LMFDB - Embedded newform 8041.2.a.i.1.8

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			1.8
Character	$\chi$	$=$	8041.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.35944 q^{2} +3.36081 q^{3} +3.56697 q^{4} -2.07702 q^{5} -7.92965 q^{6} -0.337523 q^{7} -3.69718 q^{8} +8.29507 q^{9} +O(q^{10})$	\(q-2.35944 q^{2} +3.36081 q^{3} +3.56697 q^{4} -2.07702 q^{5} -7.92965 q^{6} -0.337523 q^{7} -3.69718 q^{8} +8.29507 q^{9} +4.90061 q^{10} +1.00000 q^{11} +11.9879 q^{12} -4.41805 q^{13} +0.796366 q^{14} -6.98048 q^{15} +1.58935 q^{16} -1.00000 q^{17} -19.5718 q^{18} -3.97263 q^{19} -7.40868 q^{20} -1.13435 q^{21} -2.35944 q^{22} -1.36597 q^{23} -12.4255 q^{24} -0.685985 q^{25} +10.4241 q^{26} +17.7958 q^{27} -1.20393 q^{28} -3.07221 q^{29} +16.4700 q^{30} +10.8484 q^{31} +3.64439 q^{32} +3.36081 q^{33} +2.35944 q^{34} +0.701042 q^{35} +29.5883 q^{36} +8.29228 q^{37} +9.37320 q^{38} -14.8482 q^{39} +7.67912 q^{40} +7.25830 q^{41} +2.67644 q^{42} -1.00000 q^{43} +3.56697 q^{44} -17.2290 q^{45} +3.22293 q^{46} -1.36584 q^{47} +5.34150 q^{48} -6.88608 q^{49} +1.61854 q^{50} -3.36081 q^{51} -15.7590 q^{52} +5.56854 q^{53} -41.9881 q^{54} -2.07702 q^{55} +1.24788 q^{56} -13.3513 q^{57} +7.24871 q^{58} -6.38624 q^{59} -24.8992 q^{60} -4.07858 q^{61} -25.5962 q^{62} -2.79978 q^{63} -11.7774 q^{64} +9.17637 q^{65} -7.92965 q^{66} +8.90319 q^{67} -3.56697 q^{68} -4.59078 q^{69} -1.65407 q^{70} +2.21407 q^{71} -30.6684 q^{72} -8.86341 q^{73} -19.5652 q^{74} -2.30547 q^{75} -14.1703 q^{76} -0.337523 q^{77} +35.0336 q^{78} +12.6005 q^{79} -3.30111 q^{80} +34.9230 q^{81} -17.1255 q^{82} -2.84870 q^{83} -4.04620 q^{84} +2.07702 q^{85} +2.35944 q^{86} -10.3251 q^{87} -3.69718 q^{88} -2.02201 q^{89} +40.6509 q^{90} +1.49119 q^{91} -4.87238 q^{92} +36.4594 q^{93} +3.22263 q^{94} +8.25124 q^{95} +12.2481 q^{96} -4.54717 q^{97} +16.2473 q^{98} +8.29507 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.35944	−1.66838	−0.834189	−	0.551478i	$-0.814064\pi$
$2$	−2.35944	−1.66838	−0.834189	+	0.551478i	$0.814064\pi$
$3$	3.36081	1.94037	0.970184	−	0.242372i	$-0.0779253\pi$
$3$	3.36081	1.94037	0.970184	+	0.242372i	$0.0779253\pi$
$4$	3.56697	1.78349
$5$	−2.07702	−0.928872	−0.464436	−	0.885607i	$-0.653743\pi$
$5$	−2.07702	−0.928872	−0.464436	+	0.885607i	$0.653743\pi$
$6$	−7.92965	−3.23727
$7$	−0.337523	−0.127572	−0.0637858	−	0.997964i	$-0.520317\pi$
$7$	−0.337523	−0.127572	−0.0637858	+	0.997964i	$0.520317\pi$
$8$	−3.69718	−1.30715
$9$	8.29507	2.76502
$10$	4.90061	1.54971
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	11.9879	3.46062
$13$	−4.41805	−1.22535	−0.612673	−	0.790337i	$-0.709906\pi$
$13$	−4.41805	−1.22535	−0.612673	+	0.790337i	$0.709906\pi$
$14$	0.796366	0.212838
$15$	−6.98048	−1.80235
$16$	1.58935	0.397337
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−19.5718	−4.61311
$19$	−3.97263	−0.911384	−0.455692	−	0.890137i	$-0.650608\pi$
$19$	−3.97263	−0.911384	−0.455692	+	0.890137i	$0.650608\pi$
$20$	−7.40868	−1.65663
$21$	−1.13435	−0.247536
$22$	−2.35944	−0.503035
$23$	−1.36597	−0.284825	−0.142412	−	0.989807i	$-0.545486\pi$
$23$	−1.36597	−0.284825	−0.142412	+	0.989807i	$0.545486\pi$
$24$	−12.4255	−2.53635
$25$	−0.685985	−0.137197
$26$	10.4241	2.04434
$27$	17.7958	3.42479
$28$	−1.20393	−0.227522
$29$	−3.07221	−0.570495	−0.285248	−	0.958454i	$-0.592076\pi$
$29$	−3.07221	−0.570495	−0.285248	+	0.958454i	$0.592076\pi$
$30$	16.4700	3.00701
$31$	10.8484	1.94843	0.974214	−	0.225624i	$-0.0724422\pi$
$31$	10.8484	1.94843	0.974214	+	0.225624i	$0.0724422\pi$
$32$	3.64439	0.644243
$33$	3.36081	0.585043
$34$	2.35944	0.404641
$35$	0.701042	0.118498
$36$	29.5883	4.93138
$37$	8.29228	1.36324	0.681621	−	0.731706i	$-0.261275\pi$
$37$	8.29228	1.36324	0.681621	+	0.731706i	$0.261275\pi$
$38$	9.37320	1.52053
$39$	−14.8482	−2.37762
$40$	7.67912	1.21418
$41$	7.25830	1.13356	0.566778	−	0.823871i	$-0.308190\pi$
$41$	7.25830	1.13356	0.566778	+	0.823871i	$0.308190\pi$
$42$	2.67644	0.412983
$43$	−1.00000	−0.152499
$43$	−1.00000	−0.152499
$44$	3.56697	0.537741
$45$	−17.2290	−2.56835
$46$	3.22293	0.475195
$47$	−1.36584	−0.199229	−0.0996143	−	0.995026i	$-0.531761\pi$
$47$	−1.36584	−0.199229	−0.0996143	+	0.995026i	$0.531761\pi$
$48$	5.34150	0.770979
$49$	−6.88608	−0.983725
$50$	1.61854	0.228897
$51$	−3.36081	−0.470608
$52$	−15.7590	−2.18539
$53$	5.56854	0.764898	0.382449	−	0.923977i	$-0.375081\pi$
$53$	5.56854	0.764898	0.382449	+	0.923977i	$0.375081\pi$
$54$	−41.9881	−5.71385
$55$	−2.07702	−0.280065
$56$	1.24788	0.166755
$57$	−13.3513	−1.76842
$58$	7.24871	0.951802
$59$	−6.38624	−0.831418	−0.415709	−	0.909498i	$-0.636467\pi$
$59$	−6.38624	−0.831418	−0.415709	+	0.909498i	$0.636467\pi$
$60$	−24.8992	−3.21447
$61$	−4.07858	−0.522208	−0.261104	−	0.965311i	$-0.584087\pi$
$61$	−4.07858	−0.522208	−0.261104	+	0.965311i	$0.584087\pi$
$62$	−25.5962	−3.25072
$63$	−2.79978	−0.352739
$64$	−11.7774	−1.47218
$65$	9.17637	1.13819
$66$	−7.92965	−0.976072
$67$	8.90319	1.08770	0.543849	−	0.839183i	$-0.316966\pi$
$67$	8.90319	1.08770	0.543849	+	0.839183i	$0.316966\pi$
$68$	−3.56697	−0.432559
$69$	−4.59078	−0.552664
$70$	−1.65407	−0.197699
$71$	2.21407	0.262762	0.131381	−	0.991332i	$-0.458059\pi$
$71$	2.21407	0.262762	0.131381	+	0.991332i	$0.458059\pi$
$72$	−30.6684	−3.61430
$73$	−8.86341	−1.03738	−0.518692	−	0.854961i	$-0.673581\pi$
$73$	−8.86341	−1.03738	−0.518692	+	0.854961i	$0.673581\pi$
$74$	−19.5652	−2.27440
$75$	−2.30547	−0.266213
$76$	−14.1703	−1.62544
$77$	−0.337523	−0.0384643
$78$	35.0336	3.96677
$79$	12.6005	1.41767	0.708835	−	0.705374i	$-0.249221\pi$
$79$	12.6005	1.41767	0.708835	+	0.705374i	$0.249221\pi$
$80$	−3.30111	−0.369075
$81$	34.9230	3.88033
$82$	−17.1255	−1.89120
$83$	−2.84870	−0.312686	−0.156343	−	0.987703i	$-0.549971\pi$
$83$	−2.84870	−0.312686	−0.156343	+	0.987703i	$0.549971\pi$
$84$	−4.04620	−0.441477
$85$	2.07702	0.225285
$86$	2.35944	0.254425
$87$	−10.3251	−1.10697
$88$	−3.69718	−0.394121
$89$	−2.02201	−0.214332	−0.107166	−	0.994241i	$-0.534178\pi$
$89$	−2.02201	−0.214332	−0.107166	+	0.994241i	$0.534178\pi$
$90$	40.6509	4.28498
$91$	1.49119	0.156319
$92$	−4.87238	−0.507981
$93$	36.4594	3.78067
$94$	3.22263	0.332389
$95$	8.25124	0.846559
$96$	12.2481	1.25007
$97$	−4.54717	−0.461695	−0.230848	−	0.972990i	$-0.574150\pi$
$97$	−4.54717	−0.461695	−0.230848	+	0.972990i	$0.574150\pi$
$98$	16.2473	1.64123
$99$	8.29507	0.833686
$100$	−2.44689	−0.244689
$101$	9.41960	0.937285	0.468642	−	0.883388i	$-0.344743\pi$
$101$	9.41960	0.937285	0.468642	+	0.883388i	$0.344743\pi$
$102$	7.92965	0.785152
$103$	−6.17442	−0.608384	−0.304192	−	0.952611i	$-0.598386\pi$
$103$	−6.17442	−0.608384	−0.304192	+	0.952611i	$0.598386\pi$
$104$	16.3343	1.60171
$105$	2.35607	0.229929
$106$	−13.1386	−1.27614
$107$	9.65230	0.933123	0.466561	−	0.884489i	$-0.345493\pi$
$107$	9.65230	0.933123	0.466561	+	0.884489i	$0.345493\pi$
$108$	63.4770	6.10807
$109$	−2.50036	−0.239491	−0.119745	−	0.992805i	$-0.538208\pi$
$109$	−2.50036	−0.239491	−0.119745	+	0.992805i	$0.538208\pi$
$110$	4.90061	0.467255
$111$	27.8688	2.64519
$112$	−0.536441	−0.0506889
$113$	−6.96650	−0.655353	−0.327677	−	0.944790i	$-0.606266\pi$
$113$	−6.96650	−0.655353	−0.327677	+	0.944790i	$0.606266\pi$
$114$	31.5016	2.95039
$115$	2.83715	0.264566
$116$	−10.9585	−1.01747
$117$	−36.6480	−3.38811
$118$	15.0680	1.38712
$119$	0.337523	0.0309407
$120$	25.8081	2.35595
$121$	1.00000	0.0909091
$122$	9.62317	0.871241
$123$	24.3938	2.19951
$124$	38.6959	3.47500
$125$	11.8099	1.05631
$126$	6.60591	0.588502
$127$	2.95295	0.262032	0.131016	−	0.991380i	$-0.458176\pi$
$127$	2.95295	0.262032	0.131016	+	0.991380i	$0.458176\pi$
$128$	20.4994	1.81191
$129$	−3.36081	−0.295903
$130$	−21.6511	−1.89893
$131$	12.9188	1.12872	0.564360	−	0.825529i	$-0.309123\pi$
$131$	12.9188	1.12872	0.564360	+	0.825529i	$0.309123\pi$
$132$	11.9879	1.04342
$133$	1.34085	0.116267
$134$	−21.0066	−1.81469
$135$	−36.9622	−3.18120
$136$	3.69718	0.317031
$137$	17.3914	1.48585	0.742925	−	0.669375i	$-0.233438\pi$
$137$	17.3914	1.48585	0.742925	+	0.669375i	$0.233438\pi$
$138$	10.8317	0.922053
$139$	−16.9105	−1.43433	−0.717165	−	0.696904i	$-0.754561\pi$
$139$	−16.9105	−1.43433	−0.717165	+	0.696904i	$0.754561\pi$
$140$	2.50060	0.211339
$141$	−4.59034	−0.386577
$142$	−5.22397	−0.438386
$143$	−4.41805	−0.369456
$144$	13.1837	1.09865
$145$	6.38105	0.529917
$146$	20.9127	1.73075
$147$	−23.1428	−1.90879
$148$	29.5783	2.43132
$149$	21.5320	1.76397	0.881984	−	0.471280i	$-0.156208\pi$
$149$	21.5320	1.76397	0.881984	+	0.471280i	$0.156208\pi$
$150$	5.43962	0.444143
$151$	2.06410	0.167974	0.0839872	−	0.996467i	$-0.473235\pi$
$151$	2.06410	0.167974	0.0839872	+	0.996467i	$0.473235\pi$
$152$	14.6875	1.19132
$153$	−8.29507	−0.670617
$154$	0.796366	0.0641730
$155$	−22.5323	−1.80984
$156$	−52.9632	−4.24045
$157$	13.4726	1.07523	0.537616	−	0.843190i	$-0.319325\pi$
$157$	13.4726	1.07523	0.537616	+	0.843190i	$0.319325\pi$
$158$	−29.7302	−2.36521
$159$	18.7148	1.48418
$160$	−7.56948	−0.598420
$161$	0.461046	0.0363356
$162$	−82.3989	−6.47387
$163$	6.11928	0.479299	0.239650	−	0.970859i	$-0.422967\pi$
$163$	6.11928	0.479299	0.239650	+	0.970859i	$0.422967\pi$
$164$	25.8902	2.02168
$165$	−6.98048	−0.543430
$166$	6.72136	0.521678
$167$	13.4644	1.04191	0.520953	−	0.853585i	$-0.325577\pi$
$167$	13.4644	1.04191	0.520953	+	0.853585i	$0.325577\pi$
$168$	4.19390	0.323567
$169$	6.51914	0.501472
$170$	−4.90061	−0.375860
$171$	−32.9533	−2.52000
$172$	−3.56697	−0.271979
$173$	17.8587	1.35777	0.678886	−	0.734243i	$-0.262463\pi$
$173$	17.8587	1.35777	0.678886	+	0.734243i	$0.262463\pi$
$174$	24.3616	1.84685
$175$	0.231536	0.0175025
$176$	1.58935	0.119802
$177$	−21.4630	−1.61326
$178$	4.77081	0.357587
$179$	13.4325	1.00399	0.501994	−	0.864871i	$-0.332600\pi$
$179$	13.4325	1.00399	0.501994	+	0.864871i	$0.332600\pi$
$180$	−61.4555	−4.58062
$181$	−10.8415	−0.805842	−0.402921	−	0.915235i	$-0.632005\pi$
$181$	−10.8415	−0.805842	−0.402921	+	0.915235i	$0.632005\pi$
$182$	−3.51838	−0.260800
$183$	−13.7073	−1.01328
$184$	5.05024	0.372309
$185$	−17.2232	−1.26628
$186$	−86.0240	−6.30758
$187$	−1.00000	−0.0731272
$188$	−4.87192	−0.355321
$189$	−6.00647	−0.436907
$190$	−19.4683	−1.41238
$191$	0.770083	0.0557212	0.0278606	−	0.999612i	$-0.491131\pi$
$191$	0.770083	0.0557212	0.0278606	+	0.999612i	$0.491131\pi$
$192$	−39.5817	−2.85657
$193$	1.00907	0.0726342	0.0363171	−	0.999340i	$-0.488437\pi$
$193$	1.00907	0.0726342	0.0363171	+	0.999340i	$0.488437\pi$
$194$	10.7288	0.770282
$195$	30.8401	2.20850
$196$	−24.5625	−1.75446
$197$	−3.76355	−0.268141	−0.134071	−	0.990972i	$-0.542805\pi$
$197$	−3.76355	−0.268141	−0.134071	+	0.990972i	$0.542805\pi$
$198$	−19.5718	−1.39090
$199$	8.12239	0.575781	0.287891	−	0.957663i	$-0.407046\pi$
$199$	8.12239	0.575781	0.287891	+	0.957663i	$0.407046\pi$
$200$	2.53621	0.179337
$201$	29.9220	2.11053
$202$	−22.2250	−1.56375
$203$	1.03694	0.0727790
$204$	−11.9879	−0.839323
$205$	−15.0756	−1.05293
$206$	14.5682	1.01501
$207$	−11.3308	−0.787547
$208$	−7.02181	−0.486875
$209$	−3.97263	−0.274793
$210$	−5.55902	−0.383609
$211$	−12.3384	−0.849407	−0.424704	−	0.905332i	$-0.639622\pi$
$211$	−12.3384	−0.849407	−0.424704	+	0.905332i	$0.639622\pi$
$212$	19.8628	1.36418
$213$	7.44108	0.509854
$214$	−22.7740	−1.55680
$215$	2.07702	0.141652
$216$	−65.7941	−4.47672
$217$	−3.66158	−0.248564
$218$	5.89945	0.399561
$219$	−29.7883	−2.01291
$220$	−7.40868	−0.499493
$221$	4.41805	0.297190
$222$	−65.7548	−4.41318
$223$	14.1723	0.949044	0.474522	−	0.880244i	$-0.342621\pi$
$223$	14.1723	0.949044	0.474522	+	0.880244i	$0.342621\pi$
$224$	−1.23007	−0.0821872
$225$	−5.69030	−0.379353
$226$	16.4371	1.09338
$227$	10.7318	0.712297	0.356149	−	0.934429i	$-0.384090\pi$
$227$	10.7318	0.712297	0.356149	+	0.934429i	$0.384090\pi$
$228$	−47.6236	−3.15395
$229$	16.9360	1.11916	0.559580	−	0.828776i	$-0.310962\pi$
$229$	16.9360	1.11916	0.559580	+	0.828776i	$0.310962\pi$
$230$	−6.69410	−0.441396
$231$	−1.13435	−0.0746349
$232$	11.3585	0.745724
$233$	−9.96306	−0.652702	−0.326351	−	0.945249i	$-0.605819\pi$
$233$	−9.96306	−0.652702	−0.326351	+	0.945249i	$0.605819\pi$
$234$	86.4689	5.65265
$235$	2.83688	0.185058
$236$	−22.7795	−1.48282
$237$	42.3480	2.75080
$238$	−0.796366	−0.0516207
$239$	−1.81570	−0.117448	−0.0587240	−	0.998274i	$-0.518703\pi$
$239$	−1.81570	−0.117448	−0.0587240	+	0.998274i	$0.518703\pi$
$240$	−11.0944	−0.716141
$241$	−3.91834	−0.252402	−0.126201	−	0.992005i	$-0.540279\pi$
$241$	−3.91834	−0.252402	−0.126201	+	0.992005i	$0.540279\pi$
$242$	−2.35944	−0.151671
$243$	63.9825	4.10448
$244$	−14.5482	−0.931351
$245$	14.3025	0.913755
$246$	−57.5558	−3.66962
$247$	17.5513	1.11676
$248$	−40.1085	−2.54689
$249$	−9.57397	−0.606725
$250$	−27.8648	−1.76233
$251$	−20.5519	−1.29722	−0.648611	−	0.761120i	$-0.724650\pi$
$251$	−20.5519	−1.29722	−0.648611	+	0.761120i	$0.724650\pi$
$252$	−9.98672	−0.629105
$253$	−1.36597	−0.0858779
$254$	−6.96732	−0.437169
$255$	6.98048	0.437135
$256$	−24.8123	−1.55077
$257$	−20.4704	−1.27691	−0.638453	−	0.769660i	$-0.720426\pi$
$257$	−20.4704	−1.27691	−0.638453	+	0.769660i	$0.720426\pi$
$258$	7.92965	0.493678
$259$	−2.79883	−0.173911
$260$	32.7319	2.02994
$261$	−25.4842	−1.57743
$262$	−30.4812	−1.88313
$263$	12.9079	0.795938	0.397969	−	0.917399i	$-0.369715\pi$
$263$	12.9079	0.795938	0.397969	+	0.917399i	$0.369715\pi$
$264$	−12.4255	−0.764739
$265$	−11.5660	−0.710492
$266$	−3.16367	−0.193977
$267$	−6.79559	−0.415883
$268$	31.7574	1.93989
$269$	22.5383	1.37419	0.687093	−	0.726570i	$-0.258887\pi$
$269$	22.5383	1.37419	0.687093	+	0.726570i	$0.258887\pi$
$270$	87.2101	5.30744
$271$	9.55883	0.580658	0.290329	−	0.956927i	$-0.406235\pi$
$271$	9.55883	0.580658	0.290329	+	0.956927i	$0.406235\pi$
$272$	−1.58935	−0.0963683
$273$	5.01162	0.303317
$274$	−41.0341	−2.47896
$275$	−0.685985	−0.0413665
$276$	−16.3752	−0.985669
$277$	30.9053	1.85692	0.928459	−	0.371434i	$-0.121134\pi$
$277$	30.9053	1.85692	0.928459	+	0.371434i	$0.121134\pi$
$278$	39.8994	2.39300
$279$	89.9882	5.38745
$280$	−2.59188	−0.154894
$281$	−4.37637	−0.261073	−0.130536	−	0.991444i	$-0.541670\pi$
$281$	−4.37637	−0.261073	−0.130536	+	0.991444i	$0.541670\pi$
$282$	10.8307	0.644956
$283$	−2.52979	−0.150380	−0.0751902	−	0.997169i	$-0.523956\pi$
$283$	−2.52979	−0.150380	−0.0751902	+	0.997169i	$0.523956\pi$
$284$	7.89753	0.468632
$285$	27.7309	1.64264
$286$	10.4241	0.616392
$287$	−2.44984	−0.144610
$288$	30.2305	1.78135
$289$	1.00000	0.0588235
$290$	−15.0557	−0.884102
$291$	−15.2822	−0.895858
$292$	−31.6156	−1.85016
$293$	−13.9521	−0.815090	−0.407545	−	0.913185i	$-0.633615\pi$
$293$	−13.9521	−0.815090	−0.407545	+	0.913185i	$0.633615\pi$
$294$	54.6042	3.18458
$295$	13.2644	0.772281
$296$	−30.6581	−1.78196
$297$	17.7958	1.03261
$298$	−50.8034	−2.94296
$299$	6.03492	0.349009
$300$	−8.22354	−0.474786
$301$	0.337523	0.0194545
$302$	−4.87014	−0.280245
$303$	31.6575	1.81868
$304$	−6.31389	−0.362126
$305$	8.47129	0.485065
$306$	19.5718	1.11884
$307$	−27.4919	−1.56904	−0.784522	−	0.620101i	$-0.787092\pi$
$307$	−27.4919	−1.56904	−0.784522	+	0.620101i	$0.787092\pi$
$308$	−1.20393	−0.0686005
$309$	−20.7511	−1.18049
$310$	53.1638	3.01950
$311$	−6.52604	−0.370058	−0.185029	−	0.982733i	$-0.559238\pi$
$311$	−6.52604	−0.370058	−0.185029	+	0.982733i	$0.559238\pi$
$312$	54.8966	3.10791
$313$	12.7582	0.721139	0.360569	−	0.932732i	$-0.382582\pi$
$313$	12.7582	0.721139	0.360569	+	0.932732i	$0.382582\pi$
$314$	−31.7879	−1.79389
$315$	5.81519	0.327649
$316$	44.9457	2.52840
$317$	25.2961	1.42077	0.710385	−	0.703814i	$-0.248521\pi$
$317$	25.2961	1.42077	0.710385	+	0.703814i	$0.248521\pi$
$318$	−44.1566	−2.47618
$319$	−3.07221	−0.172011
$320$	24.4620	1.36747
$321$	32.4396	1.81060
$322$	−1.08781	−0.0606214
$323$	3.97263	0.221043
$324$	124.569	6.92052
$325$	3.03071	0.168114
$326$	−14.4381	−0.799652
$327$	−8.40323	−0.464700
$328$	−26.8353	−1.48173
$329$	0.461003	0.0254159
$330$	16.4700	0.906646
$331$	25.9915	1.42862	0.714312	−	0.699827i	$-0.246740\pi$
$331$	25.9915	1.42862	0.714312	+	0.699827i	$0.246740\pi$
$332$	−10.1612	−0.557671
$333$	68.7850	3.76940
$334$	−31.7685	−1.73829
$335$	−18.4921	−1.01033
$336$	−1.80288	−0.0983550
$337$	−11.3756	−0.619671	−0.309835	−	0.950790i	$-0.600274\pi$
$337$	−11.3756	−0.619671	−0.309835	+	0.950790i	$0.600274\pi$
$338$	−15.3815	−0.836645
$339$	−23.4131	−1.27163
$340$	7.40868	0.401792
$341$	10.8484	0.587473
$342$	77.7514	4.20431
$343$	4.68687	0.253067
$344$	3.69718	0.199339
$345$	9.53514	0.513354
$346$	−42.1366	−2.26528
$347$	17.1926	0.922945	0.461472	−	0.887155i	$-0.347321\pi$
$347$	17.1926	0.922945	0.461472	+	0.887155i	$0.347321\pi$
$348$	−36.8295	−1.97427
$349$	4.40790	0.235949	0.117975	−	0.993017i	$-0.462360\pi$
$349$	4.40790	0.235949	0.117975	+	0.993017i	$0.462360\pi$
$350$	−0.546295	−0.0292007
$351$	−78.6225	−4.19656
$352$	3.64439	0.194247
$353$	−12.6940	−0.675636	−0.337818	−	0.941211i	$-0.609689\pi$
$353$	−12.6940	−0.675636	−0.337818	+	0.941211i	$0.609689\pi$
$354$	50.6407	2.69152
$355$	−4.59867	−0.244072
$356$	−7.21244	−0.382259
$357$	1.13435	0.0600363
$358$	−31.6931	−1.67503
$359$	35.6820	1.88323	0.941613	−	0.336697i	$-0.109310\pi$
$359$	35.6820	1.88323	0.941613	+	0.336697i	$0.109310\pi$
$360$	63.6989	3.35723
$361$	−3.21820	−0.169379
$362$	25.5799	1.34445
$363$	3.36081	0.176397
$364$	5.31904	0.278793
$365$	18.4095	0.963597
$366$	32.3417	1.69053
$367$	−36.2408	−1.89175	−0.945877	−	0.324524i	$-0.894796\pi$
$367$	−36.2408	−1.89175	−0.945877	+	0.324524i	$0.894796\pi$
$368$	−2.17100	−0.113171
$369$	60.2081	3.13431
$370$	40.6372	2.11263
$371$	−1.87951	−0.0975792
$372$	130.050	6.74277
$373$	−21.2432	−1.09993	−0.549967	−	0.835187i	$-0.685360\pi$
$373$	−21.2432	−1.09993	−0.549967	+	0.835187i	$0.685360\pi$
$374$	2.35944	0.122004
$375$	39.6909	2.04963
$376$	5.04977	0.260422
$377$	13.5732	0.699054
$378$	14.1719	0.728926
$379$	−4.01803	−0.206393	−0.103196	−	0.994661i	$-0.532907\pi$
$379$	−4.01803	−0.206393	−0.103196	+	0.994661i	$0.532907\pi$
$380$	29.4319	1.50983
$381$	9.92432	0.508438
$382$	−1.81697	−0.0929641
$383$	−17.3698	−0.887556	−0.443778	−	0.896137i	$-0.646362\pi$
$383$	−17.3698	−0.887556	−0.443778	+	0.896137i	$0.646362\pi$
$384$	68.8946	3.51576
$385$	0.701042	0.0357284
$386$	−2.38083	−0.121181
$387$	−8.29507	−0.421662
$388$	−16.2196	−0.823427
$389$	12.7440	0.646147	0.323074	−	0.946374i	$-0.395284\pi$
$389$	12.7440	0.646147	0.323074	+	0.946374i	$0.395284\pi$
$390$	−72.7654	−3.68462
$391$	1.36597	0.0690801
$392$	25.4591	1.28588
$393$	43.4177	2.19013
$394$	8.87987	0.447361
$395$	−26.1716	−1.31683
$396$	29.5883	1.48687
$397$	−30.0644	−1.50889	−0.754445	−	0.656363i	$-0.772094\pi$
$397$	−30.0644	−1.50889	−0.754445	+	0.656363i	$0.772094\pi$
$398$	−19.1643	−0.960621
$399$	4.50636	0.225600
$400$	−1.09027	−0.0545134
$401$	14.6341	0.730794	0.365397	−	0.930852i	$-0.380933\pi$
$401$	14.6341	0.730794	0.365397	+	0.930852i	$0.380933\pi$
$402$	−70.5992	−3.52117
$403$	−47.9287	−2.38750
$404$	33.5994	1.67163
$405$	−72.5358	−3.60433
$406$	−2.44661	−0.121423
$407$	8.29228	0.411033
$408$	12.4255	0.615156
$409$	−5.37086	−0.265572	−0.132786	−	0.991145i	$-0.542392\pi$
$409$	−5.37086	−0.265572	−0.132786	+	0.991145i	$0.542392\pi$
$410$	35.5701	1.75668
$411$	58.4494	2.88309
$412$	−22.0240	−1.08504
$413$	2.15550	0.106065
$414$	26.7345	1.31393
$415$	5.91682	0.290445
$416$	−16.1011	−0.789421
$417$	−56.8330	−2.78313
$418$	9.37320	0.458458
$419$	−20.6886	−1.01070	−0.505352	−	0.862914i	$-0.668637\pi$
$419$	−20.6886	−1.01070	−0.505352	+	0.862914i	$0.668637\pi$
$420$	8.40404	0.410075
$421$	30.3001	1.47674	0.738369	−	0.674397i	$-0.235596\pi$
$421$	30.3001	1.47674	0.738369	+	0.674397i	$0.235596\pi$
$422$	29.1116	1.41713
$423$	−11.3298	−0.550872
$424$	−20.5879	−0.999837
$425$	0.685985	0.0332752
$426$	−17.5568	−0.850630
$427$	1.37661	0.0666190
$428$	34.4295	1.66421
$429$	−14.8482	−0.716879
$430$	−4.90061	−0.236329
$431$	19.5301	0.940734	0.470367	−	0.882471i	$-0.344122\pi$
$431$	19.5301	0.940734	0.470367	+	0.882471i	$0.344122\pi$
$432$	28.2836	1.36080
$433$	16.0481	0.771224	0.385612	−	0.922661i	$-0.373990\pi$
$433$	16.0481	0.771224	0.385612	+	0.922661i	$0.373990\pi$
$434$	8.63929	0.414699
$435$	21.4455	1.02823
$436$	−8.91870	−0.427128
$437$	5.42650	0.259585
$438$	70.2838	3.35829
$439$	−2.35071	−0.112193	−0.0560966	−	0.998425i	$-0.517865\pi$
$439$	−2.35071	−0.112193	−0.0560966	+	0.998425i	$0.517865\pi$
$440$	7.67912	0.366088
$441$	−57.1205	−2.72002
$442$	−10.4241	−0.495825
$443$	−0.379417	−0.0180266	−0.00901331	−	0.999959i	$-0.502869\pi$
$443$	−0.379417	−0.0180266	−0.00901331	+	0.999959i	$0.502869\pi$
$444$	99.4072	4.71766
$445$	4.19975	0.199087
$446$	−33.4386	−1.58336
$447$	72.3649	3.42274
$448$	3.97515	0.187808
$449$	−17.1371	−0.808750	−0.404375	−	0.914593i	$-0.632511\pi$
$449$	−17.1371	−0.808750	−0.404375	+	0.914593i	$0.632511\pi$
$450$	13.4259	0.632905
$451$	7.25830	0.341780
$452$	−24.8493	−1.16881
$453$	6.93707	0.325932
$454$	−25.3212	−1.18838
$455$	−3.09724	−0.145201
$456$	49.3621	2.31159
$457$	−26.6400	−1.24617	−0.623084	−	0.782155i	$-0.714121\pi$
$457$	−26.6400	−1.24617	−0.623084	+	0.782155i	$0.714121\pi$
$458$	−39.9594	−1.86718
$459$	−17.7958	−0.830635
$460$	10.1200	0.471849
$461$	−16.2355	−0.756162	−0.378081	−	0.925773i	$-0.623416\pi$
$461$	−16.2355	−0.756162	−0.378081	+	0.925773i	$0.623416\pi$
$462$	2.67644	0.124519
$463$	−11.0304	−0.512628	−0.256314	−	0.966594i	$-0.582508\pi$
$463$	−11.0304	−0.512628	−0.256314	+	0.966594i	$0.582508\pi$
$464$	−4.88281	−0.226679
$465$	−75.7270	−3.51176
$466$	23.5073	1.08895
$467$	−29.4707	−1.36374	−0.681870	−	0.731473i	$-0.738833\pi$
$467$	−29.4707	−1.36374	−0.681870	+	0.731473i	$0.738833\pi$
$468$	−130.722	−6.04265
$469$	−3.00503	−0.138759
$470$	−6.69347	−0.308747
$471$	45.2790	2.08635
$472$	23.6111	1.08679
$473$	−1.00000	−0.0459800
$474$	−99.9178	−4.58938
$475$	2.72517	0.125039
$476$	1.20393	0.0551823
$477$	46.1914	2.11496
$478$	4.28404	0.195948
$479$	4.34472	0.198515	0.0992576	−	0.995062i	$-0.468353\pi$
$479$	4.34472	0.198515	0.0992576	+	0.995062i	$0.468353\pi$
$480$	−25.4396	−1.16115
$481$	−36.6357	−1.67044
$482$	9.24510	0.421103
$483$	1.54949	0.0705043
$484$	3.56697	0.162135
$485$	9.44456	0.428856
$486$	−150.963	−6.84782
$487$	13.3720	0.605944	0.302972	−	0.952999i	$-0.402021\pi$
$487$	13.3720	0.605944	0.302972	+	0.952999i	$0.402021\pi$
$488$	15.0792	0.682605
$489$	20.5658	0.930016
$490$	−33.7460	−1.52449
$491$	25.4078	1.14664	0.573319	−	0.819333i	$-0.305656\pi$
$491$	25.4078	1.14664	0.573319	+	0.819333i	$0.305656\pi$
$492$	87.0120	3.92280
$493$	3.07221	0.138365
$494$	−41.4112	−1.86318
$495$	−17.2290	−0.774388
$496$	17.2419	0.774182
$497$	−0.747299	−0.0335210
$498$	22.5892	1.01225
$499$	7.54504	0.337762	0.168881	−	0.985636i	$-0.445985\pi$
$499$	7.54504	0.337762	0.168881	+	0.985636i	$0.445985\pi$
$500$	42.1256	1.88391
$501$	45.2514	2.02168
$502$	48.4909	2.16426
$503$	−17.2015	−0.766975	−0.383488	−	0.923546i	$-0.625277\pi$
$503$	−17.2015	−0.766975	−0.383488	+	0.923546i	$0.625277\pi$
$504$	10.3513	0.461083
$505$	−19.5647	−0.870618
$506$	3.22293	0.143277
$507$	21.9096	0.973040
$508$	10.5331	0.467330
$509$	39.4081	1.74674	0.873368	−	0.487062i	$-0.161931\pi$
$509$	39.4081	1.74674	0.873368	+	0.487062i	$0.161931\pi$
$510$	−16.4700	−0.729306
$511$	2.99160	0.132341
$512$	17.5444	0.775361
$513$	−70.6960	−3.12130
$514$	48.2987	2.13036
$515$	12.8244	0.565111
$516$	−11.9879	−0.527739
$517$	−1.36584	−0.0600697
$518$	6.60369	0.290149
$519$	60.0198	2.63458
$520$	−33.9267	−1.48779
$521$	−12.2266	−0.535656	−0.267828	−	0.963467i	$-0.586306\pi$
$521$	−12.2266	−0.535656	−0.267828	+	0.963467i	$0.586306\pi$
$522$	60.1286	2.63176
$523$	−23.0443	−1.00766	−0.503828	−	0.863804i	$-0.668075\pi$
$523$	−23.0443	−1.00766	−0.503828	+	0.863804i	$0.668075\pi$
$524$	46.0810	2.01306
$525$	0.778148	0.0339612
$526$	−30.4556	−1.32793
$527$	−10.8484	−0.472563
$528$	5.34150	0.232459
$529$	−21.1341	−0.918875
$530$	27.2892	1.18537
$531$	−52.9743	−2.29889
$532$	4.78279	0.207360
$533$	−32.0675	−1.38900
$534$	16.0338	0.693850
$535$	−20.0480	−0.866751
$536$	−32.9167	−1.42179
$537$	45.1440	1.94811
$538$	−53.1779	−2.29266
$539$	−6.88608	−0.296604
$540$	−131.843	−5.67362
$541$	−2.70828	−0.116438	−0.0582189	−	0.998304i	$-0.518542\pi$
$541$	−2.70828	−0.116438	−0.0582189	+	0.998304i	$0.518542\pi$
$542$	−22.5535	−0.968757
$543$	−36.4363	−1.56363
$544$	−3.64439	−0.156252
$545$	5.19329	0.222456
$546$	−11.8246	−0.506047
$547$	5.03151	0.215132	0.107566	−	0.994198i	$-0.465694\pi$
$547$	5.03151	0.215132	0.107566	+	0.994198i	$0.465694\pi$
$548$	62.0347	2.64999
$549$	−33.8321	−1.44392
$550$	1.61854	0.0690149
$551$	12.2048	0.519941
$552$	16.9729	0.722416
$553$	−4.25297	−0.180855
$554$	−72.9193	−3.09804
$555$	−57.8841	−2.45704
$556$	−60.3193	−2.55811
$557$	0.182720	0.00774211	0.00387106	−	0.999993i	$-0.498768\pi$
$557$	0.182720	0.00774211	0.00387106	+	0.999993i	$0.498768\pi$
$558$	−212.322	−8.98831
$559$	4.41805	0.186863
$560$	1.11420	0.0470835
$561$	−3.36081	−0.141894
$562$	10.3258	0.435568
$563$	−0.876473	−0.0369389	−0.0184695	−	0.999829i	$-0.505879\pi$
$563$	−0.876473	−0.0369389	−0.0184695	+	0.999829i	$0.505879\pi$
$564$	−16.3736	−0.689454
$565$	14.4696	0.608739
$566$	5.96890	0.250891
$567$	−11.7873	−0.495021
$568$	−8.18582	−0.343469
$569$	24.0649	1.00885	0.504426	−	0.863455i	$-0.331704\pi$
$569$	24.0649	1.00885	0.504426	+	0.863455i	$0.331704\pi$
$570$	−65.4294	−2.74054
$571$	2.91979	0.122189	0.0610947	−	0.998132i	$-0.480541\pi$
$571$	2.91979	0.122189	0.0610947	+	0.998132i	$0.480541\pi$
$572$	−15.7590	−0.658919
$573$	2.58811	0.108120
$574$	5.78026	0.241264
$575$	0.937036	0.0390771
$576$	−97.6946	−4.07061
$577$	33.2108	1.38258	0.691291	−	0.722576i	$-0.257042\pi$
$577$	33.2108	1.38258	0.691291	+	0.722576i	$0.257042\pi$
$578$	−2.35944	−0.0981399
$579$	3.39128	0.140937
$580$	22.7610	0.945100
$581$	0.961503	0.0398899
$582$	36.0575	1.49463
$583$	5.56854	0.230625
$584$	32.7697	1.35602
$585$	76.1187	3.14712
$586$	32.9192	1.35988
$587$	11.3106	0.466838	0.233419	−	0.972376i	$-0.425009\pi$
$587$	11.3106	0.466838	0.233419	+	0.972376i	$0.425009\pi$
$588$	−82.5498	−3.40430
$589$	−43.0967	−1.77577
$590$	−31.2965	−1.28846
$591$	−12.6486	−0.520293
$592$	13.1793	0.541666
$593$	22.2422	0.913376	0.456688	−	0.889627i	$-0.349036\pi$
$593$	22.2422	0.913376	0.456688	+	0.889627i	$0.349036\pi$
$594$	−41.9881	−1.72279
$595$	−0.701042	−0.0287399
$596$	76.8039	3.14601
$597$	27.2979	1.11723
$598$	−14.2391	−0.582279
$599$	43.8440	1.79142	0.895709	−	0.444640i	$-0.146669\pi$
$599$	43.8440	1.79142	0.895709	+	0.444640i	$0.146669\pi$
$600$	8.52374	0.347980
$601$	−39.7992	−1.62344	−0.811722	−	0.584043i	$-0.801470\pi$
$601$	−39.7992	−1.62344	−0.811722	+	0.584043i	$0.801470\pi$
$602$	−0.796366	−0.0324575
$603$	73.8526	3.00751
$604$	7.36260	0.299580
$605$	−2.07702	−0.0844429
$606$	−74.6941	−3.03424
$607$	−1.22924	−0.0498934	−0.0249467	−	0.999689i	$-0.507942\pi$
$607$	−1.22924	−0.0498934	−0.0249467	+	0.999689i	$0.507942\pi$
$608$	−14.4778	−0.587153
$609$	3.48497	0.141218
$610$	−19.9875	−0.809271
$611$	6.03436	0.244124
$612$	−29.5883	−1.19604
$613$	−30.0021	−1.21177	−0.605887	−	0.795551i	$-0.707181\pi$
$613$	−30.0021	−1.21177	−0.605887	+	0.795551i	$0.707181\pi$
$614$	64.8655	2.61776
$615$	−50.6664	−2.04307
$616$	1.24788	0.0502787
$617$	37.2819	1.50091	0.750456	−	0.660920i	$-0.229834\pi$
$617$	37.2819	1.50091	0.750456	+	0.660920i	$0.229834\pi$
$618$	48.9610	1.96950
$619$	20.8779	0.839153	0.419577	−	0.907720i	$-0.362179\pi$
$619$	20.8779	0.839153	0.419577	+	0.907720i	$0.362179\pi$
$620$	−80.3722	−3.22783
$621$	−24.3085	−0.975466
$622$	15.3978	0.617397
$623$	0.682473	0.0273427
$624$	−23.5990	−0.944716
$625$	−21.0995	−0.843980
$626$	−30.1024	−1.20313
$627$	−13.3513	−0.533199
$628$	48.0565	1.91766
$629$	−8.29228	−0.330635
$630$	−13.7206	−0.546643
$631$	41.5113	1.65254	0.826270	−	0.563275i	$-0.190459\pi$
$631$	41.5113	1.65254	0.826270	+	0.563275i	$0.190459\pi$
$632$	−46.5865	−1.85311
$633$	−41.4669	−1.64816
$634$	−59.6847	−2.37038
$635$	−6.13334	−0.243394
$636$	66.7553	2.64702
$637$	30.4230	1.20540
$638$	7.24871	0.286979
$639$	18.3659	0.726543
$640$	−42.5777	−1.68303
$641$	24.9781	0.986574	0.493287	−	0.869867i	$-0.335795\pi$
$641$	24.9781	0.986574	0.493287	+	0.869867i	$0.335795\pi$
$642$	−76.5393	−3.02077
$643$	−44.5545	−1.75706	−0.878528	−	0.477691i	$-0.841474\pi$
$643$	−44.5545	−1.75706	−0.878528	+	0.477691i	$0.841474\pi$
$644$	1.64454	0.0648040
$645$	6.98048	0.274856
$646$	−9.37320	−0.368784
$647$	−22.1384	−0.870352	−0.435176	−	0.900345i	$-0.643314\pi$
$647$	−22.1384	−0.870352	−0.435176	+	0.900345i	$0.643314\pi$
$648$	−129.117	−5.07218
$649$	−6.38624	−0.250682
$650$	−7.15080	−0.280477
$651$	−12.3059	−0.482306
$652$	21.8273	0.854823
$653$	−31.4314	−1.23001	−0.615004	−	0.788524i	$-0.710846\pi$
$653$	−31.4314	−1.23001	−0.615004	+	0.788524i	$0.710846\pi$
$654$	19.8269	0.775295
$655$	−26.8326	−1.04844
$656$	11.5360	0.450403
$657$	−73.5227	−2.86839
$658$	−1.08771	−0.0424034
$659$	1.53993	0.0599872	0.0299936	−	0.999550i	$-0.490451\pi$
$659$	1.53993	0.0599872	0.0299936	+	0.999550i	$0.490451\pi$
$660$	−24.8992	−0.969199
$661$	−3.03722	−0.118134	−0.0590670	−	0.998254i	$-0.518813\pi$
$661$	−3.03722	−0.118134	−0.0590670	+	0.998254i	$0.518813\pi$
$662$	−61.3256	−2.38349
$663$	14.8482	0.576658
$664$	10.5322	0.408728
$665$	−2.78498	−0.107997
$666$	−162.294	−6.28878
$667$	4.19655	0.162491
$668$	48.0271	1.85823
$669$	47.6303	1.84149
$670$	43.6311	1.68562
$671$	−4.07858	−0.157452
$672$	−4.13402	−0.159473
$673$	−33.5405	−1.29289	−0.646445	−	0.762960i	$-0.723745\pi$
$673$	−33.5405	−1.29289	−0.646445	+	0.762960i	$0.723745\pi$
$674$	26.8402	1.03385
$675$	−12.2076	−0.469872
$676$	23.2536	0.894368
$677$	−1.78472	−0.0685922	−0.0342961	−	0.999412i	$-0.510919\pi$
$677$	−1.78472	−0.0685922	−0.0342961	+	0.999412i	$0.510919\pi$
$678$	55.2419	2.12155
$679$	1.53477	0.0588992
$680$	−7.67912	−0.294481
$681$	36.0677	1.38212
$682$	−25.5962	−0.980128
$683$	4.28474	0.163951	0.0819756	−	0.996634i	$-0.473877\pi$
$683$	4.28474	0.163951	0.0819756	+	0.996634i	$0.473877\pi$
$684$	−117.543	−4.49438
$685$	−36.1224	−1.38016
$686$	−11.0584	−0.422212
$687$	56.9186	2.17158
$688$	−1.58935	−0.0605933
$689$	−24.6021	−0.937264
$690$	−22.4976	−0.856469
$691$	48.2437	1.83528	0.917639	−	0.397415i	$-0.130093\pi$
$691$	48.2437	1.83528	0.917639	+	0.397415i	$0.130093\pi$
$692$	63.7015	2.42157
$693$	−2.79978	−0.106355
$694$	−40.5649	−1.53982
$695$	35.1234	1.33231
$696$	38.1739	1.44698
$697$	−7.25830	−0.274928
$698$	−10.4002	−0.393653
$699$	−33.4840	−1.26648
$700$	0.825881	0.0312154
$701$	31.9011	1.20489	0.602444	−	0.798161i	$-0.294194\pi$
$701$	31.9011	1.20489	0.602444	+	0.798161i	$0.294194\pi$
$702$	185.505	7.00144
$703$	−32.9422	−1.24244
$704$	−11.7774	−0.443878
$705$	9.53424	0.359080
$706$	29.9509	1.12722
$707$	−3.17933	−0.119571
$708$	−76.5578	−2.87722
$709$	−13.9798	−0.525021	−0.262511	−	0.964929i	$-0.584551\pi$
$709$	−13.9798	−0.525021	−0.262511	+	0.964929i	$0.584551\pi$
$710$	10.8503	0.407205
$711$	104.522	3.91989
$712$	7.47572	0.280165
$713$	−14.8186	−0.554961
$714$	−2.67644	−0.100163
$715$	9.17637	0.343177
$716$	47.9132	1.79060
$717$	−6.10224	−0.227892
$718$	−84.1898	−3.14193
$719$	−11.9355	−0.445119	−0.222560	−	0.974919i	$-0.571441\pi$
$719$	−11.9355	−0.445119	−0.222560	+	0.974919i	$0.571441\pi$
$720$	−27.3829	−1.02050
$721$	2.08401	0.0776125
$722$	7.59316	0.282588
$723$	−13.1688	−0.489753
$724$	−38.6713	−1.43721
$725$	2.10749	0.0782703
$726$	−7.92965	−0.294297
$727$	−27.7919	−1.03074	−0.515372	−	0.856967i	$-0.672346\pi$
$727$	−27.7919	−1.03074	−0.515372	+	0.856967i	$0.672346\pi$
$728$	−5.51321	−0.204333
$729$	110.264	4.08386
$730$	−43.4362	−1.60764
$731$	1.00000	0.0369863
$732$	−48.8937	−1.80716
$733$	40.5665	1.49836	0.749179	−	0.662368i	$-0.230448\pi$
$733$	40.5665	1.49836	0.749179	+	0.662368i	$0.230448\pi$
$734$	85.5081	3.15616
$735$	48.0681	1.77302
$736$	−4.97813	−0.183496
$737$	8.90319	0.327953
$738$	−142.058	−5.22921
$739$	15.8992	0.584861	0.292430	−	0.956287i	$-0.405536\pi$
$739$	15.8992	0.584861	0.292430	+	0.956287i	$0.405536\pi$
$740$	−61.4348	−2.25839
$741$	58.9866	2.16693
$742$	4.43459	0.162799
$743$	40.0958	1.47097	0.735486	−	0.677540i	$-0.236954\pi$
$743$	40.0958	1.47097	0.735486	+	0.677540i	$0.236954\pi$
$744$	−134.797	−4.94190
$745$	−44.7223	−1.63850
$746$	50.1222	1.83510
$747$	−23.6302	−0.864584
$748$	−3.56697	−0.130421
$749$	−3.25787	−0.119040
$750$	−93.6484	−3.41956
$751$	−5.93359	−0.216520	−0.108260	−	0.994123i	$-0.534528\pi$
$751$	−5.93359	−0.216520	−0.108260	+	0.994123i	$0.534528\pi$
$752$	−2.17080	−0.0791608
$753$	−69.0710	−2.51709
$754$	−32.0251	−1.16629
$755$	−4.28719	−0.156027
$756$	−21.4249	−0.779217
$757$	51.6664	1.87785	0.938924	−	0.344125i	$-0.111824\pi$
$757$	51.6664	1.87785	0.938924	+	0.344125i	$0.111824\pi$
$758$	9.48032	0.344341
$759$	−4.59078	−0.166635
$760$	−30.5063	−1.10658
$761$	2.99731	0.108652	0.0543262	−	0.998523i	$-0.482699\pi$
$761$	2.99731	0.108652	0.0543262	+	0.998523i	$0.482699\pi$
$762$	−23.4159	−0.848267
$763$	0.843927	0.0305522
$764$	2.74686	0.0993780
$765$	17.2290	0.622917
$766$	40.9831	1.48078
$767$	28.2147	1.01877
$768$	−83.3895	−3.00906
$769$	10.3755	0.374150	0.187075	−	0.982346i	$-0.440099\pi$
$769$	10.3755	0.374150	0.187075	+	0.982346i	$0.440099\pi$
$770$	−1.65407	−0.0596085
$771$	−68.7971	−2.47767
$772$	3.59931	0.129542
$773$	14.3298	0.515408	0.257704	−	0.966224i	$-0.417034\pi$
$773$	14.3298	0.515408	0.257704	+	0.966224i	$0.417034\pi$
$774$	19.5718	0.703492
$775$	−7.44184	−0.267319
$776$	16.8117	0.603505
$777$	−9.40636	−0.337451
$778$	−30.0688	−1.07802
$779$	−28.8345	−1.03310
$780$	110.006	3.93884
$781$	2.21407	0.0792257
$782$	−3.22293	−0.115252
$783$	−54.6723	−1.95383
$784$	−10.9444	−0.390870
$785$	−27.9829	−0.998753
$786$	−102.442	−3.65397
$787$	1.35046	0.0481386	0.0240693	−	0.999710i	$-0.492338\pi$
$787$	1.35046	0.0481386	0.0240693	+	0.999710i	$0.492338\pi$
$788$	−13.4245	−0.478227
$789$	43.3812	1.54441
$790$	61.7503	2.19698
$791$	2.35135	0.0836045
$792$	−30.6684	−1.08975
$793$	18.0193	0.639886
$794$	70.9353	2.51740
$795$	−38.8711	−1.37861
$796$	28.9723	1.02690
$797$	−17.0552	−0.604125	−0.302063	−	0.953288i	$-0.597675\pi$
$797$	−17.0552	−0.604125	−0.302063	+	0.953288i	$0.597675\pi$
$798$	−10.6325	−0.376386
$799$	1.36584	0.0483200
$800$	−2.50000	−0.0883883
$801$	−16.7727	−0.592634
$802$	−34.5284	−1.21924
$803$	−8.86341	−0.312783
$804$	106.731	3.76411
$805$	−0.957603	−0.0337511
$806$	113.085	3.98325
$807$	75.7471	2.66642
$808$	−34.8260	−1.22517
$809$	20.0216	0.703921	0.351960	−	0.936015i	$-0.385515\pi$
$809$	20.0216	0.703921	0.351960	+	0.936015i	$0.385515\pi$
$810$	171.144	6.01339
$811$	45.0362	1.58144	0.790718	−	0.612180i	$-0.209707\pi$
$811$	45.0362	1.58144	0.790718	+	0.612180i	$0.209707\pi$
$812$	3.69874	0.129800
$813$	32.1255	1.12669
$814$	−19.5652	−0.685758
$815$	−12.7099	−0.445207
$816$	−5.34150	−0.186990
$817$	3.97263	0.138985
$818$	12.6722	0.443074
$819$	12.3695	0.432227
$820$	−53.7744	−1.87788
$821$	−30.3782	−1.06021	−0.530104	−	0.847933i	$-0.677847\pi$
$821$	−30.3782	−1.06021	−0.530104	+	0.847933i	$0.677847\pi$
$822$	−137.908	−4.81009
$823$	−52.8826	−1.84337	−0.921686	−	0.387936i	$-0.873188\pi$
$823$	−52.8826	−1.84337	−0.921686	+	0.387936i	$0.873188\pi$
$824$	22.8280	0.795250
$825$	−2.30547	−0.0802661
$826$	−5.08579	−0.176957
$827$	−12.6229	−0.438942	−0.219471	−	0.975619i	$-0.570433\pi$
$827$	−12.6229	−0.438942	−0.219471	+	0.975619i	$0.570433\pi$
$828$	−40.4168	−1.40458
$829$	−25.8805	−0.898865	−0.449433	−	0.893314i	$-0.648374\pi$
$829$	−25.8805	−0.898865	−0.449433	+	0.893314i	$0.648374\pi$
$830$	−13.9604	−0.484572
$831$	103.867	3.60310
$832$	52.0332	1.80393
$833$	6.88608	0.238588
$834$	134.094	4.64331
$835$	−27.9658	−0.967798
$836$	−14.1703	−0.490089
$837$	193.055	6.67297
$838$	48.8135	1.68623
$839$	−26.1294	−0.902085	−0.451043	−	0.892502i	$-0.648948\pi$
$839$	−26.1294	−0.902085	−0.451043	+	0.892502i	$0.648948\pi$
$840$	−8.71083	−0.300552
$841$	−19.5615	−0.674535
$842$	−71.4914	−2.46376
$843$	−14.7082	−0.506576
$844$	−44.0106	−1.51491
$845$	−13.5404	−0.465803
$846$	26.7319	0.919063
$847$	−0.337523	−0.0115974
$848$	8.85034	0.303922
$849$	−8.50215	−0.291793
$850$	−1.61854	−0.0555156
$851$	−11.3270	−0.388285
$852$	26.5421	0.909318
$853$	26.0421	0.891666	0.445833	−	0.895116i	$-0.352908\pi$
$853$	26.0421	0.891666	0.445833	+	0.895116i	$0.352908\pi$
$854$	−3.24804	−0.111146
$855$	68.4446	2.34076
$856$	−35.6863	−1.21973
$857$	46.5265	1.58931	0.794657	−	0.607059i	$-0.207651\pi$
$857$	46.5265	1.58931	0.794657	+	0.607059i	$0.207651\pi$
$858$	35.0336	1.19603
$859$	−27.4136	−0.935340	−0.467670	−	0.883903i	$-0.654906\pi$
$859$	−27.4136	−0.935340	−0.467670	+	0.883903i	$0.654906\pi$
$860$	7.40868	0.252634
$861$	−8.23346	−0.280596
$862$	−46.0803	−1.56950
$863$	28.5879	0.973143	0.486571	−	0.873641i	$-0.338247\pi$
$863$	28.5879	0.973143	0.486571	+	0.873641i	$0.338247\pi$
$864$	64.8547	2.20640
$865$	−37.0929	−1.26120
$866$	−37.8647	−1.28669
$867$	3.36081	0.114139
$868$	−13.0608	−0.443311
$869$	12.6005	0.427444
$870$	−50.5995	−1.71548
$871$	−39.3347	−1.33281
$872$	9.24427	0.313050
$873$	−37.7191	−1.27660
$874$	−12.8035	−0.433085
$875$	−3.98611	−0.134755
$876$	−106.254	−3.58999
$877$	−21.0458	−0.710667	−0.355334	−	0.934740i	$-0.615633\pi$
$877$	−21.0458	−0.710667	−0.355334	+	0.934740i	$0.615633\pi$
$878$	5.54636	0.187181
$879$	−46.8904	−1.58157
$880$	−3.30111	−0.111280
$881$	50.2925	1.69440	0.847199	−	0.531275i	$-0.178287\pi$
$881$	50.2925	1.69440	0.847199	+	0.531275i	$0.178287\pi$
$882$	134.773	4.53803
$883$	−8.48445	−0.285525	−0.142762	−	0.989757i	$-0.545598\pi$
$883$	−8.48445	−0.285525	−0.142762	+	0.989757i	$0.545598\pi$
$884$	15.7590	0.530034
$885$	44.5790	1.49851
$886$	0.895212	0.0300752
$887$	−43.9041	−1.47416	−0.737078	−	0.675807i	$-0.763795\pi$
$887$	−43.9041	−1.47416	−0.737078	+	0.675807i	$0.763795\pi$
$888$	−103.036	−3.45766
$889$	−0.996688	−0.0334279
$890$	−9.90907	−0.332153
$891$	34.9230	1.16996
$892$	50.5520	1.69261
$893$	5.42599	0.181574
$894$	−170.741	−5.71043
$895$	−27.8995	−0.932577
$896$	−6.91901	−0.231148
$897$	20.2823	0.677205
$898$	40.4341	1.34930
$899$	−33.3286	−1.11157
$900$	−20.2971	−0.676571
$901$	−5.56854	−0.185515
$902$	−17.1255	−0.570218
$903$	1.13435	0.0377489
$904$	25.7564	0.856646
$905$	22.5180	0.748524
$906$	−16.3676	−0.543778
$907$	13.1570	0.436870	0.218435	−	0.975852i	$-0.429905\pi$
$907$	13.1570	0.436870	0.218435	+	0.975852i	$0.429905\pi$
$908$	38.2802	1.27037
$909$	78.1362	2.59162
$910$	7.30775	0.242250
$911$	−51.9515	−1.72123	−0.860616	−	0.509255i	$-0.829921\pi$
$911$	−51.9515	−1.72123	−0.860616	+	0.509255i	$0.829921\pi$
$912$	−21.2198	−0.702658
$913$	−2.84870	−0.0942784
$914$	62.8556	2.07908
$915$	28.4704	0.941203
$916$	60.4101	1.99601
$917$	−4.36039	−0.143993
$918$	41.9881	1.38581
$919$	37.0574	1.22241	0.611206	−	0.791472i	$-0.290685\pi$
$919$	37.0574	1.22241	0.611206	+	0.791472i	$0.290685\pi$
$920$	−10.4895	−0.345827
$921$	−92.3951	−3.04452
$922$	38.3067	1.26156
$923$	−9.78187	−0.321974
$924$	−4.04620	−0.133110
$925$	−5.68838	−0.187033
$926$	26.0257	0.855258
$927$	−51.2173	−1.68220
$928$	−11.1963	−0.367538
$929$	41.6931	1.36791	0.683953	−	0.729526i	$-0.260259\pi$
$929$	41.6931	1.36791	0.683953	+	0.729526i	$0.260259\pi$
$930$	178.674	5.85894
$931$	27.3559	0.896552
$932$	−35.5380	−1.16408
$933$	−21.9328	−0.718048
$934$	69.5344	2.27524
$935$	2.07702	0.0679258
$936$	135.494	4.42877
$937$	38.0417	1.24277	0.621384	−	0.783506i	$-0.286571\pi$
$937$	38.0417	1.24277	0.621384	+	0.783506i	$0.286571\pi$
$938$	7.09020	0.231503
$939$	42.8781	1.39927
$940$	10.1191	0.330048
$941$	−48.6921	−1.58732	−0.793658	−	0.608364i	$-0.791826\pi$
$941$	−48.6921	−1.58732	−0.793658	+	0.608364i	$0.791826\pi$
$942$	−106.833	−3.48081
$943$	−9.91463	−0.322865
$944$	−10.1500	−0.330353
$945$	12.4756	0.405830
$946$	2.35944	0.0767121
$947$	−6.18677	−0.201043	−0.100522	−	0.994935i	$-0.532051\pi$
$947$	−6.18677	−0.201043	−0.100522	+	0.994935i	$0.532051\pi$
$948$	151.054	4.90602
$949$	39.1590	1.27115
$950$	−6.42988	−0.208613
$951$	85.0154	2.75681
$952$	−1.24788	−0.0404441
$953$	−27.0302	−0.875594	−0.437797	−	0.899074i	$-0.644241\pi$
$953$	−27.0302	−0.875594	−0.437797	+	0.899074i	$0.644241\pi$
$954$	−108.986	−3.52855
$955$	−1.59948	−0.0517579
$956$	−6.47656	−0.209467
$957$	−10.3251	−0.333764
$958$	−10.2511	−0.331198
$959$	−5.87000	−0.189552
$960$	82.2121	2.65338
$961$	86.6876	2.79637
$962$	86.4398	2.78693
$963$	80.0665	2.58011
$964$	−13.9766	−0.450156
$965$	−2.09585	−0.0674678
$966$	−3.65594	−0.117628
$967$	35.3552	1.13695	0.568473	−	0.822702i	$-0.307534\pi$
$967$	35.3552	1.13695	0.568473	+	0.822702i	$0.307534\pi$
$968$	−3.69718	−0.118832
$969$	13.3513	0.428905
$970$	−22.2839	−0.715493
$971$	46.4813	1.49165	0.745827	−	0.666139i	$-0.232054\pi$
$971$	46.4813	1.49165	0.745827	+	0.666139i	$0.232054\pi$
$972$	228.224	7.32028
$973$	5.70768	0.182980
$974$	−31.5505	−1.01094
$975$	10.1857	0.326202
$976$	−6.48227	−0.207492
$977$	−5.89654	−0.188647	−0.0943235	−	0.995542i	$-0.530069\pi$
$977$	−5.89654	−0.188647	−0.0943235	+	0.995542i	$0.530069\pi$
$978$	−48.5238	−1.55162
$979$	−2.02201	−0.0646236
$980$	51.0167	1.62967
$981$	−20.7406	−0.662197
$982$	−59.9482	−1.91302
$983$	6.13640	0.195721	0.0978604	−	0.995200i	$-0.468800\pi$
$983$	6.13640	0.195721	0.0978604	+	0.995200i	$0.468800\pi$
$984$	−90.1883	−2.87510
$985$	7.81696	0.249069
$986$	−7.24871	−0.230846
$987$	1.54935	0.0493162
$988$	62.6049	1.99173
$989$	1.36597	0.0434354
$990$	40.6509	1.29197
$991$	18.5991	0.590819	0.295409	−	0.955371i	$-0.404544\pi$
$991$	18.5991	0.590819	0.295409	+	0.955371i	$0.404544\pi$
$992$	39.5358	1.25526
$993$	87.3527	2.77206
$994$	1.76321	0.0559256
$995$	−16.8704	−0.534827
$996$	−34.1501	−1.08209
$997$	2.40123	0.0760476	0.0380238	−	0.999277i	$-0.487894\pi$
$997$	2.40123	0.0760476	0.0380238	+	0.999277i	$0.487894\pi$
$998$	−17.8021	−0.563515
$999$	147.567	4.66882

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8041.2.a.i.1.8	✓	78

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8041.2.a.i.1.8	✓	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)

\(f(q)\)	\(=\)	\(q-2.35944 q^{2} +3.36081 q^{3} +3.56697 q^{4} -2.07702 q^{5} -7.92965 q^{6} -0.337523 q^{7} -3.69718 q^{8} +8.29507 q^{9} +O(q^{10})\)	\(q-2.35944 q^{2} +3.36081 q^{3} +3.56697 q^{4} -2.07702 q^{5} -7.92965 q^{6} -0.337523 q^{7} -3.69718 q^{8} +8.29507 q^{9} +4.90061 q^{10} +1.00000 q^{11} +11.9879 q^{12} -4.41805 q^{13} +0.796366 q^{14} -6.98048 q^{15} +1.58935 q^{16} -1.00000 q^{17} -19.5718 q^{18} -3.97263 q^{19} -7.40868 q^{20} -1.13435 q^{21} -2.35944 q^{22} -1.36597 q^{23} -12.4255 q^{24} -0.685985 q^{25} +10.4241 q^{26} +17.7958 q^{27} -1.20393 q^{28} -3.07221 q^{29} +16.4700 q^{30} +10.8484 q^{31} +3.64439 q^{32} +3.36081 q^{33} +2.35944 q^{34} +0.701042 q^{35} +29.5883 q^{36} +8.29228 q^{37} +9.37320 q^{38} -14.8482 q^{39} +7.67912 q^{40} +7.25830 q^{41} +2.67644 q^{42} -1.00000 q^{43} +3.56697 q^{44} -17.2290 q^{45} +3.22293 q^{46} -1.36584 q^{47} +5.34150 q^{48} -6.88608 q^{49} +1.61854 q^{50} -3.36081 q^{51} -15.7590 q^{52} +5.56854 q^{53} -41.9881 q^{54} -2.07702 q^{55} +1.24788 q^{56} -13.3513 q^{57} +7.24871 q^{58} -6.38624 q^{59} -24.8992 q^{60} -4.07858 q^{61} -25.5962 q^{62} -2.79978 q^{63} -11.7774 q^{64} +9.17637 q^{65} -7.92965 q^{66} +8.90319 q^{67} -3.56697 q^{68} -4.59078 q^{69} -1.65407 q^{70} +2.21407 q^{71} -30.6684 q^{72} -8.86341 q^{73} -19.5652 q^{74} -2.30547 q^{75} -14.1703 q^{76} -0.337523 q^{77} +35.0336 q^{78} +12.6005 q^{79} -3.30111 q^{80} +34.9230 q^{81} -17.1255 q^{82} -2.84870 q^{83} -4.04620 q^{84} +2.07702 q^{85} +2.35944 q^{86} -10.3251 q^{87} -3.69718 q^{88} -2.02201 q^{89} +40.6509 q^{90} +1.49119 q^{91} -4.87238 q^{92} +36.4594 q^{93} +3.22263 q^{94} +8.25124 q^{95} +12.2481 q^{96} -4.54717 q^{97} +16.2473 q^{98} +8.29507 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 78 q + 7 q^{2} + 10 q^{3} + 91 q^{4} + 17 q^{5} + 12 q^{6} + 11 q^{7} + 33 q^{8} + 102 q^{9}+O(q^{10}) \) 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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