LMFDB - Embedded newform 1441.2.a.f.1.2

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			1.2
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)

$f(q)$	$=$	$q-2.51757 q^{2} -0.0469654 q^{3} +4.33818 q^{4} +2.78146 q^{5} +0.118239 q^{6} +3.17303 q^{7} -5.88653 q^{8} -2.99779 q^{9} +O(q^{10})$	\(q-2.51757 q^{2} -0.0469654 q^{3} +4.33818 q^{4} +2.78146 q^{5} +0.118239 q^{6} +3.17303 q^{7} -5.88653 q^{8} -2.99779 q^{9} -7.00252 q^{10} -1.00000 q^{11} -0.203744 q^{12} -3.12098 q^{13} -7.98834 q^{14} -0.130632 q^{15} +6.14343 q^{16} +1.69371 q^{17} +7.54717 q^{18} -6.80748 q^{19} +12.0665 q^{20} -0.149023 q^{21} +2.51757 q^{22} +5.59709 q^{23} +0.276464 q^{24} +2.73650 q^{25} +7.85729 q^{26} +0.281689 q^{27} +13.7652 q^{28} +0.262203 q^{29} +0.328876 q^{30} +10.5568 q^{31} -3.69347 q^{32} +0.0469654 q^{33} -4.26405 q^{34} +8.82564 q^{35} -13.0050 q^{36} +0.913895 q^{37} +17.1383 q^{38} +0.146578 q^{39} -16.3731 q^{40} +10.1347 q^{41} +0.375175 q^{42} +0.898928 q^{43} -4.33818 q^{44} -8.33823 q^{45} -14.0911 q^{46} -1.97251 q^{47} -0.288529 q^{48} +3.06811 q^{49} -6.88934 q^{50} -0.0795459 q^{51} -13.5394 q^{52} +12.2703 q^{53} -0.709173 q^{54} -2.78146 q^{55} -18.6781 q^{56} +0.319716 q^{57} -0.660116 q^{58} +1.45566 q^{59} -0.566706 q^{60} +9.70235 q^{61} -26.5774 q^{62} -9.51209 q^{63} -2.98828 q^{64} -8.68086 q^{65} -0.118239 q^{66} -5.64376 q^{67} +7.34763 q^{68} -0.262870 q^{69} -22.2192 q^{70} +15.3259 q^{71} +17.6466 q^{72} +5.38902 q^{73} -2.30080 q^{74} -0.128521 q^{75} -29.5320 q^{76} -3.17303 q^{77} -0.369021 q^{78} -12.5453 q^{79} +17.0877 q^{80} +8.98015 q^{81} -25.5149 q^{82} -7.57893 q^{83} -0.646487 q^{84} +4.71099 q^{85} -2.26312 q^{86} -0.0123145 q^{87} +5.88653 q^{88} +14.1630 q^{89} +20.9921 q^{90} -9.90295 q^{91} +24.2812 q^{92} -0.495803 q^{93} +4.96594 q^{94} -18.9347 q^{95} +0.173465 q^{96} -10.3501 q^{97} -7.72420 q^{98} +2.99779 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.51757	−1.78019	−0.890097	−	0.455772i	$-0.849363\pi$
$2$	−2.51757	−1.78019	−0.890097	+	0.455772i	$0.849363\pi$
$3$	−0.0469654	−0.0271155	−0.0135577	−	0.999908i	$-0.504316\pi$
$3$	−0.0469654	−0.0271155	−0.0135577	+	0.999908i	$0.504316\pi$
$4$	4.33818	2.16909
$5$	2.78146	1.24391	0.621953	−	0.783055i	$-0.286340\pi$
$5$	2.78146	1.24391	0.621953	+	0.783055i	$0.286340\pi$
$6$	0.118239	0.0482708
$7$	3.17303	1.19929	0.599646	−	0.800265i	$-0.295308\pi$
$7$	3.17303	1.19929	0.599646	+	0.800265i	$0.295308\pi$
$8$	−5.88653	−2.08120
$9$	−2.99779	−0.999265
$10$	−7.00252	−2.21439
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−0.203744	−0.0588159
$13$	−3.12098	−0.865603	−0.432802	−	0.901489i	$-0.642475\pi$
$13$	−3.12098	−0.865603	−0.432802	+	0.901489i	$0.642475\pi$
$14$	−7.98834	−2.13497
$15$	−0.130632	−0.0337291
$16$	6.14343	1.53586
$17$	1.69371	0.410786	0.205393	−	0.978680i	$-0.434153\pi$
$17$	1.69371	0.410786	0.205393	+	0.978680i	$0.434153\pi$
$18$	7.54717	1.77888
$19$	−6.80748	−1.56174	−0.780871	−	0.624692i	$-0.785225\pi$
$19$	−6.80748	−1.56174	−0.780871	+	0.624692i	$0.785225\pi$
$20$	12.0665	2.69814
$21$	−0.149023	−0.0325194
$22$	2.51757	0.536749
$23$	5.59709	1.16707	0.583537	−	0.812087i	$-0.301668\pi$
$23$	5.59709	1.16707	0.583537	+	0.812087i	$0.301668\pi$
$24$	0.276464	0.0564329
$25$	2.73650	0.547300
$26$	7.85729	1.54094
$27$	0.281689	0.0542111
$28$	13.7652	2.60137
$29$	0.262203	0.0486899	0.0243450	−	0.999704i	$-0.492250\pi$
$29$	0.262203	0.0486899	0.0243450	+	0.999704i	$0.492250\pi$
$30$	0.328876	0.0600443
$31$	10.5568	1.89605	0.948026	−	0.318193i	$-0.103076\pi$
$31$	10.5568	1.89605	0.948026	+	0.318193i	$0.103076\pi$
$32$	−3.69347	−0.652919
$33$	0.0469654	0.00817563
$34$	−4.26405	−0.731278
$35$	8.82564	1.49181
$36$	−13.0050	−2.16749
$37$	0.913895	0.150243	0.0751217	−	0.997174i	$-0.476065\pi$
$37$	0.913895	0.150243	0.0751217	+	0.997174i	$0.476065\pi$
$38$	17.1383	2.78020
$39$	0.146578	0.0234713
$40$	−16.3731	−2.58882
$41$	10.1347	1.58278	0.791389	−	0.611313i	$-0.209359\pi$
$41$	10.1347	1.58278	0.791389	+	0.611313i	$0.209359\pi$
$42$	0.375175	0.0578908
$43$	0.898928	0.137085	0.0685426	−	0.997648i	$-0.478165\pi$
$43$	0.898928	0.137085	0.0685426	+	0.997648i	$0.478165\pi$
$44$	−4.33818	−0.654005
$45$	−8.33823	−1.24299
$46$	−14.0911	−2.07762
$47$	−1.97251	−0.287720	−0.143860	−	0.989598i	$-0.545952\pi$
$47$	−1.97251	−0.287720	−0.143860	+	0.989598i	$0.545952\pi$
$48$	−0.288529	−0.0416455
$49$	3.06811	0.438302
$50$	−6.88934	−0.974299
$51$	−0.0795459	−0.0111387
$52$	−13.5394	−1.87757
$53$	12.2703	1.68546	0.842729	−	0.538339i	$-0.180948\pi$
$53$	12.2703	1.68546	0.842729	+	0.538339i	$0.180948\pi$
$54$	−0.709173	−0.0965062
$55$	−2.78146	−0.375051
$56$	−18.6781	−2.49597
$57$	0.319716	0.0423474
$58$	−0.660116	−0.0866775
$59$	1.45566	0.189510	0.0947552	−	0.995501i	$-0.469793\pi$
$59$	1.45566	0.189510	0.0947552	+	0.995501i	$0.469793\pi$
$60$	−0.566706	−0.0731614
$61$	9.70235	1.24226	0.621129	−	0.783708i	$-0.286674\pi$
$61$	9.70235	1.24226	0.621129	+	0.783708i	$0.286674\pi$
$62$	−26.5774	−3.37534
$63$	−9.51209	−1.19841
$64$	−2.98828	−0.373535
$65$	−8.68086	−1.07673
$66$	−0.118239	−0.0145542
$67$	−5.64376	−0.689495	−0.344747	−	0.938696i	$-0.612035\pi$
$67$	−5.64376	−0.689495	−0.344747	+	0.938696i	$0.612035\pi$
$68$	7.34763	0.891031
$69$	−0.262870	−0.0316458
$70$	−22.2192	−2.65570
$71$	15.3259	1.81885	0.909423	−	0.415873i	$-0.136524\pi$
$71$	15.3259	1.81885	0.909423	+	0.415873i	$0.136524\pi$
$72$	17.6466	2.07967
$73$	5.38902	0.630737	0.315369	−	0.948969i	$-0.397872\pi$
$73$	5.38902	0.630737	0.315369	+	0.948969i	$0.397872\pi$
$74$	−2.30080	−0.267462
$75$	−0.128521	−0.0148403
$76$	−29.5320	−3.38756
$77$	−3.17303	−0.361600
$78$	−0.369021	−0.0417834
$79$	−12.5453	−1.41146	−0.705729	−	0.708482i	$-0.749380\pi$
$79$	−12.5453	−1.41146	−0.705729	+	0.708482i	$0.749380\pi$
$80$	17.0877	1.91046
$81$	8.98015	0.997795
$82$	−25.5149	−2.81765
$83$	−7.57893	−0.831896	−0.415948	−	0.909388i	$-0.636550\pi$
$83$	−7.57893	−0.831896	−0.415948	+	0.909388i	$0.636550\pi$
$84$	−0.646487	−0.0705375
$85$	4.71099	0.510979
$86$	−2.26312	−0.244038
$87$	−0.0123145	−0.00132025
$88$	5.88653	0.627507
$89$	14.1630	1.50128	0.750638	−	0.660713i	$-0.229746\pi$
$89$	14.1630	1.50128	0.750638	+	0.660713i	$0.229746\pi$
$90$	20.9921	2.21276
$91$	−9.90295	−1.03811
$92$	24.2812	2.53149
$93$	−0.495803	−0.0514124
$94$	4.96594	0.512198
$95$	−18.9347	−1.94266
$96$	0.173465	0.0177042
$97$	−10.3501	−1.05090	−0.525448	−	0.850826i	$-0.676102\pi$
$97$	−10.3501	−1.05090	−0.525448	+	0.850826i	$0.676102\pi$
$98$	−7.72420	−0.780263
$99$	2.99779	0.301290
$100$	11.8714	1.18714
$101$	−6.20029	−0.616952	−0.308476	−	0.951232i	$-0.599819\pi$
$101$	−6.20029	−0.616952	−0.308476	+	0.951232i	$0.599819\pi$
$102$	0.200263	0.0198290
$103$	11.8866	1.17122	0.585610	−	0.810593i	$-0.300855\pi$
$103$	11.8866	1.17122	0.585610	+	0.810593i	$0.300855\pi$
$104$	18.3717	1.80150
$105$	−0.414500	−0.0404511
$106$	−30.8914	−3.00044
$107$	6.41451	0.620114	0.310057	−	0.950718i	$-0.399652\pi$
$107$	6.41451	0.620114	0.310057	+	0.950718i	$0.399652\pi$
$108$	1.22202	0.117589
$109$	1.99114	0.190716	0.0953581	−	0.995443i	$-0.469600\pi$
$109$	1.99114	0.190716	0.0953581	+	0.995443i	$0.469600\pi$
$110$	7.00252	0.667664
$111$	−0.0429215	−0.00407393
$112$	19.4933	1.84194
$113$	6.84780	0.644187	0.322093	−	0.946708i	$-0.395613\pi$
$113$	6.84780	0.644187	0.322093	+	0.946708i	$0.395613\pi$
$114$	−0.804909	−0.0753866
$115$	15.5681	1.45173
$116$	1.13748	0.105613
$117$	9.35605	0.864967
$118$	−3.66472	−0.337365
$119$	5.37420	0.492652
$120$	0.768971	0.0701971
$121$	1.00000	0.0909091
$122$	−24.4264	−2.21146
$123$	−0.475981	−0.0429178
$124$	45.7971	4.11270
$125$	−6.29583	−0.563116
$126$	23.9474	2.13340
$127$	4.64596	0.412263	0.206131	−	0.978524i	$-0.433913\pi$
$127$	4.64596	0.412263	0.206131	+	0.978524i	$0.433913\pi$
$128$	14.9102	1.31788
$129$	−0.0422185	−0.00371714
$130$	21.8547	1.91678
$131$	1.00000	0.0873704
$131$	1.00000	0.0873704
$132$	0.203744	0.0177337
$133$	−21.6003	−1.87299
$134$	14.2086	1.22743
$135$	0.783505	0.0674334
$136$	−9.97010	−0.854929
$137$	9.13518	0.780471	0.390235	−	0.920715i	$-0.372394\pi$
$137$	9.13518	0.780471	0.390235	+	0.920715i	$0.372394\pi$
$138$	0.661794	0.0563356
$139$	11.2144	0.951196	0.475598	−	0.879663i	$-0.342232\pi$
$139$	11.2144	0.951196	0.475598	+	0.879663i	$0.342232\pi$
$140$	38.2872	3.23586
$141$	0.0926398	0.00780168
$142$	−38.5840	−3.23790
$143$	3.12098	0.260989
$144$	−18.4167	−1.53473
$145$	0.729307	0.0605656
$146$	−13.5673	−1.12283
$147$	−0.144095	−0.0118848
$148$	3.96464	0.325891
$149$	−16.5694	−1.35742	−0.678709	−	0.734408i	$-0.737460\pi$
$149$	−16.5694	−1.35742	−0.678709	+	0.734408i	$0.737460\pi$
$150$	0.323561	0.0264186
$151$	23.7768	1.93493	0.967466	−	0.253003i	$-0.0814181\pi$
$151$	23.7768	1.93493	0.967466	+	0.253003i	$0.0814181\pi$
$152$	40.0725	3.25031
$153$	−5.07740	−0.410484
$154$	7.98834	0.643718
$155$	29.3632	2.35851
$156$	0.635881	0.0509113
$157$	−13.4537	−1.07372	−0.536862	−	0.843670i	$-0.680390\pi$
$157$	−13.4537	−1.07372	−0.536862	+	0.843670i	$0.680390\pi$
$158$	31.5837	2.51267
$159$	−0.576280	−0.0457020
$160$	−10.2732	−0.812169
$161$	17.7597	1.39966
$162$	−22.6082	−1.77627
$163$	−15.4810	−1.21257	−0.606284	−	0.795248i	$-0.707341\pi$
$163$	−15.4810	−1.21257	−0.606284	+	0.795248i	$0.707341\pi$
$164$	43.9662	3.43318
$165$	0.130632	0.0101697
$166$	19.0805	1.48094
$167$	−3.14428	−0.243312	−0.121656	−	0.992572i	$-0.538820\pi$
$167$	−3.14428	−0.243312	−0.121656	+	0.992572i	$0.538820\pi$
$168$	0.877227	0.0676795
$169$	−3.25950	−0.250731
$170$	−11.8603	−0.909641
$171$	20.4074	1.56059
$172$	3.89971	0.297350
$173$	−17.3185	−1.31670	−0.658350	−	0.752712i	$-0.728745\pi$
$173$	−17.3185	−1.31670	−0.658350	+	0.752712i	$0.728745\pi$
$174$	0.0310026	0.00235030
$175$	8.68299	0.656372
$176$	−6.14343	−0.463078
$177$	−0.0683655	−0.00513867
$178$	−35.6564	−2.67256
$179$	21.3593	1.59647	0.798236	−	0.602345i	$-0.205767\pi$
$179$	21.3593	1.59647	0.798236	+	0.602345i	$0.205767\pi$
$180$	−36.1727	−2.69616
$181$	−0.488126	−0.0362821	−0.0181411	−	0.999835i	$-0.505775\pi$
$181$	−0.488126	−0.0362821	−0.0181411	+	0.999835i	$0.505775\pi$
$182$	24.9314	1.84804
$183$	−0.455675	−0.0336845
$184$	−32.9475	−2.42892
$185$	2.54196	0.186889
$186$	1.24822	0.0915240
$187$	−1.69371	−0.123857
$188$	−8.55710	−0.624091
$189$	0.893807	0.0650149
$190$	47.6695	3.45831
$191$	−19.4681	−1.40867	−0.704333	−	0.709870i	$-0.748754\pi$
$191$	−19.4681	−1.40867	−0.704333	+	0.709870i	$0.748754\pi$
$192$	0.140346	0.0101286
$193$	−7.99295	−0.575345	−0.287673	−	0.957729i	$-0.592881\pi$
$193$	−7.99295	−0.575345	−0.287673	+	0.957729i	$0.592881\pi$
$194$	26.0572	1.87080
$195$	0.407700	0.0291960
$196$	13.3100	0.950716
$197$	−17.5728	−1.25201	−0.626007	−	0.779818i	$-0.715312\pi$
$197$	−17.5728	−1.25201	−0.626007	+	0.779818i	$0.715312\pi$
$198$	−7.54717	−0.536354
$199$	5.69208	0.403501	0.201750	−	0.979437i	$-0.435337\pi$
$199$	5.69208	0.403501	0.201750	+	0.979437i	$0.435337\pi$
$200$	−16.1085	−1.13904
$201$	0.265061	0.0186960
$202$	15.6097	1.09829
$203$	0.831978	0.0583934
$204$	−0.345084	−0.0241607
$205$	28.1893	1.96882
$206$	−29.9253	−2.08500
$207$	−16.7789	−1.16622
$208$	−19.1735	−1.32944
$209$	6.80748	0.470883
$210$	1.04353	0.0720107
$211$	−21.1186	−1.45386	−0.726931	−	0.686711i	$-0.759054\pi$
$211$	−21.1186	−1.45386	−0.726931	+	0.686711i	$0.759054\pi$
$212$	53.2308	3.65591
$213$	−0.719786	−0.0493189
$214$	−16.1490	−1.10392
$215$	2.50033	0.170521
$216$	−1.65817	−0.112824
$217$	33.4969	2.27392
$218$	−5.01283	−0.339512
$219$	−0.253098	−0.0171028
$220$	−12.0665	−0.813520
$221$	−5.28604	−0.355578
$222$	0.108058	0.00725237
$223$	12.3442	0.826631	0.413316	−	0.910588i	$-0.364371\pi$
$223$	12.3442	0.826631	0.413316	+	0.910588i	$0.364371\pi$
$224$	−11.7195	−0.783041
$225$	−8.20346	−0.546897
$226$	−17.2398	−1.14678
$227$	−23.1762	−1.53826	−0.769130	−	0.639092i	$-0.779310\pi$
$227$	−23.1762	−1.53826	−0.769130	+	0.639092i	$0.779310\pi$
$228$	1.38698	0.0918553
$229$	6.82842	0.451235	0.225617	−	0.974216i	$-0.427560\pi$
$229$	6.82842	0.451235	0.225617	+	0.974216i	$0.427560\pi$
$230$	−39.1937	−2.58436
$231$	0.149023	0.00980497
$232$	−1.54347	−0.101334
$233$	18.0665	1.18358	0.591788	−	0.806094i	$-0.298422\pi$
$233$	18.0665	1.18358	0.591788	+	0.806094i	$0.298422\pi$
$234$	−23.5545	−1.53981
$235$	−5.48645	−0.357897
$236$	6.31490	0.411065
$237$	0.589196	0.0382724
$238$	−13.5299	−0.877016
$239$	19.1342	1.23769	0.618844	−	0.785514i	$-0.287601\pi$
$239$	19.1342	1.23769	0.618844	+	0.785514i	$0.287601\pi$
$240$	−0.802530	−0.0518031
$241$	−12.5772	−0.810170	−0.405085	−	0.914279i	$-0.632758\pi$
$241$	−12.5772	−0.810170	−0.405085	+	0.914279i	$0.632758\pi$
$242$	−2.51757	−0.161836
$243$	−1.26682	−0.0812667
$244$	42.0905	2.69457
$245$	8.53383	0.545206
$246$	1.19832	0.0764020
$247$	21.2460	1.35185
$248$	−62.1428	−3.94607
$249$	0.355948	0.0225573
$250$	15.8502	1.00246
$251$	16.0840	1.01522	0.507608	−	0.861588i	$-0.330530\pi$
$251$	16.0840	1.01522	0.507608	+	0.861588i	$0.330530\pi$
$252$	−41.2651	−2.59946
$253$	−5.59709	−0.351886
$254$	−11.6966	−0.733907
$255$	−0.221254	−0.0138554
$256$	−31.5609	−1.97255
$257$	4.01075	0.250184	0.125092	−	0.992145i	$-0.460077\pi$
$257$	4.01075	0.250184	0.125092	+	0.992145i	$0.460077\pi$
$258$	0.106288	0.00661722
$259$	2.89982	0.180186
$260$	−37.6591	−2.33552
$261$	−0.786031	−0.0486541
$262$	−2.51757	−0.155536
$263$	−6.30380	−0.388709	−0.194355	−	0.980931i	$-0.562261\pi$
$263$	−6.30380	−0.388709	−0.194355	+	0.980931i	$0.562261\pi$
$264$	−0.276464	−0.0170152
$265$	34.1293	2.09655
$266$	54.3804	3.33428
$267$	−0.665172	−0.0407079
$268$	−24.4836	−1.49558
$269$	19.0933	1.16414	0.582068	−	0.813140i	$-0.302244\pi$
$269$	19.0933	1.16414	0.582068	+	0.813140i	$0.302244\pi$
$270$	−1.97253	−0.120044
$271$	8.63112	0.524303	0.262152	−	0.965027i	$-0.415568\pi$
$271$	8.63112	0.524303	0.262152	+	0.965027i	$0.415568\pi$
$272$	10.4052	0.630908
$273$	0.465096	0.0281489
$274$	−22.9985	−1.38939
$275$	−2.73650	−0.165017
$276$	−1.14038	−0.0686425
$277$	−18.8542	−1.13284	−0.566421	−	0.824116i	$-0.691672\pi$
$277$	−18.8542	−1.13284	−0.566421	+	0.824116i	$0.691672\pi$
$278$	−28.2332	−1.69331
$279$	−31.6470	−1.89466
$280$	−51.9524	−3.10475
$281$	−14.4103	−0.859648	−0.429824	−	0.902913i	$-0.641424\pi$
$281$	−14.4103	−0.859648	−0.429824	+	0.902913i	$0.641424\pi$
$282$	−0.233228	−0.0138885
$283$	5.11684	0.304164	0.152082	−	0.988368i	$-0.451402\pi$
$283$	5.11684	0.304164	0.152082	+	0.988368i	$0.451402\pi$
$284$	66.4863	3.94524
$285$	0.889276	0.0526762
$286$	−7.85729	−0.464611
$287$	32.1578	1.89821
$288$	11.0723	0.652439
$289$	−14.1313	−0.831255
$290$	−1.83608	−0.107819
$291$	0.486098	0.0284956
$292$	23.3785	1.36813
$293$	−10.4467	−0.610301	−0.305150	−	0.952304i	$-0.598707\pi$
$293$	−10.4467	−0.610301	−0.305150	+	0.952304i	$0.598707\pi$
$294$	0.362770	0.0211572
$295$	4.04885	0.235733
$296$	−5.37968	−0.312687
$297$	−0.281689	−0.0163452
$298$	41.7147	2.41647
$299$	−17.4684	−1.01022
$300$	−0.557546	−0.0321899
$301$	2.85233	0.164405
$302$	−59.8599	−3.44455
$303$	0.291199	0.0167290
$304$	−41.8213	−2.39861
$305$	26.9867	1.54525
$306$	12.7827	0.730741
$307$	−4.07876	−0.232787	−0.116394	−	0.993203i	$-0.537133\pi$
$307$	−4.07876	−0.232787	−0.116394	+	0.993203i	$0.537133\pi$
$308$	−13.7652	−0.784343
$309$	−0.558258	−0.0317582
$310$	−73.9240	−4.19860
$311$	14.8682	0.843101	0.421550	−	0.906805i	$-0.361486\pi$
$311$	14.8682	0.843101	0.421550	+	0.906805i	$0.361486\pi$
$312$	−0.862836	−0.0488485
$313$	−26.6883	−1.50851	−0.754257	−	0.656579i	$-0.772003\pi$
$313$	−26.6883	−1.50851	−0.754257	+	0.656579i	$0.772003\pi$
$314$	33.8707	1.91144
$315$	−26.4575	−1.49071
$316$	−54.4238	−3.06158
$317$	−30.9599	−1.73888	−0.869440	−	0.494038i	$-0.835520\pi$
$317$	−30.9599	−1.73888	−0.869440	+	0.494038i	$0.835520\pi$
$318$	1.45083	0.0813584
$319$	−0.262203	−0.0146806
$320$	−8.31178	−0.464642
$321$	−0.301260	−0.0168147
$322$	−44.7114	−2.49167
$323$	−11.5299	−0.641542
$324$	38.9575	2.16431
$325$	−8.54055	−0.473745
$326$	38.9747	2.15861
$327$	−0.0935145	−0.00517136
$328$	−59.6584	−3.29408
$329$	−6.25884	−0.345061
$330$	−0.328876	−0.0181040
$331$	−5.60072	−0.307843	−0.153922	−	0.988083i	$-0.549190\pi$
$331$	−5.60072	−0.307843	−0.153922	+	0.988083i	$0.549190\pi$
$332$	−32.8787	−1.80446
$333$	−2.73967	−0.150133
$334$	7.91597	0.433142
$335$	−15.6979	−0.857666
$336$	−0.915510	−0.0499452
$337$	−4.10055	−0.223371	−0.111686	−	0.993744i	$-0.535625\pi$
$337$	−4.10055	−0.223371	−0.111686	+	0.993744i	$0.535625\pi$
$338$	8.20603	0.446349
$339$	−0.321610	−0.0174674
$340$	20.4371	1.10836
$341$	−10.5568	−0.571681
$342$	−51.3772	−2.77816
$343$	−12.4760	−0.673640
$344$	−5.29157	−0.285302
$345$	−0.731160	−0.0393644
$346$	43.6006	2.34398
$347$	24.4725	1.31375	0.656876	−	0.753999i	$-0.271878\pi$
$347$	24.4725	1.31375	0.656876	+	0.753999i	$0.271878\pi$
$348$	−0.0534224	−0.00286374
$349$	−3.40810	−0.182432	−0.0912158	−	0.995831i	$-0.529075\pi$
$349$	−3.40810	−0.182432	−0.0912158	+	0.995831i	$0.529075\pi$
$350$	−21.8601	−1.16847
$351$	−0.879145	−0.0469253
$352$	3.69347	0.196862
$353$	16.2358	0.864142	0.432071	−	0.901839i	$-0.357783\pi$
$353$	16.2358	0.864142	0.432071	+	0.901839i	$0.357783\pi$
$354$	0.172115	0.00914782
$355$	42.6282	2.26247
$356$	61.4417	3.25640
$357$	−0.252402	−0.0133585
$358$	−53.7737	−2.84203
$359$	18.3031	0.966000	0.483000	−	0.875620i	$-0.339547\pi$
$359$	18.3031	0.966000	0.483000	+	0.875620i	$0.339547\pi$
$360$	49.0833	2.58692
$361$	27.3418	1.43904
$362$	1.22889	0.0645892
$363$	−0.0469654	−0.00246504
$364$	−42.9608	−2.25176
$365$	14.9893	0.784577
$366$	1.14720	0.0599649
$367$	−34.9177	−1.82269	−0.911343	−	0.411647i	$-0.864954\pi$
$367$	−34.9177	−1.82269	−0.911343	+	0.411647i	$0.864954\pi$
$368$	34.3853	1.79246
$369$	−30.3818	−1.58161
$370$	−6.39957	−0.332698
$371$	38.9341	2.02136
$372$	−2.15088	−0.111518
$373$	10.6459	0.551226	0.275613	−	0.961269i	$-0.411119\pi$
$373$	10.6459	0.551226	0.275613	+	0.961269i	$0.411119\pi$
$374$	4.26405	0.220489
$375$	0.295686	0.0152692
$376$	11.6113	0.598805
$377$	−0.818330	−0.0421462
$378$	−2.25023	−0.115739
$379$	32.8449	1.68713	0.843563	−	0.537030i	$-0.180454\pi$
$379$	32.8449	1.68713	0.843563	+	0.537030i	$0.180454\pi$
$380$	−82.1421	−4.21380
$381$	−0.218200	−0.0111787
$382$	49.0125	2.50770
$383$	−0.133606	−0.00682695	−0.00341348	−	0.999994i	$-0.501087\pi$
$383$	−0.133606	−0.00682695	−0.00341348	+	0.999994i	$0.501087\pi$
$384$	−0.700262	−0.0357351
$385$	−8.82564	−0.449796
$386$	20.1228	1.02423
$387$	−2.69480	−0.136985
$388$	−44.9007	−2.27949
$389$	−19.0392	−0.965325	−0.482662	−	0.875807i	$-0.660330\pi$
$389$	−19.0392	−0.965325	−0.482662	+	0.875807i	$0.660330\pi$
$390$	−1.02642	−0.0519746
$391$	9.47987	0.479417
$392$	−18.0606	−0.912196
$393$	−0.0469654	−0.00236909
$394$	44.2409	2.22883
$395$	−34.8942	−1.75572
$396$	13.0050	0.653524
$397$	2.09184	0.104986	0.0524931	−	0.998621i	$-0.483283\pi$
$397$	2.09184	0.104986	0.0524931	+	0.998621i	$0.483283\pi$
$398$	−14.3302	−0.718309
$399$	1.01447	0.0507869
$400$	16.8115	0.840574
$401$	−17.6116	−0.879484	−0.439742	−	0.898124i	$-0.644930\pi$
$401$	−17.6116	−0.879484	−0.439742	+	0.898124i	$0.644930\pi$
$402$	−0.667312	−0.0332825
$403$	−32.9474	−1.64123
$404$	−26.8980	−1.33822
$405$	24.9779	1.24116
$406$	−2.09457	−0.103952
$407$	−0.913895	−0.0453001
$408$	0.468250	0.0231818
$409$	3.15487	0.155999	0.0779993	−	0.996953i	$-0.475147\pi$
$409$	3.15487	0.155999	0.0779993	+	0.996953i	$0.475147\pi$
$410$	−70.9686	−3.50489
$411$	−0.429037	−0.0211629
$412$	51.5661	2.54048
$413$	4.61884	0.227278
$414$	42.2422	2.07609
$415$	−21.0805	−1.03480
$416$	11.5272	0.565169
$417$	−0.526691	−0.0257921
$418$	−17.1383	−0.838263
$419$	−14.2135	−0.694377	−0.347188	−	0.937795i	$-0.612864\pi$
$419$	−14.2135	−0.694377	−0.347188	+	0.937795i	$0.612864\pi$
$420$	−1.79817	−0.0877419
$421$	9.56690	0.466262	0.233131	−	0.972445i	$-0.425103\pi$
$421$	9.56690	0.466262	0.233131	+	0.972445i	$0.425103\pi$
$422$	53.1675	2.58815
$423$	5.91318	0.287509
$424$	−72.2296	−3.50778
$425$	4.63484	0.224823
$426$	1.81211	0.0877972
$427$	30.7858	1.48983
$428$	27.8273	1.34508
$429$	−0.146578	−0.00707685
$430$	−6.29477	−0.303561
$431$	9.69154	0.466825	0.233413	−	0.972378i	$-0.425011\pi$
$431$	9.69154	0.466825	0.233413	+	0.972378i	$0.425011\pi$
$432$	1.73054	0.0832604
$433$	−15.2339	−0.732096	−0.366048	−	0.930596i	$-0.619289\pi$
$433$	−15.2339	−0.732096	−0.366048	+	0.930596i	$0.619289\pi$
$434$	−84.3310	−4.04802
$435$	−0.0342522	−0.00164227
$436$	8.63790	0.413680
$437$	−38.1021	−1.82267
$438$	0.637192	0.0304462
$439$	13.9271	0.664707	0.332353	−	0.943155i	$-0.392157\pi$
$439$	13.9271	0.664707	0.332353	+	0.943155i	$0.392157\pi$
$440$	16.3731	0.780559
$441$	−9.19758	−0.437980
$442$	13.3080	0.632997
$443$	1.05271	0.0500156	0.0250078	−	0.999687i	$-0.492039\pi$
$443$	1.05271	0.0500156	0.0250078	+	0.999687i	$0.492039\pi$
$444$	−0.186201	−0.00883671
$445$	39.3938	1.86745
$446$	−31.0775	−1.47156
$447$	0.778188	0.0368070
$448$	−9.48191	−0.447978
$449$	−8.25735	−0.389689	−0.194844	−	0.980834i	$-0.562420\pi$
$449$	−8.25735	−0.389689	−0.194844	+	0.980834i	$0.562420\pi$
$450$	20.6528	0.973583
$451$	−10.1347	−0.477225
$452$	29.7070	1.39730
$453$	−1.11669	−0.0524666
$454$	58.3479	2.73840
$455$	−27.5446	−1.29131
$456$	−1.88202	−0.0881336
$457$	−3.69263	−0.172734	−0.0863669	−	0.996263i	$-0.527526\pi$
$457$	−3.69263	−0.172734	−0.0863669	+	0.996263i	$0.527526\pi$
$458$	−17.1911	−0.803285
$459$	0.477100	0.0222691
$460$	67.5370	3.14893
$461$	−21.4826	−1.00054	−0.500271	−	0.865869i	$-0.666766\pi$
$461$	−21.4826	−1.00054	−0.500271	+	0.865869i	$0.666766\pi$
$462$	−0.375175	−0.0174547
$463$	−2.57128	−0.119497	−0.0597487	−	0.998213i	$-0.519030\pi$
$463$	−2.57128	−0.119497	−0.0597487	+	0.998213i	$0.519030\pi$
$464$	1.61083	0.0747808
$465$	−1.37905	−0.0639521
$466$	−45.4838	−2.10699
$467$	−36.7782	−1.70189	−0.850947	−	0.525252i	$-0.823971\pi$
$467$	−36.7782	−1.70189	−0.850947	+	0.525252i	$0.823971\pi$
$468$	40.5882	1.87619
$469$	−17.9078	−0.826906
$470$	13.8126	0.637125
$471$	0.631859	0.0291145
$472$	−8.56877	−0.394410
$473$	−0.898928	−0.0413328
$474$	−1.48334	−0.0681322
$475$	−18.6287	−0.854741
$476$	23.3142	1.06861
$477$	−36.7839	−1.68422
$478$	−48.1717	−2.20332
$479$	−3.31533	−0.151482	−0.0757408	−	0.997128i	$-0.524132\pi$
$479$	−3.31533	−0.151482	−0.0757408	+	0.997128i	$0.524132\pi$
$480$	0.482486	0.0220224
$481$	−2.85225	−0.130051
$482$	31.6641	1.44226
$483$	−0.834093	−0.0379525
$484$	4.33818	0.197190
$485$	−28.7884	−1.30721
$486$	3.18932	0.144671
$487$	0.602575	0.0273053	0.0136526	−	0.999907i	$-0.495654\pi$
$487$	0.602575	0.0273053	0.0136526	+	0.999907i	$0.495654\pi$
$488$	−57.1132	−2.58539
$489$	0.727073	0.0328794
$490$	−21.4845	−0.970572
$491$	23.3629	1.05435	0.527176	−	0.849756i	$-0.323251\pi$
$491$	23.3629	1.05435	0.527176	+	0.849756i	$0.323251\pi$
$492$	−2.06489	−0.0930925
$493$	0.444097	0.0200011
$494$	−53.4883	−2.40655
$495$	8.33823	0.374776
$496$	64.8548	2.91206
$497$	48.6294	2.18133
$498$	−0.896124	−0.0401563
$499$	11.5641	0.517682	0.258841	−	0.965920i	$-0.416659\pi$
$499$	11.5641	0.517682	0.258841	+	0.965920i	$0.416659\pi$
$500$	−27.3124	−1.22145
$501$	0.147673	0.00659752
$502$	−40.4928	−1.80728
$503$	−17.6659	−0.787686	−0.393843	−	0.919178i	$-0.628855\pi$
$503$	−17.6659	−0.787686	−0.393843	+	0.919178i	$0.628855\pi$
$504$	55.9932	2.49414
$505$	−17.2458	−0.767430
$506$	14.0911	0.626425
$507$	0.153084	0.00679869
$508$	20.1550	0.894234
$509$	−9.18213	−0.406991	−0.203495	−	0.979076i	$-0.565230\pi$
$509$	−9.18213	−0.406991	−0.203495	+	0.979076i	$0.565230\pi$
$510$	0.557022	0.0246654
$511$	17.0995	0.756439
$512$	49.6365	2.19364
$513$	−1.91759	−0.0846637
$514$	−10.0974	−0.445376
$515$	33.0620	1.45689
$516$	−0.183152	−0.00806280
$517$	1.97251	0.0867509
$518$	−7.30050	−0.320766
$519$	0.813370	0.0357030
$520$	51.1002	2.24089
$521$	42.6659	1.86923	0.934614	−	0.355665i	$-0.115746\pi$
$521$	42.6659	1.86923	0.934614	+	0.355665i	$0.115746\pi$
$522$	1.97889	0.0866137
$523$	31.9428	1.39676	0.698380	−	0.715727i	$-0.253904\pi$
$523$	31.9428	1.39676	0.698380	+	0.715727i	$0.253904\pi$
$524$	4.33818	0.189514
$525$	−0.407800	−0.0177979
$526$	15.8703	0.691978
$527$	17.8801	0.778871
$528$	0.288529	0.0125566
$529$	8.32742	0.362062
$530$	−85.9231	−3.73226
$531$	−4.36376	−0.189371
$532$	−93.7061	−4.06267
$533$	−31.6302	−1.37006
$534$	1.67462	0.0724679
$535$	17.8417	0.771363
$536$	33.2222	1.43498
$537$	−1.00315	−0.0432891
$538$	−48.0687	−2.07239
$539$	−3.06811	−0.132153
$540$	3.39899	0.146269
$541$	−11.6887	−0.502536	−0.251268	−	0.967918i	$-0.580848\pi$
$541$	−11.6887	−0.502536	−0.251268	+	0.967918i	$0.580848\pi$
$542$	−21.7295	−0.933361
$543$	0.0229250	0.000983807 0
$544$	−6.25567	−0.268210
$545$	5.53826	0.237233
$546$	−1.17091	−0.0501105
$547$	29.3344	1.25425	0.627124	−	0.778919i	$-0.284232\pi$
$547$	29.3344	1.25425	0.627124	+	0.778919i	$0.284232\pi$
$548$	39.6300	1.69291
$549$	−29.0857	−1.24135
$550$	6.88934	0.293762
$551$	−1.78494	−0.0760411
$552$	1.54739	0.0658613
$553$	−39.8066	−1.69275
$554$	47.4670	2.01668
$555$	−0.119384	−0.00506758
$556$	48.6502	2.06323
$557$	41.4876	1.75789	0.878943	−	0.476927i	$-0.158249\pi$
$557$	41.4876	1.75789	0.878943	+	0.476927i	$0.158249\pi$
$558$	79.6737	3.37286
$559$	−2.80554	−0.118661
$560$	54.2197	2.29120
$561$	0.0795459	0.00335843
$562$	36.2791	1.53034
$563$	7.01042	0.295454	0.147727	−	0.989028i	$-0.452804\pi$
$563$	7.01042	0.295454	0.147727	+	0.989028i	$0.452804\pi$
$564$	0.401888	0.0169225
$565$	19.0469	0.801307
$566$	−12.8820	−0.541471
$567$	28.4943	1.19665
$568$	−90.2162	−3.78539
$569$	37.1479	1.55732	0.778660	−	0.627446i	$-0.215900\pi$
$569$	37.1479	1.55732	0.778660	+	0.627446i	$0.215900\pi$
$570$	−2.23882	−0.0937738
$571$	34.1911	1.43085	0.715426	−	0.698689i	$-0.246233\pi$
$571$	34.1911	1.43085	0.715426	+	0.698689i	$0.246233\pi$
$572$	13.5394	0.566109
$573$	0.914330	0.0381967
$574$	−80.9595	−3.37919
$575$	15.3164	0.638739
$576$	8.95825	0.373261
$577$	−5.88069	−0.244816	−0.122408	−	0.992480i	$-0.539062\pi$
$577$	−5.88069	−0.244816	−0.122408	+	0.992480i	$0.539062\pi$
$578$	35.5767	1.47979
$579$	0.375392	0.0156008
$580$	3.16386	0.131372
$581$	−24.0482	−0.997686
$582$	−1.22379	−0.0507276
$583$	−12.2703	−0.508184
$584$	−31.7227	−1.31269
$585$	26.0234	1.07594
$586$	26.3002	1.08645
$587$	−2.00019	−0.0825568	−0.0412784	−	0.999148i	$-0.513143\pi$
$587$	−2.00019	−0.0825568	−0.0412784	+	0.999148i	$0.513143\pi$
$588$	−0.625111	−0.0257791
$589$	−71.8650	−2.96114
$590$	−10.1933	−0.419650
$591$	0.825316	0.0339490
$592$	5.61445	0.230752
$593$	−14.1828	−0.582420	−0.291210	−	0.956659i	$-0.594058\pi$
$593$	−14.1828	−0.582420	−0.291210	+	0.956659i	$0.594058\pi$
$594$	0.709173	0.0290977
$595$	14.9481	0.612813
$596$	−71.8809	−2.94436
$597$	−0.267331	−0.0109411
$598$	43.9780	1.79839
$599$	−43.1297	−1.76223	−0.881115	−	0.472902i	$-0.843206\pi$
$599$	−43.1297	−1.76223	−0.881115	+	0.472902i	$0.843206\pi$
$600$	0.756542	0.0308857
$601$	9.49573	0.387339	0.193669	−	0.981067i	$-0.437961\pi$
$601$	9.49573	0.387339	0.193669	+	0.981067i	$0.437961\pi$
$602$	−7.18094	−0.292673
$603$	16.9188	0.688988
$604$	103.148	4.19704
$605$	2.78146	0.113082
$606$	−0.733116	−0.0297808
$607$	22.6942	0.921130	0.460565	−	0.887626i	$-0.347647\pi$
$607$	22.6942	0.921130	0.460565	+	0.887626i	$0.347647\pi$
$608$	25.1432	1.01969
$609$	−0.0390742	−0.00158337
$610$	−67.9409	−2.75085
$611$	6.15616	0.249052
$612$	−22.0267	−0.890376
$613$	29.4704	1.19030	0.595149	−	0.803615i	$-0.297093\pi$
$613$	29.4704	1.19030	0.595149	+	0.803615i	$0.297093\pi$
$614$	10.2686	0.414406
$615$	−1.32392	−0.0533856
$616$	18.6781	0.752564
$617$	−19.1427	−0.770656	−0.385328	−	0.922780i	$-0.625912\pi$
$617$	−19.1427	−0.770656	−0.385328	+	0.922780i	$0.625912\pi$
$618$	1.40546	0.0565357
$619$	−14.8539	−0.597028	−0.298514	−	0.954405i	$-0.596491\pi$
$619$	−14.8539	−0.597028	−0.298514	+	0.954405i	$0.596491\pi$
$620$	127.383	5.11581
$621$	1.57664	0.0632683
$622$	−37.4319	−1.50088
$623$	44.9397	1.80047
$624$	0.900492	0.0360485
$625$	−31.1941	−1.24776
$626$	67.1899	2.68545
$627$	−0.319716	−0.0127682
$628$	−58.3646	−2.32900
$629$	1.54788	0.0617179
$630$	66.6086	2.65375
$631$	−27.4090	−1.09114	−0.545568	−	0.838066i	$-0.683686\pi$
$631$	−27.4090	−1.09114	−0.545568	+	0.838066i	$0.683686\pi$
$632$	73.8484	2.93753
$633$	0.991842	0.0394222
$634$	77.9438	3.09554
$635$	12.9225	0.512816
$636$	−2.50001	−0.0991317
$637$	−9.57552	−0.379396
$638$	0.660116	0.0261342
$639$	−45.9438	−1.81751
$640$	41.4719	1.63932
$641$	−21.8080	−0.861363	−0.430681	−	0.902504i	$-0.641727\pi$
$641$	−21.8080	−0.861363	−0.430681	+	0.902504i	$0.641727\pi$
$642$	0.758444	0.0299334
$643$	40.5113	1.59761	0.798805	−	0.601590i	$-0.205466\pi$
$643$	40.5113	1.59761	0.798805	+	0.601590i	$0.205466\pi$
$644$	77.0449	3.03599
$645$	−0.117429	−0.00462376
$646$	29.0274	1.14207
$647$	−34.6135	−1.36080	−0.680399	−	0.732842i	$-0.738193\pi$
$647$	−34.6135	−1.36080	−0.680399	+	0.732842i	$0.738193\pi$
$648$	−52.8620	−2.07661
$649$	−1.45566	−0.0571395
$650$	21.5015	0.843357
$651$	−1.57320	−0.0616585
$652$	−67.1595	−2.63017
$653$	48.9394	1.91514	0.957572	−	0.288193i	$-0.0930544\pi$
$653$	48.9394	1.91514	0.957572	+	0.288193i	$0.0930544\pi$
$654$	0.235430	0.00920603
$655$	2.78146	0.108680
$656$	62.2619	2.43092
$657$	−16.1552	−0.630274
$658$	15.7571	0.614275
$659$	−2.97733	−0.115980	−0.0579901	−	0.998317i	$-0.518469\pi$
$659$	−2.97733	−0.115980	−0.0579901	+	0.998317i	$0.518469\pi$
$660$	0.566706	0.0220590
$661$	−37.6502	−1.46442	−0.732211	−	0.681078i	$-0.761512\pi$
$661$	−37.6502	−1.46442	−0.732211	+	0.681078i	$0.761512\pi$
$662$	14.1002	0.548021
$663$	0.248261	0.00964166
$664$	44.6136	1.73134
$665$	−60.0804	−2.32982
$666$	6.89732	0.267266
$667$	1.46757	0.0568247
$668$	−13.6405	−0.527765
$669$	−0.579752	−0.0224145
$670$	39.5205	1.52681
$671$	−9.70235	−0.374555
$672$	0.550410	0.0212325
$673$	6.34901	0.244736	0.122368	−	0.992485i	$-0.460951\pi$
$673$	6.34901	0.244736	0.122368	+	0.992485i	$0.460951\pi$
$674$	10.3234	0.397644
$675$	0.770841	0.0296697
$676$	−14.1403	−0.543857
$677$	10.1630	0.390595	0.195298	−	0.980744i	$-0.437433\pi$
$677$	10.1630	0.390595	0.195298	+	0.980744i	$0.437433\pi$
$678$	0.809676	0.0310954
$679$	−32.8412	−1.26033
$680$	−27.7314	−1.06345
$681$	1.08848	0.0417107
$682$	26.5774	1.01770
$683$	38.2914	1.46518	0.732590	−	0.680670i	$-0.238311\pi$
$683$	38.2914	1.46518	0.732590	+	0.680670i	$0.238311\pi$
$684$	88.5310	3.38507
$685$	25.4091	0.970832
$686$	31.4092	1.19921
$687$	−0.320700	−0.0122355
$688$	5.52250	0.210543
$689$	−38.2954	−1.45894
$690$	1.84075	0.0700762
$691$	31.7251	1.20688	0.603439	−	0.797409i	$-0.293797\pi$
$691$	31.7251	1.20688	0.603439	+	0.797409i	$0.293797\pi$
$692$	−75.1307	−2.85604
$693$	9.51209	0.361334
$694$	−61.6112	−2.33873
$695$	31.1925	1.18320
$696$	0.0724896	0.00274771
$697$	17.1653	0.650182
$698$	8.58015	0.324764
$699$	−0.848501	−0.0320932
$700$	37.6684	1.42373
$701$	20.0397	0.756890	0.378445	−	0.925624i	$-0.376459\pi$
$701$	20.0397	0.756890	0.378445	+	0.925624i	$0.376459\pi$
$702$	2.21331	0.0835361
$703$	−6.22132	−0.234642
$704$	2.98828	0.112625
$705$	0.257674	0.00970455
$706$	−40.8747	−1.53834
$707$	−19.6737	−0.739906
$708$	−0.296582	−0.0111462
$709$	−34.0422	−1.27848	−0.639240	−	0.769007i	$-0.720751\pi$
$709$	−34.0422	−1.27848	−0.639240	+	0.769007i	$0.720751\pi$
$710$	−107.320	−4.02764
$711$	37.6083	1.41042
$712$	−83.3711	−3.12446
$713$	59.0872	2.21283
$714$	0.635440	0.0237807
$715$	8.68086	0.324646
$716$	92.6606	3.46289
$717$	−0.898645	−0.0335605
$718$	−46.0794	−1.71967
$719$	30.1973	1.12617	0.563085	−	0.826399i	$-0.309614\pi$
$719$	30.1973	1.12617	0.563085	+	0.826399i	$0.309614\pi$
$720$	−51.2253	−1.90906
$721$	37.7165	1.40463
$722$	−68.8349	−2.56177
$723$	0.590694	0.0219682
$724$	−2.11758	−0.0786991
$725$	0.717519	0.0266480
$726$	0.118239	0.00438826
$727$	−25.3434	−0.939935	−0.469967	−	0.882684i	$-0.655734\pi$
$727$	−25.3434	−0.939935	−0.469967	+	0.882684i	$0.655734\pi$
$728$	58.2941	2.16052
$729$	−26.8810	−0.995591
$730$	−37.7367	−1.39670
$731$	1.52253	0.0563127
$732$	−1.97680	−0.0730646
$733$	−11.5879	−0.428008	−0.214004	−	0.976833i	$-0.568651\pi$
$733$	−11.5879	−0.428008	−0.214004	+	0.976833i	$0.568651\pi$
$734$	87.9078	3.24474
$735$	−0.400795	−0.0147835
$736$	−20.6727	−0.762005
$737$	5.64376	0.207890
$738$	76.4884	2.81558
$739$	−4.40898	−0.162187	−0.0810935	−	0.996706i	$-0.525841\pi$
$739$	−4.40898	−0.162187	−0.0810935	+	0.996706i	$0.525841\pi$
$740$	11.0275	0.405378
$741$	−0.997826	−0.0366561
$742$	−98.0194	−3.59840
$743$	−14.3363	−0.525948	−0.262974	−	0.964803i	$-0.584703\pi$
$743$	−14.3363	−0.525948	−0.262974	+	0.964803i	$0.584703\pi$
$744$	2.91856	0.107000
$745$	−46.0870	−1.68850
$746$	−26.8019	−0.981288
$747$	22.7201	0.831284
$748$	−7.34763	−0.268656
$749$	20.3534	0.743698
$750$	−0.744412	−0.0271821
$751$	−13.4353	−0.490260	−0.245130	−	0.969490i	$-0.578831\pi$
$751$	−13.4353	−0.490260	−0.245130	+	0.969490i	$0.578831\pi$
$752$	−12.1180	−0.441897
$753$	−0.755394	−0.0275281
$754$	2.06021	0.0750283
$755$	66.1342	2.40687
$756$	3.87749	0.141023
$757$	−42.3422	−1.53895	−0.769476	−	0.638676i	$-0.779483\pi$
$757$	−42.3422	−1.53895	−0.769476	+	0.638676i	$0.779483\pi$
$758$	−82.6893	−3.00341
$759$	0.262870	0.00954156
$760$	111.460	4.04307
$761$	−13.4199	−0.486470	−0.243235	−	0.969967i	$-0.578209\pi$
$761$	−13.4199	−0.486470	−0.243235	+	0.969967i	$0.578209\pi$
$762$	0.549334	0.0199003
$763$	6.31793	0.228724
$764$	−84.4563	−3.05552
$765$	−14.1226	−0.510603
$766$	0.336363	0.0121533
$767$	−4.54307	−0.164041
$768$	1.48227	0.0534868
$769$	−18.3032	−0.660029	−0.330015	−	0.943976i	$-0.607054\pi$
$769$	−18.3032	−0.660029	−0.330015	+	0.943976i	$0.607054\pi$
$770$	22.2192	0.800725
$771$	−0.188367	−0.00678386
$772$	−34.6748	−1.24797
$773$	−31.3248	−1.12667	−0.563336	−	0.826228i	$-0.690483\pi$
$773$	−31.3248	−1.12667	−0.563336	+	0.826228i	$0.690483\pi$
$774$	6.78436	0.243859
$775$	28.8886	1.03771
$776$	60.9264	2.18713
$777$	−0.136191	−0.00488583
$778$	47.9325	1.71846
$779$	−68.9919	−2.47189
$780$	1.76868	0.0633288
$781$	−15.3259	−0.548403
$782$	−23.8663	−0.853456
$783$	0.0738597	0.00263953
$784$	18.8487	0.673169
$785$	−37.4209	−1.33561
$786$	0.118239	0.00421744
$787$	−6.47761	−0.230902	−0.115451	−	0.993313i	$-0.536831\pi$
$787$	−6.47761	−0.230902	−0.115451	+	0.993313i	$0.536831\pi$
$788$	−76.2341	−2.71573
$789$	0.296061	0.0105400
$790$	87.8488	3.12552
$791$	21.7283	0.772568
$792$	−17.6466	−0.627045
$793$	−30.2808	−1.07530
$794$	−5.26635	−0.186896
$795$	−1.60290	−0.0568490
$796$	24.6932	0.875229
$797$	−19.8653	−0.703665	−0.351832	−	0.936063i	$-0.614441\pi$
$797$	−19.8653	−0.703665	−0.351832	+	0.936063i	$0.614441\pi$
$798$	−2.55400	−0.0904106
$799$	−3.34087	−0.118191
$800$	−10.1072	−0.357342
$801$	−42.4578	−1.50017
$802$	44.3386	1.56565
$803$	−5.38902	−0.190174
$804$	1.14988	0.0405533
$805$	49.3979	1.74105
$806$	82.9476	2.92170
$807$	−0.896723	−0.0315661
$808$	36.4982	1.28400
$809$	−37.7871	−1.32852	−0.664262	−	0.747500i	$-0.731254\pi$
$809$	−37.7871	−1.32852	−0.664262	+	0.747500i	$0.731254\pi$
$810$	−62.8837	−2.20951
$811$	2.96881	0.104249	0.0521244	−	0.998641i	$-0.483401\pi$
$811$	2.96881	0.104249	0.0521244	+	0.998641i	$0.483401\pi$
$812$	3.60927	0.126661
$813$	−0.405364	−0.0142167
$814$	2.30080	0.0806429
$815$	−43.0598	−1.50832
$816$	−0.488685	−0.0171074
$817$	−6.11944	−0.214092
$818$	−7.94263	−0.277708
$819$	29.6870	1.03735
$820$	122.290	4.27055
$821$	10.0762	0.351663	0.175832	−	0.984420i	$-0.443739\pi$
$821$	10.0762	0.351663	0.175832	+	0.984420i	$0.443739\pi$
$822$	1.08013	0.0376740
$823$	−43.3488	−1.51104	−0.755521	−	0.655124i	$-0.772616\pi$
$823$	−43.3488	−1.51104	−0.755521	+	0.655124i	$0.772616\pi$
$824$	−69.9708	−2.43755
$825$	0.128521	0.00447452
$826$	−11.6283	−0.404599
$827$	−24.7676	−0.861252	−0.430626	−	0.902530i	$-0.641707\pi$
$827$	−24.7676	−0.861252	−0.430626	+	0.902530i	$0.641707\pi$
$828$	−72.7900	−2.52963
$829$	10.6074	0.368410	0.184205	−	0.982888i	$-0.441029\pi$
$829$	10.6074	0.368410	0.184205	+	0.982888i	$0.441029\pi$
$830$	53.0716	1.84214
$831$	0.885498	0.0307176
$832$	9.32636	0.323333
$833$	5.19651	0.180048
$834$	1.32598	0.0459150
$835$	−8.74569	−0.302657
$836$	29.5320	1.02139
$837$	2.97372	0.102787
$838$	35.7836	1.23612
$839$	−52.5107	−1.81287	−0.906435	−	0.422346i	$-0.861207\pi$
$839$	−52.5107	−1.81287	−0.906435	+	0.422346i	$0.861207\pi$
$840$	2.43997	0.0841869
$841$	−28.9312	−0.997629
$842$	−24.0854	−0.830037
$843$	0.676787	0.0233098
$844$	−91.6160	−3.15355
$845$	−9.06616	−0.311885
$846$	−14.8869	−0.511821
$847$	3.17303	0.109027
$848$	75.3818	2.58862
$849$	−0.240314	−0.00824756
$850$	−11.6686	−0.400228
$851$	5.11515	0.175345
$852$	−3.12256	−0.106977
$853$	3.69806	0.126619	0.0633096	−	0.997994i	$-0.479834\pi$
$853$	3.69806	0.126619	0.0633096	+	0.997994i	$0.479834\pi$
$854$	−77.5056	−2.65219
$855$	56.7623	1.94123
$856$	−37.7592	−1.29058
$857$	3.04834	0.104129	0.0520646	−	0.998644i	$-0.483420\pi$
$857$	3.04834	0.104129	0.0520646	+	0.998644i	$0.483420\pi$
$858$	0.369021	0.0125982
$859$	4.23867	0.144621	0.0723107	−	0.997382i	$-0.476963\pi$
$859$	4.23867	0.144621	0.0723107	+	0.997382i	$0.476963\pi$
$860$	10.8469	0.369875
$861$	−1.51030	−0.0514710
$862$	−24.3992	−0.831039
$863$	0.242492	0.00825452	0.00412726	−	0.999991i	$-0.498686\pi$
$863$	0.242492	0.00825452	0.00412726	+	0.999991i	$0.498686\pi$
$864$	−1.04041	−0.0353954
$865$	−48.1706	−1.63785
$866$	38.3526	1.30327
$867$	0.663684	0.0225399
$868$	145.316	4.93233
$869$	12.5453	0.425570
$870$	0.0862324	0.00292355
$871$	17.6140	0.596829
$872$	−11.7209	−0.396919
$873$	31.0275	1.05012
$874$	95.9248	3.24470
$875$	−19.9769	−0.675341
$876$	−1.09798	−0.0370974
$877$	−20.3217	−0.686214	−0.343107	−	0.939296i	$-0.611479\pi$
$877$	−20.3217	−0.686214	−0.343107	+	0.939296i	$0.611479\pi$
$878$	−35.0626	−1.18331
$879$	0.490632	0.0165486
$880$	−17.0877	−0.576026
$881$	−39.6208	−1.33486	−0.667430	−	0.744673i	$-0.732606\pi$
$881$	−39.6208	−1.33486	−0.667430	+	0.744673i	$0.732606\pi$
$882$	23.1556	0.779689
$883$	19.8870	0.669252	0.334626	−	0.942351i	$-0.391390\pi$
$883$	19.8870	0.669252	0.334626	+	0.942351i	$0.391390\pi$
$884$	−22.9318	−0.771279
$885$	−0.190156	−0.00639201
$886$	−2.65027	−0.0890375
$887$	31.2209	1.04830	0.524148	−	0.851627i	$-0.324384\pi$
$887$	31.2209	1.04830	0.524148	+	0.851627i	$0.324384\pi$
$888$	0.252659	0.00847867
$889$	14.7418	0.494423
$890$	−99.1768	−3.32441
$891$	−8.98015	−0.300846
$892$	53.5515	1.79304
$893$	13.4278	0.449345
$894$	−1.95915	−0.0655236
$895$	59.4100	1.98586
$896$	47.3104	1.58053
$897$	0.820410	0.0273927
$898$	20.7885	0.693721
$899$	2.76802	0.0923186
$900$	−35.5881	−1.18627
$901$	20.7824	0.692362
$902$	25.5149	0.849553
$903$	−0.133961	−0.00445793
$904$	−40.3098	−1.34068
$905$	−1.35770	−0.0451315
$906$	2.81135	0.0934007
$907$	−38.7326	−1.28609	−0.643047	−	0.765827i	$-0.722330\pi$
$907$	−38.7326	−1.28609	−0.643047	+	0.765827i	$0.722330\pi$
$908$	−100.543	−3.33662
$909$	18.5872	0.616499
$910$	69.3456	2.29879
$911$	−38.9977	−1.29205	−0.646026	−	0.763316i	$-0.723570\pi$
$911$	−38.9977	−1.29205	−0.646026	+	0.763316i	$0.723570\pi$
$912$	1.96415	0.0650396
$913$	7.57893	0.250826
$914$	9.29646	0.307500
$915$	−1.26744	−0.0419003
$916$	29.6229	0.978769
$917$	3.17303	0.104783
$918$	−1.20113	−0.0396434
$919$	−22.5952	−0.745347	−0.372673	−	0.927963i	$-0.621559\pi$
$919$	−22.5952	−0.745347	−0.372673	+	0.927963i	$0.621559\pi$
$920$	−91.6419	−3.02134
$921$	0.191561	0.00631214
$922$	54.0839	1.78116
$923$	−47.8317	−1.57440
$924$	0.646487	0.0212678
$925$	2.50087	0.0822282
$926$	6.47338	0.212729
$927$	−35.6335	−1.17036
$928$	−0.968439	−0.0317906
$929$	52.9403	1.73691	0.868457	−	0.495765i	$-0.165112\pi$
$929$	52.9403	1.73691	0.868457	+	0.495765i	$0.165112\pi$
$930$	3.47187	0.113847
$931$	−20.8861	−0.684515
$932$	78.3757	2.56728
$933$	−0.698293	−0.0228611
$934$	92.5919	3.02970
$935$	−4.71099	−0.154066
$936$	−55.0747	−1.80017
$937$	38.0513	1.24308	0.621541	−	0.783381i	$-0.286507\pi$
$937$	38.0513	1.24308	0.621541	+	0.783381i	$0.286507\pi$
$938$	45.0842	1.47205
$939$	1.25343	0.0409041
$940$	−23.8012	−0.776310
$941$	19.4908	0.635381	0.317691	−	0.948194i	$-0.397093\pi$
$941$	19.4908	0.635381	0.317691	+	0.948194i	$0.397093\pi$
$942$	−1.59075	−0.0518295
$943$	56.7249	1.84722
$944$	8.94272	0.291061
$945$	2.48609	0.0808724
$946$	2.26312	0.0735803
$947$	−1.69513	−0.0550845	−0.0275422	−	0.999621i	$-0.508768\pi$
$947$	−1.69513	−0.0550845	−0.0275422	+	0.999621i	$0.508768\pi$
$948$	2.55604	0.0830162
$949$	−16.8190	−0.545968
$950$	46.8990	1.52161
$951$	1.45404	0.0471506
$952$	−31.6354	−1.02531
$953$	−38.7305	−1.25460	−0.627302	−	0.778776i	$-0.715841\pi$
$953$	−38.7305	−1.25460	−0.627302	+	0.778776i	$0.715841\pi$
$954$	92.6061	2.99823
$955$	−54.1498	−1.75225
$956$	83.0075	2.68465
$957$	0.0123145	0.000398071 0
$958$	8.34660	0.269666
$959$	28.9862	0.936013
$960$	0.390366	0.0125990
$961$	80.4454	2.59501
$962$	7.18074	0.231516
$963$	−19.2294	−0.619658
$964$	−54.5622	−1.75733
$965$	−22.2320	−0.715675
$966$	2.09989	0.0675629
$967$	13.1156	0.421768	0.210884	−	0.977511i	$-0.432366\pi$
$967$	13.1156	0.421768	0.210884	+	0.977511i	$0.432366\pi$
$968$	−5.88653	−0.189200
$969$	0.541507	0.0173957
$970$	72.4770	2.32710
$971$	−2.65520	−0.0852094	−0.0426047	−	0.999092i	$-0.513566\pi$
$971$	−2.65520	−0.0852094	−0.0426047	+	0.999092i	$0.513566\pi$
$972$	−5.49570	−0.176275
$973$	35.5837	1.14076
$974$	−1.51703	−0.0486086
$975$	0.401111	0.0128458
$976$	59.6057	1.90793
$977$	−19.2988	−0.617424	−0.308712	−	0.951155i	$-0.599898\pi$
$977$	−19.2988	−0.617424	−0.308712	+	0.951155i	$0.599898\pi$
$978$	−1.83046	−0.0585317
$979$	−14.1630	−0.452652
$980$	37.0213	1.18260
$981$	−5.96901	−0.190576
$982$	−58.8178	−1.87695
$983$	−44.8887	−1.43173	−0.715864	−	0.698239i	$-0.753967\pi$
$983$	−44.8887	−1.43173	−0.715864	+	0.698239i	$0.753967\pi$
$984$	2.80188	0.0893207
$985$	−48.8781	−1.55739
$986$	−1.11805	−0.0356059
$987$	0.293949	0.00935649
$988$	92.1689	2.93228
$989$	5.03138	0.159989
$990$	−20.9921	−0.667173
$991$	−34.3843	−1.09225	−0.546126	−	0.837703i	$-0.683898\pi$
$991$	−34.3843	−1.09225	−0.546126	+	0.837703i	$0.683898\pi$
$992$	−38.9911	−1.23797
$993$	0.263040	0.00834733
$994$	−122.428	−3.88319
$995$	15.8323	0.501916
$996$	1.54416	0.0489287
$997$	−40.1054	−1.27015	−0.635076	−	0.772450i	$-0.719031\pi$
$997$	−40.1054	−1.27015	−0.635076	+	0.772450i	$0.719031\pi$
$998$	−29.1136	−0.921574
$999$	0.257434	0.00814485

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1441.2.a.f.1.2	✓	31

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1441.2.a.f.1.2	✓	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)

\(f(q)\)	\(=\)	\(q-2.51757 q^{2} -0.0469654 q^{3} +4.33818 q^{4} +2.78146 q^{5} +0.118239 q^{6} +3.17303 q^{7} -5.88653 q^{8} -2.99779 q^{9} +O(q^{10})\)	\(q-2.51757 q^{2} -0.0469654 q^{3} +4.33818 q^{4} +2.78146 q^{5} +0.118239 q^{6} +3.17303 q^{7} -5.88653 q^{8} -2.99779 q^{9} -7.00252 q^{10} -1.00000 q^{11} -0.203744 q^{12} -3.12098 q^{13} -7.98834 q^{14} -0.130632 q^{15} +6.14343 q^{16} +1.69371 q^{17} +7.54717 q^{18} -6.80748 q^{19} +12.0665 q^{20} -0.149023 q^{21} +2.51757 q^{22} +5.59709 q^{23} +0.276464 q^{24} +2.73650 q^{25} +7.85729 q^{26} +0.281689 q^{27} +13.7652 q^{28} +0.262203 q^{29} +0.328876 q^{30} +10.5568 q^{31} -3.69347 q^{32} +0.0469654 q^{33} -4.26405 q^{34} +8.82564 q^{35} -13.0050 q^{36} +0.913895 q^{37} +17.1383 q^{38} +0.146578 q^{39} -16.3731 q^{40} +10.1347 q^{41} +0.375175 q^{42} +0.898928 q^{43} -4.33818 q^{44} -8.33823 q^{45} -14.0911 q^{46} -1.97251 q^{47} -0.288529 q^{48} +3.06811 q^{49} -6.88934 q^{50} -0.0795459 q^{51} -13.5394 q^{52} +12.2703 q^{53} -0.709173 q^{54} -2.78146 q^{55} -18.6781 q^{56} +0.319716 q^{57} -0.660116 q^{58} +1.45566 q^{59} -0.566706 q^{60} +9.70235 q^{61} -26.5774 q^{62} -9.51209 q^{63} -2.98828 q^{64} -8.68086 q^{65} -0.118239 q^{66} -5.64376 q^{67} +7.34763 q^{68} -0.262870 q^{69} -22.2192 q^{70} +15.3259 q^{71} +17.6466 q^{72} +5.38902 q^{73} -2.30080 q^{74} -0.128521 q^{75} -29.5320 q^{76} -3.17303 q^{77} -0.369021 q^{78} -12.5453 q^{79} +17.0877 q^{80} +8.98015 q^{81} -25.5149 q^{82} -7.57893 q^{83} -0.646487 q^{84} +4.71099 q^{85} -2.26312 q^{86} -0.0123145 q^{87} +5.88653 q^{88} +14.1630 q^{89} +20.9921 q^{90} -9.90295 q^{91} +24.2812 q^{92} -0.495803 q^{93} +4.96594 q^{94} -18.9347 q^{95} +0.173465 q^{96} -10.3501 q^{97} -7.72420 q^{98} +2.99779 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 31 q + 6 q^{2} + 4 q^{3} + 38 q^{4} + 8 q^{5} + 7 q^{6} + 4 q^{7} + 24 q^{8} + 45 q^{9}+O(q^{10}) \) 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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