LMFDB - Embedded newform 6026.2.a.m.1.6

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:	$41$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
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)

$f(q)$	$=$	$q+1.00000 q^{2} -2.68141 q^{3} +1.00000 q^{4} +3.69693 q^{5} -2.68141 q^{6} +1.66171 q^{7} +1.00000 q^{8} +4.18994 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.68141 q^{3} +1.00000 q^{4} +3.69693 q^{5} -2.68141 q^{6} +1.66171 q^{7} +1.00000 q^{8} +4.18994 q^{9} +3.69693 q^{10} +1.08901 q^{11} -2.68141 q^{12} +5.01517 q^{13} +1.66171 q^{14} -9.91298 q^{15} +1.00000 q^{16} +2.99305 q^{17} +4.18994 q^{18} -6.33032 q^{19} +3.69693 q^{20} -4.45572 q^{21} +1.08901 q^{22} +1.00000 q^{23} -2.68141 q^{24} +8.66732 q^{25} +5.01517 q^{26} -3.19070 q^{27} +1.66171 q^{28} +6.93445 q^{29} -9.91298 q^{30} -1.48739 q^{31} +1.00000 q^{32} -2.92007 q^{33} +2.99305 q^{34} +6.14323 q^{35} +4.18994 q^{36} +8.98143 q^{37} -6.33032 q^{38} -13.4477 q^{39} +3.69693 q^{40} -10.6268 q^{41} -4.45572 q^{42} +9.71374 q^{43} +1.08901 q^{44} +15.4899 q^{45} +1.00000 q^{46} -7.23746 q^{47} -2.68141 q^{48} -4.23872 q^{49} +8.66732 q^{50} -8.02558 q^{51} +5.01517 q^{52} +11.4468 q^{53} -3.19070 q^{54} +4.02599 q^{55} +1.66171 q^{56} +16.9742 q^{57} +6.93445 q^{58} -7.58942 q^{59} -9.91298 q^{60} -2.74208 q^{61} -1.48739 q^{62} +6.96246 q^{63} +1.00000 q^{64} +18.5407 q^{65} -2.92007 q^{66} +10.7864 q^{67} +2.99305 q^{68} -2.68141 q^{69} +6.14323 q^{70} -0.695015 q^{71} +4.18994 q^{72} +0.967537 q^{73} +8.98143 q^{74} -23.2406 q^{75} -6.33032 q^{76} +1.80961 q^{77} -13.4477 q^{78} +1.77179 q^{79} +3.69693 q^{80} -4.01424 q^{81} -10.6268 q^{82} +4.69305 q^{83} -4.45572 q^{84} +11.0651 q^{85} +9.71374 q^{86} -18.5941 q^{87} +1.08901 q^{88} -12.9474 q^{89} +15.4899 q^{90} +8.33375 q^{91} +1.00000 q^{92} +3.98831 q^{93} -7.23746 q^{94} -23.4028 q^{95} -2.68141 q^{96} +3.19159 q^{97} -4.23872 q^{98} +4.56287 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 41 q + 41 q^{2} + 4 q^{3} + 41 q^{4} + 9 q^{5} + 4 q^{6} + 12 q^{7} + 41 q^{8} + 63 q^{9}+O(q^{10}) $ 41 * q + 41 * q^2 + 4 * q^3 + 41 * q^4 + 9 * q^5 + 4 * q^6 + 12 * q^7 + 41 * q^8 + 63 * q^9	\( 41 q + 41 q^{2} + 4 q^{3} + 41 q^{4} + 9 q^{5} + 4 q^{6} + 12 q^{7} + 41 q^{8} + 63 q^{9} + 9 q^{10} + 4 q^{11} + 4 q^{12} + 16 q^{13} + 12 q^{14} + 10 q^{15} + 41 q^{16} + 10 q^{17} + 63 q^{18} + 16 q^{19} + 9 q^{20} + 16 q^{21} + 4 q^{22} + 41 q^{23} + 4 q^{24} + 76 q^{25} + 16 q^{26} + 7 q^{27} + 12 q^{28} + 28 q^{29} + 10 q^{30} + 25 q^{31} + 41 q^{32} + 5 q^{33} + 10 q^{34} + 4 q^{35} + 63 q^{36} + 26 q^{37} + 16 q^{38} + 50 q^{39} + 9 q^{40} + 27 q^{41} + 16 q^{42} + 12 q^{43} + 4 q^{44} + 44 q^{45} + 41 q^{46} + 18 q^{47} + 4 q^{48} + 87 q^{49} + 76 q^{50} + 24 q^{51} + 16 q^{52} + 63 q^{53} + 7 q^{54} + 18 q^{55} + 12 q^{56} - 12 q^{57} + 28 q^{58} + 33 q^{59} + 10 q^{60} + 24 q^{61} + 25 q^{62} + 48 q^{63} + 41 q^{64} + 21 q^{65} + 5 q^{66} - 9 q^{67} + 10 q^{68} + 4 q^{69} + 4 q^{70} + 36 q^{71} + 63 q^{72} + 36 q^{73} + 26 q^{74} + 6 q^{75} + 16 q^{76} + 48 q^{77} + 50 q^{78} + 51 q^{79} + 9 q^{80} + 149 q^{81} + 27 q^{82} - 27 q^{83} + 16 q^{84} + 52 q^{85} + 12 q^{86} - 3 q^{87} + 4 q^{88} + 68 q^{89} + 44 q^{90} + 22 q^{91} + 41 q^{92} + 45 q^{93} + 18 q^{94} + 46 q^{95} + 4 q^{96} + 16 q^{97} + 87 q^{98} - 10 q^{99}+O(q^{100}) \) 41 * q + 41 * q^2 + 4 * q^3 + 41 * q^4 + 9 * q^5 + 4 * q^6 + 12 * q^7 + 41 * q^8 + 63 * q^9 + 9 * q^10 + 4 * q^11 + 4 * q^12 + 16 * q^13 + 12 * q^14 + 10 * q^15 + 41 * q^16 + 10 * q^17 + 63 * q^18 + 16 * q^19 + 9 * q^20 + 16 * q^21 + 4 * q^22 + 41 * q^23 + 4 * q^24 + 76 * q^25 + 16 * q^26 + 7 * q^27 + 12 * q^28 + 28 * q^29 + 10 * q^30 + 25 * q^31 + 41 * q^32 + 5 * q^33 + 10 * q^34 + 4 * q^35 + 63 * q^36 + 26 * q^37 + 16 * q^38 + 50 * q^39 + 9 * q^40 + 27 * q^41 + 16 * q^42 + 12 * q^43 + 4 * q^44 + 44 * q^45 + 41 * q^46 + 18 * q^47 + 4 * q^48 + 87 * q^49 + 76 * q^50 + 24 * q^51 + 16 * q^52 + 63 * q^53 + 7 * q^54 + 18 * q^55 + 12 * q^56 - 12 * q^57 + 28 * q^58 + 33 * q^59 + 10 * q^60 + 24 * q^61 + 25 * q^62 + 48 * q^63 + 41 * q^64 + 21 * q^65 + 5 * q^66 - 9 * q^67 + 10 * q^68 + 4 * q^69 + 4 * q^70 + 36 * q^71 + 63 * q^72 + 36 * q^73 + 26 * q^74 + 6 * q^75 + 16 * q^76 + 48 * q^77 + 50 * q^78 + 51 * q^79 + 9 * q^80 + 149 * q^81 + 27 * q^82 - 27 * q^83 + 16 * q^84 + 52 * q^85 + 12 * q^86 - 3 * q^87 + 4 * q^88 + 68 * q^89 + 44 * q^90 + 22 * q^91 + 41 * q^92 + 45 * q^93 + 18 * q^94 + 46 * q^95 + 4 * q^96 + 16 * q^97 + 87 * q^98 - 10 * 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
$3$	−2.68141	−1.54811	−0.774055	−	0.633118i	$-0.781775\pi$
$3$	−2.68141	−1.54811	−0.774055	+	0.633118i	$0.781775\pi$
$4$	1.00000	0.500000
$5$	3.69693	1.65332	0.826659	−	0.562703i	$-0.190238\pi$
$5$	3.69693	1.65332	0.826659	+	0.562703i	$0.190238\pi$
$6$	−2.68141	−1.09468
$7$	1.66171	0.628067	0.314033	−	0.949412i	$-0.398320\pi$
$7$	1.66171	0.628067	0.314033	+	0.949412i	$0.398320\pi$
$8$	1.00000	0.353553
$9$	4.18994	1.39665
$10$	3.69693	1.16907
$11$	1.08901	0.328348	0.164174	−	0.986431i	$-0.447504\pi$
$11$	1.08901	0.328348	0.164174	+	0.986431i	$0.447504\pi$
$12$	−2.68141	−0.774055
$13$	5.01517	1.39096	0.695479	−	0.718547i	$-0.255192\pi$
$13$	5.01517	1.39096	0.695479	+	0.718547i	$0.255192\pi$
$14$	1.66171	0.444110
$15$	−9.91298	−2.55952
$16$	1.00000	0.250000
$17$	2.99305	0.725922	0.362961	−	0.931804i	$-0.381766\pi$
$17$	2.99305	0.725922	0.362961	+	0.931804i	$0.381766\pi$
$18$	4.18994	0.987578
$19$	−6.33032	−1.45228	−0.726138	−	0.687549i	$-0.758686\pi$
$19$	−6.33032	−1.45228	−0.726138	+	0.687549i	$0.758686\pi$
$20$	3.69693	0.826659
$21$	−4.45572	−0.972317
$22$	1.08901	0.232177
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	−2.68141	−0.547340
$25$	8.66732	1.73346
$26$	5.01517	0.983555
$27$	−3.19070	−0.614051
$28$	1.66171	0.314033
$29$	6.93445	1.28769	0.643847	−	0.765154i	$-0.277337\pi$
$29$	6.93445	1.28769	0.643847	+	0.765154i	$0.277337\pi$
$30$	−9.91298	−1.80985
$31$	−1.48739	−0.267144	−0.133572	−	0.991039i	$-0.542645\pi$
$31$	−1.48739	−0.267144	−0.133572	+	0.991039i	$0.542645\pi$
$32$	1.00000	0.176777
$33$	−2.92007	−0.508319
$34$	2.99305	0.513304
$35$	6.14323	1.03839
$36$	4.18994	0.698323
$37$	8.98143	1.47654	0.738269	−	0.674506i	$-0.235643\pi$
$37$	8.98143	1.47654	0.738269	+	0.674506i	$0.235643\pi$
$38$	−6.33032	−1.02691
$39$	−13.4477	−2.15336
$40$	3.69693	0.584536
$41$	−10.6268	−1.65963	−0.829816	−	0.558037i	$-0.811555\pi$
$41$	−10.6268	−1.65963	−0.829816	+	0.558037i	$0.811555\pi$
$42$	−4.45572	−0.687532
$43$	9.71374	1.48133	0.740666	−	0.671873i	$-0.234510\pi$
$43$	9.71374	1.48133	0.740666	+	0.671873i	$0.234510\pi$
$44$	1.08901	0.164174
$45$	15.4899	2.30910
$46$	1.00000	0.147442
$47$	−7.23746	−1.05569	−0.527846	−	0.849340i	$-0.677000\pi$
$47$	−7.23746	−1.05569	−0.527846	+	0.849340i	$0.677000\pi$
$48$	−2.68141	−0.387028
$49$	−4.23872	−0.605532
$50$	8.66732	1.22574
$51$	−8.02558	−1.12381
$52$	5.01517	0.695479
$53$	11.4468	1.57234	0.786172	−	0.618008i	$-0.212060\pi$
$53$	11.4468	1.57234	0.786172	+	0.618008i	$0.212060\pi$
$54$	−3.19070	−0.434200
$55$	4.02599	0.542864
$56$	1.66171	0.222055
$57$	16.9742	2.24828
$58$	6.93445	0.910538
$59$	−7.58942	−0.988058	−0.494029	−	0.869445i	$-0.664476\pi$
$59$	−7.58942	−0.988058	−0.494029	+	0.869445i	$0.664476\pi$
$60$	−9.91298	−1.27976
$61$	−2.74208	−0.351088	−0.175544	−	0.984472i	$-0.556168\pi$
$61$	−2.74208	−0.351088	−0.175544	+	0.984472i	$0.556168\pi$
$62$	−1.48739	−0.188899
$63$	6.96246	0.877187
$64$	1.00000	0.125000
$65$	18.5407	2.29970
$66$	−2.92007	−0.359436
$67$	10.7864	1.31777	0.658883	−	0.752245i	$-0.271029\pi$
$67$	10.7864	1.31777	0.658883	+	0.752245i	$0.271029\pi$
$68$	2.99305	0.362961
$69$	−2.68141	−0.322803
$70$	6.14323	0.734256
$71$	−0.695015	−0.0824831	−0.0412415	−	0.999149i	$-0.513131\pi$
$71$	−0.695015	−0.0824831	−0.0412415	+	0.999149i	$0.513131\pi$
$72$	4.18994	0.493789
$73$	0.967537	0.113242	0.0566208	−	0.998396i	$-0.481967\pi$
$73$	0.967537	0.113242	0.0566208	+	0.998396i	$0.481967\pi$
$74$	8.98143	1.04407
$75$	−23.2406	−2.68359
$76$	−6.33032	−0.726138
$77$	1.80961	0.206225
$78$	−13.4477	−1.52265
$79$	1.77179	0.199342	0.0996709	−	0.995020i	$-0.468221\pi$
$79$	1.77179	0.199342	0.0996709	+	0.995020i	$0.468221\pi$
$80$	3.69693	0.413330
$81$	−4.01424	−0.446027
$82$	−10.6268	−1.17354
$83$	4.69305	0.515129	0.257564	−	0.966261i	$-0.417080\pi$
$83$	4.69305	0.515129	0.257564	+	0.966261i	$0.417080\pi$
$84$	−4.45572	−0.486158
$85$	11.0651	1.20018
$86$	9.71374	1.04746
$87$	−18.5941	−1.99349
$88$	1.08901	0.116089
$89$	−12.9474	−1.37242	−0.686208	−	0.727405i	$-0.740726\pi$
$89$	−12.9474	−1.37242	−0.686208	+	0.727405i	$0.740726\pi$
$90$	15.4899	1.63278
$91$	8.33375	0.873614
$92$	1.00000	0.104257
$93$	3.98831	0.413568
$94$	−7.23746	−0.746487
$95$	−23.4028	−2.40107
$96$	−2.68141	−0.273670
$97$	3.19159	0.324057	0.162028	−	0.986786i	$-0.448196\pi$
$97$	3.19159	0.324057	0.162028	+	0.986786i	$0.448196\pi$
$98$	−4.23872	−0.428176
$99$	4.56287	0.458586
$100$	8.66732	0.866732
$101$	−3.46021	−0.344304	−0.172152	−	0.985070i	$-0.555072\pi$
$101$	−3.46021	−0.344304	−0.172152	+	0.985070i	$0.555072\pi$
$102$	−8.02558	−0.794651
$103$	−12.6403	−1.24549	−0.622743	−	0.782427i	$-0.713982\pi$
$103$	−12.6403	−1.24549	−0.622743	+	0.782427i	$0.713982\pi$
$104$	5.01517	0.491778
$105$	−16.4725	−1.60755
$106$	11.4468	1.11181
$107$	−0.476525	−0.0460674	−0.0230337	−	0.999735i	$-0.507332\pi$
$107$	−0.476525	−0.0460674	−0.0230337	+	0.999735i	$0.507332\pi$
$108$	−3.19070	−0.307026
$109$	−1.58771	−0.152075	−0.0760375	−	0.997105i	$-0.524227\pi$
$109$	−1.58771	−0.152075	−0.0760375	+	0.997105i	$0.524227\pi$
$110$	4.02599	0.383863
$111$	−24.0829	−2.28584
$112$	1.66171	0.157017
$113$	−13.8576	−1.30361	−0.651805	−	0.758387i	$-0.725988\pi$
$113$	−13.8576	−1.30361	−0.651805	+	0.758387i	$0.725988\pi$
$114$	16.9742	1.58978
$115$	3.69693	0.344741
$116$	6.93445	0.643847
$117$	21.0132	1.94267
$118$	−7.58942	−0.698662
$119$	4.97358	0.455927
$120$	−9.91298	−0.904927
$121$	−9.81406	−0.892187
$122$	−2.74208	−0.248257
$123$	28.4948	2.56929
$124$	−1.48739	−0.133572
$125$	13.5578	1.21265
$126$	6.96246	0.620265
$127$	−6.02838	−0.534932	−0.267466	−	0.963567i	$-0.586186\pi$
$127$	−6.02838	−0.534932	−0.267466	+	0.963567i	$0.586186\pi$
$128$	1.00000	0.0883883
$129$	−26.0465	−2.29327
$130$	18.5407	1.62613
$131$	1.00000	0.0873704
$131$	1.00000	0.0873704
$132$	−2.92007	−0.254160
$133$	−10.5192	−0.912126
$134$	10.7864	0.931802
$135$	−11.7958	−1.01522
$136$	2.99305	0.256652
$137$	0.652623	0.0557573	0.0278787	−	0.999611i	$-0.491125\pi$
$137$	0.652623	0.0557573	0.0278787	+	0.999611i	$0.491125\pi$
$138$	−2.68141	−0.228256
$139$	−9.98125	−0.846599	−0.423299	−	0.905990i	$-0.639128\pi$
$139$	−9.98125	−0.846599	−0.423299	+	0.905990i	$0.639128\pi$
$140$	6.14323	0.519197
$141$	19.4066	1.63433
$142$	−0.695015	−0.0583244
$143$	5.46156	0.456718
$144$	4.18994	0.349161
$145$	25.6362	2.12897
$146$	0.967537	0.0800739
$147$	11.3657	0.937430
$148$	8.98143	0.738269
$149$	20.9944	1.71993	0.859966	−	0.510352i	$-0.170485\pi$
$149$	20.9944	1.71993	0.859966	+	0.510352i	$0.170485\pi$
$150$	−23.2406	−1.89759
$151$	−14.5513	−1.18417	−0.592085	−	0.805875i	$-0.701695\pi$
$151$	−14.5513	−1.18417	−0.592085	+	0.805875i	$0.701695\pi$
$152$	−6.33032	−0.513457
$153$	12.5407	1.01386
$154$	1.80961	0.145823
$155$	−5.49880	−0.441674
$156$	−13.4477	−1.07668
$157$	4.20557	0.335641	0.167820	−	0.985818i	$-0.446327\pi$
$157$	4.20557	0.335641	0.167820	+	0.985818i	$0.446327\pi$
$158$	1.77179	0.140956
$159$	−30.6936	−2.43416
$160$	3.69693	0.292268
$161$	1.66171	0.130961
$162$	−4.01424	−0.315389
$163$	−10.8159	−0.847164	−0.423582	−	0.905858i	$-0.639228\pi$
$163$	−10.8159	−0.847164	−0.423582	+	0.905858i	$0.639228\pi$
$164$	−10.6268	−0.829816
$165$	−10.7953	−0.840414
$166$	4.69305	0.364251
$167$	9.51457	0.736260	0.368130	−	0.929774i	$-0.379998\pi$
$167$	9.51457	0.736260	0.368130	+	0.929774i	$0.379998\pi$
$168$	−4.45572	−0.343766
$169$	12.1519	0.934762
$170$	11.0651	0.848655
$171$	−26.5236	−2.02831
$172$	9.71374	0.740666
$173$	0.149602	0.0113740	0.00568702	−	0.999984i	$-0.498190\pi$
$173$	0.149602	0.0113740	0.00568702	+	0.999984i	$0.498190\pi$
$174$	−18.5941	−1.40961
$175$	14.4026	1.08873
$176$	1.08901	0.0820871
$177$	20.3503	1.52962
$178$	−12.9474	−0.970445
$179$	−23.5519	−1.76035	−0.880174	−	0.474651i	$-0.842574\pi$
$179$	−23.5519	−1.76035	−0.880174	+	0.474651i	$0.842574\pi$
$180$	15.4899	1.15455
$181$	−1.06669	−0.0792867	−0.0396433	−	0.999214i	$-0.512622\pi$
$181$	−1.06669	−0.0792867	−0.0396433	+	0.999214i	$0.512622\pi$
$182$	8.33375	0.617739
$183$	7.35264	0.543523
$184$	1.00000	0.0737210
$185$	33.2038	2.44119
$186$	3.98831	0.292437
$187$	3.25946	0.238355
$188$	−7.23746	−0.527846
$189$	−5.30202	−0.385665
$190$	−23.4028	−1.69782
$191$	20.0762	1.45266	0.726330	−	0.687346i	$-0.241225\pi$
$191$	20.0762	1.45266	0.726330	+	0.687346i	$0.241225\pi$
$192$	−2.68141	−0.193514
$193$	−5.82053	−0.418971	−0.209485	−	0.977812i	$-0.567179\pi$
$193$	−5.82053	−0.418971	−0.209485	+	0.977812i	$0.567179\pi$
$194$	3.19159	0.229143
$195$	−49.7152	−3.56018
$196$	−4.23872	−0.302766
$197$	−5.35782	−0.381729	−0.190864	−	0.981616i	$-0.561129\pi$
$197$	−5.35782	−0.381729	−0.190864	+	0.981616i	$0.561129\pi$
$198$	4.56287	0.324269
$199$	5.77556	0.409419	0.204709	−	0.978823i	$-0.434375\pi$
$199$	5.77556	0.409419	0.204709	+	0.978823i	$0.434375\pi$
$200$	8.66732	0.612872
$201$	−28.9227	−2.04005
$202$	−3.46021	−0.243460
$203$	11.5230	0.808758
$204$	−8.02558	−0.561903
$205$	−39.2867	−2.74390
$206$	−12.6403	−0.880691
$207$	4.18994	0.291221
$208$	5.01517	0.347739
$209$	−6.89377	−0.476852
$210$	−16.4725	−1.13671
$211$	26.4089	1.81807	0.909033	−	0.416724i	$-0.136822\pi$
$211$	26.4089	1.81807	0.909033	+	0.416724i	$0.136822\pi$
$212$	11.4468	0.786172
$213$	1.86362	0.127693
$214$	−0.476525	−0.0325746
$215$	35.9111	2.44911
$216$	−3.19070	−0.217100
$217$	−2.47162	−0.167784
$218$	−1.58771	−0.107533
$219$	−2.59436	−0.175310
$220$	4.02599	0.271432
$221$	15.0107	1.00973
$222$	−24.0829	−1.61634
$223$	8.69125	0.582009	0.291005	−	0.956722i	$-0.406011\pi$
$223$	8.69125	0.582009	0.291005	+	0.956722i	$0.406011\pi$
$224$	1.66171	0.111028
$225$	36.3155	2.42103
$226$	−13.8576	−0.921791
$227$	−9.12147	−0.605414	−0.302707	−	0.953084i	$-0.597890\pi$
$227$	−9.12147	−0.605414	−0.302707	+	0.953084i	$0.597890\pi$
$228$	16.9742	1.12414
$229$	9.00477	0.595052	0.297526	−	0.954714i	$-0.403839\pi$
$229$	9.00477	0.595052	0.297526	+	0.954714i	$0.403839\pi$
$230$	3.69693	0.243769
$231$	−4.85231	−0.319259
$232$	6.93445	0.455269
$233$	−15.3077	−1.00284	−0.501421	−	0.865203i	$-0.667189\pi$
$233$	−15.3077	−1.00284	−0.501421	+	0.865203i	$0.667189\pi$
$234$	21.0132	1.37368
$235$	−26.7564	−1.74540
$236$	−7.58942	−0.494029
$237$	−4.75088	−0.308603
$238$	4.97358	0.322389
$239$	13.5363	0.875589	0.437795	−	0.899075i	$-0.355760\pi$
$239$	13.5363	0.875589	0.437795	+	0.899075i	$0.355760\pi$
$240$	−9.91298	−0.639880
$241$	8.58434	0.552966	0.276483	−	0.961019i	$-0.410831\pi$
$241$	8.58434	0.552966	0.276483	+	0.961019i	$0.410831\pi$
$242$	−9.81406	−0.630872
$243$	20.3359	1.30455
$244$	−2.74208	−0.175544
$245$	−15.6703	−1.00114
$246$	28.4948	1.81676
$247$	−31.7476	−2.02005
$248$	−1.48739	−0.0944496
$249$	−12.5840	−0.797476
$250$	13.5578	0.857472
$251$	−17.3653	−1.09609	−0.548043	−	0.836450i	$-0.684627\pi$
$251$	−17.3653	−1.09609	−0.548043	+	0.836450i	$0.684627\pi$
$252$	6.96246	0.438593
$253$	1.08901	0.0684653
$254$	−6.02838	−0.378254
$255$	−29.6701	−1.85801
$256$	1.00000	0.0625000
$257$	−3.47284	−0.216630	−0.108315	−	0.994117i	$-0.534546\pi$
$257$	−3.47284	−0.216630	−0.108315	+	0.994117i	$0.534546\pi$
$258$	−26.0465	−1.62158
$259$	14.9245	0.927365
$260$	18.5407	1.14985
$261$	29.0549	1.79845
$262$	1.00000	0.0617802
$263$	13.4886	0.831746	0.415873	−	0.909423i	$-0.363476\pi$
$263$	13.4886	0.831746	0.415873	+	0.909423i	$0.363476\pi$
$264$	−2.92007	−0.179718
$265$	42.3182	2.59959
$266$	−10.5192	−0.644970
$267$	34.7171	2.12465
$268$	10.7864	0.658883
$269$	−21.2981	−1.29857	−0.649284	−	0.760546i	$-0.724931\pi$
$269$	−21.2981	−1.29857	−0.649284	+	0.760546i	$0.724931\pi$
$270$	−11.7958	−0.717871
$271$	−7.87545	−0.478399	−0.239200	−	0.970970i	$-0.576885\pi$
$271$	−7.87545	−0.478399	−0.239200	+	0.970970i	$0.576885\pi$
$272$	2.99305	0.181480
$273$	−22.3462	−1.35245
$274$	0.652623	0.0394264
$275$	9.43878	0.569180
$276$	−2.68141	−0.161402
$277$	1.49148	0.0896146	0.0448073	−	0.998996i	$-0.485733\pi$
$277$	1.49148	0.0896146	0.0448073	+	0.998996i	$0.485733\pi$
$278$	−9.98125	−0.598636
$279$	−6.23209	−0.373105
$280$	6.14323	0.367128
$281$	9.20204	0.548948	0.274474	−	0.961595i	$-0.411496\pi$
$281$	9.20204	0.548948	0.274474	+	0.961595i	$0.411496\pi$
$282$	19.4066	1.15564
$283$	18.2617	1.08555	0.542774	−	0.839879i	$-0.317374\pi$
$283$	18.2617	1.08555	0.542774	+	0.839879i	$0.317374\pi$
$284$	−0.695015	−0.0412415
$285$	62.7523	3.71713
$286$	5.46156	0.322949
$287$	−17.6587	−1.04236
$288$	4.18994	0.246894
$289$	−8.04164	−0.473038
$290$	25.6362	1.50541
$291$	−8.55794	−0.501675
$292$	0.967537	0.0566208
$293$	−11.5952	−0.677401	−0.338701	−	0.940894i	$-0.609987\pi$
$293$	−11.5952	−0.677401	−0.338701	+	0.940894i	$0.609987\pi$
$294$	11.3657	0.662863
$295$	−28.0576	−1.63357
$296$	8.98143	0.522035
$297$	−3.47470	−0.201623
$298$	20.9944	1.21618
$299$	5.01517	0.290035
$300$	−23.2406	−1.34180
$301$	16.1414	0.930376
$302$	−14.5513	−0.837335
$303$	9.27823	0.533021
$304$	−6.33032	−0.363069
$305$	−10.1373	−0.580460
$306$	12.5407	0.716904
$307$	−12.6131	−0.719866	−0.359933	−	0.932978i	$-0.617200\pi$
$307$	−12.6131	−0.719866	−0.359933	+	0.932978i	$0.617200\pi$
$308$	1.80961	0.103112
$309$	33.8938	1.92815
$310$	−5.49880	−0.312311
$311$	10.4953	0.595133	0.297566	−	0.954701i	$-0.403825\pi$
$311$	10.4953	0.595133	0.297566	+	0.954701i	$0.403825\pi$
$312$	−13.4477	−0.761326
$313$	7.77338	0.439378	0.219689	−	0.975570i	$-0.429496\pi$
$313$	7.77338	0.439378	0.219689	+	0.975570i	$0.429496\pi$
$314$	4.20557	0.237334
$315$	25.7397	1.45027
$316$	1.77179	0.0996709
$317$	19.8686	1.11593	0.557967	−	0.829863i	$-0.311582\pi$
$317$	19.8686	1.11593	0.557967	+	0.829863i	$0.311582\pi$
$318$	−30.6936	−1.72121
$319$	7.55167	0.422812
$320$	3.69693	0.206665
$321$	1.27776	0.0713174
$322$	1.66171	0.0926034
$323$	−18.9470	−1.05424
$324$	−4.01424	−0.223013
$325$	43.4680	2.41117
$326$	−10.8159	−0.599036
$327$	4.25729	0.235429
$328$	−10.6268	−0.586768
$329$	−12.0266	−0.663046
$330$	−10.7953	−0.594262
$331$	−5.53675	−0.304327	−0.152164	−	0.988355i	$-0.548624\pi$
$331$	−5.53675	−0.304327	−0.152164	+	0.988355i	$0.548624\pi$
$332$	4.69305	0.257564
$333$	37.6316	2.06220
$334$	9.51457	0.520614
$335$	39.8766	2.17869
$336$	−4.45572	−0.243079
$337$	6.17499	0.336373	0.168186	−	0.985755i	$-0.446209\pi$
$337$	6.17499	0.336373	0.168186	+	0.985755i	$0.446209\pi$
$338$	12.1519	0.660976
$339$	37.1577	2.01813
$340$	11.0651	0.600090
$341$	−1.61978	−0.0877162
$342$	−26.5236	−1.43423
$343$	−18.6755	−1.00838
$344$	9.71374	0.523730
$345$	−9.91298	−0.533697
$346$	0.149602	0.00804267
$347$	17.0527	0.915437	0.457719	−	0.889097i	$-0.348667\pi$
$347$	17.0527	0.915437	0.457719	+	0.889097i	$0.348667\pi$
$348$	−18.5941	−0.996747
$349$	−26.6603	−1.42709	−0.713545	−	0.700609i	$-0.752912\pi$
$349$	−26.6603	−1.42709	−0.713545	+	0.700609i	$0.752912\pi$
$350$	14.4026	0.769849
$351$	−16.0019	−0.854119
$352$	1.08901	0.0580443
$353$	36.4757	1.94140	0.970702	−	0.240288i	$-0.0772420\pi$
$353$	36.4757	1.94140	0.970702	+	0.240288i	$0.0772420\pi$
$354$	20.3503	1.08161
$355$	−2.56942	−0.136371
$356$	−12.9474	−0.686208
$357$	−13.3362	−0.705826
$358$	−23.5519	−1.24475
$359$	−6.42819	−0.339267	−0.169634	−	0.985507i	$-0.554258\pi$
$359$	−6.42819	−0.339267	−0.169634	+	0.985507i	$0.554258\pi$
$360$	15.4899	0.816390
$361$	21.0730	1.10910
$362$	−1.06669	−0.0560641
$363$	26.3155	1.38120
$364$	8.33375	0.436807
$365$	3.57692	0.187224
$366$	7.35264	0.384329
$367$	29.6146	1.54587	0.772935	−	0.634485i	$-0.218788\pi$
$367$	29.6146	1.54587	0.772935	+	0.634485i	$0.218788\pi$
$368$	1.00000	0.0521286
$369$	−44.5257	−2.31792
$370$	33.2038	1.72618
$371$	19.0213	0.987537
$372$	3.98831	0.206784
$373$	−19.1154	−0.989760	−0.494880	−	0.868961i	$-0.664788\pi$
$373$	−19.1154	−0.989760	−0.494880	+	0.868961i	$0.664788\pi$
$374$	3.25946	0.168542
$375$	−36.3540	−1.87731
$376$	−7.23746	−0.373244
$377$	34.7774	1.79113
$378$	−5.30202	−0.272706
$379$	−17.6976	−0.909066	−0.454533	−	0.890730i	$-0.650194\pi$
$379$	−17.6976	−0.909066	−0.454533	+	0.890730i	$0.650194\pi$
$380$	−23.4028	−1.20054
$381$	16.1645	0.828134
$382$	20.0762	1.02719
$383$	7.79563	0.398338	0.199169	−	0.979965i	$-0.436176\pi$
$383$	7.79563	0.398338	0.199169	+	0.979965i	$0.436176\pi$
$384$	−2.68141	−0.136835
$385$	6.69002	0.340955
$386$	−5.82053	−0.296257
$387$	40.7000	2.06890
$388$	3.19159	0.162028
$389$	−0.0914446	−0.00463643	−0.00231821	−	0.999997i	$-0.500738\pi$
$389$	−0.0914446	−0.00463643	−0.00231821	+	0.999997i	$0.500738\pi$
$390$	−49.7152	−2.51743
$391$	2.99305	0.151365
$392$	−4.23872	−0.214088
$393$	−2.68141	−0.135259
$394$	−5.35782	−0.269923
$395$	6.55018	0.329575
$396$	4.56287	0.229293
$397$	2.52040	0.126495	0.0632477	−	0.997998i	$-0.479854\pi$
$397$	2.52040	0.126495	0.0632477	+	0.997998i	$0.479854\pi$
$398$	5.77556	0.289503
$399$	28.2061	1.41207
$400$	8.66732	0.433366
$401$	14.9678	0.747457	0.373728	−	0.927538i	$-0.378079\pi$
$401$	14.9678	0.747457	0.373728	+	0.927538i	$0.378079\pi$
$402$	−28.9227	−1.44253
$403$	−7.45953	−0.371586
$404$	−3.46021	−0.172152
$405$	−14.8404	−0.737424
$406$	11.5230	0.571879
$407$	9.78085	0.484819
$408$	−8.02558	−0.397326
$409$	−17.3283	−0.856831	−0.428415	−	0.903582i	$-0.640928\pi$
$409$	−17.3283	−0.856831	−0.428415	+	0.903582i	$0.640928\pi$
$410$	−39.2867	−1.94023
$411$	−1.74995	−0.0863185
$412$	−12.6403	−0.622743
$413$	−12.6114	−0.620567
$414$	4.18994	0.205924
$415$	17.3499	0.851672
$416$	5.01517	0.245889
$417$	26.7638	1.31063
$418$	−6.89377	−0.337185
$419$	−1.17631	−0.0574664	−0.0287332	−	0.999587i	$-0.509147\pi$
$419$	−1.17631	−0.0574664	−0.0287332	+	0.999587i	$0.509147\pi$
$420$	−16.4725	−0.803775
$421$	−12.6702	−0.617505	−0.308753	−	0.951142i	$-0.599912\pi$
$421$	−12.6702	−0.617505	−0.308753	+	0.951142i	$0.599912\pi$
$422$	26.4089	1.28557
$423$	−30.3245	−1.47443
$424$	11.4468	0.555907
$425$	25.9417	1.25836
$426$	1.86362	0.0902925
$427$	−4.55654	−0.220507
$428$	−0.476525	−0.0230337
$429$	−14.6446	−0.707050
$430$	35.9111	1.73179
$431$	24.8859	1.19871	0.599355	−	0.800484i	$-0.295424\pi$
$431$	24.8859	1.19871	0.599355	+	0.800484i	$0.295424\pi$
$432$	−3.19070	−0.153513
$433$	34.6479	1.66507	0.832535	−	0.553972i	$-0.186889\pi$
$433$	34.6479	1.66507	0.832535	+	0.553972i	$0.186889\pi$
$434$	−2.47162	−0.118641
$435$	−68.7410	−3.29588
$436$	−1.58771	−0.0760375
$437$	−6.33032	−0.302820
$438$	−2.59436	−0.123963
$439$	12.3436	0.589127	0.294563	−	0.955632i	$-0.404826\pi$
$439$	12.3436	0.589127	0.294563	+	0.955632i	$0.404826\pi$
$440$	4.02599	0.191932
$441$	−17.7600	−0.845713
$442$	15.0107	0.713984
$443$	−4.49638	−0.213629	−0.106815	−	0.994279i	$-0.534065\pi$
$443$	−4.49638	−0.213629	−0.106815	+	0.994279i	$0.534065\pi$
$444$	−24.0829	−1.14292
$445$	−47.8655	−2.26904
$446$	8.69125	0.411543
$447$	−56.2946	−2.66264
$448$	1.66171	0.0785084
$449$	18.7419	0.884485	0.442242	−	0.896896i	$-0.354183\pi$
$449$	18.7419	0.884485	0.442242	+	0.896896i	$0.354183\pi$
$450$	36.3155	1.71193
$451$	−11.5727	−0.544937
$452$	−13.8576	−0.651805
$453$	39.0180	1.83323
$454$	−9.12147	−0.428092
$455$	30.8093	1.44436
$456$	16.9742	0.794888
$457$	34.2518	1.60223	0.801115	−	0.598511i	$-0.204241\pi$
$457$	34.2518	1.60223	0.801115	+	0.598511i	$0.204241\pi$
$458$	9.00477	0.420765
$459$	−9.54994	−0.445753
$460$	3.69693	0.172370
$461$	1.67906	0.0782014	0.0391007	−	0.999235i	$-0.487551\pi$
$461$	1.67906	0.0782014	0.0391007	+	0.999235i	$0.487551\pi$
$462$	−4.85231	−0.225750
$463$	15.3605	0.713864	0.356932	−	0.934130i	$-0.383823\pi$
$463$	15.3605	0.713864	0.356932	+	0.934130i	$0.383823\pi$
$464$	6.93445	0.321924
$465$	14.7445	0.683760
$466$	−15.3077	−0.709117
$467$	−10.0313	−0.464192	−0.232096	−	0.972693i	$-0.574558\pi$
$467$	−10.0313	−0.464192	−0.232096	+	0.972693i	$0.574558\pi$
$468$	21.0132	0.971337
$469$	17.9238	0.827646
$470$	−26.7564	−1.23418
$471$	−11.2768	−0.519609
$472$	−7.58942	−0.349331
$473$	10.5783	0.486393
$474$	−4.75088	−0.218215
$475$	−54.8669	−2.51747
$476$	4.97358	0.227964
$477$	47.9615	2.19601
$478$	13.5363	0.619135
$479$	3.80368	0.173794	0.0868972	−	0.996217i	$-0.472305\pi$
$479$	3.80368	0.173794	0.0868972	+	0.996217i	$0.472305\pi$
$480$	−9.91298	−0.452463
$481$	45.0434	2.05380
$482$	8.58434	0.391006
$483$	−4.45572	−0.202742
$484$	−9.81406	−0.446094
$485$	11.7991	0.535769
$486$	20.3359	0.922456
$487$	−12.6344	−0.572518	−0.286259	−	0.958152i	$-0.592412\pi$
$487$	−12.6344	−0.572518	−0.286259	+	0.958152i	$0.592412\pi$
$488$	−2.74208	−0.124128
$489$	29.0017	1.31150
$490$	−15.6703	−0.707911
$491$	9.95538	0.449280	0.224640	−	0.974442i	$-0.427879\pi$
$491$	9.95538	0.449280	0.224640	+	0.974442i	$0.427879\pi$
$492$	28.4948	1.28465
$493$	20.7552	0.934765
$494$	−31.7476	−1.42839
$495$	16.8686	0.758189
$496$	−1.48739	−0.0667860
$497$	−1.15491	−0.0518049
$498$	−12.5840	−0.563901
$499$	3.23165	0.144668	0.0723342	−	0.997380i	$-0.476955\pi$
$499$	3.23165	0.144668	0.0723342	+	0.997380i	$0.476955\pi$
$500$	13.5578	0.606324
$501$	−25.5124	−1.13981
$502$	−17.3653	−0.775049
$503$	−20.6210	−0.919444	−0.459722	−	0.888063i	$-0.652051\pi$
$503$	−20.6210	−0.919444	−0.459722	+	0.888063i	$0.652051\pi$
$504$	6.96246	0.310132
$505$	−12.7922	−0.569244
$506$	1.08901	0.0484123
$507$	−32.5842	−1.44711
$508$	−6.02838	−0.267466
$509$	13.8783	0.615145	0.307573	−	0.951525i	$-0.400483\pi$
$509$	13.8783	0.615145	0.307573	+	0.951525i	$0.400483\pi$
$510$	−29.6701	−1.31381
$511$	1.60776	0.0711233
$512$	1.00000	0.0441942
$513$	20.1982	0.891771
$514$	−3.47284	−0.153181
$515$	−46.7303	−2.05918
$516$	−26.0465	−1.14663
$517$	−7.88166	−0.346635
$518$	14.9245	0.655746
$519$	−0.401144	−0.0176083
$520$	18.5407	0.813065
$521$	−9.08129	−0.397858	−0.198929	−	0.980014i	$-0.563746\pi$
$521$	−9.08129	−0.397858	−0.198929	+	0.980014i	$0.563746\pi$
$522$	29.0549	1.27170
$523$	24.3758	1.06588	0.532939	−	0.846154i	$-0.321088\pi$
$523$	24.3758	1.06588	0.532939	+	0.846154i	$0.321088\pi$
$524$	1.00000	0.0436852
$525$	−38.6191	−1.68548
$526$	13.4886	0.588133
$527$	−4.45185	−0.193926
$528$	−2.92007	−0.127080
$529$	1.00000	0.0434783
$530$	42.3182	1.83818
$531$	−31.7992	−1.37997
$532$	−10.5192	−0.456063
$533$	−53.2953	−2.30848
$534$	34.7171	1.50236
$535$	−1.76168	−0.0761641
$536$	10.7864	0.465901
$537$	63.1521	2.72521
$538$	−21.2981	−0.918227
$539$	−4.61600	−0.198825
$540$	−11.7958	−0.507611
$541$	−13.2929	−0.571505	−0.285753	−	0.958303i	$-0.592244\pi$
$541$	−13.2929	−0.571505	−0.285753	+	0.958303i	$0.592244\pi$
$542$	−7.87545	−0.338279
$543$	2.86024	0.122744
$544$	2.99305	0.128326
$545$	−5.86965	−0.251428
$546$	−22.3462	−0.956327
$547$	−22.7075	−0.970904	−0.485452	−	0.874263i	$-0.661345\pi$
$547$	−22.7075	−0.970904	−0.485452	+	0.874263i	$0.661345\pi$
$548$	0.652623	0.0278787
$549$	−11.4892	−0.490345
$550$	9.43878	0.402471
$551$	−43.8973	−1.87009
$552$	−2.68141	−0.114128
$553$	2.94420	0.125200
$554$	1.49148	0.0633671
$555$	−89.0327	−3.77923
$556$	−9.98125	−0.423299
$557$	−15.3281	−0.649474	−0.324737	−	0.945804i	$-0.605276\pi$
$557$	−15.3281	−0.649474	−0.324737	+	0.945804i	$0.605276\pi$
$558$	−6.23209	−0.263825
$559$	48.7160	2.06047
$560$	6.14323	0.259599
$561$	−8.73992	−0.369000
$562$	9.20204	0.388165
$563$	−0.709523	−0.0299028	−0.0149514	−	0.999888i	$-0.504759\pi$
$563$	−0.709523	−0.0299028	−0.0149514	+	0.999888i	$0.504759\pi$
$564$	19.4066	0.817164
$565$	−51.2305	−2.15528
$566$	18.2617	0.767599
$567$	−6.67050	−0.280135
$568$	−0.695015	−0.0291622
$569$	−6.34739	−0.266096	−0.133048	−	0.991110i	$-0.542477\pi$
$569$	−6.34739	−0.266096	−0.133048	+	0.991110i	$0.542477\pi$
$570$	62.7523	2.62841
$571$	33.9289	1.41988	0.709939	−	0.704263i	$-0.248722\pi$
$571$	33.9289	1.41988	0.709939	+	0.704263i	$0.248722\pi$
$572$	5.46156	0.228359
$573$	−53.8323	−2.24888
$574$	−17.6587	−0.737060
$575$	8.66732	0.361452
$576$	4.18994	0.174581
$577$	−9.81592	−0.408642	−0.204321	−	0.978904i	$-0.565499\pi$
$577$	−9.81592	−0.408642	−0.204321	+	0.978904i	$0.565499\pi$
$578$	−8.04164	−0.334488
$579$	15.6072	0.648613
$580$	25.6362	1.06448
$581$	7.79848	0.323535
$582$	−8.55794	−0.354738
$583$	12.4657	0.516276
$584$	0.967537	0.0400369
$585$	77.6845	3.21186
$586$	−11.5952	−0.478995
$587$	−9.65493	−0.398501	−0.199251	−	0.979949i	$-0.563851\pi$
$587$	−9.65493	−0.398501	−0.199251	+	0.979949i	$0.563851\pi$
$588$	11.3657	0.468715
$589$	9.41568	0.387966
$590$	−28.0576	−1.15511
$591$	14.3665	0.590958
$592$	8.98143	0.369135
$593$	−46.0712	−1.89192	−0.945959	−	0.324285i	$-0.894876\pi$
$593$	−46.0712	−1.89192	−0.945959	+	0.324285i	$0.894876\pi$
$594$	−3.47470	−0.142569
$595$	18.3870	0.753793
$596$	20.9944	0.859966
$597$	−15.4866	−0.633826
$598$	5.01517	0.205085
$599$	33.5254	1.36981	0.684905	−	0.728632i	$-0.259844\pi$
$599$	33.5254	1.36981	0.684905	+	0.728632i	$0.259844\pi$
$600$	−23.2406	−0.948793
$601$	−35.4325	−1.44532	−0.722661	−	0.691203i	$-0.757081\pi$
$601$	−35.4325	−1.44532	−0.722661	+	0.691203i	$0.757081\pi$
$602$	16.1414	0.657875
$603$	45.1943	1.84045
$604$	−14.5513	−0.592085
$605$	−36.2819	−1.47507
$606$	9.27823	0.376902
$607$	23.5831	0.957209	0.478604	−	0.878031i	$-0.341143\pi$
$607$	23.5831	0.957209	0.478604	+	0.878031i	$0.341143\pi$
$608$	−6.33032	−0.256728
$609$	−30.8979	−1.25205
$610$	−10.1373	−0.410447
$611$	−36.2971	−1.46842
$612$	12.5407	0.506928
$613$	12.4052	0.501043	0.250522	−	0.968111i	$-0.419398\pi$
$613$	12.4052	0.501043	0.250522	+	0.968111i	$0.419398\pi$
$614$	−12.6131	−0.509022
$615$	105.344	4.24786
$616$	1.80961	0.0729114
$617$	−47.4032	−1.90838	−0.954191	−	0.299197i	$-0.903281\pi$
$617$	−47.4032	−1.90838	−0.954191	+	0.299197i	$0.903281\pi$
$618$	33.8938	1.36341
$619$	12.3024	0.494476	0.247238	−	0.968955i	$-0.420477\pi$
$619$	12.3024	0.494476	0.247238	+	0.968955i	$0.420477\pi$
$620$	−5.49880	−0.220837
$621$	−3.19070	−0.128039
$622$	10.4953	0.420822
$623$	−21.5147	−0.861970
$624$	−13.4477	−0.538339
$625$	6.78579	0.271432
$626$	7.77338	0.310687
$627$	18.4850	0.738219
$628$	4.20557	0.167820
$629$	26.8819	1.07185
$630$	25.7397	1.02550
$631$	−7.29057	−0.290233	−0.145117	−	0.989415i	$-0.546356\pi$
$631$	−7.29057	−0.290233	−0.145117	+	0.989415i	$0.546356\pi$
$632$	1.77179	0.0704779
$633$	−70.8131	−2.81457
$634$	19.8686	0.789084
$635$	−22.2865	−0.884413
$636$	−30.6936	−1.21708
$637$	−21.2579	−0.842269
$638$	7.55167	0.298973
$639$	−2.91207	−0.115200
$640$	3.69693	0.146134
$641$	−20.7985	−0.821492	−0.410746	−	0.911750i	$-0.634732\pi$
$641$	−20.7985	−0.821492	−0.410746	+	0.911750i	$0.634732\pi$
$642$	1.27776	0.0504290
$643$	−17.6758	−0.697064	−0.348532	−	0.937297i	$-0.613320\pi$
$643$	−17.6758	−0.697064	−0.348532	+	0.937297i	$0.613320\pi$
$644$	1.66171	0.0654805
$645$	−96.2921	−3.79150
$646$	−18.9470	−0.745459
$647$	2.65894	0.104534	0.0522669	−	0.998633i	$-0.483355\pi$
$647$	2.65894	0.104534	0.0522669	+	0.998633i	$0.483355\pi$
$648$	−4.01424	−0.157694
$649$	−8.26494	−0.324427
$650$	43.4680	1.70496
$651$	6.62741	0.259749
$652$	−10.8159	−0.423582
$653$	13.9095	0.544322	0.272161	−	0.962252i	$-0.412262\pi$
$653$	13.9095	0.544322	0.272161	+	0.962252i	$0.412262\pi$
$654$	4.25729	0.166473
$655$	3.69693	0.144451
$656$	−10.6268	−0.414908
$657$	4.05392	0.158158
$658$	−12.0266	−0.468844
$659$	−12.5949	−0.490627	−0.245313	−	0.969444i	$-0.578891\pi$
$659$	−12.5949	−0.490627	−0.245313	+	0.969444i	$0.578891\pi$
$660$	−10.7953	−0.420207
$661$	48.8290	1.89923	0.949613	−	0.313424i	$-0.101476\pi$
$661$	48.8290	1.89923	0.949613	+	0.313424i	$0.101476\pi$
$662$	−5.53675	−0.215192
$663$	−40.2496	−1.56317
$664$	4.69305	0.182126
$665$	−38.8886	−1.50804
$666$	37.6316	1.45820
$667$	6.93445	0.268503
$668$	9.51457	0.368130
$669$	−23.3048	−0.901014
$670$	39.8766	1.54057
$671$	−2.98615	−0.115279
$672$	−4.45572	−0.171883
$673$	−48.5602	−1.87186	−0.935929	−	0.352188i	$-0.885438\pi$
$673$	−48.5602	−1.87186	−0.935929	+	0.352188i	$0.885438\pi$
$674$	6.17499	0.237852
$675$	−27.6548	−1.06444
$676$	12.1519	0.467381
$677$	−12.5332	−0.481690	−0.240845	−	0.970564i	$-0.577425\pi$
$677$	−12.5332	−0.481690	−0.240845	+	0.970564i	$0.577425\pi$
$678$	37.1577	1.42703
$679$	5.30349	0.203529
$680$	11.0651	0.424328
$681$	24.4584	0.937247
$682$	−1.61978	−0.0620247
$683$	−17.0962	−0.654166	−0.327083	−	0.944996i	$-0.606066\pi$
$683$	−17.0962	−0.654166	−0.327083	+	0.944996i	$0.606066\pi$
$684$	−26.5236	−1.01416
$685$	2.41270	0.0921847
$686$	−18.6755	−0.713033
$687$	−24.1454	−0.921206
$688$	9.71374	0.370333
$689$	57.4078	2.18706
$690$	−9.91298	−0.377381
$691$	46.9453	1.78588	0.892942	−	0.450171i	$-0.148637\pi$
$691$	46.9453	1.78588	0.892942	+	0.450171i	$0.148637\pi$
$692$	0.149602	0.00568702
$693$	7.58217	0.288023
$694$	17.0527	0.647312
$695$	−36.9000	−1.39970
$696$	−18.5941	−0.704806
$697$	−31.8066	−1.20476
$698$	−26.6603	−1.00911
$699$	41.0462	1.55251
$700$	14.4026	0.544365
$701$	41.1269	1.55334	0.776670	−	0.629907i	$-0.216907\pi$
$701$	41.1269	1.55334	0.776670	+	0.629907i	$0.216907\pi$
$702$	−16.0019	−0.603953
$703$	−56.8553	−2.14434
$704$	1.08901	0.0410435
$705$	71.7448	2.70207
$706$	36.4757	1.37278
$707$	−5.74987	−0.216246
$708$	20.3503	0.764811
$709$	−34.0308	−1.27805	−0.639027	−	0.769184i	$-0.720663\pi$
$709$	−34.0308	−1.27805	−0.639027	+	0.769184i	$0.720663\pi$
$710$	−2.56942	−0.0964288
$711$	7.42368	0.278410
$712$	−12.9474	−0.485223
$713$	−1.48739	−0.0557034
$714$	−13.3362	−0.499094
$715$	20.1910	0.755101
$716$	−23.5519	−0.880174
$717$	−36.2963	−1.35551
$718$	−6.42819	−0.239898
$719$	5.73673	0.213944	0.106972	−	0.994262i	$-0.465884\pi$
$719$	5.73673	0.213944	0.106972	+	0.994262i	$0.465884\pi$
$720$	15.4899	0.577275
$721$	−21.0045	−0.782248
$722$	21.0730	0.784254
$723$	−23.0181	−0.856053
$724$	−1.06669	−0.0396433
$725$	60.1030	2.23217
$726$	26.3155	0.976659
$727$	17.9538	0.665869	0.332934	−	0.942950i	$-0.391961\pi$
$727$	17.9538	0.665869	0.332934	+	0.942950i	$0.391961\pi$
$728$	8.33375	0.308869
$729$	−42.4861	−1.57356
$730$	3.57692	0.132388
$731$	29.0737	1.07533
$732$	7.35264	0.271761
$733$	−33.4322	−1.23485	−0.617423	−	0.786631i	$-0.711823\pi$
$733$	−33.4322	−1.23485	−0.617423	+	0.786631i	$0.711823\pi$
$734$	29.6146	1.09310
$735$	42.0184	1.54987
$736$	1.00000	0.0368605
$737$	11.7465	0.432686
$738$	−44.5257	−1.63902
$739$	−28.7748	−1.05850	−0.529249	−	0.848466i	$-0.677526\pi$
$739$	−28.7748	−1.05850	−0.529249	+	0.848466i	$0.677526\pi$
$740$	33.2038	1.22059
$741$	85.1282	3.12726
$742$	19.0213	0.698294
$743$	−42.9715	−1.57647	−0.788236	−	0.615373i	$-0.789005\pi$
$743$	−42.9715	−1.57647	−0.788236	+	0.615373i	$0.789005\pi$
$744$	3.98831	0.146218
$745$	77.6150	2.84360
$746$	−19.1154	−0.699866
$747$	19.6636	0.719452
$748$	3.25946	0.119178
$749$	−0.791845	−0.0289334
$750$	−36.3540	−1.32746
$751$	−19.7661	−0.721273	−0.360637	−	0.932706i	$-0.617441\pi$
$751$	−19.7661	−0.721273	−0.360637	+	0.932706i	$0.617441\pi$
$752$	−7.23746	−0.263923
$753$	46.5633	1.69686
$754$	34.7774	1.26652
$755$	−53.7953	−1.95781
$756$	−5.30202	−0.192833
$757$	−5.04903	−0.183510	−0.0917551	−	0.995782i	$-0.529248\pi$
$757$	−5.04903	−0.183510	−0.0917551	+	0.995782i	$0.529248\pi$
$758$	−17.6976	−0.642807
$759$	−2.92007	−0.105992
$760$	−23.4028	−0.848908
$761$	−5.03035	−0.182350	−0.0911751	−	0.995835i	$-0.529062\pi$
$761$	−5.03035	−0.182350	−0.0911751	+	0.995835i	$0.529062\pi$
$762$	16.1645	0.585579
$763$	−2.63831	−0.0955132
$764$	20.0762	0.726330
$765$	46.3621	1.67623
$766$	7.79563	0.281667
$767$	−38.0622	−1.37435
$768$	−2.68141	−0.0967569
$769$	3.03255	0.109356	0.0546782	−	0.998504i	$-0.482587\pi$
$769$	3.03255	0.109356	0.0546782	+	0.998504i	$0.482587\pi$
$770$	6.69002	0.241092
$771$	9.31210	0.335367
$772$	−5.82053	−0.209485
$773$	−53.5381	−1.92563	−0.962815	−	0.270160i	$-0.912923\pi$
$773$	−53.5381	−1.92563	−0.962815	+	0.270160i	$0.912923\pi$
$774$	40.7000	1.46293
$775$	−12.8917	−0.463084
$776$	3.19159	0.114571
$777$	−40.0187	−1.43566
$778$	−0.0914446	−0.00327845
$779$	67.2712	2.41024
$780$	−49.7152	−1.78009
$781$	−0.756877	−0.0270832
$782$	2.99305	0.107031
$783$	−22.1258	−0.790710
$784$	−4.23872	−0.151383
$785$	15.5477	0.554921
$786$	−2.68141	−0.0956426
$787$	17.8688	0.636952	0.318476	−	0.947931i	$-0.396829\pi$
$787$	17.8688	0.636952	0.318476	+	0.947931i	$0.396829\pi$
$788$	−5.35782	−0.190864
$789$	−36.1685	−1.28763
$790$	6.55018	0.233045
$791$	−23.0272	−0.818754
$792$	4.56287	0.162135
$793$	−13.7520	−0.488348
$794$	2.52040	0.0894457
$795$	−113.472	−4.02444
$796$	5.77556	0.204709
$797$	8.43370	0.298737	0.149368	−	0.988782i	$-0.452276\pi$
$797$	8.43370	0.298737	0.149368	+	0.988782i	$0.452276\pi$
$798$	28.2061	0.998485
$799$	−21.6621	−0.766350
$800$	8.66732	0.306436
$801$	−54.2486	−1.91678
$802$	14.9678	0.528532
$803$	1.05365	0.0371827
$804$	−28.9227	−1.02002
$805$	6.14323	0.216520
$806$	−7.45953	−0.262751
$807$	57.1089	2.01033
$808$	−3.46021	−0.121730
$809$	−32.5261	−1.14356	−0.571778	−	0.820408i	$-0.693746\pi$
$809$	−32.5261	−1.14356	−0.571778	+	0.820408i	$0.693746\pi$
$810$	−14.8404	−0.521438
$811$	−54.7159	−1.92133	−0.960667	−	0.277703i	$-0.910427\pi$
$811$	−54.7159	−1.92133	−0.960667	+	0.277703i	$0.910427\pi$
$812$	11.5230	0.404379
$813$	21.1173	0.740615
$814$	9.78085	0.342819
$815$	−39.9856	−1.40063
$816$	−8.02558	−0.280952
$817$	−61.4911	−2.15130
$818$	−17.3283	−0.605871
$819$	34.9179	1.22013
$820$	−39.2867	−1.37195
$821$	−11.6774	−0.407543	−0.203771	−	0.979019i	$-0.565320\pi$
$821$	−11.6774	−0.407543	−0.203771	+	0.979019i	$0.565320\pi$
$822$	−1.74995	−0.0610364
$823$	44.2793	1.54348	0.771739	−	0.635939i	$-0.219387\pi$
$823$	44.2793	1.54348	0.771739	+	0.635939i	$0.219387\pi$
$824$	−12.6403	−0.440346
$825$	−25.3092	−0.881153
$826$	−12.6114	−0.438807
$827$	−14.5798	−0.506990	−0.253495	−	0.967337i	$-0.581580\pi$
$827$	−14.5798	−0.506990	−0.253495	+	0.967337i	$0.581580\pi$
$828$	4.18994	0.145610
$829$	−41.9602	−1.45734	−0.728669	−	0.684866i	$-0.759861\pi$
$829$	−41.9602	−1.45734	−0.728669	+	0.684866i	$0.759861\pi$
$830$	17.3499	0.602223
$831$	−3.99927	−0.138733
$832$	5.01517	0.173870
$833$	−12.6867	−0.439569
$834$	26.7638	0.926754
$835$	35.1747	1.21727
$836$	−6.89377	−0.238426
$837$	4.74583	0.164040
$838$	−1.17631	−0.0406349
$839$	39.1179	1.35050	0.675250	−	0.737589i	$-0.264036\pi$
$839$	39.1179	1.35050	0.675250	+	0.737589i	$0.264036\pi$
$840$	−16.4725	−0.568355
$841$	19.0866	0.658157
$842$	−12.6702	−0.436642
$843$	−24.6744	−0.849832
$844$	26.4089	0.909033
$845$	44.9248	1.54546
$846$	−30.3245	−1.04258
$847$	−16.3081	−0.560353
$848$	11.4468	0.393086
$849$	−48.9672	−1.68055
$850$	25.9417	0.889794
$851$	8.98143	0.307880
$852$	1.86362	0.0638465
$853$	−8.54342	−0.292521	−0.146261	−	0.989246i	$-0.546724\pi$
$853$	−8.54342	−0.292521	−0.146261	+	0.989246i	$0.546724\pi$
$854$	−4.55654	−0.155922
$855$	−98.0561	−3.35345
$856$	−0.476525	−0.0162873
$857$	−28.7788	−0.983064	−0.491532	−	0.870859i	$-0.663563\pi$
$857$	−28.7788	−0.983064	−0.491532	+	0.870859i	$0.663563\pi$
$858$	−14.6446	−0.499960
$859$	−24.7949	−0.845992	−0.422996	−	0.906131i	$-0.639022\pi$
$859$	−24.7949	−0.845992	−0.422996	+	0.906131i	$0.639022\pi$
$860$	35.9111	1.22456
$861$	47.3501	1.61369
$862$	24.8859	0.847616
$863$	55.4404	1.88721	0.943607	−	0.331067i	$-0.107408\pi$
$863$	55.4404	1.88721	0.943607	+	0.331067i	$0.107408\pi$
$864$	−3.19070	−0.108550
$865$	0.553070	0.0188049
$866$	34.6479	1.17738
$867$	21.5629	0.732315
$868$	−2.47162	−0.0838921
$869$	1.92949	0.0654535
$870$	−68.7410	−2.33054
$871$	54.0955	1.83296
$872$	−1.58771	−0.0537666
$873$	13.3725	0.452592
$874$	−6.33032	−0.214126
$875$	22.5292	0.761625
$876$	−2.59436	−0.0876552
$877$	44.7351	1.51060	0.755298	−	0.655382i	$-0.227492\pi$
$877$	44.7351	1.51060	0.755298	+	0.655382i	$0.227492\pi$
$878$	12.3436	0.416576
$879$	31.0916	1.04869
$880$	4.02599	0.135716
$881$	21.8990	0.737796	0.368898	−	0.929470i	$-0.379735\pi$
$881$	21.8990	0.737796	0.368898	+	0.929470i	$0.379735\pi$
$882$	−17.7600	−0.598010
$883$	4.88526	0.164402	0.0822010	−	0.996616i	$-0.473805\pi$
$883$	4.88526	0.164402	0.0822010	+	0.996616i	$0.473805\pi$
$884$	15.0107	0.504863
$885$	75.2337	2.52895
$886$	−4.49638	−0.151059
$887$	−32.1354	−1.07900	−0.539501	−	0.841985i	$-0.681387\pi$
$887$	−32.1354	−1.07900	−0.539501	+	0.841985i	$0.681387\pi$
$888$	−24.0829	−0.808168
$889$	−10.0174	−0.335973
$890$	−47.8655	−1.60446
$891$	−4.37154	−0.146452
$892$	8.69125	0.291005
$893$	45.8155	1.53316
$894$	−56.2946	−1.88277
$895$	−87.0697	−2.91042
$896$	1.66171	0.0555138
$897$	−13.4477	−0.449006
$898$	18.7419	0.625425
$899$	−10.3143	−0.344000
$900$	36.3155	1.21052
$901$	34.2610	1.14140
$902$	−11.5727	−0.385329
$903$	−43.2817	−1.44032
$904$	−13.8576	−0.460896
$905$	−3.94349	−0.131086
$906$	39.0180	1.29629
$907$	55.3531	1.83797	0.918985	−	0.394292i	$-0.129010\pi$
$907$	55.3531	1.83797	0.918985	+	0.394292i	$0.129010\pi$
$908$	−9.12147	−0.302707
$909$	−14.4981	−0.480871
$910$	30.8093	1.02132
$911$	31.3925	1.04008	0.520040	−	0.854142i	$-0.325917\pi$
$911$	31.3925	1.04008	0.520040	+	0.854142i	$0.325917\pi$
$912$	16.9742	0.562071
$913$	5.11076	0.169142
$914$	34.2518	1.13295
$915$	27.1822	0.898616
$916$	9.00477	0.297526
$917$	1.66171	0.0548745
$918$	−9.54994	−0.315195
$919$	−53.0592	−1.75026	−0.875130	−	0.483887i	$-0.839224\pi$
$919$	−53.0592	−1.75026	−0.875130	+	0.483887i	$0.839224\pi$
$920$	3.69693	0.121884
$921$	33.8208	1.11443
$922$	1.67906	0.0552967
$923$	−3.48562	−0.114730
$924$	−4.85231	−0.159629
$925$	77.8449	2.55953
$926$	15.3605	0.504778
$927$	−52.9620	−1.73950
$928$	6.93445	0.227634
$929$	58.4233	1.91681	0.958403	−	0.285417i	$-0.0921321\pi$
$929$	58.4233	1.91681	0.958403	+	0.285417i	$0.0921321\pi$
$930$	14.7445	0.483491
$931$	26.8325	0.879399
$932$	−15.3077	−0.501421
$933$	−28.1421	−0.921331
$934$	−10.0313	−0.328233
$935$	12.0500	0.394077
$936$	21.0132	0.686839
$937$	12.9685	0.423661	0.211830	−	0.977306i	$-0.432058\pi$
$937$	12.9685	0.423661	0.211830	+	0.977306i	$0.432058\pi$
$938$	17.9238	0.585234
$939$	−20.8436	−0.680205
$940$	−26.7564	−0.872698
$941$	56.5907	1.84480	0.922402	−	0.386232i	$-0.126224\pi$
$941$	56.5907	1.84480	0.922402	+	0.386232i	$0.126224\pi$
$942$	−11.2768	−0.367419
$943$	−10.6268	−0.346057
$944$	−7.58942	−0.247014
$945$	−19.6012	−0.637628
$946$	10.5783	0.343932
$947$	−37.6397	−1.22313	−0.611564	−	0.791195i	$-0.709459\pi$
$947$	−37.6397	−1.22313	−0.611564	+	0.791195i	$0.709459\pi$
$948$	−4.75088	−0.154301
$949$	4.85236	0.157514
$950$	−54.8669	−1.78012
$951$	−53.2759	−1.72759
$952$	4.97358	0.161195
$953$	−55.0491	−1.78322	−0.891608	−	0.452808i	$-0.850422\pi$
$953$	−55.0491	−1.78322	−0.891608	+	0.452808i	$0.850422\pi$
$954$	47.9615	1.55281
$955$	74.2202	2.40171
$956$	13.5363	0.437795
$957$	−20.2491	−0.654560
$958$	3.80368	0.122891
$959$	1.08447	0.0350193
$960$	−9.91298	−0.319940
$961$	−28.7877	−0.928634
$962$	45.0434	1.45226
$963$	−1.99661	−0.0643398
$964$	8.58434	0.276483
$965$	−21.5181	−0.692692
$966$	−4.45572	−0.143360
$967$	16.1574	0.519585	0.259793	−	0.965664i	$-0.416346\pi$
$967$	16.1574	0.519585	0.259793	+	0.965664i	$0.416346\pi$
$968$	−9.81406	−0.315436
$969$	50.8045	1.63208
$970$	11.7991	0.378846
$971$	−56.5743	−1.81556	−0.907778	−	0.419451i	$-0.862223\pi$
$971$	−56.5743	−1.81556	−0.907778	+	0.419451i	$0.862223\pi$
$972$	20.3359	0.652275
$973$	−16.5859	−0.531721
$974$	−12.6344	−0.404831
$975$	−116.555	−3.73276
$976$	−2.74208	−0.0877719
$977$	4.84557	0.155023	0.0775117	−	0.996991i	$-0.475302\pi$
$977$	4.84557	0.155023	0.0775117	+	0.996991i	$0.475302\pi$
$978$	29.0017	0.927373
$979$	−14.0998	−0.450631
$980$	−15.6703	−0.500569
$981$	−6.65240	−0.212395
$982$	9.95538	0.317689
$983$	−19.1235	−0.609945	−0.304973	−	0.952361i	$-0.598647\pi$
$983$	−19.1235	−0.609945	−0.304973	+	0.952361i	$0.598647\pi$
$984$	28.4948	0.908382
$985$	−19.8075	−0.631119
$986$	20.7552	0.660979
$987$	32.2481	1.02647
$988$	−31.7476	−1.01003
$989$	9.71374	0.308879
$990$	16.8686	0.536121
$991$	3.27745	0.104112	0.0520558	−	0.998644i	$-0.483423\pi$
$991$	3.27745	0.104112	0.0520558	+	0.998644i	$0.483423\pi$
$992$	−1.48739	−0.0472248
$993$	14.8463	0.471132
$994$	−1.15491	−0.0366316
$995$	21.3519	0.676900
$996$	−12.5840	−0.398738
$997$	43.7250	1.38478	0.692392	−	0.721522i	$-0.256557\pi$
$997$	43.7250	1.38478	0.692392	+	0.721522i	$0.256557\pi$
$998$	3.23165	0.102296
$999$	−28.6571	−0.906670

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6026.2.a.m.1.6	✓	41

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6026.2.a.m.1.6	✓	41	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.68141 q^{3} +1.00000 q^{4} +3.69693 q^{5} -2.68141 q^{6} +1.66171 q^{7} +1.00000 q^{8} +4.18994 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.68141 q^{3} +1.00000 q^{4} +3.69693 q^{5} -2.68141 q^{6} +1.66171 q^{7} +1.00000 q^{8} +4.18994 q^{9} +3.69693 q^{10} +1.08901 q^{11} -2.68141 q^{12} +5.01517 q^{13} +1.66171 q^{14} -9.91298 q^{15} +1.00000 q^{16} +2.99305 q^{17} +4.18994 q^{18} -6.33032 q^{19} +3.69693 q^{20} -4.45572 q^{21} +1.08901 q^{22} +1.00000 q^{23} -2.68141 q^{24} +8.66732 q^{25} +5.01517 q^{26} -3.19070 q^{27} +1.66171 q^{28} +6.93445 q^{29} -9.91298 q^{30} -1.48739 q^{31} +1.00000 q^{32} -2.92007 q^{33} +2.99305 q^{34} +6.14323 q^{35} +4.18994 q^{36} +8.98143 q^{37} -6.33032 q^{38} -13.4477 q^{39} +3.69693 q^{40} -10.6268 q^{41} -4.45572 q^{42} +9.71374 q^{43} +1.08901 q^{44} +15.4899 q^{45} +1.00000 q^{46} -7.23746 q^{47} -2.68141 q^{48} -4.23872 q^{49} +8.66732 q^{50} -8.02558 q^{51} +5.01517 q^{52} +11.4468 q^{53} -3.19070 q^{54} +4.02599 q^{55} +1.66171 q^{56} +16.9742 q^{57} +6.93445 q^{58} -7.58942 q^{59} -9.91298 q^{60} -2.74208 q^{61} -1.48739 q^{62} +6.96246 q^{63} +1.00000 q^{64} +18.5407 q^{65} -2.92007 q^{66} +10.7864 q^{67} +2.99305 q^{68} -2.68141 q^{69} +6.14323 q^{70} -0.695015 q^{71} +4.18994 q^{72} +0.967537 q^{73} +8.98143 q^{74} -23.2406 q^{75} -6.33032 q^{76} +1.80961 q^{77} -13.4477 q^{78} +1.77179 q^{79} +3.69693 q^{80} -4.01424 q^{81} -10.6268 q^{82} +4.69305 q^{83} -4.45572 q^{84} +11.0651 q^{85} +9.71374 q^{86} -18.5941 q^{87} +1.08901 q^{88} -12.9474 q^{89} +15.4899 q^{90} +8.33375 q^{91} +1.00000 q^{92} +3.98831 q^{93} -7.23746 q^{94} -23.4028 q^{95} -2.68141 q^{96} +3.19159 q^{97} -4.23872 q^{98} +4.56287 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 41 q + 41 q^{2} + 4 q^{3} + 41 q^{4} + 9 q^{5} + 4 q^{6} + 12 q^{7} + 41 q^{8} + 63 q^{9}+O(q^{10}) \) 41 * q + 41 * q^2 + 4 * q^3 + 41 * q^4 + 9 * q^5 + 4 * q^6 + 12 * q^7 + 41 * q^8 + 63 * q^9	\( 41 q + 41 q^{2} + 4 q^{3} + 41 q^{4} + 9 q^{5} + 4 q^{6} + 12 q^{7} + 41 q^{8} + 63 q^{9} + 9 q^{10} + 4 q^{11} + 4 q^{12} + 16 q^{13} + 12 q^{14} + 10 q^{15} + 41 q^{16} + 10 q^{17} + 63 q^{18} + 16 q^{19} + 9 q^{20} + 16 q^{21} + 4 q^{22} + 41 q^{23} + 4 q^{24} + 76 q^{25} + 16 q^{26} + 7 q^{27} + 12 q^{28} + 28 q^{29} + 10 q^{30} + 25 q^{31} + 41 q^{32} + 5 q^{33} + 10 q^{34} + 4 q^{35} + 63 q^{36} + 26 q^{37} + 16 q^{38} + 50 q^{39} + 9 q^{40} + 27 q^{41} + 16 q^{42} + 12 q^{43} + 4 q^{44} + 44 q^{45} + 41 q^{46} + 18 q^{47} + 4 q^{48} + 87 q^{49} + 76 q^{50} + 24 q^{51} + 16 q^{52} + 63 q^{53} + 7 q^{54} + 18 q^{55} + 12 q^{56} - 12 q^{57} + 28 q^{58} + 33 q^{59} + 10 q^{60} + 24 q^{61} + 25 q^{62} + 48 q^{63} + 41 q^{64} + 21 q^{65} + 5 q^{66} - 9 q^{67} + 10 q^{68} + 4 q^{69} + 4 q^{70} + 36 q^{71} + 63 q^{72} + 36 q^{73} + 26 q^{74} + 6 q^{75} + 16 q^{76} + 48 q^{77} + 50 q^{78} + 51 q^{79} + 9 q^{80} + 149 q^{81} + 27 q^{82} - 27 q^{83} + 16 q^{84} + 52 q^{85} + 12 q^{86} - 3 q^{87} + 4 q^{88} + 68 q^{89} + 44 q^{90} + 22 q^{91} + 41 q^{92} + 45 q^{93} + 18 q^{94} + 46 q^{95} + 4 q^{96} + 16 q^{97} + 87 q^{98} - 10 q^{99}+O(q^{100}) \) 41 * q + 41 * q^2 + 4 * q^3 + 41 * q^4 + 9 * q^5 + 4 * q^6 + 12 * q^7 + 41 * q^8 + 63 * q^9 + 9 * q^10 + 4 * q^11 + 4 * q^12 + 16 * q^13 + 12 * q^14 + 10 * q^15 + 41 * q^16 + 10 * q^17 + 63 * q^18 + 16 * q^19 + 9 * q^20 + 16 * q^21 + 4 * q^22 + 41 * q^23 + 4 * q^24 + 76 * q^25 + 16 * q^26 + 7 * q^27 + 12 * q^28 + 28 * q^29 + 10 * q^30 + 25 * q^31 + 41 * q^32 + 5 * q^33 + 10 * q^34 + 4 * q^35 + 63 * q^36 + 26 * q^37 + 16 * q^38 + 50 * q^39 + 9 * q^40 + 27 * q^41 + 16 * q^42 + 12 * q^43 + 4 * q^44 + 44 * q^45 + 41 * q^46 + 18 * q^47 + 4 * q^48 + 87 * q^49 + 76 * q^50 + 24 * q^51 + 16 * q^52 + 63 * q^53 + 7 * q^54 + 18 * q^55 + 12 * q^56 - 12 * q^57 + 28 * q^58 + 33 * q^59 + 10 * q^60 + 24 * q^61 + 25 * q^62 + 48 * q^63 + 41 * q^64 + 21 * q^65 + 5 * q^66 - 9 * q^67 + 10 * q^68 + 4 * q^69 + 4 * q^70 + 36 * q^71 + 63 * q^72 + 36 * q^73 + 26 * q^74 + 6 * q^75 + 16 * q^76 + 48 * q^77 + 50 * q^78 + 51 * q^79 + 9 * q^80 + 149 * q^81 + 27 * q^82 - 27 * q^83 + 16 * q^84 + 52 * q^85 + 12 * q^86 - 3 * q^87 + 4 * q^88 + 68 * q^89 + 44 * q^90 + 22 * q^91 + 41 * q^92 + 45 * q^93 + 18 * q^94 + 46 * q^95 + 4 * q^96 + 16 * q^97 + 87 * q^98 - 10 * q^99

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