LMFDB - Embedded newform 6026.2.a.l.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("6026.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$48.1178522580$
Analytic rank:	$0$
Dimension:	$36$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
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)

$f(q)$	$=$	$q-1.00000 q^{2} -2.51058 q^{3} +1.00000 q^{4} -0.511257 q^{5} +2.51058 q^{6} +2.88576 q^{7} -1.00000 q^{8} +3.30300 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.51058 q^{3} +1.00000 q^{4} -0.511257 q^{5} +2.51058 q^{6} +2.88576 q^{7} -1.00000 q^{8} +3.30300 q^{9} +0.511257 q^{10} -5.38722 q^{11} -2.51058 q^{12} +3.75595 q^{13} -2.88576 q^{14} +1.28355 q^{15} +1.00000 q^{16} -6.96786 q^{17} -3.30300 q^{18} -8.21277 q^{19} -0.511257 q^{20} -7.24492 q^{21} +5.38722 q^{22} -1.00000 q^{23} +2.51058 q^{24} -4.73862 q^{25} -3.75595 q^{26} -0.760712 q^{27} +2.88576 q^{28} -5.85786 q^{29} -1.28355 q^{30} -5.58407 q^{31} -1.00000 q^{32} +13.5250 q^{33} +6.96786 q^{34} -1.47537 q^{35} +3.30300 q^{36} -3.38415 q^{37} +8.21277 q^{38} -9.42960 q^{39} +0.511257 q^{40} -3.72210 q^{41} +7.24492 q^{42} +11.3059 q^{43} -5.38722 q^{44} -1.68868 q^{45} +1.00000 q^{46} -7.08924 q^{47} -2.51058 q^{48} +1.32761 q^{49} +4.73862 q^{50} +17.4934 q^{51} +3.75595 q^{52} +7.83201 q^{53} +0.760712 q^{54} +2.75425 q^{55} -2.88576 q^{56} +20.6188 q^{57} +5.85786 q^{58} +1.50893 q^{59} +1.28355 q^{60} -11.6715 q^{61} +5.58407 q^{62} +9.53167 q^{63} +1.00000 q^{64} -1.92025 q^{65} -13.5250 q^{66} +14.0127 q^{67} -6.96786 q^{68} +2.51058 q^{69} +1.47537 q^{70} -2.01306 q^{71} -3.30300 q^{72} +2.53245 q^{73} +3.38415 q^{74} +11.8967 q^{75} -8.21277 q^{76} -15.5462 q^{77} +9.42960 q^{78} +1.71441 q^{79} -0.511257 q^{80} -7.99918 q^{81} +3.72210 q^{82} -2.22661 q^{83} -7.24492 q^{84} +3.56237 q^{85} -11.3059 q^{86} +14.7066 q^{87} +5.38722 q^{88} +8.71618 q^{89} +1.68868 q^{90} +10.8388 q^{91} -1.00000 q^{92} +14.0192 q^{93} +7.08924 q^{94} +4.19884 q^{95} +2.51058 q^{96} -9.11934 q^{97} -1.32761 q^{98} -17.7940 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 36 q^{2} + 4 q^{3} + 36 q^{4} + q^{5} - 4 q^{6} + 13 q^{7} - 36 q^{8} + 46 q^{9}+O(q^{10}) $ 36 * q - 36 * q^2 + 4 * q^3 + 36 * q^4 + q^5 - 4 * q^6 + 13 * q^7 - 36 * q^8 + 46 * q^9	\( 36 q - 36 q^{2} + 4 q^{3} + 36 q^{4} + q^{5} - 4 q^{6} + 13 q^{7} - 36 q^{8} + 46 q^{9} - q^{10} + 14 q^{11} + 4 q^{12} + 4 q^{13} - 13 q^{14} + 10 q^{15} + 36 q^{16} - 4 q^{17} - 46 q^{18} + 29 q^{19} + q^{20} + 24 q^{21} - 14 q^{22} - 36 q^{23} - 4 q^{24} + 49 q^{25} - 4 q^{26} + 19 q^{27} + 13 q^{28} - 13 q^{29} - 10 q^{30} + 21 q^{31} - 36 q^{32} - 5 q^{33} + 4 q^{34} + 30 q^{35} + 46 q^{36} + 13 q^{37} - 29 q^{38} + 30 q^{39} - q^{40} - 8 q^{41} - 24 q^{42} + 42 q^{43} + 14 q^{44} + 30 q^{45} + 36 q^{46} - 14 q^{47} + 4 q^{48} + 61 q^{49} - 49 q^{50} + 46 q^{51} + 4 q^{52} - 3 q^{53} - 19 q^{54} + 26 q^{55} - 13 q^{56} + 26 q^{57} + 13 q^{58} + 45 q^{59} + 10 q^{60} + 34 q^{61} - 21 q^{62} + 63 q^{63} + 36 q^{64} - 25 q^{65} + 5 q^{66} + 42 q^{67} - 4 q^{68} - 4 q^{69} - 30 q^{70} - 2 q^{71} - 46 q^{72} + 16 q^{73} - 13 q^{74} + 72 q^{75} + 29 q^{76} - 36 q^{77} - 30 q^{78} + 33 q^{79} + q^{80} + 96 q^{81} + 8 q^{82} + 8 q^{83} + 24 q^{84} + 18 q^{85} - 42 q^{86} + 11 q^{87} - 14 q^{88} + 21 q^{89} - 30 q^{90} + 60 q^{91} - 36 q^{92} - 27 q^{93} + 14 q^{94} - 44 q^{95} - 4 q^{96} + 20 q^{97} - 61 q^{98} + 76 q^{99}+O(q^{100}) \) 36 * q - 36 * q^2 + 4 * q^3 + 36 * q^4 + q^5 - 4 * q^6 + 13 * q^7 - 36 * q^8 + 46 * q^9 - q^10 + 14 * q^11 + 4 * q^12 + 4 * q^13 - 13 * q^14 + 10 * q^15 + 36 * q^16 - 4 * q^17 - 46 * q^18 + 29 * q^19 + q^20 + 24 * q^21 - 14 * q^22 - 36 * q^23 - 4 * q^24 + 49 * q^25 - 4 * q^26 + 19 * q^27 + 13 * q^28 - 13 * q^29 - 10 * q^30 + 21 * q^31 - 36 * q^32 - 5 * q^33 + 4 * q^34 + 30 * q^35 + 46 * q^36 + 13 * q^37 - 29 * q^38 + 30 * q^39 - q^40 - 8 * q^41 - 24 * q^42 + 42 * q^43 + 14 * q^44 + 30 * q^45 + 36 * q^46 - 14 * q^47 + 4 * q^48 + 61 * q^49 - 49 * q^50 + 46 * q^51 + 4 * q^52 - 3 * q^53 - 19 * q^54 + 26 * q^55 - 13 * q^56 + 26 * q^57 + 13 * q^58 + 45 * q^59 + 10 * q^60 + 34 * q^61 - 21 * q^62 + 63 * q^63 + 36 * q^64 - 25 * q^65 + 5 * q^66 + 42 * q^67 - 4 * q^68 - 4 * q^69 - 30 * q^70 - 2 * q^71 - 46 * q^72 + 16 * q^73 - 13 * q^74 + 72 * q^75 + 29 * q^76 - 36 * q^77 - 30 * q^78 + 33 * q^79 + q^80 + 96 * q^81 + 8 * q^82 + 8 * q^83 + 24 * q^84 + 18 * q^85 - 42 * q^86 + 11 * q^87 - 14 * q^88 + 21 * q^89 - 30 * q^90 + 60 * q^91 - 36 * q^92 - 27 * q^93 + 14 * q^94 - 44 * q^95 - 4 * q^96 + 20 * q^97 - 61 * q^98 + 76 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−2.51058	−1.44948	−0.724741	−	0.689021i	$-0.758041\pi$
$3$	−2.51058	−1.44948	−0.724741	+	0.689021i	$0.758041\pi$
$4$	1.00000	0.500000
$5$	−0.511257	−0.228641	−0.114321	−	0.993444i	$-0.536469\pi$
$5$	−0.511257	−0.228641	−0.114321	+	0.993444i	$0.536469\pi$
$6$	2.51058	1.02494
$7$	2.88576	1.09071	0.545357	−	0.838204i	$-0.316394\pi$
$7$	2.88576	1.09071	0.545357	+	0.838204i	$0.316394\pi$
$8$	−1.00000	−0.353553
$9$	3.30300	1.10100
$10$	0.511257	0.161674
$11$	−5.38722	−1.62431	−0.812154	−	0.583444i	$-0.801705\pi$
$11$	−5.38722	−1.62431	−0.812154	+	0.583444i	$0.801705\pi$
$12$	−2.51058	−0.724741
$13$	3.75595	1.04171	0.520856	−	0.853645i	$-0.325613\pi$
$13$	3.75595	1.04171	0.520856	+	0.853645i	$0.325613\pi$
$14$	−2.88576	−0.771252
$15$	1.28355	0.331412
$16$	1.00000	0.250000
$17$	−6.96786	−1.68995	−0.844977	−	0.534802i	$-0.820386\pi$
$17$	−6.96786	−1.68995	−0.844977	+	0.534802i	$0.820386\pi$
$18$	−3.30300	−0.778525
$19$	−8.21277	−1.88414	−0.942069	−	0.335418i	$-0.891122\pi$
$19$	−8.21277	−1.88414	−0.942069	+	0.335418i	$0.891122\pi$
$20$	−0.511257	−0.114321
$21$	−7.24492	−1.58097
$22$	5.38722	1.14856
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	2.51058	0.512470
$25$	−4.73862	−0.947723
$26$	−3.75595	−0.736602
$27$	−0.760712	−0.146399
$28$	2.88576	0.545357
$29$	−5.85786	−1.08778	−0.543889	−	0.839157i	$-0.683049\pi$
$29$	−5.85786	−1.08778	−0.543889	+	0.839157i	$0.683049\pi$
$30$	−1.28355	−0.234343
$31$	−5.58407	−1.00293	−0.501464	−	0.865178i	$-0.667205\pi$
$31$	−5.58407	−1.00293	−0.501464	+	0.865178i	$0.667205\pi$
$32$	−1.00000	−0.176777
$33$	13.5250	2.35441
$34$	6.96786	1.19498
$35$	−1.47537	−0.249382
$36$	3.30300	0.550500
$37$	−3.38415	−0.556350	−0.278175	−	0.960530i	$-0.589730\pi$
$37$	−3.38415	−0.556350	−0.278175	+	0.960530i	$0.589730\pi$
$38$	8.21277	1.33229
$39$	−9.42960	−1.50994
$40$	0.511257	0.0808369
$41$	−3.72210	−0.581294	−0.290647	−	0.956830i	$-0.593871\pi$
$41$	−3.72210	−0.581294	−0.290647	+	0.956830i	$0.593871\pi$
$42$	7.24492	1.11792
$43$	11.3059	1.72413	0.862066	−	0.506796i	$-0.169170\pi$
$43$	11.3059	1.72413	0.862066	+	0.506796i	$0.169170\pi$
$44$	−5.38722	−0.812154
$45$	−1.68868	−0.251734
$46$	1.00000	0.147442
$47$	−7.08924	−1.03407	−0.517036	−	0.855963i	$-0.672965\pi$
$47$	−7.08924	−1.03407	−0.517036	+	0.855963i	$0.672965\pi$
$48$	−2.51058	−0.362371
$49$	1.32761	0.189658
$50$	4.73862	0.670141
$51$	17.4934	2.44956
$52$	3.75595	0.520856
$53$	7.83201	1.07581	0.537905	−	0.843006i	$-0.319216\pi$
$53$	7.83201	1.07581	0.537905	+	0.843006i	$0.319216\pi$
$54$	0.760712	0.103520
$55$	2.75425	0.371384
$56$	−2.88576	−0.385626
$57$	20.6188	2.73103
$58$	5.85786	0.769175
$59$	1.50893	0.196446	0.0982232	−	0.995164i	$-0.468684\pi$
$59$	1.50893	0.196446	0.0982232	+	0.995164i	$0.468684\pi$
$60$	1.28355	0.165706
$61$	−11.6715	−1.49439	−0.747194	−	0.664606i	$-0.768599\pi$
$61$	−11.6715	−1.49439	−0.747194	+	0.664606i	$0.768599\pi$
$62$	5.58407	0.709177
$63$	9.53167	1.20088
$64$	1.00000	0.125000
$65$	−1.92025	−0.238178
$66$	−13.5250	−1.66482
$67$	14.0127	1.71193	0.855963	−	0.517037i	$-0.172965\pi$
$67$	14.0127	1.71193	0.855963	+	0.517037i	$0.172965\pi$
$68$	−6.96786	−0.844977
$69$	2.51058	0.302238
$70$	1.47537	0.176340
$71$	−2.01306	−0.238906	−0.119453	−	0.992840i	$-0.538114\pi$
$71$	−2.01306	−0.238906	−0.119453	+	0.992840i	$0.538114\pi$
$72$	−3.30300	−0.389263
$73$	2.53245	0.296401	0.148201	−	0.988957i	$-0.452652\pi$
$73$	2.53245	0.296401	0.148201	+	0.988957i	$0.452652\pi$
$74$	3.38415	0.393399
$75$	11.8967	1.37371
$76$	−8.21277	−0.942069
$77$	−15.5462	−1.77166
$78$	9.42960	1.06769
$79$	1.71441	0.192886	0.0964431	−	0.995339i	$-0.469253\pi$
$79$	1.71441	0.192886	0.0964431	+	0.995339i	$0.469253\pi$
$80$	−0.511257	−0.0571603
$81$	−7.99918	−0.888798
$82$	3.72210	0.411037
$83$	−2.22661	−0.244402	−0.122201	−	0.992505i	$-0.538995\pi$
$83$	−2.22661	−0.244402	−0.122201	+	0.992505i	$0.538995\pi$
$84$	−7.24492	−0.790486
$85$	3.56237	0.386393
$86$	−11.3059	−1.21915
$87$	14.7066	1.57672
$88$	5.38722	0.574279
$89$	8.71618	0.923913	0.461957	−	0.886903i	$-0.347148\pi$
$89$	8.71618	0.923913	0.461957	+	0.886903i	$0.347148\pi$
$90$	1.68868	0.178003
$91$	10.8388	1.13621
$92$	−1.00000	−0.104257
$93$	14.0192	1.45373
$94$	7.08924	0.731200
$95$	4.19884	0.430792
$96$	2.51058	0.256235
$97$	−9.11934	−0.925929	−0.462964	−	0.886377i	$-0.653214\pi$
$97$	−9.11934	−0.925929	−0.462964	+	0.886377i	$0.653214\pi$
$98$	−1.32761	−0.134108
$99$	−17.7940	−1.78836
$100$	−4.73862	−0.473862
$101$	−10.4611	−1.04092	−0.520461	−	0.853885i	$-0.674240\pi$
$101$	−10.4611	−1.04092	−0.520461	+	0.853885i	$0.674240\pi$
$102$	−17.4934	−1.73210
$103$	−14.6660	−1.44508	−0.722542	−	0.691327i	$-0.757026\pi$
$103$	−14.6660	−1.44508	−0.722542	+	0.691327i	$0.757026\pi$
$104$	−3.75595	−0.368301
$105$	3.70402	0.361475
$106$	−7.83201	−0.760712
$107$	8.56794	0.828294	0.414147	−	0.910210i	$-0.364080\pi$
$107$	8.56794	0.828294	0.414147	+	0.910210i	$0.364080\pi$
$108$	−0.760712	−0.0731996
$109$	2.08211	0.199430	0.0997148	−	0.995016i	$-0.468207\pi$
$109$	2.08211	0.199430	0.0997148	+	0.995016i	$0.468207\pi$
$110$	−2.75425	−0.262608
$111$	8.49616	0.806420
$112$	2.88576	0.272679
$113$	−7.38213	−0.694453	−0.347226	−	0.937781i	$-0.612876\pi$
$113$	−7.38213	−0.694453	−0.347226	+	0.937781i	$0.612876\pi$
$114$	−20.6188	−1.93113
$115$	0.511257	0.0476750
$116$	−5.85786	−0.543889
$117$	12.4059	1.14693
$118$	−1.50893	−0.138909
$119$	−20.1076	−1.84326
$120$	−1.28355	−0.117172
$121$	18.0221	1.63837
$122$	11.6715	1.05669
$123$	9.34462	0.842576
$124$	−5.58407	−0.501464
$125$	4.97894	0.445330
$126$	−9.53167	−0.849149
$127$	5.44124	0.482832	0.241416	−	0.970422i	$-0.422388\pi$
$127$	5.44124	0.482832	0.241416	+	0.970422i	$0.422388\pi$
$128$	−1.00000	−0.0883883
$129$	−28.3843	−2.49910
$130$	1.92025	0.168417
$131$	1.00000	0.0873704
$131$	1.00000	0.0873704
$132$	13.5250	1.17720
$133$	−23.7001	−2.05506
$134$	−14.0127	−1.21051
$135$	0.388920	0.0334729
$136$	6.96786	0.597489
$137$	8.10163	0.692169	0.346084	−	0.938203i	$-0.387511\pi$
$137$	8.10163	0.692169	0.346084	+	0.938203i	$0.387511\pi$
$138$	−2.51058	−0.213715
$139$	−3.65855	−0.310314	−0.155157	−	0.987890i	$-0.549588\pi$
$139$	−3.65855	−0.310314	−0.155157	+	0.987890i	$0.549588\pi$
$140$	−1.47537	−0.124691
$141$	17.7981	1.49887
$142$	2.01306	0.168932
$143$	−20.2341	−1.69206
$144$	3.30300	0.275250
$145$	2.99488	0.248711
$146$	−2.53245	−0.209587
$147$	−3.33306	−0.274906
$148$	−3.38415	−0.278175
$149$	−2.38664	−0.195521	−0.0977606	−	0.995210i	$-0.531168\pi$
$149$	−2.38664	−0.195521	−0.0977606	+	0.995210i	$0.531168\pi$
$150$	−11.8967	−0.971359
$151$	18.3602	1.49413	0.747067	−	0.664749i	$-0.231461\pi$
$151$	18.3602	1.49413	0.747067	+	0.664749i	$0.231461\pi$
$152$	8.21277	0.666144
$153$	−23.0149	−1.86064
$154$	15.5462	1.25275
$155$	2.85490	0.229311
$156$	−9.42960	−0.754972
$157$	−10.8659	−0.867190	−0.433595	−	0.901108i	$-0.642755\pi$
$157$	−10.8659	−0.867190	−0.433595	+	0.901108i	$0.642755\pi$
$158$	−1.71441	−0.136391
$159$	−19.6629	−1.55937
$160$	0.511257	0.0404184
$161$	−2.88576	−0.227430
$162$	7.99918	0.628475
$163$	16.8013	1.31598	0.657989	−	0.753027i	$-0.271407\pi$
$163$	16.8013	1.31598	0.657989	+	0.753027i	$0.271407\pi$
$164$	−3.72210	−0.290647
$165$	−6.91477	−0.538314
$166$	2.22661	0.172818
$167$	11.0107	0.852030	0.426015	−	0.904716i	$-0.359917\pi$
$167$	11.0107	0.852030	0.426015	+	0.904716i	$0.359917\pi$
$168$	7.24492	0.558958
$169$	1.10713	0.0851637
$170$	−3.56237	−0.273221
$171$	−27.1268	−2.07444
$172$	11.3059	0.862066
$173$	−0.663353	−0.0504338	−0.0252169	−	0.999682i	$-0.508028\pi$
$173$	−0.663353	−0.0504338	−0.0252169	+	0.999682i	$0.508028\pi$
$174$	−14.7066	−1.11491
$175$	−13.6745	−1.03370
$176$	−5.38722	−0.406077
$177$	−3.78829	−0.284746
$178$	−8.71618	−0.653305
$179$	−23.9850	−1.79273	−0.896363	−	0.443321i	$-0.853800\pi$
$179$	−23.9850	−1.79273	−0.896363	+	0.443321i	$0.853800\pi$
$180$	−1.68868	−0.125867
$181$	−0.0162749	−0.00120970	−0.000604851	−	1.00000i	$-0.500193\pi$
$181$	−0.0162749	−0.00120970	−0.000604851		1.00000i	$0.500193\pi$
$182$	−10.8388	−0.803422
$183$	29.3023	2.16609
$184$	1.00000	0.0737210
$185$	1.73017	0.127205
$186$	−14.0192	−1.02794
$187$	37.5374	2.74501
$188$	−7.08924	−0.517036
$189$	−2.19523	−0.159680
$190$	−4.19884	−0.304616
$191$	−0.471480	−0.0341151	−0.0170576	−	0.999855i	$-0.505430\pi$
$191$	−0.471480	−0.0341151	−0.0170576	+	0.999855i	$0.505430\pi$
$192$	−2.51058	−0.181185
$193$	−23.8221	−1.71475	−0.857375	−	0.514693i	$-0.827906\pi$
$193$	−23.8221	−1.71475	−0.857375	+	0.514693i	$0.827906\pi$
$194$	9.11934	0.654731
$195$	4.82095	0.345235
$196$	1.32761	0.0948290
$197$	−19.6639	−1.40099	−0.700496	−	0.713656i	$-0.747038\pi$
$197$	−19.6639	−1.40099	−0.700496	+	0.713656i	$0.747038\pi$
$198$	17.7940	1.26456
$199$	8.20565	0.581683	0.290841	−	0.956771i	$-0.406065\pi$
$199$	8.20565	0.581683	0.290841	+	0.956771i	$0.406065\pi$
$200$	4.73862	0.335071
$201$	−35.1800	−2.48141
$202$	10.4611	0.736043
$203$	−16.9044	−1.18646
$204$	17.4934	1.22478
$205$	1.90295	0.132908
$206$	14.6660	1.02183
$207$	−3.30300	−0.229575
$208$	3.75595	0.260428
$209$	44.2440	3.06042
$210$	−3.70402	−0.255602
$211$	27.5086	1.89377	0.946886	−	0.321568i	$-0.104210\pi$
$211$	27.5086	1.89377	0.946886	+	0.321568i	$0.104210\pi$
$212$	7.83201	0.537905
$213$	5.05394	0.346291
$214$	−8.56794	−0.585692
$215$	−5.78022	−0.394208
$216$	0.760712	0.0517599
$217$	−16.1143	−1.09391
$218$	−2.08211	−0.141018
$219$	−6.35792	−0.429628
$220$	2.75425	0.185692
$221$	−26.1709	−1.76045
$222$	−8.49616	−0.570225
$223$	5.80952	0.389034	0.194517	−	0.980899i	$-0.437686\pi$
$223$	5.80952	0.389034	0.194517	+	0.980899i	$0.437686\pi$
$224$	−2.88576	−0.192813
$225$	−15.6517	−1.04344
$226$	7.38213	0.491052
$227$	−14.4506	−0.959120	−0.479560	−	0.877509i	$-0.659204\pi$
$227$	−14.4506	−0.959120	−0.479560	+	0.877509i	$0.659204\pi$
$228$	20.6188	1.36551
$229$	−15.9119	−1.05149	−0.525744	−	0.850643i	$-0.676213\pi$
$229$	−15.9119	−1.05149	−0.525744	+	0.850643i	$0.676213\pi$
$230$	−0.511257	−0.0337113
$231$	39.0300	2.56798
$232$	5.85786	0.384588
$233$	−14.5827	−0.955345	−0.477672	−	0.878538i	$-0.658519\pi$
$233$	−14.5827	−0.955345	−0.477672	+	0.878538i	$0.658519\pi$
$234$	−12.4059	−0.810999
$235$	3.62443	0.236432
$236$	1.50893	0.0982232
$237$	−4.30416	−0.279585
$238$	20.1076	1.30338
$239$	−17.8680	−1.15579	−0.577893	−	0.816113i	$-0.696125\pi$
$239$	−17.8680	−1.15579	−0.577893	+	0.816113i	$0.696125\pi$
$240$	1.28355	0.0828529
$241$	14.4767	0.932526	0.466263	−	0.884646i	$-0.345600\pi$
$241$	14.4767	0.932526	0.466263	+	0.884646i	$0.345600\pi$
$242$	−18.0221	−1.15851
$243$	22.3647	1.43470
$244$	−11.6715	−0.747194
$245$	−0.678748	−0.0433636
$246$	−9.34462	−0.595791
$247$	−30.8467	−1.96273
$248$	5.58407	0.354589
$249$	5.59007	0.354256
$250$	−4.97894	−0.314896
$251$	16.4959	1.04121	0.520606	−	0.853797i	$-0.325706\pi$
$251$	16.4959	1.04121	0.520606	+	0.853797i	$0.325706\pi$
$252$	9.53167	0.600439
$253$	5.38722	0.338691
$254$	−5.44124	−0.341414
$255$	−8.94361	−0.560071
$256$	1.00000	0.0625000
$257$	10.5985	0.661115	0.330557	−	0.943786i	$-0.392763\pi$
$257$	10.5985	0.661115	0.330557	+	0.943786i	$0.392763\pi$
$258$	28.3843	1.76713
$259$	−9.76583	−0.606819
$260$	−1.92025	−0.119089
$261$	−19.3485	−1.19764
$262$	−1.00000	−0.0617802
$263$	−22.4041	−1.38149	−0.690747	−	0.723096i	$-0.742718\pi$
$263$	−22.4041	−1.38149	−0.690747	+	0.723096i	$0.742718\pi$
$264$	−13.5250	−0.832408
$265$	−4.00417	−0.245974
$266$	23.7001	1.45314
$267$	−21.8826	−1.33920
$268$	14.0127	0.855963
$269$	20.9540	1.27759	0.638793	−	0.769379i	$-0.279434\pi$
$269$	20.9540	1.27759	0.638793	+	0.769379i	$0.279434\pi$
$270$	−0.388920	−0.0236689
$271$	−0.509602	−0.0309561	−0.0154781	−	0.999880i	$-0.504927\pi$
$271$	−0.509602	−0.0309561	−0.0154781	+	0.999880i	$0.504927\pi$
$272$	−6.96786	−0.422489
$273$	−27.2115	−1.64692
$274$	−8.10163	−0.489437
$275$	25.5280	1.53939
$276$	2.51058	0.151119
$277$	2.78169	0.167136	0.0835679	−	0.996502i	$-0.473368\pi$
$277$	2.78169	0.167136	0.0835679	+	0.996502i	$0.473368\pi$
$278$	3.65855	0.219425
$279$	−18.4442	−1.10422
$280$	1.47537	0.0881700
$281$	30.7848	1.83646	0.918232	−	0.396042i	$-0.129617\pi$
$281$	30.7848	1.83646	0.918232	+	0.396042i	$0.129617\pi$
$282$	−17.7981	−1.05986
$283$	15.5982	0.927218	0.463609	−	0.886040i	$-0.346554\pi$
$283$	15.5982	0.927218	0.463609	+	0.886040i	$0.346554\pi$
$284$	−2.01306	−0.119453
$285$	−10.5415	−0.624425
$286$	20.2341	1.19647
$287$	−10.7411	−0.634026
$288$	−3.30300	−0.194631
$289$	31.5511	1.85595
$290$	−2.99488	−0.175865
$291$	22.8948	1.34212
$292$	2.53245	0.148201
$293$	1.30357	0.0761556	0.0380778	−	0.999275i	$-0.487877\pi$
$293$	1.30357	0.0761556	0.0380778	+	0.999275i	$0.487877\pi$
$294$	3.33306	0.194388
$295$	−0.771453	−0.0449157
$296$	3.38415	0.196699
$297$	4.09812	0.237797
$298$	2.38664	0.138254
$299$	−3.75595	−0.217212
$300$	11.8967	0.686854
$301$	32.6261	1.88054
$302$	−18.3602	−1.05651
$303$	26.2635	1.50880
$304$	−8.21277	−0.471035
$305$	5.96716	0.341679
$306$	23.0149	1.31567
$307$	−24.5643	−1.40196	−0.700979	−	0.713182i	$-0.747253\pi$
$307$	−24.5643	−1.40196	−0.700979	+	0.713182i	$0.747253\pi$
$308$	−15.5462	−0.885828
$309$	36.8202	2.09463
$310$	−2.85490	−0.162147
$311$	12.1608	0.689574	0.344787	−	0.938681i	$-0.387951\pi$
$311$	12.1608	0.689574	0.344787	+	0.938681i	$0.387951\pi$
$312$	9.42960	0.533846
$313$	−12.4268	−0.702403	−0.351202	−	0.936300i	$-0.614227\pi$
$313$	−12.4268	−0.702403	−0.351202	+	0.936300i	$0.614227\pi$
$314$	10.8659	0.613196
$315$	−4.87314	−0.274570
$316$	1.71441	0.0964431
$317$	−10.3369	−0.580577	−0.290289	−	0.956939i	$-0.593751\pi$
$317$	−10.3369	−0.580577	−0.290289	+	0.956939i	$0.593751\pi$
$318$	19.6629	1.10264
$319$	31.5576	1.76689
$320$	−0.511257	−0.0285802
$321$	−21.5105	−1.20060
$322$	2.88576	0.160817
$323$	57.2254	3.18411
$324$	−7.99918	−0.444399
$325$	−17.7980	−0.987255
$326$	−16.8013	−0.930537
$327$	−5.22729	−0.289070
$328$	3.72210	0.205518
$329$	−20.4579	−1.12788
$330$	6.91477	0.380646
$331$	27.0413	1.48632	0.743161	−	0.669112i	$-0.233325\pi$
$331$	27.0413	1.48632	0.743161	+	0.669112i	$0.233325\pi$
$332$	−2.22661	−0.122201
$333$	−11.1778	−0.612542
$334$	−11.0107	−0.602476
$335$	−7.16411	−0.391417
$336$	−7.24492	−0.395243
$337$	24.0784	1.31164	0.655818	−	0.754919i	$-0.272324\pi$
$337$	24.0784	1.31164	0.655818	+	0.754919i	$0.272324\pi$
$338$	−1.10713	−0.0602198
$339$	18.5334	1.00660
$340$	3.56237	0.193197
$341$	30.0826	1.62906
$342$	27.1268	1.46685
$343$	−16.3692	−0.883852
$344$	−11.3059	−0.609573
$345$	−1.28355	−0.0691041
$346$	0.663353	0.0356621
$347$	−18.5624	−0.996482	−0.498241	−	0.867039i	$-0.666021\pi$
$347$	−18.5624	−0.996482	−0.498241	+	0.867039i	$0.666021\pi$
$348$	14.7066	0.788358
$349$	−1.67029	−0.0894084	−0.0447042	−	0.999000i	$-0.514235\pi$
$349$	−1.67029	−0.0894084	−0.0447042	+	0.999000i	$0.514235\pi$
$350$	13.6745	0.730933
$351$	−2.85719	−0.152506
$352$	5.38722	0.287140
$353$	7.13355	0.379681	0.189840	−	0.981815i	$-0.439203\pi$
$353$	7.13355	0.379681	0.189840	+	0.981815i	$0.439203\pi$
$354$	3.78829	0.201346
$355$	1.02919	0.0546238
$356$	8.71618	0.461957
$357$	50.4816	2.67177
$358$	23.9850	1.26765
$359$	−12.9461	−0.683267	−0.341633	−	0.939833i	$-0.610980\pi$
$359$	−12.9461	−0.683267	−0.341633	+	0.939833i	$0.610980\pi$
$360$	1.68868	0.0890015
$361$	48.4496	2.54998
$362$	0.0162749	0.000855388 0
$363$	−45.2459	−2.37480
$364$	10.8388	0.568105
$365$	−1.29474	−0.0677695
$366$	−29.3023	−1.53166
$367$	−0.629538	−0.0328616	−0.0164308	−	0.999865i	$-0.505230\pi$
$367$	−0.629538	−0.0328616	−0.0164308	+	0.999865i	$0.505230\pi$
$368$	−1.00000	−0.0521286
$369$	−12.2941	−0.640005
$370$	−1.73017	−0.0899472
$371$	22.6013	1.17340
$372$	14.0192	0.726864
$373$	18.3933	0.952367	0.476184	−	0.879346i	$-0.342020\pi$
$373$	18.3933	0.952367	0.476184	+	0.879346i	$0.342020\pi$
$374$	−37.5374	−1.94101
$375$	−12.5000	−0.645498
$376$	7.08924	0.365600
$377$	−22.0018	−1.13315
$378$	2.19523	0.112911
$379$	−18.4020	−0.945245	−0.472623	−	0.881265i	$-0.656693\pi$
$379$	−18.4020	−0.945245	−0.472623	+	0.881265i	$0.656693\pi$
$380$	4.19884	0.215396
$381$	−13.6607	−0.699857
$382$	0.471480	0.0241230
$383$	−1.58184	−0.0808283	−0.0404141	−	0.999183i	$-0.512868\pi$
$383$	−1.58184	−0.0808283	−0.0404141	+	0.999183i	$0.512868\pi$
$384$	2.51058	0.128117
$385$	7.94812	0.405073
$386$	23.8221	1.21251
$387$	37.3434	1.89827
$388$	−9.11934	−0.462964
$389$	−33.4209	−1.69451	−0.847254	−	0.531188i	$-0.821746\pi$
$389$	−33.4209	−1.69451	−0.847254	+	0.531188i	$0.821746\pi$
$390$	−4.82095	−0.244118
$391$	6.96786	0.352380
$392$	−1.32761	−0.0670542
$393$	−2.51058	−0.126642
$394$	19.6639	0.990651
$395$	−0.876505	−0.0441017
$396$	−17.7940	−0.894182
$397$	−0.554580	−0.0278336	−0.0139168	−	0.999903i	$-0.504430\pi$
$397$	−0.554580	−0.0278336	−0.0139168	+	0.999903i	$0.504430\pi$
$398$	−8.20565	−0.411312
$399$	59.5009	2.97877
$400$	−4.73862	−0.236931
$401$	−21.7117	−1.08423	−0.542116	−	0.840304i	$-0.682377\pi$
$401$	−21.7117	−1.08423	−0.542116	+	0.840304i	$0.682377\pi$
$402$	35.1800	1.75462
$403$	−20.9735	−1.04476
$404$	−10.4611	−0.520461
$405$	4.08964	0.203216
$406$	16.9044	0.838951
$407$	18.2311	0.903684
$408$	−17.4934	−0.866050
$409$	7.78555	0.384970	0.192485	−	0.981300i	$-0.438345\pi$
$409$	7.78555	0.384970	0.192485	+	0.981300i	$0.438345\pi$
$410$	−1.90295	−0.0939800
$411$	−20.3398	−1.00329
$412$	−14.6660	−0.722542
$413$	4.35442	0.214267
$414$	3.30300	0.162334
$415$	1.13837	0.0558803
$416$	−3.75595	−0.184150
$417$	9.18507	0.449795
$418$	−44.2440	−2.16404
$419$	13.4977	0.659404	0.329702	−	0.944085i	$-0.393052\pi$
$419$	13.4977	0.659404	0.329702	+	0.944085i	$0.393052\pi$
$420$	3.70402	0.180738
$421$	6.20566	0.302446	0.151223	−	0.988500i	$-0.451679\pi$
$421$	6.20566	0.302446	0.151223	+	0.988500i	$0.451679\pi$
$422$	−27.5086	−1.33910
$423$	−23.4158	−1.13851
$424$	−7.83201	−0.380356
$425$	33.0180	1.60161
$426$	−5.05394	−0.244864
$427$	−33.6813	−1.62995
$428$	8.56794	0.414147
$429$	50.7993	2.45261
$430$	5.78022	0.278747
$431$	−39.3002	−1.89303	−0.946513	−	0.322667i	$-0.895421\pi$
$431$	−39.3002	−1.89303	−0.946513	+	0.322667i	$0.895421\pi$
$432$	−0.760712	−0.0365998
$433$	−23.0486	−1.10765	−0.553823	−	0.832635i	$-0.686831\pi$
$433$	−23.0486	−1.10765	−0.553823	+	0.832635i	$0.686831\pi$
$434$	16.1143	0.773510
$435$	−7.51887	−0.360502
$436$	2.08211	0.0997148
$437$	8.21277	0.392870
$438$	6.35792	0.303793
$439$	−37.3139	−1.78090	−0.890448	−	0.455086i	$-0.849609\pi$
$439$	−37.3139	−1.78090	−0.890448	+	0.455086i	$0.849609\pi$
$440$	−2.75425	−0.131304
$441$	4.38509	0.208814
$442$	26.1709	1.24482
$443$	40.4081	1.91984	0.959922	−	0.280266i	$-0.0904227\pi$
$443$	40.4081	1.91984	0.959922	+	0.280266i	$0.0904227\pi$
$444$	8.49616	0.403210
$445$	−4.45621	−0.211245
$446$	−5.80952	−0.275089
$447$	5.99185	0.283405
$448$	2.88576	0.136339
$449$	−1.40362	−0.0662411	−0.0331206	−	0.999451i	$-0.510545\pi$
$449$	−1.40362	−0.0662411	−0.0331206	+	0.999451i	$0.510545\pi$
$450$	15.6517	0.737826
$451$	20.0518	0.944200
$452$	−7.38213	−0.347226
$453$	−46.0948	−2.16572
$454$	14.4506	0.678201
$455$	−5.54139	−0.259785
$456$	−20.6188	−0.965564
$457$	−3.46295	−0.161990	−0.0809950	−	0.996715i	$-0.525810\pi$
$457$	−3.46295	−0.161990	−0.0809950	+	0.996715i	$0.525810\pi$
$458$	15.9119	0.743514
$459$	5.30054	0.247408
$460$	0.511257	0.0238375
$461$	1.61097	0.0750301	0.0375151	−	0.999296i	$-0.488056\pi$
$461$	1.61097	0.0750301	0.0375151	+	0.999296i	$0.488056\pi$
$462$	−39.0300	−1.81584
$463$	11.2376	0.522256	0.261128	−	0.965304i	$-0.415906\pi$
$463$	11.2376	0.522256	0.261128	+	0.965304i	$0.415906\pi$
$464$	−5.85786	−0.271945
$465$	−7.16744	−0.332382
$466$	14.5827	0.675531
$467$	23.9013	1.10602	0.553009	−	0.833175i	$-0.313479\pi$
$467$	23.9013	1.10602	0.553009	+	0.833175i	$0.313479\pi$
$468$	12.4059	0.573463
$469$	40.4373	1.86722
$470$	−3.62443	−0.167182
$471$	27.2796	1.25698
$472$	−1.50893	−0.0694543
$473$	−60.9073	−2.80052
$474$	4.30416	0.197697
$475$	38.9172	1.78564
$476$	−20.1076	−0.921629
$477$	25.8692	1.18447
$478$	17.8680	0.817264
$479$	11.8375	0.540870	0.270435	−	0.962738i	$-0.412833\pi$
$479$	11.8375	0.540870	0.270435	+	0.962738i	$0.412833\pi$
$480$	−1.28355	−0.0585858
$481$	−12.7107	−0.579557
$482$	−14.4767	−0.659396
$483$	7.24492	0.329655
$484$	18.0221	0.819187
$485$	4.66233	0.211705
$486$	−22.3647	−1.01448
$487$	35.9670	1.62982	0.814909	−	0.579588i	$-0.196787\pi$
$487$	35.9670	1.62982	0.814909	+	0.579588i	$0.196787\pi$
$488$	11.6715	0.528346
$489$	−42.1809	−1.90749
$490$	0.678748	0.0306627
$491$	−12.9770	−0.585645	−0.292822	−	0.956167i	$-0.594594\pi$
$491$	−12.9770	−0.585645	−0.292822	+	0.956167i	$0.594594\pi$
$492$	9.34462	0.421288
$493$	40.8168	1.83830
$494$	30.8467	1.38786
$495$	9.09731	0.408894
$496$	−5.58407	−0.250732
$497$	−5.80921	−0.260578
$498$	−5.59007	−0.250497
$499$	16.6841	0.746881	0.373440	−	0.927654i	$-0.378178\pi$
$499$	16.6841	0.746881	0.373440	+	0.927654i	$0.378178\pi$
$500$	4.97894	0.222665
$501$	−27.6431	−1.23500
$502$	−16.4959	−0.736249
$503$	18.4348	0.821967	0.410984	−	0.911643i	$-0.365185\pi$
$503$	18.4348	0.821967	0.410984	+	0.911643i	$0.365185\pi$
$504$	−9.53167	−0.424574
$505$	5.34833	0.237998
$506$	−5.38722	−0.239491
$507$	−2.77953	−0.123443
$508$	5.44124	0.241416
$509$	29.0183	1.28621	0.643107	−	0.765776i	$-0.277645\pi$
$509$	29.0183	1.28621	0.643107	+	0.765776i	$0.277645\pi$
$510$	8.94361	0.396030
$511$	7.30805	0.323289
$512$	−1.00000	−0.0441942
$513$	6.24755	0.275836
$514$	−10.5985	−0.467479
$515$	7.49810	0.330406
$516$	−28.3843	−1.24955
$517$	38.1913	1.67965
$518$	9.76583	0.429086
$519$	1.66540	0.0731030
$520$	1.92025	0.0842087
$521$	−13.8139	−0.605200	−0.302600	−	0.953118i	$-0.597855\pi$
$521$	−13.8139	−0.605200	−0.302600	+	0.953118i	$0.597855\pi$
$522$	19.3485	0.846863
$523$	33.1710	1.45047	0.725234	−	0.688503i	$-0.241732\pi$
$523$	33.1710	1.45047	0.725234	+	0.688503i	$0.241732\pi$
$524$	1.00000	0.0436852
$525$	34.3309	1.49832
$526$	22.4041	0.976864
$527$	38.9090	1.69490
$528$	13.5250	0.588601
$529$	1.00000	0.0434783
$530$	4.00417	0.173930
$531$	4.98401	0.216288
$532$	−23.7001	−1.02753
$533$	−13.9800	−0.605541
$534$	21.8826	0.946955
$535$	−4.38042	−0.189382
$536$	−14.0127	−0.605257
$537$	60.2163	2.59853
$538$	−20.9540	−0.903390
$539$	−7.15210	−0.308063
$540$	0.388920	0.0167364
$541$	44.6719	1.92060	0.960298	−	0.278978i	$-0.0899955\pi$
$541$	44.6719	1.92060	0.960298	+	0.278978i	$0.0899955\pi$
$542$	0.509602	0.0218893
$543$	0.0408593	0.00175344
$544$	6.96786	0.298745
$545$	−1.06449	−0.0455978
$546$	27.2115	1.16455
$547$	26.6173	1.13807	0.569037	−	0.822312i	$-0.307316\pi$
$547$	26.6173	1.13807	0.569037	+	0.822312i	$0.307316\pi$
$548$	8.10163	0.346084
$549$	−38.5511	−1.64532
$550$	−25.5280	−1.08852
$551$	48.1093	2.04952
$552$	−2.51058	−0.106857
$553$	4.94737	0.210384
$554$	−2.78169	−0.118183
$555$	−4.34373	−0.184381
$556$	−3.65855	−0.155157
$557$	17.7216	0.750890	0.375445	−	0.926845i	$-0.377490\pi$
$557$	17.7216	0.750890	0.375445	+	0.926845i	$0.377490\pi$
$558$	18.4442	0.780805
$559$	42.4643	1.79605
$560$	−1.47537	−0.0623456
$561$	−94.2405	−3.97884
$562$	−30.7848	−1.29858
$563$	−2.85794	−0.120448	−0.0602240	−	0.998185i	$-0.519181\pi$
$563$	−2.85794	−0.120448	−0.0602240	+	0.998185i	$0.519181\pi$
$564$	17.7981	0.749435
$565$	3.77417	0.158781
$566$	−15.5982	−0.655642
$567$	−23.0837	−0.969425
$568$	2.01306	0.0844661
$569$	35.9603	1.50754	0.753768	−	0.657141i	$-0.228234\pi$
$569$	35.9603	1.50754	0.753768	+	0.657141i	$0.228234\pi$
$570$	10.5415	0.441535
$571$	−39.8518	−1.66774	−0.833872	−	0.551957i	$-0.813881\pi$
$571$	−39.8518	−1.66774	−0.833872	+	0.551957i	$0.813881\pi$
$572$	−20.2341	−0.846030
$573$	1.18369	0.0494493
$574$	10.7411	0.448324
$575$	4.73862	0.197614
$576$	3.30300	0.137625
$577$	−38.1380	−1.58770	−0.793852	−	0.608111i	$-0.791928\pi$
$577$	−38.1380	−1.58770	−0.793852	+	0.608111i	$0.791928\pi$
$578$	−31.5511	−1.31235
$579$	59.8072	2.48550
$580$	2.99488	0.124355
$581$	−6.42545	−0.266573
$582$	−22.8948	−0.949021
$583$	−42.1928	−1.74745
$584$	−2.53245	−0.104794
$585$	−6.34261	−0.262235
$586$	−1.30357	−0.0538502
$587$	22.9409	0.946870	0.473435	−	0.880829i	$-0.343014\pi$
$587$	22.9409	0.946870	0.473435	+	0.880829i	$0.343014\pi$
$588$	−3.33306	−0.137453
$589$	45.8607	1.88966
$590$	0.771453	0.0317602
$591$	49.3677	2.03071
$592$	−3.38415	−0.139088
$593$	−44.2667	−1.81782	−0.908909	−	0.416995i	$-0.863083\pi$
$593$	−44.2667	−1.81782	−0.908909	+	0.416995i	$0.863083\pi$
$594$	−4.09812	−0.168148
$595$	10.2801	0.421445
$596$	−2.38664	−0.0977606
$597$	−20.6009	−0.843139
$598$	3.75595	0.153592
$599$	37.9935	1.55237	0.776186	−	0.630504i	$-0.217152\pi$
$599$	37.9935	1.55237	0.776186	+	0.630504i	$0.217152\pi$
$600$	−11.8967	−0.485679
$601$	−0.377633	−0.0154040	−0.00770199	−	0.999970i	$-0.502452\pi$
$601$	−0.377633	−0.0154040	−0.00770199	+	0.999970i	$0.502452\pi$
$602$	−32.6261	−1.32974
$603$	46.2841	1.88483
$604$	18.3602	0.747067
$605$	−9.21394	−0.374600
$606$	−26.2635	−1.06688
$607$	−15.4605	−0.627522	−0.313761	−	0.949502i	$-0.601589\pi$
$607$	−15.4605	−0.627522	−0.313761	+	0.949502i	$0.601589\pi$
$608$	8.21277	0.333072
$609$	42.4398	1.71975
$610$	−5.96716	−0.241603
$611$	−26.6268	−1.07721
$612$	−23.0149	−0.930321
$613$	−29.1329	−1.17666	−0.588332	−	0.808619i	$-0.700215\pi$
$613$	−29.1329	−1.17666	−0.588332	+	0.808619i	$0.700215\pi$
$614$	24.5643	0.991334
$615$	−4.77750	−0.192648
$616$	15.5462	0.626375
$617$	13.7378	0.553062	0.276531	−	0.961005i	$-0.410815\pi$
$617$	13.7378	0.553062	0.276531	+	0.961005i	$0.410815\pi$
$618$	−36.8202	−1.48112
$619$	−20.4654	−0.822574	−0.411287	−	0.911506i	$-0.634921\pi$
$619$	−20.4654	−0.822574	−0.411287	+	0.911506i	$0.634921\pi$
$620$	2.85490	0.114655
$621$	0.760712	0.0305263
$622$	−12.1608	−0.487603
$623$	25.1528	1.00773
$624$	−9.42960	−0.377486
$625$	21.1476	0.845902
$626$	12.4268	0.496674
$627$	−111.078	−4.43603
$628$	−10.8659	−0.433595
$629$	23.5803	0.940206
$630$	4.87314	0.194150
$631$	−40.2318	−1.60160	−0.800802	−	0.598929i	$-0.795593\pi$
$631$	−40.2318	−1.60160	−0.800802	+	0.598929i	$0.795593\pi$
$632$	−1.71441	−0.0681956
$633$	−69.0626	−2.74499
$634$	10.3369	0.410530
$635$	−2.78188	−0.110395
$636$	−19.6629	−0.779684
$637$	4.98642	0.197569
$638$	−31.5576	−1.24938
$639$	−6.64914	−0.263036
$640$	0.511257	0.0202092
$641$	−24.9677	−0.986165	−0.493083	−	0.869982i	$-0.664130\pi$
$641$	−24.9677	−0.986165	−0.493083	+	0.869982i	$0.664130\pi$
$642$	21.5105	0.848951
$643$	38.8290	1.53127	0.765633	−	0.643277i	$-0.222426\pi$
$643$	38.8290	1.53127	0.765633	+	0.643277i	$0.222426\pi$
$644$	−2.88576	−0.113715
$645$	14.5117	0.571397
$646$	−57.2254	−2.25150
$647$	15.2376	0.599052	0.299526	−	0.954088i	$-0.403171\pi$
$647$	15.2376	0.599052	0.299526	+	0.954088i	$0.403171\pi$
$648$	7.99918	0.314237
$649$	−8.12895	−0.319089
$650$	17.7980	0.698094
$651$	40.4561	1.58560
$652$	16.8013	0.657989
$653$	−23.6868	−0.926938	−0.463469	−	0.886113i	$-0.653395\pi$
$653$	−23.6868	−0.926938	−0.463469	+	0.886113i	$0.653395\pi$
$654$	5.22729	0.204403
$655$	−0.511257	−0.0199765
$656$	−3.72210	−0.145323
$657$	8.36470	0.326338
$658$	20.4579	0.797530
$659$	45.9088	1.78835	0.894176	−	0.447716i	$-0.147763\pi$
$659$	45.9088	1.78835	0.894176	+	0.447716i	$0.147763\pi$
$660$	−6.91477	−0.269157
$661$	−12.0783	−0.469793	−0.234897	−	0.972020i	$-0.575475\pi$
$661$	−12.0783	−0.469793	−0.234897	+	0.972020i	$0.575475\pi$
$662$	−27.0413	−1.05099
$663$	65.7041	2.55174
$664$	2.22661	0.0864091
$665$	12.1168	0.469871
$666$	11.1778	0.433133
$667$	5.85786	0.226817
$668$	11.0107	0.426015
$669$	−14.5853	−0.563899
$670$	7.16411	0.276774
$671$	62.8771	2.42735
$672$	7.24492	0.279479
$673$	−12.0192	−0.463306	−0.231653	−	0.972799i	$-0.574413\pi$
$673$	−12.0192	−0.463306	−0.231653	+	0.972799i	$0.574413\pi$
$674$	−24.0784	−0.927466
$675$	3.60472	0.138746
$676$	1.10713	0.0425818
$677$	41.4928	1.59470	0.797349	−	0.603518i	$-0.206235\pi$
$677$	41.4928	1.59470	0.797349	+	0.603518i	$0.206235\pi$
$678$	−18.5334	−0.711772
$679$	−26.3162	−1.00992
$680$	−3.56237	−0.136611
$681$	36.2794	1.39023
$682$	−30.0826	−1.15192
$683$	3.89229	0.148934	0.0744671	−	0.997223i	$-0.476274\pi$
$683$	3.89229	0.148934	0.0744671	+	0.997223i	$0.476274\pi$
$684$	−27.1268	−1.03722
$685$	−4.14202	−0.158258
$686$	16.3692	0.624978
$687$	39.9480	1.52411
$688$	11.3059	0.431033
$689$	29.4166	1.12068
$690$	1.28355	0.0488640
$691$	−42.4732	−1.61576	−0.807879	−	0.589348i	$-0.799385\pi$
$691$	−42.4732	−1.61576	−0.807879	+	0.589348i	$0.799385\pi$
$692$	−0.663353	−0.0252169
$693$	−51.3492	−1.95059
$694$	18.5624	0.704619
$695$	1.87046	0.0709506
$696$	−14.7066	−0.557453
$697$	25.9351	0.982360
$698$	1.67029	0.0632213
$699$	36.6110	1.38476
$700$	−13.6745	−0.516848
$701$	23.8526	0.900899	0.450449	−	0.892802i	$-0.351264\pi$
$701$	23.8526	0.900899	0.450449	+	0.892802i	$0.351264\pi$
$702$	2.85719	0.107838
$703$	27.7932	1.04824
$704$	−5.38722	−0.203038
$705$	−9.09941	−0.342704
$706$	−7.13355	−0.268475
$707$	−30.1883	−1.13535
$708$	−3.78829	−0.142373
$709$	1.89921	0.0713264	0.0356632	−	0.999364i	$-0.488646\pi$
$709$	1.89921	0.0713264	0.0356632	+	0.999364i	$0.488646\pi$
$710$	−1.02919	−0.0386249
$711$	5.66270	0.212368
$712$	−8.71618	−0.326653
$713$	5.58407	0.209125
$714$	−50.4816	−1.88923
$715$	10.3448	0.386875
$716$	−23.9850	−0.896363
$717$	44.8590	1.67529
$718$	12.9461	0.483143
$719$	−41.0968	−1.53265	−0.766326	−	0.642452i	$-0.777917\pi$
$719$	−41.0968	−1.53265	−0.766326	+	0.642452i	$0.777917\pi$
$720$	−1.68868	−0.0629336
$721$	−42.3226	−1.57617
$722$	−48.4496	−1.80311
$723$	−36.3449	−1.35168
$724$	−0.0162749	−0.000604851 0
$725$	27.7582	1.03091
$726$	45.2459	1.67923
$727$	−14.0067	−0.519480	−0.259740	−	0.965679i	$-0.583637\pi$
$727$	−14.0067	−0.519480	−0.259740	+	0.965679i	$0.583637\pi$
$728$	−10.8388	−0.401711
$729$	−32.1508	−1.19077
$730$	1.29474	0.0479203
$731$	−78.7779	−2.91370
$732$	29.3023	1.08304
$733$	32.1662	1.18809	0.594044	−	0.804433i	$-0.297531\pi$
$733$	32.1662	1.18809	0.594044	+	0.804433i	$0.297531\pi$
$734$	0.629538	0.0232367
$735$	1.70405	0.0628549
$736$	1.00000	0.0368605
$737$	−75.4896	−2.78069
$738$	12.2941	0.452552
$739$	7.75446	0.285252	0.142626	−	0.989777i	$-0.454445\pi$
$739$	7.75446	0.285252	0.142626	+	0.989777i	$0.454445\pi$
$740$	1.73017	0.0636023
$741$	77.4431	2.84494
$742$	−22.6013	−0.829720
$743$	39.0174	1.43141	0.715705	−	0.698402i	$-0.246105\pi$
$743$	39.0174	1.43141	0.715705	+	0.698402i	$0.246105\pi$
$744$	−14.0192	−0.513970
$745$	1.22019	0.0447042
$746$	−18.3933	−0.673426
$747$	−7.35449	−0.269087
$748$	37.5374	1.37250
$749$	24.7250	0.903432
$750$	12.5000	0.456436
$751$	−33.3095	−1.21548	−0.607740	−	0.794136i	$-0.707924\pi$
$751$	−33.3095	−1.21548	−0.607740	+	0.794136i	$0.707924\pi$
$752$	−7.08924	−0.258518
$753$	−41.4143	−1.50922
$754$	22.0018	0.801259
$755$	−9.38680	−0.341621
$756$	−2.19523	−0.0798398
$757$	21.4170	0.778413	0.389207	−	0.921150i	$-0.372749\pi$
$757$	21.4170	0.778413	0.389207	+	0.921150i	$0.372749\pi$
$758$	18.4020	0.668389
$759$	−13.5250	−0.490928
$760$	−4.19884	−0.152308
$761$	−2.84495	−0.103130	−0.0515648	−	0.998670i	$-0.516421\pi$
$761$	−2.84495	−0.103130	−0.0515648	+	0.998670i	$0.516421\pi$
$762$	13.6607	0.494874
$763$	6.00846	0.217521
$764$	−0.471480	−0.0170576
$765$	11.7665	0.425419
$766$	1.58184	0.0571542
$767$	5.66747	0.204641
$768$	−2.51058	−0.0905927
$769$	0.419197	0.0151166	0.00755832	−	0.999971i	$-0.497594\pi$
$769$	0.419197	0.0151166	0.00755832	+	0.999971i	$0.497594\pi$
$770$	−7.94812	−0.286430
$771$	−26.6083	−0.958274
$772$	−23.8221	−0.857375
$773$	−26.5846	−0.956183	−0.478092	−	0.878310i	$-0.658671\pi$
$773$	−26.5846	−0.956183	−0.478092	+	0.878310i	$0.658671\pi$
$774$	−37.3434	−1.34228
$775$	26.4608	0.950498
$776$	9.11934	0.327365
$777$	24.5179	0.879574
$778$	33.4209	1.19820
$779$	30.5687	1.09524
$780$	4.82095	0.172618
$781$	10.8448	0.388057
$782$	−6.96786	−0.249170
$783$	4.45615	0.159250
$784$	1.32761	0.0474145
$785$	5.55525	0.198275
$786$	2.51058	0.0895494
$787$	−9.77703	−0.348513	−0.174257	−	0.984700i	$-0.555752\pi$
$787$	−9.77703	−0.348513	−0.174257	+	0.984700i	$0.555752\pi$
$788$	−19.6639	−0.700496
$789$	56.2472	2.00245
$790$	0.876505	0.0311846
$791$	−21.3031	−0.757450
$792$	17.7940	0.632282
$793$	−43.8377	−1.55672
$794$	0.554580	0.0196813
$795$	10.0528	0.356536
$796$	8.20565	0.290841
$797$	−41.9248	−1.48505	−0.742527	−	0.669817i	$-0.766373\pi$
$797$	−41.9248	−1.48505	−0.742527	+	0.669817i	$0.766373\pi$
$798$	−59.5009	−2.10631
$799$	49.3969	1.74754
$800$	4.73862	0.167535
$801$	28.7896	1.01723
$802$	21.7117	0.766668
$803$	−13.6429	−0.481447
$804$	−35.1800	−1.24070
$805$	1.47537	0.0519998
$806$	20.9735	0.738758
$807$	−52.6066	−1.85184
$808$	10.4611	0.368021
$809$	−21.0922	−0.741561	−0.370781	−	0.928720i	$-0.620910\pi$
$809$	−21.0922	−0.741561	−0.370781	+	0.928720i	$0.620910\pi$
$810$	−4.08964	−0.143695
$811$	48.4981	1.70300	0.851499	−	0.524356i	$-0.175694\pi$
$811$	48.4981	1.70300	0.851499	+	0.524356i	$0.175694\pi$
$812$	−16.9044	−0.593228
$813$	1.27940	0.0448703
$814$	−18.2311	−0.639001
$815$	−8.58978	−0.300887
$816$	17.4934	0.612390
$817$	−92.8527	−3.24850
$818$	−7.78555	−0.272215
$819$	35.8004	1.25097
$820$	1.90295	0.0664539
$821$	25.5230	0.890757	0.445379	−	0.895342i	$-0.353069\pi$
$821$	25.5230	0.890757	0.445379	+	0.895342i	$0.353069\pi$
$822$	20.3398	0.709431
$823$	−38.5857	−1.34501	−0.672507	−	0.740091i	$-0.734782\pi$
$823$	−38.5857	−1.34501	−0.672507	+	0.740091i	$0.734782\pi$
$824$	14.6660	0.510914
$825$	−64.0899	−2.23133
$826$	−4.35442	−0.151510
$827$	−9.36807	−0.325760	−0.162880	−	0.986646i	$-0.552078\pi$
$827$	−9.36807	−0.325760	−0.162880	+	0.986646i	$0.552078\pi$
$828$	−3.30300	−0.114787
$829$	−42.8474	−1.48815	−0.744076	−	0.668095i	$-0.767110\pi$
$829$	−42.8474	−1.48815	−0.744076	+	0.668095i	$0.767110\pi$
$830$	−1.13837	−0.0395134
$831$	−6.98366	−0.242260
$832$	3.75595	0.130214
$833$	−9.25057	−0.320513
$834$	−9.18507	−0.318053
$835$	−5.62928	−0.194809
$836$	44.2440	1.53021
$837$	4.24787	0.146828
$838$	−13.4977	−0.466269
$839$	30.7268	1.06081	0.530404	−	0.847745i	$-0.322040\pi$
$839$	30.7268	1.06081	0.530404	+	0.847745i	$0.322040\pi$
$840$	−3.70402	−0.127801
$841$	5.31457	0.183261
$842$	−6.20566	−0.213861
$843$	−77.2875	−2.66192
$844$	27.5086	0.946886
$845$	−0.566027	−0.0194719
$846$	23.4158	0.805052
$847$	52.0075	1.78700
$848$	7.83201	0.268952
$849$	−39.1605	−1.34399
$850$	−33.0180	−1.13251
$851$	3.38415	0.116007
$852$	5.05394	0.173145
$853$	44.2511	1.51513	0.757565	−	0.652760i	$-0.226389\pi$
$853$	44.2511	1.51513	0.757565	+	0.652760i	$0.226389\pi$
$854$	33.6813	1.15255
$855$	13.8688	0.474302
$856$	−8.56794	−0.292846
$857$	15.9063	0.543350	0.271675	−	0.962389i	$-0.412422\pi$
$857$	15.9063	0.543350	0.271675	+	0.962389i	$0.412422\pi$
$858$	−50.7993	−1.73426
$859$	−8.07507	−0.275518	−0.137759	−	0.990466i	$-0.543990\pi$
$859$	−8.07507	−0.275518	−0.137759	+	0.990466i	$0.543990\pi$
$860$	−5.78022	−0.197104
$861$	26.9663	0.919010
$862$	39.3002	1.33857
$863$	−26.4360	−0.899891	−0.449946	−	0.893056i	$-0.648557\pi$
$863$	−26.4360	−0.899891	−0.449946	+	0.893056i	$0.648557\pi$
$864$	0.760712	0.0258800
$865$	0.339144	0.0115312
$866$	23.0486	0.783224
$867$	−79.2115	−2.69016
$868$	−16.1143	−0.546954
$869$	−9.23590	−0.313306
$870$	7.51887	0.254914
$871$	52.6310	1.78333
$872$	−2.08211	−0.0705090
$873$	−30.1212	−1.01945
$874$	−8.21277	−0.277801
$875$	14.3680	0.485728
$876$	−6.35792	−0.214814
$877$	−39.1192	−1.32096	−0.660481	−	0.750842i	$-0.729648\pi$
$877$	−39.1192	−1.32096	−0.660481	+	0.750842i	$0.729648\pi$
$878$	37.3139	1.25928
$879$	−3.27273	−0.110386
$880$	2.75425	0.0928459
$881$	−20.8635	−0.702911	−0.351455	−	0.936205i	$-0.614313\pi$
$881$	−20.8635	−0.702911	−0.351455	+	0.936205i	$0.614313\pi$
$882$	−4.38509	−0.147654
$883$	28.0795	0.944950	0.472475	−	0.881344i	$-0.343361\pi$
$883$	28.0795	0.944950	0.472475	+	0.881344i	$0.343361\pi$
$884$	−26.1709	−0.880223
$885$	1.93679	0.0651046
$886$	−40.4081	−1.35754
$887$	−7.64049	−0.256543	−0.128271	−	0.991739i	$-0.540943\pi$
$887$	−7.64049	−0.256543	−0.128271	+	0.991739i	$0.540943\pi$
$888$	−8.49616	−0.285113
$889$	15.7021	0.526632
$890$	4.45621	0.149373
$891$	43.0933	1.44368
$892$	5.80952	0.194517
$893$	58.2223	1.94834
$894$	−5.99185	−0.200397
$895$	12.2625	0.409891
$896$	−2.88576	−0.0964064
$897$	9.42960	0.314845
$898$	1.40362	0.0468395
$899$	32.7107	1.09096
$900$	−15.6517	−0.521722
$901$	−54.5724	−1.81807
$902$	−20.0518	−0.667650
$903$	−81.9103	−2.72580
$904$	7.38213	0.245526
$905$	0.00832065	0.000276588 0
$906$	46.0948	1.53140
$907$	−53.0524	−1.76158	−0.880789	−	0.473509i	$-0.842987\pi$
$907$	−53.0524	−1.76158	−0.880789	+	0.473509i	$0.842987\pi$
$908$	−14.4506	−0.479560
$909$	−34.5532	−1.14606
$910$	5.54139	0.183695
$911$	23.8822	0.791252	0.395626	−	0.918412i	$-0.370528\pi$
$911$	23.8822	0.791252	0.395626	+	0.918412i	$0.370528\pi$
$912$	20.6188	0.682757
$913$	11.9952	0.396984
$914$	3.46295	0.114544
$915$	−14.9810	−0.495257
$916$	−15.9119	−0.525744
$917$	2.88576	0.0952962
$918$	−5.30054	−0.174944
$919$	−5.59573	−0.184586	−0.0922930	−	0.995732i	$-0.529420\pi$
$919$	−5.59573	−0.184586	−0.0922930	+	0.995732i	$0.529420\pi$
$920$	−0.511257	−0.0168557
$921$	61.6706	2.03211
$922$	−1.61097	−0.0530543
$923$	−7.56094	−0.248871
$924$	39.0300	1.28399
$925$	16.0362	0.527266
$926$	−11.2376	−0.369291
$927$	−48.4419	−1.59104
$928$	5.85786	0.192294
$929$	41.3350	1.35616	0.678079	−	0.734989i	$-0.262813\pi$
$929$	41.3350	1.35616	0.678079	+	0.734989i	$0.262813\pi$
$930$	7.16744	0.235030
$931$	−10.9033	−0.357342
$932$	−14.5827	−0.477672
$933$	−30.5306	−0.999526
$934$	−23.9013	−0.782073
$935$	−19.1913	−0.627621
$936$	−12.4059	−0.405500
$937$	−10.2085	−0.333496	−0.166748	−	0.986000i	$-0.553327\pi$
$937$	−10.2085	−0.333496	−0.166748	+	0.986000i	$0.553327\pi$
$938$	−40.4373	−1.32033
$939$	31.1984	1.01812
$940$	3.62443	0.118216
$941$	14.5064	0.472894	0.236447	−	0.971644i	$-0.424017\pi$
$941$	14.5064	0.472894	0.236447	+	0.971644i	$0.424017\pi$
$942$	−27.2796	−0.888817
$943$	3.72210	0.121208
$944$	1.50893	0.0491116
$945$	1.12233	0.0365094
$946$	60.9073	1.98027
$947$	19.8686	0.645644	0.322822	−	0.946460i	$-0.395368\pi$
$947$	19.8686	0.645644	0.322822	+	0.946460i	$0.395368\pi$
$948$	−4.30416	−0.139793
$949$	9.51175	0.308765
$950$	−38.9172	−1.26264
$951$	25.9515	0.841537
$952$	20.1076	0.651690
$953$	35.1323	1.13805	0.569023	−	0.822322i	$-0.307322\pi$
$953$	35.1323	1.13805	0.569023	+	0.822322i	$0.307322\pi$
$954$	−25.8692	−0.837545
$955$	0.241048	0.00780012
$956$	−17.8680	−0.577893
$957$	−79.2278	−2.56107
$958$	−11.8375	−0.382453
$959$	23.3793	0.754959
$960$	1.28355	0.0414264
$961$	0.181814	0.00586497
$962$	12.7107	0.409808
$963$	28.2999	0.911953
$964$	14.4767	0.466263
$965$	12.1792	0.392062
$966$	−7.24492	−0.233102
$967$	−25.0067	−0.804160	−0.402080	−	0.915605i	$-0.631713\pi$
$967$	−25.0067	−0.804160	−0.402080	+	0.915605i	$0.631713\pi$
$968$	−18.0221	−0.579253
$969$	−143.669	−4.61531
$970$	−4.66233	−0.149698
$971$	9.19051	0.294938	0.147469	−	0.989067i	$-0.452887\pi$
$971$	9.19051	0.294938	0.147469	+	0.989067i	$0.452887\pi$
$972$	22.3647	0.717348
$973$	−10.5577	−0.338464
$974$	−35.9670	−1.15246
$975$	44.6832	1.43101
$976$	−11.6715	−0.373597
$977$	−7.37425	−0.235923	−0.117962	−	0.993018i	$-0.537636\pi$
$977$	−7.37425	−0.235923	−0.117962	+	0.993018i	$0.537636\pi$
$978$	42.1809	1.34880
$979$	−46.9560	−1.50072
$980$	−0.678748	−0.0216818
$981$	6.87720	0.219572
$982$	12.9770	0.414113
$983$	−19.8561	−0.633310	−0.316655	−	0.948541i	$-0.602560\pi$
$983$	−19.8561	−0.633310	−0.316655	+	0.948541i	$0.602560\pi$
$984$	−9.34462	−0.297896
$985$	10.0533	0.320325
$986$	−40.8168	−1.29987
$987$	51.3610	1.63484
$988$	−30.8467	−0.981365
$989$	−11.3059	−0.359506
$990$	−9.09731	−0.289132
$991$	−39.1941	−1.24504	−0.622520	−	0.782604i	$-0.713891\pi$
$991$	−39.1941	−1.24504	−0.622520	+	0.782604i	$0.713891\pi$
$992$	5.58407	0.177294
$993$	−67.8892	−2.15440
$994$	5.80921	0.184257
$995$	−4.19520	−0.132997
$996$	5.59007	0.177128
$997$	50.0872	1.58628	0.793138	−	0.609042i	$-0.208446\pi$
$997$	50.0872	1.58628	0.793138	+	0.609042i	$0.208446\pi$
$998$	−16.6841	−0.528125
$999$	2.57436	0.0814492

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6026.2.a.l.1.5	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6026.2.a.l.1.5	✓	36	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.51058 q^{3} +1.00000 q^{4} -0.511257 q^{5} +2.51058 q^{6} +2.88576 q^{7} -1.00000 q^{8} +3.30300 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.51058 q^{3} +1.00000 q^{4} -0.511257 q^{5} +2.51058 q^{6} +2.88576 q^{7} -1.00000 q^{8} +3.30300 q^{9} +0.511257 q^{10} -5.38722 q^{11} -2.51058 q^{12} +3.75595 q^{13} -2.88576 q^{14} +1.28355 q^{15} +1.00000 q^{16} -6.96786 q^{17} -3.30300 q^{18} -8.21277 q^{19} -0.511257 q^{20} -7.24492 q^{21} +5.38722 q^{22} -1.00000 q^{23} +2.51058 q^{24} -4.73862 q^{25} -3.75595 q^{26} -0.760712 q^{27} +2.88576 q^{28} -5.85786 q^{29} -1.28355 q^{30} -5.58407 q^{31} -1.00000 q^{32} +13.5250 q^{33} +6.96786 q^{34} -1.47537 q^{35} +3.30300 q^{36} -3.38415 q^{37} +8.21277 q^{38} -9.42960 q^{39} +0.511257 q^{40} -3.72210 q^{41} +7.24492 q^{42} +11.3059 q^{43} -5.38722 q^{44} -1.68868 q^{45} +1.00000 q^{46} -7.08924 q^{47} -2.51058 q^{48} +1.32761 q^{49} +4.73862 q^{50} +17.4934 q^{51} +3.75595 q^{52} +7.83201 q^{53} +0.760712 q^{54} +2.75425 q^{55} -2.88576 q^{56} +20.6188 q^{57} +5.85786 q^{58} +1.50893 q^{59} +1.28355 q^{60} -11.6715 q^{61} +5.58407 q^{62} +9.53167 q^{63} +1.00000 q^{64} -1.92025 q^{65} -13.5250 q^{66} +14.0127 q^{67} -6.96786 q^{68} +2.51058 q^{69} +1.47537 q^{70} -2.01306 q^{71} -3.30300 q^{72} +2.53245 q^{73} +3.38415 q^{74} +11.8967 q^{75} -8.21277 q^{76} -15.5462 q^{77} +9.42960 q^{78} +1.71441 q^{79} -0.511257 q^{80} -7.99918 q^{81} +3.72210 q^{82} -2.22661 q^{83} -7.24492 q^{84} +3.56237 q^{85} -11.3059 q^{86} +14.7066 q^{87} +5.38722 q^{88} +8.71618 q^{89} +1.68868 q^{90} +10.8388 q^{91} -1.00000 q^{92} +14.0192 q^{93} +7.08924 q^{94} +4.19884 q^{95} +2.51058 q^{96} -9.11934 q^{97} -1.32761 q^{98} -17.7940 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 36 q^{2} + 4 q^{3} + 36 q^{4} + q^{5} - 4 q^{6} + 13 q^{7} - 36 q^{8} + 46 q^{9}+O(q^{10}) \) 36 * q - 36 * q^2 + 4 * q^3 + 36 * q^4 + q^5 - 4 * q^6 + 13 * q^7 - 36 * q^8 + 46 * q^9	\( 36 q - 36 q^{2} + 4 q^{3} + 36 q^{4} + q^{5} - 4 q^{6} + 13 q^{7} - 36 q^{8} + 46 q^{9} - q^{10} + 14 q^{11} + 4 q^{12} + 4 q^{13} - 13 q^{14} + 10 q^{15} + 36 q^{16} - 4 q^{17} - 46 q^{18} + 29 q^{19} + q^{20} + 24 q^{21} - 14 q^{22} - 36 q^{23} - 4 q^{24} + 49 q^{25} - 4 q^{26} + 19 q^{27} + 13 q^{28} - 13 q^{29} - 10 q^{30} + 21 q^{31} - 36 q^{32} - 5 q^{33} + 4 q^{34} + 30 q^{35} + 46 q^{36} + 13 q^{37} - 29 q^{38} + 30 q^{39} - q^{40} - 8 q^{41} - 24 q^{42} + 42 q^{43} + 14 q^{44} + 30 q^{45} + 36 q^{46} - 14 q^{47} + 4 q^{48} + 61 q^{49} - 49 q^{50} + 46 q^{51} + 4 q^{52} - 3 q^{53} - 19 q^{54} + 26 q^{55} - 13 q^{56} + 26 q^{57} + 13 q^{58} + 45 q^{59} + 10 q^{60} + 34 q^{61} - 21 q^{62} + 63 q^{63} + 36 q^{64} - 25 q^{65} + 5 q^{66} + 42 q^{67} - 4 q^{68} - 4 q^{69} - 30 q^{70} - 2 q^{71} - 46 q^{72} + 16 q^{73} - 13 q^{74} + 72 q^{75} + 29 q^{76} - 36 q^{77} - 30 q^{78} + 33 q^{79} + q^{80} + 96 q^{81} + 8 q^{82} + 8 q^{83} + 24 q^{84} + 18 q^{85} - 42 q^{86} + 11 q^{87} - 14 q^{88} + 21 q^{89} - 30 q^{90} + 60 q^{91} - 36 q^{92} - 27 q^{93} + 14 q^{94} - 44 q^{95} - 4 q^{96} + 20 q^{97} - 61 q^{98} + 76 q^{99}+O(q^{100}) \) 36 * q - 36 * q^2 + 4 * q^3 + 36 * q^4 + q^5 - 4 * q^6 + 13 * q^7 - 36 * q^8 + 46 * q^9 - q^10 + 14 * q^11 + 4 * q^12 + 4 * q^13 - 13 * q^14 + 10 * q^15 + 36 * q^16 - 4 * q^17 - 46 * q^18 + 29 * q^19 + q^20 + 24 * q^21 - 14 * q^22 - 36 * q^23 - 4 * q^24 + 49 * q^25 - 4 * q^26 + 19 * q^27 + 13 * q^28 - 13 * q^29 - 10 * q^30 + 21 * q^31 - 36 * q^32 - 5 * q^33 + 4 * q^34 + 30 * q^35 + 46 * q^36 + 13 * q^37 - 29 * q^38 + 30 * q^39 - q^40 - 8 * q^41 - 24 * q^42 + 42 * q^43 + 14 * q^44 + 30 * q^45 + 36 * q^46 - 14 * q^47 + 4 * q^48 + 61 * q^49 - 49 * q^50 + 46 * q^51 + 4 * q^52 - 3 * q^53 - 19 * q^54 + 26 * q^55 - 13 * q^56 + 26 * q^57 + 13 * q^58 + 45 * q^59 + 10 * q^60 + 34 * q^61 - 21 * q^62 + 63 * q^63 + 36 * q^64 - 25 * q^65 + 5 * q^66 + 42 * q^67 - 4 * q^68 - 4 * q^69 - 30 * q^70 - 2 * q^71 - 46 * q^72 + 16 * q^73 - 13 * q^74 + 72 * q^75 + 29 * q^76 - 36 * q^77 - 30 * q^78 + 33 * q^79 + q^80 + 96 * q^81 + 8 * q^82 + 8 * q^83 + 24 * q^84 + 18 * q^85 - 42 * q^86 + 11 * q^87 - 14 * q^88 + 21 * q^89 - 30 * q^90 + 60 * q^91 - 36 * q^92 - 27 * q^93 + 14 * q^94 - 44 * q^95 - 4 * q^96 + 20 * q^97 - 61 * q^98 + 76 * q^99

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