LMFDB - Embedded newform 8033.2.a.d.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8033,2,Mod(1,8033)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8033, 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("8033.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8033 = 29 \cdot 277 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8033.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:	$64.1438279437$
Analytic rank:	$0$
Dimension:	$168$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Character	$\chi$	$=$	8033.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.69133 q^{2} -1.56780 q^{3} +5.24327 q^{4} +1.58955 q^{5} +4.21948 q^{6} -0.425755 q^{7} -8.72870 q^{8} -0.541992 q^{9} +O(q^{10})$	\(q-2.69133 q^{2} -1.56780 q^{3} +5.24327 q^{4} +1.58955 q^{5} +4.21948 q^{6} -0.425755 q^{7} -8.72870 q^{8} -0.541992 q^{9} -4.27800 q^{10} -3.42167 q^{11} -8.22041 q^{12} -1.13639 q^{13} +1.14585 q^{14} -2.49210 q^{15} +13.0053 q^{16} -3.29165 q^{17} +1.45868 q^{18} +3.62159 q^{19} +8.33442 q^{20} +0.667500 q^{21} +9.20885 q^{22} -1.43574 q^{23} +13.6849 q^{24} -2.47334 q^{25} +3.05840 q^{26} +5.55315 q^{27} -2.23235 q^{28} +1.00000 q^{29} +6.70707 q^{30} +4.85296 q^{31} -17.5442 q^{32} +5.36451 q^{33} +8.85892 q^{34} -0.676758 q^{35} -2.84181 q^{36} +11.8248 q^{37} -9.74689 q^{38} +1.78164 q^{39} -13.8747 q^{40} -1.68740 q^{41} -1.79646 q^{42} +9.99287 q^{43} -17.9407 q^{44} -0.861523 q^{45} +3.86406 q^{46} +4.93642 q^{47} -20.3898 q^{48} -6.81873 q^{49} +6.65657 q^{50} +5.16066 q^{51} -5.95839 q^{52} +10.1080 q^{53} -14.9454 q^{54} -5.43891 q^{55} +3.71629 q^{56} -5.67793 q^{57} -2.69133 q^{58} -10.6209 q^{59} -13.0667 q^{60} -0.119205 q^{61} -13.0609 q^{62} +0.230756 q^{63} +21.2066 q^{64} -1.80635 q^{65} -14.4377 q^{66} -13.6054 q^{67} -17.2590 q^{68} +2.25096 q^{69} +1.82138 q^{70} -8.80138 q^{71} +4.73089 q^{72} +2.32818 q^{73} -31.8243 q^{74} +3.87771 q^{75} +18.9889 q^{76} +1.45679 q^{77} -4.79497 q^{78} -4.83562 q^{79} +20.6726 q^{80} -7.08027 q^{81} +4.54136 q^{82} +5.21294 q^{83} +3.49988 q^{84} -5.23223 q^{85} -26.8941 q^{86} -1.56780 q^{87} +29.8667 q^{88} -11.9542 q^{89} +2.31864 q^{90} +0.483824 q^{91} -7.52798 q^{92} -7.60849 q^{93} -13.2855 q^{94} +5.75668 q^{95} +27.5058 q^{96} -13.1262 q^{97} +18.3515 q^{98} +1.85452 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 168 q + 12 q^{2} + 35 q^{3} + 184 q^{4} + 12 q^{5} + 10 q^{6} + 74 q^{7} + 39 q^{8} + 183 q^{9}+O(q^{10}) $ 168 * q + 12 * q^2 + 35 * q^3 + 184 * q^4 + 12 * q^5 + 10 * q^6 + 74 * q^7 + 39 * q^8 + 183 * q^9	\( 168 q + 12 q^{2} + 35 q^{3} + 184 q^{4} + 12 q^{5} + 10 q^{6} + 74 q^{7} + 39 q^{8} + 183 q^{9} + 41 q^{10} + 29 q^{11} + 82 q^{12} + 62 q^{13} + 23 q^{14} + 31 q^{15} + 204 q^{16} + 56 q^{17} + 35 q^{18} + 83 q^{19} + 6 q^{20} + 30 q^{21} + 56 q^{22} + 54 q^{23} + 28 q^{24} + 210 q^{25} + 21 q^{26} + 140 q^{27} + 151 q^{28} + 168 q^{29} + 29 q^{30} + 72 q^{31} + 40 q^{32} + 32 q^{33} + 34 q^{34} + 18 q^{35} + 152 q^{36} + 42 q^{37} + 29 q^{38} + 70 q^{39} + 97 q^{40} + 41 q^{41} - 20 q^{42} + 119 q^{43} + 37 q^{44} + 22 q^{45} + 24 q^{46} + 119 q^{47} + 135 q^{48} + 216 q^{49} + 38 q^{50} + 18 q^{51} + 154 q^{52} - 7 q^{53} + 35 q^{54} + 224 q^{55} + 46 q^{56} + 12 q^{57} + 12 q^{58} + 25 q^{59} + 13 q^{60} + 82 q^{61} + 27 q^{62} + 211 q^{63} + 217 q^{64} + 8 q^{65} - 6 q^{66} + 76 q^{67} + 132 q^{68} + 36 q^{69} + 39 q^{70} + 32 q^{71} + 39 q^{72} + 89 q^{73} - q^{74} + 123 q^{75} + 180 q^{76} + 68 q^{77} - 54 q^{78} + 176 q^{79} - 11 q^{80} + 192 q^{81} + 51 q^{82} + 76 q^{83} + 86 q^{84} + 65 q^{85} - 72 q^{86} + 35 q^{87} + 178 q^{88} + 55 q^{89} + 2 q^{90} + 80 q^{91} + 44 q^{92} + 39 q^{93} + 89 q^{94} + 77 q^{95} - 68 q^{96} + 82 q^{97} + 80 q^{98} + 67 q^{99}+O(q^{100}) \) 168 * q + 12 * q^2 + 35 * q^3 + 184 * q^4 + 12 * q^5 + 10 * q^6 + 74 * q^7 + 39 * q^8 + 183 * q^9 + 41 * q^10 + 29 * q^11 + 82 * q^12 + 62 * q^13 + 23 * q^14 + 31 * q^15 + 204 * q^16 + 56 * q^17 + 35 * q^18 + 83 * q^19 + 6 * q^20 + 30 * q^21 + 56 * q^22 + 54 * q^23 + 28 * q^24 + 210 * q^25 + 21 * q^26 + 140 * q^27 + 151 * q^28 + 168 * q^29 + 29 * q^30 + 72 * q^31 + 40 * q^32 + 32 * q^33 + 34 * q^34 + 18 * q^35 + 152 * q^36 + 42 * q^37 + 29 * q^38 + 70 * q^39 + 97 * q^40 + 41 * q^41 - 20 * q^42 + 119 * q^43 + 37 * q^44 + 22 * q^45 + 24 * q^46 + 119 * q^47 + 135 * q^48 + 216 * q^49 + 38 * q^50 + 18 * q^51 + 154 * q^52 - 7 * q^53 + 35 * q^54 + 224 * q^55 + 46 * q^56 + 12 * q^57 + 12 * q^58 + 25 * q^59 + 13 * q^60 + 82 * q^61 + 27 * q^62 + 211 * q^63 + 217 * q^64 + 8 * q^65 - 6 * q^66 + 76 * q^67 + 132 * q^68 + 36 * q^69 + 39 * q^70 + 32 * q^71 + 39 * q^72 + 89 * q^73 - q^74 + 123 * q^75 + 180 * q^76 + 68 * q^77 - 54 * q^78 + 176 * q^79 - 11 * q^80 + 192 * q^81 + 51 * q^82 + 76 * q^83 + 86 * q^84 + 65 * q^85 - 72 * q^86 + 35 * q^87 + 178 * q^88 + 55 * q^89 + 2 * q^90 + 80 * q^91 + 44 * q^92 + 39 * q^93 + 89 * q^94 + 77 * q^95 - 68 * q^96 + 82 * q^97 + 80 * q^98 + 67 * 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 $

$2$	−2.69133	−1.90306	−0.951529	−	0.307558i	$-0.900488\pi$
$2$	−2.69133	−1.90306	−0.951529	+	0.307558i	$0.900488\pi$
$3$	−1.56780	−0.905172	−0.452586	−	0.891721i	$-0.649498\pi$
$3$	−1.56780	−0.905172	−0.452586	+	0.891721i	$0.649498\pi$
$4$	5.24327	2.62163
$5$	1.58955	0.710868	0.355434	−	0.934701i	$-0.384333\pi$
$5$	1.58955	0.710868	0.355434	+	0.934701i	$0.384333\pi$
$6$	4.21948	1.72260
$7$	−0.425755	−0.160920	−0.0804601	−	0.996758i	$-0.525639\pi$
$7$	−0.425755	−0.160920	−0.0804601	+	0.996758i	$0.525639\pi$
$8$	−8.72870	−3.08606
$9$	−0.541992	−0.180664
$10$	−4.27800	−1.35282
$11$	−3.42167	−1.03167	−0.515836	−	0.856687i	$-0.672519\pi$
$11$	−3.42167	−1.03167	−0.515836	+	0.856687i	$0.672519\pi$
$12$	−8.22041	−2.37303
$13$	−1.13639	−0.315178	−0.157589	−	0.987505i	$-0.550372\pi$
$13$	−1.13639	−0.315178	−0.157589	+	0.987505i	$0.550372\pi$
$14$	1.14585	0.306241
$15$	−2.49210	−0.643457
$16$	13.0053	3.25133
$17$	−3.29165	−0.798342	−0.399171	−	0.916876i	$-0.630702\pi$
$17$	−3.29165	−0.798342	−0.399171	+	0.916876i	$0.630702\pi$
$18$	1.45868	0.343814
$19$	3.62159	0.830849	0.415424	−	0.909628i	$-0.363633\pi$
$19$	3.62159	0.830849	0.415424	+	0.909628i	$0.363633\pi$
$20$	8.33442	1.86363
$21$	0.667500	0.145660
$22$	9.20885	1.96333
$23$	−1.43574	−0.299373	−0.149686	−	0.988734i	$-0.547826\pi$
$23$	−1.43574	−0.299373	−0.149686	+	0.988734i	$0.547826\pi$
$24$	13.6849	2.79342
$25$	−2.47334	−0.494667
$26$	3.05840	0.599802
$27$	5.55315	1.06870
$28$	−2.23235	−0.421874
$29$	1.00000	0.185695
$29$	1.00000	0.185695
$30$	6.70707	1.22454
$31$	4.85296	0.871618	0.435809	−	0.900039i	$-0.356462\pi$
$31$	4.85296	0.871618	0.435809	+	0.900039i	$0.356462\pi$
$32$	−17.5442	−3.10140
$33$	5.36451	0.933841
$34$	8.85892	1.51929
$35$	−0.676758	−0.114393
$36$	−2.84181	−0.473635
$37$	11.8248	1.94398	0.971989	−	0.235025i	$-0.0755173\pi$
$37$	11.8248	1.94398	0.971989	+	0.235025i	$0.0755173\pi$
$38$	−9.74689	−1.58115
$39$	1.78164	0.285290
$40$	−13.8747	−2.19378
$41$	−1.68740	−0.263528	−0.131764	−	0.991281i	$-0.542064\pi$
$41$	−1.68740	−0.263528	−0.131764	+	0.991281i	$0.542064\pi$
$42$	−1.79646	−0.277200
$43$	9.99287	1.52390	0.761949	−	0.647637i	$-0.224243\pi$
$43$	9.99287	1.52390	0.761949	+	0.647637i	$0.224243\pi$
$44$	−17.9407	−2.70467
$45$	−0.861523	−0.128428
$46$	3.86406	0.569724
$47$	4.93642	0.720051	0.360025	−	0.932943i	$-0.382768\pi$
$47$	4.93642	0.720051	0.360025	+	0.932943i	$0.382768\pi$
$48$	−20.3898	−2.94301
$49$	−6.81873	−0.974105
$50$	6.65657	0.941381
$51$	5.16066	0.722637
$52$	−5.95839	−0.826280
$53$	10.1080	1.38845	0.694223	−	0.719760i	$-0.255748\pi$
$53$	10.1080	1.38845	0.694223	+	0.719760i	$0.255748\pi$
$54$	−14.9454	−2.03381
$55$	−5.43891	−0.733382
$56$	3.71629	0.496610
$57$	−5.67793	−0.752061
$58$	−2.69133	−0.353389
$59$	−10.6209	−1.38273	−0.691363	−	0.722507i	$-0.742990\pi$
$59$	−10.6209	−1.38273	−0.691363	+	0.722507i	$0.742990\pi$
$60$	−13.0667	−1.68691
$61$	−0.119205	−0.0152626	−0.00763131	−	0.999971i	$-0.502429\pi$
$61$	−0.119205	−0.0152626	−0.00763131	+	0.999971i	$0.502429\pi$
$62$	−13.0609	−1.65874
$63$	0.230756	0.0290725
$64$	21.2066	2.65082
$65$	−1.80635	−0.224050
$66$	−14.4377	−1.77715
$67$	−13.6054	−1.66217	−0.831084	−	0.556147i	$-0.812279\pi$
$67$	−13.6054	−1.66217	−0.831084	+	0.556147i	$0.812279\pi$
$68$	−17.2590	−2.09296
$69$	2.25096	0.270984
$70$	1.82138	0.217697
$71$	−8.80138	−1.04453	−0.522266	−	0.852783i	$-0.674913\pi$
$71$	−8.80138	−1.04453	−0.522266	+	0.852783i	$0.674913\pi$
$72$	4.73089	0.557541
$73$	2.32818	0.272493	0.136246	−	0.990675i	$-0.456496\pi$
$73$	2.32818	0.272493	0.136246	+	0.990675i	$0.456496\pi$
$74$	−31.8243	−3.69951
$75$	3.87771	0.447759
$76$	18.9889	2.17818
$77$	1.45679	0.166017
$78$	−4.79497	−0.542924
$79$	−4.83562	−0.544050	−0.272025	−	0.962290i	$-0.587693\pi$
$79$	−4.83562	−0.544050	−0.272025	+	0.962290i	$0.587693\pi$
$80$	20.6726	2.31126
$81$	−7.08027	−0.786696
$82$	4.54136	0.501509
$83$	5.21294	0.572195	0.286097	−	0.958201i	$-0.407642\pi$
$83$	5.21294	0.572195	0.286097	+	0.958201i	$0.407642\pi$
$84$	3.49988	0.381868
$85$	−5.23223	−0.567516
$86$	−26.8941	−2.90007
$87$	−1.56780	−0.168086
$88$	29.8667	3.18381
$89$	−11.9542	−1.26714	−0.633572	−	0.773683i	$-0.718412\pi$
$89$	−11.9542	−1.26714	−0.633572	+	0.773683i	$0.718412\pi$
$90$	2.31864	0.244406
$91$	0.483824	0.0507185
$92$	−7.52798	−0.784846
$93$	−7.60849	−0.788964
$94$	−13.2855	−1.37030
$95$	5.75668	0.590623
$96$	27.5058	2.80730
$97$	−13.1262	−1.33276	−0.666381	−	0.745611i	$-0.732158\pi$
$97$	−13.1262	−1.33276	−0.666381	+	0.745611i	$0.732158\pi$
$98$	18.3515	1.85378
$99$	1.85452	0.186386
$100$	−12.9684	−1.29684
$101$	−5.13298	−0.510750	−0.255375	−	0.966842i	$-0.582199\pi$
$101$	−5.13298	−0.510750	−0.255375	+	0.966842i	$0.582199\pi$
$102$	−13.8890	−1.37522
$103$	−3.48080	−0.342974	−0.171487	−	0.985186i	$-0.554857\pi$
$103$	−3.48080	−0.342974	−0.171487	+	0.985186i	$0.554857\pi$
$104$	9.91921	0.972658
$105$	1.06102	0.103545
$106$	−27.2041	−2.64229
$107$	−11.2641	−1.08894	−0.544472	−	0.838779i	$-0.683270\pi$
$107$	−11.2641	−1.08894	−0.544472	+	0.838779i	$0.683270\pi$
$108$	29.1166	2.80175
$109$	9.90276	0.948512	0.474256	−	0.880387i	$-0.342717\pi$
$109$	9.90276	0.948512	0.474256	+	0.880387i	$0.342717\pi$
$110$	14.6379	1.39567
$111$	−18.5389	−1.75963
$112$	−5.53707	−0.523204
$113$	13.9137	1.30890	0.654448	−	0.756107i	$-0.272901\pi$
$113$	13.9137	1.30890	0.654448	+	0.756107i	$0.272901\pi$
$114$	15.2812	1.43122
$115$	−2.28218	−0.212814
$116$	5.24327	0.486825
$117$	0.615914	0.0569413
$118$	28.5844	2.63141
$119$	1.40144	0.128469
$120$	21.7528	1.98575
$121$	0.707829	0.0643481
$122$	0.320820	0.0290457
$123$	2.64551	0.238538
$124$	25.4454	2.28506
$125$	−11.8792	−1.06251
$126$	−0.621041	−0.0553267
$127$	−10.0827	−0.894699	−0.447349	−	0.894359i	$-0.647632\pi$
$127$	−10.0827	−0.894699	−0.447349	+	0.894359i	$0.647632\pi$
$128$	−21.9856	−1.94327
$129$	−15.6669	−1.37939
$130$	4.86148	0.426380
$131$	−11.6059	−1.01401	−0.507005	−	0.861943i	$-0.669248\pi$
$131$	−11.6059	−1.01401	−0.507005	+	0.861943i	$0.669248\pi$
$132$	28.1275	2.44819
$133$	−1.54191	−0.133700
$134$	36.6167	3.16320
$135$	8.82700	0.759707
$136$	28.7318	2.46373
$137$	−0.498688	−0.0426058	−0.0213029	−	0.999773i	$-0.506781\pi$
$137$	−0.498688	−0.0426058	−0.0213029	+	0.999773i	$0.506781\pi$
$138$	−6.05808	−0.515698
$139$	−1.84932	−0.156858	−0.0784288	−	0.996920i	$-0.524990\pi$
$139$	−1.84932	−0.156858	−0.0784288	+	0.996920i	$0.524990\pi$
$140$	−3.54842	−0.299896
$141$	−7.73933	−0.651770
$142$	23.6874	1.98781
$143$	3.88835	0.325160
$144$	−7.04877	−0.587398
$145$	1.58955	0.132005
$146$	−6.26590	−0.518569
$147$	10.6904	0.881732
$148$	62.0004	5.09640
$149$	−7.79473	−0.638569	−0.319285	−	0.947659i	$-0.603443\pi$
$149$	−7.79473	−0.638569	−0.319285	+	0.947659i	$0.603443\pi$
$150$	−10.4362	−0.852111
$151$	9.43657	0.767937	0.383969	−	0.923346i	$-0.374557\pi$
$151$	9.43657	0.767937	0.383969	+	0.923346i	$0.374557\pi$
$152$	−31.6117	−2.56405
$153$	1.78405	0.144232
$154$	−3.92071	−0.315940
$155$	7.71402	0.619605
$156$	9.34159	0.747926
$157$	5.01780	0.400464	0.200232	−	0.979749i	$-0.435830\pi$
$157$	5.01780	0.400464	0.200232	+	0.979749i	$0.435830\pi$
$158$	13.0143	1.03536
$159$	−15.8474	−1.25678
$160$	−27.8873	−2.20469
$161$	0.611274	0.0481752
$162$	19.0553	1.49713
$163$	14.9600	1.17176	0.585879	−	0.810399i	$-0.300749\pi$
$163$	14.9600	1.17176	0.585879	+	0.810399i	$0.300749\pi$
$164$	−8.84750	−0.690873
$165$	8.52714	0.663837
$166$	−14.0298	−1.08892
$167$	9.38558	0.726278	0.363139	−	0.931735i	$-0.381705\pi$
$167$	9.38558	0.726278	0.363139	+	0.931735i	$0.381705\pi$
$168$	−5.82641	−0.449517
$169$	−11.7086	−0.900663
$170$	14.0817	1.08002
$171$	−1.96287	−0.150105
$172$	52.3953	3.99510
$173$	−13.2848	−1.01003	−0.505013	−	0.863112i	$-0.668512\pi$
$173$	−13.2848	−1.01003	−0.505013	+	0.863112i	$0.668512\pi$
$174$	4.21948	0.319878
$175$	1.05304	0.0796020
$176$	−44.4999	−3.35430
$177$	16.6515	1.25161
$178$	32.1728	2.41145
$179$	−8.92245	−0.666896	−0.333448	−	0.942769i	$-0.608212\pi$
$179$	−8.92245	−0.666896	−0.333448	+	0.942769i	$0.608212\pi$
$180$	−4.51719	−0.336692
$181$	13.4134	0.997009	0.498505	−	0.866887i	$-0.333883\pi$
$181$	13.4134	0.997009	0.498505	+	0.866887i	$0.333883\pi$
$182$	−1.30213	−0.0965203
$183$	0.186890	0.0138153
$184$	12.5322	0.923883
$185$	18.7960	1.38191
$186$	20.4770	1.50144
$187$	11.2629	0.823628
$188$	25.8830	1.88771
$189$	−2.36428	−0.171976
$190$	−15.4931	−1.12399
$191$	−7.58230	−0.548636	−0.274318	−	0.961639i	$-0.588452\pi$
$191$	−7.58230	−0.548636	−0.274318	+	0.961639i	$0.588452\pi$
$192$	−33.2477	−2.39945
$193$	5.83519	0.420026	0.210013	−	0.977699i	$-0.432649\pi$
$193$	5.83519	0.420026	0.210013	+	0.977699i	$0.432649\pi$
$194$	35.3269	2.53633
$195$	2.83200	0.202803
$196$	−35.7524	−2.55374
$197$	2.07236	0.147649	0.0738246	−	0.997271i	$-0.476479\pi$
$197$	2.07236	0.147649	0.0738246	+	0.997271i	$0.476479\pi$
$198$	−4.99113	−0.354704
$199$	4.82242	0.341853	0.170926	−	0.985284i	$-0.445324\pi$
$199$	4.82242	0.341853	0.170926	+	0.985284i	$0.445324\pi$
$200$	21.5890	1.52657
$201$	21.3306	1.50455
$202$	13.8145	0.971988
$203$	−0.425755	−0.0298821
$204$	27.0587	1.89449
$205$	−2.68221	−0.187333
$206$	9.36799	0.652699
$207$	0.778161	0.0540859
$208$	−14.7791	−1.02475
$209$	−12.3919	−0.857164
$210$	−2.85557	−0.197053
$211$	−8.20946	−0.565163	−0.282581	−	0.959243i	$-0.591191\pi$
$211$	−8.20946	−0.565163	−0.282581	+	0.959243i	$0.591191\pi$
$212$	52.9991	3.63999
$213$	13.7988	0.945481
$214$	30.3155	2.07233
$215$	15.8841	1.08329
$216$	−48.4718	−3.29809
$217$	−2.06617	−0.140261
$218$	−26.6516	−1.80507
$219$	−3.65012	−0.246653
$220$	−28.5176	−1.92266
$221$	3.74060	0.251620
$222$	49.8943	3.34869
$223$	−7.51977	−0.503561	−0.251781	−	0.967784i	$-0.581016\pi$
$223$	−7.51977	−0.503561	−0.251781	+	0.967784i	$0.581016\pi$
$224$	7.46952	0.499078
$225$	1.34053	0.0893686
$226$	−37.4465	−2.49090
$227$	22.6877	1.50584	0.752918	−	0.658114i	$-0.228645\pi$
$227$	22.6877	1.50584	0.752918	+	0.658114i	$0.228645\pi$
$228$	−29.7709	−1.97163
$229$	−15.5447	−1.02722	−0.513610	−	0.858023i	$-0.671692\pi$
$229$	−15.5447	−1.02722	−0.513610	+	0.858023i	$0.671692\pi$
$230$	6.14211	0.404998
$231$	−2.28397	−0.150274
$232$	−8.72870	−0.573067
$233$	−14.1931	−0.929818	−0.464909	−	0.885358i	$-0.653913\pi$
$233$	−14.1931	−0.929818	−0.464909	+	0.885358i	$0.653913\pi$
$234$	−1.65763	−0.108363
$235$	7.84668	0.511861
$236$	−55.6883	−3.62500
$237$	7.58131	0.492459
$238$	−3.77173	−0.244485
$239$	17.2015	1.11267	0.556335	−	0.830958i	$-0.312207\pi$
$239$	17.2015	1.11267	0.556335	+	0.830958i	$0.312207\pi$
$240$	−32.4105	−2.09209
$241$	13.8347	0.891174	0.445587	−	0.895239i	$-0.352995\pi$
$241$	13.8347	0.891174	0.445587	+	0.895239i	$0.352995\pi$
$242$	−1.90500	−0.122458
$243$	−5.55898	−0.356608
$244$	−0.625023	−0.0400130
$245$	−10.8387	−0.692459
$246$	−7.11996	−0.453952
$247$	−4.11553	−0.261865
$248$	−42.3601	−2.68987
$249$	−8.17287	−0.517935
$250$	31.9709	2.02202
$251$	11.2702	0.711366	0.355683	−	0.934607i	$-0.384248\pi$
$251$	11.2702	0.711366	0.355683	+	0.934607i	$0.384248\pi$
$252$	1.20991	0.0762175
$253$	4.91264	0.308855
$254$	27.1360	1.70266
$255$	8.20312	0.513699
$256$	16.7574	1.04734
$257$	4.91340	0.306489	0.153245	−	0.988188i	$-0.451028\pi$
$257$	4.91340	0.306489	0.153245	+	0.988188i	$0.451028\pi$
$258$	42.1647	2.62506
$259$	−5.03445	−0.312826
$260$	−9.47115	−0.587376
$261$	−0.541992	−0.0335485
$262$	31.2353	1.92972
$263$	−1.04365	−0.0643545	−0.0321772	−	0.999482i	$-0.510244\pi$
$263$	−1.04365	−0.0643545	−0.0321772	+	0.999482i	$0.510244\pi$
$264$	−46.8252	−2.88189
$265$	16.0672	0.987001
$266$	4.14979	0.254440
$267$	18.7419	1.14698
$268$	−71.3369	−4.35759
$269$	2.17338	0.132513	0.0662567	−	0.997803i	$-0.478894\pi$
$269$	2.17338	0.132513	0.0662567	+	0.997803i	$0.478894\pi$
$270$	−23.7564	−1.44577
$271$	−21.5355	−1.30819	−0.654094	−	0.756413i	$-0.726950\pi$
$271$	−21.5355	−1.30819	−0.654094	+	0.756413i	$0.726950\pi$
$272$	−42.8089	−2.59567
$273$	−0.758540	−0.0459090
$274$	1.34213	0.0810813
$275$	8.46294	0.510335
$276$	11.8024	0.710420
$277$	−1.00000	−0.0600842
$277$	−1.00000	−0.0600842
$278$	4.97714	0.298509
$279$	−2.63027	−0.157470
$280$	5.90722	0.353024
$281$	−4.04192	−0.241121	−0.120561	−	0.992706i	$-0.538469\pi$
$281$	−4.04192	−0.241121	−0.120561	+	0.992706i	$0.538469\pi$
$282$	20.8291	1.24036
$283$	24.2489	1.44145	0.720725	−	0.693221i	$-0.243809\pi$
$283$	24.2489	1.44145	0.720725	+	0.693221i	$0.243809\pi$
$284$	−46.1480	−2.73838
$285$	−9.02535	−0.534616
$286$	−10.4648	−0.618799
$287$	0.718420	0.0424070
$288$	9.50881	0.560312
$289$	−6.16505	−0.362650
$290$	−4.27800	−0.251213
$291$	20.5793	1.20638
$292$	12.2073	0.714375
$293$	5.73991	0.335329	0.167665	−	0.985844i	$-0.446377\pi$
$293$	5.73991	0.335329	0.167665	+	0.985844i	$0.446377\pi$
$294$	−28.7715	−1.67799
$295$	−16.8825	−0.982936
$296$	−103.215	−5.99924
$297$	−19.0010	−1.10255
$298$	20.9782	1.21523
$299$	1.63156	0.0943557
$300$	20.3318	1.17386
$301$	−4.25451	−0.245226
$302$	−25.3969	−1.46143
$303$	8.04750	0.462317
$304$	47.0998	2.70136
$305$	−0.189482	−0.0108497
$306$	−4.80147	−0.274482
$307$	32.7060	1.86663	0.933314	−	0.359060i	$-0.116903\pi$
$307$	32.7060	1.86663	0.933314	+	0.359060i	$0.116903\pi$
$308$	7.63835	0.435236
$309$	5.45721	0.310450
$310$	−20.7610	−1.17914
$311$	13.5480	0.768235	0.384117	−	0.923284i	$-0.374506\pi$
$311$	13.5480	0.768235	0.384117	+	0.923284i	$0.374506\pi$
$312$	−15.5514	−0.880423
$313$	4.75182	0.268589	0.134294	−	0.990941i	$-0.457123\pi$
$313$	4.75182	0.268589	0.134294	+	0.990941i	$0.457123\pi$
$314$	−13.5046	−0.762107
$315$	0.366798	0.0206667
$316$	−25.3545	−1.42630
$317$	22.8662	1.28429	0.642146	−	0.766583i	$-0.278044\pi$
$317$	22.8662	1.28429	0.642146	+	0.766583i	$0.278044\pi$
$318$	42.6506	2.39173
$319$	−3.42167	−0.191577
$320$	33.7089	1.88438
$321$	17.6599	0.985682
$322$	−1.64514	−0.0916802
$323$	−11.9210	−0.663301
$324$	−37.1237	−2.06243
$325$	2.81067	0.155908
$326$	−40.2623	−2.22992
$327$	−15.5256	−0.858567
$328$	14.7288	0.813264
$329$	−2.10171	−0.115871
$330$	−22.9494	−1.26332
$331$	−22.9238	−1.26001	−0.630004	−	0.776592i	$-0.716947\pi$
$331$	−22.9238	−1.26001	−0.630004	+	0.776592i	$0.716947\pi$
$332$	27.3329	1.50009
$333$	−6.40893	−0.351207
$334$	−25.2597	−1.38215
$335$	−21.6265	−1.18158
$336$	8.68104	0.473590
$337$	−8.53326	−0.464836	−0.232418	−	0.972616i	$-0.574664\pi$
$337$	−8.53326	−0.464836	−0.232418	+	0.972616i	$0.574664\pi$
$338$	31.5118	1.71401
$339$	−21.8140	−1.18478
$340$	−27.4340	−1.48782
$341$	−16.6052	−0.899224
$342$	5.28274	0.285658
$343$	5.88340	0.317673
$344$	−87.2248	−4.70285
$345$	3.57801	0.192634
$346$	35.7538	1.92214
$347$	−26.2396	−1.40861	−0.704307	−	0.709896i	$-0.748742\pi$
$347$	−26.2396	−1.40861	−0.704307	+	0.709896i	$0.748742\pi$
$348$	−8.22041	−0.440660
$349$	12.7087	0.680282	0.340141	−	0.940374i	$-0.389525\pi$
$349$	12.7087	0.680282	0.340141	+	0.940374i	$0.389525\pi$
$350$	−2.83407	−0.151487
$351$	−6.31054	−0.336832
$352$	60.0304	3.19963
$353$	−10.5825	−0.563249	−0.281624	−	0.959525i	$-0.590873\pi$
$353$	−10.5825	−0.563249	−0.281624	+	0.959525i	$0.590873\pi$
$354$	−44.8148	−2.38188
$355$	−13.9902	−0.742524
$356$	−62.6791	−3.32199
$357$	−2.19718	−0.116287
$358$	24.0133	1.26914
$359$	−17.0698	−0.900910	−0.450455	−	0.892799i	$-0.648738\pi$
$359$	−17.0698	−0.900910	−0.450455	+	0.892799i	$0.648738\pi$
$360$	7.51998	0.396338
$361$	−5.88412	−0.309691
$362$	−36.0999	−1.89737
$363$	−1.10974	−0.0582460
$364$	2.53682	0.132965
$365$	3.70075	0.193706
$366$	−0.502982	−0.0262913
$367$	13.8104	0.720896	0.360448	−	0.932779i	$-0.382624\pi$
$367$	13.8104	0.720896	0.360448	+	0.932779i	$0.382624\pi$
$368$	−18.6723	−0.973359
$369$	0.914559	0.0476100
$370$	−50.5863	−2.62986
$371$	−4.30355	−0.223429
$372$	−39.8933	−2.06837
$373$	−23.1203	−1.19712	−0.598562	−	0.801076i	$-0.704261\pi$
$373$	−23.1203	−1.19712	−0.598562	+	0.801076i	$0.704261\pi$
$374$	−30.3123	−1.56741
$375$	18.6243	0.961755
$376$	−43.0885	−2.22212
$377$	−1.13639	−0.0585270
$378$	6.36306	0.327281
$379$	23.4316	1.20360	0.601800	−	0.798647i	$-0.294450\pi$
$379$	23.4316	1.20360	0.601800	+	0.798647i	$0.294450\pi$
$380$	30.1838	1.54840
$381$	15.8078	0.809856
$382$	20.4065	1.04409
$383$	−30.9928	−1.58366	−0.791829	−	0.610743i	$-0.790871\pi$
$383$	−30.9928	−1.58366	−0.791829	+	0.610743i	$0.790871\pi$
$384$	34.4691	1.75899
$385$	2.31564	0.118016
$386$	−15.7044	−0.799335
$387$	−5.41606	−0.275314
$388$	−68.8241	−3.49401
$389$	30.2699	1.53474	0.767372	−	0.641202i	$-0.221564\pi$
$389$	30.2699	1.53474	0.767372	+	0.641202i	$0.221564\pi$
$390$	−7.62184	−0.385947
$391$	4.72596	0.239002
$392$	59.5187	3.00615
$393$	18.1957	0.917854
$394$	−5.57740	−0.280985
$395$	−7.68646	−0.386748
$396$	9.72374	0.488636
$397$	−11.6673	−0.585564	−0.292782	−	0.956179i	$-0.594581\pi$
$397$	−11.6673	−0.585564	−0.292782	+	0.956179i	$0.594581\pi$
$398$	−12.9787	−0.650565
$399$	2.41741	0.121022
$400$	−32.1665	−1.60832
$401$	12.8143	0.639916	0.319958	−	0.947432i	$-0.396331\pi$
$401$	12.8143	0.639916	0.319958	+	0.947432i	$0.396331\pi$
$402$	−57.4078	−2.86324
$403$	−5.51485	−0.274714
$404$	−26.9136	−1.33900
$405$	−11.2544	−0.559237
$406$	1.14585	0.0568675
$407$	−40.4604	−2.00555
$408$	−45.0459	−2.23010
$409$	−7.16641	−0.354356	−0.177178	−	0.984179i	$-0.556697\pi$
$409$	−7.16641	−0.354356	−0.177178	+	0.984179i	$0.556697\pi$
$410$	7.21871	0.356507
$411$	0.781845	0.0385655
$412$	−18.2508	−0.899151
$413$	4.52191	0.222509
$414$	−2.09429	−0.102929
$415$	8.28623	0.406755
$416$	19.9370	0.977493
$417$	2.89938	0.141983
$418$	33.3506	1.63123
$419$	32.2421	1.57513	0.787565	−	0.616232i	$-0.211342\pi$
$419$	32.2421	1.57513	0.787565	+	0.616232i	$0.211342\pi$
$420$	5.56323	0.271458
$421$	25.1227	1.22441	0.612203	−	0.790701i	$-0.290284\pi$
$421$	25.1227	1.22441	0.612203	+	0.790701i	$0.290284\pi$
$422$	22.0944	1.07554
$423$	−2.67550	−0.130087
$424$	−88.2300	−4.28483
$425$	8.14136	0.394914
$426$	−37.1372	−1.79931
$427$	0.0507521	0.00245607
$428$	−59.0608	−2.85481
$429$	−6.09617	−0.294326
$430$	−42.7495	−2.06156
$431$	14.6730	0.706773	0.353387	−	0.935477i	$-0.385030\pi$
$431$	14.6730	0.706773	0.353387	+	0.935477i	$0.385030\pi$
$432$	72.2204	3.47470
$433$	4.20417	0.202040	0.101020	−	0.994884i	$-0.467789\pi$
$433$	4.20417	0.202040	0.101020	+	0.994884i	$0.467789\pi$
$434$	5.56076	0.266925
$435$	−2.49210	−0.119487
$436$	51.9228	2.48665
$437$	−5.19966	−0.248734
$438$	9.82369	0.469394
$439$	26.5581	1.26755	0.633774	−	0.773519i	$-0.281505\pi$
$439$	26.5581	1.26755	0.633774	+	0.773519i	$0.281505\pi$
$440$	47.4746	2.26326
$441$	3.69570	0.175986
$442$	−10.0672	−0.478847
$443$	27.0303	1.28425	0.642123	−	0.766601i	$-0.278054\pi$
$443$	27.0303	1.28425	0.642123	+	0.766601i	$0.278054\pi$
$444$	−97.2044	−4.61311
$445$	−19.0018	−0.900772
$446$	20.2382	0.958306
$447$	12.2206	0.578015
$448$	−9.02881	−0.426571
$449$	−37.2085	−1.75598	−0.877990	−	0.478680i	$-0.841115\pi$
$449$	−37.2085	−1.75598	−0.877990	+	0.478680i	$0.841115\pi$
$450$	−3.60781	−0.170074
$451$	5.77373	0.271874
$452$	72.9535	3.43144
$453$	−14.7947	−0.695115
$454$	−61.0602	−2.86570
$455$	0.769061	0.0360541
$456$	49.5610	2.32091
$457$	−9.27875	−0.434042	−0.217021	−	0.976167i	$-0.569634\pi$
$457$	−9.27875	−0.434042	−0.217021	+	0.976167i	$0.569634\pi$
$458$	41.8359	1.95486
$459$	−18.2790	−0.853191
$460$	−11.9661	−0.557921
$461$	8.83320	0.411403	0.205702	−	0.978615i	$-0.434052\pi$
$461$	8.83320	0.411403	0.205702	+	0.978615i	$0.434052\pi$
$462$	6.14691	0.285980
$463$	2.20349	0.102405	0.0512025	−	0.998688i	$-0.483695\pi$
$463$	2.20349	0.102405	0.0512025	+	0.998688i	$0.483695\pi$
$464$	13.0053	0.603756
$465$	−12.0941	−0.560849
$466$	38.1982	1.76950
$467$	3.62359	0.167680	0.0838399	−	0.996479i	$-0.473282\pi$
$467$	3.62359	0.167680	0.0838399	+	0.996479i	$0.473282\pi$
$468$	3.22940	0.149279
$469$	5.79258	0.267477
$470$	−21.1180	−0.974101
$471$	−7.86693	−0.362489
$472$	92.7069	4.26718
$473$	−34.1923	−1.57216
$474$	−20.4038	−0.937178
$475$	−8.95740	−0.410994
$476$	7.34810	0.336800
$477$	−5.47848	−0.250842
$478$	−46.2948	−2.11748
$479$	−2.86210	−0.130773	−0.0653864	−	0.997860i	$-0.520828\pi$
$479$	−2.86210	−0.130773	−0.0653864	+	0.997860i	$0.520828\pi$
$480$	43.7218	1.99562
$481$	−13.4375	−0.612699
$482$	−37.2339	−1.69596
$483$	−0.958358	−0.0436068
$484$	3.71133	0.168697
$485$	−20.8647	−0.947418
$486$	14.9610	0.678647
$487$	6.53315	0.296046	0.148023	−	0.988984i	$-0.452709\pi$
$487$	6.53315	0.296046	0.148023	+	0.988984i	$0.452709\pi$
$488$	1.04050	0.0471014
$489$	−23.4543	−1.06064
$490$	29.1705	1.31779
$491$	32.8362	1.48188	0.740939	−	0.671572i	$-0.234381\pi$
$491$	32.8362	1.48188	0.740939	+	0.671572i	$0.234381\pi$
$492$	13.8711	0.625359
$493$	−3.29165	−0.148248
$494$	11.0763	0.498345
$495$	2.94785	0.132496
$496$	63.1142	2.83391
$497$	3.74723	0.168086
$498$	21.9959	0.985660
$499$	−6.89100	−0.308483	−0.154242	−	0.988033i	$-0.549293\pi$
$499$	−6.89100	−0.308483	−0.154242	+	0.988033i	$0.549293\pi$
$500$	−62.2859	−2.78551
$501$	−14.7147	−0.657406
$502$	−30.3317	−1.35377
$503$	5.04087	0.224761	0.112381	−	0.993665i	$-0.464152\pi$
$503$	5.04087	0.224761	0.112381	+	0.993665i	$0.464152\pi$
$504$	−2.01420	−0.0897196
$505$	−8.15912	−0.363076
$506$	−13.2215	−0.587769
$507$	18.3568	0.815255
$508$	−52.8665	−2.34557
$509$	27.6906	1.22737	0.613683	−	0.789553i	$-0.289687\pi$
$509$	27.6906	1.22737	0.613683	+	0.789553i	$0.289687\pi$
$510$	−22.0773	−0.977599
$511$	−0.991233	−0.0438496
$512$	−1.12843	−0.0498699
$513$	20.1112	0.887931
$514$	−13.2236	−0.583267
$515$	−5.53290	−0.243809
$516$	−82.1455	−3.61625
$517$	−16.8908	−0.742856
$518$	13.5494	0.595325
$519$	20.8280	0.914247
$520$	15.7671	0.691431
$521$	39.1816	1.71658	0.858288	−	0.513169i	$-0.171528\pi$
$521$	39.1816	1.71658	0.858288	+	0.513169i	$0.171528\pi$
$522$	1.45868	0.0638447
$523$	30.2127	1.32111	0.660554	−	0.750778i	$-0.270321\pi$
$523$	30.2127	1.32111	0.660554	+	0.750778i	$0.270321\pi$
$524$	−60.8527	−2.65836
$525$	−1.65095	−0.0720535
$526$	2.80882	0.122470
$527$	−15.9742	−0.695849
$528$	69.7670	3.03622
$529$	−20.9386	−0.910376
$530$	−43.2422	−1.87832
$531$	5.75646	0.249809
$532$	−8.08463	−0.350513
$533$	1.91755	0.0830581
$534$	−50.4406	−2.18278
$535$	−17.9049	−0.774095
$536$	118.758	5.12955
$537$	13.9887	0.603655
$538$	−5.84929	−0.252181
$539$	23.3315	1.00496
$540$	46.2823	1.99167
$541$	39.6017	1.70261	0.851305	−	0.524670i	$-0.175811\pi$
$541$	39.6017	1.70261	0.851305	+	0.524670i	$0.175811\pi$
$542$	57.9592	2.48956
$543$	−21.0296	−0.902465
$544$	57.7493	2.47598
$545$	15.7409	0.674267
$546$	2.04148	0.0873674
$547$	44.4727	1.90151	0.950757	−	0.309937i	$-0.100308\pi$
$547$	44.4727	1.90151	0.950757	+	0.309937i	$0.100308\pi$
$548$	−2.61475	−0.111697
$549$	0.0646081	0.00275741
$550$	−22.7766	−0.971197
$551$	3.62159	0.154285
$552$	−19.6480	−0.836273
$553$	2.05879	0.0875487
$554$	2.69133	0.114344
$555$	−29.4685	−1.25087
$556$	−9.69650	−0.411223
$557$	−16.9213	−0.716977	−0.358489	−	0.933534i	$-0.616708\pi$
$557$	−16.9213	−0.716977	−0.358489	+	0.933534i	$0.616708\pi$
$558$	7.07892	0.299675
$559$	−11.3558	−0.480299
$560$	−8.80144	−0.371929
$561$	−17.6581	−0.745524
$562$	10.8782	0.458867
$563$	18.9093	0.796930	0.398465	−	0.917184i	$-0.369543\pi$
$563$	18.9093	0.796930	0.398465	+	0.917184i	$0.369543\pi$
$564$	−40.5794	−1.70870
$565$	22.1166	0.930451
$566$	−65.2619	−2.74316
$567$	3.01446	0.126595
$568$	76.8246	3.22349
$569$	26.7470	1.12129	0.560647	−	0.828055i	$-0.310553\pi$
$569$	26.7470	1.12129	0.560647	+	0.828055i	$0.310553\pi$
$570$	24.2902	1.01740
$571$	25.9209	1.08476	0.542378	−	0.840134i	$-0.317524\pi$
$571$	25.9209	1.08476	0.542378	+	0.840134i	$0.317524\pi$
$572$	20.3877	0.852451
$573$	11.8876	0.496610
$574$	−1.93351	−0.0807030
$575$	3.55107	0.148090
$576$	−11.4938	−0.478908
$577$	−19.1726	−0.798165	−0.399083	−	0.916915i	$-0.630671\pi$
$577$	−19.1726	−0.798165	−0.399083	+	0.916915i	$0.630671\pi$
$578$	16.5922	0.690144
$579$	−9.14843	−0.380196
$580$	8.33442	0.346068
$581$	−2.21944	−0.0920778
$582$	−55.3857	−2.29581
$583$	−34.5864	−1.43242
$584$	−20.3220	−0.840929
$585$	0.979026	0.0404777
$586$	−15.4480	−0.638151
$587$	18.7859	0.775379	0.387690	−	0.921790i	$-0.373273\pi$
$587$	18.7859	0.775379	0.387690	+	0.921790i	$0.373273\pi$
$588$	56.0528	2.31158
$589$	17.5754	0.724182
$590$	45.4363	1.87058
$591$	−3.24905	−0.133648
$592$	153.785	6.32051
$593$	−25.3901	−1.04265	−0.521324	−	0.853359i	$-0.674562\pi$
$593$	−25.3901	−1.04265	−0.521324	+	0.853359i	$0.674562\pi$
$594$	51.1381	2.09822
$595$	2.22765	0.0913248
$596$	−40.8698	−1.67409
$597$	−7.56061	−0.309435
$598$	−4.39107	−0.179564
$599$	13.3638	0.546029	0.273015	−	0.962010i	$-0.411979\pi$
$599$	13.3638	0.546029	0.273015	+	0.962010i	$0.411979\pi$
$600$	−33.8473	−1.38181
$601$	0.294926	0.0120303	0.00601514	−	0.999982i	$-0.498085\pi$
$601$	0.294926	0.0120303	0.00601514	+	0.999982i	$0.498085\pi$
$602$	11.4503	0.466680
$603$	7.37404	0.300294
$604$	49.4784	2.01325
$605$	1.12513	0.0457429
$606$	−21.6585	−0.879816
$607$	4.66063	0.189169	0.0945845	−	0.995517i	$-0.469848\pi$
$607$	4.66063	0.189169	0.0945845	+	0.995517i	$0.469848\pi$
$608$	−63.5377	−2.57679
$609$	0.667500	0.0270485
$610$	0.509959	0.0206476
$611$	−5.60970	−0.226944
$612$	9.35424	0.378123
$613$	−9.37953	−0.378836	−0.189418	−	0.981897i	$-0.560660\pi$
$613$	−9.37953	−0.378836	−0.189418	+	0.981897i	$0.560660\pi$
$614$	−88.0226	−3.55230
$615$	4.20517	0.169569
$616$	−12.7159	−0.512339
$617$	46.2119	1.86042	0.930211	−	0.367025i	$-0.119624\pi$
$617$	46.2119	1.86042	0.930211	+	0.367025i	$0.119624\pi$
$618$	−14.6872	−0.590805
$619$	34.3986	1.38260	0.691298	−	0.722570i	$-0.257039\pi$
$619$	34.3986	1.38260	0.691298	+	0.722570i	$0.257039\pi$
$620$	40.4466	1.62438
$621$	−7.97289	−0.319941
$622$	−36.4621	−1.46200
$623$	5.08957	0.203909
$624$	23.1707	0.927571
$625$	−6.51592	−0.260637
$626$	−12.7887	−0.511140
$627$	19.4280	0.775880
$628$	26.3097	1.04987
$629$	−38.9230	−1.55196
$630$	−0.987174	−0.0393300
$631$	−34.4589	−1.37179	−0.685894	−	0.727701i	$-0.740589\pi$
$631$	−34.4589	−1.37179	−0.685894	+	0.727701i	$0.740589\pi$
$632$	42.2087	1.67897
$633$	12.8708	0.511569
$634$	−61.5404	−2.44408
$635$	−16.0270	−0.636012
$636$	−83.0922	−3.29482
$637$	7.74874	0.307016
$638$	9.20885	0.364582
$639$	4.77028	0.188709
$640$	−34.9472	−1.38141
$641$	−39.2925	−1.55196	−0.775979	−	0.630758i	$-0.782744\pi$
$641$	−39.2925	−1.55196	−0.775979	+	0.630758i	$0.782744\pi$
$642$	−47.5288	−1.87581
$643$	7.01591	0.276681	0.138340	−	0.990385i	$-0.455823\pi$
$643$	7.01591	0.276681	0.138340	+	0.990385i	$0.455823\pi$
$644$	3.20507	0.126298
$645$	−24.9032	−0.980563
$646$	32.0833	1.26230
$647$	15.9443	0.626833	0.313417	−	0.949616i	$-0.398526\pi$
$647$	15.9443	0.626833	0.313417	+	0.949616i	$0.398526\pi$
$648$	61.8015	2.42779
$649$	36.3413	1.42652
$650$	−7.56446	−0.296702
$651$	3.23935	0.126960
$652$	78.4393	3.07192
$653$	12.7896	0.500496	0.250248	−	0.968182i	$-0.419488\pi$
$653$	12.7896	0.500496	0.250248	+	0.968182i	$0.419488\pi$
$654$	41.7845	1.63390
$655$	−18.4481	−0.720827
$656$	−21.9452	−0.856815
$657$	−1.26185	−0.0492296
$658$	5.65639	0.220509
$659$	17.5837	0.684964	0.342482	−	0.939524i	$-0.388732\pi$
$659$	17.5837	0.684964	0.342482	+	0.939524i	$0.388732\pi$
$660$	44.7101	1.74034
$661$	39.5072	1.53665	0.768326	−	0.640059i	$-0.221090\pi$
$661$	39.5072	1.53665	0.768326	+	0.640059i	$0.221090\pi$
$662$	61.6956	2.39787
$663$	−5.86452	−0.227759
$664$	−45.5022	−1.76583
$665$	−2.45094	−0.0950433
$666$	17.2486	0.668368
$667$	−1.43574	−0.0555921
$668$	49.2111	1.90403
$669$	11.7895	0.455809
$670$	58.2041	2.24862
$671$	0.407880	0.0157460
$672$	−11.7107	−0.451752
$673$	10.4304	0.402064	0.201032	−	0.979585i	$-0.435571\pi$
$673$	10.4304	0.402064	0.201032	+	0.979585i	$0.435571\pi$
$674$	22.9658	0.884611
$675$	−13.7348	−0.528653
$676$	−61.3914	−2.36121
$677$	−31.6913	−1.21800	−0.608999	−	0.793171i	$-0.708429\pi$
$677$	−31.6913	−1.21800	−0.608999	+	0.793171i	$0.708429\pi$
$678$	58.7088	2.25470
$679$	5.58854	0.214469
$680$	45.6706	1.75139
$681$	−35.5699	−1.36304
$682$	44.6902	1.71128
$683$	3.52277	0.134795	0.0673976	−	0.997726i	$-0.478530\pi$
$683$	3.52277	0.134795	0.0673976	+	0.997726i	$0.478530\pi$
$684$	−10.2919	−0.393519
$685$	−0.792688	−0.0302871
$686$	−15.8342	−0.604551
$687$	24.3710	0.929811
$688$	129.960	4.95469
$689$	−11.4867	−0.437607
$690$	−9.62961	−0.366593
$691$	21.6113	0.822131	0.411065	−	0.911606i	$-0.365157\pi$
$691$	21.6113	0.822131	0.411065	+	0.911606i	$0.365157\pi$
$692$	−69.6558	−2.64792
$693$	−0.789571	−0.0299933
$694$	70.6193	2.68067
$695$	−2.93959	−0.111505
$696$	13.6849	0.518724
$697$	5.55434	0.210385
$698$	−34.2034	−1.29462
$699$	22.2519	0.841645
$700$	5.52134	0.208687
$701$	−2.45727	−0.0928099	−0.0464049	−	0.998923i	$-0.514776\pi$
$701$	−2.45727	−0.0928099	−0.0464049	+	0.998923i	$0.514776\pi$
$702$	16.9838	0.641010
$703$	42.8244	1.61515
$704$	−72.5619	−2.73478
$705$	−12.3020	−0.463322
$706$	28.4810	1.07190
$707$	2.18539	0.0821901
$708$	87.3084	3.28125
$709$	−2.09285	−0.0785988	−0.0392994	−	0.999227i	$-0.512513\pi$
$709$	−2.09285	−0.0785988	−0.0392994	+	0.999227i	$0.512513\pi$
$710$	37.6523	1.41307
$711$	2.62087	0.0982903
$712$	104.345	3.91049
$713$	−6.96760	−0.260939
$714$	5.91333	0.221301
$715$	6.18072	0.231146
$716$	−46.7828	−1.74836
$717$	−26.9685	−1.00716
$718$	45.9405	1.71449
$719$	−51.5354	−1.92194	−0.960972	−	0.276645i	$-0.910778\pi$
$719$	−51.5354	−1.92194	−0.960972	+	0.276645i	$0.910778\pi$
$720$	−11.2044	−0.417562
$721$	1.48197	0.0551914
$722$	15.8361	0.589359
$723$	−21.6901	−0.806665
$724$	70.3299	2.61379
$725$	−2.47334	−0.0918574
$726$	2.98667	0.110846
$727$	−14.1389	−0.524382	−0.262191	−	0.965016i	$-0.584445\pi$
$727$	−14.1389	−0.524382	−0.262191	+	0.965016i	$0.584445\pi$
$728$	−4.22315	−0.156520
$729$	29.9562	1.10949
$730$	−9.95994	−0.368634
$731$	−32.8930	−1.21659
$732$	0.979913	0.0362186
$733$	18.8923	0.697804	0.348902	−	0.937159i	$-0.386555\pi$
$733$	18.8923	0.697804	0.348902	+	0.937159i	$0.386555\pi$
$734$	−37.1683	−1.37191
$735$	16.9930	0.626795
$736$	25.1889	0.928475
$737$	46.5533	1.71481
$738$	−2.46138	−0.0906047
$739$	−5.33007	−0.196070	−0.0980349	−	0.995183i	$-0.531256\pi$
$739$	−5.33007	−0.196070	−0.0980349	+	0.995183i	$0.531256\pi$
$740$	98.5525	3.62286
$741$	6.45235	0.237033
$742$	11.5823	0.425199
$743$	7.79351	0.285916	0.142958	−	0.989729i	$-0.454339\pi$
$743$	7.79351	0.285916	0.142958	+	0.989729i	$0.454339\pi$
$744$	66.4122	2.43479
$745$	−12.3901	−0.453938
$746$	62.2244	2.27820
$747$	−2.82538	−0.103375
$748$	59.0546	2.15925
$749$	4.79576	0.175233
$750$	−50.1242	−1.83028
$751$	−7.14828	−0.260844	−0.130422	−	0.991459i	$-0.541633\pi$
$751$	−7.14828	−0.260844	−0.130422	+	0.991459i	$0.541633\pi$
$752$	64.1996	2.34112
$753$	−17.6694	−0.643908
$754$	3.05840	0.111380
$755$	14.9999	0.545902
$756$	−12.3966	−0.450858
$757$	−1.68386	−0.0612008	−0.0306004	−	0.999532i	$-0.509742\pi$
$757$	−1.68386	−0.0612008	−0.0306004	+	0.999532i	$0.509742\pi$
$758$	−63.0622	−2.29052
$759$	−7.70205	−0.279567
$760$	−50.2484	−1.82270
$761$	−22.6872	−0.822410	−0.411205	−	0.911543i	$-0.634892\pi$
$761$	−22.6872	−0.822410	−0.411205	+	0.911543i	$0.634892\pi$
$762$	−42.5439	−1.54120
$763$	−4.21615	−0.152635
$764$	−39.7560	−1.43832
$765$	2.83583	0.102530
$766$	83.4119	3.01379
$767$	12.0695	0.435805
$768$	−26.2722	−0.948018
$769$	0.428356	0.0154469	0.00772345	−	0.999970i	$-0.497542\pi$
$769$	0.428356	0.0154469	0.00772345	+	0.999970i	$0.497542\pi$
$770$	−6.23216	−0.224592
$771$	−7.70325	−0.277426
$772$	30.5955	1.10115
$773$	−45.9435	−1.65247	−0.826236	−	0.563324i	$-0.809522\pi$
$773$	−45.9435	−1.65247	−0.826236	+	0.563324i	$0.809522\pi$
$774$	14.5764	0.523938
$775$	−12.0030	−0.431161
$776$	114.575	4.11299
$777$	7.89303	0.283161
$778$	−81.4663	−2.92071
$779$	−6.11107	−0.218952
$780$	14.8489	0.531676
$781$	30.1154	1.07761
$782$	−12.7191	−0.454835
$783$	5.55315	0.198453
$784$	−88.6797	−3.16713
$785$	7.97604	0.284677
$786$	−48.9708	−1.74673
$787$	53.5527	1.90895	0.954474	−	0.298293i	$-0.0964172\pi$
$787$	53.5527	1.90895	0.954474	+	0.298293i	$0.0964172\pi$
$788$	10.8659	0.387082
$789$	1.63624	0.0582518
$790$	20.6868	0.736003
$791$	−5.92385	−0.210628
$792$	−16.1875	−0.575199
$793$	0.135463	0.00481044
$794$	31.4005	1.11436
$795$	−25.1902	−0.893405
$796$	25.2852	0.896212
$797$	−53.4222	−1.89231	−0.946157	−	0.323709i	$-0.895070\pi$
$797$	−53.4222	−1.89231	−0.946157	+	0.323709i	$0.895070\pi$
$798$	−6.50605	−0.230312
$799$	−16.2490	−0.574847
$800$	43.3926	1.53416
$801$	6.47909	0.228928
$802$	−34.4875	−1.21780
$803$	−7.96626	−0.281123
$804$	111.842	3.94437
$805$	0.971650	0.0342462
$806$	14.8423	0.522798
$807$	−3.40743	−0.119947
$808$	44.8042	1.57621
$809$	−6.34953	−0.223238	−0.111619	−	0.993751i	$-0.535604\pi$
$809$	−6.34953	−0.223238	−0.111619	+	0.993751i	$0.535604\pi$
$810$	30.2894	1.06426
$811$	−1.05357	−0.0369958	−0.0184979	−	0.999829i	$-0.505888\pi$
$811$	−1.05357	−0.0369958	−0.0184979	+	0.999829i	$0.505888\pi$
$812$	−2.23235	−0.0783400
$813$	33.7634	1.18414
$814$	108.892	3.81668
$815$	23.7796	0.832965
$816$	67.1159	2.34953
$817$	36.1900	1.26613
$818$	19.2872	0.674361
$819$	−0.262229	−0.00916301
$820$	−14.0635	−0.491119
$821$	−28.8316	−1.00623	−0.503115	−	0.864220i	$-0.667813\pi$
$821$	−28.8316	−1.00623	−0.503115	+	0.864220i	$0.667813\pi$
$822$	−2.10420	−0.0733925
$823$	16.1698	0.563644	0.281822	−	0.959467i	$-0.409061\pi$
$823$	16.1698	0.563644	0.281822	+	0.959467i	$0.409061\pi$
$824$	30.3829	1.05844
$825$	−13.2682	−0.461940
$826$	−12.1700	−0.423447
$827$	21.6307	0.752174	0.376087	−	0.926584i	$-0.377269\pi$
$827$	21.6307	0.752174	0.376087	+	0.926584i	$0.377269\pi$
$828$	4.08010	0.141793
$829$	−20.9541	−0.727766	−0.363883	−	0.931445i	$-0.618549\pi$
$829$	−20.9541	−0.727766	−0.363883	+	0.931445i	$0.618549\pi$
$830$	−22.3010	−0.774078
$831$	1.56780	0.0543865
$832$	−24.0989	−0.835480
$833$	22.4449	0.777669
$834$	−7.80318	−0.270202
$835$	14.9188	0.516287
$836$	−64.9739	−2.24717
$837$	26.9492	0.931501
$838$	−86.7742	−2.99756
$839$	50.2776	1.73578	0.867888	−	0.496760i	$-0.165477\pi$
$839$	50.2776	1.73578	0.867888	+	0.496760i	$0.165477\pi$
$840$	−9.26136	−0.319547
$841$	1.00000	0.0344828
$842$	−67.6135	−2.33012
$843$	6.33694	0.218256
$844$	−43.0444	−1.48165
$845$	−18.6114	−0.640252
$846$	7.20066	0.247564
$847$	−0.301362	−0.0103549
$848$	131.458	4.51429
$849$	−38.0176	−1.30476
$850$	−21.9111	−0.751544
$851$	−16.9773	−0.581974
$852$	72.3510	2.47870
$853$	30.0010	1.02722	0.513608	−	0.858025i	$-0.328309\pi$
$853$	30.0010	1.02722	0.513608	+	0.858025i	$0.328309\pi$
$854$	−0.136591	−0.00467404
$855$	−3.12008	−0.106704
$856$	98.3213	3.36055
$857$	16.4306	0.561259	0.280629	−	0.959816i	$-0.409457\pi$
$857$	16.4306	0.561259	0.280629	+	0.959816i	$0.409457\pi$
$858$	16.4068	0.560119
$859$	23.5462	0.803385	0.401693	−	0.915775i	$-0.368422\pi$
$859$	23.5462	0.803385	0.401693	+	0.915775i	$0.368422\pi$
$860$	83.2848	2.83999
$861$	−1.12634	−0.0383856
$862$	−39.4899	−1.34503
$863$	−54.3798	−1.85111	−0.925555	−	0.378614i	$-0.876401\pi$
$863$	−54.3798	−1.85111	−0.925555	+	0.378614i	$0.876401\pi$
$864$	−97.4254	−3.31448
$865$	−21.1169	−0.717995
$866$	−11.3148	−0.384493
$867$	9.66558	0.328260
$868$	−10.8335	−0.367713
$869$	16.5459	0.561281
$870$	6.70707	0.227391
$871$	15.4611	0.523878
$872$	−86.4382	−2.92717
$873$	7.11430	0.240782
$874$	13.9940	0.473355
$875$	5.05764	0.170979
$876$	−19.1386	−0.646632
$877$	54.9387	1.85515	0.927573	−	0.373641i	$-0.121891\pi$
$877$	54.9387	1.85515	0.927573	+	0.373641i	$0.121891\pi$
$878$	−71.4766	−2.41222
$879$	−8.99906	−0.303531
$880$	−70.7347	−2.38446
$881$	−13.7315	−0.462627	−0.231314	−	0.972879i	$-0.574302\pi$
$881$	−13.7315	−0.462627	−0.231314	+	0.972879i	$0.574302\pi$
$882$	−9.94636	−0.334911
$883$	7.73416	0.260275	0.130138	−	0.991496i	$-0.458458\pi$
$883$	7.73416	0.260275	0.130138	+	0.991496i	$0.458458\pi$
$884$	19.6129	0.659654
$885$	26.4684	0.889726
$886$	−72.7474	−2.44400
$887$	−10.1652	−0.341315	−0.170657	−	0.985330i	$-0.554589\pi$
$887$	−10.1652	−0.341315	−0.170657	+	0.985330i	$0.554589\pi$
$888$	161.821	5.43034
$889$	4.29278	0.143975
$890$	51.1402	1.71422
$891$	24.2263	0.811613
$892$	−39.4281	−1.32015
$893$	17.8777	0.598253
$894$	−32.8897	−1.10000
$895$	−14.1827	−0.474074
$896$	9.36048	0.312712
$897$	−2.55797	−0.0854081
$898$	100.140	3.34173
$899$	4.85296	0.161855
$900$	7.02875	0.234292
$901$	−33.2721	−1.10845
$902$	−15.5390	−0.517393
$903$	6.67024	0.221972
$904$	−121.449	−4.03933
$905$	21.3212	0.708741
$906$	39.8174	1.32284
$907$	−12.2761	−0.407622	−0.203811	−	0.979010i	$-0.565333\pi$
$907$	−12.2761	−0.407622	−0.203811	+	0.979010i	$0.565333\pi$
$908$	118.958	3.94775
$909$	2.78203	0.0922743
$910$	−2.06980	−0.0686131
$911$	10.6858	0.354035	0.177018	−	0.984208i	$-0.443355\pi$
$911$	10.6858	0.354035	0.177018	+	0.984208i	$0.443355\pi$
$912$	−73.8432	−2.44519
$913$	−17.8370	−0.590318
$914$	24.9722	0.826007
$915$	0.297070	0.00982084
$916$	−81.5048	−2.69300
$917$	4.94126	0.163175
$918$	49.1949	1.62367
$919$	22.4009	0.738939	0.369469	−	0.929243i	$-0.379539\pi$
$919$	22.4009	0.738939	0.369469	+	0.929243i	$0.379539\pi$
$920$	19.9205	0.656759
$921$	−51.2766	−1.68962
$922$	−23.7731	−0.782924
$923$	10.0018	0.329213
$924$	−11.9754	−0.393963
$925$	−29.2466	−0.961623
$926$	−5.93033	−0.194883
$927$	1.88657	0.0619630
$928$	−17.5442	−0.575916
$929$	12.7723	0.419047	0.209523	−	0.977804i	$-0.432809\pi$
$929$	12.7723	0.419047	0.209523	+	0.977804i	$0.432809\pi$
$930$	32.5491	1.06733
$931$	−24.6946	−0.809334
$932$	−74.4180	−2.43764
$933$	−21.2405	−0.695384
$934$	−9.75229	−0.319105
$935$	17.9030	0.585490
$936$	−5.37613	−0.175724
$937$	−20.7817	−0.678909	−0.339454	−	0.940623i	$-0.610242\pi$
$937$	−20.7817	−0.678909	−0.339454	+	0.940623i	$0.610242\pi$
$938$	−15.5898	−0.509024
$939$	−7.44992	−0.243119
$940$	41.1422	1.34191
$941$	11.1089	0.362139	0.181070	−	0.983470i	$-0.442044\pi$
$941$	11.1089	0.362139	0.181070	+	0.983470i	$0.442044\pi$
$942$	21.1725	0.689837
$943$	2.42267	0.0788931
$944$	−138.128	−4.49569
$945$	−3.75814	−0.122252
$946$	92.0228	2.99192
$947$	48.7674	1.58473	0.792364	−	0.610048i	$-0.208850\pi$
$947$	48.7674	1.58473	0.792364	+	0.610048i	$0.208850\pi$
$948$	39.7508	1.29105
$949$	−2.64572	−0.0858836
$950$	24.1073	0.782145
$951$	−35.8496	−1.16250
$952$	−12.2327	−0.396465
$953$	8.30337	0.268973	0.134486	−	0.990915i	$-0.457062\pi$
$953$	8.30337	0.268973	0.134486	+	0.990915i	$0.457062\pi$
$954$	14.7444	0.477368
$955$	−12.0524	−0.390007
$956$	90.1918	2.91701
$957$	5.36451	0.173410
$958$	7.70287	0.248868
$959$	0.212319	0.00685613
$960$	−52.8489	−1.70569
$961$	−7.44877	−0.240283
$962$	36.1649	1.16600
$963$	6.10507	0.196733
$964$	72.5392	2.33633
$965$	9.27532	0.298583
$966$	2.57926	0.0829863
$967$	27.7456	0.892238	0.446119	−	0.894974i	$-0.352806\pi$
$967$	27.7456	0.892238	0.446119	+	0.894974i	$0.352806\pi$
$968$	−6.17843	−0.198582
$969$	18.6898	0.600402
$970$	56.1539	1.80299
$971$	−35.5235	−1.14000	−0.570002	−	0.821644i	$-0.693057\pi$
$971$	−35.5235	−1.14000	−0.570002	+	0.821644i	$0.693057\pi$
$972$	−29.1472	−0.934896
$973$	0.787359	0.0252416
$974$	−17.5829	−0.563392
$975$	−4.40658	−0.141124
$976$	−1.55030	−0.0496237
$977$	−47.5312	−1.52066	−0.760329	−	0.649538i	$-0.774962\pi$
$977$	−47.5312	−1.52066	−0.760329	+	0.649538i	$0.774962\pi$
$978$	63.1234	2.01846
$979$	40.9034	1.30728
$980$	−56.8302	−1.81537
$981$	−5.36722	−0.171362
$982$	−88.3732	−2.82010
$983$	−43.6800	−1.39318	−0.696588	−	0.717472i	$-0.745299\pi$
$983$	−43.6800	−1.39318	−0.696588	+	0.717472i	$0.745299\pi$
$984$	−23.0919	−0.736143
$985$	3.29411	0.104959
$986$	8.85892	0.282125
$987$	3.29506	0.104883
$988$	−21.5788	−0.686514
$989$	−14.3472	−0.456214
$990$	−7.93363	−0.252147
$991$	−6.40798	−0.203556	−0.101778	−	0.994807i	$-0.532453\pi$
$991$	−6.40798	−0.203556	−0.101778	+	0.994807i	$0.532453\pi$
$992$	−85.1412	−2.70324
$993$	35.9401	1.14052
$994$	−10.0850	−0.319878
$995$	7.66547	0.243012
$996$	−42.8525	−1.35783
$997$	−16.5844	−0.525234	−0.262617	−	0.964900i	$-0.584586\pi$
$997$	−16.5844	−0.525234	−0.262617	+	0.964900i	$0.584586\pi$
$998$	18.5460	0.587062
$999$	65.6646	2.07754

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8033.2.a.d.1.5	✓	168

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8033.2.a.d.1.5	✓	168	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:	\( N \)	\(=\)	\( 8033 = 29 \cdot 277 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8033.a (trivial)

\(f(q)\)	\(=\)	\(q-2.69133 q^{2} -1.56780 q^{3} +5.24327 q^{4} +1.58955 q^{5} +4.21948 q^{6} -0.425755 q^{7} -8.72870 q^{8} -0.541992 q^{9} +O(q^{10})\)	\(q-2.69133 q^{2} -1.56780 q^{3} +5.24327 q^{4} +1.58955 q^{5} +4.21948 q^{6} -0.425755 q^{7} -8.72870 q^{8} -0.541992 q^{9} -4.27800 q^{10} -3.42167 q^{11} -8.22041 q^{12} -1.13639 q^{13} +1.14585 q^{14} -2.49210 q^{15} +13.0053 q^{16} -3.29165 q^{17} +1.45868 q^{18} +3.62159 q^{19} +8.33442 q^{20} +0.667500 q^{21} +9.20885 q^{22} -1.43574 q^{23} +13.6849 q^{24} -2.47334 q^{25} +3.05840 q^{26} +5.55315 q^{27} -2.23235 q^{28} +1.00000 q^{29} +6.70707 q^{30} +4.85296 q^{31} -17.5442 q^{32} +5.36451 q^{33} +8.85892 q^{34} -0.676758 q^{35} -2.84181 q^{36} +11.8248 q^{37} -9.74689 q^{38} +1.78164 q^{39} -13.8747 q^{40} -1.68740 q^{41} -1.79646 q^{42} +9.99287 q^{43} -17.9407 q^{44} -0.861523 q^{45} +3.86406 q^{46} +4.93642 q^{47} -20.3898 q^{48} -6.81873 q^{49} +6.65657 q^{50} +5.16066 q^{51} -5.95839 q^{52} +10.1080 q^{53} -14.9454 q^{54} -5.43891 q^{55} +3.71629 q^{56} -5.67793 q^{57} -2.69133 q^{58} -10.6209 q^{59} -13.0667 q^{60} -0.119205 q^{61} -13.0609 q^{62} +0.230756 q^{63} +21.2066 q^{64} -1.80635 q^{65} -14.4377 q^{66} -13.6054 q^{67} -17.2590 q^{68} +2.25096 q^{69} +1.82138 q^{70} -8.80138 q^{71} +4.73089 q^{72} +2.32818 q^{73} -31.8243 q^{74} +3.87771 q^{75} +18.9889 q^{76} +1.45679 q^{77} -4.79497 q^{78} -4.83562 q^{79} +20.6726 q^{80} -7.08027 q^{81} +4.54136 q^{82} +5.21294 q^{83} +3.49988 q^{84} -5.23223 q^{85} -26.8941 q^{86} -1.56780 q^{87} +29.8667 q^{88} -11.9542 q^{89} +2.31864 q^{90} +0.483824 q^{91} -7.52798 q^{92} -7.60849 q^{93} -13.2855 q^{94} +5.75668 q^{95} +27.5058 q^{96} -13.1262 q^{97} +18.3515 q^{98} +1.85452 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 168 q + 12 q^{2} + 35 q^{3} + 184 q^{4} + 12 q^{5} + 10 q^{6} + 74 q^{7} + 39 q^{8} + 183 q^{9}+O(q^{10}) \) 168 * q + 12 * q^2 + 35 * q^3 + 184 * q^4 + 12 * q^5 + 10 * q^6 + 74 * q^7 + 39 * q^8 + 183 * q^9	\( 168 q + 12 q^{2} + 35 q^{3} + 184 q^{4} + 12 q^{5} + 10 q^{6} + 74 q^{7} + 39 q^{8} + 183 q^{9} + 41 q^{10} + 29 q^{11} + 82 q^{12} + 62 q^{13} + 23 q^{14} + 31 q^{15} + 204 q^{16} + 56 q^{17} + 35 q^{18} + 83 q^{19} + 6 q^{20} + 30 q^{21} + 56 q^{22} + 54 q^{23} + 28 q^{24} + 210 q^{25} + 21 q^{26} + 140 q^{27} + 151 q^{28} + 168 q^{29} + 29 q^{30} + 72 q^{31} + 40 q^{32} + 32 q^{33} + 34 q^{34} + 18 q^{35} + 152 q^{36} + 42 q^{37} + 29 q^{38} + 70 q^{39} + 97 q^{40} + 41 q^{41} - 20 q^{42} + 119 q^{43} + 37 q^{44} + 22 q^{45} + 24 q^{46} + 119 q^{47} + 135 q^{48} + 216 q^{49} + 38 q^{50} + 18 q^{51} + 154 q^{52} - 7 q^{53} + 35 q^{54} + 224 q^{55} + 46 q^{56} + 12 q^{57} + 12 q^{58} + 25 q^{59} + 13 q^{60} + 82 q^{61} + 27 q^{62} + 211 q^{63} + 217 q^{64} + 8 q^{65} - 6 q^{66} + 76 q^{67} + 132 q^{68} + 36 q^{69} + 39 q^{70} + 32 q^{71} + 39 q^{72} + 89 q^{73} - q^{74} + 123 q^{75} + 180 q^{76} + 68 q^{77} - 54 q^{78} + 176 q^{79} - 11 q^{80} + 192 q^{81} + 51 q^{82} + 76 q^{83} + 86 q^{84} + 65 q^{85} - 72 q^{86} + 35 q^{87} + 178 q^{88} + 55 q^{89} + 2 q^{90} + 80 q^{91} + 44 q^{92} + 39 q^{93} + 89 q^{94} + 77 q^{95} - 68 q^{96} + 82 q^{97} + 80 q^{98} + 67 q^{99}+O(q^{100}) \) 168 * q + 12 * q^2 + 35 * q^3 + 184 * q^4 + 12 * q^5 + 10 * q^6 + 74 * q^7 + 39 * q^8 + 183 * q^9 + 41 * q^10 + 29 * q^11 + 82 * q^12 + 62 * q^13 + 23 * q^14 + 31 * q^15 + 204 * q^16 + 56 * q^17 + 35 * q^18 + 83 * q^19 + 6 * q^20 + 30 * q^21 + 56 * q^22 + 54 * q^23 + 28 * q^24 + 210 * q^25 + 21 * q^26 + 140 * q^27 + 151 * q^28 + 168 * q^29 + 29 * q^30 + 72 * q^31 + 40 * q^32 + 32 * q^33 + 34 * q^34 + 18 * q^35 + 152 * q^36 + 42 * q^37 + 29 * q^38 + 70 * q^39 + 97 * q^40 + 41 * q^41 - 20 * q^42 + 119 * q^43 + 37 * q^44 + 22 * q^45 + 24 * q^46 + 119 * q^47 + 135 * q^48 + 216 * q^49 + 38 * q^50 + 18 * q^51 + 154 * q^52 - 7 * q^53 + 35 * q^54 + 224 * q^55 + 46 * q^56 + 12 * q^57 + 12 * q^58 + 25 * q^59 + 13 * q^60 + 82 * q^61 + 27 * q^62 + 211 * q^63 + 217 * q^64 + 8 * q^65 - 6 * q^66 + 76 * q^67 + 132 * q^68 + 36 * q^69 + 39 * q^70 + 32 * q^71 + 39 * q^72 + 89 * q^73 - q^74 + 123 * q^75 + 180 * q^76 + 68 * q^77 - 54 * q^78 + 176 * q^79 - 11 * q^80 + 192 * q^81 + 51 * q^82 + 76 * q^83 + 86 * q^84 + 65 * q^85 - 72 * q^86 + 35 * q^87 + 178 * q^88 + 55 * q^89 + 2 * q^90 + 80 * q^91 + 44 * q^92 + 39 * q^93 + 89 * q^94 + 77 * q^95 - 68 * q^96 + 82 * q^97 + 80 * q^98 + 67 * q^99

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