LMFDB - Embedded newform 8015.2.a.l.1.43

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8015,2,Mod(1,8015)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8015, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("8015.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8015 = 5 \cdot 7 \cdot 229 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8015.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:	$64.0000972201$
Analytic rank:	$0$
Dimension:	$62$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.43
Character	$\chi$	$=$	8015.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.24614 q^{2} +2.46236 q^{3} -0.447139 q^{4} -1.00000 q^{5} +3.06845 q^{6} -1.00000 q^{7} -3.04947 q^{8} +3.06324 q^{9} +O(q^{10})$	\(q+1.24614 q^{2} +2.46236 q^{3} -0.447139 q^{4} -1.00000 q^{5} +3.06845 q^{6} -1.00000 q^{7} -3.04947 q^{8} +3.06324 q^{9} -1.24614 q^{10} +1.46291 q^{11} -1.10102 q^{12} -4.42027 q^{13} -1.24614 q^{14} -2.46236 q^{15} -2.90579 q^{16} -0.0499232 q^{17} +3.81722 q^{18} -0.658238 q^{19} +0.447139 q^{20} -2.46236 q^{21} +1.82298 q^{22} +4.57297 q^{23} -7.50891 q^{24} +1.00000 q^{25} -5.50827 q^{26} +0.155708 q^{27} +0.447139 q^{28} +4.16152 q^{29} -3.06845 q^{30} -5.17544 q^{31} +2.47793 q^{32} +3.60220 q^{33} -0.0622113 q^{34} +1.00000 q^{35} -1.36969 q^{36} +2.60005 q^{37} -0.820255 q^{38} -10.8843 q^{39} +3.04947 q^{40} +6.25946 q^{41} -3.06845 q^{42} +5.47750 q^{43} -0.654122 q^{44} -3.06324 q^{45} +5.69855 q^{46} +10.4755 q^{47} -7.15511 q^{48} +1.00000 q^{49} +1.24614 q^{50} -0.122929 q^{51} +1.97647 q^{52} +8.42397 q^{53} +0.194034 q^{54} -1.46291 q^{55} +3.04947 q^{56} -1.62082 q^{57} +5.18582 q^{58} +8.86491 q^{59} +1.10102 q^{60} +9.68144 q^{61} -6.44931 q^{62} -3.06324 q^{63} +8.89942 q^{64} +4.42027 q^{65} +4.48885 q^{66} -1.18665 q^{67} +0.0223226 q^{68} +11.2603 q^{69} +1.24614 q^{70} -4.70654 q^{71} -9.34126 q^{72} +8.22538 q^{73} +3.24002 q^{74} +2.46236 q^{75} +0.294324 q^{76} -1.46291 q^{77} -13.5634 q^{78} +15.8964 q^{79} +2.90579 q^{80} -8.80630 q^{81} +7.80015 q^{82} -8.75408 q^{83} +1.10102 q^{84} +0.0499232 q^{85} +6.82572 q^{86} +10.2472 q^{87} -4.46109 q^{88} +13.3176 q^{89} -3.81722 q^{90} +4.42027 q^{91} -2.04475 q^{92} -12.7438 q^{93} +13.0539 q^{94} +0.658238 q^{95} +6.10157 q^{96} +5.42424 q^{97} +1.24614 q^{98} +4.48122 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 62 q + 2 q^{2} + 11 q^{3} + 64 q^{4} - 62 q^{5} + 3 q^{6} - 62 q^{7} + 15 q^{8} + 69 q^{9}+O(q^{10}) $ 62 * q + 2 * q^2 + 11 * q^3 + 64 * q^4 - 62 * q^5 + 3 * q^6 - 62 * q^7 + 15 * q^8 + 69 * q^9	\( 62 q + 2 q^{2} + 11 q^{3} + 64 q^{4} - 62 q^{5} + 3 q^{6} - 62 q^{7} + 15 q^{8} + 69 q^{9} - 2 q^{10} - 13 q^{11} + 37 q^{12} + 31 q^{13} - 2 q^{14} - 11 q^{15} + 64 q^{16} + 30 q^{17} + 18 q^{18} + 20 q^{19} - 64 q^{20} - 11 q^{21} + 7 q^{22} + 29 q^{24} + 62 q^{25} + 59 q^{27} - 64 q^{28} - 29 q^{29} - 3 q^{30} + 20 q^{31} + 22 q^{32} + 72 q^{33} + 13 q^{34} + 62 q^{35} + 53 q^{36} + 35 q^{37} + 34 q^{38} - 6 q^{39} - 15 q^{40} + 13 q^{41} - 3 q^{42} - 4 q^{43} - 44 q^{44} - 69 q^{45} - 19 q^{46} + 58 q^{47} + 64 q^{48} + 62 q^{49} + 2 q^{50} - 30 q^{51} + 82 q^{52} + 18 q^{53} + 22 q^{54} + 13 q^{55} - 15 q^{56} + 21 q^{57} + 18 q^{58} - 11 q^{59} - 37 q^{60} + 24 q^{61} + 48 q^{62} - 69 q^{63} + 65 q^{64} - 31 q^{65} + 25 q^{66} - 6 q^{67} + 65 q^{68} + 27 q^{69} + 2 q^{70} - 35 q^{71} + 53 q^{72} + 116 q^{73} - 69 q^{74} + 11 q^{75} + 65 q^{76} + 13 q^{77} + 102 q^{78} - 83 q^{79} - 64 q^{80} + 126 q^{81} + 71 q^{82} + 84 q^{83} - 37 q^{84} - 30 q^{85} + 24 q^{86} + 49 q^{87} + 20 q^{88} - 16 q^{89} - 18 q^{90} - 31 q^{91} + 19 q^{92} + 65 q^{93} + 54 q^{94} - 20 q^{95} + 17 q^{96} + 155 q^{97} + 2 q^{98} + 6 q^{99}+O(q^{100}) \) 62 * q + 2 * q^2 + 11 * q^3 + 64 * q^4 - 62 * q^5 + 3 * q^6 - 62 * q^7 + 15 * q^8 + 69 * q^9 - 2 * q^10 - 13 * q^11 + 37 * q^12 + 31 * q^13 - 2 * q^14 - 11 * q^15 + 64 * q^16 + 30 * q^17 + 18 * q^18 + 20 * q^19 - 64 * q^20 - 11 * q^21 + 7 * q^22 + 29 * q^24 + 62 * q^25 + 59 * q^27 - 64 * q^28 - 29 * q^29 - 3 * q^30 + 20 * q^31 + 22 * q^32 + 72 * q^33 + 13 * q^34 + 62 * q^35 + 53 * q^36 + 35 * q^37 + 34 * q^38 - 6 * q^39 - 15 * q^40 + 13 * q^41 - 3 * q^42 - 4 * q^43 - 44 * q^44 - 69 * q^45 - 19 * q^46 + 58 * q^47 + 64 * q^48 + 62 * q^49 + 2 * q^50 - 30 * q^51 + 82 * q^52 + 18 * q^53 + 22 * q^54 + 13 * q^55 - 15 * q^56 + 21 * q^57 + 18 * q^58 - 11 * q^59 - 37 * q^60 + 24 * q^61 + 48 * q^62 - 69 * q^63 + 65 * q^64 - 31 * q^65 + 25 * q^66 - 6 * q^67 + 65 * q^68 + 27 * q^69 + 2 * q^70 - 35 * q^71 + 53 * q^72 + 116 * q^73 - 69 * q^74 + 11 * q^75 + 65 * q^76 + 13 * q^77 + 102 * q^78 - 83 * q^79 - 64 * q^80 + 126 * q^81 + 71 * q^82 + 84 * q^83 - 37 * q^84 - 30 * q^85 + 24 * q^86 + 49 * q^87 + 20 * q^88 - 16 * q^89 - 18 * q^90 - 31 * q^91 + 19 * q^92 + 65 * q^93 + 54 * q^94 - 20 * q^95 + 17 * q^96 + 155 * q^97 + 2 * q^98 + 6 * 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 $

$2$	1.24614	0.881153	0.440576	−	0.897715i	$-0.354774\pi$
$2$	1.24614	0.881153	0.440576	+	0.897715i	$0.354774\pi$
$3$	2.46236	1.42165	0.710823	−	0.703371i	$-0.248323\pi$
$3$	2.46236	1.42165	0.710823	+	0.703371i	$0.248323\pi$
$4$	−0.447139	−0.223569
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	3.06845	1.25269
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−3.04947	−1.07815
$9$	3.06324	1.02108
$10$	−1.24614	−0.394064
$11$	1.46291	0.441082	0.220541	−	0.975378i	$-0.429218\pi$
$11$	1.46291	0.441082	0.220541	+	0.975378i	$0.429218\pi$
$12$	−1.10102	−0.317837
$13$	−4.42027	−1.22596	−0.612981	−	0.790098i	$-0.710030\pi$
$13$	−4.42027	−1.22596	−0.612981	+	0.790098i	$0.710030\pi$
$14$	−1.24614	−0.333045
$15$	−2.46236	−0.635780
$16$	−2.90579	−0.726447
$17$	−0.0499232	−0.0121082	−0.00605408	−	0.999982i	$-0.501927\pi$
$17$	−0.0499232	−0.0121082	−0.00605408	+	0.999982i	$0.501927\pi$
$18$	3.81722	0.899726
$19$	−0.658238	−0.151010	−0.0755050	−	0.997145i	$-0.524057\pi$
$19$	−0.658238	−0.151010	−0.0755050	+	0.997145i	$0.524057\pi$
$20$	0.447139	0.0999833
$21$	−2.46236	−0.537332
$22$	1.82298	0.388661
$23$	4.57297	0.953529	0.476765	−	0.879031i	$-0.341809\pi$
$23$	4.57297	0.953529	0.476765	+	0.879031i	$0.341809\pi$
$24$	−7.50891	−1.53275
$25$	1.00000	0.200000
$26$	−5.50827	−1.08026
$27$	0.155708	0.0299660
$28$	0.447139	0.0845013
$29$	4.16152	0.772774	0.386387	−	0.922337i	$-0.373723\pi$
$29$	4.16152	0.772774	0.386387	+	0.922337i	$0.373723\pi$
$30$	−3.06845	−0.560219
$31$	−5.17544	−0.929536	−0.464768	−	0.885432i	$-0.653862\pi$
$31$	−5.17544	−0.929536	−0.464768	+	0.885432i	$0.653862\pi$
$32$	2.47793	0.438041
$33$	3.60220	0.627063
$34$	−0.0622113	−0.0106691
$35$	1.00000	0.169031
$36$	−1.36969	−0.228282
$37$	2.60005	0.427445	0.213722	−	0.976894i	$-0.431441\pi$
$37$	2.60005	0.427445	0.213722	+	0.976894i	$0.431441\pi$
$38$	−0.820255	−0.133063
$39$	−10.8843	−1.74288
$40$	3.04947	0.482164
$41$	6.25946	0.977563	0.488782	−	0.872406i	$-0.337441\pi$
$41$	6.25946	0.977563	0.488782	+	0.872406i	$0.337441\pi$
$42$	−3.06845	−0.473472
$43$	5.47750	0.835310	0.417655	−	0.908606i	$-0.362852\pi$
$43$	5.47750	0.835310	0.417655	+	0.908606i	$0.362852\pi$
$44$	−0.654122	−0.0986126
$45$	−3.06324	−0.456640
$46$	5.69855	0.840205
$47$	10.4755	1.52801	0.764003	−	0.645212i	$-0.223231\pi$
$47$	10.4755	1.52801	0.764003	+	0.645212i	$0.223231\pi$
$48$	−7.15511	−1.03275
$49$	1.00000	0.142857
$50$	1.24614	0.176231
$51$	−0.122929	−0.0172135
$52$	1.97647	0.274088
$53$	8.42397	1.15712	0.578561	−	0.815639i	$-0.303615\pi$
$53$	8.42397	1.15712	0.578561	+	0.815639i	$0.303615\pi$
$54$	0.194034	0.0264046
$55$	−1.46291	−0.197258
$56$	3.04947	0.407503
$57$	−1.62082	−0.214683
$58$	5.18582	0.680932
$59$	8.86491	1.15411	0.577056	−	0.816704i	$-0.304201\pi$
$59$	8.86491	1.15411	0.577056	+	0.816704i	$0.304201\pi$
$60$	1.10102	0.142141
$61$	9.68144	1.23958	0.619790	−	0.784767i	$-0.287218\pi$
$61$	9.68144	1.23958	0.619790	+	0.784767i	$0.287218\pi$
$62$	−6.44931	−0.819064
$63$	−3.06324	−0.385931
$64$	8.89942	1.11243
$65$	4.42027	0.548267
$66$	4.48885	0.552539
$67$	−1.18665	−0.144972	−0.0724859	−	0.997369i	$-0.523093\pi$
$67$	−1.18665	−0.144972	−0.0724859	+	0.997369i	$0.523093\pi$
$68$	0.0223226	0.00270702
$69$	11.2603	1.35558
$70$	1.24614	0.148942
$71$	−4.70654	−0.558563	−0.279282	−	0.960209i	$-0.590096\pi$
$71$	−4.70654	−0.558563	−0.279282	+	0.960209i	$0.590096\pi$
$72$	−9.34126	−1.10088
$73$	8.22538	0.962708	0.481354	−	0.876526i	$-0.340145\pi$
$73$	8.22538	0.962708	0.481354	+	0.876526i	$0.340145\pi$
$74$	3.24002	0.376644
$75$	2.46236	0.284329
$76$	0.294324	0.0337612
$77$	−1.46291	−0.166714
$78$	−13.5634	−1.53575
$79$	15.8964	1.78849	0.894243	−	0.447583i	$-0.147715\pi$
$79$	15.8964	1.78849	0.894243	+	0.447583i	$0.147715\pi$
$80$	2.90579	0.324877
$81$	−8.80630	−0.978477
$82$	7.80015	0.861383
$83$	−8.75408	−0.960885	−0.480442	−	0.877026i	$-0.659524\pi$
$83$	−8.75408	−0.960885	−0.480442	+	0.877026i	$0.659524\pi$
$84$	1.10102	0.120131
$85$	0.0499232	0.00541493
$86$	6.82572	0.736036
$87$	10.2472	1.09861
$88$	−4.46109	−0.475554
$89$	13.3176	1.41167	0.705834	−	0.708377i	$-0.250573\pi$
$89$	13.3176	1.41167	0.705834	+	0.708377i	$0.250573\pi$
$90$	−3.81722	−0.402370
$91$	4.42027	0.463370
$92$	−2.04475	−0.213180
$93$	−12.7438	−1.32147
$94$	13.0539	1.34641
$95$	0.658238	0.0675337
$96$	6.10157	0.622739
$97$	5.42424	0.550748	0.275374	−	0.961337i	$-0.411198\pi$
$97$	5.42424	0.550748	0.275374	+	0.961337i	$0.411198\pi$
$98$	1.24614	0.125879
$99$	4.48122	0.450380
$100$	−0.447139	−0.0447139
$101$	17.7053	1.76175	0.880873	−	0.473353i	$-0.156956\pi$
$101$	17.7053	1.76175	0.880873	+	0.473353i	$0.156956\pi$
$102$	−0.153187	−0.0151677
$103$	1.42123	0.140038	0.0700189	−	0.997546i	$-0.477694\pi$
$103$	1.42123	0.140038	0.0700189	+	0.997546i	$0.477694\pi$
$104$	13.4795	1.32177
$105$	2.46236	0.240302
$106$	10.4974	1.01960
$107$	−6.61729	−0.639718	−0.319859	−	0.947465i	$-0.603635\pi$
$107$	−6.61729	−0.639718	−0.319859	+	0.947465i	$0.603635\pi$
$108$	−0.0696231	−0.00669948
$109$	−17.9093	−1.71540	−0.857698	−	0.514154i	$-0.828106\pi$
$109$	−17.9093	−1.71540	−0.857698	+	0.514154i	$0.828106\pi$
$110$	−1.82298	−0.173815
$111$	6.40226	0.607676
$112$	2.90579	0.274571
$113$	−17.5204	−1.64818	−0.824092	−	0.566457i	$-0.808314\pi$
$113$	−17.5204	−1.64818	−0.824092	+	0.566457i	$0.808314\pi$
$114$	−2.01977	−0.189168
$115$	−4.57297	−0.426431
$116$	−1.86078	−0.172769
$117$	−13.5403	−1.25180
$118$	11.0469	1.01695
$119$	0.0499232	0.00457645
$120$	7.50891	0.685467
$121$	−8.85991	−0.805446
$122$	12.0644	1.09226
$123$	15.4131	1.38975
$124$	2.31414	0.207816
$125$	−1.00000	−0.0894427
$126$	−3.81722	−0.340065
$127$	−4.97063	−0.441072	−0.220536	−	0.975379i	$-0.570781\pi$
$127$	−4.97063	−0.441072	−0.220536	+	0.975379i	$0.570781\pi$
$128$	6.13405	0.542179
$129$	13.4876	1.18752
$130$	5.50827	0.483107
$131$	−4.51695	−0.394648	−0.197324	−	0.980338i	$-0.563225\pi$
$131$	−4.51695	−0.394648	−0.197324	+	0.980338i	$0.563225\pi$
$132$	−1.61069	−0.140192
$133$	0.658238	0.0570764
$134$	−1.47873	−0.127742
$135$	−0.155708	−0.0134012
$136$	0.152240	0.0130544
$137$	11.0480	0.943895	0.471947	−	0.881627i	$-0.343551\pi$
$137$	11.0480	0.943895	0.471947	+	0.881627i	$0.343551\pi$
$138$	14.0319	1.19447
$139$	−0.473739	−0.0401820	−0.0200910	−	0.999798i	$-0.506396\pi$
$139$	−0.473739	−0.0401820	−0.0200910	+	0.999798i	$0.506396\pi$
$140$	−0.447139	−0.0377901
$141$	25.7945	2.17229
$142$	−5.86500	−0.492180
$143$	−6.46643	−0.540750
$144$	−8.90111	−0.741760
$145$	−4.16152	−0.345595
$146$	10.2500	0.848293
$147$	2.46236	0.203092
$148$	−1.16258	−0.0955636
$149$	−8.81604	−0.722238	−0.361119	−	0.932520i	$-0.617605\pi$
$149$	−8.81604	−0.722238	−0.361119	+	0.932520i	$0.617605\pi$
$150$	3.06845	0.250538
$151$	−11.0369	−0.898171	−0.449086	−	0.893489i	$-0.648250\pi$
$151$	−11.0369	−0.898171	−0.449086	+	0.893489i	$0.648250\pi$
$152$	2.00728	0.162812
$153$	−0.152927	−0.0123634
$154$	−1.82298	−0.146900
$155$	5.17544	0.415701
$156$	4.86680	0.389656
$157$	−4.94050	−0.394295	−0.197147	−	0.980374i	$-0.563168\pi$
$157$	−4.94050	−0.394295	−0.197147	+	0.980374i	$0.563168\pi$
$158$	19.8091	1.57593
$159$	20.7429	1.64502
$160$	−2.47793	−0.195898
$161$	−4.57297	−0.360400
$162$	−10.9739	−0.862188
$163$	−20.6345	−1.61622	−0.808109	−	0.589033i	$-0.799509\pi$
$163$	−20.6345	−1.61622	−0.808109	+	0.589033i	$0.799509\pi$
$164$	−2.79885	−0.218553
$165$	−3.60220	−0.280431
$166$	−10.9088	−0.846686
$167$	−8.98507	−0.695286	−0.347643	−	0.937627i	$-0.613018\pi$
$167$	−8.98507	−0.695286	−0.347643	+	0.937627i	$0.613018\pi$
$168$	7.50891	0.579325
$169$	6.53876	0.502982
$170$	0.0622113	0.00477139
$171$	−2.01634	−0.154193
$172$	−2.44920	−0.186750
$173$	10.5897	0.805118	0.402559	−	0.915394i	$-0.368121\pi$
$173$	10.5897	0.805118	0.402559	+	0.915394i	$0.368121\pi$
$174$	12.7694	0.968045
$175$	−1.00000	−0.0755929
$176$	−4.25089	−0.320423
$177$	21.8286	1.64074
$178$	16.5956	1.24390
$179$	−0.907167	−0.0678048	−0.0339024	−	0.999425i	$-0.510794\pi$
$179$	−0.907167	−0.0678048	−0.0339024	+	0.999425i	$0.510794\pi$
$180$	1.36969	0.102091
$181$	−25.6659	−1.90773	−0.953866	−	0.300234i	$-0.902935\pi$
$181$	−25.6659	−1.90773	−0.953866	+	0.300234i	$0.902935\pi$
$182$	5.50827	0.408300
$183$	23.8392	1.76225
$184$	−13.9451	−1.02805
$185$	−2.60005	−0.191159
$186$	−15.8806	−1.16442
$187$	−0.0730329	−0.00534070
$188$	−4.68400	−0.341616
$189$	−0.155708	−0.0113261
$190$	0.820255	0.0595076
$191$	2.53195	0.183206	0.0916028	−	0.995796i	$-0.470801\pi$
$191$	2.53195	0.183206	0.0916028	+	0.995796i	$0.470801\pi$
$192$	21.9136	1.58148
$193$	15.2175	1.09538	0.547689	−	0.836682i	$-0.315508\pi$
$193$	15.2175	1.09538	0.547689	+	0.836682i	$0.315508\pi$
$194$	6.75935	0.485293
$195$	10.8843	0.779441
$196$	−0.447139	−0.0319385
$197$	23.6872	1.68764	0.843821	−	0.536625i	$-0.180301\pi$
$197$	23.6872	1.68764	0.843821	+	0.536625i	$0.180301\pi$
$198$	5.58422	0.396853
$199$	−19.3994	−1.37519	−0.687593	−	0.726096i	$-0.741333\pi$
$199$	−19.3994	−1.37519	−0.687593	+	0.726096i	$0.741333\pi$
$200$	−3.04947	−0.215630
$201$	−2.92195	−0.206099
$202$	22.0633	1.55237
$203$	−4.16152	−0.292081
$204$	0.0549664	0.00384842
$205$	−6.25946	−0.437180
$206$	1.77105	0.123395
$207$	14.0081	0.973628
$208$	12.8444	0.890596
$209$	−0.962939	−0.0666079
$210$	3.06845	0.211743
$211$	10.3328	0.711340	0.355670	−	0.934612i	$-0.384253\pi$
$211$	10.3328	0.711340	0.355670	+	0.934612i	$0.384253\pi$
$212$	−3.76669	−0.258697
$213$	−11.5892	−0.794079
$214$	−8.24606	−0.563689
$215$	−5.47750	−0.373562
$216$	−0.474827	−0.0323079
$217$	5.17544	0.351332
$218$	−22.3174	−1.51153
$219$	20.2539	1.36863
$220$	0.654122	0.0441009
$221$	0.220674	0.0148441
$222$	7.97810	0.535455
$223$	−11.0550	−0.740294	−0.370147	−	0.928973i	$-0.620693\pi$
$223$	−11.0550	−0.740294	−0.370147	+	0.928973i	$0.620693\pi$
$224$	−2.47793	−0.165564
$225$	3.06324	0.204216
$226$	−21.8329	−1.45230
$227$	28.3039	1.87859	0.939297	−	0.343106i	$-0.111479\pi$
$227$	28.3039	1.87859	0.939297	+	0.343106i	$0.111479\pi$
$228$	0.724732	0.0479965
$229$	1.00000	0.0660819
$229$	1.00000	0.0660819
$230$	−5.69855	−0.375751
$231$	−3.60220	−0.237008
$232$	−12.6904	−0.833168
$233$	28.0706	1.83896	0.919482	−	0.393133i	$-0.128609\pi$
$233$	28.0706	1.83896	0.919482	+	0.393133i	$0.128609\pi$
$234$	−16.8731	−1.10303
$235$	−10.4755	−0.683345
$236$	−3.96385	−0.258024
$237$	39.1427	2.54259
$238$	0.0622113	0.00403256
$239$	2.82887	0.182985	0.0914923	−	0.995806i	$-0.470836\pi$
$239$	2.82887	0.182985	0.0914923	+	0.995806i	$0.470836\pi$
$240$	7.15511	0.461860
$241$	5.22088	0.336307	0.168153	−	0.985761i	$-0.446220\pi$
$241$	5.22088	0.336307	0.168153	+	0.985761i	$0.446220\pi$
$242$	−11.0407	−0.709721
$243$	−22.1514	−1.42101
$244$	−4.32895	−0.277132
$245$	−1.00000	−0.0638877
$246$	19.2068	1.22458
$247$	2.90959	0.185133
$248$	15.7824	1.00218
$249$	−21.5557	−1.36604
$250$	−1.24614	−0.0788127
$251$	7.51392	0.474275	0.237137	−	0.971476i	$-0.423791\pi$
$251$	7.51392	0.474275	0.237137	+	0.971476i	$0.423791\pi$
$252$	1.36969	0.0862825
$253$	6.68982	0.420585
$254$	−6.19409	−0.388652
$255$	0.122929	0.00769812
$256$	−10.1550	−0.634686
$257$	−8.34268	−0.520402	−0.260201	−	0.965554i	$-0.583789\pi$
$257$	−8.34268	−0.520402	−0.260201	+	0.965554i	$0.583789\pi$
$258$	16.8074	1.04638
$259$	−2.60005	−0.161559
$260$	−1.97647	−0.122576
$261$	12.7477	0.789063
$262$	−5.62875	−0.347745
$263$	−20.8310	−1.28450	−0.642249	−	0.766496i	$-0.721998\pi$
$263$	−20.8310	−1.28450	−0.642249	+	0.766496i	$0.721998\pi$
$264$	−10.9848	−0.676069
$265$	−8.42397	−0.517480
$266$	0.820255	0.0502931
$267$	32.7929	2.00689
$268$	0.530596	0.0324113
$269$	16.6297	1.01393	0.506964	−	0.861967i	$-0.330768\pi$
$269$	16.6297	1.01393	0.506964	+	0.861967i	$0.330768\pi$
$270$	−0.194034	−0.0118085
$271$	14.0574	0.853924	0.426962	−	0.904270i	$-0.359584\pi$
$271$	14.0574	0.853924	0.426962	+	0.904270i	$0.359584\pi$
$272$	0.145066	0.00879594
$273$	10.8843	0.658748
$274$	13.7673	0.831716
$275$	1.46291	0.0882165
$276$	−5.03492	−0.303067
$277$	−20.9685	−1.25987	−0.629937	−	0.776647i	$-0.716919\pi$
$277$	−20.9685	−1.25987	−0.629937	+	0.776647i	$0.716919\pi$
$278$	−0.590344	−0.0354065
$279$	−15.8536	−0.949130
$280$	−3.04947	−0.182241
$281$	−1.21515	−0.0724900	−0.0362450	−	0.999343i	$-0.511540\pi$
$281$	−1.21515	−0.0724900	−0.0362450	+	0.999343i	$0.511540\pi$
$282$	32.1435	1.91412
$283$	−14.6614	−0.871528	−0.435764	−	0.900061i	$-0.643522\pi$
$283$	−14.6614	−0.871528	−0.435764	+	0.900061i	$0.643522\pi$
$284$	2.10448	0.124878
$285$	1.62082	0.0960091
$286$	−8.05807	−0.476484
$287$	−6.25946	−0.369484
$288$	7.59049	0.447274
$289$	−16.9975	−0.999853
$290$	−5.18582	−0.304522
$291$	13.3564	0.782969
$292$	−3.67789	−0.215232
$293$	1.81819	0.106220	0.0531099	−	0.998589i	$-0.483087\pi$
$293$	1.81819	0.106220	0.0531099	+	0.998589i	$0.483087\pi$
$294$	3.06845	0.178955
$295$	−8.86491	−0.516135
$296$	−7.92877	−0.460851
$297$	0.227786	0.0132175
$298$	−10.9860	−0.636402
$299$	−20.2137	−1.16899
$300$	−1.10102	−0.0635674
$301$	−5.47750	−0.315718
$302$	−13.7535	−0.791426
$303$	43.5970	2.50458
$304$	1.91270	0.109701
$305$	−9.68144	−0.554357
$306$	−0.190568	−0.0108940
$307$	6.47220	0.369388	0.184694	−	0.982796i	$-0.440871\pi$
$307$	6.47220	0.369388	0.184694	+	0.982796i	$0.440871\pi$
$308$	0.654122	0.0372721
$309$	3.49958	0.199084
$310$	6.44931	0.366296
$311$	−3.98045	−0.225711	−0.112855	−	0.993611i	$-0.536000\pi$
$311$	−3.98045	−0.225711	−0.112855	+	0.993611i	$0.536000\pi$
$312$	33.1914	1.87909
$313$	15.3360	0.866840	0.433420	−	0.901192i	$-0.357307\pi$
$313$	15.3360	0.866840	0.433420	+	0.901192i	$0.357307\pi$
$314$	−6.15655	−0.347434
$315$	3.06324	0.172594
$316$	−7.10790	−0.399851
$317$	29.3652	1.64931	0.824656	−	0.565635i	$-0.191369\pi$
$317$	29.3652	1.64931	0.824656	+	0.565635i	$0.191369\pi$
$318$	25.8485	1.44951
$319$	6.08790	0.340857
$320$	−8.89942	−0.497493
$321$	−16.2942	−0.909452
$322$	−5.69855	−0.317568
$323$	0.0328613	0.00182845
$324$	3.93764	0.218758
$325$	−4.42027	−0.245192
$326$	−25.7134	−1.42414
$327$	−44.0991	−2.43869
$328$	−19.0881	−1.05396
$329$	−10.4755	−0.577532
$330$	−4.48885	−0.247103
$331$	9.56626	0.525809	0.262905	−	0.964822i	$-0.415320\pi$
$331$	9.56626	0.525809	0.262905	+	0.964822i	$0.415320\pi$
$332$	3.91429	0.214825
$333$	7.96455	0.436455
$334$	−11.1966	−0.612653
$335$	1.18665	0.0648334
$336$	7.15511	0.390343
$337$	26.0666	1.41994	0.709970	−	0.704232i	$-0.248709\pi$
$337$	26.0666	1.41994	0.709970	+	0.704232i	$0.248709\pi$
$338$	8.14821	0.443204
$339$	−43.1417	−2.34313
$340$	−0.0223226	−0.00121061
$341$	−7.57118	−0.410002
$342$	−2.51263	−0.135868
$343$	−1.00000	−0.0539949
$344$	−16.7035	−0.900591
$345$	−11.2603	−0.606235
$346$	13.1962	0.709432
$347$	−22.3314	−1.19881	−0.599407	−	0.800444i	$-0.704597\pi$
$347$	−22.3314	−1.19881	−0.599407	+	0.800444i	$0.704597\pi$
$348$	−4.58191	−0.245616
$349$	21.8905	1.17177	0.585886	−	0.810393i	$-0.300746\pi$
$349$	21.8905	1.17177	0.585886	+	0.810393i	$0.300746\pi$
$350$	−1.24614	−0.0666089
$351$	−0.688271	−0.0367372
$352$	3.62498	0.193212
$353$	11.3822	0.605812	0.302906	−	0.953020i	$-0.402043\pi$
$353$	11.3822	0.605812	0.302906	+	0.953020i	$0.402043\pi$
$354$	27.2015	1.44574
$355$	4.70654	0.249797
$356$	−5.95484	−0.315606
$357$	0.122929	0.00650610
$358$	−1.13046	−0.0597464
$359$	14.6229	0.771769	0.385885	−	0.922547i	$-0.373896\pi$
$359$	14.6229	0.771769	0.385885	+	0.922547i	$0.373896\pi$
$360$	9.34126	0.492327
$361$	−18.5667	−0.977196
$362$	−31.9833	−1.68100
$363$	−21.8163	−1.14506
$364$	−1.97647	−0.103595
$365$	−8.22538	−0.430536
$366$	29.7070	1.55281
$367$	9.42730	0.492101	0.246051	−	0.969257i	$-0.420867\pi$
$367$	9.42730	0.492101	0.246051	+	0.969257i	$0.420867\pi$
$368$	−13.2881	−0.692689
$369$	19.1742	0.998169
$370$	−3.24002	−0.168440
$371$	−8.42397	−0.437351
$372$	5.69826	0.295441
$373$	−32.6395	−1.69001	−0.845005	−	0.534759i	$-0.820402\pi$
$373$	−32.6395	−1.69001	−0.845005	+	0.534759i	$0.820402\pi$
$374$	−0.0910092	−0.00470597
$375$	−2.46236	−0.127156
$376$	−31.9447	−1.64742
$377$	−18.3950	−0.947391
$378$	−0.194034	−0.00998001
$379$	6.14818	0.315811	0.157905	−	0.987454i	$-0.449526\pi$
$379$	6.14818	0.315811	0.157905	+	0.987454i	$0.449526\pi$
$380$	−0.294324	−0.0150985
$381$	−12.2395	−0.627049
$382$	3.15516	0.161432
$383$	36.8177	1.88130	0.940648	−	0.339382i	$-0.110218\pi$
$383$	36.8177	1.88130	0.940648	+	0.339382i	$0.110218\pi$
$384$	15.1043	0.770786
$385$	1.46291	0.0745565
$386$	18.9631	0.965196
$387$	16.7789	0.852917
$388$	−2.42539	−0.123130
$389$	14.6758	0.744093	0.372046	−	0.928214i	$-0.378656\pi$
$389$	14.6758	0.744093	0.372046	+	0.928214i	$0.378656\pi$
$390$	13.5634	0.686807
$391$	−0.228297	−0.0115455
$392$	−3.04947	−0.154022
$393$	−11.1224	−0.561050
$394$	29.5175	1.48707
$395$	−15.8964	−0.799835
$396$	−2.00373	−0.100691
$397$	−12.6910	−0.636943	−0.318472	−	0.947932i	$-0.603170\pi$
$397$	−12.6910	−0.636943	−0.318472	+	0.947932i	$0.603170\pi$
$398$	−24.1743	−1.21175
$399$	1.62082	0.0811425
$400$	−2.90579	−0.145289
$401$	12.6280	0.630610	0.315305	−	0.948990i	$-0.397893\pi$
$401$	12.6280	0.630610	0.315305	+	0.948990i	$0.397893\pi$
$402$	−3.64116	−0.181605
$403$	22.8768	1.13958
$404$	−7.91674	−0.393873
$405$	8.80630	0.437588
$406$	−5.18582	−0.257368
$407$	3.80362	0.188538
$408$	0.374869	0.0185588
$409$	9.17000	0.453427	0.226714	−	0.973961i	$-0.427202\pi$
$409$	9.17000	0.453427	0.226714	+	0.973961i	$0.427202\pi$
$410$	−7.80015	−0.385222
$411$	27.2042	1.34188
$412$	−0.635486	−0.0313082
$413$	−8.86491	−0.436214
$414$	17.4560	0.857915
$415$	8.75408	0.429721
$416$	−10.9531	−0.537021
$417$	−1.16652	−0.0571246
$418$	−1.19996	−0.0586917
$419$	37.5140	1.83268	0.916340	−	0.400400i	$-0.131129\pi$
$419$	37.5140	1.83268	0.916340	+	0.400400i	$0.131129\pi$
$420$	−1.10102	−0.0537242
$421$	−40.2654	−1.96242	−0.981209	−	0.192949i	$-0.938195\pi$
$421$	−40.2654	−1.96242	−0.981209	+	0.192949i	$0.938195\pi$
$422$	12.8761	0.626799
$423$	32.0889	1.56021
$424$	−25.6887	−1.24755
$425$	−0.0499232	−0.00242163
$426$	−14.4418	−0.699705
$427$	−9.68144	−0.468518
$428$	2.95885	0.143021
$429$	−15.9227	−0.768756
$430$	−6.82572	−0.329165
$431$	−20.7022	−0.997189	−0.498594	−	0.866835i	$-0.666150\pi$
$431$	−20.7022	−0.997189	−0.498594	+	0.866835i	$0.666150\pi$
$432$	−0.452454	−0.0217687
$433$	30.1961	1.45113	0.725565	−	0.688153i	$-0.241578\pi$
$433$	30.1961	1.45113	0.725565	+	0.688153i	$0.241578\pi$
$434$	6.44931	0.309577
$435$	−10.2472	−0.491314
$436$	8.00793	0.383510
$437$	−3.01010	−0.143993
$438$	25.2391	1.20597
$439$	38.9141	1.85727	0.928635	−	0.370996i	$-0.120984\pi$
$439$	38.9141	1.85727	0.928635	+	0.370996i	$0.120984\pi$
$440$	4.46109	0.212674
$441$	3.06324	0.145868
$442$	0.274990	0.0130800
$443$	9.72130	0.461873	0.230936	−	0.972969i	$-0.425821\pi$
$443$	9.72130	0.461873	0.230936	+	0.972969i	$0.425821\pi$
$444$	−2.86270	−0.135858
$445$	−13.3176	−0.631317
$446$	−13.7760	−0.652312
$447$	−21.7083	−1.02677
$448$	−8.89942	−0.420458
$449$	23.3906	1.10387	0.551935	−	0.833887i	$-0.313890\pi$
$449$	23.3906	1.10387	0.551935	+	0.833887i	$0.313890\pi$
$450$	3.81722	0.179945
$451$	9.15699	0.431186
$452$	7.83407	0.368483
$453$	−27.1769	−1.27688
$454$	35.2705	1.65533
$455$	−4.42027	−0.207225
$456$	4.94265	0.231461
$457$	40.7818	1.90769	0.953846	−	0.300297i	$-0.0970859\pi$
$457$	40.7818	1.90769	0.953846	+	0.300297i	$0.0970859\pi$
$458$	1.24614	0.0582282
$459$	−0.00777344	−0.000362833 0
$460$	2.04475	0.0953370
$461$	−38.7404	−1.80432	−0.902161	−	0.431399i	$-0.858020\pi$
$461$	−38.7404	−1.80432	−0.902161	+	0.431399i	$0.858020\pi$
$462$	−4.48885	−0.208840
$463$	−10.0870	−0.468783	−0.234391	−	0.972142i	$-0.575310\pi$
$463$	−10.0870	−0.468783	−0.234391	+	0.972142i	$0.575310\pi$
$464$	−12.0925	−0.561379
$465$	12.7438	0.590980
$466$	34.9798	1.62041
$467$	27.1624	1.25693	0.628464	−	0.777839i	$-0.283684\pi$
$467$	27.1624	1.25693	0.628464	+	0.777839i	$0.283684\pi$
$468$	6.05440	0.279865
$469$	1.18665	0.0547942
$470$	−13.0539	−0.602132
$471$	−12.1653	−0.560548
$472$	−27.0333	−1.24431
$473$	8.01306	0.368441
$474$	48.7773	2.24041
$475$	−0.658238	−0.0302020
$476$	−0.0223226	−0.00102316
$477$	25.8046	1.18151
$478$	3.52517	0.161237
$479$	−21.8972	−1.00051	−0.500255	−	0.865878i	$-0.666760\pi$
$479$	−21.8972	−1.00051	−0.500255	+	0.865878i	$0.666760\pi$
$480$	−6.10157	−0.278497
$481$	−11.4929	−0.524031
$482$	6.50594	0.296338
$483$	−11.2603	−0.512362
$484$	3.96161	0.180073
$485$	−5.42424	−0.246302
$486$	−27.6037	−1.25213
$487$	−31.8642	−1.44390	−0.721952	−	0.691943i	$-0.756755\pi$
$487$	−31.8642	−1.44390	−0.721952	+	0.691943i	$0.756755\pi$
$488$	−29.5233	−1.33646
$489$	−50.8096	−2.29769
$490$	−1.24614	−0.0562948
$491$	−3.89185	−0.175637	−0.0878183	−	0.996137i	$-0.527989\pi$
$491$	−3.89185	−0.175637	−0.0878183	+	0.996137i	$0.527989\pi$
$492$	−6.89178	−0.310706
$493$	−0.207756	−0.00935687
$494$	3.62575	0.163130
$495$	−4.48122	−0.201416
$496$	15.0387	0.675259
$497$	4.70654	0.211117
$498$	−26.8614	−1.20369
$499$	9.56614	0.428239	0.214120	−	0.976807i	$-0.431312\pi$
$499$	9.56614	0.428239	0.214120	+	0.976807i	$0.431312\pi$
$500$	0.447139	0.0199967
$501$	−22.1245	−0.988450
$502$	9.36339	0.417908
$503$	24.2825	1.08271	0.541353	−	0.840796i	$-0.317912\pi$
$503$	24.2825	1.08271	0.541353	+	0.840796i	$0.317912\pi$
$504$	9.34126	0.416093
$505$	−17.7053	−0.787877
$506$	8.33644	0.370600
$507$	16.1008	0.715062
$508$	2.22256	0.0986103
$509$	14.8541	0.658396	0.329198	−	0.944261i	$-0.393222\pi$
$509$	14.8541	0.658396	0.329198	+	0.944261i	$0.393222\pi$
$510$	0.153187	0.00678322
$511$	−8.22538	−0.363869
$512$	−24.9226	−1.10143
$513$	−0.102493	−0.00452517
$514$	−10.3961	−0.458554
$515$	−1.42123	−0.0626268
$516$	−6.03083	−0.265492
$517$	15.3246	0.673977
$518$	−3.24002	−0.142358
$519$	26.0756	1.14459
$520$	−13.4795	−0.591115
$521$	−41.5556	−1.82058	−0.910292	−	0.413966i	$-0.864143\pi$
$521$	−41.5556	−1.82058	−0.910292	+	0.413966i	$0.864143\pi$
$522$	15.8854	0.695285
$523$	−34.0040	−1.48689	−0.743446	−	0.668796i	$-0.766810\pi$
$523$	−34.0040	−1.48689	−0.743446	+	0.668796i	$0.766810\pi$
$524$	2.01971	0.0882313
$525$	−2.46236	−0.107466
$526$	−25.9584	−1.13184
$527$	0.258375	0.0112550
$528$	−10.4672	−0.455528
$529$	−2.08798	−0.0907816
$530$	−10.4974	−0.455979
$531$	27.1553	1.17844
$532$	−0.294324	−0.0127605
$533$	−27.6685	−1.19845
$534$	40.8645	1.76838
$535$	6.61729	0.286090
$536$	3.61865	0.156302
$537$	−2.23377	−0.0963945
$538$	20.7229	0.893426
$539$	1.46291	0.0630118
$540$	0.0696231	0.00299610
$541$	−8.88257	−0.381891	−0.190946	−	0.981601i	$-0.561155\pi$
$541$	−8.88257	−0.381891	−0.190946	+	0.981601i	$0.561155\pi$
$542$	17.5174	0.752437
$543$	−63.1988	−2.71212
$544$	−0.123706	−0.00530387
$545$	17.9093	0.767149
$546$	13.5634	0.580458
$547$	26.0102	1.11212	0.556058	−	0.831143i	$-0.312313\pi$
$547$	26.0102	1.11212	0.556058	+	0.831143i	$0.312313\pi$
$548$	−4.93999	−0.211026
$549$	29.6565	1.26571
$550$	1.82298	0.0777322
$551$	−2.73927	−0.116697
$552$	−34.3380	−1.46152
$553$	−15.8964	−0.675984
$554$	−26.1296	−1.11014
$555$	−6.40226	−0.271761
$556$	0.211827	0.00898347
$557$	17.6210	0.746627	0.373313	−	0.927705i	$-0.378222\pi$
$557$	17.6210	0.746627	0.373313	+	0.927705i	$0.378222\pi$
$558$	−19.7558	−0.836328
$559$	−24.2120	−1.02406
$560$	−2.90579	−0.122792
$561$	−0.179834	−0.00759258
$562$	−1.51425	−0.0638748
$563$	18.1411	0.764556	0.382278	−	0.924047i	$-0.375140\pi$
$563$	18.1411	0.764556	0.382278	+	0.924047i	$0.375140\pi$
$564$	−11.5337	−0.485657
$565$	17.5204	0.737090
$566$	−18.2701	−0.767949
$567$	8.80630	0.369830
$568$	14.3525	0.602216
$569$	12.3029	0.515764	0.257882	−	0.966176i	$-0.416975\pi$
$569$	12.3029	0.515764	0.257882	+	0.966176i	$0.416975\pi$
$570$	2.01977	0.0845987
$571$	26.7895	1.12111	0.560553	−	0.828118i	$-0.310588\pi$
$571$	26.7895	1.12111	0.560553	+	0.828118i	$0.310588\pi$
$572$	2.89139	0.120895
$573$	6.23458	0.260454
$574$	−7.80015	−0.325572
$575$	4.57297	0.190706
$576$	27.2610	1.13588
$577$	28.2833	1.17745	0.588724	−	0.808334i	$-0.299631\pi$
$577$	28.2833	1.17745	0.588724	+	0.808334i	$0.299631\pi$
$578$	−21.1812	−0.881024
$579$	37.4710	1.55724
$580$	1.86078	0.0772645
$581$	8.75408	0.363180
$582$	16.6440	0.689915
$583$	12.3235	0.510386
$584$	−25.0831	−1.03794
$585$	13.5403	0.559823
$586$	2.26572	0.0935960
$587$	25.3798	1.04754	0.523768	−	0.851861i	$-0.324526\pi$
$587$	25.3798	1.04754	0.523768	+	0.851861i	$0.324526\pi$
$588$	−1.10102	−0.0454053
$589$	3.40667	0.140369
$590$	−11.0469	−0.454794
$591$	58.3264	2.39923
$592$	−7.55518	−0.310516
$593$	−5.13745	−0.210970	−0.105485	−	0.994421i	$-0.533639\pi$
$593$	−5.13745	−0.210970	−0.105485	+	0.994421i	$0.533639\pi$
$594$	0.283853	0.0116466
$595$	−0.0499232	−0.00204665
$596$	3.94200	0.161470
$597$	−47.7683	−1.95503
$598$	−25.1891	−1.03006
$599$	12.1205	0.495228	0.247614	−	0.968859i	$-0.420353\pi$
$599$	12.1205	0.495228	0.247614	+	0.968859i	$0.420353\pi$
$600$	−7.50891	−0.306550
$601$	25.5231	1.04111	0.520555	−	0.853828i	$-0.325725\pi$
$601$	25.5231	1.04111	0.520555	+	0.853828i	$0.325725\pi$
$602$	−6.82572	−0.278196
$603$	−3.63498	−0.148028
$604$	4.93503	0.200804
$605$	8.85991	0.360207
$606$	54.3278	2.20692
$607$	−37.9248	−1.53932	−0.769661	−	0.638453i	$-0.779575\pi$
$607$	−37.9248	−1.53932	−0.769661	+	0.638453i	$0.779575\pi$
$608$	−1.63107	−0.0661486
$609$	−10.2472	−0.415236
$610$	−12.0644	−0.488474
$611$	−46.3045	−1.87328
$612$	0.0683794	0.00276407
$613$	−17.5547	−0.709026	−0.354513	−	0.935051i	$-0.615353\pi$
$613$	−17.5547	−0.709026	−0.354513	+	0.935051i	$0.615353\pi$
$614$	8.06526	0.325487
$615$	−15.4131	−0.621515
$616$	4.46109	0.179742
$617$	−5.89116	−0.237169	−0.118585	−	0.992944i	$-0.537836\pi$
$617$	−5.89116	−0.237169	−0.118585	+	0.992944i	$0.537836\pi$
$618$	4.36096	0.175424
$619$	42.3799	1.70339	0.851695	−	0.524038i	$-0.175575\pi$
$619$	42.3799	1.70339	0.851695	+	0.524038i	$0.175575\pi$
$620$	−2.31414	−0.0929381
$621$	0.712047	0.0285735
$622$	−4.96019	−0.198886
$623$	−13.3176	−0.533560
$624$	31.6275	1.26611
$625$	1.00000	0.0400000
$626$	19.1107	0.763819
$627$	−2.37111	−0.0946929
$628$	2.20909	0.0881523
$629$	−0.129803	−0.00517557
$630$	3.81722	0.152081
$631$	−6.13013	−0.244037	−0.122018	−	0.992528i	$-0.538937\pi$
$631$	−6.13013	−0.244037	−0.122018	+	0.992528i	$0.538937\pi$
$632$	−48.4757	−1.92826
$633$	25.4431	1.01127
$634$	36.5930	1.45330
$635$	4.97063	0.197253
$636$	−9.27495	−0.367776
$637$	−4.42027	−0.175137
$638$	7.58637	0.300347
$639$	−14.4172	−0.570337
$640$	−6.13405	−0.242470
$641$	−0.919866	−0.0363325	−0.0181663	−	0.999835i	$-0.505783\pi$
$641$	−0.919866	−0.0363325	−0.0181663	+	0.999835i	$0.505783\pi$
$642$	−20.3048	−0.801366
$643$	−21.8237	−0.860642	−0.430321	−	0.902676i	$-0.641600\pi$
$643$	−21.8237	−0.860642	−0.430321	+	0.902676i	$0.641600\pi$
$644$	2.04475	0.0805745
$645$	−13.4876	−0.531073
$646$	0.0409498	0.00161115
$647$	24.0684	0.946227	0.473114	−	0.881001i	$-0.343130\pi$
$647$	24.0684	0.946227	0.473114	+	0.881001i	$0.343130\pi$
$648$	26.8546	1.05495
$649$	12.9685	0.509059
$650$	−5.50827	−0.216052
$651$	12.7438	0.499470
$652$	9.22648	0.361337
$653$	23.3108	0.912221	0.456111	−	0.889923i	$-0.349242\pi$
$653$	23.3108	0.912221	0.456111	+	0.889923i	$0.349242\pi$
$654$	−54.9536	−2.14886
$655$	4.51695	0.176492
$656$	−18.1887	−0.710148
$657$	25.1963	0.983000
$658$	−13.0539	−0.508894
$659$	15.3521	0.598033	0.299016	−	0.954248i	$-0.403341\pi$
$659$	15.3521	0.598033	0.299016	+	0.954248i	$0.403341\pi$
$660$	1.61069	0.0626959
$661$	−22.8289	−0.887941	−0.443970	−	0.896041i	$-0.646430\pi$
$661$	−22.8289	−0.887941	−0.443970	+	0.896041i	$0.646430\pi$
$662$	11.9209	0.463318
$663$	0.543380	0.0211031
$664$	26.6953	1.03598
$665$	−0.658238	−0.0255254
$666$	9.92493	0.384583
$667$	19.0305	0.736863
$668$	4.01758	0.155445
$669$	−27.2213	−1.05244
$670$	1.47873	0.0571281
$671$	14.1630	0.546757
$672$	−6.10157	−0.235373
$673$	6.58459	0.253817	0.126909	−	0.991914i	$-0.459494\pi$
$673$	6.58459	0.253817	0.126909	+	0.991914i	$0.459494\pi$
$674$	32.4826	1.25118
$675$	0.155708	0.00599320
$676$	−2.92374	−0.112451
$677$	−37.6023	−1.44517	−0.722587	−	0.691280i	$-0.757047\pi$
$677$	−37.6023	−1.44517	−0.722587	+	0.691280i	$0.757047\pi$
$678$	−53.7605	−2.06466
$679$	−5.42424	−0.208163
$680$	−0.152240	−0.00583812
$681$	69.6944	2.67070
$682$	−9.43474	−0.361275
$683$	−8.83601	−0.338101	−0.169050	−	0.985607i	$-0.554070\pi$
$683$	−8.83601	−0.338101	−0.169050	+	0.985607i	$0.554070\pi$
$684$	0.901583	0.0344729
$685$	−11.0480	−0.422123
$686$	−1.24614	−0.0475778
$687$	2.46236	0.0939450
$688$	−15.9164	−0.606809
$689$	−37.2362	−1.41859
$690$	−14.0319	−0.534185
$691$	−30.8214	−1.17250	−0.586250	−	0.810130i	$-0.699396\pi$
$691$	−30.8214	−1.17250	−0.586250	+	0.810130i	$0.699396\pi$
$692$	−4.73506	−0.180000
$693$	−4.48122	−0.170228
$694$	−27.8281	−1.05634
$695$	0.473739	0.0179699
$696$	−31.2485	−1.18447
$697$	−0.312492	−0.0118365
$698$	27.2786	1.03251
$699$	69.1199	2.61436
$700$	0.447139	0.0169003
$701$	29.2705	1.10553	0.552766	−	0.833336i	$-0.313572\pi$
$701$	29.2705	1.10553	0.552766	+	0.833336i	$0.313572\pi$
$702$	−0.857680	−0.0323711
$703$	−1.71145	−0.0645485
$704$	13.0190	0.490673
$705$	−25.7945	−0.971476
$706$	14.1838	0.533813
$707$	−17.7053	−0.665877
$708$	−9.76043	−0.366819
$709$	−52.2672	−1.96293	−0.981467	−	0.191630i	$-0.938623\pi$
$709$	−52.2672	−1.96293	−0.981467	+	0.191630i	$0.938623\pi$
$710$	5.86500	0.220109
$711$	48.6944	1.82618
$712$	−40.6118	−1.52199
$713$	−23.6671	−0.886340
$714$	0.153187	0.00573287
$715$	6.46643	0.241831
$716$	0.405630	0.0151591
$717$	6.96571	0.260139
$718$	18.2222	0.680047
$719$	−23.7345	−0.885148	−0.442574	−	0.896732i	$-0.645935\pi$
$719$	−23.7345	−0.885148	−0.442574	+	0.896732i	$0.645935\pi$
$720$	8.90111	0.331725
$721$	−1.42123	−0.0529293
$722$	−23.1367	−0.861059
$723$	12.8557	0.478109
$724$	11.4762	0.426510
$725$	4.16152	0.154555
$726$	−27.1862	−1.00897
$727$	14.3640	0.532730	0.266365	−	0.963872i	$-0.414177\pi$
$727$	14.3640	0.532730	0.266365	+	0.963872i	$0.414177\pi$
$728$	−13.4795	−0.499583
$729$	−28.1260	−1.04170
$730$	−10.2500	−0.379368
$731$	−0.273454	−0.0101141
$732$	−10.6594	−0.393984
$733$	28.0463	1.03591	0.517957	−	0.855407i	$-0.326693\pi$
$733$	28.0463	1.03591	0.517957	+	0.855407i	$0.326693\pi$
$734$	11.7477	0.433616
$735$	−2.46236	−0.0908257
$736$	11.3315	0.417685
$737$	−1.73595	−0.0639446
$738$	23.8937	0.879539
$739$	−23.4194	−0.861496	−0.430748	−	0.902472i	$-0.641750\pi$
$739$	−23.4194	−0.861496	−0.430748	+	0.902472i	$0.641750\pi$
$740$	1.16258	0.0427374
$741$	7.16446	0.263193
$742$	−10.4974	−0.385373
$743$	−7.55917	−0.277319	−0.138660	−	0.990340i	$-0.544279\pi$
$743$	−7.55917	−0.277319	−0.138660	+	0.990340i	$0.544279\pi$
$744$	38.8619	1.42475
$745$	8.81604	0.322995
$746$	−40.6733	−1.48916
$747$	−26.8158	−0.981139
$748$	0.0326559	0.00119402
$749$	6.61729	0.241790
$750$	−3.06845	−0.112044
$751$	−43.5914	−1.59067	−0.795336	−	0.606169i	$-0.792706\pi$
$751$	−43.5914	−1.59067	−0.795336	+	0.606169i	$0.792706\pi$
$752$	−30.4396	−1.11002
$753$	18.5020	0.674251
$754$	−22.9227	−0.834797
$755$	11.0369	0.401674
$756$	0.0696231	0.00253217
$757$	33.2588	1.20881	0.604405	−	0.796677i	$-0.293411\pi$
$757$	33.2588	1.20881	0.604405	+	0.796677i	$0.293411\pi$
$758$	7.66149	0.278278
$759$	16.4728	0.597923
$760$	−2.00728	−0.0728116
$761$	−45.9238	−1.66474	−0.832369	−	0.554222i	$-0.813016\pi$
$761$	−45.9238	−1.66474	−0.832369	+	0.554222i	$0.813016\pi$
$762$	−15.2521	−0.552526
$763$	17.9093	0.648359
$764$	−1.13213	−0.0409592
$765$	0.152927	0.00552907
$766$	45.8800	1.65771
$767$	−39.1853	−1.41490
$768$	−25.0052	−0.902299
$769$	−36.3144	−1.30953	−0.654765	−	0.755833i	$-0.727232\pi$
$769$	−36.3144	−1.30953	−0.654765	+	0.755833i	$0.727232\pi$
$770$	1.82298	0.0656957
$771$	−20.5427	−0.739828
$772$	−6.80433	−0.244893
$773$	−3.29503	−0.118514	−0.0592570	−	0.998243i	$-0.518873\pi$
$773$	−3.29503	−0.118514	−0.0592570	+	0.998243i	$0.518873\pi$
$774$	20.9088	0.751551
$775$	−5.17544	−0.185907
$776$	−16.5411	−0.593790
$777$	−6.40226	−0.229680
$778$	18.2881	0.655660
$779$	−4.12021	−0.147622
$780$	−4.86680	−0.174259
$781$	−6.88522	−0.246372
$782$	−0.284490	−0.0101733
$783$	0.647981	0.0231569
$784$	−2.90579	−0.103778
$785$	4.94050	0.176334
$786$	−13.8600	−0.494371
$787$	16.6352	0.592982	0.296491	−	0.955036i	$-0.404183\pi$
$787$	16.6352	0.592982	0.296491	+	0.955036i	$0.404183\pi$
$788$	−10.5915	−0.377305
$789$	−51.2936	−1.82610
$790$	−19.8091	−0.704777
$791$	17.5204	0.622955
$792$	−13.6654	−0.485578
$793$	−42.7945	−1.51968
$794$	−15.8147	−0.561244
$795$	−20.7429	−0.735674
$796$	8.67422	0.307450
$797$	23.1724	0.820809	0.410404	−	0.911904i	$-0.365388\pi$
$797$	23.1724	0.820809	0.410404	+	0.911904i	$0.365388\pi$
$798$	2.01977	0.0714990
$799$	−0.522970	−0.0185014
$800$	2.47793	0.0876082
$801$	40.7951	1.44142
$802$	15.7362	0.555664
$803$	12.0329	0.424633
$804$	1.30652	0.0460774
$805$	4.57297	0.161176
$806$	28.5077	1.00414
$807$	40.9483	1.44145
$808$	−53.9919	−1.89943
$809$	−4.99812	−0.175725	−0.0878623	−	0.996133i	$-0.528004\pi$
$809$	−4.99812	−0.175725	−0.0878623	+	0.996133i	$0.528004\pi$
$810$	10.9739	0.385582
$811$	−35.4858	−1.24607	−0.623037	−	0.782193i	$-0.714101\pi$
$811$	−35.4858	−1.24607	−0.623037	+	0.782193i	$0.714101\pi$
$812$	1.86078	0.0653004
$813$	34.6143	1.21398
$814$	4.73984	0.166131
$815$	20.6345	0.722795
$816$	0.357206	0.0125047
$817$	−3.60549	−0.126140
$818$	11.4271	0.399539
$819$	13.5403	0.473137
$820$	2.79885	0.0977400
$821$	30.5028	1.06456	0.532278	−	0.846569i	$-0.321336\pi$
$821$	30.5028	1.06456	0.532278	+	0.846569i	$0.321336\pi$
$822$	33.9002	1.18241
$823$	−6.09578	−0.212486	−0.106243	−	0.994340i	$-0.533882\pi$
$823$	−6.09578	−0.212486	−0.106243	+	0.994340i	$0.533882\pi$
$824$	−4.33400	−0.150982
$825$	3.60220	0.125413
$826$	−11.0469	−0.384371
$827$	−18.3520	−0.638160	−0.319080	−	0.947728i	$-0.603374\pi$
$827$	−18.3520	−0.638160	−0.319080	+	0.947728i	$0.603374\pi$
$828$	−6.26356	−0.217674
$829$	11.0345	0.383243	0.191622	−	0.981469i	$-0.438625\pi$
$829$	11.0345	0.383243	0.191622	+	0.981469i	$0.438625\pi$
$830$	10.9088	0.378650
$831$	−51.6320	−1.79109
$832$	−39.3378	−1.36379
$833$	−0.0499232	−0.00172974
$834$	−1.45364	−0.0503355
$835$	8.98507	0.310941
$836$	0.430568	0.0148915
$837$	−0.805857	−0.0278545
$838$	46.7477	1.61487
$839$	22.3307	0.770940	0.385470	−	0.922720i	$-0.374039\pi$
$839$	22.3307	0.770940	0.385470	+	0.922720i	$0.374039\pi$
$840$	−7.50891	−0.259082
$841$	−11.6818	−0.402820
$842$	−50.1763	−1.72919
$843$	−2.99215	−0.103055
$844$	−4.62020	−0.159034
$845$	−6.53876	−0.224940
$846$	39.9872	1.37479
$847$	8.85991	0.304430
$848$	−24.4783	−0.840588
$849$	−36.1016	−1.23900
$850$	−0.0622113	−0.00213383
$851$	11.8899	0.407581
$852$	5.18198	0.177532
$853$	−23.9554	−0.820219	−0.410109	−	0.912036i	$-0.634509\pi$
$853$	−23.9554	−0.820219	−0.410109	+	0.912036i	$0.634509\pi$
$854$	−12.0644	−0.412836
$855$	2.01634	0.0689572
$856$	20.1793	0.689713
$857$	2.84743	0.0972664	0.0486332	−	0.998817i	$-0.484513\pi$
$857$	2.84743	0.0972664	0.0486332	+	0.998817i	$0.484513\pi$
$858$	−19.8419	−0.677391
$859$	18.6463	0.636203	0.318101	−	0.948057i	$-0.396955\pi$
$859$	18.6463	0.636203	0.318101	+	0.948057i	$0.396955\pi$
$860$	2.44920	0.0835171
$861$	−15.4131	−0.525276
$862$	−25.7978	−0.878676
$863$	10.6560	0.362734	0.181367	−	0.983416i	$-0.441948\pi$
$863$	10.6560	0.362734	0.181367	+	0.983416i	$0.441948\pi$
$864$	0.385834	0.0131263
$865$	−10.5897	−0.360060
$866$	37.6285	1.27867
$867$	−41.8540	−1.42144
$868$	−2.31414	−0.0785471
$869$	23.2549	0.788869
$870$	−12.7694	−0.432923
$871$	5.24529	0.177730
$872$	54.6138	1.84946
$873$	16.6157	0.562357
$874$	−3.75100	−0.126879
$875$	1.00000	0.0338062
$876$	−9.05629	−0.305984
$877$	−48.3368	−1.63222	−0.816109	−	0.577899i	$-0.803873\pi$
$877$	−48.3368	−1.63222	−0.816109	+	0.577899i	$0.803873\pi$
$878$	48.4924	1.63654
$879$	4.47705	0.151007
$880$	4.25089	0.143298
$881$	3.76075	0.126703	0.0633514	−	0.997991i	$-0.479821\pi$
$881$	3.76075	0.126703	0.0633514	+	0.997991i	$0.479821\pi$
$882$	3.81722	0.128532
$883$	−24.2839	−0.817219	−0.408609	−	0.912709i	$-0.633986\pi$
$883$	−24.2839	−0.817219	−0.408609	+	0.912709i	$0.633986\pi$
$884$	−0.0986720	−0.00331870
$885$	−21.8286	−0.733761
$886$	12.1141	0.406981
$887$	−40.4748	−1.35901	−0.679505	−	0.733671i	$-0.737805\pi$
$887$	−40.4748	−1.35901	−0.679505	+	0.733671i	$0.737805\pi$
$888$	−19.5235	−0.655166
$889$	4.97063	0.166710
$890$	−16.5956	−0.556287
$891$	−12.8828	−0.431589
$892$	4.94310	0.165507
$893$	−6.89536	−0.230744
$894$	−27.0515	−0.904739
$895$	0.907167	0.0303232
$896$	−6.13405	−0.204924
$897$	−49.7736	−1.66189
$898$	29.1479	0.972679
$899$	−21.5377	−0.718322
$900$	−1.36969	−0.0456564
$901$	−0.420552	−0.0140106
$902$	11.4109	0.379941
$903$	−13.4876	−0.448839
$904$	53.4281	1.77699
$905$	25.6659	0.853163
$906$	−33.8662	−1.12513
$907$	−10.2924	−0.341754	−0.170877	−	0.985292i	$-0.554660\pi$
$907$	−10.2924	−0.341754	−0.170877	+	0.985292i	$0.554660\pi$
$908$	−12.6558	−0.419996
$909$	54.2356	1.79888
$910$	−5.50827	−0.182597
$911$	−41.4665	−1.37385	−0.686923	−	0.726731i	$-0.741039\pi$
$911$	−41.4665	−1.37385	−0.686923	+	0.726731i	$0.741039\pi$
$912$	4.70976	0.155956
$913$	−12.8064	−0.423829
$914$	50.8197	1.68097
$915$	−23.8392	−0.788100
$916$	−0.447139	−0.0147739
$917$	4.51695	0.149163
$918$	−0.00968678	−0.000319712 0
$919$	36.2294	1.19510	0.597549	−	0.801832i	$-0.296141\pi$
$919$	36.2294	1.19510	0.597549	+	0.801832i	$0.296141\pi$
$920$	13.9451	0.459758
$921$	15.9369	0.525139
$922$	−48.2760	−1.58988
$923$	20.8041	0.684777
$924$	1.61069	0.0529877
$925$	2.60005	0.0854890
$926$	−12.5698	−0.413069
$927$	4.35356	0.142990
$928$	10.3120	0.338507
$929$	−26.2810	−0.862253	−0.431126	−	0.902292i	$-0.641884\pi$
$929$	−26.2810	−0.862253	−0.431126	+	0.902292i	$0.641884\pi$
$930$	15.8806	0.520744
$931$	−0.658238	−0.0215729
$932$	−12.5514	−0.411136
$933$	−9.80132	−0.320881
$934$	33.8482	1.10755
$935$	0.0730329	0.00238843
$936$	41.2908	1.34963
$937$	−45.2152	−1.47712	−0.738558	−	0.674190i	$-0.764493\pi$
$937$	−45.2152	−1.47712	−0.738558	+	0.674190i	$0.764493\pi$
$938$	1.47873	0.0482821
$939$	37.7627	1.23234
$940$	4.68400	0.152775
$941$	−41.9913	−1.36888	−0.684438	−	0.729071i	$-0.739953\pi$
$941$	−41.9913	−1.36888	−0.684438	+	0.729071i	$0.739953\pi$
$942$	−15.1597	−0.493928
$943$	28.6243	0.932135
$944$	−25.7596	−0.838402
$945$	0.155708	0.00506518
$946$	9.98538	0.324653
$947$	−16.3529	−0.531396	−0.265698	−	0.964056i	$-0.585602\pi$
$947$	−16.3529	−0.531396	−0.265698	+	0.964056i	$0.585602\pi$
$948$	−17.5022	−0.568446
$949$	−36.3584	−1.18024
$950$	−0.820255	−0.0266126
$951$	72.3077	2.34474
$952$	−0.152240	−0.00493411
$953$	−56.4313	−1.82799	−0.913995	−	0.405725i	$-0.867019\pi$
$953$	−56.4313	−1.82799	−0.913995	+	0.405725i	$0.867019\pi$
$954$	32.1561	1.04109
$955$	−2.53195	−0.0819320
$956$	−1.26490	−0.0409098
$957$	14.9906	0.484578
$958$	−27.2870	−0.881602
$959$	−11.0480	−0.356759
$960$	−21.9136	−0.707259
$961$	−4.21482	−0.135962
$962$	−14.3217	−0.461752
$963$	−20.2703	−0.653202
$964$	−2.33446	−0.0751879
$965$	−15.2175	−0.489868
$966$	−14.0319	−0.451469
$967$	−9.96427	−0.320429	−0.160215	−	0.987082i	$-0.551219\pi$
$967$	−9.96427	−0.320429	−0.160215	+	0.987082i	$0.551219\pi$
$968$	27.0181	0.868393
$969$	0.0809166	0.00259941
$970$	−6.75935	−0.217030
$971$	50.6361	1.62499	0.812495	−	0.582969i	$-0.198109\pi$
$971$	50.6361	1.62499	0.812495	+	0.582969i	$0.198109\pi$
$972$	9.90477	0.317696
$973$	0.473739	0.0151874
$974$	−39.7072	−1.27230
$975$	−10.8843	−0.348577
$976$	−28.1322	−0.900490
$977$	36.0245	1.15252	0.576262	−	0.817265i	$-0.304511\pi$
$977$	36.0245	1.15252	0.576262	+	0.817265i	$0.304511\pi$
$978$	−63.3158	−2.02462
$979$	19.4825	0.622662
$980$	0.447139	0.0142833
$981$	−54.8603	−1.75155
$982$	−4.84978	−0.154763
$983$	−51.3856	−1.63895	−0.819473	−	0.573118i	$-0.805734\pi$
$983$	−51.3856	−1.63895	−0.819473	+	0.573118i	$0.805734\pi$
$984$	−47.0017	−1.49836
$985$	−23.6872	−0.754736
$986$	−0.258893	−0.00824484
$987$	−25.7945	−0.821047
$988$	−1.30099	−0.0413900
$989$	25.0484	0.796493
$990$	−5.58422	−0.177478
$991$	−31.4982	−1.00057	−0.500287	−	0.865859i	$-0.666772\pi$
$991$	−31.4982	−1.00057	−0.500287	+	0.865859i	$0.666772\pi$
$992$	−12.8244	−0.407175
$993$	23.5556	0.747515
$994$	5.86500	0.186026
$995$	19.3994	0.615002
$996$	9.63840	0.305405
$997$	27.4756	0.870163	0.435081	−	0.900391i	$-0.356720\pi$
$997$	27.4756	0.870163	0.435081	+	0.900391i	$0.356720\pi$
$998$	11.9207	0.377344
$999$	0.404848	0.0128088

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8015.2.a.l.1.43	✓	62

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8015.2.a.l.1.43	✓	62	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:	\( N \)	\(=\)	\( 8015 = 5 \cdot 7 \cdot 229 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8015.a (trivial)

\(f(q)\)	\(=\)	\(q+1.24614 q^{2} +2.46236 q^{3} -0.447139 q^{4} -1.00000 q^{5} +3.06845 q^{6} -1.00000 q^{7} -3.04947 q^{8} +3.06324 q^{9} +O(q^{10})\)	\(q+1.24614 q^{2} +2.46236 q^{3} -0.447139 q^{4} -1.00000 q^{5} +3.06845 q^{6} -1.00000 q^{7} -3.04947 q^{8} +3.06324 q^{9} -1.24614 q^{10} +1.46291 q^{11} -1.10102 q^{12} -4.42027 q^{13} -1.24614 q^{14} -2.46236 q^{15} -2.90579 q^{16} -0.0499232 q^{17} +3.81722 q^{18} -0.658238 q^{19} +0.447139 q^{20} -2.46236 q^{21} +1.82298 q^{22} +4.57297 q^{23} -7.50891 q^{24} +1.00000 q^{25} -5.50827 q^{26} +0.155708 q^{27} +0.447139 q^{28} +4.16152 q^{29} -3.06845 q^{30} -5.17544 q^{31} +2.47793 q^{32} +3.60220 q^{33} -0.0622113 q^{34} +1.00000 q^{35} -1.36969 q^{36} +2.60005 q^{37} -0.820255 q^{38} -10.8843 q^{39} +3.04947 q^{40} +6.25946 q^{41} -3.06845 q^{42} +5.47750 q^{43} -0.654122 q^{44} -3.06324 q^{45} +5.69855 q^{46} +10.4755 q^{47} -7.15511 q^{48} +1.00000 q^{49} +1.24614 q^{50} -0.122929 q^{51} +1.97647 q^{52} +8.42397 q^{53} +0.194034 q^{54} -1.46291 q^{55} +3.04947 q^{56} -1.62082 q^{57} +5.18582 q^{58} +8.86491 q^{59} +1.10102 q^{60} +9.68144 q^{61} -6.44931 q^{62} -3.06324 q^{63} +8.89942 q^{64} +4.42027 q^{65} +4.48885 q^{66} -1.18665 q^{67} +0.0223226 q^{68} +11.2603 q^{69} +1.24614 q^{70} -4.70654 q^{71} -9.34126 q^{72} +8.22538 q^{73} +3.24002 q^{74} +2.46236 q^{75} +0.294324 q^{76} -1.46291 q^{77} -13.5634 q^{78} +15.8964 q^{79} +2.90579 q^{80} -8.80630 q^{81} +7.80015 q^{82} -8.75408 q^{83} +1.10102 q^{84} +0.0499232 q^{85} +6.82572 q^{86} +10.2472 q^{87} -4.46109 q^{88} +13.3176 q^{89} -3.81722 q^{90} +4.42027 q^{91} -2.04475 q^{92} -12.7438 q^{93} +13.0539 q^{94} +0.658238 q^{95} +6.10157 q^{96} +5.42424 q^{97} +1.24614 q^{98} +4.48122 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 62 q + 2 q^{2} + 11 q^{3} + 64 q^{4} - 62 q^{5} + 3 q^{6} - 62 q^{7} + 15 q^{8} + 69 q^{9}+O(q^{10}) \) 62 * q + 2 * q^2 + 11 * q^3 + 64 * q^4 - 62 * q^5 + 3 * q^6 - 62 * q^7 + 15 * q^8 + 69 * q^9	\( 62 q + 2 q^{2} + 11 q^{3} + 64 q^{4} - 62 q^{5} + 3 q^{6} - 62 q^{7} + 15 q^{8} + 69 q^{9} - 2 q^{10} - 13 q^{11} + 37 q^{12} + 31 q^{13} - 2 q^{14} - 11 q^{15} + 64 q^{16} + 30 q^{17} + 18 q^{18} + 20 q^{19} - 64 q^{20} - 11 q^{21} + 7 q^{22} + 29 q^{24} + 62 q^{25} + 59 q^{27} - 64 q^{28} - 29 q^{29} - 3 q^{30} + 20 q^{31} + 22 q^{32} + 72 q^{33} + 13 q^{34} + 62 q^{35} + 53 q^{36} + 35 q^{37} + 34 q^{38} - 6 q^{39} - 15 q^{40} + 13 q^{41} - 3 q^{42} - 4 q^{43} - 44 q^{44} - 69 q^{45} - 19 q^{46} + 58 q^{47} + 64 q^{48} + 62 q^{49} + 2 q^{50} - 30 q^{51} + 82 q^{52} + 18 q^{53} + 22 q^{54} + 13 q^{55} - 15 q^{56} + 21 q^{57} + 18 q^{58} - 11 q^{59} - 37 q^{60} + 24 q^{61} + 48 q^{62} - 69 q^{63} + 65 q^{64} - 31 q^{65} + 25 q^{66} - 6 q^{67} + 65 q^{68} + 27 q^{69} + 2 q^{70} - 35 q^{71} + 53 q^{72} + 116 q^{73} - 69 q^{74} + 11 q^{75} + 65 q^{76} + 13 q^{77} + 102 q^{78} - 83 q^{79} - 64 q^{80} + 126 q^{81} + 71 q^{82} + 84 q^{83} - 37 q^{84} - 30 q^{85} + 24 q^{86} + 49 q^{87} + 20 q^{88} - 16 q^{89} - 18 q^{90} - 31 q^{91} + 19 q^{92} + 65 q^{93} + 54 q^{94} - 20 q^{95} + 17 q^{96} + 155 q^{97} + 2 q^{98} + 6 q^{99}+O(q^{100}) \) 62 * q + 2 * q^2 + 11 * q^3 + 64 * q^4 - 62 * q^5 + 3 * q^6 - 62 * q^7 + 15 * q^8 + 69 * q^9 - 2 * q^10 - 13 * q^11 + 37 * q^12 + 31 * q^13 - 2 * q^14 - 11 * q^15 + 64 * q^16 + 30 * q^17 + 18 * q^18 + 20 * q^19 - 64 * q^20 - 11 * q^21 + 7 * q^22 + 29 * q^24 + 62 * q^25 + 59 * q^27 - 64 * q^28 - 29 * q^29 - 3 * q^30 + 20 * q^31 + 22 * q^32 + 72 * q^33 + 13 * q^34 + 62 * q^35 + 53 * q^36 + 35 * q^37 + 34 * q^38 - 6 * q^39 - 15 * q^40 + 13 * q^41 - 3 * q^42 - 4 * q^43 - 44 * q^44 - 69 * q^45 - 19 * q^46 + 58 * q^47 + 64 * q^48 + 62 * q^49 + 2 * q^50 - 30 * q^51 + 82 * q^52 + 18 * q^53 + 22 * q^54 + 13 * q^55 - 15 * q^56 + 21 * q^57 + 18 * q^58 - 11 * q^59 - 37 * q^60 + 24 * q^61 + 48 * q^62 - 69 * q^63 + 65 * q^64 - 31 * q^65 + 25 * q^66 - 6 * q^67 + 65 * q^68 + 27 * q^69 + 2 * q^70 - 35 * q^71 + 53 * q^72 + 116 * q^73 - 69 * q^74 + 11 * q^75 + 65 * q^76 + 13 * q^77 + 102 * q^78 - 83 * q^79 - 64 * q^80 + 126 * q^81 + 71 * q^82 + 84 * q^83 - 37 * q^84 - 30 * q^85 + 24 * q^86 + 49 * q^87 + 20 * q^88 - 16 * q^89 - 18 * q^90 - 31 * q^91 + 19 * q^92 + 65 * q^93 + 54 * q^94 - 20 * q^95 + 17 * q^96 + 155 * q^97 + 2 * q^98 + 6 * q^99

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