LMFDB - Embedded newform 6026.2.a.m.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6026,2,Mod(1,6026)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6026, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("6026.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6026 = 2 \cdot 23 \cdot 131 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6026.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:	$48.1178522580$
Analytic rank:	$0$
Dimension:	$41$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Character	$\chi$	$=$	6026.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -3.22313 q^{3} +1.00000 q^{4} -0.601968 q^{5} -3.22313 q^{6} -4.66050 q^{7} +1.00000 q^{8} +7.38856 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -3.22313 q^{3} +1.00000 q^{4} -0.601968 q^{5} -3.22313 q^{6} -4.66050 q^{7} +1.00000 q^{8} +7.38856 q^{9} -0.601968 q^{10} +5.32153 q^{11} -3.22313 q^{12} +1.09324 q^{13} -4.66050 q^{14} +1.94022 q^{15} +1.00000 q^{16} -0.187895 q^{17} +7.38856 q^{18} +7.97941 q^{19} -0.601968 q^{20} +15.0214 q^{21} +5.32153 q^{22} +1.00000 q^{23} -3.22313 q^{24} -4.63763 q^{25} +1.09324 q^{26} -14.1449 q^{27} -4.66050 q^{28} -8.43702 q^{29} +1.94022 q^{30} -3.70101 q^{31} +1.00000 q^{32} -17.1520 q^{33} -0.187895 q^{34} +2.80548 q^{35} +7.38856 q^{36} +9.99519 q^{37} +7.97941 q^{38} -3.52364 q^{39} -0.601968 q^{40} -1.80066 q^{41} +15.0214 q^{42} +6.14508 q^{43} +5.32153 q^{44} -4.44768 q^{45} +1.00000 q^{46} -10.6149 q^{47} -3.22313 q^{48} +14.7203 q^{49} -4.63763 q^{50} +0.605610 q^{51} +1.09324 q^{52} +8.90981 q^{53} -14.1449 q^{54} -3.20339 q^{55} -4.66050 q^{56} -25.7187 q^{57} -8.43702 q^{58} -5.16023 q^{59} +1.94022 q^{60} +8.21286 q^{61} -3.70101 q^{62} -34.4344 q^{63} +1.00000 q^{64} -0.658093 q^{65} -17.1520 q^{66} -6.93155 q^{67} -0.187895 q^{68} -3.22313 q^{69} +2.80548 q^{70} -12.3902 q^{71} +7.38856 q^{72} -6.97958 q^{73} +9.99519 q^{74} +14.9477 q^{75} +7.97941 q^{76} -24.8010 q^{77} -3.52364 q^{78} +7.45177 q^{79} -0.601968 q^{80} +23.4251 q^{81} -1.80066 q^{82} -14.3598 q^{83} +15.0214 q^{84} +0.113107 q^{85} +6.14508 q^{86} +27.1936 q^{87} +5.32153 q^{88} -0.650144 q^{89} -4.44768 q^{90} -5.09503 q^{91} +1.00000 q^{92} +11.9288 q^{93} -10.6149 q^{94} -4.80335 q^{95} -3.22313 q^{96} -11.4871 q^{97} +14.7203 q^{98} +39.3184 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 41 q + 41 q^{2} + 4 q^{3} + 41 q^{4} + 9 q^{5} + 4 q^{6} + 12 q^{7} + 41 q^{8} + 63 q^{9}+O(q^{10}) $ 41 * q + 41 * q^2 + 4 * q^3 + 41 * q^4 + 9 * q^5 + 4 * q^6 + 12 * q^7 + 41 * q^8 + 63 * q^9	\( 41 q + 41 q^{2} + 4 q^{3} + 41 q^{4} + 9 q^{5} + 4 q^{6} + 12 q^{7} + 41 q^{8} + 63 q^{9} + 9 q^{10} + 4 q^{11} + 4 q^{12} + 16 q^{13} + 12 q^{14} + 10 q^{15} + 41 q^{16} + 10 q^{17} + 63 q^{18} + 16 q^{19} + 9 q^{20} + 16 q^{21} + 4 q^{22} + 41 q^{23} + 4 q^{24} + 76 q^{25} + 16 q^{26} + 7 q^{27} + 12 q^{28} + 28 q^{29} + 10 q^{30} + 25 q^{31} + 41 q^{32} + 5 q^{33} + 10 q^{34} + 4 q^{35} + 63 q^{36} + 26 q^{37} + 16 q^{38} + 50 q^{39} + 9 q^{40} + 27 q^{41} + 16 q^{42} + 12 q^{43} + 4 q^{44} + 44 q^{45} + 41 q^{46} + 18 q^{47} + 4 q^{48} + 87 q^{49} + 76 q^{50} + 24 q^{51} + 16 q^{52} + 63 q^{53} + 7 q^{54} + 18 q^{55} + 12 q^{56} - 12 q^{57} + 28 q^{58} + 33 q^{59} + 10 q^{60} + 24 q^{61} + 25 q^{62} + 48 q^{63} + 41 q^{64} + 21 q^{65} + 5 q^{66} - 9 q^{67} + 10 q^{68} + 4 q^{69} + 4 q^{70} + 36 q^{71} + 63 q^{72} + 36 q^{73} + 26 q^{74} + 6 q^{75} + 16 q^{76} + 48 q^{77} + 50 q^{78} + 51 q^{79} + 9 q^{80} + 149 q^{81} + 27 q^{82} - 27 q^{83} + 16 q^{84} + 52 q^{85} + 12 q^{86} - 3 q^{87} + 4 q^{88} + 68 q^{89} + 44 q^{90} + 22 q^{91} + 41 q^{92} + 45 q^{93} + 18 q^{94} + 46 q^{95} + 4 q^{96} + 16 q^{97} + 87 q^{98} - 10 q^{99}+O(q^{100}) \) 41 * q + 41 * q^2 + 4 * q^3 + 41 * q^4 + 9 * q^5 + 4 * q^6 + 12 * q^7 + 41 * q^8 + 63 * q^9 + 9 * q^10 + 4 * q^11 + 4 * q^12 + 16 * q^13 + 12 * q^14 + 10 * q^15 + 41 * q^16 + 10 * q^17 + 63 * q^18 + 16 * q^19 + 9 * q^20 + 16 * q^21 + 4 * q^22 + 41 * q^23 + 4 * q^24 + 76 * q^25 + 16 * q^26 + 7 * q^27 + 12 * q^28 + 28 * q^29 + 10 * q^30 + 25 * q^31 + 41 * q^32 + 5 * q^33 + 10 * q^34 + 4 * q^35 + 63 * q^36 + 26 * q^37 + 16 * q^38 + 50 * q^39 + 9 * q^40 + 27 * q^41 + 16 * q^42 + 12 * q^43 + 4 * q^44 + 44 * q^45 + 41 * q^46 + 18 * q^47 + 4 * q^48 + 87 * q^49 + 76 * q^50 + 24 * q^51 + 16 * q^52 + 63 * q^53 + 7 * q^54 + 18 * q^55 + 12 * q^56 - 12 * q^57 + 28 * q^58 + 33 * q^59 + 10 * q^60 + 24 * q^61 + 25 * q^62 + 48 * q^63 + 41 * q^64 + 21 * q^65 + 5 * q^66 - 9 * q^67 + 10 * q^68 + 4 * q^69 + 4 * q^70 + 36 * q^71 + 63 * q^72 + 36 * q^73 + 26 * q^74 + 6 * q^75 + 16 * q^76 + 48 * q^77 + 50 * q^78 + 51 * q^79 + 9 * q^80 + 149 * q^81 + 27 * q^82 - 27 * q^83 + 16 * q^84 + 52 * q^85 + 12 * q^86 - 3 * q^87 + 4 * q^88 + 68 * q^89 + 44 * q^90 + 22 * q^91 + 41 * q^92 + 45 * q^93 + 18 * q^94 + 46 * q^95 + 4 * q^96 + 16 * q^97 + 87 * q^98 - 10 * 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 $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−3.22313	−1.86087	−0.930437	−	0.366451i	$-0.880573\pi$
$3$	−3.22313	−1.86087	−0.930437	+	0.366451i	$0.880573\pi$
$4$	1.00000	0.500000
$5$	−0.601968	−0.269208	−0.134604	−	0.990899i	$-0.542976\pi$
$5$	−0.601968	−0.269208	−0.134604	+	0.990899i	$0.542976\pi$
$6$	−3.22313	−1.31584
$7$	−4.66050	−1.76150	−0.880752	−	0.473577i	$-0.842962\pi$
$7$	−4.66050	−1.76150	−0.880752	+	0.473577i	$0.842962\pi$
$8$	1.00000	0.353553
$9$	7.38856	2.46285
$10$	−0.601968	−0.190359
$11$	5.32153	1.60450	0.802251	−	0.596987i	$-0.203636\pi$
$11$	5.32153	1.60450	0.802251	+	0.596987i	$0.203636\pi$
$12$	−3.22313	−0.930437
$13$	1.09324	0.303209	0.151604	−	0.988441i	$-0.451556\pi$
$13$	1.09324	0.303209	0.151604	+	0.988441i	$0.451556\pi$
$14$	−4.66050	−1.24557
$15$	1.94022	0.500963
$16$	1.00000	0.250000
$17$	−0.187895	−0.0455713	−0.0227856	−	0.999740i	$-0.507254\pi$
$17$	−0.187895	−0.0455713	−0.0227856	+	0.999740i	$0.507254\pi$
$18$	7.38856	1.74150
$19$	7.97941	1.83060	0.915301	−	0.402770i	$-0.131952\pi$
$19$	7.97941	1.83060	0.915301	+	0.402770i	$0.131952\pi$
$20$	−0.601968	−0.134604
$21$	15.0214	3.27794
$22$	5.32153	1.13455
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	−3.22313	−0.657918
$25$	−4.63763	−0.927527
$26$	1.09324	0.214401
$27$	−14.1449	−2.72219
$28$	−4.66050	−0.880752
$29$	−8.43702	−1.56671	−0.783357	−	0.621572i	$-0.786494\pi$
$29$	−8.43702	−1.56671	−0.783357	+	0.621572i	$0.786494\pi$
$30$	1.94022	0.354234
$31$	−3.70101	−0.664721	−0.332360	−	0.943152i	$-0.607845\pi$
$31$	−3.70101	−0.664721	−0.332360	+	0.943152i	$0.607845\pi$
$32$	1.00000	0.176777
$33$	−17.1520	−2.98578
$34$	−0.187895	−0.0322237
$35$	2.80548	0.474212
$36$	7.38856	1.23143
$37$	9.99519	1.64320	0.821600	−	0.570065i	$-0.193082\pi$
$37$	9.99519	1.64320	0.821600	+	0.570065i	$0.193082\pi$
$38$	7.97941	1.29443
$39$	−3.52364	−0.564234
$40$	−0.601968	−0.0951796
$41$	−1.80066	−0.281216	−0.140608	−	0.990065i	$-0.544906\pi$
$41$	−1.80066	−0.281216	−0.140608	+	0.990065i	$0.544906\pi$
$42$	15.0214	2.31785
$43$	6.14508	0.937117	0.468558	−	0.883433i	$-0.344774\pi$
$43$	6.14508	0.937117	0.468558	+	0.883433i	$0.344774\pi$
$44$	5.32153	0.802251
$45$	−4.44768	−0.663021
$46$	1.00000	0.147442
$47$	−10.6149	−1.54834	−0.774170	−	0.632978i	$-0.781832\pi$
$47$	−10.6149	−1.54834	−0.774170	+	0.632978i	$0.781832\pi$
$48$	−3.22313	−0.465219
$49$	14.7203	2.10290
$50$	−4.63763	−0.655861
$51$	0.605610	0.0848024
$52$	1.09324	0.151604
$53$	8.90981	1.22386	0.611928	−	0.790913i	$-0.290394\pi$
$53$	8.90981	1.22386	0.611928	+	0.790913i	$0.290394\pi$
$54$	−14.1449	−1.92488
$55$	−3.20339	−0.431945
$56$	−4.66050	−0.622786
$57$	−25.7187	−3.40652
$58$	−8.43702	−1.10783
$59$	−5.16023	−0.671805	−0.335902	−	0.941897i	$-0.609041\pi$
$59$	−5.16023	−0.671805	−0.335902	+	0.941897i	$0.609041\pi$
$60$	1.94022	0.250482
$61$	8.21286	1.05155	0.525774	−	0.850624i	$-0.323776\pi$
$61$	8.21286	1.05155	0.525774	+	0.850624i	$0.323776\pi$
$62$	−3.70101	−0.470029
$63$	−34.4344	−4.33833
$64$	1.00000	0.125000
$65$	−0.658093	−0.0816264
$66$	−17.1520	−2.11126
$67$	−6.93155	−0.846824	−0.423412	−	0.905937i	$-0.639168\pi$
$67$	−6.93155	−0.846824	−0.423412	+	0.905937i	$0.639168\pi$
$68$	−0.187895	−0.0227856
$69$	−3.22313	−0.388019
$70$	2.80548	0.335318
$71$	−12.3902	−1.47045	−0.735224	−	0.677824i	$-0.762923\pi$
$71$	−12.3902	−1.47045	−0.735224	+	0.677824i	$0.762923\pi$
$72$	7.38856	0.870750
$73$	−6.97958	−0.816898	−0.408449	−	0.912781i	$-0.633930\pi$
$73$	−6.97958	−0.816898	−0.408449	+	0.912781i	$0.633930\pi$
$74$	9.99519	1.16192
$75$	14.9477	1.72601
$76$	7.97941	0.915301
$77$	−24.8010	−2.82634
$78$	−3.52364	−0.398973
$79$	7.45177	0.838390	0.419195	−	0.907896i	$-0.362312\pi$
$79$	7.45177	0.838390	0.419195	+	0.907896i	$0.362312\pi$
$80$	−0.601968	−0.0673021
$81$	23.4251	2.60279
$82$	−1.80066	−0.198849
$83$	−14.3598	−1.57619	−0.788095	−	0.615554i	$-0.788932\pi$
$83$	−14.3598	−1.57619	−0.788095	+	0.615554i	$0.788932\pi$
$84$	15.0214	1.63897
$85$	0.113107	0.0122682
$86$	6.14508	0.662641
$87$	27.1936	2.91546
$88$	5.32153	0.567277
$89$	−0.650144	−0.0689152	−0.0344576	−	0.999406i	$-0.510970\pi$
$89$	−0.650144	−0.0689152	−0.0344576	+	0.999406i	$0.510970\pi$
$90$	−4.44768	−0.468827
$91$	−5.09503	−0.534104
$92$	1.00000	0.104257
$93$	11.9288	1.23696
$94$	−10.6149	−1.09484
$95$	−4.80335	−0.492814
$96$	−3.22313	−0.328959
$97$	−11.4871	−1.16634	−0.583169	−	0.812351i	$-0.698187\pi$
$97$	−11.4871	−1.16634	−0.583169	+	0.812351i	$0.698187\pi$
$98$	14.7203	1.48697
$99$	39.3184	3.95165
$100$	−4.63763	−0.463763
$101$	7.50918	0.747192	0.373596	−	0.927592i	$-0.378125\pi$
$101$	7.50918	0.747192	0.373596	+	0.927592i	$0.378125\pi$
$102$	0.605610	0.0599643
$103$	2.81882	0.277746	0.138873	−	0.990310i	$-0.455652\pi$
$103$	2.81882	0.277746	0.138873	+	0.990310i	$0.455652\pi$
$104$	1.09324	0.107201
$105$	−9.04241	−0.882449
$106$	8.90981	0.865397
$107$	−3.39174	−0.327891	−0.163946	−	0.986469i	$-0.552422\pi$
$107$	−3.39174	−0.327891	−0.163946	+	0.986469i	$0.552422\pi$
$108$	−14.1449	−1.36109
$109$	20.1773	1.93263	0.966317	−	0.257356i	$-0.0828512\pi$
$109$	20.1773	1.93263	0.966317	+	0.257356i	$0.0828512\pi$
$110$	−3.20339	−0.305432
$111$	−32.2158	−3.05779
$112$	−4.66050	−0.440376
$113$	0.580065	0.0545679	0.0272840	−	0.999628i	$-0.491314\pi$
$113$	0.580065	0.0545679	0.0272840	+	0.999628i	$0.491314\pi$
$114$	−25.7187	−2.40877
$115$	−0.601968	−0.0561338
$116$	−8.43702	−0.783357
$117$	8.07743	0.746759
$118$	−5.16023	−0.475038
$119$	0.875686	0.0802740
$120$	1.94022	0.177117
$121$	17.3187	1.57443
$122$	8.21286	0.743557
$123$	5.80375	0.523307
$124$	−3.70101	−0.332360
$125$	5.80155	0.518906
$126$	−34.4344	−3.06766
$127$	3.96341	0.351696	0.175848	−	0.984417i	$-0.443733\pi$
$127$	3.96341	0.351696	0.175848	+	0.984417i	$0.443733\pi$
$128$	1.00000	0.0883883
$129$	−19.8064	−1.74386
$130$	−0.658093	−0.0577186
$131$	1.00000	0.0873704
$131$	1.00000	0.0873704
$132$	−17.1520	−1.49289
$133$	−37.1881	−3.22462
$134$	−6.93155	−0.598795
$135$	8.51478	0.732835
$136$	−0.187895	−0.0161119
$137$	12.5160	1.06931	0.534655	−	0.845070i	$-0.320441\pi$
$137$	12.5160	1.06931	0.534655	+	0.845070i	$0.320441\pi$
$138$	−3.22313	−0.274371
$139$	16.2454	1.37792	0.688959	−	0.724800i	$-0.258068\pi$
$139$	16.2454	1.37792	0.688959	+	0.724800i	$0.258068\pi$
$140$	2.80548	0.237106
$141$	34.2131	2.88127
$142$	−12.3902	−1.03976
$143$	5.81769	0.486499
$144$	7.38856	0.615713
$145$	5.07882	0.421773
$146$	−6.97958	−0.577634
$147$	−47.4454	−3.91323
$148$	9.99519	0.821600
$149$	14.4540	1.18412	0.592059	−	0.805894i	$-0.298315\pi$
$149$	14.4540	1.18412	0.592059	+	0.805894i	$0.298315\pi$
$150$	14.9477	1.22047
$151$	−7.70453	−0.626985	−0.313493	−	0.949591i	$-0.601499\pi$
$151$	−7.70453	−0.626985	−0.313493	+	0.949591i	$0.601499\pi$
$152$	7.97941	0.647216
$153$	−1.38827	−0.112235
$154$	−24.8010	−1.99852
$155$	2.22789	0.178948
$156$	−3.52364	−0.282117
$157$	3.25966	0.260149	0.130075	−	0.991504i	$-0.458478\pi$
$157$	3.25966	0.260149	0.130075	+	0.991504i	$0.458478\pi$
$158$	7.45177	0.592831
$159$	−28.7175	−2.27744
$160$	−0.601968	−0.0475898
$161$	−4.66050	−0.367299
$162$	23.4251	1.84045
$163$	−17.7081	−1.38700	−0.693502	−	0.720455i	$-0.743933\pi$
$163$	−17.7081	−1.38700	−0.693502	+	0.720455i	$0.743933\pi$
$164$	−1.80066	−0.140608
$165$	10.3249	0.803796
$166$	−14.3598	−1.11453
$167$	−7.83502	−0.606292	−0.303146	−	0.952944i	$-0.598037\pi$
$167$	−7.83502	−0.606292	−0.303146	+	0.952944i	$0.598037\pi$
$168$	15.0214	1.15893
$169$	−11.8048	−0.908064
$170$	0.113107	0.00867490
$171$	58.9564	4.50851
$172$	6.14508	0.468558
$173$	12.3545	0.939298	0.469649	−	0.882853i	$-0.344380\pi$
$173$	12.3545	0.939298	0.469649	+	0.882853i	$0.344380\pi$
$174$	27.1936	2.06154
$175$	21.6137	1.63384
$176$	5.32153	0.401125
$177$	16.6321	1.25014
$178$	−0.650144	−0.0487304
$179$	11.6933	0.873996	0.436998	−	0.899462i	$-0.356042\pi$
$179$	11.6933	0.873996	0.436998	+	0.899462i	$0.356042\pi$
$180$	−4.44768	−0.331510
$181$	1.33962	0.0995731	0.0497866	−	0.998760i	$-0.484146\pi$
$181$	1.33962	0.0995731	0.0497866	+	0.998760i	$0.484146\pi$
$182$	−5.09503	−0.377668
$183$	−26.4711	−1.95680
$184$	1.00000	0.0737210
$185$	−6.01679	−0.442363
$186$	11.9288	0.874664
$187$	−0.999890	−0.0731192
$188$	−10.6149	−0.774170
$189$	65.9223	4.79514
$190$	−4.80335	−0.348472
$191$	11.1776	0.808783	0.404392	−	0.914586i	$-0.367483\pi$
$191$	11.1776	0.808783	0.404392	+	0.914586i	$0.367483\pi$
$192$	−3.22313	−0.232609
$193$	−8.62430	−0.620791	−0.310396	−	0.950607i	$-0.600461\pi$
$193$	−8.62430	−0.620791	−0.310396	+	0.950607i	$0.600461\pi$
$194$	−11.4871	−0.824725
$195$	2.12112	0.151896
$196$	14.7203	1.05145
$197$	25.5695	1.82175	0.910876	−	0.412680i	$-0.135407\pi$
$197$	25.5695	1.82175	0.910876	+	0.412680i	$0.135407\pi$
$198$	39.3184	2.79424
$199$	−2.68426	−0.190282	−0.0951410	−	0.995464i	$-0.530330\pi$
$199$	−2.68426	−0.190282	−0.0951410	+	0.995464i	$0.530330\pi$
$200$	−4.63763	−0.327930
$201$	22.3413	1.57583
$202$	7.50918	0.528344
$203$	39.3207	2.75977
$204$	0.605610	0.0424012
$205$	1.08394	0.0757056
$206$	2.81882	0.196396
$207$	7.38856	0.513540
$208$	1.09324	0.0758022
$209$	42.4627	2.93721
$210$	−9.04241	−0.623985
$211$	−6.97951	−0.480489	−0.240245	−	0.970712i	$-0.577228\pi$
$211$	−6.97951	−0.480489	−0.240245	+	0.970712i	$0.577228\pi$
$212$	8.90981	0.611928
$213$	39.9353	2.73632
$214$	−3.39174	−0.231854
$215$	−3.69915	−0.252280
$216$	−14.1449	−0.962438
$217$	17.2486	1.17091
$218$	20.1773	1.36658
$219$	22.4961	1.52014
$220$	−3.20339	−0.215973
$221$	−0.205414	−0.0138176
$222$	−32.2158	−2.16218
$223$	28.5096	1.90914	0.954571	−	0.297984i	$-0.0963142\pi$
$223$	28.5096	1.90914	0.954571	+	0.297984i	$0.0963142\pi$
$224$	−4.66050	−0.311393
$225$	−34.2654	−2.28436
$226$	0.580065	0.0385854
$227$	12.3571	0.820168	0.410084	−	0.912048i	$-0.365499\pi$
$227$	12.3571	0.820168	0.410084	+	0.912048i	$0.365499\pi$
$228$	−25.7187	−1.70326
$229$	28.1130	1.85776	0.928879	−	0.370383i	$-0.120774\pi$
$229$	28.1130	1.85776	0.928879	+	0.370383i	$0.120774\pi$
$230$	−0.601968	−0.0396926
$231$	79.9369	5.25946
$232$	−8.43702	−0.553917
$233$	8.70329	0.570171	0.285086	−	0.958502i	$-0.407978\pi$
$233$	8.70329	0.570171	0.285086	+	0.958502i	$0.407978\pi$
$234$	8.07743	0.528038
$235$	6.38982	0.416826
$236$	−5.16023	−0.335902
$237$	−24.0180	−1.56014
$238$	0.875686	0.0567623
$239$	−5.76445	−0.372871	−0.186436	−	0.982467i	$-0.559694\pi$
$239$	−5.76445	−0.372871	−0.186436	+	0.982467i	$0.559694\pi$
$240$	1.94022	0.125241
$241$	−0.304809	−0.0196345	−0.00981723	−	0.999952i	$-0.503125\pi$
$241$	−0.304809	−0.0196345	−0.00981723	+	0.999952i	$0.503125\pi$
$242$	17.3187	1.11329
$243$	−33.0675	−2.12128
$244$	8.21286	0.525774
$245$	−8.86115	−0.566118
$246$	5.80375	0.370034
$247$	8.72338	0.555055
$248$	−3.70101	−0.235014
$249$	46.2834	2.93309
$250$	5.80155	0.366922
$251$	−9.36639	−0.591201	−0.295601	−	0.955312i	$-0.595520\pi$
$251$	−9.36639	−0.591201	−0.295601	+	0.955312i	$0.595520\pi$
$252$	−34.4344	−2.16916
$253$	5.32153	0.334562
$254$	3.96341	0.248686
$255$	−0.364558	−0.0228295
$256$	1.00000	0.0625000
$257$	−17.3764	−1.08391	−0.541954	−	0.840408i	$-0.682315\pi$
$257$	−17.3764	−1.08391	−0.541954	+	0.840408i	$0.682315\pi$
$258$	−19.8064	−1.23309
$259$	−46.5826	−2.89450
$260$	−0.658093	−0.0408132
$261$	−62.3374	−3.85859
$262$	1.00000	0.0617802
$263$	10.8104	0.666599	0.333299	−	0.942821i	$-0.391838\pi$
$263$	10.8104	0.666599	0.333299	+	0.942821i	$0.391838\pi$
$264$	−17.1520	−1.05563
$265$	−5.36342	−0.329472
$266$	−37.1881	−2.28015
$267$	2.09550	0.128242
$268$	−6.93155	−0.423412
$269$	−10.1082	−0.616307	−0.308153	−	0.951337i	$-0.599711\pi$
$269$	−10.1082	−0.616307	−0.308153	+	0.951337i	$0.599711\pi$
$270$	8.51478	0.518193
$271$	9.18068	0.557687	0.278843	−	0.960337i	$-0.410049\pi$
$271$	9.18068	0.557687	0.278843	+	0.960337i	$0.410049\pi$
$272$	−0.187895	−0.0113928
$273$	16.4219	0.993900
$274$	12.5160	0.756117
$275$	−24.6793	−1.48822
$276$	−3.22313	−0.194010
$277$	2.64706	0.159047	0.0795233	−	0.996833i	$-0.474660\pi$
$277$	2.64706	0.159047	0.0795233	+	0.996833i	$0.474660\pi$
$278$	16.2454	0.974335
$279$	−27.3451	−1.63711
$280$	2.80548	0.167659
$281$	4.68757	0.279637	0.139818	−	0.990177i	$-0.455348\pi$
$281$	4.68757	0.279637	0.139818	+	0.990177i	$0.455348\pi$
$282$	34.2131	2.03736
$283$	−4.72530	−0.280890	−0.140445	−	0.990088i	$-0.544853\pi$
$283$	−4.72530	−0.280890	−0.140445	+	0.990088i	$0.544853\pi$
$284$	−12.3902	−0.735224
$285$	15.4818	0.917064
$286$	5.81769	0.344007
$287$	8.39197	0.495362
$288$	7.38856	0.435375
$289$	−16.9647	−0.997923
$290$	5.07882	0.298238
$291$	37.0244	2.17041
$292$	−6.97958	−0.408449
$293$	10.4346	0.609595	0.304797	−	0.952417i	$-0.401411\pi$
$293$	10.4346	0.609595	0.304797	+	0.952417i	$0.401411\pi$
$294$	−47.4454	−2.76707
$295$	3.10629	0.180855
$296$	9.99519	0.580959
$297$	−75.2725	−4.36775
$298$	14.4540	0.837298
$299$	1.09324	0.0632234
$300$	14.9477	0.863005
$301$	−28.6392	−1.65074
$302$	−7.70453	−0.443346
$303$	−24.2031	−1.39043
$304$	7.97941	0.457651
$305$	−4.94388	−0.283086
$306$	−1.38827	−0.0793623
$307$	−28.4582	−1.62419	−0.812097	−	0.583522i	$-0.801674\pi$
$307$	−28.4582	−1.62419	−0.812097	+	0.583522i	$0.801674\pi$
$308$	−24.8010	−1.41317
$309$	−9.08541	−0.516851
$310$	2.22789	0.126536
$311$	19.3322	1.09623	0.548113	−	0.836404i	$-0.315346\pi$
$311$	19.3322	1.09623	0.548113	+	0.836404i	$0.315346\pi$
$312$	−3.52364	−0.199487
$313$	−5.29786	−0.299453	−0.149726	−	0.988727i	$-0.547839\pi$
$313$	−5.29786	−0.299453	−0.149726	+	0.988727i	$0.547839\pi$
$314$	3.25966	0.183953
$315$	20.7284	1.16791
$316$	7.45177	0.419195
$317$	−20.8056	−1.16856	−0.584281	−	0.811552i	$-0.698623\pi$
$317$	−20.8056	−1.16856	−0.584281	+	0.811552i	$0.698623\pi$
$318$	−28.7175	−1.61040
$319$	−44.8978	−2.51380
$320$	−0.601968	−0.0336511
$321$	10.9320	0.610165
$322$	−4.66050	−0.259720
$323$	−1.49929	−0.0834229
$324$	23.4251	1.30140
$325$	−5.07003	−0.281234
$326$	−17.7081	−0.980760
$327$	−65.0340	−3.59639
$328$	−1.80066	−0.0994247
$329$	49.4707	2.72741
$330$	10.3249	0.568370
$331$	35.2110	1.93537	0.967686	−	0.252157i	$-0.0811398\pi$
$331$	35.2110	1.93537	0.967686	+	0.252157i	$0.0811398\pi$
$332$	−14.3598	−0.788095
$333$	73.8501	4.04696
$334$	−7.83502	−0.428713
$335$	4.17258	0.227972
$336$	15.0214	0.819485
$337$	8.12877	0.442802	0.221401	−	0.975183i	$-0.428937\pi$
$337$	8.12877	0.442802	0.221401	+	0.975183i	$0.428937\pi$
$338$	−11.8048	−0.642098
$339$	−1.86962	−0.101544
$340$	0.113107	0.00613408
$341$	−19.6950	−1.06655
$342$	58.9564	3.18800
$343$	−35.9804	−1.94276
$344$	6.14508	0.331321
$345$	1.94022	0.104458
$346$	12.3545	0.664184
$347$	−1.20584	−0.0647328	−0.0323664	−	0.999476i	$-0.510304\pi$
$347$	−1.20584	−0.0647328	−0.0323664	+	0.999476i	$0.510304\pi$
$348$	27.1936	1.45773
$349$	−17.4356	−0.933305	−0.466652	−	0.884441i	$-0.654540\pi$
$349$	−17.4356	−0.933305	−0.466652	+	0.884441i	$0.654540\pi$
$350$	21.6137	1.15530
$351$	−15.4637	−0.825391
$352$	5.32153	0.283639
$353$	29.3527	1.56228	0.781142	−	0.624353i	$-0.214637\pi$
$353$	29.3527	1.56228	0.781142	+	0.624353i	$0.214637\pi$
$354$	16.6321	0.883985
$355$	7.45852	0.395857
$356$	−0.650144	−0.0344576
$357$	−2.82245	−0.149380
$358$	11.6933	0.618009
$359$	−4.51481	−0.238283	−0.119141	−	0.992877i	$-0.538014\pi$
$359$	−4.51481	−0.238283	−0.119141	+	0.992877i	$0.538014\pi$
$360$	−4.44768	−0.234413
$361$	44.6710	2.35111
$362$	1.33962	0.0704088
$363$	−55.8204	−2.92981
$364$	−5.09503	−0.267052
$365$	4.20149	0.219916
$366$	−26.4711	−1.38367
$367$	−3.40392	−0.177683	−0.0888416	−	0.996046i	$-0.528317\pi$
$367$	−3.40392	−0.177683	−0.0888416	+	0.996046i	$0.528317\pi$
$368$	1.00000	0.0521286
$369$	−13.3043	−0.692593
$370$	−6.01679	−0.312798
$371$	−41.5242	−2.15583
$372$	11.9288	0.618481
$373$	24.9981	1.29435	0.647177	−	0.762339i	$-0.275949\pi$
$373$	24.9981	1.29435	0.647177	+	0.762339i	$0.275949\pi$
$374$	−0.999890	−0.0517031
$375$	−18.6991	−0.965620
$376$	−10.6149	−0.547421
$377$	−9.22364	−0.475042
$378$	65.9223	3.39068
$379$	−0.299021	−0.0153597	−0.00767985	−	0.999971i	$-0.502445\pi$
$379$	−0.299021	−0.0153597	−0.00767985	+	0.999971i	$0.502445\pi$
$380$	−4.80335	−0.246407
$381$	−12.7746	−0.654461
$382$	11.1776	0.571896
$383$	−7.17339	−0.366543	−0.183272	−	0.983062i	$-0.558669\pi$
$383$	−7.17339	−0.366543	−0.183272	+	0.983062i	$0.558669\pi$
$384$	−3.22313	−0.164480
$385$	14.9294	0.760874
$386$	−8.62430	−0.438966
$387$	45.4033	2.30798
$388$	−11.4871	−0.583169
$389$	−7.21235	−0.365681	−0.182840	−	0.983143i	$-0.558529\pi$
$389$	−7.21235	−0.365681	−0.182840	+	0.983143i	$0.558529\pi$
$390$	2.12112	0.107407
$391$	−0.187895	−0.00950226
$392$	14.7203	0.743487
$393$	−3.22313	−0.162585
$394$	25.5695	1.28817
$395$	−4.48573	−0.225702
$396$	39.3184	1.97583
$397$	31.8495	1.59848	0.799240	−	0.601013i	$-0.205236\pi$
$397$	31.8495	1.59848	0.799240	+	0.601013i	$0.205236\pi$
$398$	−2.68426	−0.134550
$399$	119.862	6.00060
$400$	−4.63763	−0.231882
$401$	6.12411	0.305823	0.152912	−	0.988240i	$-0.451135\pi$
$401$	6.12411	0.305823	0.152912	+	0.988240i	$0.451135\pi$
$402$	22.3413	1.11428
$403$	−4.04607	−0.201549
$404$	7.50918	0.373596
$405$	−14.1012	−0.700694
$406$	39.3207	1.95146
$407$	53.1897	2.63652
$408$	0.605610	0.0299822
$409$	0.879801	0.0435034	0.0217517	−	0.999763i	$-0.493076\pi$
$409$	0.879801	0.0435034	0.0217517	+	0.999763i	$0.493076\pi$
$410$	1.08394	0.0535319
$411$	−40.3406	−1.98985
$412$	2.81882	0.138873
$413$	24.0493	1.18339
$414$	7.38856	0.363128
$415$	8.64413	0.424324
$416$	1.09324	0.0536003
$417$	−52.3611	−2.56413
$418$	42.4627	2.07692
$419$	−8.00850	−0.391241	−0.195620	−	0.980680i	$-0.562672\pi$
$419$	−8.00850	−0.391241	−0.195620	+	0.980680i	$0.562672\pi$
$420$	−9.04241	−0.441224
$421$	0.921809	0.0449262	0.0224631	−	0.999748i	$-0.492849\pi$
$421$	0.921809	0.0449262	0.0224631	+	0.999748i	$0.492849\pi$
$422$	−6.97951	−0.339757
$423$	−78.4287	−3.81333
$424$	8.90981	0.432699
$425$	0.871389	0.0422686
$426$	39.9353	1.93487
$427$	−38.2760	−1.85231
$428$	−3.39174	−0.163946
$429$	−18.7512	−0.905314
$430$	−3.69915	−0.178389
$431$	34.4143	1.65768	0.828839	−	0.559487i	$-0.189002\pi$
$431$	34.4143	1.65768	0.828839	+	0.559487i	$0.189002\pi$
$432$	−14.1449	−0.680546
$433$	22.5031	1.08143	0.540714	−	0.841206i	$-0.318154\pi$
$433$	22.5031	1.08143	0.540714	+	0.841206i	$0.318154\pi$
$434$	17.2486	0.827957
$435$	−16.3697	−0.784866
$436$	20.1773	0.966317
$437$	7.97941	0.381707
$438$	22.4961	1.07490
$439$	−26.8337	−1.28070	−0.640351	−	0.768083i	$-0.721211\pi$
$439$	−26.8337	−1.28070	−0.640351	+	0.768083i	$0.721211\pi$
$440$	−3.20339	−0.152716
$441$	108.762	5.17913
$442$	−0.205414	−0.00977053
$443$	−27.8023	−1.32093	−0.660463	−	0.750858i	$-0.729640\pi$
$443$	−27.8023	−1.32093	−0.660463	+	0.750858i	$0.729640\pi$
$444$	−32.2158	−1.52889
$445$	0.391366	0.0185525
$446$	28.5096	1.34997
$447$	−46.5871	−2.20350
$448$	−4.66050	−0.220188
$449$	17.2299	0.813129	0.406564	−	0.913622i	$-0.366727\pi$
$449$	17.2299	0.813129	0.406564	+	0.913622i	$0.366727\pi$
$450$	−34.2654	−1.61529
$451$	−9.58226	−0.451211
$452$	0.580065	0.0272840
$453$	24.8327	1.16674
$454$	12.3571	0.579947
$455$	3.06704	0.143785
$456$	−25.7187	−1.20439
$457$	−41.4403	−1.93849	−0.969247	−	0.246091i	$-0.920854\pi$
$457$	−41.4403	−1.93849	−0.969247	+	0.246091i	$0.920854\pi$
$458$	28.1130	1.31363
$459$	2.65776	0.124053
$460$	−0.601968	−0.0280669
$461$	−20.9272	−0.974676	−0.487338	−	0.873213i	$-0.662032\pi$
$461$	−20.9272	−0.974676	−0.487338	+	0.873213i	$0.662032\pi$
$462$	79.9369	3.71900
$463$	41.1006	1.91011	0.955054	−	0.296432i	$-0.0957968\pi$
$463$	41.1006	1.91011	0.955054	+	0.296432i	$0.0957968\pi$
$464$	−8.43702	−0.391679
$465$	−7.18078	−0.333001
$466$	8.70329	0.403172
$467$	5.62522	0.260304	0.130152	−	0.991494i	$-0.458453\pi$
$467$	5.62522	0.260304	0.130152	+	0.991494i	$0.458453\pi$
$468$	8.07743	0.373380
$469$	32.3045	1.49168
$470$	6.38982	0.294741
$471$	−10.5063	−0.484105
$472$	−5.16023	−0.237519
$473$	32.7013	1.50361
$474$	−24.0180	−1.10318
$475$	−37.0056	−1.69793
$476$	0.875686	0.0401370
$477$	65.8306	3.01418
$478$	−5.76445	−0.263660
$479$	−20.6354	−0.942854	−0.471427	−	0.881905i	$-0.656261\pi$
$479$	−20.6354	−0.942854	−0.471427	+	0.881905i	$0.656261\pi$
$480$	1.94022	0.0885586
$481$	10.9271	0.498233
$482$	−0.304809	−0.0138837
$483$	15.0214	0.683497
$484$	17.3187	0.787213
$485$	6.91487	0.313988
$486$	−33.0675	−1.49997
$487$	−8.32189	−0.377101	−0.188550	−	0.982064i	$-0.560379\pi$
$487$	−8.32189	−0.377101	−0.188550	+	0.982064i	$0.560379\pi$
$488$	8.21286	0.371779
$489$	57.0754	2.58104
$490$	−8.86115	−0.400306
$491$	−0.172547	−0.00778692	−0.00389346	−	0.999992i	$-0.501239\pi$
$491$	−0.172547	−0.00778692	−0.00389346	+	0.999992i	$0.501239\pi$
$492$	5.80375	0.261653
$493$	1.58527	0.0713971
$494$	8.72338	0.392483
$495$	−23.6685	−1.06382
$496$	−3.70101	−0.166180
$497$	57.7447	2.59020
$498$	46.2834	2.07401
$499$	16.6453	0.745147	0.372574	−	0.928003i	$-0.378475\pi$
$499$	16.6453	0.745147	0.372574	+	0.928003i	$0.378475\pi$
$500$	5.80155	0.259453
$501$	25.2533	1.12823
$502$	−9.36639	−0.418042
$503$	−19.9668	−0.890274	−0.445137	−	0.895463i	$-0.646845\pi$
$503$	−19.9668	−0.890274	−0.445137	+	0.895463i	$0.646845\pi$
$504$	−34.4344	−1.53383
$505$	−4.52029	−0.201150
$506$	5.32153	0.236571
$507$	38.0485	1.68979
$508$	3.96341	0.175848
$509$	8.92284	0.395498	0.197749	−	0.980253i	$-0.436637\pi$
$509$	8.92284	0.395498	0.197749	+	0.980253i	$0.436637\pi$
$510$	−0.364558	−0.0161429
$511$	32.5284	1.43897
$512$	1.00000	0.0441942
$513$	−112.868	−4.98324
$514$	−17.3764	−0.766439
$515$	−1.69684	−0.0747716
$516$	−19.8064	−0.871928
$517$	−56.4874	−2.48431
$518$	−46.5826	−2.04672
$519$	−39.8203	−1.74792
$520$	−0.658093	−0.0288593
$521$	−28.5299	−1.24992	−0.624959	−	0.780658i	$-0.714884\pi$
$521$	−28.5299	−1.24992	−0.624959	+	0.780658i	$0.714884\pi$
$522$	−62.3374	−2.72843
$523$	30.1852	1.31990	0.659952	−	0.751307i	$-0.270576\pi$
$523$	30.1852	1.31990	0.659952	+	0.751307i	$0.270576\pi$
$524$	1.00000	0.0436852
$525$	−69.6638	−3.04038
$526$	10.8104	0.471356
$527$	0.695401	0.0302922
$528$	−17.1520	−0.746444
$529$	1.00000	0.0434783
$530$	−5.36342	−0.232972
$531$	−38.1267	−1.65456
$532$	−37.1881	−1.61231
$533$	−1.96854	−0.0852671
$534$	2.09550	0.0906811
$535$	2.04172	0.0882712
$536$	−6.93155	−0.299397
$537$	−37.6889	−1.62640
$538$	−10.1082	−0.435795
$539$	78.3345	3.37410
$540$	8.51478	0.366418
$541$	−22.6965	−0.975799	−0.487900	−	0.872900i	$-0.662237\pi$
$541$	−22.6965	−0.975799	−0.487900	+	0.872900i	$0.662237\pi$
$542$	9.18068	0.394344
$543$	−4.31777	−0.185293
$544$	−0.187895	−0.00805594
$545$	−12.1461	−0.520281
$546$	16.4219	0.702794
$547$	−12.6781	−0.542075	−0.271037	−	0.962569i	$-0.587367\pi$
$547$	−12.6781	−0.542075	−0.271037	+	0.962569i	$0.587367\pi$
$548$	12.5160	0.534655
$549$	60.6812	2.58981
$550$	−24.6793	−1.05233
$551$	−67.3224	−2.86803
$552$	−3.22313	−0.137185
$553$	−34.7290	−1.47683
$554$	2.64706	0.112463
$555$	19.3929	0.823182
$556$	16.2454	0.688959
$557$	15.0665	0.638387	0.319194	−	0.947689i	$-0.396588\pi$
$557$	15.0665	0.638387	0.319194	+	0.947689i	$0.396588\pi$
$558$	−27.3451	−1.15761
$559$	6.71802	0.284142
$560$	2.80548	0.118553
$561$	3.22277	0.136066
$562$	4.68757	0.197733
$563$	17.0854	0.720062	0.360031	−	0.932940i	$-0.382766\pi$
$563$	17.0854	0.720062	0.360031	+	0.932940i	$0.382766\pi$
$564$	34.2131	1.44063
$565$	−0.349181	−0.0146901
$566$	−4.72530	−0.198619
$567$	−109.173	−4.58483
$568$	−12.3902	−0.519882
$569$	8.71452	0.365332	0.182666	−	0.983175i	$-0.441527\pi$
$569$	8.71452	0.365332	0.182666	+	0.983175i	$0.441527\pi$
$570$	15.4818	0.648462
$571$	5.91398	0.247493	0.123746	−	0.992314i	$-0.460509\pi$
$571$	5.91398	0.247493	0.123746	+	0.992314i	$0.460509\pi$
$572$	5.81769	0.243250
$573$	−36.0269	−1.50504
$574$	8.39197	0.350274
$575$	−4.63763	−0.193403
$576$	7.38856	0.307857
$577$	33.8828	1.41056	0.705280	−	0.708928i	$-0.250821\pi$
$577$	33.8828	1.41056	0.705280	+	0.708928i	$0.250821\pi$
$578$	−16.9647	−0.705638
$579$	27.7972	1.15521
$580$	5.07882	0.210886
$581$	66.9238	2.77647
$582$	37.0244	1.53471
$583$	47.4138	1.96368
$584$	−6.97958	−0.288817
$585$	−4.86236	−0.201034
$586$	10.4346	0.431049
$587$	32.7187	1.35044	0.675222	−	0.737615i	$-0.264048\pi$
$587$	32.7187	1.35044	0.675222	+	0.737615i	$0.264048\pi$
$588$	−47.4454	−1.95661
$589$	−29.5319	−1.21684
$590$	3.10629	0.127884
$591$	−82.4138	−3.39005
$592$	9.99519	0.410800
$593$	36.8310	1.51247	0.756234	−	0.654301i	$-0.227037\pi$
$593$	36.8310	1.51247	0.756234	+	0.654301i	$0.227037\pi$
$594$	−75.2725	−3.08847
$595$	−0.527135	−0.0216104
$596$	14.4540	0.592059
$597$	8.65171	0.354091
$598$	1.09324	0.0447057
$599$	−17.1336	−0.700058	−0.350029	−	0.936739i	$-0.613828\pi$
$599$	−17.1336	−0.700058	−0.350029	+	0.936739i	$0.613828\pi$
$600$	14.9477	0.610237
$601$	−21.5705	−0.879878	−0.439939	−	0.898028i	$-0.645000\pi$
$601$	−21.5705	−0.879878	−0.439939	+	0.898028i	$0.645000\pi$
$602$	−28.6392	−1.16725
$603$	−51.2142	−2.08560
$604$	−7.70453	−0.313493
$605$	−10.4253	−0.423849
$606$	−24.2031	−0.983182
$607$	38.1782	1.54961	0.774803	−	0.632202i	$-0.217849\pi$
$607$	38.1782	1.54961	0.774803	+	0.632202i	$0.217849\pi$
$608$	7.97941	0.323608
$609$	−126.736	−5.13559
$610$	−4.94388	−0.200172
$611$	−11.6046	−0.469471
$612$	−1.38827	−0.0561177
$613$	27.0495	1.09252	0.546259	−	0.837616i	$-0.316051\pi$
$613$	27.0495	1.09252	0.546259	+	0.837616i	$0.316051\pi$
$614$	−28.4582	−1.14848
$615$	−3.49368	−0.140879
$616$	−24.8010	−0.999261
$617$	48.3671	1.94718	0.973592	−	0.228294i	$-0.0733147\pi$
$617$	48.3671	1.94718	0.973592	+	0.228294i	$0.0733147\pi$
$618$	−9.08541	−0.365469
$619$	13.7683	0.553394	0.276697	−	0.960957i	$-0.410760\pi$
$619$	13.7683	0.553394	0.276697	+	0.960957i	$0.410760\pi$
$620$	2.22789	0.0894742
$621$	−14.1449	−0.567615
$622$	19.3322	0.775149
$623$	3.03000	0.121394
$624$	−3.52364	−0.141058
$625$	19.6958	0.787833
$626$	−5.29786	−0.211745
$627$	−136.863	−5.46577
$628$	3.25966	0.130075
$629$	−1.87805	−0.0748826
$630$	20.7284	0.825840
$631$	26.2775	1.04609	0.523045	−	0.852305i	$-0.324796\pi$
$631$	26.2775	1.04609	0.523045	+	0.852305i	$0.324796\pi$
$632$	7.45177	0.296416
$633$	22.4958	0.894130
$634$	−20.8056	−0.826297
$635$	−2.38585	−0.0946794
$636$	−28.7175	−1.13872
$637$	16.0927	0.637618
$638$	−44.8978	−1.77752
$639$	−91.5459	−3.62150
$640$	−0.601968	−0.0237949
$641$	1.13546	0.0448481	0.0224240	−	0.999749i	$-0.492862\pi$
$641$	1.13546	0.0448481	0.0224240	+	0.999749i	$0.492862\pi$
$642$	10.9320	0.431452
$643$	−5.39768	−0.212864	−0.106432	−	0.994320i	$-0.533943\pi$
$643$	−5.39768	−0.212864	−0.106432	+	0.994320i	$0.533943\pi$
$644$	−4.66050	−0.183650
$645$	11.9228	0.469461
$646$	−1.49929	−0.0589889
$647$	−29.8711	−1.17436	−0.587178	−	0.809458i	$-0.699761\pi$
$647$	−29.8711	−1.17436	−0.587178	+	0.809458i	$0.699761\pi$
$648$	23.4251	0.920226
$649$	−27.4603	−1.07791
$650$	−5.07003	−0.198863
$651$	−55.5943	−2.17891
$652$	−17.7081	−0.693502
$653$	−5.89724	−0.230777	−0.115388	−	0.993320i	$-0.536811\pi$
$653$	−5.89724	−0.230777	−0.115388	+	0.993320i	$0.536811\pi$
$654$	−65.0340	−2.54303
$655$	−0.601968	−0.0235209
$656$	−1.80066	−0.0703039
$657$	−51.5690	−2.01190
$658$	49.4707	1.92857
$659$	−12.3810	−0.482294	−0.241147	−	0.970489i	$-0.577524\pi$
$659$	−12.3810	−0.482294	−0.241147	+	0.970489i	$0.577524\pi$
$660$	10.3249	0.401898
$661$	19.1339	0.744222	0.372111	−	0.928188i	$-0.378634\pi$
$661$	19.1339	0.744222	0.372111	+	0.928188i	$0.378634\pi$
$662$	35.2110	1.36852
$663$	0.662074	0.0257128
$664$	−14.3598	−0.557267
$665$	22.3860	0.868094
$666$	73.8501	2.86163
$667$	−8.43702	−0.326683
$668$	−7.83502	−0.303146
$669$	−91.8900	−3.55267
$670$	4.17258	0.161201
$671$	43.7050	1.68721
$672$	15.0214	0.579463
$673$	−28.2811	−1.09016	−0.545079	−	0.838385i	$-0.683500\pi$
$673$	−28.2811	−1.09016	−0.545079	+	0.838385i	$0.683500\pi$
$674$	8.12877	0.313108
$675$	65.5988	2.52490
$676$	−11.8048	−0.454032
$677$	43.2693	1.66297	0.831486	−	0.555545i	$-0.187490\pi$
$677$	43.2693	1.66297	0.831486	+	0.555545i	$0.187490\pi$
$678$	−1.86962	−0.0718025
$679$	53.5356	2.05451
$680$	0.113107	0.00433745
$681$	−39.8285	−1.52623
$682$	−19.6950	−0.754162
$683$	−36.8689	−1.41075	−0.705374	−	0.708835i	$-0.749221\pi$
$683$	−36.8689	−1.41075	−0.705374	+	0.708835i	$0.749221\pi$
$684$	58.9564	2.25425
$685$	−7.53421	−0.287868
$686$	−35.9804	−1.37374
$687$	−90.6118	−3.45705
$688$	6.14508	0.234279
$689$	9.74052	0.371084
$690$	1.94022	0.0738630
$691$	37.8371	1.43939	0.719696	−	0.694289i	$-0.244281\pi$
$691$	37.8371	1.43939	0.719696	+	0.694289i	$0.244281\pi$
$692$	12.3545	0.469649
$693$	−183.244	−6.96085
$694$	−1.20584	−0.0457730
$695$	−9.77923	−0.370947
$696$	27.1936	1.03077
$697$	0.338335	0.0128153
$698$	−17.4356	−0.659946
$699$	−28.0518	−1.06102
$700$	21.6137	0.816921
$701$	−13.6521	−0.515631	−0.257815	−	0.966194i	$-0.583003\pi$
$701$	−13.6521	−0.515631	−0.257815	+	0.966194i	$0.583003\pi$
$702$	−15.4637	−0.583640
$703$	79.7557	3.00805
$704$	5.32153	0.200563
$705$	−20.5952	−0.775661
$706$	29.3527	1.10470
$707$	−34.9966	−1.31618
$708$	16.6321	0.625072
$709$	−5.01696	−0.188416	−0.0942080	−	0.995553i	$-0.530032\pi$
$709$	−5.01696	−0.188416	−0.0942080	+	0.995553i	$0.530032\pi$
$710$	7.45852	0.279913
$711$	55.0579	2.06483
$712$	−0.650144	−0.0243652
$713$	−3.70101	−0.138604
$714$	−2.82245	−0.105627
$715$	−3.50206	−0.130970
$716$	11.6933	0.436998
$717$	18.5796	0.693867
$718$	−4.51481	−0.168491
$719$	33.2633	1.24051	0.620255	−	0.784400i	$-0.287029\pi$
$719$	33.2633	1.24051	0.620255	+	0.784400i	$0.287029\pi$
$720$	−4.44768	−0.165755
$721$	−13.1371	−0.489251
$722$	44.6710	1.66248
$723$	0.982438	0.0365372
$724$	1.33962	0.0497866
$725$	39.1278	1.45317
$726$	−55.8204	−2.07169
$727$	−46.2238	−1.71435	−0.857173	−	0.515029i	$-0.827781\pi$
$727$	−46.2238	−1.71435	−0.857173	+	0.515029i	$0.827781\pi$
$728$	−5.09503	−0.188834
$729$	36.3056	1.34465
$730$	4.20149	0.155504
$731$	−1.15463	−0.0427056
$732$	−26.4711	−0.978400
$733$	10.0289	0.370427	0.185214	−	0.982698i	$-0.440702\pi$
$733$	10.0289	0.370427	0.185214	+	0.982698i	$0.440702\pi$
$734$	−3.40392	−0.125641
$735$	28.5606	1.05347
$736$	1.00000	0.0368605
$737$	−36.8865	−1.35873
$738$	−13.3043	−0.489737
$739$	14.7907	0.544086	0.272043	−	0.962285i	$-0.412301\pi$
$739$	14.7907	0.544086	0.272043	+	0.962285i	$0.412301\pi$
$740$	−6.01679	−0.221182
$741$	−28.1166	−1.03289
$742$	−41.5242	−1.52440
$743$	−46.7890	−1.71652	−0.858260	−	0.513215i	$-0.828454\pi$
$743$	−46.7890	−1.71652	−0.858260	+	0.513215i	$0.828454\pi$
$744$	11.9288	0.437332
$745$	−8.70085	−0.318775
$746$	24.9981	0.915247
$747$	−106.098	−3.88192
$748$	−0.999890	−0.0365596
$749$	15.8072	0.577582
$750$	−18.6991	−0.682796
$751$	10.1953	0.372030	0.186015	−	0.982547i	$-0.440443\pi$
$751$	10.1953	0.372030	0.186015	+	0.982547i	$0.440443\pi$
$752$	−10.6149	−0.387085
$753$	30.1891	1.10015
$754$	−9.22364	−0.335905
$755$	4.63788	0.168790
$756$	65.9223	2.39757
$757$	2.24502	0.0815965	0.0407983	−	0.999167i	$-0.487010\pi$
$757$	2.24502	0.0815965	0.0407983	+	0.999167i	$0.487010\pi$
$758$	−0.299021	−0.0108609
$759$	−17.1520	−0.622577
$760$	−4.80335	−0.174236
$761$	−35.2201	−1.27673	−0.638363	−	0.769736i	$-0.720388\pi$
$761$	−35.2201	−1.27673	−0.638363	+	0.769736i	$0.720388\pi$
$762$	−12.7746	−0.462774
$763$	−94.0363	−3.40434
$764$	11.1776	0.404392
$765$	0.835697	0.0302147
$766$	−7.17339	−0.259185
$767$	−5.64135	−0.203697
$768$	−3.22313	−0.116305
$769$	−14.4591	−0.521408	−0.260704	−	0.965419i	$-0.583955\pi$
$769$	−14.4591	−0.521408	−0.260704	+	0.965419i	$0.583955\pi$
$770$	14.9294	0.538019
$771$	56.0063	2.01702
$772$	−8.62430	−0.310396
$773$	17.4856	0.628912	0.314456	−	0.949272i	$-0.398178\pi$
$773$	17.4856	0.628912	0.314456	+	0.949272i	$0.398178\pi$
$774$	45.4033	1.63199
$775$	17.1639	0.616546
$776$	−11.4871	−0.412363
$777$	150.142	5.38631
$778$	−7.21235	−0.258575
$779$	−14.3682	−0.514794
$780$	2.12112	0.0759482
$781$	−65.9350	−2.35934
$782$	−0.187895	−0.00671911
$783$	119.341	4.26489
$784$	14.7203	0.525725
$785$	−1.96221	−0.0700344
$786$	−3.22313	−0.114965
$787$	10.2756	0.366284	0.183142	−	0.983086i	$-0.441373\pi$
$787$	10.2756	0.366284	0.183142	+	0.983086i	$0.441373\pi$
$788$	25.5695	0.910876
$789$	−34.8434	−1.24046
$790$	−4.48573	−0.159595
$791$	−2.70340	−0.0961217
$792$	39.3184	1.39712
$793$	8.97859	0.318839
$794$	31.8495	1.13030
$795$	17.2870	0.613107
$796$	−2.68426	−0.0951410
$797$	39.5653	1.40148	0.700738	−	0.713419i	$-0.252854\pi$
$797$	39.5653	1.40148	0.700738	+	0.713419i	$0.252854\pi$
$798$	119.862	4.24307
$799$	1.99448	0.0705598
$800$	−4.63763	−0.163965
$801$	−4.80363	−0.169728
$802$	6.12411	0.216250
$803$	−37.1420	−1.31071
$804$	22.3413	0.787916
$805$	2.80548	0.0988800
$806$	−4.04607	−0.142517
$807$	32.5800	1.14687
$808$	7.50918	0.264172
$809$	28.3988	0.998447	0.499224	−	0.866473i	$-0.333619\pi$
$809$	28.3988	0.998447	0.499224	+	0.866473i	$0.333619\pi$
$810$	−14.1012	−0.495465
$811$	−30.4157	−1.06804	−0.534020	−	0.845472i	$-0.679319\pi$
$811$	−30.4157	−1.06804	−0.534020	+	0.845472i	$0.679319\pi$
$812$	39.3207	1.37989
$813$	−29.5905	−1.03778
$814$	53.1897	1.86430
$815$	10.6597	0.373393
$816$	0.605610	0.0212006
$817$	49.0342	1.71549
$818$	0.879801	0.0307615
$819$	−37.6449	−1.31542
$820$	1.08394	0.0378528
$821$	32.9892	1.15133	0.575665	−	0.817685i	$-0.304743\pi$
$821$	32.9892	1.15133	0.575665	+	0.817685i	$0.304743\pi$
$822$	−40.3406	−1.40704
$823$	24.1472	0.841719	0.420860	−	0.907126i	$-0.361729\pi$
$823$	24.1472	0.841719	0.420860	+	0.907126i	$0.361729\pi$
$824$	2.81882	0.0981981
$825$	79.5446	2.76939
$826$	24.0493	0.836781
$827$	−30.5545	−1.06248	−0.531242	−	0.847220i	$-0.678274\pi$
$827$	−30.5545	−1.06248	−0.531242	+	0.847220i	$0.678274\pi$
$828$	7.38856	0.256770
$829$	52.5351	1.82462	0.912309	−	0.409502i	$-0.134297\pi$
$829$	52.5351	1.82462	0.912309	+	0.409502i	$0.134297\pi$
$830$	8.64413	0.300042
$831$	−8.53183	−0.295966
$832$	1.09324	0.0379011
$833$	−2.76587	−0.0958317
$834$	−52.3611	−1.81312
$835$	4.71643	0.163219
$836$	42.4627	1.46860
$837$	52.3504	1.80949
$838$	−8.00850	−0.276649
$839$	36.1424	1.24778	0.623888	−	0.781514i	$-0.285552\pi$
$839$	36.1424	1.24778	0.623888	+	0.781514i	$0.285552\pi$
$840$	−9.04241	−0.311993
$841$	42.1832	1.45459
$842$	0.921809	0.0317676
$843$	−15.1086	−0.520369
$844$	−6.97951	−0.240245
$845$	7.10614	0.244459
$846$	−78.4287	−2.69643
$847$	−80.7138	−2.77336
$848$	8.90981	0.305964
$849$	15.2303	0.522701
$850$	0.871389	0.0298884
$851$	9.99519	0.342631
$852$	39.9353	1.36816
$853$	−25.1311	−0.860473	−0.430237	−	0.902716i	$-0.641570\pi$
$853$	−25.1311	−0.860473	−0.430237	+	0.902716i	$0.641570\pi$
$854$	−38.2760	−1.30978
$855$	−35.4899	−1.21373
$856$	−3.39174	−0.115927
$857$	−43.3831	−1.48194	−0.740969	−	0.671540i	$-0.765633\pi$
$857$	−43.3831	−1.48194	−0.740969	+	0.671540i	$0.765633\pi$
$858$	−18.7512	−0.640154
$859$	26.2440	0.895432	0.447716	−	0.894176i	$-0.352238\pi$
$859$	26.2440	0.895432	0.447716	+	0.894176i	$0.352238\pi$
$860$	−3.69915	−0.126140
$861$	−27.0484	−0.921807
$862$	34.4143	1.17216
$863$	29.2686	0.996315	0.498158	−	0.867086i	$-0.334010\pi$
$863$	29.2686	0.996315	0.498158	+	0.867086i	$0.334010\pi$
$864$	−14.1449	−0.481219
$865$	−7.43704	−0.252867
$866$	22.5031	0.764686
$867$	54.6794	1.85701
$868$	17.2486	0.585454
$869$	39.6548	1.34520
$870$	−16.3697	−0.554984
$871$	−7.57782	−0.256765
$872$	20.1773	0.683289
$873$	−84.8731	−2.87252
$874$	7.97941	0.269908
$875$	−27.0381	−0.914056
$876$	22.4961	0.760072
$877$	17.1894	0.580443	0.290222	−	0.956959i	$-0.406271\pi$
$877$	17.1894	0.580443	0.290222	+	0.956959i	$0.406271\pi$
$878$	−26.8337	−0.905593
$879$	−33.6320	−1.13438
$880$	−3.20339	−0.107986
$881$	−30.3679	−1.02312	−0.511559	−	0.859248i	$-0.670932\pi$
$881$	−30.3679	−1.02312	−0.511559	+	0.859248i	$0.670932\pi$
$882$	108.762	3.66220
$883$	−32.4262	−1.09123	−0.545614	−	0.838037i	$-0.683703\pi$
$883$	−32.4262	−1.09123	−0.545614	+	0.838037i	$0.683703\pi$
$884$	−0.205414	−0.00690881
$885$	−10.0120	−0.336549
$886$	−27.8023	−0.934036
$887$	22.0531	0.740470	0.370235	−	0.928938i	$-0.379277\pi$
$887$	22.0531	0.740470	0.370235	+	0.928938i	$0.379277\pi$
$888$	−32.2158	−1.08109
$889$	−18.4715	−0.619513
$890$	0.391366	0.0131186
$891$	124.658	4.17619
$892$	28.5096	0.954571
$893$	−84.7005	−2.83440
$894$	−46.5871	−1.55811
$895$	−7.03898	−0.235287
$896$	−4.66050	−0.155696
$897$	−3.52364	−0.117651
$898$	17.2299	0.574969
$899$	31.2255	1.04143
$900$	−34.2654	−1.14218
$901$	−1.67411	−0.0557727
$902$	−9.58226	−0.319054
$903$	92.3078	3.07181
$904$	0.580065	0.0192927
$905$	−0.806408	−0.0268059
$906$	24.8327	0.825010
$907$	−12.6012	−0.418416	−0.209208	−	0.977871i	$-0.567089\pi$
$907$	−12.6012	−0.418416	−0.209208	+	0.977871i	$0.567089\pi$
$908$	12.3571	0.410084
$909$	55.4820	1.84022
$910$	3.06704	0.101672
$911$	23.7234	0.785990	0.392995	−	0.919541i	$-0.371439\pi$
$911$	23.7234	0.785990	0.392995	+	0.919541i	$0.371439\pi$
$912$	−25.7187	−0.851630
$913$	−76.4160	−2.52900
$914$	−41.4403	−1.37072
$915$	15.9348	0.526787
$916$	28.1130	0.928879
$917$	−4.66050	−0.153903
$918$	2.65776	0.0877190
$919$	7.16741	0.236431	0.118216	−	0.992988i	$-0.462283\pi$
$919$	7.16741	0.236431	0.118216	+	0.992988i	$0.462283\pi$
$920$	−0.601968	−0.0198463
$921$	91.7244	3.02242
$922$	−20.9272	−0.689200
$923$	−13.5454	−0.445853
$924$	79.9369	2.62973
$925$	−46.3540	−1.52411
$926$	41.1006	1.35065
$927$	20.8270	0.684048
$928$	−8.43702	−0.276959
$929$	−28.8160	−0.945422	−0.472711	−	0.881217i	$-0.656725\pi$
$929$	−28.8160	−0.945422	−0.472711	+	0.881217i	$0.656725\pi$
$930$	−7.18078	−0.235467
$931$	117.459	3.84957
$932$	8.70329	0.285086
$933$	−62.3100	−2.03994
$934$	5.62522	0.184063
$935$	0.601902	0.0196843
$936$	8.07743	0.264019
$937$	−16.0835	−0.525424	−0.262712	−	0.964874i	$-0.584617\pi$
$937$	−16.0835	−0.525424	−0.262712	+	0.964874i	$0.584617\pi$
$938$	32.3045	1.05478
$939$	17.0757	0.557244
$940$	6.38982	0.208413
$941$	−41.8000	−1.36264	−0.681320	−	0.731986i	$-0.738594\pi$
$941$	−41.8000	−1.36264	−0.681320	+	0.731986i	$0.738594\pi$
$942$	−10.5063	−0.342314
$943$	−1.80066	−0.0586375
$944$	−5.16023	−0.167951
$945$	−39.6831	−1.29089
$946$	32.7013	1.06321
$947$	29.5192	0.959246	0.479623	−	0.877475i	$-0.340773\pi$
$947$	29.5192	0.959246	0.479623	+	0.877475i	$0.340773\pi$
$948$	−24.0180	−0.780069
$949$	−7.63032	−0.247691
$950$	−37.0056	−1.20062
$951$	67.0593	2.17455
$952$	0.875686	0.0283811
$953$	42.8446	1.38787	0.693937	−	0.720036i	$-0.255875\pi$
$953$	42.8446	1.38787	0.693937	+	0.720036i	$0.255875\pi$
$954$	65.8306	2.13135
$955$	−6.72857	−0.217731
$956$	−5.76445	−0.186436
$957$	144.712	4.67786
$958$	−20.6354	−0.666698
$959$	−58.3307	−1.88360
$960$	1.94022	0.0626204
$961$	−17.3025	−0.558146
$962$	10.9271	0.352304
$963$	−25.0600	−0.807549
$964$	−0.304809	−0.00981723
$965$	5.19156	0.167122
$966$	15.0214	0.483306
$967$	−12.3555	−0.397326	−0.198663	−	0.980068i	$-0.563660\pi$
$967$	−12.3555	−0.397326	−0.198663	+	0.980068i	$0.563660\pi$
$968$	17.3187	0.556644
$969$	4.83241	0.155239
$970$	6.91487	0.222023
$971$	27.9989	0.898528	0.449264	−	0.893399i	$-0.351686\pi$
$971$	27.9989	0.898528	0.449264	+	0.893399i	$0.351686\pi$
$972$	−33.0675	−1.06064
$973$	−75.7118	−2.42721
$974$	−8.32189	−0.266651
$975$	16.3413	0.523342
$976$	8.21286	0.262887
$977$	−38.3085	−1.22560	−0.612798	−	0.790239i	$-0.709956\pi$
$977$	−38.3085	−1.22560	−0.612798	+	0.790239i	$0.709956\pi$
$978$	57.0754	1.82507
$979$	−3.45976	−0.110574
$980$	−8.86115	−0.283059
$981$	149.081	4.75979
$982$	−0.172547	−0.00550618
$983$	−32.7585	−1.04483	−0.522417	−	0.852690i	$-0.674970\pi$
$983$	−32.7585	−1.04483	−0.522417	+	0.852690i	$0.674970\pi$
$984$	5.80375	0.185017
$985$	−15.3920	−0.490431
$986$	1.58527	0.0504854
$987$	−159.450	−5.07536
$988$	8.72338	0.277528
$989$	6.14508	0.195402
$990$	−23.6685	−0.752233
$991$	−21.2433	−0.674815	−0.337408	−	0.941359i	$-0.609550\pi$
$991$	−21.2433	−0.674815	−0.337408	+	0.941359i	$0.609550\pi$
$992$	−3.70101	−0.117507
$993$	−113.490	−3.60149
$994$	57.7447	1.83155
$995$	1.61584	0.0512255
$996$	46.2834	1.46655
$997$	−58.7577	−1.86088	−0.930438	−	0.366450i	$-0.880573\pi$
$997$	−58.7577	−1.86088	−0.930438	+	0.366450i	$0.880573\pi$
$998$	16.6453	0.526899
$999$	−141.381	−4.47309

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6026.2.a.m.1.3	✓	41

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6026.2.a.m.1.3	✓	41	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:	\( N \)	\(=\)	\( 6026 = 2 \cdot 23 \cdot 131 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6026.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -3.22313 q^{3} +1.00000 q^{4} -0.601968 q^{5} -3.22313 q^{6} -4.66050 q^{7} +1.00000 q^{8} +7.38856 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -3.22313 q^{3} +1.00000 q^{4} -0.601968 q^{5} -3.22313 q^{6} -4.66050 q^{7} +1.00000 q^{8} +7.38856 q^{9} -0.601968 q^{10} +5.32153 q^{11} -3.22313 q^{12} +1.09324 q^{13} -4.66050 q^{14} +1.94022 q^{15} +1.00000 q^{16} -0.187895 q^{17} +7.38856 q^{18} +7.97941 q^{19} -0.601968 q^{20} +15.0214 q^{21} +5.32153 q^{22} +1.00000 q^{23} -3.22313 q^{24} -4.63763 q^{25} +1.09324 q^{26} -14.1449 q^{27} -4.66050 q^{28} -8.43702 q^{29} +1.94022 q^{30} -3.70101 q^{31} +1.00000 q^{32} -17.1520 q^{33} -0.187895 q^{34} +2.80548 q^{35} +7.38856 q^{36} +9.99519 q^{37} +7.97941 q^{38} -3.52364 q^{39} -0.601968 q^{40} -1.80066 q^{41} +15.0214 q^{42} +6.14508 q^{43} +5.32153 q^{44} -4.44768 q^{45} +1.00000 q^{46} -10.6149 q^{47} -3.22313 q^{48} +14.7203 q^{49} -4.63763 q^{50} +0.605610 q^{51} +1.09324 q^{52} +8.90981 q^{53} -14.1449 q^{54} -3.20339 q^{55} -4.66050 q^{56} -25.7187 q^{57} -8.43702 q^{58} -5.16023 q^{59} +1.94022 q^{60} +8.21286 q^{61} -3.70101 q^{62} -34.4344 q^{63} +1.00000 q^{64} -0.658093 q^{65} -17.1520 q^{66} -6.93155 q^{67} -0.187895 q^{68} -3.22313 q^{69} +2.80548 q^{70} -12.3902 q^{71} +7.38856 q^{72} -6.97958 q^{73} +9.99519 q^{74} +14.9477 q^{75} +7.97941 q^{76} -24.8010 q^{77} -3.52364 q^{78} +7.45177 q^{79} -0.601968 q^{80} +23.4251 q^{81} -1.80066 q^{82} -14.3598 q^{83} +15.0214 q^{84} +0.113107 q^{85} +6.14508 q^{86} +27.1936 q^{87} +5.32153 q^{88} -0.650144 q^{89} -4.44768 q^{90} -5.09503 q^{91} +1.00000 q^{92} +11.9288 q^{93} -10.6149 q^{94} -4.80335 q^{95} -3.22313 q^{96} -11.4871 q^{97} +14.7203 q^{98} +39.3184 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 41 q + 41 q^{2} + 4 q^{3} + 41 q^{4} + 9 q^{5} + 4 q^{6} + 12 q^{7} + 41 q^{8} + 63 q^{9}+O(q^{10}) \) 41 * q + 41 * q^2 + 4 * q^3 + 41 * q^4 + 9 * q^5 + 4 * q^6 + 12 * q^7 + 41 * q^8 + 63 * q^9	\( 41 q + 41 q^{2} + 4 q^{3} + 41 q^{4} + 9 q^{5} + 4 q^{6} + 12 q^{7} + 41 q^{8} + 63 q^{9} + 9 q^{10} + 4 q^{11} + 4 q^{12} + 16 q^{13} + 12 q^{14} + 10 q^{15} + 41 q^{16} + 10 q^{17} + 63 q^{18} + 16 q^{19} + 9 q^{20} + 16 q^{21} + 4 q^{22} + 41 q^{23} + 4 q^{24} + 76 q^{25} + 16 q^{26} + 7 q^{27} + 12 q^{28} + 28 q^{29} + 10 q^{30} + 25 q^{31} + 41 q^{32} + 5 q^{33} + 10 q^{34} + 4 q^{35} + 63 q^{36} + 26 q^{37} + 16 q^{38} + 50 q^{39} + 9 q^{40} + 27 q^{41} + 16 q^{42} + 12 q^{43} + 4 q^{44} + 44 q^{45} + 41 q^{46} + 18 q^{47} + 4 q^{48} + 87 q^{49} + 76 q^{50} + 24 q^{51} + 16 q^{52} + 63 q^{53} + 7 q^{54} + 18 q^{55} + 12 q^{56} - 12 q^{57} + 28 q^{58} + 33 q^{59} + 10 q^{60} + 24 q^{61} + 25 q^{62} + 48 q^{63} + 41 q^{64} + 21 q^{65} + 5 q^{66} - 9 q^{67} + 10 q^{68} + 4 q^{69} + 4 q^{70} + 36 q^{71} + 63 q^{72} + 36 q^{73} + 26 q^{74} + 6 q^{75} + 16 q^{76} + 48 q^{77} + 50 q^{78} + 51 q^{79} + 9 q^{80} + 149 q^{81} + 27 q^{82} - 27 q^{83} + 16 q^{84} + 52 q^{85} + 12 q^{86} - 3 q^{87} + 4 q^{88} + 68 q^{89} + 44 q^{90} + 22 q^{91} + 41 q^{92} + 45 q^{93} + 18 q^{94} + 46 q^{95} + 4 q^{96} + 16 q^{97} + 87 q^{98} - 10 q^{99}+O(q^{100}) \) 41 * q + 41 * q^2 + 4 * q^3 + 41 * q^4 + 9 * q^5 + 4 * q^6 + 12 * q^7 + 41 * q^8 + 63 * q^9 + 9 * q^10 + 4 * q^11 + 4 * q^12 + 16 * q^13 + 12 * q^14 + 10 * q^15 + 41 * q^16 + 10 * q^17 + 63 * q^18 + 16 * q^19 + 9 * q^20 + 16 * q^21 + 4 * q^22 + 41 * q^23 + 4 * q^24 + 76 * q^25 + 16 * q^26 + 7 * q^27 + 12 * q^28 + 28 * q^29 + 10 * q^30 + 25 * q^31 + 41 * q^32 + 5 * q^33 + 10 * q^34 + 4 * q^35 + 63 * q^36 + 26 * q^37 + 16 * q^38 + 50 * q^39 + 9 * q^40 + 27 * q^41 + 16 * q^42 + 12 * q^43 + 4 * q^44 + 44 * q^45 + 41 * q^46 + 18 * q^47 + 4 * q^48 + 87 * q^49 + 76 * q^50 + 24 * q^51 + 16 * q^52 + 63 * q^53 + 7 * q^54 + 18 * q^55 + 12 * q^56 - 12 * q^57 + 28 * q^58 + 33 * q^59 + 10 * q^60 + 24 * q^61 + 25 * q^62 + 48 * q^63 + 41 * q^64 + 21 * q^65 + 5 * q^66 - 9 * q^67 + 10 * q^68 + 4 * q^69 + 4 * q^70 + 36 * q^71 + 63 * q^72 + 36 * q^73 + 26 * q^74 + 6 * q^75 + 16 * q^76 + 48 * q^77 + 50 * q^78 + 51 * q^79 + 9 * q^80 + 149 * q^81 + 27 * q^82 - 27 * q^83 + 16 * q^84 + 52 * q^85 + 12 * q^86 - 3 * q^87 + 4 * q^88 + 68 * q^89 + 44 * q^90 + 22 * q^91 + 41 * q^92 + 45 * q^93 + 18 * q^94 + 46 * q^95 + 4 * q^96 + 16 * q^97 + 87 * q^98 - 10 * q^99

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