LMFDB - Embedded newform 8041.2.a.i.1.14

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:	$78$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
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)

$f(q)$	$=$	$q-1.93129 q^{2} -1.02169 q^{3} +1.72989 q^{4} +3.42042 q^{5} +1.97319 q^{6} -3.76946 q^{7} +0.521655 q^{8} -1.95614 q^{9} +O(q^{10})$	\(q-1.93129 q^{2} -1.02169 q^{3} +1.72989 q^{4} +3.42042 q^{5} +1.97319 q^{6} -3.76946 q^{7} +0.521655 q^{8} -1.95614 q^{9} -6.60584 q^{10} +1.00000 q^{11} -1.76742 q^{12} -3.64938 q^{13} +7.27994 q^{14} -3.49462 q^{15} -4.46726 q^{16} -1.00000 q^{17} +3.77789 q^{18} -5.82980 q^{19} +5.91697 q^{20} +3.85123 q^{21} -1.93129 q^{22} +6.80071 q^{23} -0.532970 q^{24} +6.69929 q^{25} +7.04803 q^{26} +5.06365 q^{27} -6.52077 q^{28} +8.99508 q^{29} +6.74914 q^{30} +8.93511 q^{31} +7.58427 q^{32} -1.02169 q^{33} +1.93129 q^{34} -12.8932 q^{35} -3.38392 q^{36} +5.86524 q^{37} +11.2591 q^{38} +3.72854 q^{39} +1.78428 q^{40} -12.1917 q^{41} -7.43785 q^{42} -1.00000 q^{43} +1.72989 q^{44} -6.69084 q^{45} -13.1342 q^{46} -8.53866 q^{47} +4.56416 q^{48} +7.20884 q^{49} -12.9383 q^{50} +1.02169 q^{51} -6.31304 q^{52} -1.76229 q^{53} -9.77940 q^{54} +3.42042 q^{55} -1.96636 q^{56} +5.95626 q^{57} -17.3721 q^{58} -8.40601 q^{59} -6.04532 q^{60} -13.7622 q^{61} -17.2563 q^{62} +7.37361 q^{63} -5.71294 q^{64} -12.4824 q^{65} +1.97319 q^{66} +10.2727 q^{67} -1.72989 q^{68} -6.94823 q^{69} +24.9005 q^{70} +6.02117 q^{71} -1.02043 q^{72} -9.17547 q^{73} -11.3275 q^{74} -6.84462 q^{75} -10.0849 q^{76} -3.76946 q^{77} -7.20091 q^{78} -6.50847 q^{79} -15.2799 q^{80} +0.694938 q^{81} +23.5458 q^{82} +13.6004 q^{83} +6.66222 q^{84} -3.42042 q^{85} +1.93129 q^{86} -9.19021 q^{87} +0.521655 q^{88} -6.66144 q^{89} +12.9220 q^{90} +13.7562 q^{91} +11.7645 q^{92} -9.12893 q^{93} +16.4907 q^{94} -19.9404 q^{95} -7.74879 q^{96} +2.21727 q^{97} -13.9224 q^{98} -1.95614 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 78 q + 7 q^{2} + 10 q^{3} + 91 q^{4} + 17 q^{5} + 12 q^{6} + 11 q^{7} + 33 q^{8} + 102 q^{9}+O(q^{10}) $ 78 * q + 7 * q^2 + 10 * q^3 + 91 * q^4 + 17 * q^5 + 12 * q^6 + 11 * q^7 + 33 * q^8 + 102 * q^9	\( 78 q + 7 q^{2} + 10 q^{3} + 91 q^{4} + 17 q^{5} + 12 q^{6} + 11 q^{7} + 33 q^{8} + 102 q^{9} + 3 q^{10} + 78 q^{11} + 31 q^{12} - 16 q^{13} + 31 q^{14} + 38 q^{15} + 121 q^{16} - 78 q^{17} + 11 q^{18} + 51 q^{20} + 6 q^{21} + 7 q^{22} + 48 q^{23} + 11 q^{24} + 101 q^{25} + 18 q^{26} + 46 q^{27} + 27 q^{28} + 22 q^{29} + 14 q^{30} + 56 q^{31} + 83 q^{32} + 10 q^{33} - 7 q^{34} + 24 q^{35} + 139 q^{36} + 53 q^{37} + 10 q^{38} + 79 q^{39} - q^{40} + 23 q^{41} + 17 q^{42} - 78 q^{43} + 91 q^{44} + 76 q^{45} + 21 q^{46} + 57 q^{47} + 78 q^{48} + 115 q^{49} + 58 q^{50} - 10 q^{51} - 63 q^{52} + 22 q^{53} - 18 q^{54} + 17 q^{55} + 111 q^{56} - 11 q^{57} + 36 q^{58} + 71 q^{59} + 36 q^{60} + 4 q^{61} - 5 q^{62} + 71 q^{63} + 183 q^{64} + 47 q^{65} + 12 q^{66} + 11 q^{67} - 91 q^{68} + 31 q^{69} + 33 q^{70} + 159 q^{71} + 59 q^{72} + 2 q^{73} - 4 q^{74} + 83 q^{75} - 44 q^{76} + 11 q^{77} + 101 q^{78} + 35 q^{79} + 85 q^{80} + 170 q^{81} + 98 q^{82} - 32 q^{83} + 44 q^{84} - 17 q^{85} - 7 q^{86} - 6 q^{87} + 33 q^{88} + 50 q^{89} - 5 q^{90} + 86 q^{91} + 106 q^{92} + 68 q^{93} - q^{94} + 109 q^{95} - 50 q^{96} + 40 q^{97} + 106 q^{98} + 102 q^{99}+O(q^{100}) \) 78 * q + 7 * q^2 + 10 * q^3 + 91 * q^4 + 17 * q^5 + 12 * q^6 + 11 * q^7 + 33 * q^8 + 102 * q^9 + 3 * q^10 + 78 * q^11 + 31 * q^12 - 16 * q^13 + 31 * q^14 + 38 * q^15 + 121 * q^16 - 78 * q^17 + 11 * q^18 + 51 * q^20 + 6 * q^21 + 7 * q^22 + 48 * q^23 + 11 * q^24 + 101 * q^25 + 18 * q^26 + 46 * q^27 + 27 * q^28 + 22 * q^29 + 14 * q^30 + 56 * q^31 + 83 * q^32 + 10 * q^33 - 7 * q^34 + 24 * q^35 + 139 * q^36 + 53 * q^37 + 10 * q^38 + 79 * q^39 - q^40 + 23 * q^41 + 17 * q^42 - 78 * q^43 + 91 * q^44 + 76 * q^45 + 21 * q^46 + 57 * q^47 + 78 * q^48 + 115 * q^49 + 58 * q^50 - 10 * q^51 - 63 * q^52 + 22 * q^53 - 18 * q^54 + 17 * q^55 + 111 * q^56 - 11 * q^57 + 36 * q^58 + 71 * q^59 + 36 * q^60 + 4 * q^61 - 5 * q^62 + 71 * q^63 + 183 * q^64 + 47 * q^65 + 12 * q^66 + 11 * q^67 - 91 * q^68 + 31 * q^69 + 33 * q^70 + 159 * q^71 + 59 * q^72 + 2 * q^73 - 4 * q^74 + 83 * q^75 - 44 * q^76 + 11 * q^77 + 101 * q^78 + 35 * q^79 + 85 * q^80 + 170 * q^81 + 98 * q^82 - 32 * q^83 + 44 * q^84 - 17 * q^85 - 7 * q^86 - 6 * q^87 + 33 * q^88 + 50 * q^89 - 5 * q^90 + 86 * q^91 + 106 * q^92 + 68 * q^93 - q^94 + 109 * q^95 - 50 * q^96 + 40 * q^97 + 106 * q^98 + 102 * 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 $

$2$	−1.93129	−1.36563	−0.682815	−	0.730591i	$-0.739245\pi$
$2$	−1.93129	−1.36563	−0.682815	+	0.730591i	$0.739245\pi$
$3$	−1.02169	−0.589874	−0.294937	−	0.955517i	$-0.595299\pi$
$3$	−1.02169	−0.589874	−0.294937	+	0.955517i	$0.595299\pi$
$4$	1.72989	0.864947
$5$	3.42042	1.52966	0.764830	−	0.644232i	$-0.222823\pi$
$5$	3.42042	1.52966	0.764830	+	0.644232i	$0.222823\pi$
$6$	1.97319	0.805550
$7$	−3.76946	−1.42472	−0.712361	−	0.701813i	$-0.752374\pi$
$7$	−3.76946	−1.42472	−0.712361	+	0.701813i	$0.752374\pi$
$8$	0.521655	0.184433
$9$	−1.95614	−0.652048
$10$	−6.60584	−2.08895
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−1.76742	−0.510210
$13$	−3.64938	−1.01216	−0.506078	−	0.862488i	$-0.668905\pi$
$13$	−3.64938	−1.01216	−0.506078	+	0.862488i	$0.668905\pi$
$14$	7.27994	1.94564
$15$	−3.49462	−0.902307
$16$	−4.46726	−1.11681
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	3.77789	0.890457
$19$	−5.82980	−1.33745	−0.668724	−	0.743511i	$-0.733159\pi$
$19$	−5.82980	−1.33745	−0.668724	+	0.743511i	$0.733159\pi$
$20$	5.91697	1.32307
$21$	3.85123	0.840407
$22$	−1.93129	−0.411753
$23$	6.80071	1.41805	0.709023	−	0.705185i	$-0.249136\pi$
$23$	6.80071	1.41805	0.709023	+	0.705185i	$0.249136\pi$
$24$	−0.532970	−0.108792
$25$	6.69929	1.33986
$26$	7.04803	1.38223
$27$	5.06365	0.974501
$28$	−6.52077	−1.23231
$29$	8.99508	1.67035	0.835173	−	0.549988i	$-0.185368\pi$
$29$	8.99508	1.67035	0.835173	+	0.549988i	$0.185368\pi$
$30$	6.74914	1.23222
$31$	8.93511	1.60479	0.802396	−	0.596792i	$-0.203558\pi$
$31$	8.93511	1.60479	0.802396	+	0.596792i	$0.203558\pi$
$32$	7.58427	1.34072
$33$	−1.02169	−0.177854
$34$	1.93129	0.331214
$35$	−12.8932	−2.17934
$36$	−3.38392	−0.563987
$37$	5.86524	0.964240	0.482120	−	0.876105i	$-0.339867\pi$
$37$	5.86524	0.964240	0.482120	+	0.876105i	$0.339867\pi$
$38$	11.2591	1.82646
$39$	3.72854	0.597045
$40$	1.78428	0.282119
$41$	−12.1917	−1.90403	−0.952016	−	0.306049i	$-0.900993\pi$
$41$	−12.1917	−1.90403	−0.952016	+	0.306049i	$0.900993\pi$
$42$	−7.43785	−1.14769
$43$	−1.00000	−0.152499
$43$	−1.00000	−0.152499
$44$	1.72989	0.260791
$45$	−6.69084	−0.997412
$46$	−13.1342	−1.93653
$47$	−8.53866	−1.24549	−0.622746	−	0.782424i	$-0.713983\pi$
$47$	−8.53866	−1.24549	−0.622746	+	0.782424i	$0.713983\pi$
$48$	4.56416	0.658780
$49$	7.20884	1.02983
$50$	−12.9383	−1.82975
$51$	1.02169	0.143066
$52$	−6.31304	−0.875461
$53$	−1.76229	−0.242070	−0.121035	−	0.992648i	$-0.538621\pi$
$53$	−1.76229	−0.242070	−0.121035	+	0.992648i	$0.538621\pi$
$54$	−9.77940	−1.33081
$55$	3.42042	0.461210
$56$	−1.96636	−0.262765
$57$	5.95626	0.788926
$58$	−17.3721	−2.28107
$59$	−8.40601	−1.09437	−0.547184	−	0.837012i	$-0.684300\pi$
$59$	−8.40601	−1.09437	−0.547184	+	0.837012i	$0.684300\pi$
$60$	−6.04532	−0.780447
$61$	−13.7622	−1.76207	−0.881033	−	0.473054i	$-0.843152\pi$
$61$	−13.7622	−1.76207	−0.881033	+	0.473054i	$0.843152\pi$
$62$	−17.2563	−2.19155
$63$	7.37361	0.928988
$64$	−5.71294	−0.714118
$65$	−12.4824	−1.54825
$66$	1.97319	0.242883
$67$	10.2727	1.25501	0.627505	−	0.778613i	$-0.284076\pi$
$67$	10.2727	1.25501	0.627505	+	0.778613i	$0.284076\pi$
$68$	−1.72989	−0.209780
$69$	−6.94823	−0.836469
$70$	24.9005	2.97617
$71$	6.02117	0.714582	0.357291	−	0.933993i	$-0.383700\pi$
$71$	6.02117	0.714582	0.357291	+	0.933993i	$0.383700\pi$
$72$	−1.02043	−0.120259
$73$	−9.17547	−1.07391	−0.536954	−	0.843612i	$-0.680425\pi$
$73$	−9.17547	−1.07391	−0.536954	+	0.843612i	$0.680425\pi$
$74$	−11.3275	−1.31680
$75$	−6.84462	−0.790348
$76$	−10.0849	−1.15682
$77$	−3.76946	−0.429570
$78$	−7.20091	−0.815343
$79$	−6.50847	−0.732260	−0.366130	−	0.930564i	$-0.619317\pi$
$79$	−6.50847	−0.732260	−0.366130	+	0.930564i	$0.619317\pi$
$80$	−15.2799	−1.70835
$81$	0.694938	0.0772153
$82$	23.5458	2.60020
$83$	13.6004	1.49284	0.746419	−	0.665477i	$-0.231772\pi$
$83$	13.6004	1.49284	0.746419	+	0.665477i	$0.231772\pi$
$84$	6.66222	0.726907
$85$	−3.42042	−0.370997
$86$	1.93129	0.208257
$87$	−9.19021	−0.985294
$88$	0.521655	0.0556086
$89$	−6.66144	−0.706112	−0.353056	−	0.935602i	$-0.614857\pi$
$89$	−6.66144	−0.706112	−0.353056	+	0.935602i	$0.614857\pi$
$90$	12.9220	1.36210
$91$	13.7562	1.44204
$92$	11.7645	1.22653
$93$	−9.12893	−0.946626
$94$	16.4907	1.70088
$95$	−19.9404	−2.04584
$96$	−7.74879	−0.790858
$97$	2.21727	0.225130	0.112565	−	0.993644i	$-0.464093\pi$
$97$	2.21727	0.225130	0.112565	+	0.993644i	$0.464093\pi$
$98$	−13.9224	−1.40637
$99$	−1.95614	−0.196600
$100$	11.5891	1.15891
$101$	5.24444	0.521841	0.260920	−	0.965360i	$-0.415974\pi$
$101$	5.24444	0.521841	0.260920	+	0.965360i	$0.415974\pi$
$102$	−1.97319	−0.195375
$103$	−9.95886	−0.981276	−0.490638	−	0.871364i	$-0.663236\pi$
$103$	−9.95886	−0.981276	−0.490638	+	0.871364i	$0.663236\pi$
$104$	−1.90372	−0.186675
$105$	13.1728	1.28554
$106$	3.40351	0.330578
$107$	−7.62475	−0.737113	−0.368556	−	0.929605i	$-0.620148\pi$
$107$	−7.62475	−0.737113	−0.368556	+	0.929605i	$0.620148\pi$
$108$	8.75958	0.842891
$109$	7.18893	0.688575	0.344287	−	0.938864i	$-0.388121\pi$
$109$	7.18893	0.688575	0.344287	+	0.938864i	$0.388121\pi$
$110$	−6.60584	−0.629842
$111$	−5.99247	−0.568780
$112$	16.8391	1.59115
$113$	−15.6487	−1.47211	−0.736053	−	0.676923i	$-0.763313\pi$
$113$	−15.6487	−1.47211	−0.736053	+	0.676923i	$0.763313\pi$
$114$	−11.5033	−1.07738
$115$	23.2613	2.16913
$116$	15.5605	1.44476
$117$	7.13872	0.659975
$118$	16.2345	1.49450
$119$	3.76946	0.345546
$120$	−1.82298	−0.166415
$121$	1.00000	0.0909091
$122$	26.5788	2.40633
$123$	12.4562	1.12314
$124$	15.4568	1.38806
$125$	5.81230	0.519868
$126$	−14.2406	−1.26865
$127$	−10.1601	−0.901564	−0.450782	−	0.892634i	$-0.648855\pi$
$127$	−10.1601	−0.901564	−0.450782	+	0.892634i	$0.648855\pi$
$128$	−4.13518	−0.365502
$129$	1.02169	0.0899550
$130$	24.1072	2.11434
$131$	8.02982	0.701568	0.350784	−	0.936456i	$-0.385915\pi$
$131$	8.02982	0.701568	0.350784	+	0.936456i	$0.385915\pi$
$132$	−1.76742	−0.153834
$133$	21.9752	1.90549
$134$	−19.8396	−1.71388
$135$	17.3198	1.49065
$136$	−0.521655	−0.0447315
$137$	−11.7124	−1.00065	−0.500327	−	0.865836i	$-0.666787\pi$
$137$	−11.7124	−1.00065	−0.500327	+	0.865836i	$0.666787\pi$
$138$	13.4191	1.14231
$139$	5.23493	0.444021	0.222010	−	0.975044i	$-0.428738\pi$
$139$	5.23493	0.444021	0.222010	+	0.975044i	$0.428738\pi$
$140$	−22.3038	−1.88501
$141$	8.72388	0.734683
$142$	−11.6287	−0.975855
$143$	−3.64938	−0.305177
$144$	8.73860	0.728217
$145$	30.7670	2.55506
$146$	17.7205	1.46656
$147$	−7.36521	−0.607473
$148$	10.1462	0.834016
$149$	−0.961166	−0.0787418	−0.0393709	−	0.999225i	$-0.512535\pi$
$149$	−0.961166	−0.0787418	−0.0393709	+	0.999225i	$0.512535\pi$
$150$	13.2190	1.07932
$151$	−17.0146	−1.38463	−0.692315	−	0.721595i	$-0.743409\pi$
$151$	−17.0146	−1.38463	−0.692315	+	0.721595i	$0.743409\pi$
$152$	−3.04114	−0.246669
$153$	1.95614	0.158145
$154$	7.27994	0.586634
$155$	30.5618	2.45479
$156$	6.44999	0.516412
$157$	22.4675	1.79311	0.896553	−	0.442937i	$-0.146064\pi$
$157$	22.4675	1.79311	0.896553	+	0.442937i	$0.146064\pi$
$158$	12.5698	0.999997
$159$	1.80052	0.142791
$160$	25.9414	2.05085
$161$	−25.6350	−2.02032
$162$	−1.34213	−0.105448
$163$	−13.4178	−1.05096	−0.525481	−	0.850805i	$-0.676115\pi$
$163$	−13.4178	−1.05096	−0.525481	+	0.850805i	$0.676115\pi$
$164$	−21.0904	−1.64689
$165$	−3.49462	−0.272056
$166$	−26.2664	−2.03866
$167$	−7.54783	−0.584068	−0.292034	−	0.956408i	$-0.594332\pi$
$167$	−7.54783	−0.584068	−0.292034	+	0.956408i	$0.594332\pi$
$168$	2.00901	0.154999
$169$	0.317983	0.0244602
$170$	6.60584	0.506645
$171$	11.4039	0.872081
$172$	−1.72989	−0.131903
$173$	8.09816	0.615692	0.307846	−	0.951436i	$-0.400392\pi$
$173$	8.09816	0.615692	0.307846	+	0.951436i	$0.400392\pi$
$174$	17.7490	1.34555
$175$	−25.2527	−1.90893
$176$	−4.46726	−0.336732
$177$	8.58835	0.645540
$178$	12.8652	0.964287
$179$	−2.36120	−0.176484	−0.0882422	−	0.996099i	$-0.528125\pi$
$179$	−2.36120	−0.176484	−0.0882422	+	0.996099i	$0.528125\pi$
$180$	−11.5744	−0.862708
$181$	15.5183	1.15346	0.576732	−	0.816933i	$-0.304328\pi$
$181$	15.5183	1.15346	0.576732	+	0.816933i	$0.304328\pi$
$182$	−26.5673	−1.96930
$183$	14.0607	1.03940
$184$	3.54762	0.261534
$185$	20.0616	1.47496
$186$	17.6306	1.29274
$187$	−1.00000	−0.0731272
$188$	−14.7710	−1.07728
$189$	−19.0873	−1.38839
$190$	38.5107	2.79386
$191$	17.0247	1.23187	0.615934	−	0.787798i	$-0.288779\pi$
$191$	17.0247	1.23187	0.615934	+	0.787798i	$0.288779\pi$
$192$	5.83687	0.421240
$193$	18.9266	1.36237	0.681185	−	0.732111i	$-0.261465\pi$
$193$	18.9266	1.36237	0.681185	+	0.732111i	$0.261465\pi$
$194$	−4.28220	−0.307444
$195$	12.7532	0.913276
$196$	12.4705	0.890752
$197$	−15.9397	−1.13566	−0.567828	−	0.823147i	$-0.692216\pi$
$197$	−15.9397	−1.13566	−0.567828	+	0.823147i	$0.692216\pi$
$198$	3.77789	0.268483
$199$	9.77181	0.692705	0.346353	−	0.938104i	$-0.387420\pi$
$199$	9.77181	0.692705	0.346353	+	0.938104i	$0.387420\pi$
$200$	3.49472	0.247114
$201$	−10.4955	−0.740298
$202$	−10.1285	−0.712642
$203$	−33.9066	−2.37978
$204$	1.76742	0.123744
$205$	−41.7009	−2.91252
$206$	19.2335	1.34006
$207$	−13.3032	−0.924635
$208$	16.3027	1.13039
$209$	−5.82980	−0.403256
$210$	−25.4406	−1.75557
$211$	22.1858	1.52733	0.763667	−	0.645610i	$-0.223397\pi$
$211$	22.1858	1.52733	0.763667	+	0.645610i	$0.223397\pi$
$212$	−3.04858	−0.209377
$213$	−6.15179	−0.421513
$214$	14.7256	1.00662
$215$	−3.42042	−0.233271
$216$	2.64148	0.179730
$217$	−33.6805	−2.28638
$218$	−13.8839	−0.940338
$219$	9.37451	0.633470
$220$	5.91697	0.398922
$221$	3.64938	0.245484
$222$	11.5732	0.776744
$223$	−21.8547	−1.46350	−0.731750	−	0.681573i	$-0.761296\pi$
$223$	−21.8547	−1.46350	−0.731750	+	0.681573i	$0.761296\pi$
$224$	−28.5886	−1.91016
$225$	−13.1048	−0.873653
$226$	30.2222	2.01035
$227$	5.06855	0.336411	0.168206	−	0.985752i	$-0.446203\pi$
$227$	5.06855	0.336411	0.168206	+	0.985752i	$0.446203\pi$
$228$	10.3037	0.682379
$229$	0.194465	0.0128506	0.00642531	−	0.999979i	$-0.497955\pi$
$229$	0.194465	0.0128506	0.00642531	+	0.999979i	$0.497955\pi$
$230$	−44.9244	−2.96223
$231$	3.85123	0.253392
$232$	4.69233	0.308066
$233$	−23.3548	−1.53002	−0.765011	−	0.644018i	$-0.777266\pi$
$233$	−23.3548	−1.53002	−0.765011	+	0.644018i	$0.777266\pi$
$234$	−13.7870	−0.901282
$235$	−29.2058	−1.90518
$236$	−14.5415	−0.946571
$237$	6.64965	0.431941
$238$	−7.27994	−0.471888
$239$	13.9058	0.899492	0.449746	−	0.893157i	$-0.351515\pi$
$239$	13.9058	0.899492	0.449746	+	0.893157i	$0.351515\pi$
$240$	15.6114	1.00771
$241$	19.5543	1.25960	0.629800	−	0.776757i	$-0.283137\pi$
$241$	19.5543	1.25960	0.629800	+	0.776757i	$0.283137\pi$
$242$	−1.93129	−0.124148
$243$	−15.9010	−1.02005
$244$	−23.8071	−1.52409
$245$	24.6573	1.57530
$246$	−24.0566	−1.53379
$247$	21.2752	1.35371
$248$	4.66104	0.295976
$249$	−13.8954	−0.880586
$250$	−11.2253	−0.709948
$251$	−11.3731	−0.717865	−0.358932	−	0.933364i	$-0.616859\pi$
$251$	−11.3731	−0.717865	−0.358932	+	0.933364i	$0.616859\pi$
$252$	12.7556	0.803525
$253$	6.80071	0.427557
$254$	19.6222	1.23120
$255$	3.49462	0.218842
$256$	19.4121	1.21326
$257$	13.8509	0.863995	0.431998	−	0.901875i	$-0.357809\pi$
$257$	13.8509	0.863995	0.431998	+	0.901875i	$0.357809\pi$
$258$	−1.97319	−0.122845
$259$	−22.1088	−1.37377
$260$	−21.5933	−1.33916
$261$	−17.5957	−1.08915
$262$	−15.5079	−0.958083
$263$	0.255501	0.0157549	0.00787743	−	0.999969i	$-0.497493\pi$
$263$	0.255501	0.0157549	0.00787743	+	0.999969i	$0.497493\pi$
$264$	−0.532970	−0.0328021
$265$	−6.02779	−0.370284
$266$	−42.4406	−2.60220
$267$	6.80594	0.416517
$268$	17.7707	1.08552
$269$	−12.2374	−0.746129	−0.373065	−	0.927805i	$-0.621693\pi$
$269$	−12.2374	−0.746129	−0.373065	+	0.927805i	$0.621693\pi$
$270$	−33.4497	−2.03568
$271$	18.3874	1.11696	0.558478	−	0.829519i	$-0.311385\pi$
$271$	18.3874	1.11696	0.558478	+	0.829519i	$0.311385\pi$
$272$	4.46726	0.270867
$273$	−14.0546	−0.850623
$274$	22.6200	1.36652
$275$	6.69929	0.403983
$276$	−12.0197	−0.723501
$277$	14.1613	0.850872	0.425436	−	0.904988i	$-0.360121\pi$
$277$	14.1613	0.850872	0.425436	+	0.904988i	$0.360121\pi$
$278$	−10.1102	−0.606369
$279$	−17.4784	−1.04640
$280$	−6.72577	−0.401942
$281$	0.898035	0.0535723	0.0267861	−	0.999641i	$-0.491473\pi$
$281$	0.898035	0.0535723	0.0267861	+	0.999641i	$0.491473\pi$
$282$	−16.8484	−1.00331
$283$	−2.41574	−0.143601	−0.0718003	−	0.997419i	$-0.522874\pi$
$283$	−2.41574	−0.143601	−0.0718003	+	0.997419i	$0.522874\pi$
$284$	10.4160	0.618075
$285$	20.3729	1.20679
$286$	7.04803	0.416758
$287$	45.9563	2.71272
$288$	−14.8359	−0.874216
$289$	1.00000	0.0588235
$290$	−59.4201	−3.48927
$291$	−2.26537	−0.132798
$292$	−15.8726	−0.928873
$293$	8.41438	0.491573	0.245787	−	0.969324i	$-0.420954\pi$
$293$	8.41438	0.491573	0.245787	+	0.969324i	$0.420954\pi$
$294$	14.2244	0.829583
$295$	−28.7521	−1.67401
$296$	3.05963	0.177837
$297$	5.06365	0.293823
$298$	1.85629	0.107532
$299$	−24.8184	−1.43528
$300$	−11.8405	−0.683609
$301$	3.76946	0.217268
$302$	32.8602	1.89089
$303$	−5.35820	−0.307821
$304$	26.0432	1.49368
$305$	−47.0725	−2.69536
$306$	−3.77789	−0.215968
$307$	24.0642	1.37342	0.686708	−	0.726933i	$-0.259055\pi$
$307$	24.0642	1.37342	0.686708	+	0.726933i	$0.259055\pi$
$308$	−6.52077	−0.371555
$309$	10.1749	0.578829
$310$	−59.0239	−3.35233
$311$	31.5879	1.79119	0.895593	−	0.444875i	$-0.146752\pi$
$311$	31.5879	1.79119	0.895593	+	0.444875i	$0.146752\pi$
$312$	1.94501	0.110115
$313$	−13.9224	−0.786943	−0.393472	−	0.919337i	$-0.628726\pi$
$313$	−13.9224	−0.786943	−0.393472	+	0.919337i	$0.628726\pi$
$314$	−43.3914	−2.44872
$315$	25.2209	1.42104
$316$	−11.2590	−0.633366
$317$	−6.38616	−0.358682	−0.179341	−	0.983787i	$-0.557397\pi$
$317$	−6.38616	−0.358682	−0.179341	+	0.983787i	$0.557397\pi$
$318$	−3.47734	−0.194999
$319$	8.99508	0.503628
$320$	−19.5407	−1.09236
$321$	7.79015	0.434804
$322$	49.5087	2.75901
$323$	5.82980	0.324379
$324$	1.20217	0.0667872
$325$	−24.4483	−1.35615
$326$	25.9137	1.43523
$327$	−7.34487	−0.406172
$328$	−6.35988	−0.351166
$329$	32.1861	1.77448
$330$	6.74914	0.371528
$331$	22.9611	1.26205	0.631027	−	0.775761i	$-0.282634\pi$
$331$	22.9611	1.26205	0.631027	+	0.775761i	$0.282634\pi$
$332$	23.5272	1.29122
$333$	−11.4733	−0.628731
$334$	14.5771	0.797622
$335$	35.1370	1.91974
$336$	−17.2044	−0.938578
$337$	13.3485	0.727141	0.363570	−	0.931567i	$-0.381558\pi$
$337$	13.3485	0.727141	0.363570	+	0.931567i	$0.381558\pi$
$338$	−0.614118	−0.0334036
$339$	15.9882	0.868358
$340$	−5.91697	−0.320893
$341$	8.93511	0.483863
$342$	−22.0243	−1.19094
$343$	−0.787207	−0.0425052
$344$	−0.521655	−0.0281257
$345$	−23.7659	−1.27951
$346$	−15.6399	−0.840807
$347$	1.90774	0.102413	0.0512065	−	0.998688i	$-0.483693\pi$
$347$	1.90774	0.102413	0.0512065	+	0.998688i	$0.483693\pi$
$348$	−15.8981	−0.852227
$349$	−1.79108	−0.0958746	−0.0479373	−	0.998850i	$-0.515265\pi$
$349$	−1.79108	−0.0958746	−0.0479373	+	0.998850i	$0.515265\pi$
$350$	48.7704	2.60689
$351$	−18.4792	−0.986347
$352$	7.58427	0.404243
$353$	−4.88142	−0.259812	−0.129906	−	0.991526i	$-0.541468\pi$
$353$	−4.88142	−0.259812	−0.129906	+	0.991526i	$0.541468\pi$
$354$	−16.5866	−0.881569
$355$	20.5950	1.09307
$356$	−11.5236	−0.610749
$357$	−3.85123	−0.203829
$358$	4.56017	0.241013
$359$	31.9392	1.68568	0.842842	−	0.538161i	$-0.180881\pi$
$359$	31.9392	1.68568	0.842842	+	0.538161i	$0.180881\pi$
$360$	−3.49031	−0.183955
$361$	14.9866	0.788767
$362$	−29.9704	−1.57521
$363$	−1.02169	−0.0536249
$364$	23.7968	1.24729
$365$	−31.3840	−1.64271
$366$	−27.1554	−1.41943
$367$	3.54576	0.185087	0.0925435	−	0.995709i	$-0.470500\pi$
$367$	3.54576	0.185087	0.0925435	+	0.995709i	$0.470500\pi$
$368$	−30.3805	−1.58369
$369$	23.8488	1.24152
$370$	−38.7449	−2.01425
$371$	6.64290	0.344882
$372$	−15.7921	−0.818781
$373$	−9.40947	−0.487204	−0.243602	−	0.969875i	$-0.578329\pi$
$373$	−9.40947	−0.487204	−0.243602	+	0.969875i	$0.578329\pi$
$374$	1.93129	0.0998648
$375$	−5.93838	−0.306657
$376$	−4.45423	−0.229709
$377$	−32.8265	−1.69065
$378$	36.8631	1.89603
$379$	−4.19081	−0.215267	−0.107634	−	0.994191i	$-0.534327\pi$
$379$	−4.19081	−0.215267	−0.107634	+	0.994191i	$0.534327\pi$
$380$	−34.4947	−1.76954
$381$	10.3805	0.531809
$382$	−32.8798	−1.68228
$383$	1.80572	0.0922680	0.0461340	−	0.998935i	$-0.485310\pi$
$383$	1.80572	0.0922680	0.0461340	+	0.998935i	$0.485310\pi$
$384$	4.22488	0.215600
$385$	−12.8932	−0.657096
$386$	−36.5529	−1.86049
$387$	1.95614	0.0994364
$388$	3.83565	0.194725
$389$	6.60879	0.335079	0.167539	−	0.985865i	$-0.446418\pi$
$389$	6.60879	0.335079	0.167539	+	0.985865i	$0.446418\pi$
$390$	−24.6302	−1.24720
$391$	−6.80071	−0.343927
$392$	3.76052	0.189935
$393$	−8.20400	−0.413837
$394$	30.7842	1.55089
$395$	−22.2617	−1.12011
$396$	−3.38392	−0.170049
$397$	−31.2363	−1.56770	−0.783851	−	0.620948i	$-0.786748\pi$
$397$	−31.2363	−1.56770	−0.783851	+	0.620948i	$0.786748\pi$
$398$	−18.8722	−0.945980
$399$	−22.4519	−1.12400
$400$	−29.9275	−1.49637
$401$	17.7698	0.887381	0.443690	−	0.896180i	$-0.353669\pi$
$401$	17.7698	0.887381	0.443690	+	0.896180i	$0.353669\pi$
$402$	20.2700	1.01097
$403$	−32.6076	−1.62430
$404$	9.07232	0.451365
$405$	2.37698	0.118113
$406$	65.4836	3.24990
$407$	5.86524	0.290729
$408$	0.532970	0.0263860
$409$	17.4893	0.864793	0.432396	−	0.901684i	$-0.357668\pi$
$409$	17.4893	0.864793	0.432396	+	0.901684i	$0.357668\pi$
$410$	80.5367	3.97743
$411$	11.9664	0.590260
$412$	−17.2278	−0.848751
$413$	31.6861	1.55917
$414$	25.6923	1.26271
$415$	46.5191	2.28353
$416$	−27.6779	−1.35702
$417$	−5.34849	−0.261917
$418$	11.2591	0.550698
$419$	20.4807	1.00055	0.500274	−	0.865867i	$-0.333233\pi$
$419$	20.4807	1.00055	0.500274	+	0.865867i	$0.333233\pi$
$420$	22.7876	1.11192
$421$	9.21966	0.449339	0.224669	−	0.974435i	$-0.427870\pi$
$421$	9.21966	0.449339	0.224669	+	0.974435i	$0.427870\pi$
$422$	−42.8473	−2.08578
$423$	16.7029	0.812121
$424$	−0.919309	−0.0446456
$425$	−6.69929	−0.324963
$426$	11.8809	0.575632
$427$	51.8760	2.51046
$428$	−13.1900	−0.637563
$429$	3.72854	0.180016
$430$	6.60584	0.318562
$431$	−12.7939	−0.616261	−0.308130	−	0.951344i	$-0.599703\pi$
$431$	−12.7939	−0.616261	−0.308130	+	0.951344i	$0.599703\pi$
$432$	−22.6206	−1.08834
$433$	−32.6914	−1.57105	−0.785524	−	0.618831i	$-0.787607\pi$
$433$	−32.6914	−1.57105	−0.785524	+	0.618831i	$0.787607\pi$
$434$	65.0470	3.12236
$435$	−31.4344	−1.50716
$436$	12.4361	0.595580
$437$	−39.6468	−1.89656
$438$	−18.1049	−0.865086
$439$	−37.1147	−1.77139	−0.885695	−	0.464267i	$-0.846318\pi$
$439$	−37.1147	−1.77139	−0.885695	+	0.464267i	$0.846318\pi$
$440$	1.78428	0.0850622
$441$	−14.1015	−0.671502
$442$	−7.04803	−0.335240
$443$	5.41595	0.257319	0.128660	−	0.991689i	$-0.458933\pi$
$443$	5.41595	0.257319	0.128660	+	0.991689i	$0.458933\pi$
$444$	−10.3663	−0.491965
$445$	−22.7850	−1.08011
$446$	42.2079	1.99860
$447$	0.982016	0.0464478
$448$	21.5347	1.01742
$449$	−0.222969	−0.0105226	−0.00526129	−	0.999986i	$-0.501675\pi$
$449$	−0.222969	−0.0105226	−0.00526129	+	0.999986i	$0.501675\pi$
$450$	25.3092	1.19309
$451$	−12.1917	−0.574087
$452$	−27.0706	−1.27329
$453$	17.3837	0.816758
$454$	−9.78885	−0.459413
$455$	47.0520	2.20583
$456$	3.10711	0.145504
$457$	20.6408	0.965537	0.482769	−	0.875748i	$-0.339631\pi$
$457$	20.6408	0.965537	0.482769	+	0.875748i	$0.339631\pi$
$458$	−0.375569	−0.0175492
$459$	−5.06365	−0.236351
$460$	40.2396	1.87618
$461$	4.38320	0.204146	0.102073	−	0.994777i	$-0.467452\pi$
$461$	4.38320	0.204146	0.102073	+	0.994777i	$0.467452\pi$
$462$	−7.43785	−0.346040
$463$	18.8999	0.878351	0.439176	−	0.898401i	$-0.355271\pi$
$463$	18.8999	0.878351	0.439176	+	0.898401i	$0.355271\pi$
$464$	−40.1833	−1.86546
$465$	−31.2248	−1.44802
$466$	45.1049	2.08944
$467$	34.8619	1.61322	0.806609	−	0.591085i	$-0.201300\pi$
$467$	34.8619	1.61322	0.806609	+	0.591085i	$0.201300\pi$
$468$	12.3492	0.570843
$469$	−38.7225	−1.78804
$470$	56.4050	2.60177
$471$	−22.9549	−1.05771
$472$	−4.38503	−0.201837
$473$	−1.00000	−0.0459800
$474$	−12.8424	−0.589872
$475$	−39.0555	−1.79199
$476$	6.52077	0.298879
$477$	3.44730	0.157841
$478$	−26.8562	−1.22837
$479$	19.7107	0.900607	0.450304	−	0.892876i	$-0.351316\pi$
$479$	19.7107	0.900607	0.450304	+	0.892876i	$0.351316\pi$
$480$	−26.5041	−1.20974
$481$	−21.4045	−0.975962
$482$	−37.7650	−1.72015
$483$	26.1911	1.19174
$484$	1.72989	0.0786315
$485$	7.58401	0.344372
$486$	30.7095	1.39301
$487$	−22.3747	−1.01389	−0.506947	−	0.861977i	$-0.669226\pi$
$487$	−22.3747	−1.01389	−0.506947	+	0.861977i	$0.669226\pi$
$488$	−7.17910	−0.324983
$489$	13.7089	0.619936
$490$	−47.6204	−2.15127
$491$	33.7975	1.52526	0.762630	−	0.646835i	$-0.223908\pi$
$491$	33.7975	1.52526	0.762630	+	0.646835i	$0.223908\pi$
$492$	21.5479	0.971456
$493$	−8.99508	−0.405118
$494$	−41.0886	−1.84866
$495$	−6.69084	−0.300731
$496$	−39.9154	−1.79225
$497$	−22.6966	−1.01808
$498$	26.8361	1.20256
$499$	24.7803	1.10932	0.554659	−	0.832078i	$-0.312849\pi$
$499$	24.7803	1.10932	0.554659	+	0.832078i	$0.312849\pi$
$500$	10.0547	0.449658
$501$	7.71156	0.344527
$502$	21.9648	0.980338
$503$	24.6990	1.10127	0.550636	−	0.834745i	$-0.314385\pi$
$503$	24.6990	1.10127	0.550636	+	0.834745i	$0.314385\pi$
$504$	3.84648	0.171336
$505$	17.9382	0.798239
$506$	−13.1342	−0.583885
$507$	−0.324881	−0.0144285
$508$	−17.5759	−0.779805
$509$	2.71097	0.120161	0.0600807	−	0.998194i	$-0.480864\pi$
$509$	2.71097	0.120161	0.0600807	+	0.998194i	$0.480864\pi$
$510$	−6.74914	−0.298857
$511$	34.5866	1.53002
$512$	−29.2201	−1.29136
$513$	−29.5201	−1.30334
$514$	−26.7501	−1.17990
$515$	−34.0635	−1.50102
$516$	1.76742	0.0778063
$517$	−8.53866	−0.375530
$518$	42.6986	1.87607
$519$	−8.27383	−0.363181
$520$	−6.51151	−0.285549
$521$	−27.3984	−1.20035	−0.600174	−	0.799870i	$-0.704902\pi$
$521$	−27.3984	−1.20035	−0.600174	+	0.799870i	$0.704902\pi$
$522$	33.9824	1.48737
$523$	3.46716	0.151608	0.0758042	−	0.997123i	$-0.475848\pi$
$523$	3.46716	0.151608	0.0758042	+	0.997123i	$0.475848\pi$
$524$	13.8907	0.606819
$525$	25.8005	1.12603
$526$	−0.493447	−0.0215153
$527$	−8.93511	−0.389219
$528$	4.56416	0.198630
$529$	23.2497	1.01086
$530$	11.6414	0.505672
$531$	16.4434	0.713581
$532$	38.0148	1.64815
$533$	44.4923	1.92718
$534$	−13.1443	−0.568808
$535$	−26.0799	−1.12753
$536$	5.35880	0.231465
$537$	2.41242	0.104104
$538$	23.6341	1.01894
$539$	7.20884	0.310507
$540$	29.9615	1.28934
$541$	26.8951	1.15631	0.578156	−	0.815926i	$-0.303773\pi$
$541$	26.8951	1.15631	0.578156	+	0.815926i	$0.303773\pi$
$542$	−35.5115	−1.52535
$543$	−15.8549	−0.680399
$544$	−7.58427	−0.325173
$545$	24.5892	1.05328
$546$	27.1436	1.16164
$547$	−9.20692	−0.393660	−0.196830	−	0.980438i	$-0.563065\pi$
$547$	−9.20692	−0.393660	−0.196830	+	0.980438i	$0.563065\pi$
$548$	−20.2611	−0.865513
$549$	26.9208	1.14895
$550$	−12.9383	−0.551691
$551$	−52.4395	−2.23400
$552$	−3.62458	−0.154272
$553$	24.5334	1.04327
$554$	−27.3497	−1.16198
$555$	−20.4968	−0.870040
$556$	9.05587	0.384055
$557$	−42.2262	−1.78918	−0.894591	−	0.446886i	$-0.852533\pi$
$557$	−42.2262	−1.78918	−0.894591	+	0.446886i	$0.852533\pi$
$558$	33.7558	1.42900
$559$	3.64938	0.154352
$560$	57.5970	2.43392
$561$	1.02169	0.0431359
$562$	−1.73437	−0.0731599
$563$	41.5016	1.74908	0.874541	−	0.484952i	$-0.161163\pi$
$563$	41.5016	1.74908	0.874541	+	0.484952i	$0.161163\pi$
$564$	15.0914	0.635462
$565$	−53.5252	−2.25182
$566$	4.66549	0.196105
$567$	−2.61954	−0.110010
$568$	3.14097	0.131792
$569$	5.80289	0.243270	0.121635	−	0.992575i	$-0.461186\pi$
$569$	5.80289	0.243270	0.121635	+	0.992575i	$0.461186\pi$
$570$	−39.3461	−1.64803
$571$	−9.85080	−0.412243	−0.206121	−	0.978526i	$-0.566084\pi$
$571$	−9.85080	−0.412243	−0.206121	+	0.978526i	$0.566084\pi$
$572$	−6.31304	−0.263962
$573$	−17.3941	−0.726647
$574$	−88.7551	−3.70457
$575$	45.5600	1.89998
$576$	11.1753	0.465639
$577$	−18.3695	−0.764732	−0.382366	−	0.924011i	$-0.624891\pi$
$577$	−18.3695	−0.764732	−0.382366	+	0.924011i	$0.624891\pi$
$578$	−1.93129	−0.0803312
$579$	−19.3372	−0.803627
$580$	53.2236	2.20999
$581$	−51.2662	−2.12688
$582$	4.37509	0.181353
$583$	−1.76229	−0.0729868
$584$	−4.78642	−0.198064
$585$	24.4174	1.00954
$586$	−16.2506	−0.671308
$587$	3.33679	0.137724	0.0688621	−	0.997626i	$-0.478063\pi$
$587$	3.33679	0.137724	0.0688621	+	0.997626i	$0.478063\pi$
$588$	−12.7410	−0.525431
$589$	−52.0899	−2.14633
$590$	55.5287	2.28608
$591$	16.2855	0.669895
$592$	−26.2015	−1.07688
$593$	26.1905	1.07551	0.537757	−	0.843100i	$-0.319272\pi$
$593$	26.1905	1.07551	0.537757	+	0.843100i	$0.319272\pi$
$594$	−9.77940	−0.401254
$595$	12.8932	0.528568
$596$	−1.66272	−0.0681075
$597$	−9.98379	−0.408609
$598$	47.9316	1.96007
$599$	20.4406	0.835182	0.417591	−	0.908635i	$-0.362874\pi$
$599$	20.4406	0.835182	0.417591	+	0.908635i	$0.362874\pi$
$600$	−3.57052	−0.145766
$601$	0.260039	0.0106072	0.00530360	−	0.999986i	$-0.498312\pi$
$601$	0.260039	0.0106072	0.00530360	+	0.999986i	$0.498312\pi$
$602$	−7.27994	−0.296708
$603$	−20.0949	−0.818327
$604$	−29.4335	−1.19763
$605$	3.42042	0.139060
$606$	10.3483	0.420369
$607$	4.00843	0.162697	0.0813485	−	0.996686i	$-0.474077\pi$
$607$	4.00843	0.162697	0.0813485	+	0.996686i	$0.474077\pi$
$608$	−44.2148	−1.79315
$609$	34.6421	1.40377
$610$	90.9108	3.68087
$611$	31.1608	1.26063
$612$	3.38392	0.136787
$613$	39.2250	1.58428	0.792141	−	0.610338i	$-0.208966\pi$
$613$	39.2250	1.58428	0.792141	+	0.610338i	$0.208966\pi$
$614$	−46.4750	−1.87558
$615$	42.6055	1.71802
$616$	−1.96636	−0.0792268
$617$	−17.2989	−0.696428	−0.348214	−	0.937415i	$-0.613212\pi$
$617$	−17.2989	−0.696428	−0.348214	+	0.937415i	$0.613212\pi$
$618$	−19.6507	−0.790467
$619$	−25.2206	−1.01370	−0.506850	−	0.862034i	$-0.669190\pi$
$619$	−25.2206	−1.01370	−0.506850	+	0.862034i	$0.669190\pi$
$620$	52.8687	2.12326
$621$	34.4365	1.38189
$622$	−61.0055	−2.44610
$623$	25.1101	1.00601
$624$	−16.6564	−0.666788
$625$	−13.6159	−0.544638
$626$	26.8883	1.07467
$627$	5.95626	0.237870
$628$	38.8665	1.55094
$629$	−5.86524	−0.233863
$630$	−48.7089	−1.94061
$631$	31.7362	1.26340	0.631699	−	0.775214i	$-0.282358\pi$
$631$	31.7362	1.26340	0.631699	+	0.775214i	$0.282358\pi$
$632$	−3.39517	−0.135053
$633$	−22.6671	−0.900936
$634$	12.3335	0.489827
$635$	−34.7519	−1.37909
$636$	3.11471	0.123506
$637$	−26.3078	−1.04235
$638$	−17.3721	−0.687770
$639$	−11.7783	−0.465942
$640$	−14.1441	−0.559093
$641$	6.15248	0.243008	0.121504	−	0.992591i	$-0.461228\pi$
$641$	6.15248	0.243008	0.121504	+	0.992591i	$0.461228\pi$
$642$	−15.0451	−0.593781
$643$	12.4271	0.490077	0.245039	−	0.969513i	$-0.421199\pi$
$643$	12.4271	0.490077	0.245039	+	0.969513i	$0.421199\pi$
$644$	−44.3459	−1.74747
$645$	3.49462	0.137601
$646$	−11.2591	−0.442982
$647$	−34.7380	−1.36569	−0.682845	−	0.730563i	$-0.739258\pi$
$647$	−34.7380	−1.36569	−0.682845	+	0.730563i	$0.739258\pi$
$648$	0.362518	0.0142410
$649$	−8.40601	−0.329965
$650$	47.2168	1.85199
$651$	34.4111	1.34868
$652$	−23.2114	−0.909027
$653$	−17.7273	−0.693722	−0.346861	−	0.937917i	$-0.612752\pi$
$653$	−17.7273	−0.693722	−0.346861	+	0.937917i	$0.612752\pi$
$654$	14.1851	0.554681
$655$	27.4654	1.07316
$656$	54.4637	2.12645
$657$	17.9485	0.700240
$658$	−62.1609	−2.42328
$659$	33.4208	1.30189	0.650945	−	0.759125i	$-0.274373\pi$
$659$	33.4208	1.30189	0.650945	+	0.759125i	$0.274373\pi$
$660$	−6.04532	−0.235314
$661$	36.1367	1.40556	0.702778	−	0.711409i	$-0.251943\pi$
$661$	36.1367	1.40556	0.702778	+	0.711409i	$0.251943\pi$
$662$	−44.3445	−1.72350
$663$	−3.72854	−0.144805
$664$	7.09471	0.275328
$665$	75.1645	2.91475
$666$	22.1582	0.858614
$667$	61.1730	2.36863
$668$	−13.0569	−0.505188
$669$	22.3288	0.863281
$670$	−67.8598	−2.62165
$671$	−13.7622	−0.531283
$672$	29.2088	1.12675
$673$	−7.49134	−0.288770	−0.144385	−	0.989522i	$-0.546120\pi$
$673$	−7.49134	−0.288770	−0.144385	+	0.989522i	$0.546120\pi$
$674$	−25.7799	−0.993006
$675$	33.9229	1.30569
$676$	0.550077	0.0211568
$677$	−24.2124	−0.930559	−0.465279	−	0.885164i	$-0.654046\pi$
$677$	−24.2124	−0.930559	−0.465279	+	0.885164i	$0.654046\pi$
$678$	−30.8778	−1.18586
$679$	−8.35792	−0.320748
$680$	−1.78428	−0.0684240
$681$	−5.17849	−0.198440
$682$	−17.2563	−0.660778
$683$	18.4436	0.705724	0.352862	−	0.935675i	$-0.385208\pi$
$683$	18.4436	0.705724	0.352862	+	0.935675i	$0.385208\pi$
$684$	19.7276	0.754303
$685$	−40.0612	−1.53066
$686$	1.52033	0.0580464
$687$	−0.198683	−0.00758025
$688$	4.46726	0.170313
$689$	6.43128	0.245012
$690$	45.8989	1.74734
$691$	42.2587	1.60760	0.803799	−	0.594902i	$-0.202809\pi$
$691$	42.2587	1.60760	0.803799	+	0.594902i	$0.202809\pi$
$692$	14.0090	0.532540
$693$	7.37361	0.280100
$694$	−3.68441	−0.139858
$695$	17.9057	0.679201
$696$	−4.79411	−0.181720
$697$	12.1917	0.461795
$698$	3.45911	0.130929
$699$	23.8614	0.902520
$700$	−43.6845	−1.65112
$701$	15.2137	0.574613	0.287306	−	0.957839i	$-0.407240\pi$
$701$	15.2137	0.574613	0.287306	+	0.957839i	$0.407240\pi$
$702$	35.6888	1.34699
$703$	−34.1932	−1.28962
$704$	−5.71294	−0.215315
$705$	29.8394	1.12382
$706$	9.42746	0.354807
$707$	−19.7687	−0.743479
$708$	14.8569	0.558358
$709$	16.0512	0.602814	0.301407	−	0.953496i	$-0.402544\pi$
$709$	16.0512	0.602814	0.301407	+	0.953496i	$0.402544\pi$
$710$	−39.7749	−1.49273
$711$	12.7315	0.477469
$712$	−3.47497	−0.130230
$713$	60.7651	2.27567
$714$	7.43785	0.278355
$715$	−12.4824	−0.466816
$716$	−4.08463	−0.152650
$717$	−14.2075	−0.530587
$718$	−61.6839	−2.30202
$719$	−10.4185	−0.388543	−0.194271	−	0.980948i	$-0.562234\pi$
$719$	−10.4185	−0.388543	−0.194271	+	0.980948i	$0.562234\pi$
$720$	29.8897	1.11392
$721$	37.5395	1.39805
$722$	−28.9435	−1.07716
$723$	−19.9784	−0.743006
$724$	26.8450	0.997686
$725$	60.2607	2.23803
$726$	1.97319	0.0732319
$727$	17.2552	0.639960	0.319980	−	0.947424i	$-0.396324\pi$
$727$	17.2552	0.639960	0.319980	+	0.947424i	$0.396324\pi$
$728$	7.17598	0.265960
$729$	14.1611	0.524485
$730$	60.6117	2.24334
$731$	1.00000	0.0369863
$732$	24.3235	0.899024
$733$	−46.1287	−1.70380	−0.851901	−	0.523703i	$-0.824550\pi$
$733$	−46.1287	−1.70380	−0.851901	+	0.523703i	$0.824550\pi$
$734$	−6.84790	−0.252761
$735$	−25.1921	−0.929226
$736$	51.5784	1.90121
$737$	10.2727	0.378400
$738$	−46.0591	−1.69546
$739$	17.2437	0.634319	0.317159	−	0.948372i	$-0.397271\pi$
$739$	17.2437	0.634319	0.317159	+	0.948372i	$0.397271\pi$
$740$	34.7045	1.27576
$741$	−21.7367	−0.798517
$742$	−12.8294	−0.470982
$743$	−21.1967	−0.777633	−0.388816	−	0.921315i	$-0.627116\pi$
$743$	−21.1967	−0.777633	−0.388816	+	0.921315i	$0.627116\pi$
$744$	−4.76215	−0.174589
$745$	−3.28759	−0.120448
$746$	18.1724	0.665340
$747$	−26.6043	−0.973402
$748$	−1.72989	−0.0632512
$749$	28.7412	1.05018
$750$	11.4688	0.418780
$751$	43.5191	1.58804	0.794018	−	0.607894i	$-0.207986\pi$
$751$	43.5191	1.58804	0.794018	+	0.607894i	$0.207986\pi$
$752$	38.1444	1.39098
$753$	11.6198	0.423450
$754$	63.3976	2.30880
$755$	−58.1972	−2.11801
$756$	−33.0189	−1.20089
$757$	−27.8734	−1.01308	−0.506538	−	0.862217i	$-0.669075\pi$
$757$	−27.8734	−1.01308	−0.506538	+	0.862217i	$0.669075\pi$
$758$	8.09368	0.293976
$759$	−6.94823	−0.252205
$760$	−10.4020	−0.377320
$761$	−47.8990	−1.73634	−0.868169	−	0.496269i	$-0.834703\pi$
$761$	−47.8990	−1.73634	−0.868169	+	0.496269i	$0.834703\pi$
$762$	−20.0478	−0.726255
$763$	−27.0984	−0.981028
$764$	29.4510	1.06550
$765$	6.69084	0.241908
$766$	−3.48737	−0.126004
$767$	30.6767	1.10767
$768$	−19.8332	−0.715669
$769$	−34.7810	−1.25423	−0.627117	−	0.778925i	$-0.715765\pi$
$769$	−34.7810	−1.25423	−0.627117	+	0.778925i	$0.715765\pi$
$770$	24.9005	0.897350
$771$	−14.1514	−0.509649
$772$	32.7411	1.17838
$773$	27.7518	0.998161	0.499081	−	0.866556i	$-0.333671\pi$
$773$	27.7518	0.998161	0.499081	+	0.866556i	$0.333671\pi$
$774$	−3.77789	−0.135793
$775$	59.8589	2.15020
$776$	1.15665	0.0415213
$777$	22.5884	0.810354
$778$	−12.7635	−0.457594
$779$	71.0755	2.54654
$780$	22.0617	0.789935
$781$	6.02117	0.215455
$782$	13.1342	0.469677
$783$	45.5480	1.62775
$784$	−32.2037	−1.15013
$785$	76.8485	2.74284
$786$	15.8443	0.565149
$787$	30.5023	1.08729	0.543645	−	0.839315i	$-0.317044\pi$
$787$	30.5023	1.08729	0.543645	+	0.839315i	$0.317044\pi$
$788$	−27.5740	−0.982282
$789$	−0.261043	−0.00929339
$790$	42.9939	1.52965
$791$	58.9872	2.09734
$792$	−1.02043	−0.0362595
$793$	50.2234	1.78349
$794$	60.3264	2.14090
$795$	6.15855	0.218421
$796$	16.9042	0.599153
$797$	−25.7925	−0.913619	−0.456809	−	0.889565i	$-0.651008\pi$
$797$	−25.7925	−0.913619	−0.456809	+	0.889565i	$0.651008\pi$
$798$	43.3612	1.53497
$799$	8.53866	0.302076
$800$	50.8093	1.79638
$801$	13.0307	0.460419
$802$	−34.3187	−1.21183
$803$	−9.17547	−0.323795
$804$	−18.1562	−0.640318
$805$	−87.6826	−3.09041
$806$	62.9749	2.21819
$807$	12.5029	0.440122
$808$	2.73578	0.0962446
$809$	0.926092	0.0325596	0.0162798	−	0.999867i	$-0.494818\pi$
$809$	0.926092	0.0325596	0.0162798	+	0.999867i	$0.494818\pi$
$810$	−4.59065	−0.161299
$811$	−13.0943	−0.459803	−0.229901	−	0.973214i	$-0.573840\pi$
$811$	−13.0943	−0.459803	−0.229901	+	0.973214i	$0.573840\pi$
$812$	−58.6549	−2.05838
$813$	−18.7863	−0.658864
$814$	−11.3275	−0.397029
$815$	−45.8945	−1.60762
$816$	−4.56416	−0.159778
$817$	5.82980	0.203959
$818$	−33.7771	−1.18099
$819$	−26.9091	−0.940281
$820$	−72.1382	−2.51917
$821$	−9.87585	−0.344669	−0.172335	−	0.985038i	$-0.555131\pi$
$821$	−9.87585	−0.344669	−0.172335	+	0.985038i	$0.555131\pi$
$822$	−23.1107	−0.806077
$823$	−52.9875	−1.84703	−0.923515	−	0.383563i	$-0.874697\pi$
$823$	−52.9875	−1.84703	−0.923515	+	0.383563i	$0.874697\pi$
$824$	−5.19508	−0.180979
$825$	−6.84462	−0.238299
$826$	−61.1952	−2.12925
$827$	49.3467	1.71595	0.857976	−	0.513690i	$-0.171722\pi$
$827$	49.3467	1.71595	0.857976	+	0.513690i	$0.171722\pi$
$828$	−23.0131	−0.799760
$829$	−46.7956	−1.62528	−0.812639	−	0.582767i	$-0.801970\pi$
$829$	−46.7956	−1.62528	−0.812639	+	0.582767i	$0.801970\pi$
$830$	−89.8420	−3.11846
$831$	−14.4685	−0.501908
$832$	20.8487	0.722799
$833$	−7.20884	−0.249771
$834$	10.3295	0.357681
$835$	−25.8168	−0.893426
$836$	−10.0849	−0.348795
$837$	45.2443	1.56387
$838$	−39.5543	−1.36638
$839$	−29.9248	−1.03312	−0.516560	−	0.856251i	$-0.672788\pi$
$839$	−29.9248	−1.03312	−0.516560	+	0.856251i	$0.672788\pi$
$840$	6.87167	0.237095
$841$	51.9115	1.79005
$842$	−17.8059	−0.613631
$843$	−0.917515	−0.0316009
$844$	38.3791	1.32106
$845$	1.08764	0.0374158
$846$	−32.2581	−1.10906
$847$	−3.76946	−0.129520
$848$	7.87262	0.270347
$849$	2.46814	0.0847063
$850$	12.9383	0.443780
$851$	39.8878	1.36734
$852$	−10.6419	−0.364587
$853$	29.3458	1.00478	0.502390	−	0.864641i	$-0.332454\pi$
$853$	29.3458	1.00478	0.502390	+	0.864641i	$0.332454\pi$
$854$	−100.188	−3.42836
$855$	39.0063	1.33399
$856$	−3.97749	−0.135948
$857$	14.8651	0.507781	0.253891	−	0.967233i	$-0.418290\pi$
$857$	14.8651	0.507781	0.253891	+	0.967233i	$0.418290\pi$
$858$	−7.20091	−0.245835
$859$	51.4083	1.75403	0.877014	−	0.480465i	$-0.159532\pi$
$859$	51.4083	1.75403	0.877014	+	0.480465i	$0.159532\pi$
$860$	−5.91697	−0.201767
$861$	−46.9532	−1.60016
$862$	24.7088	0.841585
$863$	43.4321	1.47845	0.739223	−	0.673460i	$-0.235193\pi$
$863$	43.4321	1.47845	0.739223	+	0.673460i	$0.235193\pi$
$864$	38.4041	1.30654
$865$	27.6991	0.941799
$866$	63.1367	2.14547
$867$	−1.02169	−0.0346985
$868$	−58.2637	−1.97760
$869$	−6.50847	−0.220785
$870$	60.7090	2.05823
$871$	−37.4890	−1.27027
$872$	3.75014	0.126996
$873$	−4.33731	−0.146796
$874$	76.5696	2.59000
$875$	−21.9092	−0.740668
$876$	16.2169	0.547918
$877$	46.8935	1.58348	0.791740	−	0.610858i	$-0.209175\pi$
$877$	46.8935	1.58348	0.791740	+	0.610858i	$0.209175\pi$
$878$	71.6795	2.41906
$879$	−8.59691	−0.289967
$880$	−15.2799	−0.515085
$881$	17.0668	0.574995	0.287497	−	0.957781i	$-0.407177\pi$
$881$	17.0668	0.574995	0.287497	+	0.957781i	$0.407177\pi$
$882$	27.2342	0.917023
$883$	38.2164	1.28608	0.643042	−	0.765831i	$-0.277672\pi$
$883$	38.2164	1.28608	0.643042	+	0.765831i	$0.277672\pi$
$884$	6.31304	0.212331
$885$	29.3758	0.987457
$886$	−10.4598	−0.351403
$887$	−40.9640	−1.37544	−0.687718	−	0.725978i	$-0.741387\pi$
$887$	−40.9640	−1.37544	−0.687718	+	0.725978i	$0.741387\pi$
$888$	−3.12600	−0.104902
$889$	38.2981	1.28448
$890$	44.0044	1.47503
$891$	0.694938	0.0232813
$892$	−37.8063	−1.26585
$893$	49.7787	1.66578
$894$	−1.89656	−0.0634305
$895$	−8.07631	−0.269961
$896$	15.5874	0.520738
$897$	25.3568	0.846637
$898$	0.430619	0.0143699
$899$	80.3720	2.68056
$900$	−22.6699	−0.755663
$901$	1.76229	0.0587105
$902$	23.5458	0.783991
$903$	−3.85123	−0.128161
$904$	−8.16322	−0.271505
$905$	53.0791	1.76441
$906$	−33.5731	−1.11539
$907$	39.9965	1.32806	0.664031	−	0.747705i	$-0.268844\pi$
$907$	39.9965	1.32806	0.664031	+	0.747705i	$0.268844\pi$
$908$	8.76805	0.290978
$909$	−10.2589	−0.340266
$910$	−90.8713	−3.01235
$911$	36.0926	1.19580	0.597900	−	0.801571i	$-0.296002\pi$
$911$	36.0926	1.19580	0.597900	+	0.801571i	$0.296002\pi$
$912$	−26.6081	−0.881084
$913$	13.6004	0.450107
$914$	−39.8635	−1.31857
$915$	48.0936	1.58993
$916$	0.336404	0.0111151
$917$	−30.2681	−0.999540
$918$	9.77940	0.322768
$919$	−0.880867	−0.0290571	−0.0145286	−	0.999894i	$-0.504625\pi$
$919$	−0.880867	−0.0290571	−0.0145286	+	0.999894i	$0.504625\pi$
$920$	12.1344	0.400058
$921$	−24.5862	−0.810143
$922$	−8.46525	−0.278788
$923$	−21.9736	−0.723268
$924$	6.66222	0.219171
$925$	39.2930	1.29195
$926$	−36.5012	−1.19950
$927$	19.4810	0.639839
$928$	68.2212	2.23947
$929$	56.0330	1.83838	0.919191	−	0.393812i	$-0.128844\pi$
$929$	56.0330	1.83838	0.919191	+	0.393812i	$0.128844\pi$
$930$	60.3042	1.97745
$931$	−42.0261	−1.37735
$932$	−40.4013	−1.32339
$933$	−32.2731	−1.05657
$934$	−67.3286	−2.20306
$935$	−3.42042	−0.111860
$936$	3.72394	0.121721
$937$	−43.1219	−1.40873	−0.704366	−	0.709837i	$-0.748768\pi$
$937$	−43.1219	−1.40873	−0.704366	+	0.709837i	$0.748768\pi$
$938$	74.7846	2.44180
$939$	14.2245	0.464198
$940$	−50.5230	−1.64788
$941$	38.1153	1.24252	0.621261	−	0.783603i	$-0.286621\pi$
$941$	38.1153	1.24252	0.621261	+	0.783603i	$0.286621\pi$
$942$	44.3327	1.44444
$943$	−82.9126	−2.70000
$944$	37.5518	1.22221
$945$	−65.2865	−2.12377
$946$	1.93129	0.0627918
$947$	−10.7696	−0.349966	−0.174983	−	0.984571i	$-0.555987\pi$
$947$	−10.7696	−0.349966	−0.174983	+	0.984571i	$0.555987\pi$
$948$	11.5032	0.373606
$949$	33.4848	1.08696
$950$	75.4277	2.44720
$951$	6.52469	0.211577
$952$	1.96636	0.0637300
$953$	42.2032	1.36710	0.683548	−	0.729906i	$-0.260436\pi$
$953$	42.2032	1.36710	0.683548	+	0.729906i	$0.260436\pi$
$954$	−6.65775	−0.215553
$955$	58.2318	1.88434
$956$	24.0556	0.778013
$957$	−9.19021	−0.297077
$958$	−38.0672	−1.22990
$959$	44.1493	1.42565
$960$	19.9646	0.644353
$961$	48.8361	1.57536
$962$	41.3384	1.33280
$963$	14.9151	0.480633
$964$	33.8268	1.08949
$965$	64.7371	2.08396
$966$	−50.5827	−1.62747
$967$	−57.7994	−1.85870	−0.929351	−	0.369197i	$-0.879633\pi$
$967$	−57.7994	−1.85870	−0.929351	+	0.369197i	$0.879633\pi$
$968$	0.521655	0.0167666
$969$	−5.95626	−0.191343
$970$	−14.6469	−0.470285
$971$	−58.9849	−1.89292	−0.946458	−	0.322827i	$-0.895367\pi$
$971$	−58.9849	−1.89292	−0.946458	+	0.322827i	$0.895367\pi$
$972$	−27.5070	−0.882287
$973$	−19.7329	−0.632607
$974$	43.2121	1.38460
$975$	24.9786	0.799956
$976$	61.4792	1.96790
$977$	−9.45071	−0.302355	−0.151178	−	0.988507i	$-0.548307\pi$
$977$	−9.45071	−0.302355	−0.151178	+	0.988507i	$0.548307\pi$
$978$	−26.4758	−0.846604
$979$	−6.66144	−0.212901
$980$	42.6545	1.36255
$981$	−14.0626	−0.448984
$982$	−65.2729	−2.08294
$983$	28.3445	0.904049	0.452024	−	0.892006i	$-0.350702\pi$
$983$	28.3445	0.904049	0.452024	+	0.892006i	$0.350702\pi$
$984$	6.49784	0.207144
$985$	−54.5205	−1.73717
$986$	17.3721	0.553242
$987$	−32.8843	−1.04672
$988$	36.8038	1.17088
$989$	−6.80071	−0.216250
$990$	12.9220	0.410687
$991$	−29.5356	−0.938231	−0.469115	−	0.883137i	$-0.655427\pi$
$991$	−29.5356	−0.938231	−0.469115	+	0.883137i	$0.655427\pi$
$992$	67.7663	2.15158
$993$	−23.4591	−0.744453
$994$	43.8338	1.39032
$995$	33.4237	1.05960
$996$	−24.0376	−0.761660
$997$	37.8583	1.19898	0.599492	−	0.800381i	$-0.295369\pi$
$997$	37.8583	1.19898	0.599492	+	0.800381i	$0.295369\pi$
$998$	−47.8580	−1.51492
$999$	29.6996	0.939653

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8041.2.a.i.1.14	✓	78

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8041.2.a.i.1.14	✓	78	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)

\(f(q)\)	\(=\)	\(q-1.93129 q^{2} -1.02169 q^{3} +1.72989 q^{4} +3.42042 q^{5} +1.97319 q^{6} -3.76946 q^{7} +0.521655 q^{8} -1.95614 q^{9} +O(q^{10})\)	\(q-1.93129 q^{2} -1.02169 q^{3} +1.72989 q^{4} +3.42042 q^{5} +1.97319 q^{6} -3.76946 q^{7} +0.521655 q^{8} -1.95614 q^{9} -6.60584 q^{10} +1.00000 q^{11} -1.76742 q^{12} -3.64938 q^{13} +7.27994 q^{14} -3.49462 q^{15} -4.46726 q^{16} -1.00000 q^{17} +3.77789 q^{18} -5.82980 q^{19} +5.91697 q^{20} +3.85123 q^{21} -1.93129 q^{22} +6.80071 q^{23} -0.532970 q^{24} +6.69929 q^{25} +7.04803 q^{26} +5.06365 q^{27} -6.52077 q^{28} +8.99508 q^{29} +6.74914 q^{30} +8.93511 q^{31} +7.58427 q^{32} -1.02169 q^{33} +1.93129 q^{34} -12.8932 q^{35} -3.38392 q^{36} +5.86524 q^{37} +11.2591 q^{38} +3.72854 q^{39} +1.78428 q^{40} -12.1917 q^{41} -7.43785 q^{42} -1.00000 q^{43} +1.72989 q^{44} -6.69084 q^{45} -13.1342 q^{46} -8.53866 q^{47} +4.56416 q^{48} +7.20884 q^{49} -12.9383 q^{50} +1.02169 q^{51} -6.31304 q^{52} -1.76229 q^{53} -9.77940 q^{54} +3.42042 q^{55} -1.96636 q^{56} +5.95626 q^{57} -17.3721 q^{58} -8.40601 q^{59} -6.04532 q^{60} -13.7622 q^{61} -17.2563 q^{62} +7.37361 q^{63} -5.71294 q^{64} -12.4824 q^{65} +1.97319 q^{66} +10.2727 q^{67} -1.72989 q^{68} -6.94823 q^{69} +24.9005 q^{70} +6.02117 q^{71} -1.02043 q^{72} -9.17547 q^{73} -11.3275 q^{74} -6.84462 q^{75} -10.0849 q^{76} -3.76946 q^{77} -7.20091 q^{78} -6.50847 q^{79} -15.2799 q^{80} +0.694938 q^{81} +23.5458 q^{82} +13.6004 q^{83} +6.66222 q^{84} -3.42042 q^{85} +1.93129 q^{86} -9.19021 q^{87} +0.521655 q^{88} -6.66144 q^{89} +12.9220 q^{90} +13.7562 q^{91} +11.7645 q^{92} -9.12893 q^{93} +16.4907 q^{94} -19.9404 q^{95} -7.74879 q^{96} +2.21727 q^{97} -13.9224 q^{98} -1.95614 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 78 q + 7 q^{2} + 10 q^{3} + 91 q^{4} + 17 q^{5} + 12 q^{6} + 11 q^{7} + 33 q^{8} + 102 q^{9}+O(q^{10}) \) 78 * q + 7 * q^2 + 10 * q^3 + 91 * q^4 + 17 * q^5 + 12 * q^6 + 11 * q^7 + 33 * q^8 + 102 * q^9	\( 78 q + 7 q^{2} + 10 q^{3} + 91 q^{4} + 17 q^{5} + 12 q^{6} + 11 q^{7} + 33 q^{8} + 102 q^{9} + 3 q^{10} + 78 q^{11} + 31 q^{12} - 16 q^{13} + 31 q^{14} + 38 q^{15} + 121 q^{16} - 78 q^{17} + 11 q^{18} + 51 q^{20} + 6 q^{21} + 7 q^{22} + 48 q^{23} + 11 q^{24} + 101 q^{25} + 18 q^{26} + 46 q^{27} + 27 q^{28} + 22 q^{29} + 14 q^{30} + 56 q^{31} + 83 q^{32} + 10 q^{33} - 7 q^{34} + 24 q^{35} + 139 q^{36} + 53 q^{37} + 10 q^{38} + 79 q^{39} - q^{40} + 23 q^{41} + 17 q^{42} - 78 q^{43} + 91 q^{44} + 76 q^{45} + 21 q^{46} + 57 q^{47} + 78 q^{48} + 115 q^{49} + 58 q^{50} - 10 q^{51} - 63 q^{52} + 22 q^{53} - 18 q^{54} + 17 q^{55} + 111 q^{56} - 11 q^{57} + 36 q^{58} + 71 q^{59} + 36 q^{60} + 4 q^{61} - 5 q^{62} + 71 q^{63} + 183 q^{64} + 47 q^{65} + 12 q^{66} + 11 q^{67} - 91 q^{68} + 31 q^{69} + 33 q^{70} + 159 q^{71} + 59 q^{72} + 2 q^{73} - 4 q^{74} + 83 q^{75} - 44 q^{76} + 11 q^{77} + 101 q^{78} + 35 q^{79} + 85 q^{80} + 170 q^{81} + 98 q^{82} - 32 q^{83} + 44 q^{84} - 17 q^{85} - 7 q^{86} - 6 q^{87} + 33 q^{88} + 50 q^{89} - 5 q^{90} + 86 q^{91} + 106 q^{92} + 68 q^{93} - q^{94} + 109 q^{95} - 50 q^{96} + 40 q^{97} + 106 q^{98} + 102 q^{99}+O(q^{100}) \) 78 * q + 7 * q^2 + 10 * q^3 + 91 * q^4 + 17 * q^5 + 12 * q^6 + 11 * q^7 + 33 * q^8 + 102 * q^9 + 3 * q^10 + 78 * q^11 + 31 * q^12 - 16 * q^13 + 31 * q^14 + 38 * q^15 + 121 * q^16 - 78 * q^17 + 11 * q^18 + 51 * q^20 + 6 * q^21 + 7 * q^22 + 48 * q^23 + 11 * q^24 + 101 * q^25 + 18 * q^26 + 46 * q^27 + 27 * q^28 + 22 * q^29 + 14 * q^30 + 56 * q^31 + 83 * q^32 + 10 * q^33 - 7 * q^34 + 24 * q^35 + 139 * q^36 + 53 * q^37 + 10 * q^38 + 79 * q^39 - q^40 + 23 * q^41 + 17 * q^42 - 78 * q^43 + 91 * q^44 + 76 * q^45 + 21 * q^46 + 57 * q^47 + 78 * q^48 + 115 * q^49 + 58 * q^50 - 10 * q^51 - 63 * q^52 + 22 * q^53 - 18 * q^54 + 17 * q^55 + 111 * q^56 - 11 * q^57 + 36 * q^58 + 71 * q^59 + 36 * q^60 + 4 * q^61 - 5 * q^62 + 71 * q^63 + 183 * q^64 + 47 * q^65 + 12 * q^66 + 11 * q^67 - 91 * q^68 + 31 * q^69 + 33 * q^70 + 159 * q^71 + 59 * q^72 + 2 * q^73 - 4 * q^74 + 83 * q^75 - 44 * q^76 + 11 * q^77 + 101 * q^78 + 35 * q^79 + 85 * q^80 + 170 * q^81 + 98 * q^82 - 32 * q^83 + 44 * q^84 - 17 * q^85 - 7 * q^86 - 6 * q^87 + 33 * q^88 + 50 * q^89 - 5 * q^90 + 86 * q^91 + 106 * q^92 + 68 * q^93 - q^94 + 109 * q^95 - 50 * q^96 + 40 * q^97 + 106 * q^98 + 102 * q^99

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