 37 q^{31} + 62 q^{32} + 12 q^{34} + 40 q^{35} + 107 q^{36} - 34 q^{37} + 22 q^{38} + 61 q^{39} + 37 q^{40} + 41 q^{41} + 19 q^{42} - 66 q^{43} - 66 q^{44} + 10 q^{45} + 43 q^{46} + 61 q^{47} + 29 q^{48} + 33 q^{49} + 59 q^{50} + 51 q^{52} - 35 q^{53} - 37 q^{54} - 6 q^{55} + 37 q^{56} - 7 q^{57} + 17 q^{58} + 48 q^{59} - 56 q^{60} + q^{61} + 37 q^{62} + 43 q^{63} + 68 q^{64} + 41 q^{65} - 7 q^{66} + 10 q^{67} + 66 q^{68} + 18 q^{69} + 77 q^{70} + 84 q^{71} + 83 q^{72} + 5 q^{73} + 36 q^{74} + 14 q^{75} + 14 q^{76} - 13 q^{77} + 41 q^{78} + 58 q^{79} + 25 q^{80} + 78 q^{81} - 28 q^{82} + 47 q^{83} + 44 q^{84} + 6 q^{85} - 12 q^{86} + 101 q^{87} - 30 q^{88} + 53 q^{89} + q^{90} + 2 q^{91} + 34 q^{92} - 3 q^{93} + 17 q^{94} + 91 q^{95} + 27 q^{96} - 28 q^{97} + 87 q^{98} - 58 q^{99}+O(q^{100}) \) 66 * q + 12 * q^2 + 66 * q^4 + 6 * q^5 + 7 * q^6 + 13 * q^7 + 30 * q^8 + 58 * q^9 + 7 * q^10 - 66 * q^11 + 12 * q^12 + 12 * q^13 + 13 * q^14 + 35 * q^15 + 58 * q^16 + 66 * q^17 + 37 * q^18 + 24 * q^19 + 17 * q^20 + 16 * q^21 - 12 * q^22 + 25 * q^23 + 22 * q^24 + 56 * q^25 + 36 * q^26 + 17 * q^28 + 29 * q^29 + 28 * q^30 + 37 * q^31 + 62 * q^32 + 12 * q^34 + 40 * q^35 + 107 * q^36 - 34 * q^37 + 22 * q^38 + 61 * q^39 + 37 * q^40 + 41 * q^41 + 19 * q^42 - 66 * q^43 - 66 * q^44 + 10 * q^45 + 43 * q^46 + 61 * q^47 + 29 * q^48 + 33 * q^49 + 59 * q^50 + 51 * q^52 - 35 * q^53 - 37 * q^54 - 6 * q^55 + 37 * q^56 - 7 * q^57 + 17 * q^58 + 48 * q^59 - 56 * q^60 + q^61 + 37 * q^62 + 43 * q^63 + 68 * q^64 + 41 * q^65 - 7 * q^66 + 10 * q^67 + 66 * q^68 + 18 * q^69 + 77 * q^70 + 84 * q^71 + 83 * q^72 + 5 * q^73 + 36 * q^74 + 14 * q^75 + 14 * q^76 - 13 * q^77 + 41 * q^78 + 58 * q^79 + 25 * q^80 + 78 * q^81 - 28 * q^82 + 47 * q^83 + 44 * q^84 + 6 * q^85 - 12 * q^86 + 101 * q^87 - 30 * q^88 + 53 * q^89 + q^90 + 2 * q^91 + 34 * q^92 - 3 * q^93 + 17 * q^94 + 91 * q^95 + 27 * q^96 - 28 * q^97 + 87 * q^98 - 58 * 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 $

$2$	−2.69318	−1.90437	−0.952184	−	0.305526i	$-0.901168\pi$
$2$	−2.69318	−1.90437	−0.952184	+	0.305526i	$0.901168\pi$
$3$	−2.72821	−1.57513	−0.787567	−	0.616229i	$-0.788659\pi$
$3$	−2.72821	−1.57513	−0.787567	+	0.616229i	$0.788659\pi$
$4$	5.25323	2.62662
$5$	0.571799	0.255716	0.127858	−	0.991792i	$-0.459190\pi$
$5$	0.571799	0.255716	0.127858	+	0.991792i	$0.459190\pi$
$6$	7.34757	2.99963
$7$	0.634478	0.239810	0.119905	−	0.992785i	$-0.461741\pi$
$7$	0.634478	0.239810	0.119905	+	0.992785i	$0.461741\pi$
$8$	−8.76155	−3.09768
$9$	4.44313	1.48104
$10$	−1.53996	−0.486977
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−14.3319	−4.13727
$13$	−2.83881	−0.787345	−0.393673	−	0.919251i	$-0.628796\pi$
$13$	−2.83881	−0.787345	−0.393673	+	0.919251i	$0.628796\pi$
$14$	−1.70877	−0.456687
$15$	−1.55999	−0.402787
$16$	13.0900	3.27250
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−11.9662	−2.82045
$19$	−2.49012	−0.571272	−0.285636	−	0.958338i	$-0.592205\pi$
$19$	−2.49012	−0.571272	−0.285636	+	0.958338i	$0.592205\pi$
$20$	3.00379	0.671668
$21$	−1.73099	−0.377733
$22$	2.69318	0.574188
$23$	1.33564	0.278501	0.139251	−	0.990257i	$-0.455531\pi$
$23$	1.33564	0.278501	0.139251	+	0.990257i	$0.455531\pi$
$24$	23.9034	4.87925
$25$	−4.67305	−0.934609
$26$	7.64544	1.49939
$27$	−3.93718	−0.757710
$28$	3.33306	0.629890
$29$	5.52657	1.02626	0.513129	−	0.858311i	$-0.328486\pi$
$29$	5.52657	1.02626	0.513129	+	0.858311i	$0.328486\pi$
$30$	4.20133	0.767054
$31$	6.72024	1.20699	0.603495	−	0.797367i	$-0.293774\pi$
$31$	6.72024	1.20699	0.603495	+	0.797367i	$0.293774\pi$
$32$	−17.7306	−3.13436
$33$	2.72821	0.474921
$34$	−2.69318	−0.461877
$35$	0.362794	0.0613233
$36$	23.3408	3.89014
$37$	−3.75694	−0.617637	−0.308818	−	0.951121i	$-0.599933\pi$
$37$	−3.75694	−0.617637	−0.308818	+	0.951121i	$0.599933\pi$
$38$	6.70634	1.08791
$39$	7.74488	1.24017
$40$	−5.00984	−0.792126
$41$	−1.22976	−0.192057	−0.0960285	−	0.995379i	$-0.530614\pi$
$41$	−1.22976	−0.192057	−0.0960285	+	0.995379i	$0.530614\pi$
$42$	4.66187	0.719343
$43$	−1.00000	−0.152499
$43$	−1.00000	−0.152499
$44$	−5.25323	−0.791955
$45$	2.54058	0.378727
$46$	−3.59714	−0.530369
$47$	−12.2325	−1.78429	−0.892144	−	0.451751i	$-0.850799\pi$
$47$	−12.2325	−1.78429	−0.892144	+	0.451751i	$0.850799\pi$
$48$	−35.7123	−5.15462
$49$	−6.59744	−0.942491
$50$	12.5854	1.77984
$51$	−2.72821	−0.382026
$52$	−14.9129	−2.06805
$53$	−1.54189	−0.211795	−0.105898	−	0.994377i	$-0.533772\pi$
$53$	−1.54189	−0.211795	−0.105898	+	0.994377i	$0.533772\pi$
$54$	10.6035	1.44296
$55$	−0.571799	−0.0771013
$56$	−5.55901	−0.742855
$57$	6.79356	0.899829
$58$	−14.8841	−1.95437
$59$	−1.52524	−0.198570	−0.0992849	−	0.995059i	$-0.531656\pi$
$59$	−1.52524	−0.198570	−0.0992849	+	0.995059i	$0.531656\pi$
$60$	−8.19498	−1.05797
$61$	−8.50086	−1.08842	−0.544212	−	0.838948i	$-0.683171\pi$
$61$	−8.50086	−1.08842	−0.544212	+	0.838948i	$0.683171\pi$
$62$	−18.0988	−2.29855
$63$	2.81907	0.355170
$64$	21.5719	2.69648
$65$	−1.62323	−0.201337
$66$	−7.34757	−0.904423
$67$	−4.37172	−0.534091	−0.267045	−	0.963684i	$-0.586047\pi$
$67$	−4.37172	−0.534091	−0.267045	+	0.963684i	$0.586047\pi$
$68$	5.25323	0.637048
$69$	−3.64392	−0.438676
$70$	−0.977070	−0.116782
$71$	12.4681	1.47970	0.739848	−	0.672774i	$-0.234897\pi$
$71$	12.4681	1.47970	0.739848	+	0.672774i	$0.234897\pi$
$72$	−38.9287	−4.58780
$73$	12.5933	1.47393	0.736966	−	0.675930i	$-0.236258\pi$
$73$	12.5933	1.47393	0.736966	+	0.675930i	$0.236258\pi$
$74$	10.1181	1.17621
$75$	12.7491	1.47213
$76$	−13.0812	−1.50051
$77$	−0.634478	−0.0723055
$78$	−20.8584	−2.36175
$79$	−4.82690	−0.543068	−0.271534	−	0.962429i	$-0.587531\pi$
$79$	−4.82690	−0.543068	−0.271534	+	0.962429i	$0.587531\pi$
$80$	7.48484	0.836830
$81$	−2.58796	−0.287551
$82$	3.31198	0.365747
$83$	2.01465	0.221137	0.110568	−	0.993869i	$-0.464733\pi$
$83$	2.01465	0.221137	0.110568	+	0.993869i	$0.464733\pi$
$84$	−9.09330	−0.992160
$85$	0.571799	0.0620203
$86$	2.69318	0.290413
$87$	−15.0777	−1.61649
$88$	8.76155	0.933984
$89$	7.32848	0.776818	0.388409	−	0.921487i	$-0.373025\pi$
$89$	7.32848	0.776818	0.388409	+	0.921487i	$0.373025\pi$
$90$	−6.84224	−0.721235
$91$	−1.80117	−0.188813
$92$	7.01645	0.731516
$93$	−18.3342	−1.90117
$94$	32.9443	3.39794
$95$	−1.42384	−0.146083
$96$	48.3729	4.93704
$97$	−0.697040	−0.0707737	−0.0353868	−	0.999374i	$-0.511266\pi$
$97$	−0.697040	−0.0707737	−0.0353868	+	0.999374i	$0.511266\pi$
$98$	17.7681	1.79485
$99$	−4.44313	−0.446552
$100$	−24.5486	−2.45486
$101$	10.0649	1.00150	0.500748	−	0.865593i	$-0.333058\pi$
$101$	10.0649	1.00150	0.500748	+	0.865593i	$0.333058\pi$
$102$	7.34757	0.727518
$103$	−15.6741	−1.54442	−0.772209	−	0.635369i	$-0.780848\pi$
$103$	−15.6741	−1.54442	−0.772209	+	0.635369i	$0.780848\pi$
$104$	24.8724	2.43894
$105$	−0.989778	−0.0965924
$106$	4.15260	0.403336
$107$	−2.94600	−0.284801	−0.142400	−	0.989809i	$-0.545482\pi$
$107$	−2.94600	−0.284801	−0.142400	+	0.989809i	$0.545482\pi$
$108$	−20.6829	−1.99021
$109$	1.17417	0.112465	0.0562325	−	0.998418i	$-0.482091\pi$
$109$	1.17417	0.112465	0.0562325	+	0.998418i	$0.482091\pi$
$110$	1.53996	0.146829
$111$	10.2497	0.972860
$112$	8.30532	0.784779
$113$	−8.42941	−0.792972	−0.396486	−	0.918041i	$-0.629771\pi$
$113$	−8.42941	−0.792972	−0.396486	+	0.918041i	$0.629771\pi$
$114$	−18.2963	−1.71361
$115$	0.763720	0.0712172
$116$	29.0324	2.69559
$117$	−12.6132	−1.16609
$118$	4.10776	0.378150
$119$	0.634478	0.0581625
$120$	13.6679	1.24770
$121$	1.00000	0.0909091
$122$	22.8944	2.07276
$123$	3.35506	0.302515
$124$	35.3030	3.17030
$125$	−5.53103	−0.494711
$126$	−7.59228	−0.676374
$127$	5.89223	0.522851	0.261425	−	0.965224i	$-0.415807\pi$
$127$	5.89223	0.522851	0.261425	+	0.965224i	$0.415807\pi$
$128$	−22.6357	−2.00073
$129$	2.72821	0.240206
$130$	4.37165	0.383419
$131$	14.3267	1.25173	0.625863	−	0.779933i	$-0.284747\pi$
$131$	14.3267	1.25173	0.625863	+	0.779933i	$0.284747\pi$
$132$	14.3319	1.24743
$133$	−1.57992	−0.136997
$134$	11.7738	1.01711
$135$	−2.25127	−0.193759
$136$	−8.76155	−0.751297
$137$	13.8531	1.18355	0.591775	−	0.806103i	$-0.298427\pi$
$137$	13.8531	1.18355	0.591775	+	0.806103i	$0.298427\pi$
$138$	9.81374	0.835401
$139$	−2.95538	−0.250672	−0.125336	−	0.992114i	$-0.540001\pi$
$139$	−2.95538	−0.250672	−0.125336	+	0.992114i	$0.540001\pi$
$140$	1.90584	0.161073
$141$	33.3727	2.81049
$142$	−33.5790	−2.81788
$143$	2.83881	0.237393
$144$	58.1606	4.84672
$145$	3.16009	0.262431
$146$	−33.9160	−2.80691
$147$	17.9992	1.48455
$148$	−19.7361	−1.62229
$149$	−15.4596	−1.26650	−0.633251	−	0.773946i	$-0.718280\pi$
$149$	−15.4596	−1.26650	−0.633251	+	0.773946i	$0.718280\pi$
$150$	−34.3355	−2.80348
$151$	21.4621	1.74656	0.873279	−	0.487221i	$-0.161989\pi$
$151$	21.4621	1.74656	0.873279	+	0.487221i	$0.161989\pi$
$152$	21.8173	1.76961
$153$	4.44313	0.359206
$154$	1.70877	0.137696
$155$	3.84262	0.308647
$156$	40.6857	3.25746
$157$	−4.16596	−0.332479	−0.166240	−	0.986085i	$-0.553163\pi$
$157$	−4.16596	−0.332479	−0.166240	+	0.986085i	$0.553163\pi$
$158$	12.9997	1.03420
$159$	4.20661	0.333606
$160$	−10.1384	−0.801507
$161$	0.847438	0.0667874
$162$	6.96984	0.547603
$163$	1.59862	0.125214	0.0626069	−	0.998038i	$-0.480059\pi$
$163$	1.59862	0.125214	0.0626069	+	0.998038i	$0.480059\pi$
$164$	−6.46024	−0.504460
$165$	1.55999	0.121445
$166$	−5.42583	−0.421126
$167$	12.6756	0.980866	0.490433	−	0.871479i	$-0.336839\pi$
$167$	12.6756	0.980866	0.490433	+	0.871479i	$0.336839\pi$
$168$	15.1662	1.17009
$169$	−4.94114	−0.380088
$170$	−1.53996	−0.118109
$171$	−11.0639	−0.846079
$172$	−5.25323	−0.400555
$173$	15.8996	1.20883	0.604413	−	0.796671i	$-0.293408\pi$
$173$	15.8996	1.20883	0.604413	+	0.796671i	$0.293408\pi$
$174$	40.6069	3.07840
$175$	−2.96495	−0.224129
$176$	−13.0900	−0.986695
$177$	4.16119	0.312774
$178$	−19.7369	−1.47935
$179$	−9.65848	−0.721909	−0.360955	−	0.932583i	$-0.617549\pi$
$179$	−9.65848	−0.721909	−0.360955	+	0.932583i	$0.617549\pi$
$180$	13.3462	0.994771
$181$	6.64246	0.493730	0.246865	−	0.969050i	$-0.420600\pi$
$181$	6.64246	0.493730	0.246865	+	0.969050i	$0.420600\pi$
$182$	4.85087	0.359570
$183$	23.1921	1.71441
$184$	−11.7023	−0.862706
$185$	−2.14821	−0.157940
$186$	49.3774	3.62053
$187$	−1.00000	−0.0731272
$188$	−64.2600	−4.68664
$189$	−2.49805	−0.181707
$190$	3.83467	0.278196
$191$	−14.2710	−1.03262	−0.516308	−	0.856403i	$-0.672694\pi$
$191$	−14.2710	−1.03262	−0.516308	+	0.856403i	$0.672694\pi$
$192$	−58.8526	−4.24732
$193$	−24.5441	−1.76672	−0.883361	−	0.468693i	$-0.844725\pi$
$193$	−24.5441	−1.76672	−0.883361	+	0.468693i	$0.844725\pi$
$194$	1.87726	0.134779
$195$	4.42851	0.317132
$196$	−34.6579	−2.47556
$197$	−22.8281	−1.62643	−0.813217	−	0.581960i	$-0.802286\pi$
$197$	−22.8281	−1.62643	−0.813217	+	0.581960i	$0.802286\pi$
$198$	11.9662	0.850399
$199$	1.01539	0.0719790	0.0359895	−	0.999352i	$-0.488542\pi$
$199$	1.01539	0.0719790	0.0359895	+	0.999352i	$0.488542\pi$
$200$	40.9431	2.89512
$201$	11.9270	0.841264
$202$	−27.1066	−1.90722
$203$	3.50649	0.246107
$204$	−14.3319	−1.00344
$205$	−0.703178	−0.0491121
$206$	42.2133	2.94114
$207$	5.93445	0.412473
$208$	−37.1600	−2.57658
$209$	2.49012	0.172245
$210$	2.66565	0.183948
$211$	20.6975	1.42488	0.712438	−	0.701735i	$-0.247591\pi$
$211$	20.6975	1.42488	0.712438	+	0.701735i	$0.247591\pi$
$212$	−8.09992	−0.556305
$213$	−34.0157	−2.33072
$214$	7.93413	0.542366
$215$	−0.571799	−0.0389963
$216$	34.4958	2.34714
$217$	4.26384	0.289449
$218$	−3.16225	−0.214175
$219$	−34.3571	−2.32164
$220$	−3.00379	−0.202516
$221$	−2.83881	−0.190959
$222$	−27.6044	−1.85268
$223$	−12.9170	−0.864987	−0.432493	−	0.901637i	$-0.642366\pi$
$223$	−12.9170	−0.864987	−0.432493	+	0.901637i	$0.642366\pi$
$224$	−11.2497	−0.751652
$225$	−20.7630	−1.38420
$226$	22.7019	1.51011
$227$	15.8424	1.05150	0.525749	−	0.850640i	$-0.323785\pi$
$227$	15.8424	1.05150	0.525749	+	0.850640i	$0.323785\pi$
$228$	35.6881	2.36351
$229$	−5.35454	−0.353838	−0.176919	−	0.984225i	$-0.556613\pi$
$229$	−5.35454	−0.353838	−0.176919	+	0.984225i	$0.556613\pi$
$230$	−2.05684	−0.135624
$231$	1.73099	0.113891
$232$	−48.4213	−3.17902
$233$	8.13560	0.532981	0.266491	−	0.963838i	$-0.414136\pi$
$233$	8.13560	0.532981	0.266491	+	0.963838i	$0.414136\pi$
$234$	33.9697	2.22067
$235$	−6.99450	−0.456271
$236$	−8.01246	−0.521567
$237$	13.1688	0.855405
$238$	−1.70877	−0.110763
$239$	2.55791	0.165458	0.0827288	−	0.996572i	$-0.473636\pi$
$239$	2.55791	0.165458	0.0827288	+	0.996572i	$0.473636\pi$
$240$	−20.4202	−1.31812
$241$	−19.4036	−1.24990	−0.624948	−	0.780667i	$-0.714880\pi$
$241$	−19.4036	−1.24990	−0.624948	+	0.780667i	$0.714880\pi$
$242$	−2.69318	−0.173124
$243$	18.8720	1.21064
$244$	−44.6570	−2.85887
$245$	−3.77241	−0.241010
$246$	−9.03578	−0.576101
$247$	7.06897	0.449788
$248$	−58.8797	−3.73886
$249$	−5.49640	−0.348320
$250$	14.8961	0.942111
$251$	2.91283	0.183856	0.0919280	−	0.995766i	$-0.470697\pi$
$251$	2.91283	0.183856	0.0919280	+	0.995766i	$0.470697\pi$
$252$	14.8092	0.932895
$253$	−1.33564	−0.0839713
$254$	−15.8689	−0.995700
$255$	−1.55999	−0.0976902
$256$	17.8183	1.11364
$257$	−12.2685	−0.765287	−0.382643	−	0.923896i	$-0.624986\pi$
$257$	−12.2685	−0.765287	−0.382643	+	0.923896i	$0.624986\pi$
$258$	−7.34757	−0.457440
$259$	−2.38369	−0.148116
$260$	−8.52720	−0.528835
$261$	24.5553	1.51994
$262$	−38.5843	−2.38375
$263$	18.3950	1.13428	0.567141	−	0.823620i	$-0.308049\pi$
$263$	18.3950	1.13428	0.567141	+	0.823620i	$0.308049\pi$
$264$	−23.9034	−1.47115
$265$	−0.881652	−0.0541595
$266$	4.25502	0.260892
$267$	−19.9936	−1.22359
$268$	−22.9657	−1.40285
$269$	16.0497	0.978566	0.489283	−	0.872125i	$-0.337259\pi$
$269$	16.0497	0.978566	0.489283	+	0.872125i	$0.337259\pi$
$270$	6.06308	0.368988
$271$	5.70010	0.346256	0.173128	−	0.984899i	$-0.444613\pi$
$271$	5.70010	0.346256	0.173128	+	0.984899i	$0.444613\pi$
$272$	13.0900	0.793697
$273$	4.91396	0.297406
$274$	−37.3089	−2.25391
$275$	4.67305	0.281795
$276$	−19.1424	−1.15223
$277$	−11.9900	−0.720410	−0.360205	−	0.932873i	$-0.617293\pi$
$277$	−11.9900	−0.720410	−0.360205	+	0.932873i	$0.617293\pi$
$278$	7.95937	0.477371
$279$	29.8589	1.78761
$280$	−3.17864	−0.189960
$281$	25.0748	1.49583	0.747917	−	0.663792i	$-0.231054\pi$
$281$	25.0748	1.49583	0.747917	+	0.663792i	$0.231054\pi$
$282$	−89.8789	−5.35221
$283$	−14.7205	−0.875044	−0.437522	−	0.899208i	$-0.644144\pi$
$283$	−14.7205	−0.875044	−0.437522	+	0.899208i	$0.644144\pi$
$284$	65.4980	3.88659
$285$	3.88455	0.230101
$286$	−7.64544	−0.452084
$287$	−0.780259	−0.0460572
$288$	−78.7796	−4.64213
$289$	1.00000	0.0588235
$290$	−8.51069	−0.499765
$291$	1.90167	0.111478
$292$	66.1554	3.87145
$293$	−20.5088	−1.19814	−0.599069	−	0.800698i	$-0.704462\pi$
$293$	−20.5088	−1.19814	−0.599069	+	0.800698i	$0.704462\pi$
$294$	−48.4751	−2.82713
$295$	−0.872132	−0.0507775
$296$	32.9166	1.91324
$297$	3.93718	0.228458
$298$	41.6356	2.41189
$299$	−3.79165	−0.219277
$300$	66.9738	3.86673
$301$	−0.634478	−0.0365707
$302$	−57.8012	−3.32609
$303$	−27.4592	−1.57749
$304$	−32.5956	−1.86948
$305$	−4.86078	−0.278328
$306$	−11.9662	−0.684061
$307$	−18.4730	−1.05431	−0.527155	−	0.849769i	$-0.676741\pi$
$307$	−18.4730	−1.05431	−0.527155	+	0.849769i	$0.676741\pi$
$308$	−3.33306	−0.189919
$309$	42.7623	2.43266
$310$	−10.3489	−0.587777
$311$	−6.37650	−0.361578	−0.180789	−	0.983522i	$-0.557865\pi$
$311$	−6.37650	−0.361578	−0.180789	+	0.983522i	$0.557865\pi$
$312$	−67.8572	−3.84166
$313$	−9.82650	−0.555427	−0.277713	−	0.960664i	$-0.589577\pi$
$313$	−9.82650	−0.555427	−0.277713	+	0.960664i	$0.589577\pi$
$314$	11.2197	0.633163
$315$	1.61194	0.0908226
$316$	−25.3568	−1.42643
$317$	17.7862	0.998970	0.499485	−	0.866323i	$-0.333523\pi$
$317$	17.7862	0.998970	0.499485	+	0.866323i	$0.333523\pi$
$318$	−11.3292	−0.635308
$319$	−5.52657	−0.309429
$320$	12.3348	0.689534
$321$	8.03732	0.448599
$322$	−2.28230	−0.127188
$323$	−2.49012	−0.138554
$324$	−13.5951	−0.755286
$325$	13.2659	0.735860
$326$	−4.30539	−0.238453
$327$	−3.20338	−0.177147
$328$	10.7746	0.594930
$329$	−7.76123	−0.427891
$330$	−4.20133	−0.231276
$331$	−23.6834	−1.30176	−0.650879	−	0.759181i	$-0.725600\pi$
$331$	−23.6834	−1.30176	−0.650879	+	0.759181i	$0.725600\pi$
$332$	10.5834	0.580842
$333$	−16.6926	−0.914747
$334$	−34.1377	−1.86793
$335$	−2.49974	−0.136576
$336$	−22.6587	−1.23613
$337$	14.2306	0.775192	0.387596	−	0.921829i	$-0.373306\pi$
$337$	14.2306	0.775192	0.387596	+	0.921829i	$0.373306\pi$
$338$	13.3074	0.723827
$339$	22.9972	1.24904
$340$	3.00379	0.162903
$341$	−6.72024	−0.363921
$342$	29.7971	1.61125
$343$	−8.62728	−0.465829
$344$	8.76155	0.472391
$345$	−2.08359	−0.112177
$346$	−42.8206	−2.30205
$347$	1.62314	0.0871348	0.0435674	−	0.999050i	$-0.486128\pi$
$347$	1.62314	0.0871348	0.0435674	+	0.999050i	$0.486128\pi$
$348$	−79.2064	−4.24591
$349$	2.81077	0.150457	0.0752286	−	0.997166i	$-0.476031\pi$
$349$	2.81077	0.150457	0.0752286	+	0.997166i	$0.476031\pi$
$350$	7.98514	0.426824
$351$	11.1769	0.596579
$352$	17.7306	0.945046
$353$	−5.19613	−0.276562	−0.138281	−	0.990393i	$-0.544158\pi$
$353$	−5.19613	−0.276562	−0.138281	+	0.990393i	$0.544158\pi$
$354$	−11.2068	−0.595637
$355$	7.12926	0.378382
$356$	38.4982	2.04040
$357$	−1.73099	−0.0916137
$358$	26.0121	1.37478
$359$	27.0570	1.42801	0.714007	−	0.700138i	$-0.246878\pi$
$359$	27.0570	1.42801	0.714007	+	0.700138i	$0.246878\pi$
$360$	−22.2594	−1.17317
$361$	−12.7993	−0.673649
$362$	−17.8894	−0.940244
$363$	−2.72821	−0.143194
$364$	−9.46194	−0.495940
$365$	7.20082	0.376908
$366$	−62.4607	−3.26487
$367$	15.5369	0.811017	0.405509	−	0.914091i	$-0.367094\pi$
$367$	15.5369	0.811017	0.405509	+	0.914091i	$0.367094\pi$
$368$	17.4836	0.911394
$369$	−5.46401	−0.284445
$370$	5.78552	0.300775
$371$	−0.978298	−0.0507907
$372$	−96.3139	−4.99364
$373$	26.8314	1.38928	0.694638	−	0.719360i	$-0.255565\pi$
$373$	26.8314	1.38928	0.694638	+	0.719360i	$0.255565\pi$
$374$	2.69318	0.139261
$375$	15.0898	0.779235
$376$	107.175	5.52715
$377$	−15.6889	−0.808020
$378$	6.72771	0.346036
$379$	−12.9338	−0.664364	−0.332182	−	0.943215i	$-0.607785\pi$
$379$	−12.9338	−0.664364	−0.332182	+	0.943215i	$0.607785\pi$
$380$	−7.47979	−0.383705
$381$	−16.0752	−0.823560
$382$	38.4345	1.96648
$383$	4.70751	0.240543	0.120271	−	0.992741i	$-0.461624\pi$
$383$	4.70751	0.240543	0.120271	+	0.992741i	$0.461624\pi$
$384$	61.7549	3.15142
$385$	−0.362794	−0.0184897
$386$	66.1017	3.36449
$387$	−4.44313	−0.225857
$388$	−3.66171	−0.185895
$389$	−12.3308	−0.625197	−0.312599	−	0.949885i	$-0.601199\pi$
$389$	−12.3308	−0.625197	−0.312599	+	0.949885i	$0.601199\pi$
$390$	−11.9268	−0.603936
$391$	1.33564	0.0675465
$392$	57.8038	2.91953
$393$	−39.0862	−1.97164
$394$	61.4802	3.09733
$395$	−2.76001	−0.138871
$396$	−23.3408	−1.17292
$397$	−36.5058	−1.83217	−0.916087	−	0.400979i	$-0.868670\pi$
$397$	−36.5058	−1.83217	−0.916087	+	0.400979i	$0.868670\pi$
$398$	−2.73463	−0.137074
$399$	4.31037	0.215788
$400$	−61.1701	−3.05851
$401$	−2.22081	−0.110902	−0.0554511	−	0.998461i	$-0.517660\pi$
$401$	−2.22081	−0.110902	−0.0554511	+	0.998461i	$0.517660\pi$
$402$	−32.1215	−1.60208
$403$	−19.0775	−0.950317
$404$	52.8733	2.63054
$405$	−1.47979	−0.0735314
$406$	−9.44362	−0.468679
$407$	3.75694	0.186224
$408$	23.9034	1.18339
$409$	−2.03480	−0.100615	−0.0503073	−	0.998734i	$-0.516020\pi$
$409$	−2.03480	−0.100615	−0.0503073	+	0.998734i	$0.516020\pi$
$410$	1.89379	0.0935274
$411$	−37.7942	−1.86425
$412$	−82.3399	−4.05659
$413$	−0.967734	−0.0476191
$414$	−15.9826	−0.785500
$415$	1.15198	0.0565483
$416$	50.3340	2.46782
$417$	8.06289	0.394841
$418$	−6.70634	−0.328018
$419$	−6.66140	−0.325431	−0.162715	−	0.986673i	$-0.552025\pi$
$419$	−6.66140	−0.325431	−0.162715	+	0.986673i	$0.552025\pi$
$420$	−5.19953	−0.253711
$421$	−12.9495	−0.631119	−0.315560	−	0.948906i	$-0.602192\pi$
$421$	−12.9495	−0.631119	−0.315560	+	0.948906i	$0.602192\pi$
$422$	−55.7422	−2.71349
$423$	−54.3505	−2.64261
$424$	13.5094	0.656073
$425$	−4.67305	−0.226676
$426$	91.6105	4.43854
$427$	−5.39361	−0.261015
$428$	−15.4760	−0.748063
$429$	−7.74488	−0.373926
$430$	1.53996	0.0742634
$431$	−32.9867	−1.58892	−0.794458	−	0.607319i	$-0.792245\pi$
$431$	−32.9867	−1.58892	−0.794458	+	0.607319i	$0.792245\pi$
$432$	−51.5376	−2.47960
$433$	12.5779	0.604453	0.302227	−	0.953236i	$-0.402270\pi$
$433$	12.5779	0.604453	0.302227	+	0.953236i	$0.402270\pi$
$434$	−11.4833	−0.551217
$435$	−8.62138	−0.413364
$436$	6.16818	0.295402
$437$	−3.32591	−0.159100
$438$	92.5300	4.42126
$439$	20.4808	0.977496	0.488748	−	0.872425i	$-0.337454\pi$
$439$	20.4808	0.977496	0.488748	+	0.872425i	$0.337454\pi$
$440$	5.00984	0.238835
$441$	−29.3133	−1.39587
$442$	7.64544	0.363657
$443$	19.1921	0.911846	0.455923	−	0.890019i	$-0.349309\pi$
$443$	19.1921	0.911846	0.455923	+	0.890019i	$0.349309\pi$
$444$	53.8441	2.55533
$445$	4.19042	0.198645
$446$	34.7879	1.64725
$447$	42.1771	1.99491
$448$	13.6869	0.646644
$449$	−1.19999	−0.0566312	−0.0283156	−	0.999599i	$-0.509014\pi$
$449$	−1.19999	−0.0566312	−0.0283156	+	0.999599i	$0.509014\pi$
$450$	55.9185	2.63602
$451$	1.22976	0.0579074
$452$	−44.2817	−2.08283
$453$	−58.5530	−2.75106
$454$	−42.6665	−2.00244
$455$	−1.02990	−0.0482826
$456$	−59.5221	−2.78738
$457$	−36.0360	−1.68569	−0.842847	−	0.538154i	$-0.819122\pi$
$457$	−36.0360	−1.68569	−0.842847	+	0.538154i	$0.819122\pi$
$458$	14.4208	0.673838
$459$	−3.93718	−0.183772
$460$	4.01200	0.187060
$461$	−13.4579	−0.626797	−0.313399	−	0.949622i	$-0.601468\pi$
$461$	−13.4579	−0.626797	−0.313399	+	0.949622i	$0.601468\pi$
$462$	−4.66187	−0.216890
$463$	12.1085	0.562730	0.281365	−	0.959601i	$-0.409213\pi$
$463$	12.1085	0.562730	0.281365	+	0.959601i	$0.409213\pi$
$464$	72.3428	3.35843
$465$	−10.4835	−0.486160
$466$	−21.9107	−1.01499
$467$	−27.3149	−1.26399	−0.631993	−	0.774974i	$-0.717763\pi$
$467$	−27.3149	−1.26399	−0.631993	+	0.774974i	$0.717763\pi$
$468$	−66.2602	−3.06288
$469$	−2.77376	−0.128080
$470$	18.8375	0.868908
$471$	11.3656	0.523699
$472$	13.3635	0.615105
$473$	1.00000	0.0459800
$474$	−35.4660	−1.62901
$475$	11.6364	0.533916
$476$	3.33306	0.152771
$477$	−6.85084	−0.313678
$478$	−6.88892	−0.315092
$479$	−12.0723	−0.551597	−0.275798	−	0.961216i	$-0.588942\pi$
$479$	−12.0723	−0.551597	−0.275798	+	0.961216i	$0.588942\pi$
$480$	27.6596	1.26248
$481$	10.6652	0.486293
$482$	52.2574	2.38026
$483$	−2.31199	−0.105199
$484$	5.25323	0.238783
$485$	−0.398566	−0.0180980
$486$	−50.8258	−2.30551
$487$	−6.58779	−0.298521	−0.149261	−	0.988798i	$-0.547689\pi$
$487$	−6.58779	−0.298521	−0.149261	+	0.988798i	$0.547689\pi$
$488$	74.4807	3.37158
$489$	−4.36138	−0.197229
$490$	10.1598	0.458972
$491$	−39.4269	−1.77931	−0.889656	−	0.456632i	$-0.849056\pi$
$491$	−39.4269	−1.77931	−0.889656	+	0.456632i	$0.849056\pi$
$492$	17.6249	0.794592
$493$	5.52657	0.248904
$494$	−19.0380	−0.856561
$495$	−2.54058	−0.114190
$496$	87.9678	3.94987
$497$	7.91076	0.354846
$498$	14.8028	0.663329
$499$	25.9219	1.16042	0.580212	−	0.814465i	$-0.302970\pi$
$499$	25.9219	1.16042	0.580212	+	0.814465i	$0.302970\pi$
$500$	−29.0558	−1.29942
$501$	−34.5817	−1.54499
$502$	−7.84477	−0.350129
$503$	2.56796	0.114500	0.0572499	−	0.998360i	$-0.481767\pi$
$503$	2.56796	0.114500	0.0572499	+	0.998360i	$0.481767\pi$
$504$	−24.6994	−1.10020
$505$	5.75510	0.256098
$506$	3.59714	0.159912
$507$	13.4805	0.598689
$508$	30.9533	1.37333
$509$	5.53467	0.245320	0.122660	−	0.992449i	$-0.460858\pi$
$509$	5.53467	0.245320	0.122660	+	0.992449i	$0.460858\pi$
$510$	4.20133	0.186038
$511$	7.99017	0.353464
$512$	−2.71660	−0.120058
$513$	9.80402	0.432858
$514$	33.0412	1.45739
$515$	−8.96245	−0.394933
$516$	14.3319	0.630928
$517$	12.2325	0.537983
$518$	6.41973	0.282067
$519$	−43.3775	−1.90406
$520$	14.2220	0.623676
$521$	8.21405	0.359864	0.179932	−	0.983679i	$-0.442412\pi$
$521$	8.21405	0.359864	0.179932	+	0.983679i	$0.442412\pi$
$522$	−66.1319	−2.89452
$523$	−22.7071	−0.992913	−0.496457	−	0.868061i	$-0.665366\pi$
$523$	−22.7071	−0.992913	−0.496457	+	0.868061i	$0.665366\pi$
$524$	75.2613	3.28781
$525$	8.08900	0.353033
$526$	−49.5410	−2.16009
$527$	6.72024	0.292738
$528$	35.7123	1.55418
$529$	−21.2161	−0.922437
$530$	2.37445	0.103140
$531$	−6.77686	−0.294091
$532$	−8.29971	−0.359838
$533$	3.49107	0.151215
$534$	53.8465	2.33017
$535$	−1.68452	−0.0728282
$536$	38.3031	1.65444
$537$	26.3504	1.13710
$538$	−43.2247	−1.86355
$539$	6.59744	0.284172
$540$	−11.8265	−0.508929
$541$	−8.26335	−0.355269	−0.177635	−	0.984097i	$-0.556844\pi$
$541$	−8.26335	−0.355269	−0.177635	+	0.984097i	$0.556844\pi$
$542$	−15.3514	−0.659400
$543$	−18.1220	−0.777691
$544$	−17.7306	−0.760195
$545$	0.671388	0.0287591
$546$	−13.2342	−0.566371
$547$	−24.8205	−1.06125	−0.530624	−	0.847607i	$-0.678042\pi$
$547$	−24.8205	−1.06125	−0.530624	+	0.847607i	$0.678042\pi$
$548$	72.7736	3.10873
$549$	−37.7705	−1.61200
$550$	−12.5854	−0.536642
$551$	−13.7618	−0.586273
$552$	31.9264	1.35888
$553$	−3.06256	−0.130233
$554$	32.2913	1.37193
$555$	5.86077	0.248776
$556$	−15.5253	−0.658418
$557$	−24.2474	−1.02740	−0.513698	−	0.857971i	$-0.671725\pi$
$557$	−24.2474	−1.02740	−0.513698	+	0.857971i	$0.671725\pi$
$558$	−80.4155	−3.40426
$559$	2.83881	0.120069
$560$	4.74897	0.200681
$561$	2.72821	0.115185
$562$	−67.5309	−2.84862
$563$	−30.8271	−1.29921	−0.649605	−	0.760272i	$-0.725066\pi$
$563$	−30.8271	−1.29921	−0.649605	+	0.760272i	$0.725066\pi$
$564$	175.315	7.38208
$565$	−4.81993	−0.202776
$566$	39.6451	1.66641
$567$	−1.64200	−0.0689577
$568$	−109.240	−4.58362
$569$	41.1164	1.72369	0.861845	−	0.507172i	$-0.169309\pi$
$569$	41.1164	1.72369	0.861845	+	0.507172i	$0.169309\pi$
$570$	−10.4618	−0.438196
$571$	31.6796	1.32575	0.662874	−	0.748731i	$-0.269336\pi$
$571$	31.6796	1.32575	0.662874	+	0.748731i	$0.269336\pi$
$572$	14.9129	0.623542
$573$	38.9344	1.62651
$574$	2.10138	0.0877099
$575$	−6.24153	−0.260290
$576$	95.8467	3.99361
$577$	17.2344	0.717479	0.358740	−	0.933438i	$-0.383207\pi$
$577$	17.2344	0.717479	0.358740	+	0.933438i	$0.383207\pi$
$578$	−2.69318	−0.112022
$579$	66.9615	2.78282
$580$	16.6007	0.689305
$581$	1.27825	0.0530309
$582$	−5.12155	−0.212295
$583$	1.54189	0.0638587
$584$	−110.337	−4.56576
$585$	−7.21223	−0.298189
$586$	55.2340	2.28169
$587$	−7.36961	−0.304176	−0.152088	−	0.988367i	$-0.548600\pi$
$587$	−7.36961	−0.304176	−0.152088	+	0.988367i	$0.548600\pi$
$588$	94.5540	3.89934
$589$	−16.7342	−0.689519
$590$	2.34881	0.0966990
$591$	62.2798	2.56185
$592$	−49.1783	−2.02121
$593$	43.7756	1.79765	0.898824	−	0.438309i	$-0.144422\pi$
$593$	43.7756	1.79765	0.898824	+	0.438309i	$0.144422\pi$
$594$	−10.6035	−0.435068
$595$	0.362794	0.0148731
$596$	−81.2130	−3.32662
$597$	−2.77019	−0.113376
$598$	10.2116	0.417583
$599$	17.2671	0.705515	0.352757	−	0.935715i	$-0.385244\pi$
$599$	17.2671	0.705515	0.352757	+	0.935715i	$0.385244\pi$
$600$	−111.701	−4.56019
$601$	11.9149	0.486020	0.243010	−	0.970024i	$-0.421865\pi$
$601$	11.9149	0.486020	0.243010	+	0.970024i	$0.421865\pi$
$602$	1.70877	0.0696441
$603$	−19.4242	−0.791013
$604$	112.745	4.58754
$605$	0.571799	0.0232469
$606$	73.9526	3.00412
$607$	41.6135	1.68904	0.844520	−	0.535524i	$-0.179886\pi$
$607$	41.6135	1.68904	0.844520	+	0.535524i	$0.179886\pi$
$608$	44.1513	1.79057
$609$	−9.56645	−0.387652
$610$	13.0910	0.530038
$611$	34.7257	1.40485
$612$	23.3408	0.943497
$613$	−3.28589	−0.132716	−0.0663579	−	0.997796i	$-0.521138\pi$
$613$	−3.28589	−0.132716	−0.0663579	+	0.997796i	$0.521138\pi$
$614$	49.7511	2.00779
$615$	1.91842	0.0773581
$616$	5.55901	0.223979
$617$	−33.5848	−1.35207	−0.676037	−	0.736868i	$-0.736304\pi$
$617$	−33.5848	−1.35207	−0.676037	+	0.736868i	$0.736304\pi$
$618$	−115.167	−4.63269
$619$	9.28323	0.373124	0.186562	−	0.982443i	$-0.440265\pi$
$619$	9.28323	0.373124	0.186562	+	0.982443i	$0.440265\pi$
$620$	20.1862	0.810697
$621$	−5.25867	−0.211023
$622$	17.1731	0.688577
$623$	4.64976	0.186289
$624$	101.380	4.05846
$625$	20.2026	0.808104
$626$	26.4646	1.05774
$627$	−6.79356	−0.271309
$628$	−21.8847	−0.873296
$629$	−3.75694	−0.149799
$630$	−4.34125	−0.172960
$631$	15.4445	0.614834	0.307417	−	0.951575i	$-0.400535\pi$
$631$	15.4445	0.614834	0.307417	+	0.951575i	$0.400535\pi$
$632$	42.2911	1.68225
$633$	−56.4672	−2.24437
$634$	−47.9014	−1.90241
$635$	3.36917	0.133701
$636$	22.0983	0.876254
$637$	18.7289	0.742066
$638$	14.8841	0.589266
$639$	55.3976	2.19150
$640$	−12.9430	−0.511619
$641$	38.1609	1.50727	0.753633	−	0.657296i	$-0.228300\pi$
$641$	38.1609	1.50727	0.753633	+	0.657296i	$0.228300\pi$
$642$	−21.6460	−0.854298
$643$	33.3459	1.31503	0.657516	−	0.753441i	$-0.271607\pi$
$643$	33.3459	1.31503	0.657516	+	0.753441i	$0.271607\pi$
$644$	4.45179	0.175425
$645$	1.55999	0.0614244
$646$	6.70634	0.263857
$647$	13.6643	0.537197	0.268599	−	0.963252i	$-0.413439\pi$
$647$	13.6643	0.537197	0.268599	+	0.963252i	$0.413439\pi$
$648$	22.6745	0.890740
$649$	1.52524	0.0598711
$650$	−35.7275	−1.40135
$651$	−11.6327	−0.455920
$652$	8.39794	0.328889
$653$	19.1938	0.751113	0.375557	−	0.926799i	$-0.377452\pi$
$653$	19.1938	0.751113	0.375557	+	0.926799i	$0.377452\pi$
$654$	8.62728	0.337353
$655$	8.19197	0.320087
$656$	−16.0976	−0.628506
$657$	55.9537	2.18296
$658$	20.9024	0.814861
$659$	44.6369	1.73881	0.869403	−	0.494103i	$-0.164504\pi$
$659$	44.6369	1.73881	0.869403	+	0.494103i	$0.164504\pi$
$660$	8.19498	0.318989
$661$	−20.3703	−0.792312	−0.396156	−	0.918183i	$-0.629656\pi$
$661$	−20.3703	−0.792312	−0.396156	+	0.918183i	$0.629656\pi$
$662$	63.7838	2.47903
$663$	7.74488	0.300786
$664$	−17.6515	−0.685010
$665$	−0.903398	−0.0350323
$666$	44.9562	1.74202
$667$	7.38154	0.285814
$668$	66.5878	2.57636
$669$	35.2403	1.36247
$670$	6.73227	0.260090
$671$	8.50086	0.328172
$672$	30.6916	1.18395
$673$	21.0635	0.811939	0.405970	−	0.913887i	$-0.366934\pi$
$673$	21.0635	0.811939	0.405970	+	0.913887i	$0.366934\pi$
$674$	−38.3257	−1.47625
$675$	18.3986	0.708163
$676$	−25.9570	−0.998345
$677$	−24.2760	−0.933003	−0.466502	−	0.884520i	$-0.654486\pi$
$677$	−24.2760	−0.933003	−0.466502	+	0.884520i	$0.654486\pi$
$678$	−61.9357	−2.37863
$679$	−0.442257	−0.0169723
$680$	−5.00984	−0.192119
$681$	−43.2215	−1.65625
$682$	18.0988	0.693040
$683$	43.2453	1.65473	0.827367	−	0.561662i	$-0.189838\pi$
$683$	43.2453	1.65473	0.827367	+	0.561662i	$0.189838\pi$
$684$	−58.1213	−2.22232
$685$	7.92118	0.302653
$686$	23.2348	0.887110
$687$	14.6083	0.557342
$688$	−13.0900	−0.499051
$689$	4.37715	0.166756
$690$	5.61148	0.213626
$691$	−2.18622	−0.0831675	−0.0415838	−	0.999135i	$-0.513240\pi$
$691$	−2.18622	−0.0831675	−0.0415838	+	0.999135i	$0.513240\pi$
$692$	83.5244	3.17512
$693$	−2.81907	−0.107088
$694$	−4.37142	−0.165937
$695$	−1.68988	−0.0641008
$696$	132.104	5.00738
$697$	−1.22976	−0.0465807
$698$	−7.56992	−0.286526
$699$	−22.1956	−0.839516
$700$	−15.5756	−0.588701
$701$	−42.9667	−1.62283	−0.811415	−	0.584471i	$-0.801302\pi$
$701$	−42.9667	−1.62283	−0.811415	+	0.584471i	$0.801302\pi$
$702$	−30.1014	−1.13611
$703$	9.35520	0.352838
$704$	−21.5719	−0.813020
$705$	19.0825	0.718688
$706$	13.9941	0.526676
$707$	6.38596	0.240169
$708$	21.8597	0.821537
$709$	−6.81565	−0.255967	−0.127984	−	0.991776i	$-0.540850\pi$
$709$	−6.81565	−0.255967	−0.127984	+	0.991776i	$0.540850\pi$
$710$	−19.2004	−0.720578
$711$	−21.4465	−0.804308
$712$	−64.2089	−2.40633
$713$	8.97585	0.336148
$714$	4.66187	0.174466
$715$	1.62323	0.0607053
$716$	−50.7383	−1.89618
$717$	−6.97852	−0.260618
$718$	−72.8695	−2.71946
$719$	31.6410	1.18001	0.590006	−	0.807399i	$-0.299125\pi$
$719$	31.6410	1.18001	0.590006	+	0.807399i	$0.299125\pi$
$720$	33.2561	1.23938
$721$	−9.94490	−0.370367
$722$	34.4709	1.28287
$723$	52.9371	1.96875
$724$	34.8944	1.29684
$725$	−25.8259	−0.959151
$726$	7.34757	0.272694
$727$	50.3254	1.86646	0.933232	−	0.359274i	$-0.116976\pi$
$727$	50.3254	1.86646	0.933232	+	0.359274i	$0.116976\pi$
$728$	15.7810	0.584883
$729$	−43.7230	−1.61937
$730$	−19.3931	−0.717772
$731$	−1.00000	−0.0369863
$732$	121.834	4.50310
$733$	−6.37480	−0.235458	−0.117729	−	0.993046i	$-0.537561\pi$
$733$	−6.37480	−0.235458	−0.117729	+	0.993046i	$0.537561\pi$
$734$	−41.8436	−1.54448
$735$	10.2919	0.379623
$736$	−23.6818	−0.872924
$737$	4.37172	0.161034
$738$	14.7156	0.541688
$739$	17.6219	0.648232	0.324116	−	0.946017i	$-0.394933\pi$
$739$	17.6219	0.648232	0.324116	+	0.946017i	$0.394933\pi$
$740$	−11.2851	−0.414847
$741$	−19.2856	−0.708476
$742$	2.63473	0.0967241
$743$	28.3054	1.03843	0.519213	−	0.854645i	$-0.326225\pi$
$743$	28.3054	1.03843	0.519213	+	0.854645i	$0.326225\pi$
$744$	160.636	5.88921
$745$	−8.83979	−0.323865
$746$	−72.2618	−2.64569
$747$	8.95137	0.327514
$748$	−5.25323	−0.192077
$749$	−1.86918	−0.0682982
$750$	−40.6397	−1.48395
$751$	−50.8638	−1.85605	−0.928023	−	0.372524i	$-0.878492\pi$
$751$	−50.8638	−1.85605	−0.928023	+	0.372524i	$0.878492\pi$
$752$	−160.123	−5.83908
$753$	−7.94681	−0.289598
$754$	42.2531	1.53877
$755$	12.2720	0.446623
$756$	−13.1229	−0.477274
$757$	−22.2385	−0.808274	−0.404137	−	0.914699i	$-0.632428\pi$
$757$	−22.2385	−0.808274	−0.404137	+	0.914699i	$0.632428\pi$
$758$	34.8331	1.26519
$759$	3.64392	0.132266
$760$	12.4751	0.452519
$761$	−20.0171	−0.725619	−0.362809	−	0.931863i	$-0.618182\pi$
$761$	−20.0171	−0.725619	−0.362809	+	0.931863i	$0.618182\pi$
$762$	43.2936	1.56836
$763$	0.744984	0.0269702
$764$	−74.9691	−2.71229
$765$	2.54058	0.0918548
$766$	−12.6782	−0.458082
$767$	4.32988	0.156343
$768$	−48.6121	−1.75414
$769$	−10.1687	−0.366692	−0.183346	−	0.983048i	$-0.558693\pi$
$769$	−10.1687	−0.366692	−0.183346	+	0.983048i	$0.558693\pi$
$770$	0.977070	0.0352112
$771$	33.4710	1.20543
$772$	−128.936	−4.64050
$773$	9.36606	0.336874	0.168437	−	0.985712i	$-0.446128\pi$
$773$	9.36606	0.336874	0.168437	+	0.985712i	$0.446128\pi$
$774$	11.9662	0.430115
$775$	−31.4040	−1.12806
$776$	6.10715	0.219234
$777$	6.50322	0.233302
$778$	33.2091	1.19061
$779$	3.06226	0.109717
$780$	23.2640	0.832985
$781$	−12.4681	−0.446145
$782$	−3.59714	−0.128633
$783$	−21.7591	−0.777606
$784$	−86.3604	−3.08430
$785$	−2.38209	−0.0850203
$786$	105.266	3.75472
$787$	−35.4734	−1.26449	−0.632245	−	0.774769i	$-0.717866\pi$
$787$	−35.4734	−1.26449	−0.632245	+	0.774769i	$0.717866\pi$
$788$	−119.921	−4.27202
$789$	−50.1854	−1.78665
$790$	7.43322	0.264462
$791$	−5.34828	−0.190163
$792$	38.9287	1.38327
$793$	24.1324	0.856965
$794$	98.3168	3.48913
$795$	2.40533	0.0853084
$796$	5.33407	0.189061
$797$	26.2706	0.930554	0.465277	−	0.885165i	$-0.345955\pi$
$797$	26.2706	0.930554	0.465277	+	0.885165i	$0.345955\pi$
$798$	−11.6086	−0.410940
$799$	−12.2325	−0.432753
$800$	82.8561	2.92940
$801$	32.5614	1.15050
$802$	5.98106	0.211199
$803$	−12.5933	−0.444407
$804$	62.6552	2.20968
$805$	0.484564	0.0170786
$806$	51.3792	1.80975
$807$	−43.7869	−1.54137
$808$	−88.1842	−3.10231
$809$	48.5062	1.70539	0.852694	−	0.522411i	$-0.174967\pi$
$809$	48.5062	1.70539	0.852694	+	0.522411i	$0.174967\pi$
$810$	3.98535	0.140031
$811$	20.2234	0.710140	0.355070	−	0.934840i	$-0.384457\pi$
$811$	20.2234	0.710140	0.355070	+	0.934840i	$0.384457\pi$
$812$	18.4204	0.646430
$813$	−15.5511	−0.545400
$814$	−10.1181	−0.354640
$815$	0.914091	0.0320192
$816$	−35.7123	−1.25018
$817$	2.49012	0.0871181
$818$	5.48010	0.191607
$819$	−8.00282	−0.279641
$820$	−3.69396	−0.128999
$821$	38.2036	1.33331	0.666657	−	0.745365i	$-0.267725\pi$
$821$	38.2036	1.33331	0.666657	+	0.745365i	$0.267725\pi$
$822$	101.787	3.55022
$823$	−1.55429	−0.0541791	−0.0270895	−	0.999633i	$-0.508624\pi$
$823$	−1.55429	−0.0541791	−0.0270895	+	0.999633i	$0.508624\pi$
$824$	137.330	4.78411
$825$	−12.7491	−0.443865
$826$	2.60629	0.0906843
$827$	26.3290	0.915550	0.457775	−	0.889068i	$-0.348647\pi$
$827$	26.3290	0.915550	0.457775	+	0.889068i	$0.348647\pi$
$828$	31.1750	1.08341
$829$	−1.79574	−0.0623686	−0.0311843	−	0.999514i	$-0.509928\pi$
$829$	−1.79574	−0.0623686	−0.0311843	+	0.999514i	$0.509928\pi$
$830$	−3.10248	−0.107689
$831$	32.7113	1.13474
$832$	−61.2385	−2.12306
$833$	−6.59744	−0.228588
$834$	−21.7148	−0.751923
$835$	7.24788	0.250823
$836$	13.0812	0.452421
$837$	−26.4587	−0.914548
$838$	17.9404	0.619740
$839$	−29.6417	−1.02334	−0.511672	−	0.859181i	$-0.670974\pi$
$839$	−29.6417	−1.02334	−0.511672	+	0.859181i	$0.670974\pi$
$840$	8.67199	0.299212
$841$	1.54301	0.0532071
$842$	34.8753	1.20188
$843$	−68.4092	−2.35614
$844$	108.729	3.74260
$845$	−2.82534	−0.0971946
$846$	146.376	5.03250
$847$	0.634478	0.0218009
$848$	−20.1834	−0.693099
$849$	40.1607	1.37831
$850$	12.5854	0.431675
$851$	−5.01793	−0.172013
$852$	−178.692	−6.12190
$853$	−13.4299	−0.459830	−0.229915	−	0.973211i	$-0.573845\pi$
$853$	−13.4299	−0.459830	−0.229915	+	0.973211i	$0.573845\pi$
$854$	14.5260	0.497069
$855$	−6.32633	−0.216356
$856$	25.8116	0.882221
$857$	−14.1948	−0.484884	−0.242442	−	0.970166i	$-0.577948\pi$
$857$	−14.1948	−0.484884	−0.242442	+	0.970166i	$0.577948\pi$
$858$	20.8584	0.712093
$859$	40.3760	1.37761	0.688806	−	0.724945i	$-0.258135\pi$
$859$	40.3760	1.37761	0.688806	+	0.724945i	$0.258135\pi$
$860$	−3.00379	−0.102428
$861$	2.12871	0.0725463
$862$	88.8393	3.02588
$863$	31.8042	1.08263	0.541313	−	0.840821i	$-0.317927\pi$
$863$	31.8042	1.08263	0.541313	+	0.840821i	$0.317927\pi$
$864$	69.8086	2.37494
$865$	9.09138	0.309116
$866$	−33.8745	−1.15110
$867$	−2.72821	−0.0926549
$868$	22.3990	0.760270
$869$	4.82690	0.163741
$870$	23.2190	0.787196
$871$	12.4105	0.420514
$872$	−10.2875	−0.348380
$873$	−3.09704	−0.104819
$874$	8.95728	0.302985
$875$	−3.50932	−0.118637
$876$	−180.486	−6.09806
$877$	19.9927	0.675105	0.337553	−	0.941307i	$-0.390401\pi$
$877$	19.9927	0.675105	0.337553	+	0.941307i	$0.390401\pi$
$878$	−55.1586	−1.86151
$879$	55.9524	1.88723
$880$	−7.48484	−0.252314
$881$	−35.9683	−1.21180	−0.605901	−	0.795540i	$-0.707187\pi$
$881$	−35.9683	−1.21180	−0.605901	+	0.795540i	$0.707187\pi$
$882$	78.9461	2.65825
$883$	−27.6942	−0.931985	−0.465992	−	0.884789i	$-0.654303\pi$
$883$	−27.6942	−0.931985	−0.465992	+	0.884789i	$0.654303\pi$
$884$	−14.9129	−0.501577
$885$	2.37936	0.0799813
$886$	−51.6879	−1.73649
$887$	−37.7277	−1.26677	−0.633387	−	0.773836i	$-0.718336\pi$
$887$	−37.7277	−1.26677	−0.633387	+	0.773836i	$0.718336\pi$
$888$	−89.8034	−3.01360
$889$	3.73849	0.125385
$890$	−11.2856	−0.378293
$891$	2.58796	0.0866999
$892$	−67.8560	−2.27199
$893$	30.4602	1.01931
$894$	−113.591	−3.79904
$895$	−5.52271	−0.184604
$896$	−14.3618	−0.479796
$897$	10.3444	0.345390
$898$	3.23180	0.107847
$899$	37.1399	1.23868
$900$	−109.073	−3.63576
$901$	−1.54189	−0.0513679
$902$	−3.31198	−0.110277
$903$	1.73099	0.0576038
$904$	73.8547	2.45637
$905$	3.79815	0.126255
$906$	157.694	5.23903
$907$	33.6803	1.11833	0.559167	−	0.829055i	$-0.311121\pi$
$907$	33.6803	1.11833	0.559167	+	0.829055i	$0.311121\pi$
$908$	83.2239	2.76188
$909$	44.7197	1.48326
$910$	2.77372	0.0919479
$911$	−8.00069	−0.265075	−0.132537	−	0.991178i	$-0.542312\pi$
$911$	−8.00069	−0.265075	−0.132537	+	0.991178i	$0.542312\pi$
$912$	88.9276	2.94469
$913$	−2.01465	−0.0666753
$914$	97.0515	3.21018
$915$	13.2612	0.438403
$916$	−28.1287	−0.929397
$917$	9.08996	0.300177
$918$	10.6035	0.349969
$919$	14.4451	0.476500	0.238250	−	0.971204i	$-0.423426\pi$
$919$	14.4451	0.476500	0.238250	+	0.971204i	$0.423426\pi$
$920$	−6.69137	−0.220608
$921$	50.3982	1.66068
$922$	36.2446	1.19365
$923$	−35.3947	−1.16503
$924$	9.09330	0.299148
$925$	17.5563	0.577249
$926$	−32.6104	−1.07164
$927$	−69.6423	−2.28735
$928$	−97.9896	−3.21667
$929$	−18.7184	−0.614131	−0.307065	−	0.951688i	$-0.599347\pi$
$929$	−18.7184	−0.614131	−0.307065	+	0.951688i	$0.599347\pi$
$930$	28.2339	0.925827
$931$	16.4284	0.538418
$932$	42.7382	1.39994
$933$	17.3964	0.569533
$934$	73.5641	2.40709
$935$	−0.571799	−0.0186998
$936$	110.511	3.61218
$937$	−37.8300	−1.23585	−0.617926	−	0.786236i	$-0.712027\pi$
$937$	−37.8300	−1.23585	−0.617926	+	0.786236i	$0.712027\pi$
$938$	7.47025	0.243912
$939$	26.8088	0.874871
$940$	−36.7438	−1.19845
$941$	55.1881	1.79908	0.899540	−	0.436837i	$-0.143902\pi$
$941$	55.1881	1.79908	0.899540	+	0.436837i	$0.143902\pi$
$942$	−30.6097	−0.997316
$943$	−1.64253	−0.0534881
$944$	−19.9654	−0.649819
$945$	−1.42838	−0.0464653
$946$	−2.69318	−0.0875629
$947$	8.79261	0.285721	0.142861	−	0.989743i	$-0.454370\pi$
$947$	8.79261	0.285721	0.142861	+	0.989743i	$0.454370\pi$
$948$	69.1787	2.24682
$949$	−35.7500	−1.16049
$950$	−31.3390	−1.01677
$951$	−48.5244	−1.57351
$952$	−5.55901	−0.180169
$953$	31.5806	1.02299	0.511497	−	0.859285i	$-0.329091\pi$
$953$	31.5806	1.02299	0.511497	+	0.859285i	$0.329091\pi$
$954$	18.4506	0.597359
$955$	−8.16016	−0.264057
$956$	13.4373	0.434593
$957$	15.0777	0.487391
$958$	32.5129	1.05044
$959$	8.78949	0.283827
$960$	−33.6518	−1.08611
$961$	14.1616	0.456825
$962$	−28.7234	−0.926081
$963$	−13.0895	−0.421803
$964$	−101.932	−3.28300
$965$	−14.0343	−0.451779
$966$	6.22661	0.200338
$967$	24.5968	0.790981	0.395491	−	0.918470i	$-0.370575\pi$
$967$	24.5968	0.790981	0.395491	+	0.918470i	$0.370575\pi$
$968$	−8.76155	−0.281607
$969$	6.79356	0.218241
$970$	1.07341	0.0344652
$971$	−15.7325	−0.504881	−0.252440	−	0.967612i	$-0.581233\pi$
$971$	−15.7325	−0.504881	−0.252440	+	0.967612i	$0.581233\pi$
$972$	99.1391	3.17989
$973$	−1.87512	−0.0601137
$974$	17.7421	0.568494
$975$	−36.1922	−1.15908
$976$	−111.276	−3.56186
$977$	17.2959	0.553346	0.276673	−	0.960964i	$-0.410768\pi$
$977$	17.2959	0.553346	0.276673	+	0.960964i	$0.410768\pi$
$978$	11.7460	0.375596
$979$	−7.32848	−0.234219
$980$	−19.8173	−0.633041
$981$	5.21699	0.166566
$982$	106.184	3.38846
$983$	39.7867	1.26900	0.634500	−	0.772923i	$-0.281206\pi$
$983$	39.7867	1.26900	0.634500	+	0.772923i	$0.281206\pi$
$984$	−29.3955	−0.937095
$985$	−13.0531	−0.415905
$986$	−14.8841	−0.474005
$987$	21.1743	0.673985
$988$	37.1350	1.18142
$989$	−1.33564	−0.0424710
$990$	6.84224	0.217461
$991$	14.6854	0.466496	0.233248	−	0.972417i	$-0.425065\pi$
$991$	14.6854	0.466496	0.233248	+	0.972417i	$0.425065\pi$
$992$	−119.154	−3.78314
$993$	64.6133	2.05044
$994$	−21.3051	−0.675758
$995$	0.580598	0.0184062
$996$	−28.8739	−0.914903
$997$	5.55279	0.175859	0.0879293	−	0.996127i	$-0.471975\pi$
$997$	5.55279	0.175859	0.0879293	+	0.996127i	$0.471975\pi$
$998$	−69.8124	−2.20987
$999$	14.7917	0.467989

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8041.2.a.f.1.1	✓	66

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8041.2.a.f.1.1	✓	66	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:	\( N \)	\(=\)	\( 8041 = 11 \cdot 17 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8041.a (trivial)

\(f(q)\)	\(=\)	\(q-2.69318 q^{2} -2.72821 q^{3} +5.25323 q^{4} +0.571799 q^{5} +7.34757 q^{6} +0.634478 q^{7} -8.76155 q^{8} +4.44313 q^{9} +O(q^{10})\)	\(q-2.69318 q^{2} -2.72821 q^{3} +5.25323 q^{4} +0.571799 q^{5} +7.34757 q^{6} +0.634478 q^{7} -8.76155 q^{8} +4.44313 q^{9} -1.53996 q^{10} -1.00000 q^{11} -14.3319 q^{12} -2.83881 q^{13} -1.70877 q^{14} -1.55999 q^{15} +13.0900 q^{16} +1.00000 q^{17} -11.9662 q^{18} -2.49012 q^{19} +3.00379 q^{20} -1.73099 q^{21} +2.69318 q^{22} +1.33564 q^{23} +23.9034 q^{24} -4.67305 q^{25} +7.64544 q^{26} -3.93718 q^{27} +3.33306 q^{28} +5.52657 q^{29} +4.20133 q^{30} +6.72024 q^{31} -17.7306 q^{32} +2.72821 q^{33} -2.69318 q^{34} +0.362794 q^{35} +23.3408 q^{36} -3.75694 q^{37} +6.70634 q^{38} +7.74488 q^{39} -5.00984 q^{40} -1.22976 q^{41} +4.66187 q^{42} -1.00000 q^{43} -5.25323 q^{44} +2.54058 q^{45} -3.59714 q^{46} -12.2325 q^{47} -35.7123 q^{48} -6.59744 q^{49} +12.5854 q^{50} -2.72821 q^{51} -14.9129 q^{52} -1.54189 q^{53} +10.6035 q^{54} -0.571799 q^{55} -5.55901 q^{56} +6.79356 q^{57} -14.8841 q^{58} -1.52524 q^{59} -8.19498 q^{60} -8.50086 q^{61} -18.0988 q^{62} +2.81907 q^{63} +21.5719 q^{64} -1.62323 q^{65} -7.34757 q^{66} -4.37172 q^{67} +5.25323 q^{68} -3.64392 q^{69} -0.977070 q^{70} +12.4681 q^{71} -38.9287 q^{72} +12.5933 q^{73} +10.1181 q^{74} +12.7491 q^{75} -13.0812 q^{76} -0.634478 q^{77} -20.8584 q^{78} -4.82690 q^{79} +7.48484 q^{80} -2.58796 q^{81} +3.31198 q^{82} +2.01465 q^{83} -9.09330 q^{84} +0.571799 q^{85} +2.69318 q^{86} -15.0777 q^{87} +8.76155 q^{88} +7.32848 q^{89} -6.84224 q^{90} -1.80117 q^{91} +7.01645 q^{92} -18.3342 q^{93} +32.9443 q^{94} -1.42384 q^{95} +48.3729 q^{96} -0.697040 q^{97} +17.7681 q^{98} -4.44313 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 66 q + 12 q^{2} + 66 q^{4} + 6 q^{5} + 7 q^{6} + 13 q^{7} + 30 q^{8} + 58 q^{9}+O(q^{10}) \) 66 * q + 12 * q^2 + 66 * q^4 + 6 * q^5 + 7 * q^6 + 13 * q^7 + 30 * q^8 + 58 * q^9	\( 66 q + 12 q^{2} + 66 q^{4} + 6 q^{5} + 7 q^{6} + 13 q^{7} + 30 q^{8} + 58 q^{9} + 7 q^{10} - 66 q^{11} + 12 q^{12} + 12 q^{13} + 13 q^{14} + 35 q^{15} + 58 q^{16} + 66 q^{17} + 37 q^{18} + 24 q^{19} + 17 q^{20} + 16 q^{21} - 12 q^{22} + 25 q^{23} + 22 q^{24} + 56 q^{25} + 36 q^{26} + 17 q^{28} + 29 q^{29} + 28 q^{30} + 37 q^{31} + 62 q^{32} + 12 q^{34} + 40 q^{35} + 107 q^{36} - 34 q^{37} + 22 q^{38} + 61 q^{39} + 37 q^{40} + 41 q^{41} + 19 q^{42} - 66 q^{43} - 66 q^{44} + 10 q^{45} + 43 q^{46} + 61 q^{47} + 29 q^{48} + 33 q^{49} + 59 q^{50} + 51 q^{52} - 35 q^{53} - 37 q^{54} - 6 q^{55} + 37 q^{56} - 7 q^{57} + 17 q^{58} + 48 q^{59} - 56 q^{60} + q^{61} + 37 q^{62} + 43 q^{63} + 68 q^{64} + 41 q^{65} - 7 q^{66} + 10 q^{67} + 66 q^{68} + 18 q^{69} + 77 q^{70} + 84 q^{71} + 83 q^{72} + 5 q^{73} + 36 q^{74} + 14 q^{75} + 14 q^{76} - 13 q^{77} + 41 q^{78} + 58 q^{79} + 25 q^{80} + 78 q^{81} - 28 q^{82} + 47 q^{83} + 44 q^{84} + 6 q^{85} - 12 q^{86} + 101 q^{87} - 30 q^{88} + 53 q^{89} + q^{90} + 2 q^{91} + 34 q^{92} - 3 q^{93} + 17 q^{94} + 91 q^{95} + 27 q^{96} - 28 q^{97} + 87 q^{98} - 58 q^{99}+O(q^{100}) \) 66 * q + 12 * q^2 + 66 * q^4 + 6 * q^5 + 7 * q^6 + 13 * q^7 + 30 * q^8 + 58 * q^9 + 7 * q^10 - 66 * q^11 + 12 * q^12 + 12 * q^13 + 13 * q^14 + 35 * q^15 + 58 * q^16 + 66 * q^17 + 37 * q^18 + 24 * q^19 + 17 * q^20 + 16 * q^21 - 12 * q^22 + 25 * q^23 + 22 * q^24 + 56 * q^25 + 36 * q^26 + 17 * q^28 + 29 * q^29 + 28 * q^30 + 37 * q^31 + 62 * q^32 + 12 * q^34 + 40 * q^35 + 107 * q^36 - 34 * q^37 + 22 * q^38 + 61 * q^39 + 37 * q^40 + 41 * q^41 + 19 * q^42 - 66 * q^43 - 66 * q^44 + 10 * q^45 + 43 * q^46 + 61 * q^47 + 29 * q^48 + 33 * q^49 + 59 * q^50 + 51 * q^52 - 35 * q^53 - 37 * q^54 - 6 * q^55 + 37 * q^56 - 7 * q^57 + 17 * q^58 + 48 * q^59 - 56 * q^60 + q^61 + 37 * q^62 + 43 * q^63 + 68 * q^64 + 41 * q^65 - 7 * q^66 + 10 * q^67 + 66 * q^68 + 18 * q^69 + 77 * q^70 + 84 * q^71 + 83 * q^72 + 5 * q^73 + 36 * q^74 + 14 * q^75 + 14 * q^76 - 13 * q^77 + 41 * q^78 + 58 * q^79 + 25 * q^80 + 78 * q^81 - 28 * q^82 + 47 * q^83 + 44 * q^84 + 6 * q^85 - 12 * q^86 + 101 * q^87 - 30 * q^88 + 53 * q^89 + q^90 + 2 * q^91 + 34 * q^92 - 3 * q^93 + 17 * q^94 + 91 * q^95 + 27 * q^96 - 28 * q^97 + 87 * q^98 - 58 * q^99

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