LMFDB - Embedded newform 8041.2.a.h.1.3

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:	$1$
Dimension:	$74$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Character	$\chi$	$=$	8041.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.72314 q^{2} +3.10551 q^{3} +5.41549 q^{4} -3.61264 q^{5} -8.45674 q^{6} -4.38477 q^{7} -9.30085 q^{8} +6.64419 q^{9} +O(q^{10})$	\(q-2.72314 q^{2} +3.10551 q^{3} +5.41549 q^{4} -3.61264 q^{5} -8.45674 q^{6} -4.38477 q^{7} -9.30085 q^{8} +6.64419 q^{9} +9.83772 q^{10} -1.00000 q^{11} +16.8179 q^{12} +2.27156 q^{13} +11.9403 q^{14} -11.2191 q^{15} +14.4965 q^{16} -1.00000 q^{17} -18.0931 q^{18} +4.60946 q^{19} -19.5642 q^{20} -13.6169 q^{21} +2.72314 q^{22} +2.86541 q^{23} -28.8839 q^{24} +8.05116 q^{25} -6.18577 q^{26} +11.3171 q^{27} -23.7456 q^{28} -4.20834 q^{29} +30.5511 q^{30} -6.52550 q^{31} -20.8744 q^{32} -3.10551 q^{33} +2.72314 q^{34} +15.8406 q^{35} +35.9815 q^{36} -2.77855 q^{37} -12.5522 q^{38} +7.05435 q^{39} +33.6006 q^{40} -0.370177 q^{41} +37.0808 q^{42} -1.00000 q^{43} -5.41549 q^{44} -24.0031 q^{45} -7.80292 q^{46} +9.19629 q^{47} +45.0191 q^{48} +12.2262 q^{49} -21.9244 q^{50} -3.10551 q^{51} +12.3016 q^{52} +7.33670 q^{53} -30.8180 q^{54} +3.61264 q^{55} +40.7820 q^{56} +14.3147 q^{57} +11.4599 q^{58} -12.3607 q^{59} -60.7568 q^{60} +2.29319 q^{61} +17.7699 q^{62} -29.1332 q^{63} +27.8508 q^{64} -8.20632 q^{65} +8.45674 q^{66} +13.7736 q^{67} -5.41549 q^{68} +8.89857 q^{69} -43.1361 q^{70} -9.92454 q^{71} -61.7966 q^{72} -8.37295 q^{73} +7.56639 q^{74} +25.0030 q^{75} +24.9625 q^{76} +4.38477 q^{77} -19.2100 q^{78} -1.86134 q^{79} -52.3708 q^{80} +15.2127 q^{81} +1.00804 q^{82} -6.00373 q^{83} -73.7423 q^{84} +3.61264 q^{85} +2.72314 q^{86} -13.0690 q^{87} +9.30085 q^{88} +11.2735 q^{89} +65.3637 q^{90} -9.96025 q^{91} +15.5176 q^{92} -20.2650 q^{93} -25.0428 q^{94} -16.6523 q^{95} -64.8256 q^{96} +4.42008 q^{97} -33.2936 q^{98} -6.64419 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 74 q - 7 q^{2} - 3 q^{3} + 79 q^{4} - 6 q^{5} - 12 q^{6} - 16 q^{7} - 21 q^{8} + 75 q^{9}+O(q^{10}) $ 74 * q - 7 * q^2 - 3 * q^3 + 79 * q^4 - 6 * q^5 - 12 * q^6 - 16 * q^7 - 21 * q^8 + 75 * q^9	\( 74 q - 7 q^{2} - 3 q^{3} + 79 q^{4} - 6 q^{5} - 12 q^{6} - 16 q^{7} - 21 q^{8} + 75 q^{9} - 9 q^{10} - 74 q^{11} - 3 q^{12} + 4 q^{13} - 5 q^{14} - 17 q^{15} + 85 q^{16} - 74 q^{17} - 23 q^{18} - 21 q^{20} - 22 q^{21} + 7 q^{22} - 23 q^{23} - 51 q^{24} + 90 q^{25} - 46 q^{26} - 27 q^{27} - 61 q^{28} - 63 q^{29} - 22 q^{30} - 31 q^{31} - 69 q^{32} + 3 q^{33} + 7 q^{34} - 20 q^{35} + 51 q^{36} + 8 q^{37} - 2 q^{38} - 77 q^{39} - 37 q^{40} - 64 q^{41} + 13 q^{42} - 74 q^{43} - 79 q^{44} - 12 q^{45} - 53 q^{46} - 32 q^{47} + 2 q^{48} + 78 q^{49} - 104 q^{50} + 3 q^{51} + 13 q^{52} + 25 q^{53} - 110 q^{54} + 6 q^{55} - 29 q^{56} - 29 q^{57} - 14 q^{58} - 61 q^{59} - 82 q^{60} - 36 q^{61} - 63 q^{62} - 104 q^{63} + 107 q^{64} - 65 q^{65} + 12 q^{66} + 33 q^{67} - 79 q^{68} - 34 q^{69} - 3 q^{70} - 168 q^{71} - 67 q^{72} - 47 q^{73} - 54 q^{74} - 53 q^{75} - 4 q^{76} + 16 q^{77} - 3 q^{78} - 79 q^{79} - 59 q^{80} + 70 q^{81} - 18 q^{82} - 36 q^{83} - 118 q^{84} + 6 q^{85} + 7 q^{86} - 24 q^{87} + 21 q^{88} - 24 q^{89} + 25 q^{90} - 14 q^{91} - 18 q^{92} - 13 q^{93} + 9 q^{94} - 155 q^{95} - 50 q^{96} + q^{97} - 60 q^{98} - 75 q^{99}+O(q^{100}) \) 74 * q - 7 * q^2 - 3 * q^3 + 79 * q^4 - 6 * q^5 - 12 * q^6 - 16 * q^7 - 21 * q^8 + 75 * q^9 - 9 * q^10 - 74 * q^11 - 3 * q^12 + 4 * q^13 - 5 * q^14 - 17 * q^15 + 85 * q^16 - 74 * q^17 - 23 * q^18 - 21 * q^20 - 22 * q^21 + 7 * q^22 - 23 * q^23 - 51 * q^24 + 90 * q^25 - 46 * q^26 - 27 * q^27 - 61 * q^28 - 63 * q^29 - 22 * q^30 - 31 * q^31 - 69 * q^32 + 3 * q^33 + 7 * q^34 - 20 * q^35 + 51 * q^36 + 8 * q^37 - 2 * q^38 - 77 * q^39 - 37 * q^40 - 64 * q^41 + 13 * q^42 - 74 * q^43 - 79 * q^44 - 12 * q^45 - 53 * q^46 - 32 * q^47 + 2 * q^48 + 78 * q^49 - 104 * q^50 + 3 * q^51 + 13 * q^52 + 25 * q^53 - 110 * q^54 + 6 * q^55 - 29 * q^56 - 29 * q^57 - 14 * q^58 - 61 * q^59 - 82 * q^60 - 36 * q^61 - 63 * q^62 - 104 * q^63 + 107 * q^64 - 65 * q^65 + 12 * q^66 + 33 * q^67 - 79 * q^68 - 34 * q^69 - 3 * q^70 - 168 * q^71 - 67 * q^72 - 47 * q^73 - 54 * q^74 - 53 * q^75 - 4 * q^76 + 16 * q^77 - 3 * q^78 - 79 * q^79 - 59 * q^80 + 70 * q^81 - 18 * q^82 - 36 * q^83 - 118 * q^84 + 6 * q^85 + 7 * q^86 - 24 * q^87 + 21 * q^88 - 24 * q^89 + 25 * q^90 - 14 * q^91 - 18 * q^92 - 13 * q^93 + 9 * q^94 - 155 * q^95 - 50 * q^96 + q^97 - 60 * q^98 - 75 * 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 $

$2$	−2.72314	−1.92555	−0.962775	−	0.270304i	$-0.912876\pi$
$2$	−2.72314	−1.92555	−0.962775	+	0.270304i	$0.912876\pi$
$3$	3.10551	1.79297	0.896483	−	0.443077i	$-0.146113\pi$
$3$	3.10551	1.79297	0.896483	+	0.443077i	$0.146113\pi$
$4$	5.41549	2.70774
$5$	−3.61264	−1.61562	−0.807811	−	0.589442i	$-0.799348\pi$
$5$	−3.61264	−1.61562	−0.807811	+	0.589442i	$0.799348\pi$
$6$	−8.45674	−3.45245
$7$	−4.38477	−1.65729	−0.828643	−	0.559778i	$-0.810887\pi$
$7$	−4.38477	−1.65729	−0.828643	+	0.559778i	$0.810887\pi$
$8$	−9.30085	−3.28835
$9$	6.64419	2.21473
$10$	9.83772	3.11096
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	16.8179	4.85490
$13$	2.27156	0.630017	0.315009	−	0.949089i	$-0.397993\pi$
$13$	2.27156	0.630017	0.315009	+	0.949089i	$0.397993\pi$
$14$	11.9403	3.19119
$15$	−11.2191	−2.89676
$16$	14.4965	3.62413
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−18.0931	−4.26457
$19$	4.60946	1.05748	0.528742	−	0.848783i	$-0.322664\pi$
$19$	4.60946	1.05748	0.528742	+	0.848783i	$0.322664\pi$
$20$	−19.5642	−4.37469
$21$	−13.6169	−2.97146
$22$	2.72314	0.580575
$23$	2.86541	0.597480	0.298740	−	0.954335i	$-0.403434\pi$
$23$	2.86541	0.597480	0.298740	+	0.954335i	$0.403434\pi$
$24$	−28.8839	−5.89590
$25$	8.05116	1.61023
$26$	−6.18577	−1.21313
$27$	11.3171	2.17797
$28$	−23.7456	−4.48751
$29$	−4.20834	−0.781469	−0.390735	−	0.920503i	$-0.627779\pi$
$29$	−4.20834	−0.781469	−0.390735	+	0.920503i	$0.627779\pi$
$30$	30.5511	5.57785
$31$	−6.52550	−1.17202	−0.586008	−	0.810306i	$-0.699301\pi$
$31$	−6.52550	−1.17202	−0.586008	+	0.810306i	$0.699301\pi$
$32$	−20.8744	−3.69010
$33$	−3.10551	−0.540600
$34$	2.72314	0.467015
$35$	15.8406	2.67755
$36$	35.9815	5.99692
$37$	−2.77855	−0.456791	−0.228396	−	0.973568i	$-0.573348\pi$
$37$	−2.77855	−0.456791	−0.228396	+	0.973568i	$0.573348\pi$
$38$	−12.5522	−2.03624
$39$	7.05435	1.12960
$40$	33.6006	5.31272
$41$	−0.370177	−0.0578119	−0.0289060	−	0.999582i	$-0.509202\pi$
$41$	−0.370177	−0.0578119	−0.0289060	+	0.999582i	$0.509202\pi$
$42$	37.0808	5.72169
$43$	−1.00000	−0.152499
$43$	−1.00000	−0.152499
$44$	−5.41549	−0.816416
$45$	−24.0031	−3.57817
$46$	−7.80292	−1.15048
$47$	9.19629	1.34142	0.670708	−	0.741721i	$-0.265990\pi$
$47$	9.19629	1.34142	0.670708	+	0.741721i	$0.265990\pi$
$48$	45.0191	6.49795
$49$	12.2262	1.74660
$50$	−21.9244	−3.10058
$51$	−3.10551	−0.434858
$52$	12.3016	1.70593
$53$	7.33670	1.00777	0.503887	−	0.863770i	$-0.331903\pi$
$53$	7.33670	1.00777	0.503887	+	0.863770i	$0.331903\pi$
$54$	−30.8180	−4.19379
$55$	3.61264	0.487128
$56$	40.7820	5.44973
$57$	14.3147	1.89603
$58$	11.4599	1.50476
$59$	−12.3607	−1.60922	−0.804611	−	0.593803i	$-0.797626\pi$
$59$	−12.3607	−1.60922	−0.804611	+	0.593803i	$0.797626\pi$
$60$	−60.7568	−7.84367
$61$	2.29319	0.293613	0.146806	−	0.989165i	$-0.453101\pi$
$61$	2.29319	0.293613	0.146806	+	0.989165i	$0.453101\pi$
$62$	17.7699	2.25677
$63$	−29.1332	−3.67044
$64$	27.8508	3.48135
$65$	−8.20632	−1.01787
$66$	8.45674	1.04095
$67$	13.7736	1.68271	0.841356	−	0.540481i	$-0.181758\pi$
$67$	13.7736	1.68271	0.841356	+	0.540481i	$0.181758\pi$
$68$	−5.41549	−0.656724
$69$	8.89857	1.07126
$70$	−43.1361	−5.15575
$71$	−9.92454	−1.17783	−0.588913	−	0.808196i	$-0.700444\pi$
$71$	−9.92454	−1.17783	−0.588913	+	0.808196i	$0.700444\pi$
$72$	−61.7966	−7.28280
$73$	−8.37295	−0.979979	−0.489990	−	0.871728i	$-0.662999\pi$
$73$	−8.37295	−0.979979	−0.489990	+	0.871728i	$0.662999\pi$
$74$	7.56639	0.879575
$75$	25.0030	2.88709
$76$	24.9625	2.86339
$77$	4.38477	0.499690
$78$	−19.2100	−2.17510
$79$	−1.86134	−0.209417	−0.104709	−	0.994503i	$-0.533391\pi$
$79$	−1.86134	−0.209417	−0.104709	+	0.994503i	$0.533391\pi$
$80$	−52.3708	−5.85523
$81$	15.2127	1.69030
$82$	1.00804	0.111320
$83$	−6.00373	−0.658995	−0.329498	−	0.944156i	$-0.606879\pi$
$83$	−6.00373	−0.658995	−0.329498	+	0.944156i	$0.606879\pi$
$84$	−73.7423	−8.04595
$85$	3.61264	0.391846
$86$	2.72314	0.293644
$87$	−13.0690	−1.40115
$88$	9.30085	0.991474
$89$	11.2735	1.19499	0.597496	−	0.801872i	$-0.296162\pi$
$89$	11.2735	1.19499	0.597496	+	0.801872i	$0.296162\pi$
$90$	65.3637	6.88994
$91$	−9.96025	−1.04412
$92$	15.5176	1.61782
$93$	−20.2650	−2.10138
$94$	−25.0428	−2.58297
$95$	−16.6523	−1.70849
$96$	−64.8256	−6.61624
$97$	4.42008	0.448791	0.224396	−	0.974498i	$-0.427959\pi$
$97$	4.42008	0.448791	0.224396	+	0.974498i	$0.427959\pi$
$98$	−33.2936	−3.36316
$99$	−6.64419	−0.667766
$100$	43.6010	4.36010
$101$	−17.4813	−1.73945	−0.869725	−	0.493537i	$-0.835704\pi$
$101$	−17.4813	−1.73945	−0.869725	+	0.493537i	$0.835704\pi$
$102$	8.45674	0.837342
$103$	4.03674	0.397752	0.198876	−	0.980025i	$-0.436271\pi$
$103$	4.03674	0.397752	0.198876	+	0.980025i	$0.436271\pi$
$104$	−21.1274	−2.07172
$105$	49.1931	4.80075
$106$	−19.9789	−1.94052
$107$	−12.6257	−1.22058	−0.610288	−	0.792180i	$-0.708946\pi$
$107$	−12.6257	−1.22058	−0.610288	+	0.792180i	$0.708946\pi$
$108$	61.2874	5.89739
$109$	8.64111	0.827668	0.413834	−	0.910352i	$-0.364189\pi$
$109$	8.64111	0.827668	0.413834	+	0.910352i	$0.364189\pi$
$110$	−9.83772	−0.937990
$111$	−8.62882	−0.819012
$112$	−63.5639	−6.00623
$113$	1.71246	0.161095	0.0805474	−	0.996751i	$-0.474333\pi$
$113$	1.71246	0.161095	0.0805474	+	0.996751i	$0.474333\pi$
$114$	−38.9810	−3.65091
$115$	−10.3517	−0.965301
$116$	−22.7902	−2.11602
$117$	15.0927	1.39532
$118$	33.6598	3.09864
$119$	4.38477	0.401951
$120$	104.347	9.52554
$121$	1.00000	0.0909091
$122$	−6.24467	−0.565366
$123$	−1.14959	−0.103655
$124$	−35.3388	−3.17352
$125$	−11.0227	−0.985904
$126$	79.3338	7.06762
$127$	13.3731	1.18667	0.593334	−	0.804957i	$-0.297812\pi$
$127$	13.3731	1.18667	0.593334	+	0.804957i	$0.297812\pi$
$128$	−34.0928	−3.01341
$129$	−3.10551	−0.273425
$130$	22.3470	1.95996
$131$	18.8093	1.64337	0.821686	−	0.569940i	$-0.193034\pi$
$131$	18.8093	1.64337	0.821686	+	0.569940i	$0.193034\pi$
$132$	−16.8179	−1.46381
$133$	−20.2114	−1.75255
$134$	−37.5074	−3.24015
$135$	−40.8845	−3.51878
$136$	9.30085	0.797541
$137$	−0.950198	−0.0811809	−0.0405904	−	0.999176i	$-0.512924\pi$
$137$	−0.950198	−0.0811809	−0.0405904	+	0.999176i	$0.512924\pi$
$138$	−24.2320	−2.06277
$139$	2.87809	0.244117	0.122058	−	0.992523i	$-0.461051\pi$
$139$	2.87809	0.244117	0.122058	+	0.992523i	$0.461051\pi$
$140$	85.7845	7.25011
$141$	28.5592	2.40512
$142$	27.0259	2.26796
$143$	−2.27156	−0.189957
$144$	96.3177	8.02648
$145$	15.2032	1.26256
$146$	22.8007	1.88700
$147$	37.9685	3.13159
$148$	−15.0472	−1.23687
$149$	1.15390	0.0945313	0.0472657	−	0.998882i	$-0.484949\pi$
$149$	1.15390	0.0945313	0.0472657	+	0.998882i	$0.484949\pi$
$150$	−68.0865	−5.55924
$151$	15.4735	1.25922	0.629610	−	0.776912i	$-0.283215\pi$
$151$	15.4735	1.25922	0.629610	+	0.776912i	$0.283215\pi$
$152$	−42.8719	−3.47737
$153$	−6.64419	−0.537151
$154$	−11.9403	−0.962179
$155$	23.5743	1.89353
$156$	38.2027	3.05867
$157$	−22.8352	−1.82245	−0.911224	−	0.411910i	$-0.864862\pi$
$157$	−22.8352	−1.82245	−0.911224	+	0.411910i	$0.864862\pi$
$158$	5.06869	0.403243
$159$	22.7842	1.80690
$160$	75.4116	5.96181
$161$	−12.5642	−0.990195
$162$	−41.4263	−3.25476
$163$	19.4195	1.52105	0.760525	−	0.649309i	$-0.224942\pi$
$163$	19.4195	1.52105	0.760525	+	0.649309i	$0.224942\pi$
$164$	−2.00469	−0.156540
$165$	11.2191	0.873405
$166$	16.3490	1.26893
$167$	10.2739	0.795015	0.397507	−	0.917599i	$-0.369875\pi$
$167$	10.2739	0.795015	0.397507	+	0.917599i	$0.369875\pi$
$168$	126.649	9.77119
$169$	−7.84002	−0.603078
$170$	−9.83772	−0.754519
$171$	30.6262	2.34204
$172$	−5.41549	−0.412927
$173$	−19.7755	−1.50350	−0.751752	−	0.659446i	$-0.770791\pi$
$173$	−19.7755	−1.50350	−0.751752	+	0.659446i	$0.770791\pi$
$174$	35.5888	2.69798
$175$	−35.3025	−2.66861
$176$	−14.4965	−1.09272
$177$	−38.3862	−2.88528
$178$	−30.6994	−2.30102
$179$	−8.78370	−0.656525	−0.328262	−	0.944587i	$-0.606463\pi$
$179$	−8.78370	−0.656525	−0.328262	+	0.944587i	$0.606463\pi$
$180$	−129.988	−9.68876
$181$	25.1714	1.87098	0.935489	−	0.353357i	$-0.114960\pi$
$181$	25.1714	1.87098	0.935489	+	0.353357i	$0.114960\pi$
$182$	27.1232	2.01050
$183$	7.12152	0.526438
$184$	−26.6508	−1.96472
$185$	10.0379	0.738002
$186$	55.1845	4.04632
$187$	1.00000	0.0731272
$188$	49.8024	3.63221
$189$	−49.6227	−3.60952
$190$	45.3466	3.28979
$191$	−12.7517	−0.922682	−0.461341	−	0.887223i	$-0.652632\pi$
$191$	−12.7517	−0.922682	−0.461341	+	0.887223i	$0.652632\pi$
$192$	86.4909	6.24194
$193$	14.9086	1.07314	0.536572	−	0.843854i	$-0.319719\pi$
$193$	14.9086	1.07314	0.536572	+	0.843854i	$0.319719\pi$
$194$	−12.0365	−0.864170
$195$	−25.4848	−1.82501
$196$	66.2107	4.72933
$197$	−0.382678	−0.0272647	−0.0136323	−	0.999907i	$-0.504339\pi$
$197$	−0.382678	−0.0272647	−0.0136323	+	0.999907i	$0.504339\pi$
$198$	18.0931	1.28582
$199$	−0.882424	−0.0625534	−0.0312767	−	0.999511i	$-0.509957\pi$
$199$	−0.882424	−0.0625534	−0.0312767	+	0.999511i	$0.509957\pi$
$200$	−74.8826	−5.29500
$201$	42.7740	3.01705
$202$	47.6039	3.34940
$203$	18.4526	1.29512
$204$	−16.8179	−1.17749
$205$	1.33732	0.0934021
$206$	−10.9926	−0.765891
$207$	19.0383	1.32326
$208$	32.9297	2.28327
$209$	−4.60946	−0.318843
$210$	−133.960	−9.24409
$211$	−23.8301	−1.64053	−0.820267	−	0.571980i	$-0.806175\pi$
$211$	−23.8301	−1.64053	−0.820267	+	0.571980i	$0.806175\pi$
$212$	39.7318	2.72879
$213$	−30.8208	−2.11180
$214$	34.3816	2.35028
$215$	3.61264	0.246380
$216$	−105.258	−7.16192
$217$	28.6128	1.94236
$218$	−23.5310	−1.59372
$219$	−26.0023	−1.75707
$220$	19.5642	1.31902
$221$	−2.27156	−0.152802
$222$	23.4975	1.57705
$223$	−12.9680	−0.868399	−0.434200	−	0.900817i	$-0.642969\pi$
$223$	−12.9680	−0.868399	−0.434200	+	0.900817i	$0.642969\pi$
$224$	91.5293	6.11556
$225$	53.4934	3.56623
$226$	−4.66327	−0.310196
$227$	22.5425	1.49620	0.748099	−	0.663587i	$-0.230967\pi$
$227$	22.5425	1.49620	0.748099	+	0.663587i	$0.230967\pi$
$228$	77.5213	5.13397
$229$	−20.5942	−1.36091	−0.680453	−	0.732792i	$-0.738217\pi$
$229$	−20.5942	−1.36091	−0.680453	+	0.732792i	$0.738217\pi$
$230$	28.1891	1.85874
$231$	13.6169	0.895928
$232$	39.1411	2.56974
$233$	−15.2538	−0.999309	−0.499655	−	0.866225i	$-0.666540\pi$
$233$	−15.2538	−0.999309	−0.499655	+	0.866225i	$0.666540\pi$
$234$	−41.0994	−2.68675
$235$	−33.2229	−2.16722
$236$	−66.9390	−4.35736
$237$	−5.78041	−0.375478
$238$	−11.9403	−0.773977
$239$	−17.7586	−1.14871	−0.574353	−	0.818608i	$-0.694746\pi$
$239$	−17.7586	−1.14871	−0.574353	+	0.818608i	$0.694746\pi$
$240$	−162.638	−10.4982
$241$	−13.1580	−0.847580	−0.423790	−	0.905761i	$-0.639300\pi$
$241$	−13.1580	−0.847580	−0.423790	+	0.905761i	$0.639300\pi$
$242$	−2.72314	−0.175050
$243$	13.2920	0.852680
$244$	12.4187	0.795028
$245$	−44.1687	−2.82184
$246$	3.13049	0.199593
$247$	10.4707	0.666233
$248$	60.6927	3.85399
$249$	−18.6447	−1.18156
$250$	30.0165	1.89841
$251$	−3.66701	−0.231460	−0.115730	−	0.993281i	$-0.536921\pi$
$251$	−3.66701	−0.231460	−0.115730	+	0.993281i	$0.536921\pi$
$252$	−157.771	−9.93861
$253$	−2.86541	−0.180147
$254$	−36.4167	−2.28499
$255$	11.2191	0.702566
$256$	37.1379	2.32112
$257$	1.45708	0.0908899	0.0454449	−	0.998967i	$-0.485529\pi$
$257$	1.45708	0.0908899	0.0454449	+	0.998967i	$0.485529\pi$
$258$	8.45674	0.526493
$259$	12.1833	0.757034
$260$	−44.4412	−2.75613
$261$	−27.9610	−1.73074
$262$	−51.2202	−3.16440
$263$	−32.0341	−1.97530	−0.987652	−	0.156662i	$-0.949927\pi$
$263$	−32.0341	−1.97530	−0.987652	+	0.156662i	$0.949927\pi$
$264$	28.8839	1.77768
$265$	−26.5049	−1.62818
$266$	55.0385	3.37463
$267$	35.0101	2.14258
$268$	74.5908	4.55636
$269$	24.2134	1.47632	0.738159	−	0.674627i	$-0.235696\pi$
$269$	24.2134	1.47632	0.738159	+	0.674627i	$0.235696\pi$
$270$	111.334	6.77558
$271$	−19.8994	−1.20880	−0.604402	−	0.796679i	$-0.706588\pi$
$271$	−19.8994	−1.20880	−0.604402	+	0.796679i	$0.706588\pi$
$272$	−14.4965	−0.878982
$273$	−30.9317	−1.87207
$274$	2.58752	0.156318
$275$	−8.05116	−0.485503
$276$	48.1901	2.90070
$277$	−11.4551	−0.688271	−0.344135	−	0.938920i	$-0.611828\pi$
$277$	−11.4551	−0.688271	−0.344135	+	0.938920i	$0.611828\pi$
$278$	−7.83745	−0.470059
$279$	−43.3567	−2.59570
$280$	−147.331	−8.80470
$281$	12.4283	0.741408	0.370704	−	0.928751i	$-0.379116\pi$
$281$	12.4283	0.741408	0.370704	+	0.928751i	$0.379116\pi$
$282$	−77.7706	−4.63117
$283$	7.15869	0.425540	0.212770	−	0.977102i	$-0.431751\pi$
$283$	7.15869	0.425540	0.212770	+	0.977102i	$0.431751\pi$
$284$	−53.7462	−3.18925
$285$	−51.7140	−3.06327
$286$	6.18577	0.365772
$287$	1.62314	0.0958108
$288$	−138.693	−8.17259
$289$	1.00000	0.0588235
$290$	−41.4005	−2.43112
$291$	13.7266	0.804668
$292$	−45.3436	−2.65353
$293$	−9.40026	−0.549169	−0.274585	−	0.961563i	$-0.588540\pi$
$293$	−9.40026	−0.549169	−0.274585	+	0.961563i	$0.588540\pi$
$294$	−103.393	−6.03003
$295$	44.6546	2.59989
$296$	25.8429	1.50209
$297$	−11.3171	−0.656683
$298$	−3.14224	−0.182025
$299$	6.50895	0.376423
$300$	135.403	7.81751
$301$	4.38477	0.252734
$302$	−42.1366	−2.42469
$303$	−54.2882	−3.11878
$304$	66.8213	3.83246
$305$	−8.28446	−0.474367
$306$	18.0931	1.03431
$307$	29.9862	1.71140	0.855701	−	0.517470i	$-0.173126\pi$
$307$	29.9862	1.71140	0.855701	+	0.517470i	$0.173126\pi$
$308$	23.7456	1.35303
$309$	12.5361	0.713155
$310$	−64.1961	−3.64609
$311$	−27.1396	−1.53894	−0.769472	−	0.638680i	$-0.779481\pi$
$311$	−27.1396	−1.53894	−0.769472	+	0.638680i	$0.779481\pi$
$312$	−65.6114	−3.71452
$313$	−17.9197	−1.01288	−0.506440	−	0.862275i	$-0.669039\pi$
$313$	−17.9197	−1.01288	−0.506440	+	0.862275i	$0.669039\pi$
$314$	62.1835	3.50922
$315$	105.248	5.93004
$316$	−10.0801	−0.567048
$317$	−2.75496	−0.154734	−0.0773669	−	0.997003i	$-0.524651\pi$
$317$	−2.75496	−0.154734	−0.0773669	+	0.997003i	$0.524651\pi$
$318$	−62.0445	−3.47929
$319$	4.20834	0.235622
$320$	−100.615	−5.62454
$321$	−39.2093	−2.18845
$322$	34.2140	1.90667
$323$	−4.60946	−0.256477
$324$	82.3842	4.57690
$325$	18.2887	1.01447
$326$	−52.8819	−2.92886
$327$	26.8351	1.48398
$328$	3.44296	0.190106
$329$	−40.3236	−2.22311
$330$	−30.5511	−1.68178
$331$	−1.84707	−0.101524	−0.0507621	−	0.998711i	$-0.516165\pi$
$331$	−1.84707	−0.101524	−0.0507621	+	0.998711i	$0.516165\pi$
$332$	−32.5131	−1.78439
$333$	−18.4612	−1.01167
$334$	−27.9771	−1.53084
$335$	−49.7590	−2.71863
$336$	−197.398	−10.7690
$337$	−25.9294	−1.41247	−0.706233	−	0.707979i	$-0.749607\pi$
$337$	−25.9294	−1.41247	−0.706233	+	0.707979i	$0.749607\pi$
$338$	21.3495	1.16126
$339$	5.31806	0.288838
$340$	19.5642	1.06102
$341$	6.52550	0.353376
$342$	−83.3993	−4.50972
$343$	−22.9155	−1.23732
$344$	9.30085	0.501468
$345$	−32.1473	−1.73075
$346$	53.8514	2.89507
$347$	−26.2051	−1.40677	−0.703383	−	0.710811i	$-0.748328\pi$
$347$	−26.2051	−1.40677	−0.703383	+	0.710811i	$0.748328\pi$
$348$	−70.7752	−3.79395
$349$	−30.3199	−1.62299	−0.811494	−	0.584361i	$-0.801345\pi$
$349$	−30.3199	−1.62299	−0.811494	+	0.584361i	$0.801345\pi$
$350$	96.1335	5.13855
$351$	25.7074	1.37216
$352$	20.8744	1.11261
$353$	12.4955	0.665069	0.332535	−	0.943091i	$-0.392096\pi$
$353$	12.4955	0.665069	0.332535	+	0.943091i	$0.392096\pi$
$354$	104.531	5.55575
$355$	35.8538	1.90292
$356$	61.0517	3.23573
$357$	13.6169	0.720684
$358$	23.9192	1.26417
$359$	−10.0378	−0.529773	−0.264886	−	0.964280i	$-0.585334\pi$
$359$	−10.0378	−0.529773	−0.264886	+	0.964280i	$0.585334\pi$
$360$	223.249	11.7662
$361$	2.24716	0.118271
$362$	−68.5453	−3.60266
$363$	3.10551	0.162997
$364$	−53.9396	−2.82721
$365$	30.2484	1.58328
$366$	−19.3929	−1.01368
$367$	−11.9870	−0.625718	−0.312859	−	0.949800i	$-0.601287\pi$
$367$	−11.9870	−0.625718	−0.312859	+	0.949800i	$0.601287\pi$
$368$	41.5386	2.16535
$369$	−2.45953	−0.128038
$370$	−27.3346	−1.42106
$371$	−32.1697	−1.67017
$372$	−109.745	−5.69001
$373$	−18.4821	−0.956965	−0.478483	−	0.878097i	$-0.658813\pi$
$373$	−18.4821	−0.956965	−0.478483	+	0.878097i	$0.658813\pi$
$374$	−2.72314	−0.140810
$375$	−34.2312	−1.76769
$376$	−85.5333	−4.41104
$377$	−9.55949	−0.492339
$378$	135.130	6.95031
$379$	−13.3937	−0.687989	−0.343994	−	0.938972i	$-0.611780\pi$
$379$	−13.3937	−0.687989	−0.343994	+	0.938972i	$0.611780\pi$
$380$	−90.1805	−4.62616
$381$	41.5302	2.12765
$382$	34.7247	1.77667
$383$	−1.59346	−0.0814221	−0.0407111	−	0.999171i	$-0.512962\pi$
$383$	−1.59346	−0.0814221	−0.0407111	+	0.999171i	$0.512962\pi$
$384$	−105.876	−5.40294
$385$	−15.8406	−0.807311
$386$	−40.5982	−2.06639
$387$	−6.64419	−0.337743
$388$	23.9369	1.21521
$389$	−9.16094	−0.464478	−0.232239	−	0.972659i	$-0.574605\pi$
$389$	−9.16094	−0.464478	−0.232239	+	0.972659i	$0.574605\pi$
$390$	69.3987	3.51414
$391$	−2.86541	−0.144910
$392$	−113.714	−5.74341
$393$	58.4123	2.94651
$394$	1.04209	0.0524995
$395$	6.72435	0.338339
$396$	−35.9815	−1.80814
$397$	−26.6944	−1.33975	−0.669876	−	0.742473i	$-0.733653\pi$
$397$	−26.6944	−1.33975	−0.669876	+	0.742473i	$0.733653\pi$
$398$	2.40296	0.120450
$399$	−62.7668	−3.14227
$400$	116.714	5.83570
$401$	−13.8776	−0.693017	−0.346508	−	0.938047i	$-0.612633\pi$
$401$	−13.8776	−0.693017	−0.346508	+	0.938047i	$0.612633\pi$
$402$	−116.480	−5.80948
$403$	−14.8231	−0.738390
$404$	−94.6695	−4.70998
$405$	−54.9580	−2.73088
$406$	−50.2490	−2.49381
$407$	2.77855	0.137728
$408$	28.8839	1.42997
$409$	31.8091	1.57286	0.786429	−	0.617681i	$-0.211928\pi$
$409$	31.8091	1.57286	0.786429	+	0.617681i	$0.211928\pi$
$410$	−3.64170	−0.179851
$411$	−2.95085	−0.145555
$412$	21.8609	1.07701
$413$	54.1986	2.66694
$414$	−51.8441	−2.54800
$415$	21.6893	1.06469
$416$	−47.4174	−2.32483
$417$	8.93795	0.437693
$418$	12.5522	0.613949
$419$	14.8186	0.723935	0.361967	−	0.932191i	$-0.382105\pi$
$419$	14.8186	0.723935	0.361967	+	0.932191i	$0.382105\pi$
$420$	266.404	12.9992
$421$	7.78369	0.379354	0.189677	−	0.981847i	$-0.439256\pi$
$421$	7.78369	0.379354	0.189677	+	0.981847i	$0.439256\pi$
$422$	64.8928	3.15893
$423$	61.1019	2.97088
$424$	−68.2376	−3.31391
$425$	−8.05116	−0.390539
$426$	83.9292	4.06639
$427$	−10.0551	−0.486600
$428$	−68.3745	−3.30501
$429$	−7.05435	−0.340587
$430$	−9.83772	−0.474417
$431$	31.1195	1.49897	0.749487	−	0.662019i	$-0.230300\pi$
$431$	31.1195	1.49897	0.749487	+	0.662019i	$0.230300\pi$
$432$	164.058	7.89326
$433$	−14.2977	−0.687102	−0.343551	−	0.939134i	$-0.611630\pi$
$433$	−14.2977	−0.687102	−0.343551	+	0.939134i	$0.611630\pi$
$434$	−77.9167	−3.74012
$435$	47.2137	2.26373
$436$	46.7958	2.24111
$437$	13.2080	0.631825
$438$	70.8078	3.38333
$439$	−28.1897	−1.34542	−0.672710	−	0.739906i	$-0.734870\pi$
$439$	−28.1897	−1.34542	−0.672710	+	0.739906i	$0.734870\pi$
$440$	−33.6006	−1.60185
$441$	81.2330	3.86824
$442$	6.18577	0.294227
$443$	19.9125	0.946072	0.473036	−	0.881043i	$-0.343158\pi$
$443$	19.9125	0.946072	0.473036	+	0.881043i	$0.343158\pi$
$444$	−46.7293	−2.21767
$445$	−40.7272	−1.93066
$446$	35.3136	1.67215
$447$	3.58345	0.169491
$448$	−122.119	−5.76959
$449$	−21.9373	−1.03529	−0.517643	−	0.855597i	$-0.673190\pi$
$449$	−21.9373	−1.03529	−0.517643	+	0.855597i	$0.673190\pi$
$450$	−145.670	−6.86695
$451$	0.370177	0.0174309
$452$	9.27381	0.436203
$453$	48.0533	2.25774
$454$	−61.3864	−2.88101
$455$	35.9828	1.68690
$456$	−133.139	−6.23481
$457$	10.0001	0.467784	0.233892	−	0.972263i	$-0.424854\pi$
$457$	10.0001	0.467784	0.233892	+	0.972263i	$0.424854\pi$
$458$	56.0810	2.62049
$459$	−11.3171	−0.528235
$460$	−56.0595	−2.61379
$461$	3.72297	0.173396	0.0866980	−	0.996235i	$-0.472368\pi$
$461$	3.72297	0.173396	0.0866980	+	0.996235i	$0.472368\pi$
$462$	−37.0808	−1.72516
$463$	21.8991	1.01774	0.508868	−	0.860844i	$-0.330064\pi$
$463$	21.8991	1.01774	0.508868	+	0.860844i	$0.330064\pi$
$464$	−61.0064	−2.83215
$465$	73.2102	3.39504
$466$	41.5382	1.92422
$467$	−40.7163	−1.88413	−0.942063	−	0.335435i	$-0.891117\pi$
$467$	−40.7163	−1.88413	−0.942063	+	0.335435i	$0.891117\pi$
$468$	81.7342	3.77816
$469$	−60.3940	−2.78874
$470$	90.4705	4.17309
$471$	−70.9150	−3.26759
$472$	114.965	5.29168
$473$	1.00000	0.0459800
$474$	15.7409	0.723002
$475$	37.1115	1.70279
$476$	23.7456	1.08838
$477$	48.7464	2.23195
$478$	48.3590	2.21189
$479$	−36.6124	−1.67287	−0.836433	−	0.548070i	$-0.815363\pi$
$479$	−36.6124	−1.67287	−0.836433	+	0.548070i	$0.815363\pi$
$480$	234.192	10.6893
$481$	−6.31165	−0.287786
$482$	35.8310	1.63206
$483$	−39.0181	−1.77539
$484$	5.41549	0.246159
$485$	−15.9682	−0.725077
$486$	−36.1959	−1.64188
$487$	22.7726	1.03193	0.515963	−	0.856611i	$-0.327434\pi$
$487$	22.7726	1.03193	0.515963	+	0.856611i	$0.327434\pi$
$488$	−21.3286	−0.965501
$489$	60.3073	2.72719
$490$	120.278	5.43359
$491$	−24.2571	−1.09471	−0.547355	−	0.836901i	$-0.684365\pi$
$491$	−24.2571	−1.09471	−0.547355	+	0.836901i	$0.684365\pi$
$492$	−6.22558	−0.280671
$493$	4.20834	0.189534
$494$	−28.5131	−1.28286
$495$	24.0031	1.07886
$496$	−94.5972	−4.24754
$497$	43.5168	1.95200
$498$	50.7720	2.27515
$499$	−33.3756	−1.49410	−0.747048	−	0.664770i	$-0.768529\pi$
$499$	−33.3756	−1.49410	−0.747048	+	0.664770i	$0.768529\pi$
$500$	−59.6935	−2.66958
$501$	31.9055	1.42543
$502$	9.98578	0.445687
$503$	−40.3894	−1.80087	−0.900437	−	0.434987i	$-0.856753\pi$
$503$	−40.3894	−1.80087	−0.900437	+	0.434987i	$0.856753\pi$
$504$	270.964	12.0697
$505$	63.1535	2.81029
$506$	7.80292	0.346882
$507$	−24.3473	−1.08130
$508$	72.4216	3.21319
$509$	−34.9891	−1.55087	−0.775433	−	0.631430i	$-0.782468\pi$
$509$	−34.9891	−1.55087	−0.775433	+	0.631430i	$0.782468\pi$
$510$	−30.5511	−1.35283
$511$	36.7134	1.62411
$512$	−32.9461	−1.45602
$513$	52.1656	2.30317
$514$	−3.96782	−0.175013
$515$	−14.5833	−0.642616
$516$	−16.8179	−0.740365
$517$	−9.19629	−0.404452
$518$	−33.1768	−1.45771
$519$	−61.4130	−2.69573
$520$	76.3258	3.34711
$521$	−9.03160	−0.395682	−0.197841	−	0.980234i	$-0.563393\pi$
$521$	−9.03160	−0.395682	−0.197841	+	0.980234i	$0.563393\pi$
$522$	76.1417	3.33263
$523$	19.0728	0.833997	0.416999	−	0.908907i	$-0.363082\pi$
$523$	19.0728	0.833997	0.416999	+	0.908907i	$0.363082\pi$
$524$	101.861	4.44983
$525$	−109.632	−4.78474
$526$	87.2332	3.80355
$527$	6.52550	0.284255
$528$	−45.0191	−1.95921
$529$	−14.7894	−0.643018
$530$	72.1764	3.13514
$531$	−82.1266	−3.56399
$532$	−109.455	−4.74546
$533$	−0.840879	−0.0364225
$534$	−95.3373	−4.12565
$535$	45.6122	1.97199
$536$	−128.106	−5.53334
$537$	−27.2779	−1.17713
$538$	−65.9365	−2.84272
$539$	−12.2262	−0.526618
$540$	−221.409	−9.52794
$541$	−22.4190	−0.963868	−0.481934	−	0.876208i	$-0.660065\pi$
$541$	−22.4190	−0.963868	−0.481934	+	0.876208i	$0.660065\pi$
$542$	54.1890	2.32761
$543$	78.1701	3.35460
$544$	20.8744	0.894982
$545$	−31.2172	−1.33720
$546$	84.2312	3.60476
$547$	−9.87343	−0.422157	−0.211079	−	0.977469i	$-0.567698\pi$
$547$	−9.87343	−0.422157	−0.211079	+	0.977469i	$0.567698\pi$
$548$	−5.14578	−0.219817
$549$	15.2364	0.650273
$550$	21.9244	0.934861
$551$	−19.3982	−0.826391
$552$	−82.7642	−3.52268
$553$	8.16154	0.347064
$554$	31.1939	1.32530
$555$	31.1728	1.32321
$556$	15.5863	0.661005
$557$	29.1200	1.23385	0.616927	−	0.787020i	$-0.288377\pi$
$557$	29.1200	1.23385	0.616927	+	0.787020i	$0.288377\pi$
$558$	118.066	4.99815
$559$	−2.27156	−0.0960767
$560$	229.633	9.70379
$561$	3.10551	0.131115
$562$	−33.8439	−1.42762
$563$	1.29138	0.0544250	0.0272125	−	0.999630i	$-0.491337\pi$
$563$	1.29138	0.0544250	0.0272125	+	0.999630i	$0.491337\pi$
$564$	154.662	6.51244
$565$	−6.18650	−0.260268
$566$	−19.4941	−0.819399
$567$	−66.7041	−2.80131
$568$	92.3067	3.87310
$569$	10.0232	0.420195	0.210097	−	0.977680i	$-0.432622\pi$
$569$	10.0232	0.420195	0.210097	+	0.977680i	$0.432622\pi$
$570$	140.824	5.89848
$571$	25.0994	1.05038	0.525188	−	0.850986i	$-0.323995\pi$
$571$	25.0994	1.05038	0.525188	+	0.850986i	$0.323995\pi$
$572$	−12.3016	−0.514356
$573$	−39.6006	−1.65434
$574$	−4.42003	−0.184489
$575$	23.0699	0.962081
$576$	185.046	7.71025
$577$	−42.7920	−1.78145	−0.890726	−	0.454540i	$-0.849804\pi$
$577$	−42.7920	−1.78145	−0.890726	+	0.454540i	$0.849804\pi$
$578$	−2.72314	−0.113268
$579$	46.2988	1.92411
$580$	82.3328	3.41869
$581$	26.3250	1.09214
$582$	−37.3795	−1.54943
$583$	−7.33670	−0.303855
$584$	77.8755	3.22251
$585$	−54.5244	−2.25431
$586$	25.5982	1.05745
$587$	−7.64506	−0.315545	−0.157773	−	0.987475i	$-0.550431\pi$
$587$	−7.64506	−0.315545	−0.157773	+	0.987475i	$0.550431\pi$
$588$	205.618	8.47954
$589$	−30.0791	−1.23939
$590$	−121.601	−5.00622
$591$	−1.18841	−0.0488847
$592$	−40.2794	−1.65547
$593$	35.9547	1.47648	0.738241	−	0.674537i	$-0.235657\pi$
$593$	35.9547	1.47648	0.738241	+	0.674537i	$0.235657\pi$
$594$	30.8180	1.26448
$595$	−15.8406	−0.649400
$596$	6.24894	0.255967
$597$	−2.74038	−0.112156
$598$	−17.7248	−0.724821
$599$	−42.6138	−1.74115	−0.870576	−	0.492035i	$-0.836253\pi$
$599$	−42.6138	−1.74115	−0.870576	+	0.492035i	$0.836253\pi$
$600$	−232.549	−9.49376
$601$	−19.3366	−0.788756	−0.394378	−	0.918948i	$-0.629040\pi$
$601$	−19.3366	−0.788756	−0.394378	+	0.918948i	$0.629040\pi$
$602$	−11.9403	−0.486651
$603$	91.5144	3.72675
$604$	83.7968	3.40964
$605$	−3.61264	−0.146875
$606$	147.834	6.00536
$607$	37.9475	1.54024	0.770121	−	0.637898i	$-0.220196\pi$
$607$	37.9475	1.54024	0.770121	+	0.637898i	$0.220196\pi$
$608$	−96.2197	−3.90223
$609$	57.3047	2.32210
$610$	22.5598	0.913418
$611$	20.8899	0.845116
$612$	−35.9815	−1.45447
$613$	−18.9235	−0.764312	−0.382156	−	0.924098i	$-0.624818\pi$
$613$	−18.9235	−0.764312	−0.382156	+	0.924098i	$0.624818\pi$
$614$	−81.6566	−3.29539
$615$	4.15305	0.167467
$616$	−40.7820	−1.64316
$617$	−12.9345	−0.520724	−0.260362	−	0.965511i	$-0.583842\pi$
$617$	−12.9345	−0.520724	−0.260362	+	0.965511i	$0.583842\pi$
$618$	−34.1376	−1.37322
$619$	−2.22291	−0.0893464	−0.0446732	−	0.999002i	$-0.514225\pi$
$619$	−2.22291	−0.0893464	−0.0446732	+	0.999002i	$0.514225\pi$
$620$	127.666	5.12720
$621$	32.4281	1.30129
$622$	73.9049	2.96332
$623$	−49.4318	−1.98044
$624$	102.264	4.09382
$625$	−0.434611	−0.0173844
$626$	48.7978	1.95035
$627$	−14.3147	−0.571675
$628$	−123.664	−4.93473
$629$	2.77855	0.110788
$630$	−286.604	−11.4186
$631$	−9.61848	−0.382906	−0.191453	−	0.981502i	$-0.561320\pi$
$631$	−9.61848	−0.382906	−0.191453	+	0.981502i	$0.561320\pi$
$632$	17.3121	0.688636
$633$	−74.0047	−2.94142
$634$	7.50213	0.297948
$635$	−48.3120	−1.91720
$636$	123.388	4.89263
$637$	27.7725	1.10039
$638$	−11.4599	−0.453702
$639$	−65.9406	−2.60857
$640$	123.165	4.86853
$641$	10.0620	0.397424	0.198712	−	0.980058i	$-0.436324\pi$
$641$	10.0620	0.397424	0.198712	+	0.980058i	$0.436324\pi$
$642$	106.772	4.21397
$643$	−37.1749	−1.46604	−0.733018	−	0.680209i	$-0.761889\pi$
$643$	−37.1749	−1.46604	−0.733018	+	0.680209i	$0.761889\pi$
$644$	−68.0411	−2.68119
$645$	11.2191	0.441751
$646$	12.5522	0.493860
$647$	0.167490	0.00658470	0.00329235	−	0.999995i	$-0.498952\pi$
$647$	0.167490	0.00658470	0.00329235	+	0.999995i	$0.498952\pi$
$648$	−141.491	−5.55829
$649$	12.3607	0.485198
$650$	−49.8026	−1.95342
$651$	88.8574	3.48259
$652$	105.166	4.11861
$653$	5.81705	0.227639	0.113819	−	0.993501i	$-0.463691\pi$
$653$	5.81705	0.227639	0.113819	+	0.993501i	$0.463691\pi$
$654$	−73.0756	−2.85748
$655$	−67.9511	−2.65507
$656$	−5.36628	−0.209518
$657$	−55.6315	−2.17039
$658$	109.807	4.28071
$659$	−41.8265	−1.62933	−0.814665	−	0.579932i	$-0.803079\pi$
$659$	−41.8265	−1.62933	−0.814665	+	0.579932i	$0.803079\pi$
$660$	60.7568	2.36496
$661$	−28.9608	−1.12644	−0.563222	−	0.826306i	$-0.690438\pi$
$661$	−28.9608	−1.12644	−0.563222	+	0.826306i	$0.690438\pi$
$662$	5.02983	0.195490
$663$	−7.05435	−0.273968
$664$	55.8398	2.16701
$665$	73.0166	2.83146
$666$	50.2725	1.94802
$667$	−12.0586	−0.466912
$668$	55.6379	2.15270
$669$	−40.2721	−1.55701
$670$	135.501	5.23485
$671$	−2.29319	−0.0885276
$672$	284.245	10.9650
$673$	−22.6524	−0.873185	−0.436593	−	0.899659i	$-0.643815\pi$
$673$	−22.6524	−0.873185	−0.436593	+	0.899659i	$0.643815\pi$
$674$	70.6095	2.71978
$675$	91.1155	3.50704
$676$	−42.4575	−1.63298
$677$	35.7707	1.37478	0.687390	−	0.726289i	$-0.258756\pi$
$677$	35.7707	1.37478	0.687390	+	0.726289i	$0.258756\pi$
$678$	−14.4818	−0.556171
$679$	−19.3810	−0.743776
$680$	−33.6006	−1.28852
$681$	70.0060	2.68263
$682$	−17.7699	−0.680443
$683$	28.7293	1.09930	0.549648	−	0.835396i	$-0.314762\pi$
$683$	28.7293	1.09930	0.549648	+	0.835396i	$0.314762\pi$
$684$	165.856	6.34165
$685$	3.43272	0.131158
$686$	62.4022	2.38253
$687$	−63.9556	−2.44006
$688$	−14.4965	−0.552675
$689$	16.6658	0.634915
$690$	87.5416	3.33265
$691$	−24.8950	−0.947049	−0.473525	−	0.880781i	$-0.657018\pi$
$691$	−24.8950	−0.947049	−0.473525	+	0.880781i	$0.657018\pi$
$692$	−107.094	−4.07110
$693$	29.1332	1.10668
$694$	71.3603	2.70880
$695$	−10.3975	−0.394400
$696$	121.553	4.60746
$697$	0.370177	0.0140214
$698$	82.5653	3.12514
$699$	−47.3708	−1.79173
$700$	−191.180	−7.22593
$701$	6.54452	0.247183	0.123592	−	0.992333i	$-0.460559\pi$
$701$	6.54452	0.247183	0.123592	+	0.992333i	$0.460559\pi$
$702$	−70.0048	−2.64216
$703$	−12.8076	−0.483049
$704$	−27.8508	−1.04967
$705$	−103.174	−3.88576
$706$	−34.0270	−1.28062
$707$	76.6512	2.88277
$708$	−207.880	−7.81260
$709$	36.4573	1.36918	0.684590	−	0.728928i	$-0.259981\pi$
$709$	36.4573	1.36918	0.684590	+	0.728928i	$0.259981\pi$
$710$	−97.6349	−3.66417
$711$	−12.3671	−0.463803
$712$	−104.853	−3.92955
$713$	−18.6983	−0.700255
$714$	−37.0808	−1.38771
$715$	8.20632	0.306899
$716$	−47.5680	−1.77770
$717$	−55.1494	−2.05959
$718$	27.3342	1.02010
$719$	−14.8547	−0.553985	−0.276993	−	0.960872i	$-0.589338\pi$
$719$	−14.8547	−0.553985	−0.276993	+	0.960872i	$0.589338\pi$
$720$	−347.961	−12.9677
$721$	−17.7001	−0.659188
$722$	−6.11932	−0.227737
$723$	−40.8622	−1.51968
$724$	136.316	5.06613
$725$	−33.8820	−1.25835
$726$	−8.45674	−0.313859
$727$	31.2673	1.15964	0.579821	−	0.814744i	$-0.303123\pi$
$727$	31.2673	1.15964	0.579821	+	0.814744i	$0.303123\pi$
$728$	92.6388	3.43342
$729$	−4.35977	−0.161473
$730$	−82.3707	−3.04868
$731$	1.00000	0.0369863
$732$	38.5665	1.42546
$733$	−17.3295	−0.640078	−0.320039	−	0.947404i	$-0.603696\pi$
$733$	−17.3295	−0.640078	−0.320039	+	0.947404i	$0.603696\pi$
$734$	32.6424	1.20485
$735$	−137.166	−5.05946
$736$	−59.8137	−2.20476
$737$	−13.7736	−0.507357
$738$	6.69763	0.246543
$739$	−37.4892	−1.37906	−0.689531	−	0.724256i	$-0.742183\pi$
$739$	−37.4892	−1.37906	−0.689531	+	0.724256i	$0.742183\pi$
$740$	54.3602	1.99832
$741$	32.5168	1.19453
$742$	87.6026	3.21599
$743$	26.4081	0.968819	0.484410	−	0.874841i	$-0.339034\pi$
$743$	26.4081	0.968819	0.484410	+	0.874841i	$0.339034\pi$
$744$	188.482	6.91008
$745$	−4.16863	−0.152727
$746$	50.3293	1.84269
$747$	−39.8899	−1.45950
$748$	5.41549	0.198010
$749$	55.3609	2.02284
$750$	93.2164	3.40378
$751$	3.88500	0.141766	0.0708829	−	0.997485i	$-0.477418\pi$
$751$	3.88500	0.141766	0.0708829	+	0.997485i	$0.477418\pi$
$752$	133.314	4.86147
$753$	−11.3879	−0.414999
$754$	26.0318	0.948024
$755$	−55.9003	−2.03442
$756$	−268.731	−9.77366
$757$	−2.96497	−0.107764	−0.0538819	−	0.998547i	$-0.517159\pi$
$757$	−2.96497	−0.107764	−0.0538819	+	0.998547i	$0.517159\pi$
$758$	36.4730	1.32476
$759$	−8.89857	−0.322997
$760$	154.881	5.61812
$761$	11.4016	0.413306	0.206653	−	0.978414i	$-0.433743\pi$
$761$	11.4016	0.413306	0.206653	+	0.978414i	$0.433743\pi$
$762$	−113.092	−4.09691
$763$	−37.8892	−1.37168
$764$	−69.0568	−2.49839
$765$	24.0031	0.867833
$766$	4.33922	0.156782
$767$	−28.0780	−1.01384
$768$	115.332	4.16169
$769$	10.2091	0.368150	0.184075	−	0.982912i	$-0.441071\pi$
$769$	10.2091	0.368150	0.184075	+	0.982912i	$0.441071\pi$
$770$	43.1361	1.55452
$771$	4.52496	0.162963
$772$	80.7374	2.90580
$773$	22.6110	0.813261	0.406631	−	0.913593i	$-0.366704\pi$
$773$	22.6110	0.813261	0.406631	+	0.913593i	$0.366704\pi$
$774$	18.0931	0.650341
$775$	−52.5379	−1.88722
$776$	−41.1105	−1.47578
$777$	37.8354	1.35734
$778$	24.9465	0.894376
$779$	−1.70632	−0.0611351
$780$	−138.013	−4.94165
$781$	9.92454	0.355128
$782$	7.80292	0.279032
$783$	−47.6261	−1.70202
$784$	177.237	6.32990
$785$	82.4954	2.94439
$786$	−159.065	−5.67366
$787$	6.54535	0.233316	0.116658	−	0.993172i	$-0.462782\pi$
$787$	6.54535	0.233316	0.116658	+	0.993172i	$0.462782\pi$
$788$	−2.07239	−0.0738258
$789$	−99.4821	−3.54166
$790$	−18.3113	−0.651489
$791$	−7.50874	−0.266980
$792$	61.7966	2.19585
$793$	5.20911	0.184981
$794$	72.6925	2.57976
$795$	−82.3111	−2.91927
$796$	−4.77876	−0.169379
$797$	53.8811	1.90857	0.954283	−	0.298906i	$-0.0966217\pi$
$797$	53.8811	1.90857	0.954283	+	0.298906i	$0.0966217\pi$
$798$	170.923	6.05060
$799$	−9.19629	−0.325341
$800$	−168.063	−5.94193
$801$	74.9035	2.64659
$802$	37.7908	1.33444
$803$	8.37295	0.295475
$804$	231.642	8.16940
$805$	45.3898	1.59978
$806$	40.3653	1.42181
$807$	75.1950	2.64699
$808$	162.591	5.71991
$809$	44.4233	1.56184	0.780920	−	0.624631i	$-0.214751\pi$
$809$	44.4233	1.56184	0.780920	+	0.624631i	$0.214751\pi$
$810$	149.658	5.25845
$811$	−26.0917	−0.916204	−0.458102	−	0.888900i	$-0.651471\pi$
$811$	−26.0917	−0.916204	−0.458102	+	0.888900i	$0.651471\pi$
$812$	99.9298	3.50685
$813$	−61.7979	−2.16735
$814$	−7.56639	−0.265202
$815$	−70.1555	−2.45744
$816$	−45.0191	−1.57598
$817$	−4.60946	−0.161265
$818$	−86.6206	−3.02862
$819$	−66.1778	−2.31244
$820$	7.24221	0.252909
$821$	13.5220	0.471922	0.235961	−	0.971762i	$-0.424176\pi$
$821$	13.5220	0.471922	0.235961	+	0.971762i	$0.424176\pi$
$822$	8.03557	0.280273
$823$	−25.5703	−0.891324	−0.445662	−	0.895201i	$-0.647032\pi$
$823$	−25.5703	−0.891324	−0.445662	+	0.895201i	$0.647032\pi$
$824$	−37.5451	−1.30795
$825$	−25.0030	−0.870491
$826$	−147.590	−5.13533
$827$	−15.4428	−0.536998	−0.268499	−	0.963280i	$-0.586528\pi$
$827$	−15.4428	−0.536998	−0.268499	+	0.963280i	$0.586528\pi$
$828$	103.102	3.58304
$829$	48.7399	1.69281	0.846404	−	0.532542i	$-0.178763\pi$
$829$	48.7399	1.69281	0.846404	+	0.532542i	$0.178763\pi$
$830$	−59.0630	−2.05011
$831$	−35.5740	−1.23405
$832$	63.2647	2.19331
$833$	−12.2262	−0.423612
$834$	−24.3393	−0.842800
$835$	−37.1157	−1.28444
$836$	−24.9625	−0.863346
$837$	−73.8496	−2.55261
$838$	−40.3530	−1.39397
$839$	15.2428	0.526239	0.263120	−	0.964763i	$-0.415249\pi$
$839$	15.2428	0.526239	0.263120	+	0.964763i	$0.415249\pi$
$840$	−457.537	−15.7865
$841$	−11.2899	−0.389306
$842$	−21.1961	−0.730465
$843$	38.5961	1.32932
$844$	−129.052	−4.44215
$845$	28.3232	0.974346
$846$	−166.389	−5.72057
$847$	−4.38477	−0.150662
$848$	106.357	3.65231
$849$	22.2314	0.762979
$850$	21.9244	0.752002
$851$	−7.96170	−0.272924
$852$	−166.909	−5.71822
$853$	33.5084	1.14731	0.573653	−	0.819098i	$-0.305526\pi$
$853$	33.5084	1.14731	0.573653	+	0.819098i	$0.305526\pi$
$854$	27.3814	0.936973
$855$	−110.641	−3.78385
$856$	117.430	4.01368
$857$	−36.2269	−1.23749	−0.618744	−	0.785593i	$-0.712358\pi$
$857$	−36.2269	−1.23749	−0.618744	+	0.785593i	$0.712358\pi$
$858$	19.2100	0.655818
$859$	−6.65354	−0.227016	−0.113508	−	0.993537i	$-0.536209\pi$
$859$	−6.65354	−0.227016	−0.113508	+	0.993537i	$0.536209\pi$
$860$	19.5642	0.667134
$861$	5.04067	0.171786
$862$	−84.7428	−2.88635
$863$	−21.2986	−0.725013	−0.362506	−	0.931981i	$-0.618079\pi$
$863$	−21.2986	−0.725013	−0.362506	+	0.931981i	$0.618079\pi$
$864$	−236.237	−8.03694
$865$	71.4417	2.42909
$866$	38.9345	1.32305
$867$	3.10551	0.105469
$868$	154.952	5.25942
$869$	1.86134	0.0631417
$870$	−128.570	−4.35892
$871$	31.2875	1.06014
$872$	−80.3697	−2.72166
$873$	29.3679	0.993952
$874$	−35.9673	−1.21661
$875$	48.3321	1.63392
$876$	−140.815	−4.75770
$877$	−7.44481	−0.251394	−0.125697	−	0.992069i	$-0.540117\pi$
$877$	−7.44481	−0.251394	−0.125697	+	0.992069i	$0.540117\pi$
$878$	76.7644	2.59067
$879$	−29.1926	−0.984642
$880$	52.3708	1.76542
$881$	34.9631	1.17794	0.588968	−	0.808156i	$-0.299534\pi$
$881$	34.9631	1.17794	0.588968	+	0.808156i	$0.299534\pi$
$882$	−221.209	−7.44849
$883$	25.4962	0.858015	0.429007	−	0.903301i	$-0.358863\pi$
$883$	25.4962	0.858015	0.429007	+	0.903301i	$0.358863\pi$
$884$	−12.3016	−0.413748
$885$	138.675	4.66152
$886$	−54.2246	−1.82171
$887$	34.0592	1.14360	0.571798	−	0.820395i	$-0.306246\pi$
$887$	34.0592	1.14360	0.571798	+	0.820395i	$0.306246\pi$
$888$	80.2554	2.69320
$889$	−58.6377	−1.96665
$890$	110.906	3.71757
$891$	−15.2127	−0.509644
$892$	−70.2279	−2.35140
$893$	42.3900	1.41853
$894$	−9.75824	−0.326364
$895$	31.7323	1.06070
$896$	149.489	4.99408
$897$	20.2136	0.674913
$898$	59.7384	1.99349
$899$	27.4615	0.915894
$900$	289.693	9.65644
$901$	−7.33670	−0.244421
$902$	−1.00804	−0.0335642
$903$	13.6169	0.453143
$904$	−15.9273	−0.529736
$905$	−90.9353	−3.02279
$906$	−130.856	−4.34739
$907$	−37.8873	−1.25803	−0.629013	−	0.777395i	$-0.716541\pi$
$907$	−37.8873	−1.25803	−0.629013	+	0.777395i	$0.716541\pi$
$908$	122.079	4.05132
$909$	−116.149	−3.85241
$910$	−97.9862	−3.24821
$911$	−4.32202	−0.143195	−0.0715975	−	0.997434i	$-0.522810\pi$
$911$	−4.32202	−0.143195	−0.0715975	+	0.997434i	$0.522810\pi$
$912$	207.514	6.87148
$913$	6.00373	0.198695
$914$	−27.2316	−0.900742
$915$	−25.7275	−0.850524
$916$	−111.528	−3.68498
$917$	−82.4742	−2.72354
$918$	30.8180	1.01714
$919$	−22.8594	−0.754062	−0.377031	−	0.926201i	$-0.623055\pi$
$919$	−22.8594	−0.754062	−0.377031	+	0.926201i	$0.623055\pi$
$920$	96.2796	3.17425
$921$	93.1224	3.06849
$922$	−10.1382	−0.333883
$923$	−22.5442	−0.742051
$924$	73.7423	2.42594
$925$	−22.3706	−0.735540
$926$	−59.6342	−1.95970
$927$	26.8209	0.880912
$928$	87.8465	2.88370
$929$	−53.4155	−1.75251	−0.876253	−	0.481852i	$-0.839964\pi$
$929$	−53.4155	−1.75251	−0.876253	+	0.481852i	$0.839964\pi$
$930$	−199.362	−6.53732
$931$	56.3561	1.84700
$932$	−82.6067	−2.70587
$933$	−84.2822	−2.75928
$934$	110.876	3.62798
$935$	−3.61264	−0.118146
$936$	−140.375	−4.58829
$937$	36.7520	1.20064	0.600318	−	0.799761i	$-0.295041\pi$
$937$	36.7520	1.20064	0.600318	+	0.799761i	$0.295041\pi$
$938$	164.461	5.36985
$939$	−55.6498	−1.81606
$940$	−179.918	−5.86828
$941$	7.65576	0.249571	0.124785	−	0.992184i	$-0.460176\pi$
$941$	7.65576	0.249571	0.124785	+	0.992184i	$0.460176\pi$
$942$	193.111	6.29191
$943$	−1.06071	−0.0345414
$944$	−179.187	−5.83203
$945$	179.269	5.83162
$946$	−2.72314	−0.0885369
$947$	−10.6692	−0.346701	−0.173351	−	0.984860i	$-0.555459\pi$
$947$	−10.6692	−0.346701	−0.173351	+	0.984860i	$0.555459\pi$
$948$	−31.3038	−1.01670
$949$	−19.0196	−0.617404
$950$	−101.060	−3.27882
$951$	−8.55554	−0.277433
$952$	−40.7820	−1.32175
$953$	45.2372	1.46538	0.732688	−	0.680565i	$-0.238266\pi$
$953$	45.2372	1.46538	0.732688	+	0.680565i	$0.238266\pi$
$954$	−132.743	−4.29772
$955$	46.0674	1.49070
$956$	−96.1712	−3.11040
$957$	13.0690	0.422462
$958$	99.7008	3.22119
$959$	4.16639	0.134540
$960$	−312.460	−10.0846
$961$	11.5822	0.373620
$962$	17.1875	0.554147
$963$	−83.8878	−2.70325
$964$	−71.2569	−2.29503
$965$	−53.8594	−1.73380
$966$	106.252	3.41860
$967$	−11.1030	−0.357049	−0.178524	−	0.983936i	$-0.557132\pi$
$967$	−11.1030	−0.357049	−0.178524	+	0.983936i	$0.557132\pi$
$968$	−9.30085	−0.298941
$969$	−14.3147	−0.459856
$970$	43.4835	1.39617
$971$	17.8314	0.572238	0.286119	−	0.958194i	$-0.407635\pi$
$971$	17.8314	0.572238	0.286119	+	0.958194i	$0.407635\pi$
$972$	71.9825	2.30884
$973$	−12.6198	−0.404571
$974$	−62.0130	−1.98702
$975$	56.7957	1.81892
$976$	33.2433	1.06409
$977$	9.49623	0.303811	0.151906	−	0.988395i	$-0.451459\pi$
$977$	9.49623	0.303811	0.151906	+	0.988395i	$0.451459\pi$
$978$	−164.225	−5.25134
$979$	−11.2735	−0.360304
$980$	−239.195	−7.64081
$981$	57.4132	1.83306
$982$	66.0556	2.10792
$983$	−38.8828	−1.24017	−0.620085	−	0.784535i	$-0.712902\pi$
$983$	−38.8828	−1.24017	−0.620085	+	0.784535i	$0.712902\pi$
$984$	10.6921	0.340853
$985$	1.38248	0.0440494
$986$	−11.4599	−0.364958
$987$	−125.225	−3.98596
$988$	56.7038	1.80399
$989$	−2.86541	−0.0911148
$990$	−65.3637	−2.07739
$991$	−24.0283	−0.763285	−0.381643	−	0.924310i	$-0.624642\pi$
$991$	−24.0283	−0.763285	−0.381643	+	0.924310i	$0.624642\pi$
$992$	136.216	4.32486
$993$	−5.73610	−0.182030
$994$	−118.502	−3.75866
$995$	3.18788	0.101063
$996$	−100.970	−3.19935
$997$	13.7737	0.436219	0.218110	−	0.975924i	$-0.430011\pi$
$997$	13.7737	0.436219	0.218110	+	0.975924i	$0.430011\pi$
$998$	90.8863	2.87696
$999$	−31.4451	−0.994878

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8041.2.a.h.1.3	✓	74

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8041.2.a.h.1.3	✓	74	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 8041 = 11 \cdot 17 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8041.a (trivial)

\(f(q)\)	\(=\)	\(q-2.72314 q^{2} +3.10551 q^{3} +5.41549 q^{4} -3.61264 q^{5} -8.45674 q^{6} -4.38477 q^{7} -9.30085 q^{8} +6.64419 q^{9} +O(q^{10})\)	\(q-2.72314 q^{2} +3.10551 q^{3} +5.41549 q^{4} -3.61264 q^{5} -8.45674 q^{6} -4.38477 q^{7} -9.30085 q^{8} +6.64419 q^{9} +9.83772 q^{10} -1.00000 q^{11} +16.8179 q^{12} +2.27156 q^{13} +11.9403 q^{14} -11.2191 q^{15} +14.4965 q^{16} -1.00000 q^{17} -18.0931 q^{18} +4.60946 q^{19} -19.5642 q^{20} -13.6169 q^{21} +2.72314 q^{22} +2.86541 q^{23} -28.8839 q^{24} +8.05116 q^{25} -6.18577 q^{26} +11.3171 q^{27} -23.7456 q^{28} -4.20834 q^{29} +30.5511 q^{30} -6.52550 q^{31} -20.8744 q^{32} -3.10551 q^{33} +2.72314 q^{34} +15.8406 q^{35} +35.9815 q^{36} -2.77855 q^{37} -12.5522 q^{38} +7.05435 q^{39} +33.6006 q^{40} -0.370177 q^{41} +37.0808 q^{42} -1.00000 q^{43} -5.41549 q^{44} -24.0031 q^{45} -7.80292 q^{46} +9.19629 q^{47} +45.0191 q^{48} +12.2262 q^{49} -21.9244 q^{50} -3.10551 q^{51} +12.3016 q^{52} +7.33670 q^{53} -30.8180 q^{54} +3.61264 q^{55} +40.7820 q^{56} +14.3147 q^{57} +11.4599 q^{58} -12.3607 q^{59} -60.7568 q^{60} +2.29319 q^{61} +17.7699 q^{62} -29.1332 q^{63} +27.8508 q^{64} -8.20632 q^{65} +8.45674 q^{66} +13.7736 q^{67} -5.41549 q^{68} +8.89857 q^{69} -43.1361 q^{70} -9.92454 q^{71} -61.7966 q^{72} -8.37295 q^{73} +7.56639 q^{74} +25.0030 q^{75} +24.9625 q^{76} +4.38477 q^{77} -19.2100 q^{78} -1.86134 q^{79} -52.3708 q^{80} +15.2127 q^{81} +1.00804 q^{82} -6.00373 q^{83} -73.7423 q^{84} +3.61264 q^{85} +2.72314 q^{86} -13.0690 q^{87} +9.30085 q^{88} +11.2735 q^{89} +65.3637 q^{90} -9.96025 q^{91} +15.5176 q^{92} -20.2650 q^{93} -25.0428 q^{94} -16.6523 q^{95} -64.8256 q^{96} +4.42008 q^{97} -33.2936 q^{98} -6.64419 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 74 q - 7 q^{2} - 3 q^{3} + 79 q^{4} - 6 q^{5} - 12 q^{6} - 16 q^{7} - 21 q^{8} + 75 q^{9}+O(q^{10}) \) 74 * q - 7 * q^2 - 3 * q^3 + 79 * q^4 - 6 * q^5 - 12 * q^6 - 16 * q^7 - 21 * q^8 + 75 * q^9	\( 74 q - 7 q^{2} - 3 q^{3} + 79 q^{4} - 6 q^{5} - 12 q^{6} - 16 q^{7} - 21 q^{8} + 75 q^{9} - 9 q^{10} - 74 q^{11} - 3 q^{12} + 4 q^{13} - 5 q^{14} - 17 q^{15} + 85 q^{16} - 74 q^{17} - 23 q^{18} - 21 q^{20} - 22 q^{21} + 7 q^{22} - 23 q^{23} - 51 q^{24} + 90 q^{25} - 46 q^{26} - 27 q^{27} - 61 q^{28} - 63 q^{29} - 22 q^{30} - 31 q^{31} - 69 q^{32} + 3 q^{33} + 7 q^{34} - 20 q^{35} + 51 q^{36} + 8 q^{37} - 2 q^{38} - 77 q^{39} - 37 q^{40} - 64 q^{41} + 13 q^{42} - 74 q^{43} - 79 q^{44} - 12 q^{45} - 53 q^{46} - 32 q^{47} + 2 q^{48} + 78 q^{49} - 104 q^{50} + 3 q^{51} + 13 q^{52} + 25 q^{53} - 110 q^{54} + 6 q^{55} - 29 q^{56} - 29 q^{57} - 14 q^{58} - 61 q^{59} - 82 q^{60} - 36 q^{61} - 63 q^{62} - 104 q^{63} + 107 q^{64} - 65 q^{65} + 12 q^{66} + 33 q^{67} - 79 q^{68} - 34 q^{69} - 3 q^{70} - 168 q^{71} - 67 q^{72} - 47 q^{73} - 54 q^{74} - 53 q^{75} - 4 q^{76} + 16 q^{77} - 3 q^{78} - 79 q^{79} - 59 q^{80} + 70 q^{81} - 18 q^{82} - 36 q^{83} - 118 q^{84} + 6 q^{85} + 7 q^{86} - 24 q^{87} + 21 q^{88} - 24 q^{89} + 25 q^{90} - 14 q^{91} - 18 q^{92} - 13 q^{93} + 9 q^{94} - 155 q^{95} - 50 q^{96} + q^{97} - 60 q^{98} - 75 q^{99}+O(q^{100}) \) 74 * q - 7 * q^2 - 3 * q^3 + 79 * q^4 - 6 * q^5 - 12 * q^6 - 16 * q^7 - 21 * q^8 + 75 * q^9 - 9 * q^10 - 74 * q^11 - 3 * q^12 + 4 * q^13 - 5 * q^14 - 17 * q^15 + 85 * q^16 - 74 * q^17 - 23 * q^18 - 21 * q^20 - 22 * q^21 + 7 * q^22 - 23 * q^23 - 51 * q^24 + 90 * q^25 - 46 * q^26 - 27 * q^27 - 61 * q^28 - 63 * q^29 - 22 * q^30 - 31 * q^31 - 69 * q^32 + 3 * q^33 + 7 * q^34 - 20 * q^35 + 51 * q^36 + 8 * q^37 - 2 * q^38 - 77 * q^39 - 37 * q^40 - 64 * q^41 + 13 * q^42 - 74 * q^43 - 79 * q^44 - 12 * q^45 - 53 * q^46 - 32 * q^47 + 2 * q^48 + 78 * q^49 - 104 * q^50 + 3 * q^51 + 13 * q^52 + 25 * q^53 - 110 * q^54 + 6 * q^55 - 29 * q^56 - 29 * q^57 - 14 * q^58 - 61 * q^59 - 82 * q^60 - 36 * q^61 - 63 * q^62 - 104 * q^63 + 107 * q^64 - 65 * q^65 + 12 * q^66 + 33 * q^67 - 79 * q^68 - 34 * q^69 - 3 * q^70 - 168 * q^71 - 67 * q^72 - 47 * q^73 - 54 * q^74 - 53 * q^75 - 4 * q^76 + 16 * q^77 - 3 * q^78 - 79 * q^79 - 59 * q^80 + 70 * q^81 - 18 * q^82 - 36 * q^83 - 118 * q^84 + 6 * q^85 + 7 * q^86 - 24 * q^87 + 21 * q^88 - 24 * q^89 + 25 * q^90 - 14 * q^91 - 18 * q^92 - 13 * q^93 + 9 * q^94 - 155 * q^95 - 50 * q^96 + q^97 - 60 * q^98 - 75 * q^99

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