LMFDB - Embedded newform 8015.2.a.l.1.58

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			1.58
Character	$\chi$	$=$	8015.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.53639 q^{2} +3.11385 q^{3} +4.43329 q^{4} -1.00000 q^{5} +7.89795 q^{6} -1.00000 q^{7} +6.17179 q^{8} +6.69607 q^{9} +O(q^{10})$	\(q+2.53639 q^{2} +3.11385 q^{3} +4.43329 q^{4} -1.00000 q^{5} +7.89795 q^{6} -1.00000 q^{7} +6.17179 q^{8} +6.69607 q^{9} -2.53639 q^{10} +0.694118 q^{11} +13.8046 q^{12} +6.89482 q^{13} -2.53639 q^{14} -3.11385 q^{15} +6.78751 q^{16} -1.07371 q^{17} +16.9839 q^{18} -6.93839 q^{19} -4.43329 q^{20} -3.11385 q^{21} +1.76056 q^{22} -6.40773 q^{23} +19.2180 q^{24} +1.00000 q^{25} +17.4880 q^{26} +11.5090 q^{27} -4.43329 q^{28} +8.17452 q^{29} -7.89795 q^{30} -3.45726 q^{31} +4.87221 q^{32} +2.16138 q^{33} -2.72336 q^{34} +1.00000 q^{35} +29.6857 q^{36} +3.20904 q^{37} -17.5985 q^{38} +21.4694 q^{39} -6.17179 q^{40} +12.4117 q^{41} -7.89795 q^{42} +3.20569 q^{43} +3.07723 q^{44} -6.69607 q^{45} -16.2525 q^{46} -7.35044 q^{47} +21.1353 q^{48} +1.00000 q^{49} +2.53639 q^{50} -3.34339 q^{51} +30.5667 q^{52} -4.64026 q^{53} +29.1914 q^{54} -0.694118 q^{55} -6.17179 q^{56} -21.6051 q^{57} +20.7338 q^{58} +4.98998 q^{59} -13.8046 q^{60} +8.72134 q^{61} -8.76897 q^{62} -6.69607 q^{63} -1.21717 q^{64} -6.89482 q^{65} +5.48211 q^{66} +1.23346 q^{67} -4.76009 q^{68} -19.9527 q^{69} +2.53639 q^{70} -6.96428 q^{71} +41.3268 q^{72} -0.707397 q^{73} +8.13938 q^{74} +3.11385 q^{75} -30.7599 q^{76} -0.694118 q^{77} +54.4549 q^{78} -10.5072 q^{79} -6.78751 q^{80} +15.7492 q^{81} +31.4809 q^{82} +4.46033 q^{83} -13.8046 q^{84} +1.07371 q^{85} +8.13089 q^{86} +25.4543 q^{87} +4.28395 q^{88} -10.6281 q^{89} -16.9839 q^{90} -6.89482 q^{91} -28.4074 q^{92} -10.7654 q^{93} -18.6436 q^{94} +6.93839 q^{95} +15.1713 q^{96} +16.7029 q^{97} +2.53639 q^{98} +4.64786 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	2.53639	1.79350	0.896751	−	0.442536i	$-0.145921\pi$
$2$	2.53639	1.79350	0.896751	+	0.442536i	$0.145921\pi$
$3$	3.11385	1.79778	0.898892	−	0.438171i	$-0.144374\pi$
$3$	3.11385	1.79778	0.898892	+	0.438171i	$0.144374\pi$
$4$	4.43329	2.21665
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	7.89795	3.22433
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	6.17179	2.18206
$9$	6.69607	2.23202
$10$	−2.53639	−0.802078
$11$	0.694118	0.209284	0.104642	−	0.994510i	$-0.466630\pi$
$11$	0.694118	0.209284	0.104642	+	0.994510i	$0.466630\pi$
$12$	13.8046	3.98505
$13$	6.89482	1.91228	0.956139	−	0.292914i	$-0.0946249\pi$
$13$	6.89482	1.91228	0.956139	+	0.292914i	$0.0946249\pi$
$14$	−2.53639	−0.677880
$15$	−3.11385	−0.803993
$16$	6.78751	1.69688
$17$	−1.07371	−0.260414	−0.130207	−	0.991487i	$-0.541564\pi$
$17$	−1.07371	−0.260414	−0.130207	+	0.991487i	$0.541564\pi$
$18$	16.9839	4.00314
$19$	−6.93839	−1.59178	−0.795888	−	0.605444i	$-0.792996\pi$
$19$	−6.93839	−1.59178	−0.795888	+	0.605444i	$0.792996\pi$
$20$	−4.43329	−0.991315
$21$	−3.11385	−0.679498
$22$	1.76056	0.375352
$23$	−6.40773	−1.33610	−0.668052	−	0.744115i	$-0.732872\pi$
$23$	−6.40773	−1.33610	−0.668052	+	0.744115i	$0.732872\pi$
$24$	19.2180	3.92287
$25$	1.00000	0.200000
$26$	17.4880	3.42967
$27$	11.5090	2.21491
$28$	−4.43329	−0.837814
$29$	8.17452	1.51797	0.758986	−	0.651107i	$-0.225695\pi$
$29$	8.17452	1.51797	0.758986	+	0.651107i	$0.225695\pi$
$30$	−7.89795	−1.44196
$31$	−3.45726	−0.620942	−0.310471	−	0.950583i	$-0.600487\pi$
$31$	−3.45726	−0.620942	−0.310471	+	0.950583i	$0.600487\pi$
$32$	4.87221	0.861294
$33$	2.16138	0.376248
$34$	−2.72336	−0.467053
$35$	1.00000	0.169031
$36$	29.6857	4.94761
$37$	3.20904	0.527562	0.263781	−	0.964583i	$-0.415030\pi$
$37$	3.20904	0.527562	0.263781	+	0.964583i	$0.415030\pi$
$38$	−17.5985	−2.85485
$39$	21.4694	3.43786
$40$	−6.17179	−0.975846
$41$	12.4117	1.93838	0.969189	−	0.246317i	$-0.0792204\pi$
$41$	12.4117	1.93838	0.969189	+	0.246317i	$0.0792204\pi$
$42$	−7.89795	−1.21868
$43$	3.20569	0.488863	0.244431	−	0.969667i	$-0.421399\pi$
$43$	3.20569	0.488863	0.244431	+	0.969667i	$0.421399\pi$
$44$	3.07723	0.463909
$45$	−6.69607	−0.998192
$46$	−16.2525	−2.39630
$47$	−7.35044	−1.07217	−0.536086	−	0.844163i	$-0.680098\pi$
$47$	−7.35044	−1.07217	−0.536086	+	0.844163i	$0.680098\pi$
$48$	21.1353	3.05062
$49$	1.00000	0.142857
$50$	2.53639	0.358700
$51$	−3.34339	−0.468168
$52$	30.5667	4.23885
$53$	−4.64026	−0.637388	−0.318694	−	0.947858i	$-0.603244\pi$
$53$	−4.64026	−0.637388	−0.318694	+	0.947858i	$0.603244\pi$
$54$	29.1914	3.97245
$55$	−0.694118	−0.0935948
$56$	−6.17179	−0.824741
$57$	−21.6051	−2.86167
$58$	20.7338	2.72248
$59$	4.98998	0.649640	0.324820	−	0.945776i	$-0.394696\pi$
$59$	4.98998	0.649640	0.324820	+	0.945776i	$0.394696\pi$
$60$	−13.8046	−1.78217
$61$	8.72134	1.11665	0.558326	−	0.829621i	$-0.311444\pi$
$61$	8.72134	1.11665	0.558326	+	0.829621i	$0.311444\pi$
$62$	−8.76897	−1.11366
$63$	−6.69607	−0.843626
$64$	−1.21717	−0.152146
$65$	−6.89482	−0.855197
$66$	5.48211	0.674801
$67$	1.23346	0.150692	0.0753458	−	0.997157i	$-0.475994\pi$
$67$	1.23346	0.150692	0.0753458	+	0.997157i	$0.475994\pi$
$68$	−4.76009	−0.577246
$69$	−19.9527	−2.40203
$70$	2.53639	0.303157
$71$	−6.96428	−0.826508	−0.413254	−	0.910616i	$-0.635608\pi$
$71$	−6.96428	−0.826508	−0.413254	+	0.910616i	$0.635608\pi$
$72$	41.3268	4.87041
$73$	−0.707397	−0.0827946	−0.0413973	−	0.999143i	$-0.513181\pi$
$73$	−0.707397	−0.0827946	−0.0413973	+	0.999143i	$0.513181\pi$
$74$	8.13938	0.946184
$75$	3.11385	0.359557
$76$	−30.7599	−3.52841
$77$	−0.694118	−0.0791020
$78$	54.4549	6.16581
$79$	−10.5072	−1.18215	−0.591075	−	0.806616i	$-0.701296\pi$
$79$	−10.5072	−1.18215	−0.591075	+	0.806616i	$0.701296\pi$
$80$	−6.78751	−0.758867
$81$	15.7492	1.74991
$82$	31.4809	3.47648
$83$	4.46033	0.489584	0.244792	−	0.969576i	$-0.421280\pi$
$83$	4.46033	0.489584	0.244792	+	0.969576i	$0.421280\pi$
$84$	−13.8046	−1.50621
$85$	1.07371	0.116461
$86$	8.13089	0.876776
$87$	25.4543	2.72898
$88$	4.28395	0.456671
$89$	−10.6281	−1.12657	−0.563287	−	0.826261i	$-0.690464\pi$
$89$	−10.6281	−1.12657	−0.563287	+	0.826261i	$0.690464\pi$
$90$	−16.9839	−1.79026
$91$	−6.89482	−0.722773
$92$	−28.4074	−2.96167
$93$	−10.7654	−1.11632
$94$	−18.6436	−1.92294
$95$	6.93839	0.711864
$96$	15.1713	1.54842
$97$	16.7029	1.69592	0.847961	−	0.530059i	$-0.177830\pi$
$97$	16.7029	1.69592	0.847961	+	0.530059i	$0.177830\pi$
$98$	2.53639	0.256214
$99$	4.64786	0.467128
$100$	4.43329	0.443329
$101$	−19.0840	−1.89893	−0.949465	−	0.313874i	$-0.898373\pi$
$101$	−19.0840	−1.89893	−0.949465	+	0.313874i	$0.898373\pi$
$102$	−8.48015	−0.839660
$103$	−3.71668	−0.366215	−0.183108	−	0.983093i	$-0.558616\pi$
$103$	−3.71668	−0.366215	−0.183108	+	0.983093i	$0.558616\pi$
$104$	42.5534	4.17270
$105$	3.11385	0.303881
$106$	−11.7695	−1.14316
$107$	−13.6558	−1.32015	−0.660077	−	0.751198i	$-0.729476\pi$
$107$	−13.6558	−1.32015	−0.660077	+	0.751198i	$0.729476\pi$
$108$	51.0229	4.90968
$109$	0.0225205	0.00215707	0.00107853	−	0.999999i	$-0.499657\pi$
$109$	0.0225205	0.00215707	0.00107853	+	0.999999i	$0.499657\pi$
$110$	−1.76056	−0.167862
$111$	9.99246	0.948443
$112$	−6.78751	−0.641359
$113$	−9.15269	−0.861013	−0.430506	−	0.902588i	$-0.641665\pi$
$113$	−9.15269	−0.861013	−0.430506	+	0.902588i	$0.641665\pi$
$114$	−54.7991	−5.13241
$115$	6.40773	0.597524
$116$	36.2401	3.36481
$117$	46.1682	4.26825
$118$	12.6566	1.16513
$119$	1.07371	0.0984272
$120$	−19.2180	−1.75436
$121$	−10.5182	−0.956200
$122$	22.1207	2.00272
$123$	38.6481	3.48478
$124$	−15.3270	−1.37641
$125$	−1.00000	−0.0894427
$126$	−16.9839	−1.51304
$127$	7.14187	0.633738	0.316869	−	0.948469i	$-0.397368\pi$
$127$	7.14187	0.633738	0.316869	+	0.948469i	$0.397368\pi$
$128$	−12.8316	−1.13417
$129$	9.98204	0.878869
$130$	−17.4880	−1.53380
$131$	−2.62484	−0.229333	−0.114667	−	0.993404i	$-0.536580\pi$
$131$	−2.62484	−0.229333	−0.114667	+	0.993404i	$0.536580\pi$
$132$	9.58203	0.834009
$133$	6.93839	0.601635
$134$	3.12855	0.270265
$135$	−11.5090	−0.990539
$136$	−6.62674	−0.568238
$137$	−3.40028	−0.290506	−0.145253	−	0.989395i	$-0.546400\pi$
$137$	−3.40028	−0.290506	−0.145253	+	0.989395i	$0.546400\pi$
$138$	−50.6080	−4.30804
$139$	15.1275	1.28310	0.641548	−	0.767083i	$-0.278292\pi$
$139$	15.1275	1.28310	0.641548	+	0.767083i	$0.278292\pi$
$140$	4.43329	0.374682
$141$	−22.8882	−1.92753
$142$	−17.6642	−1.48234
$143$	4.78581	0.400210
$144$	45.4497	3.78747
$145$	−8.17452	−0.678857
$146$	−1.79424	−0.148492
$147$	3.11385	0.256826
$148$	14.2266	1.16942
$149$	2.39105	0.195883	0.0979414	−	0.995192i	$-0.468774\pi$
$149$	2.39105	0.195883	0.0979414	+	0.995192i	$0.468774\pi$
$150$	7.89795	0.644865
$151$	13.7810	1.12148	0.560742	−	0.827991i	$-0.310516\pi$
$151$	13.7810	1.12148	0.560742	+	0.827991i	$0.310516\pi$
$152$	−42.8223	−3.47335
$153$	−7.18967	−0.581250
$154$	−1.76056	−0.141870
$155$	3.45726	0.277694
$156$	95.1803	7.62052
$157$	−14.4724	−1.15503	−0.577513	−	0.816382i	$-0.695977\pi$
$157$	−14.4724	−1.15503	−0.577513	+	0.816382i	$0.695977\pi$
$158$	−26.6504	−2.12019
$159$	−14.4491	−1.14589
$160$	−4.87221	−0.385182
$161$	6.40773	0.505000
$162$	39.9461	3.13846
$163$	−11.3530	−0.889236	−0.444618	−	0.895720i	$-0.646661\pi$
$163$	−11.3530	−0.889236	−0.444618	+	0.895720i	$0.646661\pi$
$164$	55.0246	4.29670
$165$	−2.16138	−0.168263
$166$	11.3131	0.878070
$167$	−23.9335	−1.85203	−0.926014	−	0.377489i	$-0.876788\pi$
$167$	−23.9335	−1.85203	−0.926014	+	0.377489i	$0.876788\pi$
$168$	−19.2180	−1.48270
$169$	34.5385	2.65681
$170$	2.72336	0.208872
$171$	−46.4600	−3.55288
$172$	14.2118	1.08364
$173$	22.1259	1.68220	0.841101	−	0.540879i	$-0.181908\pi$
$173$	22.1259	1.68220	0.841101	+	0.540879i	$0.181908\pi$
$174$	64.5620	4.89443
$175$	−1.00000	−0.0755929
$176$	4.71133	0.355130
$177$	15.5381	1.16791
$178$	−26.9570	−2.02051
$179$	−13.2390	−0.989526	−0.494763	−	0.869028i	$-0.664745\pi$
$179$	−13.2390	−0.989526	−0.494763	+	0.869028i	$0.664745\pi$
$180$	−29.6857	−2.21264
$181$	−24.5051	−1.82145	−0.910724	−	0.413015i	$-0.864476\pi$
$181$	−24.5051	−1.82145	−0.910724	+	0.413015i	$0.864476\pi$
$182$	−17.4880	−1.29629
$183$	27.1569	2.00750
$184$	−39.5472	−2.91546
$185$	−3.20904	−0.235933
$186$	−27.3053	−2.00212
$187$	−0.745284	−0.0545006
$188$	−32.5867	−2.37663
$189$	−11.5090	−0.837158
$190$	17.5985	1.27673
$191$	−6.29692	−0.455629	−0.227814	−	0.973705i	$-0.573158\pi$
$191$	−6.29692	−0.455629	−0.227814	+	0.973705i	$0.573158\pi$
$192$	−3.79008	−0.273526
$193$	9.76342	0.702787	0.351393	−	0.936228i	$-0.385708\pi$
$193$	9.76342	0.702787	0.351393	+	0.936228i	$0.385708\pi$
$194$	42.3651	3.04164
$195$	−21.4694	−1.53746
$196$	4.43329	0.316664
$197$	9.83007	0.700364	0.350182	−	0.936682i	$-0.386120\pi$
$197$	9.83007	0.700364	0.350182	+	0.936682i	$0.386120\pi$
$198$	11.7888	0.837794
$199$	11.5793	0.820836	0.410418	−	0.911898i	$-0.365383\pi$
$199$	11.5793	0.820836	0.410418	+	0.911898i	$0.365383\pi$
$200$	6.17179	0.436412
$201$	3.84082	0.270911
$202$	−48.4045	−3.40573
$203$	−8.17452	−0.573739
$204$	−14.8222	−1.03776
$205$	−12.4117	−0.866869
$206$	−9.42696	−0.656807
$207$	−42.9066	−2.98222
$208$	46.7986	3.24490
$209$	−4.81606	−0.333134
$210$	7.89795	0.545011
$211$	−28.9280	−1.99149	−0.995744	−	0.0921609i	$-0.970623\pi$
$211$	−28.9280	−1.99149	−0.995744	+	0.0921609i	$0.970623\pi$
$212$	−20.5716	−1.41286
$213$	−21.6857	−1.48588
$214$	−34.6364	−2.36770
$215$	−3.20569	−0.218626
$216$	71.0313	4.83307
$217$	3.45726	0.234694
$218$	0.0571207	0.00386870
$219$	−2.20273	−0.148847
$220$	−3.07723	−0.207467
$221$	−7.40306	−0.497984
$222$	25.3448	1.70103
$223$	−16.2888	−1.09078	−0.545389	−	0.838183i	$-0.683618\pi$
$223$	−16.2888	−1.09078	−0.545389	+	0.838183i	$0.683618\pi$
$224$	−4.87221	−0.325538
$225$	6.69607	0.446405
$226$	−23.2148	−1.54423
$227$	9.63959	0.639802	0.319901	−	0.947451i	$-0.396350\pi$
$227$	9.63959	0.639802	0.319901	+	0.947451i	$0.396350\pi$
$228$	−95.7819	−6.34331
$229$	1.00000	0.0660819
$229$	1.00000	0.0660819
$230$	16.2525	1.07166
$231$	−2.16138	−0.142208
$232$	50.4515	3.31230
$233$	8.65226	0.566829	0.283414	−	0.958998i	$-0.408533\pi$
$233$	8.65226	0.566829	0.283414	+	0.958998i	$0.408533\pi$
$234$	117.101	7.65511
$235$	7.35044	0.479490
$236$	22.1221	1.44002
$237$	−32.7178	−2.12525
$238$	2.72336	0.176529
$239$	20.5627	1.33009	0.665046	−	0.746803i	$-0.268412\pi$
$239$	20.5627	1.33009	0.665046	+	0.746803i	$0.268412\pi$
$240$	−21.1353	−1.36428
$241$	0.271703	0.0175019	0.00875096	−	0.999962i	$-0.497214\pi$
$241$	0.271703	0.0175019	0.00875096	+	0.999962i	$0.497214\pi$
$242$	−26.6783	−1.71495
$243$	14.5135	0.931042
$244$	38.6643	2.47523
$245$	−1.00000	−0.0638877
$246$	98.0269	6.24997
$247$	−47.8389	−3.04392
$248$	−21.3375	−1.35493
$249$	13.8888	0.880167
$250$	−2.53639	−0.160416
$251$	−9.97546	−0.629646	−0.314823	−	0.949150i	$-0.601945\pi$
$251$	−9.97546	−0.629646	−0.314823	+	0.949150i	$0.601945\pi$
$252$	−29.6857	−1.87002
$253$	−4.44772	−0.279626
$254$	18.1146	1.13661
$255$	3.34339	0.209371
$256$	−30.1118	−1.88199
$257$	4.57395	0.285315	0.142657	−	0.989772i	$-0.454435\pi$
$257$	4.57395	0.285315	0.142657	+	0.989772i	$0.454435\pi$
$258$	25.3184	1.57625
$259$	−3.20904	−0.199400
$260$	−30.5667	−1.89567
$261$	54.7372	3.38815
$262$	−6.65763	−0.411310
$263$	−4.40317	−0.271511	−0.135755	−	0.990742i	$-0.543346\pi$
$263$	−4.40317	−0.271511	−0.135755	+	0.990742i	$0.543346\pi$
$264$	13.3396	0.820995
$265$	4.64026	0.285049
$266$	17.5985	1.07903
$267$	−33.0943	−2.02534
$268$	5.46831	0.334030
$269$	29.2799	1.78523	0.892613	−	0.450824i	$-0.148870\pi$
$269$	29.2799	1.78523	0.892613	+	0.450824i	$0.148870\pi$
$270$	−29.1914	−1.77653
$271$	−14.4079	−0.875219	−0.437610	−	0.899165i	$-0.644175\pi$
$271$	−14.4079	−0.875219	−0.437610	+	0.899165i	$0.644175\pi$
$272$	−7.28785	−0.441891
$273$	−21.4694	−1.29939
$274$	−8.62446	−0.521023
$275$	0.694118	0.0418569
$276$	−88.4563	−5.32444
$277$	16.4969	0.991202	0.495601	−	0.868550i	$-0.334948\pi$
$277$	16.4969	0.991202	0.495601	+	0.868550i	$0.334948\pi$
$278$	38.3693	2.30124
$279$	−23.1501	−1.38596
$280$	6.17179	0.368835
$281$	−19.2992	−1.15129	−0.575647	−	0.817698i	$-0.695250\pi$
$281$	−19.2992	−1.15129	−0.575647	+	0.817698i	$0.695250\pi$
$282$	−58.0535	−3.45703
$283$	4.38026	0.260380	0.130190	−	0.991489i	$-0.458441\pi$
$283$	4.38026	0.260380	0.130190	+	0.991489i	$0.458441\pi$
$284$	−30.8747	−1.83208
$285$	21.6051	1.27978
$286$	12.1387	0.717777
$287$	−12.4117	−0.732638
$288$	32.6247	1.92243
$289$	−15.8471	−0.932185
$290$	−20.7338	−1.21753
$291$	52.0103	3.04890
$292$	−3.13610	−0.183526
$293$	−9.28530	−0.542453	−0.271227	−	0.962516i	$-0.587429\pi$
$293$	−9.28530	−0.542453	−0.271227	+	0.962516i	$0.587429\pi$
$294$	7.89795	0.460618
$295$	−4.98998	−0.290528
$296$	19.8055	1.15117
$297$	7.98861	0.463546
$298$	6.06466	0.351316
$299$	−44.1801	−2.55500
$300$	13.8046	0.797010
$301$	−3.20569	−0.184773
$302$	34.9541	2.01138
$303$	−59.4248	−3.41386
$304$	−47.0944	−2.70105
$305$	−8.72134	−0.499382
$306$	−18.2358	−1.04247
$307$	11.9072	0.679580	0.339790	−	0.940501i	$-0.389644\pi$
$307$	11.9072	0.679580	0.339790	+	0.940501i	$0.389644\pi$
$308$	−3.07723	−0.175341
$309$	−11.5732	−0.658375
$310$	8.76897	0.498044
$311$	9.34999	0.530189	0.265095	−	0.964222i	$-0.414597\pi$
$311$	9.34999	0.530189	0.265095	+	0.964222i	$0.414597\pi$
$312$	132.505	7.50161
$313$	−3.30987	−0.187085	−0.0935423	−	0.995615i	$-0.529819\pi$
$313$	−3.30987	−0.187085	−0.0935423	+	0.995615i	$0.529819\pi$
$314$	−36.7078	−2.07154
$315$	6.69607	0.377281
$316$	−46.5814	−2.62041
$317$	−0.410312	−0.0230454	−0.0115227	−	0.999934i	$-0.503668\pi$
$317$	−0.410312	−0.0230454	−0.0115227	+	0.999934i	$0.503668\pi$
$318$	−36.6485	−2.05515
$319$	5.67408	0.317688
$320$	1.21717	0.0680418
$321$	−42.5221	−2.37335
$322$	16.2525	0.905718
$323$	7.44985	0.414521
$324$	69.8207	3.87893
$325$	6.89482	0.382456
$326$	−28.7957	−1.59485
$327$	0.0701253	0.00387794
$328$	76.6023	4.22966
$329$	7.35044	0.405243
$330$	−5.48211	−0.301780
$331$	3.36690	0.185061	0.0925307	−	0.995710i	$-0.470504\pi$
$331$	3.36690	0.185061	0.0925307	+	0.995710i	$0.470504\pi$
$332$	19.7739	1.08524
$333$	21.4879	1.17753
$334$	−60.7047	−3.32162
$335$	−1.23346	−0.0673913
$336$	−21.1353	−1.15303
$337$	−18.9603	−1.03283	−0.516415	−	0.856338i	$-0.672734\pi$
$337$	−18.9603	−1.03283	−0.516415	+	0.856338i	$0.672734\pi$
$338$	87.6032	4.76499
$339$	−28.5001	−1.54791
$340$	4.76009	0.258152
$341$	−2.39974	−0.129953
$342$	−117.841	−6.37210
$343$	−1.00000	−0.0539949
$344$	19.7848	1.06673
$345$	19.9527	1.07422
$346$	56.1200	3.01703
$347$	2.04321	0.109685	0.0548427	−	0.998495i	$-0.482534\pi$
$347$	2.04321	0.109685	0.0548427	+	0.998495i	$0.482534\pi$
$348$	112.846	6.04919
$349$	−17.4134	−0.932116	−0.466058	−	0.884754i	$-0.654326\pi$
$349$	−17.4134	−0.932116	−0.466058	+	0.884754i	$0.654326\pi$
$350$	−2.53639	−0.135576
$351$	79.3526	4.23553
$352$	3.38189	0.180255
$353$	16.3755	0.871578	0.435789	−	0.900049i	$-0.356469\pi$
$353$	16.3755	0.871578	0.435789	+	0.900049i	$0.356469\pi$
$354$	39.4107	2.09465
$355$	6.96428	0.369626
$356$	−47.1174	−2.49722
$357$	3.34339	0.176951
$358$	−33.5792	−1.77472
$359$	18.7159	0.987789	0.493894	−	0.869522i	$-0.335573\pi$
$359$	18.7159	0.987789	0.493894	+	0.869522i	$0.335573\pi$
$360$	−41.3268	−2.17811
$361$	29.1413	1.53375
$362$	−62.1546	−3.26677
$363$	−32.7521	−1.71904
$364$	−30.5667	−1.60213
$365$	0.707397	0.0370269
$366$	68.8807	3.60045
$367$	7.13403	0.372394	0.186197	−	0.982512i	$-0.440384\pi$
$367$	7.13403	0.372394	0.186197	+	0.982512i	$0.440384\pi$
$368$	−43.4925	−2.26720
$369$	83.1095	4.32651
$370$	−8.13938	−0.423146
$371$	4.64026	0.240910
$372$	−47.7262	−2.47449
$373$	−10.4582	−0.541504	−0.270752	−	0.962649i	$-0.587272\pi$
$373$	−10.4582	−0.541504	−0.270752	+	0.962649i	$0.587272\pi$
$374$	−1.89033	−0.0977468
$375$	−3.11385	−0.160799
$376$	−45.3654	−2.33954
$377$	56.3618	2.90278
$378$	−29.1914	−1.50144
$379$	−10.0073	−0.514042	−0.257021	−	0.966406i	$-0.582741\pi$
$379$	−10.0073	−0.514042	−0.257021	+	0.966406i	$0.582741\pi$
$380$	30.7599	1.57795
$381$	22.2387	1.13932
$382$	−15.9715	−0.817171
$383$	−12.0370	−0.615061	−0.307531	−	0.951538i	$-0.599503\pi$
$383$	−12.0370	−0.615061	−0.307531	+	0.951538i	$0.599503\pi$
$384$	−39.9558	−2.03899
$385$	0.694118	0.0353755
$386$	24.7639	1.26045
$387$	21.4655	1.09115
$388$	74.0488	3.75926
$389$	6.24817	0.316795	0.158397	−	0.987375i	$-0.449367\pi$
$389$	6.24817	0.316795	0.158397	+	0.987375i	$0.449367\pi$
$390$	−54.4549	−2.75743
$391$	6.88007	0.347940
$392$	6.17179	0.311723
$393$	−8.17336	−0.412292
$394$	24.9329	1.25610
$395$	10.5072	0.528674
$396$	20.6053	1.03546
$397$	23.2972	1.16925	0.584626	−	0.811303i	$-0.301241\pi$
$397$	23.2972	1.16925	0.584626	+	0.811303i	$0.301241\pi$
$398$	29.3697	1.47217
$399$	21.6051	1.08161
$400$	6.78751	0.339375
$401$	−12.8957	−0.643980	−0.321990	−	0.946743i	$-0.604352\pi$
$401$	−12.8957	−0.643980	−0.321990	+	0.946743i	$0.604352\pi$
$402$	9.74184	0.485879
$403$	−23.8372	−1.18741
$404$	−84.6050	−4.20926
$405$	−15.7492	−0.782583
$406$	−20.7338	−1.02900
$407$	2.22745	0.110411
$408$	−20.6347	−1.02157
$409$	12.4018	0.613230	0.306615	−	0.951834i	$-0.400804\pi$
$409$	12.4018	0.613230	0.306615	+	0.951834i	$0.400804\pi$
$410$	−31.4809	−1.55473
$411$	−10.5880	−0.522267
$412$	−16.4771	−0.811770
$413$	−4.98998	−0.245541
$414$	−108.828	−5.34861
$415$	−4.46033	−0.218949
$416$	33.5930	1.64703
$417$	47.1048	2.30673
$418$	−12.2154	−0.597476
$419$	25.4805	1.24481	0.622403	−	0.782697i	$-0.286156\pi$
$419$	25.4805	1.24481	0.622403	+	0.782697i	$0.286156\pi$
$420$	13.8046	0.673597
$421$	15.8522	0.772591	0.386296	−	0.922375i	$-0.373754\pi$
$421$	15.8522	0.772591	0.386296	+	0.922375i	$0.373754\pi$
$422$	−73.3729	−3.57174
$423$	−49.2191	−2.39311
$424$	−28.6387	−1.39082
$425$	−1.07371	−0.0520828
$426$	−55.0036	−2.66493
$427$	−8.72134	−0.422055
$428$	−60.5401	−2.92631
$429$	14.9023	0.719490
$430$	−8.13089	−0.392106
$431$	27.1499	1.30776	0.653881	−	0.756597i	$-0.273140\pi$
$431$	27.1499	1.30776	0.653881	+	0.756597i	$0.273140\pi$
$432$	78.1176	3.75843
$433$	37.4869	1.80150	0.900752	−	0.434335i	$-0.143016\pi$
$433$	37.4869	1.80150	0.900752	+	0.434335i	$0.143016\pi$
$434$	8.76897	0.420924
$435$	−25.4543	−1.22044
$436$	0.0998398	0.00478146
$437$	44.4593	2.12678
$438$	−5.58699	−0.266957
$439$	27.6510	1.31971	0.659855	−	0.751393i	$-0.270618\pi$
$439$	27.6510	1.31971	0.659855	+	0.751393i	$0.270618\pi$
$440$	−4.28395	−0.204229
$441$	6.69607	0.318861
$442$	−18.7771	−0.893135
$443$	16.4609	0.782080	0.391040	−	0.920374i	$-0.372115\pi$
$443$	16.4609	0.782080	0.391040	+	0.920374i	$0.372115\pi$
$444$	44.2995	2.10236
$445$	10.6281	0.503819
$446$	−41.3148	−1.95631
$447$	7.44539	0.352155
$448$	1.21717	0.0575058
$449$	−33.9770	−1.60347	−0.801737	−	0.597677i	$-0.796091\pi$
$449$	−33.9770	−1.60347	−0.801737	+	0.597677i	$0.796091\pi$
$450$	16.9839	0.800628
$451$	8.61516	0.405672
$452$	−40.5766	−1.90856
$453$	42.9121	2.01619
$454$	24.4498	1.14749
$455$	6.89482	0.323234
$456$	−133.342	−6.24433
$457$	8.90711	0.416657	0.208328	−	0.978059i	$-0.433198\pi$
$457$	8.90711	0.416657	0.208328	+	0.978059i	$0.433198\pi$
$458$	2.53639	0.118518
$459$	−12.3574	−0.576794
$460$	28.4074	1.32450
$461$	0.253730	0.0118174	0.00590870	−	0.999983i	$-0.498119\pi$
$461$	0.253730	0.0118174	0.00590870	+	0.999983i	$0.498119\pi$
$462$	−5.48211	−0.255051
$463$	−22.3456	−1.03849	−0.519244	−	0.854626i	$-0.673786\pi$
$463$	−22.3456	−1.03849	−0.519244	+	0.854626i	$0.673786\pi$
$464$	55.4847	2.57581
$465$	10.7654	0.499233
$466$	21.9456	1.01661
$467$	35.9456	1.66337	0.831683	−	0.555251i	$-0.187378\pi$
$467$	35.9456	1.66337	0.831683	+	0.555251i	$0.187378\pi$
$468$	204.677	9.46120
$469$	−1.23346	−0.0569560
$470$	18.6436	0.859966
$471$	−45.0650	−2.07649
$472$	30.7971	1.41755
$473$	2.22512	0.102311
$474$	−82.9853	−3.81164
$475$	−6.93839	−0.318355
$476$	4.76009	0.218178
$477$	−31.0715	−1.42267
$478$	52.1552	2.38552
$479$	−14.2792	−0.652434	−0.326217	−	0.945295i	$-0.605774\pi$
$479$	−14.2792	−0.652434	−0.326217	+	0.945295i	$0.605774\pi$
$480$	−15.1713	−0.692474
$481$	22.1257	1.00885
$482$	0.689145	0.0313897
$483$	19.9527	0.907880
$484$	−46.6303	−2.11956
$485$	−16.7029	−0.758439
$486$	36.8120	1.66983
$487$	−2.74442	−0.124361	−0.0621807	−	0.998065i	$-0.519805\pi$
$487$	−2.74442	−0.124361	−0.0621807	+	0.998065i	$0.519805\pi$
$488$	53.8263	2.43660
$489$	−35.3516	−1.59865
$490$	−2.53639	−0.114583
$491$	−9.75967	−0.440448	−0.220224	−	0.975449i	$-0.570679\pi$
$491$	−9.75967	−0.440448	−0.220224	+	0.975449i	$0.570679\pi$
$492$	171.339	7.72454
$493$	−8.77710	−0.395301
$494$	−121.338	−5.45927
$495$	−4.64786	−0.208906
$496$	−23.4662	−1.05366
$497$	6.96428	0.312391
$498$	35.2275	1.57858
$499$	−13.3965	−0.599709	−0.299854	−	0.953985i	$-0.596938\pi$
$499$	−13.3965	−0.599709	−0.299854	+	0.953985i	$0.596938\pi$
$500$	−4.43329	−0.198263
$501$	−74.5253	−3.32955
$502$	−25.3017	−1.12927
$503$	−38.5846	−1.72040	−0.860201	−	0.509954i	$-0.829662\pi$
$503$	−38.5846	−1.72040	−0.860201	+	0.509954i	$0.829662\pi$
$504$	−41.3268	−1.84084
$505$	19.0840	0.849227
$506$	−11.2812	−0.501509
$507$	107.548	4.77636
$508$	31.6620	1.40477
$509$	22.6354	1.00329	0.501647	−	0.865072i	$-0.332728\pi$
$509$	22.6354	1.00329	0.501647	+	0.865072i	$0.332728\pi$
$510$	8.48015	0.375507
$511$	0.707397	0.0312934
$512$	−50.7120	−2.24118
$513$	−79.8541	−3.52564
$514$	11.6013	0.511713
$515$	3.71668	0.163776
$516$	44.2533	1.94814
$517$	−5.10207	−0.224389
$518$	−8.13938	−0.357624
$519$	68.8968	3.02423
$520$	−42.5534	−1.86609
$521$	13.9472	0.611037	0.305518	−	0.952186i	$-0.401170\pi$
$521$	13.9472	0.611037	0.305518	+	0.952186i	$0.401170\pi$
$522$	138.835	6.07665
$523$	5.46489	0.238963	0.119482	−	0.992836i	$-0.461877\pi$
$523$	5.46489	0.238963	0.119482	+	0.992836i	$0.461877\pi$
$524$	−11.6367	−0.508351
$525$	−3.11385	−0.135900
$526$	−11.1682	−0.486955
$527$	3.71211	0.161702
$528$	14.6704	0.638446
$529$	18.0590	0.785174
$530$	11.7695	0.511235
$531$	33.4133	1.45001
$532$	30.7599	1.33361
$533$	85.5762	3.70672
$534$	−83.9401	−3.63244
$535$	13.6558	0.590391
$536$	7.61268	0.328818
$537$	−41.2242	−1.77895
$538$	74.2653	3.20181
$539$	0.694118	0.0298978
$540$	−51.0229	−2.19568
$541$	12.4275	0.534300	0.267150	−	0.963655i	$-0.413918\pi$
$541$	12.4275	0.534300	0.267150	+	0.963655i	$0.413918\pi$
$542$	−36.5442	−1.56971
$543$	−76.3052	−3.27457
$544$	−5.23136	−0.224293
$545$	−0.0225205	−0.000964670 0
$546$	−54.4549	−2.33046
$547$	−26.3836	−1.12808	−0.564040	−	0.825748i	$-0.690754\pi$
$547$	−26.3836	−1.12808	−0.564040	+	0.825748i	$0.690754\pi$
$548$	−15.0745	−0.643949
$549$	58.3987	2.49240
$550$	1.76056	0.0750703
$551$	−56.7180	−2.41627
$552$	−123.144	−5.24136
$553$	10.5072	0.446811
$554$	41.8426	1.77772
$555$	−9.99246	−0.424156
$556$	67.0646	2.84417
$557$	−35.8380	−1.51850	−0.759252	−	0.650797i	$-0.774435\pi$
$557$	−35.8380	−1.51850	−0.759252	+	0.650797i	$0.774435\pi$
$558$	−58.7177	−2.48572
$559$	22.1026	0.934841
$560$	6.78751	0.286825
$561$	−2.32070	−0.0979802
$562$	−48.9504	−2.06485
$563$	28.7783	1.21286	0.606430	−	0.795137i	$-0.292601\pi$
$563$	28.7783	1.21286	0.606430	+	0.795137i	$0.292601\pi$
$564$	−101.470	−4.27266
$565$	9.15269	0.385057
$566$	11.1101	0.466991
$567$	−15.7492	−0.661403
$568$	−42.9821	−1.80349
$569$	19.2339	0.806327	0.403164	−	0.915128i	$-0.367911\pi$
$569$	19.2339	0.806327	0.403164	+	0.915128i	$0.367911\pi$
$570$	54.7991	2.29528
$571$	4.18337	0.175068	0.0875342	−	0.996162i	$-0.472101\pi$
$571$	4.18337	0.175068	0.0875342	+	0.996162i	$0.472101\pi$
$572$	21.2169	0.887124
$573$	−19.6077	−0.819122
$574$	−31.4809	−1.31399
$575$	−6.40773	−0.267221
$576$	−8.15025	−0.339594
$577$	23.3122	0.970501	0.485251	−	0.874375i	$-0.338728\pi$
$577$	23.3122	0.970501	0.485251	+	0.874375i	$0.338728\pi$
$578$	−40.1946	−1.67187
$579$	30.4019	1.26346
$580$	−36.2401	−1.50479
$581$	−4.46033	−0.185046
$582$	131.919	5.46820
$583$	−3.22088	−0.133395
$584$	−4.36591	−0.180663
$585$	−46.1682	−1.90882
$586$	−23.5512	−0.972891
$587$	7.83786	0.323503	0.161752	−	0.986832i	$-0.448286\pi$
$587$	7.83786	0.323503	0.161752	+	0.986832i	$0.448286\pi$
$588$	13.8046	0.569293
$589$	23.9878	0.988401
$590$	−12.6566	−0.521062
$591$	30.6094	1.25910
$592$	21.7814	0.895209
$593$	−34.7711	−1.42788	−0.713939	−	0.700208i	$-0.753091\pi$
$593$	−34.7711	−1.42788	−0.713939	+	0.700208i	$0.753091\pi$
$594$	20.2623	0.831371
$595$	−1.07371	−0.0440180
$596$	10.6002	0.434203
$597$	36.0563	1.47569
$598$	−112.058	−4.58240
$599$	−45.6310	−1.86443	−0.932217	−	0.361900i	$-0.882128\pi$
$599$	−45.6310	−1.86443	−0.932217	+	0.361900i	$0.882128\pi$
$600$	19.2180	0.784574
$601$	−31.1708	−1.27148	−0.635742	−	0.771902i	$-0.719306\pi$
$601$	−31.1708	−1.27148	−0.635742	+	0.771902i	$0.719306\pi$
$602$	−8.13089	−0.331390
$603$	8.25936	0.336347
$604$	61.0954	2.48593
$605$	10.5182	0.427626
$606$	−150.725	−6.12277
$607$	−22.3766	−0.908237	−0.454119	−	0.890941i	$-0.650046\pi$
$607$	−22.3766	−0.908237	−0.454119	+	0.890941i	$0.650046\pi$
$608$	−33.8053	−1.37099
$609$	−25.4543	−1.03146
$610$	−22.1207	−0.895643
$611$	−50.6799	−2.05029
$612$	−31.8739	−1.28843
$613$	39.7573	1.60578	0.802891	−	0.596126i	$-0.203294\pi$
$613$	39.7573	1.60578	0.802891	+	0.596126i	$0.203294\pi$
$614$	30.2013	1.21883
$615$	−38.6481	−1.55844
$616$	−4.28395	−0.172605
$617$	−34.8823	−1.40431	−0.702155	−	0.712024i	$-0.747779\pi$
$617$	−34.8823	−1.40431	−0.702155	+	0.712024i	$0.747779\pi$
$618$	−29.3541	−1.18080
$619$	−16.6609	−0.669659	−0.334829	−	0.942279i	$-0.608679\pi$
$619$	−16.6609	−0.669659	−0.334829	+	0.942279i	$0.608679\pi$
$620$	15.3270	0.615549
$621$	−73.7467	−2.95935
$622$	23.7153	0.950895
$623$	10.6281	0.425805
$624$	145.724	5.83363
$625$	1.00000	0.0400000
$626$	−8.39512	−0.335537
$627$	−14.9965	−0.598902
$628$	−64.1605	−2.56028
$629$	−3.44559	−0.137385
$630$	16.9839	0.676654
$631$	36.1944	1.44088	0.720438	−	0.693519i	$-0.243941\pi$
$631$	36.1944	1.44088	0.720438	+	0.693519i	$0.243941\pi$
$632$	−64.8482	−2.57952
$633$	−90.0776	−3.58026
$634$	−1.04071	−0.0413320
$635$	−7.14187	−0.283416
$636$	−64.0570	−2.54002
$637$	6.89482	0.273183
$638$	14.3917	0.569773
$639$	−46.6333	−1.84479
$640$	12.8316	0.507215
$641$	−41.5036	−1.63929	−0.819647	−	0.572869i	$-0.805830\pi$
$641$	−41.5036	−1.63929	−0.819647	+	0.572869i	$0.805830\pi$
$642$	−107.853	−4.25661
$643$	10.9258	0.430873	0.215436	−	0.976518i	$-0.430883\pi$
$643$	10.9258	0.430873	0.215436	+	0.976518i	$0.430883\pi$
$644$	28.4074	1.11941
$645$	−9.98204	−0.393042
$646$	18.8958	0.743443
$647$	−24.0338	−0.944866	−0.472433	−	0.881367i	$-0.656624\pi$
$647$	−24.0338	−0.944866	−0.472433	+	0.881367i	$0.656624\pi$
$648$	97.2006	3.81840
$649$	3.46363	0.135960
$650$	17.4880	0.685935
$651$	10.7654	0.421929
$652$	−50.3312	−1.97112
$653$	−44.6154	−1.74594	−0.872968	−	0.487778i	$-0.837807\pi$
$653$	−44.6154	−1.74594	−0.872968	+	0.487778i	$0.837807\pi$
$654$	0.177866	0.00695509
$655$	2.62484	0.102561
$656$	84.2444	3.28919
$657$	−4.73678	−0.184799
$658$	18.6436	0.726804
$659$	32.1860	1.25379	0.626894	−	0.779105i	$-0.284326\pi$
$659$	32.1860	1.25379	0.626894	+	0.779105i	$0.284326\pi$
$660$	−9.58203	−0.372980
$661$	−26.9824	−1.04949	−0.524747	−	0.851258i	$-0.675840\pi$
$661$	−26.9824	−1.04949	−0.524747	+	0.851258i	$0.675840\pi$
$662$	8.53978	0.331908
$663$	−23.0520	−0.895267
$664$	27.5282	1.06830
$665$	−6.93839	−0.269059
$666$	54.5019	2.11190
$667$	−52.3801	−2.02817
$668$	−106.104	−4.10529
$669$	−50.7209	−1.96098
$670$	−3.12855	−0.120866
$671$	6.05363	0.233698
$672$	−15.1713	−0.585247
$673$	33.5732	1.29415	0.647076	−	0.762426i	$-0.275992\pi$
$673$	33.5732	1.29415	0.647076	+	0.762426i	$0.275992\pi$
$674$	−48.0907	−1.85238
$675$	11.5090	0.442982
$676$	153.119	5.88920
$677$	28.8307	1.10805	0.554026	−	0.832499i	$-0.313091\pi$
$677$	28.8307	1.10805	0.554026	+	0.832499i	$0.313091\pi$
$678$	−72.2875	−2.77619
$679$	−16.7029	−0.640998
$680$	6.62674	0.254124
$681$	30.0162	1.15022
$682$	−6.08670	−0.233072
$683$	10.7047	0.409602	0.204801	−	0.978804i	$-0.434345\pi$
$683$	10.7047	0.409602	0.204801	+	0.978804i	$0.434345\pi$
$684$	−205.971	−7.87549
$685$	3.40028	0.129918
$686$	−2.53639	−0.0968400
$687$	3.11385	0.118801
$688$	21.7586	0.829540
$689$	−31.9937	−1.21886
$690$	50.6080	1.92661
$691$	−6.28528	−0.239103	−0.119552	−	0.992828i	$-0.538146\pi$
$691$	−6.28528	−0.239103	−0.119552	+	0.992828i	$0.538146\pi$
$692$	98.0906	3.72885
$693$	−4.64786	−0.176558
$694$	5.18239	0.196721
$695$	−15.1275	−0.573818
$696$	157.098	5.95480
$697$	−13.3266	−0.504781
$698$	−44.1671	−1.67175
$699$	26.9419	1.01904
$700$	−4.43329	−0.167563
$701$	45.0514	1.70157	0.850783	−	0.525516i	$-0.176128\pi$
$701$	45.0514	1.70157	0.850783	+	0.525516i	$0.176128\pi$
$702$	201.269	7.59642
$703$	−22.2655	−0.839761
$704$	−0.844858	−0.0318418
$705$	22.8882	0.862019
$706$	41.5346	1.56318
$707$	19.0840	0.717728
$708$	68.8848	2.58885
$709$	14.3281	0.538104	0.269052	−	0.963126i	$-0.413290\pi$
$709$	14.3281	0.538104	0.269052	+	0.963126i	$0.413290\pi$
$710$	17.6642	0.662924
$711$	−70.3569	−2.63859
$712$	−65.5943	−2.45825
$713$	22.1532	0.829643
$714$	8.48015	0.317362
$715$	−4.78581	−0.178979
$716$	−58.6922	−2.19343
$717$	64.0293	2.39122
$718$	47.4710	1.77160
$719$	−32.2886	−1.20416	−0.602081	−	0.798435i	$-0.705662\pi$
$719$	−32.2886	−1.20416	−0.602081	+	0.798435i	$0.705662\pi$
$720$	−45.4497	−1.69381
$721$	3.71668	0.138416
$722$	73.9137	2.75078
$723$	0.846042	0.0314647
$724$	−108.638	−4.03751
$725$	8.17452	0.303594
$726$	−83.0723	−3.08310
$727$	14.2026	0.526744	0.263372	−	0.964694i	$-0.415165\pi$
$727$	14.2026	0.526744	0.263372	+	0.964694i	$0.415165\pi$
$728$	−42.5534	−1.57713
$729$	−2.05458	−0.0760954
$730$	1.79424	0.0664077
$731$	−3.44199	−0.127307
$732$	120.395	4.44992
$733$	−2.19744	−0.0811642	−0.0405821	−	0.999176i	$-0.512921\pi$
$733$	−2.19744	−0.0811642	−0.0405821	+	0.999176i	$0.512921\pi$
$734$	18.0947	0.667888
$735$	−3.11385	−0.114856
$736$	−31.2198	−1.15078
$737$	0.856168	0.0315374
$738$	210.798	7.75960
$739$	−25.9961	−0.956283	−0.478141	−	0.878283i	$-0.658689\pi$
$739$	−25.9961	−0.956283	−0.478141	+	0.878283i	$0.658689\pi$
$740$	−14.2266	−0.522980
$741$	−148.963	−5.47230
$742$	11.7695	0.432073
$743$	−8.73693	−0.320527	−0.160263	−	0.987074i	$-0.551234\pi$
$743$	−8.73693	−0.320527	−0.160263	+	0.987074i	$0.551234\pi$
$744$	−66.4418	−2.43587
$745$	−2.39105	−0.0876014
$746$	−26.5261	−0.971189
$747$	29.8667	1.09276
$748$	−3.30406	−0.120808
$749$	13.6558	0.498971
$750$	−7.89795	−0.288393
$751$	31.8729	1.16306	0.581530	−	0.813525i	$-0.302454\pi$
$751$	31.8729	1.16306	0.581530	+	0.813525i	$0.302454\pi$
$752$	−49.8912	−1.81934
$753$	−31.0621	−1.13197
$754$	142.956	5.20614
$755$	−13.7810	−0.501543
$756$	−51.0229	−1.85568
$757$	−27.4187	−0.996548	−0.498274	−	0.867020i	$-0.666033\pi$
$757$	−27.4187	−0.996548	−0.498274	+	0.867020i	$0.666033\pi$
$758$	−25.3825	−0.921934
$759$	−13.8495	−0.502706
$760$	42.8223	1.55333
$761$	2.80527	0.101691	0.0508455	−	0.998707i	$-0.483808\pi$
$761$	2.80527	0.101691	0.0508455	+	0.998707i	$0.483808\pi$
$762$	56.4061	2.04338
$763$	−0.0225205	−0.000815295 0
$764$	−27.9161	−1.00997
$765$	7.18967	0.259943
$766$	−30.5305	−1.10311
$767$	34.4050	1.24229
$768$	−93.7636	−3.38340
$769$	35.1929	1.26909	0.634544	−	0.772886i	$-0.281188\pi$
$769$	35.1929	1.26909	0.634544	+	0.772886i	$0.281188\pi$
$770$	1.76056	0.0634460
$771$	14.2426	0.512934
$772$	43.2841	1.55783
$773$	−41.9774	−1.50982	−0.754910	−	0.655828i	$-0.772320\pi$
$773$	−41.9774	−1.50982	−0.754910	+	0.655828i	$0.772320\pi$
$774$	54.4450	1.95699
$775$	−3.45726	−0.124188
$776$	103.087	3.70060
$777$	−9.99246	−0.358478
$778$	15.8478	0.568172
$779$	−86.1171	−3.08546
$780$	−95.1803	−3.40800
$781$	−4.83403	−0.172975
$782$	17.4506	0.624031
$783$	94.0808	3.36217
$784$	6.78751	0.242411
$785$	14.4724	0.516543
$786$	−20.7309	−0.739445
$787$	19.3395	0.689377	0.344689	−	0.938717i	$-0.387985\pi$
$787$	19.3395	0.689377	0.344689	+	0.938717i	$0.387985\pi$
$788$	43.5796	1.55246
$789$	−13.7108	−0.488118
$790$	26.6504	0.948177
$791$	9.15269	0.325432
$792$	28.6856	1.01930
$793$	60.1320	2.13535
$794$	59.0908	2.09706
$795$	14.4491	0.512456
$796$	51.3345	1.81950
$797$	28.6379	1.01441	0.507203	−	0.861827i	$-0.330680\pi$
$797$	28.6379	1.01441	0.507203	+	0.861827i	$0.330680\pi$
$798$	54.7991	1.93987
$799$	7.89227	0.279209
$800$	4.87221	0.172259
$801$	−71.1664	−2.51454
$802$	−32.7086	−1.15498
$803$	−0.491017	−0.0173276
$804$	17.0275	0.600513
$805$	−6.40773	−0.225843
$806$	−60.4604	−2.12963
$807$	91.1732	3.20945
$808$	−117.783	−4.14357
$809$	51.2405	1.80152	0.900760	−	0.434317i	$-0.143010\pi$
$809$	51.2405	1.80152	0.900760	+	0.434317i	$0.143010\pi$
$810$	−39.9461	−1.40356
$811$	−21.6619	−0.760652	−0.380326	−	0.924852i	$-0.624188\pi$
$811$	−21.6619	−0.760652	−0.380326	+	0.924852i	$0.624188\pi$
$812$	−36.2401	−1.27178
$813$	−44.8642	−1.57345
$814$	5.64969	0.198021
$815$	11.3530	0.397678
$816$	−22.6933	−0.794423
$817$	−22.2423	−0.778160
$818$	31.4559	1.09983
$819$	−46.1682	−1.61325
$820$	−55.0246	−1.92154
$821$	44.4385	1.55091	0.775457	−	0.631400i	$-0.217520\pi$
$821$	44.4385	1.55091	0.775457	+	0.631400i	$0.217520\pi$
$822$	−26.8553	−0.936686
$823$	−45.4173	−1.58315	−0.791574	−	0.611073i	$-0.790738\pi$
$823$	−45.4173	−1.58315	−0.791574	+	0.611073i	$0.790738\pi$
$824$	−22.9386	−0.799103
$825$	2.16138	0.0752496
$826$	−12.6566	−0.440378
$827$	5.27897	0.183568	0.0917840	−	0.995779i	$-0.470743\pi$
$827$	5.27897	0.183568	0.0917840	+	0.995779i	$0.470743\pi$
$828$	−190.218	−6.61052
$829$	−5.27399	−0.183173	−0.0915866	−	0.995797i	$-0.529194\pi$
$829$	−5.27399	−0.183173	−0.0915866	+	0.995797i	$0.529194\pi$
$830$	−11.3131	−0.392685
$831$	51.3688	1.78197
$832$	−8.39215	−0.290945
$833$	−1.07371	−0.0372020
$834$	119.476	4.13712
$835$	23.9335	0.828252
$836$	−21.3510	−0.738440
$837$	−39.7897	−1.37533
$838$	64.6287	2.23256
$839$	−9.41643	−0.325091	−0.162546	−	0.986701i	$-0.551970\pi$
$839$	−9.41643	−0.325091	−0.162546	+	0.986701i	$0.551970\pi$
$840$	19.2180	0.663086
$841$	37.8228	1.30424
$842$	40.2075	1.38564
$843$	−60.0949	−2.06978
$844$	−128.247	−4.41443
$845$	−34.5385	−1.18816
$846$	−124.839	−4.29205
$847$	10.5182	0.361410
$848$	−31.4958	−1.08157
$849$	13.6395	0.468106
$850$	−2.72336	−0.0934106
$851$	−20.5626	−0.704878
$852$	−96.1392	−3.29368
$853$	25.9727	0.889287	0.444643	−	0.895708i	$-0.353330\pi$
$853$	25.9727	0.889287	0.444643	+	0.895708i	$0.353330\pi$
$854$	−22.1207	−0.756956
$855$	46.4600	1.58890
$856$	−84.2806	−2.88065
$857$	36.0150	1.23025	0.615125	−	0.788429i	$-0.289105\pi$
$857$	36.0150	1.23025	0.615125	+	0.788429i	$0.289105\pi$
$858$	37.7981	1.29041
$859$	5.11809	0.174627	0.0873134	−	0.996181i	$-0.472172\pi$
$859$	5.11809	0.174627	0.0873134	+	0.996181i	$0.472172\pi$
$860$	−14.2118	−0.484617
$861$	−38.6481	−1.31712
$862$	68.8627	2.34547
$863$	−30.1432	−1.02609	−0.513043	−	0.858363i	$-0.671482\pi$
$863$	−30.1432	−1.02609	−0.513043	+	0.858363i	$0.671482\pi$
$864$	56.0744	1.90769
$865$	−22.1259	−0.752303
$866$	95.0814	3.23100
$867$	−49.3456	−1.67587
$868$	15.3270	0.520234
$869$	−7.29322	−0.247406
$870$	−64.5620	−2.18886
$871$	8.50450	0.288164
$872$	0.138992	0.00470685
$873$	111.844	3.78534
$874$	112.766	3.81438
$875$	1.00000	0.0338062
$876$	−9.76535	−0.329941
$877$	−4.50267	−0.152044	−0.0760221	−	0.997106i	$-0.524222\pi$
$877$	−4.50267	−0.152044	−0.0760221	+	0.997106i	$0.524222\pi$
$878$	70.1338	2.36690
$879$	−28.9131	−0.975213
$880$	−4.71133	−0.158819
$881$	−5.48375	−0.184752	−0.0923761	−	0.995724i	$-0.529446\pi$
$881$	−5.48375	−0.184752	−0.0923761	+	0.995724i	$0.529446\pi$
$882$	16.9839	0.571877
$883$	−1.62232	−0.0545954	−0.0272977	−	0.999627i	$-0.508690\pi$
$883$	−1.62232	−0.0545954	−0.0272977	+	0.999627i	$0.508690\pi$
$884$	−32.8200	−1.10385
$885$	−15.5381	−0.522306
$886$	41.7513	1.40266
$887$	3.13140	0.105142	0.0525710	−	0.998617i	$-0.483258\pi$
$887$	3.13140	0.105142	0.0525710	+	0.998617i	$0.483258\pi$
$888$	61.6714	2.06956
$889$	−7.14187	−0.239531
$890$	26.9570	0.903601
$891$	10.9318	0.366228
$892$	−72.2130	−2.41787
$893$	51.0002	1.70666
$894$	18.8844	0.631590
$895$	13.2390	0.442530
$896$	12.8316	0.428675
$897$	−137.570	−4.59334
$898$	−86.1791	−2.87583
$899$	−28.2614	−0.942572
$900$	29.6857	0.989522
$901$	4.98231	0.165985
$902$	21.8515	0.727574
$903$	−9.98204	−0.332181
$904$	−56.4885	−1.87878
$905$	24.5051	0.814577
$906$	108.842	3.61603
$907$	41.6263	1.38218	0.691090	−	0.722769i	$-0.257131\pi$
$907$	41.6263	1.38218	0.691090	+	0.722769i	$0.257131\pi$
$908$	42.7351	1.41821
$909$	−127.788	−4.23846
$910$	17.4880	0.579721
$911$	−19.8906	−0.659004	−0.329502	−	0.944155i	$-0.606881\pi$
$911$	−19.8906	−0.659004	−0.329502	+	0.944155i	$0.606881\pi$
$912$	−146.645	−4.85590
$913$	3.09599	0.102462
$914$	22.5919	0.747275
$915$	−27.1569	−0.897781
$916$	4.43329	0.146480
$917$	2.62484	0.0866798
$918$	−31.3432	−1.03448
$919$	−43.0877	−1.42133	−0.710667	−	0.703529i	$-0.751607\pi$
$919$	−43.0877	−1.42133	−0.710667	+	0.703529i	$0.751607\pi$
$920$	39.5472	1.30383
$921$	37.0773	1.22174
$922$	0.643560	0.0211945
$923$	−48.0174	−1.58051
$924$	−9.58203	−0.315226
$925$	3.20904	0.105512
$926$	−56.6772	−1.86253
$927$	−24.8871	−0.817401
$928$	39.8280	1.30742
$929$	−20.6800	−0.678490	−0.339245	−	0.940698i	$-0.610172\pi$
$929$	−20.6800	−0.678490	−0.339245	+	0.940698i	$0.610172\pi$
$930$	27.3053	0.895375
$931$	−6.93839	−0.227397
$932$	38.3580	1.25646
$933$	29.1145	0.953166
$934$	91.1723	2.98325
$935$	0.745284	0.0243734
$936$	284.940	9.31357
$937$	35.2520	1.15163	0.575816	−	0.817579i	$-0.304684\pi$
$937$	35.2520	1.15163	0.575816	+	0.817579i	$0.304684\pi$
$938$	−3.12855	−0.102151
$939$	−10.3064	−0.336338
$940$	32.5867	1.06286
$941$	38.6480	1.25989	0.629945	−	0.776640i	$-0.283077\pi$
$941$	38.6480	1.25989	0.629945	+	0.776640i	$0.283077\pi$
$942$	−114.303	−3.72418
$943$	−79.5307	−2.58988
$944$	33.8696	1.10236
$945$	11.5090	0.374389
$946$	5.64379	0.183495
$947$	49.5153	1.60903	0.804516	−	0.593932i	$-0.202425\pi$
$947$	49.5153	1.60903	0.804516	+	0.593932i	$0.202425\pi$
$948$	−145.048	−4.71093
$949$	−4.87737	−0.158326
$950$	−17.5985	−0.570970
$951$	−1.27765	−0.0414306
$952$	6.62674	0.214774
$953$	28.4065	0.920176	0.460088	−	0.887873i	$-0.347818\pi$
$953$	28.4065	0.920176	0.460088	+	0.887873i	$0.347818\pi$
$954$	−78.8096	−2.55155
$955$	6.29692	0.203763
$956$	91.1606	2.94834
$957$	17.6682	0.571133
$958$	−36.2177	−1.17014
$959$	3.40028	0.109801
$960$	3.79008	0.122324
$961$	−19.0474	−0.614431
$962$	56.1195	1.80937
$963$	−91.4401	−2.94661
$964$	1.20454	0.0387956
$965$	−9.76342	−0.314296
$966$	50.6080	1.62828
$967$	0.0613950	0.00197433	0.000987166	−	1.00000i	$-0.499686\pi$
$967$	0.0613950	0.00197433	0.000987166		1.00000i	$0.499686\pi$
$968$	−64.9162	−2.08648
$969$	23.1977	0.745218
$970$	−42.3651	−1.36026
$971$	−3.13614	−0.100643	−0.0503217	−	0.998733i	$-0.516025\pi$
$971$	−3.13614	−0.100643	−0.0503217	+	0.998733i	$0.516025\pi$
$972$	64.3427	2.06379
$973$	−15.1275	−0.484965
$974$	−6.96092	−0.223042
$975$	21.4694	0.687572
$976$	59.1962	1.89482
$977$	−58.3101	−1.86551	−0.932753	−	0.360517i	$-0.882600\pi$
$977$	−58.3101	−1.86551	−0.932753	+	0.360517i	$0.882600\pi$
$978$	−89.6655	−2.86719
$979$	−7.37714	−0.235774
$980$	−4.43329	−0.141616
$981$	0.150799	0.00481463
$982$	−24.7544	−0.789944
$983$	6.56017	0.209237	0.104618	−	0.994512i	$-0.466638\pi$
$983$	6.56017	0.209237	0.104618	+	0.994512i	$0.466638\pi$
$984$	238.528	7.60400
$985$	−9.83007	−0.313212
$986$	−22.2622	−0.708973
$987$	22.8882	0.728539
$988$	−212.084	−6.74729
$989$	−20.5412	−0.653172
$990$	−11.7888	−0.374673
$991$	−43.4062	−1.37884	−0.689422	−	0.724360i	$-0.742135\pi$
$991$	−43.4062	−1.37884	−0.689422	+	0.724360i	$0.742135\pi$
$992$	−16.8445	−0.534813
$993$	10.4840	0.332700
$994$	17.6642	0.560273
$995$	−11.5793	−0.367089
$996$	61.5731	1.95102
$997$	−27.4582	−0.869611	−0.434805	−	0.900524i	$-0.643183\pi$
$997$	−27.4582	−0.869611	−0.434805	+	0.900524i	$0.643183\pi$
$998$	−33.9787	−1.07558
$999$	36.9329	1.16850

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8015.2.a.l.1.58	✓	62

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8015.2.a.l.1.58	✓	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)

\(f(q)\)	\(=\)	\(q+2.53639 q^{2} +3.11385 q^{3} +4.43329 q^{4} -1.00000 q^{5} +7.89795 q^{6} -1.00000 q^{7} +6.17179 q^{8} +6.69607 q^{9} +O(q^{10})\)	\(q+2.53639 q^{2} +3.11385 q^{3} +4.43329 q^{4} -1.00000 q^{5} +7.89795 q^{6} -1.00000 q^{7} +6.17179 q^{8} +6.69607 q^{9} -2.53639 q^{10} +0.694118 q^{11} +13.8046 q^{12} +6.89482 q^{13} -2.53639 q^{14} -3.11385 q^{15} +6.78751 q^{16} -1.07371 q^{17} +16.9839 q^{18} -6.93839 q^{19} -4.43329 q^{20} -3.11385 q^{21} +1.76056 q^{22} -6.40773 q^{23} +19.2180 q^{24} +1.00000 q^{25} +17.4880 q^{26} +11.5090 q^{27} -4.43329 q^{28} +8.17452 q^{29} -7.89795 q^{30} -3.45726 q^{31} +4.87221 q^{32} +2.16138 q^{33} -2.72336 q^{34} +1.00000 q^{35} +29.6857 q^{36} +3.20904 q^{37} -17.5985 q^{38} +21.4694 q^{39} -6.17179 q^{40} +12.4117 q^{41} -7.89795 q^{42} +3.20569 q^{43} +3.07723 q^{44} -6.69607 q^{45} -16.2525 q^{46} -7.35044 q^{47} +21.1353 q^{48} +1.00000 q^{49} +2.53639 q^{50} -3.34339 q^{51} +30.5667 q^{52} -4.64026 q^{53} +29.1914 q^{54} -0.694118 q^{55} -6.17179 q^{56} -21.6051 q^{57} +20.7338 q^{58} +4.98998 q^{59} -13.8046 q^{60} +8.72134 q^{61} -8.76897 q^{62} -6.69607 q^{63} -1.21717 q^{64} -6.89482 q^{65} +5.48211 q^{66} +1.23346 q^{67} -4.76009 q^{68} -19.9527 q^{69} +2.53639 q^{70} -6.96428 q^{71} +41.3268 q^{72} -0.707397 q^{73} +8.13938 q^{74} +3.11385 q^{75} -30.7599 q^{76} -0.694118 q^{77} +54.4549 q^{78} -10.5072 q^{79} -6.78751 q^{80} +15.7492 q^{81} +31.4809 q^{82} +4.46033 q^{83} -13.8046 q^{84} +1.07371 q^{85} +8.13089 q^{86} +25.4543 q^{87} +4.28395 q^{88} -10.6281 q^{89} -16.9839 q^{90} -6.89482 q^{91} -28.4074 q^{92} -10.7654 q^{93} -18.6436 q^{94} +6.93839 q^{95} +15.1713 q^{96} +16.7029 q^{97} +2.53639 q^{98} +4.64786 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 62 q + 2 q^{2} + 11 q^{3} + 64 q^{4} - 62 q^{5} + 3 q^{6} - 62 q^{7} + 15 q^{8} + 69 q^{9}+O(q^{10}) \) 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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