LMFDB - Embedded newform 6037.2.a.b.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6037,2,Mod(1,6037)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6037, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6037.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6037 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6037.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:	$48.2056877002$
Analytic rank:	$0$
Dimension:	$259$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Character	$\chi$	$=$	6037.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.60071 q^{2} -0.749599 q^{3} +4.76372 q^{4} -3.60076 q^{5} +1.94949 q^{6} -2.40322 q^{7} -7.18764 q^{8} -2.43810 q^{9} +O(q^{10})$	\(q-2.60071 q^{2} -0.749599 q^{3} +4.76372 q^{4} -3.60076 q^{5} +1.94949 q^{6} -2.40322 q^{7} -7.18764 q^{8} -2.43810 q^{9} +9.36455 q^{10} +2.22014 q^{11} -3.57088 q^{12} -2.00163 q^{13} +6.25010 q^{14} +2.69912 q^{15} +9.16557 q^{16} +4.82130 q^{17} +6.34081 q^{18} -2.15015 q^{19} -17.1530 q^{20} +1.80145 q^{21} -5.77395 q^{22} +1.89464 q^{23} +5.38785 q^{24} +7.96546 q^{25} +5.20568 q^{26} +4.07639 q^{27} -11.4483 q^{28} -2.11811 q^{29} -7.01965 q^{30} +0.688943 q^{31} -9.46175 q^{32} -1.66421 q^{33} -12.5388 q^{34} +8.65343 q^{35} -11.6144 q^{36} +4.93426 q^{37} +5.59193 q^{38} +1.50042 q^{39} +25.8810 q^{40} -1.43704 q^{41} -4.68507 q^{42} -9.03240 q^{43} +10.5761 q^{44} +8.77902 q^{45} -4.92742 q^{46} +7.66993 q^{47} -6.87050 q^{48} -1.22452 q^{49} -20.7159 q^{50} -3.61404 q^{51} -9.53522 q^{52} -1.61201 q^{53} -10.6015 q^{54} -7.99419 q^{55} +17.2735 q^{56} +1.61175 q^{57} +5.50859 q^{58} -6.77799 q^{59} +12.8579 q^{60} -9.48597 q^{61} -1.79174 q^{62} +5.85930 q^{63} +6.27617 q^{64} +7.20740 q^{65} +4.32814 q^{66} +3.30456 q^{67} +22.9673 q^{68} -1.42022 q^{69} -22.5051 q^{70} +4.23793 q^{71} +17.5242 q^{72} +4.90703 q^{73} -12.8326 q^{74} -5.97090 q^{75} -10.2427 q^{76} -5.33549 q^{77} -3.90217 q^{78} -13.0263 q^{79} -33.0030 q^{80} +4.25865 q^{81} +3.73732 q^{82} -14.0724 q^{83} +8.58161 q^{84} -17.3603 q^{85} +23.4907 q^{86} +1.58773 q^{87} -15.9576 q^{88} -10.5387 q^{89} -22.8317 q^{90} +4.81038 q^{91} +9.02553 q^{92} -0.516431 q^{93} -19.9473 q^{94} +7.74217 q^{95} +7.09251 q^{96} -17.5159 q^{97} +3.18462 q^{98} -5.41293 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 259 q + 47 q^{2} + 29 q^{3} + 273 q^{4} + 38 q^{5} + 24 q^{6} + 42 q^{7} + 141 q^{8} + 286 q^{9}+O(q^{10}) $ 259 * q + 47 * q^2 + 29 * q^3 + 273 * q^4 + 38 * q^5 + 24 * q^6 + 42 * q^7 + 141 * q^8 + 286 * q^9	\( 259 q + 47 q^{2} + 29 q^{3} + 273 q^{4} + 38 q^{5} + 24 q^{6} + 42 q^{7} + 141 q^{8} + 286 q^{9} + 18 q^{10} + 108 q^{11} + 46 q^{12} + 33 q^{13} + 35 q^{14} + 40 q^{15} + 301 q^{16} + 67 q^{17} + 117 q^{18} + 69 q^{19} + 103 q^{20} + 24 q^{21} + 42 q^{22} + 162 q^{23} + 45 q^{24} + 291 q^{25} + 41 q^{26} + 101 q^{27} + 87 q^{28} + 78 q^{29} + 48 q^{30} + 25 q^{31} + 314 q^{32} + 67 q^{33} + 9 q^{34} + 252 q^{35} + 337 q^{36} + 49 q^{37} + 59 q^{38} + 93 q^{39} + 44 q^{40} + 60 q^{41} + 38 q^{42} + 178 q^{43} + 171 q^{44} + 67 q^{45} + 43 q^{46} + 185 q^{47} + 67 q^{48} + 273 q^{49} + 204 q^{50} + 145 q^{51} + 83 q^{52} + 112 q^{53} + 60 q^{54} + 57 q^{55} + 93 q^{56} + 109 q^{57} + 63 q^{58} + 228 q^{59} + 53 q^{60} + 20 q^{61} + 126 q^{62} + 153 q^{63} + 345 q^{64} + 113 q^{65} + 5 q^{66} + 208 q^{67} + 166 q^{68} + 10 q^{69} + 69 q^{70} + 150 q^{71} + 331 q^{72} + 75 q^{73} + 84 q^{74} + 72 q^{75} + 102 q^{76} + 166 q^{77} + 69 q^{78} + 52 q^{79} + 180 q^{80} + 327 q^{81} + 43 q^{82} + 434 q^{83} + 75 q^{85} + 133 q^{86} + 144 q^{87} + 111 q^{88} + 78 q^{89} - 8 q^{90} + 35 q^{91} + 372 q^{92} + 160 q^{93} + 36 q^{94} + 154 q^{95} + 60 q^{96} + 35 q^{97} + 254 q^{98} + 234 q^{99}+O(q^{100}) \) 259 * q + 47 * q^2 + 29 * q^3 + 273 * q^4 + 38 * q^5 + 24 * q^6 + 42 * q^7 + 141 * q^8 + 286 * q^9 + 18 * q^10 + 108 * q^11 + 46 * q^12 + 33 * q^13 + 35 * q^14 + 40 * q^15 + 301 * q^16 + 67 * q^17 + 117 * q^18 + 69 * q^19 + 103 * q^20 + 24 * q^21 + 42 * q^22 + 162 * q^23 + 45 * q^24 + 291 * q^25 + 41 * q^26 + 101 * q^27 + 87 * q^28 + 78 * q^29 + 48 * q^30 + 25 * q^31 + 314 * q^32 + 67 * q^33 + 9 * q^34 + 252 * q^35 + 337 * q^36 + 49 * q^37 + 59 * q^38 + 93 * q^39 + 44 * q^40 + 60 * q^41 + 38 * q^42 + 178 * q^43 + 171 * q^44 + 67 * q^45 + 43 * q^46 + 185 * q^47 + 67 * q^48 + 273 * q^49 + 204 * q^50 + 145 * q^51 + 83 * q^52 + 112 * q^53 + 60 * q^54 + 57 * q^55 + 93 * q^56 + 109 * q^57 + 63 * q^58 + 228 * q^59 + 53 * q^60 + 20 * q^61 + 126 * q^62 + 153 * q^63 + 345 * q^64 + 113 * q^65 + 5 * q^66 + 208 * q^67 + 166 * q^68 + 10 * q^69 + 69 * q^70 + 150 * q^71 + 331 * q^72 + 75 * q^73 + 84 * q^74 + 72 * q^75 + 102 * q^76 + 166 * q^77 + 69 * q^78 + 52 * q^79 + 180 * q^80 + 327 * q^81 + 43 * q^82 + 434 * q^83 + 75 * q^85 + 133 * q^86 + 144 * q^87 + 111 * q^88 + 78 * q^89 - 8 * q^90 + 35 * q^91 + 372 * q^92 + 160 * q^93 + 36 * q^94 + 154 * q^95 + 60 * q^96 + 35 * q^97 + 254 * q^98 + 234 * 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 $

$2$	−2.60071	−1.83898	−0.919492	−	0.393110i	$-0.871399\pi$
$2$	−2.60071	−1.83898	−0.919492	+	0.393110i	$0.871399\pi$
$3$	−0.749599	−0.432781	−0.216390	−	0.976307i	$-0.569428\pi$
$3$	−0.749599	−0.432781	−0.216390	+	0.976307i	$0.569428\pi$
$4$	4.76372	2.38186
$5$	−3.60076	−1.61031	−0.805154	−	0.593066i	$-0.797917\pi$
$5$	−3.60076	−1.61031	−0.805154	+	0.593066i	$0.797917\pi$
$6$	1.94949	0.795877
$7$	−2.40322	−0.908333	−0.454167	−	0.890917i	$-0.650063\pi$
$7$	−2.40322	−0.908333	−0.454167	+	0.890917i	$0.650063\pi$
$8$	−7.18764	−2.54121
$9$	−2.43810	−0.812701
$10$	9.36455	2.96133
$11$	2.22014	0.669397	0.334699	−	0.942325i	$-0.391366\pi$
$11$	2.22014	0.669397	0.334699	+	0.942325i	$0.391366\pi$
$12$	−3.57088	−1.03082
$13$	−2.00163	−0.555154	−0.277577	−	0.960703i	$-0.589531\pi$
$13$	−2.00163	−0.555154	−0.277577	+	0.960703i	$0.589531\pi$
$14$	6.25010	1.67041
$15$	2.69912	0.696911
$16$	9.16557	2.29139
$17$	4.82130	1.16934	0.584669	−	0.811272i	$-0.301225\pi$
$17$	4.82130	1.16934	0.584669	+	0.811272i	$0.301225\pi$
$18$	6.34081	1.49454
$19$	−2.15015	−0.493278	−0.246639	−	0.969107i	$-0.579326\pi$
$19$	−2.15015	−0.493278	−0.246639	+	0.969107i	$0.579326\pi$
$20$	−17.1530	−3.83553
$21$	1.80145	0.393109
$22$	−5.77395	−1.23101
$23$	1.89464	0.395060	0.197530	−	0.980297i	$-0.436708\pi$
$23$	1.89464	0.395060	0.197530	+	0.980297i	$0.436708\pi$
$24$	5.38785	1.09979
$25$	7.96546	1.59309
$26$	5.20568	1.02092
$27$	4.07639	0.784502
$28$	−11.4483	−2.16352
$29$	−2.11811	−0.393322	−0.196661	−	0.980472i	$-0.563010\pi$
$29$	−2.11811	−0.393322	−0.196661	+	0.980472i	$0.563010\pi$
$30$	−7.01965	−1.28161
$31$	0.688943	0.123738	0.0618689	−	0.998084i	$-0.480294\pi$
$31$	0.688943	0.123738	0.0618689	+	0.998084i	$0.480294\pi$
$32$	−9.46175	−1.67262
$33$	−1.66421	−0.289702
$34$	−12.5388	−2.15039
$35$	8.65343	1.46270
$36$	−11.6144	−1.93574
$37$	4.93426	0.811188	0.405594	−	0.914053i	$-0.367065\pi$
$37$	4.93426	0.811188	0.405594	+	0.914053i	$0.367065\pi$
$38$	5.59193	0.907131
$39$	1.50042	0.240260
$40$	25.8810	4.09214
$41$	−1.43704	−0.224427	−0.112214	−	0.993684i	$-0.535794\pi$
$41$	−1.43704	−0.224427	−0.112214	+	0.993684i	$0.535794\pi$
$42$	−4.68507	−0.722921
$43$	−9.03240	−1.37743	−0.688714	−	0.725033i	$-0.741824\pi$
$43$	−9.03240	−1.37743	−0.688714	+	0.725033i	$0.741824\pi$
$44$	10.5761	1.59441
$45$	8.77902	1.30870
$46$	−4.92742	−0.726509
$47$	7.66993	1.11877	0.559387	−	0.828907i	$-0.311037\pi$
$47$	7.66993	1.11877	0.559387	+	0.828907i	$0.311037\pi$
$48$	−6.87050	−0.991671
$49$	−1.22452	−0.174931
$50$	−20.7159	−2.92967
$51$	−3.61404	−0.506067
$52$	−9.53522	−1.32230
$53$	−1.61201	−0.221427	−0.110714	−	0.993852i	$-0.535314\pi$
$53$	−1.61201	−0.221427	−0.110714	+	0.993852i	$0.535314\pi$
$54$	−10.6015	−1.44269
$55$	−7.99419	−1.07794
$56$	17.2735	2.30827
$57$	1.61175	0.213481
$58$	5.50859	0.723313
$59$	−6.77799	−0.882419	−0.441209	−	0.897404i	$-0.645450\pi$
$59$	−6.77799	−0.882419	−0.441209	+	0.897404i	$0.645450\pi$
$60$	12.8579	1.65994
$61$	−9.48597	−1.21455	−0.607277	−	0.794490i	$-0.707738\pi$
$61$	−9.48597	−1.21455	−0.607277	+	0.794490i	$0.707738\pi$
$62$	−1.79174	−0.227552
$63$	5.85930	0.738203
$64$	6.27617	0.784522
$65$	7.20740	0.893969
$66$	4.32814	0.532758
$67$	3.30456	0.403717	0.201858	−	0.979415i	$-0.435302\pi$
$67$	3.30456	0.403717	0.201858	+	0.979415i	$0.435302\pi$
$68$	22.9673	2.78520
$69$	−1.42022	−0.170974
$70$	−22.5051	−2.68987
$71$	4.23793	0.502950	0.251475	−	0.967864i	$-0.419084\pi$
$71$	4.23793	0.502950	0.251475	+	0.967864i	$0.419084\pi$
$72$	17.5242	2.06525
$73$	4.90703	0.574325	0.287162	−	0.957882i	$-0.407288\pi$
$73$	4.90703	0.574325	0.287162	+	0.957882i	$0.407288\pi$
$74$	−12.8326	−1.49176
$75$	−5.97090	−0.689460
$76$	−10.2427	−1.17492
$77$	−5.33549	−0.608036
$78$	−3.90217	−0.441834
$79$	−13.0263	−1.46558	−0.732789	−	0.680456i	$-0.761782\pi$
$79$	−13.0263	−1.46558	−0.732789	+	0.680456i	$0.761782\pi$
$80$	−33.0030	−3.68985
$81$	4.25865	0.473183
$82$	3.73732	0.412718
$83$	−14.0724	−1.54465	−0.772324	−	0.635229i	$-0.780906\pi$
$83$	−14.0724	−1.54465	−0.772324	+	0.635229i	$0.780906\pi$
$84$	8.58161	0.936331
$85$	−17.3603	−1.88299
$86$	23.4907	2.53307
$87$	1.58773	0.170222
$88$	−15.9576	−1.70108
$89$	−10.5387	−1.11710	−0.558550	−	0.829471i	$-0.688642\pi$
$89$	−10.5387	−1.11710	−0.558550	+	0.829471i	$0.688642\pi$
$90$	−22.8317	−2.40667
$91$	4.81038	0.504264
$92$	9.02553	0.940977
$93$	−0.516431	−0.0535513
$94$	−19.9473	−2.05741
$95$	7.74217	0.794330
$96$	7.09251	0.723877
$97$	−17.5159	−1.77847	−0.889236	−	0.457448i	$-0.848763\pi$
$97$	−17.5159	−1.77847	−0.889236	+	0.457448i	$0.848763\pi$
$98$	3.18462	0.321695
$99$	−5.41293	−0.544019
$100$	37.9452	3.79452
$101$	−14.1313	−1.40612	−0.703061	−	0.711130i	$-0.748184\pi$
$101$	−14.1313	−1.40612	−0.703061	+	0.711130i	$0.748184\pi$
$102$	9.39909	0.930648
$103$	−11.3083	−1.11424	−0.557119	−	0.830433i	$-0.688093\pi$
$103$	−11.3083	−1.11424	−0.557119	+	0.830433i	$0.688093\pi$
$104$	14.3870	1.41076
$105$	−6.48660	−0.633027
$106$	4.19239	0.407201
$107$	8.81988	0.852650	0.426325	−	0.904570i	$-0.359808\pi$
$107$	8.81988	0.852650	0.426325	+	0.904570i	$0.359808\pi$
$108$	19.4188	1.86857
$109$	9.55008	0.914731	0.457366	−	0.889279i	$-0.348793\pi$
$109$	9.55008	0.914731	0.457366	+	0.889279i	$0.348793\pi$
$110$	20.7906	1.98231
$111$	−3.69872	−0.351067
$112$	−22.0269	−2.08135
$113$	−5.40354	−0.508322	−0.254161	−	0.967162i	$-0.581799\pi$
$113$	−5.40354	−0.508322	−0.254161	+	0.967162i	$0.581799\pi$
$114$	−4.19170	−0.392589
$115$	−6.82214	−0.636168
$116$	−10.0901	−0.936838
$117$	4.88019	0.451174
$118$	17.6276	1.62275
$119$	−11.5867	−1.06215
$120$	−19.4003	−1.77100
$121$	−6.07098	−0.551907
$122$	24.6703	2.23354
$123$	1.07720	0.0971279
$124$	3.28193	0.294726
$125$	−10.6779	−0.955063
$126$	−15.2384	−1.35754
$127$	−12.4562	−1.10531	−0.552656	−	0.833410i	$-0.686386\pi$
$127$	−12.4562	−1.10531	−0.552656	+	0.833410i	$0.686386\pi$
$128$	2.60096	0.229895
$129$	6.77067	0.596125
$130$	−18.7444	−1.64399
$131$	14.6621	1.28103	0.640517	−	0.767944i	$-0.278720\pi$
$131$	14.6621	1.28103	0.640517	+	0.767944i	$0.278720\pi$
$132$	−7.92784	−0.690030
$133$	5.16729	0.448061
$134$	−8.59422	−0.742428
$135$	−14.6781	−1.26329
$136$	−34.6538	−2.97154
$137$	2.45492	0.209738	0.104869	−	0.994486i	$-0.466558\pi$
$137$	2.45492	0.209738	0.104869	+	0.994486i	$0.466558\pi$
$138$	3.69359	0.314419
$139$	−0.0244488	−0.00207372	−0.00103686	−	0.999999i	$-0.500330\pi$
$139$	−0.0244488	−0.00207372	−0.00103686	+	0.999999i	$0.500330\pi$
$140$	41.2225	3.48394
$141$	−5.74937	−0.484184
$142$	−11.0216	−0.924916
$143$	−4.44391	−0.371618
$144$	−22.3466	−1.86222
$145$	7.62679	0.633370
$146$	−12.7618	−1.05617
$147$	0.917896	0.0757068
$148$	23.5054	1.93213
$149$	7.07311	0.579451	0.289726	−	0.957110i	$-0.406436\pi$
$149$	7.07311	0.579451	0.289726	+	0.957110i	$0.406436\pi$
$150$	15.5286	1.26791
$151$	−3.14779	−0.256163	−0.128082	−	0.991764i	$-0.540882\pi$
$151$	−3.14779	−0.256163	−0.128082	+	0.991764i	$0.540882\pi$
$152$	15.4545	1.25353
$153$	−11.7548	−0.950321
$154$	13.8761	1.11817
$155$	−2.48072	−0.199256
$156$	7.14759	0.572265
$157$	−6.32853	−0.505072	−0.252536	−	0.967588i	$-0.581265\pi$
$157$	−6.32853	−0.505072	−0.252536	+	0.967588i	$0.581265\pi$
$158$	33.8778	2.69517
$159$	1.20836	0.0958295
$160$	34.0695	2.69343
$161$	−4.55325	−0.358846
$162$	−11.0755	−0.870176
$163$	2.47104	0.193547	0.0967733	−	0.995306i	$-0.469148\pi$
$163$	2.47104	0.193547	0.0967733	+	0.995306i	$0.469148\pi$
$164$	−6.84564	−0.534555
$165$	5.99243	0.466510
$166$	36.5983	2.84058
$167$	4.65532	0.360240	0.180120	−	0.983645i	$-0.442351\pi$
$167$	4.65532	0.360240	0.180120	+	0.983645i	$0.442351\pi$
$168$	−12.9482	−0.998975
$169$	−8.99346	−0.691804
$170$	45.1493	3.46279
$171$	5.24229	0.400888
$172$	−43.0278	−3.28084
$173$	16.9623	1.28962	0.644811	−	0.764342i	$-0.276936\pi$
$173$	16.9623	1.28962	0.644811	+	0.764342i	$0.276936\pi$
$174$	−4.12923	−0.313036
$175$	−19.1428	−1.44706
$176$	20.3488	1.53385
$177$	5.08077	0.381894
$178$	27.4082	2.05433
$179$	−2.81310	−0.210261	−0.105131	−	0.994458i	$-0.533526\pi$
$179$	−2.81310	−0.210261	−0.105131	+	0.994458i	$0.533526\pi$
$180$	41.8208	3.11714
$181$	7.92772	0.589263	0.294631	−	0.955611i	$-0.404803\pi$
$181$	7.92772	0.589263	0.294631	+	0.955611i	$0.404803\pi$
$182$	−12.5104	−0.927334
$183$	7.11067	0.525636
$184$	−13.6180	−1.00393
$185$	−17.7671	−1.30626
$186$	1.34309	0.0984800
$187$	10.7040	0.782751
$188$	36.5374	2.66476
$189$	−9.79648	−0.712589
$190$	−20.1352	−1.46076
$191$	−26.0936	−1.88807	−0.944033	−	0.329851i	$-0.893001\pi$
$191$	−26.0936	−1.88807	−0.944033	+	0.329851i	$0.893001\pi$
$192$	−4.70461	−0.339526
$193$	−1.58426	−0.114037	−0.0570187	−	0.998373i	$-0.518159\pi$
$193$	−1.58426	−0.114037	−0.0570187	+	0.998373i	$0.518159\pi$
$194$	45.5539	3.27058
$195$	−5.40266	−0.386893
$196$	−5.83325	−0.416661
$197$	10.3233	0.735508	0.367754	−	0.929923i	$-0.380127\pi$
$197$	10.3233	0.735508	0.367754	+	0.929923i	$0.380127\pi$
$198$	14.0775	1.00044
$199$	−3.30085	−0.233991	−0.116996	−	0.993132i	$-0.537326\pi$
$199$	−3.30085	−0.233991	−0.116996	+	0.993132i	$0.537326\pi$
$200$	−57.2529	−4.04839
$201$	−2.47710	−0.174721
$202$	36.7516	2.58583
$203$	5.09028	0.357268
$204$	−17.2163	−1.20538
$205$	5.17442	0.361397
$206$	29.4096	2.04907
$207$	−4.61933	−0.321065
$208$	−18.3461	−1.27207
$209$	−4.77363	−0.330199
$210$	16.8698	1.16413
$211$	3.58875	0.247060	0.123530	−	0.992341i	$-0.460579\pi$
$211$	3.58875	0.247060	0.123530	+	0.992341i	$0.460579\pi$
$212$	−7.67918	−0.527408
$213$	−3.17675	−0.217667
$214$	−22.9380	−1.56801
$215$	32.5235	2.21808
$216$	−29.2997	−1.99359
$217$	−1.65568	−0.112395
$218$	−24.8370	−1.68218
$219$	−3.67830	−0.248557
$220$	−38.0820	−2.56749
$221$	−9.65048	−0.649162
$222$	9.61930	0.645605
$223$	−9.95968	−0.666949	−0.333475	−	0.942759i	$-0.608221\pi$
$223$	−9.95968	−0.666949	−0.333475	+	0.942759i	$0.608221\pi$
$224$	22.7387	1.51929
$225$	−19.4206	−1.29471
$226$	14.0531	0.934796
$227$	17.4185	1.15610	0.578052	−	0.816000i	$-0.303813\pi$
$227$	17.4185	1.15610	0.578052	+	0.816000i	$0.303813\pi$
$228$	7.67792	0.508483
$229$	−13.8102	−0.912603	−0.456302	−	0.889825i	$-0.650826\pi$
$229$	−13.8102	−0.912603	−0.456302	+	0.889825i	$0.650826\pi$
$230$	17.7425	1.16990
$231$	3.99948	0.263146
$232$	15.2242	0.999516
$233$	3.23572	0.211979	0.105989	−	0.994367i	$-0.466199\pi$
$233$	3.23572	0.211979	0.105989	+	0.994367i	$0.466199\pi$
$234$	−12.6920	−0.829701
$235$	−27.6176	−1.80157
$236$	−32.2884	−2.10180
$237$	9.76452	0.634274
$238$	30.1336	1.95327
$239$	17.9609	1.16179	0.580896	−	0.813978i	$-0.302702\pi$
$239$	17.9609	1.16179	0.580896	+	0.813978i	$0.302702\pi$
$240$	24.7390	1.59690
$241$	17.3752	1.11924	0.559619	−	0.828750i	$-0.310948\pi$
$241$	17.3752	1.11924	0.559619	+	0.828750i	$0.310948\pi$
$242$	15.7889	1.01495
$243$	−15.4215	−0.989287
$244$	−45.1885	−2.89290
$245$	4.40919	0.281693
$246$	−2.80149	−0.178617
$247$	4.30382	0.273845
$248$	−4.95187	−0.314444
$249$	10.5487	0.668494
$250$	27.7702	1.75634
$251$	1.62952	0.102855	0.0514273	−	0.998677i	$-0.483623\pi$
$251$	1.62952	0.102855	0.0514273	+	0.998677i	$0.483623\pi$
$252$	27.9121	1.75830
$253$	4.20637	0.264452
$254$	32.3951	2.03265
$255$	13.0133	0.814924
$256$	−19.3167	−1.20729
$257$	6.18870	0.386041	0.193020	−	0.981195i	$-0.438172\pi$
$257$	6.18870	0.386041	0.193020	+	0.981195i	$0.438172\pi$
$258$	−17.6086	−1.09626
$259$	−11.8581	−0.736829
$260$	34.3340	2.12931
$261$	5.16416	0.319653
$262$	−38.1319	−2.35580
$263$	3.91256	0.241259	0.120629	−	0.992698i	$-0.461509\pi$
$263$	3.91256	0.241259	0.120629	+	0.992698i	$0.461509\pi$
$264$	11.9618	0.736196
$265$	5.80448	0.356566
$266$	−13.4387	−0.823977
$267$	7.89980	0.483460
$268$	15.7420	0.961596
$269$	−7.57471	−0.461838	−0.230919	−	0.972973i	$-0.574173\pi$
$269$	−7.57471	−0.461838	−0.230919	+	0.972973i	$0.574173\pi$
$270$	38.1736	2.32317
$271$	−18.5223	−1.12515	−0.562575	−	0.826746i	$-0.690189\pi$
$271$	−18.5223	−1.12515	−0.562575	+	0.826746i	$0.690189\pi$
$272$	44.1900	2.67941
$273$	−3.60585	−0.218236
$274$	−6.38455	−0.385705
$275$	17.6844	1.06641
$276$	−6.76553	−0.407237
$277$	12.5043	0.751311	0.375655	−	0.926759i	$-0.377418\pi$
$277$	12.5043	0.751311	0.375655	+	0.926759i	$0.377418\pi$
$278$	0.0635843	0.00381353
$279$	−1.67971	−0.100562
$280$	−62.1977	−3.71703
$281$	−4.42222	−0.263807	−0.131904	−	0.991263i	$-0.542109\pi$
$281$	−4.42222	−0.263807	−0.131904	+	0.991263i	$0.542109\pi$
$282$	14.9525	0.890406
$283$	17.1801	1.02125	0.510625	−	0.859803i	$-0.329414\pi$
$283$	17.1801	1.02125	0.510625	+	0.859803i	$0.329414\pi$
$284$	20.1883	1.19796
$285$	−5.80352	−0.343771
$286$	11.5573	0.683400
$287$	3.45352	0.203855
$288$	23.0687	1.35934
$289$	6.24494	0.367349
$290$	−19.8351	−1.16476
$291$	13.1299	0.769689
$292$	23.3757	1.36796
$293$	−4.68421	−0.273654	−0.136827	−	0.990595i	$-0.543691\pi$
$293$	−4.68421	−0.273654	−0.136827	+	0.990595i	$0.543691\pi$
$294$	−2.38719	−0.139223
$295$	24.4059	1.42097
$296$	−35.4657	−2.06140
$297$	9.05016	0.525144
$298$	−18.3951	−1.06560
$299$	−3.79238	−0.219319
$300$	−28.4437	−1.64220
$301$	21.7069	1.25116
$302$	8.18650	0.471080
$303$	10.5928	0.608542
$304$	−19.7074	−1.13029
$305$	34.1567	1.95581
$306$	30.5709	1.74762
$307$	−28.6823	−1.63699	−0.818494	−	0.574515i	$-0.805191\pi$
$307$	−28.6823	−1.63699	−0.818494	+	0.574515i	$0.805191\pi$
$308$	−25.4168	−1.44825
$309$	8.47667	0.482221
$310$	6.45164	0.366428
$311$	−16.3627	−0.927844	−0.463922	−	0.885876i	$-0.653558\pi$
$311$	−16.3627	−0.927844	−0.463922	+	0.885876i	$0.653558\pi$
$312$	−10.7845	−0.610552
$313$	15.5165	0.877042	0.438521	−	0.898721i	$-0.355502\pi$
$313$	15.5165	0.877042	0.438521	+	0.898721i	$0.355502\pi$
$314$	16.4587	0.928818
$315$	−21.0979	−1.18873
$316$	−62.0538	−3.49080
$317$	−17.3276	−0.973214	−0.486607	−	0.873621i	$-0.661766\pi$
$317$	−17.3276	−0.973214	−0.486607	+	0.873621i	$0.661766\pi$
$318$	−3.14261	−0.176229
$319$	−4.70249	−0.263289
$320$	−22.5990	−1.26332
$321$	−6.61137	−0.369010
$322$	11.8417	0.659912
$323$	−10.3665	−0.576809
$324$	20.2870	1.12706
$325$	−15.9440	−0.884411
$326$	−6.42647	−0.355929
$327$	−7.15872	−0.395878
$328$	10.3289	0.570318
$329$	−18.4325	−1.01622
$330$	−15.5846	−0.857904
$331$	5.82367	0.320098	0.160049	−	0.987109i	$-0.448835\pi$
$331$	5.82367	0.320098	0.160049	+	0.987109i	$0.448835\pi$
$332$	−67.0370	−3.67913
$333$	−12.0302	−0.659253
$334$	−12.1072	−0.662475
$335$	−11.8989	−0.650108
$336$	16.5113	0.900767
$337$	−7.52521	−0.409924	−0.204962	−	0.978770i	$-0.565707\pi$
$337$	−7.52521	−0.409924	−0.204962	+	0.978770i	$0.565707\pi$
$338$	23.3894	1.27222
$339$	4.05049	0.219992
$340$	−82.6998	−4.48502
$341$	1.52955	0.0828297
$342$	−13.6337	−0.737226
$343$	19.7654	1.06723
$344$	64.9216	3.50034
$345$	5.11387	0.275322
$346$	−44.1142	−2.37159
$347$	2.79302	0.149937	0.0749687	−	0.997186i	$-0.476114\pi$
$347$	2.79302	0.149937	0.0749687	+	0.997186i	$0.476114\pi$
$348$	7.56349	0.405446
$349$	−33.1385	−1.77387	−0.886933	−	0.461898i	$-0.847169\pi$
$349$	−33.1385	−1.77387	−0.886933	+	0.461898i	$0.847169\pi$
$350$	49.7849	2.66112
$351$	−8.15945	−0.435519
$352$	−21.0064	−1.11964
$353$	4.63827	0.246870	0.123435	−	0.992353i	$-0.460609\pi$
$353$	4.63827	0.246870	0.123435	+	0.992353i	$0.460609\pi$
$354$	−13.2136	−0.702296
$355$	−15.2598	−0.809904
$356$	−50.2034	−2.66077
$357$	8.68535	0.459677
$358$	7.31608	0.386667
$359$	−26.0910	−1.37703	−0.688515	−	0.725222i	$-0.741737\pi$
$359$	−26.0910	−1.37703	−0.688515	+	0.725222i	$0.741737\pi$
$360$	−63.1004	−3.32568
$361$	−14.3769	−0.756676
$362$	−20.6177	−1.08364
$363$	4.55080	0.238855
$364$	22.9153	1.20109
$365$	−17.6690	−0.924840
$366$	−18.4928	−0.966635
$367$	−18.7059	−0.976440	−0.488220	−	0.872721i	$-0.662354\pi$
$367$	−18.7059	−0.976440	−0.488220	+	0.872721i	$0.662354\pi$
$368$	17.3655	0.905237
$369$	3.50364	0.182392
$370$	46.2071	2.40219
$371$	3.87403	0.201130
$372$	−2.46013	−0.127552
$373$	−3.42892	−0.177543	−0.0887714	−	0.996052i	$-0.528294\pi$
$373$	−3.42892	−0.177543	−0.0887714	+	0.996052i	$0.528294\pi$
$374$	−27.8379	−1.43947
$375$	8.00416	0.413333
$376$	−55.1287	−2.84304
$377$	4.23967	0.218354
$378$	25.4779	1.31044
$379$	−30.5237	−1.56790	−0.783949	−	0.620825i	$-0.786798\pi$
$379$	−30.5237	−1.56790	−0.783949	+	0.620825i	$0.786798\pi$
$380$	36.8815	1.89198
$381$	9.33717	0.478358
$382$	67.8620	3.47212
$383$	−6.67146	−0.340896	−0.170448	−	0.985367i	$-0.554521\pi$
$383$	−6.67146	−0.340896	−0.170448	+	0.985367i	$0.554521\pi$
$384$	−1.94968	−0.0994940
$385$	19.2118	0.979125
$386$	4.12020	0.209713
$387$	22.0219	1.11944
$388$	−83.4409	−4.23607
$389$	−18.0381	−0.914569	−0.457284	−	0.889321i	$-0.651178\pi$
$389$	−18.0381	−0.914569	−0.457284	+	0.889321i	$0.651178\pi$
$390$	14.0508	0.711489
$391$	9.13463	0.461958
$392$	8.80138	0.444537
$393$	−10.9907	−0.554407
$394$	−26.8481	−1.35259
$395$	46.9047	2.36003
$396$	−25.7856	−1.29578
$397$	14.9013	0.747874	0.373937	−	0.927454i	$-0.378008\pi$
$397$	14.9013	0.747874	0.373937	+	0.927454i	$0.378008\pi$
$398$	8.58458	0.430306
$399$	−3.87340	−0.193912
$400$	73.0080	3.65040
$401$	−10.0752	−0.503132	−0.251566	−	0.967840i	$-0.580946\pi$
$401$	−10.0752	−0.503132	−0.251566	+	0.967840i	$0.580946\pi$
$402$	6.44222	0.321309
$403$	−1.37901	−0.0686935
$404$	−67.3177	−3.34918
$405$	−15.3344	−0.761971
$406$	−13.2384	−0.657009
$407$	10.9547	0.543007
$408$	25.9764	1.28602
$409$	−10.8222	−0.535122	−0.267561	−	0.963541i	$-0.586218\pi$
$409$	−10.8222	−0.535122	−0.267561	+	0.963541i	$0.586218\pi$
$410$	−13.4572	−0.664604
$411$	−1.84020	−0.0907706
$412$	−53.8695	−2.65396
$413$	16.2890	0.801530
$414$	12.0136	0.590434
$415$	50.6714	2.48736
$416$	18.9390	0.928559
$417$	0.0183268	0.000897465 0
$418$	12.4149	0.607231
$419$	17.0887	0.834838	0.417419	−	0.908714i	$-0.362935\pi$
$419$	17.0887	0.834838	0.417419	+	0.908714i	$0.362935\pi$
$420$	−30.9003	−1.50778
$421$	17.9307	0.873891	0.436946	−	0.899488i	$-0.356060\pi$
$421$	17.9307	0.873891	0.436946	+	0.899488i	$0.356060\pi$
$422$	−9.33331	−0.454338
$423$	−18.7001	−0.909228
$424$	11.5866	0.562694
$425$	38.4039	1.86286
$426$	8.26181	0.400286
$427$	22.7969	1.10322
$428$	42.0154	2.03089
$429$	3.33115	0.160829
$430$	−84.5843	−4.07902
$431$	22.0254	1.06092	0.530462	−	0.847708i	$-0.322018\pi$
$431$	22.0254	1.06092	0.530462	+	0.847708i	$0.322018\pi$
$432$	37.3625	1.79760
$433$	29.2860	1.40739	0.703697	−	0.710501i	$-0.251531\pi$
$433$	29.2860	1.40739	0.703697	+	0.710501i	$0.251531\pi$
$434$	4.30596	0.206693
$435$	−5.71703	−0.274111
$436$	45.4939	2.17876
$437$	−4.07376	−0.194875
$438$	9.56622	0.457092
$439$	−22.1269	−1.05606	−0.528031	−	0.849225i	$-0.677069\pi$
$439$	−22.1269	−1.05606	−0.528031	+	0.849225i	$0.677069\pi$
$440$	57.4593	2.73927
$441$	2.98550	0.142166
$442$	25.0982	1.19380
$443$	−18.8566	−0.895903	−0.447951	−	0.894058i	$-0.647846\pi$
$443$	−18.8566	−0.895903	−0.447951	+	0.894058i	$0.647846\pi$
$444$	−17.6196	−0.836191
$445$	37.9473	1.79888
$446$	25.9023	1.22651
$447$	−5.30199	−0.250775
$448$	−15.0830	−0.712607
$449$	24.0191	1.13353	0.566766	−	0.823879i	$-0.308195\pi$
$449$	24.0191	1.13353	0.566766	+	0.823879i	$0.308195\pi$
$450$	50.5075	2.38095
$451$	−3.19042	−0.150231
$452$	−25.7409	−1.21075
$453$	2.35958	0.110863
$454$	−45.3005	−2.12606
$455$	−17.3210	−0.812021
$456$	−11.5847	−0.542502
$457$	19.8939	0.930597	0.465298	−	0.885154i	$-0.345947\pi$
$457$	19.8939	0.930597	0.465298	+	0.885154i	$0.345947\pi$
$458$	35.9164	1.67826
$459$	19.6535	0.917348
$460$	−32.4988	−1.51526
$461$	38.3823	1.78764	0.893821	−	0.448425i	$-0.148015\pi$
$461$	38.3823	1.78764	0.893821	+	0.448425i	$0.148015\pi$
$462$	−10.4015	−0.483921
$463$	−16.1933	−0.752567	−0.376283	−	0.926505i	$-0.622798\pi$
$463$	−16.1933	−0.752567	−0.376283	+	0.926505i	$0.622798\pi$
$464$	−19.4136	−0.901256
$465$	1.85954	0.0862342
$466$	−8.41518	−0.389826
$467$	−8.67187	−0.401286	−0.200643	−	0.979664i	$-0.564303\pi$
$467$	−8.67187	−0.401286	−0.200643	+	0.979664i	$0.564303\pi$
$468$	23.2478	1.07463
$469$	−7.94160	−0.366709
$470$	71.8254	3.31306
$471$	4.74386	0.218585
$472$	48.7177	2.24242
$473$	−20.0532	−0.922046
$474$	−25.3947	−1.16642
$475$	−17.1270	−0.785838
$476$	−55.1956	−2.52989
$477$	3.93026	0.179954
$478$	−46.7111	−2.13652
$479$	3.99940	0.182737	0.0913687	−	0.995817i	$-0.470876\pi$
$479$	3.99940	0.182737	0.0913687	+	0.995817i	$0.470876\pi$
$480$	−25.5384	−1.16566
$481$	−9.87659	−0.450334
$482$	−45.1881	−2.05826
$483$	3.41311	0.155302
$484$	−28.9204	−1.31457
$485$	63.0706	2.86389
$486$	40.1068	1.81928
$487$	14.9384	0.676925	0.338463	−	0.940980i	$-0.390093\pi$
$487$	14.9384	0.676925	0.338463	+	0.940980i	$0.390093\pi$
$488$	68.1817	3.08644
$489$	−1.85229	−0.0837633
$490$	−11.4670	−0.518028
$491$	13.8028	0.622913	0.311457	−	0.950260i	$-0.399183\pi$
$491$	13.8028	0.622913	0.311457	+	0.950260i	$0.399183\pi$
$492$	5.13148	0.231345
$493$	−10.2120	−0.459926
$494$	−11.1930	−0.503597
$495$	19.4906	0.876039
$496$	6.31455	0.283532
$497$	−10.1847	−0.456846
$498$	−27.4341	−1.22935
$499$	35.6685	1.59674	0.798371	−	0.602166i	$-0.205695\pi$
$499$	35.6685	1.59674	0.798371	+	0.602166i	$0.205695\pi$
$500$	−50.8666	−2.27482
$501$	−3.48962	−0.155905
$502$	−4.23793	−0.189148
$503$	−30.0654	−1.34055	−0.670275	−	0.742113i	$-0.733824\pi$
$503$	−30.0654	−1.34055	−0.670275	+	0.742113i	$0.733824\pi$
$504$	−42.1146	−1.87593
$505$	50.8836	2.26429
$506$	−10.9396	−0.486323
$507$	6.74148	0.299400
$508$	−59.3379	−2.63270
$509$	−16.0537	−0.711569	−0.355785	−	0.934568i	$-0.615786\pi$
$509$	−16.0537	−0.711569	−0.355785	+	0.934568i	$0.615786\pi$
$510$	−33.8438	−1.49863
$511$	−11.7927	−0.521678
$512$	45.0353	1.99030
$513$	−8.76486	−0.386978
$514$	−16.0950	−0.709922
$515$	40.7184	1.79427
$516$	32.2536	1.41988
$517$	17.0283	0.748904
$518$	30.8396	1.35502
$519$	−12.7149	−0.558124
$520$	−51.8042	−2.27177
$521$	−42.8894	−1.87902	−0.939508	−	0.342526i	$-0.888718\pi$
$521$	−42.8894	−1.87902	−0.939508	+	0.342526i	$0.888718\pi$
$522$	−13.4305	−0.587837
$523$	5.15590	0.225452	0.112726	−	0.993626i	$-0.464042\pi$
$523$	5.15590	0.225452	0.112726	+	0.993626i	$0.464042\pi$
$524$	69.8461	3.05124
$525$	14.3494	0.626260
$526$	−10.1754	−0.443670
$527$	3.32160	0.144691
$528$	−15.2535	−0.663822
$529$	−19.4103	−0.843928
$530$	−15.0958	−0.655719
$531$	16.5254	0.717142
$532$	24.6155	1.06722
$533$	2.87642	0.124592
$534$	−20.5451	−0.889074
$535$	−31.7582	−1.37303
$536$	−23.7520	−1.02593
$537$	2.10870	0.0909970
$538$	19.6997	0.849313
$539$	−2.71860	−0.117098
$540$	−69.9224	−3.00898
$541$	−10.7502	−0.462188	−0.231094	−	0.972931i	$-0.574230\pi$
$541$	−10.7502	−0.462188	−0.231094	+	0.972931i	$0.574230\pi$
$542$	48.1712	2.06913
$543$	−5.94261	−0.255022
$544$	−45.6179	−1.95585
$545$	−34.3875	−1.47300
$546$	9.37779	0.401332
$547$	28.5128	1.21912	0.609559	−	0.792741i	$-0.291347\pi$
$547$	28.5128	1.21912	0.609559	+	0.792741i	$0.291347\pi$
$548$	11.6945	0.499566
$549$	23.1278	0.987069
$550$	−45.9922	−1.96111
$551$	4.55425	0.194017
$552$	10.2080	0.434483
$553$	31.3052	1.33123
$554$	−32.5201	−1.38165
$555$	13.3182	0.565325
$556$	−0.116467	−0.00493930
$557$	15.7892	0.669010	0.334505	−	0.942394i	$-0.391431\pi$
$557$	15.7892	0.669010	0.334505	+	0.942394i	$0.391431\pi$
$558$	4.36845	0.184931
$559$	18.0796	0.764684
$560$	79.3136	3.35161
$561$	−8.02367	−0.338760
$562$	11.5009	0.485137
$563$	7.82334	0.329714	0.164857	−	0.986317i	$-0.447284\pi$
$563$	7.82334	0.329714	0.164857	+	0.986317i	$0.447284\pi$
$564$	−27.3884	−1.15326
$565$	19.4568	0.818556
$566$	−44.6805	−1.87806
$567$	−10.2345	−0.429808
$568$	−30.4607	−1.27810
$569$	−25.9007	−1.08581	−0.542907	−	0.839793i	$-0.682676\pi$
$569$	−25.9007	−1.08581	−0.542907	+	0.839793i	$0.682676\pi$
$570$	15.0933	0.632189
$571$	−1.20933	−0.0506087	−0.0253044	−	0.999680i	$-0.508055\pi$
$571$	−1.20933	−0.0506087	−0.0253044	+	0.999680i	$0.508055\pi$
$572$	−21.1695	−0.885142
$573$	19.5597	0.817119
$574$	−8.98162	−0.374886
$575$	15.0917	0.629367
$576$	−15.3020	−0.637581
$577$	36.0838	1.50219	0.751095	−	0.660194i	$-0.229526\pi$
$577$	36.0838	1.50219	0.751095	+	0.660194i	$0.229526\pi$
$578$	−16.2413	−0.675549
$579$	1.18756	0.0493532
$580$	36.3319	1.50860
$581$	33.8192	1.40305
$582$	−34.1472	−1.41544
$583$	−3.57890	−0.148223
$584$	−35.2700	−1.45948
$585$	−17.5724	−0.726529
$586$	12.1823	0.503246
$587$	−7.23567	−0.298648	−0.149324	−	0.988788i	$-0.547710\pi$
$587$	−7.23567	−0.298648	−0.149324	+	0.988788i	$0.547710\pi$
$588$	4.37260	0.180323
$589$	−1.48133	−0.0610372
$590$	−63.4728	−2.61313
$591$	−7.73837	−0.318314
$592$	45.2253	1.85875
$593$	−11.6987	−0.480408	−0.240204	−	0.970722i	$-0.577214\pi$
$593$	−11.6987	−0.480408	−0.240204	+	0.970722i	$0.577214\pi$
$594$	−23.5369	−0.965730
$595$	41.7208	1.71039
$596$	33.6943	1.38017
$597$	2.47432	0.101267
$598$	9.86290	0.403324
$599$	−14.9465	−0.610696	−0.305348	−	0.952241i	$-0.598773\pi$
$599$	−14.9465	−0.610696	−0.305348	+	0.952241i	$0.598773\pi$
$600$	42.9167	1.75207
$601$	−7.63701	−0.311520	−0.155760	−	0.987795i	$-0.549783\pi$
$601$	−7.63701	−0.311520	−0.155760	+	0.987795i	$0.549783\pi$
$602$	−56.4534	−2.30087
$603$	−8.05686	−0.328101
$604$	−14.9952	−0.610145
$605$	21.8601	0.888741
$606$	−27.5489	−1.11910
$607$	19.2133	0.779845	0.389923	−	0.920848i	$-0.372502\pi$
$607$	19.2133	0.779845	0.389923	+	0.920848i	$0.372502\pi$
$608$	20.3442	0.825066
$609$	−3.81567	−0.154619
$610$	−88.8318	−3.59669
$611$	−15.3524	−0.621091
$612$	−55.9967	−2.26353
$613$	16.3596	0.660758	0.330379	−	0.943848i	$-0.392823\pi$
$613$	16.3596	0.660758	0.330379	+	0.943848i	$0.392823\pi$
$614$	74.5946	3.01039
$615$	−3.87874	−0.156406
$616$	38.3496	1.54515
$617$	48.0225	1.93331	0.966656	−	0.256077i	$-0.0824302\pi$
$617$	48.0225	1.93331	0.966656	+	0.256077i	$0.0824302\pi$
$618$	−22.0454	−0.886796
$619$	−6.57799	−0.264392	−0.132196	−	0.991224i	$-0.542203\pi$
$619$	−6.57799	−0.264392	−0.132196	+	0.991224i	$0.542203\pi$
$620$	−11.8174	−0.474600
$621$	7.72330	0.309925
$622$	42.5547	1.70629
$623$	25.3269	1.01470
$624$	13.7522	0.550530
$625$	−1.37869	−0.0551477
$626$	−40.3539	−1.61287
$627$	3.57831	0.142904
$628$	−30.1473	−1.20301
$629$	23.7896	0.948552
$630$	54.8697	2.18606
$631$	−44.0453	−1.75341	−0.876707	−	0.481025i	$-0.840265\pi$
$631$	−44.0453	−1.75341	−0.876707	+	0.481025i	$0.840265\pi$
$632$	93.6286	3.72435
$633$	−2.69012	−0.106923
$634$	45.0641	1.78972
$635$	44.8519	1.77989
$636$	5.75630	0.228252
$637$	2.45103	0.0971135
$638$	12.2298	0.484184
$639$	−10.3325	−0.408748
$640$	−9.36544	−0.370201
$641$	23.4674	0.926909	0.463454	−	0.886121i	$-0.346610\pi$
$641$	23.4674	0.926909	0.463454	+	0.886121i	$0.346610\pi$
$642$	17.1943	0.678604
$643$	1.32958	0.0524334	0.0262167	−	0.999656i	$-0.491654\pi$
$643$	1.32958	0.0524334	0.0262167	+	0.999656i	$0.491654\pi$
$644$	−21.6904	−0.854721
$645$	−24.3796	−0.959944
$646$	26.9604	1.06074
$647$	−9.42766	−0.370640	−0.185320	−	0.982678i	$-0.559332\pi$
$647$	−9.42766	−0.370640	−0.185320	+	0.982678i	$0.559332\pi$
$648$	−30.6096	−1.20246
$649$	−15.0481	−0.590688
$650$	41.4657	1.62642
$651$	1.24110	0.0486425
$652$	11.7713	0.461001
$653$	25.5048	0.998080	0.499040	−	0.866579i	$-0.333686\pi$
$653$	25.5048	0.998080	0.499040	+	0.866579i	$0.333686\pi$
$654$	18.6178	0.728014
$655$	−52.7947	−2.06286
$656$	−13.1713	−0.514251
$657$	−11.9638	−0.466754
$658$	47.9378	1.86881
$659$	21.6617	0.843820	0.421910	−	0.906638i	$-0.361360\pi$
$659$	21.6617	0.843820	0.421910	+	0.906638i	$0.361360\pi$
$660$	28.5462	1.11116
$661$	37.3586	1.45308	0.726541	−	0.687123i	$-0.241127\pi$
$661$	37.3586	1.45308	0.726541	+	0.687123i	$0.241127\pi$
$662$	−15.1457	−0.588655
$663$	7.23399	0.280945
$664$	101.147	3.92528
$665$	−18.6062	−0.721517
$666$	31.2872	1.21235
$667$	−4.01305	−0.155386
$668$	22.1766	0.858040
$669$	7.46576	0.288643
$670$	30.9457	1.19554
$671$	−21.0602	−0.813019
$672$	−17.0449	−0.657521
$673$	−3.20604	−0.123584	−0.0617918	−	0.998089i	$-0.519681\pi$
$673$	−3.20604	−0.123584	−0.0617918	+	0.998089i	$0.519681\pi$
$674$	19.5709	0.753844
$675$	32.4704	1.24979
$676$	−42.8423	−1.64778
$677$	−4.16865	−0.160214	−0.0801071	−	0.996786i	$-0.525526\pi$
$677$	−4.16865	−0.160214	−0.0801071	+	0.996786i	$0.525526\pi$
$678$	−10.5342	−0.404562
$679$	42.0947	1.61545
$680$	124.780	4.78509
$681$	−13.0569	−0.500340
$682$	−3.97792	−0.152322
$683$	−1.11078	−0.0425029	−0.0212514	−	0.999774i	$-0.506765\pi$
$683$	−1.11078	−0.0425029	−0.0212514	+	0.999774i	$0.506765\pi$
$684$	24.9728	0.954858
$685$	−8.83958	−0.337743
$686$	−51.4040	−1.96262
$687$	10.3521	0.394957
$688$	−82.7871	−3.15623
$689$	3.22666	0.122926
$690$	−13.2997	−0.506312
$691$	45.7674	1.74107	0.870537	−	0.492104i	$-0.163772\pi$
$691$	45.7674	1.74107	0.870537	+	0.492104i	$0.163772\pi$
$692$	80.8038	3.07170
$693$	13.0085	0.494151
$694$	−7.26386	−0.275732
$695$	0.0880341	0.00333932
$696$	−11.4120	−0.432572
$697$	−6.92839	−0.262431
$698$	86.1839	3.26211
$699$	−2.42549	−0.0917404
$700$	−91.1909	−3.44669
$701$	13.7643	0.519872	0.259936	−	0.965626i	$-0.416298\pi$
$701$	13.7643	0.519872	0.259936	+	0.965626i	$0.416298\pi$
$702$	21.2204	0.800913
$703$	−10.6094	−0.400141
$704$	13.9340	0.525157
$705$	20.7021	0.779685
$706$	−12.0628	−0.453991
$707$	33.9608	1.27723
$708$	24.2033	0.909617
$709$	49.9855	1.87724	0.938622	−	0.344947i	$-0.112103\pi$
$709$	49.9855	1.87724	0.938622	+	0.344947i	$0.112103\pi$
$710$	39.6863	1.48940
$711$	31.7595	1.19108
$712$	75.7484	2.83879
$713$	1.30530	0.0488838
$714$	−22.5881	−0.845339
$715$	16.0014	0.598420
$716$	−13.4008	−0.500813
$717$	−13.4634	−0.502801
$718$	67.8552	2.53233
$719$	4.38691	0.163604	0.0818022	−	0.996649i	$-0.473932\pi$
$719$	4.38691	0.163604	0.0818022	+	0.996649i	$0.473932\pi$
$720$	80.4647	2.99874
$721$	27.1763	1.01210
$722$	37.3901	1.39152
$723$	−13.0245	−0.484385
$724$	37.7654	1.40354
$725$	−16.8717	−0.626599
$726$	−11.8353	−0.439250
$727$	−8.21876	−0.304817	−0.152409	−	0.988318i	$-0.548703\pi$
$727$	−8.21876	−0.304817	−0.152409	+	0.988318i	$0.548703\pi$
$728$	−34.5753	−1.28144
$729$	−1.21604	−0.0450386
$730$	45.9521	1.70076
$731$	−43.5479	−1.61068
$732$	33.8732	1.25199
$733$	−31.7146	−1.17140	−0.585702	−	0.810526i	$-0.699181\pi$
$733$	−31.7146	−1.17140	−0.585702	+	0.810526i	$0.699181\pi$
$734$	48.6487	1.79566
$735$	−3.30512	−0.121911
$736$	−17.9266	−0.660784
$737$	7.33659	0.270247
$738$	−9.11198	−0.335416
$739$	14.5846	0.536504	0.268252	−	0.963349i	$-0.413554\pi$
$739$	14.5846	0.536504	0.268252	+	0.963349i	$0.413554\pi$
$740$	−84.6374	−3.11133
$741$	−3.22613	−0.118515
$742$	−10.0753	−0.369874
$743$	16.7750	0.615415	0.307708	−	0.951481i	$-0.400438\pi$
$743$	16.7750	0.615415	0.307708	+	0.951481i	$0.400438\pi$
$744$	3.71192	0.136085
$745$	−25.4685	−0.933095
$746$	8.91764	0.326498
$747$	34.3100	1.25534
$748$	50.9906	1.86440
$749$	−21.1961	−0.774490
$750$	−20.8165	−0.760112
$751$	−23.3405	−0.851706	−0.425853	−	0.904792i	$-0.640026\pi$
$751$	−23.3405	−0.851706	−0.425853	+	0.904792i	$0.640026\pi$
$752$	70.2992	2.56355
$753$	−1.22149	−0.0445135
$754$	−11.0262	−0.401550
$755$	11.3344	0.412502
$756$	−46.6677	−1.69729
$757$	−0.728092	−0.0264630	−0.0132315	−	0.999912i	$-0.504212\pi$
$757$	−0.728092	−0.0264630	−0.0132315	+	0.999912i	$0.504212\pi$
$758$	79.3835	2.88334
$759$	−3.15309	−0.114450
$760$	−55.6480	−2.01856
$761$	37.8199	1.37097	0.685485	−	0.728087i	$-0.259590\pi$
$761$	37.8199	1.37097	0.685485	+	0.728087i	$0.259590\pi$
$762$	−24.2833	−0.879692
$763$	−22.9510	−0.830881
$764$	−124.302	−4.49711
$765$	42.3263	1.53031
$766$	17.3506	0.626902
$767$	13.5671	0.489878
$768$	14.4798	0.522494
$769$	7.96338	0.287167	0.143583	−	0.989638i	$-0.454137\pi$
$769$	7.96338	0.287167	0.143583	+	0.989638i	$0.454137\pi$
$770$	−49.9645	−1.80059
$771$	−4.63904	−0.167071
$772$	−7.54695	−0.271621
$773$	15.3892	0.553511	0.276756	−	0.960940i	$-0.410741\pi$
$773$	15.3892	0.553511	0.276756	+	0.960940i	$0.410741\pi$
$774$	−57.2727	−2.05863
$775$	5.48775	0.197126
$776$	125.898	4.51948
$777$	8.88884	0.318885
$778$	46.9120	1.68188
$779$	3.08985	0.110705
$780$	−25.7367	−0.921523
$781$	9.40879	0.336673
$782$	−23.7566	−0.849533
$783$	−8.63423	−0.308562
$784$	−11.2234	−0.400835
$785$	22.7875	0.813321
$786$	28.5837	1.01955
$787$	−41.2252	−1.46952	−0.734761	−	0.678327i	$-0.762705\pi$
$787$	−41.2252	−1.46952	−0.734761	+	0.678327i	$0.762705\pi$
$788$	49.1775	1.75188
$789$	−2.93285	−0.104412
$790$	−121.986	−4.34006
$791$	12.9859	0.461726
$792$	38.9062	1.38247
$793$	18.9874	0.674264
$794$	−38.7540	−1.37533
$795$	−4.35103	−0.154315
$796$	−15.7243	−0.557334
$797$	−29.2361	−1.03560	−0.517798	−	0.855503i	$-0.673248\pi$
$797$	−29.2361	−1.03560	−0.517798	+	0.855503i	$0.673248\pi$
$798$	10.0736	0.356601
$799$	36.9790	1.30822
$800$	−75.3672	−2.66463
$801$	25.6944	0.907868
$802$	26.2027	0.925251
$803$	10.8943	0.384451
$804$	−11.8002	−0.416160
$805$	16.3951	0.577853
$806$	3.58642	0.126326
$807$	5.67799	0.199875
$808$	101.571	3.57326
$809$	−12.4998	−0.439470	−0.219735	−	0.975560i	$-0.570519\pi$
$809$	−12.4998	−0.439470	−0.219735	+	0.975560i	$0.570519\pi$
$810$	39.8803	1.40125
$811$	−33.4708	−1.17532	−0.587660	−	0.809108i	$-0.699951\pi$
$811$	−33.4708	−1.17532	−0.587660	+	0.809108i	$0.699951\pi$
$812$	24.2487	0.850961
$813$	13.8843	0.486944
$814$	−28.4902	−0.998580
$815$	−8.89761	−0.311670
$816$	−33.1247	−1.15960
$817$	19.4210	0.679456
$818$	28.1454	0.984080
$819$	−11.7282	−0.409816
$820$	24.6495	0.860798
$821$	−38.9331	−1.35878	−0.679388	−	0.733779i	$-0.737755\pi$
$821$	−38.9331	−1.35878	−0.679388	+	0.733779i	$0.737755\pi$
$822$	4.78585	0.166926
$823$	21.3407	0.743889	0.371944	−	0.928255i	$-0.378691\pi$
$823$	21.3407	0.743889	0.371944	+	0.928255i	$0.378691\pi$
$824$	81.2799	2.83152
$825$	−13.2562	−0.461523
$826$	−42.3631	−1.47400
$827$	35.2637	1.22624	0.613120	−	0.789990i	$-0.289914\pi$
$827$	35.2637	1.22624	0.613120	+	0.789990i	$0.289914\pi$
$828$	−22.0052	−0.764733
$829$	44.0741	1.53076	0.765379	−	0.643580i	$-0.222552\pi$
$829$	44.0741	1.53076	0.765379	+	0.643580i	$0.222552\pi$
$830$	−131.782	−4.57421
$831$	−9.37321	−0.325153
$832$	−12.5626	−0.435530
$833$	−5.90376	−0.204553
$834$	−0.0476627	−0.00165042
$835$	−16.7627	−0.580097
$836$	−22.7402	−0.786488
$837$	2.80840	0.0970726
$838$	−44.4429	−1.53525
$839$	−25.4543	−0.878779	−0.439389	−	0.898297i	$-0.644805\pi$
$839$	−25.4543	−0.878779	−0.439389	+	0.898297i	$0.644805\pi$
$840$	46.6233	1.60866
$841$	−24.5136	−0.845298
$842$	−46.6328	−1.60707
$843$	3.31489	0.114171
$844$	17.0958	0.588461
$845$	32.3833	1.11402
$846$	48.6335	1.67206
$847$	14.5899	0.501316
$848$	−14.7750	−0.507377
$849$	−12.8782	−0.441978
$850$	−99.8776	−3.42577
$851$	9.34865	0.320468
$852$	−15.1331	−0.518452
$853$	−2.16771	−0.0742210	−0.0371105	−	0.999311i	$-0.511815\pi$
$853$	−2.16771	−0.0742210	−0.0371105	+	0.999311i	$0.511815\pi$
$854$	−59.2882	−2.02880
$855$	−18.8762	−0.645553
$856$	−63.3941	−2.16677
$857$	−4.45040	−0.152023	−0.0760114	−	0.997107i	$-0.524219\pi$
$857$	−4.45040	−0.152023	−0.0760114	+	0.997107i	$0.524219\pi$
$858$	−8.66336	−0.295762
$859$	25.8007	0.880309	0.440155	−	0.897922i	$-0.354924\pi$
$859$	25.8007	0.880309	0.440155	+	0.897922i	$0.354924\pi$
$860$	154.933	5.28316
$861$	−2.58875	−0.0882245
$862$	−57.2817	−1.95102
$863$	31.8885	1.08550	0.542748	−	0.839896i	$-0.317384\pi$
$863$	31.8885	1.08550	0.542748	+	0.839896i	$0.317384\pi$
$864$	−38.5698	−1.31217
$865$	−61.0773	−2.07669
$866$	−76.1644	−2.58817
$867$	−4.68120	−0.158982
$868$	−7.88721	−0.267709
$869$	−28.9203	−0.981053
$870$	14.8684	0.504085
$871$	−6.61453	−0.224125
$872$	−68.6425	−2.32453
$873$	42.7056	1.44537
$874$	10.5947	0.358371
$875$	25.6614	0.867515
$876$	−17.5224	−0.592027
$877$	−14.0514	−0.474483	−0.237241	−	0.971451i	$-0.576243\pi$
$877$	−14.0514	−0.474483	−0.237241	+	0.971451i	$0.576243\pi$
$878$	57.5459	1.94208
$879$	3.51128	0.118432
$880$	−73.2713	−2.46997
$881$	19.0071	0.640366	0.320183	−	0.947356i	$-0.396256\pi$
$881$	19.0071	0.640366	0.320183	+	0.947356i	$0.396256\pi$
$882$	−7.76442	−0.261442
$883$	14.1755	0.477044	0.238522	−	0.971137i	$-0.423337\pi$
$883$	14.1755	0.477044	0.238522	+	0.971137i	$0.423337\pi$
$884$	−45.9722	−1.54621
$885$	−18.2946	−0.614967
$886$	49.0406	1.64755
$887$	38.8125	1.30320	0.651598	−	0.758564i	$-0.274099\pi$
$887$	38.8125	1.30320	0.651598	+	0.758564i	$0.274099\pi$
$888$	26.5850	0.892136
$889$	29.9351	1.00399
$890$	−98.6902	−3.30810
$891$	9.45479	0.316747
$892$	−47.4451	−1.58858
$893$	−16.4915	−0.551867
$894$	13.7890	0.461172
$895$	10.1293	0.338585
$896$	−6.25069	−0.208821
$897$	2.84276	0.0949171
$898$	−62.4668	−2.08454
$899$	−1.45925	−0.0486688
$900$	−92.5143	−3.08381
$901$	−7.77201	−0.258923
$902$	8.29738	0.276272
$903$	−16.2714	−0.541480
$904$	38.8387	1.29176
$905$	−28.5458	−0.948895
$906$	−6.13659	−0.203874
$907$	−29.5282	−0.980468	−0.490234	−	0.871591i	$-0.663089\pi$
$907$	−29.5282	−0.980468	−0.490234	+	0.871591i	$0.663089\pi$
$908$	82.9767	2.75368
$909$	34.4537	1.14276
$910$	45.0470	1.49329
$911$	5.98340	0.198239	0.0991194	−	0.995076i	$-0.468397\pi$
$911$	5.98340	0.198239	0.0991194	+	0.995076i	$0.468397\pi$
$912$	14.7726	0.489170
$913$	−31.2427	−1.03398
$914$	−51.7383	−1.71135
$915$	−25.6038	−0.846435
$916$	−65.7878	−2.17369
$917$	−35.2363	−1.16361
$918$	−51.1132	−1.68699
$919$	14.1985	0.468366	0.234183	−	0.972193i	$-0.424759\pi$
$919$	14.1985	0.468366	0.234183	+	0.972193i	$0.424759\pi$
$920$	49.0351	1.61664
$921$	21.5002	0.708457
$922$	−99.8214	−3.28744
$923$	−8.48279	−0.279214
$924$	19.0524	0.626777
$925$	39.3037	1.29230
$926$	42.1142	1.38396
$927$	27.5707	0.905542
$928$	20.0410	0.657877
$929$	20.5986	0.675819	0.337909	−	0.941179i	$-0.390280\pi$
$929$	20.5986	0.675819	0.337909	+	0.941179i	$0.390280\pi$
$930$	−4.83614	−0.158583
$931$	2.63290	0.0862896
$932$	15.4140	0.504904
$933$	12.2655	0.401553
$934$	22.5531	0.737959
$935$	−38.5424	−1.26047
$936$	−35.0771	−1.14653
$937$	−24.9845	−0.816207	−0.408103	−	0.912936i	$-0.633810\pi$
$937$	−24.9845	−0.816207	−0.408103	+	0.912936i	$0.633810\pi$
$938$	20.6538	0.674372
$939$	−11.6311	−0.379567
$940$	−131.562	−4.29109
$941$	−54.8706	−1.78873	−0.894366	−	0.447337i	$-0.852373\pi$
$941$	−54.8706	−1.78873	−0.894366	+	0.447337i	$0.852373\pi$
$942$	−12.3374	−0.401975
$943$	−2.72267	−0.0886623
$944$	−62.1241	−2.02197
$945$	35.2748	1.14749
$946$	52.1526	1.69563
$947$	−17.8703	−0.580706	−0.290353	−	0.956920i	$-0.593773\pi$
$947$	−17.8703	−0.580706	−0.290353	+	0.956920i	$0.593773\pi$
$948$	46.5154	1.51075
$949$	−9.82208	−0.318838
$950$	44.5423	1.44514
$951$	12.9887	0.421188
$952$	83.2808	2.69915
$953$	−10.1087	−0.327454	−0.163727	−	0.986506i	$-0.552352\pi$
$953$	−10.1087	−0.327454	−0.163727	+	0.986506i	$0.552352\pi$
$954$	−10.2215	−0.330932
$955$	93.9567	3.04037
$956$	85.5605	2.76722
$957$	3.52498	0.113946
$958$	−10.4013	−0.336051
$959$	−5.89972	−0.190512
$960$	16.9402	0.546742
$961$	−30.5254	−0.984689
$962$	25.6862	0.828156
$963$	−21.5038	−0.692949
$964$	82.7707	2.66587
$965$	5.70453	0.183635
$966$	−8.87652	−0.285597
$967$	−6.79599	−0.218544	−0.109272	−	0.994012i	$-0.534852\pi$
$967$	−6.79599	−0.218544	−0.109272	+	0.994012i	$0.534852\pi$
$968$	43.6360	1.40252
$969$	7.77073	0.249632
$970$	−164.029	−5.26664
$971$	16.8683	0.541329	0.270664	−	0.962674i	$-0.412757\pi$
$971$	16.8683	0.541329	0.270664	+	0.962674i	$0.412757\pi$
$972$	−73.4635	−2.35634
$973$	0.0587558	0.00188363
$974$	−38.8506	−1.24485
$975$	11.9516	0.382756
$976$	−86.9443	−2.78302
$977$	−36.4954	−1.16759	−0.583796	−	0.811900i	$-0.698433\pi$
$977$	−36.4954	−1.16759	−0.583796	+	0.811900i	$0.698433\pi$
$978$	4.81727	0.154039
$979$	−23.3974	−0.747784
$980$	21.0041	0.670952
$981$	−23.2841	−0.743403
$982$	−35.8972	−1.14553
$983$	13.0504	0.416242	0.208121	−	0.978103i	$-0.433265\pi$
$983$	13.0504	0.416242	0.208121	+	0.978103i	$0.433265\pi$
$984$	−7.74253	−0.246823
$985$	−37.1719	−1.18439
$986$	26.5586	0.845797
$987$	13.8170	0.439800
$988$	20.5022	0.652261
$989$	−17.1132	−0.544167
$990$	−50.6896	−1.61102
$991$	14.0462	0.446193	0.223096	−	0.974796i	$-0.428384\pi$
$991$	14.0462	0.446193	0.223096	+	0.974796i	$0.428384\pi$
$992$	−6.51860	−0.206966
$993$	−4.36542	−0.138532
$994$	26.4875	0.840132
$995$	11.8856	0.376798
$996$	50.2508	1.59226
$997$	−39.4626	−1.24979	−0.624896	−	0.780708i	$-0.714859\pi$
$997$	−39.4626	−1.24979	−0.624896	+	0.780708i	$0.714859\pi$
$998$	−92.7637	−2.93638
$999$	20.1140	0.636379

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6037.2.a.b.1.8	✓	259

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6037.2.a.b.1.8	✓	259	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:	\( N \)	\(=\)	\( 6037 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6037.a (trivial)

\(f(q)\)	\(=\)	\(q-2.60071 q^{2} -0.749599 q^{3} +4.76372 q^{4} -3.60076 q^{5} +1.94949 q^{6} -2.40322 q^{7} -7.18764 q^{8} -2.43810 q^{9} +O(q^{10})\)	\(q-2.60071 q^{2} -0.749599 q^{3} +4.76372 q^{4} -3.60076 q^{5} +1.94949 q^{6} -2.40322 q^{7} -7.18764 q^{8} -2.43810 q^{9} +9.36455 q^{10} +2.22014 q^{11} -3.57088 q^{12} -2.00163 q^{13} +6.25010 q^{14} +2.69912 q^{15} +9.16557 q^{16} +4.82130 q^{17} +6.34081 q^{18} -2.15015 q^{19} -17.1530 q^{20} +1.80145 q^{21} -5.77395 q^{22} +1.89464 q^{23} +5.38785 q^{24} +7.96546 q^{25} +5.20568 q^{26} +4.07639 q^{27} -11.4483 q^{28} -2.11811 q^{29} -7.01965 q^{30} +0.688943 q^{31} -9.46175 q^{32} -1.66421 q^{33} -12.5388 q^{34} +8.65343 q^{35} -11.6144 q^{36} +4.93426 q^{37} +5.59193 q^{38} +1.50042 q^{39} +25.8810 q^{40} -1.43704 q^{41} -4.68507 q^{42} -9.03240 q^{43} +10.5761 q^{44} +8.77902 q^{45} -4.92742 q^{46} +7.66993 q^{47} -6.87050 q^{48} -1.22452 q^{49} -20.7159 q^{50} -3.61404 q^{51} -9.53522 q^{52} -1.61201 q^{53} -10.6015 q^{54} -7.99419 q^{55} +17.2735 q^{56} +1.61175 q^{57} +5.50859 q^{58} -6.77799 q^{59} +12.8579 q^{60} -9.48597 q^{61} -1.79174 q^{62} +5.85930 q^{63} +6.27617 q^{64} +7.20740 q^{65} +4.32814 q^{66} +3.30456 q^{67} +22.9673 q^{68} -1.42022 q^{69} -22.5051 q^{70} +4.23793 q^{71} +17.5242 q^{72} +4.90703 q^{73} -12.8326 q^{74} -5.97090 q^{75} -10.2427 q^{76} -5.33549 q^{77} -3.90217 q^{78} -13.0263 q^{79} -33.0030 q^{80} +4.25865 q^{81} +3.73732 q^{82} -14.0724 q^{83} +8.58161 q^{84} -17.3603 q^{85} +23.4907 q^{86} +1.58773 q^{87} -15.9576 q^{88} -10.5387 q^{89} -22.8317 q^{90} +4.81038 q^{91} +9.02553 q^{92} -0.516431 q^{93} -19.9473 q^{94} +7.74217 q^{95} +7.09251 q^{96} -17.5159 q^{97} +3.18462 q^{98} -5.41293 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 259 q + 47 q^{2} + 29 q^{3} + 273 q^{4} + 38 q^{5} + 24 q^{6} + 42 q^{7} + 141 q^{8} + 286 q^{9}+O(q^{10}) \) 259 * q + 47 * q^2 + 29 * q^3 + 273 * q^4 + 38 * q^5 + 24 * q^6 + 42 * q^7 + 141 * q^8 + 286 * q^9	\( 259 q + 47 q^{2} + 29 q^{3} + 273 q^{4} + 38 q^{5} + 24 q^{6} + 42 q^{7} + 141 q^{8} + 286 q^{9} + 18 q^{10} + 108 q^{11} + 46 q^{12} + 33 q^{13} + 35 q^{14} + 40 q^{15} + 301 q^{16} + 67 q^{17} + 117 q^{18} + 69 q^{19} + 103 q^{20} + 24 q^{21} + 42 q^{22} + 162 q^{23} + 45 q^{24} + 291 q^{25} + 41 q^{26} + 101 q^{27} + 87 q^{28} + 78 q^{29} + 48 q^{30} + 25 q^{31} + 314 q^{32} + 67 q^{33} + 9 q^{34} + 252 q^{35} + 337 q^{36} + 49 q^{37} + 59 q^{38} + 93 q^{39} + 44 q^{40} + 60 q^{41} + 38 q^{42} + 178 q^{43} + 171 q^{44} + 67 q^{45} + 43 q^{46} + 185 q^{47} + 67 q^{48} + 273 q^{49} + 204 q^{50} + 145 q^{51} + 83 q^{52} + 112 q^{53} + 60 q^{54} + 57 q^{55} + 93 q^{56} + 109 q^{57} + 63 q^{58} + 228 q^{59} + 53 q^{60} + 20 q^{61} + 126 q^{62} + 153 q^{63} + 345 q^{64} + 113 q^{65} + 5 q^{66} + 208 q^{67} + 166 q^{68} + 10 q^{69} + 69 q^{70} + 150 q^{71} + 331 q^{72} + 75 q^{73} + 84 q^{74} + 72 q^{75} + 102 q^{76} + 166 q^{77} + 69 q^{78} + 52 q^{79} + 180 q^{80} + 327 q^{81} + 43 q^{82} + 434 q^{83} + 75 q^{85} + 133 q^{86} + 144 q^{87} + 111 q^{88} + 78 q^{89} - 8 q^{90} + 35 q^{91} + 372 q^{92} + 160 q^{93} + 36 q^{94} + 154 q^{95} + 60 q^{96} + 35 q^{97} + 254 q^{98} + 234 q^{99}+O(q^{100}) \) 259 * q + 47 * q^2 + 29 * q^3 + 273 * q^4 + 38 * q^5 + 24 * q^6 + 42 * q^7 + 141 * q^8 + 286 * q^9 + 18 * q^10 + 108 * q^11 + 46 * q^12 + 33 * q^13 + 35 * q^14 + 40 * q^15 + 301 * q^16 + 67 * q^17 + 117 * q^18 + 69 * q^19 + 103 * q^20 + 24 * q^21 + 42 * q^22 + 162 * q^23 + 45 * q^24 + 291 * q^25 + 41 * q^26 + 101 * q^27 + 87 * q^28 + 78 * q^29 + 48 * q^30 + 25 * q^31 + 314 * q^32 + 67 * q^33 + 9 * q^34 + 252 * q^35 + 337 * q^36 + 49 * q^37 + 59 * q^38 + 93 * q^39 + 44 * q^40 + 60 * q^41 + 38 * q^42 + 178 * q^43 + 171 * q^44 + 67 * q^45 + 43 * q^46 + 185 * q^47 + 67 * q^48 + 273 * q^49 + 204 * q^50 + 145 * q^51 + 83 * q^52 + 112 * q^53 + 60 * q^54 + 57 * q^55 + 93 * q^56 + 109 * q^57 + 63 * q^58 + 228 * q^59 + 53 * q^60 + 20 * q^61 + 126 * q^62 + 153 * q^63 + 345 * q^64 + 113 * q^65 + 5 * q^66 + 208 * q^67 + 166 * q^68 + 10 * q^69 + 69 * q^70 + 150 * q^71 + 331 * q^72 + 75 * q^73 + 84 * q^74 + 72 * q^75 + 102 * q^76 + 166 * q^77 + 69 * q^78 + 52 * q^79 + 180 * q^80 + 327 * q^81 + 43 * q^82 + 434 * q^83 + 75 * q^85 + 133 * q^86 + 144 * q^87 + 111 * q^88 + 78 * q^89 - 8 * q^90 + 35 * q^91 + 372 * q^92 + 160 * q^93 + 36 * q^94 + 154 * q^95 + 60 * q^96 + 35 * q^97 + 254 * q^98 + 234 * q^99

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