LMFDB - Embedded newform 1441.2.a.f.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1441,2,Mod(1,1441)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1441, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1441.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1441 = 11 \cdot 131 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1441.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:	$11.5064429313$
Analytic rank:	$0$
Dimension:	$31$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Character	$\chi$	$=$	1441.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.31847 q^{2} -2.88980 q^{3} -0.261634 q^{4} -1.34376 q^{5} +3.81011 q^{6} +0.384750 q^{7} +2.98190 q^{8} +5.35092 q^{9} +O(q^{10})$	\(q-1.31847 q^{2} -2.88980 q^{3} -0.261634 q^{4} -1.34376 q^{5} +3.81011 q^{6} +0.384750 q^{7} +2.98190 q^{8} +5.35092 q^{9} +1.77171 q^{10} -1.00000 q^{11} +0.756070 q^{12} +6.11632 q^{13} -0.507281 q^{14} +3.88320 q^{15} -3.40828 q^{16} -5.49693 q^{17} -7.05503 q^{18} -6.99481 q^{19} +0.351574 q^{20} -1.11185 q^{21} +1.31847 q^{22} +9.47900 q^{23} -8.61708 q^{24} -3.19430 q^{25} -8.06420 q^{26} -6.79368 q^{27} -0.100664 q^{28} -3.10401 q^{29} -5.11989 q^{30} +3.96088 q^{31} -1.47008 q^{32} +2.88980 q^{33} +7.24755 q^{34} -0.517012 q^{35} -1.39998 q^{36} -11.3376 q^{37} +9.22245 q^{38} -17.6749 q^{39} -4.00697 q^{40} +5.98983 q^{41} +1.46594 q^{42} -8.37891 q^{43} +0.261634 q^{44} -7.19037 q^{45} -12.4978 q^{46} -1.61030 q^{47} +9.84923 q^{48} -6.85197 q^{49} +4.21159 q^{50} +15.8850 q^{51} -1.60024 q^{52} -5.83561 q^{53} +8.95727 q^{54} +1.34376 q^{55} +1.14728 q^{56} +20.2136 q^{57} +4.09254 q^{58} +9.38957 q^{59} -1.01598 q^{60} -0.231717 q^{61} -5.22231 q^{62} +2.05876 q^{63} +8.75482 q^{64} -8.21889 q^{65} -3.81011 q^{66} +3.76405 q^{67} +1.43819 q^{68} -27.3924 q^{69} +0.681666 q^{70} +10.9335 q^{71} +15.9559 q^{72} +6.85220 q^{73} +14.9483 q^{74} +9.23088 q^{75} +1.83008 q^{76} -0.384750 q^{77} +23.3039 q^{78} +11.9499 q^{79} +4.57992 q^{80} +3.57958 q^{81} -7.89741 q^{82} +5.51272 q^{83} +0.290897 q^{84} +7.38658 q^{85} +11.0473 q^{86} +8.96994 q^{87} -2.98190 q^{88} -12.6399 q^{89} +9.48029 q^{90} +2.35325 q^{91} -2.48003 q^{92} -11.4461 q^{93} +2.12313 q^{94} +9.39937 q^{95} +4.24823 q^{96} -10.5412 q^{97} +9.03412 q^{98} -5.35092 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 31 q + 6 q^{2} + 4 q^{3} + 38 q^{4} + 8 q^{5} + 7 q^{6} + 4 q^{7} + 24 q^{8} + 45 q^{9}+O(q^{10}) $ 31 * q + 6 * q^2 + 4 * q^3 + 38 * q^4 + 8 * q^5 + 7 * q^6 + 4 * q^7 + 24 * q^8 + 45 * q^9	\( 31 q + 6 q^{2} + 4 q^{3} + 38 q^{4} + 8 q^{5} + 7 q^{6} + 4 q^{7} + 24 q^{8} + 45 q^{9} - 8 q^{10} - 31 q^{11} + 10 q^{12} - 8 q^{13} + 29 q^{14} + 36 q^{15} + 52 q^{16} - q^{17} + 33 q^{18} - 2 q^{19} + 22 q^{20} - 13 q^{21} - 6 q^{22} + 45 q^{23} + 16 q^{24} + 41 q^{25} + 24 q^{26} + 22 q^{27} + 17 q^{28} + 5 q^{29} + 29 q^{30} + 28 q^{31} + 69 q^{32} - 4 q^{33} + 14 q^{34} + 36 q^{35} + 63 q^{36} - 3 q^{37} + 4 q^{38} + 40 q^{39} - 48 q^{40} + 21 q^{41} - 9 q^{42} - 20 q^{43} - 38 q^{44} + 28 q^{45} - 24 q^{46} + 57 q^{47} - 46 q^{48} + 37 q^{49} + 64 q^{50} + 17 q^{51} - 11 q^{52} + 32 q^{53} - 26 q^{54} - 8 q^{55} + 84 q^{56} + 10 q^{57} - 17 q^{58} + 70 q^{59} - 33 q^{60} - 51 q^{61} - 34 q^{62} + 32 q^{63} + 80 q^{64} - q^{65} - 7 q^{66} + 24 q^{67} - 13 q^{68} + 19 q^{69} - 9 q^{70} + 128 q^{71} + 118 q^{72} - 27 q^{73} - 23 q^{74} + 41 q^{75} - 34 q^{76} - 4 q^{77} + 9 q^{78} + 2 q^{79} - 45 q^{80} + 43 q^{81} - 18 q^{82} + 46 q^{83} - 103 q^{84} - 50 q^{85} + 78 q^{86} - 9 q^{87} - 24 q^{88} + 52 q^{89} - 46 q^{90} + 38 q^{91} + 54 q^{92} + 4 q^{93} + 3 q^{94} + 70 q^{95} - 21 q^{96} + 3 q^{97} - 120 q^{98} - 45 q^{99}+O(q^{100}) \) 31 * q + 6 * q^2 + 4 * q^3 + 38 * q^4 + 8 * q^5 + 7 * q^6 + 4 * q^7 + 24 * q^8 + 45 * q^9 - 8 * q^10 - 31 * q^11 + 10 * q^12 - 8 * q^13 + 29 * q^14 + 36 * q^15 + 52 * q^16 - q^17 + 33 * q^18 - 2 * q^19 + 22 * q^20 - 13 * q^21 - 6 * q^22 + 45 * q^23 + 16 * q^24 + 41 * q^25 + 24 * q^26 + 22 * q^27 + 17 * q^28 + 5 * q^29 + 29 * q^30 + 28 * q^31 + 69 * q^32 - 4 * q^33 + 14 * q^34 + 36 * q^35 + 63 * q^36 - 3 * q^37 + 4 * q^38 + 40 * q^39 - 48 * q^40 + 21 * q^41 - 9 * q^42 - 20 * q^43 - 38 * q^44 + 28 * q^45 - 24 * q^46 + 57 * q^47 - 46 * q^48 + 37 * q^49 + 64 * q^50 + 17 * q^51 - 11 * q^52 + 32 * q^53 - 26 * q^54 - 8 * q^55 + 84 * q^56 + 10 * q^57 - 17 * q^58 + 70 * q^59 - 33 * q^60 - 51 * q^61 - 34 * q^62 + 32 * q^63 + 80 * q^64 - q^65 - 7 * q^66 + 24 * q^67 - 13 * q^68 + 19 * q^69 - 9 * q^70 + 128 * q^71 + 118 * q^72 - 27 * q^73 - 23 * q^74 + 41 * q^75 - 34 * q^76 - 4 * q^77 + 9 * q^78 + 2 * q^79 - 45 * q^80 + 43 * q^81 - 18 * q^82 + 46 * q^83 - 103 * q^84 - 50 * q^85 + 78 * q^86 - 9 * q^87 - 24 * q^88 + 52 * q^89 - 46 * q^90 + 38 * q^91 + 54 * q^92 + 4 * q^93 + 3 * q^94 + 70 * q^95 - 21 * q^96 + 3 * q^97 - 120 * q^98 - 45 * 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 $

$2$	−1.31847	−0.932300	−0.466150	−	0.884706i	$-0.654359\pi$
$2$	−1.31847	−0.932300	−0.466150	+	0.884706i	$0.654359\pi$
$3$	−2.88980	−1.66842	−0.834212	−	0.551444i	$-0.814077\pi$
$3$	−2.88980	−1.66842	−0.834212	+	0.551444i	$0.814077\pi$
$4$	−0.261634	−0.130817
$5$	−1.34376	−0.600949	−0.300475	−	0.953790i	$-0.597145\pi$
$5$	−1.34376	−0.600949	−0.300475	+	0.953790i	$0.597145\pi$
$6$	3.81011	1.55547
$7$	0.384750	0.145422	0.0727108	−	0.997353i	$-0.476835\pi$
$7$	0.384750	0.145422	0.0727108	+	0.997353i	$0.476835\pi$
$8$	2.98190	1.05426
$9$	5.35092	1.78364
$10$	1.77171	0.560265
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	0.756070	0.218258
$13$	6.11632	1.69636	0.848182	−	0.529706i	$-0.177698\pi$
$13$	6.11632	1.69636	0.848182	+	0.529706i	$0.177698\pi$
$14$	−0.507281	−0.135577
$15$	3.88320	1.00264
$16$	−3.40828	−0.852070
$17$	−5.49693	−1.33320	−0.666601	−	0.745415i	$-0.732252\pi$
$17$	−5.49693	−1.33320	−0.666601	+	0.745415i	$0.732252\pi$
$18$	−7.05503	−1.66289
$19$	−6.99481	−1.60472	−0.802360	−	0.596841i	$-0.796422\pi$
$19$	−6.99481	−1.60472	−0.802360	+	0.596841i	$0.796422\pi$
$20$	0.351574	0.0786144
$21$	−1.11185	−0.242625
$22$	1.31847	0.281099
$23$	9.47900	1.97651	0.988254	−	0.152819i	$-0.0488351\pi$
$23$	9.47900	1.97651	0.988254	+	0.152819i	$0.0488351\pi$
$24$	−8.61708	−1.75895
$25$	−3.19430	−0.638860
$26$	−8.06420	−1.58152
$27$	−6.79368	−1.30744
$28$	−0.100664	−0.0190236
$29$	−3.10401	−0.576399	−0.288200	−	0.957570i	$-0.593057\pi$
$29$	−3.10401	−0.576399	−0.288200	+	0.957570i	$0.593057\pi$
$30$	−5.11989	−0.934759
$31$	3.96088	0.711395	0.355698	−	0.934601i	$-0.384243\pi$
$31$	3.96088	0.711395	0.355698	+	0.934601i	$0.384243\pi$
$32$	−1.47008	−0.259876
$33$	2.88980	0.503049
$34$	7.24755	1.24294
$35$	−0.517012	−0.0873910
$36$	−1.39998	−0.233331
$37$	−11.3376	−1.86389	−0.931946	−	0.362597i	$-0.881890\pi$
$37$	−11.3376	−1.86389	−0.931946	+	0.362597i	$0.881890\pi$
$38$	9.22245	1.49608
$39$	−17.6749	−2.83025
$40$	−4.00697	−0.633557
$41$	5.98983	0.935454	0.467727	−	0.883873i	$-0.345073\pi$
$41$	5.98983	0.935454	0.467727	+	0.883873i	$0.345073\pi$
$42$	1.46594	0.226199
$43$	−8.37891	−1.27777	−0.638886	−	0.769302i	$-0.720604\pi$
$43$	−8.37891	−1.27777	−0.638886	+	0.769302i	$0.720604\pi$
$44$	0.261634	0.0394428
$45$	−7.19037	−1.07188
$46$	−12.4978	−1.84270
$47$	−1.61030	−0.234886	−0.117443	−	0.993080i	$-0.537470\pi$
$47$	−1.61030	−0.234886	−0.117443	+	0.993080i	$0.537470\pi$
$48$	9.84923	1.42161
$49$	−6.85197	−0.978853
$50$	4.21159	0.595609
$51$	15.8850	2.22435
$52$	−1.60024	−0.221913
$53$	−5.83561	−0.801582	−0.400791	−	0.916169i	$-0.631265\pi$
$53$	−5.83561	−0.801582	−0.400791	+	0.916169i	$0.631265\pi$
$54$	8.95727	1.21893
$55$	1.34376	0.181193
$56$	1.14728	0.153312
$57$	20.2136	2.67735
$58$	4.09254	0.537377
$59$	9.38957	1.22242	0.611209	−	0.791469i	$-0.290684\pi$
$59$	9.38957	1.22242	0.611209	+	0.791469i	$0.290684\pi$
$60$	−1.01598	−0.131162
$61$	−0.231717	−0.0296683	−0.0148342	−	0.999890i	$-0.504722\pi$
$61$	−0.231717	−0.0296683	−0.0148342	+	0.999890i	$0.504722\pi$
$62$	−5.22231	−0.663234
$63$	2.05876	0.259380
$64$	8.75482	1.09435
$65$	−8.21889	−1.01943
$66$	−3.81011	−0.468992
$67$	3.76405	0.459853	0.229926	−	0.973208i	$-0.426152\pi$
$67$	3.76405	0.459853	0.229926	+	0.973208i	$0.426152\pi$
$68$	1.43819	0.174406
$69$	−27.3924	−3.29765
$70$	0.681666	0.0814746
$71$	10.9335	1.29757	0.648786	−	0.760971i	$-0.275277\pi$
$71$	10.9335	1.29757	0.648786	+	0.760971i	$0.275277\pi$
$72$	15.9559	1.88042
$73$	6.85220	0.801990	0.400995	−	0.916080i	$-0.368664\pi$
$73$	6.85220	0.801990	0.400995	+	0.916080i	$0.368664\pi$
$74$	14.9483	1.73771
$75$	9.23088	1.06589
$76$	1.83008	0.209925
$77$	−0.384750	−0.0438463
$78$	23.3039	2.63864
$79$	11.9499	1.34447	0.672235	−	0.740338i	$-0.265334\pi$
$79$	11.9499	1.34447	0.672235	+	0.740338i	$0.265334\pi$
$80$	4.57992	0.512051
$81$	3.57958	0.397731
$82$	−7.89741	−0.872123
$83$	5.51272	0.605100	0.302550	−	0.953134i	$-0.402162\pi$
$83$	5.51272	0.605100	0.302550	+	0.953134i	$0.402162\pi$
$84$	0.290897	0.0317395
$85$	7.38658	0.801187
$86$	11.0473	1.19127
$87$	8.96994	0.961679
$88$	−2.98190	−0.317872
$89$	−12.6399	−1.33983	−0.669916	−	0.742437i	$-0.733670\pi$
$89$	−12.6399	−1.33983	−0.669916	+	0.742437i	$0.733670\pi$
$90$	9.48029	0.999311
$91$	2.35325	0.246688
$92$	−2.48003	−0.258561
$93$	−11.4461	−1.18691
$94$	2.12313	0.218984
$95$	9.39937	0.964355
$96$	4.24823	0.433584
$97$	−10.5412	−1.07030	−0.535150	−	0.844757i	$-0.679745\pi$
$97$	−10.5412	−1.07030	−0.535150	+	0.844757i	$0.679745\pi$
$98$	9.03412	0.912584
$99$	−5.35092	−0.537788
$100$	0.835738	0.0835738
$101$	1.63507	0.162696	0.0813480	−	0.996686i	$-0.474077\pi$
$101$	1.63507	0.162696	0.0813480	+	0.996686i	$0.474077\pi$
$102$	−20.9439	−2.07376
$103$	−10.5749	−1.04198	−0.520989	−	0.853563i	$-0.674437\pi$
$103$	−10.5749	−1.04198	−0.520989	+	0.853563i	$0.674437\pi$
$104$	18.2383	1.78841
$105$	1.49406	0.145805
$106$	7.69408	0.747315
$107$	−4.44882	−0.430084	−0.215042	−	0.976605i	$-0.568989\pi$
$107$	−4.44882	−0.430084	−0.215042	+	0.976605i	$0.568989\pi$
$108$	1.77746	0.171036
$109$	−14.6570	−1.40388	−0.701942	−	0.712234i	$-0.747684\pi$
$109$	−14.6570	−1.40388	−0.701942	+	0.712234i	$0.747684\pi$
$110$	−1.77171	−0.168926
$111$	32.7634	3.10976
$112$	−1.31133	−0.123909
$113$	2.25869	0.212480	0.106240	−	0.994341i	$-0.466119\pi$
$113$	2.25869	0.212480	0.106240	+	0.994341i	$0.466119\pi$
$114$	−26.6510	−2.49610
$115$	−12.7375	−1.18778
$116$	0.812114	0.0754029
$117$	32.7280	3.02570
$118$	−12.3799	−1.13966
$119$	−2.11494	−0.193876
$120$	11.5793	1.05704
$121$	1.00000	0.0909091
$122$	0.305512	0.0276598
$123$	−17.3094	−1.56073
$124$	−1.03630	−0.0930627
$125$	11.0112	0.984872
$126$	−2.71442	−0.241820
$127$	20.8510	1.85023	0.925113	−	0.379691i	$-0.123970\pi$
$127$	20.8510	1.85023	0.925113	+	0.379691i	$0.123970\pi$
$128$	−8.60281	−0.760388
$129$	24.2133	2.13186
$130$	10.8364	0.950413
$131$	1.00000	0.0873704
$131$	1.00000	0.0873704
$132$	−0.756070	−0.0658074
$133$	−2.69125	−0.233361
$134$	−4.96280	−0.428720
$135$	9.12909	0.785707
$136$	−16.3913	−1.40554
$137$	7.44832	0.636353	0.318176	−	0.948032i	$-0.396930\pi$
$137$	7.44832	0.636353	0.318176	+	0.948032i	$0.396930\pi$
$138$	36.1161	3.07440
$139$	12.0724	1.02397	0.511985	−	0.858994i	$-0.328910\pi$
$139$	12.0724	1.02397	0.511985	+	0.858994i	$0.328910\pi$
$140$	0.135268	0.0114322
$141$	4.65343	0.391890
$142$	−14.4156	−1.20973
$143$	−6.11632	−0.511473
$144$	−18.2374	−1.51979
$145$	4.17105	0.346387
$146$	−9.03443	−0.747695
$147$	19.8008	1.63314
$148$	2.96631	0.243829
$149$	17.9876	1.47360	0.736799	−	0.676112i	$-0.236336\pi$
$149$	17.9876	1.47360	0.736799	+	0.676112i	$0.236336\pi$
$150$	−12.1706	−0.993729
$151$	−13.6163	−1.10808	−0.554040	−	0.832490i	$-0.686915\pi$
$151$	−13.6163	−1.10808	−0.554040	+	0.832490i	$0.686915\pi$
$152$	−20.8578	−1.69179
$153$	−29.4136	−2.37795
$154$	0.507281	0.0408779
$155$	−5.32249	−0.427512
$156$	4.62437	0.370246
$157$	−5.47369	−0.436848	−0.218424	−	0.975854i	$-0.570092\pi$
$157$	−5.47369	−0.436848	−0.218424	+	0.975854i	$0.570092\pi$
$158$	−15.7556	−1.25345
$159$	16.8637	1.33738
$160$	1.97544	0.156172
$161$	3.64704	0.287427
$162$	−4.71957	−0.370805
$163$	0.393309	0.0308063	0.0154032	−	0.999881i	$-0.495097\pi$
$163$	0.393309	0.0308063	0.0154032	+	0.999881i	$0.495097\pi$
$164$	−1.56714	−0.122373
$165$	−3.88320	−0.302307
$166$	−7.26836	−0.564134
$167$	−16.4533	−1.27320	−0.636599	−	0.771195i	$-0.719659\pi$
$167$	−16.4533	−1.27320	−0.636599	+	0.771195i	$0.719659\pi$
$168$	−3.31542	−0.255790
$169$	24.4094	1.87765
$170$	−9.73899	−0.746946
$171$	−37.4287	−2.86224
$172$	2.19221	0.167154
$173$	−3.31287	−0.251873	−0.125937	−	0.992038i	$-0.540194\pi$
$173$	−3.31287	−0.251873	−0.125937	+	0.992038i	$0.540194\pi$
$174$	−11.8266	−0.896573
$175$	−1.22901	−0.0929041
$176$	3.40828	0.256909
$177$	−27.1339	−2.03951
$178$	16.6654	1.24912
$179$	14.9898	1.12039	0.560196	−	0.828360i	$-0.310726\pi$
$179$	14.9898	1.12039	0.560196	+	0.828360i	$0.310726\pi$
$180$	1.88125	0.140220
$181$	13.8252	1.02762	0.513811	−	0.857904i	$-0.328233\pi$
$181$	13.8252	1.02762	0.513811	+	0.857904i	$0.328233\pi$
$182$	−3.10270	−0.229987
$183$	0.669614	0.0494993
$184$	28.2654	2.08375
$185$	15.2351	1.12010
$186$	15.0914	1.10656
$187$	5.49693	0.401976
$188$	0.421309	0.0307271
$189$	−2.61386	−0.190131
$190$	−12.3928	−0.899068
$191$	8.96584	0.648745	0.324373	−	0.945929i	$-0.394847\pi$
$191$	8.96584	0.648745	0.324373	+	0.945929i	$0.394847\pi$
$192$	−25.2996	−1.82584
$193$	7.58333	0.545860	0.272930	−	0.962034i	$-0.412007\pi$
$193$	7.58333	0.545860	0.272930	+	0.962034i	$0.412007\pi$
$194$	13.8983	0.997840
$195$	23.7509	1.70084
$196$	1.79271	0.128051
$197$	1.14939	0.0818909	0.0409455	−	0.999161i	$-0.486963\pi$
$197$	1.14939	0.0818909	0.0409455	+	0.999161i	$0.486963\pi$
$198$	7.05503	0.501379
$199$	−1.65399	−0.117248	−0.0586242	−	0.998280i	$-0.518671\pi$
$199$	−1.65399	−0.117248	−0.0586242	+	0.998280i	$0.518671\pi$
$200$	−9.52508	−0.673525
$201$	−10.8773	−0.767229
$202$	−2.15580	−0.151681
$203$	−1.19426	−0.0838210
$204$	−4.15606	−0.290983
$205$	−8.04891	−0.562160
$206$	13.9427	0.971436
$207$	50.7214	3.52538
$208$	−20.8461	−1.44542
$209$	6.99481	0.483841
$210$	−1.96987	−0.135934
$211$	−2.42952	−0.167255	−0.0836275	−	0.996497i	$-0.526651\pi$
$211$	−2.42952	−0.167255	−0.0836275	+	0.996497i	$0.526651\pi$
$212$	1.52679	0.104861
$213$	−31.5957	−2.16490
$214$	5.86564	0.400967
$215$	11.2593	0.767875
$216$	−20.2581	−1.37839
$217$	1.52395	0.103452
$218$	19.3248	1.30884
$219$	−19.8015	−1.33806
$220$	−0.351574	−0.0237031
$221$	−33.6210	−2.26160
$222$	−43.1976	−2.89923
$223$	−10.6009	−0.709891	−0.354945	−	0.934887i	$-0.615501\pi$
$223$	−10.6009	−0.709891	−0.354945	+	0.934887i	$0.615501\pi$
$224$	−0.565613	−0.0377916
$225$	−17.0924	−1.13950
$226$	−2.97802	−0.198095
$227$	−19.3212	−1.28239	−0.641195	−	0.767378i	$-0.721561\pi$
$227$	−19.3212	−1.28239	−0.641195	+	0.767378i	$0.721561\pi$
$228$	−5.28856	−0.350244
$229$	16.8297	1.11214	0.556068	−	0.831137i	$-0.312309\pi$
$229$	16.8297	1.11214	0.556068	+	0.831137i	$0.312309\pi$
$230$	16.7941	1.10737
$231$	1.11185	0.0731542
$232$	−9.25583	−0.607675
$233$	22.8052	1.49402	0.747008	−	0.664815i	$-0.231490\pi$
$233$	22.8052	1.49402	0.747008	+	0.664815i	$0.231490\pi$
$234$	−43.1509	−2.82086
$235$	2.16386	0.141155
$236$	−2.45663	−0.159913
$237$	−34.5328	−2.24315
$238$	2.78849	0.180751
$239$	3.52631	0.228098	0.114049	−	0.993475i	$-0.463618\pi$
$239$	3.52631	0.228098	0.114049	+	0.993475i	$0.463618\pi$
$240$	−13.2350	−0.854318
$241$	11.2812	0.726686	0.363343	−	0.931656i	$-0.381635\pi$
$241$	11.2812	0.726686	0.363343	+	0.931656i	$0.381635\pi$
$242$	−1.31847	−0.0847545
$243$	10.0368	0.643859
$244$	0.0606251	0.00388112
$245$	9.20742	0.588241
$246$	22.8219	1.45507
$247$	−42.7825	−2.72219
$248$	11.8109	0.749996
$249$	−15.9306	−1.00956
$250$	−14.5179	−0.918196
$251$	23.8221	1.50364	0.751819	−	0.659369i	$-0.229177\pi$
$251$	23.8221	1.50364	0.751819	+	0.659369i	$0.229177\pi$
$252$	−0.538643	−0.0339313
$253$	−9.47900	−0.595940
$254$	−27.4914	−1.72497
$255$	−21.3457	−1.33672
$256$	−6.16708	−0.385442
$257$	8.51613	0.531222	0.265611	−	0.964080i	$-0.414426\pi$
$257$	8.51613	0.531222	0.265611	+	0.964080i	$0.414426\pi$
$258$	−31.9246	−1.98754
$259$	−4.36214	−0.271050
$260$	2.15034	0.133359
$261$	−16.6093	−1.02809
$262$	−1.31847	−0.0814554
$263$	14.7860	0.911745	0.455873	−	0.890045i	$-0.349327\pi$
$263$	14.7860	0.911745	0.455873	+	0.890045i	$0.349327\pi$
$264$	8.61708	0.530345
$265$	7.84168	0.481710
$266$	3.54833	0.217562
$267$	36.5269	2.23541
$268$	−0.984806	−0.0601566
$269$	−12.4788	−0.760845	−0.380422	−	0.924813i	$-0.624221\pi$
$269$	−12.4788	−0.760845	−0.380422	+	0.924813i	$0.624221\pi$
$270$	−12.0364	−0.732515
$271$	−9.36095	−0.568637	−0.284319	−	0.958730i	$-0.591767\pi$
$271$	−9.36095	−0.568637	−0.284319	+	0.958730i	$0.591767\pi$
$272$	18.7351	1.13598
$273$	−6.80042	−0.411580
$274$	−9.82039	−0.593271
$275$	3.19430	0.192624
$276$	7.16678	0.431390
$277$	−11.4638	−0.688793	−0.344396	−	0.938824i	$-0.611916\pi$
$277$	−11.4638	−0.688793	−0.344396	+	0.938824i	$0.611916\pi$
$278$	−15.9172	−0.954648
$279$	21.1944	1.26887
$280$	−1.54168	−0.0921329
$281$	1.83975	0.109750	0.0548750	−	0.998493i	$-0.482524\pi$
$281$	1.83975	0.109750	0.0548750	+	0.998493i	$0.482524\pi$
$282$	−6.13542	−0.365359
$283$	9.68105	0.575479	0.287739	−	0.957709i	$-0.407096\pi$
$283$	9.68105	0.575479	0.287739	+	0.957709i	$0.407096\pi$
$284$	−2.86059	−0.169745
$285$	−27.1623	−1.60895
$286$	8.06420	0.476846
$287$	2.30458	0.136035
$288$	−7.86629	−0.463525
$289$	13.2163	0.777428
$290$	−5.49941	−0.322936
$291$	30.4620	1.78571
$292$	−1.79277	−0.104914
$293$	−18.3091	−1.06963	−0.534816	−	0.844969i	$-0.679619\pi$
$293$	−18.3091	−1.06963	−0.534816	+	0.844969i	$0.679619\pi$
$294$	−26.1068	−1.52258
$295$	−12.6174	−0.734611
$296$	−33.8076	−1.96503
$297$	6.79368	0.394209
$298$	−23.7161	−1.37384
$299$	57.9766	3.35288
$300$	−2.41511	−0.139437
$301$	−3.22378	−0.185816
$302$	17.9527	1.03306
$303$	−4.72503	−0.271446
$304$	23.8403	1.36733
$305$	0.311373	0.0178291
$306$	38.7810	2.21696
$307$	−2.75934	−0.157484	−0.0787418	−	0.996895i	$-0.525090\pi$
$307$	−2.75934	−0.157484	−0.0787418	+	0.996895i	$0.525090\pi$
$308$	0.100664	0.00573584
$309$	30.5594	1.73846
$310$	7.01754	0.398570
$311$	11.4246	0.647829	0.323915	−	0.946086i	$-0.395001\pi$
$311$	11.4246	0.647829	0.323915	+	0.946086i	$0.395001\pi$
$312$	−52.7049	−2.98382
$313$	−28.7364	−1.62428	−0.812138	−	0.583466i	$-0.801696\pi$
$313$	−28.7364	−1.62428	−0.812138	+	0.583466i	$0.801696\pi$
$314$	7.21690	0.407273
$315$	−2.76649	−0.155874
$316$	−3.12651	−0.175880
$317$	31.3161	1.75889	0.879444	−	0.476003i	$-0.157915\pi$
$317$	31.3161	1.75889	0.879444	+	0.476003i	$0.157915\pi$
$318$	−22.2343	−1.24684
$319$	3.10401	0.173791
$320$	−11.7644	−0.657650
$321$	12.8562	0.717562
$322$	−4.80852	−0.267968
$323$	38.4500	2.13942
$324$	−0.936541	−0.0520300
$325$	−19.5374	−1.08374
$326$	−0.518566	−0.0287207
$327$	42.3557	2.34227
$328$	17.8611	0.986212
$329$	−0.619562	−0.0341575
$330$	5.11989	0.281841
$331$	10.1244	0.556485	0.278243	−	0.960511i	$-0.410248\pi$
$331$	10.1244	0.556485	0.278243	+	0.960511i	$0.410248\pi$
$332$	−1.44232	−0.0791574
$333$	−60.6666	−3.32451
$334$	21.6933	1.18700
$335$	−5.05800	−0.276348
$336$	3.78949	0.206733
$337$	15.1749	0.826627	0.413314	−	0.910589i	$-0.364371\pi$
$337$	15.1749	0.826627	0.413314	+	0.910589i	$0.364371\pi$
$338$	−32.1831	−1.75053
$339$	−6.52715	−0.354506
$340$	−1.93258	−0.104809
$341$	−3.96088	−0.214494
$342$	49.3486	2.66847
$343$	−5.32954	−0.287768
$344$	−24.9851	−1.34710
$345$	36.8089	1.98172
$346$	4.36793	0.234821
$347$	14.7261	0.790540	0.395270	−	0.918565i	$-0.370651\pi$
$347$	14.7261	0.790540	0.395270	+	0.918565i	$0.370651\pi$
$348$	−2.34684	−0.125804
$349$	23.9172	1.28026	0.640129	−	0.768267i	$-0.278881\pi$
$349$	23.9172	1.28026	0.640129	+	0.768267i	$0.278881\pi$
$350$	1.62041	0.0866145
$351$	−41.5523	−2.21790
$352$	1.47008	0.0783556
$353$	10.7072	0.569887	0.284944	−	0.958544i	$-0.408025\pi$
$353$	10.7072	0.569887	0.284944	+	0.958544i	$0.408025\pi$
$354$	35.7753	1.90144
$355$	−14.6921	−0.779775
$356$	3.30704	0.175273
$357$	6.11175	0.323468
$358$	−19.7636	−1.04454
$359$	21.0530	1.11113	0.555566	−	0.831472i	$-0.312501\pi$
$359$	21.0530	1.11113	0.555566	+	0.831472i	$0.312501\pi$
$360$	−21.4410	−1.13004
$361$	29.9274	1.57512
$362$	−18.2282	−0.958051
$363$	−2.88980	−0.151675
$364$	−0.615692	−0.0322710
$365$	−9.20774	−0.481955
$366$	−0.882867	−0.0461482
$367$	−20.1235	−1.05044	−0.525220	−	0.850967i	$-0.676017\pi$
$367$	−20.1235	−1.05044	−0.525220	+	0.850967i	$0.676017\pi$
$368$	−32.3071	−1.68412
$369$	32.0511	1.66851
$370$	−20.0870	−1.04427
$371$	−2.24525	−0.116567
$372$	2.99470	0.155268
$373$	−2.72976	−0.141342	−0.0706709	−	0.997500i	$-0.522514\pi$
$373$	−2.72976	−0.141342	−0.0706709	+	0.997500i	$0.522514\pi$
$374$	−7.24755	−0.374762
$375$	−31.8201	−1.64318
$376$	−4.80175	−0.247631
$377$	−18.9851	−0.977783
$378$	3.44630	0.177259
$379$	−14.1245	−0.725526	−0.362763	−	0.931881i	$-0.618166\pi$
$379$	−14.1245	−0.725526	−0.362763	+	0.931881i	$0.618166\pi$
$380$	−2.45920	−0.126154
$381$	−60.2551	−3.08696
$382$	−11.8212	−0.604825
$383$	3.70465	0.189299	0.0946495	−	0.995511i	$-0.469827\pi$
$383$	3.70465	0.189299	0.0946495	+	0.995511i	$0.469827\pi$
$384$	24.8604	1.26865
$385$	0.517012	0.0263494
$386$	−9.99840	−0.508905
$387$	−44.8348	−2.27908
$388$	2.75795	0.140014
$389$	−11.8789	−0.602284	−0.301142	−	0.953579i	$-0.597368\pi$
$389$	−11.8789	−0.602284	−0.301142	+	0.953579i	$0.597368\pi$
$390$	−31.3149	−1.58569
$391$	−52.1054	−2.63509
$392$	−20.4319	−1.03197
$393$	−2.88980	−0.145771
$394$	−1.51544	−0.0763469
$395$	−16.0579	−0.807958
$396$	1.39998	0.0703518
$397$	−39.3441	−1.97463	−0.987313	−	0.158789i	$-0.949241\pi$
$397$	−39.3441	−1.97463	−0.987313	+	0.158789i	$0.949241\pi$
$398$	2.18074	0.109311
$399$	7.77716	0.389345
$400$	10.8871	0.544353
$401$	36.9626	1.84582	0.922912	−	0.385012i	$-0.125803\pi$
$401$	36.9626	1.84582	0.922912	+	0.385012i	$0.125803\pi$
$402$	14.3415	0.715288
$403$	24.2260	1.20678
$404$	−0.427792	−0.0212834
$405$	−4.81011	−0.239016
$406$	1.57460	0.0781463
$407$	11.3376	0.561985
$408$	47.3675	2.34504
$409$	28.0751	1.38822	0.694112	−	0.719867i	$-0.255797\pi$
$409$	28.0751	1.38822	0.694112	+	0.719867i	$0.255797\pi$
$410$	10.6123	0.524102
$411$	−21.5241	−1.06171
$412$	2.76676	0.136309
$413$	3.61263	0.177766
$414$	−66.8747	−3.28671
$415$	−7.40779	−0.363634
$416$	−8.99149	−0.440844
$417$	−34.8869	−1.70842
$418$	−9.22245	−0.451085
$419$	−19.3388	−0.944763	−0.472382	−	0.881394i	$-0.656606\pi$
$419$	−19.3388	−0.944763	−0.472382	+	0.881394i	$0.656606\pi$
$420$	−0.390897	−0.0190738
$421$	25.4379	1.23977	0.619883	−	0.784694i	$-0.287180\pi$
$421$	25.4379	1.23977	0.619883	+	0.784694i	$0.287180\pi$
$422$	3.20325	0.155932
$423$	−8.61658	−0.418952
$424$	−17.4012	−0.845077
$425$	17.5589	0.851730
$426$	41.6580	2.01834
$427$	−0.0891530	−0.00431441
$428$	1.16396	0.0562623
$429$	17.6749	0.853354
$430$	−14.8450	−0.715890
$431$	22.1229	1.06562	0.532810	−	0.846235i	$-0.321136\pi$
$431$	22.1229	1.06562	0.532810	+	0.846235i	$0.321136\pi$
$432$	23.1547	1.11403
$433$	−22.7669	−1.09411	−0.547053	−	0.837098i	$-0.684250\pi$
$433$	−22.7669	−1.09411	−0.547053	+	0.837098i	$0.684250\pi$
$434$	−2.00928	−0.0964485
$435$	−12.0535	−0.577920
$436$	3.83477	0.183652
$437$	−66.3038	−3.17174
$438$	26.1077	1.24747
$439$	−1.75784	−0.0838970	−0.0419485	−	0.999120i	$-0.513357\pi$
$439$	−1.75784	−0.0838970	−0.0419485	+	0.999120i	$0.513357\pi$
$440$	4.00697	0.191025
$441$	−36.6643	−1.74592
$442$	44.3284	2.10848
$443$	22.8383	1.08508	0.542539	−	0.840030i	$-0.317463\pi$
$443$	22.8383	1.08508	0.542539	+	0.840030i	$0.317463\pi$
$444$	−8.57202	−0.406810
$445$	16.9851	0.805170
$446$	13.9770	0.661831
$447$	−51.9804	−2.45859
$448$	3.36841	0.159142
$449$	−9.54552	−0.450481	−0.225240	−	0.974303i	$-0.572317\pi$
$449$	−9.54552	−0.450481	−0.225240	+	0.974303i	$0.572317\pi$
$450$	22.5359	1.06235
$451$	−5.98983	−0.282050
$452$	−0.590951	−0.0277960
$453$	39.3484	1.84875
$454$	25.4744	1.19557
$455$	−3.16221	−0.148247
$456$	60.2748	2.82263
$457$	28.2396	1.32099	0.660497	−	0.750829i	$-0.270346\pi$
$457$	28.2396	1.32099	0.660497	+	0.750829i	$0.270346\pi$
$458$	−22.1894	−1.03684
$459$	37.3444	1.74309
$460$	3.33257	0.155382
$461$	−36.5188	−1.70085	−0.850425	−	0.526096i	$-0.823655\pi$
$461$	−36.5188	−1.70085	−0.850425	+	0.526096i	$0.823655\pi$
$462$	−1.46594	−0.0682016
$463$	35.0990	1.63119	0.815595	−	0.578624i	$-0.196410\pi$
$463$	35.0990	1.63119	0.815595	+	0.578624i	$0.196410\pi$
$464$	10.5793	0.491133
$465$	15.3809	0.713272
$466$	−30.0680	−1.39287
$467$	5.82268	0.269441	0.134721	−	0.990884i	$-0.456986\pi$
$467$	5.82268	0.269441	0.134721	+	0.990884i	$0.456986\pi$
$468$	−8.56276	−0.395814
$469$	1.44822	0.0668725
$470$	−2.85299	−0.131598
$471$	15.8178	0.728847
$472$	27.9987	1.28875
$473$	8.37891	0.385262
$474$	45.5305	2.09129
$475$	22.3435	1.02519
$476$	0.553341	0.0253624
$477$	−31.2259	−1.42973
$478$	−4.64934	−0.212656
$479$	36.1296	1.65080	0.825402	−	0.564546i	$-0.190949\pi$
$479$	36.1296	1.65080	0.825402	+	0.564546i	$0.190949\pi$
$480$	−5.70862	−0.260562
$481$	−69.3445	−3.16184
$482$	−14.8739	−0.677489
$483$	−10.5392	−0.479550
$484$	−0.261634	−0.0118925
$485$	14.1649	0.643196
$486$	−13.2332	−0.600270
$487$	20.2577	0.917963	0.458981	−	0.888446i	$-0.348214\pi$
$487$	20.2577	0.917963	0.458981	+	0.888446i	$0.348214\pi$
$488$	−0.690956	−0.0312781
$489$	−1.13658	−0.0513980
$490$	−12.1397	−0.548417
$491$	9.76525	0.440700	0.220350	−	0.975421i	$-0.429280\pi$
$491$	9.76525	0.440700	0.220350	+	0.975421i	$0.429280\pi$
$492$	4.52872	0.204171
$493$	17.0625	0.768457
$494$	56.4075	2.53789
$495$	7.19037	0.323183
$496$	−13.4998	−0.606158
$497$	4.20667	0.188695
$498$	21.0041	0.941215
$499$	−0.279781	−0.0125247	−0.00626236	−	0.999980i	$-0.501993\pi$
$499$	−0.279781	−0.0125247	−0.00626236	+	0.999980i	$0.501993\pi$
$500$	−2.88091	−0.128838
$501$	47.5468	2.12424
$502$	−31.4088	−1.40184
$503$	−30.3533	−1.35339	−0.676694	−	0.736264i	$-0.736588\pi$
$503$	−30.3533	−1.35339	−0.676694	+	0.736264i	$0.736588\pi$
$504$	6.13903	0.273454
$505$	−2.19715	−0.0977721
$506$	12.4978	0.555594
$507$	−70.5383	−3.13271
$508$	−5.45534	−0.242041
$509$	31.2311	1.38429	0.692146	−	0.721757i	$-0.256665\pi$
$509$	31.2311	1.38429	0.692146	+	0.721757i	$0.256665\pi$
$510$	28.1437	1.24622
$511$	2.63638	0.116627
$512$	25.3367	1.11974
$513$	47.5205	2.09808
$514$	−11.2283	−0.495258
$515$	14.2102	0.626176
$516$	−6.33504	−0.278884
$517$	1.61030	0.0708209
$518$	5.75136	0.252700
$519$	9.57353	0.420231
$520$	−24.5079	−1.07474
$521$	39.3262	1.72291	0.861456	−	0.507831i	$-0.169553\pi$
$521$	39.3262	1.72291	0.861456	+	0.507831i	$0.169553\pi$
$522$	21.8989	0.958487
$523$	−29.6043	−1.29451	−0.647253	−	0.762275i	$-0.724082\pi$
$523$	−29.6043	−1.29451	−0.647253	+	0.762275i	$0.724082\pi$
$524$	−0.261634	−0.0114295
$525$	3.55157	0.155003
$526$	−19.4949	−0.850020
$527$	−21.7727	−0.948434
$528$	−9.84923	−0.428633
$529$	66.8515	2.90659
$530$	−10.3390	−0.449098
$531$	50.2428	2.18035
$532$	0.704123	0.0305276
$533$	36.6357	1.58687
$534$	−48.1596	−2.08407
$535$	5.97816	0.258459
$536$	11.2240	0.484804
$537$	−43.3175	−1.86929
$538$	16.4529	0.709335
$539$	6.85197	0.295135
$540$	−2.38848	−0.102784
$541$	4.17591	0.179537	0.0897683	−	0.995963i	$-0.471387\pi$
$541$	4.17591	0.179537	0.0897683	+	0.995963i	$0.471387\pi$
$542$	12.3421	0.530140
$543$	−39.9521	−1.71451
$544$	8.08094	0.346467
$545$	19.6955	0.843663
$546$	8.96616	0.383716
$547$	27.8301	1.18993	0.594965	−	0.803751i	$-0.297166\pi$
$547$	27.8301	1.18993	0.594965	+	0.803751i	$0.297166\pi$
$548$	−1.94873	−0.0832458
$549$	−1.23990	−0.0529176
$550$	−4.21159	−0.179583
$551$	21.7119	0.924959
$552$	−81.6813	−3.47659
$553$	4.59772	0.195515
$554$	15.1147	0.642161
$555$	−44.0262	−1.86881
$556$	−3.15856	−0.133953
$557$	−18.8442	−0.798453	−0.399226	−	0.916852i	$-0.630721\pi$
$557$	−18.8442	−0.798453	−0.399226	+	0.916852i	$0.630721\pi$
$558$	−27.9441	−1.18297
$559$	−51.2481	−2.16756
$560$	1.76212	0.0744632
$561$	−15.8850	−0.670666
$562$	−2.42565	−0.102320
$563$	5.31026	0.223801	0.111900	−	0.993719i	$-0.464306\pi$
$563$	5.31026	0.223801	0.111900	+	0.993719i	$0.464306\pi$
$564$	−1.21750	−0.0512659
$565$	−3.03515	−0.127690
$566$	−12.7642	−0.536519
$567$	1.37724	0.0578387
$568$	32.6027	1.36798
$569$	−12.1662	−0.510033	−0.255016	−	0.966937i	$-0.582081\pi$
$569$	−12.1662	−0.510033	−0.255016	+	0.966937i	$0.582081\pi$
$570$	35.8126	1.50003
$571$	−0.928529	−0.0388577	−0.0194289	−	0.999811i	$-0.506185\pi$
$571$	−0.928529	−0.0388577	−0.0194289	+	0.999811i	$0.506185\pi$
$572$	1.60024	0.0669094
$573$	−25.9094	−1.08238
$574$	−3.03853	−0.126826
$575$	−30.2788	−1.26271
$576$	46.8463	1.95193
$577$	−29.8195	−1.24140	−0.620701	−	0.784047i	$-0.713152\pi$
$577$	−29.8195	−1.24140	−0.620701	+	0.784047i	$0.713152\pi$
$578$	−17.4253	−0.724796
$579$	−21.9143	−0.910726
$580$	−1.09129	−0.0453133
$581$	2.12102	0.0879946
$582$	−40.1633	−1.66482
$583$	5.83561	0.241686
$584$	20.4326	0.845506
$585$	−43.9786	−1.81829
$586$	24.1401	0.997217
$587$	29.3568	1.21169	0.605843	−	0.795584i	$-0.292836\pi$
$587$	29.3568	1.21169	0.605843	+	0.795584i	$0.292836\pi$
$588$	−5.18056	−0.213643
$589$	−27.7056	−1.14159
$590$	16.6356	0.684878
$591$	−3.32151	−0.136629
$592$	38.6417	1.58817
$593$	18.1563	0.745590	0.372795	−	0.927914i	$-0.378399\pi$
$593$	18.1563	0.745590	0.372795	+	0.927914i	$0.378399\pi$
$594$	−8.95727	−0.367521
$595$	2.84198	0.116510
$596$	−4.70616	−0.192772
$597$	4.77970	0.195620
$598$	−76.4405	−3.12589
$599$	22.9746	0.938718	0.469359	−	0.883007i	$-0.344485\pi$
$599$	22.9746	0.938718	0.469359	+	0.883007i	$0.344485\pi$
$600$	27.5255	1.12373
$601$	12.2944	0.501499	0.250750	−	0.968052i	$-0.419323\pi$
$601$	12.2944	0.501499	0.250750	+	0.968052i	$0.419323\pi$
$602$	4.25046	0.173236
$603$	20.1412	0.820211
$604$	3.56250	0.144956
$605$	−1.34376	−0.0546317
$606$	6.22982	0.253069
$607$	−6.90014	−0.280068	−0.140034	−	0.990147i	$-0.544721\pi$
$607$	−6.90014	−0.280068	−0.140034	+	0.990147i	$0.544721\pi$
$608$	10.2829	0.417028
$609$	3.45118	0.139849
$610$	−0.410536	−0.0166221
$611$	−9.84911	−0.398452
$612$	7.69562	0.311077
$613$	9.64459	0.389541	0.194771	−	0.980849i	$-0.437604\pi$
$613$	9.64459	0.389541	0.194771	+	0.980849i	$0.437604\pi$
$614$	3.63810	0.146822
$615$	23.2597	0.937922
$616$	−1.14728	−0.0462254
$617$	−12.6904	−0.510895	−0.255448	−	0.966823i	$-0.582223\pi$
$617$	−12.6904	−0.510895	−0.255448	+	0.966823i	$0.582223\pi$
$618$	−40.2917	−1.62077
$619$	−22.9671	−0.923126	−0.461563	−	0.887107i	$-0.652711\pi$
$619$	−22.9671	−0.923126	−0.461563	+	0.887107i	$0.652711\pi$
$620$	1.39254	0.0559259
$621$	−64.3973	−2.58417
$622$	−15.0630	−0.603971
$623$	−4.86321	−0.194840
$624$	60.2411	2.41157
$625$	1.17506	0.0470023
$626$	37.8881	1.51431
$627$	−20.2136	−0.807252
$628$	1.43210	0.0571472
$629$	62.3221	2.48494
$630$	3.64754	0.145321
$631$	18.0333	0.717894	0.358947	−	0.933358i	$-0.383136\pi$
$631$	18.0333	0.717894	0.358947	+	0.933358i	$0.383136\pi$
$632$	35.6334	1.41742
$633$	7.02082	0.279052
$634$	−41.2894	−1.63981
$635$	−28.0188	−1.11189
$636$	−4.41213	−0.174952
$637$	−41.9089	−1.66049
$638$	−4.09254	−0.162025
$639$	58.5045	2.31440
$640$	11.5601	0.456955
$641$	24.2495	0.957796	0.478898	−	0.877870i	$-0.341036\pi$
$641$	24.2495	0.957796	0.478898	+	0.877870i	$0.341036\pi$
$642$	−16.9505	−0.668983
$643$	19.5028	0.769116	0.384558	−	0.923101i	$-0.374354\pi$
$643$	19.5028	0.769116	0.384558	+	0.923101i	$0.374354\pi$
$644$	−0.954191	−0.0376004
$645$	−32.5370	−1.28114
$646$	−50.6952	−1.99458
$647$	24.2098	0.951787	0.475893	−	0.879503i	$-0.342125\pi$
$647$	24.2098	0.951787	0.475893	+	0.879503i	$0.342125\pi$
$648$	10.6739	0.419312
$649$	−9.38957	−0.368573
$650$	25.7595	1.01037
$651$	−4.40390	−0.172602
$652$	−0.102903	−0.00403000
$653$	−12.7733	−0.499859	−0.249930	−	0.968264i	$-0.580407\pi$
$653$	−12.7733	−0.499859	−0.249930	+	0.968264i	$0.580407\pi$
$654$	−55.8447	−2.18370
$655$	−1.34376	−0.0525052
$656$	−20.4150	−0.797072
$657$	36.6656	1.43046
$658$	0.816874	0.0318451
$659$	−11.9065	−0.463813	−0.231906	−	0.972738i	$-0.574496\pi$
$659$	−11.9065	−0.463813	−0.231906	+	0.972738i	$0.574496\pi$
$660$	1.01598	0.0395469
$661$	−15.9158	−0.619054	−0.309527	−	0.950891i	$-0.600171\pi$
$661$	−15.9158	−0.619054	−0.309527	+	0.950891i	$0.600171\pi$
$662$	−13.3487	−0.518811
$663$	97.1579	3.77330
$664$	16.4384	0.637933
$665$	3.61640	0.140238
$666$	79.9872	3.09944
$667$	−29.4229	−1.13926
$668$	4.30476	0.166556
$669$	30.6345	1.18440
$670$	6.66882	0.257639
$671$	0.231717	0.00894533
$672$	1.63451	0.0630524
$673$	11.1851	0.431154	0.215577	−	0.976487i	$-0.430837\pi$
$673$	11.1851	0.431154	0.215577	+	0.976487i	$0.430837\pi$
$674$	−20.0076	−0.770665
$675$	21.7010	0.835274
$676$	−6.38634	−0.245629
$677$	−19.4636	−0.748047	−0.374023	−	0.927419i	$-0.622022\pi$
$677$	−19.4636	−0.748047	−0.374023	+	0.927419i	$0.622022\pi$
$678$	8.60586	0.330506
$679$	−4.05573	−0.155645
$680$	22.0260	0.844660
$681$	55.8342	2.13957
$682$	5.22231	0.199972
$683$	22.4871	0.860446	0.430223	−	0.902723i	$-0.358435\pi$
$683$	22.4871	0.860446	0.430223	+	0.902723i	$0.358435\pi$
$684$	9.79262	0.374430
$685$	−10.0088	−0.382416
$686$	7.02684	0.268286
$687$	−48.6343	−1.85552
$688$	28.5576	1.08875
$689$	−35.6925	−1.35977
$690$	−48.5314	−1.84756
$691$	−29.8117	−1.13409	−0.567046	−	0.823686i	$-0.691914\pi$
$691$	−29.8117	−1.13409	−0.567046	+	0.823686i	$0.691914\pi$
$692$	0.866761	0.0329493
$693$	−2.05876	−0.0782060
$694$	−19.4160	−0.737021
$695$	−16.2225	−0.615354
$696$	26.7475	1.01386
$697$	−32.9257	−1.24715
$698$	−31.5341	−1.19358
$699$	−65.9023	−2.49265
$700$	0.321550	0.0121534
$701$	−33.7791	−1.27582	−0.637910	−	0.770111i	$-0.720201\pi$
$701$	−33.7791	−1.27582	−0.637910	+	0.770111i	$0.720201\pi$
$702$	54.7855	2.06775
$703$	79.3044	2.99102
$704$	−8.75482	−0.329960
$705$	−6.25311	−0.235506
$706$	−14.1171	−0.531306
$707$	0.629094	0.0236595
$708$	7.09917	0.266803
$709$	28.4259	1.06756	0.533779	−	0.845624i	$-0.320771\pi$
$709$	28.4259	1.06756	0.533779	+	0.845624i	$0.320771\pi$
$710$	19.3711	0.726984
$711$	63.9430	2.39805
$712$	−37.6910	−1.41253
$713$	37.5452	1.40608
$714$	−8.05817	−0.301569
$715$	8.21889	0.307369
$716$	−3.92185	−0.146566
$717$	−10.1903	−0.380565
$718$	−27.7577	−1.03591
$719$	15.3150	0.571154	0.285577	−	0.958356i	$-0.407815\pi$
$719$	15.3150	0.571154	0.285577	+	0.958356i	$0.407815\pi$
$720$	24.5068	0.913314
$721$	−4.06870	−0.151526
$722$	−39.4584	−1.46849
$723$	−32.6003	−1.21242
$724$	−3.61715	−0.134430
$725$	9.91513	0.368239
$726$	3.81011	0.141407
$727$	24.4418	0.906497	0.453248	−	0.891384i	$-0.350265\pi$
$727$	24.4418	0.906497	0.453248	+	0.891384i	$0.350265\pi$
$728$	7.01716	0.260073
$729$	−39.7430	−1.47196
$730$	12.1401	0.449327
$731$	46.0583	1.70353
$732$	−0.175194	−0.00647536
$733$	39.5384	1.46038	0.730191	−	0.683243i	$-0.239431\pi$
$733$	39.5384	1.46038	0.730191	+	0.683243i	$0.239431\pi$
$734$	26.5323	0.979325
$735$	−26.6076	−0.981435
$736$	−13.9349	−0.513647
$737$	−3.76405	−0.138651
$738$	−42.2584	−1.55555
$739$	13.2860	0.488734	0.244367	−	0.969683i	$-0.421420\pi$
$739$	13.2860	0.488734	0.244367	+	0.969683i	$0.421420\pi$
$740$	−3.98601	−0.146529
$741$	123.633	4.54176
$742$	2.96029	0.108676
$743$	−28.0387	−1.02864	−0.514319	−	0.857599i	$-0.671955\pi$
$743$	−28.0387	−1.02864	−0.514319	+	0.857599i	$0.671955\pi$
$744$	−34.1312	−1.25131
$745$	−24.1710	−0.885558
$746$	3.59911	0.131773
$747$	29.4981	1.07928
$748$	−1.43819	−0.0525853
$749$	−1.71168	−0.0625435
$750$	41.9539	1.53194
$751$	−48.7400	−1.77855	−0.889273	−	0.457377i	$-0.848789\pi$
$751$	−48.7400	−1.77855	−0.889273	+	0.457377i	$0.848789\pi$
$752$	5.48835	0.200139
$753$	−68.8411	−2.50871
$754$	25.0313	0.911587
$755$	18.2971	0.665900
$756$	0.683876	0.0248723
$757$	14.8498	0.539724	0.269862	−	0.962899i	$-0.413022\pi$
$757$	14.8498	0.539724	0.269862	+	0.962899i	$0.413022\pi$
$758$	18.6227	0.676407
$759$	27.3924	0.994280
$760$	28.0280	1.01668
$761$	−50.4781	−1.82983	−0.914915	−	0.403646i	$-0.867743\pi$
$761$	−50.4781	−1.82983	−0.914915	+	0.403646i	$0.867743\pi$
$762$	79.4446	2.87798
$763$	−5.63927	−0.204155
$764$	−2.34577	−0.0848670
$765$	39.5250	1.42903
$766$	−4.88448	−0.176483
$767$	57.4297	2.07366
$768$	17.8216	0.643082
$769$	−9.19830	−0.331699	−0.165850	−	0.986151i	$-0.553037\pi$
$769$	−9.19830	−0.331699	−0.165850	+	0.986151i	$0.553037\pi$
$770$	−0.681666	−0.0245655
$771$	−24.6099	−0.886303
$772$	−1.98406	−0.0714079
$773$	−29.9362	−1.07673	−0.538364	−	0.842712i	$-0.680958\pi$
$773$	−29.9362	−1.07673	−0.538364	+	0.842712i	$0.680958\pi$
$774$	59.1134	2.12479
$775$	−12.6522	−0.454482
$776$	−31.4329	−1.12837
$777$	12.6057	0.452227
$778$	15.6620	0.561509
$779$	−41.8977	−1.50114
$780$	−6.21405	−0.222499
$781$	−10.9335	−0.391233
$782$	68.6995	2.45669
$783$	21.0876	0.753610
$784$	23.3534	0.834051
$785$	7.35534	0.262523
$786$	3.81011	0.135902
$787$	−22.2059	−0.791556	−0.395778	−	0.918346i	$-0.629525\pi$
$787$	−22.2059	−0.791556	−0.395778	+	0.918346i	$0.629525\pi$
$788$	−0.300721	−0.0107127
$789$	−42.7286	−1.52118
$790$	21.1718	0.753259
$791$	0.869030	0.0308992
$792$	−15.9559	−0.566968
$793$	−1.41726	−0.0503282
$794$	51.8741	1.84094
$795$	−22.6608	−0.803697
$796$	0.432741	0.0153381
$797$	7.44535	0.263728	0.131864	−	0.991268i	$-0.457904\pi$
$797$	7.44535	0.263728	0.131864	+	0.991268i	$0.457904\pi$
$798$	−10.2540	−0.362986
$799$	8.85171	0.313151
$800$	4.69588	0.166024
$801$	−67.6353	−2.38978
$802$	−48.7341	−1.72086
$803$	−6.85220	−0.241809
$804$	2.84589	0.100367
$805$	−4.90076	−0.172729
$806$	−31.9413	−1.12509
$807$	36.0611	1.26941
$808$	4.87563	0.171524
$809$	22.9336	0.806301	0.403150	−	0.915134i	$-0.367915\pi$
$809$	22.9336	0.806301	0.403150	+	0.915134i	$0.367915\pi$
$810$	6.34199	0.222835
$811$	−11.0672	−0.388623	−0.194312	−	0.980940i	$-0.562247\pi$
$811$	−11.0672	−0.388623	−0.194312	+	0.980940i	$0.562247\pi$
$812$	0.312461	0.0109652
$813$	27.0512	0.948728
$814$	−14.9483	−0.523938
$815$	−0.528514	−0.0185130
$816$	−54.1406	−1.89530
$817$	58.6088	2.05046
$818$	−37.0162	−1.29424
$819$	12.5921	0.440002
$820$	2.10587	0.0735402
$821$	−34.2243	−1.19444	−0.597218	−	0.802079i	$-0.703727\pi$
$821$	−34.2243	−1.19444	−0.597218	+	0.802079i	$0.703727\pi$
$822$	28.3789	0.989828
$823$	−34.0862	−1.18817	−0.594085	−	0.804402i	$-0.702486\pi$
$823$	−34.0862	−1.18817	−0.594085	+	0.804402i	$0.702486\pi$
$824$	−31.5334	−1.09852
$825$	−9.23088	−0.321378
$826$	−4.76315	−0.165731
$827$	24.6775	0.858120	0.429060	−	0.903276i	$-0.358845\pi$
$827$	24.6775	0.858120	0.429060	+	0.903276i	$0.358845\pi$
$828$	−13.2704	−0.461180
$829$	18.9594	0.658487	0.329244	−	0.944245i	$-0.393206\pi$
$829$	18.9594	0.658487	0.329244	+	0.944245i	$0.393206\pi$
$830$	9.76695	0.339016
$831$	33.1280	1.14920
$832$	53.5473	1.85642
$833$	37.6648	1.30501
$834$	45.9973	1.59276
$835$	22.1094	0.765127
$836$	−1.83008	−0.0632947
$837$	−26.9089	−0.930109
$838$	25.4977	0.880803
$839$	−26.5290	−0.915883	−0.457942	−	0.888982i	$-0.651413\pi$
$839$	−26.5290	−0.915883	−0.457942	+	0.888982i	$0.651413\pi$
$840$	4.45514	0.153717
$841$	−19.3651	−0.667764
$842$	−33.5391	−1.15583
$843$	−5.31649	−0.183110
$844$	0.635646	0.0218798
$845$	−32.8005	−1.12837
$846$	11.3607	0.390589
$847$	0.384750	0.0132201
$848$	19.8894	0.683004
$849$	−27.9763	−0.960143
$850$	−23.1508	−0.794067
$851$	−107.469	−3.68400
$852$	8.26652	0.283206
$853$	7.39321	0.253139	0.126569	−	0.991958i	$-0.459603\pi$
$853$	7.39321	0.253139	0.126569	+	0.991958i	$0.459603\pi$
$854$	0.117546	0.00402233
$855$	50.2953	1.72006
$856$	−13.2659	−0.453420
$857$	−21.5507	−0.736160	−0.368080	−	0.929794i	$-0.619985\pi$
$857$	−21.5507	−0.736160	−0.368080	+	0.929794i	$0.619985\pi$
$858$	−23.3039	−0.795581
$859$	−14.0919	−0.480811	−0.240405	−	0.970673i	$-0.577280\pi$
$859$	−14.0919	−0.480811	−0.240405	+	0.970673i	$0.577280\pi$
$860$	−2.94581	−0.100451
$861$	−6.65977	−0.226964
$862$	−29.1683	−0.993478
$863$	−29.2506	−0.995703	−0.497852	−	0.867262i	$-0.665878\pi$
$863$	−29.2506	−0.995703	−0.497852	+	0.867262i	$0.665878\pi$
$864$	9.98726	0.339773
$865$	4.45172	0.151363
$866$	30.0175	1.02004
$867$	−38.1924	−1.29708
$868$	−0.398717	−0.0135333
$869$	−11.9499	−0.405373
$870$	15.8922	0.538795
$871$	23.0222	0.780077
$872$	−43.7056	−1.48006
$873$	−56.4053	−1.90903
$874$	87.4196	2.95701
$875$	4.23655	0.143222
$876$	5.18074	0.175041
$877$	39.1427	1.32176	0.660878	−	0.750494i	$-0.270184\pi$
$877$	39.1427	1.32176	0.660878	+	0.750494i	$0.270184\pi$
$878$	2.31766	0.0782172
$879$	52.9097	1.78460
$880$	−4.57992	−0.154389
$881$	−17.0867	−0.575665	−0.287832	−	0.957681i	$-0.592935\pi$
$881$	−17.0867	−0.575665	−0.287832	+	0.957681i	$0.592935\pi$
$882$	48.3409	1.62772
$883$	−4.17607	−0.140536	−0.0702680	−	0.997528i	$-0.522385\pi$
$883$	−4.17607	−0.140536	−0.0702680	+	0.997528i	$0.522385\pi$
$884$	8.79641	0.295855
$885$	36.4616	1.22564
$886$	−30.1116	−1.01162
$887$	−42.6912	−1.43343	−0.716715	−	0.697367i	$-0.754355\pi$
$887$	−42.6912	−1.43343	−0.716715	+	0.697367i	$0.754355\pi$
$888$	97.6971	3.27850
$889$	8.02241	0.269063
$890$	−22.3943	−0.750660
$891$	−3.57958	−0.119920
$892$	2.77357	0.0928659
$893$	11.2637	0.376926
$894$	68.5346	2.29214
$895$	−20.1428	−0.673298
$896$	−3.30993	−0.110577
$897$	−167.541	−5.59402
$898$	12.5855	0.419983
$899$	−12.2946	−0.410048
$900$	4.47197	0.149066
$901$	32.0780	1.06867
$902$	7.89741	0.262955
$903$	9.31606	0.310019
$904$	6.73519	0.224009
$905$	−18.5778	−0.617548
$906$	−51.8797	−1.72359
$907$	57.8047	1.91937	0.959687	−	0.281071i	$-0.0906896\pi$
$907$	57.8047	1.91937	0.959687	+	0.281071i	$0.0906896\pi$
$908$	5.05507	0.167759
$909$	8.74915	0.290191
$910$	4.16929	0.138211
$911$	3.88632	0.128760	0.0643798	−	0.997925i	$-0.479493\pi$
$911$	3.88632	0.128760	0.0643798	+	0.997925i	$0.479493\pi$
$912$	−68.8935	−2.28129
$913$	−5.51272	−0.182444
$914$	−37.2331	−1.23156
$915$	−0.899803	−0.0297466
$916$	−4.40322	−0.145486
$917$	0.384750	0.0127055
$918$	−49.2375	−1.62508
$919$	13.3970	0.441926	0.220963	−	0.975282i	$-0.429080\pi$
$919$	13.3970	0.441926	0.220963	+	0.975282i	$0.429080\pi$
$920$	−37.9820	−1.25223
$921$	7.97392	0.262750
$922$	48.1490	1.58570
$923$	66.8731	2.20115
$924$	−0.290897	−0.00956982
$925$	36.2157	1.19077
$926$	−46.2770	−1.52076
$927$	−56.5856	−1.85851
$928$	4.56314	0.149792
$929$	−2.69653	−0.0884704	−0.0442352	−	0.999021i	$-0.514085\pi$
$929$	−2.69653	−0.0884704	−0.0442352	+	0.999021i	$0.514085\pi$
$930$	−20.2793	−0.664983
$931$	47.9282	1.57078
$932$	−5.96661	−0.195443
$933$	−33.0147	−1.08085
$934$	−7.67703	−0.251200
$935$	−7.38658	−0.241567
$936$	97.5915	3.18988
$937$	43.9285	1.43508	0.717540	−	0.696517i	$-0.245268\pi$
$937$	43.9285	1.43508	0.717540	+	0.696517i	$0.245268\pi$
$938$	−1.90943	−0.0623452
$939$	83.0422	2.70998
$940$	−0.566140	−0.0184654
$941$	32.4391	1.05748	0.528742	−	0.848782i	$-0.322664\pi$
$941$	32.4391	1.05748	0.528742	+	0.848782i	$0.322664\pi$
$942$	−20.8554	−0.679504
$943$	56.7776	1.84893
$944$	−32.0023	−1.04159
$945$	3.51241	0.114259
$946$	−11.0473	−0.359180
$947$	−15.8686	−0.515659	−0.257830	−	0.966190i	$-0.583007\pi$
$947$	−15.8686	−0.515659	−0.257830	+	0.966190i	$0.583007\pi$
$948$	9.03497	0.293442
$949$	41.9103	1.36047
$950$	−29.4593	−0.955785
$951$	−90.4971	−2.93457
$952$	−6.30655	−0.204396
$953$	−27.0174	−0.875181	−0.437590	−	0.899174i	$-0.644168\pi$
$953$	−27.0174	−0.875181	−0.437590	+	0.899174i	$0.644168\pi$
$954$	41.1704	1.33294
$955$	−12.0480	−0.389863
$956$	−0.922605	−0.0298392
$957$	−8.96994	−0.289957
$958$	−47.6358	−1.53904
$959$	2.86574	0.0925394
$960$	33.9967	1.09724
$961$	−15.3114	−0.493917
$962$	91.4287	2.94778
$963$	−23.8053	−0.767115
$964$	−2.95155	−0.0950629
$965$	−10.1902	−0.328034
$966$	13.8956	0.447085
$967$	−3.96891	−0.127632	−0.0638158	−	0.997962i	$-0.520327\pi$
$967$	−3.96891	−0.127632	−0.0638158	+	0.997962i	$0.520327\pi$
$968$	2.98190	0.0958419
$969$	−111.113	−3.56945
$970$	−18.6760	−0.599651
$971$	51.7963	1.66222	0.831110	−	0.556107i	$-0.187706\pi$
$971$	51.7963	1.66222	0.831110	+	0.556107i	$0.187706\pi$
$972$	−2.62596	−0.0842278
$973$	4.64486	0.148908
$974$	−26.7092	−0.855817
$975$	56.4590	1.80814
$976$	0.789756	0.0252795
$977$	−4.97614	−0.159201	−0.0796004	−	0.996827i	$-0.525364\pi$
$977$	−4.97614	−0.159201	−0.0796004	+	0.996827i	$0.525364\pi$
$978$	1.49855	0.0479184
$979$	12.6399	0.403974
$980$	−2.40898	−0.0769519
$981$	−78.4283	−2.50402
$982$	−12.8752	−0.410864
$983$	39.6363	1.26420	0.632101	−	0.774886i	$-0.282193\pi$
$983$	39.6363	1.26420	0.632101	+	0.774886i	$0.282193\pi$
$984$	−51.6148	−1.64542
$985$	−1.54451	−0.0492123
$986$	−22.4964	−0.716432
$987$	1.79041	0.0569893
$988$	11.1934	0.356109
$989$	−79.4237	−2.52553
$990$	−9.48029	−0.301303
$991$	57.2037	1.81713	0.908567	−	0.417738i	$-0.137177\pi$
$991$	57.2037	1.81713	0.908567	+	0.417738i	$0.137177\pi$
$992$	−5.82282	−0.184875
$993$	−29.2573	−0.928454
$994$	−5.54638	−0.175920
$995$	2.22257	0.0704604
$996$	4.16800	0.132068
$997$	−45.6622	−1.44614	−0.723068	−	0.690777i	$-0.757269\pi$
$997$	−45.6622	−1.44614	−0.723068	+	0.690777i	$0.757269\pi$
$998$	0.368883	0.0116768
$999$	77.0241	2.43693

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1441.2.a.f.1.9	✓	31

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1441.2.a.f.1.9	✓	31	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:	\( N \)	\(=\)	\( 1441 = 11 \cdot 131 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1441.a (trivial)

\(f(q)\)	\(=\)	\(q-1.31847 q^{2} -2.88980 q^{3} -0.261634 q^{4} -1.34376 q^{5} +3.81011 q^{6} +0.384750 q^{7} +2.98190 q^{8} +5.35092 q^{9} +O(q^{10})\)	\(q-1.31847 q^{2} -2.88980 q^{3} -0.261634 q^{4} -1.34376 q^{5} +3.81011 q^{6} +0.384750 q^{7} +2.98190 q^{8} +5.35092 q^{9} +1.77171 q^{10} -1.00000 q^{11} +0.756070 q^{12} +6.11632 q^{13} -0.507281 q^{14} +3.88320 q^{15} -3.40828 q^{16} -5.49693 q^{17} -7.05503 q^{18} -6.99481 q^{19} +0.351574 q^{20} -1.11185 q^{21} +1.31847 q^{22} +9.47900 q^{23} -8.61708 q^{24} -3.19430 q^{25} -8.06420 q^{26} -6.79368 q^{27} -0.100664 q^{28} -3.10401 q^{29} -5.11989 q^{30} +3.96088 q^{31} -1.47008 q^{32} +2.88980 q^{33} +7.24755 q^{34} -0.517012 q^{35} -1.39998 q^{36} -11.3376 q^{37} +9.22245 q^{38} -17.6749 q^{39} -4.00697 q^{40} +5.98983 q^{41} +1.46594 q^{42} -8.37891 q^{43} +0.261634 q^{44} -7.19037 q^{45} -12.4978 q^{46} -1.61030 q^{47} +9.84923 q^{48} -6.85197 q^{49} +4.21159 q^{50} +15.8850 q^{51} -1.60024 q^{52} -5.83561 q^{53} +8.95727 q^{54} +1.34376 q^{55} +1.14728 q^{56} +20.2136 q^{57} +4.09254 q^{58} +9.38957 q^{59} -1.01598 q^{60} -0.231717 q^{61} -5.22231 q^{62} +2.05876 q^{63} +8.75482 q^{64} -8.21889 q^{65} -3.81011 q^{66} +3.76405 q^{67} +1.43819 q^{68} -27.3924 q^{69} +0.681666 q^{70} +10.9335 q^{71} +15.9559 q^{72} +6.85220 q^{73} +14.9483 q^{74} +9.23088 q^{75} +1.83008 q^{76} -0.384750 q^{77} +23.3039 q^{78} +11.9499 q^{79} +4.57992 q^{80} +3.57958 q^{81} -7.89741 q^{82} +5.51272 q^{83} +0.290897 q^{84} +7.38658 q^{85} +11.0473 q^{86} +8.96994 q^{87} -2.98190 q^{88} -12.6399 q^{89} +9.48029 q^{90} +2.35325 q^{91} -2.48003 q^{92} -11.4461 q^{93} +2.12313 q^{94} +9.39937 q^{95} +4.24823 q^{96} -10.5412 q^{97} +9.03412 q^{98} -5.35092 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 31 q + 6 q^{2} + 4 q^{3} + 38 q^{4} + 8 q^{5} + 7 q^{6} + 4 q^{7} + 24 q^{8} + 45 q^{9}+O(q^{10}) \) 31 * q + 6 * q^2 + 4 * q^3 + 38 * q^4 + 8 * q^5 + 7 * q^6 + 4 * q^7 + 24 * q^8 + 45 * q^9	\( 31 q + 6 q^{2} + 4 q^{3} + 38 q^{4} + 8 q^{5} + 7 q^{6} + 4 q^{7} + 24 q^{8} + 45 q^{9} - 8 q^{10} - 31 q^{11} + 10 q^{12} - 8 q^{13} + 29 q^{14} + 36 q^{15} + 52 q^{16} - q^{17} + 33 q^{18} - 2 q^{19} + 22 q^{20} - 13 q^{21} - 6 q^{22} + 45 q^{23} + 16 q^{24} + 41 q^{25} + 24 q^{26} + 22 q^{27} + 17 q^{28} + 5 q^{29} + 29 q^{30} + 28 q^{31} + 69 q^{32} - 4 q^{33} + 14 q^{34} + 36 q^{35} + 63 q^{36} - 3 q^{37} + 4 q^{38} + 40 q^{39} - 48 q^{40} + 21 q^{41} - 9 q^{42} - 20 q^{43} - 38 q^{44} + 28 q^{45} - 24 q^{46} + 57 q^{47} - 46 q^{48} + 37 q^{49} + 64 q^{50} + 17 q^{51} - 11 q^{52} + 32 q^{53} - 26 q^{54} - 8 q^{55} + 84 q^{56} + 10 q^{57} - 17 q^{58} + 70 q^{59} - 33 q^{60} - 51 q^{61} - 34 q^{62} + 32 q^{63} + 80 q^{64} - q^{65} - 7 q^{66} + 24 q^{67} - 13 q^{68} + 19 q^{69} - 9 q^{70} + 128 q^{71} + 118 q^{72} - 27 q^{73} - 23 q^{74} + 41 q^{75} - 34 q^{76} - 4 q^{77} + 9 q^{78} + 2 q^{79} - 45 q^{80} + 43 q^{81} - 18 q^{82} + 46 q^{83} - 103 q^{84} - 50 q^{85} + 78 q^{86} - 9 q^{87} - 24 q^{88} + 52 q^{89} - 46 q^{90} + 38 q^{91} + 54 q^{92} + 4 q^{93} + 3 q^{94} + 70 q^{95} - 21 q^{96} + 3 q^{97} - 120 q^{98} - 45 q^{99}+O(q^{100}) \) 31 * q + 6 * q^2 + 4 * q^3 + 38 * q^4 + 8 * q^5 + 7 * q^6 + 4 * q^7 + 24 * q^8 + 45 * q^9 - 8 * q^10 - 31 * q^11 + 10 * q^12 - 8 * q^13 + 29 * q^14 + 36 * q^15 + 52 * q^16 - q^17 + 33 * q^18 - 2 * q^19 + 22 * q^20 - 13 * q^21 - 6 * q^22 + 45 * q^23 + 16 * q^24 + 41 * q^25 + 24 * q^26 + 22 * q^27 + 17 * q^28 + 5 * q^29 + 29 * q^30 + 28 * q^31 + 69 * q^32 - 4 * q^33 + 14 * q^34 + 36 * q^35 + 63 * q^36 - 3 * q^37 + 4 * q^38 + 40 * q^39 - 48 * q^40 + 21 * q^41 - 9 * q^42 - 20 * q^43 - 38 * q^44 + 28 * q^45 - 24 * q^46 + 57 * q^47 - 46 * q^48 + 37 * q^49 + 64 * q^50 + 17 * q^51 - 11 * q^52 + 32 * q^53 - 26 * q^54 - 8 * q^55 + 84 * q^56 + 10 * q^57 - 17 * q^58 + 70 * q^59 - 33 * q^60 - 51 * q^61 - 34 * q^62 + 32 * q^63 + 80 * q^64 - q^65 - 7 * q^66 + 24 * q^67 - 13 * q^68 + 19 * q^69 - 9 * q^70 + 128 * q^71 + 118 * q^72 - 27 * q^73 - 23 * q^74 + 41 * q^75 - 34 * q^76 - 4 * q^77 + 9 * q^78 + 2 * q^79 - 45 * q^80 + 43 * q^81 - 18 * q^82 + 46 * q^83 - 103 * q^84 - 50 * q^85 + 78 * q^86 - 9 * q^87 - 24 * q^88 + 52 * q^89 - 46 * q^90 + 38 * q^91 + 54 * q^92 + 4 * q^93 + 3 * q^94 + 70 * q^95 - 21 * q^96 + 3 * q^97 - 120 * q^98 - 45 * q^99

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