LMFDB - Embedded newform 6026.2.a.k.1.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("6026.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6026 = 2 \cdot 23 \cdot 131 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6026.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$48.1178522580$
Analytic rank:	$0$
Dimension:	$35$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
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)

$f(q)$	$=$	$q+1.00000 q^{2} -0.783973 q^{3} +1.00000 q^{4} +4.00344 q^{5} -0.783973 q^{6} +0.255131 q^{7} +1.00000 q^{8} -2.38539 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -0.783973 q^{3} +1.00000 q^{4} +4.00344 q^{5} -0.783973 q^{6} +0.255131 q^{7} +1.00000 q^{8} -2.38539 q^{9} +4.00344 q^{10} -1.94238 q^{11} -0.783973 q^{12} +0.466261 q^{13} +0.255131 q^{14} -3.13859 q^{15} +1.00000 q^{16} -1.68830 q^{17} -2.38539 q^{18} +0.0117739 q^{19} +4.00344 q^{20} -0.200016 q^{21} -1.94238 q^{22} -1.00000 q^{23} -0.783973 q^{24} +11.0276 q^{25} +0.466261 q^{26} +4.22200 q^{27} +0.255131 q^{28} +9.98092 q^{29} -3.13859 q^{30} -5.78947 q^{31} +1.00000 q^{32} +1.52278 q^{33} -1.68830 q^{34} +1.02140 q^{35} -2.38539 q^{36} -1.60526 q^{37} +0.0117739 q^{38} -0.365536 q^{39} +4.00344 q^{40} +9.61215 q^{41} -0.200016 q^{42} -10.1444 q^{43} -1.94238 q^{44} -9.54976 q^{45} -1.00000 q^{46} +6.76180 q^{47} -0.783973 q^{48} -6.93491 q^{49} +11.0276 q^{50} +1.32358 q^{51} +0.466261 q^{52} +7.24983 q^{53} +4.22200 q^{54} -7.77622 q^{55} +0.255131 q^{56} -0.00923039 q^{57} +9.98092 q^{58} +10.5297 q^{59} -3.13859 q^{60} +12.3158 q^{61} -5.78947 q^{62} -0.608587 q^{63} +1.00000 q^{64} +1.86665 q^{65} +1.52278 q^{66} +15.3011 q^{67} -1.68830 q^{68} +0.783973 q^{69} +1.02140 q^{70} +11.6523 q^{71} -2.38539 q^{72} -11.0578 q^{73} -1.60526 q^{74} -8.64530 q^{75} +0.0117739 q^{76} -0.495563 q^{77} -0.365536 q^{78} -0.104042 q^{79} +4.00344 q^{80} +3.84623 q^{81} +9.61215 q^{82} +16.9631 q^{83} -0.200016 q^{84} -6.75900 q^{85} -10.1444 q^{86} -7.82477 q^{87} -1.94238 q^{88} +0.362499 q^{89} -9.54976 q^{90} +0.118958 q^{91} -1.00000 q^{92} +4.53879 q^{93} +6.76180 q^{94} +0.0471360 q^{95} -0.783973 q^{96} +6.04655 q^{97} -6.93491 q^{98} +4.63333 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 35 q + 35 q^{2} - 3 q^{3} + 35 q^{4} + 10 q^{5} - 3 q^{6} + 14 q^{7} + 35 q^{8} + 54 q^{9}+O(q^{10}) $ 35 * q + 35 * q^2 - 3 * q^3 + 35 * q^4 + 10 * q^5 - 3 * q^6 + 14 * q^7 + 35 * q^8 + 54 * q^9	\( 35 q + 35 q^{2} - 3 q^{3} + 35 q^{4} + 10 q^{5} - 3 q^{6} + 14 q^{7} + 35 q^{8} + 54 q^{9} + 10 q^{10} + 9 q^{11} - 3 q^{12} + 19 q^{13} + 14 q^{14} + 14 q^{15} + 35 q^{16} + 28 q^{17} + 54 q^{18} + 21 q^{19} + 10 q^{20} + 28 q^{21} + 9 q^{22} - 35 q^{23} - 3 q^{24} + 81 q^{25} + 19 q^{26} - 21 q^{27} + 14 q^{28} + 35 q^{29} + 14 q^{30} + 5 q^{31} + 35 q^{32} + 26 q^{33} + 28 q^{34} - 7 q^{35} + 54 q^{36} + 51 q^{37} + 21 q^{38} + 21 q^{39} + 10 q^{40} + 3 q^{41} + 28 q^{42} + 43 q^{43} + 9 q^{44} + 2 q^{45} - 35 q^{46} + 10 q^{47} - 3 q^{48} + 85 q^{49} + 81 q^{50} + 26 q^{51} + 19 q^{52} + 39 q^{53} - 21 q^{54} + 2 q^{55} + 14 q^{56} + 50 q^{57} + 35 q^{58} - 42 q^{59} + 14 q^{60} + 47 q^{61} + 5 q^{62} + 23 q^{63} + 35 q^{64} + 61 q^{65} + 26 q^{66} + 22 q^{67} + 28 q^{68} + 3 q^{69} - 7 q^{70} + 54 q^{72} + 30 q^{73} + 51 q^{74} - 26 q^{75} + 21 q^{76} + 2 q^{77} + 21 q^{78} + 55 q^{79} + 10 q^{80} + 67 q^{81} + 3 q^{82} + 20 q^{83} + 28 q^{84} + 28 q^{85} + 43 q^{86} + 29 q^{87} + 9 q^{88} - 31 q^{89} + 2 q^{90} + 32 q^{91} - 35 q^{92} + 11 q^{93} + 10 q^{94} + 16 q^{95} - 3 q^{96} + 36 q^{97} + 85 q^{98} - 9 q^{99}+O(q^{100}) \) 35 * q + 35 * q^2 - 3 * q^3 + 35 * q^4 + 10 * q^5 - 3 * q^6 + 14 * q^7 + 35 * q^8 + 54 * q^9 + 10 * q^10 + 9 * q^11 - 3 * q^12 + 19 * q^13 + 14 * q^14 + 14 * q^15 + 35 * q^16 + 28 * q^17 + 54 * q^18 + 21 * q^19 + 10 * q^20 + 28 * q^21 + 9 * q^22 - 35 * q^23 - 3 * q^24 + 81 * q^25 + 19 * q^26 - 21 * q^27 + 14 * q^28 + 35 * q^29 + 14 * q^30 + 5 * q^31 + 35 * q^32 + 26 * q^33 + 28 * q^34 - 7 * q^35 + 54 * q^36 + 51 * q^37 + 21 * q^38 + 21 * q^39 + 10 * q^40 + 3 * q^41 + 28 * q^42 + 43 * q^43 + 9 * q^44 + 2 * q^45 - 35 * q^46 + 10 * q^47 - 3 * q^48 + 85 * q^49 + 81 * q^50 + 26 * q^51 + 19 * q^52 + 39 * q^53 - 21 * q^54 + 2 * q^55 + 14 * q^56 + 50 * q^57 + 35 * q^58 - 42 * q^59 + 14 * q^60 + 47 * q^61 + 5 * q^62 + 23 * q^63 + 35 * q^64 + 61 * q^65 + 26 * q^66 + 22 * q^67 + 28 * q^68 + 3 * q^69 - 7 * q^70 + 54 * q^72 + 30 * q^73 + 51 * q^74 - 26 * q^75 + 21 * q^76 + 2 * q^77 + 21 * q^78 + 55 * q^79 + 10 * q^80 + 67 * q^81 + 3 * q^82 + 20 * q^83 + 28 * q^84 + 28 * q^85 + 43 * q^86 + 29 * q^87 + 9 * q^88 - 31 * q^89 + 2 * q^90 + 32 * q^91 - 35 * q^92 + 11 * q^93 + 10 * q^94 + 16 * q^95 - 3 * q^96 + 36 * q^97 + 85 * q^98 - 9 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−0.783973	−0.452627	−0.226314	−	0.974055i	$-0.572667\pi$
$3$	−0.783973	−0.452627	−0.226314	+	0.974055i	$0.572667\pi$
$4$	1.00000	0.500000
$5$	4.00344	1.79039	0.895197	−	0.445671i	$-0.147035\pi$
$5$	4.00344	1.79039	0.895197	+	0.445671i	$0.147035\pi$
$6$	−0.783973	−0.320056
$7$	0.255131	0.0964306	0.0482153	−	0.998837i	$-0.484647\pi$
$7$	0.255131	0.0964306	0.0482153	+	0.998837i	$0.484647\pi$
$8$	1.00000	0.353553
$9$	−2.38539	−0.795129
$10$	4.00344	1.26600
$11$	−1.94238	−0.585650	−0.292825	−	0.956166i	$-0.594595\pi$
$11$	−1.94238	−0.585650	−0.292825	+	0.956166i	$0.594595\pi$
$12$	−0.783973	−0.226314
$13$	0.466261	0.129318	0.0646588	−	0.997907i	$-0.479404\pi$
$13$	0.466261	0.129318	0.0646588	+	0.997907i	$0.479404\pi$
$14$	0.255131	0.0681867
$15$	−3.13859	−0.810381
$16$	1.00000	0.250000
$17$	−1.68830	−0.409472	−0.204736	−	0.978817i	$-0.565634\pi$
$17$	−1.68830	−0.409472	−0.204736	+	0.978817i	$0.565634\pi$
$18$	−2.38539	−0.562241
$19$	0.0117739	0.00270111	0.00135055	−	0.999999i	$-0.499570\pi$
$19$	0.0117739	0.00270111	0.00135055	+	0.999999i	$0.499570\pi$
$20$	4.00344	0.895197
$21$	−0.200016	−0.0436471
$22$	−1.94238	−0.414117
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	−0.783973	−0.160028
$25$	11.0276	2.20551
$26$	0.466261	0.0914413
$27$	4.22200	0.812524
$28$	0.255131	0.0482153
$29$	9.98092	1.85341	0.926705	−	0.375789i	$-0.122628\pi$
$29$	9.98092	1.85341	0.926705	+	0.375789i	$0.122628\pi$
$30$	−3.13859	−0.573026
$31$	−5.78947	−1.03982	−0.519910	−	0.854221i	$-0.674034\pi$
$31$	−5.78947	−1.03982	−0.519910	+	0.854221i	$0.674034\pi$
$32$	1.00000	0.176777
$33$	1.52278	0.265081
$34$	−1.68830	−0.289541
$35$	1.02140	0.172649
$36$	−2.38539	−0.397564
$37$	−1.60526	−0.263903	−0.131951	−	0.991256i	$-0.542124\pi$
$37$	−1.60526	−0.263903	−0.131951	+	0.991256i	$0.542124\pi$
$38$	0.0117739	0.00190997
$39$	−0.365536	−0.0585326
$40$	4.00344	0.633000
$41$	9.61215	1.50116	0.750582	−	0.660777i	$-0.229773\pi$
$41$	9.61215	1.50116	0.750582	+	0.660777i	$0.229773\pi$
$42$	−0.200016	−0.0308632
$43$	−10.1444	−1.54700	−0.773501	−	0.633796i	$-0.781496\pi$
$43$	−10.1444	−1.54700	−0.773501	+	0.633796i	$0.781496\pi$
$44$	−1.94238	−0.292825
$45$	−9.54976	−1.42359
$46$	−1.00000	−0.147442
$47$	6.76180	0.986310	0.493155	−	0.869941i	$-0.335844\pi$
$47$	6.76180	0.986310	0.493155	+	0.869941i	$0.335844\pi$
$48$	−0.783973	−0.113157
$49$	−6.93491	−0.990701
$50$	11.0276	1.55953
$51$	1.32358	0.185338
$52$	0.466261	0.0646588
$53$	7.24983	0.995841	0.497920	−	0.867223i	$-0.334097\pi$
$53$	7.24983	0.995841	0.497920	+	0.867223i	$0.334097\pi$
$54$	4.22200	0.574541
$55$	−7.77622	−1.04854
$56$	0.255131	0.0340934
$57$	−0.00923039	−0.00122260
$58$	9.98092	1.31056
$59$	10.5297	1.37085	0.685425	−	0.728143i	$-0.259616\pi$
$59$	10.5297	1.37085	0.685425	+	0.728143i	$0.259616\pi$
$60$	−3.13859	−0.405190
$61$	12.3158	1.57687	0.788437	−	0.615115i	$-0.210891\pi$
$61$	12.3158	1.57687	0.788437	+	0.615115i	$0.210891\pi$
$62$	−5.78947	−0.735264
$63$	−0.608587	−0.0766747
$64$	1.00000	0.125000
$65$	1.86665	0.231529
$66$	1.52278	0.187441
$67$	15.3011	1.86933	0.934664	−	0.355534i	$-0.115701\pi$
$67$	15.3011	1.86933	0.934664	+	0.355534i	$0.115701\pi$
$68$	−1.68830	−0.204736
$69$	0.783973	0.0943793
$70$	1.02140	0.122081
$71$	11.6523	1.38288	0.691438	−	0.722435i	$-0.256977\pi$
$71$	11.6523	1.38288	0.691438	+	0.722435i	$0.256977\pi$
$72$	−2.38539	−0.281120
$73$	−11.0578	−1.29421	−0.647107	−	0.762400i	$-0.724021\pi$
$73$	−11.0578	−1.29421	−0.647107	+	0.762400i	$0.724021\pi$
$74$	−1.60526	−0.186608
$75$	−8.64530	−0.998274
$76$	0.0117739	0.00135055
$77$	−0.495563	−0.0564746
$78$	−0.365536	−0.0413888
$79$	−0.104042	−0.0117057	−0.00585283	−	0.999983i	$-0.501863\pi$
$79$	−0.104042	−0.0117057	−0.00585283	+	0.999983i	$0.501863\pi$
$80$	4.00344	0.447598
$81$	3.84623	0.427358
$82$	9.61215	1.06148
$83$	16.9631	1.86194	0.930968	−	0.365100i	$-0.118965\pi$
$83$	16.9631	1.86194	0.930968	+	0.365100i	$0.118965\pi$
$84$	−0.200016	−0.0218236
$85$	−6.75900	−0.733117
$86$	−10.1444	−1.09390
$87$	−7.82477	−0.838904
$88$	−1.94238	−0.207059
$89$	0.362499	0.0384248	0.0192124	−	0.999815i	$-0.493884\pi$
$89$	0.362499	0.0384248	0.0192124	+	0.999815i	$0.493884\pi$
$90$	−9.54976	−1.00663
$91$	0.118958	0.0124702
$92$	−1.00000	−0.104257
$93$	4.53879	0.470651
$94$	6.76180	0.697427
$95$	0.0471360	0.00483605
$96$	−0.783973	−0.0800139
$97$	6.04655	0.613934	0.306967	−	0.951720i	$-0.400686\pi$
$97$	6.04655	0.613934	0.306967	+	0.951720i	$0.400686\pi$
$98$	−6.93491	−0.700531
$99$	4.63333	0.465667
$100$	11.0276	1.10276
$101$	3.13526	0.311970	0.155985	−	0.987759i	$-0.450145\pi$
$101$	3.13526	0.311970	0.155985	+	0.987759i	$0.450145\pi$
$102$	1.32358	0.131054
$103$	−2.97809	−0.293440	−0.146720	−	0.989178i	$-0.546872\pi$
$103$	−2.97809	−0.293440	−0.146720	+	0.989178i	$0.546872\pi$
$104$	0.466261	0.0457206
$105$	−0.800753	−0.0781455
$106$	7.24983	0.704166
$107$	−13.9992	−1.35335	−0.676676	−	0.736281i	$-0.736580\pi$
$107$	−13.9992	−1.35335	−0.676676	+	0.736281i	$0.736580\pi$
$108$	4.22200	0.406262
$109$	12.3435	1.18229	0.591147	−	0.806564i	$-0.298675\pi$
$109$	12.3435	1.18229	0.591147	+	0.806564i	$0.298675\pi$
$110$	−7.77622	−0.741433
$111$	1.25848	0.119450
$112$	0.255131	0.0241077
$113$	−0.291662	−0.0274373	−0.0137186	−	0.999906i	$-0.504367\pi$
$113$	−0.291662	−0.0274373	−0.0137186	+	0.999906i	$0.504367\pi$
$114$	−0.00923039	−0.000864505 0
$115$	−4.00344	−0.373323
$116$	9.98092	0.926705
$117$	−1.11221	−0.102824
$118$	10.5297	0.969337
$119$	−0.430738	−0.0394857
$120$	−3.13859	−0.286513
$121$	−7.22715	−0.657014
$122$	12.3158	1.11502
$123$	−7.53566	−0.679468
$124$	−5.78947	−0.519910
$125$	24.1310	2.15834
$126$	−0.608587	−0.0542172
$127$	−9.98191	−0.885752	−0.442876	−	0.896583i	$-0.646042\pi$
$127$	−9.98191	−0.885752	−0.442876	+	0.896583i	$0.646042\pi$
$128$	1.00000	0.0883883
$129$	7.95291	0.700215
$130$	1.86665	0.163716
$131$	−1.00000	−0.0873704
$131$	−1.00000	−0.0873704
$132$	1.52278	0.132541
$133$	0.00300388	0.000260470 0
$134$	15.3011	1.32181
$135$	16.9025	1.45474
$136$	−1.68830	−0.144770
$137$	10.4227	0.890468	0.445234	−	0.895414i	$-0.353120\pi$
$137$	10.4227	0.890468	0.445234	+	0.895414i	$0.353120\pi$
$138$	0.783973	0.0667362
$139$	−6.72530	−0.570433	−0.285216	−	0.958463i	$-0.592065\pi$
$139$	−6.72530	−0.570433	−0.285216	+	0.958463i	$0.592065\pi$
$140$	1.02140	0.0863244
$141$	−5.30107	−0.446431
$142$	11.6523	0.977842
$143$	−0.905657	−0.0757349
$144$	−2.38539	−0.198782
$145$	39.9580	3.31833
$146$	−11.0578	−0.915147
$147$	5.43678	0.448418
$148$	−1.60526	−0.131951
$149$	17.8945	1.46597	0.732986	−	0.680243i	$-0.238126\pi$
$149$	17.8945	1.46597	0.732986	+	0.680243i	$0.238126\pi$
$150$	−8.64530	−0.705886
$151$	5.74258	0.467324	0.233662	−	0.972318i	$-0.424929\pi$
$151$	5.74258	0.467324	0.233662	+	0.972318i	$0.424929\pi$
$152$	0.0117739	0.000954986 0
$153$	4.02724	0.325583
$154$	−0.495563	−0.0399336
$155$	−23.1778	−1.86169
$156$	−0.365536	−0.0292663
$157$	−1.21137	−0.0966780	−0.0483390	−	0.998831i	$-0.515393\pi$
$157$	−1.21137	−0.0966780	−0.0483390	+	0.998831i	$0.515393\pi$
$158$	−0.104042	−0.00827715
$159$	−5.68367	−0.450744
$160$	4.00344	0.316500
$161$	−0.255131	−0.0201072
$162$	3.84623	0.302188
$163$	−17.7175	−1.38774	−0.693871	−	0.720100i	$-0.744096\pi$
$163$	−17.7175	−1.38774	−0.693871	+	0.720100i	$0.744096\pi$
$164$	9.61215	0.750582
$165$	6.09635	0.474600
$166$	16.9631	1.31659
$167$	−15.1559	−1.17280	−0.586401	−	0.810021i	$-0.699456\pi$
$167$	−15.1559	−1.17280	−0.586401	+	0.810021i	$0.699456\pi$
$168$	−0.200016	−0.0154316
$169$	−12.7826	−0.983277
$170$	−6.75900	−0.518392
$171$	−0.0280852	−0.00214773
$172$	−10.1444	−0.773501
$173$	9.86364	0.749919	0.374960	−	0.927041i	$-0.377657\pi$
$173$	9.86364	0.749919	0.374960	+	0.927041i	$0.377657\pi$
$174$	−7.82477	−0.593194
$175$	2.81348	0.212679
$176$	−1.94238	−0.146413
$177$	−8.25500	−0.620484
$178$	0.362499	0.0271704
$179$	1.50957	0.112830	0.0564152	−	0.998407i	$-0.482033\pi$
$179$	1.50957	0.112830	0.0564152	+	0.998407i	$0.482033\pi$
$180$	−9.54976	−0.711797
$181$	−9.83700	−0.731179	−0.365589	−	0.930776i	$-0.619133\pi$
$181$	−9.83700	−0.731179	−0.365589	+	0.930776i	$0.619133\pi$
$182$	0.118958	0.00881774
$183$	−9.65524	−0.713736
$184$	−1.00000	−0.0737210
$185$	−6.42656	−0.472490
$186$	4.53879	0.332800
$187$	3.27932	0.239808
$188$	6.76180	0.493155
$189$	1.07716	0.0783522
$190$	0.0471360	0.00341960
$191$	−13.8090	−0.999188	−0.499594	−	0.866260i	$-0.666517\pi$
$191$	−13.8090	−0.999188	−0.499594	+	0.866260i	$0.666517\pi$
$192$	−0.783973	−0.0565784
$193$	7.48134	0.538519	0.269259	−	0.963068i	$-0.413221\pi$
$193$	7.48134	0.538519	0.269259	+	0.963068i	$0.413221\pi$
$194$	6.04655	0.434117
$195$	−1.46340	−0.104796
$196$	−6.93491	−0.495351
$197$	−11.7697	−0.838559	−0.419279	−	0.907857i	$-0.637717\pi$
$197$	−11.7697	−0.838559	−0.419279	+	0.907857i	$0.637717\pi$
$198$	4.63333	0.329277
$199$	−22.2622	−1.57813	−0.789064	−	0.614311i	$-0.789434\pi$
$199$	−22.2622	−1.57813	−0.789064	+	0.614311i	$0.789434\pi$
$200$	11.0276	0.779766
$201$	−11.9957	−0.846108
$202$	3.13526	0.220596
$203$	2.54645	0.178725
$204$	1.32358	0.0926691
$205$	38.4817	2.68768
$206$	−2.97809	−0.207494
$207$	2.38539	0.165796
$208$	0.466261	0.0323294
$209$	−0.0228693	−0.00158191
$210$	−0.800753	−0.0552572
$211$	3.95314	0.272146	0.136073	−	0.990699i	$-0.456552\pi$
$211$	3.95314	0.272146	0.136073	+	0.990699i	$0.456552\pi$
$212$	7.24983	0.497920
$213$	−9.13511	−0.625927
$214$	−13.9992	−0.956965
$215$	−40.6124	−2.76974
$216$	4.22200	0.287271
$217$	−1.47708	−0.100270
$218$	12.3435	0.836008
$219$	8.66899	0.585796
$220$	−7.77622	−0.524272
$221$	−0.787187	−0.0529519
$222$	1.25848	0.0844636
$223$	−6.00715	−0.402268	−0.201134	−	0.979564i	$-0.564463\pi$
$223$	−6.00715	−0.402268	−0.201134	+	0.979564i	$0.564463\pi$
$224$	0.255131	0.0170467
$225$	−26.3050	−1.75366
$226$	−0.291662	−0.0194011
$227$	−4.10863	−0.272699	−0.136350	−	0.990661i	$-0.543537\pi$
$227$	−4.10863	−0.272699	−0.136350	+	0.990661i	$0.543537\pi$
$228$	−0.00923039	−0.000611298 0
$229$	−3.90138	−0.257810	−0.128905	−	0.991657i	$-0.541146\pi$
$229$	−3.90138	−0.257810	−0.128905	+	0.991657i	$0.541146\pi$
$230$	−4.00344	−0.263979
$231$	0.388508	0.0255619
$232$	9.98092	0.655279
$233$	−8.70668	−0.570394	−0.285197	−	0.958469i	$-0.592059\pi$
$233$	−8.70668	−0.570394	−0.285197	+	0.958469i	$0.592059\pi$
$234$	−1.11221	−0.0727076
$235$	27.0705	1.76588
$236$	10.5297	0.685425
$237$	0.0815662	0.00529830
$238$	−0.430738	−0.0279206
$239$	15.6877	1.01475	0.507375	−	0.861725i	$-0.330616\pi$
$239$	15.6877	1.01475	0.507375	+	0.861725i	$0.330616\pi$
$240$	−3.13859	−0.202595
$241$	−11.9594	−0.770374	−0.385187	−	0.922839i	$-0.625863\pi$
$241$	−11.9594	−0.770374	−0.385187	+	0.922839i	$0.625863\pi$
$242$	−7.22715	−0.464579
$243$	−15.6813	−1.00596
$244$	12.3158	0.788437
$245$	−27.7635	−1.77375
$246$	−7.53566	−0.480456
$247$	0.00548969	0.000349301 0
$248$	−5.78947	−0.367632
$249$	−13.2986	−0.842763
$250$	24.1310	1.52618
$251$	−14.6299	−0.923431	−0.461715	−	0.887028i	$-0.652766\pi$
$251$	−14.6299	−0.923431	−0.461715	+	0.887028i	$0.652766\pi$
$252$	−0.608587	−0.0383374
$253$	1.94238	0.122117
$254$	−9.98191	−0.626321
$255$	5.29888	0.331828
$256$	1.00000	0.0625000
$257$	−6.61788	−0.412812	−0.206406	−	0.978466i	$-0.566177\pi$
$257$	−6.61788	−0.412812	−0.206406	+	0.978466i	$0.566177\pi$
$258$	7.95291	0.495127
$259$	−0.409552	−0.0254483
$260$	1.86665	0.115765
$261$	−23.8083	−1.47370
$262$	−1.00000	−0.0617802
$263$	−7.20406	−0.444221	−0.222111	−	0.975021i	$-0.571295\pi$
$263$	−7.20406	−0.444221	−0.222111	+	0.975021i	$0.571295\pi$
$264$	1.52278	0.0937204
$265$	29.0243	1.78295
$266$	0.00300388	0.000184180 0
$267$	−0.284189	−0.0173921
$268$	15.3011	0.934664
$269$	13.7764	0.839963	0.419982	−	0.907533i	$-0.362036\pi$
$269$	13.7764	0.839963	0.419982	+	0.907533i	$0.362036\pi$
$270$	16.9025	1.02865
$271$	−6.65829	−0.404463	−0.202231	−	0.979338i	$-0.564819\pi$
$271$	−6.65829	−0.404463	−0.202231	+	0.979338i	$0.564819\pi$
$272$	−1.68830	−0.102368
$273$	−0.0932597	−0.00564434
$274$	10.4227	0.629656
$275$	−21.4197	−1.29166
$276$	0.783973	0.0471896
$277$	−16.0260	−0.962906	−0.481453	−	0.876472i	$-0.659891\pi$
$277$	−16.0260	−0.962906	−0.481453	+	0.876472i	$0.659891\pi$
$278$	−6.72530	−0.403357
$279$	13.8101	0.826791
$280$	1.02140	0.0610406
$281$	−0.354592	−0.0211532	−0.0105766	−	0.999944i	$-0.503367\pi$
$281$	−0.354592	−0.0211532	−0.0105766	+	0.999944i	$0.503367\pi$
$282$	−5.30107	−0.315674
$283$	−10.1929	−0.605907	−0.302954	−	0.953005i	$-0.597973\pi$
$283$	−10.1929	−0.605907	−0.302954	+	0.953005i	$0.597973\pi$
$284$	11.6523	0.691438
$285$	−0.0369533	−0.00218893
$286$	−0.905657	−0.0535526
$287$	2.45236	0.144758
$288$	−2.38539	−0.140560
$289$	−14.1497	−0.832332
$290$	39.9580	2.34642
$291$	−4.74033	−0.277883
$292$	−11.0578	−0.647107
$293$	2.13905	0.124965	0.0624823	−	0.998046i	$-0.480098\pi$
$293$	2.13905	0.124965	0.0624823	+	0.998046i	$0.480098\pi$
$294$	5.43678	0.317080
$295$	42.1550	2.45436
$296$	−1.60526	−0.0933038
$297$	−8.20074	−0.475855
$298$	17.8945	1.03660
$299$	−0.466261	−0.0269646
$300$	−8.64530	−0.499137
$301$	−2.58815	−0.149178
$302$	5.74258	0.330448
$303$	−2.45796	−0.141206
$304$	0.0117739	0.000675277 0
$305$	49.3055	2.82323
$306$	4.02724	0.230222
$307$	10.6462	0.607609	0.303805	−	0.952734i	$-0.401743\pi$
$307$	10.6462	0.607609	0.303805	+	0.952734i	$0.401743\pi$
$308$	−0.495563	−0.0282373
$309$	2.33475	0.132819
$310$	−23.1778	−1.31641
$311$	21.8677	1.24001	0.620003	−	0.784599i	$-0.287131\pi$
$311$	21.8677	1.24001	0.620003	+	0.784599i	$0.287131\pi$
$312$	−0.365536	−0.0206944
$313$	0.633659	0.0358165	0.0179083	−	0.999840i	$-0.494299\pi$
$313$	0.633659	0.0358165	0.0179083	+	0.999840i	$0.494299\pi$
$314$	−1.21137	−0.0683617
$315$	−2.43644	−0.137278
$316$	−0.104042	−0.00585283
$317$	−22.2100	−1.24744	−0.623720	−	0.781648i	$-0.714379\pi$
$317$	−22.2100	−1.24744	−0.623720	+	0.781648i	$0.714379\pi$
$318$	−5.68367	−0.318724
$319$	−19.3868	−1.08545
$320$	4.00344	0.223799
$321$	10.9750	0.612564
$322$	−0.255131	−0.0142179
$323$	−0.0198778	−0.00110603
$324$	3.84623	0.213679
$325$	5.14172	0.285211
$326$	−17.7175	−0.981281
$327$	−9.67698	−0.535138
$328$	9.61215	0.530742
$329$	1.72515	0.0951105
$330$	6.09635	0.335593
$331$	29.1590	1.60272	0.801362	−	0.598179i	$-0.204109\pi$
$331$	29.1590	1.60272	0.801362	+	0.598179i	$0.204109\pi$
$332$	16.9631	0.930968
$333$	3.82916	0.209837
$334$	−15.1559	−0.829296
$335$	61.2571	3.34683
$336$	−0.200016	−0.0109118
$337$	35.0611	1.90990	0.954950	−	0.296766i	$-0.0959082\pi$
$337$	35.0611	1.90990	0.954950	+	0.296766i	$0.0959082\pi$
$338$	−12.7826	−0.695282
$339$	0.228655	0.0124189
$340$	−6.75900	−0.366558
$341$	11.2454	0.608971
$342$	−0.0280852	−0.00151867
$343$	−3.55523	−0.191965
$344$	−10.1444	−0.546948
$345$	3.13859	0.168976
$346$	9.86364	0.530273
$347$	7.00486	0.376040	0.188020	−	0.982165i	$-0.439793\pi$
$347$	7.00486	0.376040	0.188020	+	0.982165i	$0.439793\pi$
$348$	−7.82477	−0.419452
$349$	9.88228	0.528986	0.264493	−	0.964388i	$-0.414795\pi$
$349$	9.88228	0.528986	0.264493	+	0.964388i	$0.414795\pi$
$350$	2.81348	0.150387
$351$	1.96855	0.105074
$352$	−1.94238	−0.103529
$353$	−31.6827	−1.68630	−0.843151	−	0.537677i	$-0.819302\pi$
$353$	−31.6827	−1.68630	−0.843151	+	0.537677i	$0.819302\pi$
$354$	−8.25500	−0.438748
$355$	46.6494	2.47589
$356$	0.362499	0.0192124
$357$	0.337687	0.0178723
$358$	1.50957	0.0797831
$359$	−34.9300	−1.84353	−0.921767	−	0.387744i	$-0.873255\pi$
$359$	−34.9300	−1.84353	−0.921767	+	0.387744i	$0.873255\pi$
$360$	−9.54976	−0.503316
$361$	−18.9999	−0.999993
$362$	−9.83700	−0.517021
$363$	5.66589	0.297382
$364$	0.118958	0.00623508
$365$	−44.2691	−2.31715
$366$	−9.65524	−0.504687
$367$	18.7276	0.977570	0.488785	−	0.872404i	$-0.337440\pi$
$367$	18.7276	0.977570	0.488785	+	0.872404i	$0.337440\pi$
$368$	−1.00000	−0.0521286
$369$	−22.9287	−1.19362
$370$	−6.42656	−0.334101
$371$	1.84966	0.0960295
$372$	4.53879	0.235325
$373$	0.459717	0.0238033	0.0119016	−	0.999929i	$-0.496212\pi$
$373$	0.459717	0.0238033	0.0119016	+	0.999929i	$0.496212\pi$
$374$	3.27932	0.169570
$375$	−18.9180	−0.976923
$376$	6.76180	0.348713
$377$	4.65371	0.239678
$378$	1.07716	0.0554034
$379$	−22.7606	−1.16913	−0.584566	−	0.811346i	$-0.698735\pi$
$379$	−22.7606	−1.16913	−0.584566	+	0.811346i	$0.698735\pi$
$380$	0.0471360	0.00241802
$381$	7.82555	0.400915
$382$	−13.8090	−0.706532
$383$	1.44681	0.0739287	0.0369644	−	0.999317i	$-0.488231\pi$
$383$	1.44681	0.0739287	0.0369644	+	0.999317i	$0.488231\pi$
$384$	−0.783973	−0.0400070
$385$	−1.98396	−0.101112
$386$	7.48134	0.380790
$387$	24.1982	1.23007
$388$	6.04655	0.306967
$389$	21.4558	1.08785	0.543925	−	0.839134i	$-0.316938\pi$
$389$	21.4558	1.08785	0.543925	+	0.839134i	$0.316938\pi$
$390$	−1.46340	−0.0741023
$391$	1.68830	0.0853809
$392$	−6.93491	−0.350266
$393$	0.783973	0.0395462
$394$	−11.7697	−0.592951
$395$	−0.416527	−0.0209577
$396$	4.63333	0.232834
$397$	32.9961	1.65603	0.828013	−	0.560710i	$-0.189472\pi$
$397$	32.9961	1.65603	0.828013	+	0.560710i	$0.189472\pi$
$398$	−22.2622	−1.11591
$399$	−0.00235496	−0.000117896 0
$400$	11.0276	0.551378
$401$	−15.1768	−0.757894	−0.378947	−	0.925418i	$-0.623714\pi$
$401$	−15.1768	−0.757894	−0.378947	+	0.925418i	$0.623714\pi$
$402$	−11.9957	−0.598289
$403$	−2.69940	−0.134467
$404$	3.13526	0.155985
$405$	15.3981	0.765140
$406$	2.54645	0.126378
$407$	3.11803	0.154555
$408$	1.32358	0.0655270
$409$	−19.3002	−0.954333	−0.477166	−	0.878813i	$-0.658336\pi$
$409$	−19.3002	−0.954333	−0.477166	+	0.878813i	$0.658336\pi$
$410$	38.4817	1.90047
$411$	−8.17109	−0.403050
$412$	−2.97809	−0.146720
$413$	2.68646	0.132192
$414$	2.38539	0.117235
$415$	67.9106	3.33360
$416$	0.466261	0.0228603
$417$	5.27246	0.258193
$418$	−0.0228693	−0.00111858
$419$	−9.80676	−0.479092	−0.239546	−	0.970885i	$-0.576999\pi$
$419$	−9.80676	−0.479092	−0.239546	+	0.970885i	$0.576999\pi$
$420$	−0.800753	−0.0390728
$421$	20.9642	1.02173	0.510867	−	0.859660i	$-0.329324\pi$
$421$	20.9642	1.02173	0.510867	+	0.859660i	$0.329324\pi$
$422$	3.95314	0.192436
$423$	−16.1295	−0.784244
$424$	7.24983	0.352083
$425$	−18.6178	−0.903095
$426$	−9.13511	−0.442598
$427$	3.14214	0.152059
$428$	−13.9992	−0.676676
$429$	0.710011	0.0342796
$430$	−40.6124	−1.95850
$431$	−22.2128	−1.06995	−0.534976	−	0.844868i	$-0.679679\pi$
$431$	−22.2128	−1.06995	−0.534976	+	0.844868i	$0.679679\pi$
$432$	4.22200	0.203131
$433$	−0.367227	−0.0176478	−0.00882391	−	0.999961i	$-0.502809\pi$
$433$	−0.367227	−0.0176478	−0.00882391	+	0.999961i	$0.502809\pi$
$434$	−1.47708	−0.0709019
$435$	−31.3260	−1.50197
$436$	12.3435	0.591147
$437$	−0.0117739	−0.000563220 0
$438$	8.66899	0.414220
$439$	17.8063	0.849851	0.424925	−	0.905228i	$-0.360300\pi$
$439$	17.8063	0.849851	0.424925	+	0.905228i	$0.360300\pi$
$440$	−7.77622	−0.370717
$441$	16.5424	0.787735
$442$	−0.787187	−0.0374427
$443$	38.0009	1.80548	0.902738	−	0.430190i	$-0.141553\pi$
$443$	38.0009	1.80548	0.902738	+	0.430190i	$0.141553\pi$
$444$	1.25848	0.0597248
$445$	1.45124	0.0687955
$446$	−6.00715	−0.284447
$447$	−14.0288	−0.663539
$448$	0.255131	0.0120538
$449$	−8.75817	−0.413324	−0.206662	−	0.978412i	$-0.566260\pi$
$449$	−8.75817	−0.413324	−0.206662	+	0.978412i	$0.566260\pi$
$450$	−26.3050	−1.24003
$451$	−18.6705	−0.879158
$452$	−0.291662	−0.0137186
$453$	−4.50202	−0.211524
$454$	−4.10863	−0.192827
$455$	0.476241	0.0223265
$456$	−0.00923039	−0.000432253 0
$457$	4.53889	0.212320	0.106160	−	0.994349i	$-0.466144\pi$
$457$	4.53889	0.212320	0.106160	+	0.994349i	$0.466144\pi$
$458$	−3.90138	−0.182299
$459$	−7.12799	−0.332706
$460$	−4.00344	−0.186661
$461$	38.5403	1.79500	0.897499	−	0.441016i	$-0.145382\pi$
$461$	38.5403	1.79500	0.897499	+	0.441016i	$0.145382\pi$
$462$	0.388508	0.0180750
$463$	−20.0806	−0.933226	−0.466613	−	0.884462i	$-0.654526\pi$
$463$	−20.0806	−0.933226	−0.466613	+	0.884462i	$0.654526\pi$
$464$	9.98092	0.463353
$465$	18.1708	0.842650
$466$	−8.70668	−0.403329
$467$	24.3250	1.12563	0.562813	−	0.826584i	$-0.309719\pi$
$467$	24.3250	1.12563	0.562813	+	0.826584i	$0.309719\pi$
$468$	−1.11221	−0.0514120
$469$	3.90379	0.180260
$470$	27.0705	1.24867
$471$	0.949683	0.0437591
$472$	10.5297	0.484669
$473$	19.7042	0.906002
$474$	0.0815662	0.00374646
$475$	0.129837	0.00595732
$476$	−0.430738	−0.0197428
$477$	−17.2936	−0.791821
$478$	15.6877	0.717537
$479$	−9.06957	−0.414399	−0.207200	−	0.978299i	$-0.566435\pi$
$479$	−9.06957	−0.414399	−0.207200	+	0.978299i	$0.566435\pi$
$480$	−3.13859	−0.143256
$481$	−0.748470	−0.0341273
$482$	−11.9594	−0.544736
$483$	0.200016	0.00910105
$484$	−7.22715	−0.328507
$485$	24.2070	1.09918
$486$	−15.6813	−0.711320
$487$	−8.24316	−0.373533	−0.186767	−	0.982404i	$-0.559801\pi$
$487$	−8.24316	−0.373533	−0.186767	+	0.982404i	$0.559801\pi$
$488$	12.3158	0.557509
$489$	13.8900	0.628129
$490$	−27.7635	−1.25423
$491$	−32.7407	−1.47757	−0.738784	−	0.673942i	$-0.764600\pi$
$491$	−32.7407	−1.47757	−0.738784	+	0.673942i	$0.764600\pi$
$492$	−7.53566	−0.339734
$493$	−16.8508	−0.758920
$494$	0.00548969	0.000246993 0
$495$	18.5493	0.833728
$496$	−5.78947	−0.259955
$497$	2.97287	0.133352
$498$	−13.2986	−0.595923
$499$	17.2996	0.774436	0.387218	−	0.921988i	$-0.373436\pi$
$499$	17.2996	0.774436	0.387218	+	0.921988i	$0.373436\pi$
$500$	24.1310	1.07917
$501$	11.8819	0.530842
$502$	−14.6299	−0.652964
$503$	−11.6372	−0.518875	−0.259438	−	0.965760i	$-0.583537\pi$
$503$	−11.6372	−0.518875	−0.259438	+	0.965760i	$0.583537\pi$
$504$	−0.608587	−0.0271086
$505$	12.5518	0.558550
$506$	1.94238	0.0863494
$507$	10.0212	0.445058
$508$	−9.98191	−0.442876
$509$	27.2632	1.20842	0.604210	−	0.796825i	$-0.293489\pi$
$509$	27.2632	1.20842	0.604210	+	0.796825i	$0.293489\pi$
$510$	5.29888	0.234638
$511$	−2.82118	−0.124802
$512$	1.00000	0.0441942
$513$	0.0497092	0.00219472
$514$	−6.61788	−0.291902
$515$	−11.9226	−0.525374
$516$	7.95291	0.350107
$517$	−13.1340	−0.577633
$518$	−0.409552	−0.0179947
$519$	−7.73283	−0.339434
$520$	1.86665	0.0818580
$521$	10.8361	0.474740	0.237370	−	0.971419i	$-0.423715\pi$
$521$	10.8361	0.474740	0.237370	+	0.971419i	$0.423715\pi$
$522$	−23.8083	−1.04206
$523$	−38.0221	−1.66259	−0.831295	−	0.555832i	$-0.812400\pi$
$523$	−38.0221	−1.66259	−0.831295	+	0.555832i	$0.812400\pi$
$524$	−1.00000	−0.0436852
$525$	−2.20569	−0.0962642
$526$	−7.20406	−0.314112
$527$	9.77435	0.425777
$528$	1.52278	0.0662703
$529$	1.00000	0.0434783
$530$	29.0243	1.26073
$531$	−25.1174	−1.09000
$532$	0.00300388	0.000130235 0
$533$	4.48177	0.194127
$534$	−0.284189	−0.0122981
$535$	−56.0450	−2.42303
$536$	15.3011	0.660907
$537$	−1.18346	−0.0510701
$538$	13.7764	0.593944
$539$	13.4702	0.580205
$540$	16.9025	0.727369
$541$	−41.1099	−1.76745	−0.883725	−	0.468006i	$-0.844973\pi$
$541$	−41.1099	−1.76745	−0.883725	+	0.468006i	$0.844973\pi$
$542$	−6.65829	−0.285998
$543$	7.71195	0.330951
$544$	−1.68830	−0.0723852
$545$	49.4165	2.11677
$546$	−0.0932597	−0.00399115
$547$	12.1453	0.519297	0.259648	−	0.965703i	$-0.416393\pi$
$547$	12.1453	0.519297	0.259648	+	0.965703i	$0.416393\pi$
$548$	10.4227	0.445234
$549$	−29.3779	−1.25382
$550$	−21.4197	−0.913340
$551$	0.117514	0.00500626
$552$	0.783973	0.0333681
$553$	−0.0265444	−0.00112878
$554$	−16.0260	−0.680878
$555$	5.03825	0.213862
$556$	−6.72530	−0.285216
$557$	14.8644	0.629823	0.314912	−	0.949121i	$-0.398025\pi$
$557$	14.8644	0.629823	0.314912	+	0.949121i	$0.398025\pi$
$558$	13.8101	0.584629
$559$	−4.72992	−0.200054
$560$	1.02140	0.0431622
$561$	−2.57090	−0.108543
$562$	−0.354592	−0.0149576
$563$	32.3889	1.36503	0.682514	−	0.730873i	$-0.260887\pi$
$563$	32.3889	1.36503	0.682514	+	0.730873i	$0.260887\pi$
$564$	−5.30107	−0.223215
$565$	−1.16765	−0.0491235
$566$	−10.1929	−0.428441
$567$	0.981293	0.0412104
$568$	11.6523	0.488921
$569$	4.15596	0.174227	0.0871135	−	0.996198i	$-0.472236\pi$
$569$	4.15596	0.174227	0.0871135	+	0.996198i	$0.472236\pi$
$570$	−0.0369533	−0.00154781
$571$	−10.4795	−0.438554	−0.219277	−	0.975663i	$-0.570370\pi$
$571$	−10.4795	−0.438554	−0.219277	+	0.975663i	$0.570370\pi$
$572$	−0.905657	−0.0378674
$573$	10.8259	0.452259
$574$	2.45236	0.102360
$575$	−11.0276	−0.459881
$576$	−2.38539	−0.0993911
$577$	−19.6079	−0.816289	−0.408145	−	0.912917i	$-0.633824\pi$
$577$	−19.6079	−0.816289	−0.408145	+	0.912917i	$0.633824\pi$
$578$	−14.1497	−0.588548
$579$	−5.86517	−0.243748
$580$	39.9580	1.65917
$581$	4.32781	0.179548
$582$	−4.74033	−0.196493
$583$	−14.0819	−0.583214
$584$	−11.0578	−0.457573
$585$	−4.45268	−0.184096
$586$	2.13905	0.0883633
$587$	10.8884	0.449411	0.224705	−	0.974427i	$-0.427858\pi$
$587$	10.8884	0.449411	0.224705	+	0.974427i	$0.427858\pi$
$588$	5.43678	0.224209
$589$	−0.0681644	−0.00280867
$590$	42.1550	1.73550
$591$	9.22715	0.379554
$592$	−1.60526	−0.0659757
$593$	30.6086	1.25694	0.628472	−	0.777832i	$-0.283681\pi$
$593$	30.6086	1.25694	0.628472	+	0.777832i	$0.283681\pi$
$594$	−8.20074	−0.336480
$595$	−1.72443	−0.0706949
$596$	17.8945	0.732986
$597$	17.4530	0.714304
$598$	−0.466261	−0.0190668
$599$	43.6793	1.78469	0.892345	−	0.451354i	$-0.149059\pi$
$599$	43.6793	1.78469	0.892345	+	0.451354i	$0.149059\pi$
$600$	−8.64530	−0.352943
$601$	1.91022	0.0779194	0.0389597	−	0.999241i	$-0.487596\pi$
$601$	1.91022	0.0779194	0.0389597	+	0.999241i	$0.487596\pi$
$602$	−2.58815	−0.105485
$603$	−36.4990	−1.48636
$604$	5.74258	0.233662
$605$	−28.9335	−1.17631
$606$	−2.45796	−0.0998478
$607$	−27.0466	−1.09779	−0.548895	−	0.835892i	$-0.684951\pi$
$607$	−27.0466	−1.09779	−0.548895	+	0.835892i	$0.684951\pi$
$608$	0.0117739	0.000477493 0
$609$	−1.99635	−0.0808960
$610$	49.3055	1.99632
$611$	3.15276	0.127547
$612$	4.02724	0.162792
$613$	−12.9735	−0.523996	−0.261998	−	0.965068i	$-0.584381\pi$
$613$	−12.9735	−0.523996	−0.261998	+	0.965068i	$0.584381\pi$
$614$	10.6462	0.429645
$615$	−30.1686	−1.21652
$616$	−0.495563	−0.0199668
$617$	−20.9374	−0.842908	−0.421454	−	0.906850i	$-0.638480\pi$
$617$	−20.9374	−0.842908	−0.421454	+	0.906850i	$0.638480\pi$
$618$	2.33475	0.0939173
$619$	7.78593	0.312943	0.156471	−	0.987682i	$-0.449988\pi$
$619$	7.78593	0.312943	0.156471	+	0.987682i	$0.449988\pi$
$620$	−23.1778	−0.930843
$621$	−4.22200	−0.169423
$622$	21.8677	0.876817
$623$	0.0924848	0.00370533
$624$	−0.365536	−0.0146332
$625$	41.4692	1.65877
$626$	0.633659	0.0253261
$627$	0.0179290	0.000716013 0
$628$	−1.21137	−0.0483390
$629$	2.71015	0.108061
$630$	−2.43644	−0.0970702
$631$	9.39091	0.373846	0.186923	−	0.982375i	$-0.440148\pi$
$631$	9.39091	0.373846	0.186923	+	0.982375i	$0.440148\pi$
$632$	−0.104042	−0.00413857
$633$	−3.09916	−0.123180
$634$	−22.2100	−0.882073
$635$	−39.9620	−1.58584
$636$	−5.68367	−0.225372
$637$	−3.23348	−0.128115
$638$	−19.3868	−0.767529
$639$	−27.7953	−1.09957
$640$	4.00344	0.158250
$641$	−27.6093	−1.09050	−0.545252	−	0.838272i	$-0.683566\pi$
$641$	−27.6093	−1.09050	−0.545252	+	0.838272i	$0.683566\pi$
$642$	10.9750	0.433148
$643$	−0.836429	−0.0329856	−0.0164928	−	0.999864i	$-0.505250\pi$
$643$	−0.836429	−0.0329856	−0.0164928	+	0.999864i	$0.505250\pi$
$644$	−0.255131	−0.0100536
$645$	31.8390	1.25366
$646$	−0.0198778	−0.000782081 0
$647$	−27.0201	−1.06227	−0.531135	−	0.847287i	$-0.678234\pi$
$647$	−27.0201	−1.06227	−0.531135	+	0.847287i	$0.678234\pi$
$648$	3.84623	0.151094
$649$	−20.4527	−0.802839
$650$	5.14172	0.201675
$651$	1.15799	0.0453851
$652$	−17.7175	−0.693871
$653$	−47.8573	−1.87280	−0.936401	−	0.350931i	$-0.885865\pi$
$653$	−47.8573	−1.87280	−0.936401	+	0.350931i	$0.885865\pi$
$654$	−9.67698	−0.378400
$655$	−4.00344	−0.156427
$656$	9.61215	0.375291
$657$	26.3770	1.02907
$658$	1.72515	0.0672533
$659$	6.63889	0.258614	0.129307	−	0.991605i	$-0.458725\pi$
$659$	6.63889	0.258614	0.129307	+	0.991605i	$0.458725\pi$
$660$	6.09635	0.237300
$661$	20.4780	0.796504	0.398252	−	0.917276i	$-0.369617\pi$
$661$	20.4780	0.796504	0.398252	+	0.917276i	$0.369617\pi$
$662$	29.1590	1.13330
$663$	0.617134	0.0239675
$664$	16.9631	0.658294
$665$	0.0120259	0.000466343 0
$666$	3.82916	0.148377
$667$	−9.98092	−0.386463
$668$	−15.1559	−0.586401
$669$	4.70944	0.182078
$670$	61.2571	2.36657
$671$	−23.9220	−0.923497
$672$	−0.200016	−0.00771579
$673$	17.4686	0.673366	0.336683	−	0.941618i	$-0.390695\pi$
$673$	17.4686	0.673366	0.336683	+	0.941618i	$0.390695\pi$
$674$	35.0611	1.35050
$675$	46.5583	1.79203
$676$	−12.7826	−0.491638
$677$	30.9331	1.18886	0.594428	−	0.804149i	$-0.297379\pi$
$677$	30.9331	1.18886	0.594428	+	0.804149i	$0.297379\pi$
$678$	0.228655	0.00878146
$679$	1.54266	0.0592020
$680$	−6.75900	−0.259196
$681$	3.22105	0.123431
$682$	11.2454	0.430607
$683$	−10.5671	−0.404340	−0.202170	−	0.979350i	$-0.564799\pi$
$683$	−10.5671	−0.404340	−0.202170	+	0.979350i	$0.564799\pi$
$684$	−0.0280852	−0.00107386
$685$	41.7265	1.59429
$686$	−3.55523	−0.135739
$687$	3.05857	0.116692
$688$	−10.1444	−0.386750
$689$	3.38031	0.128780
$690$	3.13859	0.119484
$691$	22.9336	0.872435	0.436217	−	0.899841i	$-0.356318\pi$
$691$	22.9336	0.872435	0.436217	+	0.899841i	$0.356318\pi$
$692$	9.86364	0.374960
$693$	1.18211	0.0449046
$694$	7.00486	0.265901
$695$	−26.9244	−1.02130
$696$	−7.82477	−0.296597
$697$	−16.2282	−0.614685
$698$	9.88228	0.374050
$699$	6.82580	0.258176
$700$	2.81348	0.106339
$701$	−24.0762	−0.909345	−0.454672	−	0.890659i	$-0.650244\pi$
$701$	−24.0762	−0.909345	−0.454672	+	0.890659i	$0.650244\pi$
$702$	1.96855	0.0742982
$703$	−0.0189001	−0.000712831 0
$704$	−1.94238	−0.0732063
$705$	−21.2225	−0.799287
$706$	−31.6827	−1.19240
$707$	0.799904	0.0300835
$708$	−8.25500	−0.310242
$709$	−48.9550	−1.83854	−0.919272	−	0.393624i	$-0.871221\pi$
$709$	−48.9550	−1.83854	−0.919272	+	0.393624i	$0.871221\pi$
$710$	46.6494	1.75072
$711$	0.248181	0.00930750
$712$	0.362499	0.0135852
$713$	5.78947	0.216817
$714$	0.337687	0.0126376
$715$	−3.62575	−0.135595
$716$	1.50957	0.0564152
$717$	−12.2987	−0.459303
$718$	−34.9300	−1.30358
$719$	7.11139	0.265210	0.132605	−	0.991169i	$-0.457666\pi$
$719$	7.11139	0.265210	0.132605	+	0.991169i	$0.457666\pi$
$720$	−9.54976	−0.355898
$721$	−0.759805	−0.0282966
$722$	−18.9999	−0.707102
$723$	9.37586	0.348692
$724$	−9.83700	−0.365589
$725$	110.065	4.08772
$726$	5.66589	0.210281
$727$	−35.8352	−1.32906	−0.664528	−	0.747264i	$-0.731367\pi$
$727$	−35.8352	−1.32906	−0.664528	+	0.747264i	$0.731367\pi$
$728$	0.118958	0.00440887
$729$	0.755064	0.0279653
$730$	−44.2691	−1.63847
$731$	17.1267	0.633454
$732$	−9.65524	−0.356868
$733$	−2.46839	−0.0911722	−0.0455861	−	0.998960i	$-0.514516\pi$
$733$	−2.46839	−0.0911722	−0.0455861	+	0.998960i	$0.514516\pi$
$734$	18.7276	0.691246
$735$	21.7658	0.802845
$736$	−1.00000	−0.0368605
$737$	−29.7206	−1.09477
$738$	−22.9287	−0.844016
$739$	−40.4859	−1.48930	−0.744648	−	0.667457i	$-0.767383\pi$
$739$	−40.4859	−1.48930	−0.744648	+	0.667457i	$0.767383\pi$
$740$	−6.42656	−0.236245
$741$	−0.00430377	−0.000158103 0
$742$	1.84966	0.0679031
$743$	24.6121	0.902931	0.451465	−	0.892289i	$-0.350901\pi$
$743$	24.6121	0.902931	0.451465	+	0.892289i	$0.350901\pi$
$744$	4.53879	0.166400
$745$	71.6395	2.62467
$746$	0.459717	0.0168315
$747$	−40.4634	−1.48048
$748$	3.27932	0.119904
$749$	−3.57163	−0.130505
$750$	−18.9180	−0.690789
$751$	29.4017	1.07288	0.536441	−	0.843938i	$-0.319768\pi$
$751$	29.4017	1.07288	0.536441	+	0.843938i	$0.319768\pi$
$752$	6.76180	0.246578
$753$	11.4694	0.417970
$754$	4.65371	0.169478
$755$	22.9901	0.836694
$756$	1.07716	0.0391761
$757$	−1.25583	−0.0456440	−0.0228220	−	0.999740i	$-0.507265\pi$
$757$	−1.25583	−0.0456440	−0.0228220	+	0.999740i	$0.507265\pi$
$758$	−22.7606	−0.826702
$759$	−1.52278	−0.0552733
$760$	0.0471360	0.00170980
$761$	0.105336	0.00381843	0.00190922	−	0.999998i	$-0.499392\pi$
$761$	0.105336	0.00381843	0.00190922	+	0.999998i	$0.499392\pi$
$762$	7.82555	0.283490
$763$	3.14922	0.114009
$764$	−13.8090	−0.499594
$765$	16.1228	0.582922
$766$	1.44681	0.0522755
$767$	4.90959	0.177275
$768$	−0.783973	−0.0282892
$769$	−8.01699	−0.289100	−0.144550	−	0.989497i	$-0.546173\pi$
$769$	−8.01699	−0.289100	−0.144550	+	0.989497i	$0.546173\pi$
$770$	−1.98396	−0.0714969
$771$	5.18824	0.186850
$772$	7.48134	0.269259
$773$	23.7772	0.855206	0.427603	−	0.903967i	$-0.359358\pi$
$773$	23.7772	0.855206	0.427603	+	0.903967i	$0.359358\pi$
$774$	24.1982	0.869787
$775$	−63.8437	−2.29333
$776$	6.04655	0.217058
$777$	0.321078	0.0115186
$778$	21.4558	0.769226
$779$	0.113172	0.00405481
$780$	−1.46340	−0.0523982
$781$	−22.6333	−0.809882
$782$	1.68830	0.0603734
$783$	42.1394	1.50594
$784$	−6.93491	−0.247675
$785$	−4.84966	−0.173092
$786$	0.783973	0.0279634
$787$	36.1447	1.28842	0.644209	−	0.764850i	$-0.277187\pi$
$787$	36.1447	1.28842	0.644209	+	0.764850i	$0.277187\pi$
$788$	−11.7697	−0.419279
$789$	5.64779	0.201067
$790$	−0.416527	−0.0148194
$791$	−0.0744122	−0.00264579
$792$	4.63333	0.164638
$793$	5.74237	0.203917
$794$	32.9961	1.17099
$795$	−22.7542	−0.807010
$796$	−22.2622	−0.789064
$797$	9.84261	0.348643	0.174322	−	0.984689i	$-0.444227\pi$
$797$	9.84261	0.348643	0.174322	+	0.984689i	$0.444227\pi$
$798$	−0.00235496	−8.33648e−5 0
$799$	−11.4159	−0.403867
$800$	11.0276	0.389883
$801$	−0.864700	−0.0305527
$802$	−15.1768	−0.535912
$803$	21.4784	0.757957
$804$	−11.9957	−0.423054
$805$	−1.02140	−0.0359998
$806$	−2.69940	−0.0950825
$807$	−10.8003	−0.380190
$808$	3.13526	0.110298
$809$	55.4312	1.94886	0.974428	−	0.224699i	$-0.0721399\pi$
$809$	55.4312	1.94886	0.974428	+	0.224699i	$0.0721399\pi$
$810$	15.3981	0.541036
$811$	9.90158	0.347691	0.173846	−	0.984773i	$-0.444381\pi$
$811$	9.90158	0.347691	0.173846	+	0.984773i	$0.444381\pi$
$812$	2.54645	0.0893627
$813$	5.21992	0.183071
$814$	3.11803	0.109287
$815$	−70.9310	−2.48460
$816$	1.32358	0.0463346
$817$	−0.119438	−0.00417862
$818$	−19.3002	−0.674815
$819$	−0.283760	−0.00991539
$820$	38.4817	1.34384
$821$	−13.3338	−0.465354	−0.232677	−	0.972554i	$-0.574748\pi$
$821$	−13.3338	−0.465354	−0.232677	+	0.972554i	$0.574748\pi$
$822$	−8.17109	−0.284999
$823$	−37.2805	−1.29952	−0.649759	−	0.760140i	$-0.725130\pi$
$823$	−37.2805	−1.29952	−0.649759	+	0.760140i	$0.725130\pi$
$824$	−2.97809	−0.103747
$825$	16.7925	0.584639
$826$	2.68646	0.0934738
$827$	−18.5991	−0.646756	−0.323378	−	0.946270i	$-0.604818\pi$
$827$	−18.5991	−0.646756	−0.323378	+	0.946270i	$0.604818\pi$
$828$	2.38539	0.0828979
$829$	−28.9648	−1.00599	−0.502994	−	0.864290i	$-0.667768\pi$
$829$	−28.9648	−1.00599	−0.502994	+	0.864290i	$0.667768\pi$
$830$	67.9106	2.35721
$831$	12.5639	0.435837
$832$	0.466261	0.0161647
$833$	11.7082	0.405665
$834$	5.27246	0.182570
$835$	−60.6760	−2.09978
$836$	−0.0228693	−0.000790953 0
$837$	−24.4431	−0.844878
$838$	−9.80676	−0.338769
$839$	−45.8394	−1.58255	−0.791276	−	0.611460i	$-0.790583\pi$
$839$	−45.8394	−1.58255	−0.791276	+	0.611460i	$0.790583\pi$
$840$	−0.800753	−0.0276286
$841$	70.6187	2.43513
$842$	20.9642	0.722475
$843$	0.277990	0.00957450
$844$	3.95314	0.136073
$845$	−51.1744	−1.76045
$846$	−16.1295	−0.554544
$847$	−1.84387	−0.0633562
$848$	7.24983	0.248960
$849$	7.99099	0.274250
$850$	−18.6178	−0.638585
$851$	1.60526	0.0550276
$852$	−9.13511	−0.312964
$853$	−29.7384	−1.01822	−0.509112	−	0.860700i	$-0.670026\pi$
$853$	−29.7384	−1.01822	−0.509112	+	0.860700i	$0.670026\pi$
$854$	3.14214	0.107522
$855$	−0.112438	−0.00384528
$856$	−13.9992	−0.478482
$857$	44.2953	1.51310	0.756549	−	0.653937i	$-0.226884\pi$
$857$	44.2953	1.51310	0.756549	+	0.653937i	$0.226884\pi$
$858$	0.710011	0.0242394
$859$	−5.49640	−0.187535	−0.0937674	−	0.995594i	$-0.529891\pi$
$859$	−5.49640	−0.187535	−0.0937674	+	0.995594i	$0.529891\pi$
$860$	−40.6124	−1.38487
$861$	−1.92258	−0.0655215
$862$	−22.2128	−0.756570
$863$	−46.3408	−1.57746	−0.788729	−	0.614741i	$-0.789261\pi$
$863$	−46.3408	−1.57746	−0.788729	+	0.614741i	$0.789261\pi$
$864$	4.22200	0.143635
$865$	39.4885	1.34265
$866$	−0.367227	−0.0124789
$867$	11.0929	0.376736
$868$	−1.47708	−0.0501352
$869$	0.202090	0.00685542
$870$	−31.3260	−1.06205
$871$	7.13431	0.241737
$872$	12.3435	0.418004
$873$	−14.4234	−0.488157
$874$	−0.0117739	−0.000398257 0
$875$	6.15657	0.208130
$876$	8.66899	0.292898
$877$	−8.59962	−0.290389	−0.145194	−	0.989403i	$-0.546381\pi$
$877$	−8.59962	−0.290389	−0.145194	+	0.989403i	$0.546381\pi$
$878$	17.8063	0.600935
$879$	−1.67696	−0.0565623
$880$	−7.77622	−0.262136
$881$	−20.9009	−0.704168	−0.352084	−	0.935968i	$-0.614527\pi$
$881$	−20.9009	−0.704168	−0.352084	+	0.935968i	$0.614527\pi$
$882$	16.5424	0.557013
$883$	−0.787646	−0.0265064	−0.0132532	−	0.999912i	$-0.504219\pi$
$883$	−0.787646	−0.0265064	−0.0132532	+	0.999912i	$0.504219\pi$
$884$	−0.787187	−0.0264760
$885$	−33.0484	−1.11091
$886$	38.0009	1.27666
$887$	−12.8636	−0.431918	−0.215959	−	0.976402i	$-0.569288\pi$
$887$	−12.8636	−0.431918	−0.215959	+	0.976402i	$0.569288\pi$
$888$	1.25848	0.0422318
$889$	−2.54670	−0.0854136
$890$	1.45124	0.0486458
$891$	−7.47084	−0.250283
$892$	−6.00715	−0.201134
$893$	0.0796125	0.00266413
$894$	−14.0288	−0.469193
$895$	6.04347	0.202011
$896$	0.255131	0.00852334
$897$	0.365536	0.0122049
$898$	−8.75817	−0.292264
$899$	−57.7842	−1.92721
$900$	−26.3050	−0.876832
$901$	−12.2399	−0.407769
$902$	−18.6705	−0.621659
$903$	2.02904	0.0675221
$904$	−0.291662	−0.00970054
$905$	−39.3819	−1.30910
$906$	−4.50202	−0.149570
$907$	51.7727	1.71908	0.859542	−	0.511065i	$-0.170749\pi$
$907$	51.7727	1.71908	0.859542	+	0.511065i	$0.170749\pi$
$908$	−4.10863	−0.136350
$909$	−7.47881	−0.248056
$910$	0.476241	0.0157872
$911$	46.6632	1.54602	0.773010	−	0.634394i	$-0.218750\pi$
$911$	46.6632	1.54602	0.773010	+	0.634394i	$0.218750\pi$
$912$	−0.00923039	−0.000305649 0
$913$	−32.9487	−1.09044
$914$	4.53889	0.150133
$915$	−38.6542	−1.27787
$916$	−3.90138	−0.128905
$917$	−0.255131	−0.00842518
$918$	−7.12799	−0.235259
$919$	−4.26556	−0.140708	−0.0703539	−	0.997522i	$-0.522413\pi$
$919$	−4.26556	−0.140708	−0.0703539	+	0.997522i	$0.522413\pi$
$920$	−4.00344	−0.131990
$921$	−8.34631	−0.275020
$922$	38.5403	1.26926
$923$	5.43303	0.178830
$924$	0.388508	0.0127810
$925$	−17.7021	−0.582041
$926$	−20.0806	−0.659891
$927$	7.10391	0.233323
$928$	9.98092	0.327640
$929$	−34.8971	−1.14494	−0.572468	−	0.819927i	$-0.694014\pi$
$929$	−34.8971	−1.14494	−0.572468	+	0.819927i	$0.694014\pi$
$930$	18.1708	0.595843
$931$	−0.0816506	−0.00267599
$932$	−8.70668	−0.285197
$933$	−17.1437	−0.561260
$934$	24.3250	0.795938
$935$	13.1286	0.429350
$936$	−1.11221	−0.0363538
$937$	−55.8816	−1.82557	−0.912786	−	0.408438i	$-0.866074\pi$
$937$	−55.8816	−1.82557	−0.912786	+	0.408438i	$0.866074\pi$
$938$	3.90379	0.127463
$939$	−0.496771	−0.0162115
$940$	27.0705	0.882942
$941$	−1.35249	−0.0440900	−0.0220450	−	0.999757i	$-0.507018\pi$
$941$	−1.35249	−0.0440900	−0.0220450	+	0.999757i	$0.507018\pi$
$942$	0.949683	0.0309423
$943$	−9.61215	−0.313015
$944$	10.5297	0.342713
$945$	4.31237	0.140281
$946$	19.7042	0.640640
$947$	20.4401	0.664213	0.332106	−	0.943242i	$-0.392241\pi$
$947$	20.4401	0.664213	0.332106	+	0.943242i	$0.392241\pi$
$948$	0.0815662	0.00264915
$949$	−5.15580	−0.167364
$950$	0.129837	0.00421246
$951$	17.4121	0.564625
$952$	−0.430738	−0.0139603
$953$	−7.11984	−0.230634	−0.115317	−	0.993329i	$-0.536788\pi$
$953$	−7.11984	−0.230634	−0.115317	+	0.993329i	$0.536788\pi$
$954$	−17.2936	−0.559902
$955$	−55.2837	−1.78894
$956$	15.6877	0.507375
$957$	15.1987	0.491304
$958$	−9.06957	−0.293025
$959$	2.65915	0.0858684
$960$	−3.13859	−0.101298
$961$	2.51798	0.0812251
$962$	−0.748470	−0.0241316
$963$	33.3935	1.07609
$964$	−11.9594	−0.385187
$965$	29.9511	0.964161
$966$	0.200016	0.00643541
$967$	−56.7178	−1.82392	−0.911961	−	0.410276i	$-0.865432\pi$
$967$	−56.7178	−1.82392	−0.911961	+	0.410276i	$0.865432\pi$
$968$	−7.22715	−0.232289
$969$	0.0155836	0.000500619 0
$970$	24.2070	0.777240
$971$	5.89885	0.189303	0.0946515	−	0.995510i	$-0.469826\pi$
$971$	5.89885	0.189303	0.0946515	+	0.995510i	$0.469826\pi$
$972$	−15.6813	−0.502979
$973$	−1.71584	−0.0550072
$974$	−8.24316	−0.264128
$975$	−4.03097	−0.129094
$976$	12.3158	0.394219
$977$	−6.50862	−0.208229	−0.104115	−	0.994565i	$-0.533201\pi$
$977$	−6.50862	−0.208229	−0.104115	+	0.994565i	$0.533201\pi$
$978$	13.8900	0.444155
$979$	−0.704111	−0.0225035
$980$	−27.7635	−0.886873
$981$	−29.4440	−0.940076
$982$	−32.7407	−1.04480
$983$	−16.7191	−0.533257	−0.266628	−	0.963799i	$-0.585910\pi$
$983$	−16.7191	−0.533257	−0.266628	+	0.963799i	$0.585910\pi$
$984$	−7.53566	−0.240228
$985$	−47.1195	−1.50135
$986$	−16.8508	−0.536638
$987$	−1.35247	−0.0430496
$988$	0.00548969	0.000174650 0
$989$	10.1444	0.322572
$990$	18.5493	0.589535
$991$	−8.70067	−0.276386	−0.138193	−	0.990405i	$-0.544129\pi$
$991$	−8.70067	−0.276386	−0.138193	+	0.990405i	$0.544129\pi$
$992$	−5.78947	−0.183816
$993$	−22.8599	−0.725437
$994$	2.97287	0.0942939
$995$	−89.1256	−2.82547
$996$	−13.2986	−0.421382
$997$	28.4165	0.899958	0.449979	−	0.893039i	$-0.351431\pi$
$997$	28.4165	0.899958	0.449979	+	0.893039i	$0.351431\pi$
$998$	17.2996	0.547609
$999$	−6.77740	−0.214427

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6026.2.a.k.1.15	✓	35

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6026.2.a.k.1.15	✓	35	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -0.783973 q^{3} +1.00000 q^{4} +4.00344 q^{5} -0.783973 q^{6} +0.255131 q^{7} +1.00000 q^{8} -2.38539 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -0.783973 q^{3} +1.00000 q^{4} +4.00344 q^{5} -0.783973 q^{6} +0.255131 q^{7} +1.00000 q^{8} -2.38539 q^{9} +4.00344 q^{10} -1.94238 q^{11} -0.783973 q^{12} +0.466261 q^{13} +0.255131 q^{14} -3.13859 q^{15} +1.00000 q^{16} -1.68830 q^{17} -2.38539 q^{18} +0.0117739 q^{19} +4.00344 q^{20} -0.200016 q^{21} -1.94238 q^{22} -1.00000 q^{23} -0.783973 q^{24} +11.0276 q^{25} +0.466261 q^{26} +4.22200 q^{27} +0.255131 q^{28} +9.98092 q^{29} -3.13859 q^{30} -5.78947 q^{31} +1.00000 q^{32} +1.52278 q^{33} -1.68830 q^{34} +1.02140 q^{35} -2.38539 q^{36} -1.60526 q^{37} +0.0117739 q^{38} -0.365536 q^{39} +4.00344 q^{40} +9.61215 q^{41} -0.200016 q^{42} -10.1444 q^{43} -1.94238 q^{44} -9.54976 q^{45} -1.00000 q^{46} +6.76180 q^{47} -0.783973 q^{48} -6.93491 q^{49} +11.0276 q^{50} +1.32358 q^{51} +0.466261 q^{52} +7.24983 q^{53} +4.22200 q^{54} -7.77622 q^{55} +0.255131 q^{56} -0.00923039 q^{57} +9.98092 q^{58} +10.5297 q^{59} -3.13859 q^{60} +12.3158 q^{61} -5.78947 q^{62} -0.608587 q^{63} +1.00000 q^{64} +1.86665 q^{65} +1.52278 q^{66} +15.3011 q^{67} -1.68830 q^{68} +0.783973 q^{69} +1.02140 q^{70} +11.6523 q^{71} -2.38539 q^{72} -11.0578 q^{73} -1.60526 q^{74} -8.64530 q^{75} +0.0117739 q^{76} -0.495563 q^{77} -0.365536 q^{78} -0.104042 q^{79} +4.00344 q^{80} +3.84623 q^{81} +9.61215 q^{82} +16.9631 q^{83} -0.200016 q^{84} -6.75900 q^{85} -10.1444 q^{86} -7.82477 q^{87} -1.94238 q^{88} +0.362499 q^{89} -9.54976 q^{90} +0.118958 q^{91} -1.00000 q^{92} +4.53879 q^{93} +6.76180 q^{94} +0.0471360 q^{95} -0.783973 q^{96} +6.04655 q^{97} -6.93491 q^{98} +4.63333 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 35 q + 35 q^{2} - 3 q^{3} + 35 q^{4} + 10 q^{5} - 3 q^{6} + 14 q^{7} + 35 q^{8} + 54 q^{9}+O(q^{10}) \) 35 * q + 35 * q^2 - 3 * q^3 + 35 * q^4 + 10 * q^5 - 3 * q^6 + 14 * q^7 + 35 * q^8 + 54 * q^9	\( 35 q + 35 q^{2} - 3 q^{3} + 35 q^{4} + 10 q^{5} - 3 q^{6} + 14 q^{7} + 35 q^{8} + 54 q^{9} + 10 q^{10} + 9 q^{11} - 3 q^{12} + 19 q^{13} + 14 q^{14} + 14 q^{15} + 35 q^{16} + 28 q^{17} + 54 q^{18} + 21 q^{19} + 10 q^{20} + 28 q^{21} + 9 q^{22} - 35 q^{23} - 3 q^{24} + 81 q^{25} + 19 q^{26} - 21 q^{27} + 14 q^{28} + 35 q^{29} + 14 q^{30} + 5 q^{31} + 35 q^{32} + 26 q^{33} + 28 q^{34} - 7 q^{35} + 54 q^{36} + 51 q^{37} + 21 q^{38} + 21 q^{39} + 10 q^{40} + 3 q^{41} + 28 q^{42} + 43 q^{43} + 9 q^{44} + 2 q^{45} - 35 q^{46} + 10 q^{47} - 3 q^{48} + 85 q^{49} + 81 q^{50} + 26 q^{51} + 19 q^{52} + 39 q^{53} - 21 q^{54} + 2 q^{55} + 14 q^{56} + 50 q^{57} + 35 q^{58} - 42 q^{59} + 14 q^{60} + 47 q^{61} + 5 q^{62} + 23 q^{63} + 35 q^{64} + 61 q^{65} + 26 q^{66} + 22 q^{67} + 28 q^{68} + 3 q^{69} - 7 q^{70} + 54 q^{72} + 30 q^{73} + 51 q^{74} - 26 q^{75} + 21 q^{76} + 2 q^{77} + 21 q^{78} + 55 q^{79} + 10 q^{80} + 67 q^{81} + 3 q^{82} + 20 q^{83} + 28 q^{84} + 28 q^{85} + 43 q^{86} + 29 q^{87} + 9 q^{88} - 31 q^{89} + 2 q^{90} + 32 q^{91} - 35 q^{92} + 11 q^{93} + 10 q^{94} + 16 q^{95} - 3 q^{96} + 36 q^{97} + 85 q^{98} - 9 q^{99}+O(q^{100}) \) 35 * q + 35 * q^2 - 3 * q^3 + 35 * q^4 + 10 * q^5 - 3 * q^6 + 14 * q^7 + 35 * q^8 + 54 * q^9 + 10 * q^10 + 9 * q^11 - 3 * q^12 + 19 * q^13 + 14 * q^14 + 14 * q^15 + 35 * q^16 + 28 * q^17 + 54 * q^18 + 21 * q^19 + 10 * q^20 + 28 * q^21 + 9 * q^22 - 35 * q^23 - 3 * q^24 + 81 * q^25 + 19 * q^26 - 21 * q^27 + 14 * q^28 + 35 * q^29 + 14 * q^30 + 5 * q^31 + 35 * q^32 + 26 * q^33 + 28 * q^34 - 7 * q^35 + 54 * q^36 + 51 * q^37 + 21 * q^38 + 21 * q^39 + 10 * q^40 + 3 * q^41 + 28 * q^42 + 43 * q^43 + 9 * q^44 + 2 * q^45 - 35 * q^46 + 10 * q^47 - 3 * q^48 + 85 * q^49 + 81 * q^50 + 26 * q^51 + 19 * q^52 + 39 * q^53 - 21 * q^54 + 2 * q^55 + 14 * q^56 + 50 * q^57 + 35 * q^58 - 42 * q^59 + 14 * q^60 + 47 * q^61 + 5 * q^62 + 23 * q^63 + 35 * q^64 + 61 * q^65 + 26 * q^66 + 22 * q^67 + 28 * q^68 + 3 * q^69 - 7 * q^70 + 54 * q^72 + 30 * q^73 + 51 * q^74 - 26 * q^75 + 21 * q^76 + 2 * q^77 + 21 * q^78 + 55 * q^79 + 10 * q^80 + 67 * q^81 + 3 * q^82 + 20 * q^83 + 28 * q^84 + 28 * q^85 + 43 * q^86 + 29 * q^87 + 9 * q^88 - 31 * q^89 + 2 * q^90 + 32 * q^91 - 35 * q^92 + 11 * q^93 + 10 * q^94 + 16 * q^95 - 3 * q^96 + 36 * q^97 + 85 * q^98 - 9 * q^99

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