LMFDB - Embedded newform 6031.2.a.d.1.11

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			1.11
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)

$f(q)$	$=$	$q-2.39714 q^{2} +0.221428 q^{3} +3.74630 q^{4} -0.354828 q^{5} -0.530796 q^{6} +3.04567 q^{7} -4.18612 q^{8} -2.95097 q^{9} +O(q^{10})$	\(q-2.39714 q^{2} +0.221428 q^{3} +3.74630 q^{4} -0.354828 q^{5} -0.530796 q^{6} +3.04567 q^{7} -4.18612 q^{8} -2.95097 q^{9} +0.850573 q^{10} -5.99473 q^{11} +0.829536 q^{12} -5.16580 q^{13} -7.30091 q^{14} -0.0785690 q^{15} +2.54214 q^{16} +3.05666 q^{17} +7.07390 q^{18} -1.62254 q^{19} -1.32929 q^{20} +0.674398 q^{21} +14.3702 q^{22} +5.98216 q^{23} -0.926926 q^{24} -4.87410 q^{25} +12.3832 q^{26} -1.31771 q^{27} +11.4100 q^{28} +0.214184 q^{29} +0.188341 q^{30} -6.69718 q^{31} +2.27837 q^{32} -1.32740 q^{33} -7.32724 q^{34} -1.08069 q^{35} -11.0552 q^{36} -1.00000 q^{37} +3.88946 q^{38} -1.14386 q^{39} +1.48535 q^{40} +9.05919 q^{41} -1.61663 q^{42} -2.12678 q^{43} -22.4580 q^{44} +1.04709 q^{45} -14.3401 q^{46} -6.03829 q^{47} +0.562902 q^{48} +2.27610 q^{49} +11.6839 q^{50} +0.676831 q^{51} -19.3526 q^{52} -2.56041 q^{53} +3.15875 q^{54} +2.12710 q^{55} -12.7495 q^{56} -0.359276 q^{57} -0.513429 q^{58} -10.4942 q^{59} -0.294343 q^{60} -8.62685 q^{61} +16.0541 q^{62} -8.98768 q^{63} -10.5459 q^{64} +1.83297 q^{65} +3.18198 q^{66} +9.81060 q^{67} +11.4511 q^{68} +1.32462 q^{69} +2.59057 q^{70} -4.88786 q^{71} +12.3531 q^{72} +9.38750 q^{73} +2.39714 q^{74} -1.07926 q^{75} -6.07851 q^{76} -18.2580 q^{77} +2.74198 q^{78} -10.3356 q^{79} -0.902021 q^{80} +8.56113 q^{81} -21.7162 q^{82} -6.51303 q^{83} +2.52649 q^{84} -1.08459 q^{85} +5.09820 q^{86} +0.0474264 q^{87} +25.0947 q^{88} +12.6065 q^{89} -2.51002 q^{90} -15.7333 q^{91} +22.4109 q^{92} -1.48295 q^{93} +14.4746 q^{94} +0.575722 q^{95} +0.504496 q^{96} +4.63031 q^{97} -5.45614 q^{98} +17.6903 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.39714	−1.69504	−0.847518	−	0.530767i	$-0.821904\pi$
$2$	−2.39714	−1.69504	−0.847518	+	0.530767i	$0.821904\pi$
$3$	0.221428	0.127842	0.0639209	−	0.997955i	$-0.479639\pi$
$3$	0.221428	0.127842	0.0639209	+	0.997955i	$0.479639\pi$
$4$	3.74630	1.87315
$5$	−0.354828	−0.158684	−0.0793420	−	0.996847i	$-0.525282\pi$
$5$	−0.354828	−0.158684	−0.0793420	+	0.996847i	$0.525282\pi$
$6$	−0.530796	−0.216696
$7$	3.04567	1.15115	0.575577	−	0.817747i	$-0.304777\pi$
$7$	3.04567	1.15115	0.575577	+	0.817747i	$0.304777\pi$
$8$	−4.18612	−1.48002
$9$	−2.95097	−0.983656
$10$	0.850573	0.268975
$11$	−5.99473	−1.80748	−0.903740	−	0.428083i	$-0.859189\pi$
$11$	−5.99473	−1.80748	−0.903740	+	0.428083i	$0.859189\pi$
$12$	0.829536	0.239467
$13$	−5.16580	−1.43274	−0.716368	−	0.697723i	$-0.754197\pi$
$13$	−5.16580	−1.43274	−0.716368	+	0.697723i	$0.754197\pi$
$14$	−7.30091	−1.95125
$15$	−0.0785690	−0.0202864
$16$	2.54214	0.635534
$17$	3.05666	0.741348	0.370674	−	0.928763i	$-0.379127\pi$
$17$	3.05666	0.741348	0.370674	+	0.928763i	$0.379127\pi$
$18$	7.07390	1.66733
$19$	−1.62254	−0.372236	−0.186118	−	0.982527i	$-0.559591\pi$
$19$	−1.62254	−0.372236	−0.186118	+	0.982527i	$0.559591\pi$
$20$	−1.32929	−0.297238
$21$	0.674398	0.147166
$22$	14.3702	3.06374
$23$	5.98216	1.24737	0.623684	−	0.781677i	$-0.285635\pi$
$23$	5.98216	1.24737	0.623684	+	0.781677i	$0.285635\pi$
$24$	−0.926926	−0.189208
$25$	−4.87410	−0.974819
$26$	12.3832	2.42854
$27$	−1.31771	−0.253594
$28$	11.4100	2.15628
$29$	0.214184	0.0397729	0.0198865	−	0.999802i	$-0.493670\pi$
$29$	0.214184	0.0397729	0.0198865	+	0.999802i	$0.493670\pi$
$30$	0.188341	0.0343862
$31$	−6.69718	−1.20285	−0.601425	−	0.798930i	$-0.705400\pi$
$31$	−6.69718	−1.20285	−0.601425	+	0.798930i	$0.705400\pi$
$32$	2.27837	0.402763
$33$	−1.32740	−0.231071
$34$	−7.32724	−1.25661
$35$	−1.08069	−0.182670
$36$	−11.0552	−1.84253
$37$	−1.00000	−0.164399
$37$	−1.00000	−0.164399
$38$	3.88946	0.630953
$39$	−1.14386	−0.183163
$40$	1.48535	0.234855
$41$	9.05919	1.41481	0.707404	−	0.706809i	$-0.249866\pi$
$41$	9.05919	1.41481	0.707404	+	0.706809i	$0.249866\pi$
$42$	−1.61663	−0.249451
$43$	−2.12678	−0.324331	−0.162166	−	0.986764i	$-0.551848\pi$
$43$	−2.12678	−0.324331	−0.162166	+	0.986764i	$0.551848\pi$
$44$	−22.4580	−3.38568
$45$	1.04709	0.156090
$46$	−14.3401	−2.11433
$47$	−6.03829	−0.880775	−0.440387	−	0.897808i	$-0.645159\pi$
$47$	−6.03829	−0.880775	−0.440387	+	0.897808i	$0.645159\pi$
$48$	0.562902	0.0812478
$49$	2.27610	0.325157
$50$	11.6839	1.65235
$51$	0.676831	0.0947752
$52$	−19.3526	−2.68372
$53$	−2.56041	−0.351699	−0.175849	−	0.984417i	$-0.556267\pi$
$53$	−2.56041	−0.351699	−0.175849	+	0.984417i	$0.556267\pi$
$54$	3.15875	0.429851
$55$	2.12710	0.286818
$56$	−12.7495	−1.70373
$57$	−0.359276	−0.0475873
$58$	−0.513429	−0.0674165
$59$	−10.4942	−1.36622	−0.683112	−	0.730313i	$-0.739374\pi$
$59$	−10.4942	−1.36622	−0.683112	+	0.730313i	$0.739374\pi$
$60$	−0.294343	−0.0379995
$61$	−8.62685	−1.10455	−0.552277	−	0.833660i	$-0.686241\pi$
$61$	−8.62685	−1.10455	−0.552277	+	0.833660i	$0.686241\pi$
$62$	16.0541	2.03887
$63$	−8.98768	−1.13234
$64$	−10.5459	−1.31823
$65$	1.83297	0.227352
$66$	3.18198	0.391674
$67$	9.81060	1.19856	0.599278	−	0.800541i	$-0.295455\pi$
$67$	9.81060	1.19856	0.599278	+	0.800541i	$0.295455\pi$
$68$	11.4511	1.38865
$69$	1.32462	0.159466
$70$	2.59057	0.309632
$71$	−4.88786	−0.580082	−0.290041	−	0.957014i	$-0.593669\pi$
$71$	−4.88786	−0.580082	−0.290041	+	0.957014i	$0.593669\pi$
$72$	12.3531	1.45583
$73$	9.38750	1.09872	0.549362	−	0.835585i	$-0.314871\pi$
$73$	9.38750	1.09872	0.549362	+	0.835585i	$0.314871\pi$
$74$	2.39714	0.278662
$75$	−1.07926	−0.124623
$76$	−6.07851	−0.697253
$77$	−18.2580	−2.08069
$78$	2.74198	0.310469
$79$	−10.3356	−1.16285	−0.581424	−	0.813601i	$-0.697504\pi$
$79$	−10.3356	−1.16285	−0.581424	+	0.813601i	$0.697504\pi$
$80$	−0.902021	−0.100849
$81$	8.56113	0.951237
$82$	−21.7162	−2.39815
$83$	−6.51303	−0.714897	−0.357449	−	0.933933i	$-0.616353\pi$
$83$	−6.51303	−0.714897	−0.357449	+	0.933933i	$0.616353\pi$
$84$	2.52649	0.275663
$85$	−1.08459	−0.117640
$86$	5.09820	0.549753
$87$	0.0474264	0.00508464
$88$	25.0947	2.67510
$89$	12.6065	1.33629	0.668145	−	0.744031i	$-0.267089\pi$
$89$	12.6065	1.33629	0.668145	+	0.744031i	$0.267089\pi$
$90$	−2.51002	−0.264579
$91$	−15.7333	−1.64930
$92$	22.4109	2.33650
$93$	−1.48295	−0.153774
$94$	14.4746	1.49294
$95$	0.575722	0.0590678
$96$	0.504496	0.0514900
$97$	4.63031	0.470137	0.235068	−	0.971979i	$-0.424469\pi$
$97$	4.63031	0.470137	0.235068	+	0.971979i	$0.424469\pi$
$98$	−5.45614	−0.551153
$99$	17.6903	1.77794
$100$	−18.2598	−1.82598
$101$	−9.28873	−0.924264	−0.462132	−	0.886811i	$-0.652915\pi$
$101$	−9.28873	−0.924264	−0.462132	+	0.886811i	$0.652915\pi$
$102$	−1.62246	−0.160647
$103$	8.68801	0.856055	0.428028	−	0.903766i	$-0.359209\pi$
$103$	8.68801	0.856055	0.428028	+	0.903766i	$0.359209\pi$
$104$	21.6247	2.12047
$105$	−0.239295	−0.0233528
$106$	6.13766	0.596142
$107$	10.4042	1.00582	0.502908	−	0.864340i	$-0.332263\pi$
$107$	10.4042	1.00582	0.502908	+	0.864340i	$0.332263\pi$
$108$	−4.93655	−0.475019
$109$	−12.8882	−1.23446	−0.617232	−	0.786782i	$-0.711746\pi$
$109$	−12.8882	−1.23446	−0.617232	+	0.786782i	$0.711746\pi$
$110$	−5.09896	−0.486167
$111$	−0.221428	−0.0210171
$112$	7.74251	0.731598
$113$	17.0877	1.60747	0.803736	−	0.594986i	$-0.202843\pi$
$113$	17.0877	1.60747	0.803736	+	0.594986i	$0.202843\pi$
$114$	0.861236	0.0806622
$115$	−2.12264	−0.197937
$116$	0.802395	0.0745005
$117$	15.2441	1.40932
$118$	25.1560	2.31580
$119$	9.30956	0.853406
$120$	0.328899	0.0300243
$121$	24.9368	2.26698
$122$	20.6798	1.87226
$123$	2.00596	0.180872
$124$	−25.0896	−2.25311
$125$	3.50361	0.313372
$126$	21.5447	1.91936
$127$	1.43202	0.127071	0.0635355	−	0.997980i	$-0.479762\pi$
$127$	1.43202	0.127071	0.0635355	+	0.997980i	$0.479762\pi$
$128$	20.7232	1.83169
$129$	−0.470930	−0.0414631
$130$	−4.39389	−0.385370
$131$	−0.0760977	−0.00664868	−0.00332434	−	0.999994i	$-0.501058\pi$
$131$	−0.0760977	−0.00664868	−0.00332434	+	0.999994i	$0.501058\pi$
$132$	−4.97285	−0.432831
$133$	−4.94172	−0.428501
$134$	−23.5174	−2.03159
$135$	0.467562	0.0402413
$136$	−12.7955	−1.09721
$137$	20.6701	1.76597	0.882984	−	0.469404i	$-0.155531\pi$
$137$	20.6701	1.76597	0.882984	+	0.469404i	$0.155531\pi$
$138$	−3.17531	−0.270300
$139$	−1.18756	−0.100728	−0.0503640	−	0.998731i	$-0.516038\pi$
$139$	−1.18756	−0.100728	−0.0503640	+	0.998731i	$0.516038\pi$
$140$	−4.04858	−0.342167
$141$	−1.33705	−0.112600
$142$	11.7169	0.983260
$143$	30.9676	2.58964
$144$	−7.50177	−0.625147
$145$	−0.0759984	−0.00631132
$146$	−22.5032	−1.86238
$147$	0.503994	0.0415687
$148$	−3.74630	−0.307944
$149$	−21.0147	−1.72159	−0.860796	−	0.508950i	$-0.830034\pi$
$149$	−21.0147	−1.72159	−0.860796	+	0.508950i	$0.830034\pi$
$150$	2.58715	0.211240
$151$	16.3078	1.32711	0.663553	−	0.748129i	$-0.269048\pi$
$151$	16.3078	1.32711	0.663553	+	0.748129i	$0.269048\pi$
$152$	6.79214	0.550915
$153$	−9.02010	−0.729232
$154$	43.7670	3.52684
$155$	2.37635	0.190873
$156$	−4.28522	−0.343092
$157$	−22.4543	−1.79205	−0.896025	−	0.444005i	$-0.853557\pi$
$157$	−22.4543	−1.79205	−0.896025	+	0.444005i	$0.853557\pi$
$158$	24.7759	1.97107
$159$	−0.566947	−0.0449618
$160$	−0.808430	−0.0639120
$161$	18.2197	1.43591
$162$	−20.5223	−1.61238
$163$	1.00000	0.0783260
$163$	1.00000	0.0783260
$164$	33.9384	2.65014
$165$	0.471000	0.0366673
$166$	15.6127	1.21178
$167$	10.3628	0.801899	0.400949	−	0.916100i	$-0.368680\pi$
$167$	10.3628	0.801899	0.400949	+	0.916100i	$0.368680\pi$
$168$	−2.82311	−0.217808
$169$	13.6855	1.05273
$170$	2.59991	0.199404
$171$	4.78806	0.366152
$172$	−7.96755	−0.607520
$173$	8.10885	0.616504	0.308252	−	0.951305i	$-0.400256\pi$
$173$	8.10885	0.616504	0.308252	+	0.951305i	$0.400256\pi$
$174$	−0.113688	−0.00861865
$175$	−14.8449	−1.12217
$176$	−15.2394	−1.14871
$177$	−2.32371	−0.174661
$178$	−30.2197	−2.26506
$179$	1.89150	0.141378	0.0706889	−	0.997498i	$-0.477480\pi$
$179$	1.89150	0.141378	0.0706889	+	0.997498i	$0.477480\pi$
$180$	3.92270	0.292380
$181$	−10.2878	−0.764689	−0.382344	−	0.924020i	$-0.624883\pi$
$181$	−10.2878	−0.764689	−0.382344	+	0.924020i	$0.624883\pi$
$182$	37.7150	2.79562
$183$	−1.91023	−0.141208
$184$	−25.0420	−1.84612
$185$	0.354828	0.0260875
$186$	3.55483	0.260653
$187$	−18.3238	−1.33997
$188$	−22.6212	−1.64982
$189$	−4.01332	−0.291926
$190$	−1.38009	−0.100122
$191$	−14.9004	−1.07815	−0.539077	−	0.842257i	$-0.681227\pi$
$191$	−14.9004	−1.07815	−0.539077	+	0.842257i	$0.681227\pi$
$192$	−2.33515	−0.168525
$193$	2.59410	0.186727	0.0933636	−	0.995632i	$-0.470238\pi$
$193$	2.59410	0.186727	0.0933636	+	0.995632i	$0.470238\pi$
$194$	−11.0995	−0.796899
$195$	0.405872	0.0290651
$196$	8.52695	0.609068
$197$	−9.74684	−0.694433	−0.347217	−	0.937785i	$-0.612873\pi$
$197$	−9.74684	−0.694433	−0.347217	+	0.937785i	$0.612873\pi$
$198$	−42.4061	−3.01367
$199$	−24.1410	−1.71131	−0.855654	−	0.517548i	$-0.826845\pi$
$199$	−24.1410	−1.71131	−0.855654	+	0.517548i	$0.826845\pi$
$200$	20.4036	1.44275
$201$	2.17235	0.153225
$202$	22.2664	1.56666
$203$	0.652333	0.0457848
$204$	2.53561	0.177528
$205$	−3.21446	−0.224507
$206$	−20.8264	−1.45104
$207$	−17.6532	−1.22698
$208$	−13.1322	−0.910552
$209$	9.72668	0.672808
$210$	0.573625	0.0395839
$211$	−4.89409	−0.336923	−0.168461	−	0.985708i	$-0.553880\pi$
$211$	−4.89409	−0.336923	−0.168461	+	0.985708i	$0.553880\pi$
$212$	−9.59204	−0.658784
$213$	−1.08231	−0.0741587
$214$	−24.9405	−1.70490
$215$	0.754642	0.0514661
$216$	5.51611	0.375324
$217$	−20.3974	−1.38467
$218$	30.8948	2.09246
$219$	2.07866	0.140463
$220$	7.96874	0.537252
$221$	−15.7901	−1.06216
$222$	0.530796	0.0356247
$223$	25.9733	1.73930	0.869650	−	0.493669i	$-0.164344\pi$
$223$	25.9733	1.73930	0.869650	+	0.493669i	$0.164344\pi$
$224$	6.93917	0.463643
$225$	14.3833	0.958887
$226$	−40.9616	−2.72472
$227$	13.5150	0.897020	0.448510	−	0.893778i	$-0.351955\pi$
$227$	13.5150	0.897020	0.448510	+	0.893778i	$0.351955\pi$
$228$	−1.34595	−0.0891380
$229$	22.6387	1.49601	0.748005	−	0.663693i	$-0.231012\pi$
$229$	22.6387	1.49601	0.748005	+	0.663693i	$0.231012\pi$
$230$	5.08827	0.335510
$231$	−4.04283	−0.265999
$232$	−0.896598	−0.0588646
$233$	−1.74870	−0.114561	−0.0572804	−	0.998358i	$-0.518243\pi$
$233$	−1.74870	−0.114561	−0.0572804	+	0.998358i	$0.518243\pi$
$234$	−36.5423	−2.38885
$235$	2.14255	0.139765
$236$	−39.3143	−2.55914
$237$	−2.28860	−0.148661
$238$	−22.3164	−1.44655
$239$	13.7416	0.888867	0.444434	−	0.895812i	$-0.353405\pi$
$239$	13.7416	0.888867	0.444434	+	0.895812i	$0.353405\pi$
$240$	−0.199733	−0.0128927
$241$	−11.9163	−0.767594	−0.383797	−	0.923417i	$-0.625384\pi$
$241$	−11.9163	−0.767594	−0.383797	+	0.923417i	$0.625384\pi$
$242$	−59.7770	−3.84261
$243$	5.84882	0.375202
$244$	−32.3187	−2.06899
$245$	−0.807625	−0.0515972
$246$	−4.80858	−0.306584
$247$	8.38171	0.533315
$248$	28.0352	1.78024
$249$	−1.44217	−0.0913938
$250$	−8.39865	−0.531177
$251$	3.36873	0.212632	0.106316	−	0.994332i	$-0.466094\pi$
$251$	3.36873	0.212632	0.106316	+	0.994332i	$0.466094\pi$
$252$	−33.6705	−2.12104
$253$	−35.8614	−2.25459
$254$	−3.43275	−0.215390
$255$	−0.240158	−0.0150393
$256$	−28.5847	−1.78655
$257$	28.2207	1.76036	0.880178	−	0.474643i	$-0.157423\pi$
$257$	28.2207	1.76036	0.880178	+	0.474643i	$0.157423\pi$
$258$	1.12889	0.0702814
$259$	−3.04567	−0.189249
$260$	6.86685	0.425864
$261$	−0.632049	−0.0391229
$262$	0.182417	0.0112698
$263$	11.1169	0.685498	0.342749	−	0.939427i	$-0.388642\pi$
$263$	11.1169	0.685498	0.342749	+	0.939427i	$0.388642\pi$
$264$	5.55667	0.341989
$265$	0.908504	0.0558090
$266$	11.8460	0.726325
$267$	2.79145	0.170834
$268$	36.7534	2.24507
$269$	26.6240	1.62329	0.811647	−	0.584148i	$-0.198571\pi$
$269$	26.6240	1.62329	0.811647	+	0.584148i	$0.198571\pi$
$270$	−1.12081	−0.0682105
$271$	−0.984698	−0.0598162	−0.0299081	−	0.999553i	$-0.509521\pi$
$271$	−0.984698	−0.0598162	−0.0299081	+	0.999553i	$0.509521\pi$
$272$	7.77044	0.471152
$273$	−3.48380	−0.210849
$274$	−49.5492	−2.99338
$275$	29.2189	1.76197
$276$	4.96242	0.298703
$277$	−3.63121	−0.218178	−0.109089	−	0.994032i	$-0.534793\pi$
$277$	−3.63121	−0.218178	−0.109089	+	0.994032i	$0.534793\pi$
$278$	2.84676	0.170737
$279$	19.7632	1.18319
$280$	4.52389	0.270354
$281$	4.87312	0.290706	0.145353	−	0.989380i	$-0.453568\pi$
$281$	4.87312	0.290706	0.145353	+	0.989380i	$0.453568\pi$
$282$	3.20510	0.190861
$283$	12.5680	0.747090	0.373545	−	0.927612i	$-0.378142\pi$
$283$	12.5680	0.747090	0.373545	+	0.927612i	$0.378142\pi$
$284$	−18.3114	−1.08658
$285$	0.127481	0.00755134
$286$	−74.2337	−4.38953
$287$	27.5913	1.62866
$288$	−6.72341	−0.396181
$289$	−7.65686	−0.450403
$290$	0.182179	0.0106979
$291$	1.02528	0.0601031
$292$	35.1683	2.05807
$293$	−11.9702	−0.699308	−0.349654	−	0.936879i	$-0.613701\pi$
$293$	−11.9702	−0.699308	−0.349654	+	0.936879i	$0.613701\pi$
$294$	−1.20814	−0.0704604
$295$	3.72363	0.216798
$296$	4.18612	0.243313
$297$	7.89934	0.458366
$298$	50.3753	2.91816
$299$	−30.9027	−1.78715
$300$	−4.04324	−0.233437
$301$	−6.47748	−0.373355
$302$	−39.0920	−2.24949
$303$	−2.05679	−0.118160
$304$	−4.12472	−0.236569
$305$	3.06105	0.175275
$306$	21.6225	1.23607
$307$	−24.8331	−1.41730	−0.708651	−	0.705560i	$-0.750696\pi$
$307$	−24.8331	−1.41730	−0.708651	+	0.705560i	$0.750696\pi$
$308$	−68.3997	−3.89744
$309$	1.92377	0.109440
$310$	−5.69644	−0.323536
$311$	18.7446	1.06291	0.531455	−	0.847087i	$-0.321645\pi$
$311$	18.7446	1.06291	0.531455	+	0.847087i	$0.321645\pi$
$312$	4.78831	0.271085
$313$	15.2452	0.861707	0.430854	−	0.902422i	$-0.358213\pi$
$313$	15.2452	0.861707	0.430854	+	0.902422i	$0.358213\pi$
$314$	53.8262	3.03759
$315$	3.18908	0.179684
$316$	−38.7203	−2.17819
$317$	−32.5697	−1.82929	−0.914647	−	0.404253i	$-0.867531\pi$
$317$	−32.5697	−1.82929	−0.914647	+	0.404253i	$0.867531\pi$
$318$	1.35905	0.0762119
$319$	−1.28397	−0.0718887
$320$	3.74197	0.209182
$321$	2.30380	0.128585
$322$	−43.6752	−2.43392
$323$	−4.95954	−0.275956
$324$	32.0725	1.78181
$325$	25.1786	1.39666
$326$	−2.39714	−0.132765
$327$	−2.85381	−0.157816
$328$	−37.9229	−2.09394
$329$	−18.3906	−1.01391
$330$	−1.12905	−0.0621524
$331$	17.7306	0.974561	0.487281	−	0.873245i	$-0.337989\pi$
$331$	17.7306	0.974561	0.487281	+	0.873245i	$0.337989\pi$
$332$	−24.3997	−1.33911
$333$	2.95097	0.161712
$334$	−24.8411	−1.35925
$335$	−3.48107	−0.190191
$336$	1.71441	0.0935288
$337$	20.5671	1.12036	0.560182	−	0.828370i	$-0.310731\pi$
$337$	20.5671	1.12036	0.560182	+	0.828370i	$0.310731\pi$
$338$	−32.8061	−1.78442
$339$	3.78369	0.205502
$340$	−4.06318	−0.220357
$341$	40.1478	2.17412
$342$	−11.4777	−0.620641
$343$	−14.3874	−0.776848
$344$	8.90296	0.480016
$345$	−0.470013	−0.0253046
$346$	−19.4381	−1.04500
$347$	15.1445	0.812998	0.406499	−	0.913651i	$-0.366749\pi$
$347$	15.1445	0.812998	0.406499	+	0.913651i	$0.366749\pi$
$348$	0.177673	0.00952428
$349$	−3.58914	−0.192122	−0.0960610	−	0.995375i	$-0.530624\pi$
$349$	−3.58914	−0.192122	−0.0960610	+	0.995375i	$0.530624\pi$
$350$	35.5853	1.90212
$351$	6.80705	0.363333
$352$	−13.6582	−0.727986
$353$	−2.19879	−0.117030	−0.0585148	−	0.998287i	$-0.518636\pi$
$353$	−2.19879	−0.117030	−0.0585148	+	0.998287i	$0.518636\pi$
$354$	5.57026	0.296056
$355$	1.73435	0.0920496
$356$	47.2278	2.50307
$357$	2.06140	0.109101
$358$	−4.53421	−0.239640
$359$	−9.10869	−0.480738	−0.240369	−	0.970682i	$-0.577269\pi$
$359$	−9.10869	−0.480738	−0.240369	+	0.970682i	$0.577269\pi$
$360$	−4.38323	−0.231016
$361$	−16.3674	−0.861440
$362$	24.6614	1.29618
$363$	5.52171	0.289815
$364$	−58.9417	−3.08938
$365$	−3.33095	−0.174350
$366$	4.57909	0.239353
$367$	2.54568	0.132883	0.0664417	−	0.997790i	$-0.478835\pi$
$367$	2.54568	0.132883	0.0664417	+	0.997790i	$0.478835\pi$
$368$	15.2075	0.792745
$369$	−26.7334	−1.39169
$370$	−0.850573	−0.0442192
$371$	−7.79815	−0.404860
$372$	−5.55555	−0.288042
$373$	10.5332	0.545387	0.272694	−	0.962101i	$-0.412085\pi$
$373$	10.5332	0.545387	0.272694	+	0.962101i	$0.412085\pi$
$374$	43.9248	2.27130
$375$	0.775798	0.0400620
$376$	25.2770	1.30356
$377$	−1.10643	−0.0569840
$378$	9.62051	0.494825
$379$	−14.8431	−0.762441	−0.381220	−	0.924484i	$-0.624496\pi$
$379$	−14.8431	−0.762441	−0.381220	+	0.924484i	$0.624496\pi$
$380$	2.15682	0.110643
$381$	0.317089	0.0162450
$382$	35.7183	1.82751
$383$	17.5421	0.896360	0.448180	−	0.893943i	$-0.352072\pi$
$383$	17.5421	0.896360	0.448180	+	0.893943i	$0.352072\pi$
$384$	4.58870	0.234166
$385$	6.47844	0.330172
$386$	−6.21842	−0.316509
$387$	6.27607	0.319031
$388$	17.3465	0.880635
$389$	37.3914	1.89582	0.947910	−	0.318538i	$-0.103192\pi$
$389$	37.3914	1.89582	0.947910	+	0.318538i	$0.103192\pi$
$390$	−0.972933	−0.0492664
$391$	18.2854	0.924733
$392$	−9.52803	−0.481238
$393$	−0.0168502	−0.000849980 0
$394$	23.3646	1.17709
$395$	3.66737	0.184525
$396$	66.2730	3.33034
$397$	−29.4026	−1.47567	−0.737836	−	0.674980i	$-0.764152\pi$
$397$	−29.4026	−1.47567	−0.737836	+	0.674980i	$0.764152\pi$
$398$	57.8694	2.90073
$399$	−1.09424	−0.0547803
$400$	−12.3906	−0.619531
$401$	−25.2272	−1.25979	−0.629893	−	0.776682i	$-0.716901\pi$
$401$	−25.2272	−1.25979	−0.629893	+	0.776682i	$0.716901\pi$
$402$	−5.20742	−0.259723
$403$	34.5963	1.72336
$404$	−34.7983	−1.73128
$405$	−3.03773	−0.150946
$406$	−1.56373	−0.0776069
$407$	5.99473	0.297148
$408$	−2.83329	−0.140269
$409$	12.1846	0.602490	0.301245	−	0.953547i	$-0.402598\pi$
$409$	12.1846	0.602490	0.301245	+	0.953547i	$0.402598\pi$
$410$	7.70551	0.380548
$411$	4.57695	0.225764
$412$	32.5479	1.60352
$413$	−31.9618	−1.57274
$414$	42.3172	2.07978
$415$	2.31100	0.113443
$416$	−11.7696	−0.577053
$417$	−0.262961	−0.0128772
$418$	−23.3162	−1.14043
$419$	14.0143	0.684645	0.342322	−	0.939583i	$-0.388786\pi$
$419$	14.0143	0.684645	0.342322	+	0.939583i	$0.388786\pi$
$420$	−0.896471	−0.0437433
$421$	−4.65499	−0.226870	−0.113435	−	0.993545i	$-0.536185\pi$
$421$	−4.65499	−0.226870	−0.113435	+	0.993545i	$0.536185\pi$
$422$	11.7318	0.571096
$423$	17.8188	0.866380
$424$	10.7182	0.520520
$425$	−14.8984	−0.722680
$426$	2.59445	0.125702
$427$	−26.2745	−1.27151
$428$	38.9774	1.88404
$429$	6.85710	0.331064
$430$	−1.80898	−0.0872370
$431$	−27.5002	−1.32464	−0.662320	−	0.749221i	$-0.730428\pi$
$431$	−27.5002	−1.32464	−0.662320	+	0.749221i	$0.730428\pi$
$432$	−3.34981	−0.161168
$433$	−23.2226	−1.11601	−0.558003	−	0.829839i	$-0.688432\pi$
$433$	−23.2226	−1.11601	−0.558003	+	0.829839i	$0.688432\pi$
$434$	48.8955	2.34706
$435$	−0.0168282	−0.000806850 0
$436$	−48.2829	−2.31233
$437$	−9.70629	−0.464315
$438$	−4.98284	−0.238089
$439$	16.7839	0.801053	0.400526	−	0.916285i	$-0.368827\pi$
$439$	16.7839	0.801053	0.400526	+	0.916285i	$0.368827\pi$
$440$	−8.90429	−0.424495
$441$	−6.71671	−0.319843
$442$	37.8511	1.80039
$443$	15.6823	0.745087	0.372543	−	0.928015i	$-0.378486\pi$
$443$	15.6823	0.745087	0.372543	+	0.928015i	$0.378486\pi$
$444$	−0.829536	−0.0393681
$445$	−4.47315	−0.212048
$446$	−62.2617	−2.94818
$447$	−4.65325	−0.220091
$448$	−32.1192	−1.51749
$449$	10.8569	0.512368	0.256184	−	0.966628i	$-0.417535\pi$
$449$	10.8569	0.512368	0.256184	+	0.966628i	$0.417535\pi$
$450$	−34.4789	−1.62535
$451$	−54.3074	−2.55724
$452$	64.0154	3.01103
$453$	3.61100	0.169660
$454$	−32.3973	−1.52048
$455$	5.58262	0.261717
$456$	1.50397	0.0704300
$457$	−4.84633	−0.226702	−0.113351	−	0.993555i	$-0.536158\pi$
$457$	−4.84633	−0.226702	−0.113351	+	0.993555i	$0.536158\pi$
$458$	−54.2683	−2.53579
$459$	−4.02780	−0.188002
$460$	−7.95203	−0.370765
$461$	16.2069	0.754831	0.377416	−	0.926044i	$-0.376813\pi$
$461$	16.2069	0.754831	0.377416	+	0.926044i	$0.376813\pi$
$462$	9.69125	0.450878
$463$	5.55901	0.258349	0.129175	−	0.991622i	$-0.458767\pi$
$463$	5.55901	0.258349	0.129175	+	0.991622i	$0.458767\pi$
$464$	0.544484	0.0252770
$465$	0.526191	0.0244015
$466$	4.19187	0.194185
$467$	30.8448	1.42733	0.713664	−	0.700488i	$-0.247034\pi$
$467$	30.8448	1.42733	0.713664	+	0.700488i	$0.247034\pi$
$468$	57.1090	2.63986
$469$	29.8798	1.37972
$470$	−5.13601	−0.236906
$471$	−4.97202	−0.229099
$472$	43.9299	2.02204
$473$	12.7495	0.586222
$474$	5.48610	0.251985
$475$	7.90841	0.362863
$476$	34.8764	1.59856
$477$	7.55568	0.345951
$478$	−32.9405	−1.50666
$479$	0.189577	0.00866200	0.00433100	−	0.999991i	$-0.498621\pi$
$479$	0.189577	0.00866200	0.00433100	+	0.999991i	$0.498621\pi$
$480$	−0.179009	−0.00817063
$481$	5.16580	0.235540
$482$	28.5650	1.30110
$483$	4.03436	0.183570
$484$	93.4206	4.24639
$485$	−1.64296	−0.0746031
$486$	−14.0205	−0.635981
$487$	−22.6320	−1.02556	−0.512778	−	0.858521i	$-0.671384\pi$
$487$	−22.6320	−1.02556	−0.512778	+	0.858521i	$0.671384\pi$
$488$	36.1130	1.63476
$489$	0.221428	0.0100133
$490$	1.93599	0.0874592
$491$	0.647174	0.0292065	0.0146033	−	0.999893i	$-0.495351\pi$
$491$	0.647174	0.0292065	0.0146033	+	0.999893i	$0.495351\pi$
$492$	7.51493	0.338799
$493$	0.654686	0.0294856
$494$	−20.0922	−0.903989
$495$	−6.27700	−0.282130
$496$	−17.0252	−0.764452
$497$	−14.8868	−0.667764
$498$	3.45709	0.154916
$499$	23.9341	1.07144	0.535718	−	0.844397i	$-0.320041\pi$
$499$	23.9341	1.07144	0.535718	+	0.844397i	$0.320041\pi$
$500$	13.1255	0.586992
$501$	2.29462	0.102516
$502$	−8.07533	−0.360420
$503$	−20.1640	−0.899066	−0.449533	−	0.893264i	$-0.648410\pi$
$503$	−20.1640	−0.899066	−0.449533	+	0.893264i	$0.648410\pi$
$504$	37.6235	1.67588
$505$	3.29590	0.146666
$506$	85.9650	3.82161
$507$	3.03036	0.134583
$508$	5.36476	0.238023
$509$	30.2751	1.34192	0.670961	−	0.741493i	$-0.265882\pi$
$509$	30.2751	1.34192	0.670961	+	0.741493i	$0.265882\pi$
$510$	0.575694	0.0254922
$511$	28.5912	1.26480
$512$	27.0753	1.19657
$513$	2.13804	0.0943968
$514$	−67.6490	−2.98387
$515$	−3.08275	−0.135842
$516$	−1.76424	−0.0776665
$517$	36.1979	1.59198
$518$	7.30091	0.320783
$519$	1.79553	0.0788150
$520$	−7.67303	−0.336485
$521$	−34.1798	−1.49744	−0.748721	−	0.662885i	$-0.769332\pi$
$521$	−34.1798	−1.49744	−0.748721	+	0.662885i	$0.769332\pi$
$522$	1.51511	0.0663147
$523$	41.3784	1.80935	0.904675	−	0.426101i	$-0.140113\pi$
$523$	41.3784	1.80935	0.904675	+	0.426101i	$0.140113\pi$
$524$	−0.285084	−0.0124540
$525$	−3.28708	−0.143460
$526$	−26.6488	−1.16194
$527$	−20.4710	−0.891730
$528$	−3.37444	−0.146854
$529$	12.7863	0.555925
$530$	−2.17781	−0.0945982
$531$	30.9680	1.34390
$532$	−18.5131	−0.802646
$533$	−46.7980	−2.02705
$534$	−6.69149	−0.289569
$535$	−3.69172	−0.159607
$536$	−41.0683	−1.77388
$537$	0.418833	0.0180740
$538$	−63.8216	−2.75154
$539$	−13.6446	−0.587715
$540$	1.75162	0.0753779
$541$	27.8964	1.19936	0.599680	−	0.800240i	$-0.295295\pi$
$541$	27.8964	1.19936	0.599680	+	0.800240i	$0.295295\pi$
$542$	2.36046	0.101391
$543$	−2.27802	−0.0977592
$544$	6.96420	0.298588
$545$	4.57309	0.195889
$546$	8.35118	0.357397
$547$	−3.64763	−0.155962	−0.0779808	−	0.996955i	$-0.524847\pi$
$547$	−3.64763	−0.155962	−0.0779808	+	0.996955i	$0.524847\pi$
$548$	77.4364	3.30792
$549$	25.4576	1.08650
$550$	−70.0419	−2.98660
$551$	−0.347521	−0.0148049
$552$	−5.54502	−0.236012
$553$	−31.4789	−1.33862
$554$	8.70452	0.369820
$555$	0.0785690	0.00333507
$556$	−4.44897	−0.188678
$557$	−10.1360	−0.429478	−0.214739	−	0.976672i	$-0.568890\pi$
$557$	−10.1360	−0.429478	−0.214739	+	0.976672i	$0.568890\pi$
$558$	−47.3752	−2.00555
$559$	10.9865	0.464681
$560$	−2.74726	−0.116093
$561$	−4.05742	−0.171304
$562$	−11.6816	−0.492757
$563$	22.2162	0.936302	0.468151	−	0.883648i	$-0.344920\pi$
$563$	22.2162	0.936302	0.468151	+	0.883648i	$0.344920\pi$
$564$	−5.00898	−0.210916
$565$	−6.06318	−0.255080
$566$	−30.1273	−1.26634
$567$	26.0744	1.09502
$568$	20.4612	0.858531
$569$	8.76396	0.367404	0.183702	−	0.982982i	$-0.441192\pi$
$569$	8.76396	0.367404	0.183702	+	0.982982i	$0.441192\pi$
$570$	−0.305591	−0.0127998
$571$	−32.3406	−1.35341	−0.676707	−	0.736253i	$-0.736594\pi$
$571$	−32.3406	−1.35341	−0.676707	+	0.736253i	$0.736594\pi$
$572$	116.014	4.85078
$573$	−3.29937	−0.137833
$574$	−66.1403	−2.76064
$575$	−29.1576	−1.21596
$576$	31.1205	1.29669
$577$	−21.8028	−0.907663	−0.453832	−	0.891087i	$-0.649943\pi$
$577$	−21.8028	−0.907663	−0.453832	+	0.891087i	$0.649943\pi$
$578$	18.3546	0.763450
$579$	0.574407	0.0238715
$580$	−0.284712	−0.0118220
$581$	−19.8365	−0.822958
$582$	−2.45775	−0.101877
$583$	15.3489	0.635689
$584$	−39.2972	−1.62613
$585$	−5.40904	−0.223636
$586$	28.6943	1.18535
$587$	−17.3689	−0.716890	−0.358445	−	0.933551i	$-0.616693\pi$
$587$	−17.3689	−0.716890	−0.358445	+	0.933551i	$0.616693\pi$
$588$	1.88811	0.0778643
$589$	10.8664	0.447744
$590$	−8.92607	−0.367480
$591$	−2.15823	−0.0887776
$592$	−2.54214	−0.104481
$593$	−38.7708	−1.59213	−0.796064	−	0.605213i	$-0.793088\pi$
$593$	−38.7708	−1.59213	−0.796064	+	0.605213i	$0.793088\pi$
$594$	−18.9358	−0.776947
$595$	−3.30329	−0.135422
$596$	−78.7273	−3.22480
$597$	−5.34550	−0.218777
$598$	74.0781	3.02928
$599$	6.51104	0.266034	0.133017	−	0.991114i	$-0.457534\pi$
$599$	6.51104	0.266034	0.133017	+	0.991114i	$0.457534\pi$
$600$	4.51793	0.184444
$601$	11.0457	0.450565	0.225282	−	0.974294i	$-0.427670\pi$
$601$	11.0457	0.450565	0.225282	+	0.974294i	$0.427670\pi$
$602$	15.5274	0.632851
$603$	−28.9508	−1.17897
$604$	61.0936	2.48587
$605$	−8.84827	−0.359733
$606$	4.93042	0.200285
$607$	−46.1480	−1.87309	−0.936544	−	0.350550i	$-0.885995\pi$
$607$	−46.1480	−1.87309	−0.936544	+	0.350550i	$0.885995\pi$
$608$	−3.69675	−0.149923
$609$	0.144445	0.00585321
$610$	−7.33777	−0.297098
$611$	31.1926	1.26192
$612$	−33.7919	−1.36596
$613$	−0.458267	−0.0185092	−0.00925462	−	0.999957i	$-0.502946\pi$
$613$	−0.458267	−0.0185092	−0.00925462	+	0.999957i	$0.502946\pi$
$614$	59.5285	2.40238
$615$	−0.711772	−0.0287014
$616$	76.4300	3.07945
$617$	23.3794	0.941220	0.470610	−	0.882341i	$-0.344034\pi$
$617$	23.3794	0.941220	0.470610	+	0.882341i	$0.344034\pi$
$618$	−4.61156	−0.185504
$619$	−28.3228	−1.13839	−0.569195	−	0.822203i	$-0.692745\pi$
$619$	−28.3228	−1.13839	−0.569195	+	0.822203i	$0.692745\pi$
$620$	8.90250	0.357533
$621$	−7.88278	−0.316325
$622$	−44.9335	−1.80167
$623$	38.3953	1.53828
$624$	−2.90784	−0.116407
$625$	23.1273	0.925092
$626$	−36.5448	−1.46063
$627$	2.15376	0.0860130
$628$	−84.1205	−3.35677
$629$	−3.05666	−0.121877
$630$	−7.64468	−0.304571
$631$	19.4911	0.775928	0.387964	−	0.921675i	$-0.373179\pi$
$631$	19.4911	0.775928	0.387964	+	0.921675i	$0.373179\pi$
$632$	43.2661	1.72103
$633$	−1.08369	−0.0430728
$634$	78.0741	3.10072
$635$	−0.508120	−0.0201641
$636$	−2.12395	−0.0842201
$637$	−11.7579	−0.465864
$638$	3.07787	0.121854
$639$	14.4239	0.570601
$640$	−7.35317	−0.290659
$641$	27.2389	1.07587	0.537937	−	0.842985i	$-0.319204\pi$
$641$	27.2389	1.07587	0.537937	+	0.842985i	$0.319204\pi$
$642$	−5.52253	−0.217957
$643$	23.7322	0.935906	0.467953	−	0.883753i	$-0.344992\pi$
$643$	23.7322	0.935906	0.467953	+	0.883753i	$0.344992\pi$
$644$	68.2563	2.68968
$645$	0.167099	0.00657952
$646$	11.8887	0.467756
$647$	20.9134	0.822189	0.411095	−	0.911593i	$-0.365147\pi$
$647$	20.9134	0.822189	0.411095	+	0.911593i	$0.365147\pi$
$648$	−35.8379	−1.40785
$649$	62.9097	2.46942
$650$	−60.3567	−2.36739
$651$	−4.51656	−0.177018
$652$	3.74630	0.146716
$653$	30.5679	1.19621	0.598107	−	0.801416i	$-0.295920\pi$
$653$	30.5679	1.19621	0.598107	+	0.801416i	$0.295920\pi$
$654$	6.84099	0.267504
$655$	0.0270016	0.00105504
$656$	23.0297	0.899159
$657$	−27.7022	−1.08077
$658$	44.0850	1.71861
$659$	−40.6814	−1.58472	−0.792360	−	0.610053i	$-0.791148\pi$
$659$	−40.6814	−1.58472	−0.792360	+	0.610053i	$0.791148\pi$
$660$	1.76451	0.0686833
$661$	−24.0073	−0.933776	−0.466888	−	0.884316i	$-0.654625\pi$
$661$	−24.0073	−0.933776	−0.466888	+	0.884316i	$0.654625\pi$
$662$	−42.5028	−1.65192
$663$	−3.49637	−0.135788
$664$	27.2643	1.05806
$665$	1.75346	0.0679962
$666$	−7.07390	−0.274108
$667$	1.28128	0.0496114
$668$	38.8222	1.50207
$669$	5.75123	0.222355
$670$	8.34463	0.322381
$671$	51.7156	1.99646
$672$	1.53653	0.0592729
$673$	9.26811	0.357259	0.178630	−	0.983916i	$-0.442834\pi$
$673$	9.26811	0.357259	0.178630	+	0.983916i	$0.442834\pi$
$674$	−49.3024	−1.89906
$675$	6.42267	0.247209
$676$	51.2699	1.97192
$677$	−1.79652	−0.0690459	−0.0345229	−	0.999404i	$-0.510991\pi$
$677$	−1.79652	−0.0690459	−0.0345229	+	0.999404i	$0.510991\pi$
$678$	−9.07006	−0.348333
$679$	14.1024	0.541200
$680$	4.54021	0.174109
$681$	2.99260	0.114677
$682$	−96.2400	−3.68522
$683$	−9.09290	−0.347930	−0.173965	−	0.984752i	$-0.555658\pi$
$683$	−9.09290	−0.347930	−0.173965	+	0.984752i	$0.555658\pi$
$684$	17.9375	0.685857
$685$	−7.33434	−0.280231
$686$	34.4887	1.31679
$687$	5.01286	0.191253
$688$	−5.40657	−0.206124
$689$	13.2266	0.503891
$690$	1.12669	0.0428923
$691$	38.4315	1.46200	0.731001	−	0.682376i	$-0.239053\pi$
$691$	38.4315	1.46200	0.731001	+	0.682376i	$0.239053\pi$
$692$	30.3781	1.15480
$693$	53.8787	2.04668
$694$	−36.3035	−1.37806
$695$	0.421381	0.0159839
$696$	−0.198532	−0.00752535
$697$	27.6908	1.04887
$698$	8.60367	0.325654
$699$	−0.387211	−0.0146457
$700$	−55.6133	−2.10199
$701$	33.4290	1.26259	0.631297	−	0.775541i	$-0.282523\pi$
$701$	33.4290	1.26259	0.631297	+	0.775541i	$0.282523\pi$
$702$	−16.3175	−0.615863
$703$	1.62254	0.0611952
$704$	63.2196	2.38268
$705$	0.474422	0.0178678
$706$	5.27081	0.198369
$707$	−28.2904	−1.06397
$708$	−8.70530	−0.327165
$709$	27.4365	1.03040	0.515200	−	0.857070i	$-0.327718\pi$
$709$	27.4365	1.03040	0.515200	+	0.857070i	$0.327718\pi$
$710$	−4.15748	−0.156027
$711$	30.5001	1.14384
$712$	−52.7725	−1.97773
$713$	−40.0636	−1.50039
$714$	−4.94148	−0.184930
$715$	−10.9882	−0.410934
$716$	7.08614	0.264821
$717$	3.04277	0.113634
$718$	21.8348	0.814869
$719$	−8.92415	−0.332815	−0.166407	−	0.986057i	$-0.553217\pi$
$719$	−8.92415	−0.332815	−0.166407	+	0.986057i	$0.553217\pi$
$720$	2.66184	0.0992008
$721$	26.4608	0.985452
$722$	39.2349	1.46017
$723$	−2.63860	−0.0981306
$724$	−38.5413	−1.43237
$725$	−1.04395	−0.0387714
$726$	−13.2363	−0.491247
$727$	44.7951	1.66136	0.830679	−	0.556751i	$-0.187952\pi$
$727$	44.7951	1.66136	0.830679	+	0.556751i	$0.187952\pi$
$728$	65.8615	2.44099
$729$	−24.3883	−0.903270
$730$	7.98476	0.295529
$731$	−6.50084	−0.240442
$732$	−7.15628	−0.264504
$733$	33.0229	1.21973	0.609865	−	0.792506i	$-0.291224\pi$
$733$	33.0229	1.21973	0.609865	+	0.792506i	$0.291224\pi$
$734$	−6.10236	−0.225242
$735$	−0.178831	−0.00659628
$736$	13.6296	0.502393
$737$	−58.8119	−2.16636
$738$	64.0838	2.35896
$739$	−11.0067	−0.404888	−0.202444	−	0.979294i	$-0.564888\pi$
$739$	−11.0067	−0.404888	−0.202444	+	0.979294i	$0.564888\pi$
$740$	1.32929	0.0488657
$741$	1.85595	0.0681800
$742$	18.6933	0.686252
$743$	−36.5958	−1.34257	−0.671286	−	0.741199i	$-0.734258\pi$
$743$	−36.5958	−1.34257	−0.671286	+	0.741199i	$0.734258\pi$
$744$	6.20779	0.227589
$745$	7.45661	0.273189
$746$	−25.2495	−0.924451
$747$	19.2197	0.703214
$748$	−68.6465	−2.50996
$749$	31.6879	1.15785
$750$	−1.85970	−0.0679066
$751$	−26.7671	−0.976744	−0.488372	−	0.872636i	$-0.662409\pi$
$751$	−26.7671	−0.976744	−0.488372	+	0.872636i	$0.662409\pi$
$752$	−15.3502	−0.559762
$753$	0.745933	0.0271833
$754$	2.65227	0.0965900
$755$	−5.78645	−0.210590
$756$	−15.0351	−0.546821
$757$	28.8244	1.04764	0.523821	−	0.851828i	$-0.324506\pi$
$757$	28.8244	1.04764	0.523821	+	0.851828i	$0.324506\pi$
$758$	35.5811	1.29236
$759$	−7.94075	−0.288231
$760$	−2.41004	−0.0874214
$761$	4.11804	0.149279	0.0746393	−	0.997211i	$-0.476219\pi$
$761$	4.11804	0.149279	0.0746393	+	0.997211i	$0.476219\pi$
$762$	−0.760108	−0.0275358
$763$	−39.2531	−1.42106
$764$	−55.8212	−2.01954
$765$	3.20058	0.115717
$766$	−42.0510	−1.51936
$767$	54.2108	1.95744
$768$	−6.32947	−0.228395
$769$	20.4808	0.738555	0.369278	−	0.929319i	$-0.379605\pi$
$769$	20.4808	0.738555	0.369278	+	0.929319i	$0.379605\pi$
$770$	−15.5297	−0.559653
$771$	6.24886	0.225047
$772$	9.71826	0.349768
$773$	48.3074	1.73750	0.868748	−	0.495254i	$-0.164925\pi$
$773$	48.3074	1.73750	0.868748	+	0.495254i	$0.164925\pi$
$774$	−15.0446	−0.540768
$775$	32.6427	1.17256
$776$	−19.3830	−0.695810
$777$	−0.674398	−0.0241939
$778$	−89.6326	−3.21348
$779$	−14.6989	−0.526642
$780$	1.52052	0.0544432
$781$	29.3014	1.04849
$782$	−43.8327	−1.56746
$783$	−0.282233	−0.0100862
$784$	5.78616	0.206649
$785$	7.96742	0.284369
$786$	0.0403923	0.00144075
$787$	−0.722066	−0.0257389	−0.0128694	−	0.999917i	$-0.504097\pi$
$787$	−0.722066	−0.0257389	−0.0128694	+	0.999917i	$0.504097\pi$
$788$	−36.5145	−1.30078
$789$	2.46160	0.0876353
$790$	−8.79120	−0.312777
$791$	52.0434	1.85045
$792$	−74.0536	−2.63138
$793$	44.5646	1.58253
$794$	70.4822	2.50132
$795$	0.201169	0.00713472
$796$	−90.4392	−3.20553
$797$	−47.3011	−1.67549	−0.837745	−	0.546062i	$-0.816126\pi$
$797$	−47.3011	−1.67549	−0.837745	+	0.546062i	$0.816126\pi$
$798$	2.62304	0.0928547
$799$	−18.4570	−0.652960
$800$	−11.1050	−0.392621
$801$	−37.2015	−1.31445
$802$	60.4732	2.13538
$803$	−56.2755	−1.98592
$804$	8.13825	0.287014
$805$	−6.46486	−0.227856
$806$	−82.9323	−2.92116
$807$	5.89531	0.207525
$808$	38.8838	1.36793
$809$	−43.7716	−1.53893	−0.769464	−	0.638690i	$-0.779477\pi$
$809$	−43.7716	−1.53893	−0.769464	+	0.638690i	$0.779477\pi$
$810$	7.28187	0.255859
$811$	34.6706	1.21745	0.608725	−	0.793381i	$-0.291681\pi$
$811$	34.6706	1.21745	0.608725	+	0.793381i	$0.291681\pi$
$812$	2.44383	0.0857616
$813$	−0.218040	−0.00764700
$814$	−14.3702	−0.503676
$815$	−0.354828	−0.0124291
$816$	1.72060	0.0602329
$817$	3.45079	0.120728
$818$	−29.2082	−1.02124
$819$	46.4285	1.62234
$820$	−12.0423	−0.420535
$821$	26.8042	0.935474	0.467737	−	0.883868i	$-0.345069\pi$
$821$	26.8042	0.935474	0.467737	+	0.883868i	$0.345069\pi$
$822$	−10.9716	−0.382679
$823$	5.43745	0.189538	0.0947689	−	0.995499i	$-0.469789\pi$
$823$	5.43745	0.189538	0.0947689	+	0.995499i	$0.469789\pi$
$824$	−36.3691	−1.26698
$825$	6.46990	0.225253
$826$	76.6170	2.66585
$827$	−15.9003	−0.552907	−0.276454	−	0.961027i	$-0.589159\pi$
$827$	−15.9003	−0.552907	−0.276454	+	0.961027i	$0.589159\pi$
$828$	−66.1340	−2.29832
$829$	−20.7258	−0.719837	−0.359919	−	0.932984i	$-0.617196\pi$
$829$	−20.7258	−0.719837	−0.359919	+	0.932984i	$0.617196\pi$
$830$	−5.53981	−0.192290
$831$	−0.804053	−0.0278923
$832$	54.4778	1.88868
$833$	6.95726	0.241055
$834$	0.630354	0.0218274
$835$	−3.67702	−0.127248
$836$	36.4390	1.26027
$837$	8.82497	0.305036
$838$	−33.5944	−1.16050
$839$	−16.0384	−0.553708	−0.276854	−	0.960912i	$-0.589292\pi$
$839$	−16.0384	−0.553708	−0.276854	+	0.960912i	$0.589292\pi$
$840$	1.00172	0.0345626
$841$	−28.9541	−0.998418
$842$	11.1587	0.384553
$843$	1.07905	0.0371643
$844$	−18.3347	−0.631106
$845$	−4.85599	−0.167051
$846$	−42.7142	−1.46854
$847$	75.9492	2.60965
$848$	−6.50891	−0.223517
$849$	2.78291	0.0955093
$850$	35.7137	1.22497
$851$	−5.98216	−0.205066
$852$	−4.05465	−0.138910
$853$	−5.89645	−0.201891	−0.100945	−	0.994892i	$-0.532187\pi$
$853$	−5.89645	−0.201891	−0.100945	+	0.994892i	$0.532187\pi$
$854$	62.9838	2.15526
$855$	−1.69894	−0.0581025
$856$	−43.5534	−1.48863
$857$	37.1351	1.26851	0.634256	−	0.773123i	$-0.281307\pi$
$857$	37.1351	1.26851	0.634256	+	0.773123i	$0.281307\pi$
$858$	−16.4375	−0.561166
$859$	36.7642	1.25438	0.627189	−	0.778867i	$-0.284205\pi$
$859$	36.7642	1.25438	0.627189	+	0.778867i	$0.284205\pi$
$860$	2.82711	0.0964037
$861$	6.10950	0.208211
$862$	65.9220	2.24531
$863$	16.0280	0.545600	0.272800	−	0.962071i	$-0.412050\pi$
$863$	16.0280	0.545600	0.272800	+	0.962071i	$0.412050\pi$
$864$	−3.00224	−0.102138
$865$	−2.87725	−0.0978293
$866$	55.6678	1.89167
$867$	−1.69545	−0.0575804
$868$	−76.4147	−2.59368
$869$	61.9592	2.10182
$870$	0.0403396	0.00136764
$871$	−50.6796	−1.71721
$872$	53.9514	1.82703
$873$	−13.6639	−0.462453
$874$	23.2674	0.787030
$875$	10.6708	0.360740
$876$	7.78727	0.263108
$877$	−15.9792	−0.539579	−0.269789	−	0.962919i	$-0.586954\pi$
$877$	−15.9792	−0.539579	−0.269789	+	0.962919i	$0.586954\pi$
$878$	−40.2335	−1.35781
$879$	−2.65055	−0.0894007
$880$	5.40738	0.182283
$881$	5.01570	0.168983	0.0844916	−	0.996424i	$-0.473073\pi$
$881$	5.01570	0.168983	0.0844916	+	0.996424i	$0.473073\pi$
$882$	16.1009	0.542146
$883$	−31.6343	−1.06458	−0.532290	−	0.846562i	$-0.678668\pi$
$883$	−31.6343	−1.06458	−0.532290	+	0.846562i	$0.678668\pi$
$884$	−59.1543	−1.98957
$885$	0.824517	0.0277158
$886$	−37.5926	−1.26295
$887$	4.70876	0.158105	0.0790524	−	0.996870i	$-0.474811\pi$
$887$	4.70876	0.158105	0.0790524	+	0.996870i	$0.474811\pi$
$888$	0.926926	0.0311056
$889$	4.36145	0.146278
$890$	10.7228	0.359428
$891$	−51.3217	−1.71934
$892$	97.3036	3.25797
$893$	9.79735	0.327856
$894$	11.1545	0.373063
$895$	−0.671159	−0.0224344
$896$	63.1160	2.10856
$897$	−6.84273	−0.228472
$898$	−26.0255	−0.868482
$899$	−1.43443	−0.0478408
$900$	53.8841	1.79614
$901$	−7.82628	−0.260731
$902$	130.183	4.33461
$903$	−1.43430	−0.0477304
$904$	−71.5310	−2.37908
$905$	3.65041	0.121344
$906$	−8.65608	−0.287579
$907$	56.1352	1.86394	0.931969	−	0.362539i	$-0.118090\pi$
$907$	56.1352	1.86394	0.931969	+	0.362539i	$0.118090\pi$
$908$	50.6310	1.68025
$909$	27.4108	0.909158
$910$	−13.3823	−0.443620
$911$	−45.7810	−1.51679	−0.758397	−	0.651793i	$-0.774017\pi$
$911$	−45.7810	−1.51679	−0.758397	+	0.651793i	$0.774017\pi$
$912$	−0.913329	−0.0302434
$913$	39.0438	1.29216
$914$	11.6173	0.384267
$915$	0.677803	0.0224075
$916$	84.8114	2.80225
$917$	−0.231768	−0.00765366
$918$	9.65521	0.318669
$919$	44.4958	1.46778	0.733890	−	0.679269i	$-0.237703\pi$
$919$	44.4958	1.46778	0.733890	+	0.679269i	$0.237703\pi$
$920$	8.88562	0.292950
$921$	−5.49876	−0.181190
$922$	−38.8503	−1.27947
$923$	25.2497	0.831104
$924$	−15.1456	−0.498255
$925$	4.87410	0.160259
$926$	−13.3257	−0.437911
$927$	−25.6381	−0.842064
$928$	0.487990	0.0160191
$929$	−24.7556	−0.812206	−0.406103	−	0.913827i	$-0.633113\pi$
$929$	−24.7556	−0.812206	−0.406103	+	0.913827i	$0.633113\pi$
$930$	−1.26135	−0.0413615
$931$	−3.69306	−0.121035
$932$	−6.55113	−0.214589
$933$	4.15059	0.135884
$934$	−73.9395	−2.41937
$935$	6.50181	0.212632
$936$	−63.8137	−2.08582
$937$	36.7525	1.20065	0.600326	−	0.799756i	$-0.295038\pi$
$937$	36.7525	1.20065	0.600326	+	0.799756i	$0.295038\pi$
$938$	−71.6262	−2.33868
$939$	3.37571	0.110162
$940$	8.02664	0.261800
$941$	−23.0878	−0.752642	−0.376321	−	0.926489i	$-0.622811\pi$
$941$	−23.0878	−0.752642	−0.376321	+	0.926489i	$0.622811\pi$
$942$	11.9187	0.388331
$943$	54.1936	1.76479
$944$	−26.6776	−0.868283
$945$	1.42404	0.0463240
$946$	−30.5623	−0.993667
$947$	−12.0655	−0.392075	−0.196037	−	0.980596i	$-0.562807\pi$
$947$	−12.0655	−0.392075	−0.196037	+	0.980596i	$0.562807\pi$
$948$	−8.57377	−0.278463
$949$	−48.4939	−1.57418
$950$	−18.9576	−0.615065
$951$	−7.21185	−0.233860
$952$	−38.9709	−1.26306
$953$	42.2055	1.36717	0.683586	−	0.729870i	$-0.260420\pi$
$953$	42.2055	1.36717	0.683586	+	0.729870i	$0.260420\pi$
$954$	−18.1121	−0.586399
$955$	5.28707	0.171086
$956$	51.4799	1.66498
$957$	−0.284308	−0.00919038
$958$	−0.454444	−0.0146824
$959$	62.9543	2.03290
$960$	0.828578	0.0267422
$961$	13.8522	0.446846
$962$	−12.3832	−0.399249
$963$	−30.7026	−0.989378
$964$	−44.6419	−1.43782
$965$	−0.920459	−0.0296306
$966$	−9.67093	−0.311157
$967$	19.2204	0.618088	0.309044	−	0.951048i	$-0.399991\pi$
$967$	19.2204	0.618088	0.309044	+	0.951048i	$0.399991\pi$
$968$	−104.388	−3.35517
$969$	−1.09818	−0.0352787
$970$	3.93842	0.126455
$971$	58.0289	1.86224	0.931118	−	0.364717i	$-0.118834\pi$
$971$	58.0289	1.86224	0.931118	+	0.364717i	$0.118834\pi$
$972$	21.9114	0.702809
$973$	−3.61693	−0.115953
$974$	54.2523	1.73835
$975$	5.57526	0.178551
$976$	−21.9306	−0.701982
$977$	−39.0266	−1.24857	−0.624285	−	0.781196i	$-0.714610\pi$
$977$	−39.0266	−1.24857	−0.624285	+	0.781196i	$0.714610\pi$
$978$	−0.530796	−0.0169730
$979$	−75.5728	−2.41532
$980$	−3.02560	−0.0966492
$981$	38.0326	1.21429
$982$	−1.55137	−0.0495061
$983$	−57.5874	−1.83675	−0.918377	−	0.395707i	$-0.870499\pi$
$983$	−57.5874	−1.83675	−0.918377	+	0.395707i	$0.870499\pi$
$984$	−8.39720	−0.267693
$985$	3.45845	0.110195
$986$	−1.56938	−0.0499791
$987$	−4.07221	−0.129620
$988$	31.4004	0.998978
$989$	−12.7228	−0.404560
$990$	15.0469	0.478221
$991$	2.25977	0.0717841	0.0358920	−	0.999356i	$-0.488573\pi$
$991$	2.25977	0.0717841	0.0358920	+	0.999356i	$0.488573\pi$
$992$	−15.2587	−0.484463
$993$	3.92606	0.124590
$994$	35.6858	1.13188
$995$	8.56589	0.271557
$996$	−5.40279	−0.171194
$997$	28.0259	0.887589	0.443794	−	0.896129i	$-0.353632\pi$
$997$	28.0259	0.887589	0.443794	+	0.896129i	$0.353632\pi$
$998$	−57.3734	−1.81612
$999$	1.31771	0.0416906

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6031.2.a.d.1.11	✓	133

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6031.2.a.d.1.11	✓	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)

\(f(q)\)	\(=\)	\(q-2.39714 q^{2} +0.221428 q^{3} +3.74630 q^{4} -0.354828 q^{5} -0.530796 q^{6} +3.04567 q^{7} -4.18612 q^{8} -2.95097 q^{9} +O(q^{10})\)	\(q-2.39714 q^{2} +0.221428 q^{3} +3.74630 q^{4} -0.354828 q^{5} -0.530796 q^{6} +3.04567 q^{7} -4.18612 q^{8} -2.95097 q^{9} +0.850573 q^{10} -5.99473 q^{11} +0.829536 q^{12} -5.16580 q^{13} -7.30091 q^{14} -0.0785690 q^{15} +2.54214 q^{16} +3.05666 q^{17} +7.07390 q^{18} -1.62254 q^{19} -1.32929 q^{20} +0.674398 q^{21} +14.3702 q^{22} +5.98216 q^{23} -0.926926 q^{24} -4.87410 q^{25} +12.3832 q^{26} -1.31771 q^{27} +11.4100 q^{28} +0.214184 q^{29} +0.188341 q^{30} -6.69718 q^{31} +2.27837 q^{32} -1.32740 q^{33} -7.32724 q^{34} -1.08069 q^{35} -11.0552 q^{36} -1.00000 q^{37} +3.88946 q^{38} -1.14386 q^{39} +1.48535 q^{40} +9.05919 q^{41} -1.61663 q^{42} -2.12678 q^{43} -22.4580 q^{44} +1.04709 q^{45} -14.3401 q^{46} -6.03829 q^{47} +0.562902 q^{48} +2.27610 q^{49} +11.6839 q^{50} +0.676831 q^{51} -19.3526 q^{52} -2.56041 q^{53} +3.15875 q^{54} +2.12710 q^{55} -12.7495 q^{56} -0.359276 q^{57} -0.513429 q^{58} -10.4942 q^{59} -0.294343 q^{60} -8.62685 q^{61} +16.0541 q^{62} -8.98768 q^{63} -10.5459 q^{64} +1.83297 q^{65} +3.18198 q^{66} +9.81060 q^{67} +11.4511 q^{68} +1.32462 q^{69} +2.59057 q^{70} -4.88786 q^{71} +12.3531 q^{72} +9.38750 q^{73} +2.39714 q^{74} -1.07926 q^{75} -6.07851 q^{76} -18.2580 q^{77} +2.74198 q^{78} -10.3356 q^{79} -0.902021 q^{80} +8.56113 q^{81} -21.7162 q^{82} -6.51303 q^{83} +2.52649 q^{84} -1.08459 q^{85} +5.09820 q^{86} +0.0474264 q^{87} +25.0947 q^{88} +12.6065 q^{89} -2.51002 q^{90} -15.7333 q^{91} +22.4109 q^{92} -1.48295 q^{93} +14.4746 q^{94} +0.575722 q^{95} +0.504496 q^{96} +4.63031 q^{97} -5.45614 q^{98} +17.6903 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 133 q + 14 q^{2} + 8 q^{3} + 142 q^{4} + 34 q^{5} + 20 q^{6} + 8 q^{7} + 42 q^{8} + 177 q^{9}+O(q^{10}) \) 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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