LMFDB - Embedded newform 8041.2.a.c.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8041,2,Mod(1,8041)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8041, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("8041.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$64.2077082653$
Analytic rank:	$1$
Dimension:	$60$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
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)

$f(q)$	$=$	$q-2.53062 q^{2} +2.95421 q^{3} +4.40406 q^{4} -1.92556 q^{5} -7.47600 q^{6} +2.94104 q^{7} -6.08377 q^{8} +5.72738 q^{9} +O(q^{10})$	\(q-2.53062 q^{2} +2.95421 q^{3} +4.40406 q^{4} -1.92556 q^{5} -7.47600 q^{6} +2.94104 q^{7} -6.08377 q^{8} +5.72738 q^{9} +4.87287 q^{10} +1.00000 q^{11} +13.0105 q^{12} -5.78542 q^{13} -7.44268 q^{14} -5.68852 q^{15} +6.58762 q^{16} +1.00000 q^{17} -14.4938 q^{18} +5.50311 q^{19} -8.48029 q^{20} +8.68847 q^{21} -2.53062 q^{22} +6.45923 q^{23} -17.9728 q^{24} -1.29221 q^{25} +14.6407 q^{26} +8.05725 q^{27} +12.9525 q^{28} -3.01866 q^{29} +14.3955 q^{30} -5.37420 q^{31} -4.50326 q^{32} +2.95421 q^{33} -2.53062 q^{34} -5.66316 q^{35} +25.2237 q^{36} -10.9278 q^{37} -13.9263 q^{38} -17.0914 q^{39} +11.7147 q^{40} -8.51553 q^{41} -21.9872 q^{42} -1.00000 q^{43} +4.40406 q^{44} -11.0284 q^{45} -16.3459 q^{46} -9.32808 q^{47} +19.4612 q^{48} +1.64973 q^{49} +3.27010 q^{50} +2.95421 q^{51} -25.4794 q^{52} -14.2958 q^{53} -20.3899 q^{54} -1.92556 q^{55} -17.8926 q^{56} +16.2574 q^{57} +7.63911 q^{58} -10.4863 q^{59} -25.0526 q^{60} +12.6809 q^{61} +13.6001 q^{62} +16.8445 q^{63} -1.77920 q^{64} +11.1402 q^{65} -7.47600 q^{66} -1.79065 q^{67} +4.40406 q^{68} +19.0820 q^{69} +14.3313 q^{70} -15.0536 q^{71} -34.8440 q^{72} +8.80850 q^{73} +27.6543 q^{74} -3.81747 q^{75} +24.2360 q^{76} +2.94104 q^{77} +43.2519 q^{78} -9.57549 q^{79} -12.6849 q^{80} +6.62070 q^{81} +21.5496 q^{82} -13.3213 q^{83} +38.2645 q^{84} -1.92556 q^{85} +2.53062 q^{86} -8.91778 q^{87} -6.08377 q^{88} -2.83612 q^{89} +27.9088 q^{90} -17.0152 q^{91} +28.4469 q^{92} -15.8765 q^{93} +23.6059 q^{94} -10.5966 q^{95} -13.3036 q^{96} +8.35957 q^{97} -4.17486 q^{98} +5.72738 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q - 9 q^{2} - 6 q^{3} + 43 q^{4} - 15 q^{5} - 4 q^{6} - 17 q^{7} - 21 q^{8} + 40 q^{9}+O(q^{10}) $ 60 * q - 9 * q^2 - 6 * q^3 + 43 * q^4 - 15 * q^5 - 4 * q^6 - 17 * q^7 - 21 * q^8 + 40 * q^9	\( 60 q - 9 q^{2} - 6 q^{3} + 43 q^{4} - 15 q^{5} - 4 q^{6} - 17 q^{7} - 21 q^{8} + 40 q^{9} + q^{10} + 60 q^{11} - 13 q^{12} - 2 q^{13} - 15 q^{14} - 32 q^{15} + 21 q^{16} + 60 q^{17} - 41 q^{18} - 24 q^{19} - 33 q^{20} - 12 q^{21} - 9 q^{22} - 20 q^{23} + 9 q^{24} + 25 q^{25} - 40 q^{26} - 18 q^{27} - 3 q^{28} - 54 q^{29} - 18 q^{30} - 50 q^{31} - 51 q^{32} - 6 q^{33} - 9 q^{34} - 30 q^{35} + 27 q^{36} - 63 q^{37} - 38 q^{38} - 55 q^{39} - 5 q^{40} - 53 q^{41} - 47 q^{42} - 60 q^{43} + 43 q^{44} - 36 q^{45} - 27 q^{46} - 47 q^{47} - 38 q^{48} + 5 q^{49} - 4 q^{50} - 6 q^{51} - 13 q^{52} - 24 q^{53} - 58 q^{54} - 15 q^{55} - 45 q^{56} + 23 q^{57} + 16 q^{58} - 57 q^{59} - 4 q^{60} - 8 q^{61} - 3 q^{62} - 57 q^{63} - 5 q^{64} - 27 q^{65} - 4 q^{66} - 49 q^{67} + 43 q^{68} - 57 q^{69} - 7 q^{70} - 151 q^{71} - 29 q^{72} - 12 q^{73} + 18 q^{74} - 23 q^{75} - 38 q^{76} - 17 q^{77} + 37 q^{78} - 11 q^{79} - 21 q^{80} + 28 q^{81} + 44 q^{82} - 42 q^{83} + 16 q^{84} - 15 q^{85} + 9 q^{86} - 56 q^{87} - 21 q^{88} - 88 q^{89} + 47 q^{90} - 60 q^{91} + 26 q^{92} - 16 q^{93} + 37 q^{94} - 57 q^{95} + 108 q^{96} - 22 q^{97} + 8 q^{98} + 40 q^{99}+O(q^{100}) \) 60 * q - 9 * q^2 - 6 * q^3 + 43 * q^4 - 15 * q^5 - 4 * q^6 - 17 * q^7 - 21 * q^8 + 40 * q^9 + q^10 + 60 * q^11 - 13 * q^12 - 2 * q^13 - 15 * q^14 - 32 * q^15 + 21 * q^16 + 60 * q^17 - 41 * q^18 - 24 * q^19 - 33 * q^20 - 12 * q^21 - 9 * q^22 - 20 * q^23 + 9 * q^24 + 25 * q^25 - 40 * q^26 - 18 * q^27 - 3 * q^28 - 54 * q^29 - 18 * q^30 - 50 * q^31 - 51 * q^32 - 6 * q^33 - 9 * q^34 - 30 * q^35 + 27 * q^36 - 63 * q^37 - 38 * q^38 - 55 * q^39 - 5 * q^40 - 53 * q^41 - 47 * q^42 - 60 * q^43 + 43 * q^44 - 36 * q^45 - 27 * q^46 - 47 * q^47 - 38 * q^48 + 5 * q^49 - 4 * q^50 - 6 * q^51 - 13 * q^52 - 24 * q^53 - 58 * q^54 - 15 * q^55 - 45 * q^56 + 23 * q^57 + 16 * q^58 - 57 * q^59 - 4 * q^60 - 8 * q^61 - 3 * q^62 - 57 * q^63 - 5 * q^64 - 27 * q^65 - 4 * q^66 - 49 * q^67 + 43 * q^68 - 57 * q^69 - 7 * q^70 - 151 * q^71 - 29 * q^72 - 12 * q^73 + 18 * q^74 - 23 * q^75 - 38 * q^76 - 17 * q^77 + 37 * q^78 - 11 * q^79 - 21 * q^80 + 28 * q^81 + 44 * q^82 - 42 * q^83 + 16 * q^84 - 15 * q^85 + 9 * q^86 - 56 * q^87 - 21 * q^88 - 88 * q^89 + 47 * q^90 - 60 * q^91 + 26 * q^92 - 16 * q^93 + 37 * q^94 - 57 * q^95 + 108 * q^96 - 22 * q^97 + 8 * q^98 + 40 * 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 $

$2$	−2.53062	−1.78942	−0.894711	−	0.446646i	$-0.852618\pi$
$2$	−2.53062	−1.78942	−0.894711	+	0.446646i	$0.852618\pi$
$3$	2.95421	1.70562	0.852808	−	0.522225i	$-0.174898\pi$
$3$	2.95421	1.70562	0.852808	+	0.522225i	$0.174898\pi$
$4$	4.40406	2.20203
$5$	−1.92556	−0.861137	−0.430569	−	0.902558i	$-0.641687\pi$
$5$	−1.92556	−0.861137	−0.430569	+	0.902558i	$0.641687\pi$
$6$	−7.47600	−3.05207
$7$	2.94104	1.11161	0.555805	−	0.831313i	$-0.312410\pi$
$7$	2.94104	1.11161	0.555805	+	0.831313i	$0.312410\pi$
$8$	−6.08377	−2.15094
$9$	5.72738	1.90913
$10$	4.87287	1.54094
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	13.0105	3.75582
$13$	−5.78542	−1.60459	−0.802294	−	0.596929i	$-0.796387\pi$
$13$	−5.78542	−1.60459	−0.802294	+	0.596929i	$0.796387\pi$
$14$	−7.44268	−1.98914
$15$	−5.68852	−1.46877
$16$	6.58762	1.64691
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−14.4938	−3.41623
$19$	5.50311	1.26250	0.631250	−	0.775579i	$-0.282542\pi$
$19$	5.50311	1.26250	0.631250	+	0.775579i	$0.282542\pi$
$20$	−8.48029	−1.89625
$21$	8.68847	1.89598
$22$	−2.53062	−0.539531
$23$	6.45923	1.34684	0.673422	−	0.739259i	$-0.264824\pi$
$23$	6.45923	1.34684	0.673422	+	0.739259i	$0.264824\pi$
$24$	−17.9728	−3.66867
$25$	−1.29221	−0.258442
$26$	14.6407	2.87128
$27$	8.05725	1.55062
$28$	12.9525	2.44780
$29$	−3.01866	−0.560552	−0.280276	−	0.959919i	$-0.590426\pi$
$29$	−3.01866	−0.560552	−0.280276	+	0.959919i	$0.590426\pi$
$30$	14.3955	2.62825
$31$	−5.37420	−0.965234	−0.482617	−	0.875831i	$-0.660314\pi$
$31$	−5.37420	−0.965234	−0.482617	+	0.875831i	$0.660314\pi$
$32$	−4.50326	−0.796071
$33$	2.95421	0.514263
$34$	−2.53062	−0.433999
$35$	−5.66316	−0.957249
$36$	25.2237	4.20395
$37$	−10.9278	−1.79653	−0.898264	−	0.439457i	$-0.855171\pi$
$37$	−10.9278	−1.79653	−0.898264	+	0.439457i	$0.855171\pi$
$38$	−13.9263	−2.25915
$39$	−17.0914	−2.73681
$40$	11.7147	1.85225
$41$	−8.51553	−1.32990	−0.664951	−	0.746887i	$-0.731548\pi$
$41$	−8.51553	−1.32990	−0.664951	+	0.746887i	$0.731548\pi$
$42$	−21.9872	−3.39271
$43$	−1.00000	−0.152499
$43$	−1.00000	−0.152499
$44$	4.40406	0.663937
$45$	−11.0284	−1.64402
$46$	−16.3459	−2.41007
$47$	−9.32808	−1.36064	−0.680320	−	0.732915i	$-0.738159\pi$
$47$	−9.32808	−1.36064	−0.680320	+	0.732915i	$0.738159\pi$
$48$	19.4612	2.80899
$49$	1.64973	0.235676
$50$	3.27010	0.462462
$51$	2.95421	0.413673
$52$	−25.4794	−3.53335
$53$	−14.2958	−1.96367	−0.981837	−	0.189729i	$-0.939239\pi$
$53$	−14.2958	−1.96367	−0.981837	+	0.189729i	$0.939239\pi$
$54$	−20.3899	−2.77471
$55$	−1.92556	−0.259643
$56$	−17.8926	−2.39100
$57$	16.2574	2.15334
$58$	7.63911	1.00306
$59$	−10.4863	−1.36520	−0.682602	−	0.730791i	$-0.739152\pi$
$59$	−10.4863	−1.36520	−0.682602	+	0.730791i	$0.739152\pi$
$60$	−25.0526	−3.23427
$61$	12.6809	1.62362	0.811812	−	0.583918i	$-0.198481\pi$
$61$	12.6809	1.62362	0.811812	+	0.583918i	$0.198481\pi$
$62$	13.6001	1.72721
$63$	16.8445	2.12220
$64$	−1.77920	−0.222400
$65$	11.1402	1.38177
$66$	−7.47600	−0.920232
$67$	−1.79065	−0.218763	−0.109382	−	0.994000i	$-0.534887\pi$
$67$	−1.79065	−0.218763	−0.109382	+	0.994000i	$0.534887\pi$
$68$	4.40406	0.534071
$69$	19.0820	2.29720
$70$	14.3313	1.71292
$71$	−15.0536	−1.78654	−0.893268	−	0.449524i	$-0.851594\pi$
$71$	−15.0536	−1.78654	−0.893268	+	0.449524i	$0.851594\pi$
$72$	−34.8440	−4.10641
$73$	8.80850	1.03096	0.515479	−	0.856902i	$-0.327614\pi$
$73$	8.80850	1.03096	0.515479	+	0.856902i	$0.327614\pi$
$74$	27.6543	3.21474
$75$	−3.81747	−0.440803
$76$	24.2360	2.78006
$77$	2.94104	0.335163
$78$	43.2519	4.89731
$79$	−9.57549	−1.07733	−0.538663	−	0.842521i	$-0.681070\pi$
$79$	−9.57549	−1.07733	−0.538663	+	0.842521i	$0.681070\pi$
$80$	−12.6849	−1.41821
$81$	6.62070	0.735634
$82$	21.5496	2.37976
$83$	−13.3213	−1.46220	−0.731102	−	0.682268i	$-0.760994\pi$
$83$	−13.3213	−1.46220	−0.731102	+	0.682268i	$0.760994\pi$
$84$	38.2645	4.17500
$85$	−1.92556	−0.208857
$86$	2.53062	0.272884
$87$	−8.91778	−0.956086
$88$	−6.08377	−0.648532
$89$	−2.83612	−0.300628	−0.150314	−	0.988638i	$-0.548029\pi$
$89$	−2.83612	−0.300628	−0.150314	+	0.988638i	$0.548029\pi$
$90$	27.9088	2.94184
$91$	−17.0152	−1.78368
$92$	28.4469	2.96579
$93$	−15.8765	−1.64632
$94$	23.6059	2.43476
$95$	−10.5966	−1.08719
$96$	−13.3036	−1.35779
$97$	8.35957	0.848786	0.424393	−	0.905478i	$-0.360488\pi$
$97$	8.35957	0.848786	0.424393	+	0.905478i	$0.360488\pi$
$98$	−4.17486	−0.421724
$99$	5.72738	0.575623
$100$	−5.69098	−0.569098
$101$	−5.72371	−0.569531	−0.284765	−	0.958597i	$-0.591916\pi$
$101$	−5.72371	−0.569531	−0.284765	+	0.958597i	$0.591916\pi$
$102$	−7.47600	−0.740235
$103$	−10.4657	−1.03121	−0.515607	−	0.856825i	$-0.672433\pi$
$103$	−10.4657	−1.03121	−0.515607	+	0.856825i	$0.672433\pi$
$104$	35.1972	3.45137
$105$	−16.7302	−1.63270
$106$	36.1772	3.51384
$107$	−0.837665	−0.0809801	−0.0404901	−	0.999180i	$-0.512892\pi$
$107$	−0.837665	−0.0809801	−0.0404901	+	0.999180i	$0.512892\pi$
$108$	35.4846	3.41451
$109$	7.85126	0.752014	0.376007	−	0.926617i	$-0.377297\pi$
$109$	7.85126	0.752014	0.376007	+	0.926617i	$0.377297\pi$
$110$	4.87287	0.464610
$111$	−32.2832	−3.06418
$112$	19.3745	1.83072
$113$	−4.79774	−0.451334	−0.225667	−	0.974205i	$-0.572456\pi$
$113$	−4.79774	−0.451334	−0.225667	+	0.974205i	$0.572456\pi$
$114$	−41.1413	−3.85324
$115$	−12.4377	−1.15982
$116$	−13.2944	−1.23435
$117$	−33.1353	−3.06336
$118$	26.5369	2.44292
$119$	2.94104	0.269605
$120$	34.6077	3.15923
$121$	1.00000	0.0909091
$122$	−32.0906	−2.90535
$123$	−25.1567	−2.26830
$124$	−23.6683	−2.12547
$125$	12.1160	1.08369
$126$	−42.6270	−3.79751
$127$	9.39520	0.833689	0.416845	−	0.908978i	$-0.363136\pi$
$127$	9.39520	0.833689	0.416845	+	0.908978i	$0.363136\pi$
$128$	13.5090	1.19404
$129$	−2.95421	−0.260104
$130$	−28.1916	−2.47257
$131$	−9.75911	−0.852658	−0.426329	−	0.904568i	$-0.640193\pi$
$131$	−9.75911	−0.852658	−0.426329	+	0.904568i	$0.640193\pi$
$132$	13.0105	1.13242
$133$	16.1849	1.40341
$134$	4.53147	0.391460
$135$	−15.5147	−1.33530
$136$	−6.08377	−0.521679
$137$	7.82954	0.668923	0.334462	−	0.942409i	$-0.391446\pi$
$137$	7.82954	0.668923	0.334462	+	0.942409i	$0.391446\pi$
$138$	−48.2893	−4.11065
$139$	20.1156	1.70618	0.853090	−	0.521764i	$-0.174726\pi$
$139$	20.1156	1.70618	0.853090	+	0.521764i	$0.174726\pi$
$140$	−24.9409	−2.10789
$141$	−27.5571	−2.32073
$142$	38.0951	3.19687
$143$	−5.78542	−0.483802
$144$	37.7298	3.14415
$145$	5.81263	0.482712
$146$	−22.2910	−1.84482
$147$	4.87366	0.401973
$148$	−48.1269	−3.95601
$149$	4.37987	0.358813	0.179406	−	0.983775i	$-0.442582\pi$
$149$	4.37987	0.358813	0.179406	+	0.983775i	$0.442582\pi$
$150$	9.66058	0.788783
$151$	−7.25703	−0.590569	−0.295284	−	0.955409i	$-0.595414\pi$
$151$	−7.25703	−0.590569	−0.295284	+	0.955409i	$0.595414\pi$
$152$	−33.4797	−2.71556
$153$	5.72738	0.463031
$154$	−7.44268	−0.599748
$155$	10.3484	0.831199
$156$	−75.2715	−6.02654
$157$	10.9145	0.871074	0.435537	−	0.900171i	$-0.356559\pi$
$157$	10.9145	0.871074	0.435537	+	0.900171i	$0.356559\pi$
$158$	24.2320	1.92779
$159$	−42.2327	−3.34927
$160$	8.67130	0.685526
$161$	18.9969	1.49716
$162$	−16.7545	−1.31636
$163$	15.0536	1.17909	0.589544	−	0.807737i	$-0.299308\pi$
$163$	15.0536	1.17909	0.589544	+	0.807737i	$0.299308\pi$
$164$	−37.5029	−2.92848
$165$	−5.68852	−0.442851
$166$	33.7113	2.61650
$167$	17.5882	1.36102	0.680509	−	0.732740i	$-0.261759\pi$
$167$	17.5882	1.36102	0.680509	+	0.732740i	$0.261759\pi$
$168$	−52.8587	−4.07813
$169$	20.4711	1.57470
$170$	4.87287	0.373732
$171$	31.5184	2.41027
$172$	−4.40406	−0.335806
$173$	−2.69914	−0.205212	−0.102606	−	0.994722i	$-0.532718\pi$
$173$	−2.69914	−0.205212	−0.102606	+	0.994722i	$0.532718\pi$
$174$	22.5675	1.71084
$175$	−3.80045	−0.287287
$176$	6.58762	0.496561
$177$	−30.9788	−2.32851
$178$	7.17716	0.537951
$179$	7.78799	0.582102	0.291051	−	0.956708i	$-0.405995\pi$
$179$	7.78799	0.582102	0.291051	+	0.956708i	$0.405995\pi$
$180$	−48.5698	−3.62018
$181$	−13.6344	−1.01343	−0.506717	−	0.862113i	$-0.669141\pi$
$181$	−13.6344	−1.01343	−0.506717	+	0.862113i	$0.669141\pi$
$182$	43.0590	3.19175
$183$	37.4621	2.76928
$184$	−39.2965	−2.89698
$185$	21.0422	1.54706
$186$	40.1775	2.94596
$187$	1.00000	0.0731272
$188$	−41.0814	−2.99617
$189$	23.6967	1.72368
$190$	26.8160	1.94544
$191$	3.57434	0.258630	0.129315	−	0.991604i	$-0.458722\pi$
$191$	3.57434	0.258630	0.129315	+	0.991604i	$0.458722\pi$
$192$	−5.25613	−0.379328
$193$	−26.4712	−1.90544	−0.952719	−	0.303852i	$-0.901727\pi$
$193$	−26.4712	−1.90544	−0.952719	+	0.303852i	$0.901727\pi$
$194$	−21.1549	−1.51884
$195$	32.9105	2.35677
$196$	7.26553	0.518966
$197$	−13.0764	−0.931653	−0.465826	−	0.884876i	$-0.654243\pi$
$197$	−13.0764	−0.931653	−0.465826	+	0.884876i	$0.654243\pi$
$198$	−14.4938	−1.03003
$199$	1.52659	0.108217	0.0541087	−	0.998535i	$-0.482768\pi$
$199$	1.52659	0.108217	0.0541087	+	0.998535i	$0.482768\pi$
$200$	7.86152	0.555893
$201$	−5.28998	−0.373126
$202$	14.4846	1.01913
$203$	−8.87802	−0.623115
$204$	13.0105	0.910919
$205$	16.3972	1.14523
$206$	26.4847	1.84528
$207$	36.9945	2.57129
$208$	−38.1122	−2.64261
$209$	5.50311	0.380658
$210$	42.3378	2.92159
$211$	14.1979	0.977425	0.488712	−	0.872445i	$-0.337467\pi$
$211$	14.1979	0.977425	0.488712	+	0.872445i	$0.337467\pi$
$212$	−62.9594	−4.32407
$213$	−44.4716	−3.04714
$214$	2.11982	0.144908
$215$	1.92556	0.131322
$216$	−49.0185	−3.33528
$217$	−15.8057	−1.07296
$218$	−19.8686	−1.34567
$219$	26.0222	1.75842
$220$	−8.48029	−0.571741
$221$	−5.78542	−0.389170
$222$	81.6966	5.48312
$223$	18.2942	1.22507	0.612536	−	0.790443i	$-0.290150\pi$
$223$	18.2942	1.22507	0.612536	+	0.790443i	$0.290150\pi$
$224$	−13.2443	−0.884920
$225$	−7.40098	−0.493399
$226$	12.1413	0.807626
$227$	−18.1329	−1.20352	−0.601762	−	0.798676i	$-0.705534\pi$
$227$	−18.1329	−1.20352	−0.601762	+	0.798676i	$0.705534\pi$
$228$	71.5984	4.74172
$229$	12.5644	0.830276	0.415138	−	0.909759i	$-0.363733\pi$
$229$	12.5644	0.830276	0.415138	+	0.909759i	$0.363733\pi$
$230$	31.4750	2.07540
$231$	8.68847	0.571659
$232$	18.3649	1.20571
$233$	−9.05375	−0.593131	−0.296566	−	0.955012i	$-0.595841\pi$
$233$	−9.05375	−0.593131	−0.296566	+	0.955012i	$0.595841\pi$
$234$	83.8530	5.48164
$235$	17.9618	1.17170
$236$	−46.1824	−3.00622
$237$	−28.2880	−1.83751
$238$	−7.44268	−0.482437
$239$	−21.1814	−1.37011	−0.685056	−	0.728491i	$-0.740222\pi$
$239$	−21.1814	−1.37011	−0.685056	+	0.728491i	$0.740222\pi$
$240$	−37.4738	−2.41893
$241$	3.00974	0.193874	0.0969371	−	0.995291i	$-0.469095\pi$
$241$	3.00974	0.193874	0.0969371	+	0.995291i	$0.469095\pi$
$242$	−2.53062	−0.162675
$243$	−4.61278	−0.295910
$244$	55.8475	3.57527
$245$	−3.17666	−0.202950
$246$	63.6621	4.05895
$247$	−31.8378	−2.02579
$248$	32.6954	2.07616
$249$	−39.3540	−2.49396
$250$	−30.6612	−1.93918
$251$	2.54606	0.160706	0.0803530	−	0.996766i	$-0.474395\pi$
$251$	2.54606	0.160706	0.0803530	+	0.996766i	$0.474395\pi$
$252$	74.1840	4.67315
$253$	6.45923	0.406089
$254$	−23.7757	−1.49182
$255$	−5.68852	−0.356229
$256$	−30.6278	−1.91424
$257$	16.6944	1.04137	0.520684	−	0.853749i	$-0.325677\pi$
$257$	16.6944	1.04137	0.520684	+	0.853749i	$0.325677\pi$
$258$	7.47600	0.465436
$259$	−32.1393	−1.99704
$260$	49.0621	3.04270
$261$	−17.2890	−1.07016
$262$	24.6967	1.52576
$263$	29.8757	1.84222	0.921108	−	0.389308i	$-0.127286\pi$
$263$	29.8757	1.84222	0.921108	+	0.389308i	$0.127286\pi$
$264$	−17.9728	−1.10615
$265$	27.5274	1.69099
$266$	−40.9579	−2.51129
$267$	−8.37851	−0.512757
$268$	−7.88615	−0.481723
$269$	11.6904	0.712777	0.356388	−	0.934338i	$-0.384008\pi$
$269$	11.6904	0.712777	0.356388	+	0.934338i	$0.384008\pi$
$270$	39.2620	2.38941
$271$	−11.0567	−0.671648	−0.335824	−	0.941925i	$-0.609015\pi$
$271$	−11.0567	−0.671648	−0.335824	+	0.941925i	$0.609015\pi$
$272$	6.58762	0.399433
$273$	−50.2665	−3.04227
$274$	−19.8136	−1.19699
$275$	−1.29221	−0.0779233
$276$	84.0381	5.05850
$277$	−21.9517	−1.31895	−0.659474	−	0.751727i	$-0.729221\pi$
$277$	−21.9517	−1.31895	−0.659474	+	0.751727i	$0.729221\pi$
$278$	−50.9049	−3.05308
$279$	−30.7800	−1.84275
$280$	34.4534	2.05898
$281$	9.31582	0.555735	0.277868	−	0.960619i	$-0.410372\pi$
$281$	9.31582	0.555735	0.277868	+	0.960619i	$0.410372\pi$
$282$	69.7368	4.15276
$283$	7.08054	0.420895	0.210447	−	0.977605i	$-0.432508\pi$
$283$	7.08054	0.420895	0.210447	+	0.977605i	$0.432508\pi$
$284$	−66.2971	−3.93401
$285$	−31.3046	−1.85432
$286$	14.6407	0.865725
$287$	−25.0445	−1.47833
$288$	−25.7918	−1.51980
$289$	1.00000	0.0588235
$290$	−14.7096	−0.863776
$291$	24.6959	1.44770
$292$	38.7932	2.27020
$293$	−1.25737	−0.0734563	−0.0367282	−	0.999325i	$-0.511694\pi$
$293$	−1.25737	−0.0734563	−0.0367282	+	0.999325i	$0.511694\pi$
$294$	−12.3334	−0.719299
$295$	20.1921	1.17563
$296$	66.4825	3.86422
$297$	8.05725	0.467529
$298$	−11.0838	−0.642067
$299$	−37.3694	−2.16113
$300$	−16.8124	−0.970662
$301$	−2.94104	−0.169519
$302$	18.3648	1.05678
$303$	−16.9091	−0.971400
$304$	36.2524	2.07922
$305$	−24.4179	−1.39816
$306$	−14.4938	−0.828557
$307$	19.5486	1.11570	0.557850	−	0.829942i	$-0.311626\pi$
$307$	19.5486	1.11570	0.557850	+	0.829942i	$0.311626\pi$
$308$	12.9525	0.738039
$309$	−30.9178	−1.75885
$310$	−26.1878	−1.48737
$311$	−21.5576	−1.22242	−0.611208	−	0.791470i	$-0.709316\pi$
$311$	−21.5576	−1.22242	−0.611208	+	0.791470i	$0.709316\pi$
$312$	103.980	5.88671
$313$	−15.6198	−0.882881	−0.441440	−	0.897291i	$-0.645532\pi$
$313$	−15.6198	−0.882881	−0.441440	+	0.897291i	$0.645532\pi$
$314$	−27.6206	−1.55872
$315$	−32.4350	−1.82751
$316$	−42.1710	−2.37231
$317$	−5.47660	−0.307597	−0.153798	−	0.988102i	$-0.549151\pi$
$317$	−5.47660	−0.307597	−0.153798	+	0.988102i	$0.549151\pi$
$318$	106.875	5.99326
$319$	−3.01866	−0.169013
$320$	3.42595	0.191517
$321$	−2.47464	−0.138121
$322$	−48.0740	−2.67906
$323$	5.50311	0.306201
$324$	29.1580	1.61989
$325$	7.47599	0.414693
$326$	−38.0949	−2.10988
$327$	23.1943	1.28265
$328$	51.8065	2.86054
$329$	−27.4343	−1.51250
$330$	14.3955	0.792447
$331$	12.2369	0.672603	0.336301	−	0.941754i	$-0.390824\pi$
$331$	12.2369	0.672603	0.336301	+	0.941754i	$0.390824\pi$
$332$	−58.6679	−3.21982
$333$	−62.5879	−3.42980
$334$	−44.5092	−2.43543
$335$	3.44802	0.188385
$336$	57.2364	3.12250
$337$	29.0979	1.58506	0.792531	−	0.609831i	$-0.208763\pi$
$337$	29.0979	1.58506	0.792531	+	0.609831i	$0.208763\pi$
$338$	−51.8048	−2.81781
$339$	−14.1735	−0.769802
$340$	−8.48029	−0.459908
$341$	−5.37420	−0.291029
$342$	−79.7612	−4.31299
$343$	−15.7354	−0.849630
$344$	6.08377	0.328015
$345$	−36.7435	−1.97820
$346$	6.83051	0.367210
$347$	29.6587	1.59216	0.796080	−	0.605191i	$-0.206903\pi$
$347$	29.6587	1.59216	0.796080	+	0.605191i	$0.206903\pi$
$348$	−39.2744	−2.10533
$349$	−5.76498	−0.308592	−0.154296	−	0.988025i	$-0.549311\pi$
$349$	−5.76498	−0.308592	−0.154296	+	0.988025i	$0.549311\pi$
$350$	9.61751	0.514077
$351$	−46.6146	−2.48810
$352$	−4.50326	−0.240024
$353$	−22.6699	−1.20660	−0.603299	−	0.797515i	$-0.706147\pi$
$353$	−22.6699	−1.20660	−0.603299	+	0.797515i	$0.706147\pi$
$354$	78.3958	4.16669
$355$	28.9867	1.53845
$356$	−12.4905	−0.661993
$357$	8.68847	0.459842
$358$	−19.7085	−1.04163
$359$	−35.1198	−1.85355	−0.926776	−	0.375615i	$-0.877431\pi$
$359$	−35.1198	−1.85355	−0.926776	+	0.375615i	$0.877431\pi$
$360$	67.0944	3.53618
$361$	11.2843	0.593908
$362$	34.5034	1.81346
$363$	2.95421	0.155056
$364$	−74.9359	−3.92771
$365$	−16.9613	−0.887796
$366$	−94.8026	−4.95541
$367$	19.8550	1.03642	0.518210	−	0.855253i	$-0.326599\pi$
$367$	19.8550	1.03642	0.518210	+	0.855253i	$0.326599\pi$
$368$	42.5510	2.21812
$369$	−48.7716	−2.53895
$370$	−53.2500	−2.76834
$371$	−42.0444	−2.18284
$372$	−69.9212	−3.62524
$373$	30.4673	1.57754	0.788769	−	0.614689i	$-0.210719\pi$
$373$	30.4673	1.57754	0.788769	+	0.614689i	$0.210719\pi$
$374$	−2.53062	−0.130855
$375$	35.7934	1.84836
$376$	56.7499	2.92665
$377$	17.4643	0.899455
$378$	−59.9675	−3.08439
$379$	−17.1631	−0.881611	−0.440805	−	0.897603i	$-0.645307\pi$
$379$	−17.1631	−0.881611	−0.440805	+	0.897603i	$0.645307\pi$
$380$	−46.6680	−2.39402
$381$	27.7554	1.42195
$382$	−9.04530	−0.462798
$383$	31.0595	1.58707	0.793533	−	0.608527i	$-0.208239\pi$
$383$	31.0595	1.58707	0.793533	+	0.608527i	$0.208239\pi$
$384$	39.9084	2.03657
$385$	−5.66316	−0.288621
$386$	66.9887	3.40963
$387$	−5.72738	−0.291139
$388$	36.8160	1.86905
$389$	−30.0376	−1.52297	−0.761483	−	0.648185i	$-0.775528\pi$
$389$	−30.0376	−1.52297	−0.761483	+	0.648185i	$0.775528\pi$
$390$	−83.2841	−4.21726
$391$	6.45923	0.326657
$392$	−10.0366	−0.506925
$393$	−28.8305	−1.45431
$394$	33.0914	1.66712
$395$	18.4382	0.927726
$396$	25.2237	1.26754
$397$	−9.35259	−0.469393	−0.234697	−	0.972069i	$-0.575410\pi$
$397$	−9.35259	−0.469393	−0.234697	+	0.972069i	$0.575410\pi$
$398$	−3.86324	−0.193646
$399$	47.8136	2.39367
$400$	−8.51260	−0.425630
$401$	9.69019	0.483905	0.241952	−	0.970288i	$-0.422212\pi$
$401$	9.69019	0.483905	0.241952	+	0.970288i	$0.422212\pi$
$402$	13.3869	0.667680
$403$	31.0920	1.54880
$404$	−25.2076	−1.25412
$405$	−12.7486	−0.633482
$406$	22.4669	1.11502
$407$	−10.9278	−0.541673
$408$	−17.9728	−0.889784
$409$	−16.8864	−0.834979	−0.417490	−	0.908682i	$-0.637090\pi$
$409$	−16.8864	−0.834979	−0.417490	+	0.908682i	$0.637090\pi$
$410$	−41.4951	−2.04930
$411$	23.1301	1.14093
$412$	−46.0915	−2.27076
$413$	−30.8407	−1.51757
$414$	−93.6191	−4.60113
$415$	25.6510	1.25916
$416$	26.0533	1.27737
$417$	59.4257	2.91009
$418$	−13.9263	−0.681158
$419$	−20.6516	−1.00890	−0.504448	−	0.863442i	$-0.668304\pi$
$419$	−20.6516	−1.00890	−0.504448	+	0.863442i	$0.668304\pi$
$420$	−73.6807	−3.59525
$421$	−6.44598	−0.314158	−0.157079	−	0.987586i	$-0.550208\pi$
$421$	−6.44598	−0.314158	−0.157079	+	0.987586i	$0.550208\pi$
$422$	−35.9296	−1.74902
$423$	−53.4254	−2.59763
$424$	86.9721	4.22374
$425$	−1.29221	−0.0626815
$426$	112.541	5.45263
$427$	37.2951	1.80484
$428$	−3.68913	−0.178321
$429$	−17.0914	−0.825179
$430$	−4.87287	−0.234991
$431$	−2.18587	−0.105290	−0.0526448	−	0.998613i	$-0.516765\pi$
$431$	−2.18587	−0.105290	−0.0526448	+	0.998613i	$0.516765\pi$
$432$	53.0781	2.55372
$433$	−8.83603	−0.424633	−0.212316	−	0.977201i	$-0.568101\pi$
$433$	−8.83603	−0.424633	−0.212316	+	0.977201i	$0.568101\pi$
$434$	39.9984	1.91998
$435$	17.1717	0.823322
$436$	34.5774	1.65596
$437$	35.5459	1.70039
$438$	−65.8524	−3.14655
$439$	−21.7371	−1.03745	−0.518727	−	0.854940i	$-0.673594\pi$
$439$	−21.7371	−1.03745	−0.518727	+	0.854940i	$0.673594\pi$
$440$	11.7147	0.558476
$441$	9.44864	0.449935
$442$	14.6407	0.696389
$443$	18.3003	0.869474	0.434737	−	0.900558i	$-0.356841\pi$
$443$	18.3003	0.869474	0.434737	+	0.900558i	$0.356841\pi$
$444$	−142.177	−6.74743
$445$	5.46113	0.258882
$446$	−46.2958	−2.19217
$447$	12.9391	0.611996
$448$	−5.23270	−0.247222
$449$	−12.3281	−0.581798	−0.290899	−	0.956754i	$-0.593954\pi$
$449$	−12.3281	−0.581798	−0.290899	+	0.956754i	$0.593954\pi$
$450$	18.7291	0.882898
$451$	−8.51553	−0.400981
$452$	−21.1295	−0.993850
$453$	−21.4388	−1.00728
$454$	45.8876	2.15361
$455$	32.7638	1.53599
$456$	−98.9061	−4.63170
$457$	−1.14485	−0.0535540	−0.0267770	−	0.999641i	$-0.508524\pi$
$457$	−1.14485	−0.0535540	−0.0267770	+	0.999641i	$0.508524\pi$
$458$	−31.7957	−1.48571
$459$	8.05725	0.376080
$460$	−54.7762	−2.55395
$461$	14.2052	0.661601	0.330800	−	0.943701i	$-0.392681\pi$
$461$	14.2052	0.661601	0.330800	+	0.943701i	$0.392681\pi$
$462$	−21.9872	−1.02294
$463$	−15.6065	−0.725295	−0.362648	−	0.931926i	$-0.618127\pi$
$463$	−15.6065	−0.725295	−0.362648	+	0.931926i	$0.618127\pi$
$464$	−19.8858	−0.923176
$465$	30.5712	1.41771
$466$	22.9117	1.06136
$467$	−4.85035	−0.224448	−0.112224	−	0.993683i	$-0.535797\pi$
$467$	−4.85035	−0.224448	−0.112224	+	0.993683i	$0.535797\pi$
$468$	−145.930	−6.74561
$469$	−5.26639	−0.243179
$470$	−45.4546	−2.09666
$471$	32.2438	1.48572
$472$	63.7964	2.93647
$473$	−1.00000	−0.0459800
$474$	71.5864	3.28807
$475$	−7.11118	−0.326284
$476$	12.9525	0.593678
$477$	−81.8772	−3.74890
$478$	53.6022	2.45171
$479$	19.9883	0.913290	0.456645	−	0.889649i	$-0.349051\pi$
$479$	19.9883	0.913290	0.456645	+	0.889649i	$0.349051\pi$
$480$	25.6169	1.16924
$481$	63.2222	2.88269
$482$	−7.61651	−0.346923
$483$	56.1208	2.55359
$484$	4.40406	0.200185
$485$	−16.0969	−0.730921
$486$	11.6732	0.529508
$487$	−4.86389	−0.220404	−0.110202	−	0.993909i	$-0.535150\pi$
$487$	−4.86389	−0.220404	−0.110202	+	0.993909i	$0.535150\pi$
$488$	−77.1478	−3.49232
$489$	44.4715	2.01107
$490$	8.03894	0.363162
$491$	34.0094	1.53482	0.767412	−	0.641154i	$-0.221544\pi$
$491$	34.0094	1.53482	0.767412	+	0.641154i	$0.221544\pi$
$492$	−110.792	−4.99487
$493$	−3.01866	−0.135954
$494$	80.5696	3.62500
$495$	−11.0284	−0.495690
$496$	−35.4032	−1.58965
$497$	−44.2733	−1.98593
$498$	99.5902	4.46274
$499$	33.8434	1.51504	0.757520	−	0.652812i	$-0.226411\pi$
$499$	33.8434	1.51504	0.757520	+	0.652812i	$0.226411\pi$
$500$	53.3598	2.38632
$501$	51.9594	2.32137
$502$	−6.44312	−0.287571
$503$	6.89135	0.307270	0.153635	−	0.988128i	$-0.450902\pi$
$503$	6.89135	0.307270	0.153635	+	0.988128i	$0.450902\pi$
$504$	−102.478	−4.56473
$505$	11.0214	0.490444
$506$	−16.3459	−0.726664
$507$	60.4761	2.68584
$508$	41.3770	1.83581
$509$	−43.6826	−1.93620	−0.968099	−	0.250569i	$-0.919382\pi$
$509$	−43.6826	−1.93620	−0.968099	+	0.250569i	$0.919382\pi$
$510$	14.3955	0.637444
$511$	25.9062	1.14602
$512$	50.4895	2.23134
$513$	44.3399	1.95766
$514$	−42.2473	−1.86345
$515$	20.1523	0.888017
$516$	−13.0105	−0.572757
$517$	−9.32808	−0.410248
$518$	81.3324	3.57354
$519$	−7.97383	−0.350012
$520$	−67.7744	−2.97210
$521$	−32.4793	−1.42294	−0.711471	−	0.702716i	$-0.751971\pi$
$521$	−32.4793	−1.42294	−0.711471	+	0.702716i	$0.751971\pi$
$522$	43.7520	1.91497
$523$	−35.4955	−1.55211	−0.776055	−	0.630665i	$-0.782782\pi$
$523$	−35.4955	−1.55211	−0.776055	+	0.630665i	$0.782782\pi$
$524$	−42.9797	−1.87758
$525$	−11.2273	−0.490001
$526$	−75.6042	−3.29650
$527$	−5.37420	−0.234104
$528$	19.4612	0.846942
$529$	18.7217	0.813987
$530$	−69.6614	−3.02590
$531$	−60.0591	−2.60634
$532$	71.2792	3.09035
$533$	49.2660	2.13395
$534$	21.2029	0.917538
$535$	1.61298	0.0697350
$536$	10.8939	0.470546
$537$	23.0074	0.992842
$538$	−29.5840	−1.27546
$539$	1.64973	0.0710591
$540$	−68.3278	−2.94036
$541$	22.2361	0.956006	0.478003	−	0.878358i	$-0.341361\pi$
$541$	22.2361	0.956006	0.478003	+	0.878358i	$0.341361\pi$
$542$	27.9804	1.20186
$543$	−40.2788	−1.72853
$544$	−4.50326	−0.193076
$545$	−15.1181	−0.647588
$546$	127.206	5.44390
$547$	−2.42978	−0.103890	−0.0519449	−	0.998650i	$-0.516542\pi$
$547$	−2.42978	−0.103890	−0.0519449	+	0.998650i	$0.516542\pi$
$548$	34.4818	1.47299
$549$	72.6284	3.09970
$550$	3.27010	0.139438
$551$	−16.6121	−0.707697
$552$	−116.090	−4.94113
$553$	−28.1619	−1.19757
$554$	55.5514	2.36015
$555$	62.1633	2.63868
$556$	88.5901	3.75706
$557$	16.0970	0.682053	0.341026	−	0.940054i	$-0.389225\pi$
$557$	16.0970	0.682053	0.341026	+	0.940054i	$0.389225\pi$
$558$	77.8927	3.29746
$559$	5.78542	0.244697
$560$	−37.3068	−1.57650
$561$	2.95421	0.124727
$562$	−23.5749	−0.994445
$563$	29.6634	1.25016	0.625082	−	0.780559i	$-0.285066\pi$
$563$	29.6634	1.25016	0.625082	+	0.780559i	$0.285066\pi$
$564$	−121.363	−5.11032
$565$	9.23835	0.388660
$566$	−17.9182	−0.753158
$567$	19.4718	0.817737
$568$	91.5828	3.84273
$569$	36.3865	1.52540	0.762700	−	0.646753i	$-0.223873\pi$
$569$	36.3865	1.52540	0.762700	+	0.646753i	$0.223873\pi$
$570$	79.2201	3.31817
$571$	−32.7438	−1.37029	−0.685144	−	0.728408i	$-0.740261\pi$
$571$	−32.7438	−1.37029	−0.685144	+	0.728408i	$0.740261\pi$
$572$	−25.4794	−1.06535
$573$	10.5593	0.441123
$574$	63.3783	2.64536
$575$	−8.34669	−0.348081
$576$	−10.1901	−0.424589
$577$	16.2838	0.677904	0.338952	−	0.940804i	$-0.389928\pi$
$577$	16.2838	0.677904	0.338952	+	0.940804i	$0.389928\pi$
$578$	−2.53062	−0.105260
$579$	−78.2016	−3.24995
$580$	25.5991	1.06295
$581$	−39.1786	−1.62540
$582$	−62.4962	−2.59055
$583$	−14.2958	−0.592070
$584$	−53.5889	−2.21753
$585$	63.8041	2.63797
$586$	3.18193	0.131444
$587$	11.2015	0.462334	0.231167	−	0.972914i	$-0.425746\pi$
$587$	11.2015	0.462334	0.231167	+	0.972914i	$0.425746\pi$
$588$	21.4639	0.885157
$589$	−29.5748	−1.21861
$590$	−51.0985	−2.10369
$591$	−38.6304	−1.58904
$592$	−71.9886	−2.95871
$593$	−29.2257	−1.20016	−0.600078	−	0.799942i	$-0.704864\pi$
$593$	−29.2257	−1.20016	−0.600078	+	0.799942i	$0.704864\pi$
$594$	−20.3899	−0.836606
$595$	−5.66316	−0.232167
$596$	19.2892	0.790116
$597$	4.50988	0.184577
$598$	94.5679	3.86717
$599$	−1.23413	−0.0504254	−0.0252127	−	0.999682i	$-0.508026\pi$
$599$	−1.23413	−0.0504254	−0.0252127	+	0.999682i	$0.508026\pi$
$600$	23.2246	0.948140
$601$	12.2576	0.499997	0.249999	−	0.968246i	$-0.419570\pi$
$601$	12.2576	0.499997	0.249999	+	0.968246i	$0.419570\pi$
$602$	7.44268	0.303341
$603$	−10.2558	−0.417646
$604$	−31.9604	−1.30045
$605$	−1.92556	−0.0782852
$606$	42.7905	1.73824
$607$	29.3942	1.19307	0.596536	−	0.802586i	$-0.296543\pi$
$607$	29.3942	1.19307	0.596536	+	0.802586i	$0.296543\pi$
$608$	−24.7819	−1.00504
$609$	−26.2276	−1.06279
$610$	61.7925	2.50191
$611$	53.9669	2.18327
$612$	25.2237	1.01961
$613$	4.31300	0.174200	0.0871002	−	0.996200i	$-0.472240\pi$
$613$	4.31300	0.174200	0.0871002	+	0.996200i	$0.472240\pi$
$614$	−49.4703	−1.99646
$615$	48.4408	1.95332
$616$	−17.8926	−0.720915
$617$	3.62713	0.146023	0.0730114	−	0.997331i	$-0.476739\pi$
$617$	3.62713	0.146023	0.0730114	+	0.997331i	$0.476739\pi$
$618$	78.2414	3.14733
$619$	22.2914	0.895966	0.447983	−	0.894042i	$-0.352143\pi$
$619$	22.2914	0.895966	0.447983	+	0.894042i	$0.352143\pi$
$620$	45.5748	1.83033
$621$	52.0436	2.08844
$622$	54.5541	2.18742
$623$	−8.34116	−0.334181
$624$	−112.592	−4.50727
$625$	−16.8691	−0.674765
$626$	39.5277	1.57985
$627$	16.2574	0.649257
$628$	48.0682	1.91813
$629$	−10.9278	−0.435722
$630$	82.0809	3.27018
$631$	−27.3604	−1.08920	−0.544600	−	0.838696i	$-0.683319\pi$
$631$	−27.3604	−1.08920	−0.544600	+	0.838696i	$0.683319\pi$
$632$	58.2551	2.31726
$633$	41.9437	1.66711
$634$	13.8592	0.550420
$635$	−18.0910	−0.717921
$636$	−185.995	−7.37520
$637$	−9.54441	−0.378163
$638$	7.63911	0.302435
$639$	−86.2177	−3.41072
$640$	−26.0124	−1.02823
$641$	35.1065	1.38662	0.693311	−	0.720639i	$-0.256151\pi$
$641$	35.1065	1.38662	0.693311	+	0.720639i	$0.256151\pi$
$642$	6.26239	0.247157
$643$	−16.3996	−0.646736	−0.323368	−	0.946273i	$-0.604815\pi$
$643$	−16.3996	−0.646736	−0.323368	+	0.946273i	$0.604815\pi$
$644$	83.6634	3.29680
$645$	5.68852	0.223985
$646$	−13.9263	−0.547923
$647$	−26.0771	−1.02520	−0.512599	−	0.858628i	$-0.671317\pi$
$647$	−26.0771	−1.02520	−0.512599	+	0.858628i	$0.671317\pi$
$648$	−40.2788	−1.58230
$649$	−10.4863	−0.411624
$650$	−18.9189	−0.742061
$651$	−46.6935	−1.83006
$652$	66.2968	2.59638
$653$	26.3480	1.03108	0.515539	−	0.856866i	$-0.327592\pi$
$653$	26.3480	1.03108	0.515539	+	0.856866i	$0.327592\pi$
$654$	−58.6960	−2.29520
$655$	18.7918	0.734256
$656$	−56.0971	−2.19022
$657$	50.4496	1.96823
$658$	69.4259	2.70650
$659$	12.9541	0.504619	0.252310	−	0.967647i	$-0.418810\pi$
$659$	12.9541	0.504619	0.252310	+	0.967647i	$0.418810\pi$
$660$	−25.0526	−0.975171
$661$	44.5152	1.73144	0.865720	−	0.500529i	$-0.166861\pi$
$661$	44.5152	1.73144	0.865720	+	0.500529i	$0.166861\pi$
$662$	−30.9671	−1.20357
$663$	−17.0914	−0.663774
$664$	81.0439	3.14511
$665$	−31.1650	−1.20853
$666$	158.386	6.13735
$667$	−19.4983	−0.754976
$668$	77.4596	2.99700
$669$	54.0450	2.08950
$670$	−8.72563	−0.337101
$671$	12.6809	0.489541
$672$	−39.1264	−1.50933
$673$	−44.1401	−1.70148	−0.850739	−	0.525589i	$-0.823845\pi$
$673$	−44.1401	−1.70148	−0.850739	+	0.525589i	$0.823845\pi$
$674$	−73.6358	−2.83635
$675$	−10.4117	−0.400745
$676$	90.1561	3.46754
$677$	2.53834	0.0975565	0.0487782	−	0.998810i	$-0.484467\pi$
$677$	2.53834	0.0975565	0.0487782	+	0.998810i	$0.484467\pi$
$678$	35.8679	1.37750
$679$	24.5859	0.943518
$680$	11.7147	0.449238
$681$	−53.5685	−2.05275
$682$	13.6001	0.520774
$683$	2.48349	0.0950280	0.0475140	−	0.998871i	$-0.484870\pi$
$683$	2.48349	0.0950280	0.0475140	+	0.998871i	$0.484870\pi$
$684$	138.809	5.30749
$685$	−15.0763	−0.576035
$686$	39.8203	1.52035
$687$	37.1178	1.41613
$688$	−6.58762	−0.251151
$689$	82.7070	3.15089
$690$	92.9840	3.53984
$691$	28.3399	1.07810	0.539050	−	0.842274i	$-0.318784\pi$
$691$	28.3399	1.07810	0.539050	+	0.842274i	$0.318784\pi$
$692$	−11.8872	−0.451882
$693$	16.8445	0.639868
$694$	−75.0549	−2.84905
$695$	−38.7338	−1.46926
$696$	54.2537	2.05648
$697$	−8.51553	−0.322549
$698$	14.5890	0.552202
$699$	−26.7467	−1.01165
$700$	−16.7374	−0.632614
$701$	42.8703	1.61919	0.809595	−	0.586988i	$-0.199687\pi$
$701$	42.8703	1.61919	0.809595	+	0.586988i	$0.199687\pi$
$702$	117.964	4.45227
$703$	−60.1372	−2.26812
$704$	−1.77920	−0.0670560
$705$	53.0630	1.99847
$706$	57.3691	2.15911
$707$	−16.8337	−0.633096
$708$	−136.433	−5.12745
$709$	−24.9635	−0.937523	−0.468761	−	0.883325i	$-0.655300\pi$
$709$	−24.9635	−0.937523	−0.468761	+	0.883325i	$0.655300\pi$
$710$	−73.3544	−2.75294
$711$	−54.8424	−2.05675
$712$	17.2543	0.646633
$713$	−34.7132	−1.30002
$714$	−21.9872	−0.822852
$715$	11.1402	0.416620
$716$	34.2988	1.28181
$717$	−62.5744	−2.33688
$718$	88.8750	3.31678
$719$	−16.8271	−0.627543	−0.313772	−	0.949498i	$-0.601593\pi$
$719$	−16.8271	−0.627543	−0.313772	+	0.949498i	$0.601593\pi$
$720$	−72.6511	−2.70755
$721$	−30.7800	−1.14631
$722$	−28.5562	−1.06275
$723$	8.89140	0.330675
$724$	−60.0465	−2.23161
$725$	3.90075	0.144870
$726$	−7.47600	−0.277461
$727$	−53.6920	−1.99133	−0.995664	−	0.0930250i	$-0.970346\pi$
$727$	−53.6920	−1.99133	−0.995664	+	0.0930250i	$0.970346\pi$
$728$	103.517	3.83658
$729$	−33.4892	−1.24034
$730$	42.9227	1.58864
$731$	−1.00000	−0.0369863
$732$	164.985	6.09804
$733$	1.33747	0.0494004	0.0247002	−	0.999695i	$-0.492137\pi$
$733$	1.33747	0.0494004	0.0247002	+	0.999695i	$0.492137\pi$
$734$	−50.2454	−1.85459
$735$	−9.38454	−0.346154
$736$	−29.0876	−1.07218
$737$	−1.79065	−0.0659596
$738$	123.423	4.54325
$739$	−39.1404	−1.43980	−0.719901	−	0.694077i	$-0.755813\pi$
$739$	−39.1404	−1.43980	−0.719901	+	0.694077i	$0.755813\pi$
$740$	92.6713	3.40667
$741$	−94.0558	−3.45523
$742$	106.399	3.90602
$743$	−17.7548	−0.651362	−0.325681	−	0.945480i	$-0.605594\pi$
$743$	−17.7548	−0.651362	−0.325681	+	0.945480i	$0.605594\pi$
$744$	96.5892	3.54113
$745$	−8.43370	−0.308987
$746$	−77.1014	−2.82288
$747$	−76.2962	−2.79153
$748$	4.40406	0.161028
$749$	−2.46361	−0.0900183
$750$	−90.5796	−3.30750
$751$	−32.2716	−1.17761	−0.588804	−	0.808276i	$-0.700401\pi$
$751$	−32.2716	−1.17761	−0.588804	+	0.808276i	$0.700401\pi$
$752$	−61.4499	−2.24085
$753$	7.52161	0.274103
$754$	−44.1955	−1.60950
$755$	13.9739	0.508561
$756$	104.362	3.79560
$757$	30.7621	1.11807	0.559033	−	0.829145i	$-0.311172\pi$
$757$	30.7621	1.11807	0.559033	+	0.829145i	$0.311172\pi$
$758$	43.4334	1.57757
$759$	19.0820	0.692631
$760$	64.4672	2.33847
$761$	5.34879	0.193894	0.0969468	−	0.995290i	$-0.469092\pi$
$761$	5.34879	0.193894	0.0969468	+	0.995290i	$0.469092\pi$
$762$	−70.2386	−2.54447
$763$	23.0909	0.835946
$764$	15.7416	0.569511
$765$	−11.0284	−0.398733
$766$	−78.5999	−2.83993
$767$	60.6678	2.19059
$768$	−90.4810	−3.26495
$769$	−36.7417	−1.32494	−0.662469	−	0.749089i	$-0.730491\pi$
$769$	−36.7417	−1.32494	−0.662469	+	0.749089i	$0.730491\pi$
$770$	14.3313	0.516465
$771$	49.3188	1.77617
$772$	−116.581	−4.19583
$773$	−3.89610	−0.140133	−0.0700664	−	0.997542i	$-0.522321\pi$
$773$	−3.89610	−0.140133	−0.0700664	+	0.997542i	$0.522321\pi$
$774$	14.4938	0.520970
$775$	6.94460	0.249457
$776$	−50.8577	−1.82569
$777$	−94.9463	−3.40618
$778$	76.0139	2.72523
$779$	−46.8619	−1.67900
$780$	144.940	5.18968
$781$	−15.0536	−0.538661
$782$	−16.3459	−0.584528
$783$	−24.3221	−0.869202
$784$	10.8678	0.388137
$785$	−21.0166	−0.750114
$786$	72.9592	2.60237
$787$	25.7840	0.919101	0.459551	−	0.888152i	$-0.348010\pi$
$787$	25.7840	0.919101	0.459551	+	0.888152i	$0.348010\pi$
$788$	−57.5891	−2.05153
$789$	88.2592	3.14211
$790$	−46.6601	−1.66009
$791$	−14.1104	−0.501707
$792$	−34.8440	−1.23813
$793$	−73.3645	−2.60525
$794$	23.6679	0.839942
$795$	81.3217	2.88418
$796$	6.72321	0.238298
$797$	−38.3742	−1.35928	−0.679642	−	0.733544i	$-0.737865\pi$
$797$	−38.3742	−1.35928	−0.679642	+	0.733544i	$0.737865\pi$
$798$	−120.998	−4.28329
$799$	−9.32808	−0.330004
$800$	5.81916	0.205738
$801$	−16.2435	−0.573937
$802$	−24.5222	−0.865910
$803$	8.80850	0.310845
$804$	−23.2974	−0.821635
$805$	−36.5797	−1.28926
$806$	−78.6822	−2.77146
$807$	34.5360	1.21572
$808$	34.8218	1.22503
$809$	−22.0656	−0.775785	−0.387892	−	0.921705i	$-0.626797\pi$
$809$	−22.0656	−0.775785	−0.387892	+	0.921705i	$0.626797\pi$
$810$	32.2618	1.13357
$811$	9.60537	0.337290	0.168645	−	0.985677i	$-0.446061\pi$
$811$	9.60537	0.337290	0.168645	+	0.985677i	$0.446061\pi$
$812$	−39.0993	−1.37212
$813$	−32.6639	−1.14557
$814$	27.6543	0.969282
$815$	−28.9866	−1.01536
$816$	19.4612	0.681280
$817$	−5.50311	−0.192530
$818$	42.7332	1.49413
$819$	−97.4523	−3.40526
$820$	72.2142	2.52183
$821$	−9.71839	−0.339174	−0.169587	−	0.985515i	$-0.554243\pi$
$821$	−9.71839	−0.339174	−0.169587	+	0.985515i	$0.554243\pi$
$822$	−58.5337	−2.04160
$823$	21.3961	0.745820	0.372910	−	0.927868i	$-0.378360\pi$
$823$	21.3961	0.745820	0.372910	+	0.927868i	$0.378360\pi$
$824$	63.6708	2.21808
$825$	−3.81747	−0.132907
$826$	78.0463	2.71558
$827$	−16.7192	−0.581384	−0.290692	−	0.956817i	$-0.593885\pi$
$827$	−16.7192	−0.581384	−0.290692	+	0.956817i	$0.593885\pi$
$828$	162.926	5.66206
$829$	37.2975	1.29540	0.647698	−	0.761898i	$-0.275732\pi$
$829$	37.2975	1.29540	0.647698	+	0.761898i	$0.275732\pi$
$830$	−64.9131	−2.25317
$831$	−64.8499	−2.24962
$832$	10.2934	0.356860
$833$	1.64973	0.0571599
$834$	−150.384	−5.20737
$835$	−33.8672	−1.17202
$836$	24.2360	0.838221
$837$	−43.3012	−1.49671
$838$	52.2614	1.80534
$839$	9.71689	0.335464	0.167732	−	0.985833i	$-0.446356\pi$
$839$	9.71689	0.335464	0.167732	+	0.985833i	$0.446356\pi$
$840$	101.783	3.51183
$841$	−19.8877	−0.685782
$842$	16.3124	0.562161
$843$	27.5209	0.947871
$844$	62.5285	2.15232
$845$	−39.4184	−1.35604
$846$	135.200	4.64826
$847$	2.94104	0.101055
$848$	−94.1751	−3.23398
$849$	20.9174	0.717884
$850$	3.27010	0.112164
$851$	−70.5855	−2.41964
$852$	−195.856	−6.70990
$853$	−10.3083	−0.352951	−0.176476	−	0.984305i	$-0.556470\pi$
$853$	−10.3083	−0.352951	−0.176476	+	0.984305i	$0.556470\pi$
$854$	−94.3799	−3.22961
$855$	−60.6906	−2.07558
$856$	5.09616	0.174183
$857$	18.3486	0.626775	0.313387	−	0.949625i	$-0.398536\pi$
$857$	18.3486	0.626775	0.313387	+	0.949625i	$0.398536\pi$
$858$	43.2519	1.47659
$859$	40.8353	1.39328	0.696642	−	0.717419i	$-0.254677\pi$
$859$	40.8353	1.39328	0.696642	+	0.717419i	$0.254677\pi$
$860$	8.48029	0.289175
$861$	−73.9869	−2.52147
$862$	5.53161	0.188407
$863$	0.103856	0.00353528	0.00176764	−	0.999998i	$-0.499437\pi$
$863$	0.103856	0.00353528	0.00176764	+	0.999998i	$0.499437\pi$
$864$	−36.2839	−1.23440
$865$	5.19736	0.176716
$866$	22.3607	0.759847
$867$	2.95421	0.100330
$868$	−69.6095	−2.36270
$869$	−9.57549	−0.324826
$870$	−43.4552	−1.47327
$871$	10.3597	0.351025
$872$	−47.7653	−1.61754
$873$	47.8784	1.62044
$874$	−89.9533	−3.04272
$875$	35.6338	1.20464
$876$	114.603	3.87209
$877$	−17.6284	−0.595267	−0.297634	−	0.954680i	$-0.596197\pi$
$877$	−17.6284	−0.595267	−0.297634	+	0.954680i	$0.596197\pi$
$878$	55.0084	1.85644
$879$	−3.71454	−0.125288
$880$	−12.6849	−0.427607
$881$	−6.35470	−0.214095	−0.107048	−	0.994254i	$-0.534140\pi$
$881$	−6.35470	−0.214095	−0.107048	+	0.994254i	$0.534140\pi$
$882$	−23.9110	−0.805124
$883$	2.59468	0.0873180	0.0436590	−	0.999046i	$-0.486098\pi$
$883$	2.59468	0.0873180	0.0436590	+	0.999046i	$0.486098\pi$
$884$	−25.4794	−0.856964
$885$	59.6517	2.00517
$886$	−46.3112	−1.55585
$887$	−10.2875	−0.345420	−0.172710	−	0.984973i	$-0.555252\pi$
$887$	−10.2875	−0.345420	−0.172710	+	0.984973i	$0.555252\pi$
$888$	196.404	6.59087
$889$	27.6317	0.926737
$890$	−13.8201	−0.463250
$891$	6.62070	0.221802
$892$	80.5688	2.69764
$893$	−51.3335	−1.71781
$894$	−32.7439	−1.09512
$895$	−14.9963	−0.501270
$896$	39.7305	1.32730
$897$	−110.397	−3.68606
$898$	31.1977	1.04108
$899$	16.2229	0.541064
$900$	−32.5944	−1.08648
$901$	−14.2958	−0.476261
$902$	21.5496	0.717523
$903$	−8.68847	−0.289134
$904$	29.1884	0.970791
$905$	26.2538	0.872705
$906$	54.2536	1.80246
$907$	−42.3431	−1.40598	−0.702989	−	0.711201i	$-0.748152\pi$
$907$	−42.3431	−1.40598	−0.702989	+	0.711201i	$0.748152\pi$
$908$	−79.8584	−2.65019
$909$	−32.7818	−1.08731
$910$	−82.9128	−2.74853
$911$	49.5328	1.64110	0.820548	−	0.571578i	$-0.193668\pi$
$911$	49.5328	1.64110	0.820548	+	0.571578i	$0.193668\pi$
$912$	107.097	3.54635
$913$	−13.3213	−0.440871
$914$	2.89720	0.0958308
$915$	−72.1356	−2.38473
$916$	55.3342	1.82829
$917$	−28.7020	−0.947823
$918$	−20.3899	−0.672966
$919$	17.8781	0.589743	0.294872	−	0.955537i	$-0.404723\pi$
$919$	17.8781	0.589743	0.294872	+	0.955537i	$0.404723\pi$
$920$	75.6679	2.49470
$921$	57.7508	1.90296
$922$	−35.9480	−1.18388
$923$	87.0916	2.86665
$924$	38.2645	1.25881
$925$	14.1211	0.464298
$926$	39.4942	1.29786
$927$	−59.9408	−1.96872
$928$	13.5938	0.446239
$929$	22.3096	0.731955	0.365977	−	0.930624i	$-0.380735\pi$
$929$	22.3096	0.731955	0.365977	+	0.930624i	$0.380735\pi$
$930$	−77.3643	−2.53688
$931$	9.07867	0.297541
$932$	−39.8733	−1.30609
$933$	−63.6856	−2.08497
$934$	12.2744	0.401631
$935$	−1.92556	−0.0629726
$936$	201.588	6.58910
$937$	2.81013	0.0918029	0.0459014	−	0.998946i	$-0.485384\pi$
$937$	2.81013	0.0918029	0.0459014	+	0.998946i	$0.485384\pi$
$938$	13.3273	0.435150
$939$	−46.1441	−1.50586
$940$	79.1048	2.58011
$941$	−41.8211	−1.36333	−0.681664	−	0.731665i	$-0.738744\pi$
$941$	−41.8211	−1.36333	−0.681664	+	0.731665i	$0.738744\pi$
$942$	−81.5970	−2.65857
$943$	−55.0038	−1.79117
$944$	−69.0800	−2.24836
$945$	−45.6295	−1.48433
$946$	2.53062	0.0822777
$947$	38.4057	1.24802	0.624009	−	0.781418i	$-0.285503\pi$
$947$	38.4057	1.24802	0.624009	+	0.781418i	$0.285503\pi$
$948$	−124.582	−4.04624
$949$	−50.9609	−1.65426
$950$	17.9957	0.583859
$951$	−16.1791	−0.524642
$952$	−17.8926	−0.579904
$953$	34.9557	1.13233	0.566163	−	0.824293i	$-0.308427\pi$
$953$	34.9557	1.13233	0.566163	+	0.824293i	$0.308427\pi$
$954$	207.200	6.70836
$955$	−6.88260	−0.222716
$956$	−93.2842	−3.01703
$957$	−8.91778	−0.288271
$958$	−50.5830	−1.63426
$959$	23.0270	0.743581
$960$	10.1210	0.326654
$961$	−2.11800	−0.0683226
$962$	−159.992	−5.15834
$963$	−4.79762	−0.154601
$964$	13.2551	0.426917
$965$	50.9719	1.64084
$966$	−142.021	−4.56944
$967$	−4.98302	−0.160243	−0.0801215	−	0.996785i	$-0.525531\pi$
$967$	−4.98302	−0.160243	−0.0801215	+	0.996785i	$0.525531\pi$
$968$	−6.08377	−0.195540
$969$	16.2574	0.522262
$970$	40.7351	1.30793
$971$	−28.2273	−0.905858	−0.452929	−	0.891547i	$-0.649621\pi$
$971$	−28.2273	−0.905858	−0.452929	+	0.891547i	$0.649621\pi$
$972$	−20.3150	−0.651602
$973$	59.1607	1.89661
$974$	12.3087	0.394395
$975$	22.0857	0.707308
$976$	83.5371	2.67396
$977$	−9.53862	−0.305167	−0.152584	−	0.988291i	$-0.548759\pi$
$977$	−9.53862	−0.305167	−0.152584	+	0.988291i	$0.548759\pi$
$978$	−112.541	−3.59865
$979$	−2.83612	−0.0906429
$980$	−13.9902	−0.446901
$981$	44.9671	1.43569
$982$	−86.0651	−2.74645
$983$	56.3043	1.79583	0.897914	−	0.440171i	$-0.145082\pi$
$983$	56.3043	1.79583	0.897914	+	0.440171i	$0.145082\pi$
$984$	153.048	4.87898
$985$	25.1794	0.802281
$986$	7.63911	0.243279
$987$	−81.0467	−2.57975
$988$	−140.216	−4.46086
$989$	−6.45923	−0.205392
$990$	27.9088	0.886999
$991$	27.1357	0.861994	0.430997	−	0.902353i	$-0.358162\pi$
$991$	27.1357	0.861994	0.430997	+	0.902353i	$0.358162\pi$
$992$	24.2014	0.768395
$993$	36.1505	1.14720
$994$	112.039	3.55367
$995$	−2.93955	−0.0931900
$996$	−173.317	−5.49177
$997$	12.1480	0.384732	0.192366	−	0.981323i	$-0.438384\pi$
$997$	12.1480	0.384732	0.192366	+	0.981323i	$0.438384\pi$
$998$	−85.6450	−2.71105
$999$	−88.0484	−2.78573

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8041.2.a.c.1.4	✓	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8041.2.a.c.1.4	✓	60	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)

\(f(q)\)	\(=\)	\(q-2.53062 q^{2} +2.95421 q^{3} +4.40406 q^{4} -1.92556 q^{5} -7.47600 q^{6} +2.94104 q^{7} -6.08377 q^{8} +5.72738 q^{9} +O(q^{10})\)	\(q-2.53062 q^{2} +2.95421 q^{3} +4.40406 q^{4} -1.92556 q^{5} -7.47600 q^{6} +2.94104 q^{7} -6.08377 q^{8} +5.72738 q^{9} +4.87287 q^{10} +1.00000 q^{11} +13.0105 q^{12} -5.78542 q^{13} -7.44268 q^{14} -5.68852 q^{15} +6.58762 q^{16} +1.00000 q^{17} -14.4938 q^{18} +5.50311 q^{19} -8.48029 q^{20} +8.68847 q^{21} -2.53062 q^{22} +6.45923 q^{23} -17.9728 q^{24} -1.29221 q^{25} +14.6407 q^{26} +8.05725 q^{27} +12.9525 q^{28} -3.01866 q^{29} +14.3955 q^{30} -5.37420 q^{31} -4.50326 q^{32} +2.95421 q^{33} -2.53062 q^{34} -5.66316 q^{35} +25.2237 q^{36} -10.9278 q^{37} -13.9263 q^{38} -17.0914 q^{39} +11.7147 q^{40} -8.51553 q^{41} -21.9872 q^{42} -1.00000 q^{43} +4.40406 q^{44} -11.0284 q^{45} -16.3459 q^{46} -9.32808 q^{47} +19.4612 q^{48} +1.64973 q^{49} +3.27010 q^{50} +2.95421 q^{51} -25.4794 q^{52} -14.2958 q^{53} -20.3899 q^{54} -1.92556 q^{55} -17.8926 q^{56} +16.2574 q^{57} +7.63911 q^{58} -10.4863 q^{59} -25.0526 q^{60} +12.6809 q^{61} +13.6001 q^{62} +16.8445 q^{63} -1.77920 q^{64} +11.1402 q^{65} -7.47600 q^{66} -1.79065 q^{67} +4.40406 q^{68} +19.0820 q^{69} +14.3313 q^{70} -15.0536 q^{71} -34.8440 q^{72} +8.80850 q^{73} +27.6543 q^{74} -3.81747 q^{75} +24.2360 q^{76} +2.94104 q^{77} +43.2519 q^{78} -9.57549 q^{79} -12.6849 q^{80} +6.62070 q^{81} +21.5496 q^{82} -13.3213 q^{83} +38.2645 q^{84} -1.92556 q^{85} +2.53062 q^{86} -8.91778 q^{87} -6.08377 q^{88} -2.83612 q^{89} +27.9088 q^{90} -17.0152 q^{91} +28.4469 q^{92} -15.8765 q^{93} +23.6059 q^{94} -10.5966 q^{95} -13.3036 q^{96} +8.35957 q^{97} -4.17486 q^{98} +5.72738 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - 9 q^{2} - 6 q^{3} + 43 q^{4} - 15 q^{5} - 4 q^{6} - 17 q^{7} - 21 q^{8} + 40 q^{9}+O(q^{10}) \) 60 * q - 9 * q^2 - 6 * q^3 + 43 * q^4 - 15 * q^5 - 4 * q^6 - 17 * q^7 - 21 * q^8 + 40 * q^9	\( 60 q - 9 q^{2} - 6 q^{3} + 43 q^{4} - 15 q^{5} - 4 q^{6} - 17 q^{7} - 21 q^{8} + 40 q^{9} + q^{10} + 60 q^{11} - 13 q^{12} - 2 q^{13} - 15 q^{14} - 32 q^{15} + 21 q^{16} + 60 q^{17} - 41 q^{18} - 24 q^{19} - 33 q^{20} - 12 q^{21} - 9 q^{22} - 20 q^{23} + 9 q^{24} + 25 q^{25} - 40 q^{26} - 18 q^{27} - 3 q^{28} - 54 q^{29} - 18 q^{30} - 50 q^{31} - 51 q^{32} - 6 q^{33} - 9 q^{34} - 30 q^{35} + 27 q^{36} - 63 q^{37} - 38 q^{38} - 55 q^{39} - 5 q^{40} - 53 q^{41} - 47 q^{42} - 60 q^{43} + 43 q^{44} - 36 q^{45} - 27 q^{46} - 47 q^{47} - 38 q^{48} + 5 q^{49} - 4 q^{50} - 6 q^{51} - 13 q^{52} - 24 q^{53} - 58 q^{54} - 15 q^{55} - 45 q^{56} + 23 q^{57} + 16 q^{58} - 57 q^{59} - 4 q^{60} - 8 q^{61} - 3 q^{62} - 57 q^{63} - 5 q^{64} - 27 q^{65} - 4 q^{66} - 49 q^{67} + 43 q^{68} - 57 q^{69} - 7 q^{70} - 151 q^{71} - 29 q^{72} - 12 q^{73} + 18 q^{74} - 23 q^{75} - 38 q^{76} - 17 q^{77} + 37 q^{78} - 11 q^{79} - 21 q^{80} + 28 q^{81} + 44 q^{82} - 42 q^{83} + 16 q^{84} - 15 q^{85} + 9 q^{86} - 56 q^{87} - 21 q^{88} - 88 q^{89} + 47 q^{90} - 60 q^{91} + 26 q^{92} - 16 q^{93} + 37 q^{94} - 57 q^{95} + 108 q^{96} - 22 q^{97} + 8 q^{98} + 40 q^{99}+O(q^{100}) \) 60 * q - 9 * q^2 - 6 * q^3 + 43 * q^4 - 15 * q^5 - 4 * q^6 - 17 * q^7 - 21 * q^8 + 40 * q^9 + q^10 + 60 * q^11 - 13 * q^12 - 2 * q^13 - 15 * q^14 - 32 * q^15 + 21 * q^16 + 60 * q^17 - 41 * q^18 - 24 * q^19 - 33 * q^20 - 12 * q^21 - 9 * q^22 - 20 * q^23 + 9 * q^24 + 25 * q^25 - 40 * q^26 - 18 * q^27 - 3 * q^28 - 54 * q^29 - 18 * q^30 - 50 * q^31 - 51 * q^32 - 6 * q^33 - 9 * q^34 - 30 * q^35 + 27 * q^36 - 63 * q^37 - 38 * q^38 - 55 * q^39 - 5 * q^40 - 53 * q^41 - 47 * q^42 - 60 * q^43 + 43 * q^44 - 36 * q^45 - 27 * q^46 - 47 * q^47 - 38 * q^48 + 5 * q^49 - 4 * q^50 - 6 * q^51 - 13 * q^52 - 24 * q^53 - 58 * q^54 - 15 * q^55 - 45 * q^56 + 23 * q^57 + 16 * q^58 - 57 * q^59 - 4 * q^60 - 8 * q^61 - 3 * q^62 - 57 * q^63 - 5 * q^64 - 27 * q^65 - 4 * q^66 - 49 * q^67 + 43 * q^68 - 57 * q^69 - 7 * q^70 - 151 * q^71 - 29 * q^72 - 12 * q^73 + 18 * q^74 - 23 * q^75 - 38 * q^76 - 17 * q^77 + 37 * q^78 - 11 * q^79 - 21 * q^80 + 28 * q^81 + 44 * q^82 - 42 * q^83 + 16 * q^84 - 15 * q^85 + 9 * q^86 - 56 * q^87 - 21 * q^88 - 88 * q^89 + 47 * q^90 - 60 * q^91 + 26 * q^92 - 16 * q^93 + 37 * q^94 - 57 * q^95 + 108 * q^96 - 22 * q^97 + 8 * q^98 + 40 * q^99

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