LMFDB - Embedded newform 8017.2.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8017,2,Mod(1,8017)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8017, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("8017.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8017 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8017.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:	$64.0160673005$
Analytic rank:	$1$
Dimension:	$327$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	8017.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.79695 q^{2} -1.72914 q^{3} +5.82292 q^{4} -0.405996 q^{5} +4.83631 q^{6} -2.26625 q^{7} -10.6925 q^{8} -0.0100790 q^{9} +O(q^{10})$	\(q-2.79695 q^{2} -1.72914 q^{3} +5.82292 q^{4} -0.405996 q^{5} +4.83631 q^{6} -2.26625 q^{7} -10.6925 q^{8} -0.0100790 q^{9} +1.13555 q^{10} +3.70325 q^{11} -10.0686 q^{12} -5.26692 q^{13} +6.33858 q^{14} +0.702023 q^{15} +18.2606 q^{16} -6.42557 q^{17} +0.0281904 q^{18} +3.09023 q^{19} -2.36408 q^{20} +3.91866 q^{21} -10.3578 q^{22} +1.81164 q^{23} +18.4888 q^{24} -4.83517 q^{25} +14.7313 q^{26} +5.20484 q^{27} -13.1962 q^{28} +5.52233 q^{29} -1.96352 q^{30} -5.43652 q^{31} -29.6888 q^{32} -6.40343 q^{33} +17.9720 q^{34} +0.920088 q^{35} -0.0586892 q^{36} -2.23690 q^{37} -8.64322 q^{38} +9.10724 q^{39} +4.34111 q^{40} -3.09472 q^{41} -10.9603 q^{42} +3.38961 q^{43} +21.5637 q^{44} +0.00409203 q^{45} -5.06706 q^{46} +2.42956 q^{47} -31.5751 q^{48} -1.86411 q^{49} +13.5237 q^{50} +11.1107 q^{51} -30.6689 q^{52} -0.407006 q^{53} -14.5577 q^{54} -1.50350 q^{55} +24.2319 q^{56} -5.34344 q^{57} -15.4457 q^{58} -2.82047 q^{59} +4.08782 q^{60} -2.01008 q^{61} +15.2057 q^{62} +0.0228415 q^{63} +46.5170 q^{64} +2.13835 q^{65} +17.9101 q^{66} +8.42049 q^{67} -37.4156 q^{68} -3.13258 q^{69} -2.57344 q^{70} +0.920412 q^{71} +0.107770 q^{72} +7.29879 q^{73} +6.25650 q^{74} +8.36068 q^{75} +17.9942 q^{76} -8.39249 q^{77} -25.4725 q^{78} +15.2146 q^{79} -7.41371 q^{80} -8.96966 q^{81} +8.65579 q^{82} +4.34845 q^{83} +22.8181 q^{84} +2.60875 q^{85} -9.48057 q^{86} -9.54888 q^{87} -39.5970 q^{88} -5.51144 q^{89} -0.0114452 q^{90} +11.9362 q^{91} +10.5490 q^{92} +9.40049 q^{93} -6.79536 q^{94} -1.25462 q^{95} +51.3361 q^{96} +10.6337 q^{97} +5.21382 q^{98} -0.0373250 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 327 q - 23 q^{2} - 48 q^{3} + 315 q^{4} - 55 q^{5} - 38 q^{6} - 87 q^{7} - 69 q^{8} + 303 q^{9}+O(q^{10}) $ 327 * q - 23 * q^2 - 48 * q^3 + 315 * q^4 - 55 * q^5 - 38 * q^6 - 87 * q^7 - 69 * q^8 + 303 * q^9	\( 327 q - 23 q^{2} - 48 q^{3} + 315 q^{4} - 55 q^{5} - 38 q^{6} - 87 q^{7} - 69 q^{8} + 303 q^{9} - 48 q^{10} - 70 q^{11} - 120 q^{12} - 53 q^{13} - 52 q^{14} - 77 q^{15} + 295 q^{16} - 164 q^{17} - 58 q^{18} - 47 q^{19} - 153 q^{20} - 39 q^{21} - 68 q^{22} - 256 q^{23} - 107 q^{24} + 288 q^{25} - 95 q^{26} - 189 q^{27} - 167 q^{28} - 99 q^{29} - 81 q^{30} - 71 q^{31} - 146 q^{32} - 95 q^{33} - 40 q^{34} - 192 q^{35} + 261 q^{36} - 54 q^{37} - 179 q^{38} - 115 q^{39} - 121 q^{40} - 111 q^{41} - 62 q^{42} - 110 q^{43} - 157 q^{44} - 137 q^{45} - 11 q^{46} - 324 q^{47} - 236 q^{48} + 296 q^{49} - 73 q^{50} - 88 q^{51} - 138 q^{52} - 170 q^{53} - 127 q^{54} - 151 q^{55} - 151 q^{56} - 106 q^{57} - 81 q^{58} - 123 q^{59} - 83 q^{60} - 62 q^{61} - 287 q^{62} - 400 q^{63} + 263 q^{64} - 143 q^{65} - 64 q^{66} - 95 q^{67} - 442 q^{68} - 22 q^{69} - 26 q^{70} - 210 q^{71} - 129 q^{72} - 121 q^{73} - 159 q^{74} - 194 q^{75} - 86 q^{76} - 178 q^{77} - 68 q^{78} - 145 q^{79} - 338 q^{80} + 259 q^{81} - 103 q^{82} - 418 q^{83} - 102 q^{84} - 40 q^{85} - 89 q^{86} - 372 q^{87} - 186 q^{88} - 100 q^{89} - 150 q^{90} - 69 q^{91} - 458 q^{92} - 81 q^{93} - 46 q^{94} - 377 q^{95} - 190 q^{96} - 87 q^{97} - 147 q^{98} - 171 q^{99}+O(q^{100}) \) 327 * q - 23 * q^2 - 48 * q^3 + 315 * q^4 - 55 * q^5 - 38 * q^6 - 87 * q^7 - 69 * q^8 + 303 * q^9 - 48 * q^10 - 70 * q^11 - 120 * q^12 - 53 * q^13 - 52 * q^14 - 77 * q^15 + 295 * q^16 - 164 * q^17 - 58 * q^18 - 47 * q^19 - 153 * q^20 - 39 * q^21 - 68 * q^22 - 256 * q^23 - 107 * q^24 + 288 * q^25 - 95 * q^26 - 189 * q^27 - 167 * q^28 - 99 * q^29 - 81 * q^30 - 71 * q^31 - 146 * q^32 - 95 * q^33 - 40 * q^34 - 192 * q^35 + 261 * q^36 - 54 * q^37 - 179 * q^38 - 115 * q^39 - 121 * q^40 - 111 * q^41 - 62 * q^42 - 110 * q^43 - 157 * q^44 - 137 * q^45 - 11 * q^46 - 324 * q^47 - 236 * q^48 + 296 * q^49 - 73 * q^50 - 88 * q^51 - 138 * q^52 - 170 * q^53 - 127 * q^54 - 151 * q^55 - 151 * q^56 - 106 * q^57 - 81 * q^58 - 123 * q^59 - 83 * q^60 - 62 * q^61 - 287 * q^62 - 400 * q^63 + 263 * q^64 - 143 * q^65 - 64 * q^66 - 95 * q^67 - 442 * q^68 - 22 * q^69 - 26 * q^70 - 210 * q^71 - 129 * q^72 - 121 * q^73 - 159 * q^74 - 194 * q^75 - 86 * q^76 - 178 * q^77 - 68 * q^78 - 145 * q^79 - 338 * q^80 + 259 * q^81 - 103 * q^82 - 418 * q^83 - 102 * q^84 - 40 * q^85 - 89 * q^86 - 372 * q^87 - 186 * q^88 - 100 * q^89 - 150 * q^90 - 69 * q^91 - 458 * q^92 - 81 * q^93 - 46 * q^94 - 377 * q^95 - 190 * q^96 - 87 * q^97 - 147 * q^98 - 171 * 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 $

$2$	−2.79695	−1.97774	−0.988871	−	0.148778i	$-0.952466\pi$
$2$	−2.79695	−1.97774	−0.988871	+	0.148778i	$0.952466\pi$
$3$	−1.72914	−0.998319	−0.499159	−	0.866510i	$-0.666358\pi$
$3$	−1.72914	−0.998319	−0.499159	+	0.866510i	$0.666358\pi$
$4$	5.82292	2.91146
$5$	−0.405996	−0.181567	−0.0907834	−	0.995871i	$-0.528937\pi$
$5$	−0.405996	−0.181567	−0.0907834	+	0.995871i	$0.528937\pi$
$6$	4.83631	1.97442
$7$	−2.26625	−0.856562	−0.428281	−	0.903646i	$-0.640881\pi$
$7$	−2.26625	−0.856562	−0.428281	+	0.903646i	$0.640881\pi$
$8$	−10.6925	−3.78037
$9$	−0.0100790	−0.00335966
$10$	1.13555	0.359092
$11$	3.70325	1.11657	0.558286	−	0.829649i	$-0.311459\pi$
$11$	3.70325	1.11657	0.558286	+	0.829649i	$0.311459\pi$
$12$	−10.0686	−2.90657
$13$	−5.26692	−1.46078	−0.730390	−	0.683030i	$-0.760662\pi$
$13$	−5.26692	−1.46078	−0.730390	+	0.683030i	$0.760662\pi$
$14$	6.33858	1.69406
$15$	0.702023	0.181261
$16$	18.2606	4.56514
$17$	−6.42557	−1.55843	−0.779214	−	0.626757i	$-0.784382\pi$
$17$	−6.42557	−1.55843	−0.779214	+	0.626757i	$0.784382\pi$
$18$	0.0281904	0.00664455
$19$	3.09023	0.708947	0.354474	−	0.935066i	$-0.384660\pi$
$19$	3.09023	0.708947	0.354474	+	0.935066i	$0.384660\pi$
$20$	−2.36408	−0.528624
$21$	3.91866	0.855122
$22$	−10.3578	−2.20829
$23$	1.81164	0.377753	0.188876	−	0.982001i	$-0.439515\pi$
$23$	1.81164	0.377753	0.188876	+	0.982001i	$0.439515\pi$
$24$	18.4888	3.77402
$25$	−4.83517	−0.967034
$26$	14.7313	2.88905
$27$	5.20484	1.00167
$28$	−13.1962	−2.49385
$29$	5.52233	1.02547	0.512736	−	0.858547i	$-0.328632\pi$
$29$	5.52233	1.02547	0.512736	+	0.858547i	$0.328632\pi$
$30$	−1.96352	−0.358488
$31$	−5.43652	−0.976427	−0.488214	−	0.872724i	$-0.662351\pi$
$31$	−5.43652	−0.976427	−0.488214	+	0.872724i	$0.662351\pi$
$32$	−29.6888	−5.24830
$33$	−6.40343	−1.11469
$34$	17.9720	3.08217
$35$	0.920088	0.155523
$36$	−0.0586892	−0.00978153
$37$	−2.23690	−0.367744	−0.183872	−	0.982950i	$-0.558863\pi$
$37$	−2.23690	−0.367744	−0.183872	+	0.982950i	$0.558863\pi$
$38$	−8.64322	−1.40211
$39$	9.10724	1.45833
$40$	4.34111	0.686390
$41$	−3.09472	−0.483315	−0.241657	−	0.970362i	$-0.577691\pi$
$41$	−3.09472	−0.483315	−0.241657	+	0.970362i	$0.577691\pi$
$42$	−10.9603	−1.69121
$43$	3.38961	0.516911	0.258455	−	0.966023i	$-0.416786\pi$
$43$	3.38961	0.516911	0.258455	+	0.966023i	$0.416786\pi$
$44$	21.5637	3.25085
$45$	0.00409203	0.000610003 0
$46$	−5.06706	−0.747097
$47$	2.42956	0.354388	0.177194	−	0.984176i	$-0.443298\pi$
$47$	2.42956	0.354388	0.177194	+	0.984176i	$0.443298\pi$
$48$	−31.5751	−4.55747
$49$	−1.86411	−0.266302
$50$	13.5237	1.91254
$51$	11.1107	1.55581
$52$	−30.6689	−4.25301
$53$	−0.407006	−0.0559065	−0.0279533	−	0.999609i	$-0.508899\pi$
$53$	−0.407006	−0.0559065	−0.0279533	+	0.999609i	$0.508899\pi$
$54$	−14.5577	−1.98105
$55$	−1.50350	−0.202732
$56$	24.2319	3.23813
$57$	−5.34344	−0.707756
$58$	−15.4457	−2.02812
$59$	−2.82047	−0.367194	−0.183597	−	0.983002i	$-0.558774\pi$
$59$	−2.82047	−0.367194	−0.183597	+	0.983002i	$0.558774\pi$
$60$	4.08782	0.527736
$61$	−2.01008	−0.257364	−0.128682	−	0.991686i	$-0.541075\pi$
$61$	−2.01008	−0.257364	−0.128682	+	0.991686i	$0.541075\pi$
$62$	15.2057	1.93112
$63$	0.0228415	0.00287776
$64$	46.5170	5.81463
$65$	2.13835	0.265229
$66$	17.9101	2.20458
$67$	8.42049	1.02873	0.514363	−	0.857572i	$-0.328028\pi$
$67$	8.42049	1.02873	0.514363	+	0.857572i	$0.328028\pi$
$68$	−37.4156	−4.53730
$69$	−3.13258	−0.377118
$70$	−2.57344	−0.307585
$71$	0.920412	0.109233	0.0546164	−	0.998507i	$-0.482606\pi$
$71$	0.920412	0.109233	0.0546164	+	0.998507i	$0.482606\pi$
$72$	0.107770	0.0127008
$73$	7.29879	0.854258	0.427129	−	0.904191i	$-0.359525\pi$
$73$	7.29879	0.854258	0.427129	+	0.904191i	$0.359525\pi$
$74$	6.25650	0.727303
$75$	8.36068	0.965408
$76$	17.9942	2.06407
$77$	−8.39249	−0.956413
$78$	−25.4725	−2.88419
$79$	15.2146	1.71178	0.855891	−	0.517157i	$-0.173010\pi$
$79$	15.2146	1.71178	0.855891	+	0.517157i	$0.173010\pi$
$80$	−7.41371	−0.828878
$81$	−8.96966	−0.996629
$82$	8.65579	0.955872
$83$	4.34845	0.477305	0.238652	−	0.971105i	$-0.423294\pi$
$83$	4.34845	0.477305	0.238652	+	0.971105i	$0.423294\pi$
$84$	22.8181	2.48965
$85$	2.60875	0.282959
$86$	−9.48057	−1.02232
$87$	−9.54888	−1.02375
$88$	−39.5970	−4.22106
$89$	−5.51144	−0.584211	−0.292106	−	0.956386i	$-0.594356\pi$
$89$	−5.51144	−0.584211	−0.292106	+	0.956386i	$0.594356\pi$
$90$	−0.0114452	−0.00120643
$91$	11.9362	1.25125
$92$	10.5490	1.09981
$93$	9.40049	0.974785
$94$	−6.79536	−0.700888
$95$	−1.25462	−0.128721
$96$	51.3361	5.23947
$97$	10.6337	1.07969	0.539844	−	0.841765i	$-0.318483\pi$
$97$	10.6337	1.07969	0.539844	+	0.841765i	$0.318483\pi$
$98$	5.21382	0.526675
$99$	−0.0373250	−0.00375130
$100$	−28.1548	−2.81548
$101$	−4.34244	−0.432089	−0.216045	−	0.976384i	$-0.569316\pi$
$101$	−4.34244	−0.432089	−0.216045	+	0.976384i	$0.569316\pi$
$102$	−31.0760	−3.07699
$103$	15.1006	1.48791	0.743953	−	0.668232i	$-0.232949\pi$
$103$	15.1006	1.48791	0.743953	+	0.668232i	$0.232949\pi$
$104$	56.3166	5.52230
$105$	−1.59096	−0.155262
$106$	1.13837	0.110569
$107$	0.555083	0.0536619	0.0268309	−	0.999640i	$-0.491458\pi$
$107$	0.555083	0.0536619	0.0268309	+	0.999640i	$0.491458\pi$
$108$	30.3074	2.91633
$109$	−5.86320	−0.561593	−0.280796	−	0.959767i	$-0.590599\pi$
$109$	−5.86320	−0.561593	−0.280796	+	0.959767i	$0.590599\pi$
$110$	4.20522	0.400952
$111$	3.86791	0.367126
$112$	−41.3830	−3.91033
$113$	−19.8629	−1.86854	−0.934271	−	0.356563i	$-0.883949\pi$
$113$	−19.8629	−1.86854	−0.934271	+	0.356563i	$0.883949\pi$
$114$	14.9453	1.39976
$115$	−0.735517	−0.0685874
$116$	32.1561	2.98562
$117$	0.0530853	0.00490773
$118$	7.88871	0.726214
$119$	14.5619	1.33489
$120$	−7.50639	−0.685236
$121$	2.71405	0.246732
$122$	5.62209	0.509000
$123$	5.35121	0.482502
$124$	−31.6564	−2.84283
$125$	3.99303	0.357148
$126$	−0.0638865	−0.00569147
$127$	14.8577	1.31841	0.659206	−	0.751962i	$-0.270893\pi$
$127$	14.8577	1.31841	0.659206	+	0.751962i	$0.270893\pi$
$128$	−70.7280	−6.25153
$129$	−5.86111	−0.516042
$130$	−5.98085	−0.524555
$131$	−0.477444	−0.0417145	−0.0208572	−	0.999782i	$-0.506640\pi$
$131$	−0.477444	−0.0417145	−0.0208572	+	0.999782i	$0.506640\pi$
$132$	−37.2867	−3.24539
$133$	−7.00324	−0.607257
$134$	−23.5517	−2.03456
$135$	−2.11314	−0.181870
$136$	68.7055	5.89144
$137$	9.42921	0.805592	0.402796	−	0.915290i	$-0.368038\pi$
$137$	9.42921	0.805592	0.402796	+	0.915290i	$0.368038\pi$
$138$	8.76165	0.745841
$139$	2.70593	0.229514	0.114757	−	0.993394i	$-0.463391\pi$
$139$	2.70593	0.229514	0.114757	+	0.993394i	$0.463391\pi$
$140$	5.35760	0.452800
$141$	−4.20105	−0.353792
$142$	−2.57435	−0.216034
$143$	−19.5047	−1.63107
$144$	−0.184048	−0.0153373
$145$	−2.24204	−0.186191
$146$	−20.4143	−1.68950
$147$	3.22331	0.265854
$148$	−13.0253	−1.07067
$149$	−21.1824	−1.73533	−0.867665	−	0.497149i	$-0.834380\pi$
$149$	−21.1824	−1.73533	−0.867665	+	0.497149i	$0.834380\pi$
$150$	−23.3844	−1.90933
$151$	14.2315	1.15814	0.579070	−	0.815278i	$-0.303416\pi$
$151$	14.2315	1.15814	0.579070	+	0.815278i	$0.303416\pi$
$152$	−33.0423	−2.68009
$153$	0.0647632	0.00523580
$154$	23.4734	1.89154
$155$	2.20720	0.177287
$156$	53.0307	4.24586
$157$	−5.56154	−0.443859	−0.221930	−	0.975063i	$-0.571236\pi$
$157$	−5.56154	−0.443859	−0.221930	+	0.975063i	$0.571236\pi$
$158$	−42.5546	−3.38546
$159$	0.703769	0.0558125
$160$	12.0535	0.952916
$161$	−4.10563	−0.323569
$162$	25.0877	1.97107
$163$	4.11454	0.322275	0.161138	−	0.986932i	$-0.448484\pi$
$163$	4.11454	0.322275	0.161138	+	0.986932i	$0.448484\pi$
$164$	−18.0203	−1.40715
$165$	2.59976	0.202391
$166$	−12.1624	−0.943985
$167$	−11.5660	−0.895007	−0.447504	−	0.894282i	$-0.647687\pi$
$167$	−11.5660	−0.895007	−0.447504	+	0.894282i	$0.647687\pi$
$168$	−41.9003	−3.23268
$169$	14.7405	1.13388
$170$	−7.29654	−0.559619
$171$	−0.0311464	−0.00238183
$172$	19.7374	1.50497
$173$	−9.52531	−0.724196	−0.362098	−	0.932140i	$-0.617939\pi$
$173$	−9.52531	−0.724196	−0.362098	+	0.932140i	$0.617939\pi$
$174$	26.7077	2.02471
$175$	10.9577	0.828324
$176$	67.6234	5.09731
$177$	4.87698	0.366576
$178$	15.4152	1.15542
$179$	13.2498	0.990339	0.495170	−	0.868796i	$-0.335106\pi$
$179$	13.2498	0.990339	0.495170	+	0.868796i	$0.335106\pi$
$180$	0.0238275	0.00177600
$181$	18.0924	1.34480	0.672400	−	0.740188i	$-0.265264\pi$
$181$	18.0924	1.34480	0.672400	+	0.740188i	$0.265264\pi$
$182$	−33.3848	−2.47465
$183$	3.47571	0.256932
$184$	−19.3710	−1.42805
$185$	0.908172	0.0667702
$186$	−26.2927	−1.92787
$187$	−23.7955	−1.74010
$188$	14.1472	1.03179
$189$	−11.7955	−0.857995
$190$	3.50911	0.254577
$191$	−0.808874	−0.0585281	−0.0292640	−	0.999572i	$-0.509316\pi$
$191$	−0.808874	−0.0585281	−0.0292640	+	0.999572i	$0.509316\pi$
$192$	−80.4344	−5.80485
$193$	18.5792	1.33736	0.668678	−	0.743552i	$-0.266860\pi$
$193$	18.5792	1.33736	0.668678	+	0.743552i	$0.266860\pi$
$194$	−29.7419	−2.13535
$195$	−3.69750	−0.264783
$196$	−10.8546	−0.775326
$197$	−6.02408	−0.429198	−0.214599	−	0.976702i	$-0.568844\pi$
$197$	−6.02408	−0.429198	−0.214599	+	0.976702i	$0.568844\pi$
$198$	0.104396	0.00741911
$199$	18.2414	1.29310	0.646550	−	0.762871i	$-0.276211\pi$
$199$	18.2414	1.29310	0.646550	+	0.762871i	$0.276211\pi$
$200$	51.7001	3.65575
$201$	−14.5602	−1.02700
$202$	12.1456	0.854560
$203$	−12.5150	−0.878380
$204$	64.6967	4.52968
$205$	1.25644	0.0877539
$206$	−42.2356	−2.94269
$207$	−0.0182595	−0.00126912
$208$	−96.1770	−6.66867
$209$	11.4439	0.791590
$210$	4.44983	0.307067
$211$	−27.1740	−1.87073	−0.935367	−	0.353678i	$-0.884931\pi$
$211$	−27.1740	−1.87073	−0.935367	+	0.353678i	$0.884931\pi$
$212$	−2.36996	−0.162770
$213$	−1.59152	−0.109049
$214$	−1.55254	−0.106129
$215$	−1.37617	−0.0938538
$216$	−55.6529	−3.78670
$217$	12.3205	0.836370
$218$	16.3991	1.11069
$219$	−12.6206	−0.852822
$220$	−8.75478	−0.590247
$221$	33.8429	2.27652
$222$	−10.8184	−0.726081
$223$	−16.2304	−1.08687	−0.543433	−	0.839452i	$-0.682876\pi$
$223$	−16.2304	−1.08687	−0.543433	+	0.839452i	$0.682876\pi$
$224$	67.2823	4.49549
$225$	0.0487336	0.00324891
$226$	55.5555	3.69549
$227$	16.0892	1.06788	0.533940	−	0.845523i	$-0.320711\pi$
$227$	16.0892	1.06788	0.533940	+	0.845523i	$0.320711\pi$
$228$	−31.1144	−2.06060
$229$	−19.4712	−1.28669	−0.643346	−	0.765575i	$-0.722454\pi$
$229$	−19.4712	−1.28669	−0.643346	+	0.765575i	$0.722454\pi$
$230$	2.05720	0.135648
$231$	14.5118	0.954805
$232$	−59.0476	−3.87667
$233$	−6.38497	−0.418293	−0.209147	−	0.977884i	$-0.567069\pi$
$233$	−6.38497	−0.418293	−0.209147	+	0.977884i	$0.567069\pi$
$234$	−0.148477	−0.00970623
$235$	−0.986392	−0.0643451
$236$	−16.4234	−1.06907
$237$	−26.3082	−1.70890
$238$	−40.7290	−2.64007
$239$	−8.63424	−0.558502	−0.279251	−	0.960218i	$-0.590086\pi$
$239$	−8.63424	−0.558502	−0.279251	+	0.960218i	$0.590086\pi$
$240$	12.8193	0.827484
$241$	−5.88587	−0.379142	−0.189571	−	0.981867i	$-0.560710\pi$
$241$	−5.88587	−0.379142	−0.189571	+	0.981867i	$0.560710\pi$
$242$	−7.59105	−0.487971
$243$	−0.104744	−0.00671930
$244$	−11.7045	−0.749306
$245$	0.756821	0.0483515
$246$	−14.9671	−0.954265
$247$	−16.2760	−1.03562
$248$	58.1300	3.69126
$249$	−7.51908	−0.476502
$250$	−11.1683	−0.706346
$251$	18.7560	1.18387	0.591936	−	0.805985i	$-0.298364\pi$
$251$	18.7560	1.18387	0.591936	+	0.805985i	$0.298364\pi$
$252$	0.133004	0.00837849
$253$	6.70895	0.421788
$254$	−41.5564	−2.60748
$255$	−4.51089	−0.282483
$256$	104.789	6.54929
$257$	−12.9752	−0.809369	−0.404684	−	0.914456i	$-0.632619\pi$
$257$	−12.9752	−0.809369	−0.404684	+	0.914456i	$0.632619\pi$
$258$	16.3932	1.02060
$259$	5.06938	0.314996
$260$	12.4514	0.772204
$261$	−0.0556595	−0.00344524
$262$	1.33539	0.0825005
$263$	5.74914	0.354507	0.177253	−	0.984165i	$-0.443279\pi$
$263$	5.74914	0.354507	0.177253	+	0.984165i	$0.443279\pi$
$264$	68.4688	4.21396
$265$	0.165243	0.0101508
$266$	19.5877	1.20100
$267$	9.53004	0.583229
$268$	49.0319	2.99510
$269$	−24.0972	−1.46923	−0.734616	−	0.678484i	$-0.762637\pi$
$269$	−24.0972	−1.46923	−0.734616	+	0.678484i	$0.762637\pi$
$270$	5.91035	0.359693
$271$	14.4160	0.875707	0.437853	−	0.899046i	$-0.355739\pi$
$271$	14.4160	0.875707	0.437853	+	0.899046i	$0.355739\pi$
$272$	−117.334	−7.11445
$273$	−20.6393	−1.24915
$274$	−26.3730	−1.59325
$275$	−17.9058	−1.07976
$276$	−18.2407	−1.09796
$277$	13.9245	0.836644	0.418322	−	0.908299i	$-0.362618\pi$
$277$	13.9245	0.836644	0.418322	+	0.908299i	$0.362618\pi$
$278$	−7.56834	−0.453919
$279$	0.0547946	0.00328047
$280$	−9.83805	−0.587936
$281$	32.6182	1.94584	0.972918	−	0.231149i	$-0.0742486\pi$
$281$	32.6182	1.94584	0.972918	+	0.231149i	$0.0742486\pi$
$282$	11.7501	0.699710
$283$	−20.9747	−1.24682	−0.623408	−	0.781896i	$-0.714253\pi$
$283$	−20.9747	−1.24682	−0.623408	+	0.781896i	$0.714253\pi$
$284$	5.35949	0.318027
$285$	2.16941	0.128505
$286$	54.5537	3.22583
$287$	7.01342	0.413989
$288$	0.299234	0.0176325
$289$	24.2879	1.42870
$290$	6.27088	0.368239
$291$	−18.3871	−1.07787
$292$	42.5003	2.48714
$293$	−0.540279	−0.0315634	−0.0157817	−	0.999875i	$-0.505024\pi$
$293$	−0.540279	−0.0315634	−0.0157817	+	0.999875i	$0.505024\pi$
$294$	−9.01542	−0.525790
$295$	1.14510	0.0666702
$296$	23.9181	1.39021
$297$	19.2748	1.11844
$298$	59.2461	3.43204
$299$	−9.54176	−0.551814
$300$	48.6836	2.81075
$301$	−7.68171	−0.442766
$302$	−39.8047	−2.29050
$303$	7.50868	0.431363
$304$	56.4294	3.23645
$305$	0.816083	0.0467288
$306$	−0.181139	−0.0103551
$307$	−2.58549	−0.147562	−0.0737809	−	0.997274i	$-0.523507\pi$
$307$	−2.58549	−0.147562	−0.0737809	+	0.997274i	$0.523507\pi$
$308$	−48.8688	−2.78456
$309$	−26.1110	−1.48540
$310$	−6.17343	−0.350627
$311$	−28.0353	−1.58973	−0.794867	−	0.606784i	$-0.792459\pi$
$311$	−28.0353	−1.58973	−0.794867	+	0.606784i	$0.792459\pi$
$312$	−97.3793	−5.51301
$313$	21.7451	1.22910	0.614552	−	0.788876i	$-0.289337\pi$
$313$	21.7451	1.22910	0.614552	+	0.788876i	$0.289337\pi$
$314$	15.5553	0.877839
$315$	−0.00927356	−0.000522506 0
$316$	88.5937	4.98378
$317$	28.4927	1.60031	0.800155	−	0.599793i	$-0.204750\pi$
$317$	28.4927	1.60031	0.800155	+	0.599793i	$0.204750\pi$
$318$	−1.96841	−0.110383
$319$	20.4506	1.14501
$320$	−18.8857	−1.05574
$321$	−0.959815	−0.0535716
$322$	11.4832	0.639935
$323$	−19.8565	−1.10484
$324$	−52.2296	−2.90165
$325$	25.4664	1.41262
$326$	−11.5082	−0.637377
$327$	10.1383	0.560649
$328$	33.0904	1.82711
$329$	−5.50600	−0.303555
$330$	−7.27141	−0.400278
$331$	19.4874	1.07113	0.535563	−	0.844495i	$-0.320100\pi$
$331$	19.4874	1.07113	0.535563	+	0.844495i	$0.320100\pi$
$332$	25.3207	1.38965
$333$	0.0225457	0.00123550
$334$	32.3496	1.77009
$335$	−3.41868	−0.186783
$336$	71.5570	3.90375
$337$	16.1449	0.879469	0.439735	−	0.898128i	$-0.355072\pi$
$337$	16.1449	0.879469	0.439735	+	0.898128i	$0.355072\pi$
$338$	−41.2283	−2.24252
$339$	34.3457	1.86540
$340$	15.1906	0.823823
$341$	−20.1328	−1.09025
$342$	0.0871149	0.00471063
$343$	20.0883	1.08467
$344$	−36.2435	−1.95412
$345$	1.27181	0.0684720
$346$	26.6418	1.43227
$347$	−3.54664	−0.190394	−0.0951969	−	0.995458i	$-0.530348\pi$
$347$	−3.54664	−0.190394	−0.0951969	+	0.995458i	$0.530348\pi$
$348$	−55.6024	−2.98060
$349$	21.6148	1.15702	0.578508	−	0.815677i	$-0.303635\pi$
$349$	21.6148	1.15702	0.578508	+	0.815677i	$0.303635\pi$
$350$	−30.6481	−1.63821
$351$	−27.4135	−1.46322
$352$	−109.945	−5.86010
$353$	23.1534	1.23233	0.616164	−	0.787618i	$-0.288686\pi$
$353$	23.1534	1.23233	0.616164	+	0.787618i	$0.288686\pi$
$354$	−13.6407	−0.724993
$355$	−0.373683	−0.0198331
$356$	−32.0927	−1.70091
$357$	−25.1796	−1.33265
$358$	−37.0591	−1.95863
$359$	−22.2521	−1.17442	−0.587212	−	0.809433i	$-0.699774\pi$
$359$	−22.2521	−1.17442	−0.587212	+	0.809433i	$0.699774\pi$
$360$	−0.0437540	−0.00230604
$361$	−9.45048	−0.497393
$362$	−50.6036	−2.65967
$363$	−4.69296	−0.246317
$364$	69.5033	3.64296
$365$	−2.96327	−0.155105
$366$	−9.72137	−0.508144
$367$	−13.1638	−0.687144	−0.343572	−	0.939126i	$-0.611637\pi$
$367$	−13.1638	−0.687144	−0.343572	+	0.939126i	$0.611637\pi$
$368$	33.0816	1.72450
$369$	0.0311917	0.00162378
$370$	−2.54011	−0.132054
$371$	0.922377	0.0478874
$372$	54.7383	2.83805
$373$	0.239378	0.0123945	0.00619725	−	0.999981i	$-0.498027\pi$
$373$	0.239378	0.0123945	0.00619725	+	0.999981i	$0.498027\pi$
$374$	66.5547	3.44146
$375$	−6.90451	−0.356547
$376$	−25.9781	−1.33972
$377$	−29.0857	−1.49799
$378$	32.9913	1.69689
$379$	25.8330	1.32695	0.663476	−	0.748198i	$-0.269080\pi$
$379$	25.8330	1.32695	0.663476	+	0.748198i	$0.269080\pi$
$380$	−7.30555	−0.374767
$381$	−25.6911	−1.31620
$382$	2.26238	0.115753
$383$	9.29132	0.474764	0.237382	−	0.971416i	$-0.423711\pi$
$383$	9.29132	0.474764	0.237382	+	0.971416i	$0.423711\pi$
$384$	122.299	6.24102
$385$	3.40731	0.173653
$386$	−51.9649	−2.64495
$387$	−0.0341639	−0.00173665
$388$	61.9192	3.14347
$389$	1.11747	0.0566578	0.0283289	−	0.999599i	$-0.490981\pi$
$389$	1.11747	0.0566578	0.0283289	+	0.999599i	$0.490981\pi$
$390$	10.3417	0.523673
$391$	−11.6408	−0.588701
$392$	19.9320	1.00672
$393$	0.825567	0.0416444
$394$	16.8490	0.848843
$395$	−6.17708	−0.310803
$396$	−0.217341	−0.0109218
$397$	5.14488	0.258214	0.129107	−	0.991631i	$-0.458789\pi$
$397$	5.14488	0.258214	0.129107	+	0.991631i	$0.458789\pi$
$398$	−51.0203	−2.55742
$399$	12.1096	0.606237
$400$	−88.2929	−4.41465
$401$	5.49697	0.274506	0.137253	−	0.990536i	$-0.456173\pi$
$401$	5.49697	0.274506	0.137253	+	0.990536i	$0.456173\pi$
$402$	40.7241	2.03113
$403$	28.6337	1.42635
$404$	−25.2857	−1.25801
$405$	3.64164	0.180955
$406$	35.0038	1.73721
$407$	−8.28380	−0.410613
$408$	−118.801	−5.88154
$409$	−29.5699	−1.46214	−0.731069	−	0.682304i	$-0.760978\pi$
$409$	−29.5699	−1.46214	−0.731069	+	0.682304i	$0.760978\pi$
$410$	−3.51421	−0.173555
$411$	−16.3044	−0.804238
$412$	87.9296	4.33198
$413$	6.39189	0.314524
$414$	0.0510709	0.00251000
$415$	−1.76545	−0.0866627
$416$	156.369	7.66661
$417$	−4.67893	−0.229128
$418$	−32.0080	−1.56556
$419$	−3.41916	−0.167037	−0.0835185	−	0.996506i	$-0.526616\pi$
$419$	−3.41916	−0.167037	−0.0835185	+	0.996506i	$0.526616\pi$
$420$	−9.26403	−0.452038
$421$	16.3211	0.795441	0.397721	−	0.917507i	$-0.369801\pi$
$421$	16.3211	0.795441	0.397721	+	0.917507i	$0.369801\pi$
$422$	76.0042	3.69983
$423$	−0.0244875	−0.00119063
$424$	4.35191	0.211348
$425$	31.0687	1.50705
$426$	4.45140	0.215671
$427$	4.55534	0.220448
$428$	3.23220	0.156234
$429$	33.7264	1.62832
$430$	3.84907	0.185619
$431$	21.9938	1.05940	0.529701	−	0.848184i	$-0.322304\pi$
$431$	21.9938	1.05940	0.529701	+	0.848184i	$0.322304\pi$
$432$	95.0434	4.57278
$433$	15.5917	0.749289	0.374645	−	0.927168i	$-0.377765\pi$
$433$	15.5917	0.749289	0.374645	+	0.927168i	$0.377765\pi$
$434$	−34.4598	−1.65412
$435$	3.87680	0.185878
$436$	−34.1409	−1.63505
$437$	5.59838	0.267807
$438$	35.2992	1.68666
$439$	11.1964	0.534376	0.267188	−	0.963644i	$-0.413906\pi$
$439$	11.1964	0.534376	0.267188	+	0.963644i	$0.413906\pi$
$440$	16.0762	0.766404
$441$	0.0187884	0.000894684 0
$442$	−94.6570	−4.50237
$443$	−6.87439	−0.326612	−0.163306	−	0.986575i	$-0.552216\pi$
$443$	−6.87439	−0.326612	−0.163306	+	0.986575i	$0.552216\pi$
$444$	22.5226	1.06887
$445$	2.23762	0.106073
$446$	45.3955	2.14954
$447$	36.6273	1.73241
$448$	−105.419	−4.98059
$449$	−27.0583	−1.27696	−0.638479	−	0.769639i	$-0.720436\pi$
$449$	−27.0583	−1.27696	−0.638479	+	0.769639i	$0.720436\pi$
$450$	−0.136305	−0.00642550
$451$	−11.4605	−0.539655
$452$	−115.660	−5.44019
$453$	−24.6082	−1.15619
$454$	−45.0007	−2.11199
$455$	−4.84603	−0.227185
$456$	57.1348	2.67558
$457$	−29.3315	−1.37207	−0.686034	−	0.727569i	$-0.740650\pi$
$457$	−29.3315	−1.37207	−0.686034	+	0.727569i	$0.740650\pi$
$458$	54.4599	2.54475
$459$	−33.4441	−1.56104
$460$	−4.28286	−0.199689
$461$	26.4513	1.23196	0.615981	−	0.787761i	$-0.288760\pi$
$461$	26.4513	1.23196	0.615981	+	0.787761i	$0.288760\pi$
$462$	−40.5887	−1.88836
$463$	28.4122	1.32043	0.660214	−	0.751077i	$-0.270465\pi$
$463$	28.4122	1.32043	0.660214	+	0.751077i	$0.270465\pi$
$464$	100.841	4.68142
$465$	−3.81656	−0.176989
$466$	17.8584	0.827276
$467$	4.07234	0.188445	0.0942227	−	0.995551i	$-0.469963\pi$
$467$	4.07234	0.188445	0.0942227	+	0.995551i	$0.469963\pi$
$468$	0.309111	0.0142887
$469$	−19.0829	−0.881168
$470$	2.75889	0.127258
$471$	9.61668	0.443113
$472$	30.1579	1.38813
$473$	12.5526	0.577168
$474$	73.5828	3.37977
$475$	−14.9418	−0.685576
$476$	84.7930	3.88648
$477$	0.00410221	0.000187827 0
$478$	24.1495	1.10457
$479$	−36.8553	−1.68396	−0.841982	−	0.539506i	$-0.818611\pi$
$479$	−36.8553	−1.68396	−0.841982	+	0.539506i	$0.818611\pi$
$480$	−20.8422	−0.951314
$481$	11.7816	0.537194
$482$	16.4625	0.749845
$483$	7.09920	0.323025
$484$	15.8037	0.718349
$485$	−4.31724	−0.196036
$486$	0.292962	0.0132890
$487$	17.0668	0.773372	0.386686	−	0.922211i	$-0.373620\pi$
$487$	17.0668	0.773372	0.386686	+	0.922211i	$0.373620\pi$
$488$	21.4928	0.972933
$489$	−7.11461	−0.321734
$490$	−2.11679	−0.0956268
$491$	0.267090	0.0120536	0.00602679	−	0.999982i	$-0.498082\pi$
$491$	0.267090	0.0120536	0.00602679	+	0.999982i	$0.498082\pi$
$492$	31.1597	1.40479
$493$	−35.4841	−1.59812
$494$	45.5231	2.04818
$495$	0.0151538	0.000681112 0
$496$	−99.2739	−4.45753
$497$	−2.08588	−0.0935647
$498$	21.0305	0.942398
$499$	40.2920	1.80372	0.901859	−	0.432030i	$-0.142202\pi$
$499$	40.2920	1.80372	0.901859	+	0.432030i	$0.142202\pi$
$500$	23.2511	1.03982
$501$	19.9993	0.893503
$502$	−52.4597	−2.34139
$503$	40.4756	1.80472	0.902360	−	0.430983i	$-0.141833\pi$
$503$	40.4756	1.80472	0.902360	+	0.430983i	$0.141833\pi$
$504$	−0.244233	−0.0108790
$505$	1.76301	0.0784530
$506$	−18.7646	−0.834188
$507$	−25.4883	−1.13197
$508$	86.5155	3.83850
$509$	10.5316	0.466804	0.233402	−	0.972380i	$-0.425014\pi$
$509$	10.5316	0.466804	0.233402	+	0.972380i	$0.425014\pi$
$510$	12.6167	0.558679
$511$	−16.5409	−0.731725
$512$	−151.632	−6.70127
$513$	16.0842	0.710133
$514$	36.2909	1.60072
$515$	−6.13078	−0.270154
$516$	−34.1288	−1.50244
$517$	8.99727	0.395700
$518$	−14.1788	−0.622980
$519$	16.4706	0.722979
$520$	−22.8643	−1.00267
$521$	16.2989	0.714066	0.357033	−	0.934092i	$-0.383788\pi$
$521$	16.2989	0.714066	0.357033	+	0.934092i	$0.383788\pi$
$522$	0.155677	0.00681379
$523$	−26.6055	−1.16338	−0.581690	−	0.813411i	$-0.697608\pi$
$523$	−26.6055	−1.16338	−0.581690	+	0.813411i	$0.697608\pi$
$524$	−2.78012	−0.121450
$525$	−18.9474	−0.826932
$526$	−16.0800	−0.701123
$527$	34.9327	1.52169
$528$	−116.930	−5.08874
$529$	−19.7180	−0.857303
$530$	−0.462175	−0.0200756
$531$	0.0284275	0.00123365
$532$	−40.7793	−1.76801
$533$	16.2997	0.706017
$534$	−26.6550	−1.15348
$535$	−0.225361	−0.00974321
$536$	−90.0362	−3.88897
$537$	−22.9108	−0.988674
$538$	67.3986	2.90576
$539$	−6.90326	−0.297345
$540$	−12.3047	−0.529509
$541$	−22.2582	−0.956954	−0.478477	−	0.878100i	$-0.658811\pi$
$541$	−22.2582	−0.956954	−0.478477	+	0.878100i	$0.658811\pi$
$542$	−40.3207	−1.73192
$543$	−31.2843	−1.34254
$544$	190.768	8.17909
$545$	2.38043	0.101967
$546$	57.7270	2.47049
$547$	−26.9786	−1.15352	−0.576761	−	0.816913i	$-0.695684\pi$
$547$	−26.9786	−1.15352	−0.576761	+	0.816913i	$0.695684\pi$
$548$	54.9056	2.34545
$549$	0.0202596	0.000864658 0
$550$	50.0817	2.13549
$551$	17.0653	0.727005
$552$	33.4951	1.42565
$553$	−34.4802	−1.46625
$554$	−38.9462	−1.65467
$555$	−1.57036	−0.0666579
$556$	15.7564	0.668221
$557$	−42.6810	−1.80845	−0.904227	−	0.427053i	$-0.859552\pi$
$557$	−42.6810	−1.80845	−0.904227	+	0.427053i	$0.859552\pi$
$558$	−0.153258	−0.00648792
$559$	−17.8528	−0.755094
$560$	16.8013	0.709985
$561$	41.1457	1.73717
$562$	−91.2313	−3.84836
$563$	31.8086	1.34057	0.670286	−	0.742103i	$-0.266171\pi$
$563$	31.8086	1.34057	0.670286	+	0.742103i	$0.266171\pi$
$564$	−24.4624	−1.03005
$565$	8.06424	0.339265
$566$	58.6652	2.46588
$567$	20.3275	0.853675
$568$	−9.84152	−0.412941
$569$	−14.5041	−0.608043	−0.304021	−	0.952665i	$-0.598329\pi$
$569$	−14.5041	−0.608043	−0.304021	+	0.952665i	$0.598329\pi$
$570$	−6.06773	−0.254149
$571$	−38.2542	−1.60089	−0.800445	−	0.599406i	$-0.795403\pi$
$571$	−38.2542	−1.60089	−0.800445	+	0.599406i	$0.795403\pi$
$572$	−113.574	−4.74878
$573$	1.39866	0.0584297
$574$	−19.6162	−0.818763
$575$	−8.75958	−0.365300
$576$	−0.468845	−0.0195352
$577$	3.89268	0.162054	0.0810271	−	0.996712i	$-0.474180\pi$
$577$	3.89268	0.162054	0.0810271	+	0.996712i	$0.474180\pi$
$578$	−67.9320	−2.82560
$579$	−32.1259	−1.33511
$580$	−13.0552	−0.542089
$581$	−9.85468	−0.408841
$582$	51.4279	2.13176
$583$	−1.50724	−0.0624236
$584$	−78.0424	−3.22942
$585$	−0.0215524	−0.000891081 0
$586$	1.51113	0.0624243
$587$	15.5144	0.640350	0.320175	−	0.947358i	$-0.396258\pi$
$587$	15.5144	0.640350	0.320175	+	0.947358i	$0.396258\pi$
$588$	18.7691	0.774023
$589$	−16.8001	−0.692236
$590$	−3.20278	−0.131856
$591$	10.4165	0.428476
$592$	−40.8471	−1.67881
$593$	−15.4332	−0.633767	−0.316884	−	0.948464i	$-0.602636\pi$
$593$	−15.4332	−0.633767	−0.316884	+	0.948464i	$0.602636\pi$
$594$	−53.9107	−2.21198
$595$	−5.91208	−0.242372
$596$	−123.344	−5.05235
$597$	−31.5420	−1.29093
$598$	26.6878	1.09135
$599$	14.0449	0.573861	0.286930	−	0.957951i	$-0.407365\pi$
$599$	14.0449	0.573861	0.286930	+	0.957951i	$0.407365\pi$
$600$	−89.3966	−3.64960
$601$	19.4874	0.794907	0.397454	−	0.917622i	$-0.369894\pi$
$601$	19.4874	0.794907	0.397454	+	0.917622i	$0.369894\pi$
$602$	21.4853	0.875677
$603$	−0.0848701	−0.00345618
$604$	82.8687	3.37188
$605$	−1.10189	−0.0447983
$606$	−21.0014	−0.853124
$607$	23.5614	0.956329	0.478165	−	0.878270i	$-0.341302\pi$
$607$	23.5614	0.956329	0.478165	+	0.878270i	$0.341302\pi$
$608$	−91.7454	−3.72077
$609$	21.6401	0.876903
$610$	−2.28254	−0.0924175
$611$	−12.7963	−0.517683
$612$	0.377111	0.0152438
$613$	−3.21200	−0.129732	−0.0648658	−	0.997894i	$-0.520662\pi$
$613$	−3.21200	−0.129732	−0.0648658	+	0.997894i	$0.520662\pi$
$614$	7.23149	0.291839
$615$	−2.17257	−0.0876064
$616$	89.7368	3.61560
$617$	6.07661	0.244635	0.122318	−	0.992491i	$-0.460967\pi$
$617$	6.07661	0.244635	0.122318	+	0.992491i	$0.460967\pi$
$618$	73.0312	2.93775
$619$	5.52458	0.222052	0.111026	−	0.993818i	$-0.464586\pi$
$619$	5.52458	0.222052	0.111026	+	0.993818i	$0.464586\pi$
$620$	12.8524	0.516163
$621$	9.42930	0.378385
$622$	78.4132	3.14408
$623$	12.4903	0.500413
$624$	166.303	6.65746
$625$	22.5547	0.902187
$626$	−60.8198	−2.43085
$627$	−19.7881	−0.790260
$628$	−32.3844	−1.29228
$629$	14.3734	0.573104
$630$	0.0259377	0.00103338
$631$	−33.5702	−1.33641	−0.668204	−	0.743978i	$-0.732936\pi$
$631$	−33.5702	−1.33641	−0.668204	+	0.743978i	$0.732936\pi$
$632$	−162.683	−6.47117
$633$	46.9876	1.86759
$634$	−79.6927	−3.16500
$635$	−6.03218	−0.239380
$636$	4.09799	0.162496
$637$	9.81812	0.389008
$638$	−57.1992	−2.26454
$639$	−0.00927683	−0.000366986 0
$640$	28.7153	1.13507
$641$	29.7824	1.17633	0.588167	−	0.808740i	$-0.299850\pi$
$641$	29.7824	1.17633	0.588167	+	0.808740i	$0.299850\pi$
$642$	2.68455	0.105951
$643$	−46.5176	−1.83447	−0.917237	−	0.398342i	$-0.869586\pi$
$643$	−46.5176	−1.83447	−0.917237	+	0.398342i	$0.869586\pi$
$644$	−23.9067	−0.942058
$645$	2.37958	0.0936960
$646$	55.5376	2.18510
$647$	−12.7622	−0.501735	−0.250867	−	0.968021i	$-0.580716\pi$
$647$	−12.7622	−0.501735	−0.250867	+	0.968021i	$0.580716\pi$
$648$	95.9082	3.76763
$649$	−10.4449	−0.409998
$650$	−71.2283	−2.79381
$651$	−21.3039	−0.834964
$652$	23.9586	0.938292
$653$	34.1587	1.33673	0.668367	−	0.743831i	$-0.266993\pi$
$653$	34.1587	1.33673	0.668367	+	0.743831i	$0.266993\pi$
$654$	−28.3563	−1.10882
$655$	0.193840	0.00757397
$656$	−56.5114	−2.20640
$657$	−0.0735644	−0.00287002
$658$	15.4000	0.600354
$659$	−4.89403	−0.190644	−0.0953221	−	0.995446i	$-0.530388\pi$
$659$	−4.89403	−0.190644	−0.0953221	+	0.995446i	$0.530388\pi$
$660$	15.1382	0.589255
$661$	−21.5874	−0.839652	−0.419826	−	0.907605i	$-0.637909\pi$
$661$	−21.5874	−0.839652	−0.419826	+	0.907605i	$0.637909\pi$
$662$	−54.5053	−2.11841
$663$	−58.5192	−2.27270
$664$	−46.4959	−1.80439
$665$	2.84328	0.110258
$666$	−0.0630592	−0.00244350
$667$	10.0045	0.387375
$668$	−67.3482	−2.60578
$669$	28.0646	1.08504
$670$	9.56188	0.369408
$671$	−7.44382	−0.287366
$672$	−116.340	−4.48793
$673$	−0.970518	−0.0374107	−0.0187054	−	0.999825i	$-0.505954\pi$
$673$	−0.970518	−0.0374107	−0.0187054	+	0.999825i	$0.505954\pi$
$674$	−45.1565	−1.73936
$675$	−25.1663	−0.968651
$676$	85.8325	3.30125
$677$	−12.4074	−0.476854	−0.238427	−	0.971160i	$-0.576632\pi$
$677$	−12.4074	−0.476854	−0.238427	+	0.971160i	$0.576632\pi$
$678$	−96.0631	−3.68928
$679$	−24.0986	−0.924821
$680$	−27.8941	−1.06969
$681$	−27.8205	−1.06608
$682$	56.3103	2.15623
$683$	−0.472879	−0.0180942	−0.00904710	−	0.999959i	$-0.502880\pi$
$683$	−0.472879	−0.0180942	−0.00904710	+	0.999959i	$0.502880\pi$
$684$	−0.181363	−0.00693459
$685$	−3.82822	−0.146269
$686$	−56.1859	−2.14519
$687$	33.6684	1.28453
$688$	61.8962	2.35977
$689$	2.14367	0.0816672
$690$	−3.55719	−0.135420
$691$	−16.8053	−0.639303	−0.319652	−	0.947535i	$-0.603566\pi$
$691$	−16.8053	−0.639303	−0.319652	+	0.947535i	$0.603566\pi$
$692$	−55.4651	−2.10847
$693$	0.0845878	0.00321323
$694$	9.91978	0.376550
$695$	−1.09860	−0.0416721
$696$	102.102	3.87015
$697$	19.8854	0.753212
$698$	−60.4556	−2.28828
$699$	11.0405	0.417590
$700$	63.8058	2.41163
$701$	−39.2800	−1.48358	−0.741792	−	0.670630i	$-0.766024\pi$
$701$	−39.2800	−1.48358	−0.741792	+	0.670630i	$0.766024\pi$
$702$	76.6742	2.89388
$703$	−6.91254	−0.260712
$704$	172.264	6.49245
$705$	1.70561	0.0642369
$706$	−64.7587	−2.43723
$707$	9.84106	0.370111
$708$	28.3983	1.06727
$709$	−25.9813	−0.975749	−0.487875	−	0.872914i	$-0.662228\pi$
$709$	−25.9813	−0.975749	−0.487875	+	0.872914i	$0.662228\pi$
$710$	1.04517	0.0392246
$711$	−0.153348	−0.00575101
$712$	58.9311	2.20854
$713$	−9.84900	−0.368848
$714$	70.4261	2.63563
$715$	7.91883	0.296147
$716$	77.1527	2.88333
$717$	14.9298	0.557563
$718$	62.2381	2.32271
$719$	46.3398	1.72818	0.864091	−	0.503336i	$-0.167894\pi$
$719$	46.3398	1.72818	0.864091	+	0.503336i	$0.167894\pi$
$720$	0.0747227	0.00278475
$721$	−34.2217	−1.27448
$722$	26.4325	0.983716
$723$	10.1775	0.378505
$724$	105.351	3.91533
$725$	−26.7014	−0.991665
$726$	13.1260	0.487151
$727$	14.5420	0.539335	0.269667	−	0.962954i	$-0.413086\pi$
$727$	14.5420	0.539335	0.269667	+	0.962954i	$0.413086\pi$
$728$	−127.628	−4.73019
$729$	27.0901	1.00334
$730$	8.28813	0.306757
$731$	−21.7802	−0.805569
$732$	20.2388	0.748046
$733$	−42.6547	−1.57549	−0.787743	−	0.616004i	$-0.788750\pi$
$733$	−42.6547	−1.57549	−0.787743	+	0.616004i	$0.788750\pi$
$734$	36.8184	1.35899
$735$	−1.30865	−0.0482702
$736$	−53.7855	−1.98256
$737$	31.1832	1.14865
$738$	−0.0872416	−0.00321141
$739$	−14.9803	−0.551058	−0.275529	−	0.961293i	$-0.588853\pi$
$739$	−14.9803	−0.551058	−0.275529	+	0.961293i	$0.588853\pi$
$740$	5.28822	0.194399
$741$	28.1435	1.03388
$742$	−2.57984	−0.0947089
$743$	−20.2738	−0.743774	−0.371887	−	0.928278i	$-0.621289\pi$
$743$	−20.2738	−0.743774	−0.371887	+	0.928278i	$0.621289\pi$
$744$	−100.515	−3.68505
$745$	8.59996	0.315078
$746$	−0.669527	−0.0245131
$747$	−0.0438280	−0.00160358
$748$	−138.559	−5.06622
$749$	−1.25796	−0.0459647
$750$	19.3116	0.705159
$751$	−20.5983	−0.751644	−0.375822	−	0.926692i	$-0.622640\pi$
$751$	−20.5983	−0.751644	−0.375822	+	0.926692i	$0.622640\pi$
$752$	44.3652	1.61783
$753$	−32.4318	−1.18188
$754$	81.3512	2.96263
$755$	−5.77791	−0.210280
$756$	−68.6841	−2.49802
$757$	−46.8300	−1.70207	−0.851033	−	0.525112i	$-0.824024\pi$
$757$	−46.8300	−1.70207	−0.851033	+	0.525112i	$0.824024\pi$
$758$	−72.2536	−2.62437
$759$	−11.6007	−0.421079
$760$	13.4150	0.486615
$761$	3.37936	0.122502	0.0612509	−	0.998122i	$-0.480491\pi$
$761$	3.37936	0.122502	0.0612509	+	0.998122i	$0.480491\pi$
$762$	71.8567	2.60309
$763$	13.2875	0.481039
$764$	−4.71001	−0.170402
$765$	−0.0262936	−0.000950647 0
$766$	−25.9873	−0.938961
$767$	14.8552	0.536390
$768$	−181.194	−6.53828
$769$	9.88045	0.356298	0.178149	−	0.984004i	$-0.442989\pi$
$769$	9.88045	0.356298	0.178149	+	0.984004i	$0.442989\pi$
$770$	−9.53008	−0.343440
$771$	22.4359	0.808008
$772$	108.185	3.89366
$773$	−31.6358	−1.13786	−0.568931	−	0.822385i	$-0.692643\pi$
$773$	−31.6358	−1.13786	−0.568931	+	0.822385i	$0.692643\pi$
$774$	0.0955546	0.00343464
$775$	26.2865	0.944238
$776$	−113.701	−4.08163
$777$	−8.76566	−0.314466
$778$	−3.12550	−0.112054
$779$	−9.56341	−0.342645
$780$	−21.5302	−0.770906
$781$	3.40852	0.121966
$782$	32.5587	1.16430
$783$	28.7429	1.02719
$784$	−34.0397	−1.21570
$785$	2.25796	0.0805901
$786$	−2.30907	−0.0823618
$787$	−15.9886	−0.569933	−0.284967	−	0.958537i	$-0.591982\pi$
$787$	−15.9886	−0.569933	−0.284967	+	0.958537i	$0.591982\pi$
$788$	−35.0777	−1.24959
$789$	−9.94105	−0.353911
$790$	17.2770	0.614687
$791$	45.0143	1.60052
$792$	0.399098	0.0141813
$793$	10.5869	0.375953
$794$	−14.3900	−0.510681
$795$	−0.285727	−0.0101337
$796$	106.218	3.76481
$797$	32.8878	1.16494	0.582472	−	0.812851i	$-0.302085\pi$
$797$	32.8878	1.16494	0.582472	+	0.812851i	$0.302085\pi$
$798$	−33.8698	−1.19898
$799$	−15.6113	−0.552289
$800$	143.551	5.07528
$801$	0.0555498	0.00196275
$802$	−15.3748	−0.542901
$803$	27.0292	0.953840
$804$	−84.7829	−2.99006
$805$	1.66687	0.0587493
$806$	−80.0870	−2.82094
$807$	41.6674	1.46676
$808$	46.4316	1.63346
$809$	−28.0238	−0.985263	−0.492631	−	0.870238i	$-0.663965\pi$
$809$	−28.0238	−0.985263	−0.492631	+	0.870238i	$0.663965\pi$
$810$	−10.1855	−0.357882
$811$	−41.7830	−1.46720	−0.733600	−	0.679582i	$-0.762161\pi$
$811$	−41.7830	−1.46720	−0.733600	+	0.679582i	$0.762161\pi$
$812$	−72.8738	−2.55737
$813$	−24.9272	−0.874234
$814$	23.1694	0.812086
$815$	−1.67048	−0.0585145
$816$	202.888	7.10249
$817$	10.4747	0.366463
$818$	82.7055	2.89173
$819$	−0.120304	−0.00420378
$820$	7.31618	0.255492
$821$	−13.1292	−0.458212	−0.229106	−	0.973401i	$-0.573580\pi$
$821$	−13.1292	−0.458212	−0.229106	+	0.973401i	$0.573580\pi$
$822$	45.6026	1.59057
$823$	16.8063	0.585830	0.292915	−	0.956138i	$-0.405375\pi$
$823$	16.8063	0.585830	0.292915	+	0.956138i	$0.405375\pi$
$824$	−161.463	−5.62484
$825$	30.9617	1.07795
$826$	−17.8778	−0.622047
$827$	37.7751	1.31357	0.656785	−	0.754078i	$-0.271916\pi$
$827$	37.7751	1.31357	0.656785	+	0.754078i	$0.271916\pi$
$828$	−0.106324	−0.00369500
$829$	−22.3189	−0.775168	−0.387584	−	0.921834i	$-0.626690\pi$
$829$	−22.3189	−0.775168	−0.387584	+	0.921834i	$0.626690\pi$
$830$	4.93788	0.171396
$831$	−24.0775	−0.835238
$832$	−245.001	−8.49390
$833$	11.9780	0.415012
$834$	13.0867	0.453156
$835$	4.69576	0.162504
$836$	66.6369	2.30468
$837$	−28.2962	−0.978060
$838$	9.56322	0.330356
$839$	−27.7611	−0.958421	−0.479211	−	0.877700i	$-0.659077\pi$
$839$	−27.7611	−0.958421	−0.479211	+	0.877700i	$0.659077\pi$
$840$	17.0114	0.586947
$841$	1.49615	0.0515913
$842$	−45.6493	−1.57318
$843$	−56.4013	−1.94257
$844$	−158.232	−5.44657
$845$	−5.98456	−0.205875
$846$	0.0684904	0.00235475
$847$	−6.15071	−0.211341
$848$	−7.43216	−0.255221
$849$	36.2682	1.24472
$850$	−86.8975	−2.98056
$851$	−4.05246	−0.138917
$852$	−9.26730	−0.317492
$853$	−56.8640	−1.94698	−0.973492	−	0.228720i	$-0.926546\pi$
$853$	−56.8640	−1.94698	−0.973492	+	0.228720i	$0.926546\pi$
$854$	−12.7411	−0.435990
$855$	0.0126453	0.000432460 0
$856$	−5.93523	−0.202862
$857$	−52.9394	−1.80838	−0.904188	−	0.427135i	$-0.859523\pi$
$857$	−52.9394	−1.80838	−0.904188	+	0.427135i	$0.859523\pi$
$858$	−94.3309	−3.22040
$859$	25.8408	0.881676	0.440838	−	0.897587i	$-0.354681\pi$
$859$	25.8408	0.881676	0.440838	+	0.897587i	$0.354681\pi$
$860$	−8.01331	−0.273252
$861$	−12.1272	−0.413293
$862$	−61.5155	−2.09522
$863$	−27.0879	−0.922081	−0.461041	−	0.887379i	$-0.652524\pi$
$863$	−27.0879	−0.922081	−0.461041	+	0.887379i	$0.652524\pi$
$864$	−154.526	−5.25707
$865$	3.86723	0.131490
$866$	−43.6092	−1.48190
$867$	−41.9972	−1.42630
$868$	71.7413	2.43506
$869$	56.3436	1.91133
$870$	−10.8432	−0.367619
$871$	−44.3501	−1.50274
$872$	62.6923	2.12303
$873$	−0.107177	−0.00362739
$874$	−15.6584	−0.529653
$875$	−9.04921	−0.305919
$876$	−73.4888	−2.48296
$877$	51.4573	1.73759	0.868795	−	0.495172i	$-0.164895\pi$
$877$	51.4573	1.73759	0.868795	+	0.495172i	$0.164895\pi$
$878$	−31.3158	−1.05686
$879$	0.934217	0.0315104
$880$	−27.4548	−0.925501
$881$	−41.3292	−1.39241	−0.696207	−	0.717841i	$-0.745131\pi$
$881$	−41.3292	−1.39241	−0.696207	+	0.717841i	$0.745131\pi$
$882$	−0.0525501	−0.00176945
$883$	10.1029	0.339989	0.169994	−	0.985445i	$-0.445625\pi$
$883$	10.1029	0.339989	0.169994	+	0.985445i	$0.445625\pi$
$884$	197.065	6.62801
$885$	−1.98003	−0.0665581
$886$	19.2273	0.645954
$887$	−23.7317	−0.796833	−0.398416	−	0.917205i	$-0.630440\pi$
$887$	−23.7317	−0.796833	−0.398416	+	0.917205i	$0.630440\pi$
$888$	−41.3577	−1.38787
$889$	−33.6714	−1.12930
$890$	−6.25851	−0.209786
$891$	−33.2169	−1.11281
$892$	−94.5082	−3.16437
$893$	7.50791	0.251243
$894$	−102.445	−3.42626
$895$	−5.37937	−0.179813
$896$	160.287	5.35483
$897$	16.4990	0.550886
$898$	75.6806	2.52549
$899$	−30.0222	−1.00130
$900$	0.283772	0.00945907
$901$	2.61524	0.0871264
$902$	32.0545	1.06730
$903$	13.2827	0.442022
$904$	212.384	7.06379
$905$	−7.34544	−0.244171
$906$	68.8278	2.28665
$907$	31.2878	1.03889	0.519447	−	0.854503i	$-0.326138\pi$
$907$	31.2878	1.03889	0.519447	+	0.854503i	$0.326138\pi$
$908$	93.6863	3.10909
$909$	0.0437674	0.00145167
$910$	13.5541	0.449314
$911$	−51.9764	−1.72205	−0.861027	−	0.508559i	$-0.830178\pi$
$911$	−51.9764	−1.72205	−0.861027	+	0.508559i	$0.830178\pi$
$912$	−97.5742	−3.23100
$913$	16.1034	0.532945
$914$	82.0386	2.71360
$915$	−1.41112	−0.0466502
$916$	−113.379	−3.74616
$917$	1.08201	0.0357311
$918$	93.5414	3.08732
$919$	22.3468	0.737151	0.368576	−	0.929598i	$-0.379846\pi$
$919$	22.3468	0.737151	0.368576	+	0.929598i	$0.379846\pi$
$920$	7.86453	0.259286
$921$	4.47068	0.147314
$922$	−73.9830	−2.43650
$923$	−4.84774	−0.159565
$924$	84.5009	2.77988
$925$	10.8158	0.355621
$926$	−79.4676	−2.61147
$927$	−0.152199	−0.00499886
$928$	−163.952	−5.38198
$929$	31.6788	1.03935	0.519673	−	0.854365i	$-0.326054\pi$
$929$	31.6788	1.03935	0.519673	+	0.854365i	$0.326054\pi$
$930$	10.6747	0.350038
$931$	−5.76053	−0.188794
$932$	−37.1792	−1.21784
$933$	48.4769	1.58706
$934$	−11.3901	−0.372696
$935$	9.66085	0.315944
$936$	−0.567615	−0.0185531
$937$	0.692346	0.0226180	0.0113090	−	0.999936i	$-0.496400\pi$
$937$	0.692346	0.0226180	0.0113090	+	0.999936i	$0.496400\pi$
$938$	53.3740	1.74272
$939$	−37.6002	−1.22704
$940$	−5.74368	−0.187338
$941$	−2.74984	−0.0896422	−0.0448211	−	0.998995i	$-0.514272\pi$
$941$	−2.74984	−0.0896422	−0.0448211	+	0.998995i	$0.514272\pi$
$942$	−26.8973	−0.876363
$943$	−5.60652	−0.182574
$944$	−51.5034	−1.67629
$945$	4.78891	0.155783
$946$	−35.1089	−1.14149
$947$	23.1091	0.750946	0.375473	−	0.926833i	$-0.377480\pi$
$947$	23.1091	0.750946	0.375473	+	0.926833i	$0.377480\pi$
$948$	−153.191	−4.97540
$949$	−38.4421	−1.24788
$950$	41.7914	1.35589
$951$	−49.2679	−1.59762
$952$	−155.704	−5.04639
$953$	−33.5439	−1.08659	−0.543297	−	0.839540i	$-0.682824\pi$
$953$	−33.5439	−1.08659	−0.543297	+	0.839540i	$0.682824\pi$
$954$	−0.0114737	−0.000371474 0
$955$	0.328399	0.0106268
$956$	−50.2765	−1.62606
$957$	−35.3619	−1.14309
$958$	103.082	3.33044
$959$	−21.3690	−0.690040
$960$	32.6560	1.05397
$961$	−1.44430	−0.0465902
$962$	−32.9525	−1.06243
$963$	−0.00559467	−0.000180286 0
$964$	−34.2730	−1.10386
$965$	−7.54305	−0.242820
$966$	−19.8561	−0.638859
$967$	−31.9678	−1.02801	−0.514007	−	0.857786i	$-0.671839\pi$
$967$	−31.9678	−1.02801	−0.514007	+	0.857786i	$0.671839\pi$
$968$	−29.0200	−0.932738
$969$	34.3346	1.10299
$970$	12.0751	0.387708
$971$	−52.7365	−1.69239	−0.846197	−	0.532869i	$-0.821114\pi$
$971$	−52.7365	−1.69239	−0.846197	+	0.532869i	$0.821114\pi$
$972$	−0.609913	−0.0195630
$973$	−6.13231	−0.196593
$974$	−47.7351	−1.52953
$975$	−44.0350	−1.41025
$976$	−36.7052	−1.17490
$977$	8.39726	0.268652	0.134326	−	0.990937i	$-0.457113\pi$
$977$	8.39726	0.268652	0.134326	+	0.990937i	$0.457113\pi$
$978$	19.8992	0.636306
$979$	−20.4102	−0.652314
$980$	4.40691	0.140773
$981$	0.0590951	0.00188676
$982$	−0.747036	−0.0238389
$983$	−30.4181	−0.970186	−0.485093	−	0.874463i	$-0.661214\pi$
$983$	−30.4181	−0.970186	−0.485093	+	0.874463i	$0.661214\pi$
$984$	−57.2179	−1.82404
$985$	2.44575	0.0779281
$986$	99.2472	3.16068
$987$	9.52063	0.303045
$988$	−94.7739	−3.01516
$989$	6.14075	0.195265
$990$	−0.0423844	−0.00134706
$991$	24.0658	0.764476	0.382238	−	0.924064i	$-0.375153\pi$
$991$	24.0658	0.764476	0.382238	+	0.924064i	$0.375153\pi$
$992$	161.404	5.12458
$993$	−33.6965	−1.06932
$994$	5.83411	0.185047
$995$	−7.40594	−0.234784
$996$	−43.7830	−1.38732
$997$	−6.24136	−0.197666	−0.0988329	−	0.995104i	$-0.531511\pi$
$997$	−6.24136	−0.197666	−0.0988329	+	0.995104i	$0.531511\pi$
$998$	−112.695	−3.56729
$999$	−11.6427	−0.368360

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8017.2.a.a.1.1	✓	327

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8017.2.a.a.1.1	✓	327	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:	\( N \)	\(=\)	\( 8017 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8017.a (trivial)

\(f(q)\)	\(=\)	\(q-2.79695 q^{2} -1.72914 q^{3} +5.82292 q^{4} -0.405996 q^{5} +4.83631 q^{6} -2.26625 q^{7} -10.6925 q^{8} -0.0100790 q^{9} +O(q^{10})\)	\(q-2.79695 q^{2} -1.72914 q^{3} +5.82292 q^{4} -0.405996 q^{5} +4.83631 q^{6} -2.26625 q^{7} -10.6925 q^{8} -0.0100790 q^{9} +1.13555 q^{10} +3.70325 q^{11} -10.0686 q^{12} -5.26692 q^{13} +6.33858 q^{14} +0.702023 q^{15} +18.2606 q^{16} -6.42557 q^{17} +0.0281904 q^{18} +3.09023 q^{19} -2.36408 q^{20} +3.91866 q^{21} -10.3578 q^{22} +1.81164 q^{23} +18.4888 q^{24} -4.83517 q^{25} +14.7313 q^{26} +5.20484 q^{27} -13.1962 q^{28} +5.52233 q^{29} -1.96352 q^{30} -5.43652 q^{31} -29.6888 q^{32} -6.40343 q^{33} +17.9720 q^{34} +0.920088 q^{35} -0.0586892 q^{36} -2.23690 q^{37} -8.64322 q^{38} +9.10724 q^{39} +4.34111 q^{40} -3.09472 q^{41} -10.9603 q^{42} +3.38961 q^{43} +21.5637 q^{44} +0.00409203 q^{45} -5.06706 q^{46} +2.42956 q^{47} -31.5751 q^{48} -1.86411 q^{49} +13.5237 q^{50} +11.1107 q^{51} -30.6689 q^{52} -0.407006 q^{53} -14.5577 q^{54} -1.50350 q^{55} +24.2319 q^{56} -5.34344 q^{57} -15.4457 q^{58} -2.82047 q^{59} +4.08782 q^{60} -2.01008 q^{61} +15.2057 q^{62} +0.0228415 q^{63} +46.5170 q^{64} +2.13835 q^{65} +17.9101 q^{66} +8.42049 q^{67} -37.4156 q^{68} -3.13258 q^{69} -2.57344 q^{70} +0.920412 q^{71} +0.107770 q^{72} +7.29879 q^{73} +6.25650 q^{74} +8.36068 q^{75} +17.9942 q^{76} -8.39249 q^{77} -25.4725 q^{78} +15.2146 q^{79} -7.41371 q^{80} -8.96966 q^{81} +8.65579 q^{82} +4.34845 q^{83} +22.8181 q^{84} +2.60875 q^{85} -9.48057 q^{86} -9.54888 q^{87} -39.5970 q^{88} -5.51144 q^{89} -0.0114452 q^{90} +11.9362 q^{91} +10.5490 q^{92} +9.40049 q^{93} -6.79536 q^{94} -1.25462 q^{95} +51.3361 q^{96} +10.6337 q^{97} +5.21382 q^{98} -0.0373250 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 327 q - 23 q^{2} - 48 q^{3} + 315 q^{4} - 55 q^{5} - 38 q^{6} - 87 q^{7} - 69 q^{8} + 303 q^{9}+O(q^{10}) \) 327 * q - 23 * q^2 - 48 * q^3 + 315 * q^4 - 55 * q^5 - 38 * q^6 - 87 * q^7 - 69 * q^8 + 303 * q^9	\( 327 q - 23 q^{2} - 48 q^{3} + 315 q^{4} - 55 q^{5} - 38 q^{6} - 87 q^{7} - 69 q^{8} + 303 q^{9} - 48 q^{10} - 70 q^{11} - 120 q^{12} - 53 q^{13} - 52 q^{14} - 77 q^{15} + 295 q^{16} - 164 q^{17} - 58 q^{18} - 47 q^{19} - 153 q^{20} - 39 q^{21} - 68 q^{22} - 256 q^{23} - 107 q^{24} + 288 q^{25} - 95 q^{26} - 189 q^{27} - 167 q^{28} - 99 q^{29} - 81 q^{30} - 71 q^{31} - 146 q^{32} - 95 q^{33} - 40 q^{34} - 192 q^{35} + 261 q^{36} - 54 q^{37} - 179 q^{38} - 115 q^{39} - 121 q^{40} - 111 q^{41} - 62 q^{42} - 110 q^{43} - 157 q^{44} - 137 q^{45} - 11 q^{46} - 324 q^{47} - 236 q^{48} + 296 q^{49} - 73 q^{50} - 88 q^{51} - 138 q^{52} - 170 q^{53} - 127 q^{54} - 151 q^{55} - 151 q^{56} - 106 q^{57} - 81 q^{58} - 123 q^{59} - 83 q^{60} - 62 q^{61} - 287 q^{62} - 400 q^{63} + 263 q^{64} - 143 q^{65} - 64 q^{66} - 95 q^{67} - 442 q^{68} - 22 q^{69} - 26 q^{70} - 210 q^{71} - 129 q^{72} - 121 q^{73} - 159 q^{74} - 194 q^{75} - 86 q^{76} - 178 q^{77} - 68 q^{78} - 145 q^{79} - 338 q^{80} + 259 q^{81} - 103 q^{82} - 418 q^{83} - 102 q^{84} - 40 q^{85} - 89 q^{86} - 372 q^{87} - 186 q^{88} - 100 q^{89} - 150 q^{90} - 69 q^{91} - 458 q^{92} - 81 q^{93} - 46 q^{94} - 377 q^{95} - 190 q^{96} - 87 q^{97} - 147 q^{98} - 171 q^{99}+O(q^{100}) \) 327 * q - 23 * q^2 - 48 * q^3 + 315 * q^4 - 55 * q^5 - 38 * q^6 - 87 * q^7 - 69 * q^8 + 303 * q^9 - 48 * q^10 - 70 * q^11 - 120 * q^12 - 53 * q^13 - 52 * q^14 - 77 * q^15 + 295 * q^16 - 164 * q^17 - 58 * q^18 - 47 * q^19 - 153 * q^20 - 39 * q^21 - 68 * q^22 - 256 * q^23 - 107 * q^24 + 288 * q^25 - 95 * q^26 - 189 * q^27 - 167 * q^28 - 99 * q^29 - 81 * q^30 - 71 * q^31 - 146 * q^32 - 95 * q^33 - 40 * q^34 - 192 * q^35 + 261 * q^36 - 54 * q^37 - 179 * q^38 - 115 * q^39 - 121 * q^40 - 111 * q^41 - 62 * q^42 - 110 * q^43 - 157 * q^44 - 137 * q^45 - 11 * q^46 - 324 * q^47 - 236 * q^48 + 296 * q^49 - 73 * q^50 - 88 * q^51 - 138 * q^52 - 170 * q^53 - 127 * q^54 - 151 * q^55 - 151 * q^56 - 106 * q^57 - 81 * q^58 - 123 * q^59 - 83 * q^60 - 62 * q^61 - 287 * q^62 - 400 * q^63 + 263 * q^64 - 143 * q^65 - 64 * q^66 - 95 * q^67 - 442 * q^68 - 22 * q^69 - 26 * q^70 - 210 * q^71 - 129 * q^72 - 121 * q^73 - 159 * q^74 - 194 * q^75 - 86 * q^76 - 178 * q^77 - 68 * q^78 - 145 * q^79 - 338 * q^80 + 259 * q^81 - 103 * q^82 - 418 * q^83 - 102 * q^84 - 40 * q^85 - 89 * q^86 - 372 * q^87 - 186 * q^88 - 100 * q^89 - 150 * q^90 - 69 * q^91 - 458 * q^92 - 81 * q^93 - 46 * q^94 - 377 * q^95 - 190 * q^96 - 87 * q^97 - 147 * q^98 - 171 * q^99

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