LMFDB - Embedded newform 6026.2.a.i.1.11

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:	$1$
Dimension:	$25$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
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)

$f(q)$	$=$	$q-1.00000 q^{2} -0.932148 q^{3} +1.00000 q^{4} -0.513090 q^{5} +0.932148 q^{6} +0.0983188 q^{7} -1.00000 q^{8} -2.13110 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -0.932148 q^{3} +1.00000 q^{4} -0.513090 q^{5} +0.932148 q^{6} +0.0983188 q^{7} -1.00000 q^{8} -2.13110 q^{9} +0.513090 q^{10} +1.76350 q^{11} -0.932148 q^{12} +1.94413 q^{13} -0.0983188 q^{14} +0.478276 q^{15} +1.00000 q^{16} +0.106083 q^{17} +2.13110 q^{18} +5.57408 q^{19} -0.513090 q^{20} -0.0916477 q^{21} -1.76350 q^{22} +1.00000 q^{23} +0.932148 q^{24} -4.73674 q^{25} -1.94413 q^{26} +4.78294 q^{27} +0.0983188 q^{28} -2.46668 q^{29} -0.478276 q^{30} -6.26753 q^{31} -1.00000 q^{32} -1.64384 q^{33} -0.106083 q^{34} -0.0504464 q^{35} -2.13110 q^{36} -7.32825 q^{37} -5.57408 q^{38} -1.81222 q^{39} +0.513090 q^{40} -6.09707 q^{41} +0.0916477 q^{42} +4.09661 q^{43} +1.76350 q^{44} +1.09345 q^{45} -1.00000 q^{46} -3.63401 q^{47} -0.932148 q^{48} -6.99033 q^{49} +4.73674 q^{50} -0.0988850 q^{51} +1.94413 q^{52} +0.949157 q^{53} -4.78294 q^{54} -0.904833 q^{55} -0.0983188 q^{56} -5.19587 q^{57} +2.46668 q^{58} +15.1915 q^{59} +0.478276 q^{60} -6.05297 q^{61} +6.26753 q^{62} -0.209527 q^{63} +1.00000 q^{64} -0.997513 q^{65} +1.64384 q^{66} +9.31760 q^{67} +0.106083 q^{68} -0.932148 q^{69} +0.0504464 q^{70} +11.6016 q^{71} +2.13110 q^{72} +3.21738 q^{73} +7.32825 q^{74} +4.41534 q^{75} +5.57408 q^{76} +0.173385 q^{77} +1.81222 q^{78} +4.67534 q^{79} -0.513090 q^{80} +1.93489 q^{81} +6.09707 q^{82} +6.74942 q^{83} -0.0916477 q^{84} -0.0544301 q^{85} -4.09661 q^{86} +2.29931 q^{87} -1.76350 q^{88} -7.62846 q^{89} -1.09345 q^{90} +0.191144 q^{91} +1.00000 q^{92} +5.84226 q^{93} +3.63401 q^{94} -2.86001 q^{95} +0.932148 q^{96} +10.6127 q^{97} +6.99033 q^{98} -3.75819 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 25 q - 25 q^{2} - 4 q^{3} + 25 q^{4} - 3 q^{5} + 4 q^{6} - 11 q^{7} - 25 q^{8} + 19 q^{9}+O(q^{10}) $ 25 * q - 25 * q^2 - 4 * q^3 + 25 * q^4 - 3 * q^5 + 4 * q^6 - 11 * q^7 - 25 * q^8 + 19 * q^9	\( 25 q - 25 q^{2} - 4 q^{3} + 25 q^{4} - 3 q^{5} + 4 q^{6} - 11 q^{7} - 25 q^{8} + 19 q^{9} + 3 q^{10} - 12 q^{11} - 4 q^{12} - 6 q^{13} + 11 q^{14} + 25 q^{16} + 8 q^{17} - 19 q^{18} - 23 q^{19} - 3 q^{20} - 16 q^{21} + 12 q^{22} + 25 q^{23} + 4 q^{24} + 4 q^{25} + 6 q^{26} - 13 q^{27} - 11 q^{28} - 7 q^{29} - 7 q^{31} - 25 q^{32} + 3 q^{33} - 8 q^{34} - 18 q^{35} + 19 q^{36} - 7 q^{37} + 23 q^{38} - 2 q^{39} + 3 q^{40} - 10 q^{41} + 16 q^{42} - 26 q^{43} - 12 q^{44} + 20 q^{45} - 25 q^{46} - 2 q^{47} - 4 q^{48} + 2 q^{49} - 4 q^{50} - 28 q^{51} - 6 q^{52} + 47 q^{53} + 13 q^{54} - 38 q^{55} + 11 q^{56} - 4 q^{57} + 7 q^{58} - 19 q^{59} - 26 q^{61} + 7 q^{62} - 15 q^{63} + 25 q^{64} + 13 q^{65} - 3 q^{66} - 34 q^{67} + 8 q^{68} - 4 q^{69} + 18 q^{70} - 10 q^{71} - 19 q^{72} - 22 q^{73} + 7 q^{74} - 8 q^{75} - 23 q^{76} + 28 q^{77} + 2 q^{78} - 21 q^{79} - 3 q^{80} - 27 q^{81} + 10 q^{82} - 16 q^{83} - 16 q^{84} - 42 q^{85} + 26 q^{86} - 17 q^{87} + 12 q^{88} + 27 q^{89} - 20 q^{90} - 26 q^{91} + 25 q^{92} - 27 q^{93} + 2 q^{94} + 4 q^{96} + 4 q^{97} - 2 q^{98} - 2 q^{99}+O(q^{100}) \) 25 * q - 25 * q^2 - 4 * q^3 + 25 * q^4 - 3 * q^5 + 4 * q^6 - 11 * q^7 - 25 * q^8 + 19 * q^9 + 3 * q^10 - 12 * q^11 - 4 * q^12 - 6 * q^13 + 11 * q^14 + 25 * q^16 + 8 * q^17 - 19 * q^18 - 23 * q^19 - 3 * q^20 - 16 * q^21 + 12 * q^22 + 25 * q^23 + 4 * q^24 + 4 * q^25 + 6 * q^26 - 13 * q^27 - 11 * q^28 - 7 * q^29 - 7 * q^31 - 25 * q^32 + 3 * q^33 - 8 * q^34 - 18 * q^35 + 19 * q^36 - 7 * q^37 + 23 * q^38 - 2 * q^39 + 3 * q^40 - 10 * q^41 + 16 * q^42 - 26 * q^43 - 12 * q^44 + 20 * q^45 - 25 * q^46 - 2 * q^47 - 4 * q^48 + 2 * q^49 - 4 * q^50 - 28 * q^51 - 6 * q^52 + 47 * q^53 + 13 * q^54 - 38 * q^55 + 11 * q^56 - 4 * q^57 + 7 * q^58 - 19 * q^59 - 26 * q^61 + 7 * q^62 - 15 * q^63 + 25 * q^64 + 13 * q^65 - 3 * q^66 - 34 * q^67 + 8 * q^68 - 4 * q^69 + 18 * q^70 - 10 * q^71 - 19 * q^72 - 22 * q^73 + 7 * q^74 - 8 * q^75 - 23 * q^76 + 28 * q^77 + 2 * q^78 - 21 * q^79 - 3 * q^80 - 27 * q^81 + 10 * q^82 - 16 * q^83 - 16 * q^84 - 42 * q^85 + 26 * q^86 - 17 * q^87 + 12 * q^88 + 27 * q^89 - 20 * q^90 - 26 * q^91 + 25 * q^92 - 27 * q^93 + 2 * q^94 + 4 * q^96 + 4 * q^97 - 2 * q^98 - 2 * 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
$3$	−0.932148	−0.538176	−0.269088	−	0.963116i	$-0.586722\pi$
$3$	−0.932148	−0.538176	−0.269088	+	0.963116i	$0.586722\pi$
$4$	1.00000	0.500000
$5$	−0.513090	−0.229461	−0.114730	−	0.993397i	$-0.536600\pi$
$5$	−0.513090	−0.229461	−0.114730	+	0.993397i	$0.536600\pi$
$6$	0.932148	0.380548
$7$	0.0983188	0.0371610	0.0185805	−	0.999827i	$-0.494085\pi$
$7$	0.0983188	0.0371610	0.0185805	+	0.999827i	$0.494085\pi$
$8$	−1.00000	−0.353553
$9$	−2.13110	−0.710367
$10$	0.513090	0.162253
$11$	1.76350	0.531715	0.265857	−	0.964012i	$-0.414345\pi$
$11$	1.76350	0.531715	0.265857	+	0.964012i	$0.414345\pi$
$12$	−0.932148	−0.269088
$13$	1.94413	0.539204	0.269602	−	0.962972i	$-0.413108\pi$
$13$	1.94413	0.539204	0.269602	+	0.962972i	$0.413108\pi$
$14$	−0.0983188	−0.0262768
$15$	0.478276	0.123490
$16$	1.00000	0.250000
$17$	0.106083	0.0257289	0.0128644	−	0.999917i	$-0.495905\pi$
$17$	0.106083	0.0257289	0.0128644	+	0.999917i	$0.495905\pi$
$18$	2.13110	0.502305
$19$	5.57408	1.27878	0.639391	−	0.768882i	$-0.279186\pi$
$19$	5.57408	1.27878	0.639391	+	0.768882i	$0.279186\pi$
$20$	−0.513090	−0.114730
$21$	−0.0916477	−0.0199992
$22$	−1.76350	−0.375979
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	0.932148	0.190274
$25$	−4.73674	−0.947348
$26$	−1.94413	−0.381275
$27$	4.78294	0.920478
$28$	0.0983188	0.0185805
$29$	−2.46668	−0.458051	−0.229025	−	0.973420i	$-0.573554\pi$
$29$	−2.46668	−0.458051	−0.229025	+	0.973420i	$0.573554\pi$
$30$	−0.478276	−0.0873208
$31$	−6.26753	−1.12568	−0.562841	−	0.826565i	$-0.690292\pi$
$31$	−6.26753	−1.12568	−0.562841	+	0.826565i	$0.690292\pi$
$32$	−1.00000	−0.176777
$33$	−1.64384	−0.286156
$34$	−0.106083	−0.0181931
$35$	−0.0504464	−0.00852700
$36$	−2.13110	−0.355183
$37$	−7.32825	−1.20476	−0.602379	−	0.798210i	$-0.705780\pi$
$37$	−7.32825	−1.20476	−0.602379	+	0.798210i	$0.705780\pi$
$38$	−5.57408	−0.904236
$39$	−1.81222	−0.290187
$40$	0.513090	0.0811266
$41$	−6.09707	−0.952202	−0.476101	−	0.879391i	$-0.657950\pi$
$41$	−6.09707	−0.952202	−0.476101	+	0.879391i	$0.657950\pi$
$42$	0.0916477	0.0141415
$43$	4.09661	0.624727	0.312363	−	0.949963i	$-0.398879\pi$
$43$	4.09661	0.624727	0.312363	+	0.949963i	$0.398879\pi$
$44$	1.76350	0.265857
$45$	1.09345	0.163001
$46$	−1.00000	−0.147442
$47$	−3.63401	−0.530075	−0.265038	−	0.964238i	$-0.585384\pi$
$47$	−3.63401	−0.530075	−0.265038	+	0.964238i	$0.585384\pi$
$48$	−0.932148	−0.134544
$49$	−6.99033	−0.998619
$50$	4.73674	0.669876
$51$	−0.0988850	−0.0138467
$52$	1.94413	0.269602
$53$	0.949157	0.130377	0.0651884	−	0.997873i	$-0.479235\pi$
$53$	0.949157	0.130377	0.0651884	+	0.997873i	$0.479235\pi$
$54$	−4.78294	−0.650876
$55$	−0.904833	−0.122008
$56$	−0.0983188	−0.0131384
$57$	−5.19587	−0.688210
$58$	2.46668	0.323891
$59$	15.1915	1.97777	0.988885	−	0.148683i	$-0.0475035\pi$
$59$	15.1915	1.97777	0.988885	+	0.148683i	$0.0475035\pi$
$60$	0.478276	0.0617451
$61$	−6.05297	−0.775004	−0.387502	−	0.921869i	$-0.626662\pi$
$61$	−6.05297	−0.775004	−0.387502	+	0.921869i	$0.626662\pi$
$62$	6.26753	0.795977
$63$	−0.209527	−0.0263980
$64$	1.00000	0.125000
$65$	−0.997513	−0.123726
$66$	1.64384	0.202343
$67$	9.31760	1.13833	0.569163	−	0.822225i	$-0.307267\pi$
$67$	9.31760	1.13833	0.569163	+	0.822225i	$0.307267\pi$
$68$	0.106083	0.0128644
$69$	−0.932148	−0.112217
$70$	0.0504464	0.00602950
$71$	11.6016	1.37686	0.688428	−	0.725305i	$-0.258301\pi$
$71$	11.6016	1.37686	0.688428	+	0.725305i	$0.258301\pi$
$72$	2.13110	0.251153
$73$	3.21738	0.376565	0.188283	−	0.982115i	$-0.439708\pi$
$73$	3.21738	0.376565	0.188283	+	0.982115i	$0.439708\pi$
$74$	7.32825	0.851892
$75$	4.41534	0.509840
$76$	5.57408	0.639391
$77$	0.173385	0.0197591
$78$	1.81222	0.205193
$79$	4.67534	0.526017	0.263008	−	0.964794i	$-0.415285\pi$
$79$	4.67534	0.526017	0.263008	+	0.964794i	$0.415285\pi$
$80$	−0.513090	−0.0573652
$81$	1.93489	0.214988
$82$	6.09707	0.673309
$83$	6.74942	0.740845	0.370422	−	0.928863i	$-0.379213\pi$
$83$	6.74942	0.740845	0.370422	+	0.928863i	$0.379213\pi$
$84$	−0.0916477	−0.00999958
$85$	−0.0544301	−0.00590377
$86$	−4.09661	−0.441748
$87$	2.29931	0.246512
$88$	−1.76350	−0.187990
$89$	−7.62846	−0.808616	−0.404308	−	0.914623i	$-0.632488\pi$
$89$	−7.62846	−0.808616	−0.404308	+	0.914623i	$0.632488\pi$
$90$	−1.09345	−0.115259
$91$	0.191144	0.0200374
$92$	1.00000	0.104257
$93$	5.84226	0.605815
$94$	3.63401	0.374820
$95$	−2.86001	−0.293430
$96$	0.932148	0.0951369
$97$	10.6127	1.07756	0.538779	−	0.842447i	$-0.318886\pi$
$97$	10.6127	1.07756	0.538779	+	0.842447i	$0.318886\pi$
$98$	6.99033	0.706130
$99$	−3.75819	−0.377712
$100$	−4.73674	−0.473674
$101$	2.04141	0.203128	0.101564	−	0.994829i	$-0.467615\pi$
$101$	2.04141	0.203128	0.101564	+	0.994829i	$0.467615\pi$
$102$	0.0988850	0.00979107
$103$	−17.7356	−1.74754	−0.873770	−	0.486339i	$-0.838332\pi$
$103$	−17.7356	−1.74754	−0.873770	+	0.486339i	$0.838332\pi$
$104$	−1.94413	−0.190637
$105$	0.0470235	0.00458902
$106$	−0.949157	−0.0921902
$107$	−13.2071	−1.27677	−0.638387	−	0.769715i	$-0.720398\pi$
$107$	−13.2071	−1.27677	−0.638387	+	0.769715i	$0.720398\pi$
$108$	4.78294	0.460239
$109$	8.85329	0.847992	0.423996	−	0.905664i	$-0.360627\pi$
$109$	8.85329	0.847992	0.423996	+	0.905664i	$0.360627\pi$
$110$	0.904833	0.0862724
$111$	6.83102	0.648371
$112$	0.0983188	0.00929026
$113$	−3.21901	−0.302819	−0.151409	−	0.988471i	$-0.548381\pi$
$113$	−3.21901	−0.302819	−0.151409	+	0.988471i	$0.548381\pi$
$114$	5.19587	0.486638
$115$	−0.513090	−0.0478459
$116$	−2.46668	−0.229025
$117$	−4.14313	−0.383033
$118$	−15.1915	−1.39849
$119$	0.0104300	0.000956112 0
$120$	−0.478276	−0.0436604
$121$	−7.89007	−0.717279
$122$	6.05297	0.548011
$123$	5.68337	0.512452
$124$	−6.26753	−0.562841
$125$	4.99582	0.446840
$126$	0.209527	0.0186662
$127$	−16.2749	−1.44417	−0.722084	−	0.691805i	$-0.756816\pi$
$127$	−16.2749	−1.44417	−0.722084	+	0.691805i	$0.756816\pi$
$128$	−1.00000	−0.0883883
$129$	−3.81864	−0.336213
$130$	0.997513	0.0874876
$131$	1.00000	0.0873704
$131$	1.00000	0.0873704
$132$	−1.64384	−0.143078
$133$	0.548037	0.0475209
$134$	−9.31760	−0.804918
$135$	−2.45408	−0.211214
$136$	−0.106083	−0.00909654
$137$	−12.3517	−1.05528	−0.527639	−	0.849469i	$-0.676923\pi$
$137$	−12.3517	−1.05528	−0.527639	+	0.849469i	$0.676923\pi$
$138$	0.932148	0.0793497
$139$	−2.02855	−0.172060	−0.0860298	−	0.996293i	$-0.527418\pi$
$139$	−2.02855	−0.172060	−0.0860298	+	0.996293i	$0.527418\pi$
$140$	−0.0504464	−0.00426350
$141$	3.38744	0.285274
$142$	−11.6016	−0.973584
$143$	3.42847	0.286703
$144$	−2.13110	−0.177592
$145$	1.26563	0.105105
$146$	−3.21738	−0.266272
$147$	6.51602	0.537433
$148$	−7.32825	−0.602379
$149$	13.1522	1.07747	0.538733	−	0.842476i	$-0.318903\pi$
$149$	13.1522	1.07747	0.538733	+	0.842476i	$0.318903\pi$
$150$	−4.41534	−0.360511
$151$	8.60668	0.700401	0.350201	−	0.936675i	$-0.386113\pi$
$151$	8.60668	0.700401	0.350201	+	0.936675i	$0.386113\pi$
$152$	−5.57408	−0.452118
$153$	−0.226073	−0.0182770
$154$	−0.173385	−0.0139718
$155$	3.21581	0.258300
$156$	−1.81222	−0.145093
$157$	7.59165	0.605880	0.302940	−	0.953010i	$-0.402032\pi$
$157$	7.59165	0.605880	0.302940	+	0.953010i	$0.402032\pi$
$158$	−4.67534	−0.371950
$159$	−0.884754	−0.0701656
$160$	0.513090	0.0405633
$161$	0.0983188	0.00774861
$162$	−1.93489	−0.152019
$163$	−7.06902	−0.553689	−0.276844	−	0.960915i	$-0.589289\pi$
$163$	−7.06902	−0.553689	−0.276844	+	0.960915i	$0.589289\pi$
$164$	−6.09707	−0.476101
$165$	0.843438	0.0656616
$166$	−6.74942	−0.523856
$167$	5.77948	0.447230	0.223615	−	0.974678i	$-0.428214\pi$
$167$	5.77948	0.447230	0.223615	+	0.974678i	$0.428214\pi$
$168$	0.0916477	0.00707077
$169$	−9.22036	−0.709259
$170$	0.0544301	0.00417460
$171$	−11.8789	−0.908405
$172$	4.09661	0.312363
$173$	11.0590	0.840797	0.420398	−	0.907340i	$-0.361890\pi$
$173$	11.0590	0.840797	0.420398	+	0.907340i	$0.361890\pi$
$174$	−2.29931	−0.174310
$175$	−0.465711	−0.0352044
$176$	1.76350	0.132929
$177$	−14.1608	−1.06439
$178$	7.62846	0.571778
$179$	−14.1530	−1.05784	−0.528922	−	0.848670i	$-0.677404\pi$
$179$	−14.1530	−1.05784	−0.528922	+	0.848670i	$0.677404\pi$
$180$	1.09345	0.0815007
$181$	3.46254	0.257369	0.128684	−	0.991686i	$-0.458925\pi$
$181$	3.46254	0.257369	0.128684	+	0.991686i	$0.458925\pi$
$182$	−0.191144	−0.0141686
$183$	5.64227	0.417088
$184$	−1.00000	−0.0737210
$185$	3.76005	0.276445
$186$	−5.84226	−0.428376
$187$	0.187077	0.0136804
$188$	−3.63401	−0.265038
$189$	0.470254	0.0342059
$190$	2.86001	0.207487
$191$	−0.396258	−0.0286722	−0.0143361	−	0.999897i	$-0.504563\pi$
$191$	−0.396258	−0.0286722	−0.0143361	+	0.999897i	$0.504563\pi$
$192$	−0.932148	−0.0672720
$193$	−3.64510	−0.262380	−0.131190	−	0.991357i	$-0.541880\pi$
$193$	−3.64510	−0.262380	−0.131190	+	0.991357i	$0.541880\pi$
$194$	−10.6127	−0.761948
$195$	0.929829	0.0665864
$196$	−6.99033	−0.499310
$197$	26.3209	1.87528	0.937642	−	0.347603i	$-0.113004\pi$
$197$	26.3209	1.87528	0.937642	+	0.347603i	$0.113004\pi$
$198$	3.75819	0.267083
$199$	−21.1271	−1.49766	−0.748831	−	0.662761i	$-0.769385\pi$
$199$	−21.1271	−1.49766	−0.748831	+	0.662761i	$0.769385\pi$
$200$	4.73674	0.334938
$201$	−8.68538	−0.612620
$202$	−2.04141	−0.143633
$203$	−0.242521	−0.0170216
$204$	−0.0988850	−0.00692333
$205$	3.12834	0.218493
$206$	17.7356	1.23570
$207$	−2.13110	−0.148122
$208$	1.94413	0.134801
$209$	9.82989	0.679947
$210$	−0.0470235	−0.00324493
$211$	−5.02165	−0.345705	−0.172852	−	0.984948i	$-0.555298\pi$
$211$	−5.02165	−0.345705	−0.172852	+	0.984948i	$0.555298\pi$
$212$	0.949157	0.0651884
$213$	−10.8144	−0.740990
$214$	13.2071	0.902816
$215$	−2.10193	−0.143350
$216$	−4.78294	−0.325438
$217$	−0.616216	−0.0418315
$218$	−8.85329	−0.599621
$219$	−2.99907	−0.202658
$220$	−0.904833	−0.0610038
$221$	0.206239	0.0138731
$222$	−6.83102	−0.458468
$223$	−2.98097	−0.199621	−0.0998103	−	0.995006i	$-0.531824\pi$
$223$	−2.98097	−0.199621	−0.0998103	+	0.995006i	$0.531824\pi$
$224$	−0.0983188	−0.00656920
$225$	10.0945	0.672964
$226$	3.21901	0.214125
$227$	−27.8779	−1.85032	−0.925160	−	0.379576i	$-0.876070\pi$
$227$	−27.8779	−1.85032	−0.925160	+	0.379576i	$0.876070\pi$
$228$	−5.19587	−0.344105
$229$	8.67574	0.573309	0.286655	−	0.958034i	$-0.407457\pi$
$229$	8.67574	0.573309	0.286655	+	0.958034i	$0.407457\pi$
$230$	0.513090	0.0338321
$231$	−0.161621	−0.0106339
$232$	2.46668	0.161945
$233$	2.48734	0.162951	0.0814756	−	0.996675i	$-0.474037\pi$
$233$	2.48734	0.162951	0.0814756	+	0.996675i	$0.474037\pi$
$234$	4.14313	0.270845
$235$	1.86457	0.121631
$236$	15.1915	0.988885
$237$	−4.35811	−0.283089
$238$	−0.0104300	−0.000676073 0
$239$	10.8334	0.700757	0.350379	−	0.936608i	$-0.386053\pi$
$239$	10.8334	0.700757	0.350379	+	0.936608i	$0.386053\pi$
$240$	0.478276	0.0308726
$241$	−30.2691	−1.94980	−0.974901	−	0.222638i	$-0.928533\pi$
$241$	−30.2691	−1.94980	−0.974901	+	0.222638i	$0.928533\pi$
$242$	7.89007	0.507193
$243$	−16.1524	−1.03618
$244$	−6.05297	−0.387502
$245$	3.58667	0.229144
$246$	−5.68337	−0.362358
$247$	10.8367	0.689525
$248$	6.26753	0.397989
$249$	−6.29145	−0.398705
$250$	−4.99582	−0.315964
$251$	−16.4332	−1.03726	−0.518628	−	0.855000i	$-0.673557\pi$
$251$	−16.4332	−1.03726	−0.518628	+	0.855000i	$0.673557\pi$
$252$	−0.209527	−0.0131990
$253$	1.76350	0.110870
$254$	16.2749	1.02118
$255$	0.0507369	0.00317727
$256$	1.00000	0.0625000
$257$	−14.9307	−0.931351	−0.465676	−	0.884956i	$-0.654189\pi$
$257$	−14.9307	−0.931351	−0.465676	+	0.884956i	$0.654189\pi$
$258$	3.81864	0.237738
$259$	−0.720505	−0.0447700
$260$	−0.997513	−0.0618631
$261$	5.25674	0.325384
$262$	−1.00000	−0.0617802
$263$	15.7074	0.968558	0.484279	−	0.874914i	$-0.339082\pi$
$263$	15.7074	0.968558	0.484279	+	0.874914i	$0.339082\pi$
$264$	1.64384	0.101171
$265$	−0.487003	−0.0299163
$266$	−0.548037	−0.0336023
$267$	7.11086	0.435177
$268$	9.31760	0.569163
$269$	25.6443	1.56356	0.781779	−	0.623556i	$-0.214313\pi$
$269$	25.6443	1.56356	0.781779	+	0.623556i	$0.214313\pi$
$270$	2.45408	0.149351
$271$	−17.1604	−1.04242	−0.521209	−	0.853429i	$-0.674519\pi$
$271$	−17.1604	−1.04242	−0.521209	+	0.853429i	$0.674519\pi$
$272$	0.106083	0.00643222
$273$	−0.178175	−0.0107836
$274$	12.3517	0.746194
$275$	−8.35323	−0.503719
$276$	−0.932148	−0.0561087
$277$	−30.4299	−1.82835	−0.914177	−	0.405316i	$-0.867162\pi$
$277$	−30.4299	−1.82835	−0.914177	+	0.405316i	$0.867162\pi$
$278$	2.02855	0.121665
$279$	13.3567	0.799647
$280$	0.0504464	0.00301475
$281$	6.51695	0.388769	0.194384	−	0.980925i	$-0.437729\pi$
$281$	6.51695	0.388769	0.194384	+	0.980925i	$0.437729\pi$
$282$	−3.38744	−0.201719
$283$	12.6219	0.750296	0.375148	−	0.926965i	$-0.377592\pi$
$283$	12.6219	0.750296	0.375148	+	0.926965i	$0.377592\pi$
$284$	11.6016	0.688428
$285$	2.66595	0.157917
$286$	−3.42847	−0.202730
$287$	−0.599457	−0.0353848
$288$	2.13110	0.125576
$289$	−16.9887	−0.999338
$290$	−1.26563	−0.0743202
$291$	−9.89261	−0.579915
$292$	3.21738	0.188283
$293$	−15.3701	−0.897932	−0.448966	−	0.893549i	$-0.648208\pi$
$293$	−15.3701	−0.897932	−0.448966	+	0.893549i	$0.648208\pi$
$294$	−6.51602	−0.380022
$295$	−7.79462	−0.453821
$296$	7.32825	0.425946
$297$	8.43471	0.489432
$298$	−13.1522	−0.761884
$299$	1.94413	0.112432
$300$	4.41534	0.254920
$301$	0.402774	0.0232155
$302$	−8.60668	−0.495259
$303$	−1.90290	−0.109319
$304$	5.57408	0.319696
$305$	3.10572	0.177833
$306$	0.226073	0.0129238
$307$	15.7267	0.897570	0.448785	−	0.893640i	$-0.351857\pi$
$307$	15.7267	0.897570	0.448785	+	0.893640i	$0.351857\pi$
$308$	0.173385	0.00987953
$309$	16.5322	0.940484
$310$	−3.21581	−0.182646
$311$	−34.4984	−1.95622	−0.978112	−	0.208079i	$-0.933279\pi$
$311$	−34.4984	−1.95622	−0.978112	+	0.208079i	$0.933279\pi$
$312$	1.81222	0.102596
$313$	−4.63612	−0.262049	−0.131025	−	0.991379i	$-0.541827\pi$
$313$	−4.63612	−0.262049	−0.131025	+	0.991379i	$0.541827\pi$
$314$	−7.59165	−0.428422
$315$	0.107506	0.00605730
$316$	4.67534	0.263008
$317$	21.8326	1.22624	0.613119	−	0.789990i	$-0.289914\pi$
$317$	21.8326	1.22624	0.613119	+	0.789990i	$0.289914\pi$
$318$	0.884754	0.0496146
$319$	−4.34998	−0.243552
$320$	−0.513090	−0.0286826
$321$	12.3109	0.687129
$322$	−0.0983188	−0.00547909
$323$	0.591315	0.0329017
$324$	1.93489	0.107494
$325$	−9.20883	−0.510814
$326$	7.06902	0.391517
$327$	−8.25258	−0.456369
$328$	6.09707	0.336654
$329$	−0.357292	−0.0196981
$330$	−0.843438	−0.0464297
$331$	6.75135	0.371088	0.185544	−	0.982636i	$-0.440595\pi$
$331$	6.75135	0.371088	0.185544	+	0.982636i	$0.440595\pi$
$332$	6.74942	0.370422
$333$	15.6172	0.855820
$334$	−5.77948	−0.316239
$335$	−4.78077	−0.261201
$336$	−0.0916477	−0.00499979
$337$	−7.77881	−0.423739	−0.211869	−	0.977298i	$-0.567955\pi$
$337$	−7.77881	−0.423739	−0.211869	+	0.977298i	$0.567955\pi$
$338$	9.22036	0.501522
$339$	3.00059	0.162970
$340$	−0.0544301	−0.00295189
$341$	−11.0528	−0.598541
$342$	11.8789	0.642339
$343$	−1.37551	−0.0742707
$344$	−4.09661	−0.220874
$345$	0.478276	0.0257495
$346$	−11.0590	−0.594533
$347$	3.94396	0.211723	0.105862	−	0.994381i	$-0.466240\pi$
$347$	3.94396	0.211723	0.105862	+	0.994381i	$0.466240\pi$
$348$	2.29931	0.123256
$349$	−17.2435	−0.923023	−0.461511	−	0.887134i	$-0.652693\pi$
$349$	−17.2435	−0.923023	−0.461511	+	0.887134i	$0.652693\pi$
$350$	0.465711	0.0248933
$351$	9.29866	0.496326
$352$	−1.76350	−0.0939948
$353$	−2.61370	−0.139113	−0.0695565	−	0.997578i	$-0.522158\pi$
$353$	−2.61370	−0.139113	−0.0695565	+	0.997578i	$0.522158\pi$
$354$	14.1608	0.752636
$355$	−5.95266	−0.315934
$356$	−7.62846	−0.404308
$357$	−0.00972226	−0.000514556 0
$358$	14.1530	0.748009
$359$	0.221086	0.0116685	0.00583423	−	0.999983i	$-0.498143\pi$
$359$	0.221086	0.0116685	0.00583423	+	0.999983i	$0.498143\pi$
$360$	−1.09345	−0.0576297
$361$	12.0704	0.635284
$362$	−3.46254	−0.181987
$363$	7.35472	0.386022
$364$	0.191144	0.0100187
$365$	−1.65080	−0.0864070
$366$	−5.64227	−0.294926
$367$	−2.70938	−0.141429	−0.0707143	−	0.997497i	$-0.522528\pi$
$367$	−2.70938	−0.141429	−0.0707143	+	0.997497i	$0.522528\pi$
$368$	1.00000	0.0521286
$369$	12.9935	0.676413
$370$	−3.76005	−0.195476
$371$	0.0933200	0.00484493
$372$	5.84226	0.302907
$373$	−12.7238	−0.658815	−0.329408	−	0.944188i	$-0.606849\pi$
$373$	−12.7238	−0.658815	−0.329408	+	0.944188i	$0.606849\pi$
$374$	−0.187077	−0.00967353
$375$	−4.65684	−0.240478
$376$	3.63401	0.187410
$377$	−4.79554	−0.246983
$378$	−0.470254	−0.0241872
$379$	−17.5973	−0.903914	−0.451957	−	0.892040i	$-0.649274\pi$
$379$	−17.5973	−0.903914	−0.451957	+	0.892040i	$0.649274\pi$
$380$	−2.86001	−0.146715
$381$	15.1707	0.777216
$382$	0.396258	0.0202743
$383$	−6.01438	−0.307321	−0.153660	−	0.988124i	$-0.549106\pi$
$383$	−6.01438	−0.307321	−0.153660	+	0.988124i	$0.549106\pi$
$384$	0.932148	0.0475685
$385$	−0.0889621	−0.00453393
$386$	3.64510	0.185530
$387$	−8.73028	−0.443785
$388$	10.6127	0.538779
$389$	−24.6541	−1.25001	−0.625007	−	0.780619i	$-0.714904\pi$
$389$	−24.6541	−1.25001	−0.625007	+	0.780619i	$0.714904\pi$
$390$	−0.929829	−0.0470837
$391$	0.106083	0.00536484
$392$	6.99033	0.353065
$393$	−0.932148	−0.0470206
$394$	−26.3209	−1.32603
$395$	−2.39887	−0.120700
$396$	−3.75819	−0.188856
$397$	−20.0548	−1.00652	−0.503261	−	0.864134i	$-0.667867\pi$
$397$	−20.0548	−1.00652	−0.503261	+	0.864134i	$0.667867\pi$
$398$	21.1271	1.05901
$399$	−0.510852	−0.0255746
$400$	−4.73674	−0.236837
$401$	−34.0924	−1.70249	−0.851247	−	0.524765i	$-0.824153\pi$
$401$	−34.0924	−1.70249	−0.851247	+	0.524765i	$0.824153\pi$
$402$	8.68538	0.433188
$403$	−12.1849	−0.606972
$404$	2.04141	0.101564
$405$	−0.992773	−0.0493313
$406$	0.242521	0.0120361
$407$	−12.9234	−0.640587
$408$	0.0988850	0.00489554
$409$	12.5220	0.619171	0.309585	−	0.950872i	$-0.399810\pi$
$409$	12.5220	0.619171	0.309585	+	0.950872i	$0.399810\pi$
$410$	−3.12834	−0.154498
$411$	11.5136	0.567925
$412$	−17.7356	−0.873770
$413$	1.49361	0.0734960
$414$	2.13110	0.104738
$415$	−3.46306	−0.169995
$416$	−1.94413	−0.0953187
$417$	1.89091	0.0925983
$418$	−9.82989	−0.480795
$419$	−24.1069	−1.17770	−0.588849	−	0.808243i	$-0.700419\pi$
$419$	−24.1069	−1.17770	−0.588849	+	0.808243i	$0.700419\pi$
$420$	0.0470235	0.00229451
$421$	−14.3417	−0.698972	−0.349486	−	0.936942i	$-0.613644\pi$
$421$	−14.3417	−0.698972	−0.349486	+	0.936942i	$0.613644\pi$
$422$	5.02165	0.244450
$423$	7.74445	0.376548
$424$	−0.949157	−0.0460951
$425$	−0.502487	−0.0243742
$426$	10.8144	0.523959
$427$	−0.595121	−0.0287999
$428$	−13.2071	−0.638387
$429$	−3.19584	−0.154297
$430$	2.10193	0.101364
$431$	20.7787	1.00088	0.500438	−	0.865773i	$-0.333172\pi$
$431$	20.7787	1.00088	0.500438	+	0.865773i	$0.333172\pi$
$432$	4.78294	0.230120
$433$	−28.2502	−1.35762	−0.678810	−	0.734314i	$-0.737504\pi$
$433$	−28.2502	−1.35762	−0.678810	+	0.734314i	$0.737504\pi$
$434$	0.616216	0.0295793
$435$	−1.17975	−0.0565648
$436$	8.85329	0.423996
$437$	5.57408	0.266645
$438$	2.99907	0.143301
$439$	−11.0153	−0.525731	−0.262865	−	0.964833i	$-0.584667\pi$
$439$	−11.0153	−0.525731	−0.262865	+	0.964833i	$0.584667\pi$
$440$	0.904833	0.0431362
$441$	14.8971	0.709386
$442$	−0.206239	−0.00980978
$443$	5.22423	0.248211	0.124105	−	0.992269i	$-0.460394\pi$
$443$	5.22423	0.248211	0.124105	+	0.992269i	$0.460394\pi$
$444$	6.83102	0.324186
$445$	3.91409	0.185546
$446$	2.98097	0.141153
$447$	−12.2598	−0.579866
$448$	0.0983188	0.00464513
$449$	−40.2241	−1.89829	−0.949147	−	0.314833i	$-0.898052\pi$
$449$	−40.2241	−1.89829	−0.949147	+	0.314833i	$0.898052\pi$
$450$	−10.0945	−0.475858
$451$	−10.7522	−0.506300
$452$	−3.21901	−0.151409
$453$	−8.02269	−0.376939
$454$	27.8779	1.30837
$455$	−0.0980743	−0.00459779
$456$	5.19587	0.243319
$457$	9.25575	0.432966	0.216483	−	0.976286i	$-0.430541\pi$
$457$	9.25575	0.432966	0.216483	+	0.976286i	$0.430541\pi$
$458$	−8.67574	−0.405391
$459$	0.507389	0.0236829
$460$	−0.513090	−0.0239229
$461$	20.0758	0.935023	0.467511	−	0.883987i	$-0.345151\pi$
$461$	20.0758	0.935023	0.467511	+	0.883987i	$0.345151\pi$
$462$	0.161621	0.00751927
$463$	13.5756	0.630914	0.315457	−	0.948940i	$-0.397842\pi$
$463$	13.5756	0.630914	0.315457	+	0.948940i	$0.397842\pi$
$464$	−2.46668	−0.114513
$465$	−2.99761	−0.139011
$466$	−2.48734	−0.115224
$467$	38.9289	1.80141	0.900707	−	0.434427i	$-0.143049\pi$
$467$	38.9289	1.80141	0.900707	+	0.434427i	$0.143049\pi$
$468$	−4.14313	−0.191516
$469$	0.916096	0.0423014
$470$	−1.86457	−0.0860064
$471$	−7.07654	−0.326070
$472$	−15.1915	−0.699247
$473$	7.22436	0.332176
$474$	4.35811	0.200174
$475$	−26.4030	−1.21145
$476$	0.0104300	0.000478056 0
$477$	−2.02275	−0.0926153
$478$	−10.8334	−0.495510
$479$	−10.4185	−0.476034	−0.238017	−	0.971261i	$-0.576497\pi$
$479$	−10.4185	−0.476034	−0.238017	+	0.971261i	$0.576497\pi$
$480$	−0.478276	−0.0218302
$481$	−14.2471	−0.649610
$482$	30.2691	1.37872
$483$	−0.0916477	−0.00417011
$484$	−7.89007	−0.358640
$485$	−5.44527	−0.247257
$486$	16.1524	0.732689
$487$	−12.3536	−0.559797	−0.279898	−	0.960030i	$-0.590301\pi$
$487$	−12.3536	−0.559797	−0.279898	+	0.960030i	$0.590301\pi$
$488$	6.05297	0.274005
$489$	6.58937	0.297982
$490$	−3.58667	−0.162029
$491$	−2.11026	−0.0952345	−0.0476173	−	0.998866i	$-0.515163\pi$
$491$	−2.11026	−0.0952345	−0.0476173	+	0.998866i	$0.515163\pi$
$492$	5.68337	0.256226
$493$	−0.261673	−0.0117851
$494$	−10.8367	−0.487568
$495$	1.92829	0.0866702
$496$	−6.26753	−0.281420
$497$	1.14065	0.0511654
$498$	6.29145	0.281927
$499$	13.5076	0.604682	0.302341	−	0.953200i	$-0.402232\pi$
$499$	13.5076	0.604682	0.302341	+	0.953200i	$0.402232\pi$
$500$	4.99582	0.223420
$501$	−5.38733	−0.240688
$502$	16.4332	0.733451
$503$	−24.2987	−1.08342	−0.541712	−	0.840564i	$-0.682224\pi$
$503$	−24.2987	−1.08342	−0.541712	+	0.840564i	$0.682224\pi$
$504$	0.209527	0.00933309
$505$	−1.04743	−0.0466099
$506$	−1.76350	−0.0783971
$507$	8.59474	0.381706
$508$	−16.2749	−0.722084
$509$	6.59346	0.292250	0.146125	−	0.989266i	$-0.453320\pi$
$509$	6.59346	0.292250	0.146125	+	0.989266i	$0.453320\pi$
$510$	−0.0507369	−0.00224667
$511$	0.316329	0.0139936
$512$	−1.00000	−0.0441942
$513$	26.6605	1.17709
$514$	14.9307	0.658565
$515$	9.09995	0.400992
$516$	−3.81864	−0.168106
$517$	−6.40857	−0.281849
$518$	0.720505	0.0316572
$519$	−10.3086	−0.452496
$520$	0.997513	0.0437438
$521$	−9.01633	−0.395013	−0.197506	−	0.980302i	$-0.563284\pi$
$521$	−9.01633	−0.395013	−0.197506	+	0.980302i	$0.563284\pi$
$522$	−5.25674	−0.230081
$523$	−18.4767	−0.807931	−0.403965	−	0.914774i	$-0.632368\pi$
$523$	−18.4767	−0.807931	−0.403965	+	0.914774i	$0.632368\pi$
$524$	1.00000	0.0436852
$525$	0.434111	0.0189462
$526$	−15.7074	−0.684874
$527$	−0.664878	−0.0289625
$528$	−1.64384	−0.0715390
$529$	1.00000	0.0434783
$530$	0.487003	0.0211540
$531$	−32.3747	−1.40494
$532$	0.548037	0.0237604
$533$	−11.8535	−0.513431
$534$	−7.11086	−0.307717
$535$	6.77641	0.292970
$536$	−9.31760	−0.402459
$537$	13.1927	0.569306
$538$	−25.6443	−1.10560
$539$	−12.3274	−0.530980
$540$	−2.45408	−0.105607
$541$	−0.125397	−0.00539124	−0.00269562	−	0.999996i	$-0.500858\pi$
$541$	−0.125397	−0.00539124	−0.00269562	+	0.999996i	$0.500858\pi$
$542$	17.1604	0.737101
$543$	−3.22760	−0.138510
$544$	−0.106083	−0.00454827
$545$	−4.54254	−0.194581
$546$	0.178175	0.00762518
$547$	24.9486	1.06673	0.533363	−	0.845887i	$-0.320928\pi$
$547$	24.9486	1.06673	0.533363	+	0.845887i	$0.320928\pi$
$548$	−12.3517	−0.527639
$549$	12.8995	0.550537
$550$	8.35323	0.356183
$551$	−13.7495	−0.585747
$552$	0.932148	0.0396748
$553$	0.459674	0.0195473
$554$	30.4299	1.29284
$555$	−3.50492	−0.148776
$556$	−2.02855	−0.0860298
$557$	−34.5318	−1.46316	−0.731579	−	0.681757i	$-0.761216\pi$
$557$	−34.5318	−1.46316	−0.731579	+	0.681757i	$0.761216\pi$
$558$	−13.3567	−0.565436
$559$	7.96433	0.336855
$560$	−0.0504464	−0.00213175
$561$	−0.174383	−0.00736248
$562$	−6.51695	−0.274901
$563$	8.18846	0.345102	0.172551	−	0.985001i	$-0.444799\pi$
$563$	8.18846	0.345102	0.172551	+	0.985001i	$0.444799\pi$
$564$	3.38744	0.142637
$565$	1.65164	0.0694850
$566$	−12.6219	−0.530539
$567$	0.190236	0.00798917
$568$	−11.6016	−0.486792
$569$	−31.6922	−1.32861	−0.664303	−	0.747463i	$-0.731272\pi$
$569$	−31.6922	−1.32861	−0.664303	+	0.747463i	$0.731272\pi$
$570$	−2.66595	−0.111664
$571$	12.5688	0.525986	0.262993	−	0.964798i	$-0.415290\pi$
$571$	12.5688	0.525986	0.262993	+	0.964798i	$0.415290\pi$
$572$	3.42847	0.143351
$573$	0.369371	0.0154307
$574$	0.599457	0.0250208
$575$	−4.73674	−0.197536
$576$	−2.13110	−0.0887959
$577$	29.8320	1.24192	0.620962	−	0.783840i	$-0.286742\pi$
$577$	29.8320	1.24192	0.620962	+	0.783840i	$0.286742\pi$
$578$	16.9887	0.706639
$579$	3.39777	0.141206
$580$	1.26563	0.0525523
$581$	0.663595	0.0275305
$582$	9.89261	0.410062
$583$	1.67384	0.0693232
$584$	−3.21738	−0.133136
$585$	2.12580	0.0878910
$586$	15.3701	0.634934
$587$	12.0481	0.497279	0.248640	−	0.968596i	$-0.420017\pi$
$587$	12.0481	0.497279	0.248640	+	0.968596i	$0.420017\pi$
$588$	6.51602	0.268716
$589$	−34.9357	−1.43950
$590$	7.79462	0.320900
$591$	−24.5349	−1.00923
$592$	−7.32825	−0.301189
$593$	−31.5007	−1.29358	−0.646789	−	0.762669i	$-0.723889\pi$
$593$	−31.5007	−1.29358	−0.646789	+	0.762669i	$0.723889\pi$
$594$	−8.43471	−0.346080
$595$	−0.00535150	−0.000219390 0
$596$	13.1522	0.538733
$597$	19.6936	0.806006
$598$	−1.94413	−0.0795013
$599$	−42.6727	−1.74356	−0.871780	−	0.489898i	$-0.837034\pi$
$599$	−42.6727	−1.74356	−0.871780	+	0.489898i	$0.837034\pi$
$600$	−4.41534	−0.180256
$601$	−0.490616	−0.0200126	−0.0100063	−	0.999950i	$-0.503185\pi$
$601$	−0.490616	−0.0200126	−0.0100063	+	0.999950i	$0.503185\pi$
$602$	−0.402774	−0.0164158
$603$	−19.8567	−0.808629
$604$	8.60668	0.350201
$605$	4.04832	0.164587
$606$	1.90290	0.0773000
$607$	−1.21928	−0.0494892	−0.0247446	−	0.999694i	$-0.507877\pi$
$607$	−1.21928	−0.0494892	−0.0247446	+	0.999694i	$0.507877\pi$
$608$	−5.57408	−0.226059
$609$	0.226065	0.00916063
$610$	−3.10572	−0.125747
$611$	−7.06499	−0.285819
$612$	−0.226073	−0.00913848
$613$	−30.8954	−1.24786	−0.623928	−	0.781482i	$-0.714464\pi$
$613$	−30.8954	−1.24786	−0.623928	+	0.781482i	$0.714464\pi$
$614$	−15.7267	−0.634678
$615$	−2.91608	−0.117588
$616$	−0.173385	−0.00698588
$617$	17.8401	0.718216	0.359108	−	0.933296i	$-0.383081\pi$
$617$	17.8401	0.718216	0.359108	+	0.933296i	$0.383081\pi$
$618$	−16.5322	−0.665022
$619$	16.4586	0.661526	0.330763	−	0.943714i	$-0.392694\pi$
$619$	16.4586	0.661526	0.330763	+	0.943714i	$0.392694\pi$
$620$	3.21581	0.129150
$621$	4.78294	0.191933
$622$	34.4984	1.38326
$623$	−0.750022	−0.0300490
$624$	−1.81222	−0.0725467
$625$	21.1204	0.844816
$626$	4.63612	0.185297
$627$	−9.16291	−0.365931
$628$	7.59165	0.302940
$629$	−0.777403	−0.0309971
$630$	−0.107506	−0.00428316
$631$	−29.7876	−1.18583	−0.592913	−	0.805266i	$-0.702022\pi$
$631$	−29.7876	−1.18583	−0.592913	+	0.805266i	$0.702022\pi$
$632$	−4.67534	−0.185975
$633$	4.68092	0.186050
$634$	−21.8326	−0.867082
$635$	8.35051	0.331380
$636$	−0.884754	−0.0350828
$637$	−13.5901	−0.538460
$638$	4.34998	0.172218
$639$	−24.7242	−0.978072
$640$	0.513090	0.0202817
$641$	3.80678	0.150359	0.0751795	−	0.997170i	$-0.476047\pi$
$641$	3.80678	0.150359	0.0751795	+	0.997170i	$0.476047\pi$
$642$	−12.3109	−0.485874
$643$	−26.2794	−1.03636	−0.518179	−	0.855272i	$-0.673390\pi$
$643$	−26.2794	−1.03636	−0.518179	+	0.855272i	$0.673390\pi$
$644$	0.0983188	0.00387430
$645$	1.95931	0.0771476
$646$	−0.591315	−0.0232650
$647$	31.8279	1.25128	0.625642	−	0.780110i	$-0.284837\pi$
$647$	31.8279	1.25128	0.625642	+	0.780110i	$0.284837\pi$
$648$	−1.93489	−0.0760097
$649$	26.7903	1.05161
$650$	9.20883	0.361200
$651$	0.574405	0.0225127
$652$	−7.06902	−0.276844
$653$	36.8484	1.44199	0.720994	−	0.692941i	$-0.243685\pi$
$653$	36.8484	1.44199	0.720994	+	0.692941i	$0.243685\pi$
$654$	8.25258	0.322701
$655$	−0.513090	−0.0200481
$656$	−6.09707	−0.238051
$657$	−6.85655	−0.267500
$658$	0.357292	0.0139287
$659$	−38.4786	−1.49891	−0.749456	−	0.662054i	$-0.769685\pi$
$659$	−38.4786	−1.49891	−0.749456	+	0.662054i	$0.769685\pi$
$660$	0.843438	0.0328308
$661$	−21.2349	−0.825940	−0.412970	−	0.910745i	$-0.635509\pi$
$661$	−21.2349	−0.825940	−0.412970	+	0.910745i	$0.635509\pi$
$662$	−6.75135	−0.262399
$663$	−0.192245	−0.00746618
$664$	−6.74942	−0.261928
$665$	−0.281192	−0.0109042
$666$	−15.6172	−0.605156
$667$	−2.46668	−0.0955102
$668$	5.77948	0.223615
$669$	2.77871	0.107431
$670$	4.78077	0.184697
$671$	−10.6744	−0.412081
$672$	0.0916477	0.00353539
$673$	11.7931	0.454589	0.227294	−	0.973826i	$-0.427012\pi$
$673$	11.7931	0.454589	0.227294	+	0.973826i	$0.427012\pi$
$674$	7.77881	0.299628
$675$	−22.6556	−0.872013
$676$	−9.22036	−0.354629
$677$	35.9761	1.38267	0.691336	−	0.722533i	$-0.257022\pi$
$677$	35.9761	1.38267	0.691336	+	0.722533i	$0.257022\pi$
$678$	−3.00059	−0.115237
$679$	1.04343	0.0400431
$680$	0.0544301	0.00208730
$681$	25.9863	0.995798
$682$	11.0528	0.423233
$683$	3.99954	0.153038	0.0765192	−	0.997068i	$-0.475619\pi$
$683$	3.99954	0.153038	0.0765192	+	0.997068i	$0.475619\pi$
$684$	−11.8789	−0.454202
$685$	6.33754	0.242145
$686$	1.37551	0.0525173
$687$	−8.08708	−0.308541
$688$	4.09661	0.156182
$689$	1.84528	0.0702997
$690$	−0.478276	−0.0182076
$691$	15.8844	0.604272	0.302136	−	0.953265i	$-0.402300\pi$
$691$	15.8844	0.604272	0.302136	+	0.953265i	$0.402300\pi$
$692$	11.0590	0.420398
$693$	−0.369501	−0.0140362
$694$	−3.94396	−0.149711
$695$	1.04083	0.0394809
$696$	−2.29931	−0.0871551
$697$	−0.646795	−0.0244991
$698$	17.2435	0.652676
$699$	−2.31857	−0.0876964
$700$	−0.465711	−0.0176022
$701$	0.670179	0.0253123	0.0126562	−	0.999920i	$-0.495971\pi$
$701$	0.670179	0.0253123	0.0126562	+	0.999920i	$0.495971\pi$
$702$	−9.29866	−0.350955
$703$	−40.8483	−1.54062
$704$	1.76350	0.0664643
$705$	−1.73806	−0.0654591
$706$	2.61370	0.0983678
$707$	0.200709	0.00754845
$708$	−14.1608	−0.532194
$709$	27.8747	1.04685	0.523427	−	0.852070i	$-0.324653\pi$
$709$	27.8747	1.04685	0.523427	+	0.852070i	$0.324653\pi$
$710$	5.95266	0.223399
$711$	−9.96362	−0.373665
$712$	7.62846	0.285889
$713$	−6.26753	−0.234721
$714$	0.00972226	0.000363846 0
$715$	−1.75911	−0.0657870
$716$	−14.1530	−0.528922
$717$	−10.0984	−0.377131
$718$	−0.221086	−0.00825084
$719$	−37.7795	−1.40894	−0.704469	−	0.709734i	$-0.748815\pi$
$719$	−37.7795	−1.40894	−0.704469	+	0.709734i	$0.748815\pi$
$720$	1.09345	0.0407503
$721$	−1.74374	−0.0649404
$722$	−12.0704	−0.449214
$723$	28.2152	1.04934
$724$	3.46254	0.128684
$725$	11.6840	0.433933
$726$	−7.35472	−0.272959
$727$	−32.1529	−1.19249	−0.596243	−	0.802804i	$-0.703341\pi$
$727$	−32.1529	−1.19249	−0.596243	+	0.802804i	$0.703341\pi$
$728$	−0.191144	−0.00708428
$729$	9.25179	0.342659
$730$	1.65080	0.0610990
$731$	0.434580	0.0160735
$732$	5.64227	0.208544
$733$	8.83362	0.326277	0.163139	−	0.986603i	$-0.447838\pi$
$733$	8.83362	0.326277	0.163139	+	0.986603i	$0.447838\pi$
$734$	2.70938	0.100005
$735$	−3.34331	−0.123320
$736$	−1.00000	−0.0368605
$737$	16.4316	0.605265
$738$	−12.9935	−0.478296
$739$	−32.1232	−1.18167	−0.590835	−	0.806793i	$-0.701201\pi$
$739$	−32.1232	−1.18167	−0.590835	+	0.806793i	$0.701201\pi$
$740$	3.76005	0.138222
$741$	−10.1014	−0.371086
$742$	−0.0933200	−0.00342588
$743$	−0.361862	−0.0132754	−0.00663772	−	0.999978i	$-0.502113\pi$
$743$	−0.361862	−0.0132754	−0.00663772	+	0.999978i	$0.502113\pi$
$744$	−5.84226	−0.214188
$745$	−6.74824	−0.247236
$746$	12.7238	0.465853
$747$	−14.3837	−0.526271
$748$	0.187077	0.00684022
$749$	−1.29850	−0.0474462
$750$	4.65684	0.170044
$751$	4.90666	0.179047	0.0895233	−	0.995985i	$-0.471466\pi$
$751$	4.90666	0.179047	0.0895233	+	0.995985i	$0.471466\pi$
$752$	−3.63401	−0.132519
$753$	15.3182	0.558226
$754$	4.79554	0.174643
$755$	−4.41600	−0.160715
$756$	0.470254	0.0171030
$757$	−11.8860	−0.432005	−0.216003	−	0.976393i	$-0.569302\pi$
$757$	−11.8860	−0.432005	−0.216003	+	0.976393i	$0.569302\pi$
$758$	17.5973	0.639164
$759$	−1.64384	−0.0596677
$760$	2.86001	0.103743
$761$	24.8316	0.900143	0.450072	−	0.892993i	$-0.351398\pi$
$761$	24.8316	0.900143	0.450072	+	0.892993i	$0.351398\pi$
$762$	−15.1707	−0.549575
$763$	0.870446	0.0315122
$764$	−0.396258	−0.0143361
$765$	0.115996	0.00419384
$766$	6.01438	0.217309
$767$	29.5343	1.06642
$768$	−0.932148	−0.0336360
$769$	7.65492	0.276043	0.138022	−	0.990429i	$-0.455926\pi$
$769$	7.65492	0.276043	0.138022	+	0.990429i	$0.455926\pi$
$770$	0.0889621	0.00320597
$771$	13.9176	0.501231
$772$	−3.64510	−0.131190
$773$	39.9471	1.43680	0.718399	−	0.695632i	$-0.244875\pi$
$773$	39.9471	1.43680	0.718399	+	0.695632i	$0.244875\pi$
$774$	8.73028	0.313803
$775$	29.6877	1.06641
$776$	−10.6127	−0.380974
$777$	0.671618	0.0240941
$778$	24.6541	0.883893
$779$	−33.9856	−1.21766
$780$	0.929829	0.0332932
$781$	20.4594	0.732094
$782$	−0.106083	−0.00379352
$783$	−11.7980	−0.421626
$784$	−6.99033	−0.249655
$785$	−3.89520	−0.139026
$786$	0.932148	0.0332486
$787$	−8.27965	−0.295138	−0.147569	−	0.989052i	$-0.547145\pi$
$787$	−8.27965	−0.295138	−0.147569	+	0.989052i	$0.547145\pi$
$788$	26.3209	0.937642
$789$	−14.6416	−0.521255
$790$	2.39887	0.0853479
$791$	−0.316489	−0.0112531
$792$	3.75819	0.133542
$793$	−11.7678	−0.417885
$794$	20.0548	0.711719
$795$	0.453958	0.0161002
$796$	−21.1271	−0.748831
$797$	−14.4902	−0.513268	−0.256634	−	0.966509i	$-0.582614\pi$
$797$	−14.4902	−0.513268	−0.256634	+	0.966509i	$0.582614\pi$
$798$	0.510852	0.0180840
$799$	−0.385507	−0.0136382
$800$	4.73674	0.167469
$801$	16.2570	0.574414
$802$	34.0924	1.20384
$803$	5.67384	0.200225
$804$	−8.68538	−0.306310
$805$	−0.0504464	−0.00177800
$806$	12.1849	0.429194
$807$	−23.9042	−0.841469
$808$	−2.04141	−0.0718167
$809$	18.9987	0.667960	0.333980	−	0.942580i	$-0.391608\pi$
$809$	18.9987	0.667960	0.333980	+	0.942580i	$0.391608\pi$
$810$	0.992773	0.0348825
$811$	−43.9705	−1.54401	−0.772007	−	0.635614i	$-0.780747\pi$
$811$	−43.9705	−1.54401	−0.772007	+	0.635614i	$0.780747\pi$
$812$	−0.242521	−0.00851082
$813$	15.9960	0.561004
$814$	12.9234	0.452964
$815$	3.62704	0.127050
$816$	−0.0988850	−0.00346167
$817$	22.8348	0.798889
$818$	−12.5220	−0.437820
$819$	−0.407348	−0.0142339
$820$	3.12834	0.109247
$821$	−31.2007	−1.08891	−0.544456	−	0.838790i	$-0.683264\pi$
$821$	−31.2007	−1.08891	−0.544456	+	0.838790i	$0.683264\pi$
$822$	−11.5136	−0.401584
$823$	−15.0831	−0.525764	−0.262882	−	0.964828i	$-0.584673\pi$
$823$	−15.0831	−0.525764	−0.262882	+	0.964828i	$0.584673\pi$
$824$	17.7356	0.617849
$825$	7.78645	0.271089
$826$	−1.49361	−0.0519695
$827$	29.7431	1.03427	0.517135	−	0.855904i	$-0.326999\pi$
$827$	29.7431	1.03427	0.517135	+	0.855904i	$0.326999\pi$
$828$	−2.13110	−0.0740609
$829$	−16.9184	−0.587600	−0.293800	−	0.955867i	$-0.594920\pi$
$829$	−16.9184	−0.587600	−0.293800	+	0.955867i	$0.594920\pi$
$830$	3.46306	0.120204
$831$	28.3651	0.983976
$832$	1.94413	0.0674005
$833$	−0.741555	−0.0256934
$834$	−1.89091	−0.0654769
$835$	−2.96540	−0.102622
$836$	9.82989	0.339974
$837$	−29.9772	−1.03617
$838$	24.1069	0.832758
$839$	41.7923	1.44283	0.721416	−	0.692502i	$-0.243492\pi$
$839$	41.7923	1.44283	0.721416	+	0.692502i	$0.243492\pi$
$840$	−0.0470235	−0.00162246
$841$	−22.9155	−0.790189
$842$	14.3417	0.494248
$843$	−6.07476	−0.209226
$844$	−5.02165	−0.172852
$845$	4.73088	0.162747
$846$	−7.74445	−0.266260
$847$	−0.775743	−0.0266548
$848$	0.949157	0.0325942
$849$	−11.7655	−0.403791
$850$	0.502487	0.0172352
$851$	−7.32825	−0.251209
$852$	−10.8144	−0.370495
$853$	16.6582	0.570364	0.285182	−	0.958473i	$-0.407946\pi$
$853$	16.6582	0.570364	0.285182	+	0.958473i	$0.407946\pi$
$854$	0.595121	0.0203646
$855$	6.09496	0.208443
$856$	13.2071	0.451408
$857$	−24.2190	−0.827306	−0.413653	−	0.910435i	$-0.635747\pi$
$857$	−24.2190	−0.827306	−0.413653	+	0.910435i	$0.635747\pi$
$858$	3.19584	0.109104
$859$	−36.8280	−1.25656	−0.628278	−	0.777989i	$-0.716240\pi$
$859$	−36.8280	−1.25656	−0.628278	+	0.777989i	$0.716240\pi$
$860$	−2.10193	−0.0716751
$861$	0.558782	0.0190433
$862$	−20.7787	−0.707726
$863$	11.8916	0.404795	0.202397	−	0.979303i	$-0.435127\pi$
$863$	11.8916	0.404795	0.202397	+	0.979303i	$0.435127\pi$
$864$	−4.78294	−0.162719
$865$	−5.67424	−0.192930
$866$	28.2502	0.959983
$867$	15.8360	0.537820
$868$	−0.616216	−0.0209157
$869$	8.24495	0.279691
$870$	1.17975	0.0399974
$871$	18.1146	0.613790
$872$	−8.85329	−0.299810
$873$	−22.6167	−0.765461
$874$	−5.57408	−0.188546
$875$	0.491183	0.0166050
$876$	−2.99907	−0.101329
$877$	19.3786	0.654369	0.327184	−	0.944961i	$-0.393900\pi$
$877$	19.3786	0.654369	0.327184	+	0.944961i	$0.393900\pi$
$878$	11.0153	0.371748
$879$	14.3272	0.483245
$880$	−0.904833	−0.0305019
$881$	−25.5138	−0.859582	−0.429791	−	0.902928i	$-0.641413\pi$
$881$	−25.5138	−0.859582	−0.429791	+	0.902928i	$0.641413\pi$
$882$	−14.8971	−0.501612
$883$	−13.8350	−0.465584	−0.232792	−	0.972527i	$-0.574786\pi$
$883$	−13.8350	−0.465584	−0.232792	+	0.972527i	$0.574786\pi$
$884$	0.206239	0.00693656
$885$	7.26574	0.244235
$886$	−5.22423	−0.175512
$887$	7.10366	0.238517	0.119259	−	0.992863i	$-0.461948\pi$
$887$	7.10366	0.238517	0.119259	+	0.992863i	$0.461948\pi$
$888$	−6.83102	−0.229234
$889$	−1.60013	−0.0536668
$890$	−3.91409	−0.131201
$891$	3.41218	0.114312
$892$	−2.98097	−0.0998103
$893$	−20.2563	−0.677851
$894$	12.2598	0.410027
$895$	7.26176	0.242734
$896$	−0.0983188	−0.00328460
$897$	−1.81222	−0.0605081
$898$	40.2241	1.34230
$899$	15.4600	0.515619
$900$	10.0945	0.336482
$901$	0.100689	0.00335445
$902$	10.7522	0.358008
$903$	−0.375445	−0.0124940
$904$	3.21901	0.107063
$905$	−1.77659	−0.0590560
$906$	8.02269	0.266536
$907$	8.42017	0.279587	0.139794	−	0.990181i	$-0.455356\pi$
$907$	8.42017	0.279587	0.139794	+	0.990181i	$0.455356\pi$
$908$	−27.8779	−0.925160
$909$	−4.35046	−0.144296
$910$	0.0980743	0.00325113
$911$	11.7259	0.388497	0.194248	−	0.980952i	$-0.437773\pi$
$911$	11.7259	0.388497	0.194248	+	0.980952i	$0.437773\pi$
$912$	−5.19587	−0.172052
$913$	11.9026	0.393918
$914$	−9.25575	−0.306153
$915$	−2.89499	−0.0957054
$916$	8.67574	0.286655
$917$	0.0983188	0.00324677
$918$	−0.507389	−0.0167463
$919$	−45.1929	−1.49077	−0.745387	−	0.666632i	$-0.767735\pi$
$919$	−45.1929	−1.49077	−0.745387	+	0.666632i	$0.767735\pi$
$920$	0.513090	0.0169161
$921$	−14.6596	−0.483051
$922$	−20.0758	−0.661161
$923$	22.5550	0.742406
$924$	−0.161621	−0.00531693
$925$	34.7120	1.14132
$926$	−13.5756	−0.446123
$927$	37.7963	1.24139
$928$	2.46668	0.0809727
$929$	−44.0576	−1.44548	−0.722742	−	0.691118i	$-0.757118\pi$
$929$	−44.0576	−1.44548	−0.722742	+	0.691118i	$0.757118\pi$
$930$	2.99761	0.0982954
$931$	−38.9647	−1.27702
$932$	2.48734	0.0814756
$933$	32.1576	1.05279
$934$	−38.9289	−1.27379
$935$	−0.0959874	−0.00313912
$936$	4.14313	0.135423
$937$	17.9028	0.584859	0.292430	−	0.956287i	$-0.405536\pi$
$937$	17.9028	0.584859	0.292430	+	0.956287i	$0.405536\pi$
$938$	−0.916096	−0.0299116
$939$	4.32155	0.141028
$940$	1.86457	0.0608157
$941$	12.1445	0.395900	0.197950	−	0.980212i	$-0.436572\pi$
$941$	12.1445	0.395900	0.197950	+	0.980212i	$0.436572\pi$
$942$	7.07654	0.230566
$943$	−6.09707	−0.198548
$944$	15.1915	0.494442
$945$	−0.241282	−0.00784891
$946$	−7.22436	−0.234884
$947$	40.1063	1.30328	0.651640	−	0.758528i	$-0.274081\pi$
$947$	40.1063	1.30328	0.651640	+	0.758528i	$0.274081\pi$
$948$	−4.35811	−0.141545
$949$	6.25499	0.203046
$950$	26.4030	0.856626
$951$	−20.3512	−0.659932
$952$	−0.0104300	−0.000338037 0
$953$	19.1677	0.620902	0.310451	−	0.950589i	$-0.399520\pi$
$953$	19.1677	0.620902	0.310451	+	0.950589i	$0.399520\pi$
$954$	2.02275	0.0654889
$955$	0.203316	0.00657914
$956$	10.8334	0.350379
$957$	4.05483	0.131074
$958$	10.4185	0.336607
$959$	−1.21441	−0.0392152
$960$	0.478276	0.0154363
$961$	8.28193	0.267159
$962$	14.2471	0.459344
$963$	28.1456	0.906978
$964$	−30.2691	−0.974901
$965$	1.87026	0.0602058
$966$	0.0916477	0.00294872
$967$	41.4739	1.33371	0.666856	−	0.745187i	$-0.267640\pi$
$967$	41.4739	1.33371	0.666856	+	0.745187i	$0.267640\pi$
$968$	7.89007	0.253597
$969$	−0.551193	−0.0177069
$970$	5.44527	0.174837
$971$	−12.3194	−0.395348	−0.197674	−	0.980268i	$-0.563339\pi$
$971$	−12.3194	−0.395348	−0.197674	+	0.980268i	$0.563339\pi$
$972$	−16.1524	−0.518090
$973$	−0.199445	−0.00639391
$974$	12.3536	0.395836
$975$	8.58399	0.274908
$976$	−6.05297	−0.193751
$977$	2.09975	0.0671769	0.0335885	−	0.999436i	$-0.489306\pi$
$977$	2.09975	0.0671769	0.0335885	+	0.999436i	$0.489306\pi$
$978$	−6.58937	−0.210705
$979$	−13.4528	−0.429953
$980$	3.58667	0.114572
$981$	−18.8673	−0.602385
$982$	2.11026	0.0673410
$983$	27.1713	0.866629	0.433314	−	0.901243i	$-0.357344\pi$
$983$	27.1713	0.866629	0.433314	+	0.901243i	$0.357344\pi$
$984$	−5.68337	−0.181179
$985$	−13.5050	−0.430304
$986$	0.261673	0.00833335
$987$	0.333049	0.0106011
$988$	10.8367	0.344762
$989$	4.09661	0.130265
$990$	−1.92829	−0.0612851
$991$	−39.5928	−1.25771	−0.628854	−	0.777524i	$-0.716476\pi$
$991$	−39.5928	−1.25771	−0.628854	+	0.777524i	$0.716476\pi$
$992$	6.26753	0.198994
$993$	−6.29325	−0.199710
$994$	−1.14065	−0.0361794
$995$	10.8401	0.343655
$996$	−6.29145	−0.199352
$997$	−7.35412	−0.232907	−0.116454	−	0.993196i	$-0.537153\pi$
$997$	−7.35412	−0.232907	−0.116454	+	0.993196i	$0.537153\pi$
$998$	−13.5076	−0.427575
$999$	−35.0506	−1.10895

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6026.2.a.i.1.11	✓	25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6026.2.a.i.1.11	✓	25	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -0.932148 q^{3} +1.00000 q^{4} -0.513090 q^{5} +0.932148 q^{6} +0.0983188 q^{7} -1.00000 q^{8} -2.13110 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -0.932148 q^{3} +1.00000 q^{4} -0.513090 q^{5} +0.932148 q^{6} +0.0983188 q^{7} -1.00000 q^{8} -2.13110 q^{9} +0.513090 q^{10} +1.76350 q^{11} -0.932148 q^{12} +1.94413 q^{13} -0.0983188 q^{14} +0.478276 q^{15} +1.00000 q^{16} +0.106083 q^{17} +2.13110 q^{18} +5.57408 q^{19} -0.513090 q^{20} -0.0916477 q^{21} -1.76350 q^{22} +1.00000 q^{23} +0.932148 q^{24} -4.73674 q^{25} -1.94413 q^{26} +4.78294 q^{27} +0.0983188 q^{28} -2.46668 q^{29} -0.478276 q^{30} -6.26753 q^{31} -1.00000 q^{32} -1.64384 q^{33} -0.106083 q^{34} -0.0504464 q^{35} -2.13110 q^{36} -7.32825 q^{37} -5.57408 q^{38} -1.81222 q^{39} +0.513090 q^{40} -6.09707 q^{41} +0.0916477 q^{42} +4.09661 q^{43} +1.76350 q^{44} +1.09345 q^{45} -1.00000 q^{46} -3.63401 q^{47} -0.932148 q^{48} -6.99033 q^{49} +4.73674 q^{50} -0.0988850 q^{51} +1.94413 q^{52} +0.949157 q^{53} -4.78294 q^{54} -0.904833 q^{55} -0.0983188 q^{56} -5.19587 q^{57} +2.46668 q^{58} +15.1915 q^{59} +0.478276 q^{60} -6.05297 q^{61} +6.26753 q^{62} -0.209527 q^{63} +1.00000 q^{64} -0.997513 q^{65} +1.64384 q^{66} +9.31760 q^{67} +0.106083 q^{68} -0.932148 q^{69} +0.0504464 q^{70} +11.6016 q^{71} +2.13110 q^{72} +3.21738 q^{73} +7.32825 q^{74} +4.41534 q^{75} +5.57408 q^{76} +0.173385 q^{77} +1.81222 q^{78} +4.67534 q^{79} -0.513090 q^{80} +1.93489 q^{81} +6.09707 q^{82} +6.74942 q^{83} -0.0916477 q^{84} -0.0544301 q^{85} -4.09661 q^{86} +2.29931 q^{87} -1.76350 q^{88} -7.62846 q^{89} -1.09345 q^{90} +0.191144 q^{91} +1.00000 q^{92} +5.84226 q^{93} +3.63401 q^{94} -2.86001 q^{95} +0.932148 q^{96} +10.6127 q^{97} +6.99033 q^{98} -3.75819 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q - 25 q^{2} - 4 q^{3} + 25 q^{4} - 3 q^{5} + 4 q^{6} - 11 q^{7} - 25 q^{8} + 19 q^{9}+O(q^{10}) \) 25 * q - 25 * q^2 - 4 * q^3 + 25 * q^4 - 3 * q^5 + 4 * q^6 - 11 * q^7 - 25 * q^8 + 19 * q^9	\( 25 q - 25 q^{2} - 4 q^{3} + 25 q^{4} - 3 q^{5} + 4 q^{6} - 11 q^{7} - 25 q^{8} + 19 q^{9} + 3 q^{10} - 12 q^{11} - 4 q^{12} - 6 q^{13} + 11 q^{14} + 25 q^{16} + 8 q^{17} - 19 q^{18} - 23 q^{19} - 3 q^{20} - 16 q^{21} + 12 q^{22} + 25 q^{23} + 4 q^{24} + 4 q^{25} + 6 q^{26} - 13 q^{27} - 11 q^{28} - 7 q^{29} - 7 q^{31} - 25 q^{32} + 3 q^{33} - 8 q^{34} - 18 q^{35} + 19 q^{36} - 7 q^{37} + 23 q^{38} - 2 q^{39} + 3 q^{40} - 10 q^{41} + 16 q^{42} - 26 q^{43} - 12 q^{44} + 20 q^{45} - 25 q^{46} - 2 q^{47} - 4 q^{48} + 2 q^{49} - 4 q^{50} - 28 q^{51} - 6 q^{52} + 47 q^{53} + 13 q^{54} - 38 q^{55} + 11 q^{56} - 4 q^{57} + 7 q^{58} - 19 q^{59} - 26 q^{61} + 7 q^{62} - 15 q^{63} + 25 q^{64} + 13 q^{65} - 3 q^{66} - 34 q^{67} + 8 q^{68} - 4 q^{69} + 18 q^{70} - 10 q^{71} - 19 q^{72} - 22 q^{73} + 7 q^{74} - 8 q^{75} - 23 q^{76} + 28 q^{77} + 2 q^{78} - 21 q^{79} - 3 q^{80} - 27 q^{81} + 10 q^{82} - 16 q^{83} - 16 q^{84} - 42 q^{85} + 26 q^{86} - 17 q^{87} + 12 q^{88} + 27 q^{89} - 20 q^{90} - 26 q^{91} + 25 q^{92} - 27 q^{93} + 2 q^{94} + 4 q^{96} + 4 q^{97} - 2 q^{98} - 2 q^{99}+O(q^{100}) \) 25 * q - 25 * q^2 - 4 * q^3 + 25 * q^4 - 3 * q^5 + 4 * q^6 - 11 * q^7 - 25 * q^8 + 19 * q^9 + 3 * q^10 - 12 * q^11 - 4 * q^12 - 6 * q^13 + 11 * q^14 + 25 * q^16 + 8 * q^17 - 19 * q^18 - 23 * q^19 - 3 * q^20 - 16 * q^21 + 12 * q^22 + 25 * q^23 + 4 * q^24 + 4 * q^25 + 6 * q^26 - 13 * q^27 - 11 * q^28 - 7 * q^29 - 7 * q^31 - 25 * q^32 + 3 * q^33 - 8 * q^34 - 18 * q^35 + 19 * q^36 - 7 * q^37 + 23 * q^38 - 2 * q^39 + 3 * q^40 - 10 * q^41 + 16 * q^42 - 26 * q^43 - 12 * q^44 + 20 * q^45 - 25 * q^46 - 2 * q^47 - 4 * q^48 + 2 * q^49 - 4 * q^50 - 28 * q^51 - 6 * q^52 + 47 * q^53 + 13 * q^54 - 38 * q^55 + 11 * q^56 - 4 * q^57 + 7 * q^58 - 19 * q^59 - 26 * q^61 + 7 * q^62 - 15 * q^63 + 25 * q^64 + 13 * q^65 - 3 * q^66 - 34 * q^67 + 8 * q^68 - 4 * q^69 + 18 * q^70 - 10 * q^71 - 19 * q^72 - 22 * q^73 + 7 * q^74 - 8 * q^75 - 23 * q^76 + 28 * q^77 + 2 * q^78 - 21 * q^79 - 3 * q^80 - 27 * q^81 + 10 * q^82 - 16 * q^83 - 16 * q^84 - 42 * q^85 + 26 * q^86 - 17 * q^87 + 12 * q^88 + 27 * q^89 - 20 * q^90 - 26 * q^91 + 25 * q^92 - 27 * q^93 + 2 * q^94 + 4 * q^96 + 4 * q^97 - 2 * q^98 - 2 * q^99

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