LMFDB - Embedded newform 8041.2.a.j.1.29

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			1.29
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)

$f(q)$	$=$	$q-0.793545 q^{2} -2.25123 q^{3} -1.37029 q^{4} +3.65930 q^{5} +1.78645 q^{6} -0.286787 q^{7} +2.67447 q^{8} +2.06805 q^{9} +O(q^{10})$	\(q-0.793545 q^{2} -2.25123 q^{3} -1.37029 q^{4} +3.65930 q^{5} +1.78645 q^{6} -0.286787 q^{7} +2.67447 q^{8} +2.06805 q^{9} -2.90382 q^{10} +1.00000 q^{11} +3.08483 q^{12} -4.96078 q^{13} +0.227578 q^{14} -8.23793 q^{15} +0.618259 q^{16} +1.00000 q^{17} -1.64109 q^{18} -3.37246 q^{19} -5.01429 q^{20} +0.645623 q^{21} -0.793545 q^{22} +8.02823 q^{23} -6.02086 q^{24} +8.39047 q^{25} +3.93660 q^{26} +2.09804 q^{27} +0.392980 q^{28} -7.23827 q^{29} +6.53717 q^{30} -9.15450 q^{31} -5.83956 q^{32} -2.25123 q^{33} -0.793545 q^{34} -1.04944 q^{35} -2.83382 q^{36} +1.92710 q^{37} +2.67620 q^{38} +11.1679 q^{39} +9.78670 q^{40} -1.29446 q^{41} -0.512331 q^{42} +1.00000 q^{43} -1.37029 q^{44} +7.56761 q^{45} -6.37076 q^{46} -6.41042 q^{47} -1.39185 q^{48} -6.91775 q^{49} -6.65821 q^{50} -2.25123 q^{51} +6.79769 q^{52} +8.87383 q^{53} -1.66489 q^{54} +3.65930 q^{55} -0.767003 q^{56} +7.59220 q^{57} +5.74389 q^{58} +0.744477 q^{59} +11.2883 q^{60} -3.95812 q^{61} +7.26451 q^{62} -0.593088 q^{63} +3.39744 q^{64} -18.1530 q^{65} +1.78645 q^{66} -2.29750 q^{67} -1.37029 q^{68} -18.0734 q^{69} +0.832776 q^{70} +14.5566 q^{71} +5.53094 q^{72} +8.89106 q^{73} -1.52924 q^{74} -18.8889 q^{75} +4.62124 q^{76} -0.286787 q^{77} -8.86220 q^{78} -6.58596 q^{79} +2.26240 q^{80} -10.9273 q^{81} +1.02721 q^{82} +10.5404 q^{83} -0.884689 q^{84} +3.65930 q^{85} -0.793545 q^{86} +16.2950 q^{87} +2.67447 q^{88} +15.2232 q^{89} -6.00523 q^{90} +1.42268 q^{91} -11.0010 q^{92} +20.6089 q^{93} +5.08695 q^{94} -12.3408 q^{95} +13.1462 q^{96} +9.86803 q^{97} +5.48955 q^{98} +2.06805 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−0.793545	−0.561121	−0.280560	−	0.959836i	$-0.590520\pi$
$2$	−0.793545	−0.561121	−0.280560	+	0.959836i	$0.590520\pi$
$3$	−2.25123	−1.29975	−0.649875	−	0.760041i	$-0.725179\pi$
$3$	−2.25123	−1.29975	−0.649875	+	0.760041i	$0.725179\pi$
$4$	−1.37029	−0.685143
$5$	3.65930	1.63649	0.818244	−	0.574871i	$-0.194948\pi$
$5$	3.65930	1.63649	0.818244	+	0.574871i	$0.194948\pi$
$6$	1.78645	0.729317
$7$	−0.286787	−0.108395	−0.0541976	−	0.998530i	$-0.517260\pi$
$7$	−0.286787	−0.108395	−0.0541976	+	0.998530i	$0.517260\pi$
$8$	2.67447	0.945569
$9$	2.06805	0.689349
$10$	−2.90382	−0.918268
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	3.08483	0.890515
$13$	−4.96078	−1.37587	−0.687936	−	0.725771i	$-0.741483\pi$
$13$	−4.96078	−1.37587	−0.687936	+	0.725771i	$0.741483\pi$
$14$	0.227578	0.0608228
$15$	−8.23793	−2.12703
$16$	0.618259	0.154565
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−1.64109	−0.386808
$19$	−3.37246	−0.773696	−0.386848	−	0.922144i	$-0.626436\pi$
$19$	−3.37246	−0.773696	−0.386848	+	0.922144i	$0.626436\pi$
$20$	−5.01429	−1.12123
$21$	0.645623	0.140887
$22$	−0.793545	−0.169184
$23$	8.02823	1.67400	0.837001	−	0.547201i	$-0.184307\pi$
$23$	8.02823	1.67400	0.837001	+	0.547201i	$0.184307\pi$
$24$	−6.02086	−1.22900
$25$	8.39047	1.67809
$26$	3.93660	0.772031
$27$	2.09804	0.403768
$28$	0.392980	0.0742662
$29$	−7.23827	−1.34411	−0.672057	−	0.740500i	$-0.734589\pi$
$29$	−7.23827	−1.34411	−0.672057	+	0.740500i	$0.734589\pi$
$30$	6.53717	1.19352
$31$	−9.15450	−1.64420	−0.822098	−	0.569345i	$-0.807197\pi$
$31$	−9.15450	−1.64420	−0.822098	+	0.569345i	$0.807197\pi$
$32$	−5.83956	−1.03230
$33$	−2.25123	−0.391889
$34$	−0.793545	−0.136092
$35$	−1.04944	−0.177387
$36$	−2.83382	−0.472303
$37$	1.92710	0.316813	0.158406	−	0.987374i	$-0.449364\pi$
$37$	1.92710	0.316813	0.158406	+	0.987374i	$0.449364\pi$
$38$	2.67620	0.434137
$39$	11.1679	1.78829
$40$	9.78670	1.54741
$41$	−1.29446	−0.202161	−0.101080	−	0.994878i	$-0.532230\pi$
$41$	−1.29446	−0.202161	−0.101080	+	0.994878i	$0.532230\pi$
$42$	−0.512331	−0.0790544
$43$	1.00000	0.152499
$43$	1.00000	0.152499
$44$	−1.37029	−0.206579
$45$	7.56761	1.12811
$46$	−6.37076	−0.939317
$47$	−6.41042	−0.935055	−0.467528	−	0.883978i	$-0.654855\pi$
$47$	−6.41042	−0.935055	−0.467528	+	0.883978i	$0.654855\pi$
$48$	−1.39185	−0.200896
$49$	−6.91775	−0.988250
$50$	−6.65821	−0.941613
$51$	−2.25123	−0.315236
$52$	6.79769	0.942670
$53$	8.87383	1.21891	0.609457	−	0.792819i	$-0.291387\pi$
$53$	8.87383	1.21891	0.609457	+	0.792819i	$0.291387\pi$
$54$	−1.66489	−0.226563
$55$	3.65930	0.493420
$56$	−0.767003	−0.102495
$57$	7.59220	1.00561
$58$	5.74389	0.754210
$59$	0.744477	0.0969226	0.0484613	−	0.998825i	$-0.484568\pi$
$59$	0.744477	0.0969226	0.0484613	+	0.998825i	$0.484568\pi$
$60$	11.2883	1.45732
$61$	−3.95812	−0.506785	−0.253392	−	0.967364i	$-0.581546\pi$
$61$	−3.95812	−0.506785	−0.253392	+	0.967364i	$0.581546\pi$
$62$	7.26451	0.922593
$63$	−0.593088	−0.0747221
$64$	3.39744	0.424679
$65$	−18.1530	−2.25160
$66$	1.78645	0.219897
$67$	−2.29750	−0.280684	−0.140342	−	0.990103i	$-0.544820\pi$
$67$	−2.29750	−0.280684	−0.140342	+	0.990103i	$0.544820\pi$
$68$	−1.37029	−0.166172
$69$	−18.0734	−2.17578
$70$	0.832776	0.0995357
$71$	14.5566	1.72756	0.863778	−	0.503873i	$-0.168092\pi$
$71$	14.5566	1.72756	0.863778	+	0.503873i	$0.168092\pi$
$72$	5.53094	0.651828
$73$	8.89106	1.04062	0.520310	−	0.853977i	$-0.325816\pi$
$73$	8.89106	1.04062	0.520310	+	0.853977i	$0.325816\pi$
$74$	−1.52924	−0.177770
$75$	−18.8889	−2.18110
$76$	4.62124	0.530093
$77$	−0.286787	−0.0326824
$78$	−8.86220	−1.00345
$79$	−6.58596	−0.740979	−0.370489	−	0.928837i	$-0.620810\pi$
$79$	−6.58596	−0.740979	−0.370489	+	0.928837i	$0.620810\pi$
$80$	2.26240	0.252944
$81$	−10.9273	−1.21415
$82$	1.02721	0.113436
$83$	10.5404	1.15696	0.578479	−	0.815697i	$-0.303646\pi$
$83$	10.5404	1.15696	0.578479	+	0.815697i	$0.303646\pi$
$84$	−0.884689	−0.0965275
$85$	3.65930	0.396907
$86$	−0.793545	−0.0855701
$87$	16.2950	1.74701
$88$	2.67447	0.285100
$89$	15.2232	1.61365	0.806826	−	0.590789i	$-0.201183\pi$
$89$	15.2232	1.61365	0.806826	+	0.590789i	$0.201183\pi$
$90$	−6.00523	−0.633007
$91$	1.42268	0.149138
$92$	−11.0010	−1.14693
$93$	20.6089	2.13704
$94$	5.08695	0.524679
$95$	−12.3408	−1.26614
$96$	13.1462	1.34173
$97$	9.86803	1.00195	0.500974	−	0.865463i	$-0.332975\pi$
$97$	9.86803	1.00195	0.500974	+	0.865463i	$0.332975\pi$
$98$	5.48955	0.554528
$99$	2.06805	0.207847
$100$	−11.4973	−1.14973
$101$	−14.9133	−1.48393	−0.741964	−	0.670440i	$-0.766105\pi$
$101$	−14.9133	−1.48393	−0.741964	+	0.670440i	$0.766105\pi$
$102$	1.78645	0.176885
$103$	−4.50924	−0.444308	−0.222154	−	0.975012i	$-0.571309\pi$
$103$	−4.50924	−0.444308	−0.222154	+	0.975012i	$0.571309\pi$
$104$	−13.2675	−1.30098
$105$	2.36253	0.230559
$106$	−7.04178	−0.683959
$107$	14.7982	1.43060	0.715299	−	0.698819i	$-0.246291\pi$
$107$	14.7982	1.43060	0.715299	+	0.698819i	$0.246291\pi$
$108$	−2.87492	−0.276639
$109$	5.41813	0.518962	0.259481	−	0.965748i	$-0.416448\pi$
$109$	5.41813	0.518962	0.259481	+	0.965748i	$0.416448\pi$
$110$	−2.90382	−0.276868
$111$	−4.33835	−0.411778
$112$	−0.177308	−0.0167541
$113$	6.59981	0.620858	0.310429	−	0.950597i	$-0.399527\pi$
$113$	6.59981	0.620858	0.310429	+	0.950597i	$0.399527\pi$
$114$	−6.02475	−0.564269
$115$	29.3777	2.73948
$116$	9.91851	0.920910
$117$	−10.2591	−0.948457
$118$	−0.590776	−0.0543853
$119$	−0.286787	−0.0262897
$120$	−22.0321	−2.01125
$121$	1.00000	0.0909091
$122$	3.14094	0.284368
$123$	2.91413	0.262758
$124$	12.5443	1.12651
$125$	12.4067	1.10969
$126$	0.470642	0.0419281
$127$	18.4257	1.63502	0.817510	−	0.575914i	$-0.195354\pi$
$127$	18.4257	1.63502	0.817510	+	0.575914i	$0.195354\pi$
$128$	8.98311	0.794002
$129$	−2.25123	−0.198210
$130$	14.4052	1.26342
$131$	−8.95479	−0.782384	−0.391192	−	0.920309i	$-0.627937\pi$
$131$	−8.95479	−0.782384	−0.391192	+	0.920309i	$0.627937\pi$
$132$	3.08483	0.268500
$133$	0.967177	0.0838648
$134$	1.82317	0.157498
$135$	7.67736	0.660762
$136$	2.67447	0.229334
$137$	−19.4444	−1.66125	−0.830623	−	0.556835i	$-0.812016\pi$
$137$	−19.4444	−1.66125	−0.830623	+	0.556835i	$0.812016\pi$
$138$	14.3421	1.22088
$139$	−9.23805	−0.783561	−0.391780	−	0.920059i	$-0.628141\pi$
$139$	−9.23805	−0.783561	−0.391780	+	0.920059i	$0.628141\pi$
$140$	1.43803	0.121536
$141$	14.4313	1.21534
$142$	−11.5513	−0.969368
$143$	−4.96078	−0.414841
$144$	1.27859	0.106549
$145$	−26.4870	−2.19963
$146$	−7.05546	−0.583914
$147$	15.5735	1.28448
$148$	−2.64068	−0.217062
$149$	−9.42264	−0.771933	−0.385966	−	0.922513i	$-0.626132\pi$
$149$	−9.42264	−0.771933	−0.385966	+	0.922513i	$0.626132\pi$
$150$	14.9892	1.22386
$151$	−14.4700	−1.17755	−0.588777	−	0.808296i	$-0.700390\pi$
$151$	−14.4700	−1.17755	−0.588777	+	0.808296i	$0.700390\pi$
$152$	−9.01956	−0.731583
$153$	2.06805	0.167192
$154$	0.227578	0.0183388
$155$	−33.4991	−2.69071
$156$	−15.3032	−1.22524
$157$	−23.8901	−1.90664	−0.953318	−	0.301968i	$-0.902356\pi$
$157$	−23.8901	−1.90664	−0.953318	+	0.301968i	$0.902356\pi$
$158$	5.22626	0.415779
$159$	−19.9771	−1.58428
$160$	−21.3687	−1.68934
$161$	−2.30239	−0.181454
$162$	8.67132	0.681283
$163$	13.9590	1.09335	0.546675	−	0.837345i	$-0.315893\pi$
$163$	13.9590	1.09335	0.546675	+	0.837345i	$0.315893\pi$
$164$	1.77378	0.138509
$165$	−8.23793	−0.641322
$166$	−8.36428	−0.649194
$167$	−0.0154827	−0.00119809	−0.000599043	−	1.00000i	$-0.500191\pi$
$167$	−0.0154827	−0.00119809	−0.000599043		1.00000i	$0.500191\pi$
$168$	1.72670	0.133218
$169$	11.6093	0.893025
$170$	−2.90382	−0.222713
$171$	−6.97441	−0.533347
$172$	−1.37029	−0.104483
$173$	−5.64318	−0.429043	−0.214522	−	0.976719i	$-0.568819\pi$
$173$	−5.64318	−0.429043	−0.214522	+	0.976719i	$0.568819\pi$
$174$	−12.9308	−0.980284
$175$	−2.40627	−0.181897
$176$	0.618259	0.0466030
$177$	−1.67599	−0.125975
$178$	−12.0803	−0.905454
$179$	22.0296	1.64657	0.823285	−	0.567628i	$-0.192139\pi$
$179$	22.0296	1.64657	0.823285	+	0.567628i	$0.192139\pi$
$180$	−10.3698	−0.772919
$181$	25.3178	1.88186	0.940929	−	0.338604i	$-0.109955\pi$
$181$	25.3178	1.88186	0.940929	+	0.338604i	$0.109955\pi$
$182$	−1.12896	−0.0836844
$183$	8.91064	0.658694
$184$	21.4713	1.58288
$185$	7.05183	0.518461
$186$	−16.3541	−1.19914
$187$	1.00000	0.0731272
$188$	8.78411	0.640647
$189$	−0.601690	−0.0437665
$190$	9.79301	0.710460
$191$	−12.4209	−0.898746	−0.449373	−	0.893344i	$-0.648353\pi$
$191$	−12.4209	−0.898746	−0.449373	+	0.893344i	$0.648353\pi$
$192$	−7.64842	−0.551977
$193$	−13.8359	−0.995932	−0.497966	−	0.867197i	$-0.665920\pi$
$193$	−13.8359	−0.995932	−0.497966	+	0.867197i	$0.665920\pi$
$194$	−7.83073	−0.562213
$195$	40.8666	2.92652
$196$	9.47931	0.677093
$197$	−11.8065	−0.841179	−0.420590	−	0.907251i	$-0.638177\pi$
$197$	−11.8065	−0.841179	−0.420590	+	0.907251i	$0.638177\pi$
$198$	−1.64109	−0.116627
$199$	23.2813	1.65037	0.825184	−	0.564864i	$-0.191072\pi$
$199$	23.2813	1.65037	0.825184	+	0.564864i	$0.191072\pi$
$200$	22.4401	1.58675
$201$	5.17220	0.364819
$202$	11.8344	0.832663
$203$	2.07584	0.145695
$204$	3.08483	0.215982
$205$	−4.73681	−0.330833
$206$	3.57828	0.249311
$207$	16.6028	1.15397
$208$	−3.06705	−0.212661
$209$	−3.37246	−0.233278
$210$	−1.87477	−0.129372
$211$	10.7765	0.741884	0.370942	−	0.928656i	$-0.379035\pi$
$211$	10.7765	0.741884	0.370942	+	0.928656i	$0.379035\pi$
$212$	−12.1597	−0.835131
$213$	−32.7704	−2.24539
$214$	−11.7430	−0.802738
$215$	3.65930	0.249562
$216$	5.61115	0.381791
$217$	2.62539	0.178223
$218$	−4.29952	−0.291201
$219$	−20.0158	−1.35255
$220$	−5.01429	−0.338063
$221$	−4.96078	−0.333698
$222$	3.44267	0.231057
$223$	9.27387	0.621024	0.310512	−	0.950569i	$-0.399499\pi$
$223$	9.27387	0.621024	0.310512	+	0.950569i	$0.399499\pi$
$224$	1.67471	0.111896
$225$	17.3519	1.15679
$226$	−5.23724	−0.348376
$227$	−18.4112	−1.22199	−0.610997	−	0.791633i	$-0.709231\pi$
$227$	−18.4112	−1.22199	−0.610997	+	0.791633i	$0.709231\pi$
$228$	−10.4035	−0.688988
$229$	9.57811	0.632939	0.316470	−	0.948603i	$-0.397502\pi$
$229$	9.57811	0.632939	0.316470	+	0.948603i	$0.397502\pi$
$230$	−23.3125	−1.53718
$231$	0.645623	0.0424789
$232$	−19.3586	−1.27095
$233$	−18.1083	−1.18631	−0.593156	−	0.805087i	$-0.702118\pi$
$233$	−18.1083	−1.18631	−0.593156	+	0.805087i	$0.702118\pi$
$234$	8.14108	0.532199
$235$	−23.4576	−1.53021
$236$	−1.02015	−0.0664059
$237$	14.8265	0.963087
$238$	0.227578	0.0147517
$239$	7.25129	0.469047	0.234524	−	0.972110i	$-0.424647\pi$
$239$	7.25129	0.469047	0.234524	+	0.972110i	$0.424647\pi$
$240$	−5.09318	−0.328763
$241$	−2.72187	−0.175331	−0.0876654	−	0.996150i	$-0.527941\pi$
$241$	−2.72187	−0.175331	−0.0876654	+	0.996150i	$0.527941\pi$
$242$	−0.793545	−0.0510110
$243$	18.3058	1.17432
$244$	5.42375	0.347220
$245$	−25.3141	−1.61726
$246$	−2.31249	−0.147439
$247$	16.7300	1.06451
$248$	−24.4835	−1.55470
$249$	−23.7289	−1.50376
$250$	−9.84530	−0.622671
$251$	−1.79337	−0.113197	−0.0565984	−	0.998397i	$-0.518025\pi$
$251$	−1.79337	−0.113197	−0.0565984	+	0.998397i	$0.518025\pi$
$252$	0.812701	0.0511954
$253$	8.02823	0.504731
$254$	−14.6216	−0.917444
$255$	−8.23793	−0.515879
$256$	−13.9234	−0.870211
$257$	−15.4852	−0.965941	−0.482970	−	0.875637i	$-0.660442\pi$
$257$	−15.4852	−0.965941	−0.482970	+	0.875637i	$0.660442\pi$
$258$	1.78645	0.111220
$259$	−0.552666	−0.0343410
$260$	24.8748	1.54267
$261$	−14.9691	−0.926564
$262$	7.10603	0.439012
$263$	8.81357	0.543468	0.271734	−	0.962372i	$-0.412403\pi$
$263$	8.81357	0.543468	0.271734	+	0.962372i	$0.412403\pi$
$264$	−6.02086	−0.370558
$265$	32.4720	1.99474
$266$	−0.767498	−0.0470583
$267$	−34.2709	−2.09734
$268$	3.14823	0.192309
$269$	−1.95710	−0.119326	−0.0596632	−	0.998219i	$-0.519003\pi$
$269$	−1.95710	−0.119326	−0.0596632	+	0.998219i	$0.519003\pi$
$270$	−6.09233	−0.370767
$271$	5.61450	0.341056	0.170528	−	0.985353i	$-0.445453\pi$
$271$	5.61450	0.341056	0.170528	+	0.985353i	$0.445453\pi$
$272$	0.618259	0.0374875
$273$	−3.20279	−0.193842
$274$	15.4300	0.932160
$275$	8.39047	0.505964
$276$	24.7658	1.49072
$277$	−17.6601	−1.06109	−0.530547	−	0.847655i	$-0.678014\pi$
$277$	−17.6601	−1.06109	−0.530547	+	0.847655i	$0.678014\pi$
$278$	7.33080	0.439672
$279$	−18.9319	−1.13343
$280$	−2.80669	−0.167732
$281$	−31.5242	−1.88058	−0.940289	−	0.340376i	$-0.889446\pi$
$281$	−31.5242	−1.88058	−0.940289	+	0.340376i	$0.889446\pi$
$282$	−11.4519	−0.681951
$283$	−18.2329	−1.08384	−0.541918	−	0.840431i	$-0.682302\pi$
$283$	−18.2329	−1.08384	−0.541918	+	0.840431i	$0.682302\pi$
$284$	−19.9468	−1.18362
$285$	27.7821	1.64567
$286$	3.93660	0.232776
$287$	0.371233	0.0219132
$288$	−12.0765	−0.711614
$289$	1.00000	0.0588235
$290$	21.0186	1.23426
$291$	−22.2152	−1.30228
$292$	−12.1833	−0.712974
$293$	26.5807	1.55286	0.776430	−	0.630203i	$-0.217028\pi$
$293$	26.5807	1.55286	0.776430	+	0.630203i	$0.217028\pi$
$294$	−12.3582	−0.720748
$295$	2.72426	0.158613
$296$	5.15397	0.299569
$297$	2.09804	0.121741
$298$	7.47728	0.433147
$299$	−39.8263	−2.30321
$300$	25.8832	1.49437
$301$	−0.286787	−0.0165301
$302$	11.4826	0.660750
$303$	33.5733	1.92873
$304$	−2.08506	−0.119586
$305$	−14.4839	−0.829348
$306$	−1.64109	−0.0938148
$307$	13.6217	0.777430	0.388715	−	0.921358i	$-0.372919\pi$
$307$	13.6217	0.777430	0.388715	+	0.921358i	$0.372919\pi$
$308$	0.392980	0.0223921
$309$	10.1513	0.577489
$310$	26.5830	1.50981
$311$	2.25466	0.127850	0.0639250	−	0.997955i	$-0.479638\pi$
$311$	2.25466	0.127850	0.0639250	+	0.997955i	$0.479638\pi$
$312$	29.8682	1.69095
$313$	20.8220	1.17693	0.588466	−	0.808522i	$-0.299732\pi$
$313$	20.8220	1.17693	0.588466	+	0.808522i	$0.299732\pi$
$314$	18.9578	1.06985
$315$	−2.17029	−0.122282
$316$	9.02466	0.507677
$317$	−9.59548	−0.538936	−0.269468	−	0.963009i	$-0.586848\pi$
$317$	−9.59548	−0.538936	−0.269468	+	0.963009i	$0.586848\pi$
$318$	15.8527	0.888975
$319$	−7.23827	−0.405265
$320$	12.4322	0.694983
$321$	−33.3142	−1.85942
$322$	1.82705	0.101817
$323$	−3.37246	−0.187649
$324$	14.9736	0.831865
$325$	−41.6233	−2.30884
$326$	−11.0771	−0.613501
$327$	−12.1975	−0.674521
$328$	−3.46200	−0.191157
$329$	1.83842	0.101355
$330$	6.53717	0.359859
$331$	−10.6548	−0.585643	−0.292822	−	0.956167i	$-0.594594\pi$
$331$	−10.6548	−0.585643	−0.292822	+	0.956167i	$0.594594\pi$
$332$	−14.4434	−0.792683
$333$	3.98533	0.218395
$334$	0.0122862	0.000672271 0
$335$	−8.40723	−0.459336
$336$	0.399163	0.0217761
$337$	34.4008	1.87393	0.936966	−	0.349420i	$-0.113621\pi$
$337$	34.4008	1.87393	0.936966	+	0.349420i	$0.113621\pi$
$338$	−9.21252	−0.501095
$339$	−14.8577	−0.806960
$340$	−5.01429	−0.271938
$341$	−9.15450	−0.495744
$342$	5.53451	0.299272
$343$	3.99142	0.215517
$344$	2.67447	0.144198
$345$	−66.1360	−3.56064
$346$	4.47812	0.240745
$347$	20.6159	1.10672	0.553359	−	0.832943i	$-0.313346\pi$
$347$	20.6159	1.10672	0.553359	+	0.832943i	$0.313346\pi$
$348$	−22.3289	−1.19695
$349$	6.10149	0.326605	0.163303	−	0.986576i	$-0.447785\pi$
$349$	6.10149	0.326605	0.163303	+	0.986576i	$0.447785\pi$
$350$	1.90949	0.102066
$351$	−10.4079	−0.555533
$352$	−5.83956	−0.311250
$353$	7.31460	0.389317	0.194658	−	0.980871i	$-0.437640\pi$
$353$	7.31460	0.389317	0.194658	+	0.980871i	$0.437640\pi$
$354$	1.32997	0.0706873
$355$	53.2671	2.82713
$356$	−20.8601	−1.10558
$357$	0.645623	0.0341700
$358$	−17.4815	−0.923925
$359$	8.22178	0.433929	0.216964	−	0.976180i	$-0.430384\pi$
$359$	8.22178	0.433929	0.216964	+	0.976180i	$0.430384\pi$
$360$	20.2394	1.06671
$361$	−7.62650	−0.401395
$362$	−20.0908	−1.05595
$363$	−2.25123	−0.118159
$364$	−1.94949	−0.102181
$365$	32.5351	1.70296
$366$	−7.07099	−0.369607
$367$	1.47694	0.0770955	0.0385478	−	0.999257i	$-0.487727\pi$
$367$	1.47694	0.0770955	0.0385478	+	0.999257i	$0.487727\pi$
$368$	4.96353	0.258742
$369$	−2.67700	−0.139359
$370$	−5.59594	−0.290919
$371$	−2.54490	−0.132124
$372$	−28.2401	−1.46418
$373$	−1.17199	−0.0606832	−0.0303416	−	0.999540i	$-0.509660\pi$
$373$	−1.17199	−0.0606832	−0.0303416	+	0.999540i	$0.509660\pi$
$374$	−0.793545	−0.0410332
$375$	−27.9304	−1.44232
$376$	−17.1445	−0.884159
$377$	35.9075	1.84933
$378$	0.477468	0.0245583
$379$	35.9135	1.84475	0.922377	−	0.386291i	$-0.126244\pi$
$379$	35.9135	1.84475	0.922377	+	0.386291i	$0.126244\pi$
$380$	16.9105	0.867490
$381$	−41.4806	−2.12512
$382$	9.85655	0.504305
$383$	−19.8338	−1.01346	−0.506731	−	0.862104i	$-0.669146\pi$
$383$	−19.8338	−1.01346	−0.506731	+	0.862104i	$0.669146\pi$
$384$	−20.2231	−1.03200
$385$	−1.04944	−0.0534843
$386$	10.9794	0.558838
$387$	2.06805	0.105125
$388$	−13.5220	−0.686477
$389$	24.4696	1.24066	0.620329	−	0.784342i	$-0.286999\pi$
$389$	24.4696	1.24066	0.620329	+	0.784342i	$0.286999\pi$
$390$	−32.4294	−1.64213
$391$	8.02823	0.406005
$392$	−18.5013	−0.934459
$393$	20.1593	1.01690
$394$	9.36900	0.472003
$395$	−24.1000	−1.21260
$396$	−2.83382	−0.142405
$397$	−2.43639	−0.122279	−0.0611395	−	0.998129i	$-0.519473\pi$
$397$	−2.43639	−0.122279	−0.0611395	+	0.998129i	$0.519473\pi$
$398$	−18.4748	−0.926056
$399$	−2.17734	−0.109003
$400$	5.18748	0.259374
$401$	7.61480	0.380265	0.190132	−	0.981758i	$-0.439108\pi$
$401$	7.61480	0.380265	0.190132	+	0.981758i	$0.439108\pi$
$402$	−4.10438	−0.204708
$403$	45.4135	2.26221
$404$	20.4355	1.01670
$405$	−39.9863	−1.98694
$406$	−1.64727	−0.0817527
$407$	1.92710	0.0955227
$408$	−6.02086	−0.298077
$409$	11.2443	0.555996	0.277998	−	0.960582i	$-0.410329\pi$
$409$	11.2443	0.555996	0.277998	+	0.960582i	$0.410329\pi$
$410$	3.75887	0.185637
$411$	43.7739	2.15920
$412$	6.17895	0.304415
$413$	−0.213506	−0.0105059
$414$	−13.1750	−0.647518
$415$	38.5705	1.89335
$416$	28.9688	1.42031
$417$	20.7970	1.01843
$418$	2.67620	0.130897
$419$	−2.95561	−0.144391	−0.0721956	−	0.997390i	$-0.523001\pi$
$419$	−2.95561	−0.144391	−0.0721956	+	0.997390i	$0.523001\pi$
$420$	−3.23734	−0.157966
$421$	11.5675	0.563766	0.281883	−	0.959449i	$-0.409041\pi$
$421$	11.5675	0.563766	0.281883	+	0.959449i	$0.409041\pi$
$422$	−8.55163	−0.416287
$423$	−13.2570	−0.644580
$424$	23.7328	1.15257
$425$	8.39047	0.406997
$426$	26.0048	1.25994
$427$	1.13513	0.0549330
$428$	−20.2778	−0.980164
$429$	11.1679	0.539190
$430$	−2.90382	−0.140035
$431$	31.4377	1.51430	0.757151	−	0.653240i	$-0.226591\pi$
$431$	31.4377	1.51430	0.757151	+	0.653240i	$0.226591\pi$
$432$	1.29713	0.0624083
$433$	−10.4286	−0.501168	−0.250584	−	0.968095i	$-0.580623\pi$
$433$	−10.4286	−0.501168	−0.250584	+	0.968095i	$0.580623\pi$
$434$	−2.08336	−0.100005
$435$	59.6284	2.85896
$436$	−7.42439	−0.355564
$437$	−27.0749	−1.29517
$438$	15.8835	0.758942
$439$	−15.6699	−0.747883	−0.373942	−	0.927452i	$-0.621994\pi$
$439$	−15.6699	−0.747883	−0.373942	+	0.927452i	$0.621994\pi$
$440$	9.78670	0.466562
$441$	−14.3062	−0.681250
$442$	3.93660	0.187245
$443$	−4.79343	−0.227743	−0.113871	−	0.993495i	$-0.536325\pi$
$443$	−4.79343	−0.227743	−0.113871	+	0.993495i	$0.536325\pi$
$444$	5.94478	0.282127
$445$	55.7061	2.64072
$446$	−7.35923	−0.348470
$447$	21.2125	1.00332
$448$	−0.974339	−0.0460332
$449$	23.1976	1.09476	0.547380	−	0.836884i	$-0.315625\pi$
$449$	23.1976	1.09476	0.547380	+	0.836884i	$0.315625\pi$
$450$	−13.7695	−0.649101
$451$	−1.29446	−0.0609537
$452$	−9.04363	−0.425376
$453$	32.5754	1.53053
$454$	14.6101	0.685686
$455$	5.20603	0.244062
$456$	20.3051	0.950875
$457$	16.9869	0.794614	0.397307	−	0.917686i	$-0.369945\pi$
$457$	16.9869	0.794614	0.397307	+	0.917686i	$0.369945\pi$
$458$	−7.60066	−0.355155
$459$	2.09804	0.0979281
$460$	−40.2559	−1.87694
$461$	−19.0272	−0.886185	−0.443093	−	0.896476i	$-0.646119\pi$
$461$	−19.0272	−0.886185	−0.443093	+	0.896476i	$0.646119\pi$
$462$	−0.512331	−0.0238358
$463$	17.6489	0.820215	0.410107	−	0.912037i	$-0.365491\pi$
$463$	17.6489	0.820215	0.410107	+	0.912037i	$0.365491\pi$
$464$	−4.47513	−0.207753
$465$	75.4142	3.49725
$466$	14.3697	0.665665
$467$	0.740522	0.0342673	0.0171336	−	0.999853i	$-0.494546\pi$
$467$	0.740522	0.0342673	0.0171336	+	0.999853i	$0.494546\pi$
$468$	14.0579	0.649829
$469$	0.658892	0.0304248
$470$	18.6147	0.858631
$471$	53.7821	2.47815
$472$	1.99108	0.0916470
$473$	1.00000	0.0459800
$474$	−11.7655	−0.540408
$475$	−28.2965	−1.29833
$476$	0.392980	0.0180122
$477$	18.3515	0.840258
$478$	−5.75422	−0.263192
$479$	24.2312	1.10715	0.553576	−	0.832799i	$-0.313263\pi$
$479$	24.2312	1.10715	0.553576	+	0.832799i	$0.313263\pi$
$480$	48.1059	2.19573
$481$	−9.55991	−0.435894
$482$	2.15992	0.0983818
$483$	5.18321	0.235844
$484$	−1.37029	−0.0622858
$485$	36.1101	1.63967
$486$	−14.5265	−0.658935
$487$	−6.40748	−0.290350	−0.145175	−	0.989406i	$-0.546375\pi$
$487$	−6.40748	−0.290350	−0.145175	+	0.989406i	$0.546375\pi$
$488$	−10.5859	−0.479200
$489$	−31.4249	−1.42108
$490$	20.0879	0.907478
$491$	36.4702	1.64587	0.822937	−	0.568132i	$-0.192334\pi$
$491$	36.4702	1.64587	0.822937	+	0.568132i	$0.192334\pi$
$492$	−3.99319	−0.180027
$493$	−7.23827	−0.325995
$494$	−13.2760	−0.597317
$495$	7.56761	0.340139
$496$	−5.65985	−0.254135
$497$	−4.17465	−0.187259
$498$	18.8299	0.843789
$499$	32.4178	1.45122	0.725610	−	0.688106i	$-0.241558\pi$
$499$	32.4178	1.45122	0.725610	+	0.688106i	$0.241558\pi$
$500$	−17.0008	−0.760298
$501$	0.0348551	0.00155721
$502$	1.42312	0.0635171
$503$	10.6799	0.476195	0.238098	−	0.971241i	$-0.423476\pi$
$503$	10.6799	0.476195	0.238098	+	0.971241i	$0.423476\pi$
$504$	−1.58620	−0.0706549
$505$	−54.5722	−2.42843
$506$	−6.37076	−0.283215
$507$	−26.1353	−1.16071
$508$	−25.2485	−1.12022
$509$	−9.10549	−0.403594	−0.201797	−	0.979427i	$-0.564678\pi$
$509$	−9.10549	−0.403594	−0.201797	+	0.979427i	$0.564678\pi$
$510$	6.53717	0.289471
$511$	−2.54984	−0.112798
$512$	−6.91740	−0.305709
$513$	−7.07556	−0.312394
$514$	12.2882	0.542010
$515$	−16.5006	−0.727105
$516$	3.08483	0.135802
$517$	−6.41042	−0.281930
$518$	0.438565	0.0192694
$519$	12.7041	0.557649
$520$	−48.5496	−2.12904
$521$	26.6945	1.16951	0.584753	−	0.811211i	$-0.301191\pi$
$521$	26.6945	1.16951	0.584753	+	0.811211i	$0.301191\pi$
$522$	11.8786	0.519914
$523$	−11.4753	−0.501778	−0.250889	−	0.968016i	$-0.580723\pi$
$523$	−11.4753	−0.501778	−0.250889	+	0.968016i	$0.580723\pi$
$524$	12.2706	0.536045
$525$	5.41708	0.236421
$526$	−6.99397	−0.304951
$527$	−9.15450	−0.398776
$528$	−1.39185	−0.0605723
$529$	41.4525	1.80228
$530$	−25.7680	−1.11929
$531$	1.53961	0.0668135
$532$	−1.32531	−0.0574594
$533$	6.42152	0.278147
$534$	27.1955	1.17686
$535$	54.1511	2.34116
$536$	−6.14460	−0.265406
$537$	−49.5938	−2.14013
$538$	1.55305	0.0669566
$539$	−6.91775	−0.297969
$540$	−10.5202	−0.452716
$541$	27.1018	1.16520	0.582599	−	0.812760i	$-0.302036\pi$
$541$	27.1018	1.16520	0.582599	+	0.812760i	$0.302036\pi$
$542$	−4.45535	−0.191374
$543$	−56.9963	−2.44594
$544$	−5.83956	−0.250369
$545$	19.8265	0.849276
$546$	2.54156	0.108769
$547$	38.2897	1.63715	0.818575	−	0.574399i	$-0.194764\pi$
$547$	38.2897	1.63715	0.818575	+	0.574399i	$0.194764\pi$
$548$	26.6444	1.13819
$549$	−8.18558	−0.349352
$550$	−6.65821	−0.283907
$551$	24.4108	1.03993
$552$	−48.3369	−2.05735
$553$	1.88877	0.0803185
$554$	14.0141	0.595402
$555$	−15.8753	−0.673869
$556$	12.6588	0.536852
$557$	−33.2127	−1.40727	−0.703635	−	0.710562i	$-0.748441\pi$
$557$	−33.2127	−1.40727	−0.703635	+	0.710562i	$0.748441\pi$
$558$	15.0233	0.635989
$559$	−4.96078	−0.209819
$560$	−0.648825	−0.0274178
$561$	−2.25123	−0.0950471
$562$	25.0159	1.05523
$563$	−32.0995	−1.35283	−0.676416	−	0.736520i	$-0.736468\pi$
$563$	−32.0995	−1.35283	−0.676416	+	0.736520i	$0.736468\pi$
$564$	−19.7751	−0.832681
$565$	24.1507	1.01603
$566$	14.4687	0.608163
$567$	3.13381	0.131608
$568$	38.9314	1.63352
$569$	2.25740	0.0946353	0.0473176	−	0.998880i	$-0.484933\pi$
$569$	2.25740	0.0946353	0.0473176	+	0.998880i	$0.484933\pi$
$570$	−22.0464	−0.923420
$571$	13.6033	0.569280	0.284640	−	0.958634i	$-0.408126\pi$
$571$	13.6033	0.569280	0.284640	+	0.958634i	$0.408126\pi$
$572$	6.79769	0.284226
$573$	27.9624	1.16814
$574$	−0.294590	−0.0122960
$575$	67.3606	2.80913
$576$	7.02606	0.292753
$577$	−13.9832	−0.582126	−0.291063	−	0.956704i	$-0.594009\pi$
$577$	−13.9832	−0.582126	−0.291063	+	0.956704i	$0.594009\pi$
$578$	−0.793545	−0.0330071
$579$	31.1479	1.29446
$580$	36.2948	1.50706
$581$	−3.02284	−0.125409
$582$	17.6288	0.730737
$583$	8.87383	0.367517
$584$	23.7789	0.983978
$585$	−37.5412	−1.55214
$586$	−21.0930	−0.871343
$587$	−24.8834	−1.02705	−0.513523	−	0.858076i	$-0.671660\pi$
$587$	−24.8834	−1.02705	−0.513523	+	0.858076i	$0.671660\pi$
$588$	−21.3401	−0.880052
$589$	30.8732	1.27211
$590$	−2.16182	−0.0890009
$591$	26.5792	1.09332
$592$	1.19145	0.0489681
$593$	−13.5865	−0.557929	−0.278965	−	0.960301i	$-0.589991\pi$
$593$	−13.5865	−0.557929	−0.278965	+	0.960301i	$0.589991\pi$
$594$	−1.66489	−0.0683112
$595$	−1.04944	−0.0430227
$596$	12.9117	0.528884
$597$	−52.4116	−2.14506
$598$	31.6039	1.29238
$599$	−12.0840	−0.493739	−0.246869	−	0.969049i	$-0.579402\pi$
$599$	−12.0840	−0.493739	−0.246869	+	0.969049i	$0.579402\pi$
$600$	−50.5178	−2.06238
$601$	44.0643	1.79742	0.898710	−	0.438544i	$-0.144506\pi$
$601$	44.0643	1.79742	0.898710	+	0.438544i	$0.144506\pi$
$602$	0.227578	0.00927538
$603$	−4.75134	−0.193489
$604$	19.8281	0.806793
$605$	3.65930	0.148772
$606$	−26.6419	−1.08225
$607$	18.0665	0.733295	0.366647	−	0.930360i	$-0.380506\pi$
$607$	18.0665	0.733295	0.366647	+	0.930360i	$0.380506\pi$
$608$	19.6937	0.798685
$609$	−4.67320	−0.189367
$610$	11.4936	0.465364
$611$	31.8007	1.28652
$612$	−2.83382	−0.114550
$613$	−18.8697	−0.762139	−0.381069	−	0.924546i	$-0.624444\pi$
$613$	−18.8697	−0.762139	−0.381069	+	0.924546i	$0.624444\pi$
$614$	−10.8094	−0.436232
$615$	10.6637	0.430001
$616$	−0.767003	−0.0309034
$617$	11.5197	0.463767	0.231883	−	0.972744i	$-0.425511\pi$
$617$	11.5197	0.463767	0.231883	+	0.972744i	$0.425511\pi$
$618$	−8.05554	−0.324041
$619$	14.1241	0.567694	0.283847	−	0.958870i	$-0.408389\pi$
$619$	14.1241	0.567694	0.283847	+	0.958870i	$0.408389\pi$
$620$	45.9033	1.84352
$621$	16.8436	0.675908
$622$	−1.78917	−0.0717393
$623$	−4.36580	−0.174912
$624$	6.90464	0.276407
$625$	3.44761	0.137904
$626$	−16.5232	−0.660401
$627$	7.59220	0.303203
$628$	32.7363	1.30632
$629$	1.92710	0.0768384
$630$	1.72222	0.0686149
$631$	−8.11272	−0.322962	−0.161481	−	0.986876i	$-0.551627\pi$
$631$	−8.11272	−0.322962	−0.161481	+	0.986876i	$0.551627\pi$
$632$	−17.6140	−0.700647
$633$	−24.2604	−0.964264
$634$	7.61444	0.302408
$635$	67.4253	2.67569
$636$	27.3743	1.08546
$637$	34.3174	1.35971
$638$	5.74389	0.227403
$639$	30.1038	1.19089
$640$	32.8719	1.29938
$641$	−48.2873	−1.90724	−0.953618	−	0.301021i	$-0.902673\pi$
$641$	−48.2873	−1.90724	−0.953618	+	0.301021i	$0.902673\pi$
$642$	26.4363	1.04336
$643$	−40.9302	−1.61413	−0.807066	−	0.590462i	$-0.798946\pi$
$643$	−40.9302	−1.61413	−0.807066	+	0.590462i	$0.798946\pi$
$644$	3.15493	0.124322
$645$	−8.23793	−0.324368
$646$	2.67620	0.105294
$647$	−18.7047	−0.735357	−0.367679	−	0.929953i	$-0.619847\pi$
$647$	−18.7047	−0.735357	−0.367679	+	0.929953i	$0.619847\pi$
$648$	−29.2248	−1.14806
$649$	0.744477	0.0292233
$650$	33.0299	1.29554
$651$	−5.91036	−0.231645
$652$	−19.1278	−0.749101
$653$	38.5701	1.50937	0.754683	−	0.656090i	$-0.227791\pi$
$653$	38.5701	1.50937	0.754683	+	0.656090i	$0.227791\pi$
$654$	9.67923	0.378488
$655$	−32.7683	−1.28036
$656$	−0.800311	−0.0312469
$657$	18.3871	0.717351
$658$	−1.45887	−0.0568726
$659$	40.2280	1.56706	0.783530	−	0.621354i	$-0.213417\pi$
$659$	40.2280	1.56706	0.783530	+	0.621354i	$0.213417\pi$
$660$	11.2883	0.439398
$661$	−22.3696	−0.870076	−0.435038	−	0.900412i	$-0.643265\pi$
$661$	−22.3696	−0.870076	−0.435038	+	0.900412i	$0.643265\pi$
$662$	8.45510	0.328617
$663$	11.1679	0.433724
$664$	28.1900	1.09398
$665$	3.53919	0.137244
$666$	−3.16254	−0.122546
$667$	−58.1105	−2.25005
$668$	0.0212157	0.000820861 0
$669$	−20.8776	−0.807176
$670$	6.67152	0.257743
$671$	−3.95812	−0.152801
$672$	−3.77016	−0.145437
$673$	39.8297	1.53532	0.767662	−	0.640855i	$-0.221420\pi$
$673$	39.8297	1.53532	0.767662	+	0.640855i	$0.221420\pi$
$674$	−27.2986	−1.05150
$675$	17.6035	0.677561
$676$	−15.9081	−0.611850
$677$	25.9049	0.995607	0.497804	−	0.867290i	$-0.334140\pi$
$677$	25.9049	0.995607	0.497804	+	0.867290i	$0.334140\pi$
$678$	11.7903	0.452802
$679$	−2.83002	−0.108606
$680$	9.78670	0.375303
$681$	41.4479	1.58829
$682$	7.26451	0.278172
$683$	24.9952	0.956414	0.478207	−	0.878247i	$-0.341287\pi$
$683$	24.9952	0.956414	0.478207	+	0.878247i	$0.341287\pi$
$684$	9.55695	0.365419
$685$	−71.1528	−2.71861
$686$	−3.16737	−0.120931
$687$	−21.5626	−0.822663
$688$	0.618259	0.0235709
$689$	−44.0211	−1.67707
$690$	52.4819	1.99795
$691$	27.7930	1.05730	0.528648	−	0.848841i	$-0.322699\pi$
$691$	27.7930	1.05730	0.528648	+	0.848841i	$0.322699\pi$
$692$	7.73278	0.293956
$693$	−0.593088	−0.0225296
$694$	−16.3596	−0.621003
$695$	−33.8048	−1.28229
$696$	43.5806	1.65192
$697$	−1.29446	−0.0490311
$698$	−4.84181	−0.183265
$699$	40.7659	1.54191
$700$	3.29728	0.124626
$701$	−21.0002	−0.793165	−0.396583	−	0.917999i	$-0.629804\pi$
$701$	−21.0002	−0.793165	−0.396583	+	0.917999i	$0.629804\pi$
$702$	8.25915	0.311721
$703$	−6.49906	−0.245117
$704$	3.39744	0.128046
$705$	52.8086	1.98889
$706$	−5.80446	−0.218454
$707$	4.27693	0.160851
$708$	2.29659	0.0863110
$709$	33.8397	1.27088	0.635438	−	0.772152i	$-0.280819\pi$
$709$	33.8397	1.27088	0.635438	+	0.772152i	$0.280819\pi$
$710$	−42.2698	−1.58636
$711$	−13.6201	−0.510793
$712$	40.7140	1.52582
$713$	−73.4944	−2.75239
$714$	−0.512331	−0.0191735
$715$	−18.1530	−0.678883
$716$	−30.1869	−1.12814
$717$	−16.3243	−0.609644
$718$	−6.52435	−0.243487
$719$	51.2630	1.91179	0.955894	−	0.293711i	$-0.0948902\pi$
$719$	51.2630	1.91179	0.955894	+	0.293711i	$0.0948902\pi$
$720$	4.67874	0.174366
$721$	1.29319	0.0481608
$722$	6.05197	0.225231
$723$	6.12755	0.227886
$724$	−34.6927	−1.28934
$725$	−60.7325	−2.25555
$726$	1.78645	0.0663015
$727$	28.1067	1.04242	0.521209	−	0.853429i	$-0.325481\pi$
$727$	28.1067	1.04242	0.521209	+	0.853429i	$0.325481\pi$
$728$	3.80493	0.141020
$729$	−8.42870	−0.312174
$730$	−25.8180	−0.955568
$731$	1.00000	0.0369863
$732$	−12.2101	−0.451300
$733$	17.0943	0.631393	0.315696	−	0.948860i	$-0.397762\pi$
$733$	17.0943	0.631393	0.315696	+	0.948860i	$0.397762\pi$
$734$	−1.17202	−0.0432599
$735$	56.9880	2.10203
$736$	−46.8814	−1.72807
$737$	−2.29750	−0.0846295
$738$	2.12432	0.0781974
$739$	23.4551	0.862808	0.431404	−	0.902159i	$-0.358018\pi$
$739$	23.4551	0.862808	0.431404	+	0.902159i	$0.358018\pi$
$740$	−9.66303	−0.355220
$741$	−37.6632	−1.38359
$742$	2.01949	0.0741378
$743$	46.1875	1.69445	0.847227	−	0.531231i	$-0.178271\pi$
$743$	46.1875	1.69445	0.847227	+	0.531231i	$0.178271\pi$
$744$	55.1180	2.02072
$745$	−34.4802	−1.26326
$746$	0.930024	0.0340506
$747$	21.7980	0.797549
$748$	−1.37029	−0.0501026
$749$	−4.24393	−0.155070
$750$	22.1641	0.809317
$751$	−31.4266	−1.14677	−0.573386	−	0.819285i	$-0.694371\pi$
$751$	−31.4266	−1.14677	−0.573386	+	0.819285i	$0.694371\pi$
$752$	−3.96330	−0.144527
$753$	4.03730	0.147127
$754$	−28.4942	−1.03770
$755$	−52.9501	−1.92705
$756$	0.824487	0.0299863
$757$	−14.2784	−0.518957	−0.259478	−	0.965749i	$-0.583551\pi$
$757$	−14.2784	−0.518957	−0.259478	+	0.965749i	$0.583551\pi$
$758$	−28.4990	−1.03513
$759$	−18.0734	−0.656023
$760$	−33.0053	−1.19723
$761$	−21.7427	−0.788174	−0.394087	−	0.919073i	$-0.628939\pi$
$761$	−21.7427	−0.788174	−0.394087	+	0.919073i	$0.628939\pi$
$762$	32.9167	1.19245
$763$	−1.55385	−0.0562530
$764$	17.0202	0.615770
$765$	7.56761	0.273607
$766$	15.7390	0.568674
$767$	−3.69318	−0.133353
$768$	31.3447	1.13106
$769$	27.8526	1.00439	0.502196	−	0.864754i	$-0.332526\pi$
$769$	27.8526	1.00439	0.502196	+	0.864754i	$0.332526\pi$
$770$	0.832776	0.0300112
$771$	34.8608	1.25548
$772$	18.9592	0.682356
$773$	−25.8896	−0.931183	−0.465592	−	0.885000i	$-0.654158\pi$
$773$	−25.8896	−0.931183	−0.465592	+	0.885000i	$0.654158\pi$
$774$	−1.64109	−0.0589877
$775$	−76.8105	−2.75912
$776$	26.3918	0.947410
$777$	1.24418	0.0446347
$778$	−19.4177	−0.696159
$779$	4.36551	0.156411
$780$	−55.9989	−2.00508
$781$	14.5566	0.520878
$782$	−6.37076	−0.227818
$783$	−15.1862	−0.542710
$784$	−4.27697	−0.152749
$785$	−87.4209	−3.12019
$786$	−15.9973	−0.570605
$787$	−9.17913	−0.327201	−0.163600	−	0.986527i	$-0.552311\pi$
$787$	−9.17913	−0.327201	−0.163600	+	0.986527i	$0.552311\pi$
$788$	16.1783	0.576328
$789$	−19.8414	−0.706373
$790$	19.1244	0.680417
$791$	−1.89274	−0.0672979
$792$	5.53094	0.196533
$793$	19.6353	0.697271
$794$	1.93339	0.0686133
$795$	−73.1020	−2.59266
$796$	−31.9021	−1.13074
$797$	−13.8453	−0.490425	−0.245212	−	0.969469i	$-0.578858\pi$
$797$	−13.8453	−0.490425	−0.245212	+	0.969469i	$0.578858\pi$
$798$	1.72782	0.0611640
$799$	−6.41042	−0.226784
$800$	−48.9967	−1.73229
$801$	31.4822	1.11237
$802$	−6.04268	−0.213375
$803$	8.89106	0.313759
$804$	−7.08740	−0.249953
$805$	−8.42513	−0.296947
$806$	−36.0376	−1.26937
$807$	4.40589	0.155095
$808$	−39.8852	−1.40316
$809$	−14.2722	−0.501785	−0.250893	−	0.968015i	$-0.580724\pi$
$809$	−14.2722	−0.501785	−0.250893	+	0.968015i	$0.580724\pi$
$810$	31.7309	1.11491
$811$	−34.2359	−1.20218	−0.601092	−	0.799180i	$-0.705267\pi$
$811$	−34.2359	−1.20218	−0.601092	+	0.799180i	$0.705267\pi$
$812$	−2.84449	−0.0998222
$813$	−12.6395	−0.443288
$814$	−1.52924	−0.0535998
$815$	51.0800	1.78925
$816$	−1.39185	−0.0487243
$817$	−3.37246	−0.117988
$818$	−8.92287	−0.311981
$819$	2.94218	0.102808
$820$	6.49079	0.226668
$821$	22.7352	0.793464	0.396732	−	0.917934i	$-0.370144\pi$
$821$	22.7352	0.793464	0.396732	+	0.917934i	$0.370144\pi$
$822$	−34.7365	−1.21157
$823$	−6.39716	−0.222991	−0.111496	−	0.993765i	$-0.535564\pi$
$823$	−6.39716	−0.222991	−0.111496	+	0.993765i	$0.535564\pi$
$824$	−12.0598	−0.420124
$825$	−18.8889	−0.657627
$826$	0.169426	0.00589510
$827$	−1.08716	−0.0378042	−0.0189021	−	0.999821i	$-0.506017\pi$
$827$	−1.08716	−0.0378042	−0.0189021	+	0.999821i	$0.506017\pi$
$828$	−22.7506	−0.790636
$829$	53.9633	1.87422	0.937112	−	0.349030i	$-0.113489\pi$
$829$	53.9633	1.87422	0.937112	+	0.349030i	$0.113489\pi$
$830$	−30.6074	−1.06240
$831$	39.7571	1.37916
$832$	−16.8539	−0.584305
$833$	−6.91775	−0.239686
$834$	−16.5033	−0.571464
$835$	−0.0566558	−0.00196065
$836$	4.62124	0.159829
$837$	−19.2065	−0.663874
$838$	2.34541	0.0810209
$839$	24.0433	0.830069	0.415034	−	0.909806i	$-0.363770\pi$
$839$	24.0433	0.830069	0.415034	+	0.909806i	$0.363770\pi$
$840$	6.31852	0.218010
$841$	23.3926	0.806640
$842$	−9.17933	−0.316341
$843$	70.9684	2.44428
$844$	−14.7669	−0.508297
$845$	42.4820	1.46143
$846$	10.5201	0.361687
$847$	−0.286787	−0.00985410
$848$	5.48633	0.188401
$849$	41.0466	1.40872
$850$	−6.65821	−0.228375
$851$	15.4712	0.530345
$852$	44.9048	1.53841
$853$	−33.5265	−1.14793	−0.573963	−	0.818881i	$-0.694595\pi$
$853$	−33.5265	−1.14793	−0.573963	+	0.818881i	$0.694595\pi$
$854$	−0.900780	−0.0308241
$855$	−25.5215	−0.872816
$856$	39.5774	1.35273
$857$	17.7555	0.606516	0.303258	−	0.952909i	$-0.401926\pi$
$857$	17.7555	0.606516	0.303258	+	0.952909i	$0.401926\pi$
$858$	−8.86220	−0.302551
$859$	−31.1339	−1.06228	−0.531138	−	0.847285i	$-0.678235\pi$
$859$	−31.1339	−1.06228	−0.531138	+	0.847285i	$0.678235\pi$
$860$	−5.01429	−0.170986
$861$	−0.835733	−0.0284817
$862$	−24.9472	−0.849707
$863$	35.6322	1.21294	0.606468	−	0.795108i	$-0.292586\pi$
$863$	35.6322	1.21294	0.606468	+	0.795108i	$0.292586\pi$
$864$	−12.2516	−0.416809
$865$	−20.6501	−0.702124
$866$	8.27559	0.281216
$867$	−2.25123	−0.0764559
$868$	−3.59753	−0.122108
$869$	−6.58596	−0.223413
$870$	−47.3178	−1.60422
$871$	11.3974	0.386186
$872$	14.4906	0.490715
$873$	20.4076	0.690692
$874$	21.4851	0.726746
$875$	−3.55808	−0.120285
$876$	27.4275	0.926688
$877$	−12.8894	−0.435246	−0.217623	−	0.976033i	$-0.569830\pi$
$877$	−12.8894	−0.435246	−0.217623	+	0.976033i	$0.569830\pi$
$878$	12.4348	0.419653
$879$	−59.8393	−2.01833
$880$	2.26240	0.0762653
$881$	8.13489	0.274071	0.137036	−	0.990566i	$-0.456243\pi$
$881$	8.13489	0.274071	0.137036	+	0.990566i	$0.456243\pi$
$882$	11.3526	0.382264
$883$	−43.5831	−1.46669	−0.733343	−	0.679858i	$-0.762041\pi$
$883$	−43.5831	−1.46669	−0.733343	+	0.679858i	$0.762041\pi$
$884$	6.79769	0.228631
$885$	−6.13295	−0.206157
$886$	3.80380	0.127791
$887$	3.97143	0.133348	0.0666738	−	0.997775i	$-0.478761\pi$
$887$	3.97143	0.133348	0.0666738	+	0.997775i	$0.478761\pi$
$888$	−11.6028	−0.389364
$889$	−5.28425	−0.177228
$890$	−44.2053	−1.48176
$891$	−10.9273	−0.366079
$892$	−12.7079	−0.425491
$893$	21.6189	0.723448
$894$	−16.8331	−0.562983
$895$	80.6129	2.69459
$896$	−2.57623	−0.0860660
$897$	89.6582	2.99360
$898$	−18.4083	−0.614293
$899$	66.2627	2.20999
$900$	−23.7771	−0.792569
$901$	8.87383	0.295630
$902$	1.02721	0.0342024
$903$	0.645623	0.0214850
$904$	17.6510	0.587064
$905$	92.6454	3.07964
$906$	−25.8500	−0.858810
$907$	−34.2098	−1.13592	−0.567959	−	0.823057i	$-0.692267\pi$
$907$	−34.2098	−1.13592	−0.567959	+	0.823057i	$0.692267\pi$
$908$	25.2286	0.837241
$909$	−30.8414	−1.02294
$910$	−4.13122	−0.136948
$911$	48.8792	1.61944	0.809720	−	0.586816i	$-0.199619\pi$
$911$	48.8792	1.61944	0.809720	+	0.586816i	$0.199619\pi$
$912$	4.69395	0.155432
$913$	10.5404	0.348836
$914$	−13.4799	−0.445874
$915$	32.6067	1.07794
$916$	−13.1248	−0.433654
$917$	2.56811	0.0848066
$918$	−1.66489	−0.0549495
$919$	−36.8745	−1.21638	−0.608189	−	0.793792i	$-0.708104\pi$
$919$	−36.8745	−1.21638	−0.608189	+	0.793792i	$0.708104\pi$
$920$	78.5699	2.59037
$921$	−30.6656	−1.01047
$922$	15.0989	0.497257
$923$	−72.2123	−2.37690
$924$	−0.884689	−0.0291041
$925$	16.1693	0.531642
$926$	−14.0052	−0.460240
$927$	−9.32532	−0.306284
$928$	42.2683	1.38753
$929$	6.18661	0.202976	0.101488	−	0.994837i	$-0.467640\pi$
$929$	6.18661	0.202976	0.101488	+	0.994837i	$0.467640\pi$
$930$	−59.8445	−1.96238
$931$	23.3299	0.764605
$932$	24.8135	0.812794
$933$	−5.07576	−0.166173
$934$	−0.587638	−0.0192281
$935$	3.65930	0.119672
$936$	−27.4378	−0.896832
$937$	38.7993	1.26752	0.633758	−	0.773531i	$-0.281511\pi$
$937$	38.7993	1.26752	0.633758	+	0.773531i	$0.281511\pi$
$938$	−0.522860	−0.0170720
$939$	−46.8753	−1.52972
$940$	32.1437	1.04841
$941$	−42.5089	−1.38575	−0.692875	−	0.721057i	$-0.743656\pi$
$941$	−42.5089	−1.38575	−0.692875	+	0.721057i	$0.743656\pi$
$942$	−42.6785	−1.39054
$943$	−10.3922	−0.338417
$944$	0.460280	0.0149808
$945$	−2.20176	−0.0716233
$946$	−0.793545	−0.0258004
$947$	5.18828	0.168596	0.0842982	−	0.996441i	$-0.473135\pi$
$947$	5.18828	0.168596	0.0842982	+	0.996441i	$0.473135\pi$
$948$	−20.3166	−0.659853
$949$	−44.1066	−1.43176
$950$	22.4546	0.728522
$951$	21.6016	0.700481
$952$	−0.767003	−0.0248587
$953$	37.5594	1.21667	0.608334	−	0.793681i	$-0.291838\pi$
$953$	37.5594	1.21667	0.608334	+	0.793681i	$0.291838\pi$
$954$	−14.5627	−0.471486
$955$	−45.4518	−1.47079
$956$	−9.93635	−0.321365
$957$	16.2950	0.526744
$958$	−19.2285	−0.621246
$959$	5.57639	0.180071
$960$	−27.9878	−0.903304
$961$	52.8049	1.70338
$962$	7.58621	0.244589
$963$	30.6034	0.986181
$964$	3.72974	0.120127
$965$	−50.6298	−1.62983
$966$	−4.11311	−0.132337
$967$	34.5141	1.10990	0.554949	−	0.831885i	$-0.312738\pi$
$967$	34.5141	1.10990	0.554949	+	0.831885i	$0.312738\pi$
$968$	2.67447	0.0859608
$969$	7.59220	0.243896
$970$	−28.6550	−0.920056
$971$	−9.17517	−0.294445	−0.147223	−	0.989103i	$-0.547033\pi$
$971$	−9.17517	−0.294445	−0.147223	+	0.989103i	$0.547033\pi$
$972$	−25.0842	−0.804577
$973$	2.64935	0.0849342
$974$	5.08462	0.162922
$975$	93.7036	3.00092
$976$	−2.44714	−0.0783311
$977$	43.9975	1.40760	0.703802	−	0.710397i	$-0.251484\pi$
$977$	43.9975	1.40760	0.703802	+	0.710397i	$0.251484\pi$
$978$	24.9370	0.797398
$979$	15.2232	0.486535
$980$	34.6876	1.10806
$981$	11.2049	0.357746
$982$	−28.9407	−0.923535
$983$	49.2842	1.57192	0.785961	−	0.618276i	$-0.212168\pi$
$983$	49.2842	1.57192	0.785961	+	0.618276i	$0.212168\pi$
$984$	7.79376	0.248456
$985$	−43.2036	−1.37658
$986$	5.74389	0.182923
$987$	−4.13871	−0.131737
$988$	−22.9249	−0.729340
$989$	8.02823	0.255283
$990$	−6.00523	−0.190859
$991$	15.1467	0.481152	0.240576	−	0.970630i	$-0.422664\pi$
$991$	15.1467	0.481152	0.240576	+	0.970630i	$0.422664\pi$
$992$	53.4583	1.69730
$993$	23.9865	0.761190
$994$	3.31277	0.105075
$995$	85.1932	2.70081
$996$	32.5154	1.03029
$997$	20.2269	0.640592	0.320296	−	0.947318i	$-0.396218\pi$
$997$	20.2269	0.640592	0.320296	+	0.947318i	$0.396218\pi$
$998$	−25.7250	−0.814309
$999$	4.04313	0.127919

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8041.2.a.j.1.29	✓	82

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8041.2.a.j.1.29	✓	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)

\(f(q)\)	\(=\)	\(q-0.793545 q^{2} -2.25123 q^{3} -1.37029 q^{4} +3.65930 q^{5} +1.78645 q^{6} -0.286787 q^{7} +2.67447 q^{8} +2.06805 q^{9} +O(q^{10})\)	\(q-0.793545 q^{2} -2.25123 q^{3} -1.37029 q^{4} +3.65930 q^{5} +1.78645 q^{6} -0.286787 q^{7} +2.67447 q^{8} +2.06805 q^{9} -2.90382 q^{10} +1.00000 q^{11} +3.08483 q^{12} -4.96078 q^{13} +0.227578 q^{14} -8.23793 q^{15} +0.618259 q^{16} +1.00000 q^{17} -1.64109 q^{18} -3.37246 q^{19} -5.01429 q^{20} +0.645623 q^{21} -0.793545 q^{22} +8.02823 q^{23} -6.02086 q^{24} +8.39047 q^{25} +3.93660 q^{26} +2.09804 q^{27} +0.392980 q^{28} -7.23827 q^{29} +6.53717 q^{30} -9.15450 q^{31} -5.83956 q^{32} -2.25123 q^{33} -0.793545 q^{34} -1.04944 q^{35} -2.83382 q^{36} +1.92710 q^{37} +2.67620 q^{38} +11.1679 q^{39} +9.78670 q^{40} -1.29446 q^{41} -0.512331 q^{42} +1.00000 q^{43} -1.37029 q^{44} +7.56761 q^{45} -6.37076 q^{46} -6.41042 q^{47} -1.39185 q^{48} -6.91775 q^{49} -6.65821 q^{50} -2.25123 q^{51} +6.79769 q^{52} +8.87383 q^{53} -1.66489 q^{54} +3.65930 q^{55} -0.767003 q^{56} +7.59220 q^{57} +5.74389 q^{58} +0.744477 q^{59} +11.2883 q^{60} -3.95812 q^{61} +7.26451 q^{62} -0.593088 q^{63} +3.39744 q^{64} -18.1530 q^{65} +1.78645 q^{66} -2.29750 q^{67} -1.37029 q^{68} -18.0734 q^{69} +0.832776 q^{70} +14.5566 q^{71} +5.53094 q^{72} +8.89106 q^{73} -1.52924 q^{74} -18.8889 q^{75} +4.62124 q^{76} -0.286787 q^{77} -8.86220 q^{78} -6.58596 q^{79} +2.26240 q^{80} -10.9273 q^{81} +1.02721 q^{82} +10.5404 q^{83} -0.884689 q^{84} +3.65930 q^{85} -0.793545 q^{86} +16.2950 q^{87} +2.67447 q^{88} +15.2232 q^{89} -6.00523 q^{90} +1.42268 q^{91} -11.0010 q^{92} +20.6089 q^{93} +5.08695 q^{94} -12.3408 q^{95} +13.1462 q^{96} +9.86803 q^{97} +5.48955 q^{98} +2.06805 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 82 q + 8 q^{2} + 6 q^{3} + 98 q^{4} + 11 q^{5} + 10 q^{6} + 8 q^{7} + 30 q^{8} + 108 q^{9}+O(q^{10}) \) 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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