LMFDB - Embedded newform 8021.2.a.a.1.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8021,2,Mod(1,8021)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8021, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8021.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8021 = 13 \cdot 617 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8021.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:	$64.0480074613$
Analytic rank:	$1$
Dimension:	$134$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.18
Character	$\chi$	$=$	8021.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.20714 q^{2} -0.230793 q^{3} +2.87148 q^{4} -0.451913 q^{5} +0.509393 q^{6} +5.18852 q^{7} -1.92347 q^{8} -2.94673 q^{9} +O(q^{10})$	\(q-2.20714 q^{2} -0.230793 q^{3} +2.87148 q^{4} -0.451913 q^{5} +0.509393 q^{6} +5.18852 q^{7} -1.92347 q^{8} -2.94673 q^{9} +0.997437 q^{10} +2.89647 q^{11} -0.662717 q^{12} +1.00000 q^{13} -11.4518 q^{14} +0.104298 q^{15} -1.49757 q^{16} -6.47981 q^{17} +6.50386 q^{18} -6.93737 q^{19} -1.29766 q^{20} -1.19747 q^{21} -6.39293 q^{22} +0.917653 q^{23} +0.443924 q^{24} -4.79577 q^{25} -2.20714 q^{26} +1.37246 q^{27} +14.8987 q^{28} +9.62541 q^{29} -0.230201 q^{30} +1.11456 q^{31} +7.15231 q^{32} -0.668486 q^{33} +14.3019 q^{34} -2.34476 q^{35} -8.46148 q^{36} +2.16270 q^{37} +15.3118 q^{38} -0.230793 q^{39} +0.869243 q^{40} -6.86239 q^{41} +2.64300 q^{42} -8.50616 q^{43} +8.31715 q^{44} +1.33167 q^{45} -2.02539 q^{46} +4.07184 q^{47} +0.345630 q^{48} +19.9208 q^{49} +10.5850 q^{50} +1.49549 q^{51} +2.87148 q^{52} +9.40538 q^{53} -3.02922 q^{54} -1.30895 q^{55} -9.97999 q^{56} +1.60110 q^{57} -21.2446 q^{58} +2.46817 q^{59} +0.299490 q^{60} +9.03616 q^{61} -2.46000 q^{62} -15.2892 q^{63} -12.7910 q^{64} -0.451913 q^{65} +1.47544 q^{66} -5.94482 q^{67} -18.6066 q^{68} -0.211788 q^{69} +5.17522 q^{70} -9.15770 q^{71} +5.66797 q^{72} -5.61288 q^{73} -4.77338 q^{74} +1.10683 q^{75} -19.9205 q^{76} +15.0284 q^{77} +0.509393 q^{78} -5.60015 q^{79} +0.676774 q^{80} +8.52345 q^{81} +15.1463 q^{82} +9.21822 q^{83} -3.43852 q^{84} +2.92831 q^{85} +18.7743 q^{86} -2.22148 q^{87} -5.57129 q^{88} -5.97374 q^{89} -2.93918 q^{90} +5.18852 q^{91} +2.63502 q^{92} -0.257233 q^{93} -8.98713 q^{94} +3.13509 q^{95} -1.65070 q^{96} -6.15598 q^{97} -43.9680 q^{98} -8.53514 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 134 q - 6 q^{2} - 33 q^{3} + 98 q^{4} - 8 q^{5} - 16 q^{6} - 32 q^{7} - 15 q^{8} + 101 q^{9}+O(q^{10}) $ 134 * q - 6 * q^2 - 33 * q^3 + 98 * q^4 - 8 * q^5 - 16 * q^6 - 32 * q^7 - 15 * q^8 + 101 * q^9	\( 134 q - 6 q^{2} - 33 q^{3} + 98 q^{4} - 8 q^{5} - 16 q^{6} - 32 q^{7} - 15 q^{8} + 101 q^{9} - 33 q^{10} - 47 q^{11} - 53 q^{12} + 134 q^{13} - 28 q^{14} - 30 q^{15} + 30 q^{16} - 17 q^{17} - 14 q^{18} - 87 q^{19} - 12 q^{20} - 24 q^{21} - 52 q^{22} - 44 q^{23} - 36 q^{24} + 58 q^{25} - 6 q^{26} - 117 q^{27} - 71 q^{28} - 42 q^{29} - 21 q^{30} - 82 q^{31} - 31 q^{32} + 12 q^{33} - 30 q^{34} - 54 q^{35} + 32 q^{36} - 55 q^{37} - 12 q^{38} - 33 q^{39} - 86 q^{40} - 16 q^{41} + 6 q^{42} - 148 q^{43} - 54 q^{44} - 24 q^{45} - 57 q^{46} - 21 q^{47} - 82 q^{48} + 12 q^{49} - 17 q^{50} - 123 q^{51} + 98 q^{52} - 17 q^{53} - 10 q^{54} - 148 q^{55} - 47 q^{56} - q^{57} - 58 q^{58} - 64 q^{59} - 16 q^{60} - 112 q^{61} - 15 q^{62} - 58 q^{63} - 65 q^{64} - 8 q^{65} - 20 q^{66} - 110 q^{67} - 8 q^{68} - 57 q^{69} - 40 q^{70} - 78 q^{71} - 28 q^{72} - 43 q^{73} - 52 q^{74} - 150 q^{75} - 96 q^{76} - 24 q^{77} - 16 q^{78} - 228 q^{79} + 20 q^{80} + 54 q^{81} - 89 q^{82} - 12 q^{83} + 6 q^{84} - 77 q^{85} + 29 q^{86} - 77 q^{87} - 95 q^{88} - 32 q^{89} - 46 q^{90} - 32 q^{91} - 62 q^{92} - 9 q^{93} - 87 q^{94} - 61 q^{95} - 54 q^{96} - 38 q^{97} + 6 q^{98} - 193 q^{99}+O(q^{100}) \) 134 * q - 6 * q^2 - 33 * q^3 + 98 * q^4 - 8 * q^5 - 16 * q^6 - 32 * q^7 - 15 * q^8 + 101 * q^9 - 33 * q^10 - 47 * q^11 - 53 * q^12 + 134 * q^13 - 28 * q^14 - 30 * q^15 + 30 * q^16 - 17 * q^17 - 14 * q^18 - 87 * q^19 - 12 * q^20 - 24 * q^21 - 52 * q^22 - 44 * q^23 - 36 * q^24 + 58 * q^25 - 6 * q^26 - 117 * q^27 - 71 * q^28 - 42 * q^29 - 21 * q^30 - 82 * q^31 - 31 * q^32 + 12 * q^33 - 30 * q^34 - 54 * q^35 + 32 * q^36 - 55 * q^37 - 12 * q^38 - 33 * q^39 - 86 * q^40 - 16 * q^41 + 6 * q^42 - 148 * q^43 - 54 * q^44 - 24 * q^45 - 57 * q^46 - 21 * q^47 - 82 * q^48 + 12 * q^49 - 17 * q^50 - 123 * q^51 + 98 * q^52 - 17 * q^53 - 10 * q^54 - 148 * q^55 - 47 * q^56 - q^57 - 58 * q^58 - 64 * q^59 - 16 * q^60 - 112 * q^61 - 15 * q^62 - 58 * q^63 - 65 * q^64 - 8 * q^65 - 20 * q^66 - 110 * q^67 - 8 * q^68 - 57 * q^69 - 40 * q^70 - 78 * q^71 - 28 * q^72 - 43 * q^73 - 52 * q^74 - 150 * q^75 - 96 * q^76 - 24 * q^77 - 16 * q^78 - 228 * q^79 + 20 * q^80 + 54 * q^81 - 89 * q^82 - 12 * q^83 + 6 * q^84 - 77 * q^85 + 29 * q^86 - 77 * q^87 - 95 * q^88 - 32 * q^89 - 46 * q^90 - 32 * q^91 - 62 * q^92 - 9 * q^93 - 87 * q^94 - 61 * q^95 - 54 * q^96 - 38 * q^97 + 6 * q^98 - 193 * 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 $

$2$	−2.20714	−1.56069	−0.780343	−	0.625352i	$-0.784955\pi$
$2$	−2.20714	−1.56069	−0.780343	+	0.625352i	$0.784955\pi$
$3$	−0.230793	−0.133248	−0.0666242	−	0.997778i	$-0.521223\pi$
$3$	−0.230793	−0.133248	−0.0666242	+	0.997778i	$0.521223\pi$
$4$	2.87148	1.43574
$5$	−0.451913	−0.202102	−0.101051	−	0.994881i	$-0.532220\pi$
$5$	−0.451913	−0.202102	−0.101051	+	0.994881i	$0.532220\pi$
$6$	0.509393	0.207959
$7$	5.18852	1.96108	0.980539	−	0.196326i	$-0.0629010\pi$
$7$	5.18852	1.96108	0.980539	+	0.196326i	$0.0629010\pi$
$8$	−1.92347	−0.680051
$9$	−2.94673	−0.982245
$10$	0.997437	0.315417
$11$	2.89647	0.873319	0.436660	−	0.899627i	$-0.356161\pi$
$11$	2.89647	0.873319	0.436660	+	0.899627i	$0.356161\pi$
$12$	−0.662717	−0.191310
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	−11.4518	−3.06062
$15$	0.104298	0.0269297
$16$	−1.49757	−0.374394
$17$	−6.47981	−1.57158	−0.785792	−	0.618491i	$-0.787745\pi$
$17$	−6.47981	−1.57158	−0.785792	+	0.618491i	$0.787745\pi$
$18$	6.50386	1.53298
$19$	−6.93737	−1.59154	−0.795771	−	0.605598i	$-0.792934\pi$
$19$	−6.93737	−1.59154	−0.795771	+	0.605598i	$0.792934\pi$
$20$	−1.29766	−0.290165
$21$	−1.19747	−0.261310
$22$	−6.39293	−1.36298
$23$	0.917653	0.191344	0.0956720	−	0.995413i	$-0.469500\pi$
$23$	0.917653	0.191344	0.0956720	+	0.995413i	$0.469500\pi$
$24$	0.443924	0.0906156
$25$	−4.79577	−0.959155
$26$	−2.20714	−0.432856
$27$	1.37246	0.264131
$28$	14.8987	2.81559
$29$	9.62541	1.78739	0.893697	−	0.448671i	$-0.148103\pi$
$29$	9.62541	1.78739	0.893697	+	0.448671i	$0.148103\pi$
$30$	−0.230201	−0.0420288
$31$	1.11456	0.200181	0.100091	−	0.994978i	$-0.468087\pi$
$31$	1.11456	0.200181	0.100091	+	0.994978i	$0.468087\pi$
$32$	7.15231	1.26436
$33$	−0.668486	−0.116368
$34$	14.3019	2.45275
$35$	−2.34476	−0.396337
$36$	−8.46148	−1.41025
$37$	2.16270	0.355546	0.177773	−	0.984072i	$-0.443111\pi$
$37$	2.16270	0.355546	0.177773	+	0.984072i	$0.443111\pi$
$38$	15.3118	2.48390
$39$	−0.230793	−0.0369565
$40$	0.869243	0.137439
$41$	−6.86239	−1.07172	−0.535862	−	0.844305i	$-0.680013\pi$
$41$	−6.86239	−1.07172	−0.535862	+	0.844305i	$0.680013\pi$
$42$	2.64300	0.407823
$43$	−8.50616	−1.29718	−0.648589	−	0.761139i	$-0.724640\pi$
$43$	−8.50616	−1.29718	−0.648589	+	0.761139i	$0.724640\pi$
$44$	8.31715	1.25386
$45$	1.33167	0.198513
$46$	−2.02539	−0.298628
$47$	4.07184	0.593939	0.296970	−	0.954887i	$-0.404024\pi$
$47$	4.07184	0.593939	0.296970	+	0.954887i	$0.404024\pi$
$48$	0.345630	0.0498874
$49$	19.9208	2.84583
$50$	10.5850	1.49694
$51$	1.49549	0.209411
$52$	2.87148	0.398202
$53$	9.40538	1.29193	0.645964	−	0.763367i	$-0.276455\pi$
$53$	9.40538	1.29193	0.645964	+	0.763367i	$0.276455\pi$
$54$	−3.02922	−0.412225
$55$	−1.30895	−0.176499
$56$	−9.97999	−1.33363
$57$	1.60110	0.212070
$58$	−21.2446	−2.78956
$59$	2.46817	0.321328	0.160664	−	0.987009i	$-0.448636\pi$
$59$	2.46817	0.321328	0.160664	+	0.987009i	$0.448636\pi$
$60$	0.299490	0.0386640
$61$	9.03616	1.15696	0.578481	−	0.815696i	$-0.303646\pi$
$61$	9.03616	1.15696	0.578481	+	0.815696i	$0.303646\pi$
$62$	−2.46000	−0.312420
$63$	−15.2892	−1.92626
$64$	−12.7910	−1.59888
$65$	−0.451913	−0.0560529
$66$	1.47544	0.181614
$67$	−5.94482	−0.726275	−0.363137	−	0.931736i	$-0.618294\pi$
$67$	−5.94482	−0.726275	−0.363137	+	0.931736i	$0.618294\pi$
$68$	−18.6066	−2.25638
$69$	−0.211788	−0.0254963
$70$	5.17522	0.618557
$71$	−9.15770	−1.08682	−0.543410	−	0.839468i	$-0.682867\pi$
$71$	−9.15770	−1.08682	−0.543410	+	0.839468i	$0.682867\pi$
$72$	5.66797	0.667976
$73$	−5.61288	−0.656937	−0.328469	−	0.944515i	$-0.606533\pi$
$73$	−5.61288	−0.656937	−0.328469	+	0.944515i	$0.606533\pi$
$74$	−4.77338	−0.554895
$75$	1.10683	0.127806
$76$	−19.9205	−2.28504
$77$	15.0284	1.71265
$78$	0.509393	0.0576774
$79$	−5.60015	−0.630067	−0.315033	−	0.949081i	$-0.602016\pi$
$79$	−5.60015	−0.630067	−0.315033	+	0.949081i	$0.602016\pi$
$80$	0.676774	0.0756656
$81$	8.52345	0.947050
$82$	15.1463	1.67263
$83$	9.21822	1.01183	0.505915	−	0.862583i	$-0.331155\pi$
$83$	9.21822	1.01183	0.505915	+	0.862583i	$0.331155\pi$
$84$	−3.43852	−0.375173
$85$	2.92831	0.317620
$86$	18.7743	2.02449
$87$	−2.22148	−0.238167
$88$	−5.57129	−0.593901
$89$	−5.97374	−0.633215	−0.316608	−	0.948557i	$-0.602544\pi$
$89$	−5.97374	−0.633215	−0.316608	+	0.948557i	$0.602544\pi$
$90$	−2.93918	−0.309817
$91$	5.18852	0.543905
$92$	2.63502	0.274720
$93$	−0.257233	−0.0266739
$94$	−8.98713	−0.926952
$95$	3.13509	0.321653
$96$	−1.65070	−0.168474
$97$	−6.15598	−0.625045	−0.312523	−	0.949910i	$-0.601174\pi$
$97$	−6.15598	−0.625045	−0.312523	+	0.949910i	$0.601174\pi$
$98$	−43.9680	−4.44144
$99$	−8.53514	−0.857813
$100$	−13.7710	−1.37710
$101$	−11.4666	−1.14097	−0.570486	−	0.821307i	$-0.693245\pi$
$101$	−11.4666	−1.14097	−0.570486	+	0.821307i	$0.693245\pi$
$102$	−3.30077	−0.326825
$103$	−0.123323	−0.0121513	−0.00607566	−	0.999982i	$-0.501934\pi$
$103$	−0.123323	−0.0121513	−0.00607566	+	0.999982i	$0.501934\pi$
$104$	−1.92347	−0.188612
$105$	0.541155	0.0528113
$106$	−20.7590	−2.01629
$107$	7.59741	0.734469	0.367235	−	0.930128i	$-0.380305\pi$
$107$	7.59741	0.734469	0.367235	+	0.930128i	$0.380305\pi$
$108$	3.94100	0.379223
$109$	−14.5547	−1.39409	−0.697043	−	0.717029i	$-0.745501\pi$
$109$	−14.5547	−1.39409	−0.697043	+	0.717029i	$0.745501\pi$
$110$	2.88905	0.275460
$111$	−0.499136	−0.0473759
$112$	−7.77020	−0.734215
$113$	−7.23308	−0.680431	−0.340216	−	0.940347i	$-0.610500\pi$
$113$	−7.23308	−0.680431	−0.340216	+	0.940347i	$0.610500\pi$
$114$	−3.53385	−0.330975
$115$	−0.414700	−0.0386709
$116$	27.6391	2.56623
$117$	−2.94673	−0.272426
$118$	−5.44760	−0.501493
$119$	−33.6206	−3.08200
$120$	−0.200615	−0.0183136
$121$	−2.61045	−0.237313
$122$	−19.9441	−1.80565
$123$	1.58379	0.142806
$124$	3.20044	0.287408
$125$	4.42684	0.395949
$126$	33.7454	3.00628
$127$	−18.1924	−1.61432	−0.807158	−	0.590336i	$-0.798995\pi$
$127$	−18.1924	−1.61432	−0.807158	+	0.590336i	$0.798995\pi$
$128$	13.9270	1.23098
$129$	1.96316	0.172847
$130$	0.997437	0.0874810
$131$	−10.3108	−0.900855	−0.450428	−	0.892813i	$-0.648728\pi$
$131$	−10.3108	−0.900855	−0.450428	+	0.892813i	$0.648728\pi$
$132$	−1.91954	−0.167075
$133$	−35.9947	−3.12114
$134$	13.1211	1.13349
$135$	−0.620235	−0.0533813
$136$	12.4637	1.06876
$137$	−22.0323	−1.88235	−0.941173	−	0.337925i	$-0.890275\pi$
$137$	−22.0323	−1.88235	−0.941173	+	0.337925i	$0.890275\pi$
$138$	0.467446	0.0397917
$139$	21.1692	1.79555	0.897775	−	0.440454i	$-0.145183\pi$
$139$	21.1692	1.79555	0.897775	+	0.440454i	$0.145183\pi$
$140$	−6.73293	−0.569036
$141$	−0.939752	−0.0791414
$142$	20.2123	1.69618
$143$	2.89647	0.242215
$144$	4.41295	0.367746
$145$	−4.34985	−0.361235
$146$	12.3884	1.02527
$147$	−4.59758	−0.379202
$148$	6.21014	0.510470
$149$	14.0316	1.14952	0.574759	−	0.818323i	$-0.305096\pi$
$149$	14.0316	1.14952	0.574759	+	0.818323i	$0.305096\pi$
$150$	−2.44293	−0.199465
$151$	8.86436	0.721371	0.360686	−	0.932687i	$-0.382543\pi$
$151$	8.86436	0.721371	0.360686	+	0.932687i	$0.382543\pi$
$152$	13.3438	1.08233
$153$	19.0943	1.54368
$154$	−33.1699	−2.67290
$155$	−0.503686	−0.0404570
$156$	−0.662717	−0.0530598
$157$	−13.8308	−1.10382	−0.551910	−	0.833904i	$-0.686101\pi$
$157$	−13.8308	−1.10382	−0.551910	+	0.833904i	$0.686101\pi$
$158$	12.3603	0.983336
$159$	−2.17070	−0.172147
$160$	−3.23222	−0.255530
$161$	4.76127	0.375240
$162$	−18.8125	−1.47805
$163$	0.182995	0.0143333	0.00716666	−	0.999974i	$-0.497719\pi$
$163$	0.182995	0.0143333	0.00716666	+	0.999974i	$0.497719\pi$
$164$	−19.7052	−1.53872
$165$	0.302097	0.0235183
$166$	−20.3459	−1.57915
$167$	20.8957	1.61696	0.808480	−	0.588524i	$-0.200291\pi$
$167$	20.8957	1.61696	0.808480	+	0.588524i	$0.200291\pi$
$168$	2.30331	0.177704
$169$	1.00000	0.0769231
$170$	−6.46320	−0.495705
$171$	20.4426	1.56328
$172$	−24.4252	−1.86241
$173$	21.3231	1.62116	0.810582	−	0.585625i	$-0.199151\pi$
$173$	21.3231	1.62116	0.810582	+	0.585625i	$0.199151\pi$
$174$	4.90312	0.371704
$175$	−24.8830	−1.88098
$176$	−4.33768	−0.326965
$177$	−0.569636	−0.0428165
$178$	13.1849	0.988250
$179$	−15.7724	−1.17888	−0.589441	−	0.807812i	$-0.700652\pi$
$179$	−15.7724	−1.17888	−0.589441	+	0.807812i	$0.700652\pi$
$180$	3.82385	0.285013
$181$	8.77353	0.652131	0.326066	−	0.945347i	$-0.394277\pi$
$181$	8.77353	0.652131	0.326066	+	0.945347i	$0.394277\pi$
$182$	−11.4518	−0.848865
$183$	−2.08548	−0.154163
$184$	−1.76508	−0.130124
$185$	−0.977352	−0.0718564
$186$	0.567751	0.0416295
$187$	−18.7686	−1.37250
$188$	11.6922	0.852741
$189$	7.12107	0.517981
$190$	−6.91959	−0.502000
$191$	14.6526	1.06023	0.530113	−	0.847927i	$-0.322149\pi$
$191$	14.6526	1.06023	0.530113	+	0.847927i	$0.322149\pi$
$192$	2.95208	0.213048
$193$	−23.2228	−1.67162	−0.835808	−	0.549022i	$-0.815000\pi$
$193$	−23.2228	−1.67162	−0.835808	+	0.549022i	$0.815000\pi$
$194$	13.5871	0.975499
$195$	0.104298	0.00746896
$196$	57.2020	4.08586
$197$	25.3728	1.80774	0.903870	−	0.427807i	$-0.140714\pi$
$197$	25.3728	1.80774	0.903870	+	0.427807i	$0.140714\pi$
$198$	18.8383	1.33878
$199$	−2.46775	−0.174934	−0.0874670	−	0.996167i	$-0.527877\pi$
$199$	−2.46775	−0.174934	−0.0874670	+	0.996167i	$0.527877\pi$
$200$	9.22454	0.652274
$201$	1.37202	0.0967750
$202$	25.3085	1.78070
$203$	49.9417	3.50522
$204$	4.29428	0.300660
$205$	3.10120	0.216597
$206$	0.272190	0.0189644
$207$	−2.70408	−0.187947
$208$	−1.49757	−0.103838
$209$	−20.0939	−1.38992
$210$	−1.19441	−0.0824218
$211$	13.7867	0.949114	0.474557	−	0.880225i	$-0.342608\pi$
$211$	13.7867	0.949114	0.474557	+	0.880225i	$0.342608\pi$
$212$	27.0073	1.85487
$213$	2.11353	0.144817
$214$	−16.7686	−1.14628
$215$	3.84405	0.262162
$216$	−2.63990	−0.179622
$217$	5.78294	0.392571
$218$	32.1243	2.17573
$219$	1.29541	0.0875359
$220$	−3.75863	−0.253407
$221$	−6.47981	−0.435879
$222$	1.10166	0.0739388
$223$	5.21306	0.349092	0.174546	−	0.984649i	$-0.444154\pi$
$223$	5.21306	0.349092	0.174546	+	0.984649i	$0.444154\pi$
$224$	37.1099	2.47951
$225$	14.1319	0.942125
$226$	15.9644	1.06194
$227$	−23.8489	−1.58291	−0.791455	−	0.611228i	$-0.790676\pi$
$227$	−23.8489	−1.58291	−0.791455	+	0.611228i	$0.790676\pi$
$228$	4.59751	0.304478
$229$	−9.31905	−0.615820	−0.307910	−	0.951415i	$-0.599630\pi$
$229$	−9.31905	−0.615820	−0.307910	+	0.951415i	$0.599630\pi$
$230$	0.915301	0.0603532
$231$	−3.46845	−0.228207
$232$	−18.5142	−1.21552
$233$	−14.2564	−0.933971	−0.466985	−	0.884265i	$-0.654660\pi$
$233$	−14.2564	−0.933971	−0.466985	+	0.884265i	$0.654660\pi$
$234$	6.50386	0.425171
$235$	−1.84012	−0.120036
$236$	7.08729	0.461344
$237$	1.29248	0.0839554
$238$	74.2055	4.81003
$239$	−4.39129	−0.284049	−0.142025	−	0.989863i	$-0.545361\pi$
$239$	−4.39129	−0.284049	−0.142025	+	0.989863i	$0.545361\pi$
$240$	−0.156195	−0.0100823
$241$	−16.4675	−1.06076	−0.530382	−	0.847759i	$-0.677952\pi$
$241$	−16.4675	−1.06076	−0.530382	+	0.847759i	$0.677952\pi$
$242$	5.76163	0.370371
$243$	−6.08455	−0.390324
$244$	25.9471	1.66109
$245$	−9.00246	−0.575146
$246$	−3.49565	−0.222875
$247$	−6.93737	−0.441414
$248$	−2.14383	−0.136133
$249$	−2.12750	−0.134825
$250$	−9.77066	−0.617951
$251$	−23.8218	−1.50362	−0.751811	−	0.659379i	$-0.770819\pi$
$251$	−23.8218	−1.50362	−0.751811	+	0.659379i	$0.770819\pi$
$252$	−43.9026	−2.76560
$253$	2.65796	0.167104
$254$	40.1532	2.51944
$255$	−0.675834	−0.0423223
$256$	−5.15677	−0.322298
$257$	6.71002	0.418559	0.209280	−	0.977856i	$-0.432888\pi$
$257$	6.71002	0.418559	0.209280	+	0.977856i	$0.432888\pi$
$258$	−4.33298	−0.269760
$259$	11.2212	0.697252
$260$	−1.29766	−0.0804773
$261$	−28.3635	−1.75566
$262$	22.7573	1.40595
$263$	−17.3872	−1.07214	−0.536069	−	0.844174i	$-0.680091\pi$
$263$	−17.3872	−1.07214	−0.536069	+	0.844174i	$0.680091\pi$
$264$	1.28581	0.0791364
$265$	−4.25042	−0.261101
$266$	79.4454	4.87111
$267$	1.37870	0.0843749
$268$	−17.0704	−1.04274
$269$	31.7981	1.93876	0.969382	−	0.245558i	$-0.0789712\pi$
$269$	31.7981	1.93876	0.969382	+	0.245558i	$0.0789712\pi$
$270$	1.36895	0.0833114
$271$	−8.95422	−0.543930	−0.271965	−	0.962307i	$-0.587674\pi$
$271$	−8.95422	−0.543930	−0.271965	+	0.962307i	$0.587674\pi$
$272$	9.70400	0.588391
$273$	−1.19747	−0.0724745
$274$	48.6284	2.93775
$275$	−13.8908	−0.837649
$276$	−0.608144	−0.0366060
$277$	−0.866674	−0.0520734	−0.0260367	−	0.999661i	$-0.508289\pi$
$277$	−0.866674	−0.0520734	−0.0260367	+	0.999661i	$0.508289\pi$
$278$	−46.7235	−2.80229
$279$	−3.28432	−0.196627
$280$	4.51009	0.269529
$281$	−0.757503	−0.0451888	−0.0225944	−	0.999745i	$-0.507193\pi$
$281$	−0.757503	−0.0451888	−0.0225944	+	0.999745i	$0.507193\pi$
$282$	2.07417	0.123515
$283$	−24.3210	−1.44573	−0.722867	−	0.690987i	$-0.757176\pi$
$283$	−24.3210	−1.44573	−0.722867	+	0.690987i	$0.757176\pi$
$284$	−26.2961	−1.56039
$285$	−0.723557	−0.0428598
$286$	−6.39293	−0.378022
$287$	−35.6057	−2.10174
$288$	−21.0759	−1.24191
$289$	24.9879	1.46988
$290$	9.60073	0.563775
$291$	1.42076	0.0832863
$292$	−16.1172	−0.943190
$293$	−14.5387	−0.849359	−0.424680	−	0.905344i	$-0.639613\pi$
$293$	−14.5387	−0.849359	−0.424680	+	0.905344i	$0.639613\pi$
$294$	10.1475	0.591814
$295$	−1.11540	−0.0649410
$296$	−4.15989	−0.241789
$297$	3.97531	0.230671
$298$	−30.9698	−1.79403
$299$	0.917653	0.0530693
$300$	3.17824	0.183496
$301$	−44.1344	−2.54387
$302$	−19.5649	−1.12583
$303$	2.64642	0.152033
$304$	10.3892	0.595863
$305$	−4.08356	−0.233824
$306$	−42.1438	−2.40920
$307$	−7.06633	−0.403297	−0.201648	−	0.979458i	$-0.564630\pi$
$307$	−7.06633	−0.403297	−0.201648	+	0.979458i	$0.564630\pi$
$308$	43.1537	2.45891
$309$	0.0284620	0.00161914
$310$	1.11171	0.0631407
$311$	−20.7299	−1.17549	−0.587744	−	0.809047i	$-0.699984\pi$
$311$	−20.7299	−1.17549	−0.587744	+	0.809047i	$0.699984\pi$
$312$	0.443924	0.0251323
$313$	−22.6817	−1.28205	−0.641023	−	0.767522i	$-0.721490\pi$
$313$	−22.6817	−1.28205	−0.641023	+	0.767522i	$0.721490\pi$
$314$	30.5266	1.72272
$315$	6.90939	0.389300
$316$	−16.0807	−0.904611
$317$	−28.8368	−1.61964	−0.809819	−	0.586680i	$-0.800435\pi$
$317$	−28.8368	−1.61964	−0.809819	+	0.586680i	$0.800435\pi$
$318$	4.79104	0.268668
$319$	27.8797	1.56097
$320$	5.78043	0.323136
$321$	−1.75343	−0.0978668
$322$	−10.5088	−0.585632
$323$	44.9528	2.50124
$324$	24.4749	1.35972
$325$	−4.79577	−0.266022
$326$	−0.403897	−0.0223698
$327$	3.35912	0.185760
$328$	13.1996	0.728827
$329$	21.1268	1.16476
$330$	−0.666772	−0.0367046
$331$	−0.847509	−0.0465833	−0.0232916	−	0.999729i	$-0.507415\pi$
$331$	−0.847509	−0.0465833	−0.0232916	+	0.999729i	$0.507415\pi$
$332$	26.4699	1.45272
$333$	−6.37290	−0.349233
$334$	−46.1198	−2.52357
$335$	2.68654	0.146781
$336$	1.79331	0.0978330
$337$	9.44715	0.514619	0.257310	−	0.966329i	$-0.417164\pi$
$337$	9.44715	0.514619	0.257310	+	0.966329i	$0.417164\pi$
$338$	−2.20714	−0.120053
$339$	1.66935	0.0906664
$340$	8.40858	0.456019
$341$	3.22830	0.174822
$342$	−45.1197	−2.43979
$343$	67.0397	3.61981
$344$	16.3614	0.882146
$345$	0.0957098	0.00515284
$346$	−47.0631	−2.53013
$347$	6.58388	0.353441	0.176720	−	0.984261i	$-0.443451\pi$
$347$	6.58388	0.353441	0.176720	+	0.984261i	$0.443451\pi$
$348$	−6.37892	−0.341946
$349$	11.0286	0.590349	0.295175	−	0.955443i	$-0.404622\pi$
$349$	11.0286	0.590349	0.295175	+	0.955443i	$0.404622\pi$
$350$	54.9203	2.93561
$351$	1.37246	0.0732567
$352$	20.7165	1.10419
$353$	−9.01941	−0.480055	−0.240027	−	0.970766i	$-0.577156\pi$
$353$	−9.01941	−0.480055	−0.240027	+	0.970766i	$0.577156\pi$
$354$	1.25727	0.0668231
$355$	4.13849	0.219648
$356$	−17.1535	−0.909131
$357$	7.75941	0.410671
$358$	34.8118	1.83986
$359$	15.1776	0.801044	0.400522	−	0.916287i	$-0.368829\pi$
$359$	15.1776	0.801044	0.400522	+	0.916287i	$0.368829\pi$
$360$	−2.56143	−0.134999
$361$	29.1271	1.53301
$362$	−19.3644	−1.01777
$363$	0.602473	0.0316216
$364$	14.8987	0.780905
$365$	2.53653	0.132768
$366$	4.60296	0.240600
$367$	−13.2199	−0.690074	−0.345037	−	0.938589i	$-0.612134\pi$
$367$	−13.2199	−0.690074	−0.345037	+	0.938589i	$0.612134\pi$
$368$	−1.37425	−0.0716379
$369$	20.2216	1.05270
$370$	2.15716	0.112145
$371$	48.8001	2.53357
$372$	−0.738640	−0.0382967
$373$	−22.4884	−1.16441	−0.582203	−	0.813043i	$-0.697809\pi$
$373$	−22.4884	−1.16441	−0.582203	+	0.813043i	$0.697809\pi$
$374$	41.4249	2.14203
$375$	−1.02168	−0.0527595
$376$	−7.83208	−0.403909
$377$	9.62541	0.495734
$378$	−15.7172	−0.808406
$379$	−21.7511	−1.11728	−0.558640	−	0.829411i	$-0.688676\pi$
$379$	−21.7511	−1.11728	−0.558640	+	0.829411i	$0.688676\pi$
$380$	9.00234	0.461810
$381$	4.19868	0.215105
$382$	−32.3404	−1.65468
$383$	16.6148	0.848977	0.424489	−	0.905433i	$-0.360454\pi$
$383$	16.6148	0.848977	0.424489	+	0.905433i	$0.360454\pi$
$384$	−3.21425	−0.164026
$385$	−6.79154	−0.346129
$386$	51.2561	2.60887
$387$	25.0654	1.27415
$388$	−17.6768	−0.897401
$389$	21.9478	1.11280	0.556399	−	0.830915i	$-0.312183\pi$
$389$	21.9478	1.11280	0.556399	+	0.830915i	$0.312183\pi$
$390$	−0.230201	−0.0116567
$391$	−5.94622	−0.300713
$392$	−38.3171	−1.93530
$393$	2.37965	0.120037
$394$	−56.0015	−2.82131
$395$	2.53078	0.127338
$396$	−24.5084	−1.23160
$397$	−22.1924	−1.11380	−0.556902	−	0.830578i	$-0.688010\pi$
$397$	−22.1924	−1.11380	−0.556902	+	0.830578i	$0.688010\pi$
$398$	5.44667	0.273017
$399$	8.30733	0.415887
$400$	7.18203	0.359101
$401$	−8.91085	−0.444987	−0.222493	−	0.974934i	$-0.571420\pi$
$401$	−8.91085	−0.444987	−0.222493	+	0.974934i	$0.571420\pi$
$402$	−3.02825	−0.151035
$403$	1.11456	0.0555203
$404$	−32.9262	−1.63814
$405$	−3.85186	−0.191400
$406$	−110.228	−5.47054
$407$	6.26420	0.310505
$408$	−2.87654	−0.142410
$409$	−22.3996	−1.10759	−0.553795	−	0.832653i	$-0.686821\pi$
$409$	−22.3996	−1.10759	−0.553795	+	0.832653i	$0.686821\pi$
$410$	−6.84480	−0.338040
$411$	5.08490	0.250820
$412$	−0.354118	−0.0174461
$413$	12.8062	0.630150
$414$	5.96829	0.293325
$415$	−4.16583	−0.204493
$416$	7.15231	0.350671
$417$	−4.88571	−0.239254
$418$	44.3501	2.16923
$419$	29.4001	1.43629	0.718143	−	0.695895i	$-0.244992\pi$
$419$	29.4001	1.43629	0.718143	+	0.695895i	$0.244992\pi$
$420$	1.55391	0.0758232
$421$	−3.05866	−0.149070	−0.0745350	−	0.997218i	$-0.523747\pi$
$421$	−3.05866	−0.149070	−0.0745350	+	0.997218i	$0.523747\pi$
$422$	−30.4292	−1.48127
$423$	−11.9986	−0.583394
$424$	−18.0910	−0.878577
$425$	31.0757	1.50739
$426$	−4.66487	−0.226014
$427$	46.8843	2.26889
$428$	21.8158	1.05451
$429$	−0.668486	−0.0322748
$430$	−8.48436	−0.409152
$431$	−18.3840	−0.885528	−0.442764	−	0.896638i	$-0.646002\pi$
$431$	−18.3840	−0.885528	−0.442764	+	0.896638i	$0.646002\pi$
$432$	−2.05537	−0.0988889
$433$	−29.3297	−1.40950	−0.704748	−	0.709458i	$-0.748940\pi$
$433$	−29.3297	−1.40950	−0.704748	+	0.709458i	$0.748940\pi$
$434$	−12.7638	−0.612680
$435$	1.00391	0.0481340
$436$	−41.7934	−2.00154
$437$	−6.36610	−0.304532
$438$	−2.85916	−0.136616
$439$	−8.44414	−0.403017	−0.201508	−	0.979487i	$-0.564584\pi$
$439$	−8.44414	−0.403017	−0.201508	+	0.979487i	$0.564584\pi$
$440$	2.51774	0.120028
$441$	−58.7012	−2.79530
$442$	14.3019	0.680270
$443$	−16.3396	−0.776316	−0.388158	−	0.921593i	$-0.626888\pi$
$443$	−16.3396	−0.776316	−0.388158	+	0.921593i	$0.626888\pi$
$444$	−1.43326	−0.0680194
$445$	2.69961	0.127974
$446$	−11.5060	−0.544823
$447$	−3.23841	−0.153171
$448$	−66.3664	−3.13552
$449$	−27.1713	−1.28229	−0.641147	−	0.767418i	$-0.721541\pi$
$449$	−27.1713	−1.28229	−0.641147	+	0.767418i	$0.721541\pi$
$450$	−31.1911	−1.47036
$451$	−19.8767	−0.935958
$452$	−20.7696	−0.976921
$453$	−2.04583	−0.0961216
$454$	52.6380	2.47042
$455$	−2.34476	−0.109924
$456$	−3.07967	−0.144219
$457$	−8.60104	−0.402339	−0.201170	−	0.979556i	$-0.564474\pi$
$457$	−8.60104	−0.402339	−0.201170	+	0.979556i	$0.564474\pi$
$458$	20.5685	0.961102
$459$	−8.89331	−0.415104
$460$	−1.19080	−0.0555213
$461$	−15.7227	−0.732280	−0.366140	−	0.930560i	$-0.619321\pi$
$461$	−15.7227	−0.732280	−0.366140	+	0.930560i	$0.619321\pi$
$462$	7.65537	0.356160
$463$	29.0659	1.35081	0.675403	−	0.737449i	$-0.263970\pi$
$463$	29.0659	1.35081	0.675403	+	0.737449i	$0.263970\pi$
$464$	−14.4148	−0.669189
$465$	0.116247	0.00539083
$466$	31.4660	1.45763
$467$	33.0720	1.53039	0.765194	−	0.643800i	$-0.222643\pi$
$467$	33.0720	1.53039	0.765194	+	0.643800i	$0.222643\pi$
$468$	−8.46148	−0.391132
$469$	−30.8448	−1.42428
$470$	4.06140	0.187339
$471$	3.19206	0.147082
$472$	−4.74746	−0.218520
$473$	−24.6379	−1.13285
$474$	−2.85268	−0.131028
$475$	33.2701	1.52654
$476$	−96.5409	−4.42494
$477$	−27.7152	−1.26899
$478$	9.69221	0.443311
$479$	31.9150	1.45823	0.729116	−	0.684391i	$-0.239932\pi$
$479$	31.9150	1.45823	0.729116	+	0.684391i	$0.239932\pi$
$480$	0.745974	0.0340489
$481$	2.16270	0.0986106
$482$	36.3461	1.65552
$483$	−1.09887	−0.0500002
$484$	−7.49584	−0.340720
$485$	2.78197	0.126323
$486$	13.4295	0.609173
$487$	29.8057	1.35063	0.675314	−	0.737531i	$-0.264008\pi$
$487$	29.8057	1.35063	0.675314	+	0.737531i	$0.264008\pi$
$488$	−17.3808	−0.786792
$489$	−0.0422341	−0.00190989
$490$	19.8697	0.897622
$491$	38.3926	1.73263	0.866317	−	0.499495i	$-0.166481\pi$
$491$	38.3926	1.73263	0.866317	+	0.499495i	$0.166481\pi$
$492$	4.54782	0.205032
$493$	−62.3708	−2.80904
$494$	15.3118	0.688909
$495$	3.85714	0.173366
$496$	−1.66914	−0.0749466
$497$	−47.5149	−2.13134
$498$	4.69569	0.210419
$499$	−33.2783	−1.48974	−0.744871	−	0.667209i	$-0.767489\pi$
$499$	−33.2783	−1.48974	−0.744871	+	0.667209i	$0.767489\pi$
$500$	12.7116	0.568479
$501$	−4.82259	−0.215457
$502$	52.5782	2.34668
$503$	−0.221166	−0.00986131	−0.00493066	−	0.999988i	$-0.501569\pi$
$503$	−0.221166	−0.00986131	−0.00493066	+	0.999988i	$0.501569\pi$
$504$	29.4084	1.30995
$505$	5.18192	0.230593
$506$	−5.86649	−0.260797
$507$	−0.230793	−0.0102499
$508$	−52.2391	−2.31774
$509$	24.7361	1.09641	0.548205	−	0.836344i	$-0.315311\pi$
$509$	24.7361	1.09641	0.548205	+	0.836344i	$0.315311\pi$
$510$	1.49166	0.0660519
$511$	−29.1225	−1.28831
$512$	−16.4722	−0.727975
$513$	−9.52130	−0.420376
$514$	−14.8100	−0.653239
$515$	0.0557311	0.00245580
$516$	5.63718	0.248163
$517$	11.7940	0.518698
$518$	−24.7668	−1.08819
$519$	−4.92122	−0.216017
$520$	0.869243	0.0381188
$521$	−8.52549	−0.373508	−0.186754	−	0.982407i	$-0.559797\pi$
$521$	−8.52549	−0.373508	−0.186754	+	0.982407i	$0.559797\pi$
$522$	62.6023	2.74003
$523$	−14.4011	−0.629714	−0.314857	−	0.949139i	$-0.601957\pi$
$523$	−14.4011	−0.629714	−0.314857	+	0.949139i	$0.601957\pi$
$524$	−29.6071	−1.29339
$525$	5.74282	0.250637
$526$	38.3760	1.67327
$527$	−7.22216	−0.314602
$528$	1.00111	0.0435676
$529$	−22.1579	−0.963388
$530$	9.38127	0.407497
$531$	−7.27304	−0.315623
$532$	−103.358	−4.48114
$533$	−6.86239	−0.297243
$534$	−3.04298	−0.131683
$535$	−3.43337	−0.148437
$536$	11.4347	0.493904
$537$	3.64015	0.157084
$538$	−70.1829	−3.02580
$539$	57.7000	2.48531
$540$	−1.78099	−0.0766416
$541$	12.9539	0.556931	0.278466	−	0.960446i	$-0.410174\pi$
$541$	12.9539	0.556931	0.278466	+	0.960446i	$0.410174\pi$
$542$	19.7632	0.848904
$543$	−2.02487	−0.0868954
$544$	−46.3456	−1.98705
$545$	6.57745	0.281747
$546$	2.64300	0.113110
$547$	−9.18558	−0.392747	−0.196374	−	0.980529i	$-0.562917\pi$
$547$	−9.18558	−0.392747	−0.196374	+	0.980529i	$0.562917\pi$
$548$	−63.2652	−2.70256
$549$	−26.6272	−1.13642
$550$	30.6590	1.30731
$551$	−66.7750	−2.84471
$552$	0.407368	0.0173388
$553$	−29.0565	−1.23561
$554$	1.91287	0.0812701
$555$	0.225566	0.00957474
$556$	60.7869	2.57794
$557$	27.3137	1.15732	0.578659	−	0.815569i	$-0.303576\pi$
$557$	27.3137	1.15732	0.578659	+	0.815569i	$0.303576\pi$
$558$	7.24896	0.306873
$559$	−8.50616	−0.359772
$560$	3.51146	0.148386
$561$	4.33166	0.182883
$562$	1.67192	0.0705255
$563$	32.4641	1.36820	0.684100	−	0.729388i	$-0.260195\pi$
$563$	32.4641	1.36820	0.684100	+	0.729388i	$0.260195\pi$
$564$	−2.69848	−0.113626
$565$	3.26873	0.137516
$566$	53.6799	2.25634
$567$	44.2241	1.85724
$568$	17.6146	0.739092
$569$	−1.55276	−0.0650950	−0.0325475	−	0.999470i	$-0.510362\pi$
$569$	−1.55276	−0.0650950	−0.0325475	+	0.999470i	$0.510362\pi$
$570$	1.59699	0.0668907
$571$	−20.4524	−0.855906	−0.427953	−	0.903801i	$-0.640765\pi$
$571$	−20.4524	−0.855906	−0.427953	+	0.903801i	$0.640765\pi$
$572$	8.31715	0.347758
$573$	−3.38172	−0.141273
$574$	78.5868	3.28015
$575$	−4.40086	−0.183528
$576$	37.6917	1.57049
$577$	22.5207	0.937550	0.468775	−	0.883318i	$-0.344695\pi$
$577$	22.5207	0.937550	0.468775	+	0.883318i	$0.344695\pi$
$578$	−55.1519	−2.29402
$579$	5.35966	0.222740
$580$	−12.4905	−0.518639
$581$	47.8289	1.98428
$582$	−3.13581	−0.129984
$583$	27.2424	1.12827
$584$	10.7962	0.446751
$585$	1.33167	0.0550577
$586$	32.0890	1.32558
$587$	20.1048	0.829814	0.414907	−	0.909864i	$-0.363814\pi$
$587$	20.1048	0.829814	0.414907	+	0.909864i	$0.363814\pi$
$588$	−13.2018	−0.544434
$589$	−7.73214	−0.318597
$590$	2.46184	0.101352
$591$	−5.85587	−0.240878
$592$	−3.23880	−0.133114
$593$	−15.1131	−0.620620	−0.310310	−	0.950635i	$-0.600433\pi$
$593$	−15.1131	−0.620620	−0.310310	+	0.950635i	$0.600433\pi$
$594$	−8.77407	−0.360004
$595$	15.1936	0.622877
$596$	40.2916	1.65041
$597$	0.569539	0.0233097
$598$	−2.02539	−0.0828244
$599$	−41.5753	−1.69872	−0.849360	−	0.527814i	$-0.823012\pi$
$599$	−41.5753	−1.69872	−0.849360	+	0.527814i	$0.823012\pi$
$600$	−2.12896	−0.0869144
$601$	−12.7449	−0.519874	−0.259937	−	0.965626i	$-0.583702\pi$
$601$	−12.7449	−0.519874	−0.259937	+	0.965626i	$0.583702\pi$
$602$	97.4109	3.97017
$603$	17.5178	0.713380
$604$	25.4538	1.03570
$605$	1.17969	0.0479614
$606$	−5.84102	−0.237275
$607$	−44.9819	−1.82576	−0.912880	−	0.408228i	$-0.866147\pi$
$607$	−44.9819	−1.82576	−0.912880	+	0.408228i	$0.866147\pi$
$608$	−49.6182	−2.01228
$609$	−11.5262	−0.467065
$610$	9.01300	0.364926
$611$	4.07184	0.164729
$612$	54.8288	2.21632
$613$	−0.374742	−0.0151357	−0.00756785	−	0.999971i	$-0.502409\pi$
$613$	−0.374742	−0.0151357	−0.00756785	+	0.999971i	$0.502409\pi$
$614$	15.5964	0.629419
$615$	−0.715736	−0.0288613
$616$	−28.9068	−1.16469
$617$	1.00000	0.0402585
$617$	1.00000	0.0402585
$618$	−0.0628196	−0.00252698
$619$	44.3902	1.78419	0.892096	−	0.451847i	$-0.149235\pi$
$619$	44.3902	1.78419	0.892096	+	0.451847i	$0.149235\pi$
$620$	−1.44632	−0.0580857
$621$	1.25945	0.0505399
$622$	45.7539	1.83457
$623$	−30.9949	−1.24178
$624$	0.345630	0.0138363
$625$	21.9783	0.879133
$626$	50.0618	2.00087
$627$	4.63753	0.185205
$628$	−39.7149	−1.58480
$629$	−14.0139	−0.558770
$630$	−15.2500	−0.607575
$631$	5.33695	0.212461	0.106230	−	0.994342i	$-0.466122\pi$
$631$	5.33695	0.212461	0.106230	+	0.994342i	$0.466122\pi$
$632$	10.7717	0.428477
$633$	−3.18187	−0.126468
$634$	63.6470	2.52774
$635$	8.22139	0.326256
$636$	−6.23311	−0.247159
$637$	19.9208	0.789290
$638$	−61.5345	−2.43618
$639$	26.9853	1.06752
$640$	−6.29378	−0.248783
$641$	−3.28074	−0.129582	−0.0647908	−	0.997899i	$-0.520638\pi$
$641$	−3.28074	−0.129582	−0.0647908	+	0.997899i	$0.520638\pi$
$642$	3.87007	0.152739
$643$	25.8702	1.02022	0.510110	−	0.860109i	$-0.329605\pi$
$643$	25.8702	1.02022	0.510110	+	0.860109i	$0.329605\pi$
$644$	13.6719	0.538747
$645$	−0.887179	−0.0349326
$646$	−99.2173	−3.90365
$647$	16.5720	0.651512	0.325756	−	0.945454i	$-0.394381\pi$
$647$	16.5720	0.651512	0.325756	+	0.945454i	$0.394381\pi$
$648$	−16.3946	−0.644042
$649$	7.14899	0.280622
$650$	10.5850	0.415176
$651$	−1.33466	−0.0523095
$652$	0.525467	0.0205789
$653$	−32.8220	−1.28443	−0.642213	−	0.766526i	$-0.721983\pi$
$653$	−32.8220	−1.28443	−0.642213	+	0.766526i	$0.721983\pi$
$654$	−7.41405	−0.289912
$655$	4.65957	0.182064
$656$	10.2769	0.401247
$657$	16.5397	0.645273
$658$	−46.6299	−1.81782
$659$	−15.3609	−0.598375	−0.299187	−	0.954194i	$-0.596716\pi$
$659$	−15.3609	−0.598375	−0.299187	+	0.954194i	$0.596716\pi$
$660$	0.867466	0.0337661
$661$	33.2527	1.29338	0.646690	−	0.762753i	$-0.276153\pi$
$661$	33.2527	1.29338	0.646690	+	0.762753i	$0.276153\pi$
$662$	1.87057	0.0727019
$663$	1.49549	0.0580802
$664$	−17.7310	−0.688096
$665$	16.2665	0.630787
$666$	14.0659	0.545042
$667$	8.83279	0.342007
$668$	60.0016	2.32153
$669$	−1.20314	−0.0465160
$670$	−5.92958	−0.229080
$671$	26.1730	1.01040
$672$	−8.56471	−0.330391
$673$	38.5568	1.48626	0.743128	−	0.669149i	$-0.233341\pi$
$673$	38.5568	1.48626	0.743128	+	0.669149i	$0.233341\pi$
$674$	−20.8512	−0.803159
$675$	−6.58203	−0.253343
$676$	2.87148	0.110441
$677$	−35.1867	−1.35234	−0.676168	−	0.736747i	$-0.736361\pi$
$677$	−35.1867	−1.35234	−0.676168	+	0.736747i	$0.736361\pi$
$678$	−3.68448	−0.141502
$679$	−31.9405	−1.22576
$680$	−5.63253	−0.215998
$681$	5.50417	0.210920
$682$	−7.12532	−0.272843
$683$	12.1155	0.463587	0.231794	−	0.972765i	$-0.425541\pi$
$683$	12.1155	0.463587	0.231794	+	0.972765i	$0.425541\pi$
$684$	58.7004	2.24447
$685$	9.95669	0.380425
$686$	−147.966	−5.64938
$687$	2.15077	0.0820571
$688$	12.7386	0.485655
$689$	9.40538	0.358317
$690$	−0.211245	−0.00804196
$691$	−34.5838	−1.31563	−0.657816	−	0.753179i	$-0.728519\pi$
$691$	−34.5838	−1.31563	−0.657816	+	0.753179i	$0.728519\pi$
$692$	61.2287	2.32757
$693$	−44.2848	−1.68224
$694$	−14.5316	−0.551610
$695$	−9.56665	−0.362884
$696$	4.27295	0.161966
$697$	44.4670	1.68431
$698$	−24.3418	−0.921349
$699$	3.29029	0.124450
$700$	−71.4509	−2.70059
$701$	−50.0941	−1.89203	−0.946015	−	0.324124i	$-0.894931\pi$
$701$	−50.0941	−1.89203	−0.946015	+	0.324124i	$0.894931\pi$
$702$	−3.02922	−0.114331
$703$	−15.0034	−0.565866
$704$	−37.0488	−1.39633
$705$	0.424686	0.0159946
$706$	19.9071	0.749214
$707$	−59.4949	−2.23754
$708$	−1.63570	−0.0614733
$709$	−25.7897	−0.968554	−0.484277	−	0.874915i	$-0.660917\pi$
$709$	−25.7897	−0.968554	−0.484277	+	0.874915i	$0.660917\pi$
$710$	−9.13423	−0.342801
$711$	16.5022	0.618880
$712$	11.4903	0.430618
$713$	1.02278	0.0383035
$714$	−17.1261	−0.640929
$715$	−1.30895	−0.0489521
$716$	−45.2899	−1.69256
$717$	1.01348	0.0378491
$718$	−33.4992	−1.25018
$719$	−8.31557	−0.310118	−0.155059	−	0.987905i	$-0.549557\pi$
$719$	−8.31557	−0.310118	−0.155059	+	0.987905i	$0.549557\pi$
$720$	−1.99427	−0.0743221
$721$	−0.639862	−0.0238297
$722$	−64.2877	−2.39254
$723$	3.80058	0.141345
$724$	25.1930	0.936290
$725$	−46.1613	−1.71439
$726$	−1.32974	−0.0493514
$727$	37.2502	1.38153	0.690767	−	0.723078i	$-0.257273\pi$
$727$	37.2502	1.38153	0.690767	+	0.723078i	$0.257273\pi$
$728$	−9.97999	−0.369883
$729$	−24.1661	−0.895040
$730$	−5.59849	−0.207209
$731$	55.1183	2.03862
$732$	−5.98841	−0.221338
$733$	−32.0896	−1.18526	−0.592629	−	0.805476i	$-0.701910\pi$
$733$	−32.0896	−1.18526	−0.592629	+	0.805476i	$0.701910\pi$
$734$	29.1783	1.07699
$735$	2.07770	0.0766373
$736$	6.56334	0.241928
$737$	−17.2190	−0.634270
$738$	−44.6320	−1.64293
$739$	1.58107	0.0581605	0.0290802	−	0.999577i	$-0.490742\pi$
$739$	1.58107	0.0581605	0.0290802	+	0.999577i	$0.490742\pi$
$740$	−2.80644	−0.103167
$741$	1.60110	0.0588178
$742$	−107.709	−3.95411
$743$	6.16705	0.226247	0.113124	−	0.993581i	$-0.463914\pi$
$743$	6.16705	0.226247	0.113124	+	0.993581i	$0.463914\pi$
$744$	0.494781	0.0181396
$745$	−6.34109	−0.232319
$746$	49.6351	1.81727
$747$	−27.1636	−0.993865
$748$	−53.8936	−1.97054
$749$	39.4193	1.44035
$750$	2.25500	0.0823410
$751$	17.8887	0.652767	0.326384	−	0.945237i	$-0.394170\pi$
$751$	17.8887	0.652767	0.326384	+	0.945237i	$0.394170\pi$
$752$	−6.09789	−0.222367
$753$	5.49792	0.200355
$754$	−21.2446	−0.773684
$755$	−4.00592	−0.145790
$756$	20.4480	0.743686
$757$	−44.5820	−1.62036	−0.810181	−	0.586180i	$-0.800631\pi$
$757$	−44.5820	−1.62036	−0.810181	+	0.586180i	$0.800631\pi$
$758$	48.0078	1.74372
$759$	−0.613438	−0.0222664
$760$	−6.03026	−0.218741
$761$	−5.35003	−0.193938	−0.0969692	−	0.995287i	$-0.530915\pi$
$761$	−5.35003	−0.193938	−0.0969692	+	0.995287i	$0.530915\pi$
$762$	−9.26709	−0.335711
$763$	−75.5173	−2.73391
$764$	42.0747	1.52221
$765$	−8.62896	−0.311981
$766$	−36.6712	−1.32499
$767$	2.46817	0.0891205
$768$	1.19015	0.0429457
$769$	40.4466	1.45854	0.729271	−	0.684225i	$-0.239859\pi$
$769$	40.4466	1.45854	0.729271	+	0.684225i	$0.239859\pi$
$770$	14.9899	0.540198
$771$	−1.54862	−0.0557724
$772$	−66.6838	−2.40000
$773$	−26.3856	−0.949024	−0.474512	−	0.880249i	$-0.657376\pi$
$773$	−26.3856	−0.949024	−0.474512	+	0.880249i	$0.657376\pi$
$774$	−55.3229	−1.98854
$775$	−5.34519	−0.192005
$776$	11.8409	0.425062
$777$	−2.58978	−0.0929078
$778$	−48.4419	−1.73673
$779$	47.6069	1.70570
$780$	0.299490	0.0107235
$781$	−26.5250	−0.949140
$782$	13.1241	0.469319
$783$	13.2105	0.472106
$784$	−29.8328	−1.06546
$785$	6.25033	0.223084
$786$	−5.25223	−0.187341
$787$	−12.2158	−0.435447	−0.217724	−	0.976010i	$-0.569863\pi$
$787$	−12.2158	−0.435447	−0.217724	+	0.976010i	$0.569863\pi$
$788$	72.8575	2.59544
$789$	4.01284	0.142861
$790$	−5.58580	−0.198734
$791$	−37.5290	−1.33438
$792$	16.4171	0.583356
$793$	9.03616	0.320883
$794$	48.9817	1.73830
$795$	0.980966	0.0347913
$796$	−7.08608	−0.251159
$797$	6.49392	0.230026	0.115013	−	0.993364i	$-0.463309\pi$
$797$	6.49392	0.230026	0.115013	+	0.993364i	$0.463309\pi$
$798$	−18.3355	−0.649068
$799$	−26.3848	−0.933425
$800$	−34.3008	−1.21272
$801$	17.6030	0.621972
$802$	19.6675	0.694484
$803$	−16.2575	−0.573716
$804$	3.93973	0.138944
$805$	−2.15168	−0.0758367
$806$	−2.46000	−0.0866498
$807$	−7.33878	−0.258337
$808$	22.0558	0.775919
$809$	7.94231	0.279237	0.139618	−	0.990205i	$-0.455412\pi$
$809$	7.94231	0.279237	0.139618	+	0.990205i	$0.455412\pi$
$810$	8.50160	0.298716
$811$	−39.5023	−1.38711	−0.693557	−	0.720402i	$-0.743957\pi$
$811$	−39.5023	−1.38711	−0.693557	+	0.720402i	$0.743957\pi$
$812$	143.406	5.03258
$813$	2.06657	0.0724779
$814$	−13.8260	−0.484600
$815$	−0.0826981	−0.00289679
$816$	−2.23961	−0.0784022
$817$	59.0104	2.06451
$818$	49.4391	1.72860
$819$	−15.2892	−0.534248
$820$	8.90503	0.310977
$821$	−41.8775	−1.46154	−0.730768	−	0.682626i	$-0.760838\pi$
$821$	−41.8775	−1.46154	−0.730768	+	0.682626i	$0.760838\pi$
$822$	−11.2231	−0.391451
$823$	−9.68439	−0.337576	−0.168788	−	0.985652i	$-0.553985\pi$
$823$	−9.68439	−0.337576	−0.168788	+	0.985652i	$0.553985\pi$
$824$	0.237208	0.00826352
$825$	3.20591	0.111615
$826$	−28.2650	−0.983466
$827$	43.9943	1.52983	0.764916	−	0.644130i	$-0.222780\pi$
$827$	43.9943	1.52983	0.764916	+	0.644130i	$0.222780\pi$
$828$	−7.76470	−0.269842
$829$	−16.6075	−0.576803	−0.288401	−	0.957510i	$-0.593124\pi$
$829$	−16.6075	−0.576803	−0.288401	+	0.957510i	$0.593124\pi$
$830$	9.19459	0.319149
$831$	0.200022	0.00693869
$832$	−12.7910	−0.443448
$833$	−129.083	−4.47245
$834$	10.7835	0.373400
$835$	−9.44305	−0.326790
$836$	−57.6992	−1.99557
$837$	1.52970	0.0528741
$838$	−64.8901	−2.24159
$839$	−19.6040	−0.676806	−0.338403	−	0.941001i	$-0.609887\pi$
$839$	−19.6040	−0.676806	−0.338403	+	0.941001i	$0.609887\pi$
$840$	−1.04090	−0.0359143
$841$	63.6485	2.19478
$842$	6.75090	0.232651
$843$	0.174826	0.00602134
$844$	39.5881	1.36268
$845$	−0.451913	−0.0155463
$846$	26.4827	0.910494
$847$	−13.5444	−0.465390
$848$	−14.0853	−0.483690
$849$	5.61312	0.192642
$850$	−68.5885	−2.35257
$851$	1.98461	0.0680315
$852$	6.06896	0.207919
$853$	−55.3427	−1.89490	−0.947448	−	0.319909i	$-0.896348\pi$
$853$	−55.3427	−1.89490	−0.947448	+	0.319909i	$0.896348\pi$
$854$	−103.480	−3.54103
$855$	−9.23828	−0.315942
$856$	−14.6134	−0.499476
$857$	−19.3328	−0.660397	−0.330199	−	0.943912i	$-0.607116\pi$
$857$	−19.3328	−0.660397	−0.330199	+	0.943912i	$0.607116\pi$
$858$	1.47544	0.0503708
$859$	8.19201	0.279508	0.139754	−	0.990186i	$-0.455369\pi$
$859$	8.19201	0.279508	0.139754	+	0.990186i	$0.455369\pi$
$860$	11.0381	0.376396
$861$	8.21754	0.280053
$862$	40.5762	1.38203
$863$	10.7047	0.364391	0.182195	−	0.983262i	$-0.441680\pi$
$863$	10.7047	0.364391	0.182195	+	0.983262i	$0.441680\pi$
$864$	9.81629	0.333957
$865$	−9.63618	−0.327640
$866$	64.7348	2.19978
$867$	−5.76704	−0.195859
$868$	16.6056	0.563630
$869$	−16.2207	−0.550249
$870$	−2.21578	−0.0751221
$871$	−5.94482	−0.201432
$872$	27.9955	0.948049
$873$	18.1400	0.613947
$874$	14.0509	0.475278
$875$	22.9688	0.776486
$876$	3.71975	0.125679
$877$	41.1685	1.39016	0.695081	−	0.718931i	$-0.255369\pi$
$877$	41.1685	1.39016	0.695081	+	0.718931i	$0.255369\pi$
$878$	18.6374	0.628982
$879$	3.35543	0.113176
$880$	1.96026	0.0660802
$881$	−23.4651	−0.790561	−0.395280	−	0.918561i	$-0.629353\pi$
$881$	−23.4651	−0.790561	−0.395280	+	0.918561i	$0.629353\pi$
$882$	129.562	4.36258
$883$	5.77980	0.194506	0.0972529	−	0.995260i	$-0.468994\pi$
$883$	5.77980	0.194506	0.0972529	+	0.995260i	$0.468994\pi$
$884$	−18.6066	−0.625808
$885$	0.257426	0.00865329
$886$	36.0637	1.21158
$887$	29.6720	0.996288	0.498144	−	0.867094i	$-0.334015\pi$
$887$	29.6720	0.996288	0.498144	+	0.867094i	$0.334015\pi$
$888$	0.960074	0.0322180
$889$	−94.3918	−3.16580
$890$	−5.95843	−0.199727
$891$	24.6879	0.827077
$892$	14.9692	0.501205
$893$	−28.2479	−0.945279
$894$	7.14762	0.239052
$895$	7.12773	0.238254
$896$	72.2604	2.41405
$897$	−0.211788	−0.00707139
$898$	59.9710	2.00126
$899$	10.7281	0.357803
$900$	40.5794	1.35265
$901$	−60.9451	−2.03038
$902$	43.8707	1.46074
$903$	10.1859	0.338966
$904$	13.9126	0.462728
$905$	−3.96487	−0.131797
$906$	4.51544	0.150016
$907$	−8.77916	−0.291507	−0.145754	−	0.989321i	$-0.546561\pi$
$907$	−8.77916	−0.291507	−0.145754	+	0.989321i	$0.546561\pi$
$908$	−68.4817	−2.27264
$909$	33.7891	1.12071
$910$	5.17522	0.171557
$911$	−28.1042	−0.931133	−0.465567	−	0.885013i	$-0.654149\pi$
$911$	−28.1042	−0.931133	−0.465567	+	0.885013i	$0.654149\pi$
$912$	−2.39776	−0.0793978
$913$	26.7003	0.883651
$914$	18.9837	0.627925
$915$	0.942457	0.0311567
$916$	−26.7594	−0.884157
$917$	−53.4976	−1.76665
$918$	19.6288	0.647847
$919$	1.25336	0.0413445	0.0206723	−	0.999786i	$-0.493419\pi$
$919$	1.25336	0.0413445	0.0206723	+	0.999786i	$0.493419\pi$
$920$	0.797664	0.0262982
$921$	1.63086	0.0537386
$922$	34.7023	1.14286
$923$	−9.15770	−0.301429
$924$	−9.95958	−0.327646
$925$	−10.3718	−0.341023
$926$	−64.1525	−2.10818
$927$	0.363399	0.0119356
$928$	68.8439	2.25991
$929$	18.1790	0.596435	0.298218	−	0.954498i	$-0.403608\pi$
$929$	18.1790	0.596435	0.298218	+	0.954498i	$0.403608\pi$
$930$	−0.256574	−0.00841339
$931$	−138.198	−4.52925
$932$	−40.9371	−1.34094
$933$	4.78433	0.156632
$934$	−72.9945	−2.38845
$935$	8.48177	0.277384
$936$	5.66797	0.185263
$937$	55.9049	1.82633	0.913166	−	0.407587i	$-0.133630\pi$
$937$	55.9049	1.82633	0.913166	+	0.407587i	$0.133630\pi$
$938$	68.0789	2.22285
$939$	5.23478	0.170831
$940$	−5.28386	−0.172340
$941$	−34.4470	−1.12294	−0.561469	−	0.827498i	$-0.689764\pi$
$941$	−34.4470	−1.12294	−0.561469	+	0.827498i	$0.689764\pi$
$942$	−7.04533	−0.229549
$943$	−6.29729	−0.205068
$944$	−3.69627	−0.120303
$945$	−3.21810	−0.104685
$946$	54.3793	1.76802
$947$	34.4899	1.12077	0.560385	−	0.828232i	$-0.310653\pi$
$947$	34.4899	1.12077	0.560385	+	0.828232i	$0.310653\pi$
$948$	3.71132	0.120538
$949$	−5.61288	−0.182202
$950$	−73.4318	−2.38244
$951$	6.65534	0.215814
$952$	64.6684	2.09592
$953$	27.9044	0.903913	0.451956	−	0.892040i	$-0.350726\pi$
$953$	27.9044	0.903913	0.451956	+	0.892040i	$0.350726\pi$
$954$	61.1713	1.98049
$955$	−6.62171	−0.214274
$956$	−12.6095	−0.407820
$957$	−6.43445	−0.207996
$958$	−70.4408	−2.27584
$959$	−114.315	−3.69143
$960$	−1.33408	−0.0430573
$961$	−29.7577	−0.959927
$962$	−4.77338	−0.153900
$963$	−22.3875	−0.721429
$964$	−47.2860	−1.52298
$965$	10.4947	0.337836
$966$	2.42536	0.0780345
$967$	27.2711	0.876981	0.438490	−	0.898736i	$-0.355513\pi$
$967$	27.2711	0.876981	0.438490	+	0.898736i	$0.355513\pi$
$968$	5.02112	0.161385
$969$	−10.3748	−0.333287
$970$	−6.14020	−0.197150
$971$	1.84724	0.0592806	0.0296403	−	0.999561i	$-0.490564\pi$
$971$	1.84724	0.0592806	0.0296403	+	0.999561i	$0.490564\pi$
$972$	−17.4716	−0.560403
$973$	109.837	3.52121
$974$	−65.7855	−2.10790
$975$	1.10683	0.0354470
$976$	−13.5323	−0.433159
$977$	14.7656	0.472393	0.236197	−	0.971705i	$-0.424099\pi$
$977$	14.7656	0.472393	0.236197	+	0.971705i	$0.424099\pi$
$978$	0.0932166	0.00298074
$979$	−17.3028	−0.552999
$980$	−25.8504	−0.825759
$981$	42.8888	1.36933
$982$	−84.7379	−2.70410
$983$	−56.1946	−1.79233	−0.896165	−	0.443721i	$-0.853658\pi$
$983$	−56.1946	−1.79233	−0.896165	+	0.443721i	$0.853658\pi$
$984$	−3.04638	−0.0971150
$985$	−11.4663	−0.365347
$986$	137.661	4.38403
$987$	−4.87593	−0.155202
$988$	−19.9205	−0.633756
$989$	−7.80571	−0.248207
$990$	−8.51326	−0.270569
$991$	−5.21079	−0.165526	−0.0827630	−	0.996569i	$-0.526374\pi$
$991$	−5.21079	−0.165526	−0.0827630	+	0.996569i	$0.526374\pi$
$992$	7.97170	0.253102
$993$	0.195599	0.00620715
$994$	104.872	3.32635
$995$	1.11521	0.0353544
$996$	−6.10907	−0.193573
$997$	−11.8446	−0.375123	−0.187561	−	0.982253i	$-0.560058\pi$
$997$	−11.8446	−0.375123	−0.187561	+	0.982253i	$0.560058\pi$
$998$	73.4499	2.32502
$999$	2.96823	0.0939106

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8021.2.a.a.1.18	✓	134

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8021.2.a.a.1.18	✓	134	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:	\( N \)	\(=\)	\( 8021 = 13 \cdot 617 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8021.a (trivial)

\(f(q)\)	\(=\)	\(q-2.20714 q^{2} -0.230793 q^{3} +2.87148 q^{4} -0.451913 q^{5} +0.509393 q^{6} +5.18852 q^{7} -1.92347 q^{8} -2.94673 q^{9} +O(q^{10})\)	\(q-2.20714 q^{2} -0.230793 q^{3} +2.87148 q^{4} -0.451913 q^{5} +0.509393 q^{6} +5.18852 q^{7} -1.92347 q^{8} -2.94673 q^{9} +0.997437 q^{10} +2.89647 q^{11} -0.662717 q^{12} +1.00000 q^{13} -11.4518 q^{14} +0.104298 q^{15} -1.49757 q^{16} -6.47981 q^{17} +6.50386 q^{18} -6.93737 q^{19} -1.29766 q^{20} -1.19747 q^{21} -6.39293 q^{22} +0.917653 q^{23} +0.443924 q^{24} -4.79577 q^{25} -2.20714 q^{26} +1.37246 q^{27} +14.8987 q^{28} +9.62541 q^{29} -0.230201 q^{30} +1.11456 q^{31} +7.15231 q^{32} -0.668486 q^{33} +14.3019 q^{34} -2.34476 q^{35} -8.46148 q^{36} +2.16270 q^{37} +15.3118 q^{38} -0.230793 q^{39} +0.869243 q^{40} -6.86239 q^{41} +2.64300 q^{42} -8.50616 q^{43} +8.31715 q^{44} +1.33167 q^{45} -2.02539 q^{46} +4.07184 q^{47} +0.345630 q^{48} +19.9208 q^{49} +10.5850 q^{50} +1.49549 q^{51} +2.87148 q^{52} +9.40538 q^{53} -3.02922 q^{54} -1.30895 q^{55} -9.97999 q^{56} +1.60110 q^{57} -21.2446 q^{58} +2.46817 q^{59} +0.299490 q^{60} +9.03616 q^{61} -2.46000 q^{62} -15.2892 q^{63} -12.7910 q^{64} -0.451913 q^{65} +1.47544 q^{66} -5.94482 q^{67} -18.6066 q^{68} -0.211788 q^{69} +5.17522 q^{70} -9.15770 q^{71} +5.66797 q^{72} -5.61288 q^{73} -4.77338 q^{74} +1.10683 q^{75} -19.9205 q^{76} +15.0284 q^{77} +0.509393 q^{78} -5.60015 q^{79} +0.676774 q^{80} +8.52345 q^{81} +15.1463 q^{82} +9.21822 q^{83} -3.43852 q^{84} +2.92831 q^{85} +18.7743 q^{86} -2.22148 q^{87} -5.57129 q^{88} -5.97374 q^{89} -2.93918 q^{90} +5.18852 q^{91} +2.63502 q^{92} -0.257233 q^{93} -8.98713 q^{94} +3.13509 q^{95} -1.65070 q^{96} -6.15598 q^{97} -43.9680 q^{98} -8.53514 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 134 q - 6 q^{2} - 33 q^{3} + 98 q^{4} - 8 q^{5} - 16 q^{6} - 32 q^{7} - 15 q^{8} + 101 q^{9}+O(q^{10}) \) 134 * q - 6 * q^2 - 33 * q^3 + 98 * q^4 - 8 * q^5 - 16 * q^6 - 32 * q^7 - 15 * q^8 + 101 * q^9	\( 134 q - 6 q^{2} - 33 q^{3} + 98 q^{4} - 8 q^{5} - 16 q^{6} - 32 q^{7} - 15 q^{8} + 101 q^{9} - 33 q^{10} - 47 q^{11} - 53 q^{12} + 134 q^{13} - 28 q^{14} - 30 q^{15} + 30 q^{16} - 17 q^{17} - 14 q^{18} - 87 q^{19} - 12 q^{20} - 24 q^{21} - 52 q^{22} - 44 q^{23} - 36 q^{24} + 58 q^{25} - 6 q^{26} - 117 q^{27} - 71 q^{28} - 42 q^{29} - 21 q^{30} - 82 q^{31} - 31 q^{32} + 12 q^{33} - 30 q^{34} - 54 q^{35} + 32 q^{36} - 55 q^{37} - 12 q^{38} - 33 q^{39} - 86 q^{40} - 16 q^{41} + 6 q^{42} - 148 q^{43} - 54 q^{44} - 24 q^{45} - 57 q^{46} - 21 q^{47} - 82 q^{48} + 12 q^{49} - 17 q^{50} - 123 q^{51} + 98 q^{52} - 17 q^{53} - 10 q^{54} - 148 q^{55} - 47 q^{56} - q^{57} - 58 q^{58} - 64 q^{59} - 16 q^{60} - 112 q^{61} - 15 q^{62} - 58 q^{63} - 65 q^{64} - 8 q^{65} - 20 q^{66} - 110 q^{67} - 8 q^{68} - 57 q^{69} - 40 q^{70} - 78 q^{71} - 28 q^{72} - 43 q^{73} - 52 q^{74} - 150 q^{75} - 96 q^{76} - 24 q^{77} - 16 q^{78} - 228 q^{79} + 20 q^{80} + 54 q^{81} - 89 q^{82} - 12 q^{83} + 6 q^{84} - 77 q^{85} + 29 q^{86} - 77 q^{87} - 95 q^{88} - 32 q^{89} - 46 q^{90} - 32 q^{91} - 62 q^{92} - 9 q^{93} - 87 q^{94} - 61 q^{95} - 54 q^{96} - 38 q^{97} + 6 q^{98} - 193 q^{99}+O(q^{100}) \) 134 * q - 6 * q^2 - 33 * q^3 + 98 * q^4 - 8 * q^5 - 16 * q^6 - 32 * q^7 - 15 * q^8 + 101 * q^9 - 33 * q^10 - 47 * q^11 - 53 * q^12 + 134 * q^13 - 28 * q^14 - 30 * q^15 + 30 * q^16 - 17 * q^17 - 14 * q^18 - 87 * q^19 - 12 * q^20 - 24 * q^21 - 52 * q^22 - 44 * q^23 - 36 * q^24 + 58 * q^25 - 6 * q^26 - 117 * q^27 - 71 * q^28 - 42 * q^29 - 21 * q^30 - 82 * q^31 - 31 * q^32 + 12 * q^33 - 30 * q^34 - 54 * q^35 + 32 * q^36 - 55 * q^37 - 12 * q^38 - 33 * q^39 - 86 * q^40 - 16 * q^41 + 6 * q^42 - 148 * q^43 - 54 * q^44 - 24 * q^45 - 57 * q^46 - 21 * q^47 - 82 * q^48 + 12 * q^49 - 17 * q^50 - 123 * q^51 + 98 * q^52 - 17 * q^53 - 10 * q^54 - 148 * q^55 - 47 * q^56 - q^57 - 58 * q^58 - 64 * q^59 - 16 * q^60 - 112 * q^61 - 15 * q^62 - 58 * q^63 - 65 * q^64 - 8 * q^65 - 20 * q^66 - 110 * q^67 - 8 * q^68 - 57 * q^69 - 40 * q^70 - 78 * q^71 - 28 * q^72 - 43 * q^73 - 52 * q^74 - 150 * q^75 - 96 * q^76 - 24 * q^77 - 16 * q^78 - 228 * q^79 + 20 * q^80 + 54 * q^81 - 89 * q^82 - 12 * q^83 + 6 * q^84 - 77 * q^85 + 29 * q^86 - 77 * q^87 - 95 * q^88 - 32 * q^89 - 46 * q^90 - 32 * q^91 - 62 * q^92 - 9 * q^93 - 87 * q^94 - 61 * q^95 - 54 * q^96 - 38 * q^97 + 6 * q^98 - 193 * q^99

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