LMFDB - Embedded newform 6026.2.a.l.1.16

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:	$36$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
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)

$f(q)$	$=$	$q-1.00000 q^{2} -0.303391 q^{3} +1.00000 q^{4} +0.0493123 q^{5} +0.303391 q^{6} -2.29306 q^{7} -1.00000 q^{8} -2.90795 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -0.303391 q^{3} +1.00000 q^{4} +0.0493123 q^{5} +0.303391 q^{6} -2.29306 q^{7} -1.00000 q^{8} -2.90795 q^{9} -0.0493123 q^{10} -4.83555 q^{11} -0.303391 q^{12} -5.48009 q^{13} +2.29306 q^{14} -0.0149609 q^{15} +1.00000 q^{16} +1.01419 q^{17} +2.90795 q^{18} -1.82837 q^{19} +0.0493123 q^{20} +0.695693 q^{21} +4.83555 q^{22} -1.00000 q^{23} +0.303391 q^{24} -4.99757 q^{25} +5.48009 q^{26} +1.79242 q^{27} -2.29306 q^{28} +1.97556 q^{29} +0.0149609 q^{30} -9.42673 q^{31} -1.00000 q^{32} +1.46706 q^{33} -1.01419 q^{34} -0.113076 q^{35} -2.90795 q^{36} +2.10519 q^{37} +1.82837 q^{38} +1.66261 q^{39} -0.0493123 q^{40} -8.83563 q^{41} -0.695693 q^{42} -3.46509 q^{43} -4.83555 q^{44} -0.143398 q^{45} +1.00000 q^{46} +7.60704 q^{47} -0.303391 q^{48} -1.74188 q^{49} +4.99757 q^{50} -0.307695 q^{51} -5.48009 q^{52} +1.40630 q^{53} -1.79242 q^{54} -0.238452 q^{55} +2.29306 q^{56} +0.554710 q^{57} -1.97556 q^{58} +4.15555 q^{59} -0.0149609 q^{60} -14.1902 q^{61} +9.42673 q^{62} +6.66811 q^{63} +1.00000 q^{64} -0.270236 q^{65} -1.46706 q^{66} -10.6365 q^{67} +1.01419 q^{68} +0.303391 q^{69} +0.113076 q^{70} -10.9283 q^{71} +2.90795 q^{72} -7.54117 q^{73} -2.10519 q^{74} +1.51622 q^{75} -1.82837 q^{76} +11.0882 q^{77} -1.66261 q^{78} +0.850972 q^{79} +0.0493123 q^{80} +8.18006 q^{81} +8.83563 q^{82} -5.36345 q^{83} +0.695693 q^{84} +0.0500119 q^{85} +3.46509 q^{86} -0.599365 q^{87} +4.83555 q^{88} +5.39264 q^{89} +0.143398 q^{90} +12.5662 q^{91} -1.00000 q^{92} +2.85998 q^{93} -7.60704 q^{94} -0.0901612 q^{95} +0.303391 q^{96} -0.459267 q^{97} +1.74188 q^{98} +14.0615 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 36 q^{2} + 4 q^{3} + 36 q^{4} + q^{5} - 4 q^{6} + 13 q^{7} - 36 q^{8} + 46 q^{9}+O(q^{10}) $ 36 * q - 36 * q^2 + 4 * q^3 + 36 * q^4 + q^5 - 4 * q^6 + 13 * q^7 - 36 * q^8 + 46 * q^9	\( 36 q - 36 q^{2} + 4 q^{3} + 36 q^{4} + q^{5} - 4 q^{6} + 13 q^{7} - 36 q^{8} + 46 q^{9} - q^{10} + 14 q^{11} + 4 q^{12} + 4 q^{13} - 13 q^{14} + 10 q^{15} + 36 q^{16} - 4 q^{17} - 46 q^{18} + 29 q^{19} + q^{20} + 24 q^{21} - 14 q^{22} - 36 q^{23} - 4 q^{24} + 49 q^{25} - 4 q^{26} + 19 q^{27} + 13 q^{28} - 13 q^{29} - 10 q^{30} + 21 q^{31} - 36 q^{32} - 5 q^{33} + 4 q^{34} + 30 q^{35} + 46 q^{36} + 13 q^{37} - 29 q^{38} + 30 q^{39} - q^{40} - 8 q^{41} - 24 q^{42} + 42 q^{43} + 14 q^{44} + 30 q^{45} + 36 q^{46} - 14 q^{47} + 4 q^{48} + 61 q^{49} - 49 q^{50} + 46 q^{51} + 4 q^{52} - 3 q^{53} - 19 q^{54} + 26 q^{55} - 13 q^{56} + 26 q^{57} + 13 q^{58} + 45 q^{59} + 10 q^{60} + 34 q^{61} - 21 q^{62} + 63 q^{63} + 36 q^{64} - 25 q^{65} + 5 q^{66} + 42 q^{67} - 4 q^{68} - 4 q^{69} - 30 q^{70} - 2 q^{71} - 46 q^{72} + 16 q^{73} - 13 q^{74} + 72 q^{75} + 29 q^{76} - 36 q^{77} - 30 q^{78} + 33 q^{79} + q^{80} + 96 q^{81} + 8 q^{82} + 8 q^{83} + 24 q^{84} + 18 q^{85} - 42 q^{86} + 11 q^{87} - 14 q^{88} + 21 q^{89} - 30 q^{90} + 60 q^{91} - 36 q^{92} - 27 q^{93} + 14 q^{94} - 44 q^{95} - 4 q^{96} + 20 q^{97} - 61 q^{98} + 76 q^{99}+O(q^{100}) \) 36 * q - 36 * q^2 + 4 * q^3 + 36 * q^4 + q^5 - 4 * q^6 + 13 * q^7 - 36 * q^8 + 46 * q^9 - q^10 + 14 * q^11 + 4 * q^12 + 4 * q^13 - 13 * q^14 + 10 * q^15 + 36 * q^16 - 4 * q^17 - 46 * q^18 + 29 * q^19 + q^20 + 24 * q^21 - 14 * q^22 - 36 * q^23 - 4 * q^24 + 49 * q^25 - 4 * q^26 + 19 * q^27 + 13 * q^28 - 13 * q^29 - 10 * q^30 + 21 * q^31 - 36 * q^32 - 5 * q^33 + 4 * q^34 + 30 * q^35 + 46 * q^36 + 13 * q^37 - 29 * q^38 + 30 * q^39 - q^40 - 8 * q^41 - 24 * q^42 + 42 * q^43 + 14 * q^44 + 30 * q^45 + 36 * q^46 - 14 * q^47 + 4 * q^48 + 61 * q^49 - 49 * q^50 + 46 * q^51 + 4 * q^52 - 3 * q^53 - 19 * q^54 + 26 * q^55 - 13 * q^56 + 26 * q^57 + 13 * q^58 + 45 * q^59 + 10 * q^60 + 34 * q^61 - 21 * q^62 + 63 * q^63 + 36 * q^64 - 25 * q^65 + 5 * q^66 + 42 * q^67 - 4 * q^68 - 4 * q^69 - 30 * q^70 - 2 * q^71 - 46 * q^72 + 16 * q^73 - 13 * q^74 + 72 * q^75 + 29 * q^76 - 36 * q^77 - 30 * q^78 + 33 * q^79 + q^80 + 96 * q^81 + 8 * q^82 + 8 * q^83 + 24 * q^84 + 18 * q^85 - 42 * q^86 + 11 * q^87 - 14 * q^88 + 21 * q^89 - 30 * q^90 + 60 * q^91 - 36 * q^92 - 27 * q^93 + 14 * q^94 - 44 * q^95 - 4 * q^96 + 20 * q^97 - 61 * q^98 + 76 * 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
$3$	−0.303391	−0.175163	−0.0875813	−	0.996157i	$-0.527914\pi$
$3$	−0.303391	−0.175163	−0.0875813	+	0.996157i	$0.527914\pi$
$4$	1.00000	0.500000
$5$	0.0493123	0.0220531	0.0110266	−	0.999939i	$-0.496490\pi$
$5$	0.0493123	0.0220531	0.0110266	+	0.999939i	$0.496490\pi$
$6$	0.303391	0.123859
$7$	−2.29306	−0.866695	−0.433348	−	0.901227i	$-0.642668\pi$
$7$	−2.29306	−0.866695	−0.433348	+	0.901227i	$0.642668\pi$
$8$	−1.00000	−0.353553
$9$	−2.90795	−0.969318
$10$	−0.0493123	−0.0155939
$11$	−4.83555	−1.45797	−0.728986	−	0.684529i	$-0.760008\pi$
$11$	−4.83555	−1.45797	−0.728986	+	0.684529i	$0.760008\pi$
$12$	−0.303391	−0.0875813
$13$	−5.48009	−1.51990	−0.759952	−	0.649979i	$-0.774778\pi$
$13$	−5.48009	−1.51990	−0.759952	+	0.649979i	$0.774778\pi$
$14$	2.29306	0.612846
$15$	−0.0149609	−0.00386289
$16$	1.00000	0.250000
$17$	1.01419	0.245977	0.122988	−	0.992408i	$-0.460752\pi$
$17$	1.01419	0.245977	0.122988	+	0.992408i	$0.460752\pi$
$18$	2.90795	0.685411
$19$	−1.82837	−0.419457	−0.209728	−	0.977760i	$-0.567258\pi$
$19$	−1.82837	−0.419457	−0.209728	+	0.977760i	$0.567258\pi$
$20$	0.0493123	0.0110266
$21$	0.695693	0.151813
$22$	4.83555	1.03094
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	0.303391	0.0619293
$25$	−4.99757	−0.999514
$26$	5.48009	1.07473
$27$	1.79242	0.344951
$28$	−2.29306	−0.433348
$29$	1.97556	0.366852	0.183426	−	0.983034i	$-0.441281\pi$
$29$	1.97556	0.366852	0.183426	+	0.983034i	$0.441281\pi$
$30$	0.0149609	0.00273147
$31$	−9.42673	−1.69309	−0.846545	−	0.532317i	$-0.821321\pi$
$31$	−9.42673	−1.69309	−0.846545	+	0.532317i	$0.821321\pi$
$32$	−1.00000	−0.176777
$33$	1.46706	0.255382
$34$	−1.01419	−0.173932
$35$	−0.113076	−0.0191134
$36$	−2.90795	−0.484659
$37$	2.10519	0.346092	0.173046	−	0.984914i	$-0.444639\pi$
$37$	2.10519	0.346092	0.173046	+	0.984914i	$0.444639\pi$
$38$	1.82837	0.296601
$39$	1.66261	0.266230
$40$	−0.0493123	−0.00779696
$41$	−8.83563	−1.37989	−0.689946	−	0.723860i	$-0.742366\pi$
$41$	−8.83563	−1.37989	−0.689946	+	0.723860i	$0.742366\pi$
$42$	−0.695693	−0.107348
$43$	−3.46509	−0.528421	−0.264211	−	0.964465i	$-0.585111\pi$
$43$	−3.46509	−0.528421	−0.264211	+	0.964465i	$0.585111\pi$
$44$	−4.83555	−0.728986
$45$	−0.143398	−0.0213765
$46$	1.00000	0.147442
$47$	7.60704	1.10960	0.554800	−	0.831983i	$-0.312795\pi$
$47$	7.60704	1.10960	0.554800	+	0.831983i	$0.312795\pi$
$48$	−0.303391	−0.0437907
$49$	−1.74188	−0.248839
$50$	4.99757	0.706763
$51$	−0.307695	−0.0430859
$52$	−5.48009	−0.759952
$53$	1.40630	0.193170	0.0965850	−	0.995325i	$-0.469208\pi$
$53$	1.40630	0.193170	0.0965850	+	0.995325i	$0.469208\pi$
$54$	−1.79242	−0.243917
$55$	−0.238452	−0.0321529
$56$	2.29306	0.306423
$57$	0.554710	0.0734732
$58$	−1.97556	−0.259403
$59$	4.15555	0.541006	0.270503	−	0.962719i	$-0.412810\pi$
$59$	4.15555	0.541006	0.270503	+	0.962719i	$0.412810\pi$
$60$	−0.0149609	−0.00193144
$61$	−14.1902	−1.81687	−0.908435	−	0.418026i	$-0.862722\pi$
$61$	−14.1902	−1.81687	−0.908435	+	0.418026i	$0.862722\pi$
$62$	9.42673	1.19720
$63$	6.66811	0.840103
$64$	1.00000	0.125000
$65$	−0.270236	−0.0335187
$66$	−1.46706	−0.180582
$67$	−10.6365	−1.29946	−0.649728	−	0.760167i	$-0.725117\pi$
$67$	−10.6365	−1.29946	−0.649728	+	0.760167i	$0.725117\pi$
$68$	1.01419	0.122988
$69$	0.303391	0.0365239
$70$	0.113076	0.0135152
$71$	−10.9283	−1.29695	−0.648475	−	0.761236i	$-0.724593\pi$
$71$	−10.9283	−1.29695	−0.648475	+	0.761236i	$0.724593\pi$
$72$	2.90795	0.342706
$73$	−7.54117	−0.882627	−0.441313	−	0.897353i	$-0.645487\pi$
$73$	−7.54117	−0.882627	−0.441313	+	0.897353i	$0.645487\pi$
$74$	−2.10519	−0.244724
$75$	1.51622	0.175077
$76$	−1.82837	−0.209728
$77$	11.0882	1.26362
$78$	−1.66261	−0.188253
$79$	0.850972	0.0957418	0.0478709	−	0.998854i	$-0.484756\pi$
$79$	0.850972	0.0957418	0.0478709	+	0.998854i	$0.484756\pi$
$80$	0.0493123	0.00551329
$81$	8.18006	0.908896
$82$	8.83563	0.975732
$83$	−5.36345	−0.588715	−0.294357	−	0.955695i	$-0.595106\pi$
$83$	−5.36345	−0.588715	−0.294357	+	0.955695i	$0.595106\pi$
$84$	0.695693	0.0759063
$85$	0.0500119	0.00542456
$86$	3.46509	0.373650
$87$	−0.599365	−0.0642587
$88$	4.83555	0.515471
$89$	5.39264	0.571618	0.285809	−	0.958287i	$-0.407738\pi$
$89$	5.39264	0.571618	0.285809	+	0.958287i	$0.407738\pi$
$90$	0.143398	0.0151155
$91$	12.5662	1.31729
$92$	−1.00000	−0.104257
$93$	2.85998	0.296566
$94$	−7.60704	−0.784606
$95$	−0.0901612	−0.00925034
$96$	0.303391	0.0309647
$97$	−0.459267	−0.0466315	−0.0233157	−	0.999728i	$-0.507422\pi$
$97$	−0.459267	−0.0466315	−0.0233157	+	0.999728i	$0.507422\pi$
$98$	1.74188	0.175956
$99$	14.0615	1.41324
$100$	−4.99757	−0.499757
$101$	−15.6684	−1.55907	−0.779533	−	0.626362i	$-0.784543\pi$
$101$	−15.6684	−1.55907	−0.779533	+	0.626362i	$0.784543\pi$
$102$	0.307695	0.0304663
$103$	−10.2671	−1.01165	−0.505826	−	0.862636i	$-0.668812\pi$
$103$	−10.2671	−1.01165	−0.505826	+	0.862636i	$0.668812\pi$
$104$	5.48009	0.537367
$105$	0.0343062	0.00334795
$106$	−1.40630	−0.136592
$107$	8.89376	0.859792	0.429896	−	0.902878i	$-0.358550\pi$
$107$	8.89376	0.859792	0.429896	+	0.902878i	$0.358550\pi$
$108$	1.79242	0.172475
$109$	17.7166	1.69695	0.848473	−	0.529239i	$-0.177522\pi$
$109$	17.7166	1.69695	0.848473	+	0.529239i	$0.177522\pi$
$110$	0.238452	0.0227355
$111$	−0.638696	−0.0606224
$112$	−2.29306	−0.216674
$113$	−17.8413	−1.67836	−0.839182	−	0.543850i	$-0.816966\pi$
$113$	−17.8413	−1.67836	−0.839182	+	0.543850i	$0.816966\pi$
$114$	−0.554710	−0.0519534
$115$	−0.0493123	−0.00459840
$116$	1.97556	0.183426
$117$	15.9359	1.47327
$118$	−4.15555	−0.382549
$119$	−2.32559	−0.213187
$120$	0.0149609	0.00136574
$121$	12.3825	1.12568
$122$	14.1902	1.28472
$123$	2.68065	0.241706
$124$	−9.42673	−0.846545
$125$	−0.493003	−0.0440956
$126$	−6.66811	−0.594043
$127$	19.0803	1.69310	0.846552	−	0.532306i	$-0.178674\pi$
$127$	19.0803	1.69310	0.846552	+	0.532306i	$0.178674\pi$
$128$	−1.00000	−0.0883883
$129$	1.05128	0.0925597
$130$	0.270236	0.0237013
$131$	1.00000	0.0873704
$131$	1.00000	0.0873704
$132$	1.46706	0.127691
$133$	4.19256	0.363541
$134$	10.6365	0.918854
$135$	0.0883883	0.00760725
$136$	−1.01419	−0.0869659
$137$	2.60361	0.222441	0.111221	−	0.993796i	$-0.464524\pi$
$137$	2.60361	0.222441	0.111221	+	0.993796i	$0.464524\pi$
$138$	−0.303391	−0.0258263
$139$	4.31577	0.366058	0.183029	−	0.983107i	$-0.441410\pi$
$139$	4.31577	0.366058	0.183029	+	0.983107i	$0.441410\pi$
$140$	−0.113076	−0.00955668
$141$	−2.30790	−0.194361
$142$	10.9283	0.917082
$143$	26.4992	2.21598
$144$	−2.90795	−0.242330
$145$	0.0974193	0.00809023
$146$	7.54117	0.624111
$147$	0.528469	0.0435874
$148$	2.10519	0.173046
$149$	−14.3267	−1.17369	−0.586844	−	0.809700i	$-0.699630\pi$
$149$	−14.3267	−1.17369	−0.586844	+	0.809700i	$0.699630\pi$
$150$	−1.51622	−0.123798
$151$	8.25270	0.671595	0.335798	−	0.941934i	$-0.390994\pi$
$151$	8.25270	0.671595	0.335798	+	0.941934i	$0.390994\pi$
$152$	1.82837	0.148300
$153$	−2.94921	−0.238430
$154$	−11.0882	−0.893512
$155$	−0.464854	−0.0373380
$156$	1.66261	0.133115
$157$	7.87890	0.628805	0.314402	−	0.949290i	$-0.398196\pi$
$157$	7.87890	0.628805	0.314402	+	0.949290i	$0.398196\pi$
$158$	−0.850972	−0.0676997
$159$	−0.426658	−0.0338362
$160$	−0.0493123	−0.00389848
$161$	2.29306	0.180718
$162$	−8.18006	−0.642686
$163$	−4.16377	−0.326132	−0.163066	−	0.986615i	$-0.552138\pi$
$163$	−4.16377	−0.326132	−0.163066	+	0.986615i	$0.552138\pi$
$164$	−8.83563	−0.689946
$165$	0.0723441	0.00563198
$166$	5.36345	0.416284
$167$	8.86668	0.686125	0.343062	−	0.939313i	$-0.388536\pi$
$167$	8.86668	0.686125	0.343062	+	0.939313i	$0.388536\pi$
$168$	−0.695693	−0.0536739
$169$	17.0314	1.31011
$170$	−0.0500119	−0.00383574
$171$	5.31682	0.406587
$172$	−3.46509	−0.264211
$173$	−5.33733	−0.405789	−0.202895	−	0.979201i	$-0.565035\pi$
$173$	−5.33733	−0.405789	−0.202895	+	0.979201i	$0.565035\pi$
$174$	0.599365	0.0454378
$175$	11.4597	0.866274
$176$	−4.83555	−0.364493
$177$	−1.26075	−0.0947641
$178$	−5.39264	−0.404195
$179$	13.7373	1.02678	0.513389	−	0.858156i	$-0.328390\pi$
$179$	13.7373	1.02678	0.513389	+	0.858156i	$0.328390\pi$
$180$	−0.143398	−0.0106883
$181$	22.0779	1.64103	0.820517	−	0.571622i	$-0.193686\pi$
$181$	22.0779	1.64103	0.820517	+	0.571622i	$0.193686\pi$
$182$	−12.5662	−0.931467
$183$	4.30518	0.318248
$184$	1.00000	0.0737210
$185$	0.103812	0.00763241
$186$	−2.85998	−0.209704
$187$	−4.90415	−0.358627
$188$	7.60704	0.554800
$189$	−4.11012	−0.298967
$190$	0.0901612	0.00654098
$191$	−17.1122	−1.23819	−0.619097	−	0.785315i	$-0.712501\pi$
$191$	−17.1122	−1.23819	−0.619097	+	0.785315i	$0.712501\pi$
$192$	−0.303391	−0.0218953
$193$	20.2772	1.45958	0.729791	−	0.683671i	$-0.239617\pi$
$193$	20.2772	1.45958	0.729791	+	0.683671i	$0.239617\pi$
$194$	0.459267	0.0329734
$195$	0.0819871	0.00587122
$196$	−1.74188	−0.124420
$197$	−16.1605	−1.15139	−0.575693	−	0.817666i	$-0.695268\pi$
$197$	−16.1605	−1.15139	−0.575693	+	0.817666i	$0.695268\pi$
$198$	−14.0615	−0.999310
$199$	17.9621	1.27330	0.636648	−	0.771154i	$-0.280320\pi$
$199$	17.9621	1.27330	0.636648	+	0.771154i	$0.280320\pi$
$200$	4.99757	0.353381
$201$	3.22701	0.227616
$202$	15.6684	1.10243
$203$	−4.53007	−0.317949
$204$	−0.307695	−0.0215430
$205$	−0.435705	−0.0304310
$206$	10.2671	0.715346
$207$	2.90795	0.202117
$208$	−5.48009	−0.379976
$209$	8.84116	0.611556
$210$	−0.0343062	−0.00236735
$211$	−11.9549	−0.823009	−0.411505	−	0.911408i	$-0.634997\pi$
$211$	−11.9549	−0.823009	−0.411505	+	0.911408i	$0.634997\pi$
$212$	1.40630	0.0965850
$213$	3.31554	0.227177
$214$	−8.89376	−0.607965
$215$	−0.170872	−0.0116534
$216$	−1.79242	−0.121959
$217$	21.6160	1.46739
$218$	−17.7166	−1.19992
$219$	2.28792	0.154603
$220$	−0.238452	−0.0160764
$221$	−5.55784	−0.373861
$222$	0.638696	0.0428665
$223$	11.7778	0.788700	0.394350	−	0.918960i	$-0.370970\pi$
$223$	11.7778	0.788700	0.394350	+	0.918960i	$0.370970\pi$
$224$	2.29306	0.153212
$225$	14.5327	0.968847
$226$	17.8413	1.18678
$227$	−26.2986	−1.74550	−0.872750	−	0.488167i	$-0.837666\pi$
$227$	−26.2986	−1.74550	−0.872750	+	0.488167i	$0.837666\pi$
$228$	0.554710	0.0367366
$229$	−25.1776	−1.66378	−0.831891	−	0.554939i	$-0.812741\pi$
$229$	−25.1776	−1.66378	−0.831891	+	0.554939i	$0.812741\pi$
$230$	0.0493123	0.00325156
$231$	−3.36405	−0.221339
$232$	−1.97556	−0.129702
$233$	8.44130	0.553008	0.276504	−	0.961013i	$-0.410824\pi$
$233$	8.44130	0.553008	0.276504	+	0.961013i	$0.410824\pi$
$234$	−15.9359	−1.04176
$235$	0.375121	0.0244702
$236$	4.15555	0.270503
$237$	−0.258177	−0.0167704
$238$	2.32559	0.150746
$239$	14.5017	0.938034	0.469017	−	0.883189i	$-0.344608\pi$
$239$	14.5017	0.938034	0.469017	+	0.883189i	$0.344608\pi$
$240$	−0.0149609	−0.000965722 0
$241$	3.56989	0.229957	0.114978	−	0.993368i	$-0.463320\pi$
$241$	3.56989	0.229957	0.114978	+	0.993368i	$0.463320\pi$
$242$	−12.3825	−0.795977
$243$	−7.85901	−0.504155
$244$	−14.1902	−0.908435
$245$	−0.0858959	−0.00548769
$246$	−2.68065	−0.170912
$247$	10.0196	0.637534
$248$	9.42673	0.598598
$249$	1.62722	0.103121
$250$	0.493003	0.0311803
$251$	−15.5630	−0.982330	−0.491165	−	0.871067i	$-0.663429\pi$
$251$	−15.5630	−0.982330	−0.491165	+	0.871067i	$0.663429\pi$
$252$	6.66811	0.420052
$253$	4.83555	0.304008
$254$	−19.0803	−1.19721
$255$	−0.0151732	−0.000950180 0
$256$	1.00000	0.0625000
$257$	−22.0007	−1.37236	−0.686182	−	0.727430i	$-0.740715\pi$
$257$	−22.0007	−1.37236	−0.686182	+	0.727430i	$0.740715\pi$
$258$	−1.05128	−0.0654496
$259$	−4.82734	−0.299956
$260$	−0.270236	−0.0167593
$261$	−5.74483	−0.355596
$262$	−1.00000	−0.0617802
$263$	1.03250	0.0636666	0.0318333	−	0.999493i	$-0.489865\pi$
$263$	1.03250	0.0636666	0.0318333	+	0.999493i	$0.489865\pi$
$264$	−1.46706	−0.0902912
$265$	0.0693479	0.00426001
$266$	−4.19256	−0.257062
$267$	−1.63607	−0.100126
$268$	−10.6365	−0.649728
$269$	−14.8314	−0.904289	−0.452144	−	0.891945i	$-0.649341\pi$
$269$	−14.8314	−0.904289	−0.452144	+	0.891945i	$0.649341\pi$
$270$	−0.0883883	−0.00537914
$271$	−17.0836	−1.03776	−0.518878	−	0.854848i	$-0.673650\pi$
$271$	−17.0836	−1.03776	−0.518878	+	0.854848i	$0.673650\pi$
$272$	1.01419	0.0614942
$273$	−3.81246	−0.230741
$274$	−2.60361	−0.157290
$275$	24.1660	1.45726
$276$	0.303391	0.0182620
$277$	−30.5888	−1.83790	−0.918950	−	0.394373i	$-0.870962\pi$
$277$	−30.5888	−1.83790	−0.918950	+	0.394373i	$0.870962\pi$
$278$	−4.31577	−0.258842
$279$	27.4125	1.64114
$280$	0.113076	0.00675759
$281$	13.2412	0.789904	0.394952	−	0.918702i	$-0.370761\pi$
$281$	13.2412	0.789904	0.394952	+	0.918702i	$0.370761\pi$
$282$	2.30790	0.137434
$283$	−25.8430	−1.53621	−0.768104	−	0.640325i	$-0.778800\pi$
$283$	−25.8430	−1.53621	−0.768104	+	0.640325i	$0.778800\pi$
$284$	−10.9283	−0.648475
$285$	0.0273540	0.00162031
$286$	−26.4992	−1.56693
$287$	20.2606	1.19595
$288$	2.90795	0.171353
$289$	−15.9714	−0.939495
$290$	−0.0974193	−0.00572066
$291$	0.139337	0.00816809
$292$	−7.54117	−0.441313
$293$	−3.15708	−0.184438	−0.0922192	−	0.995739i	$-0.529396\pi$
$293$	−3.15708	−0.184438	−0.0922192	+	0.995739i	$0.529396\pi$
$294$	−0.528469	−0.0308209
$295$	0.204920	0.0119309
$296$	−2.10519	−0.122362
$297$	−8.66732	−0.502929
$298$	14.3267	0.829923
$299$	5.48009	0.316922
$300$	1.51622	0.0875387
$301$	7.94566	0.457980
$302$	−8.25270	−0.474889
$303$	4.75365	0.273090
$304$	−1.82837	−0.104864
$305$	−0.699752	−0.0400677
$306$	2.94921	0.168595
$307$	22.4053	1.27874	0.639370	−	0.768899i	$-0.279195\pi$
$307$	22.4053	1.27874	0.639370	+	0.768899i	$0.279195\pi$
$308$	11.0882	0.631809
$309$	3.11495	0.177204
$310$	0.464854	0.0264019
$311$	−22.6680	−1.28538	−0.642692	−	0.766125i	$-0.722182\pi$
$311$	−22.6680	−1.28538	−0.642692	+	0.766125i	$0.722182\pi$
$312$	−1.66261	−0.0941266
$313$	−9.88169	−0.558546	−0.279273	−	0.960212i	$-0.590093\pi$
$313$	−9.88169	−0.558546	−0.279273	+	0.960212i	$0.590093\pi$
$314$	−7.87890	−0.444632
$315$	0.328820	0.0185269
$316$	0.850972	0.0478709
$317$	−11.6932	−0.656754	−0.328377	−	0.944547i	$-0.606502\pi$
$317$	−11.6932	−0.656754	−0.328377	+	0.944547i	$0.606502\pi$
$318$	0.426658	0.0239258
$319$	−9.55289	−0.534859
$320$	0.0493123	0.00275664
$321$	−2.69828	−0.150603
$322$	−2.29306	−0.127787
$323$	−1.85431	−0.103177
$324$	8.18006	0.454448
$325$	27.3871	1.51916
$326$	4.16377	0.230610
$327$	−5.37506	−0.297242
$328$	8.83563	0.487866
$329$	−17.4434	−0.961686
$330$	−0.0723441	−0.00398241
$331$	30.8171	1.69386	0.846930	−	0.531705i	$-0.178448\pi$
$331$	30.8171	1.69386	0.846930	+	0.531705i	$0.178448\pi$
$332$	−5.36345	−0.294357
$333$	−6.12181	−0.335473
$334$	−8.86668	−0.485163
$335$	−0.524510	−0.0286571
$336$	0.695693	0.0379532
$337$	−25.5279	−1.39060	−0.695298	−	0.718722i	$-0.744728\pi$
$337$	−25.5279	−1.39060	−0.695298	+	0.718722i	$0.744728\pi$
$338$	−17.0314	−0.926386
$339$	5.41287	0.293987
$340$	0.0500119	0.00271228
$341$	45.5834	2.46848
$342$	−5.31682	−0.287500
$343$	20.0456	1.08236
$344$	3.46509	0.186825
$345$	0.0149609	0.000805468 0
$346$	5.33733	0.286936
$347$	27.1754	1.45885	0.729427	−	0.684059i	$-0.239787\pi$
$347$	27.1754	1.45885	0.729427	+	0.684059i	$0.239787\pi$
$348$	−0.599365	−0.0321293
$349$	30.0849	1.61041	0.805203	−	0.592999i	$-0.202056\pi$
$349$	30.0849	1.61041	0.805203	+	0.592999i	$0.202056\pi$
$350$	−11.4597	−0.612548
$351$	−9.82261	−0.524292
$352$	4.83555	0.257735
$353$	1.26897	0.0675403	0.0337701	−	0.999430i	$-0.489249\pi$
$353$	1.26897	0.0675403	0.0337701	+	0.999430i	$0.489249\pi$
$354$	1.26075	0.0670084
$355$	−0.538900	−0.0286018
$356$	5.39264	0.285809
$357$	0.705563	0.0373424
$358$	−13.7373	−0.726041
$359$	2.78173	0.146814	0.0734070	−	0.997302i	$-0.476613\pi$
$359$	2.78173	0.146814	0.0734070	+	0.997302i	$0.476613\pi$
$360$	0.143398	0.00755774
$361$	−15.6571	−0.824056
$362$	−22.0779	−1.16039
$363$	−3.75673	−0.197177
$364$	12.5662	0.658647
$365$	−0.371872	−0.0194647
$366$	−4.30518	−0.225035
$367$	12.9527	0.676128	0.338064	−	0.941123i	$-0.390228\pi$
$367$	12.9527	0.676128	0.338064	+	0.941123i	$0.390228\pi$
$368$	−1.00000	−0.0521286
$369$	25.6936	1.33756
$370$	−0.103812	−0.00539693
$371$	−3.22473	−0.167420
$372$	2.85998	0.148283
$373$	22.0923	1.14389	0.571947	−	0.820290i	$-0.306188\pi$
$373$	22.0923	1.14389	0.571947	+	0.820290i	$0.306188\pi$
$374$	4.90415	0.253588
$375$	0.149573	0.00772389
$376$	−7.60704	−0.392303
$377$	−10.8262	−0.557579
$378$	4.11012	0.211402
$379$	−34.4965	−1.77197	−0.885983	−	0.463718i	$-0.846515\pi$
$379$	−34.4965	−1.77197	−0.885983	+	0.463718i	$0.846515\pi$
$380$	−0.0901612	−0.00462517
$381$	−5.78879	−0.296569
$382$	17.1122	0.875535
$383$	9.57256	0.489135	0.244567	−	0.969632i	$-0.421354\pi$
$383$	9.57256	0.489135	0.244567	+	0.969632i	$0.421354\pi$
$384$	0.303391	0.0154823
$385$	0.546785	0.0278667
$386$	−20.2772	−1.03208
$387$	10.0763	0.512208
$388$	−0.459267	−0.0233157
$389$	0.343192	0.0174005	0.00870025	−	0.999962i	$-0.497231\pi$
$389$	0.343192	0.0174005	0.00870025	+	0.999962i	$0.497231\pi$
$390$	−0.0819871	−0.00415158
$391$	−1.01419	−0.0512897
$392$	1.74188	0.0879780
$393$	−0.303391	−0.0153040
$394$	16.1605	0.814153
$395$	0.0419634	0.00211141
$396$	14.0615	0.706619
$397$	−11.4402	−0.574169	−0.287084	−	0.957905i	$-0.592686\pi$
$397$	−11.4402	−0.574169	−0.287084	+	0.957905i	$0.592686\pi$
$398$	−17.9621	−0.900357
$399$	−1.27198	−0.0636788
$400$	−4.99757	−0.249878
$401$	−8.87998	−0.443445	−0.221723	−	0.975110i	$-0.571168\pi$
$401$	−8.87998	−0.443445	−0.221723	+	0.975110i	$0.571168\pi$
$402$	−3.22701	−0.160949
$403$	51.6593	2.57333
$404$	−15.6684	−0.779533
$405$	0.403378	0.0200440
$406$	4.53007	0.224824
$407$	−10.1798	−0.504592
$408$	0.307695	0.0152332
$409$	−20.5079	−1.01405	−0.507025	−	0.861931i	$-0.669255\pi$
$409$	−20.5079	−1.01405	−0.507025	+	0.861931i	$0.669255\pi$
$410$	0.435705	0.0215179
$411$	−0.789911	−0.0389634
$412$	−10.2671	−0.505826
$413$	−9.52892	−0.468888
$414$	−2.90795	−0.142918
$415$	−0.264484	−0.0129830
$416$	5.48009	0.268684
$417$	−1.30936	−0.0641198
$418$	−8.84116	−0.432435
$419$	4.59806	0.224630	0.112315	−	0.993673i	$-0.464173\pi$
$419$	4.59806	0.224630	0.112315	+	0.993673i	$0.464173\pi$
$420$	0.0343062	0.00167397
$421$	23.4290	1.14186	0.570929	−	0.820999i	$-0.306583\pi$
$421$	23.4290	1.14186	0.570929	+	0.820999i	$0.306583\pi$
$422$	11.9549	0.581955
$423$	−22.1209	−1.07556
$424$	−1.40630	−0.0682959
$425$	−5.06847	−0.245857
$426$	−3.31554	−0.160639
$427$	32.5390	1.57467
$428$	8.89376	0.429896
$429$	−8.03962	−0.388156
$430$	0.170872	0.00824017
$431$	2.61691	0.126052	0.0630259	−	0.998012i	$-0.479925\pi$
$431$	2.61691	0.126052	0.0630259	+	0.998012i	$0.479925\pi$
$432$	1.79242	0.0862377
$433$	−24.4886	−1.17685	−0.588423	−	0.808553i	$-0.700251\pi$
$433$	−24.4886	−1.17685	−0.588423	+	0.808553i	$0.700251\pi$
$434$	−21.6160	−1.03760
$435$	−0.0295561	−0.00141711
$436$	17.7166	0.848473
$437$	1.82837	0.0874628
$438$	−2.28792	−0.109321
$439$	−26.2291	−1.25185	−0.625924	−	0.779884i	$-0.715278\pi$
$439$	−26.2291	−1.25185	−0.625924	+	0.779884i	$0.715278\pi$
$440$	0.238452	0.0113678
$441$	5.06530	0.241205
$442$	5.55784	0.264360
$443$	−26.6077	−1.26417	−0.632085	−	0.774899i	$-0.717801\pi$
$443$	−26.6077	−1.26417	−0.632085	+	0.774899i	$0.717801\pi$
$444$	−0.638696	−0.0303112
$445$	0.265923	0.0126060
$446$	−11.7778	−0.557695
$447$	4.34658	0.205586
$448$	−2.29306	−0.108337
$449$	35.3211	1.66691	0.833453	−	0.552591i	$-0.186361\pi$
$449$	35.3211	1.66691	0.833453	+	0.552591i	$0.186361\pi$
$450$	−14.5327	−0.685078
$451$	42.7251	2.01184
$452$	−17.8413	−0.839182
$453$	−2.50379	−0.117638
$454$	26.2986	1.23425
$455$	0.619667	0.0290505
$456$	−0.554710	−0.0259767
$457$	18.8060	0.879708	0.439854	−	0.898069i	$-0.355030\pi$
$457$	18.8060	0.879708	0.439854	+	0.898069i	$0.355030\pi$
$458$	25.1776	1.17647
$459$	1.81785	0.0848499
$460$	−0.0493123	−0.00229920
$461$	40.8937	1.90461	0.952304	−	0.305150i	$-0.0987066\pi$
$461$	40.8937	1.90461	0.952304	+	0.305150i	$0.0987066\pi$
$462$	3.36405	0.156510
$463$	−17.2288	−0.800691	−0.400345	−	0.916364i	$-0.631110\pi$
$463$	−17.2288	−0.800691	−0.400345	+	0.916364i	$0.631110\pi$
$464$	1.97556	0.0917129
$465$	0.141032	0.00654021
$466$	−8.44130	−0.391036
$467$	−32.8361	−1.51947	−0.759737	−	0.650231i	$-0.774672\pi$
$467$	−32.8361	−1.51947	−0.759737	+	0.650231i	$0.774672\pi$
$468$	15.9359	0.736635
$469$	24.3901	1.12623
$470$	−0.375121	−0.0173030
$471$	−2.39038	−0.110143
$472$	−4.15555	−0.191275
$473$	16.7556	0.770424
$474$	0.258177	0.0118585
$475$	9.13740	0.419253
$476$	−2.32559	−0.106593
$477$	−4.08945	−0.187243
$478$	−14.5017	−0.663290
$479$	3.86764	0.176717	0.0883586	−	0.996089i	$-0.471838\pi$
$479$	3.86764	0.176717	0.0883586	+	0.996089i	$0.471838\pi$
$480$	0.0149609	0.000682868 0
$481$	−11.5367	−0.526026
$482$	−3.56989	−0.162604
$483$	−0.695693	−0.0316551
$484$	12.3825	0.562841
$485$	−0.0226475	−0.00102837
$486$	7.85901	0.356492
$487$	−28.9045	−1.30979	−0.654893	−	0.755721i	$-0.727286\pi$
$487$	−28.9045	−1.30979	−0.654893	+	0.755721i	$0.727286\pi$
$488$	14.1902	0.642361
$489$	1.26325	0.0571261
$490$	0.0858959	0.00388038
$491$	13.0250	0.587810	0.293905	−	0.955835i	$-0.405045\pi$
$491$	13.0250	0.587810	0.293905	+	0.955835i	$0.405045\pi$
$492$	2.68065	0.120853
$493$	2.00358	0.0902369
$494$	−10.0196	−0.450805
$495$	0.693407	0.0311663
$496$	−9.42673	−0.423273
$497$	25.0592	1.12406
$498$	−1.62722	−0.0729175
$499$	36.2182	1.62135	0.810674	−	0.585498i	$-0.199101\pi$
$499$	36.2182	1.62135	0.810674	+	0.585498i	$0.199101\pi$
$500$	−0.493003	−0.0220478
$501$	−2.69007	−0.120183
$502$	15.5630	0.694612
$503$	0.980285	0.0437088	0.0218544	−	0.999761i	$-0.493043\pi$
$503$	0.980285	0.0437088	0.0218544	+	0.999761i	$0.493043\pi$
$504$	−6.66811	−0.297021
$505$	−0.772646	−0.0343823
$506$	−4.83555	−0.214966
$507$	−5.16717	−0.229482
$508$	19.0803	0.846552
$509$	24.8235	1.10028	0.550141	−	0.835072i	$-0.314574\pi$
$509$	24.8235	1.10028	0.550141	+	0.835072i	$0.314574\pi$
$510$	0.0151732	0.000671879 0
$511$	17.2923	0.764968
$512$	−1.00000	−0.0441942
$513$	−3.27720	−0.144692
$514$	22.0007	0.970408
$515$	−0.506297	−0.0223101
$516$	1.05128	0.0462799
$517$	−36.7842	−1.61777
$518$	4.82734	0.212101
$519$	1.61929	0.0710791
$520$	0.270236	0.0118506
$521$	−3.19276	−0.139877	−0.0699386	−	0.997551i	$-0.522280\pi$
$521$	−3.19276	−0.139877	−0.0699386	+	0.997551i	$0.522280\pi$
$522$	5.74483	0.251444
$523$	13.2464	0.579224	0.289612	−	0.957144i	$-0.406474\pi$
$523$	13.2464	0.579224	0.289612	+	0.957144i	$0.406474\pi$
$524$	1.00000	0.0436852
$525$	−3.47677	−0.151739
$526$	−1.03250	−0.0450191
$527$	−9.56047	−0.416461
$528$	1.46706	0.0638455
$529$	1.00000	0.0434783
$530$	−0.0693479	−0.00301228
$531$	−12.0841	−0.524407
$532$	4.19256	0.181771
$533$	48.4200	2.09730
$534$	1.63607	0.0707999
$535$	0.438572	0.0189611
$536$	10.6365	0.459427
$537$	−4.16778	−0.179853
$538$	14.8314	0.639429
$539$	8.42292	0.362801
$540$	0.0883883	0.00380363
$541$	−38.6101	−1.65998	−0.829989	−	0.557780i	$-0.811653\pi$
$541$	−38.6101	−1.65998	−0.829989	+	0.557780i	$0.811653\pi$
$542$	17.0836	0.733805
$543$	−6.69821	−0.287448
$544$	−1.01419	−0.0434829
$545$	0.873649	0.0374230
$546$	3.81246	0.163158
$547$	−1.65570	−0.0707928	−0.0353964	−	0.999373i	$-0.511269\pi$
$547$	−1.65570	−0.0707928	−0.0353964	+	0.999373i	$0.511269\pi$
$548$	2.60361	0.111221
$549$	41.2645	1.76112
$550$	−24.1660	−1.03044
$551$	−3.61205	−0.153878
$552$	−0.303391	−0.0129132
$553$	−1.95133	−0.0829790
$554$	30.5888	1.29959
$555$	−0.0314956	−0.00133691
$556$	4.31577	0.183029
$557$	7.26610	0.307875	0.153937	−	0.988081i	$-0.450805\pi$
$557$	7.26610	0.307875	0.153937	+	0.988081i	$0.450805\pi$
$558$	−27.4125	−1.16046
$559$	18.9890	0.803150
$560$	−0.113076	−0.00477834
$561$	1.48787	0.0628180
$562$	−13.2412	−0.558546
$563$	−32.9324	−1.38793	−0.693967	−	0.720007i	$-0.744138\pi$
$563$	−32.9324	−1.38793	−0.693967	+	0.720007i	$0.744138\pi$
$564$	−2.30790	−0.0971803
$565$	−0.879794	−0.0370132
$566$	25.8430	1.08626
$567$	−18.7574	−0.787735
$568$	10.9283	0.458541
$569$	−26.6975	−1.11922	−0.559608	−	0.828757i	$-0.689048\pi$
$569$	−26.6975	−1.11922	−0.559608	+	0.828757i	$0.689048\pi$
$570$	−0.0273540	−0.00114573
$571$	24.6547	1.03177	0.515883	−	0.856659i	$-0.327464\pi$
$571$	24.6547	1.03177	0.515883	+	0.856659i	$0.327464\pi$
$572$	26.4992	1.10799
$573$	5.19167	0.216885
$574$	−20.2606	−0.845662
$575$	4.99757	0.208413
$576$	−2.90795	−0.121165
$577$	−6.14102	−0.255654	−0.127827	−	0.991796i	$-0.540800\pi$
$577$	−6.14102	−0.255654	−0.127827	+	0.991796i	$0.540800\pi$
$578$	15.9714	0.664324
$579$	−6.15190	−0.255664
$580$	0.0974193	0.00404512
$581$	12.2987	0.510236
$582$	−0.139337	−0.00577571
$583$	−6.80022	−0.281636
$584$	7.54117	0.312056
$585$	0.785834	0.0324902
$586$	3.15708	0.130418
$587$	16.1473	0.666471	0.333235	−	0.942844i	$-0.391860\pi$
$587$	16.1473	0.666471	0.333235	+	0.942844i	$0.391860\pi$
$588$	0.528469	0.0217937
$589$	17.2355	0.710178
$590$	−0.204920	−0.00843641
$591$	4.90294	0.201680
$592$	2.10519	0.0865230
$593$	24.6307	1.01146	0.505732	−	0.862691i	$-0.331223\pi$
$593$	24.6307	1.01146	0.505732	+	0.862691i	$0.331223\pi$
$594$	8.66732	0.355624
$595$	−0.114680	−0.00470144
$596$	−14.3267	−0.586844
$597$	−5.44952	−0.223034
$598$	−5.48009	−0.224098
$599$	−4.70072	−0.192066	−0.0960331	−	0.995378i	$-0.530615\pi$
$599$	−4.70072	−0.192066	−0.0960331	+	0.995378i	$0.530615\pi$
$600$	−1.51622	−0.0618992
$601$	−12.1603	−0.496028	−0.248014	−	0.968756i	$-0.579778\pi$
$601$	−12.1603	−0.496028	−0.248014	+	0.968756i	$0.579778\pi$
$602$	−7.94566	−0.323841
$603$	30.9304	1.25959
$604$	8.25270	0.335798
$605$	0.610610	0.0248248
$606$	−4.75365	−0.193104
$607$	25.0852	1.01818	0.509088	−	0.860714i	$-0.329983\pi$
$607$	25.0852	1.01818	0.509088	+	0.860714i	$0.329983\pi$
$608$	1.82837	0.0741502
$609$	1.37438	0.0556927
$610$	0.699752	0.0283321
$611$	−41.6873	−1.68649
$612$	−2.94921	−0.119215
$613$	−10.2819	−0.415283	−0.207642	−	0.978205i	$-0.566579\pi$
$613$	−10.2819	−0.415283	−0.207642	+	0.978205i	$0.566579\pi$
$614$	−22.4053	−0.904206
$615$	0.132189	0.00533037
$616$	−11.0882	−0.446756
$617$	−31.2048	−1.25626	−0.628129	−	0.778110i	$-0.716179\pi$
$617$	−31.2048	−1.25626	−0.628129	+	0.778110i	$0.716179\pi$
$618$	−3.11495	−0.125302
$619$	7.82034	0.314326	0.157163	−	0.987573i	$-0.449765\pi$
$619$	7.82034	0.314326	0.157163	+	0.987573i	$0.449765\pi$
$620$	−0.464854	−0.0186690
$621$	−1.79242	−0.0719272
$622$	22.6680	0.908903
$623$	−12.3656	−0.495419
$624$	1.66261	0.0665576
$625$	24.9635	0.998541
$626$	9.88169	0.394952
$627$	−2.68233	−0.107122
$628$	7.87890	0.314402
$629$	2.13506	0.0851305
$630$	−0.328820	−0.0131005
$631$	2.13651	0.0850533	0.0425266	−	0.999095i	$-0.486459\pi$
$631$	2.13651	0.0850533	0.0425266	+	0.999095i	$0.486459\pi$
$632$	−0.850972	−0.0338498
$633$	3.62700	0.144160
$634$	11.6932	0.464395
$635$	0.940894	0.0373383
$636$	−0.426658	−0.0169181
$637$	9.54564	0.378212
$638$	9.55289	0.378203
$639$	31.7790	1.25716
$640$	−0.0493123	−0.00194924
$641$	−43.5946	−1.72188	−0.860941	−	0.508705i	$-0.830124\pi$
$641$	−43.5946	−1.72188	−0.860941	+	0.508705i	$0.830124\pi$
$642$	2.69828	0.106493
$643$	−14.9494	−0.589548	−0.294774	−	0.955567i	$-0.595244\pi$
$643$	−14.9494	−0.589548	−0.294774	+	0.955567i	$0.595244\pi$
$644$	2.29306	0.0903592
$645$	0.0518409	0.00204123
$646$	1.85431	0.0729568
$647$	−31.1189	−1.22341	−0.611705	−	0.791086i	$-0.709516\pi$
$647$	−31.1189	−1.22341	−0.611705	+	0.791086i	$0.709516\pi$
$648$	−8.18006	−0.321343
$649$	−20.0943	−0.788772
$650$	−27.3871	−1.07421
$651$	−6.55811	−0.257032
$652$	−4.16377	−0.163066
$653$	−33.9058	−1.32684	−0.663419	−	0.748248i	$-0.730895\pi$
$653$	−33.9058	−1.32684	−0.663419	+	0.748248i	$0.730895\pi$
$654$	5.37506	0.210182
$655$	0.0493123	0.00192679
$656$	−8.83563	−0.344973
$657$	21.9294	0.855546
$658$	17.4434	0.680014
$659$	42.5907	1.65910	0.829549	−	0.558434i	$-0.188597\pi$
$659$	42.5907	1.65910	0.829549	+	0.558434i	$0.188597\pi$
$660$	0.0723441	0.00281599
$661$	−10.3663	−0.403201	−0.201600	−	0.979468i	$-0.564614\pi$
$661$	−10.3663	−0.403201	−0.201600	+	0.979468i	$0.564614\pi$
$662$	−30.8171	−1.19774
$663$	1.68620	0.0654865
$664$	5.36345	0.208142
$665$	0.206745	0.00801722
$666$	6.12181	0.237215
$667$	−1.97556	−0.0764939
$668$	8.86668	0.343062
$669$	−3.57328	−0.138151
$670$	0.524510	0.0202636
$671$	68.6174	2.64895
$672$	−0.695693	−0.0268369
$673$	13.6344	0.525566	0.262783	−	0.964855i	$-0.415360\pi$
$673$	13.6344	0.525566	0.262783	+	0.964855i	$0.415360\pi$
$674$	25.5279	0.983300
$675$	−8.95773	−0.344783
$676$	17.0314	0.655054
$677$	9.32887	0.358538	0.179269	−	0.983800i	$-0.442627\pi$
$677$	9.32887	0.358538	0.179269	+	0.983800i	$0.442627\pi$
$678$	−5.41287	−0.207880
$679$	1.05313	0.0404153
$680$	−0.0500119	−0.00191787
$681$	7.97875	0.305746
$682$	−45.5834	−1.74548
$683$	11.4650	0.438696	0.219348	−	0.975647i	$-0.429607\pi$
$683$	11.4650	0.438696	0.219348	+	0.975647i	$0.429607\pi$
$684$	5.31682	0.203294
$685$	0.128390	0.00490553
$686$	−20.0456	−0.765346
$687$	7.63864	0.291432
$688$	−3.46509	−0.132105
$689$	−7.70665	−0.293600
$690$	−0.0149609	−0.000569552 0
$691$	16.9058	0.643128	0.321564	−	0.946888i	$-0.395791\pi$
$691$	16.9058	0.643128	0.321564	+	0.946888i	$0.395791\pi$
$692$	−5.33733	−0.202895
$693$	−32.2440	−1.22485
$694$	−27.1754	−1.03157
$695$	0.212820	0.00807274
$696$	0.599365	0.0227189
$697$	−8.96098	−0.339421
$698$	−30.0849	−1.13873
$699$	−2.56101	−0.0968663
$700$	11.4597	0.433137
$701$	−40.5541	−1.53171	−0.765854	−	0.643015i	$-0.777683\pi$
$701$	−40.5541	−1.53171	−0.765854	+	0.643015i	$0.777683\pi$
$702$	9.82261	0.370731
$703$	−3.84907	−0.145171
$704$	−4.83555	−0.182246
$705$	−0.113808	−0.00428626
$706$	−1.26897	−0.0477582
$707$	35.9286	1.35123
$708$	−1.26075	−0.0473821
$709$	32.9831	1.23871	0.619353	−	0.785113i	$-0.287395\pi$
$709$	32.9831	1.23871	0.619353	+	0.785113i	$0.287395\pi$
$710$	0.538900	0.0202245
$711$	−2.47459	−0.0928043
$712$	−5.39264	−0.202098
$713$	9.42673	0.353034
$714$	−0.705563	−0.0264050
$715$	1.30674	0.0488692
$716$	13.7373	0.513389
$717$	−4.39967	−0.164309
$718$	−2.78173	−0.103813
$719$	0.852064	0.0317766	0.0158883	−	0.999874i	$-0.494942\pi$
$719$	0.852064	0.0317766	0.0158883	+	0.999874i	$0.494942\pi$
$720$	−0.143398	−0.00534413
$721$	23.5432	0.876794
$722$	15.6571	0.582696
$723$	−1.08307	−0.0402799
$724$	22.0779	0.820517
$725$	−9.87298	−0.366673
$726$	3.75673	0.139425
$727$	44.3318	1.64417	0.822087	−	0.569362i	$-0.192810\pi$
$727$	44.3318	1.64417	0.822087	+	0.569362i	$0.192810\pi$
$728$	−12.5662	−0.465734
$729$	−22.1558	−0.820586
$730$	0.371872	0.0137636
$731$	−3.51425	−0.129979
$732$	4.30518	0.159124
$733$	−36.8836	−1.36233	−0.681163	−	0.732132i	$-0.738525\pi$
$733$	−36.8836	−1.36233	−0.681163	+	0.732132i	$0.738525\pi$
$734$	−12.9527	−0.478095
$735$	0.0260600	0.000961238 0
$736$	1.00000	0.0368605
$737$	51.4333	1.89457
$738$	−25.6936	−0.945794
$739$	22.2067	0.816888	0.408444	−	0.912783i	$-0.366072\pi$
$739$	22.2067	0.816888	0.408444	+	0.912783i	$0.366072\pi$
$740$	0.103812	0.00381621
$741$	−3.03986	−0.111672
$742$	3.22473	0.118383
$743$	−49.6339	−1.82089	−0.910446	−	0.413629i	$-0.864261\pi$
$743$	−49.6339	−1.82089	−0.910446	+	0.413629i	$0.864261\pi$
$744$	−2.85998	−0.104852
$745$	−0.706483	−0.0258835
$746$	−22.0923	−0.808855
$747$	15.5967	0.570652
$748$	−4.90415	−0.179313
$749$	−20.3939	−0.745177
$750$	−0.149573	−0.00546162
$751$	39.4441	1.43934	0.719668	−	0.694318i	$-0.244294\pi$
$751$	39.4441	1.43934	0.719668	+	0.694318i	$0.244294\pi$
$752$	7.60704	0.277400
$753$	4.72168	0.172068
$754$	10.8262	0.394268
$755$	0.406960	0.0148108
$756$	−4.11012	−0.149484
$757$	−24.2218	−0.880356	−0.440178	−	0.897911i	$-0.645085\pi$
$757$	−24.2218	−0.880356	−0.440178	+	0.897911i	$0.645085\pi$
$758$	34.4965	1.25297
$759$	−1.46706	−0.0532509
$760$	0.0901612	0.00327049
$761$	−30.8126	−1.11696	−0.558479	−	0.829519i	$-0.688615\pi$
$761$	−30.8126	−1.11696	−0.558479	+	0.829519i	$0.688615\pi$
$762$	5.78879	0.209706
$763$	−40.6253	−1.47074
$764$	−17.1122	−0.619097
$765$	−0.145432	−0.00525812
$766$	−9.57256	−0.345871
$767$	−22.7728	−0.822278
$768$	−0.303391	−0.0109477
$769$	31.8092	1.14707	0.573534	−	0.819182i	$-0.305572\pi$
$769$	31.8092	1.14707	0.573534	+	0.819182i	$0.305572\pi$
$770$	−0.546785	−0.0197048
$771$	6.67480	0.240387
$772$	20.2772	0.729791
$773$	−1.51961	−0.0546567	−0.0273283	−	0.999627i	$-0.508700\pi$
$773$	−1.51961	−0.0546567	−0.0273283	+	0.999627i	$0.508700\pi$
$774$	−10.0763	−0.362186
$775$	47.1107	1.69227
$776$	0.459267	0.0164867
$777$	1.46457	0.0525411
$778$	−0.343192	−0.0123040
$779$	16.1548	0.578805
$780$	0.0819871	0.00293561
$781$	52.8443	1.89092
$782$	1.01419	0.0362673
$783$	3.54102	0.126546
$784$	−1.74188	−0.0622099
$785$	0.388527	0.0138671
$786$	0.303391	0.0108216
$787$	−34.9444	−1.24563	−0.622817	−	0.782368i	$-0.714012\pi$
$787$	−34.9444	−1.24563	−0.622817	+	0.782368i	$0.714012\pi$
$788$	−16.1605	−0.575693
$789$	−0.313251	−0.0111520
$790$	−0.0419634	−0.00149299
$791$	40.9111	1.45463
$792$	−14.0615	−0.499655
$793$	77.7636	2.76147
$794$	11.4402	0.405998
$795$	−0.0210395	−0.000746194 0
$796$	17.9621	0.636648
$797$	−14.6989	−0.520663	−0.260332	−	0.965519i	$-0.583832\pi$
$797$	−14.6989	−0.520663	−0.260332	+	0.965519i	$0.583832\pi$
$798$	1.27198	0.0450277
$799$	7.71497	0.272936
$800$	4.99757	0.176691
$801$	−15.6815	−0.554080
$802$	8.87998	0.313563
$803$	36.4656	1.28684
$804$	3.22701	0.113808
$805$	0.113076	0.00398541
$806$	−51.6593	−1.81962
$807$	4.49972	0.158398
$808$	15.6684	0.551213
$809$	−42.0503	−1.47841	−0.739205	−	0.673480i	$-0.764799\pi$
$809$	−42.0503	−1.47841	−0.739205	+	0.673480i	$0.764799\pi$
$810$	−0.403378	−0.0141732
$811$	6.11707	0.214799	0.107400	−	0.994216i	$-0.465748\pi$
$811$	6.11707	0.214799	0.107400	+	0.994216i	$0.465748\pi$
$812$	−4.53007	−0.158974
$813$	5.18301	0.181776
$814$	10.1798	0.356801
$815$	−0.205325	−0.00719223
$816$	−0.307695	−0.0107715
$817$	6.33547	0.221650
$818$	20.5079	0.717041
$819$	−36.5419	−1.27688
$820$	−0.435705	−0.0152155
$821$	−32.5379	−1.13558	−0.567791	−	0.823173i	$-0.692202\pi$
$821$	−32.5379	−1.13558	−0.567791	+	0.823173i	$0.692202\pi$
$822$	0.789911	0.0275513
$823$	−51.7303	−1.80320	−0.901602	−	0.432567i	$-0.857608\pi$
$823$	−51.7303	−1.80320	−0.901602	+	0.432567i	$0.857608\pi$
$824$	10.2671	0.357673
$825$	−7.33173	−0.255258
$826$	9.52892	0.331554
$827$	−26.2551	−0.912981	−0.456490	−	0.889728i	$-0.650894\pi$
$827$	−26.2551	−0.912981	−0.456490	+	0.889728i	$0.650894\pi$
$828$	2.90795	0.101058
$829$	−33.1849	−1.15256	−0.576280	−	0.817252i	$-0.695496\pi$
$829$	−33.1849	−1.15256	−0.576280	+	0.817252i	$0.695496\pi$
$830$	0.264484	0.00918038
$831$	9.28034	0.321932
$832$	−5.48009	−0.189988
$833$	−1.76659	−0.0612087
$834$	1.30936	0.0453395
$835$	0.437237	0.0151312
$836$	8.84116	0.305778
$837$	−16.8966	−0.584033
$838$	−4.59806	−0.158837
$839$	−20.7194	−0.715314	−0.357657	−	0.933853i	$-0.616424\pi$
$839$	−20.7194	−0.715314	−0.357657	+	0.933853i	$0.616424\pi$
$840$	−0.0343062	−0.00118368
$841$	−25.0972	−0.865420
$842$	−23.4290	−0.807416
$843$	−4.01726	−0.138362
$844$	−11.9549	−0.411505
$845$	0.839858	0.0288920
$846$	22.1209	0.760533
$847$	−28.3938	−0.975623
$848$	1.40630	0.0482925
$849$	7.84053	0.269086
$850$	5.06847	0.173847
$851$	−2.10519	−0.0721651
$852$	3.31554	0.113589
$853$	−55.2601	−1.89207	−0.946035	−	0.324066i	$-0.894950\pi$
$853$	−55.2601	−1.89207	−0.946035	+	0.324066i	$0.894950\pi$
$854$	−32.5390	−1.11346
$855$	0.262185	0.00896652
$856$	−8.89376	−0.303982
$857$	−42.0304	−1.43573	−0.717866	−	0.696181i	$-0.754881\pi$
$857$	−42.0304	−1.43573	−0.717866	+	0.696181i	$0.754881\pi$
$858$	8.03962	0.274468
$859$	37.0983	1.26578	0.632888	−	0.774243i	$-0.281869\pi$
$859$	37.0983	1.26578	0.632888	+	0.774243i	$0.281869\pi$
$860$	−0.170872	−0.00582668
$861$	−6.14688	−0.209485
$862$	−2.61691	−0.0891322
$863$	0.245583	0.00835976	0.00417988	−	0.999991i	$-0.498669\pi$
$863$	0.245583	0.00835976	0.00417988	+	0.999991i	$0.498669\pi$
$864$	−1.79242	−0.0609793
$865$	−0.263196	−0.00894893
$866$	24.4886	0.832156
$867$	4.84558	0.164565
$868$	21.6160	0.733697
$869$	−4.11491	−0.139589
$870$	0.0295561	0.00100205
$871$	58.2890	1.97505
$872$	−17.7166	−0.599961
$873$	1.33553	0.0452007
$874$	−1.82837	−0.0618455
$875$	1.13049	0.0382174
$876$	2.28792	0.0773016
$877$	31.1652	1.05238	0.526188	−	0.850368i	$-0.323621\pi$
$877$	31.1652	1.05238	0.526188	+	0.850368i	$0.323621\pi$
$878$	26.2291	0.885190
$879$	0.957828	0.0323067
$880$	−0.238452	−0.00803821
$881$	37.1804	1.25264	0.626319	−	0.779567i	$-0.284561\pi$
$881$	37.1804	1.25264	0.626319	+	0.779567i	$0.284561\pi$
$882$	−5.06530	−0.170557
$883$	−35.2123	−1.18499	−0.592493	−	0.805575i	$-0.701856\pi$
$883$	−35.2123	−1.18499	−0.592493	+	0.805575i	$0.701856\pi$
$884$	−5.55784	−0.186930
$885$	−0.0621707	−0.00208985
$886$	26.6077	0.893904
$887$	1.00463	0.0337320	0.0168660	−	0.999858i	$-0.494631\pi$
$887$	1.00463	0.0337320	0.0168660	+	0.999858i	$0.494631\pi$
$888$	0.638696	0.0214332
$889$	−43.7523	−1.46740
$890$	−0.265923	−0.00891377
$891$	−39.5550	−1.32514
$892$	11.7778	0.394350
$893$	−13.9085	−0.465430
$894$	−4.34658	−0.145372
$895$	0.677421	0.0226437
$896$	2.29306	0.0766058
$897$	−1.66261	−0.0555129
$898$	−35.3211	−1.17868
$899$	−18.6230	−0.621113
$900$	14.5327	0.484423
$901$	1.42625	0.0475153
$902$	−42.7251	−1.42259
$903$	−2.41064	−0.0802211
$904$	17.8413	0.593392
$905$	1.08871	0.0361900
$906$	2.50379	0.0831829
$907$	−14.7771	−0.490667	−0.245333	−	0.969439i	$-0.578897\pi$
$907$	−14.7771	−0.490667	−0.245333	+	0.969439i	$0.578897\pi$
$908$	−26.2986	−0.872750
$909$	45.5630	1.51123
$910$	−0.619667	−0.0205418
$911$	−32.8900	−1.08969	−0.544846	−	0.838536i	$-0.683412\pi$
$911$	−32.8900	−1.08969	−0.544846	+	0.838536i	$0.683412\pi$
$912$	0.554710	0.0183683
$913$	25.9352	0.858330
$914$	−18.8060	−0.622048
$915$	0.212298	0.00701836
$916$	−25.1776	−0.831891
$917$	−2.29306	−0.0757235
$918$	−1.81785	−0.0599979
$919$	37.4142	1.23418	0.617090	−	0.786893i	$-0.288312\pi$
$919$	37.4142	1.23418	0.617090	+	0.786893i	$0.288312\pi$
$920$	0.0493123	0.00162578
$921$	−6.79757	−0.223987
$922$	−40.8937	−1.34676
$923$	59.8881	1.97124
$924$	−3.36405	−0.110669
$925$	−10.5209	−0.345924
$926$	17.2288	0.566174
$927$	29.8564	0.980612
$928$	−1.97556	−0.0648508
$929$	−43.5336	−1.42829	−0.714145	−	0.699998i	$-0.753184\pi$
$929$	−43.5336	−1.42829	−0.714145	+	0.699998i	$0.753184\pi$
$930$	−0.141032	−0.00462463
$931$	3.18479	0.104377
$932$	8.44130	0.276504
$933$	6.87725	0.225151
$934$	32.8361	1.07443
$935$	−0.241835	−0.00790885
$936$	−15.9359	−0.520880
$937$	−28.6733	−0.936715	−0.468357	−	0.883539i	$-0.655154\pi$
$937$	−28.6733	−0.936715	−0.468357	+	0.883539i	$0.655154\pi$
$938$	−24.3901	−0.796366
$939$	2.99801	0.0978364
$940$	0.375121	0.0122351
$941$	24.3791	0.794736	0.397368	−	0.917659i	$-0.369924\pi$
$941$	24.3791	0.794736	0.397368	+	0.917659i	$0.369924\pi$
$942$	2.39038	0.0778829
$943$	8.83563	0.287728
$944$	4.15555	0.135252
$945$	−0.202680	−0.00659317
$946$	−16.7556	−0.544772
$947$	5.69627	0.185104	0.0925519	−	0.995708i	$-0.470498\pi$
$947$	5.69627	0.185104	0.0925519	+	0.995708i	$0.470498\pi$
$948$	−0.258177	−0.00838519
$949$	41.3263	1.34151
$950$	−9.13740	−0.296456
$951$	3.54760	0.115039
$952$	2.32559	0.0753729
$953$	36.8983	1.19525	0.597627	−	0.801774i	$-0.296110\pi$
$953$	36.8983	1.19525	0.597627	+	0.801774i	$0.296110\pi$
$954$	4.08945	0.132401
$955$	−0.843841	−0.0273060
$956$	14.5017	0.469017
$957$	2.89826	0.0936874
$958$	−3.86764	−0.124958
$959$	−5.97023	−0.192789
$960$	−0.0149609	−0.000482861 0
$961$	57.8632	1.86655
$962$	11.5367	0.371957
$963$	−25.8626	−0.833412
$964$	3.56989	0.114978
$965$	0.999914	0.0321884
$966$	0.695693	0.0223835
$967$	4.94738	0.159097	0.0795485	−	0.996831i	$-0.474652\pi$
$967$	4.94738	0.159097	0.0795485	+	0.996831i	$0.474652\pi$
$968$	−12.3825	−0.397989
$969$	0.562580	0.0180727
$970$	0.0226475	0.000727168 0
$971$	−0.243267	−0.00780681	−0.00390341	−	0.999992i	$-0.501242\pi$
$971$	−0.243267	−0.00780681	−0.00390341	+	0.999992i	$0.501242\pi$
$972$	−7.85901	−0.252078
$973$	−9.89631	−0.317261
$974$	28.9045	0.926159
$975$	−8.30900	−0.266101
$976$	−14.1902	−0.454218
$977$	−46.3338	−1.48235	−0.741176	−	0.671311i	$-0.765731\pi$
$977$	−46.3338	−1.48235	−0.741176	+	0.671311i	$0.765731\pi$
$978$	−1.26325	−0.0403943
$979$	−26.0763	−0.833403
$980$	−0.0858959	−0.00274385
$981$	−51.5192	−1.64488
$982$	−13.0250	−0.415644
$983$	4.68685	0.149487	0.0747437	−	0.997203i	$-0.476186\pi$
$983$	4.68685	0.149487	0.0747437	+	0.997203i	$0.476186\pi$
$984$	−2.68065	−0.0854559
$985$	−0.796911	−0.0253917
$986$	−2.00358	−0.0638071
$987$	5.29216	0.168451
$988$	10.0196	0.318767
$989$	3.46509	0.110183
$990$	−0.693407	−0.0220379
$991$	46.0720	1.46352	0.731762	−	0.681560i	$-0.238698\pi$
$991$	46.0720	1.46352	0.731762	+	0.681560i	$0.238698\pi$
$992$	9.42673	0.299299
$993$	−9.34961	−0.296701
$994$	−25.0592	−0.794831
$995$	0.885751	0.0280802
$996$	1.62722	0.0515604
$997$	4.09904	0.129818	0.0649090	−	0.997891i	$-0.479324\pi$
$997$	4.09904	0.129818	0.0649090	+	0.997891i	$0.479324\pi$
$998$	−36.2182	−1.14647
$999$	3.77339	0.119385

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6026.2.a.l.1.16	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6026.2.a.l.1.16	✓	36	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -0.303391 q^{3} +1.00000 q^{4} +0.0493123 q^{5} +0.303391 q^{6} -2.29306 q^{7} -1.00000 q^{8} -2.90795 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -0.303391 q^{3} +1.00000 q^{4} +0.0493123 q^{5} +0.303391 q^{6} -2.29306 q^{7} -1.00000 q^{8} -2.90795 q^{9} -0.0493123 q^{10} -4.83555 q^{11} -0.303391 q^{12} -5.48009 q^{13} +2.29306 q^{14} -0.0149609 q^{15} +1.00000 q^{16} +1.01419 q^{17} +2.90795 q^{18} -1.82837 q^{19} +0.0493123 q^{20} +0.695693 q^{21} +4.83555 q^{22} -1.00000 q^{23} +0.303391 q^{24} -4.99757 q^{25} +5.48009 q^{26} +1.79242 q^{27} -2.29306 q^{28} +1.97556 q^{29} +0.0149609 q^{30} -9.42673 q^{31} -1.00000 q^{32} +1.46706 q^{33} -1.01419 q^{34} -0.113076 q^{35} -2.90795 q^{36} +2.10519 q^{37} +1.82837 q^{38} +1.66261 q^{39} -0.0493123 q^{40} -8.83563 q^{41} -0.695693 q^{42} -3.46509 q^{43} -4.83555 q^{44} -0.143398 q^{45} +1.00000 q^{46} +7.60704 q^{47} -0.303391 q^{48} -1.74188 q^{49} +4.99757 q^{50} -0.307695 q^{51} -5.48009 q^{52} +1.40630 q^{53} -1.79242 q^{54} -0.238452 q^{55} +2.29306 q^{56} +0.554710 q^{57} -1.97556 q^{58} +4.15555 q^{59} -0.0149609 q^{60} -14.1902 q^{61} +9.42673 q^{62} +6.66811 q^{63} +1.00000 q^{64} -0.270236 q^{65} -1.46706 q^{66} -10.6365 q^{67} +1.01419 q^{68} +0.303391 q^{69} +0.113076 q^{70} -10.9283 q^{71} +2.90795 q^{72} -7.54117 q^{73} -2.10519 q^{74} +1.51622 q^{75} -1.82837 q^{76} +11.0882 q^{77} -1.66261 q^{78} +0.850972 q^{79} +0.0493123 q^{80} +8.18006 q^{81} +8.83563 q^{82} -5.36345 q^{83} +0.695693 q^{84} +0.0500119 q^{85} +3.46509 q^{86} -0.599365 q^{87} +4.83555 q^{88} +5.39264 q^{89} +0.143398 q^{90} +12.5662 q^{91} -1.00000 q^{92} +2.85998 q^{93} -7.60704 q^{94} -0.0901612 q^{95} +0.303391 q^{96} -0.459267 q^{97} +1.74188 q^{98} +14.0615 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 36 q^{2} + 4 q^{3} + 36 q^{4} + q^{5} - 4 q^{6} + 13 q^{7} - 36 q^{8} + 46 q^{9}+O(q^{10}) \) 36 * q - 36 * q^2 + 4 * q^3 + 36 * q^4 + q^5 - 4 * q^6 + 13 * q^7 - 36 * q^8 + 46 * q^9	\( 36 q - 36 q^{2} + 4 q^{3} + 36 q^{4} + q^{5} - 4 q^{6} + 13 q^{7} - 36 q^{8} + 46 q^{9} - q^{10} + 14 q^{11} + 4 q^{12} + 4 q^{13} - 13 q^{14} + 10 q^{15} + 36 q^{16} - 4 q^{17} - 46 q^{18} + 29 q^{19} + q^{20} + 24 q^{21} - 14 q^{22} - 36 q^{23} - 4 q^{24} + 49 q^{25} - 4 q^{26} + 19 q^{27} + 13 q^{28} - 13 q^{29} - 10 q^{30} + 21 q^{31} - 36 q^{32} - 5 q^{33} + 4 q^{34} + 30 q^{35} + 46 q^{36} + 13 q^{37} - 29 q^{38} + 30 q^{39} - q^{40} - 8 q^{41} - 24 q^{42} + 42 q^{43} + 14 q^{44} + 30 q^{45} + 36 q^{46} - 14 q^{47} + 4 q^{48} + 61 q^{49} - 49 q^{50} + 46 q^{51} + 4 q^{52} - 3 q^{53} - 19 q^{54} + 26 q^{55} - 13 q^{56} + 26 q^{57} + 13 q^{58} + 45 q^{59} + 10 q^{60} + 34 q^{61} - 21 q^{62} + 63 q^{63} + 36 q^{64} - 25 q^{65} + 5 q^{66} + 42 q^{67} - 4 q^{68} - 4 q^{69} - 30 q^{70} - 2 q^{71} - 46 q^{72} + 16 q^{73} - 13 q^{74} + 72 q^{75} + 29 q^{76} - 36 q^{77} - 30 q^{78} + 33 q^{79} + q^{80} + 96 q^{81} + 8 q^{82} + 8 q^{83} + 24 q^{84} + 18 q^{85} - 42 q^{86} + 11 q^{87} - 14 q^{88} + 21 q^{89} - 30 q^{90} + 60 q^{91} - 36 q^{92} - 27 q^{93} + 14 q^{94} - 44 q^{95} - 4 q^{96} + 20 q^{97} - 61 q^{98} + 76 q^{99}+O(q^{100}) \) 36 * q - 36 * q^2 + 4 * q^3 + 36 * q^4 + q^5 - 4 * q^6 + 13 * q^7 - 36 * q^8 + 46 * q^9 - q^10 + 14 * q^11 + 4 * q^12 + 4 * q^13 - 13 * q^14 + 10 * q^15 + 36 * q^16 - 4 * q^17 - 46 * q^18 + 29 * q^19 + q^20 + 24 * q^21 - 14 * q^22 - 36 * q^23 - 4 * q^24 + 49 * q^25 - 4 * q^26 + 19 * q^27 + 13 * q^28 - 13 * q^29 - 10 * q^30 + 21 * q^31 - 36 * q^32 - 5 * q^33 + 4 * q^34 + 30 * q^35 + 46 * q^36 + 13 * q^37 - 29 * q^38 + 30 * q^39 - q^40 - 8 * q^41 - 24 * q^42 + 42 * q^43 + 14 * q^44 + 30 * q^45 + 36 * q^46 - 14 * q^47 + 4 * q^48 + 61 * q^49 - 49 * q^50 + 46 * q^51 + 4 * q^52 - 3 * q^53 - 19 * q^54 + 26 * q^55 - 13 * q^56 + 26 * q^57 + 13 * q^58 + 45 * q^59 + 10 * q^60 + 34 * q^61 - 21 * q^62 + 63 * q^63 + 36 * q^64 - 25 * q^65 + 5 * q^66 + 42 * q^67 - 4 * q^68 - 4 * q^69 - 30 * q^70 - 2 * q^71 - 46 * q^72 + 16 * q^73 - 13 * q^74 + 72 * q^75 + 29 * q^76 - 36 * q^77 - 30 * q^78 + 33 * q^79 + q^80 + 96 * q^81 + 8 * q^82 + 8 * q^83 + 24 * q^84 + 18 * q^85 - 42 * q^86 + 11 * q^87 - 14 * q^88 + 21 * q^89 - 30 * q^90 + 60 * q^91 - 36 * q^92 - 27 * q^93 + 14 * q^94 - 44 * q^95 - 4 * q^96 + 20 * q^97 - 61 * q^98 + 76 * q^99

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