LMFDB - Embedded newform 8015.2.a.l.1.62

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			1.62
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)

$f(q)$	$=$	$q+2.79293 q^{2} -1.06735 q^{3} +5.80048 q^{4} -1.00000 q^{5} -2.98104 q^{6} -1.00000 q^{7} +10.6145 q^{8} -1.86076 q^{9} +O(q^{10})$	\(q+2.79293 q^{2} -1.06735 q^{3} +5.80048 q^{4} -1.00000 q^{5} -2.98104 q^{6} -1.00000 q^{7} +10.6145 q^{8} -1.86076 q^{9} -2.79293 q^{10} +0.504421 q^{11} -6.19116 q^{12} +2.67005 q^{13} -2.79293 q^{14} +1.06735 q^{15} +18.0446 q^{16} +0.222483 q^{17} -5.19698 q^{18} +3.37331 q^{19} -5.80048 q^{20} +1.06735 q^{21} +1.40881 q^{22} -8.15087 q^{23} -11.3294 q^{24} +1.00000 q^{25} +7.45727 q^{26} +5.18814 q^{27} -5.80048 q^{28} -7.54939 q^{29} +2.98104 q^{30} +9.86730 q^{31} +29.1685 q^{32} -0.538394 q^{33} +0.621382 q^{34} +1.00000 q^{35} -10.7933 q^{36} -5.73261 q^{37} +9.42144 q^{38} -2.84988 q^{39} -10.6145 q^{40} +11.2262 q^{41} +2.98104 q^{42} +2.74059 q^{43} +2.92588 q^{44} +1.86076 q^{45} -22.7648 q^{46} +8.69917 q^{47} -19.2600 q^{48} +1.00000 q^{49} +2.79293 q^{50} -0.237468 q^{51} +15.4876 q^{52} +12.3367 q^{53} +14.4901 q^{54} -0.504421 q^{55} -10.6145 q^{56} -3.60051 q^{57} -21.0850 q^{58} -14.5599 q^{59} +6.19116 q^{60} +5.57857 q^{61} +27.5587 q^{62} +1.86076 q^{63} +45.3763 q^{64} -2.67005 q^{65} -1.50370 q^{66} +8.95098 q^{67} +1.29051 q^{68} +8.69984 q^{69} +2.79293 q^{70} -0.120147 q^{71} -19.7510 q^{72} +6.77351 q^{73} -16.0108 q^{74} -1.06735 q^{75} +19.5668 q^{76} -0.504421 q^{77} -7.95953 q^{78} +13.5337 q^{79} -18.0446 q^{80} +0.0447058 q^{81} +31.3539 q^{82} -4.74510 q^{83} +6.19116 q^{84} -0.222483 q^{85} +7.65428 q^{86} +8.05786 q^{87} +5.35417 q^{88} -0.176402 q^{89} +5.19698 q^{90} -2.67005 q^{91} -47.2789 q^{92} -10.5319 q^{93} +24.2962 q^{94} -3.37331 q^{95} -31.1330 q^{96} +13.1772 q^{97} +2.79293 q^{98} -0.938605 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	2.79293	1.97490	0.987451	−	0.157924i	$-0.0504799\pi$
$2$	2.79293	1.97490	0.987451	+	0.157924i	$0.0504799\pi$
$3$	−1.06735	−0.616236	−0.308118	−	0.951348i	$-0.599699\pi$
$3$	−1.06735	−0.616236	−0.308118	+	0.951348i	$0.599699\pi$
$4$	5.80048	2.90024
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−2.98104	−1.21701
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	10.6145	3.75279
$9$	−1.86076	−0.620253
$10$	−2.79293	−0.883203
$11$	0.504421	0.152089	0.0760443	−	0.997104i	$-0.475771\pi$
$11$	0.504421	0.152089	0.0760443	+	0.997104i	$0.475771\pi$
$12$	−6.19116	−1.78723
$13$	2.67005	0.740538	0.370269	−	0.928925i	$-0.379266\pi$
$13$	2.67005	0.740538	0.370269	+	0.928925i	$0.379266\pi$
$14$	−2.79293	−0.746443
$15$	1.06735	0.275589
$16$	18.0446	4.51116
$17$	0.222483	0.0539602	0.0269801	−	0.999636i	$-0.491411\pi$
$17$	0.222483	0.0539602	0.0269801	+	0.999636i	$0.491411\pi$
$18$	−5.19698	−1.22494
$19$	3.37331	0.773891	0.386945	−	0.922103i	$-0.373530\pi$
$19$	3.37331	0.773891	0.386945	+	0.922103i	$0.373530\pi$
$20$	−5.80048	−1.29703
$21$	1.06735	0.232915
$22$	1.40881	0.300360
$23$	−8.15087	−1.69957	−0.849787	−	0.527127i	$-0.823269\pi$
$23$	−8.15087	−1.69957	−0.849787	+	0.527127i	$0.823269\pi$
$24$	−11.3294	−2.31260
$25$	1.00000	0.200000
$26$	7.45727	1.46249
$27$	5.18814	0.998458
$28$	−5.80048	−1.09619
$29$	−7.54939	−1.40189	−0.700943	−	0.713217i	$-0.747237\pi$
$29$	−7.54939	−1.40189	−0.700943	+	0.713217i	$0.747237\pi$
$30$	2.98104	0.544262
$31$	9.86730	1.77222	0.886110	−	0.463475i	$-0.153398\pi$
$31$	9.86730	1.77222	0.886110	+	0.463475i	$0.153398\pi$
$32$	29.1685	5.15630
$33$	−0.538394	−0.0937224
$34$	0.621382	0.106566
$35$	1.00000	0.169031
$36$	−10.7933	−1.79888
$37$	−5.73261	−0.942435	−0.471217	−	0.882017i	$-0.656185\pi$
$37$	−5.73261	−0.942435	−0.471217	+	0.882017i	$0.656185\pi$
$38$	9.42144	1.52836
$39$	−2.84988	−0.456346
$40$	−10.6145	−1.67830
$41$	11.2262	1.75323	0.876616	−	0.481191i	$-0.159796\pi$
$41$	11.2262	1.75323	0.876616	+	0.481191i	$0.159796\pi$
$42$	2.98104	0.459985
$43$	2.74059	0.417936	0.208968	−	0.977923i	$-0.432990\pi$
$43$	2.74059	0.417936	0.208968	+	0.977923i	$0.432990\pi$
$44$	2.92588	0.441093
$45$	1.86076	0.277386
$46$	−22.7648	−3.35649
$47$	8.69917	1.26890	0.634452	−	0.772962i	$-0.281226\pi$
$47$	8.69917	1.26890	0.634452	+	0.772962i	$0.281226\pi$
$48$	−19.2600	−2.77994
$49$	1.00000	0.142857
$50$	2.79293	0.394981
$51$	−0.237468	−0.0332522
$52$	15.4876	2.14774
$53$	12.3367	1.69458	0.847291	−	0.531129i	$-0.178232\pi$
$53$	12.3367	1.69458	0.847291	+	0.531129i	$0.178232\pi$
$54$	14.4901	1.97186
$55$	−0.504421	−0.0680161
$56$	−10.6145	−1.41842
$57$	−3.60051	−0.476899
$58$	−21.0850	−2.76859
$59$	−14.5599	−1.89554	−0.947771	−	0.318952i	$-0.896669\pi$
$59$	−14.5599	−1.89554	−0.947771	+	0.318952i	$0.896669\pi$
$60$	6.19116	0.799275
$61$	5.57857	0.714262	0.357131	−	0.934054i	$-0.383755\pi$
$61$	5.57857	0.714262	0.357131	+	0.934054i	$0.383755\pi$
$62$	27.5587	3.49996
$63$	1.86076	0.234434
$64$	45.3763	5.67204
$65$	−2.67005	−0.331179
$66$	−1.50370	−0.185093
$67$	8.95098	1.09354	0.546768	−	0.837284i	$-0.315858\pi$
$67$	8.95098	1.09354	0.546768	+	0.837284i	$0.315858\pi$
$68$	1.29051	0.156497
$69$	8.69984	1.04734
$70$	2.79293	0.333819
$71$	−0.120147	−0.0142589	−0.00712943	−	0.999975i	$-0.502269\pi$
$71$	−0.120147	−0.0142589	−0.00712943	+	0.999975i	$0.502269\pi$
$72$	−19.7510	−2.32768
$73$	6.77351	0.792779	0.396390	−	0.918082i	$-0.370263\pi$
$73$	6.77351	0.792779	0.396390	+	0.918082i	$0.370263\pi$
$74$	−16.0108	−1.86122
$75$	−1.06735	−0.123247
$76$	19.5668	2.24447
$77$	−0.504421	−0.0574841
$78$	−7.95953	−0.901239
$79$	13.5337	1.52266	0.761328	−	0.648367i	$-0.224548\pi$
$79$	13.5337	1.52266	0.761328	+	0.648367i	$0.224548\pi$
$80$	−18.0446	−2.01745
$81$	0.0447058	0.00496731
$82$	31.3539	3.46246
$83$	−4.74510	−0.520842	−0.260421	−	0.965495i	$-0.583861\pi$
$83$	−4.74510	−0.520842	−0.260421	+	0.965495i	$0.583861\pi$
$84$	6.19116	0.675510
$85$	−0.222483	−0.0241317
$86$	7.65428	0.825382
$87$	8.05786	0.863893
$88$	5.35417	0.570756
$89$	−0.176402	−0.0186985	−0.00934927	−	0.999956i	$-0.502976\pi$
$89$	−0.176402	−0.0186985	−0.00934927	+	0.999956i	$0.502976\pi$
$90$	5.19698	0.547810
$91$	−2.67005	−0.279897
$92$	−47.2789	−4.92917
$93$	−10.5319	−1.09211
$94$	24.2962	2.50596
$95$	−3.37331	−0.346094
$96$	−31.1330	−3.17750
$97$	13.1772	1.33794	0.668971	−	0.743289i	$-0.266735\pi$
$97$	13.1772	1.33794	0.668971	+	0.743289i	$0.266735\pi$
$98$	2.79293	0.282129
$99$	−0.938605	−0.0943334
$100$	5.80048	0.580048
$101$	−8.22460	−0.818378	−0.409189	−	0.912450i	$-0.634188\pi$
$101$	−8.22460	−0.818378	−0.409189	+	0.912450i	$0.634188\pi$
$102$	−0.663233	−0.0656698
$103$	1.71653	0.169135	0.0845676	−	0.996418i	$-0.473049\pi$
$103$	1.71653	0.169135	0.0845676	+	0.996418i	$0.473049\pi$
$104$	28.3412	2.77908
$105$	−1.06735	−0.104163
$106$	34.4557	3.34663
$107$	−16.0681	−1.55337	−0.776683	−	0.629891i	$-0.783099\pi$
$107$	−16.0681	−1.55337	−0.776683	+	0.629891i	$0.783099\pi$
$108$	30.0937	2.89577
$109$	5.98418	0.573181	0.286590	−	0.958053i	$-0.407478\pi$
$109$	5.98418	0.573181	0.286590	+	0.958053i	$0.407478\pi$
$110$	−1.40881	−0.134325
$111$	6.11871	0.580762
$112$	−18.0446	−1.70506
$113$	−6.25651	−0.588563	−0.294281	−	0.955719i	$-0.595080\pi$
$113$	−6.25651	−0.588563	−0.294281	+	0.955719i	$0.595080\pi$
$114$	−10.0560	−0.941830
$115$	8.15087	0.760072
$116$	−43.7901	−4.06581
$117$	−4.96832	−0.459321
$118$	−40.6649	−3.74351
$119$	−0.222483	−0.0203950
$120$	11.3294	1.03423
$121$	−10.7456	−0.976869
$122$	15.5806	1.41060
$123$	−11.9823	−1.08040
$124$	57.2351	5.13986
$125$	−1.00000	−0.0894427
$126$	5.19698	0.462984
$127$	−7.46000	−0.661968	−0.330984	−	0.943636i	$-0.607381\pi$
$127$	−7.46000	−0.661968	−0.330984	+	0.943636i	$0.607381\pi$
$128$	68.3962	6.04542
$129$	−2.92517	−0.257547
$130$	−7.45727	−0.654046
$131$	−14.3762	−1.25605	−0.628027	−	0.778192i	$-0.716137\pi$
$131$	−14.3762	−1.25605	−0.628027	+	0.778192i	$0.716137\pi$
$132$	−3.12295	−0.271818
$133$	−3.37331	−0.292503
$134$	24.9995	2.15963
$135$	−5.18814	−0.446524
$136$	2.36155	0.202501
$137$	0.0595141	0.00508464	0.00254232	−	0.999997i	$-0.499191\pi$
$137$	0.0595141	0.00508464	0.00254232	+	0.999997i	$0.499191\pi$
$138$	24.2981	2.06839
$139$	−15.1831	−1.28781	−0.643906	−	0.765105i	$-0.722687\pi$
$139$	−15.1831	−1.28781	−0.643906	+	0.765105i	$0.722687\pi$
$140$	5.80048	0.490230
$141$	−9.28508	−0.781945
$142$	−0.335563	−0.0281599
$143$	1.34683	0.112627
$144$	−33.5767	−2.79806
$145$	7.54939	0.626943
$146$	18.9180	1.56566
$147$	−1.06735	−0.0880337
$148$	−33.2519	−2.73329
$149$	−10.6241	−0.870363	−0.435181	−	0.900343i	$-0.643316\pi$
$149$	−10.6241	−0.870363	−0.435181	+	0.900343i	$0.643316\pi$
$150$	−2.98104	−0.243401
$151$	19.5077	1.58752	0.793758	−	0.608234i	$-0.208122\pi$
$151$	19.5077	1.58752	0.793758	+	0.608234i	$0.208122\pi$
$152$	35.8060	2.90425
$153$	−0.413988	−0.0334690
$154$	−1.40881	−0.113525
$155$	−9.86730	−0.792561
$156$	−16.5307	−1.32351
$157$	2.92294	0.233276	0.116638	−	0.993174i	$-0.462788\pi$
$157$	2.92294	0.233276	0.116638	+	0.993174i	$0.462788\pi$
$158$	37.7986	3.00710
$159$	−13.1676	−1.04426
$160$	−29.1685	−2.30597
$161$	8.15087	0.642378
$162$	0.124860	0.00980996
$163$	12.3357	0.966207	0.483104	−	0.875563i	$-0.339509\pi$
$163$	12.3357	0.966207	0.483104	+	0.875563i	$0.339509\pi$
$164$	65.1171	5.08479
$165$	0.538394	0.0419139
$166$	−13.2527	−1.02861
$167$	−2.33883	−0.180984	−0.0904921	−	0.995897i	$-0.528844\pi$
$167$	−2.33883	−0.180984	−0.0904921	+	0.995897i	$0.528844\pi$
$168$	11.3294	0.874082
$169$	−5.87084	−0.451603
$170$	−0.621382	−0.0476578
$171$	−6.27692	−0.480008
$172$	15.8967	1.21211
$173$	20.7325	1.57626	0.788132	−	0.615506i	$-0.211048\pi$
$173$	20.7325	1.57626	0.788132	+	0.615506i	$0.211048\pi$
$174$	22.5051	1.70610
$175$	−1.00000	−0.0755929
$176$	9.10208	0.686095
$177$	15.5406	1.16810
$178$	−0.492678	−0.0369278
$179$	6.32207	0.472534	0.236267	−	0.971688i	$-0.424076\pi$
$179$	6.32207	0.472534	0.236267	+	0.971688i	$0.424076\pi$
$180$	10.7933	0.804485
$181$	3.28207	0.243954	0.121977	−	0.992533i	$-0.461077\pi$
$181$	3.28207	0.243954	0.121977	+	0.992533i	$0.461077\pi$
$182$	−7.45727	−0.552769
$183$	−5.95429	−0.440154
$184$	−86.5173	−6.37814
$185$	5.73261	0.421470
$186$	−29.4149	−2.15680
$187$	0.112225	0.00820672
$188$	50.4594	3.68013
$189$	−5.18814	−0.377382
$190$	−9.42144	−0.683503
$191$	21.5432	1.55881	0.779404	−	0.626522i	$-0.215522\pi$
$191$	21.5432	1.55881	0.779404	+	0.626522i	$0.215522\pi$
$192$	−48.4325	−3.49532
$193$	3.20665	0.230820	0.115410	−	0.993318i	$-0.463182\pi$
$193$	3.20665	0.230820	0.115410	+	0.993318i	$0.463182\pi$
$194$	36.8030	2.64230
$195$	2.84988	0.204084
$196$	5.80048	0.414320
$197$	−23.7466	−1.69187	−0.845937	−	0.533283i	$-0.820958\pi$
$197$	−23.7466	−1.69187	−0.845937	+	0.533283i	$0.820958\pi$
$198$	−2.62146	−0.186299
$199$	10.0607	0.713186	0.356593	−	0.934260i	$-0.383938\pi$
$199$	10.0607	0.713186	0.356593	+	0.934260i	$0.383938\pi$
$200$	10.6145	0.750558
$201$	−9.55385	−0.673877
$202$	−22.9708	−1.61622
$203$	7.54939	0.529863
$204$	−1.37743	−0.0964393
$205$	−11.2262	−0.784069
$206$	4.79417	0.334025
$207$	15.1668	1.05417
$208$	48.1800	3.34068
$209$	1.70157	0.117700
$210$	−2.98104	−0.205712
$211$	6.78078	0.466808	0.233404	−	0.972380i	$-0.425014\pi$
$211$	6.78078	0.466808	0.233404	+	0.972380i	$0.425014\pi$
$212$	71.5590	4.91469
$213$	0.128239	0.00878682
$214$	−44.8773	−3.06775
$215$	−2.74059	−0.186907
$216$	55.0695	3.74700
$217$	−9.86730	−0.669836
$218$	16.7134	1.13198
$219$	−7.22972	−0.488539
$220$	−2.92588	−0.197263
$221$	0.594041	0.0399595
$222$	17.0891	1.14695
$223$	4.95086	0.331534	0.165767	−	0.986165i	$-0.446990\pi$
$223$	4.95086	0.331534	0.165767	+	0.986165i	$0.446990\pi$
$224$	−29.1685	−1.94890
$225$	−1.86076	−0.124051
$226$	−17.4740	−1.16235
$227$	12.9617	0.860298	0.430149	−	0.902758i	$-0.358461\pi$
$227$	12.9617	0.860298	0.430149	+	0.902758i	$0.358461\pi$
$228$	−20.8847	−1.38312
$229$	1.00000	0.0660819
$229$	1.00000	0.0660819
$230$	22.7648	1.50107
$231$	0.538394	0.0354237
$232$	−80.1330	−5.26099
$233$	−4.06811	−0.266511	−0.133255	−	0.991082i	$-0.542543\pi$
$233$	−4.06811	−0.266511	−0.133255	+	0.991082i	$0.542543\pi$
$234$	−13.8762	−0.907114
$235$	−8.69917	−0.567471
$236$	−84.4546	−5.49753
$237$	−14.4452	−0.938316
$238$	−0.621382	−0.0402782
$239$	−6.92927	−0.448217	−0.224109	−	0.974564i	$-0.571947\pi$
$239$	−6.92927	−0.448217	−0.224109	+	0.974564i	$0.571947\pi$
$240$	19.2600	1.24323
$241$	−5.89243	−0.379565	−0.189782	−	0.981826i	$-0.560778\pi$
$241$	−5.89243	−0.379565	−0.189782	+	0.981826i	$0.560778\pi$
$242$	−30.0116	−1.92922
$243$	−15.6121	−1.00152
$244$	32.3584	2.07153
$245$	−1.00000	−0.0638877
$246$	−33.4657	−2.13369
$247$	9.00690	0.573096
$248$	104.736	6.65077
$249$	5.06469	0.320962
$250$	−2.79293	−0.176641
$251$	−12.1235	−0.765231	−0.382615	−	0.923908i	$-0.624977\pi$
$251$	−12.1235	−0.765231	−0.382615	+	0.923908i	$0.624977\pi$
$252$	10.7933	0.679914
$253$	−4.11146	−0.258486
$254$	−20.8353	−1.30732
$255$	0.237468	0.0148708
$256$	100.273	6.26709
$257$	18.2290	1.13709	0.568545	−	0.822652i	$-0.307506\pi$
$257$	18.2290	1.13709	0.568545	+	0.822652i	$0.307506\pi$
$258$	−8.16981	−0.508630
$259$	5.73261	0.356207
$260$	−15.4876	−0.960498
$261$	14.0476	0.869525
$262$	−40.1517	−2.48058
$263$	3.05391	0.188312	0.0941559	−	0.995557i	$-0.469985\pi$
$263$	3.05391	0.188312	0.0941559	+	0.995557i	$0.469985\pi$
$264$	−5.71478	−0.351721
$265$	−12.3367	−0.757840
$266$	−9.42144	−0.577665
$267$	0.188283	0.0115227
$268$	51.9200	3.17152
$269$	6.64052	0.404880	0.202440	−	0.979295i	$-0.435113\pi$
$269$	6.64052	0.404880	0.202440	+	0.979295i	$0.435113\pi$
$270$	−14.4901	−0.881842
$271$	3.63182	0.220618	0.110309	−	0.993897i	$-0.464816\pi$
$271$	3.63182	0.220618	0.110309	+	0.993897i	$0.464816\pi$
$272$	4.01463	0.243423
$273$	2.84988	0.172483
$274$	0.166219	0.0100417
$275$	0.504421	0.0304177
$276$	50.4633	3.03753
$277$	−17.0129	−1.02221	−0.511103	−	0.859520i	$-0.670763\pi$
$277$	−17.0129	−1.02221	−0.511103	+	0.859520i	$0.670763\pi$
$278$	−42.4053	−2.54330
$279$	−18.3607	−1.09923
$280$	10.6145	0.634337
$281$	−18.7836	−1.12054	−0.560268	−	0.828311i	$-0.689302\pi$
$281$	−18.7836	−1.12054	−0.560268	+	0.828311i	$0.689302\pi$
$282$	−25.9326	−1.54426
$283$	8.51860	0.506378	0.253189	−	0.967417i	$-0.418520\pi$
$283$	8.51860	0.506378	0.253189	+	0.967417i	$0.418520\pi$
$284$	−0.696912	−0.0413541
$285$	3.60051	0.213276
$286$	3.76160	0.222428
$287$	−11.2262	−0.662659
$288$	−54.2755	−3.19821
$289$	−16.9505	−0.997088
$290$	21.0850	1.23815
$291$	−14.0647	−0.824488
$292$	39.2896	2.29925
$293$	19.8242	1.15814	0.579072	−	0.815277i	$-0.303415\pi$
$293$	19.8242	1.15814	0.579072	+	0.815277i	$0.303415\pi$
$294$	−2.98104	−0.173858
$295$	14.5599	0.847712
$296$	−60.8487	−3.53676
$297$	2.61701	0.151854
$298$	−29.6725	−1.71888
$299$	−21.7632	−1.25860
$300$	−6.19116	−0.357447
$301$	−2.74059	−0.157965
$302$	54.4838	3.13519
$303$	8.77854	0.504314
$304$	60.8701	3.49114
$305$	−5.57857	−0.319428
$306$	−1.15624	−0.0660979
$307$	26.3052	1.50132	0.750659	−	0.660690i	$-0.229736\pi$
$307$	26.3052	1.50132	0.750659	+	0.660690i	$0.229736\pi$
$308$	−2.92588	−0.166718
$309$	−1.83215	−0.104227
$310$	−27.5587	−1.56523
$311$	−18.9844	−1.07651	−0.538253	−	0.842783i	$-0.680916\pi$
$311$	−18.9844	−1.07651	−0.538253	+	0.842783i	$0.680916\pi$
$312$	−30.2500	−1.71257
$313$	8.71751	0.492743	0.246371	−	0.969175i	$-0.420762\pi$
$313$	8.71751	0.492743	0.246371	+	0.969175i	$0.420762\pi$
$314$	8.16358	0.460697
$315$	−1.86076	−0.104842
$316$	78.5018	4.41607
$317$	−16.9226	−0.950471	−0.475235	−	0.879859i	$-0.657637\pi$
$317$	−16.9226	−0.950471	−0.475235	+	0.879859i	$0.657637\pi$
$318$	−36.7764	−2.06232
$319$	−3.80807	−0.213211
$320$	−45.3763	−2.53661
$321$	17.1504	0.957240
$322$	22.7648	1.26863
$323$	0.750506	0.0417593
$324$	0.259315	0.0144064
$325$	2.67005	0.148108
$326$	34.4528	1.90816
$327$	−6.38723	−0.353215
$328$	119.160	6.57951
$329$	−8.69917	−0.479601
$330$	1.50370	0.0827760
$331$	15.2488	0.838149	0.419075	−	0.907952i	$-0.362355\pi$
$331$	15.2488	0.838149	0.419075	+	0.907952i	$0.362355\pi$
$332$	−27.5239	−1.51057
$333$	10.6670	0.584548
$334$	−6.53220	−0.357426
$335$	−8.95098	−0.489044
$336$	19.2600	1.05072
$337$	−1.93417	−0.105361	−0.0526804	−	0.998611i	$-0.516776\pi$
$337$	−1.93417	−0.105361	−0.0526804	+	0.998611i	$0.516776\pi$
$338$	−16.3969	−0.891873
$339$	6.67790	0.362694
$340$	−1.29051	−0.0699878
$341$	4.97727	0.269534
$342$	−17.5310	−0.947970
$343$	−1.00000	−0.0539949
$344$	29.0900	1.56843
$345$	−8.69984	−0.468384
$346$	57.9046	3.11297
$347$	10.7025	0.574542	0.287271	−	0.957849i	$-0.407252\pi$
$347$	10.7025	0.574542	0.287271	+	0.957849i	$0.407252\pi$
$348$	46.7395	2.50550
$349$	−17.5969	−0.941940	−0.470970	−	0.882149i	$-0.656096\pi$
$349$	−17.5969	−0.941940	−0.470970	+	0.882149i	$0.656096\pi$
$350$	−2.79293	−0.149289
$351$	13.8526	0.739396
$352$	14.7132	0.784214
$353$	21.5008	1.14437	0.572185	−	0.820124i	$-0.306096\pi$
$353$	21.5008	1.14437	0.572185	+	0.820124i	$0.306096\pi$
$354$	43.4038	2.30689
$355$	0.120147	0.00637676
$356$	−1.02321	−0.0542303
$357$	0.237468	0.0125681
$358$	17.6571	0.933208
$359$	16.3532	0.863091	0.431546	−	0.902091i	$-0.357968\pi$
$359$	16.3532	0.863091	0.431546	+	0.902091i	$0.357968\pi$
$360$	19.7510	1.04097
$361$	−7.62077	−0.401093
$362$	9.16661	0.481786
$363$	11.4693	0.601982
$364$	−15.4876	−0.811769
$365$	−6.77351	−0.354542
$366$	−16.6299	−0.869261
$367$	−9.24858	−0.482772	−0.241386	−	0.970429i	$-0.577602\pi$
$367$	−9.24858	−0.482772	−0.241386	+	0.970429i	$0.577602\pi$
$368$	−147.079	−7.66704
$369$	−20.8892	−1.08745
$370$	16.0108	0.832361
$371$	−12.3367	−0.640492
$372$	−61.0900	−3.16737
$373$	−29.2548	−1.51475	−0.757377	−	0.652977i	$-0.773520\pi$
$373$	−29.2548	−1.51475	−0.757377	+	0.652977i	$0.773520\pi$
$374$	0.313438	0.0162075
$375$	1.06735	0.0551178
$376$	92.3373	4.76193
$377$	−20.1572	−1.03815
$378$	−14.4901	−0.745292
$379$	−7.31748	−0.375874	−0.187937	−	0.982181i	$-0.560180\pi$
$379$	−7.31748	−0.375874	−0.187937	+	0.982181i	$0.560180\pi$
$380$	−19.5668	−1.00376
$381$	7.96245	0.407928
$382$	60.1686	3.07849
$383$	−17.2247	−0.880142	−0.440071	−	0.897963i	$-0.645047\pi$
$383$	−17.2247	−0.880142	−0.440071	+	0.897963i	$0.645047\pi$
$384$	−73.0028	−3.72541
$385$	0.504421	0.0257077
$386$	8.95597	0.455847
$387$	−5.09958	−0.259226
$388$	76.4341	3.88035
$389$	21.0960	1.06961	0.534806	−	0.844975i	$-0.320385\pi$
$389$	21.0960	1.06961	0.534806	+	0.844975i	$0.320385\pi$
$390$	7.95953	0.403046
$391$	−1.81343	−0.0917092
$392$	10.6145	0.536113
$393$	15.3444	0.774025
$394$	−66.3227	−3.34129
$395$	−13.5337	−0.680953
$396$	−5.44436	−0.273590
$397$	−21.6705	−1.08761	−0.543806	−	0.839211i	$-0.683017\pi$
$397$	−21.6705	−1.08761	−0.543806	+	0.839211i	$0.683017\pi$
$398$	28.0989	1.40847
$399$	3.60051	0.180251
$400$	18.0446	0.902231
$401$	20.1668	1.00708	0.503541	−	0.863971i	$-0.332030\pi$
$401$	20.1668	1.00708	0.503541	+	0.863971i	$0.332030\pi$
$402$	−26.6833	−1.33084
$403$	26.3462	1.31240
$404$	−47.7066	−2.37349
$405$	−0.0447058	−0.00222145
$406$	21.0850	1.04643
$407$	−2.89164	−0.143333
$408$	−2.52060	−0.124788
$409$	−27.5364	−1.36159	−0.680794	−	0.732475i	$-0.738365\pi$
$409$	−27.5364	−1.36159	−0.680794	+	0.732475i	$0.738365\pi$
$410$	−31.3539	−1.54846
$411$	−0.0635225	−0.00313334
$412$	9.95672	0.490533
$413$	14.5599	0.716447
$414$	42.3599	2.08187
$415$	4.74510	0.232928
$416$	77.8812	3.81844
$417$	16.2057	0.793596
$418$	4.75237	0.232446
$419$	−15.6433	−0.764223	−0.382112	−	0.924116i	$-0.624803\pi$
$419$	−15.6433	−0.764223	−0.382112	+	0.924116i	$0.624803\pi$
$420$	−6.19116	−0.302097
$421$	28.2512	1.37688	0.688440	−	0.725293i	$-0.258296\pi$
$421$	28.2512	1.37688	0.688440	+	0.725293i	$0.258296\pi$
$422$	18.9383	0.921901
$423$	−16.1871	−0.787042
$424$	130.948	6.35941
$425$	0.222483	0.0107920
$426$	0.358164	0.0173531
$427$	−5.57857	−0.269966
$428$	−93.2030	−4.50514
$429$	−1.43754	−0.0694050
$430$	−7.65428	−0.369122
$431$	−12.7155	−0.612483	−0.306241	−	0.951954i	$-0.599071\pi$
$431$	−12.7155	−0.612483	−0.306241	+	0.951954i	$0.599071\pi$
$432$	93.6180	4.50420
$433$	10.0648	0.483685	0.241842	−	0.970316i	$-0.422248\pi$
$433$	10.0648	0.483685	0.241842	+	0.970316i	$0.422248\pi$
$434$	−27.5587	−1.32286
$435$	−8.05786	−0.386345
$436$	34.7111	1.66236
$437$	−27.4954	−1.31528
$438$	−20.1921	−0.964817
$439$	−16.3004	−0.777973	−0.388987	−	0.921243i	$-0.627175\pi$
$439$	−16.3004	−0.777973	−0.388987	+	0.921243i	$0.627175\pi$
$440$	−5.35417	−0.255250
$441$	−1.86076	−0.0886076
$442$	1.65912	0.0789162
$443$	0.988554	0.0469676	0.0234838	−	0.999724i	$-0.492524\pi$
$443$	0.988554	0.0469676	0.0234838	+	0.999724i	$0.492524\pi$
$444$	35.4915	1.68435
$445$	0.176402	0.00836224
$446$	13.8274	0.654748
$447$	11.3397	0.536349
$448$	−45.3763	−2.14383
$449$	−25.9528	−1.22479	−0.612395	−	0.790552i	$-0.709794\pi$
$449$	−25.9528	−1.22479	−0.612395	+	0.790552i	$0.709794\pi$
$450$	−5.19698	−0.244988
$451$	5.66271	0.266646
$452$	−36.2908	−1.70697
$453$	−20.8216	−0.978284
$454$	36.2012	1.69900
$455$	2.67005	0.125174
$456$	−38.2176	−1.78970
$457$	−0.576076	−0.0269477	−0.0134739	−	0.999909i	$-0.504289\pi$
$457$	−0.576076	−0.0269477	−0.0134739	+	0.999909i	$0.504289\pi$
$458$	2.79293	0.130505
$459$	1.15428	0.0538770
$460$	47.2789	2.20439
$461$	−0.725377	−0.0337842	−0.0168921	−	0.999857i	$-0.505377\pi$
$461$	−0.725377	−0.0337842	−0.0168921	+	0.999857i	$0.505377\pi$
$462$	1.50370	0.0699585
$463$	10.0709	0.468034	0.234017	−	0.972232i	$-0.424813\pi$
$463$	10.0709	0.468034	0.234017	+	0.972232i	$0.424813\pi$
$464$	−136.226	−6.32413
$465$	10.5319	0.488405
$466$	−11.3620	−0.526333
$467$	−34.7490	−1.60799	−0.803996	−	0.594635i	$-0.797297\pi$
$467$	−34.7490	−1.60799	−0.803996	+	0.594635i	$0.797297\pi$
$468$	−28.8186	−1.33214
$469$	−8.95098	−0.413318
$470$	−24.2962	−1.12070
$471$	−3.11981	−0.143753
$472$	−154.546	−7.11357
$473$	1.38241	0.0635632
$474$	−40.3445	−1.85308
$475$	3.37331	0.154778
$476$	−1.29051	−0.0591505
$477$	−22.9557	−1.05107
$478$	−19.3530	−0.885185
$479$	4.17971	0.190976	0.0954879	−	0.995431i	$-0.469559\pi$
$479$	4.17971	0.190976	0.0954879	+	0.995431i	$0.469559\pi$
$480$	31.1330	1.42102
$481$	−15.3063	−0.697909
$482$	−16.4572	−0.749603
$483$	−8.69984	−0.395857
$484$	−62.3294	−2.83316
$485$	−13.1772	−0.598346
$486$	−43.6037	−1.97790
$487$	−19.8156	−0.897931	−0.448966	−	0.893549i	$-0.648207\pi$
$487$	−19.8156	−0.897931	−0.448966	+	0.893549i	$0.648207\pi$
$488$	59.2136	2.68048
$489$	−13.1665	−0.595412
$490$	−2.79293	−0.126172
$491$	9.83568	0.443878	0.221939	−	0.975061i	$-0.428761\pi$
$491$	9.83568	0.443878	0.221939	+	0.975061i	$0.428761\pi$
$492$	−69.5029	−3.13343
$493$	−1.67961	−0.0756460
$494$	25.1557	1.13181
$495$	0.938605	0.0421872
$496$	178.052	7.99476
$497$	0.120147	0.00538934
$498$	14.1453	0.633868
$499$	−28.8496	−1.29148	−0.645742	−	0.763556i	$-0.723452\pi$
$499$	−28.8496	−1.29148	−0.645742	+	0.763556i	$0.723452\pi$
$500$	−5.80048	−0.259405
$501$	2.49636	0.111529
$502$	−33.8602	−1.51126
$503$	−12.9751	−0.578532	−0.289266	−	0.957249i	$-0.593411\pi$
$503$	−12.9751	−0.578532	−0.289266	+	0.957249i	$0.593411\pi$
$504$	19.7510	0.879780
$505$	8.22460	0.365990
$506$	−11.4831	−0.510484
$507$	6.26626	0.278294
$508$	−43.2716	−1.91987
$509$	18.9209	0.838655	0.419327	−	0.907835i	$-0.362266\pi$
$509$	18.9209	0.838655	0.419327	+	0.907835i	$0.362266\pi$
$510$	0.663233	0.0293684
$511$	−6.77351	−0.299642
$512$	143.265	6.33146
$513$	17.5012	0.772698
$514$	50.9123	2.24564
$515$	−1.71653	−0.0756395
$516$	−16.9674	−0.746948
$517$	4.38804	0.192986
$518$	16.0108	0.703474
$519$	−22.1289	−0.971351
$520$	−28.3412	−1.24284
$521$	−42.6480	−1.86844	−0.934222	−	0.356693i	$-0.883904\pi$
$521$	−42.6480	−1.86844	−0.934222	+	0.356693i	$0.883904\pi$
$522$	39.2340	1.71723
$523$	−11.8360	−0.517550	−0.258775	−	0.965938i	$-0.583319\pi$
$523$	−11.8360	−0.517550	−0.258775	+	0.965938i	$0.583319\pi$
$524$	−83.3888	−3.64286
$525$	1.06735	0.0465831
$526$	8.52936	0.371898
$527$	2.19531	0.0956293
$528$	−9.71512	−0.422796
$529$	43.4366	1.88855
$530$	−34.4557	−1.49666
$531$	27.0925	1.17572
$532$	−19.5668	−0.848330
$533$	29.9744	1.29833
$534$	0.525861	0.0227562
$535$	16.0681	0.694687
$536$	95.0102	4.10381
$537$	−6.74787	−0.291192
$538$	18.5465	0.799598
$539$	0.504421	0.0217269
$540$	−30.0937	−1.29503
$541$	9.36010	0.402422	0.201211	−	0.979548i	$-0.435512\pi$
$541$	9.36010	0.402422	0.201211	+	0.979548i	$0.435512\pi$
$542$	10.1434	0.435698
$543$	−3.50312	−0.150333
$544$	6.48950	0.278235
$545$	−5.98418	−0.256334
$546$	7.95953	0.340636
$547$	−26.6114	−1.13782	−0.568910	−	0.822400i	$-0.692635\pi$
$547$	−26.6114	−1.13782	−0.568910	+	0.822400i	$0.692635\pi$
$548$	0.345211	0.0147467
$549$	−10.3804	−0.443023
$550$	1.40881	0.0600720
$551$	−25.4664	−1.08491
$552$	92.3444	3.93044
$553$	−13.5337	−0.575510
$554$	−47.5159	−2.01876
$555$	−6.11871	−0.259725
$556$	−88.0691	−3.73496
$557$	−34.2583	−1.45157	−0.725786	−	0.687920i	$-0.758524\pi$
$557$	−34.2583	−1.45157	−0.725786	+	0.687920i	$0.758524\pi$
$558$	−51.2802	−2.17086
$559$	7.31750	0.309497
$560$	18.0446	0.762524
$561$	−0.119784	−0.00505728
$562$	−52.4614	−2.21295
$563$	−9.29337	−0.391669	−0.195834	−	0.980637i	$-0.562741\pi$
$563$	−9.29337	−0.391669	−0.195834	+	0.980637i	$0.562741\pi$
$564$	−53.8579	−2.26783
$565$	6.25651	0.263213
$566$	23.7919	1.00005
$567$	−0.0447058	−0.00187747
$568$	−1.27530	−0.0535105
$569$	−45.8862	−1.92365	−0.961825	−	0.273664i	$-0.911765\pi$
$569$	−45.8862	−1.92365	−0.961825	+	0.273664i	$0.911765\pi$
$570$	10.0560	0.421199
$571$	−22.5665	−0.944377	−0.472189	−	0.881498i	$-0.656536\pi$
$571$	−22.5665	−0.944377	−0.472189	+	0.881498i	$0.656536\pi$
$572$	7.81225	0.326646
$573$	−22.9941	−0.960594
$574$	−31.3539	−1.30869
$575$	−8.15087	−0.339915
$576$	−84.4344	−3.51810
$577$	23.5063	0.978580	0.489290	−	0.872121i	$-0.337256\pi$
$577$	23.5063	0.978580	0.489290	+	0.872121i	$0.337256\pi$
$578$	−47.3416	−1.96915
$579$	−3.42263	−0.142240
$580$	43.7901	1.81829
$581$	4.74510	0.196860
$582$	−39.2818	−1.62828
$583$	6.22291	0.257726
$584$	71.8973	2.97513
$585$	4.96832	0.205415
$586$	55.3678	2.28722
$587$	−30.0282	−1.23940	−0.619699	−	0.784840i	$-0.712745\pi$
$587$	−30.0282	−1.23940	−0.619699	+	0.784840i	$0.712745\pi$
$588$	−6.19116	−0.255319
$589$	33.2855	1.37150
$590$	40.6649	1.67415
$591$	25.3460	1.04259
$592$	−103.443	−4.25147
$593$	2.79249	0.114674	0.0573368	−	0.998355i	$-0.481739\pi$
$593$	2.79249	0.114674	0.0573368	+	0.998355i	$0.481739\pi$
$594$	7.30912	0.299897
$595$	0.222483	0.00912093
$596$	−61.6251	−2.52426
$597$	−10.7383	−0.439491
$598$	−60.7832	−2.48561
$599$	30.8909	1.26217	0.631084	−	0.775714i	$-0.282610\pi$
$599$	30.8909	1.26217	0.631084	+	0.775714i	$0.282610\pi$
$600$	−11.3294	−0.462521
$601$	25.7315	1.04961	0.524805	−	0.851222i	$-0.324138\pi$
$601$	25.7315	1.04961	0.524805	+	0.851222i	$0.324138\pi$
$602$	−7.65428	−0.311965
$603$	−16.6556	−0.678270
$604$	113.154	4.60418
$605$	10.7456	0.436869
$606$	24.5179	0.995971
$607$	23.6914	0.961605	0.480802	−	0.876829i	$-0.340345\pi$
$607$	23.6914	0.961605	0.480802	+	0.876829i	$0.340345\pi$
$608$	98.3943	3.99041
$609$	−8.05786	−0.326521
$610$	−15.5806	−0.630839
$611$	23.2272	0.939672
$612$	−2.40133	−0.0970680
$613$	0.848584	0.0342740	0.0171370	−	0.999853i	$-0.494545\pi$
$613$	0.848584	0.0342740	0.0171370	+	0.999853i	$0.494545\pi$
$614$	73.4687	2.96496
$615$	11.9823	0.483172
$616$	−5.35417	−0.215726
$617$	22.9027	0.922029	0.461014	−	0.887393i	$-0.347486\pi$
$617$	22.9027	0.922029	0.461014	+	0.887393i	$0.347486\pi$
$618$	−5.11706	−0.205838
$619$	−41.5809	−1.67128	−0.835640	−	0.549278i	$-0.814903\pi$
$619$	−41.5809	−1.67128	−0.835640	+	0.549278i	$0.814903\pi$
$620$	−57.2351	−2.29862
$621$	−42.2879	−1.69695
$622$	−53.0222	−2.12600
$623$	0.176402	0.00706738
$624$	−51.4250	−2.05865
$625$	1.00000	0.0400000
$626$	24.3474	0.973119
$627$	−1.81617	−0.0725309
$628$	16.9545	0.676556
$629$	−1.27541	−0.0508539
$630$	−5.19698	−0.207053
$631$	−21.6184	−0.860614	−0.430307	−	0.902683i	$-0.641595\pi$
$631$	−21.6184	−0.860614	−0.430307	+	0.902683i	$0.641595\pi$
$632$	143.653	5.71421
$633$	−7.23748	−0.287664
$634$	−47.2638	−1.87709
$635$	7.46000	0.296041
$636$	−76.3787	−3.02861
$637$	2.67005	0.105791
$638$	−10.6357	−0.421071
$639$	0.223565	0.00884410
$640$	−68.3962	−2.70360
$641$	7.17011	0.283202	0.141601	−	0.989924i	$-0.454775\pi$
$641$	7.17011	0.283202	0.141601	+	0.989924i	$0.454775\pi$
$642$	47.8999	1.89046
$643$	−7.74714	−0.305517	−0.152759	−	0.988264i	$-0.548816\pi$
$643$	−7.74714	−0.305517	−0.152759	+	0.988264i	$0.548816\pi$
$644$	47.2789	1.86305
$645$	2.92517	0.115179
$646$	2.09611	0.0824705
$647$	−31.7059	−1.24649	−0.623243	−	0.782028i	$-0.714185\pi$
$647$	−31.7059	−1.24649	−0.623243	+	0.782028i	$0.714185\pi$
$648$	0.474530	0.0186413
$649$	−7.34433	−0.288290
$650$	7.45727	0.292498
$651$	10.5319	0.412777
$652$	71.5530	2.80223
$653$	15.9434	0.623915	0.311957	−	0.950096i	$-0.399015\pi$
$653$	15.9434	0.623915	0.311957	+	0.950096i	$0.399015\pi$
$654$	−17.8391	−0.697565
$655$	14.3762	0.561724
$656$	202.572	7.90910
$657$	−12.6039	−0.491724
$658$	−24.2962	−0.947165
$659$	−35.3813	−1.37826	−0.689130	−	0.724638i	$-0.742007\pi$
$659$	−35.3813	−1.37826	−0.689130	+	0.724638i	$0.742007\pi$
$660$	3.12295	0.121561
$661$	−13.1239	−0.510460	−0.255230	−	0.966880i	$-0.582151\pi$
$661$	−13.1239	−0.510460	−0.255230	+	0.966880i	$0.582151\pi$
$662$	42.5889	1.65526
$663$	−0.634051	−0.0246245
$664$	−50.3668	−1.95461
$665$	3.37331	0.130811
$666$	29.7922	1.15443
$667$	61.5341	2.38261
$668$	−13.5664	−0.524898
$669$	−5.28431	−0.204303
$670$	−24.9995	−0.965815
$671$	2.81394	0.108631
$672$	31.1330	1.20098
$673$	−40.9151	−1.57716	−0.788581	−	0.614931i	$-0.789184\pi$
$673$	−40.9151	−1.57716	−0.788581	+	0.614931i	$0.789184\pi$
$674$	−5.40200	−0.208077
$675$	5.18814	0.199692
$676$	−34.0537	−1.30976
$677$	−3.54633	−0.136297	−0.0681484	−	0.997675i	$-0.521709\pi$
$677$	−3.54633	−0.136297	−0.0681484	+	0.997675i	$0.521709\pi$
$678$	18.6509	0.716285
$679$	−13.1772	−0.505694
$680$	−2.36155	−0.0905613
$681$	−13.8347	−0.530146
$682$	13.9012	0.532304
$683$	−2.22325	−0.0850703	−0.0425352	−	0.999095i	$-0.513543\pi$
$683$	−2.22325	−0.0850703	−0.0425352	+	0.999095i	$0.513543\pi$
$684$	−36.4092	−1.39214
$685$	−0.0595141	−0.00227392
$686$	−2.79293	−0.106635
$687$	−1.06735	−0.0407220
$688$	49.4529	1.88537
$689$	32.9397	1.25490
$690$	−24.2981	−0.925013
$691$	32.2910	1.22841	0.614203	−	0.789148i	$-0.289478\pi$
$691$	32.2910	1.22841	0.614203	+	0.789148i	$0.289478\pi$
$692$	120.259	4.57155
$693$	0.938605	0.0356547
$694$	29.8914	1.13466
$695$	15.1831	0.575927
$696$	85.5301	3.24201
$697$	2.49763	0.0946047
$698$	−49.1469	−1.86024
$699$	4.34210	0.164233
$700$	−5.80048	−0.219238
$701$	3.23802	0.122298	0.0611492	−	0.998129i	$-0.480523\pi$
$701$	3.23802	0.122298	0.0611492	+	0.998129i	$0.480523\pi$
$702$	38.6894	1.46024
$703$	−19.3379	−0.729341
$704$	22.8887	0.862652
$705$	9.28508	0.349696
$706$	60.0502	2.26002
$707$	8.22460	0.309318
$708$	90.1428	3.38777
$709$	41.8220	1.57066	0.785329	−	0.619078i	$-0.212494\pi$
$709$	41.8220	1.57066	0.785329	+	0.619078i	$0.212494\pi$
$710$	0.335563	0.0125935
$711$	−25.1829	−0.944433
$712$	−1.87241	−0.0701717
$713$	−80.4271	−3.01202
$714$	0.663233	0.0248209
$715$	−1.34683	−0.0503685
$716$	36.6710	1.37046
$717$	7.39597	0.276207
$718$	45.6735	1.70452
$719$	−20.7107	−0.772379	−0.386189	−	0.922419i	$-0.626209\pi$
$719$	−20.7107	−0.772379	−0.386189	+	0.922419i	$0.626209\pi$
$720$	33.5767	1.25133
$721$	−1.71653	−0.0639271
$722$	−21.2843	−0.792120
$723$	6.28929	0.233901
$724$	19.0376	0.707526
$725$	−7.54939	−0.280377
$726$	32.0330	1.18886
$727$	−10.0567	−0.372981	−0.186490	−	0.982457i	$-0.559711\pi$
$727$	−10.0567	−0.372981	−0.186490	+	0.982457i	$0.559711\pi$
$728$	−28.3412	−1.05040
$729$	16.5295	0.612205
$730$	−18.9180	−0.700185
$731$	0.609735	0.0225519
$732$	−34.5378	−1.27655
$733$	−34.1110	−1.25992	−0.629960	−	0.776628i	$-0.716929\pi$
$733$	−34.1110	−1.25992	−0.629960	+	0.776628i	$0.716929\pi$
$734$	−25.8307	−0.953428
$735$	1.06735	0.0393699
$736$	−237.748	−8.76351
$737$	4.51506	0.166314
$738$	−58.3421	−2.14760
$739$	14.8374	0.545802	0.272901	−	0.962042i	$-0.412017\pi$
$739$	14.8374	0.545802	0.272901	+	0.962042i	$0.412017\pi$
$740$	33.2519	1.22236
$741$	−9.61354	−0.353162
$742$	−34.4557	−1.26491
$743$	−26.0718	−0.956481	−0.478241	−	0.878229i	$-0.658725\pi$
$743$	−26.0718	−0.956481	−0.478241	+	0.878229i	$0.658725\pi$
$744$	−111.791	−4.09844
$745$	10.6241	0.389238
$746$	−81.7067	−2.99149
$747$	8.82949	0.323054
$748$	0.650960	0.0238015
$749$	16.0681	0.587117
$750$	2.98104	0.108852
$751$	−28.3565	−1.03474	−0.517371	−	0.855761i	$-0.673089\pi$
$751$	−28.3565	−1.03474	−0.517371	+	0.855761i	$0.673089\pi$
$752$	156.973	5.72423
$753$	12.9401	0.471563
$754$	−56.2978	−2.05025
$755$	−19.5077	−0.709959
$756$	−30.0937	−1.09450
$757$	36.4519	1.32487	0.662433	−	0.749121i	$-0.269524\pi$
$757$	36.4519	1.32487	0.662433	+	0.749121i	$0.269524\pi$
$758$	−20.4372	−0.742314
$759$	4.38838	0.159288
$760$	−35.8060	−1.29882
$761$	2.42204	0.0877990	0.0438995	−	0.999036i	$-0.486022\pi$
$761$	2.42204	0.0877990	0.0438995	+	0.999036i	$0.486022\pi$
$762$	22.2386	0.805619
$763$	−5.98418	−0.216642
$764$	124.961	4.52092
$765$	0.413988	0.0149678
$766$	−48.1075	−1.73819
$767$	−38.8757	−1.40372
$768$	−107.027	−3.86200
$769$	36.5506	1.31805	0.659024	−	0.752122i	$-0.270970\pi$
$769$	36.5506	1.31805	0.659024	+	0.752122i	$0.270970\pi$
$770$	1.40881	0.0507701
$771$	−19.4567	−0.700716
$772$	18.6001	0.669433
$773$	40.3857	1.45257	0.726286	−	0.687392i	$-0.241245\pi$
$773$	40.3857	1.45257	0.726286	+	0.687392i	$0.241245\pi$
$774$	−14.2428	−0.511946
$775$	9.86730	0.354444
$776$	139.869	5.02102
$777$	−6.11871	−0.219507
$778$	58.9198	2.11238
$779$	37.8693	1.35681
$780$	16.5307	0.591893
$781$	−0.0606048	−0.00216861
$782$	−5.06480	−0.181117
$783$	−39.1673	−1.39973
$784$	18.0446	0.644451
$785$	−2.92294	−0.104324
$786$	42.8560	1.52862
$787$	−48.8519	−1.74138	−0.870691	−	0.491831i	$-0.836328\pi$
$787$	−48.8519	−1.74138	−0.870691	+	0.491831i	$0.836328\pi$
$788$	−137.742	−4.90684
$789$	−3.25959	−0.116045
$790$	−37.7986	−1.34482
$791$	6.25651	0.222456
$792$	−9.96282	−0.354013
$793$	14.8950	0.528938
$794$	−60.5243	−2.14793
$795$	13.1676	0.467008
$796$	58.3571	2.06841
$797$	−1.20937	−0.0428382	−0.0214191	−	0.999771i	$-0.506818\pi$
$797$	−1.20937	−0.0428382	−0.0214191	+	0.999771i	$0.506818\pi$
$798$	10.0560	0.355978
$799$	1.93542	0.0684703
$800$	29.1685	1.03126
$801$	0.328241	0.0115978
$802$	56.3245	1.98889
$803$	3.41670	0.120573
$804$	−55.4169	−1.95440
$805$	−8.15087	−0.287280
$806$	73.5831	2.59185
$807$	−7.08777	−0.249501
$808$	−87.2999	−3.07120
$809$	26.0775	0.916835	0.458417	−	0.888737i	$-0.348417\pi$
$809$	26.0775	0.916835	0.458417	+	0.888737i	$0.348417\pi$
$810$	−0.124860	−0.00438715
$811$	−9.69833	−0.340554	−0.170277	−	0.985396i	$-0.554466\pi$
$811$	−9.69833	−0.340554	−0.170277	+	0.985396i	$0.554466\pi$
$812$	43.7901	1.53673
$813$	−3.87644	−0.135953
$814$	−8.07617	−0.283070
$815$	−12.3357	−0.432101
$816$	−4.28502	−0.150006
$817$	9.24486	0.323437
$818$	−76.9074	−2.68901
$819$	4.96832	0.173607
$820$	−65.1171	−2.27399
$821$	−50.1723	−1.75102	−0.875512	−	0.483196i	$-0.839476\pi$
$821$	−50.1723	−1.75102	−0.875512	+	0.483196i	$0.839476\pi$
$822$	−0.177414	−0.00618803
$823$	−23.6021	−0.822719	−0.411360	−	0.911473i	$-0.634946\pi$
$823$	−23.6021	−0.822719	−0.411360	+	0.911473i	$0.634946\pi$
$824$	18.2201	0.634729
$825$	−0.538394	−0.0187445
$826$	40.6649	1.41491
$827$	51.7386	1.79913	0.899563	−	0.436791i	$-0.143885\pi$
$827$	51.7386	1.79913	0.899563	+	0.436791i	$0.143885\pi$
$828$	87.9748	3.05733
$829$	3.08709	0.107219	0.0536095	−	0.998562i	$-0.482927\pi$
$829$	3.08709	0.107219	0.0536095	+	0.998562i	$0.482927\pi$
$830$	13.2527	0.460010
$831$	18.1587	0.629920
$832$	121.157	4.20036
$833$	0.222483	0.00770859
$834$	45.2614	1.56727
$835$	2.33883	0.0809386
$836$	9.86991	0.341358
$837$	51.1930	1.76949
$838$	−43.6906	−1.50927
$839$	−35.9323	−1.24052	−0.620260	−	0.784396i	$-0.712973\pi$
$839$	−35.9323	−1.24052	−0.620260	+	0.784396i	$0.712973\pi$
$840$	−11.3294	−0.390901
$841$	27.9933	0.965286
$842$	78.9038	2.71920
$843$	20.0487	0.690515
$844$	39.3318	1.35386
$845$	5.87084	0.201963
$846$	−45.2094	−1.55433
$847$	10.7456	0.369222
$848$	222.612	7.64452
$849$	−9.09235	−0.312049
$850$	0.621382	0.0213132
$851$	46.7257	1.60174
$852$	0.743851	0.0254839
$853$	−4.75056	−0.162656	−0.0813281	−	0.996687i	$-0.525916\pi$
$853$	−4.75056	−0.162656	−0.0813281	+	0.996687i	$0.525916\pi$
$854$	−15.5806	−0.533156
$855$	6.27692	0.214666
$856$	−170.555	−5.82946
$857$	−30.5487	−1.04352	−0.521762	−	0.853091i	$-0.674725\pi$
$857$	−30.5487	−1.04352	−0.521762	+	0.853091i	$0.674725\pi$
$858$	−4.01495	−0.137068
$859$	39.7302	1.35558	0.677789	−	0.735257i	$-0.262938\pi$
$859$	39.7302	1.35558	0.677789	+	0.735257i	$0.262938\pi$
$860$	−15.8967	−0.542074
$861$	11.9823	0.408355
$862$	−35.5135	−1.20959
$863$	−33.0975	−1.12665	−0.563325	−	0.826235i	$-0.690478\pi$
$863$	−33.0975	−1.12665	−0.563325	+	0.826235i	$0.690478\pi$
$864$	151.330	5.14835
$865$	−20.7325	−0.704927
$866$	28.1104	0.955230
$867$	18.0922	0.614442
$868$	−57.2351	−1.94269
$869$	6.82666	0.231579
$870$	−22.5051	−0.762993
$871$	23.8996	0.809805
$872$	63.5191	2.15103
$873$	−24.5196	−0.829863
$874$	−76.7929	−2.59756
$875$	1.00000	0.0338062
$876$	−41.9358	−1.41688
$877$	−43.0854	−1.45489	−0.727446	−	0.686165i	$-0.759293\pi$
$877$	−43.0854	−1.45489	−0.727446	+	0.686165i	$0.759293\pi$
$878$	−45.5258	−1.53642
$879$	−21.1594	−0.713690
$880$	−9.10208	−0.306831
$881$	−44.8177	−1.50995	−0.754974	−	0.655755i	$-0.772351\pi$
$881$	−44.8177	−1.50995	−0.754974	+	0.655755i	$0.772351\pi$
$882$	−5.19698	−0.174991
$883$	29.8559	1.00473	0.502366	−	0.864655i	$-0.332463\pi$
$883$	29.8559	1.00473	0.502366	+	0.864655i	$0.332463\pi$
$884$	3.44573	0.115892
$885$	−15.5406	−0.522391
$886$	2.76097	0.0927565
$887$	26.9891	0.906207	0.453103	−	0.891458i	$-0.350317\pi$
$887$	26.9891	0.906207	0.453103	+	0.891458i	$0.350317\pi$
$888$	64.9470	2.17948
$889$	7.46000	0.250200
$890$	0.492678	0.0165146
$891$	0.0225505	0.000755471 0
$892$	28.7174	0.961529
$893$	29.3450	0.981993
$894$	31.6710	1.05924
$895$	−6.32207	−0.211323
$896$	−68.3962	−2.28496
$897$	23.2290	0.775594
$898$	−72.4845	−2.41884
$899$	−74.4921	−2.48445
$900$	−10.7933	−0.359777
$901$	2.74472	0.0914399
$902$	15.8156	0.526601
$903$	2.92517	0.0973436
$904$	−66.4097	−2.20875
$905$	−3.28207	−0.109100
$906$	−58.1534	−1.93202
$907$	43.6688	1.45000	0.725000	−	0.688749i	$-0.241840\pi$
$907$	43.6688	1.45000	0.725000	+	0.688749i	$0.241840\pi$
$908$	75.1841	2.49507
$909$	15.3040	0.507602
$910$	7.45727	0.247206
$911$	0.376434	0.0124718	0.00623591	−	0.999981i	$-0.498015\pi$
$911$	0.376434	0.0124718	0.00623591	+	0.999981i	$0.498015\pi$
$912$	−64.9699	−2.15137
$913$	−2.39353	−0.0792141
$914$	−1.60894	−0.0532191
$915$	5.95429	0.196843
$916$	5.80048	0.191653
$917$	14.3762	0.474743
$918$	3.22382	0.106402
$919$	9.96284	0.328644	0.164322	−	0.986407i	$-0.447456\pi$
$919$	9.96284	0.328644	0.164322	+	0.986407i	$0.447456\pi$
$920$	86.5173	2.85239
$921$	−28.0769	−0.925166
$922$	−2.02593	−0.0667205
$923$	−0.320799	−0.0105592
$924$	3.12295	0.102737
$925$	−5.73261	−0.188487
$926$	28.1274	0.924322
$927$	−3.19406	−0.104907
$928$	−220.204	−7.22855
$929$	60.1465	1.97334	0.986671	−	0.162728i	$-0.0520294\pi$
$929$	60.1465	1.97334	0.986671	+	0.162728i	$0.0520294\pi$
$930$	29.4149	0.964551
$931$	3.37331	0.110556
$932$	−23.5970	−0.772945
$933$	20.2630	0.663382
$934$	−97.0517	−3.17563
$935$	−0.112225	−0.00367016
$936$	−52.7362	−1.72374
$937$	−41.3668	−1.35140	−0.675698	−	0.737179i	$-0.736157\pi$
$937$	−41.3668	−1.35140	−0.675698	+	0.737179i	$0.736157\pi$
$938$	−24.9995	−0.816263
$939$	−9.30466	−0.303646
$940$	−50.4594	−1.64580
$941$	−60.3573	−1.96759	−0.983796	−	0.179290i	$-0.942620\pi$
$941$	−60.3573	−1.96759	−0.983796	+	0.179290i	$0.942620\pi$
$942$	−8.71341	−0.283898
$943$	−91.5029	−2.97975
$944$	−262.728	−8.55108
$945$	5.18814	0.168770
$946$	3.86098	0.125531
$947$	37.8252	1.22915	0.614577	−	0.788857i	$-0.289327\pi$
$947$	37.8252	1.22915	0.614577	+	0.788857i	$0.289327\pi$
$948$	−83.7890	−2.72134
$949$	18.0856	0.587083
$950$	9.42144	0.305672
$951$	18.0624	0.585714
$952$	−2.36155	−0.0765382
$953$	33.0740	1.07137	0.535686	−	0.844417i	$-0.320053\pi$
$953$	33.0740	1.07137	0.535686	+	0.844417i	$0.320053\pi$
$954$	−64.1138	−2.07576
$955$	−21.5432	−0.697120
$956$	−40.1931	−1.29994
$957$	4.06455	0.131388
$958$	11.6737	0.377159
$959$	−0.0595141	−0.00192181
$960$	48.4325	1.56315
$961$	66.3637	2.14076
$962$	−42.7496	−1.37830
$963$	29.8990	0.963481
$964$	−34.1789	−1.10083
$965$	−3.20665	−0.103226
$966$	−24.2981	−0.781778
$967$	−15.4449	−0.496675	−0.248338	−	0.968674i	$-0.579884\pi$
$967$	−15.4449	−0.496675	−0.248338	+	0.968674i	$0.579884\pi$
$968$	−114.059	−3.66598
$969$	−0.801054	−0.0257336
$970$	−36.8030	−1.18167
$971$	46.1134	1.47985	0.739924	−	0.672690i	$-0.234861\pi$
$971$	46.1134	1.47985	0.739924	+	0.672690i	$0.234861\pi$
$972$	−90.5579	−2.90465
$973$	15.1831	0.486747
$974$	−55.3437	−1.77333
$975$	−2.84988	−0.0912692
$976$	100.663	3.22215
$977$	0.261368	0.00836189	0.00418095	−	0.999991i	$-0.498669\pi$
$977$	0.261368	0.00836189	0.00418095	+	0.999991i	$0.498669\pi$
$978$	−36.7733	−1.17588
$979$	−0.0889806	−0.00284383
$980$	−5.80048	−0.185290
$981$	−11.1351	−0.355517
$982$	27.4704	0.876616
$983$	2.27071	0.0724243	0.0362121	−	0.999344i	$-0.488471\pi$
$983$	2.27071	0.0724243	0.0362121	+	0.999344i	$0.488471\pi$
$984$	−127.186	−4.05453
$985$	23.7466	0.756629
$986$	−4.69105	−0.149394
$987$	9.28508	0.295547
$988$	52.2444	1.66212
$989$	−22.3382	−0.710312
$990$	2.62146	0.0833156
$991$	−60.9788	−1.93706	−0.968528	−	0.248903i	$-0.919930\pi$
$991$	−60.9788	−1.93706	−0.968528	+	0.248903i	$0.919930\pi$
$992$	287.814	9.13810
$993$	−16.2758	−0.516498
$994$	0.335563	0.0106434
$995$	−10.0607	−0.318946
$996$	29.3776	0.930866
$997$	−2.82451	−0.0894531	−0.0447265	−	0.998999i	$-0.514242\pi$
$997$	−2.82451	−0.0894531	−0.0447265	+	0.998999i	$0.514242\pi$
$998$	−80.5749	−2.55055
$999$	−29.7416	−0.940982

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8015.2.a.l.1.62	✓	62

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8015.2.a.l.1.62	✓	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)

\(f(q)\)	\(=\)	\(q+2.79293 q^{2} -1.06735 q^{3} +5.80048 q^{4} -1.00000 q^{5} -2.98104 q^{6} -1.00000 q^{7} +10.6145 q^{8} -1.86076 q^{9} +O(q^{10})\)	\(q+2.79293 q^{2} -1.06735 q^{3} +5.80048 q^{4} -1.00000 q^{5} -2.98104 q^{6} -1.00000 q^{7} +10.6145 q^{8} -1.86076 q^{9} -2.79293 q^{10} +0.504421 q^{11} -6.19116 q^{12} +2.67005 q^{13} -2.79293 q^{14} +1.06735 q^{15} +18.0446 q^{16} +0.222483 q^{17} -5.19698 q^{18} +3.37331 q^{19} -5.80048 q^{20} +1.06735 q^{21} +1.40881 q^{22} -8.15087 q^{23} -11.3294 q^{24} +1.00000 q^{25} +7.45727 q^{26} +5.18814 q^{27} -5.80048 q^{28} -7.54939 q^{29} +2.98104 q^{30} +9.86730 q^{31} +29.1685 q^{32} -0.538394 q^{33} +0.621382 q^{34} +1.00000 q^{35} -10.7933 q^{36} -5.73261 q^{37} +9.42144 q^{38} -2.84988 q^{39} -10.6145 q^{40} +11.2262 q^{41} +2.98104 q^{42} +2.74059 q^{43} +2.92588 q^{44} +1.86076 q^{45} -22.7648 q^{46} +8.69917 q^{47} -19.2600 q^{48} +1.00000 q^{49} +2.79293 q^{50} -0.237468 q^{51} +15.4876 q^{52} +12.3367 q^{53} +14.4901 q^{54} -0.504421 q^{55} -10.6145 q^{56} -3.60051 q^{57} -21.0850 q^{58} -14.5599 q^{59} +6.19116 q^{60} +5.57857 q^{61} +27.5587 q^{62} +1.86076 q^{63} +45.3763 q^{64} -2.67005 q^{65} -1.50370 q^{66} +8.95098 q^{67} +1.29051 q^{68} +8.69984 q^{69} +2.79293 q^{70} -0.120147 q^{71} -19.7510 q^{72} +6.77351 q^{73} -16.0108 q^{74} -1.06735 q^{75} +19.5668 q^{76} -0.504421 q^{77} -7.95953 q^{78} +13.5337 q^{79} -18.0446 q^{80} +0.0447058 q^{81} +31.3539 q^{82} -4.74510 q^{83} +6.19116 q^{84} -0.222483 q^{85} +7.65428 q^{86} +8.05786 q^{87} +5.35417 q^{88} -0.176402 q^{89} +5.19698 q^{90} -2.67005 q^{91} -47.2789 q^{92} -10.5319 q^{93} +24.2962 q^{94} -3.37331 q^{95} -31.1330 q^{96} +13.1772 q^{97} +2.79293 q^{98} -0.938605 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 62 q + 2 q^{2} + 11 q^{3} + 64 q^{4} - 62 q^{5} + 3 q^{6} - 62 q^{7} + 15 q^{8} + 69 q^{9}+O(q^{10}) \) 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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