LMFDB - Embedded newform 2005.2.a.g.1.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2005,2,Mod(1,2005)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2005, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("2005.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2005 = 5 \cdot 401 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2005.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:	$16.0100056053$
Analytic rank:	$0$
Dimension:	$37$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
Character	$\chi$	$=$	2005.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.791118 q^{2} +0.403039 q^{3} -1.37413 q^{4} +1.00000 q^{5} -0.318852 q^{6} +4.95364 q^{7} +2.66934 q^{8} -2.83756 q^{9} +O(q^{10})$	\(q-0.791118 q^{2} +0.403039 q^{3} -1.37413 q^{4} +1.00000 q^{5} -0.318852 q^{6} +4.95364 q^{7} +2.66934 q^{8} -2.83756 q^{9} -0.791118 q^{10} +1.72776 q^{11} -0.553829 q^{12} -6.32477 q^{13} -3.91892 q^{14} +0.403039 q^{15} +0.636504 q^{16} +4.42985 q^{17} +2.24484 q^{18} +1.59498 q^{19} -1.37413 q^{20} +1.99651 q^{21} -1.36686 q^{22} +3.09979 q^{23} +1.07585 q^{24} +1.00000 q^{25} +5.00364 q^{26} -2.35277 q^{27} -6.80696 q^{28} +3.59013 q^{29} -0.318852 q^{30} +6.53030 q^{31} -5.84222 q^{32} +0.696356 q^{33} -3.50453 q^{34} +4.95364 q^{35} +3.89918 q^{36} +8.41087 q^{37} -1.26182 q^{38} -2.54913 q^{39} +2.66934 q^{40} -9.81215 q^{41} -1.57948 q^{42} -4.70480 q^{43} -2.37418 q^{44} -2.83756 q^{45} -2.45230 q^{46} +0.745105 q^{47} +0.256536 q^{48} +17.5386 q^{49} -0.791118 q^{50} +1.78540 q^{51} +8.69106 q^{52} -10.8723 q^{53} +1.86132 q^{54} +1.72776 q^{55} +13.2229 q^{56} +0.642840 q^{57} -2.84021 q^{58} -0.447188 q^{59} -0.553829 q^{60} +13.3194 q^{61} -5.16624 q^{62} -14.0563 q^{63} +3.34888 q^{64} -6.32477 q^{65} -0.550900 q^{66} -12.5970 q^{67} -6.08719 q^{68} +1.24934 q^{69} -3.91892 q^{70} -2.48751 q^{71} -7.57440 q^{72} +5.13106 q^{73} -6.65399 q^{74} +0.403039 q^{75} -2.19172 q^{76} +8.55872 q^{77} +2.01666 q^{78} -11.6933 q^{79} +0.636504 q^{80} +7.56442 q^{81} +7.76257 q^{82} +6.32739 q^{83} -2.74347 q^{84} +4.42985 q^{85} +3.72205 q^{86} +1.44696 q^{87} +4.61198 q^{88} -0.806572 q^{89} +2.24484 q^{90} -31.3306 q^{91} -4.25952 q^{92} +2.63197 q^{93} -0.589466 q^{94} +1.59498 q^{95} -2.35465 q^{96} -2.17849 q^{97} -13.8751 q^{98} -4.90263 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 37 q + 11 q^{2} + 13 q^{3} + 43 q^{4} + 37 q^{5} - 2 q^{6} + 34 q^{7} + 27 q^{8} + 50 q^{9}+O(q^{10}) $ 37 * q + 11 * q^2 + 13 * q^3 + 43 * q^4 + 37 * q^5 - 2 * q^6 + 34 * q^7 + 27 * q^8 + 50 * q^9	\( 37 q + 11 q^{2} + 13 q^{3} + 43 q^{4} + 37 q^{5} - 2 q^{6} + 34 q^{7} + 27 q^{8} + 50 q^{9} + 11 q^{10} + 38 q^{11} + 24 q^{12} + 17 q^{13} + 14 q^{14} + 13 q^{15} + 47 q^{16} + 22 q^{17} + 18 q^{18} + 6 q^{19} + 43 q^{20} + 4 q^{21} + 18 q^{22} + 45 q^{23} - 19 q^{24} + 37 q^{25} - q^{26} + 43 q^{27} + 46 q^{28} + 17 q^{29} - 2 q^{30} - 13 q^{31} + 50 q^{32} + 12 q^{33} - 30 q^{34} + 34 q^{35} + 43 q^{36} + 9 q^{37} + q^{38} - 7 q^{39} + 27 q^{40} + 12 q^{41} - 38 q^{42} + 53 q^{43} + 36 q^{44} + 50 q^{45} - 15 q^{46} + 39 q^{47} - 6 q^{48} + 37 q^{49} + 11 q^{50} + 38 q^{51} + 17 q^{52} + 19 q^{53} - 62 q^{54} + 38 q^{55} + 18 q^{56} + 6 q^{57} - 13 q^{58} + 33 q^{59} + 24 q^{60} - 11 q^{61} + q^{62} + 98 q^{63} + 15 q^{64} + 17 q^{65} - 70 q^{66} + 49 q^{67} + 32 q^{68} - 36 q^{69} + 14 q^{70} + 19 q^{71} + 5 q^{72} + 39 q^{73} + 21 q^{74} + 13 q^{75} - 33 q^{76} + 34 q^{77} - 22 q^{78} - 9 q^{79} + 47 q^{80} + 49 q^{81} + 14 q^{82} + 114 q^{83} - 50 q^{84} + 22 q^{85} + 9 q^{86} + 56 q^{87} + 14 q^{88} + 2 q^{89} + 18 q^{90} - 29 q^{91} + 47 q^{92} - 7 q^{93} - 52 q^{94} + 6 q^{95} - 89 q^{96} + 4 q^{97} + 14 q^{98} + 57 q^{99}+O(q^{100}) \) 37 * q + 11 * q^2 + 13 * q^3 + 43 * q^4 + 37 * q^5 - 2 * q^6 + 34 * q^7 + 27 * q^8 + 50 * q^9 + 11 * q^10 + 38 * q^11 + 24 * q^12 + 17 * q^13 + 14 * q^14 + 13 * q^15 + 47 * q^16 + 22 * q^17 + 18 * q^18 + 6 * q^19 + 43 * q^20 + 4 * q^21 + 18 * q^22 + 45 * q^23 - 19 * q^24 + 37 * q^25 - q^26 + 43 * q^27 + 46 * q^28 + 17 * q^29 - 2 * q^30 - 13 * q^31 + 50 * q^32 + 12 * q^33 - 30 * q^34 + 34 * q^35 + 43 * q^36 + 9 * q^37 + q^38 - 7 * q^39 + 27 * q^40 + 12 * q^41 - 38 * q^42 + 53 * q^43 + 36 * q^44 + 50 * q^45 - 15 * q^46 + 39 * q^47 - 6 * q^48 + 37 * q^49 + 11 * q^50 + 38 * q^51 + 17 * q^52 + 19 * q^53 - 62 * q^54 + 38 * q^55 + 18 * q^56 + 6 * q^57 - 13 * q^58 + 33 * q^59 + 24 * q^60 - 11 * q^61 + q^62 + 98 * q^63 + 15 * q^64 + 17 * q^65 - 70 * q^66 + 49 * q^67 + 32 * q^68 - 36 * q^69 + 14 * q^70 + 19 * q^71 + 5 * q^72 + 39 * q^73 + 21 * q^74 + 13 * q^75 - 33 * q^76 + 34 * q^77 - 22 * q^78 - 9 * q^79 + 47 * q^80 + 49 * q^81 + 14 * q^82 + 114 * q^83 - 50 * q^84 + 22 * q^85 + 9 * q^86 + 56 * q^87 + 14 * q^88 + 2 * q^89 + 18 * q^90 - 29 * q^91 + 47 * q^92 - 7 * q^93 - 52 * q^94 + 6 * q^95 - 89 * q^96 + 4 * q^97 + 14 * q^98 + 57 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−0.791118	−0.559405	−0.279702	−	0.960087i	$-0.590236\pi$
$2$	−0.791118	−0.559405	−0.279702	+	0.960087i	$0.590236\pi$
$3$	0.403039	0.232695	0.116347	−	0.993209i	$-0.462881\pi$
$3$	0.403039	0.232695	0.116347	+	0.993209i	$0.462881\pi$
$4$	−1.37413	−0.687066
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−0.318852	−0.130171
$7$	4.95364	1.87230	0.936150	−	0.351600i	$-0.114362\pi$
$7$	4.95364	1.87230	0.936150	+	0.351600i	$0.114362\pi$
$8$	2.66934	0.943753
$9$	−2.83756	−0.945853
$10$	−0.791118	−0.250173
$11$	1.72776	0.520940	0.260470	−	0.965482i	$-0.416122\pi$
$11$	1.72776	0.520940	0.260470	+	0.965482i	$0.416122\pi$
$12$	−0.553829	−0.159877
$13$	−6.32477	−1.75417	−0.877087	−	0.480331i	$-0.840516\pi$
$13$	−6.32477	−1.75417	−0.877087	+	0.480331i	$0.840516\pi$
$14$	−3.91892	−1.04737
$15$	0.403039	0.104064
$16$	0.636504	0.159126
$17$	4.42985	1.07440	0.537198	−	0.843456i	$-0.319483\pi$
$17$	4.42985	1.07440	0.537198	+	0.843456i	$0.319483\pi$
$18$	2.24484	0.529115
$19$	1.59498	0.365914	0.182957	−	0.983121i	$-0.441433\pi$
$19$	1.59498	0.365914	0.182957	+	0.983121i	$0.441433\pi$
$20$	−1.37413	−0.307265
$21$	1.99651	0.435675
$22$	−1.36686	−0.291417
$23$	3.09979	0.646351	0.323176	−	0.946339i	$-0.395250\pi$
$23$	3.09979	0.646351	0.323176	+	0.946339i	$0.395250\pi$
$24$	1.07585	0.219606
$25$	1.00000	0.200000
$26$	5.00364	0.981294
$27$	−2.35277	−0.452790
$28$	−6.80696	−1.28639
$29$	3.59013	0.666670	0.333335	−	0.942809i	$-0.391826\pi$
$29$	3.59013	0.666670	0.333335	+	0.942809i	$0.391826\pi$
$30$	−0.318852	−0.0582141
$31$	6.53030	1.17288	0.586438	−	0.809994i	$-0.300530\pi$
$31$	6.53030	1.17288	0.586438	+	0.809994i	$0.300530\pi$
$32$	−5.84222	−1.03277
$33$	0.696356	0.121220
$34$	−3.50453	−0.601022
$35$	4.95364	0.837318
$36$	3.89918	0.649864
$37$	8.41087	1.38274	0.691370	−	0.722501i	$-0.257008\pi$
$37$	8.41087	1.38274	0.691370	+	0.722501i	$0.257008\pi$
$38$	−1.26182	−0.204694
$39$	−2.54913	−0.408187
$40$	2.66934	0.422059
$41$	−9.81215	−1.53240	−0.766200	−	0.642602i	$-0.777855\pi$
$41$	−9.81215	−1.53240	−0.766200	+	0.642602i	$0.777855\pi$
$42$	−1.57948	−0.243719
$43$	−4.70480	−0.717475	−0.358737	−	0.933439i	$-0.616793\pi$
$43$	−4.70480	−0.717475	−0.358737	+	0.933439i	$0.616793\pi$
$44$	−2.37418	−0.357920
$45$	−2.83756	−0.422998
$46$	−2.45230	−0.361572
$47$	0.745105	0.108685	0.0543424	−	0.998522i	$-0.482694\pi$
$47$	0.745105	0.108685	0.0543424	+	0.998522i	$0.482694\pi$
$48$	0.256536	0.0370278
$49$	17.5386	2.50551
$50$	−0.791118	−0.111881
$51$	1.78540	0.250006
$52$	8.69106	1.20523
$53$	−10.8723	−1.49342	−0.746712	−	0.665147i	$-0.768369\pi$
$53$	−10.8723	−1.49342	−0.746712	+	0.665147i	$0.768369\pi$
$54$	1.86132	0.253293
$55$	1.72776	0.232972
$56$	13.2229	1.76699
$57$	0.642840	0.0851463
$58$	−2.84021	−0.372938
$59$	−0.447188	−0.0582190	−0.0291095	−	0.999576i	$-0.509267\pi$
$59$	−0.447188	−0.0582190	−0.0291095	+	0.999576i	$0.509267\pi$
$60$	−0.553829	−0.0714990
$61$	13.3194	1.70537	0.852684	−	0.522426i	$-0.174973\pi$
$61$	13.3194	1.70537	0.852684	+	0.522426i	$0.174973\pi$
$62$	−5.16624	−0.656113
$63$	−14.0563	−1.77092
$64$	3.34888	0.418610
$65$	−6.32477	−0.784491
$66$	−0.550900	−0.0678111
$67$	−12.5970	−1.53897	−0.769485	−	0.638665i	$-0.779487\pi$
$67$	−12.5970	−1.53897	−0.769485	+	0.638665i	$0.779487\pi$
$68$	−6.08719	−0.738181
$69$	1.24934	0.150403
$70$	−3.91892	−0.468400
$71$	−2.48751	−0.295213	−0.147607	−	0.989046i	$-0.547157\pi$
$71$	−2.48751	−0.295213	−0.147607	+	0.989046i	$0.547157\pi$
$72$	−7.57440	−0.892652
$73$	5.13106	0.600545	0.300273	−	0.953853i	$-0.402922\pi$
$73$	5.13106	0.600545	0.300273	+	0.953853i	$0.402922\pi$
$74$	−6.65399	−0.773511
$75$	0.403039	0.0465390
$76$	−2.19172	−0.251407
$77$	8.55872	0.975357
$78$	2.01666	0.228342
$79$	−11.6933	−1.31560	−0.657802	−	0.753191i	$-0.728514\pi$
$79$	−11.6933	−1.31560	−0.657802	+	0.753191i	$0.728514\pi$
$80$	0.636504	0.0711633
$81$	7.56442	0.840491
$82$	7.76257	0.857232
$83$	6.32739	0.694521	0.347261	−	0.937769i	$-0.387112\pi$
$83$	6.32739	0.694521	0.347261	+	0.937769i	$0.387112\pi$
$84$	−2.74347	−0.299337
$85$	4.42985	0.480484
$86$	3.72205	0.401359
$87$	1.44696	0.155131
$88$	4.61198	0.491639
$89$	−0.806572	−0.0854965	−0.0427482	−	0.999086i	$-0.513611\pi$
$89$	−0.806572	−0.0854965	−0.0427482	+	0.999086i	$0.513611\pi$
$90$	2.24484	0.236627
$91$	−31.3306	−3.28434
$92$	−4.25952	−0.444086
$93$	2.63197	0.272922
$94$	−0.589466	−0.0607988
$95$	1.59498	0.163642
$96$	−2.35465	−0.240320
$97$	−2.17849	−0.221192	−0.110596	−	0.993865i	$-0.535276\pi$
$97$	−2.17849	−0.221192	−0.110596	+	0.993865i	$0.535276\pi$
$98$	−13.8751	−1.40159
$99$	−4.90263	−0.492733
$100$	−1.37413	−0.137413
$101$	10.8567	1.08028	0.540141	−	0.841574i	$-0.318371\pi$
$101$	10.8567	1.08028	0.540141	+	0.841574i	$0.318371\pi$
$102$	−1.41246	−0.139855
$103$	9.57034	0.942993	0.471497	−	0.881868i	$-0.343714\pi$
$103$	9.57034	0.942993	0.471497	+	0.881868i	$0.343714\pi$
$104$	−16.8829	−1.65551
$105$	1.99651	0.194840
$106$	8.60127	0.835429
$107$	8.38383	0.810496	0.405248	−	0.914207i	$-0.367185\pi$
$107$	8.38383	0.810496	0.405248	+	0.914207i	$0.367185\pi$
$108$	3.23301	0.311097
$109$	18.2028	1.74352	0.871758	−	0.489936i	$-0.162980\pi$
$109$	18.2028	1.74352	0.871758	+	0.489936i	$0.162980\pi$
$110$	−1.36686	−0.130325
$111$	3.38991	0.321756
$112$	3.15301	0.297932
$113$	14.8386	1.39590	0.697948	−	0.716148i	$-0.254097\pi$
$113$	14.8386	1.39590	0.697948	+	0.716148i	$0.254097\pi$
$114$	−0.508563	−0.0476313
$115$	3.09979	0.289057
$116$	−4.93331	−0.458046
$117$	17.9469	1.65919
$118$	0.353779	0.0325680
$119$	21.9439	2.01159
$120$	1.07585	0.0982110
$121$	−8.01483	−0.728621
$122$	−10.5372	−0.953992
$123$	−3.95468	−0.356582
$124$	−8.97349	−0.805844
$125$	1.00000	0.0894427
$126$	11.1202	0.990662
$127$	11.0541	0.980889	0.490444	−	0.871472i	$-0.336834\pi$
$127$	11.0541	0.980889	0.490444	+	0.871472i	$0.336834\pi$
$128$	9.03509	0.798596
$129$	−1.89622	−0.166953
$130$	5.00364	0.438848
$131$	11.0907	0.968995	0.484497	−	0.874793i	$-0.339002\pi$
$131$	11.0907	0.968995	0.484497	+	0.874793i	$0.339002\pi$
$132$	−0.956886	−0.0832862
$133$	7.90097	0.685101
$134$	9.96573	0.860908
$135$	−2.35277	−0.202494
$136$	11.8247	1.01396
$137$	−16.8526	−1.43981	−0.719907	−	0.694070i	$-0.755816\pi$
$137$	−16.8526	−1.43981	−0.719907	+	0.694070i	$0.755816\pi$
$138$	−0.988374	−0.0841360
$139$	9.33306	0.791620	0.395810	−	0.918332i	$-0.370464\pi$
$139$	9.33306	0.791620	0.395810	+	0.918332i	$0.370464\pi$
$140$	−6.80696	−0.575293
$141$	0.300307	0.0252904
$142$	1.96792	0.165144
$143$	−10.9277	−0.913820
$144$	−1.80612	−0.150510
$145$	3.59013	0.298144
$146$	−4.05927	−0.335948
$147$	7.06873	0.583019
$148$	−11.5577	−0.950033
$149$	17.7819	1.45675	0.728373	−	0.685181i	$-0.240277\pi$
$149$	17.7819	1.45675	0.728373	+	0.685181i	$0.240277\pi$
$150$	−0.318852	−0.0260341
$151$	−18.9046	−1.53844	−0.769218	−	0.638987i	$-0.779354\pi$
$151$	−18.9046	−1.53844	−0.769218	+	0.638987i	$0.779354\pi$
$152$	4.25754	0.345332
$153$	−12.5699	−1.01622
$154$	−6.77096	−0.545619
$155$	6.53030	0.524526
$156$	3.50284	0.280452
$157$	15.0201	1.19873	0.599366	−	0.800475i	$-0.295420\pi$
$157$	15.0201	1.19873	0.599366	+	0.800475i	$0.295420\pi$
$158$	9.25081	0.735955
$159$	−4.38196	−0.347512
$160$	−5.84222	−0.461868
$161$	15.3553	1.21016
$162$	−5.98435	−0.470175
$163$	−3.80340	−0.297906	−0.148953	−	0.988844i	$-0.547590\pi$
$163$	−3.80340	−0.297906	−0.148953	+	0.988844i	$0.547590\pi$
$164$	13.4832	1.05286
$165$	0.696356	0.0542113
$166$	−5.00571	−0.388519
$167$	11.8657	0.918199	0.459099	−	0.888385i	$-0.348172\pi$
$167$	11.8657	0.918199	0.459099	+	0.888385i	$0.348172\pi$
$168$	5.32936	0.411169
$169$	27.0027	2.07713
$170$	−3.50453	−0.268785
$171$	−4.52586	−0.346101
$172$	6.46501	0.492953
$173$	7.73327	0.587950	0.293975	−	0.955813i	$-0.405022\pi$
$173$	7.73327	0.587950	0.293975	+	0.955813i	$0.405022\pi$
$174$	−1.14472	−0.0867808
$175$	4.95364	0.374460
$176$	1.09973	0.0828951
$177$	−0.180234	−0.0135473
$178$	0.638094	0.0478272
$179$	11.5713	0.864877	0.432439	−	0.901663i	$-0.357653\pi$
$179$	11.5713	0.864877	0.432439	+	0.901663i	$0.357653\pi$
$180$	3.89918	0.290628
$181$	−5.86839	−0.436194	−0.218097	−	0.975927i	$-0.569985\pi$
$181$	−5.86839	−0.436194	−0.218097	+	0.975927i	$0.569985\pi$
$182$	24.7862	1.83728
$183$	5.36822	0.396830
$184$	8.27439	0.609996
$185$	8.41087	0.618380
$186$	−2.08220	−0.152674
$187$	7.65372	0.559696
$188$	−1.02387	−0.0746736
$189$	−11.6548	−0.847759
$190$	−1.26182	−0.0915420
$191$	23.5487	1.70392	0.851961	−	0.523605i	$-0.175413\pi$
$191$	23.5487	1.70392	0.851961	+	0.523605i	$0.175413\pi$
$192$	1.34973	0.0974084
$193$	−7.66512	−0.551748	−0.275874	−	0.961194i	$-0.588967\pi$
$193$	−7.66512	−0.551748	−0.275874	+	0.961194i	$0.588967\pi$
$194$	1.72344	0.123736
$195$	−2.54913	−0.182547
$196$	−24.1003	−1.72145
$197$	2.06382	0.147041	0.0735204	−	0.997294i	$-0.476577\pi$
$197$	2.06382	0.147041	0.0735204	+	0.997294i	$0.476577\pi$
$198$	3.87856	0.275637
$199$	−17.2937	−1.22592	−0.612960	−	0.790114i	$-0.710021\pi$
$199$	−17.2937	−1.22592	−0.612960	+	0.790114i	$0.710021\pi$
$200$	2.66934	0.188751
$201$	−5.07709	−0.358110
$202$	−8.58893	−0.604315
$203$	17.7842	1.24821
$204$	−2.45338	−0.171771
$205$	−9.81215	−0.685310
$206$	−7.57127	−0.527515
$207$	−8.79584	−0.611353
$208$	−4.02574	−0.279135
$209$	2.75575	0.190619
$210$	−1.57948	−0.108994
$211$	−26.6546	−1.83498	−0.917488	−	0.397764i	$-0.869786\pi$
$211$	−26.6546	−1.83498	−0.917488	+	0.397764i	$0.869786\pi$
$212$	14.9400	1.02608
$213$	−1.00256	−0.0686946
$214$	−6.63260	−0.453395
$215$	−4.70480	−0.320864
$216$	−6.28032	−0.427322
$217$	32.3488	2.19598
$218$	−14.4006	−0.975332
$219$	2.06802	0.139744
$220$	−2.37418	−0.160067
$221$	−28.0177	−1.88468
$222$	−2.68182	−0.179992
$223$	−16.1968	−1.08462	−0.542308	−	0.840180i	$-0.682449\pi$
$223$	−16.1968	−1.08462	−0.542308	+	0.840180i	$0.682449\pi$
$224$	−28.9403	−1.93365
$225$	−2.83756	−0.189171
$226$	−11.7391	−0.780871
$227$	−3.18113	−0.211139	−0.105569	−	0.994412i	$-0.533667\pi$
$227$	−3.18113	−0.211139	−0.105569	+	0.994412i	$0.533667\pi$
$228$	−0.883348	−0.0585011
$229$	−16.5328	−1.09252	−0.546258	−	0.837617i	$-0.683948\pi$
$229$	−16.5328	−1.09252	−0.546258	+	0.837617i	$0.683948\pi$
$230$	−2.45230	−0.161700
$231$	3.44950	0.226960
$232$	9.58325	0.629171
$233$	−22.4135	−1.46836	−0.734179	−	0.678956i	$-0.762433\pi$
$233$	−22.4135	−1.46836	−0.734179	+	0.678956i	$0.762433\pi$
$234$	−14.1981	−0.928160
$235$	0.745105	0.0486053
$236$	0.614496	0.0400003
$237$	−4.71288	−0.306134
$238$	−17.3602	−1.12529
$239$	−20.2498	−1.30985	−0.654926	−	0.755693i	$-0.727300\pi$
$239$	−20.2498	−1.30985	−0.654926	+	0.755693i	$0.727300\pi$
$240$	0.256536	0.0165593
$241$	−22.9933	−1.48113	−0.740564	−	0.671986i	$-0.765442\pi$
$241$	−22.9933	−1.48113	−0.740564	+	0.671986i	$0.765442\pi$
$242$	6.34068	0.407594
$243$	10.1071	0.648368
$244$	−18.3026	−1.17170
$245$	17.5386	1.12050
$246$	3.12862	0.199474
$247$	−10.0879	−0.641877
$248$	17.4316	1.10691
$249$	2.55019	0.161612
$250$	−0.791118	−0.0500347
$251$	22.7699	1.43722	0.718611	−	0.695412i	$-0.244778\pi$
$251$	22.7699	1.43722	0.718611	+	0.695412i	$0.244778\pi$
$252$	19.3152	1.21674
$253$	5.35571	0.336710
$254$	−8.74506	−0.548714
$255$	1.78540	0.111806
$256$	−13.8456	−0.865349
$257$	14.9262	0.931073	0.465537	−	0.885029i	$-0.345861\pi$
$257$	14.9262	0.931073	0.465537	+	0.885029i	$0.345861\pi$
$258$	1.50013	0.0933941
$259$	41.6645	2.58890
$260$	8.69106	0.538997
$261$	−10.1872	−0.630571
$262$	−8.77402	−0.542061
$263$	23.0909	1.42384	0.711922	−	0.702259i	$-0.247825\pi$
$263$	23.0909	1.42384	0.711922	+	0.702259i	$0.247825\pi$
$264$	1.85881	0.114402
$265$	−10.8723	−0.667880
$266$	−6.25060	−0.383249
$267$	−0.325080	−0.0198946
$268$	17.3100	1.05737
$269$	−17.3612	−1.05853	−0.529266	−	0.848456i	$-0.677533\pi$
$269$	−17.3612	−1.05853	−0.529266	+	0.848456i	$0.677533\pi$
$270$	1.86132	0.113276
$271$	−31.1875	−1.89450	−0.947252	−	0.320489i	$-0.896153\pi$
$271$	−31.1875	−1.89450	−0.947252	+	0.320489i	$0.896153\pi$
$272$	2.81961	0.170964
$273$	−12.6275	−0.764249
$274$	13.3324	0.805439
$275$	1.72776	0.104188
$276$	−1.71676	−0.103337
$277$	23.3615	1.40366	0.701828	−	0.712347i	$-0.252368\pi$
$277$	23.3615	1.40366	0.701828	+	0.712347i	$0.252368\pi$
$278$	−7.38355	−0.442836
$279$	−18.5301	−1.10937
$280$	13.2229	0.790222
$281$	−25.4784	−1.51991	−0.759957	−	0.649973i	$-0.774780\pi$
$281$	−25.4784	−1.51991	−0.759957	+	0.649973i	$0.774780\pi$
$282$	−0.237578	−0.0141476
$283$	7.78545	0.462797	0.231398	−	0.972859i	$-0.425670\pi$
$283$	7.78545	0.462797	0.231398	+	0.972859i	$0.425670\pi$
$284$	3.41817	0.202831
$285$	0.642840	0.0380786
$286$	8.64510	0.511195
$287$	−48.6059	−2.86911
$288$	16.5777	0.976848
$289$	2.62353	0.154325
$290$	−2.84021	−0.166783
$291$	−0.878016	−0.0514702
$292$	−7.05075	−0.412614
$293$	3.91287	0.228592	0.114296	−	0.993447i	$-0.463539\pi$
$293$	3.91287	0.228592	0.114296	+	0.993447i	$0.463539\pi$
$294$	−5.59220	−0.326144
$295$	−0.447188	−0.0260363
$296$	22.4515	1.30496
$297$	−4.06502	−0.235876
$298$	−14.0675	−0.814911
$299$	−19.6055	−1.13381
$300$	−0.553829	−0.0319753
$301$	−23.3059	−1.34333
$302$	14.9558	0.860608
$303$	4.37568	0.251376
$304$	1.01521	0.0582264
$305$	13.3194	0.762664
$306$	9.94431	0.568479
$307$	−4.54519	−0.259408	−0.129704	−	0.991553i	$-0.541403\pi$
$307$	−4.54519	−0.259408	−0.129704	+	0.991553i	$0.541403\pi$
$308$	−11.7608	−0.670135
$309$	3.85722	0.219430
$310$	−5.16624	−0.293423
$311$	8.67993	0.492194	0.246097	−	0.969245i	$-0.420852\pi$
$311$	8.67993	0.492194	0.246097	+	0.969245i	$0.420852\pi$
$312$	−6.80448	−0.385228
$313$	18.5037	1.04589	0.522946	−	0.852366i	$-0.324833\pi$
$313$	18.5037	1.04589	0.522946	+	0.852366i	$0.324833\pi$
$314$	−11.8826	−0.670576
$315$	−14.0563	−0.791980
$316$	16.0682	0.903907
$317$	3.23273	0.181568	0.0907840	−	0.995871i	$-0.471063\pi$
$317$	3.23273	0.181568	0.0907840	+	0.995871i	$0.471063\pi$
$318$	3.46665	0.194400
$319$	6.20289	0.347295
$320$	3.34888	0.187208
$321$	3.37901	0.188598
$322$	−12.1478	−0.676972
$323$	7.06552	0.393136
$324$	−10.3945	−0.577473
$325$	−6.32477	−0.350835
$326$	3.00894	0.166650
$327$	7.33646	0.405707
$328$	−26.1919	−1.44621
$329$	3.69098	0.203491
$330$	−0.550900	−0.0303261
$331$	27.6065	1.51739	0.758695	−	0.651446i	$-0.225837\pi$
$331$	27.6065	1.51739	0.758695	+	0.651446i	$0.225837\pi$
$332$	−8.69467	−0.477182
$333$	−23.8664	−1.30787
$334$	−9.38721	−0.513645
$335$	−12.5970	−0.688249
$336$	1.27079	0.0693272
$337$	18.6221	1.01441	0.507205	−	0.861826i	$-0.330679\pi$
$337$	18.6221	1.01441	0.507205	+	0.861826i	$0.330679\pi$
$338$	−21.3623	−1.16196
$339$	5.98053	0.324818
$340$	−6.08719	−0.330124
$341$	11.2828	0.610998
$342$	3.58049	0.193611
$343$	52.2043	2.81877
$344$	−12.5587	−0.677119
$345$	1.24934	0.0672621
$346$	−6.11793	−0.328902
$347$	4.53156	0.243267	0.121633	−	0.992575i	$-0.461187\pi$
$347$	4.53156	0.243267	0.121633	+	0.992575i	$0.461187\pi$
$348$	−1.98832	−0.106585
$349$	3.49557	0.187114	0.0935569	−	0.995614i	$-0.470176\pi$
$349$	3.49557	0.187114	0.0935569	+	0.995614i	$0.470176\pi$
$350$	−3.91892	−0.209475
$351$	14.8807	0.794272
$352$	−10.0940	−0.538011
$353$	15.5586	0.828100	0.414050	−	0.910254i	$-0.364114\pi$
$353$	15.5586	0.828100	0.414050	+	0.910254i	$0.364114\pi$
$354$	0.142587	0.00757840
$355$	−2.48751	−0.132023
$356$	1.10834	0.0587417
$357$	8.84424	0.468087
$358$	−9.15424	−0.483817
$359$	−13.8048	−0.728588	−0.364294	−	0.931284i	$-0.618690\pi$
$359$	−13.8048	−0.728588	−0.364294	+	0.931284i	$0.618690\pi$
$360$	−7.57440	−0.399206
$361$	−16.4560	−0.866107
$362$	4.64259	0.244009
$363$	−3.23029	−0.169546
$364$	43.0524	2.25656
$365$	5.13106	0.268572
$366$	−4.24690	−0.221989
$367$	−12.4553	−0.650159	−0.325080	−	0.945687i	$-0.605391\pi$
$367$	−12.4553	−0.650159	−0.325080	+	0.945687i	$0.605391\pi$
$368$	1.97303	0.102851
$369$	27.8426	1.44943
$370$	−6.65399	−0.345925
$371$	−53.8575	−2.79614
$372$	−3.61667	−0.187516
$373$	−20.1265	−1.04211	−0.521056	−	0.853522i	$-0.674462\pi$
$373$	−20.1265	−1.04211	−0.521056	+	0.853522i	$0.674462\pi$
$374$	−6.05500	−0.313097
$375$	0.403039	0.0208129
$376$	1.98894	0.102572
$377$	−22.7067	−1.16945
$378$	9.22029	0.474241
$379$	−18.4846	−0.949490	−0.474745	−	0.880124i	$-0.657460\pi$
$379$	−18.4846	−0.949490	−0.474745	+	0.880124i	$0.657460\pi$
$380$	−2.19172	−0.112433
$381$	4.45522	0.228248
$382$	−18.6298	−0.953182
$383$	−20.7568	−1.06062	−0.530312	−	0.847803i	$-0.677925\pi$
$383$	−20.7568	−1.06062	−0.530312	+	0.847803i	$0.677925\pi$
$384$	3.64149	0.185829
$385$	8.55872	0.436193
$386$	6.06402	0.308650
$387$	13.3501	0.678626
$388$	2.99353	0.151973
$389$	23.4938	1.19118	0.595592	−	0.803287i	$-0.296918\pi$
$389$	23.4938	1.19118	0.595592	+	0.803287i	$0.296918\pi$
$390$	2.01666	0.102118
$391$	13.7316	0.694437
$392$	46.8164	2.36458
$393$	4.46997	0.225480
$394$	−1.63272	−0.0822553
$395$	−11.6933	−0.588356
$396$	6.73686	0.338540
$397$	−15.8748	−0.796735	−0.398367	−	0.917226i	$-0.630423\pi$
$397$	−15.8748	−0.796735	−0.398367	+	0.917226i	$0.630423\pi$
$398$	13.6814	0.685786
$399$	3.18440	0.159419
$400$	0.636504	0.0318252
$401$	−1.00000	−0.0499376
$401$	−1.00000	−0.0499376
$402$	4.01658	0.200329
$403$	−41.3026	−2.05743
$404$	−14.9185	−0.742225
$405$	7.56442	0.375879
$406$	−14.0694	−0.698253
$407$	14.5320	0.720325
$408$	4.76584	0.235944
$409$	−1.43507	−0.0709597	−0.0354798	−	0.999370i	$-0.511296\pi$
$409$	−1.43507	−0.0709597	−0.0354798	+	0.999370i	$0.511296\pi$
$410$	7.76257	0.383366
$411$	−6.79226	−0.335037
$412$	−13.1509	−0.647899
$413$	−2.21521	−0.109003
$414$	6.95855	0.341994
$415$	6.32739	0.310599
$416$	36.9507	1.81166
$417$	3.76159	0.184206
$418$	−2.18012	−0.106633
$419$	15.7197	0.767957	0.383978	−	0.923342i	$-0.374554\pi$
$419$	15.7197	0.767957	0.383978	+	0.923342i	$0.374554\pi$
$420$	−2.74347	−0.133868
$421$	34.0320	1.65862	0.829309	−	0.558791i	$-0.188734\pi$
$421$	34.0320	1.65862	0.829309	+	0.558791i	$0.188734\pi$
$422$	21.0869	1.02649
$423$	−2.11428	−0.102800
$424$	−29.0218	−1.40942
$425$	4.42985	0.214879
$426$	0.793147	0.0384281
$427$	65.9793	3.19296
$428$	−11.5205	−0.556864
$429$	−4.40429	−0.212641
$430$	3.72205	0.179493
$431$	9.40553	0.453048	0.226524	−	0.974006i	$-0.427264\pi$
$431$	9.40553	0.453048	0.226524	+	0.974006i	$0.427264\pi$
$432$	−1.49754	−0.0720506
$433$	−8.54869	−0.410824	−0.205412	−	0.978676i	$-0.565853\pi$
$433$	−8.54869	−0.410824	−0.205412	+	0.978676i	$0.565853\pi$
$434$	−25.5917	−1.22844
$435$	1.44696	0.0693765
$436$	−25.0131	−1.19791
$437$	4.94411	0.236509
$438$	−1.63605	−0.0781733
$439$	−33.6464	−1.60585	−0.802927	−	0.596077i	$-0.796725\pi$
$439$	−33.6464	−1.60585	−0.802927	+	0.596077i	$0.796725\pi$
$440$	4.61198	0.219868
$441$	−49.7667	−2.36984
$442$	22.1653	1.05430
$443$	7.27920	0.345845	0.172923	−	0.984935i	$-0.444679\pi$
$443$	7.27920	0.345845	0.172923	+	0.984935i	$0.444679\pi$
$444$	−4.65819	−0.221068
$445$	−0.806572	−0.0382352
$446$	12.8136	0.606739
$447$	7.16678	0.338977
$448$	16.5892	0.783764
$449$	−36.8917	−1.74103	−0.870513	−	0.492145i	$-0.836213\pi$
$449$	−36.8917	−1.74103	−0.870513	+	0.492145i	$0.836213\pi$
$450$	2.24484	0.105823
$451$	−16.9531	−0.798289
$452$	−20.3902	−0.959073
$453$	−7.61930	−0.357986
$454$	2.51665	0.118112
$455$	−31.3306	−1.46880
$456$	1.71596	0.0803571
$457$	16.4408	0.769067	0.384533	−	0.923111i	$-0.374362\pi$
$457$	16.4408	0.769067	0.384533	+	0.923111i	$0.374362\pi$
$458$	13.0794	0.611158
$459$	−10.4224	−0.486475
$460$	−4.25952	−0.198601
$461$	14.1042	0.656899	0.328450	−	0.944522i	$-0.393474\pi$
$461$	14.1042	0.656899	0.328450	+	0.944522i	$0.393474\pi$
$462$	−2.72896	−0.126963
$463$	−7.43444	−0.345508	−0.172754	−	0.984965i	$-0.555267\pi$
$463$	−7.43444	−0.345508	−0.172754	+	0.984965i	$0.555267\pi$
$464$	2.28513	0.106084
$465$	2.63197	0.122055
$466$	17.7317	0.821407
$467$	−31.4636	−1.45596	−0.727982	−	0.685596i	$-0.759541\pi$
$467$	−31.4636	−1.45596	−0.727982	+	0.685596i	$0.759541\pi$
$468$	−24.6614	−1.13997
$469$	−62.4011	−2.88142
$470$	−0.589466	−0.0271900
$471$	6.05367	0.278939
$472$	−1.19370	−0.0549443
$473$	−8.12878	−0.373762
$474$	3.72844	0.171253
$475$	1.59498	0.0731828
$476$	−30.1538	−1.38210
$477$	30.8508	1.41256
$478$	16.0200	0.732738
$479$	19.0153	0.868834	0.434417	−	0.900712i	$-0.356955\pi$
$479$	19.0153	0.868834	0.434417	+	0.900712i	$0.356955\pi$
$480$	−2.35465	−0.107474
$481$	−53.1968	−2.42557
$482$	18.1904	0.828550
$483$	6.18877	0.281599
$484$	11.0134	0.500611
$485$	−2.17849	−0.0989200
$486$	−7.99587	−0.362700
$487$	12.6325	0.572435	0.286217	−	0.958165i	$-0.407602\pi$
$487$	12.6325	0.572435	0.286217	+	0.958165i	$0.407602\pi$
$488$	35.5539	1.60945
$489$	−1.53292	−0.0693211
$490$	−13.8751	−0.626812
$491$	−2.57204	−0.116075	−0.0580374	−	0.998314i	$-0.518484\pi$
$491$	−2.57204	−0.116075	−0.0580374	+	0.998314i	$0.518484\pi$
$492$	5.43426	0.244995
$493$	15.9037	0.716267
$494$	7.98071	0.359069
$495$	−4.90263	−0.220357
$496$	4.15656	0.186635
$497$	−12.3222	−0.552728
$498$	−2.01750	−0.0904063
$499$	−4.93956	−0.221125	−0.110562	−	0.993869i	$-0.535265\pi$
$499$	−4.93956	−0.221125	−0.110562	+	0.993869i	$0.535265\pi$
$500$	−1.37413	−0.0614531
$501$	4.78236	0.213660
$502$	−18.0137	−0.803989
$503$	−24.6438	−1.09881	−0.549406	−	0.835555i	$-0.685146\pi$
$503$	−24.6438	−1.09881	−0.549406	+	0.835555i	$0.685146\pi$
$504$	−37.5209	−1.67131
$505$	10.8567	0.483117
$506$	−4.23700	−0.188357
$507$	10.8831	0.483337
$508$	−15.1897	−0.673935
$509$	−6.99963	−0.310253	−0.155126	−	0.987895i	$-0.549579\pi$
$509$	−6.99963	−0.310253	−0.155126	+	0.987895i	$0.549579\pi$
$510$	−1.41246	−0.0625449
$511$	25.4174	1.12440
$512$	−7.11668	−0.314516
$513$	−3.75262	−0.165682
$514$	−11.8084	−0.520847
$515$	9.57034	0.421719
$516$	2.60565	0.114708
$517$	1.28737	0.0566183
$518$	−32.9615	−1.44825
$519$	3.11681	0.136813
$520$	−16.8829	−0.740365
$521$	−1.51222	−0.0662514	−0.0331257	−	0.999451i	$-0.510546\pi$
$521$	−1.51222	−0.0662514	−0.0331257	+	0.999451i	$0.510546\pi$
$522$	8.05927	0.352745
$523$	−25.9884	−1.13640	−0.568198	−	0.822892i	$-0.692359\pi$
$523$	−25.9884	−1.13640	−0.568198	+	0.822892i	$0.692359\pi$
$524$	−15.2400	−0.665764
$525$	1.99651	0.0871349
$526$	−18.2676	−0.796505
$527$	28.9282	1.26013
$528$	0.443234	0.0192893
$529$	−13.3913	−0.582230
$530$	8.60127	0.373615
$531$	1.26892	0.0550666
$532$	−10.8570	−0.470710
$533$	62.0596	2.68810
$534$	0.257177	0.0111291
$535$	8.38383	0.362465
$536$	−33.6257	−1.45241
$537$	4.66368	0.201252
$538$	13.7348	0.592148
$539$	30.3025	1.30522
$540$	3.23301	0.139127
$541$	−2.36953	−0.101874	−0.0509371	−	0.998702i	$-0.516221\pi$
$541$	−2.36953	−0.101874	−0.0509371	+	0.998702i	$0.516221\pi$
$542$	24.6730	1.05980
$543$	−2.36519	−0.101500
$544$	−25.8801	−1.10960
$545$	18.2028	0.779724
$546$	9.98982	0.427525
$547$	19.4388	0.831142	0.415571	−	0.909561i	$-0.363582\pi$
$547$	19.4388	0.831142	0.415571	+	0.909561i	$0.363582\pi$
$548$	23.1577	0.989247
$549$	−37.7945	−1.61303
$550$	−1.36686	−0.0582833
$551$	5.72619	0.243944
$552$	3.33490	0.141943
$553$	−57.9246	−2.46321
$554$	−18.4817	−0.785212
$555$	3.38991	0.143894
$556$	−12.8249	−0.543895
$557$	−25.1792	−1.06688	−0.533439	−	0.845839i	$-0.679101\pi$
$557$	−25.1792	−1.06688	−0.533439	+	0.845839i	$0.679101\pi$
$558$	14.6595	0.620586
$559$	29.7567	1.25858
$560$	3.15301	0.133239
$561$	3.08475	0.130238
$562$	20.1564	0.850248
$563$	33.6123	1.41659	0.708295	−	0.705916i	$-0.249465\pi$
$563$	33.6123	1.41659	0.708295	+	0.705916i	$0.249465\pi$
$564$	−0.412661	−0.0173762
$565$	14.8386	0.624264
$566$	−6.15921	−0.258891
$567$	37.4714	1.57365
$568$	−6.64001	−0.278609
$569$	−46.2866	−1.94044	−0.970218	−	0.242233i	$-0.922120\pi$
$569$	−46.2866	−1.94044	−0.970218	+	0.242233i	$0.922120\pi$
$570$	−0.508563	−0.0213013
$571$	−2.95950	−0.123851	−0.0619256	−	0.998081i	$-0.519724\pi$
$571$	−2.95950	−0.123851	−0.0619256	+	0.998081i	$0.519724\pi$
$572$	15.0161	0.627855
$573$	9.49104	0.396494
$574$	38.4530	1.60500
$575$	3.09979	0.129270
$576$	−9.50265	−0.395944
$577$	−42.5650	−1.77200	−0.886001	−	0.463683i	$-0.846528\pi$
$577$	−42.5650	−1.77200	−0.886001	+	0.463683i	$0.846528\pi$
$578$	−2.07552	−0.0863303
$579$	−3.08935	−0.128389
$580$	−4.93331	−0.204844
$581$	31.3436	1.30035
$582$	0.694614	0.0287927
$583$	−18.7848	−0.777985
$584$	13.6965	0.566766
$585$	17.9469	0.742013
$586$	−3.09554	−0.127876
$587$	−19.1259	−0.789410	−0.394705	−	0.918808i	$-0.629153\pi$
$587$	−19.1259	−0.789410	−0.394705	+	0.918808i	$0.629153\pi$
$588$	−9.71337	−0.400573
$589$	10.4157	0.429172
$590$	0.353779	0.0145648
$591$	0.831798	0.0342156
$592$	5.35355	0.220030
$593$	−24.6059	−1.01044	−0.505222	−	0.862990i	$-0.668589\pi$
$593$	−24.6059	−1.01044	−0.505222	+	0.862990i	$0.668589\pi$
$594$	3.21591	0.131950
$595$	21.9439	0.899611
$596$	−24.4346	−1.00088
$597$	−6.97005	−0.285265
$598$	15.5102	0.634261
$599$	14.3745	0.587327	0.293664	−	0.955909i	$-0.405125\pi$
$599$	14.3745	0.587327	0.293664	+	0.955909i	$0.405125\pi$
$600$	1.07585	0.0439213
$601$	33.0817	1.34943	0.674715	−	0.738079i	$-0.264267\pi$
$601$	33.0817	1.34943	0.674715	+	0.738079i	$0.264267\pi$
$602$	18.4377	0.751465
$603$	35.7448	1.45564
$604$	25.9774	1.05701
$605$	−8.01483	−0.325849
$606$	−3.46168	−0.140621
$607$	−29.6315	−1.20271	−0.601353	−	0.798984i	$-0.705371\pi$
$607$	−29.6315	−1.20271	−0.601353	+	0.798984i	$0.705371\pi$
$608$	−9.31824	−0.377905
$609$	7.16773	0.290451
$610$	−10.5372	−0.426638
$611$	−4.71262	−0.190652
$612$	17.2728	0.698210
$613$	−27.8079	−1.12315	−0.561574	−	0.827426i	$-0.689804\pi$
$613$	−27.8079	−1.12315	−0.561574	+	0.827426i	$0.689804\pi$
$614$	3.59578	0.145114
$615$	−3.95468	−0.159468
$616$	22.8461	0.920496
$617$	−26.8672	−1.08163	−0.540816	−	0.841141i	$-0.681884\pi$
$617$	−26.8672	−1.08163	−0.540816	+	0.841141i	$0.681884\pi$
$618$	−3.05152	−0.122750
$619$	−30.8836	−1.24132	−0.620659	−	0.784081i	$-0.713135\pi$
$619$	−30.8836	−1.24132	−0.620659	+	0.784081i	$0.713135\pi$
$620$	−8.97349	−0.360384
$621$	−7.29308	−0.292661
$622$	−6.86685	−0.275336
$623$	−3.99547	−0.160075
$624$	−1.62253	−0.0649532
$625$	1.00000	0.0400000
$626$	−14.6386	−0.585077
$627$	1.11068	0.0443561
$628$	−20.6395	−0.823608
$629$	37.2589	1.48561
$630$	11.1202	0.443038
$631$	−10.6309	−0.423209	−0.211604	−	0.977355i	$-0.567869\pi$
$631$	−10.6309	−0.423209	−0.211604	+	0.977355i	$0.567869\pi$
$632$	−31.2135	−1.24161
$633$	−10.7428	−0.426989
$634$	−2.55747	−0.101570
$635$	11.0541	0.438667
$636$	6.02139	0.238764
$637$	−110.927	−4.39510
$638$	−4.90722	−0.194279
$639$	7.05846	0.279229
$640$	9.03509	0.357143
$641$	−6.59386	−0.260442	−0.130221	−	0.991485i	$-0.541569\pi$
$641$	−6.59386	−0.260442	−0.130221	+	0.991485i	$0.541569\pi$
$642$	−2.67320	−0.105503
$643$	17.1107	0.674780	0.337390	−	0.941365i	$-0.390456\pi$
$643$	17.1107	0.674780	0.337390	+	0.941365i	$0.390456\pi$
$644$	−21.1002	−0.831463
$645$	−1.89622	−0.0746635
$646$	−5.58966	−0.219922
$647$	11.8817	0.467116	0.233558	−	0.972343i	$-0.424963\pi$
$647$	11.8817	0.467116	0.233558	+	0.972343i	$0.424963\pi$
$648$	20.1920	0.793216
$649$	−0.772636	−0.0303286
$650$	5.00364	0.196259
$651$	13.0378	0.510992
$652$	5.22638	0.204681
$653$	−2.22101	−0.0869147	−0.0434574	−	0.999055i	$-0.513837\pi$
$653$	−2.22101	−0.0869147	−0.0434574	+	0.999055i	$0.513837\pi$
$654$	−5.80401	−0.226955
$655$	11.0907	0.433348
$656$	−6.24547	−0.243845
$657$	−14.5597	−0.568027
$658$	−2.92000	−0.113834
$659$	−8.88731	−0.346200	−0.173100	−	0.984904i	$-0.555378\pi$
$659$	−8.88731	−0.346200	−0.173100	+	0.984904i	$0.555378\pi$
$660$	−0.956886	−0.0372467
$661$	4.42403	0.172075	0.0860374	−	0.996292i	$-0.472580\pi$
$661$	4.42403	0.172075	0.0860374	+	0.996292i	$0.472580\pi$
$662$	−21.8400	−0.848835
$663$	−11.2922	−0.438554
$664$	16.8899	0.655457
$665$	7.90097	0.306387
$666$	18.8811	0.731628
$667$	11.1286	0.430903
$668$	−16.3051	−0.630863
$669$	−6.52793	−0.252384
$670$	9.96573	0.385010
$671$	23.0127	0.888395
$672$	−11.6641	−0.449951
$673$	−15.0230	−0.579096	−0.289548	−	0.957164i	$-0.593505\pi$
$673$	−15.0230	−0.579096	−0.289548	+	0.957164i	$0.593505\pi$
$674$	−14.7323	−0.567466
$675$	−2.35277	−0.0905580
$676$	−37.1052	−1.42712
$677$	−32.6871	−1.25627	−0.628133	−	0.778106i	$-0.716181\pi$
$677$	−32.6871	−1.25627	−0.628133	+	0.778106i	$0.716181\pi$
$678$	−4.73130	−0.181705
$679$	−10.7914	−0.414138
$680$	11.8247	0.453458
$681$	−1.28212	−0.0491309
$682$	−8.92604	−0.341796
$683$	−20.5083	−0.784730	−0.392365	−	0.919810i	$-0.628343\pi$
$683$	−20.5083	−0.784730	−0.392365	+	0.919810i	$0.628343\pi$
$684$	6.21913	0.237794
$685$	−16.8526	−0.643904
$686$	−41.2998	−1.57683
$687$	−6.66335	−0.254223
$688$	−2.99462	−0.114169
$689$	68.7647	2.61973
$690$	−0.988374	−0.0376267
$691$	−30.5279	−1.16134	−0.580668	−	0.814140i	$-0.697209\pi$
$691$	−30.5279	−1.16134	−0.580668	+	0.814140i	$0.697209\pi$
$692$	−10.6265	−0.403961
$693$	−24.2859	−0.922544
$694$	−3.58500	−0.136085
$695$	9.33306	0.354023
$696$	3.86243	0.146405
$697$	−43.4663	−1.64640
$698$	−2.76541	−0.104672
$699$	−9.03352	−0.341679
$700$	−6.80696	−0.257279
$701$	20.6468	0.779818	0.389909	−	0.920853i	$-0.372506\pi$
$701$	20.6468	0.779818	0.389909	+	0.920853i	$0.372506\pi$
$702$	−11.7724	−0.444320
$703$	13.4152	0.505964
$704$	5.78607	0.218071
$705$	0.300307	0.0113102
$706$	−12.3087	−0.463243
$707$	53.7802	2.02261
$708$	0.247666	0.00930786
$709$	−11.5216	−0.432703	−0.216351	−	0.976316i	$-0.569416\pi$
$709$	−11.5216	−0.432703	−0.216351	+	0.976316i	$0.569416\pi$
$710$	1.96792	0.0738546
$711$	33.1806	1.24437
$712$	−2.15301	−0.0806876
$713$	20.2426	0.758090
$714$	−6.99684	−0.261850
$715$	−10.9277	−0.408673
$716$	−15.9005	−0.594228
$717$	−8.16147	−0.304796
$718$	10.9212	0.407576
$719$	15.3500	0.572459	0.286230	−	0.958161i	$-0.407598\pi$
$719$	15.3500	0.572459	0.286230	+	0.958161i	$0.407598\pi$
$720$	−1.80612	−0.0673100
$721$	47.4080	1.76557
$722$	13.0187	0.484504
$723$	−9.26720	−0.344651
$724$	8.06394	0.299694
$725$	3.59013	0.133334
$726$	2.55554	0.0948451
$727$	32.5846	1.20850	0.604248	−	0.796796i	$-0.293474\pi$
$727$	32.5846	1.20850	0.604248	+	0.796796i	$0.293474\pi$
$728$	−83.6320	−3.09961
$729$	−18.6197	−0.689619
$730$	−4.05927	−0.150240
$731$	−20.8415	−0.770852
$732$	−7.37665	−0.272649
$733$	16.0646	0.593361	0.296681	−	0.954977i	$-0.404120\pi$
$733$	16.0646	0.593361	0.296681	+	0.954977i	$0.404120\pi$
$734$	9.85358	0.363702
$735$	7.06873	0.260734
$736$	−18.1097	−0.667532
$737$	−21.7647	−0.801712
$738$	−22.0268	−0.810816
$739$	−13.3648	−0.491632	−0.245816	−	0.969317i	$-0.579056\pi$
$739$	−13.3648	−0.491632	−0.245816	+	0.969317i	$0.579056\pi$
$740$	−11.5577	−0.424868
$741$	−4.06581	−0.149361
$742$	42.6076	1.56417
$743$	−8.91587	−0.327092	−0.163546	−	0.986536i	$-0.552293\pi$
$743$	−8.91587	−0.327092	−0.163546	+	0.986536i	$0.552293\pi$
$744$	7.02560	0.257571
$745$	17.7819	0.651477
$746$	15.9225	0.582963
$747$	−17.9543	−0.656915
$748$	−10.5172	−0.384548
$749$	41.5305	1.51749
$750$	−0.318852	−0.0116428
$751$	−7.97845	−0.291138	−0.145569	−	0.989348i	$-0.546501\pi$
$751$	−7.97845	−0.291138	−0.145569	+	0.989348i	$0.546501\pi$
$752$	0.474262	0.0172946
$753$	9.17715	0.334434
$754$	17.9637	0.654199
$755$	−18.9046	−0.688009
$756$	16.0152	0.582466
$757$	−5.29562	−0.192472	−0.0962362	−	0.995359i	$-0.530680\pi$
$757$	−5.29562	−0.192472	−0.0962362	+	0.995359i	$0.530680\pi$
$758$	14.6235	0.531149
$759$	2.15856	0.0783508
$760$	4.25754	0.154437
$761$	6.99717	0.253647	0.126824	−	0.991925i	$-0.459522\pi$
$761$	6.99717	0.253647	0.126824	+	0.991925i	$0.459522\pi$
$762$	−3.52460	−0.127683
$763$	90.1704	3.26439
$764$	−32.3590	−1.17071
$765$	−12.5699	−0.454467
$766$	16.4211	0.593318
$767$	2.82836	0.102126
$768$	−5.58031	−0.201362
$769$	−6.26206	−0.225816	−0.112908	−	0.993605i	$-0.536016\pi$
$769$	−6.26206	−0.225816	−0.112908	+	0.993605i	$0.536016\pi$
$770$	−6.77096	−0.244008
$771$	6.01586	0.216656
$772$	10.5329	0.379087
$773$	29.1057	1.04686	0.523429	−	0.852069i	$-0.324653\pi$
$773$	29.1057	1.04686	0.523429	+	0.852069i	$0.324653\pi$
$774$	−10.5615	−0.379627
$775$	6.53030	0.234575
$776$	−5.81512	−0.208751
$777$	16.7924	0.602424
$778$	−18.5864	−0.666354
$779$	−15.6502	−0.560727
$780$	3.50284	0.125422
$781$	−4.29783	−0.153789
$782$	−10.8633	−0.388471
$783$	−8.44672	−0.301861
$784$	11.1634	0.398692
$785$	15.0201	0.536089
$786$	−3.53627	−0.126135
$787$	9.11600	0.324950	0.162475	−	0.986713i	$-0.448052\pi$
$787$	9.11600	0.324950	0.162475	+	0.986713i	$0.448052\pi$
$788$	−2.83595	−0.101027
$789$	9.30652	0.331321
$790$	9.25081	0.329129
$791$	73.5050	2.61354
$792$	−13.0868	−0.465018
$793$	−84.2418	−2.99151
$794$	12.5589	0.445697
$795$	−4.38196	−0.155412
$796$	23.7639	0.842288
$797$	26.8508	0.951106	0.475553	−	0.879687i	$-0.342248\pi$
$797$	26.8508	0.951106	0.475553	+	0.879687i	$0.342248\pi$
$798$	−2.51924	−0.0891800
$799$	3.30070	0.116770
$800$	−5.84222	−0.206554
$801$	2.28870	0.0808671
$802$	0.791118	0.0279353
$803$	8.86526	0.312848
$804$	6.97660	0.246046
$805$	15.3553	0.541202
$806$	32.6752	1.15094
$807$	−6.99725	−0.246315
$808$	28.9802	1.01952
$809$	−35.3657	−1.24339	−0.621697	−	0.783258i	$-0.713556\pi$
$809$	−35.3657	−1.24339	−0.621697	+	0.783258i	$0.713556\pi$
$810$	−5.98435	−0.210269
$811$	−36.6352	−1.28644	−0.643219	−	0.765682i	$-0.722401\pi$
$811$	−36.6352	−1.28644	−0.643219	+	0.765682i	$0.722401\pi$
$812$	−24.4378	−0.857600
$813$	−12.5698	−0.440841
$814$	−11.4965	−0.402953
$815$	−3.80340	−0.133227
$816$	1.13641	0.0397825
$817$	−7.50407	−0.262534
$818$	1.13531	0.0396952
$819$	88.9025	3.10651
$820$	13.4832	0.470854
$821$	6.62208	0.231112	0.115556	−	0.993301i	$-0.463135\pi$
$821$	6.62208	0.231112	0.115556	+	0.993301i	$0.463135\pi$
$822$	5.37348	0.187421
$823$	−6.62270	−0.230853	−0.115426	−	0.993316i	$-0.536823\pi$
$823$	−6.62270	−0.230853	−0.115426	+	0.993316i	$0.536823\pi$
$824$	25.5465	0.889953
$825$	0.696356	0.0242440
$826$	1.75249	0.0609771
$827$	49.5262	1.72219	0.861097	−	0.508441i	$-0.169778\pi$
$827$	49.5262	1.72219	0.861097	+	0.508441i	$0.169778\pi$
$828$	12.0867	0.420040
$829$	−6.03111	−0.209469	−0.104735	−	0.994500i	$-0.533399\pi$
$829$	−6.03111	−0.209469	−0.104735	+	0.994500i	$0.533399\pi$
$830$	−5.00571	−0.173751
$831$	9.41559	0.326623
$832$	−21.1809	−0.734315
$833$	77.6932	2.69191
$834$	−2.97586	−0.103046
$835$	11.8657	0.410631
$836$	−3.78677	−0.130968
$837$	−15.3643	−0.531067
$838$	−12.4361	−0.429599
$839$	−22.7726	−0.786196	−0.393098	−	0.919497i	$-0.628597\pi$
$839$	−22.7726	−0.786196	−0.393098	+	0.919497i	$0.628597\pi$
$840$	5.32936	0.183881
$841$	−16.1110	−0.555552
$842$	−26.9233	−0.927839
$843$	−10.2688	−0.353676
$844$	36.6269	1.26075
$845$	27.0027	0.928920
$846$	1.67265	0.0575067
$847$	−39.7026	−1.36420
$848$	−6.92026	−0.237643
$849$	3.13784	0.107690
$850$	−3.50453	−0.120204
$851$	26.0720	0.893735
$852$	1.37766	0.0471977
$853$	36.7565	1.25852	0.629259	−	0.777195i	$-0.283358\pi$
$853$	36.7565	1.25852	0.629259	+	0.777195i	$0.283358\pi$
$854$	−52.1974	−1.78616
$855$	−4.52586	−0.154781
$856$	22.3793	0.764908
$857$	−47.6321	−1.62708	−0.813541	−	0.581507i	$-0.802463\pi$
$857$	−47.6321	−1.62708	−0.813541	+	0.581507i	$0.802463\pi$
$858$	3.48431	0.118953
$859$	−46.1021	−1.57298	−0.786491	−	0.617602i	$-0.788104\pi$
$859$	−46.1021	−1.57298	−0.786491	+	0.617602i	$0.788104\pi$
$860$	6.46501	0.220455
$861$	−19.5901	−0.667628
$862$	−7.44088	−0.253437
$863$	−33.7855	−1.15007	−0.575036	−	0.818128i	$-0.695012\pi$
$863$	−33.7855	−1.15007	−0.575036	+	0.818128i	$0.695012\pi$
$864$	13.7454	0.467627
$865$	7.73327	0.262939
$866$	6.76302	0.229817
$867$	1.05738	0.0359107
$868$	−44.4515	−1.50878
$869$	−20.2033	−0.685351
$870$	−1.14472	−0.0388095
$871$	79.6732	2.69962
$872$	48.5895	1.64545
$873$	6.18159	0.209215
$874$	−3.91138	−0.132304
$875$	4.95364	0.167464
$876$	−2.84173	−0.0960132
$877$	−27.0938	−0.914893	−0.457447	−	0.889237i	$-0.651236\pi$
$877$	−27.0938	−0.914893	−0.457447	+	0.889237i	$0.651236\pi$
$878$	26.6183	0.898323
$879$	1.57704	0.0531923
$880$	1.09973	0.0370718
$881$	17.6809	0.595684	0.297842	−	0.954615i	$-0.403733\pi$
$881$	17.6809	0.595684	0.297842	+	0.954615i	$0.403733\pi$
$882$	39.3714	1.32570
$883$	4.44245	0.149500	0.0747502	−	0.997202i	$-0.476184\pi$
$883$	4.44245	0.149500	0.0747502	+	0.997202i	$0.476184\pi$
$884$	38.5001	1.29490
$885$	−0.180234	−0.00605852
$886$	−5.75871	−0.193468
$887$	23.8414	0.800517	0.400259	−	0.916402i	$-0.368920\pi$
$887$	23.8414	0.800517	0.400259	+	0.916402i	$0.368920\pi$
$888$	9.04882	0.303658
$889$	54.7578	1.83652
$890$	0.638094	0.0213890
$891$	13.0695	0.437846
$892$	22.2565	0.745203
$893$	1.18843	0.0397693
$894$	−5.66977	−0.189626
$895$	11.5713	0.386785
$896$	44.7566	1.49521
$897$	−7.90177	−0.263832
$898$	29.1857	0.973939
$899$	23.4446	0.781921
$900$	3.89918	0.129973
$901$	−48.1626	−1.60453
$902$	13.4119	0.446567
$903$	−9.39318	−0.312586
$904$	39.6092	1.31738
$905$	−5.86839	−0.195072
$906$	6.02777	0.200259
$907$	7.61914	0.252989	0.126495	−	0.991967i	$-0.459627\pi$
$907$	7.61914	0.252989	0.126495	+	0.991967i	$0.459627\pi$
$908$	4.37129	0.145066
$909$	−30.8065	−1.02179
$910$	24.7862	0.821655
$911$	48.3257	1.60110	0.800551	−	0.599264i	$-0.204540\pi$
$911$	48.3257	1.60110	0.800551	+	0.599264i	$0.204540\pi$
$912$	0.409170	0.0135490
$913$	10.9322	0.361804
$914$	−13.0066	−0.430220
$915$	5.36822	0.177468
$916$	22.7182	0.750630
$917$	54.9391	1.81425
$918$	8.24534	0.272137
$919$	6.38938	0.210766	0.105383	−	0.994432i	$-0.466393\pi$
$919$	6.38938	0.210766	0.105383	+	0.994432i	$0.466393\pi$
$920$	8.27439	0.272799
$921$	−1.83189	−0.0603628
$922$	−11.1581	−0.367473
$923$	15.7329	0.517856
$924$	−4.74007	−0.155937
$925$	8.41087	0.276548
$926$	5.88152	0.193279
$927$	−27.1564	−0.891933
$928$	−20.9743	−0.688516
$929$	−15.8242	−0.519177	−0.259588	−	0.965719i	$-0.583587\pi$
$929$	−15.8242	−0.519177	−0.259588	+	0.965719i	$0.583587\pi$
$930$	−2.08220	−0.0682779
$931$	27.9737	0.916801
$932$	30.7991	1.00886
$933$	3.49835	0.114531
$934$	24.8915	0.814473
$935$	7.65372	0.250304
$936$	47.9063	1.56587
$937$	−50.8146	−1.66004	−0.830020	−	0.557734i	$-0.811671\pi$
$937$	−50.8146	−1.66004	−0.830020	+	0.557734i	$0.811671\pi$
$938$	49.3666	1.61188
$939$	7.45772	0.243373
$940$	−1.02387	−0.0333951
$941$	8.94611	0.291635	0.145817	−	0.989312i	$-0.453419\pi$
$941$	8.94611	0.291635	0.145817	+	0.989312i	$0.453419\pi$
$942$	−4.78917	−0.156040
$943$	−30.4156	−0.990469
$944$	−0.284637	−0.00926415
$945$	−11.6548	−0.379129
$946$	6.43082	0.209084
$947$	4.64822	0.151047	0.0755234	−	0.997144i	$-0.475937\pi$
$947$	4.64822	0.151047	0.0755234	+	0.997144i	$0.475937\pi$
$948$	6.47611	0.210334
$949$	−32.4527	−1.05346
$950$	−1.26182	−0.0409388
$951$	1.30292	0.0422499
$952$	58.5756	1.89845
$953$	13.5252	0.438123	0.219062	−	0.975711i	$-0.429700\pi$
$953$	13.5252	0.438123	0.219062	+	0.975711i	$0.429700\pi$
$954$	−24.4066	−0.790193
$955$	23.5487	0.762017
$956$	27.8259	0.899955
$957$	2.50001	0.0808137
$958$	−15.0434	−0.486030
$959$	−83.4817	−2.69577
$960$	1.34973	0.0435624
$961$	11.6448	0.375639
$962$	42.0850	1.35687
$963$	−23.7896	−0.766610
$964$	31.5958	1.01763
$965$	−7.66512	−0.246749
$966$	−4.89605	−0.157528
$967$	−16.5816	−0.533229	−0.266614	−	0.963803i	$-0.585905\pi$
$967$	−16.5816	−0.533229	−0.266614	+	0.963803i	$0.585905\pi$
$968$	−21.3943	−0.687639
$969$	2.84768	0.0914808
$970$	1.72344	0.0553364
$971$	13.3713	0.429106	0.214553	−	0.976712i	$-0.431171\pi$
$971$	13.3713	0.429106	0.214553	+	0.976712i	$0.431171\pi$
$972$	−13.8884	−0.445472
$973$	46.2326	1.48215
$974$	−9.99383	−0.320223
$975$	−2.54913	−0.0816375
$976$	8.47782	0.271368
$977$	34.5728	1.10608	0.553040	−	0.833155i	$-0.313468\pi$
$977$	34.5728	1.10608	0.553040	+	0.833155i	$0.313468\pi$
$978$	1.21272	0.0387786
$979$	−1.39357	−0.0445386
$980$	−24.1003	−0.769856
$981$	−51.6517	−1.64911
$982$	2.03479	0.0649328
$983$	4.75895	0.151787	0.0758935	−	0.997116i	$-0.475819\pi$
$983$	4.75895	0.151787	0.0758935	+	0.997116i	$0.475819\pi$
$984$	−10.5564	−0.336525
$985$	2.06382	0.0657586
$986$	−12.5817	−0.400683
$987$	1.48761	0.0473512
$988$	13.8621	0.441012
$989$	−14.5839	−0.463741
$990$	3.87856	0.123269
$991$	22.7111	0.721440	0.360720	−	0.932674i	$-0.382531\pi$
$991$	22.7111	0.721440	0.360720	+	0.932674i	$0.382531\pi$
$992$	−38.1515	−1.21131
$993$	11.1265	0.353089
$994$	9.74835	0.309199
$995$	−17.2937	−0.548248
$996$	−3.50429	−0.111038
$997$	−11.2973	−0.357790	−0.178895	−	0.983868i	$-0.557252\pi$
$997$	−11.2973	−0.357790	−0.178895	+	0.983868i	$0.557252\pi$
$998$	3.90777	0.123698
$999$	−19.7888	−0.626090

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2005.2.a.g.1.13	✓	37

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2005.2.a.g.1.13	✓	37	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:	\( N \)	\(=\)	\( 2005 = 5 \cdot 401 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2005.a (trivial)

\(f(q)\)	\(=\)	\(q-0.791118 q^{2} +0.403039 q^{3} -1.37413 q^{4} +1.00000 q^{5} -0.318852 q^{6} +4.95364 q^{7} +2.66934 q^{8} -2.83756 q^{9} +O(q^{10})\)	\(q-0.791118 q^{2} +0.403039 q^{3} -1.37413 q^{4} +1.00000 q^{5} -0.318852 q^{6} +4.95364 q^{7} +2.66934 q^{8} -2.83756 q^{9} -0.791118 q^{10} +1.72776 q^{11} -0.553829 q^{12} -6.32477 q^{13} -3.91892 q^{14} +0.403039 q^{15} +0.636504 q^{16} +4.42985 q^{17} +2.24484 q^{18} +1.59498 q^{19} -1.37413 q^{20} +1.99651 q^{21} -1.36686 q^{22} +3.09979 q^{23} +1.07585 q^{24} +1.00000 q^{25} +5.00364 q^{26} -2.35277 q^{27} -6.80696 q^{28} +3.59013 q^{29} -0.318852 q^{30} +6.53030 q^{31} -5.84222 q^{32} +0.696356 q^{33} -3.50453 q^{34} +4.95364 q^{35} +3.89918 q^{36} +8.41087 q^{37} -1.26182 q^{38} -2.54913 q^{39} +2.66934 q^{40} -9.81215 q^{41} -1.57948 q^{42} -4.70480 q^{43} -2.37418 q^{44} -2.83756 q^{45} -2.45230 q^{46} +0.745105 q^{47} +0.256536 q^{48} +17.5386 q^{49} -0.791118 q^{50} +1.78540 q^{51} +8.69106 q^{52} -10.8723 q^{53} +1.86132 q^{54} +1.72776 q^{55} +13.2229 q^{56} +0.642840 q^{57} -2.84021 q^{58} -0.447188 q^{59} -0.553829 q^{60} +13.3194 q^{61} -5.16624 q^{62} -14.0563 q^{63} +3.34888 q^{64} -6.32477 q^{65} -0.550900 q^{66} -12.5970 q^{67} -6.08719 q^{68} +1.24934 q^{69} -3.91892 q^{70} -2.48751 q^{71} -7.57440 q^{72} +5.13106 q^{73} -6.65399 q^{74} +0.403039 q^{75} -2.19172 q^{76} +8.55872 q^{77} +2.01666 q^{78} -11.6933 q^{79} +0.636504 q^{80} +7.56442 q^{81} +7.76257 q^{82} +6.32739 q^{83} -2.74347 q^{84} +4.42985 q^{85} +3.72205 q^{86} +1.44696 q^{87} +4.61198 q^{88} -0.806572 q^{89} +2.24484 q^{90} -31.3306 q^{91} -4.25952 q^{92} +2.63197 q^{93} -0.589466 q^{94} +1.59498 q^{95} -2.35465 q^{96} -2.17849 q^{97} -13.8751 q^{98} -4.90263 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 37 q + 11 q^{2} + 13 q^{3} + 43 q^{4} + 37 q^{5} - 2 q^{6} + 34 q^{7} + 27 q^{8} + 50 q^{9}+O(q^{10}) \) 37 * q + 11 * q^2 + 13 * q^3 + 43 * q^4 + 37 * q^5 - 2 * q^6 + 34 * q^7 + 27 * q^8 + 50 * q^9	\( 37 q + 11 q^{2} + 13 q^{3} + 43 q^{4} + 37 q^{5} - 2 q^{6} + 34 q^{7} + 27 q^{8} + 50 q^{9} + 11 q^{10} + 38 q^{11} + 24 q^{12} + 17 q^{13} + 14 q^{14} + 13 q^{15} + 47 q^{16} + 22 q^{17} + 18 q^{18} + 6 q^{19} + 43 q^{20} + 4 q^{21} + 18 q^{22} + 45 q^{23} - 19 q^{24} + 37 q^{25} - q^{26} + 43 q^{27} + 46 q^{28} + 17 q^{29} - 2 q^{30} - 13 q^{31} + 50 q^{32} + 12 q^{33} - 30 q^{34} + 34 q^{35} + 43 q^{36} + 9 q^{37} + q^{38} - 7 q^{39} + 27 q^{40} + 12 q^{41} - 38 q^{42} + 53 q^{43} + 36 q^{44} + 50 q^{45} - 15 q^{46} + 39 q^{47} - 6 q^{48} + 37 q^{49} + 11 q^{50} + 38 q^{51} + 17 q^{52} + 19 q^{53} - 62 q^{54} + 38 q^{55} + 18 q^{56} + 6 q^{57} - 13 q^{58} + 33 q^{59} + 24 q^{60} - 11 q^{61} + q^{62} + 98 q^{63} + 15 q^{64} + 17 q^{65} - 70 q^{66} + 49 q^{67} + 32 q^{68} - 36 q^{69} + 14 q^{70} + 19 q^{71} + 5 q^{72} + 39 q^{73} + 21 q^{74} + 13 q^{75} - 33 q^{76} + 34 q^{77} - 22 q^{78} - 9 q^{79} + 47 q^{80} + 49 q^{81} + 14 q^{82} + 114 q^{83} - 50 q^{84} + 22 q^{85} + 9 q^{86} + 56 q^{87} + 14 q^{88} + 2 q^{89} + 18 q^{90} - 29 q^{91} + 47 q^{92} - 7 q^{93} - 52 q^{94} + 6 q^{95} - 89 q^{96} + 4 q^{97} + 14 q^{98} + 57 q^{99}+O(q^{100}) \) 37 * q + 11 * q^2 + 13 * q^3 + 43 * q^4 + 37 * q^5 - 2 * q^6 + 34 * q^7 + 27 * q^8 + 50 * q^9 + 11 * q^10 + 38 * q^11 + 24 * q^12 + 17 * q^13 + 14 * q^14 + 13 * q^15 + 47 * q^16 + 22 * q^17 + 18 * q^18 + 6 * q^19 + 43 * q^20 + 4 * q^21 + 18 * q^22 + 45 * q^23 - 19 * q^24 + 37 * q^25 - q^26 + 43 * q^27 + 46 * q^28 + 17 * q^29 - 2 * q^30 - 13 * q^31 + 50 * q^32 + 12 * q^33 - 30 * q^34 + 34 * q^35 + 43 * q^36 + 9 * q^37 + q^38 - 7 * q^39 + 27 * q^40 + 12 * q^41 - 38 * q^42 + 53 * q^43 + 36 * q^44 + 50 * q^45 - 15 * q^46 + 39 * q^47 - 6 * q^48 + 37 * q^49 + 11 * q^50 + 38 * q^51 + 17 * q^52 + 19 * q^53 - 62 * q^54 + 38 * q^55 + 18 * q^56 + 6 * q^57 - 13 * q^58 + 33 * q^59 + 24 * q^60 - 11 * q^61 + q^62 + 98 * q^63 + 15 * q^64 + 17 * q^65 - 70 * q^66 + 49 * q^67 + 32 * q^68 - 36 * q^69 + 14 * q^70 + 19 * q^71 + 5 * q^72 + 39 * q^73 + 21 * q^74 + 13 * q^75 - 33 * q^76 + 34 * q^77 - 22 * q^78 - 9 * q^79 + 47 * q^80 + 49 * q^81 + 14 * q^82 + 114 * q^83 - 50 * q^84 + 22 * q^85 + 9 * q^86 + 56 * q^87 + 14 * q^88 + 2 * q^89 + 18 * q^90 - 29 * q^91 + 47 * q^92 - 7 * q^93 - 52 * q^94 + 6 * q^95 - 89 * q^96 + 4 * q^97 + 14 * q^98 + 57 * q^99

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