LMFDB - Embedded newform 8015.2.a.l.1.22

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			1.22
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)

$f(q)$	$=$	$q-1.01597 q^{2} +3.29298 q^{3} -0.967811 q^{4} -1.00000 q^{5} -3.34556 q^{6} -1.00000 q^{7} +3.01520 q^{8} +7.84372 q^{9} +O(q^{10})$	\(q-1.01597 q^{2} +3.29298 q^{3} -0.967811 q^{4} -1.00000 q^{5} -3.34556 q^{6} -1.00000 q^{7} +3.01520 q^{8} +7.84372 q^{9} +1.01597 q^{10} -6.31839 q^{11} -3.18698 q^{12} -5.68874 q^{13} +1.01597 q^{14} -3.29298 q^{15} -1.12772 q^{16} +1.61361 q^{17} -7.96896 q^{18} +2.13466 q^{19} +0.967811 q^{20} -3.29298 q^{21} +6.41928 q^{22} -2.24317 q^{23} +9.92899 q^{24} +1.00000 q^{25} +5.77957 q^{26} +15.9503 q^{27} +0.967811 q^{28} -7.73433 q^{29} +3.34556 q^{30} +8.36953 q^{31} -4.88467 q^{32} -20.8063 q^{33} -1.63937 q^{34} +1.00000 q^{35} -7.59124 q^{36} +2.74919 q^{37} -2.16875 q^{38} -18.7329 q^{39} -3.01520 q^{40} +4.98382 q^{41} +3.34556 q^{42} -2.61371 q^{43} +6.11501 q^{44} -7.84372 q^{45} +2.27899 q^{46} +1.87840 q^{47} -3.71356 q^{48} +1.00000 q^{49} -1.01597 q^{50} +5.31358 q^{51} +5.50562 q^{52} +11.8377 q^{53} -16.2050 q^{54} +6.31839 q^{55} -3.01520 q^{56} +7.02941 q^{57} +7.85783 q^{58} +0.907289 q^{59} +3.18698 q^{60} +2.44556 q^{61} -8.50317 q^{62} -7.84372 q^{63} +7.21810 q^{64} +5.68874 q^{65} +21.1386 q^{66} -8.81817 q^{67} -1.56167 q^{68} -7.38672 q^{69} -1.01597 q^{70} -9.46632 q^{71} +23.6504 q^{72} +6.06503 q^{73} -2.79309 q^{74} +3.29298 q^{75} -2.06595 q^{76} +6.31839 q^{77} +19.0320 q^{78} -13.0557 q^{79} +1.12772 q^{80} +28.9928 q^{81} -5.06340 q^{82} -2.44346 q^{83} +3.18698 q^{84} -1.61361 q^{85} +2.65544 q^{86} -25.4690 q^{87} -19.0512 q^{88} +12.5853 q^{89} +7.96896 q^{90} +5.68874 q^{91} +2.17097 q^{92} +27.5607 q^{93} -1.90839 q^{94} -2.13466 q^{95} -16.0851 q^{96} +13.5945 q^{97} -1.01597 q^{98} -49.5597 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.01597	−0.718397	−0.359199	−	0.933261i	$-0.616950\pi$
$2$	−1.01597	−0.718397	−0.359199	+	0.933261i	$0.616950\pi$
$3$	3.29298	1.90120	0.950602	−	0.310414i	$-0.100468\pi$
$3$	3.29298	1.90120	0.950602	+	0.310414i	$0.100468\pi$
$4$	−0.967811	−0.483905
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−3.34556	−1.36582
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	3.01520	1.06603
$9$	7.84372	2.61457
$10$	1.01597	0.321277
$11$	−6.31839	−1.90507	−0.952533	−	0.304435i	$-0.901532\pi$
$11$	−6.31839	−1.90507	−0.952533	+	0.304435i	$0.901532\pi$
$12$	−3.18698	−0.920002
$13$	−5.68874	−1.57777	−0.788886	−	0.614540i	$-0.789342\pi$
$13$	−5.68874	−1.57777	−0.788886	+	0.614540i	$0.789342\pi$
$14$	1.01597	0.271529
$15$	−3.29298	−0.850244
$16$	−1.12772	−0.281930
$17$	1.61361	0.391357	0.195679	−	0.980668i	$-0.437309\pi$
$17$	1.61361	0.391357	0.195679	+	0.980668i	$0.437309\pi$
$18$	−7.96896	−1.87830
$19$	2.13466	0.489725	0.244863	−	0.969558i	$-0.421257\pi$
$19$	2.13466	0.489725	0.244863	+	0.969558i	$0.421257\pi$
$20$	0.967811	0.216409
$21$	−3.29298	−0.718587
$22$	6.41928	1.36859
$23$	−2.24317	−0.467734	−0.233867	−	0.972269i	$-0.575138\pi$
$23$	−2.24317	−0.467734	−0.233867	+	0.972269i	$0.575138\pi$
$24$	9.92899	2.02675
$25$	1.00000	0.200000
$26$	5.77957	1.13347
$27$	15.9503	3.06963
$28$	0.967811	0.182899
$29$	−7.73433	−1.43623	−0.718115	−	0.695925i	$-0.754995\pi$
$29$	−7.73433	−1.43623	−0.718115	+	0.695925i	$0.754995\pi$
$30$	3.34556	0.610813
$31$	8.36953	1.50321	0.751606	−	0.659613i	$-0.229280\pi$
$31$	8.36953	1.50321	0.751606	+	0.659613i	$0.229280\pi$
$32$	−4.88467	−0.863496
$33$	−20.8063	−3.62192
$34$	−1.63937	−0.281150
$35$	1.00000	0.169031
$36$	−7.59124	−1.26521
$37$	2.74919	0.451965	0.225982	−	0.974131i	$-0.427441\pi$
$37$	2.74919	0.451965	0.225982	+	0.974131i	$0.427441\pi$
$38$	−2.16875	−0.351817
$39$	−18.7329	−2.99966
$40$	−3.01520	−0.476745
$41$	4.98382	0.778342	0.389171	−	0.921165i	$-0.372761\pi$
$41$	4.98382	0.778342	0.389171	+	0.921165i	$0.372761\pi$
$42$	3.34556	0.516231
$43$	−2.61371	−0.398587	−0.199294	−	0.979940i	$-0.563865\pi$
$43$	−2.61371	−0.398587	−0.199294	+	0.979940i	$0.563865\pi$
$44$	6.11501	0.921872
$45$	−7.84372	−1.16927
$46$	2.27899	0.336019
$47$	1.87840	0.273993	0.136996	−	0.990572i	$-0.456255\pi$
$47$	1.87840	0.273993	0.136996	+	0.990572i	$0.456255\pi$
$48$	−3.71356	−0.536007
$49$	1.00000	0.142857
$50$	−1.01597	−0.143679
$51$	5.31358	0.744049
$52$	5.50562	0.763492
$53$	11.8377	1.62603	0.813017	−	0.582240i	$-0.197824\pi$
$53$	11.8377	1.62603	0.813017	+	0.582240i	$0.197824\pi$
$54$	−16.2050	−2.20522
$55$	6.31839	0.851972
$56$	−3.01520	−0.402923
$57$	7.02941	0.931068
$58$	7.85783	1.03178
$59$	0.907289	0.118119	0.0590595	−	0.998254i	$-0.481190\pi$
$59$	0.907289	0.118119	0.0590595	+	0.998254i	$0.481190\pi$
$60$	3.18698	0.411438
$61$	2.44556	0.313122	0.156561	−	0.987668i	$-0.449959\pi$
$61$	2.44556	0.313122	0.156561	+	0.987668i	$0.449959\pi$
$62$	−8.50317	−1.07990
$63$	−7.84372	−0.988216
$64$	7.21810	0.902263
$65$	5.68874	0.705601
$66$	21.1386	2.60198
$67$	−8.81817	−1.07731	−0.538655	−	0.842526i	$-0.681068\pi$
$67$	−8.81817	−1.07731	−0.538655	+	0.842526i	$0.681068\pi$
$68$	−1.56167	−0.189380
$69$	−7.38672	−0.889257
$70$	−1.01597	−0.121431
$71$	−9.46632	−1.12345	−0.561723	−	0.827325i	$-0.689861\pi$
$71$	−9.46632	−1.12345	−0.561723	+	0.827325i	$0.689861\pi$
$72$	23.6504	2.78722
$73$	6.06503	0.709858	0.354929	−	0.934893i	$-0.384505\pi$
$73$	6.06503	0.709858	0.354929	+	0.934893i	$0.384505\pi$
$74$	−2.79309	−0.324690
$75$	3.29298	0.380241
$76$	−2.06595	−0.236981
$77$	6.31839	0.720047
$78$	19.0320	2.15495
$79$	−13.0557	−1.46888	−0.734440	−	0.678674i	$-0.762555\pi$
$79$	−13.0557	−1.46888	−0.734440	+	0.678674i	$0.762555\pi$
$80$	1.12772	0.126083
$81$	28.9928	3.22142
$82$	−5.06340	−0.559159
$83$	−2.44346	−0.268204	−0.134102	−	0.990968i	$-0.542815\pi$
$83$	−2.44346	−0.268204	−0.134102	+	0.990968i	$0.542815\pi$
$84$	3.18698	0.347728
$85$	−1.61361	−0.175020
$86$	2.65544	0.286344
$87$	−25.4690	−2.73056
$88$	−19.0512	−2.03086
$89$	12.5853	1.33404	0.667020	−	0.745040i	$-0.267570\pi$
$89$	12.5853	1.33404	0.667020	+	0.745040i	$0.267570\pi$
$90$	7.96896	0.840002
$91$	5.68874	0.596342
$92$	2.17097	0.226339
$93$	27.5607	2.85791
$94$	−1.90839	−0.196836
$95$	−2.13466	−0.219012
$96$	−16.0851	−1.64168
$97$	13.5945	1.38031	0.690156	−	0.723661i	$-0.257542\pi$
$97$	13.5945	1.38031	0.690156	+	0.723661i	$0.257542\pi$
$98$	−1.01597	−0.102628
$99$	−49.5597	−4.98094
$100$	−0.967811	−0.0967811
$101$	5.21352	0.518764	0.259382	−	0.965775i	$-0.416481\pi$
$101$	5.21352	0.518764	0.259382	+	0.965775i	$0.416481\pi$
$102$	−5.39842	−0.534523
$103$	−9.87704	−0.973213	−0.486607	−	0.873621i	$-0.661766\pi$
$103$	−9.87704	−0.973213	−0.486607	+	0.873621i	$0.661766\pi$
$104$	−17.1527	−1.68196
$105$	3.29298	0.321362
$106$	−12.0267	−1.16814
$107$	−2.78424	−0.269162	−0.134581	−	0.990903i	$-0.542969\pi$
$107$	−2.78424	−0.269162	−0.134581	+	0.990903i	$0.542969\pi$
$108$	−15.4369	−1.48541
$109$	7.30708	0.699891	0.349946	−	0.936770i	$-0.386200\pi$
$109$	7.30708	0.699891	0.349946	+	0.936770i	$0.386200\pi$
$110$	−6.41928	−0.612054
$111$	9.05305	0.859277
$112$	1.12772	0.106560
$113$	9.62182	0.905145	0.452572	−	0.891728i	$-0.350506\pi$
$113$	9.62182	0.905145	0.452572	+	0.891728i	$0.350506\pi$
$114$	−7.14165	−0.668876
$115$	2.24317	0.209177
$116$	7.48537	0.694999
$117$	−44.6209	−4.12520
$118$	−0.921776	−0.0848564
$119$	−1.61361	−0.147919
$120$	−9.92899	−0.906389
$121$	28.9221	2.62928
$122$	−2.48461	−0.224946
$123$	16.4116	1.47979
$124$	−8.10012	−0.727412
$125$	−1.00000	−0.0894427
$126$	7.96896	0.709932
$127$	20.1099	1.78447	0.892233	−	0.451575i	$-0.149138\pi$
$127$	20.1099	1.78447	0.892233	+	0.451575i	$0.149138\pi$
$128$	2.43598	0.215312
$129$	−8.60690	−0.757795
$130$	−5.77957	−0.506902
$131$	−16.7769	−1.46580	−0.732901	−	0.680335i	$-0.761834\pi$
$131$	−16.7769	−1.46580	−0.732901	+	0.680335i	$0.761834\pi$
$132$	20.1366	1.75267
$133$	−2.13466	−0.185099
$134$	8.95897	0.773937
$135$	−15.9503	−1.37278
$136$	4.86534	0.417200
$137$	9.23069	0.788631	0.394315	−	0.918975i	$-0.370982\pi$
$137$	9.23069	0.788631	0.394315	+	0.918975i	$0.370982\pi$
$138$	7.50467	0.638840
$139$	15.4136	1.30736	0.653682	−	0.756770i	$-0.273224\pi$
$139$	15.4136	1.30736	0.653682	+	0.756770i	$0.273224\pi$
$140$	−0.967811	−0.0817949
$141$	6.18554	0.520916
$142$	9.61748	0.807081
$143$	35.9437	3.00576
$144$	−8.84553	−0.737127
$145$	7.73433	0.642301
$146$	−6.16187	−0.509960
$147$	3.29298	0.271600
$148$	−2.66070	−0.218708
$149$	−16.5159	−1.35303	−0.676517	−	0.736427i	$-0.736511\pi$
$149$	−16.5159	−1.35303	−0.676517	+	0.736427i	$0.736511\pi$
$150$	−3.34556	−0.273164
$151$	14.8509	1.20855	0.604275	−	0.796776i	$-0.293463\pi$
$151$	14.8509	1.20855	0.604275	+	0.796776i	$0.293463\pi$
$152$	6.43643	0.522064
$153$	12.6567	1.02323
$154$	−6.41928	−0.517280
$155$	−8.36953	−0.672257
$156$	18.1299	1.45155
$157$	2.69423	0.215023	0.107512	−	0.994204i	$-0.465712\pi$
$157$	2.69423	0.215023	0.107512	+	0.994204i	$0.465712\pi$
$158$	13.2642	1.05524
$159$	38.9813	3.09142
$160$	4.88467	0.386167
$161$	2.24317	0.176787
$162$	−29.4557	−2.31426
$163$	19.6605	1.53993	0.769963	−	0.638088i	$-0.220274\pi$
$163$	19.6605	1.53993	0.769963	+	0.638088i	$0.220274\pi$
$164$	−4.82340	−0.376644
$165$	20.8063	1.61977
$166$	2.48247	0.192677
$167$	−8.86477	−0.685976	−0.342988	−	0.939340i	$-0.611439\pi$
$167$	−8.86477	−0.685976	−0.342988	+	0.939340i	$0.611439\pi$
$168$	−9.92899	−0.766038
$169$	19.3617	1.48936
$170$	1.63937	0.125734
$171$	16.7437	1.28042
$172$	2.52958	0.192878
$173$	−5.04724	−0.383734	−0.191867	−	0.981421i	$-0.561454\pi$
$173$	−5.04724	−0.383734	−0.191867	+	0.981421i	$0.561454\pi$
$174$	25.8757	1.96163
$175$	−1.00000	−0.0755929
$176$	7.12538	0.537096
$177$	2.98769	0.224568
$178$	−12.7863	−0.958370
$179$	16.8738	1.26121	0.630605	−	0.776104i	$-0.282807\pi$
$179$	16.8738	1.26121	0.630605	+	0.776104i	$0.282807\pi$
$180$	7.59124	0.565817
$181$	6.92207	0.514513	0.257257	−	0.966343i	$-0.417181\pi$
$181$	6.92207	0.514513	0.257257	+	0.966343i	$0.417181\pi$
$182$	−5.77957	−0.428410
$183$	8.05319	0.595309
$184$	−6.76361	−0.498620
$185$	−2.74919	−0.202125
$186$	−28.0008	−2.05312
$187$	−10.1954	−0.745561
$188$	−1.81794	−0.132587
$189$	−15.9503	−1.16021
$190$	2.16875	0.157338
$191$	16.9601	1.22719	0.613594	−	0.789622i	$-0.289723\pi$
$191$	16.9601	1.22719	0.613594	+	0.789622i	$0.289723\pi$
$192$	23.7691	1.71539
$193$	20.0077	1.44018	0.720092	−	0.693879i	$-0.244100\pi$
$193$	20.0077	1.44018	0.720092	+	0.693879i	$0.244100\pi$
$194$	−13.8116	−0.991612
$195$	18.7329	1.34149
$196$	−0.967811	−0.0691293
$197$	10.0601	0.716754	0.358377	−	0.933577i	$-0.383330\pi$
$197$	10.0601	0.716754	0.358377	+	0.933577i	$0.383330\pi$
$198$	50.3510	3.57829
$199$	−6.78095	−0.480689	−0.240344	−	0.970688i	$-0.577260\pi$
$199$	−6.78095	−0.480689	−0.240344	+	0.970688i	$0.577260\pi$
$200$	3.01520	0.213207
$201$	−29.0381	−2.04819
$202$	−5.29676	−0.372679
$203$	7.73433	0.542844
$204$	−5.14254	−0.360050
$205$	−4.98382	−0.348085
$206$	10.0347	0.699154
$207$	−17.5948	−1.22292
$208$	6.41531	0.444822
$209$	−13.4876	−0.932959
$210$	−3.34556	−0.230866
$211$	−6.26952	−0.431612	−0.215806	−	0.976436i	$-0.569238\pi$
$211$	−6.26952	−0.431612	−0.215806	+	0.976436i	$0.569238\pi$
$212$	−11.4567	−0.786847
$213$	−31.1724	−2.13590
$214$	2.82869	0.193365
$215$	2.61371	0.178254
$216$	48.0932	3.27233
$217$	−8.36953	−0.568161
$218$	−7.42375	−0.502800
$219$	19.9720	1.34958
$220$	−6.11501	−0.412274
$221$	−9.17939	−0.617472
$222$	−9.19760	−0.617302
$223$	−27.2744	−1.82643	−0.913214	−	0.407481i	$-0.866407\pi$
$223$	−27.2744	−1.82643	−0.913214	+	0.407481i	$0.866407\pi$
$224$	4.88467	0.326371
$225$	7.84372	0.522915
$226$	−9.77545	−0.650254
$227$	−29.8729	−1.98273	−0.991367	−	0.131113i	$-0.958145\pi$
$227$	−29.8729	−1.98273	−0.991367	+	0.131113i	$0.958145\pi$
$228$	−6.80313	−0.450549
$229$	1.00000	0.0660819
$229$	1.00000	0.0660819
$230$	−2.27899	−0.150272
$231$	20.8063	1.36896
$232$	−23.3205	−1.53107
$233$	25.7669	1.68805	0.844024	−	0.536306i	$-0.180181\pi$
$233$	25.7669	1.68805	0.844024	+	0.536306i	$0.180181\pi$
$234$	45.3333	2.96353
$235$	−1.87840	−0.122533
$236$	−0.878084	−0.0571584
$237$	−42.9921	−2.79264
$238$	1.63937	0.106265
$239$	10.1204	0.654633	0.327316	−	0.944915i	$-0.393856\pi$
$239$	10.1204	0.654633	0.327316	+	0.944915i	$0.393856\pi$
$240$	3.71356	0.239709
$241$	−11.2252	−0.723079	−0.361539	−	0.932357i	$-0.617749\pi$
$241$	−11.2252	−0.723079	−0.361539	+	0.932357i	$0.617749\pi$
$242$	−29.3839	−1.88887
$243$	47.6219	3.05494
$244$	−2.36684	−0.151522
$245$	−1.00000	−0.0638877
$246$	−16.6737	−1.06308
$247$	−12.1435	−0.772675
$248$	25.2358	1.60247
$249$	−8.04626	−0.509911
$250$	1.01597	0.0642554
$251$	−17.8922	−1.12935	−0.564674	−	0.825314i	$-0.690998\pi$
$251$	−17.8922	−1.12935	−0.564674	+	0.825314i	$0.690998\pi$
$252$	7.59124	0.478203
$253$	14.1732	0.891064
$254$	−20.4310	−1.28196
$255$	−5.31358	−0.332749
$256$	−16.9111	−1.05694
$257$	9.99749	0.623626	0.311813	−	0.950143i	$-0.399064\pi$
$257$	9.99749	0.623626	0.311813	+	0.950143i	$0.399064\pi$
$258$	8.74432	0.544398
$259$	−2.74919	−0.170827
$260$	−5.50562	−0.341444
$261$	−60.6659	−3.75513
$262$	17.0447	1.05303
$263$	−16.2638	−1.00287	−0.501435	−	0.865195i	$-0.667194\pi$
$263$	−16.2638	−1.00287	−0.501435	+	0.865195i	$0.667194\pi$
$264$	−62.7352	−3.86109
$265$	−11.8377	−0.727184
$266$	2.16875	0.132974
$267$	41.4432	2.53628
$268$	8.53432	0.521317
$269$	−3.28699	−0.200411	−0.100206	−	0.994967i	$-0.531950\pi$
$269$	−3.28699	−0.200411	−0.100206	+	0.994967i	$0.531950\pi$
$270$	16.2050	0.986202
$271$	25.6005	1.55512	0.777561	−	0.628808i	$-0.216457\pi$
$271$	25.6005	1.55512	0.777561	+	0.628808i	$0.216457\pi$
$272$	−1.81970	−0.110335
$273$	18.7329	1.13377
$274$	−9.37807	−0.566550
$275$	−6.31839	−0.381013
$276$	7.14895	0.430316
$277$	−5.08975	−0.305813	−0.152907	−	0.988241i	$-0.548863\pi$
$277$	−5.08975	−0.305813	−0.152907	+	0.988241i	$0.548863\pi$
$278$	−15.6597	−0.939206
$279$	65.6482	3.93026
$280$	3.01520	0.180193
$281$	13.1386	0.783786	0.391893	−	0.920011i	$-0.371820\pi$
$281$	13.1386	0.783786	0.391893	+	0.920011i	$0.371820\pi$
$282$	−6.28430	−0.374225
$283$	−5.30575	−0.315394	−0.157697	−	0.987488i	$-0.550407\pi$
$283$	−5.30575	−0.315394	−0.157697	+	0.987488i	$0.550407\pi$
$284$	9.16161	0.543642
$285$	−7.02941	−0.416386
$286$	−36.5176	−2.15933
$287$	−4.98382	−0.294186
$288$	−38.3140	−2.25767
$289$	−14.3963	−0.846840
$290$	−7.85783	−0.461428
$291$	44.7664	2.62425
$292$	−5.86980	−0.343504
$293$	16.5534	0.967061	0.483530	−	0.875328i	$-0.339354\pi$
$293$	16.5534	0.967061	0.483530	+	0.875328i	$0.339354\pi$
$294$	−3.34556	−0.195117
$295$	−0.907289	−0.0528244
$296$	8.28937	0.481810
$297$	−100.780	−5.84785
$298$	16.7796	0.972016
$299$	12.7608	0.737977
$300$	−3.18698	−0.184000
$301$	2.61371	0.150652
$302$	−15.0880	−0.868220
$303$	17.1680	0.986276
$304$	−2.40730	−0.138068
$305$	−2.44556	−0.140033
$306$	−12.8588	−0.735087
$307$	20.7049	1.18169	0.590846	−	0.806785i	$-0.298794\pi$
$307$	20.7049	1.18169	0.590846	+	0.806785i	$0.298794\pi$
$308$	−6.11501	−0.348435
$309$	−32.5249	−1.85028
$310$	8.50317	0.482947
$311$	24.9358	1.41398	0.706989	−	0.707224i	$-0.250053\pi$
$311$	24.9358	1.41398	0.706989	+	0.707224i	$0.250053\pi$
$312$	−56.4834	−3.19774
$313$	21.6911	1.22605	0.613027	−	0.790062i	$-0.289952\pi$
$313$	21.6911	1.22605	0.613027	+	0.790062i	$0.289952\pi$
$314$	−2.73725	−0.154472
$315$	7.84372	0.441944
$316$	12.6354	0.710799
$317$	9.40569	0.528276	0.264138	−	0.964485i	$-0.414913\pi$
$317$	9.40569	0.528276	0.264138	+	0.964485i	$0.414913\pi$
$318$	−39.6038	−2.22087
$319$	48.8685	2.73611
$320$	−7.21810	−0.403504
$321$	−9.16844	−0.511732
$322$	−2.27899	−0.127003
$323$	3.44451	0.191658
$324$	−28.0595	−1.55886
$325$	−5.68874	−0.315554
$326$	−19.9744	−1.10628
$327$	24.0621	1.33064
$328$	15.0272	0.829739
$329$	−1.87840	−0.103560
$330$	−21.1386	−1.16364
$331$	18.9819	1.04334	0.521669	−	0.853148i	$-0.325310\pi$
$331$	18.9819	1.04334	0.521669	+	0.853148i	$0.325310\pi$
$332$	2.36481	0.129786
$333$	21.5639	1.18170
$334$	9.00631	0.492803
$335$	8.81817	0.481788
$336$	3.71356	0.202591
$337$	−16.9403	−0.922800	−0.461400	−	0.887192i	$-0.652653\pi$
$337$	−16.9403	−0.922800	−0.461400	+	0.887192i	$0.652653\pi$
$338$	−19.6709	−1.06996
$339$	31.6845	1.72086
$340$	1.56167	0.0846932
$341$	−52.8819	−2.86372
$342$	−17.0111	−0.919852
$343$	−1.00000	−0.0539949
$344$	−7.88085	−0.424907
$345$	7.38672	0.397688
$346$	5.12783	0.275674
$347$	−32.9041	−1.76638	−0.883192	−	0.469011i	$-0.844610\pi$
$347$	−32.9041	−1.76638	−0.883192	+	0.469011i	$0.844610\pi$
$348$	24.6492	1.32133
$349$	10.3882	0.556070	0.278035	−	0.960571i	$-0.410317\pi$
$349$	10.3882	0.556070	0.278035	+	0.960571i	$0.410317\pi$
$350$	1.01597	0.0543057
$351$	−90.7369	−4.84318
$352$	30.8632	1.64502
$353$	12.1743	0.647971	0.323986	−	0.946062i	$-0.394977\pi$
$353$	12.1743	0.647971	0.323986	+	0.946062i	$0.394977\pi$
$354$	−3.03539	−0.161329
$355$	9.46632	0.502420
$356$	−12.1802	−0.645549
$357$	−5.31358	−0.281224
$358$	−17.1433	−0.906049
$359$	7.28344	0.384405	0.192203	−	0.981355i	$-0.438437\pi$
$359$	7.28344	0.384405	0.192203	+	0.981355i	$0.438437\pi$
$360$	−23.6504	−1.24648
$361$	−14.4432	−0.760169
$362$	−7.03260	−0.369625
$363$	95.2398	4.99879
$364$	−5.50562	−0.288573
$365$	−6.06503	−0.317458
$366$	−8.18178	−0.427668
$367$	−15.5822	−0.813383	−0.406692	−	0.913565i	$-0.633318\pi$
$367$	−15.5822	−0.813383	−0.406692	+	0.913565i	$0.633318\pi$
$368$	2.52967	0.131868
$369$	39.0917	2.03503
$370$	2.79309	0.145206
$371$	−11.8377	−0.614583
$372$	−26.6735	−1.38296
$373$	−15.2450	−0.789355	−0.394677	−	0.918820i	$-0.629144\pi$
$373$	−15.2450	−0.789355	−0.394677	+	0.918820i	$0.629144\pi$
$374$	10.3582	0.535609
$375$	−3.29298	−0.170049
$376$	5.66375	0.292086
$377$	43.9986	2.26604
$378$	16.2050	0.833493
$379$	−33.0298	−1.69663	−0.848314	−	0.529494i	$-0.822382\pi$
$379$	−33.0298	−1.69663	−0.848314	+	0.529494i	$0.822382\pi$
$380$	2.06595	0.105981
$381$	66.2216	3.39263
$382$	−17.2309	−0.881609
$383$	−4.23856	−0.216580	−0.108290	−	0.994119i	$-0.534538\pi$
$383$	−4.23856	−0.216580	−0.108290	+	0.994119i	$0.534538\pi$
$384$	8.02164	0.409352
$385$	−6.31839	−0.322015
$386$	−20.3271	−1.03462
$387$	−20.5012	−1.04214
$388$	−13.1569	−0.667940
$389$	−17.1906	−0.871600	−0.435800	−	0.900043i	$-0.643535\pi$
$389$	−17.1906	−0.871600	−0.435800	+	0.900043i	$0.643535\pi$
$390$	−19.0320	−0.963723
$391$	−3.61960	−0.183051
$392$	3.01520	0.152291
$393$	−55.2459	−2.78679
$394$	−10.2208	−0.514914
$395$	13.0557	0.656903
$396$	47.9644	2.41030
$397$	−23.3017	−1.16948	−0.584740	−	0.811221i	$-0.698803\pi$
$397$	−23.3017	−1.16948	−0.584740	+	0.811221i	$0.698803\pi$
$398$	6.88922	0.345325
$399$	−7.02941	−0.351910
$400$	−1.12772	−0.0563860
$401$	29.6515	1.48073	0.740363	−	0.672207i	$-0.234654\pi$
$401$	29.6515	1.48073	0.740363	+	0.672207i	$0.234654\pi$
$402$	29.5017	1.47141
$403$	−47.6120	−2.37173
$404$	−5.04570	−0.251033
$405$	−28.9928	−1.44066
$406$	−7.85783	−0.389977
$407$	−17.3705	−0.861023
$408$	16.0215	0.793182
$409$	−5.58939	−0.276378	−0.138189	−	0.990406i	$-0.544128\pi$
$409$	−5.58939	−0.276378	−0.138189	+	0.990406i	$0.544128\pi$
$410$	5.06340	0.250064
$411$	30.3965	1.49935
$412$	9.55910	0.470943
$413$	−0.907289	−0.0446448
$414$	17.8758	0.878545
$415$	2.44346	0.119945
$416$	27.7876	1.36240
$417$	50.7566	2.48556
$418$	13.7030	0.670236
$419$	−18.0697	−0.882762	−0.441381	−	0.897320i	$-0.645511\pi$
$419$	−18.0697	−0.882762	−0.441381	+	0.897320i	$0.645511\pi$
$420$	−3.18698	−0.155509
$421$	19.2290	0.937166	0.468583	−	0.883419i	$-0.344765\pi$
$421$	19.2290	0.937166	0.468583	+	0.883419i	$0.344765\pi$
$422$	6.36963	0.310069
$423$	14.7336	0.716375
$424$	35.6930	1.73341
$425$	1.61361	0.0782714
$426$	31.6702	1.53442
$427$	−2.44556	−0.118349
$428$	2.69461	0.130249
$429$	118.362	5.71456
$430$	−2.65544	−0.128057
$431$	11.7335	0.565181	0.282591	−	0.959241i	$-0.408806\pi$
$431$	11.7335	0.565181	0.282591	+	0.959241i	$0.408806\pi$
$432$	−17.9875	−0.865422
$433$	7.41003	0.356103	0.178052	−	0.984021i	$-0.443021\pi$
$433$	7.41003	0.356103	0.178052	+	0.984021i	$0.443021\pi$
$434$	8.50317	0.408165
$435$	25.4690	1.22115
$436$	−7.07187	−0.338681
$437$	−4.78842	−0.229061
$438$	−20.2909	−0.969537
$439$	−7.88688	−0.376420	−0.188210	−	0.982129i	$-0.560269\pi$
$439$	−7.88688	−0.376420	−0.188210	+	0.982129i	$0.560269\pi$
$440$	19.0512	0.908230
$441$	7.84372	0.373511
$442$	9.32595	0.443590
$443$	37.6005	1.78645	0.893226	−	0.449607i	$-0.148436\pi$
$443$	37.6005	1.78645	0.893226	+	0.449607i	$0.148436\pi$
$444$	−8.76163	−0.415809
$445$	−12.5853	−0.596601
$446$	27.7099	1.31210
$447$	−54.3865	−2.57239
$448$	−7.21810	−0.341023
$449$	35.9048	1.69445	0.847226	−	0.531233i	$-0.178271\pi$
$449$	35.9048	1.69445	0.847226	+	0.531233i	$0.178271\pi$
$450$	−7.96896	−0.375660
$451$	−31.4897	−1.48279
$452$	−9.31210	−0.438004
$453$	48.9038	2.29770
$454$	30.3499	1.42439
$455$	−5.68874	−0.266692
$456$	21.1951	0.992549
$457$	−11.7213	−0.548299	−0.274149	−	0.961687i	$-0.588396\pi$
$457$	−11.7213	−0.548299	−0.274149	+	0.961687i	$0.588396\pi$
$458$	−1.01597	−0.0474730
$459$	25.7375	1.20132
$460$	−2.17097	−0.101222
$461$	−35.9816	−1.67583	−0.837916	−	0.545800i	$-0.816226\pi$
$461$	−35.9816	−1.67583	−0.837916	+	0.545800i	$0.816226\pi$
$462$	−21.1386	−0.983454
$463$	−3.76576	−0.175010	−0.0875049	−	0.996164i	$-0.527889\pi$
$463$	−3.76576	−0.175010	−0.0875049	+	0.996164i	$0.527889\pi$
$464$	8.72217	0.404916
$465$	−27.5607	−1.27810
$466$	−26.1784	−1.21269
$467$	−15.5329	−0.718776	−0.359388	−	0.933188i	$-0.617014\pi$
$467$	−15.5329	−0.718776	−0.359388	+	0.933188i	$0.617014\pi$
$468$	43.1846	1.99621
$469$	8.81817	0.407185
$470$	1.90839	0.0880276
$471$	8.87206	0.408803
$472$	2.73566	0.125919
$473$	16.5144	0.759335
$474$	43.6786	2.00622
$475$	2.13466	0.0979451
$476$	1.56167	0.0715788
$477$	92.8517	4.25139
$478$	−10.2820	−0.470286
$479$	43.4103	1.98347	0.991733	−	0.128316i	$-0.0409573\pi$
$479$	43.4103	1.98347	0.991733	+	0.128316i	$0.0409573\pi$
$480$	16.0851	0.734182
$481$	−15.6394	−0.713097
$482$	11.4044	0.519458
$483$	7.38672	0.336107
$484$	−27.9911	−1.27232
$485$	−13.5945	−0.617294
$486$	−48.3822	−2.19466
$487$	−0.771424	−0.0349566	−0.0174783	−	0.999847i	$-0.505564\pi$
$487$	−0.771424	−0.0349566	−0.0174783	+	0.999847i	$0.505564\pi$
$488$	7.37386	0.333799
$489$	64.7415	2.92771
$490$	1.01597	0.0458967
$491$	1.25434	0.0566074	0.0283037	−	0.999599i	$-0.490989\pi$
$491$	1.25434	0.0566074	0.0283037	+	0.999599i	$0.490989\pi$
$492$	−15.8834	−0.716077
$493$	−12.4802	−0.562079
$494$	12.3374	0.555088
$495$	49.5597	2.22754
$496$	−9.43849	−0.423801
$497$	9.46632	0.424623
$498$	8.17474	0.366319
$499$	34.5239	1.54550	0.772750	−	0.634710i	$-0.218881\pi$
$499$	34.5239	1.54550	0.772750	+	0.634710i	$0.218881\pi$
$500$	0.967811	0.0432818
$501$	−29.1915	−1.30418
$502$	18.1779	0.811321
$503$	10.2212	0.455741	0.227870	−	0.973691i	$-0.426824\pi$
$503$	10.2212	0.455741	0.227870	+	0.973691i	$0.426824\pi$
$504$	−23.6504	−1.05347
$505$	−5.21352	−0.231998
$506$	−14.3995	−0.640138
$507$	63.7578	2.83158
$508$	−19.4626	−0.863513
$509$	12.3039	0.545359	0.272680	−	0.962105i	$-0.412090\pi$
$509$	12.3039	0.545359	0.272680	+	0.962105i	$0.412090\pi$
$510$	5.39842	0.239046
$511$	−6.06503	−0.268301
$512$	12.3091	0.543993
$513$	34.0485	1.50328
$514$	−10.1571	−0.448011
$515$	9.87704	0.435234
$516$	8.32985	0.366701
$517$	−11.8685	−0.521975
$518$	2.79309	0.122721
$519$	−16.6204	−0.729557
$520$	17.1527	0.752194
$521$	17.8194	0.780682	0.390341	−	0.920670i	$-0.372357\pi$
$521$	17.8194	0.780682	0.390341	+	0.920670i	$0.372357\pi$
$522$	61.6346	2.69767
$523$	1.67232	0.0731254	0.0365627	−	0.999331i	$-0.488359\pi$
$523$	1.67232	0.0731254	0.0365627	+	0.999331i	$0.488359\pi$
$524$	16.2368	0.709309
$525$	−3.29298	−0.143717
$526$	16.5235	0.720459
$527$	13.5051	0.588293
$528$	23.4637	1.02113
$529$	−17.9682	−0.781225
$530$	12.0267	0.522407
$531$	7.11652	0.308831
$532$	2.06595	0.0895703
$533$	−28.3517	−1.22805
$534$	−42.1049	−1.82206
$535$	2.78424	0.120373
$536$	−26.5885	−1.14845
$537$	55.5652	2.39781
$538$	3.33948	0.143975
$539$	−6.31839	−0.272152
$540$	15.4369	0.664296
$541$	27.7249	1.19199	0.595994	−	0.802989i	$-0.296758\pi$
$541$	27.7249	1.19199	0.595994	+	0.802989i	$0.296758\pi$
$542$	−26.0093	−1.11720
$543$	22.7942	0.978195
$544$	−7.88194	−0.337935
$545$	−7.30708	−0.313001
$546$	−19.0320	−0.814495
$547$	−18.1333	−0.775323	−0.387662	−	0.921802i	$-0.626717\pi$
$547$	−18.1333	−0.775323	−0.387662	+	0.921802i	$0.626717\pi$
$548$	−8.93356	−0.381623
$549$	19.1823	0.818681
$550$	6.41928	0.273719
$551$	−16.5102	−0.703358
$552$	−22.2724	−0.947978
$553$	13.0557	0.555184
$554$	5.17101	0.219695
$555$	−9.05305	−0.384280
$556$	−14.9174	−0.632640
$557$	−25.3337	−1.07342	−0.536712	−	0.843765i	$-0.680334\pi$
$557$	−25.3337	−1.07342	−0.536712	+	0.843765i	$0.680334\pi$
$558$	−66.6965	−2.82349
$559$	14.8687	0.628879
$560$	−1.12772	−0.0476549
$561$	−33.5732	−1.41746
$562$	−13.3484	−0.563070
$563$	−21.2954	−0.897492	−0.448746	−	0.893659i	$-0.648129\pi$
$563$	−21.2954	−0.897492	−0.448746	+	0.893659i	$0.648129\pi$
$564$	−5.98643	−0.252074
$565$	−9.62182	−0.404793
$566$	5.39047	0.226578
$567$	−28.9928	−1.21758
$568$	−28.5428	−1.19763
$569$	−35.1776	−1.47472	−0.737361	−	0.675499i	$-0.763928\pi$
$569$	−35.1776	−1.47472	−0.737361	+	0.675499i	$0.763928\pi$
$570$	7.14165	0.299131
$571$	−33.5101	−1.40236	−0.701178	−	0.712987i	$-0.747342\pi$
$571$	−33.5101	−1.40236	−0.701178	+	0.712987i	$0.747342\pi$
$572$	−34.7867	−1.45450
$573$	55.8492	2.33313
$574$	5.06340	0.211342
$575$	−2.24317	−0.0935467
$576$	56.6168	2.35903
$577$	−24.3175	−1.01235	−0.506176	−	0.862430i	$-0.668941\pi$
$577$	−24.3175	−1.01235	−0.506176	+	0.862430i	$0.668941\pi$
$578$	14.6261	0.608367
$579$	65.8849	2.73808
$580$	−7.48537	−0.310813
$581$	2.44346	0.101372
$582$	−45.4812	−1.88526
$583$	−74.7952	−3.09770
$584$	18.2873	0.756732
$585$	44.6209	1.84485
$586$	−16.8177	−0.694734
$587$	31.3520	1.29403	0.647017	−	0.762475i	$-0.276016\pi$
$587$	31.3520	1.29403	0.647017	+	0.762475i	$0.276016\pi$
$588$	−3.18698	−0.131429
$589$	17.8661	0.736161
$590$	0.921776	0.0379489
$591$	33.1278	1.36270
$592$	−3.10032	−0.127423
$593$	−46.5771	−1.91269	−0.956346	−	0.292236i	$-0.905601\pi$
$593$	−46.5771	−1.91269	−0.956346	+	0.292236i	$0.905601\pi$
$594$	102.389	4.20108
$595$	1.61361	0.0661514
$596$	15.9842	0.654740
$597$	−22.3295	−0.913887
$598$	−12.9646	−0.530161
$599$	−17.9722	−0.734323	−0.367161	−	0.930157i	$-0.619670\pi$
$599$	−17.9722	−0.734323	−0.367161	+	0.930157i	$0.619670\pi$
$600$	9.92899	0.405349
$601$	7.80235	0.318265	0.159132	−	0.987257i	$-0.449130\pi$
$601$	7.80235	0.318265	0.159132	+	0.987257i	$0.449130\pi$
$602$	−2.65544	−0.108228
$603$	−69.1673	−2.81671
$604$	−14.3729	−0.584824
$605$	−28.9221	−1.17585
$606$	−17.4421	−0.708538
$607$	28.6507	1.16290	0.581449	−	0.813583i	$-0.302486\pi$
$607$	28.6507	1.16290	0.581449	+	0.813583i	$0.302486\pi$
$608$	−10.4271	−0.422876
$609$	25.4690	1.03206
$610$	2.48461	0.100599
$611$	−10.6857	−0.432298
$612$	−12.2493	−0.495147
$613$	11.5405	0.466115	0.233058	−	0.972463i	$-0.425127\pi$
$613$	11.5405	0.466115	0.233058	+	0.972463i	$0.425127\pi$
$614$	−21.0355	−0.848924
$615$	−16.4116	−0.661781
$616$	19.0512	0.767595
$617$	43.4486	1.74917	0.874587	−	0.484869i	$-0.161133\pi$
$617$	43.4486	1.74917	0.874587	+	0.484869i	$0.161133\pi$
$618$	33.0442	1.32923
$619$	34.3689	1.38140	0.690702	−	0.723139i	$-0.257302\pi$
$619$	34.3689	1.38140	0.690702	+	0.723139i	$0.257302\pi$
$620$	8.10012	0.325309
$621$	−35.7792	−1.43577
$622$	−25.3339	−1.01580
$623$	−12.5853	−0.504219
$624$	21.1255	0.845696
$625$	1.00000	0.0400000
$626$	−22.0374	−0.880793
$627$	−44.4145	−1.77375
$628$	−2.60751	−0.104051
$629$	4.43612	0.176880
$630$	−7.96896	−0.317491
$631$	28.1085	1.11898	0.559491	−	0.828836i	$-0.310996\pi$
$631$	28.1085	1.11898	0.559491	+	0.828836i	$0.310996\pi$
$632$	−39.3655	−1.56588
$633$	−20.6454	−0.820581
$634$	−9.55587	−0.379512
$635$	−20.1099	−0.798038
$636$	−37.7266	−1.49596
$637$	−5.68874	−0.225396
$638$	−49.6488	−1.96562
$639$	−74.2512	−2.93733
$640$	−2.43598	−0.0962906
$641$	37.6643	1.48765	0.743826	−	0.668373i	$-0.233009\pi$
$641$	37.6643	1.48765	0.743826	+	0.668373i	$0.233009\pi$
$642$	9.31483	0.367627
$643$	18.5643	0.732106	0.366053	−	0.930594i	$-0.380709\pi$
$643$	18.5643	0.732106	0.366053	+	0.930594i	$0.380709\pi$
$644$	−2.17097	−0.0855481
$645$	8.60690	0.338896
$646$	−3.49951	−0.137686
$647$	−44.5607	−1.75186	−0.875930	−	0.482438i	$-0.839751\pi$
$647$	−44.5607	−1.75186	−0.875930	+	0.482438i	$0.839751\pi$
$648$	87.4190	3.43414
$649$	−5.73261	−0.225025
$650$	5.77957	0.226693
$651$	−27.5607	−1.08019
$652$	−19.0276	−0.745179
$653$	26.8931	1.05241	0.526204	−	0.850359i	$-0.323615\pi$
$653$	26.8931	1.05241	0.526204	+	0.850359i	$0.323615\pi$
$654$	−24.4463	−0.955925
$655$	16.7769	0.655526
$656$	−5.62036	−0.219438
$657$	47.5724	1.85598
$658$	1.90839	0.0743969
$659$	4.68623	0.182549	0.0912747	−	0.995826i	$-0.470906\pi$
$659$	4.68623	0.182549	0.0912747	+	0.995826i	$0.470906\pi$
$660$	−20.1366	−0.783816
$661$	5.91209	0.229954	0.114977	−	0.993368i	$-0.463321\pi$
$661$	5.91209	0.229954	0.114977	+	0.993368i	$0.463321\pi$
$662$	−19.2849	−0.749531
$663$	−30.2275	−1.17394
$664$	−7.36751	−0.285915
$665$	2.13466	0.0827787
$666$	−21.9082	−0.848927
$667$	17.3494	0.671773
$668$	8.57942	0.331948
$669$	−89.8140	−3.47241
$670$	−8.95897	−0.346115
$671$	−15.4520	−0.596519
$672$	16.0851	0.620497
$673$	37.3520	1.43981	0.719907	−	0.694070i	$-0.244184\pi$
$673$	37.3520	1.43981	0.719907	+	0.694070i	$0.244184\pi$
$674$	17.2108	0.662937
$675$	15.9503	0.613926
$676$	−18.7385	−0.720711
$677$	16.3677	0.629063	0.314532	−	0.949247i	$-0.398153\pi$
$677$	16.3677	0.629063	0.314532	+	0.949247i	$0.398153\pi$
$678$	−32.1904	−1.23626
$679$	−13.5945	−0.521709
$680$	−4.86534	−0.186577
$681$	−98.3709	−3.76958
$682$	53.7263	2.05729
$683$	−37.6564	−1.44088	−0.720441	−	0.693516i	$-0.756061\pi$
$683$	−37.6564	−1.44088	−0.720441	+	0.693516i	$0.756061\pi$
$684$	−16.2047	−0.619604
$685$	−9.23069	−0.352686
$686$	1.01597	0.0387898
$687$	3.29298	0.125635
$688$	2.94754	0.112374
$689$	−67.3416	−2.56551
$690$	−7.50467	−0.285698
$691$	−15.3103	−0.582431	−0.291215	−	0.956657i	$-0.594060\pi$
$691$	−15.3103	−0.582431	−0.291215	+	0.956657i	$0.594060\pi$
$692$	4.88477	0.185691
$693$	49.5597	1.88262
$694$	33.4295	1.26897
$695$	−15.4136	−0.584671
$696$	−76.7941	−2.91087
$697$	8.04193	0.304610
$698$	−10.5541	−0.399479
$699$	84.8500	3.20932
$700$	0.967811	0.0365798
$701$	47.9878	1.81248	0.906238	−	0.422769i	$-0.138942\pi$
$701$	47.9878	1.81248	0.906238	+	0.422769i	$0.138942\pi$
$702$	92.1857	3.47933
$703$	5.86861	0.221339
$704$	−45.6068	−1.71887
$705$	−6.18554	−0.232961
$706$	−12.3687	−0.465501
$707$	−5.21352	−0.196074
$708$	−2.89151	−0.108670
$709$	−3.73742	−0.140362	−0.0701808	−	0.997534i	$-0.522358\pi$
$709$	−3.73742	−0.140362	−0.0701808	+	0.997534i	$0.522358\pi$
$710$	−9.61748	−0.360937
$711$	−102.405	−3.84049
$712$	37.9472	1.42213
$713$	−18.7743	−0.703103
$714$	5.39842	0.202031
$715$	−35.9437	−1.34422
$716$	−16.3307	−0.610306
$717$	33.3262	1.24459
$718$	−7.39973	−0.276156
$719$	3.52836	0.131586	0.0657929	−	0.997833i	$-0.479042\pi$
$719$	3.52836	0.131586	0.0657929	+	0.997833i	$0.479042\pi$
$720$	8.84553	0.329653
$721$	9.87704	0.367840
$722$	14.6738	0.546103
$723$	−36.9644	−1.37472
$724$	−6.69925	−0.248976
$725$	−7.73433	−0.287246
$726$	−96.7605	−3.59112
$727$	−1.70109	−0.0630898	−0.0315449	−	0.999502i	$-0.510043\pi$
$727$	−1.70109	−0.0630898	−0.0315449	+	0.999502i	$0.510043\pi$
$728$	17.1527	0.635720
$729$	69.8395	2.58665
$730$	6.16187	0.228061
$731$	−4.21750	−0.155990
$732$	−7.79396	−0.288073
$733$	18.6527	0.688955	0.344477	−	0.938795i	$-0.388056\pi$
$733$	18.6527	0.688955	0.344477	+	0.938795i	$0.388056\pi$
$734$	15.8310	0.584332
$735$	−3.29298	−0.121463
$736$	10.9572	0.403886
$737$	55.7166	2.05235
$738$	−39.7159	−1.46196
$739$	−23.6173	−0.868777	−0.434389	−	0.900726i	$-0.643036\pi$
$739$	−23.6173	−0.868777	−0.434389	+	0.900726i	$0.643036\pi$
$740$	2.66070	0.0978093
$741$	−39.9884	−1.46901
$742$	12.0267	0.441515
$743$	−5.26847	−0.193281	−0.0966406	−	0.995319i	$-0.530810\pi$
$743$	−5.26847	−0.193281	−0.0966406	+	0.995319i	$0.530810\pi$
$744$	83.1010	3.04663
$745$	16.5159	0.605095
$746$	15.4884	0.567070
$747$	−19.1658	−0.701240
$748$	9.86722	0.360781
$749$	2.78424	0.101734
$750$	3.34556	0.122163
$751$	−26.6578	−0.972758	−0.486379	−	0.873748i	$-0.661683\pi$
$751$	−26.6578	−0.972758	−0.486379	+	0.873748i	$0.661683\pi$
$752$	−2.11831	−0.0772469
$753$	−58.9188	−2.14712
$754$	−44.7011	−1.62792
$755$	−14.8509	−0.540480
$756$	15.4369	0.561433
$757$	9.05913	0.329260	0.164630	−	0.986355i	$-0.447357\pi$
$757$	9.05913	0.329260	0.164630	+	0.986355i	$0.447357\pi$
$758$	33.5572	1.21885
$759$	46.6722	1.69409
$760$	−6.43643	−0.233474
$761$	−18.8796	−0.684384	−0.342192	−	0.939630i	$-0.611169\pi$
$761$	−18.8796	−0.684384	−0.342192	+	0.939630i	$0.611169\pi$
$762$	−67.2789	−2.43726
$763$	−7.30708	−0.264534
$764$	−16.4141	−0.593843
$765$	−12.6567	−0.457603
$766$	4.30623	0.155591
$767$	−5.16133	−0.186365
$768$	−55.6879	−2.00946
$769$	−43.9318	−1.58422	−0.792110	−	0.610379i	$-0.791017\pi$
$769$	−43.9318	−1.58422	−0.792110	+	0.610379i	$0.791017\pi$
$770$	6.41928	0.231335
$771$	32.9215	1.18564
$772$	−19.3636	−0.696913
$773$	−30.9174	−1.11202	−0.556012	−	0.831174i	$-0.687669\pi$
$773$	−30.9174	−1.11202	−0.556012	+	0.831174i	$0.687669\pi$
$774$	20.8286	0.748667
$775$	8.36953	0.300642
$776$	40.9901	1.47146
$777$	−9.05305	−0.324776
$778$	17.4651	0.626155
$779$	10.6388	0.381174
$780$	−18.1299	−0.649155
$781$	59.8119	2.14024
$782$	3.67739	0.131503
$783$	−123.365	−4.40870
$784$	−1.12772	−0.0402757
$785$	−2.69423	−0.0961614
$786$	56.1280	2.00202
$787$	38.8018	1.38314	0.691568	−	0.722312i	$-0.256920\pi$
$787$	38.8018	1.38314	0.691568	+	0.722312i	$0.256920\pi$
$788$	−9.73630	−0.346841
$789$	−53.5564	−1.90666
$790$	−13.2642	−0.471917
$791$	−9.62182	−0.342113
$792$	−149.432	−5.30984
$793$	−13.9122	−0.494035
$794$	23.6738	0.840151
$795$	−38.9813	−1.38253
$796$	6.56267	0.232608
$797$	−33.5262	−1.18756	−0.593780	−	0.804628i	$-0.702365\pi$
$797$	−33.5262	−1.18756	−0.593780	+	0.804628i	$0.702365\pi$
$798$	7.14165	0.252812
$799$	3.03100	0.107229
$800$	−4.88467	−0.172699
$801$	98.7156	3.48794
$802$	−30.1250	−1.06375
$803$	−38.3212	−1.35233
$804$	28.1034	0.991129
$805$	−2.24317	−0.0790614
$806$	48.3723	1.70384
$807$	−10.8240	−0.381023
$808$	15.7198	0.553020
$809$	10.3643	0.364390	0.182195	−	0.983262i	$-0.441680\pi$
$809$	10.3643	0.364390	0.182195	+	0.983262i	$0.441680\pi$
$810$	29.4557	1.03497
$811$	23.3528	0.820029	0.410015	−	0.912079i	$-0.365524\pi$
$811$	23.3528	0.820029	0.410015	+	0.912079i	$0.365524\pi$
$812$	−7.48537	−0.262685
$813$	84.3021	2.95660
$814$	17.6478	0.618557
$815$	−19.6605	−0.688676
$816$	−5.99223	−0.209770
$817$	−5.57939	−0.195198
$818$	5.67864	0.198549
$819$	44.6209	1.55918
$820$	4.82340	0.168440
$821$	−15.3408	−0.535399	−0.267699	−	0.963502i	$-0.586263\pi$
$821$	−15.3408	−0.535399	−0.267699	+	0.963502i	$0.586263\pi$
$822$	−30.8818	−1.07713
$823$	−27.6997	−0.965549	−0.482775	−	0.875745i	$-0.660371\pi$
$823$	−27.6997	−0.965549	−0.482775	+	0.875745i	$0.660371\pi$
$824$	−29.7812	−1.03748
$825$	−20.8063	−0.724384
$826$	0.921776	0.0320727
$827$	12.0039	0.417415	0.208708	−	0.977978i	$-0.433074\pi$
$827$	12.0039	0.417415	0.208708	+	0.977978i	$0.433074\pi$
$828$	17.0285	0.591780
$829$	−2.56630	−0.0891314	−0.0445657	−	0.999006i	$-0.514190\pi$
$829$	−2.56630	−0.0891314	−0.0445657	+	0.999006i	$0.514190\pi$
$830$	−2.48247	−0.0861679
$831$	−16.7604	−0.581413
$832$	−41.0619	−1.42357
$833$	1.61361	0.0559082
$834$	−51.5671	−1.78562
$835$	8.86477	0.306778
$836$	13.0535	0.451464
$837$	133.496	4.61431
$838$	18.3582	0.634174
$839$	1.41712	0.0489245	0.0244623	−	0.999701i	$-0.492213\pi$
$839$	1.41712	0.0489245	0.0244623	+	0.999701i	$0.492213\pi$
$840$	9.92899	0.342583
$841$	30.8199	1.06275
$842$	−19.5361	−0.673258
$843$	43.2653	1.49014
$844$	6.06771	0.208859
$845$	−19.3617	−0.666064
$846$	−14.9689	−0.514641
$847$	−28.9221	−0.993774
$848$	−13.3496	−0.458428
$849$	−17.4717	−0.599629
$850$	−1.63937	−0.0562300
$851$	−6.16692	−0.211399
$852$	30.1690	1.03357
$853$	−4.92765	−0.168720	−0.0843598	−	0.996435i	$-0.526885\pi$
$853$	−4.92765	−0.168720	−0.0843598	+	0.996435i	$0.526885\pi$
$854$	2.48461	0.0850217
$855$	−16.7437	−0.572623
$856$	−8.39502	−0.286936
$857$	30.7269	1.04961	0.524805	−	0.851223i	$-0.324138\pi$
$857$	30.7269	1.04961	0.524805	+	0.851223i	$0.324138\pi$
$858$	−120.252	−4.10532
$859$	10.5675	0.360557	0.180279	−	0.983616i	$-0.442300\pi$
$859$	10.5675	0.360557	0.180279	+	0.983616i	$0.442300\pi$
$860$	−2.52958	−0.0862578
$861$	−16.4116	−0.559307
$862$	−11.9208	−0.406025
$863$	−47.6106	−1.62068	−0.810342	−	0.585957i	$-0.800719\pi$
$863$	−47.6106	−1.62068	−0.810342	+	0.585957i	$0.800719\pi$
$864$	−77.9118	−2.65061
$865$	5.04724	0.171611
$866$	−7.52835	−0.255824
$867$	−47.4066	−1.61001
$868$	8.10012	0.274936
$869$	82.4909	2.79831
$870$	−25.8757	−0.877267
$871$	50.1643	1.69975
$872$	22.0323	0.746107
$873$	106.631	3.60893
$874$	4.86488	0.164557
$875$	1.00000	0.0338062
$876$	−19.3291	−0.653071
$877$	−16.7822	−0.566694	−0.283347	−	0.959017i	$-0.591445\pi$
$877$	−16.7822	−0.566694	−0.283347	+	0.959017i	$0.591445\pi$
$878$	8.01281	0.270419
$879$	54.5101	1.83858
$880$	−7.12538	−0.240197
$881$	9.77832	0.329440	0.164720	−	0.986340i	$-0.447328\pi$
$881$	9.77832	0.329440	0.164720	+	0.986340i	$0.447328\pi$
$882$	−7.96896	−0.268329
$883$	36.9449	1.24330	0.621648	−	0.783297i	$-0.286464\pi$
$883$	36.9449	1.24330	0.621648	+	0.783297i	$0.286464\pi$
$884$	8.88391	0.298798
$885$	−2.98769	−0.100430
$886$	−38.2009	−1.28338
$887$	−38.1648	−1.28145	−0.640725	−	0.767771i	$-0.721366\pi$
$887$	−38.1648	−1.28145	−0.640725	+	0.767771i	$0.721366\pi$
$888$	27.2967	0.916018
$889$	−20.1099	−0.674465
$890$	12.7863	0.428596
$891$	−183.188	−6.13702
$892$	26.3964	0.883818
$893$	4.00975	0.134181
$894$	55.2549	1.84800
$895$	−16.8738	−0.564030
$896$	−2.43598	−0.0813804
$897$	42.0211	1.40304
$898$	−36.4781	−1.21729
$899$	−64.7327	−2.15896
$900$	−7.59124	−0.253041
$901$	19.1014	0.636360
$902$	31.9925	1.06524
$903$	8.60690	0.286420
$904$	29.0117	0.964915
$905$	−6.92207	−0.230097
$906$	−49.6846	−1.65066
$907$	48.9170	1.62426	0.812131	−	0.583475i	$-0.198307\pi$
$907$	48.9170	1.62426	0.812131	+	0.583475i	$0.198307\pi$
$908$	28.9113	0.959456
$909$	40.8934	1.35635
$910$	5.77957	0.191591
$911$	−5.11665	−0.169522	−0.0847611	−	0.996401i	$-0.527013\pi$
$911$	−5.11665	−0.169522	−0.0847611	+	0.996401i	$0.527013\pi$
$912$	−7.92721	−0.262496
$913$	15.4387	0.510947
$914$	11.9084	0.393896
$915$	−8.05319	−0.266230
$916$	−0.967811	−0.0319774
$917$	16.7769	0.554021
$918$	−26.1484	−0.863027
$919$	−11.9663	−0.394731	−0.197366	−	0.980330i	$-0.563239\pi$
$919$	−11.9663	−0.394731	−0.197366	+	0.980330i	$0.563239\pi$
$920$	6.76361	0.222990
$921$	68.1809	2.24664
$922$	36.5561	1.20391
$923$	53.8514	1.77254
$924$	−20.1366	−0.662445
$925$	2.74919	0.0903930
$926$	3.82589	0.125727
$927$	−77.4727	−2.54454
$928$	37.7797	1.24018
$929$	−42.2904	−1.38750	−0.693751	−	0.720215i	$-0.744043\pi$
$929$	−42.2904	−1.38750	−0.693751	+	0.720215i	$0.744043\pi$
$930$	28.0008	0.918181
$931$	2.13466	0.0699608
$932$	−24.9375	−0.816855
$933$	82.1131	2.68826
$934$	15.7809	0.516366
$935$	10.1954	0.333425
$936$	−134.541	−4.39760
$937$	5.27378	0.172287	0.0861434	−	0.996283i	$-0.472546\pi$
$937$	5.27378	0.172287	0.0861434	+	0.996283i	$0.472546\pi$
$938$	−8.95897	−0.292521
$939$	71.4284	2.33098
$940$	1.81794	0.0592945
$941$	−3.18610	−0.103864	−0.0519319	−	0.998651i	$-0.516538\pi$
$941$	−3.18610	−0.103864	−0.0519319	+	0.998651i	$0.516538\pi$
$942$	−9.01372	−0.293683
$943$	−11.1796	−0.364057
$944$	−1.02317	−0.0333013
$945$	15.9503	0.518863
$946$	−16.7781	−0.545504
$947$	23.0059	0.747592	0.373796	−	0.927511i	$-0.378056\pi$
$947$	23.0059	0.747592	0.373796	+	0.927511i	$0.378056\pi$
$948$	41.6082	1.35137
$949$	−34.5023	−1.11999
$950$	−2.16875	−0.0703635
$951$	30.9728	1.00436
$952$	−4.86534	−0.157687
$953$	−0.254204	−0.00823449	−0.00411725	−	0.999992i	$-0.501311\pi$
$953$	−0.254204	−0.00823449	−0.00411725	+	0.999992i	$0.501311\pi$
$954$	−94.3342	−3.05418
$955$	−16.9601	−0.548815
$956$	−9.79461	−0.316780
$957$	160.923	5.20191
$958$	−44.1034	−1.42492
$959$	−9.23069	−0.298074
$960$	−23.7691	−0.767144
$961$	39.0490	1.25965
$962$	15.8892	0.512287
$963$	−21.8388	−0.703745
$964$	10.8639	0.349902
$965$	−20.0077	−0.644070
$966$	−7.50467	−0.241459
$967$	17.4491	0.561126	0.280563	−	0.959836i	$-0.409479\pi$
$967$	17.4491	0.561126	0.280563	+	0.959836i	$0.409479\pi$
$968$	87.2057	2.80290
$969$	11.3427	0.364380
$970$	13.8116	0.443462
$971$	−46.4827	−1.49170	−0.745851	−	0.666113i	$-0.767957\pi$
$971$	−46.4827	−1.49170	−0.745851	+	0.666113i	$0.767957\pi$
$972$	−46.0890	−1.47830
$973$	−15.4136	−0.494137
$974$	0.783742	0.0251127
$975$	−18.7329	−0.599933
$976$	−2.75791	−0.0882786
$977$	1.25071	0.0400136	0.0200068	−	0.999800i	$-0.493631\pi$
$977$	1.25071	0.0400136	0.0200068	+	0.999800i	$0.493631\pi$
$978$	−65.7753	−2.10326
$979$	−79.5188	−2.54143
$980$	0.967811	0.0309156
$981$	57.3147	1.82992
$982$	−1.27436	−0.0406666
$983$	23.1933	0.739752	0.369876	−	0.929081i	$-0.379400\pi$
$983$	23.1933	0.739752	0.369876	+	0.929081i	$0.379400\pi$
$984$	49.4843	1.57750
$985$	−10.0601	−0.320542
$986$	12.6794	0.403796
$987$	−6.18554	−0.196888
$988$	11.7527	0.373902
$989$	5.86300	0.186433
$990$	−50.3510	−1.60026
$991$	13.4093	0.425960	0.212980	−	0.977057i	$-0.431683\pi$
$991$	13.4093	0.425960	0.212980	+	0.977057i	$0.431683\pi$
$992$	−40.8824	−1.29802
$993$	62.5069	1.98360
$994$	−9.61748	−0.305048
$995$	6.78095	0.214970
$996$	7.78726	0.246749
$997$	12.8080	0.405635	0.202817	−	0.979217i	$-0.434990\pi$
$997$	12.8080	0.405635	0.202817	+	0.979217i	$0.434990\pi$
$998$	−35.0751	−1.11028
$999$	43.8504	1.38737

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8015.2.a.l.1.22	✓	62

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8015.2.a.l.1.22	✓	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)

\(f(q)\)	\(=\)	\(q-1.01597 q^{2} +3.29298 q^{3} -0.967811 q^{4} -1.00000 q^{5} -3.34556 q^{6} -1.00000 q^{7} +3.01520 q^{8} +7.84372 q^{9} +O(q^{10})\)	\(q-1.01597 q^{2} +3.29298 q^{3} -0.967811 q^{4} -1.00000 q^{5} -3.34556 q^{6} -1.00000 q^{7} +3.01520 q^{8} +7.84372 q^{9} +1.01597 q^{10} -6.31839 q^{11} -3.18698 q^{12} -5.68874 q^{13} +1.01597 q^{14} -3.29298 q^{15} -1.12772 q^{16} +1.61361 q^{17} -7.96896 q^{18} +2.13466 q^{19} +0.967811 q^{20} -3.29298 q^{21} +6.41928 q^{22} -2.24317 q^{23} +9.92899 q^{24} +1.00000 q^{25} +5.77957 q^{26} +15.9503 q^{27} +0.967811 q^{28} -7.73433 q^{29} +3.34556 q^{30} +8.36953 q^{31} -4.88467 q^{32} -20.8063 q^{33} -1.63937 q^{34} +1.00000 q^{35} -7.59124 q^{36} +2.74919 q^{37} -2.16875 q^{38} -18.7329 q^{39} -3.01520 q^{40} +4.98382 q^{41} +3.34556 q^{42} -2.61371 q^{43} +6.11501 q^{44} -7.84372 q^{45} +2.27899 q^{46} +1.87840 q^{47} -3.71356 q^{48} +1.00000 q^{49} -1.01597 q^{50} +5.31358 q^{51} +5.50562 q^{52} +11.8377 q^{53} -16.2050 q^{54} +6.31839 q^{55} -3.01520 q^{56} +7.02941 q^{57} +7.85783 q^{58} +0.907289 q^{59} +3.18698 q^{60} +2.44556 q^{61} -8.50317 q^{62} -7.84372 q^{63} +7.21810 q^{64} +5.68874 q^{65} +21.1386 q^{66} -8.81817 q^{67} -1.56167 q^{68} -7.38672 q^{69} -1.01597 q^{70} -9.46632 q^{71} +23.6504 q^{72} +6.06503 q^{73} -2.79309 q^{74} +3.29298 q^{75} -2.06595 q^{76} +6.31839 q^{77} +19.0320 q^{78} -13.0557 q^{79} +1.12772 q^{80} +28.9928 q^{81} -5.06340 q^{82} -2.44346 q^{83} +3.18698 q^{84} -1.61361 q^{85} +2.65544 q^{86} -25.4690 q^{87} -19.0512 q^{88} +12.5853 q^{89} +7.96896 q^{90} +5.68874 q^{91} +2.17097 q^{92} +27.5607 q^{93} -1.90839 q^{94} -2.13466 q^{95} -16.0851 q^{96} +13.5945 q^{97} -1.01597 q^{98} -49.5597 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 62 q + 2 q^{2} + 11 q^{3} + 64 q^{4} - 62 q^{5} + 3 q^{6} - 62 q^{7} + 15 q^{8} + 69 q^{9}+O(q^{10}) \) 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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