LMFDB - Embedded newform 8015.2.a.l.1.51

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			1.51
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)

$f(q)$	$=$	$q+2.00507 q^{2} -2.97462 q^{3} +2.02029 q^{4} -1.00000 q^{5} -5.96432 q^{6} -1.00000 q^{7} +0.0406892 q^{8} +5.84839 q^{9} +O(q^{10})$	\(q+2.00507 q^{2} -2.97462 q^{3} +2.02029 q^{4} -1.00000 q^{5} -5.96432 q^{6} -1.00000 q^{7} +0.0406892 q^{8} +5.84839 q^{9} -2.00507 q^{10} -4.21808 q^{11} -6.00961 q^{12} +0.537768 q^{13} -2.00507 q^{14} +2.97462 q^{15} -3.95900 q^{16} +5.04173 q^{17} +11.7264 q^{18} -1.80467 q^{19} -2.02029 q^{20} +2.97462 q^{21} -8.45753 q^{22} +0.0595591 q^{23} -0.121035 q^{24} +1.00000 q^{25} +1.07826 q^{26} -8.47289 q^{27} -2.02029 q^{28} +3.07069 q^{29} +5.96432 q^{30} -3.60353 q^{31} -8.01944 q^{32} +12.5472 q^{33} +10.1090 q^{34} +1.00000 q^{35} +11.8155 q^{36} -10.8597 q^{37} -3.61849 q^{38} -1.59966 q^{39} -0.0406892 q^{40} -4.34933 q^{41} +5.96432 q^{42} -7.91072 q^{43} -8.52176 q^{44} -5.84839 q^{45} +0.119420 q^{46} -2.71923 q^{47} +11.7765 q^{48} +1.00000 q^{49} +2.00507 q^{50} -14.9973 q^{51} +1.08645 q^{52} -6.21568 q^{53} -16.9887 q^{54} +4.21808 q^{55} -0.0406892 q^{56} +5.36822 q^{57} +6.15693 q^{58} -3.72905 q^{59} +6.00961 q^{60} -2.31653 q^{61} -7.22533 q^{62} -5.84839 q^{63} -8.16151 q^{64} -0.537768 q^{65} +25.1580 q^{66} +1.76203 q^{67} +10.1858 q^{68} -0.177166 q^{69} +2.00507 q^{70} -6.64223 q^{71} +0.237966 q^{72} +3.46914 q^{73} -21.7745 q^{74} -2.97462 q^{75} -3.64597 q^{76} +4.21808 q^{77} -3.20742 q^{78} +16.1254 q^{79} +3.95900 q^{80} +7.65849 q^{81} -8.72069 q^{82} +9.34281 q^{83} +6.00961 q^{84} -5.04173 q^{85} -15.8615 q^{86} -9.13414 q^{87} -0.171630 q^{88} +12.1526 q^{89} -11.7264 q^{90} -0.537768 q^{91} +0.120327 q^{92} +10.7192 q^{93} -5.45224 q^{94} +1.80467 q^{95} +23.8548 q^{96} +4.40673 q^{97} +2.00507 q^{98} -24.6690 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	2.00507	1.41780	0.708898	−	0.705311i	$-0.249193\pi$
$2$	2.00507	1.41780	0.708898	+	0.705311i	$0.249193\pi$
$3$	−2.97462	−1.71740	−0.858700	−	0.512478i	$-0.828727\pi$
$3$	−2.97462	−1.71740	−0.858700	+	0.512478i	$0.828727\pi$
$4$	2.02029	1.01015
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−5.96432	−2.43492
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	0.0406892	0.0143858
$9$	5.84839	1.94946
$10$	−2.00507	−0.634058
$11$	−4.21808	−1.27180	−0.635900	−	0.771772i	$-0.719371\pi$
$11$	−4.21808	−1.27180	−0.635900	+	0.771772i	$0.719371\pi$
$12$	−6.00961	−1.73483
$13$	0.537768	0.149150	0.0745750	−	0.997215i	$-0.476240\pi$
$13$	0.537768	0.149150	0.0745750	+	0.997215i	$0.476240\pi$
$14$	−2.00507	−0.535877
$15$	2.97462	0.768045
$16$	−3.95900	−0.989750
$17$	5.04173	1.22280	0.611400	−	0.791322i	$-0.290607\pi$
$17$	5.04173	1.22280	0.611400	+	0.791322i	$0.290607\pi$
$18$	11.7264	2.76394
$19$	−1.80467	−0.414020	−0.207010	−	0.978339i	$-0.566373\pi$
$19$	−1.80467	−0.414020	−0.207010	+	0.978339i	$0.566373\pi$
$20$	−2.02029	−0.451751
$21$	2.97462	0.649116
$22$	−8.45753	−1.80315
$23$	0.0595591	0.0124189	0.00620946	−	0.999981i	$-0.498023\pi$
$23$	0.0595591	0.0124189	0.00620946	+	0.999981i	$0.498023\pi$
$24$	−0.121035	−0.0247062
$25$	1.00000	0.200000
$26$	1.07826	0.211464
$27$	−8.47289	−1.63061
$28$	−2.02029	−0.381800
$29$	3.07069	0.570212	0.285106	−	0.958496i	$-0.407971\pi$
$29$	3.07069	0.570212	0.285106	+	0.958496i	$0.407971\pi$
$30$	5.96432	1.08893
$31$	−3.60353	−0.647214	−0.323607	−	0.946192i	$-0.604896\pi$
$31$	−3.60353	−0.647214	−0.323607	+	0.946192i	$0.604896\pi$
$32$	−8.01944	−1.41765
$33$	12.5472	2.18419
$34$	10.1090	1.73368
$35$	1.00000	0.169031
$36$	11.8155	1.96924
$37$	−10.8597	−1.78533	−0.892666	−	0.450719i	$-0.851168\pi$
$37$	−10.8597	−1.78533	−0.892666	+	0.450719i	$0.851168\pi$
$38$	−3.61849	−0.586997
$39$	−1.59966	−0.256150
$40$	−0.0406892	−0.00643352
$41$	−4.34933	−0.679250	−0.339625	−	0.940561i	$-0.610300\pi$
$41$	−4.34933	−0.679250	−0.339625	+	0.940561i	$0.610300\pi$
$42$	5.96432	0.920315
$43$	−7.91072	−1.20637	−0.603187	−	0.797600i	$-0.706103\pi$
$43$	−7.91072	−1.20637	−0.603187	+	0.797600i	$0.706103\pi$
$44$	−8.52176	−1.28470
$45$	−5.84839	−0.871826
$46$	0.119420	0.0176075
$47$	−2.71923	−0.396640	−0.198320	−	0.980137i	$-0.563549\pi$
$47$	−2.71923	−0.396640	−0.198320	+	0.980137i	$0.563549\pi$
$48$	11.7765	1.69980
$49$	1.00000	0.142857
$50$	2.00507	0.283559
$51$	−14.9973	−2.10004
$52$	1.08645	0.150663
$53$	−6.21568	−0.853789	−0.426895	−	0.904301i	$-0.640392\pi$
$53$	−6.21568	−0.853789	−0.426895	+	0.904301i	$0.640392\pi$
$54$	−16.9887	−2.31187
$55$	4.21808	0.568766
$56$	−0.0406892	−0.00543732
$57$	5.36822	0.711039
$58$	6.15693	0.808445
$59$	−3.72905	−0.485482	−0.242741	−	0.970091i	$-0.578046\pi$
$59$	−3.72905	−0.485482	−0.242741	+	0.970091i	$0.578046\pi$
$60$	6.00961	0.775838
$61$	−2.31653	−0.296602	−0.148301	−	0.988942i	$-0.547380\pi$
$61$	−2.31653	−0.296602	−0.148301	+	0.988942i	$0.547380\pi$
$62$	−7.22533	−0.917618
$63$	−5.84839	−0.736828
$64$	−8.16151	−1.02019
$65$	−0.537768	−0.0667019
$66$	25.1580	3.09673
$67$	1.76203	0.215266	0.107633	−	0.994191i	$-0.465673\pi$
$67$	1.76203	0.215266	0.107633	+	0.994191i	$0.465673\pi$
$68$	10.1858	1.23521
$69$	−0.177166	−0.0213283
$70$	2.00507	0.239651
$71$	−6.64223	−0.788287	−0.394144	−	0.919049i	$-0.628959\pi$
$71$	−6.64223	−0.788287	−0.394144	+	0.919049i	$0.628959\pi$
$72$	0.237966	0.0280446
$73$	3.46914	0.406033	0.203016	−	0.979175i	$-0.434926\pi$
$73$	3.46914	0.406033	0.203016	+	0.979175i	$0.434926\pi$
$74$	−21.7745	−2.53124
$75$	−2.97462	−0.343480
$76$	−3.64597	−0.418221
$77$	4.21808	0.480695
$78$	−3.20742	−0.363169
$79$	16.1254	1.81425	0.907126	−	0.420859i	$-0.138271\pi$
$79$	16.1254	1.81425	0.907126	+	0.420859i	$0.138271\pi$
$80$	3.95900	0.442630
$81$	7.65849	0.850943
$82$	−8.72069	−0.963039
$83$	9.34281	1.02551	0.512754	−	0.858536i	$-0.328625\pi$
$83$	9.34281	1.02551	0.512754	+	0.858536i	$0.328625\pi$
$84$	6.00961	0.655703
$85$	−5.04173	−0.546853
$86$	−15.8615	−1.71039
$87$	−9.13414	−0.979282
$88$	−0.171630	−0.0182958
$89$	12.1526	1.28817	0.644087	−	0.764952i	$-0.277238\pi$
$89$	12.1526	1.28817	0.644087	+	0.764952i	$0.277238\pi$
$90$	−11.7264	−1.23607
$91$	−0.537768	−0.0563734
$92$	0.120327	0.0125449
$93$	10.7192	1.11153
$94$	−5.45224	−0.562355
$95$	1.80467	0.185156
$96$	23.8548	2.43467
$97$	4.40673	0.447436	0.223718	−	0.974654i	$-0.428181\pi$
$97$	4.40673	0.447436	0.223718	+	0.974654i	$0.428181\pi$
$98$	2.00507	0.202542
$99$	−24.6690	−2.47933
$100$	2.02029	0.202029
$101$	3.68268	0.366440	0.183220	−	0.983072i	$-0.441348\pi$
$101$	3.68268	0.366440	0.183220	+	0.983072i	$0.441348\pi$
$102$	−30.0705	−2.97742
$103$	12.9844	1.27939	0.639694	−	0.768630i	$-0.279061\pi$
$103$	12.9844	1.27939	0.639694	+	0.768630i	$0.279061\pi$
$104$	0.0218813	0.00214564
$105$	−2.97462	−0.290294
$106$	−12.4628	−1.21050
$107$	−17.6012	−1.70157	−0.850785	−	0.525513i	$-0.823873\pi$
$107$	−17.6012	−1.70157	−0.850785	+	0.525513i	$0.823873\pi$
$108$	−17.1177	−1.64715
$109$	−5.15431	−0.493693	−0.246846	−	0.969055i	$-0.579394\pi$
$109$	−5.15431	−0.493693	−0.246846	+	0.969055i	$0.579394\pi$
$110$	8.45753	0.806394
$111$	32.3037	3.06613
$112$	3.95900	0.374091
$113$	−1.23862	−0.116520	−0.0582599	−	0.998301i	$-0.518555\pi$
$113$	−1.23862	−0.116520	−0.0582599	+	0.998301i	$0.518555\pi$
$114$	10.7636	1.00811
$115$	−0.0595591	−0.00555391
$116$	6.20369	0.575998
$117$	3.14508	0.290762
$118$	−7.47700	−0.688314
$119$	−5.04173	−0.462175
$120$	0.121035	0.0110489
$121$	6.79220	0.617473
$122$	−4.64481	−0.420521
$123$	12.9376	1.16654
$124$	−7.28020	−0.653781
$125$	−1.00000	−0.0894427
$126$	−11.7264	−1.04467
$127$	18.8785	1.67520	0.837598	−	0.546287i	$-0.183959\pi$
$127$	18.8785	1.67520	0.837598	+	0.546287i	$0.183959\pi$
$128$	−0.325496	−0.0287701
$129$	23.5314	2.07183
$130$	−1.07826	−0.0945697
$131$	−5.27999	−0.461315	−0.230658	−	0.973035i	$-0.574088\pi$
$131$	−5.27999	−0.461315	−0.230658	+	0.973035i	$0.574088\pi$
$132$	25.3490	2.20635
$133$	1.80467	0.156485
$134$	3.53298	0.305203
$135$	8.47289	0.729230
$136$	0.205144	0.0175909
$137$	−0.940881	−0.0803849	−0.0401924	−	0.999192i	$-0.512797\pi$
$137$	−0.940881	−0.0803849	−0.0401924	+	0.999192i	$0.512797\pi$
$138$	−0.355229	−0.0302391
$139$	−10.5016	−0.890731	−0.445365	−	0.895349i	$-0.646926\pi$
$139$	−10.5016	−0.890731	−0.445365	+	0.895349i	$0.646926\pi$
$140$	2.02029	0.170746
$141$	8.08869	0.681190
$142$	−13.3181	−1.11763
$143$	−2.26835	−0.189689
$144$	−23.1538	−1.92948
$145$	−3.07069	−0.255007
$146$	6.95587	0.575672
$147$	−2.97462	−0.245343
$148$	−21.9399	−1.80345
$149$	4.02623	0.329842	0.164921	−	0.986307i	$-0.447263\pi$
$149$	4.02623	0.329842	0.164921	+	0.986307i	$0.447263\pi$
$150$	−5.96432	−0.486985
$151$	10.9291	0.889397	0.444698	−	0.895680i	$-0.353311\pi$
$151$	10.9291	0.889397	0.444698	+	0.895680i	$0.353311\pi$
$152$	−0.0734306	−0.00595601
$153$	29.4860	2.38380
$154$	8.45753	0.681527
$155$	3.60353	0.289443
$156$	−3.23178	−0.258749
$157$	8.20693	0.654985	0.327492	−	0.944854i	$-0.393796\pi$
$157$	8.20693	0.654985	0.327492	+	0.944854i	$0.393796\pi$
$158$	32.3326	2.57224
$159$	18.4893	1.46630
$160$	8.01944	0.633993
$161$	−0.0595591	−0.00469391
$162$	15.3558	1.20646
$163$	3.61002	0.282758	0.141379	−	0.989956i	$-0.454846\pi$
$163$	3.61002	0.282758	0.141379	+	0.989956i	$0.454846\pi$
$164$	−8.78691	−0.686143
$165$	−12.5472	−0.976799
$166$	18.7330	1.45396
$167$	16.5517	1.28081	0.640405	−	0.768038i	$-0.278767\pi$
$167$	16.5517	1.28081	0.640405	+	0.768038i	$0.278767\pi$
$168$	0.121035	0.00933805
$169$	−12.7108	−0.977754
$170$	−10.1090	−0.775326
$171$	−10.5544	−0.807117
$172$	−15.9820	−1.21861
$173$	20.0193	1.52204	0.761018	−	0.648731i	$-0.224700\pi$
$173$	20.0193	1.52204	0.761018	+	0.648731i	$0.224700\pi$
$174$	−18.3146	−1.38842
$175$	−1.00000	−0.0755929
$176$	16.6994	1.25876
$177$	11.0925	0.833766
$178$	24.3668	1.82637
$179$	−9.85328	−0.736469	−0.368234	−	0.929733i	$-0.620038\pi$
$179$	−9.85328	−0.736469	−0.368234	+	0.929733i	$0.620038\pi$
$180$	−11.8155	−0.880672
$181$	19.1524	1.42359	0.711794	−	0.702389i	$-0.247883\pi$
$181$	19.1524	1.42359	0.711794	+	0.702389i	$0.247883\pi$
$182$	−1.07826	−0.0799260
$183$	6.89082	0.509384
$184$	0.00242341	0.000178656 0
$185$	10.8597	0.798425
$186$	21.4926	1.57592
$187$	−21.2664	−1.55516
$188$	−5.49364	−0.400665
$189$	8.47289	0.616312
$190$	3.61849	0.262513
$191$	4.78905	0.346524	0.173262	−	0.984876i	$-0.444569\pi$
$191$	4.78905	0.346524	0.173262	+	0.984876i	$0.444569\pi$
$192$	24.2774	1.75207
$193$	−6.03763	−0.434598	−0.217299	−	0.976105i	$-0.569725\pi$
$193$	−6.03763	−0.434598	−0.217299	+	0.976105i	$0.569725\pi$
$194$	8.83580	0.634373
$195$	1.59966	0.114554
$196$	2.02029	0.144307
$197$	10.1442	0.722741	0.361371	−	0.932422i	$-0.382309\pi$
$197$	10.1442	0.722741	0.361371	+	0.932422i	$0.382309\pi$
$198$	−49.4630	−3.51518
$199$	6.70984	0.475648	0.237824	−	0.971308i	$-0.423566\pi$
$199$	6.70984	0.475648	0.237824	+	0.971308i	$0.423566\pi$
$200$	0.0406892	0.00287716
$201$	−5.24137	−0.369698
$202$	7.38402	0.519538
$203$	−3.07069	−0.215520
$204$	−30.2989	−2.12134
$205$	4.34933	0.303770
$206$	26.0345	1.81391
$207$	0.348325	0.0242102
$208$	−2.12902	−0.147621
$209$	7.61226	0.526551
$210$	−5.96432	−0.411577
$211$	−20.0259	−1.37864	−0.689321	−	0.724456i	$-0.742091\pi$
$211$	−20.0259	−1.37864	−0.689321	+	0.724456i	$0.742091\pi$
$212$	−12.5575	−0.862452
$213$	19.7581	1.35380
$214$	−35.2916	−2.41248
$215$	7.91072	0.539507
$216$	−0.344755	−0.0234576
$217$	3.60353	0.244624
$218$	−10.3347	−0.699956
$219$	−10.3194	−0.697320
$220$	8.52176	0.574537
$221$	2.71128	0.182381
$222$	64.7710	4.34715
$223$	4.60789	0.308567	0.154284	−	0.988027i	$-0.450693\pi$
$223$	4.60789	0.308567	0.154284	+	0.988027i	$0.450693\pi$
$224$	8.01944	0.535821
$225$	5.84839	0.389893
$226$	−2.48352	−0.165201
$227$	−9.82621	−0.652189	−0.326094	−	0.945337i	$-0.605733\pi$
$227$	−9.82621	−0.652189	−0.326094	+	0.945337i	$0.605733\pi$
$228$	10.8454	0.718253
$229$	1.00000	0.0660819
$229$	1.00000	0.0660819
$230$	−0.119420	−0.00787431
$231$	−12.5472	−0.825545
$232$	0.124944	0.00820295
$233$	26.5562	1.73975	0.869876	−	0.493271i	$-0.164199\pi$
$233$	26.5562	1.73975	0.869876	+	0.493271i	$0.164199\pi$
$234$	6.30609	0.412242
$235$	2.71923	0.177383
$236$	−7.53378	−0.490408
$237$	−47.9671	−3.11580
$238$	−10.1090	−0.655270
$239$	0.0705261	0.00456196	0.00228098	−	0.999997i	$-0.499274\pi$
$239$	0.0705261	0.00456196	0.00228098	+	0.999997i	$0.499274\pi$
$240$	−11.7765	−0.760173
$241$	6.36305	0.409880	0.204940	−	0.978774i	$-0.434300\pi$
$241$	6.36305	0.409880	0.204940	+	0.978774i	$0.434300\pi$
$242$	13.6188	0.875451
$243$	2.63753	0.169198
$244$	−4.68008	−0.299611
$245$	−1.00000	−0.0638877
$246$	25.9408	1.65392
$247$	−0.970495	−0.0617511
$248$	−0.146625	−0.00931068
$249$	−27.7914	−1.76121
$250$	−2.00507	−0.126812
$251$	−26.6127	−1.67978	−0.839888	−	0.542759i	$-0.817380\pi$
$251$	−26.6127	−1.67978	−0.839888	+	0.542759i	$0.817380\pi$
$252$	−11.8155	−0.744304
$253$	−0.251225	−0.0157944
$254$	37.8527	2.37509
$255$	14.9973	0.939165
$256$	15.6704	0.979399
$257$	27.4541	1.71254	0.856271	−	0.516526i	$-0.172775\pi$
$257$	27.4541	1.71254	0.856271	+	0.516526i	$0.172775\pi$
$258$	47.1821	2.93743
$259$	10.8597	0.674792
$260$	−1.08645	−0.0673787
$261$	17.9586	1.11161
$262$	−10.5867	−0.654051
$263$	−16.0791	−0.991478	−0.495739	−	0.868471i	$-0.665103\pi$
$263$	−16.0791	−0.991478	−0.495739	+	0.868471i	$0.665103\pi$
$264$	0.510535	0.0314213
$265$	6.21568	0.381826
$266$	3.61849	0.221864
$267$	−36.1494	−2.21231
$268$	3.55981	0.217450
$269$	25.4706	1.55297	0.776486	−	0.630135i	$-0.217000\pi$
$269$	25.4706	1.55297	0.776486	+	0.630135i	$0.217000\pi$
$270$	16.9887	1.03390
$271$	19.4672	1.18255	0.591274	−	0.806471i	$-0.298625\pi$
$271$	19.4672	1.18255	0.591274	+	0.806471i	$0.298625\pi$
$272$	−19.9602	−1.21027
$273$	1.59966	0.0968157
$274$	−1.88653	−0.113969
$275$	−4.21808	−0.254360
$276$	−0.357927	−0.0215447
$277$	−1.94385	−0.116794	−0.0583972	−	0.998293i	$-0.518599\pi$
$277$	−1.94385	−0.116794	−0.0583972	+	0.998293i	$0.518599\pi$
$278$	−21.0563	−1.26287
$279$	−21.0749	−1.26172
$280$	0.0406892	0.00243164
$281$	0.724470	0.0432182	0.0216091	−	0.999766i	$-0.493121\pi$
$281$	0.724470	0.0432182	0.0216091	+	0.999766i	$0.493121\pi$
$282$	16.2184	0.965789
$283$	−15.5685	−0.925449	−0.462724	−	0.886502i	$-0.653128\pi$
$283$	−15.5685	−0.925449	−0.462724	+	0.886502i	$0.653128\pi$
$284$	−13.4192	−0.796286
$285$	−5.36822	−0.317986
$286$	−4.54819	−0.268940
$287$	4.34933	0.256733
$288$	−46.9008	−2.76366
$289$	8.41906	0.495239
$290$	−6.15693	−0.361547
$291$	−13.1084	−0.768427
$292$	7.00869	0.410152
$293$	−3.24922	−0.189822	−0.0949108	−	0.995486i	$-0.530257\pi$
$293$	−3.24922	−0.189822	−0.0949108	+	0.995486i	$0.530257\pi$
$294$	−5.96432	−0.347846
$295$	3.72905	0.217114
$296$	−0.441874	−0.0256834
$297$	35.7393	2.07381
$298$	8.07287	0.467649
$299$	0.0320290	0.00185228
$300$	−6.00961	−0.346965
$301$	7.91072	0.455966
$302$	21.9136	1.26098
$303$	−10.9546	−0.629325
$304$	7.14470	0.409777
$305$	2.31653	0.132644
$306$	59.1214	3.37975
$307$	−25.7115	−1.46743	−0.733717	−	0.679455i	$-0.762216\pi$
$307$	−25.7115	−1.46743	−0.733717	+	0.679455i	$0.762216\pi$
$308$	8.52176	0.485572
$309$	−38.6236	−2.19722
$310$	7.22533	0.410371
$311$	−13.4262	−0.761330	−0.380665	−	0.924713i	$-0.624305\pi$
$311$	−13.4262	−0.761330	−0.380665	+	0.924713i	$0.624305\pi$
$312$	−0.0650887	−0.00368492
$313$	−10.9285	−0.617718	−0.308859	−	0.951108i	$-0.599947\pi$
$313$	−10.9285	−0.617718	−0.308859	+	0.951108i	$0.599947\pi$
$314$	16.4555	0.928635
$315$	5.84839	0.329519
$316$	32.5781	1.83266
$317$	34.2758	1.92512	0.962560	−	0.271068i	$-0.0873767\pi$
$317$	34.2758	1.92512	0.962560	+	0.271068i	$0.0873767\pi$
$318$	37.0723	2.07891
$319$	−12.9524	−0.725195
$320$	8.16151	0.456242
$321$	52.3569	2.92228
$322$	−0.119420	−0.00665501
$323$	−9.09868	−0.506264
$324$	15.4724	0.859578
$325$	0.537768	0.0298300
$326$	7.23832	0.400894
$327$	15.3321	0.847868
$328$	−0.176970	−0.00977155
$329$	2.71923	0.149916
$330$	−25.1580	−1.38490
$331$	31.2613	1.71828	0.859138	−	0.511744i	$-0.171000\pi$
$331$	31.2613	1.71828	0.859138	+	0.511744i	$0.171000\pi$
$332$	18.8752	1.03591
$333$	−63.5120	−3.48044
$334$	33.1873	1.81593
$335$	−1.76203	−0.0962699
$336$	−11.7765	−0.642463
$337$	−19.7364	−1.07511	−0.537554	−	0.843229i	$-0.680652\pi$
$337$	−19.7364	−1.07511	−0.537554	+	0.843229i	$0.680652\pi$
$338$	−25.4860	−1.38626
$339$	3.68444	0.200111
$340$	−10.1858	−0.552401
$341$	15.2000	0.823126
$342$	−21.1623	−1.14433
$343$	−1.00000	−0.0539949
$344$	−0.321880	−0.0173546
$345$	0.177166	0.00953829
$346$	40.1400	2.15794
$347$	14.2612	0.765581	0.382790	−	0.923835i	$-0.374963\pi$
$347$	14.2612	0.765581	0.382790	+	0.923835i	$0.374963\pi$
$348$	−18.4536	−0.989219
$349$	26.0146	1.39253	0.696266	−	0.717784i	$-0.254843\pi$
$349$	26.0146	1.39253	0.696266	+	0.717784i	$0.254843\pi$
$350$	−2.00507	−0.107175
$351$	−4.55645	−0.243205
$352$	33.8267	1.80297
$353$	25.7693	1.37156	0.685781	−	0.727808i	$-0.259461\pi$
$353$	25.7693	1.37156	0.685781	+	0.727808i	$0.259461\pi$
$354$	22.2413	1.18211
$355$	6.64223	0.352533
$356$	24.5518	1.30124
$357$	14.9973	0.793739
$358$	−19.7565	−1.04416
$359$	3.32748	0.175618	0.0878089	−	0.996137i	$-0.472014\pi$
$359$	3.32748	0.175618	0.0878089	+	0.996137i	$0.472014\pi$
$360$	−0.237966	−0.0125419
$361$	−15.7432	−0.828587
$362$	38.4019	2.01836
$363$	−20.2043	−1.06045
$364$	−1.08645	−0.0569454
$365$	−3.46914	−0.181583
$366$	13.8166	0.722203
$367$	25.1398	1.31229	0.656144	−	0.754635i	$-0.272186\pi$
$367$	25.1398	1.31229	0.656144	+	0.754635i	$0.272186\pi$
$368$	−0.235794	−0.0122916
$369$	−25.4365	−1.32417
$370$	21.7745	1.13200
$371$	6.21568	0.322702
$372$	21.6558	1.12280
$373$	6.46116	0.334546	0.167273	−	0.985911i	$-0.446504\pi$
$373$	6.46116	0.334546	0.167273	+	0.985911i	$0.446504\pi$
$374$	−42.6406	−2.20489
$375$	2.97462	0.153609
$376$	−0.110643	−0.00570599
$377$	1.65132	0.0850471
$378$	16.9887	0.873805
$379$	−34.4818	−1.77121	−0.885604	−	0.464440i	$-0.846256\pi$
$379$	−34.4818	−1.77121	−0.885604	+	0.464440i	$0.846256\pi$
$380$	3.64597	0.187034
$381$	−56.1565	−2.87698
$382$	9.60237	0.491300
$383$	−34.4404	−1.75982	−0.879911	−	0.475139i	$-0.842398\pi$
$383$	−34.4404	−1.75982	−0.879911	+	0.475139i	$0.842398\pi$
$384$	0.968230	0.0494098
$385$	−4.21808	−0.214973
$386$	−12.1059	−0.616172
$387$	−46.2650	−2.35178
$388$	8.90290	0.451976
$389$	−8.42958	−0.427397	−0.213698	−	0.976900i	$-0.568551\pi$
$389$	−8.42958	−0.427397	−0.213698	+	0.976900i	$0.568551\pi$
$390$	3.20742	0.162414
$391$	0.300281	0.0151859
$392$	0.0406892	0.00205511
$393$	15.7060	0.792263
$394$	20.3397	1.02470
$395$	−16.1254	−0.811358
$396$	−49.8386	−2.50448
$397$	−2.36237	−0.118564	−0.0592820	−	0.998241i	$-0.518881\pi$
$397$	−2.36237	−0.118564	−0.0592820	+	0.998241i	$0.518881\pi$
$398$	13.4537	0.674372
$399$	−5.36822	−0.268747
$400$	−3.95900	−0.197950
$401$	−4.92460	−0.245923	−0.122961	−	0.992411i	$-0.539239\pi$
$401$	−4.92460	−0.245923	−0.122961	+	0.992411i	$0.539239\pi$
$402$	−10.5093	−0.524156
$403$	−1.93787	−0.0965320
$404$	7.44009	0.370158
$405$	−7.65849	−0.380553
$406$	−6.15693	−0.305563
$407$	45.8073	2.27058
$408$	−0.610226	−0.0302107
$409$	−13.7940	−0.682067	−0.341034	−	0.940051i	$-0.610777\pi$
$409$	−13.7940	−0.682067	−0.341034	+	0.940051i	$0.610777\pi$
$410$	8.72069	0.430684
$411$	2.79877	0.138053
$412$	26.2322	1.29237
$413$	3.72905	0.183495
$414$	0.698414	0.0343252
$415$	−9.34281	−0.458621
$416$	−4.31260	−0.211443
$417$	31.2382	1.52974
$418$	15.2631	0.746542
$419$	−5.80673	−0.283678	−0.141839	−	0.989890i	$-0.545301\pi$
$419$	−5.80673	−0.283678	−0.141839	+	0.989890i	$0.545301\pi$
$420$	−6.00961	−0.293239
$421$	12.5564	0.611959	0.305980	−	0.952038i	$-0.401016\pi$
$421$	12.5564	0.611959	0.305980	+	0.952038i	$0.401016\pi$
$422$	−40.1533	−1.95463
$423$	−15.9031	−0.773236
$424$	−0.252911	−0.0122824
$425$	5.04173	0.244560
$426$	39.6164	1.91942
$427$	2.31653	0.112105
$428$	−35.5596	−1.71884
$429$	6.74748	0.325772
$430$	15.8615	0.764910
$431$	1.04885	0.0505211	0.0252606	−	0.999681i	$-0.491958\pi$
$431$	1.04885	0.0505211	0.0252606	+	0.999681i	$0.491958\pi$
$432$	33.5442	1.61390
$433$	−20.8286	−1.00096	−0.500480	−	0.865748i	$-0.666843\pi$
$433$	−20.8286	−1.00096	−0.500480	+	0.865748i	$0.666843\pi$
$434$	7.22533	0.346827
$435$	9.13414	0.437948
$436$	−10.4132	−0.498702
$437$	−0.107485	−0.00514169
$438$	−20.6911	−0.988658
$439$	−30.8376	−1.47180	−0.735899	−	0.677091i	$-0.763240\pi$
$439$	−30.8376	−1.47180	−0.735899	+	0.677091i	$0.763240\pi$
$440$	0.171630	0.00818214
$441$	5.84839	0.278495
$442$	5.43630	0.258578
$443$	5.46977	0.259877	0.129938	−	0.991522i	$-0.458522\pi$
$443$	5.46977	0.259877	0.129938	+	0.991522i	$0.458522\pi$
$444$	65.2629	3.09724
$445$	−12.1526	−0.576089
$446$	9.23913	0.437485
$447$	−11.9765	−0.566470
$448$	8.16151	0.385595
$449$	5.27563	0.248972	0.124486	−	0.992221i	$-0.460272\pi$
$449$	5.27563	0.248972	0.124486	+	0.992221i	$0.460272\pi$
$450$	11.7264	0.552788
$451$	18.3458	0.863870
$452$	−2.50238	−0.117702
$453$	−32.5099	−1.52745
$454$	−19.7022	−0.924671
$455$	0.537768	0.0252109
$456$	0.218428	0.0102289
$457$	−10.2876	−0.481235	−0.240617	−	0.970620i	$-0.577350\pi$
$457$	−10.2876	−0.481235	−0.240617	+	0.970620i	$0.577350\pi$
$458$	2.00507	0.0936906
$459$	−42.7180	−1.99391
$460$	−0.120327	−0.00561026
$461$	21.4763	1.00025	0.500126	−	0.865953i	$-0.333287\pi$
$461$	21.4763	1.00025	0.500126	+	0.865953i	$0.333287\pi$
$462$	−25.1580	−1.17046
$463$	−0.554878	−0.0257874	−0.0128937	−	0.999917i	$-0.504104\pi$
$463$	−0.554878	−0.0257874	−0.0128937	+	0.999917i	$0.504104\pi$
$464$	−12.1569	−0.564368
$465$	−10.7192	−0.497089
$466$	53.2469	2.46661
$467$	13.4722	0.623418	0.311709	−	0.950178i	$-0.399099\pi$
$467$	13.4722	0.623418	0.311709	+	0.950178i	$0.399099\pi$
$468$	6.35398	0.293713
$469$	−1.76203	−0.0813629
$470$	5.45224	0.251493
$471$	−24.4125	−1.12487
$472$	−0.151732	−0.00698403
$473$	33.3681	1.53426
$474$	−96.1772	−4.41757
$475$	−1.80467	−0.0828041
$476$	−10.1858	−0.466864
$477$	−36.3517	−1.66443
$478$	0.141410	0.00646792
$479$	−3.22190	−0.147212	−0.0736062	−	0.997287i	$-0.523451\pi$
$479$	−3.22190	−0.147212	−0.0736062	+	0.997287i	$0.523451\pi$
$480$	−23.8548	−1.08882
$481$	−5.84002	−0.266282
$482$	12.7584	0.581127
$483$	0.177166	0.00806132
$484$	13.7222	0.623738
$485$	−4.40673	−0.200100
$486$	5.28843	0.239888
$487$	−15.6127	−0.707481	−0.353740	−	0.935344i	$-0.615090\pi$
$487$	−15.6127	−0.707481	−0.353740	+	0.935344i	$0.615090\pi$
$488$	−0.0942578	−0.00426685
$489$	−10.7384	−0.485609
$490$	−2.00507	−0.0905797
$491$	39.8739	1.79948	0.899742	−	0.436422i	$-0.143755\pi$
$491$	39.8739	1.79948	0.899742	+	0.436422i	$0.143755\pi$
$492$	26.1378	1.17838
$493$	15.4816	0.697255
$494$	−1.94591	−0.0875505
$495$	24.6690	1.10879
$496$	14.2664	0.640580
$497$	6.64223	0.297945
$498$	−55.7235	−2.49703
$499$	36.1402	1.61786	0.808929	−	0.587906i	$-0.200048\pi$
$499$	36.1402	1.61786	0.808929	+	0.587906i	$0.200048\pi$
$500$	−2.02029	−0.0903503
$501$	−49.2351	−2.19966
$502$	−53.3602	−2.38158
$503$	−29.1419	−1.29937	−0.649686	−	0.760203i	$-0.725100\pi$
$503$	−29.1419	−1.29937	−0.649686	+	0.760203i	$0.725100\pi$
$504$	−0.237966	−0.0105998
$505$	−3.68268	−0.163877
$506$	−0.503723	−0.0223932
$507$	37.8099	1.67920
$508$	38.1401	1.69219
$509$	−5.02226	−0.222608	−0.111304	−	0.993786i	$-0.535503\pi$
$509$	−5.02226	−0.222608	−0.111304	+	0.993786i	$0.535503\pi$
$510$	30.0705	1.33154
$511$	−3.46914	−0.153466
$512$	32.0712	1.41736
$513$	15.2908	0.675105
$514$	55.0474	2.42804
$515$	−12.9844	−0.572160
$516$	47.5404	2.09285
$517$	11.4699	0.504447
$518$	21.7745	0.956718
$519$	−59.5498	−2.61394
$520$	−0.0218813	−0.000959559 0
$521$	−25.1235	−1.10068	−0.550341	−	0.834940i	$-0.685502\pi$
$521$	−25.1235	−1.10068	−0.550341	+	0.834940i	$0.685502\pi$
$522$	36.0081	1.57603
$523$	38.1779	1.66940	0.834702	−	0.550702i	$-0.185640\pi$
$523$	38.1779	1.66940	0.834702	+	0.550702i	$0.185640\pi$
$524$	−10.6671	−0.465996
$525$	2.97462	0.129823
$526$	−32.2396	−1.40571
$527$	−18.1681	−0.791413
$528$	−49.6744	−2.16180
$529$	−22.9965	−0.999846
$530$	12.4628	0.541352
$531$	−21.8090	−0.946428
$532$	3.64597	0.158073
$533$	−2.33893	−0.101310
$534$	−72.4820	−3.13660
$535$	17.6012	0.760966
$536$	0.0716954	0.00309677
$537$	29.3098	1.26481
$538$	51.0703	2.20180
$539$	−4.21808	−0.181686
$540$	17.1177	0.736629
$541$	35.4011	1.52201	0.761007	−	0.648744i	$-0.224705\pi$
$541$	35.4011	1.52201	0.761007	+	0.648744i	$0.224705\pi$
$542$	39.0330	1.67661
$543$	−56.9712	−2.44487
$544$	−40.4319	−1.73350
$545$	5.15431	0.220786
$546$	3.20742	0.137265
$547$	−28.2855	−1.20940	−0.604699	−	0.796454i	$-0.706707\pi$
$547$	−28.2855	−1.20940	−0.604699	+	0.796454i	$0.706707\pi$
$548$	−1.90086	−0.0812005
$549$	−13.5480	−0.578214
$550$	−8.45753	−0.360630
$551$	−5.54159	−0.236079
$552$	−0.00720873	−0.000306824 0
$553$	−16.1254	−0.685723
$554$	−3.89754	−0.165591
$555$	−32.3037	−1.37121
$556$	−21.2162	−0.899768
$557$	2.45585	0.104058	0.0520288	−	0.998646i	$-0.483431\pi$
$557$	2.45585	0.104058	0.0520288	+	0.998646i	$0.483431\pi$
$558$	−42.2565	−1.78886
$559$	−4.25413	−0.179931
$560$	−3.95900	−0.167298
$561$	63.2596	2.67082
$562$	1.45261	0.0612746
$563$	30.2286	1.27399	0.636993	−	0.770870i	$-0.280178\pi$
$563$	30.2286	1.27399	0.636993	+	0.770870i	$0.280178\pi$
$564$	16.3415	0.688102
$565$	1.23862	0.0521093
$566$	−31.2158	−1.31210
$567$	−7.65849	−0.321626
$568$	−0.270266	−0.0113401
$569$	−13.8470	−0.580495	−0.290248	−	0.956952i	$-0.593738\pi$
$569$	−13.8470	−0.580495	−0.290248	+	0.956952i	$0.593738\pi$
$570$	−10.7636	−0.450840
$571$	−26.0706	−1.09102	−0.545511	−	0.838104i	$-0.683664\pi$
$571$	−26.0706	−1.09102	−0.545511	+	0.838104i	$0.683664\pi$
$572$	−4.58273	−0.191614
$573$	−14.2456	−0.595120
$574$	8.72069	0.363994
$575$	0.0595591	0.00248378
$576$	−47.7317	−1.98882
$577$	43.7245	1.82027	0.910137	−	0.414308i	$-0.135976\pi$
$577$	43.7245	1.82027	0.910137	+	0.414308i	$0.135976\pi$
$578$	16.8808	0.702148
$579$	17.9597	0.746379
$580$	−6.20369	−0.257594
$581$	−9.34281	−0.387605
$582$	−26.2832	−1.08947
$583$	26.2182	1.08585
$584$	0.141157	0.00584110
$585$	−3.14508	−0.130033
$586$	−6.51491	−0.269129
$587$	33.4838	1.38202	0.691012	−	0.722844i	$-0.257165\pi$
$587$	33.4838	1.38202	0.691012	+	0.722844i	$0.257165\pi$
$588$	−6.00961	−0.247832
$589$	6.50320	0.267960
$590$	7.47700	0.307823
$591$	−30.1751	−1.24124
$592$	42.9938	1.76703
$593$	23.6782	0.972345	0.486173	−	0.873863i	$-0.338393\pi$
$593$	23.6782	0.972345	0.486173	+	0.873863i	$0.338393\pi$
$594$	71.6597	2.94023
$595$	5.04173	0.206691
$596$	8.13417	0.333189
$597$	−19.9593	−0.816878
$598$	0.0642202	0.00262616
$599$	1.85993	0.0759946	0.0379973	−	0.999278i	$-0.487902\pi$
$599$	1.85993	0.0759946	0.0379973	+	0.999278i	$0.487902\pi$
$600$	−0.121035	−0.00494123
$601$	−9.18487	−0.374659	−0.187329	−	0.982297i	$-0.559983\pi$
$601$	−9.18487	−0.374659	−0.187329	+	0.982297i	$0.559983\pi$
$602$	15.8615	0.646467
$603$	10.3050	0.419653
$604$	22.0800	0.898421
$605$	−6.79220	−0.276142
$606$	−21.9647	−0.892254
$607$	28.5474	1.15870	0.579351	−	0.815078i	$-0.303306\pi$
$607$	28.5474	1.15870	0.579351	+	0.815078i	$0.303306\pi$
$608$	14.4725	0.586936
$609$	9.13414	0.370134
$610$	4.64481	0.188063
$611$	−1.46231	−0.0591589
$612$	59.5704	2.40799
$613$	−13.3492	−0.539168	−0.269584	−	0.962977i	$-0.586886\pi$
$613$	−13.3492	−0.539168	−0.269584	+	0.962977i	$0.586886\pi$
$614$	−51.5533	−2.08052
$615$	−12.9376	−0.521695
$616$	0.171630	0.00691517
$617$	−5.06353	−0.203850	−0.101925	−	0.994792i	$-0.532500\pi$
$617$	−5.06353	−0.203850	−0.101925	+	0.994792i	$0.532500\pi$
$618$	−77.4430	−3.11521
$619$	16.9850	0.682683	0.341342	−	0.939939i	$-0.389119\pi$
$619$	16.9850	0.682683	0.341342	+	0.939939i	$0.389119\pi$
$620$	7.28020	0.292380
$621$	−0.504637	−0.0202504
$622$	−26.9204	−1.07941
$623$	−12.1526	−0.486884
$624$	6.33305	0.253525
$625$	1.00000	0.0400000
$626$	−21.9125	−0.875798
$627$	−22.6436	−0.904298
$628$	16.5804	0.661630
$629$	−54.7519	−2.18310
$630$	11.7264	0.467191
$631$	11.2203	0.446673	0.223336	−	0.974741i	$-0.428305\pi$
$631$	11.2203	0.446673	0.223336	+	0.974741i	$0.428305\pi$
$632$	0.656130	0.0260994
$633$	59.5696	2.36768
$634$	68.7253	2.72943
$635$	−18.8785	−0.749171
$636$	37.3538	1.48118
$637$	0.537768	0.0213071
$638$	−25.9704	−1.02818
$639$	−38.8463	−1.53674
$640$	0.325496	0.0128664
$641$	−3.24683	−0.128242	−0.0641210	−	0.997942i	$-0.520424\pi$
$641$	−3.24683	−0.128242	−0.0641210	+	0.997942i	$0.520424\pi$
$642$	104.979	4.14320
$643$	27.5358	1.08590	0.542952	−	0.839763i	$-0.317306\pi$
$643$	27.5358	1.08590	0.542952	+	0.839763i	$0.317306\pi$
$644$	−0.120327	−0.00474154
$645$	−23.5314	−0.926549
$646$	−18.2435	−0.717779
$647$	−2.70474	−0.106334	−0.0531671	−	0.998586i	$-0.516932\pi$
$647$	−2.70474	−0.106334	−0.0531671	+	0.998586i	$0.516932\pi$
$648$	0.311618	0.0122415
$649$	15.7295	0.617435
$650$	1.07826	0.0422929
$651$	−10.7192	−0.420117
$652$	7.29329	0.285627
$653$	3.77151	0.147591	0.0737954	−	0.997273i	$-0.476489\pi$
$653$	3.77151	0.147591	0.0737954	+	0.997273i	$0.476489\pi$
$654$	30.7419	1.20210
$655$	5.27999	0.206306
$656$	17.2190	0.672288
$657$	20.2889	0.791546
$658$	5.45224	0.212550
$659$	32.0382	1.24803	0.624015	−	0.781412i	$-0.285500\pi$
$659$	32.0382	1.24803	0.624015	+	0.781412i	$0.285500\pi$
$660$	−25.3490	−0.986710
$661$	14.5424	0.565634	0.282817	−	0.959174i	$-0.408731\pi$
$661$	14.5424	0.565634	0.282817	+	0.959174i	$0.408731\pi$
$662$	62.6810	2.43617
$663$	−8.06504	−0.313220
$664$	0.380151	0.0147527
$665$	−1.80467	−0.0699822
$666$	−127.346	−4.93455
$667$	0.182887	0.00708142
$668$	33.4393	1.29380
$669$	−13.7067	−0.529933
$670$	−3.53298	−0.136491
$671$	9.77133	0.377218
$672$	−23.8548	−0.920220
$673$	30.4908	1.17533	0.587667	−	0.809103i	$-0.300046\pi$
$673$	30.4908	1.17533	0.587667	+	0.809103i	$0.300046\pi$
$674$	−39.5728	−1.52429
$675$	−8.47289	−0.326122
$676$	−25.6796	−0.987675
$677$	5.48274	0.210719	0.105359	−	0.994434i	$-0.466401\pi$
$677$	5.48274	0.210719	0.105359	+	0.994434i	$0.466401\pi$
$678$	7.38755	0.283717
$679$	−4.40673	−0.169115
$680$	−0.205144	−0.00786691
$681$	29.2293	1.12007
$682$	30.4770	1.16703
$683$	39.2025	1.50004	0.750022	−	0.661413i	$-0.230043\pi$
$683$	39.2025	1.50004	0.750022	+	0.661413i	$0.230043\pi$
$684$	−21.3230	−0.815307
$685$	0.940881	0.0359492
$686$	−2.00507	−0.0765538
$687$	−2.97462	−0.113489
$688$	31.3186	1.19401
$689$	−3.34259	−0.127343
$690$	0.355229	0.0135233
$691$	−10.6839	−0.406434	−0.203217	−	0.979134i	$-0.565140\pi$
$691$	−10.6839	−0.406434	−0.203217	+	0.979134i	$0.565140\pi$
$692$	40.4448	1.53748
$693$	24.6690	0.937097
$694$	28.5946	1.08544
$695$	10.5016	0.398347
$696$	−0.371660	−0.0140877
$697$	−21.9281	−0.830587
$698$	52.1611	1.97433
$699$	−78.9946	−2.98785
$700$	−2.02029	−0.0763599
$701$	0.208068	0.00785862	0.00392931	−	0.999992i	$-0.498749\pi$
$701$	0.208068	0.00785862	0.00392931	+	0.999992i	$0.498749\pi$
$702$	−9.13598	−0.344815
$703$	19.5983	0.739164
$704$	34.4259	1.29748
$705$	−8.08869	−0.304638
$706$	51.6692	1.94460
$707$	−3.68268	−0.138501
$708$	22.4102	0.842226
$709$	−18.6005	−0.698557	−0.349278	−	0.937019i	$-0.613573\pi$
$709$	−18.6005	−0.698557	−0.349278	+	0.937019i	$0.613573\pi$
$710$	13.3181	0.499820
$711$	94.3078	3.53682
$712$	0.494479	0.0185314
$713$	−0.214623	−0.00803770
$714$	30.0705	1.12536
$715$	2.26835	0.0848314
$716$	−19.9065	−0.743941
$717$	−0.209789	−0.00783470
$718$	6.67182	0.248990
$719$	−30.8939	−1.15215	−0.576074	−	0.817398i	$-0.695416\pi$
$719$	−30.8939	−1.15215	−0.576074	+	0.817398i	$0.695416\pi$
$720$	23.1538	0.862891
$721$	−12.9844	−0.483563
$722$	−31.5661	−1.17477
$723$	−18.9277	−0.703929
$724$	38.6935	1.43803
$725$	3.07069	0.114042
$726$	−40.5109	−1.50350
$727$	−33.1830	−1.23069	−0.615344	−	0.788259i	$-0.710983\pi$
$727$	−33.1830	−1.23069	−0.615344	+	0.788259i	$0.710983\pi$
$728$	−0.0218813	−0.000810976 0
$729$	−30.8211	−1.14152
$730$	−6.95587	−0.257448
$731$	−39.8837	−1.47515
$732$	13.9215	0.514553
$733$	31.8446	1.17621	0.588104	−	0.808785i	$-0.299874\pi$
$733$	31.8446	1.17621	0.588104	+	0.808785i	$0.299874\pi$
$734$	50.4070	1.86056
$735$	2.97462	0.109721
$736$	−0.477630	−0.0176057
$737$	−7.43238	−0.273775
$738$	−51.0020	−1.87741
$739$	12.2176	0.449433	0.224716	−	0.974424i	$-0.427854\pi$
$739$	12.2176	0.449433	0.224716	+	0.974424i	$0.427854\pi$
$740$	21.9399	0.806526
$741$	2.88686	0.106051
$742$	12.4628	0.457526
$743$	10.8666	0.398658	0.199329	−	0.979933i	$-0.436124\pi$
$743$	10.8666	0.398658	0.199329	+	0.979933i	$0.436124\pi$
$744$	0.436154	0.0159902
$745$	−4.02623	−0.147510
$746$	12.9551	0.474318
$747$	54.6404	1.99919
$748$	−42.9644	−1.57094
$749$	17.6012	0.643133
$750$	5.96432	0.217786
$751$	11.8906	0.433893	0.216946	−	0.976184i	$-0.430390\pi$
$751$	11.8906	0.433893	0.216946	+	0.976184i	$0.430390\pi$
$752$	10.7654	0.392575
$753$	79.1627	2.88485
$754$	3.31100	0.120580
$755$	−10.9291	−0.397750
$756$	17.1177	0.622565
$757$	29.1979	1.06122	0.530608	−	0.847618i	$-0.321964\pi$
$757$	29.1979	1.06122	0.530608	+	0.847618i	$0.321964\pi$
$758$	−69.1382	−2.51121
$759$	0.747300	0.0271253
$760$	0.0734306	0.00266361
$761$	−27.7343	−1.00537	−0.502684	−	0.864470i	$-0.667654\pi$
$761$	−27.7343	−1.00537	−0.502684	+	0.864470i	$0.667654\pi$
$762$	−112.597	−4.07898
$763$	5.15431	0.186598
$764$	9.67529	0.350040
$765$	−29.4860	−1.06607
$766$	−69.0553	−2.49507
$767$	−2.00537	−0.0724096
$768$	−46.6135	−1.68202
$769$	4.91549	0.177257	0.0886285	−	0.996065i	$-0.471752\pi$
$769$	4.91549	0.177257	0.0886285	+	0.996065i	$0.471752\pi$
$770$	−8.45753	−0.304788
$771$	−81.6658	−2.94112
$772$	−12.1978	−0.439008
$773$	−28.3561	−1.01990	−0.509949	−	0.860205i	$-0.670336\pi$
$773$	−28.3561	−1.01990	−0.509949	+	0.860205i	$0.670336\pi$
$774$	−92.7644	−3.33435
$775$	−3.60353	−0.129443
$776$	0.179306	0.00643672
$777$	−32.3037	−1.15889
$778$	−16.9019	−0.605961
$779$	7.84911	0.281224
$780$	3.23178	0.115716
$781$	28.0174	1.00254
$782$	0.602083	0.0215304
$783$	−26.0176	−0.929793
$784$	−3.95900	−0.141393
$785$	−8.20693	−0.292918
$786$	31.4916	1.12327
$787$	−1.92615	−0.0686598	−0.0343299	−	0.999411i	$-0.510930\pi$
$787$	−1.92615	−0.0686598	−0.0343299	+	0.999411i	$0.510930\pi$
$788$	20.4942	0.730075
$789$	47.8292	1.70276
$790$	−32.3326	−1.15034
$791$	1.23862	0.0440404
$792$	−1.00376	−0.0356671
$793$	−1.24576	−0.0442382
$794$	−4.73671	−0.168100
$795$	−18.4893	−0.655748
$796$	13.5558	0.480474
$797$	−10.7617	−0.381197	−0.190599	−	0.981668i	$-0.561043\pi$
$797$	−10.7617	−0.381197	−0.190599	+	0.981668i	$0.561043\pi$
$798$	−10.7636	−0.381029
$799$	−13.7096	−0.485012
$800$	−8.01944	−0.283530
$801$	71.0732	2.51125
$802$	−9.87415	−0.348668
$803$	−14.6331	−0.516392
$804$	−10.5891	−0.373449
$805$	0.0595591	0.00209918
$806$	−3.88555	−0.136863
$807$	−75.7655	−2.66707
$808$	0.149845	0.00527153
$809$	−6.30481	−0.221665	−0.110833	−	0.993839i	$-0.535352\pi$
$809$	−6.30481	−0.221665	−0.110833	+	0.993839i	$0.535352\pi$
$810$	−15.3558	−0.539547
$811$	−7.36136	−0.258492	−0.129246	−	0.991613i	$-0.541256\pi$
$811$	−7.36136	−0.258492	−0.129246	+	0.991613i	$0.541256\pi$
$812$	−6.20369	−0.217707
$813$	−57.9076	−2.03091
$814$	91.8467	3.21922
$815$	−3.61002	−0.126453
$816$	59.3742	2.07851
$817$	14.2763	0.499463
$818$	−27.6578	−0.967032
$819$	−3.14508	−0.109898
$820$	8.78691	0.306852
$821$	−16.1155	−0.562435	−0.281218	−	0.959644i	$-0.590738\pi$
$821$	−16.1155	−0.562435	−0.281218	+	0.959644i	$0.590738\pi$
$822$	5.61172	0.195731
$823$	30.9022	1.07718	0.538592	−	0.842567i	$-0.318957\pi$
$823$	30.9022	1.07718	0.538592	+	0.842567i	$0.318957\pi$
$824$	0.528323	0.0184050
$825$	12.5472	0.436838
$826$	7.47700	0.260158
$827$	−19.2827	−0.670527	−0.335263	−	0.942124i	$-0.608825\pi$
$827$	−19.2827	−0.670527	−0.335263	+	0.942124i	$0.608825\pi$
$828$	0.703718	0.0244559
$829$	−31.4656	−1.09284	−0.546422	−	0.837510i	$-0.684010\pi$
$829$	−31.4656	−1.09284	−0.546422	+	0.837510i	$0.684010\pi$
$830$	−18.7330	−0.650231
$831$	5.78221	0.200583
$832$	−4.38900	−0.152161
$833$	5.04173	0.174686
$834$	62.6347	2.16886
$835$	−16.5517	−0.572795
$836$	15.3790	0.531893
$837$	30.5323	1.05535
$838$	−11.6429	−0.402197
$839$	−39.9857	−1.38046	−0.690230	−	0.723590i	$-0.742491\pi$
$839$	−39.9857	−1.38046	−0.690230	+	0.723590i	$0.742491\pi$
$840$	−0.121035	−0.00417610
$841$	−19.5709	−0.674858
$842$	25.1763	0.867634
$843$	−2.15502	−0.0742230
$844$	−40.4582	−1.39263
$845$	12.7108	0.437265
$846$	−31.8868	−1.09629
$847$	−6.79220	−0.233383
$848$	24.6079	0.845038
$849$	46.3103	1.58937
$850$	10.1090	0.346736
$851$	−0.646796	−0.0221719
$852$	39.9172	1.36754
$853$	−4.62619	−0.158398	−0.0791988	−	0.996859i	$-0.525236\pi$
$853$	−4.62619	−0.158398	−0.0791988	+	0.996859i	$0.525236\pi$
$854$	4.64481	0.158942
$855$	10.5544	0.360954
$856$	−0.716177	−0.0244784
$857$	−19.2967	−0.659161	−0.329581	−	0.944127i	$-0.606907\pi$
$857$	−19.2967	−0.659161	−0.329581	+	0.944127i	$0.606907\pi$
$858$	13.5292	0.461878
$859$	−28.1006	−0.958781	−0.479391	−	0.877602i	$-0.659142\pi$
$859$	−28.1006	−0.958781	−0.479391	+	0.877602i	$0.659142\pi$
$860$	15.9820	0.544981
$861$	−12.9376	−0.440913
$862$	2.10301	0.0716287
$863$	−3.26753	−0.111228	−0.0556140	−	0.998452i	$-0.517712\pi$
$863$	−3.26753	−0.111228	−0.0556140	+	0.998452i	$0.517712\pi$
$864$	67.9478	2.31163
$865$	−20.0193	−0.680675
$866$	−41.7628	−1.41916
$867$	−25.0435	−0.850523
$868$	7.28020	0.247106
$869$	−68.0183	−2.30736
$870$	18.3146	0.620922
$871$	0.947562	0.0321069
$872$	−0.209724	−0.00710216
$873$	25.7723	0.872260
$874$	−0.215514	−0.00728987
$875$	1.00000	0.0338062
$876$	−20.8482	−0.704396
$877$	−2.03846	−0.0688339	−0.0344169	−	0.999408i	$-0.510957\pi$
$877$	−2.03846	−0.0688339	−0.0344169	+	0.999408i	$0.510957\pi$
$878$	−61.8314	−2.08671
$879$	9.66522	0.326000
$880$	−16.6994	−0.562936
$881$	−59.1070	−1.99137	−0.995684	−	0.0928132i	$-0.970414\pi$
$881$	−59.1070	−1.99137	−0.995684	+	0.0928132i	$0.970414\pi$
$882$	11.7264	0.394849
$883$	−10.8542	−0.365274	−0.182637	−	0.983180i	$-0.558463\pi$
$883$	−10.8542	−0.365274	−0.182637	+	0.983180i	$0.558463\pi$
$884$	5.47758	0.184231
$885$	−11.0925	−0.372872
$886$	10.9673	0.368452
$887$	23.0551	0.774114	0.387057	−	0.922056i	$-0.373492\pi$
$887$	23.0551	0.774114	0.387057	+	0.922056i	$0.373492\pi$
$888$	1.31441	0.0441087
$889$	−18.8785	−0.633165
$890$	−24.3668	−0.816776
$891$	−32.3041	−1.08223
$892$	9.30929	0.311698
$893$	4.90732	0.164217
$894$	−24.0137	−0.803140
$895$	9.85328	0.329359
$896$	0.325496	0.0108741
$897$	−0.0952741	−0.00318111
$898$	10.5780	0.352992
$899$	−11.0653	−0.369049
$900$	11.8155	0.393849
$901$	−31.3378	−1.04401
$902$	36.7846	1.22479
$903$	−23.5314	−0.783077
$904$	−0.0503985	−0.00167623
$905$	−19.1524	−0.636648
$906$	−65.1846	−2.16561
$907$	19.7985	0.657398	0.328699	−	0.944435i	$-0.393390\pi$
$907$	19.7985	0.657398	0.328699	+	0.944435i	$0.393390\pi$
$908$	−19.8518	−0.658806
$909$	21.5377	0.714362
$910$	1.07826	0.0357440
$911$	−20.7775	−0.688388	−0.344194	−	0.938899i	$-0.611848\pi$
$911$	−20.7775	−0.688388	−0.344194	+	0.938899i	$0.611848\pi$
$912$	−21.2528	−0.703751
$913$	−39.4087	−1.30424
$914$	−20.6274	−0.682293
$915$	−6.89082	−0.227803
$916$	2.02029	0.0667524
$917$	5.27999	0.174361
$918$	−85.6525	−2.82695
$919$	−17.1507	−0.565750	−0.282875	−	0.959157i	$-0.591288\pi$
$919$	−17.1507	−0.565750	−0.282875	+	0.959157i	$0.591288\pi$
$920$	−0.00242341	−7.98974e−5 0
$921$	76.4821	2.52017
$922$	43.0615	1.41815
$923$	−3.57198	−0.117573
$924$	−25.3490	−0.833922
$925$	−10.8597	−0.357066
$926$	−1.11257	−0.0365613
$927$	75.9377	2.49412
$928$	−24.6252	−0.808362
$929$	−18.8004	−0.616821	−0.308411	−	0.951253i	$-0.599797\pi$
$929$	−18.8004	−0.616821	−0.308411	+	0.951253i	$0.599797\pi$
$930$	−21.4926	−0.704771
$931$	−1.80467	−0.0591458
$932$	53.6512	1.75740
$933$	39.9379	1.30751
$934$	27.0126	0.883879
$935$	21.2664	0.695487
$936$	0.127970	0.00418285
$937$	4.31292	0.140897	0.0704485	−	0.997515i	$-0.477557\pi$
$937$	4.31292	0.140897	0.0704485	+	0.997515i	$0.477557\pi$
$938$	−3.53298	−0.115356
$939$	32.5083	1.06087
$940$	5.49364	0.179183
$941$	−35.2484	−1.14906	−0.574532	−	0.818482i	$-0.694816\pi$
$941$	−35.2484	−1.14906	−0.574532	+	0.818482i	$0.694816\pi$
$942$	−48.9488	−1.59484
$943$	−0.259042	−0.00843556
$944$	14.7633	0.480506
$945$	−8.47289	−0.275623
$946$	66.9052	2.17527
$947$	20.6912	0.672373	0.336187	−	0.941795i	$-0.390863\pi$
$947$	20.6912	0.672373	0.336187	+	0.941795i	$0.390863\pi$
$948$	−96.9076	−3.14741
$949$	1.86559	0.0605598
$950$	−3.61849	−0.117399
$951$	−101.958	−3.30620
$952$	−0.205144	−0.00664875
$953$	−61.0154	−1.97648	−0.988241	−	0.152904i	$-0.951138\pi$
$953$	−61.0154	−1.97648	−0.988241	+	0.152904i	$0.951138\pi$
$954$	−72.8876	−2.35982
$955$	−4.78905	−0.154970
$956$	0.142483	0.00460824
$957$	38.5285	1.24545
$958$	−6.46013	−0.208717
$959$	0.940881	0.0303826
$960$	−24.2774	−0.783551
$961$	−18.0145	−0.581114
$962$	−11.7096	−0.377534
$963$	−102.939	−3.31715
$964$	12.8552	0.414039
$965$	6.03763	0.194358
$966$	0.355229	0.0114293
$967$	24.9242	0.801508	0.400754	−	0.916186i	$-0.368748\pi$
$967$	24.9242	0.801508	0.400754	+	0.916186i	$0.368748\pi$
$968$	0.276369	0.00888284
$969$	27.0651	0.869458
$970$	−8.83580	−0.283700
$971$	13.9355	0.447210	0.223605	−	0.974680i	$-0.428217\pi$
$971$	13.9355	0.447210	0.223605	+	0.974680i	$0.428217\pi$
$972$	5.32859	0.170915
$973$	10.5016	0.336664
$974$	−31.3046	−1.00306
$975$	−1.59966	−0.0512300
$976$	9.17116	0.293562
$977$	55.6211	1.77948	0.889738	−	0.456471i	$-0.150887\pi$
$977$	55.6211	1.77948	0.889738	+	0.456471i	$0.150887\pi$
$978$	−21.5313	−0.688495
$979$	−51.2607	−1.63830
$980$	−2.02029	−0.0645359
$981$	−30.1444	−0.962436
$982$	79.9498	2.55130
$983$	−33.3702	−1.06435	−0.532173	−	0.846636i	$-0.678624\pi$
$983$	−33.3702	−1.06435	−0.532173	+	0.846636i	$0.678624\pi$
$984$	0.526420	0.0167817
$985$	−10.1442	−0.323220
$986$	31.0416	0.988566
$987$	−8.08869	−0.257466
$988$	−1.96068	−0.0623777
$989$	−0.471155	−0.0149819
$990$	49.4630	1.57204
$991$	17.7506	0.563867	0.281934	−	0.959434i	$-0.409024\pi$
$991$	17.7506	0.563867	0.281934	+	0.959434i	$0.409024\pi$
$992$	28.8983	0.917523
$993$	−92.9906	−2.95097
$994$	13.3181	0.422425
$995$	−6.70984	−0.212716
$996$	−56.1467	−1.77908
$997$	−61.4602	−1.94647	−0.973233	−	0.229822i	$-0.926186\pi$
$997$	−61.4602	−1.94647	−0.973233	+	0.229822i	$0.926186\pi$
$998$	72.4635	2.29379
$999$	92.0134	2.91118

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8015.2.a.l.1.51	✓	62

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8015.2.a.l.1.51	✓	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)

\(f(q)\)	\(=\)	\(q+2.00507 q^{2} -2.97462 q^{3} +2.02029 q^{4} -1.00000 q^{5} -5.96432 q^{6} -1.00000 q^{7} +0.0406892 q^{8} +5.84839 q^{9} +O(q^{10})\)	\(q+2.00507 q^{2} -2.97462 q^{3} +2.02029 q^{4} -1.00000 q^{5} -5.96432 q^{6} -1.00000 q^{7} +0.0406892 q^{8} +5.84839 q^{9} -2.00507 q^{10} -4.21808 q^{11} -6.00961 q^{12} +0.537768 q^{13} -2.00507 q^{14} +2.97462 q^{15} -3.95900 q^{16} +5.04173 q^{17} +11.7264 q^{18} -1.80467 q^{19} -2.02029 q^{20} +2.97462 q^{21} -8.45753 q^{22} +0.0595591 q^{23} -0.121035 q^{24} +1.00000 q^{25} +1.07826 q^{26} -8.47289 q^{27} -2.02029 q^{28} +3.07069 q^{29} +5.96432 q^{30} -3.60353 q^{31} -8.01944 q^{32} +12.5472 q^{33} +10.1090 q^{34} +1.00000 q^{35} +11.8155 q^{36} -10.8597 q^{37} -3.61849 q^{38} -1.59966 q^{39} -0.0406892 q^{40} -4.34933 q^{41} +5.96432 q^{42} -7.91072 q^{43} -8.52176 q^{44} -5.84839 q^{45} +0.119420 q^{46} -2.71923 q^{47} +11.7765 q^{48} +1.00000 q^{49} +2.00507 q^{50} -14.9973 q^{51} +1.08645 q^{52} -6.21568 q^{53} -16.9887 q^{54} +4.21808 q^{55} -0.0406892 q^{56} +5.36822 q^{57} +6.15693 q^{58} -3.72905 q^{59} +6.00961 q^{60} -2.31653 q^{61} -7.22533 q^{62} -5.84839 q^{63} -8.16151 q^{64} -0.537768 q^{65} +25.1580 q^{66} +1.76203 q^{67} +10.1858 q^{68} -0.177166 q^{69} +2.00507 q^{70} -6.64223 q^{71} +0.237966 q^{72} +3.46914 q^{73} -21.7745 q^{74} -2.97462 q^{75} -3.64597 q^{76} +4.21808 q^{77} -3.20742 q^{78} +16.1254 q^{79} +3.95900 q^{80} +7.65849 q^{81} -8.72069 q^{82} +9.34281 q^{83} +6.00961 q^{84} -5.04173 q^{85} -15.8615 q^{86} -9.13414 q^{87} -0.171630 q^{88} +12.1526 q^{89} -11.7264 q^{90} -0.537768 q^{91} +0.120327 q^{92} +10.7192 q^{93} -5.45224 q^{94} +1.80467 q^{95} +23.8548 q^{96} +4.40673 q^{97} +2.00507 q^{98} -24.6690 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 62 q + 2 q^{2} + 11 q^{3} + 64 q^{4} - 62 q^{5} + 3 q^{6} - 62 q^{7} + 15 q^{8} + 69 q^{9}+O(q^{10}) \) 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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