LMFDB - Embedded newform 6023.2.a.d.1.25

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6023,2,Mod(1,6023)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6023, 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("6023.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6023 = 19 \cdot 317 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6023.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:	$48.0938971374$
Analytic rank:	$0$
Dimension:	$140$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.25
Character	$\chi$	$=$	6023.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.02168 q^{2} +1.61986 q^{3} +2.08717 q^{4} -1.19952 q^{5} -3.27484 q^{6} +0.0155924 q^{7} -0.176233 q^{8} -0.376042 q^{9} +O(q^{10})$	\(q-2.02168 q^{2} +1.61986 q^{3} +2.08717 q^{4} -1.19952 q^{5} -3.27484 q^{6} +0.0155924 q^{7} -0.176233 q^{8} -0.376042 q^{9} +2.42503 q^{10} +5.32822 q^{11} +3.38093 q^{12} -4.20187 q^{13} -0.0315228 q^{14} -1.94305 q^{15} -3.81806 q^{16} +6.93614 q^{17} +0.760235 q^{18} -1.00000 q^{19} -2.50360 q^{20} +0.0252576 q^{21} -10.7719 q^{22} -2.89006 q^{23} -0.285473 q^{24} -3.56116 q^{25} +8.49482 q^{26} -5.46873 q^{27} +0.0325440 q^{28} -7.33242 q^{29} +3.92822 q^{30} +3.18394 q^{31} +8.07134 q^{32} +8.63100 q^{33} -14.0226 q^{34} -0.0187033 q^{35} -0.784864 q^{36} -5.41180 q^{37} +2.02168 q^{38} -6.80646 q^{39} +0.211394 q^{40} +9.11138 q^{41} -0.0510626 q^{42} +4.74478 q^{43} +11.1209 q^{44} +0.451068 q^{45} +5.84276 q^{46} -0.137903 q^{47} -6.18473 q^{48} -6.99976 q^{49} +7.19951 q^{50} +11.2356 q^{51} -8.77003 q^{52} +11.3480 q^{53} +11.0560 q^{54} -6.39129 q^{55} -0.00274789 q^{56} -1.61986 q^{57} +14.8238 q^{58} +7.90796 q^{59} -4.05548 q^{60} +1.80813 q^{61} -6.43689 q^{62} -0.00586340 q^{63} -8.68151 q^{64} +5.04021 q^{65} -17.4491 q^{66} -0.452250 q^{67} +14.4769 q^{68} -4.68150 q^{69} +0.0378121 q^{70} -8.19915 q^{71} +0.0662709 q^{72} +14.1099 q^{73} +10.9409 q^{74} -5.76860 q^{75} -2.08717 q^{76} +0.0830799 q^{77} +13.7605 q^{78} +10.9055 q^{79} +4.57982 q^{80} -7.73047 q^{81} -18.4203 q^{82} +11.8185 q^{83} +0.0527169 q^{84} -8.32001 q^{85} -9.59240 q^{86} -11.8775 q^{87} -0.939007 q^{88} +3.41736 q^{89} -0.911914 q^{90} -0.0655173 q^{91} -6.03205 q^{92} +5.15754 q^{93} +0.278795 q^{94} +1.19952 q^{95} +13.0745 q^{96} -7.34060 q^{97} +14.1512 q^{98} -2.00364 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 140 q + 4 q^{2} + 3 q^{3} + 162 q^{4} + 13 q^{5} + 12 q^{6} + 25 q^{7} + 12 q^{8} + 181 q^{9}+O(q^{10}) $ 140 * q + 4 * q^2 + 3 * q^3 + 162 * q^4 + 13 * q^5 + 12 * q^6 + 25 * q^7 + 12 * q^8 + 181 * q^9	\( 140 q + 4 q^{2} + 3 q^{3} + 162 q^{4} + 13 q^{5} + 12 q^{6} + 25 q^{7} + 12 q^{8} + 181 q^{9} + 8 q^{10} + 19 q^{11} + 17 q^{12} + 28 q^{13} + 5 q^{14} + 14 q^{15} + 202 q^{16} + 38 q^{17} + 26 q^{18} - 140 q^{19} + 36 q^{20} + 4 q^{21} + 53 q^{22} + 58 q^{23} + 47 q^{24} + 279 q^{25} + 29 q^{26} + 21 q^{27} + 69 q^{28} + 18 q^{29} + 50 q^{30} + 20 q^{31} + 13 q^{32} + 47 q^{33} + 6 q^{34} + 35 q^{35} + 230 q^{36} + 88 q^{37} - 4 q^{38} + 32 q^{39} + 32 q^{40} + 24 q^{41} + 75 q^{42} + 100 q^{43} + 63 q^{44} + 87 q^{45} + 23 q^{46} + 35 q^{47} + 46 q^{48} + 255 q^{49} + 11 q^{50} - 6 q^{51} + 47 q^{52} + 77 q^{53} + 16 q^{54} + 63 q^{55} + 21 q^{56} - 3 q^{57} + 165 q^{58} + 18 q^{59} + 28 q^{60} + 99 q^{61} + 34 q^{62} + 89 q^{63} + 298 q^{64} + 78 q^{65} - 3 q^{66} + 28 q^{67} + 93 q^{68} + 19 q^{69} + 16 q^{70} + q^{71} + 43 q^{72} + 201 q^{73} + 32 q^{74} + 22 q^{75} - 162 q^{76} + 86 q^{77} + 122 q^{78} + 58 q^{79} + 92 q^{80} + 288 q^{81} + 143 q^{82} + 57 q^{83} + q^{84} + 136 q^{85} - 6 q^{86} + 43 q^{87} + 198 q^{88} + 46 q^{89} + 30 q^{90} + 26 q^{91} + 129 q^{92} + 111 q^{93} + 44 q^{94} - 13 q^{95} + 32 q^{96} + 110 q^{97} - 34 q^{98} + 62 q^{99}+O(q^{100}) \) 140 * q + 4 * q^2 + 3 * q^3 + 162 * q^4 + 13 * q^5 + 12 * q^6 + 25 * q^7 + 12 * q^8 + 181 * q^9 + 8 * q^10 + 19 * q^11 + 17 * q^12 + 28 * q^13 + 5 * q^14 + 14 * q^15 + 202 * q^16 + 38 * q^17 + 26 * q^18 - 140 * q^19 + 36 * q^20 + 4 * q^21 + 53 * q^22 + 58 * q^23 + 47 * q^24 + 279 * q^25 + 29 * q^26 + 21 * q^27 + 69 * q^28 + 18 * q^29 + 50 * q^30 + 20 * q^31 + 13 * q^32 + 47 * q^33 + 6 * q^34 + 35 * q^35 + 230 * q^36 + 88 * q^37 - 4 * q^38 + 32 * q^39 + 32 * q^40 + 24 * q^41 + 75 * q^42 + 100 * q^43 + 63 * q^44 + 87 * q^45 + 23 * q^46 + 35 * q^47 + 46 * q^48 + 255 * q^49 + 11 * q^50 - 6 * q^51 + 47 * q^52 + 77 * q^53 + 16 * q^54 + 63 * q^55 + 21 * q^56 - 3 * q^57 + 165 * q^58 + 18 * q^59 + 28 * q^60 + 99 * q^61 + 34 * q^62 + 89 * q^63 + 298 * q^64 + 78 * q^65 - 3 * q^66 + 28 * q^67 + 93 * q^68 + 19 * q^69 + 16 * q^70 + q^71 + 43 * q^72 + 201 * q^73 + 32 * q^74 + 22 * q^75 - 162 * q^76 + 86 * q^77 + 122 * q^78 + 58 * q^79 + 92 * q^80 + 288 * q^81 + 143 * q^82 + 57 * q^83 + q^84 + 136 * q^85 - 6 * q^86 + 43 * q^87 + 198 * q^88 + 46 * q^89 + 30 * q^90 + 26 * q^91 + 129 * q^92 + 111 * q^93 + 44 * q^94 - 13 * q^95 + 32 * q^96 + 110 * q^97 - 34 * q^98 + 62 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−2.02168	−1.42954	−0.714770	−	0.699359i	$-0.753469\pi$
$2$	−2.02168	−1.42954	−0.714770	+	0.699359i	$0.753469\pi$
$3$	1.61986	0.935229	0.467614	−	0.883933i	$-0.345114\pi$
$3$	1.61986	0.935229	0.467614	+	0.883933i	$0.345114\pi$
$4$	2.08717	1.04359
$5$	−1.19952	−0.536440	−0.268220	−	0.963358i	$-0.586435\pi$
$5$	−1.19952	−0.536440	−0.268220	+	0.963358i	$0.586435\pi$
$6$	−3.27484	−1.33695
$7$	0.0155924	0.00589338	0.00294669	−	0.999996i	$-0.499062\pi$
$7$	0.0155924	0.00589338	0.00294669	+	0.999996i	$0.499062\pi$
$8$	−0.176233	−0.0623076
$9$	−0.376042	−0.125347
$10$	2.42503	0.766862
$11$	5.32822	1.60652	0.803260	−	0.595629i	$-0.203097\pi$
$11$	5.32822	1.60652	0.803260	+	0.595629i	$0.203097\pi$
$12$	3.38093	0.975991
$13$	−4.20187	−1.16539	−0.582695	−	0.812691i	$-0.698002\pi$
$13$	−4.20187	−1.16539	−0.582695	+	0.812691i	$0.698002\pi$
$14$	−0.0315228	−0.00842482
$15$	−1.94305	−0.501694
$16$	−3.81806	−0.954515
$17$	6.93614	1.68226	0.841131	−	0.540832i	$-0.181890\pi$
$17$	6.93614	1.68226	0.841131	+	0.540832i	$0.181890\pi$
$18$	0.760235	0.179189
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	−2.50360	−0.559821
$21$	0.0252576	0.00551166
$22$	−10.7719	−2.29659
$23$	−2.89006	−0.602619	−0.301309	−	0.953526i	$-0.597424\pi$
$23$	−2.89006	−0.602619	−0.301309	+	0.953526i	$0.597424\pi$
$24$	−0.285473	−0.0582719
$25$	−3.56116	−0.712232
$26$	8.49482	1.66597
$27$	−5.46873	−1.05246
$28$	0.0325440	0.00615025
$29$	−7.33242	−1.36160	−0.680798	−	0.732471i	$-0.738367\pi$
$29$	−7.33242	−1.36160	−0.680798	+	0.732471i	$0.738367\pi$
$30$	3.92822	0.717192
$31$	3.18394	0.571852	0.285926	−	0.958252i	$-0.407699\pi$
$31$	3.18394	0.571852	0.285926	+	0.958252i	$0.407699\pi$
$32$	8.07134	1.42682
$33$	8.63100	1.50246
$34$	−14.0226	−2.40486
$35$	−0.0187033	−0.00316144
$36$	−0.784864	−0.130811
$37$	−5.41180	−0.889695	−0.444847	−	0.895606i	$-0.646742\pi$
$37$	−5.41180	−0.889695	−0.444847	+	0.895606i	$0.646742\pi$
$38$	2.02168	0.327959
$39$	−6.80646	−1.08991
$40$	0.211394	0.0334243
$41$	9.11138	1.42296	0.711479	−	0.702707i	$-0.248026\pi$
$41$	9.11138	1.42296	0.711479	+	0.702707i	$0.248026\pi$
$42$	−0.0510626	−0.00787914
$43$	4.74478	0.723572	0.361786	−	0.932261i	$-0.382167\pi$
$43$	4.74478	0.723572	0.361786	+	0.932261i	$0.382167\pi$
$44$	11.1209	1.67654
$45$	0.451068	0.0672413
$46$	5.84276	0.861468
$47$	−0.137903	−0.0201152	−0.0100576	−	0.999949i	$-0.503201\pi$
$47$	−0.137903	−0.0201152	−0.0100576	+	0.999949i	$0.503201\pi$
$48$	−6.18473	−0.892689
$49$	−6.99976	−0.999965
$50$	7.19951	1.01816
$51$	11.2356	1.57330
$52$	−8.77003	−1.21618
$53$	11.3480	1.55877	0.779385	−	0.626545i	$-0.215531\pi$
$53$	11.3480	1.55877	0.779385	+	0.626545i	$0.215531\pi$
$54$	11.0560	1.50453
$55$	−6.39129	−0.861801
$56$	−0.00274789	−0.000367202 0
$57$	−1.61986	−0.214556
$58$	14.8238	1.94646
$59$	7.90796	1.02953	0.514765	−	0.857332i	$-0.327879\pi$
$59$	7.90796	1.02953	0.514765	+	0.857332i	$0.327879\pi$
$60$	−4.05548	−0.523561
$61$	1.80813	0.231507	0.115753	−	0.993278i	$-0.463072\pi$
$61$	1.80813	0.231507	0.115753	+	0.993278i	$0.463072\pi$
$62$	−6.43689	−0.817485
$63$	−0.00586340	−0.000738719 0
$64$	−8.68151	−1.08519
$65$	5.04021	0.625161
$66$	−17.4491	−2.14783
$67$	−0.452250	−0.0552511	−0.0276255	−	0.999618i	$-0.508795\pi$
$67$	−0.452250	−0.0552511	−0.0276255	+	0.999618i	$0.508795\pi$
$68$	14.4769	1.75558
$69$	−4.68150	−0.563586
$70$	0.0378121	0.00451941
$71$	−8.19915	−0.973060	−0.486530	−	0.873664i	$-0.661737\pi$
$71$	−8.19915	−0.973060	−0.486530	+	0.873664i	$0.661737\pi$
$72$	0.0662709	0.00781010
$73$	14.1099	1.65144	0.825720	−	0.564080i	$-0.190769\pi$
$73$	14.1099	1.65144	0.825720	+	0.564080i	$0.190769\pi$
$74$	10.9409	1.27185
$75$	−5.76860	−0.666100
$76$	−2.08717	−0.239415
$77$	0.0830799	0.00946783
$78$	13.7605	1.55806
$79$	10.9055	1.22696	0.613481	−	0.789710i	$-0.289769\pi$
$79$	10.9055	1.22696	0.613481	+	0.789710i	$0.289769\pi$
$80$	4.57982	0.512040
$81$	−7.73047	−0.858941
$82$	−18.4203	−2.03418
$83$	11.8185	1.29725	0.648624	−	0.761109i	$-0.275345\pi$
$83$	11.8185	1.29725	0.648624	+	0.761109i	$0.275345\pi$
$84$	0.0527169	0.00575189
$85$	−8.32001	−0.902432
$86$	−9.59240	−1.03438
$87$	−11.8775	−1.27340
$88$	−0.939007	−0.100098
$89$	3.41736	0.362240	0.181120	−	0.983461i	$-0.442028\pi$
$89$	3.41736	0.362240	0.181120	+	0.983461i	$0.442028\pi$
$90$	−0.911914	−0.0961242
$91$	−0.0655173	−0.00686808
$92$	−6.03205	−0.628884
$93$	5.15754	0.534812
$94$	0.278795	0.0287555
$95$	1.19952	0.123068
$96$	13.0745	1.33441
$97$	−7.34060	−0.745325	−0.372662	−	0.927967i	$-0.621555\pi$
$97$	−7.34060	−0.745325	−0.372662	+	0.927967i	$0.621555\pi$
$98$	14.1512	1.42949
$99$	−2.00364	−0.201373
$100$	−7.43276	−0.743276
$101$	17.6725	1.75848	0.879241	−	0.476378i	$-0.158051\pi$
$101$	17.6725	1.75848	0.879241	+	0.476378i	$0.158051\pi$
$102$	−22.7147	−2.24910
$103$	9.45120	0.931255	0.465627	−	0.884981i	$-0.345829\pi$
$103$	9.45120	0.931255	0.465627	+	0.884981i	$0.345829\pi$
$104$	0.740507	0.0726127
$105$	−0.0302969	−0.00295667
$106$	−22.9420	−2.22833
$107$	−18.1030	−1.75008	−0.875042	−	0.484046i	$-0.839167\pi$
$107$	−18.1030	−1.75008	−0.875042	+	0.484046i	$0.839167\pi$
$108$	−11.4142	−1.09833
$109$	−5.91699	−0.566744	−0.283372	−	0.959010i	$-0.591453\pi$
$109$	−5.91699	−0.566744	−0.283372	+	0.959010i	$0.591453\pi$
$110$	12.9211	1.23198
$111$	−8.76638	−0.832068
$112$	−0.0595327	−0.00562532
$113$	−14.5977	−1.37324	−0.686618	−	0.727018i	$-0.740905\pi$
$113$	−14.5977	−1.37324	−0.686618	+	0.727018i	$0.740905\pi$
$114$	3.27484	0.306717
$115$	3.46667	0.323269
$116$	−15.3040	−1.42094
$117$	1.58008	0.146078
$118$	−15.9873	−1.47175
$119$	0.108151	0.00991421
$120$	0.342429	0.0312594
$121$	17.3900	1.58091
$122$	−3.65545	−0.330949
$123$	14.7592	1.33079
$124$	6.64542	0.596777
$125$	10.2692	0.918510
$126$	0.0118539	0.00105603
$127$	1.99849	0.177337	0.0886686	−	0.996061i	$-0.471739\pi$
$127$	1.99849	0.177337	0.0886686	+	0.996061i	$0.471739\pi$
$128$	1.40852	0.124497
$129$	7.68589	0.676705
$130$	−10.1897	−0.893693
$131$	−13.9706	−1.22062	−0.610310	−	0.792162i	$-0.708955\pi$
$131$	−13.9706	−1.22062	−0.610310	+	0.792162i	$0.708955\pi$
$132$	18.0144	1.56795
$133$	−0.0155924	−0.00135203
$134$	0.914302	0.0789837
$135$	6.55982	0.564580
$136$	−1.22237	−0.104818
$137$	−14.2799	−1.22002	−0.610008	−	0.792395i	$-0.708834\pi$
$137$	−14.2799	−1.22002	−0.610008	+	0.792395i	$0.708834\pi$
$138$	9.46447	0.805670
$139$	13.4310	1.13920	0.569599	−	0.821922i	$-0.307098\pi$
$139$	13.4310	1.13920	0.569599	+	0.821922i	$0.307098\pi$
$140$	−0.0390371	−0.00329924
$141$	−0.223384	−0.0188123
$142$	16.5760	1.39103
$143$	−22.3885	−1.87222
$144$	1.43575	0.119646
$145$	8.79536	0.730415
$146$	−28.5257	−2.36080
$147$	−11.3387	−0.935196
$148$	−11.2954	−0.928473
$149$	5.48001	0.448940	0.224470	−	0.974481i	$-0.427935\pi$
$149$	5.48001	0.448940	0.224470	+	0.974481i	$0.427935\pi$
$150$	11.6622	0.952217
$151$	4.16795	0.339183	0.169591	−	0.985514i	$-0.445755\pi$
$151$	4.16795	0.339183	0.169591	+	0.985514i	$0.445755\pi$
$152$	0.176233	0.0142943
$153$	−2.60828	−0.210867
$154$	−0.167961	−0.0135346
$155$	−3.81918	−0.306764
$156$	−14.2062	−1.13741
$157$	2.08697	0.166559	0.0832794	−	0.996526i	$-0.473461\pi$
$157$	2.08697	0.166559	0.0832794	+	0.996526i	$0.473461\pi$
$158$	−22.0473	−1.75399
$159$	18.3822	1.45781
$160$	−9.68170	−0.765406
$161$	−0.0450630	−0.00355146
$162$	15.6285	1.22789
$163$	2.04470	0.160153	0.0800766	−	0.996789i	$-0.474484\pi$
$163$	2.04470	0.160153	0.0800766	+	0.996789i	$0.474484\pi$
$164$	19.0170	1.48498
$165$	−10.3530	−0.805981
$166$	−23.8931	−1.85447
$167$	7.70824	0.596482	0.298241	−	0.954491i	$-0.403600\pi$
$167$	7.70824	0.596482	0.298241	+	0.954491i	$0.403600\pi$
$168$	−0.00445121	−0.000343418 0
$169$	4.65573	0.358133
$170$	16.8204	1.29006
$171$	0.376042	0.0287567
$172$	9.90316	0.755109
$173$	−16.3589	−1.24375	−0.621873	−	0.783118i	$-0.713628\pi$
$173$	−16.3589	−1.24375	−0.621873	+	0.783118i	$0.713628\pi$
$174$	24.0125	1.82038
$175$	−0.0555271	−0.00419745
$176$	−20.3435	−1.53345
$177$	12.8098	0.962845
$178$	−6.90880	−0.517836
$179$	−3.96360	−0.296253	−0.148127	−	0.988968i	$-0.547324\pi$
$179$	−3.96360	−0.296253	−0.148127	+	0.988968i	$0.547324\pi$
$180$	0.941457	0.0701721
$181$	−22.8231	−1.69643	−0.848214	−	0.529654i	$-0.822322\pi$
$181$	−22.8231	−1.69643	−0.848214	+	0.529654i	$0.822322\pi$
$182$	0.132455	0.00981820
$183$	2.92892	0.216512
$184$	0.509322	0.0375478
$185$	6.49154	0.477268
$186$	−10.4269	−0.764536
$187$	36.9573	2.70259
$188$	−0.287827	−0.0209919
$189$	−0.0852707	−0.00620253
$190$	−2.42503	−0.175930
$191$	−7.68907	−0.556362	−0.278181	−	0.960529i	$-0.589731\pi$
$191$	−7.68907	−0.556362	−0.278181	+	0.960529i	$0.589731\pi$
$192$	−14.0629	−1.01490
$193$	22.4864	1.61860	0.809302	−	0.587392i	$-0.199845\pi$
$193$	22.4864	1.61860	0.809302	+	0.587392i	$0.199845\pi$
$194$	14.8403	1.06547
$195$	8.16445	0.584669
$196$	−14.6097	−1.04355
$197$	24.3244	1.73304	0.866520	−	0.499143i	$-0.166352\pi$
$197$	24.3244	1.73304	0.866520	+	0.499143i	$0.166352\pi$
$198$	4.05070	0.287871
$199$	−6.01864	−0.426650	−0.213325	−	0.976981i	$-0.568429\pi$
$199$	−6.01864	−0.426650	−0.213325	+	0.976981i	$0.568429\pi$
$200$	0.627593	0.0443775
$201$	−0.732583	−0.0516724
$202$	−35.7281	−2.51382
$203$	−0.114330	−0.00802441
$204$	23.4506	1.64187
$205$	−10.9292	−0.763331
$206$	−19.1073	−1.33127
$207$	1.08678	0.0755367
$208$	16.0430	1.11238
$209$	−5.32822	−0.368561
$210$	0.0612504	0.00422668
$211$	11.7361	0.807949	0.403975	−	0.914770i	$-0.367628\pi$
$211$	11.7361	0.807949	0.403975	+	0.914770i	$0.367628\pi$
$212$	23.6853	1.62671
$213$	−13.2815	−0.910033
$214$	36.5984	2.50182
$215$	−5.69144	−0.388153
$216$	0.963768	0.0655761
$217$	0.0496453	0.00337014
$218$	11.9622	0.810184
$219$	22.8561	1.54447
$220$	−13.3397	−0.899363
$221$	−29.1448	−1.96049
$222$	17.7228	1.18947
$223$	16.4617	1.10236	0.551180	−	0.834387i	$-0.314178\pi$
$223$	16.4617	1.10236	0.551180	+	0.834387i	$0.314178\pi$
$224$	0.125852	0.00840882
$225$	1.33915	0.0892764
$226$	29.5118	1.96310
$227$	4.00512	0.265829	0.132915	−	0.991128i	$-0.457566\pi$
$227$	4.00512	0.265829	0.132915	+	0.991128i	$0.457566\pi$
$228$	−3.38093	−0.223908
$229$	−8.53179	−0.563796	−0.281898	−	0.959444i	$-0.590964\pi$
$229$	−8.53179	−0.563796	−0.281898	+	0.959444i	$0.590964\pi$
$230$	−7.00848	−0.462126
$231$	0.134578	0.00885459
$232$	1.29221	0.0848379
$233$	−13.4621	−0.881930	−0.440965	−	0.897524i	$-0.645364\pi$
$233$	−13.4621	−0.881930	−0.440965	+	0.897524i	$0.645364\pi$
$234$	−3.19441	−0.208825
$235$	0.165417	0.0107906
$236$	16.5053	1.07440
$237$	17.6654	1.14749
$238$	−0.218647	−0.0141728
$239$	20.7905	1.34482	0.672412	−	0.740177i	$-0.265259\pi$
$239$	20.7905	1.34482	0.672412	+	0.740177i	$0.265259\pi$
$240$	7.41868	0.478874
$241$	12.7578	0.821800	0.410900	−	0.911680i	$-0.365215\pi$
$241$	12.7578	0.821800	0.410900	+	0.911680i	$0.365215\pi$
$242$	−35.1569	−2.25997
$243$	3.88388	0.249151
$244$	3.77387	0.241597
$245$	8.39632	0.536421
$246$	−29.8383	−1.90242
$247$	4.20187	0.267359
$248$	−0.561113	−0.0356307
$249$	19.1443	1.21322
$250$	−20.7611	−1.31305
$251$	17.3530	1.09531	0.547655	−	0.836704i	$-0.315521\pi$
$251$	17.3530	1.09531	0.547655	+	0.836704i	$0.315521\pi$
$252$	−0.0122379	−0.000770917 0
$253$	−15.3989	−0.968119
$254$	−4.04030	−0.253511
$255$	−13.4773	−0.843980
$256$	14.5155	0.907216
$257$	20.8671	1.30165	0.650826	−	0.759227i	$-0.274423\pi$
$257$	20.8671	1.30165	0.650826	+	0.759227i	$0.274423\pi$
$258$	−15.5384	−0.967377
$259$	−0.0843830	−0.00524331
$260$	10.5198	0.652409
$261$	2.75730	0.170673
$262$	28.2441	1.74493
$263$	−10.9070	−0.672553	−0.336277	−	0.941763i	$-0.609168\pi$
$263$	−10.9070	−0.672553	−0.336277	+	0.941763i	$0.609168\pi$
$264$	−1.52106	−0.0936149
$265$	−13.6121	−0.836187
$266$	0.0315228	0.00193279
$267$	5.53566	0.338777
$268$	−0.943923	−0.0576592
$269$	14.0206	0.854850	0.427425	−	0.904051i	$-0.359421\pi$
$269$	14.0206	0.854850	0.427425	+	0.904051i	$0.359421\pi$
$270$	−13.2618	−0.807090
$271$	12.8446	0.780253	0.390127	−	0.920761i	$-0.372431\pi$
$271$	12.8446	0.780253	0.390127	+	0.920761i	$0.372431\pi$
$272$	−26.4826	−1.60574
$273$	−0.106129	−0.00642323
$274$	28.8694	1.74406
$275$	−18.9747	−1.14422
$276$	−9.77109	−0.588151
$277$	−28.4049	−1.70669	−0.853343	−	0.521350i	$-0.825428\pi$
$277$	−28.4049	−1.70669	−0.853343	+	0.521350i	$0.825428\pi$
$278$	−27.1530	−1.62853
$279$	−1.19729	−0.0716801
$280$	0.00329614	0.000196982 0
$281$	−24.1741	−1.44211	−0.721054	−	0.692879i	$-0.756342\pi$
$281$	−24.1741	−1.44211	−0.721054	+	0.692879i	$0.756342\pi$
$282$	0.451609	0.0268930
$283$	18.2083	1.08237	0.541184	−	0.840904i	$-0.317976\pi$
$283$	18.2083	1.08237	0.541184	+	0.840904i	$0.317976\pi$
$284$	−17.1130	−1.01547
$285$	1.94305	0.115096
$286$	45.2623	2.67642
$287$	0.142068	0.00838603
$288$	−3.03516	−0.178849
$289$	31.1101	1.83000
$290$	−17.7814	−1.04416
$291$	−11.8908	−0.697049
$292$	29.4498	1.72342
$293$	29.6240	1.73065	0.865326	−	0.501210i	$-0.167112\pi$
$293$	29.6240	1.73065	0.865326	+	0.501210i	$0.167112\pi$
$294$	22.9231	1.33690
$295$	−9.48573	−0.552280
$296$	0.953736	0.0554348
$297$	−29.1386	−1.69079
$298$	−11.0788	−0.641778
$299$	12.1437	0.702286
$300$	−12.0401	−0.695133
$301$	0.0739825	0.00426428
$302$	−8.42624	−0.484876
$303$	28.6271	1.64458
$304$	3.81806	0.218981
$305$	−2.16888	−0.124190
$306$	5.27310	0.301443
$307$	−0.238186	−0.0135940	−0.00679699	−	0.999977i	$-0.502164\pi$
$307$	−0.238186	−0.0135940	−0.00679699	+	0.999977i	$0.502164\pi$
$308$	0.173402	0.00988049
$309$	15.3097	0.870936
$310$	7.72115	0.438532
$311$	2.52664	0.143272	0.0716362	−	0.997431i	$-0.477178\pi$
$311$	2.52664	0.143272	0.0716362	+	0.997431i	$0.477178\pi$
$312$	1.19952	0.0679094
$313$	13.7715	0.778409	0.389204	−	0.921151i	$-0.372750\pi$
$313$	13.7715	0.778409	0.389204	+	0.921151i	$0.372750\pi$
$314$	−4.21919	−0.238102
$315$	0.00703325	0.000396278 0
$316$	22.7616	1.28044
$317$	1.00000	0.0561656
$317$	1.00000	0.0561656
$318$	−37.1629	−2.08399
$319$	−39.0688	−2.18743
$320$	10.4136	0.582139
$321$	−29.3244	−1.63673
$322$	0.0911027	0.00507696
$323$	−6.93614	−0.385937
$324$	−16.1348	−0.896378
$325$	14.9635	0.830028
$326$	−4.13372	−0.228945
$327$	−9.58471	−0.530036
$328$	−1.60572	−0.0886612
$329$	−0.00215024	−0.000118546 0
$330$	20.9304	1.15218
$331$	31.5925	1.73648	0.868241	−	0.496143i	$-0.165251\pi$
$331$	31.5925	1.73648	0.868241	+	0.496143i	$0.165251\pi$
$332$	24.6672	1.35379
$333$	2.03506	0.111521
$334$	−15.5836	−0.852695
$335$	0.542481	0.0296389
$336$	−0.0964349	−0.00526096
$337$	−14.8905	−0.811136	−0.405568	−	0.914065i	$-0.632926\pi$
$337$	−14.8905	−0.811136	−0.405568	+	0.914065i	$0.632926\pi$
$338$	−9.41237	−0.511965
$339$	−23.6463	−1.28429
$340$	−17.3653	−0.941765
$341$	16.9647	0.918692
$342$	−0.760235	−0.0411088
$343$	−0.218290	−0.0117866
$344$	−0.836184	−0.0450840
$345$	5.61553	0.302330
$346$	33.0725	1.77799
$347$	31.0684	1.66784	0.833920	−	0.551885i	$-0.186091\pi$
$347$	31.0684	1.66784	0.833920	+	0.551885i	$0.186091\pi$
$348$	−24.7904	−1.32891
$349$	−31.0868	−1.66404	−0.832018	−	0.554748i	$-0.812815\pi$
$349$	−31.0868	−1.66404	−0.832018	+	0.554748i	$0.812815\pi$
$350$	0.112258	0.00600043
$351$	22.9789	1.22652
$352$	43.0059	2.29222
$353$	23.5044	1.25101	0.625507	−	0.780218i	$-0.284892\pi$
$353$	23.5044	1.25101	0.625507	+	0.780218i	$0.284892\pi$
$354$	−25.8973	−1.37643
$355$	9.83500	0.521988
$356$	7.13262	0.378028
$357$	0.175190	0.00927205
$358$	8.01312	0.423506
$359$	16.7710	0.885138	0.442569	−	0.896735i	$-0.354067\pi$
$359$	16.7710	0.885138	0.442569	+	0.896735i	$0.354067\pi$
$360$	−0.0794929	−0.00418965
$361$	1.00000	0.0526316
$362$	46.1409	2.42511
$363$	28.1694	1.47851
$364$	−0.136746	−0.00716743
$365$	−16.9251	−0.885898
$366$	−5.92132	−0.309513
$367$	6.90989	0.360693	0.180347	−	0.983603i	$-0.442278\pi$
$367$	6.90989	0.360693	0.180347	+	0.983603i	$0.442278\pi$
$368$	11.0344	0.575208
$369$	−3.42626	−0.178364
$370$	−13.1238	−0.682273
$371$	0.176943	0.00918643
$372$	10.7647	0.558123
$373$	26.6662	1.38072	0.690362	−	0.723464i	$-0.257451\pi$
$373$	26.6662	1.38072	0.690362	+	0.723464i	$0.257451\pi$
$374$	−74.7157	−3.86346
$375$	16.6348	0.859016
$376$	0.0243030	0.00125333
$377$	30.8099	1.58679
$378$	0.172390	0.00886676
$379$	−25.2880	−1.29896	−0.649478	−	0.760380i	$-0.725013\pi$
$379$	−25.2880	−1.29896	−0.649478	+	0.760380i	$0.725013\pi$
$380$	2.50360	0.128432
$381$	3.23728	0.165851
$382$	15.5448	0.795342
$383$	−12.1319	−0.619913	−0.309956	−	0.950751i	$-0.600314\pi$
$383$	−12.1319	−0.619913	−0.309956	+	0.950751i	$0.600314\pi$
$384$	2.28161	0.116433
$385$	−0.0996556	−0.00507892
$386$	−45.4601	−2.31386
$387$	−1.78424	−0.0906978
$388$	−15.3211	−0.777810
$389$	−3.08242	−0.156285	−0.0781425	−	0.996942i	$-0.524899\pi$
$389$	−3.08242	−0.156285	−0.0781425	+	0.996942i	$0.524899\pi$
$390$	−16.5059	−0.835808
$391$	−20.0459	−1.01376
$392$	1.23359	0.0623055
$393$	−22.6305	−1.14156
$394$	−49.1760	−2.47745
$395$	−13.0813	−0.658191
$396$	−4.18193	−0.210150
$397$	−17.5036	−0.878479	−0.439240	−	0.898370i	$-0.644752\pi$
$397$	−17.5036	−0.878479	−0.439240	+	0.898370i	$0.644752\pi$
$398$	12.1677	0.609914
$399$	−0.0252576	−0.00126446
$400$	13.5967	0.679836
$401$	29.5435	1.47533	0.737666	−	0.675166i	$-0.235928\pi$
$401$	29.5435	1.47533	0.737666	+	0.675166i	$0.235928\pi$
$402$	1.48104	0.0738678
$403$	−13.3785	−0.666430
$404$	36.8856	1.83513
$405$	9.27282	0.460770
$406$	0.231139	0.0114712
$407$	−28.8353	−1.42931
$408$	−1.98008	−0.0980286
$409$	29.6653	1.46685	0.733427	−	0.679769i	$-0.237920\pi$
$409$	29.6653	1.46685	0.733427	+	0.679769i	$0.237920\pi$
$410$	22.0954	1.09121
$411$	−23.1315	−1.14099
$412$	19.7263	0.971844
$413$	0.123304	0.00606740
$414$	−2.19712	−0.107983
$415$	−14.1765	−0.695895
$416$	−33.9147	−1.66281
$417$	21.7563	1.06541
$418$	10.7719	0.526873
$419$	−4.23303	−0.206797	−0.103399	−	0.994640i	$-0.532972\pi$
$419$	−4.23303	−0.206797	−0.103399	+	0.994640i	$0.532972\pi$
$420$	−0.0632348	−0.00308554
$421$	−20.9063	−1.01891	−0.509456	−	0.860497i	$-0.670153\pi$
$421$	−20.9063	−1.01891	−0.509456	+	0.860497i	$0.670153\pi$
$422$	−23.7267	−1.15500
$423$	0.0518573	0.00252139
$424$	−1.99989	−0.0971233
$425$	−24.7007	−1.19816
$426$	26.8509	1.30093
$427$	0.0281931	0.00136436
$428$	−37.7841	−1.82636
$429$	−36.2663	−1.75096
$430$	11.5062	0.554880
$431$	−34.1792	−1.64635	−0.823177	−	0.567785i	$-0.807800\pi$
$431$	−34.1792	−1.64635	−0.823177	+	0.567785i	$0.807800\pi$
$432$	20.8799	1.00459
$433$	−30.8256	−1.48138	−0.740692	−	0.671845i	$-0.765502\pi$
$433$	−30.8256	−1.48138	−0.740692	+	0.671845i	$0.765502\pi$
$434$	−0.100367	−0.00481775
$435$	14.2473	0.683105
$436$	−12.3498	−0.591446
$437$	2.89006	0.138250
$438$	−46.2077	−2.20789
$439$	3.50545	0.167306	0.0836530	−	0.996495i	$-0.473341\pi$
$439$	3.50545	0.167306	0.0836530	+	0.996495i	$0.473341\pi$
$440$	1.12635	0.0536968
$441$	2.63220	0.125343
$442$	58.9213	2.80260
$443$	−6.30985	−0.299790	−0.149895	−	0.988702i	$-0.547894\pi$
$443$	−6.30985	−0.299790	−0.149895	+	0.988702i	$0.547894\pi$
$444$	−18.2969	−0.868334
$445$	−4.09918	−0.194320
$446$	−33.2803	−1.57587
$447$	8.87687	0.419862
$448$	−0.135366	−0.00639543
$449$	−40.6648	−1.91909	−0.959545	−	0.281554i	$-0.909150\pi$
$449$	−40.6648	−1.91909	−0.959545	+	0.281554i	$0.909150\pi$
$450$	−2.70732	−0.127624
$451$	48.5475	2.28601
$452$	−30.4679	−1.43309
$453$	6.75151	0.317214
$454$	−8.09705	−0.380013
$455$	0.0785891	0.00368431
$456$	0.285473	0.0133685
$457$	33.6858	1.57576	0.787879	−	0.615830i	$-0.211179\pi$
$457$	33.6858	1.57576	0.787879	+	0.615830i	$0.211179\pi$
$458$	17.2485	0.805969
$459$	−37.9319	−1.77051
$460$	7.23554	0.337359
$461$	15.3474	0.714800	0.357400	−	0.933951i	$-0.383663\pi$
$461$	15.3474	0.714800	0.357400	+	0.933951i	$0.383663\pi$
$462$	−0.272073	−0.0126580
$463$	34.9611	1.62478	0.812391	−	0.583113i	$-0.198166\pi$
$463$	34.9611	1.62478	0.812391	+	0.583113i	$0.198166\pi$
$464$	27.9956	1.29966
$465$	−6.18655	−0.286895
$466$	27.2160	1.26075
$467$	17.3949	0.804941	0.402470	−	0.915433i	$-0.368152\pi$
$467$	17.3949	0.804941	0.402470	+	0.915433i	$0.368152\pi$
$468$	3.29790	0.152445
$469$	−0.00705166	−0.000325616 0
$470$	−0.334419	−0.0154256
$471$	3.38061	0.155770
$472$	−1.39364	−0.0641475
$473$	25.2812	1.16243
$474$	−35.7137	−1.64038
$475$	3.56116	0.163397
$476$	0.225730	0.0103463
$477$	−4.26733	−0.195388
$478$	−42.0316	−1.92248
$479$	−30.3218	−1.38544	−0.692719	−	0.721208i	$-0.743587\pi$
$479$	−30.3218	−1.38544	−0.692719	+	0.721208i	$0.743587\pi$
$480$	−15.6830	−0.715829
$481$	22.7397	1.03684
$482$	−25.7921	−1.17480
$483$	−0.0729959	−0.00332143
$484$	36.2958	1.64981
$485$	8.80516	0.399822
$486$	−7.85195	−0.356172
$487$	0.922667	0.0418101	0.0209050	−	0.999781i	$-0.493345\pi$
$487$	0.922667	0.0418101	0.0209050	+	0.999781i	$0.493345\pi$
$488$	−0.318651	−0.0144247
$489$	3.31213	0.149780
$490$	−16.9746	−0.766836
$491$	35.2509	1.59085	0.795424	−	0.606053i	$-0.207248\pi$
$491$	35.2509	1.59085	0.795424	+	0.606053i	$0.207248\pi$
$492$	30.8050	1.38880
$493$	−50.8587	−2.29056
$494$	−8.49482	−0.382200
$495$	2.40339	0.108025
$496$	−12.1565	−0.545841
$497$	−0.127844	−0.00573461
$498$	−38.7036	−1.73435
$499$	20.5279	0.918956	0.459478	−	0.888189i	$-0.348036\pi$
$499$	20.5279	0.918956	0.459478	+	0.888189i	$0.348036\pi$
$500$	21.4337	0.958543
$501$	12.4863	0.557847
$502$	−35.0821	−1.56579
$503$	8.24863	0.367788	0.183894	−	0.982946i	$-0.441130\pi$
$503$	8.24863	0.367788	0.183894	+	0.982946i	$0.441130\pi$
$504$	0.00103332	4.60279e−5 0
$505$	−21.1985	−0.943319
$506$	31.1315	1.38397
$507$	7.54164	0.334936
$508$	4.17119	0.185067
$509$	3.19497	0.141615	0.0708073	−	0.997490i	$-0.477442\pi$
$509$	3.19497	0.141615	0.0708073	+	0.997490i	$0.477442\pi$
$510$	27.2467	1.20650
$511$	0.220008	0.00973256
$512$	−32.1626	−1.42140
$513$	5.46873	0.241450
$514$	−42.1865	−1.86076
$515$	−11.3369	−0.499562
$516$	16.0418	0.706200
$517$	−0.734777	−0.0323155
$518$	0.170595	0.00749552
$519$	−26.4992	−1.16319
$520$	−0.888249	−0.0389523
$521$	31.5850	1.38376	0.691882	−	0.722010i	$-0.256782\pi$
$521$	31.5850	1.38376	0.691882	+	0.722010i	$0.256782\pi$
$522$	−5.57437	−0.243983
$523$	1.07612	0.0470553	0.0235277	−	0.999723i	$-0.492510\pi$
$523$	1.07612	0.0470553	0.0235277	+	0.999723i	$0.492510\pi$
$524$	−29.1591	−1.27382
$525$	−0.0899463	−0.00392558
$526$	22.0504	0.961442
$527$	22.0842	0.962005
$528$	−32.9536	−1.43412
$529$	−14.6476	−0.636851
$530$	27.5193	1.19536
$531$	−2.97373	−0.129049
$532$	−0.0325440	−0.00141096
$533$	−38.2848	−1.65830
$534$	−11.1913	−0.484295
$535$	21.7149	0.938815
$536$	0.0797011	0.00344256
$537$	−6.42049	−0.277065
$538$	−28.3451	−1.22204
$539$	−37.2963	−1.60646
$540$	13.6915	0.589187
$541$	8.60196	0.369827	0.184914	−	0.982755i	$-0.440799\pi$
$541$	8.60196	0.369827	0.184914	+	0.982755i	$0.440799\pi$
$542$	−25.9676	−1.11540
$543$	−36.9703	−1.58655
$544$	55.9840	2.40029
$545$	7.09752	0.304024
$546$	0.214559	0.00918226
$547$	10.1226	0.432809	0.216405	−	0.976304i	$-0.430567\pi$
$547$	10.1226	0.432809	0.216405	+	0.976304i	$0.430567\pi$
$548$	−29.8047	−1.27319
$549$	−0.679932	−0.0290188
$550$	38.3606	1.63570
$551$	7.33242	0.312372
$552$	0.825033	0.0351157
$553$	0.170043	0.00723095
$554$	57.4255	2.43978
$555$	10.5154	0.446354
$556$	28.0327	1.18885
$557$	−27.9592	−1.18467	−0.592334	−	0.805693i	$-0.701793\pi$
$557$	−27.9592	−1.18467	−0.592334	+	0.805693i	$0.701793\pi$
$558$	2.42054	0.102470
$559$	−19.9369	−0.843243
$560$	0.0714105	0.00301764
$561$	59.8658	2.52754
$562$	48.8722	2.06155
$563$	−24.8208	−1.04607	−0.523035	−	0.852311i	$-0.675200\pi$
$563$	−24.8208	−1.04607	−0.523035	+	0.852311i	$0.675200\pi$
$564$	−0.466240	−0.0196323
$565$	17.5102	0.736658
$566$	−36.8112	−1.54729
$567$	−0.120537	−0.00506206
$568$	1.44496	0.0606290
$569$	−21.8553	−0.916223	−0.458112	−	0.888895i	$-0.651474\pi$
$569$	−21.8553	−0.916223	−0.458112	+	0.888895i	$0.651474\pi$
$570$	−3.92822	−0.164535
$571$	−8.37833	−0.350622	−0.175311	−	0.984513i	$-0.556093\pi$
$571$	−8.37833	−0.350622	−0.175311	+	0.984513i	$0.556093\pi$
$572$	−46.7287	−1.95382
$573$	−12.4553	−0.520326
$574$	−0.287216	−0.0119882
$575$	10.2920	0.429205
$576$	3.26461	0.136026
$577$	5.01874	0.208933	0.104466	−	0.994528i	$-0.466687\pi$
$577$	5.01874	0.208933	0.104466	+	0.994528i	$0.466687\pi$
$578$	−62.8945	−2.61607
$579$	36.4249	1.51377
$580$	18.3574	0.762250
$581$	0.184279	0.00764517
$582$	24.0393	0.996460
$583$	60.4648	2.50420
$584$	−2.48663	−0.102897
$585$	−1.89533	−0.0783623
$586$	−59.8901	−2.47404
$587$	−10.6394	−0.439133	−0.219567	−	0.975598i	$-0.570464\pi$
$587$	−10.6394	−0.439133	−0.219567	+	0.975598i	$0.570464\pi$
$588$	−23.6657	−0.975957
$589$	−3.18394	−0.131192
$590$	19.1771	0.789507
$591$	39.4022	1.62079
$592$	20.6626	0.849226
$593$	−4.44019	−0.182337	−0.0911685	−	0.995835i	$-0.529060\pi$
$593$	−4.44019	−0.182337	−0.0911685	+	0.995835i	$0.529060\pi$
$594$	58.9088	2.41706
$595$	−0.129729	−0.00531837
$596$	11.4377	0.468507
$597$	−9.74938	−0.399016
$598$	−24.5505	−1.00395
$599$	3.85310	0.157433	0.0787167	−	0.996897i	$-0.474918\pi$
$599$	3.85310	0.157433	0.0787167	+	0.996897i	$0.474918\pi$
$600$	1.01661	0.0415031
$601$	−4.63538	−0.189081	−0.0945405	−	0.995521i	$-0.530138\pi$
$601$	−4.63538	−0.189081	−0.0945405	+	0.995521i	$0.530138\pi$
$602$	−0.149569	−0.00609596
$603$	0.170065	0.00692558
$604$	8.69923	0.353966
$605$	−20.8595	−0.848061
$606$	−57.8746	−2.35100
$607$	7.40949	0.300742	0.150371	−	0.988630i	$-0.451953\pi$
$607$	7.40949	0.300742	0.150371	+	0.988630i	$0.451953\pi$
$608$	−8.07134	−0.327336
$609$	−0.185199	−0.00750465
$610$	4.38477	0.177534
$611$	0.579450	0.0234420
$612$	−5.44393	−0.220058
$613$	31.6593	1.27871	0.639354	−	0.768912i	$-0.279202\pi$
$613$	31.6593	1.27871	0.639354	+	0.768912i	$0.279202\pi$
$614$	0.481534	0.0194331
$615$	−17.7039	−0.713889
$616$	−0.0146414	−0.000589918 0
$617$	−6.79984	−0.273751	−0.136876	−	0.990588i	$-0.543706\pi$
$617$	−6.79984	−0.273751	−0.136876	+	0.990588i	$0.543706\pi$
$618$	−30.9512	−1.24504
$619$	36.1523	1.45308	0.726542	−	0.687122i	$-0.241126\pi$
$619$	36.1523	1.45308	0.726542	+	0.687122i	$0.241126\pi$
$620$	−7.97129	−0.320135
$621$	15.8049	0.634231
$622$	−5.10804	−0.204814
$623$	0.0532849	0.00213482
$624$	25.9875	1.04033
$625$	5.48768	0.219507
$626$	−27.8414	−1.11277
$627$	−8.63100	−0.344689
$628$	4.35587	0.173818
$629$	−37.5370	−1.49670
$630$	−0.0142189	−0.000566496 0
$631$	39.5383	1.57400	0.786998	−	0.616956i	$-0.211634\pi$
$631$	39.5383	1.57400	0.786998	+	0.616956i	$0.211634\pi$
$632$	−1.92190	−0.0764491
$633$	19.0109	0.755617
$634$	−2.02168	−0.0802910
$635$	−2.39722	−0.0951307
$636$	38.3669	1.52135
$637$	29.4121	1.16535
$638$	78.9844	3.12702
$639$	3.08322	0.121970
$640$	−1.68954	−0.0667851
$641$	−27.8412	−1.09966	−0.549830	−	0.835277i	$-0.685307\pi$
$641$	−27.8412	−1.09966	−0.549830	+	0.835277i	$0.685307\pi$
$642$	59.2845	2.33977
$643$	43.9277	1.73234	0.866169	−	0.499750i	$-0.166575\pi$
$643$	43.9277	1.73234	0.866169	+	0.499750i	$0.166575\pi$
$644$	−0.0940542	−0.00370625
$645$	−9.21935	−0.363011
$646$	14.0226	0.551713
$647$	21.2676	0.836116	0.418058	−	0.908420i	$-0.362711\pi$
$647$	21.2676	0.836116	0.418058	+	0.908420i	$0.362711\pi$
$648$	1.36236	0.0535186
$649$	42.1354	1.65396
$650$	−30.2514	−1.18656
$651$	0.0804186	0.00315185
$652$	4.26764	0.167134
$653$	−15.1410	−0.592514	−0.296257	−	0.955108i	$-0.595738\pi$
$653$	−15.1410	−0.592514	−0.296257	+	0.955108i	$0.595738\pi$
$654$	19.3772	0.757707
$655$	16.7580	0.654789
$656$	−34.7878	−1.35823
$657$	−5.30592	−0.207004
$658$	0.00434708	0.000169467 0
$659$	44.0808	1.71715	0.858573	−	0.512691i	$-0.171351\pi$
$659$	44.0808	1.71715	0.858573	+	0.512691i	$0.171351\pi$
$660$	−21.6085	−0.841110
$661$	24.0526	0.935539	0.467769	−	0.883851i	$-0.345058\pi$
$661$	24.0526	0.935539	0.467769	+	0.883851i	$0.345058\pi$
$662$	−63.8698	−2.48237
$663$	−47.2106	−1.83351
$664$	−2.08280	−0.0808284
$665$	0.0187033	0.000725285 0
$666$	−4.11424	−0.159424
$667$	21.1911	0.820524
$668$	16.0884	0.622480
$669$	26.6658	1.03096
$670$	−1.09672	−0.0423700
$671$	9.63411	0.371921
$672$	0.203863	0.00786417
$673$	10.3789	0.400076	0.200038	−	0.979788i	$-0.435893\pi$
$673$	10.3789	0.400076	0.200038	+	0.979788i	$0.435893\pi$
$674$	30.1037	1.15955
$675$	19.4750	0.749594
$676$	9.71730	0.373742
$677$	1.25944	0.0484041	0.0242020	−	0.999707i	$-0.492296\pi$
$677$	1.25944	0.0484041	0.0242020	+	0.999707i	$0.492296\pi$
$678$	47.8051	1.83594
$679$	−0.114458	−0.00439248
$680$	1.46626	0.0562284
$681$	6.48774	0.248611
$682$	−34.2972	−1.31331
$683$	26.3454	1.00808	0.504039	−	0.863681i	$-0.331847\pi$
$683$	26.3454	1.00808	0.504039	+	0.863681i	$0.331847\pi$
$684$	0.784864	0.0300100
$685$	17.1290	0.654465
$686$	0.441312	0.0168494
$687$	−13.8203	−0.527278
$688$	−18.1158	−0.690660
$689$	−47.6829	−1.81658
$690$	−11.3528	−0.432193
$691$	−0.800981	−0.0304708	−0.0152354	−	0.999884i	$-0.504850\pi$
$691$	−0.800981	−0.0304708	−0.0152354	+	0.999884i	$0.504850\pi$
$692$	−34.1439	−1.29796
$693$	−0.0312415	−0.00118677
$694$	−62.8103	−2.38425
$695$	−16.1106	−0.611112
$696$	2.09321	0.0793428
$697$	63.1978	2.39379
$698$	62.8474	2.37881
$699$	−21.8067	−0.824806
$700$	−0.115895	−0.00438040
$701$	−6.59244	−0.248993	−0.124497	−	0.992220i	$-0.539732\pi$
$701$	−6.59244	−0.248993	−0.124497	+	0.992220i	$0.539732\pi$
$702$	−46.4559	−1.75336
$703$	5.41180	0.204110
$704$	−46.2570	−1.74338
$705$	0.267952	0.0100917
$706$	−47.5183	−1.78838
$707$	0.275557	0.0103634
$708$	26.7363	1.00481
$709$	−29.3027	−1.10049	−0.550244	−	0.835004i	$-0.685465\pi$
$709$	−29.3027	−1.10049	−0.550244	+	0.835004i	$0.685465\pi$
$710$	−19.8832	−0.746203
$711$	−4.10092	−0.153796
$712$	−0.602251	−0.0225703
$713$	−9.20176	−0.344609
$714$	−0.354178	−0.0132548
$715$	26.8554	1.00433
$716$	−8.27272	−0.309166
$717$	33.6777	1.25772
$718$	−33.9055	−1.26534
$719$	−11.6450	−0.434287	−0.217143	−	0.976140i	$-0.569674\pi$
$719$	−11.6450	−0.434287	−0.217143	+	0.976140i	$0.569674\pi$
$720$	−1.72221	−0.0641828
$721$	0.147367	0.00548824
$722$	−2.02168	−0.0752390
$723$	20.6658	0.768571
$724$	−47.6357	−1.77037
$725$	26.1119	0.969773
$726$	−56.9493	−2.11359
$727$	−49.6572	−1.84169	−0.920843	−	0.389934i	$-0.872498\pi$
$727$	−49.6572	−1.84169	−0.920843	+	0.389934i	$0.872498\pi$
$728$	0.0115463	0.000427934 0
$729$	29.4828	1.09195
$730$	34.2170	1.26643
$731$	32.9105	1.21724
$732$	6.11316	0.225949
$733$	−19.7587	−0.729805	−0.364902	−	0.931046i	$-0.618898\pi$
$733$	−19.7587	−0.729805	−0.364902	+	0.931046i	$0.618898\pi$
$734$	−13.9696	−0.515626
$735$	13.6009	0.501676
$736$	−23.3266	−0.859831
$737$	−2.40969	−0.0887620
$738$	6.92679	0.254979
$739$	−2.21765	−0.0815777	−0.0407888	−	0.999168i	$-0.512987\pi$
$739$	−2.21765	−0.0815777	−0.0407888	+	0.999168i	$0.512987\pi$
$740$	13.5490	0.498070
$741$	6.80646	0.250042
$742$	−0.357721	−0.0131324
$743$	34.0422	1.24889	0.624444	−	0.781070i	$-0.285326\pi$
$743$	34.0422	1.24889	0.624444	+	0.781070i	$0.285326\pi$
$744$	−0.908927	−0.0333229
$745$	−6.57336	−0.240829
$746$	−53.9104	−1.97380
$747$	−4.44425	−0.162607
$748$	77.1363	2.82038
$749$	−0.282270	−0.0103139
$750$	−33.6301	−1.22800
$751$	−7.72073	−0.281733	−0.140867	−	0.990029i	$-0.544989\pi$
$751$	−7.72073	−0.281733	−0.140867	+	0.990029i	$0.544989\pi$
$752$	0.526521	0.0192002
$753$	28.1094	1.02436
$754$	−62.2876	−2.26838
$755$	−4.99952	−0.181951
$756$	−0.177975	−0.00647287
$757$	−49.9423	−1.81518	−0.907592	−	0.419853i	$-0.862082\pi$
$757$	−49.9423	−1.81518	−0.907592	+	0.419853i	$0.862082\pi$
$758$	51.1241	1.85691
$759$	−24.9441	−0.905413
$760$	−0.211394	−0.00766806
$761$	−2.70897	−0.0982001	−0.0491001	−	0.998794i	$-0.515635\pi$
$761$	−2.70897	−0.0982001	−0.0491001	+	0.998794i	$0.515635\pi$
$762$	−6.54473	−0.237091
$763$	−0.0922601	−0.00334004
$764$	−16.0484	−0.580611
$765$	3.12868	0.113117
$766$	24.5268	0.886190
$767$	−33.2282	−1.19980
$768$	23.5131	0.848454
$769$	−36.1349	−1.30306	−0.651529	−	0.758624i	$-0.725872\pi$
$769$	−36.1349	−1.30306	−0.651529	+	0.758624i	$0.725872\pi$
$770$	0.201471	0.00726052
$771$	33.8018	1.21734
$772$	46.9329	1.68915
$773$	43.9268	1.57994	0.789969	−	0.613147i	$-0.210097\pi$
$773$	43.9268	1.57994	0.789969	+	0.613147i	$0.210097\pi$
$774$	3.60715	0.129656
$775$	−11.3385	−0.407291
$776$	1.29365	0.0464394
$777$	−0.136689	−0.00490369
$778$	6.23166	0.223416
$779$	−9.11138	−0.326449
$780$	17.0406	0.610152
$781$	−43.6869	−1.56324
$782$	40.5262	1.44921
$783$	40.0990	1.43302
$784$	26.7255	0.954481
$785$	−2.50336	−0.0893487
$786$	45.7516	1.63191
$787$	−9.43882	−0.336458	−0.168229	−	0.985748i	$-0.553805\pi$
$787$	−9.43882	−0.336458	−0.168229	+	0.985748i	$0.553805\pi$
$788$	50.7691	1.80858
$789$	−17.6678	−0.628991
$790$	26.4461	0.940911
$791$	−0.227613	−0.00809300
$792$	0.353106	0.0125471
$793$	−7.59752	−0.269796
$794$	35.3865	1.25582
$795$	−22.0498	−0.782026
$796$	−12.5619	−0.445246
$797$	−3.17869	−0.112595	−0.0562974	−	0.998414i	$-0.517930\pi$
$797$	−3.17869	−0.112595	−0.0562974	+	0.998414i	$0.517930\pi$
$798$	0.0510626	0.00180760
$799$	−0.956514	−0.0338390
$800$	−28.7433	−1.01623
$801$	−1.28507	−0.0454058
$802$	−59.7273	−2.10905
$803$	75.1807	2.65307
$804$	−1.52903	−0.0539246
$805$	0.0540538	0.00190514
$806$	27.0470	0.952689
$807$	22.7114	0.799480
$808$	−3.11447	−0.109567
$809$	32.6344	1.14736	0.573682	−	0.819078i	$-0.305514\pi$
$809$	32.6344	1.14736	0.573682	+	0.819078i	$0.305514\pi$
$810$	−18.7466	−0.658689
$811$	26.5834	0.933469	0.466734	−	0.884398i	$-0.345430\pi$
$811$	26.5834	0.933469	0.466734	+	0.884398i	$0.345430\pi$
$812$	−0.238627	−0.00837416
$813$	20.8065	0.729715
$814$	58.2956	2.04326
$815$	−2.45265	−0.0859125
$816$	−42.8982	−1.50174
$817$	−4.74478	−0.165999
$818$	−59.9736	−2.09693
$819$	0.0246373	0.000860896 0
$820$	−22.8112	−0.796602
$821$	−52.6441	−1.83729	−0.918646	−	0.395081i	$-0.870717\pi$
$821$	−52.6441	−1.83729	−0.918646	+	0.395081i	$0.870717\pi$
$822$	46.7645	1.63110
$823$	0.131878	0.00459698	0.00229849	−	0.999997i	$-0.499268\pi$
$823$	0.131878	0.00459698	0.00229849	+	0.999997i	$0.499268\pi$
$824$	−1.66561	−0.0580243
$825$	−30.7364	−1.07010
$826$	−0.249281	−0.00867360
$827$	35.4915	1.23416	0.617080	−	0.786901i	$-0.288316\pi$
$827$	35.4915	1.23416	0.617080	+	0.786901i	$0.288316\pi$
$828$	2.26830	0.0788290
$829$	−3.17893	−0.110409	−0.0552043	−	0.998475i	$-0.517581\pi$
$829$	−3.17893	−0.110409	−0.0552043	+	0.998475i	$0.517581\pi$
$830$	28.6602	0.994810
$831$	−46.0121	−1.59614
$832$	36.4786	1.26467
$833$	−48.5513	−1.68220
$834$	−43.9842	−1.52305
$835$	−9.24616	−0.319977
$836$	−11.1209	−0.384625
$837$	−17.4121	−0.601850
$838$	8.55782	0.295625
$839$	48.9498	1.68993	0.844967	−	0.534818i	$-0.179620\pi$
$839$	48.9498	1.68993	0.844967	+	0.534818i	$0.179620\pi$
$840$	0.00533930	0.000184223 0
$841$	24.7644	0.853946
$842$	42.2658	1.45658
$843$	−39.1588	−1.34870
$844$	24.4953	0.843164
$845$	−5.58462	−0.192117
$846$	−0.104839	−0.00360442
$847$	0.271152	0.00931688
$848$	−43.3274	−1.48787
$849$	29.4949	1.01226
$850$	49.9369	1.71282
$851$	15.6404	0.536147
$852$	−27.7208	−0.949698
$853$	−35.3713	−1.21109	−0.605545	−	0.795811i	$-0.707045\pi$
$853$	−35.3713	−1.21109	−0.605545	+	0.795811i	$0.707045\pi$
$854$	−0.0569972	−0.00195041
$855$	−0.451068	−0.0154262
$856$	3.19034	0.109044
$857$	33.7673	1.15347	0.576734	−	0.816932i	$-0.304327\pi$
$857$	33.7673	1.15347	0.576734	+	0.816932i	$0.304327\pi$
$858$	73.3188	2.50306
$859$	40.6756	1.38783	0.693916	−	0.720056i	$-0.255884\pi$
$859$	40.6756	1.38783	0.693916	+	0.720056i	$0.255884\pi$
$860$	−11.8790	−0.405071
$861$	0.230131	0.00784286
$862$	69.0992	2.35353
$863$	−7.65062	−0.260430	−0.130215	−	0.991486i	$-0.541567\pi$
$863$	−7.65062	−0.260430	−0.130215	+	0.991486i	$0.541567\pi$
$864$	−44.1400	−1.50167
$865$	19.6228	0.667195
$866$	62.3193	2.11770
$867$	50.3941	1.71147
$868$	0.103618	0.00351703
$869$	58.1068	1.97114
$870$	−28.8034	−0.976526
$871$	1.90029	0.0643890
$872$	1.04277	0.0353125
$873$	2.76037	0.0934245
$874$	−5.84276	−0.197634
$875$	0.160122	0.00541312
$876$	47.7046	1.61179
$877$	−34.2839	−1.15769	−0.578843	−	0.815439i	$-0.696495\pi$
$877$	−34.2839	−1.15769	−0.578843	+	0.815439i	$0.696495\pi$
$878$	−7.08688	−0.239171
$879$	47.9868	1.61855
$880$	24.4023	0.822602
$881$	13.8190	0.465575	0.232788	−	0.972528i	$-0.425215\pi$
$881$	13.8190	0.465575	0.232788	+	0.972528i	$0.425215\pi$
$882$	−5.32146	−0.179183
$883$	−41.6522	−1.40171	−0.700855	−	0.713304i	$-0.747198\pi$
$883$	−41.6522	−1.40171	−0.700855	+	0.713304i	$0.747198\pi$
$884$	−60.8302	−2.04594
$885$	−15.3656	−0.516508
$886$	12.7565	0.428562
$887$	58.7872	1.97388	0.986941	−	0.161082i	$-0.0514985\pi$
$887$	58.7872	1.97388	0.986941	+	0.161082i	$0.0514985\pi$
$888$	1.54492	0.0518442
$889$	0.0311613	0.00104512
$890$	8.28721	0.277788
$891$	−41.1897	−1.37991
$892$	34.3585	1.15041
$893$	0.137903	0.00461474
$894$	−17.9462	−0.600209
$895$	4.75440	0.158922
$896$	0.0219622	0.000733707 0
$897$	19.6711	0.656798
$898$	82.2110	2.74342
$899$	−23.3460	−0.778632
$900$	2.79503	0.0931676
$901$	78.7115	2.62226
$902$	−98.1472	−3.26795
$903$	0.119842	0.00398808
$904$	2.57259	0.0855631
$905$	27.3767	0.910031
$906$	−13.6494	−0.453470
$907$	57.2752	1.90179	0.950896	−	0.309510i	$-0.100165\pi$
$907$	57.2752	1.90179	0.950896	+	0.309510i	$0.100165\pi$
$908$	8.35937	0.277415
$909$	−6.64561	−0.220421
$910$	−0.158882	−0.00526687
$911$	−50.2164	−1.66374	−0.831871	−	0.554969i	$-0.812730\pi$
$911$	−50.2164	−1.66374	−0.831871	+	0.554969i	$0.812730\pi$
$912$	6.18473	0.204797
$913$	62.9715	2.08405
$914$	−68.1018	−2.25261
$915$	−3.51329	−0.116146
$916$	−17.8073	−0.588370
$917$	−0.217836	−0.00719358
$918$	76.6859	2.53101
$919$	0.471076	0.0155394	0.00776968	−	0.999970i	$-0.497527\pi$
$919$	0.471076	0.0155394	0.00776968	+	0.999970i	$0.497527\pi$
$920$	−0.610940	−0.0201421
$921$	−0.385828	−0.0127135
$922$	−31.0275	−1.02184
$923$	34.4518	1.13399
$924$	0.280887	0.00924052
$925$	19.2723	0.633669
$926$	−70.6801	−2.32269
$927$	−3.55405	−0.116730
$928$	−59.1825	−1.94276
$929$	20.4188	0.669920	0.334960	−	0.942232i	$-0.391277\pi$
$929$	20.4188	0.669920	0.334960	+	0.942232i	$0.391277\pi$
$930$	12.5072	0.410127
$931$	6.99976	0.229408
$932$	−28.0977	−0.920370
$933$	4.09281	0.133993
$934$	−35.1669	−1.15070
$935$	−44.3309	−1.44978
$936$	−0.278462	−0.00910180
$937$	50.6900	1.65597	0.827984	−	0.560751i	$-0.189488\pi$
$937$	50.6900	1.65597	0.827984	+	0.560751i	$0.189488\pi$
$938$	0.0142562	0.000465481 0
$939$	22.3079	0.727990
$940$	0.345253	0.0112609
$941$	19.4890	0.635325	0.317662	−	0.948204i	$-0.397102\pi$
$941$	19.4890	0.635325	0.317662	+	0.948204i	$0.397102\pi$
$942$	−6.83450	−0.222680
$943$	−26.3324	−0.857502
$944$	−30.1931	−0.982700
$945$	0.102284	0.00332728
$946$	−51.1105	−1.66174
$947$	−12.2715	−0.398769	−0.199384	−	0.979921i	$-0.563894\pi$
$947$	−12.2715	−0.398769	−0.199384	+	0.979921i	$0.563894\pi$
$948$	36.8707	1.19750
$949$	−59.2880	−1.92457
$950$	−7.19951	−0.233583
$951$	1.61986	0.0525277
$952$	−0.0190598	−0.000617731 0
$953$	−37.2884	−1.20789	−0.603945	−	0.797026i	$-0.706405\pi$
$953$	−37.2884	−1.20789	−0.603945	+	0.797026i	$0.706405\pi$
$954$	8.62716	0.279315
$955$	9.22317	0.298455
$956$	43.3933	1.40344
$957$	−63.2861	−2.04575
$958$	61.3008	1.98054
$959$	−0.222659	−0.00719002
$960$	16.8686	0.544433
$961$	−20.8625	−0.672985
$962$	−45.9723	−1.48221
$963$	6.80750	0.219369
$964$	26.6276	0.857619
$965$	−26.9728	−0.868284
$966$	0.147574	0.00474812
$967$	19.0106	0.611338	0.305669	−	0.952138i	$-0.401120\pi$
$967$	19.0106	0.611338	0.305669	+	0.952138i	$0.401120\pi$
$968$	−3.06468	−0.0985025
$969$	−11.2356	−0.360940
$970$	−17.8012	−0.571561
$971$	−48.9698	−1.57152	−0.785758	−	0.618533i	$-0.787727\pi$
$971$	−48.9698	−1.57152	−0.785758	+	0.618533i	$0.787727\pi$
$972$	8.10633	0.260011
$973$	0.209421	0.00671373
$974$	−1.86533	−0.0597692
$975$	24.2389	0.776266
$976$	−6.90353	−0.220977
$977$	−10.2981	−0.329465	−0.164733	−	0.986338i	$-0.552676\pi$
$977$	−10.2981	−0.329465	−0.164733	+	0.986338i	$0.552676\pi$
$978$	−6.69606	−0.214116
$979$	18.2085	0.581945
$980$	17.5246	0.559801
$981$	2.22504	0.0710399
$982$	−71.2658	−2.27418
$983$	3.05893	0.0975647	0.0487824	−	0.998809i	$-0.484466\pi$
$983$	3.05893	0.0975647	0.0487824	+	0.998809i	$0.484466\pi$
$984$	−2.60105	−0.0829185
$985$	−29.1775	−0.929671
$986$	102.820	3.27445
$987$	−0.00348309	−0.000110868 0
$988$	8.77003	0.279012
$989$	−13.7127	−0.436038
$990$	−4.85888	−0.154425
$991$	48.3144	1.53476	0.767379	−	0.641194i	$-0.221560\pi$
$991$	48.3144	1.53476	0.767379	+	0.641194i	$0.221560\pi$
$992$	25.6986	0.815932
$993$	51.1756	1.62401
$994$	0.258460	0.00819785
$995$	7.21946	0.228872
$996$	39.9575	1.26610
$997$	−16.5777	−0.525022	−0.262511	−	0.964929i	$-0.584551\pi$
$997$	−16.5777	−0.525022	−0.262511	+	0.964929i	$0.584551\pi$
$998$	−41.5008	−1.31368
$999$	29.5957	0.936365

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6023.2.a.d.1.25	✓	140

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6023.2.a.d.1.25	✓	140	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:	\( N \)	\(=\)	\( 6023 = 19 \cdot 317 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6023.a (trivial)

\(f(q)\)	\(=\)	\(q-2.02168 q^{2} +1.61986 q^{3} +2.08717 q^{4} -1.19952 q^{5} -3.27484 q^{6} +0.0155924 q^{7} -0.176233 q^{8} -0.376042 q^{9} +O(q^{10})\)	\(q-2.02168 q^{2} +1.61986 q^{3} +2.08717 q^{4} -1.19952 q^{5} -3.27484 q^{6} +0.0155924 q^{7} -0.176233 q^{8} -0.376042 q^{9} +2.42503 q^{10} +5.32822 q^{11} +3.38093 q^{12} -4.20187 q^{13} -0.0315228 q^{14} -1.94305 q^{15} -3.81806 q^{16} +6.93614 q^{17} +0.760235 q^{18} -1.00000 q^{19} -2.50360 q^{20} +0.0252576 q^{21} -10.7719 q^{22} -2.89006 q^{23} -0.285473 q^{24} -3.56116 q^{25} +8.49482 q^{26} -5.46873 q^{27} +0.0325440 q^{28} -7.33242 q^{29} +3.92822 q^{30} +3.18394 q^{31} +8.07134 q^{32} +8.63100 q^{33} -14.0226 q^{34} -0.0187033 q^{35} -0.784864 q^{36} -5.41180 q^{37} +2.02168 q^{38} -6.80646 q^{39} +0.211394 q^{40} +9.11138 q^{41} -0.0510626 q^{42} +4.74478 q^{43} +11.1209 q^{44} +0.451068 q^{45} +5.84276 q^{46} -0.137903 q^{47} -6.18473 q^{48} -6.99976 q^{49} +7.19951 q^{50} +11.2356 q^{51} -8.77003 q^{52} +11.3480 q^{53} +11.0560 q^{54} -6.39129 q^{55} -0.00274789 q^{56} -1.61986 q^{57} +14.8238 q^{58} +7.90796 q^{59} -4.05548 q^{60} +1.80813 q^{61} -6.43689 q^{62} -0.00586340 q^{63} -8.68151 q^{64} +5.04021 q^{65} -17.4491 q^{66} -0.452250 q^{67} +14.4769 q^{68} -4.68150 q^{69} +0.0378121 q^{70} -8.19915 q^{71} +0.0662709 q^{72} +14.1099 q^{73} +10.9409 q^{74} -5.76860 q^{75} -2.08717 q^{76} +0.0830799 q^{77} +13.7605 q^{78} +10.9055 q^{79} +4.57982 q^{80} -7.73047 q^{81} -18.4203 q^{82} +11.8185 q^{83} +0.0527169 q^{84} -8.32001 q^{85} -9.59240 q^{86} -11.8775 q^{87} -0.939007 q^{88} +3.41736 q^{89} -0.911914 q^{90} -0.0655173 q^{91} -6.03205 q^{92} +5.15754 q^{93} +0.278795 q^{94} +1.19952 q^{95} +13.0745 q^{96} -7.34060 q^{97} +14.1512 q^{98} -2.00364 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 140 q + 4 q^{2} + 3 q^{3} + 162 q^{4} + 13 q^{5} + 12 q^{6} + 25 q^{7} + 12 q^{8} + 181 q^{9}+O(q^{10}) \) 140 * q + 4 * q^2 + 3 * q^3 + 162 * q^4 + 13 * q^5 + 12 * q^6 + 25 * q^7 + 12 * q^8 + 181 * q^9	\( 140 q + 4 q^{2} + 3 q^{3} + 162 q^{4} + 13 q^{5} + 12 q^{6} + 25 q^{7} + 12 q^{8} + 181 q^{9} + 8 q^{10} + 19 q^{11} + 17 q^{12} + 28 q^{13} + 5 q^{14} + 14 q^{15} + 202 q^{16} + 38 q^{17} + 26 q^{18} - 140 q^{19} + 36 q^{20} + 4 q^{21} + 53 q^{22} + 58 q^{23} + 47 q^{24} + 279 q^{25} + 29 q^{26} + 21 q^{27} + 69 q^{28} + 18 q^{29} + 50 q^{30} + 20 q^{31} + 13 q^{32} + 47 q^{33} + 6 q^{34} + 35 q^{35} + 230 q^{36} + 88 q^{37} - 4 q^{38} + 32 q^{39} + 32 q^{40} + 24 q^{41} + 75 q^{42} + 100 q^{43} + 63 q^{44} + 87 q^{45} + 23 q^{46} + 35 q^{47} + 46 q^{48} + 255 q^{49} + 11 q^{50} - 6 q^{51} + 47 q^{52} + 77 q^{53} + 16 q^{54} + 63 q^{55} + 21 q^{56} - 3 q^{57} + 165 q^{58} + 18 q^{59} + 28 q^{60} + 99 q^{61} + 34 q^{62} + 89 q^{63} + 298 q^{64} + 78 q^{65} - 3 q^{66} + 28 q^{67} + 93 q^{68} + 19 q^{69} + 16 q^{70} + q^{71} + 43 q^{72} + 201 q^{73} + 32 q^{74} + 22 q^{75} - 162 q^{76} + 86 q^{77} + 122 q^{78} + 58 q^{79} + 92 q^{80} + 288 q^{81} + 143 q^{82} + 57 q^{83} + q^{84} + 136 q^{85} - 6 q^{86} + 43 q^{87} + 198 q^{88} + 46 q^{89} + 30 q^{90} + 26 q^{91} + 129 q^{92} + 111 q^{93} + 44 q^{94} - 13 q^{95} + 32 q^{96} + 110 q^{97} - 34 q^{98} + 62 q^{99}+O(q^{100}) \) 140 * q + 4 * q^2 + 3 * q^3 + 162 * q^4 + 13 * q^5 + 12 * q^6 + 25 * q^7 + 12 * q^8 + 181 * q^9 + 8 * q^10 + 19 * q^11 + 17 * q^12 + 28 * q^13 + 5 * q^14 + 14 * q^15 + 202 * q^16 + 38 * q^17 + 26 * q^18 - 140 * q^19 + 36 * q^20 + 4 * q^21 + 53 * q^22 + 58 * q^23 + 47 * q^24 + 279 * q^25 + 29 * q^26 + 21 * q^27 + 69 * q^28 + 18 * q^29 + 50 * q^30 + 20 * q^31 + 13 * q^32 + 47 * q^33 + 6 * q^34 + 35 * q^35 + 230 * q^36 + 88 * q^37 - 4 * q^38 + 32 * q^39 + 32 * q^40 + 24 * q^41 + 75 * q^42 + 100 * q^43 + 63 * q^44 + 87 * q^45 + 23 * q^46 + 35 * q^47 + 46 * q^48 + 255 * q^49 + 11 * q^50 - 6 * q^51 + 47 * q^52 + 77 * q^53 + 16 * q^54 + 63 * q^55 + 21 * q^56 - 3 * q^57 + 165 * q^58 + 18 * q^59 + 28 * q^60 + 99 * q^61 + 34 * q^62 + 89 * q^63 + 298 * q^64 + 78 * q^65 - 3 * q^66 + 28 * q^67 + 93 * q^68 + 19 * q^69 + 16 * q^70 + q^71 + 43 * q^72 + 201 * q^73 + 32 * q^74 + 22 * q^75 - 162 * q^76 + 86 * q^77 + 122 * q^78 + 58 * q^79 + 92 * q^80 + 288 * q^81 + 143 * q^82 + 57 * q^83 + q^84 + 136 * q^85 - 6 * q^86 + 43 * q^87 + 198 * q^88 + 46 * q^89 + 30 * q^90 + 26 * q^91 + 129 * q^92 + 111 * q^93 + 44 * q^94 - 13 * q^95 + 32 * q^96 + 110 * q^97 - 34 * q^98 + 62 * q^99

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