LMFDB - Embedded newform 8043.2.a.t.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8043,2,Mod(1,8043)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8043, 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("8043.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8043 = 3 \cdot 7 \cdot 383 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8043.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:	$64.2236783457$
Analytic rank:	$0$
Dimension:	$52$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Character	$\chi$	$=$	8043.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.28128 q^{2} -1.00000 q^{3} +3.20426 q^{4} +2.19375 q^{5} +2.28128 q^{6} +1.00000 q^{7} -2.74725 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.28128 q^{2} -1.00000 q^{3} +3.20426 q^{4} +2.19375 q^{5} +2.28128 q^{6} +1.00000 q^{7} -2.74725 q^{8} +1.00000 q^{9} -5.00457 q^{10} -5.46288 q^{11} -3.20426 q^{12} -1.92610 q^{13} -2.28128 q^{14} -2.19375 q^{15} -0.141251 q^{16} -3.39222 q^{17} -2.28128 q^{18} +4.43083 q^{19} +7.02934 q^{20} -1.00000 q^{21} +12.4624 q^{22} -5.61925 q^{23} +2.74725 q^{24} -0.187455 q^{25} +4.39397 q^{26} -1.00000 q^{27} +3.20426 q^{28} -4.28623 q^{29} +5.00457 q^{30} +3.43056 q^{31} +5.81674 q^{32} +5.46288 q^{33} +7.73862 q^{34} +2.19375 q^{35} +3.20426 q^{36} -8.18210 q^{37} -10.1080 q^{38} +1.92610 q^{39} -6.02679 q^{40} -6.81620 q^{41} +2.28128 q^{42} +1.40342 q^{43} -17.5045 q^{44} +2.19375 q^{45} +12.8191 q^{46} -7.83905 q^{47} +0.141251 q^{48} +1.00000 q^{49} +0.427638 q^{50} +3.39222 q^{51} -6.17171 q^{52} +3.13136 q^{53} +2.28128 q^{54} -11.9842 q^{55} -2.74725 q^{56} -4.43083 q^{57} +9.77810 q^{58} -1.91066 q^{59} -7.02934 q^{60} -5.52236 q^{61} -7.82609 q^{62} +1.00000 q^{63} -12.9871 q^{64} -4.22538 q^{65} -12.4624 q^{66} -4.20815 q^{67} -10.8695 q^{68} +5.61925 q^{69} -5.00457 q^{70} -7.79993 q^{71} -2.74725 q^{72} +12.9587 q^{73} +18.6657 q^{74} +0.187455 q^{75} +14.1975 q^{76} -5.46288 q^{77} -4.39397 q^{78} -14.7769 q^{79} -0.309871 q^{80} +1.00000 q^{81} +15.5497 q^{82} +11.1649 q^{83} -3.20426 q^{84} -7.44169 q^{85} -3.20161 q^{86} +4.28623 q^{87} +15.0079 q^{88} +2.89981 q^{89} -5.00457 q^{90} -1.92610 q^{91} -18.0055 q^{92} -3.43056 q^{93} +17.8831 q^{94} +9.72014 q^{95} -5.81674 q^{96} +0.436297 q^{97} -2.28128 q^{98} -5.46288 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 52 q + 3 q^{2} - 52 q^{3} + 61 q^{4} - 7 q^{5} - 3 q^{6} + 52 q^{7} + 24 q^{8} + 52 q^{9}+O(q^{10}) $ 52 * q + 3 * q^2 - 52 * q^3 + 61 * q^4 - 7 * q^5 - 3 * q^6 + 52 * q^7 + 24 * q^8 + 52 * q^9	\( 52 q + 3 q^{2} - 52 q^{3} + 61 q^{4} - 7 q^{5} - 3 q^{6} + 52 q^{7} + 24 q^{8} + 52 q^{9} - 2 q^{10} + 9 q^{11} - 61 q^{12} + 44 q^{13} + 3 q^{14} + 7 q^{15} + 95 q^{16} - 6 q^{17} + 3 q^{18} + 7 q^{19} - 21 q^{20} - 52 q^{21} + 19 q^{22} - 4 q^{23} - 24 q^{24} + 83 q^{25} - 5 q^{26} - 52 q^{27} + 61 q^{28} + 31 q^{29} + 2 q^{30} + 11 q^{31} + 71 q^{32} - 9 q^{33} + 17 q^{34} - 7 q^{35} + 61 q^{36} + 71 q^{37} - 8 q^{38} - 44 q^{39} + 20 q^{40} - 25 q^{41} - 3 q^{42} + 75 q^{43} + 14 q^{44} - 7 q^{45} + 36 q^{46} - 20 q^{47} - 95 q^{48} + 52 q^{49} + 26 q^{50} + 6 q^{51} + 88 q^{52} + 70 q^{53} - 3 q^{54} + 12 q^{55} + 24 q^{56} - 7 q^{57} + 48 q^{58} - 27 q^{59} + 21 q^{60} + 59 q^{61} - 23 q^{62} + 52 q^{63} + 138 q^{64} + 44 q^{65} - 19 q^{66} + 65 q^{67} - 8 q^{68} + 4 q^{69} - 2 q^{70} - 11 q^{71} + 24 q^{72} + 34 q^{73} + 38 q^{74} - 83 q^{75} + 31 q^{76} + 9 q^{77} + 5 q^{78} + 74 q^{79} - 5 q^{80} + 52 q^{81} + 51 q^{82} - 30 q^{83} - 61 q^{84} + 70 q^{85} + 29 q^{86} - 31 q^{87} + 90 q^{88} - q^{89} - 2 q^{90} + 44 q^{91} + 34 q^{92} - 11 q^{93} + 27 q^{94} + 9 q^{95} - 71 q^{96} + 73 q^{97} + 3 q^{98} + 9 q^{99}+O(q^{100}) \) 52 * q + 3 * q^2 - 52 * q^3 + 61 * q^4 - 7 * q^5 - 3 * q^6 + 52 * q^7 + 24 * q^8 + 52 * q^9 - 2 * q^10 + 9 * q^11 - 61 * q^12 + 44 * q^13 + 3 * q^14 + 7 * q^15 + 95 * q^16 - 6 * q^17 + 3 * q^18 + 7 * q^19 - 21 * q^20 - 52 * q^21 + 19 * q^22 - 4 * q^23 - 24 * q^24 + 83 * q^25 - 5 * q^26 - 52 * q^27 + 61 * q^28 + 31 * q^29 + 2 * q^30 + 11 * q^31 + 71 * q^32 - 9 * q^33 + 17 * q^34 - 7 * q^35 + 61 * q^36 + 71 * q^37 - 8 * q^38 - 44 * q^39 + 20 * q^40 - 25 * q^41 - 3 * q^42 + 75 * q^43 + 14 * q^44 - 7 * q^45 + 36 * q^46 - 20 * q^47 - 95 * q^48 + 52 * q^49 + 26 * q^50 + 6 * q^51 + 88 * q^52 + 70 * q^53 - 3 * q^54 + 12 * q^55 + 24 * q^56 - 7 * q^57 + 48 * q^58 - 27 * q^59 + 21 * q^60 + 59 * q^61 - 23 * q^62 + 52 * q^63 + 138 * q^64 + 44 * q^65 - 19 * q^66 + 65 * q^67 - 8 * q^68 + 4 * q^69 - 2 * q^70 - 11 * q^71 + 24 * q^72 + 34 * q^73 + 38 * q^74 - 83 * q^75 + 31 * q^76 + 9 * q^77 + 5 * q^78 + 74 * q^79 - 5 * q^80 + 52 * q^81 + 51 * q^82 - 30 * q^83 - 61 * q^84 + 70 * q^85 + 29 * q^86 - 31 * q^87 + 90 * q^88 - q^89 - 2 * q^90 + 44 * q^91 + 34 * q^92 - 11 * q^93 + 27 * q^94 + 9 * q^95 - 71 * q^96 + 73 * q^97 + 3 * q^98 + 9 * 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 $

$2$	−2.28128	−1.61311	−0.806556	−	0.591158i	$-0.798671\pi$
$2$	−2.28128	−1.61311	−0.806556	+	0.591158i	$0.798671\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	3.20426	1.60213
$5$	2.19375	0.981075	0.490538	−	0.871420i	$-0.336800\pi$
$5$	2.19375	0.981075	0.490538	+	0.871420i	$0.336800\pi$
$6$	2.28128	0.931330
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−2.74725	−0.971300
$9$	1.00000	0.333333
$10$	−5.00457	−1.58258
$11$	−5.46288	−1.64712	−0.823560	−	0.567228i	$-0.808016\pi$
$11$	−5.46288	−1.64712	−0.823560	+	0.567228i	$0.808016\pi$
$12$	−3.20426	−0.924989
$13$	−1.92610	−0.534203	−0.267102	−	0.963668i	$-0.586066\pi$
$13$	−1.92610	−0.534203	−0.267102	+	0.963668i	$0.586066\pi$
$14$	−2.28128	−0.609699
$15$	−2.19375	−0.566424
$16$	−0.141251	−0.0353129
$17$	−3.39222	−0.822734	−0.411367	−	0.911470i	$-0.634949\pi$
$17$	−3.39222	−0.822734	−0.411367	+	0.911470i	$0.634949\pi$
$18$	−2.28128	−0.537704
$19$	4.43083	1.01650	0.508251	−	0.861209i	$-0.330292\pi$
$19$	4.43083	1.01650	0.508251	+	0.861209i	$0.330292\pi$
$20$	7.02934	1.57181
$21$	−1.00000	−0.218218
$22$	12.4624	2.65699
$23$	−5.61925	−1.17169	−0.585847	−	0.810422i	$-0.699238\pi$
$23$	−5.61925	−1.17169	−0.585847	+	0.810422i	$0.699238\pi$
$24$	2.74725	0.560780
$25$	−0.187455	−0.0374909
$26$	4.39397	0.861729
$27$	−1.00000	−0.192450
$28$	3.20426	0.605548
$29$	−4.28623	−0.795932	−0.397966	−	0.917400i	$-0.630284\pi$
$29$	−4.28623	−0.795932	−0.397966	+	0.917400i	$0.630284\pi$
$30$	5.00457	0.913705
$31$	3.43056	0.616148	0.308074	−	0.951362i	$-0.400316\pi$
$31$	3.43056	0.616148	0.308074	+	0.951362i	$0.400316\pi$
$32$	5.81674	1.02826
$33$	5.46288	0.950966
$34$	7.73862	1.32716
$35$	2.19375	0.370812
$36$	3.20426	0.534043
$37$	−8.18210	−1.34513	−0.672565	−	0.740038i	$-0.734807\pi$
$37$	−8.18210	−1.34513	−0.672565	+	0.740038i	$0.734807\pi$
$38$	−10.1080	−1.63973
$39$	1.92610	0.308422
$40$	−6.02679	−0.952919
$41$	−6.81620	−1.06451	−0.532256	−	0.846584i	$-0.678655\pi$
$41$	−6.81620	−1.06451	−0.532256	+	0.846584i	$0.678655\pi$
$42$	2.28128	0.352010
$43$	1.40342	0.214020	0.107010	−	0.994258i	$-0.465872\pi$
$43$	1.40342	0.214020	0.107010	+	0.994258i	$0.465872\pi$
$44$	−17.5045	−2.63890
$45$	2.19375	0.327025
$46$	12.8191	1.89007
$47$	−7.83905	−1.14344	−0.571721	−	0.820448i	$-0.693724\pi$
$47$	−7.83905	−1.14344	−0.571721	+	0.820448i	$0.693724\pi$
$48$	0.141251	0.0203879
$49$	1.00000	0.142857
$50$	0.427638	0.0604771
$51$	3.39222	0.475006
$52$	−6.17171	−0.855862
$53$	3.13136	0.430126	0.215063	−	0.976600i	$-0.431004\pi$
$53$	3.13136	0.430126	0.215063	+	0.976600i	$0.431004\pi$
$54$	2.28128	0.310443
$55$	−11.9842	−1.61595
$56$	−2.74725	−0.367117
$57$	−4.43083	−0.586878
$58$	9.77810	1.28393
$59$	−1.91066	−0.248746	−0.124373	−	0.992236i	$-0.539692\pi$
$59$	−1.91066	−0.248746	−0.124373	+	0.992236i	$0.539692\pi$
$60$	−7.02934	−0.907484
$61$	−5.52236	−0.707065	−0.353533	−	0.935422i	$-0.615020\pi$
$61$	−5.52236	−0.707065	−0.353533	+	0.935422i	$0.615020\pi$
$62$	−7.82609	−0.993915
$63$	1.00000	0.125988
$64$	−12.9871	−1.62339
$65$	−4.22538	−0.524094
$66$	−12.4624	−1.53401
$67$	−4.20815	−0.514107	−0.257054	−	0.966397i	$-0.582752\pi$
$67$	−4.20815	−0.514107	−0.257054	+	0.966397i	$0.582752\pi$
$68$	−10.8695	−1.31813
$69$	5.61925	0.676478
$70$	−5.00457	−0.598161
$71$	−7.79993	−0.925682	−0.462841	−	0.886441i	$-0.653170\pi$
$71$	−7.79993	−0.925682	−0.462841	+	0.886441i	$0.653170\pi$
$72$	−2.74725	−0.323767
$73$	12.9587	1.51670	0.758351	−	0.651847i	$-0.226005\pi$
$73$	12.9587	1.51670	0.758351	+	0.651847i	$0.226005\pi$
$74$	18.6657	2.16984
$75$	0.187455	0.0216454
$76$	14.1975	1.62857
$77$	−5.46288	−0.622553
$78$	−4.39397	−0.497520
$79$	−14.7769	−1.66253	−0.831265	−	0.555876i	$-0.812383\pi$
$79$	−14.7769	−1.66253	−0.831265	+	0.555876i	$0.812383\pi$
$80$	−0.309871	−0.0346446
$81$	1.00000	0.111111
$82$	15.5497	1.71718
$83$	11.1649	1.22551	0.612753	−	0.790275i	$-0.290062\pi$
$83$	11.1649	1.22551	0.612753	+	0.790275i	$0.290062\pi$
$84$	−3.20426	−0.349613
$85$	−7.44169	−0.807164
$86$	−3.20161	−0.345238
$87$	4.28623	0.459532
$88$	15.0079	1.59985
$89$	2.89981	0.307380	0.153690	−	0.988119i	$-0.450884\pi$
$89$	2.89981	0.307380	0.153690	+	0.988119i	$0.450884\pi$
$90$	−5.00457	−0.527528
$91$	−1.92610	−0.201910
$92$	−18.0055	−1.87720
$93$	−3.43056	−0.355733
$94$	17.8831	1.84450
$95$	9.72014	0.997265
$96$	−5.81674	−0.593668
$97$	0.436297	0.0442993	0.0221496	−	0.999755i	$-0.492949\pi$
$97$	0.436297	0.0442993	0.0221496	+	0.999755i	$0.492949\pi$
$98$	−2.28128	−0.230444
$99$	−5.46288	−0.549040
$100$	−0.600653	−0.0600653
$101$	14.3744	1.43030	0.715152	−	0.698969i	$-0.246358\pi$
$101$	14.3744	1.43030	0.715152	+	0.698969i	$0.246358\pi$
$102$	−7.73862	−0.766237
$103$	8.82271	0.869328	0.434664	−	0.900593i	$-0.356867\pi$
$103$	8.82271	0.869328	0.434664	+	0.900593i	$0.356867\pi$
$104$	5.29147	0.518872
$105$	−2.19375	−0.214088
$106$	−7.14352	−0.693840
$107$	6.13689	0.593275	0.296638	−	0.954990i	$-0.404135\pi$
$107$	6.13689	0.593275	0.296638	+	0.954990i	$0.404135\pi$
$108$	−3.20426	−0.308330
$109$	−9.50038	−0.909972	−0.454986	−	0.890499i	$-0.650356\pi$
$109$	−9.50038	−0.909972	−0.454986	+	0.890499i	$0.650356\pi$
$110$	27.3394	2.60671
$111$	8.18210	0.776611
$112$	−0.141251	−0.0133470
$113$	5.69556	0.535793	0.267896	−	0.963448i	$-0.413672\pi$
$113$	5.69556	0.535793	0.267896	+	0.963448i	$0.413672\pi$
$114$	10.1080	0.946699
$115$	−12.3272	−1.14952
$116$	−13.7342	−1.27519
$117$	−1.92610	−0.178068
$118$	4.35875	0.401256
$119$	−3.39222	−0.310964
$120$	6.02679	0.550168
$121$	18.8431	1.71301
$122$	12.5981	1.14058
$123$	6.81620	0.614596
$124$	10.9924	0.987148
$125$	−11.3800	−1.01786
$126$	−2.28128	−0.203233
$127$	8.28600	0.735263	0.367632	−	0.929971i	$-0.380169\pi$
$127$	8.28600	0.735263	0.367632	+	0.929971i	$0.380169\pi$
$128$	17.9939	1.59045
$129$	−1.40342	−0.123565
$130$	9.63929	0.845422
$131$	1.05531	0.0922027	0.0461014	−	0.998937i	$-0.485320\pi$
$131$	1.05531	0.0922027	0.0461014	+	0.998937i	$0.485320\pi$
$132$	17.5045	1.52357
$133$	4.43083	0.384202
$134$	9.59998	0.829312
$135$	−2.19375	−0.188808
$136$	9.31928	0.799122
$137$	17.6510	1.50803	0.754015	−	0.656857i	$-0.228115\pi$
$137$	17.6510	1.50803	0.754015	+	0.656857i	$0.228115\pi$
$138$	−12.8191	−1.09123
$139$	6.79197	0.576087	0.288044	−	0.957617i	$-0.406995\pi$
$139$	6.79197	0.576087	0.288044	+	0.957617i	$0.406995\pi$
$140$	7.02934	0.594088
$141$	7.83905	0.660167
$142$	17.7939	1.49323
$143$	10.5220	0.879897
$144$	−0.141251	−0.0117710
$145$	−9.40292	−0.780870
$146$	−29.5625	−2.44661
$147$	−1.00000	−0.0824786
$148$	−26.2176	−2.15507
$149$	−3.84397	−0.314910	−0.157455	−	0.987526i	$-0.550329\pi$
$149$	−3.84397	−0.314910	−0.157455	+	0.987526i	$0.550329\pi$
$150$	−0.427638	−0.0349165
$151$	16.4355	1.33750	0.668752	−	0.743485i	$-0.266829\pi$
$151$	16.4355	1.33750	0.668752	+	0.743485i	$0.266829\pi$
$152$	−12.1726	−0.987329
$153$	−3.39222	−0.274245
$154$	12.4624	1.00425
$155$	7.52581	0.604487
$156$	6.17171	0.494132
$157$	10.7735	0.859819	0.429909	−	0.902872i	$-0.358545\pi$
$157$	10.7735	0.859819	0.429909	+	0.902872i	$0.358545\pi$
$158$	33.7103	2.68185
$159$	−3.13136	−0.248333
$160$	12.7605	1.00880
$161$	−5.61925	−0.442859
$162$	−2.28128	−0.179235
$163$	3.40427	0.266643	0.133322	−	0.991073i	$-0.457436\pi$
$163$	3.40427	0.266643	0.133322	+	0.991073i	$0.457436\pi$
$164$	−21.8408	−1.70548
$165$	11.9842	0.932969
$166$	−25.4703	−1.97688
$167$	−0.0615062	−0.00475949	−0.00237975	−	0.999997i	$-0.500757\pi$
$167$	−0.0615062	−0.00475949	−0.00237975	+	0.999997i	$0.500757\pi$
$168$	2.74725	0.211955
$169$	−9.29015	−0.714627
$170$	16.9766	1.30205
$171$	4.43083	0.338834
$172$	4.49693	0.342888
$173$	7.48230	0.568869	0.284435	−	0.958695i	$-0.408194\pi$
$173$	7.48230	0.568869	0.284435	+	0.958695i	$0.408194\pi$
$174$	−9.77810	−0.741276
$175$	−0.187455	−0.0141702
$176$	0.771640	0.0581646
$177$	1.91066	0.143614
$178$	−6.61530	−0.495837
$179$	13.8749	1.03706	0.518529	−	0.855060i	$-0.326480\pi$
$179$	13.8749	1.03706	0.518529	+	0.855060i	$0.326480\pi$
$180$	7.02934	0.523936
$181$	18.1717	1.35069	0.675346	−	0.737501i	$-0.263994\pi$
$181$	18.1717	1.35069	0.675346	+	0.737501i	$0.263994\pi$
$182$	4.39397	0.325703
$183$	5.52236	0.408224
$184$	15.4375	1.13807
$185$	−17.9495	−1.31967
$186$	7.82609	0.573837
$187$	18.5313	1.35514
$188$	−25.1183	−1.83194
$189$	−1.00000	−0.0727393
$190$	−22.1744	−1.60870
$191$	−12.1055	−0.875926	−0.437963	−	0.898993i	$-0.644300\pi$
$191$	−12.1055	−0.875926	−0.437963	+	0.898993i	$0.644300\pi$
$192$	12.9871	0.937265
$193$	17.8606	1.28564	0.642819	−	0.766018i	$-0.277765\pi$
$193$	17.8606	1.28564	0.642819	+	0.766018i	$0.277765\pi$
$194$	−0.995318	−0.0714597
$195$	4.22538	0.302586
$196$	3.20426	0.228875
$197$	0.905420	0.0645085	0.0322542	−	0.999480i	$-0.489731\pi$
$197$	0.905420	0.0645085	0.0322542	+	0.999480i	$0.489731\pi$
$198$	12.4624	0.885663
$199$	28.0185	1.98618	0.993089	−	0.117368i	$-0.0374456\pi$
$199$	28.0185	1.98618	0.993089	+	0.117368i	$0.0374456\pi$
$200$	0.514985	0.0364150
$201$	4.20815	0.296820
$202$	−32.7920	−2.30724
$203$	−4.28623	−0.300834
$204$	10.8695	0.761020
$205$	−14.9530	−1.04437
$206$	−20.1271	−1.40232
$207$	−5.61925	−0.390565
$208$	0.272064	0.0188642
$209$	−24.2051	−1.67430
$210$	5.00457	0.345348
$211$	1.39710	0.0961806	0.0480903	−	0.998843i	$-0.484686\pi$
$211$	1.39710	0.0961806	0.0480903	+	0.998843i	$0.484686\pi$
$212$	10.0337	0.689116
$213$	7.79993	0.534442
$214$	−14.0000	−0.957019
$215$	3.07876	0.209970
$216$	2.74725	0.186927
$217$	3.43056	0.232882
$218$	21.6731	1.46789
$219$	−12.9587	−0.875668
$220$	−38.4005	−2.58896
$221$	6.53374	0.439507
$222$	−18.6657	−1.25276
$223$	−2.97094	−0.198949	−0.0994744	−	0.995040i	$-0.531716\pi$
$223$	−2.97094	−0.198949	−0.0994744	+	0.995040i	$0.531716\pi$
$224$	5.81674	0.388647
$225$	−0.187455	−0.0124970
$226$	−12.9932	−0.864293
$227$	−20.5827	−1.36612	−0.683062	−	0.730360i	$-0.739352\pi$
$227$	−20.5827	−1.36612	−0.683062	+	0.730360i	$0.739352\pi$
$228$	−14.1975	−0.940254
$229$	29.7267	1.96439	0.982196	−	0.187857i	$-0.0601542\pi$
$229$	29.7267	1.96439	0.982196	+	0.187857i	$0.0601542\pi$
$230$	28.1219	1.85430
$231$	5.46288	0.359431
$232$	11.7753	0.773089
$233$	−20.3326	−1.33203	−0.666017	−	0.745937i	$-0.732002\pi$
$233$	−20.3326	−1.33203	−0.666017	+	0.745937i	$0.732002\pi$
$234$	4.39397	0.287243
$235$	−17.1969	−1.12180
$236$	−6.12224	−0.398524
$237$	14.7769	0.959862
$238$	7.73862	0.501620
$239$	−12.7437	−0.824324	−0.412162	−	0.911111i	$-0.635226\pi$
$239$	−12.7437	−0.824324	−0.412162	+	0.911111i	$0.635226\pi$
$240$	0.309871	0.0200021
$241$	13.5865	0.875183	0.437592	−	0.899174i	$-0.355832\pi$
$241$	13.5865	0.875183	0.437592	+	0.899174i	$0.355832\pi$
$242$	−42.9864	−2.76327
$243$	−1.00000	−0.0641500
$244$	−17.6951	−1.13281
$245$	2.19375	0.140154
$246$	−15.5497	−0.991412
$247$	−8.53421	−0.543019
$248$	−9.42463	−0.598464
$249$	−11.1649	−0.707546
$250$	25.9610	1.64192
$251$	−28.3298	−1.78816	−0.894080	−	0.447907i	$-0.852169\pi$
$251$	−28.3298	−1.78816	−0.894080	+	0.447907i	$0.852169\pi$
$252$	3.20426	0.201849
$253$	30.6973	1.92992
$254$	−18.9027	−1.18606
$255$	7.44169	0.466016
$256$	−15.0748	−0.942177
$257$	28.0780	1.75146	0.875730	−	0.482801i	$-0.160380\pi$
$257$	28.0780	1.75146	0.875730	+	0.482801i	$0.160380\pi$
$258$	3.20161	0.199323
$259$	−8.18210	−0.508411
$260$	−13.5392	−0.839665
$261$	−4.28623	−0.265311
$262$	−2.40746	−0.148733
$263$	−18.0835	−1.11508	−0.557540	−	0.830150i	$-0.688255\pi$
$263$	−18.0835	−1.11508	−0.557540	+	0.830150i	$0.688255\pi$
$264$	−15.0079	−0.923673
$265$	6.86943	0.421986
$266$	−10.1080	−0.619760
$267$	−2.89981	−0.177466
$268$	−13.4840	−0.823666
$269$	16.8302	1.02616	0.513078	−	0.858342i	$-0.328505\pi$
$269$	16.8302	1.02616	0.513078	+	0.858342i	$0.328505\pi$
$270$	5.00457	0.304568
$271$	11.4478	0.695405	0.347702	−	0.937605i	$-0.386962\pi$
$271$	11.4478	0.695405	0.347702	+	0.937605i	$0.386962\pi$
$272$	0.479156	0.0290531
$273$	1.92610	0.116573
$274$	−40.2670	−2.43262
$275$	1.02404	0.0617521
$276$	18.0055	1.08380
$277$	−4.25874	−0.255883	−0.127941	−	0.991782i	$-0.540837\pi$
$277$	−4.25874	−0.255883	−0.127941	+	0.991782i	$0.540837\pi$
$278$	−15.4944	−0.929293
$279$	3.43056	0.205383
$280$	−6.02679	−0.360169
$281$	5.79790	0.345874	0.172937	−	0.984933i	$-0.444674\pi$
$281$	5.79790	0.345874	0.172937	+	0.984933i	$0.444674\pi$
$282$	−17.8831	−1.06492
$283$	−28.1059	−1.67072	−0.835360	−	0.549704i	$-0.814741\pi$
$283$	−28.1059	−1.67072	−0.835360	+	0.549704i	$0.814741\pi$
$284$	−24.9930	−1.48306
$285$	−9.72014	−0.575771
$286$	−24.0038	−1.41937
$287$	−6.81620	−0.402347
$288$	5.81674	0.342755
$289$	−5.49285	−0.323109
$290$	21.4507	1.25963
$291$	−0.436297	−0.0255762
$292$	41.5230	2.42995
$293$	16.5857	0.968946	0.484473	−	0.874806i	$-0.339011\pi$
$293$	16.5857	0.968946	0.484473	+	0.874806i	$0.339011\pi$
$294$	2.28128	0.133047
$295$	−4.19151	−0.244039
$296$	22.4783	1.30652
$297$	5.46288	0.316989
$298$	8.76919	0.507985
$299$	10.8232	0.625923
$300$	0.600653	0.0346787
$301$	1.40342	0.0808920
$302$	−37.4941	−2.15754
$303$	−14.3744	−0.825786
$304$	−0.625861	−0.0358956
$305$	−12.1147	−0.693685
$306$	7.73862	0.442387
$307$	21.2542	1.21304	0.606519	−	0.795069i	$-0.292565\pi$
$307$	21.2542	1.21304	0.606519	+	0.795069i	$0.292565\pi$
$308$	−17.5045	−0.997410
$309$	−8.82271	−0.501907
$310$	−17.1685	−0.975105
$311$	2.45714	0.139332	0.0696659	−	0.997570i	$-0.477807\pi$
$311$	2.45714	0.139332	0.0696659	+	0.997570i	$0.477807\pi$
$312$	−5.29147	−0.299571
$313$	8.75490	0.494856	0.247428	−	0.968906i	$-0.420415\pi$
$313$	8.75490	0.494856	0.247428	+	0.968906i	$0.420415\pi$
$314$	−24.5774	−1.38698
$315$	2.19375	0.123604
$316$	−47.3489	−2.66359
$317$	−4.77605	−0.268250	−0.134125	−	0.990964i	$-0.542822\pi$
$317$	−4.77605	−0.268250	−0.134125	+	0.990964i	$0.542822\pi$
$318$	7.14352	0.400589
$319$	23.4152	1.31100
$320$	−28.4905	−1.59267
$321$	−6.13689	−0.342528
$322$	12.8191	0.714380
$323$	−15.0303	−0.836311
$324$	3.20426	0.178014
$325$	0.361056	0.0200278
$326$	−7.76611	−0.430125
$327$	9.50038	0.525372
$328$	18.7258	1.03396
$329$	−7.83905	−0.432181
$330$	−27.3394	−1.50498
$331$	8.21512	0.451544	0.225772	−	0.974180i	$-0.427510\pi$
$331$	8.21512	0.451544	0.225772	+	0.974180i	$0.427510\pi$
$332$	35.7752	1.96342
$333$	−8.18210	−0.448377
$334$	0.140313	0.00767759
$335$	−9.23163	−0.504378
$336$	0.141251	0.00770590
$337$	10.0724	0.548681	0.274341	−	0.961633i	$-0.411540\pi$
$337$	10.0724	0.548681	0.274341	+	0.961633i	$0.411540\pi$
$338$	21.1935	1.15277
$339$	−5.69556	−0.309340
$340$	−23.8451	−1.29318
$341$	−18.7408	−1.01487
$342$	−10.1080	−0.546577
$343$	1.00000	0.0539949
$344$	−3.85556	−0.207878
$345$	12.3272	0.663676
$346$	−17.0693	−0.917649
$347$	10.9984	0.590425	0.295212	−	0.955432i	$-0.404610\pi$
$347$	10.9984	0.590425	0.295212	+	0.955432i	$0.404610\pi$
$348$	13.7342	0.736229
$349$	11.3989	0.610167	0.305084	−	0.952326i	$-0.401316\pi$
$349$	11.3989	0.610167	0.305084	+	0.952326i	$0.401316\pi$
$350$	0.427638	0.0228582
$351$	1.92610	0.102807
$352$	−31.7762	−1.69367
$353$	−18.4733	−0.983235	−0.491618	−	0.870811i	$-0.663594\pi$
$353$	−18.4733	−0.983235	−0.491618	+	0.870811i	$0.663594\pi$
$354$	−4.35875	−0.231665
$355$	−17.1111	−0.908163
$356$	9.29174	0.492461
$357$	3.39222	0.179535
$358$	−31.6526	−1.67289
$359$	−29.9687	−1.58169	−0.790844	−	0.612018i	$-0.790358\pi$
$359$	−29.9687	−1.58169	−0.790844	+	0.612018i	$0.790358\pi$
$360$	−6.02679	−0.317640
$361$	0.632252	0.0332764
$362$	−41.4548	−2.17882
$363$	−18.8431	−0.989005
$364$	−6.17171	−0.323486
$365$	28.4282	1.48800
$366$	−12.5981	−0.658511
$367$	25.6218	1.33745	0.668725	−	0.743510i	$-0.266840\pi$
$367$	25.6218	1.33745	0.668725	+	0.743510i	$0.266840\pi$
$368$	0.793727	0.0413759
$369$	−6.81620	−0.354837
$370$	40.9479	2.12878
$371$	3.13136	0.162572
$372$	−10.9924	−0.569930
$373$	−26.6011	−1.37735	−0.688675	−	0.725070i	$-0.741807\pi$
$373$	−26.6011	−1.37735	−0.688675	+	0.725070i	$0.741807\pi$
$374$	−42.2751	−2.18600
$375$	11.3800	0.587660
$376$	21.5358	1.11063
$377$	8.25569	0.425190
$378$	2.28128	0.117337
$379$	−25.3810	−1.30374	−0.651868	−	0.758332i	$-0.726014\pi$
$379$	−25.3810	−1.30374	−0.651868	+	0.758332i	$0.726014\pi$
$380$	31.1458	1.59775
$381$	−8.28600	−0.424505
$382$	27.6162	1.41297
$383$	−1.00000	−0.0510976
$383$	−1.00000	−0.0510976
$384$	−17.9939	−0.918245
$385$	−11.9842	−0.610772
$386$	−40.7452	−2.07388
$387$	1.40342	0.0713400
$388$	1.39801	0.0709732
$389$	−10.3706	−0.525811	−0.262906	−	0.964822i	$-0.584681\pi$
$389$	−10.3706	−0.525811	−0.262906	+	0.964822i	$0.584681\pi$
$390$	−9.63929	−0.488104
$391$	19.0617	0.963992
$392$	−2.74725	−0.138757
$393$	−1.05531	−0.0532333
$394$	−2.06552	−0.104059
$395$	−32.4168	−1.63107
$396$	−17.5045	−0.879633
$397$	−24.1372	−1.21141	−0.605705	−	0.795689i	$-0.707109\pi$
$397$	−24.1372	−1.21141	−0.605705	+	0.795689i	$0.707109\pi$
$398$	−63.9181	−3.20392
$399$	−4.43083	−0.221819
$400$	0.0264783	0.00132391
$401$	−29.8872	−1.49250	−0.746249	−	0.665667i	$-0.768147\pi$
$401$	−29.8872	−1.49250	−0.746249	+	0.665667i	$0.768147\pi$
$402$	−9.59998	−0.478804
$403$	−6.60760	−0.329148
$404$	46.0592	2.29153
$405$	2.19375	0.109008
$406$	9.77810	0.485279
$407$	44.6979	2.21559
$408$	−9.31928	−0.461373
$409$	−11.5768	−0.572437	−0.286219	−	0.958164i	$-0.592398\pi$
$409$	−11.5768	−0.572437	−0.286219	+	0.958164i	$0.592398\pi$
$410$	34.1121	1.68468
$411$	−17.6510	−0.870662
$412$	28.2702	1.39277
$413$	−1.91066	−0.0940173
$414$	12.8191	0.630024
$415$	24.4930	1.20231
$416$	−11.2036	−0.549302
$417$	−6.79197	−0.332604
$418$	55.2187	2.70084
$419$	−16.0627	−0.784716	−0.392358	−	0.919813i	$-0.628340\pi$
$419$	−16.0627	−0.784716	−0.392358	+	0.919813i	$0.628340\pi$
$420$	−7.02934	−0.342997
$421$	−10.5434	−0.513854	−0.256927	−	0.966431i	$-0.582710\pi$
$421$	−10.5434	−0.513854	−0.256927	+	0.966431i	$0.582710\pi$
$422$	−3.18719	−0.155150
$423$	−7.83905	−0.381148
$424$	−8.60264	−0.417781
$425$	0.635888	0.0308451
$426$	−17.7939	−0.862115
$427$	−5.52236	−0.267246
$428$	19.6642	0.950503
$429$	−10.5220	−0.508009
$430$	−7.02353	−0.338705
$431$	22.8062	1.09853	0.549267	−	0.835647i	$-0.314907\pi$
$431$	22.8062	1.09853	0.549267	+	0.835647i	$0.314907\pi$
$432$	0.141251	0.00679596
$433$	−8.04282	−0.386513	−0.193257	−	0.981148i	$-0.561905\pi$
$433$	−8.04282	−0.386513	−0.193257	+	0.981148i	$0.561905\pi$
$434$	−7.82609	−0.375664
$435$	9.40292	0.450835
$436$	−30.4417	−1.45789
$437$	−24.8979	−1.19103
$438$	29.5625	1.41255
$439$	15.0166	0.716701	0.358351	−	0.933587i	$-0.383339\pi$
$439$	15.0166	0.716701	0.358351	+	0.933587i	$0.383339\pi$
$440$	32.9236	1.56957
$441$	1.00000	0.0476190
$442$	−14.9053	−0.708974
$443$	7.00952	0.333032	0.166516	−	0.986039i	$-0.446748\pi$
$443$	7.00952	0.333032	0.166516	+	0.986039i	$0.446748\pi$
$444$	26.2176	1.24423
$445$	6.36147	0.301562
$446$	6.77755	0.320927
$447$	3.84397	0.181814
$448$	−12.9871	−0.613584
$449$	30.5637	1.44239	0.721195	−	0.692732i	$-0.243593\pi$
$449$	30.5637	1.44239	0.721195	+	0.692732i	$0.243593\pi$
$450$	0.427638	0.0201590
$451$	37.2361	1.75338
$452$	18.2500	0.858409
$453$	−16.4355	−0.772209
$454$	46.9551	2.20371
$455$	−4.22538	−0.198089
$456$	12.1726	0.570035
$457$	18.3199	0.856970	0.428485	−	0.903549i	$-0.359048\pi$
$457$	18.3199	0.856970	0.428485	+	0.903549i	$0.359048\pi$
$458$	−67.8149	−3.16878
$459$	3.39222	0.158335
$460$	−39.4996	−1.84168
$461$	25.4410	1.18490	0.592452	−	0.805605i	$-0.298160\pi$
$461$	25.4410	1.18490	0.592452	+	0.805605i	$0.298160\pi$
$462$	−12.4624	−0.579803
$463$	9.08976	0.422437	0.211219	−	0.977439i	$-0.432257\pi$
$463$	9.08976	0.422437	0.211219	+	0.977439i	$0.432257\pi$
$464$	0.605436	0.0281066
$465$	−7.52581	−0.349001
$466$	46.3845	2.14872
$467$	14.9405	0.691365	0.345683	−	0.938351i	$-0.387647\pi$
$467$	14.9405	0.691365	0.345683	+	0.938351i	$0.387647\pi$
$468$	−6.17171	−0.285287
$469$	−4.20815	−0.194314
$470$	39.2311	1.80959
$471$	−10.7735	−0.496417
$472$	5.24906	0.241607
$473$	−7.66674	−0.352517
$474$	−33.7103	−1.54836
$475$	−0.830580	−0.0381096
$476$	−10.8695	−0.498205
$477$	3.13136	0.143375
$478$	29.0721	1.32973
$479$	6.43845	0.294180	0.147090	−	0.989123i	$-0.453009\pi$
$479$	6.43845	0.294180	0.147090	+	0.989123i	$0.453009\pi$
$480$	−12.7605	−0.582434
$481$	15.7595	0.718573
$482$	−30.9947	−1.41177
$483$	5.61925	0.255685
$484$	60.3781	2.74446
$485$	0.957128	0.0434609
$486$	2.28128	0.103481
$487$	−20.3815	−0.923575	−0.461788	−	0.886991i	$-0.652792\pi$
$487$	−20.3815	−0.923575	−0.461788	+	0.886991i	$0.652792\pi$
$488$	15.1713	0.686773
$489$	−3.40427	−0.153946
$490$	−5.00457	−0.226083
$491$	38.1855	1.72329	0.861644	−	0.507514i	$-0.169435\pi$
$491$	38.1855	1.72329	0.861644	+	0.507514i	$0.169435\pi$
$492$	21.8408	0.984662
$493$	14.5398	0.654841
$494$	19.4690	0.875950
$495$	−11.9842	−0.538650
$496$	−0.484572	−0.0217579
$497$	−7.79993	−0.349875
$498$	25.4703	1.14135
$499$	−13.1560	−0.588944	−0.294472	−	0.955660i	$-0.595144\pi$
$499$	−13.1560	−0.588944	−0.294472	+	0.955660i	$0.595144\pi$
$500$	−36.4644	−1.63074
$501$	0.0615062	0.00274790
$502$	64.6283	2.88450
$503$	33.6597	1.50081	0.750406	−	0.660977i	$-0.229858\pi$
$503$	33.6597	1.50081	0.750406	+	0.660977i	$0.229858\pi$
$504$	−2.74725	−0.122372
$505$	31.5338	1.40324
$506$	−70.0292	−3.11318
$507$	9.29015	0.412590
$508$	26.5505	1.17799
$509$	2.55359	0.113186	0.0565930	−	0.998397i	$-0.481976\pi$
$509$	2.55359	0.113186	0.0565930	+	0.998397i	$0.481976\pi$
$510$	−16.9766	−0.751736
$511$	12.9587	0.573259
$512$	−1.59773	−0.0706103
$513$	−4.43083	−0.195626
$514$	−64.0540	−2.82530
$515$	19.3548	0.852876
$516$	−4.49693	−0.197966
$517$	42.8238	1.88339
$518$	18.6657	0.820124
$519$	−7.48230	−0.328437
$520$	11.6082	0.509052
$521$	−9.53258	−0.417630	−0.208815	−	0.977955i	$-0.566961\pi$
$521$	−9.53258	−0.417630	−0.208815	+	0.977955i	$0.566961\pi$
$522$	9.77810	0.427976
$523$	−16.2112	−0.708868	−0.354434	−	0.935081i	$-0.615326\pi$
$523$	−16.2112	−0.708868	−0.354434	+	0.935081i	$0.615326\pi$
$524$	3.38148	0.147721
$525$	0.187455	0.00818120
$526$	41.2537	1.79875
$527$	−11.6372	−0.506926
$528$	−0.771640	−0.0335813
$529$	8.57592	0.372866
$530$	−15.6711	−0.680710
$531$	−1.91066	−0.0829155
$532$	14.1975	0.615540
$533$	13.1287	0.568665
$534$	6.61530	0.286272
$535$	13.4628	0.582048
$536$	11.5608	0.499353
$537$	−13.8749	−0.598746
$538$	−38.3945	−1.65530
$539$	−5.46288	−0.235303
$540$	−7.02934	−0.302495
$541$	0.345102	0.0148371	0.00741855	−	0.999972i	$-0.497639\pi$
$541$	0.345102	0.0148371	0.00741855	+	0.999972i	$0.497639\pi$
$542$	−26.1157	−1.12177
$543$	−18.1717	−0.779823
$544$	−19.7317	−0.845988
$545$	−20.8415	−0.892751
$546$	−4.39397	−0.188045
$547$	−9.76904	−0.417694	−0.208847	−	0.977948i	$-0.566971\pi$
$547$	−9.76904	−0.417694	−0.208847	+	0.977948i	$0.566971\pi$
$548$	56.5585	2.41606
$549$	−5.52236	−0.235688
$550$	−2.33613	−0.0996131
$551$	−18.9915	−0.809067
$552$	−15.4375	−0.657063
$553$	−14.7769	−0.628377
$554$	9.71539	0.412767
$555$	17.9495	0.761914
$556$	21.7632	0.922966
$557$	13.4070	0.568071	0.284036	−	0.958814i	$-0.408327\pi$
$557$	13.4070	0.568071	0.284036	+	0.958814i	$0.408327\pi$
$558$	−7.82609	−0.331305
$559$	−2.70313	−0.114330
$560$	−0.309871	−0.0130944
$561$	−18.5313	−0.782392
$562$	−13.2267	−0.557933
$563$	13.4824	0.568217	0.284109	−	0.958792i	$-0.408302\pi$
$563$	13.4824	0.568217	0.284109	+	0.958792i	$0.408302\pi$
$564$	25.1183	1.05767
$565$	12.4946	0.525653
$566$	64.1174	2.69506
$567$	1.00000	0.0419961
$568$	21.4284	0.899115
$569$	−39.0815	−1.63838	−0.819191	−	0.573521i	$-0.805577\pi$
$569$	−39.0815	−1.63838	−0.819191	+	0.573521i	$0.805577\pi$
$570$	22.1744	0.928783
$571$	−20.1576	−0.843570	−0.421785	−	0.906696i	$-0.638596\pi$
$571$	−20.1576	−0.843570	−0.421785	+	0.906696i	$0.638596\pi$
$572$	33.7153	1.40971
$573$	12.1055	0.505716
$574$	15.5497	0.649031
$575$	1.05335	0.0439279
$576$	−12.9871	−0.541130
$577$	20.6831	0.861048	0.430524	−	0.902579i	$-0.358329\pi$
$577$	20.6831	0.861048	0.430524	+	0.902579i	$0.358329\pi$
$578$	12.5307	0.521210
$579$	−17.8606	−0.742263
$580$	−30.1294	−1.25105
$581$	11.1649	0.463197
$582$	0.995318	0.0412573
$583$	−17.1063	−0.708469
$584$	−35.6008	−1.47317
$585$	−4.22538	−0.174698
$586$	−37.8367	−1.56302
$587$	9.31754	0.384576	0.192288	−	0.981339i	$-0.438409\pi$
$587$	9.31754	0.384576	0.192288	+	0.981339i	$0.438409\pi$
$588$	−3.20426	−0.132141
$589$	15.2002	0.626315
$590$	9.56202	0.393662
$591$	−0.905420	−0.0372440
$592$	1.15573	0.0475004
$593$	−25.8868	−1.06305	−0.531523	−	0.847044i	$-0.678380\pi$
$593$	−25.8868	−1.06305	−0.531523	+	0.847044i	$0.678380\pi$
$594$	−12.4624	−0.511338
$595$	−7.44169	−0.305079
$596$	−12.3171	−0.504527
$597$	−28.0185	−1.14672
$598$	−24.6908	−1.00968
$599$	−18.3707	−0.750606	−0.375303	−	0.926902i	$-0.622461\pi$
$599$	−18.3707	−0.750606	−0.375303	+	0.926902i	$0.622461\pi$
$600$	−0.514985	−0.0210242
$601$	10.5435	0.430076	0.215038	−	0.976606i	$-0.431012\pi$
$601$	10.5435	0.430076	0.215038	+	0.976606i	$0.431012\pi$
$602$	−3.20161	−0.130488
$603$	−4.20815	−0.171369
$604$	52.6637	2.14285
$605$	41.3370	1.68059
$606$	32.7920	1.33208
$607$	13.6682	0.554777	0.277388	−	0.960758i	$-0.410531\pi$
$607$	13.6682	0.554777	0.277388	+	0.960758i	$0.410531\pi$
$608$	25.7730	1.04523
$609$	4.28623	0.173687
$610$	27.6370	1.11899
$611$	15.0988	0.610831
$612$	−10.8695	−0.439375
$613$	40.9081	1.65226	0.826131	−	0.563478i	$-0.190537\pi$
$613$	40.9081	1.65226	0.826131	+	0.563478i	$0.190537\pi$
$614$	−48.4868	−1.95677
$615$	14.9530	0.602965
$616$	15.0079	0.604686
$617$	38.7478	1.55993	0.779964	−	0.625824i	$-0.215237\pi$
$617$	38.7478	1.55993	0.779964	+	0.625824i	$0.215237\pi$
$618$	20.1271	0.809631
$619$	−38.9712	−1.56638	−0.783192	−	0.621780i	$-0.786410\pi$
$619$	−38.9712	−1.56638	−0.783192	+	0.621780i	$0.786410\pi$
$620$	24.1146	0.968466
$621$	5.61925	0.225493
$622$	−5.60544	−0.224758
$623$	2.89981	0.116179
$624$	−0.272064	−0.0108913
$625$	−24.0276	−0.961103
$626$	−19.9724	−0.798258
$627$	24.2051	0.966659
$628$	34.5211	1.37754
$629$	27.7555	1.10668
$630$	−5.00457	−0.199387
$631$	−32.0129	−1.27441	−0.637206	−	0.770693i	$-0.719910\pi$
$631$	−32.0129	−1.27441	−0.637206	+	0.770693i	$0.719910\pi$
$632$	40.5958	1.61482
$633$	−1.39710	−0.0555299
$634$	10.8955	0.432716
$635$	18.1774	0.721349
$636$	−10.0337	−0.397861
$637$	−1.92610	−0.0763147
$638$	−53.4166	−2.11478
$639$	−7.79993	−0.308561
$640$	39.4740	1.56035
$641$	10.6974	0.422522	0.211261	−	0.977430i	$-0.432243\pi$
$641$	10.6974	0.422522	0.211261	+	0.977430i	$0.432243\pi$
$642$	14.0000	0.552535
$643$	−30.3063	−1.19516	−0.597581	−	0.801809i	$-0.703871\pi$
$643$	−30.3063	−1.19516	−0.597581	+	0.801809i	$0.703871\pi$
$644$	−18.0055	−0.709516
$645$	−3.07876	−0.121226
$646$	34.2885	1.34906
$647$	10.7901	0.424205	0.212102	−	0.977247i	$-0.431969\pi$
$647$	10.7901	0.424205	0.212102	+	0.977247i	$0.431969\pi$
$648$	−2.74725	−0.107922
$649$	10.4377	0.409715
$650$	−0.823671	−0.0323071
$651$	−3.43056	−0.134454
$652$	10.9082	0.427196
$653$	−27.2266	−1.06546	−0.532730	−	0.846285i	$-0.678834\pi$
$653$	−27.2266	−1.06546	−0.532730	+	0.846285i	$0.678834\pi$
$654$	−21.6731	−0.847484
$655$	2.31508	0.0904579
$656$	0.962798	0.0375909
$657$	12.9587	0.505567
$658$	17.8831	0.697156
$659$	−37.1884	−1.44865	−0.724326	−	0.689457i	$-0.757849\pi$
$659$	−37.1884	−1.44865	−0.724326	+	0.689457i	$0.757849\pi$
$660$	38.4005	1.49474
$661$	46.0608	1.79156	0.895779	−	0.444500i	$-0.146619\pi$
$661$	46.0608	1.79156	0.895779	+	0.444500i	$0.146619\pi$
$662$	−18.7410	−0.728391
$663$	−6.53374	−0.253750
$664$	−30.6728	−1.19033
$665$	9.72014	0.376931
$666$	18.6657	0.723281
$667$	24.0854	0.932589
$668$	−0.197082	−0.00762532
$669$	2.97094	0.114863
$670$	21.0600	0.813618
$671$	30.1680	1.16462
$672$	−5.81674	−0.224386
$673$	0.419999	0.0161898	0.00809488	−	0.999967i	$-0.497423\pi$
$673$	0.419999	0.0161898	0.00809488	+	0.999967i	$0.497423\pi$
$674$	−22.9781	−0.885084
$675$	0.187455	0.00721514
$676$	−29.7680	−1.14492
$677$	−36.8349	−1.41568	−0.707840	−	0.706373i	$-0.750330\pi$
$677$	−36.8349	−1.41568	−0.707840	+	0.706373i	$0.750330\pi$
$678$	12.9932	0.499000
$679$	0.436297	0.0167436
$680$	20.4442	0.783999
$681$	20.5827	0.788733
$682$	42.7530	1.63710
$683$	10.5538	0.403830	0.201915	−	0.979403i	$-0.435284\pi$
$683$	10.5538	0.403830	0.201915	+	0.979403i	$0.435284\pi$
$684$	14.1975	0.542856
$685$	38.7220	1.47949
$686$	−2.28128	−0.0870998
$687$	−29.7267	−1.13414
$688$	−0.198236	−0.00755766
$689$	−6.03131	−0.229774
$690$	−28.1219	−1.07058
$691$	−19.4193	−0.738744	−0.369372	−	0.929282i	$-0.620427\pi$
$691$	−19.4193	−0.738744	−0.369372	+	0.929282i	$0.620427\pi$
$692$	23.9752	0.911401
$693$	−5.46288	−0.207518
$694$	−25.0905	−0.952421
$695$	14.8999	0.565185
$696$	−11.7753	−0.446343
$697$	23.1220	0.875810
$698$	−26.0040	−0.984268
$699$	20.3326	0.769050
$700$	−0.600653	−0.0227026
$701$	−20.9067	−0.789633	−0.394817	−	0.918760i	$-0.629192\pi$
$701$	−20.9067	−0.789633	−0.394817	+	0.918760i	$0.629192\pi$
$702$	−4.39397	−0.165840
$703$	−36.2535	−1.36733
$704$	70.9472	2.67392
$705$	17.1969	0.647674
$706$	42.1429	1.58607
$707$	14.3744	0.540604
$708$	6.12224	0.230088
$709$	36.8601	1.38431	0.692155	−	0.721749i	$-0.256661\pi$
$709$	36.8601	1.38431	0.692155	+	0.721749i	$0.256661\pi$
$710$	39.0353	1.46497
$711$	−14.7769	−0.554177
$712$	−7.96652	−0.298558
$713$	−19.2772	−0.721936
$714$	−7.73862	−0.289610
$715$	23.0827	0.863246
$716$	44.4587	1.66150
$717$	12.7437	0.475923
$718$	68.3672	2.55144
$719$	2.04824	0.0763864	0.0381932	−	0.999270i	$-0.487840\pi$
$719$	2.04824	0.0763864	0.0381932	+	0.999270i	$0.487840\pi$
$720$	−0.309871	−0.0115482
$721$	8.82271	0.328575
$722$	−1.44235	−0.0536786
$723$	−13.5865	−0.505287
$724$	58.2268	2.16398
$725$	0.803474	0.0298403
$726$	42.9864	1.59538
$727$	−4.22436	−0.156673	−0.0783365	−	0.996927i	$-0.524961\pi$
$727$	−4.22436	−0.156673	−0.0783365	+	0.996927i	$0.524961\pi$
$728$	5.29147	0.196115
$729$	1.00000	0.0370370
$730$	−64.8528	−2.40031
$731$	−4.76072	−0.176082
$732$	17.6951	0.654028
$733$	16.1955	0.598196	0.299098	−	0.954222i	$-0.403314\pi$
$733$	16.1955	0.598196	0.299098	+	0.954222i	$0.403314\pi$
$734$	−58.4507	−2.15745
$735$	−2.19375	−0.0809177
$736$	−32.6857	−1.20481
$737$	22.9886	0.846797
$738$	15.5497	0.572392
$739$	−8.26782	−0.304137	−0.152068	−	0.988370i	$-0.548593\pi$
$739$	−8.26782	−0.304137	−0.152068	+	0.988370i	$0.548593\pi$
$740$	−57.5148	−2.11429
$741$	8.53421	0.313512
$742$	−7.14352	−0.262247
$743$	26.3038	0.964994	0.482497	−	0.875898i	$-0.339730\pi$
$743$	26.3038	0.964994	0.482497	+	0.875898i	$0.339730\pi$
$744$	9.42463	0.345524
$745$	−8.43272	−0.308951
$746$	60.6846	2.22182
$747$	11.1649	0.408502
$748$	59.3790	2.17111
$749$	6.13689	0.224237
$750$	−25.9610	−0.947961
$751$	−5.73891	−0.209416	−0.104708	−	0.994503i	$-0.533391\pi$
$751$	−5.73891	−0.209416	−0.104708	+	0.994503i	$0.533391\pi$
$752$	1.10728	0.0403782
$753$	28.3298	1.03239
$754$	−18.8336	−0.685878
$755$	36.0555	1.31219
$756$	−3.20426	−0.116538
$757$	2.40581	0.0874407	0.0437204	−	0.999044i	$-0.486079\pi$
$757$	2.40581	0.0874407	0.0437204	+	0.999044i	$0.486079\pi$
$758$	57.9013	2.10307
$759$	−30.6973	−1.11424
$760$	−26.7037	−0.968644
$761$	11.6920	0.423836	0.211918	−	0.977287i	$-0.432029\pi$
$761$	11.6920	0.423836	0.211918	+	0.977287i	$0.432029\pi$
$762$	18.9027	0.684773
$763$	−9.50038	−0.343937
$764$	−38.7893	−1.40335
$765$	−7.44169	−0.269055
$766$	2.28128	0.0824261
$767$	3.68011	0.132881
$768$	15.0748	0.543966
$769$	16.8320	0.606978	0.303489	−	0.952835i	$-0.401848\pi$
$769$	16.8320	0.606978	0.303489	+	0.952835i	$0.401848\pi$
$770$	27.3394	0.985243
$771$	−28.0780	−1.01121
$772$	57.2301	2.05976
$773$	2.75083	0.0989406	0.0494703	−	0.998776i	$-0.484247\pi$
$773$	2.75083	0.0989406	0.0494703	+	0.998776i	$0.484247\pi$
$774$	−3.20161	−0.115079
$775$	−0.643076	−0.0231000
$776$	−1.19862	−0.0430279
$777$	8.18210	0.293531
$778$	23.6583	0.848192
$779$	−30.2014	−1.08208
$780$	13.5392	0.484781
$781$	42.6101	1.52471
$782$	−43.4852	−1.55503
$783$	4.28623	0.153177
$784$	−0.141251	−0.00504469
$785$	23.6344	0.843547
$786$	2.40746	0.0858712
$787$	17.5721	0.626379	0.313190	−	0.949691i	$-0.398602\pi$
$787$	17.5721	0.626379	0.313190	+	0.949691i	$0.398602\pi$
$788$	2.90120	0.103351
$789$	18.0835	0.643791
$790$	73.9520	2.63109
$791$	5.69556	0.202511
$792$	15.0079	0.533283
$793$	10.6366	0.377717
$794$	55.0638	1.95414
$795$	−6.86943	−0.243633
$796$	89.7784	3.18211
$797$	27.6712	0.980163	0.490082	−	0.871676i	$-0.336967\pi$
$797$	27.6712	0.980163	0.490082	+	0.871676i	$0.336967\pi$
$798$	10.1080	0.357819
$799$	26.5918	0.940749
$800$	−1.09038	−0.0385506
$801$	2.89981	0.102460
$802$	68.1813	2.40757
$803$	−70.7919	−2.49819
$804$	13.4840	0.475544
$805$	−12.3272	−0.434478
$806$	15.0738	0.530952
$807$	−16.8302	−0.592451
$808$	−39.4900	−1.38925
$809$	−30.9280	−1.08737	−0.543685	−	0.839290i	$-0.682971\pi$
$809$	−30.9280	−1.08737	−0.543685	+	0.839290i	$0.682971\pi$
$810$	−5.00457	−0.175843
$811$	−42.6182	−1.49653	−0.748263	−	0.663402i	$-0.769112\pi$
$811$	−42.6182	−1.49653	−0.748263	+	0.663402i	$0.769112\pi$
$812$	−13.7342	−0.481975
$813$	−11.4478	−0.401492
$814$	−101.969	−3.57400
$815$	7.46812	0.261597
$816$	−0.479156	−0.0167738
$817$	6.21833	0.217552
$818$	26.4100	0.923405
$819$	−1.92610	−0.0673033
$820$	−47.9134	−1.67321
$821$	35.4160	1.23603	0.618013	−	0.786168i	$-0.287938\pi$
$821$	35.4160	1.23603	0.618013	+	0.786168i	$0.287938\pi$
$822$	40.2670	1.40447
$823$	10.8636	0.378682	0.189341	−	0.981911i	$-0.439365\pi$
$823$	10.8636	0.378682	0.189341	+	0.981911i	$0.439365\pi$
$824$	−24.2382	−0.844378
$825$	−1.02404	−0.0356526
$826$	4.35875	0.151660
$827$	−1.05651	−0.0367383	−0.0183692	−	0.999831i	$-0.505847\pi$
$827$	−1.05651	−0.0367383	−0.0183692	+	0.999831i	$0.505847\pi$
$828$	−18.0055	−0.625735
$829$	−1.48088	−0.0514331	−0.0257165	−	0.999669i	$-0.508187\pi$
$829$	−1.48088	−0.0514331	−0.0257165	+	0.999669i	$0.508187\pi$
$830$	−55.8755	−1.93947
$831$	4.25874	0.147734
$832$	25.0145	0.867221
$833$	−3.39222	−0.117533
$834$	15.4944	0.536527
$835$	−0.134929	−0.00466942
$836$	−77.5594	−2.68245
$837$	−3.43056	−0.118578
$838$	36.6436	1.26583
$839$	−45.4542	−1.56925	−0.784627	−	0.619968i	$-0.787146\pi$
$839$	−45.4542	−1.56925	−0.784627	+	0.619968i	$0.787146\pi$
$840$	6.02679	0.207944
$841$	−10.6283	−0.366492
$842$	24.0525	0.828904
$843$	−5.79790	−0.199690
$844$	4.47668	0.154094
$845$	−20.3803	−0.701103
$846$	17.8831	0.614833
$847$	18.8431	0.647456
$848$	−0.442309	−0.0151890
$849$	28.1059	0.964590
$850$	−1.45064	−0.0497566
$851$	45.9773	1.57608
$852$	24.9930	0.856246
$853$	38.1836	1.30738	0.653690	−	0.756762i	$-0.273220\pi$
$853$	38.1836	1.30738	0.653690	+	0.756762i	$0.273220\pi$
$854$	12.5981	0.431097
$855$	9.72014	0.332422
$856$	−16.8596	−0.576249
$857$	0.761898	0.0260259	0.0130130	−	0.999915i	$-0.495858\pi$
$857$	0.761898	0.0260259	0.0130130	+	0.999915i	$0.495858\pi$
$858$	24.0038	0.819475
$859$	31.9384	1.08972	0.544862	−	0.838526i	$-0.316582\pi$
$859$	31.9384	1.08972	0.544862	+	0.838526i	$0.316582\pi$
$860$	9.86515	0.336399
$861$	6.81620	0.232295
$862$	−52.0273	−1.77206
$863$	−43.8945	−1.49419	−0.747094	−	0.664719i	$-0.768551\pi$
$863$	−43.8945	−1.49419	−0.747094	+	0.664719i	$0.768551\pi$
$864$	−5.81674	−0.197889
$865$	16.4143	0.558103
$866$	18.3480	0.623489
$867$	5.49285	0.186547
$868$	10.9924	0.373107
$869$	80.7244	2.73839
$870$	−21.4507	−0.727248
$871$	8.10530	0.274638
$872$	26.0999	0.883856
$873$	0.436297	0.0147664
$874$	56.7992	1.92126
$875$	−11.3800	−0.384714
$876$	−41.5230	−1.40293
$877$	29.7703	1.00527	0.502636	−	0.864498i	$-0.332364\pi$
$877$	29.7703	1.00527	0.502636	+	0.864498i	$0.332364\pi$
$878$	−34.2570	−1.15612
$879$	−16.5857	−0.559421
$880$	1.69279	0.0570638
$881$	19.9190	0.671087	0.335544	−	0.942025i	$-0.391080\pi$
$881$	19.9190	0.671087	0.335544	+	0.942025i	$0.391080\pi$
$882$	−2.28128	−0.0768148
$883$	26.5329	0.892902	0.446451	−	0.894808i	$-0.352688\pi$
$883$	26.5329	0.892902	0.446451	+	0.894808i	$0.352688\pi$
$884$	20.9358	0.704147
$885$	4.19151	0.140896
$886$	−15.9907	−0.537218
$887$	−38.0119	−1.27632	−0.638158	−	0.769905i	$-0.720303\pi$
$887$	−38.0119	−1.27632	−0.638158	+	0.769905i	$0.720303\pi$
$888$	−22.4783	−0.754322
$889$	8.28600	0.277903
$890$	−14.5123	−0.486454
$891$	−5.46288	−0.183013
$892$	−9.51965	−0.318741
$893$	−34.7335	−1.16231
$894$	−8.76919	−0.293286
$895$	30.4381	1.01743
$896$	17.9939	0.601133
$897$	−10.8232	−0.361377
$898$	−69.7245	−2.32674
$899$	−14.7042	−0.490412
$900$	−0.600653	−0.0200218
$901$	−10.6223	−0.353879
$902$	−84.9461	−2.82840
$903$	−1.40342	−0.0467030
$904$	−15.6471	−0.520416
$905$	39.8642	1.32513
$906$	37.4941	1.24566
$907$	−29.2416	−0.970951	−0.485476	−	0.874250i	$-0.661354\pi$
$907$	−29.2416	−0.970951	−0.485476	+	0.874250i	$0.661354\pi$
$908$	−65.9524	−2.18871
$909$	14.3744	0.476768
$910$	9.63929	0.319539
$911$	−23.2938	−0.771758	−0.385879	−	0.922549i	$-0.626102\pi$
$911$	−23.2938	−0.771758	−0.385879	+	0.922549i	$0.626102\pi$
$912$	0.625861	0.0207243
$913$	−60.9925	−2.01856
$914$	−41.7929	−1.38239
$915$	12.1147	0.400499
$916$	95.2518	3.14721
$917$	1.05531	0.0348494
$918$	−7.73862	−0.255412
$919$	−46.0969	−1.52060	−0.760298	−	0.649574i	$-0.774947\pi$
$919$	−46.0969	−1.52060	−0.760298	+	0.649574i	$0.774947\pi$
$920$	33.8660	1.11653
$921$	−21.2542	−0.700348
$922$	−58.0381	−1.91138
$923$	15.0234	0.494502
$924$	17.5045	0.575855
$925$	1.53377	0.0504302
$926$	−20.7363	−0.681438
$927$	8.82271	0.289776
$928$	−24.9319	−0.818429
$929$	−1.32804	−0.0435716	−0.0217858	−	0.999763i	$-0.506935\pi$
$929$	−1.32804	−0.0435716	−0.0217858	+	0.999763i	$0.506935\pi$
$930$	17.1685	0.562977
$931$	4.43083	0.145215
$932$	−65.1509	−2.13409
$933$	−2.45714	−0.0804432
$934$	−34.0836	−1.11525
$935$	40.6531	1.32950
$936$	5.29147	0.172957
$937$	18.4171	0.601660	0.300830	−	0.953678i	$-0.402736\pi$
$937$	18.4171	0.601660	0.300830	+	0.953678i	$0.402736\pi$
$938$	9.59998	0.313451
$939$	−8.75490	−0.285705
$940$	−55.1034	−1.79727
$941$	−17.0217	−0.554891	−0.277445	−	0.960741i	$-0.589488\pi$
$941$	−17.0217	−0.554891	−0.277445	+	0.960741i	$0.589488\pi$
$942$	24.5774	0.800775
$943$	38.3019	1.24728
$944$	0.269883	0.00878395
$945$	−2.19375	−0.0713627
$946$	17.4900	0.568649
$947$	20.4681	0.665125	0.332563	−	0.943081i	$-0.392087\pi$
$947$	20.4681	0.665125	0.332563	+	0.943081i	$0.392087\pi$
$948$	47.3489	1.53782
$949$	−24.9597	−0.810227
$950$	1.89479	0.0614751
$951$	4.77605	0.154874
$952$	9.31928	0.302040
$953$	−32.1294	−1.04077	−0.520387	−	0.853930i	$-0.674212\pi$
$953$	−32.1294	−1.04077	−0.520387	+	0.853930i	$0.674212\pi$
$954$	−7.14352	−0.231280
$955$	−26.5566	−0.859350
$956$	−40.8342	−1.32067
$957$	−23.4152	−0.756904
$958$	−14.6879	−0.474546
$959$	17.6510	0.569982
$960$	28.4905	0.919528
$961$	−19.2312	−0.620362
$962$	−35.9520	−1.15914
$963$	6.13689	0.197758
$964$	43.5346	1.40216
$965$	39.1818	1.26131
$966$	−12.8191	−0.412448
$967$	18.5651	0.597014	0.298507	−	0.954407i	$-0.403511\pi$
$967$	18.5651	0.597014	0.298507	+	0.954407i	$0.403511\pi$
$968$	−51.7667	−1.66384
$969$	15.0303	0.482844
$970$	−2.18348	−0.0701073
$971$	−3.32985	−0.106860	−0.0534300	−	0.998572i	$-0.517015\pi$
$971$	−3.32985	−0.106860	−0.0534300	+	0.998572i	$0.517015\pi$
$972$	−3.20426	−0.102777
$973$	6.79197	0.217740
$974$	46.4961	1.48983
$975$	−0.361056	−0.0115630
$976$	0.780041	0.0249685
$977$	51.1646	1.63690	0.818449	−	0.574578i	$-0.194834\pi$
$977$	51.1646	1.63690	0.818449	+	0.574578i	$0.194834\pi$
$978$	7.76611	0.248333
$979$	−15.8413	−0.506291
$980$	7.02934	0.224544
$981$	−9.50038	−0.303324
$982$	−87.1120	−2.77985
$983$	−37.1740	−1.18567	−0.592834	−	0.805325i	$-0.701991\pi$
$983$	−37.1740	−1.18567	−0.592834	+	0.805325i	$0.701991\pi$
$984$	−18.7258	−0.596957
$985$	1.98627	0.0632877
$986$	−33.1695	−1.05633
$987$	7.83905	0.249520
$988$	−27.3458	−0.869986
$989$	−7.88618	−0.250766
$990$	27.3394	0.868902
$991$	7.79804	0.247713	0.123856	−	0.992300i	$-0.460474\pi$
$991$	7.79804	0.247713	0.123856	+	0.992300i	$0.460474\pi$
$992$	19.9547	0.633562
$993$	−8.21512	−0.260699
$994$	17.7939	0.564387
$995$	61.4656	1.94859
$996$	−35.7752	−1.13358
$997$	−54.1840	−1.71602	−0.858011	−	0.513631i	$-0.828300\pi$
$997$	−54.1840	−1.71602	−0.858011	+	0.513631i	$0.828300\pi$
$998$	30.0126	0.950032
$999$	8.18210	0.258870

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8043.2.a.t.1.7	✓	52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8043.2.a.t.1.7	✓	52	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:	\( N \)	\(=\)	\( 8043 = 3 \cdot 7 \cdot 383 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8043.a (trivial)

\(f(q)\)	\(=\)	\(q-2.28128 q^{2} -1.00000 q^{3} +3.20426 q^{4} +2.19375 q^{5} +2.28128 q^{6} +1.00000 q^{7} -2.74725 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.28128 q^{2} -1.00000 q^{3} +3.20426 q^{4} +2.19375 q^{5} +2.28128 q^{6} +1.00000 q^{7} -2.74725 q^{8} +1.00000 q^{9} -5.00457 q^{10} -5.46288 q^{11} -3.20426 q^{12} -1.92610 q^{13} -2.28128 q^{14} -2.19375 q^{15} -0.141251 q^{16} -3.39222 q^{17} -2.28128 q^{18} +4.43083 q^{19} +7.02934 q^{20} -1.00000 q^{21} +12.4624 q^{22} -5.61925 q^{23} +2.74725 q^{24} -0.187455 q^{25} +4.39397 q^{26} -1.00000 q^{27} +3.20426 q^{28} -4.28623 q^{29} +5.00457 q^{30} +3.43056 q^{31} +5.81674 q^{32} +5.46288 q^{33} +7.73862 q^{34} +2.19375 q^{35} +3.20426 q^{36} -8.18210 q^{37} -10.1080 q^{38} +1.92610 q^{39} -6.02679 q^{40} -6.81620 q^{41} +2.28128 q^{42} +1.40342 q^{43} -17.5045 q^{44} +2.19375 q^{45} +12.8191 q^{46} -7.83905 q^{47} +0.141251 q^{48} +1.00000 q^{49} +0.427638 q^{50} +3.39222 q^{51} -6.17171 q^{52} +3.13136 q^{53} +2.28128 q^{54} -11.9842 q^{55} -2.74725 q^{56} -4.43083 q^{57} +9.77810 q^{58} -1.91066 q^{59} -7.02934 q^{60} -5.52236 q^{61} -7.82609 q^{62} +1.00000 q^{63} -12.9871 q^{64} -4.22538 q^{65} -12.4624 q^{66} -4.20815 q^{67} -10.8695 q^{68} +5.61925 q^{69} -5.00457 q^{70} -7.79993 q^{71} -2.74725 q^{72} +12.9587 q^{73} +18.6657 q^{74} +0.187455 q^{75} +14.1975 q^{76} -5.46288 q^{77} -4.39397 q^{78} -14.7769 q^{79} -0.309871 q^{80} +1.00000 q^{81} +15.5497 q^{82} +11.1649 q^{83} -3.20426 q^{84} -7.44169 q^{85} -3.20161 q^{86} +4.28623 q^{87} +15.0079 q^{88} +2.89981 q^{89} -5.00457 q^{90} -1.92610 q^{91} -18.0055 q^{92} -3.43056 q^{93} +17.8831 q^{94} +9.72014 q^{95} -5.81674 q^{96} +0.436297 q^{97} -2.28128 q^{98} -5.46288 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q + 3 q^{2} - 52 q^{3} + 61 q^{4} - 7 q^{5} - 3 q^{6} + 52 q^{7} + 24 q^{8} + 52 q^{9}+O(q^{10}) \) 52 * q + 3 * q^2 - 52 * q^3 + 61 * q^4 - 7 * q^5 - 3 * q^6 + 52 * q^7 + 24 * q^8 + 52 * q^9	\( 52 q + 3 q^{2} - 52 q^{3} + 61 q^{4} - 7 q^{5} - 3 q^{6} + 52 q^{7} + 24 q^{8} + 52 q^{9} - 2 q^{10} + 9 q^{11} - 61 q^{12} + 44 q^{13} + 3 q^{14} + 7 q^{15} + 95 q^{16} - 6 q^{17} + 3 q^{18} + 7 q^{19} - 21 q^{20} - 52 q^{21} + 19 q^{22} - 4 q^{23} - 24 q^{24} + 83 q^{25} - 5 q^{26} - 52 q^{27} + 61 q^{28} + 31 q^{29} + 2 q^{30} + 11 q^{31} + 71 q^{32} - 9 q^{33} + 17 q^{34} - 7 q^{35} + 61 q^{36} + 71 q^{37} - 8 q^{38} - 44 q^{39} + 20 q^{40} - 25 q^{41} - 3 q^{42} + 75 q^{43} + 14 q^{44} - 7 q^{45} + 36 q^{46} - 20 q^{47} - 95 q^{48} + 52 q^{49} + 26 q^{50} + 6 q^{51} + 88 q^{52} + 70 q^{53} - 3 q^{54} + 12 q^{55} + 24 q^{56} - 7 q^{57} + 48 q^{58} - 27 q^{59} + 21 q^{60} + 59 q^{61} - 23 q^{62} + 52 q^{63} + 138 q^{64} + 44 q^{65} - 19 q^{66} + 65 q^{67} - 8 q^{68} + 4 q^{69} - 2 q^{70} - 11 q^{71} + 24 q^{72} + 34 q^{73} + 38 q^{74} - 83 q^{75} + 31 q^{76} + 9 q^{77} + 5 q^{78} + 74 q^{79} - 5 q^{80} + 52 q^{81} + 51 q^{82} - 30 q^{83} - 61 q^{84} + 70 q^{85} + 29 q^{86} - 31 q^{87} + 90 q^{88} - q^{89} - 2 q^{90} + 44 q^{91} + 34 q^{92} - 11 q^{93} + 27 q^{94} + 9 q^{95} - 71 q^{96} + 73 q^{97} + 3 q^{98} + 9 q^{99}+O(q^{100}) \) 52 * q + 3 * q^2 - 52 * q^3 + 61 * q^4 - 7 * q^5 - 3 * q^6 + 52 * q^7 + 24 * q^8 + 52 * q^9 - 2 * q^10 + 9 * q^11 - 61 * q^12 + 44 * q^13 + 3 * q^14 + 7 * q^15 + 95 * q^16 - 6 * q^17 + 3 * q^18 + 7 * q^19 - 21 * q^20 - 52 * q^21 + 19 * q^22 - 4 * q^23 - 24 * q^24 + 83 * q^25 - 5 * q^26 - 52 * q^27 + 61 * q^28 + 31 * q^29 + 2 * q^30 + 11 * q^31 + 71 * q^32 - 9 * q^33 + 17 * q^34 - 7 * q^35 + 61 * q^36 + 71 * q^37 - 8 * q^38 - 44 * q^39 + 20 * q^40 - 25 * q^41 - 3 * q^42 + 75 * q^43 + 14 * q^44 - 7 * q^45 + 36 * q^46 - 20 * q^47 - 95 * q^48 + 52 * q^49 + 26 * q^50 + 6 * q^51 + 88 * q^52 + 70 * q^53 - 3 * q^54 + 12 * q^55 + 24 * q^56 - 7 * q^57 + 48 * q^58 - 27 * q^59 + 21 * q^60 + 59 * q^61 - 23 * q^62 + 52 * q^63 + 138 * q^64 + 44 * q^65 - 19 * q^66 + 65 * q^67 - 8 * q^68 + 4 * q^69 - 2 * q^70 - 11 * q^71 + 24 * q^72 + 34 * q^73 + 38 * q^74 - 83 * q^75 + 31 * q^76 + 9 * q^77 + 5 * q^78 + 74 * q^79 - 5 * q^80 + 52 * q^81 + 51 * q^82 - 30 * q^83 - 61 * q^84 + 70 * q^85 + 29 * q^86 - 31 * q^87 + 90 * q^88 - q^89 - 2 * q^90 + 44 * q^91 + 34 * q^92 - 11 * q^93 + 27 * q^94 + 9 * q^95 - 71 * q^96 + 73 * q^97 + 3 * q^98 + 9 * q^99

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