LMFDB - Embedded newform 6031.2.a.d.1.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6031,2,Mod(1,6031)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6031, 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("6031.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6031 = 37 \cdot 163 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6031.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:	$48.1577774590$
Analytic rank:	$0$
Dimension:	$133$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.17
Character	$\chi$	$=$	6031.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.27645 q^{2} -1.27799 q^{3} +3.18222 q^{4} +2.39479 q^{5} +2.90928 q^{6} +2.25162 q^{7} -2.69127 q^{8} -1.36674 q^{9} +O(q^{10})$	\(q-2.27645 q^{2} -1.27799 q^{3} +3.18222 q^{4} +2.39479 q^{5} +2.90928 q^{6} +2.25162 q^{7} -2.69127 q^{8} -1.36674 q^{9} -5.45162 q^{10} -0.742995 q^{11} -4.06686 q^{12} +4.07276 q^{13} -5.12571 q^{14} -3.06052 q^{15} -0.237904 q^{16} +5.58079 q^{17} +3.11131 q^{18} +4.21305 q^{19} +7.62076 q^{20} -2.87756 q^{21} +1.69139 q^{22} -1.08616 q^{23} +3.43942 q^{24} +0.735028 q^{25} -9.27144 q^{26} +5.58065 q^{27} +7.16517 q^{28} +6.12158 q^{29} +6.96713 q^{30} +9.57044 q^{31} +5.92412 q^{32} +0.949541 q^{33} -12.7044 q^{34} +5.39217 q^{35} -4.34926 q^{36} -1.00000 q^{37} -9.59079 q^{38} -5.20496 q^{39} -6.44503 q^{40} +0.942866 q^{41} +6.55061 q^{42} -7.10690 q^{43} -2.36437 q^{44} -3.27305 q^{45} +2.47258 q^{46} -0.861900 q^{47} +0.304039 q^{48} -1.93019 q^{49} -1.67325 q^{50} -7.13220 q^{51} +12.9604 q^{52} +7.39616 q^{53} -12.7041 q^{54} -1.77932 q^{55} -6.05973 q^{56} -5.38424 q^{57} -13.9355 q^{58} -9.57670 q^{59} -9.73927 q^{60} -1.29175 q^{61} -21.7866 q^{62} -3.07738 q^{63} -13.0101 q^{64} +9.75342 q^{65} -2.16158 q^{66} +0.722309 q^{67} +17.7593 q^{68} +1.38810 q^{69} -12.2750 q^{70} +8.08850 q^{71} +3.67826 q^{72} +11.6006 q^{73} +2.27645 q^{74} -0.939359 q^{75} +13.4069 q^{76} -1.67294 q^{77} +11.8488 q^{78} +0.619227 q^{79} -0.569729 q^{80} -3.03182 q^{81} -2.14639 q^{82} +12.7127 q^{83} -9.15702 q^{84} +13.3648 q^{85} +16.1785 q^{86} -7.82332 q^{87} +1.99960 q^{88} +6.16638 q^{89} +7.45093 q^{90} +9.17033 q^{91} -3.45639 q^{92} -12.2309 q^{93} +1.96207 q^{94} +10.0894 q^{95} -7.57097 q^{96} +6.18807 q^{97} +4.39399 q^{98} +1.01548 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 133 q + 14 q^{2} + 8 q^{3} + 142 q^{4} + 34 q^{5} + 20 q^{6} + 8 q^{7} + 42 q^{8} + 177 q^{9}+O(q^{10}) $ 133 * q + 14 * q^2 + 8 * q^3 + 142 * q^4 + 34 * q^5 + 20 * q^6 + 8 * q^7 + 42 * q^8 + 177 * q^9	\( 133 q + 14 q^{2} + 8 q^{3} + 142 q^{4} + 34 q^{5} + 20 q^{6} + 8 q^{7} + 42 q^{8} + 177 q^{9} + 9 q^{10} + 23 q^{11} + 24 q^{12} + 23 q^{13} + 31 q^{14} + 9 q^{15} + 168 q^{16} + 98 q^{17} + 38 q^{18} + 29 q^{19} + 83 q^{20} + 26 q^{21} + 2 q^{22} + 34 q^{23} + 75 q^{24} + 177 q^{25} + 67 q^{26} + 32 q^{27} + 32 q^{28} + 91 q^{29} + 12 q^{30} + 24 q^{31} + 88 q^{32} + 27 q^{33} + 23 q^{34} + 66 q^{35} + 232 q^{36} - 133 q^{37} + 26 q^{38} + 28 q^{39} + 41 q^{40} + 132 q^{41} + 13 q^{42} + 11 q^{43} + 65 q^{44} + 107 q^{45} + 20 q^{46} + 10 q^{47} + 27 q^{48} + 229 q^{49} + 78 q^{50} + 19 q^{51} + 71 q^{52} + 7 q^{53} + 43 q^{54} + 41 q^{55} + 67 q^{56} + 45 q^{57} + 25 q^{58} + 97 q^{59} - 42 q^{60} + 65 q^{61} + 24 q^{62} + 39 q^{63} + 200 q^{64} + 60 q^{65} + 35 q^{66} + 25 q^{67} + 227 q^{68} + 120 q^{69} + 37 q^{70} + 26 q^{71} + 93 q^{72} + 55 q^{73} - 14 q^{74} + 5 q^{75} + 34 q^{76} + 21 q^{77} - 2 q^{78} + 50 q^{79} + 162 q^{80} + 341 q^{81} + 66 q^{82} + 30 q^{83} - 89 q^{84} + 30 q^{85} - 12 q^{86} + 80 q^{87} - 85 q^{88} + 225 q^{89} - 86 q^{90} + q^{91} + 82 q^{92} + 42 q^{93} - 17 q^{94} + 70 q^{95} + 55 q^{96} + 12 q^{97} + 90 q^{98} + 17 q^{99}+O(q^{100}) \) 133 * q + 14 * q^2 + 8 * q^3 + 142 * q^4 + 34 * q^5 + 20 * q^6 + 8 * q^7 + 42 * q^8 + 177 * q^9 + 9 * q^10 + 23 * q^11 + 24 * q^12 + 23 * q^13 + 31 * q^14 + 9 * q^15 + 168 * q^16 + 98 * q^17 + 38 * q^18 + 29 * q^19 + 83 * q^20 + 26 * q^21 + 2 * q^22 + 34 * q^23 + 75 * q^24 + 177 * q^25 + 67 * q^26 + 32 * q^27 + 32 * q^28 + 91 * q^29 + 12 * q^30 + 24 * q^31 + 88 * q^32 + 27 * q^33 + 23 * q^34 + 66 * q^35 + 232 * q^36 - 133 * q^37 + 26 * q^38 + 28 * q^39 + 41 * q^40 + 132 * q^41 + 13 * q^42 + 11 * q^43 + 65 * q^44 + 107 * q^45 + 20 * q^46 + 10 * q^47 + 27 * q^48 + 229 * q^49 + 78 * q^50 + 19 * q^51 + 71 * q^52 + 7 * q^53 + 43 * q^54 + 41 * q^55 + 67 * q^56 + 45 * q^57 + 25 * q^58 + 97 * q^59 - 42 * q^60 + 65 * q^61 + 24 * q^62 + 39 * q^63 + 200 * q^64 + 60 * q^65 + 35 * q^66 + 25 * q^67 + 227 * q^68 + 120 * q^69 + 37 * q^70 + 26 * q^71 + 93 * q^72 + 55 * q^73 - 14 * q^74 + 5 * q^75 + 34 * q^76 + 21 * q^77 - 2 * q^78 + 50 * q^79 + 162 * q^80 + 341 * q^81 + 66 * q^82 + 30 * q^83 - 89 * q^84 + 30 * q^85 - 12 * q^86 + 80 * q^87 - 85 * q^88 + 225 * q^89 - 86 * q^90 + q^91 + 82 * q^92 + 42 * q^93 - 17 * q^94 + 70 * q^95 + 55 * q^96 + 12 * q^97 + 90 * q^98 + 17 * 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 $

$2$	−2.27645	−1.60969	−0.804846	−	0.593483i	$-0.797752\pi$
$2$	−2.27645	−1.60969	−0.804846	+	0.593483i	$0.797752\pi$
$3$	−1.27799	−0.737849	−0.368924	−	0.929459i	$-0.620274\pi$
$3$	−1.27799	−0.737849	−0.368924	+	0.929459i	$0.620274\pi$
$4$	3.18222	1.59111
$5$	2.39479	1.07098	0.535492	−	0.844540i	$-0.320126\pi$
$5$	2.39479	1.07098	0.535492	+	0.844540i	$0.320126\pi$
$6$	2.90928	1.18771
$7$	2.25162	0.851034	0.425517	−	0.904951i	$-0.360092\pi$
$7$	2.25162	0.851034	0.425517	+	0.904951i	$0.360092\pi$
$8$	−2.69127	−0.951508
$9$	−1.36674	−0.455579
$10$	−5.45162	−1.72395
$11$	−0.742995	−0.224021	−0.112011	−	0.993707i	$-0.535729\pi$
$11$	−0.742995	−0.224021	−0.112011	+	0.993707i	$0.535729\pi$
$12$	−4.06686	−1.17400
$13$	4.07276	1.12958	0.564791	−	0.825234i	$-0.308957\pi$
$13$	4.07276	1.12958	0.564791	+	0.825234i	$0.308957\pi$
$14$	−5.12571	−1.36990
$15$	−3.06052	−0.790224
$16$	−0.237904	−0.0594759
$17$	5.58079	1.35354	0.676770	−	0.736195i	$-0.263379\pi$
$17$	5.58079	1.35354	0.676770	+	0.736195i	$0.263379\pi$
$18$	3.11131	0.733342
$19$	4.21305	0.966540	0.483270	−	0.875471i	$-0.339449\pi$
$19$	4.21305	0.966540	0.483270	+	0.875471i	$0.339449\pi$
$20$	7.62076	1.70405
$21$	−2.87756	−0.627934
$22$	1.69139	0.360605
$23$	−1.08616	−0.226479	−0.113240	−	0.993568i	$-0.536123\pi$
$23$	−1.08616	−0.226479	−0.113240	+	0.993568i	$0.536123\pi$
$24$	3.43942	0.702069
$25$	0.735028	0.147006
$26$	−9.27144	−1.81828
$27$	5.58065	1.07400
$28$	7.16517	1.35409
$29$	6.12158	1.13675	0.568374	−	0.822770i	$-0.307573\pi$
$29$	6.12158	1.13675	0.568374	+	0.822770i	$0.307573\pi$
$30$	6.96713	1.27202
$31$	9.57044	1.71890	0.859451	−	0.511219i	$-0.170806\pi$
$31$	9.57044	1.71890	0.859451	+	0.511219i	$0.170806\pi$
$32$	5.92412	1.04725
$33$	0.949541	0.165294
$34$	−12.7044	−2.17878
$35$	5.39217	0.911443
$36$	−4.34926	−0.724877
$37$	−1.00000	−0.164399
$37$	−1.00000	−0.164399
$38$	−9.59079	−1.55583
$39$	−5.20496	−0.833461
$40$	−6.44503	−1.01905
$41$	0.942866	0.147251	0.0736255	−	0.997286i	$-0.476543\pi$
$41$	0.942866	0.147251	0.0736255	+	0.997286i	$0.476543\pi$
$42$	6.55061	1.01078
$43$	−7.10690	−1.08379	−0.541896	−	0.840445i	$-0.682293\pi$
$43$	−7.10690	−1.08379	−0.541896	+	0.840445i	$0.682293\pi$
$44$	−2.36437	−0.356443
$45$	−3.27305	−0.487917
$46$	2.47258	0.364562
$47$	−0.861900	−0.125721	−0.0628605	−	0.998022i	$-0.520022\pi$
$47$	−0.861900	−0.125721	−0.0628605	+	0.998022i	$0.520022\pi$
$48$	0.304039	0.0438842
$49$	−1.93019	−0.275742
$50$	−1.67325	−0.236634
$51$	−7.13220	−0.998708
$52$	12.9604	1.79729
$53$	7.39616	1.01594	0.507970	−	0.861375i	$-0.330396\pi$
$53$	7.39616	1.01594	0.507970	+	0.861375i	$0.330396\pi$
$54$	−12.7041	−1.72881
$55$	−1.77932	−0.239923
$56$	−6.05973	−0.809765
$57$	−5.38424	−0.713160
$58$	−13.9355	−1.82982
$59$	−9.57670	−1.24678	−0.623390	−	0.781911i	$-0.714245\pi$
$59$	−9.57670	−1.24678	−0.623390	+	0.781911i	$0.714245\pi$
$60$	−9.73927	−1.25733
$61$	−1.29175	−0.165391	−0.0826955	−	0.996575i	$-0.526353\pi$
$61$	−1.29175	−0.165391	−0.0826955	+	0.996575i	$0.526353\pi$
$62$	−21.7866	−2.76690
$63$	−3.07738	−0.387713
$64$	−13.0101	−1.62627
$65$	9.75342	1.20976
$66$	−2.16158	−0.266072
$67$	0.722309	0.0882441	0.0441221	−	0.999026i	$-0.485951\pi$
$67$	0.722309	0.0882441	0.0441221	+	0.999026i	$0.485951\pi$
$68$	17.7593	2.15363
$69$	1.38810	0.167108
$70$	−12.2750	−1.46714
$71$	8.08850	0.959929	0.479964	−	0.877288i	$-0.340650\pi$
$71$	8.08850	0.959929	0.479964	+	0.877288i	$0.340650\pi$
$72$	3.67826	0.433487
$73$	11.6006	1.35775	0.678873	−	0.734256i	$-0.262469\pi$
$73$	11.6006	1.35775	0.678873	+	0.734256i	$0.262469\pi$
$74$	2.27645	0.264632
$75$	−0.939359	−0.108468
$76$	13.4069	1.53787
$77$	−1.67294	−0.190650
$78$	11.8488	1.34162
$79$	0.619227	0.0696684	0.0348342	−	0.999393i	$-0.488910\pi$
$79$	0.619227	0.0696684	0.0348342	+	0.999393i	$0.488910\pi$
$80$	−0.569729	−0.0636977
$81$	−3.03182	−0.336869
$82$	−2.14639	−0.237029
$83$	12.7127	1.39540	0.697701	−	0.716389i	$-0.254206\pi$
$83$	12.7127	1.39540	0.697701	+	0.716389i	$0.254206\pi$
$84$	−9.15702	−0.999113
$85$	13.3648	1.44962
$86$	16.1785	1.74457
$87$	−7.82332	−0.838748
$88$	1.99960	0.213158
$89$	6.16638	0.653635	0.326817	−	0.945087i	$-0.394024\pi$
$89$	6.16638	0.653635	0.326817	+	0.945087i	$0.394024\pi$
$90$	7.45093	0.785397
$91$	9.17033	0.961312
$92$	−3.45639	−0.360354
$93$	−12.2309	−1.26829
$94$	1.96207	0.202372
$95$	10.0894	1.03515
$96$	−7.57097	−0.772709
$97$	6.18807	0.628303	0.314152	−	0.949373i	$-0.398280\pi$
$97$	6.18807	0.628303	0.314152	+	0.949373i	$0.398280\pi$
$98$	4.39399	0.443860
$99$	1.01548	0.102059
$100$	2.33902	0.233902
$101$	3.08328	0.306798	0.153399	−	0.988164i	$-0.450978\pi$
$101$	3.08328	0.306798	0.153399	+	0.988164i	$0.450978\pi$
$102$	16.2361	1.60761
$103$	6.36182	0.626849	0.313425	−	0.949613i	$-0.398524\pi$
$103$	6.36182	0.626849	0.313425	+	0.949613i	$0.398524\pi$
$104$	−10.9609	−1.07481
$105$	−6.89115	−0.672507
$106$	−16.8370	−1.63535
$107$	7.64633	0.739199	0.369599	−	0.929191i	$-0.379495\pi$
$107$	7.64633	0.739199	0.369599	+	0.929191i	$0.379495\pi$
$108$	17.7589	1.70885
$109$	−19.0875	−1.82825	−0.914124	−	0.405436i	$-0.867120\pi$
$109$	−19.0875	−1.82825	−0.914124	+	0.405436i	$0.867120\pi$
$110$	4.05053	0.386202
$111$	1.27799	0.121302
$112$	−0.535669	−0.0506160
$113$	11.7352	1.10396	0.551978	−	0.833858i	$-0.313873\pi$
$113$	11.7352	1.10396	0.551978	+	0.833858i	$0.313873\pi$
$114$	12.2570	1.14797
$115$	−2.60112	−0.242556
$116$	19.4802	1.80869
$117$	−5.56640	−0.514614
$118$	21.8009	2.00693
$119$	12.5658	1.15191
$120$	8.23670	0.751904
$121$	−10.4480	−0.949814
$122$	2.94059	0.266229
$123$	−1.20498	−0.108649
$124$	30.4553	2.73496
$125$	−10.2137	−0.913543
$126$	7.00549	0.624099
$127$	−9.25105	−0.820898	−0.410449	−	0.911883i	$-0.634628\pi$
$127$	−9.25105	−0.820898	−0.410449	+	0.911883i	$0.634628\pi$
$128$	17.7687	1.57055
$129$	9.08257	0.799675
$130$	−22.2032	−1.94735
$131$	5.64110	0.492865	0.246433	−	0.969160i	$-0.420742\pi$
$131$	5.64110	0.492865	0.246433	+	0.969160i	$0.420742\pi$
$132$	3.02165	0.263001
$133$	9.48620	0.822558
$134$	−1.64430	−0.142046
$135$	13.3645	1.15023
$136$	−15.0194	−1.28790
$137$	−18.2616	−1.56019	−0.780097	−	0.625658i	$-0.784830\pi$
$137$	−18.2616	−1.56019	−0.780097	+	0.625658i	$0.784830\pi$
$138$	−3.15994	−0.268992
$139$	−13.2812	−1.12649	−0.563247	−	0.826288i	$-0.690448\pi$
$139$	−13.2812	−1.12649	−0.563247	+	0.826288i	$0.690448\pi$
$140$	17.1591	1.45021
$141$	1.10150	0.0927632
$142$	−18.4131	−1.54519
$143$	−3.02604	−0.253050
$144$	0.325151	0.0270960
$145$	14.6599	1.21744
$146$	−26.4081	−2.18555
$147$	2.46677	0.203456
$148$	−3.18222	−0.261577
$149$	17.4652	1.43080	0.715401	−	0.698714i	$-0.246244\pi$
$149$	17.4652	1.43080	0.715401	+	0.698714i	$0.246244\pi$
$150$	2.13840	0.174600
$151$	−3.71209	−0.302086	−0.151043	−	0.988527i	$-0.548263\pi$
$151$	−3.71209	−0.302086	−0.151043	+	0.988527i	$0.548263\pi$
$152$	−11.3385	−0.919670
$153$	−7.62747	−0.616644
$154$	3.80837	0.306887
$155$	22.9192	1.84091
$156$	−16.5633	−1.32613
$157$	8.55721	0.682940	0.341470	−	0.939893i	$-0.389075\pi$
$157$	8.55721	0.682940	0.341470	+	0.939893i	$0.389075\pi$
$158$	−1.40964	−0.112145
$159$	−9.45223	−0.749610
$160$	14.1870	1.12158
$161$	−2.44562	−0.192742
$162$	6.90179	0.542256
$163$	1.00000	0.0783260
$163$	1.00000	0.0783260
$164$	3.00041	0.234293
$165$	2.27395	0.177027
$166$	−28.9399	−2.24617
$167$	−12.0363	−0.931400	−0.465700	−	0.884943i	$-0.654197\pi$
$167$	−12.0363	−0.931400	−0.465700	+	0.884943i	$0.654197\pi$
$168$	7.74428	0.597484
$169$	3.58741	0.275954
$170$	−30.4243	−2.33344
$171$	−5.75813	−0.440335
$172$	−22.6158	−1.72443
$173$	11.5538	0.878420	0.439210	−	0.898385i	$-0.355258\pi$
$173$	11.5538	0.878420	0.439210	+	0.898385i	$0.355258\pi$
$174$	17.8094	1.35013
$175$	1.65500	0.125107
$176$	0.176761	0.0133239
$177$	12.2389	0.919936
$178$	−14.0375	−1.05215
$179$	−23.2724	−1.73946	−0.869730	−	0.493528i	$-0.835707\pi$
$179$	−23.2724	−1.73946	−0.869730	+	0.493528i	$0.835707\pi$
$180$	−10.4156	−0.776331
$181$	12.6094	0.937250	0.468625	−	0.883397i	$-0.344750\pi$
$181$	12.6094	0.937250	0.468625	+	0.883397i	$0.344750\pi$
$182$	−20.8758	−1.54742
$183$	1.65084	0.122034
$184$	2.92314	0.215497
$185$	−2.39479	−0.176069
$186$	27.8431	2.04156
$187$	−4.14649	−0.303222
$188$	−2.74276	−0.200036
$189$	12.5655	0.914008
$190$	−22.9680	−1.66627
$191$	−13.6777	−0.989681	−0.494841	−	0.868984i	$-0.664774\pi$
$191$	−13.6777	−0.989681	−0.494841	+	0.868984i	$0.664774\pi$
$192$	16.6269	1.19994
$193$	−19.4362	−1.39904	−0.699522	−	0.714611i	$-0.746604\pi$
$193$	−19.4362	−1.39904	−0.699522	+	0.714611i	$0.746604\pi$
$194$	−14.0868	−1.01138
$195$	−12.4648	−0.892622
$196$	−6.14231	−0.438736
$197$	−1.23288	−0.0878393	−0.0439197	−	0.999035i	$-0.513985\pi$
$197$	−1.23288	−0.0878393	−0.0439197	+	0.999035i	$0.513985\pi$
$198$	−2.31168	−0.164284
$199$	8.77764	0.622230	0.311115	−	0.950372i	$-0.399297\pi$
$199$	8.77764	0.622230	0.311115	+	0.950372i	$0.399297\pi$
$200$	−1.97816	−0.139877
$201$	−0.923106	−0.0651108
$202$	−7.01893	−0.493850
$203$	13.7835	0.967411
$204$	−22.6963	−1.58906
$205$	2.25797	0.157703
$206$	−14.4824	−1.00903
$207$	1.48449	0.103179
$208$	−0.968925	−0.0671829
$209$	−3.13027	−0.216525
$210$	15.6873	1.08253
$211$	0.871819	0.0600185	0.0300093	−	0.999550i	$-0.490446\pi$
$211$	0.871819	0.0600185	0.0300093	+	0.999550i	$0.490446\pi$
$212$	23.5362	1.61647
$213$	−10.3370	−0.708282
$214$	−17.4065	−1.18988
$215$	−17.0196	−1.16072
$216$	−15.0191	−1.02192
$217$	21.5490	1.46284
$218$	43.4516	2.94292
$219$	−14.8255	−1.00181
$220$	−5.66218	−0.381744
$221$	22.7292	1.52893
$222$	−2.90928	−0.195258
$223$	1.06390	0.0712437	0.0356218	−	0.999365i	$-0.488659\pi$
$223$	1.06390	0.0712437	0.0356218	+	0.999365i	$0.488659\pi$
$224$	13.3389	0.891241
$225$	−1.00459	−0.0669726
$226$	−26.7146	−1.77703
$227$	−17.1079	−1.13549	−0.567747	−	0.823203i	$-0.692185\pi$
$227$	−17.1079	−1.13549	−0.567747	+	0.823203i	$0.692185\pi$
$228$	−17.1339	−1.13472
$229$	9.39892	0.621098	0.310549	−	0.950557i	$-0.399487\pi$
$229$	9.39892	0.621098	0.310549	+	0.950557i	$0.399487\pi$
$230$	5.92132	0.390440
$231$	2.13801	0.140671
$232$	−16.4748	−1.08162
$233$	6.76753	0.443356	0.221678	−	0.975120i	$-0.428847\pi$
$233$	6.76753	0.443356	0.221678	+	0.975120i	$0.428847\pi$
$234$	12.6716	0.828370
$235$	−2.06407	−0.134645
$236$	−30.4752	−1.98377
$237$	−0.791367	−0.0514048
$238$	−28.6055	−1.85422
$239$	25.1380	1.62604	0.813022	−	0.582233i	$-0.197821\pi$
$239$	25.1380	1.62604	0.813022	+	0.582233i	$0.197821\pi$
$240$	0.728110	0.0469993
$241$	3.11751	0.200816	0.100408	−	0.994946i	$-0.467985\pi$
$241$	3.11751	0.200816	0.100408	+	0.994946i	$0.467985\pi$
$242$	23.7843	1.52891
$243$	−12.8673	−0.825439
$244$	−4.11062	−0.263156
$245$	−4.62241	−0.295315
$246$	2.74307	0.174891
$247$	17.1588	1.09179
$248$	−25.7566	−1.63555
$249$	−16.2468	−1.02960
$250$	23.2510	1.47052
$251$	−7.07702	−0.446698	−0.223349	−	0.974739i	$-0.571699\pi$
$251$	−7.07702	−0.446698	−0.223349	+	0.974739i	$0.571699\pi$
$252$	−9.79290	−0.616894
$253$	0.807009	0.0507362
$254$	21.0596	1.32139
$255$	−17.0801	−1.06960
$256$	−14.4293	−0.901830
$257$	9.72696	0.606751	0.303376	−	0.952871i	$-0.401886\pi$
$257$	9.72696	0.606751	0.303376	+	0.952871i	$0.401886\pi$
$258$	−20.6760	−1.28723
$259$	−2.25162	−0.139909
$260$	31.0376	1.92487
$261$	−8.36658	−0.517878
$262$	−12.8417	−0.793362
$263$	−22.9610	−1.41583	−0.707917	−	0.706295i	$-0.750365\pi$
$263$	−22.9610	−1.41583	−0.707917	+	0.706295i	$0.750365\pi$
$264$	−2.55547	−0.157278
$265$	17.7123	1.08805
$266$	−21.5949	−1.32407
$267$	−7.88058	−0.482284
$268$	2.29855	0.140406
$269$	−4.45323	−0.271518	−0.135759	−	0.990742i	$-0.543347\pi$
$269$	−4.45323	−0.271518	−0.135759	+	0.990742i	$0.543347\pi$
$270$	−30.4236	−1.85152
$271$	−8.19695	−0.497929	−0.248965	−	0.968513i	$-0.580090\pi$
$271$	−8.19695	−0.497929	−0.248965	+	0.968513i	$0.580090\pi$
$272$	−1.32769	−0.0805030
$273$	−11.7196	−0.709303
$274$	41.5716	2.51143
$275$	−0.546121	−0.0329324
$276$	4.41724	0.265887
$277$	−4.11746	−0.247394	−0.123697	−	0.992320i	$-0.539475\pi$
$277$	−4.11746	−0.247394	−0.123697	+	0.992320i	$0.539475\pi$
$278$	30.2339	1.81331
$279$	−13.0803	−0.783095
$280$	−14.5118	−0.867245
$281$	−6.77475	−0.404148	−0.202074	−	0.979370i	$-0.564768\pi$
$281$	−6.77475	−0.404148	−0.202074	+	0.979370i	$0.564768\pi$
$282$	−2.50751	−0.149320
$283$	−25.5890	−1.52111	−0.760553	−	0.649276i	$-0.775072\pi$
$283$	−25.5890	−1.52111	−0.760553	+	0.649276i	$0.775072\pi$
$284$	25.7394	1.52735
$285$	−12.8941	−0.763783
$286$	6.88863	0.407333
$287$	2.12298	0.125315
$288$	−8.09671	−0.477103
$289$	14.1452	0.832070
$290$	−33.3725	−1.95970
$291$	−7.90830	−0.463593
$292$	36.9156	2.16032
$293$	−23.6487	−1.38157	−0.690787	−	0.723058i	$-0.742736\pi$
$293$	−23.6487	−1.38157	−0.690787	+	0.723058i	$0.742736\pi$
$294$	−5.61548	−0.327502
$295$	−22.9342	−1.33528
$296$	2.69127	0.156427
$297$	−4.14640	−0.240598
$298$	−39.7586	−2.30315
$299$	−4.42366	−0.255827
$300$	−2.98925	−0.172584
$301$	−16.0021	−0.922344
$302$	8.45039	0.486266
$303$	−3.94041	−0.226370
$304$	−1.00230	−0.0574858
$305$	−3.09346	−0.177131
$306$	17.3635	0.992608
$307$	14.3748	0.820411	0.410206	−	0.911993i	$-0.365457\pi$
$307$	14.3748	0.820411	0.410206	+	0.911993i	$0.365457\pi$
$308$	−5.32368	−0.303345
$309$	−8.13036	−0.462520
$310$	−52.1744	−2.96331
$311$	−15.2425	−0.864323	−0.432161	−	0.901796i	$-0.642249\pi$
$311$	−15.2425	−0.864323	−0.432161	+	0.901796i	$0.642249\pi$
$312$	14.0080	0.793044
$313$	−2.30922	−0.130525	−0.0652625	−	0.997868i	$-0.520788\pi$
$313$	−2.30922	−0.130525	−0.0652625	+	0.997868i	$0.520788\pi$
$314$	−19.4801	−1.09932
$315$	−7.36967	−0.415234
$316$	1.97052	0.110850
$317$	8.48861	0.476768	0.238384	−	0.971171i	$-0.423382\pi$
$317$	8.48861	0.476768	0.238384	+	0.971171i	$0.423382\pi$
$318$	21.5175	1.20664
$319$	−4.54830	−0.254656
$320$	−31.1566	−1.74171
$321$	−9.77195	−0.545417
$322$	5.56732	0.310255
$323$	23.5121	1.30825
$324$	−9.64793	−0.535996
$325$	2.99359	0.166055
$326$	−2.27645	−0.126081
$327$	24.3936	1.34897
$328$	−2.53751	−0.140110
$329$	−1.94067	−0.106993
$330$	−5.17654	−0.284959
$331$	−14.5706	−0.800874	−0.400437	−	0.916324i	$-0.631142\pi$
$331$	−14.5706	−0.800874	−0.400437	+	0.916324i	$0.631142\pi$
$332$	40.4547	2.22024
$333$	1.36674	0.0748967
$334$	27.4001	1.49927
$335$	1.72978	0.0945080
$336$	0.684581	0.0373469
$337$	−4.69438	−0.255719	−0.127860	−	0.991792i	$-0.540811\pi$
$337$	−4.69438	−0.255719	−0.127860	+	0.991792i	$0.540811\pi$
$338$	−8.16655	−0.444202
$339$	−14.9975	−0.814553
$340$	42.5298	2.30650
$341$	−7.11078	−0.385070
$342$	13.1081	0.708804
$343$	−20.1074	−1.08570
$344$	19.1266	1.03124
$345$	3.32421	0.178970
$346$	−26.3017	−1.41399
$347$	−18.2019	−0.977128	−0.488564	−	0.872528i	$-0.662479\pi$
$347$	−18.2019	−0.977128	−0.488564	+	0.872528i	$0.662479\pi$
$348$	−24.8956	−1.33454
$349$	9.73936	0.521336	0.260668	−	0.965429i	$-0.416057\pi$
$349$	9.73936	0.521336	0.260668	+	0.965429i	$0.416057\pi$
$350$	−3.76754	−0.201383
$351$	22.7287	1.21317
$352$	−4.40159	−0.234605
$353$	−6.15793	−0.327753	−0.163877	−	0.986481i	$-0.552400\pi$
$353$	−6.15793	−0.327753	−0.163877	+	0.986481i	$0.552400\pi$
$354$	−27.8614	−1.48081
$355$	19.3703	1.02807
$356$	19.6228	1.04001
$357$	−16.0590	−0.849934
$358$	52.9784	2.80000
$359$	7.57796	0.399949	0.199975	−	0.979801i	$-0.435914\pi$
$359$	7.57796	0.399949	0.199975	+	0.979801i	$0.435914\pi$
$360$	8.80866	0.464257
$361$	−1.25022	−0.0658009
$362$	−28.7047	−1.50868
$363$	13.3524	0.700820
$364$	29.1820	1.52955
$365$	27.7810	1.45412
$366$	−3.75805	−0.196437
$367$	−0.246034	−0.0128429	−0.00642144	−	0.999979i	$-0.502044\pi$
$367$	−0.246034	−0.0128429	−0.00642144	+	0.999979i	$0.502044\pi$
$368$	0.258401	0.0134701
$369$	−1.28865	−0.0670844
$370$	5.45162	0.283416
$371$	16.6534	0.864599
$372$	−38.9216	−2.01799
$373$	−29.1186	−1.50770	−0.753852	−	0.657045i	$-0.771806\pi$
$373$	−29.1186	−1.50770	−0.753852	+	0.657045i	$0.771806\pi$
$374$	9.43928	0.488094
$375$	13.0531	0.674057
$376$	2.31961	0.119625
$377$	24.9317	1.28405
$378$	−28.6048	−1.47127
$379$	29.7325	1.52726	0.763629	−	0.645655i	$-0.223416\pi$
$379$	29.7325	1.52726	0.763629	+	0.645655i	$0.223416\pi$
$380$	32.1066	1.64704
$381$	11.8228	0.605699
$382$	31.1365	1.59308
$383$	18.7324	0.957179	0.478589	−	0.878039i	$-0.341148\pi$
$383$	18.7324	0.957179	0.478589	+	0.878039i	$0.341148\pi$
$384$	−22.7083	−1.15883
$385$	−4.00635	−0.204183
$386$	44.2454	2.25203
$387$	9.71327	0.493753
$388$	19.6918	0.999700
$389$	18.1187	0.918655	0.459327	−	0.888267i	$-0.348090\pi$
$389$	18.1187	0.918655	0.459327	+	0.888267i	$0.348090\pi$
$390$	28.3755	1.43685
$391$	−6.06161	−0.306549
$392$	5.19467	0.262371
$393$	−7.20928	−0.363660
$394$	2.80660	0.141394
$395$	1.48292	0.0746137
$396$	3.23148	0.162388
$397$	−33.4415	−1.67838	−0.839191	−	0.543837i	$-0.816971\pi$
$397$	−33.4415	−1.67838	−0.839191	+	0.543837i	$0.816971\pi$
$398$	−19.9819	−1.00160
$399$	−12.1233	−0.606923
$400$	−0.174866	−0.00874328
$401$	21.7998	1.08863	0.544316	−	0.838880i	$-0.316789\pi$
$401$	21.7998	1.08863	0.544316	+	0.838880i	$0.316789\pi$
$402$	2.10140	0.104808
$403$	38.9781	1.94164
$404$	9.81168	0.488149
$405$	−7.26058	−0.360781
$406$	−31.3774	−1.55723
$407$	0.742995	0.0368289
$408$	19.1947	0.950278
$409$	−7.20410	−0.356220	−0.178110	−	0.984011i	$-0.556998\pi$
$409$	−7.20410	−0.356220	−0.178110	+	0.984011i	$0.556998\pi$
$410$	−5.14015	−0.253854
$411$	23.3382	1.15119
$412$	20.2447	0.997387
$413$	−21.5631	−1.06105
$414$	−3.37937	−0.166087
$415$	30.4443	1.49445
$416$	24.1275	1.18295
$417$	16.9732	0.831183
$418$	7.12591	0.348540
$419$	13.6621	0.667437	0.333719	−	0.942673i	$-0.391696\pi$
$419$	13.6621	0.667437	0.333719	+	0.942673i	$0.391696\pi$
$420$	−21.9292	−1.07003
$421$	−9.91380	−0.483169	−0.241584	−	0.970380i	$-0.577667\pi$
$421$	−9.91380	−0.483169	−0.241584	+	0.970380i	$0.577667\pi$
$422$	−1.98465	−0.0966114
$423$	1.17799	0.0572759
$424$	−19.9051	−0.966675
$425$	4.10203	0.198978
$426$	23.5318	1.14012
$427$	−2.90852	−0.140753
$428$	24.3323	1.17615
$429$	3.86726	0.186713
$430$	38.7442	1.86841
$431$	−29.7661	−1.43378	−0.716892	−	0.697184i	$-0.754436\pi$
$431$	−29.7661	−1.43378	−0.716892	+	0.697184i	$0.754436\pi$
$432$	−1.32766	−0.0638769
$433$	−28.4134	−1.36546	−0.682731	−	0.730670i	$-0.739208\pi$
$433$	−28.4134	−1.36546	−0.682731	+	0.730670i	$0.739208\pi$
$434$	−49.0552	−2.35473
$435$	−18.7352	−0.898286
$436$	−60.7406	−2.90894
$437$	−4.57603	−0.218901
$438$	33.7494	1.61261
$439$	−6.59442	−0.314734	−0.157367	−	0.987540i	$-0.550301\pi$
$439$	−6.59442	−0.314734	−0.157367	+	0.987540i	$0.550301\pi$
$440$	4.78862	0.228289
$441$	2.63807	0.125622
$442$	−51.7419	−2.46111
$443$	3.07508	0.146101	0.0730506	−	0.997328i	$-0.476727\pi$
$443$	3.07508	0.146101	0.0730506	+	0.997328i	$0.476727\pi$
$444$	4.06686	0.193004
$445$	14.7672	0.700032
$446$	−2.42190	−0.114680
$447$	−22.3203	−1.05572
$448$	−29.2939	−1.38401
$449$	10.5521	0.497983	0.248991	−	0.968506i	$-0.419901\pi$
$449$	10.5521	0.497983	0.248991	+	0.968506i	$0.419901\pi$
$450$	2.28690	0.107805
$451$	−0.700544	−0.0329873
$452$	37.3441	1.75652
$453$	4.74403	0.222894
$454$	38.9454	1.82780
$455$	21.9610	1.02955
$456$	14.4905	0.678578
$457$	14.6625	0.685881	0.342941	−	0.939357i	$-0.388577\pi$
$457$	14.6625	0.685881	0.342941	+	0.939357i	$0.388577\pi$
$458$	−21.3962	−0.999778
$459$	31.1444	1.45370
$460$	−8.27735	−0.385933
$461$	6.20780	0.289126	0.144563	−	0.989496i	$-0.453822\pi$
$461$	6.20780	0.289126	0.144563	+	0.989496i	$0.453822\pi$
$462$	−4.86707	−0.226437
$463$	3.33835	0.155146	0.0775732	−	0.996987i	$-0.475283\pi$
$463$	3.33835	0.155146	0.0775732	+	0.996987i	$0.475283\pi$
$464$	−1.45634	−0.0676091
$465$	−29.2906	−1.35832
$466$	−15.4059	−0.713667
$467$	−7.47243	−0.345783	−0.172891	−	0.984941i	$-0.555311\pi$
$467$	−7.47243	−0.345783	−0.172891	+	0.984941i	$0.555311\pi$
$468$	−17.7135	−0.818807
$469$	1.62637	0.0750987
$470$	4.69876	0.216737
$471$	−10.9361	−0.503907
$472$	25.7735	1.18632
$473$	5.28039	0.242793
$474$	1.80151	0.0827459
$475$	3.09671	0.142087
$476$	39.9873	1.83281
$477$	−10.1086	−0.462841
$478$	−57.2255	−2.61743
$479$	32.2817	1.47499	0.737495	−	0.675353i	$-0.236009\pi$
$479$	32.2817	1.47499	0.737495	+	0.675353i	$0.236009\pi$
$480$	−18.1309	−0.827559
$481$	−4.07276	−0.185702
$482$	−7.09685	−0.323253
$483$	3.12548	0.142214
$484$	−33.2477	−1.51126
$485$	14.8191	0.672902
$486$	29.2918	1.32870
$487$	−31.8841	−1.44481	−0.722403	−	0.691472i	$-0.756963\pi$
$487$	−31.8841	−1.44481	−0.722403	+	0.691472i	$0.756963\pi$
$488$	3.47644	0.157371
$489$	−1.27799	−0.0577928
$490$	10.5227	0.475367
$491$	2.95825	0.133504	0.0667520	−	0.997770i	$-0.478736\pi$
$491$	2.95825	0.133504	0.0667520	+	0.997770i	$0.478736\pi$
$492$	−3.83450	−0.172873
$493$	34.1632	1.53863
$494$	−39.0610	−1.75744
$495$	2.43186	0.109304
$496$	−2.27684	−0.102233
$497$	18.2123	0.816931
$498$	36.9849	1.65733
$499$	20.1392	0.901555	0.450778	−	0.892636i	$-0.351147\pi$
$499$	20.1392	0.901555	0.450778	+	0.892636i	$0.351147\pi$
$500$	−32.5023	−1.45355
$501$	15.3823	0.687233
$502$	16.1105	0.719046
$503$	19.9322	0.888734	0.444367	−	0.895845i	$-0.353429\pi$
$503$	19.9322	0.888734	0.444367	+	0.895845i	$0.353429\pi$
$504$	8.28205	0.368912
$505$	7.38381	0.328575
$506$	−1.83712	−0.0816697
$507$	−4.58468	−0.203613
$508$	−29.4389	−1.30614
$509$	32.3142	1.43230	0.716152	−	0.697945i	$-0.245902\pi$
$509$	32.3142	1.43230	0.716152	+	0.697945i	$0.245902\pi$
$510$	38.8821	1.72173
$511$	26.1201	1.15549
$512$	−2.68989	−0.118878
$513$	23.5116	1.03806
$514$	−22.1429	−0.976683
$515$	15.2352	0.671345
$516$	28.9027	1.27237
$517$	0.640387	0.0281642
$518$	5.12571	0.225211
$519$	−14.7657	−0.648141
$520$	−26.2491	−1.15110
$521$	35.5345	1.55679	0.778397	−	0.627772i	$-0.216033\pi$
$521$	35.5345	1.55679	0.778397	+	0.627772i	$0.216033\pi$
$522$	19.0461	0.833625
$523$	−39.3205	−1.71936	−0.859682	−	0.510830i	$-0.829338\pi$
$523$	−39.3205	−1.71936	−0.859682	+	0.510830i	$0.829338\pi$
$524$	17.9512	0.784204
$525$	−2.11508	−0.0923098
$526$	52.2695	2.27906
$527$	53.4106	2.32660
$528$	−0.225899	−0.00983100
$529$	−21.8203	−0.948707
$530$	−40.3210	−1.75143
$531$	13.0888	0.568007
$532$	30.1872	1.30878
$533$	3.84007	0.166332
$534$	17.9397	0.776329
$535$	18.3114	0.791670
$536$	−1.94393	−0.0839650
$537$	29.7419	1.28346
$538$	10.1376	0.437061
$539$	1.43412	0.0617721
$540$	42.5288	1.83015
$541$	3.21387	0.138175	0.0690876	−	0.997611i	$-0.477991\pi$
$541$	3.21387	0.138175	0.0690876	+	0.997611i	$0.477991\pi$
$542$	18.6599	0.801513
$543$	−16.1147	−0.691549
$544$	33.0612	1.41749
$545$	−45.7105	−1.95802
$546$	26.6791	1.14176
$547$	−25.0108	−1.06939	−0.534693	−	0.845047i	$-0.679573\pi$
$547$	−25.0108	−1.06939	−0.534693	+	0.845047i	$0.679573\pi$
$548$	−58.1125	−2.48244
$549$	1.76548	0.0753487
$550$	1.24322	0.0530110
$551$	25.7905	1.09871
$552$	−3.73575	−0.159004
$553$	1.39427	0.0592902
$554$	9.37319	0.398228
$555$	3.06052	0.129912
$556$	−42.2637	−1.79238
$557$	4.07119	0.172502	0.0862509	−	0.996273i	$-0.472511\pi$
$557$	4.07119	0.172502	0.0862509	+	0.996273i	$0.472511\pi$
$558$	29.7766	1.26054
$559$	−28.9447	−1.22423
$560$	−1.28282	−0.0542089
$561$	5.29919	0.223732
$562$	15.4224	0.650554
$563$	15.3604	0.647363	0.323682	−	0.946166i	$-0.395079\pi$
$563$	15.3604	0.647363	0.323682	+	0.946166i	$0.395079\pi$
$564$	3.50522	0.147597
$565$	28.1034	1.18232
$566$	58.2520	2.44851
$567$	−6.82652	−0.286687
$568$	−21.7683	−0.913380
$569$	7.41186	0.310721	0.155361	−	0.987858i	$-0.450346\pi$
$569$	7.41186	0.310721	0.155361	+	0.987858i	$0.450346\pi$
$570$	29.3529	1.22946
$571$	−17.4951	−0.732146	−0.366073	−	0.930586i	$-0.619298\pi$
$571$	−17.4951	−0.732146	−0.366073	+	0.930586i	$0.619298\pi$
$572$	−9.62954	−0.402631
$573$	17.4799	0.730235
$574$	−4.83285	−0.201719
$575$	−0.798356	−0.0332937
$576$	17.7814	0.740894
$577$	20.5647	0.856120	0.428060	−	0.903750i	$-0.359197\pi$
$577$	20.5647	0.856120	0.428060	+	0.903750i	$0.359197\pi$
$578$	−32.2008	−1.33938
$579$	24.8392	1.03228
$580$	46.6511	1.93708
$581$	28.6243	1.18753
$582$	18.0029	0.746242
$583$	−5.49530	−0.227592
$584$	−31.2203	−1.29191
$585$	−13.3304	−0.551143
$586$	53.8352	2.22391
$587$	−24.2965	−1.00282	−0.501412	−	0.865208i	$-0.667186\pi$
$587$	−24.2965	−1.00282	−0.501412	+	0.865208i	$0.667186\pi$
$588$	7.84982	0.323721
$589$	40.3207	1.66139
$590$	52.2086	2.14939
$591$	1.57561	0.0648121
$592$	0.237904	0.00977778
$593$	21.8620	0.897765	0.448882	−	0.893591i	$-0.351822\pi$
$593$	21.8620	0.897765	0.448882	+	0.893591i	$0.351822\pi$
$594$	9.43906	0.387289
$595$	30.0925	1.23367
$596$	55.5781	2.27657
$597$	−11.2178	−0.459112
$598$	10.0702	0.411803
$599$	−13.6893	−0.559328	−0.279664	−	0.960098i	$-0.590223\pi$
$599$	−13.6893	−0.559328	−0.279664	+	0.960098i	$0.590223\pi$
$600$	2.52807	0.103208
$601$	24.3933	0.995025	0.497513	−	0.867457i	$-0.334247\pi$
$601$	24.3933	0.995025	0.497513	+	0.867457i	$0.334247\pi$
$602$	36.4279	1.48469
$603$	−0.987207	−0.0402022
$604$	−11.8127	−0.480652
$605$	−25.0207	−1.01724
$606$	8.97014	0.364387
$607$	−22.2913	−0.904774	−0.452387	−	0.891822i	$-0.649427\pi$
$607$	−22.2913	−0.904774	−0.452387	+	0.891822i	$0.649427\pi$
$608$	24.9586	1.01220
$609$	−17.6152	−0.713803
$610$	7.04211	0.285127
$611$	−3.51032	−0.142012
$612$	−24.2723	−0.981149
$613$	5.48029	0.221347	0.110673	−	0.993857i	$-0.464699\pi$
$613$	5.48029	0.221347	0.110673	+	0.993857i	$0.464699\pi$
$614$	−32.7234	−1.32061
$615$	−2.88566	−0.116361
$616$	4.50234	0.181405
$617$	−5.82930	−0.234679	−0.117339	−	0.993092i	$-0.537437\pi$
$617$	−5.82930	−0.234679	−0.117339	+	0.993092i	$0.537437\pi$
$618$	18.5084	0.744515
$619$	11.4760	0.461261	0.230631	−	0.973041i	$-0.425921\pi$
$619$	11.4760	0.461261	0.230631	+	0.973041i	$0.425921\pi$
$620$	72.9340	2.92910
$621$	−6.06147	−0.243238
$622$	34.6988	1.39129
$623$	13.8844	0.556265
$624$	1.23828	0.0495708
$625$	−28.1349	−1.12539
$626$	5.25683	0.210105
$627$	4.00046	0.159763
$628$	27.2310	1.08663
$629$	−5.58079	−0.222521
$630$	16.7767	0.668399
$631$	26.6257	1.05995	0.529976	−	0.848012i	$-0.322201\pi$
$631$	26.6257	1.05995	0.529976	+	0.848012i	$0.322201\pi$
$632$	−1.66651	−0.0662901
$633$	−1.11418	−0.0442846
$634$	−19.3239	−0.767450
$635$	−22.1543	−0.879168
$636$	−30.0791	−1.19271
$637$	−7.86122	−0.311473
$638$	10.3540	0.409918
$639$	−11.0549	−0.437323
$640$	42.5524	1.68203
$641$	41.7856	1.65043	0.825216	−	0.564818i	$-0.191054\pi$
$641$	41.7856	1.65043	0.825216	+	0.564818i	$0.191054\pi$
$642$	22.2454	0.877954
$643$	13.2733	0.523448	0.261724	−	0.965143i	$-0.415709\pi$
$643$	13.2733	0.523448	0.261724	+	0.965143i	$0.415709\pi$
$644$	−7.78250	−0.306673
$645$	21.7509	0.856439
$646$	−53.5242	−2.10588
$647$	16.9514	0.666427	0.333213	−	0.942851i	$-0.391867\pi$
$647$	16.9514	0.666427	0.333213	+	0.942851i	$0.391867\pi$
$648$	8.15945	0.320533
$649$	7.11544	0.279305
$650$	−6.81477	−0.267297
$651$	−27.5395	−1.07936
$652$	3.18222	0.124625
$653$	7.99903	0.313026	0.156513	−	0.987676i	$-0.449975\pi$
$653$	7.99903	0.313026	0.156513	+	0.987676i	$0.449975\pi$
$654$	−55.5308	−2.17143
$655$	13.5093	0.527851
$656$	−0.224311	−0.00875788
$657$	−15.8549	−0.618560
$658$	4.41785	0.172226
$659$	24.3353	0.947970	0.473985	−	0.880533i	$-0.342815\pi$
$659$	24.3353	0.947970	0.473985	+	0.880533i	$0.342815\pi$
$660$	7.23622	0.281670
$661$	31.4947	1.22500	0.612500	−	0.790470i	$-0.290164\pi$
$661$	31.4947	1.22500	0.612500	+	0.790470i	$0.290164\pi$
$662$	33.1693	1.28916
$663$	−29.0478	−1.12812
$664$	−34.2134	−1.32774
$665$	22.7175	0.880946
$666$	−3.11131	−0.120561
$667$	−6.64899	−0.257450
$668$	−38.3023	−1.48196
$669$	−1.35965	−0.0525671
$670$	−3.93776	−0.152129
$671$	0.959760	0.0370511
$672$	−17.0470	−0.657601
$673$	22.4484	0.865324	0.432662	−	0.901556i	$-0.357574\pi$
$673$	22.4484	0.865324	0.432662	+	0.901556i	$0.357574\pi$
$674$	10.6865	0.411630
$675$	4.10193	0.157884
$676$	11.4159	0.439074
$677$	−30.4065	−1.16862	−0.584308	−	0.811532i	$-0.698634\pi$
$677$	−30.4065	−1.16862	−0.584308	+	0.811532i	$0.698634\pi$
$678$	34.1411	1.31118
$679$	13.9332	0.534707
$680$	−35.9684	−1.37932
$681$	21.8638	0.837823
$682$	16.1873	0.619845
$683$	25.2873	0.967593	0.483796	−	0.875181i	$-0.339258\pi$
$683$	25.2873	0.967593	0.483796	+	0.875181i	$0.339258\pi$
$684$	−18.3236	−0.700622
$685$	−43.7327	−1.67094
$686$	45.7736	1.74764
$687$	−12.0117	−0.458277
$688$	1.69076	0.0644595
$689$	30.1228	1.14759
$690$	−7.56740	−0.288086
$691$	−3.80279	−0.144665	−0.0723324	−	0.997381i	$-0.523044\pi$
$691$	−3.80279	−0.144665	−0.0723324	+	0.997381i	$0.523044\pi$
$692$	36.7668	1.39766
$693$	2.28647	0.0868559
$694$	41.4357	1.57288
$695$	−31.8057	−1.20646
$696$	21.0547	0.798076
$697$	5.26194	0.199310
$698$	−22.1712	−0.839191
$699$	−8.64885	−0.327130
$700$	5.26659	0.199059
$701$	19.7039	0.744206	0.372103	−	0.928191i	$-0.378637\pi$
$701$	19.7039	0.744206	0.372103	+	0.928191i	$0.378637\pi$
$702$	−51.7407	−1.95283
$703$	−4.21305	−0.158898
$704$	9.66647	0.364319
$705$	2.63787	0.0993478
$706$	14.0182	0.527582
$707$	6.94238	0.261095
$708$	38.9471	1.46372
$709$	−7.05929	−0.265117	−0.132559	−	0.991175i	$-0.542319\pi$
$709$	−7.05929	−0.265117	−0.132559	+	0.991175i	$0.542319\pi$
$710$	−44.0955	−1.65487
$711$	−0.846320	−0.0317395
$712$	−16.5954	−0.621939
$713$	−10.3950	−0.389296
$714$	36.5576	1.36813
$715$	−7.24674	−0.271013
$716$	−74.0579	−2.76767
$717$	−32.1262	−1.19978
$718$	−17.2508	−0.643796
$719$	−13.4273	−0.500752	−0.250376	−	0.968149i	$-0.580554\pi$
$719$	−13.4273	−0.500752	−0.250376	+	0.968149i	$0.580554\pi$
$720$	0.778670	0.0290193
$721$	14.3244	0.533470
$722$	2.84606	0.105919
$723$	−3.98415	−0.148172
$724$	40.1259	1.49127
$725$	4.49953	0.167108
$726$	−30.3961	−1.12810
$727$	−18.1136	−0.671798	−0.335899	−	0.941898i	$-0.609040\pi$
$727$	−18.1136	−0.671798	−0.335899	+	0.941898i	$0.609040\pi$
$728$	−24.6798	−0.914696
$729$	25.5398	0.945918
$730$	−63.2420	−2.34069
$731$	−39.6621	−1.46696
$732$	5.25334	0.194169
$733$	4.61943	0.170623	0.0853113	−	0.996354i	$-0.472812\pi$
$733$	4.61943	0.170623	0.0853113	+	0.996354i	$0.472812\pi$
$734$	0.560084	0.0206731
$735$	5.90741	0.217898
$736$	−6.43452	−0.237180
$737$	−0.536672	−0.0197686
$738$	2.93355	0.107985
$739$	−7.04181	−0.259037	−0.129519	−	0.991577i	$-0.541343\pi$
$739$	−7.04181	−0.259037	−0.129519	+	0.991577i	$0.541343\pi$
$740$	−7.62076	−0.280145
$741$	−21.9288	−0.805573
$742$	−37.9105	−1.39174
$743$	−10.8647	−0.398586	−0.199293	−	0.979940i	$-0.563865\pi$
$743$	−10.8647	−0.398586	−0.199293	+	0.979940i	$0.563865\pi$
$744$	32.9168	1.20679
$745$	41.8254	1.53237
$746$	66.2870	2.42694
$747$	−17.3749	−0.635716
$748$	−13.1951	−0.482459
$749$	17.2167	0.629083
$750$	−29.7146	−1.08502
$751$	−2.96777	−0.108296	−0.0541478	−	0.998533i	$-0.517244\pi$
$751$	−2.96777	−0.108296	−0.0541478	+	0.998533i	$0.517244\pi$
$752$	0.205049	0.00747737
$753$	9.04438	0.329595
$754$	−56.7558	−2.06693
$755$	−8.88969	−0.323529
$756$	39.9863	1.45429
$757$	31.3731	1.14027	0.570137	−	0.821550i	$-0.306890\pi$
$757$	31.3731	1.14027	0.570137	+	0.821550i	$0.306890\pi$
$758$	−67.6846	−2.45842
$759$	−1.03135	−0.0374357
$760$	−27.1532	−0.984952
$761$	−47.7935	−1.73251	−0.866257	−	0.499599i	$-0.833481\pi$
$761$	−47.7935	−1.73251	−0.866257	+	0.499599i	$0.833481\pi$
$762$	−26.9139	−0.974989
$763$	−42.9778	−1.55590
$764$	−43.5254	−1.57469
$765$	−18.2662	−0.660416
$766$	−42.6433	−1.54076
$767$	−39.0037	−1.40834
$768$	18.4405	0.665414
$769$	−28.6647	−1.03368	−0.516838	−	0.856083i	$-0.672891\pi$
$769$	−28.6647	−1.03368	−0.516838	+	0.856083i	$0.672891\pi$
$770$	9.12026	0.328671
$771$	−12.4310	−0.447691
$772$	−61.8502	−2.22604
$773$	−42.0344	−1.51187	−0.755936	−	0.654646i	$-0.772818\pi$
$773$	−42.0344	−1.51187	−0.755936	+	0.654646i	$0.772818\pi$
$774$	−22.1118	−0.794791
$775$	7.03453	0.252688
$776$	−16.6538	−0.597835
$777$	2.87756	0.103232
$778$	−41.2463	−1.47875
$779$	3.97234	0.142324
$780$	−39.6658	−1.42026
$781$	−6.00971	−0.215044
$782$	13.7990	0.493450
$783$	34.1624	1.22086
$784$	0.459200	0.0164000
$785$	20.4927	0.731418
$786$	16.4116	0.585381
$787$	41.1567	1.46708	0.733539	−	0.679648i	$-0.237867\pi$
$787$	41.1567	1.46708	0.733539	+	0.679648i	$0.237867\pi$
$788$	−3.92331	−0.139762
$789$	29.3439	1.04467
$790$	−3.37579	−0.120105
$791$	26.4233	0.939504
$792$	−2.73293	−0.0971103
$793$	−5.26097	−0.186823
$794$	76.1279	2.70168
$795$	−22.6361	−0.802820
$796$	27.9324	0.990038
$797$	33.1011	1.17250	0.586251	−	0.810130i	$-0.300603\pi$
$797$	33.1011	1.17250	0.586251	+	0.810130i	$0.300603\pi$
$798$	27.5980	0.976960
$799$	−4.81008	−0.170168
$800$	4.35439	0.153951
$801$	−8.42782	−0.297782
$802$	−49.6263	−1.75236
$803$	−8.61917	−0.304164
$804$	−2.93753	−0.103599
$805$	−5.85674	−0.206423
$806$	−88.7317	−3.12544
$807$	5.69119	0.200339
$808$	−8.29794	−0.291920
$809$	−18.9976	−0.667918	−0.333959	−	0.942588i	$-0.608385\pi$
$809$	−18.9976	−0.667918	−0.333959	+	0.942588i	$0.608385\pi$
$810$	16.5283	0.580747
$811$	−10.7086	−0.376031	−0.188015	−	0.982166i	$-0.560205\pi$
$811$	−10.7086	−0.376031	−0.188015	+	0.982166i	$0.560205\pi$
$812$	43.8621	1.53926
$813$	10.4756	0.367396
$814$	−1.69139	−0.0592832
$815$	2.39479	0.0838859
$816$	1.69678	0.0593990
$817$	−29.9417	−1.04753
$818$	16.3998	0.573404
$819$	−12.5334	−0.437953
$820$	7.18536	0.250924
$821$	6.80683	0.237560	0.118780	−	0.992921i	$-0.462102\pi$
$821$	6.80683	0.237560	0.118780	+	0.992921i	$0.462102\pi$
$822$	−53.1282	−1.85306
$823$	−13.4429	−0.468591	−0.234295	−	0.972165i	$-0.575278\pi$
$823$	−13.4429	−0.468591	−0.234295	+	0.972165i	$0.575278\pi$
$824$	−17.1214	−0.596452
$825$	0.697939	0.0242991
$826$	49.0874	1.70797
$827$	−30.9259	−1.07540	−0.537699	−	0.843137i	$-0.680706\pi$
$827$	−30.9259	−1.07540	−0.537699	+	0.843137i	$0.680706\pi$
$828$	4.72398	0.164170
$829$	14.1748	0.492311	0.246156	−	0.969230i	$-0.420833\pi$
$829$	14.1748	0.492311	0.246156	+	0.969230i	$0.420833\pi$
$830$	−69.3050	−2.40561
$831$	5.26208	0.182539
$832$	−52.9873	−1.83700
$833$	−10.7720	−0.373228
$834$	−38.6387	−1.33795
$835$	−28.8245	−0.997514
$836$	−9.96122	−0.344516
$837$	53.4093	1.84610
$838$	−31.1011	−1.07437
$839$	10.6140	0.366436	0.183218	−	0.983072i	$-0.441349\pi$
$839$	10.6140	0.366436	0.183218	+	0.983072i	$0.441349\pi$
$840$	18.5459	0.639896
$841$	8.47369	0.292196
$842$	22.5683	0.777754
$843$	8.65808	0.298200
$844$	2.77432	0.0954962
$845$	8.59110	0.295543
$846$	−2.68164	−0.0921966
$847$	−23.5249	−0.808324
$848$	−1.75957	−0.0604239
$849$	32.7025	1.12235
$850$	−9.33807	−0.320293
$851$	1.08616	0.0372330
$852$	−32.8948	−1.12696
$853$	40.8639	1.39915	0.699577	−	0.714557i	$-0.253372\pi$
$853$	40.8639	1.39915	0.699577	+	0.714557i	$0.253372\pi$
$854$	6.62111	0.226570
$855$	−13.7895	−0.471592
$856$	−20.5784	−0.703354
$857$	28.0960	0.959743	0.479871	−	0.877339i	$-0.340683\pi$
$857$	28.0960	0.959743	0.479871	+	0.877339i	$0.340683\pi$
$858$	−8.80361	−0.300550
$859$	−8.87848	−0.302930	−0.151465	−	0.988463i	$-0.548399\pi$
$859$	−8.87848	−0.302930	−0.151465	+	0.988463i	$0.548399\pi$
$860$	−54.1600	−1.84684
$861$	−2.71315	−0.0924639
$862$	67.7611	2.30795
$863$	41.6765	1.41869	0.709343	−	0.704864i	$-0.248992\pi$
$863$	41.6765	1.41869	0.709343	+	0.704864i	$0.248992\pi$
$864$	33.0604	1.12474
$865$	27.6690	0.940773
$866$	64.6817	2.19798
$867$	−18.0774	−0.613942
$868$	68.5738	2.32755
$869$	−0.460082	−0.0156072
$870$	42.6498	1.44596
$871$	2.94180	0.0996789
$872$	51.3695	1.73959
$873$	−8.45746	−0.286242
$874$	10.4171	0.352364
$875$	−22.9974	−0.777456
$876$	−47.1779	−1.59399
$877$	−1.01324	−0.0342147	−0.0171074	−	0.999854i	$-0.505446\pi$
$877$	−1.01324	−0.0342147	−0.0171074	+	0.999854i	$0.505446\pi$
$878$	15.0119	0.506626
$879$	30.2229	1.01939
$880$	0.423306	0.0142696
$881$	25.4949	0.858943	0.429472	−	0.903080i	$-0.358700\pi$
$881$	25.4949	0.858943	0.429472	+	0.903080i	$0.358700\pi$
$882$	−6.00543	−0.202213
$883$	17.3279	0.583130	0.291565	−	0.956551i	$-0.405824\pi$
$883$	17.3279	0.583130	0.291565	+	0.956551i	$0.405824\pi$
$884$	72.3295	2.43270
$885$	29.3097	0.985236
$886$	−7.00026	−0.235178
$887$	−55.9455	−1.87847	−0.939233	−	0.343279i	$-0.888462\pi$
$887$	−55.9455	−1.87847	−0.939233	+	0.343279i	$0.888462\pi$
$888$	−3.43942	−0.115419
$889$	−20.8299	−0.698612
$890$	−33.6168	−1.12684
$891$	2.25263	0.0754658
$892$	3.38555	0.113357
$893$	−3.63123	−0.121514
$894$	50.8111	1.69938
$895$	−55.7325	−1.86293
$896$	40.0084	1.33659
$897$	5.65341	0.188762
$898$	−24.0212	−0.801599
$899$	58.5862	1.95396
$900$	−3.19683	−0.106561
$901$	41.2764	1.37512
$902$	1.59475	0.0530995
$903$	20.4505	0.680550
$904$	−31.5827	−1.05042
$905$	30.1969	1.00378
$906$	−10.7995	−0.358791
$907$	−22.0920	−0.733552	−0.366776	−	0.930309i	$-0.619538\pi$
$907$	−22.0920	−0.733552	−0.366776	+	0.930309i	$0.619538\pi$
$908$	−54.4413	−1.80670
$909$	−4.21403	−0.139771
$910$	−49.9932	−1.65726
$911$	51.7596	1.71487	0.857435	−	0.514592i	$-0.172056\pi$
$911$	51.7596	1.71487	0.857435	+	0.514592i	$0.172056\pi$
$912$	1.28093	0.0424158
$913$	−9.44548	−0.312600
$914$	−33.3784	−1.10406
$915$	3.95342	0.130696
$916$	29.9095	0.988237
$917$	12.7016	0.419445
$918$	−70.8988	−2.34001
$919$	17.0129	0.561203	0.280601	−	0.959824i	$-0.409466\pi$
$919$	17.0129	0.561203	0.280601	+	0.959824i	$0.409466\pi$
$920$	7.00032	0.230794
$921$	−18.3708	−0.605340
$922$	−14.1317	−0.465404
$923$	32.9426	1.08432
$924$	6.80362	0.223823
$925$	−0.735028	−0.0241676
$926$	−7.59959	−0.249738
$927$	−8.69494	−0.285579
$928$	36.2649	1.19045
$929$	−53.2858	−1.74825	−0.874124	−	0.485702i	$-0.838564\pi$
$929$	−53.2858	−1.74825	−0.874124	+	0.485702i	$0.838564\pi$
$930$	66.6785	2.18647
$931$	−8.13200	−0.266516
$932$	21.5358	0.705428
$933$	19.4798	0.637740
$934$	17.0106	0.556604
$935$	−9.92999	−0.324745
$936$	14.9807	0.489659
$937$	−31.9915	−1.04512	−0.522558	−	0.852604i	$-0.675022\pi$
$937$	−31.9915	−1.04512	−0.522558	+	0.852604i	$0.675022\pi$
$938$	−3.70235	−0.120886
$939$	2.95117	0.0963077
$940$	−6.56834	−0.214235
$941$	25.5796	0.833872	0.416936	−	0.908936i	$-0.363104\pi$
$941$	25.5796	0.833872	0.416936	+	0.908936i	$0.363104\pi$
$942$	24.8954	0.811135
$943$	−1.02410	−0.0333493
$944$	2.27833	0.0741534
$945$	30.0918	0.978887
$946$	−12.0205	−0.390822
$947$	−11.0240	−0.358232	−0.179116	−	0.983828i	$-0.557324\pi$
$947$	−11.0240	−0.358232	−0.179116	+	0.983828i	$0.557324\pi$
$948$	−2.51831	−0.0817907
$949$	47.2464	1.53368
$950$	−7.04950	−0.228716
$951$	−10.8484	−0.351783
$952$	−33.8180	−1.09605
$953$	41.2784	1.33714	0.668569	−	0.743650i	$-0.266907\pi$
$953$	41.2784	1.33714	0.668569	+	0.743650i	$0.266907\pi$
$954$	23.0117	0.745032
$955$	−32.7552	−1.05993
$956$	79.9948	2.58722
$957$	5.81269	0.187897
$958$	−73.4877	−2.37428
$959$	−41.1183	−1.32778
$960$	39.8179	1.28512
$961$	60.5932	1.95462
$962$	9.27144	0.298923
$963$	−10.4505	−0.336763
$964$	9.92060	0.319521
$965$	−46.5455	−1.49835
$966$	−7.11499	−0.228921
$967$	34.6842	1.11537	0.557685	−	0.830053i	$-0.311690\pi$
$967$	34.6842	1.11537	0.557685	+	0.830053i	$0.311690\pi$
$968$	28.1183	0.903756
$969$	−30.0483	−0.965291
$970$	−33.7350	−1.08317
$971$	−30.5550	−0.980556	−0.490278	−	0.871566i	$-0.663105\pi$
$971$	−30.5550	−0.980556	−0.490278	+	0.871566i	$0.663105\pi$
$972$	−40.9467	−1.31337
$973$	−29.9042	−0.958685
$974$	72.5826	2.32570
$975$	−3.82579	−0.122523
$976$	0.307311	0.00983678
$977$	−1.99917	−0.0639591	−0.0319796	−	0.999489i	$-0.510181\pi$
$977$	−1.99917	−0.0639591	−0.0319796	+	0.999489i	$0.510181\pi$
$978$	2.90928	0.0930286
$979$	−4.58159	−0.146428
$980$	−14.7095	−0.469879
$981$	26.0875	0.832911
$982$	−6.73431	−0.214900
$983$	−21.9483	−0.700041	−0.350021	−	0.936742i	$-0.613825\pi$
$983$	−21.9483	−0.700041	−0.350021	+	0.936742i	$0.613825\pi$
$984$	3.24291	0.103380
$985$	−2.95250	−0.0940744
$986$	−77.7708	−2.47673
$987$	2.48017	0.0789446
$988$	54.6030	1.73715
$989$	7.71922	0.245457
$990$	−5.53600	−0.175946
$991$	−47.9070	−1.52182	−0.760908	−	0.648860i	$-0.775246\pi$
$991$	−47.9070	−1.52182	−0.760908	+	0.648860i	$0.775246\pi$
$992$	56.6964	1.80011
$993$	18.6211	0.590924
$994$	−41.4593	−1.31501
$995$	21.0206	0.666399
$996$	−51.7008	−1.63820
$997$	−2.48794	−0.0787940	−0.0393970	−	0.999224i	$-0.512544\pi$
$997$	−2.48794	−0.0787940	−0.0393970	+	0.999224i	$0.512544\pi$
$998$	−45.8459	−1.45123
$999$	−5.58065	−0.176564

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6031.2.a.d.1.17	✓	133

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6031.2.a.d.1.17	✓	133	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:	\( N \)	\(=\)	\( 6031 = 37 \cdot 163 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6031.a (trivial)

\(f(q)\)	\(=\)	\(q-2.27645 q^{2} -1.27799 q^{3} +3.18222 q^{4} +2.39479 q^{5} +2.90928 q^{6} +2.25162 q^{7} -2.69127 q^{8} -1.36674 q^{9} +O(q^{10})\)	\(q-2.27645 q^{2} -1.27799 q^{3} +3.18222 q^{4} +2.39479 q^{5} +2.90928 q^{6} +2.25162 q^{7} -2.69127 q^{8} -1.36674 q^{9} -5.45162 q^{10} -0.742995 q^{11} -4.06686 q^{12} +4.07276 q^{13} -5.12571 q^{14} -3.06052 q^{15} -0.237904 q^{16} +5.58079 q^{17} +3.11131 q^{18} +4.21305 q^{19} +7.62076 q^{20} -2.87756 q^{21} +1.69139 q^{22} -1.08616 q^{23} +3.43942 q^{24} +0.735028 q^{25} -9.27144 q^{26} +5.58065 q^{27} +7.16517 q^{28} +6.12158 q^{29} +6.96713 q^{30} +9.57044 q^{31} +5.92412 q^{32} +0.949541 q^{33} -12.7044 q^{34} +5.39217 q^{35} -4.34926 q^{36} -1.00000 q^{37} -9.59079 q^{38} -5.20496 q^{39} -6.44503 q^{40} +0.942866 q^{41} +6.55061 q^{42} -7.10690 q^{43} -2.36437 q^{44} -3.27305 q^{45} +2.47258 q^{46} -0.861900 q^{47} +0.304039 q^{48} -1.93019 q^{49} -1.67325 q^{50} -7.13220 q^{51} +12.9604 q^{52} +7.39616 q^{53} -12.7041 q^{54} -1.77932 q^{55} -6.05973 q^{56} -5.38424 q^{57} -13.9355 q^{58} -9.57670 q^{59} -9.73927 q^{60} -1.29175 q^{61} -21.7866 q^{62} -3.07738 q^{63} -13.0101 q^{64} +9.75342 q^{65} -2.16158 q^{66} +0.722309 q^{67} +17.7593 q^{68} +1.38810 q^{69} -12.2750 q^{70} +8.08850 q^{71} +3.67826 q^{72} +11.6006 q^{73} +2.27645 q^{74} -0.939359 q^{75} +13.4069 q^{76} -1.67294 q^{77} +11.8488 q^{78} +0.619227 q^{79} -0.569729 q^{80} -3.03182 q^{81} -2.14639 q^{82} +12.7127 q^{83} -9.15702 q^{84} +13.3648 q^{85} +16.1785 q^{86} -7.82332 q^{87} +1.99960 q^{88} +6.16638 q^{89} +7.45093 q^{90} +9.17033 q^{91} -3.45639 q^{92} -12.2309 q^{93} +1.96207 q^{94} +10.0894 q^{95} -7.57097 q^{96} +6.18807 q^{97} +4.39399 q^{98} +1.01548 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 133 q + 14 q^{2} + 8 q^{3} + 142 q^{4} + 34 q^{5} + 20 q^{6} + 8 q^{7} + 42 q^{8} + 177 q^{9}+O(q^{10}) \) 133 * q + 14 * q^2 + 8 * q^3 + 142 * q^4 + 34 * q^5 + 20 * q^6 + 8 * q^7 + 42 * q^8 + 177 * q^9	\( 133 q + 14 q^{2} + 8 q^{3} + 142 q^{4} + 34 q^{5} + 20 q^{6} + 8 q^{7} + 42 q^{8} + 177 q^{9} + 9 q^{10} + 23 q^{11} + 24 q^{12} + 23 q^{13} + 31 q^{14} + 9 q^{15} + 168 q^{16} + 98 q^{17} + 38 q^{18} + 29 q^{19} + 83 q^{20} + 26 q^{21} + 2 q^{22} + 34 q^{23} + 75 q^{24} + 177 q^{25} + 67 q^{26} + 32 q^{27} + 32 q^{28} + 91 q^{29} + 12 q^{30} + 24 q^{31} + 88 q^{32} + 27 q^{33} + 23 q^{34} + 66 q^{35} + 232 q^{36} - 133 q^{37} + 26 q^{38} + 28 q^{39} + 41 q^{40} + 132 q^{41} + 13 q^{42} + 11 q^{43} + 65 q^{44} + 107 q^{45} + 20 q^{46} + 10 q^{47} + 27 q^{48} + 229 q^{49} + 78 q^{50} + 19 q^{51} + 71 q^{52} + 7 q^{53} + 43 q^{54} + 41 q^{55} + 67 q^{56} + 45 q^{57} + 25 q^{58} + 97 q^{59} - 42 q^{60} + 65 q^{61} + 24 q^{62} + 39 q^{63} + 200 q^{64} + 60 q^{65} + 35 q^{66} + 25 q^{67} + 227 q^{68} + 120 q^{69} + 37 q^{70} + 26 q^{71} + 93 q^{72} + 55 q^{73} - 14 q^{74} + 5 q^{75} + 34 q^{76} + 21 q^{77} - 2 q^{78} + 50 q^{79} + 162 q^{80} + 341 q^{81} + 66 q^{82} + 30 q^{83} - 89 q^{84} + 30 q^{85} - 12 q^{86} + 80 q^{87} - 85 q^{88} + 225 q^{89} - 86 q^{90} + q^{91} + 82 q^{92} + 42 q^{93} - 17 q^{94} + 70 q^{95} + 55 q^{96} + 12 q^{97} + 90 q^{98} + 17 q^{99}+O(q^{100}) \) 133 * q + 14 * q^2 + 8 * q^3 + 142 * q^4 + 34 * q^5 + 20 * q^6 + 8 * q^7 + 42 * q^8 + 177 * q^9 + 9 * q^10 + 23 * q^11 + 24 * q^12 + 23 * q^13 + 31 * q^14 + 9 * q^15 + 168 * q^16 + 98 * q^17 + 38 * q^18 + 29 * q^19 + 83 * q^20 + 26 * q^21 + 2 * q^22 + 34 * q^23 + 75 * q^24 + 177 * q^25 + 67 * q^26 + 32 * q^27 + 32 * q^28 + 91 * q^29 + 12 * q^30 + 24 * q^31 + 88 * q^32 + 27 * q^33 + 23 * q^34 + 66 * q^35 + 232 * q^36 - 133 * q^37 + 26 * q^38 + 28 * q^39 + 41 * q^40 + 132 * q^41 + 13 * q^42 + 11 * q^43 + 65 * q^44 + 107 * q^45 + 20 * q^46 + 10 * q^47 + 27 * q^48 + 229 * q^49 + 78 * q^50 + 19 * q^51 + 71 * q^52 + 7 * q^53 + 43 * q^54 + 41 * q^55 + 67 * q^56 + 45 * q^57 + 25 * q^58 + 97 * q^59 - 42 * q^60 + 65 * q^61 + 24 * q^62 + 39 * q^63 + 200 * q^64 + 60 * q^65 + 35 * q^66 + 25 * q^67 + 227 * q^68 + 120 * q^69 + 37 * q^70 + 26 * q^71 + 93 * q^72 + 55 * q^73 - 14 * q^74 + 5 * q^75 + 34 * q^76 + 21 * q^77 - 2 * q^78 + 50 * q^79 + 162 * q^80 + 341 * q^81 + 66 * q^82 + 30 * q^83 - 89 * q^84 + 30 * q^85 - 12 * q^86 + 80 * q^87 - 85 * q^88 + 225 * q^89 - 86 * q^90 + q^91 + 82 * q^92 + 42 * q^93 - 17 * q^94 + 70 * q^95 + 55 * q^96 + 12 * q^97 + 90 * q^98 + 17 * q^99

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