LMFDB - Embedded newform 8015.2.a.l.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:	$0$
Dimension:	$62$
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)

$f(q)$	$=$	$q-1.21148 q^{2} +1.67937 q^{3} -0.532324 q^{4} -1.00000 q^{5} -2.03452 q^{6} -1.00000 q^{7} +3.06785 q^{8} -0.179714 q^{9} +O(q^{10})$	\(q-1.21148 q^{2} +1.67937 q^{3} -0.532324 q^{4} -1.00000 q^{5} -2.03452 q^{6} -1.00000 q^{7} +3.06785 q^{8} -0.179714 q^{9} +1.21148 q^{10} -5.20420 q^{11} -0.893970 q^{12} +4.41019 q^{13} +1.21148 q^{14} -1.67937 q^{15} -2.65198 q^{16} -0.830757 q^{17} +0.217720 q^{18} -7.19999 q^{19} +0.532324 q^{20} -1.67937 q^{21} +6.30476 q^{22} -1.03249 q^{23} +5.15206 q^{24} +1.00000 q^{25} -5.34284 q^{26} -5.33992 q^{27} +0.532324 q^{28} -6.71927 q^{29} +2.03452 q^{30} +0.399125 q^{31} -2.92289 q^{32} -8.73977 q^{33} +1.00644 q^{34} +1.00000 q^{35} +0.0956662 q^{36} +6.46999 q^{37} +8.72262 q^{38} +7.40634 q^{39} -3.06785 q^{40} +6.34004 q^{41} +2.03452 q^{42} -1.63582 q^{43} +2.77032 q^{44} +0.179714 q^{45} +1.25084 q^{46} -5.69334 q^{47} -4.45366 q^{48} +1.00000 q^{49} -1.21148 q^{50} -1.39515 q^{51} -2.34765 q^{52} -10.3766 q^{53} +6.46919 q^{54} +5.20420 q^{55} -3.06785 q^{56} -12.0915 q^{57} +8.14024 q^{58} -14.5415 q^{59} +0.893970 q^{60} +8.62838 q^{61} -0.483530 q^{62} +0.179714 q^{63} +8.84498 q^{64} -4.41019 q^{65} +10.5880 q^{66} -2.55982 q^{67} +0.442232 q^{68} -1.73393 q^{69} -1.21148 q^{70} +15.5322 q^{71} -0.551337 q^{72} +6.22453 q^{73} -7.83824 q^{74} +1.67937 q^{75} +3.83273 q^{76} +5.20420 q^{77} -8.97261 q^{78} +8.09991 q^{79} +2.65198 q^{80} -8.42856 q^{81} -7.68081 q^{82} +11.9391 q^{83} +0.893970 q^{84} +0.830757 q^{85} +1.98176 q^{86} -11.2841 q^{87} -15.9657 q^{88} -5.80329 q^{89} -0.217720 q^{90} -4.41019 q^{91} +0.549619 q^{92} +0.670278 q^{93} +6.89735 q^{94} +7.19999 q^{95} -4.90861 q^{96} -8.15777 q^{97} -1.21148 q^{98} +0.935268 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 62 q + 2 q^{2} + 11 q^{3} + 64 q^{4} - 62 q^{5} + 3 q^{6} - 62 q^{7} + 15 q^{8} + 69 q^{9}+O(q^{10}) $ 62 * q + 2 * q^2 + 11 * q^3 + 64 * q^4 - 62 * q^5 + 3 * q^6 - 62 * q^7 + 15 * q^8 + 69 * q^9	\( 62 q + 2 q^{2} + 11 q^{3} + 64 q^{4} - 62 q^{5} + 3 q^{6} - 62 q^{7} + 15 q^{8} + 69 q^{9} - 2 q^{10} - 13 q^{11} + 37 q^{12} + 31 q^{13} - 2 q^{14} - 11 q^{15} + 64 q^{16} + 30 q^{17} + 18 q^{18} + 20 q^{19} - 64 q^{20} - 11 q^{21} + 7 q^{22} + 29 q^{24} + 62 q^{25} + 59 q^{27} - 64 q^{28} - 29 q^{29} - 3 q^{30} + 20 q^{31} + 22 q^{32} + 72 q^{33} + 13 q^{34} + 62 q^{35} + 53 q^{36} + 35 q^{37} + 34 q^{38} - 6 q^{39} - 15 q^{40} + 13 q^{41} - 3 q^{42} - 4 q^{43} - 44 q^{44} - 69 q^{45} - 19 q^{46} + 58 q^{47} + 64 q^{48} + 62 q^{49} + 2 q^{50} - 30 q^{51} + 82 q^{52} + 18 q^{53} + 22 q^{54} + 13 q^{55} - 15 q^{56} + 21 q^{57} + 18 q^{58} - 11 q^{59} - 37 q^{60} + 24 q^{61} + 48 q^{62} - 69 q^{63} + 65 q^{64} - 31 q^{65} + 25 q^{66} - 6 q^{67} + 65 q^{68} + 27 q^{69} + 2 q^{70} - 35 q^{71} + 53 q^{72} + 116 q^{73} - 69 q^{74} + 11 q^{75} + 65 q^{76} + 13 q^{77} + 102 q^{78} - 83 q^{79} - 64 q^{80} + 126 q^{81} + 71 q^{82} + 84 q^{83} - 37 q^{84} - 30 q^{85} + 24 q^{86} + 49 q^{87} + 20 q^{88} - 16 q^{89} - 18 q^{90} - 31 q^{91} + 19 q^{92} + 65 q^{93} + 54 q^{94} - 20 q^{95} + 17 q^{96} + 155 q^{97} + 2 q^{98} + 6 q^{99}+O(q^{100}) \) 62 * q + 2 * q^2 + 11 * q^3 + 64 * q^4 - 62 * q^5 + 3 * q^6 - 62 * q^7 + 15 * q^8 + 69 * q^9 - 2 * q^10 - 13 * q^11 + 37 * q^12 + 31 * q^13 - 2 * q^14 - 11 * q^15 + 64 * q^16 + 30 * q^17 + 18 * q^18 + 20 * q^19 - 64 * q^20 - 11 * q^21 + 7 * q^22 + 29 * q^24 + 62 * q^25 + 59 * q^27 - 64 * q^28 - 29 * q^29 - 3 * q^30 + 20 * q^31 + 22 * q^32 + 72 * q^33 + 13 * q^34 + 62 * q^35 + 53 * q^36 + 35 * q^37 + 34 * q^38 - 6 * q^39 - 15 * q^40 + 13 * q^41 - 3 * q^42 - 4 * q^43 - 44 * q^44 - 69 * q^45 - 19 * q^46 + 58 * q^47 + 64 * q^48 + 62 * q^49 + 2 * q^50 - 30 * q^51 + 82 * q^52 + 18 * q^53 + 22 * q^54 + 13 * q^55 - 15 * q^56 + 21 * q^57 + 18 * q^58 - 11 * q^59 - 37 * q^60 + 24 * q^61 + 48 * q^62 - 69 * q^63 + 65 * q^64 - 31 * q^65 + 25 * q^66 - 6 * q^67 + 65 * q^68 + 27 * q^69 + 2 * q^70 - 35 * q^71 + 53 * q^72 + 116 * q^73 - 69 * q^74 + 11 * q^75 + 65 * q^76 + 13 * q^77 + 102 * q^78 - 83 * q^79 - 64 * q^80 + 126 * q^81 + 71 * q^82 + 84 * q^83 - 37 * q^84 - 30 * q^85 + 24 * q^86 + 49 * q^87 + 20 * q^88 - 16 * q^89 - 18 * q^90 - 31 * q^91 + 19 * q^92 + 65 * q^93 + 54 * q^94 - 20 * q^95 + 17 * q^96 + 155 * q^97 + 2 * q^98 + 6 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.21148	−0.856643	−0.428322	−	0.903626i	$-0.640895\pi$
$2$	−1.21148	−0.856643	−0.428322	+	0.903626i	$0.640895\pi$
$3$	1.67937	0.969585	0.484793	−	0.874629i	$-0.338895\pi$
$3$	1.67937	0.969585	0.484793	+	0.874629i	$0.338895\pi$
$4$	−0.532324	−0.266162
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−2.03452	−0.830589
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	3.06785	1.08465
$9$	−0.179714	−0.0599047
$10$	1.21148	0.383103
$11$	−5.20420	−1.56912	−0.784562	−	0.620050i	$-0.787112\pi$
$11$	−5.20420	−1.56912	−0.784562	+	0.620050i	$0.787112\pi$
$12$	−0.893970	−0.258067
$13$	4.41019	1.22317	0.611583	−	0.791180i	$-0.290533\pi$
$13$	4.41019	1.22317	0.611583	+	0.791180i	$0.290533\pi$
$14$	1.21148	0.323781
$15$	−1.67937	−0.433612
$16$	−2.65198	−0.662996
$17$	−0.830757	−0.201488	−0.100744	−	0.994912i	$-0.532122\pi$
$17$	−0.830757	−0.201488	−0.100744	+	0.994912i	$0.532122\pi$
$18$	0.217720	0.0513170
$19$	−7.19999	−1.65179	−0.825896	−	0.563823i	$-0.809330\pi$
$19$	−7.19999	−1.65179	−0.825896	+	0.563823i	$0.809330\pi$
$20$	0.532324	0.119031
$21$	−1.67937	−0.366469
$22$	6.30476	1.34418
$23$	−1.03249	−0.215289	−0.107644	−	0.994189i	$-0.534331\pi$
$23$	−1.03249	−0.215289	−0.107644	+	0.994189i	$0.534331\pi$
$24$	5.15206	1.05166
$25$	1.00000	0.200000
$26$	−5.34284	−1.04782
$27$	−5.33992	−1.02767
$28$	0.532324	0.100600
$29$	−6.71927	−1.24774	−0.623868	−	0.781529i	$-0.714440\pi$
$29$	−6.71927	−1.24774	−0.623868	+	0.781529i	$0.714440\pi$
$30$	2.03452	0.371451
$31$	0.399125	0.0716849	0.0358424	−	0.999357i	$-0.488589\pi$
$31$	0.399125	0.0716849	0.0358424	+	0.999357i	$0.488589\pi$
$32$	−2.92289	−0.516699
$33$	−8.73977	−1.52140
$34$	1.00644	0.172604
$35$	1.00000	0.169031
$36$	0.0956662	0.0159444
$37$	6.46999	1.06366	0.531830	−	0.846851i	$-0.321505\pi$
$37$	6.46999	1.06366	0.531830	+	0.846851i	$0.321505\pi$
$38$	8.72262	1.41500
$39$	7.40634	1.18596
$40$	−3.06785	−0.485070
$41$	6.34004	0.990148	0.495074	−	0.868851i	$-0.335141\pi$
$41$	6.34004	0.990148	0.495074	+	0.868851i	$0.335141\pi$
$42$	2.03452	0.313933
$43$	−1.63582	−0.249461	−0.124730	−	0.992191i	$-0.539807\pi$
$43$	−1.63582	−0.249461	−0.124730	+	0.992191i	$0.539807\pi$
$44$	2.77032	0.417641
$45$	0.179714	0.0267902
$46$	1.25084	0.184426
$47$	−5.69334	−0.830459	−0.415229	−	0.909717i	$-0.636299\pi$
$47$	−5.69334	−0.830459	−0.415229	+	0.909717i	$0.636299\pi$
$48$	−4.45366	−0.642831
$49$	1.00000	0.142857
$50$	−1.21148	−0.171329
$51$	−1.39515	−0.195360
$52$	−2.34765	−0.325561
$53$	−10.3766	−1.42533	−0.712665	−	0.701504i	$-0.752512\pi$
$53$	−10.3766	−1.42533	−0.712665	+	0.701504i	$0.752512\pi$
$54$	6.46919	0.880345
$55$	5.20420	0.701734
$56$	−3.06785	−0.409959
$57$	−12.0915	−1.60155
$58$	8.14024	1.06887
$59$	−14.5415	−1.89315	−0.946574	−	0.322487i	$-0.895481\pi$
$59$	−14.5415	−1.89315	−0.946574	+	0.322487i	$0.895481\pi$
$60$	0.893970	0.115411
$61$	8.62838	1.10475	0.552375	−	0.833596i	$-0.313722\pi$
$61$	8.62838	1.10475	0.552375	+	0.833596i	$0.313722\pi$
$62$	−0.483530	−0.0614084
$63$	0.179714	0.0226419
$64$	8.84498	1.10562
$65$	−4.41019	−0.547017
$66$	10.5880	1.30330
$67$	−2.55982	−0.312732	−0.156366	−	0.987699i	$-0.549978\pi$
$67$	−2.55982	−0.312732	−0.156366	+	0.987699i	$0.549978\pi$
$68$	0.442232	0.0536285
$69$	−1.73393	−0.208741
$70$	−1.21148	−0.144799
$71$	15.5322	1.84334	0.921668	−	0.387981i	$-0.126827\pi$
$71$	15.5322	1.84334	0.921668	+	0.387981i	$0.126827\pi$
$72$	−0.551337	−0.0649756
$73$	6.22453	0.728527	0.364263	−	0.931296i	$-0.381321\pi$
$73$	6.22453	0.728527	0.364263	+	0.931296i	$0.381321\pi$
$74$	−7.83824	−0.911177
$75$	1.67937	0.193917
$76$	3.83273	0.439644
$77$	5.20420	0.593073
$78$	−8.97261	−1.01595
$79$	8.09991	0.911311	0.455655	−	0.890156i	$-0.349405\pi$
$79$	8.09991	0.911311	0.455655	+	0.890156i	$0.349405\pi$
$80$	2.65198	0.296501
$81$	−8.42856	−0.936507
$82$	−7.68081	−0.848204
$83$	11.9391	1.31048	0.655242	−	0.755419i	$-0.272567\pi$
$83$	11.9391	1.31048	0.655242	+	0.755419i	$0.272567\pi$
$84$	0.893970	0.0975401
$85$	0.830757	0.0901083
$86$	1.98176	0.213699
$87$	−11.2841	−1.20979
$88$	−15.9657	−1.70195
$89$	−5.80329	−0.615147	−0.307574	−	0.951524i	$-0.599517\pi$
$89$	−5.80329	−0.615147	−0.307574	+	0.951524i	$0.599517\pi$
$90$	−0.217720	−0.0229497
$91$	−4.41019	−0.462313
$92$	0.549619	0.0573017
$93$	0.670278	0.0695046
$94$	6.89735	0.711407
$95$	7.19999	0.738703
$96$	−4.90861	−0.500983
$97$	−8.15777	−0.828296	−0.414148	−	0.910210i	$-0.635920\pi$
$97$	−8.15777	−0.828296	−0.414148	+	0.910210i	$0.635920\pi$
$98$	−1.21148	−0.122378
$99$	0.935268	0.0939980
$100$	−0.532324	−0.0532324
$101$	9.42696	0.938017	0.469009	−	0.883194i	$-0.344611\pi$
$101$	9.42696	0.938017	0.469009	+	0.883194i	$0.344611\pi$
$102$	1.69019	0.167354
$103$	−0.699690	−0.0689425	−0.0344713	−	0.999406i	$-0.510975\pi$
$103$	−0.699690	−0.0689425	−0.0344713	+	0.999406i	$0.510975\pi$
$104$	13.5298	1.32671
$105$	1.67937	0.163890
$106$	12.5710	1.22100
$107$	−7.12220	−0.688529	−0.344264	−	0.938873i	$-0.611872\pi$
$107$	−7.12220	−0.688529	−0.344264	+	0.938873i	$0.611872\pi$
$108$	2.84257	0.273526
$109$	−5.44814	−0.521837	−0.260919	−	0.965361i	$-0.584025\pi$
$109$	−5.44814	−0.521837	−0.260919	+	0.965361i	$0.584025\pi$
$110$	−6.30476	−0.601136
$111$	10.8655	1.03131
$112$	2.65198	0.250589
$113$	−1.58231	−0.148851	−0.0744255	−	0.997227i	$-0.523712\pi$
$113$	−1.58231	−0.148851	−0.0744255	+	0.997227i	$0.523712\pi$
$114$	14.6485	1.37196
$115$	1.03249	0.0962801
$116$	3.57683	0.332100
$117$	−0.792574	−0.0732735
$118$	17.6167	1.62175
$119$	0.830757	0.0761554
$120$	−5.15206	−0.470317
$121$	16.0837	1.46215
$122$	−10.4531	−0.946377
$123$	10.6473	0.960033
$124$	−0.212464	−0.0190798
$125$	−1.00000	−0.0894427
$126$	−0.217720	−0.0193960
$127$	−5.30748	−0.470963	−0.235482	−	0.971879i	$-0.575667\pi$
$127$	−5.30748	−0.470963	−0.235482	+	0.971879i	$0.575667\pi$
$128$	−4.86970	−0.430425
$129$	−2.74715	−0.241873
$130$	5.34284	0.468598
$131$	9.34518	0.816492	0.408246	−	0.912872i	$-0.366141\pi$
$131$	9.34518	0.816492	0.408246	+	0.912872i	$0.366141\pi$
$132$	4.65239	0.404939
$133$	7.19999	0.624318
$134$	3.10117	0.267900
$135$	5.33992	0.459587
$136$	−2.54864	−0.218544
$137$	−12.7964	−1.09327	−0.546637	−	0.837370i	$-0.684092\pi$
$137$	−12.7964	−1.09327	−0.546637	+	0.837370i	$0.684092\pi$
$138$	2.10062	0.178816
$139$	1.58170	0.134158	0.0670790	−	0.997748i	$-0.478632\pi$
$139$	1.58170	0.134158	0.0670790	+	0.997748i	$0.478632\pi$
$140$	−0.532324	−0.0449896
$141$	−9.56122	−0.805200
$142$	−18.8169	−1.57908
$143$	−22.9515	−1.91930
$144$	0.476599	0.0397166
$145$	6.71927	0.558005
$146$	−7.54088	−0.624087
$147$	1.67937	0.138512
$148$	−3.44413	−0.283106
$149$	1.46551	0.120059	0.0600296	−	0.998197i	$-0.480880\pi$
$149$	1.46551	0.120059	0.0600296	+	0.998197i	$0.480880\pi$
$150$	−2.03452	−0.166118
$151$	10.8842	0.885748	0.442874	−	0.896584i	$-0.353959\pi$
$151$	10.8842	0.885748	0.442874	+	0.896584i	$0.353959\pi$
$152$	−22.0885	−1.79161
$153$	0.149299	0.0120701
$154$	−6.30476	−0.508052
$155$	−0.399125	−0.0320585
$156$	−3.94258	−0.315659
$157$	−3.90830	−0.311917	−0.155958	−	0.987764i	$-0.549847\pi$
$157$	−3.90830	−0.311917	−0.155958	+	0.987764i	$0.549847\pi$
$158$	−9.81285	−0.780668
$159$	−17.4261	−1.38198
$160$	2.92289	0.231075
$161$	1.03249	0.0813715
$162$	10.2110	0.802252
$163$	8.96770	0.702405	0.351202	−	0.936300i	$-0.385773\pi$
$163$	8.96770	0.702405	0.351202	+	0.936300i	$0.385773\pi$
$164$	−3.37496	−0.263540
$165$	8.73977	0.680391
$166$	−14.4639	−1.12262
$167$	3.62653	0.280630	0.140315	−	0.990107i	$-0.455189\pi$
$167$	3.62653	0.280630	0.140315	+	0.990107i	$0.455189\pi$
$168$	−5.15206	−0.397490
$169$	6.44977	0.496136
$170$	−1.00644	−0.0771906
$171$	1.29394	0.0989501
$172$	0.870788	0.0663970
$173$	7.05442	0.536338	0.268169	−	0.963372i	$-0.413581\pi$
$173$	7.05442	0.536338	0.268169	+	0.963372i	$0.413581\pi$
$174$	13.6705	1.03636
$175$	−1.00000	−0.0755929
$176$	13.8014	1.04032
$177$	−24.4206	−1.83557
$178$	7.03055	0.526962
$179$	3.13166	0.234071	0.117036	−	0.993128i	$-0.462661\pi$
$179$	3.13166	0.234071	0.117036	+	0.993128i	$0.462661\pi$
$180$	−0.0956662	−0.00713054
$181$	22.4452	1.66834	0.834168	−	0.551510i	$-0.185948\pi$
$181$	22.4452	1.66834	0.834168	+	0.551510i	$0.185948\pi$
$182$	5.34284	0.396038
$183$	14.4902	1.07115
$184$	−3.16752	−0.233513
$185$	−6.46999	−0.475683
$186$	−0.812026	−0.0595407
$187$	4.32342	0.316160
$188$	3.03070	0.221037
$189$	5.33992	0.388422
$190$	−8.72262	−0.632805
$191$	−25.4447	−1.84112	−0.920558	−	0.390606i	$-0.872266\pi$
$191$	−25.4447	−1.84112	−0.920558	+	0.390606i	$0.872266\pi$
$192$	14.8540	1.07199
$193$	−16.0136	−1.15268	−0.576341	−	0.817210i	$-0.695520\pi$
$193$	−16.0136	−1.15268	−0.576341	+	0.817210i	$0.695520\pi$
$194$	9.88295	0.709554
$195$	−7.40634	−0.530379
$196$	−0.532324	−0.0380232
$197$	24.7300	1.76194	0.880971	−	0.473170i	$-0.156890\pi$
$197$	24.7300	1.76194	0.880971	+	0.473170i	$0.156890\pi$
$198$	−1.13306	−0.0805228
$199$	−1.74351	−0.123594	−0.0617972	−	0.998089i	$-0.519683\pi$
$199$	−1.74351	−0.123594	−0.0617972	+	0.998089i	$0.519683\pi$
$200$	3.06785	0.216930
$201$	−4.29889	−0.303221
$202$	−11.4205	−0.803546
$203$	6.71927	0.471600
$204$	0.742672	0.0519974
$205$	−6.34004	−0.442808
$206$	0.847658	0.0590592
$207$	0.185553	0.0128968
$208$	−11.6957	−0.810954
$209$	37.4702	2.59187
$210$	−2.03452	−0.140395
$211$	−10.5180	−0.724088	−0.362044	−	0.932161i	$-0.617921\pi$
$211$	−10.5180	−0.724088	−0.362044	+	0.932161i	$0.617921\pi$
$212$	5.52370	0.379369
$213$	26.0843	1.78727
$214$	8.62838	0.589824
$215$	1.63582	0.111562
$216$	−16.3821	−1.11466
$217$	−0.399125	−0.0270943
$218$	6.60029	0.447028
$219$	10.4533	0.706368
$220$	−2.77032	−0.186775
$221$	−3.66380	−0.246454
$222$	−13.1633	−0.883464
$223$	4.06215	0.272021	0.136011	−	0.990707i	$-0.456572\pi$
$223$	4.06215	0.272021	0.136011	+	0.990707i	$0.456572\pi$
$224$	2.92289	0.195294
$225$	−0.179714	−0.0119809
$226$	1.91693	0.127512
$227$	−13.3462	−0.885820	−0.442910	−	0.896566i	$-0.646054\pi$
$227$	−13.3462	−0.885820	−0.442910	+	0.896566i	$0.646054\pi$
$228$	6.43657	0.426273
$229$	1.00000	0.0660819
$229$	1.00000	0.0660819
$230$	−1.25084	−0.0824777
$231$	8.73977	0.575035
$232$	−20.6137	−1.35336
$233$	15.2104	0.996465	0.498232	−	0.867044i	$-0.333983\pi$
$233$	15.2104	0.996465	0.498232	+	0.867044i	$0.333983\pi$
$234$	0.960185	0.0627692
$235$	5.69334	0.371392
$236$	7.74082	0.503884
$237$	13.6027	0.883593
$238$	−1.00644	−0.0652380
$239$	−12.8861	−0.833536	−0.416768	−	0.909013i	$-0.636837\pi$
$239$	−12.8861	−0.833536	−0.416768	+	0.909013i	$0.636837\pi$
$240$	4.45366	0.287483
$241$	6.39447	0.411904	0.205952	−	0.978562i	$-0.433971\pi$
$241$	6.39447	0.411904	0.205952	+	0.978562i	$0.433971\pi$
$242$	−19.4850	−1.25254
$243$	1.86508	0.119645
$244$	−4.59310	−0.294043
$245$	−1.00000	−0.0638877
$246$	−12.8989	−0.822406
$247$	−31.7533	−2.02042
$248$	1.22446	0.0777530
$249$	20.0501	1.27062
$250$	1.21148	0.0766205
$251$	−9.03909	−0.570542	−0.285271	−	0.958447i	$-0.592084\pi$
$251$	−9.03909	−0.570542	−0.285271	+	0.958447i	$0.592084\pi$
$252$	−0.0956662	−0.00602641
$253$	5.37327	0.337815
$254$	6.42989	0.403447
$255$	1.39515	0.0873676
$256$	−11.7904	−0.736901
$257$	−17.6408	−1.10040	−0.550200	−	0.835033i	$-0.685449\pi$
$257$	−17.6408	−1.10040	−0.550200	+	0.835033i	$0.685449\pi$
$258$	3.32811	0.207199
$259$	−6.46999	−0.402026
$260$	2.34765	0.145595
$261$	1.20755	0.0747453
$262$	−11.3215	−0.699442
$263$	18.1765	1.12081	0.560405	−	0.828219i	$-0.310646\pi$
$263$	18.1765	1.12081	0.560405	+	0.828219i	$0.310646\pi$
$264$	−26.8123	−1.65019
$265$	10.3766	0.637427
$266$	−8.72262	−0.534818
$267$	−9.74587	−0.596438
$268$	1.36266	0.0832375
$269$	−5.15450	−0.314276	−0.157138	−	0.987577i	$-0.550227\pi$
$269$	−5.15450	−0.314276	−0.157138	+	0.987577i	$0.550227\pi$
$270$	−6.46919	−0.393702
$271$	16.4518	0.999374	0.499687	−	0.866206i	$-0.333448\pi$
$271$	16.4518	0.999374	0.499687	+	0.866206i	$0.333448\pi$
$272$	2.20315	0.133586
$273$	−7.40634	−0.448252
$274$	15.5026	0.936546
$275$	−5.20420	−0.313825
$276$	0.923014	0.0555589
$277$	29.5923	1.77803	0.889015	−	0.457877i	$-0.151390\pi$
$277$	29.5923	1.77803	0.889015	+	0.457877i	$0.151390\pi$
$278$	−1.91619	−0.114926
$279$	−0.0717284	−0.00429427
$280$	3.06785	0.183339
$281$	6.48794	0.387038	0.193519	−	0.981097i	$-0.438010\pi$
$281$	6.48794	0.387038	0.193519	+	0.981097i	$0.438010\pi$
$282$	11.5832	0.689770
$283$	−20.9612	−1.24601	−0.623007	−	0.782217i	$-0.714089\pi$
$283$	−20.9612	−1.24601	−0.623007	+	0.782217i	$0.714089\pi$
$284$	−8.26818	−0.490626
$285$	12.0915	0.716236
$286$	27.8052	1.64416
$287$	−6.34004	−0.374241
$288$	0.525285	0.0309527
$289$	−16.3098	−0.959403
$290$	−8.14024	−0.478011
$291$	−13.6999	−0.803104
$292$	−3.31347	−0.193906
$293$	−9.48074	−0.553871	−0.276935	−	0.960889i	$-0.589319\pi$
$293$	−9.48074	−0.553871	−0.276935	+	0.960889i	$0.589319\pi$
$294$	−2.03452	−0.118656
$295$	14.5415	0.846641
$296$	19.8490	1.15370
$297$	27.7900	1.61254
$298$	−1.77543	−0.102848
$299$	−4.55347	−0.263334
$300$	−0.893970	−0.0516134
$301$	1.63582	0.0942872
$302$	−13.1860	−0.758770
$303$	15.8314	0.909487
$304$	19.0942	1.09513
$305$	−8.62838	−0.494059
$306$	−0.180872	−0.0103398
$307$	−14.2468	−0.813109	−0.406554	−	0.913627i	$-0.633270\pi$
$307$	−14.2468	−0.813109	−0.406554	+	0.913627i	$0.633270\pi$
$308$	−2.77032	−0.157854
$309$	−1.17504	−0.0668457
$310$	0.483530	0.0274627
$311$	3.14087	0.178102	0.0890512	−	0.996027i	$-0.471617\pi$
$311$	3.14087	0.178102	0.0890512	+	0.996027i	$0.471617\pi$
$312$	22.7216	1.28636
$313$	29.6973	1.67859	0.839295	−	0.543677i	$-0.182968\pi$
$313$	29.6973	1.67859	0.839295	+	0.543677i	$0.182968\pi$
$314$	4.73482	0.267201
$315$	−0.179714	−0.0101257
$316$	−4.31178	−0.242556
$317$	26.3993	1.48273	0.741367	−	0.671100i	$-0.234178\pi$
$317$	26.3993	1.48273	0.741367	+	0.671100i	$0.234178\pi$
$318$	21.1113	1.18386
$319$	34.9684	1.95785
$320$	−8.84498	−0.494449
$321$	−11.9608	−0.667587
$322$	−1.25084	−0.0697064
$323$	5.98144	0.332816
$324$	4.48673	0.249263
$325$	4.41019	0.244633
$326$	−10.8642	−0.601710
$327$	−9.14944	−0.505965
$328$	19.4503	1.07396
$329$	5.69334	0.313884
$330$	−10.5880	−0.582852
$331$	17.4298	0.958029	0.479015	−	0.877807i	$-0.340994\pi$
$331$	17.4298	0.958029	0.479015	+	0.877807i	$0.340994\pi$
$332$	−6.35546	−0.348801
$333$	−1.16275	−0.0637183
$334$	−4.39346	−0.240399
$335$	2.55982	0.139858
$336$	4.45366	0.242967
$337$	16.5637	0.902282	0.451141	−	0.892453i	$-0.351017\pi$
$337$	16.5637	0.902282	0.451141	+	0.892453i	$0.351017\pi$
$338$	−7.81375	−0.425012
$339$	−2.65728	−0.144324
$340$	−0.442232	−0.0239834
$341$	−2.07712	−0.112483
$342$	−1.56758	−0.0847650
$343$	−1.00000	−0.0539949
$344$	−5.01846	−0.270577
$345$	1.73393	0.0933517
$346$	−8.54627	−0.459450
$347$	23.3487	1.25342	0.626712	−	0.779251i	$-0.284400\pi$
$347$	23.3487	1.25342	0.626712	+	0.779251i	$0.284400\pi$
$348$	6.00682	0.321999
$349$	24.2150	1.29620	0.648101	−	0.761555i	$-0.275564\pi$
$349$	24.2150	1.29620	0.648101	+	0.761555i	$0.275564\pi$
$350$	1.21148	0.0647562
$351$	−23.5501	−1.25701
$352$	15.2113	0.810764
$353$	6.44993	0.343295	0.171647	−	0.985158i	$-0.445091\pi$
$353$	6.44993	0.343295	0.171647	+	0.985158i	$0.445091\pi$
$354$	29.5850	1.57243
$355$	−15.5322	−0.824365
$356$	3.08923	0.163729
$357$	1.39515	0.0738391
$358$	−3.79394	−0.200516
$359$	32.5794	1.71948	0.859739	−	0.510734i	$-0.170626\pi$
$359$	32.5794	1.71948	0.859739	+	0.510734i	$0.170626\pi$
$360$	0.551337	0.0290580
$361$	32.8399	1.72841
$362$	−27.1918	−1.42917
$363$	27.0104	1.41768
$364$	2.34765	0.123050
$365$	−6.22453	−0.325807
$366$	−17.5546	−0.917593
$367$	−3.67511	−0.191839	−0.0959197	−	0.995389i	$-0.530579\pi$
$367$	−3.67511	−0.191839	−0.0959197	+	0.995389i	$0.530579\pi$
$368$	2.73814	0.142736
$369$	−1.13940	−0.0593146
$370$	7.83824	0.407491
$371$	10.3766	0.538724
$372$	−0.356805	−0.0184995
$373$	0.818134	0.0423614	0.0211807	−	0.999776i	$-0.493257\pi$
$373$	0.818134	0.0423614	0.0211807	+	0.999776i	$0.493257\pi$
$374$	−5.23773	−0.270836
$375$	−1.67937	−0.0867223
$376$	−17.4663	−0.900757
$377$	−29.6332	−1.52619
$378$	−6.46919	−0.332739
$379$	7.86409	0.403951	0.201976	−	0.979391i	$-0.435264\pi$
$379$	7.86409	0.403951	0.201976	+	0.979391i	$0.435264\pi$
$380$	−3.83273	−0.196615
$381$	−8.91323	−0.456639
$382$	30.8257	1.57718
$383$	−16.6110	−0.848784	−0.424392	−	0.905479i	$-0.639512\pi$
$383$	−16.6110	−0.848784	−0.424392	+	0.905479i	$0.639512\pi$
$384$	−8.17804	−0.417334
$385$	−5.20420	−0.265230
$386$	19.4001	0.987437
$387$	0.293981	0.0149439
$388$	4.34258	0.220461
$389$	16.1772	0.820219	0.410110	−	0.912036i	$-0.365490\pi$
$389$	16.1772	0.820219	0.410110	+	0.912036i	$0.365490\pi$
$390$	8.97261	0.454346
$391$	0.857747	0.0433781
$392$	3.06785	0.154950
$393$	15.6940	0.791658
$394$	−29.9599	−1.50936
$395$	−8.09991	−0.407551
$396$	−0.497866	−0.0250187
$397$	1.58954	0.0797767	0.0398884	−	0.999204i	$-0.487300\pi$
$397$	1.58954	0.0797767	0.0398884	+	0.999204i	$0.487300\pi$
$398$	2.11223	0.105876
$399$	12.0915	0.605330
$400$	−2.65198	−0.132599
$401$	0.780173	0.0389600	0.0194800	−	0.999810i	$-0.493799\pi$
$401$	0.780173	0.0389600	0.0194800	+	0.999810i	$0.493799\pi$
$402$	5.20801	0.259752
$403$	1.76022	0.0876826
$404$	−5.01820	−0.249665
$405$	8.42856	0.418819
$406$	−8.14024	−0.403993
$407$	−33.6711	−1.66901
$408$	−4.28011	−0.211897
$409$	−31.1049	−1.53804	−0.769018	−	0.639227i	$-0.779254\pi$
$409$	−31.1049	−1.53804	−0.769018	+	0.639227i	$0.779254\pi$
$410$	7.68081	0.379328
$411$	−21.4900	−1.06002
$412$	0.372462	0.0183499
$413$	14.5415	0.715543
$414$	−0.224793	−0.0110480
$415$	−11.9391	−0.586066
$416$	−12.8905	−0.632008
$417$	2.65626	0.130078
$418$	−45.3942	−2.22030
$419$	−11.7006	−0.571611	−0.285806	−	0.958288i	$-0.592261\pi$
$419$	−11.7006	−0.571611	−0.285806	+	0.958288i	$0.592261\pi$
$420$	−0.893970	−0.0436213
$421$	−31.0490	−1.51323	−0.756617	−	0.653858i	$-0.773149\pi$
$421$	−31.0490	−1.51323	−0.756617	+	0.653858i	$0.773149\pi$
$422$	12.7423	0.620285
$423$	1.02317	0.0497484
$424$	−31.8338	−1.54598
$425$	−0.830757	−0.0402976
$426$	−31.6006	−1.53105
$427$	−8.62838	−0.417556
$428$	3.79132	0.183260
$429$	−38.5441	−1.86092
$430$	−1.98176	−0.0955690
$431$	7.44759	0.358738	0.179369	−	0.983782i	$-0.442594\pi$
$431$	7.44759	0.358738	0.179369	+	0.983782i	$0.442594\pi$
$432$	14.1614	0.681339
$433$	18.3812	0.883344	0.441672	−	0.897177i	$-0.354385\pi$
$433$	18.3812	0.883344	0.441672	+	0.897177i	$0.354385\pi$
$434$	0.483530	0.0232102
$435$	11.2841	0.541033
$436$	2.90018	0.138893
$437$	7.43391	0.355612
$438$	−12.6639	−0.605106
$439$	9.57580	0.457028	0.228514	−	0.973541i	$-0.426613\pi$
$439$	9.57580	0.457028	0.228514	+	0.973541i	$0.426613\pi$
$440$	15.9657	0.761135
$441$	−0.179714	−0.00855782
$442$	4.43860	0.211123
$443$	−10.9484	−0.520174	−0.260087	−	0.965585i	$-0.583751\pi$
$443$	−10.9484	−0.520174	−0.260087	+	0.965585i	$0.583751\pi$
$444$	−5.78397	−0.274495
$445$	5.80329	0.275102
$446$	−4.92119	−0.233025
$447$	2.46113	0.116408
$448$	−8.84498	−0.417886
$449$	27.2355	1.28532	0.642661	−	0.766150i	$-0.277830\pi$
$449$	27.2355	1.28532	0.642661	+	0.766150i	$0.277830\pi$
$450$	0.217720	0.0102634
$451$	−32.9948	−1.55367
$452$	0.842301	0.0396185
$453$	18.2787	0.858808
$454$	16.1686	0.758832
$455$	4.41019	0.206753
$456$	−37.0948	−1.73712
$457$	−0.651536	−0.0304776	−0.0152388	−	0.999884i	$-0.504851\pi$
$457$	−0.651536	−0.0304776	−0.0152388	+	0.999884i	$0.504851\pi$
$458$	−1.21148	−0.0566086
$459$	4.43618	0.207063
$460$	−0.549619	−0.0256261
$461$	14.3290	0.667369	0.333684	−	0.942685i	$-0.391708\pi$
$461$	14.3290	0.667369	0.333684	+	0.942685i	$0.391708\pi$
$462$	−10.5880	−0.492600
$463$	−8.87000	−0.412224	−0.206112	−	0.978528i	$-0.566081\pi$
$463$	−8.87000	−0.412224	−0.206112	+	0.978528i	$0.566081\pi$
$464$	17.8194	0.827244
$465$	−0.670278	−0.0310834
$466$	−18.4270	−0.853615
$467$	14.8062	0.685150	0.342575	−	0.939491i	$-0.388701\pi$
$467$	14.8062	0.685150	0.342575	+	0.939491i	$0.388701\pi$
$468$	0.421906	0.0195026
$469$	2.55982	0.118202
$470$	−6.89735	−0.318151
$471$	−6.56349	−0.302430
$472$	−44.6113	−2.05340
$473$	8.51314	0.391435
$474$	−16.4794	−0.756924
$475$	−7.19999	−0.330358
$476$	−0.442232	−0.0202697
$477$	1.86482	0.0853841
$478$	15.6113	0.714043
$479$	21.2236	0.969730	0.484865	−	0.874589i	$-0.338869\pi$
$479$	21.2236	0.969730	0.484865	+	0.874589i	$0.338869\pi$
$480$	4.90861	0.224047
$481$	28.5339	1.30103
$482$	−7.74675	−0.352855
$483$	1.73393	0.0788966
$484$	−8.56172	−0.389169
$485$	8.15777	0.370425
$486$	−2.25950	−0.102493
$487$	31.8562	1.44354	0.721770	−	0.692132i	$-0.243329\pi$
$487$	31.8562	1.44354	0.721770	+	0.692132i	$0.243329\pi$
$488$	26.4706	1.19827
$489$	15.0601	0.681041
$490$	1.21148	0.0547289
$491$	−18.6585	−0.842046	−0.421023	−	0.907050i	$-0.638329\pi$
$491$	−18.6585	−0.842046	−0.421023	+	0.907050i	$0.638329\pi$
$492$	−5.66781	−0.255524
$493$	5.58208	0.251404
$494$	38.4684	1.73078
$495$	−0.935268	−0.0420372
$496$	−1.05847	−0.0475268
$497$	−15.5322	−0.696715
$498$	−24.2903	−1.08847
$499$	−12.6494	−0.566264	−0.283132	−	0.959081i	$-0.591373\pi$
$499$	−12.6494	−0.566264	−0.283132	+	0.959081i	$0.591373\pi$
$500$	0.532324	0.0238063
$501$	6.09029	0.272094
$502$	10.9506	0.488751
$503$	29.5547	1.31778	0.658889	−	0.752240i	$-0.271027\pi$
$503$	29.5547	1.31778	0.658889	+	0.752240i	$0.271027\pi$
$504$	0.551337	0.0245585
$505$	−9.42696	−0.419494
$506$	−6.50960	−0.289387
$507$	10.8316	0.481046
$508$	2.82530	0.125353
$509$	−16.4136	−0.727520	−0.363760	−	0.931493i	$-0.618507\pi$
$509$	−16.4136	−0.727520	−0.363760	+	0.931493i	$0.618507\pi$
$510$	−1.69019	−0.0748429
$511$	−6.22453	−0.275357
$512$	24.0232	1.06169
$513$	38.4474	1.69749
$514$	21.3714	0.942651
$515$	0.699690	0.0308320
$516$	1.46238	0.0643775
$517$	29.6292	1.30309
$518$	7.83824	0.344392
$519$	11.8470	0.520025
$520$	−13.5298	−0.593321
$521$	−12.0011	−0.525776	−0.262888	−	0.964826i	$-0.584675\pi$
$521$	−12.0011	−0.525776	−0.262888	+	0.964826i	$0.584675\pi$
$522$	−1.46292	−0.0640301
$523$	−37.2948	−1.63079	−0.815393	−	0.578907i	$-0.803479\pi$
$523$	−37.2948	−1.63079	−0.815393	+	0.578907i	$0.803479\pi$
$524$	−4.97466	−0.217319
$525$	−1.67937	−0.0732937
$526$	−22.0204	−0.960134
$527$	−0.331576	−0.0144437
$528$	23.1777	1.00868
$529$	−21.9340	−0.953651
$530$	−12.5710	−0.546048
$531$	2.61332	0.113409
$532$	−3.83273	−0.166170
$533$	27.9608	1.21112
$534$	11.8069	0.510934
$535$	7.12220	0.307919
$536$	−7.85316	−0.339205
$537$	5.25922	0.226952
$538$	6.24456	0.269222
$539$	−5.20420	−0.224161
$540$	−2.84257	−0.122325
$541$	16.4106	0.705549	0.352774	−	0.935708i	$-0.385238\pi$
$541$	16.4106	0.705549	0.352774	+	0.935708i	$0.385238\pi$
$542$	−19.9309	−0.856107
$543$	37.6938	1.61759
$544$	2.42821	0.104109
$545$	5.44814	0.233373
$546$	8.97261	0.383992
$547$	−3.72065	−0.159084	−0.0795418	−	0.996832i	$-0.525346\pi$
$547$	−3.72065	−0.159084	−0.0795418	+	0.996832i	$0.525346\pi$
$548$	6.81186	0.290988
$549$	−1.55064	−0.0661798
$550$	6.30476	0.268836
$551$	48.3787	2.06100
$552$	−5.31944	−0.226411
$553$	−8.09991	−0.344443
$554$	−35.8504	−1.52314
$555$	−10.8655	−0.461215
$556$	−0.841977	−0.0357078
$557$	−18.5330	−0.785268	−0.392634	−	0.919695i	$-0.628436\pi$
$557$	−18.5330	−0.785268	−0.392634	+	0.919695i	$0.628436\pi$
$558$	0.0868972	0.00367865
$559$	−7.21429	−0.305132
$560$	−2.65198	−0.112067
$561$	7.26063	0.306544
$562$	−7.85999	−0.331554
$563$	−22.1107	−0.931857	−0.465928	−	0.884822i	$-0.654280\pi$
$563$	−22.1107	−0.931857	−0.465928	+	0.884822i	$0.654280\pi$
$564$	5.08967	0.214314
$565$	1.58231	0.0665682
$566$	25.3940	1.06739
$567$	8.42856	0.353966
$568$	47.6505	1.99937
$569$	0.831052	0.0348395	0.0174198	−	0.999848i	$-0.494455\pi$
$569$	0.831052	0.0348395	0.0174198	+	0.999848i	$0.494455\pi$
$570$	−14.6485	−0.613559
$571$	23.5897	0.987200	0.493600	−	0.869689i	$-0.335681\pi$
$571$	23.5897	0.987200	0.493600	+	0.869689i	$0.335681\pi$
$572$	12.2176	0.510845
$573$	−42.7311	−1.78512
$574$	7.68081	0.320591
$575$	−1.03249	−0.0430578
$576$	−1.58957	−0.0662320
$577$	46.7857	1.94771	0.973857	−	0.227163i	$-0.0729450\pi$
$577$	46.7857	1.94771	0.973857	+	0.227163i	$0.0729450\pi$
$578$	19.7590	0.821866
$579$	−26.8927	−1.11762
$580$	−3.57683	−0.148520
$581$	−11.9391	−0.495316
$582$	16.5971	0.687973
$583$	54.0017	2.23652
$584$	19.0959	0.790196
$585$	0.792574	0.0327689
$586$	11.4857	0.474469
$587$	−22.4244	−0.925552	−0.462776	−	0.886475i	$-0.653147\pi$
$587$	−22.4244	−0.925552	−0.462776	+	0.886475i	$0.653147\pi$
$588$	−0.893970	−0.0368667
$589$	−2.87369	−0.118408
$590$	−17.6167	−0.725270
$591$	41.5309	1.70835
$592$	−17.1583	−0.705202
$593$	18.9139	0.776700	0.388350	−	0.921512i	$-0.373045\pi$
$593$	18.9139	0.776700	0.388350	+	0.921512i	$0.373045\pi$
$594$	−33.6669	−1.38137
$595$	−0.830757	−0.0340577
$596$	−0.780126	−0.0319552
$597$	−2.92801	−0.119835
$598$	5.51642	0.225583
$599$	27.9809	1.14327	0.571635	−	0.820508i	$-0.306309\pi$
$599$	27.9809	1.14327	0.571635	+	0.820508i	$0.306309\pi$
$600$	5.15206	0.210332
$601$	−23.5211	−0.959444	−0.479722	−	0.877420i	$-0.659263\pi$
$601$	−23.5211	−0.959444	−0.479722	+	0.877420i	$0.659263\pi$
$602$	−1.98176	−0.0807705
$603$	0.460037	0.0187341
$604$	−5.79395	−0.235752
$605$	−16.0837	−0.653894
$606$	−19.1793	−0.779106
$607$	24.4743	0.993383	0.496691	−	0.867927i	$-0.334548\pi$
$607$	24.4743	0.993383	0.496691	+	0.867927i	$0.334548\pi$
$608$	21.0448	0.853478
$609$	11.2841	0.457256
$610$	10.4531	0.423233
$611$	−25.1087	−1.01579
$612$	−0.0794754	−0.00321260
$613$	−28.3221	−1.14392	−0.571959	−	0.820283i	$-0.693816\pi$
$613$	−28.3221	−1.14392	−0.571959	+	0.820283i	$0.693816\pi$
$614$	17.2597	0.696544
$615$	−10.6473	−0.429340
$616$	15.9657	0.643277
$617$	4.95914	0.199647	0.0998237	−	0.995005i	$-0.468172\pi$
$617$	4.95914	0.199647	0.0998237	+	0.995005i	$0.468172\pi$
$618$	1.42353	0.0572629
$619$	−18.2756	−0.734557	−0.367278	−	0.930111i	$-0.619710\pi$
$619$	−18.2756	−0.734557	−0.367278	+	0.930111i	$0.619710\pi$
$620$	0.212464	0.00853275
$621$	5.51341	0.221245
$622$	−3.80509	−0.152570
$623$	5.80329	0.232504
$624$	−19.6415	−0.786289
$625$	1.00000	0.0400000
$626$	−35.9776	−1.43795
$627$	62.9263	2.51303
$628$	2.08048	0.0830204
$629$	−5.37499	−0.214315
$630$	0.217720	0.00867416
$631$	37.5771	1.49592	0.747960	−	0.663744i	$-0.231034\pi$
$631$	37.5771	1.49592	0.747960	+	0.663744i	$0.231034\pi$
$632$	24.8493	0.988453
$633$	−17.6636	−0.702065
$634$	−31.9822	−1.27017
$635$	5.30748	0.210621
$636$	9.27633	0.367831
$637$	4.41019	0.174738
$638$	−42.3634	−1.67718
$639$	−2.79136	−0.110425
$640$	4.86970	0.192492
$641$	39.1973	1.54820	0.774100	−	0.633063i	$-0.218203\pi$
$641$	39.1973	1.54820	0.774100	+	0.633063i	$0.218203\pi$
$642$	14.4902	0.571884
$643$	11.1838	0.441044	0.220522	−	0.975382i	$-0.429224\pi$
$643$	11.1838	0.441044	0.220522	+	0.975382i	$0.429224\pi$
$644$	−0.549619	−0.0216580
$645$	2.74715	0.108169
$646$	−7.24638	−0.285105
$647$	8.01306	0.315026	0.157513	−	0.987517i	$-0.449652\pi$
$647$	8.01306	0.315026	0.157513	+	0.987517i	$0.449652\pi$
$648$	−25.8576	−1.01578
$649$	75.6770	2.97058
$650$	−5.34284	−0.209563
$651$	−0.670278	−0.0262703
$652$	−4.77373	−0.186954
$653$	−31.1546	−1.21917	−0.609586	−	0.792720i	$-0.708664\pi$
$653$	−31.1546	−1.21917	−0.609586	+	0.792720i	$0.708664\pi$
$654$	11.0843	0.433432
$655$	−9.34518	−0.365146
$656$	−16.8137	−0.656464
$657$	−1.11864	−0.0436422
$658$	−6.89735	−0.268887
$659$	−5.48445	−0.213644	−0.106822	−	0.994278i	$-0.534067\pi$
$659$	−5.48445	−0.213644	−0.106822	+	0.994278i	$0.534067\pi$
$660$	−4.65239	−0.181094
$661$	40.0157	1.55643	0.778215	−	0.627998i	$-0.216125\pi$
$661$	40.0157	1.55643	0.778215	+	0.627998i	$0.216125\pi$
$662$	−21.1158	−0.820690
$663$	−6.15287	−0.238958
$664$	36.6273	1.42141
$665$	−7.19999	−0.279204
$666$	1.40864	0.0545838
$667$	6.93757	0.268624
$668$	−1.93049	−0.0746930
$669$	6.82185	0.263748
$670$	−3.10117	−0.119809
$671$	−44.9038	−1.73349
$672$	4.90861	0.189354
$673$	−30.4785	−1.17486	−0.587431	−	0.809274i	$-0.699861\pi$
$673$	−30.4785	−1.17486	−0.587431	+	0.809274i	$0.699861\pi$
$674$	−20.0665	−0.772933
$675$	−5.33992	−0.205534
$676$	−3.43337	−0.132053
$677$	14.6811	0.564241	0.282121	−	0.959379i	$-0.408962\pi$
$677$	14.6811	0.564241	0.282121	+	0.959379i	$0.408962\pi$
$678$	3.21923	0.123634
$679$	8.15777	0.313067
$680$	2.54864	0.0977359
$681$	−22.4133	−0.858878
$682$	2.51639	0.0963574
$683$	13.7959	0.527886	0.263943	−	0.964538i	$-0.414977\pi$
$683$	13.7959	0.527886	0.263943	+	0.964538i	$0.414977\pi$
$684$	−0.688796	−0.0263368
$685$	12.7964	0.488927
$686$	1.21148	0.0462544
$687$	1.67937	0.0640720
$688$	4.33817	0.165391
$689$	−45.7626	−1.74342
$690$	−2.10062	−0.0799691
$691$	33.3779	1.26975	0.634877	−	0.772614i	$-0.281051\pi$
$691$	33.3779	1.26975	0.634877	+	0.772614i	$0.281051\pi$
$692$	−3.75524	−0.142753
$693$	−0.935268	−0.0355279
$694$	−28.2864	−1.07374
$695$	−1.58170	−0.0599973
$696$	−34.6181	−1.31219
$697$	−5.26703	−0.199503
$698$	−29.3360	−1.11038
$699$	25.5439	0.966157
$700$	0.532324	0.0201200
$701$	−5.55442	−0.209787	−0.104894	−	0.994483i	$-0.533450\pi$
$701$	−5.55442	−0.209787	−0.104894	+	0.994483i	$0.533450\pi$
$702$	28.5303	1.07681
$703$	−46.5839	−1.75694
$704$	−46.0310	−1.73486
$705$	9.56122	0.360097
$706$	−7.81393	−0.294081
$707$	−9.42696	−0.354537
$708$	12.9997	0.488559
$709$	31.4048	1.17943	0.589717	−	0.807610i	$-0.299239\pi$
$709$	31.4048	1.17943	0.589717	+	0.807610i	$0.299239\pi$
$710$	18.8169	0.706186
$711$	−1.45567	−0.0545918
$712$	−17.8036	−0.667219
$713$	−0.412092	−0.0154330
$714$	−1.69019	−0.0632538
$715$	22.9515	0.858337
$716$	−1.66706	−0.0623010
$717$	−21.6406	−0.808184
$718$	−39.4692	−1.47298
$719$	−36.5380	−1.36264	−0.681318	−	0.731987i	$-0.738593\pi$
$719$	−36.5380	−1.36264	−0.681318	+	0.731987i	$0.738593\pi$
$720$	−0.476599	−0.0177618
$721$	0.699690	0.0260578
$722$	−39.7847	−1.48063
$723$	10.7387	0.399376
$724$	−11.9481	−0.444048
$725$	−6.71927	−0.249547
$726$	−32.7225	−1.21445
$727$	31.0389	1.15117	0.575585	−	0.817742i	$-0.304774\pi$
$727$	31.0389	1.15117	0.575585	+	0.817742i	$0.304774\pi$
$728$	−13.5298	−0.501448
$729$	28.4178	1.05251
$730$	7.54088	0.279100
$731$	1.35897	0.0502634
$732$	−7.71351	−0.285099
$733$	1.66939	0.0616602	0.0308301	−	0.999525i	$-0.490185\pi$
$733$	1.66939	0.0616602	0.0308301	+	0.999525i	$0.490185\pi$
$734$	4.45231	0.164338
$735$	−1.67937	−0.0619445
$736$	3.01785	0.111239
$737$	13.3218	0.490716
$738$	1.38035	0.0508114
$739$	−40.7099	−1.49754	−0.748769	−	0.662831i	$-0.769355\pi$
$739$	−40.7099	−1.49754	−0.748769	+	0.662831i	$0.769355\pi$
$740$	3.44413	0.126609
$741$	−53.3256	−1.95896
$742$	−12.5710	−0.461495
$743$	2.42226	0.0888639	0.0444320	−	0.999012i	$-0.485852\pi$
$743$	2.42226	0.0888639	0.0444320	+	0.999012i	$0.485852\pi$
$744$	2.05631	0.0753881
$745$	−1.46551	−0.0536921
$746$	−0.991150	−0.0362886
$747$	−2.14562	−0.0785042
$748$	−2.30146	−0.0841498
$749$	7.12220	0.260239
$750$	2.03452	0.0742901
$751$	−28.5100	−1.04034	−0.520172	−	0.854061i	$-0.674132\pi$
$751$	−28.5100	−1.04034	−0.520172	+	0.854061i	$0.674132\pi$
$752$	15.0986	0.550590
$753$	−15.1800	−0.553189
$754$	35.9000	1.30740
$755$	−10.8842	−0.396118
$756$	−2.84257	−0.103383
$757$	26.2780	0.955089	0.477544	−	0.878608i	$-0.341527\pi$
$757$	26.2780	0.955089	0.477544	+	0.878608i	$0.341527\pi$
$758$	−9.52717	−0.346042
$759$	9.02372	0.327540
$760$	22.0885	0.801234
$761$	−44.1265	−1.59958	−0.799792	−	0.600277i	$-0.795057\pi$
$761$	−44.1265	−1.59958	−0.799792	+	0.600277i	$0.795057\pi$
$762$	10.7982	0.391177
$763$	5.44814	0.197236
$764$	13.5448	0.490035
$765$	−0.149299	−0.00539791
$766$	20.1239	0.727105
$767$	−64.1310	−2.31563
$768$	−19.8005	−0.714488
$769$	50.7840	1.83132	0.915659	−	0.401956i	$-0.131670\pi$
$769$	50.7840	1.83132	0.915659	+	0.401956i	$0.131670\pi$
$770$	6.30476	0.227208
$771$	−29.6254	−1.06693
$772$	8.52441	0.306800
$773$	−33.1988	−1.19408	−0.597038	−	0.802213i	$-0.703656\pi$
$773$	−33.1988	−1.19408	−0.597038	+	0.802213i	$0.703656\pi$
$774$	−0.356151	−0.0128016
$775$	0.399125	0.0143370
$776$	−25.0268	−0.898411
$777$	−10.8655	−0.389798
$778$	−19.5984	−0.702635
$779$	−45.6482	−1.63552
$780$	3.94258	0.141167
$781$	−80.8327	−2.89242
$782$	−1.03914	−0.0371596
$783$	35.8803	1.28226
$784$	−2.65198	−0.0947137
$785$	3.90830	0.139493
$786$	−19.0129	−0.678169
$787$	−45.7887	−1.63219	−0.816096	−	0.577916i	$-0.803866\pi$
$787$	−45.7887	−1.63219	−0.816096	+	0.577916i	$0.803866\pi$
$788$	−13.1644	−0.468962
$789$	30.5250	1.08672
$790$	9.81285	0.349126
$791$	1.58231	0.0562604
$792$	2.86926	0.101955
$793$	38.0528	1.35129
$794$	−1.92569	−0.0683402
$795$	17.4261	0.618040
$796$	0.928115	0.0328962
$797$	19.1935	0.679868	0.339934	−	0.940449i	$-0.389595\pi$
$797$	19.1935	0.679868	0.339934	+	0.940449i	$0.389595\pi$
$798$	−14.6485	−0.518552
$799$	4.72978	0.167328
$800$	−2.92289	−0.103340
$801$	1.04293	0.0368503
$802$	−0.945161	−0.0333748
$803$	−32.3937	−1.14315
$804$	2.28840	0.0807058
$805$	−1.03249	−0.0363905
$806$	−2.13246	−0.0751127
$807$	−8.65632	−0.304717
$808$	28.9205	1.01742
$809$	−3.73090	−0.131171	−0.0655857	−	0.997847i	$-0.520892\pi$
$809$	−3.73090	−0.131171	−0.0655857	+	0.997847i	$0.520892\pi$
$810$	−10.2110	−0.358778
$811$	−50.0738	−1.75833	−0.879165	−	0.476518i	$-0.841899\pi$
$811$	−50.0738	−1.75833	−0.879165	+	0.476518i	$0.841899\pi$
$812$	−3.57683	−0.125522
$813$	27.6286	0.968978
$814$	40.7917	1.42975
$815$	−8.96770	−0.314125
$816$	3.69991	0.129523
$817$	11.7779	0.412057
$818$	37.6828	1.31755
$819$	0.792574	0.0276948
$820$	3.37496	0.117859
$821$	41.5748	1.45097	0.725485	−	0.688238i	$-0.241615\pi$
$821$	41.5748	1.45097	0.725485	+	0.688238i	$0.241615\pi$
$822$	26.0346	0.908061
$823$	−32.8745	−1.14593	−0.572967	−	0.819578i	$-0.694208\pi$
$823$	−32.8745	−1.14593	−0.572967	+	0.819578i	$0.694208\pi$
$824$	−2.14655	−0.0747785
$825$	−8.73977	−0.304280
$826$	−17.6167	−0.612965
$827$	15.5065	0.539214	0.269607	−	0.962970i	$-0.413106\pi$
$827$	15.5065	0.539214	0.269607	+	0.962970i	$0.413106\pi$
$828$	−0.0987743	−0.00343265
$829$	43.5863	1.51382	0.756908	−	0.653522i	$-0.226709\pi$
$829$	43.5863	1.51382	0.756908	+	0.653522i	$0.226709\pi$
$830$	14.4639	0.502049
$831$	49.6965	1.72395
$832$	39.0080	1.35236
$833$	−0.830757	−0.0287840
$834$	−3.21800	−0.111430
$835$	−3.62653	−0.125501
$836$	−19.9463	−0.689857
$837$	−2.13129	−0.0736683
$838$	14.1750	0.489667
$839$	−8.93743	−0.308554	−0.154277	−	0.988028i	$-0.549305\pi$
$839$	−8.93743	−0.308554	−0.154277	+	0.988028i	$0.549305\pi$
$840$	5.15206	0.177763
$841$	16.1486	0.556847
$842$	37.6151	1.29630
$843$	10.8957	0.375267
$844$	5.59898	0.192725
$845$	−6.44977	−0.221879
$846$	−1.23955	−0.0426167
$847$	−16.0837	−0.552641
$848$	27.5185	0.944988
$849$	−35.2016	−1.20812
$850$	1.00644	0.0345207
$851$	−6.68019	−0.228994
$852$	−13.8853	−0.475704
$853$	−20.3463	−0.696646	−0.348323	−	0.937375i	$-0.613249\pi$
$853$	−20.3463	−0.696646	−0.348323	+	0.937375i	$0.613249\pi$
$854$	10.4531	0.357697
$855$	−1.29394	−0.0442518
$856$	−21.8498	−0.746812
$857$	−24.2576	−0.828622	−0.414311	−	0.910135i	$-0.635977\pi$
$857$	−24.2576	−0.828622	−0.414311	+	0.910135i	$0.635977\pi$
$858$	46.6952	1.59415
$859$	−58.1446	−1.98387	−0.991933	−	0.126761i	$-0.959542\pi$
$859$	−58.1446	−1.98387	−0.991933	+	0.126761i	$0.959542\pi$
$860$	−0.870788	−0.0296936
$861$	−10.6473	−0.362858
$862$	−9.02258	−0.307310
$863$	−12.4828	−0.424920	−0.212460	−	0.977170i	$-0.568148\pi$
$863$	−12.4828	−0.424920	−0.212460	+	0.977170i	$0.568148\pi$
$864$	15.6080	0.530995
$865$	−7.05442	−0.239858
$866$	−22.2684	−0.756711
$867$	−27.3903	−0.930222
$868$	0.212464	0.00721149
$869$	−42.1535	−1.42996
$870$	−13.6705	−0.463472
$871$	−11.2893	−0.382524
$872$	−16.7141	−0.566010
$873$	1.46607	0.0496189
$874$	−9.00601	−0.304633
$875$	1.00000	0.0338062
$876$	−5.56454	−0.188009
$877$	28.4690	0.961330	0.480665	−	0.876904i	$-0.340395\pi$
$877$	28.4690	0.961330	0.480665	+	0.876904i	$0.340395\pi$
$878$	−11.6009	−0.391510
$879$	−15.9217	−0.537025
$880$	−13.8014	−0.465246
$881$	19.1957	0.646719	0.323360	−	0.946276i	$-0.395188\pi$
$881$	19.1957	0.646719	0.323360	+	0.946276i	$0.395188\pi$
$882$	0.217720	0.00733100
$883$	2.63445	0.0886561	0.0443281	−	0.999017i	$-0.485885\pi$
$883$	2.63445	0.0886561	0.0443281	+	0.999017i	$0.485885\pi$
$884$	1.95033	0.0655966
$885$	24.4206	0.820891
$886$	13.2637	0.445603
$887$	−21.7274	−0.729533	−0.364767	−	0.931099i	$-0.618851\pi$
$887$	−21.7274	−0.729533	−0.364767	+	0.931099i	$0.618851\pi$
$888$	33.3338	1.11861
$889$	5.30748	0.178007
$890$	−7.03055	−0.235665
$891$	43.8639	1.46950
$892$	−2.16238	−0.0724018
$893$	40.9920	1.37174
$894$	−2.98161	−0.0997198
$895$	−3.13166	−0.104680
$896$	4.86970	0.162685
$897$	−7.64697	−0.255325
$898$	−32.9952	−1.10106
$899$	−2.68182	−0.0894439
$900$	0.0956662	0.00318887
$901$	8.62040	0.287187
$902$	39.9725	1.33094
$903$	2.74715	0.0914195
$904$	−4.85428	−0.161451
$905$	−22.4452	−0.746103
$906$	−22.1442	−0.735692
$907$	−24.4192	−0.810826	−0.405413	−	0.914134i	$-0.632872\pi$
$907$	−24.4192	−0.810826	−0.405413	+	0.914134i	$0.632872\pi$
$908$	7.10452	0.235772
$909$	−1.69416	−0.0561917
$910$	−5.34284	−0.177113
$911$	33.0116	1.09372	0.546862	−	0.837223i	$-0.315822\pi$
$911$	33.0116	1.09372	0.546862	+	0.837223i	$0.315822\pi$
$912$	32.0663	1.06182
$913$	−62.1333	−2.05631
$914$	0.789321	0.0261084
$915$	−14.4902	−0.479033
$916$	−0.532324	−0.0175885
$917$	−9.34518	−0.308605
$918$	−5.37432	−0.177379
$919$	42.2800	1.39469	0.697344	−	0.716736i	$-0.254365\pi$
$919$	42.2800	1.39469	0.697344	+	0.716736i	$0.254365\pi$
$920$	3.16752	0.104430
$921$	−23.9257	−0.788378
$922$	−17.3593	−0.571697
$923$	68.5000	2.25471
$924$	−4.65239	−0.153053
$925$	6.46999	0.212732
$926$	10.7458	0.353129
$927$	0.125744	0.00412998
$928$	19.6397	0.644704
$929$	7.20203	0.236291	0.118145	−	0.992996i	$-0.462305\pi$
$929$	7.20203	0.236291	0.118145	+	0.992996i	$0.462305\pi$
$930$	0.812026	0.0266274
$931$	−7.19999	−0.235970
$932$	−8.09685	−0.265221
$933$	5.27469	0.172685
$934$	−17.9374	−0.586929
$935$	−4.32342	−0.141391
$936$	−2.43150	−0.0794760
$937$	41.1492	1.34428	0.672142	−	0.740422i	$-0.265374\pi$
$937$	41.1492	1.34428	0.672142	+	0.740422i	$0.265374\pi$
$938$	−3.10117	−0.101257
$939$	49.8727	1.62754
$940$	−3.03070	−0.0988506
$941$	−26.8462	−0.875161	−0.437580	−	0.899179i	$-0.644164\pi$
$941$	−26.8462	−0.875161	−0.437580	+	0.899179i	$0.644164\pi$
$942$	7.95151	0.259074
$943$	−6.54602	−0.213168
$944$	38.5639	1.25515
$945$	−5.33992	−0.173708
$946$	−10.3135	−0.335320
$947$	−40.7037	−1.32269	−0.661347	−	0.750080i	$-0.730015\pi$
$947$	−40.7037	−1.32269	−0.661347	+	0.750080i	$0.730015\pi$
$948$	−7.24107	−0.235179
$949$	27.4514	0.891109
$950$	8.72262	0.282999
$951$	44.3342	1.43764
$952$	2.54864	0.0826019
$953$	−40.7762	−1.32087	−0.660435	−	0.750883i	$-0.729628\pi$
$953$	−40.7762	−1.32087	−0.660435	+	0.750883i	$0.729628\pi$
$954$	−2.25918	−0.0731437
$955$	25.4447	0.823372
$956$	6.85961	0.221856
$957$	58.7249	1.89831
$958$	−25.7119	−0.830713
$959$	12.7964	0.413219
$960$	−14.8540	−0.479411
$961$	−30.8407	−0.994861
$962$	−34.5681	−1.11452
$963$	1.27996	0.0412461
$964$	−3.40393	−0.109633
$965$	16.0136	0.515495
$966$	−2.10062	−0.0675863
$967$	25.7602	0.828393	0.414197	−	0.910187i	$-0.364063\pi$
$967$	25.7602	0.828393	0.414197	+	0.910187i	$0.364063\pi$
$968$	49.3423	1.58592
$969$	10.0451	0.322694
$970$	−9.88295	−0.317322
$971$	3.89442	0.124978	0.0624890	−	0.998046i	$-0.480096\pi$
$971$	3.89442	0.124978	0.0624890	+	0.998046i	$0.480096\pi$
$972$	−0.992827	−0.0318449
$973$	−1.58170	−0.0507069
$974$	−38.5930	−1.23660
$975$	7.40634	0.237193
$976$	−22.8823	−0.732445
$977$	−41.5162	−1.32822	−0.664111	−	0.747634i	$-0.731190\pi$
$977$	−41.5162	−1.32822	−0.664111	+	0.747634i	$0.731190\pi$
$978$	−18.2450	−0.583409
$979$	30.2015	0.965243
$980$	0.532324	0.0170045
$981$	0.979108	0.0312605
$982$	22.6043	0.721333
$983$	−53.0915	−1.69336	−0.846679	−	0.532105i	$-0.821401\pi$
$983$	−53.0915	−1.69336	−0.846679	+	0.532105i	$0.821401\pi$
$984$	32.6643	1.04130
$985$	−24.7300	−0.787965
$986$	−6.76256	−0.215364
$987$	9.56122	0.304337
$988$	16.9031	0.537758
$989$	1.68897	0.0537061
$990$	1.13306	0.0360109
$991$	−6.81162	−0.216378	−0.108189	−	0.994130i	$-0.534505\pi$
$991$	−6.81162	−0.216378	−0.108189	+	0.994130i	$0.534505\pi$
$992$	−1.16660	−0.0370395
$993$	29.2711	0.928891
$994$	18.8169	0.596836
$995$	1.74351	0.0552731
$996$	−10.6732	−0.338192
$997$	41.2097	1.30512	0.652561	−	0.757736i	$-0.273694\pi$
$997$	41.2097	1.30512	0.652561	+	0.757736i	$0.273694\pi$
$998$	15.3244	0.485086
$999$	−34.5492	−1.09309

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8015.2.a.l.1.20	✓	62

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8015.2.a.l.1.20	✓	62	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 8015 = 5 \cdot 7 \cdot 229 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8015.a (trivial)

\(f(q)\)	\(=\)	\(q-1.21148 q^{2} +1.67937 q^{3} -0.532324 q^{4} -1.00000 q^{5} -2.03452 q^{6} -1.00000 q^{7} +3.06785 q^{8} -0.179714 q^{9} +O(q^{10})\)	\(q-1.21148 q^{2} +1.67937 q^{3} -0.532324 q^{4} -1.00000 q^{5} -2.03452 q^{6} -1.00000 q^{7} +3.06785 q^{8} -0.179714 q^{9} +1.21148 q^{10} -5.20420 q^{11} -0.893970 q^{12} +4.41019 q^{13} +1.21148 q^{14} -1.67937 q^{15} -2.65198 q^{16} -0.830757 q^{17} +0.217720 q^{18} -7.19999 q^{19} +0.532324 q^{20} -1.67937 q^{21} +6.30476 q^{22} -1.03249 q^{23} +5.15206 q^{24} +1.00000 q^{25} -5.34284 q^{26} -5.33992 q^{27} +0.532324 q^{28} -6.71927 q^{29} +2.03452 q^{30} +0.399125 q^{31} -2.92289 q^{32} -8.73977 q^{33} +1.00644 q^{34} +1.00000 q^{35} +0.0956662 q^{36} +6.46999 q^{37} +8.72262 q^{38} +7.40634 q^{39} -3.06785 q^{40} +6.34004 q^{41} +2.03452 q^{42} -1.63582 q^{43} +2.77032 q^{44} +0.179714 q^{45} +1.25084 q^{46} -5.69334 q^{47} -4.45366 q^{48} +1.00000 q^{49} -1.21148 q^{50} -1.39515 q^{51} -2.34765 q^{52} -10.3766 q^{53} +6.46919 q^{54} +5.20420 q^{55} -3.06785 q^{56} -12.0915 q^{57} +8.14024 q^{58} -14.5415 q^{59} +0.893970 q^{60} +8.62838 q^{61} -0.483530 q^{62} +0.179714 q^{63} +8.84498 q^{64} -4.41019 q^{65} +10.5880 q^{66} -2.55982 q^{67} +0.442232 q^{68} -1.73393 q^{69} -1.21148 q^{70} +15.5322 q^{71} -0.551337 q^{72} +6.22453 q^{73} -7.83824 q^{74} +1.67937 q^{75} +3.83273 q^{76} +5.20420 q^{77} -8.97261 q^{78} +8.09991 q^{79} +2.65198 q^{80} -8.42856 q^{81} -7.68081 q^{82} +11.9391 q^{83} +0.893970 q^{84} +0.830757 q^{85} +1.98176 q^{86} -11.2841 q^{87} -15.9657 q^{88} -5.80329 q^{89} -0.217720 q^{90} -4.41019 q^{91} +0.549619 q^{92} +0.670278 q^{93} +6.89735 q^{94} +7.19999 q^{95} -4.90861 q^{96} -8.15777 q^{97} -1.21148 q^{98} +0.935268 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 62 q + 2 q^{2} + 11 q^{3} + 64 q^{4} - 62 q^{5} + 3 q^{6} - 62 q^{7} + 15 q^{8} + 69 q^{9}+O(q^{10}) \) 62 * q + 2 * q^2 + 11 * q^3 + 64 * q^4 - 62 * q^5 + 3 * q^6 - 62 * q^7 + 15 * q^8 + 69 * q^9	\( 62 q + 2 q^{2} + 11 q^{3} + 64 q^{4} - 62 q^{5} + 3 q^{6} - 62 q^{7} + 15 q^{8} + 69 q^{9} - 2 q^{10} - 13 q^{11} + 37 q^{12} + 31 q^{13} - 2 q^{14} - 11 q^{15} + 64 q^{16} + 30 q^{17} + 18 q^{18} + 20 q^{19} - 64 q^{20} - 11 q^{21} + 7 q^{22} + 29 q^{24} + 62 q^{25} + 59 q^{27} - 64 q^{28} - 29 q^{29} - 3 q^{30} + 20 q^{31} + 22 q^{32} + 72 q^{33} + 13 q^{34} + 62 q^{35} + 53 q^{36} + 35 q^{37} + 34 q^{38} - 6 q^{39} - 15 q^{40} + 13 q^{41} - 3 q^{42} - 4 q^{43} - 44 q^{44} - 69 q^{45} - 19 q^{46} + 58 q^{47} + 64 q^{48} + 62 q^{49} + 2 q^{50} - 30 q^{51} + 82 q^{52} + 18 q^{53} + 22 q^{54} + 13 q^{55} - 15 q^{56} + 21 q^{57} + 18 q^{58} - 11 q^{59} - 37 q^{60} + 24 q^{61} + 48 q^{62} - 69 q^{63} + 65 q^{64} - 31 q^{65} + 25 q^{66} - 6 q^{67} + 65 q^{68} + 27 q^{69} + 2 q^{70} - 35 q^{71} + 53 q^{72} + 116 q^{73} - 69 q^{74} + 11 q^{75} + 65 q^{76} + 13 q^{77} + 102 q^{78} - 83 q^{79} - 64 q^{80} + 126 q^{81} + 71 q^{82} + 84 q^{83} - 37 q^{84} - 30 q^{85} + 24 q^{86} + 49 q^{87} + 20 q^{88} - 16 q^{89} - 18 q^{90} - 31 q^{91} + 19 q^{92} + 65 q^{93} + 54 q^{94} - 20 q^{95} + 17 q^{96} + 155 q^{97} + 2 q^{98} + 6 q^{99}+O(q^{100}) \) 62 * q + 2 * q^2 + 11 * q^3 + 64 * q^4 - 62 * q^5 + 3 * q^6 - 62 * q^7 + 15 * q^8 + 69 * q^9 - 2 * q^10 - 13 * q^11 + 37 * q^12 + 31 * q^13 - 2 * q^14 - 11 * q^15 + 64 * q^16 + 30 * q^17 + 18 * q^18 + 20 * q^19 - 64 * q^20 - 11 * q^21 + 7 * q^22 + 29 * q^24 + 62 * q^25 + 59 * q^27 - 64 * q^28 - 29 * q^29 - 3 * q^30 + 20 * q^31 + 22 * q^32 + 72 * q^33 + 13 * q^34 + 62 * q^35 + 53 * q^36 + 35 * q^37 + 34 * q^38 - 6 * q^39 - 15 * q^40 + 13 * q^41 - 3 * q^42 - 4 * q^43 - 44 * q^44 - 69 * q^45 - 19 * q^46 + 58 * q^47 + 64 * q^48 + 62 * q^49 + 2 * q^50 - 30 * q^51 + 82 * q^52 + 18 * q^53 + 22 * q^54 + 13 * q^55 - 15 * q^56 + 21 * q^57 + 18 * q^58 - 11 * q^59 - 37 * q^60 + 24 * q^61 + 48 * q^62 - 69 * q^63 + 65 * q^64 - 31 * q^65 + 25 * q^66 - 6 * q^67 + 65 * q^68 + 27 * q^69 + 2 * q^70 - 35 * q^71 + 53 * q^72 + 116 * q^73 - 69 * q^74 + 11 * q^75 + 65 * q^76 + 13 * q^77 + 102 * q^78 - 83 * q^79 - 64 * q^80 + 126 * q^81 + 71 * q^82 + 84 * q^83 - 37 * q^84 - 30 * q^85 + 24 * q^86 + 49 * q^87 + 20 * q^88 - 16 * q^89 - 18 * q^90 - 31 * q^91 + 19 * q^92 + 65 * q^93 + 54 * q^94 - 20 * q^95 + 17 * q^96 + 155 * q^97 + 2 * q^98 + 6 * q^99

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