LMFDB - Embedded newform 8041.2.a.j.1.20

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:	$82$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.20
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)

$f(q)$	$=$	$q-1.62861 q^{2} -2.08850 q^{3} +0.652359 q^{4} -3.32951 q^{5} +3.40134 q^{6} -5.07571 q^{7} +2.19478 q^{8} +1.36181 q^{9} +O(q^{10})$	\(q-1.62861 q^{2} -2.08850 q^{3} +0.652359 q^{4} -3.32951 q^{5} +3.40134 q^{6} -5.07571 q^{7} +2.19478 q^{8} +1.36181 q^{9} +5.42246 q^{10} +1.00000 q^{11} -1.36245 q^{12} -0.291030 q^{13} +8.26634 q^{14} +6.95367 q^{15} -4.87915 q^{16} +1.00000 q^{17} -2.21786 q^{18} +7.07744 q^{19} -2.17204 q^{20} +10.6006 q^{21} -1.62861 q^{22} +1.66635 q^{23} -4.58378 q^{24} +6.08564 q^{25} +0.473973 q^{26} +3.42135 q^{27} -3.31119 q^{28} -4.92017 q^{29} -11.3248 q^{30} -5.61097 q^{31} +3.55666 q^{32} -2.08850 q^{33} -1.62861 q^{34} +16.8996 q^{35} +0.888390 q^{36} +8.06861 q^{37} -11.5264 q^{38} +0.607814 q^{39} -7.30753 q^{40} -2.39391 q^{41} -17.2642 q^{42} +1.00000 q^{43} +0.652359 q^{44} -4.53417 q^{45} -2.71383 q^{46} +6.60547 q^{47} +10.1901 q^{48} +18.7629 q^{49} -9.91112 q^{50} -2.08850 q^{51} -0.189856 q^{52} +9.64367 q^{53} -5.57203 q^{54} -3.32951 q^{55} -11.1401 q^{56} -14.7812 q^{57} +8.01303 q^{58} +13.7484 q^{59} +4.53629 q^{60} +14.9930 q^{61} +9.13806 q^{62} -6.91216 q^{63} +3.96590 q^{64} +0.968986 q^{65} +3.40134 q^{66} +1.40254 q^{67} +0.652359 q^{68} -3.48017 q^{69} -27.5229 q^{70} +7.30119 q^{71} +2.98887 q^{72} -12.2232 q^{73} -13.1406 q^{74} -12.7098 q^{75} +4.61703 q^{76} -5.07571 q^{77} -0.989890 q^{78} -6.07658 q^{79} +16.2452 q^{80} -11.2309 q^{81} +3.89874 q^{82} -1.31345 q^{83} +6.91540 q^{84} -3.32951 q^{85} -1.62861 q^{86} +10.2758 q^{87} +2.19478 q^{88} -4.77370 q^{89} +7.38437 q^{90} +1.47718 q^{91} +1.08706 q^{92} +11.7185 q^{93} -10.7577 q^{94} -23.5644 q^{95} -7.42806 q^{96} +1.25500 q^{97} -30.5573 q^{98} +1.36181 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 82 q + 8 q^{2} + 6 q^{3} + 98 q^{4} + 11 q^{5} + 10 q^{6} + 8 q^{7} + 30 q^{8} + 108 q^{9}+O(q^{10}) $ 82 * q + 8 * q^2 + 6 * q^3 + 98 * q^4 + 11 * q^5 + 10 * q^6 + 8 * q^7 + 30 * q^8 + 108 * q^9	\( 82 q + 8 q^{2} + 6 q^{3} + 98 q^{4} + 11 q^{5} + 10 q^{6} + 8 q^{7} + 30 q^{8} + 108 q^{9} + q^{10} + 82 q^{11} + 3 q^{12} + 26 q^{13} + 17 q^{14} + 66 q^{15} + 122 q^{16} + 82 q^{17} + 18 q^{18} + 12 q^{19} + 9 q^{20} + 22 q^{21} + 8 q^{22} + 50 q^{23} + 15 q^{24} + 117 q^{25} + 36 q^{26} + 30 q^{27} + 11 q^{28} + 33 q^{29} - 26 q^{30} + 40 q^{31} + 58 q^{32} + 6 q^{33} + 8 q^{34} + 16 q^{35} + 160 q^{36} + 31 q^{37} + 18 q^{38} + 41 q^{39} - 29 q^{40} + 42 q^{41} - 51 q^{42} + 82 q^{43} + 98 q^{44} - 2 q^{45} - 19 q^{46} + 84 q^{47} - 46 q^{48} + 136 q^{49} + 59 q^{50} + 6 q^{51} + 45 q^{52} + 83 q^{53} + 24 q^{54} + 11 q^{55} + 21 q^{56} + 23 q^{57} + 14 q^{58} + 96 q^{59} + 184 q^{60} - 6 q^{61} - 23 q^{62} + 8 q^{63} + 148 q^{64} + 5 q^{65} + 10 q^{66} + 78 q^{67} + 98 q^{68} + 61 q^{69} - 3 q^{70} + 155 q^{71} + 50 q^{72} - 23 q^{73} + 10 q^{74} - 19 q^{75} + 44 q^{76} + 8 q^{77} - 27 q^{78} + 31 q^{79} + 19 q^{80} + 150 q^{81} - 12 q^{82} + 54 q^{83} + 8 q^{84} + 11 q^{85} + 8 q^{86} + 20 q^{87} + 30 q^{88} + 25 q^{89} - 81 q^{90} - 14 q^{91} + 60 q^{92} + 36 q^{93} + 19 q^{94} + 111 q^{95} - 6 q^{96} + 2 q^{97} - 5 q^{98} + 108 q^{99}+O(q^{100}) \) 82 * q + 8 * q^2 + 6 * q^3 + 98 * q^4 + 11 * q^5 + 10 * q^6 + 8 * q^7 + 30 * q^8 + 108 * q^9 + q^10 + 82 * q^11 + 3 * q^12 + 26 * q^13 + 17 * q^14 + 66 * q^15 + 122 * q^16 + 82 * q^17 + 18 * q^18 + 12 * q^19 + 9 * q^20 + 22 * q^21 + 8 * q^22 + 50 * q^23 + 15 * q^24 + 117 * q^25 + 36 * q^26 + 30 * q^27 + 11 * q^28 + 33 * q^29 - 26 * q^30 + 40 * q^31 + 58 * q^32 + 6 * q^33 + 8 * q^34 + 16 * q^35 + 160 * q^36 + 31 * q^37 + 18 * q^38 + 41 * q^39 - 29 * q^40 + 42 * q^41 - 51 * q^42 + 82 * q^43 + 98 * q^44 - 2 * q^45 - 19 * q^46 + 84 * q^47 - 46 * q^48 + 136 * q^49 + 59 * q^50 + 6 * q^51 + 45 * q^52 + 83 * q^53 + 24 * q^54 + 11 * q^55 + 21 * q^56 + 23 * q^57 + 14 * q^58 + 96 * q^59 + 184 * q^60 - 6 * q^61 - 23 * q^62 + 8 * q^63 + 148 * q^64 + 5 * q^65 + 10 * q^66 + 78 * q^67 + 98 * q^68 + 61 * q^69 - 3 * q^70 + 155 * q^71 + 50 * q^72 - 23 * q^73 + 10 * q^74 - 19 * q^75 + 44 * q^76 + 8 * q^77 - 27 * q^78 + 31 * q^79 + 19 * q^80 + 150 * q^81 - 12 * q^82 + 54 * q^83 + 8 * q^84 + 11 * q^85 + 8 * q^86 + 20 * q^87 + 30 * q^88 + 25 * q^89 - 81 * q^90 - 14 * q^91 + 60 * q^92 + 36 * q^93 + 19 * q^94 + 111 * q^95 - 6 * q^96 + 2 * q^97 - 5 * q^98 + 108 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.62861	−1.15160	−0.575799	−	0.817591i	$-0.695309\pi$
$2$	−1.62861	−1.15160	−0.575799	+	0.817591i	$0.695309\pi$
$3$	−2.08850	−1.20579	−0.602897	−	0.797819i	$-0.705987\pi$
$3$	−2.08850	−1.20579	−0.602897	+	0.797819i	$0.705987\pi$
$4$	0.652359	0.326180
$5$	−3.32951	−1.48900	−0.744501	−	0.667621i	$-0.767313\pi$
$5$	−3.32951	−1.48900	−0.744501	+	0.667621i	$0.767313\pi$
$6$	3.40134	1.38859
$7$	−5.07571	−1.91844	−0.959219	−	0.282663i	$-0.908782\pi$
$7$	−5.07571	−1.91844	−0.959219	+	0.282663i	$0.908782\pi$
$8$	2.19478	0.775971
$9$	1.36181	0.453937
$10$	5.42246	1.71473
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−1.36245	−0.393305
$13$	−0.291030	−0.0807171	−0.0403586	−	0.999185i	$-0.512850\pi$
$13$	−0.291030	−0.0807171	−0.0403586	+	0.999185i	$0.512850\pi$
$14$	8.26634	2.20927
$15$	6.95367	1.79543
$16$	−4.87915	−1.21979
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−2.21786	−0.522754
$19$	7.07744	1.62368	0.811838	−	0.583883i	$-0.198467\pi$
$19$	7.07744	1.62368	0.811838	+	0.583883i	$0.198467\pi$
$20$	−2.17204	−0.485682
$21$	10.6006	2.31324
$22$	−1.62861	−0.347220
$23$	1.66635	0.347459	0.173729	−	0.984793i	$-0.444418\pi$
$23$	1.66635	0.347459	0.173729	+	0.984793i	$0.444418\pi$
$24$	−4.58378	−0.935660
$25$	6.08564	1.21713
$26$	0.473973	0.0929537
$27$	3.42135	0.658439
$28$	−3.31119	−0.625756
$29$	−4.92017	−0.913654	−0.456827	−	0.889556i	$-0.651014\pi$
$29$	−4.92017	−0.913654	−0.456827	+	0.889556i	$0.651014\pi$
$30$	−11.3248	−2.06761
$31$	−5.61097	−1.00776	−0.503880	−	0.863774i	$-0.668095\pi$
$31$	−5.61097	−1.00776	−0.503880	+	0.863774i	$0.668095\pi$
$32$	3.55666	0.628734
$33$	−2.08850	−0.363560
$34$	−1.62861	−0.279304
$35$	16.8996	2.85656
$36$	0.888390	0.148065
$37$	8.06861	1.32647	0.663236	−	0.748410i	$-0.269183\pi$
$37$	8.06861	1.32647	0.663236	+	0.748410i	$0.269183\pi$
$38$	−11.5264	−1.86982
$39$	0.607814	0.0973281
$40$	−7.30753	−1.15542
$41$	−2.39391	−0.373866	−0.186933	−	0.982373i	$-0.559855\pi$
$41$	−2.39391	−0.373866	−0.186933	+	0.982373i	$0.559855\pi$
$42$	−17.2642	−2.66392
$43$	1.00000	0.152499
$43$	1.00000	0.152499
$44$	0.652359	0.0983468
$45$	−4.53417	−0.675914
$46$	−2.71383	−0.400133
$47$	6.60547	0.963507	0.481753	−	0.876307i	$-0.340000\pi$
$47$	6.60547	0.963507	0.481753	+	0.876307i	$0.340000\pi$
$48$	10.1901	1.47081
$49$	18.7629	2.68041
$50$	−9.91112	−1.40164
$51$	−2.08850	−0.292448
$52$	−0.189856	−0.0263283
$53$	9.64367	1.32466	0.662330	−	0.749212i	$-0.269568\pi$
$53$	9.64367	1.32466	0.662330	+	0.749212i	$0.269568\pi$
$54$	−5.57203	−0.758257
$55$	−3.32951	−0.448951
$56$	−11.1401	−1.48865
$57$	−14.7812	−1.95782
$58$	8.01303	1.05216
$59$	13.7484	1.78989	0.894947	−	0.446173i	$-0.147213\pi$
$59$	13.7484	1.78989	0.894947	+	0.446173i	$0.147213\pi$
$60$	4.53629	0.585632
$61$	14.9930	1.91966	0.959828	−	0.280590i	$-0.0905302\pi$
$61$	14.9930	1.91966	0.959828	+	0.280590i	$0.0905302\pi$
$62$	9.13806	1.16054
$63$	−6.91216	−0.870851
$64$	3.96590	0.495737
$65$	0.968986	0.120188
$66$	3.40134	0.418676
$67$	1.40254	0.171347	0.0856735	−	0.996323i	$-0.472696\pi$
$67$	1.40254	0.171347	0.0856735	+	0.996323i	$0.472696\pi$
$68$	0.652359	0.0791102
$69$	−3.48017	−0.418963
$70$	−27.5229	−3.28961
$71$	7.30119	0.866492	0.433246	−	0.901276i	$-0.357368\pi$
$71$	7.30119	0.866492	0.433246	+	0.901276i	$0.357368\pi$
$72$	2.98887	0.352242
$73$	−12.2232	−1.43061	−0.715307	−	0.698810i	$-0.753713\pi$
$73$	−12.2232	−1.43061	−0.715307	+	0.698810i	$0.753713\pi$
$74$	−13.1406	−1.52756
$75$	−12.7098	−1.46761
$76$	4.61703	0.529610
$77$	−5.07571	−0.578431
$78$	−0.989890	−0.112083
$79$	−6.07658	−0.683668	−0.341834	−	0.939760i	$-0.611048\pi$
$79$	−6.07658	−0.683668	−0.341834	+	0.939760i	$0.611048\pi$
$80$	16.2452	1.81627
$81$	−11.2309	−1.24788
$82$	3.89874	0.430544
$83$	−1.31345	−0.144170	−0.0720851	−	0.997398i	$-0.522965\pi$
$83$	−1.31345	−0.144170	−0.0720851	+	0.997398i	$0.522965\pi$
$84$	6.91540	0.754532
$85$	−3.32951	−0.361136
$86$	−1.62861	−0.175617
$87$	10.2758	1.10168
$88$	2.19478	0.233964
$89$	−4.77370	−0.506011	−0.253006	−	0.967465i	$-0.581419\pi$
$89$	−4.77370	−0.506011	−0.253006	+	0.967465i	$0.581419\pi$
$90$	7.38437	0.778381
$91$	1.47718	0.154851
$92$	1.08706	0.113334
$93$	11.7185	1.21515
$94$	−10.7577	−1.10957
$95$	−23.5644	−2.41766
$96$	−7.42806	−0.758123
$97$	1.25500	0.127426	0.0637130	−	0.997968i	$-0.479706\pi$
$97$	1.25500	0.127426	0.0637130	+	0.997968i	$0.479706\pi$
$98$	−30.5573	−3.08675
$99$	1.36181	0.136867
$100$	3.97003	0.397003
$101$	10.9162	1.08620	0.543099	−	0.839669i	$-0.317251\pi$
$101$	10.9162	1.08620	0.543099	+	0.839669i	$0.317251\pi$
$102$	3.40134	0.336783
$103$	−11.9102	−1.17355	−0.586775	−	0.809750i	$-0.699603\pi$
$103$	−11.9102	−1.17355	−0.586775	+	0.809750i	$0.699603\pi$
$104$	−0.638745	−0.0626341
$105$	−35.2948	−3.44442
$106$	−15.7057	−1.52548
$107$	−12.9562	−1.25252	−0.626262	−	0.779613i	$-0.715416\pi$
$107$	−12.9562	−1.25252	−0.626262	+	0.779613i	$0.715416\pi$
$108$	2.23195	0.214769
$109$	19.3440	1.85281	0.926407	−	0.376523i	$-0.122880\pi$
$109$	19.3440	1.85281	0.926407	+	0.376523i	$0.122880\pi$
$110$	5.42246	0.517012
$111$	−16.8513	−1.59945
$112$	24.7651	2.34009
$113$	−10.0690	−0.947209	−0.473605	−	0.880738i	$-0.657047\pi$
$113$	−10.0690	−0.947209	−0.473605	+	0.880738i	$0.657047\pi$
$114$	24.0727	2.25462
$115$	−5.54814	−0.517367
$116$	−3.20972	−0.298015
$117$	−0.396328	−0.0366405
$118$	−22.3908	−2.06124
$119$	−5.07571	−0.465290
$120$	15.2617	1.39320
$121$	1.00000	0.0909091
$122$	−24.4177	−2.21067
$123$	4.99967	0.450805
$124$	−3.66037	−0.328711
$125$	−3.61466	−0.323305
$126$	11.2572	1.00287
$127$	14.7795	1.31147	0.655733	−	0.754993i	$-0.272360\pi$
$127$	14.7795	1.31147	0.655733	+	0.754993i	$0.272360\pi$
$128$	−13.5722	−1.19962
$129$	−2.08850	−0.183882
$130$	−1.57810	−0.138408
$131$	−21.9985	−1.92202	−0.961010	−	0.276514i	$-0.910821\pi$
$131$	−21.9985	−1.92202	−0.961010	+	0.276514i	$0.910821\pi$
$132$	−1.36245	−0.118586
$133$	−35.9230	−3.11492
$134$	−2.28418	−0.197323
$135$	−11.3914	−0.980417
$136$	2.19478	0.188201
$137$	−11.4506	−0.978294	−0.489147	−	0.872201i	$-0.662692\pi$
$137$	−11.4506	−0.978294	−0.489147	+	0.872201i	$0.662692\pi$
$138$	5.66783	0.482478
$139$	−6.06668	−0.514569	−0.257284	−	0.966336i	$-0.582828\pi$
$139$	−6.06668	−0.514569	−0.257284	+	0.966336i	$0.582828\pi$
$140$	11.0246	0.931752
$141$	−13.7955	−1.16179
$142$	−11.8908	−0.997851
$143$	−0.291030	−0.0243371
$144$	−6.64448	−0.553706
$145$	16.3818	1.36043
$146$	19.9067	1.64749
$147$	−39.1861	−3.23202
$148$	5.26363	0.432668
$149$	−6.38373	−0.522975	−0.261488	−	0.965207i	$-0.584213\pi$
$149$	−6.38373	−0.522975	−0.261488	+	0.965207i	$0.584213\pi$
$150$	20.6993	1.69009
$151$	1.42651	0.116088	0.0580439	−	0.998314i	$-0.481514\pi$
$151$	1.42651	0.116088	0.0580439	+	0.998314i	$0.481514\pi$
$152$	15.5334	1.25992
$153$	1.36181	0.110096
$154$	8.26634	0.666120
$155$	18.6818	1.50056
$156$	0.396513	0.0317464
$157$	−1.02272	−0.0816221	−0.0408110	−	0.999167i	$-0.512994\pi$
$157$	−1.02272	−0.0816221	−0.0408110	+	0.999167i	$0.512994\pi$
$158$	9.89635	0.787311
$159$	−20.1408	−1.59727
$160$	−11.8419	−0.936186
$161$	−8.45793	−0.666578
$162$	18.2907	1.43705
$163$	19.0310	1.49063	0.745313	−	0.666715i	$-0.232300\pi$
$163$	19.0310	1.49063	0.745313	+	0.666715i	$0.232300\pi$
$164$	−1.56169	−0.121947
$165$	6.95367	0.541342
$166$	2.13910	0.166026
$167$	1.56173	0.120850	0.0604252	−	0.998173i	$-0.480754\pi$
$167$	1.56173	0.120850	0.0604252	+	0.998173i	$0.480754\pi$
$168$	23.2659	1.79501
$169$	−12.9153	−0.993485
$170$	5.42246	0.415884
$171$	9.63814	0.737047
$172$	0.652359	0.0497419
$173$	9.72343	0.739259	0.369629	−	0.929179i	$-0.379485\pi$
$173$	9.72343	0.739259	0.369629	+	0.929179i	$0.379485\pi$
$174$	−16.7352	−1.26869
$175$	−30.8890	−2.33499
$176$	−4.87915	−0.367779
$177$	−28.7135	−2.15824
$178$	7.77448	0.582722
$179$	3.23929	0.242116	0.121058	−	0.992645i	$-0.461371\pi$
$179$	3.23929	0.242116	0.121058	+	0.992645i	$0.461371\pi$
$180$	−2.95791	−0.220469
$181$	11.2818	0.838572	0.419286	−	0.907854i	$-0.362280\pi$
$181$	11.2818	0.838572	0.419286	+	0.907854i	$0.362280\pi$
$182$	−2.40575	−0.178326
$183$	−31.3128	−2.31471
$184$	3.65727	0.269618
$185$	−26.8645	−1.97512
$186$	−19.0848	−1.39937
$187$	1.00000	0.0731272
$188$	4.30914	0.314276
$189$	−17.3658	−1.26317
$190$	38.3771	2.78417
$191$	19.3859	1.40271	0.701357	−	0.712810i	$-0.252578\pi$
$191$	19.3859	1.40271	0.701357	+	0.712810i	$0.252578\pi$
$192$	−8.28276	−0.597757
$193$	−14.8428	−1.06841	−0.534205	−	0.845355i	$-0.679389\pi$
$193$	−14.8428	−1.06841	−0.534205	+	0.845355i	$0.679389\pi$
$194$	−2.04390	−0.146744
$195$	−2.02372	−0.144922
$196$	12.2401	0.874294
$197$	11.5745	0.824653	0.412326	−	0.911036i	$-0.364716\pi$
$197$	11.5745	0.824653	0.412326	+	0.911036i	$0.364716\pi$
$198$	−2.21786	−0.157616
$199$	−8.60612	−0.610072	−0.305036	−	0.952341i	$-0.598668\pi$
$199$	−8.60612	−0.610072	−0.305036	+	0.952341i	$0.598668\pi$
$200$	13.3566	0.944456
$201$	−2.92919	−0.206609
$202$	−17.7781	−1.25086
$203$	24.9734	1.75279
$204$	−1.36245	−0.0953905
$205$	7.97055	0.556687
$206$	19.3971	1.35146
$207$	2.26926	0.157724
$208$	1.41998	0.0984576
$209$	7.07744	0.489557
$210$	57.4814	3.96659
$211$	−4.22581	−0.290916	−0.145458	−	0.989364i	$-0.546466\pi$
$211$	−4.22581	−0.290916	−0.145458	+	0.989364i	$0.546466\pi$
$212$	6.29114	0.432077
$213$	−15.2485	−1.04481
$214$	21.1005	1.44240
$215$	−3.32951	−0.227071
$216$	7.50910	0.510929
$217$	28.4797	1.93333
$218$	−31.5037	−2.13370
$219$	25.5280	1.72503
$220$	−2.17204	−0.146439
$221$	−0.291030	−0.0195768
$222$	27.4441	1.84193
$223$	−27.5315	−1.84364	−0.921822	−	0.387613i	$-0.873300\pi$
$223$	−27.5315	−1.84364	−0.921822	+	0.387613i	$0.873300\pi$
$224$	−18.0526	−1.20619
$225$	8.28750	0.552500
$226$	16.3984	1.09080
$227$	12.0603	0.800473	0.400236	−	0.916412i	$-0.368928\pi$
$227$	12.0603	0.800473	0.400236	+	0.916412i	$0.368928\pi$
$228$	−9.64265	−0.638600
$229$	10.5284	0.695734	0.347867	−	0.937544i	$-0.386906\pi$
$229$	10.5284	0.695734	0.347867	+	0.937544i	$0.386906\pi$
$230$	9.03574	0.595799
$231$	10.6006	0.697468
$232$	−10.7987	−0.708968
$233$	−9.44338	−0.618656	−0.309328	−	0.950955i	$-0.600104\pi$
$233$	−9.44338	−0.618656	−0.309328	+	0.950955i	$0.600104\pi$
$234$	0.645462	0.0421952
$235$	−21.9930	−1.43466
$236$	8.96892	0.583827
$237$	12.6909	0.824363
$238$	8.26634	0.535827
$239$	21.1275	1.36662	0.683312	−	0.730126i	$-0.260539\pi$
$239$	21.1275	1.36662	0.683312	+	0.730126i	$0.260539\pi$
$240$	−33.9280	−2.19004
$241$	10.9561	0.705741	0.352871	−	0.935672i	$-0.385206\pi$
$241$	10.9561	0.705741	0.352871	+	0.935672i	$0.385206\pi$
$242$	−1.62861	−0.104691
$243$	13.1916	0.846244
$244$	9.78081	0.626152
$245$	−62.4711	−3.99113
$246$	−8.14249	−0.519146
$247$	−2.05974	−0.131058
$248$	−12.3148	−0.781992
$249$	2.74314	0.173839
$250$	5.88686	0.372318
$251$	14.5228	0.916673	0.458336	−	0.888779i	$-0.348446\pi$
$251$	14.5228	0.916673	0.458336	+	0.888779i	$0.348446\pi$
$252$	−4.50921	−0.284054
$253$	1.66635	0.104763
$254$	−24.0700	−1.51028
$255$	6.95367	0.435456
$256$	14.1720	0.885748
$257$	−21.4777	−1.33974	−0.669872	−	0.742476i	$-0.733651\pi$
$257$	−21.4777	−1.33974	−0.669872	+	0.742476i	$0.733651\pi$
$258$	3.40134	0.211758
$259$	−40.9540	−2.54476
$260$	0.632127	0.0392029
$261$	−6.70035	−0.414741
$262$	35.8269	2.21340
$263$	−5.46042	−0.336704	−0.168352	−	0.985727i	$-0.553844\pi$
$263$	−5.46042	−0.336704	−0.168352	+	0.985727i	$0.553844\pi$
$264$	−4.58378	−0.282112
$265$	−32.1087	−1.97242
$266$	58.5045	3.58714
$267$	9.96985	0.610145
$268$	0.914957	0.0558899
$269$	−0.0887634	−0.00541200	−0.00270600	−	0.999996i	$-0.500861\pi$
$269$	−0.0887634	−0.00541200	−0.00270600	+	0.999996i	$0.500861\pi$
$270$	18.5521	1.12905
$271$	−16.3443	−0.992843	−0.496422	−	0.868082i	$-0.665353\pi$
$271$	−16.3443	−0.992843	−0.496422	+	0.868082i	$0.665353\pi$
$272$	−4.87915	−0.295842
$273$	−3.08509	−0.186718
$274$	18.6486	1.12660
$275$	6.08564	0.366978
$276$	−2.27032	−0.136657
$277$	21.8189	1.31097	0.655486	−	0.755207i	$-0.272464\pi$
$277$	21.8189	1.31097	0.655486	+	0.755207i	$0.272464\pi$
$278$	9.88023	0.592577
$279$	−7.64108	−0.457460
$280$	37.0909	2.21661
$281$	11.3532	0.677276	0.338638	−	0.940917i	$-0.390034\pi$
$281$	11.3532	0.677276	0.338638	+	0.940917i	$0.390034\pi$
$282$	22.4674	1.33792
$283$	27.6296	1.64241	0.821203	−	0.570636i	$-0.193303\pi$
$283$	27.6296	1.64241	0.821203	+	0.570636i	$0.193303\pi$
$284$	4.76300	0.282632
$285$	49.2141	2.91519
$286$	0.473973	0.0280266
$287$	12.1508	0.717239
$288$	4.84349	0.285406
$289$	1.00000	0.0588235
$290$	−26.6795	−1.56667
$291$	−2.62106	−0.153649
$292$	−7.97390	−0.466637
$293$	13.6011	0.794584	0.397292	−	0.917692i	$-0.369950\pi$
$293$	13.6011	0.794584	0.397292	+	0.917692i	$0.369950\pi$
$294$	63.8188	3.72199
$295$	−45.7756	−2.66516
$296$	17.7088	1.02930
$297$	3.42135	0.198527
$298$	10.3966	0.602258
$299$	−0.484958	−0.0280459
$300$	−8.29138	−0.478703
$301$	−5.07571	−0.292559
$302$	−2.32323	−0.133687
$303$	−22.7983	−1.30973
$304$	−34.5318	−1.98054
$305$	−49.9193	−2.85837
$306$	−2.21786	−0.126786
$307$	−24.0368	−1.37185	−0.685926	−	0.727671i	$-0.740603\pi$
$307$	−24.0368	−1.37185	−0.685926	+	0.727671i	$0.740603\pi$
$308$	−3.31119	−0.188672
$309$	24.8745	1.41506
$310$	−30.4253	−1.72804
$311$	32.4528	1.84023	0.920115	−	0.391648i	$-0.128095\pi$
$311$	32.4528	1.84023	0.920115	+	0.391648i	$0.128095\pi$
$312$	1.33402	0.0755238
$313$	0.741689	0.0419227	0.0209614	−	0.999780i	$-0.493327\pi$
$313$	0.741689	0.0419227	0.0209614	+	0.999780i	$0.493327\pi$
$314$	1.66561	0.0939959
$315$	23.0141	1.29670
$316$	−3.96411	−0.222999
$317$	−22.9895	−1.29122	−0.645609	−	0.763668i	$-0.723396\pi$
$317$	−22.9895	−1.29122	−0.645609	+	0.763668i	$0.723396\pi$
$318$	32.8014	1.83941
$319$	−4.92017	−0.275477
$320$	−13.2045	−0.738154
$321$	27.0590	1.51028
$322$	13.7746	0.767631
$323$	7.07744	0.393799
$324$	−7.32658	−0.407032
$325$	−1.77110	−0.0982431
$326$	−30.9941	−1.71660
$327$	−40.3998	−2.23411
$328$	−5.25410	−0.290109
$329$	−33.5275	−1.84843
$330$	−11.3248	−0.623409
$331$	8.56674	0.470870	0.235435	−	0.971890i	$-0.424348\pi$
$331$	8.56674	0.470870	0.235435	+	0.971890i	$0.424348\pi$
$332$	−0.856843	−0.0470254
$333$	10.9879	0.602135
$334$	−2.54344	−0.139171
$335$	−4.66976	−0.255136
$336$	−51.7219	−2.82166
$337$	−9.85838	−0.537020	−0.268510	−	0.963277i	$-0.586531\pi$
$337$	−9.85838	−0.537020	−0.268510	+	0.963277i	$0.586531\pi$
$338$	21.0339	1.14410
$339$	21.0290	1.14214
$340$	−2.17204	−0.117795
$341$	−5.61097	−0.303851
$342$	−15.6967	−0.848782
$343$	−59.7048	−3.22376
$344$	2.19478	0.118334
$345$	11.5873	0.623837
$346$	−15.8356	−0.851330
$347$	−32.9701	−1.76993	−0.884963	−	0.465661i	$-0.845817\pi$
$347$	−32.9701	−1.76993	−0.884963	+	0.465661i	$0.845817\pi$
$348$	6.70349	0.359345
$349$	−6.16526	−0.330019	−0.165009	−	0.986292i	$-0.552765\pi$
$349$	−6.16526	−0.330019	−0.165009	+	0.986292i	$0.552765\pi$
$350$	50.3060	2.68897
$351$	−0.995714	−0.0531473
$352$	3.55666	0.189570
$353$	9.70048	0.516304	0.258152	−	0.966104i	$-0.416886\pi$
$353$	9.70048	0.516304	0.258152	+	0.966104i	$0.416886\pi$
$354$	46.7631	2.48543
$355$	−24.3094	−1.29021
$356$	−3.11417	−0.165051
$357$	10.6006	0.561043
$358$	−5.27553	−0.278821
$359$	22.9708	1.21235	0.606176	−	0.795331i	$-0.292703\pi$
$359$	22.9708	1.21235	0.606176	+	0.795331i	$0.292703\pi$
$360$	−9.95148	−0.524489
$361$	31.0901	1.63632
$362$	−18.3737	−0.965698
$363$	−2.08850	−0.109618
$364$	0.963654	0.0505092
$365$	40.6972	2.13019
$366$	50.9962	2.66561
$367$	17.4307	0.909875	0.454938	−	0.890523i	$-0.349662\pi$
$367$	17.4307	0.909875	0.454938	+	0.890523i	$0.349662\pi$
$368$	−8.13038	−0.423825
$369$	−3.26005	−0.169712
$370$	43.7518	2.27455
$371$	−48.9485	−2.54128
$372$	7.64466	0.396357
$373$	−6.92606	−0.358618	−0.179309	−	0.983793i	$-0.557386\pi$
$373$	−6.92606	−0.358618	−0.179309	+	0.983793i	$0.557386\pi$
$374$	−1.62861	−0.0842132
$375$	7.54920	0.389839
$376$	14.4975	0.747653
$377$	1.43192	0.0737475
$378$	28.2820	1.45467
$379$	14.6675	0.753419	0.376709	−	0.926331i	$-0.377056\pi$
$379$	14.6675	0.753419	0.376709	+	0.926331i	$0.377056\pi$
$380$	−15.3725	−0.788590
$381$	−30.8669	−1.58136
$382$	−31.5720	−1.61536
$383$	−0.404206	−0.0206540	−0.0103270	−	0.999947i	$-0.503287\pi$
$383$	−0.404206	−0.0206540	−0.0103270	+	0.999947i	$0.503287\pi$
$384$	28.3455	1.44650
$385$	16.8996	0.861285
$386$	24.1731	1.23038
$387$	1.36181	0.0692248
$388$	0.818711	0.0415637
$389$	11.7715	0.596837	0.298418	−	0.954435i	$-0.403541\pi$
$389$	11.7715	0.596837	0.298418	+	0.954435i	$0.403541\pi$
$390$	3.29585	0.166892
$391$	1.66635	0.0842711
$392$	41.1803	2.07992
$393$	45.9438	2.31756
$394$	−18.8504	−0.949669
$395$	20.2320	1.01798
$396$	0.888390	0.0446433
$397$	−14.7110	−0.738325	−0.369162	−	0.929365i	$-0.620355\pi$
$397$	−14.7110	−0.738325	−0.369162	+	0.929365i	$0.620355\pi$
$398$	14.0160	0.702558
$399$	75.0251	3.75595
$400$	−29.6927	−1.48464
$401$	36.0545	1.80048	0.900238	−	0.435398i	$-0.143392\pi$
$401$	36.0545	1.80048	0.900238	+	0.435398i	$0.143392\pi$
$402$	4.77049	0.237931
$403$	1.63296	0.0813435
$404$	7.12125	0.354296
$405$	37.3934	1.85809
$406$	−40.6718	−2.01851
$407$	8.06861	0.399946
$408$	−4.58378	−0.226931
$409$	26.8478	1.32754	0.663770	−	0.747937i	$-0.268956\pi$
$409$	26.8478	1.32754	0.663770	+	0.747937i	$0.268956\pi$
$410$	−12.9809	−0.641080
$411$	23.9146	1.17962
$412$	−7.76975	−0.382788
$413$	−69.7831	−3.43380
$414$	−3.69573	−0.181635
$415$	4.37316	0.214670
$416$	−1.03509	−0.0507496
$417$	12.6702	0.620464
$418$	−11.5264	−0.563773
$419$	−7.71081	−0.376698	−0.188349	−	0.982102i	$-0.560314\pi$
$419$	−7.71081	−0.376698	−0.188349	+	0.982102i	$0.560314\pi$
$420$	−23.0249	−1.12350
$421$	21.0274	1.02481	0.512405	−	0.858744i	$-0.328755\pi$
$421$	21.0274	1.02481	0.512405	+	0.858744i	$0.328755\pi$
$422$	6.88217	0.335019
$423$	8.99541	0.437372
$424$	21.1657	1.02790
$425$	6.08564	0.295197
$426$	24.8338	1.20320
$427$	−76.1001	−3.68274
$428$	−8.45209	−0.408547
$429$	0.607814	0.0293455
$430$	5.42246	0.261494
$431$	9.31784	0.448824	0.224412	−	0.974494i	$-0.427954\pi$
$431$	9.31784	0.448824	0.224412	+	0.974494i	$0.427954\pi$
$432$	−16.6933	−0.803155
$433$	−2.56641	−0.123334	−0.0616669	−	0.998097i	$-0.519642\pi$
$433$	−2.56641	−0.123334	−0.0616669	+	0.998097i	$0.519642\pi$
$434$	−46.3822	−2.22642
$435$	−34.2133	−1.64040
$436$	12.6192	0.604350
$437$	11.7935	0.564160
$438$	−41.5751	−1.98654
$439$	3.05425	0.145772	0.0728858	−	0.997340i	$-0.476779\pi$
$439$	3.05425	0.145772	0.0728858	+	0.997340i	$0.476779\pi$
$440$	−7.30753	−0.348373
$441$	25.5515	1.21674
$442$	0.473973	0.0225446
$443$	33.9273	1.61194	0.805968	−	0.591960i	$-0.201645\pi$
$443$	33.9273	1.61194	0.805968	+	0.591960i	$0.201645\pi$
$444$	−10.9931	−0.521708
$445$	15.8941	0.753452
$446$	44.8380	2.12314
$447$	13.3324	0.630600
$448$	−20.1298	−0.951042
$449$	4.81672	0.227315	0.113657	−	0.993520i	$-0.463743\pi$
$449$	4.81672	0.227315	0.113657	+	0.993520i	$0.463743\pi$
$450$	−13.4971	−0.636258
$451$	−2.39391	−0.112725
$452$	−6.56859	−0.308960
$453$	−2.97926	−0.139978
$454$	−19.6415	−0.921823
$455$	−4.91830	−0.230573
$456$	−32.4414	−1.51921
$457$	14.9884	0.701129	0.350565	−	0.936539i	$-0.385990\pi$
$457$	14.9884	0.701129	0.350565	+	0.936539i	$0.385990\pi$
$458$	−17.1466	−0.801206
$459$	3.42135	0.159695
$460$	−3.61938	−0.168755
$461$	−27.4947	−1.28056	−0.640279	−	0.768142i	$-0.721181\pi$
$461$	−27.4947	−1.28056	−0.640279	+	0.768142i	$0.721181\pi$
$462$	−17.2642	−0.803204
$463$	−38.9588	−1.81057	−0.905284	−	0.424808i	$-0.860342\pi$
$463$	−38.9588	−1.81057	−0.905284	+	0.424808i	$0.860342\pi$
$464$	24.0063	1.11446
$465$	−39.0168	−1.80936
$466$	15.3795	0.712444
$467$	19.1118	0.884388	0.442194	−	0.896919i	$-0.354200\pi$
$467$	19.1118	0.884388	0.442194	+	0.896919i	$0.354200\pi$
$468$	−0.258548	−0.0119514
$469$	−7.11886	−0.328719
$470$	35.8179	1.65216
$471$	2.13595	0.0984193
$472$	30.1747	1.38891
$473$	1.00000	0.0459800
$474$	−20.6685	−0.949335
$475$	43.0708	1.97622
$476$	−3.31119	−0.151768
$477$	13.1329	0.601312
$478$	−34.4084	−1.57380
$479$	15.3476	0.701250	0.350625	−	0.936516i	$-0.385969\pi$
$479$	15.3476	0.701250	0.350625	+	0.936516i	$0.385969\pi$
$480$	24.7318	1.12885
$481$	−2.34821	−0.107069
$482$	−17.8431	−0.812731
$483$	17.6643	0.803755
$484$	0.652359	0.0296527
$485$	−4.17854	−0.189738
$486$	−21.4840	−0.974534
$487$	8.22456	0.372690	0.186345	−	0.982484i	$-0.440336\pi$
$487$	8.22456	0.372690	0.186345	+	0.982484i	$0.440336\pi$
$488$	32.9063	1.48960
$489$	−39.7462	−1.79739
$490$	101.741	4.59618
$491$	36.4639	1.64559	0.822797	−	0.568335i	$-0.192412\pi$
$491$	36.4639	1.64559	0.822797	+	0.568335i	$0.192412\pi$
$492$	3.26158	0.147043
$493$	−4.92017	−0.221594
$494$	3.35451	0.150927
$495$	−4.53417	−0.203796
$496$	27.3767	1.22925
$497$	−37.0588	−1.66231
$498$	−4.46750	−0.200193
$499$	−33.1026	−1.48188	−0.740938	−	0.671573i	$-0.765619\pi$
$499$	−33.1026	−1.48188	−0.740938	+	0.671573i	$0.765619\pi$
$500$	−2.35806	−0.105456
$501$	−3.26167	−0.145721
$502$	−23.6520	−1.05564
$503$	−0.683501	−0.0304758	−0.0152379	−	0.999884i	$-0.504851\pi$
$503$	−0.683501	−0.0304758	−0.0152379	+	0.999884i	$0.504851\pi$
$504$	−15.1707	−0.675755
$505$	−36.3455	−1.61735
$506$	−2.71383	−0.120645
$507$	26.9735	1.19794
$508$	9.64153	0.427774
$509$	−34.2606	−1.51857	−0.759286	−	0.650757i	$-0.774452\pi$
$509$	−34.2606	−1.51857	−0.759286	+	0.650757i	$0.774452\pi$
$510$	−11.3248	−0.501470
$511$	62.0413	2.74455
$512$	4.06383	0.179598
$513$	24.2144	1.06909
$514$	34.9788	1.54285
$515$	39.6553	1.74742
$516$	−1.36245	−0.0599785
$517$	6.60547	0.290508
$518$	66.6979	2.93054
$519$	−20.3073	−0.891393
$520$	2.12671	0.0932624
$521$	8.32135	0.364565	0.182283	−	0.983246i	$-0.441651\pi$
$521$	8.32135	0.364565	0.182283	+	0.983246i	$0.441651\pi$
$522$	10.9122	0.477616
$523$	21.8533	0.955578	0.477789	−	0.878475i	$-0.341438\pi$
$523$	21.8533	0.955578	0.477789	+	0.878475i	$0.341438\pi$
$524$	−14.3509	−0.626924
$525$	64.5115	2.81551
$526$	8.89287	0.387747
$527$	−5.61097	−0.244418
$528$	10.1901	0.443466
$529$	−20.2233	−0.879272
$530$	52.2924	2.27144
$531$	18.7228	0.812499
$532$	−23.4347	−1.01602
$533$	0.696699	0.0301774
$534$	−16.2370	−0.702642
$535$	43.1378	1.86501
$536$	3.07825	0.132960
$537$	−6.76525	−0.291942
$538$	0.144561	0.00623245
$539$	18.7629	0.808173
$540$	−7.43129	−0.319792
$541$	−43.2293	−1.85857	−0.929287	−	0.369358i	$-0.879578\pi$
$541$	−43.2293	−1.85857	−0.929287	+	0.369358i	$0.879578\pi$
$542$	26.6184	1.14336
$543$	−23.5621	−1.01114
$544$	3.55666	0.152490
$545$	−64.4059	−2.75885
$546$	5.02440	0.215024
$547$	12.9473	0.553585	0.276792	−	0.960930i	$-0.410729\pi$
$547$	12.9473	0.553585	0.276792	+	0.960930i	$0.410729\pi$
$548$	−7.46993	−0.319099
$549$	20.4176	0.871403
$550$	−9.91112	−0.422612
$551$	−34.8222	−1.48348
$552$	−7.63820	−0.325103
$553$	30.8430	1.31158
$554$	−35.5344	−1.50971
$555$	56.1065	2.38159
$556$	−3.95765	−0.167842
$557$	−45.2180	−1.91595	−0.957975	−	0.286852i	$-0.907391\pi$
$557$	−45.2180	−1.91595	−0.957975	+	0.286852i	$0.907391\pi$
$558$	12.4443	0.526810
$559$	−0.291030	−0.0123092
$560$	−82.4558	−3.48439
$561$	−2.08850	−0.0881763
$562$	−18.4899	−0.779950
$563$	28.6961	1.20940	0.604698	−	0.796455i	$-0.293294\pi$
$563$	28.6961	1.20940	0.604698	+	0.796455i	$0.293294\pi$
$564$	−8.99962	−0.378952
$565$	33.5248	1.41040
$566$	−44.9977	−1.89139
$567$	57.0048	2.39398
$568$	16.0245	0.672373
$569$	43.7394	1.83365	0.916826	−	0.399288i	$-0.130743\pi$
$569$	43.7394	1.83365	0.916826	+	0.399288i	$0.130743\pi$
$570$	−80.1505	−3.35713
$571$	−45.5937	−1.90804	−0.954019	−	0.299747i	$-0.903098\pi$
$571$	−45.5937	−1.90804	−0.954019	+	0.299747i	$0.903098\pi$
$572$	−0.189856	−0.00793827
$573$	−40.4873	−1.69138
$574$	−19.7889	−0.825971
$575$	10.1408	0.422902
$576$	5.40081	0.225034
$577$	−21.6913	−0.903020	−0.451510	−	0.892266i	$-0.649115\pi$
$577$	−21.6913	−0.903020	−0.451510	+	0.892266i	$0.649115\pi$
$578$	−1.62861	−0.0677411
$579$	30.9992	1.28828
$580$	10.6868	0.443745
$581$	6.66671	0.276582
$582$	4.26868	0.176942
$583$	9.64367	0.399400
$584$	−26.8271	−1.11011
$585$	1.31958	0.0545578
$586$	−22.1508	−0.915042
$587$	−46.4306	−1.91640	−0.958198	−	0.286106i	$-0.907639\pi$
$587$	−46.4306	−1.91640	−0.958198	+	0.286106i	$0.907639\pi$
$588$	−25.5634	−1.05422
$589$	−39.7113	−1.63628
$590$	74.5504	3.06919
$591$	−24.1734	−0.994360
$592$	−39.3679	−1.61801
$593$	7.37552	0.302876	0.151438	−	0.988467i	$-0.451610\pi$
$593$	7.37552	0.302876	0.151438	+	0.988467i	$0.451610\pi$
$594$	−5.57203	−0.228623
$595$	16.8996	0.692818
$596$	−4.16448	−0.170584
$597$	17.9738	0.735620
$598$	0.789806	0.0322976
$599$	−5.20415	−0.212636	−0.106318	−	0.994332i	$-0.533906\pi$
$599$	−5.20415	−0.212636	−0.106318	+	0.994332i	$0.533906\pi$
$600$	−27.8953	−1.13882
$601$	−3.93573	−0.160542	−0.0802709	−	0.996773i	$-0.525579\pi$
$601$	−3.93573	−0.160542	−0.0802709	+	0.996773i	$0.525579\pi$
$602$	8.26634	0.336911
$603$	1.90999	0.0777808
$604$	0.930598	0.0378655
$605$	−3.32951	−0.135364
$606$	37.1295	1.50828
$607$	10.2445	0.415813	0.207906	−	0.978149i	$-0.433335\pi$
$607$	10.2445	0.415813	0.207906	+	0.978149i	$0.433335\pi$
$608$	25.1720	1.02086
$609$	−52.1568	−2.11350
$610$	81.2989	3.29170
$611$	−1.92239	−0.0777715
$612$	0.888390	0.0359110
$613$	26.3194	1.06303	0.531515	−	0.847049i	$-0.321623\pi$
$613$	26.3194	1.06303	0.531515	+	0.847049i	$0.321623\pi$
$614$	39.1465	1.57982
$615$	−16.6465	−0.671250
$616$	−11.1401	−0.448846
$617$	−9.39245	−0.378126	−0.189063	−	0.981965i	$-0.560545\pi$
$617$	−9.39245	−0.378126	−0.189063	+	0.981965i	$0.560545\pi$
$618$	−40.5107	−1.62958
$619$	0.610849	0.0245521	0.0122761	−	0.999925i	$-0.496092\pi$
$619$	0.610849	0.0245521	0.0122761	+	0.999925i	$0.496092\pi$
$620$	12.1872	0.489451
$621$	5.70118	0.228780
$622$	−52.8529	−2.11921
$623$	24.2299	0.970752
$624$	−2.96561	−0.118720
$625$	−18.3932	−0.735726
$626$	−1.20792	−0.0482782
$627$	−14.7812	−0.590304
$628$	−0.667182	−0.0266235
$629$	8.06861	0.321717
$630$	−37.4810	−1.49328
$631$	12.2961	0.489501	0.244751	−	0.969586i	$-0.421294\pi$
$631$	12.2961	0.489501	0.244751	+	0.969586i	$0.421294\pi$
$632$	−13.3367	−0.530507
$633$	8.82557	0.350785
$634$	37.4408	1.48696
$635$	−49.2084	−1.95278
$636$	−13.1390	−0.520996
$637$	−5.46055	−0.216355
$638$	8.01303	0.317239
$639$	9.94285	0.393333
$640$	45.1888	1.78624
$641$	9.14232	0.361100	0.180550	−	0.983566i	$-0.442212\pi$
$641$	9.14232	0.361100	0.180550	+	0.983566i	$0.442212\pi$
$642$	−44.0684	−1.73924
$643$	14.0019	0.552179	0.276090	−	0.961132i	$-0.410961\pi$
$643$	14.0019	0.552179	0.276090	+	0.961132i	$0.410961\pi$
$644$	−5.51761	−0.217424
$645$	6.95367	0.273800
$646$	−11.5264	−0.453499
$647$	−26.7200	−1.05047	−0.525235	−	0.850957i	$-0.676023\pi$
$647$	−26.7200	−1.05047	−0.525235	+	0.850957i	$0.676023\pi$
$648$	−24.6493	−0.968317
$649$	13.7484	0.539673
$650$	2.88443	0.113137
$651$	−59.4796	−2.33119
$652$	12.4151	0.486212
$653$	9.86080	0.385883	0.192941	−	0.981210i	$-0.438197\pi$
$653$	9.86080	0.385883	0.192941	+	0.981210i	$0.438197\pi$
$654$	65.7953	2.57280
$655$	73.2443	2.86189
$656$	11.6802	0.456037
$657$	−16.6457	−0.649409
$658$	54.6030	2.12865
$659$	−27.6231	−1.07604	−0.538022	−	0.842931i	$-0.680828\pi$
$659$	−27.6231	−1.07604	−0.538022	+	0.842931i	$0.680828\pi$
$660$	4.53629	0.176575
$661$	−14.3226	−0.557086	−0.278543	−	0.960424i	$-0.589852\pi$
$661$	−14.3226	−0.557086	−0.278543	+	0.960424i	$0.589852\pi$
$662$	−13.9518	−0.542254
$663$	0.607814	0.0236055
$664$	−2.88274	−0.111872
$665$	119.606	4.63813
$666$	−17.8950	−0.693418
$667$	−8.19875	−0.317457
$668$	1.01881	0.0394189
$669$	57.4994	2.22305
$670$	7.60520	0.293814
$671$	14.9930	0.578798
$672$	37.7027	1.45441
$673$	−38.2857	−1.47581	−0.737903	−	0.674907i	$-0.764184\pi$
$673$	−38.2857	−1.47581	−0.737903	+	0.674907i	$0.764184\pi$
$674$	16.0554	0.618432
$675$	20.8211	0.801405
$676$	−8.42542	−0.324054
$677$	25.7670	0.990307	0.495154	−	0.868806i	$-0.335112\pi$
$677$	25.7670	0.990307	0.495154	+	0.868806i	$0.335112\pi$
$678$	−34.2480	−1.31529
$679$	−6.37002	−0.244459
$680$	−7.30753	−0.280231
$681$	−25.1880	−0.965205
$682$	9.13806	0.349914
$683$	22.4740	0.859944	0.429972	−	0.902842i	$-0.358523\pi$
$683$	22.4740	0.859944	0.429972	+	0.902842i	$0.358523\pi$
$684$	6.28753	0.240410
$685$	38.1250	1.45668
$686$	97.2357	3.71248
$687$	−21.9884	−0.838911
$688$	−4.87915	−0.186016
$689$	−2.80659	−0.106923
$690$	−18.8711	−0.718410
$691$	10.1459	0.385970	0.192985	−	0.981202i	$-0.438183\pi$
$691$	10.1459	0.385970	0.192985	+	0.981202i	$0.438183\pi$
$692$	6.34317	0.241131
$693$	−6.91216	−0.262571
$694$	53.6953	2.03824
$695$	20.1991	0.766194
$696$	22.5530	0.854869
$697$	−2.39391	−0.0906758
$698$	10.0408	0.380049
$699$	19.7224	0.745971
$700$	−20.1507	−0.761625
$701$	38.8986	1.46918	0.734589	−	0.678512i	$-0.237375\pi$
$701$	38.8986	1.46918	0.734589	+	0.678512i	$0.237375\pi$
$702$	1.62163	0.0612043
$703$	57.1051	2.15376
$704$	3.96590	0.149470
$705$	45.9322	1.72991
$706$	−15.7983	−0.594576
$707$	−55.4073	−2.08380
$708$	−18.7315	−0.703974
$709$	−39.1055	−1.46864	−0.734318	−	0.678805i	$-0.762498\pi$
$709$	−39.1055	−1.46864	−0.734318	+	0.678805i	$0.762498\pi$
$710$	39.5905	1.48580
$711$	−8.27515	−0.310342
$712$	−10.4772	−0.392650
$713$	−9.34986	−0.350155
$714$	−17.2642	−0.646097
$715$	0.968986	0.0362380
$716$	2.11318	0.0789733
$717$	−44.1247	−1.64787
$718$	−37.4104	−1.39614
$719$	34.7211	1.29488	0.647439	−	0.762117i	$-0.275840\pi$
$719$	34.7211	1.29488	0.647439	+	0.762117i	$0.275840\pi$
$720$	22.1229	0.824470
$721$	60.4529	2.25138
$722$	−50.6336	−1.88439
$723$	−22.8817	−0.850978
$724$	7.35981	0.273525
$725$	−29.9424	−1.11203
$726$	3.40134	0.126235
$727$	7.13207	0.264514	0.132257	−	0.991215i	$-0.457778\pi$
$727$	7.13207	0.264514	0.132257	+	0.991215i	$0.457778\pi$
$728$	3.24209	0.120160
$729$	6.14203	0.227483
$730$	−66.2797	−2.45312
$731$	1.00000	0.0369863
$732$	−20.4272	−0.755010
$733$	−36.6739	−1.35458	−0.677291	−	0.735716i	$-0.736846\pi$
$733$	−36.6739	−1.35458	−0.677291	+	0.735716i	$0.736846\pi$
$734$	−28.3878	−1.04781
$735$	130.471	4.81248
$736$	5.92664	0.218459
$737$	1.40254	0.0516630
$738$	5.30935	0.195440
$739$	−1.61499	−0.0594084	−0.0297042	−	0.999559i	$-0.509457\pi$
$739$	−1.61499	−0.0594084	−0.0297042	+	0.999559i	$0.509457\pi$
$740$	−17.5253	−0.644244
$741$	4.30177	0.158029
$742$	79.7178	2.92653
$743$	−3.21151	−0.117819	−0.0589094	−	0.998263i	$-0.518762\pi$
$743$	−3.21151	−0.117819	−0.0589094	+	0.998263i	$0.518762\pi$
$744$	25.7195	0.942921
$745$	21.2547	0.778712
$746$	11.2798	0.412984
$747$	−1.78868	−0.0654442
$748$	0.652359	0.0238526
$749$	65.7619	2.40289
$750$	−12.2947	−0.448938
$751$	31.7034	1.15687	0.578436	−	0.815728i	$-0.303663\pi$
$751$	31.7034	1.15687	0.578436	+	0.815728i	$0.303663\pi$
$752$	−32.2291	−1.17527
$753$	−30.3308	−1.10532
$754$	−2.33203	−0.0849275
$755$	−4.74958	−0.172855
$756$	−11.3287	−0.412022
$757$	−17.5773	−0.638857	−0.319429	−	0.947610i	$-0.603491\pi$
$757$	−17.5773	−0.638857	−0.319429	+	0.947610i	$0.603491\pi$
$758$	−23.8876	−0.867636
$759$	−3.48017	−0.126322
$760$	−51.7186	−1.87603
$761$	−18.6364	−0.675569	−0.337784	−	0.941223i	$-0.609677\pi$
$761$	−18.6364	−0.675569	−0.337784	+	0.941223i	$0.609677\pi$
$762$	50.2700	1.82109
$763$	−98.1843	−3.55451
$764$	12.6466	0.457537
$765$	−4.53417	−0.163933
$766$	0.658293	0.0237851
$767$	−4.00120	−0.144475
$768$	−29.5981	−1.06803
$769$	4.64011	0.167327	0.0836633	−	0.996494i	$-0.473338\pi$
$769$	4.64011	0.167327	0.0836633	+	0.996494i	$0.473338\pi$
$770$	−27.5229	−0.991855
$771$	44.8562	1.61546
$772$	−9.68286	−0.348494
$773$	−18.9078	−0.680068	−0.340034	−	0.940413i	$-0.610439\pi$
$773$	−18.9078	−0.680068	−0.340034	+	0.940413i	$0.610439\pi$
$774$	−2.21786	−0.0797192
$775$	−34.1464	−1.22657
$776$	2.75445	0.0988788
$777$	85.5321	3.06845
$778$	−19.1711	−0.687316
$779$	−16.9427	−0.607037
$780$	−1.32019	−0.0472705
$781$	7.30119	0.261257
$782$	−2.71383	−0.0970465
$783$	−16.8336	−0.601585
$784$	−91.5467	−3.26952
$785$	3.40516	0.121535
$786$	−74.8244	−2.66890
$787$	30.0731	1.07199	0.535994	−	0.844222i	$-0.319937\pi$
$787$	30.0731	1.07199	0.535994	+	0.844222i	$0.319937\pi$
$788$	7.55076	0.268985
$789$	11.4041	0.405995
$790$	−32.9500	−1.17231
$791$	51.1072	1.81716
$792$	2.98887	0.106205
$793$	−4.36340	−0.154949
$794$	23.9585	0.850254
$795$	67.0589	2.37833
$796$	−5.61428	−0.198993
$797$	31.1217	1.10239	0.551194	−	0.834377i	$-0.314172\pi$
$797$	31.1217	1.10239	0.551194	+	0.834377i	$0.314172\pi$
$798$	−122.186	−4.32535
$799$	6.60547	0.233685
$800$	21.6445	0.765250
$801$	−6.50088	−0.229697
$802$	−58.7186	−2.07343
$803$	−12.2232	−0.431347
$804$	−1.91088	−0.0673916
$805$	28.1608	0.992537
$806$	−2.65945	−0.0936750
$807$	0.185382	0.00652575
$808$	23.9585	0.842858
$809$	25.7767	0.906262	0.453131	−	0.891444i	$-0.350307\pi$
$809$	25.7767	0.906262	0.453131	+	0.891444i	$0.350307\pi$
$810$	−60.8992	−2.13978
$811$	13.1142	0.460501	0.230250	−	0.973131i	$-0.426046\pi$
$811$	13.1142	0.460501	0.230250	+	0.973131i	$0.426046\pi$
$812$	16.2916	0.571724
$813$	34.1349	1.19716
$814$	−13.1406	−0.460578
$815$	−63.3640	−2.21955
$816$	10.1901	0.356724
$817$	7.07744	0.247608
$818$	−43.7245	−1.52879
$819$	2.01164	0.0702926
$820$	5.19966	0.181580
$821$	20.0522	0.699828	0.349914	−	0.936782i	$-0.386211\pi$
$821$	20.0522	0.699828	0.349914	+	0.936782i	$0.386211\pi$
$822$	−38.9475	−1.35845
$823$	13.8477	0.482702	0.241351	−	0.970438i	$-0.422410\pi$
$823$	13.8477	0.482702	0.241351	+	0.970438i	$0.422410\pi$
$824$	−26.1403	−0.910641
$825$	−12.7098	−0.442500
$826$	113.649	3.95436
$827$	−32.5826	−1.13301	−0.566503	−	0.824059i	$-0.691704\pi$
$827$	−32.5826	−1.13301	−0.566503	+	0.824059i	$0.691704\pi$
$828$	1.48037	0.0514465
$829$	−20.0534	−0.696482	−0.348241	−	0.937405i	$-0.613221\pi$
$829$	−20.0534	−0.696482	−0.348241	+	0.937405i	$0.613221\pi$
$830$	−7.12215	−0.247214
$831$	−45.5687	−1.58076
$832$	−1.15419	−0.0400145
$833$	18.7629	0.650094
$834$	−20.6348	−0.714525
$835$	−5.19980	−0.179946
$836$	4.61703	0.159683
$837$	−19.1971	−0.663548
$838$	12.5579	0.433805
$839$	−8.47812	−0.292697	−0.146349	−	0.989233i	$-0.546752\pi$
$839$	−8.47812	−0.292697	−0.146349	+	0.989233i	$0.546752\pi$
$840$	−77.4642	−2.67277
$841$	−4.79188	−0.165237
$842$	−34.2453	−1.18017
$843$	−23.7111	−0.816654
$844$	−2.75674	−0.0948910
$845$	43.0016	1.47930
$846$	−14.6500	−0.503677
$847$	−5.07571	−0.174404
$848$	−47.0529	−1.61580
$849$	−57.7042	−1.98040
$850$	−9.91112	−0.339949
$851$	13.4452	0.460894
$852$	−9.94750	−0.340796
$853$	−47.7144	−1.63371	−0.816855	−	0.576842i	$-0.804285\pi$
$853$	−47.7144	−1.63371	−0.816855	+	0.576842i	$0.804285\pi$
$854$	123.937	4.24104
$855$	−32.0903	−1.09746
$856$	−28.4360	−0.971921
$857$	−24.3088	−0.830373	−0.415186	−	0.909736i	$-0.636284\pi$
$857$	−24.3088	−0.830373	−0.415186	+	0.909736i	$0.636284\pi$
$858$	−0.989890	−0.0337943
$859$	9.53462	0.325317	0.162658	−	0.986682i	$-0.447993\pi$
$859$	9.53462	0.325317	0.162658	+	0.986682i	$0.447993\pi$
$860$	−2.17204	−0.0740658
$861$	−25.3769	−0.864842
$862$	−15.1751	−0.516866
$863$	29.5973	1.00750	0.503752	−	0.863848i	$-0.331953\pi$
$863$	29.5973	1.00750	0.503752	+	0.863848i	$0.331953\pi$
$864$	12.1686	0.413983
$865$	−32.3743	−1.10076
$866$	4.17968	0.142031
$867$	−2.08850	−0.0709290
$868$	18.5790	0.630611
$869$	−6.07658	−0.206134
$870$	55.7199	1.88908
$871$	−0.408179	−0.0138306
$872$	42.4557	1.43773
$873$	1.70907	0.0578434
$874$	−19.2070	−0.649686
$875$	18.3470	0.620241
$876$	16.6535	0.562668
$877$	−38.0420	−1.28459	−0.642294	−	0.766459i	$-0.722017\pi$
$877$	−38.0420	−1.28459	−0.642294	+	0.766459i	$0.722017\pi$
$878$	−4.97418	−0.167870
$879$	−28.4058	−0.958104
$880$	16.2452	0.547625
$881$	−33.7151	−1.13589	−0.567946	−	0.823066i	$-0.692262\pi$
$881$	−33.7151	−1.13589	−0.567946	+	0.823066i	$0.692262\pi$
$882$	−41.6133	−1.40119
$883$	−21.0002	−0.706711	−0.353356	−	0.935489i	$-0.614959\pi$
$883$	−21.0002	−0.706711	−0.353356	+	0.935489i	$0.614959\pi$
$884$	−0.189856	−0.00638554
$885$	95.6020	3.21363
$886$	−55.2542	−1.85630
$887$	34.0722	1.14403	0.572016	−	0.820243i	$-0.306162\pi$
$887$	34.0722	1.14403	0.572016	+	0.820243i	$0.306162\pi$
$888$	−36.9848	−1.24113
$889$	−75.0164	−2.51597
$890$	−25.8852	−0.867674
$891$	−11.2309	−0.376249
$892$	−17.9604	−0.601359
$893$	46.7498	1.56442
$894$	−21.7132	−0.726198
$895$	−10.7853	−0.360512
$896$	68.8886	2.30141
$897$	1.01283	0.0338175
$898$	−7.84454	−0.261776
$899$	27.6070	0.920743
$900$	5.40643	0.180214
$901$	9.64367	0.321277
$902$	3.89874	0.129814
$903$	10.6006	0.352766
$904$	−22.0991	−0.735007
$905$	−37.5630	−1.24864
$906$	4.85205	0.161198
$907$	29.4640	0.978337	0.489168	−	0.872189i	$-0.337300\pi$
$907$	29.4640	0.978337	0.489168	+	0.872189i	$0.337300\pi$
$908$	7.86767	0.261098
$909$	14.8657	0.493066
$910$	8.00997	0.265528
$911$	3.26857	0.108293	0.0541463	−	0.998533i	$-0.482756\pi$
$911$	3.26857	0.108293	0.0541463	+	0.998533i	$0.482756\pi$
$912$	72.1196	2.38812
$913$	−1.31345	−0.0434690
$914$	−24.4103	−0.807420
$915$	104.256	3.44661
$916$	6.86828	0.226934
$917$	111.658	3.68728
$918$	−5.57203	−0.183904
$919$	−0.643250	−0.0212189	−0.0106094	−	0.999944i	$-0.503377\pi$
$919$	−0.643250	−0.0212189	−0.0106094	+	0.999944i	$0.503377\pi$
$920$	−12.1769	−0.401462
$921$	50.2007	1.65417
$922$	44.7781	1.47469
$923$	−2.12486	−0.0699408
$924$	6.91540	0.227500
$925$	49.1027	1.61449
$926$	63.4485	2.08505
$927$	−16.2195	−0.532718
$928$	−17.4994	−0.574445
$929$	15.5564	0.510390	0.255195	−	0.966890i	$-0.417860\pi$
$929$	15.5564	0.510390	0.255195	+	0.966890i	$0.417860\pi$
$930$	63.5430	2.08366
$931$	132.793	4.35211
$932$	−6.16047	−0.201793
$933$	−67.7775	−2.21894
$934$	−31.1256	−1.01846
$935$	−3.32951	−0.108887
$936$	−0.869851	−0.0284320
$937$	−52.4852	−1.71462	−0.857309	−	0.514802i	$-0.827865\pi$
$937$	−52.4852	−1.71462	−0.857309	+	0.514802i	$0.827865\pi$
$938$	11.5938	0.378552
$939$	−1.54901	−0.0505501
$940$	−14.3473	−0.467958
$941$	−16.1525	−0.526556	−0.263278	−	0.964720i	$-0.584804\pi$
$941$	−16.1525	−0.526556	−0.263278	+	0.964720i	$0.584804\pi$
$942$	−3.47862	−0.113340
$943$	−3.98910	−0.129903
$944$	−67.0806	−2.18329
$945$	57.8195	1.88087
$946$	−1.62861	−0.0529506
$947$	−12.8320	−0.416984	−0.208492	−	0.978024i	$-0.566855\pi$
$947$	−12.8320	−0.416984	−0.208492	+	0.978024i	$0.566855\pi$
$948$	8.27902	0.268890
$949$	3.55731	0.115475
$950$	−70.1453	−2.27581
$951$	48.0134	1.55694
$952$	−11.1401	−0.361051
$953$	−21.9532	−0.711133	−0.355566	−	0.934651i	$-0.615712\pi$
$953$	−21.9532	−0.711133	−0.355566	+	0.934651i	$0.615712\pi$
$954$	−21.3883	−0.692471
$955$	−64.5455	−2.08864
$956$	13.7827	0.445765
$957$	10.2758	0.332168
$958$	−24.9952	−0.807558
$959$	58.1201	1.87680
$960$	27.5775	0.890062
$961$	0.482983	0.0155801
$962$	3.82430	0.123301
$963$	−17.6439	−0.568567
$964$	7.14728	0.230198
$965$	49.4194	1.59087
$966$	−28.7683	−0.925604
$967$	−14.4592	−0.464977	−0.232488	−	0.972599i	$-0.574687\pi$
$967$	−14.4592	−0.464977	−0.232488	+	0.972599i	$0.574687\pi$
$968$	2.19478	0.0705428
$969$	−14.7812	−0.474840
$970$	6.80519	0.218502
$971$	−37.1369	−1.19178	−0.595890	−	0.803066i	$-0.703201\pi$
$971$	−37.1369	−1.19178	−0.595890	+	0.803066i	$0.703201\pi$
$972$	8.60569	0.276028
$973$	30.7927	0.987169
$974$	−13.3946	−0.429190
$975$	3.69894	0.118461
$976$	−73.1530	−2.34157
$977$	−40.3189	−1.28992	−0.644958	−	0.764218i	$-0.723125\pi$
$977$	−40.3189	−1.28992	−0.644958	+	0.764218i	$0.723125\pi$
$978$	64.7310	2.06987
$979$	−4.77370	−0.152568
$980$	−40.7536	−1.30183
$981$	26.3428	0.841062
$982$	−59.3854	−1.89506
$983$	28.5515	0.910651	0.455326	−	0.890325i	$-0.349523\pi$
$983$	28.5515	0.910651	0.455326	+	0.890325i	$0.349523\pi$
$984$	10.9732	0.349812
$985$	−38.5376	−1.22791
$986$	8.01303	0.255187
$987$	70.0219	2.22882
$988$	−1.34369	−0.0427486
$989$	1.66635	0.0529870
$990$	7.38437	0.234691
$991$	28.5652	0.907405	0.453702	−	0.891153i	$-0.350103\pi$
$991$	28.5652	0.907405	0.453702	+	0.891153i	$0.350103\pi$
$992$	−19.9563	−0.633613
$993$	−17.8916	−0.567772
$994$	60.3541	1.91432
$995$	28.6542	0.908398
$996$	1.78951	0.0567029
$997$	4.98477	0.157869	0.0789346	−	0.996880i	$-0.474848\pi$
$997$	4.98477	0.157869	0.0789346	+	0.996880i	$0.474848\pi$
$998$	53.9111	1.70653
$999$	27.6055	0.873401

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8041.2.a.j.1.20	✓	82

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8041.2.a.j.1.20	✓	82	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)

\(f(q)\)	\(=\)	\(q-1.62861 q^{2} -2.08850 q^{3} +0.652359 q^{4} -3.32951 q^{5} +3.40134 q^{6} -5.07571 q^{7} +2.19478 q^{8} +1.36181 q^{9} +O(q^{10})\)	\(q-1.62861 q^{2} -2.08850 q^{3} +0.652359 q^{4} -3.32951 q^{5} +3.40134 q^{6} -5.07571 q^{7} +2.19478 q^{8} +1.36181 q^{9} +5.42246 q^{10} +1.00000 q^{11} -1.36245 q^{12} -0.291030 q^{13} +8.26634 q^{14} +6.95367 q^{15} -4.87915 q^{16} +1.00000 q^{17} -2.21786 q^{18} +7.07744 q^{19} -2.17204 q^{20} +10.6006 q^{21} -1.62861 q^{22} +1.66635 q^{23} -4.58378 q^{24} +6.08564 q^{25} +0.473973 q^{26} +3.42135 q^{27} -3.31119 q^{28} -4.92017 q^{29} -11.3248 q^{30} -5.61097 q^{31} +3.55666 q^{32} -2.08850 q^{33} -1.62861 q^{34} +16.8996 q^{35} +0.888390 q^{36} +8.06861 q^{37} -11.5264 q^{38} +0.607814 q^{39} -7.30753 q^{40} -2.39391 q^{41} -17.2642 q^{42} +1.00000 q^{43} +0.652359 q^{44} -4.53417 q^{45} -2.71383 q^{46} +6.60547 q^{47} +10.1901 q^{48} +18.7629 q^{49} -9.91112 q^{50} -2.08850 q^{51} -0.189856 q^{52} +9.64367 q^{53} -5.57203 q^{54} -3.32951 q^{55} -11.1401 q^{56} -14.7812 q^{57} +8.01303 q^{58} +13.7484 q^{59} +4.53629 q^{60} +14.9930 q^{61} +9.13806 q^{62} -6.91216 q^{63} +3.96590 q^{64} +0.968986 q^{65} +3.40134 q^{66} +1.40254 q^{67} +0.652359 q^{68} -3.48017 q^{69} -27.5229 q^{70} +7.30119 q^{71} +2.98887 q^{72} -12.2232 q^{73} -13.1406 q^{74} -12.7098 q^{75} +4.61703 q^{76} -5.07571 q^{77} -0.989890 q^{78} -6.07658 q^{79} +16.2452 q^{80} -11.2309 q^{81} +3.89874 q^{82} -1.31345 q^{83} +6.91540 q^{84} -3.32951 q^{85} -1.62861 q^{86} +10.2758 q^{87} +2.19478 q^{88} -4.77370 q^{89} +7.38437 q^{90} +1.47718 q^{91} +1.08706 q^{92} +11.7185 q^{93} -10.7577 q^{94} -23.5644 q^{95} -7.42806 q^{96} +1.25500 q^{97} -30.5573 q^{98} +1.36181 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 82 q + 8 q^{2} + 6 q^{3} + 98 q^{4} + 11 q^{5} + 10 q^{6} + 8 q^{7} + 30 q^{8} + 108 q^{9}+O(q^{10}) \) 82 * q + 8 * q^2 + 6 * q^3 + 98 * q^4 + 11 * q^5 + 10 * q^6 + 8 * q^7 + 30 * q^8 + 108 * q^9	\( 82 q + 8 q^{2} + 6 q^{3} + 98 q^{4} + 11 q^{5} + 10 q^{6} + 8 q^{7} + 30 q^{8} + 108 q^{9} + q^{10} + 82 q^{11} + 3 q^{12} + 26 q^{13} + 17 q^{14} + 66 q^{15} + 122 q^{16} + 82 q^{17} + 18 q^{18} + 12 q^{19} + 9 q^{20} + 22 q^{21} + 8 q^{22} + 50 q^{23} + 15 q^{24} + 117 q^{25} + 36 q^{26} + 30 q^{27} + 11 q^{28} + 33 q^{29} - 26 q^{30} + 40 q^{31} + 58 q^{32} + 6 q^{33} + 8 q^{34} + 16 q^{35} + 160 q^{36} + 31 q^{37} + 18 q^{38} + 41 q^{39} - 29 q^{40} + 42 q^{41} - 51 q^{42} + 82 q^{43} + 98 q^{44} - 2 q^{45} - 19 q^{46} + 84 q^{47} - 46 q^{48} + 136 q^{49} + 59 q^{50} + 6 q^{51} + 45 q^{52} + 83 q^{53} + 24 q^{54} + 11 q^{55} + 21 q^{56} + 23 q^{57} + 14 q^{58} + 96 q^{59} + 184 q^{60} - 6 q^{61} - 23 q^{62} + 8 q^{63} + 148 q^{64} + 5 q^{65} + 10 q^{66} + 78 q^{67} + 98 q^{68} + 61 q^{69} - 3 q^{70} + 155 q^{71} + 50 q^{72} - 23 q^{73} + 10 q^{74} - 19 q^{75} + 44 q^{76} + 8 q^{77} - 27 q^{78} + 31 q^{79} + 19 q^{80} + 150 q^{81} - 12 q^{82} + 54 q^{83} + 8 q^{84} + 11 q^{85} + 8 q^{86} + 20 q^{87} + 30 q^{88} + 25 q^{89} - 81 q^{90} - 14 q^{91} + 60 q^{92} + 36 q^{93} + 19 q^{94} + 111 q^{95} - 6 q^{96} + 2 q^{97} - 5 q^{98} + 108 q^{99}+O(q^{100}) \) 82 * q + 8 * q^2 + 6 * q^3 + 98 * q^4 + 11 * q^5 + 10 * q^6 + 8 * q^7 + 30 * q^8 + 108 * q^9 + q^10 + 82 * q^11 + 3 * q^12 + 26 * q^13 + 17 * q^14 + 66 * q^15 + 122 * q^16 + 82 * q^17 + 18 * q^18 + 12 * q^19 + 9 * q^20 + 22 * q^21 + 8 * q^22 + 50 * q^23 + 15 * q^24 + 117 * q^25 + 36 * q^26 + 30 * q^27 + 11 * q^28 + 33 * q^29 - 26 * q^30 + 40 * q^31 + 58 * q^32 + 6 * q^33 + 8 * q^34 + 16 * q^35 + 160 * q^36 + 31 * q^37 + 18 * q^38 + 41 * q^39 - 29 * q^40 + 42 * q^41 - 51 * q^42 + 82 * q^43 + 98 * q^44 - 2 * q^45 - 19 * q^46 + 84 * q^47 - 46 * q^48 + 136 * q^49 + 59 * q^50 + 6 * q^51 + 45 * q^52 + 83 * q^53 + 24 * q^54 + 11 * q^55 + 21 * q^56 + 23 * q^57 + 14 * q^58 + 96 * q^59 + 184 * q^60 - 6 * q^61 - 23 * q^62 + 8 * q^63 + 148 * q^64 + 5 * q^65 + 10 * q^66 + 78 * q^67 + 98 * q^68 + 61 * q^69 - 3 * q^70 + 155 * q^71 + 50 * q^72 - 23 * q^73 + 10 * q^74 - 19 * q^75 + 44 * q^76 + 8 * q^77 - 27 * q^78 + 31 * q^79 + 19 * q^80 + 150 * q^81 - 12 * q^82 + 54 * q^83 + 8 * q^84 + 11 * q^85 + 8 * q^86 + 20 * q^87 + 30 * q^88 + 25 * q^89 - 81 * q^90 - 14 * q^91 + 60 * q^92 + 36 * q^93 + 19 * q^94 + 111 * q^95 - 6 * q^96 + 2 * q^97 - 5 * q^98 + 108 * q^99

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