LMFDB - Embedded newform 8015.2.a.n.1.12

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:	$68$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
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)

$f(q)$	$=$	$q-2.04947 q^{2} -1.65528 q^{3} +2.20033 q^{4} -1.00000 q^{5} +3.39245 q^{6} +1.00000 q^{7} -0.410568 q^{8} -0.260041 q^{9} +O(q^{10})$	\(q-2.04947 q^{2} -1.65528 q^{3} +2.20033 q^{4} -1.00000 q^{5} +3.39245 q^{6} +1.00000 q^{7} -0.410568 q^{8} -0.260041 q^{9} +2.04947 q^{10} +3.07599 q^{11} -3.64217 q^{12} -6.96455 q^{13} -2.04947 q^{14} +1.65528 q^{15} -3.55921 q^{16} +2.59404 q^{17} +0.532946 q^{18} -5.65948 q^{19} -2.20033 q^{20} -1.65528 q^{21} -6.30414 q^{22} -2.20232 q^{23} +0.679606 q^{24} +1.00000 q^{25} +14.2736 q^{26} +5.39629 q^{27} +2.20033 q^{28} -9.39223 q^{29} -3.39245 q^{30} -8.85195 q^{31} +8.11563 q^{32} -5.09163 q^{33} -5.31641 q^{34} -1.00000 q^{35} -0.572175 q^{36} -9.77015 q^{37} +11.5989 q^{38} +11.5283 q^{39} +0.410568 q^{40} -3.61685 q^{41} +3.39245 q^{42} -1.57071 q^{43} +6.76818 q^{44} +0.260041 q^{45} +4.51359 q^{46} -12.8789 q^{47} +5.89150 q^{48} +1.00000 q^{49} -2.04947 q^{50} -4.29387 q^{51} -15.3243 q^{52} +10.5760 q^{53} -11.0595 q^{54} -3.07599 q^{55} -0.410568 q^{56} +9.36804 q^{57} +19.2491 q^{58} +8.59806 q^{59} +3.64217 q^{60} -14.7665 q^{61} +18.1418 q^{62} -0.260041 q^{63} -9.51433 q^{64} +6.96455 q^{65} +10.4351 q^{66} -5.31962 q^{67} +5.70774 q^{68} +3.64546 q^{69} +2.04947 q^{70} -8.41810 q^{71} +0.106764 q^{72} -6.22527 q^{73} +20.0236 q^{74} -1.65528 q^{75} -12.4527 q^{76} +3.07599 q^{77} -23.6269 q^{78} +12.4141 q^{79} +3.55921 q^{80} -8.15226 q^{81} +7.41263 q^{82} -8.59977 q^{83} -3.64217 q^{84} -2.59404 q^{85} +3.21912 q^{86} +15.5468 q^{87} -1.26290 q^{88} +5.10322 q^{89} -0.532946 q^{90} -6.96455 q^{91} -4.84583 q^{92} +14.6525 q^{93} +26.3950 q^{94} +5.65948 q^{95} -13.4337 q^{96} +2.38854 q^{97} -2.04947 q^{98} -0.799881 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q + 9 q^{2} + 83 q^{4} - 68 q^{5} + 5 q^{6} + 68 q^{7} + 30 q^{8} + 86 q^{9}+O(q^{10}) $ 68 * q + 9 * q^2 + 83 * q^4 - 68 * q^5 + 5 * q^6 + 68 * q^7 + 30 * q^8 + 86 * q^9	\( 68 q + 9 q^{2} + 83 q^{4} - 68 q^{5} + 5 q^{6} + 68 q^{7} + 30 q^{8} + 86 q^{9} - 9 q^{10} + 5 q^{11} + 9 q^{12} + 15 q^{13} + 9 q^{14} + 109 q^{16} + 7 q^{17} + 39 q^{18} + 20 q^{19} - 83 q^{20} + 56 q^{22} + 36 q^{23} + q^{24} + 68 q^{25} + q^{26} + 12 q^{27} + 83 q^{28} - 16 q^{29} - 5 q^{30} + 31 q^{31} + 79 q^{32} + 45 q^{33} + 31 q^{34} - 68 q^{35} + 114 q^{36} + 72 q^{37} + 8 q^{38} + 47 q^{39} - 30 q^{40} + 6 q^{41} + 5 q^{42} + 75 q^{43} + 15 q^{44} - 86 q^{45} + 29 q^{46} - 10 q^{47} + 44 q^{48} + 68 q^{49} + 9 q^{50} + 23 q^{51} + 37 q^{52} + 41 q^{53} + 4 q^{54} - 5 q^{55} + 30 q^{56} + 55 q^{57} + 66 q^{58} - 5 q^{59} - 9 q^{60} - 2 q^{61} + 3 q^{62} + 86 q^{63} + 162 q^{64} - 15 q^{65} - 23 q^{66} + 92 q^{67} + 35 q^{68} - 25 q^{69} - 9 q^{70} - 2 q^{71} + 128 q^{72} + 80 q^{73} + 18 q^{74} + 71 q^{76} + 5 q^{77} + 20 q^{78} + 100 q^{79} - 109 q^{80} + 140 q^{81} + 36 q^{82} - 60 q^{83} + 9 q^{84} - 7 q^{85} - 27 q^{86} + 24 q^{87} + 175 q^{88} + 19 q^{89} - 39 q^{90} + 15 q^{91} + 75 q^{92} + 37 q^{93} + 11 q^{94} - 20 q^{95} + 15 q^{96} + 96 q^{97} + 9 q^{98} + 3 q^{99}+O(q^{100}) \) 68 * q + 9 * q^2 + 83 * q^4 - 68 * q^5 + 5 * q^6 + 68 * q^7 + 30 * q^8 + 86 * q^9 - 9 * q^10 + 5 * q^11 + 9 * q^12 + 15 * q^13 + 9 * q^14 + 109 * q^16 + 7 * q^17 + 39 * q^18 + 20 * q^19 - 83 * q^20 + 56 * q^22 + 36 * q^23 + q^24 + 68 * q^25 + q^26 + 12 * q^27 + 83 * q^28 - 16 * q^29 - 5 * q^30 + 31 * q^31 + 79 * q^32 + 45 * q^33 + 31 * q^34 - 68 * q^35 + 114 * q^36 + 72 * q^37 + 8 * q^38 + 47 * q^39 - 30 * q^40 + 6 * q^41 + 5 * q^42 + 75 * q^43 + 15 * q^44 - 86 * q^45 + 29 * q^46 - 10 * q^47 + 44 * q^48 + 68 * q^49 + 9 * q^50 + 23 * q^51 + 37 * q^52 + 41 * q^53 + 4 * q^54 - 5 * q^55 + 30 * q^56 + 55 * q^57 + 66 * q^58 - 5 * q^59 - 9 * q^60 - 2 * q^61 + 3 * q^62 + 86 * q^63 + 162 * q^64 - 15 * q^65 - 23 * q^66 + 92 * q^67 + 35 * q^68 - 25 * q^69 - 9 * q^70 - 2 * q^71 + 128 * q^72 + 80 * q^73 + 18 * q^74 + 71 * q^76 + 5 * q^77 + 20 * q^78 + 100 * q^79 - 109 * q^80 + 140 * q^81 + 36 * q^82 - 60 * q^83 + 9 * q^84 - 7 * q^85 - 27 * q^86 + 24 * q^87 + 175 * q^88 + 19 * q^89 - 39 * q^90 + 15 * q^91 + 75 * q^92 + 37 * q^93 + 11 * q^94 - 20 * q^95 + 15 * q^96 + 96 * q^97 + 9 * q^98 + 3 * 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 $

$2$	−2.04947	−1.44919	−0.724597	−	0.689173i	$-0.757974\pi$
$2$	−2.04947	−1.44919	−0.724597	+	0.689173i	$0.757974\pi$
$3$	−1.65528	−0.955678	−0.477839	−	0.878448i	$-0.658580\pi$
$3$	−1.65528	−0.955678	−0.477839	+	0.878448i	$0.658580\pi$
$4$	2.20033	1.10016
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	3.39245	1.38496
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−0.410568	−0.145158
$9$	−0.260041	−0.0866802
$10$	2.04947	0.648099
$11$	3.07599	0.927445	0.463722	−	0.885981i	$-0.346513\pi$
$11$	3.07599	0.927445	0.463722	+	0.885981i	$0.346513\pi$
$12$	−3.64217	−1.05140
$13$	−6.96455	−1.93162	−0.965809	−	0.259255i	$-0.916523\pi$
$13$	−6.96455	−1.93162	−0.965809	+	0.259255i	$0.916523\pi$
$14$	−2.04947	−0.547744
$15$	1.65528	0.427392
$16$	−3.55921	−0.889803
$17$	2.59404	0.629147	0.314574	−	0.949233i	$-0.398138\pi$
$17$	2.59404	0.629147	0.314574	+	0.949233i	$0.398138\pi$
$18$	0.532946	0.125616
$19$	−5.65948	−1.29837	−0.649187	−	0.760629i	$-0.724891\pi$
$19$	−5.65948	−1.29837	−0.649187	+	0.760629i	$0.724891\pi$
$20$	−2.20033	−0.492009
$21$	−1.65528	−0.361212
$22$	−6.30414	−1.34405
$23$	−2.20232	−0.459215	−0.229608	−	0.973283i	$-0.573744\pi$
$23$	−2.20232	−0.459215	−0.229608	+	0.973283i	$0.573744\pi$
$24$	0.679606	0.138724
$25$	1.00000	0.200000
$26$	14.2736	2.79929
$27$	5.39629	1.03852
$28$	2.20033	0.415823
$29$	−9.39223	−1.74409	−0.872047	−	0.489423i	$-0.837208\pi$
$29$	−9.39223	−1.74409	−0.872047	+	0.489423i	$0.837208\pi$
$30$	−3.39245	−0.619374
$31$	−8.85195	−1.58986	−0.794929	−	0.606702i	$-0.792492\pi$
$31$	−8.85195	−1.58986	−0.794929	+	0.606702i	$0.792492\pi$
$32$	8.11563	1.43465
$33$	−5.09163	−0.886338
$34$	−5.31641	−0.911757
$35$	−1.00000	−0.169031
$36$	−0.572175	−0.0953625
$37$	−9.77015	−1.60620	−0.803102	−	0.595842i	$-0.796818\pi$
$37$	−9.77015	−1.60620	−0.803102	+	0.595842i	$0.796818\pi$
$38$	11.5989	1.88160
$39$	11.5283	1.84600
$40$	0.410568	0.0649165
$41$	−3.61685	−0.564857	−0.282429	−	0.959288i	$-0.591140\pi$
$41$	−3.61685	−0.564857	−0.282429	+	0.959288i	$0.591140\pi$
$42$	3.39245	0.523467
$43$	−1.57071	−0.239531	−0.119765	−	0.992802i	$-0.538214\pi$
$43$	−1.57071	−0.239531	−0.119765	+	0.992802i	$0.538214\pi$
$44$	6.76818	1.02034
$45$	0.260041	0.0387646
$46$	4.51359	0.665493
$47$	−12.8789	−1.87859	−0.939293	−	0.343115i	$-0.888518\pi$
$47$	−12.8789	−1.87859	−0.939293	+	0.343115i	$0.888518\pi$
$48$	5.89150	0.850364
$49$	1.00000	0.142857
$50$	−2.04947	−0.289839
$51$	−4.29387	−0.601262
$52$	−15.3243	−2.12510
$53$	10.5760	1.45272	0.726360	−	0.687315i	$-0.241211\pi$
$53$	10.5760	1.45272	0.726360	+	0.687315i	$0.241211\pi$
$54$	−11.0595	−1.50501
$55$	−3.07599	−0.414766
$56$	−0.410568	−0.0548645
$57$	9.36804	1.24083
$58$	19.2491	2.52753
$59$	8.59806	1.11937	0.559686	−	0.828705i	$-0.310922\pi$
$59$	8.59806	1.11937	0.559686	+	0.828705i	$0.310922\pi$
$60$	3.64217	0.470202
$61$	−14.7665	−1.89066	−0.945329	−	0.326118i	$-0.894259\pi$
$61$	−14.7665	−1.89066	−0.945329	+	0.326118i	$0.894259\pi$
$62$	18.1418	2.30401
$63$	−0.260041	−0.0327620
$64$	−9.51433	−1.18929
$65$	6.96455	0.863846
$66$	10.4351	1.28448
$67$	−5.31962	−0.649895	−0.324947	−	0.945732i	$-0.605347\pi$
$67$	−5.31962	−0.649895	−0.324947	+	0.945732i	$0.605347\pi$
$68$	5.70774	0.692166
$69$	3.64546	0.438862
$70$	2.04947	0.244959
$71$	−8.41810	−0.999045	−0.499522	−	0.866301i	$-0.666491\pi$
$71$	−8.41810	−0.999045	−0.499522	+	0.866301i	$0.666491\pi$
$72$	0.106764	0.0125823
$73$	−6.22527	−0.728613	−0.364307	−	0.931279i	$-0.618694\pi$
$73$	−6.22527	−0.728613	−0.364307	+	0.931279i	$0.618694\pi$
$74$	20.0236	2.32770
$75$	−1.65528	−0.191136
$76$	−12.4527	−1.42843
$77$	3.07599	0.350541
$78$	−23.6269	−2.67522
$79$	12.4141	1.39670	0.698349	−	0.715758i	$-0.253919\pi$
$79$	12.4141	1.39670	0.698349	+	0.715758i	$0.253919\pi$
$80$	3.55921	0.397932
$81$	−8.15226	−0.905806
$82$	7.41263	0.818588
$83$	−8.59977	−0.943947	−0.471974	−	0.881613i	$-0.656458\pi$
$83$	−8.59977	−0.943947	−0.471974	+	0.881613i	$0.656458\pi$
$84$	−3.64217	−0.397393
$85$	−2.59404	−0.281363
$86$	3.21912	0.347127
$87$	15.5468	1.66679
$88$	−1.26290	−0.134626
$89$	5.10322	0.540940	0.270470	−	0.962728i	$-0.412821\pi$
$89$	5.10322	0.540940	0.270470	+	0.962728i	$0.412821\pi$
$90$	−0.532946	−0.0561774
$91$	−6.96455	−0.730083
$92$	−4.84583	−0.505213
$93$	14.6525	1.51939
$94$	26.3950	2.72244
$95$	5.65948	0.580651
$96$	−13.4337	−1.37107
$97$	2.38854	0.242520	0.121260	−	0.992621i	$-0.461307\pi$
$97$	2.38854	0.242520	0.121260	+	0.992621i	$0.461307\pi$
$98$	−2.04947	−0.207028
$99$	−0.799881	−0.0803911
$100$	2.20033	0.220033
$101$	−16.3202	−1.62392	−0.811962	−	0.583710i	$-0.801601\pi$
$101$	−16.3202	−1.62392	−0.811962	+	0.583710i	$0.801601\pi$
$102$	8.80016	0.871346
$103$	9.25451	0.911874	0.455937	−	0.890012i	$-0.349304\pi$
$103$	9.25451	0.911874	0.455937	+	0.890012i	$0.349304\pi$
$104$	2.85942	0.280389
$105$	1.65528	0.161539
$106$	−21.6751	−2.10527
$107$	3.96790	0.383592	0.191796	−	0.981435i	$-0.438569\pi$
$107$	3.96790	0.383592	0.191796	+	0.981435i	$0.438569\pi$
$108$	11.8736	1.14254
$109$	−5.33851	−0.511337	−0.255668	−	0.966765i	$-0.582296\pi$
$109$	−5.33851	−0.511337	−0.255668	+	0.966765i	$0.582296\pi$
$110$	6.30414	0.601076
$111$	16.1724	1.53501
$112$	−3.55921	−0.336314
$113$	2.55746	0.240586	0.120293	−	0.992738i	$-0.461617\pi$
$113$	2.55746	0.240586	0.120293	+	0.992738i	$0.461617\pi$
$114$	−19.1995	−1.79820
$115$	2.20232	0.205367
$116$	−20.6660	−1.91879
$117$	1.81107	0.167433
$118$	−17.6215	−1.62219
$119$	2.59404	0.237795
$120$	−0.679606	−0.0620393
$121$	−1.53831	−0.139846
$122$	30.2635	2.73993
$123$	5.98691	0.539821
$124$	−19.4772	−1.74911
$125$	−1.00000	−0.0894427
$126$	0.532946	0.0474786
$127$	12.9738	1.15124	0.575619	−	0.817718i	$-0.304761\pi$
$127$	12.9738	1.15124	0.575619	+	0.817718i	$0.304761\pi$
$128$	3.26807	0.288859
$129$	2.59997	0.228914
$130$	−14.2736	−1.25188
$131$	−17.0650	−1.49097	−0.745487	−	0.666520i	$-0.767783\pi$
$131$	−17.0650	−1.49097	−0.745487	+	0.666520i	$0.767783\pi$
$132$	−11.2033	−0.975118
$133$	−5.65948	−0.490739
$134$	10.9024	0.941824
$135$	−5.39629	−0.464438
$136$	−1.06503	−0.0913257
$137$	19.4528	1.66197	0.830984	−	0.556296i	$-0.187778\pi$
$137$	19.4528	1.66197	0.830984	+	0.556296i	$0.187778\pi$
$138$	−7.47127	−0.635996
$139$	2.63491	0.223490	0.111745	−	0.993737i	$-0.464356\pi$
$139$	2.63491	0.223490	0.111745	+	0.993737i	$0.464356\pi$
$140$	−2.20033	−0.185962
$141$	21.3183	1.79532
$142$	17.2526	1.44781
$143$	−21.4229	−1.79147
$144$	0.925539	0.0771283
$145$	9.39223	0.779982
$146$	12.7585	1.05590
$147$	−1.65528	−0.136525
$148$	−21.4976	−1.76709
$149$	−9.39115	−0.769353	−0.384677	−	0.923051i	$-0.625687\pi$
$149$	−9.39115	−0.769353	−0.384677	+	0.923051i	$0.625687\pi$
$150$	3.39245	0.276993
$151$	1.11243	0.0905281	0.0452640	−	0.998975i	$-0.485587\pi$
$151$	1.11243	0.0905281	0.0452640	+	0.998975i	$0.485587\pi$
$152$	2.32360	0.188469
$153$	−0.674556	−0.0545346
$154$	−6.30414	−0.508002
$155$	8.85195	0.711006
$156$	25.3660	2.03091
$157$	−7.75706	−0.619080	−0.309540	−	0.950886i	$-0.600175\pi$
$157$	−7.75706	−0.619080	−0.309540	+	0.950886i	$0.600175\pi$
$158$	−25.4424	−2.02409
$159$	−17.5062	−1.38833
$160$	−8.11563	−0.641597
$161$	−2.20232	−0.173567
$162$	16.7078	1.31269
$163$	13.7377	1.07602	0.538011	−	0.842938i	$-0.319176\pi$
$163$	13.7377	1.07602	0.538011	+	0.842938i	$0.319176\pi$
$164$	−7.95826	−0.621436
$165$	5.09163	0.396383
$166$	17.6250	1.36796
$167$	6.00009	0.464301	0.232150	−	0.972680i	$-0.425424\pi$
$167$	6.00009	0.464301	0.232150	+	0.972680i	$0.425424\pi$
$168$	0.679606	0.0524328
$169$	35.5049	2.73115
$170$	5.31641	0.407750
$171$	1.47170	0.112543
$172$	−3.45608	−0.263523
$173$	14.1260	1.07398	0.536990	−	0.843588i	$-0.319561\pi$
$173$	14.1260	1.07398	0.536990	+	0.843588i	$0.319561\pi$
$174$	−31.8627	−2.41550
$175$	1.00000	0.0755929
$176$	−10.9481	−0.825243
$177$	−14.2322	−1.06976
$178$	−10.4589	−0.783927
$179$	−17.6250	−1.31736	−0.658678	−	0.752425i	$-0.728884\pi$
$179$	−17.6250	−1.31736	−0.658678	+	0.752425i	$0.728884\pi$
$180$	0.572175	0.0426474
$181$	−20.8984	−1.55337	−0.776685	−	0.629890i	$-0.783100\pi$
$181$	−20.8984	−1.55337	−0.776685	+	0.629890i	$0.783100\pi$
$182$	14.2736	1.05803
$183$	24.4427	1.80686
$184$	0.904203	0.0666587
$185$	9.77015	0.718316
$186$	−30.0298	−2.20189
$187$	7.97924	0.583500
$188$	−28.3379	−2.06675
$189$	5.39629	0.392522
$190$	−11.5989	−0.841476
$191$	−16.4141	−1.18768	−0.593841	−	0.804582i	$-0.702389\pi$
$191$	−16.4141	−1.18768	−0.593841	+	0.804582i	$0.702389\pi$
$192$	15.7489	1.13658
$193$	−21.1233	−1.52048	−0.760242	−	0.649639i	$-0.774920\pi$
$193$	−21.1233	−1.52048	−0.760242	+	0.649639i	$0.774920\pi$
$194$	−4.89524	−0.351458
$195$	−11.5283	−0.825558
$196$	2.20033	0.157166
$197$	−22.4665	−1.60067	−0.800336	−	0.599551i	$-0.795346\pi$
$197$	−22.4665	−1.60067	−0.800336	+	0.599551i	$0.795346\pi$
$198$	1.63933	0.116502
$199$	11.6681	0.827132	0.413566	−	0.910474i	$-0.364283\pi$
$199$	11.6681	0.827132	0.413566	+	0.910474i	$0.364283\pi$
$200$	−0.410568	−0.0290316
$201$	8.80547	0.621090
$202$	33.4479	2.35338
$203$	−9.39223	−0.659205
$204$	−9.44793	−0.661487
$205$	3.61685	0.252612
$206$	−18.9669	−1.32148
$207$	0.572693	0.0398049
$208$	24.7883	1.71876
$209$	−17.4085	−1.20417
$210$	−3.39245	−0.234101
$211$	−3.57294	−0.245971	−0.122986	−	0.992408i	$-0.539247\pi$
$211$	−3.57294	−0.245971	−0.122986	+	0.992408i	$0.539247\pi$
$212$	23.2706	1.59823
$213$	13.9343	0.954765
$214$	−8.13210	−0.555899
$215$	1.57071	0.107122
$216$	−2.21554	−0.150749
$217$	−8.85195	−0.600910
$218$	10.9411	0.741027
$219$	10.3046	0.696319
$220$	−6.76818	−0.456311
$221$	−18.0663	−1.21527
$222$	−33.1448	−2.22453
$223$	14.5832	0.976564	0.488282	−	0.872686i	$-0.337624\pi$
$223$	14.5832	0.976564	0.488282	+	0.872686i	$0.337624\pi$
$224$	8.11563	0.542249
$225$	−0.260041	−0.0173360
$226$	−5.24144	−0.348655
$227$	−13.4862	−0.895110	−0.447555	−	0.894256i	$-0.647705\pi$
$227$	−13.4862	−0.895110	−0.447555	+	0.894256i	$0.647705\pi$
$228$	20.6128	1.36511
$229$	−1.00000	−0.0660819
$229$	−1.00000	−0.0660819
$230$	−4.51359	−0.297617
$231$	−5.09163	−0.335004
$232$	3.85615	0.253169
$233$	−5.67709	−0.371918	−0.185959	−	0.982557i	$-0.559539\pi$
$233$	−5.67709	−0.371918	−0.185959	+	0.982557i	$0.559539\pi$
$234$	−3.71172	−0.242643
$235$	12.8789	0.840130
$236$	18.9186	1.23149
$237$	−20.5489	−1.33479
$238$	−5.31641	−0.344612
$239$	−13.3075	−0.860789	−0.430394	−	0.902641i	$-0.641626\pi$
$239$	−13.3075	−0.860789	−0.430394	+	0.902641i	$0.641626\pi$
$240$	−5.89150	−0.380295
$241$	−14.6454	−0.943392	−0.471696	−	0.881761i	$-0.656358\pi$
$241$	−14.6454	−0.943392	−0.471696	+	0.881761i	$0.656358\pi$
$242$	3.15271	0.202664
$243$	−2.69458	−0.172857
$244$	−32.4912	−2.08003
$245$	−1.00000	−0.0638877
$246$	−12.2700	−0.782306
$247$	39.4157	2.50796
$248$	3.63433	0.230780
$249$	14.2350	0.902109
$250$	2.04947	0.129620
$251$	11.1342	0.702784	0.351392	−	0.936229i	$-0.385709\pi$
$251$	11.1342	0.702784	0.351392	+	0.936229i	$0.385709\pi$
$252$	−0.572175	−0.0360436
$253$	−6.77431	−0.425897
$254$	−26.5894	−1.66837
$255$	4.29387	0.268893
$256$	12.3308	0.770678
$257$	−10.7262	−0.669080	−0.334540	−	0.942382i	$-0.608581\pi$
$257$	−10.7262	−0.669080	−0.334540	+	0.942382i	$0.608581\pi$
$258$	−5.32856	−0.331741
$259$	−9.77015	−0.607088
$260$	15.3243	0.950372
$261$	2.44236	0.151178
$262$	34.9742	2.16071
$263$	−5.68688	−0.350668	−0.175334	−	0.984509i	$-0.556101\pi$
$263$	−5.68688	−0.350668	−0.175334	+	0.984509i	$0.556101\pi$
$264$	2.09046	0.128659
$265$	−10.5760	−0.649676
$266$	11.5989	0.711177
$267$	−8.44727	−0.516964
$268$	−11.7049	−0.714991
$269$	−6.08152	−0.370797	−0.185398	−	0.982663i	$-0.559358\pi$
$269$	−6.08152	−0.370797	−0.185398	+	0.982663i	$0.559358\pi$
$270$	11.0595	0.673062
$271$	14.6950	0.892658	0.446329	−	0.894869i	$-0.352731\pi$
$271$	14.6950	0.892658	0.446329	+	0.894869i	$0.352731\pi$
$272$	−9.23274	−0.559817
$273$	11.5283	0.697724
$274$	−39.8680	−2.40852
$275$	3.07599	0.185489
$276$	8.02121	0.482820
$277$	−16.5986	−0.997312	−0.498656	−	0.866800i	$-0.666173\pi$
$277$	−16.5986	−0.997312	−0.498656	+	0.866800i	$0.666173\pi$
$278$	−5.40017	−0.323881
$279$	2.30187	0.137809
$280$	0.410568	0.0245361
$281$	−27.8245	−1.65987	−0.829935	−	0.557861i	$-0.811622\pi$
$281$	−27.8245	−1.65987	−0.829935	+	0.557861i	$0.811622\pi$
$282$	−43.6912	−2.60177
$283$	4.12955	0.245476	0.122738	−	0.992439i	$-0.460832\pi$
$283$	4.12955	0.245476	0.122738	+	0.992439i	$0.460832\pi$
$284$	−18.5226	−1.09911
$285$	−9.36804	−0.554915
$286$	43.9055	2.59619
$287$	−3.61685	−0.213496
$288$	−2.11039	−0.124356
$289$	−10.2709	−0.604173
$290$	−19.2491	−1.13035
$291$	−3.95371	−0.231771
$292$	−13.6977	−0.801594
$293$	9.34494	0.545937	0.272969	−	0.962023i	$-0.411994\pi$
$293$	9.34494	0.545937	0.272969	+	0.962023i	$0.411994\pi$
$294$	3.39245	0.197852
$295$	−8.59806	−0.500599
$296$	4.01132	0.233153
$297$	16.5989	0.963166
$298$	19.2469	1.11494
$299$	15.3382	0.887029
$300$	−3.64217	−0.210281
$301$	−1.57071	−0.0905342
$302$	−2.27989	−0.131193
$303$	27.0146	1.55195
$304$	20.1433	1.15530
$305$	14.7665	0.845528
$306$	1.38248	0.0790313
$307$	−9.64456	−0.550444	−0.275222	−	0.961381i	$-0.588751\pi$
$307$	−9.64456	−0.550444	−0.275222	+	0.961381i	$0.588751\pi$
$308$	6.76818	0.385653
$309$	−15.3188	−0.871458
$310$	−18.1418	−1.03039
$311$	−0.947453	−0.0537251	−0.0268626	−	0.999639i	$-0.508552\pi$
$311$	−0.947453	−0.0537251	−0.0268626	+	0.999639i	$0.508552\pi$
$312$	−4.73315	−0.267962
$313$	−20.7010	−1.17009	−0.585044	−	0.811002i	$-0.698923\pi$
$313$	−20.7010	−1.17009	−0.585044	+	0.811002i	$0.698923\pi$
$314$	15.8979	0.897168
$315$	0.260041	0.0146516
$316$	27.3151	1.53660
$317$	−6.74921	−0.379073	−0.189537	−	0.981874i	$-0.560699\pi$
$317$	−6.74921	−0.379073	−0.189537	+	0.981874i	$0.560699\pi$
$318$	35.8784	2.01196
$319$	−28.8904	−1.61755
$320$	9.51433	0.531867
$321$	−6.56800	−0.366590
$322$	4.51359	0.251533
$323$	−14.6809	−0.816869
$324$	−17.9376	−0.996536
$325$	−6.96455	−0.386324
$326$	−28.1551	−1.55936
$327$	8.83675	0.488673
$328$	1.48496	0.0819934
$329$	−12.8789	−0.710039
$330$	−10.4351	−0.574435
$331$	6.89598	0.379037	0.189519	−	0.981877i	$-0.439307\pi$
$331$	6.89598	0.379037	0.189519	+	0.981877i	$0.439307\pi$
$332$	−18.9223	−1.03850
$333$	2.54064	0.139226
$334$	−12.2970	−0.672862
$335$	5.31962	0.290642
$336$	5.89150	0.321408
$337$	−34.4338	−1.87573	−0.937865	−	0.346999i	$-0.887201\pi$
$337$	−34.4338	−1.87573	−0.937865	+	0.346999i	$0.887201\pi$
$338$	−72.7663	−3.95796
$339$	−4.23332	−0.229922
$340$	−5.70774	−0.309546
$341$	−27.2285	−1.47451
$342$	−3.01620	−0.163097
$343$	1.00000	0.0539949
$344$	0.644884	0.0347698
$345$	−3.64546	−0.196265
$346$	−28.9508	−1.55641
$347$	18.2698	0.980773	0.490386	−	0.871505i	$-0.336856\pi$
$347$	18.2698	0.980773	0.490386	+	0.871505i	$0.336856\pi$
$348$	34.2081	1.83374
$349$	−9.66908	−0.517574	−0.258787	−	0.965934i	$-0.583323\pi$
$349$	−9.66908	−0.517574	−0.258787	+	0.965934i	$0.583323\pi$
$350$	−2.04947	−0.109549
$351$	−37.5827	−2.00602
$352$	24.9636	1.33056
$353$	28.2080	1.50136	0.750680	−	0.660666i	$-0.229726\pi$
$353$	28.2080	1.50136	0.750680	+	0.660666i	$0.229726\pi$
$354$	29.1685	1.55029
$355$	8.41810	0.446786
$356$	11.2288	0.595123
$357$	−4.29387	−0.227256
$358$	36.1220	1.90911
$359$	18.4787	0.975266	0.487633	−	0.873049i	$-0.337860\pi$
$359$	18.4787	0.975266	0.487633	+	0.873049i	$0.337860\pi$
$360$	−0.106764	−0.00562698
$361$	13.0297	0.685776
$362$	42.8307	2.25113
$363$	2.54633	0.133648
$364$	−15.3243	−0.803211
$365$	6.22527	0.325846
$366$	−50.0947	−2.61849
$367$	−17.6617	−0.921935	−0.460967	−	0.887417i	$-0.652497\pi$
$367$	−17.6617	−0.921935	−0.460967	+	0.887417i	$0.652497\pi$
$368$	7.83852	0.408611
$369$	0.940528	0.0489619
$370$	−20.0236	−1.04098
$371$	10.5760	0.549076
$372$	32.2403	1.67158
$373$	29.1711	1.51042	0.755212	−	0.655481i	$-0.227534\pi$
$373$	29.1711	1.51042	0.755212	+	0.655481i	$0.227534\pi$
$374$	−16.3532	−0.845604
$375$	1.65528	0.0854784
$376$	5.28769	0.272692
$377$	65.4126	3.36892
$378$	−11.0595	−0.568841
$379$	22.8228	1.17233	0.586164	−	0.810193i	$-0.300638\pi$
$379$	22.8228	1.17233	0.586164	+	0.810193i	$0.300638\pi$
$380$	12.4527	0.638811
$381$	−21.4753	−1.10021
$382$	33.6402	1.72118
$383$	−12.1838	−0.622564	−0.311282	−	0.950318i	$-0.600758\pi$
$383$	−12.1838	−0.622564	−0.311282	+	0.950318i	$0.600758\pi$
$384$	−5.40958	−0.276056
$385$	−3.07599	−0.156767
$386$	43.2915	2.20348
$387$	0.408448	0.0207626
$388$	5.25558	0.266811
$389$	23.0652	1.16945	0.584727	−	0.811230i	$-0.301202\pi$
$389$	23.0652	1.16945	0.584727	+	0.811230i	$0.301202\pi$
$390$	23.6269	1.19639
$391$	−5.71291	−0.288914
$392$	−0.410568	−0.0207368
$393$	28.2474	1.42489
$394$	46.0445	2.31969
$395$	−12.4141	−0.624622
$396$	−1.76000	−0.0884434
$397$	−20.6660	−1.03720	−0.518599	−	0.855017i	$-0.673546\pi$
$397$	−20.6660	−1.03720	−0.518599	+	0.855017i	$0.673546\pi$
$398$	−23.9135	−1.19868
$399$	9.36804	0.468989
$400$	−3.55921	−0.177961
$401$	11.8690	0.592711	0.296355	−	0.955078i	$-0.404229\pi$
$401$	11.8690	0.592711	0.296355	+	0.955078i	$0.404229\pi$
$402$	−18.0466	−0.900080
$403$	61.6499	3.07100
$404$	−35.9099	−1.78658
$405$	8.15226	0.405089
$406$	19.2491	0.955317
$407$	−30.0529	−1.48966
$408$	1.76293	0.0872779
$409$	11.0016	0.543994	0.271997	−	0.962298i	$-0.412316\pi$
$409$	11.0016	0.543994	0.271997	+	0.962298i	$0.412316\pi$
$410$	−7.41263	−0.366084
$411$	−32.1999	−1.58831
$412$	20.3630	1.00321
$413$	8.59806	0.423083
$414$	−1.17372	−0.0576850
$415$	8.59977	0.422146
$416$	−56.5217	−2.77120
$417$	−4.36152	−0.213585
$418$	35.6782	1.74508
$419$	−31.2065	−1.52454	−0.762268	−	0.647261i	$-0.775914\pi$
$419$	−31.2065	−1.52454	−0.762268	+	0.647261i	$0.775914\pi$
$420$	3.64217	0.177719
$421$	−14.8919	−0.725785	−0.362893	−	0.931831i	$-0.618211\pi$
$421$	−14.8919	−0.725785	−0.362893	+	0.931831i	$0.618211\pi$
$422$	7.32263	0.356460
$423$	3.34905	0.162836
$424$	−4.34215	−0.210874
$425$	2.59404	0.125829
$426$	−28.5580	−1.38364
$427$	−14.7665	−0.714602
$428$	8.73069	0.422014
$429$	35.4609	1.71207
$430$	−3.21912	−0.155240
$431$	−34.8670	−1.67949	−0.839743	−	0.542984i	$-0.817294\pi$
$431$	−34.8670	−1.67949	−0.839743	+	0.542984i	$0.817294\pi$
$432$	−19.2065	−0.924074
$433$	−20.5393	−0.987056	−0.493528	−	0.869730i	$-0.664293\pi$
$433$	−20.5393	−0.987056	−0.493528	+	0.869730i	$0.664293\pi$
$434$	18.1418	0.870835
$435$	−15.5468	−0.745412
$436$	−11.7465	−0.562555
$437$	12.4640	0.596234
$438$	−21.1189	−1.00910
$439$	−34.7253	−1.65735	−0.828674	−	0.559731i	$-0.810904\pi$
$439$	−34.7253	−1.65735	−0.828674	+	0.559731i	$0.810904\pi$
$440$	1.26290	0.0602065
$441$	−0.260041	−0.0123829
$442$	37.0264	1.76117
$443$	3.66593	0.174174	0.0870869	−	0.996201i	$-0.472244\pi$
$443$	3.66593	0.174174	0.0870869	+	0.996201i	$0.472244\pi$
$444$	35.5845	1.68877
$445$	−5.10322	−0.241916
$446$	−29.8879	−1.41523
$447$	15.5450	0.735254
$448$	−9.51433	−0.449510
$449$	17.8247	0.841198	0.420599	−	0.907247i	$-0.361820\pi$
$449$	17.8247	0.841198	0.420599	+	0.907247i	$0.361820\pi$
$450$	0.532946	0.0251233
$451$	−11.1254	−0.523874
$452$	5.62725	0.264684
$453$	−1.84138	−0.0865157
$454$	27.6395	1.29719
$455$	6.96455	0.326503
$456$	−3.84622	−0.180116
$457$	21.7161	1.01583	0.507917	−	0.861406i	$-0.330416\pi$
$457$	21.7161	1.01583	0.507917	+	0.861406i	$0.330416\pi$
$458$	2.04947	0.0957655
$459$	13.9982	0.653380
$460$	4.84583	0.225938
$461$	−8.79549	−0.409647	−0.204823	−	0.978799i	$-0.565662\pi$
$461$	−8.79549	−0.409647	−0.204823	+	0.978799i	$0.565662\pi$
$462$	10.4351	0.485487
$463$	40.4584	1.88026	0.940130	−	0.340817i	$-0.110704\pi$
$463$	40.4584	1.88026	0.940130	+	0.340817i	$0.110704\pi$
$464$	33.4289	1.55190
$465$	−14.6525	−0.679493
$466$	11.6350	0.538982
$467$	8.05065	0.372540	0.186270	−	0.982499i	$-0.440360\pi$
$467$	8.05065	0.372540	0.186270	+	0.982499i	$0.440360\pi$
$468$	3.98494	0.184204
$469$	−5.31962	−0.245637
$470$	−26.3950	−1.21751
$471$	12.8401	0.591641
$472$	−3.53009	−0.162486
$473$	−4.83148	−0.222152
$474$	42.1143	1.93437
$475$	−5.65948	−0.259675
$476$	5.70774	0.261614
$477$	−2.75018	−0.125922
$478$	27.2733	1.24745
$479$	11.1351	0.508775	0.254387	−	0.967102i	$-0.418126\pi$
$479$	11.1351	0.508775	0.254387	+	0.967102i	$0.418126\pi$
$480$	13.4337	0.613160
$481$	68.0447	3.10257
$482$	30.0153	1.36716
$483$	3.64546	0.165874
$484$	−3.38478	−0.153854
$485$	−2.38854	−0.108458
$486$	5.52245	0.250504
$487$	14.4889	0.656554	0.328277	−	0.944582i	$-0.393532\pi$
$487$	14.4889	0.656554	0.328277	+	0.944582i	$0.393532\pi$
$488$	6.06266	0.274444
$489$	−22.7398	−1.02833
$490$	2.04947	0.0925856
$491$	15.2398	0.687762	0.343881	−	0.939013i	$-0.388258\pi$
$491$	15.2398	0.687762	0.343881	+	0.939013i	$0.388258\pi$
$492$	13.1732	0.593892
$493$	−24.3638	−1.09729
$494$	−80.7814	−3.63453
$495$	0.799881	0.0359520
$496$	31.5060	1.41466
$497$	−8.41810	−0.377603
$498$	−29.1743	−1.30733
$499$	17.2108	0.770463	0.385231	−	0.922820i	$-0.374122\pi$
$499$	17.2108	0.770463	0.385231	+	0.922820i	$0.374122\pi$
$500$	−2.20033	−0.0984017
$501$	−9.93184	−0.443722
$502$	−22.8192	−1.01847
$503$	−16.4443	−0.733213	−0.366606	−	0.930376i	$-0.619480\pi$
$503$	−16.4443	−0.733213	−0.366606	+	0.930376i	$0.619480\pi$
$504$	0.106764	0.00475567
$505$	16.3202	0.726241
$506$	13.8837	0.617208
$507$	−58.7707	−2.61010
$508$	28.5466	1.26655
$509$	−24.2394	−1.07439	−0.537197	−	0.843457i	$-0.680517\pi$
$509$	−24.2394	−1.07439	−0.537197	+	0.843457i	$0.680517\pi$
$510$	−8.80016	−0.389678
$511$	−6.22527	−0.275390
$512$	−31.8078	−1.40572
$513$	−30.5402	−1.34838
$514$	21.9829	0.969626
$515$	−9.25451	−0.407803
$516$	5.72078	0.251843
$517$	−39.6155	−1.74229
$518$	20.0236	0.879788
$519$	−23.3825	−1.02638
$520$	−2.85942	−0.125394
$521$	7.51468	0.329224	0.164612	−	0.986358i	$-0.447363\pi$
$521$	7.51468	0.329224	0.164612	+	0.986358i	$0.447363\pi$
$522$	−5.00555	−0.219087
$523$	33.1396	1.44909	0.724546	−	0.689226i	$-0.242049\pi$
$523$	33.1396	1.44909	0.724546	+	0.689226i	$0.242049\pi$
$524$	−37.5486	−1.64032
$525$	−1.65528	−0.0722424
$526$	11.6551	0.508186
$527$	−22.9623	−1.00026
$528$	18.1222	0.788666
$529$	−18.1498	−0.789121
$530$	21.6751	0.941507
$531$	−2.23585	−0.0970274
$532$	−12.4527	−0.539894
$533$	25.1897	1.09109
$534$	17.3124	0.749182
$535$	−3.96790	−0.171547
$536$	2.18407	0.0943373
$537$	29.1744	1.25897
$538$	12.4639	0.537356
$539$	3.07599	0.132492
$540$	−11.8736	−0.510959
$541$	39.7582	1.70934	0.854670	−	0.519172i	$-0.173760\pi$
$541$	39.7582	1.70934	0.854670	+	0.519172i	$0.173760\pi$
$542$	−30.1170	−1.29363
$543$	34.5928	1.48452
$544$	21.0523	0.902609
$545$	5.33851	0.228677
$546$	−23.6269	−1.01114
$547$	−31.9965	−1.36807	−0.684036	−	0.729449i	$-0.739777\pi$
$547$	−31.9965	−1.36807	−0.684036	+	0.729449i	$0.739777\pi$
$548$	42.8026	1.82844
$549$	3.83989	0.163883
$550$	−6.30414	−0.268810
$551$	53.1552	2.26449
$552$	−1.49671	−0.0637042
$553$	12.4141	0.527902
$554$	34.0183	1.44530
$555$	−16.1724	−0.686479
$556$	5.79767	0.245876
$557$	19.4956	0.826054	0.413027	−	0.910719i	$-0.364471\pi$
$557$	19.4956	0.826054	0.413027	+	0.910719i	$0.364471\pi$
$558$	−4.71761	−0.199712
$559$	10.9393	0.462682
$560$	3.55921	0.150404
$561$	−13.2079	−0.557638
$562$	57.0254	2.40547
$563$	−15.7722	−0.664720	−0.332360	−	0.943153i	$-0.607845\pi$
$563$	−15.7722	−0.664720	−0.332360	+	0.943153i	$0.607845\pi$
$564$	46.9072	1.97515
$565$	−2.55746	−0.107593
$566$	−8.46339	−0.355743
$567$	−8.15226	−0.342363
$568$	3.45621	0.145019
$569$	8.15082	0.341700	0.170850	−	0.985297i	$-0.445349\pi$
$569$	8.15082	0.341700	0.170850	+	0.985297i	$0.445349\pi$
$570$	19.1995	0.804180
$571$	−29.1215	−1.21869	−0.609347	−	0.792903i	$-0.708569\pi$
$571$	−29.1215	−1.21869	−0.609347	+	0.792903i	$0.708569\pi$
$572$	−47.1373	−1.97091
$573$	27.1700	1.13504
$574$	7.41263	0.309397
$575$	−2.20232	−0.0918431
$576$	2.47411	0.103088
$577$	6.95595	0.289580	0.144790	−	0.989462i	$-0.453749\pi$
$577$	6.95595	0.289580	0.144790	+	0.989462i	$0.453749\pi$
$578$	21.0500	0.875565
$579$	34.9649	1.45309
$580$	20.6660	0.858109
$581$	−8.59977	−0.356778
$582$	8.10301	0.335881
$583$	32.5315	1.34732
$584$	2.55590	0.105764
$585$	−1.81107	−0.0748783
$586$	−19.1522	−0.791169
$587$	34.7636	1.43485	0.717423	−	0.696638i	$-0.245321\pi$
$587$	34.7636	1.43485	0.717423	+	0.696638i	$0.245321\pi$
$588$	−3.64217	−0.150200
$589$	50.0975	2.06423
$590$	17.6215	0.725465
$591$	37.1884	1.52973
$592$	34.7740	1.42920
$593$	−31.5410	−1.29523	−0.647617	−	0.761966i	$-0.724234\pi$
$593$	−31.5410	−1.29523	−0.647617	+	0.761966i	$0.724234\pi$
$594$	−34.0190	−1.39582
$595$	−2.59404	−0.106345
$596$	−20.6636	−0.846415
$597$	−19.3141	−0.790472
$598$	−31.4351	−1.28548
$599$	−35.1552	−1.43640	−0.718201	−	0.695836i	$-0.755034\pi$
$599$	−35.1552	−1.43640	−0.718201	+	0.695836i	$0.755034\pi$
$600$	0.679606	0.0277448
$601$	18.7845	0.766235	0.383118	−	0.923700i	$-0.374850\pi$
$601$	18.7845	0.766235	0.383118	+	0.923700i	$0.374850\pi$
$602$	3.21912	0.131202
$603$	1.38332	0.0563330
$604$	2.44771	0.0995958
$605$	1.53831	0.0625411
$606$	−55.3656	−2.24908
$607$	33.9488	1.37794	0.688970	−	0.724790i	$-0.258063\pi$
$607$	33.9488	1.37794	0.688970	+	0.724790i	$0.258063\pi$
$608$	−45.9303	−1.86272
$609$	15.5468	0.629988
$610$	−30.2635	−1.22533
$611$	89.6960	3.62871
$612$	−1.48425	−0.0599971
$613$	38.2603	1.54532	0.772659	−	0.634822i	$-0.218926\pi$
$613$	38.2603	1.54532	0.772659	+	0.634822i	$0.218926\pi$
$614$	19.7662	0.797701
$615$	−5.98691	−0.241416
$616$	−1.26290	−0.0508838
$617$	−42.7562	−1.72130	−0.860649	−	0.509198i	$-0.829942\pi$
$617$	−42.7562	−1.72130	−0.860649	+	0.509198i	$0.829942\pi$
$618$	31.3955	1.26291
$619$	−44.2766	−1.77963	−0.889813	−	0.456325i	$-0.849166\pi$
$619$	−44.2766	−1.77963	−0.889813	+	0.456325i	$0.849166\pi$
$620$	19.4772	0.782224
$621$	−11.8844	−0.476903
$622$	1.94178	0.0778582
$623$	5.10322	0.204456
$624$	−41.0316	−1.64258
$625$	1.00000	0.0400000
$626$	42.4260	1.69568
$627$	28.8160	1.15080
$628$	−17.0681	−0.681090
$629$	−25.3442	−1.01054
$630$	−0.532946	−0.0212331
$631$	−8.34822	−0.332337	−0.166169	−	0.986097i	$-0.553140\pi$
$631$	−8.34822	−0.332337	−0.166169	+	0.986097i	$0.553140\pi$
$632$	−5.09684	−0.202742
$633$	5.91422	0.235069
$634$	13.8323	0.549351
$635$	−12.9738	−0.514849
$636$	−38.5194	−1.52739
$637$	−6.96455	−0.275945
$638$	59.2100	2.34415
$639$	2.18905	0.0865974
$640$	−3.26807	−0.129182
$641$	17.3957	0.687090	0.343545	−	0.939136i	$-0.388372\pi$
$641$	17.3957	0.687090	0.343545	+	0.939136i	$0.388372\pi$
$642$	13.4609	0.531260
$643$	−6.33390	−0.249785	−0.124892	−	0.992170i	$-0.539859\pi$
$643$	−6.33390	−0.249785	−0.124892	+	0.992170i	$0.539859\pi$
$644$	−4.84583	−0.190952
$645$	−2.59997	−0.102374
$646$	30.0881	1.18380
$647$	−13.5351	−0.532120	−0.266060	−	0.963957i	$-0.585722\pi$
$647$	−13.5351	−0.532120	−0.266060	+	0.963957i	$0.585722\pi$
$648$	3.34706	0.131485
$649$	26.4475	1.03816
$650$	14.2736	0.559858
$651$	14.6525	0.574276
$652$	30.2275	1.18380
$653$	−36.4724	−1.42727	−0.713637	−	0.700516i	$-0.752953\pi$
$653$	−36.4724	−1.42727	−0.713637	+	0.700516i	$0.752953\pi$
$654$	−18.1107	−0.708183
$655$	17.0650	0.666784
$656$	12.8731	0.502611
$657$	1.61882	0.0631563
$658$	26.3950	1.02898
$659$	−15.1141	−0.588760	−0.294380	−	0.955688i	$-0.595113\pi$
$659$	−15.1141	−0.588760	−0.294380	+	0.955688i	$0.595113\pi$
$660$	11.2033	0.436086
$661$	1.28356	0.0499246	0.0249623	−	0.999688i	$-0.492053\pi$
$661$	1.28356	0.0499246	0.0249623	+	0.999688i	$0.492053\pi$
$662$	−14.1331	−0.549299
$663$	29.9049	1.16141
$664$	3.53079	0.137021
$665$	5.65948	0.219465
$666$	−5.20696	−0.201766
$667$	20.6847	0.800915
$668$	13.2022	0.510807
$669$	−24.1393	−0.933281
$670$	−10.9024	−0.421197
$671$	−45.4216	−1.75348
$672$	−13.4337	−0.518215
$673$	−43.7113	−1.68495	−0.842473	−	0.538739i	$-0.818901\pi$
$673$	−43.7113	−1.68495	−0.842473	+	0.538739i	$0.818901\pi$
$674$	70.5711	2.71830
$675$	5.39629	0.207703
$676$	78.1225	3.00471
$677$	−6.74014	−0.259045	−0.129522	−	0.991577i	$-0.541344\pi$
$677$	−6.74014	−0.259045	−0.129522	+	0.991577i	$0.541344\pi$
$678$	8.67606	0.333202
$679$	2.38854	0.0916638
$680$	1.06503	0.0408421
$681$	22.3235	0.855437
$682$	55.8040	2.13685
$683$	20.4685	0.783204	0.391602	−	0.920135i	$-0.371921\pi$
$683$	20.4685	0.783204	0.391602	+	0.920135i	$0.371921\pi$
$684$	3.23821	0.123816
$685$	−19.4528	−0.743255
$686$	−2.04947	−0.0782491
$687$	1.65528	0.0631530
$688$	5.59049	0.213135
$689$	−73.6568	−2.80610
$690$	7.47127	0.284426
$691$	−18.3238	−0.697071	−0.348535	−	0.937296i	$-0.613321\pi$
$691$	−18.3238	−0.697071	−0.348535	+	0.937296i	$0.613321\pi$
$692$	31.0819	1.18156
$693$	−0.799881	−0.0303850
$694$	−37.4434	−1.42133
$695$	−2.63491	−0.0999478
$696$	−6.38302	−0.241948
$697$	−9.38226	−0.355379
$698$	19.8165	0.750066
$699$	9.39718	0.355434
$700$	2.20033	0.0831646
$701$	12.0241	0.454145	0.227072	−	0.973878i	$-0.427085\pi$
$701$	12.0241	0.454145	0.227072	+	0.973878i	$0.427085\pi$
$702$	77.0246	2.90711
$703$	55.2940	2.08545
$704$	−29.2659	−1.10300
$705$	−21.3183	−0.802893
$706$	−57.8115	−2.17576
$707$	−16.3202	−0.613786
$708$	−31.3156	−1.17691
$709$	23.6644	0.888735	0.444367	−	0.895845i	$-0.353428\pi$
$709$	23.6644	0.888735	0.444367	+	0.895845i	$0.353428\pi$
$710$	−17.2526	−0.647480
$711$	−3.22817	−0.121066
$712$	−2.09522	−0.0785217
$713$	19.4948	0.730087
$714$	8.80016	0.329338
$715$	21.4229	0.801169
$716$	−38.7809	−1.44931
$717$	22.0276	0.822637
$718$	−37.8714	−1.41335
$719$	−19.9337	−0.743402	−0.371701	−	0.928353i	$-0.621225\pi$
$719$	−19.9337	−0.743402	−0.371701	+	0.928353i	$0.621225\pi$
$720$	−0.925539	−0.0344928
$721$	9.25451	0.344656
$722$	−26.7041	−0.993823
$723$	24.2423	0.901579
$724$	−45.9835	−1.70896
$725$	−9.39223	−0.348819
$726$	−5.21863	−0.193682
$727$	−6.91897	−0.256610	−0.128305	−	0.991735i	$-0.540954\pi$
$727$	−6.91897	−0.256610	−0.128305	+	0.991735i	$0.540954\pi$
$728$	2.85942	0.105977
$729$	28.9171	1.07100
$730$	−12.7585	−0.472214
$731$	−4.07449	−0.150700
$732$	53.7821	1.98784
$733$	−23.9411	−0.884284	−0.442142	−	0.896945i	$-0.645781\pi$
$733$	−23.9411	−0.884284	−0.442142	+	0.896945i	$0.645781\pi$
$734$	36.1972	1.33606
$735$	1.65528	0.0610560
$736$	−17.8732	−0.658816
$737$	−16.3631	−0.602742
$738$	−1.92758	−0.0709554
$739$	14.7560	0.542810	0.271405	−	0.962465i	$-0.412512\pi$
$739$	14.7560	0.542810	0.271405	+	0.962465i	$0.412512\pi$
$740$	21.4976	0.790266
$741$	−65.2442	−2.39680
$742$	−21.6751	−0.795718
$743$	19.0756	0.699815	0.349908	−	0.936784i	$-0.386213\pi$
$743$	19.0756	0.699815	0.349908	+	0.936784i	$0.386213\pi$
$744$	−6.01585	−0.220552
$745$	9.39115	0.344065
$746$	−59.7854	−2.18890
$747$	2.23629	0.0818215
$748$	17.5569	0.641946
$749$	3.96790	0.144984
$750$	−3.39245	−0.123875
$751$	21.4028	0.780999	0.390499	−	0.920603i	$-0.372302\pi$
$751$	21.4028	0.780999	0.390499	+	0.920603i	$0.372302\pi$
$752$	45.8389	1.67157
$753$	−18.4302	−0.671635
$754$	−134.061	−4.88222
$755$	−1.11243	−0.0404854
$756$	11.8736	0.431839
$757$	33.8449	1.23011	0.615056	−	0.788483i	$-0.289133\pi$
$757$	33.8449	1.23011	0.615056	+	0.788483i	$0.289133\pi$
$758$	−46.7746	−1.69893
$759$	11.2134	0.407020
$760$	−2.32360	−0.0842860
$761$	30.4881	1.10519	0.552597	−	0.833449i	$-0.313637\pi$
$761$	30.4881	1.10519	0.552597	+	0.833449i	$0.313637\pi$
$762$	44.0130	1.59442
$763$	−5.33851	−0.193267
$764$	−36.1164	−1.30665
$765$	0.674556	0.0243886
$766$	24.9704	0.902217
$767$	−59.8816	−2.16220
$768$	−20.4110	−0.736520
$769$	−9.51229	−0.343022	−0.171511	−	0.985182i	$-0.554865\pi$
$769$	−9.51229	−0.343022	−0.171511	+	0.985182i	$0.554865\pi$
$770$	6.30414	0.227186
$771$	17.7548	0.639424
$772$	−46.4781	−1.67278
$773$	−22.7975	−0.819970	−0.409985	−	0.912092i	$-0.634466\pi$
$773$	−22.7975	−0.819970	−0.409985	+	0.912092i	$0.634466\pi$
$774$	−0.837103	−0.0300890
$775$	−8.85195	−0.317972
$776$	−0.980659	−0.0352036
$777$	16.1724	0.580180
$778$	−47.2715	−1.69477
$779$	20.4695	0.733396
$780$	−25.3660	−0.908250
$781$	−25.8940	−0.926559
$782$	11.7084	0.418693
$783$	−50.6832	−1.81127
$784$	−3.55921	−0.127115
$785$	7.75706	0.276861
$786$	−57.8921	−2.06494
$787$	−1.86034	−0.0663139	−0.0331569	−	0.999450i	$-0.510556\pi$
$787$	−1.86034	−0.0663139	−0.0331569	+	0.999450i	$0.510556\pi$
$788$	−49.4337	−1.76100
$789$	9.41339	0.335125
$790$	25.4424	0.905199
$791$	2.55746	0.0909328
$792$	0.328406	0.0116694
$793$	102.842	3.65203
$794$	42.3544	1.50310
$795$	17.5062	0.620881
$796$	25.6737	0.909981
$797$	50.8349	1.80066	0.900332	−	0.435204i	$-0.143324\pi$
$797$	50.8349	1.80066	0.900332	+	0.435204i	$0.143324\pi$
$798$	−19.1995	−0.679656
$799$	−33.4085	−1.18191
$800$	8.11563	0.286931
$801$	−1.32704	−0.0468888
$802$	−24.3252	−0.858953
$803$	−19.1489	−0.675749
$804$	19.3749	0.683301
$805$	2.20232	0.0776216
$806$	−126.350	−4.45047
$807$	10.0666	0.354362
$808$	6.70057	0.235725
$809$	16.5460	0.581727	0.290863	−	0.956765i	$-0.406057\pi$
$809$	16.5460	0.581727	0.290863	+	0.956765i	$0.406057\pi$
$810$	−16.7078	−0.587053
$811$	12.6567	0.444436	0.222218	−	0.974997i	$-0.428670\pi$
$811$	12.6567	0.444436	0.222218	+	0.974997i	$0.428670\pi$
$812$	−20.6660	−0.725234
$813$	−24.3244	−0.853093
$814$	61.5924	2.15881
$815$	−13.7377	−0.481212
$816$	15.2828	0.535005
$817$	8.88940	0.311001
$818$	−22.5474	−0.788353
$819$	1.81107	0.0632837
$820$	7.95826	0.277915
$821$	−54.8024	−1.91262	−0.956308	−	0.292360i	$-0.905559\pi$
$821$	−54.8024	−1.91262	−0.956308	+	0.292360i	$0.905559\pi$
$822$	65.9928	2.30176
$823$	−22.2895	−0.776963	−0.388481	−	0.921457i	$-0.627000\pi$
$823$	−22.2895	−0.776963	−0.388481	+	0.921457i	$0.627000\pi$
$824$	−3.79961	−0.132366
$825$	−5.09163	−0.177268
$826$	−17.6215	−0.613129
$827$	27.1933	0.945603	0.472802	−	0.881169i	$-0.343243\pi$
$827$	27.1933	0.945603	0.472802	+	0.881169i	$0.343243\pi$
$828$	1.26011	0.0437919
$829$	37.7031	1.30948	0.654741	−	0.755853i	$-0.272778\pi$
$829$	37.7031	1.30948	0.654741	+	0.755853i	$0.272778\pi$
$830$	−17.6250	−0.611772
$831$	27.4753	0.953109
$832$	66.2630	2.29726
$833$	2.59404	0.0898782
$834$	8.93881	0.309526
$835$	−6.00009	−0.207642
$836$	−38.3044	−1.32479
$837$	−47.7677	−1.65109
$838$	63.9568	2.20935
$839$	5.98708	0.206697	0.103349	−	0.994645i	$-0.467044\pi$
$839$	5.98708	0.206697	0.103349	+	0.994645i	$0.467044\pi$
$840$	−0.679606	−0.0234486
$841$	59.2140	2.04186
$842$	30.5205	1.05180
$843$	46.0574	1.58630
$844$	−7.86163	−0.270609
$845$	−35.5049	−1.22141
$846$	−6.86377	−0.235981
$847$	−1.53831	−0.0528568
$848$	−37.6421	−1.29263
$849$	−6.83557	−0.234596
$850$	−5.31641	−0.182351
$851$	21.5170	0.737593
$852$	30.6601	1.05040
$853$	11.3735	0.389421	0.194710	−	0.980861i	$-0.437623\pi$
$853$	11.3735	0.389421	0.194710	+	0.980861i	$0.437623\pi$
$854$	30.2635	1.03560
$855$	−1.47170	−0.0503309
$856$	−1.62909	−0.0556813
$857$	9.51534	0.325038	0.162519	−	0.986705i	$-0.448038\pi$
$857$	9.51534	0.325038	0.162519	+	0.986705i	$0.448038\pi$
$858$	−72.6760	−2.48112
$859$	−22.9502	−0.783049	−0.391525	−	0.920168i	$-0.628052\pi$
$859$	−22.9502	−0.783049	−0.391525	+	0.920168i	$0.628052\pi$
$860$	3.45608	0.117851
$861$	5.98691	0.204033
$862$	71.4590	2.43390
$863$	27.7917	0.946041	0.473020	−	0.881052i	$-0.343164\pi$
$863$	27.7917	0.946041	0.473020	+	0.881052i	$0.343164\pi$
$864$	43.7943	1.48991
$865$	−14.1260	−0.480299
$866$	42.0947	1.43044
$867$	17.0013	0.577395
$868$	−19.4772	−0.661100
$869$	38.1857	1.29536
$870$	31.8627	1.08025
$871$	37.0487	1.25535
$872$	2.19182	0.0742245
$873$	−0.621118	−0.0210216
$874$	−25.5446	−0.864058
$875$	−1.00000	−0.0338062
$876$	22.6735	0.766066
$877$	−47.6334	−1.60847	−0.804233	−	0.594314i	$-0.797424\pi$
$877$	−47.6334	−1.60847	−0.804233	+	0.594314i	$0.797424\pi$
$878$	71.1685	2.40182
$879$	−15.4685	−0.521740
$880$	10.9481	0.369060
$881$	30.3857	1.02372	0.511861	−	0.859068i	$-0.328956\pi$
$881$	30.3857	1.02372	0.511861	+	0.859068i	$0.328956\pi$
$882$	0.532946	0.0179452
$883$	54.0425	1.81867	0.909337	−	0.416059i	$-0.136589\pi$
$883$	54.0425	1.81867	0.909337	+	0.416059i	$0.136589\pi$
$884$	−39.7519	−1.33700
$885$	14.2322	0.478411
$886$	−7.51322	−0.252412
$887$	19.3546	0.649865	0.324932	−	0.945737i	$-0.394658\pi$
$887$	19.3546	0.649865	0.324932	+	0.945737i	$0.394658\pi$
$888$	−6.63986	−0.222819
$889$	12.9738	0.435127
$890$	10.4589	0.350583
$891$	−25.0762	−0.840085
$892$	32.0879	1.07438
$893$	72.8882	2.43911
$894$	−31.8590	−1.06553
$895$	17.6250	0.589140
$896$	3.26807	0.109179
$897$	−25.3890	−0.847714
$898$	−36.5311	−1.21906
$899$	83.1396	2.77286
$900$	−0.572175	−0.0190725
$901$	27.4345	0.913975
$902$	22.8011	0.759195
$903$	2.59997	0.0865215
$904$	−1.05001	−0.0349229
$905$	20.8984	0.694688
$906$	3.77386	0.125378
$907$	6.08257	0.201969	0.100984	−	0.994888i	$-0.467801\pi$
$907$	6.08257	0.201969	0.100984	+	0.994888i	$0.467801\pi$
$908$	−29.6741	−0.984768
$909$	4.24393	0.140762
$910$	−14.2736	−0.473166
$911$	−7.94655	−0.263281	−0.131640	−	0.991298i	$-0.542024\pi$
$911$	−7.94655	−0.263281	−0.131640	+	0.991298i	$0.542024\pi$
$912$	−33.3428	−1.10409
$913$	−26.4528	−0.875459
$914$	−44.5064	−1.47214
$915$	−24.4427	−0.808052
$916$	−2.20033	−0.0727009
$917$	−17.0650	−0.563535
$918$	−28.6889	−0.946874
$919$	−33.0429	−1.08999	−0.544993	−	0.838441i	$-0.683468\pi$
$919$	−33.0429	−1.08999	−0.544993	+	0.838441i	$0.683468\pi$
$920$	−0.904203	−0.0298107
$921$	15.9645	0.526047
$922$	18.0261	0.593658
$923$	58.6283	1.92977
$924$	−11.2033	−0.368560
$925$	−9.77015	−0.321241
$926$	−82.9182	−2.72486
$927$	−2.40655	−0.0790414
$928$	−76.2239	−2.50217
$929$	43.6616	1.43249	0.716246	−	0.697848i	$-0.245859\pi$
$929$	43.6616	1.43249	0.716246	+	0.697848i	$0.245859\pi$
$930$	30.0298	0.984717
$931$	−5.65948	−0.185482
$932$	−12.4915	−0.409171
$933$	1.56830	0.0513439
$934$	−16.4996	−0.539882
$935$	−7.97924	−0.260949
$936$	−0.743566	−0.0243042
$937$	55.8960	1.82604	0.913021	−	0.407913i	$-0.133743\pi$
$937$	55.8960	1.82604	0.913021	+	0.407913i	$0.133743\pi$
$938$	10.9024	0.355976
$939$	34.2659	1.11823
$940$	28.3379	0.924281
$941$	35.6927	1.16355	0.581775	−	0.813350i	$-0.302358\pi$
$941$	35.6927	1.16355	0.581775	+	0.813350i	$0.302358\pi$
$942$	−26.3154	−0.857403
$943$	7.96546	0.259391
$944$	−30.6023	−0.996020
$945$	−5.39629	−0.175541
$946$	9.90198	0.321941
$947$	26.9384	0.875381	0.437690	−	0.899126i	$-0.355797\pi$
$947$	26.9384	0.875381	0.437690	+	0.899126i	$0.355797\pi$
$948$	−45.2143	−1.46849
$949$	43.3562	1.40740
$950$	11.5989	0.376319
$951$	11.1718	0.362272
$952$	−1.06503	−0.0345179
$953$	−4.02006	−0.130223	−0.0651113	−	0.997878i	$-0.520740\pi$
$953$	−4.02006	−0.130223	−0.0651113	+	0.997878i	$0.520740\pi$
$954$	5.63641	0.182485
$955$	16.4141	0.531147
$956$	−29.2808	−0.947009
$957$	47.8217	1.54586
$958$	−22.8210	−0.737314
$959$	19.4528	0.628165
$960$	−15.7489	−0.508294
$961$	47.3571	1.52765
$962$	−139.456	−4.49623
$963$	−1.03182	−0.0332498
$964$	−32.2247	−1.03789
$965$	21.1233	0.679982
$966$	−7.47127	−0.240384
$967$	−36.3806	−1.16992	−0.584961	−	0.811061i	$-0.698890\pi$
$967$	−36.3806	−1.16992	−0.584961	+	0.811061i	$0.698890\pi$
$968$	0.631580	0.0202997
$969$	24.3011	0.780663
$970$	4.89524	0.157177
$971$	−51.7487	−1.66069	−0.830347	−	0.557247i	$-0.811858\pi$
$971$	−51.7487	−1.66069	−0.830347	+	0.557247i	$0.811858\pi$
$972$	−5.92895	−0.190171
$973$	2.63491	0.0844713
$974$	−29.6945	−0.951474
$975$	11.5283	0.369201
$976$	52.5571	1.68231
$977$	59.1147	1.89125	0.945624	−	0.325262i	$-0.105452\pi$
$977$	59.1147	1.89125	0.945624	+	0.325262i	$0.105452\pi$
$978$	46.6046	1.49025
$979$	15.6974	0.501692
$980$	−2.20033	−0.0702869
$981$	1.38823	0.0443228
$982$	−31.2335	−0.996701
$983$	−11.6520	−0.371642	−0.185821	−	0.982584i	$-0.559495\pi$
$983$	−11.6520	−0.371642	−0.185821	+	0.982584i	$0.559495\pi$
$984$	−2.45804	−0.0783593
$985$	22.4665	0.715843
$986$	49.9330	1.59019
$987$	21.3183	0.678569
$988$	86.7276	2.75917
$989$	3.45921	0.109996
$990$	−1.63933	−0.0521014
$991$	12.6645	0.402302	0.201151	−	0.979560i	$-0.435532\pi$
$991$	12.6645	0.402302	0.201151	+	0.979560i	$0.435532\pi$
$992$	−71.8392	−2.28090
$993$	−11.4148	−0.362237
$994$	17.2526	0.547221
$995$	−11.6681	−0.369905
$996$	31.3218	0.992468
$997$	−10.4164	−0.329891	−0.164946	−	0.986303i	$-0.552745\pi$
$997$	−10.4164	−0.329891	−0.164946	+	0.986303i	$0.552745\pi$
$998$	−35.2731	−1.11655
$999$	−52.7226	−1.66807

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8015.2.a.n.1.12	✓	68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8015.2.a.n.1.12	✓	68	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)

\(f(q)\)	\(=\)	\(q-2.04947 q^{2} -1.65528 q^{3} +2.20033 q^{4} -1.00000 q^{5} +3.39245 q^{6} +1.00000 q^{7} -0.410568 q^{8} -0.260041 q^{9} +O(q^{10})\)	\(q-2.04947 q^{2} -1.65528 q^{3} +2.20033 q^{4} -1.00000 q^{5} +3.39245 q^{6} +1.00000 q^{7} -0.410568 q^{8} -0.260041 q^{9} +2.04947 q^{10} +3.07599 q^{11} -3.64217 q^{12} -6.96455 q^{13} -2.04947 q^{14} +1.65528 q^{15} -3.55921 q^{16} +2.59404 q^{17} +0.532946 q^{18} -5.65948 q^{19} -2.20033 q^{20} -1.65528 q^{21} -6.30414 q^{22} -2.20232 q^{23} +0.679606 q^{24} +1.00000 q^{25} +14.2736 q^{26} +5.39629 q^{27} +2.20033 q^{28} -9.39223 q^{29} -3.39245 q^{30} -8.85195 q^{31} +8.11563 q^{32} -5.09163 q^{33} -5.31641 q^{34} -1.00000 q^{35} -0.572175 q^{36} -9.77015 q^{37} +11.5989 q^{38} +11.5283 q^{39} +0.410568 q^{40} -3.61685 q^{41} +3.39245 q^{42} -1.57071 q^{43} +6.76818 q^{44} +0.260041 q^{45} +4.51359 q^{46} -12.8789 q^{47} +5.89150 q^{48} +1.00000 q^{49} -2.04947 q^{50} -4.29387 q^{51} -15.3243 q^{52} +10.5760 q^{53} -11.0595 q^{54} -3.07599 q^{55} -0.410568 q^{56} +9.36804 q^{57} +19.2491 q^{58} +8.59806 q^{59} +3.64217 q^{60} -14.7665 q^{61} +18.1418 q^{62} -0.260041 q^{63} -9.51433 q^{64} +6.96455 q^{65} +10.4351 q^{66} -5.31962 q^{67} +5.70774 q^{68} +3.64546 q^{69} +2.04947 q^{70} -8.41810 q^{71} +0.106764 q^{72} -6.22527 q^{73} +20.0236 q^{74} -1.65528 q^{75} -12.4527 q^{76} +3.07599 q^{77} -23.6269 q^{78} +12.4141 q^{79} +3.55921 q^{80} -8.15226 q^{81} +7.41263 q^{82} -8.59977 q^{83} -3.64217 q^{84} -2.59404 q^{85} +3.21912 q^{86} +15.5468 q^{87} -1.26290 q^{88} +5.10322 q^{89} -0.532946 q^{90} -6.96455 q^{91} -4.84583 q^{92} +14.6525 q^{93} +26.3950 q^{94} +5.65948 q^{95} -13.4337 q^{96} +2.38854 q^{97} -2.04947 q^{98} -0.799881 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q + 9 q^{2} + 83 q^{4} - 68 q^{5} + 5 q^{6} + 68 q^{7} + 30 q^{8} + 86 q^{9}+O(q^{10}) \) 68 * q + 9 * q^2 + 83 * q^4 - 68 * q^5 + 5 * q^6 + 68 * q^7 + 30 * q^8 + 86 * q^9	\( 68 q + 9 q^{2} + 83 q^{4} - 68 q^{5} + 5 q^{6} + 68 q^{7} + 30 q^{8} + 86 q^{9} - 9 q^{10} + 5 q^{11} + 9 q^{12} + 15 q^{13} + 9 q^{14} + 109 q^{16} + 7 q^{17} + 39 q^{18} + 20 q^{19} - 83 q^{20} + 56 q^{22} + 36 q^{23} + q^{24} + 68 q^{25} + q^{26} + 12 q^{27} + 83 q^{28} - 16 q^{29} - 5 q^{30} + 31 q^{31} + 79 q^{32} + 45 q^{33} + 31 q^{34} - 68 q^{35} + 114 q^{36} + 72 q^{37} + 8 q^{38} + 47 q^{39} - 30 q^{40} + 6 q^{41} + 5 q^{42} + 75 q^{43} + 15 q^{44} - 86 q^{45} + 29 q^{46} - 10 q^{47} + 44 q^{48} + 68 q^{49} + 9 q^{50} + 23 q^{51} + 37 q^{52} + 41 q^{53} + 4 q^{54} - 5 q^{55} + 30 q^{56} + 55 q^{57} + 66 q^{58} - 5 q^{59} - 9 q^{60} - 2 q^{61} + 3 q^{62} + 86 q^{63} + 162 q^{64} - 15 q^{65} - 23 q^{66} + 92 q^{67} + 35 q^{68} - 25 q^{69} - 9 q^{70} - 2 q^{71} + 128 q^{72} + 80 q^{73} + 18 q^{74} + 71 q^{76} + 5 q^{77} + 20 q^{78} + 100 q^{79} - 109 q^{80} + 140 q^{81} + 36 q^{82} - 60 q^{83} + 9 q^{84} - 7 q^{85} - 27 q^{86} + 24 q^{87} + 175 q^{88} + 19 q^{89} - 39 q^{90} + 15 q^{91} + 75 q^{92} + 37 q^{93} + 11 q^{94} - 20 q^{95} + 15 q^{96} + 96 q^{97} + 9 q^{98} + 3 q^{99}+O(q^{100}) \) 68 * q + 9 * q^2 + 83 * q^4 - 68 * q^5 + 5 * q^6 + 68 * q^7 + 30 * q^8 + 86 * q^9 - 9 * q^10 + 5 * q^11 + 9 * q^12 + 15 * q^13 + 9 * q^14 + 109 * q^16 + 7 * q^17 + 39 * q^18 + 20 * q^19 - 83 * q^20 + 56 * q^22 + 36 * q^23 + q^24 + 68 * q^25 + q^26 + 12 * q^27 + 83 * q^28 - 16 * q^29 - 5 * q^30 + 31 * q^31 + 79 * q^32 + 45 * q^33 + 31 * q^34 - 68 * q^35 + 114 * q^36 + 72 * q^37 + 8 * q^38 + 47 * q^39 - 30 * q^40 + 6 * q^41 + 5 * q^42 + 75 * q^43 + 15 * q^44 - 86 * q^45 + 29 * q^46 - 10 * q^47 + 44 * q^48 + 68 * q^49 + 9 * q^50 + 23 * q^51 + 37 * q^52 + 41 * q^53 + 4 * q^54 - 5 * q^55 + 30 * q^56 + 55 * q^57 + 66 * q^58 - 5 * q^59 - 9 * q^60 - 2 * q^61 + 3 * q^62 + 86 * q^63 + 162 * q^64 - 15 * q^65 - 23 * q^66 + 92 * q^67 + 35 * q^68 - 25 * q^69 - 9 * q^70 - 2 * q^71 + 128 * q^72 + 80 * q^73 + 18 * q^74 + 71 * q^76 + 5 * q^77 + 20 * q^78 + 100 * q^79 - 109 * q^80 + 140 * q^81 + 36 * q^82 - 60 * q^83 + 9 * q^84 - 7 * q^85 - 27 * q^86 + 24 * q^87 + 175 * q^88 + 19 * q^89 - 39 * q^90 + 15 * q^91 + 75 * q^92 + 37 * q^93 + 11 * q^94 - 20 * q^95 + 15 * q^96 + 96 * q^97 + 9 * q^98 + 3 * q^99

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