LMFDB - Embedded newform 8041.2.a.i.1.61

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8041,2,Mod(1,8041)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8041, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8041.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8041 = 11 \cdot 17 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8041.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:	$64.2077082653$
Analytic rank:	$0$
Dimension:	$78$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.61
Character	$\chi$	$=$	8041.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.88003 q^{2} -0.403145 q^{3} +1.53450 q^{4} -2.96266 q^{5} -0.757923 q^{6} +2.73707 q^{7} -0.875149 q^{8} -2.83747 q^{9} +O(q^{10})$	\(q+1.88003 q^{2} -0.403145 q^{3} +1.53450 q^{4} -2.96266 q^{5} -0.757923 q^{6} +2.73707 q^{7} -0.875149 q^{8} -2.83747 q^{9} -5.56989 q^{10} +1.00000 q^{11} -0.618626 q^{12} -4.24576 q^{13} +5.14577 q^{14} +1.19438 q^{15} -4.71431 q^{16} -1.00000 q^{17} -5.33453 q^{18} +4.36765 q^{19} -4.54621 q^{20} -1.10344 q^{21} +1.88003 q^{22} -6.82432 q^{23} +0.352812 q^{24} +3.77737 q^{25} -7.98214 q^{26} +2.35335 q^{27} +4.20004 q^{28} -0.653224 q^{29} +2.24547 q^{30} +8.20214 q^{31} -7.11273 q^{32} -0.403145 q^{33} -1.88003 q^{34} -8.10902 q^{35} -4.35411 q^{36} -10.9519 q^{37} +8.21131 q^{38} +1.71165 q^{39} +2.59277 q^{40} +6.51004 q^{41} -2.07449 q^{42} -1.00000 q^{43} +1.53450 q^{44} +8.40648 q^{45} -12.8299 q^{46} +8.54322 q^{47} +1.90055 q^{48} +0.491569 q^{49} +7.10155 q^{50} +0.403145 q^{51} -6.51512 q^{52} +2.99398 q^{53} +4.42435 q^{54} -2.96266 q^{55} -2.39535 q^{56} -1.76080 q^{57} -1.22808 q^{58} -2.20739 q^{59} +1.83278 q^{60} +2.30853 q^{61} +15.4202 q^{62} -7.76637 q^{63} -3.94351 q^{64} +12.5787 q^{65} -0.757923 q^{66} +13.8878 q^{67} -1.53450 q^{68} +2.75119 q^{69} -15.2452 q^{70} +11.8247 q^{71} +2.48321 q^{72} +8.74150 q^{73} -20.5898 q^{74} -1.52282 q^{75} +6.70217 q^{76} +2.73707 q^{77} +3.21795 q^{78} -15.6191 q^{79} +13.9669 q^{80} +7.56368 q^{81} +12.2391 q^{82} +10.9660 q^{83} -1.69322 q^{84} +2.96266 q^{85} -1.88003 q^{86} +0.263344 q^{87} -0.875149 q^{88} -6.78747 q^{89} +15.8044 q^{90} -11.6209 q^{91} -10.4719 q^{92} -3.30665 q^{93} +16.0615 q^{94} -12.9399 q^{95} +2.86746 q^{96} +4.62390 q^{97} +0.924163 q^{98} -2.83747 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 78 q + 7 q^{2} + 10 q^{3} + 91 q^{4} + 17 q^{5} + 12 q^{6} + 11 q^{7} + 33 q^{8} + 102 q^{9}+O(q^{10}) $ 78 * q + 7 * q^2 + 10 * q^3 + 91 * q^4 + 17 * q^5 + 12 * q^6 + 11 * q^7 + 33 * q^8 + 102 * q^9	\( 78 q + 7 q^{2} + 10 q^{3} + 91 q^{4} + 17 q^{5} + 12 q^{6} + 11 q^{7} + 33 q^{8} + 102 q^{9} + 3 q^{10} + 78 q^{11} + 31 q^{12} - 16 q^{13} + 31 q^{14} + 38 q^{15} + 121 q^{16} - 78 q^{17} + 11 q^{18} + 51 q^{20} + 6 q^{21} + 7 q^{22} + 48 q^{23} + 11 q^{24} + 101 q^{25} + 18 q^{26} + 46 q^{27} + 27 q^{28} + 22 q^{29} + 14 q^{30} + 56 q^{31} + 83 q^{32} + 10 q^{33} - 7 q^{34} + 24 q^{35} + 139 q^{36} + 53 q^{37} + 10 q^{38} + 79 q^{39} - q^{40} + 23 q^{41} + 17 q^{42} - 78 q^{43} + 91 q^{44} + 76 q^{45} + 21 q^{46} + 57 q^{47} + 78 q^{48} + 115 q^{49} + 58 q^{50} - 10 q^{51} - 63 q^{52} + 22 q^{53} - 18 q^{54} + 17 q^{55} + 111 q^{56} - 11 q^{57} + 36 q^{58} + 71 q^{59} + 36 q^{60} + 4 q^{61} - 5 q^{62} + 71 q^{63} + 183 q^{64} + 47 q^{65} + 12 q^{66} + 11 q^{67} - 91 q^{68} + 31 q^{69} + 33 q^{70} + 159 q^{71} + 59 q^{72} + 2 q^{73} - 4 q^{74} + 83 q^{75} - 44 q^{76} + 11 q^{77} + 101 q^{78} + 35 q^{79} + 85 q^{80} + 170 q^{81} + 98 q^{82} - 32 q^{83} + 44 q^{84} - 17 q^{85} - 7 q^{86} - 6 q^{87} + 33 q^{88} + 50 q^{89} - 5 q^{90} + 86 q^{91} + 106 q^{92} + 68 q^{93} - q^{94} + 109 q^{95} - 50 q^{96} + 40 q^{97} + 106 q^{98} + 102 q^{99}+O(q^{100}) \) 78 * q + 7 * q^2 + 10 * q^3 + 91 * q^4 + 17 * q^5 + 12 * q^6 + 11 * q^7 + 33 * q^8 + 102 * q^9 + 3 * q^10 + 78 * q^11 + 31 * q^12 - 16 * q^13 + 31 * q^14 + 38 * q^15 + 121 * q^16 - 78 * q^17 + 11 * q^18 + 51 * q^20 + 6 * q^21 + 7 * q^22 + 48 * q^23 + 11 * q^24 + 101 * q^25 + 18 * q^26 + 46 * q^27 + 27 * q^28 + 22 * q^29 + 14 * q^30 + 56 * q^31 + 83 * q^32 + 10 * q^33 - 7 * q^34 + 24 * q^35 + 139 * q^36 + 53 * q^37 + 10 * q^38 + 79 * q^39 - q^40 + 23 * q^41 + 17 * q^42 - 78 * q^43 + 91 * q^44 + 76 * q^45 + 21 * q^46 + 57 * q^47 + 78 * q^48 + 115 * q^49 + 58 * q^50 - 10 * q^51 - 63 * q^52 + 22 * q^53 - 18 * q^54 + 17 * q^55 + 111 * q^56 - 11 * q^57 + 36 * q^58 + 71 * q^59 + 36 * q^60 + 4 * q^61 - 5 * q^62 + 71 * q^63 + 183 * q^64 + 47 * q^65 + 12 * q^66 + 11 * q^67 - 91 * q^68 + 31 * q^69 + 33 * q^70 + 159 * q^71 + 59 * q^72 + 2 * q^73 - 4 * q^74 + 83 * q^75 - 44 * q^76 + 11 * q^77 + 101 * q^78 + 35 * q^79 + 85 * q^80 + 170 * q^81 + 98 * q^82 - 32 * q^83 + 44 * q^84 - 17 * q^85 - 7 * q^86 - 6 * q^87 + 33 * q^88 + 50 * q^89 - 5 * q^90 + 86 * q^91 + 106 * q^92 + 68 * q^93 - q^94 + 109 * q^95 - 50 * q^96 + 40 * q^97 + 106 * q^98 + 102 * 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 $

$2$	1.88003	1.32938	0.664690	−	0.747119i	$-0.268564\pi$
$2$	1.88003	1.32938	0.664690	+	0.747119i	$0.268564\pi$
$3$	−0.403145	−0.232756	−0.116378	−	0.993205i	$-0.537128\pi$
$3$	−0.403145	−0.232756	−0.116378	+	0.993205i	$0.537128\pi$
$4$	1.53450	0.767251
$5$	−2.96266	−1.32494	−0.662471	−	0.749087i	$-0.730492\pi$
$5$	−2.96266	−1.32494	−0.662471	+	0.749087i	$0.730492\pi$
$6$	−0.757923	−0.309421
$7$	2.73707	1.03452	0.517258	−	0.855829i	$-0.326953\pi$
$7$	2.73707	1.03452	0.517258	+	0.855829i	$0.326953\pi$
$8$	−0.875149	−0.309412
$9$	−2.83747	−0.945825
$10$	−5.56989	−1.76135
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−0.618626	−0.178582
$13$	−4.24576	−1.17756	−0.588780	−	0.808293i	$-0.700392\pi$
$13$	−4.24576	−1.17756	−0.588780	+	0.808293i	$0.700392\pi$
$14$	5.14577	1.37527
$15$	1.19438	0.308388
$16$	−4.71431	−1.17858
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−5.33453	−1.25736
$19$	4.36765	1.00201	0.501004	−	0.865445i	$-0.332964\pi$
$19$	4.36765	1.00201	0.501004	+	0.865445i	$0.332964\pi$
$20$	−4.54621	−1.01656
$21$	−1.10344	−0.240789
$22$	1.88003	0.400823
$23$	−6.82432	−1.42297	−0.711484	−	0.702702i	$-0.751977\pi$
$23$	−6.82432	−1.42297	−0.711484	+	0.702702i	$0.751977\pi$
$24$	0.352812	0.0720174
$25$	3.77737	0.755473
$26$	−7.98214	−1.56543
$27$	2.35335	0.452902
$28$	4.20004	0.793734
$29$	−0.653224	−0.121301	−0.0606503	−	0.998159i	$-0.519317\pi$
$29$	−0.653224	−0.121301	−0.0606503	+	0.998159i	$0.519317\pi$
$30$	2.24547	0.409965
$31$	8.20214	1.47315	0.736574	−	0.676357i	$-0.236442\pi$
$31$	8.20214	1.47315	0.736574	+	0.676357i	$0.236442\pi$
$32$	−7.11273	−1.25736
$33$	−0.403145	−0.0701785
$34$	−1.88003	−0.322422
$35$	−8.10902	−1.37068
$36$	−4.35411	−0.725685
$37$	−10.9519	−1.80047	−0.900237	−	0.435401i	$-0.856607\pi$
$37$	−10.9519	−1.80047	−0.900237	+	0.435401i	$0.856607\pi$
$38$	8.21131	1.33205
$39$	1.71165	0.274084
$40$	2.59277	0.409953
$41$	6.51004	1.01670	0.508349	−	0.861151i	$-0.330256\pi$
$41$	6.51004	1.01670	0.508349	+	0.861151i	$0.330256\pi$
$42$	−2.07449	−0.320101
$43$	−1.00000	−0.152499
$43$	−1.00000	−0.152499
$44$	1.53450	0.231335
$45$	8.40648	1.25316
$46$	−12.8299	−1.89167
$47$	8.54322	1.24616	0.623079	−	0.782159i	$-0.285882\pi$
$47$	8.54322	1.24616	0.623079	+	0.782159i	$0.285882\pi$
$48$	1.90055	0.274320
$49$	0.491569	0.0702241
$50$	7.10155	1.00431
$51$	0.403145	0.0564515
$52$	−6.51512	−0.903485
$53$	2.99398	0.411254	0.205627	−	0.978630i	$-0.434077\pi$
$53$	2.99398	0.411254	0.205627	+	0.978630i	$0.434077\pi$
$54$	4.42435	0.602078
$55$	−2.96266	−0.399485
$56$	−2.39535	−0.320092
$57$	−1.76080	−0.233223
$58$	−1.22808	−0.161255
$59$	−2.20739	−0.287378	−0.143689	−	0.989623i	$-0.545896\pi$
$59$	−2.20739	−0.287378	−0.143689	+	0.989623i	$0.545896\pi$
$60$	1.83278	0.236611
$61$	2.30853	0.295577	0.147788	−	0.989019i	$-0.452785\pi$
$61$	2.30853	0.295577	0.147788	+	0.989019i	$0.452785\pi$
$62$	15.4202	1.95837
$63$	−7.76637	−0.978471
$64$	−3.94351	−0.492938
$65$	12.5787	1.56020
$66$	−0.757923	−0.0932938
$67$	13.8878	1.69667	0.848334	−	0.529462i	$-0.177606\pi$
$67$	13.8878	1.69667	0.848334	+	0.529462i	$0.177606\pi$
$68$	−1.53450	−0.186086
$69$	2.75119	0.331204
$70$	−15.2452	−1.82215
$71$	11.8247	1.40333	0.701665	−	0.712507i	$-0.252440\pi$
$71$	11.8247	1.40333	0.701665	+	0.712507i	$0.252440\pi$
$72$	2.48321	0.292650
$73$	8.74150	1.02312	0.511558	−	0.859249i	$-0.329069\pi$
$73$	8.74150	1.02312	0.511558	+	0.859249i	$0.329069\pi$
$74$	−20.5898	−2.39351
$75$	−1.52282	−0.175841
$76$	6.70217	0.768792
$77$	2.73707	0.311918
$78$	3.21795	0.364362
$79$	−15.6191	−1.75729	−0.878644	−	0.477477i	$-0.841552\pi$
$79$	−15.6191	−1.75729	−0.878644	+	0.477477i	$0.841552\pi$
$80$	13.9669	1.56155
$81$	7.56368	0.840409
$82$	12.2391	1.35158
$83$	10.9660	1.20368	0.601840	−	0.798617i	$-0.294434\pi$
$83$	10.9660	1.20368	0.601840	+	0.798617i	$0.294434\pi$
$84$	−1.69322	−0.184746
$85$	2.96266	0.321346
$86$	−1.88003	−0.202729
$87$	0.263344	0.0282334
$88$	−0.875149	−0.0932912
$89$	−6.78747	−0.719470	−0.359735	−	0.933054i	$-0.617133\pi$
$89$	−6.78747	−0.719470	−0.359735	+	0.933054i	$0.617133\pi$
$90$	15.8044	1.66593
$91$	−11.6209	−1.21821
$92$	−10.4719	−1.09177
$93$	−3.30665	−0.342883
$94$	16.0615	1.65662
$95$	−12.9399	−1.32760
$96$	2.86746	0.292659
$97$	4.62390	0.469486	0.234743	−	0.972057i	$-0.424575\pi$
$97$	4.62390	0.469486	0.234743	+	0.972057i	$0.424575\pi$
$98$	0.924163	0.0933546
$99$	−2.83747	−0.285177
$100$	5.79638	0.579638
$101$	−9.23631	−0.919047	−0.459523	−	0.888166i	$-0.651980\pi$
$101$	−9.23631	−0.919047	−0.459523	+	0.888166i	$0.651980\pi$
$102$	0.757923	0.0750455
$103$	15.1258	1.49039	0.745194	−	0.666848i	$-0.232357\pi$
$103$	15.1258	1.49039	0.745194	+	0.666848i	$0.232357\pi$
$104$	3.71567	0.364351
$105$	3.26911	0.319032
$106$	5.62876	0.546713
$107$	6.02403	0.582364	0.291182	−	0.956668i	$-0.405951\pi$
$107$	6.02403	0.582364	0.291182	+	0.956668i	$0.405951\pi$
$108$	3.61121	0.347489
$109$	−11.8333	−1.13342	−0.566712	−	0.823916i	$-0.691785\pi$
$109$	−11.8333	−1.13342	−0.566712	+	0.823916i	$0.691785\pi$
$110$	−5.56989	−0.531068
$111$	4.41518	0.419070
$112$	−12.9034	−1.21926
$113$	−4.56842	−0.429761	−0.214881	−	0.976640i	$-0.568936\pi$
$113$	−4.56842	−0.429761	−0.214881	+	0.976640i	$0.568936\pi$
$114$	−3.31034	−0.310042
$115$	20.2182	1.88535
$116$	−1.00237	−0.0930681
$117$	12.0472	1.11377
$118$	−4.14995	−0.382034
$119$	−2.73707	−0.250907
$120$	−1.04526	−0.0954189
$121$	1.00000	0.0909091
$122$	4.34009	0.392933
$123$	−2.62449	−0.236642
$124$	12.5862	1.13027
$125$	3.62225	0.323984
$126$	−14.6010	−1.30076
$127$	−5.47385	−0.485726	−0.242863	−	0.970061i	$-0.578086\pi$
$127$	−5.47385	−0.485726	−0.242863	+	0.970061i	$0.578086\pi$
$128$	6.81156	0.602062
$129$	0.403145	0.0354949
$130$	23.6484	2.07410
$131$	−12.4336	−1.08633	−0.543165	−	0.839626i	$-0.682774\pi$
$131$	−12.4336	−1.08633	−0.543165	+	0.839626i	$0.682774\pi$
$132$	−0.618626	−0.0538445
$133$	11.9546	1.03659
$134$	26.1095	2.25552
$135$	−6.97217	−0.600069
$136$	0.875149	0.0750434
$137$	−1.73826	−0.148509	−0.0742547	−	0.997239i	$-0.523658\pi$
$137$	−1.73826	−0.148509	−0.0742547	+	0.997239i	$0.523658\pi$
$138$	5.17231	0.440296
$139$	−18.4947	−1.56870	−0.784350	−	0.620319i	$-0.787003\pi$
$139$	−18.4947	−1.56870	−0.784350	+	0.620319i	$0.787003\pi$
$140$	−12.4433	−1.05165
$141$	−3.44415	−0.290050
$142$	22.2307	1.86556
$143$	−4.24576	−0.355048
$144$	13.3767	1.11473
$145$	1.93528	0.160716
$146$	16.4343	1.36011
$147$	−0.198173	−0.0163451
$148$	−16.8056	−1.38141
$149$	18.6318	1.52638	0.763188	−	0.646177i	$-0.223633\pi$
$149$	18.6318	1.52638	0.763188	+	0.646177i	$0.223633\pi$
$150$	−2.86295	−0.233759
$151$	10.9944	0.894712	0.447356	−	0.894356i	$-0.352366\pi$
$151$	10.9944	0.894712	0.447356	+	0.894356i	$0.352366\pi$
$152$	−3.82235	−0.310033
$153$	2.83747	0.229396
$154$	5.14577	0.414658
$155$	−24.3002	−1.95184
$156$	2.62653	0.210291
$157$	−17.3084	−1.38136	−0.690679	−	0.723161i	$-0.742688\pi$
$157$	−17.3084	−1.38136	−0.690679	+	0.723161i	$0.742688\pi$
$158$	−29.3644	−2.33610
$159$	−1.20701	−0.0957218
$160$	21.0726	1.66594
$161$	−18.6787	−1.47208
$162$	14.2199	1.11722
$163$	8.99966	0.704908	0.352454	−	0.935829i	$-0.385347\pi$
$163$	8.99966	0.704908	0.352454	+	0.935829i	$0.385347\pi$
$164$	9.98967	0.780063
$165$	1.19438	0.0929824
$166$	20.6165	1.60015
$167$	12.3095	0.952537	0.476268	−	0.879300i	$-0.341989\pi$
$167$	12.3095	0.952537	0.476268	+	0.879300i	$0.341989\pi$
$168$	0.965671	0.0745031
$169$	5.02644	0.386649
$170$	5.56989	0.427191
$171$	−12.3931	−0.947724
$172$	−1.53450	−0.117005
$173$	7.35501	0.559191	0.279595	−	0.960118i	$-0.409800\pi$
$173$	7.35501	0.559191	0.279595	+	0.960118i	$0.409800\pi$
$174$	0.495093	0.0375329
$175$	10.3389	0.781550
$176$	−4.71431	−0.355354
$177$	0.889897	0.0668888
$178$	−12.7606	−0.956449
$179$	12.6952	0.948884	0.474442	−	0.880287i	$-0.342650\pi$
$179$	12.6952	0.948884	0.474442	+	0.880287i	$0.342650\pi$
$180$	12.8998	0.961491
$181$	1.61349	0.119930	0.0599649	−	0.998200i	$-0.480901\pi$
$181$	1.61349	0.119930	0.0599649	+	0.998200i	$0.480901\pi$
$182$	−21.8477	−1.61946
$183$	−0.930670	−0.0687971
$184$	5.97230	0.440284
$185$	32.4466	2.38552
$186$	−6.21659	−0.455822
$187$	−1.00000	−0.0731272
$188$	13.1096	0.956115
$189$	6.44128	0.468534
$190$	−24.3273	−1.76489
$191$	11.3959	0.824576	0.412288	−	0.911054i	$-0.364730\pi$
$191$	11.3959	0.824576	0.412288	+	0.911054i	$0.364730\pi$
$192$	1.58980	0.114734
$193$	−10.4972	−0.755605	−0.377803	−	0.925886i	$-0.623320\pi$
$193$	−10.4972	−0.755605	−0.377803	+	0.925886i	$0.623320\pi$
$194$	8.69306	0.624125
$195$	−5.07105	−0.363145
$196$	0.754313	0.0538795
$197$	19.8579	1.41482	0.707409	−	0.706804i	$-0.249864\pi$
$197$	19.8579	1.41482	0.707409	+	0.706804i	$0.249864\pi$
$198$	−5.33453	−0.379108
$199$	7.62782	0.540722	0.270361	−	0.962759i	$-0.412857\pi$
$199$	7.62782	0.540722	0.270361	+	0.962759i	$0.412857\pi$
$200$	−3.30576	−0.233753
$201$	−5.59880	−0.394909
$202$	−17.3645	−1.22176
$203$	−1.78792	−0.125488
$204$	0.618626	0.0433125
$205$	−19.2871	−1.34707
$206$	28.4369	1.98129
$207$	19.3638	1.34588
$208$	20.0158	1.38785
$209$	4.36765	0.302117
$210$	6.14601	0.424115
$211$	−5.05920	−0.348290	−0.174145	−	0.984720i	$-0.555716\pi$
$211$	−5.05920	−0.348290	−0.174145	+	0.984720i	$0.555716\pi$
$212$	4.59426	0.315535
$213$	−4.76705	−0.326633
$214$	11.3253	0.774184
$215$	2.96266	0.202052
$216$	−2.05953	−0.140133
$217$	22.4499	1.52400
$218$	−22.2469	−1.50675
$219$	−3.52409	−0.238136
$220$	−4.54621	−0.306505
$221$	4.24576	0.285600
$222$	8.30066	0.557104
$223$	9.05942	0.606664	0.303332	−	0.952885i	$-0.401901\pi$
$223$	9.05942	0.606664	0.303332	+	0.952885i	$0.401901\pi$
$224$	−19.4681	−1.30076
$225$	−10.7182	−0.714546
$226$	−8.58876	−0.571316
$227$	−2.75887	−0.183113	−0.0915565	−	0.995800i	$-0.529184\pi$
$227$	−2.75887	−0.183113	−0.0915565	+	0.995800i	$0.529184\pi$
$228$	−2.70194	−0.178941
$229$	−15.0269	−0.993008	−0.496504	−	0.868035i	$-0.665383\pi$
$229$	−15.0269	−0.993008	−0.496504	+	0.868035i	$0.665383\pi$
$230$	38.0107	2.50635
$231$	−1.10344	−0.0726008
$232$	0.571669	0.0375319
$233$	26.5844	1.74160	0.870801	−	0.491635i	$-0.163601\pi$
$233$	26.5844	1.74160	0.870801	+	0.491635i	$0.163601\pi$
$234$	22.6491	1.48062
$235$	−25.3107	−1.65109
$236$	−3.38724	−0.220491
$237$	6.29676	0.409019
$238$	−5.14577	−0.333551
$239$	2.01028	0.130034	0.0650170	−	0.997884i	$-0.479290\pi$
$239$	2.01028	0.130034	0.0650170	+	0.997884i	$0.479290\pi$
$240$	−5.63068	−0.363459
$241$	15.1940	0.978731	0.489366	−	0.872079i	$-0.337228\pi$
$241$	15.1940	0.978731	0.489366	+	0.872079i	$0.337228\pi$
$242$	1.88003	0.120853
$243$	−10.1093	−0.648512
$244$	3.54244	0.226781
$245$	−1.45635	−0.0930430
$246$	−4.93411	−0.314587
$247$	−18.5440	−1.17993
$248$	−7.17809	−0.455809
$249$	−4.42090	−0.280163
$250$	6.80992	0.430697
$251$	−0.930473	−0.0587309	−0.0293655	−	0.999569i	$-0.509349\pi$
$251$	−0.930473	−0.0587309	−0.0293655	+	0.999569i	$0.509349\pi$
$252$	−11.9175	−0.750733
$253$	−6.82432	−0.429041
$254$	−10.2910	−0.645714
$255$	−1.19438	−0.0747950
$256$	20.6929	1.29331
$257$	20.9180	1.30483	0.652414	−	0.757863i	$-0.273756\pi$
$257$	20.9180	1.30483	0.652414	+	0.757863i	$0.273756\pi$
$258$	0.757923	0.0471862
$259$	−29.9760	−1.86262
$260$	19.3021	1.19707
$261$	1.85351	0.114729
$262$	−23.3755	−1.44415
$263$	22.2622	1.37275	0.686374	−	0.727249i	$-0.259201\pi$
$263$	22.2622	1.37275	0.686374	+	0.727249i	$0.259201\pi$
$264$	0.352812	0.0217141
$265$	−8.87014	−0.544889
$266$	22.4749	1.37803
$267$	2.73633	0.167461
$268$	21.3109	1.30177
$269$	29.3330	1.78846	0.894232	−	0.447604i	$-0.147722\pi$
$269$	29.3330	1.78846	0.894232	+	0.447604i	$0.147722\pi$
$270$	−13.1079	−0.797719
$271$	6.00197	0.364593	0.182297	−	0.983244i	$-0.441647\pi$
$271$	6.00197	0.364593	0.182297	+	0.983244i	$0.441647\pi$
$272$	4.71431	0.285847
$273$	4.68492	0.283544
$274$	−3.26797	−0.197426
$275$	3.77737	0.227784
$276$	4.22170	0.254117
$277$	7.74906	0.465596	0.232798	−	0.972525i	$-0.425212\pi$
$277$	7.74906	0.465596	0.232798	+	0.972525i	$0.425212\pi$
$278$	−34.7705	−2.08540
$279$	−23.2734	−1.39334
$280$	7.09660	0.424103
$281$	−28.4160	−1.69515	−0.847577	−	0.530673i	$-0.821939\pi$
$281$	−28.4160	−1.69515	−0.847577	+	0.530673i	$0.821939\pi$
$282$	−6.47510	−0.385587
$283$	−16.4959	−0.980579	−0.490289	−	0.871560i	$-0.663109\pi$
$283$	−16.4959	−0.980579	−0.490289	+	0.871560i	$0.663109\pi$
$284$	18.1450	1.07671
$285$	5.21664	0.309007
$286$	−7.98214	−0.471994
$287$	17.8185	1.05179
$288$	20.1822	1.18925
$289$	1.00000	0.0588235
$290$	3.63838	0.213653
$291$	−1.86410	−0.109275
$292$	13.4139	0.784986
$293$	−2.87076	−0.167711	−0.0838557	−	0.996478i	$-0.526723\pi$
$293$	−2.87076	−0.167711	−0.0838557	+	0.996478i	$0.526723\pi$
$294$	−0.372571	−0.0217288
$295$	6.53975	0.380759
$296$	9.58450	0.557088
$297$	2.35335	0.136555
$298$	35.0283	2.02913
$299$	28.9744	1.67563
$300$	−2.33678	−0.134914
$301$	−2.73707	−0.157762
$302$	20.6698	1.18941
$303$	3.72357	0.213913
$304$	−20.5905	−1.18094
$305$	−6.83938	−0.391622
$306$	5.33453	0.304955
$307$	2.25140	0.128494	0.0642471	−	0.997934i	$-0.479535\pi$
$307$	2.25140	0.128494	0.0642471	+	0.997934i	$0.479535\pi$
$308$	4.20004	0.239320
$309$	−6.09788	−0.346896
$310$	−45.6850	−2.59473
$311$	−13.9660	−0.791940	−0.395970	−	0.918263i	$-0.629592\pi$
$311$	−13.9660	−0.791940	−0.395970	+	0.918263i	$0.629592\pi$
$312$	−1.49795	−0.0848048
$313$	11.8796	0.671472	0.335736	−	0.941956i	$-0.391015\pi$
$313$	11.8796	0.671472	0.335736	+	0.941956i	$0.391015\pi$
$314$	−32.5402	−1.83635
$315$	23.0091	1.29642
$316$	−23.9676	−1.34828
$317$	27.4919	1.54410	0.772048	−	0.635564i	$-0.219232\pi$
$317$	27.4919	1.54410	0.772048	+	0.635564i	$0.219232\pi$
$318$	−2.26920	−0.127251
$319$	−0.653224	−0.0365735
$320$	11.6833	0.653115
$321$	−2.42855	−0.135549
$322$	−35.1164	−1.95696
$323$	−4.36765	−0.243023
$324$	11.6065	0.644805
$325$	−16.0378	−0.889616
$326$	16.9196	0.937091
$327$	4.77053	0.263811
$328$	−5.69726	−0.314579
$329$	23.3834	1.28917
$330$	2.24547	0.123609
$331$	23.0534	1.26713	0.633566	−	0.773689i	$-0.281591\pi$
$331$	23.0534	1.26713	0.633566	+	0.773689i	$0.281591\pi$
$332$	16.8274	0.923525
$333$	31.0756	1.70293
$334$	23.1422	1.26628
$335$	−41.1449	−2.24799
$336$	5.20194	0.283789
$337$	−1.57007	−0.0855271	−0.0427636	−	0.999085i	$-0.513616\pi$
$337$	−1.57007	−0.0855271	−0.0427636	+	0.999085i	$0.513616\pi$
$338$	9.44985	0.514004
$339$	1.84174	0.100029
$340$	4.54621	0.246553
$341$	8.20214	0.444171
$342$	−23.2994	−1.25989
$343$	−17.8141	−0.961868
$344$	0.875149	0.0471849
$345$	−8.15084	−0.438826
$346$	13.8276	0.743377
$347$	−18.1212	−0.972799	−0.486399	−	0.873737i	$-0.661690\pi$
$347$	−18.1212	−0.972799	−0.486399	+	0.873737i	$0.661690\pi$
$348$	0.404101	0.0216621
$349$	21.9179	1.17324	0.586620	−	0.809863i	$-0.300458\pi$
$349$	21.9179	1.17324	0.586620	+	0.809863i	$0.300458\pi$
$350$	19.4375	1.03898
$351$	−9.99173	−0.533319
$352$	−7.11273	−0.379110
$353$	−11.0621	−0.588774	−0.294387	−	0.955686i	$-0.595115\pi$
$353$	−11.0621	−0.588774	−0.294387	+	0.955686i	$0.595115\pi$
$354$	1.67303	0.0889206
$355$	−35.0325	−1.85933
$356$	−10.4154	−0.552014
$357$	1.10344	0.0584000
$358$	23.8673	1.26143
$359$	−36.4754	−1.92510	−0.962549	−	0.271109i	$-0.912610\pi$
$359$	−36.4754	−1.92510	−0.962549	+	0.271109i	$0.912610\pi$
$360$	−7.35692	−0.387744
$361$	0.0763944	0.00402076
$362$	3.03341	0.159432
$363$	−0.403145	−0.0211596
$364$	−17.8324	−0.934670
$365$	−25.8981	−1.35557
$366$	−1.74968	−0.0914575
$367$	19.5658	1.02133	0.510664	−	0.859780i	$-0.329399\pi$
$367$	19.5658	1.02133	0.510664	+	0.859780i	$0.329399\pi$
$368$	32.1719	1.67708
$369$	−18.4721	−0.961618
$370$	61.0006	3.17127
$371$	8.19474	0.425449
$372$	−5.07406	−0.263078
$373$	−4.21415	−0.218200	−0.109100	−	0.994031i	$-0.534797\pi$
$373$	−4.21415	−0.218200	−0.109100	+	0.994031i	$0.534797\pi$
$374$	−1.88003	−0.0972139
$375$	−1.46029	−0.0754090
$376$	−7.47659	−0.385576
$377$	2.77343	0.142839
$378$	12.1098	0.622860
$379$	−31.2283	−1.60409	−0.802045	−	0.597263i	$-0.796255\pi$
$379$	−31.2283	−1.60409	−0.802045	+	0.597263i	$0.796255\pi$
$380$	−19.8563	−1.01861
$381$	2.20675	0.113055
$382$	21.4245	1.09617
$383$	3.90734	0.199656	0.0998279	−	0.995005i	$-0.468171\pi$
$383$	3.90734	0.199656	0.0998279	+	0.995005i	$0.468171\pi$
$384$	−2.74604	−0.140133
$385$	−8.10902	−0.413274
$386$	−19.7350	−1.00449
$387$	2.83747	0.144237
$388$	7.09538	0.360213
$389$	2.18848	0.110960	0.0554802	−	0.998460i	$-0.482331\pi$
$389$	2.18848	0.110960	0.0554802	+	0.998460i	$0.482331\pi$
$390$	−9.53371	−0.482758
$391$	6.82432	0.345121
$392$	−0.430196	−0.0217282
$393$	5.01255	0.252850
$394$	37.3334	1.88083
$395$	46.2742	2.32831
$396$	−4.35411	−0.218802
$397$	14.8586	0.745732	0.372866	−	0.927885i	$-0.378375\pi$
$397$	14.8586	0.745732	0.372866	+	0.927885i	$0.378375\pi$
$398$	14.3405	0.718825
$399$	−4.81943	−0.241273
$400$	−17.8077	−0.890384
$401$	14.4459	0.721396	0.360698	−	0.932683i	$-0.382539\pi$
$401$	14.4459	0.721396	0.360698	+	0.932683i	$0.382539\pi$
$402$	−10.5259	−0.524984
$403$	−34.8243	−1.73472
$404$	−14.1731	−0.705139
$405$	−22.4086	−1.11349
$406$	−3.36134	−0.166821
$407$	−10.9519	−0.542863
$408$	−0.352812	−0.0174668
$409$	1.57161	0.0777114	0.0388557	−	0.999245i	$-0.487629\pi$
$409$	1.57161	0.0777114	0.0388557	+	0.999245i	$0.487629\pi$
$410$	−36.2602	−1.79076
$411$	0.700770	0.0345664
$412$	23.2105	1.14350
$413$	−6.04179	−0.297297
$414$	36.4045	1.78918
$415$	−32.4887	−1.59481
$416$	30.1989	1.48062
$417$	7.45604	0.365124
$418$	8.21131	0.401628
$419$	21.0944	1.03053	0.515265	−	0.857031i	$-0.327693\pi$
$419$	21.0944	1.03053	0.515265	+	0.857031i	$0.327693\pi$
$420$	5.01645	0.244778
$421$	−17.6809	−0.861716	−0.430858	−	0.902420i	$-0.641789\pi$
$421$	−17.6809	−0.861716	−0.430858	+	0.902420i	$0.641789\pi$
$422$	−9.51143	−0.463009
$423$	−24.2412	−1.17865
$424$	−2.62018	−0.127247
$425$	−3.77737	−0.183229
$426$	−8.96218	−0.434219
$427$	6.31861	0.305779
$428$	9.24388	0.446820
$429$	1.71165	0.0826394
$430$	5.56989	0.268604
$431$	26.9285	1.29710	0.648551	−	0.761171i	$-0.275375\pi$
$431$	26.9285	1.29710	0.648551	+	0.761171i	$0.275375\pi$
$432$	−11.0944	−0.533779
$433$	−35.5925	−1.71047	−0.855233	−	0.518244i	$-0.826586\pi$
$433$	−35.5925	−1.71047	−0.855233	+	0.518244i	$0.826586\pi$
$434$	42.2063	2.02597
$435$	−0.780199	−0.0374077
$436$	−18.1582	−0.869621
$437$	−29.8063	−1.42583
$438$	−6.62538	−0.316573
$439$	7.48768	0.357367	0.178684	−	0.983907i	$-0.442816\pi$
$439$	7.48768	0.357367	0.178684	+	0.983907i	$0.442816\pi$
$440$	2.59277	0.123606
$441$	−1.39481	−0.0664197
$442$	7.98214	0.379671
$443$	−15.5987	−0.741117	−0.370559	−	0.928809i	$-0.620834\pi$
$443$	−15.5987	−0.741117	−0.370559	+	0.928809i	$0.620834\pi$
$444$	6.77510	0.321532
$445$	20.1090	0.953257
$446$	17.0320	0.806486
$447$	−7.51130	−0.355272
$448$	−10.7937	−0.509953
$449$	5.30996	0.250592	0.125296	−	0.992119i	$-0.460012\pi$
$449$	5.30996	0.250592	0.125296	+	0.992119i	$0.460012\pi$
$450$	−20.1505	−0.949902
$451$	6.51004	0.306546
$452$	−7.01025	−0.329735
$453$	−4.43233	−0.208249
$454$	−5.18676	−0.243427
$455$	34.4289	1.61405
$456$	1.54096	0.0721620
$457$	−17.3625	−0.812184	−0.406092	−	0.913832i	$-0.633109\pi$
$457$	−17.3625	−0.812184	−0.406092	+	0.913832i	$0.633109\pi$
$458$	−28.2510	−1.32008
$459$	−2.35335	−0.109845
$460$	31.0248	1.44654
$461$	20.1931	0.940489	0.470244	−	0.882536i	$-0.344166\pi$
$461$	20.1931	0.940489	0.470244	+	0.882536i	$0.344166\pi$
$462$	−2.07449	−0.0965140
$463$	−39.5355	−1.83737	−0.918686	−	0.394988i	$-0.870749\pi$
$463$	−39.5355	−1.83737	−0.918686	+	0.394988i	$0.870749\pi$
$464$	3.07950	0.142962
$465$	9.79648	0.454301
$466$	49.9794	2.31525
$467$	−11.1093	−0.514079	−0.257039	−	0.966401i	$-0.582747\pi$
$467$	−11.1093	−0.514079	−0.257039	+	0.966401i	$0.582747\pi$
$468$	18.4865	0.854538
$469$	38.0120	1.75523
$470$	−47.5848	−2.19492
$471$	6.97778	0.321519
$472$	1.93180	0.0889181
$473$	−1.00000	−0.0459800
$474$	11.8381	0.543741
$475$	16.4982	0.756991
$476$	−4.20004	−0.192509
$477$	−8.49534	−0.388975
$478$	3.77938	0.172865
$479$	3.73070	0.170460	0.0852300	−	0.996361i	$-0.472837\pi$
$479$	3.73070	0.170460	0.0852300	+	0.996361i	$0.472837\pi$
$480$	−8.49531	−0.387756
$481$	46.4989	2.12017
$482$	28.5651	1.30111
$483$	7.53020	0.342636
$484$	1.53450	0.0697501
$485$	−13.6991	−0.622042
$486$	−19.0058	−0.862118
$487$	37.0435	1.67860	0.839300	−	0.543669i	$-0.182965\pi$
$487$	37.0435	1.67860	0.839300	+	0.543669i	$0.182965\pi$
$488$	−2.02030	−0.0914549
$489$	−3.62816	−0.164071
$490$	−2.73798	−0.123689
$491$	−29.0353	−1.31034	−0.655171	−	0.755480i	$-0.727404\pi$
$491$	−29.0353	−1.31034	−0.655171	+	0.755480i	$0.727404\pi$
$492$	−4.02728	−0.181564
$493$	0.653224	0.0294197
$494$	−34.8632	−1.56857
$495$	8.40648	0.377843
$496$	−38.6674	−1.73622
$497$	32.3650	1.45177
$498$	−8.31142	−0.372443
$499$	−26.8577	−1.20232	−0.601158	−	0.799131i	$-0.705294\pi$
$499$	−26.8577	−1.20232	−0.601158	+	0.799131i	$0.705294\pi$
$500$	5.55835	0.248577
$501$	−4.96250	−0.221708
$502$	−1.74931	−0.0780757
$503$	−33.9614	−1.51426	−0.757132	−	0.653262i	$-0.773400\pi$
$503$	−33.9614	−1.51426	−0.757132	+	0.653262i	$0.773400\pi$
$504$	6.79674	0.302751
$505$	27.3641	1.21768
$506$	−12.8299	−0.570359
$507$	−2.02638	−0.0899948
$508$	−8.39963	−0.372673
$509$	10.8491	0.480876	0.240438	−	0.970665i	$-0.422709\pi$
$509$	10.8491	0.480876	0.240438	+	0.970665i	$0.422709\pi$
$510$	−2.24547	−0.0994310
$511$	23.9261	1.05843
$512$	25.2801	1.11724
$513$	10.2786	0.453811
$514$	39.3264	1.73461
$515$	−44.8126	−1.97468
$516$	0.618626	0.0272335
$517$	8.54322	0.375731
$518$	−56.3557	−2.47613
$519$	−2.96513	−0.130155
$520$	−11.0083	−0.482745
$521$	9.15584	0.401125	0.200562	−	0.979681i	$-0.435723\pi$
$521$	9.15584	0.401125	0.200562	+	0.979681i	$0.435723\pi$
$522$	3.48464	0.152519
$523$	−35.7727	−1.56423	−0.782115	−	0.623134i	$-0.785859\pi$
$523$	−35.7727	−1.56423	−0.782115	+	0.623134i	$0.785859\pi$
$524$	−19.0794	−0.833488
$525$	−4.16808	−0.181910
$526$	41.8536	1.82490
$527$	−8.20214	−0.357291
$528$	1.90055	0.0827107
$529$	23.5713	1.02484
$530$	−16.6761	−0.724364
$531$	6.26341	0.271809
$532$	18.3443	0.795328
$533$	−27.6401	−1.19722
$534$	5.14438	0.222619
$535$	−17.8472	−0.771600
$536$	−12.1539	−0.524969
$537$	−5.11800	−0.220858
$538$	55.1468	2.37755
$539$	0.491569	0.0211734
$540$	−10.6988	−0.460403
$541$	29.8496	1.28333	0.641667	−	0.766984i	$-0.278243\pi$
$541$	29.8496	1.28333	0.641667	+	0.766984i	$0.278243\pi$
$542$	11.2839	0.484683
$543$	−0.650470	−0.0279143
$544$	7.11273	0.304956
$545$	35.0581	1.50172
$546$	8.80778	0.376938
$547$	42.7151	1.82637	0.913183	−	0.407550i	$-0.133617\pi$
$547$	42.7151	1.82637	0.913183	+	0.407550i	$0.133617\pi$
$548$	−2.66736	−0.113944
$549$	−6.55038	−0.279564
$550$	7.10155	0.302811
$551$	−2.85306	−0.121544
$552$	−2.40770	−0.102478
$553$	−42.7507	−1.81794
$554$	14.5684	0.618954
$555$	−13.0807	−0.555244
$556$	−28.3802	−1.20359
$557$	18.8125	0.797111	0.398555	−	0.917144i	$-0.369512\pi$
$557$	18.8125	0.797111	0.398555	+	0.917144i	$0.369512\pi$
$558$	−43.7545	−1.85228
$559$	4.24576	0.179576
$560$	38.2284	1.61545
$561$	0.403145	0.0170208
$562$	−53.4228	−2.25350
$563$	−42.1412	−1.77604	−0.888020	−	0.459806i	$-0.847919\pi$
$563$	−42.1412	−1.77604	−0.888020	+	0.459806i	$0.847919\pi$
$564$	−5.28506	−0.222541
$565$	13.5347	0.569409
$566$	−31.0127	−1.30356
$567$	20.7024	0.869417
$568$	−10.3483	−0.434207
$569$	18.1684	0.761658	0.380829	−	0.924646i	$-0.375639\pi$
$569$	18.1684	0.761658	0.380829	+	0.924646i	$0.375639\pi$
$570$	9.80743	0.410788
$571$	−36.1928	−1.51462	−0.757310	−	0.653055i	$-0.773487\pi$
$571$	−36.1928	−1.51462	−0.757310	+	0.653055i	$0.773487\pi$
$572$	−6.51512	−0.272411
$573$	−4.59418	−0.191925
$574$	33.4992	1.39823
$575$	−25.7780	−1.07502
$576$	11.1896	0.466233
$577$	−24.9745	−1.03970	−0.519851	−	0.854257i	$-0.674013\pi$
$577$	−24.9745	−1.03970	−0.519851	+	0.854257i	$0.674013\pi$
$578$	1.88003	0.0781988
$579$	4.23189	0.175871
$580$	2.96969	0.123310
$581$	30.0149	1.24523
$582$	−3.50456	−0.145269
$583$	2.99398	0.123998
$584$	−7.65012	−0.316564
$585$	−35.6919	−1.47568
$586$	−5.39710	−0.222952
$587$	−30.1862	−1.24592	−0.622959	−	0.782255i	$-0.714070\pi$
$587$	−30.1862	−1.24592	−0.622959	+	0.782255i	$0.714070\pi$
$588$	−0.304097	−0.0125408
$589$	35.8241	1.47611
$590$	12.2949	0.506173
$591$	−8.00561	−0.329307
$592$	51.6304	2.12200
$593$	−23.1145	−0.949197	−0.474599	−	0.880202i	$-0.657407\pi$
$593$	−23.1145	−0.949197	−0.474599	+	0.880202i	$0.657407\pi$
$594$	4.42435	0.181533
$595$	8.10902	0.332438
$596$	28.5905	1.17111
$597$	−3.07511	−0.125856
$598$	54.4726	2.22755
$599$	19.2784	0.787692	0.393846	−	0.919176i	$-0.371144\pi$
$599$	19.2784	0.787692	0.393846	+	0.919176i	$0.371144\pi$
$600$	1.33270	0.0544072
$601$	−43.0910	−1.75772	−0.878858	−	0.477083i	$-0.841694\pi$
$601$	−43.0910	−1.75772	−0.878858	+	0.477083i	$0.841694\pi$
$602$	−5.14577	−0.209726
$603$	−39.4063	−1.60475
$604$	16.8709	0.686468
$605$	−2.96266	−0.120449
$606$	7.00041	0.284372
$607$	−21.7338	−0.882147	−0.441073	−	0.897471i	$-0.645402\pi$
$607$	−21.7338	−0.882147	−0.441073	+	0.897471i	$0.645402\pi$
$608$	−31.0659	−1.25989
$609$	0.720791	0.0292079
$610$	−12.8582	−0.520614
$611$	−36.2724	−1.46743
$612$	4.35411	0.176004
$613$	−15.7682	−0.636871	−0.318435	−	0.947945i	$-0.603157\pi$
$613$	−15.7682	−0.636871	−0.318435	+	0.947945i	$0.603157\pi$
$614$	4.23269	0.170818
$615$	7.77547	0.313537
$616$	−2.39535	−0.0965113
$617$	36.6659	1.47612	0.738058	−	0.674738i	$-0.235743\pi$
$617$	36.6659	1.47612	0.738058	+	0.674738i	$0.235743\pi$
$618$	−11.4642	−0.461157
$619$	37.7066	1.51556	0.757779	−	0.652512i	$-0.226285\pi$
$619$	37.7066	1.51556	0.757779	+	0.652512i	$0.226285\pi$
$620$	−37.2886	−1.49755
$621$	−16.0600	−0.644465
$622$	−26.2565	−1.05279
$623$	−18.5778	−0.744304
$624$	−8.06926	−0.323029
$625$	−29.6183	−1.18473
$626$	22.3339	0.892642
$627$	−1.76080	−0.0703194
$628$	−26.5597	−1.05985
$629$	10.9519	0.436679
$630$	43.2578	1.72343
$631$	9.00774	0.358592	0.179296	−	0.983795i	$-0.442618\pi$
$631$	9.00774	0.358592	0.179296	+	0.983795i	$0.442618\pi$
$632$	13.6691	0.543726
$633$	2.03959	0.0810664
$634$	51.6854	2.05269
$635$	16.2172	0.643559
$636$	−1.85215	−0.0734426
$637$	−2.08708	−0.0826932
$638$	−1.22808	−0.0486201
$639$	−33.5522	−1.32730
$640$	−20.1803	−0.797698
$641$	−4.77678	−0.188671	−0.0943357	−	0.995540i	$-0.530073\pi$
$641$	−4.77678	−0.188671	−0.0943357	+	0.995540i	$0.530073\pi$
$642$	−4.56574	−0.180196
$643$	6.58590	0.259722	0.129861	−	0.991532i	$-0.458547\pi$
$643$	6.58590	0.259722	0.129861	+	0.991532i	$0.458547\pi$
$644$	−28.6624	−1.12946
$645$	−1.19438	−0.0470287
$646$	−8.21131	−0.323070
$647$	21.8895	0.860566	0.430283	−	0.902694i	$-0.358414\pi$
$647$	21.8895	0.860566	0.430283	+	0.902694i	$0.358414\pi$
$648$	−6.61935	−0.260033
$649$	−2.20739	−0.0866476
$650$	−30.1515	−1.18264
$651$	−9.05054	−0.354718
$652$	13.8100	0.540841
$653$	12.9951	0.508536	0.254268	−	0.967134i	$-0.418165\pi$
$653$	12.9951	0.508536	0.254268	+	0.967134i	$0.418165\pi$
$654$	8.96872	0.350705
$655$	36.8366	1.43933
$656$	−30.6904	−1.19826
$657$	−24.8038	−0.967688
$658$	43.9615	1.71380
$659$	−16.5121	−0.643220	−0.321610	−	0.946872i	$-0.604224\pi$
$659$	−16.5121	−0.643220	−0.321610	+	0.946872i	$0.604224\pi$
$660$	1.83278	0.0713409
$661$	−31.2854	−1.21686	−0.608430	−	0.793607i	$-0.708201\pi$
$661$	−31.2854	−1.21686	−0.608430	+	0.793607i	$0.708201\pi$
$662$	43.3411	1.68450
$663$	−1.71165	−0.0664751
$664$	−9.59693	−0.372433
$665$	−35.4174	−1.37343
$666$	58.4230	2.26384
$667$	4.45781	0.172607
$668$	18.8889	0.730835
$669$	−3.65226	−0.141204
$670$	−77.3536	−2.98843
$671$	2.30853	0.0891197
$672$	7.84844	0.302760
$673$	22.2091	0.856097	0.428049	−	0.903756i	$-0.359201\pi$
$673$	22.2091	0.856097	0.428049	+	0.903756i	$0.359201\pi$
$674$	−2.95177	−0.113698
$675$	8.88945	0.342155
$676$	7.71308	0.296657
$677$	26.6003	1.02233	0.511167	−	0.859482i	$-0.329213\pi$
$677$	26.6003	1.02233	0.511167	+	0.859482i	$0.329213\pi$
$678$	3.46251	0.132977
$679$	12.6560	0.485691
$680$	−2.59277	−0.0994282
$681$	1.11223	0.0426206
$682$	15.4202	0.590472
$683$	−32.7447	−1.25294	−0.626471	−	0.779445i	$-0.715501\pi$
$683$	−32.7447	−1.25294	−0.626471	+	0.779445i	$0.715501\pi$
$684$	−19.0172	−0.727142
$685$	5.14987	0.196767
$686$	−33.4909	−1.27869
$687$	6.05803	0.231128
$688$	4.71431	0.179731
$689$	−12.7117	−0.484277
$690$	−15.3238	−0.583367
$691$	47.3672	1.80193	0.900967	−	0.433888i	$-0.142859\pi$
$691$	47.3672	1.80193	0.900967	+	0.433888i	$0.142859\pi$
$692$	11.2863	0.429040
$693$	−7.76637	−0.295020
$694$	−34.0684	−1.29322
$695$	54.7935	2.07844
$696$	−0.230465	−0.00873576
$697$	−6.51004	−0.246586
$698$	41.2063	1.55968
$699$	−10.7174	−0.405368
$700$	15.8651	0.599645
$701$	−6.10515	−0.230588	−0.115294	−	0.993331i	$-0.536781\pi$
$701$	−6.10515	−0.230588	−0.115294	+	0.993331i	$0.536781\pi$
$702$	−18.7847	−0.708984
$703$	−47.8339	−1.80409
$704$	−3.94351	−0.148626
$705$	10.2039	0.384300
$706$	−20.7970	−0.782704
$707$	−25.2804	−0.950769
$708$	1.36555	0.0513205
$709$	−20.7459	−0.779130	−0.389565	−	0.920999i	$-0.627375\pi$
$709$	−20.7459	−0.779130	−0.389565	+	0.920999i	$0.627375\pi$
$710$	−65.8620	−2.47176
$711$	44.3189	1.66209
$712$	5.94005	0.222613
$713$	−55.9740	−2.09624
$714$	2.07449	0.0776358
$715$	12.5787	0.470418
$716$	19.4808	0.728032
$717$	−0.810432	−0.0302661
$718$	−68.5747	−2.55919
$719$	12.7555	0.475701	0.237851	−	0.971302i	$-0.423557\pi$
$719$	12.7555	0.475701	0.237851	+	0.971302i	$0.423557\pi$
$720$	−39.6307	−1.47695
$721$	41.4004	1.54183
$722$	0.143624	0.00534512
$723$	−6.12537	−0.227805
$724$	2.47590	0.0920162
$725$	−2.46747	−0.0916395
$726$	−0.757923	−0.0281291
$727$	−12.4673	−0.462386	−0.231193	−	0.972908i	$-0.574263\pi$
$727$	−12.4673	−0.462386	−0.231193	+	0.972908i	$0.574263\pi$
$728$	10.1701	0.376927
$729$	−18.6155	−0.689465
$730$	−48.6892	−1.80207
$731$	1.00000	0.0369863
$732$	−1.42811	−0.0527846
$733$	17.0673	0.630395	0.315197	−	0.949026i	$-0.397929\pi$
$733$	17.0673	0.630395	0.315197	+	0.949026i	$0.397929\pi$
$734$	36.7843	1.35773
$735$	0.587121	0.0216563
$736$	48.5395	1.78919
$737$	13.8878	0.511565
$738$	−34.7280	−1.27836
$739$	31.4318	1.15624	0.578119	−	0.815952i	$-0.303787\pi$
$739$	31.4318	1.15624	0.578119	+	0.815952i	$0.303787\pi$
$740$	49.7894	1.83030
$741$	7.47591	0.274634
$742$	15.4063	0.565584
$743$	−17.8009	−0.653050	−0.326525	−	0.945188i	$-0.605878\pi$
$743$	−17.8009	−0.653050	−0.326525	+	0.945188i	$0.605878\pi$
$744$	2.89381	0.106092
$745$	−55.1997	−2.02236
$746$	−7.92271	−0.290071
$747$	−31.1159	−1.13847
$748$	−1.53450	−0.0561069
$749$	16.4882	0.602466
$750$	−2.74538	−0.100247
$751$	10.8525	0.396012	0.198006	−	0.980201i	$-0.436554\pi$
$751$	10.8525	0.396012	0.198006	+	0.980201i	$0.436554\pi$
$752$	−40.2754	−1.46869
$753$	0.375115	0.0136700
$754$	5.21412	0.189887
$755$	−32.5727	−1.18544
$756$	9.88416	0.359483
$757$	25.9980	0.944912	0.472456	−	0.881354i	$-0.343368\pi$
$757$	25.9980	0.944912	0.472456	+	0.881354i	$0.343368\pi$
$758$	−58.7101	−2.13245
$759$	2.75119	0.0998618
$760$	11.3243	0.410776
$761$	2.18692	0.0792757	0.0396379	−	0.999214i	$-0.487380\pi$
$761$	2.18692	0.0792757	0.0396379	+	0.999214i	$0.487380\pi$
$762$	4.14876	0.150294
$763$	−32.3886	−1.17255
$764$	17.4870	0.632656
$765$	−8.40648	−0.303937
$766$	7.34591	0.265418
$767$	9.37204	0.338405
$768$	−8.34224	−0.301025
$769$	−8.86196	−0.319571	−0.159785	−	0.987152i	$-0.551080\pi$
$769$	−8.86196	−0.319571	−0.159785	+	0.987152i	$0.551080\pi$
$770$	−15.2452	−0.549398
$771$	−8.43297	−0.303706
$772$	−16.1080	−0.579739
$773$	25.0606	0.901368	0.450684	−	0.892684i	$-0.351180\pi$
$773$	25.0606	0.901368	0.450684	+	0.892684i	$0.351180\pi$
$774$	5.33453	0.191746
$775$	30.9825	1.11292
$776$	−4.04660	−0.145265
$777$	12.0847	0.433535
$778$	4.11440	0.147508
$779$	28.4336	1.01874
$780$	−7.78154	−0.278624
$781$	11.8247	0.423120
$782$	12.8299	0.458796
$783$	−1.53726	−0.0549373
$784$	−2.31741	−0.0827645
$785$	51.2789	1.83022
$786$	9.42372	0.336133
$787$	−31.9856	−1.14016	−0.570081	−	0.821589i	$-0.693088\pi$
$787$	−31.9856	−1.14016	−0.570081	+	0.821589i	$0.693088\pi$
$788$	30.4720	1.08552
$789$	−8.97489	−0.319515
$790$	86.9967	3.09520
$791$	−12.5041	−0.444595
$792$	2.48321	0.0882372
$793$	−9.80144	−0.348059
$794$	27.9346	0.991361
$795$	3.57595	0.126826
$796$	11.7049	0.414869
$797$	−27.4137	−0.971044	−0.485522	−	0.874224i	$-0.661370\pi$
$797$	−27.4137	−0.971044	−0.485522	+	0.874224i	$0.661370\pi$
$798$	−9.06065	−0.320744
$799$	−8.54322	−0.302237
$800$	−26.8674	−0.949905
$801$	19.2593	0.680493
$802$	27.1588	0.959009
$803$	8.74150	0.308481
$804$	−8.59137	−0.302994
$805$	55.3386	1.95043
$806$	−65.4706	−2.30610
$807$	−11.8254	−0.416275
$808$	8.08315	0.284364
$809$	32.9418	1.15817	0.579086	−	0.815266i	$-0.303409\pi$
$809$	32.9418	1.15817	0.579086	+	0.815266i	$0.303409\pi$
$810$	−42.1289	−1.48026
$811$	52.6925	1.85028	0.925142	−	0.379622i	$-0.123946\pi$
$811$	52.6925	1.85028	0.925142	+	0.379622i	$0.123946\pi$
$812$	−2.74357	−0.0962804
$813$	−2.41966	−0.0848612
$814$	−20.5898	−0.721671
$815$	−26.6630	−0.933963
$816$	−1.90055	−0.0665325
$817$	−4.36765	−0.152805
$818$	2.95468	0.103308
$819$	32.9741	1.15221
$820$	−29.5960	−1.03354
$821$	54.4728	1.90111	0.950557	−	0.310550i	$-0.100513\pi$
$821$	54.4728	1.90111	0.950557	+	0.310550i	$0.100513\pi$
$822$	1.31747	0.0459519
$823$	39.9327	1.39197	0.695983	−	0.718058i	$-0.254969\pi$
$823$	39.9327	1.39197	0.695983	+	0.718058i	$0.254969\pi$
$824$	−13.2373	−0.461144
$825$	−1.52282	−0.0530180
$826$	−11.3587	−0.395221
$827$	−56.3943	−1.96102	−0.980510	−	0.196468i	$-0.937053\pi$
$827$	−56.3943	−1.96102	−0.980510	+	0.196468i	$0.937053\pi$
$828$	29.7138	1.03263
$829$	32.5819	1.13161	0.565807	−	0.824537i	$-0.308565\pi$
$829$	32.5819	1.13161	0.565807	+	0.824537i	$0.308565\pi$
$830$	−61.0796	−2.12010
$831$	−3.12399	−0.108370
$832$	16.7432	0.580465
$833$	−0.491569	−0.0170319
$834$	14.0176	0.485388
$835$	−36.4688	−1.26206
$836$	6.70217	0.231799
$837$	19.3025	0.667191
$838$	39.6581	1.36997
$839$	−1.70542	−0.0588775	−0.0294387	−	0.999567i	$-0.509372\pi$
$839$	−1.70542	−0.0588775	−0.0294387	+	0.999567i	$0.509372\pi$
$840$	−2.86096	−0.0987124
$841$	−28.5733	−0.985286
$842$	−33.2406	−1.14555
$843$	11.4557	0.394557
$844$	−7.76335	−0.267226
$845$	−14.8917	−0.512288
$846$	−45.5741	−1.56687
$847$	2.73707	0.0940469
$848$	−14.1145	−0.484695
$849$	6.65023	0.228235
$850$	−7.10155	−0.243581
$851$	74.7389	2.56202
$852$	−7.31505	−0.250609
$853$	16.2093	0.554995	0.277497	−	0.960726i	$-0.410495\pi$
$853$	16.2093	0.554995	0.277497	+	0.960726i	$0.410495\pi$
$854$	11.8791	0.406496
$855$	36.7166	1.25568
$856$	−5.27192	−0.180191
$857$	39.1411	1.33704	0.668518	−	0.743696i	$-0.266929\pi$
$857$	39.1411	1.33704	0.668518	+	0.743696i	$0.266929\pi$
$858$	3.21795	0.109859
$859$	−24.9664	−0.851842	−0.425921	−	0.904760i	$-0.640050\pi$
$859$	−24.9664	−0.851842	−0.425921	+	0.904760i	$0.640050\pi$
$860$	4.54621	0.155024
$861$	−7.18342	−0.244810
$862$	50.6264	1.72434
$863$	35.6366	1.21308	0.606541	−	0.795052i	$-0.292556\pi$
$863$	35.6366	1.21308	0.606541	+	0.795052i	$0.292556\pi$
$864$	−16.7387	−0.569462
$865$	−21.7904	−0.740896
$866$	−66.9149	−2.27386
$867$	−0.403145	−0.0136915
$868$	34.4493	1.16929
$869$	−15.6191	−0.529843
$870$	−1.46679	−0.0497290
$871$	−58.9643	−1.99793
$872$	10.3559	0.350695
$873$	−13.1202	−0.444051
$874$	−56.0366	−1.89547
$875$	9.91436	0.335166
$876$	−5.40772	−0.182710
$877$	−29.0725	−0.981709	−0.490855	−	0.871241i	$-0.663315\pi$
$877$	−29.0725	−0.981709	−0.490855	+	0.871241i	$0.663315\pi$
$878$	14.0770	0.475077
$879$	1.15733	0.0390358
$880$	13.9669	0.470824
$881$	51.3230	1.72912	0.864558	−	0.502532i	$-0.167598\pi$
$881$	51.3230	1.72912	0.864558	+	0.502532i	$0.167598\pi$
$882$	−2.62229	−0.0882971
$883$	38.1435	1.28363	0.641815	−	0.766860i	$-0.278182\pi$
$883$	38.1435	1.28363	0.641815	+	0.766860i	$0.278182\pi$
$884$	6.51512	0.219127
$885$	−2.63647	−0.0886238
$886$	−29.3260	−0.985226
$887$	5.94737	0.199693	0.0998465	−	0.995003i	$-0.468165\pi$
$887$	5.94737	0.199693	0.0998465	+	0.995003i	$0.468165\pi$
$888$	−3.86394	−0.129665
$889$	−14.9823	−0.502491
$890$	37.8054	1.26724
$891$	7.56368	0.253393
$892$	13.9017	0.465463
$893$	37.3138	1.24866
$894$	−14.1215	−0.472292
$895$	−37.6116	−1.25722
$896$	18.6437	0.622843
$897$	−11.6809	−0.390013
$898$	9.98286	0.333132
$899$	−5.35784	−0.178694
$900$	−16.4471	−0.548236
$901$	−2.99398	−0.0997439
$902$	12.2391	0.407516
$903$	1.10344	0.0367201
$904$	3.99805	0.132973
$905$	−4.78023	−0.158900
$906$	−8.33291	−0.276842
$907$	57.4890	1.90889	0.954445	−	0.298386i	$-0.0964482\pi$
$907$	57.4890	1.90889	0.954445	+	0.298386i	$0.0964482\pi$
$908$	−4.23350	−0.140494
$909$	26.2078	0.869257
$910$	64.7273	2.14569
$911$	38.1263	1.26318	0.631590	−	0.775302i	$-0.282402\pi$
$911$	38.1263	1.26318	0.631590	+	0.775302i	$0.282402\pi$
$912$	8.30093	0.274871
$913$	10.9660	0.362923
$914$	−32.6420	−1.07970
$915$	2.75726	0.0911522
$916$	−23.0589	−0.761886
$917$	−34.0317	−1.12383
$918$	−4.42435	−0.146025
$919$	20.2603	0.668325	0.334163	−	0.942515i	$-0.391547\pi$
$919$	20.2603	0.668325	0.334163	+	0.942515i	$0.391547\pi$
$920$	−17.6939	−0.583351
$921$	−0.907640	−0.0299077
$922$	37.9637	1.25027
$923$	−50.2046	−1.65251
$924$	−1.69322	−0.0557030
$925$	−41.3692	−1.36021
$926$	−74.3279	−2.44257
$927$	−42.9190	−1.40965
$928$	4.64621	0.152519
$929$	−16.9861	−0.557295	−0.278647	−	0.960394i	$-0.589886\pi$
$929$	−16.9861	−0.557295	−0.278647	+	0.960394i	$0.589886\pi$
$930$	18.4176	0.603938
$931$	2.14700	0.0703652
$932$	40.7938	1.33625
$933$	5.63032	0.184329
$934$	−20.8859	−0.683406
$935$	2.96266	0.0968894
$936$	−10.5431	−0.344613
$937$	3.81588	0.124659	0.0623296	−	0.998056i	$-0.480147\pi$
$937$	3.81588	0.124659	0.0623296	+	0.998056i	$0.480147\pi$
$938$	71.4636	2.33337
$939$	−4.78918	−0.156289
$940$	−38.8393	−1.26680
$941$	−16.4940	−0.537690	−0.268845	−	0.963183i	$-0.586642\pi$
$941$	−16.4940	−0.537690	−0.268845	+	0.963183i	$0.586642\pi$
$942$	13.1184	0.427421
$943$	−44.4266	−1.44673
$944$	10.4063	0.338697
$945$	−19.0833	−0.620781
$946$	−1.88003	−0.0611250
$947$	−15.3546	−0.498957	−0.249479	−	0.968380i	$-0.580259\pi$
$947$	−15.3546	−0.498957	−0.249479	+	0.968380i	$0.580259\pi$
$948$	9.66240	0.313820
$949$	−37.1143	−1.20478
$950$	31.0171	1.00633
$951$	−11.0832	−0.359397
$952$	2.39535	0.0776337
$953$	15.1796	0.491715	0.245858	−	0.969306i	$-0.420930\pi$
$953$	15.1796	0.491715	0.245858	+	0.969306i	$0.420930\pi$
$954$	−15.9715	−0.517095
$955$	−33.7621	−1.09252
$956$	3.08477	0.0997687
$957$	0.263344	0.00851270
$958$	7.01382	0.226606
$959$	−4.75774	−0.153635
$960$	−4.71005	−0.152016
$961$	36.2751	1.17016
$962$	87.4192	2.81851
$963$	−17.0930	−0.550815
$964$	23.3152	0.750932
$965$	31.0997	1.00113
$966$	14.1570	0.455493
$967$	44.8990	1.44385	0.721927	−	0.691969i	$-0.243257\pi$
$967$	44.8990	1.44385	0.721927	+	0.691969i	$0.243257\pi$
$968$	−0.875149	−0.0281284
$969$	1.76080	0.0565649
$970$	−25.7546	−0.826930
$971$	−37.4722	−1.20254	−0.601269	−	0.799046i	$-0.705338\pi$
$971$	−37.4722	−1.20254	−0.601269	+	0.799046i	$0.705338\pi$
$972$	−15.5127	−0.497571
$973$	−50.6213	−1.62285
$974$	69.6427	2.23150
$975$	6.46554	0.207063
$976$	−10.8831	−0.348360
$977$	−5.94305	−0.190135	−0.0950676	−	0.995471i	$-0.530307\pi$
$977$	−5.94305	−0.190135	−0.0950676	+	0.995471i	$0.530307\pi$
$978$	−6.82105	−0.218113
$979$	−6.78747	−0.216928
$980$	−2.23478	−0.0713873
$981$	33.5767	1.07202
$982$	−54.5871	−1.74194
$983$	−60.1349	−1.91801	−0.959003	−	0.283395i	$-0.908539\pi$
$983$	−60.1349	−1.91801	−0.959003	+	0.283395i	$0.908539\pi$
$984$	2.29682	0.0732199
$985$	−58.8323	−1.87455
$986$	1.22808	0.0391100
$987$	−9.42690	−0.300062
$988$	−28.4558	−0.905299
$989$	6.82432	0.217001
$990$	15.8044	0.502297
$991$	−24.5031	−0.778366	−0.389183	−	0.921160i	$-0.627243\pi$
$991$	−24.5031	−0.778366	−0.389183	+	0.921160i	$0.627243\pi$
$992$	−58.3396	−1.85228
$993$	−9.29386	−0.294932
$994$	60.8470	1.92995
$995$	−22.5987	−0.716426
$996$	−6.78388	−0.214956
$997$	40.0773	1.26926	0.634630	−	0.772816i	$-0.281152\pi$
$997$	40.0773	1.26926	0.634630	+	0.772816i	$0.281152\pi$
$998$	−50.4932	−1.59833
$999$	−25.7735	−0.815437

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8041.2.a.i.1.61	✓	78

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8041.2.a.i.1.61	✓	78	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:	\( N \)	\(=\)	\( 8041 = 11 \cdot 17 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8041.a (trivial)

\(f(q)\)	\(=\)	\(q+1.88003 q^{2} -0.403145 q^{3} +1.53450 q^{4} -2.96266 q^{5} -0.757923 q^{6} +2.73707 q^{7} -0.875149 q^{8} -2.83747 q^{9} +O(q^{10})\)	\(q+1.88003 q^{2} -0.403145 q^{3} +1.53450 q^{4} -2.96266 q^{5} -0.757923 q^{6} +2.73707 q^{7} -0.875149 q^{8} -2.83747 q^{9} -5.56989 q^{10} +1.00000 q^{11} -0.618626 q^{12} -4.24576 q^{13} +5.14577 q^{14} +1.19438 q^{15} -4.71431 q^{16} -1.00000 q^{17} -5.33453 q^{18} +4.36765 q^{19} -4.54621 q^{20} -1.10344 q^{21} +1.88003 q^{22} -6.82432 q^{23} +0.352812 q^{24} +3.77737 q^{25} -7.98214 q^{26} +2.35335 q^{27} +4.20004 q^{28} -0.653224 q^{29} +2.24547 q^{30} +8.20214 q^{31} -7.11273 q^{32} -0.403145 q^{33} -1.88003 q^{34} -8.10902 q^{35} -4.35411 q^{36} -10.9519 q^{37} +8.21131 q^{38} +1.71165 q^{39} +2.59277 q^{40} +6.51004 q^{41} -2.07449 q^{42} -1.00000 q^{43} +1.53450 q^{44} +8.40648 q^{45} -12.8299 q^{46} +8.54322 q^{47} +1.90055 q^{48} +0.491569 q^{49} +7.10155 q^{50} +0.403145 q^{51} -6.51512 q^{52} +2.99398 q^{53} +4.42435 q^{54} -2.96266 q^{55} -2.39535 q^{56} -1.76080 q^{57} -1.22808 q^{58} -2.20739 q^{59} +1.83278 q^{60} +2.30853 q^{61} +15.4202 q^{62} -7.76637 q^{63} -3.94351 q^{64} +12.5787 q^{65} -0.757923 q^{66} +13.8878 q^{67} -1.53450 q^{68} +2.75119 q^{69} -15.2452 q^{70} +11.8247 q^{71} +2.48321 q^{72} +8.74150 q^{73} -20.5898 q^{74} -1.52282 q^{75} +6.70217 q^{76} +2.73707 q^{77} +3.21795 q^{78} -15.6191 q^{79} +13.9669 q^{80} +7.56368 q^{81} +12.2391 q^{82} +10.9660 q^{83} -1.69322 q^{84} +2.96266 q^{85} -1.88003 q^{86} +0.263344 q^{87} -0.875149 q^{88} -6.78747 q^{89} +15.8044 q^{90} -11.6209 q^{91} -10.4719 q^{92} -3.30665 q^{93} +16.0615 q^{94} -12.9399 q^{95} +2.86746 q^{96} +4.62390 q^{97} +0.924163 q^{98} -2.83747 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 78 q + 7 q^{2} + 10 q^{3} + 91 q^{4} + 17 q^{5} + 12 q^{6} + 11 q^{7} + 33 q^{8} + 102 q^{9}+O(q^{10}) \) 78 * q + 7 * q^2 + 10 * q^3 + 91 * q^4 + 17 * q^5 + 12 * q^6 + 11 * q^7 + 33 * q^8 + 102 * q^9	\( 78 q + 7 q^{2} + 10 q^{3} + 91 q^{4} + 17 q^{5} + 12 q^{6} + 11 q^{7} + 33 q^{8} + 102 q^{9} + 3 q^{10} + 78 q^{11} + 31 q^{12} - 16 q^{13} + 31 q^{14} + 38 q^{15} + 121 q^{16} - 78 q^{17} + 11 q^{18} + 51 q^{20} + 6 q^{21} + 7 q^{22} + 48 q^{23} + 11 q^{24} + 101 q^{25} + 18 q^{26} + 46 q^{27} + 27 q^{28} + 22 q^{29} + 14 q^{30} + 56 q^{31} + 83 q^{32} + 10 q^{33} - 7 q^{34} + 24 q^{35} + 139 q^{36} + 53 q^{37} + 10 q^{38} + 79 q^{39} - q^{40} + 23 q^{41} + 17 q^{42} - 78 q^{43} + 91 q^{44} + 76 q^{45} + 21 q^{46} + 57 q^{47} + 78 q^{48} + 115 q^{49} + 58 q^{50} - 10 q^{51} - 63 q^{52} + 22 q^{53} - 18 q^{54} + 17 q^{55} + 111 q^{56} - 11 q^{57} + 36 q^{58} + 71 q^{59} + 36 q^{60} + 4 q^{61} - 5 q^{62} + 71 q^{63} + 183 q^{64} + 47 q^{65} + 12 q^{66} + 11 q^{67} - 91 q^{68} + 31 q^{69} + 33 q^{70} + 159 q^{71} + 59 q^{72} + 2 q^{73} - 4 q^{74} + 83 q^{75} - 44 q^{76} + 11 q^{77} + 101 q^{78} + 35 q^{79} + 85 q^{80} + 170 q^{81} + 98 q^{82} - 32 q^{83} + 44 q^{84} - 17 q^{85} - 7 q^{86} - 6 q^{87} + 33 q^{88} + 50 q^{89} - 5 q^{90} + 86 q^{91} + 106 q^{92} + 68 q^{93} - q^{94} + 109 q^{95} - 50 q^{96} + 40 q^{97} + 106 q^{98} + 102 q^{99}+O(q^{100}) \) 78 * q + 7 * q^2 + 10 * q^3 + 91 * q^4 + 17 * q^5 + 12 * q^6 + 11 * q^7 + 33 * q^8 + 102 * q^9 + 3 * q^10 + 78 * q^11 + 31 * q^12 - 16 * q^13 + 31 * q^14 + 38 * q^15 + 121 * q^16 - 78 * q^17 + 11 * q^18 + 51 * q^20 + 6 * q^21 + 7 * q^22 + 48 * q^23 + 11 * q^24 + 101 * q^25 + 18 * q^26 + 46 * q^27 + 27 * q^28 + 22 * q^29 + 14 * q^30 + 56 * q^31 + 83 * q^32 + 10 * q^33 - 7 * q^34 + 24 * q^35 + 139 * q^36 + 53 * q^37 + 10 * q^38 + 79 * q^39 - q^40 + 23 * q^41 + 17 * q^42 - 78 * q^43 + 91 * q^44 + 76 * q^45 + 21 * q^46 + 57 * q^47 + 78 * q^48 + 115 * q^49 + 58 * q^50 - 10 * q^51 - 63 * q^52 + 22 * q^53 - 18 * q^54 + 17 * q^55 + 111 * q^56 - 11 * q^57 + 36 * q^58 + 71 * q^59 + 36 * q^60 + 4 * q^61 - 5 * q^62 + 71 * q^63 + 183 * q^64 + 47 * q^65 + 12 * q^66 + 11 * q^67 - 91 * q^68 + 31 * q^69 + 33 * q^70 + 159 * q^71 + 59 * q^72 + 2 * q^73 - 4 * q^74 + 83 * q^75 - 44 * q^76 + 11 * q^77 + 101 * q^78 + 35 * q^79 + 85 * q^80 + 170 * q^81 + 98 * q^82 - 32 * q^83 + 44 * q^84 - 17 * q^85 - 7 * q^86 - 6 * q^87 + 33 * q^88 + 50 * q^89 - 5 * q^90 + 86 * q^91 + 106 * q^92 + 68 * q^93 - q^94 + 109 * q^95 - 50 * q^96 + 40 * q^97 + 106 * q^98 + 102 * q^99

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