LMFDB - Embedded newform 8041.2.a.h.1.53

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:	$1$
Dimension:	$74$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.53
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)

$f(q)$	$=$	$q+1.34534 q^{2} -2.29674 q^{3} -0.190071 q^{4} -3.94764 q^{5} -3.08989 q^{6} -5.02160 q^{7} -2.94638 q^{8} +2.27502 q^{9} +O(q^{10})$	\(q+1.34534 q^{2} -2.29674 q^{3} -0.190071 q^{4} -3.94764 q^{5} -3.08989 q^{6} -5.02160 q^{7} -2.94638 q^{8} +2.27502 q^{9} -5.31090 q^{10} -1.00000 q^{11} +0.436545 q^{12} -2.87402 q^{13} -6.75573 q^{14} +9.06671 q^{15} -3.58373 q^{16} -1.00000 q^{17} +3.06066 q^{18} +6.17411 q^{19} +0.750334 q^{20} +11.5333 q^{21} -1.34534 q^{22} -4.25047 q^{23} +6.76707 q^{24} +10.5839 q^{25} -3.86652 q^{26} +1.66509 q^{27} +0.954462 q^{28} -2.72997 q^{29} +12.1978 q^{30} -3.69516 q^{31} +1.07144 q^{32} +2.29674 q^{33} -1.34534 q^{34} +19.8235 q^{35} -0.432416 q^{36} +8.93416 q^{37} +8.30626 q^{38} +6.60088 q^{39} +11.6313 q^{40} -6.98910 q^{41} +15.5162 q^{42} -1.00000 q^{43} +0.190071 q^{44} -8.98096 q^{45} -5.71831 q^{46} -0.315812 q^{47} +8.23090 q^{48} +18.2164 q^{49} +14.2389 q^{50} +2.29674 q^{51} +0.546269 q^{52} -9.81199 q^{53} +2.24011 q^{54} +3.94764 q^{55} +14.7955 q^{56} -14.1803 q^{57} -3.67273 q^{58} -5.66297 q^{59} -1.72332 q^{60} -11.8956 q^{61} -4.97124 q^{62} -11.4242 q^{63} +8.60891 q^{64} +11.3456 q^{65} +3.08989 q^{66} +9.17320 q^{67} +0.190071 q^{68} +9.76223 q^{69} +26.6692 q^{70} -15.0595 q^{71} -6.70307 q^{72} +11.1383 q^{73} +12.0194 q^{74} -24.3084 q^{75} -1.17352 q^{76} +5.02160 q^{77} +8.88040 q^{78} +10.7151 q^{79} +14.1473 q^{80} -10.6493 q^{81} -9.40269 q^{82} +10.2363 q^{83} -2.19215 q^{84} +3.94764 q^{85} -1.34534 q^{86} +6.27004 q^{87} +2.94638 q^{88} +16.2578 q^{89} -12.0824 q^{90} +14.4322 q^{91} +0.807893 q^{92} +8.48683 q^{93} -0.424873 q^{94} -24.3732 q^{95} -2.46083 q^{96} +12.5340 q^{97} +24.5072 q^{98} -2.27502 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 74 q - 7 q^{2} - 3 q^{3} + 79 q^{4} - 6 q^{5} - 12 q^{6} - 16 q^{7} - 21 q^{8} + 75 q^{9}+O(q^{10}) $ 74 * q - 7 * q^2 - 3 * q^3 + 79 * q^4 - 6 * q^5 - 12 * q^6 - 16 * q^7 - 21 * q^8 + 75 * q^9	\( 74 q - 7 q^{2} - 3 q^{3} + 79 q^{4} - 6 q^{5} - 12 q^{6} - 16 q^{7} - 21 q^{8} + 75 q^{9} - 9 q^{10} - 74 q^{11} - 3 q^{12} + 4 q^{13} - 5 q^{14} - 17 q^{15} + 85 q^{16} - 74 q^{17} - 23 q^{18} - 21 q^{20} - 22 q^{21} + 7 q^{22} - 23 q^{23} - 51 q^{24} + 90 q^{25} - 46 q^{26} - 27 q^{27} - 61 q^{28} - 63 q^{29} - 22 q^{30} - 31 q^{31} - 69 q^{32} + 3 q^{33} + 7 q^{34} - 20 q^{35} + 51 q^{36} + 8 q^{37} - 2 q^{38} - 77 q^{39} - 37 q^{40} - 64 q^{41} + 13 q^{42} - 74 q^{43} - 79 q^{44} - 12 q^{45} - 53 q^{46} - 32 q^{47} + 2 q^{48} + 78 q^{49} - 104 q^{50} + 3 q^{51} + 13 q^{52} + 25 q^{53} - 110 q^{54} + 6 q^{55} - 29 q^{56} - 29 q^{57} - 14 q^{58} - 61 q^{59} - 82 q^{60} - 36 q^{61} - 63 q^{62} - 104 q^{63} + 107 q^{64} - 65 q^{65} + 12 q^{66} + 33 q^{67} - 79 q^{68} - 34 q^{69} - 3 q^{70} - 168 q^{71} - 67 q^{72} - 47 q^{73} - 54 q^{74} - 53 q^{75} - 4 q^{76} + 16 q^{77} - 3 q^{78} - 79 q^{79} - 59 q^{80} + 70 q^{81} - 18 q^{82} - 36 q^{83} - 118 q^{84} + 6 q^{85} + 7 q^{86} - 24 q^{87} + 21 q^{88} - 24 q^{89} + 25 q^{90} - 14 q^{91} - 18 q^{92} - 13 q^{93} + 9 q^{94} - 155 q^{95} - 50 q^{96} + q^{97} - 60 q^{98} - 75 q^{99}+O(q^{100}) \) 74 * q - 7 * q^2 - 3 * q^3 + 79 * q^4 - 6 * q^5 - 12 * q^6 - 16 * q^7 - 21 * q^8 + 75 * q^9 - 9 * q^10 - 74 * q^11 - 3 * q^12 + 4 * q^13 - 5 * q^14 - 17 * q^15 + 85 * q^16 - 74 * q^17 - 23 * q^18 - 21 * q^20 - 22 * q^21 + 7 * q^22 - 23 * q^23 - 51 * q^24 + 90 * q^25 - 46 * q^26 - 27 * q^27 - 61 * q^28 - 63 * q^29 - 22 * q^30 - 31 * q^31 - 69 * q^32 + 3 * q^33 + 7 * q^34 - 20 * q^35 + 51 * q^36 + 8 * q^37 - 2 * q^38 - 77 * q^39 - 37 * q^40 - 64 * q^41 + 13 * q^42 - 74 * q^43 - 79 * q^44 - 12 * q^45 - 53 * q^46 - 32 * q^47 + 2 * q^48 + 78 * q^49 - 104 * q^50 + 3 * q^51 + 13 * q^52 + 25 * q^53 - 110 * q^54 + 6 * q^55 - 29 * q^56 - 29 * q^57 - 14 * q^58 - 61 * q^59 - 82 * q^60 - 36 * q^61 - 63 * q^62 - 104 * q^63 + 107 * q^64 - 65 * q^65 + 12 * q^66 + 33 * q^67 - 79 * q^68 - 34 * q^69 - 3 * q^70 - 168 * q^71 - 67 * q^72 - 47 * q^73 - 54 * q^74 - 53 * q^75 - 4 * q^76 + 16 * q^77 - 3 * q^78 - 79 * q^79 - 59 * q^80 + 70 * q^81 - 18 * q^82 - 36 * q^83 - 118 * q^84 + 6 * q^85 + 7 * q^86 - 24 * q^87 + 21 * q^88 - 24 * q^89 + 25 * q^90 - 14 * q^91 - 18 * q^92 - 13 * q^93 + 9 * q^94 - 155 * q^95 - 50 * q^96 + q^97 - 60 * q^98 - 75 * 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 $

$2$	1.34534	0.951296	0.475648	−	0.879636i	$-0.342214\pi$
$2$	1.34534	0.951296	0.475648	+	0.879636i	$0.342214\pi$
$3$	−2.29674	−1.32602	−0.663012	−	0.748609i	$-0.730722\pi$
$3$	−2.29674	−1.32602	−0.663012	+	0.748609i	$0.730722\pi$
$4$	−0.190071	−0.0950357
$5$	−3.94764	−1.76544	−0.882720	−	0.469900i	$-0.844290\pi$
$5$	−3.94764	−1.76544	−0.882720	+	0.469900i	$0.844290\pi$
$6$	−3.08989	−1.26144
$7$	−5.02160	−1.89799	−0.948993	−	0.315298i	$-0.897895\pi$
$7$	−5.02160	−1.89799	−0.948993	+	0.315298i	$0.897895\pi$
$8$	−2.94638	−1.04170
$9$	2.27502	0.758340
$10$	−5.31090	−1.67946
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	0.436545	0.126020
$13$	−2.87402	−0.797109	−0.398555	−	0.917145i	$-0.630488\pi$
$13$	−2.87402	−0.797109	−0.398555	+	0.917145i	$0.630488\pi$
$14$	−6.75573	−1.80555
$15$	9.06671	2.34101
$16$	−3.58373	−0.895933
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	3.06066	0.721405
$19$	6.17411	1.41644	0.708219	−	0.705992i	$-0.249499\pi$
$19$	6.17411	1.41644	0.708219	+	0.705992i	$0.249499\pi$
$20$	0.750334	0.167780
$21$	11.5333	2.51677
$22$	−1.34534	−0.286827
$23$	−4.25047	−0.886285	−0.443142	−	0.896451i	$-0.646136\pi$
$23$	−4.25047	−0.886285	−0.443142	+	0.896451i	$0.646136\pi$
$24$	6.76707	1.38132
$25$	10.5839	2.11678
$26$	−3.86652	−0.758287
$27$	1.66509	0.320448
$28$	0.954462	0.180376
$29$	−2.72997	−0.506943	−0.253472	−	0.967343i	$-0.581572\pi$
$29$	−2.72997	−0.506943	−0.253472	+	0.967343i	$0.581572\pi$
$30$	12.1978	2.22700
$31$	−3.69516	−0.663671	−0.331835	−	0.943337i	$-0.607668\pi$
$31$	−3.69516	−0.663671	−0.331835	+	0.943337i	$0.607668\pi$
$32$	1.07144	0.189406
$33$	2.29674	0.399811
$34$	−1.34534	−0.230723
$35$	19.8235	3.35078
$36$	−0.432416	−0.0720693
$37$	8.93416	1.46877	0.734383	−	0.678735i	$-0.237471\pi$
$37$	8.93416	1.46877	0.734383	+	0.678735i	$0.237471\pi$
$38$	8.30626	1.34745
$39$	6.60088	1.05699
$40$	11.6313	1.83906
$41$	−6.98910	−1.09151	−0.545757	−	0.837943i	$-0.683758\pi$
$41$	−6.98910	−1.09151	−0.545757	+	0.837943i	$0.683758\pi$
$42$	15.5162	2.39420
$43$	−1.00000	−0.152499
$43$	−1.00000	−0.152499
$44$	0.190071	0.0286543
$45$	−8.98096	−1.33880
$46$	−5.71831	−0.843119
$47$	−0.315812	−0.0460659	−0.0230330	−	0.999735i	$-0.507332\pi$
$47$	−0.315812	−0.0460659	−0.0230330	+	0.999735i	$0.507332\pi$
$48$	8.23090	1.18803
$49$	18.2164	2.60235
$50$	14.2389	2.01368
$51$	2.29674	0.321608
$52$	0.546269	0.0757538
$53$	−9.81199	−1.34778	−0.673890	−	0.738831i	$-0.735378\pi$
$53$	−9.81199	−1.34778	−0.673890	+	0.738831i	$0.735378\pi$
$54$	2.24011	0.304841
$55$	3.94764	0.532300
$56$	14.7955	1.97714
$57$	−14.1803	−1.87823
$58$	−3.67273	−0.482253
$59$	−5.66297	−0.737256	−0.368628	−	0.929577i	$-0.620172\pi$
$59$	−5.66297	−0.737256	−0.368628	+	0.929577i	$0.620172\pi$
$60$	−1.72332	−0.222480
$61$	−11.8956	−1.52308	−0.761540	−	0.648118i	$-0.775556\pi$
$61$	−11.8956	−1.52308	−0.761540	+	0.648118i	$0.775556\pi$
$62$	−4.97124	−0.631348
$63$	−11.4242	−1.43932
$64$	8.60891	1.07611
$65$	11.3456	1.40725
$66$	3.08989	0.380339
$67$	9.17320	1.12068	0.560342	−	0.828261i	$-0.310670\pi$
$67$	9.17320	1.12068	0.560342	+	0.828261i	$0.310670\pi$
$68$	0.190071	0.0230495
$69$	9.76223	1.17523
$70$	26.6692	3.18758
$71$	−15.0595	−1.78723	−0.893617	−	0.448831i	$-0.851841\pi$
$71$	−15.0595	−1.78723	−0.893617	+	0.448831i	$0.851841\pi$
$72$	−6.70307	−0.789965
$73$	11.1383	1.30363	0.651817	−	0.758376i	$-0.274007\pi$
$73$	11.1383	1.30363	0.651817	+	0.758376i	$0.274007\pi$
$74$	12.0194	1.39723
$75$	−24.3084	−2.80689
$76$	−1.17352	−0.134612
$77$	5.02160	0.572264
$78$	8.88040	1.00551
$79$	10.7151	1.20554	0.602772	−	0.797914i	$-0.294063\pi$
$79$	10.7151	1.20554	0.602772	+	0.797914i	$0.294063\pi$
$80$	14.1473	1.58171
$81$	−10.6493	−1.18326
$82$	−9.40269	−1.03835
$83$	10.2363	1.12358	0.561788	−	0.827281i	$-0.310113\pi$
$83$	10.2363	1.12358	0.561788	+	0.827281i	$0.310113\pi$
$84$	−2.19215	−0.239183
$85$	3.94764	0.428182
$86$	−1.34534	−0.145071
$87$	6.27004	0.672219
$88$	2.94638	0.314085
$89$	16.2578	1.72332	0.861662	−	0.507482i	$-0.169424\pi$
$89$	16.2578	1.72332	0.861662	+	0.507482i	$0.169424\pi$
$90$	−12.0824	−1.27360
$91$	14.4322	1.51290
$92$	0.807893	0.0842286
$93$	8.48683	0.880044
$94$	−0.424873	−0.0438223
$95$	−24.3732	−2.50064
$96$	−2.46083	−0.251157
$97$	12.5340	1.27263	0.636317	−	0.771428i	$-0.280457\pi$
$97$	12.5340	1.27263	0.636317	+	0.771428i	$0.280457\pi$
$98$	24.5072	2.47560
$99$	−2.27502	−0.228648
$100$	−2.01169	−0.201169
$101$	2.80719	0.279326	0.139663	−	0.990199i	$-0.455398\pi$
$101$	2.80719	0.279326	0.139663	+	0.990199i	$0.455398\pi$
$102$	3.08989	0.305944
$103$	14.7669	1.45502	0.727512	−	0.686095i	$-0.240677\pi$
$103$	14.7669	1.45502	0.727512	+	0.686095i	$0.240677\pi$
$104$	8.46796	0.830351
$105$	−45.5294	−4.44321
$106$	−13.2004	−1.28214
$107$	−5.88769	−0.569185	−0.284592	−	0.958649i	$-0.591858\pi$
$107$	−5.88769	−0.569185	−0.284592	+	0.958649i	$0.591858\pi$
$108$	−0.316487	−0.0304540
$109$	3.70746	0.355110	0.177555	−	0.984111i	$-0.443181\pi$
$109$	3.70746	0.355110	0.177555	+	0.984111i	$0.443181\pi$
$110$	5.31090	0.506375
$111$	−20.5194	−1.94762
$112$	17.9960	1.70047
$113$	−10.1266	−0.952626	−0.476313	−	0.879276i	$-0.658027\pi$
$113$	−10.1266	−0.952626	−0.476313	+	0.879276i	$0.658027\pi$
$114$	−19.0773	−1.78675
$115$	16.7793	1.56468
$116$	0.518889	0.0481777
$117$	−6.53845	−0.604480
$118$	−7.61860	−0.701349
$119$	5.02160	0.460329
$120$	−26.7140	−2.43864
$121$	1.00000	0.0909091
$122$	−16.0036	−1.44890
$123$	16.0522	1.44737
$124$	0.702345	0.0630724
$125$	−22.0431	−1.97160
$126$	−15.3694	−1.36922
$127$	−10.0409	−0.890989	−0.445495	−	0.895285i	$-0.646972\pi$
$127$	−10.0409	−0.890989	−0.445495	+	0.895285i	$0.646972\pi$
$128$	9.43899	0.834297
$129$	2.29674	0.202217
$130$	15.2636	1.33871
$131$	−11.3467	−0.991365	−0.495682	−	0.868504i	$-0.665082\pi$
$131$	−11.3467	−0.991365	−0.495682	+	0.868504i	$0.665082\pi$
$132$	−0.436545	−0.0379963
$133$	−31.0039	−2.68838
$134$	12.3410	1.06610
$135$	−6.57320	−0.565731
$136$	2.94638	0.252650
$137$	−14.2142	−1.21440	−0.607200	−	0.794549i	$-0.707707\pi$
$137$	−14.2142	−1.21440	−0.607200	+	0.794549i	$0.707707\pi$
$138$	13.1335	1.11800
$139$	−15.9844	−1.35578	−0.677888	−	0.735166i	$-0.737104\pi$
$139$	−15.9844	−1.35578	−0.677888	+	0.735166i	$0.737104\pi$
$140$	−3.76787	−0.318443
$141$	0.725339	0.0610845
$142$	−20.2601	−1.70019
$143$	2.87402	0.240338
$144$	−8.15305	−0.679421
$145$	10.7770	0.894977
$146$	14.9847	1.24014
$147$	−41.8384	−3.45078
$148$	−1.69813	−0.139585
$149$	−13.5039	−1.10628	−0.553140	−	0.833089i	$-0.686570\pi$
$149$	−13.5039	−1.10628	−0.553140	+	0.833089i	$0.686570\pi$
$150$	−32.7030	−2.67019
$151$	−2.71048	−0.220575	−0.110288	−	0.993900i	$-0.535177\pi$
$151$	−2.71048	−0.220575	−0.110288	+	0.993900i	$0.535177\pi$
$152$	−18.1913	−1.47551
$153$	−2.27502	−0.183924
$154$	6.75573	0.544393
$155$	14.5872	1.17167
$156$	−1.25464	−0.100451
$157$	−7.84790	−0.626330	−0.313165	−	0.949699i	$-0.601389\pi$
$157$	−7.84790	−0.626330	−0.313165	+	0.949699i	$0.601389\pi$
$158$	14.4154	1.14683
$159$	22.5356	1.78719
$160$	−4.22967	−0.334385
$161$	21.3442	1.68215
$162$	−14.3269	−1.12563
$163$	15.6637	1.22688	0.613440	−	0.789742i	$-0.289785\pi$
$163$	15.6637	1.22688	0.613440	+	0.789742i	$0.289785\pi$
$164$	1.32843	0.103733
$165$	−9.06671	−0.705842
$166$	13.7712	1.06885
$167$	8.25443	0.638747	0.319374	−	0.947629i	$-0.396527\pi$
$167$	8.25443	0.638747	0.319374	+	0.947629i	$0.396527\pi$
$168$	−33.9815	−2.62173
$169$	−4.74002	−0.364617
$170$	5.31090	0.407328
$171$	14.0462	1.07414
$172$	0.190071	0.0144928
$173$	−8.66363	−0.658684	−0.329342	−	0.944211i	$-0.606827\pi$
$173$	−8.66363	−0.658684	−0.329342	+	0.944211i	$0.606827\pi$
$174$	8.43531	0.639479
$175$	−53.1480	−4.01761
$176$	3.58373	0.270134
$177$	13.0064	0.977620
$178$	21.8722	1.63939
$179$	−16.3612	−1.22289	−0.611446	−	0.791286i	$-0.709412\pi$
$179$	−16.3612	−1.22289	−0.611446	+	0.791286i	$0.709412\pi$
$180$	1.70702	0.127234
$181$	−2.81184	−0.209002	−0.104501	−	0.994525i	$-0.533325\pi$
$181$	−2.81184	−0.209002	−0.104501	+	0.994525i	$0.533325\pi$
$182$	19.4161	1.43922
$183$	27.3212	2.01964
$184$	12.5235	0.923245
$185$	−35.2689	−2.59302
$186$	11.4176	0.837182
$187$	1.00000	0.0731272
$188$	0.0600268	0.00437791
$189$	−8.36143	−0.608205
$190$	−32.7901	−2.37885
$191$	−13.3840	−0.968435	−0.484217	−	0.874948i	$-0.660896\pi$
$191$	−13.3840	−0.968435	−0.484217	+	0.874948i	$0.660896\pi$
$192$	−19.7724	−1.42695
$193$	3.26526	0.235039	0.117519	−	0.993071i	$-0.462506\pi$
$193$	3.26526	0.235039	0.117519	+	0.993071i	$0.462506\pi$
$194$	16.8624	1.21065
$195$	−26.0579	−1.86604
$196$	−3.46242	−0.247316
$197$	18.8958	1.34627	0.673133	−	0.739521i	$-0.264948\pi$
$197$	18.8958	1.34627	0.673133	+	0.739521i	$0.264948\pi$
$198$	−3.06066	−0.217512
$199$	−5.59601	−0.396690	−0.198345	−	0.980132i	$-0.563557\pi$
$199$	−5.59601	−0.396690	−0.198345	+	0.980132i	$0.563557\pi$
$200$	−31.1841	−2.20505
$201$	−21.0685	−1.48605
$202$	3.77662	0.265722
$203$	13.7088	0.962170
$204$	−0.436545	−0.0305642
$205$	27.5905	1.92700
$206$	19.8664	1.38416
$207$	−9.66990	−0.672105
$208$	10.2997	0.714156
$209$	−6.17411	−0.427072
$210$	−61.2523	−4.22681
$211$	27.4410	1.88912	0.944559	−	0.328340i	$-0.106489\pi$
$211$	27.4410	1.88912	0.944559	+	0.328340i	$0.106489\pi$
$212$	1.86498	0.128087
$213$	34.5878	2.36991
$214$	−7.92092	−0.541463
$215$	3.94764	0.269227
$216$	−4.90600	−0.333811
$217$	18.5556	1.25964
$218$	4.98777	0.337815
$219$	−25.5817	−1.72865
$220$	−0.750334	−0.0505875
$221$	2.87402	0.193327
$222$	−27.6056	−1.85276
$223$	−5.69575	−0.381416	−0.190708	−	0.981647i	$-0.561078\pi$
$223$	−5.69575	−0.381416	−0.190708	+	0.981647i	$0.561078\pi$
$224$	−5.38035	−0.359490
$225$	24.0785	1.60523
$226$	−13.6236	−0.906229
$227$	6.08499	0.403875	0.201937	−	0.979398i	$-0.435276\pi$
$227$	6.08499	0.403875	0.201937	+	0.979398i	$0.435276\pi$
$228$	2.69528	0.178499
$229$	2.14701	0.141879	0.0709394	−	0.997481i	$-0.477400\pi$
$229$	2.14701	0.141879	0.0709394	+	0.997481i	$0.477400\pi$
$230$	22.5738	1.48848
$231$	−11.5333	−0.758836
$232$	8.04354	0.528084
$233$	25.7545	1.68723	0.843617	−	0.536946i	$-0.180422\pi$
$233$	25.7545	1.68723	0.843617	+	0.536946i	$0.180422\pi$
$234$	−8.79641	−0.575039
$235$	1.24671	0.0813266
$236$	1.07637	0.0700657
$237$	−24.6098	−1.59858
$238$	6.75573	0.437909
$239$	12.5789	0.813659	0.406830	−	0.913504i	$-0.366634\pi$
$239$	12.5789	0.813659	0.406830	+	0.913504i	$0.366634\pi$
$240$	−32.4926	−2.09739
$241$	4.80728	0.309664	0.154832	−	0.987941i	$-0.450516\pi$
$241$	4.80728	0.309664	0.154832	+	0.987941i	$0.450516\pi$
$242$	1.34534	0.0864815
$243$	19.4635	1.24858
$244$	2.26102	0.144747
$245$	−71.9120	−4.59429
$246$	21.5955	1.37688
$247$	−17.7445	−1.12906
$248$	10.8874	0.691348
$249$	−23.5101	−1.48989
$250$	−29.6554	−1.87557
$251$	−19.1466	−1.20852	−0.604261	−	0.796787i	$-0.706531\pi$
$251$	−19.1466	−1.20852	−0.604261	+	0.796787i	$0.706531\pi$
$252$	2.17142	0.136786
$253$	4.25047	0.267225
$254$	−13.5084	−0.847595
$255$	−9.06671	−0.567779
$256$	−4.51921	−0.282450
$257$	21.7031	1.35380	0.676902	−	0.736073i	$-0.263322\pi$
$257$	21.7031	1.35380	0.676902	+	0.736073i	$0.263322\pi$
$258$	3.08989	0.192368
$259$	−44.8637	−2.78770
$260$	−2.15647	−0.133739
$261$	−6.21074	−0.384435
$262$	−15.2651	−0.943081
$263$	−0.895397	−0.0552125	−0.0276063	−	0.999619i	$-0.508788\pi$
$263$	−0.895397	−0.0552125	−0.0276063	+	0.999619i	$0.508788\pi$
$264$	−6.76707	−0.416485
$265$	38.7342	2.37942
$266$	−41.7107	−2.55745
$267$	−37.3400	−2.28517
$268$	−1.74356	−0.106505
$269$	18.9228	1.15375	0.576873	−	0.816834i	$-0.304273\pi$
$269$	18.9228	1.15375	0.576873	+	0.816834i	$0.304273\pi$
$270$	−8.84316	−0.538177
$271$	28.0050	1.70118	0.850592	−	0.525826i	$-0.176244\pi$
$271$	28.0050	1.70118	0.850592	+	0.525826i	$0.176244\pi$
$272$	3.58373	0.217296
$273$	−33.1469	−2.00614
$274$	−19.1228	−1.15525
$275$	−10.5839	−0.638232
$276$	−1.85552	−0.111689
$277$	5.80909	0.349034	0.174517	−	0.984654i	$-0.444164\pi$
$277$	5.80909	0.349034	0.174517	+	0.984654i	$0.444164\pi$
$278$	−21.5043	−1.28974
$279$	−8.40657	−0.503288
$280$	−58.4075	−3.49052
$281$	−18.7383	−1.11784	−0.558918	−	0.829223i	$-0.688783\pi$
$281$	−18.7383	−1.11784	−0.558918	+	0.829223i	$0.688783\pi$
$282$	0.975824	0.0581095
$283$	11.3523	0.674822	0.337411	−	0.941357i	$-0.390449\pi$
$283$	11.3523	0.674822	0.337411	+	0.941357i	$0.390449\pi$
$284$	2.86238	0.169851
$285$	55.9789	3.31590
$286$	3.86652	0.228632
$287$	35.0965	2.07168
$288$	2.43755	0.143634
$289$	1.00000	0.0588235
$290$	14.4986	0.851388
$291$	−28.7873	−1.68754
$292$	−2.11706	−0.123892
$293$	3.49617	0.204249	0.102124	−	0.994772i	$-0.467436\pi$
$293$	3.49617	0.204249	0.102124	+	0.994772i	$0.467436\pi$
$294$	−56.2867	−3.28271
$295$	22.3554	1.30158
$296$	−26.3234	−1.53002
$297$	−1.66509	−0.0966186
$298$	−18.1672	−1.05240
$299$	12.2159	0.706466
$300$	4.62033	0.266755
$301$	5.02160	0.289440
$302$	−3.64650	−0.209832
$303$	−6.44740	−0.370393
$304$	−22.1264	−1.26903
$305$	46.9597	2.68890
$306$	−3.06066	−0.174967
$307$	−1.41100	−0.0805301	−0.0402650	−	0.999189i	$-0.512820\pi$
$307$	−1.41100	−0.0805301	−0.0402650	+	0.999189i	$0.512820\pi$
$308$	−0.954462	−0.0543855
$309$	−33.9157	−1.92940
$310$	19.6247	1.11461
$311$	5.64698	0.320211	0.160105	−	0.987100i	$-0.448817\pi$
$311$	5.64698	0.320211	0.160105	+	0.987100i	$0.448817\pi$
$312$	−19.4487	−1.10107
$313$	−8.24069	−0.465791	−0.232896	−	0.972502i	$-0.574820\pi$
$313$	−8.24069	−0.465791	−0.232896	+	0.972502i	$0.574820\pi$
$314$	−10.5581	−0.595826
$315$	45.0988	2.54103
$316$	−2.03664	−0.114570
$317$	18.5696	1.04297	0.521486	−	0.853260i	$-0.325378\pi$
$317$	18.5696	1.04297	0.521486	+	0.853260i	$0.325378\pi$
$318$	30.3179	1.70015
$319$	2.72997	0.152849
$320$	−33.9849	−1.89981
$321$	13.5225	0.754752
$322$	28.7151	1.60023
$323$	−6.17411	−0.343537
$324$	2.02414	0.112452
$325$	−30.4183	−1.68730
$326$	21.0730	1.16713
$327$	−8.51507	−0.470884
$328$	20.5926	1.13703
$329$	1.58588	0.0874324
$330$	−12.1978	−0.671465
$331$	19.0085	1.04480	0.522402	−	0.852699i	$-0.325036\pi$
$331$	19.0085	1.04480	0.522402	+	0.852699i	$0.325036\pi$
$332$	−1.94562	−0.106780
$333$	20.3254	1.11382
$334$	11.1050	0.607638
$335$	−36.2125	−1.97850
$336$	−41.3323	−2.25486
$337$	0.647963	0.0352968	0.0176484	−	0.999844i	$-0.494382\pi$
$337$	0.647963	0.0352968	0.0176484	+	0.999844i	$0.494382\pi$
$338$	−6.37691	−0.346858
$339$	23.2581	1.26320
$340$	−0.750334	−0.0406926
$341$	3.69516	0.200104
$342$	18.8969	1.02183
$343$	−56.3244	−3.04123
$344$	2.94638	0.158858
$345$	−38.5378	−2.07480
$346$	−11.6555	−0.626603
$347$	−22.5810	−1.21221	−0.606105	−	0.795385i	$-0.707269\pi$
$347$	−22.5810	−1.21221	−0.606105	+	0.795385i	$0.707269\pi$
$348$	−1.19175	−0.0638848
$349$	7.37709	0.394887	0.197443	−	0.980314i	$-0.436736\pi$
$349$	7.37709	0.394887	0.197443	+	0.980314i	$0.436736\pi$
$350$	−71.5019	−3.82194
$351$	−4.78551	−0.255432
$352$	−1.07144	−0.0571081
$353$	20.9381	1.11443	0.557213	−	0.830370i	$-0.311871\pi$
$353$	20.9381	1.11443	0.557213	+	0.830370i	$0.311871\pi$
$354$	17.4980	0.930006
$355$	59.4495	3.15525
$356$	−3.09014	−0.163777
$357$	−11.5333	−0.610407
$358$	−22.0113	−1.16333
$359$	−26.7551	−1.41208	−0.706040	−	0.708172i	$-0.749520\pi$
$359$	−26.7551	−1.41208	−0.706040	+	0.708172i	$0.749520\pi$
$360$	26.4613	1.39463
$361$	19.1197	1.00630
$362$	−3.78286	−0.198823
$363$	−2.29674	−0.120548
$364$	−2.74314	−0.143780
$365$	−43.9698	−2.30149
$366$	36.7562	1.92128
$367$	−4.26076	−0.222410	−0.111205	−	0.993797i	$-0.535471\pi$
$367$	−4.26076	−0.222410	−0.111205	+	0.993797i	$0.535471\pi$
$368$	15.2325	0.794051
$369$	−15.9003	−0.827739
$370$	−47.4485	−2.46673
$371$	49.2719	2.55807
$372$	−1.61310	−0.0836355
$373$	6.51088	0.337121	0.168560	−	0.985691i	$-0.446088\pi$
$373$	6.51088	0.337121	0.168560	+	0.985691i	$0.446088\pi$
$374$	1.34534	0.0695657
$375$	50.6274	2.61439
$376$	0.930503	0.0479870
$377$	7.84599	0.404089
$378$	−11.2489	−0.578583
$379$	22.5270	1.15713	0.578567	−	0.815635i	$-0.303612\pi$
$379$	22.5270	1.15713	0.578567	+	0.815635i	$0.303612\pi$
$380$	4.63264	0.237650
$381$	23.0614	1.18147
$382$	−18.0060	−0.921268
$383$	−25.5082	−1.30341	−0.651705	−	0.758473i	$-0.725946\pi$
$383$	−25.5082	−1.30341	−0.651705	+	0.758473i	$0.725946\pi$
$384$	−21.6789	−1.10630
$385$	−19.8235	−1.01030
$386$	4.39287	0.223591
$387$	−2.27502	−0.115646
$388$	−2.38235	−0.120946
$389$	25.6210	1.29904	0.649518	−	0.760346i	$-0.274971\pi$
$389$	25.6210	1.29904	0.649518	+	0.760346i	$0.274971\pi$
$390$	−35.0566	−1.77516
$391$	4.25047	0.214956
$392$	−53.6726	−2.71087
$393$	26.0604	1.31457
$394$	25.4211	1.28070
$395$	−42.2994	−2.12831
$396$	0.432416	0.0217297
$397$	9.05300	0.454357	0.227179	−	0.973853i	$-0.427050\pi$
$397$	9.05300	0.454357	0.227179	+	0.973853i	$0.427050\pi$
$398$	−7.52851	−0.377370
$399$	71.2079	3.56486
$400$	−37.9298	−1.89649
$401$	6.35397	0.317302	0.158651	−	0.987335i	$-0.449285\pi$
$401$	6.35397	0.317302	0.158651	+	0.987335i	$0.449285\pi$
$402$	−28.3441	−1.41368
$403$	10.6200	0.529018
$404$	−0.533567	−0.0265459
$405$	42.0398	2.08897
$406$	18.4430	0.915309
$407$	−8.93416	−0.442850
$408$	−6.76707	−0.335020
$409$	−19.8523	−0.981633	−0.490817	−	0.871263i	$-0.663301\pi$
$409$	−19.8523	−0.981633	−0.490817	+	0.871263i	$0.663301\pi$
$410$	37.1185	1.83315
$411$	32.6463	1.61032
$412$	−2.80676	−0.138279
$413$	28.4372	1.39930
$414$	−13.0093	−0.639370
$415$	−40.4091	−1.98361
$416$	−3.07935	−0.150977
$417$	36.7119	1.79779
$418$	−8.30626	−0.406272
$419$	−28.1747	−1.37643	−0.688213	−	0.725509i	$-0.741604\pi$
$419$	−28.1747	−1.37643	−0.688213	+	0.725509i	$0.741604\pi$
$420$	8.65383	0.422264
$421$	−24.3932	−1.18885	−0.594425	−	0.804151i	$-0.702620\pi$
$421$	−24.3932	−1.18885	−0.594425	+	0.804151i	$0.702620\pi$
$422$	36.9174	1.79711
$423$	−0.718478	−0.0349336
$424$	28.9099	1.40399
$425$	−10.5839	−0.513393
$426$	46.5322	2.25449
$427$	59.7351	2.89078
$428$	1.11908	0.0540928
$429$	−6.60088	−0.318693
$430$	5.31090	0.256115
$431$	26.9487	1.29807	0.649037	−	0.760757i	$-0.275172\pi$
$431$	26.9487	1.29807	0.649037	+	0.760757i	$0.275172\pi$
$432$	−5.96725	−0.287099
$433$	12.6081	0.605908	0.302954	−	0.953005i	$-0.402027\pi$
$433$	12.6081	0.605908	0.302954	+	0.953005i	$0.402027\pi$
$434$	24.9635	1.19829
$435$	−24.7519	−1.18676
$436$	−0.704681	−0.0337481
$437$	−26.2429	−1.25537
$438$	−34.4160	−1.64446
$439$	20.5713	0.981813	0.490906	−	0.871212i	$-0.336666\pi$
$439$	20.5713	0.981813	0.490906	+	0.871212i	$0.336666\pi$
$440$	−11.6313	−0.554499
$441$	41.4427	1.97346
$442$	3.86652	0.183912
$443$	−31.1156	−1.47835	−0.739174	−	0.673514i	$-0.764784\pi$
$443$	−31.1156	−1.47835	−0.739174	+	0.673514i	$0.764784\pi$
$444$	3.90016	0.185093
$445$	−64.1800	−3.04242
$446$	−7.66270	−0.362839
$447$	31.0149	1.46695
$448$	−43.2305	−2.04245
$449$	39.2184	1.85083	0.925414	−	0.378957i	$-0.123717\pi$
$449$	39.2184	1.85083	0.925414	+	0.378957i	$0.123717\pi$
$450$	32.3937	1.52705
$451$	6.98910	0.329104
$452$	1.92477	0.0905335
$453$	6.22526	0.292488
$454$	8.18635	0.384204
$455$	−56.9730	−2.67094
$456$	41.7807	1.95656
$457$	−32.0595	−1.49968	−0.749841	−	0.661618i	$-0.769870\pi$
$457$	−32.0595	−1.49968	−0.749841	+	0.661618i	$0.769870\pi$
$458$	2.88846	0.134969
$459$	−1.66509	−0.0777200
$460$	−3.18927	−0.148701
$461$	−18.5297	−0.863014	−0.431507	−	0.902110i	$-0.642018\pi$
$461$	−18.5297	−0.863014	−0.431507	+	0.902110i	$0.642018\pi$
$462$	−15.5162	−0.721878
$463$	−2.63767	−0.122583	−0.0612915	−	0.998120i	$-0.519522\pi$
$463$	−2.63767	−0.122583	−0.0612915	+	0.998120i	$0.519522\pi$
$464$	9.78348	0.454187
$465$	−33.5030	−1.55366
$466$	34.6485	1.60506
$467$	36.9931	1.71184	0.855919	−	0.517110i	$-0.172992\pi$
$467$	36.9931	1.71184	0.855919	+	0.517110i	$0.172992\pi$
$468$	1.24277	0.0574471
$469$	−46.0641	−2.12704
$470$	1.67725	0.0773657
$471$	18.0246	0.830529
$472$	16.6853	0.768002
$473$	1.00000	0.0459800
$474$	−33.1085	−1.52072
$475$	65.3461	2.99828
$476$	−0.954462	−0.0437477
$477$	−22.3225	−1.02208
$478$	16.9228	0.774031
$479$	−10.4565	−0.477770	−0.238885	−	0.971048i	$-0.576782\pi$
$479$	−10.4565	−0.477770	−0.238885	+	0.971048i	$0.576782\pi$
$480$	9.71446	0.443402
$481$	−25.6769	−1.17077
$482$	6.46740	0.294582
$483$	−49.0220	−2.23058
$484$	−0.190071	−0.00863961
$485$	−49.4797	−2.24676
$486$	26.1850	1.18777
$487$	5.87803	0.266359	0.133180	−	0.991092i	$-0.457481\pi$
$487$	5.87803	0.266359	0.133180	+	0.991092i	$0.457481\pi$
$488$	35.0491	1.58660
$489$	−35.9756	−1.62687
$490$	−96.7457	−4.37053
$491$	18.8242	0.849523	0.424762	−	0.905305i	$-0.360358\pi$
$491$	18.8242	0.849523	0.424762	+	0.905305i	$0.360358\pi$
$492$	−3.05106	−0.137552
$493$	2.72997	0.122952
$494$	−23.8723	−1.07407
$495$	8.98096	0.403664
$496$	13.2425	0.594604
$497$	75.6227	3.39214
$498$	−31.6289	−1.41733
$499$	−6.38044	−0.285628	−0.142814	−	0.989750i	$-0.545615\pi$
$499$	−6.38044	−0.285628	−0.142814	+	0.989750i	$0.545615\pi$
$500$	4.18977	0.187372
$501$	−18.9583	−0.846994
$502$	−25.7586	−1.14966
$503$	32.2630	1.43853	0.719267	−	0.694733i	$-0.244478\pi$
$503$	32.2630	1.43853	0.719267	+	0.694733i	$0.244478\pi$
$504$	33.6601	1.49934
$505$	−11.0818	−0.493133
$506$	5.71831	0.254210
$507$	10.8866	0.483490
$508$	1.90850	0.0846758
$509$	34.7812	1.54165	0.770825	−	0.637048i	$-0.219845\pi$
$509$	34.7812	1.54165	0.770825	+	0.637048i	$0.219845\pi$
$510$	−12.1978	−0.540126
$511$	−55.9318	−2.47428
$512$	−24.9578	−1.10299
$513$	10.2805	0.453894
$514$	29.1980	1.28787
$515$	−58.2943	−2.56876
$516$	−0.436545	−0.0192178
$517$	0.315812	0.0138894
$518$	−60.3568	−2.65193
$519$	19.8981	0.873431
$520$	−33.4285	−1.46593
$521$	−34.9168	−1.52973	−0.764866	−	0.644189i	$-0.777195\pi$
$521$	−34.9168	−1.52973	−0.764866	+	0.644189i	$0.777195\pi$
$522$	−8.35553	−0.365711
$523$	26.9699	1.17931	0.589656	−	0.807655i	$-0.299263\pi$
$523$	26.9699	1.17931	0.589656	+	0.807655i	$0.299263\pi$
$524$	2.15668	0.0942150
$525$	122.067	5.32744
$526$	−1.20461	−0.0525235
$527$	3.69516	0.160964
$528$	−8.23090	−0.358204
$529$	−4.93349	−0.214500
$530$	52.1105	2.26354
$531$	−12.8834	−0.559091
$532$	5.89295	0.255492
$533$	20.0868	0.870056
$534$	−50.2348	−2.17387
$535$	23.2425	1.00486
$536$	−27.0277	−1.16742
$537$	37.5774	1.62158
$538$	25.4576	1.09755
$539$	−18.2164	−0.784637
$540$	1.24938	0.0537646
$541$	−12.4439	−0.535006	−0.267503	−	0.963557i	$-0.586199\pi$
$541$	−12.4439	−0.535006	−0.267503	+	0.963557i	$0.586199\pi$
$542$	37.6762	1.61833
$543$	6.45806	0.277142
$544$	−1.07144	−0.0459377
$545$	−14.6357	−0.626925
$546$	−44.5938	−1.90844
$547$	−17.2282	−0.736625	−0.368312	−	0.929702i	$-0.620064\pi$
$547$	−17.2282	−0.736625	−0.368312	+	0.929702i	$0.620064\pi$
$548$	2.70171	0.115411
$549$	−27.0628	−1.15501
$550$	−14.2389	−0.607147
$551$	−16.8552	−0.718054
$552$	−28.7633	−1.22425
$553$	−53.8070	−2.28810
$554$	7.81517	0.332035
$555$	81.0034	3.43840
$556$	3.03817	0.128847
$557$	−25.4945	−1.08024	−0.540119	−	0.841589i	$-0.681621\pi$
$557$	−25.4945	−1.08024	−0.540119	+	0.841589i	$0.681621\pi$
$558$	−11.3097	−0.478776
$559$	2.87402	0.121558
$560$	−71.0420	−3.00207
$561$	−2.29674	−0.0969685
$562$	−25.2094	−1.06339
$563$	−15.0479	−0.634192	−0.317096	−	0.948393i	$-0.602708\pi$
$563$	−15.0479	−0.634192	−0.317096	+	0.948393i	$0.602708\pi$
$564$	−0.137866	−0.00580521
$565$	39.9760	1.68180
$566$	15.2726	0.641956
$567$	53.4767	2.24581
$568$	44.3710	1.86177
$569$	19.2103	0.805337	0.402668	−	0.915346i	$-0.368083\pi$
$569$	19.2103	0.805337	0.402668	+	0.915346i	$0.368083\pi$
$570$	75.3104	3.15441
$571$	−43.0275	−1.80065	−0.900323	−	0.435223i	$-0.856670\pi$
$571$	−43.0275	−1.80065	−0.900323	+	0.435223i	$0.856670\pi$
$572$	−0.546269	−0.0228406
$573$	30.7397	1.28417
$574$	47.2165	1.97078
$575$	−44.9865	−1.87607
$576$	19.5854	0.816060
$577$	12.5383	0.521977	0.260989	−	0.965342i	$-0.415951\pi$
$577$	12.5383	0.521977	0.260989	+	0.965342i	$0.415951\pi$
$578$	1.34534	0.0559586
$579$	−7.49946	−0.311667
$580$	−2.04839	−0.0850548
$581$	−51.4024	−2.13253
$582$	−38.7286	−1.60535
$583$	9.81199	0.406371
$584$	−32.8176	−1.35800
$585$	25.8114	1.06717
$586$	4.70353	0.194301
$587$	44.1353	1.82166	0.910830	−	0.412783i	$-0.135443\pi$
$587$	44.1353	1.82166	0.910830	+	0.412783i	$0.135443\pi$
$588$	7.95229	0.327947
$589$	−22.8144	−0.940049
$590$	30.0755	1.23819
$591$	−43.3986	−1.78518
$592$	−32.0176	−1.31592
$593$	10.3711	0.425892	0.212946	−	0.977064i	$-0.431694\pi$
$593$	10.3711	0.425892	0.212946	+	0.977064i	$0.431694\pi$
$594$	−2.24011	−0.0919129
$595$	−19.8235	−0.812683
$596$	2.56670	0.105136
$597$	12.8526	0.526021
$598$	16.4345	0.672058
$599$	−8.34256	−0.340868	−0.170434	−	0.985369i	$-0.554517\pi$
$599$	−8.34256	−0.340868	−0.170434	+	0.985369i	$0.554517\pi$
$600$	71.6219	2.92395
$601$	−7.38104	−0.301079	−0.150539	−	0.988604i	$-0.548101\pi$
$601$	−7.38104	−0.301079	−0.150539	+	0.988604i	$0.548101\pi$
$602$	6.75573	0.275343
$603$	20.8692	0.849859
$604$	0.515184	0.0209625
$605$	−3.94764	−0.160494
$606$	−8.67391	−0.352354
$607$	−16.3932	−0.665379	−0.332689	−	0.943036i	$-0.607956\pi$
$607$	−16.3932	−0.665379	−0.332689	+	0.943036i	$0.607956\pi$
$608$	6.61521	0.268282
$609$	−31.4856	−1.27586
$610$	63.1765	2.55794
$611$	0.907650	0.0367196
$612$	0.432416	0.0174794
$613$	20.8361	0.841561	0.420780	−	0.907163i	$-0.361756\pi$
$613$	20.8361	0.841561	0.420780	+	0.907163i	$0.361756\pi$
$614$	−1.89827	−0.0766079
$615$	−63.3682	−2.55525
$616$	−14.7955	−0.596129
$617$	−10.3944	−0.418463	−0.209231	−	0.977866i	$-0.567096\pi$
$617$	−10.3944	−0.418463	−0.209231	+	0.977866i	$0.567096\pi$
$618$	−45.6280	−1.83543
$619$	−7.87345	−0.316461	−0.158230	−	0.987402i	$-0.550579\pi$
$619$	−7.87345	−0.316461	−0.158230	+	0.987402i	$0.550579\pi$
$620$	−2.77261	−0.111351
$621$	−7.07744	−0.284008
$622$	7.59708	0.304615
$623$	−81.6402	−3.27084
$624$	−23.6558	−0.946988
$625$	34.0991	1.36396
$626$	−11.0865	−0.443105
$627$	14.1803	0.566308
$628$	1.49166	0.0595237
$629$	−8.93416	−0.356228
$630$	60.6730	2.41727
$631$	−35.1286	−1.39845	−0.699225	−	0.714902i	$-0.746471\pi$
$631$	−35.1286	−1.39845	−0.699225	+	0.714902i	$0.746471\pi$
$632$	−31.5708	−1.25582
$633$	−63.0250	−2.50502
$634$	24.9823	0.992176
$635$	39.6380	1.57299
$636$	−4.28337	−0.169847
$637$	−52.3544	−2.07436
$638$	3.67273	0.145405
$639$	−34.2606	−1.35533
$640$	−37.2618	−1.47290
$641$	46.7080	1.84485	0.922427	−	0.386172i	$-0.126203\pi$
$641$	46.7080	1.84485	0.922427	+	0.386172i	$0.126203\pi$
$642$	18.1923	0.717993
$643$	−12.1314	−0.478414	−0.239207	−	0.970969i	$-0.576887\pi$
$643$	−12.1314	−0.478414	−0.239207	+	0.970969i	$0.576887\pi$
$644$	−4.05691	−0.159865
$645$	−9.06671	−0.357001
$646$	−8.30626	−0.326805
$647$	33.4546	1.31523	0.657617	−	0.753352i	$-0.271564\pi$
$647$	33.4546	1.31523	0.657617	+	0.753352i	$0.271564\pi$
$648$	31.3770	1.23261
$649$	5.66297	0.222291
$650$	−40.9228	−1.60512
$651$	−42.6175	−1.67031
$652$	−2.97723	−0.116597
$653$	−27.8619	−1.09032	−0.545160	−	0.838332i	$-0.683531\pi$
$653$	−27.8619	−1.09032	−0.545160	+	0.838332i	$0.683531\pi$
$654$	−11.4556	−0.447950
$655$	44.7927	1.75019
$656$	25.0471	0.977923
$657$	25.3397	0.988597
$658$	2.13354	0.0831742
$659$	20.6782	0.805508	0.402754	−	0.915308i	$-0.368053\pi$
$659$	20.6782	0.805508	0.402754	+	0.915308i	$0.368053\pi$
$660$	1.72332	0.0670802
$661$	33.8300	1.31584	0.657918	−	0.753090i	$-0.271437\pi$
$661$	33.8300	1.31584	0.657918	+	0.753090i	$0.271437\pi$
$662$	25.5729	0.993918
$663$	−6.60088	−0.256357
$664$	−30.1600	−1.17043
$665$	122.392	4.74617
$666$	27.3445	1.05958
$667$	11.6037	0.449296
$668$	−1.56893	−0.0607038
$669$	13.0817	0.505766
$670$	−48.7180	−1.88214
$671$	11.8956	0.459226
$672$	12.3573	0.476692
$673$	−34.0543	−1.31270	−0.656348	−	0.754458i	$-0.727900\pi$
$673$	−34.0543	−1.31270	−0.656348	+	0.754458i	$0.727900\pi$
$674$	0.871727	0.0335777
$675$	17.6232	0.678316
$676$	0.900941	0.0346516
$677$	−30.2146	−1.16124	−0.580620	−	0.814175i	$-0.697190\pi$
$677$	−30.2146	−1.16124	−0.580620	+	0.814175i	$0.697190\pi$
$678$	31.2899	1.20168
$679$	−62.9406	−2.41544
$680$	−11.6313	−0.446038
$681$	−13.9756	−0.535547
$682$	4.97124	0.190358
$683$	11.3128	0.432874	0.216437	−	0.976297i	$-0.430556\pi$
$683$	11.3128	0.432874	0.216437	+	0.976297i	$0.430556\pi$
$684$	−2.66978	−0.102082
$685$	56.1125	2.14395
$686$	−75.7753	−2.89311
$687$	−4.93114	−0.188135
$688$	3.58373	0.136628
$689$	28.1998	1.07433
$690$	−51.8463	−1.97375
$691$	17.5011	0.665772	0.332886	−	0.942967i	$-0.391978\pi$
$691$	17.5011	0.665772	0.332886	+	0.942967i	$0.391978\pi$
$692$	1.64671	0.0625985
$693$	11.4242	0.433970
$694$	−30.3790	−1.15317
$695$	63.1005	2.39354
$696$	−18.4739	−0.700252
$697$	6.98910	0.264731
$698$	9.92467	0.375654
$699$	−59.1514	−2.23731
$700$	10.1019	0.381816
$701$	23.3579	0.882216	0.441108	−	0.897454i	$-0.354586\pi$
$701$	23.3579	0.882216	0.441108	+	0.897454i	$0.354586\pi$
$702$	−6.43812	−0.242991
$703$	55.1605	2.08042
$704$	−8.60891	−0.324461
$705$	−2.86338	−0.107841
$706$	28.1688	1.06015
$707$	−14.0966	−0.530157
$708$	−2.47214	−0.0929087
$709$	44.6655	1.67745	0.838724	−	0.544557i	$-0.183302\pi$
$709$	44.6655	1.67745	0.838724	+	0.544557i	$0.183302\pi$
$710$	79.9795	3.00158
$711$	24.3771	0.914212
$712$	−47.9017	−1.79519
$713$	15.7062	0.588201
$714$	−15.5162	−0.580678
$715$	−11.3456	−0.424301
$716$	3.10979	0.116218
$717$	−28.8904	−1.07893
$718$	−35.9946	−1.34331
$719$	−23.1279	−0.862527	−0.431263	−	0.902226i	$-0.641932\pi$
$719$	−23.1279	−0.862527	−0.431263	+	0.902226i	$0.641932\pi$
$720$	32.1853	1.19948
$721$	−74.1533	−2.76161
$722$	25.7224	0.957288
$723$	−11.0411	−0.410622
$724$	0.534450	0.0198627
$725$	−28.8937	−1.07308
$726$	−3.08989	−0.114676
$727$	17.9808	0.666870	0.333435	−	0.942773i	$-0.391792\pi$
$727$	17.9808	0.666870	0.333435	+	0.942773i	$0.391792\pi$
$728$	−42.5227	−1.57599
$729$	−12.7546	−0.472392
$730$	−59.1542	−2.18940
$731$	1.00000	0.0369863
$732$	−5.19297	−0.191938
$733$	−20.4673	−0.755976	−0.377988	−	0.925811i	$-0.623384\pi$
$733$	−20.4673	−0.755976	−0.377988	+	0.925811i	$0.623384\pi$
$734$	−5.73215	−0.211578
$735$	165.163	6.09213
$736$	−4.55413	−0.167868
$737$	−9.17320	−0.337899
$738$	−21.3913	−0.787424
$739$	−30.2194	−1.11164	−0.555819	−	0.831303i	$-0.687595\pi$
$739$	−30.2194	−1.11164	−0.555819	+	0.831303i	$0.687595\pi$
$740$	6.70360	0.246429
$741$	40.7546	1.49716
$742$	66.2872	2.43348
$743$	−12.4187	−0.455596	−0.227798	−	0.973708i	$-0.573153\pi$
$743$	−12.4187	−0.455596	−0.227798	+	0.973708i	$0.573153\pi$
$744$	−25.0054	−0.916744
$745$	53.3084	1.95307
$746$	8.75932	0.320702
$747$	23.2877	0.852053
$748$	−0.190071	−0.00694970
$749$	29.5656	1.08030
$750$	68.1109	2.48706
$751$	35.2503	1.28630	0.643151	−	0.765740i	$-0.277627\pi$
$751$	35.2503	1.28630	0.643151	+	0.765740i	$0.277627\pi$
$752$	1.13179	0.0412720
$753$	43.9747	1.60253
$754$	10.5555	0.384408
$755$	10.7000	0.389412
$756$	1.58927	0.0578012
$757$	−5.75383	−0.209127	−0.104563	−	0.994518i	$-0.533344\pi$
$757$	−5.75383	−0.209127	−0.104563	+	0.994518i	$0.533344\pi$
$758$	30.3064	1.10078
$759$	−9.76223	−0.354347
$760$	71.8127	2.60492
$761$	−34.4533	−1.24893	−0.624466	−	0.781052i	$-0.714683\pi$
$761$	−34.4533	−1.24893	−0.624466	+	0.781052i	$0.714683\pi$
$762$	31.0254	1.12393
$763$	−18.6174	−0.673993
$764$	2.54392	0.0920358
$765$	8.98096	0.324707
$766$	−34.3171	−1.23993
$767$	16.2755	0.587674
$768$	10.3794	0.374536
$769$	23.5094	0.847772	0.423886	−	0.905716i	$-0.360666\pi$
$769$	23.5094	0.847772	0.423886	+	0.905716i	$0.360666\pi$
$770$	−26.6692	−0.961092
$771$	−49.8465	−1.79518
$772$	−0.620632	−0.0223371
$773$	26.3138	0.946443	0.473221	−	0.880943i	$-0.343091\pi$
$773$	26.3138	0.946443	0.473221	+	0.880943i	$0.343091\pi$
$774$	−3.06066	−0.110013
$775$	−39.1092	−1.40484
$776$	−36.9299	−1.32571
$777$	103.040	3.69655
$778$	34.4688	1.23577
$779$	−43.1515	−1.54606
$780$	4.95286	0.177341
$781$	15.0595	0.538871
$782$	5.71831	0.204486
$783$	−4.54566	−0.162449
$784$	−65.2828	−2.33153
$785$	30.9807	1.10575
$786$	35.0600	1.25055
$787$	−19.2287	−0.685429	−0.342715	−	0.939440i	$-0.611346\pi$
$787$	−19.2287	−0.685429	−0.342715	+	0.939440i	$0.611346\pi$
$788$	−3.59154	−0.127943
$789$	2.05649	0.0732131
$790$	−56.9069	−2.02466
$791$	50.8515	1.80807
$792$	6.70307	0.238183
$793$	34.1883	1.21406
$794$	12.1793	0.432228
$795$	−88.9625	−3.15517
$796$	1.06364	0.0376997
$797$	30.2962	1.07315	0.536574	−	0.843854i	$-0.319718\pi$
$797$	30.2962	1.07315	0.536574	+	0.843854i	$0.319718\pi$
$798$	95.7986	3.39123
$799$	0.315812	0.0111726
$800$	11.3400	0.400930
$801$	36.9868	1.30687
$802$	8.54823	0.301849
$803$	−11.1383	−0.393061
$804$	4.00451	0.141228
$805$	−84.2591	−2.96974
$806$	14.2874	0.503253
$807$	−43.4609	−1.52989
$808$	−8.27106	−0.290975
$809$	−5.95482	−0.209360	−0.104680	−	0.994506i	$-0.533382\pi$
$809$	−5.95482	−0.209360	−0.104680	+	0.994506i	$0.533382\pi$
$810$	56.5577	1.98723
$811$	32.4865	1.14075	0.570377	−	0.821383i	$-0.306797\pi$
$811$	32.4865	1.14075	0.570377	+	0.821383i	$0.306797\pi$
$812$	−2.60565	−0.0914405
$813$	−64.3203	−2.25581
$814$	−12.0194	−0.421281
$815$	−61.8349	−2.16598
$816$	−8.23090	−0.288139
$817$	−6.17411	−0.216005
$818$	−26.7080	−0.933824
$819$	32.8334	1.14729
$820$	−5.24416	−0.183134
$821$	−37.4986	−1.30871	−0.654354	−	0.756188i	$-0.727060\pi$
$821$	−37.4986	−1.30871	−0.654354	+	0.756188i	$0.727060\pi$
$822$	43.9202	1.53189
$823$	−8.99217	−0.313447	−0.156724	−	0.987642i	$-0.550093\pi$
$823$	−8.99217	−0.313447	−0.156724	+	0.987642i	$0.550093\pi$
$824$	−43.5088	−1.51570
$825$	24.3084	0.846311
$826$	38.2575	1.33115
$827$	35.3902	1.23064	0.615318	−	0.788279i	$-0.289028\pi$
$827$	35.3902	1.23064	0.615318	+	0.788279i	$0.289028\pi$
$828$	1.83797	0.0638739
$829$	−13.1795	−0.457742	−0.228871	−	0.973457i	$-0.573503\pi$
$829$	−13.1795	−0.457742	−0.228871	+	0.973457i	$0.573503\pi$
$830$	−54.3639	−1.88700
$831$	−13.3420	−0.462828
$832$	−24.7422	−0.857780
$833$	−18.2164	−0.631162
$834$	49.3899	1.71023
$835$	−32.5856	−1.12767
$836$	1.17352	0.0405871
$837$	−6.15280	−0.212672
$838$	−37.9045	−1.30939
$839$	16.8199	0.580686	0.290343	−	0.956923i	$-0.406231\pi$
$839$	16.8199	0.580686	0.290343	+	0.956923i	$0.406231\pi$
$840$	134.147	4.62851
$841$	−21.5473	−0.743009
$842$	−32.8170	−1.13095
$843$	43.0371	1.48228
$844$	−5.21575	−0.179534
$845$	18.7119	0.643709
$846$	−0.966595	−0.0332322
$847$	−5.02160	−0.172544
$848$	35.1635	1.20752
$849$	−26.0732	−0.894830
$850$	−14.2389	−0.488389
$851$	−37.9744	−1.30175
$852$	−6.57414	−0.225226
$853$	−21.5218	−0.736893	−0.368447	−	0.929649i	$-0.620110\pi$
$853$	−21.5218	−0.736893	−0.368447	+	0.929649i	$0.620110\pi$
$854$	80.3637	2.74999
$855$	−55.4495	−1.89633
$856$	17.3474	0.592921
$857$	51.3857	1.75530	0.877652	−	0.479299i	$-0.159109\pi$
$857$	51.3857	1.75530	0.877652	+	0.479299i	$0.159109\pi$
$858$	−8.88040	−0.303172
$859$	−36.6020	−1.24884	−0.624422	−	0.781087i	$-0.714666\pi$
$859$	−36.6020	−1.24884	−0.624422	+	0.781087i	$0.714666\pi$
$860$	−0.750334	−0.0255862
$861$	−80.6075	−2.74710
$862$	36.2551	1.23485
$863$	−26.8246	−0.913120	−0.456560	−	0.889693i	$-0.650919\pi$
$863$	−26.8246	−0.913120	−0.456560	+	0.889693i	$0.650919\pi$
$864$	1.78405	0.0606947
$865$	34.2009	1.16287
$866$	16.9622	0.576398
$867$	−2.29674	−0.0780014
$868$	−3.52689	−0.119711
$869$	−10.7151	−0.363485
$870$	−33.2996	−1.12896
$871$	−26.3639	−0.893308
$872$	−10.9236	−0.369919
$873$	28.5151	0.965088
$874$	−35.3055	−1.19423
$875$	110.692	3.74207
$876$	4.86235	0.164283
$877$	46.1670	1.55895	0.779475	−	0.626434i	$-0.215486\pi$
$877$	46.1670	1.55895	0.779475	+	0.626434i	$0.215486\pi$
$878$	27.6753	0.933995
$879$	−8.02980	−0.270839
$880$	−14.1473	−0.476905
$881$	40.0734	1.35011	0.675053	−	0.737769i	$-0.264121\pi$
$881$	40.0734	1.35011	0.675053	+	0.737769i	$0.264121\pi$
$882$	55.7544	1.87735
$883$	30.6355	1.03097	0.515483	−	0.856900i	$-0.327613\pi$
$883$	30.6355	1.03097	0.515483	+	0.856900i	$0.327613\pi$
$884$	−0.546269	−0.0183730
$885$	−51.3445	−1.72593
$886$	−41.8610	−1.40635
$887$	−19.7019	−0.661524	−0.330762	−	0.943714i	$-0.607306\pi$
$887$	−19.7019	−0.661524	−0.330762	+	0.943714i	$0.607306\pi$
$888$	60.4581	2.02884
$889$	50.4216	1.69108
$890$	−86.3437	−2.89425
$891$	10.6493	0.356767
$892$	1.08260	0.0362481
$893$	−1.94986	−0.0652496
$894$	41.7254	1.39551
$895$	64.5881	2.15894
$896$	−47.3988	−1.58348
$897$	−28.0568	−0.936790
$898$	52.7619	1.76069
$899$	10.0877	0.336443
$900$	−4.57664	−0.152555
$901$	9.81199	0.326885
$902$	9.40269	0.313075
$903$	−11.5333	−0.383804
$904$	29.8367	0.992354
$905$	11.1001	0.368981
$906$	8.37507	0.278243
$907$	−25.2552	−0.838585	−0.419293	−	0.907851i	$-0.637722\pi$
$907$	−25.2552	−0.838585	−0.419293	+	0.907851i	$0.637722\pi$
$908$	−1.15658	−0.0383825
$909$	6.38642	0.211824
$910$	−76.6478	−2.54085
$911$	−46.1531	−1.52912	−0.764560	−	0.644552i	$-0.777044\pi$
$911$	−46.1531	−1.52912	−0.764560	+	0.644552i	$0.777044\pi$
$912$	50.8185	1.68277
$913$	−10.2363	−0.338771
$914$	−43.1309	−1.42664
$915$	−107.854	−3.56555
$916$	−0.408086	−0.0134835
$917$	56.9785	1.88160
$918$	−2.24011	−0.0739347
$919$	−14.5901	−0.481285	−0.240642	−	0.970614i	$-0.577358\pi$
$919$	−14.5901	−0.481285	−0.240642	+	0.970614i	$0.577358\pi$
$920$	−49.4383	−1.62993
$921$	3.24070	0.106785
$922$	−24.9287	−0.820982
$923$	43.2813	1.42462
$924$	2.19215	0.0721165
$925$	94.5580	3.10905
$926$	−3.54856	−0.116613
$927$	33.5949	1.10340
$928$	−2.92501	−0.0960181
$929$	−25.0091	−0.820523	−0.410261	−	0.911968i	$-0.634563\pi$
$929$	−25.0091	−0.820523	−0.410261	+	0.911968i	$0.634563\pi$
$930$	−45.0728	−1.47799
$931$	112.470	3.68607
$932$	−4.89519	−0.160347
$933$	−12.9696	−0.424607
$934$	49.7682	1.62846
$935$	−3.94764	−0.129102
$936$	19.2648	0.629688
$937$	26.0324	0.850442	0.425221	−	0.905090i	$-0.360196\pi$
$937$	26.0324	0.850442	0.425221	+	0.905090i	$0.360196\pi$
$938$	−61.9717	−2.02345
$939$	18.9267	0.617650
$940$	−0.236964	−0.00772893
$941$	45.6686	1.48875	0.744376	−	0.667760i	$-0.232747\pi$
$941$	45.6686	1.48875	0.744376	+	0.667760i	$0.232747\pi$
$942$	24.2491	0.790079
$943$	29.7070	0.967392
$944$	20.2946	0.660532
$945$	33.0079	1.07375
$946$	1.34534	0.0437406
$947$	−40.1943	−1.30614	−0.653069	−	0.757298i	$-0.726519\pi$
$947$	−40.1943	−1.30614	−0.653069	+	0.757298i	$0.726519\pi$
$948$	4.67762	0.151922
$949$	−32.0116	−1.03914
$950$	87.9124	2.85225
$951$	−42.6496	−1.38301
$952$	−14.7955	−0.479526
$953$	−22.2483	−0.720692	−0.360346	−	0.932819i	$-0.617341\pi$
$953$	−22.2483	−0.720692	−0.360346	+	0.932819i	$0.617341\pi$
$954$	−30.0312	−0.972296
$955$	52.8354	1.70971
$956$	−2.39088	−0.0773267
$957$	−6.27004	−0.202682
$958$	−14.0675	−0.454501
$959$	71.3779	2.30491
$960$	78.0545	2.51920
$961$	−17.3458	−0.559541
$962$	−34.5441	−1.11375
$963$	−13.3946	−0.431635
$964$	−0.913726	−0.0294291
$965$	−12.8901	−0.414946
$966$	−65.9510	−2.12194
$967$	−3.56737	−0.114719	−0.0573594	−	0.998354i	$-0.518268\pi$
$967$	−3.56737	−0.114719	−0.0573594	+	0.998354i	$0.518268\pi$
$968$	−2.94638	−0.0947003
$969$	14.1803	0.455538
$970$	−66.5668	−2.13733
$971$	8.54947	0.274365	0.137183	−	0.990546i	$-0.456195\pi$
$971$	8.54947	0.274365	0.137183	+	0.990546i	$0.456195\pi$
$972$	−3.69945	−0.118660
$973$	80.2670	2.57324
$974$	7.90793	0.253386
$975$	69.8629	2.23740
$976$	42.6307	1.36458
$977$	49.2436	1.57544	0.787721	−	0.616033i	$-0.211261\pi$
$977$	49.2436	1.57544	0.787721	+	0.616033i	$0.211261\pi$
$978$	−48.3992	−1.54764
$979$	−16.2578	−0.519602
$980$	13.6684	0.436621
$981$	8.43453	0.269294
$982$	25.3248	0.808148
$983$	−35.3994	−1.12907	−0.564533	−	0.825410i	$-0.690944\pi$
$983$	−35.3994	−1.12907	−0.564533	+	0.825410i	$0.690944\pi$
$984$	−47.2958	−1.50773
$985$	−74.5937	−2.37675
$986$	3.67273	0.116964
$987$	−3.64236	−0.115938
$988$	3.37272	0.107301
$989$	4.25047	0.135157
$990$	12.0824	0.384004
$991$	−61.5869	−1.95637	−0.978186	−	0.207733i	$-0.933392\pi$
$991$	−61.5869	−1.95637	−0.978186	+	0.207733i	$0.933392\pi$
$992$	−3.95915	−0.125703
$993$	−43.6577	−1.38543
$994$	101.738	3.22693
$995$	22.0910	0.700333
$996$	4.46859	0.141593
$997$	24.0316	0.761088	0.380544	−	0.924763i	$-0.375737\pi$
$997$	24.0316	0.761088	0.380544	+	0.924763i	$0.375737\pi$
$998$	−8.58383	−0.271716
$999$	14.8762	0.470663

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8041.2.a.h.1.53	✓	74

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8041.2.a.h.1.53	✓	74	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)

\(f(q)\)	\(=\)	\(q+1.34534 q^{2} -2.29674 q^{3} -0.190071 q^{4} -3.94764 q^{5} -3.08989 q^{6} -5.02160 q^{7} -2.94638 q^{8} +2.27502 q^{9} +O(q^{10})\)	\(q+1.34534 q^{2} -2.29674 q^{3} -0.190071 q^{4} -3.94764 q^{5} -3.08989 q^{6} -5.02160 q^{7} -2.94638 q^{8} +2.27502 q^{9} -5.31090 q^{10} -1.00000 q^{11} +0.436545 q^{12} -2.87402 q^{13} -6.75573 q^{14} +9.06671 q^{15} -3.58373 q^{16} -1.00000 q^{17} +3.06066 q^{18} +6.17411 q^{19} +0.750334 q^{20} +11.5333 q^{21} -1.34534 q^{22} -4.25047 q^{23} +6.76707 q^{24} +10.5839 q^{25} -3.86652 q^{26} +1.66509 q^{27} +0.954462 q^{28} -2.72997 q^{29} +12.1978 q^{30} -3.69516 q^{31} +1.07144 q^{32} +2.29674 q^{33} -1.34534 q^{34} +19.8235 q^{35} -0.432416 q^{36} +8.93416 q^{37} +8.30626 q^{38} +6.60088 q^{39} +11.6313 q^{40} -6.98910 q^{41} +15.5162 q^{42} -1.00000 q^{43} +0.190071 q^{44} -8.98096 q^{45} -5.71831 q^{46} -0.315812 q^{47} +8.23090 q^{48} +18.2164 q^{49} +14.2389 q^{50} +2.29674 q^{51} +0.546269 q^{52} -9.81199 q^{53} +2.24011 q^{54} +3.94764 q^{55} +14.7955 q^{56} -14.1803 q^{57} -3.67273 q^{58} -5.66297 q^{59} -1.72332 q^{60} -11.8956 q^{61} -4.97124 q^{62} -11.4242 q^{63} +8.60891 q^{64} +11.3456 q^{65} +3.08989 q^{66} +9.17320 q^{67} +0.190071 q^{68} +9.76223 q^{69} +26.6692 q^{70} -15.0595 q^{71} -6.70307 q^{72} +11.1383 q^{73} +12.0194 q^{74} -24.3084 q^{75} -1.17352 q^{76} +5.02160 q^{77} +8.88040 q^{78} +10.7151 q^{79} +14.1473 q^{80} -10.6493 q^{81} -9.40269 q^{82} +10.2363 q^{83} -2.19215 q^{84} +3.94764 q^{85} -1.34534 q^{86} +6.27004 q^{87} +2.94638 q^{88} +16.2578 q^{89} -12.0824 q^{90} +14.4322 q^{91} +0.807893 q^{92} +8.48683 q^{93} -0.424873 q^{94} -24.3732 q^{95} -2.46083 q^{96} +12.5340 q^{97} +24.5072 q^{98} -2.27502 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 74 q - 7 q^{2} - 3 q^{3} + 79 q^{4} - 6 q^{5} - 12 q^{6} - 16 q^{7} - 21 q^{8} + 75 q^{9}+O(q^{10}) \) 74 * q - 7 * q^2 - 3 * q^3 + 79 * q^4 - 6 * q^5 - 12 * q^6 - 16 * q^7 - 21 * q^8 + 75 * q^9	\( 74 q - 7 q^{2} - 3 q^{3} + 79 q^{4} - 6 q^{5} - 12 q^{6} - 16 q^{7} - 21 q^{8} + 75 q^{9} - 9 q^{10} - 74 q^{11} - 3 q^{12} + 4 q^{13} - 5 q^{14} - 17 q^{15} + 85 q^{16} - 74 q^{17} - 23 q^{18} - 21 q^{20} - 22 q^{21} + 7 q^{22} - 23 q^{23} - 51 q^{24} + 90 q^{25} - 46 q^{26} - 27 q^{27} - 61 q^{28} - 63 q^{29} - 22 q^{30} - 31 q^{31} - 69 q^{32} + 3 q^{33} + 7 q^{34} - 20 q^{35} + 51 q^{36} + 8 q^{37} - 2 q^{38} - 77 q^{39} - 37 q^{40} - 64 q^{41} + 13 q^{42} - 74 q^{43} - 79 q^{44} - 12 q^{45} - 53 q^{46} - 32 q^{47} + 2 q^{48} + 78 q^{49} - 104 q^{50} + 3 q^{51} + 13 q^{52} + 25 q^{53} - 110 q^{54} + 6 q^{55} - 29 q^{56} - 29 q^{57} - 14 q^{58} - 61 q^{59} - 82 q^{60} - 36 q^{61} - 63 q^{62} - 104 q^{63} + 107 q^{64} - 65 q^{65} + 12 q^{66} + 33 q^{67} - 79 q^{68} - 34 q^{69} - 3 q^{70} - 168 q^{71} - 67 q^{72} - 47 q^{73} - 54 q^{74} - 53 q^{75} - 4 q^{76} + 16 q^{77} - 3 q^{78} - 79 q^{79} - 59 q^{80} + 70 q^{81} - 18 q^{82} - 36 q^{83} - 118 q^{84} + 6 q^{85} + 7 q^{86} - 24 q^{87} + 21 q^{88} - 24 q^{89} + 25 q^{90} - 14 q^{91} - 18 q^{92} - 13 q^{93} + 9 q^{94} - 155 q^{95} - 50 q^{96} + q^{97} - 60 q^{98} - 75 q^{99}+O(q^{100}) \) 74 * q - 7 * q^2 - 3 * q^3 + 79 * q^4 - 6 * q^5 - 12 * q^6 - 16 * q^7 - 21 * q^8 + 75 * q^9 - 9 * q^10 - 74 * q^11 - 3 * q^12 + 4 * q^13 - 5 * q^14 - 17 * q^15 + 85 * q^16 - 74 * q^17 - 23 * q^18 - 21 * q^20 - 22 * q^21 + 7 * q^22 - 23 * q^23 - 51 * q^24 + 90 * q^25 - 46 * q^26 - 27 * q^27 - 61 * q^28 - 63 * q^29 - 22 * q^30 - 31 * q^31 - 69 * q^32 + 3 * q^33 + 7 * q^34 - 20 * q^35 + 51 * q^36 + 8 * q^37 - 2 * q^38 - 77 * q^39 - 37 * q^40 - 64 * q^41 + 13 * q^42 - 74 * q^43 - 79 * q^44 - 12 * q^45 - 53 * q^46 - 32 * q^47 + 2 * q^48 + 78 * q^49 - 104 * q^50 + 3 * q^51 + 13 * q^52 + 25 * q^53 - 110 * q^54 + 6 * q^55 - 29 * q^56 - 29 * q^57 - 14 * q^58 - 61 * q^59 - 82 * q^60 - 36 * q^61 - 63 * q^62 - 104 * q^63 + 107 * q^64 - 65 * q^65 + 12 * q^66 + 33 * q^67 - 79 * q^68 - 34 * q^69 - 3 * q^70 - 168 * q^71 - 67 * q^72 - 47 * q^73 - 54 * q^74 - 53 * q^75 - 4 * q^76 + 16 * q^77 - 3 * q^78 - 79 * q^79 - 59 * q^80 + 70 * q^81 - 18 * q^82 - 36 * q^83 - 118 * q^84 + 6 * q^85 + 7 * q^86 - 24 * q^87 + 21 * q^88 - 24 * q^89 + 25 * q^90 - 14 * q^91 - 18 * q^92 - 13 * q^93 + 9 * q^94 - 155 * q^95 - 50 * q^96 + q^97 - 60 * q^98 - 75 * q^99

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