LMFDB - Embedded newform 8015.2.a.k.1.5

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:	$1$
Dimension:	$49$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
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)

$f(q)$	$=$	$q-2.52338 q^{2} -1.42453 q^{3} +4.36744 q^{4} -1.00000 q^{5} +3.59462 q^{6} -1.00000 q^{7} -5.97394 q^{8} -0.970719 q^{9} +O(q^{10})$	\(q-2.52338 q^{2} -1.42453 q^{3} +4.36744 q^{4} -1.00000 q^{5} +3.59462 q^{6} -1.00000 q^{7} -5.97394 q^{8} -0.970719 q^{9} +2.52338 q^{10} -0.848727 q^{11} -6.22154 q^{12} -0.668666 q^{13} +2.52338 q^{14} +1.42453 q^{15} +6.33964 q^{16} +5.10314 q^{17} +2.44949 q^{18} -4.66612 q^{19} -4.36744 q^{20} +1.42453 q^{21} +2.14166 q^{22} -6.42229 q^{23} +8.51005 q^{24} +1.00000 q^{25} +1.68730 q^{26} +5.65640 q^{27} -4.36744 q^{28} -1.41680 q^{29} -3.59462 q^{30} +7.95008 q^{31} -4.04942 q^{32} +1.20904 q^{33} -12.8771 q^{34} +1.00000 q^{35} -4.23956 q^{36} -7.24020 q^{37} +11.7744 q^{38} +0.952534 q^{39} +5.97394 q^{40} +6.84226 q^{41} -3.59462 q^{42} -7.81976 q^{43} -3.70676 q^{44} +0.970719 q^{45} +16.2059 q^{46} -6.23502 q^{47} -9.03099 q^{48} +1.00000 q^{49} -2.52338 q^{50} -7.26956 q^{51} -2.92036 q^{52} -6.56867 q^{53} -14.2732 q^{54} +0.848727 q^{55} +5.97394 q^{56} +6.64702 q^{57} +3.57513 q^{58} +2.55402 q^{59} +6.22154 q^{60} +8.83007 q^{61} -20.0611 q^{62} +0.970719 q^{63} -2.46105 q^{64} +0.668666 q^{65} -3.05086 q^{66} +5.96788 q^{67} +22.2876 q^{68} +9.14874 q^{69} -2.52338 q^{70} +11.6721 q^{71} +5.79902 q^{72} -0.0230230 q^{73} +18.2698 q^{74} -1.42453 q^{75} -20.3790 q^{76} +0.848727 q^{77} -2.40360 q^{78} -6.57570 q^{79} -6.33964 q^{80} -5.14555 q^{81} -17.2656 q^{82} +9.04107 q^{83} +6.22154 q^{84} -5.10314 q^{85} +19.7322 q^{86} +2.01828 q^{87} +5.07025 q^{88} +9.49552 q^{89} -2.44949 q^{90} +0.668666 q^{91} -28.0490 q^{92} -11.3251 q^{93} +15.7333 q^{94} +4.66612 q^{95} +5.76852 q^{96} -13.5986 q^{97} -2.52338 q^{98} +0.823876 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 49 q - 3 q^{2} - 10 q^{3} + 49 q^{4} - 49 q^{5} + 10 q^{6} - 49 q^{7} - 6 q^{8} + 39 q^{9}+O(q^{10}) $ 49 * q - 3 * q^2 - 10 * q^3 + 49 * q^4 - 49 * q^5 + 10 * q^6 - 49 * q^7 - 6 * q^8 + 39 * q^9	\( 49 q - 3 q^{2} - 10 q^{3} + 49 q^{4} - 49 q^{5} + 10 q^{6} - 49 q^{7} - 6 q^{8} + 39 q^{9} + 3 q^{10} + 16 q^{11} - 26 q^{12} - 31 q^{13} + 3 q^{14} + 10 q^{15} + 49 q^{16} - 18 q^{17} + 4 q^{18} - 16 q^{19} - 49 q^{20} + 10 q^{21} + 10 q^{22} + 10 q^{23} + 2 q^{24} + 49 q^{25} - 22 q^{26} - 58 q^{27} - 49 q^{28} + 31 q^{29} - 10 q^{30} - 35 q^{31} - 5 q^{32} - 82 q^{33} - 41 q^{34} + 49 q^{35} + 49 q^{36} - 24 q^{37} - 20 q^{38} + 41 q^{39} + 6 q^{40} + 30 q^{41} - 10 q^{42} - 19 q^{43} + 27 q^{44} - 39 q^{45} + 15 q^{46} - 39 q^{47} - 51 q^{48} + 49 q^{49} - 3 q^{50} + 46 q^{51} - 94 q^{52} - 17 q^{53} + 9 q^{54} - 16 q^{55} + 6 q^{56} - 23 q^{57} - 46 q^{58} + 11 q^{59} + 26 q^{60} - 9 q^{61} - 49 q^{62} - 39 q^{63} + 10 q^{64} + 31 q^{65} - 10 q^{66} - 2 q^{67} - 73 q^{68} - 47 q^{69} - 3 q^{70} + 26 q^{71} - 39 q^{72} - 100 q^{73} + 8 q^{74} - 10 q^{75} - 71 q^{76} - 16 q^{77} - 51 q^{78} + 50 q^{79} - 49 q^{80} + 61 q^{81} - 36 q^{82} - 67 q^{83} + 26 q^{84} + 18 q^{85} + 33 q^{86} - 45 q^{87} - q^{88} - 19 q^{89} - 4 q^{90} + 31 q^{91} + 7 q^{92} + 9 q^{93} - 33 q^{94} + 16 q^{95} - 8 q^{96} - 85 q^{97} - 3 q^{98} + 27 q^{99}+O(q^{100}) \) 49 * q - 3 * q^2 - 10 * q^3 + 49 * q^4 - 49 * q^5 + 10 * q^6 - 49 * q^7 - 6 * q^8 + 39 * q^9 + 3 * q^10 + 16 * q^11 - 26 * q^12 - 31 * q^13 + 3 * q^14 + 10 * q^15 + 49 * q^16 - 18 * q^17 + 4 * q^18 - 16 * q^19 - 49 * q^20 + 10 * q^21 + 10 * q^22 + 10 * q^23 + 2 * q^24 + 49 * q^25 - 22 * q^26 - 58 * q^27 - 49 * q^28 + 31 * q^29 - 10 * q^30 - 35 * q^31 - 5 * q^32 - 82 * q^33 - 41 * q^34 + 49 * q^35 + 49 * q^36 - 24 * q^37 - 20 * q^38 + 41 * q^39 + 6 * q^40 + 30 * q^41 - 10 * q^42 - 19 * q^43 + 27 * q^44 - 39 * q^45 + 15 * q^46 - 39 * q^47 - 51 * q^48 + 49 * q^49 - 3 * q^50 + 46 * q^51 - 94 * q^52 - 17 * q^53 + 9 * q^54 - 16 * q^55 + 6 * q^56 - 23 * q^57 - 46 * q^58 + 11 * q^59 + 26 * q^60 - 9 * q^61 - 49 * q^62 - 39 * q^63 + 10 * q^64 + 31 * q^65 - 10 * q^66 - 2 * q^67 - 73 * q^68 - 47 * q^69 - 3 * q^70 + 26 * q^71 - 39 * q^72 - 100 * q^73 + 8 * q^74 - 10 * q^75 - 71 * q^76 - 16 * q^77 - 51 * q^78 + 50 * q^79 - 49 * q^80 + 61 * q^81 - 36 * q^82 - 67 * q^83 + 26 * q^84 + 18 * q^85 + 33 * q^86 - 45 * q^87 - q^88 - 19 * q^89 - 4 * q^90 + 31 * q^91 + 7 * q^92 + 9 * q^93 - 33 * q^94 + 16 * q^95 - 8 * q^96 - 85 * q^97 - 3 * q^98 + 27 * 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 $

$2$	−2.52338	−1.78430	−0.892149	−	0.451741i	$-0.850803\pi$
$2$	−2.52338	−1.78430	−0.892149	+	0.451741i	$0.850803\pi$
$3$	−1.42453	−0.822452	−0.411226	−	0.911533i	$-0.634899\pi$
$3$	−1.42453	−0.822452	−0.411226	+	0.911533i	$0.634899\pi$
$4$	4.36744	2.18372
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	3.59462	1.46750
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−5.97394	−2.11211
$9$	−0.970719	−0.323573
$10$	2.52338	0.797962
$11$	−0.848727	−0.255901	−0.127950	−	0.991781i	$-0.540840\pi$
$11$	−0.848727	−0.255901	−0.127950	+	0.991781i	$0.540840\pi$
$12$	−6.22154	−1.79600
$13$	−0.668666	−0.185455	−0.0927273	−	0.995692i	$-0.529558\pi$
$13$	−0.668666	−0.185455	−0.0927273	+	0.995692i	$0.529558\pi$
$14$	2.52338	0.674401
$15$	1.42453	0.367812
$16$	6.33964	1.58491
$17$	5.10314	1.23769	0.618846	−	0.785512i	$-0.287600\pi$
$17$	5.10314	1.23769	0.618846	+	0.785512i	$0.287600\pi$
$18$	2.44949	0.577351
$19$	−4.66612	−1.07048	−0.535240	−	0.844700i	$-0.679779\pi$
$19$	−4.66612	−1.07048	−0.535240	+	0.844700i	$0.679779\pi$
$20$	−4.36744	−0.976589
$21$	1.42453	0.310858
$22$	2.14166	0.456604
$23$	−6.42229	−1.33914	−0.669570	−	0.742749i	$-0.733522\pi$
$23$	−6.42229	−1.33914	−0.669570	+	0.742749i	$0.733522\pi$
$24$	8.51005	1.73711
$25$	1.00000	0.200000
$26$	1.68730	0.330906
$27$	5.65640	1.08858
$28$	−4.36744	−0.825368
$29$	−1.41680	−0.263094	−0.131547	−	0.991310i	$-0.541994\pi$
$29$	−1.41680	−0.263094	−0.131547	+	0.991310i	$0.541994\pi$
$30$	−3.59462	−0.656285
$31$	7.95008	1.42788	0.713938	−	0.700209i	$-0.246910\pi$
$31$	7.95008	1.42788	0.713938	+	0.700209i	$0.246910\pi$
$32$	−4.04942	−0.715843
$33$	1.20904	0.210466
$34$	−12.8771	−2.20841
$35$	1.00000	0.169031
$36$	−4.23956	−0.706593
$37$	−7.24020	−1.19028	−0.595141	−	0.803621i	$-0.702904\pi$
$37$	−7.24020	−1.19028	−0.595141	+	0.803621i	$0.702904\pi$
$38$	11.7744	1.91006
$39$	0.952534	0.152528
$40$	5.97394	0.944563
$41$	6.84226	1.06858	0.534291	−	0.845301i	$-0.320579\pi$
$41$	6.84226	1.06858	0.534291	+	0.845301i	$0.320579\pi$
$42$	−3.59462	−0.554662
$43$	−7.81976	−1.19250	−0.596251	−	0.802798i	$-0.703344\pi$
$43$	−7.81976	−1.19250	−0.596251	+	0.802798i	$0.703344\pi$
$44$	−3.70676	−0.558816
$45$	0.970719	0.144706
$46$	16.2059	2.38943
$47$	−6.23502	−0.909470	−0.454735	−	0.890627i	$-0.650266\pi$
$47$	−6.23502	−0.909470	−0.454735	+	0.890627i	$0.650266\pi$
$48$	−9.03099	−1.30351
$49$	1.00000	0.142857
$50$	−2.52338	−0.356860
$51$	−7.26956	−1.01794
$52$	−2.92036	−0.404981
$53$	−6.56867	−0.902277	−0.451138	−	0.892454i	$-0.648982\pi$
$53$	−6.56867	−0.902277	−0.451138	+	0.892454i	$0.648982\pi$
$54$	−14.2732	−1.94234
$55$	0.848727	0.114442
$56$	5.97394	0.798301
$57$	6.64702	0.880419
$58$	3.57513	0.469437
$59$	2.55402	0.332505	0.166253	−	0.986083i	$-0.446833\pi$
$59$	2.55402	0.332505	0.166253	+	0.986083i	$0.446833\pi$
$60$	6.22154	0.803197
$61$	8.83007	1.13057	0.565287	−	0.824894i	$-0.308765\pi$
$61$	8.83007	1.13057	0.565287	+	0.824894i	$0.308765\pi$
$62$	−20.0611	−2.54776
$63$	0.970719	0.122299
$64$	−2.46105	−0.307632
$65$	0.668666	0.0829378
$66$	−3.05086	−0.375534
$67$	5.96788	0.729093	0.364546	−	0.931185i	$-0.381224\pi$
$67$	5.96788	0.729093	0.364546	+	0.931185i	$0.381224\pi$
$68$	22.2876	2.70277
$69$	9.14874	1.10138
$70$	−2.52338	−0.301601
$71$	11.6721	1.38522	0.692612	−	0.721311i	$-0.256460\pi$
$71$	11.6721	1.38522	0.692612	+	0.721311i	$0.256460\pi$
$72$	5.79902	0.683421
$73$	−0.0230230	−0.00269464	−0.00134732	−	0.999999i	$-0.500429\pi$
$73$	−0.0230230	−0.00269464	−0.00134732	+	0.999999i	$0.500429\pi$
$74$	18.2698	2.12382
$75$	−1.42453	−0.164490
$76$	−20.3790	−2.33763
$77$	0.848727	0.0967215
$78$	−2.40360	−0.272155
$79$	−6.57570	−0.739824	−0.369912	−	0.929067i	$-0.620612\pi$
$79$	−6.57570	−0.739824	−0.369912	+	0.929067i	$0.620612\pi$
$80$	−6.33964	−0.708793
$81$	−5.14555	−0.571727
$82$	−17.2656	−1.90667
$83$	9.04107	0.992387	0.496193	−	0.868212i	$-0.334731\pi$
$83$	9.04107	0.992387	0.496193	+	0.868212i	$0.334731\pi$
$84$	6.22154	0.678826
$85$	−5.10314	−0.553513
$86$	19.7322	2.12778
$87$	2.01828	0.216382
$88$	5.07025	0.540490
$89$	9.49552	1.00652	0.503262	−	0.864134i	$-0.332133\pi$
$89$	9.49552	1.00652	0.503262	+	0.864134i	$0.332133\pi$
$90$	−2.44949	−0.258199
$91$	0.668666	0.0700953
$92$	−28.0490	−2.92431
$93$	−11.3251	−1.17436
$94$	15.7333	1.62277
$95$	4.66612	0.478733
$96$	5.76852	0.588747
$97$	−13.5986	−1.38073	−0.690366	−	0.723460i	$-0.742551\pi$
$97$	−13.5986	−1.38073	−0.690366	+	0.723460i	$0.742551\pi$
$98$	−2.52338	−0.254900
$99$	0.823876	0.0828027
$100$	4.36744	0.436744
$101$	0.419005	0.0416925	0.0208463	−	0.999783i	$-0.493364\pi$
$101$	0.419005	0.0416925	0.0208463	+	0.999783i	$0.493364\pi$
$102$	18.3439	1.81631
$103$	−1.31565	−0.129635	−0.0648174	−	0.997897i	$-0.520646\pi$
$103$	−1.31565	−0.129635	−0.0648174	+	0.997897i	$0.520646\pi$
$104$	3.99457	0.391700
$105$	−1.42453	−0.139020
$106$	16.5752	1.60993
$107$	17.2065	1.66342	0.831708	−	0.555213i	$-0.187363\pi$
$107$	17.2065	1.66342	0.831708	+	0.555213i	$0.187363\pi$
$108$	24.7040	2.37714
$109$	2.64535	0.253379	0.126689	−	0.991942i	$-0.459565\pi$
$109$	2.64535	0.253379	0.126689	+	0.991942i	$0.459565\pi$
$110$	−2.14166	−0.204199
$111$	10.3139	0.978949
$112$	−6.33964	−0.599039
$113$	4.98217	0.468684	0.234342	−	0.972154i	$-0.424707\pi$
$113$	4.98217	0.468684	0.234342	+	0.972154i	$0.424707\pi$
$114$	−16.7729	−1.57093
$115$	6.42229	0.598882
$116$	−6.18780	−0.574523
$117$	0.649087	0.0600081
$118$	−6.44477	−0.593289
$119$	−5.10314	−0.467804
$120$	−8.51005	−0.776858
$121$	−10.2797	−0.934515
$122$	−22.2816	−2.01728
$123$	−9.74700	−0.878857
$124$	34.7215	3.11808
$125$	−1.00000	−0.0894427
$126$	−2.44949	−0.218218
$127$	−11.2305	−0.996548	−0.498274	−	0.867020i	$-0.666033\pi$
$127$	−11.2305	−0.996548	−0.498274	+	0.867020i	$0.666033\pi$
$128$	14.3090	1.26475
$129$	11.1395	0.980776
$130$	−1.68730	−0.147986
$131$	0.274771	0.0240068	0.0120034	−	0.999928i	$-0.496179\pi$
$131$	0.274771	0.0240068	0.0120034	+	0.999928i	$0.496179\pi$
$132$	5.28039	0.459599
$133$	4.66612	0.404604
$134$	−15.0592	−1.30092
$135$	−5.65640	−0.486826
$136$	−30.4858	−2.61414
$137$	−6.00003	−0.512617	−0.256309	−	0.966595i	$-0.582506\pi$
$137$	−6.00003	−0.512617	−0.256309	+	0.966595i	$0.582506\pi$
$138$	−23.0857	−1.96519
$139$	−1.76516	−0.149719	−0.0748595	−	0.997194i	$-0.523851\pi$
$139$	−1.76516	−0.149719	−0.0748595	+	0.997194i	$0.523851\pi$
$140$	4.36744	0.369116
$141$	8.88196	0.747996
$142$	−29.4531	−2.47165
$143$	0.567515	0.0474580
$144$	−6.15401	−0.512834
$145$	1.41680	0.117659
$146$	0.0580957	0.00480804
$147$	−1.42453	−0.117493
$148$	−31.6211	−2.59924
$149$	−13.6841	−1.12105	−0.560524	−	0.828138i	$-0.689400\pi$
$149$	−13.6841	−1.12105	−0.560524	+	0.828138i	$0.689400\pi$
$150$	3.59462	0.293500
$151$	18.7963	1.52962	0.764810	−	0.644256i	$-0.222833\pi$
$151$	18.7963	1.52962	0.764810	+	0.644256i	$0.222833\pi$
$152$	27.8751	2.26097
$153$	−4.95371	−0.400484
$154$	−2.14166	−0.172580
$155$	−7.95008	−0.638566
$156$	4.16013	0.333077
$157$	−13.4881	−1.07646	−0.538232	−	0.842796i	$-0.680908\pi$
$157$	−13.4881	−1.07646	−0.538232	+	0.842796i	$0.680908\pi$
$158$	16.5930	1.32007
$159$	9.35726	0.742079
$160$	4.04942	0.320135
$161$	6.42229	0.506148
$162$	12.9842	1.02013
$163$	12.3141	0.964513	0.482256	−	0.876030i	$-0.339817\pi$
$163$	12.3141	0.964513	0.482256	+	0.876030i	$0.339817\pi$
$164$	29.8832	2.33348
$165$	−1.20904	−0.0941233
$166$	−22.8141	−1.77071
$167$	16.4019	1.26922	0.634608	−	0.772835i	$-0.281162\pi$
$167$	16.4019	1.26922	0.634608	+	0.772835i	$0.281162\pi$
$168$	−8.51005	−0.656564
$169$	−12.5529	−0.965607
$170$	12.8771	0.987632
$171$	4.52949	0.346379
$172$	−34.1523	−2.60409
$173$	−2.13203	−0.162096	−0.0810478	−	0.996710i	$-0.525827\pi$
$173$	−2.13203	−0.162096	−0.0810478	+	0.996710i	$0.525827\pi$
$174$	−5.09287	−0.386090
$175$	−1.00000	−0.0755929
$176$	−5.38062	−0.405580
$177$	−3.63828	−0.273470
$178$	−23.9608	−1.79594
$179$	19.4447	1.45337	0.726684	−	0.686972i	$-0.241061\pi$
$179$	19.4447	1.45337	0.726684	+	0.686972i	$0.241061\pi$
$180$	4.23956	0.315998
$181$	15.3076	1.13780	0.568902	−	0.822405i	$-0.307368\pi$
$181$	15.3076	1.13780	0.568902	+	0.822405i	$0.307368\pi$
$182$	−1.68730	−0.125071
$183$	−12.5787	−0.929843
$184$	38.3664	2.82841
$185$	7.24020	0.532310
$186$	28.5775	2.09541
$187$	−4.33117	−0.316727
$188$	−27.2310	−1.98603
$189$	−5.65640	−0.411443
$190$	−11.7744	−0.854203
$191$	−0.236355	−0.0171021	−0.00855103	−	0.999963i	$-0.502722\pi$
$191$	−0.236355	−0.0171021	−0.00855103	+	0.999963i	$0.502722\pi$
$192$	3.50584	0.253012
$193$	−10.8077	−0.777953	−0.388977	−	0.921248i	$-0.627171\pi$
$193$	−10.8077	−0.777953	−0.388977	+	0.921248i	$0.627171\pi$
$194$	34.3145	2.46364
$195$	−0.952534	−0.0682124
$196$	4.36744	0.311960
$197$	18.3318	1.30608	0.653042	−	0.757322i	$-0.273493\pi$
$197$	18.3318	1.30608	0.653042	+	0.757322i	$0.273493\pi$
$198$	−2.07895	−0.147745
$199$	18.4261	1.30619	0.653096	−	0.757275i	$-0.273470\pi$
$199$	18.4261	1.30619	0.653096	+	0.757275i	$0.273470\pi$
$200$	−5.97394	−0.422421
$201$	−8.50142	−0.599644
$202$	−1.05731	−0.0743919
$203$	1.41680	0.0994401
$204$	−31.7494	−2.22290
$205$	−6.84226	−0.477884
$206$	3.31988	0.231307
$207$	6.23424	0.433310
$208$	−4.23910	−0.293929
$209$	3.96026	0.273937
$210$	3.59462	0.248053
$211$	−4.40445	−0.303215	−0.151607	−	0.988441i	$-0.548445\pi$
$211$	−4.40445	−0.303215	−0.151607	+	0.988441i	$0.548445\pi$
$212$	−28.6883	−1.97032
$213$	−16.6272	−1.13928
$214$	−43.4185	−2.96803
$215$	7.81976	0.533303
$216$	−33.7910	−2.29919
$217$	−7.95008	−0.539686
$218$	−6.67522	−0.452103
$219$	0.0327969	0.00221621
$220$	3.70676	0.249910
$221$	−3.41230	−0.229536
$222$	−26.0258	−1.74674
$223$	14.7979	0.990943	0.495472	−	0.868624i	$-0.334995\pi$
$223$	14.7979	0.990943	0.495472	+	0.868624i	$0.334995\pi$
$224$	4.04942	0.270563
$225$	−0.970719	−0.0647146
$226$	−12.5719	−0.836271
$227$	−15.9137	−1.05623	−0.528114	−	0.849173i	$-0.677101\pi$
$227$	−15.9137	−1.05623	−0.528114	+	0.849173i	$0.677101\pi$
$228$	29.0304	1.92259
$229$	−1.00000	−0.0660819
$229$	−1.00000	−0.0660819
$230$	−16.2059	−1.06858
$231$	−1.20904	−0.0795487
$232$	8.46390	0.555682
$233$	−26.7303	−1.75116	−0.875580	−	0.483073i	$-0.839521\pi$
$233$	−26.7303	−1.75116	−0.875580	+	0.483073i	$0.839521\pi$
$234$	−1.63789	−0.107072
$235$	6.23502	0.406728
$236$	11.1545	0.726098
$237$	9.36727	0.608469
$238$	12.8771	0.834701
$239$	−23.4040	−1.51388	−0.756939	−	0.653486i	$-0.773306\pi$
$239$	−23.4040	−1.51388	−0.756939	+	0.653486i	$0.773306\pi$
$240$	9.03099	0.582948
$241$	−16.1340	−1.03928	−0.519641	−	0.854385i	$-0.673934\pi$
$241$	−16.1340	−1.03928	−0.519641	+	0.854385i	$0.673934\pi$
$242$	25.9395	1.66745
$243$	−9.63923	−0.618357
$244$	38.5648	2.46886
$245$	−1.00000	−0.0638877
$246$	24.5954	1.56814
$247$	3.12007	0.198526
$248$	−47.4933	−3.01583
$249$	−12.8793	−0.816190
$250$	2.52338	0.159592
$251$	28.4713	1.79709	0.898547	−	0.438877i	$-0.144624\pi$
$251$	28.4713	1.79709	0.898547	+	0.438877i	$0.144624\pi$
$252$	4.23956	0.267067
$253$	5.45078	0.342687
$254$	28.3389	1.77814
$255$	7.26956	0.455238
$256$	−31.1849	−1.94906
$257$	20.4842	1.27777	0.638884	−	0.769303i	$-0.279396\pi$
$257$	20.4842	1.27777	0.638884	+	0.769303i	$0.279396\pi$
$258$	−28.1091	−1.75000
$259$	7.24020	0.449884
$260$	2.92036	0.181113
$261$	1.37532	0.0851300
$262$	−0.693351	−0.0428354
$263$	−18.9296	−1.16725	−0.583625	−	0.812023i	$-0.698366\pi$
$263$	−18.9296	−1.16725	−0.583625	+	0.812023i	$0.698366\pi$
$264$	−7.22271	−0.444527
$265$	6.56867	0.403510
$266$	−11.7744	−0.721933
$267$	−13.5266	−0.827817
$268$	26.0644	1.59213
$269$	6.28753	0.383357	0.191679	−	0.981458i	$-0.438607\pi$
$269$	6.28753	0.383357	0.191679	+	0.981458i	$0.438607\pi$
$270$	14.2732	0.868642
$271$	−11.6850	−0.709815	−0.354908	−	0.934901i	$-0.615488\pi$
$271$	−11.6850	−0.709815	−0.354908	+	0.934901i	$0.615488\pi$
$272$	32.3520	1.96163
$273$	−0.952534	−0.0576500
$274$	15.1404	0.914662
$275$	−0.848727	−0.0511802
$276$	39.9565	2.40510
$277$	23.8663	1.43399	0.716994	−	0.697079i	$-0.245517\pi$
$277$	23.8663	1.43399	0.716994	+	0.697079i	$0.245517\pi$
$278$	4.45417	0.267143
$279$	−7.71729	−0.462022
$280$	−5.97394	−0.357011
$281$	4.80738	0.286784	0.143392	−	0.989666i	$-0.454199\pi$
$281$	4.80738	0.286784	0.143392	+	0.989666i	$0.454199\pi$
$282$	−22.4125	−1.33465
$283$	8.35831	0.496850	0.248425	−	0.968651i	$-0.420087\pi$
$283$	8.35831	0.496850	0.248425	+	0.968651i	$0.420087\pi$
$284$	50.9772	3.02494
$285$	−6.64702	−0.393735
$286$	−1.43206	−0.0846793
$287$	−6.84226	−0.403886
$288$	3.93085	0.231628
$289$	9.04200	0.531882
$290$	−3.57513	−0.209939
$291$	19.3716	1.13559
$292$	−0.100551	−0.00588433
$293$	−16.7423	−0.978096	−0.489048	−	0.872257i	$-0.662656\pi$
$293$	−16.7423	−0.978096	−0.489048	+	0.872257i	$0.662656\pi$
$294$	3.59462	0.209643
$295$	−2.55402	−0.148701
$296$	43.2525	2.51400
$297$	−4.80074	−0.278567
$298$	34.5302	2.00028
$299$	4.29437	0.248350
$300$	−6.22154	−0.359201
$301$	7.81976	0.450724
$302$	−47.4301	−2.72930
$303$	−0.596884	−0.0342901
$304$	−29.5815	−1.69661
$305$	−8.83007	−0.505608
$306$	12.5001	0.714583
$307$	14.3653	0.819873	0.409936	−	0.912114i	$-0.365551\pi$
$307$	14.3653	0.819873	0.409936	+	0.912114i	$0.365551\pi$
$308$	3.70676	0.211213
$309$	1.87418	0.106618
$310$	20.0611	1.13939
$311$	17.2621	0.978844	0.489422	−	0.872047i	$-0.337208\pi$
$311$	17.2621	0.978844	0.489422	+	0.872047i	$0.337208\pi$
$312$	−5.69038	−0.322154
$313$	−16.3325	−0.923166	−0.461583	−	0.887097i	$-0.652718\pi$
$313$	−16.3325	−0.923166	−0.461583	+	0.887097i	$0.652718\pi$
$314$	34.0355	1.92073
$315$	−0.970719	−0.0546938
$316$	−28.7189	−1.61557
$317$	−9.66009	−0.542564	−0.271282	−	0.962500i	$-0.587448\pi$
$317$	−9.66009	−0.542564	−0.271282	+	0.962500i	$0.587448\pi$
$318$	−23.6119	−1.32409
$319$	1.20248	0.0673259
$320$	2.46105	0.137577
$321$	−24.5112	−1.36808
$322$	−16.2059	−0.903118
$323$	−23.8118	−1.32493
$324$	−22.4729	−1.24849
$325$	−0.668666	−0.0370909
$326$	−31.0731	−1.72098
$327$	−3.76838	−0.208392
$328$	−40.8753	−2.25696
$329$	6.23502	0.343748
$330$	3.05086	0.167944
$331$	1.80356	0.0991329	0.0495664	−	0.998771i	$-0.484216\pi$
$331$	1.80356	0.0991329	0.0495664	+	0.998771i	$0.484216\pi$
$332$	39.4863	2.16709
$333$	7.02820	0.385143
$334$	−41.3881	−2.26466
$335$	−5.96788	−0.326060
$336$	9.03099	0.492681
$337$	26.1807	1.42615	0.713076	−	0.701087i	$-0.247301\pi$
$337$	26.1807	1.42615	0.713076	+	0.701087i	$0.247301\pi$
$338$	31.6757	1.72293
$339$	−7.09725	−0.385470
$340$	−22.2876	−1.20872
$341$	−6.74745	−0.365395
$342$	−11.4296	−0.618043
$343$	−1.00000	−0.0539949
$344$	46.7148	2.51869
$345$	−9.14874	−0.492552
$346$	5.37993	0.289227
$347$	−1.71612	−0.0921264	−0.0460632	−	0.998939i	$-0.514668\pi$
$347$	−1.71612	−0.0921264	−0.0460632	+	0.998939i	$0.514668\pi$
$348$	8.81469	0.472517
$349$	31.6008	1.69155	0.845775	−	0.533540i	$-0.179139\pi$
$349$	31.6008	1.69155	0.845775	+	0.533540i	$0.179139\pi$
$350$	2.52338	0.134880
$351$	−3.78225	−0.201881
$352$	3.43686	0.183185
$353$	−24.9372	−1.32727	−0.663637	−	0.748055i	$-0.730988\pi$
$353$	−24.9372	−1.32727	−0.663637	+	0.748055i	$0.730988\pi$
$354$	9.18075	0.487951
$355$	−11.6721	−0.619491
$356$	41.4711	2.19796
$357$	7.26956	0.384746
$358$	−49.0664	−2.59324
$359$	32.9291	1.73793	0.868965	−	0.494873i	$-0.164786\pi$
$359$	32.9291	1.73793	0.868965	+	0.494873i	$0.164786\pi$
$360$	−5.79902	−0.305635
$361$	2.77264	0.145929
$362$	−38.6269	−2.03018
$363$	14.6437	0.768593
$364$	2.92036	0.153068
$365$	0.0230230	0.00120508
$366$	31.7408	1.65912
$367$	−15.0452	−0.785355	−0.392678	−	0.919676i	$-0.628451\pi$
$367$	−15.0452	−0.785355	−0.392678	+	0.919676i	$0.628451\pi$
$368$	−40.7150	−2.12242
$369$	−6.64192	−0.345764
$370$	−18.2698	−0.949800
$371$	6.56867	0.341029
$372$	−49.4617	−2.56447
$373$	33.8911	1.75481	0.877407	−	0.479747i	$-0.159272\pi$
$373$	33.8911	1.75481	0.877407	+	0.479747i	$0.159272\pi$
$374$	10.9292	0.565135
$375$	1.42453	0.0735623
$376$	37.2476	1.92090
$377$	0.947368	0.0487919
$378$	14.2732	0.734136
$379$	20.1383	1.03443	0.517216	−	0.855855i	$-0.326968\pi$
$379$	20.1383	1.03443	0.517216	+	0.855855i	$0.326968\pi$
$380$	20.3790	1.04542
$381$	15.9982	0.819613
$382$	0.596414	0.0305152
$383$	28.8245	1.47286	0.736431	−	0.676513i	$-0.236510\pi$
$383$	28.8245	1.47286	0.736431	+	0.676513i	$0.236510\pi$
$384$	−20.3836	−1.04020
$385$	−0.848727	−0.0432552
$386$	27.2718	1.38810
$387$	7.59079	0.385862
$388$	−59.3912	−3.01513
$389$	20.5921	1.04406	0.522030	−	0.852927i	$-0.325175\pi$
$389$	20.5921	1.04406	0.522030	+	0.852927i	$0.325175\pi$
$390$	2.40360	0.121711
$391$	−32.7738	−1.65744
$392$	−5.97394	−0.301730
$393$	−0.391419	−0.0197445
$394$	−46.2580	−2.33044
$395$	6.57570	0.330859
$396$	3.59823	0.180818
$397$	−27.7555	−1.39301	−0.696504	−	0.717553i	$-0.745262\pi$
$397$	−27.7555	−1.39301	−0.696504	+	0.717553i	$0.745262\pi$
$398$	−46.4960	−2.33063
$399$	−6.64702	−0.332767
$400$	6.33964	0.316982
$401$	−1.94222	−0.0969898	−0.0484949	−	0.998823i	$-0.515442\pi$
$401$	−1.94222	−0.0969898	−0.0484949	+	0.998823i	$0.515442\pi$
$402$	21.4523	1.06994
$403$	−5.31595	−0.264806
$404$	1.82998	0.0910448
$405$	5.14555	0.255684
$406$	−3.57513	−0.177431
$407$	6.14496	0.304594
$408$	43.4279	2.15000
$409$	−21.1897	−1.04776	−0.523882	−	0.851791i	$-0.675517\pi$
$409$	−21.1897	−1.04776	−0.523882	+	0.851791i	$0.675517\pi$
$410$	17.2656	0.852688
$411$	8.54722	0.421603
$412$	−5.74602	−0.283086
$413$	−2.55402	−0.125675
$414$	−15.7314	−0.773154
$415$	−9.04107	−0.443809
$416$	2.70771	0.132756
$417$	2.51452	0.123137
$418$	−9.99324	−0.488785
$419$	1.53946	0.0752074	0.0376037	−	0.999293i	$-0.488028\pi$
$419$	1.53946	0.0752074	0.0376037	+	0.999293i	$0.488028\pi$
$420$	−6.22154	−0.303580
$421$	11.6903	0.569751	0.284875	−	0.958565i	$-0.408048\pi$
$421$	11.6903	0.569751	0.284875	+	0.958565i	$0.408048\pi$
$422$	11.1141	0.541025
$423$	6.05245	0.294280
$424$	39.2409	1.90571
$425$	5.10314	0.247538
$426$	41.9568	2.03281
$427$	−8.83007	−0.427317
$428$	75.1484	3.63243
$429$	−0.808442	−0.0390319
$430$	−19.7322	−0.951572
$431$	−13.8060	−0.665013	−0.332507	−	0.943101i	$-0.607894\pi$
$431$	−13.8060	−0.665013	−0.332507	+	0.943101i	$0.607894\pi$
$432$	35.8595	1.72529
$433$	−1.65373	−0.0794732	−0.0397366	−	0.999210i	$-0.512652\pi$
$433$	−1.65373	−0.0794732	−0.0397366	+	0.999210i	$0.512652\pi$
$434$	20.0611	0.962961
$435$	−2.01828	−0.0967689
$436$	11.5534	0.553308
$437$	29.9672	1.43352
$438$	−0.0827590	−0.00395438
$439$	−38.7364	−1.84879	−0.924393	−	0.381441i	$-0.875428\pi$
$439$	−38.7364	−1.84879	−0.924393	+	0.381441i	$0.875428\pi$
$440$	−5.07025	−0.241715
$441$	−0.970719	−0.0462247
$442$	8.61051	0.409560
$443$	38.5878	1.83336	0.916680	−	0.399621i	$-0.130858\pi$
$443$	38.5878	1.83336	0.916680	+	0.399621i	$0.130858\pi$
$444$	45.0452	2.13775
$445$	−9.49552	−0.450131
$446$	−37.3408	−1.76814
$447$	19.4934	0.922008
$448$	2.46105	0.116274
$449$	0.533646	0.0251843	0.0125922	−	0.999921i	$-0.495992\pi$
$449$	0.533646	0.0251843	0.0125922	+	0.999921i	$0.495992\pi$
$450$	2.44949	0.115470
$451$	−5.80722	−0.273451
$452$	21.7593	1.02347
$453$	−26.7758	−1.25804
$454$	40.1563	1.88463
$455$	−0.668666	−0.0313476
$456$	−39.7089	−1.85954
$457$	−18.3925	−0.860365	−0.430183	−	0.902742i	$-0.641551\pi$
$457$	−18.3925	−0.860365	−0.430183	+	0.902742i	$0.641551\pi$
$458$	2.52338	0.117910
$459$	28.8654	1.34732
$460$	28.0490	1.30779
$461$	21.9662	1.02307	0.511535	−	0.859263i	$-0.329077\pi$
$461$	21.9662	1.02307	0.511535	+	0.859263i	$0.329077\pi$
$462$	3.05086	0.141939
$463$	19.5288	0.907579	0.453790	−	0.891109i	$-0.350072\pi$
$463$	19.5288	0.907579	0.453790	+	0.891109i	$0.350072\pi$
$464$	−8.98202	−0.416980
$465$	11.3251	0.525189
$466$	67.4507	3.12459
$467$	14.5462	0.673116	0.336558	−	0.941663i	$-0.390737\pi$
$467$	14.5462	0.673116	0.336558	+	0.941663i	$0.390737\pi$
$468$	2.83485	0.131041
$469$	−5.96788	−0.275571
$470$	−15.7333	−0.725723
$471$	19.2141	0.885340
$472$	−15.2576	−0.702287
$473$	6.63685	0.305162
$474$	−23.6372	−1.08569
$475$	−4.66612	−0.214096
$476$	−22.2876	−1.02155
$477$	6.37634	0.291952
$478$	59.0571	2.70121
$479$	−3.26874	−0.149353	−0.0746763	−	0.997208i	$-0.523792\pi$
$479$	−3.26874	−0.149353	−0.0746763	+	0.997208i	$0.523792\pi$
$480$	−5.76852	−0.263296
$481$	4.84128	0.220743
$482$	40.7122	1.85439
$483$	−9.14874	−0.416282
$484$	−44.8958	−2.04072
$485$	13.5986	0.617482
$486$	24.3234	1.10333
$487$	−21.4367	−0.971388	−0.485694	−	0.874129i	$-0.661433\pi$
$487$	−21.4367	−0.971388	−0.485694	+	0.874129i	$0.661433\pi$
$488$	−52.7503	−2.38789
$489$	−17.5417	−0.793265
$490$	2.52338	0.113995
$491$	−25.6361	−1.15694	−0.578470	−	0.815704i	$-0.696350\pi$
$491$	−25.6361	−1.15694	−0.578470	+	0.815704i	$0.696350\pi$
$492$	−42.5694	−1.91918
$493$	−7.23014	−0.325629
$494$	−7.87313	−0.354229
$495$	−0.823876	−0.0370305
$496$	50.4006	2.26305
$497$	−11.6721	−0.523565
$498$	32.4993	1.45633
$499$	5.81272	0.260213	0.130107	−	0.991500i	$-0.458468\pi$
$499$	5.81272	0.260213	0.130107	+	0.991500i	$0.458468\pi$
$500$	−4.36744	−0.195318
$501$	−23.3649	−1.04387
$502$	−71.8439	−3.20655
$503$	3.32921	0.148442	0.0742212	−	0.997242i	$-0.476353\pi$
$503$	3.32921	0.148442	0.0742212	+	0.997242i	$0.476353\pi$
$504$	−5.79902	−0.258309
$505$	−0.419005	−0.0186455
$506$	−13.7544	−0.611456
$507$	17.8819	0.794165
$508$	−49.0486	−2.17618
$509$	34.1171	1.51221	0.756107	−	0.654448i	$-0.227099\pi$
$509$	34.1171	1.51221	0.756107	+	0.654448i	$0.227099\pi$
$510$	−18.3439	−0.812280
$511$	0.0230230	0.00101848
$512$	50.0734	2.21295
$513$	−26.3934	−1.16530
$514$	−51.6893	−2.27992
$515$	1.31565	0.0579744
$516$	48.6509	2.14174
$517$	5.29183	0.232734
$518$	−18.2698	−0.802727
$519$	3.03714	0.133316
$520$	−3.99457	−0.175174
$521$	26.4614	1.15930	0.579648	−	0.814867i	$-0.303190\pi$
$521$	26.4614	1.15930	0.579648	+	0.814867i	$0.303190\pi$
$522$	−3.47045	−0.151897
$523$	−5.84149	−0.255431	−0.127715	−	0.991811i	$-0.540764\pi$
$523$	−5.84149	−0.255431	−0.127715	+	0.991811i	$0.540764\pi$
$524$	1.20005	0.0524242
$525$	1.42453	0.0621715
$526$	47.7666	2.08272
$527$	40.5703	1.76727
$528$	7.66485	0.333570
$529$	18.2459	0.793298
$530$	−16.5752	−0.719983
$531$	−2.47924	−0.107590
$532$	20.3790	0.883541
$533$	−4.57519	−0.198173
$534$	34.1328	1.47707
$535$	−17.2065	−0.743902
$536$	−35.6518	−1.53992
$537$	−27.6996	−1.19532
$538$	−15.8658	−0.684024
$539$	−0.848727	−0.0365573
$540$	−24.7040	−1.06309
$541$	40.0355	1.72126	0.860631	−	0.509229i	$-0.170069\pi$
$541$	40.0355	1.72126	0.860631	+	0.509229i	$0.170069\pi$
$542$	29.4858	1.26652
$543$	−21.8061	−0.935790
$544$	−20.6648	−0.885994
$545$	−2.64535	−0.113314
$546$	2.40360	0.102865
$547$	−22.1171	−0.945657	−0.472829	−	0.881154i	$-0.656767\pi$
$547$	−22.1171	−0.945657	−0.472829	+	0.881154i	$0.656767\pi$
$548$	−26.2048	−1.11941
$549$	−8.57152	−0.365824
$550$	2.14166	0.0913207
$551$	6.61097	0.281637
$552$	−54.6540	−2.32623
$553$	6.57570	0.279627
$554$	−60.2238	−2.55866
$555$	−10.3139	−0.437799
$556$	−7.70923	−0.326944
$557$	23.3531	0.989502	0.494751	−	0.869035i	$-0.335259\pi$
$557$	23.3531	0.989502	0.494751	+	0.869035i	$0.335259\pi$
$558$	19.4737	0.824385
$559$	5.22881	0.221155
$560$	6.33964	0.267899
$561$	6.16988	0.260492
$562$	−12.1308	−0.511709
$563$	12.2200	0.515013	0.257507	−	0.966277i	$-0.417099\pi$
$563$	12.2200	0.515013	0.257507	+	0.966277i	$0.417099\pi$
$564$	38.7914	1.63341
$565$	−4.98217	−0.209602
$566$	−21.0912	−0.886528
$567$	5.14555	0.216093
$568$	−69.7284	−2.92574
$569$	25.5409	1.07073	0.535366	−	0.844620i	$-0.320174\pi$
$569$	25.5409	1.07073	0.535366	+	0.844620i	$0.320174\pi$
$570$	16.7729	0.702541
$571$	−43.9287	−1.83836	−0.919179	−	0.393840i	$-0.871146\pi$
$571$	−43.9287	−1.83836	−0.919179	+	0.393840i	$0.871146\pi$
$572$	2.47859	0.103635
$573$	0.336695	0.0140656
$574$	17.2656	0.720653
$575$	−6.42229	−0.267828
$576$	2.38899	0.0995413
$577$	−8.98997	−0.374257	−0.187129	−	0.982335i	$-0.559918\pi$
$577$	−8.98997	−0.374257	−0.187129	+	0.982335i	$0.559918\pi$
$578$	−22.8164	−0.949037
$579$	15.3958	0.639829
$580$	6.18780	0.256934
$581$	−9.04107	−0.375087
$582$	−48.8820	−2.02622
$583$	5.57501	0.230893
$584$	0.137538	0.00569136
$585$	−0.649087	−0.0268365
$586$	42.2472	1.74522
$587$	−9.92905	−0.409816	−0.204908	−	0.978781i	$-0.565689\pi$
$587$	−9.92905	−0.409816	−0.204908	+	0.978781i	$0.565689\pi$
$588$	−6.22154	−0.256572
$589$	−37.0960	−1.52851
$590$	6.44477	0.265327
$591$	−26.1141	−1.07419
$592$	−45.9003	−1.88649
$593$	−39.3719	−1.61681	−0.808406	−	0.588625i	$-0.799669\pi$
$593$	−39.3719	−1.61681	−0.808406	+	0.588625i	$0.799669\pi$
$594$	12.1141	0.497047
$595$	5.10314	0.209208
$596$	−59.7646	−2.44805
$597$	−26.2485	−1.07428
$598$	−10.8363	−0.443130
$599$	−23.0413	−0.941442	−0.470721	−	0.882282i	$-0.656006\pi$
$599$	−23.0413	−0.941442	−0.470721	+	0.882282i	$0.656006\pi$
$600$	8.51005	0.347421
$601$	−3.33226	−0.135926	−0.0679629	−	0.997688i	$-0.521650\pi$
$601$	−3.33226	−0.135926	−0.0679629	+	0.997688i	$0.521650\pi$
$602$	−19.7322	−0.804225
$603$	−5.79314	−0.235915
$604$	82.0916	3.34026
$605$	10.2797	0.417928
$606$	1.50616	0.0611837
$607$	−19.7552	−0.801838	−0.400919	−	0.916114i	$-0.631309\pi$
$607$	−19.7552	−0.801838	−0.400919	+	0.916114i	$0.631309\pi$
$608$	18.8951	0.766296
$609$	−2.01828	−0.0817846
$610$	22.2816	0.902156
$611$	4.16914	0.168666
$612$	−21.6350	−0.874544
$613$	27.6862	1.11824	0.559118	−	0.829088i	$-0.311140\pi$
$613$	27.6862	1.11824	0.559118	+	0.829088i	$0.311140\pi$
$614$	−36.2492	−1.46290
$615$	9.74700	0.393037
$616$	−5.07025	−0.204286
$617$	−35.7035	−1.43737	−0.718685	−	0.695336i	$-0.755256\pi$
$617$	−35.7035	−1.43737	−0.718685	+	0.695336i	$0.755256\pi$
$618$	−4.72926	−0.190239
$619$	−14.5614	−0.585273	−0.292637	−	0.956224i	$-0.594533\pi$
$619$	−14.5614	−0.585273	−0.292637	+	0.956224i	$0.594533\pi$
$620$	−34.7215	−1.39445
$621$	−36.3271	−1.45776
$622$	−43.5588	−1.74655
$623$	−9.49552	−0.380430
$624$	6.03872	0.241742
$625$	1.00000	0.0400000
$626$	41.2130	1.64720
$627$	−5.64150	−0.225300
$628$	−58.9083	−2.35070
$629$	−36.9477	−1.47320
$630$	2.44949	0.0975901
$631$	−3.97413	−0.158208	−0.0791038	−	0.996866i	$-0.525206\pi$
$631$	−3.97413	−0.158208	−0.0791038	+	0.996866i	$0.525206\pi$
$632$	39.2828	1.56259
$633$	6.27426	0.249379
$634$	24.3761	0.968097
$635$	11.2305	0.445670
$636$	40.8673	1.62049
$637$	−0.668666	−0.0264935
$638$	−3.03431	−0.120129
$639$	−11.3303	−0.448221
$640$	−14.3090	−0.565613
$641$	−23.8566	−0.942279	−0.471139	−	0.882059i	$-0.656157\pi$
$641$	−23.8566	−0.942279	−0.471139	+	0.882059i	$0.656157\pi$
$642$	61.8509	2.44106
$643$	−16.8458	−0.664334	−0.332167	−	0.943221i	$-0.607780\pi$
$643$	−16.8458	−0.664334	−0.332167	+	0.943221i	$0.607780\pi$
$644$	28.0490	1.10528
$645$	−11.1395	−0.438616
$646$	60.0863	2.36406
$647$	8.40839	0.330568	0.165284	−	0.986246i	$-0.447146\pi$
$647$	8.40839	0.330568	0.165284	+	0.986246i	$0.447146\pi$
$648$	30.7392	1.20755
$649$	−2.16767	−0.0850885
$650$	1.68730	0.0661813
$651$	11.3251	0.443866
$652$	53.7810	2.10622
$653$	17.3030	0.677118	0.338559	−	0.940945i	$-0.390060\pi$
$653$	17.3030	0.677118	0.338559	+	0.940945i	$0.390060\pi$
$654$	9.50904	0.371833
$655$	−0.274771	−0.0107362
$656$	43.3775	1.69361
$657$	0.0223489	0.000871912 0
$658$	−15.7333	−0.613348
$659$	−31.3426	−1.22094	−0.610468	−	0.792041i	$-0.709019\pi$
$659$	−31.3426	−1.22094	−0.610468	+	0.792041i	$0.709019\pi$
$660$	−5.28039	−0.205539
$661$	−38.5317	−1.49871	−0.749355	−	0.662169i	$-0.769636\pi$
$661$	−38.5317	−1.49871	−0.749355	+	0.662169i	$0.769636\pi$
$662$	−4.55108	−0.176883
$663$	4.86091	0.188782
$664$	−54.0108	−2.09603
$665$	−4.66612	−0.180944
$666$	−17.7348	−0.687210
$667$	9.09912	0.352319
$668$	71.6342	2.77161
$669$	−21.0801	−0.815003
$670$	15.0592	0.581789
$671$	−7.49432	−0.289315
$672$	−5.76852	−0.222525
$673$	−19.5187	−0.752392	−0.376196	−	0.926540i	$-0.622768\pi$
$673$	−19.5187	−0.752392	−0.376196	+	0.926540i	$0.622768\pi$
$674$	−66.0637	−2.54468
$675$	5.65640	0.217715
$676$	−54.8239	−2.10861
$677$	12.8101	0.492332	0.246166	−	0.969228i	$-0.420829\pi$
$677$	12.8101	0.492332	0.246166	+	0.969228i	$0.420829\pi$
$678$	17.9090	0.687793
$679$	13.5986	0.521868
$680$	30.4858	1.16908
$681$	22.6695	0.868697
$682$	17.0264	0.651973
$683$	−28.1023	−1.07531	−0.537653	−	0.843166i	$-0.680689\pi$
$683$	−28.1023	−1.07531	−0.537653	+	0.843166i	$0.680689\pi$
$684$	19.7823	0.756394
$685$	6.00003	0.229249
$686$	2.52338	0.0963430
$687$	1.42453	0.0543491
$688$	−49.5745	−1.89001
$689$	4.39225	0.167331
$690$	23.0857	0.878859
$691$	−38.5774	−1.46755	−0.733776	−	0.679392i	$-0.762244\pi$
$691$	−38.5774	−1.46755	−0.733776	+	0.679392i	$0.762244\pi$
$692$	−9.31153	−0.353971
$693$	−0.823876	−0.0312965
$694$	4.33043	0.164381
$695$	1.76516	0.0669564
$696$	−12.0571	−0.457022
$697$	34.9170	1.32258
$698$	−79.7407	−3.01823
$699$	38.0781	1.44024
$700$	−4.36744	−0.165074
$701$	−38.8325	−1.46668	−0.733342	−	0.679860i	$-0.762040\pi$
$701$	−38.8325	−1.46668	−0.733342	+	0.679860i	$0.762040\pi$
$702$	9.54404	0.360216
$703$	33.7836	1.27417
$704$	2.08876	0.0787232
$705$	−8.88196	−0.334514
$706$	62.9260	2.36825
$707$	−0.419005	−0.0157583
$708$	−15.8900	−0.597181
$709$	−24.5858	−0.923340	−0.461670	−	0.887052i	$-0.652750\pi$
$709$	−24.5858	−0.923340	−0.461670	+	0.887052i	$0.652750\pi$
$710$	29.4531	1.10536
$711$	6.38315	0.239387
$712$	−56.7257	−2.12588
$713$	−51.0577	−1.91213
$714$	−18.3439	−0.686502
$715$	−0.567515	−0.0212239
$716$	84.9236	3.17375
$717$	33.3396	1.24509
$718$	−83.0925	−3.10099
$719$	22.2165	0.828535	0.414267	−	0.910155i	$-0.364038\pi$
$719$	22.2165	0.828535	0.414267	+	0.910155i	$0.364038\pi$
$720$	6.15401	0.229346
$721$	1.31565	0.0489973
$722$	−6.99643	−0.260380
$723$	22.9833	0.854759
$724$	66.8550	2.48465
$725$	−1.41680	−0.0526187
$726$	−36.9515	−1.37140
$727$	−20.4443	−0.758239	−0.379119	−	0.925348i	$-0.623773\pi$
$727$	−20.4443	−0.758239	−0.379119	+	0.925348i	$0.623773\pi$
$728$	−3.99457	−0.148049
$729$	29.1680	1.08030
$730$	−0.0580957	−0.00215022
$731$	−39.9053	−1.47595
$732$	−54.9366	−2.03052
$733$	−44.1636	−1.63122	−0.815611	−	0.578601i	$-0.803599\pi$
$733$	−44.1636	−1.63122	−0.815611	+	0.578601i	$0.803599\pi$
$734$	37.9648	1.40131
$735$	1.42453	0.0525445
$736$	26.0066	0.958615
$737$	−5.06511	−0.186576
$738$	16.7601	0.616946
$739$	−3.84632	−0.141489	−0.0707446	−	0.997494i	$-0.522538\pi$
$739$	−3.84632	−0.141489	−0.0707446	+	0.997494i	$0.522538\pi$
$740$	31.6211	1.16242
$741$	−4.44463	−0.163278
$742$	−16.5752	−0.608497
$743$	13.9275	0.510950	0.255475	−	0.966816i	$-0.417768\pi$
$743$	13.9275	0.510950	0.255475	+	0.966816i	$0.417768\pi$
$744$	67.6555	2.48037
$745$	13.6841	0.501348
$746$	−85.5200	−3.13111
$747$	−8.77634	−0.321110
$748$	−18.9161	−0.691642
$749$	−17.2065	−0.628712
$750$	−3.59462	−0.131257
$751$	−1.37450	−0.0501564	−0.0250782	−	0.999685i	$-0.507983\pi$
$751$	−1.37450	−0.0501564	−0.0250782	+	0.999685i	$0.507983\pi$
$752$	−39.5277	−1.44143
$753$	−40.5582	−1.47802
$754$	−2.39057	−0.0870594
$755$	−18.7963	−0.684066
$756$	−24.7040	−0.898475
$757$	−26.9970	−0.981223	−0.490612	−	0.871378i	$-0.663227\pi$
$757$	−26.9970	−0.981223	−0.490612	+	0.871378i	$0.663227\pi$
$758$	−50.8164	−1.84574
$759$	−7.76479	−0.281844
$760$	−27.8751	−1.01114
$761$	−30.8697	−1.11903	−0.559513	−	0.828822i	$-0.689012\pi$
$761$	−30.8697	−1.11903	−0.559513	+	0.828822i	$0.689012\pi$
$762$	−40.3695	−1.46243
$763$	−2.64535	−0.0957681
$764$	−1.03227	−0.0373461
$765$	4.95371	0.179102
$766$	−72.7350	−2.62802
$767$	−1.70779	−0.0616647
$768$	44.4238	1.60301
$769$	−16.0771	−0.579753	−0.289877	−	0.957064i	$-0.593614\pi$
$769$	−16.0771	−0.579753	−0.289877	+	0.957064i	$0.593614\pi$
$770$	2.14166	0.0771801
$771$	−29.1803	−1.05090
$772$	−47.2018	−1.69883
$773$	38.3642	1.37987	0.689933	−	0.723873i	$-0.257640\pi$
$773$	38.3642	1.37987	0.689933	+	0.723873i	$0.257640\pi$
$774$	−19.1544	−0.688492
$775$	7.95008	0.285575
$776$	81.2375	2.91625
$777$	−10.3139	−0.370008
$778$	−51.9616	−1.86291
$779$	−31.9268	−1.14390
$780$	−4.16013	−0.148957
$781$	−9.90643	−0.354480
$782$	82.7008	2.95737
$783$	−8.01401	−0.286397
$784$	6.33964	0.226416
$785$	13.4881	0.481410
$786$	0.987698	0.0352300
$787$	12.2407	0.436332	0.218166	−	0.975912i	$-0.429993\pi$
$787$	12.2407	0.436332	0.218166	+	0.975912i	$0.429993\pi$
$788$	80.0628	2.85212
$789$	26.9658	0.960007
$790$	−16.5930	−0.590351
$791$	−4.98217	−0.177146
$792$	−4.92179	−0.174888
$793$	−5.90437	−0.209670
$794$	70.0376	2.48554
$795$	−9.35726	−0.331868
$796$	80.4748	2.85236
$797$	−23.6305	−0.837035	−0.418518	−	0.908209i	$-0.637450\pi$
$797$	−23.6305	−0.837035	−0.418518	+	0.908209i	$0.637450\pi$
$798$	16.7729	0.593755
$799$	−31.8181	−1.12564
$800$	−4.04942	−0.143169
$801$	−9.21748	−0.325684
$802$	4.90095	0.173059
$803$	0.0195402	0.000689560 0
$804$	−37.1294	−1.30945
$805$	−6.42229	−0.226356
$806$	13.4142	0.472493
$807$	−8.95676	−0.315293
$808$	−2.50311	−0.0880591
$809$	−15.1184	−0.531534	−0.265767	−	0.964037i	$-0.585625\pi$
$809$	−15.1184	−0.531534	−0.265767	+	0.964037i	$0.585625\pi$
$810$	−12.9842	−0.456217
$811$	−8.77456	−0.308116	−0.154058	−	0.988062i	$-0.549234\pi$
$811$	−8.77456	−0.308116	−0.154058	+	0.988062i	$0.549234\pi$
$812$	6.18780	0.217149
$813$	16.6457	0.583789
$814$	−15.5061	−0.543487
$815$	−12.3141	−0.431343
$816$	−46.0864	−1.61335
$817$	36.4879	1.27655
$818$	53.4697	1.86952
$819$	−0.649087	−0.0226809
$820$	−29.8832	−1.04356
$821$	44.5549	1.55498	0.777488	−	0.628898i	$-0.216494\pi$
$821$	44.5549	1.55498	0.777488	+	0.628898i	$0.216494\pi$
$822$	−21.5679	−0.752266
$823$	4.15176	0.144721	0.0723606	−	0.997379i	$-0.476947\pi$
$823$	4.15176	0.144721	0.0723606	+	0.997379i	$0.476947\pi$
$824$	7.85961	0.273803
$825$	1.20904	0.0420932
$826$	6.44477	0.224242
$827$	−3.77244	−0.131181	−0.0655904	−	0.997847i	$-0.520893\pi$
$827$	−3.77244	−0.131181	−0.0655904	+	0.997847i	$0.520893\pi$
$828$	27.2277	0.946227
$829$	−53.7792	−1.86783	−0.933915	−	0.357496i	$-0.883631\pi$
$829$	−53.7792	−1.86783	−0.933915	+	0.357496i	$0.883631\pi$
$830$	22.8141	0.791887
$831$	−33.9983	−1.17939
$832$	1.64562	0.0570517
$833$	5.10314	0.176813
$834$	−6.34509	−0.219713
$835$	−16.4019	−0.567610
$836$	17.2962	0.598201
$837$	44.9688	1.55435
$838$	−3.88463	−0.134192
$839$	−38.4162	−1.32627	−0.663137	−	0.748498i	$-0.730776\pi$
$839$	−38.4162	−1.32627	−0.663137	+	0.748498i	$0.730776\pi$
$840$	8.51005	0.293625
$841$	−26.9927	−0.930782
$842$	−29.4991	−1.01660
$843$	−6.84825	−0.235866
$844$	−19.2361	−0.662136
$845$	12.5529	0.431832
$846$	−15.2726	−0.525083
$847$	10.2797	0.353213
$848$	−41.6430	−1.43003
$849$	−11.9066	−0.408635
$850$	−12.8771	−0.441682
$851$	46.4987	1.59395
$852$	−72.6184	−2.48787
$853$	−40.5111	−1.38707	−0.693537	−	0.720421i	$-0.743948\pi$
$853$	−40.5111	−1.38707	−0.693537	+	0.720421i	$0.743948\pi$
$854$	22.2816	0.762461
$855$	−4.52949	−0.154905
$856$	−102.791	−3.51331
$857$	−12.3739	−0.422685	−0.211342	−	0.977412i	$-0.567783\pi$
$857$	−12.3739	−0.422685	−0.211342	+	0.977412i	$0.567783\pi$
$858$	2.04000	0.0696446
$859$	−8.89170	−0.303381	−0.151690	−	0.988428i	$-0.548472\pi$
$859$	−8.89170	−0.303381	−0.151690	+	0.988428i	$0.548472\pi$
$860$	34.1523	1.16458
$861$	9.74700	0.332177
$862$	34.8379	1.18658
$863$	−34.3946	−1.17081	−0.585403	−	0.810743i	$-0.699064\pi$
$863$	−34.3946	−1.17081	−0.585403	+	0.810743i	$0.699064\pi$
$864$	−22.9052	−0.779249
$865$	2.13203	0.0724913
$866$	4.17299	0.141804
$867$	−12.8806	−0.437448
$868$	−34.7215	−1.17852
$869$	5.58097	0.189322
$870$	5.09287	0.172665
$871$	−3.99052	−0.135214
$872$	−15.8032	−0.535163
$873$	13.2005	0.446768
$874$	−75.6185	−2.55783
$875$	1.00000	0.0338062
$876$	0.143238	0.00483958
$877$	−14.8655	−0.501972	−0.250986	−	0.967991i	$-0.580755\pi$
$877$	−14.8655	−0.501972	−0.250986	+	0.967991i	$0.580755\pi$
$878$	97.7465	3.29879
$879$	23.8499	0.804437
$880$	5.38062	0.181381
$881$	−46.4930	−1.56639	−0.783194	−	0.621778i	$-0.786411\pi$
$881$	−46.4930	−1.56639	−0.783194	+	0.621778i	$0.786411\pi$
$882$	2.44949	0.0824787
$883$	−36.7433	−1.23651	−0.618255	−	0.785978i	$-0.712160\pi$
$883$	−36.7433	−1.23651	−0.618255	+	0.785978i	$0.712160\pi$
$884$	−14.9030	−0.501242
$885$	3.63828	0.122299
$886$	−97.3716	−3.27126
$887$	40.6500	1.36489	0.682446	−	0.730936i	$-0.260916\pi$
$887$	40.6500	1.36489	0.682446	+	0.730936i	$0.260916\pi$
$888$	−61.6145	−2.06765
$889$	11.2305	0.376660
$890$	23.9608	0.803167
$891$	4.36717	0.146306
$892$	64.6291	2.16394
$893$	29.0933	0.973570
$894$	−49.1893	−1.64514
$895$	−19.4447	−0.649966
$896$	−14.3090	−0.478030
$897$	−6.11745	−0.204256
$898$	−1.34659	−0.0449363
$899$	−11.2637	−0.375665
$900$	−4.23956	−0.141319
$901$	−33.5208	−1.11674
$902$	14.6538	0.487918
$903$	−11.1395	−0.370698
$904$	−29.7632	−0.989910
$905$	−15.3076	−0.508842
$906$	67.5655	2.24471
$907$	35.6000	1.18208	0.591039	−	0.806643i	$-0.298718\pi$
$907$	35.6000	1.18208	0.591039	+	0.806643i	$0.298718\pi$
$908$	−69.5021	−2.30651
$909$	−0.406736	−0.0134906
$910$	1.68730	0.0559334
$911$	−11.5202	−0.381681	−0.190841	−	0.981621i	$-0.561121\pi$
$911$	−11.5202	−0.381681	−0.190841	+	0.981621i	$0.561121\pi$
$912$	42.1397	1.39538
$913$	−7.67341	−0.253953
$914$	46.4113	1.53515
$915$	12.5787	0.415838
$916$	−4.36744	−0.144304
$917$	−0.274771	−0.00907374
$918$	−72.8383	−2.40402
$919$	−11.2543	−0.371246	−0.185623	−	0.982621i	$-0.559430\pi$
$919$	−11.2543	−0.371246	−0.185623	+	0.982621i	$0.559430\pi$
$920$	−38.3664	−1.26490
$921$	−20.4638	−0.674306
$922$	−55.4291	−1.82546
$923$	−7.80474	−0.256896
$924$	−5.28039	−0.173712
$925$	−7.24020	−0.238056
$926$	−49.2785	−1.61939
$927$	1.27713	0.0419463
$928$	5.73723	0.188334
$929$	−47.5105	−1.55877	−0.779384	−	0.626547i	$-0.784468\pi$
$929$	−47.5105	−1.55877	−0.779384	+	0.626547i	$0.784468\pi$
$930$	−28.5775	−0.937094
$931$	−4.66612	−0.152926
$932$	−116.743	−3.82404
$933$	−24.5903	−0.805052
$934$	−36.7055	−1.20104
$935$	4.33117	0.141644
$936$	−3.87761	−0.126744
$937$	44.6900	1.45996	0.729979	−	0.683470i	$-0.239530\pi$
$937$	44.6900	1.45996	0.729979	+	0.683470i	$0.239530\pi$
$938$	15.0592	0.491701
$939$	23.2661	0.759260
$940$	27.2310	0.888179
$941$	−35.2538	−1.14924	−0.574621	−	0.818420i	$-0.694850\pi$
$941$	−35.2538	−1.14924	−0.574621	+	0.818420i	$0.694850\pi$
$942$	−48.4845	−1.57971
$943$	−43.9430	−1.43098
$944$	16.1916	0.526991
$945$	5.65640	0.184003
$946$	−16.7473	−0.544501
$947$	31.5402	1.02492	0.512460	−	0.858711i	$-0.328734\pi$
$947$	31.5402	1.02492	0.512460	+	0.858711i	$0.328734\pi$
$948$	40.9109	1.32873
$949$	0.0153947	0.000499733 0
$950$	11.7744	0.382011
$951$	13.7611	0.446233
$952$	30.4858	0.988052
$953$	−52.0857	−1.68722	−0.843611	−	0.536955i	$-0.819575\pi$
$953$	−52.0857	−1.68722	−0.843611	+	0.536955i	$0.819575\pi$
$954$	−16.0899	−0.520930
$955$	0.236355	0.00764828
$956$	−102.215	−3.30588
$957$	−1.71297	−0.0553723
$958$	8.24827	0.266489
$959$	6.00003	0.193751
$960$	−3.50584	−0.113150
$961$	32.2037	1.03883
$962$	−12.2164	−0.393872
$963$	−16.7027	−0.538237
$964$	−70.4642	−2.26950
$965$	10.8077	0.347911
$966$	23.0857	0.742771
$967$	54.9930	1.76845	0.884227	−	0.467057i	$-0.154686\pi$
$967$	54.9930	1.76845	0.884227	+	0.467057i	$0.154686\pi$
$968$	61.4101	1.97380
$969$	33.9206	1.08969
$970$	−34.3145	−1.10177
$971$	35.6879	1.14528	0.572640	−	0.819807i	$-0.305919\pi$
$971$	35.6879	1.14528	0.572640	+	0.819807i	$0.305919\pi$
$972$	−42.0987	−1.35032
$973$	1.76516	0.0565885
$974$	54.0928	1.73324
$975$	0.952534	0.0305055
$976$	55.9794	1.79186
$977$	19.5578	0.625708	0.312854	−	0.949801i	$-0.398715\pi$
$977$	19.5578	0.625708	0.312854	+	0.949801i	$0.398715\pi$
$978$	44.2645	1.41542
$979$	−8.05911	−0.257570
$980$	−4.36744	−0.139513
$981$	−2.56789	−0.0819865
$982$	64.6895	2.06432
$983$	−29.9583	−0.955522	−0.477761	−	0.878490i	$-0.658552\pi$
$983$	−29.9583	−0.955522	−0.477761	+	0.878490i	$0.658552\pi$
$984$	58.2280	1.85624
$985$	−18.3318	−0.584098
$986$	18.2444	0.581019
$987$	−8.88196	−0.282716
$988$	13.6267	0.433524
$989$	50.2208	1.59693
$990$	2.07895	0.0660734
$991$	−17.6034	−0.559189	−0.279595	−	0.960118i	$-0.590200\pi$
$991$	−17.6034	−0.559189	−0.279595	+	0.960118i	$0.590200\pi$
$992$	−32.1932	−1.02214
$993$	−2.56923	−0.0815320
$994$	29.4531	0.934196
$995$	−18.4261	−0.584147
$996$	−56.2494	−1.78233
$997$	3.33196	0.105524	0.0527622	−	0.998607i	$-0.483197\pi$
$997$	3.33196	0.105524	0.0527622	+	0.998607i	$0.483197\pi$
$998$	−14.6677	−0.464298
$999$	−40.9535	−1.29571

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8015.2.a.k.1.5	✓	49

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8015.2.a.k.1.5	✓	49	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)

\(f(q)\)	\(=\)	\(q-2.52338 q^{2} -1.42453 q^{3} +4.36744 q^{4} -1.00000 q^{5} +3.59462 q^{6} -1.00000 q^{7} -5.97394 q^{8} -0.970719 q^{9} +O(q^{10})\)	\(q-2.52338 q^{2} -1.42453 q^{3} +4.36744 q^{4} -1.00000 q^{5} +3.59462 q^{6} -1.00000 q^{7} -5.97394 q^{8} -0.970719 q^{9} +2.52338 q^{10} -0.848727 q^{11} -6.22154 q^{12} -0.668666 q^{13} +2.52338 q^{14} +1.42453 q^{15} +6.33964 q^{16} +5.10314 q^{17} +2.44949 q^{18} -4.66612 q^{19} -4.36744 q^{20} +1.42453 q^{21} +2.14166 q^{22} -6.42229 q^{23} +8.51005 q^{24} +1.00000 q^{25} +1.68730 q^{26} +5.65640 q^{27} -4.36744 q^{28} -1.41680 q^{29} -3.59462 q^{30} +7.95008 q^{31} -4.04942 q^{32} +1.20904 q^{33} -12.8771 q^{34} +1.00000 q^{35} -4.23956 q^{36} -7.24020 q^{37} +11.7744 q^{38} +0.952534 q^{39} +5.97394 q^{40} +6.84226 q^{41} -3.59462 q^{42} -7.81976 q^{43} -3.70676 q^{44} +0.970719 q^{45} +16.2059 q^{46} -6.23502 q^{47} -9.03099 q^{48} +1.00000 q^{49} -2.52338 q^{50} -7.26956 q^{51} -2.92036 q^{52} -6.56867 q^{53} -14.2732 q^{54} +0.848727 q^{55} +5.97394 q^{56} +6.64702 q^{57} +3.57513 q^{58} +2.55402 q^{59} +6.22154 q^{60} +8.83007 q^{61} -20.0611 q^{62} +0.970719 q^{63} -2.46105 q^{64} +0.668666 q^{65} -3.05086 q^{66} +5.96788 q^{67} +22.2876 q^{68} +9.14874 q^{69} -2.52338 q^{70} +11.6721 q^{71} +5.79902 q^{72} -0.0230230 q^{73} +18.2698 q^{74} -1.42453 q^{75} -20.3790 q^{76} +0.848727 q^{77} -2.40360 q^{78} -6.57570 q^{79} -6.33964 q^{80} -5.14555 q^{81} -17.2656 q^{82} +9.04107 q^{83} +6.22154 q^{84} -5.10314 q^{85} +19.7322 q^{86} +2.01828 q^{87} +5.07025 q^{88} +9.49552 q^{89} -2.44949 q^{90} +0.668666 q^{91} -28.0490 q^{92} -11.3251 q^{93} +15.7333 q^{94} +4.66612 q^{95} +5.76852 q^{96} -13.5986 q^{97} -2.52338 q^{98} +0.823876 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 49 q - 3 q^{2} - 10 q^{3} + 49 q^{4} - 49 q^{5} + 10 q^{6} - 49 q^{7} - 6 q^{8} + 39 q^{9}+O(q^{10}) \) 49 * q - 3 * q^2 - 10 * q^3 + 49 * q^4 - 49 * q^5 + 10 * q^6 - 49 * q^7 - 6 * q^8 + 39 * q^9	\( 49 q - 3 q^{2} - 10 q^{3} + 49 q^{4} - 49 q^{5} + 10 q^{6} - 49 q^{7} - 6 q^{8} + 39 q^{9} + 3 q^{10} + 16 q^{11} - 26 q^{12} - 31 q^{13} + 3 q^{14} + 10 q^{15} + 49 q^{16} - 18 q^{17} + 4 q^{18} - 16 q^{19} - 49 q^{20} + 10 q^{21} + 10 q^{22} + 10 q^{23} + 2 q^{24} + 49 q^{25} - 22 q^{26} - 58 q^{27} - 49 q^{28} + 31 q^{29} - 10 q^{30} - 35 q^{31} - 5 q^{32} - 82 q^{33} - 41 q^{34} + 49 q^{35} + 49 q^{36} - 24 q^{37} - 20 q^{38} + 41 q^{39} + 6 q^{40} + 30 q^{41} - 10 q^{42} - 19 q^{43} + 27 q^{44} - 39 q^{45} + 15 q^{46} - 39 q^{47} - 51 q^{48} + 49 q^{49} - 3 q^{50} + 46 q^{51} - 94 q^{52} - 17 q^{53} + 9 q^{54} - 16 q^{55} + 6 q^{56} - 23 q^{57} - 46 q^{58} + 11 q^{59} + 26 q^{60} - 9 q^{61} - 49 q^{62} - 39 q^{63} + 10 q^{64} + 31 q^{65} - 10 q^{66} - 2 q^{67} - 73 q^{68} - 47 q^{69} - 3 q^{70} + 26 q^{71} - 39 q^{72} - 100 q^{73} + 8 q^{74} - 10 q^{75} - 71 q^{76} - 16 q^{77} - 51 q^{78} + 50 q^{79} - 49 q^{80} + 61 q^{81} - 36 q^{82} - 67 q^{83} + 26 q^{84} + 18 q^{85} + 33 q^{86} - 45 q^{87} - q^{88} - 19 q^{89} - 4 q^{90} + 31 q^{91} + 7 q^{92} + 9 q^{93} - 33 q^{94} + 16 q^{95} - 8 q^{96} - 85 q^{97} - 3 q^{98} + 27 q^{99}+O(q^{100}) \) 49 * q - 3 * q^2 - 10 * q^3 + 49 * q^4 - 49 * q^5 + 10 * q^6 - 49 * q^7 - 6 * q^8 + 39 * q^9 + 3 * q^10 + 16 * q^11 - 26 * q^12 - 31 * q^13 + 3 * q^14 + 10 * q^15 + 49 * q^16 - 18 * q^17 + 4 * q^18 - 16 * q^19 - 49 * q^20 + 10 * q^21 + 10 * q^22 + 10 * q^23 + 2 * q^24 + 49 * q^25 - 22 * q^26 - 58 * q^27 - 49 * q^28 + 31 * q^29 - 10 * q^30 - 35 * q^31 - 5 * q^32 - 82 * q^33 - 41 * q^34 + 49 * q^35 + 49 * q^36 - 24 * q^37 - 20 * q^38 + 41 * q^39 + 6 * q^40 + 30 * q^41 - 10 * q^42 - 19 * q^43 + 27 * q^44 - 39 * q^45 + 15 * q^46 - 39 * q^47 - 51 * q^48 + 49 * q^49 - 3 * q^50 + 46 * q^51 - 94 * q^52 - 17 * q^53 + 9 * q^54 - 16 * q^55 + 6 * q^56 - 23 * q^57 - 46 * q^58 + 11 * q^59 + 26 * q^60 - 9 * q^61 - 49 * q^62 - 39 * q^63 + 10 * q^64 + 31 * q^65 - 10 * q^66 - 2 * q^67 - 73 * q^68 - 47 * q^69 - 3 * q^70 + 26 * q^71 - 39 * q^72 - 100 * q^73 + 8 * q^74 - 10 * q^75 - 71 * q^76 - 16 * q^77 - 51 * q^78 + 50 * q^79 - 49 * q^80 + 61 * q^81 - 36 * q^82 - 67 * q^83 + 26 * q^84 + 18 * q^85 + 33 * q^86 - 45 * q^87 - q^88 - 19 * q^89 - 4 * q^90 + 31 * q^91 + 7 * q^92 + 9 * q^93 - 33 * q^94 + 16 * q^95 - 8 * q^96 - 85 * q^97 - 3 * q^98 + 27 * q^99

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