LMFDB - Embedded newform 8033.2.a.e.1.14

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:	$169$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
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)

$f(q)$	$=$	$q-2.49641 q^{2} -2.16208 q^{3} +4.23205 q^{4} +4.42906 q^{5} +5.39744 q^{6} +1.14877 q^{7} -5.57210 q^{8} +1.67460 q^{9} +O(q^{10})$	\(q-2.49641 q^{2} -2.16208 q^{3} +4.23205 q^{4} +4.42906 q^{5} +5.39744 q^{6} +1.14877 q^{7} -5.57210 q^{8} +1.67460 q^{9} -11.0567 q^{10} -2.25337 q^{11} -9.15003 q^{12} +0.130045 q^{13} -2.86780 q^{14} -9.57600 q^{15} +5.44613 q^{16} -6.40012 q^{17} -4.18048 q^{18} +1.64878 q^{19} +18.7440 q^{20} -2.48374 q^{21} +5.62533 q^{22} -1.43314 q^{23} +12.0473 q^{24} +14.6166 q^{25} -0.324646 q^{26} +2.86563 q^{27} +4.86165 q^{28} -1.00000 q^{29} +23.9056 q^{30} +0.773762 q^{31} -2.45156 q^{32} +4.87197 q^{33} +15.9773 q^{34} +5.08798 q^{35} +7.08698 q^{36} +0.667456 q^{37} -4.11604 q^{38} -0.281168 q^{39} -24.6792 q^{40} -8.01689 q^{41} +6.20042 q^{42} -4.69794 q^{43} -9.53637 q^{44} +7.41690 q^{45} +3.57769 q^{46} -8.70653 q^{47} -11.7750 q^{48} -5.68033 q^{49} -36.4890 q^{50} +13.8376 q^{51} +0.550358 q^{52} -4.20358 q^{53} -7.15377 q^{54} -9.98032 q^{55} -6.40106 q^{56} -3.56481 q^{57} +2.49641 q^{58} -2.91600 q^{59} -40.5261 q^{60} -4.11884 q^{61} -1.93162 q^{62} +1.92373 q^{63} -4.77216 q^{64} +0.575979 q^{65} -12.1624 q^{66} +14.2569 q^{67} -27.0856 q^{68} +3.09856 q^{69} -12.7017 q^{70} -4.89442 q^{71} -9.33103 q^{72} +16.2009 q^{73} -1.66624 q^{74} -31.6023 q^{75} +6.97773 q^{76} -2.58861 q^{77} +0.701911 q^{78} +5.94739 q^{79} +24.1213 q^{80} -11.2195 q^{81} +20.0134 q^{82} +14.9027 q^{83} -10.5113 q^{84} -28.3465 q^{85} +11.7280 q^{86} +2.16208 q^{87} +12.5560 q^{88} -4.22004 q^{89} -18.5156 q^{90} +0.149392 q^{91} -6.06511 q^{92} -1.67294 q^{93} +21.7350 q^{94} +7.30257 q^{95} +5.30048 q^{96} -4.45567 q^{97} +14.1804 q^{98} -3.77349 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 169 q + 3 q^{2} + 8 q^{3} + 183 q^{4} + 13 q^{5} + 17 q^{6} + 76 q^{7} + 6 q^{8} + 181 q^{9}+O(q^{10}) $ 169 * q + 3 * q^2 + 8 * q^3 + 183 * q^4 + 13 * q^5 + 17 * q^6 + 76 * q^7 + 6 * q^8 + 181 * q^9	\( 169 q + 3 q^{2} + 8 q^{3} + 183 q^{4} + 13 q^{5} + 17 q^{6} + 76 q^{7} + 6 q^{8} + 181 q^{9} + 30 q^{10} + 2 q^{11} + 25 q^{12} + 63 q^{13} - 3 q^{14} + 26 q^{15} + 219 q^{16} + 14 q^{17} + 31 q^{18} + 51 q^{19} + 49 q^{20} + 16 q^{21} + 53 q^{22} + 50 q^{23} + 43 q^{24} + 214 q^{25} - 2 q^{26} + 23 q^{27} + 149 q^{28} - 169 q^{29} + 26 q^{30} + 65 q^{31} + 25 q^{32} + 57 q^{33} + 60 q^{34} + 60 q^{35} + 218 q^{36} + 52 q^{37} + 35 q^{38} + 49 q^{39} + 72 q^{40} + 3 q^{41} + 78 q^{42} + 132 q^{43} + 64 q^{45} + 32 q^{46} + 54 q^{47} + 76 q^{48} + 245 q^{49} - 6 q^{50} + 44 q^{51} + 193 q^{52} + 58 q^{53} + 54 q^{54} + 213 q^{55} + 12 q^{56} + 52 q^{57} - 3 q^{58} + 25 q^{59} + 32 q^{60} + 100 q^{61} + 78 q^{62} + 227 q^{63} + 292 q^{64} + 37 q^{65} + 59 q^{66} + 110 q^{67} + 24 q^{68} - 20 q^{69} + 47 q^{70} + 44 q^{71} + 71 q^{72} + 139 q^{73} + 35 q^{74} + 53 q^{75} + 92 q^{76} + 22 q^{77} + 83 q^{78} + 137 q^{79} + 90 q^{80} + 177 q^{81} + 91 q^{82} + 126 q^{83} + 36 q^{84} + 95 q^{85} + 21 q^{86} - 8 q^{87} + 75 q^{88} + 19 q^{89} + 130 q^{90} + 102 q^{91} + 68 q^{92} + 22 q^{93} + 82 q^{94} + 37 q^{95} + 107 q^{96} + 116 q^{97} - 13 q^{98} - 11 q^{99}+O(q^{100}) \) 169 * q + 3 * q^2 + 8 * q^3 + 183 * q^4 + 13 * q^5 + 17 * q^6 + 76 * q^7 + 6 * q^8 + 181 * q^9 + 30 * q^10 + 2 * q^11 + 25 * q^12 + 63 * q^13 - 3 * q^14 + 26 * q^15 + 219 * q^16 + 14 * q^17 + 31 * q^18 + 51 * q^19 + 49 * q^20 + 16 * q^21 + 53 * q^22 + 50 * q^23 + 43 * q^24 + 214 * q^25 - 2 * q^26 + 23 * q^27 + 149 * q^28 - 169 * q^29 + 26 * q^30 + 65 * q^31 + 25 * q^32 + 57 * q^33 + 60 * q^34 + 60 * q^35 + 218 * q^36 + 52 * q^37 + 35 * q^38 + 49 * q^39 + 72 * q^40 + 3 * q^41 + 78 * q^42 + 132 * q^43 + 64 * q^45 + 32 * q^46 + 54 * q^47 + 76 * q^48 + 245 * q^49 - 6 * q^50 + 44 * q^51 + 193 * q^52 + 58 * q^53 + 54 * q^54 + 213 * q^55 + 12 * q^56 + 52 * q^57 - 3 * q^58 + 25 * q^59 + 32 * q^60 + 100 * q^61 + 78 * q^62 + 227 * q^63 + 292 * q^64 + 37 * q^65 + 59 * q^66 + 110 * q^67 + 24 * q^68 - 20 * q^69 + 47 * q^70 + 44 * q^71 + 71 * q^72 + 139 * q^73 + 35 * q^74 + 53 * q^75 + 92 * q^76 + 22 * q^77 + 83 * q^78 + 137 * q^79 + 90 * q^80 + 177 * q^81 + 91 * q^82 + 126 * q^83 + 36 * q^84 + 95 * q^85 + 21 * q^86 - 8 * q^87 + 75 * q^88 + 19 * q^89 + 130 * q^90 + 102 * q^91 + 68 * q^92 + 22 * q^93 + 82 * q^94 + 37 * q^95 + 107 * q^96 + 116 * q^97 - 13 * q^98 - 11 * 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 $

$2$	−2.49641	−1.76523	−0.882613	−	0.470100i	$-0.844218\pi$
$2$	−2.49641	−1.76523	−0.882613	+	0.470100i	$0.844218\pi$
$3$	−2.16208	−1.24828	−0.624139	−	0.781313i	$-0.714550\pi$
$3$	−2.16208	−1.24828	−0.624139	+	0.781313i	$0.714550\pi$
$4$	4.23205	2.11602
$5$	4.42906	1.98074	0.990369	−	0.138456i	$-0.0442138\pi$
$5$	4.42906	1.98074	0.990369	+	0.138456i	$0.0442138\pi$
$6$	5.39744	2.20349
$7$	1.14877	0.434194	0.217097	−	0.976150i	$-0.430341\pi$
$7$	1.14877	0.434194	0.217097	+	0.976150i	$0.430341\pi$
$8$	−5.57210	−1.97003
$9$	1.67460	0.558200
$10$	−11.0567	−3.49645
$11$	−2.25337	−0.679417	−0.339708	−	0.940531i	$-0.610328\pi$
$11$	−2.25337	−0.679417	−0.339708	+	0.940531i	$0.610328\pi$
$12$	−9.15003	−2.64139
$13$	0.130045	0.0360681	0.0180340	−	0.999837i	$-0.494259\pi$
$13$	0.130045	0.0360681	0.0180340	+	0.999837i	$0.494259\pi$
$14$	−2.86780	−0.766452
$15$	−9.57600	−2.47251
$16$	5.44613	1.36153
$17$	−6.40012	−1.55226	−0.776129	−	0.630575i	$-0.782819\pi$
$17$	−6.40012	−1.55226	−0.776129	+	0.630575i	$0.782819\pi$
$18$	−4.18048	−0.985348
$19$	1.64878	0.378257	0.189129	−	0.981952i	$-0.439434\pi$
$19$	1.64878	0.378257	0.189129	+	0.981952i	$0.439434\pi$
$20$	18.7440	4.19129
$21$	−2.48374	−0.541996
$22$	5.62533	1.19932
$23$	−1.43314	−0.298830	−0.149415	−	0.988775i	$-0.547739\pi$
$23$	−1.43314	−0.298830	−0.149415	+	0.988775i	$0.547739\pi$
$24$	12.0473	2.45915
$25$	14.6166	2.92332
$26$	−0.324646	−0.0636683
$27$	2.86563	0.551490
$28$	4.86165	0.918766
$29$	−1.00000	−0.185695
$29$	−1.00000	−0.185695
$30$	23.9056	4.36454
$31$	0.773762	0.138972	0.0694859	−	0.997583i	$-0.477864\pi$
$31$	0.773762	0.138972	0.0694859	+	0.997583i	$0.477864\pi$
$32$	−2.45156	−0.433379
$33$	4.87197	0.848101
$34$	15.9773	2.74009
$35$	5.08798	0.860025
$36$	7.08698	1.18116
$37$	0.667456	0.109729	0.0548646	−	0.998494i	$-0.482527\pi$
$37$	0.667456	0.109729	0.0548646	+	0.998494i	$0.482527\pi$
$38$	−4.11604	−0.667709
$39$	−0.281168	−0.0450230
$40$	−24.6792	−3.90212
$41$	−8.01689	−1.25203	−0.626014	−	0.779812i	$-0.715315\pi$
$41$	−8.01689	−1.25203	−0.626014	+	0.779812i	$0.715315\pi$
$42$	6.20042	0.956745
$43$	−4.69794	−0.716429	−0.358215	−	0.933639i	$-0.616614\pi$
$43$	−4.69794	−0.716429	−0.358215	+	0.933639i	$0.616614\pi$
$44$	−9.53637	−1.43766
$45$	7.41690	1.10565
$46$	3.57769	0.527502
$47$	−8.70653	−1.26998	−0.634989	−	0.772521i	$-0.718995\pi$
$47$	−8.70653	−1.26998	−0.634989	+	0.772521i	$0.718995\pi$
$48$	−11.7750	−1.69957
$49$	−5.68033	−0.811475
$50$	−36.4890	−5.16032
$51$	13.8376	1.93765
$52$	0.550358	0.0763209
$53$	−4.20358	−0.577407	−0.288703	−	0.957419i	$-0.593224\pi$
$53$	−4.20358	−0.577407	−0.288703	+	0.957419i	$0.593224\pi$
$54$	−7.15377	−0.973505
$55$	−9.98032	−1.34575
$56$	−6.40106	−0.855378
$57$	−3.56481	−0.472170
$58$	2.49641	0.327794
$59$	−2.91600	−0.379631	−0.189816	−	0.981820i	$-0.560789\pi$
$59$	−2.91600	−0.379631	−0.189816	+	0.981820i	$0.560789\pi$
$60$	−40.5261	−5.23189
$61$	−4.11884	−0.527363	−0.263681	−	0.964610i	$-0.584937\pi$
$61$	−4.11884	−0.527363	−0.263681	+	0.964610i	$0.584937\pi$
$62$	−1.93162	−0.245317
$63$	1.92373	0.242367
$64$	−4.77216	−0.596521
$65$	0.575979	0.0714414
$66$	−12.1624	−1.49709
$67$	14.2569	1.74176	0.870879	−	0.491497i	$-0.163550\pi$
$67$	14.2569	1.74176	0.870879	+	0.491497i	$0.163550\pi$
$68$	−27.0856	−3.28461
$69$	3.09856	0.373023
$70$	−12.7017	−1.51814
$71$	−4.89442	−0.580861	−0.290431	−	0.956896i	$-0.593799\pi$
$71$	−4.89442	−0.580861	−0.290431	+	0.956896i	$0.593799\pi$
$72$	−9.33103	−1.09967
$73$	16.2009	1.89618	0.948089	−	0.318006i	$-0.103013\pi$
$73$	16.2009	1.89618	0.948089	+	0.318006i	$0.103013\pi$
$74$	−1.66624	−0.193697
$75$	−31.6023	−3.64912
$76$	6.97773	0.800401
$77$	−2.58861	−0.294999
$78$	0.701911	0.0794758
$79$	5.94739	0.669134	0.334567	−	0.942372i	$-0.391410\pi$
$79$	5.94739	0.669134	0.334567	+	0.942372i	$0.391410\pi$
$80$	24.1213	2.69684
$81$	−11.2195	−1.24661
$82$	20.0134	2.21011
$83$	14.9027	1.63578	0.817889	−	0.575376i	$-0.195144\pi$
$83$	14.9027	1.63578	0.817889	+	0.575376i	$0.195144\pi$
$84$	−10.5113	−1.14688
$85$	−28.3465	−3.07461
$86$	11.7280	1.26466
$87$	2.16208	0.231800
$88$	12.5560	1.33847
$89$	−4.22004	−0.447323	−0.223662	−	0.974667i	$-0.571801\pi$
$89$	−4.22004	−0.447323	−0.223662	+	0.974667i	$0.571801\pi$
$90$	−18.5156	−1.95172
$91$	0.149392	0.0156606
$92$	−6.06511	−0.632331
$93$	−1.67294	−0.173475
$94$	21.7350	2.24180
$95$	7.30257	0.749228
$96$	5.30048	0.540978
$97$	−4.45567	−0.452405	−0.226203	−	0.974080i	$-0.572631\pi$
$97$	−4.45567	−0.452405	−0.226203	+	0.974080i	$0.572631\pi$
$98$	14.1804	1.43244
$99$	−3.77349	−0.379250
$100$	61.8582	6.18582
$101$	−5.97881	−0.594914	−0.297457	−	0.954735i	$-0.596138\pi$
$101$	−5.97881	−0.594914	−0.297457	+	0.954735i	$0.596138\pi$
$102$	−34.5442	−3.42039
$103$	−1.98095	−0.195188	−0.0975942	−	0.995226i	$-0.531115\pi$
$103$	−1.98095	−0.195188	−0.0975942	+	0.995226i	$0.531115\pi$
$104$	−0.724625	−0.0710553
$105$	−11.0006	−1.07355
$106$	10.4939	1.01925
$107$	17.0564	1.64891	0.824455	−	0.565928i	$-0.191482\pi$
$107$	17.0564	1.64891	0.824455	+	0.565928i	$0.191482\pi$
$108$	12.1275	1.16697
$109$	−5.68429	−0.544456	−0.272228	−	0.962233i	$-0.587761\pi$
$109$	−5.68429	−0.544456	−0.272228	+	0.962233i	$0.587761\pi$
$110$	24.9149	2.37555
$111$	−1.44309	−0.136973
$112$	6.25636	0.591170
$113$	−8.21573	−0.772870	−0.386435	−	0.922317i	$-0.626294\pi$
$113$	−8.21573	−0.772870	−0.386435	+	0.922317i	$0.626294\pi$
$114$	8.89921	0.833487
$115$	−6.34746	−0.591903
$116$	−4.23205	−0.392936
$117$	0.217774	0.0201332
$118$	7.27953	0.670135
$119$	−7.35227	−0.673982
$120$	53.3584	4.87093
$121$	−5.92232	−0.538393
$122$	10.2823	0.930915
$123$	17.3332	1.56288
$124$	3.27460	0.294068
$125$	42.5925	3.80959
$126$	−4.80241	−0.427833
$127$	13.8147	1.22586	0.612929	−	0.790138i	$-0.289991\pi$
$127$	13.8147	1.22586	0.612929	+	0.790138i	$0.289991\pi$
$128$	16.8164	1.48637
$129$	10.1573	0.894303
$130$	−1.43788	−0.126110
$131$	21.1996	1.85222	0.926110	−	0.377255i	$-0.123132\pi$
$131$	21.1996	1.85222	0.926110	+	0.377255i	$0.123132\pi$
$132$	20.6184	1.79460
$133$	1.89408	0.164237
$134$	−35.5910	−3.07460
$135$	12.6920	1.09236
$136$	35.6621	3.05800
$137$	7.74276	0.661509	0.330754	−	0.943717i	$-0.392697\pi$
$137$	7.74276	0.661509	0.330754	+	0.943717i	$0.392697\pi$
$138$	−7.73527	−0.658470
$139$	−13.1167	−1.11255	−0.556274	−	0.830999i	$-0.687769\pi$
$139$	−13.1167	−1.11255	−0.556274	+	0.830999i	$0.687769\pi$
$140$	21.5326	1.81983
$141$	18.8242	1.58529
$142$	12.2185	1.02535
$143$	−0.293040	−0.0245052
$144$	9.12008	0.760007
$145$	−4.42906	−0.367814
$146$	−40.4442	−3.34718
$147$	12.2813	1.01295
$148$	2.82471	0.232189
$149$	13.7156	1.12362	0.561811	−	0.827265i	$-0.310105\pi$
$149$	13.7156	1.12362	0.561811	+	0.827265i	$0.310105\pi$
$150$	78.8922	6.44152
$151$	−4.92572	−0.400850	−0.200425	−	0.979709i	$-0.564232\pi$
$151$	−4.92572	−0.400850	−0.200425	+	0.979709i	$0.564232\pi$
$152$	−9.18719	−0.745179
$153$	−10.7176	−0.866469
$154$	6.46221	0.520740
$155$	3.42704	0.275267
$156$	−1.18992	−0.0952697
$157$	10.3850	0.828814	0.414407	−	0.910092i	$-0.363989\pi$
$157$	10.3850	0.828814	0.414407	+	0.910092i	$0.363989\pi$
$158$	−14.8471	−1.18117
$159$	9.08849	0.720764
$160$	−10.8581	−0.858410
$161$	−1.64635	−0.129750
$162$	28.0085	2.20055
$163$	21.2405	1.66369	0.831843	−	0.555011i	$-0.187286\pi$
$163$	21.2405	1.66369	0.831843	+	0.555011i	$0.187286\pi$
$164$	−33.9279	−2.64932
$165$	21.5783	1.67987
$166$	−37.2031	−2.88752
$167$	−7.10656	−0.549922	−0.274961	−	0.961455i	$-0.588665\pi$
$167$	−7.10656	−0.549922	−0.274961	+	0.961455i	$0.588665\pi$
$168$	13.8396	1.06775
$169$	−12.9831	−0.998699
$170$	70.7645	5.42739
$171$	2.76105	0.211143
$172$	−19.8819	−1.51598
$173$	−2.06196	−0.156768	−0.0783839	−	0.996923i	$-0.524976\pi$
$173$	−2.06196	−0.156768	−0.0783839	+	0.996923i	$0.524976\pi$
$174$	−5.39744	−0.409179
$175$	16.7911	1.26929
$176$	−12.2722	−0.925048
$177$	6.30464	0.473886
$178$	10.5349	0.789627
$179$	8.97387	0.670738	0.335369	−	0.942087i	$-0.391139\pi$
$179$	8.97387	0.670738	0.335369	+	0.942087i	$0.391139\pi$
$180$	31.3887	2.33957
$181$	7.87785	0.585556	0.292778	−	0.956180i	$-0.405420\pi$
$181$	7.87785	0.585556	0.292778	+	0.956180i	$0.405420\pi$
$182$	−0.372944	−0.0276444
$183$	8.90526	0.658296
$184$	7.98558	0.588705
$185$	2.95621	0.217345
$186$	4.17633	0.306223
$187$	14.4218	1.05463
$188$	−36.8465	−2.68730
$189$	3.29195	0.239454
$190$	−18.2302	−1.32256
$191$	−5.25425	−0.380184	−0.190092	−	0.981766i	$-0.560879\pi$
$191$	−5.25425	−0.380184	−0.190092	+	0.981766i	$0.560879\pi$
$192$	10.3178	0.744624
$193$	11.1165	0.800184	0.400092	−	0.916475i	$-0.368978\pi$
$193$	11.1165	0.800184	0.400092	+	0.916475i	$0.368978\pi$
$194$	11.1232	0.798597
$195$	−1.24531	−0.0891787
$196$	−24.0394	−1.71710
$197$	−3.70382	−0.263886	−0.131943	−	0.991257i	$-0.542122\pi$
$197$	−3.70382	−0.263886	−0.131943	+	0.991257i	$0.542122\pi$
$198$	9.42017	0.669462
$199$	−4.46051	−0.316197	−0.158099	−	0.987423i	$-0.550536\pi$
$199$	−4.46051	−0.316197	−0.158099	+	0.987423i	$0.550536\pi$
$200$	−81.4451	−5.75904
$201$	−30.8246	−2.17420
$202$	14.9255	1.05016
$203$	−1.14877	−0.0806279
$204$	58.5613	4.10011
$205$	−35.5073	−2.47994
$206$	4.94525	0.344552
$207$	−2.39993	−0.166807
$208$	0.708244	0.0491079
$209$	−3.71532	−0.256994
$210$	27.4620	1.89506
$211$	24.1213	1.66058	0.830289	−	0.557333i	$-0.188175\pi$
$211$	24.1213	1.66058	0.830289	+	0.557333i	$0.188175\pi$
$212$	−17.7898	−1.22181
$213$	10.5821	0.725076
$214$	−42.5798	−2.91070
$215$	−20.8075	−1.41906
$216$	−15.9676	−1.08645
$217$	0.888875	0.0603408
$218$	14.1903	0.961089
$219$	−35.0278	−2.36696
$220$	−42.2372	−2.84763
$221$	−0.832305	−0.0559869
$222$	3.60255	0.241787
$223$	−19.4238	−1.30072	−0.650358	−	0.759628i	$-0.725381\pi$
$223$	−19.4238	−1.30072	−0.650358	+	0.759628i	$0.725381\pi$
$224$	−2.81628	−0.188171
$225$	24.4769	1.63180
$226$	20.5098	1.36429
$227$	−15.3933	−1.02169	−0.510844	−	0.859673i	$-0.670667\pi$
$227$	−15.3933	−1.02169	−0.510844	+	0.859673i	$0.670667\pi$
$228$	−15.0864	−0.999123
$229$	24.3492	1.60904	0.804521	−	0.593924i	$-0.202422\pi$
$229$	24.3492	1.60904	0.804521	+	0.593924i	$0.202422\pi$
$230$	15.8458	1.04484
$231$	5.59678	0.368241
$232$	5.57210	0.365826
$233$	−16.9393	−1.10973	−0.554866	−	0.831940i	$-0.687230\pi$
$233$	−16.9393	−1.10973	−0.554866	+	0.831940i	$0.687230\pi$
$234$	−0.543651	−0.0355396
$235$	−38.5618	−2.51549
$236$	−12.3407	−0.803309
$237$	−12.8588	−0.835266
$238$	18.3543	1.18973
$239$	25.4900	1.64881	0.824406	−	0.565998i	$-0.191509\pi$
$239$	25.4900	1.64881	0.824406	+	0.565998i	$0.191509\pi$
$240$	−52.1521	−3.36641
$241$	5.40893	0.348420	0.174210	−	0.984709i	$-0.444263\pi$
$241$	5.40893	0.348420	0.174210	+	0.984709i	$0.444263\pi$
$242$	14.7845	0.950385
$243$	15.6606	1.00463
$244$	−17.4311	−1.11591
$245$	−25.1585	−1.60732
$246$	−43.2707	−2.75884
$247$	0.214417	0.0136430
$248$	−4.31148	−0.273779
$249$	−32.2208	−2.04191
$250$	−106.328	−6.72479
$251$	22.7799	1.43786	0.718928	−	0.695085i	$-0.244633\pi$
$251$	22.7799	1.43786	0.718928	+	0.695085i	$0.244633\pi$
$252$	8.14132	0.512855
$253$	3.22939	0.203030
$254$	−34.4871	−2.16392
$255$	61.2875	3.83797
$256$	−32.4362	−2.02726
$257$	28.0608	1.75039	0.875194	−	0.483773i	$-0.160734\pi$
$257$	28.0608	1.75039	0.875194	+	0.483773i	$0.160734\pi$
$258$	−25.3568	−1.57865
$259$	0.766754	0.0476438
$260$	2.43757	0.151172
$261$	−1.67460	−0.103655
$262$	−52.9229	−3.26959
$263$	11.3244	0.698290	0.349145	−	0.937069i	$-0.386472\pi$
$263$	11.3244	0.698290	0.349145	+	0.937069i	$0.386472\pi$
$264$	−27.1471	−1.67079
$265$	−18.6179	−1.14369
$266$	−4.72838	−0.289916
$267$	9.12407	0.558384
$268$	60.3359	3.68560
$269$	−7.83105	−0.477468	−0.238734	−	0.971085i	$-0.576732\pi$
$269$	−7.83105	−0.477468	−0.238734	+	0.971085i	$0.576732\pi$
$270$	−31.6845	−1.92826
$271$	12.3296	0.748973	0.374486	−	0.927232i	$-0.377819\pi$
$271$	12.3296	0.748973	0.374486	+	0.927232i	$0.377819\pi$
$272$	−34.8559	−2.11345
$273$	−0.322998	−0.0195487
$274$	−19.3291	−1.16771
$275$	−32.9366	−1.98615
$276$	13.1133	0.789325
$277$	1.00000	0.0600842
$277$	1.00000	0.0600842
$278$	32.7447	1.96390
$279$	1.29574	0.0775740
$280$	−28.3507	−1.69428
$281$	6.02151	0.359213	0.179607	−	0.983739i	$-0.442518\pi$
$281$	6.02151	0.359213	0.179607	+	0.983739i	$0.442518\pi$
$282$	−46.9929	−2.79839
$283$	30.9306	1.83864	0.919318	−	0.393515i	$-0.128741\pi$
$283$	30.9306	1.83864	0.919318	+	0.393515i	$0.128741\pi$
$284$	−20.7134	−1.22912
$285$	−15.7888	−0.935245
$286$	0.731547	0.0432573
$287$	−9.20957	−0.543624
$288$	−4.10538	−0.241912
$289$	23.9615	1.40950
$290$	11.0567	0.649274
$291$	9.63353	0.564728
$292$	68.5632	4.01236
$293$	−22.4026	−1.30878	−0.654388	−	0.756159i	$-0.727074\pi$
$293$	−22.4026	−1.30878	−0.654388	+	0.756159i	$0.727074\pi$
$294$	−30.6592	−1.78808
$295$	−12.9152	−0.751950
$296$	−3.71913	−0.216170
$297$	−6.45732	−0.374692
$298$	−34.2396	−1.98345
$299$	−0.186373	−0.0107782
$300$	−133.742	−7.72162
$301$	−5.39686	−0.311070
$302$	12.2966	0.707591
$303$	12.9267	0.742618
$304$	8.97950	0.515009
$305$	−18.2426	−1.04457
$306$	26.7556	1.52951
$307$	13.2631	0.756966	0.378483	−	0.925608i	$-0.376446\pi$
$307$	13.2631	0.756966	0.378483	+	0.925608i	$0.376446\pi$
$308$	−10.9551	−0.624225
$309$	4.28297	0.243650
$310$	−8.55529	−0.485908
$311$	−0.840150	−0.0476405	−0.0238203	−	0.999716i	$-0.507583\pi$
$311$	−0.840150	−0.0476405	−0.0238203	+	0.999716i	$0.507583\pi$
$312$	1.56670	0.0886968
$313$	5.92152	0.334704	0.167352	−	0.985897i	$-0.446478\pi$
$313$	5.92152	0.334704	0.167352	+	0.985897i	$0.446478\pi$
$314$	−25.9252	−1.46304
$315$	8.52032	0.480066
$316$	25.1697	1.41590
$317$	13.0441	0.732630	0.366315	−	0.930491i	$-0.380619\pi$
$317$	13.0441	0.732630	0.366315	+	0.930491i	$0.380619\pi$
$318$	−22.6886	−1.27231
$319$	2.25337	0.126165
$320$	−21.1362	−1.18155
$321$	−36.8774	−2.05830
$322$	4.10995	0.229039
$323$	−10.5524	−0.587152
$324$	−47.4815	−2.63786
$325$	1.90082	0.105438
$326$	−53.0250	−2.93678
$327$	12.2899	0.679633
$328$	44.6709	2.46654
$329$	−10.0018	−0.551417
$330$	−53.8681	−2.96534
$331$	15.0479	0.827105	0.413553	−	0.910480i	$-0.364288\pi$
$331$	15.0479	0.827105	0.413553	+	0.910480i	$0.364288\pi$
$332$	63.0687	3.46135
$333$	1.11772	0.0612507
$334$	17.7409	0.970737
$335$	63.1447	3.44997
$336$	−13.5268	−0.737945
$337$	−21.8335	−1.18934	−0.594672	−	0.803968i	$-0.702718\pi$
$337$	−21.8335	−1.18934	−0.594672	+	0.803968i	$0.702718\pi$
$338$	32.4111	1.76293
$339$	17.7631	0.964758
$340$	−119.964	−6.50596
$341$	−1.74357	−0.0944197
$342$	−6.89271	−0.372715
$343$	−14.5668	−0.786533
$344$	26.1774	1.41139
$345$	13.7237	0.738860
$346$	5.14749	0.276731
$347$	26.0628	1.39912	0.699561	−	0.714573i	$-0.253379\pi$
$347$	26.0628	1.39912	0.699561	+	0.714573i	$0.253379\pi$
$348$	9.15003	0.490493
$349$	23.5541	1.26082	0.630412	−	0.776261i	$-0.282886\pi$
$349$	23.5541	1.26082	0.630412	+	0.776261i	$0.282886\pi$
$350$	−41.9175	−2.24058
$351$	0.372661	0.0198912
$352$	5.52428	0.294445
$353$	24.6119	1.30996	0.654979	−	0.755647i	$-0.272677\pi$
$353$	24.6119	1.30996	0.654979	+	0.755647i	$0.272677\pi$
$354$	−15.7389	−0.836516
$355$	−21.6777	−1.15053
$356$	−17.8594	−0.946547
$357$	15.8962	0.841317
$358$	−22.4024	−1.18401
$359$	11.8923	0.627651	0.313826	−	0.949481i	$-0.398389\pi$
$359$	11.8923	0.627651	0.313826	+	0.949481i	$0.398389\pi$
$360$	−41.3277	−2.17816
$361$	−16.2815	−0.856922
$362$	−19.6663	−1.03364
$363$	12.8045	0.672064
$364$	0.632235	0.0331381
$365$	71.7550	3.75583
$366$	−22.2312	−1.16204
$367$	15.7024	0.819658	0.409829	−	0.912162i	$-0.365588\pi$
$367$	15.7024	0.819658	0.409829	+	0.912162i	$0.365588\pi$
$368$	−7.80506	−0.406867
$369$	−13.4251	−0.698882
$370$	−7.37989	−0.383662
$371$	−4.82895	−0.250707
$372$	−7.07995	−0.367078
$373$	−23.9497	−1.24007	−0.620033	−	0.784576i	$-0.712881\pi$
$373$	−23.9497	−1.24007	−0.620033	+	0.784576i	$0.712881\pi$
$374$	−36.0028	−1.86166
$375$	−92.0885	−4.75543
$376$	48.5137	2.50190
$377$	−0.130045	−0.00669767
$378$	−8.21804	−0.422690
$379$	−33.8594	−1.73924	−0.869619	−	0.493723i	$-0.835636\pi$
$379$	−33.8594	−1.73924	−0.869619	+	0.493723i	$0.835636\pi$
$380$	30.9048	1.58538
$381$	−29.8685	−1.53021
$382$	13.1167	0.671111
$383$	28.5554	1.45911	0.729557	−	0.683920i	$-0.239726\pi$
$383$	28.5554	1.45911	0.729557	+	0.683920i	$0.239726\pi$
$384$	−36.3584	−1.85541
$385$	−11.4651	−0.584315
$386$	−27.7513	−1.41251
$387$	−7.86717	−0.399911
$388$	−18.8566	−0.957300
$389$	−12.1482	−0.615937	−0.307969	−	0.951396i	$-0.599649\pi$
$389$	−12.1482	−0.615937	−0.307969	+	0.951396i	$0.599649\pi$
$390$	3.10881	0.157421
$391$	9.17225	0.463861
$392$	31.6513	1.59863
$393$	−45.8353	−2.31209
$394$	9.24624	0.465819
$395$	26.3414	1.32538
$396$	−15.9696	−0.802502
$397$	−10.1036	−0.507087	−0.253543	−	0.967324i	$-0.581596\pi$
$397$	−10.1036	−0.507087	−0.253543	+	0.967324i	$0.581596\pi$
$398$	11.1352	0.558159
$399$	−4.09515	−0.205014
$400$	79.6039	3.98020
$401$	−34.3449	−1.71510	−0.857552	−	0.514397i	$-0.828016\pi$
$401$	−34.3449	−1.71510	−0.857552	+	0.514397i	$0.828016\pi$
$402$	76.9507	3.83795
$403$	0.100624	0.00501244
$404$	−25.3026	−1.25885
$405$	−49.6919	−2.46921
$406$	2.86780	0.142326
$407$	−1.50403	−0.0745518
$408$	−77.1044	−3.81724
$409$	32.8751	1.62557	0.812784	−	0.582565i	$-0.197951\pi$
$409$	32.8751	1.62557	0.812784	+	0.582565i	$0.197951\pi$
$410$	88.6407	4.37765
$411$	−16.7405	−0.825747
$412$	−8.38346	−0.413024
$413$	−3.34982	−0.164834
$414$	5.99120	0.294452
$415$	66.0048	3.24005
$416$	−0.318814	−0.0156311
$417$	28.3595	1.38877
$418$	9.27495	0.453653
$419$	−4.10439	−0.200513	−0.100256	−	0.994962i	$-0.531966\pi$
$419$	−4.10439	−0.200513	−0.100256	+	0.994962i	$0.531966\pi$
$420$	−46.5552	−2.27166
$421$	10.2104	0.497624	0.248812	−	0.968552i	$-0.419960\pi$
$421$	10.2104	0.497624	0.248812	+	0.968552i	$0.419960\pi$
$422$	−60.2166	−2.93130
$423$	−14.5799	−0.708901
$424$	23.4228	1.13751
$425$	−93.5480	−4.53774
$426$	−26.4173	−1.27992
$427$	−4.73160	−0.228978
$428$	72.1837	3.48913
$429$	0.633577	0.0305894
$430$	51.9439	2.50496
$431$	−7.35980	−0.354509	−0.177255	−	0.984165i	$-0.556722\pi$
$431$	−7.35980	−0.354509	−0.177255	+	0.984165i	$0.556722\pi$
$432$	15.6066	0.750872
$433$	−3.63100	−0.174495	−0.0872474	−	0.996187i	$-0.527807\pi$
$433$	−3.63100	−0.174495	−0.0872474	+	0.996187i	$0.527807\pi$
$434$	−2.21899	−0.106515
$435$	9.57600	0.459134
$436$	−24.0562	−1.15208
$437$	−2.36293	−0.113034
$438$	87.4436	4.17822
$439$	−17.3277	−0.827005	−0.413502	−	0.910503i	$-0.635695\pi$
$439$	−17.3277	−0.827005	−0.413502	+	0.910503i	$0.635695\pi$
$440$	55.6113	2.65117
$441$	−9.51227	−0.452965
$442$	2.07777	0.0988296
$443$	−16.9055	−0.803206	−0.401603	−	0.915814i	$-0.631547\pi$
$443$	−16.9055	−0.803206	−0.401603	+	0.915814i	$0.631547\pi$
$444$	−6.10725	−0.289837
$445$	−18.6908	−0.886030
$446$	48.4898	2.29606
$447$	−29.6542	−1.40259
$448$	−5.48212	−0.259006
$449$	28.7225	1.35550	0.677749	−	0.735294i	$-0.262956\pi$
$449$	28.7225	1.35550	0.677749	+	0.735294i	$0.262956\pi$
$450$	−61.1044	−2.88049
$451$	18.0650	0.850649
$452$	−34.7693	−1.63541
$453$	10.6498	0.500372
$454$	38.4279	1.80351
$455$	0.661667	0.0310194
$456$	19.8635	0.930192
$457$	11.3333	0.530148	0.265074	−	0.964228i	$-0.414604\pi$
$457$	11.3333	0.530148	0.265074	+	0.964228i	$0.414604\pi$
$458$	−60.7856	−2.84032
$459$	−18.3404	−0.856055
$460$	−26.8627	−1.25248
$461$	33.8418	1.57617	0.788085	−	0.615566i	$-0.211073\pi$
$461$	33.8418	1.57617	0.788085	+	0.615566i	$0.211073\pi$
$462$	−13.9718	−0.650029
$463$	29.7274	1.38155	0.690775	−	0.723070i	$-0.257270\pi$
$463$	29.7274	1.38155	0.690775	+	0.723070i	$0.257270\pi$
$464$	−5.44613	−0.252830
$465$	−7.40954	−0.343609
$466$	42.2874	1.95893
$467$	−23.4072	−1.08316	−0.541578	−	0.840651i	$-0.682173\pi$
$467$	−23.4072	−1.08316	−0.541578	+	0.840651i	$0.682173\pi$
$468$	0.921628	0.0426023
$469$	16.3779	0.756262
$470$	96.2659	4.44041
$471$	−22.4533	−1.03459
$472$	16.2483	0.747887
$473$	10.5862	0.486754
$474$	32.1007	1.47443
$475$	24.0996	1.10577
$476$	−31.1152	−1.42616
$477$	−7.03932	−0.322308
$478$	−63.6335	−2.91053
$479$	−4.30008	−0.196476	−0.0982378	−	0.995163i	$-0.531321\pi$
$479$	−4.30008	−0.196476	−0.0982378	+	0.995163i	$0.531321\pi$
$480$	23.4762	1.07154
$481$	0.0867995	0.00395772
$482$	−13.5029	−0.615040
$483$	3.55954	0.161964
$484$	−25.0636	−1.13925
$485$	−19.7345	−0.896096
$486$	−39.0953	−1.77340
$487$	11.9807	0.542896	0.271448	−	0.962453i	$-0.412497\pi$
$487$	11.9807	0.542896	0.271448	+	0.962453i	$0.412497\pi$
$488$	22.9506	1.03892
$489$	−45.9237	−2.07674
$490$	62.8059	2.83728
$491$	19.9660	0.901053	0.450527	−	0.892763i	$-0.351236\pi$
$491$	19.9660	0.901053	0.450527	+	0.892763i	$0.351236\pi$
$492$	73.3548	3.30709
$493$	6.40012	0.288247
$494$	−0.535271	−0.0240830
$495$	−16.7130	−0.751195
$496$	4.21401	0.189215
$497$	−5.62257	−0.252207
$498$	80.4361	3.60443
$499$	−25.9465	−1.16153	−0.580764	−	0.814072i	$-0.697246\pi$
$499$	−25.9465	−1.16153	−0.580764	+	0.814072i	$0.697246\pi$
$500$	180.254	8.06119
$501$	15.3650	0.686456
$502$	−56.8679	−2.53814
$503$	−6.58078	−0.293423	−0.146711	−	0.989179i	$-0.546869\pi$
$503$	−6.58078	−0.293423	−0.146711	+	0.989179i	$0.546869\pi$
$504$	−10.7192	−0.477472
$505$	−26.4805	−1.17837
$506$	−8.06187	−0.358394
$507$	28.0705	1.24665
$508$	58.4645	2.59394
$509$	−40.7347	−1.80553	−0.902767	−	0.430130i	$-0.858468\pi$
$509$	−40.7347	−1.80553	−0.902767	+	0.430130i	$0.858468\pi$
$510$	−152.999	−6.77489
$511$	18.6112	0.823310
$512$	47.3412	2.09221
$513$	4.72480	0.208605
$514$	−70.0513	−3.08983
$515$	−8.77374	−0.386617
$516$	42.9863	1.89237
$517$	19.6190	0.862844
$518$	−1.91413	−0.0841020
$519$	4.45812	0.195690
$520$	−3.20941	−0.140742
$521$	−1.95137	−0.0854910	−0.0427455	−	0.999086i	$-0.513610\pi$
$521$	−1.95137	−0.0854910	−0.0427455	+	0.999086i	$0.513610\pi$
$522$	4.18048	0.182975
$523$	−26.3835	−1.15367	−0.576835	−	0.816861i	$-0.695712\pi$
$523$	−26.3835	−1.15367	−0.576835	+	0.816861i	$0.695712\pi$
$524$	89.7178	3.91934
$525$	−36.3038	−1.58443
$526$	−28.2702	−1.23264
$527$	−4.95217	−0.215720
$528$	26.5334	1.15472
$529$	−20.9461	−0.910701
$530$	46.4780	2.01887
$531$	−4.88314	−0.211910
$532$	8.01582	0.347530
$533$	−1.04256	−0.0451582
$534$	−22.7774	−0.985674
$535$	75.5441	3.26606
$536$	−79.4409	−3.43132
$537$	−19.4022	−0.837268
$538$	19.5495	0.842839
$539$	12.7999	0.551330
$540$	53.7133	2.31145
$541$	16.9922	0.730552	0.365276	−	0.930899i	$-0.380975\pi$
$541$	16.9922	0.730552	0.365276	+	0.930899i	$0.380975\pi$
$542$	−30.7798	−1.32211
$543$	−17.0326	−0.730937
$544$	15.6903	0.672716
$545$	−25.1761	−1.07843
$546$	0.806335	0.0345079
$547$	10.9842	0.469651	0.234825	−	0.972038i	$-0.424548\pi$
$547$	10.9842	0.469651	0.234825	+	0.972038i	$0.424548\pi$
$548$	32.7677	1.39977
$549$	−6.89740	−0.294374
$550$	82.2232	3.50601
$551$	−1.64878	−0.0702406
$552$	−17.2655	−0.734868
$553$	6.83219	0.290534
$554$	−2.49641	−0.106062
$555$	−6.39156	−0.271307
$556$	−55.5107	−2.35418
$557$	0.714725	0.0302839	0.0151419	−	0.999885i	$-0.495180\pi$
$557$	0.714725	0.0302839	0.0151419	+	0.999885i	$0.495180\pi$
$558$	−3.23470	−0.136936
$559$	−0.610945	−0.0258402
$560$	27.7098	1.17095
$561$	−31.1812	−1.31647
$562$	−15.0321	−0.634093
$563$	−18.2209	−0.767918	−0.383959	−	0.923350i	$-0.625440\pi$
$563$	−18.2209	−0.767918	−0.383959	+	0.923350i	$0.625440\pi$
$564$	79.6650	3.35450
$565$	−36.3880	−1.53085
$566$	−77.2155	−3.24561
$567$	−12.8886	−0.541272
$568$	27.2722	1.14432
$569$	−5.51858	−0.231351	−0.115675	−	0.993287i	$-0.536903\pi$
$569$	−5.51858	−0.231351	−0.115675	+	0.993287i	$0.536903\pi$
$570$	39.4152	1.65092
$571$	4.82895	0.202085	0.101043	−	0.994882i	$-0.467782\pi$
$571$	4.82895	0.202085	0.101043	+	0.994882i	$0.467782\pi$
$572$	−1.24016	−0.0518537
$573$	11.3601	0.474576
$574$	22.9908	0.959619
$575$	−20.9476	−0.873575
$576$	−7.99146	−0.332977
$577$	−0.113298	−0.00471665	−0.00235832	−	0.999997i	$-0.500751\pi$
$577$	−0.113298	−0.00471665	−0.00235832	+	0.999997i	$0.500751\pi$
$578$	−59.8178	−2.48809
$579$	−24.0348	−0.998853
$580$	−18.7440	−0.778303
$581$	17.1197	0.710246
$582$	−24.0492	−0.996872
$583$	9.47223	0.392300
$584$	−90.2733	−3.73554
$585$	0.964533	0.0398785
$586$	55.9261	2.31029
$587$	−6.57801	−0.271504	−0.135752	−	0.990743i	$-0.543345\pi$
$587$	−6.57801	−0.271504	−0.135752	+	0.990743i	$0.543345\pi$
$588$	51.9752	2.14342
$589$	1.27577	0.0525670
$590$	32.2415	1.32736
$591$	8.00796	0.329403
$592$	3.63505	0.149400
$593$	19.1109	0.784791	0.392396	−	0.919797i	$-0.371646\pi$
$593$	19.1109	0.784791	0.392396	+	0.919797i	$0.371646\pi$
$594$	16.1201	0.661415
$595$	−32.5637	−1.33498
$596$	58.0449	2.37761
$597$	9.64398	0.394702
$598$	0.465262	0.0190260
$599$	−43.3767	−1.77232	−0.886161	−	0.463377i	$-0.846638\pi$
$599$	−43.3767	−1.77232	−0.886161	+	0.463377i	$0.846638\pi$
$600$	176.091	7.18889
$601$	−6.28127	−0.256218	−0.128109	−	0.991760i	$-0.540891\pi$
$601$	−6.28127	−0.256218	−0.128109	+	0.991760i	$0.540891\pi$
$602$	13.4728	0.549108
$603$	23.8746	0.972249
$604$	−20.8459	−0.848208
$605$	−26.2303	−1.06641
$606$	−32.2702	−1.31089
$607$	−15.3487	−0.622983	−0.311491	−	0.950249i	$-0.600828\pi$
$607$	−15.3487	−0.622983	−0.311491	+	0.950249i	$0.600828\pi$
$608$	−4.04210	−0.163929
$609$	2.48374	0.100646
$610$	45.5409	1.84390
$611$	−1.13224	−0.0458056
$612$	−45.3575	−1.83347
$613$	18.0253	0.728037	0.364018	−	0.931392i	$-0.381405\pi$
$613$	18.0253	0.728037	0.364018	+	0.931392i	$0.381405\pi$
$614$	−33.1101	−1.33622
$615$	76.7697	3.09566
$616$	14.4240	0.581158
$617$	−36.0012	−1.44935	−0.724677	−	0.689089i	$-0.758011\pi$
$617$	−36.0012	−1.44935	−0.724677	+	0.689089i	$0.758011\pi$
$618$	−10.6920	−0.430097
$619$	−2.48969	−0.100069	−0.0500346	−	0.998747i	$-0.515933\pi$
$619$	−2.48969	−0.100069	−0.0500346	+	0.998747i	$0.515933\pi$
$620$	14.5034	0.582471
$621$	−4.10684	−0.164802
$622$	2.09736	0.0840963
$623$	−4.84786	−0.194225
$624$	−1.53128	−0.0613003
$625$	115.562	4.62248
$626$	−14.7825	−0.590829
$627$	8.03283	0.320800
$628$	43.9499	1.75379
$629$	−4.27180	−0.170328
$630$	−21.2702	−0.847425
$631$	−30.7153	−1.22276	−0.611378	−	0.791339i	$-0.709385\pi$
$631$	−30.7153	−1.22276	−0.611378	+	0.791339i	$0.709385\pi$
$632$	−33.1395	−1.31822
$633$	−52.1522	−2.07286
$634$	−32.5634	−1.29326
$635$	61.1862	2.42810
$636$	38.4629	1.52515
$637$	−0.738699	−0.0292683
$638$	−5.62533	−0.222709
$639$	−8.19619	−0.324236
$640$	74.4809	2.94411
$641$	−19.6771	−0.777198	−0.388599	−	0.921407i	$-0.627041\pi$
$641$	−19.6771	−0.777198	−0.388599	+	0.921407i	$0.627041\pi$
$642$	92.0611	3.63336
$643$	36.1290	1.42479	0.712395	−	0.701779i	$-0.247611\pi$
$643$	36.1290	1.42479	0.712395	+	0.701779i	$0.247611\pi$
$644$	−6.96742	−0.274555
$645$	44.9875	1.77138
$646$	26.3431	1.03646
$647$	17.5917	0.691601	0.345800	−	0.938308i	$-0.387607\pi$
$647$	17.5917	0.691601	0.345800	+	0.938308i	$0.387607\pi$
$648$	62.5163	2.45587
$649$	6.57084	0.257928
$650$	−4.74522	−0.186123
$651$	−1.92182	−0.0753221
$652$	89.8909	3.52040
$653$	41.1696	1.61109	0.805546	−	0.592533i	$-0.201872\pi$
$653$	41.1696	1.61109	0.805546	+	0.592533i	$0.201872\pi$
$654$	−30.6806	−1.19971
$655$	93.8944	3.66876
$656$	−43.6611	−1.70468
$657$	27.1301	1.05845
$658$	24.9686	0.973377
$659$	−12.3627	−0.481584	−0.240792	−	0.970577i	$-0.577407\pi$
$659$	−12.3627	−0.481584	−0.240792	+	0.970577i	$0.577407\pi$
$660$	91.3203	3.55464
$661$	12.6785	0.493137	0.246568	−	0.969125i	$-0.420697\pi$
$661$	12.6785	0.493137	0.246568	+	0.969125i	$0.420697\pi$
$662$	−37.5656	−1.46003
$663$	1.79951	0.0698873
$664$	−83.0391	−3.22254
$665$	8.38898	0.325311
$666$	−2.79029	−0.108121
$667$	1.43314	0.0554913
$668$	−30.0753	−1.16365
$669$	41.9959	1.62365
$670$	−157.635	−6.08997
$671$	9.28126	0.358299
$672$	6.08904	0.234890
$673$	−30.9241	−1.19204	−0.596018	−	0.802971i	$-0.703251\pi$
$673$	−30.9241	−1.19204	−0.596018	+	0.802971i	$0.703251\pi$
$674$	54.5052	2.09946
$675$	41.8857	1.61218
$676$	−54.9450	−2.11327
$677$	11.1548	0.428712	0.214356	−	0.976756i	$-0.431235\pi$
$677$	11.1548	0.428712	0.214356	+	0.976756i	$0.431235\pi$
$678$	−44.3439	−1.70302
$679$	−5.11855	−0.196432
$680$	157.950	6.05710
$681$	33.2815	1.27535
$682$	4.35267	0.166672
$683$	−7.19594	−0.275345	−0.137672	−	0.990478i	$-0.543962\pi$
$683$	−7.19594	−0.275345	−0.137672	+	0.990478i	$0.543962\pi$
$684$	11.6849	0.446783
$685$	34.2932	1.31027
$686$	36.3646	1.38841
$687$	−52.6450	−2.00853
$688$	−25.5856	−0.975442
$689$	−0.546656	−0.0208259
$690$	−34.2600	−1.30426
$691$	3.90719	0.148636	0.0743182	−	0.997235i	$-0.476322\pi$
$691$	3.90719	0.148636	0.0743182	+	0.997235i	$0.476322\pi$
$692$	−8.72630	−0.331724
$693$	−4.33488	−0.164668
$694$	−65.0633	−2.46977
$695$	−58.0949	−2.20366
$696$	−12.0473	−0.456653
$697$	51.3091	1.94347
$698$	−58.8007	−2.22564
$699$	36.6242	1.38525
$700$	71.0608	2.68585
$701$	−16.9444	−0.639982	−0.319991	−	0.947421i	$-0.603680\pi$
$701$	−16.9444	−0.639982	−0.319991	+	0.947421i	$0.603680\pi$
$702$	−0.930314	−0.0351124
$703$	1.10049	0.0415058
$704$	10.7535	0.405286
$705$	83.3737	3.14004
$706$	−61.4413	−2.31237
$707$	−6.86828	−0.258308
$708$	26.6815	1.00275
$709$	20.3755	0.765220	0.382610	−	0.923910i	$-0.375025\pi$
$709$	20.3755	0.765220	0.382610	+	0.923910i	$0.375025\pi$
$710$	54.1164	2.03095
$711$	9.95950	0.373510
$712$	23.5145	0.881243
$713$	−1.10891	−0.0415289
$714$	−39.6834	−1.48511
$715$	−1.29789	−0.0485384
$716$	37.9778	1.41930
$717$	−55.1115	−2.05818
$718$	−29.6880	−1.10795
$719$	−24.2083	−0.902819	−0.451409	−	0.892317i	$-0.649079\pi$
$719$	−24.2083	−0.902819	−0.451409	+	0.892317i	$0.649079\pi$
$720$	40.3934	1.50537
$721$	−2.27565	−0.0847498
$722$	40.6453	1.51266
$723$	−11.6946	−0.434925
$724$	33.3394	1.23905
$725$	−14.6166	−0.542847
$726$	−31.9654	−1.18635
$727$	22.6916	0.841585	0.420793	−	0.907157i	$-0.361752\pi$
$727$	22.6916	0.841585	0.420793	+	0.907157i	$0.361752\pi$
$728$	−0.832428	−0.0308518
$729$	−0.201025	−0.00744539
$730$	−179.130	−6.62989
$731$	30.0674	1.11208
$732$	37.6875	1.39297
$733$	22.9366	0.847182	0.423591	−	0.905853i	$-0.360769\pi$
$733$	22.9366	0.847182	0.423591	+	0.905853i	$0.360769\pi$
$734$	−39.1996	−1.44688
$735$	54.3948	2.00638
$736$	3.51343	0.129507
$737$	−32.1261	−1.18338
$738$	33.5145	1.23368
$739$	1.82275	0.0670509	0.0335254	−	0.999438i	$-0.489327\pi$
$739$	1.82275	0.0670509	0.0335254	+	0.999438i	$0.489327\pi$
$740$	12.5108	0.459906
$741$	−0.463586	−0.0170303
$742$	12.0550	0.442554
$743$	−37.7928	−1.38648	−0.693241	−	0.720706i	$-0.743818\pi$
$743$	−37.7928	−1.38648	−0.693241	+	0.720706i	$0.743818\pi$
$744$	9.32177	0.341753
$745$	60.7471	2.22560
$746$	59.7881	2.18900
$747$	24.9560	0.913091
$748$	61.0339	2.23162
$749$	19.5939	0.715947
$750$	229.890	8.39441
$751$	8.45871	0.308663	0.154331	−	0.988019i	$-0.450678\pi$
$751$	8.45871	0.308663	0.154331	+	0.988019i	$0.450678\pi$
$752$	−47.4169	−1.72912
$753$	−49.2520	−1.79484
$754$	0.324646	0.0118229
$755$	−21.8163	−0.793978
$756$	13.9317	0.506690
$757$	−13.8082	−0.501866	−0.250933	−	0.968004i	$-0.580737\pi$
$757$	−13.8082	−0.501866	−0.250933	+	0.968004i	$0.580737\pi$
$758$	84.5267	3.07015
$759$	−6.98220	−0.253438
$760$	−40.6906	−1.47600
$761$	−47.7122	−1.72956	−0.864782	−	0.502147i	$-0.832544\pi$
$761$	−47.7122	−1.72956	−0.864782	+	0.502147i	$0.832544\pi$
$762$	74.5640	2.70117
$763$	−6.52995	−0.236400
$764$	−22.2362	−0.804479
$765$	−47.4691	−1.71625
$766$	−71.2859	−2.57567
$767$	−0.379212	−0.0136926
$768$	70.1298	2.53059
$769$	16.2479	0.585913	0.292956	−	0.956126i	$-0.405361\pi$
$769$	16.2479	0.585913	0.292956	+	0.956126i	$0.405361\pi$
$770$	28.6216	1.03145
$771$	−60.6698	−2.18497
$772$	47.0456	1.69321
$773$	−21.6539	−0.778837	−0.389419	−	0.921061i	$-0.627324\pi$
$773$	−21.6539	−0.778837	−0.389419	+	0.921061i	$0.627324\pi$
$774$	19.6396	0.705933
$775$	11.3098	0.406259
$776$	24.8275	0.891254
$777$	−1.65778	−0.0594727
$778$	30.3268	1.08727
$779$	−13.2181	−0.473589
$780$	−5.27022	−0.188704
$781$	11.0289	0.394647
$782$	−22.8977	−0.818819
$783$	−2.86563	−0.102409
$784$	−30.9358	−1.10485
$785$	45.9959	1.64166
$786$	114.424	4.08135
$787$	20.5693	0.733217	0.366609	−	0.930375i	$-0.380519\pi$
$787$	20.5693	0.733217	0.366609	+	0.930375i	$0.380519\pi$
$788$	−15.6747	−0.558389
$789$	−24.4842	−0.871661
$790$	−65.7588	−2.33959
$791$	−9.43798	−0.335576
$792$	21.0263	0.747136
$793$	−0.535635	−0.0190210
$794$	25.2228	0.895123
$795$	40.2535	1.42765
$796$	−18.8771	−0.669080
$797$	38.9593	1.38001	0.690004	−	0.723806i	$-0.257609\pi$
$797$	38.9593	1.38001	0.690004	+	0.723806i	$0.257609\pi$
$798$	10.2231	0.361896
$799$	55.7228	1.97133
$800$	−35.8335	−1.26691
$801$	−7.06687	−0.249696
$802$	85.7389	3.02755
$803$	−36.5067	−1.28829
$804$	−130.451	−4.60066
$805$	−7.29177	−0.257001
$806$	−0.251199	−0.00884809
$807$	16.9314	0.596013
$808$	33.3145	1.17200
$809$	6.74272	0.237061	0.118531	−	0.992950i	$-0.462182\pi$
$809$	6.74272	0.237061	0.118531	+	0.992950i	$0.462182\pi$
$810$	124.051	4.35872
$811$	2.77355	0.0973926	0.0486963	−	0.998814i	$-0.484493\pi$
$811$	2.77355	0.0973926	0.0486963	+	0.998814i	$0.484493\pi$
$812$	−4.86165	−0.170611
$813$	−26.6577	−0.934927
$814$	3.75466	0.131601
$815$	94.0756	3.29532
$816$	75.3613	2.63817
$817$	−7.74589	−0.270994
$818$	−82.0696	−2.86950
$819$	0.250172	0.00874171
$820$	−150.269	−5.24761
$821$	42.3524	1.47811	0.739055	−	0.673645i	$-0.235272\pi$
$821$	42.3524	1.47811	0.739055	+	0.673645i	$0.235272\pi$
$822$	41.7911	1.45763
$823$	42.7420	1.48989	0.744946	−	0.667125i	$-0.232475\pi$
$823$	42.7420	1.48989	0.744946	+	0.667125i	$0.232475\pi$
$824$	11.0380	0.384528
$825$	71.2117	2.47927
$826$	8.36251	0.290969
$827$	20.1349	0.700159	0.350080	−	0.936720i	$-0.386155\pi$
$827$	20.1349	0.700159	0.350080	+	0.936720i	$0.386155\pi$
$828$	−10.1566	−0.352967
$829$	35.3455	1.22760	0.613800	−	0.789462i	$-0.289640\pi$
$829$	35.3455	1.22760	0.613800	+	0.789462i	$0.289640\pi$
$830$	−164.775	−5.71942
$831$	−2.16208	−0.0750018
$832$	−0.620597	−0.0215153
$833$	36.3548	1.25962
$834$	−70.7968	−2.45149
$835$	−31.4754	−1.08925
$836$	−15.7234	−0.543806
$837$	2.21731	0.0766415
$838$	10.2462	0.353950
$839$	−13.9804	−0.482658	−0.241329	−	0.970443i	$-0.577583\pi$
$839$	−13.9804	−0.482658	−0.241329	+	0.970443i	$0.577583\pi$
$840$	61.2966	2.11493
$841$	1.00000	0.0344828
$842$	−25.4893	−0.878419
$843$	−13.0190	−0.448398
$844$	102.082	3.51382
$845$	−57.5029	−1.97816
$846$	36.3975	1.25137
$847$	−6.80339	−0.233767
$848$	−22.8933	−0.786158
$849$	−66.8746	−2.29513
$850$	233.534	8.01015
$851$	−0.956556	−0.0327903
$852$	44.7841	1.53428
$853$	−44.3043	−1.51695	−0.758475	−	0.651702i	$-0.774055\pi$
$853$	−44.3043	−1.51695	−0.758475	+	0.651702i	$0.774055\pi$
$854$	11.8120	0.404198
$855$	12.2289	0.418219
$856$	−95.0402	−3.24841
$857$	41.8486	1.42952	0.714760	−	0.699370i	$-0.246536\pi$
$857$	41.8486	1.42952	0.714760	+	0.699370i	$0.246536\pi$
$858$	−1.58167	−0.0539972
$859$	−18.2661	−0.623232	−0.311616	−	0.950208i	$-0.600870\pi$
$859$	−18.2661	−0.623232	−0.311616	+	0.950208i	$0.600870\pi$
$860$	−88.0582	−3.00276
$861$	19.9118	0.678594
$862$	18.3731	0.625789
$863$	−37.0061	−1.25970	−0.629852	−	0.776715i	$-0.716884\pi$
$863$	−37.0061	−1.25970	−0.629852	+	0.776715i	$0.716884\pi$
$864$	−7.02526	−0.239004
$865$	−9.13254	−0.310516
$866$	9.06446	0.308023
$867$	−51.8068	−1.75945
$868$	3.76176	0.127683
$869$	−13.4017	−0.454621
$870$	−23.9056	−0.810475
$871$	1.85404	0.0628218
$872$	31.6734	1.07260
$873$	−7.46146	−0.252532
$874$	5.89885	0.199531
$875$	48.9290	1.65410
$876$	−148.239	−5.00854
$877$	−22.0008	−0.742915	−0.371457	−	0.928450i	$-0.621142\pi$
$877$	−22.0008	−0.742915	−0.371457	+	0.928450i	$0.621142\pi$
$878$	43.2569	1.45985
$879$	48.4364	1.63372
$880$	−54.3541	−1.83228
$881$	−39.4791	−1.33008	−0.665042	−	0.746806i	$-0.731586\pi$
$881$	−39.4791	−1.33008	−0.665042	+	0.746806i	$0.731586\pi$
$882$	23.7465	0.799586
$883$	32.0497	1.07856	0.539280	−	0.842127i	$-0.318697\pi$
$883$	32.0497	1.07856	0.539280	+	0.842127i	$0.318697\pi$
$884$	−3.52236	−0.118470
$885$	27.9236	0.938643
$886$	42.2031	1.41784
$887$	−35.6489	−1.19697	−0.598487	−	0.801132i	$-0.704231\pi$
$887$	−35.6489	−1.19697	−0.598487	+	0.801132i	$0.704231\pi$
$888$	8.04107	0.269841
$889$	15.8699	0.532261
$890$	46.6599	1.56404
$891$	25.2817	0.846970
$892$	−82.2025	−2.75234
$893$	−14.3552	−0.480378
$894$	74.0289	2.47590
$895$	39.7458	1.32856
$896$	19.3182	0.645375
$897$	0.402953	0.0134542
$898$	−71.7030	−2.39276
$899$	−0.773762	−0.0258064
$900$	103.588	3.45292
$901$	26.9034	0.896284
$902$	−45.0977	−1.50159
$903$	11.6684	0.388302
$904$	45.7788	1.52258
$905$	34.8915	1.15983
$906$	−26.5863	−0.883270
$907$	−46.8978	−1.55722	−0.778609	−	0.627510i	$-0.784074\pi$
$907$	−46.8978	−1.55722	−0.778609	+	0.627510i	$0.784074\pi$
$908$	−65.1451	−2.16192
$909$	−10.0121	−0.332081
$910$	−1.65179	−0.0547563
$911$	5.56380	0.184337	0.0921685	−	0.995743i	$-0.470620\pi$
$911$	5.56380	0.184337	0.0921685	+	0.995743i	$0.470620\pi$
$912$	−19.4144	−0.642875
$913$	−33.5812	−1.11138
$914$	−28.2925	−0.935832
$915$	39.4420	1.30391
$916$	103.047	3.40477
$917$	24.3535	0.804223
$918$	45.7850	1.51113
$919$	30.7578	1.01461	0.507304	−	0.861767i	$-0.330642\pi$
$919$	30.7578	1.01461	0.507304	+	0.861767i	$0.330642\pi$
$920$	35.3687	1.16607
$921$	−28.6760	−0.944905
$922$	−84.4829	−2.78230
$923$	−0.636496	−0.0209505
$924$	23.6858	0.779207
$925$	9.75594	0.320773
$926$	−74.2117	−2.43875
$927$	−3.31729	−0.108954
$928$	2.45156	0.0804765
$929$	−50.2019	−1.64707	−0.823536	−	0.567264i	$-0.808002\pi$
$929$	−50.2019	−1.64707	−0.823536	+	0.567264i	$0.808002\pi$
$930$	18.4972	0.606548
$931$	−9.36563	−0.306946
$932$	−71.6880	−2.34822
$933$	1.81647	0.0594687
$934$	58.4338	1.91201
$935$	63.8752	2.08894
$936$	−1.21346	−0.0396631
$937$	10.9148	0.356572	0.178286	−	0.983979i	$-0.442945\pi$
$937$	10.9148	0.356572	0.178286	+	0.983979i	$0.442945\pi$
$938$	−40.8859	−1.33497
$939$	−12.8028	−0.417804
$940$	−163.195	−5.32284
$941$	0.657322	0.0214281	0.0107140	−	0.999943i	$-0.496590\pi$
$941$	0.657322	0.0214281	0.0107140	+	0.999943i	$0.496590\pi$
$942$	56.0525	1.82629
$943$	11.4893	0.374143
$944$	−15.8809	−0.516881
$945$	14.5802	0.474295
$946$	−26.4275	−0.859231
$947$	8.02931	0.260917	0.130459	−	0.991454i	$-0.458355\pi$
$947$	8.02931	0.260917	0.130459	+	0.991454i	$0.458355\pi$
$948$	−54.4189	−1.76744
$949$	2.10686	0.0683915
$950$	−60.1625	−1.95193
$951$	−28.2024	−0.914526
$952$	40.9676	1.32777
$953$	26.8217	0.868840	0.434420	−	0.900710i	$-0.356953\pi$
$953$	26.8217	0.868840	0.434420	+	0.900710i	$0.356953\pi$
$954$	17.5730	0.568947
$955$	−23.2714	−0.753045
$956$	107.875	3.48893
$957$	−4.87197	−0.157488
$958$	10.7347	0.346824
$959$	8.89466	0.287223
$960$	45.6982	1.47490
$961$	−30.4013	−0.980687
$962$	−0.216687	−0.00698626
$963$	28.5627	0.920420
$964$	22.8909	0.737265
$965$	49.2357	1.58495
$966$	−8.88605	−0.285904
$967$	22.1662	0.712818	0.356409	−	0.934330i	$-0.384001\pi$
$967$	22.1662	0.712818	0.356409	+	0.934330i	$0.384001\pi$
$968$	32.9998	1.06065
$969$	22.8152	0.732930
$970$	49.2652	1.58181
$971$	−12.6459	−0.405827	−0.202914	−	0.979197i	$-0.565041\pi$
$971$	−12.6459	−0.405827	−0.202914	+	0.979197i	$0.565041\pi$
$972$	66.2765	2.12582
$973$	−15.0681	−0.483062
$974$	−29.9086	−0.958335
$975$	−4.10973	−0.131617
$976$	−22.4317	−0.718022
$977$	4.25815	0.136230	0.0681151	−	0.997677i	$-0.478301\pi$
$977$	4.25815	0.136230	0.0681151	+	0.997677i	$0.478301\pi$
$978$	114.644	3.66592
$979$	9.50931	0.303919
$980$	−106.472	−3.40113
$981$	−9.51891	−0.303915
$982$	−49.8433	−1.59056
$983$	41.7055	1.33020	0.665099	−	0.746755i	$-0.268389\pi$
$983$	41.7055	1.33020	0.665099	+	0.746755i	$0.268389\pi$
$984$	−96.5822	−3.07893
$985$	−16.4044	−0.522689
$986$	−15.9773	−0.508821
$987$	21.6247	0.688323
$988$	0.907421	0.0288689
$989$	6.73280	0.214090
$990$	41.7225	1.32603
$991$	16.5987	0.527277	0.263638	−	0.964622i	$-0.415077\pi$
$991$	16.5987	0.527277	0.263638	+	0.964622i	$0.415077\pi$
$992$	−1.89693	−0.0602275
$993$	−32.5347	−1.03246
$994$	14.0362	0.445202
$995$	−19.7559	−0.626303
$996$	−136.360	−4.32073
$997$	−23.2547	−0.736482	−0.368241	−	0.929730i	$-0.620040\pi$
$997$	−23.2547	−0.736482	−0.368241	+	0.929730i	$0.620040\pi$
$998$	64.7731	2.05036
$999$	1.91268	0.0605145

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8033.2.a.e.1.14	✓	169

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8033.2.a.e.1.14	✓	169	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)

\(f(q)\)	\(=\)	\(q-2.49641 q^{2} -2.16208 q^{3} +4.23205 q^{4} +4.42906 q^{5} +5.39744 q^{6} +1.14877 q^{7} -5.57210 q^{8} +1.67460 q^{9} +O(q^{10})\)	\(q-2.49641 q^{2} -2.16208 q^{3} +4.23205 q^{4} +4.42906 q^{5} +5.39744 q^{6} +1.14877 q^{7} -5.57210 q^{8} +1.67460 q^{9} -11.0567 q^{10} -2.25337 q^{11} -9.15003 q^{12} +0.130045 q^{13} -2.86780 q^{14} -9.57600 q^{15} +5.44613 q^{16} -6.40012 q^{17} -4.18048 q^{18} +1.64878 q^{19} +18.7440 q^{20} -2.48374 q^{21} +5.62533 q^{22} -1.43314 q^{23} +12.0473 q^{24} +14.6166 q^{25} -0.324646 q^{26} +2.86563 q^{27} +4.86165 q^{28} -1.00000 q^{29} +23.9056 q^{30} +0.773762 q^{31} -2.45156 q^{32} +4.87197 q^{33} +15.9773 q^{34} +5.08798 q^{35} +7.08698 q^{36} +0.667456 q^{37} -4.11604 q^{38} -0.281168 q^{39} -24.6792 q^{40} -8.01689 q^{41} +6.20042 q^{42} -4.69794 q^{43} -9.53637 q^{44} +7.41690 q^{45} +3.57769 q^{46} -8.70653 q^{47} -11.7750 q^{48} -5.68033 q^{49} -36.4890 q^{50} +13.8376 q^{51} +0.550358 q^{52} -4.20358 q^{53} -7.15377 q^{54} -9.98032 q^{55} -6.40106 q^{56} -3.56481 q^{57} +2.49641 q^{58} -2.91600 q^{59} -40.5261 q^{60} -4.11884 q^{61} -1.93162 q^{62} +1.92373 q^{63} -4.77216 q^{64} +0.575979 q^{65} -12.1624 q^{66} +14.2569 q^{67} -27.0856 q^{68} +3.09856 q^{69} -12.7017 q^{70} -4.89442 q^{71} -9.33103 q^{72} +16.2009 q^{73} -1.66624 q^{74} -31.6023 q^{75} +6.97773 q^{76} -2.58861 q^{77} +0.701911 q^{78} +5.94739 q^{79} +24.1213 q^{80} -11.2195 q^{81} +20.0134 q^{82} +14.9027 q^{83} -10.5113 q^{84} -28.3465 q^{85} +11.7280 q^{86} +2.16208 q^{87} +12.5560 q^{88} -4.22004 q^{89} -18.5156 q^{90} +0.149392 q^{91} -6.06511 q^{92} -1.67294 q^{93} +21.7350 q^{94} +7.30257 q^{95} +5.30048 q^{96} -4.45567 q^{97} +14.1804 q^{98} -3.77349 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 169 q + 3 q^{2} + 8 q^{3} + 183 q^{4} + 13 q^{5} + 17 q^{6} + 76 q^{7} + 6 q^{8} + 181 q^{9}+O(q^{10}) \) 169 * q + 3 * q^2 + 8 * q^3 + 183 * q^4 + 13 * q^5 + 17 * q^6 + 76 * q^7 + 6 * q^8 + 181 * q^9	\( 169 q + 3 q^{2} + 8 q^{3} + 183 q^{4} + 13 q^{5} + 17 q^{6} + 76 q^{7} + 6 q^{8} + 181 q^{9} + 30 q^{10} + 2 q^{11} + 25 q^{12} + 63 q^{13} - 3 q^{14} + 26 q^{15} + 219 q^{16} + 14 q^{17} + 31 q^{18} + 51 q^{19} + 49 q^{20} + 16 q^{21} + 53 q^{22} + 50 q^{23} + 43 q^{24} + 214 q^{25} - 2 q^{26} + 23 q^{27} + 149 q^{28} - 169 q^{29} + 26 q^{30} + 65 q^{31} + 25 q^{32} + 57 q^{33} + 60 q^{34} + 60 q^{35} + 218 q^{36} + 52 q^{37} + 35 q^{38} + 49 q^{39} + 72 q^{40} + 3 q^{41} + 78 q^{42} + 132 q^{43} + 64 q^{45} + 32 q^{46} + 54 q^{47} + 76 q^{48} + 245 q^{49} - 6 q^{50} + 44 q^{51} + 193 q^{52} + 58 q^{53} + 54 q^{54} + 213 q^{55} + 12 q^{56} + 52 q^{57} - 3 q^{58} + 25 q^{59} + 32 q^{60} + 100 q^{61} + 78 q^{62} + 227 q^{63} + 292 q^{64} + 37 q^{65} + 59 q^{66} + 110 q^{67} + 24 q^{68} - 20 q^{69} + 47 q^{70} + 44 q^{71} + 71 q^{72} + 139 q^{73} + 35 q^{74} + 53 q^{75} + 92 q^{76} + 22 q^{77} + 83 q^{78} + 137 q^{79} + 90 q^{80} + 177 q^{81} + 91 q^{82} + 126 q^{83} + 36 q^{84} + 95 q^{85} + 21 q^{86} - 8 q^{87} + 75 q^{88} + 19 q^{89} + 130 q^{90} + 102 q^{91} + 68 q^{92} + 22 q^{93} + 82 q^{94} + 37 q^{95} + 107 q^{96} + 116 q^{97} - 13 q^{98} - 11 q^{99}+O(q^{100}) \) 169 * q + 3 * q^2 + 8 * q^3 + 183 * q^4 + 13 * q^5 + 17 * q^6 + 76 * q^7 + 6 * q^8 + 181 * q^9 + 30 * q^10 + 2 * q^11 + 25 * q^12 + 63 * q^13 - 3 * q^14 + 26 * q^15 + 219 * q^16 + 14 * q^17 + 31 * q^18 + 51 * q^19 + 49 * q^20 + 16 * q^21 + 53 * q^22 + 50 * q^23 + 43 * q^24 + 214 * q^25 - 2 * q^26 + 23 * q^27 + 149 * q^28 - 169 * q^29 + 26 * q^30 + 65 * q^31 + 25 * q^32 + 57 * q^33 + 60 * q^34 + 60 * q^35 + 218 * q^36 + 52 * q^37 + 35 * q^38 + 49 * q^39 + 72 * q^40 + 3 * q^41 + 78 * q^42 + 132 * q^43 + 64 * q^45 + 32 * q^46 + 54 * q^47 + 76 * q^48 + 245 * q^49 - 6 * q^50 + 44 * q^51 + 193 * q^52 + 58 * q^53 + 54 * q^54 + 213 * q^55 + 12 * q^56 + 52 * q^57 - 3 * q^58 + 25 * q^59 + 32 * q^60 + 100 * q^61 + 78 * q^62 + 227 * q^63 + 292 * q^64 + 37 * q^65 + 59 * q^66 + 110 * q^67 + 24 * q^68 - 20 * q^69 + 47 * q^70 + 44 * q^71 + 71 * q^72 + 139 * q^73 + 35 * q^74 + 53 * q^75 + 92 * q^76 + 22 * q^77 + 83 * q^78 + 137 * q^79 + 90 * q^80 + 177 * q^81 + 91 * q^82 + 126 * q^83 + 36 * q^84 + 95 * q^85 + 21 * q^86 - 8 * q^87 + 75 * q^88 + 19 * q^89 + 130 * q^90 + 102 * q^91 + 68 * q^92 + 22 * q^93 + 82 * q^94 + 37 * q^95 + 107 * q^96 + 116 * q^97 - 13 * q^98 - 11 * q^99

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