LMFDB - Embedded newform 8015.2.a.h.1.20

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:	$38$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.20
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)

$f(q)$	$=$	$q-0.0830831 q^{2} +2.10839 q^{3} -1.99310 q^{4} +1.00000 q^{5} -0.175171 q^{6} +1.00000 q^{7} +0.331759 q^{8} +1.44530 q^{9} +O(q^{10})$	\(q-0.0830831 q^{2} +2.10839 q^{3} -1.99310 q^{4} +1.00000 q^{5} -0.175171 q^{6} +1.00000 q^{7} +0.331759 q^{8} +1.44530 q^{9} -0.0830831 q^{10} -2.34152 q^{11} -4.20222 q^{12} +0.0413492 q^{13} -0.0830831 q^{14} +2.10839 q^{15} +3.95863 q^{16} +1.41364 q^{17} -0.120080 q^{18} -3.69278 q^{19} -1.99310 q^{20} +2.10839 q^{21} +0.194541 q^{22} +3.47584 q^{23} +0.699476 q^{24} +1.00000 q^{25} -0.00343542 q^{26} -3.27792 q^{27} -1.99310 q^{28} -0.644473 q^{29} -0.175171 q^{30} -9.97589 q^{31} -0.992413 q^{32} -4.93683 q^{33} -0.117450 q^{34} +1.00000 q^{35} -2.88061 q^{36} -5.07262 q^{37} +0.306807 q^{38} +0.0871800 q^{39} +0.331759 q^{40} +1.07746 q^{41} -0.175171 q^{42} +6.22948 q^{43} +4.66687 q^{44} +1.44530 q^{45} -0.288784 q^{46} -5.17555 q^{47} +8.34633 q^{48} +1.00000 q^{49} -0.0830831 q^{50} +2.98050 q^{51} -0.0824129 q^{52} -2.60426 q^{53} +0.272340 q^{54} -2.34152 q^{55} +0.331759 q^{56} -7.78580 q^{57} +0.0535448 q^{58} +2.91134 q^{59} -4.20222 q^{60} -10.2592 q^{61} +0.828829 q^{62} +1.44530 q^{63} -7.83481 q^{64} +0.0413492 q^{65} +0.410167 q^{66} -3.76735 q^{67} -2.81752 q^{68} +7.32842 q^{69} -0.0830831 q^{70} -7.28547 q^{71} +0.479490 q^{72} +12.5684 q^{73} +0.421450 q^{74} +2.10839 q^{75} +7.36006 q^{76} -2.34152 q^{77} -0.00724319 q^{78} +8.13374 q^{79} +3.95863 q^{80} -11.2470 q^{81} -0.0895185 q^{82} -11.8585 q^{83} -4.20222 q^{84} +1.41364 q^{85} -0.517565 q^{86} -1.35880 q^{87} -0.776820 q^{88} -6.54109 q^{89} -0.120080 q^{90} +0.0413492 q^{91} -6.92769 q^{92} -21.0330 q^{93} +0.430001 q^{94} -3.69278 q^{95} -2.09239 q^{96} -0.367785 q^{97} -0.0830831 q^{98} -3.38419 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 38 q - 6 q^{2} - 9 q^{3} + 24 q^{4} + 38 q^{5} - 10 q^{6} + 38 q^{7} - 21 q^{8} + 13 q^{9}+O(q^{10}) $ 38 * q - 6 * q^2 - 9 * q^3 + 24 * q^4 + 38 * q^5 - 10 * q^6 + 38 * q^7 - 21 * q^8 + 13 * q^9	\( 38 q - 6 q^{2} - 9 q^{3} + 24 q^{4} + 38 q^{5} - 10 q^{6} + 38 q^{7} - 21 q^{8} + 13 q^{9} - 6 q^{10} - 18 q^{11} - 20 q^{12} - 25 q^{13} - 6 q^{14} - 9 q^{15} - 21 q^{17} - 7 q^{18} - 14 q^{19} + 24 q^{20} - 9 q^{21} - 11 q^{22} - 16 q^{23} - 10 q^{24} + 38 q^{25} - 21 q^{26} - 15 q^{27} + 24 q^{28} - 52 q^{29} - 10 q^{30} - 30 q^{31} - 8 q^{32} - 13 q^{33} - 9 q^{34} + 38 q^{35} - 16 q^{36} - 47 q^{37} - 10 q^{38} - 50 q^{39} - 21 q^{40} - 35 q^{41} - 10 q^{42} - 18 q^{43} - 22 q^{44} + 13 q^{45} - 17 q^{46} - 23 q^{47} - 13 q^{48} + 38 q^{49} - 6 q^{50} - 5 q^{51} - 41 q^{52} - 12 q^{53} + 35 q^{54} - 18 q^{55} - 21 q^{56} - 3 q^{57} - 16 q^{58} - 16 q^{59} - 20 q^{60} - 47 q^{61} + 14 q^{62} + 13 q^{63} - 55 q^{64} - 25 q^{65} - 6 q^{66} - 54 q^{67} + 31 q^{68} - 95 q^{69} - 6 q^{70} - 41 q^{71} - 59 q^{73} - q^{74} - 9 q^{75} - 23 q^{76} - 18 q^{77} + 19 q^{78} - 117 q^{79} - 38 q^{81} + 19 q^{82} - 21 q^{83} - 20 q^{84} - 21 q^{85} - 12 q^{86} - 14 q^{87} - 40 q^{88} - 96 q^{89} - 7 q^{90} - 25 q^{91} + 53 q^{92} - 53 q^{93} - 28 q^{94} - 14 q^{95} + 40 q^{96} - 70 q^{97} - 6 q^{98} - 52 q^{99}+O(q^{100}) \) 38 * q - 6 * q^2 - 9 * q^3 + 24 * q^4 + 38 * q^5 - 10 * q^6 + 38 * q^7 - 21 * q^8 + 13 * q^9 - 6 * q^10 - 18 * q^11 - 20 * q^12 - 25 * q^13 - 6 * q^14 - 9 * q^15 - 21 * q^17 - 7 * q^18 - 14 * q^19 + 24 * q^20 - 9 * q^21 - 11 * q^22 - 16 * q^23 - 10 * q^24 + 38 * q^25 - 21 * q^26 - 15 * q^27 + 24 * q^28 - 52 * q^29 - 10 * q^30 - 30 * q^31 - 8 * q^32 - 13 * q^33 - 9 * q^34 + 38 * q^35 - 16 * q^36 - 47 * q^37 - 10 * q^38 - 50 * q^39 - 21 * q^40 - 35 * q^41 - 10 * q^42 - 18 * q^43 - 22 * q^44 + 13 * q^45 - 17 * q^46 - 23 * q^47 - 13 * q^48 + 38 * q^49 - 6 * q^50 - 5 * q^51 - 41 * q^52 - 12 * q^53 + 35 * q^54 - 18 * q^55 - 21 * q^56 - 3 * q^57 - 16 * q^58 - 16 * q^59 - 20 * q^60 - 47 * q^61 + 14 * q^62 + 13 * q^63 - 55 * q^64 - 25 * q^65 - 6 * q^66 - 54 * q^67 + 31 * q^68 - 95 * q^69 - 6 * q^70 - 41 * q^71 - 59 * q^73 - q^74 - 9 * q^75 - 23 * q^76 - 18 * q^77 + 19 * q^78 - 117 * q^79 - 38 * q^81 + 19 * q^82 - 21 * q^83 - 20 * q^84 - 21 * q^85 - 12 * q^86 - 14 * q^87 - 40 * q^88 - 96 * q^89 - 7 * q^90 - 25 * q^91 + 53 * q^92 - 53 * q^93 - 28 * q^94 - 14 * q^95 + 40 * q^96 - 70 * q^97 - 6 * q^98 - 52 * 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 $

$2$	−0.0830831	−0.0587486	−0.0293743	−	0.999568i	$-0.509351\pi$
$2$	−0.0830831	−0.0587486	−0.0293743	+	0.999568i	$0.509351\pi$
$3$	2.10839	1.21728	0.608639	−	0.793447i	$-0.291716\pi$
$3$	2.10839	1.21728	0.608639	+	0.793447i	$0.291716\pi$
$4$	−1.99310	−0.996549
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−0.175171	−0.0715134
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	0.331759	0.117295
$9$	1.44530	0.481765
$10$	−0.0830831	−0.0262732
$11$	−2.34152	−0.705994	−0.352997	−	0.935624i	$-0.614837\pi$
$11$	−2.34152	−0.705994	−0.352997	+	0.935624i	$0.614837\pi$
$12$	−4.20222	−1.21308
$13$	0.0413492	0.0114682	0.00573410	−	0.999984i	$-0.498175\pi$
$13$	0.0413492	0.0114682	0.00573410	+	0.999984i	$0.498175\pi$
$14$	−0.0830831	−0.0222049
$15$	2.10839	0.544383
$16$	3.95863	0.989658
$17$	1.41364	0.342858	0.171429	−	0.985196i	$-0.445162\pi$
$17$	1.41364	0.342858	0.171429	+	0.985196i	$0.445162\pi$
$18$	−0.120080	−0.0283030
$19$	−3.69278	−0.847181	−0.423591	−	0.905854i	$-0.639230\pi$
$19$	−3.69278	−0.847181	−0.423591	+	0.905854i	$0.639230\pi$
$20$	−1.99310	−0.445670
$21$	2.10839	0.460088
$22$	0.194541	0.0414762
$23$	3.47584	0.724763	0.362381	−	0.932030i	$-0.381964\pi$
$23$	3.47584	0.724763	0.362381	+	0.932030i	$0.381964\pi$
$24$	0.699476	0.142780
$25$	1.00000	0.200000
$26$	−0.00343542	−0.000673741 0
$27$	−3.27792	−0.630836
$28$	−1.99310	−0.376660
$29$	−0.644473	−0.119676	−0.0598378	−	0.998208i	$-0.519058\pi$
$29$	−0.644473	−0.119676	−0.0598378	+	0.998208i	$0.519058\pi$
$30$	−0.175171	−0.0319818
$31$	−9.97589	−1.79172	−0.895862	−	0.444333i	$-0.853441\pi$
$31$	−9.97589	−1.79172	−0.895862	+	0.444333i	$0.853441\pi$
$32$	−0.992413	−0.175436
$33$	−4.93683	−0.859391
$34$	−0.117450	−0.0201424
$35$	1.00000	0.169031
$36$	−2.88061	−0.480102
$37$	−5.07262	−0.833934	−0.416967	−	0.908922i	$-0.636907\pi$
$37$	−5.07262	−0.833934	−0.416967	+	0.908922i	$0.636907\pi$
$38$	0.306807	0.0497707
$39$	0.0871800	0.0139600
$40$	0.331759	0.0524557
$41$	1.07746	0.168270	0.0841352	−	0.996454i	$-0.473187\pi$
$41$	1.07746	0.168270	0.0841352	+	0.996454i	$0.473187\pi$
$42$	−0.175171	−0.0270295
$43$	6.22948	0.949987	0.474993	−	0.879989i	$-0.342450\pi$
$43$	6.22948	0.949987	0.474993	+	0.879989i	$0.342450\pi$
$44$	4.66687	0.703558
$45$	1.44530	0.215452
$46$	−0.288784	−0.0425788
$47$	−5.17555	−0.754931	−0.377466	−	0.926024i	$-0.623204\pi$
$47$	−5.17555	−0.754931	−0.377466	+	0.926024i	$0.623204\pi$
$48$	8.34633	1.20469
$49$	1.00000	0.142857
$50$	−0.0830831	−0.0117497
$51$	2.98050	0.417353
$52$	−0.0824129	−0.0114286
$53$	−2.60426	−0.357723	−0.178861	−	0.983874i	$-0.557241\pi$
$53$	−2.60426	−0.357723	−0.178861	+	0.983874i	$0.557241\pi$
$54$	0.272340	0.0370607
$55$	−2.34152	−0.315730
$56$	0.331759	0.0443332
$57$	−7.78580	−1.03125
$58$	0.0535448	0.00703078
$59$	2.91134	0.379024	0.189512	−	0.981878i	$-0.439309\pi$
$59$	2.91134	0.379024	0.189512	+	0.981878i	$0.439309\pi$
$60$	−4.20222	−0.542504
$61$	−10.2592	−1.31355	−0.656777	−	0.754085i	$-0.728081\pi$
$61$	−10.2592	−1.31355	−0.656777	+	0.754085i	$0.728081\pi$
$62$	0.828829	0.105261
$63$	1.44530	0.182090
$64$	−7.83481	−0.979351
$65$	0.0413492	0.00512873
$66$	0.410167	0.0504881
$67$	−3.76735	−0.460255	−0.230128	−	0.973160i	$-0.573914\pi$
$67$	−3.76735	−0.460255	−0.230128	+	0.973160i	$0.573914\pi$
$68$	−2.81752	−0.341674
$69$	7.32842	0.882238
$70$	−0.0830831	−0.00993033
$71$	−7.28547	−0.864626	−0.432313	−	0.901724i	$-0.642302\pi$
$71$	−7.28547	−0.864626	−0.432313	+	0.901724i	$0.642302\pi$
$72$	0.479490	0.0565084
$73$	12.5684	1.47102	0.735510	−	0.677514i	$-0.236943\pi$
$73$	12.5684	1.47102	0.735510	+	0.677514i	$0.236943\pi$
$74$	0.421450	0.0489925
$75$	2.10839	0.243456
$76$	7.36006	0.844257
$77$	−2.34152	−0.266841
$78$	−0.00724319	−0.000820130 0
$79$	8.13374	0.915117	0.457559	−	0.889179i	$-0.348724\pi$
$79$	8.13374	0.915117	0.457559	+	0.889179i	$0.348724\pi$
$80$	3.95863	0.442588
$81$	−11.2470	−1.24967
$82$	−0.0895185	−0.00988566
$83$	−11.8585	−1.30164	−0.650819	−	0.759233i	$-0.725575\pi$
$83$	−11.8585	−1.30164	−0.650819	+	0.759233i	$0.725575\pi$
$84$	−4.20222	−0.458500
$85$	1.41364	0.153331
$86$	−0.517565	−0.0558104
$87$	−1.35880	−0.145678
$88$	−0.776820	−0.0828092
$89$	−6.54109	−0.693354	−0.346677	−	0.937985i	$-0.612690\pi$
$89$	−6.54109	−0.693354	−0.346677	+	0.937985i	$0.612690\pi$
$90$	−0.120080	−0.0126575
$91$	0.0413492	0.00433457
$92$	−6.92769	−0.722261
$93$	−21.0330	−2.18103
$94$	0.430001	0.0443512
$95$	−3.69278	−0.378871
$96$	−2.09239	−0.213554
$97$	−0.367785	−0.0373429	−0.0186715	−	0.999826i	$-0.505944\pi$
$97$	−0.367785	−0.0373429	−0.0186715	+	0.999826i	$0.505944\pi$
$98$	−0.0830831	−0.00839266
$99$	−3.38419	−0.340123
$100$	−1.99310	−0.199310
$101$	15.9619	1.58826	0.794132	−	0.607746i	$-0.207926\pi$
$101$	15.9619	1.58826	0.794132	+	0.607746i	$0.207926\pi$
$102$	−0.247629	−0.0245189
$103$	4.92591	0.485364	0.242682	−	0.970106i	$-0.421973\pi$
$103$	4.92591	0.485364	0.242682	+	0.970106i	$0.421973\pi$
$104$	0.0137180	0.00134516
$105$	2.10839	0.205757
$106$	0.216370	0.0210157
$107$	−13.0636	−1.26291	−0.631453	−	0.775414i	$-0.717541\pi$
$107$	−13.0636	−1.26291	−0.631453	+	0.775414i	$0.717541\pi$
$108$	6.53321	0.628658
$109$	−13.3631	−1.27995	−0.639974	−	0.768397i	$-0.721055\pi$
$109$	−13.3631	−1.27995	−0.639974	+	0.768397i	$0.721055\pi$
$110$	0.194541	0.0185487
$111$	−10.6951	−1.01513
$112$	3.95863	0.374055
$113$	−6.49536	−0.611032	−0.305516	−	0.952187i	$-0.598829\pi$
$113$	−6.49536	−0.611032	−0.305516	+	0.952187i	$0.598829\pi$
$114$	0.646869	0.0605848
$115$	3.47584	0.324124
$116$	1.28450	0.119263
$117$	0.0597618	0.00552498
$118$	−0.241883	−0.0222671
$119$	1.41364	0.129588
$120$	0.699476	0.0638532
$121$	−5.51729	−0.501572
$122$	0.852365	0.0771695
$123$	2.27170	0.204832
$124$	19.8829	1.78554
$125$	1.00000	0.0894427
$126$	−0.120080	−0.0106975
$127$	17.7441	1.57454	0.787268	−	0.616611i	$-0.211495\pi$
$127$	17.7441	1.57454	0.787268	+	0.616611i	$0.211495\pi$
$128$	2.63577	0.232971
$129$	13.1342	1.15640
$130$	−0.00343542	−0.000301306 0
$131$	6.94459	0.606751	0.303376	−	0.952871i	$-0.401886\pi$
$131$	6.94459	0.606751	0.303376	+	0.952871i	$0.401886\pi$
$132$	9.83957	0.856425
$133$	−3.69278	−0.320204
$134$	0.313003	0.0270394
$135$	−3.27792	−0.282118
$136$	0.468987	0.0402153
$137$	−0.850722	−0.0726821	−0.0363410	−	0.999339i	$-0.511570\pi$
$137$	−0.850722	−0.0726821	−0.0363410	+	0.999339i	$0.511570\pi$
$138$	−0.608868	−0.0518303
$139$	−4.35218	−0.369147	−0.184574	−	0.982819i	$-0.559090\pi$
$139$	−4.35218	−0.369147	−0.184574	+	0.982819i	$0.559090\pi$
$140$	−1.99310	−0.168447
$141$	−10.9121	−0.918961
$142$	0.605300	0.0507956
$143$	−0.0968198	−0.00809648
$144$	5.72139	0.476783
$145$	−0.644473	−0.0535206
$146$	−1.04422	−0.0864204
$147$	2.10839	0.173897
$148$	10.1102	0.831056
$149$	3.73823	0.306248	0.153124	−	0.988207i	$-0.451067\pi$
$149$	3.73823	0.306248	0.153124	+	0.988207i	$0.451067\pi$
$150$	−0.175171	−0.0143027
$151$	−2.84154	−0.231241	−0.115620	−	0.993293i	$-0.536886\pi$
$151$	−2.84154	−0.231241	−0.115620	+	0.993293i	$0.536886\pi$
$152$	−1.22511	−0.0993697
$153$	2.04313	0.165177
$154$	0.194541	0.0156765
$155$	−9.97589	−0.801283
$156$	−0.173758	−0.0139118
$157$	16.9685	1.35423	0.677117	−	0.735875i	$-0.263229\pi$
$157$	16.9685	1.35423	0.677117	+	0.735875i	$0.263229\pi$
$158$	−0.675777	−0.0537619
$159$	−5.49079	−0.435448
$160$	−0.992413	−0.0784572
$161$	3.47584	0.273935
$162$	0.934437	0.0734163
$163$	−12.2353	−0.958339	−0.479170	−	0.877722i	$-0.659062\pi$
$163$	−12.2353	−0.958339	−0.479170	+	0.877722i	$0.659062\pi$
$164$	−2.14748	−0.167690
$165$	−4.93683	−0.384331
$166$	0.985241	0.0764695
$167$	−9.55296	−0.739230	−0.369615	−	0.929185i	$-0.620510\pi$
$167$	−9.55296	−0.739230	−0.369615	+	0.929185i	$0.620510\pi$
$168$	0.699476	0.0539658
$169$	−12.9983	−0.999868
$170$	−0.117450	−0.00900797
$171$	−5.33715	−0.408142
$172$	−12.4160	−0.946708
$173$	−24.6426	−1.87354	−0.936772	−	0.349940i	$-0.886202\pi$
$173$	−24.6426	−1.87354	−0.936772	+	0.349940i	$0.886202\pi$
$174$	0.112893	0.00855841
$175$	1.00000	0.0755929
$176$	−9.26920	−0.698693
$177$	6.13823	0.461377
$178$	0.543454	0.0407336
$179$	10.7435	0.803009	0.401504	−	0.915857i	$-0.368487\pi$
$179$	10.7435	0.803009	0.401504	+	0.915857i	$0.368487\pi$
$180$	−2.88061	−0.214708
$181$	4.04087	0.300355	0.150178	−	0.988659i	$-0.452015\pi$
$181$	4.04087	0.300355	0.150178	+	0.988659i	$0.452015\pi$
$182$	−0.00343542	−0.000254650 0
$183$	−21.6303	−1.59896
$184$	1.15314	0.0850107
$185$	−5.07262	−0.372947
$186$	1.74749	0.128132
$187$	−3.31006	−0.242056
$188$	10.3154	0.752326
$189$	−3.27792	−0.238434
$190$	0.306807	0.0222581
$191$	−0.0949066	−0.00686720	−0.00343360	−	0.999994i	$-0.501093\pi$
$191$	−0.0949066	−0.00686720	−0.00343360	+	0.999994i	$0.501093\pi$
$192$	−16.5188	−1.19214
$193$	−2.83704	−0.204214	−0.102107	−	0.994773i	$-0.532558\pi$
$193$	−2.83704	−0.204214	−0.102107	+	0.994773i	$0.532558\pi$
$194$	0.0305568	0.00219385
$195$	0.0871800	0.00624309
$196$	−1.99310	−0.142364
$197$	−3.60846	−0.257092	−0.128546	−	0.991704i	$-0.541031\pi$
$197$	−3.60846	−0.257092	−0.128546	+	0.991704i	$0.541031\pi$
$198$	0.281169	0.0199818
$199$	0.216450	0.0153438	0.00767188	−	0.999971i	$-0.497558\pi$
$199$	0.216450	0.0153438	0.00767188	+	0.999971i	$0.497558\pi$
$200$	0.331759	0.0234589
$201$	−7.94304	−0.560259
$202$	−1.32616	−0.0933083
$203$	−0.644473	−0.0452331
$204$	−5.94042	−0.415913
$205$	1.07746	0.0752528
$206$	−0.409260	−0.0285145
$207$	5.02362	0.349165
$208$	0.163686	0.0113496
$209$	8.64670	0.598105
$210$	−0.175171	−0.0120880
$211$	−3.40580	−0.234465	−0.117232	−	0.993105i	$-0.537402\pi$
$211$	−3.40580	−0.234465	−0.117232	+	0.993105i	$0.537402\pi$
$212$	5.19054	0.356488
$213$	−15.3606	−1.05249
$214$	1.08537	0.0741940
$215$	6.22948	0.424847
$216$	−1.08748	−0.0739936
$217$	−9.97589	−0.677208
$218$	1.11024	0.0751952
$219$	26.4990	1.79064
$220$	4.66687	0.314640
$221$	0.0584528	0.00393196
$222$	0.888579	0.0596375
$223$	3.76416	0.252067	0.126033	−	0.992026i	$-0.459775\pi$
$223$	3.76416	0.252067	0.126033	+	0.992026i	$0.459775\pi$
$224$	−0.992413	−0.0663084
$225$	1.44530	0.0963530
$226$	0.539655	0.0358973
$227$	−23.3928	−1.55263	−0.776316	−	0.630343i	$-0.782914\pi$
$227$	−23.3928	−1.55263	−0.776316	+	0.630343i	$0.782914\pi$
$228$	15.5179	1.02770
$229$	−1.00000	−0.0660819
$229$	−1.00000	−0.0660819
$230$	−0.288784	−0.0190418
$231$	−4.93683	−0.324819
$232$	−0.213810	−0.0140373
$233$	−4.03852	−0.264572	−0.132286	−	0.991212i	$-0.542232\pi$
$233$	−4.03852	−0.264572	−0.132286	+	0.991212i	$0.542232\pi$
$234$	−0.00496519	−0.000324585 0
$235$	−5.17555	−0.337615
$236$	−5.80258	−0.377716
$237$	17.1491	1.11395
$238$	−0.117450	−0.00761312
$239$	−5.40418	−0.349568	−0.174784	−	0.984607i	$-0.555923\pi$
$239$	−5.40418	−0.349568	−0.174784	+	0.984607i	$0.555923\pi$
$240$	8.34633	0.538753
$241$	−29.6872	−1.91232	−0.956160	−	0.292844i	$-0.905398\pi$
$241$	−29.6872	−1.91232	−0.956160	+	0.292844i	$0.905398\pi$
$242$	0.458394	0.0294667
$243$	−13.8793	−0.890357
$244$	20.4476	1.30902
$245$	1.00000	0.0638877
$246$	−0.188740	−0.0120336
$247$	−0.152693	−0.00971564
$248$	−3.30959	−0.210159
$249$	−25.0023	−1.58446
$250$	−0.0830831	−0.00525464
$251$	24.7573	1.56267	0.781333	−	0.624114i	$-0.214540\pi$
$251$	24.7573	1.56267	0.781333	+	0.624114i	$0.214540\pi$
$252$	−2.88061	−0.181462
$253$	−8.13874	−0.511678
$254$	−1.47424	−0.0925018
$255$	2.98050	0.186646
$256$	15.4506	0.965664
$257$	−6.66040	−0.415464	−0.207732	−	0.978186i	$-0.566608\pi$
$257$	−6.66040	−0.415464	−0.207732	+	0.978186i	$0.566608\pi$
$258$	−1.09123	−0.0679368
$259$	−5.07262	−0.315198
$260$	−0.0824129	−0.00511103
$261$	−0.931454	−0.0576555
$262$	−0.576978	−0.0356458
$263$	2.88965	0.178183	0.0890916	−	0.996023i	$-0.471604\pi$
$263$	2.88965	0.178183	0.0890916	+	0.996023i	$0.471604\pi$
$264$	−1.63784	−0.100802
$265$	−2.60426	−0.159978
$266$	0.306807	0.0188116
$267$	−13.7911	−0.844005
$268$	7.50870	0.458667
$269$	5.77768	0.352271	0.176136	−	0.984366i	$-0.443640\pi$
$269$	5.77768	0.352271	0.176136	+	0.984366i	$0.443640\pi$
$270$	0.272340	0.0165741
$271$	−22.8553	−1.38836	−0.694182	−	0.719800i	$-0.744234\pi$
$271$	−22.8553	−1.38836	−0.694182	+	0.719800i	$0.744234\pi$
$272$	5.59607	0.339312
$273$	0.0871800	0.00527638
$274$	0.0706806	0.00426997
$275$	−2.34152	−0.141199
$276$	−14.6062	−0.879193
$277$	13.8330	0.831143	0.415572	−	0.909560i	$-0.363582\pi$
$277$	13.8330	0.831143	0.415572	+	0.909560i	$0.363582\pi$
$278$	0.361593	0.0216869
$279$	−14.4181	−0.863190
$280$	0.331759	0.0198264
$281$	−20.8420	−1.24333	−0.621665	−	0.783283i	$-0.713543\pi$
$281$	−20.8420	−1.24333	−0.621665	+	0.783283i	$0.713543\pi$
$282$	0.906608	0.0539877
$283$	−5.06173	−0.300889	−0.150444	−	0.988618i	$-0.548070\pi$
$283$	−5.06173	−0.300889	−0.150444	+	0.988618i	$0.548070\pi$
$284$	14.5206	0.861642
$285$	−7.78580	−0.461191
$286$	0.00804409	0.000475657 0
$287$	1.07746	0.0636002
$288$	−1.43433	−0.0845187
$289$	−15.0016	−0.882449
$290$	0.0535448	0.00314426
$291$	−0.775434	−0.0454567
$292$	−25.0500	−1.46594
$293$	−22.2848	−1.30189	−0.650946	−	0.759124i	$-0.725628\pi$
$293$	−22.2848	−1.30189	−0.650946	+	0.759124i	$0.725628\pi$
$294$	−0.175171	−0.0102162
$295$	2.91134	0.169505
$296$	−1.68289	−0.0978159
$297$	7.67531	0.445366
$298$	−0.310584	−0.0179917
$299$	0.143723	0.00831172
$300$	−4.20222	−0.242615
$301$	6.22948	0.359061
$302$	0.236084	0.0135851
$303$	33.6538	1.93336
$304$	−14.6183	−0.838419
$305$	−10.2592	−0.587439
$306$	−0.169749	−0.00970392
$307$	2.49525	0.142412	0.0712058	−	0.997462i	$-0.477315\pi$
$307$	2.49525	0.142412	0.0712058	+	0.997462i	$0.477315\pi$
$308$	4.66687	0.265920
$309$	10.3857	0.590823
$310$	0.828829	0.0470743
$311$	−3.86660	−0.219255	−0.109627	−	0.993973i	$-0.534966\pi$
$311$	−3.86660	−0.219255	−0.109627	+	0.993973i	$0.534966\pi$
$312$	0.0289228	0.00163743
$313$	25.3460	1.43264	0.716320	−	0.697772i	$-0.245825\pi$
$313$	25.3460	1.43264	0.716320	+	0.697772i	$0.245825\pi$
$314$	−1.40980	−0.0795595
$315$	1.44530	0.0814332
$316$	−16.2113	−0.911959
$317$	−12.2666	−0.688961	−0.344480	−	0.938794i	$-0.611945\pi$
$317$	−12.2666	−0.688961	−0.344480	+	0.938794i	$0.611945\pi$
$318$	0.456192	0.0255820
$319$	1.50904	0.0844903
$320$	−7.83481	−0.437979
$321$	−27.5431	−1.53731
$322$	−0.288784	−0.0160933
$323$	−5.22025	−0.290463
$324$	22.4164	1.24535
$325$	0.0413492	0.00229364
$326$	1.01654	0.0563011
$327$	−28.1745	−1.55805
$328$	0.357456	0.0197372
$329$	−5.17555	−0.285337
$330$	0.410167	0.0225789
$331$	18.0279	0.990901	0.495451	−	0.868636i	$-0.335003\pi$
$331$	18.0279	0.990901	0.495451	+	0.868636i	$0.335003\pi$
$332$	23.6351	1.29715
$333$	−7.33144	−0.401761
$334$	0.793690	0.0434288
$335$	−3.76735	−0.205832
$336$	8.34633	0.455329
$337$	−5.86361	−0.319411	−0.159706	−	0.987165i	$-0.551055\pi$
$337$	−5.86361	−0.319411	−0.159706	+	0.987165i	$0.551055\pi$
$338$	1.07994	0.0587409
$339$	−13.6947	−0.743796
$340$	−2.81752	−0.152801
$341$	23.3587	1.26495
$342$	0.443427	0.0239778
$343$	1.00000	0.0539949
$344$	2.06669	0.111428
$345$	7.32842	0.394549
$346$	2.04739	0.110068
$347$	−5.43732	−0.291891	−0.145945	−	0.989293i	$-0.546622\pi$
$347$	−5.43732	−0.291891	−0.145945	+	0.989293i	$0.546622\pi$
$348$	2.70822	0.145176
$349$	18.4132	0.985634	0.492817	−	0.870133i	$-0.335967\pi$
$349$	18.4132	0.985634	0.492817	+	0.870133i	$0.335967\pi$
$350$	−0.0830831	−0.00444098
$351$	−0.135539	−0.00723455
$352$	2.32375	0.123856
$353$	13.9340	0.741632	0.370816	−	0.928706i	$-0.379078\pi$
$353$	13.9340	0.741632	0.370816	+	0.928706i	$0.379078\pi$
$354$	−0.509983	−0.0271053
$355$	−7.28547	−0.386673
$356$	13.0370	0.690961
$357$	2.98050	0.157745
$358$	−0.892606	−0.0471757
$359$	27.0662	1.42850	0.714249	−	0.699892i	$-0.246768\pi$
$359$	27.0662	1.42850	0.714249	+	0.699892i	$0.246768\pi$
$360$	0.479490	0.0252713
$361$	−5.36340	−0.282284
$362$	−0.335728	−0.0176455
$363$	−11.6326	−0.610553
$364$	−0.0824129	−0.00431961
$365$	12.5684	0.657860
$366$	1.79712	0.0939368
$367$	−24.2262	−1.26460	−0.632299	−	0.774724i	$-0.717889\pi$
$367$	−24.2262	−1.26460	−0.632299	+	0.774724i	$0.717889\pi$
$368$	13.7596	0.717267
$369$	1.55724	0.0810668
$370$	0.421450	0.0219101
$371$	−2.60426	−0.135206
$372$	41.9209	2.17350
$373$	−27.5341	−1.42566	−0.712830	−	0.701337i	$-0.752587\pi$
$373$	−27.5341	−1.42566	−0.712830	+	0.701337i	$0.752587\pi$
$374$	0.275010	0.0142204
$375$	2.10839	0.108877
$376$	−1.71703	−0.0885493
$377$	−0.0266484	−0.00137246
$378$	0.272340	0.0140076
$379$	14.7404	0.757166	0.378583	−	0.925567i	$-0.376411\pi$
$379$	14.7404	0.757166	0.378583	+	0.925567i	$0.376411\pi$
$380$	7.36006	0.377563
$381$	37.4115	1.91665
$382$	0.00788514	0.000403439 0
$383$	−1.45138	−0.0741621	−0.0370810	−	0.999312i	$-0.511806\pi$
$383$	−1.45138	−0.0741621	−0.0370810	+	0.999312i	$0.511806\pi$
$384$	5.55722	0.283591
$385$	−2.34152	−0.119335
$386$	0.235710	0.0119973
$387$	9.00344	0.457671
$388$	0.733032	0.0372141
$389$	12.7375	0.645816	0.322908	−	0.946430i	$-0.395340\pi$
$389$	12.7375	0.645816	0.322908	+	0.946430i	$0.395340\pi$
$390$	−0.00724319	−0.000366773 0
$391$	4.91358	0.248491
$392$	0.331759	0.0167564
$393$	14.6419	0.738585
$394$	0.299802	0.0151038
$395$	8.13374	0.409253
$396$	6.74501	0.338949
$397$	−16.5465	−0.830445	−0.415222	−	0.909720i	$-0.636296\pi$
$397$	−16.5465	−0.830445	−0.415222	+	0.909720i	$0.636296\pi$
$398$	−0.0179834	−0.000901425 0
$399$	−7.78580	−0.389778
$400$	3.95863	0.197932
$401$	−9.79345	−0.489061	−0.244531	−	0.969642i	$-0.578634\pi$
$401$	−9.79345	−0.489061	−0.244531	+	0.969642i	$0.578634\pi$
$402$	0.659932	0.0329144
$403$	−0.412495	−0.0205478
$404$	−31.8135	−1.58278
$405$	−11.2470	−0.558868
$406$	0.0535448	0.00265739
$407$	11.8776	0.588753
$408$	0.988807	0.0489532
$409$	36.9511	1.82712	0.913558	−	0.406709i	$-0.133324\pi$
$409$	36.9511	1.82712	0.913558	+	0.406709i	$0.133324\pi$
$410$	−0.0895185	−0.00442100
$411$	−1.79365	−0.0884742
$412$	−9.81782	−0.483689
$413$	2.91134	0.143258
$414$	−0.417378	−0.0205130
$415$	−11.8585	−0.582111
$416$	−0.0410355	−0.00201193
$417$	−9.17609	−0.449355
$418$	−0.718395	−0.0351379
$419$	29.9218	1.46177	0.730887	−	0.682499i	$-0.239107\pi$
$419$	29.9218	1.46177	0.730887	+	0.682499i	$0.239107\pi$
$420$	−4.20222	−0.205047
$421$	−5.91647	−0.288351	−0.144175	−	0.989552i	$-0.546053\pi$
$421$	−5.91647	−0.288351	−0.144175	+	0.989552i	$0.546053\pi$
$422$	0.282964	0.0137745
$423$	−7.48019	−0.363700
$424$	−0.863987	−0.0419589
$425$	1.41364	0.0685716
$426$	1.27621	0.0618324
$427$	−10.2592	−0.496477
$428$	26.0370	1.25855
$429$	−0.204134	−0.00985566
$430$	−0.517565	−0.0249592
$431$	17.9275	0.863536	0.431768	−	0.901985i	$-0.357890\pi$
$431$	17.9275	0.863536	0.431768	+	0.901985i	$0.357890\pi$
$432$	−12.9761	−0.624311
$433$	27.7953	1.33576	0.667878	−	0.744271i	$-0.267203\pi$
$433$	27.7953	1.33576	0.667878	+	0.744271i	$0.267203\pi$
$434$	0.828829	0.0397850
$435$	−1.35880	−0.0651494
$436$	26.6339	1.27553
$437$	−12.8355	−0.614005
$438$	−2.20162	−0.105198
$439$	5.21043	0.248680	0.124340	−	0.992240i	$-0.460319\pi$
$439$	5.21043	0.248680	0.124340	+	0.992240i	$0.460319\pi$
$440$	−0.776820	−0.0370334
$441$	1.44530	0.0688236
$442$	−0.00485644	−0.000230997 0
$443$	29.6822	1.41024	0.705122	−	0.709086i	$-0.250892\pi$
$443$	29.6822	1.41024	0.705122	+	0.709086i	$0.250892\pi$
$444$	21.3163	1.01163
$445$	−6.54109	−0.310077
$446$	−0.312738	−0.0148086
$447$	7.88165	0.372789
$448$	−7.83481	−0.370160
$449$	−18.4160	−0.869103	−0.434551	−	0.900647i	$-0.643093\pi$
$449$	−18.4160	−0.869103	−0.434551	+	0.900647i	$0.643093\pi$
$450$	−0.120080	−0.00566061
$451$	−2.52288	−0.118798
$452$	12.9459	0.608923
$453$	−5.99106	−0.281484
$454$	1.94354	0.0912151
$455$	0.0413492	0.00193848
$456$	−2.58301	−0.120961
$457$	−35.3171	−1.65206	−0.826032	−	0.563623i	$-0.809407\pi$
$457$	−35.3171	−1.65206	−0.826032	+	0.563623i	$0.809407\pi$
$458$	0.0830831	0.00388222
$459$	−4.63379	−0.216287
$460$	−6.92769	−0.323005
$461$	−29.1083	−1.35571	−0.677854	−	0.735197i	$-0.737090\pi$
$461$	−29.1083	−1.35571	−0.677854	+	0.735197i	$0.737090\pi$
$462$	0.410167	0.0190827
$463$	−33.2152	−1.54364	−0.771820	−	0.635841i	$-0.780653\pi$
$463$	−33.2152	−1.54364	−0.771820	+	0.635841i	$0.780653\pi$
$464$	−2.55123	−0.118438
$465$	−21.0330	−0.975384
$466$	0.335533	0.0155433
$467$	−20.4727	−0.947362	−0.473681	−	0.880696i	$-0.657075\pi$
$467$	−20.4727	−0.947362	−0.473681	+	0.880696i	$0.657075\pi$
$468$	−0.119111	−0.00550591
$469$	−3.76735	−0.173960
$470$	0.430001	0.0198345
$471$	35.7762	1.64848
$472$	0.965863	0.0444574
$473$	−14.5864	−0.670685
$474$	−1.42480	−0.0654432
$475$	−3.69278	−0.169436
$476$	−2.81752	−0.129141
$477$	−3.76393	−0.172338
$478$	0.448996	0.0205366
$479$	21.0356	0.961143	0.480572	−	0.876956i	$-0.340429\pi$
$479$	21.0356	0.961143	0.480572	+	0.876956i	$0.340429\pi$
$480$	−2.09239	−0.0955042
$481$	−0.209749	−0.00956372
$482$	2.46651	0.112346
$483$	7.32842	0.333454
$484$	10.9965	0.499841
$485$	−0.367785	−0.0167003
$486$	1.15313	0.0523072
$487$	23.6070	1.06974	0.534869	−	0.844935i	$-0.320361\pi$
$487$	23.6070	1.06974	0.534869	+	0.844935i	$0.320361\pi$
$488$	−3.40358	−0.154073
$489$	−25.7967	−1.16657
$490$	−0.0830831	−0.00375331
$491$	−1.55524	−0.0701870	−0.0350935	−	0.999384i	$-0.511173\pi$
$491$	−1.55524	−0.0701870	−0.0350935	+	0.999384i	$0.511173\pi$
$492$	−4.52771	−0.204125
$493$	−0.911052	−0.0410317
$494$	0.0126862	0.000570780 0
$495$	−3.38419	−0.152108
$496$	−39.4909	−1.77319
$497$	−7.28547	−0.326798
$498$	2.07727	0.0930846
$499$	29.4552	1.31859	0.659297	−	0.751882i	$-0.270854\pi$
$499$	29.4552	1.31859	0.659297	+	0.751882i	$0.270854\pi$
$500$	−1.99310	−0.0891340
$501$	−20.1413	−0.899848
$502$	−2.05691	−0.0918045
$503$	−1.31542	−0.0586516	−0.0293258	−	0.999570i	$-0.509336\pi$
$503$	−1.31542	−0.0586516	−0.0293258	+	0.999570i	$0.509336\pi$
$504$	0.479490	0.0213582
$505$	15.9619	0.710293
$506$	0.676192	0.0300604
$507$	−27.4054	−1.21712
$508$	−35.3657	−1.56910
$509$	−7.16645	−0.317647	−0.158824	−	0.987307i	$-0.550770\pi$
$509$	−7.16645	−0.317647	−0.158824	+	0.987307i	$0.550770\pi$
$510$	−0.247629	−0.0109652
$511$	12.5684	0.555993
$512$	−6.55522	−0.289703
$513$	12.1046	0.534432
$514$	0.553367	0.0244080
$515$	4.92591	0.217061
$516$	−26.1777	−1.15241
$517$	12.1186	0.532977
$518$	0.421450	0.0185174
$519$	−51.9562	−2.28062
$520$	0.0137180	0.000601572 0
$521$	−14.0198	−0.614219	−0.307110	−	0.951674i	$-0.599362\pi$
$521$	−14.0198	−0.614219	−0.307110	+	0.951674i	$0.599362\pi$
$522$	0.0773881	0.00338719
$523$	−15.7457	−0.688513	−0.344256	−	0.938876i	$-0.611869\pi$
$523$	−15.7457	−0.688513	−0.344256	+	0.938876i	$0.611869\pi$
$524$	−13.8412	−0.604657
$525$	2.10839	0.0920175
$526$	−0.240081	−0.0104680
$527$	−14.1023	−0.614306
$528$	−19.5431	−0.850503
$529$	−10.9185	−0.474719
$530$	0.216370	0.00939852
$531$	4.20774	0.182601
$532$	7.36006	0.319099
$533$	0.0445519	0.00192976
$534$	1.14581	0.0495841
$535$	−13.0636	−0.564789
$536$	−1.24985	−0.0539854
$537$	22.6515	0.977485
$538$	−0.480027	−0.0206955
$539$	−2.34152	−0.100856
$540$	6.53321	0.281145
$541$	−1.27339	−0.0547471	−0.0273736	−	0.999625i	$-0.508714\pi$
$541$	−1.27339	−0.0547471	−0.0273736	+	0.999625i	$0.508714\pi$
$542$	1.89889	0.0815645
$543$	8.51971	0.365616
$544$	−1.40291	−0.0601495
$545$	−13.3631	−0.572410
$546$	−0.00724319	−0.000309980 0
$547$	−31.7361	−1.35694	−0.678468	−	0.734630i	$-0.737356\pi$
$547$	−31.7361	−1.35694	−0.678468	+	0.734630i	$0.737356\pi$
$548$	1.69557	0.0724312
$549$	−14.8276	−0.632825
$550$	0.194541	0.00829524
$551$	2.37989	0.101387
$552$	2.43127	0.103482
$553$	8.13374	0.345882
$554$	−1.14929	−0.0488285
$555$	−10.6951	−0.453980
$556$	8.67433	0.367873
$557$	1.31919	0.0558958	0.0279479	−	0.999609i	$-0.491103\pi$
$557$	1.31919	0.0558958	0.0279479	+	0.999609i	$0.491103\pi$
$558$	1.19790	0.0507112
$559$	0.257584	0.0108946
$560$	3.95863	0.167283
$561$	−6.97889	−0.294649
$562$	1.73162	0.0730439
$563$	−1.48940	−0.0627708	−0.0313854	−	0.999507i	$-0.509992\pi$
$563$	−1.48940	−0.0627708	−0.0313854	+	0.999507i	$0.509992\pi$
$564$	21.7488	0.915789
$565$	−6.49536	−0.273262
$566$	0.420544	0.0176768
$567$	−11.2470	−0.472330
$568$	−2.41702	−0.101416
$569$	−20.7982	−0.871905	−0.435952	−	0.899970i	$-0.643588\pi$
$569$	−20.7982	−0.871905	−0.435952	+	0.899970i	$0.643588\pi$
$570$	0.646869	0.0270944
$571$	−33.7025	−1.41041	−0.705203	−	0.709006i	$-0.749144\pi$
$571$	−33.7025	−1.41041	−0.705203	+	0.709006i	$0.749144\pi$
$572$	0.192971	0.00806853
$573$	−0.200100	−0.00835929
$574$	−0.0895185	−0.00373643
$575$	3.47584	0.144953
$576$	−11.3236	−0.471817
$577$	−3.18822	−0.132727	−0.0663636	−	0.997796i	$-0.521140\pi$
$577$	−3.18822	−0.132727	−0.0663636	+	0.997796i	$0.521140\pi$
$578$	1.24638	0.0518427
$579$	−5.98157	−0.248586
$580$	1.28450	0.0533358
$581$	−11.8585	−0.491973
$582$	0.0644255	0.00267052
$583$	6.09792	0.252550
$584$	4.16968	0.172543
$585$	0.0597618	0.00247084
$586$	1.85149	0.0764844
$587$	6.48970	0.267859	0.133929	−	0.990991i	$-0.457240\pi$
$587$	6.48970	0.267859	0.133929	+	0.990991i	$0.457240\pi$
$588$	−4.20222	−0.173297
$589$	36.8387	1.51791
$590$	−0.241883	−0.00995817
$591$	−7.60804	−0.312953
$592$	−20.0806	−0.825310
$593$	−16.1926	−0.664951	−0.332475	−	0.943112i	$-0.607884\pi$
$593$	−16.1926	−0.664951	−0.332475	+	0.943112i	$0.607884\pi$
$594$	−0.637688	−0.0261647
$595$	1.41364	0.0579535
$596$	−7.45067	−0.305191
$597$	0.456361	0.0186776
$598$	−0.0119410	−0.000488302 0
$599$	4.85297	0.198287	0.0991434	−	0.995073i	$-0.468390\pi$
$599$	4.85297	0.198287	0.0991434	+	0.995073i	$0.468390\pi$
$600$	0.699476	0.0285560
$601$	−5.67878	−0.231642	−0.115821	−	0.993270i	$-0.536950\pi$
$601$	−5.67878	−0.231642	−0.115821	+	0.993270i	$0.536950\pi$
$602$	−0.517565	−0.0210944
$603$	−5.44494	−0.221735
$604$	5.66346	0.230443
$605$	−5.51729	−0.224310
$606$	−2.79606	−0.113582
$607$	15.5043	0.629300	0.314650	−	0.949208i	$-0.398113\pi$
$607$	15.5043	0.629300	0.314650	+	0.949208i	$0.398113\pi$
$608$	3.66476	0.148626
$609$	−1.35880	−0.0550613
$610$	0.852365	0.0345113
$611$	−0.214005	−0.00865770
$612$	−4.07215	−0.164607
$613$	11.3435	0.458160	0.229080	−	0.973408i	$-0.426428\pi$
$613$	11.3435	0.458160	0.229080	+	0.973408i	$0.426428\pi$
$614$	−0.207313	−0.00836649
$615$	2.27170	0.0916036
$616$	−0.776820	−0.0312990
$617$	3.05583	0.123023	0.0615115	−	0.998106i	$-0.480408\pi$
$617$	3.05583	0.123023	0.0615115	+	0.998106i	$0.480408\pi$
$618$	−0.862878	−0.0347101
$619$	23.1728	0.931393	0.465696	−	0.884945i	$-0.345804\pi$
$619$	23.1728	0.931393	0.465696	+	0.884945i	$0.345804\pi$
$620$	19.8829	0.798518
$621$	−11.3935	−0.457206
$622$	0.321249	0.0128809
$623$	−6.54109	−0.262063
$624$	0.345114	0.0138156
$625$	1.00000	0.0400000
$626$	−2.10582	−0.0841657
$627$	18.2306	0.728060
$628$	−33.8199	−1.34956
$629$	−7.17086	−0.285921
$630$	−0.120080	−0.00478409
$631$	−7.24149	−0.288279	−0.144140	−	0.989557i	$-0.546041\pi$
$631$	−7.24149	−0.288279	−0.144140	+	0.989557i	$0.546041\pi$
$632$	2.69844	0.107338
$633$	−7.18074	−0.285409
$634$	1.01915	0.0404755
$635$	17.7441	0.704154
$636$	10.9437	0.433945
$637$	0.0413492	0.00163831
$638$	−0.125376	−0.00496369
$639$	−10.5297	−0.416547
$640$	2.63577	0.104188
$641$	39.4442	1.55795	0.778977	−	0.627053i	$-0.215739\pi$
$641$	39.4442	1.55795	0.778977	+	0.627053i	$0.215739\pi$
$642$	2.28837	0.0903148
$643$	31.7316	1.25137	0.625687	−	0.780074i	$-0.284819\pi$
$643$	31.7316	1.25137	0.625687	+	0.780074i	$0.284819\pi$
$644$	−6.92769	−0.272989
$645$	13.1342	0.517157
$646$	0.433715	0.0170643
$647$	−34.4984	−1.35627	−0.678137	−	0.734936i	$-0.737212\pi$
$647$	−34.4984	−1.35627	−0.678137	+	0.734936i	$0.737212\pi$
$648$	−3.73130	−0.146579
$649$	−6.81695	−0.267589
$650$	−0.00343542	−0.000134748 0
$651$	−21.0330	−0.824350
$652$	24.3861	0.955032
$653$	5.30398	0.207561	0.103780	−	0.994600i	$-0.466906\pi$
$653$	5.30398	0.207561	0.103780	+	0.994600i	$0.466906\pi$
$654$	2.34082	0.0915335
$655$	6.94459	0.271347
$656$	4.26525	0.166530
$657$	18.1650	0.708686
$658$	0.430001	0.0167632
$659$	28.9973	1.12958	0.564788	−	0.825236i	$-0.308958\pi$
$659$	28.9973	1.12958	0.564788	+	0.825236i	$0.308958\pi$
$660$	9.83957	0.383005
$661$	−16.5809	−0.644923	−0.322462	−	0.946583i	$-0.604510\pi$
$661$	−16.5809	−0.644923	−0.322462	+	0.946583i	$0.604510\pi$
$662$	−1.49781	−0.0582141
$663$	0.123241	0.00478629
$664$	−3.93416	−0.152675
$665$	−3.69278	−0.143200
$666$	0.609119	0.0236029
$667$	−2.24009	−0.0867364
$668$	19.0400	0.736679
$669$	7.93631	0.306835
$670$	0.313003	0.0120924
$671$	24.0221	0.927362
$672$	−2.09239	−0.0807158
$673$	−10.4099	−0.401273	−0.200637	−	0.979666i	$-0.564301\pi$
$673$	−10.4099	−0.401273	−0.200637	+	0.979666i	$0.564301\pi$
$674$	0.487167	0.0187650
$675$	−3.27792	−0.126167
$676$	25.9069	0.996418
$677$	−22.1442	−0.851070	−0.425535	−	0.904942i	$-0.639914\pi$
$677$	−22.1442	−0.851070	−0.425535	+	0.904942i	$0.639914\pi$
$678$	1.13780	0.0436970
$679$	−0.367785	−0.0141143
$680$	0.468987	0.0179848
$681$	−49.3210	−1.88999
$682$	−1.94072	−0.0743139
$683$	15.4229	0.590142	0.295071	−	0.955475i	$-0.404657\pi$
$683$	15.4229	0.590142	0.295071	+	0.955475i	$0.404657\pi$
$684$	10.6375	0.406734
$685$	−0.850722	−0.0325044
$686$	−0.0830831	−0.00317213
$687$	−2.10839	−0.0804400
$688$	24.6602	0.940162
$689$	−0.107684	−0.00410243
$690$	−0.608868	−0.0231792
$691$	−24.6617	−0.938176	−0.469088	−	0.883151i	$-0.655417\pi$
$691$	−24.6617	−0.938176	−0.469088	+	0.883151i	$0.655417\pi$
$692$	49.1151	1.86708
$693$	−3.38419	−0.128555
$694$	0.451749	0.0171482
$695$	−4.35218	−0.165088
$696$	−0.450794	−0.0170873
$697$	1.52313	0.0576928
$698$	−1.52982	−0.0579047
$699$	−8.51476	−0.322058
$700$	−1.99310	−0.0753320
$701$	20.6258	0.779026	0.389513	−	0.921021i	$-0.372643\pi$
$701$	20.6258	0.779026	0.389513	+	0.921021i	$0.372643\pi$
$702$	0.0112610	0.000425020 0
$703$	18.7321	0.706493
$704$	18.3453	0.691416
$705$	−10.9121	−0.410972
$706$	−1.15768	−0.0435699
$707$	15.9619	0.600307
$708$	−12.2341	−0.459785
$709$	21.1382	0.793862	0.396931	−	0.917848i	$-0.370075\pi$
$709$	21.1382	0.793862	0.396931	+	0.917848i	$0.370075\pi$
$710$	0.605300	0.0227165
$711$	11.7557	0.440872
$712$	−2.17007	−0.0813266
$713$	−34.6746	−1.29857
$714$	−0.247629	−0.00926729
$715$	−0.0968198	−0.00362086
$716$	−21.4129	−0.800237
$717$	−11.3941	−0.425521
$718$	−2.24874	−0.0839223
$719$	41.8076	1.55916	0.779581	−	0.626302i	$-0.215432\pi$
$719$	41.8076	1.55916	0.779581	+	0.626302i	$0.215432\pi$
$720$	5.72139	0.213224
$721$	4.92591	0.183450
$722$	0.445608	0.0165838
$723$	−62.5921	−2.32783
$724$	−8.05384	−0.299319
$725$	−0.644473	−0.0239351
$726$	0.966472	0.0358691
$727$	−9.70217	−0.359834	−0.179917	−	0.983682i	$-0.557583\pi$
$727$	−9.70217	−0.359834	−0.179917	+	0.983682i	$0.557583\pi$
$728$	0.0137180	0.000508421 0
$729$	4.47811	0.165856
$730$	−1.04422	−0.0386484
$731$	8.80624	0.325710
$732$	43.1114	1.59344
$733$	−4.53794	−0.167613	−0.0838063	−	0.996482i	$-0.526708\pi$
$733$	−4.53794	−0.167613	−0.0838063	+	0.996482i	$0.526708\pi$
$734$	2.01279	0.0742934
$735$	2.10839	0.0777690
$736$	−3.44947	−0.127149
$737$	8.82132	0.324938
$738$	−0.129381	−0.00476257
$739$	12.3504	0.454315	0.227158	−	0.973858i	$-0.427057\pi$
$739$	12.3504	0.454315	0.227158	+	0.973858i	$0.427057\pi$
$740$	10.1102	0.371660
$741$	−0.321936	−0.0118266
$742$	0.216370	0.00794320
$743$	−32.5879	−1.19553	−0.597767	−	0.801670i	$-0.703945\pi$
$743$	−32.5879	−1.19553	−0.597767	+	0.801670i	$0.703945\pi$
$744$	−6.97790	−0.255822
$745$	3.73823	0.136958
$746$	2.28762	0.0837555
$747$	−17.1390	−0.627084
$748$	6.59727	0.241220
$749$	−13.0636	−0.477334
$750$	−0.175171	−0.00639635
$751$	12.1187	0.442218	0.221109	−	0.975249i	$-0.429032\pi$
$751$	12.1187	0.442218	0.221109	+	0.975249i	$0.429032\pi$
$752$	−20.4881	−0.747123
$753$	52.1979	1.90220
$754$	0.00221403	8.06304e−5 0
$755$	−2.84154	−0.103414
$756$	6.53321	0.237611
$757$	20.0543	0.728885	0.364442	−	0.931226i	$-0.381260\pi$
$757$	20.0543	0.728885	0.364442	+	0.931226i	$0.381260\pi$
$758$	−1.22468	−0.0444825
$759$	−17.1596	−0.622855
$760$	−1.22511	−0.0444395
$761$	1.66674	0.0604194	0.0302097	−	0.999544i	$-0.490382\pi$
$761$	1.66674	0.0604194	0.0302097	+	0.999544i	$0.490382\pi$
$762$	−3.10826	−0.112600
$763$	−13.3631	−0.483775
$764$	0.189158	0.00684350
$765$	2.04313	0.0738694
$766$	0.120585	0.00435692
$767$	0.120381	0.00434672
$768$	32.5759	1.17548
$769$	18.5363	0.668434	0.334217	−	0.942496i	$-0.391528\pi$
$769$	18.5363	0.668434	0.334217	+	0.942496i	$0.391528\pi$
$770$	0.194541	0.00701076
$771$	−14.0427	−0.505735
$772$	5.65449	0.203510
$773$	−17.4121	−0.626270	−0.313135	−	0.949709i	$-0.601379\pi$
$773$	−17.4121	−0.626270	−0.313135	+	0.949709i	$0.601379\pi$
$774$	−0.748034	−0.0268875
$775$	−9.97589	−0.358345
$776$	−0.122016	−0.00438012
$777$	−10.6951	−0.383683
$778$	−1.05827	−0.0379408
$779$	−3.97881	−0.142556
$780$	−0.173758	−0.00622154
$781$	17.0591	0.610421
$782$	−0.408236	−0.0145985
$783$	2.11253	0.0754957
$784$	3.95863	0.141380
$785$	16.9685	0.605632
$786$	−1.21649	−0.0433909
$787$	6.68586	0.238325	0.119163	−	0.992875i	$-0.461979\pi$
$787$	6.68586	0.238325	0.119163	+	0.992875i	$0.461979\pi$
$788$	7.19202	0.256205
$789$	6.09249	0.216898
$790$	−0.675777	−0.0240431
$791$	−6.49536	−0.230949
$792$	−1.12273	−0.0398946
$793$	−0.424209	−0.0150641
$794$	1.37473	0.0487875
$795$	−5.49079	−0.194738
$796$	−0.431407	−0.0152908
$797$	3.63505	0.128760	0.0643800	−	0.997925i	$-0.479493\pi$
$797$	3.63505	0.128760	0.0643800	+	0.997925i	$0.479493\pi$
$798$	0.646869	0.0228989
$799$	−7.31636	−0.258834
$800$	−0.992413	−0.0350871
$801$	−9.45381	−0.334034
$802$	0.813670	0.0287317
$803$	−29.4291	−1.03853
$804$	15.8312	0.558325
$805$	3.47584	0.122507
$806$	0.0342714	0.00120716
$807$	12.1816	0.428812
$808$	5.29549	0.186295
$809$	19.4291	0.683092	0.341546	−	0.939865i	$-0.389050\pi$
$809$	19.4291	0.683092	0.341546	+	0.939865i	$0.389050\pi$
$810$	0.934437	0.0328328
$811$	17.9755	0.631204	0.315602	−	0.948892i	$-0.397794\pi$
$811$	17.9755	0.631204	0.315602	+	0.948892i	$0.397794\pi$
$812$	1.28450	0.0450770
$813$	−48.1879	−1.69002
$814$	−0.986832	−0.0345884
$815$	−12.2353	−0.428582
$816$	11.7987	0.413037
$817$	−23.0041	−0.804811
$818$	−3.07001	−0.107341
$819$	0.0597618	0.00208824
$820$	−2.14748	−0.0749931
$821$	−2.06013	−0.0718991	−0.0359496	−	0.999354i	$-0.511446\pi$
$821$	−2.06013	−0.0718991	−0.0359496	+	0.999354i	$0.511446\pi$
$822$	0.149022	0.00519774
$823$	−27.3219	−0.952381	−0.476190	−	0.879342i	$-0.657983\pi$
$823$	−27.3219	−0.952381	−0.476190	+	0.879342i	$0.657983\pi$
$824$	1.63421	0.0569306
$825$	−4.93683	−0.171878
$826$	−0.241883	−0.00841619
$827$	5.02249	0.174649	0.0873246	−	0.996180i	$-0.472168\pi$
$827$	5.02249	0.174649	0.0873246	+	0.996180i	$0.472168\pi$
$828$	−10.0126	−0.347960
$829$	−4.47983	−0.155591	−0.0777955	−	0.996969i	$-0.524788\pi$
$829$	−4.47983	−0.155591	−0.0777955	+	0.996969i	$0.524788\pi$
$830$	0.985241	0.0341982
$831$	29.1653	1.01173
$832$	−0.323963	−0.0112314
$833$	1.41364	0.0489797
$834$	0.762378	0.0263990
$835$	−9.55296	−0.330594
$836$	−17.2337	−0.596041
$837$	32.7002	1.13028
$838$	−2.48599	−0.0858772
$839$	−49.1757	−1.69773	−0.848867	−	0.528607i	$-0.822715\pi$
$839$	−49.1757	−1.69773	−0.848867	+	0.528607i	$0.822715\pi$
$840$	0.699476	0.0241342
$841$	−28.5847	−0.985678
$842$	0.491558	0.0169402
$843$	−43.9430	−1.51348
$844$	6.78809	0.233656
$845$	−12.9983	−0.447155
$846$	0.621478	0.0213669
$847$	−5.51729	−0.189576
$848$	−10.3093	−0.354023
$849$	−10.6721	−0.366265
$850$	−0.117450	−0.00402849
$851$	−17.6316	−0.604405
$852$	30.6151	1.04886
$853$	13.6145	0.466151	0.233075	−	0.972459i	$-0.425121\pi$
$853$	13.6145	0.466151	0.233075	+	0.972459i	$0.425121\pi$
$854$	0.852365	0.0291673
$855$	−5.33715	−0.182527
$856$	−4.33397	−0.148132
$857$	5.35359	0.182875	0.0914376	−	0.995811i	$-0.470854\pi$
$857$	5.35359	0.182875	0.0914376	+	0.995811i	$0.470854\pi$
$858$	0.0169601	0.000579007 0
$859$	55.7424	1.90191	0.950954	−	0.309334i	$-0.100106\pi$
$859$	55.7424	1.90191	0.950954	+	0.309334i	$0.100106\pi$
$860$	−12.4160	−0.423381
$861$	2.27170	0.0774192
$862$	−1.48947	−0.0507316
$863$	34.3748	1.17013	0.585066	−	0.810986i	$-0.301069\pi$
$863$	34.3748	1.17013	0.585066	+	0.810986i	$0.301069\pi$
$864$	3.25305	0.110671
$865$	−24.6426	−0.837874
$866$	−2.30932	−0.0784738
$867$	−31.6292	−1.07418
$868$	19.8829	0.674871
$869$	−19.0453	−0.646068
$870$	0.112893	0.00382744
$871$	−0.155777	−0.00527830
$872$	−4.43331	−0.150131
$873$	−0.531558	−0.0179905
$874$	1.06641	0.0360720
$875$	1.00000	0.0338062
$876$	−52.8152	−1.78446
$877$	14.9600	0.505164	0.252582	−	0.967576i	$-0.418720\pi$
$877$	14.9600	0.505164	0.252582	+	0.967576i	$0.418720\pi$
$878$	−0.432899	−0.0146096
$879$	−46.9850	−1.58476
$880$	−9.26920	−0.312465
$881$	33.8330	1.13986	0.569931	−	0.821692i	$-0.306970\pi$
$881$	33.8330	1.13986	0.569931	+	0.821692i	$0.306970\pi$
$882$	−0.120080	−0.00404329
$883$	−6.76815	−0.227767	−0.113883	−	0.993494i	$-0.536329\pi$
$883$	−6.76815	−0.227767	−0.113883	+	0.993494i	$0.536329\pi$
$884$	−0.116502	−0.00391839
$885$	6.13823	0.206334
$886$	−2.46609	−0.0828499
$887$	−50.4888	−1.69525	−0.847625	−	0.530596i	$-0.821968\pi$
$887$	−50.4888	−1.69525	−0.847625	+	0.530596i	$0.821968\pi$
$888$	−3.54818	−0.119069
$889$	17.7441	0.595118
$890$	0.543454	0.0182166
$891$	26.3351	0.882258
$892$	−7.50234	−0.251197
$893$	19.1121	0.639563
$894$	−0.654832	−0.0219009
$895$	10.7435	0.359116
$896$	2.63577	0.0880548
$897$	0.303024	0.0101177
$898$	1.53006	0.0510586
$899$	6.42919	0.214426
$900$	−2.88061	−0.0960205
$901$	−3.68148	−0.122648
$902$	0.209609	0.00697922
$903$	13.1342	0.437077
$904$	−2.15490	−0.0716708
$905$	4.04087	0.134323
$906$	0.497756	0.0165368
$907$	37.5714	1.24754	0.623770	−	0.781608i	$-0.285600\pi$
$907$	37.5714	1.24754	0.623770	+	0.781608i	$0.285600\pi$
$908$	46.6241	1.54727
$909$	23.0696	0.765170
$910$	−0.00343542	−0.000113883 0
$911$	56.9148	1.88567	0.942835	−	0.333259i	$-0.108148\pi$
$911$	56.9148	1.88567	0.942835	+	0.333259i	$0.108148\pi$
$912$	−30.8211	−1.02059
$913$	27.7669	0.918949
$914$	2.93426	0.0970565
$915$	−21.6303	−0.715077
$916$	1.99310	0.0658538
$917$	6.94459	0.229330
$918$	0.384990	0.0127066
$919$	0.957708	0.0315919	0.0157959	−	0.999875i	$-0.494972\pi$
$919$	0.957708	0.0315919	0.0157959	+	0.999875i	$0.494972\pi$
$920$	1.15314	0.0380179
$921$	5.26096	0.173355
$922$	2.41841	0.0796460
$923$	−0.301248	−0.00991570
$924$	9.83957	0.323698
$925$	−5.07262	−0.166787
$926$	2.75962	0.0906867
$927$	7.11939	0.233832
$928$	0.639584	0.0209954
$929$	−9.65385	−0.316733	−0.158366	−	0.987380i	$-0.550623\pi$
$929$	−9.65385	−0.316733	−0.158366	+	0.987380i	$0.550623\pi$
$930$	1.74749	0.0573025
$931$	−3.69278	−0.121026
$932$	8.04916	0.263659
$933$	−8.15229	−0.266894
$934$	1.70093	0.0556563
$935$	−3.31006	−0.108251
$936$	0.0198265	0.000648049 0
$937$	24.2463	0.792091	0.396046	−	0.918231i	$-0.370382\pi$
$937$	24.2463	0.792091	0.396046	+	0.918231i	$0.370382\pi$
$938$	0.313003	0.0102199
$939$	53.4392	1.74392
$940$	10.3154	0.336450
$941$	−46.2419	−1.50744	−0.753721	−	0.657195i	$-0.771743\pi$
$941$	−46.2419	−1.50744	−0.753721	+	0.657195i	$0.771743\pi$
$942$	−2.97240	−0.0968460
$943$	3.74507	0.121956
$944$	11.5249	0.375104
$945$	−3.27792	−0.106631
$946$	1.21189	0.0394018
$947$	−51.8815	−1.68592	−0.842961	−	0.537974i	$-0.819190\pi$
$947$	−51.8815	−1.68592	−0.842961	+	0.537974i	$0.819190\pi$
$948$	−34.1798	−1.11011
$949$	0.519693	0.0168699
$950$	0.306807	0.00995415
$951$	−25.8627	−0.838656
$952$	0.468987	0.0152000
$953$	58.3545	1.89029	0.945143	−	0.326656i	$-0.105922\pi$
$953$	58.3545	1.89029	0.945143	+	0.326656i	$0.105922\pi$
$954$	0.312719	0.0101246
$955$	−0.0949066	−0.00307111
$956$	10.7711	0.348361
$957$	3.18165	0.102848
$958$	−1.74771	−0.0564659
$959$	−0.850722	−0.0274712
$960$	−16.5188	−0.533142
$961$	68.5185	2.21027
$962$	0.0174266	0.000561856 0
$963$	−18.8808	−0.608424
$964$	59.1695	1.90572
$965$	−2.83704	−0.0913275
$966$	−0.608868	−0.0195900
$967$	−13.2474	−0.426008	−0.213004	−	0.977051i	$-0.568325\pi$
$967$	−13.2474	−0.426008	−0.213004	+	0.977051i	$0.568325\pi$
$968$	−1.83041	−0.0588317
$969$	−11.0063	−0.353574
$970$	0.0305568	0.000981118 0
$971$	−17.5664	−0.563734	−0.281867	−	0.959454i	$-0.590954\pi$
$971$	−17.5664	−0.563734	−0.281867	+	0.959454i	$0.590954\pi$
$972$	27.6628	0.887284
$973$	−4.35218	−0.139525
$974$	−1.96135	−0.0628456
$975$	0.0871800	0.00279200
$976$	−40.6123	−1.29997
$977$	−30.3685	−0.971576	−0.485788	−	0.874077i	$-0.661467\pi$
$977$	−30.3685	−0.971576	−0.485788	+	0.874077i	$0.661467\pi$
$978$	2.14327	0.0685341
$979$	15.3161	0.489504
$980$	−1.99310	−0.0636672
$981$	−19.3136	−0.616634
$982$	0.129214	0.00412339
$983$	44.4774	1.41861	0.709304	−	0.704903i	$-0.249009\pi$
$983$	44.4774	1.41861	0.709304	+	0.704903i	$0.249009\pi$
$984$	0.753655	0.0240257
$985$	−3.60846	−0.114975
$986$	0.0756931	0.00241056
$987$	−10.9121	−0.347335
$988$	0.304332	0.00968210
$989$	21.6527	0.688515
$990$	0.281169	0.00893613
$991$	−10.9400	−0.347520	−0.173760	−	0.984788i	$-0.555592\pi$
$991$	−10.9400	−0.347520	−0.173760	+	0.984788i	$0.555592\pi$
$992$	9.90021	0.314332
$993$	38.0097	1.20620
$994$	0.605300	0.0191989
$995$	0.216450	0.00686194
$996$	49.8320	1.57899
$997$	41.2145	1.30528	0.652638	−	0.757670i	$-0.273662\pi$
$997$	41.2145	1.30528	0.652638	+	0.757670i	$0.273662\pi$
$998$	−2.44723	−0.0774656
$999$	16.6277	0.526076

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8015.2.a.h.1.20	✓	38

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8015.2.a.h.1.20	✓	38	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)

\(f(q)\)	\(=\)	\(q-0.0830831 q^{2} +2.10839 q^{3} -1.99310 q^{4} +1.00000 q^{5} -0.175171 q^{6} +1.00000 q^{7} +0.331759 q^{8} +1.44530 q^{9} +O(q^{10})\)	\(q-0.0830831 q^{2} +2.10839 q^{3} -1.99310 q^{4} +1.00000 q^{5} -0.175171 q^{6} +1.00000 q^{7} +0.331759 q^{8} +1.44530 q^{9} -0.0830831 q^{10} -2.34152 q^{11} -4.20222 q^{12} +0.0413492 q^{13} -0.0830831 q^{14} +2.10839 q^{15} +3.95863 q^{16} +1.41364 q^{17} -0.120080 q^{18} -3.69278 q^{19} -1.99310 q^{20} +2.10839 q^{21} +0.194541 q^{22} +3.47584 q^{23} +0.699476 q^{24} +1.00000 q^{25} -0.00343542 q^{26} -3.27792 q^{27} -1.99310 q^{28} -0.644473 q^{29} -0.175171 q^{30} -9.97589 q^{31} -0.992413 q^{32} -4.93683 q^{33} -0.117450 q^{34} +1.00000 q^{35} -2.88061 q^{36} -5.07262 q^{37} +0.306807 q^{38} +0.0871800 q^{39} +0.331759 q^{40} +1.07746 q^{41} -0.175171 q^{42} +6.22948 q^{43} +4.66687 q^{44} +1.44530 q^{45} -0.288784 q^{46} -5.17555 q^{47} +8.34633 q^{48} +1.00000 q^{49} -0.0830831 q^{50} +2.98050 q^{51} -0.0824129 q^{52} -2.60426 q^{53} +0.272340 q^{54} -2.34152 q^{55} +0.331759 q^{56} -7.78580 q^{57} +0.0535448 q^{58} +2.91134 q^{59} -4.20222 q^{60} -10.2592 q^{61} +0.828829 q^{62} +1.44530 q^{63} -7.83481 q^{64} +0.0413492 q^{65} +0.410167 q^{66} -3.76735 q^{67} -2.81752 q^{68} +7.32842 q^{69} -0.0830831 q^{70} -7.28547 q^{71} +0.479490 q^{72} +12.5684 q^{73} +0.421450 q^{74} +2.10839 q^{75} +7.36006 q^{76} -2.34152 q^{77} -0.00724319 q^{78} +8.13374 q^{79} +3.95863 q^{80} -11.2470 q^{81} -0.0895185 q^{82} -11.8585 q^{83} -4.20222 q^{84} +1.41364 q^{85} -0.517565 q^{86} -1.35880 q^{87} -0.776820 q^{88} -6.54109 q^{89} -0.120080 q^{90} +0.0413492 q^{91} -6.92769 q^{92} -21.0330 q^{93} +0.430001 q^{94} -3.69278 q^{95} -2.09239 q^{96} -0.367785 q^{97} -0.0830831 q^{98} -3.38419 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 38 q - 6 q^{2} - 9 q^{3} + 24 q^{4} + 38 q^{5} - 10 q^{6} + 38 q^{7} - 21 q^{8} + 13 q^{9}+O(q^{10}) \) 38 * q - 6 * q^2 - 9 * q^3 + 24 * q^4 + 38 * q^5 - 10 * q^6 + 38 * q^7 - 21 * q^8 + 13 * q^9	\( 38 q - 6 q^{2} - 9 q^{3} + 24 q^{4} + 38 q^{5} - 10 q^{6} + 38 q^{7} - 21 q^{8} + 13 q^{9} - 6 q^{10} - 18 q^{11} - 20 q^{12} - 25 q^{13} - 6 q^{14} - 9 q^{15} - 21 q^{17} - 7 q^{18} - 14 q^{19} + 24 q^{20} - 9 q^{21} - 11 q^{22} - 16 q^{23} - 10 q^{24} + 38 q^{25} - 21 q^{26} - 15 q^{27} + 24 q^{28} - 52 q^{29} - 10 q^{30} - 30 q^{31} - 8 q^{32} - 13 q^{33} - 9 q^{34} + 38 q^{35} - 16 q^{36} - 47 q^{37} - 10 q^{38} - 50 q^{39} - 21 q^{40} - 35 q^{41} - 10 q^{42} - 18 q^{43} - 22 q^{44} + 13 q^{45} - 17 q^{46} - 23 q^{47} - 13 q^{48} + 38 q^{49} - 6 q^{50} - 5 q^{51} - 41 q^{52} - 12 q^{53} + 35 q^{54} - 18 q^{55} - 21 q^{56} - 3 q^{57} - 16 q^{58} - 16 q^{59} - 20 q^{60} - 47 q^{61} + 14 q^{62} + 13 q^{63} - 55 q^{64} - 25 q^{65} - 6 q^{66} - 54 q^{67} + 31 q^{68} - 95 q^{69} - 6 q^{70} - 41 q^{71} - 59 q^{73} - q^{74} - 9 q^{75} - 23 q^{76} - 18 q^{77} + 19 q^{78} - 117 q^{79} - 38 q^{81} + 19 q^{82} - 21 q^{83} - 20 q^{84} - 21 q^{85} - 12 q^{86} - 14 q^{87} - 40 q^{88} - 96 q^{89} - 7 q^{90} - 25 q^{91} + 53 q^{92} - 53 q^{93} - 28 q^{94} - 14 q^{95} + 40 q^{96} - 70 q^{97} - 6 q^{98} - 52 q^{99}+O(q^{100}) \) 38 * q - 6 * q^2 - 9 * q^3 + 24 * q^4 + 38 * q^5 - 10 * q^6 + 38 * q^7 - 21 * q^8 + 13 * q^9 - 6 * q^10 - 18 * q^11 - 20 * q^12 - 25 * q^13 - 6 * q^14 - 9 * q^15 - 21 * q^17 - 7 * q^18 - 14 * q^19 + 24 * q^20 - 9 * q^21 - 11 * q^22 - 16 * q^23 - 10 * q^24 + 38 * q^25 - 21 * q^26 - 15 * q^27 + 24 * q^28 - 52 * q^29 - 10 * q^30 - 30 * q^31 - 8 * q^32 - 13 * q^33 - 9 * q^34 + 38 * q^35 - 16 * q^36 - 47 * q^37 - 10 * q^38 - 50 * q^39 - 21 * q^40 - 35 * q^41 - 10 * q^42 - 18 * q^43 - 22 * q^44 + 13 * q^45 - 17 * q^46 - 23 * q^47 - 13 * q^48 + 38 * q^49 - 6 * q^50 - 5 * q^51 - 41 * q^52 - 12 * q^53 + 35 * q^54 - 18 * q^55 - 21 * q^56 - 3 * q^57 - 16 * q^58 - 16 * q^59 - 20 * q^60 - 47 * q^61 + 14 * q^62 + 13 * q^63 - 55 * q^64 - 25 * q^65 - 6 * q^66 - 54 * q^67 + 31 * q^68 - 95 * q^69 - 6 * q^70 - 41 * q^71 - 59 * q^73 - q^74 - 9 * q^75 - 23 * q^76 - 18 * q^77 + 19 * q^78 - 117 * q^79 - 38 * q^81 + 19 * q^82 - 21 * q^83 - 20 * q^84 - 21 * q^85 - 12 * q^86 - 14 * q^87 - 40 * q^88 - 96 * q^89 - 7 * q^90 - 25 * q^91 + 53 * q^92 - 53 * q^93 - 28 * q^94 - 14 * q^95 + 40 * q^96 - 70 * q^97 - 6 * q^98 - 52 * q^99

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