LMFDB - Embedded newform 8041.2.a.j.1.61

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			1.61
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)

$f(q)$	$=$	$q+1.66273 q^{2} -1.91287 q^{3} +0.764679 q^{4} -2.26060 q^{5} -3.18060 q^{6} +4.75760 q^{7} -2.05401 q^{8} +0.659084 q^{9} +O(q^{10})$	\(q+1.66273 q^{2} -1.91287 q^{3} +0.764679 q^{4} -2.26060 q^{5} -3.18060 q^{6} +4.75760 q^{7} -2.05401 q^{8} +0.659084 q^{9} -3.75878 q^{10} +1.00000 q^{11} -1.46273 q^{12} -1.49350 q^{13} +7.91062 q^{14} +4.32425 q^{15} -4.94462 q^{16} +1.00000 q^{17} +1.09588 q^{18} -7.12302 q^{19} -1.72864 q^{20} -9.10069 q^{21} +1.66273 q^{22} +6.90085 q^{23} +3.92906 q^{24} +0.110334 q^{25} -2.48329 q^{26} +4.47788 q^{27} +3.63804 q^{28} -2.62768 q^{29} +7.19007 q^{30} +4.01153 q^{31} -4.11357 q^{32} -1.91287 q^{33} +1.66273 q^{34} -10.7551 q^{35} +0.503987 q^{36} -7.39303 q^{37} -11.8437 q^{38} +2.85687 q^{39} +4.64330 q^{40} +7.46428 q^{41} -15.1320 q^{42} +1.00000 q^{43} +0.764679 q^{44} -1.48993 q^{45} +11.4743 q^{46} -11.8108 q^{47} +9.45844 q^{48} +15.6348 q^{49} +0.183456 q^{50} -1.91287 q^{51} -1.14205 q^{52} -5.45663 q^{53} +7.44551 q^{54} -2.26060 q^{55} -9.77216 q^{56} +13.6254 q^{57} -4.36913 q^{58} +4.63734 q^{59} +3.30666 q^{60} +11.0893 q^{61} +6.67010 q^{62} +3.13566 q^{63} +3.04948 q^{64} +3.37621 q^{65} -3.18060 q^{66} -8.38813 q^{67} +0.764679 q^{68} -13.2004 q^{69} -17.8828 q^{70} +4.75702 q^{71} -1.35376 q^{72} -8.86850 q^{73} -12.2926 q^{74} -0.211055 q^{75} -5.44682 q^{76} +4.75760 q^{77} +4.75022 q^{78} -4.00403 q^{79} +11.1778 q^{80} -10.5429 q^{81} +12.4111 q^{82} +0.839781 q^{83} -6.95911 q^{84} -2.26060 q^{85} +1.66273 q^{86} +5.02642 q^{87} -2.05401 q^{88} -8.98851 q^{89} -2.47735 q^{90} -7.10547 q^{91} +5.27693 q^{92} -7.67355 q^{93} -19.6383 q^{94} +16.1023 q^{95} +7.86873 q^{96} +11.0355 q^{97} +25.9965 q^{98} +0.659084 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	1.66273	1.17573	0.587865	−	0.808959i	$-0.299969\pi$
$2$	1.66273	1.17573	0.587865	+	0.808959i	$0.299969\pi$
$3$	−1.91287	−1.10440	−0.552199	−	0.833712i	$-0.686211\pi$
$3$	−1.91287	−1.10440	−0.552199	+	0.833712i	$0.686211\pi$
$4$	0.764679	0.382339
$5$	−2.26060	−1.01097	−0.505487	−	0.862834i	$-0.668687\pi$
$5$	−2.26060	−1.01097	−0.505487	+	0.862834i	$0.668687\pi$
$6$	−3.18060	−1.29847
$7$	4.75760	1.79821	0.899103	−	0.437738i	$-0.144220\pi$
$7$	4.75760	1.79821	0.899103	+	0.437738i	$0.144220\pi$
$8$	−2.05401	−0.726202
$9$	0.659084	0.219695
$10$	−3.75878	−1.18863
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−1.46273	−0.422255
$13$	−1.49350	−0.414222	−0.207111	−	0.978317i	$-0.566406\pi$
$13$	−1.49350	−0.414222	−0.207111	+	0.978317i	$0.566406\pi$
$14$	7.91062	2.11420
$15$	4.32425	1.11652
$16$	−4.94462	−1.23616
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	1.09588	0.258301
$19$	−7.12302	−1.63413	−0.817066	−	0.576544i	$-0.804401\pi$
$19$	−7.12302	−1.63413	−0.817066	+	0.576544i	$0.804401\pi$
$20$	−1.72864	−0.386535
$21$	−9.10069	−1.98593
$22$	1.66273	0.354496
$23$	6.90085	1.43893	0.719463	−	0.694531i	$-0.244388\pi$
$23$	6.90085	1.43893	0.719463	+	0.694531i	$0.244388\pi$
$24$	3.92906	0.802016
$25$	0.110334	0.0220668
$26$	−2.48329	−0.487013
$27$	4.47788	0.861768
$28$	3.63804	0.687525
$29$	−2.62768	−0.487948	−0.243974	−	0.969782i	$-0.578451\pi$
$29$	−2.62768	−0.487948	−0.243974	+	0.969782i	$0.578451\pi$
$30$	7.19007	1.31272
$31$	4.01153	0.720492	0.360246	−	0.932857i	$-0.382693\pi$
$31$	4.01153	0.720492	0.360246	+	0.932857i	$0.382693\pi$
$32$	−4.11357	−0.727183
$33$	−1.91287	−0.332988
$34$	1.66273	0.285156
$35$	−10.7551	−1.81794
$36$	0.503987	0.0839979
$37$	−7.39303	−1.21541	−0.607704	−	0.794164i	$-0.707909\pi$
$37$	−7.39303	−1.21541	−0.607704	+	0.794164i	$0.707909\pi$
$38$	−11.8437	−1.92130
$39$	2.85687	0.457466
$40$	4.64330	0.734170
$41$	7.46428	1.16572	0.582862	−	0.812571i	$-0.301933\pi$
$41$	7.46428	1.16572	0.582862	+	0.812571i	$0.301933\pi$
$42$	−15.1320	−2.33492
$43$	1.00000	0.152499
$43$	1.00000	0.152499
$44$	0.764679	0.115280
$45$	−1.48993	−0.222105
$46$	11.4743	1.69179
$47$	−11.8108	−1.72279	−0.861394	−	0.507937i	$-0.830408\pi$
$47$	−11.8108	−1.72279	−0.861394	+	0.507937i	$0.830408\pi$
$48$	9.45844	1.36521
$49$	15.6348	2.23354
$50$	0.183456	0.0259446
$51$	−1.91287	−0.267856
$52$	−1.14205	−0.158373
$53$	−5.45663	−0.749526	−0.374763	−	0.927121i	$-0.622276\pi$
$53$	−5.45663	−0.749526	−0.374763	+	0.927121i	$0.622276\pi$
$54$	7.44551	1.01321
$55$	−2.26060	−0.304820
$56$	−9.77216	−1.30586
$57$	13.6254	1.80473
$58$	−4.36913	−0.573695
$59$	4.63734	0.603730	0.301865	−	0.953351i	$-0.402391\pi$
$59$	4.63734	0.603730	0.301865	+	0.953351i	$0.402391\pi$
$60$	3.30666	0.426888
$61$	11.0893	1.41984	0.709920	−	0.704283i	$-0.248731\pi$
$61$	11.0893	1.41984	0.709920	+	0.704283i	$0.248731\pi$
$62$	6.67010	0.847104
$63$	3.13566	0.395056
$64$	3.04948	0.381186
$65$	3.37621	0.418767
$66$	−3.18060	−0.391504
$67$	−8.38813	−1.02477	−0.512387	−	0.858755i	$-0.671238\pi$
$67$	−8.38813	−1.02477	−0.512387	+	0.858755i	$0.671238\pi$
$68$	0.764679	0.0927309
$69$	−13.2004	−1.58915
$70$	−17.8828	−2.13740
$71$	4.75702	0.564555	0.282277	−	0.959333i	$-0.408910\pi$
$71$	4.75702	0.564555	0.282277	+	0.959333i	$0.408910\pi$
$72$	−1.35376	−0.159543
$73$	−8.86850	−1.03798	−0.518990	−	0.854781i	$-0.673692\pi$
$73$	−8.86850	−1.03798	−0.518990	+	0.854781i	$0.673692\pi$
$74$	−12.2926	−1.42899
$75$	−0.211055	−0.0243706
$76$	−5.44682	−0.624793
$77$	4.75760	0.542179
$78$	4.75022	0.537856
$79$	−4.00403	−0.450488	−0.225244	−	0.974302i	$-0.572318\pi$
$79$	−4.00403	−0.450488	−0.225244	+	0.974302i	$0.572318\pi$
$80$	11.1778	1.24972
$81$	−10.5429	−1.17143
$82$	12.4111	1.37058
$83$	0.839781	0.0921779	0.0460889	−	0.998937i	$-0.485324\pi$
$83$	0.839781	0.0921779	0.0460889	+	0.998937i	$0.485324\pi$
$84$	−6.95911	−0.759301
$85$	−2.26060	−0.245197
$86$	1.66273	0.179297
$87$	5.02642	0.538889
$88$	−2.05401	−0.218958
$89$	−8.98851	−0.952780	−0.476390	−	0.879234i	$-0.658055\pi$
$89$	−8.98851	−0.952780	−0.476390	+	0.879234i	$0.658055\pi$
$90$	−2.47735	−0.261136
$91$	−7.10547	−0.744856
$92$	5.27693	0.550158
$93$	−7.67355	−0.795710
$94$	−19.6383	−2.02553
$95$	16.1023	1.65206
$96$	7.86873	0.803099
$97$	11.0355	1.12048	0.560241	−	0.828329i	$-0.310708\pi$
$97$	11.0355	1.12048	0.560241	+	0.828329i	$0.310708\pi$
$98$	25.9965	2.62604
$99$	0.659084	0.0662404
$100$	0.0843701	0.00843701
$101$	−5.35214	−0.532558	−0.266279	−	0.963896i	$-0.585794\pi$
$101$	−5.35214	−0.532558	−0.266279	+	0.963896i	$0.585794\pi$
$102$	−3.18060	−0.314926
$103$	12.0799	1.19026	0.595132	−	0.803628i	$-0.297100\pi$
$103$	12.0799	1.19026	0.595132	+	0.803628i	$0.297100\pi$
$104$	3.06766	0.300809
$105$	20.5731	2.00773
$106$	−9.07292	−0.881240
$107$	3.68464	0.356208	0.178104	−	0.984012i	$-0.443004\pi$
$107$	3.68464	0.356208	0.178104	+	0.984012i	$0.443004\pi$
$108$	3.42414	0.329488
$109$	17.6132	1.68704	0.843518	−	0.537100i	$-0.180480\pi$
$109$	17.6132	1.68704	0.843518	+	0.537100i	$0.180480\pi$
$110$	−3.75878	−0.358386
$111$	14.1419	1.34229
$112$	−23.5246	−2.22286
$113$	−18.3409	−1.72537	−0.862686	−	0.505740i	$-0.831219\pi$
$113$	−18.3409	−1.72537	−0.862686	+	0.505740i	$0.831219\pi$
$114$	22.6554	2.12188
$115$	−15.6001	−1.45472
$116$	−2.00933	−0.186562
$117$	−0.984341	−0.0910024
$118$	7.71065	0.709823
$119$	4.75760	0.436129
$120$	−8.88205	−0.810816
$121$	1.00000	0.0909091
$122$	18.4385	1.66935
$123$	−14.2782	−1.28742
$124$	3.06753	0.275472
$125$	11.0536	0.988664
$126$	5.21376	0.464479
$127$	11.7773	1.04506	0.522532	−	0.852619i	$-0.324987\pi$
$127$	11.7773	1.04506	0.522532	+	0.852619i	$0.324987\pi$
$128$	13.2976	1.17535
$129$	−1.91287	−0.168419
$130$	5.61373	0.492357
$131$	16.4463	1.43692	0.718460	−	0.695569i	$-0.244847\pi$
$131$	16.4463	1.43692	0.718460	+	0.695569i	$0.244847\pi$
$132$	−1.46273	−0.127315
$133$	−33.8885	−2.93851
$134$	−13.9472	−1.20486
$135$	−10.1227	−0.871224
$136$	−2.05401	−0.176130
$137$	14.2510	1.21754	0.608772	−	0.793345i	$-0.291662\pi$
$137$	14.2510	1.21754	0.608772	+	0.793345i	$0.291662\pi$
$138$	−21.9488	−1.86841
$139$	−14.1003	−1.19597	−0.597986	−	0.801507i	$-0.704032\pi$
$139$	−14.1003	−1.19597	−0.597986	+	0.801507i	$0.704032\pi$
$140$	−8.22417	−0.695069
$141$	22.5926	1.90264
$142$	7.90965	0.663763
$143$	−1.49350	−0.124893
$144$	−3.25892	−0.271577
$145$	5.94015	0.493303
$146$	−14.7459	−1.22038
$147$	−29.9074	−2.46672
$148$	−5.65329	−0.464698
$149$	−8.73579	−0.715664	−0.357832	−	0.933786i	$-0.616484\pi$
$149$	−8.73579	−0.715664	−0.357832	+	0.933786i	$0.616484\pi$
$150$	−0.350928	−0.0286532
$151$	−6.98144	−0.568142	−0.284071	−	0.958803i	$-0.591685\pi$
$151$	−6.98144	−0.568142	−0.284071	+	0.958803i	$0.591685\pi$
$152$	14.6307	1.18671
$153$	0.659084	0.0532838
$154$	7.91062	0.637456
$155$	−9.06848	−0.728398
$156$	2.18459	0.174907
$157$	−4.53250	−0.361733	−0.180867	−	0.983508i	$-0.557890\pi$
$157$	−4.53250	−0.361733	−0.180867	+	0.983508i	$0.557890\pi$
$158$	−6.65762	−0.529652
$159$	10.4378	0.827775
$160$	9.29915	0.735163
$161$	32.8315	2.58748
$162$	−17.5300	−1.37728
$163$	6.64195	0.520238	0.260119	−	0.965577i	$-0.416238\pi$
$163$	6.64195	0.520238	0.260119	+	0.965577i	$0.416238\pi$
$164$	5.70777	0.445702
$165$	4.32425	0.336642
$166$	1.39633	0.108376
$167$	−25.4022	−1.96568	−0.982839	−	0.184466i	$-0.940944\pi$
$167$	−25.4022	−1.96568	−0.982839	+	0.184466i	$0.940944\pi$
$168$	18.6929	1.44219
$169$	−10.7695	−0.828420
$170$	−3.75878	−0.288285
$171$	−4.69467	−0.359010
$172$	0.764679	0.0583062
$173$	13.6026	1.03418	0.517092	−	0.855930i	$-0.327015\pi$
$173$	13.6026	1.03418	0.517092	+	0.855930i	$0.327015\pi$
$174$	8.35759	0.633587
$175$	0.524926	0.0396807
$176$	−4.94462	−0.372715
$177$	−8.87064	−0.666758
$178$	−14.9455	−1.12021
$179$	−5.79324	−0.433007	−0.216503	−	0.976282i	$-0.569465\pi$
$179$	−5.79324	−0.433007	−0.216503	+	0.976282i	$0.569465\pi$
$180$	−1.13932	−0.0849196
$181$	8.37942	0.622838	0.311419	−	0.950273i	$-0.399196\pi$
$181$	8.37942	0.622838	0.311419	+	0.950273i	$0.399196\pi$
$182$	−11.8145	−0.875749
$183$	−21.2124	−1.56807
$184$	−14.1744	−1.04495
$185$	16.7127	1.22874
$186$	−12.7591	−0.935539
$187$	1.00000	0.0731272
$188$	−9.03150	−0.658690
$189$	21.3040	1.54963
$190$	26.7739	1.94238
$191$	19.7170	1.42667	0.713337	−	0.700821i	$-0.247183\pi$
$191$	19.7170	1.42667	0.713337	+	0.700821i	$0.247183\pi$
$192$	−5.83328	−0.420981
$193$	22.7503	1.63761	0.818803	−	0.574075i	$-0.194638\pi$
$193$	22.7503	1.63761	0.818803	+	0.574075i	$0.194638\pi$
$194$	18.3490	1.31738
$195$	−6.45826	−0.462486
$196$	11.9556	0.853971
$197$	20.7820	1.48066	0.740328	−	0.672246i	$-0.234670\pi$
$197$	20.7820	1.48066	0.740328	+	0.672246i	$0.234670\pi$
$198$	1.09588	0.0778808
$199$	20.0742	1.42302	0.711512	−	0.702674i	$-0.248011\pi$
$199$	20.0742	1.42302	0.711512	+	0.702674i	$0.248011\pi$
$200$	−0.226627	−0.0160250
$201$	16.0454	1.13176
$202$	−8.89918	−0.626144
$203$	−12.5015	−0.877431
$204$	−1.46273	−0.102412
$205$	−16.8738	−1.17852
$206$	20.0856	1.39943
$207$	4.54824	0.316124
$208$	7.38479	0.512043
$209$	−7.12302	−0.492710
$210$	34.2075	2.36054
$211$	16.8273	1.15844	0.579221	−	0.815171i	$-0.303357\pi$
$211$	16.8273	1.15844	0.579221	+	0.815171i	$0.303357\pi$
$212$	−4.17257	−0.286573
$213$	−9.09958	−0.623493
$214$	6.12657	0.418804
$215$	−2.26060	−0.154172
$216$	−9.19760	−0.625817
$217$	19.0853	1.29559
$218$	29.2860	1.98350
$219$	16.9643	1.14634
$220$	−1.72864	−0.116545
$221$	−1.49350	−0.100464
$222$	23.5143	1.57817
$223$	−19.9390	−1.33522	−0.667608	−	0.744513i	$-0.732682\pi$
$223$	−19.9390	−1.33522	−0.667608	+	0.744513i	$0.732682\pi$
$224$	−19.5707	−1.30762
$225$	0.0727194	0.00484796
$226$	−30.4961	−2.02857
$227$	−9.20695	−0.611087	−0.305543	−	0.952178i	$-0.598838\pi$
$227$	−9.20695	−0.611087	−0.305543	+	0.952178i	$0.598838\pi$
$228$	10.4191	0.690020
$229$	22.6774	1.49856	0.749282	−	0.662251i	$-0.230399\pi$
$229$	22.6774	1.49856	0.749282	+	0.662251i	$0.230399\pi$
$230$	−25.9388	−1.71035
$231$	−9.10069	−0.598782
$232$	5.39728	0.354349
$233$	21.9569	1.43845	0.719223	−	0.694779i	$-0.244498\pi$
$233$	21.9569	1.43845	0.719223	+	0.694779i	$0.244498\pi$
$234$	−1.63670	−0.106994
$235$	26.6996	1.74169
$236$	3.54607	0.230830
$237$	7.65920	0.497518
$238$	7.91062	0.512769
$239$	19.8792	1.28588	0.642940	−	0.765916i	$-0.277714\pi$
$239$	19.8792	1.28588	0.642940	+	0.765916i	$0.277714\pi$
$240$	−21.3818	−1.38019
$241$	17.4616	1.12480	0.562401	−	0.826865i	$-0.309878\pi$
$241$	17.4616	1.12480	0.562401	+	0.826865i	$0.309878\pi$
$242$	1.66273	0.106884
$243$	6.73353	0.431956
$244$	8.47975	0.542860
$245$	−35.3441	−2.25805
$246$	−23.7408	−1.51366
$247$	10.6382	0.676894
$248$	−8.23972	−0.523223
$249$	−1.60639	−0.101801
$250$	18.3792	1.16240
$251$	14.4946	0.914889	0.457445	−	0.889238i	$-0.348765\pi$
$251$	14.4946	0.914889	0.457445	+	0.889238i	$0.348765\pi$
$252$	2.39777	0.151045
$253$	6.90085	0.433853
$254$	19.5825	1.22871
$255$	4.32425	0.270795
$256$	16.0114	1.00071
$257$	13.7238	0.856068	0.428034	−	0.903763i	$-0.359206\pi$
$257$	13.7238	0.856068	0.428034	+	0.903763i	$0.359206\pi$
$258$	−3.18060	−0.198015
$259$	−35.1731	−2.18555
$260$	2.58172	0.160111
$261$	−1.73186	−0.107200
$262$	27.3458	1.68943
$263$	12.3407	0.760962	0.380481	−	0.924789i	$-0.375758\pi$
$263$	12.3407	0.760962	0.380481	+	0.924789i	$0.375758\pi$
$264$	3.92906	0.241817
$265$	12.3353	0.757751
$266$	−56.3475	−3.45489
$267$	17.1939	1.05225
$268$	−6.41422	−0.391811
$269$	−23.4942	−1.43247	−0.716235	−	0.697859i	$-0.754136\pi$
$269$	−23.4942	−1.43247	−0.716235	+	0.697859i	$0.754136\pi$
$270$	−16.8314	−1.02432
$271$	−27.9941	−1.70052	−0.850260	−	0.526363i	$-0.823555\pi$
$271$	−27.9941	−1.70052	−0.850260	+	0.526363i	$0.823555\pi$
$272$	−4.94462	−0.299812
$273$	13.5919	0.822618
$274$	23.6956	1.43150
$275$	0.110334	0.00665340
$276$	−10.0941	−0.607593
$277$	1.09306	0.0656753	0.0328377	−	0.999461i	$-0.489546\pi$
$277$	1.09306	0.0656753	0.0328377	+	0.999461i	$0.489546\pi$
$278$	−23.4450	−1.40614
$279$	2.64393	0.158288
$280$	22.0910	1.32019
$281$	14.2193	0.848255	0.424127	−	0.905603i	$-0.360581\pi$
$281$	14.2193	0.848255	0.424127	+	0.905603i	$0.360581\pi$
$282$	37.5655	2.23699
$283$	−15.1955	−0.903278	−0.451639	−	0.892201i	$-0.649160\pi$
$283$	−15.1955	−0.903278	−0.451639	+	0.892201i	$0.649160\pi$
$284$	3.63759	0.215851
$285$	−30.8017	−1.82454
$286$	−2.48329	−0.146840
$287$	35.5121	2.09621
$288$	−2.71119	−0.159758
$289$	1.00000	0.0588235
$290$	9.87688	0.579990
$291$	−21.1095	−1.23746
$292$	−6.78155	−0.396860
$293$	−9.67665	−0.565316	−0.282658	−	0.959221i	$-0.591216\pi$
$293$	−9.67665	−0.565316	−0.282658	+	0.959221i	$0.591216\pi$
$294$	−49.7280	−2.90019
$295$	−10.4832	−0.610355
$296$	15.1854	0.882631
$297$	4.47788	0.259833
$298$	−14.5253	−0.841427
$299$	−10.3064	−0.596035
$300$	−0.161389	−0.00931782
$301$	4.75760	0.274224
$302$	−11.6083	−0.667981
$303$	10.2380	0.588156
$304$	35.2207	2.02004
$305$	−25.0685	−1.43542
$306$	1.09588	0.0626473
$307$	−3.27815	−0.187094	−0.0935470	−	0.995615i	$-0.529821\pi$
$307$	−3.27815	−0.187094	−0.0935470	+	0.995615i	$0.529821\pi$
$308$	3.63804	0.207296
$309$	−23.1072	−1.31452
$310$	−15.0785	−0.856399
$311$	24.0289	1.36256	0.681278	−	0.732025i	$-0.261425\pi$
$311$	24.0289	1.36256	0.681278	+	0.732025i	$0.261425\pi$
$312$	−5.86804	−0.332213
$313$	21.3932	1.20922	0.604608	−	0.796523i	$-0.293330\pi$
$313$	21.3932	1.20922	0.604608	+	0.796523i	$0.293330\pi$
$314$	−7.53634	−0.425300
$315$	−7.08849	−0.399391
$316$	−3.06179	−0.172239
$317$	8.35687	0.469369	0.234684	−	0.972072i	$-0.424594\pi$
$317$	8.35687	0.469369	0.234684	+	0.972072i	$0.424594\pi$
$318$	17.3553	0.973239
$319$	−2.62768	−0.147122
$320$	−6.89368	−0.385368
$321$	−7.04825	−0.393395
$322$	54.5900	3.04218
$323$	−7.12302	−0.396335
$324$	−8.06190	−0.447883
$325$	−0.164784	−0.00914056
$326$	11.0438	0.611659
$327$	−33.6918	−1.86316
$328$	−15.3317	−0.846551
$329$	−56.1913	−3.09793
$330$	7.19007	0.395800
$331$	11.5332	0.633921	0.316961	−	0.948439i	$-0.397338\pi$
$331$	11.5332	0.633921	0.316961	+	0.948439i	$0.397338\pi$
$332$	0.642162	0.0352432
$333$	−4.87263	−0.267018
$334$	−42.2370	−2.31110
$335$	18.9622	1.03602
$336$	44.9995	2.45492
$337$	20.2293	1.10196	0.550981	−	0.834518i	$-0.314254\pi$
$337$	20.2293	1.10196	0.550981	+	0.834518i	$0.314254\pi$
$338$	−17.9067	−0.973998
$339$	35.0839	1.90550
$340$	−1.72864	−0.0937485
$341$	4.01153	0.217237
$342$	−7.80598	−0.422099
$343$	41.0809	2.21816
$344$	−2.05401	−0.110745
$345$	29.8410	1.60658
$346$	22.6174	1.21592
$347$	−27.5981	−1.48154	−0.740772	−	0.671757i	$-0.765540\pi$
$347$	−27.5981	−1.48154	−0.740772	+	0.671757i	$0.765540\pi$
$348$	3.84360	0.206038
$349$	−25.2101	−1.34947	−0.674733	−	0.738062i	$-0.735741\pi$
$349$	−25.2101	−1.34947	−0.674733	+	0.738062i	$0.735741\pi$
$350$	0.872811	0.0466537
$351$	−6.68770	−0.356963
$352$	−4.11357	−0.219254
$353$	6.07861	0.323532	0.161766	−	0.986829i	$-0.448281\pi$
$353$	6.07861	0.323532	0.161766	+	0.986829i	$0.448281\pi$
$354$	−14.7495	−0.783927
$355$	−10.7537	−0.570750
$356$	−6.87332	−0.364285
$357$	−9.10069	−0.481660
$358$	−9.63260	−0.509099
$359$	27.6182	1.45763	0.728816	−	0.684709i	$-0.240071\pi$
$359$	27.6182	1.45763	0.728816	+	0.684709i	$0.240071\pi$
$360$	3.06033	0.161293
$361$	31.7374	1.67039
$362$	13.9327	0.732288
$363$	−1.91287	−0.100400
$364$	−5.43341	−0.284788
$365$	20.0482	1.04937
$366$	−35.2706	−1.84362
$367$	0.287028	0.0149827	0.00749137	−	0.999972i	$-0.497615\pi$
$367$	0.287028	0.0149827	0.00749137	+	0.999972i	$0.497615\pi$
$368$	−34.1221	−1.77874
$369$	4.91958	0.256103
$370$	27.7888	1.44467
$371$	−25.9605	−1.34780
$372$	−5.86780	−0.304231
$373$	2.36121	0.122259	0.0611295	−	0.998130i	$-0.480530\pi$
$373$	2.36121	0.122259	0.0611295	+	0.998130i	$0.480530\pi$
$374$	1.66273	0.0859778
$375$	−21.1441	−1.09188
$376$	24.2596	1.25109
$377$	3.92444	0.202119
$378$	35.4228	1.82195
$379$	24.7318	1.27039	0.635194	−	0.772352i	$-0.280920\pi$
$379$	24.7318	1.27039	0.635194	+	0.772352i	$0.280920\pi$
$380$	12.3131	0.631649
$381$	−22.5284	−1.15417
$382$	32.7841	1.67738
$383$	0.968467	0.0494863	0.0247432	−	0.999694i	$-0.492123\pi$
$383$	0.968467	0.0494863	0.0247432	+	0.999694i	$0.492123\pi$
$384$	−25.4366	−1.29806
$385$	−10.7551	−0.548129
$386$	37.8277	1.92538
$387$	0.659084	0.0335031
$388$	8.43859	0.428405
$389$	−9.20750	−0.466839	−0.233419	−	0.972376i	$-0.574992\pi$
$389$	−9.20750	−0.466839	−0.233419	+	0.972376i	$0.574992\pi$
$390$	−10.7384	−0.543758
$391$	6.90085	0.348991
$392$	−32.1140	−1.62200
$393$	−31.4597	−1.58693
$394$	34.5549	1.74085
$395$	9.05152	0.455431
$396$	0.503987	0.0253263
$397$	30.8879	1.55022	0.775110	−	0.631826i	$-0.217694\pi$
$397$	30.8879	1.55022	0.775110	+	0.631826i	$0.217694\pi$
$398$	33.3781	1.67309
$399$	64.8244	3.24528
$400$	−0.545561	−0.0272780
$401$	24.1195	1.20447	0.602235	−	0.798319i	$-0.294277\pi$
$401$	24.1195	1.20447	0.602235	+	0.798319i	$0.294277\pi$
$402$	26.6793	1.33064
$403$	−5.99121	−0.298444
$404$	−4.09267	−0.203618
$405$	23.8332	1.18428
$406$	−20.7866	−1.03162
$407$	−7.39303	−0.366459
$408$	3.92906	0.194517
$409$	−6.08352	−0.300811	−0.150405	−	0.988624i	$-0.548058\pi$
$409$	−6.08352	−0.300811	−0.150405	+	0.988624i	$0.548058\pi$
$410$	−28.0566	−1.38562
$411$	−27.2603	−1.34465
$412$	9.23721	0.455085
$413$	22.0626	1.08563
$414$	7.56250	0.371677
$415$	−1.89841	−0.0931894
$416$	6.14361	0.301215
$417$	26.9721	1.32083
$418$	−11.8437	−0.579293
$419$	−7.10970	−0.347331	−0.173666	−	0.984805i	$-0.555561\pi$
$419$	−7.10970	−0.347331	−0.173666	+	0.984805i	$0.555561\pi$
$420$	15.7318	0.767633
$421$	6.09974	0.297283	0.148642	−	0.988891i	$-0.452510\pi$
$421$	6.09974	0.297283	0.148642	+	0.988891i	$0.452510\pi$
$422$	27.9793	1.36201
$423$	−7.78433	−0.378487
$424$	11.2080	0.544307
$425$	0.110334	0.00535199
$426$	−15.1302	−0.733059
$427$	52.7585	2.55316
$428$	2.81757	0.136192
$429$	2.85687	0.137931
$430$	−3.75878	−0.181264
$431$	3.24654	0.156381	0.0781903	−	0.996938i	$-0.475086\pi$
$431$	3.24654	0.156381	0.0781903	+	0.996938i	$0.475086\pi$
$432$	−22.1414	−1.06528
$433$	−37.5522	−1.80464	−0.902321	−	0.431065i	$-0.858138\pi$
$433$	−37.5522	−1.80464	−0.902321	+	0.431065i	$0.858138\pi$
$434$	31.7337	1.52327
$435$	−11.3628	−0.544802
$436$	13.4684	0.645020
$437$	−49.1549	−2.35140
$438$	28.2071	1.34779
$439$	−9.32963	−0.445279	−0.222640	−	0.974901i	$-0.571467\pi$
$439$	−9.32963	−0.445279	−0.222640	+	0.974901i	$0.571467\pi$
$440$	4.64330	0.221361
$441$	10.3046	0.490697
$442$	−2.48329	−0.118118
$443$	26.9671	1.28125	0.640623	−	0.767855i	$-0.278676\pi$
$443$	26.9671	1.28125	0.640623	+	0.767855i	$0.278676\pi$
$444$	10.8140	0.513211
$445$	20.3195	0.963235
$446$	−33.1533	−1.56985
$447$	16.7105	0.790377
$448$	14.5082	0.685450
$449$	−16.9187	−0.798441	−0.399221	−	0.916855i	$-0.630719\pi$
$449$	−16.9187	−0.798441	−0.399221	+	0.916855i	$0.630719\pi$
$450$	0.120913	0.00569989
$451$	7.46428	0.351479
$452$	−14.0249	−0.659677
$453$	13.3546	0.627454
$454$	−15.3087	−0.718473
$455$	16.0627	0.753030
$456$	−27.9868	−1.31060
$457$	40.8529	1.91102	0.955510	−	0.294960i	$-0.0953063\pi$
$457$	40.8529	1.91102	0.955510	+	0.294960i	$0.0953063\pi$
$458$	37.7064	1.76191
$459$	4.47788	0.209009
$460$	−11.9291	−0.556195
$461$	16.6225	0.774188	0.387094	−	0.922040i	$-0.373479\pi$
$461$	16.6225	0.774188	0.387094	+	0.922040i	$0.373479\pi$
$462$	−15.1320	−0.704005
$463$	−5.36298	−0.249239	−0.124619	−	0.992205i	$-0.539771\pi$
$463$	−5.36298	−0.249239	−0.124619	+	0.992205i	$0.539771\pi$
$464$	12.9929	0.603180
$465$	17.3469	0.804441
$466$	36.5085	1.69122
$467$	4.11816	0.190566	0.0952829	−	0.995450i	$-0.469624\pi$
$467$	4.11816	0.190566	0.0952829	+	0.995450i	$0.469624\pi$
$468$	−0.752705	−0.0347938
$469$	−39.9074	−1.84275
$470$	44.3944	2.04776
$471$	8.67011	0.399497
$472$	−9.52514	−0.438430
$473$	1.00000	0.0459800
$474$	12.7352	0.584947
$475$	−0.785912	−0.0360601
$476$	3.63804	0.166749
$477$	−3.59638	−0.164667
$478$	33.0538	1.51185
$479$	−43.3506	−1.98074	−0.990370	−	0.138449i	$-0.955788\pi$
$479$	−43.3506	−1.98074	−0.990370	+	0.138449i	$0.955788\pi$
$480$	−17.7881	−0.811912
$481$	11.0415	0.503448
$482$	29.0340	1.32246
$483$	−62.8025	−2.85761
$484$	0.764679	0.0347581
$485$	−24.9469	−1.13278
$486$	11.1961	0.507863
$487$	−7.28461	−0.330097	−0.165049	−	0.986285i	$-0.552778\pi$
$487$	−7.28461	−0.330097	−0.165049	+	0.986285i	$0.552778\pi$
$488$	−22.7775	−1.03109
$489$	−12.7052	−0.574549
$490$	−58.7678	−2.65486
$491$	−20.3309	−0.917523	−0.458761	−	0.888560i	$-0.651707\pi$
$491$	−20.3309	−0.917523	−0.458761	+	0.888560i	$0.651707\pi$
$492$	−10.9182	−0.492232
$493$	−2.62768	−0.118345
$494$	17.6885	0.795844
$495$	−1.48993	−0.0669673
$496$	−19.8355	−0.890641
$497$	22.6320	1.01518
$498$	−2.67100	−0.119690
$499$	29.6614	1.32783	0.663913	−	0.747810i	$-0.268894\pi$
$499$	29.6614	1.32783	0.663913	+	0.747810i	$0.268894\pi$
$500$	8.45245	0.378005
$501$	48.5911	2.17089
$502$	24.1006	1.07566
$503$	2.67854	0.119430	0.0597152	−	0.998215i	$-0.480981\pi$
$503$	2.67854	0.119430	0.0597152	+	0.998215i	$0.480981\pi$
$504$	−6.44067	−0.286890
$505$	12.0991	0.538402
$506$	11.4743	0.510093
$507$	20.6006	0.914905
$508$	9.00584	0.399569
$509$	3.84516	0.170434	0.0852168	−	0.996362i	$-0.472842\pi$
$509$	3.84516	0.170434	0.0852168	+	0.996362i	$0.472842\pi$
$510$	7.19007	0.318382
$511$	−42.1928	−1.86650
$512$	0.0274479	0.00121304
$513$	−31.8960	−1.40824
$514$	22.8190	1.00650
$515$	−27.3078	−1.20332
$516$	−1.46273	−0.0643932
$517$	−11.8108	−0.519440
$518$	−58.4835	−2.56962
$519$	−26.0200	−1.14215
$520$	−6.93477	−0.304110
$521$	24.8035	1.08666	0.543330	−	0.839519i	$-0.317163\pi$
$521$	24.8035	1.08666	0.543330	+	0.839519i	$0.317163\pi$
$522$	−2.87962	−0.126038
$523$	−1.90390	−0.0832517	−0.0416259	−	0.999133i	$-0.513254\pi$
$523$	−1.90390	−0.0832517	−0.0416259	+	0.999133i	$0.513254\pi$
$524$	12.5761	0.549391
$525$	−1.00412	−0.0438233
$526$	20.5193	0.894685
$527$	4.01153	0.174745
$528$	9.45844	0.411626
$529$	24.6217	1.07051
$530$	20.5103	0.890910
$531$	3.05640	0.132636
$532$	−25.9138	−1.12351
$533$	−11.1479	−0.482869
$534$	28.5888	1.23716
$535$	−8.32952	−0.360117
$536$	17.2293	0.744192
$537$	11.0817	0.478212
$538$	−39.0646	−1.68420
$539$	15.6348	0.673438
$540$	−7.74062	−0.333103
$541$	8.07710	0.347261	0.173631	−	0.984811i	$-0.444450\pi$
$541$	8.07710	0.347261	0.173631	+	0.984811i	$0.444450\pi$
$542$	−46.5467	−1.99935
$543$	−16.0288	−0.687861
$544$	−4.11357	−0.176368
$545$	−39.8164	−1.70555
$546$	22.5996	0.967176
$547$	−5.75456	−0.246047	−0.123024	−	0.992404i	$-0.539259\pi$
$547$	−5.75456	−0.246047	−0.123024	+	0.992404i	$0.539259\pi$
$548$	10.8974	0.465515
$549$	7.30878	0.311931
$550$	0.183456	0.00782259
$551$	18.7170	0.797372
$552$	27.1138	1.15404
$553$	−19.0496	−0.810070
$554$	1.81746	0.0772164
$555$	−31.9693	−1.35702
$556$	−10.7822	−0.457267
$557$	32.3007	1.36862	0.684312	−	0.729189i	$-0.260103\pi$
$557$	32.3007	1.36862	0.684312	+	0.729189i	$0.260103\pi$
$558$	4.39616	0.186104
$559$	−1.49350	−0.0631683
$560$	53.1797	2.24725
$561$	−1.91287	−0.0807616
$562$	23.6430	0.997318
$563$	−15.0875	−0.635864	−0.317932	−	0.948114i	$-0.602988\pi$
$563$	−15.0875	−0.635864	−0.317932	+	0.948114i	$0.602988\pi$
$564$	17.2761	0.727455
$565$	41.4616	1.74430
$566$	−25.2660	−1.06201
$567$	−50.1587	−2.10647
$568$	−9.77096	−0.409980
$569$	30.5597	1.28113	0.640565	−	0.767904i	$-0.278700\pi$
$569$	30.5597	1.28113	0.640565	+	0.767904i	$0.278700\pi$
$570$	−51.2150	−2.14516
$571$	−13.8081	−0.577851	−0.288925	−	0.957352i	$-0.593298\pi$
$571$	−13.8081	−0.577851	−0.288925	+	0.957352i	$0.593298\pi$
$572$	−1.14205	−0.0477514
$573$	−37.7162	−1.57562
$574$	59.0471	2.46458
$575$	0.761399	0.0317525
$576$	2.00987	0.0837444
$577$	−6.16917	−0.256826	−0.128413	−	0.991721i	$-0.540988\pi$
$577$	−6.16917	−0.256826	−0.128413	+	0.991721i	$0.540988\pi$
$578$	1.66273	0.0691605
$579$	−43.5185	−1.80857
$580$	4.54231	0.188609
$581$	3.99534	0.165755
$582$	−35.0994	−1.45492
$583$	−5.45663	−0.225991
$584$	18.2160	0.753782
$585$	2.22521	0.0920009
$586$	−16.0897	−0.664658
$587$	9.06101	0.373988	0.186994	−	0.982361i	$-0.440126\pi$
$587$	9.06101	0.373988	0.186994	+	0.982361i	$0.440126\pi$
$588$	−22.8695	−0.943124
$589$	−28.5742	−1.17738
$590$	−17.4307	−0.717612
$591$	−39.7533	−1.63523
$592$	36.5558	1.50243
$593$	−45.5405	−1.87013	−0.935063	−	0.354483i	$-0.884657\pi$
$593$	−45.5405	−1.87013	−0.935063	+	0.354483i	$0.884657\pi$
$594$	7.44551	0.305493
$595$	−10.7551	−0.440915
$596$	−6.68007	−0.273626
$597$	−38.3995	−1.57159
$598$	−17.1368	−0.700776
$599$	4.00512	0.163645	0.0818224	−	0.996647i	$-0.473926\pi$
$599$	4.00512	0.163645	0.0818224	+	0.996647i	$0.473926\pi$
$600$	0.433509	0.0176979
$601$	14.5910	0.595178	0.297589	−	0.954694i	$-0.403818\pi$
$601$	14.5910	0.595178	0.297589	+	0.954694i	$0.403818\pi$
$602$	7.91062	0.322413
$603$	−5.52848	−0.225137
$604$	−5.33856	−0.217223
$605$	−2.26060	−0.0919067
$606$	17.0230	0.691512
$607$	−7.83198	−0.317890	−0.158945	−	0.987287i	$-0.550809\pi$
$607$	−7.83198	−0.317890	−0.158945	+	0.987287i	$0.550809\pi$
$608$	29.3010	1.18831
$609$	23.9137	0.969033
$610$	−41.6822	−1.68766
$611$	17.6395	0.713617
$612$	0.503987	0.0203725
$613$	22.9808	0.928186	0.464093	−	0.885787i	$-0.346380\pi$
$613$	22.9808	0.928186	0.464093	+	0.885787i	$0.346380\pi$
$614$	−5.45069	−0.219972
$615$	32.2774	1.30155
$616$	−9.77216	−0.393732
$617$	−31.8581	−1.28256	−0.641280	−	0.767307i	$-0.721596\pi$
$617$	−31.8581	−1.28256	−0.641280	+	0.767307i	$0.721596\pi$
$618$	−38.4212	−1.54553
$619$	−35.3838	−1.42220	−0.711098	−	0.703093i	$-0.751802\pi$
$619$	−35.3838	−1.42220	−0.711098	+	0.703093i	$0.751802\pi$
$620$	−6.93448	−0.278495
$621$	30.9011	1.24002
$622$	39.9537	1.60200
$623$	−42.7637	−1.71329
$624$	−14.1262	−0.565499
$625$	−25.5395	−1.02158
$626$	35.5712	1.42171
$627$	13.6254	0.544147
$628$	−3.46591	−0.138305
$629$	−7.39303	−0.294780
$630$	−11.7863	−0.469576
$631$	−17.4259	−0.693712	−0.346856	−	0.937918i	$-0.612751\pi$
$631$	−17.4259	−0.693712	−0.346856	+	0.937918i	$0.612751\pi$
$632$	8.22431	0.327145
$633$	−32.1886	−1.27938
$634$	13.8952	0.551850
$635$	−26.6238	−1.05653
$636$	7.98160	0.316491
$637$	−23.3505	−0.925182
$638$	−4.36913	−0.172976
$639$	3.13528	0.124030
$640$	−30.0606	−1.18825
$641$	−9.09197	−0.359111	−0.179556	−	0.983748i	$-0.557466\pi$
$641$	−9.09197	−0.359111	−0.179556	+	0.983748i	$0.557466\pi$
$642$	−11.7194	−0.462526
$643$	−23.7876	−0.938093	−0.469047	−	0.883173i	$-0.655402\pi$
$643$	−23.7876	−0.938093	−0.469047	+	0.883173i	$0.655402\pi$
$644$	25.1055	0.989297
$645$	4.32425	0.170267
$646$	−11.8437	−0.465983
$647$	27.4969	1.08101	0.540507	−	0.841340i	$-0.318233\pi$
$647$	27.4969	1.08101	0.540507	+	0.841340i	$0.318233\pi$
$648$	21.6551	0.850694
$649$	4.63734	0.182032
$650$	−0.273991	−0.0107468
$651$	−36.5077	−1.43085
$652$	5.07896	0.198907
$653$	26.1827	1.02461	0.512305	−	0.858804i	$-0.328792\pi$
$653$	26.1827	1.02461	0.512305	+	0.858804i	$0.328792\pi$
$654$	−56.0204	−2.19057
$655$	−37.1786	−1.45269
$656$	−36.9080	−1.44102
$657$	−5.84509	−0.228039
$658$	−93.4311	−3.64232
$659$	13.2718	0.516995	0.258498	−	0.966012i	$-0.416773\pi$
$659$	13.2718	0.516995	0.258498	+	0.966012i	$0.416773\pi$
$660$	3.30666	0.128712
$661$	15.0989	0.587279	0.293639	−	0.955916i	$-0.405134\pi$
$661$	15.0989	0.587279	0.293639	+	0.955916i	$0.405134\pi$
$662$	19.1766	0.745320
$663$	2.85687	0.110952
$664$	−1.72492	−0.0669397
$665$	76.6085	2.97075
$666$	−8.10188	−0.313941
$667$	−18.1332	−0.702121
$668$	−19.4245	−0.751556
$669$	38.1408	1.47461
$670$	31.5291	1.21808
$671$	11.0893	0.428098
$672$	37.4363	1.44414
$673$	2.17901	0.0839947	0.0419974	−	0.999118i	$-0.486628\pi$
$673$	2.17901	0.0839947	0.0419974	+	0.999118i	$0.486628\pi$
$674$	33.6360	1.29561
$675$	0.494062	0.0190165
$676$	−8.23518	−0.316738
$677$	11.2310	0.431643	0.215822	−	0.976433i	$-0.430757\pi$
$677$	11.2310	0.431643	0.215822	+	0.976433i	$0.430757\pi$
$678$	58.3352	2.24035
$679$	52.5024	2.01486
$680$	4.64330	0.178062
$681$	17.6117	0.674883
$682$	6.67010	0.255411
$683$	−7.31902	−0.280054	−0.140027	−	0.990148i	$-0.544719\pi$
$683$	−7.31902	−0.280054	−0.140027	+	0.990148i	$0.544719\pi$
$684$	−3.58991	−0.137264
$685$	−32.2159	−1.23091
$686$	68.3066	2.60796
$687$	−43.3790	−1.65501
$688$	−4.94462	−0.188512
$689$	8.14947	0.310470
$690$	49.6176	1.88891
$691$	−32.5946	−1.23996	−0.619979	−	0.784619i	$-0.712859\pi$
$691$	−32.5946	−1.23996	−0.619979	+	0.784619i	$0.712859\pi$
$692$	10.4016	0.395409
$693$	3.13566	0.119114
$694$	−45.8883	−1.74189
$695$	31.8752	1.20910
$696$	−10.3243	−0.391342
$697$	7.46428	0.282730
$698$	−41.9177	−1.58661
$699$	−42.0008	−1.58862
$700$	0.401400	0.0151715
$701$	−3.85638	−0.145653	−0.0728266	−	0.997345i	$-0.523202\pi$
$701$	−3.85638	−0.145653	−0.0728266	+	0.997345i	$0.523202\pi$
$702$	−11.1199	−0.419692
$703$	52.6607	1.98614
$704$	3.04948	0.114932
$705$	−51.0730	−1.92352
$706$	10.1071	0.380386
$707$	−25.4634	−0.957649
$708$	−6.78319	−0.254928
$709$	−51.5214	−1.93493	−0.967464	−	0.253010i	$-0.918580\pi$
$709$	−51.5214	−1.93493	−0.967464	+	0.253010i	$0.918580\pi$
$710$	−17.8806	−0.671047
$711$	−2.63899	−0.0989698
$712$	18.4625	0.691910
$713$	27.6830	1.03673
$714$	−15.1320	−0.566301
$715$	3.37621	0.126263
$716$	−4.42996	−0.165555
$717$	−38.0265	−1.42012
$718$	45.9217	1.71378
$719$	−40.9697	−1.52791	−0.763957	−	0.645267i	$-0.776746\pi$
$719$	−40.9697	−1.52791	−0.763957	+	0.645267i	$0.776746\pi$
$720$	7.36713	0.274557
$721$	57.4712	2.14034
$722$	52.7708	1.96393
$723$	−33.4019	−1.24223
$724$	6.40757	0.238135
$725$	−0.289923	−0.0107675
$726$	−3.18060	−0.118043
$727$	−44.4738	−1.64944	−0.824720	−	0.565541i	$-0.808667\pi$
$727$	−44.4738	−1.64944	−0.824720	+	0.565541i	$0.808667\pi$
$728$	14.5947	0.540916
$729$	18.7482	0.694378
$730$	33.3347	1.23377
$731$	1.00000	0.0369863
$732$	−16.2207	−0.599534
$733$	−34.0699	−1.25840	−0.629199	−	0.777244i	$-0.716617\pi$
$733$	−34.0699	−1.25840	−0.629199	+	0.777244i	$0.716617\pi$
$734$	0.477251	0.0176156
$735$	67.6088	2.49379
$736$	−28.3871	−1.04636
$737$	−8.38813	−0.308981
$738$	8.17995	0.301108
$739$	−19.2904	−0.709609	−0.354804	−	0.934941i	$-0.615453\pi$
$739$	−19.2904	−0.709609	−0.354804	+	0.934941i	$0.615453\pi$
$740$	12.7799	0.469797
$741$	−20.3496	−0.747560
$742$	−43.1653	−1.58465
$743$	40.5571	1.48790	0.743949	−	0.668237i	$-0.232951\pi$
$743$	40.5571	1.48790	0.743949	+	0.668237i	$0.232951\pi$
$744$	15.7615	0.577846
$745$	19.7482	0.723517
$746$	3.92606	0.143743
$747$	0.553486	0.0202510
$748$	0.764679	0.0279594
$749$	17.5301	0.640535
$750$	−35.1570	−1.28375
$751$	20.4305	0.745518	0.372759	−	0.927928i	$-0.378412\pi$
$751$	20.4305	0.745518	0.372759	+	0.927928i	$0.378412\pi$
$752$	58.4002	2.12963
$753$	−27.7263	−1.01040
$754$	6.52529	0.237637
$755$	15.7823	0.574376
$756$	16.2907	0.592486
$757$	−27.8584	−1.01253	−0.506266	−	0.862377i	$-0.668975\pi$
$757$	−27.8584	−1.01253	−0.506266	+	0.862377i	$0.668975\pi$
$758$	41.1224	1.49363
$759$	−13.2004	−0.479146
$760$	−33.0743	−1.19973
$761$	−11.1797	−0.405263	−0.202631	−	0.979255i	$-0.564949\pi$
$761$	−11.1797	−0.405263	−0.202631	+	0.979255i	$0.564949\pi$
$762$	−37.4588	−1.35699
$763$	83.7965	3.03364
$764$	15.0772	0.545474
$765$	−1.48993	−0.0538685
$766$	1.61030	0.0581825
$767$	−6.92586	−0.250078
$768$	−30.6278	−1.10518
$769$	−22.2531	−0.802468	−0.401234	−	0.915976i	$-0.631419\pi$
$769$	−22.2531	−0.802468	−0.401234	+	0.915976i	$0.631419\pi$
$770$	−17.8828	−0.644451
$771$	−26.2519	−0.945439
$772$	17.3967	0.626121
$773$	6.87280	0.247197	0.123599	−	0.992332i	$-0.460556\pi$
$773$	6.87280	0.247197	0.123599	+	0.992332i	$0.460556\pi$
$774$	1.09588	0.0393906
$775$	0.442609	0.0158990
$776$	−22.6670	−0.813697
$777$	67.2817	2.41372
$778$	−15.3096	−0.548876
$779$	−53.1682	−1.90495
$780$	−4.93850	−0.176827
$781$	4.75702	0.170220
$782$	11.4743	0.410319
$783$	−11.7664	−0.420498
$784$	−77.3082	−2.76101
$785$	10.2462	0.365703
$786$	−52.3090	−1.86580
$787$	7.00183	0.249588	0.124794	−	0.992183i	$-0.460173\pi$
$787$	7.00183	0.249588	0.124794	+	0.992183i	$0.460173\pi$
$788$	15.8915	0.566113
$789$	−23.6063	−0.840405
$790$	15.0503	0.535464
$791$	−87.2590	−3.10257
$792$	−1.35376	−0.0481039
$793$	−16.5619	−0.588129
$794$	51.3583	1.82264
$795$	−23.5958	−0.836858
$796$	15.3503	0.544078
$797$	39.0534	1.38334	0.691671	−	0.722212i	$-0.256875\pi$
$797$	39.0534	1.38334	0.691671	+	0.722212i	$0.256875\pi$
$798$	107.786	3.81557
$799$	−11.8108	−0.417837
$800$	−0.453867	−0.0160466
$801$	−5.92418	−0.209321
$802$	40.1043	1.41613
$803$	−8.86850	−0.312963
$804$	12.2696	0.432715
$805$	−74.2190	−2.61588
$806$	−9.96179	−0.350889
$807$	44.9415	1.58202
$808$	10.9933	0.386745
$809$	37.3313	1.31250	0.656249	−	0.754544i	$-0.272142\pi$
$809$	37.3313	1.31250	0.656249	+	0.754544i	$0.272142\pi$
$810$	39.6283	1.39240
$811$	−21.0123	−0.737842	−0.368921	−	0.929461i	$-0.620273\pi$
$811$	−21.0123	−0.737842	−0.368921	+	0.929461i	$0.620273\pi$
$812$	−9.55960	−0.335476
$813$	53.5492	1.87805
$814$	−12.2926	−0.430857
$815$	−15.0148	−0.525946
$816$	9.45844	0.331112
$817$	−7.12302	−0.249203
$818$	−10.1153	−0.353672
$819$	−4.68310	−0.163641
$820$	−12.9030	−0.450593
$821$	−33.4908	−1.16884	−0.584418	−	0.811453i	$-0.698677\pi$
$821$	−33.4908	−1.16884	−0.584418	+	0.811453i	$0.698677\pi$
$822$	−45.3267	−1.58095
$823$	8.81746	0.307357	0.153679	−	0.988121i	$-0.450888\pi$
$823$	8.81746	0.307357	0.153679	+	0.988121i	$0.450888\pi$
$824$	−24.8121	−0.864372
$825$	−0.211055	−0.00734800
$826$	36.6842	1.27641
$827$	23.8272	0.828553	0.414276	−	0.910151i	$-0.364035\pi$
$827$	23.8272	0.828553	0.414276	+	0.910151i	$0.364035\pi$
$828$	3.47794	0.120867
$829$	−40.4576	−1.40515	−0.702576	−	0.711609i	$-0.747967\pi$
$829$	−40.4576	−1.40515	−0.702576	+	0.711609i	$0.747967\pi$
$830$	−3.15655	−0.109565
$831$	−2.09088	−0.0725317
$832$	−4.55440	−0.157895
$833$	15.6348	0.541713
$834$	44.8473	1.55294
$835$	57.4242	1.98725
$836$	−5.44682	−0.188382
$837$	17.9631	0.620897
$838$	−11.8215	−0.408368
$839$	3.52555	0.121715	0.0608577	−	0.998146i	$-0.480616\pi$
$839$	3.52555	0.121715	0.0608577	+	0.998146i	$0.480616\pi$
$840$	−42.2573	−1.45801
$841$	−22.0953	−0.761907
$842$	10.1422	0.349525
$843$	−27.1998	−0.936811
$844$	12.8675	0.442918
$845$	24.3455	0.837511
$846$	−12.9433	−0.444999
$847$	4.75760	0.163473
$848$	26.9810	0.926531
$849$	29.0670	0.997578
$850$	0.183456	0.00629249
$851$	−51.0182	−1.74888
$852$	−6.95825	−0.238386
$853$	0.840517	0.0287787	0.0143894	−	0.999896i	$-0.495420\pi$
$853$	0.840517	0.0287787	0.0143894	+	0.999896i	$0.495420\pi$
$854$	87.7232	3.00183
$855$	10.6128	0.362950
$856$	−7.56829	−0.258679
$857$	23.6757	0.808748	0.404374	−	0.914594i	$-0.367489\pi$
$857$	23.6757	0.808748	0.404374	+	0.914594i	$0.367489\pi$
$858$	4.75022	0.162170
$859$	−6.44212	−0.219802	−0.109901	−	0.993943i	$-0.535053\pi$
$859$	−6.44212	−0.219802	−0.109901	+	0.993943i	$0.535053\pi$
$860$	−1.72864	−0.0589460
$861$	−67.9301	−2.31505
$862$	5.39813	0.183861
$863$	52.3413	1.78172	0.890860	−	0.454279i	$-0.150103\pi$
$863$	52.3413	1.78172	0.890860	+	0.454279i	$0.150103\pi$
$864$	−18.4200	−0.626663
$865$	−30.7500	−1.04553
$866$	−62.4392	−2.12177
$867$	−1.91287	−0.0649646
$868$	14.5941	0.495356
$869$	−4.00403	−0.135827
$870$	−18.8932	−0.640540
$871$	12.5277	0.424484
$872$	−36.1776	−1.22513
$873$	7.27331	0.246164
$874$	−81.7314	−2.76461
$875$	52.5887	1.77782
$876$	12.9722	0.438292
$877$	−5.79883	−0.195812	−0.0979062	−	0.995196i	$-0.531215\pi$
$877$	−5.79883	−0.195812	−0.0979062	+	0.995196i	$0.531215\pi$
$878$	−15.5127	−0.523528
$879$	18.5102	0.624334
$880$	11.1778	0.376805
$881$	14.4554	0.487013	0.243507	−	0.969899i	$-0.421702\pi$
$881$	14.4554	0.487013	0.243507	+	0.969899i	$0.421702\pi$
$882$	17.1339	0.576927
$883$	−13.4498	−0.452623	−0.226311	−	0.974055i	$-0.572667\pi$
$883$	−13.4498	−0.452623	−0.226311	+	0.974055i	$0.572667\pi$
$884$	−1.14205	−0.0384112
$885$	20.0530	0.674075
$886$	44.8391	1.50640
$887$	8.94759	0.300431	0.150215	−	0.988653i	$-0.452003\pi$
$887$	8.94759	0.300431	0.150215	+	0.988653i	$0.452003\pi$
$888$	−29.0477	−0.974776
$889$	56.0316	1.87924
$890$	33.7858	1.13250
$891$	−10.5429	−0.353199
$892$	−15.2470	−0.510506
$893$	84.1288	2.81526
$894$	27.7850	0.929270
$895$	13.0962	0.437758
$896$	63.2648	2.11353
$897$	19.7148	0.658260
$898$	−28.1312	−0.938751
$899$	−10.5410	−0.351563
$900$	0.0556070	0.00185357
$901$	−5.45663	−0.181787
$902$	12.4111	0.413244
$903$	−9.10069	−0.302852
$904$	37.6725	1.25297
$905$	−18.9426	−0.629672
$906$	22.2051	0.737717
$907$	−46.3296	−1.53835	−0.769175	−	0.639038i	$-0.779332\pi$
$907$	−46.3296	−1.53835	−0.769175	+	0.639038i	$0.779332\pi$
$908$	−7.04036	−0.233643
$909$	−3.52751	−0.117000
$910$	26.7079	0.885359
$911$	40.9624	1.35714	0.678572	−	0.734534i	$-0.262599\pi$
$911$	40.9624	1.35714	0.678572	+	0.734534i	$0.262599\pi$
$912$	−67.3726	−2.23093
$913$	0.839781	0.0277927
$914$	67.9275	2.24684
$915$	47.9529	1.58527
$916$	17.3409	0.572960
$917$	78.2450	2.58388
$918$	7.44551	0.245738
$919$	−24.3152	−0.802086	−0.401043	−	0.916059i	$-0.631352\pi$
$919$	−24.3152	−0.802086	−0.401043	+	0.916059i	$0.631352\pi$
$920$	32.0427	1.05642
$921$	6.27069	0.206626
$922$	27.6388	0.910236
$923$	−7.10461	−0.233851
$924$	−6.95911	−0.228938
$925$	−0.815704	−0.0268202
$926$	−8.91721	−0.293038
$927$	7.96164	0.261495
$928$	10.8091	0.354828
$929$	24.4545	0.802326	0.401163	−	0.916007i	$-0.368606\pi$
$929$	24.4545	0.802326	0.401163	+	0.916007i	$0.368606\pi$
$930$	28.8432	0.945805
$931$	−111.367	−3.64990
$932$	16.7900	0.549974
$933$	−45.9643	−1.50480
$934$	6.84740	0.224054
$935$	−2.26060	−0.0739297
$936$	2.02184	0.0660861
$937$	−33.0832	−1.08078	−0.540391	−	0.841414i	$-0.681723\pi$
$937$	−33.0832	−1.08078	−0.540391	+	0.841414i	$0.681723\pi$
$938$	−66.3553	−2.16658
$939$	−40.9225	−1.33546
$940$	20.4166	0.665917
$941$	38.2482	1.24686	0.623428	−	0.781881i	$-0.285739\pi$
$941$	38.2482	1.24686	0.623428	+	0.781881i	$0.285739\pi$
$942$	14.4161	0.469701
$943$	51.5098	1.67739
$944$	−22.9299	−0.746305
$945$	−48.1598	−1.56664
$946$	1.66273	0.0540601
$947$	20.7685	0.674885	0.337442	−	0.941346i	$-0.390438\pi$
$947$	20.7685	0.674885	0.337442	+	0.941346i	$0.390438\pi$
$948$	5.85682	0.190221
$949$	13.2451	0.429954
$950$	−1.30676	−0.0423969
$951$	−15.9856	−0.518370
$952$	−9.77216	−0.316717
$953$	−12.2623	−0.397215	−0.198608	−	0.980079i	$-0.563642\pi$
$953$	−12.2623	−0.397215	−0.198608	+	0.980079i	$0.563642\pi$
$954$	−5.97981	−0.193604
$955$	−44.5724	−1.44233
$956$	15.2012	0.491643
$957$	5.02642	0.162481
$958$	−72.0804	−2.32881
$959$	67.8006	2.18940
$960$	13.1867	0.425600
$961$	−14.9076	−0.480891
$962$	18.3590	0.591919
$963$	2.42849	0.0782570
$964$	13.3525	0.430056
$965$	−51.4295	−1.65557
$966$	−104.424	−3.35978
$967$	10.3594	0.333135	0.166567	−	0.986030i	$-0.446732\pi$
$967$	10.3594	0.333135	0.166567	+	0.986030i	$0.446732\pi$
$968$	−2.05401	−0.0660183
$969$	13.6254	0.437712
$970$	−41.4799	−1.33184
$971$	26.0489	0.835950	0.417975	−	0.908458i	$-0.362740\pi$
$971$	26.0489	0.835950	0.417975	+	0.908458i	$0.362740\pi$
$972$	5.14899	0.165154
$973$	−67.0836	−2.15060
$974$	−12.1124	−0.388105
$975$	0.315211	0.0100948
$976$	−54.8324	−1.75514
$977$	−15.2965	−0.489380	−0.244690	−	0.969601i	$-0.578686\pi$
$977$	−15.2965	−0.489380	−0.244690	+	0.969601i	$0.578686\pi$
$978$	−21.1254	−0.675514
$979$	−8.98851	−0.287274
$980$	−27.0269	−0.863342
$981$	11.6086	0.370633
$982$	−33.8049	−1.07876
$983$	−4.26952	−0.136177	−0.0680883	−	0.997679i	$-0.521690\pi$
$983$	−4.26952	−0.136177	−0.0680883	+	0.997679i	$0.521690\pi$
$984$	29.3276	0.934929
$985$	−46.9799	−1.49690
$986$	−4.36913	−0.139141
$987$	107.487	3.42134
$988$	8.13482	0.258803
$989$	6.90085	0.219434
$990$	−2.47735	−0.0787354
$991$	−55.6310	−1.76718	−0.883589	−	0.468264i	$-0.844880\pi$
$991$	−55.6310	−1.76718	−0.883589	+	0.468264i	$0.844880\pi$
$992$	−16.5017	−0.523930
$993$	−22.0615	−0.700101
$994$	37.6310	1.19358
$995$	−45.3799	−1.43864
$996$	−1.22838	−0.0389226
$997$	−17.5981	−0.557339	−0.278669	−	0.960387i	$-0.589893\pi$
$997$	−17.5981	−0.557339	−0.278669	+	0.960387i	$0.589893\pi$
$998$	49.3190	1.56116
$999$	−33.1051	−1.04740

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8041.2.a.j.1.61	✓	82

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8041.2.a.j.1.61	✓	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)

\(f(q)\)	\(=\)	\(q+1.66273 q^{2} -1.91287 q^{3} +0.764679 q^{4} -2.26060 q^{5} -3.18060 q^{6} +4.75760 q^{7} -2.05401 q^{8} +0.659084 q^{9} +O(q^{10})\)	\(q+1.66273 q^{2} -1.91287 q^{3} +0.764679 q^{4} -2.26060 q^{5} -3.18060 q^{6} +4.75760 q^{7} -2.05401 q^{8} +0.659084 q^{9} -3.75878 q^{10} +1.00000 q^{11} -1.46273 q^{12} -1.49350 q^{13} +7.91062 q^{14} +4.32425 q^{15} -4.94462 q^{16} +1.00000 q^{17} +1.09588 q^{18} -7.12302 q^{19} -1.72864 q^{20} -9.10069 q^{21} +1.66273 q^{22} +6.90085 q^{23} +3.92906 q^{24} +0.110334 q^{25} -2.48329 q^{26} +4.47788 q^{27} +3.63804 q^{28} -2.62768 q^{29} +7.19007 q^{30} +4.01153 q^{31} -4.11357 q^{32} -1.91287 q^{33} +1.66273 q^{34} -10.7551 q^{35} +0.503987 q^{36} -7.39303 q^{37} -11.8437 q^{38} +2.85687 q^{39} +4.64330 q^{40} +7.46428 q^{41} -15.1320 q^{42} +1.00000 q^{43} +0.764679 q^{44} -1.48993 q^{45} +11.4743 q^{46} -11.8108 q^{47} +9.45844 q^{48} +15.6348 q^{49} +0.183456 q^{50} -1.91287 q^{51} -1.14205 q^{52} -5.45663 q^{53} +7.44551 q^{54} -2.26060 q^{55} -9.77216 q^{56} +13.6254 q^{57} -4.36913 q^{58} +4.63734 q^{59} +3.30666 q^{60} +11.0893 q^{61} +6.67010 q^{62} +3.13566 q^{63} +3.04948 q^{64} +3.37621 q^{65} -3.18060 q^{66} -8.38813 q^{67} +0.764679 q^{68} -13.2004 q^{69} -17.8828 q^{70} +4.75702 q^{71} -1.35376 q^{72} -8.86850 q^{73} -12.2926 q^{74} -0.211055 q^{75} -5.44682 q^{76} +4.75760 q^{77} +4.75022 q^{78} -4.00403 q^{79} +11.1778 q^{80} -10.5429 q^{81} +12.4111 q^{82} +0.839781 q^{83} -6.95911 q^{84} -2.26060 q^{85} +1.66273 q^{86} +5.02642 q^{87} -2.05401 q^{88} -8.98851 q^{89} -2.47735 q^{90} -7.10547 q^{91} +5.27693 q^{92} -7.67355 q^{93} -19.6383 q^{94} +16.1023 q^{95} +7.86873 q^{96} +11.0355 q^{97} +25.9965 q^{98} +0.659084 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 82 q + 8 q^{2} + 6 q^{3} + 98 q^{4} + 11 q^{5} + 10 q^{6} + 8 q^{7} + 30 q^{8} + 108 q^{9}+O(q^{10}) \) 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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