LMFDB - Embedded newform 6422.2.a.bj.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6422,2,Mod(1,6422)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6422, 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("6422.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6422 = 2 \cdot 13^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6422.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:	$51.2799281781$
Analytic rank:	$0$
Dimension:	$9$
Coefficient field:	$\mathbb{Q}[x]/(x^{9} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{9} - x^{8} - 12x^{7} + 14x^{6} + 35x^{5} - 35x^{4} - 28x^{3} + 10x^{2} + 4x - 1 $ x^9 - x^8 - 12x^7 + 14x^6 + 35x^5 - 35x^4 - 28x^3 + 10x^2 + 4*x - 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$1.91149$ of defining polynomial
Character	$\chi$	$=$	6422.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +0.0255071 q^{3} +1.00000 q^{4} -1.15077 q^{5} -0.0255071 q^{6} -2.71462 q^{7} -1.00000 q^{8} -2.99935 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +0.0255071 q^{3} +1.00000 q^{4} -1.15077 q^{5} -0.0255071 q^{6} -2.71462 q^{7} -1.00000 q^{8} -2.99935 q^{9} +1.15077 q^{10} +2.25258 q^{11} +0.0255071 q^{12} +2.71462 q^{14} -0.0293528 q^{15} +1.00000 q^{16} -1.05257 q^{17} +2.99935 q^{18} +1.00000 q^{19} -1.15077 q^{20} -0.0692421 q^{21} -2.25258 q^{22} -4.19440 q^{23} -0.0255071 q^{24} -3.67573 q^{25} -0.153026 q^{27} -2.71462 q^{28} -9.59724 q^{29} +0.0293528 q^{30} +5.93949 q^{31} -1.00000 q^{32} +0.0574567 q^{33} +1.05257 q^{34} +3.12390 q^{35} -2.99935 q^{36} +5.76725 q^{37} -1.00000 q^{38} +1.15077 q^{40} -3.73239 q^{41} +0.0692421 q^{42} -4.42815 q^{43} +2.25258 q^{44} +3.45156 q^{45} +4.19440 q^{46} +1.18667 q^{47} +0.0255071 q^{48} +0.369164 q^{49} +3.67573 q^{50} -0.0268479 q^{51} -2.39200 q^{53} +0.153026 q^{54} -2.59220 q^{55} +2.71462 q^{56} +0.0255071 q^{57} +9.59724 q^{58} -2.95491 q^{59} -0.0293528 q^{60} -1.72623 q^{61} -5.93949 q^{62} +8.14210 q^{63} +1.00000 q^{64} -0.0574567 q^{66} +4.39417 q^{67} -1.05257 q^{68} -0.106987 q^{69} -3.12390 q^{70} -12.9641 q^{71} +2.99935 q^{72} -0.865426 q^{73} -5.76725 q^{74} -0.0937573 q^{75} +1.00000 q^{76} -6.11489 q^{77} -1.38491 q^{79} -1.15077 q^{80} +8.99414 q^{81} +3.73239 q^{82} +7.32243 q^{83} -0.0692421 q^{84} +1.21126 q^{85} +4.42815 q^{86} -0.244798 q^{87} -2.25258 q^{88} +8.81390 q^{89} -3.45156 q^{90} -4.19440 q^{92} +0.151499 q^{93} -1.18667 q^{94} -1.15077 q^{95} -0.0255071 q^{96} -3.14346 q^{97} -0.369164 q^{98} -6.75627 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q - 9 q^{2} + q^{3} + 9 q^{4} - q^{5} - q^{6} + 13 q^{7} - 9 q^{8} - 2 q^{9}+O(q^{10}) $ 9 * q - 9 * q^2 + q^3 + 9 * q^4 - q^5 - q^6 + 13 * q^7 - 9 * q^8 - 2 * q^9	$ 9 q - 9 q^{2} + q^{3} + 9 q^{4} - q^{5} - q^{6} + 13 q^{7} - 9 q^{8} - 2 q^{9} + q^{10} + 3 q^{11} + q^{12} - 13 q^{14} + 3 q^{15} + 9 q^{16} - 8 q^{17} + 2 q^{18} + 9 q^{19} - q^{20} + 24 q^{21} - 3 q^{22} - 10 q^{23} - q^{24} + 8 q^{25} + 10 q^{27} + 13 q^{28} - 20 q^{29} - 3 q^{30} + q^{31} - 9 q^{32} - 2 q^{33} + 8 q^{34} + 4 q^{35} - 2 q^{36} + 15 q^{37} - 9 q^{38} + q^{40} + 19 q^{41} - 24 q^{42} - 16 q^{43} + 3 q^{44} + 15 q^{45} + 10 q^{46} + 18 q^{47} + q^{48} + 18 q^{49} - 8 q^{50} - 11 q^{51} + 17 q^{53} - 10 q^{54} - 26 q^{55} - 13 q^{56} + q^{57} + 20 q^{58} + 24 q^{59} + 3 q^{60} + 6 q^{61} - q^{62} + q^{63} + 9 q^{64} + 2 q^{66} + 29 q^{67} - 8 q^{68} - 12 q^{69} - 4 q^{70} + 23 q^{71} + 2 q^{72} + 38 q^{73} - 15 q^{74} + 11 q^{75} + 9 q^{76} - 40 q^{77} - 20 q^{79} - q^{80} - 31 q^{81} - 19 q^{82} + 20 q^{83} + 24 q^{84} + 39 q^{85} + 16 q^{86} - 10 q^{87} - 3 q^{88} - 7 q^{89} - 15 q^{90} - 10 q^{92} + 11 q^{93} - 18 q^{94} - q^{95} - q^{96} + 28 q^{97} - 18 q^{98} + 25 q^{99}+O(q^{100}) $ 9 * q - 9 * q^2 + q^3 + 9 * q^4 - q^5 - q^6 + 13 * q^7 - 9 * q^8 - 2 * q^9 + q^10 + 3 * q^11 + q^12 - 13 * q^14 + 3 * q^15 + 9 * q^16 - 8 * q^17 + 2 * q^18 + 9 * q^19 - q^20 + 24 * q^21 - 3 * q^22 - 10 * q^23 - q^24 + 8 * q^25 + 10 * q^27 + 13 * q^28 - 20 * q^29 - 3 * q^30 + q^31 - 9 * q^32 - 2 * q^33 + 8 * q^34 + 4 * q^35 - 2 * q^36 + 15 * q^37 - 9 * q^38 + q^40 + 19 * q^41 - 24 * q^42 - 16 * q^43 + 3 * q^44 + 15 * q^45 + 10 * q^46 + 18 * q^47 + q^48 + 18 * q^49 - 8 * q^50 - 11 * q^51 + 17 * q^53 - 10 * q^54 - 26 * q^55 - 13 * q^56 + q^57 + 20 * q^58 + 24 * q^59 + 3 * q^60 + 6 * q^61 - q^62 + q^63 + 9 * q^64 + 2 * q^66 + 29 * q^67 - 8 * q^68 - 12 * q^69 - 4 * q^70 + 23 * q^71 + 2 * q^72 + 38 * q^73 - 15 * q^74 + 11 * q^75 + 9 * q^76 - 40 * q^77 - 20 * q^79 - q^80 - 31 * q^81 - 19 * q^82 + 20 * q^83 + 24 * q^84 + 39 * q^85 + 16 * q^86 - 10 * q^87 - 3 * q^88 - 7 * q^89 - 15 * q^90 - 10 * q^92 + 11 * q^93 - 18 * q^94 - q^95 - q^96 + 28 * q^97 - 18 * q^98 + 25 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	0.0255071	0.0147265	0.00736327	−	0.999973i	$-0.497656\pi$
$3$	0.0255071	0.0147265	0.00736327	+	0.999973i	$0.497656\pi$
$4$	1.00000	0.500000
$5$	−1.15077	−0.514639	−0.257320	−	0.966326i	$-0.582839\pi$
$5$	−1.15077	−0.514639	−0.257320	+	0.966326i	$0.582839\pi$
$6$	−0.0255071	−0.0104132
$7$	−2.71462	−1.02603	−0.513015	−	0.858380i	$-0.671471\pi$
$7$	−2.71462	−1.02603	−0.513015	+	0.858380i	$0.671471\pi$
$8$	−1.00000	−0.353553
$9$	−2.99935	−0.999783
$10$	1.15077	0.363905
$11$	2.25258	0.679178	0.339589	−	0.940574i	$-0.389712\pi$
$11$	2.25258	0.679178	0.339589	+	0.940574i	$0.389712\pi$
$12$	0.0255071	0.00736327
$13$	0	0
$13$	0	0
$14$	2.71462	0.725513
$15$	−0.0293528	−0.00757885
$16$	1.00000	0.250000
$17$	−1.05257	−0.255285	−0.127642	−	0.991820i	$-0.540741\pi$
$17$	−1.05257	−0.255285	−0.127642	+	0.991820i	$0.540741\pi$
$18$	2.99935	0.706953
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	−1.15077	−0.257320
$21$	−0.0692421	−0.0151099
$22$	−2.25258	−0.480251
$23$	−4.19440	−0.874593	−0.437296	−	0.899317i	$-0.644064\pi$
$23$	−4.19440	−0.874593	−0.437296	+	0.899317i	$0.644064\pi$
$24$	−0.0255071	−0.00520662
$25$	−3.67573	−0.735146
$26$	0	0
$27$	−0.153026	−0.0294499
$28$	−2.71462	−0.513015
$29$	−9.59724	−1.78216	−0.891081	−	0.453844i	$-0.850052\pi$
$29$	−9.59724	−1.78216	−0.891081	+	0.453844i	$0.850052\pi$
$30$	0.0293528	0.00535906
$31$	5.93949	1.06676	0.533382	−	0.845874i	$-0.320921\pi$
$31$	5.93949	1.06676	0.533382	+	0.845874i	$0.320921\pi$
$32$	−1.00000	−0.176777
$33$	0.0574567	0.0100019
$34$	1.05257	0.180513
$35$	3.12390	0.528035
$36$	−2.99935	−0.499892
$37$	5.76725	0.948130	0.474065	−	0.880490i	$-0.342786\pi$
$37$	5.76725	0.948130	0.474065	+	0.880490i	$0.342786\pi$
$38$	−1.00000	−0.162221
$39$	0	0
$40$	1.15077	0.181952
$41$	−3.73239	−0.582901	−0.291450	−	0.956586i	$-0.594138\pi$
$41$	−3.73239	−0.582901	−0.291450	+	0.956586i	$0.594138\pi$
$42$	0.0692421	0.0106843
$43$	−4.42815	−0.675286	−0.337643	−	0.941274i	$-0.609630\pi$
$43$	−4.42815	−0.675286	−0.337643	+	0.941274i	$0.609630\pi$
$44$	2.25258	0.339589
$45$	3.45156	0.514528
$46$	4.19440	0.618430
$47$	1.18667	0.173094	0.0865470	−	0.996248i	$-0.472417\pi$
$47$	1.18667	0.173094	0.0865470	+	0.996248i	$0.472417\pi$
$48$	0.0255071	0.00368163
$49$	0.369164	0.0527377
$50$	3.67573	0.519827
$51$	−0.0268479	−0.00375946
$52$	0	0
$53$	−2.39200	−0.328566	−0.164283	−	0.986413i	$-0.552531\pi$
$53$	−2.39200	−0.328566	−0.164283	+	0.986413i	$0.552531\pi$
$54$	0.153026	0.0208242
$55$	−2.59220	−0.349532
$56$	2.71462	0.362756
$57$	0.0255071	0.00337850
$58$	9.59724	1.26018
$59$	−2.95491	−0.384696	−0.192348	−	0.981327i	$-0.561610\pi$
$59$	−2.95491	−0.384696	−0.192348	+	0.981327i	$0.561610\pi$
$60$	−0.0293528	−0.00378943
$61$	−1.72623	−0.221021	−0.110510	−	0.993875i	$-0.535249\pi$
$61$	−1.72623	−0.221021	−0.110510	+	0.993875i	$0.535249\pi$
$62$	−5.93949	−0.754317
$63$	8.14210	1.02581
$64$	1.00000	0.125000
$65$	0	0
$66$	−0.0574567	−0.00707244
$67$	4.39417	0.536834	0.268417	−	0.963303i	$-0.413500\pi$
$67$	4.39417	0.536834	0.268417	+	0.963303i	$0.413500\pi$
$68$	−1.05257	−0.127642
$69$	−0.106987	−0.0128797
$70$	−3.12390	−0.373377
$71$	−12.9641	−1.53855	−0.769277	−	0.638915i	$-0.779384\pi$
$71$	−12.9641	−1.53855	−0.769277	+	0.638915i	$0.779384\pi$
$72$	2.99935	0.353477
$73$	−0.865426	−0.101290	−0.0506452	−	0.998717i	$-0.516128\pi$
$73$	−0.865426	−0.101290	−0.0506452	+	0.998717i	$0.516128\pi$
$74$	−5.76725	−0.670429
$75$	−0.0937573	−0.0108262
$76$	1.00000	0.114708
$77$	−6.11489	−0.696857
$78$	0	0
$79$	−1.38491	−0.155815	−0.0779073	−	0.996961i	$-0.524824\pi$
$79$	−1.38491	−0.155815	−0.0779073	+	0.996961i	$0.524824\pi$
$80$	−1.15077	−0.128660
$81$	8.99414	0.999349
$82$	3.73239	0.412173
$83$	7.32243	0.803741	0.401870	−	0.915697i	$-0.368360\pi$
$83$	7.32243	0.803741	0.401870	+	0.915697i	$0.368360\pi$
$84$	−0.0692421	−0.00755493
$85$	1.21126	0.131379
$86$	4.42815	0.477499
$87$	−0.244798	−0.0262451
$88$	−2.25258	−0.240126
$89$	8.81390	0.934272	0.467136	−	0.884186i	$-0.345286\pi$
$89$	8.81390	0.934272	0.467136	+	0.884186i	$0.345286\pi$
$90$	−3.45156	−0.363826
$91$	0	0
$92$	−4.19440	−0.437296
$93$	0.151499	0.0157097
$94$	−1.18667	−0.122396
$95$	−1.15077	−0.118066
$96$	−0.0255071	−0.00260331
$97$	−3.14346	−0.319170	−0.159585	−	0.987184i	$-0.551016\pi$
$97$	−3.14346	−0.319170	−0.159585	+	0.987184i	$0.551016\pi$
$98$	−0.369164	−0.0372912
$99$	−6.75627	−0.679030
$100$	−3.67573	−0.367573
$101$	11.5032	1.14461	0.572304	−	0.820042i	$-0.306050\pi$
$101$	11.5032	1.14461	0.572304	+	0.820042i	$0.306050\pi$
$102$	0.0268479	0.00265834
$103$	−0.710513	−0.0700089	−0.0350045	−	0.999387i	$-0.511145\pi$
$103$	−0.710513	−0.0700089	−0.0350045	+	0.999387i	$0.511145\pi$
$104$	0	0
$105$	0.0796816	0.00777613
$106$	2.39200	0.232331
$107$	−2.50730	−0.242390	−0.121195	−	0.992629i	$-0.538673\pi$
$107$	−2.50730	−0.242390	−0.121195	+	0.992629i	$0.538673\pi$
$108$	−0.153026	−0.0147249
$109$	−16.3490	−1.56595	−0.782973	−	0.622056i	$-0.786298\pi$
$109$	−16.3490	−1.56595	−0.782973	+	0.622056i	$0.786298\pi$
$110$	2.59220	0.247156
$111$	0.147106	0.0139627
$112$	−2.71462	−0.256508
$113$	−19.4844	−1.83294	−0.916471	−	0.400101i	$-0.868975\pi$
$113$	−19.4844	−1.83294	−0.916471	+	0.400101i	$0.868975\pi$
$114$	−0.0255071	−0.00238896
$115$	4.82678	0.450100
$116$	−9.59724	−0.891081
$117$	0	0
$118$	2.95491	0.272021
$119$	2.85731	0.261930
$120$	0.0293528	0.00267953
$121$	−5.92589	−0.538718
$122$	1.72623	0.156285
$123$	−0.0952024	−0.00858411
$124$	5.93949	0.533382
$125$	9.98376	0.892975
$126$	−8.14210	−0.725355
$127$	16.4464	1.45938	0.729691	−	0.683777i	$-0.239664\pi$
$127$	16.4464	1.45938	0.729691	+	0.683777i	$0.239664\pi$
$128$	−1.00000	−0.0883883
$129$	−0.112949	−0.00994462
$130$	0	0
$131$	0.947875	0.0828162	0.0414081	−	0.999142i	$-0.486816\pi$
$131$	0.947875	0.0828162	0.0414081	+	0.999142i	$0.486816\pi$
$132$	0.0574567	0.00500097
$133$	−2.71462	−0.235387
$134$	−4.39417	−0.379599
$135$	0.176098	0.0151561
$136$	1.05257	0.0902567
$137$	−5.85810	−0.500491	−0.250246	−	0.968182i	$-0.580511\pi$
$137$	−5.85810	−0.500491	−0.250246	+	0.968182i	$0.580511\pi$
$138$	0.106987	0.00910734
$139$	6.74914	0.572455	0.286227	−	0.958162i	$-0.407599\pi$
$139$	6.74914	0.572455	0.286227	+	0.958162i	$0.407599\pi$
$140$	3.12390	0.264018
$141$	0.0302686	0.00254908
$142$	12.9641	1.08792
$143$	0	0
$144$	−2.99935	−0.249946
$145$	11.0442	0.917171
$146$	0.865426	0.0716232
$147$	0.00941630	0.000776644 0
$148$	5.76725	0.474065
$149$	−16.7413	−1.37150	−0.685749	−	0.727838i	$-0.740525\pi$
$149$	−16.7413	−1.37150	−0.685749	+	0.727838i	$0.740525\pi$
$150$	0.0937573	0.00765525
$151$	−8.25725	−0.671966	−0.335983	−	0.941868i	$-0.609068\pi$
$151$	−8.25725	−0.671966	−0.335983	+	0.941868i	$0.609068\pi$
$152$	−1.00000	−0.0811107
$153$	3.15701	0.255229
$154$	6.11489	0.492752
$155$	−6.83498	−0.548999
$156$	0	0
$157$	−4.24489	−0.338779	−0.169389	−	0.985549i	$-0.554180\pi$
$157$	−4.24489	−0.338779	−0.169389	+	0.985549i	$0.554180\pi$
$158$	1.38491	0.110178
$159$	−0.0610130	−0.00483864
$160$	1.15077	0.0909762
$161$	11.3862	0.897358
$162$	−8.99414	−0.706647
$163$	−7.08938	−0.555283	−0.277642	−	0.960685i	$-0.589553\pi$
$163$	−7.08938	−0.555283	−0.277642	+	0.960685i	$0.589553\pi$
$164$	−3.73239	−0.291450
$165$	−0.0661194	−0.00514739
$166$	−7.32243	−0.568330
$167$	21.2953	1.64788	0.823942	−	0.566674i	$-0.191770\pi$
$167$	21.2953	1.64788	0.823942	+	0.566674i	$0.191770\pi$
$168$	0.0692421	0.00534214
$169$	0	0
$170$	−1.21126	−0.0928993
$171$	−2.99935	−0.229366
$172$	−4.42815	−0.337643
$173$	21.3897	1.62623	0.813116	−	0.582102i	$-0.197769\pi$
$173$	21.3897	1.62623	0.813116	+	0.582102i	$0.197769\pi$
$174$	0.244798	0.0185581
$175$	9.97822	0.754282
$176$	2.25258	0.169794
$177$	−0.0753711	−0.00566524
$178$	−8.81390	−0.660630
$179$	13.8415	1.03456	0.517280	−	0.855816i	$-0.326945\pi$
$179$	13.8415	1.03456	0.517280	+	0.855816i	$0.326945\pi$
$180$	3.45156	0.257264
$181$	−10.7106	−0.796109	−0.398055	−	0.917362i	$-0.630315\pi$
$181$	−10.7106	−0.796109	−0.398055	+	0.917362i	$0.630315\pi$
$182$	0	0
$183$	−0.0440311	−0.00325487
$184$	4.19440	0.309215
$185$	−6.63677	−0.487945
$186$	−0.151499	−0.0111085
$187$	−2.37098	−0.173384
$188$	1.18667	0.0865470
$189$	0.415408	0.0302165
$190$	1.15077	0.0834855
$191$	8.94110	0.646955	0.323478	−	0.946236i	$-0.395148\pi$
$191$	8.94110	0.646955	0.323478	+	0.946236i	$0.395148\pi$
$192$	0.0255071	0.00184082
$193$	1.42747	0.102751	0.0513757	−	0.998679i	$-0.483639\pi$
$193$	1.42747	0.102751	0.0513757	+	0.998679i	$0.483639\pi$
$194$	3.14346	0.225687
$195$	0	0
$196$	0.369164	0.0263689
$197$	8.15923	0.581321	0.290661	−	0.956826i	$-0.406125\pi$
$197$	8.15923	0.581321	0.290661	+	0.956826i	$0.406125\pi$
$198$	6.75627	0.480147
$199$	14.0903	0.998836	0.499418	−	0.866361i	$-0.333547\pi$
$199$	14.0903	0.998836	0.499418	+	0.866361i	$0.333547\pi$
$200$	3.67573	0.259913
$201$	0.112083	0.00790570
$202$	−11.5032	−0.809360
$203$	26.0529	1.82855
$204$	−0.0268479	−0.00187973
$205$	4.29511	0.299984
$206$	0.710513	0.0495038
$207$	12.5805	0.874403
$208$	0	0
$209$	2.25258	0.155814
$210$	−0.0796816	−0.00549856
$211$	−8.30609	−0.571815	−0.285907	−	0.958257i	$-0.592295\pi$
$211$	−8.30609	−0.571815	−0.285907	+	0.958257i	$0.592295\pi$
$212$	−2.39200	−0.164283
$213$	−0.330677	−0.0226576
$214$	2.50730	0.171395
$215$	5.09577	0.347529
$216$	0.153026	0.0104121
$217$	−16.1235	−1.09453
$218$	16.3490	1.10729
$219$	−0.0220745	−0.00149166
$220$	−2.59220	−0.174766
$221$	0	0
$222$	−0.147106	−0.00987310
$223$	21.1374	1.41547	0.707733	−	0.706480i	$-0.249718\pi$
$223$	21.1374	1.41547	0.707733	+	0.706480i	$0.249718\pi$
$224$	2.71462	0.181378
$225$	11.0248	0.734987
$226$	19.4844	1.29609
$227$	−13.3858	−0.888444	−0.444222	−	0.895917i	$-0.646520\pi$
$227$	−13.3858	−0.888444	−0.444222	+	0.895917i	$0.646520\pi$
$228$	0.0255071	0.00168925
$229$	27.6256	1.82555	0.912776	−	0.408460i	$-0.133934\pi$
$229$	27.6256	1.82555	0.912776	+	0.408460i	$0.133934\pi$
$230$	−4.82678	−0.318269
$231$	−0.155973	−0.0102623
$232$	9.59724	0.630089
$233$	16.2971	1.06766	0.533830	−	0.845592i	$-0.320752\pi$
$233$	16.2971	1.06766	0.533830	+	0.845592i	$0.320752\pi$
$234$	0	0
$235$	−1.36559	−0.0890810
$236$	−2.95491	−0.192348
$237$	−0.0353251	−0.00229461
$238$	−2.85731	−0.185212
$239$	−3.04743	−0.197122	−0.0985610	−	0.995131i	$-0.531424\pi$
$239$	−3.04743	−0.197122	−0.0985610	+	0.995131i	$0.531424\pi$
$240$	−0.0293528	−0.00189471
$241$	20.6690	1.33141	0.665705	−	0.746215i	$-0.268131\pi$
$241$	20.6690	1.33141	0.665705	+	0.746215i	$0.268131\pi$
$242$	5.92589	0.380931
$243$	0.688493	0.0441668
$244$	−1.72623	−0.110510
$245$	−0.424822	−0.0271409
$246$	0.0952024	0.00606988
$247$	0	0
$248$	−5.93949	−0.377158
$249$	0.186774	0.0118363
$250$	−9.98376	−0.631428
$251$	19.5303	1.23274	0.616370	−	0.787457i	$-0.288603\pi$
$251$	19.5303	1.23274	0.616370	+	0.787457i	$0.288603\pi$
$252$	8.14210	0.512904
$253$	−9.44821	−0.594004
$254$	−16.4464	−1.03194
$255$	0.0308957	0.00193476
$256$	1.00000	0.0625000
$257$	17.0046	1.06072	0.530360	−	0.847773i	$-0.322057\pi$
$257$	17.0046	1.06072	0.530360	+	0.847773i	$0.322057\pi$
$258$	0.112949	0.00703191
$259$	−15.6559	−0.972810
$260$	0	0
$261$	28.7855	1.78178
$262$	−0.947875	−0.0585599
$263$	−8.52643	−0.525762	−0.262881	−	0.964828i	$-0.584673\pi$
$263$	−8.52643	−0.525762	−0.262881	+	0.964828i	$0.584673\pi$
$264$	−0.0574567	−0.00353622
$265$	2.75264	0.169093
$266$	2.71462	0.166444
$267$	0.224817	0.0137586
$268$	4.39417	0.268417
$269$	−20.5238	−1.25136	−0.625678	−	0.780082i	$-0.715178\pi$
$269$	−20.5238	−1.25136	−0.625678	+	0.780082i	$0.715178\pi$
$270$	−0.176098	−0.0107170
$271$	28.7754	1.74798	0.873989	−	0.485946i	$-0.161525\pi$
$271$	28.7754	1.74798	0.873989	+	0.485946i	$0.161525\pi$
$272$	−1.05257	−0.0638211
$273$	0	0
$274$	5.85810	0.353901
$275$	−8.27987	−0.499295
$276$	−0.106987	−0.00643986
$277$	14.0065	0.841566	0.420783	−	0.907161i	$-0.361755\pi$
$277$	14.0065	0.841566	0.420783	+	0.907161i	$0.361755\pi$
$278$	−6.74914	−0.404787
$279$	−17.8146	−1.06653
$280$	−3.12390	−0.186689
$281$	−14.4810	−0.863862	−0.431931	−	0.901907i	$-0.642168\pi$
$281$	−14.4810	−0.863862	−0.431931	+	0.901907i	$0.642168\pi$
$282$	−0.0302686	−0.00180247
$283$	−14.7134	−0.874619	−0.437310	−	0.899311i	$-0.644069\pi$
$283$	−14.7134	−0.874619	−0.437310	+	0.899311i	$0.644069\pi$
$284$	−12.9641	−0.769277
$285$	−0.0293528	−0.00173871
$286$	0	0
$287$	10.1320	0.598074
$288$	2.99935	0.176738
$289$	−15.8921	−0.934830
$290$	−11.0442	−0.648538
$291$	−0.0801805	−0.00470026
$292$	−0.865426	−0.0506452
$293$	14.3484	0.838245	0.419122	−	0.907930i	$-0.362338\pi$
$293$	14.3484	0.838245	0.419122	+	0.907930i	$0.362338\pi$
$294$	−0.00941630	−0.000549170 0
$295$	3.40041	0.197980
$296$	−5.76725	−0.335215
$297$	−0.344703	−0.0200017
$298$	16.7413	0.969796
$299$	0	0
$300$	−0.0937573	−0.00541308
$301$	12.0207	0.692864
$302$	8.25725	0.475151
$303$	0.293412	0.0168561
$304$	1.00000	0.0573539
$305$	1.98649	0.113746
$306$	−3.15701	−0.180474
$307$	7.93805	0.453048	0.226524	−	0.974006i	$-0.427264\pi$
$307$	7.93805	0.453048	0.226524	+	0.974006i	$0.427264\pi$
$308$	−6.11489	−0.348428
$309$	−0.0181231	−0.00103099
$310$	6.83498	0.388201
$311$	−15.2395	−0.864155	−0.432077	−	0.901837i	$-0.642219\pi$
$311$	−15.2395	−0.864155	−0.432077	+	0.901837i	$0.642219\pi$
$312$	0	0
$313$	22.1114	1.24981	0.624905	−	0.780700i	$-0.285138\pi$
$313$	22.1114	1.24981	0.624905	+	0.780700i	$0.285138\pi$
$314$	4.24489	0.239553
$315$	−9.36967	−0.527921
$316$	−1.38491	−0.0779073
$317$	−8.42018	−0.472924	−0.236462	−	0.971641i	$-0.575988\pi$
$317$	−8.42018	−0.472924	−0.236462	+	0.971641i	$0.575988\pi$
$318$	0.0610130	0.00342144
$319$	−21.6185	−1.21040
$320$	−1.15077	−0.0643299
$321$	−0.0639539	−0.00356956
$322$	−11.3862	−0.634528
$323$	−1.05257	−0.0585663
$324$	8.99414	0.499675
$325$	0	0
$326$	7.08938	0.392644
$327$	−0.417015	−0.0230610
$328$	3.73239	0.206087
$329$	−3.22137	−0.177600
$330$	0.0661194	0.00363975
$331$	−0.994400	−0.0546572	−0.0273286	−	0.999627i	$-0.508700\pi$
$331$	−0.994400	−0.0546572	−0.0273286	+	0.999627i	$0.508700\pi$
$332$	7.32243	0.401870
$333$	−17.2980	−0.947924
$334$	−21.2953	−1.16523
$335$	−5.05667	−0.276276
$336$	−0.0692421	−0.00377747
$337$	−3.77065	−0.205400	−0.102700	−	0.994712i	$-0.532748\pi$
$337$	−3.77065	−0.205400	−0.102700	+	0.994712i	$0.532748\pi$
$338$	0	0
$339$	−0.496992	−0.0269929
$340$	1.21126	0.0656897
$341$	13.3792	0.724523
$342$	2.99935	0.162186
$343$	18.0002	0.971920
$344$	4.42815	0.238750
$345$	0.123117	0.00662841
$346$	−21.3897	−1.14992
$347$	−3.24661	−0.174287	−0.0871437	−	0.996196i	$-0.527774\pi$
$347$	−3.24661	−0.174287	−0.0871437	+	0.996196i	$0.527774\pi$
$348$	−0.244798	−0.0131225
$349$	−4.86399	−0.260364	−0.130182	−	0.991490i	$-0.541556\pi$
$349$	−4.86399	−0.260364	−0.130182	+	0.991490i	$0.541556\pi$
$350$	−9.97822	−0.533358
$351$	0	0
$352$	−2.25258	−0.120063
$353$	8.71382	0.463790	0.231895	−	0.972741i	$-0.425507\pi$
$353$	8.71382	0.463790	0.231895	+	0.972741i	$0.425507\pi$
$354$	0.0753711	0.00400593
$355$	14.9187	0.791801
$356$	8.81390	0.467136
$357$	0.0728818	0.00385731
$358$	−13.8415	−0.731544
$359$	10.0729	0.531630	0.265815	−	0.964024i	$-0.414359\pi$
$359$	10.0729	0.531630	0.265815	+	0.964024i	$0.414359\pi$
$360$	−3.45156	−0.181913
$361$	1.00000	0.0526316
$362$	10.7106	0.562934
$363$	−0.151152	−0.00793344
$364$	0	0
$365$	0.995905	0.0521281
$366$	0.0440311	0.00230154
$367$	9.61210	0.501748	0.250874	−	0.968020i	$-0.419282\pi$
$367$	9.61210	0.501748	0.250874	+	0.968020i	$0.419282\pi$
$368$	−4.19440	−0.218648
$369$	11.1947	0.582774
$370$	6.63677	0.345029
$371$	6.49337	0.337119
$372$	0.151499	0.00785487
$373$	21.0559	1.09023	0.545116	−	0.838361i	$-0.316486\pi$
$373$	21.0559	1.09023	0.545116	+	0.838361i	$0.316486\pi$
$374$	2.37098	0.122601
$375$	0.254657	0.0131504
$376$	−1.18667	−0.0611980
$377$	0	0
$378$	−0.415408	−0.0213663
$379$	−23.3233	−1.19804	−0.599019	−	0.800735i	$-0.704442\pi$
$379$	−23.3233	−1.19804	−0.599019	+	0.800735i	$0.704442\pi$
$380$	−1.15077	−0.0590332
$381$	0.419500	0.0214916
$382$	−8.94110	−0.457466
$383$	−30.8875	−1.57828	−0.789140	−	0.614214i	$-0.789473\pi$
$383$	−30.8875	−1.57828	−0.789140	+	0.614214i	$0.789473\pi$
$384$	−0.0255071	−0.00130165
$385$	7.03683	0.358630
$386$	−1.42747	−0.0726563
$387$	13.2816	0.675140
$388$	−3.14346	−0.159585
$389$	2.40183	0.121777	0.0608887	−	0.998145i	$-0.480607\pi$
$389$	2.40183	0.121777	0.0608887	+	0.998145i	$0.480607\pi$
$390$	0	0
$391$	4.41488	0.223270
$392$	−0.369164	−0.0186456
$393$	0.0241776	0.00121960
$394$	−8.15923	−0.411056
$395$	1.59371	0.0801883
$396$	−6.75627	−0.339515
$397$	−22.4135	−1.12490	−0.562450	−	0.826831i	$-0.690141\pi$
$397$	−22.4135	−1.12490	−0.562450	+	0.826831i	$0.690141\pi$
$398$	−14.0903	−0.706283
$399$	−0.0692421	−0.00346644
$400$	−3.67573	−0.183787
$401$	−5.79343	−0.289310	−0.144655	−	0.989482i	$-0.546207\pi$
$401$	−5.79343	−0.289310	−0.144655	+	0.989482i	$0.546207\pi$
$402$	−0.112083	−0.00559017
$403$	0	0
$404$	11.5032	0.572304
$405$	−10.3502	−0.514305
$406$	−26.0529	−1.29298
$407$	12.9912	0.643949
$408$	0.0268479	0.00132917
$409$	6.02882	0.298106	0.149053	−	0.988829i	$-0.452377\pi$
$409$	6.02882	0.298106	0.149053	+	0.988829i	$0.452377\pi$
$410$	−4.29511	−0.212121
$411$	−0.149423	−0.00737050
$412$	−0.710513	−0.0350045
$413$	8.02145	0.394710
$414$	−12.5805	−0.618296
$415$	−8.42642	−0.413637
$416$	0	0
$417$	0.172151	0.00843028
$418$	−2.25258	−0.110177
$419$	−35.3612	−1.72751	−0.863755	−	0.503912i	$-0.831893\pi$
$419$	−35.3612	−1.72751	−0.863755	+	0.503912i	$0.831893\pi$
$420$	0.0796816	0.00388807
$421$	14.9312	0.727701	0.363851	−	0.931457i	$-0.381462\pi$
$421$	14.9312	0.727701	0.363851	+	0.931457i	$0.381462\pi$
$422$	8.30609	0.404334
$423$	−3.55925	−0.173057
$424$	2.39200	0.116166
$425$	3.86895	0.187671
$426$	0.330677	0.0160213
$427$	4.68605	0.226774
$428$	−2.50730	−0.121195
$429$	0	0
$430$	−5.09577	−0.245740
$431$	−14.3600	−0.691696	−0.345848	−	0.938291i	$-0.612409\pi$
$431$	−14.3600	−0.691696	−0.345848	+	0.938291i	$0.612409\pi$
$432$	−0.153026	−0.00736247
$433$	−7.09636	−0.341029	−0.170515	−	0.985355i	$-0.554543\pi$
$433$	−7.09636	−0.341029	−0.170515	+	0.985355i	$0.554543\pi$
$434$	16.1235	0.773951
$435$	0.281705	0.0135067
$436$	−16.3490	−0.782973
$437$	−4.19440	−0.200645
$438$	0.0220745	0.00105476
$439$	−23.7941	−1.13563	−0.567816	−	0.823156i	$-0.692211\pi$
$439$	−23.7941	−1.13563	−0.567816	+	0.823156i	$0.692211\pi$
$440$	2.59220	0.123578
$441$	−1.10725	−0.0527263
$442$	0	0
$443$	−6.45547	−0.306709	−0.153354	−	0.988171i	$-0.549008\pi$
$443$	−6.45547	−0.306709	−0.153354	+	0.988171i	$0.549008\pi$
$444$	0.147106	0.00698133
$445$	−10.1428	−0.480813
$446$	−21.1374	−1.00089
$447$	−0.427021	−0.0201974
$448$	−2.71462	−0.128254
$449$	28.1063	1.32642	0.663209	−	0.748434i	$-0.269194\pi$
$449$	28.1063	1.32642	0.663209	+	0.748434i	$0.269194\pi$
$450$	−11.0248	−0.519714
$451$	−8.40749	−0.395893
$452$	−19.4844	−0.916471
$453$	−0.210619	−0.00989573
$454$	13.3858	0.628225
$455$	0	0
$456$	−0.0255071	−0.00119448
$457$	25.4808	1.19194	0.595971	−	0.803006i	$-0.296767\pi$
$457$	25.4808	1.19194	0.595971	+	0.803006i	$0.296767\pi$
$458$	−27.6256	−1.29086
$459$	0.161070	0.00751810
$460$	4.82678	0.225050
$461$	−21.5758	−1.00488	−0.502442	−	0.864611i	$-0.667565\pi$
$461$	−21.5758	−1.00488	−0.502442	+	0.864611i	$0.667565\pi$
$462$	0.155973	0.00725653
$463$	9.71185	0.451348	0.225674	−	0.974203i	$-0.427542\pi$
$463$	9.71185	0.451348	0.225674	+	0.974203i	$0.427542\pi$
$464$	−9.59724	−0.445541
$465$	−0.174341	−0.00808485
$466$	−16.2971	−0.754950
$467$	31.1018	1.43922	0.719609	−	0.694379i	$-0.244321\pi$
$467$	31.1018	1.43922	0.719609	+	0.694379i	$0.244321\pi$
$468$	0	0
$469$	−11.9285	−0.550807
$470$	1.36559	0.0629898
$471$	−0.108275	−0.00498904
$472$	2.95491	0.136011
$473$	−9.97474	−0.458639
$474$	0.0353251	0.00162253
$475$	−3.67573	−0.168654
$476$	2.85731	0.130965
$477$	7.17444	0.328495
$478$	3.04743	0.139386
$479$	9.27589	0.423826	0.211913	−	0.977289i	$-0.432031\pi$
$479$	9.27589	0.423826	0.211913	+	0.977289i	$0.432031\pi$
$480$	0.0293528	0.00133976
$481$	0	0
$482$	−20.6690	−0.941449
$483$	0.290429	0.0132150
$484$	−5.92589	−0.269359
$485$	3.61739	0.164257
$486$	−0.688493	−0.0312307
$487$	36.6877	1.66248	0.831238	−	0.555916i	$-0.187632\pi$
$487$	36.6877	1.66248	0.831238	+	0.555916i	$0.187632\pi$
$488$	1.72623	0.0781427
$489$	−0.180830	−0.00817740
$490$	0.424822	0.0191915
$491$	3.49813	0.157868	0.0789341	−	0.996880i	$-0.474848\pi$
$491$	3.49813	0.157868	0.0789341	+	0.996880i	$0.474848\pi$
$492$	−0.0952024	−0.00429205
$493$	10.1017	0.454958
$494$	0	0
$495$	7.77490	0.349456
$496$	5.93949	0.266691
$497$	35.1926	1.57860
$498$	−0.186774	−0.00836954
$499$	22.2594	0.996469	0.498235	−	0.867042i	$-0.333982\pi$
$499$	22.2594	0.996469	0.498235	+	0.867042i	$0.333982\pi$
$500$	9.98376	0.446487
$501$	0.543183	0.0242676
$502$	−19.5303	−0.871678
$503$	11.7763	0.525078	0.262539	−	0.964921i	$-0.415440\pi$
$503$	11.7763	0.525078	0.262539	+	0.964921i	$0.415440\pi$
$504$	−8.14210	−0.362678
$505$	−13.2375	−0.589060
$506$	9.44821	0.420024
$507$	0	0
$508$	16.4464	0.729691
$509$	28.2844	1.25368	0.626842	−	0.779147i	$-0.284347\pi$
$509$	28.2844	1.25368	0.626842	+	0.779147i	$0.284347\pi$
$510$	−0.0308957	−0.00136808
$511$	2.34930	0.103927
$512$	−1.00000	−0.0441942
$513$	−0.153026	−0.00675626
$514$	−17.0046	−0.750042
$515$	0.817636	0.0360293
$516$	−0.112949	−0.00497231
$517$	2.67307	0.117562
$518$	15.6559	0.687880
$519$	0.545590	0.0239488
$520$	0	0
$521$	2.50201	0.109615	0.0548075	−	0.998497i	$-0.482545\pi$
$521$	2.50201	0.109615	0.0548075	+	0.998497i	$0.482545\pi$
$522$	−28.7855	−1.25991
$523$	−13.7531	−0.601380	−0.300690	−	0.953722i	$-0.597217\pi$
$523$	−13.7531	−0.601380	−0.300690	+	0.953722i	$0.597217\pi$
$524$	0.947875	0.0414081
$525$	0.254515	0.0111080
$526$	8.52643	0.371770
$527$	−6.25170	−0.272328
$528$	0.0574567	0.00250048
$529$	−5.40702	−0.235088
$530$	−2.75264	−0.119567
$531$	8.86280	0.384613
$532$	−2.71462	−0.117694
$533$	0	0
$534$	−0.224817	−0.00972879
$535$	2.88532	0.124743
$536$	−4.39417	−0.189799
$537$	0.353056	0.0152355
$538$	20.5238	0.884842
$539$	0.831570	0.0358183
$540$	0.176098	0.00757803
$541$	11.3737	0.488993	0.244497	−	0.969650i	$-0.421377\pi$
$541$	11.3737	0.488993	0.244497	+	0.969650i	$0.421377\pi$
$542$	−28.7754	−1.23601
$543$	−0.273195	−0.0117239
$544$	1.05257	0.0451284
$545$	18.8139	0.805897
$546$	0	0
$547$	6.97009	0.298020	0.149010	−	0.988836i	$-0.452391\pi$
$547$	6.97009	0.298020	0.149010	+	0.988836i	$0.452391\pi$
$548$	−5.85810	−0.250246
$549$	5.17756	0.220973
$550$	8.27987	0.353055
$551$	−9.59724	−0.408856
$552$	0.106987	0.00455367
$553$	3.75951	0.159870
$554$	−14.0065	−0.595077
$555$	−0.169285	−0.00718574
$556$	6.74914	0.286227
$557$	−0.915444	−0.0387886	−0.0193943	−	0.999812i	$-0.506174\pi$
$557$	−0.915444	−0.0387886	−0.0193943	+	0.999812i	$0.506174\pi$
$558$	17.8146	0.754153
$559$	0	0
$560$	3.12390	0.132009
$561$	−0.0604769	−0.00255334
$562$	14.4810	0.610842
$563$	−12.3326	−0.519758	−0.259879	−	0.965641i	$-0.583683\pi$
$563$	−12.3326	−0.519758	−0.259879	+	0.965641i	$0.583683\pi$
$564$	0.0302686	0.00127454
$565$	22.4221	0.943304
$566$	14.7134	0.618449
$567$	−24.4157	−1.02536
$568$	12.9641	0.543961
$569$	28.4768	1.19381	0.596906	−	0.802312i	$-0.296397\pi$
$569$	28.4768	1.19381	0.596906	+	0.802312i	$0.296397\pi$
$570$	0.0293528	0.00122945
$571$	7.56342	0.316519	0.158260	−	0.987398i	$-0.449412\pi$
$571$	7.56342	0.316519	0.158260	+	0.987398i	$0.449412\pi$
$572$	0	0
$573$	0.228062	0.00952741
$574$	−10.1320	−0.422902
$575$	15.4175	0.642954
$576$	−2.99935	−0.124973
$577$	25.2279	1.05025	0.525126	−	0.851024i	$-0.324018\pi$
$577$	25.2279	1.05025	0.525126	+	0.851024i	$0.324018\pi$
$578$	15.8921	0.661025
$579$	0.0364106	0.00151317
$580$	11.0442	0.458585
$581$	−19.8776	−0.824662
$582$	0.0801805	0.00332359
$583$	−5.38816	−0.223155
$584$	0.865426	0.0358116
$585$	0	0
$586$	−14.3484	−0.592728
$587$	44.3906	1.83220	0.916099	−	0.400953i	$-0.131321\pi$
$587$	44.3906	1.83220	0.916099	+	0.400953i	$0.131321\pi$
$588$	0.00941630	0.000388322 0
$589$	5.93949	0.244733
$590$	−3.40041	−0.139993
$591$	0.208118	0.00856085
$592$	5.76725	0.237032
$593$	−3.34970	−0.137556	−0.0687779	−	0.997632i	$-0.521910\pi$
$593$	−3.34970	−0.137556	−0.0687779	+	0.997632i	$0.521910\pi$
$594$	0.344703	0.0141433
$595$	−3.28811	−0.134799
$596$	−16.7413	−0.685749
$597$	0.359403	0.0147094
$598$	0	0
$599$	−18.7205	−0.764899	−0.382449	−	0.923976i	$-0.624919\pi$
$599$	−18.7205	−0.764899	−0.382449	+	0.923976i	$0.624919\pi$
$600$	0.0937573	0.00382762
$601$	−7.53304	−0.307279	−0.153639	−	0.988127i	$-0.549099\pi$
$601$	−7.53304	−0.307279	−0.153639	+	0.988127i	$0.549099\pi$
$602$	−12.0207	−0.489929
$603$	−13.1797	−0.536717
$604$	−8.25725	−0.335983
$605$	6.81933	0.277245
$606$	−0.293412	−0.0119191
$607$	37.4507	1.52008	0.760039	−	0.649877i	$-0.225180\pi$
$607$	37.4507	1.52008	0.760039	+	0.649877i	$0.225180\pi$
$608$	−1.00000	−0.0405554
$609$	0.664533	0.0269282
$610$	−1.98649	−0.0804306
$611$	0	0
$612$	3.15701	0.127615
$613$	31.6875	1.27985	0.639923	−	0.768439i	$-0.278966\pi$
$613$	31.6875	1.27985	0.639923	+	0.768439i	$0.278966\pi$
$614$	−7.93805	−0.320353
$615$	0.109556	0.00441772
$616$	6.11489	0.246376
$617$	−23.6175	−0.950806	−0.475403	−	0.879768i	$-0.657698\pi$
$617$	−23.6175	−0.950806	−0.475403	+	0.879768i	$0.657698\pi$
$618$	0.0181231	0.000729019 0
$619$	−17.3471	−0.697238	−0.348619	−	0.937265i	$-0.613349\pi$
$619$	−17.3471	−0.697238	−0.348619	+	0.937265i	$0.613349\pi$
$620$	−6.83498	−0.274500
$621$	0.641852	0.0257566
$622$	15.2395	0.611050
$623$	−23.9264	−0.958591
$624$	0	0
$625$	6.88966	0.275587
$626$	−22.1114	−0.883750
$627$	0.0574567	0.00229460
$628$	−4.24489	−0.169389
$629$	−6.07040	−0.242043
$630$	9.36967	0.373296
$631$	42.1838	1.67931	0.839656	−	0.543119i	$-0.182757\pi$
$631$	42.1838	1.67931	0.839656	+	0.543119i	$0.182757\pi$
$632$	1.38491	0.0550888
$633$	−0.211864	−0.00842085
$634$	8.42018	0.334408
$635$	−18.9260	−0.751055
$636$	−0.0610130	−0.00241932
$637$	0	0
$638$	21.6185	0.855885
$639$	38.8838	1.53822
$640$	1.15077	0.0454881
$641$	−32.2793	−1.27496	−0.637478	−	0.770469i	$-0.720022\pi$
$641$	−32.2793	−1.27496	−0.637478	+	0.770469i	$0.720022\pi$
$642$	0.0639539	0.00252406
$643$	−21.3091	−0.840349	−0.420175	−	0.907443i	$-0.638031\pi$
$643$	−21.3091	−0.840349	−0.420175	+	0.907443i	$0.638031\pi$
$644$	11.3862	0.448679
$645$	0.129978	0.00511789
$646$	1.05257	0.0414126
$647$	−48.9872	−1.92589	−0.962943	−	0.269706i	$-0.913073\pi$
$647$	−48.9872	−1.92589	−0.962943	+	0.269706i	$0.913073\pi$
$648$	−8.99414	−0.353323
$649$	−6.65616	−0.261277
$650$	0	0
$651$	−0.411263	−0.0161187
$652$	−7.08938	−0.277642
$653$	−22.1790	−0.867932	−0.433966	−	0.900929i	$-0.642886\pi$
$653$	−22.1790	−0.867932	−0.433966	+	0.900929i	$0.642886\pi$
$654$	0.417015	0.0163066
$655$	−1.09078	−0.0426205
$656$	−3.73239	−0.145725
$657$	2.59572	0.101269
$658$	3.22137	0.125582
$659$	−21.8945	−0.852887	−0.426444	−	0.904514i	$-0.640234\pi$
$659$	−21.8945	−0.852887	−0.426444	+	0.904514i	$0.640234\pi$
$660$	−0.0661194	−0.00257369
$661$	12.1382	0.472120	0.236060	−	0.971739i	$-0.424144\pi$
$661$	12.1382	0.472120	0.236060	+	0.971739i	$0.424144\pi$
$662$	0.994400	0.0386485
$663$	0	0
$664$	−7.32243	−0.284165
$665$	3.12390	0.121140
$666$	17.2980	0.670284
$667$	40.2546	1.55867
$668$	21.2953	0.823942
$669$	0.539154	0.0208449
$670$	5.05667	0.195356
$671$	−3.88846	−0.150112
$672$	0.0692421	0.00267107
$673$	38.1092	1.46900	0.734501	−	0.678607i	$-0.237416\pi$
$673$	38.1092	1.46900	0.734501	+	0.678607i	$0.237416\pi$
$674$	3.77065	0.145240
$675$	0.562483	0.0216500
$676$	0	0
$677$	2.70946	0.104133	0.0520665	−	0.998644i	$-0.483419\pi$
$677$	2.70946	0.104133	0.0520665	+	0.998644i	$0.483419\pi$
$678$	0.496992	0.0190869
$679$	8.53329	0.327478
$680$	−1.21126	−0.0464496
$681$	−0.341432	−0.0130837
$682$	−13.3792	−0.512315
$683$	21.8712	0.836877	0.418438	−	0.908245i	$-0.362578\pi$
$683$	21.8712	0.836877	0.418438	+	0.908245i	$0.362578\pi$
$684$	−2.99935	−0.114683
$685$	6.74131	0.257572
$686$	−18.0002	−0.687251
$687$	0.704650	0.0268841
$688$	−4.42815	−0.168822
$689$	0	0
$690$	−0.123117	−0.00468699
$691$	10.0011	0.380459	0.190229	−	0.981740i	$-0.439077\pi$
$691$	10.0011	0.380459	0.190229	+	0.981740i	$0.439077\pi$
$692$	21.3897	0.813116
$693$	18.3407	0.696706
$694$	3.24661	0.123240
$695$	−7.76670	−0.294608
$696$	0.244798	0.00927903
$697$	3.92858	0.148806
$698$	4.86399	0.184105
$699$	0.415693	0.0157229
$700$	9.97822	0.377141
$701$	−7.09276	−0.267890	−0.133945	−	0.990989i	$-0.542765\pi$
$701$	−7.09276	−0.267890	−0.133945	+	0.990989i	$0.542765\pi$
$702$	0	0
$703$	5.76725	0.217516
$704$	2.25258	0.0848972
$705$	−0.0348321	−0.00131185
$706$	−8.71382	−0.327949
$707$	−31.2267	−1.17440
$708$	−0.0753711	−0.00283262
$709$	30.4599	1.14395	0.571973	−	0.820272i	$-0.306178\pi$
$709$	30.4599	1.14395	0.571973	+	0.820272i	$0.306178\pi$
$710$	−14.9187	−0.559888
$711$	4.15383	0.155781
$712$	−8.81390	−0.330315
$713$	−24.9126	−0.932985
$714$	−0.0728818	−0.00272753
$715$	0	0
$716$	13.8415	0.517280
$717$	−0.0777312	−0.00290292
$718$	−10.0729	−0.375919
$719$	−39.0201	−1.45521	−0.727603	−	0.685999i	$-0.759365\pi$
$719$	−39.0201	−1.45521	−0.727603	+	0.685999i	$0.759365\pi$
$720$	3.45156	0.128632
$721$	1.92877	0.0718313
$722$	−1.00000	−0.0372161
$723$	0.527207	0.0196070
$724$	−10.7106	−0.398055
$725$	35.2769	1.31015
$726$	0.151152	0.00560979
$727$	39.4422	1.46283	0.731416	−	0.681932i	$-0.238860\pi$
$727$	39.4422	1.46283	0.731416	+	0.681932i	$0.238860\pi$
$728$	0	0
$729$	−26.9649	−0.998699
$730$	−0.995905	−0.0368601
$731$	4.66091	0.172390
$732$	−0.0440311	−0.00162744
$733$	−32.3909	−1.19639	−0.598193	−	0.801352i	$-0.704114\pi$
$733$	−32.3909	−1.19639	−0.598193	+	0.801352i	$0.704114\pi$
$734$	−9.61210	−0.354789
$735$	−0.0108360	−0.000399691 0
$736$	4.19440	0.154608
$737$	9.89821	0.364605
$738$	−11.1947	−0.412084
$739$	17.5562	0.645816	0.322908	−	0.946430i	$-0.395340\pi$
$739$	17.5562	0.645816	0.322908	+	0.946430i	$0.395340\pi$
$740$	−6.63677	−0.243972
$741$	0	0
$742$	−6.49337	−0.238379
$743$	1.71339	0.0628581	0.0314291	−	0.999506i	$-0.489994\pi$
$743$	1.71339	0.0628581	0.0314291	+	0.999506i	$0.489994\pi$
$744$	−0.151499	−0.00555423
$745$	19.2653	0.705827
$746$	−21.0559	−0.770911
$747$	−21.9625	−0.803566
$748$	−2.37098	−0.0866918
$749$	6.80636	0.248699
$750$	−0.254657	−0.00929875
$751$	16.1868	0.590664	0.295332	−	0.955395i	$-0.404570\pi$
$751$	16.1868	0.590664	0.295332	+	0.955395i	$0.404570\pi$
$752$	1.18667	0.0432735
$753$	0.498161	0.0181540
$754$	0	0
$755$	9.50219	0.345820
$756$	0.415408	0.0151082
$757$	−48.6200	−1.76712	−0.883561	−	0.468316i	$-0.844861\pi$
$757$	−48.6200	−1.76712	−0.883561	+	0.468316i	$0.844861\pi$
$758$	23.3233	0.847140
$759$	−0.240996	−0.00874762
$760$	1.15077	0.0417428
$761$	−9.58447	−0.347437	−0.173718	−	0.984795i	$-0.555578\pi$
$761$	−9.58447	−0.347437	−0.173718	+	0.984795i	$0.555578\pi$
$762$	−0.419500	−0.0151969
$763$	44.3812	1.60671
$764$	8.94110	0.323478
$765$	−3.63299	−0.131351
$766$	30.8875	1.11601
$767$	0	0
$768$	0.0255071	0.000920408 0
$769$	−36.9907	−1.33392	−0.666959	−	0.745095i	$-0.732404\pi$
$769$	−36.9907	−1.33392	−0.666959	+	0.745095i	$0.732404\pi$
$770$	−7.03683	−0.253590
$771$	0.433739	0.0156207
$772$	1.42747	0.0513757
$773$	35.8711	1.29019	0.645096	−	0.764102i	$-0.276817\pi$
$773$	35.8711	1.29019	0.645096	+	0.764102i	$0.276817\pi$
$774$	−13.2816	−0.477396
$775$	−21.8320	−0.784228
$776$	3.14346	0.112844
$777$	−0.399336	−0.0143261
$778$	−2.40183	−0.0861097
$779$	−3.73239	−0.133727
$780$	0	0
$781$	−29.2026	−1.04495
$782$	−4.41488	−0.157876
$783$	1.46863	0.0524844
$784$	0.369164	0.0131844
$785$	4.88488	0.174349
$786$	−0.0241776	−0.000862385 0
$787$	29.1606	1.03946	0.519732	−	0.854329i	$-0.326032\pi$
$787$	29.1606	1.03946	0.519732	+	0.854329i	$0.326032\pi$
$788$	8.15923	0.290661
$789$	−0.217485	−0.00774266
$790$	−1.59371	−0.0567017
$791$	52.8929	1.88065
$792$	6.75627	0.240074
$793$	0	0
$794$	22.4135	0.795425
$795$	0.0702118	0.00249016
$796$	14.0903	0.499418
$797$	28.7748	1.01926	0.509628	−	0.860395i	$-0.329783\pi$
$797$	28.7748	1.01926	0.509628	+	0.860395i	$0.329783\pi$
$798$	0.0692421	0.00245114
$799$	−1.24905	−0.0441882
$800$	3.67573	0.129957
$801$	−26.4360	−0.934069
$802$	5.79343	0.204573
$803$	−1.94944	−0.0687942
$804$	0.112083	0.00395285
$805$	−13.1029	−0.461816
$806$	0	0
$807$	−0.523502	−0.0184281
$808$	−11.5032	−0.404680
$809$	30.6410	1.07728	0.538640	−	0.842536i	$-0.318938\pi$
$809$	30.6410	1.07728	0.538640	+	0.842536i	$0.318938\pi$
$810$	10.3502	0.363668
$811$	10.2616	0.360333	0.180166	−	0.983636i	$-0.442336\pi$
$811$	10.2616	0.360333	0.180166	+	0.983636i	$0.442336\pi$
$812$	26.0529	0.914276
$813$	0.733976	0.0257417
$814$	−12.9912	−0.455340
$815$	8.15823	0.285771
$816$	−0.0268479	−0.000939864 0
$817$	−4.42815	−0.154921
$818$	−6.02882	−0.210793
$819$	0	0
$820$	4.29511	0.149992
$821$	−27.3037	−0.952907	−0.476453	−	0.879200i	$-0.658078\pi$
$821$	−27.3037	−0.952907	−0.476453	+	0.879200i	$0.658078\pi$
$822$	0.149423	0.00521173
$823$	−46.0833	−1.60636	−0.803182	−	0.595734i	$-0.796861\pi$
$823$	−46.0833	−1.60636	−0.803182	+	0.595734i	$0.796861\pi$
$824$	0.710513	0.0247519
$825$	−0.211196	−0.00735289
$826$	−8.02145	−0.279102
$827$	−39.9507	−1.38922	−0.694612	−	0.719385i	$-0.744424\pi$
$827$	−39.9507	−1.38922	−0.694612	+	0.719385i	$0.744424\pi$
$828$	12.5805	0.437201
$829$	−0.731061	−0.0253908	−0.0126954	−	0.999919i	$-0.504041\pi$
$829$	−0.731061	−0.0253908	−0.0126954	+	0.999919i	$0.504041\pi$
$830$	8.42642	0.292485
$831$	0.357264	0.0123934
$832$	0	0
$833$	−0.388569	−0.0134631
$834$	−0.172151	−0.00596111
$835$	−24.5060	−0.848066
$836$	2.25258	0.0779070
$837$	−0.908897	−0.0314161
$838$	35.3612	1.22153
$839$	9.22691	0.318548	0.159274	−	0.987234i	$-0.449085\pi$
$839$	9.22691	0.318548	0.159274	+	0.987234i	$0.449085\pi$
$840$	−0.0796816	−0.00274928
$841$	63.1069	2.17610
$842$	−14.9312	−0.514563
$843$	−0.369367	−0.0127217
$844$	−8.30609	−0.285907
$845$	0	0
$846$	3.55925	0.122369
$847$	16.0866	0.552740
$848$	−2.39200	−0.0821416
$849$	−0.375295	−0.0128801
$850$	−3.86895	−0.132704
$851$	−24.1901	−0.829227
$852$	−0.330677	−0.0113288
$853$	40.9891	1.40344	0.701721	−	0.712452i	$-0.252415\pi$
$853$	40.9891	1.40344	0.701721	+	0.712452i	$0.252415\pi$
$854$	−4.68605	−0.160353
$855$	3.45156	0.118041
$856$	2.50730	0.0856977
$857$	7.41582	0.253320	0.126660	−	0.991946i	$-0.459574\pi$
$857$	7.41582	0.253320	0.126660	+	0.991946i	$0.459574\pi$
$858$	0	0
$859$	−58.1830	−1.98518	−0.992590	−	0.121515i	$-0.961225\pi$
$859$	−58.1830	−1.98518	−0.992590	+	0.121515i	$0.961225\pi$
$860$	5.09577	0.173764
$861$	0.258438	0.00880755
$862$	14.3600	0.489103
$863$	−17.0224	−0.579449	−0.289724	−	0.957110i	$-0.593564\pi$
$863$	−17.0224	−0.579449	−0.289724	+	0.957110i	$0.593564\pi$
$864$	0.153026	0.00520605
$865$	−24.6146	−0.836923
$866$	7.09636	0.241144
$867$	−0.405362	−0.0137668
$868$	−16.1235	−0.547266
$869$	−3.11962	−0.105826
$870$	−0.281705	−0.00955071
$871$	0	0
$872$	16.3490	0.553645
$873$	9.42832	0.319100
$874$	4.19440	0.141878
$875$	−27.1021	−0.916219
$876$	−0.0220745	−0.000745829 0
$877$	23.3641	0.788951	0.394475	−	0.918907i	$-0.370926\pi$
$877$	23.3641	0.788951	0.394475	+	0.918907i	$0.370926\pi$
$878$	23.7941	0.803013
$879$	0.365987	0.0123444
$880$	−2.59220	−0.0873829
$881$	38.9846	1.31343	0.656713	−	0.754141i	$-0.271946\pi$
$881$	38.9846	1.31343	0.656713	+	0.754141i	$0.271946\pi$
$882$	1.10725	0.0372831
$883$	8.78170	0.295528	0.147764	−	0.989023i	$-0.452792\pi$
$883$	8.78170	0.295528	0.147764	+	0.989023i	$0.452792\pi$
$884$	0	0
$885$	0.0867347	0.00291555
$886$	6.45547	0.216876
$887$	−0.963905	−0.0323648	−0.0161824	−	0.999869i	$-0.505151\pi$
$887$	−0.963905	−0.0323648	−0.0161824	+	0.999869i	$0.505151\pi$
$888$	−0.147106	−0.00493655
$889$	−44.6457	−1.49737
$890$	10.1428	0.339986
$891$	20.2600	0.678736
$892$	21.1374	0.707733
$893$	1.18667	0.0397105
$894$	0.427021	0.0142817
$895$	−15.9283	−0.532425
$896$	2.71462	0.0906891
$897$	0	0
$898$	−28.1063	−0.937919
$899$	−57.0027	−1.90115
$900$	11.0248	0.367493
$901$	2.51773	0.0838779
$902$	8.40749	0.279939
$903$	0.306614	0.0102035
$904$	19.4844	0.648043
$905$	12.3254	0.409709
$906$	0.210619	0.00699733
$907$	−19.6491	−0.652439	−0.326219	−	0.945294i	$-0.605775\pi$
$907$	−19.6491	−0.652439	−0.326219	+	0.945294i	$0.605775\pi$
$908$	−13.3858	−0.444222
$909$	−34.5020	−1.14436
$910$	0	0
$911$	54.4510	1.80404	0.902021	−	0.431692i	$-0.142083\pi$
$911$	54.4510	1.80404	0.902021	+	0.431692i	$0.142083\pi$
$912$	0.0255071	0.000844625 0
$913$	16.4943	0.545883
$914$	−25.4808	−0.842830
$915$	0.0506696	0.00167508
$916$	27.6256	0.912776
$917$	−2.57312	−0.0849719
$918$	−0.161070	−0.00531610
$919$	37.7935	1.24669	0.623346	−	0.781947i	$-0.285773\pi$
$919$	37.7935	1.24669	0.623346	+	0.781947i	$0.285773\pi$
$920$	−4.82678	−0.159134
$921$	0.202477	0.00667183
$922$	21.5758	0.710560
$923$	0	0
$924$	−0.155973	−0.00513114
$925$	−21.1989	−0.697014
$926$	−9.71185	−0.319151
$927$	2.13108	0.0699937
$928$	9.59724	0.315045
$929$	−57.4492	−1.88485	−0.942423	−	0.334423i	$-0.891459\pi$
$929$	−57.4492	−1.88485	−0.942423	+	0.334423i	$0.891459\pi$
$930$	0.174341	0.00571685
$931$	0.369164	0.0120989
$932$	16.2971	0.533830
$933$	−0.388716	−0.0127260
$934$	−31.1018	−1.01768
$935$	2.72845	0.0892300
$936$	0	0
$937$	51.2610	1.67462	0.837311	−	0.546726i	$-0.184126\pi$
$937$	51.2610	1.67462	0.837311	+	0.546726i	$0.184126\pi$
$938$	11.9285	0.389480
$939$	0.563998	0.0184054
$940$	−1.36559	−0.0445405
$941$	6.55228	0.213598	0.106799	−	0.994281i	$-0.465940\pi$
$941$	6.55228	0.213598	0.106799	+	0.994281i	$0.465940\pi$
$942$	0.108275	0.00352778
$943$	15.6551	0.509801
$944$	−2.95491	−0.0961740
$945$	−0.478038	−0.0155506
$946$	9.97474	0.324307
$947$	−57.3614	−1.86400	−0.931998	−	0.362463i	$-0.881936\pi$
$947$	−57.3614	−1.86400	−0.931998	+	0.362463i	$0.881936\pi$
$948$	−0.0353251	−0.00114730
$949$	0	0
$950$	3.67573	0.119256
$951$	−0.214774	−0.00696453
$952$	−2.85731	−0.0926061
$953$	−7.89306	−0.255681	−0.127841	−	0.991795i	$-0.540805\pi$
$953$	−7.89306	−0.255681	−0.127841	+	0.991795i	$0.540805\pi$
$954$	−7.17444	−0.232281
$955$	−10.2891	−0.332949
$956$	−3.04743	−0.0985610
$957$	−0.551426	−0.0178251
$958$	−9.27589	−0.299690
$959$	15.9025	0.513519
$960$	−0.0293528	−0.000947357 0
$961$	4.27759	0.137987
$962$	0	0
$963$	7.52026	0.242337
$964$	20.6690	0.665705
$965$	−1.64269	−0.0528799
$966$	−0.290429	−0.00934440
$967$	−23.5254	−0.756526	−0.378263	−	0.925698i	$-0.623479\pi$
$967$	−23.5254	−0.756526	−0.378263	+	0.925698i	$0.623479\pi$
$968$	5.92589	0.190465
$969$	−0.0268479	−0.000862478 0
$970$	−3.61739	−0.116147
$971$	23.1546	0.743067	0.371533	−	0.928420i	$-0.378832\pi$
$971$	23.1546	0.743067	0.371533	+	0.928420i	$0.378832\pi$
$972$	0.688493	0.0220834
$973$	−18.3214	−0.587356
$974$	−36.6877	−1.17555
$975$	0	0
$976$	−1.72623	−0.0552552
$977$	9.84498	0.314969	0.157484	−	0.987521i	$-0.449662\pi$
$977$	9.84498	0.314969	0.157484	+	0.987521i	$0.449662\pi$
$978$	0.180830	0.00578229
$979$	19.8540	0.634536
$980$	−0.424822	−0.0135704
$981$	49.0362	1.56561
$982$	−3.49813	−0.111630
$983$	18.2291	0.581417	0.290708	−	0.956812i	$-0.406109\pi$
$983$	18.2291	0.581417	0.290708	+	0.956812i	$0.406109\pi$
$984$	0.0952024	0.00303494
$985$	−9.38939	−0.299171
$986$	−10.1017	−0.321704
$987$	−0.0821678	−0.00261543
$988$	0	0
$989$	18.5734	0.590600
$990$	−7.77490	−0.247103
$991$	−12.4721	−0.396190	−0.198095	−	0.980183i	$-0.563475\pi$
$991$	−12.4721	−0.396190	−0.198095	+	0.980183i	$0.563475\pi$
$992$	−5.93949	−0.188579
$993$	−0.0253643	−0.000804911 0
$994$	−35.1926	−1.11624
$995$	−16.2147	−0.514040
$996$	0.186774	0.00591816
$997$	48.3651	1.53174	0.765869	−	0.642996i	$-0.222309\pi$
$997$	48.3651	1.53174	0.765869	+	0.642996i	$0.222309\pi$
$998$	−22.2594	−0.704610
$999$	−0.882539	−0.0279223

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6422.2.a.bj.1.5	✓	9
13.12	even	2		6422.2.a.bl.1.5	yes	9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6422.2.a.bj.1.5	✓	9	1.1	even	1	trivial
6422.2.a.bl.1.5	yes	9	13.12	even	2

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:	\( N \)	\(=\)	\( 6422 = 2 \cdot 13^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6422.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +0.0255071 q^{3} +1.00000 q^{4} -1.15077 q^{5} -0.0255071 q^{6} -2.71462 q^{7} -1.00000 q^{8} -2.99935 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +0.0255071 q^{3} +1.00000 q^{4} -1.15077 q^{5} -0.0255071 q^{6} -2.71462 q^{7} -1.00000 q^{8} -2.99935 q^{9} +1.15077 q^{10} +2.25258 q^{11} +0.0255071 q^{12} +2.71462 q^{14} -0.0293528 q^{15} +1.00000 q^{16} -1.05257 q^{17} +2.99935 q^{18} +1.00000 q^{19} -1.15077 q^{20} -0.0692421 q^{21} -2.25258 q^{22} -4.19440 q^{23} -0.0255071 q^{24} -3.67573 q^{25} -0.153026 q^{27} -2.71462 q^{28} -9.59724 q^{29} +0.0293528 q^{30} +5.93949 q^{31} -1.00000 q^{32} +0.0574567 q^{33} +1.05257 q^{34} +3.12390 q^{35} -2.99935 q^{36} +5.76725 q^{37} -1.00000 q^{38} +1.15077 q^{40} -3.73239 q^{41} +0.0692421 q^{42} -4.42815 q^{43} +2.25258 q^{44} +3.45156 q^{45} +4.19440 q^{46} +1.18667 q^{47} +0.0255071 q^{48} +0.369164 q^{49} +3.67573 q^{50} -0.0268479 q^{51} -2.39200 q^{53} +0.153026 q^{54} -2.59220 q^{55} +2.71462 q^{56} +0.0255071 q^{57} +9.59724 q^{58} -2.95491 q^{59} -0.0293528 q^{60} -1.72623 q^{61} -5.93949 q^{62} +8.14210 q^{63} +1.00000 q^{64} -0.0574567 q^{66} +4.39417 q^{67} -1.05257 q^{68} -0.106987 q^{69} -3.12390 q^{70} -12.9641 q^{71} +2.99935 q^{72} -0.865426 q^{73} -5.76725 q^{74} -0.0937573 q^{75} +1.00000 q^{76} -6.11489 q^{77} -1.38491 q^{79} -1.15077 q^{80} +8.99414 q^{81} +3.73239 q^{82} +7.32243 q^{83} -0.0692421 q^{84} +1.21126 q^{85} +4.42815 q^{86} -0.244798 q^{87} -2.25258 q^{88} +8.81390 q^{89} -3.45156 q^{90} -4.19440 q^{92} +0.151499 q^{93} -1.18667 q^{94} -1.15077 q^{95} -0.0255071 q^{96} -3.14346 q^{97} -0.369164 q^{98} -6.75627 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q - 9 q^{2} + q^{3} + 9 q^{4} - q^{5} - q^{6} + 13 q^{7} - 9 q^{8} - 2 q^{9}+O(q^{10}) \) 9 * q - 9 * q^2 + q^3 + 9 * q^4 - q^5 - q^6 + 13 * q^7 - 9 * q^8 - 2 * q^9	\( 9 q - 9 q^{2} + q^{3} + 9 q^{4} - q^{5} - q^{6} + 13 q^{7} - 9 q^{8} - 2 q^{9} + q^{10} + 3 q^{11} + q^{12} - 13 q^{14} + 3 q^{15} + 9 q^{16} - 8 q^{17} + 2 q^{18} + 9 q^{19} - q^{20} + 24 q^{21} - 3 q^{22} - 10 q^{23} - q^{24} + 8 q^{25} + 10 q^{27} + 13 q^{28} - 20 q^{29} - 3 q^{30} + q^{31} - 9 q^{32} - 2 q^{33} + 8 q^{34} + 4 q^{35} - 2 q^{36} + 15 q^{37} - 9 q^{38} + q^{40} + 19 q^{41} - 24 q^{42} - 16 q^{43} + 3 q^{44} + 15 q^{45} + 10 q^{46} + 18 q^{47} + q^{48} + 18 q^{49} - 8 q^{50} - 11 q^{51} + 17 q^{53} - 10 q^{54} - 26 q^{55} - 13 q^{56} + q^{57} + 20 q^{58} + 24 q^{59} + 3 q^{60} + 6 q^{61} - q^{62} + q^{63} + 9 q^{64} + 2 q^{66} + 29 q^{67} - 8 q^{68} - 12 q^{69} - 4 q^{70} + 23 q^{71} + 2 q^{72} + 38 q^{73} - 15 q^{74} + 11 q^{75} + 9 q^{76} - 40 q^{77} - 20 q^{79} - q^{80} - 31 q^{81} - 19 q^{82} + 20 q^{83} + 24 q^{84} + 39 q^{85} + 16 q^{86} - 10 q^{87} - 3 q^{88} - 7 q^{89} - 15 q^{90} - 10 q^{92} + 11 q^{93} - 18 q^{94} - q^{95} - q^{96} + 28 q^{97} - 18 q^{98} + 25 q^{99}+O(q^{100}) \) 9 * q - 9 * q^2 + q^3 + 9 * q^4 - q^5 - q^6 + 13 * q^7 - 9 * q^8 - 2 * q^9 + q^10 + 3 * q^11 + q^12 - 13 * q^14 + 3 * q^15 + 9 * q^16 - 8 * q^17 + 2 * q^18 + 9 * q^19 - q^20 + 24 * q^21 - 3 * q^22 - 10 * q^23 - q^24 + 8 * q^25 + 10 * q^27 + 13 * q^28 - 20 * q^29 - 3 * q^30 + q^31 - 9 * q^32 - 2 * q^33 + 8 * q^34 + 4 * q^35 - 2 * q^36 + 15 * q^37 - 9 * q^38 + q^40 + 19 * q^41 - 24 * q^42 - 16 * q^43 + 3 * q^44 + 15 * q^45 + 10 * q^46 + 18 * q^47 + q^48 + 18 * q^49 - 8 * q^50 - 11 * q^51 + 17 * q^53 - 10 * q^54 - 26 * q^55 - 13 * q^56 + q^57 + 20 * q^58 + 24 * q^59 + 3 * q^60 + 6 * q^61 - q^62 + q^63 + 9 * q^64 + 2 * q^66 + 29 * q^67 - 8 * q^68 - 12 * q^69 - 4 * q^70 + 23 * q^71 + 2 * q^72 + 38 * q^73 - 15 * q^74 + 11 * q^75 + 9 * q^76 - 40 * q^77 - 20 * q^79 - q^80 - 31 * q^81 - 19 * q^82 + 20 * q^83 + 24 * q^84 + 39 * q^85 + 16 * q^86 - 10 * q^87 - 3 * q^88 - 7 * q^89 - 15 * q^90 - 10 * q^92 + 11 * q^93 - 18 * q^94 - q^95 - q^96 + 28 * q^97 - 18 * q^98 + 25 * q^99

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