LMFDB - Embedded newform 6026.2.a.i.1.13

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			1.13
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)

$f(q)$	$=$	$q-1.00000 q^{2} -0.0412722 q^{3} +1.00000 q^{4} -3.47552 q^{5} +0.0412722 q^{6} -4.67489 q^{7} -1.00000 q^{8} -2.99830 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -0.0412722 q^{3} +1.00000 q^{4} -3.47552 q^{5} +0.0412722 q^{6} -4.67489 q^{7} -1.00000 q^{8} -2.99830 q^{9} +3.47552 q^{10} -0.864604 q^{11} -0.0412722 q^{12} +1.77625 q^{13} +4.67489 q^{14} +0.143443 q^{15} +1.00000 q^{16} +0.0423660 q^{17} +2.99830 q^{18} -0.190142 q^{19} -3.47552 q^{20} +0.192943 q^{21} +0.864604 q^{22} +1.00000 q^{23} +0.0412722 q^{24} +7.07925 q^{25} -1.77625 q^{26} +0.247563 q^{27} -4.67489 q^{28} +8.29029 q^{29} -0.143443 q^{30} -5.15683 q^{31} -1.00000 q^{32} +0.0356842 q^{33} -0.0423660 q^{34} +16.2477 q^{35} -2.99830 q^{36} +3.01004 q^{37} +0.190142 q^{38} -0.0733097 q^{39} +3.47552 q^{40} +5.50915 q^{41} -0.192943 q^{42} +1.97222 q^{43} -0.864604 q^{44} +10.4206 q^{45} -1.00000 q^{46} -6.19777 q^{47} -0.0412722 q^{48} +14.8546 q^{49} -7.07925 q^{50} -0.00174854 q^{51} +1.77625 q^{52} +12.3238 q^{53} -0.247563 q^{54} +3.00495 q^{55} +4.67489 q^{56} +0.00784760 q^{57} -8.29029 q^{58} -12.5038 q^{59} +0.143443 q^{60} -1.83577 q^{61} +5.15683 q^{62} +14.0167 q^{63} +1.00000 q^{64} -6.17339 q^{65} -0.0356842 q^{66} -8.37015 q^{67} +0.0423660 q^{68} -0.0412722 q^{69} -16.2477 q^{70} -8.15822 q^{71} +2.99830 q^{72} -1.53021 q^{73} -3.01004 q^{74} -0.292176 q^{75} -0.190142 q^{76} +4.04194 q^{77} +0.0733097 q^{78} +7.35334 q^{79} -3.47552 q^{80} +8.98467 q^{81} -5.50915 q^{82} +14.9726 q^{83} +0.192943 q^{84} -0.147244 q^{85} -1.97222 q^{86} -0.342159 q^{87} +0.864604 q^{88} -3.01022 q^{89} -10.4206 q^{90} -8.30377 q^{91} +1.00000 q^{92} +0.212834 q^{93} +6.19777 q^{94} +0.660844 q^{95} +0.0412722 q^{96} +9.58972 q^{97} -14.8546 q^{98} +2.59234 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−0.0412722	−0.0238285	−0.0119143	−	0.999929i	$-0.503793\pi$
$3$	−0.0412722	−0.0238285	−0.0119143	+	0.999929i	$0.503793\pi$
$4$	1.00000	0.500000
$5$	−3.47552	−1.55430	−0.777150	−	0.629315i	$-0.783335\pi$
$5$	−3.47552	−1.55430	−0.777150	+	0.629315i	$0.783335\pi$
$6$	0.0412722	0.0168493
$7$	−4.67489	−1.76694	−0.883472	−	0.468484i	$-0.844800\pi$
$7$	−4.67489	−1.76694	−0.883472	+	0.468484i	$0.844800\pi$
$8$	−1.00000	−0.353553
$9$	−2.99830	−0.999432
$10$	3.47552	1.09906
$11$	−0.864604	−0.260688	−0.130344	−	0.991469i	$-0.541608\pi$
$11$	−0.864604	−0.260688	−0.130344	+	0.991469i	$0.541608\pi$
$12$	−0.0412722	−0.0119143
$13$	1.77625	0.492642	0.246321	−	0.969188i	$-0.420778\pi$
$13$	1.77625	0.492642	0.246321	+	0.969188i	$0.420778\pi$
$14$	4.67489	1.24942
$15$	0.143443	0.0370367
$16$	1.00000	0.250000
$17$	0.0423660	0.0102753	0.00513764	−	0.999987i	$-0.498365\pi$
$17$	0.0423660	0.0102753	0.00513764	+	0.999987i	$0.498365\pi$
$18$	2.99830	0.706705
$19$	−0.190142	−0.0436216	−0.0218108	−	0.999762i	$-0.506943\pi$
$19$	−0.190142	−0.0436216	−0.0218108	+	0.999762i	$0.506943\pi$
$20$	−3.47552	−0.777150
$21$	0.192943	0.0421037
$22$	0.864604	0.184334
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	0.0412722	0.00842466
$25$	7.07925	1.41585
$26$	−1.77625	−0.348351
$27$	0.247563	0.0476436
$28$	−4.67489	−0.883472
$29$	8.29029	1.53947	0.769734	−	0.638365i	$-0.220389\pi$
$29$	8.29029	1.53947	0.769734	+	0.638365i	$0.220389\pi$
$30$	−0.143443	−0.0261889
$31$	−5.15683	−0.926194	−0.463097	−	0.886308i	$-0.653262\pi$
$31$	−5.15683	−0.926194	−0.463097	+	0.886308i	$0.653262\pi$
$32$	−1.00000	−0.176777
$33$	0.0356842	0.00621182
$34$	−0.0423660	−0.00726571
$35$	16.2477	2.74636
$36$	−2.99830	−0.499716
$37$	3.01004	0.494847	0.247424	−	0.968907i	$-0.420416\pi$
$37$	3.01004	0.494847	0.247424	+	0.968907i	$0.420416\pi$
$38$	0.190142	0.0308452
$39$	−0.0733097	−0.0117390
$40$	3.47552	0.549528
$41$	5.50915	0.860384	0.430192	−	0.902737i	$-0.358446\pi$
$41$	5.50915	0.860384	0.430192	+	0.902737i	$0.358446\pi$
$42$	−0.192943	−0.0297718
$43$	1.97222	0.300761	0.150381	−	0.988628i	$-0.451950\pi$
$43$	1.97222	0.300761	0.150381	+	0.988628i	$0.451950\pi$
$44$	−0.864604	−0.130344
$45$	10.4206	1.55342
$46$	−1.00000	−0.147442
$47$	−6.19777	−0.904037	−0.452019	−	0.892009i	$-0.649296\pi$
$47$	−6.19777	−0.904037	−0.452019	+	0.892009i	$0.649296\pi$
$48$	−0.0412722	−0.00595714
$49$	14.8546	2.12209
$50$	−7.07925	−1.00116
$51$	−0.00174854	−0.000244845 0
$52$	1.77625	0.246321
$53$	12.3238	1.69281	0.846404	−	0.532541i	$-0.178763\pi$
$53$	12.3238	1.69281	0.846404	+	0.532541i	$0.178763\pi$
$54$	−0.247563	−0.0336891
$55$	3.00495	0.405188
$56$	4.67489	0.624709
$57$	0.00784760	0.00103944
$58$	−8.29029	−1.08857
$59$	−12.5038	−1.62785	−0.813926	−	0.580968i	$-0.802674\pi$
$59$	−12.5038	−1.62785	−0.813926	+	0.580968i	$0.802674\pi$
$60$	0.143443	0.0185184
$61$	−1.83577	−0.235047	−0.117523	−	0.993070i	$-0.537495\pi$
$61$	−1.83577	−0.235047	−0.117523	+	0.993070i	$0.537495\pi$
$62$	5.15683	0.654918
$63$	14.0167	1.76594
$64$	1.00000	0.125000
$65$	−6.17339	−0.765714
$66$	−0.0356842	−0.00439242
$67$	−8.37015	−1.02258	−0.511288	−	0.859409i	$-0.670832\pi$
$67$	−8.37015	−1.02258	−0.511288	+	0.859409i	$0.670832\pi$
$68$	0.0423660	0.00513764
$69$	−0.0412722	−0.00496859
$70$	−16.2477	−1.94197
$71$	−8.15822	−0.968203	−0.484102	−	0.875012i	$-0.660853\pi$
$71$	−8.15822	−0.968203	−0.484102	+	0.875012i	$0.660853\pi$
$72$	2.99830	0.353353
$73$	−1.53021	−0.179097	−0.0895487	−	0.995982i	$-0.528542\pi$
$73$	−1.53021	−0.179097	−0.0895487	+	0.995982i	$0.528542\pi$
$74$	−3.01004	−0.349910
$75$	−0.292176	−0.0337376
$76$	−0.190142	−0.0218108
$77$	4.04194	0.460621
$78$	0.0733097	0.00830069
$79$	7.35334	0.827315	0.413657	−	0.910433i	$-0.364251\pi$
$79$	7.35334	0.827315	0.413657	+	0.910433i	$0.364251\pi$
$80$	−3.47552	−0.388575
$81$	8.98467	0.998297
$82$	−5.50915	−0.608383
$83$	14.9726	1.64346	0.821730	−	0.569878i	$-0.193009\pi$
$83$	14.9726	1.64346	0.821730	+	0.569878i	$0.193009\pi$
$84$	0.192943	0.0210519
$85$	−0.147244	−0.0159709
$86$	−1.97222	−0.212670
$87$	−0.342159	−0.0366833
$88$	0.864604	0.0921671
$89$	−3.01022	−0.319083	−0.159542	−	0.987191i	$-0.551002\pi$
$89$	−3.01022	−0.319083	−0.159542	+	0.987191i	$0.551002\pi$
$90$	−10.4206	−1.09843
$91$	−8.30377	−0.870472
$92$	1.00000	0.104257
$93$	0.212834	0.0220698
$94$	6.19777	0.639251
$95$	0.660844	0.0678011
$96$	0.0412722	0.00421233
$97$	9.58972	0.973688	0.486844	−	0.873489i	$-0.338148\pi$
$97$	9.58972	0.973688	0.486844	+	0.873489i	$0.338148\pi$
$98$	−14.8546	−1.50055
$99$	2.59234	0.260540
$100$	7.07925	0.707925
$101$	1.84549	0.183634	0.0918168	−	0.995776i	$-0.470733\pi$
$101$	1.84549	0.183634	0.0918168	+	0.995776i	$0.470733\pi$
$102$	0.00174854	0.000173131 0
$103$	3.17903	0.313239	0.156619	−	0.987659i	$-0.449940\pi$
$103$	3.17903	0.313239	0.156619	+	0.987659i	$0.449940\pi$
$104$	−1.77625	−0.174175
$105$	−0.670579	−0.0654418
$106$	−12.3238	−1.19700
$107$	8.94815	0.865050	0.432525	−	0.901622i	$-0.357623\pi$
$107$	8.94815	0.865050	0.432525	+	0.901622i	$0.357623\pi$
$108$	0.247563	0.0238218
$109$	13.9356	1.33479	0.667396	−	0.744703i	$-0.267409\pi$
$109$	13.9356	1.33479	0.667396	+	0.744703i	$0.267409\pi$
$110$	−3.00495	−0.286511
$111$	−0.124231	−0.0117915
$112$	−4.67489	−0.441736
$113$	0.872199	0.0820496	0.0410248	−	0.999158i	$-0.486938\pi$
$113$	0.872199	0.0820496	0.0410248	+	0.999158i	$0.486938\pi$
$114$	−0.00784760	−0.000734995 0
$115$	−3.47552	−0.324094
$116$	8.29029	0.769734
$117$	−5.32572	−0.492363
$118$	12.5038	1.15107
$119$	−0.198057	−0.0181558
$120$	−0.143443	−0.0130945
$121$	−10.2525	−0.932042
$122$	1.83577	0.166203
$123$	−0.227375	−0.0205017
$124$	−5.15683	−0.463097
$125$	−7.22647	−0.646355
$126$	−14.0167	−1.24871
$127$	−9.06565	−0.804446	−0.402223	−	0.915542i	$-0.631762\pi$
$127$	−9.06565	−0.804446	−0.402223	+	0.915542i	$0.631762\pi$
$128$	−1.00000	−0.0883883
$129$	−0.0813981	−0.00716671
$130$	6.17339	0.541442
$131$	1.00000	0.0873704
$131$	1.00000	0.0873704
$132$	0.0356842	0.00310591
$133$	0.888896	0.0770770
$134$	8.37015	0.723071
$135$	−0.860411	−0.0740524
$136$	−0.0423660	−0.00363286
$137$	−20.6634	−1.76540	−0.882698	−	0.469940i	$-0.844276\pi$
$137$	−20.6634	−1.76540	−0.882698	+	0.469940i	$0.844276\pi$
$138$	0.0412722	0.00351333
$139$	18.6588	1.58262	0.791311	−	0.611414i	$-0.209399\pi$
$139$	18.6588	1.58262	0.791311	+	0.611414i	$0.209399\pi$
$140$	16.2477	1.37318
$141$	0.255796	0.0215419
$142$	8.15822	0.684623
$143$	−1.53575	−0.128426
$144$	−2.99830	−0.249858
$145$	−28.8131	−2.39279
$146$	1.53021	0.126641
$147$	−0.613084	−0.0505664
$148$	3.01004	0.247424
$149$	19.9068	1.63083	0.815416	−	0.578876i	$-0.196508\pi$
$149$	19.9068	1.63083	0.815416	+	0.578876i	$0.196508\pi$
$150$	0.292176	0.0238561
$151$	−6.46915	−0.526452	−0.263226	−	0.964734i	$-0.584786\pi$
$151$	−6.46915	−0.526452	−0.263226	+	0.964734i	$0.584786\pi$
$152$	0.190142	0.0154226
$153$	−0.127026	−0.0102694
$154$	−4.04194	−0.325708
$155$	17.9227	1.43958
$156$	−0.0733097	−0.00586948
$157$	9.16519	0.731461	0.365731	−	0.930721i	$-0.380819\pi$
$157$	9.16519	0.731461	0.365731	+	0.930721i	$0.380819\pi$
$158$	−7.35334	−0.585000
$159$	−0.508632	−0.0403372
$160$	3.47552	0.274764
$161$	−4.67489	−0.368433
$162$	−8.98467	−0.705903
$163$	−14.0111	−1.09744	−0.548718	−	0.836007i	$-0.684884\pi$
$163$	−14.0111	−1.09744	−0.548718	+	0.836007i	$0.684884\pi$
$164$	5.50915	0.430192
$165$	−0.124021	−0.00965503
$166$	−14.9726	−1.16210
$167$	−12.2410	−0.947238	−0.473619	−	0.880730i	$-0.657053\pi$
$167$	−12.2410	−0.947238	−0.473619	+	0.880730i	$0.657053\pi$
$168$	−0.192943	−0.0148859
$169$	−9.84494	−0.757303
$170$	0.147244	0.0112931
$171$	0.570103	0.0435969
$172$	1.97222	0.150381
$173$	14.5343	1.10502	0.552512	−	0.833505i	$-0.313669\pi$
$173$	14.5343	1.10502	0.552512	+	0.833505i	$0.313669\pi$
$174$	0.342159	0.0259390
$175$	−33.0947	−2.50173
$176$	−0.864604	−0.0651720
$177$	0.516059	0.0387894
$178$	3.01022	0.225626
$179$	−13.8315	−1.03382	−0.516908	−	0.856041i	$-0.672917\pi$
$179$	−13.8315	−1.03382	−0.516908	+	0.856041i	$0.672917\pi$
$180$	10.4206	0.776709
$181$	−15.1875	−1.12888	−0.564440	−	0.825474i	$-0.690908\pi$
$181$	−15.1875	−1.12888	−0.564440	+	0.825474i	$0.690908\pi$
$182$	8.30377	0.615516
$183$	0.0757664	0.00560082
$184$	−1.00000	−0.0737210
$185$	−10.4615	−0.769141
$186$	−0.212834	−0.0156057
$187$	−0.0366299	−0.00267864
$188$	−6.19777	−0.452019
$189$	−1.15733	−0.0841835
$190$	−0.660844	−0.0479426
$191$	−6.00261	−0.434333	−0.217167	−	0.976135i	$-0.569682\pi$
$191$	−6.00261	−0.434333	−0.217167	+	0.976135i	$0.569682\pi$
$192$	−0.0412722	−0.00297857
$193$	−22.5349	−1.62210	−0.811050	−	0.584977i	$-0.801103\pi$
$193$	−22.5349	−1.62210	−0.811050	+	0.584977i	$0.801103\pi$
$194$	−9.58972	−0.688502
$195$	0.254790	0.0182459
$196$	14.8546	1.06105
$197$	−14.9776	−1.06711	−0.533554	−	0.845766i	$-0.679144\pi$
$197$	−14.9776	−1.06711	−0.533554	+	0.845766i	$0.679144\pi$
$198$	−2.59234	−0.184230
$199$	−15.4970	−1.09855	−0.549277	−	0.835640i	$-0.685097\pi$
$199$	−15.4970	−1.09855	−0.549277	+	0.835640i	$0.685097\pi$
$200$	−7.07925	−0.500578
$201$	0.345455	0.0243665
$202$	−1.84549	−0.129849
$203$	−38.7562	−2.72015
$204$	−0.00174854	−0.000122422 0
$205$	−19.1472	−1.33730
$206$	−3.17903	−0.221493
$207$	−2.99830	−0.208396
$208$	1.77625	0.123161
$209$	0.164398	0.0113716
$210$	0.670579	0.0462743
$211$	−11.1133	−0.765071	−0.382536	−	0.923941i	$-0.624949\pi$
$211$	−11.1133	−0.765071	−0.382536	+	0.923941i	$0.624949\pi$
$212$	12.3238	0.846404
$213$	0.336708	0.0230709
$214$	−8.94815	−0.611683
$215$	−6.85451	−0.467474
$216$	−0.247563	−0.0168445
$217$	24.1076	1.63653
$218$	−13.9356	−0.943840
$219$	0.0631552	0.00426763
$220$	3.00495	0.202594
$221$	0.0752526	0.00506203
$222$	0.124231	0.00833784
$223$	26.3115	1.76195	0.880973	−	0.473167i	$-0.156889\pi$
$223$	26.3115	1.76195	0.880973	+	0.473167i	$0.156889\pi$
$224$	4.67489	0.312355
$225$	−21.2257	−1.41505
$226$	−0.872199	−0.0580178
$227$	2.83976	0.188482	0.0942408	−	0.995549i	$-0.469958\pi$
$227$	2.83976	0.188482	0.0942408	+	0.995549i	$0.469958\pi$
$228$	0.00784760	0.000519720 0
$229$	−25.6328	−1.69386	−0.846932	−	0.531702i	$-0.821553\pi$
$229$	−25.6328	−1.69386	−0.846932	+	0.531702i	$0.821553\pi$
$230$	3.47552	0.229169
$231$	−0.166820	−0.0109759
$232$	−8.29029	−0.544284
$233$	8.73343	0.572146	0.286073	−	0.958208i	$-0.407650\pi$
$233$	8.73343	0.572146	0.286073	+	0.958208i	$0.407650\pi$
$234$	5.32572	0.348153
$235$	21.5405	1.40515
$236$	−12.5038	−0.813926
$237$	−0.303489	−0.0197137
$238$	0.198057	0.0128381
$239$	7.12982	0.461190	0.230595	−	0.973050i	$-0.425933\pi$
$239$	7.12982	0.461190	0.230595	+	0.973050i	$0.425933\pi$
$240$	0.143443	0.00925918
$241$	15.4202	0.993303	0.496651	−	0.867950i	$-0.334563\pi$
$241$	15.4202	0.993303	0.496651	+	0.867950i	$0.334563\pi$
$242$	10.2525	0.659053
$243$	−1.11351	−0.0714315
$244$	−1.83577	−0.117523
$245$	−51.6276	−3.29837
$246$	0.227375	0.0144969
$247$	−0.337740	−0.0214899
$248$	5.15683	0.327459
$249$	−0.617954	−0.0391612
$250$	7.22647	0.457042
$251$	7.09374	0.447753	0.223876	−	0.974618i	$-0.428129\pi$
$251$	7.09374	0.447753	0.223876	+	0.974618i	$0.428129\pi$
$252$	14.0167	0.882970
$253$	−0.864604	−0.0543572
$254$	9.06565	0.568829
$255$	0.00607709	0.000380562 0
$256$	1.00000	0.0625000
$257$	11.0409	0.688710	0.344355	−	0.938839i	$-0.388098\pi$
$257$	11.0409	0.688710	0.344355	+	0.938839i	$0.388098\pi$
$258$	0.0813981	0.00506763
$259$	−14.0716	−0.874368
$260$	−6.17339	−0.382857
$261$	−24.8567	−1.53859
$262$	−1.00000	−0.0617802
$263$	3.30817	0.203990	0.101995	−	0.994785i	$-0.467477\pi$
$263$	3.30817	0.203990	0.101995	+	0.994785i	$0.467477\pi$
$264$	−0.0356842	−0.00219621
$265$	−42.8317	−2.63113
$266$	−0.888896	−0.0545017
$267$	0.124239	0.00760328
$268$	−8.37015	−0.511288
$269$	7.18955	0.438354	0.219177	−	0.975685i	$-0.429663\pi$
$269$	7.18955	0.438354	0.219177	+	0.975685i	$0.429663\pi$
$270$	0.860411	0.0523629
$271$	17.3708	1.05520	0.527600	−	0.849493i	$-0.323092\pi$
$271$	17.3708	1.05520	0.527600	+	0.849493i	$0.323092\pi$
$272$	0.0423660	0.00256882
$273$	0.342715	0.0207421
$274$	20.6634	1.24832
$275$	−6.12075	−0.369095
$276$	−0.0412722	−0.00248430
$277$	−28.3063	−1.70076	−0.850381	−	0.526167i	$-0.823629\pi$
$277$	−28.3063	−1.70076	−0.850381	+	0.526167i	$0.823629\pi$
$278$	−18.6588	−1.11908
$279$	15.4617	0.925668
$280$	−16.2477	−0.970986
$281$	6.39709	0.381618	0.190809	−	0.981627i	$-0.438889\pi$
$281$	6.39709	0.381618	0.190809	+	0.981627i	$0.438889\pi$
$282$	−0.255796	−0.0152324
$283$	16.7184	0.993808	0.496904	−	0.867805i	$-0.334470\pi$
$283$	16.7184	0.993808	0.496904	+	0.867805i	$0.334470\pi$
$284$	−8.15822	−0.484102
$285$	−0.0272745	−0.00161560
$286$	1.53575	0.0908109
$287$	−25.7547	−1.52025
$288$	2.99830	0.176676
$289$	−16.9982	−0.999894
$290$	28.8131	1.69196
$291$	−0.395789	−0.0232016
$292$	−1.53021	−0.0895487
$293$	31.8350	1.85982	0.929911	−	0.367784i	$-0.119883\pi$
$293$	31.8350	1.85982	0.929911	+	0.367784i	$0.119883\pi$
$294$	0.613084	0.0357558
$295$	43.4571	2.53017
$296$	−3.01004	−0.174955
$297$	−0.214044	−0.0124201
$298$	−19.9068	−1.15317
$299$	1.77625	0.102723
$300$	−0.292176	−0.0168688
$301$	−9.21994	−0.531429
$302$	6.46915	0.372258
$303$	−0.0761677	−0.00437572
$304$	−0.190142	−0.0109054
$305$	6.38027	0.365333
$306$	0.127026	0.00726159
$307$	5.80297	0.331193	0.165596	−	0.986194i	$-0.447045\pi$
$307$	5.80297	0.331193	0.165596	+	0.986194i	$0.447045\pi$
$308$	4.04194	0.230311
$309$	−0.131206	−0.00746403
$310$	−17.9227	−1.01794
$311$	7.37807	0.418372	0.209186	−	0.977876i	$-0.432919\pi$
$311$	7.37807	0.418372	0.209186	+	0.977876i	$0.432919\pi$
$312$	0.0733097	0.00415035
$313$	−24.4896	−1.38424	−0.692118	−	0.721784i	$-0.743322\pi$
$313$	−24.4896	−1.38424	−0.692118	+	0.721784i	$0.743322\pi$
$314$	−9.16519	−0.517221
$315$	−48.7154	−2.74480
$316$	7.35334	0.413657
$317$	10.2462	0.575484	0.287742	−	0.957708i	$-0.407095\pi$
$317$	10.2462	0.575484	0.287742	+	0.957708i	$0.407095\pi$
$318$	0.508632	0.0285227
$319$	−7.16782	−0.401321
$320$	−3.47552	−0.194288
$321$	−0.369310	−0.0206129
$322$	4.67489	0.260522
$323$	−0.00805558	−0.000448224 0
$324$	8.98467	0.499148
$325$	12.5745	0.697508
$326$	14.0111	0.776005
$327$	−0.575155	−0.0318061
$328$	−5.50915	−0.304192
$329$	28.9739	1.59738
$330$	0.124021	0.00682714
$331$	−23.1127	−1.27039	−0.635195	−	0.772352i	$-0.719080\pi$
$331$	−23.1127	−1.27039	−0.635195	+	0.772352i	$0.719080\pi$
$332$	14.9726	0.821730
$333$	−9.02499	−0.494566
$334$	12.2410	0.669798
$335$	29.0906	1.58939
$336$	0.192943	0.0105259
$337$	−5.86119	−0.319279	−0.159640	−	0.987175i	$-0.551033\pi$
$337$	−5.86119	−0.319279	−0.159640	+	0.987175i	$0.551033\pi$
$338$	9.84494	0.535494
$339$	−0.0359976	−0.00195512
$340$	−0.147244	−0.00798543
$341$	4.45862	0.241448
$342$	−0.570103	−0.0308276
$343$	−36.7196	−1.98267
$344$	−1.97222	−0.106335
$345$	0.143443	0.00772269
$346$	−14.5343	−0.781370
$347$	3.30471	0.177406	0.0887030	−	0.996058i	$-0.471728\pi$
$347$	3.30471	0.177406	0.0887030	+	0.996058i	$0.471728\pi$
$348$	−0.342159	−0.0183416
$349$	−33.0618	−1.76976	−0.884880	−	0.465819i	$-0.845760\pi$
$349$	−33.0618	−1.76976	−0.884880	+	0.465819i	$0.845760\pi$
$350$	33.0947	1.76899
$351$	0.439734	0.0234712
$352$	0.864604	0.0460836
$353$	30.6985	1.63392	0.816959	−	0.576696i	$-0.195658\pi$
$353$	30.6985	1.63392	0.816959	+	0.576696i	$0.195658\pi$
$354$	−0.516059	−0.0274282
$355$	28.3541	1.50488
$356$	−3.01022	−0.159542
$357$	0.00817425	0.000432627 0
$358$	13.8315	0.731018
$359$	−18.5718	−0.980180	−0.490090	−	0.871672i	$-0.663036\pi$
$359$	−18.5718	−0.980180	−0.490090	+	0.871672i	$0.663036\pi$
$360$	−10.4206	−0.549216
$361$	−18.9638	−0.998097
$362$	15.1875	0.798239
$363$	0.423142	0.0222092
$364$	−8.30377	−0.435236
$365$	5.31827	0.278371
$366$	−0.0757664	−0.00396038
$367$	1.80375	0.0941548	0.0470774	−	0.998891i	$-0.485009\pi$
$367$	1.80375	0.0941548	0.0470774	+	0.998891i	$0.485009\pi$
$368$	1.00000	0.0521286
$369$	−16.5181	−0.859895
$370$	10.4615	0.543865
$371$	−57.6126	−2.99110
$372$	0.212834	0.0110349
$373$	33.0923	1.71345	0.856727	−	0.515771i	$-0.172494\pi$
$373$	33.0923	1.71345	0.856727	+	0.515771i	$0.172494\pi$
$374$	0.0366299	0.00189408
$375$	0.298253	0.0154017
$376$	6.19777	0.319625
$377$	14.7256	0.758407
$378$	1.15733	0.0595267
$379$	−18.7938	−0.965371	−0.482686	−	0.875794i	$-0.660339\pi$
$379$	−18.7938	−0.965371	−0.482686	+	0.875794i	$0.660339\pi$
$380$	0.660844	0.0339006
$381$	0.374160	0.0191688
$382$	6.00261	0.307120
$383$	−9.84527	−0.503070	−0.251535	−	0.967848i	$-0.580935\pi$
$383$	−9.84527	−0.503070	−0.251535	+	0.967848i	$0.580935\pi$
$384$	0.0412722	0.00210617
$385$	−14.0478	−0.715944
$386$	22.5349	1.14700
$387$	−5.91331	−0.300591
$388$	9.58972	0.486844
$389$	23.5844	1.19577	0.597887	−	0.801580i	$-0.296007\pi$
$389$	23.5844	1.19577	0.597887	+	0.801580i	$0.296007\pi$
$390$	−0.254790	−0.0129018
$391$	0.0423660	0.00214254
$392$	−14.8546	−0.750273
$393$	−0.0412722	−0.00208191
$394$	14.9776	0.754560
$395$	−25.5567	−1.28590
$396$	2.59234	0.130270
$397$	−18.0989	−0.908356	−0.454178	−	0.890911i	$-0.650067\pi$
$397$	−18.0989	−0.908356	−0.454178	+	0.890911i	$0.650067\pi$
$398$	15.4970	0.776795
$399$	−0.0366867	−0.00183663
$400$	7.07925	0.353962
$401$	18.9159	0.944617	0.472308	−	0.881433i	$-0.343421\pi$
$401$	18.9159	0.944617	0.472308	+	0.881433i	$0.343421\pi$
$402$	−0.345455	−0.0172297
$403$	−9.15980	−0.456282
$404$	1.84549	0.0918168
$405$	−31.2264	−1.55165
$406$	38.7562	1.92344
$407$	−2.60249	−0.129001
$408$	0.00174854	8.65657e−5 0
$409$	−17.9680	−0.888462	−0.444231	−	0.895912i	$-0.646523\pi$
$409$	−17.9680	−0.888462	−0.444231	+	0.895912i	$0.646523\pi$
$410$	19.1472	0.945610
$411$	0.852827	0.0420668
$412$	3.17903	0.156619
$413$	58.4538	2.87632
$414$	2.99830	0.147358
$415$	−52.0377	−2.55443
$416$	−1.77625	−0.0870877
$417$	−0.770092	−0.0377116
$418$	−0.164398	−0.00804097
$419$	32.6997	1.59748	0.798742	−	0.601674i	$-0.205499\pi$
$419$	32.6997	1.59748	0.798742	+	0.601674i	$0.205499\pi$
$420$	−0.670579	−0.0327209
$421$	33.4154	1.62857	0.814283	−	0.580469i	$-0.197131\pi$
$421$	33.4154	1.62857	0.814283	+	0.580469i	$0.197131\pi$
$422$	11.1133	0.540987
$423$	18.5827	0.903524
$424$	−12.3238	−0.598498
$425$	0.299920	0.0145482
$426$	−0.336708	−0.0163136
$427$	8.58204	0.415314
$428$	8.94815	0.432525
$429$	0.0633839	0.00306020
$430$	6.85451	0.330554
$431$	−6.27017	−0.302023	−0.151012	−	0.988532i	$-0.548253\pi$
$431$	−6.27017	−0.302023	−0.151012	+	0.988532i	$0.548253\pi$
$432$	0.247563	0.0119109
$433$	−20.6938	−0.994481	−0.497240	−	0.867613i	$-0.665653\pi$
$433$	−20.6938	−0.994481	−0.497240	+	0.867613i	$0.665653\pi$
$434$	−24.1076	−1.15720
$435$	1.18918	0.0570168
$436$	13.9356	0.667396
$437$	−0.190142	−0.00909574
$438$	−0.0631552	−0.00301767
$439$	24.4058	1.16482	0.582412	−	0.812894i	$-0.302109\pi$
$439$	24.4058	1.16482	0.582412	+	0.812894i	$0.302109\pi$
$440$	−3.00495	−0.143255
$441$	−44.5386	−2.12089
$442$	−0.0752526	−0.00357940
$443$	−31.8722	−1.51429	−0.757147	−	0.653244i	$-0.773407\pi$
$443$	−31.8722	−1.51429	−0.757147	+	0.653244i	$0.773407\pi$
$444$	−0.124231	−0.00589575
$445$	10.4621	0.495951
$446$	−26.3115	−1.24588
$447$	−0.821600	−0.0388603
$448$	−4.67489	−0.220868
$449$	−25.2156	−1.19000	−0.595000	−	0.803726i	$-0.702848\pi$
$449$	−25.2156	−1.19000	−0.595000	+	0.803726i	$0.702848\pi$
$450$	21.2257	1.00059
$451$	−4.76323	−0.224292
$452$	0.872199	0.0410248
$453$	0.266996	0.0125446
$454$	−2.83976	−0.133277
$455$	28.8599	1.35297
$456$	−0.00784760	−0.000367498 0
$457$	34.6630	1.62147	0.810733	−	0.585416i	$-0.199069\pi$
$457$	34.6630	1.62147	0.810733	+	0.585416i	$0.199069\pi$
$458$	25.6328	1.19774
$459$	0.0104883	0.000489550 0
$460$	−3.47552	−0.162047
$461$	22.9197	1.06748	0.533738	−	0.845650i	$-0.320787\pi$
$461$	22.9197	1.06748	0.533738	+	0.845650i	$0.320787\pi$
$462$	0.166820	0.00776116
$463$	24.2266	1.12590	0.562952	−	0.826489i	$-0.309665\pi$
$463$	24.2266	1.12590	0.562952	+	0.826489i	$0.309665\pi$
$464$	8.29029	0.384867
$465$	−0.739709	−0.0343032
$466$	−8.73343	−0.404568
$467$	8.44872	0.390960	0.195480	−	0.980708i	$-0.437373\pi$
$467$	8.44872	0.390960	0.195480	+	0.980708i	$0.437373\pi$
$468$	−5.32572	−0.246181
$469$	39.1296	1.80684
$470$	−21.5405	−0.993588
$471$	−0.378268	−0.0174297
$472$	12.5038	0.575533
$473$	−1.70519	−0.0784049
$474$	0.303489	0.0139397
$475$	−1.34606	−0.0617617
$476$	−0.198057	−0.00907791
$477$	−36.9505	−1.69185
$478$	−7.12982	−0.326110
$479$	−15.6448	−0.714829	−0.357415	−	0.933946i	$-0.616342\pi$
$479$	−15.6448	−0.714829	−0.357415	+	0.933946i	$0.616342\pi$
$480$	−0.143443	−0.00654723
$481$	5.34658	0.243783
$482$	−15.4202	−0.702371
$483$	0.192943	0.00877923
$484$	−10.2525	−0.466021
$485$	−33.3293	−1.51340
$486$	1.11351	0.0505097
$487$	23.5517	1.06723	0.533615	−	0.845728i	$-0.320833\pi$
$487$	23.5517	1.06723	0.533615	+	0.845728i	$0.320833\pi$
$488$	1.83577	0.0831015
$489$	0.578271	0.0261503
$490$	51.6276	2.33230
$491$	−9.07759	−0.409666	−0.204833	−	0.978797i	$-0.565665\pi$
$491$	−9.07759	−0.409666	−0.204833	+	0.978797i	$0.565665\pi$
$492$	−0.227375	−0.0102508
$493$	0.351226	0.0158184
$494$	0.337740	0.0151956
$495$	−9.00973	−0.404957
$496$	−5.15683	−0.231548
$497$	38.1388	1.71076
$498$	0.617954	0.0276912
$499$	1.08724	0.0486713	0.0243357	−	0.999704i	$-0.492253\pi$
$499$	1.08724	0.0486713	0.0243357	+	0.999704i	$0.492253\pi$
$500$	−7.22647	−0.323177
$501$	0.505214	0.0225713
$502$	−7.09374	−0.316609
$503$	33.7707	1.50576	0.752881	−	0.658157i	$-0.228664\pi$
$503$	33.7707	1.50576	0.752881	+	0.658157i	$0.228664\pi$
$504$	−14.0167	−0.624354
$505$	−6.41406	−0.285422
$506$	0.864604	0.0384364
$507$	0.406323	0.0180454
$508$	−9.06565	−0.402223
$509$	13.9629	0.618893	0.309447	−	0.950917i	$-0.399856\pi$
$509$	13.9629	0.618893	0.309447	+	0.950917i	$0.399856\pi$
$510$	−0.00607709	−0.000269098 0
$511$	7.15357	0.316455
$512$	−1.00000	−0.0441942
$513$	−0.0470722	−0.00207829
$514$	−11.0409	−0.486992
$515$	−11.0488	−0.486867
$516$	−0.0813981	−0.00358335
$517$	5.35862	0.235672
$518$	14.0716	0.618271
$519$	−0.599864	−0.0263311
$520$	6.17339	0.270721
$521$	−20.3616	−0.892060	−0.446030	−	0.895018i	$-0.647163\pi$
$521$	−20.3616	−0.892060	−0.446030	+	0.895018i	$0.647163\pi$
$522$	24.8567	1.08795
$523$	−15.9682	−0.698242	−0.349121	−	0.937078i	$-0.613520\pi$
$523$	−15.9682	−0.698242	−0.349121	+	0.937078i	$0.613520\pi$
$524$	1.00000	0.0436852
$525$	1.36589	0.0596125
$526$	−3.30817	−0.144243
$527$	−0.218474	−0.00951689
$528$	0.0356842	0.00155295
$529$	1.00000	0.0434783
$530$	42.8317	1.86049
$531$	37.4900	1.62693
$532$	0.888896	0.0385385
$533$	9.78561	0.423862
$534$	−0.124239	−0.00537633
$535$	−31.0995	−1.34455
$536$	8.37015	0.361535
$537$	0.570857	0.0246343
$538$	−7.18955	−0.309963
$539$	−12.8434	−0.553204
$540$	−0.860411	−0.0370262
$541$	−0.119484	−0.00513703	−0.00256852	−	0.999997i	$-0.500818\pi$
$541$	−0.119484	−0.00513703	−0.00256852	+	0.999997i	$0.500818\pi$
$542$	−17.3708	−0.746138
$543$	0.626823	0.0268996
$544$	−0.0423660	−0.00181643
$545$	−48.4336	−2.07467
$546$	−0.342715	−0.0146669
$547$	20.1739	0.862575	0.431287	−	0.902215i	$-0.358059\pi$
$547$	20.1739	0.862575	0.431287	+	0.902215i	$0.358059\pi$
$548$	−20.6634	−0.882698
$549$	5.50419	0.234913
$550$	6.12075	0.260990
$551$	−1.57633	−0.0671541
$552$	0.0412722	0.00175666
$553$	−34.3761	−1.46182
$554$	28.3063	1.20262
$555$	0.431768	0.0183275
$556$	18.6588	0.791311
$557$	24.4050	1.03407	0.517037	−	0.855963i	$-0.327035\pi$
$557$	24.4050	1.03407	0.517037	+	0.855963i	$0.327035\pi$
$558$	−15.4617	−0.654546
$559$	3.50316	0.148168
$560$	16.2477	0.686590
$561$	0.00151180	6.38281e−5 0
$562$	−6.39709	−0.269845
$563$	7.23851	0.305067	0.152533	−	0.988298i	$-0.451257\pi$
$563$	7.23851	0.305067	0.152533	+	0.988298i	$0.451257\pi$
$564$	0.255796	0.0107709
$565$	−3.03135	−0.127530
$566$	−16.7184	−0.702729
$567$	−42.0024	−1.76393
$568$	8.15822	0.342311
$569$	−23.5696	−0.988088	−0.494044	−	0.869437i	$-0.664482\pi$
$569$	−23.5696	−0.988088	−0.494044	+	0.869437i	$0.664482\pi$
$570$	0.0272745	0.00114240
$571$	−37.5303	−1.57059	−0.785297	−	0.619119i	$-0.787490\pi$
$571$	−37.5303	−1.57059	−0.785297	+	0.619119i	$0.787490\pi$
$572$	−1.53575	−0.0642130
$573$	0.247741	0.0103495
$574$	25.7547	1.07498
$575$	7.07925	0.295225
$576$	−2.99830	−0.124929
$577$	−32.8755	−1.36863	−0.684313	−	0.729188i	$-0.739898\pi$
$577$	−32.8755	−1.36863	−0.684313	+	0.729188i	$0.739898\pi$
$578$	16.9982	0.707032
$579$	0.930067	0.0386523
$580$	−28.8131	−1.19640
$581$	−69.9955	−2.90390
$582$	0.395789	0.0164060
$583$	−10.6552	−0.441295
$584$	1.53021	0.0633205
$585$	18.5096	0.765280
$586$	−31.8350	−1.31509
$587$	−26.5449	−1.09562	−0.547812	−	0.836601i	$-0.684539\pi$
$587$	−26.5449	−1.09562	−0.547812	+	0.836601i	$0.684539\pi$
$588$	−0.613084	−0.0252832
$589$	0.980531	0.0404021
$590$	−43.4571	−1.78910
$591$	0.618159	0.0254276
$592$	3.01004	0.123712
$593$	−15.5165	−0.637185	−0.318592	−	0.947892i	$-0.603210\pi$
$593$	−15.5165	−0.637185	−0.318592	+	0.947892i	$0.603210\pi$
$594$	0.214044	0.00878234
$595$	0.688350	0.0282196
$596$	19.9068	0.815416
$597$	0.639597	0.0261769
$598$	−1.77625	−0.0726362
$599$	41.7557	1.70609	0.853046	−	0.521836i	$-0.174753\pi$
$599$	41.7557	1.70609	0.853046	+	0.521836i	$0.174753\pi$
$600$	0.292176	0.0119281
$601$	16.3294	0.666091	0.333046	−	0.942911i	$-0.391924\pi$
$601$	16.3294	0.666091	0.333046	+	0.942911i	$0.391924\pi$
$602$	9.21994	0.375777
$603$	25.0962	1.02200
$604$	−6.46915	−0.263226
$605$	35.6326	1.44867
$606$	0.0761677	0.00309410
$607$	−26.9070	−1.09212	−0.546060	−	0.837746i	$-0.683873\pi$
$607$	−26.9070	−1.09212	−0.546060	+	0.837746i	$0.683873\pi$
$608$	0.190142	0.00771129
$609$	1.59956	0.0648173
$610$	−6.38027	−0.258329
$611$	−11.0088	−0.445367
$612$	−0.127026	−0.00513472
$613$	−22.6280	−0.913935	−0.456968	−	0.889483i	$-0.651065\pi$
$613$	−22.6280	−0.913935	−0.456968	+	0.889483i	$0.651065\pi$
$614$	−5.80297	−0.234189
$615$	0.790246	0.0318658
$616$	−4.04194	−0.162854
$617$	35.4013	1.42520	0.712602	−	0.701569i	$-0.247517\pi$
$617$	35.4013	1.42520	0.712602	+	0.701569i	$0.247517\pi$
$618$	0.131206	0.00527786
$619$	20.4815	0.823221	0.411611	−	0.911360i	$-0.364966\pi$
$619$	20.4815	0.823221	0.411611	+	0.911360i	$0.364966\pi$
$620$	17.9227	0.719791
$621$	0.247563	0.00993437
$622$	−7.37807	−0.295834
$623$	14.0725	0.563802
$624$	−0.0733097	−0.00293474
$625$	−10.2805	−0.411220
$626$	24.4896	0.978803
$627$	−0.00678507	−0.000270970 0
$628$	9.16519	0.365731
$629$	0.127523	0.00508469
$630$	48.7154	1.94087
$631$	−42.6326	−1.69718	−0.848588	−	0.529054i	$-0.822547\pi$
$631$	−42.6326	−1.69718	−0.848588	+	0.529054i	$0.822547\pi$
$632$	−7.35334	−0.292500
$633$	0.458671	0.0182305
$634$	−10.2462	−0.406929
$635$	31.5079	1.25035
$636$	−0.508632	−0.0201686
$637$	26.3855	1.04543
$638$	7.16782	0.283777
$639$	24.4608	0.967653
$640$	3.47552	0.137382
$641$	−17.9556	−0.709203	−0.354602	−	0.935018i	$-0.615383\pi$
$641$	−17.9556	−0.709203	−0.354602	+	0.935018i	$0.615383\pi$
$642$	0.369310	0.0145755
$643$	25.2299	0.994971	0.497486	−	0.867472i	$-0.334257\pi$
$643$	25.2299	0.994971	0.497486	+	0.867472i	$0.334257\pi$
$644$	−4.67489	−0.184217
$645$	0.282901	0.0111392
$646$	0.00805558	0.000316942 0
$647$	−19.3390	−0.760294	−0.380147	−	0.924926i	$-0.624127\pi$
$647$	−19.3390	−0.760294	−0.380147	+	0.924926i	$0.624127\pi$
$648$	−8.98467	−0.352951
$649$	10.8108	0.424362
$650$	−12.5745	−0.493212
$651$	−0.994976	−0.0389962
$652$	−14.0111	−0.548718
$653$	−37.3477	−1.46153	−0.730764	−	0.682630i	$-0.760836\pi$
$653$	−37.3477	−1.46153	−0.730764	+	0.682630i	$0.760836\pi$
$654$	0.575155	0.0224903
$655$	−3.47552	−0.135800
$656$	5.50915	0.215096
$657$	4.58802	0.178996
$658$	−28.9739	−1.12952
$659$	25.0911	0.977410	0.488705	−	0.872449i	$-0.337469\pi$
$659$	25.0911	0.977410	0.488705	+	0.872449i	$0.337469\pi$
$660$	−0.124021	−0.00482751
$661$	−16.2810	−0.633257	−0.316629	−	0.948550i	$-0.602551\pi$
$661$	−16.2810	−0.633257	−0.316629	+	0.948550i	$0.602551\pi$
$662$	23.1127	0.898301
$663$	−0.00310584	−0.000120621 0
$664$	−14.9726	−0.581051
$665$	−3.08938	−0.119801
$666$	9.02499	0.349711
$667$	8.29029	0.321001
$668$	−12.2410	−0.473619
$669$	−1.08593	−0.0419846
$670$	−29.0906	−1.12387
$671$	1.58722	0.0612738
$672$	−0.192943	−0.00744295
$673$	35.4722	1.36735	0.683677	−	0.729785i	$-0.260380\pi$
$673$	35.4722	1.36735	0.683677	+	0.729785i	$0.260380\pi$
$674$	5.86119	0.225765
$675$	1.75256	0.0674561
$676$	−9.84494	−0.378652
$677$	22.1996	0.853199	0.426599	−	0.904441i	$-0.359711\pi$
$677$	22.1996	0.853199	0.426599	+	0.904441i	$0.359711\pi$
$678$	0.0359976	0.00138248
$679$	−44.8309	−1.72045
$680$	0.147244	0.00564655
$681$	−0.117203	−0.00449124
$682$	−4.45862	−0.170729
$683$	−38.8502	−1.48656	−0.743281	−	0.668980i	$-0.766731\pi$
$683$	−38.8502	−1.48656	−0.743281	+	0.668980i	$0.766731\pi$
$684$	0.570103	0.0217984
$685$	71.8162	2.74396
$686$	36.7196	1.40196
$687$	1.05792	0.0403623
$688$	1.97222	0.0751904
$689$	21.8902	0.833949
$690$	−0.143443	−0.00546077
$691$	13.4523	0.511751	0.255876	−	0.966710i	$-0.417636\pi$
$691$	13.4523	0.511751	0.255876	+	0.966710i	$0.417636\pi$
$692$	14.5343	0.552512
$693$	−12.1189	−0.460360
$694$	−3.30471	−0.125445
$695$	−64.8492	−2.45987
$696$	0.342159	0.0129695
$697$	0.233401	0.00884068
$698$	33.0618	1.25141
$699$	−0.360448	−0.0136334
$700$	−33.0947	−1.25086
$701$	−20.6030	−0.778164	−0.389082	−	0.921203i	$-0.627208\pi$
$701$	−20.6030	−0.778164	−0.389082	+	0.921203i	$0.627208\pi$
$702$	−0.439734	−0.0165967
$703$	−0.572336	−0.0215861
$704$	−0.864604	−0.0325860
$705$	−0.889024	−0.0334826
$706$	−30.6985	−1.15535
$707$	−8.62749	−0.324470
$708$	0.516059	0.0193947
$709$	0.381165	0.0143149	0.00715747	−	0.999974i	$-0.497722\pi$
$709$	0.381165	0.0143149	0.00715747	+	0.999974i	$0.497722\pi$
$710$	−28.3541	−1.06411
$711$	−22.0475	−0.826845
$712$	3.01022	0.112813
$713$	−5.15683	−0.193125
$714$	−0.00817425	−0.000305913 0
$715$	5.33754	0.199613
$716$	−13.8315	−0.516908
$717$	−0.294264	−0.0109895
$718$	18.5718	0.693092
$719$	−10.4968	−0.391466	−0.195733	−	0.980657i	$-0.562709\pi$
$719$	−10.4968	−0.391466	−0.195733	+	0.980657i	$0.562709\pi$
$720$	10.4206	0.388354
$721$	−14.8616	−0.553476
$722$	18.9638	0.705761
$723$	−0.636426	−0.0236690
$724$	−15.1875	−0.564440
$725$	58.6890	2.17965
$726$	−0.423142	−0.0157043
$727$	−39.2239	−1.45474	−0.727368	−	0.686248i	$-0.759257\pi$
$727$	−39.2239	−1.45474	−0.727368	+	0.686248i	$0.759257\pi$
$728$	8.30377	0.307758
$729$	−26.9081	−0.996595
$730$	−5.31827	−0.196838
$731$	0.0835553	0.00309040
$732$	0.0757664	0.00280041
$733$	27.9896	1.03382	0.516909	−	0.856040i	$-0.327083\pi$
$733$	27.9896	1.03382	0.516909	+	0.856040i	$0.327083\pi$
$734$	−1.80375	−0.0665775
$735$	2.13079	0.0785953
$736$	−1.00000	−0.0368605
$737$	7.23687	0.266574
$738$	16.5181	0.608038
$739$	6.90180	0.253887	0.126943	−	0.991910i	$-0.459483\pi$
$739$	6.90180	0.253887	0.126943	+	0.991910i	$0.459483\pi$
$740$	−10.4615	−0.384571
$741$	0.0139393	0.000512072 0
$742$	57.6126	2.11503
$743$	15.6206	0.573066	0.286533	−	0.958070i	$-0.407497\pi$
$743$	15.6206	0.573066	0.286533	+	0.958070i	$0.407497\pi$
$744$	−0.212834	−0.00780287
$745$	−69.1866	−2.53480
$746$	−33.0923	−1.21159
$747$	−44.8924	−1.64253
$748$	−0.0366299	−0.00133932
$749$	−41.8316	−1.52849
$750$	−0.298253	−0.0108906
$751$	−35.5230	−1.29625	−0.648127	−	0.761533i	$-0.724447\pi$
$751$	−35.5230	−1.29625	−0.648127	+	0.761533i	$0.724447\pi$
$752$	−6.19777	−0.226009
$753$	−0.292775	−0.0106693
$754$	−14.7256	−0.536275
$755$	22.4837	0.818264
$756$	−1.15733	−0.0420918
$757$	31.5217	1.14568	0.572838	−	0.819668i	$-0.305842\pi$
$757$	31.5217	1.14568	0.572838	+	0.819668i	$0.305842\pi$
$758$	18.7938	0.682621
$759$	0.0356842	0.00129525
$760$	−0.660844	−0.0239713
$761$	−12.1218	−0.439414	−0.219707	−	0.975566i	$-0.570510\pi$
$761$	−12.1218	−0.439414	−0.219707	+	0.975566i	$0.570510\pi$
$762$	−0.374160	−0.0135544
$763$	−65.1476	−2.35850
$764$	−6.00261	−0.217167
$765$	0.441481	0.0159618
$766$	9.84527	0.355724
$767$	−22.2098	−0.801949
$768$	−0.0412722	−0.00148928
$769$	−34.9286	−1.25956	−0.629779	−	0.776774i	$-0.716855\pi$
$769$	−34.9286	−1.25956	−0.629779	+	0.776774i	$0.716855\pi$
$770$	14.0478	0.506249
$771$	−0.455681	−0.0164110
$772$	−22.5349	−0.811050
$773$	32.8442	1.18132	0.590662	−	0.806919i	$-0.298867\pi$
$773$	32.8442	1.18132	0.590662	+	0.806919i	$0.298867\pi$
$774$	5.91331	0.212550
$775$	−36.5065	−1.31135
$776$	−9.58972	−0.344251
$777$	0.580767	0.0208349
$778$	−23.5844	−0.845541
$779$	−1.04752	−0.0375314
$780$	0.254790	0.00912293
$781$	7.05364	0.252399
$782$	−0.0423660	−0.00151501
$783$	2.05237	0.0733457
$784$	14.8546	0.530523
$785$	−31.8538	−1.13691
$786$	0.0412722	0.00147213
$787$	1.64417	0.0586082	0.0293041	−	0.999571i	$-0.490671\pi$
$787$	1.64417	0.0586082	0.0293041	+	0.999571i	$0.490671\pi$
$788$	−14.9776	−0.533554
$789$	−0.136535	−0.00486079
$790$	25.5567	0.909266
$791$	−4.07744	−0.144977
$792$	−2.59234	−0.0921148
$793$	−3.26079	−0.115794
$794$	18.0989	0.642304
$795$	1.76776	0.0626960
$796$	−15.4970	−0.549277
$797$	−25.8675	−0.916275	−0.458137	−	0.888881i	$-0.651483\pi$
$797$	−25.8675	−0.916275	−0.458137	+	0.888881i	$0.651483\pi$
$798$	0.0366867	0.00129870
$799$	−0.262575	−0.00928923
$800$	−7.07925	−0.250289
$801$	9.02554	0.318902
$802$	−18.9159	−0.667945
$803$	1.32303	0.0466886
$804$	0.345455	0.0121833
$805$	16.2477	0.572656
$806$	9.15980	0.322640
$807$	−0.296729	−0.0104453
$808$	−1.84549	−0.0649243
$809$	−32.6307	−1.14723	−0.573616	−	0.819124i	$-0.694460\pi$
$809$	−32.6307	−1.14723	−0.573616	+	0.819124i	$0.694460\pi$
$810$	31.2264	1.09718
$811$	26.3040	0.923658	0.461829	−	0.886969i	$-0.347193\pi$
$811$	26.3040	0.923658	0.461829	+	0.886969i	$0.347193\pi$
$812$	−38.7562	−1.36008
$813$	−0.716931	−0.0251439
$814$	2.60249	0.0912173
$815$	48.6960	1.70575
$816$	−0.00174854	−6.12112e−5 0
$817$	−0.375003	−0.0131197
$818$	17.9680	0.628237
$819$	24.8972	0.869978
$820$	−19.1472	−0.668648
$821$	−27.3627	−0.954965	−0.477483	−	0.878641i	$-0.658451\pi$
$821$	−27.3627	−0.954965	−0.477483	+	0.878641i	$0.658451\pi$
$822$	−0.852827	−0.0297457
$823$	27.5890	0.961691	0.480845	−	0.876805i	$-0.340330\pi$
$823$	27.5890	0.961691	0.480845	+	0.876805i	$0.340330\pi$
$824$	−3.17903	−0.110747
$825$	0.252617	0.00879500
$826$	−58.4538	−2.03387
$827$	1.06654	0.0370873	0.0185437	−	0.999828i	$-0.494097\pi$
$827$	1.06654	0.0370873	0.0185437	+	0.999828i	$0.494097\pi$
$828$	−2.99830	−0.104198
$829$	−3.53135	−0.122649	−0.0613245	−	0.998118i	$-0.519532\pi$
$829$	−3.53135	−0.122649	−0.0613245	+	0.998118i	$0.519532\pi$
$830$	52.0377	1.80625
$831$	1.16827	0.0405267
$832$	1.77625	0.0615803
$833$	0.629332	0.0218051
$834$	0.770092	0.0266661
$835$	42.5439	1.47229
$836$	0.164398	0.00568582
$837$	−1.27664	−0.0441272
$838$	−32.6997	−1.12959
$839$	−23.8880	−0.824706	−0.412353	−	0.911024i	$-0.635293\pi$
$839$	−23.8880	−0.824706	−0.412353	+	0.911024i	$0.635293\pi$
$840$	0.670579	0.0231372
$841$	39.7288	1.36996
$842$	−33.4154	−1.15157
$843$	−0.264022	−0.00909341
$844$	−11.1133	−0.382536
$845$	34.2163	1.17708
$846$	−18.5827	−0.638888
$847$	47.9292	1.64687
$848$	12.3238	0.423202
$849$	−0.690008	−0.0236810
$850$	−0.299920	−0.0102872
$851$	3.01004	0.103183
$852$	0.336708	0.0115354
$853$	−51.2915	−1.75619	−0.878094	−	0.478487i	$-0.841185\pi$
$853$	−51.2915	−1.75619	−0.878094	+	0.478487i	$0.841185\pi$
$854$	−8.58204	−0.293671
$855$	−1.98141	−0.0677626
$856$	−8.94815	−0.305841
$857$	10.4768	0.357882	0.178941	−	0.983860i	$-0.442733\pi$
$857$	10.4768	0.357882	0.178941	+	0.983860i	$0.442733\pi$
$858$	−0.0633839	−0.00216389
$859$	10.9096	0.372232	0.186116	−	0.982528i	$-0.440410\pi$
$859$	10.9096	0.372232	0.186116	+	0.982528i	$0.440410\pi$
$860$	−6.85451	−0.233737
$861$	1.06295	0.0362254
$862$	6.27017	0.213563
$863$	31.9340	1.08705	0.543524	−	0.839394i	$-0.317090\pi$
$863$	31.9340	1.08705	0.543524	+	0.839394i	$0.317090\pi$
$864$	−0.247563	−0.00842227
$865$	−50.5144	−1.71754
$866$	20.6938	0.703204
$867$	0.701554	0.0238260
$868$	24.1076	0.818266
$869$	−6.35773	−0.215671
$870$	−1.18918	−0.0403170
$871$	−14.8675	−0.503765
$872$	−13.9356	−0.471920
$873$	−28.7528	−0.973135
$874$	0.190142	0.00643166
$875$	33.7830	1.14207
$876$	0.0631552	0.00213382
$877$	45.6266	1.54070	0.770350	−	0.637621i	$-0.220081\pi$
$877$	45.6266	1.54070	0.770350	+	0.637621i	$0.220081\pi$
$878$	−24.4058	−0.823655
$879$	−1.31390	−0.0443169
$880$	3.00495	0.101297
$881$	34.8012	1.17248	0.586242	−	0.810136i	$-0.300607\pi$
$881$	34.8012	1.17248	0.586242	+	0.810136i	$0.300607\pi$
$882$	44.5386	1.49969
$883$	−41.6654	−1.40215	−0.701077	−	0.713086i	$-0.747297\pi$
$883$	−41.6654	−1.40215	−0.701077	+	0.713086i	$0.747297\pi$
$884$	0.0752526	0.00253102
$885$	−1.79357	−0.0602903
$886$	31.8722	1.07077
$887$	−17.6236	−0.591744	−0.295872	−	0.955228i	$-0.595610\pi$
$887$	−17.6236	−0.591744	−0.295872	+	0.955228i	$0.595610\pi$
$888$	0.124231	0.00416892
$889$	42.3810	1.42141
$890$	−10.4621	−0.350690
$891$	−7.76819	−0.260244
$892$	26.3115	0.880973
$893$	1.17846	0.0394356
$894$	0.821600	0.0274784
$895$	48.0717	1.60686
$896$	4.67489	0.156177
$897$	−0.0733097	−0.00244774
$898$	25.2156	0.841457
$899$	−42.7516	−1.42584
$900$	−21.2257	−0.707523
$901$	0.522112	0.0173941
$902$	4.76323	0.158598
$903$	0.380528	0.0126632
$904$	−0.872199	−0.0290089
$905$	52.7846	1.75462
$906$	−0.266996	−0.00887036
$907$	19.0203	0.631558	0.315779	−	0.948833i	$-0.397734\pi$
$907$	19.0203	0.631558	0.315779	+	0.948833i	$0.397734\pi$
$908$	2.83976	0.0942408
$909$	−5.53334	−0.183529
$910$	−28.8599	−0.956697
$911$	−15.7797	−0.522804	−0.261402	−	0.965230i	$-0.584185\pi$
$911$	−15.7797	−0.522804	−0.261402	+	0.965230i	$0.584185\pi$
$912$	0.00784760	0.000259860 0
$913$	−12.9454	−0.428430
$914$	−34.6630	−1.14655
$915$	−0.263328	−0.00870535
$916$	−25.6328	−0.846932
$917$	−4.67489	−0.154379
$918$	−0.0104883	−0.000346164 0
$919$	−4.88291	−0.161072	−0.0805362	−	0.996752i	$-0.525663\pi$
$919$	−4.88291	−0.161072	−0.0805362	+	0.996752i	$0.525663\pi$
$920$	3.47552	0.114585
$921$	−0.239502	−0.00789184
$922$	−22.9197	−0.754819
$923$	−14.4910	−0.476978
$924$	−0.166820	−0.00548797
$925$	21.3088	0.700629
$926$	−24.2266	−0.796135
$927$	−9.53167	−0.313061
$928$	−8.29029	−0.272142
$929$	35.6581	1.16991	0.584953	−	0.811067i	$-0.301113\pi$
$929$	35.6581	1.16991	0.584953	+	0.811067i	$0.301113\pi$
$930$	0.739709	0.0242560
$931$	−2.82450	−0.0925691
$932$	8.73343	0.286073
$933$	−0.304510	−0.00996920
$934$	−8.44872	−0.276451
$935$	0.127308	0.00416341
$936$	5.32572	0.174077
$937$	32.6424	1.06638	0.533190	−	0.845996i	$-0.320993\pi$
$937$	32.6424	1.06638	0.533190	+	0.845996i	$0.320993\pi$
$938$	−39.1296	−1.27763
$939$	1.01074	0.0329843
$940$	21.5405	0.702573
$941$	−4.19759	−0.136838	−0.0684188	−	0.997657i	$-0.521795\pi$
$941$	−4.19759	−0.136838	−0.0684188	+	0.997657i	$0.521795\pi$
$942$	0.378268	0.0123246
$943$	5.50915	0.179402
$944$	−12.5038	−0.406963
$945$	4.02233	0.130846
$946$	1.70519	0.0554406
$947$	−4.51522	−0.146725	−0.0733624	−	0.997305i	$-0.523373\pi$
$947$	−4.51522	−0.146725	−0.0733624	+	0.997305i	$0.523373\pi$
$948$	−0.303489	−0.00985686
$949$	−2.71803	−0.0882310
$950$	1.34606	0.0436721
$951$	−0.422884	−0.0137130
$952$	0.198057	0.00641906
$953$	−25.9868	−0.841794	−0.420897	−	0.907108i	$-0.638285\pi$
$953$	−25.9868	−0.841794	−0.420897	+	0.907108i	$0.638285\pi$
$954$	36.9505	1.19632
$955$	20.8622	0.675085
$956$	7.12982	0.230595
$957$	0.295832	0.00956289
$958$	15.6448	0.505461
$959$	96.5994	3.11936
$960$	0.143443	0.00462959
$961$	−4.40713	−0.142165
$962$	−5.34658	−0.172381
$963$	−26.8292	−0.864559
$964$	15.4202	0.496651
$965$	78.3206	2.52123
$966$	−0.192943	−0.00620785
$967$	7.03394	0.226196	0.113098	−	0.993584i	$-0.463923\pi$
$967$	7.03394	0.226196	0.113098	+	0.993584i	$0.463923\pi$
$968$	10.2525	0.329527
$969$	0.000332472 0	1.06805e−5 0
$970$	33.3293	1.07014
$971$	−9.26587	−0.297356	−0.148678	−	0.988886i	$-0.547502\pi$
$971$	−9.26587	−0.297356	−0.148678	+	0.988886i	$0.547502\pi$
$972$	−1.11351	−0.0357158
$973$	−87.2281	−2.79640
$974$	−23.5517	−0.754645
$975$	−0.518978	−0.0166206
$976$	−1.83577	−0.0587616
$977$	12.1087	0.387393	0.193697	−	0.981061i	$-0.437952\pi$
$977$	12.1087	0.387393	0.193697	+	0.981061i	$0.437952\pi$
$978$	−0.578271	−0.0184911
$979$	2.60265	0.0831811
$980$	−51.6276	−1.64918
$981$	−41.7832	−1.33403
$982$	9.07759	0.289678
$983$	−14.0941	−0.449533	−0.224766	−	0.974413i	$-0.572162\pi$
$983$	−14.0941	−0.449533	−0.224766	+	0.974413i	$0.572162\pi$
$984$	0.227375	0.00724844
$985$	52.0549	1.65861
$986$	−0.351226	−0.0111853
$987$	−1.19582	−0.0380633
$988$	−0.337740	−0.0107449
$989$	1.97222	0.0627131
$990$	9.00973	0.286348
$991$	36.5012	1.15950	0.579749	−	0.814795i	$-0.303151\pi$
$991$	36.5012	1.15950	0.579749	+	0.814795i	$0.303151\pi$
$992$	5.15683	0.163729
$993$	0.953913	0.0302715
$994$	−38.1388	−1.20969
$995$	53.8602	1.70748
$996$	−0.617954	−0.0195806
$997$	16.0618	0.508682	0.254341	−	0.967115i	$-0.418141\pi$
$997$	16.0618	0.508682	0.254341	+	0.967115i	$0.418141\pi$
$998$	−1.08724	−0.0344158
$999$	0.745175	0.0235763

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6026.2.a.i.1.13	✓	25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6026.2.a.i.1.13	✓	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -0.0412722 q^{3} +1.00000 q^{4} -3.47552 q^{5} +0.0412722 q^{6} -4.67489 q^{7} -1.00000 q^{8} -2.99830 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -0.0412722 q^{3} +1.00000 q^{4} -3.47552 q^{5} +0.0412722 q^{6} -4.67489 q^{7} -1.00000 q^{8} -2.99830 q^{9} +3.47552 q^{10} -0.864604 q^{11} -0.0412722 q^{12} +1.77625 q^{13} +4.67489 q^{14} +0.143443 q^{15} +1.00000 q^{16} +0.0423660 q^{17} +2.99830 q^{18} -0.190142 q^{19} -3.47552 q^{20} +0.192943 q^{21} +0.864604 q^{22} +1.00000 q^{23} +0.0412722 q^{24} +7.07925 q^{25} -1.77625 q^{26} +0.247563 q^{27} -4.67489 q^{28} +8.29029 q^{29} -0.143443 q^{30} -5.15683 q^{31} -1.00000 q^{32} +0.0356842 q^{33} -0.0423660 q^{34} +16.2477 q^{35} -2.99830 q^{36} +3.01004 q^{37} +0.190142 q^{38} -0.0733097 q^{39} +3.47552 q^{40} +5.50915 q^{41} -0.192943 q^{42} +1.97222 q^{43} -0.864604 q^{44} +10.4206 q^{45} -1.00000 q^{46} -6.19777 q^{47} -0.0412722 q^{48} +14.8546 q^{49} -7.07925 q^{50} -0.00174854 q^{51} +1.77625 q^{52} +12.3238 q^{53} -0.247563 q^{54} +3.00495 q^{55} +4.67489 q^{56} +0.00784760 q^{57} -8.29029 q^{58} -12.5038 q^{59} +0.143443 q^{60} -1.83577 q^{61} +5.15683 q^{62} +14.0167 q^{63} +1.00000 q^{64} -6.17339 q^{65} -0.0356842 q^{66} -8.37015 q^{67} +0.0423660 q^{68} -0.0412722 q^{69} -16.2477 q^{70} -8.15822 q^{71} +2.99830 q^{72} -1.53021 q^{73} -3.01004 q^{74} -0.292176 q^{75} -0.190142 q^{76} +4.04194 q^{77} +0.0733097 q^{78} +7.35334 q^{79} -3.47552 q^{80} +8.98467 q^{81} -5.50915 q^{82} +14.9726 q^{83} +0.192943 q^{84} -0.147244 q^{85} -1.97222 q^{86} -0.342159 q^{87} +0.864604 q^{88} -3.01022 q^{89} -10.4206 q^{90} -8.30377 q^{91} +1.00000 q^{92} +0.212834 q^{93} +6.19777 q^{94} +0.660844 q^{95} +0.0412722 q^{96} +9.58972 q^{97} -14.8546 q^{98} +2.59234 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q - 25 q^{2} - 4 q^{3} + 25 q^{4} - 3 q^{5} + 4 q^{6} - 11 q^{7} - 25 q^{8} + 19 q^{9}+O(q^{10}) \) 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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