LMFDB - Embedded newform 8043.2.a.t.1.13

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			1.13
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)

$f(q)$	$=$	$q-1.64173 q^{2} -1.00000 q^{3} +0.695293 q^{4} +0.237832 q^{5} +1.64173 q^{6} +1.00000 q^{7} +2.14198 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.64173 q^{2} -1.00000 q^{3} +0.695293 q^{4} +0.237832 q^{5} +1.64173 q^{6} +1.00000 q^{7} +2.14198 q^{8} +1.00000 q^{9} -0.390457 q^{10} +5.78104 q^{11} -0.695293 q^{12} -2.25763 q^{13} -1.64173 q^{14} -0.237832 q^{15} -4.90715 q^{16} +1.36602 q^{17} -1.64173 q^{18} -1.08935 q^{19} +0.165363 q^{20} -1.00000 q^{21} -9.49094 q^{22} +8.19746 q^{23} -2.14198 q^{24} -4.94344 q^{25} +3.70643 q^{26} -1.00000 q^{27} +0.695293 q^{28} +4.22185 q^{29} +0.390457 q^{30} -2.42770 q^{31} +3.77228 q^{32} -5.78104 q^{33} -2.24264 q^{34} +0.237832 q^{35} +0.695293 q^{36} -1.97831 q^{37} +1.78842 q^{38} +2.25763 q^{39} +0.509432 q^{40} +4.27690 q^{41} +1.64173 q^{42} +4.64096 q^{43} +4.01952 q^{44} +0.237832 q^{45} -13.4581 q^{46} -2.78914 q^{47} +4.90715 q^{48} +1.00000 q^{49} +8.11581 q^{50} -1.36602 q^{51} -1.56971 q^{52} +4.58089 q^{53} +1.64173 q^{54} +1.37492 q^{55} +2.14198 q^{56} +1.08935 q^{57} -6.93115 q^{58} +2.07593 q^{59} -0.165363 q^{60} -2.14607 q^{61} +3.98564 q^{62} +1.00000 q^{63} +3.62123 q^{64} -0.536937 q^{65} +9.49094 q^{66} +7.93805 q^{67} +0.949783 q^{68} -8.19746 q^{69} -0.390457 q^{70} -1.57991 q^{71} +2.14198 q^{72} +9.02206 q^{73} +3.24786 q^{74} +4.94344 q^{75} -0.757417 q^{76} +5.78104 q^{77} -3.70643 q^{78} +8.22828 q^{79} -1.16708 q^{80} +1.00000 q^{81} -7.02154 q^{82} +2.94888 q^{83} -0.695293 q^{84} +0.324883 q^{85} -7.61923 q^{86} -4.22185 q^{87} +12.3829 q^{88} -2.57906 q^{89} -0.390457 q^{90} -2.25763 q^{91} +5.69964 q^{92} +2.42770 q^{93} +4.57903 q^{94} -0.259082 q^{95} -3.77228 q^{96} -5.87142 q^{97} -1.64173 q^{98} +5.78104 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.64173	−1.16088	−0.580441	−	0.814302i	$-0.697120\pi$
$2$	−1.64173	−1.16088	−0.580441	+	0.814302i	$0.697120\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	0.695293	0.347646
$5$	0.237832	0.106362	0.0531808	−	0.998585i	$-0.483064\pi$
$5$	0.237832	0.106362	0.0531808	+	0.998585i	$0.483064\pi$
$6$	1.64173	0.670235
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	2.14198	0.757305
$9$	1.00000	0.333333
$10$	−0.390457	−0.123473
$11$	5.78104	1.74305	0.871525	−	0.490352i	$-0.163132\pi$
$11$	5.78104	1.74305	0.871525	+	0.490352i	$0.163132\pi$
$12$	−0.695293	−0.200714
$13$	−2.25763	−0.626154	−0.313077	−	0.949728i	$-0.601360\pi$
$13$	−2.25763	−0.626154	−0.313077	+	0.949728i	$0.601360\pi$
$14$	−1.64173	−0.438772
$15$	−0.237832	−0.0614079
$16$	−4.90715	−1.22679
$17$	1.36602	0.331308	0.165654	−	0.986184i	$-0.447026\pi$
$17$	1.36602	0.331308	0.165654	+	0.986184i	$0.447026\pi$
$18$	−1.64173	−0.386961
$19$	−1.08935	−0.249914	−0.124957	−	0.992162i	$-0.539879\pi$
$19$	−1.08935	−0.249914	−0.124957	+	0.992162i	$0.539879\pi$
$20$	0.165363	0.0369763
$21$	−1.00000	−0.218218
$22$	−9.49094	−2.02347
$23$	8.19746	1.70929	0.854644	−	0.519214i	$-0.173775\pi$
$23$	8.19746	1.70929	0.854644	+	0.519214i	$0.173775\pi$
$24$	−2.14198	−0.437230
$25$	−4.94344	−0.988687
$26$	3.70643	0.726891
$27$	−1.00000	−0.192450
$28$	0.695293	0.131398
$29$	4.22185	0.783977	0.391989	−	0.919970i	$-0.371787\pi$
$29$	4.22185	0.783977	0.391989	+	0.919970i	$0.371787\pi$
$30$	0.390457	0.0712874
$31$	−2.42770	−0.436028	−0.218014	−	0.975946i	$-0.569958\pi$
$31$	−2.42770	−0.436028	−0.218014	+	0.975946i	$0.569958\pi$
$32$	3.77228	0.666851
$33$	−5.78104	−1.00635
$34$	−2.24264	−0.384610
$35$	0.237832	0.0402009
$36$	0.695293	0.115882
$37$	−1.97831	−0.325232	−0.162616	−	0.986689i	$-0.551993\pi$
$37$	−1.97831	−0.325232	−0.162616	+	0.986689i	$0.551993\pi$
$38$	1.78842	0.290121
$39$	2.25763	0.361510
$40$	0.509432	0.0805483
$41$	4.27690	0.667940	0.333970	−	0.942584i	$-0.391612\pi$
$41$	4.27690	0.667940	0.333970	+	0.942584i	$0.391612\pi$
$42$	1.64173	0.253325
$43$	4.64096	0.707740	0.353870	−	0.935295i	$-0.384865\pi$
$43$	4.64096	0.707740	0.353870	+	0.935295i	$0.384865\pi$
$44$	4.01952	0.605965
$45$	0.237832	0.0354539
$46$	−13.4581	−1.98428
$47$	−2.78914	−0.406838	−0.203419	−	0.979092i	$-0.565205\pi$
$47$	−2.78914	−0.406838	−0.203419	+	0.979092i	$0.565205\pi$
$48$	4.90715	0.708287
$49$	1.00000	0.142857
$50$	8.11581	1.14775
$51$	−1.36602	−0.191281
$52$	−1.56971	−0.217680
$53$	4.58089	0.629234	0.314617	−	0.949219i	$-0.398124\pi$
$53$	4.58089	0.629234	0.314617	+	0.949219i	$0.398124\pi$
$54$	1.64173	0.223412
$55$	1.37492	0.185394
$56$	2.14198	0.286235
$57$	1.08935	0.144288
$58$	−6.93115	−0.910105
$59$	2.07593	0.270263	0.135131	−	0.990828i	$-0.456854\pi$
$59$	2.07593	0.270263	0.135131	+	0.990828i	$0.456854\pi$
$60$	−0.165363	−0.0213483
$61$	−2.14607	−0.274776	−0.137388	−	0.990517i	$-0.543871\pi$
$61$	−2.14607	−0.274776	−0.137388	+	0.990517i	$0.543871\pi$
$62$	3.98564	0.506177
$63$	1.00000	0.125988
$64$	3.62123	0.452653
$65$	−0.536937	−0.0665988
$66$	9.49094	1.16825
$67$	7.93805	0.969787	0.484893	−	0.874573i	$-0.338858\pi$
$67$	7.93805	0.969787	0.484893	+	0.874573i	$0.338858\pi$
$68$	0.949783	0.115178
$69$	−8.19746	−0.986858
$70$	−0.390457	−0.0466685
$71$	−1.57991	−0.187501	−0.0937503	−	0.995596i	$-0.529886\pi$
$71$	−1.57991	−0.187501	−0.0937503	+	0.995596i	$0.529886\pi$
$72$	2.14198	0.252435
$73$	9.02206	1.05595	0.527976	−	0.849259i	$-0.322951\pi$
$73$	9.02206	1.05595	0.527976	+	0.849259i	$0.322951\pi$
$74$	3.24786	0.377556
$75$	4.94344	0.570819
$76$	−0.757417	−0.0868817
$77$	5.78104	0.658811
$78$	−3.70643	−0.419671
$79$	8.22828	0.925753	0.462877	−	0.886423i	$-0.346817\pi$
$79$	8.22828	0.925753	0.462877	+	0.886423i	$0.346817\pi$
$80$	−1.16708	−0.130483
$81$	1.00000	0.111111
$82$	−7.02154	−0.775399
$83$	2.94888	0.323682	0.161841	−	0.986817i	$-0.448257\pi$
$83$	2.94888	0.323682	0.161841	+	0.986817i	$0.448257\pi$
$84$	−0.695293	−0.0758627
$85$	0.324883	0.0352385
$86$	−7.61923	−0.821603
$87$	−4.22185	−0.452629
$88$	12.3829	1.32002
$89$	−2.57906	−0.273379	−0.136690	−	0.990614i	$-0.543646\pi$
$89$	−2.57906	−0.273379	−0.136690	+	0.990614i	$0.543646\pi$
$90$	−0.390457	−0.0411578
$91$	−2.25763	−0.236664
$92$	5.69964	0.594228
$93$	2.42770	0.251741
$94$	4.57903	0.472291
$95$	−0.259082	−0.0265813
$96$	−3.77228	−0.385007
$97$	−5.87142	−0.596152	−0.298076	−	0.954542i	$-0.596345\pi$
$97$	−5.87142	−0.596152	−0.298076	+	0.954542i	$0.596345\pi$
$98$	−1.64173	−0.165840
$99$	5.78104	0.581016
$100$	−3.43714	−0.343714
$101$	−2.77484	−0.276107	−0.138053	−	0.990425i	$-0.544085\pi$
$101$	−2.77484	−0.276107	−0.138053	+	0.990425i	$0.544085\pi$
$102$	2.24264	0.222055
$103$	−4.20839	−0.414665	−0.207333	−	0.978270i	$-0.566478\pi$
$103$	−4.20839	−0.414665	−0.207333	+	0.978270i	$0.566478\pi$
$104$	−4.83581	−0.474190
$105$	−0.237832	−0.0232100
$106$	−7.52061	−0.730466
$107$	4.66666	0.451143	0.225572	−	0.974227i	$-0.427575\pi$
$107$	4.66666	0.451143	0.225572	+	0.974227i	$0.427575\pi$
$108$	−0.695293	−0.0669046
$109$	4.78502	0.458322	0.229161	−	0.973389i	$-0.426402\pi$
$109$	4.78502	0.458322	0.229161	+	0.973389i	$0.426402\pi$
$110$	−2.25725	−0.215220
$111$	1.97831	0.187773
$112$	−4.90715	−0.463682
$113$	−8.17744	−0.769268	−0.384634	−	0.923069i	$-0.625672\pi$
$113$	−8.17744	−0.769268	−0.384634	+	0.923069i	$0.625672\pi$
$114$	−1.78842	−0.167501
$115$	1.94962	0.181803
$116$	2.93542	0.272547
$117$	−2.25763	−0.208718
$118$	−3.40812	−0.313743
$119$	1.36602	0.125223
$120$	−0.509432	−0.0465046
$121$	22.4204	2.03822
$122$	3.52327	0.318982
$123$	−4.27690	−0.385635
$124$	−1.68796	−0.151584
$125$	−2.36487	−0.211520
$126$	−1.64173	−0.146257
$127$	17.2615	1.53171	0.765855	−	0.643014i	$-0.222316\pi$
$127$	17.2615	1.53171	0.765855	+	0.643014i	$0.222316\pi$
$128$	−13.4897	−1.19233
$129$	−4.64096	−0.408614
$130$	0.881508	0.0773134
$131$	11.4196	0.997733	0.498866	−	0.866679i	$-0.333750\pi$
$131$	11.4196	0.997733	0.498866	+	0.866679i	$0.333750\pi$
$132$	−4.01952	−0.349854
$133$	−1.08935	−0.0944586
$134$	−13.0322	−1.12581
$135$	−0.237832	−0.0204693
$136$	2.92599	0.250902
$137$	−10.8164	−0.924108	−0.462054	−	0.886852i	$-0.652887\pi$
$137$	−10.8164	−0.924108	−0.462054	+	0.886852i	$0.652887\pi$
$138$	13.4581	1.14563
$139$	22.6325	1.91967	0.959833	−	0.280574i	$-0.0905247\pi$
$139$	22.6325	1.91967	0.959833	+	0.280574i	$0.0905247\pi$
$140$	0.165363	0.0139757
$141$	2.78914	0.234888
$142$	2.59379	0.217666
$143$	−13.0515	−1.09142
$144$	−4.90715	−0.408929
$145$	1.00409	0.0833851
$146$	−14.8118	−1.22584
$147$	−1.00000	−0.0824786
$148$	−1.37550	−0.113066
$149$	−22.8771	−1.87417	−0.937084	−	0.349105i	$-0.886486\pi$
$149$	−22.8771	−1.87417	−0.937084	+	0.349105i	$0.886486\pi$
$150$	−8.11581	−0.662653
$151$	18.5290	1.50787	0.753935	−	0.656949i	$-0.228153\pi$
$151$	18.5290	1.50787	0.753935	+	0.656949i	$0.228153\pi$
$152$	−2.33337	−0.189261
$153$	1.36602	0.110436
$154$	−9.49094	−0.764801
$155$	−0.577385	−0.0463767
$156$	1.56971	0.125678
$157$	−18.4086	−1.46916	−0.734582	−	0.678520i	$-0.762622\pi$
$157$	−18.4086	−1.46916	−0.734582	+	0.678520i	$0.762622\pi$
$158$	−13.5086	−1.07469
$159$	−4.58089	−0.363288
$160$	0.897168	0.0709274
$161$	8.19746	0.646050
$162$	−1.64173	−0.128987
$163$	−10.7594	−0.842744	−0.421372	−	0.906888i	$-0.638451\pi$
$163$	−10.7594	−0.842744	−0.421372	+	0.906888i	$0.638451\pi$
$164$	2.97370	0.232207
$165$	−1.37492	−0.107037
$166$	−4.84129	−0.375757
$167$	6.47908	0.501366	0.250683	−	0.968069i	$-0.419345\pi$
$167$	6.47908	0.501366	0.250683	+	0.968069i	$0.419345\pi$
$168$	−2.14198	−0.165258
$169$	−7.90310	−0.607931
$170$	−0.533372	−0.0409077
$171$	−1.08935	−0.0833047
$172$	3.22683	0.246043
$173$	20.7885	1.58052	0.790259	−	0.612774i	$-0.209946\pi$
$173$	20.7885	1.58052	0.790259	+	0.612774i	$0.209946\pi$
$174$	6.93115	0.525449
$175$	−4.94344	−0.373689
$176$	−28.3685	−2.13835
$177$	−2.07593	−0.156036
$178$	4.23413	0.317361
$179$	9.63053	0.719819	0.359910	−	0.932987i	$-0.382807\pi$
$179$	9.63053	0.719819	0.359910	+	0.932987i	$0.382807\pi$
$180$	0.165363	0.0123254
$181$	−7.91612	−0.588401	−0.294200	−	0.955744i	$-0.595053\pi$
$181$	−7.91612	−0.588401	−0.294200	+	0.955744i	$0.595053\pi$
$182$	3.70643	0.274739
$183$	2.14607	0.158642
$184$	17.5588	1.29445
$185$	−0.470505	−0.0345922
$186$	−3.98564	−0.292242
$187$	7.89701	0.577487
$188$	−1.93927	−0.141436
$189$	−1.00000	−0.0727393
$190$	0.425344	0.0308577
$191$	−2.05238	−0.148505	−0.0742526	−	0.997239i	$-0.523657\pi$
$191$	−2.05238	−0.148505	−0.0742526	+	0.997239i	$0.523657\pi$
$192$	−3.62123	−0.261340
$193$	14.1555	1.01894	0.509469	−	0.860489i	$-0.329842\pi$
$193$	14.1555	1.01894	0.509469	+	0.860489i	$0.329842\pi$
$194$	9.63931	0.692062
$195$	0.536937	0.0384509
$196$	0.695293	0.0496638
$197$	−1.36118	−0.0969803	−0.0484901	−	0.998824i	$-0.515441\pi$
$197$	−1.36118	−0.0969803	−0.0484901	+	0.998824i	$0.515441\pi$
$198$	−9.49094	−0.674491
$199$	−23.4644	−1.66334	−0.831672	−	0.555267i	$-0.812616\pi$
$199$	−23.4644	−1.66334	−0.831672	+	0.555267i	$0.812616\pi$
$200$	−10.5888	−0.748738
$201$	−7.93805	−0.559907
$202$	4.55555	0.320528
$203$	4.22185	0.296316
$204$	−0.949783	−0.0664981
$205$	1.01718	0.0710432
$206$	6.90907	0.481378
$207$	8.19746	0.569763
$208$	11.0785	0.768159
$209$	−6.29758	−0.435612
$210$	0.390457	0.0269441
$211$	−27.3996	−1.88626	−0.943132	−	0.332419i	$-0.892135\pi$
$211$	−27.3996	−1.88626	−0.943132	+	0.332419i	$0.892135\pi$
$212$	3.18506	0.218751
$213$	1.57991	0.108254
$214$	−7.66142	−0.523724
$215$	1.10377	0.0752765
$216$	−2.14198	−0.145743
$217$	−2.42770	−0.164803
$218$	−7.85573	−0.532057
$219$	−9.02206	−0.609654
$220$	0.955969	0.0644514
$221$	−3.08397	−0.207450
$222$	−3.24786	−0.217982
$223$	−2.53124	−0.169505	−0.0847523	−	0.996402i	$-0.527010\pi$
$223$	−2.53124	−0.169505	−0.0847523	+	0.996402i	$0.527010\pi$
$224$	3.77228	0.252046
$225$	−4.94344	−0.329562
$226$	13.4252	0.893030
$227$	−27.0352	−1.79439	−0.897195	−	0.441635i	$-0.854399\pi$
$227$	−27.0352	−1.79439	−0.897195	+	0.441635i	$0.854399\pi$
$228$	0.757417	0.0501612
$229$	−6.76803	−0.447244	−0.223622	−	0.974676i	$-0.571788\pi$
$229$	−6.76803	−0.447244	−0.223622	+	0.974676i	$0.571788\pi$
$230$	−3.20076	−0.211052
$231$	−5.78104	−0.380365
$232$	9.04312	0.593710
$233$	1.85586	0.121581	0.0607907	−	0.998151i	$-0.480638\pi$
$233$	1.85586	0.121581	0.0607907	+	0.998151i	$0.480638\pi$
$234$	3.70643	0.242297
$235$	−0.663346	−0.0432719
$236$	1.44338	0.0939558
$237$	−8.22828	−0.534484
$238$	−2.24264	−0.145369
$239$	−9.15287	−0.592050	−0.296025	−	0.955180i	$-0.595661\pi$
$239$	−9.15287	−0.592050	−0.296025	+	0.955180i	$0.595661\pi$
$240$	1.16708	0.0753346
$241$	2.21622	0.142759	0.0713796	−	0.997449i	$-0.477260\pi$
$241$	2.21622	0.142759	0.0713796	+	0.997449i	$0.477260\pi$
$242$	−36.8084	−2.36613
$243$	−1.00000	−0.0641500
$244$	−1.49215	−0.0955248
$245$	0.237832	0.0151945
$246$	7.02154	0.447677
$247$	2.45935	0.156485
$248$	−5.20010	−0.330206
$249$	−2.94888	−0.186878
$250$	3.88248	0.245550
$251$	−2.11671	−0.133605	−0.0668027	−	0.997766i	$-0.521280\pi$
$251$	−2.11671	−0.133605	−0.0668027	+	0.997766i	$0.521280\pi$
$252$	0.695293	0.0437993
$253$	47.3899	2.97937
$254$	−28.3388	−1.77813
$255$	−0.324883	−0.0203450
$256$	14.9040	0.931498
$257$	−19.8853	−1.24041	−0.620205	−	0.784440i	$-0.712951\pi$
$257$	−19.8853	−1.24041	−0.620205	+	0.784440i	$0.712951\pi$
$258$	7.61923	0.474353
$259$	−1.97831	−0.122926
$260$	−0.373328	−0.0231528
$261$	4.22185	0.261326
$262$	−18.7479	−1.15825
$263$	9.06635	0.559055	0.279527	−	0.960138i	$-0.409822\pi$
$263$	9.06635	0.559055	0.279527	+	0.960138i	$0.409822\pi$
$264$	−12.3829	−0.762114
$265$	1.08948	0.0669264
$266$	1.78842	0.109655
$267$	2.57906	0.157836
$268$	5.51927	0.337143
$269$	−0.433491	−0.0264304	−0.0132152	−	0.999913i	$-0.504207\pi$
$269$	−0.433491	−0.0264304	−0.0132152	+	0.999913i	$0.504207\pi$
$270$	0.390457	0.0237625
$271$	−14.7685	−0.897124	−0.448562	−	0.893752i	$-0.648064\pi$
$271$	−14.7685	−0.897124	−0.448562	+	0.893752i	$0.648064\pi$
$272$	−6.70327	−0.406445
$273$	2.25763	0.136638
$274$	17.7577	1.07278
$275$	−28.5782	−1.72333
$276$	−5.69964	−0.343078
$277$	9.88525	0.593947	0.296974	−	0.954886i	$-0.404023\pi$
$277$	9.88525	0.593947	0.296974	+	0.954886i	$0.404023\pi$
$278$	−37.1566	−2.22850
$279$	−2.42770	−0.145343
$280$	0.509432	0.0304444
$281$	17.6017	1.05003	0.525014	−	0.851094i	$-0.324060\pi$
$281$	17.6017	1.05003	0.525014	+	0.851094i	$0.324060\pi$
$282$	−4.57903	−0.272677
$283$	−16.9893	−1.00991	−0.504954	−	0.863146i	$-0.668491\pi$
$283$	−16.9893	−1.00991	−0.504954	+	0.863146i	$0.668491\pi$
$284$	−1.09850	−0.0651839
$285$	0.259082	0.0153467
$286$	21.4270	1.26701
$287$	4.27690	0.252458
$288$	3.77228	0.222284
$289$	−15.1340	−0.890235
$290$	−1.64845	−0.0968003
$291$	5.87142	0.344189
$292$	6.27297	0.367098
$293$	−2.27390	−0.132843	−0.0664214	−	0.997792i	$-0.521158\pi$
$293$	−2.27390	−0.132843	−0.0664214	+	0.997792i	$0.521158\pi$
$294$	1.64173	0.0957479
$295$	0.493722	0.0287456
$296$	−4.23750	−0.246300
$297$	−5.78104	−0.335450
$298$	37.5582	2.17569
$299$	−18.5068	−1.07028
$300$	3.43714	0.198443
$301$	4.64096	0.267501
$302$	−30.4197	−1.75046
$303$	2.77484	0.159410
$304$	5.34561	0.306592
$305$	−0.510403	−0.0292256
$306$	−2.24264	−0.128203
$307$	0.926766	0.0528933	0.0264467	−	0.999650i	$-0.491581\pi$
$307$	0.926766	0.0528933	0.0264467	+	0.999650i	$0.491581\pi$
$308$	4.01952	0.229033
$309$	4.20839	0.239407
$310$	0.947913	0.0538379
$311$	28.9611	1.64223	0.821117	−	0.570760i	$-0.193351\pi$
$311$	28.9611	1.64223	0.821117	+	0.570760i	$0.193351\pi$
$312$	4.83581	0.273774
$313$	−3.57283	−0.201948	−0.100974	−	0.994889i	$-0.532196\pi$
$313$	−3.57283	−0.201948	−0.100974	+	0.994889i	$0.532196\pi$
$314$	30.2220	1.70553
$315$	0.237832	0.0134003
$316$	5.72106	0.321835
$317$	3.05312	0.171481	0.0857403	−	0.996318i	$-0.472674\pi$
$317$	3.05312	0.171481	0.0857403	+	0.996318i	$0.472674\pi$
$318$	7.52061	0.421735
$319$	24.4067	1.36651
$320$	0.861244	0.0481450
$321$	−4.66666	−0.260468
$322$	−13.4581	−0.749988
$323$	−1.48807	−0.0827986
$324$	0.695293	0.0386274
$325$	11.1605	0.619071
$326$	17.6641	0.978326
$327$	−4.78502	−0.264612
$328$	9.16105	0.505834
$329$	−2.78914	−0.153770
$330$	2.25725	0.124257
$331$	−13.2567	−0.728655	−0.364327	−	0.931271i	$-0.618701\pi$
$331$	−13.2567	−0.728655	−0.364327	+	0.931271i	$0.618701\pi$
$332$	2.05034	0.112527
$333$	−1.97831	−0.108411
$334$	−10.6369	−0.582027
$335$	1.88792	0.103148
$336$	4.90715	0.267707
$337$	13.8112	0.752344	0.376172	−	0.926550i	$-0.377240\pi$
$337$	13.8112	0.752344	0.376172	+	0.926550i	$0.377240\pi$
$338$	12.9748	0.705736
$339$	8.17744	0.444137
$340$	0.225889	0.0122505
$341$	−14.0346	−0.760019
$342$	1.78842	0.0967069
$343$	1.00000	0.0539949
$344$	9.94087	0.535976
$345$	−1.94962	−0.104964
$346$	−34.1291	−1.83479
$347$	27.0004	1.44946	0.724730	−	0.689033i	$-0.241965\pi$
$347$	27.0004	1.44946	0.724730	+	0.689033i	$0.241965\pi$
$348$	−2.93542	−0.157355
$349$	8.00928	0.428727	0.214363	−	0.976754i	$-0.431232\pi$
$349$	8.00928	0.428727	0.214363	+	0.976754i	$0.431232\pi$
$350$	8.11581	0.433808
$351$	2.25763	0.120503
$352$	21.8077	1.16235
$353$	11.4012	0.606826	0.303413	−	0.952859i	$-0.401874\pi$
$353$	11.4012	0.606826	0.303413	+	0.952859i	$0.401874\pi$
$354$	3.40812	0.181140
$355$	−0.375753	−0.0199429
$356$	−1.79320	−0.0950394
$357$	−1.36602	−0.0722974
$358$	−15.8108	−0.835625
$359$	15.6374	0.825310	0.412655	−	0.910887i	$-0.364602\pi$
$359$	15.6374	0.825310	0.412655	+	0.910887i	$0.364602\pi$
$360$	0.509432	0.0268494
$361$	−17.8133	−0.937543
$362$	12.9962	0.683064
$363$	−22.4204	−1.17677
$364$	−1.56971	−0.0822754
$365$	2.14573	0.112313
$366$	−3.52327	−0.184164
$367$	25.4077	1.32627	0.663136	−	0.748499i	$-0.269225\pi$
$367$	25.4077	1.32627	0.663136	+	0.748499i	$0.269225\pi$
$368$	−40.2262	−2.09694
$369$	4.27690	0.222647
$370$	0.772444	0.0401575
$371$	4.58089	0.237828
$372$	1.68796	0.0875168
$373$	8.30425	0.429978	0.214989	−	0.976617i	$-0.431028\pi$
$373$	8.30425	0.429978	0.214989	+	0.976617i	$0.431028\pi$
$374$	−12.9648	−0.670394
$375$	2.36487	0.122121
$376$	−5.97429	−0.308100
$377$	−9.53137	−0.490891
$378$	1.64173	0.0844417
$379$	−8.20219	−0.421318	−0.210659	−	0.977560i	$-0.567561\pi$
$379$	−8.20219	−0.421318	−0.210659	+	0.977560i	$0.567561\pi$
$380$	−0.180138	−0.00924089
$381$	−17.2615	−0.884333
$382$	3.36947	0.172397
$383$	−1.00000	−0.0510976
$383$	−1.00000	−0.0510976
$384$	13.4897	0.688391
$385$	1.37492	0.0700722
$386$	−23.2396	−1.18287
$387$	4.64096	0.235913
$388$	−4.08235	−0.207250
$389$	32.8469	1.66541	0.832703	−	0.553720i	$-0.186792\pi$
$389$	32.8469	1.66541	0.832703	+	0.553720i	$0.186792\pi$
$390$	−0.881508	−0.0446369
$391$	11.1979	0.566302
$392$	2.14198	0.108186
$393$	−11.4196	−0.576041
$394$	2.23470	0.112583
$395$	1.95695	0.0984647
$396$	4.01952	0.201988
$397$	−6.05116	−0.303699	−0.151850	−	0.988404i	$-0.548523\pi$
$397$	−6.05116	−0.303699	−0.151850	+	0.988404i	$0.548523\pi$
$398$	38.5223	1.93095
$399$	1.08935	0.0545357
$400$	24.2582	1.21291
$401$	−39.2333	−1.95922	−0.979608	−	0.200918i	$-0.935607\pi$
$401$	−39.2333	−1.95922	−0.979608	+	0.200918i	$0.935607\pi$
$402$	13.0322	0.649986
$403$	5.48086	0.273021
$404$	−1.92933	−0.0959876
$405$	0.237832	0.0118180
$406$	−6.93115	−0.343987
$407$	−11.4367	−0.566895
$408$	−2.92599	−0.144858
$409$	5.53149	0.273515	0.136757	−	0.990605i	$-0.456332\pi$
$409$	5.53149	0.273515	0.136757	+	0.990605i	$0.456332\pi$
$410$	−1.66995	−0.0824728
$411$	10.8164	0.533534
$412$	−2.92607	−0.144157
$413$	2.07593	0.102150
$414$	−13.4581	−0.661427
$415$	0.701339	0.0344274
$416$	−8.51641	−0.417552
$417$	−22.6325	−1.10832
$418$	10.3390	0.505695
$419$	−32.6458	−1.59485	−0.797425	−	0.603418i	$-0.793805\pi$
$419$	−32.6458	−1.59485	−0.797425	+	0.603418i	$0.793805\pi$
$420$	−0.165363	−0.00806888
$421$	−8.43878	−0.411281	−0.205641	−	0.978628i	$-0.565928\pi$
$421$	−8.43878	−0.411281	−0.205641	+	0.978628i	$0.565928\pi$
$422$	44.9828	2.18973
$423$	−2.78914	−0.135613
$424$	9.81219	0.476522
$425$	−6.75283	−0.327560
$426$	−2.59379	−0.125670
$427$	−2.14607	−0.103855
$428$	3.24470	0.156838
$429$	13.0515	0.630130
$430$	−1.81210	−0.0873871
$431$	6.86425	0.330639	0.165320	−	0.986240i	$-0.447134\pi$
$431$	6.86425	0.330639	0.165320	+	0.986240i	$0.447134\pi$
$432$	4.90715	0.236096
$433$	26.5261	1.27476	0.637381	−	0.770549i	$-0.280018\pi$
$433$	26.5261	1.27476	0.637381	+	0.770549i	$0.280018\pi$
$434$	3.98564	0.191317
$435$	−1.00409	−0.0481424
$436$	3.32699	0.159334
$437$	−8.92991	−0.427175
$438$	14.8118	0.707736
$439$	39.6901	1.89431	0.947153	−	0.320784i	$-0.103946\pi$
$439$	39.6901	1.89431	0.947153	+	0.320784i	$0.103946\pi$
$440$	2.94505	0.140400
$441$	1.00000	0.0476190
$442$	5.06306	0.240825
$443$	6.52266	0.309901	0.154950	−	0.987922i	$-0.450478\pi$
$443$	6.52266	0.309901	0.154950	+	0.987922i	$0.450478\pi$
$444$	1.37550	0.0652785
$445$	−0.613382	−0.0290771
$446$	4.15563	0.196775
$447$	22.8771	1.08205
$448$	3.62123	0.171087
$449$	24.5161	1.15698	0.578492	−	0.815688i	$-0.303641\pi$
$449$	24.5161	1.15698	0.578492	+	0.815688i	$0.303641\pi$
$450$	8.11581	0.382583
$451$	24.7249	1.16425
$452$	−5.68571	−0.267433
$453$	−18.5290	−0.870569
$454$	44.3846	2.08307
$455$	−0.536937	−0.0251720
$456$	2.33337	0.109270
$457$	−40.0070	−1.87145	−0.935723	−	0.352735i	$-0.885252\pi$
$457$	−40.0070	−1.87145	−0.935723	+	0.352735i	$0.885252\pi$
$458$	11.1113	0.519197
$459$	−1.36602	−0.0637603
$460$	1.35556	0.0632031
$461$	−28.2518	−1.31582	−0.657908	−	0.753098i	$-0.728558\pi$
$461$	−28.2518	−1.31582	−0.657908	+	0.753098i	$0.728558\pi$
$462$	9.49094	0.441558
$463$	−0.0447845	−0.00208131	−0.00104066	−	0.999999i	$-0.500331\pi$
$463$	−0.0447845	−0.00208131	−0.00104066	+	0.999999i	$0.500331\pi$
$464$	−20.7173	−0.961774
$465$	0.577385	0.0267756
$466$	−3.04683	−0.141142
$467$	25.4153	1.17608	0.588040	−	0.808832i	$-0.299900\pi$
$467$	25.4153	1.17608	0.588040	+	0.808832i	$0.299900\pi$
$468$	−1.56971	−0.0725601
$469$	7.93805	0.366545
$470$	1.08904	0.0502336
$471$	18.4086	0.848222
$472$	4.44660	0.204671
$473$	26.8296	1.23363
$474$	13.5086	0.620473
$475$	5.38513	0.247087
$476$	0.949783	0.0435332
$477$	4.58089	0.209745
$478$	15.0266	0.687300
$479$	−34.4517	−1.57414	−0.787070	−	0.616864i	$-0.788403\pi$
$479$	−34.4517	−1.57414	−0.787070	+	0.616864i	$0.788403\pi$
$480$	−0.897168	−0.0409499
$481$	4.46629	0.203645
$482$	−3.63844	−0.165726
$483$	−8.19746	−0.372997
$484$	15.5888	0.708580
$485$	−1.39641	−0.0634077
$486$	1.64173	0.0744706
$487$	14.4934	0.656760	0.328380	−	0.944546i	$-0.393497\pi$
$487$	14.4934	0.656760	0.328380	+	0.944546i	$0.393497\pi$
$488$	−4.59684	−0.208089
$489$	10.7594	0.486558
$490$	−0.390457	−0.0176390
$491$	13.5744	0.612604	0.306302	−	0.951934i	$-0.400908\pi$
$491$	13.5744	0.612604	0.306302	+	0.951934i	$0.400908\pi$
$492$	−2.97370	−0.134065
$493$	5.76712	0.259738
$494$	−4.03760	−0.181660
$495$	1.37492	0.0617979
$496$	11.9131	0.534914
$497$	−1.57991	−0.0708686
$498$	4.84129	0.216943
$499$	22.9928	1.02930	0.514649	−	0.857401i	$-0.327922\pi$
$499$	22.9928	1.02930	0.514649	+	0.857401i	$0.327922\pi$
$500$	−1.64427	−0.0735342
$501$	−6.47908	−0.289464
$502$	3.47507	0.155100
$503$	37.3508	1.66539	0.832694	−	0.553733i	$-0.186797\pi$
$503$	37.3508	1.66539	0.832694	+	0.553733i	$0.186797\pi$
$504$	2.14198	0.0954115
$505$	−0.659946	−0.0293672
$506$	−77.8016	−3.45870
$507$	7.90310	0.350989
$508$	12.0018	0.532493
$509$	−29.8651	−1.32375	−0.661875	−	0.749614i	$-0.730239\pi$
$509$	−29.8651	−1.32375	−0.661875	+	0.749614i	$0.730239\pi$
$510$	0.533372	0.0236181
$511$	9.02206	0.399112
$512$	2.51093	0.110969
$513$	1.08935	0.0480960
$514$	32.6464	1.43997
$515$	−1.00089	−0.0441045
$516$	−3.22683	−0.142053
$517$	−16.1241	−0.709138
$518$	3.24786	0.142703
$519$	−20.7885	−0.912512
$520$	−1.15011	−0.0504357
$521$	−16.8500	−0.738214	−0.369107	−	0.929387i	$-0.620336\pi$
$521$	−16.8500	−0.738214	−0.369107	+	0.929387i	$0.620336\pi$
$522$	−6.93115	−0.303368
$523$	−29.5296	−1.29124	−0.645620	−	0.763659i	$-0.723401\pi$
$523$	−29.5296	−1.29124	−0.645620	+	0.763659i	$0.723401\pi$
$524$	7.93995	0.346858
$525$	4.94344	0.215749
$526$	−14.8845	−0.648997
$527$	−3.31629	−0.144460
$528$	28.3685	1.23458
$529$	44.1984	1.92167
$530$	−1.78864	−0.0776936
$531$	2.07593	0.0900875
$532$	−0.757417	−0.0328382
$533$	−9.65567	−0.418233
$534$	−4.23413	−0.183229
$535$	1.10988	0.0479844
$536$	17.0032	0.734425
$537$	−9.63053	−0.415588
$538$	0.711677	0.0306826
$539$	5.78104	0.249007
$540$	−0.165363	−0.00711608
$541$	−13.5892	−0.584244	−0.292122	−	0.956381i	$-0.594361\pi$
$541$	−13.5892	−0.584244	−0.292122	+	0.956381i	$0.594361\pi$
$542$	24.2460	1.04146
$543$	7.91612	0.339713
$544$	5.15300	0.220933
$545$	1.13803	0.0487479
$546$	−3.70643	−0.158621
$547$	10.0767	0.430847	0.215424	−	0.976521i	$-0.430887\pi$
$547$	10.0767	0.430847	0.215424	+	0.976521i	$0.430887\pi$
$548$	−7.52057	−0.321263
$549$	−2.14607	−0.0915919
$550$	46.9178	2.00058
$551$	−4.59907	−0.195927
$552$	−17.5588	−0.747353
$553$	8.22828	0.349902
$554$	−16.2290	−0.689503
$555$	0.470505	0.0199718
$556$	15.7362	0.667365
$557$	39.7523	1.68436	0.842179	−	0.539198i	$-0.181273\pi$
$557$	39.7523	1.68436	0.842179	+	0.539198i	$0.181273\pi$
$558$	3.98564	0.168726
$559$	−10.4776	−0.443155
$560$	−1.16708	−0.0493180
$561$	−7.89701	−0.333412
$562$	−28.8973	−1.21896
$563$	24.7189	1.04178	0.520889	−	0.853625i	$-0.325601\pi$
$563$	24.7189	1.04178	0.520889	+	0.853625i	$0.325601\pi$
$564$	1.93927	0.0816579
$565$	−1.94486	−0.0818207
$566$	27.8919	1.17238
$567$	1.00000	0.0419961
$568$	−3.38414	−0.141995
$569$	3.43028	0.143805	0.0719024	−	0.997412i	$-0.477093\pi$
$569$	3.43028	0.143805	0.0719024	+	0.997412i	$0.477093\pi$
$570$	−0.425344	−0.0178157
$571$	−14.3960	−0.602452	−0.301226	−	0.953553i	$-0.597396\pi$
$571$	−14.3960	−0.602452	−0.301226	+	0.953553i	$0.597396\pi$
$572$	−9.07459	−0.379428
$573$	2.05238	0.0857396
$574$	−7.02154	−0.293073
$575$	−40.5236	−1.68995
$576$	3.62123	0.150884
$577$	−30.5189	−1.27052	−0.635260	−	0.772299i	$-0.719107\pi$
$577$	−30.5189	−1.27052	−0.635260	+	0.772299i	$0.719107\pi$
$578$	24.8460	1.03346
$579$	−14.1555	−0.588284
$580$	0.698137	0.0289885
$581$	2.94888	0.122340
$582$	−9.63931	−0.399562
$583$	26.4823	1.09679
$584$	19.3251	0.799678
$585$	−0.536937	−0.0221996
$586$	3.73314	0.154215
$587$	42.0285	1.73470	0.867350	−	0.497698i	$-0.165821\pi$
$587$	42.0285	1.73470	0.867350	+	0.497698i	$0.165821\pi$
$588$	−0.695293	−0.0286734
$589$	2.64462	0.108970
$590$	−0.810560	−0.0333702
$591$	1.36118	0.0559916
$592$	9.70786	0.398991
$593$	−9.97632	−0.409678	−0.204839	−	0.978796i	$-0.565667\pi$
$593$	−9.97632	−0.409678	−0.204839	+	0.978796i	$0.565667\pi$
$594$	9.49094	0.389418
$595$	0.324883	0.0133189
$596$	−15.9063	−0.651548
$597$	23.4644	0.960333
$598$	30.3833	1.24247
$599$	36.0274	1.47204	0.736020	−	0.676960i	$-0.236703\pi$
$599$	36.0274	1.47204	0.736020	+	0.676960i	$0.236703\pi$
$600$	10.5888	0.432284
$601$	5.63556	0.229879	0.114940	−	0.993372i	$-0.463333\pi$
$601$	5.63556	0.229879	0.114940	+	0.993372i	$0.463333\pi$
$602$	−7.61923	−0.310537
$603$	7.93805	0.323262
$604$	12.8831	0.524206
$605$	5.33230	0.216789
$606$	−4.55555	−0.185057
$607$	−39.4141	−1.59977	−0.799885	−	0.600153i	$-0.795106\pi$
$607$	−39.4141	−1.59977	−0.799885	+	0.600153i	$0.795106\pi$
$608$	−4.10933	−0.166655
$609$	−4.22185	−0.171078
$610$	0.837947	0.0339275
$611$	6.29685	0.254743
$612$	0.949783	0.0383927
$613$	16.4373	0.663897	0.331949	−	0.943297i	$-0.392294\pi$
$613$	16.4373	0.663897	0.331949	+	0.943297i	$0.392294\pi$
$614$	−1.52150	−0.0614029
$615$	−1.01718	−0.0410168
$616$	12.3829	0.498921
$617$	−24.7027	−0.994492	−0.497246	−	0.867610i	$-0.665655\pi$
$617$	−24.7027	−0.994492	−0.497246	+	0.867610i	$0.665655\pi$
$618$	−6.90907	−0.277923
$619$	23.2597	0.934885	0.467443	−	0.884023i	$-0.345175\pi$
$619$	23.2597	0.934885	0.467443	+	0.884023i	$0.345175\pi$
$620$	−0.401452	−0.0161227
$621$	−8.19746	−0.328953
$622$	−47.5465	−1.90644
$623$	−2.57906	−0.103328
$624$	−11.0785	−0.443497
$625$	24.1547	0.966190
$626$	5.86564	0.234438
$627$	6.29758	0.251501
$628$	−12.7994	−0.510750
$629$	−2.70241	−0.107752
$630$	−0.390457	−0.0155562
$631$	−2.08624	−0.0830519	−0.0415260	−	0.999137i	$-0.513222\pi$
$631$	−2.08624	−0.0830519	−0.0415260	+	0.999137i	$0.513222\pi$
$632$	17.6248	0.701078
$633$	27.3996	1.08903
$634$	−5.01242	−0.199069
$635$	4.10533	0.162915
$636$	−3.18506	−0.126296
$637$	−2.25763	−0.0894506
$638$	−40.0693	−1.58636
$639$	−1.57991	−0.0625002
$640$	−3.20827	−0.126818
$641$	26.0119	1.02741	0.513704	−	0.857968i	$-0.328273\pi$
$641$	26.0119	1.02741	0.513704	+	0.857968i	$0.328273\pi$
$642$	7.66142	0.302372
$643$	−29.1598	−1.14995	−0.574975	−	0.818171i	$-0.694988\pi$
$643$	−29.1598	−1.14995	−0.574975	+	0.818171i	$0.694988\pi$
$644$	5.69964	0.224597
$645$	−1.10377	−0.0434609
$646$	2.44302	0.0961194
$647$	−9.26412	−0.364210	−0.182105	−	0.983279i	$-0.558291\pi$
$647$	−9.26412	−0.364210	−0.182105	+	0.983279i	$0.558291\pi$
$648$	2.14198	0.0841450
$649$	12.0010	0.471081
$650$	−18.3225	−0.718668
$651$	2.42770	0.0951491
$652$	−7.48095	−0.292977
$653$	5.52170	0.216081	0.108041	−	0.994146i	$-0.465542\pi$
$653$	5.52170	0.216081	0.108041	+	0.994146i	$0.465542\pi$
$654$	7.85573	0.307183
$655$	2.71594	0.106121
$656$	−20.9874	−0.819421
$657$	9.02206	0.351984
$658$	4.57903	0.178509
$659$	−13.8918	−0.541147	−0.270573	−	0.962699i	$-0.587213\pi$
$659$	−13.8918	−0.541147	−0.270573	+	0.962699i	$0.587213\pi$
$660$	−0.955969	−0.0372111
$661$	18.1436	0.705703	0.352852	−	0.935679i	$-0.385212\pi$
$661$	18.1436	0.705703	0.352852	+	0.935679i	$0.385212\pi$
$662$	21.7640	0.845882
$663$	3.08397	0.119771
$664$	6.31646	0.245126
$665$	−0.259082	−0.0100468
$666$	3.24786	0.125852
$667$	34.6084	1.34004
$668$	4.50486	0.174298
$669$	2.53124	0.0978635
$670$	−3.09947	−0.119743
$671$	−12.4065	−0.478948
$672$	−3.77228	−0.145519
$673$	11.3744	0.438452	0.219226	−	0.975674i	$-0.429647\pi$
$673$	11.3744	0.438452	0.219226	+	0.975674i	$0.429647\pi$
$674$	−22.6743	−0.873383
$675$	4.94344	0.190273
$676$	−5.49497	−0.211345
$677$	24.4944	0.941397	0.470699	−	0.882294i	$-0.344002\pi$
$677$	24.4944	0.941397	0.470699	+	0.882294i	$0.344002\pi$
$678$	−13.4252	−0.515591
$679$	−5.87142	−0.225324
$680$	0.695894	0.0266863
$681$	27.0352	1.03599
$682$	23.0412	0.882292
$683$	−9.63629	−0.368722	−0.184361	−	0.982859i	$-0.559022\pi$
$683$	−9.63629	−0.368722	−0.184361	+	0.982859i	$0.559022\pi$
$684$	−0.757417	−0.0289606
$685$	−2.57249	−0.0982896
$686$	−1.64173	−0.0626817
$687$	6.76803	0.258216
$688$	−22.7739	−0.868248
$689$	−10.3420	−0.393998
$690$	3.20076	0.121851
$691$	−15.0802	−0.573679	−0.286839	−	0.957979i	$-0.592605\pi$
$691$	−15.0802	−0.573679	−0.286839	+	0.957979i	$0.592605\pi$
$692$	14.4541	0.549461
$693$	5.78104	0.219604
$694$	−44.3276	−1.68265
$695$	5.38274	0.204179
$696$	−9.04312	−0.342779
$697$	5.84233	0.221294
$698$	−13.1491	−0.497701
$699$	−1.85586	−0.0701950
$700$	−3.43714	−0.129912
$701$	26.2730	0.992317	0.496158	−	0.868232i	$-0.334744\pi$
$701$	26.2730	0.992317	0.496158	+	0.868232i	$0.334744\pi$
$702$	−3.70643	−0.139890
$703$	2.15507	0.0812800
$704$	20.9345	0.788997
$705$	0.663346	0.0249831
$706$	−18.7178	−0.704453
$707$	−2.77484	−0.104359
$708$	−1.44338	−0.0542454
$709$	−14.4530	−0.542792	−0.271396	−	0.962468i	$-0.587485\pi$
$709$	−14.4530	−0.542792	−0.271396	+	0.962468i	$0.587485\pi$
$710$	0.616886	0.0231513
$711$	8.22828	0.308584
$712$	−5.52429	−0.207032
$713$	−19.9010	−0.745298
$714$	2.24264	0.0839287
$715$	−3.10405	−0.116085
$716$	6.69604	0.250243
$717$	9.15287	0.341820
$718$	−25.6725	−0.958087
$719$	−12.6577	−0.472051	−0.236026	−	0.971747i	$-0.575845\pi$
$719$	−12.6577	−0.472051	−0.236026	+	0.971747i	$0.575845\pi$
$720$	−1.16708	−0.0434944
$721$	−4.20839	−0.156729
$722$	29.2447	1.08838
$723$	−2.21622	−0.0824220
$724$	−5.50402	−0.204555
$725$	−20.8704	−0.775108
$726$	36.8084	1.36609
$727$	18.4504	0.684287	0.342143	−	0.939648i	$-0.388847\pi$
$727$	18.4504	0.684287	0.342143	+	0.939648i	$0.388847\pi$
$728$	−4.83581	−0.179227
$729$	1.00000	0.0370370
$730$	−3.52272	−0.130382
$731$	6.33964	0.234480
$732$	1.49215	0.0551513
$733$	0.491812	0.0181655	0.00908275	−	0.999959i	$-0.497109\pi$
$733$	0.491812	0.0181655	0.00908275	+	0.999959i	$0.497109\pi$
$734$	−41.7127	−1.53964
$735$	−0.237832	−0.00877256
$736$	30.9231	1.13984
$737$	45.8902	1.69039
$738$	−7.02154	−0.258466
$739$	−10.5570	−0.388344	−0.194172	−	0.980967i	$-0.562202\pi$
$739$	−10.5570	−0.388344	−0.194172	+	0.980967i	$0.562202\pi$
$740$	−0.327139	−0.0120259
$741$	−2.45935	−0.0903465
$742$	−7.52061	−0.276090
$743$	3.77989	0.138671	0.0693354	−	0.997593i	$-0.477912\pi$
$743$	3.77989	0.138671	0.0693354	+	0.997593i	$0.477912\pi$
$744$	5.20010	0.190645
$745$	−5.44091	−0.199340
$746$	−13.6334	−0.499153
$747$	2.94888	0.107894
$748$	5.49074	0.200761
$749$	4.66666	0.170516
$750$	−3.88248	−0.141768
$751$	−31.8886	−1.16363	−0.581815	−	0.813321i	$-0.697657\pi$
$751$	−31.8886	−1.16363	−0.581815	+	0.813321i	$0.697657\pi$
$752$	13.6867	0.499104
$753$	2.11671	0.0771371
$754$	15.6480	0.569866
$755$	4.40679	0.160380
$756$	−0.695293	−0.0252876
$757$	−29.7429	−1.08102	−0.540512	−	0.841336i	$-0.681769\pi$
$757$	−29.7429	−1.08102	−0.540512	+	0.841336i	$0.681769\pi$
$758$	13.4658	0.489101
$759$	−47.3899	−1.72014
$760$	−0.554950	−0.0201301
$761$	−14.3994	−0.521978	−0.260989	−	0.965342i	$-0.584049\pi$
$761$	−14.3994	−0.521978	−0.260989	+	0.965342i	$0.584049\pi$
$762$	28.3388	1.02661
$763$	4.78502	0.173229
$764$	−1.42701	−0.0516273
$765$	0.324883	0.0117462
$766$	1.64173	0.0593183
$767$	−4.68668	−0.169226
$768$	−14.9040	−0.537801
$769$	6.53624	0.235703	0.117851	−	0.993031i	$-0.462399\pi$
$769$	6.53624	0.235703	0.117851	+	0.993031i	$0.462399\pi$
$770$	−2.25725	−0.0813456
$771$	19.8853	0.716151
$772$	9.84224	0.354230
$773$	0.894761	0.0321823	0.0160912	−	0.999871i	$-0.494878\pi$
$773$	0.894761	0.0321823	0.0160912	+	0.999871i	$0.494878\pi$
$774$	−7.61923	−0.273868
$775$	12.0012	0.431095
$776$	−12.5765	−0.451469
$777$	1.97831	0.0709714
$778$	−53.9260	−1.93334
$779$	−4.65904	−0.166928
$780$	0.373328	0.0133673
$781$	−9.13351	−0.326823
$782$	−18.3840	−0.657409
$783$	−4.22185	−0.150876
$784$	−4.90715	−0.175255
$785$	−4.37815	−0.156263
$786$	18.7479	0.668716
$787$	43.6054	1.55436	0.777182	−	0.629275i	$-0.216648\pi$
$787$	43.6054	1.55436	0.777182	+	0.629275i	$0.216648\pi$
$788$	−0.946421	−0.0337148
$789$	−9.06635	−0.322771
$790$	−3.21279	−0.114306
$791$	−8.17744	−0.290756
$792$	12.3829	0.440007
$793$	4.84503	0.172052
$794$	9.93441	0.352559
$795$	−1.08948	−0.0386400
$796$	−16.3146	−0.578256
$797$	−21.8603	−0.774333	−0.387166	−	0.922010i	$-0.626546\pi$
$797$	−21.8603	−0.774333	−0.387166	+	0.922010i	$0.626546\pi$
$798$	−1.78842	−0.0633095
$799$	−3.81002	−0.134789
$800$	−18.6480	−0.659307
$801$	−2.57906	−0.0911265
$802$	64.4106	2.27442
$803$	52.1569	1.84058
$804$	−5.51927	−0.194650
$805$	1.94962	0.0687150
$806$	−8.99811	−0.316945
$807$	0.433491	0.0152596
$808$	−5.94366	−0.209097
$809$	16.4303	0.577658	0.288829	−	0.957381i	$-0.406734\pi$
$809$	16.4303	0.577658	0.288829	+	0.957381i	$0.406734\pi$
$810$	−0.390457	−0.0137193
$811$	9.27313	0.325623	0.162812	−	0.986657i	$-0.447944\pi$
$811$	9.27313	0.325623	0.162812	+	0.986657i	$0.447944\pi$
$812$	2.93542	0.103013
$813$	14.7685	0.517955
$814$	18.7760	0.658098
$815$	−2.55894	−0.0896356
$816$	6.70327	0.234661
$817$	−5.05563	−0.176874
$818$	−9.08124	−0.317518
$819$	−2.25763	−0.0788880
$820$	0.707241	0.0246979
$821$	−11.1906	−0.390554	−0.195277	−	0.980748i	$-0.562561\pi$
$821$	−11.1906	−0.390554	−0.195277	+	0.980748i	$0.562561\pi$
$822$	−17.7577	−0.619370
$823$	6.95247	0.242348	0.121174	−	0.992631i	$-0.461334\pi$
$823$	6.95247	0.242348	0.121174	+	0.992631i	$0.461334\pi$
$824$	−9.01431	−0.314028
$825$	28.5782	0.994965
$826$	−3.40812	−0.118584
$827$	−25.9722	−0.903142	−0.451571	−	0.892235i	$-0.649136\pi$
$827$	−25.9722	−0.903142	−0.451571	+	0.892235i	$0.649136\pi$
$828$	5.69964	0.198076
$829$	44.4629	1.54426	0.772131	−	0.635464i	$-0.219191\pi$
$829$	44.4629	1.54426	0.772131	+	0.635464i	$0.219191\pi$
$830$	−1.15141	−0.0399661
$831$	−9.88525	−0.342916
$832$	−8.17540	−0.283431
$833$	1.36602	0.0473298
$834$	37.1566	1.28663
$835$	1.54093	0.0533262
$836$	−4.37866	−0.151439
$837$	2.42770	0.0839137
$838$	53.5957	1.85143
$839$	−42.0751	−1.45259	−0.726296	−	0.687382i	$-0.758760\pi$
$839$	−42.0751	−1.45259	−0.726296	+	0.687382i	$0.758760\pi$
$840$	−0.509432	−0.0175771
$841$	−11.1760	−0.385380
$842$	13.8542	0.477449
$843$	−17.6017	−0.606234
$844$	−19.0507	−0.655753
$845$	−1.87961	−0.0646605
$846$	4.57903	0.157430
$847$	22.4204	0.770375
$848$	−22.4791	−0.771937
$849$	16.9893	0.583071
$850$	11.0864	0.380259
$851$	−16.2171	−0.555915
$852$	1.09850	0.0376339
$853$	22.3841	0.766418	0.383209	−	0.923662i	$-0.374819\pi$
$853$	22.3841	0.766418	0.383209	+	0.923662i	$0.374819\pi$
$854$	3.52327	0.120564
$855$	−0.259082	−0.00886043
$856$	9.99591	0.341653
$857$	49.7405	1.69910	0.849552	−	0.527505i	$-0.176872\pi$
$857$	49.7405	1.69910	0.849552	+	0.527505i	$0.176872\pi$
$858$	−21.4270	−0.731507
$859$	−6.12407	−0.208951	−0.104475	−	0.994527i	$-0.533316\pi$
$859$	−6.12407	−0.208951	−0.104475	+	0.994527i	$0.533316\pi$
$860$	0.767443	0.0261696
$861$	−4.27690	−0.145756
$862$	−11.2693	−0.383833
$863$	−39.6564	−1.34992	−0.674959	−	0.737855i	$-0.735839\pi$
$863$	−39.6564	−1.34992	−0.674959	+	0.737855i	$0.735839\pi$
$864$	−3.77228	−0.128336
$865$	4.94416	0.168106
$866$	−43.5488	−1.47985
$867$	15.1340	0.513977
$868$	−1.68796	−0.0572932
$869$	47.5680	1.61363
$870$	1.64845	0.0558877
$871$	−17.9212	−0.607236
$872$	10.2494	0.347089
$873$	−5.87142	−0.198717
$874$	14.6605	0.495900
$875$	−2.36487	−0.0799471
$876$	−6.27297	−0.211944
$877$	49.0629	1.65674	0.828369	−	0.560183i	$-0.189269\pi$
$877$	49.0629	1.65674	0.828369	+	0.560183i	$0.189269\pi$
$878$	−65.1606	−2.19906
$879$	2.27390	0.0766968
$880$	−6.74693	−0.227439
$881$	8.89268	0.299602	0.149801	−	0.988716i	$-0.452137\pi$
$881$	8.89268	0.299602	0.149801	+	0.988716i	$0.452137\pi$
$882$	−1.64173	−0.0552801
$883$	55.8572	1.87974	0.939872	−	0.341528i	$-0.110944\pi$
$883$	55.8572	1.87974	0.939872	+	0.341528i	$0.110944\pi$
$884$	−2.14426	−0.0721193
$885$	−0.493722	−0.0165963
$886$	−10.7085	−0.359758
$887$	16.3919	0.550387	0.275193	−	0.961389i	$-0.411258\pi$
$887$	16.3919	0.550387	0.275193	+	0.961389i	$0.411258\pi$
$888$	4.23750	0.142201
$889$	17.2615	0.578932
$890$	1.00701	0.0337551
$891$	5.78104	0.193672
$892$	−1.75995	−0.0589276
$893$	3.03835	0.101674
$894$	−37.5582	−1.25613
$895$	2.29045	0.0765612
$896$	−13.4897	−0.450658
$897$	18.5068	0.617926
$898$	−40.2489	−1.34312
$899$	−10.2494	−0.341836
$900$	−3.43714	−0.114571
$901$	6.25759	0.208470
$902$	−40.5918	−1.35156
$903$	−4.64096	−0.154442
$904$	−17.5159	−0.582571
$905$	−1.88271	−0.0625833
$906$	30.4197	1.01063
$907$	31.3764	1.04184	0.520918	−	0.853607i	$-0.325590\pi$
$907$	31.3764	1.04184	0.520918	+	0.853607i	$0.325590\pi$
$908$	−18.7974	−0.623813
$909$	−2.77484	−0.0920356
$910$	0.881508	0.0292217
$911$	−4.11265	−0.136258	−0.0681292	−	0.997677i	$-0.521703\pi$
$911$	−4.11265	−0.136258	−0.0681292	+	0.997677i	$0.521703\pi$
$912$	−5.34561	−0.177011
$913$	17.0476	0.564194
$914$	65.6808	2.17253
$915$	0.510403	0.0168734
$916$	−4.70576	−0.155483
$917$	11.4196	0.377108
$918$	2.24264	0.0740182
$919$	−7.62239	−0.251439	−0.125720	−	0.992066i	$-0.540124\pi$
$919$	−7.62239	−0.251439	−0.125720	+	0.992066i	$0.540124\pi$
$920$	4.17605	0.137680
$921$	−0.926766	−0.0305380
$922$	46.3819	1.52751
$923$	3.56685	0.117404
$924$	−4.01952	−0.132232
$925$	9.77964	0.321552
$926$	0.0735243	0.00241616
$927$	−4.20839	−0.138222
$928$	15.9260	0.522796
$929$	52.6591	1.72769	0.863845	−	0.503758i	$-0.168050\pi$
$929$	52.6591	1.72769	0.863845	+	0.503758i	$0.168050\pi$
$930$	−0.947913	−0.0310833
$931$	−1.08935	−0.0357020
$932$	1.29037	0.0422673
$933$	−28.9611	−0.948144
$934$	−41.7252	−1.36529
$935$	1.87816	0.0614225
$936$	−4.83581	−0.158063
$937$	25.4912	0.832760	0.416380	−	0.909191i	$-0.363299\pi$
$937$	25.4912	0.832760	0.416380	+	0.909191i	$0.363299\pi$
$938$	−13.0322	−0.425515
$939$	3.57283	0.116595
$940$	−0.461220	−0.0150433
$941$	−45.8401	−1.49434	−0.747172	−	0.664631i	$-0.768589\pi$
$941$	−45.8401	−1.49434	−0.747172	+	0.664631i	$0.768589\pi$
$942$	−30.2220	−0.984686
$943$	35.0597	1.14170
$944$	−10.1869	−0.331555
$945$	−0.237832	−0.00773667
$946$	−44.0471	−1.43209
$947$	−10.4076	−0.338202	−0.169101	−	0.985599i	$-0.554086\pi$
$947$	−10.4076	−0.338202	−0.169101	+	0.985599i	$0.554086\pi$
$948$	−5.72106	−0.185811
$949$	−20.3685	−0.661189
$950$	−8.84096	−0.286839
$951$	−3.05312	−0.0990043
$952$	2.92599	0.0948319
$953$	−28.7135	−0.930120	−0.465060	−	0.885279i	$-0.653967\pi$
$953$	−28.7135	−0.930120	−0.465060	+	0.885279i	$0.653967\pi$
$954$	−7.52061	−0.243489
$955$	−0.488122	−0.0157953
$956$	−6.36392	−0.205824
$957$	−24.4067	−0.788956
$958$	56.5606	1.82739
$959$	−10.8164	−0.349280
$960$	−0.861244	−0.0277965
$961$	−25.1063	−0.809879
$962$	−7.33246	−0.236408
$963$	4.66666	0.150381
$964$	1.54092	0.0496297
$965$	3.36664	0.108376
$966$	13.4581	0.433006
$967$	43.2551	1.39099	0.695495	−	0.718530i	$-0.255185\pi$
$967$	43.2551	1.39099	0.695495	+	0.718530i	$0.255185\pi$
$968$	48.0242	1.54356
$969$	1.48807	0.0478038
$970$	2.29254	0.0736089
$971$	34.8729	1.11912	0.559562	−	0.828788i	$-0.310969\pi$
$971$	34.8729	1.11912	0.559562	+	0.828788i	$0.310969\pi$
$972$	−0.695293	−0.0223015
$973$	22.6325	0.725565
$974$	−23.7944	−0.762421
$975$	−11.1605	−0.357421
$976$	10.5311	0.337092
$977$	19.6616	0.629031	0.314515	−	0.949252i	$-0.398158\pi$
$977$	19.6616	0.629031	0.314515	+	0.949252i	$0.398158\pi$
$978$	−17.6641	−0.564837
$979$	−14.9096	−0.476514
$980$	0.165363	0.00528232
$981$	4.78502	0.152774
$982$	−22.2856	−0.711161
$983$	7.83129	0.249779	0.124890	−	0.992171i	$-0.460142\pi$
$983$	7.83129	0.249779	0.124890	+	0.992171i	$0.460142\pi$
$984$	−9.16105	−0.292044
$985$	−0.323733	−0.0103150
$986$	−9.46809	−0.301525
$987$	2.78914	0.0887793
$988$	1.70997	0.0544014
$989$	38.0441	1.20973
$990$	−2.25725	−0.0717400
$991$	2.12575	0.0675267	0.0337633	−	0.999430i	$-0.489251\pi$
$991$	2.12575	0.0675267	0.0337633	+	0.999430i	$0.489251\pi$
$992$	−9.15797	−0.290766
$993$	13.2567	0.420689
$994$	2.59379	0.0822700
$995$	−5.58058	−0.176916
$996$	−2.05034	−0.0649675
$997$	7.82010	0.247665	0.123832	−	0.992303i	$-0.460481\pi$
$997$	7.82010	0.247665	0.123832	+	0.992303i	$0.460481\pi$
$998$	−37.7481	−1.19489
$999$	1.97831	0.0625909

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8043.2.a.t.1.13	✓	52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8043.2.a.t.1.13	✓	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)

\(f(q)\)	\(=\)	\(q-1.64173 q^{2} -1.00000 q^{3} +0.695293 q^{4} +0.237832 q^{5} +1.64173 q^{6} +1.00000 q^{7} +2.14198 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.64173 q^{2} -1.00000 q^{3} +0.695293 q^{4} +0.237832 q^{5} +1.64173 q^{6} +1.00000 q^{7} +2.14198 q^{8} +1.00000 q^{9} -0.390457 q^{10} +5.78104 q^{11} -0.695293 q^{12} -2.25763 q^{13} -1.64173 q^{14} -0.237832 q^{15} -4.90715 q^{16} +1.36602 q^{17} -1.64173 q^{18} -1.08935 q^{19} +0.165363 q^{20} -1.00000 q^{21} -9.49094 q^{22} +8.19746 q^{23} -2.14198 q^{24} -4.94344 q^{25} +3.70643 q^{26} -1.00000 q^{27} +0.695293 q^{28} +4.22185 q^{29} +0.390457 q^{30} -2.42770 q^{31} +3.77228 q^{32} -5.78104 q^{33} -2.24264 q^{34} +0.237832 q^{35} +0.695293 q^{36} -1.97831 q^{37} +1.78842 q^{38} +2.25763 q^{39} +0.509432 q^{40} +4.27690 q^{41} +1.64173 q^{42} +4.64096 q^{43} +4.01952 q^{44} +0.237832 q^{45} -13.4581 q^{46} -2.78914 q^{47} +4.90715 q^{48} +1.00000 q^{49} +8.11581 q^{50} -1.36602 q^{51} -1.56971 q^{52} +4.58089 q^{53} +1.64173 q^{54} +1.37492 q^{55} +2.14198 q^{56} +1.08935 q^{57} -6.93115 q^{58} +2.07593 q^{59} -0.165363 q^{60} -2.14607 q^{61} +3.98564 q^{62} +1.00000 q^{63} +3.62123 q^{64} -0.536937 q^{65} +9.49094 q^{66} +7.93805 q^{67} +0.949783 q^{68} -8.19746 q^{69} -0.390457 q^{70} -1.57991 q^{71} +2.14198 q^{72} +9.02206 q^{73} +3.24786 q^{74} +4.94344 q^{75} -0.757417 q^{76} +5.78104 q^{77} -3.70643 q^{78} +8.22828 q^{79} -1.16708 q^{80} +1.00000 q^{81} -7.02154 q^{82} +2.94888 q^{83} -0.695293 q^{84} +0.324883 q^{85} -7.61923 q^{86} -4.22185 q^{87} +12.3829 q^{88} -2.57906 q^{89} -0.390457 q^{90} -2.25763 q^{91} +5.69964 q^{92} +2.42770 q^{93} +4.57903 q^{94} -0.259082 q^{95} -3.77228 q^{96} -5.87142 q^{97} -1.64173 q^{98} +5.78104 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q + 3 q^{2} - 52 q^{3} + 61 q^{4} - 7 q^{5} - 3 q^{6} + 52 q^{7} + 24 q^{8} + 52 q^{9}+O(q^{10}) \) 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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