LMFDB - Embedded newform 6026.2.a.k.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("6026.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

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

Embedding invariants

Embedding label			1.9
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)

$f(q)$	$=$	$q+1.00000 q^{2} -2.05490 q^{3} +1.00000 q^{4} +0.786161 q^{5} -2.05490 q^{6} -2.31145 q^{7} +1.00000 q^{8} +1.22260 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.05490 q^{3} +1.00000 q^{4} +0.786161 q^{5} -2.05490 q^{6} -2.31145 q^{7} +1.00000 q^{8} +1.22260 q^{9} +0.786161 q^{10} +0.549829 q^{11} -2.05490 q^{12} +7.02447 q^{13} -2.31145 q^{14} -1.61548 q^{15} +1.00000 q^{16} -1.36147 q^{17} +1.22260 q^{18} -4.58483 q^{19} +0.786161 q^{20} +4.74979 q^{21} +0.549829 q^{22} -1.00000 q^{23} -2.05490 q^{24} -4.38195 q^{25} +7.02447 q^{26} +3.65238 q^{27} -2.31145 q^{28} -4.02196 q^{29} -1.61548 q^{30} +0.353798 q^{31} +1.00000 q^{32} -1.12984 q^{33} -1.36147 q^{34} -1.81717 q^{35} +1.22260 q^{36} +5.31013 q^{37} -4.58483 q^{38} -14.4345 q^{39} +0.786161 q^{40} +3.51154 q^{41} +4.74979 q^{42} +2.95696 q^{43} +0.549829 q^{44} +0.961158 q^{45} -1.00000 q^{46} +12.7104 q^{47} -2.05490 q^{48} -1.65719 q^{49} -4.38195 q^{50} +2.79767 q^{51} +7.02447 q^{52} +5.85896 q^{53} +3.65238 q^{54} +0.432254 q^{55} -2.31145 q^{56} +9.42134 q^{57} -4.02196 q^{58} -3.66073 q^{59} -1.61548 q^{60} -5.15900 q^{61} +0.353798 q^{62} -2.82597 q^{63} +1.00000 q^{64} +5.52236 q^{65} -1.12984 q^{66} +11.9110 q^{67} -1.36147 q^{68} +2.05490 q^{69} -1.81717 q^{70} -14.7381 q^{71} +1.22260 q^{72} -1.84671 q^{73} +5.31013 q^{74} +9.00445 q^{75} -4.58483 q^{76} -1.27090 q^{77} -14.4345 q^{78} -4.22285 q^{79} +0.786161 q^{80} -11.1730 q^{81} +3.51154 q^{82} -1.45868 q^{83} +4.74979 q^{84} -1.07033 q^{85} +2.95696 q^{86} +8.26470 q^{87} +0.549829 q^{88} +16.3057 q^{89} +0.961158 q^{90} -16.2367 q^{91} -1.00000 q^{92} -0.727018 q^{93} +12.7104 q^{94} -3.60441 q^{95} -2.05490 q^{96} -2.55578 q^{97} -1.65719 q^{98} +0.672219 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 35 q + 35 q^{2} - 3 q^{3} + 35 q^{4} + 10 q^{5} - 3 q^{6} + 14 q^{7} + 35 q^{8} + 54 q^{9}+O(q^{10}) $ 35 * q + 35 * q^2 - 3 * q^3 + 35 * q^4 + 10 * q^5 - 3 * q^6 + 14 * q^7 + 35 * q^8 + 54 * q^9	\( 35 q + 35 q^{2} - 3 q^{3} + 35 q^{4} + 10 q^{5} - 3 q^{6} + 14 q^{7} + 35 q^{8} + 54 q^{9} + 10 q^{10} + 9 q^{11} - 3 q^{12} + 19 q^{13} + 14 q^{14} + 14 q^{15} + 35 q^{16} + 28 q^{17} + 54 q^{18} + 21 q^{19} + 10 q^{20} + 28 q^{21} + 9 q^{22} - 35 q^{23} - 3 q^{24} + 81 q^{25} + 19 q^{26} - 21 q^{27} + 14 q^{28} + 35 q^{29} + 14 q^{30} + 5 q^{31} + 35 q^{32} + 26 q^{33} + 28 q^{34} - 7 q^{35} + 54 q^{36} + 51 q^{37} + 21 q^{38} + 21 q^{39} + 10 q^{40} + 3 q^{41} + 28 q^{42} + 43 q^{43} + 9 q^{44} + 2 q^{45} - 35 q^{46} + 10 q^{47} - 3 q^{48} + 85 q^{49} + 81 q^{50} + 26 q^{51} + 19 q^{52} + 39 q^{53} - 21 q^{54} + 2 q^{55} + 14 q^{56} + 50 q^{57} + 35 q^{58} - 42 q^{59} + 14 q^{60} + 47 q^{61} + 5 q^{62} + 23 q^{63} + 35 q^{64} + 61 q^{65} + 26 q^{66} + 22 q^{67} + 28 q^{68} + 3 q^{69} - 7 q^{70} + 54 q^{72} + 30 q^{73} + 51 q^{74} - 26 q^{75} + 21 q^{76} + 2 q^{77} + 21 q^{78} + 55 q^{79} + 10 q^{80} + 67 q^{81} + 3 q^{82} + 20 q^{83} + 28 q^{84} + 28 q^{85} + 43 q^{86} + 29 q^{87} + 9 q^{88} - 31 q^{89} + 2 q^{90} + 32 q^{91} - 35 q^{92} + 11 q^{93} + 10 q^{94} + 16 q^{95} - 3 q^{96} + 36 q^{97} + 85 q^{98} - 9 q^{99}+O(q^{100}) \) 35 * q + 35 * q^2 - 3 * q^3 + 35 * q^4 + 10 * q^5 - 3 * q^6 + 14 * q^7 + 35 * q^8 + 54 * q^9 + 10 * q^10 + 9 * q^11 - 3 * q^12 + 19 * q^13 + 14 * q^14 + 14 * q^15 + 35 * q^16 + 28 * q^17 + 54 * q^18 + 21 * q^19 + 10 * q^20 + 28 * q^21 + 9 * q^22 - 35 * q^23 - 3 * q^24 + 81 * q^25 + 19 * q^26 - 21 * q^27 + 14 * q^28 + 35 * q^29 + 14 * q^30 + 5 * q^31 + 35 * q^32 + 26 * q^33 + 28 * q^34 - 7 * q^35 + 54 * q^36 + 51 * q^37 + 21 * q^38 + 21 * q^39 + 10 * q^40 + 3 * q^41 + 28 * q^42 + 43 * q^43 + 9 * q^44 + 2 * q^45 - 35 * q^46 + 10 * q^47 - 3 * q^48 + 85 * q^49 + 81 * q^50 + 26 * q^51 + 19 * q^52 + 39 * q^53 - 21 * q^54 + 2 * q^55 + 14 * q^56 + 50 * q^57 + 35 * q^58 - 42 * q^59 + 14 * q^60 + 47 * q^61 + 5 * q^62 + 23 * q^63 + 35 * q^64 + 61 * q^65 + 26 * q^66 + 22 * q^67 + 28 * q^68 + 3 * q^69 - 7 * q^70 + 54 * q^72 + 30 * q^73 + 51 * q^74 - 26 * q^75 + 21 * q^76 + 2 * q^77 + 21 * q^78 + 55 * q^79 + 10 * q^80 + 67 * q^81 + 3 * q^82 + 20 * q^83 + 28 * q^84 + 28 * q^85 + 43 * q^86 + 29 * q^87 + 9 * q^88 - 31 * q^89 + 2 * q^90 + 32 * q^91 - 35 * q^92 + 11 * q^93 + 10 * q^94 + 16 * q^95 - 3 * q^96 + 36 * q^97 + 85 * q^98 - 9 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−2.05490	−1.18639	−0.593197	−	0.805057i	$-0.702135\pi$
$3$	−2.05490	−1.18639	−0.593197	+	0.805057i	$0.702135\pi$
$4$	1.00000	0.500000
$5$	0.786161	0.351582	0.175791	−	0.984428i	$-0.443752\pi$
$5$	0.786161	0.351582	0.175791	+	0.984428i	$0.443752\pi$
$6$	−2.05490	−0.838908
$7$	−2.31145	−0.873646	−0.436823	−	0.899547i	$-0.643896\pi$
$7$	−2.31145	−0.873646	−0.436823	+	0.899547i	$0.643896\pi$
$8$	1.00000	0.353553
$9$	1.22260	0.407532
$10$	0.786161	0.248606
$11$	0.549829	0.165780	0.0828898	−	0.996559i	$-0.473585\pi$
$11$	0.549829	0.165780	0.0828898	+	0.996559i	$0.473585\pi$
$12$	−2.05490	−0.593197
$13$	7.02447	1.94824	0.974118	−	0.226040i	$-0.0725779\pi$
$13$	7.02447	1.94824	0.974118	+	0.226040i	$0.0725779\pi$
$14$	−2.31145	−0.617761
$15$	−1.61548	−0.417115
$16$	1.00000	0.250000
$17$	−1.36147	−0.330204	−0.165102	−	0.986276i	$-0.552795\pi$
$17$	−1.36147	−0.330204	−0.165102	+	0.986276i	$0.552795\pi$
$18$	1.22260	0.288169
$19$	−4.58483	−1.05183	−0.525916	−	0.850537i	$-0.676277\pi$
$19$	−4.58483	−1.05183	−0.525916	+	0.850537i	$0.676277\pi$
$20$	0.786161	0.175791
$21$	4.74979	1.03649
$22$	0.549829	0.117224
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	−2.05490	−0.419454
$25$	−4.38195	−0.876390
$26$	7.02447	1.37761
$27$	3.65238	0.702901
$28$	−2.31145	−0.436823
$29$	−4.02196	−0.746859	−0.373429	−	0.927659i	$-0.621818\pi$
$29$	−4.02196	−0.746859	−0.373429	+	0.927659i	$0.621818\pi$
$30$	−1.61548	−0.294945
$31$	0.353798	0.0635440	0.0317720	−	0.999495i	$-0.489885\pi$
$31$	0.353798	0.0635440	0.0317720	+	0.999495i	$0.489885\pi$
$32$	1.00000	0.176777
$33$	−1.12984	−0.196680
$34$	−1.36147	−0.233490
$35$	−1.81717	−0.307158
$36$	1.22260	0.203766
$37$	5.31013	0.872981	0.436490	−	0.899709i	$-0.356221\pi$
$37$	5.31013	0.872981	0.436490	+	0.899709i	$0.356221\pi$
$38$	−4.58483	−0.743757
$39$	−14.4345	−2.31138
$40$	0.786161	0.124303
$41$	3.51154	0.548410	0.274205	−	0.961671i	$-0.411585\pi$
$41$	3.51154	0.548410	0.274205	+	0.961671i	$0.411585\pi$
$42$	4.74979	0.732909
$43$	2.95696	0.450933	0.225466	−	0.974251i	$-0.427609\pi$
$43$	2.95696	0.450933	0.225466	+	0.974251i	$0.427609\pi$
$44$	0.549829	0.0828898
$45$	0.961158	0.143281
$46$	−1.00000	−0.147442
$47$	12.7104	1.85400	0.927000	−	0.375061i	$-0.122378\pi$
$47$	12.7104	1.85400	0.927000	+	0.375061i	$0.122378\pi$
$48$	−2.05490	−0.296599
$49$	−1.65719	−0.236742
$50$	−4.38195	−0.619701
$51$	2.79767	0.391753
$52$	7.02447	0.974118
$53$	5.85896	0.804790	0.402395	−	0.915466i	$-0.368178\pi$
$53$	5.85896	0.804790	0.402395	+	0.915466i	$0.368178\pi$
$54$	3.65238	0.497026
$55$	0.432254	0.0582851
$56$	−2.31145	−0.308881
$57$	9.42134	1.24789
$58$	−4.02196	−0.528109
$59$	−3.66073	−0.476587	−0.238294	−	0.971193i	$-0.576588\pi$
$59$	−3.66073	−0.476587	−0.238294	+	0.971193i	$0.576588\pi$
$60$	−1.61548	−0.208557
$61$	−5.15900	−0.660542	−0.330271	−	0.943886i	$-0.607140\pi$
$61$	−5.15900	−0.660542	−0.330271	+	0.943886i	$0.607140\pi$
$62$	0.353798	0.0449324
$63$	−2.82597	−0.356039
$64$	1.00000	0.125000
$65$	5.52236	0.684965
$66$	−1.12984	−0.139074
$67$	11.9110	1.45516	0.727578	−	0.686025i	$-0.240646\pi$
$67$	11.9110	1.45516	0.727578	+	0.686025i	$0.240646\pi$
$68$	−1.36147	−0.165102
$69$	2.05490	0.247380
$70$	−1.81717	−0.217194
$71$	−14.7381	−1.74909	−0.874543	−	0.484948i	$-0.838839\pi$
$71$	−14.7381	−1.74909	−0.874543	+	0.484948i	$0.838839\pi$
$72$	1.22260	0.144084
$73$	−1.84671	−0.216141	−0.108070	−	0.994143i	$-0.534467\pi$
$73$	−1.84671	−0.216141	−0.108070	+	0.994143i	$0.534467\pi$
$74$	5.31013	0.617290
$75$	9.00445	1.03974
$76$	−4.58483	−0.525916
$77$	−1.27090	−0.144833
$78$	−14.4345	−1.63439
$79$	−4.22285	−0.475108	−0.237554	−	0.971374i	$-0.576346\pi$
$79$	−4.22285	−0.475108	−0.237554	+	0.971374i	$0.576346\pi$
$80$	0.786161	0.0878955
$81$	−11.1730	−1.24145
$82$	3.51154	0.387785
$83$	−1.45868	−0.160111	−0.0800554	−	0.996790i	$-0.525510\pi$
$83$	−1.45868	−0.160111	−0.0800554	+	0.996790i	$0.525510\pi$
$84$	4.74979	0.518245
$85$	−1.07033	−0.116094
$86$	2.95696	0.318857
$87$	8.26470	0.886069
$88$	0.549829	0.0586120
$89$	16.3057	1.72840	0.864198	−	0.503151i	$-0.167826\pi$
$89$	16.3057	1.72840	0.864198	+	0.503151i	$0.167826\pi$
$90$	0.961158	0.101315
$91$	−16.2367	−1.70207
$92$	−1.00000	−0.104257
$93$	−0.727018	−0.0753882
$94$	12.7104	1.31098
$95$	−3.60441	−0.369805
$96$	−2.05490	−0.209727
$97$	−2.55578	−0.259500	−0.129750	−	0.991547i	$-0.541418\pi$
$97$	−2.55578	−0.259500	−0.129750	+	0.991547i	$0.541418\pi$
$98$	−1.65719	−0.167402
$99$	0.672219	0.0675605
$100$	−4.38195	−0.438195
$101$	13.9532	1.38839	0.694196	−	0.719786i	$-0.255760\pi$
$101$	13.9532	1.38839	0.694196	+	0.719786i	$0.255760\pi$
$102$	2.79767	0.277011
$103$	−9.47627	−0.933725	−0.466862	−	0.884330i	$-0.654616\pi$
$103$	−9.47627	−0.933725	−0.466862	+	0.884330i	$0.654616\pi$
$104$	7.02447	0.688806
$105$	3.73410	0.364411
$106$	5.85896	0.569072
$107$	−20.3124	−1.96367	−0.981837	−	0.189728i	$-0.939239\pi$
$107$	−20.3124	−1.96367	−0.981837	+	0.189728i	$0.939239\pi$
$108$	3.65238	0.351450
$109$	5.62438	0.538718	0.269359	−	0.963040i	$-0.413188\pi$
$109$	5.62438	0.538718	0.269359	+	0.963040i	$0.413188\pi$
$110$	0.432254	0.0412138
$111$	−10.9118	−1.03570
$112$	−2.31145	−0.218412
$113$	4.88457	0.459502	0.229751	−	0.973249i	$-0.426209\pi$
$113$	4.88457	0.459502	0.229751	+	0.973249i	$0.426209\pi$
$114$	9.42134	0.882389
$115$	−0.786161	−0.0733099
$116$	−4.02196	−0.373429
$117$	8.58809	0.793969
$118$	−3.66073	−0.336998
$119$	3.14697	0.288482
$120$	−1.61548	−0.147472
$121$	−10.6977	−0.972517
$122$	−5.15900	−0.467074
$123$	−7.21585	−0.650631
$124$	0.353798	0.0317720
$125$	−7.37573	−0.659705
$126$	−2.82597	−0.251758
$127$	4.72016	0.418846	0.209423	−	0.977825i	$-0.432841\pi$
$127$	4.72016	0.418846	0.209423	+	0.977825i	$0.432841\pi$
$128$	1.00000	0.0883883
$129$	−6.07625	−0.534984
$130$	5.52236	0.484343
$131$	−1.00000	−0.0873704
$131$	−1.00000	−0.0873704
$132$	−1.12984	−0.0983400
$133$	10.5976	0.918928
$134$	11.9110	1.02895
$135$	2.87136	0.247127
$136$	−1.36147	−0.116745
$137$	4.45233	0.380388	0.190194	−	0.981747i	$-0.439088\pi$
$137$	4.45233	0.380388	0.190194	+	0.981747i	$0.439088\pi$
$138$	2.05490	0.174924
$139$	12.0230	1.01978	0.509888	−	0.860241i	$-0.329687\pi$
$139$	12.0230	1.01978	0.509888	+	0.860241i	$0.329687\pi$
$140$	−1.81717	−0.153579
$141$	−26.1185	−2.19958
$142$	−14.7381	−1.23679
$143$	3.86225	0.322978
$144$	1.22260	0.101883
$145$	−3.16191	−0.262582
$146$	−1.84671	−0.152835
$147$	3.40536	0.280869
$148$	5.31013	0.436490
$149$	7.87689	0.645300	0.322650	−	0.946518i	$-0.395426\pi$
$149$	7.87689	0.645300	0.322650	+	0.946518i	$0.395426\pi$
$150$	9.00445	0.735210
$151$	9.71506	0.790600	0.395300	−	0.918552i	$-0.370641\pi$
$151$	9.71506	0.790600	0.395300	+	0.918552i	$0.370641\pi$
$152$	−4.58483	−0.371878
$153$	−1.66452	−0.134569
$154$	−1.27090	−0.102412
$155$	0.278142	0.0223409
$156$	−14.4345	−1.15569
$157$	21.9269	1.74996	0.874979	−	0.484162i	$-0.160875\pi$
$157$	21.9269	1.74996	0.874979	+	0.484162i	$0.160875\pi$
$158$	−4.22285	−0.335952
$159$	−12.0395	−0.954798
$160$	0.786161	0.0621515
$161$	2.31145	0.182168
$162$	−11.1730	−0.877837
$163$	20.3750	1.59589	0.797947	−	0.602728i	$-0.205919\pi$
$163$	20.3750	1.59589	0.797947	+	0.602728i	$0.205919\pi$
$164$	3.51154	0.274205
$165$	−0.888237	−0.0691492
$166$	−1.45868	−0.113215
$167$	−1.74639	−0.135140	−0.0675700	−	0.997715i	$-0.521525\pi$
$167$	−1.74639	−0.135140	−0.0675700	+	0.997715i	$0.521525\pi$
$168$	4.74979	0.366454
$169$	36.3431	2.79562
$170$	−1.07033	−0.0820908
$171$	−5.60539	−0.428655
$172$	2.95696	0.225466
$173$	−0.935831	−0.0711500	−0.0355750	−	0.999367i	$-0.511326\pi$
$173$	−0.935831	−0.0711500	−0.0355750	+	0.999367i	$0.511326\pi$
$174$	8.26470	0.626546
$175$	10.1287	0.765655
$176$	0.549829	0.0414449
$177$	7.52243	0.565420
$178$	16.3057	1.22216
$179$	18.7402	1.40071	0.700354	−	0.713796i	$-0.253026\pi$
$179$	18.7402	1.40071	0.700354	+	0.713796i	$0.253026\pi$
$180$	0.961158	0.0716405
$181$	21.2634	1.58049	0.790247	−	0.612788i	$-0.209952\pi$
$181$	21.2634	1.58049	0.790247	+	0.612788i	$0.209952\pi$
$182$	−16.2367	−1.20355
$183$	10.6012	0.783664
$184$	−1.00000	−0.0737210
$185$	4.17462	0.306924
$186$	−0.727018	−0.0533075
$187$	−0.748574	−0.0547412
$188$	12.7104	0.927000
$189$	−8.44230	−0.614087
$190$	−3.60441	−0.261491
$191$	1.94321	0.140605	0.0703027	−	0.997526i	$-0.477603\pi$
$191$	1.94321	0.140605	0.0703027	+	0.997526i	$0.477603\pi$
$192$	−2.05490	−0.148299
$193$	3.80577	0.273945	0.136973	−	0.990575i	$-0.456263\pi$
$193$	3.80577	0.273945	0.136973	+	0.990575i	$0.456263\pi$
$194$	−2.55578	−0.183494
$195$	−11.3479	−0.812638
$196$	−1.65719	−0.118371
$197$	7.25287	0.516745	0.258373	−	0.966045i	$-0.416814\pi$
$197$	7.25287	0.516745	0.258373	+	0.966045i	$0.416814\pi$
$198$	0.672219	0.0477725
$199$	−0.526543	−0.0373257	−0.0186628	−	0.999826i	$-0.505941\pi$
$199$	−0.526543	−0.0373257	−0.0186628	+	0.999826i	$0.505941\pi$
$200$	−4.38195	−0.309851
$201$	−24.4758	−1.72639
$202$	13.9532	0.981742
$203$	9.29656	0.652490
$204$	2.79767	0.195876
$205$	2.76064	0.192811
$206$	−9.47627	−0.660243
$207$	−1.22260	−0.0849763
$208$	7.02447	0.487059
$209$	−2.52087	−0.174372
$210$	3.73410	0.257677
$211$	−23.1675	−1.59491	−0.797457	−	0.603375i	$-0.793822\pi$
$211$	−23.1675	−1.59491	−0.797457	+	0.603375i	$0.793822\pi$
$212$	5.85896	0.402395
$213$	30.2852	2.07511
$214$	−20.3124	−1.38853
$215$	2.32465	0.158540
$216$	3.65238	0.248513
$217$	−0.817787	−0.0555150
$218$	5.62438	0.380931
$219$	3.79479	0.256428
$220$	0.432254	0.0291426
$221$	−9.56358	−0.643316
$222$	−10.9118	−0.732350
$223$	−29.1091	−1.94929	−0.974645	−	0.223757i	$-0.928168\pi$
$223$	−29.1091	−1.94929	−0.974645	+	0.223757i	$0.928168\pi$
$224$	−2.31145	−0.154440
$225$	−5.35736	−0.357157
$226$	4.88457	0.324917
$227$	5.17806	0.343680	0.171840	−	0.985125i	$-0.445029\pi$
$227$	5.17806	0.343680	0.171840	+	0.985125i	$0.445029\pi$
$228$	9.42134	0.623943
$229$	23.0381	1.52240	0.761200	−	0.648517i	$-0.224610\pi$
$229$	23.0381	1.52240	0.761200	+	0.648517i	$0.224610\pi$
$230$	−0.786161	−0.0518379
$231$	2.61157	0.171829
$232$	−4.02196	−0.264054
$233$	17.9471	1.17575	0.587877	−	0.808950i	$-0.299964\pi$
$233$	17.9471	1.17575	0.587877	+	0.808950i	$0.299964\pi$
$234$	8.58809	0.561421
$235$	9.99241	0.651833
$236$	−3.66073	−0.238294
$237$	8.67752	0.563665
$238$	3.14697	0.203987
$239$	−1.83769	−0.118870	−0.0594351	−	0.998232i	$-0.518930\pi$
$239$	−1.83769	−0.118870	−0.0594351	+	0.998232i	$0.518930\pi$
$240$	−1.61548	−0.104279
$241$	15.0476	0.969300	0.484650	−	0.874708i	$-0.338947\pi$
$241$	15.0476	0.969300	0.484650	+	0.874708i	$0.338947\pi$
$242$	−10.6977	−0.687673
$243$	12.0023	0.769949
$244$	−5.15900	−0.330271
$245$	−1.30282	−0.0832342
$246$	−7.21585	−0.460066
$247$	−32.2059	−2.04922
$248$	0.353798	0.0224662
$249$	2.99743	0.189955
$250$	−7.37573	−0.466482
$251$	5.13628	0.324199	0.162099	−	0.986774i	$-0.448173\pi$
$251$	5.13628	0.324199	0.162099	+	0.986774i	$0.448173\pi$
$252$	−2.82597	−0.178020
$253$	−0.549829	−0.0345674
$254$	4.72016	0.296169
$255$	2.19942	0.137733
$256$	1.00000	0.0625000
$257$	−14.5816	−0.909577	−0.454788	−	0.890600i	$-0.650285\pi$
$257$	−14.5816	−0.909577	−0.454788	+	0.890600i	$0.650285\pi$
$258$	−6.07625	−0.378291
$259$	−12.2741	−0.762676
$260$	5.52236	0.342482
$261$	−4.91723	−0.304369
$262$	−1.00000	−0.0617802
$263$	17.7235	1.09288	0.546440	−	0.837498i	$-0.315983\pi$
$263$	17.7235	1.09288	0.546440	+	0.837498i	$0.315983\pi$
$264$	−1.12984	−0.0695369
$265$	4.60609	0.282950
$266$	10.5976	0.649781
$267$	−33.5064	−2.05056
$268$	11.9110	0.727578
$269$	11.5199	0.702378	0.351189	−	0.936305i	$-0.385778\pi$
$269$	11.5199	0.702378	0.351189	+	0.936305i	$0.385778\pi$
$270$	2.87136	0.174745
$271$	4.66039	0.283099	0.141549	−	0.989931i	$-0.454792\pi$
$271$	4.66039	0.283099	0.141549	+	0.989931i	$0.454792\pi$
$272$	−1.36147	−0.0825511
$273$	33.3647	2.01933
$274$	4.45233	0.268975
$275$	−2.40932	−0.145288
$276$	2.05490	0.123690
$277$	7.14403	0.429243	0.214622	−	0.976697i	$-0.431148\pi$
$277$	7.14403	0.429243	0.214622	+	0.976697i	$0.431148\pi$
$278$	12.0230	0.721091
$279$	0.432552	0.0258962
$280$	−1.81717	−0.108597
$281$	14.0083	0.835666	0.417833	−	0.908524i	$-0.362790\pi$
$281$	14.0083	0.835666	0.417833	+	0.908524i	$0.362790\pi$
$282$	−26.1185	−1.55533
$283$	9.05588	0.538316	0.269158	−	0.963096i	$-0.413255\pi$
$283$	9.05588	0.538316	0.269158	+	0.963096i	$0.413255\pi$
$284$	−14.7381	−0.874543
$285$	7.40669	0.438734
$286$	3.86225	0.228380
$287$	−8.11675	−0.479117
$288$	1.22260	0.0720422
$289$	−15.1464	−0.890965
$290$	−3.16191	−0.185674
$291$	5.25186	0.307870
$292$	−1.84671	−0.108070
$293$	23.9146	1.39711	0.698554	−	0.715557i	$-0.253827\pi$
$293$	23.9146	1.39711	0.698554	+	0.715557i	$0.253827\pi$
$294$	3.40536	0.198605
$295$	−2.87793	−0.167559
$296$	5.31013	0.308645
$297$	2.00818	0.116527
$298$	7.87689	0.456296
$299$	−7.02447	−0.406235
$300$	9.00445	0.519872
$301$	−6.83487	−0.393956
$302$	9.71506	0.559039
$303$	−28.6723	−1.64718
$304$	−4.58483	−0.262958
$305$	−4.05581	−0.232235
$306$	−1.66452	−0.0951546
$307$	14.1783	0.809197	0.404598	−	0.914494i	$-0.367411\pi$
$307$	14.1783	0.809197	0.404598	+	0.914494i	$0.367411\pi$
$308$	−1.27090	−0.0724164
$309$	19.4728	1.10777
$310$	0.278142	0.0157974
$311$	−26.9475	−1.52805	−0.764025	−	0.645187i	$-0.776780\pi$
$311$	−26.9475	−1.52805	−0.764025	+	0.645187i	$0.776780\pi$
$312$	−14.4345	−0.817195
$313$	31.9564	1.80628	0.903142	−	0.429342i	$-0.141254\pi$
$313$	31.9564	1.80628	0.903142	+	0.429342i	$0.141254\pi$
$314$	21.9269	1.23741
$315$	−2.22167	−0.125177
$316$	−4.22285	−0.237554
$317$	19.7218	1.10769	0.553843	−	0.832621i	$-0.313161\pi$
$317$	19.7218	1.10769	0.553843	+	0.832621i	$0.313161\pi$
$318$	−12.0395	−0.675144
$319$	−2.21139	−0.123814
$320$	0.786161	0.0439477
$321$	41.7399	2.32969
$322$	2.31145	0.128812
$323$	6.24209	0.347319
$324$	−11.1730	−0.620725
$325$	−30.7809	−1.70741
$326$	20.3750	1.12847
$327$	−11.5575	−0.639132
$328$	3.51154	0.193892
$329$	−29.3794	−1.61974
$330$	−0.888237	−0.0488958
$331$	−16.1354	−0.886883	−0.443441	−	0.896303i	$-0.646243\pi$
$331$	−16.1354	−0.886883	−0.443441	+	0.896303i	$0.646243\pi$
$332$	−1.45868	−0.0800554
$333$	6.49215	0.355768
$334$	−1.74639	−0.0955585
$335$	9.36393	0.511606
$336$	4.74979	0.259122
$337$	18.2587	0.994615	0.497307	−	0.867574i	$-0.334322\pi$
$337$	18.2587	0.994615	0.497307	+	0.867574i	$0.334322\pi$
$338$	36.3431	1.97680
$339$	−10.0373	−0.545151
$340$	−1.07033	−0.0580469
$341$	0.194528	0.0105343
$342$	−5.60539	−0.303105
$343$	20.0107	1.08048
$344$	2.95696	0.159429
$345$	1.61548	0.0869745
$346$	−0.935831	−0.0503106
$347$	17.7437	0.952534	0.476267	−	0.879301i	$-0.341990\pi$
$347$	17.7437	0.952534	0.476267	+	0.879301i	$0.341990\pi$
$348$	8.26470	0.443035
$349$	−15.4410	−0.826535	−0.413268	−	0.910610i	$-0.635613\pi$
$349$	−15.4410	−0.826535	−0.413268	+	0.910610i	$0.635613\pi$
$350$	10.1287	0.541400
$351$	25.6560	1.36942
$352$	0.549829	0.0293060
$353$	−31.2103	−1.66115	−0.830577	−	0.556904i	$-0.811989\pi$
$353$	−31.2103	−1.66115	−0.830577	+	0.556904i	$0.811989\pi$
$354$	7.52243	0.399813
$355$	−11.5865	−0.614947
$356$	16.3057	0.864198
$357$	−6.46669	−0.342253
$358$	18.7402	0.990450
$359$	−8.63746	−0.455868	−0.227934	−	0.973677i	$-0.573197\pi$
$359$	−8.63746	−0.455868	−0.227934	+	0.973677i	$0.573197\pi$
$360$	0.961158	0.0506575
$361$	2.02062	0.106348
$362$	21.2634	1.11758
$363$	21.9826	1.15379
$364$	−16.2367	−0.851035
$365$	−1.45181	−0.0759912
$366$	10.6012	0.554134
$367$	−19.7710	−1.03204	−0.516018	−	0.856578i	$-0.672586\pi$
$367$	−19.7710	−1.03204	−0.516018	+	0.856578i	$0.672586\pi$
$368$	−1.00000	−0.0521286
$369$	4.29320	0.223495
$370$	4.17462	0.217028
$371$	−13.5427	−0.703102
$372$	−0.727018	−0.0376941
$373$	25.2140	1.30553	0.652765	−	0.757560i	$-0.273609\pi$
$373$	25.2140	1.30553	0.652765	+	0.757560i	$0.273609\pi$
$374$	−0.748574	−0.0387078
$375$	15.1563	0.782670
$376$	12.7104	0.655488
$377$	−28.2521	−1.45506
$378$	−8.44230	−0.434225
$379$	29.4771	1.51414	0.757069	−	0.653335i	$-0.226631\pi$
$379$	29.4771	1.51414	0.757069	+	0.653335i	$0.226631\pi$
$380$	−3.60441	−0.184902
$381$	−9.69943	−0.496917
$382$	1.94321	0.0994230
$383$	3.86623	0.197555	0.0987775	−	0.995110i	$-0.468507\pi$
$383$	3.86623	0.197555	0.0987775	+	0.995110i	$0.468507\pi$
$384$	−2.05490	−0.104863
$385$	−0.999134	−0.0509206
$386$	3.80577	0.193709
$387$	3.61517	0.183769
$388$	−2.55578	−0.129750
$389$	20.0994	1.01908	0.509541	−	0.860446i	$-0.329815\pi$
$389$	20.0994	1.01908	0.509541	+	0.860446i	$0.329815\pi$
$390$	−11.3479	−0.574622
$391$	1.36147	0.0688524
$392$	−1.65719	−0.0837009
$393$	2.05490	0.103656
$394$	7.25287	0.365394
$395$	−3.31984	−0.167039
$396$	0.672219	0.0337803
$397$	−31.5637	−1.58414	−0.792069	−	0.610432i	$-0.790996\pi$
$397$	−31.5637	−1.58414	−0.792069	+	0.610432i	$0.790996\pi$
$398$	−0.526543	−0.0263932
$399$	−21.7770	−1.09021
$400$	−4.38195	−0.219098
$401$	−33.8098	−1.68838	−0.844190	−	0.536044i	$-0.819918\pi$
$401$	−33.8098	−1.68838	−0.844190	+	0.536044i	$0.819918\pi$
$402$	−24.4758	−1.22074
$403$	2.48524	0.123799
$404$	13.9532	0.694196
$405$	−8.78382	−0.436471
$406$	9.29656	0.461380
$407$	2.91966	0.144722
$408$	2.79767	0.138505
$409$	−3.79592	−0.187696	−0.0938481	−	0.995587i	$-0.529917\pi$
$409$	−3.79592	−0.187696	−0.0938481	+	0.995587i	$0.529917\pi$
$410$	2.76064	0.136338
$411$	−9.14907	−0.451290
$412$	−9.47627	−0.466862
$413$	8.46161	0.416369
$414$	−1.22260	−0.0600873
$415$	−1.14676	−0.0562921
$416$	7.02447	0.344403
$417$	−24.7060	−1.20986
$418$	−2.52087	−0.123300
$419$	31.9062	1.55872	0.779360	−	0.626576i	$-0.215544\pi$
$419$	31.9062	1.55872	0.779360	+	0.626576i	$0.215544\pi$
$420$	3.73410	0.182205
$421$	26.6511	1.29889	0.649447	−	0.760407i	$-0.275001\pi$
$421$	26.6511	1.29889	0.649447	+	0.760407i	$0.275001\pi$
$422$	−23.1675	−1.12777
$423$	15.5397	0.755565
$424$	5.85896	0.284536
$425$	5.96588	0.289388
$426$	30.2852	1.46732
$427$	11.9248	0.577081
$428$	−20.3124	−0.981837
$429$	−7.93653	−0.383179
$430$	2.32465	0.112105
$431$	−38.1003	−1.83522	−0.917612	−	0.397477i	$-0.869886\pi$
$431$	−38.1003	−1.83522	−0.917612	+	0.397477i	$0.869886\pi$
$432$	3.65238	0.175725
$433$	−15.7457	−0.756692	−0.378346	−	0.925664i	$-0.623507\pi$
$433$	−15.7457	−0.756692	−0.378346	+	0.925664i	$0.623507\pi$
$434$	−0.817787	−0.0392550
$435$	6.49739	0.311526
$436$	5.62438	0.269359
$437$	4.58483	0.219322
$438$	3.79479	0.181322
$439$	−13.7364	−0.655604	−0.327802	−	0.944746i	$-0.606308\pi$
$439$	−13.7364	−0.655604	−0.327802	+	0.944746i	$0.606308\pi$
$440$	0.432254	0.0206069
$441$	−2.02608	−0.0964799
$442$	−9.56358	−0.454893
$443$	−36.0546	−1.71301	−0.856503	−	0.516143i	$-0.827367\pi$
$443$	−36.0546	−1.71301	−0.856503	+	0.516143i	$0.827367\pi$
$444$	−10.9118	−0.517850
$445$	12.8189	0.607673
$446$	−29.1091	−1.37836
$447$	−16.1862	−0.765580
$448$	−2.31145	−0.109206
$449$	18.2902	0.863170	0.431585	−	0.902072i	$-0.357955\pi$
$449$	18.2902	0.863170	0.431585	+	0.902072i	$0.357955\pi$
$450$	−5.35736	−0.252548
$451$	1.93075	0.0909153
$452$	4.88457	0.229751
$453$	−19.9634	−0.937964
$454$	5.17806	0.243018
$455$	−12.7647	−0.598417
$456$	9.42134	0.441195
$457$	13.0539	0.610634	0.305317	−	0.952251i	$-0.401238\pi$
$457$	13.0539	0.610634	0.305317	+	0.952251i	$0.401238\pi$
$458$	23.0381	1.07650
$459$	−4.97259	−0.232101
$460$	−0.786161	−0.0366550
$461$	6.16823	0.287283	0.143642	−	0.989630i	$-0.454119\pi$
$461$	6.16823	0.287283	0.143642	+	0.989630i	$0.454119\pi$
$462$	2.61157	0.121501
$463$	21.4242	0.995668	0.497834	−	0.867272i	$-0.334129\pi$
$463$	21.4242	0.995668	0.497834	+	0.867272i	$0.334129\pi$
$464$	−4.02196	−0.186715
$465$	−0.571553	−0.0265051
$466$	17.9471	0.831384
$467$	29.7634	1.37728	0.688642	−	0.725101i	$-0.258207\pi$
$467$	29.7634	1.37728	0.688642	+	0.725101i	$0.258207\pi$
$468$	8.58809	0.396984
$469$	−27.5316	−1.27129
$470$	9.99241	0.460916
$471$	−45.0575	−2.07614
$472$	−3.66073	−0.168499
$473$	1.62582	0.0747554
$474$	8.67752	0.398572
$475$	20.0905	0.921814
$476$	3.14697	0.144241
$477$	7.16314	0.327978
$478$	−1.83769	−0.0840539
$479$	25.9135	1.18402	0.592008	−	0.805932i	$-0.298335\pi$
$479$	25.9135	1.18402	0.592008	+	0.805932i	$0.298335\pi$
$480$	−1.61548	−0.0737362
$481$	37.3009	1.70077
$482$	15.0476	0.685398
$483$	−4.74979	−0.216123
$484$	−10.6977	−0.486259
$485$	−2.00926	−0.0912356
$486$	12.0023	0.544436
$487$	30.0105	1.35991	0.679953	−	0.733256i	$-0.262000\pi$
$487$	30.0105	1.35991	0.679953	+	0.733256i	$0.262000\pi$
$488$	−5.15900	−0.233537
$489$	−41.8685	−1.89336
$490$	−1.30282	−0.0588554
$491$	−15.3509	−0.692776	−0.346388	−	0.938091i	$-0.612592\pi$
$491$	−15.3509	−0.692776	−0.346388	+	0.938091i	$0.612592\pi$
$492$	−7.21585	−0.325316
$493$	5.47576	0.246616
$494$	−32.2059	−1.44901
$495$	0.528472	0.0237531
$496$	0.353798	0.0158860
$497$	34.0663	1.52808
$498$	2.99743	0.134318
$499$	2.83531	0.126926	0.0634630	−	0.997984i	$-0.479786\pi$
$499$	2.83531	0.126926	0.0634630	+	0.997984i	$0.479786\pi$
$500$	−7.37573	−0.329852
$501$	3.58866	0.160329
$502$	5.13628	0.229243
$503$	−41.1155	−1.83325	−0.916625	−	0.399748i	$-0.869098\pi$
$503$	−41.1155	−1.83325	−0.916625	+	0.399748i	$0.869098\pi$
$504$	−2.82597	−0.125879
$505$	10.9694	0.488134
$506$	−0.549829	−0.0244429
$507$	−74.6813	−3.31671
$508$	4.72016	0.209423
$509$	1.82733	0.0809951	0.0404975	−	0.999180i	$-0.487106\pi$
$509$	1.82733	0.0809951	0.0404975	+	0.999180i	$0.487106\pi$
$510$	2.19942	0.0973920
$511$	4.26858	0.188831
$512$	1.00000	0.0441942
$513$	−16.7455	−0.739333
$514$	−14.5816	−0.643168
$515$	−7.44988	−0.328281
$516$	−6.07625	−0.267492
$517$	6.98854	0.307355
$518$	−12.2741	−0.539294
$519$	1.92304	0.0844119
$520$	5.52236	0.242172
$521$	14.4492	0.633032	0.316516	−	0.948587i	$-0.397487\pi$
$521$	14.4492	0.633032	0.316516	+	0.948587i	$0.397487\pi$
$522$	−4.91723	−0.215221
$523$	−19.2199	−0.840429	−0.420215	−	0.907425i	$-0.638045\pi$
$523$	−19.2199	−0.840429	−0.420215	+	0.907425i	$0.638045\pi$
$524$	−1.00000	−0.0436852
$525$	−20.8134	−0.908369
$526$	17.7235	0.772783
$527$	−0.481684	−0.0209825
$528$	−1.12984	−0.0491700
$529$	1.00000	0.0434783
$530$	4.60609	0.200076
$531$	−4.47560	−0.194225
$532$	10.5976	0.459464
$533$	24.6667	1.06843
$534$	−33.5064	−1.44997
$535$	−15.9688	−0.690392
$536$	11.9110	0.514475
$537$	−38.5091	−1.66179
$538$	11.5199	0.496656
$539$	−0.911173	−0.0392470
$540$	2.87136	0.123564
$541$	−19.2063	−0.825745	−0.412873	−	0.910789i	$-0.635475\pi$
$541$	−19.2063	−0.825745	−0.412873	+	0.910789i	$0.635475\pi$
$542$	4.66039	0.200181
$543$	−43.6940	−1.87509
$544$	−1.36147	−0.0583724
$545$	4.42167	0.189404
$546$	33.3647	1.42788
$547$	−37.6077	−1.60799	−0.803994	−	0.594637i	$-0.797296\pi$
$547$	−37.6077	−1.60799	−0.803994	+	0.594637i	$0.797296\pi$
$548$	4.45233	0.190194
$549$	−6.30738	−0.269192
$550$	−2.40932	−0.102734
$551$	18.4400	0.785569
$552$	2.05490	0.0874622
$553$	9.76091	0.415076
$554$	7.14403	0.303521
$555$	−8.57841	−0.364133
$556$	12.0230	0.509888
$557$	−44.0025	−1.86445	−0.932223	−	0.361884i	$-0.882133\pi$
$557$	−44.0025	−1.86445	−0.932223	+	0.361884i	$0.882133\pi$
$558$	0.432552	0.0183114
$559$	20.7711	0.878523
$560$	−1.81717	−0.0767896
$561$	1.53824	0.0649446
$562$	14.0083	0.590905
$563$	−0.261699	−0.0110293	−0.00551465	−	0.999985i	$-0.501755\pi$
$563$	−0.261699	−0.0110293	−0.00551465	+	0.999985i	$0.501755\pi$
$564$	−26.1185	−1.09979
$565$	3.84006	0.161553
$566$	9.05588	0.380647
$567$	25.8260	1.08459
$568$	−14.7381	−0.618395
$569$	−5.75667	−0.241332	−0.120666	−	0.992693i	$-0.538503\pi$
$569$	−5.75667	−0.241332	−0.120666	+	0.992693i	$0.538503\pi$
$570$	7.40669	0.310232
$571$	11.4359	0.478577	0.239288	−	0.970949i	$-0.423086\pi$
$571$	11.4359	0.478577	0.239288	+	0.970949i	$0.423086\pi$
$572$	3.86225	0.161489
$573$	−3.99308	−0.166813
$574$	−8.11675	−0.338787
$575$	4.38195	0.182740
$576$	1.22260	0.0509415
$577$	−10.2660	−0.427378	−0.213689	−	0.976902i	$-0.568548\pi$
$577$	−10.2660	−0.427378	−0.213689	+	0.976902i	$0.568548\pi$
$578$	−15.1464	−0.630007
$579$	−7.82046	−0.325007
$580$	−3.16191	−0.131291
$581$	3.37166	0.139880
$582$	5.25186	0.217697
$583$	3.22142	0.133418
$584$	−1.84671	−0.0764173
$585$	6.75162	0.279145
$586$	23.9146	0.987905
$587$	35.9039	1.48191	0.740956	−	0.671553i	$-0.234373\pi$
$587$	35.9039	1.48191	0.740956	+	0.671553i	$0.234373\pi$
$588$	3.40536	0.140435
$589$	−1.62210	−0.0668375
$590$	−2.87793	−0.118482
$591$	−14.9039	−0.613064
$592$	5.31013	0.218245
$593$	−7.70086	−0.316236	−0.158118	−	0.987420i	$-0.550543\pi$
$593$	−7.70086	−0.316236	−0.158118	+	0.987420i	$0.550543\pi$
$594$	2.00818	0.0823968
$595$	2.47402	0.101425
$596$	7.87689	0.322650
$597$	1.08199	0.0442830
$598$	−7.02447	−0.287252
$599$	−32.6393	−1.33361	−0.666803	−	0.745234i	$-0.732338\pi$
$599$	−32.6393	−1.33361	−0.666803	+	0.745234i	$0.732338\pi$
$600$	9.00445	0.367605
$601$	20.7528	0.846526	0.423263	−	0.906007i	$-0.360885\pi$
$601$	20.7528	0.846526	0.423263	+	0.906007i	$0.360885\pi$
$602$	−6.83487	−0.278569
$603$	14.5623	0.593022
$604$	9.71506	0.395300
$605$	−8.41011	−0.341919
$606$	−28.6723	−1.16473
$607$	12.6517	0.513515	0.256758	−	0.966476i	$-0.417346\pi$
$607$	12.6517	0.513515	0.256758	+	0.966476i	$0.417346\pi$
$608$	−4.58483	−0.185939
$609$	−19.1035	−0.774111
$610$	−4.05581	−0.164215
$611$	89.2837	3.61203
$612$	−1.66452	−0.0672844
$613$	4.81235	0.194369	0.0971845	−	0.995266i	$-0.469016\pi$
$613$	4.81235	0.194369	0.0971845	+	0.995266i	$0.469016\pi$
$614$	14.1783	0.572189
$615$	−5.67282	−0.228750
$616$	−1.27090	−0.0512061
$617$	−21.8176	−0.878343	−0.439171	−	0.898403i	$-0.644728\pi$
$617$	−21.8176	−0.878343	−0.439171	+	0.898403i	$0.644728\pi$
$618$	19.4728	0.783309
$619$	−5.60797	−0.225403	−0.112702	−	0.993629i	$-0.535950\pi$
$619$	−5.60797	−0.225403	−0.112702	+	0.993629i	$0.535950\pi$
$620$	0.278142	0.0111705
$621$	−3.65238	−0.146565
$622$	−26.9475	−1.08049
$623$	−37.6897	−1.51001
$624$	−14.4345	−0.577844
$625$	16.1112	0.644450
$626$	31.9564	1.27724
$627$	5.18012	0.206874
$628$	21.9269	0.874979
$629$	−7.22957	−0.288262
$630$	−2.22167	−0.0885134
$631$	−8.18983	−0.326032	−0.163016	−	0.986623i	$-0.552122\pi$
$631$	−8.18983	−0.326032	−0.163016	+	0.986623i	$0.552122\pi$
$632$	−4.22285	−0.167976
$633$	47.6067	1.89220
$634$	19.7218	0.783252
$635$	3.71080	0.147259
$636$	−12.0395	−0.477399
$637$	−11.6409	−0.461229
$638$	−2.21139	−0.0875497
$639$	−18.0187	−0.712809
$640$	0.786161	0.0310757
$641$	13.5979	0.537085	0.268542	−	0.963268i	$-0.413458\pi$
$641$	13.5979	0.537085	0.268542	+	0.963268i	$0.413458\pi$
$642$	41.7399	1.64734
$643$	−31.1973	−1.23030	−0.615151	−	0.788409i	$-0.710905\pi$
$643$	−31.1973	−1.23030	−0.615151	+	0.788409i	$0.710905\pi$
$644$	2.31145	0.0910839
$645$	−4.77691	−0.188091
$646$	6.24209	0.245592
$647$	−9.74899	−0.383272	−0.191636	−	0.981466i	$-0.561379\pi$
$647$	−9.74899	−0.383272	−0.191636	+	0.981466i	$0.561379\pi$
$648$	−11.1730	−0.438919
$649$	−2.01278	−0.0790084
$650$	−30.7809	−1.20732
$651$	1.68047	0.0658627
$652$	20.3750	0.797947
$653$	−35.2990	−1.38136	−0.690679	−	0.723162i	$-0.742688\pi$
$653$	−35.2990	−1.38136	−0.690679	+	0.723162i	$0.742688\pi$
$654$	−11.5575	−0.451935
$655$	−0.786161	−0.0307179
$656$	3.51154	0.137103
$657$	−2.25778	−0.0880844
$658$	−29.3794	−1.14533
$659$	49.9744	1.94673	0.973364	−	0.229266i	$-0.0736327\pi$
$659$	49.9744	1.94673	0.973364	+	0.229266i	$0.0736327\pi$
$660$	−0.888237	−0.0345746
$661$	−49.8779	−1.94002	−0.970012	−	0.243056i	$-0.921850\pi$
$661$	−49.8779	−1.94002	−0.970012	+	0.243056i	$0.921850\pi$
$662$	−16.1354	−0.627121
$663$	19.6522	0.763227
$664$	−1.45868	−0.0566077
$665$	8.33142	0.323079
$666$	6.49215	0.251566
$667$	4.02196	0.155731
$668$	−1.74639	−0.0675700
$669$	59.8162	2.31263
$670$	9.36393	0.361760
$671$	−2.83657	−0.109504
$672$	4.74979	0.183227
$673$	15.9800	0.615985	0.307992	−	0.951389i	$-0.400343\pi$
$673$	15.9800	0.615985	0.307992	+	0.951389i	$0.400343\pi$
$674$	18.2587	0.703299
$675$	−16.0045	−0.616015
$676$	36.3431	1.39781
$677$	−27.6364	−1.06215	−0.531076	−	0.847324i	$-0.678212\pi$
$677$	−27.6364	−1.06215	−0.531076	+	0.847324i	$0.678212\pi$
$678$	−10.0373	−0.385480
$679$	5.90756	0.226712
$680$	−1.07033	−0.0410454
$681$	−10.6404	−0.407740
$682$	0.194528	0.00744887
$683$	3.60434	0.137916	0.0689581	−	0.997620i	$-0.478033\pi$
$683$	3.60434	0.137916	0.0689581	+	0.997620i	$0.478033\pi$
$684$	−5.60539	−0.214327
$685$	3.50025	0.133738
$686$	20.0107	0.764011
$687$	−47.3409	−1.80617
$688$	2.95696	0.112733
$689$	41.1561	1.56792
$690$	1.61548	0.0615002
$691$	−35.6115	−1.35473	−0.677363	−	0.735649i	$-0.736877\pi$
$691$	−35.6115	−1.35473	−0.677363	+	0.735649i	$0.736877\pi$
$692$	−0.935831	−0.0355750
$693$	−1.55380	−0.0590240
$694$	17.7437	0.673543
$695$	9.45201	0.358535
$696$	8.26470	0.313273
$697$	−4.78085	−0.181087
$698$	−15.4410	−0.584449
$699$	−36.8794	−1.39491
$700$	10.1287	0.382828
$701$	39.2695	1.48319	0.741594	−	0.670849i	$-0.234070\pi$
$701$	39.2695	1.48319	0.741594	+	0.670849i	$0.234070\pi$
$702$	25.6560	0.968324
$703$	−24.3460	−0.918228
$704$	0.549829	0.0207225
$705$	−20.5334	−0.773331
$706$	−31.2103	−1.17461
$707$	−32.2521	−1.21296
$708$	7.52243	0.282710
$709$	−17.1991	−0.645926	−0.322963	−	0.946412i	$-0.604679\pi$
$709$	−17.1991	−0.645926	−0.322963	+	0.946412i	$0.604679\pi$
$710$	−11.5865	−0.434833
$711$	−5.16284	−0.193622
$712$	16.3057	0.611081
$713$	−0.353798	−0.0132498
$714$	−6.46669	−0.242010
$715$	3.03635	0.113553
$716$	18.7402	0.700354
$717$	3.77626	0.141027
$718$	−8.63746	−0.322347
$719$	−15.9988	−0.596653	−0.298326	−	0.954464i	$-0.596428\pi$
$719$	−15.9988	−0.596653	−0.298326	+	0.954464i	$0.596428\pi$
$720$	0.961158	0.0358202
$721$	21.9039	0.815745
$722$	2.02062	0.0751997
$723$	−30.9212	−1.14997
$724$	21.2634	0.790247
$725$	17.6240	0.654540
$726$	21.9826	0.815852
$727$	−26.6900	−0.989879	−0.494939	−	0.868928i	$-0.664810\pi$
$727$	−26.6900	−0.989879	−0.494939	+	0.868928i	$0.664810\pi$
$728$	−16.2367	−0.601773
$729$	8.85565	0.327987
$730$	−1.45181	−0.0537339
$731$	−4.02581	−0.148900
$732$	10.6012	0.391832
$733$	−38.4402	−1.41982	−0.709911	−	0.704291i	$-0.751265\pi$
$733$	−38.4402	−1.41982	−0.709911	+	0.704291i	$0.751265\pi$
$734$	−19.7710	−0.729760
$735$	2.67716	0.0987486
$736$	−1.00000	−0.0368605
$737$	6.54899	0.241235
$738$	4.29320	0.158035
$739$	36.9774	1.36024	0.680118	−	0.733102i	$-0.261928\pi$
$739$	36.9774	1.36024	0.680118	+	0.733102i	$0.261928\pi$
$740$	4.17462	0.153462
$741$	66.1799	2.43118
$742$	−13.5427	−0.497168
$743$	14.7441	0.540908	0.270454	−	0.962733i	$-0.412826\pi$
$743$	14.7441	0.540908	0.270454	+	0.962733i	$0.412826\pi$
$744$	−0.727018	−0.0266538
$745$	6.19250	0.226876
$746$	25.2140	0.923150
$747$	−1.78337	−0.0652503
$748$	−0.748574	−0.0273706
$749$	46.9511	1.71556
$750$	15.1563	0.553432
$751$	−29.2022	−1.06560	−0.532802	−	0.846240i	$-0.678861\pi$
$751$	−29.2022	−1.06560	−0.532802	+	0.846240i	$0.678861\pi$
$752$	12.7104	0.463500
$753$	−10.5545	−0.384628
$754$	−28.2521	−1.02888
$755$	7.63760	0.277961
$756$	−8.44230	−0.307043
$757$	−1.34677	−0.0489490	−0.0244745	−	0.999700i	$-0.507791\pi$
$757$	−1.34677	−0.0489490	−0.0244745	+	0.999700i	$0.507791\pi$
$758$	29.4771	1.07066
$759$	1.12984	0.0410106
$760$	−3.60441	−0.130746
$761$	11.9390	0.432790	0.216395	−	0.976306i	$-0.430570\pi$
$761$	11.9390	0.432790	0.216395	+	0.976306i	$0.430570\pi$
$762$	−9.69943	−0.351373
$763$	−13.0005	−0.470649
$764$	1.94321	0.0703027
$765$	−1.30858	−0.0473120
$766$	3.86623	0.139692
$767$	−25.7147	−0.928504
$768$	−2.05490	−0.0741497
$769$	−46.3472	−1.67132	−0.835662	−	0.549244i	$-0.814916\pi$
$769$	−46.3472	−1.67132	−0.835662	+	0.549244i	$0.814916\pi$
$770$	−0.999134	−0.0360063
$771$	29.9637	1.07912
$772$	3.80577	0.136973
$773$	−1.79620	−0.0646049	−0.0323025	−	0.999478i	$-0.510284\pi$
$773$	−1.79620	−0.0646049	−0.0323025	+	0.999478i	$0.510284\pi$
$774$	3.61517	0.129945
$775$	−1.55032	−0.0556893
$776$	−2.55578	−0.0917472
$777$	25.2220	0.904835
$778$	20.0994	0.720600
$779$	−16.0998	−0.576835
$780$	−11.3479	−0.406319
$781$	−8.10341	−0.289963
$782$	1.36147	0.0486860
$783$	−14.6897	−0.524968
$784$	−1.65719	−0.0591855
$785$	17.2381	0.615253
$786$	2.05490	0.0732957
$787$	16.5110	0.588554	0.294277	−	0.955720i	$-0.404921\pi$
$787$	16.5110	0.588554	0.294277	+	0.955720i	$0.404921\pi$
$788$	7.25287	0.258373
$789$	−36.4200	−1.29659
$790$	−3.31984	−0.118115
$791$	−11.2905	−0.401442
$792$	0.672219	0.0238863
$793$	−36.2392	−1.28689
$794$	−31.5637	−1.12015
$795$	−9.46503	−0.335690
$796$	−0.526543	−0.0186628
$797$	19.5090	0.691044	0.345522	−	0.938411i	$-0.387702\pi$
$797$	19.5090	0.691044	0.345522	+	0.938411i	$0.387702\pi$
$798$	−21.7770	−0.770896
$799$	−17.3048	−0.612199
$800$	−4.38195	−0.154925
$801$	19.9352	0.704377
$802$	−33.8098	−1.19387
$803$	−1.01537	−0.0358318
$804$	−24.4758	−0.863194
$805$	1.81717	0.0640469
$806$	2.48524	0.0875389
$807$	−23.6721	−0.833297
$808$	13.9532	0.490871
$809$	−6.47300	−0.227579	−0.113789	−	0.993505i	$-0.536299\pi$
$809$	−6.47300	−0.227579	−0.113789	+	0.993505i	$0.536299\pi$
$810$	−8.78382	−0.308632
$811$	23.3990	0.821650	0.410825	−	0.911714i	$-0.365241\pi$
$811$	23.3990	0.821650	0.410825	+	0.911714i	$0.365241\pi$
$812$	9.29656	0.326245
$813$	−9.57663	−0.335867
$814$	2.91966	0.102334
$815$	16.0180	0.561087
$816$	2.79767	0.0979382
$817$	−13.5572	−0.474305
$818$	−3.79592	−0.132721
$819$	−19.8509	−0.693648
$820$	2.76064	0.0964056
$821$	−37.0324	−1.29244	−0.646220	−	0.763151i	$-0.723651\pi$
$821$	−37.0324	−1.29244	−0.646220	+	0.763151i	$0.723651\pi$
$822$	−9.14907	−0.319110
$823$	43.4842	1.51577	0.757883	−	0.652391i	$-0.226234\pi$
$823$	43.4842	1.51577	0.757883	+	0.652391i	$0.226234\pi$
$824$	−9.47627	−0.330122
$825$	4.95091	0.172368
$826$	8.46161	0.294417
$827$	15.6472	0.544106	0.272053	−	0.962282i	$-0.412297\pi$
$827$	15.6472	0.544106	0.272053	+	0.962282i	$0.412297\pi$
$828$	−1.22260	−0.0424882
$829$	9.85044	0.342120	0.171060	−	0.985261i	$-0.445281\pi$
$829$	9.85044	0.342120	0.171060	+	0.985261i	$0.445281\pi$
$830$	−1.14676	−0.0398045
$831$	−14.6802	−0.509252
$832$	7.02447	0.243530
$833$	2.25621	0.0781732
$834$	−24.7060	−0.855499
$835$	−1.37295	−0.0475128
$836$	−2.52087	−0.0871861
$837$	1.29220	0.0446651
$838$	31.9062	1.10218
$839$	31.5950	1.09078	0.545390	−	0.838183i	$-0.316382\pi$
$839$	31.5950	1.09078	0.545390	+	0.838183i	$0.316382\pi$
$840$	3.73410	0.128839
$841$	−12.8239	−0.442202
$842$	26.6511	0.918456
$843$	−28.7856	−0.991429
$844$	−23.1675	−0.797457
$845$	28.5715	0.982891
$846$	15.5397	0.534265
$847$	24.7272	0.849636
$848$	5.85896	0.201197
$849$	−18.6089	−0.638656
$850$	5.96588	0.204628
$851$	−5.31013	−0.182029
$852$	30.2852	1.03755
$853$	−10.5650	−0.361739	−0.180870	−	0.983507i	$-0.557891\pi$
$853$	−10.5650	−0.361739	−0.180870	+	0.983507i	$0.557891\pi$
$854$	11.9248	0.408058
$855$	−4.40674	−0.150707
$856$	−20.3124	−0.694263
$857$	−0.954823	−0.0326161	−0.0163081	−	0.999867i	$-0.505191\pi$
$857$	−0.954823	−0.0326161	−0.0163081	+	0.999867i	$0.505191\pi$
$858$	−7.93653	−0.270949
$859$	33.3339	1.13734	0.568670	−	0.822566i	$-0.307458\pi$
$859$	33.3339	1.13734	0.568670	+	0.822566i	$0.307458\pi$
$860$	2.32465	0.0792699
$861$	16.6791	0.568422
$862$	−38.1003	−1.29770
$863$	−33.4131	−1.13740	−0.568698	−	0.822546i	$-0.692553\pi$
$863$	−33.4131	−1.13740	−0.568698	+	0.822546i	$0.692553\pi$
$864$	3.65238	0.124256
$865$	−0.735714	−0.0250150
$866$	−15.7457	−0.535062
$867$	31.1243	1.05704
$868$	−0.817787	−0.0277575
$869$	−2.32185	−0.0787632
$870$	6.49739	0.220282
$871$	83.6681	2.83499
$872$	5.62438	0.190466
$873$	−3.12469	−0.105755
$874$	4.58483	0.155084
$875$	17.0486	0.576349
$876$	3.79479	0.128214
$877$	−25.5401	−0.862429	−0.431215	−	0.902249i	$-0.641915\pi$
$877$	−25.5401	−0.862429	−0.431215	+	0.902249i	$0.641915\pi$
$878$	−13.7364	−0.463582
$879$	−49.1421	−1.65752
$880$	0.432254	0.0145713
$881$	10.4093	0.350699	0.175350	−	0.984506i	$-0.443894\pi$
$881$	10.4093	0.350699	0.175350	+	0.984506i	$0.443894\pi$
$882$	−2.02608	−0.0682216
$883$	10.4077	0.350246	0.175123	−	0.984547i	$-0.443968\pi$
$883$	10.4077	0.350246	0.175123	+	0.984547i	$0.443968\pi$
$884$	−9.56358	−0.321658
$885$	5.91384	0.198792
$886$	−36.0546	−1.21128
$887$	−33.2003	−1.11476	−0.557379	−	0.830258i	$-0.688193\pi$
$887$	−33.2003	−1.11476	−0.557379	+	0.830258i	$0.688193\pi$
$888$	−10.9118	−0.366175
$889$	−10.9104	−0.365923
$890$	12.8189	0.429690
$891$	−6.14326	−0.205807
$892$	−29.1091	−0.974645
$893$	−58.2749	−1.95009
$894$	−16.1862	−0.541347
$895$	14.7328	0.492464
$896$	−2.31145	−0.0772202
$897$	14.4345	0.481955
$898$	18.2902	0.610353
$899$	−1.42296	−0.0474584
$900$	−5.35736	−0.178579
$901$	−7.97678	−0.265745
$902$	1.93075	0.0642868
$903$	14.0450	0.467387
$904$	4.88457	0.162458
$905$	16.7164	0.555673
$906$	−19.9634	−0.663240
$907$	−5.99295	−0.198993	−0.0994963	−	0.995038i	$-0.531723\pi$
$907$	−5.99295	−0.198993	−0.0994963	+	0.995038i	$0.531723\pi$
$908$	5.17806	0.171840
$909$	17.0591	0.565815
$910$	−12.7647	−0.423145
$911$	28.3829	0.940367	0.470183	−	0.882569i	$-0.344188\pi$
$911$	28.3829	0.940367	0.470183	+	0.882569i	$0.344188\pi$
$912$	9.42134	0.311972
$913$	−0.802023	−0.0265431
$914$	13.0539	0.431784
$915$	8.33426	0.275522
$916$	23.0381	0.761200
$917$	2.31145	0.0763308
$918$	−4.97259	−0.164120
$919$	56.6194	1.86770	0.933851	−	0.357662i	$-0.116426\pi$
$919$	56.6194	1.86770	0.933851	+	0.357662i	$0.116426\pi$
$920$	−0.786161	−0.0259190
$921$	−29.1349	−0.960027
$922$	6.16823	0.203140
$923$	−103.527	−3.40763
$924$	2.61157	0.0859144
$925$	−23.2687	−0.765072
$926$	21.4242	0.704043
$927$	−11.5857	−0.380523
$928$	−4.02196	−0.132027
$929$	28.0694	0.920928	0.460464	−	0.887678i	$-0.347683\pi$
$929$	28.0694	0.920928	0.460464	+	0.887678i	$0.347683\pi$
$930$	−0.571553	−0.0187420
$931$	7.59794	0.249012
$932$	17.9471	0.587877
$933$	55.3742	1.81287
$934$	29.7634	0.973887
$935$	−0.588500	−0.0192460
$936$	8.58809	0.280710
$937$	−12.0564	−0.393866	−0.196933	−	0.980417i	$-0.563098\pi$
$937$	−12.0564	−0.393866	−0.196933	+	0.980417i	$0.563098\pi$
$938$	−27.5316	−0.898939
$939$	−65.6671	−2.14297
$940$	9.99241	0.325916
$941$	6.10761	0.199103	0.0995513	−	0.995032i	$-0.468259\pi$
$941$	6.10761	0.199103	0.0995513	+	0.995032i	$0.468259\pi$
$942$	−45.0575	−1.46805
$943$	−3.51154	−0.114351
$944$	−3.66073	−0.119147
$945$	−6.63701	−0.215902
$946$	1.62582	0.0528601
$947$	0.676551	0.0219850	0.0109925	−	0.999940i	$-0.496501\pi$
$947$	0.676551	0.0219850	0.0109925	+	0.999940i	$0.496501\pi$
$948$	8.67752	0.281833
$949$	−12.9721	−0.421094
$950$	20.0905	0.651821
$951$	−40.5262	−1.31415
$952$	3.14697	0.101994
$953$	52.8853	1.71312	0.856561	−	0.516046i	$-0.172597\pi$
$953$	52.8853	1.71312	0.856561	+	0.516046i	$0.172597\pi$
$954$	7.16314	0.231915
$955$	1.52767	0.0494343
$956$	−1.83769	−0.0594351
$957$	4.54417	0.146892
$958$	25.9135	0.837226
$959$	−10.2913	−0.332325
$960$	−1.61548	−0.0521394
$961$	−30.8748	−0.995962
$962$	37.3009	1.20263
$963$	−24.8339	−0.800260
$964$	15.0476	0.484650
$965$	2.99195	0.0963142
$966$	−4.74979	−0.152822
$967$	25.4144	0.817273	0.408637	−	0.912697i	$-0.366004\pi$
$967$	25.4144	0.817273	0.408637	+	0.912697i	$0.366004\pi$
$968$	−10.6977	−0.343837
$969$	−12.8268	−0.412058
$970$	−2.00926	−0.0645133
$971$	49.7014	1.59499	0.797497	−	0.603323i	$-0.206157\pi$
$971$	49.7014	1.59499	0.797497	+	0.603323i	$0.206157\pi$
$972$	12.0023	0.384974
$973$	−27.7906	−0.890924
$974$	30.0105	0.961599
$975$	63.2515	2.02567
$976$	−5.15900	−0.165136
$977$	−29.3864	−0.940154	−0.470077	−	0.882625i	$-0.655774\pi$
$977$	−29.3864	−0.940154	−0.470077	+	0.882625i	$0.655774\pi$
$978$	−41.8685	−1.33881
$979$	8.96532	0.286533
$980$	−1.30282	−0.0416171
$981$	6.87635	0.219545
$982$	−15.3509	−0.489867
$983$	−47.8085	−1.52485	−0.762427	−	0.647075i	$-0.775992\pi$
$983$	−47.8085	−1.52485	−0.762427	+	0.647075i	$0.775992\pi$
$984$	−7.21585	−0.230033
$985$	5.70192	0.181678
$986$	5.47576	0.174384
$987$	60.3717	1.92165
$988$	−32.2059	−1.02461
$989$	−2.95696	−0.0940259
$990$	0.528472	0.0167960
$991$	50.6386	1.60859	0.804293	−	0.594232i	$-0.202544\pi$
$991$	50.6386	1.60859	0.804293	+	0.594232i	$0.202544\pi$
$992$	0.353798	0.0112331
$993$	33.1566	1.05219
$994$	34.0663	1.08052
$995$	−0.413948	−0.0131230
$996$	2.99743	0.0949773
$997$	−36.6952	−1.16215	−0.581074	−	0.813851i	$-0.697367\pi$
$997$	−36.6952	−1.16215	−0.581074	+	0.813851i	$0.697367\pi$
$998$	2.83531	0.0897503
$999$	19.3946	0.613619

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6026.2.a.k.1.9	✓	35

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6026.2.a.k.1.9	✓	35	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.05490 q^{3} +1.00000 q^{4} +0.786161 q^{5} -2.05490 q^{6} -2.31145 q^{7} +1.00000 q^{8} +1.22260 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.05490 q^{3} +1.00000 q^{4} +0.786161 q^{5} -2.05490 q^{6} -2.31145 q^{7} +1.00000 q^{8} +1.22260 q^{9} +0.786161 q^{10} +0.549829 q^{11} -2.05490 q^{12} +7.02447 q^{13} -2.31145 q^{14} -1.61548 q^{15} +1.00000 q^{16} -1.36147 q^{17} +1.22260 q^{18} -4.58483 q^{19} +0.786161 q^{20} +4.74979 q^{21} +0.549829 q^{22} -1.00000 q^{23} -2.05490 q^{24} -4.38195 q^{25} +7.02447 q^{26} +3.65238 q^{27} -2.31145 q^{28} -4.02196 q^{29} -1.61548 q^{30} +0.353798 q^{31} +1.00000 q^{32} -1.12984 q^{33} -1.36147 q^{34} -1.81717 q^{35} +1.22260 q^{36} +5.31013 q^{37} -4.58483 q^{38} -14.4345 q^{39} +0.786161 q^{40} +3.51154 q^{41} +4.74979 q^{42} +2.95696 q^{43} +0.549829 q^{44} +0.961158 q^{45} -1.00000 q^{46} +12.7104 q^{47} -2.05490 q^{48} -1.65719 q^{49} -4.38195 q^{50} +2.79767 q^{51} +7.02447 q^{52} +5.85896 q^{53} +3.65238 q^{54} +0.432254 q^{55} -2.31145 q^{56} +9.42134 q^{57} -4.02196 q^{58} -3.66073 q^{59} -1.61548 q^{60} -5.15900 q^{61} +0.353798 q^{62} -2.82597 q^{63} +1.00000 q^{64} +5.52236 q^{65} -1.12984 q^{66} +11.9110 q^{67} -1.36147 q^{68} +2.05490 q^{69} -1.81717 q^{70} -14.7381 q^{71} +1.22260 q^{72} -1.84671 q^{73} +5.31013 q^{74} +9.00445 q^{75} -4.58483 q^{76} -1.27090 q^{77} -14.4345 q^{78} -4.22285 q^{79} +0.786161 q^{80} -11.1730 q^{81} +3.51154 q^{82} -1.45868 q^{83} +4.74979 q^{84} -1.07033 q^{85} +2.95696 q^{86} +8.26470 q^{87} +0.549829 q^{88} +16.3057 q^{89} +0.961158 q^{90} -16.2367 q^{91} -1.00000 q^{92} -0.727018 q^{93} +12.7104 q^{94} -3.60441 q^{95} -2.05490 q^{96} -2.55578 q^{97} -1.65719 q^{98} +0.672219 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 35 q + 35 q^{2} - 3 q^{3} + 35 q^{4} + 10 q^{5} - 3 q^{6} + 14 q^{7} + 35 q^{8} + 54 q^{9}+O(q^{10}) \) 35 * q + 35 * q^2 - 3 * q^3 + 35 * q^4 + 10 * q^5 - 3 * q^6 + 14 * q^7 + 35 * q^8 + 54 * q^9	\( 35 q + 35 q^{2} - 3 q^{3} + 35 q^{4} + 10 q^{5} - 3 q^{6} + 14 q^{7} + 35 q^{8} + 54 q^{9} + 10 q^{10} + 9 q^{11} - 3 q^{12} + 19 q^{13} + 14 q^{14} + 14 q^{15} + 35 q^{16} + 28 q^{17} + 54 q^{18} + 21 q^{19} + 10 q^{20} + 28 q^{21} + 9 q^{22} - 35 q^{23} - 3 q^{24} + 81 q^{25} + 19 q^{26} - 21 q^{27} + 14 q^{28} + 35 q^{29} + 14 q^{30} + 5 q^{31} + 35 q^{32} + 26 q^{33} + 28 q^{34} - 7 q^{35} + 54 q^{36} + 51 q^{37} + 21 q^{38} + 21 q^{39} + 10 q^{40} + 3 q^{41} + 28 q^{42} + 43 q^{43} + 9 q^{44} + 2 q^{45} - 35 q^{46} + 10 q^{47} - 3 q^{48} + 85 q^{49} + 81 q^{50} + 26 q^{51} + 19 q^{52} + 39 q^{53} - 21 q^{54} + 2 q^{55} + 14 q^{56} + 50 q^{57} + 35 q^{58} - 42 q^{59} + 14 q^{60} + 47 q^{61} + 5 q^{62} + 23 q^{63} + 35 q^{64} + 61 q^{65} + 26 q^{66} + 22 q^{67} + 28 q^{68} + 3 q^{69} - 7 q^{70} + 54 q^{72} + 30 q^{73} + 51 q^{74} - 26 q^{75} + 21 q^{76} + 2 q^{77} + 21 q^{78} + 55 q^{79} + 10 q^{80} + 67 q^{81} + 3 q^{82} + 20 q^{83} + 28 q^{84} + 28 q^{85} + 43 q^{86} + 29 q^{87} + 9 q^{88} - 31 q^{89} + 2 q^{90} + 32 q^{91} - 35 q^{92} + 11 q^{93} + 10 q^{94} + 16 q^{95} - 3 q^{96} + 36 q^{97} + 85 q^{98} - 9 q^{99}+O(q^{100}) \) 35 * q + 35 * q^2 - 3 * q^3 + 35 * q^4 + 10 * q^5 - 3 * q^6 + 14 * q^7 + 35 * q^8 + 54 * q^9 + 10 * q^10 + 9 * q^11 - 3 * q^12 + 19 * q^13 + 14 * q^14 + 14 * q^15 + 35 * q^16 + 28 * q^17 + 54 * q^18 + 21 * q^19 + 10 * q^20 + 28 * q^21 + 9 * q^22 - 35 * q^23 - 3 * q^24 + 81 * q^25 + 19 * q^26 - 21 * q^27 + 14 * q^28 + 35 * q^29 + 14 * q^30 + 5 * q^31 + 35 * q^32 + 26 * q^33 + 28 * q^34 - 7 * q^35 + 54 * q^36 + 51 * q^37 + 21 * q^38 + 21 * q^39 + 10 * q^40 + 3 * q^41 + 28 * q^42 + 43 * q^43 + 9 * q^44 + 2 * q^45 - 35 * q^46 + 10 * q^47 - 3 * q^48 + 85 * q^49 + 81 * q^50 + 26 * q^51 + 19 * q^52 + 39 * q^53 - 21 * q^54 + 2 * q^55 + 14 * q^56 + 50 * q^57 + 35 * q^58 - 42 * q^59 + 14 * q^60 + 47 * q^61 + 5 * q^62 + 23 * q^63 + 35 * q^64 + 61 * q^65 + 26 * q^66 + 22 * q^67 + 28 * q^68 + 3 * q^69 - 7 * q^70 + 54 * q^72 + 30 * q^73 + 51 * q^74 - 26 * q^75 + 21 * q^76 + 2 * q^77 + 21 * q^78 + 55 * q^79 + 10 * q^80 + 67 * q^81 + 3 * q^82 + 20 * q^83 + 28 * q^84 + 28 * q^85 + 43 * q^86 + 29 * q^87 + 9 * q^88 - 31 * q^89 + 2 * q^90 + 32 * q^91 - 35 * q^92 + 11 * q^93 + 10 * q^94 + 16 * q^95 - 3 * q^96 + 36 * q^97 + 85 * q^98 - 9 * q^99

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