LMFDB - Embedded newform 6011.2.a.f.1.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6011,2,Mod(1,6011)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6011, 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("6011.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6011 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6011.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:	$47.9980766550$
Analytic rank:	$0$
Dimension:	$275$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
Character	$\chi$	$=$	6011.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.61945 q^{2} -2.32553 q^{3} +4.86151 q^{4} +4.35353 q^{5} +6.09159 q^{6} -2.02403 q^{7} -7.49557 q^{8} +2.40807 q^{9} +O(q^{10})$	\(q-2.61945 q^{2} -2.32553 q^{3} +4.86151 q^{4} +4.35353 q^{5} +6.09159 q^{6} -2.02403 q^{7} -7.49557 q^{8} +2.40807 q^{9} -11.4039 q^{10} -0.177226 q^{11} -11.3056 q^{12} +4.78943 q^{13} +5.30183 q^{14} -10.1243 q^{15} +9.91124 q^{16} -2.97313 q^{17} -6.30781 q^{18} +2.55745 q^{19} +21.1647 q^{20} +4.70692 q^{21} +0.464235 q^{22} -3.96683 q^{23} +17.4311 q^{24} +13.9532 q^{25} -12.5457 q^{26} +1.37655 q^{27} -9.83982 q^{28} +9.86443 q^{29} +26.5199 q^{30} +0.0293395 q^{31} -10.9708 q^{32} +0.412144 q^{33} +7.78795 q^{34} -8.81166 q^{35} +11.7068 q^{36} -1.18205 q^{37} -6.69910 q^{38} -11.1379 q^{39} -32.6322 q^{40} -8.97836 q^{41} -12.3295 q^{42} -0.281229 q^{43} -0.861586 q^{44} +10.4836 q^{45} +10.3909 q^{46} +10.0343 q^{47} -23.0488 q^{48} -2.90332 q^{49} -36.5498 q^{50} +6.91408 q^{51} +23.2838 q^{52} +1.61664 q^{53} -3.60580 q^{54} -0.771560 q^{55} +15.1712 q^{56} -5.94741 q^{57} -25.8394 q^{58} -7.70280 q^{59} -49.2191 q^{60} +13.9445 q^{61} -0.0768534 q^{62} -4.87399 q^{63} +8.91504 q^{64} +20.8509 q^{65} -1.07959 q^{66} +1.50313 q^{67} -14.4539 q^{68} +9.22496 q^{69} +23.0817 q^{70} -12.6786 q^{71} -18.0498 q^{72} -11.9498 q^{73} +3.09633 q^{74} -32.4486 q^{75} +12.4330 q^{76} +0.358710 q^{77} +29.1752 q^{78} +9.20705 q^{79} +43.1489 q^{80} -10.4254 q^{81} +23.5183 q^{82} -1.57703 q^{83} +22.8827 q^{84} -12.9436 q^{85} +0.736665 q^{86} -22.9400 q^{87} +1.32841 q^{88} +18.0745 q^{89} -27.4613 q^{90} -9.69392 q^{91} -19.2848 q^{92} -0.0682299 q^{93} -26.2842 q^{94} +11.1339 q^{95} +25.5129 q^{96} +4.97875 q^{97} +7.60509 q^{98} -0.426773 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 275 q + 16 q^{2} + 9 q^{3} + 316 q^{4} + 36 q^{5} + 30 q^{6} + 41 q^{7} + 36 q^{8} + 322 q^{9}+O(q^{10}) $ 275 * q + 16 * q^2 + 9 * q^3 + 316 * q^4 + 36 * q^5 + 30 * q^6 + 41 * q^7 + 36 * q^8 + 322 * q^9	\( 275 q + 16 q^{2} + 9 q^{3} + 316 q^{4} + 36 q^{5} + 30 q^{6} + 41 q^{7} + 36 q^{8} + 322 q^{9} + 44 q^{10} + 42 q^{11} + 26 q^{12} + 97 q^{13} + 24 q^{14} + 46 q^{15} + 386 q^{16} + 35 q^{17} + 47 q^{18} + 101 q^{19} + 60 q^{20} + 187 q^{21} + 72 q^{22} + 35 q^{23} + 73 q^{24} + 373 q^{25} + 21 q^{26} + 27 q^{27} + 97 q^{28} + 162 q^{29} + 13 q^{30} + 113 q^{31} + 58 q^{32} + 16 q^{33} + 52 q^{34} + 23 q^{35} + 426 q^{36} + 257 q^{37} + 8 q^{38} + 87 q^{39} + 126 q^{40} + 77 q^{41} - 7 q^{42} + 107 q^{43} + 133 q^{44} + 140 q^{45} + 207 q^{46} + 24 q^{47} + 4 q^{48} + 418 q^{49} + 65 q^{50} + 94 q^{51} + 142 q^{52} + 81 q^{53} + 79 q^{54} + 26 q^{55} + 62 q^{56} + 112 q^{57} + 44 q^{58} + 30 q^{59} + 83 q^{60} + 347 q^{61} + 5 q^{62} + 97 q^{63} + 508 q^{64} + 94 q^{65} + 4 q^{66} + 98 q^{67} + 28 q^{68} + 91 q^{69} + 17 q^{70} + 58 q^{71} + 99 q^{72} + 157 q^{73} + 80 q^{74} + 83 q^{75} + 264 q^{76} + 61 q^{77} + 5 q^{78} + 282 q^{79} + 49 q^{80} + 403 q^{81} + 46 q^{82} + 43 q^{83} + 318 q^{84} + 396 q^{85} + 57 q^{86} + 31 q^{87} + 180 q^{88} + 98 q^{89} + 67 q^{90} + 195 q^{91} + 97 q^{92} + 83 q^{93} + 96 q^{94} + 28 q^{95} + 127 q^{96} + 167 q^{97} + 24 q^{98} + 133 q^{99}+O(q^{100}) \) 275 * q + 16 * q^2 + 9 * q^3 + 316 * q^4 + 36 * q^5 + 30 * q^6 + 41 * q^7 + 36 * q^8 + 322 * q^9 + 44 * q^10 + 42 * q^11 + 26 * q^12 + 97 * q^13 + 24 * q^14 + 46 * q^15 + 386 * q^16 + 35 * q^17 + 47 * q^18 + 101 * q^19 + 60 * q^20 + 187 * q^21 + 72 * q^22 + 35 * q^23 + 73 * q^24 + 373 * q^25 + 21 * q^26 + 27 * q^27 + 97 * q^28 + 162 * q^29 + 13 * q^30 + 113 * q^31 + 58 * q^32 + 16 * q^33 + 52 * q^34 + 23 * q^35 + 426 * q^36 + 257 * q^37 + 8 * q^38 + 87 * q^39 + 126 * q^40 + 77 * q^41 - 7 * q^42 + 107 * q^43 + 133 * q^44 + 140 * q^45 + 207 * q^46 + 24 * q^47 + 4 * q^48 + 418 * q^49 + 65 * q^50 + 94 * q^51 + 142 * q^52 + 81 * q^53 + 79 * q^54 + 26 * q^55 + 62 * q^56 + 112 * q^57 + 44 * q^58 + 30 * q^59 + 83 * q^60 + 347 * q^61 + 5 * q^62 + 97 * q^63 + 508 * q^64 + 94 * q^65 + 4 * q^66 + 98 * q^67 + 28 * q^68 + 91 * q^69 + 17 * q^70 + 58 * q^71 + 99 * q^72 + 157 * q^73 + 80 * q^74 + 83 * q^75 + 264 * q^76 + 61 * q^77 + 5 * q^78 + 282 * q^79 + 49 * q^80 + 403 * q^81 + 46 * q^82 + 43 * q^83 + 318 * q^84 + 396 * q^85 + 57 * q^86 + 31 * q^87 + 180 * q^88 + 98 * q^89 + 67 * q^90 + 195 * q^91 + 97 * q^92 + 83 * q^93 + 96 * q^94 + 28 * q^95 + 127 * q^96 + 167 * q^97 + 24 * q^98 + 133 * 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 $

$2$	−2.61945	−1.85223	−0.926115	−	0.377242i	$-0.876872\pi$
$2$	−2.61945	−1.85223	−0.926115	+	0.377242i	$0.876872\pi$
$3$	−2.32553	−1.34264	−0.671321	−	0.741166i	$-0.734273\pi$
$3$	−2.32553	−1.34264	−0.671321	+	0.741166i	$0.734273\pi$
$4$	4.86151	2.43075
$5$	4.35353	1.94696	0.973480	−	0.228774i	$-0.0734717\pi$
$5$	4.35353	1.94696	0.973480	+	0.228774i	$0.0734717\pi$
$6$	6.09159	2.48688
$7$	−2.02403	−0.765010	−0.382505	−	0.923953i	$-0.624938\pi$
$7$	−2.02403	−0.765010	−0.382505	+	0.923953i	$0.624938\pi$
$8$	−7.49557	−2.65008
$9$	2.40807	0.802690
$10$	−11.4039	−3.60621
$11$	−0.177226	−0.0534357	−0.0267178	−	0.999643i	$-0.508506\pi$
$11$	−0.177226	−0.0534357	−0.0267178	+	0.999643i	$0.508506\pi$
$12$	−11.3056	−3.26363
$13$	4.78943	1.32835	0.664174	−	0.747578i	$-0.268783\pi$
$13$	4.78943	1.32835	0.664174	+	0.747578i	$0.268783\pi$
$14$	5.30183	1.41697
$15$	−10.1243	−2.61407
$16$	9.91124	2.47781
$17$	−2.97313	−0.721089	−0.360545	−	0.932742i	$-0.617409\pi$
$17$	−2.97313	−0.721089	−0.360545	+	0.932742i	$0.617409\pi$
$18$	−6.30781	−1.48677
$19$	2.55745	0.586718	0.293359	−	0.956002i	$-0.405227\pi$
$19$	2.55745	0.586718	0.293359	+	0.956002i	$0.405227\pi$
$20$	21.1647	4.73258
$21$	4.70692	1.02713
$22$	0.464235	0.0989751
$23$	−3.96683	−0.827141	−0.413570	−	0.910472i	$-0.635718\pi$
$23$	−3.96683	−0.827141	−0.413570	+	0.910472i	$0.635718\pi$
$24$	17.4311	3.55812
$25$	13.9532	2.79065
$26$	−12.5457	−2.46040
$27$	1.37655	0.264917
$28$	−9.83982	−1.85955
$29$	9.86443	1.83178	0.915889	−	0.401431i	$-0.131487\pi$
$29$	9.86443	1.83178	0.915889	+	0.401431i	$0.131487\pi$
$30$	26.5199	4.84186
$31$	0.0293395	0.00526954	0.00263477	−	0.999997i	$-0.499161\pi$
$31$	0.0293395	0.00526954	0.00263477	+	0.999997i	$0.499161\pi$
$32$	−10.9708	−1.93939
$33$	0.412144	0.0717450
$34$	7.78795	1.33562
$35$	−8.81166	−1.48944
$36$	11.7068	1.95114
$37$	−1.18205	−0.194329	−0.0971643	−	0.995268i	$-0.530977\pi$
$37$	−1.18205	−0.194329	−0.0971643	+	0.995268i	$0.530977\pi$
$38$	−6.69910	−1.08674
$39$	−11.1379	−1.78350
$40$	−32.6322	−5.15960
$41$	−8.97836	−1.40218	−0.701092	−	0.713071i	$-0.747304\pi$
$41$	−8.97836	−1.40218	−0.701092	+	0.713071i	$0.747304\pi$
$42$	−12.3295	−1.90249
$43$	−0.281229	−0.0428870	−0.0214435	−	0.999770i	$-0.506826\pi$
$43$	−0.281229	−0.0428870	−0.0214435	+	0.999770i	$0.506826\pi$
$44$	−0.861586	−0.129889
$45$	10.4836	1.56280
$46$	10.3909	1.53205
$47$	10.0343	1.46365	0.731823	−	0.681495i	$-0.238670\pi$
$47$	10.0343	1.46365	0.731823	+	0.681495i	$0.238670\pi$
$48$	−23.0488	−3.32681
$49$	−2.90332	−0.414760
$50$	−36.5498	−5.16892
$51$	6.91408	0.968165
$52$	23.2838	3.22889
$53$	1.61664	0.222062	0.111031	−	0.993817i	$-0.464585\pi$
$53$	1.61664	0.222062	0.111031	+	0.993817i	$0.464585\pi$
$54$	−3.60580	−0.490688
$55$	−0.771560	−0.104037
$56$	15.1712	2.02734
$57$	−5.94741	−0.787753
$58$	−25.8394	−3.39287
$59$	−7.70280	−1.00282	−0.501409	−	0.865210i	$-0.667185\pi$
$59$	−7.70280	−1.00282	−0.501409	+	0.865210i	$0.667185\pi$
$60$	−49.2191	−6.35416
$61$	13.9445	1.78541	0.892704	−	0.450644i	$-0.148806\pi$
$61$	13.9445	1.78541	0.892704	+	0.450644i	$0.148806\pi$
$62$	−0.0768534	−0.00976039
$63$	−4.87399	−0.614065
$64$	8.91504	1.11438
$65$	20.8509	2.58624
$66$	−1.07959	−0.132888
$67$	1.50313	0.183637	0.0918184	−	0.995776i	$-0.470732\pi$
$67$	1.50313	0.183637	0.0918184	+	0.995776i	$0.470732\pi$
$68$	−14.4539	−1.75279
$69$	9.22496	1.11055
$70$	23.0817	2.75879
$71$	−12.6786	−1.50467	−0.752337	−	0.658778i	$-0.771074\pi$
$71$	−12.6786	−1.50467	−0.752337	+	0.658778i	$0.771074\pi$
$72$	−18.0498	−2.12719
$73$	−11.9498	−1.39862	−0.699309	−	0.714820i	$-0.746509\pi$
$73$	−11.9498	−1.39862	−0.699309	+	0.714820i	$0.746509\pi$
$74$	3.09633	0.359941
$75$	−32.4486	−3.74685
$76$	12.4330	1.42617
$77$	0.358710	0.0408788
$78$	29.1752	3.30344
$79$	9.20705	1.03587	0.517937	−	0.855419i	$-0.326700\pi$
$79$	9.20705	1.03587	0.517937	+	0.855419i	$0.326700\pi$
$80$	43.1489	4.82419
$81$	−10.4254	−1.15838
$82$	23.5183	2.59717
$83$	−1.57703	−0.173101	−0.0865507	−	0.996247i	$-0.527584\pi$
$83$	−1.57703	−0.173101	−0.0865507	+	0.996247i	$0.527584\pi$
$84$	22.8827	2.49671
$85$	−12.9436	−1.40393
$86$	0.736665	0.0794366
$87$	−22.9400	−2.45942
$88$	1.32841	0.141609
$89$	18.0745	1.91589	0.957945	−	0.286951i	$-0.0926418\pi$
$89$	18.0745	1.91589	0.957945	+	0.286951i	$0.0926418\pi$
$90$	−27.4613	−2.89467
$91$	−9.69392	−1.01620
$92$	−19.2848	−2.01057
$93$	−0.0682299	−0.00707511
$94$	−26.2842	−2.71101
$95$	11.1339	1.14232
$96$	25.5129	2.60390
$97$	4.97875	0.505515	0.252758	−	0.967530i	$-0.418663\pi$
$97$	4.97875	0.505515	0.252758	+	0.967530i	$0.418663\pi$
$98$	7.60509	0.768231
$99$	−0.426773	−0.0428923
$100$	67.8338	6.78338
$101$	14.2718	1.42010	0.710050	−	0.704151i	$-0.248672\pi$
$101$	14.2718	1.42010	0.710050	+	0.704151i	$0.248672\pi$
$102$	−18.1111	−1.79326
$103$	0.940283	0.0926489	0.0463244	−	0.998926i	$-0.485249\pi$
$103$	0.940283	0.0926489	0.0463244	+	0.998926i	$0.485249\pi$
$104$	−35.8995	−3.52023
$105$	20.4917	1.99979
$106$	−4.23469	−0.411310
$107$	−19.9413	−1.92779	−0.963897	−	0.266274i	$-0.914207\pi$
$107$	−19.9413	−1.92779	−0.963897	+	0.266274i	$0.914207\pi$
$108$	6.69211	0.643949
$109$	18.3279	1.75549	0.877747	−	0.479124i	$-0.159046\pi$
$109$	18.3279	1.75549	0.877747	+	0.479124i	$0.159046\pi$
$110$	2.02106	0.192701
$111$	2.74890	0.260914
$112$	−20.0606	−1.89555
$113$	11.0228	1.03693	0.518467	−	0.855098i	$-0.326503\pi$
$113$	11.0228	1.03693	0.518467	+	0.855098i	$0.326503\pi$
$114$	15.5789	1.45910
$115$	−17.2697	−1.61041
$116$	47.9560	4.45260
$117$	11.5333	1.06625
$118$	20.1771	1.85745
$119$	6.01769	0.551640
$120$	75.8870	6.92751
$121$	−10.9686	−0.997145
$122$	−36.5268	−3.30698
$123$	20.8794	1.88263
$124$	0.142634	0.0128089
$125$	38.9783	3.48632
$126$	12.7672	1.13739
$127$	−0.0554610	−0.00492137	−0.00246068	−	0.999997i	$-0.500783\pi$
$127$	−0.0554610	−0.00492137	−0.00246068	+	0.999997i	$0.500783\pi$
$128$	−1.41083	−0.124701
$129$	0.654006	0.0575820
$130$	−54.6179	−4.79031
$131$	15.4977	1.35404	0.677021	−	0.735964i	$-0.263271\pi$
$131$	15.4977	1.35404	0.677021	+	0.735964i	$0.263271\pi$
$132$	2.00364	0.174394
$133$	−5.17634	−0.448845
$134$	−3.93738	−0.340137
$135$	5.99286	0.515783
$136$	22.2853	1.91095
$137$	−5.56678	−0.475602	−0.237801	−	0.971314i	$-0.576427\pi$
$137$	−5.56678	−0.475602	−0.237801	+	0.971314i	$0.576427\pi$
$138$	−24.1643	−2.05700
$139$	14.4762	1.22785	0.613926	−	0.789363i	$-0.289589\pi$
$139$	14.4762	1.22785	0.613926	+	0.789363i	$0.289589\pi$
$140$	−42.8380	−3.62047
$141$	−23.3349	−1.96515
$142$	33.2110	2.78700
$143$	−0.848811	−0.0709812
$144$	23.8669	1.98891
$145$	42.9451	3.56640
$146$	31.3019	2.59056
$147$	6.75174	0.556874
$148$	−5.74657	−0.472365
$149$	13.5937	1.11364	0.556821	−	0.830633i	$-0.312021\pi$
$149$	13.5937	1.11364	0.556821	+	0.830633i	$0.312021\pi$
$150$	84.9975	6.94002
$151$	13.2815	1.08083	0.540416	−	0.841398i	$-0.318267\pi$
$151$	13.2815	1.08083	0.540416	+	0.841398i	$0.318267\pi$
$152$	−19.1695	−1.55485
$153$	−7.15949	−0.578811
$154$	−0.939623	−0.0757170
$155$	0.127731	0.0102596
$156$	−54.1471	−4.33524
$157$	3.52631	0.281430	0.140715	−	0.990050i	$-0.455060\pi$
$157$	3.52631	0.281430	0.140715	+	0.990050i	$0.455060\pi$
$158$	−24.1174	−1.91868
$159$	−3.75953	−0.298150
$160$	−47.7619	−3.77591
$161$	8.02896	0.632771
$162$	27.3088	2.14558
$163$	−20.7102	−1.62215	−0.811076	−	0.584941i	$-0.801118\pi$
$163$	−20.7102	−1.62215	−0.811076	+	0.584941i	$0.801118\pi$
$164$	−43.6483	−3.40836
$165$	1.79428	0.139685
$166$	4.13094	0.320623
$167$	−14.5887	−1.12891	−0.564456	−	0.825463i	$-0.690914\pi$
$167$	−14.5887	−1.12891	−0.564456	+	0.825463i	$0.690914\pi$
$168$	−35.2811	−2.72199
$169$	9.93861	0.764508
$170$	33.9051	2.60040
$171$	6.15850	0.470953
$172$	−1.36720	−0.104248
$173$	−22.0269	−1.67467	−0.837337	−	0.546687i	$-0.815889\pi$
$173$	−22.0269	−1.67467	−0.837337	+	0.546687i	$0.815889\pi$
$174$	60.0901	4.55542
$175$	−28.2417	−2.13487
$176$	−1.75653	−0.132403
$177$	17.9130	1.34643
$178$	−47.3451	−3.54867
$179$	−0.491118	−0.0367079	−0.0183540	−	0.999832i	$-0.505843\pi$
$179$	−0.491118	−0.0367079	−0.0183540	+	0.999832i	$0.505843\pi$
$180$	50.9661	3.79879
$181$	−23.3358	−1.73454	−0.867268	−	0.497841i	$-0.834126\pi$
$181$	−23.3358	−1.73454	−0.867268	+	0.497841i	$0.834126\pi$
$182$	25.3927	1.88223
$183$	−32.4282	−2.39716
$184$	29.7336	2.19199
$185$	−5.14611	−0.378350
$186$	0.178725	0.0131047
$187$	0.526916	0.0385319
$188$	48.7816	3.55776
$189$	−2.78618	−0.202664
$190$	−29.1647	−2.11583
$191$	7.20651	0.521444	0.260722	−	0.965414i	$-0.416039\pi$
$191$	7.20651	0.521444	0.260722	+	0.965414i	$0.416039\pi$
$192$	−20.7322	−1.49621
$193$	4.95877	0.356940	0.178470	−	0.983945i	$-0.442885\pi$
$193$	4.95877	0.356940	0.178470	+	0.983945i	$0.442885\pi$
$194$	−13.0416	−0.936330
$195$	−48.4894	−3.47240
$196$	−14.1145	−1.00818
$197$	−14.0627	−1.00193	−0.500963	−	0.865468i	$-0.667021\pi$
$197$	−14.0627	−1.00193	−0.500963	+	0.865468i	$0.667021\pi$
$198$	1.11791	0.0794463
$199$	9.46096	0.670670	0.335335	−	0.942099i	$-0.391150\pi$
$199$	9.46096	0.670670	0.335335	+	0.942099i	$0.391150\pi$
$200$	−104.588	−7.39546
$201$	−3.49557	−0.246559
$202$	−37.3843	−2.63035
$203$	−19.9659	−1.40133
$204$	33.6129	2.35337
$205$	−39.0876	−2.72999
$206$	−2.46302	−0.171607
$207$	−9.55239	−0.663937
$208$	47.4691	3.29139
$209$	−0.453246	−0.0313517
$210$	−53.6771	−3.70407
$211$	−7.58247	−0.521999	−0.260999	−	0.965339i	$-0.584052\pi$
$211$	−7.58247	−0.521999	−0.260999	+	0.965339i	$0.584052\pi$
$212$	7.85928	0.539778
$213$	29.4844	2.02024
$214$	52.2351	3.57072
$215$	−1.22434	−0.0834993
$216$	−10.3180	−0.702053
$217$	−0.0593840	−0.00403125
$218$	−48.0090	−3.25158
$219$	27.7896	1.87784
$220$	−3.75094	−0.252889
$221$	−14.2396	−0.957857
$222$	−7.20059	−0.483272
$223$	18.5881	1.24475	0.622376	−	0.782718i	$-0.286168\pi$
$223$	18.5881	1.24475	0.622376	+	0.782718i	$0.286168\pi$
$224$	22.2052	1.48365
$225$	33.6004	2.24003
$226$	−28.8735	−1.92064
$227$	16.5194	1.09643	0.548217	−	0.836336i	$-0.315307\pi$
$227$	16.5194	1.09643	0.548217	+	0.836336i	$0.315307\pi$
$228$	−28.9134	−1.91483
$229$	−7.94143	−0.524784	−0.262392	−	0.964961i	$-0.584511\pi$
$229$	−7.94143	−0.524784	−0.262392	+	0.964961i	$0.584511\pi$
$230$	45.2371	2.98285
$231$	−0.834190	−0.0548857
$232$	−73.9395	−4.85437
$233$	−10.6199	−0.695730	−0.347865	−	0.937545i	$-0.613093\pi$
$233$	−10.6199	−0.695730	−0.347865	+	0.937545i	$0.613093\pi$
$234$	−30.2108	−1.97494
$235$	43.6845	2.84966
$236$	−37.4472	−2.43760
$237$	−21.4112	−1.39081
$238$	−15.7630	−1.02176
$239$	3.69898	0.239267	0.119634	−	0.992818i	$-0.461828\pi$
$239$	3.69898	0.239267	0.119634	+	0.992818i	$0.461828\pi$
$240$	−100.344	−6.47717
$241$	−15.8000	−1.01777	−0.508885	−	0.860835i	$-0.669942\pi$
$241$	−15.8000	−1.01777	−0.508885	+	0.860835i	$0.669942\pi$
$242$	28.7317	1.84694
$243$	20.1149	1.29037
$244$	67.7912	4.33989
$245$	−12.6397	−0.807521
$246$	−54.6925	−3.48707
$247$	12.2487	0.779366
$248$	−0.219917	−0.0139647
$249$	3.66742	0.232413
$250$	−102.102	−6.45747
$251$	9.82878	0.620387	0.310194	−	0.950673i	$-0.399606\pi$
$251$	9.82878	0.620387	0.310194	+	0.950673i	$0.399606\pi$
$252$	−23.6950	−1.49264
$253$	0.703025	0.0441988
$254$	0.145277	0.00911550
$255$	30.1007	1.88498
$256$	−14.1345	−0.883405
$257$	4.44445	0.277237	0.138619	−	0.990346i	$-0.455734\pi$
$257$	4.44445	0.277237	0.138619	+	0.990346i	$0.455734\pi$
$258$	−1.71313	−0.106655
$259$	2.39251	0.148663
$260$	101.367	6.28651
$261$	23.7542	1.47035
$262$	−40.5954	−2.50799
$263$	−10.8287	−0.667726	−0.333863	−	0.942622i	$-0.608352\pi$
$263$	−10.8287	−0.667726	−0.333863	+	0.942622i	$0.608352\pi$
$264$	−3.08925	−0.190130
$265$	7.03807	0.432345
$266$	13.5591	0.831364
$267$	−42.0326	−2.57236
$268$	7.30749	0.446376
$269$	−8.53572	−0.520432	−0.260216	−	0.965550i	$-0.583794\pi$
$269$	−8.53572	−0.520432	−0.260216	+	0.965550i	$0.583794\pi$
$270$	−15.6980	−0.955349
$271$	−7.11164	−0.432001	−0.216001	−	0.976393i	$-0.569301\pi$
$271$	−7.11164	−0.432001	−0.216001	+	0.976393i	$0.569301\pi$
$272$	−29.4674	−1.78672
$273$	22.5435	1.36439
$274$	14.5819	0.880924
$275$	−2.47288	−0.149120
$276$	44.8472	2.69948
$277$	6.08358	0.365527	0.182763	−	0.983157i	$-0.441496\pi$
$277$	6.08358	0.365527	0.182763	+	0.983157i	$0.441496\pi$
$278$	−37.9196	−2.27426
$279$	0.0706516	0.00422980
$280$	66.0484	3.94715
$281$	4.58500	0.273518	0.136759	−	0.990604i	$-0.456331\pi$
$281$	4.58500	0.273518	0.136759	+	0.990604i	$0.456331\pi$
$282$	61.1246	3.63992
$283$	25.8942	1.53925	0.769626	−	0.638496i	$-0.220443\pi$
$283$	25.8942	1.53925	0.769626	+	0.638496i	$0.220443\pi$
$284$	−61.6372	−3.65749
$285$	−25.8922	−1.53372
$286$	2.22342	0.131473
$287$	18.1724	1.07268
$288$	−26.4185	−1.55673
$289$	−8.16051	−0.480030
$290$	−112.493	−6.60579
$291$	−11.5782	−0.678726
$292$	−58.0940	−3.39970
$293$	−16.6705	−0.973900	−0.486950	−	0.873430i	$-0.661891\pi$
$293$	−16.6705	−0.973900	−0.486950	+	0.873430i	$0.661891\pi$
$294$	−17.6858	−1.03146
$295$	−33.5344	−1.95245
$296$	8.86017	0.514987
$297$	−0.243961	−0.0141560
$298$	−35.6080	−2.06272
$299$	−18.9988	−1.09873
$300$	−157.749	−9.10766
$301$	0.569215	0.0328090
$302$	−34.7902	−2.00195
$303$	−33.1895	−1.90669
$304$	25.3474	1.45378
$305$	60.7078	3.47612
$306$	18.7539	1.07209
$307$	3.38654	0.193280	0.0966401	−	0.995319i	$-0.469190\pi$
$307$	3.38654	0.193280	0.0966401	+	0.995319i	$0.469190\pi$
$308$	1.74387	0.0993663
$309$	−2.18665	−0.124394
$310$	−0.334584	−0.0190031
$311$	3.70212	0.209928	0.104964	−	0.994476i	$-0.466527\pi$
$311$	3.70212	0.209928	0.104964	+	0.994476i	$0.466527\pi$
$312$	83.4851	4.72642
$313$	−19.7271	−1.11504	−0.557520	−	0.830163i	$-0.688247\pi$
$313$	−19.7271	−1.11504	−0.557520	+	0.830163i	$0.688247\pi$
$314$	−9.23697	−0.521273
$315$	−21.2191	−1.19556
$316$	44.7601	2.51795
$317$	31.9071	1.79208	0.896041	−	0.443972i	$-0.146431\pi$
$317$	31.9071	1.79208	0.896041	+	0.443972i	$0.146431\pi$
$318$	9.84788	0.552242
$319$	−1.74823	−0.0978823
$320$	38.8119	2.16965
$321$	46.3739	2.58834
$322$	−21.0314	−1.17204
$323$	−7.60361	−0.423076
$324$	−50.6832	−2.81573
$325$	66.8281	3.70695
$326$	54.2494	3.00460
$327$	−42.6220	−2.35700
$328$	67.2979	3.71590
$329$	−20.3096	−1.11970
$330$	−4.70003	−0.258728
$331$	12.0154	0.660425	0.330212	−	0.943907i	$-0.392880\pi$
$331$	12.0154	0.660425	0.330212	+	0.943907i	$0.392880\pi$
$332$	−7.66673	−0.420767
$333$	−2.84647	−0.155985
$334$	38.2145	2.09100
$335$	6.54393	0.357533
$336$	46.6514	2.54504
$337$	17.2575	0.940076	0.470038	−	0.882646i	$-0.344240\pi$
$337$	17.2575	0.940076	0.470038	+	0.882646i	$0.344240\pi$
$338$	−26.0337	−1.41604
$339$	−25.6337	−1.39223
$340$	−62.9254	−3.41261
$341$	−0.00519973	−0.000281581 0
$342$	−16.1319	−0.872312
$343$	20.0446	1.08231
$344$	2.10797	0.113654
$345$	40.1612	2.16220
$346$	57.6983	3.10188
$347$	−22.6700	−1.21699	−0.608495	−	0.793557i	$-0.708227\pi$
$347$	−22.6700	−1.21699	−0.608495	+	0.793557i	$0.708227\pi$
$348$	−111.523	−5.97825
$349$	−9.21211	−0.493113	−0.246557	−	0.969128i	$-0.579299\pi$
$349$	−9.21211	−0.493113	−0.246557	+	0.969128i	$0.579299\pi$
$350$	73.9778	3.95428
$351$	6.59289	0.351903
$352$	1.94432	0.103632
$353$	13.2368	0.704522	0.352261	−	0.935902i	$-0.385413\pi$
$353$	13.2368	0.704522	0.352261	+	0.935902i	$0.385413\pi$
$354$	−46.9223	−2.49389
$355$	−55.1968	−2.92954
$356$	87.8692	4.65706
$357$	−13.9943	−0.740656
$358$	1.28646	0.0679915
$359$	−3.71214	−0.195919	−0.0979597	−	0.995190i	$-0.531232\pi$
$359$	−3.71214	−0.195919	−0.0979597	+	0.995190i	$0.531232\pi$
$360$	−78.5806	−4.14156
$361$	−12.4595	−0.655762
$362$	61.1269	3.21276
$363$	25.5077	1.33881
$364$	−47.1271	−2.47013
$365$	−52.0238	−2.72305
$366$	84.9441	4.44010
$367$	22.6137	1.18043	0.590213	−	0.807248i	$-0.299044\pi$
$367$	22.6137	1.18043	0.590213	+	0.807248i	$0.299044\pi$
$368$	−39.3162	−2.04950
$369$	−21.6205	−1.12552
$370$	13.4800	0.700790
$371$	−3.27211	−0.169880
$372$	−0.331700	−0.0171978
$373$	1.65639	0.0857648	0.0428824	−	0.999080i	$-0.486346\pi$
$373$	1.65639	0.0857648	0.0428824	+	0.999080i	$0.486346\pi$
$374$	−1.38023	−0.0713699
$375$	−90.6450	−4.68089
$376$	−75.2124	−3.87878
$377$	47.2450	2.43324
$378$	7.29824	0.375381
$379$	6.68738	0.343508	0.171754	−	0.985140i	$-0.445057\pi$
$379$	6.68738	0.343508	0.171754	+	0.985140i	$0.445057\pi$
$380$	54.1277	2.77669
$381$	0.128976	0.00660764
$382$	−18.8771	−0.965835
$383$	−21.1631	−1.08139	−0.540693	−	0.841220i	$-0.681838\pi$
$383$	−21.1631	−1.08139	−0.540693	+	0.841220i	$0.681838\pi$
$384$	3.28093	0.167429
$385$	1.56166	0.0795894
$386$	−12.9892	−0.661135
$387$	−0.677219	−0.0344250
$388$	24.2042	1.22878
$389$	−14.8346	−0.752143	−0.376072	−	0.926591i	$-0.622725\pi$
$389$	−14.8346	−0.752143	−0.376072	+	0.926591i	$0.622725\pi$
$390$	127.015	6.43167
$391$	11.7939	0.596442
$392$	21.7620	1.09915
$393$	−36.0403	−1.81799
$394$	36.8365	1.85580
$395$	40.0832	2.01680
$396$	−2.07476	−0.104261
$397$	−19.1698	−0.962104	−0.481052	−	0.876692i	$-0.659745\pi$
$397$	−19.1698	−0.962104	−0.481052	+	0.876692i	$0.659745\pi$
$398$	−24.7825	−1.24223
$399$	12.0377	0.602639
$400$	138.294	6.91470
$401$	27.5715	1.37686	0.688428	−	0.725305i	$-0.258301\pi$
$401$	27.5715	1.37686	0.688428	+	0.725305i	$0.258301\pi$
$402$	9.15647	0.456683
$403$	0.140520	0.00699978
$404$	69.3826	3.45191
$405$	−45.3874	−2.25532
$406$	52.2995	2.59558
$407$	0.209491	0.0103841
$408$	−51.8250	−2.56572
$409$	36.4757	1.80361	0.901804	−	0.432145i	$-0.142243\pi$
$409$	36.4757	1.80361	0.901804	+	0.432145i	$0.142243\pi$
$410$	102.388	5.05658
$411$	12.9457	0.638564
$412$	4.57119	0.225207
$413$	15.5907	0.767166
$414$	25.0220	1.22976
$415$	−6.86564	−0.337021
$416$	−52.5440	−2.57618
$417$	−33.6647	−1.64857
$418$	1.18725	0.0580705
$419$	−17.5469	−0.857222	−0.428611	−	0.903489i	$-0.640997\pi$
$419$	−17.5469	−0.857222	−0.428611	+	0.903489i	$0.640997\pi$
$420$	99.6208	4.86100
$421$	20.4218	0.995295	0.497648	−	0.867379i	$-0.334197\pi$
$421$	20.4218	0.995295	0.497648	+	0.867379i	$0.334197\pi$
$422$	19.8619	0.966862
$423$	24.1632	1.17485
$424$	−12.1176	−0.588483
$425$	−41.4848	−2.01231
$426$	−77.2329	−3.74195
$427$	−28.2240	−1.36585
$428$	−96.9446	−4.68599
$429$	1.97393	0.0953024
$430$	3.20710	0.154660
$431$	−19.3437	−0.931756	−0.465878	−	0.884849i	$-0.654261\pi$
$431$	−19.3437	−0.931756	−0.465878	+	0.884849i	$0.654261\pi$
$432$	13.6433	0.656415
$433$	−19.6881	−0.946151	−0.473075	−	0.881022i	$-0.656856\pi$
$433$	−19.6881	−0.946151	−0.473075	+	0.881022i	$0.656856\pi$
$434$	0.155553	0.00746680
$435$	−99.8700	−4.78840
$436$	89.1012	4.26717
$437$	−10.1449	−0.485298
$438$	−72.7933	−3.47820
$439$	7.97359	0.380559	0.190279	−	0.981730i	$-0.439061\pi$
$439$	7.97359	0.380559	0.190279	+	0.981730i	$0.439061\pi$
$440$	5.78328	0.275707
$441$	−6.99139	−0.332923
$442$	37.2998	1.77417
$443$	0.604177	0.0287053	0.0143527	−	0.999897i	$-0.495431\pi$
$443$	0.604177	0.0287053	0.0143527	+	0.999897i	$0.495431\pi$
$444$	13.3638	0.634217
$445$	78.6878	3.73016
$446$	−48.6906	−2.30557
$447$	−31.6125	−1.49522
$448$	−18.0443	−0.852512
$449$	1.58290	0.0747016	0.0373508	−	0.999302i	$-0.488108\pi$
$449$	1.58290	0.0747016	0.0373508	+	0.999302i	$0.488108\pi$
$450$	−88.0144	−4.14904
$451$	1.59120	0.0749267
$452$	53.5872	2.52053
$453$	−30.8865	−1.45117
$454$	−43.2718	−2.03085
$455$	−42.2028	−1.97850
$456$	44.5792	2.08761
$457$	13.2863	0.621505	0.310752	−	0.950491i	$-0.399419\pi$
$457$	13.2863	0.621505	0.310752	+	0.950491i	$0.399419\pi$
$458$	20.8022	0.972021
$459$	−4.09266	−0.191029
$460$	−83.9568	−3.91451
$461$	−34.3062	−1.59780	−0.798900	−	0.601463i	$-0.794585\pi$
$461$	−34.3062	−1.59780	−0.798900	+	0.601463i	$0.794585\pi$
$462$	2.18512	0.101661
$463$	0.736043	0.0342068	0.0171034	−	0.999854i	$-0.494556\pi$
$463$	0.736043	0.0342068	0.0171034	+	0.999854i	$0.494556\pi$
$464$	97.7687	4.53880
$465$	−0.297041	−0.0137749
$466$	27.8181	1.28865
$467$	−27.7579	−1.28448	−0.642241	−	0.766503i	$-0.721995\pi$
$467$	−27.7579	−1.28448	−0.642241	+	0.766503i	$0.721995\pi$
$468$	56.0691	2.59179
$469$	−3.04238	−0.140484
$470$	−114.429	−5.27822
$471$	−8.20051	−0.377860
$472$	57.7368	2.65755
$473$	0.0498412	0.00229170
$474$	56.0856	2.57610
$475$	35.6847	1.63733
$476$	29.2550	1.34090
$477$	3.89297	0.178247
$478$	−9.68928	−0.443177
$479$	−11.8001	−0.539159	−0.269579	−	0.962978i	$-0.586885\pi$
$479$	−11.8001	−0.539159	−0.269579	+	0.962978i	$0.586885\pi$
$480$	111.071	5.06969
$481$	−5.66136	−0.258136
$482$	41.3874	1.88514
$483$	−18.6715	−0.849585
$484$	−53.3239	−2.42381
$485$	21.6751	0.984217
$486$	−52.6899	−2.39006
$487$	32.0017	1.45014	0.725069	−	0.688676i	$-0.241808\pi$
$487$	32.0017	1.45014	0.725069	+	0.688676i	$0.241808\pi$
$488$	−104.522	−4.73148
$489$	48.1622	2.17797
$490$	33.1090	1.49571
$491$	−35.8346	−1.61719	−0.808597	−	0.588363i	$-0.799773\pi$
$491$	−35.8346	−1.61719	−0.808597	+	0.588363i	$0.799773\pi$
$492$	101.505	4.57621
$493$	−29.3282	−1.32088
$494$	−32.0848	−1.44356
$495$	−1.85797	−0.0835095
$496$	0.290791	0.0130569
$497$	25.6618	1.15109
$498$	−9.60661	−0.430483
$499$	28.7883	1.28874	0.644370	−	0.764714i	$-0.277120\pi$
$499$	28.7883	1.28874	0.644370	+	0.764714i	$0.277120\pi$
$500$	189.493	8.47439
$501$	33.9265	1.51572
$502$	−25.7460	−1.14910
$503$	−2.23356	−0.0995897	−0.0497949	−	0.998759i	$-0.515857\pi$
$503$	−2.23356	−0.0995897	−0.0497949	+	0.998759i	$0.515857\pi$
$504$	36.5333	1.62732
$505$	62.1329	2.76488
$506$	−1.84154	−0.0818663
$507$	−23.1125	−1.02646
$508$	−0.269624	−0.0119626
$509$	6.87422	0.304695	0.152347	−	0.988327i	$-0.451317\pi$
$509$	6.87422	0.304695	0.152347	+	0.988327i	$0.451317\pi$
$510$	−78.8472	−3.49141
$511$	24.1867	1.06996
$512$	39.8462	1.76097
$513$	3.52046	0.155432
$514$	−11.6420	−0.513507
$515$	4.09355	0.180384
$516$	3.17945	0.139968
$517$	−1.77833	−0.0782109
$518$	−6.26705	−0.275358
$519$	51.2241	2.24849
$520$	−156.290	−6.85375
$521$	20.2409	0.886770	0.443385	−	0.896331i	$-0.353777\pi$
$521$	20.2409	0.886770	0.443385	+	0.896331i	$0.353777\pi$
$522$	−62.2229	−2.72342
$523$	30.5752	1.33696	0.668480	−	0.743730i	$-0.266945\pi$
$523$	30.5752	1.33696	0.668480	+	0.743730i	$0.266945\pi$
$524$	75.3422	3.29134
$525$	65.6769	2.86637
$526$	28.3652	1.23678
$527$	−0.0872302	−0.00379981
$528$	4.08485	0.177770
$529$	−7.26429	−0.315839
$530$	−18.4359	−0.800803
$531$	−18.5489	−0.804952
$532$	−25.1648	−1.09103
$533$	−43.0012	−1.86259
$534$	110.102	4.76459
$535$	−86.8149	−3.75334
$536$	−11.2668	−0.486653
$537$	1.14211	0.0492856
$538$	22.3589	0.963959
$539$	0.514544	0.0221630
$540$	29.1343	1.25374
$541$	27.2348	1.17092	0.585459	−	0.810702i	$-0.300914\pi$
$541$	27.2348	1.17092	0.585459	+	0.810702i	$0.300914\pi$
$542$	18.6286	0.800165
$543$	54.2680	2.32886
$544$	32.6177	1.39847
$545$	79.7911	3.41788
$546$	−59.0514	−2.52717
$547$	−6.67369	−0.285346	−0.142673	−	0.989770i	$-0.545570\pi$
$547$	−6.67369	−0.285346	−0.142673	+	0.989770i	$0.545570\pi$
$548$	−27.0629	−1.15607
$549$	33.5793	1.43313
$550$	6.47758	0.276205
$551$	25.2277	1.07474
$552$	−69.1463	−2.94306
$553$	−18.6353	−0.792454
$554$	−15.9356	−0.677040
$555$	11.9674	0.507989
$556$	70.3760	2.98461
$557$	27.9377	1.18376	0.591878	−	0.806027i	$-0.298387\pi$
$557$	27.9377	1.18376	0.591878	+	0.806027i	$0.298387\pi$
$558$	−0.185068	−0.00783457
$559$	−1.34693	−0.0569689
$560$	−87.3345	−3.69056
$561$	−1.22536	−0.0517346
$562$	−12.0102	−0.506618
$563$	18.0805	0.762003	0.381002	−	0.924574i	$-0.375579\pi$
$563$	18.0805	0.762003	0.381002	+	0.924574i	$0.375579\pi$
$564$	−113.443	−4.77681
$565$	47.9879	2.01887
$566$	−67.8285	−2.85105
$567$	21.1013	0.886171
$568$	95.0334	3.98751
$569$	−20.3966	−0.855072	−0.427536	−	0.903998i	$-0.640618\pi$
$569$	−20.3966	−0.855072	−0.427536	+	0.903998i	$0.640618\pi$
$570$	67.8233	2.84081
$571$	9.72371	0.406925	0.203462	−	0.979083i	$-0.434781\pi$
$571$	9.72371	0.406925	0.203462	+	0.979083i	$0.434781\pi$
$572$	−4.12650	−0.172538
$573$	−16.7589	−0.700114
$574$	−47.6017	−1.98686
$575$	−55.3501	−2.30826
$576$	21.4680	0.894502
$577$	−6.83818	−0.284677	−0.142338	−	0.989818i	$-0.545462\pi$
$577$	−6.83818	−0.284677	−0.142338	+	0.989818i	$0.545462\pi$
$578$	21.3760	0.889126
$579$	−11.5318	−0.479243
$580$	208.778	8.66903
$581$	3.19195	0.132424
$582$	30.3285	1.25716
$583$	−0.286510	−0.0118660
$584$	89.5705	3.70645
$585$	50.2105	2.07595
$586$	43.6674	1.80389
$587$	−25.5987	−1.05657	−0.528286	−	0.849067i	$-0.677165\pi$
$587$	−25.5987	−1.05657	−0.528286	+	0.849067i	$0.677165\pi$
$588$	32.8237	1.35362
$589$	0.0750343	0.00309173
$590$	87.8415	3.61638
$591$	32.7032	1.34523
$592$	−11.7156	−0.481509
$593$	9.54165	0.391829	0.195914	−	0.980621i	$-0.437233\pi$
$593$	9.54165	0.391829	0.195914	+	0.980621i	$0.437233\pi$
$594$	0.639043	0.0262202
$595$	26.1982	1.07402
$596$	66.0860	2.70699
$597$	−22.0017	−0.900470
$598$	49.7664	2.03510
$599$	8.37070	0.342017	0.171009	−	0.985270i	$-0.445297\pi$
$599$	8.37070	0.342017	0.171009	+	0.985270i	$0.445297\pi$
$600$	243.221	9.92945
$601$	24.9935	1.01951	0.509753	−	0.860321i	$-0.329737\pi$
$601$	24.9935	1.01951	0.509753	+	0.860321i	$0.329737\pi$
$602$	−1.49103	−0.0607698
$603$	3.61964	0.147403
$604$	64.5681	2.62724
$605$	−47.7521	−1.94140
$606$	86.9382	3.53162
$607$	38.6164	1.56739	0.783695	−	0.621146i	$-0.213333\pi$
$607$	38.6164	1.56739	0.783695	+	0.621146i	$0.213333\pi$
$608$	−28.0573	−1.13787
$609$	46.4311	1.88148
$610$	−159.021	−6.43856
$611$	48.0583	1.94423
$612$	−34.8059	−1.40695
$613$	−15.0838	−0.609228	−0.304614	−	0.952476i	$-0.598528\pi$
$613$	−15.0838	−0.609228	−0.304614	+	0.952476i	$0.598528\pi$
$614$	−8.87088	−0.357999
$615$	90.8992	3.66541
$616$	−2.68874	−0.108332
$617$	−34.7122	−1.39746	−0.698731	−	0.715384i	$-0.746252\pi$
$617$	−34.7122	−1.39746	−0.698731	+	0.715384i	$0.746252\pi$
$618$	5.72782	0.230407
$619$	−7.46923	−0.300214	−0.150107	−	0.988670i	$-0.547962\pi$
$619$	−7.46923	−0.300214	−0.150107	+	0.988670i	$0.547962\pi$
$620$	0.620964	0.0249385
$621$	−5.46054	−0.219124
$622$	−9.69752	−0.388835
$623$	−36.5832	−1.46567
$624$	−110.391	−4.41916
$625$	99.9269	3.99708
$626$	51.6740	2.06531
$627$	1.05404	0.0420941
$628$	17.1432	0.684086
$629$	3.51440	0.140128
$630$	55.5823	2.21445
$631$	−16.9954	−0.676576	−0.338288	−	0.941043i	$-0.609848\pi$
$631$	−16.9954	−0.676576	−0.338288	+	0.941043i	$0.609848\pi$
$632$	−69.0121	−2.74515
$633$	17.6332	0.700858
$634$	−83.5790	−3.31935
$635$	−0.241451	−0.00958170
$636$	−18.2770	−0.724729
$637$	−13.9052	−0.550946
$638$	4.57941	0.181301
$639$	−30.5310	−1.20779
$640$	−6.14211	−0.242788
$641$	−6.29425	−0.248608	−0.124304	−	0.992244i	$-0.539670\pi$
$641$	−6.29425	−0.248608	−0.124304	+	0.992244i	$0.539670\pi$
$642$	−121.474	−4.79420
$643$	17.4963	0.689985	0.344993	−	0.938605i	$-0.387881\pi$
$643$	17.4963	0.689985	0.344993	+	0.938605i	$0.387881\pi$
$644$	39.0328	1.53811
$645$	2.84723	0.112110
$646$	19.9173	0.783634
$647$	−32.6911	−1.28522	−0.642609	−	0.766194i	$-0.722148\pi$
$647$	−32.6911	−1.28522	−0.642609	+	0.766194i	$0.722148\pi$
$648$	78.1444	3.06980
$649$	1.36514	0.0535863
$650$	−175.053	−6.86613
$651$	0.138099	0.00541253
$652$	−100.683	−3.94305
$653$	15.4705	0.605407	0.302704	−	0.953085i	$-0.402111\pi$
$653$	15.4705	0.605407	0.302704	+	0.953085i	$0.402111\pi$
$654$	111.646	4.36571
$655$	67.4698	2.63626
$656$	−88.9866	−3.47434
$657$	−28.7759	−1.12266
$658$	53.1999	2.07395
$659$	−33.0589	−1.28779	−0.643895	−	0.765114i	$-0.722683\pi$
$659$	−33.0589	−1.28779	−0.643895	+	0.765114i	$0.722683\pi$
$660$	8.72291	0.339539
$661$	13.7524	0.534906	0.267453	−	0.963571i	$-0.413818\pi$
$661$	13.7524	0.534906	0.267453	+	0.963571i	$0.413818\pi$
$662$	−31.4737	−1.22326
$663$	33.1145	1.28606
$664$	11.8207	0.458733
$665$	−22.5353	−0.873883
$666$	7.45617	0.288921
$667$	−39.1305	−1.51514
$668$	−70.9233	−2.74411
$669$	−43.2271	−1.67126
$670$	−17.1415	−0.662234
$671$	−2.47133	−0.0954045
$672$	−51.6389	−1.99201
$673$	21.1791	0.816395	0.408198	−	0.912894i	$-0.366157\pi$
$673$	21.1791	0.816395	0.408198	+	0.912894i	$0.366157\pi$
$674$	−45.2051	−1.74124
$675$	19.2074	0.739292
$676$	48.3166	1.85833
$677$	29.7046	1.14164	0.570820	−	0.821075i	$-0.306625\pi$
$677$	29.7046	1.14164	0.570820	+	0.821075i	$0.306625\pi$
$678$	67.1461	2.57873
$679$	−10.0771	−0.386724
$680$	97.0197	3.72054
$681$	−38.4164	−1.47212
$682$	0.0136204	0.000521553 0
$683$	−24.6300	−0.942440	−0.471220	−	0.882016i	$-0.656186\pi$
$683$	−24.6300	−0.942440	−0.471220	+	0.882016i	$0.656186\pi$
$684$	29.9396	1.14477
$685$	−24.2352	−0.925978
$686$	−52.5057	−2.00468
$687$	18.4680	0.704598
$688$	−2.78733	−0.106266
$689$	7.74276	0.294975
$690$	−105.200	−4.00490
$691$	29.6513	1.12799	0.563994	−	0.825779i	$-0.309264\pi$
$691$	29.6513	1.12799	0.563994	+	0.825779i	$0.309264\pi$
$692$	−107.084	−4.07072
$693$	0.863799	0.0328130
$694$	59.3830	2.25415
$695$	63.0225	2.39058
$696$	171.948	6.51768
$697$	26.6938	1.01110
$698$	24.1307	0.913359
$699$	24.6967	0.934116
$700$	−137.297	−5.18935
$701$	−8.06082	−0.304453	−0.152227	−	0.988346i	$-0.548644\pi$
$701$	−8.06082	−0.304453	−0.152227	+	0.988346i	$0.548644\pi$
$702$	−17.2697	−0.651804
$703$	−3.02304	−0.114016
$704$	−1.57998	−0.0595477
$705$	−101.589	−3.82607
$706$	−34.6730	−1.30494
$707$	−28.8866	−1.08639
$708$	87.0844	3.27283
$709$	−35.3225	−1.32656	−0.663282	−	0.748370i	$-0.730837\pi$
$709$	−35.3225	−1.32656	−0.663282	+	0.748370i	$0.730837\pi$
$710$	144.585	5.42618
$711$	22.1712	0.831485
$712$	−135.478	−5.07727
$713$	−0.116385	−0.00435865
$714$	36.6573	1.37186
$715$	−3.69533	−0.138197
$716$	−2.38758	−0.0892279
$717$	−8.60207	−0.321250
$718$	9.72377	0.362888
$719$	20.6553	0.770312	0.385156	−	0.922851i	$-0.374148\pi$
$719$	20.6553	0.770312	0.385156	+	0.922851i	$0.374148\pi$
$720$	103.905	3.87233
$721$	−1.90316	−0.0708773
$722$	32.6369	1.21462
$723$	36.7434	1.36650
$724$	−113.447	−4.21623
$725$	137.641	5.11185
$726$	−66.8162	−2.47978
$727$	13.8722	0.514492	0.257246	−	0.966346i	$-0.417185\pi$
$727$	13.8722	0.514492	0.257246	+	0.966346i	$0.417185\pi$
$728$	72.6615	2.69301
$729$	−15.5015	−0.574129
$730$	136.274	5.04372
$731$	0.836130	0.0309254
$732$	−157.650	−5.82692
$733$	−1.75981	−0.0650000	−0.0325000	−	0.999472i	$-0.510347\pi$
$733$	−1.75981	−0.0650000	−0.0325000	+	0.999472i	$0.510347\pi$
$734$	−59.2354	−2.18642
$735$	29.3939	1.08421
$736$	43.5194	1.60415
$737$	−0.266394	−0.00981276
$738$	56.6338	2.08472
$739$	6.63281	0.243992	0.121996	−	0.992531i	$-0.461071\pi$
$739$	6.63281	0.243992	0.121996	+	0.992531i	$0.461071\pi$
$740$	−25.0179	−0.919675
$741$	−28.4847	−1.04641
$742$	8.57112	0.314656
$743$	−7.94040	−0.291305	−0.145653	−	0.989336i	$-0.546528\pi$
$743$	−7.94040	−0.291305	−0.145653	+	0.989336i	$0.546528\pi$
$744$	0.511422	0.0187496
$745$	59.1807	2.16821
$746$	−4.33884	−0.158856
$747$	−3.79759	−0.138947
$748$	2.56160	0.0936615
$749$	40.3616	1.47478
$750$	237.440	8.67007
$751$	14.9578	0.545818	0.272909	−	0.962040i	$-0.412014\pi$
$751$	14.9578	0.545818	0.272909	+	0.962040i	$0.412014\pi$
$752$	99.4519	3.62664
$753$	−22.8571	−0.832958
$754$	−123.756	−4.50692
$755$	57.8214	2.10434
$756$	−13.5450	−0.492627
$757$	1.82592	0.0663643	0.0331822	−	0.999449i	$-0.489436\pi$
$757$	1.82592	0.0663643	0.0331822	+	0.999449i	$0.489436\pi$
$758$	−17.5173	−0.636255
$759$	−1.63490	−0.0593432
$760$	−83.4551	−3.02723
$761$	−19.4349	−0.704515	−0.352257	−	0.935903i	$-0.614586\pi$
$761$	−19.4349	−0.704515	−0.352257	+	0.935903i	$0.614586\pi$
$762$	−0.337846	−0.0122389
$763$	−37.0961	−1.34297
$764$	35.0345	1.26750
$765$	−31.1691	−1.12692
$766$	55.4358	2.00298
$767$	−36.8920	−1.33209
$768$	32.8701	1.18610
$769$	47.5982	1.71644	0.858218	−	0.513286i	$-0.171572\pi$
$769$	47.5982	1.71644	0.858218	+	0.513286i	$0.171572\pi$
$770$	−4.09068	−0.147418
$771$	−10.3357	−0.372231
$772$	24.1071	0.867634
$773$	19.6148	0.705496	0.352748	−	0.935718i	$-0.385247\pi$
$773$	19.6148	0.705496	0.352748	+	0.935718i	$0.385247\pi$
$774$	1.77394	0.0637630
$775$	0.409382	0.0147054
$776$	−37.3185	−1.33966
$777$	−5.56384	−0.199602
$778$	38.8584	1.39314
$779$	−22.9617	−0.822687
$780$	−235.731	−8.44054
$781$	2.24698	0.0804033
$782$	−30.8935	−1.10475
$783$	13.5789	0.485270
$784$	−28.7755	−1.02770
$785$	15.3519	0.547932
$786$	94.4057	3.36734
$787$	21.6353	0.771217	0.385608	−	0.922663i	$-0.373992\pi$
$787$	21.6353	0.771217	0.385608	+	0.922663i	$0.373992\pi$
$788$	−68.3660	−2.43544
$789$	25.1824	0.896517
$790$	−104.996	−3.73558
$791$	−22.3103	−0.793264
$792$	3.19890	0.113668
$793$	66.7861	2.37164
$794$	50.2143	1.78204
$795$	−16.3672	−0.580486
$796$	45.9945	1.63023
$797$	−4.66740	−0.165328	−0.0826639	−	0.996577i	$-0.526343\pi$
$797$	−4.66740	−0.165328	−0.0826639	+	0.996577i	$0.526343\pi$
$798$	−31.5321	−1.11623
$799$	−29.8331	−1.05542
$800$	−153.079	−5.41215
$801$	43.5246	1.53787
$802$	−72.2221	−2.55025
$803$	2.11782	0.0747361
$804$	−16.9937	−0.599323
$805$	34.9543	1.23198
$806$	−0.368084	−0.0129652
$807$	19.8500	0.698754
$808$	−106.975	−3.76338
$809$	−29.7172	−1.04480	−0.522400	−	0.852701i	$-0.674963\pi$
$809$	−29.7172	−1.04480	−0.522400	+	0.852701i	$0.674963\pi$
$810$	118.890	4.17736
$811$	−8.73839	−0.306846	−0.153423	−	0.988161i	$-0.549030\pi$
$811$	−8.73839	−0.306846	−0.153423	+	0.988161i	$0.549030\pi$
$812$	−97.0642	−3.40628
$813$	16.5383	0.580023
$814$	−0.548750	−0.0192337
$815$	−90.1627	−3.15826
$816$	68.5271	2.39893
$817$	−0.719228	−0.0251626
$818$	−95.5463	−3.34070
$819$	−23.3436	−0.815692
$820$	−190.025	−6.63594
$821$	−28.2245	−0.985042	−0.492521	−	0.870301i	$-0.663924\pi$
$821$	−28.2245	−0.985042	−0.492521	+	0.870301i	$0.663924\pi$
$822$	−33.9105	−1.18277
$823$	−15.9772	−0.556928	−0.278464	−	0.960447i	$-0.589825\pi$
$823$	−15.9772	−0.556928	−0.278464	+	0.960447i	$0.589825\pi$
$824$	−7.04796	−0.245527
$825$	5.75075	0.200215
$826$	−40.8389	−1.42097
$827$	35.2646	1.22627	0.613135	−	0.789978i	$-0.289908\pi$
$827$	35.2646	1.22627	0.613135	+	0.789978i	$0.289908\pi$
$828$	−46.4390	−1.61387
$829$	−23.7147	−0.823647	−0.411823	−	0.911264i	$-0.635108\pi$
$829$	−23.7147	−0.823647	−0.411823	+	0.911264i	$0.635108\pi$
$830$	17.9842	0.624241
$831$	−14.1475	−0.490772
$832$	42.6979	1.48028
$833$	8.63194	0.299079
$834$	88.1829	3.05352
$835$	−63.5126	−2.19794
$836$	−2.20346	−0.0762082
$837$	0.0403874	0.00139599
$838$	45.9632	1.58777
$839$	49.9215	1.72348	0.861741	−	0.507348i	$-0.169374\pi$
$839$	49.9215	1.72348	0.861741	+	0.507348i	$0.169374\pi$
$840$	−153.597	−5.29961
$841$	68.3070	2.35541
$842$	−53.4937	−1.84352
$843$	−10.6625	−0.367237
$844$	−36.8622	−1.26885
$845$	43.2680	1.48847
$846$	−63.2942	−2.17610
$847$	22.2007	0.762825
$848$	16.0229	0.550227
$849$	−60.2176	−2.06666
$850$	108.667	3.72726
$851$	4.68900	0.160737
$852$	143.339	4.91071
$853$	36.7099	1.25692	0.628461	−	0.777841i	$-0.283685\pi$
$853$	36.7099	1.25692	0.628461	+	0.777841i	$0.283685\pi$
$854$	73.9313	2.52988
$855$	26.8113	0.916926
$856$	149.471	5.10882
$857$	−2.40983	−0.0823182	−0.0411591	−	0.999153i	$-0.513105\pi$
$857$	−2.40983	−0.0823182	−0.0411591	+	0.999153i	$0.513105\pi$
$858$	−5.17061	−0.176522
$859$	−51.9388	−1.77213	−0.886064	−	0.463564i	$-0.846571\pi$
$859$	−51.9388	−1.77213	−0.886064	+	0.463564i	$0.846571\pi$
$860$	−5.95214	−0.202966
$861$	−42.2604	−1.44023
$862$	50.6699	1.72583
$863$	14.0182	0.477184	0.238592	−	0.971120i	$-0.423314\pi$
$863$	14.0182	0.477184	0.238592	+	0.971120i	$0.423314\pi$
$864$	−15.1019	−0.513777
$865$	−95.8948	−3.26052
$866$	51.5720	1.75249
$867$	18.9775	0.644509
$868$	−0.288696	−0.00979897
$869$	−1.63173	−0.0553526
$870$	261.604	8.86921
$871$	7.19914	0.243934
$872$	−137.378	−4.65221
$873$	11.9892	0.405772
$874$	26.5742	0.898884
$875$	−78.8930	−2.66707
$876$	135.099	4.56458
$877$	15.9539	0.538727	0.269363	−	0.963039i	$-0.413187\pi$
$877$	15.9539	0.538727	0.269363	+	0.963039i	$0.413187\pi$
$878$	−20.8864	−0.704882
$879$	38.7676	1.30760
$880$	−7.64711	−0.257784
$881$	−7.90505	−0.266328	−0.133164	−	0.991094i	$-0.542514\pi$
$881$	−7.90505	−0.266328	−0.133164	+	0.991094i	$0.542514\pi$
$882$	18.3136	0.616651
$883$	−29.7630	−1.00160	−0.500802	−	0.865562i	$-0.666962\pi$
$883$	−29.7630	−1.00160	−0.500802	+	0.865562i	$0.666962\pi$
$884$	−69.2258	−2.32832
$885$	77.9850	2.62144
$886$	−1.58261	−0.0531688
$887$	28.2514	0.948589	0.474294	−	0.880366i	$-0.342703\pi$
$887$	28.2514	0.948589	0.474294	+	0.880366i	$0.342703\pi$
$888$	−20.6045	−0.691443
$889$	0.112254	0.00376489
$890$	−206.119	−6.90911
$891$	1.84766	0.0618988
$892$	90.3662	3.02569
$893$	25.6621	0.858748
$894$	82.8074	2.76949
$895$	−2.13810	−0.0714688
$896$	2.85556	0.0953976
$897$	44.1822	1.47520
$898$	−4.14632	−0.138365
$899$	0.289418	0.00965263
$900$	163.348	5.44495
$901$	−4.80646	−0.160126
$902$	−4.16806	−0.138781
$903$	−1.32372	−0.0440508
$904$	−82.6218	−2.74796
$905$	−101.593	−3.37707
$906$	80.9055	2.68790
$907$	8.89238	0.295267	0.147633	−	0.989042i	$-0.452834\pi$
$907$	8.89238	0.295267	0.147633	+	0.989042i	$0.452834\pi$
$908$	80.3094	2.66516
$909$	34.3675	1.13990
$910$	110.548	3.66463
$911$	−37.7483	−1.25066	−0.625329	−	0.780361i	$-0.715035\pi$
$911$	−37.7483	−1.25066	−0.625329	+	0.780361i	$0.715035\pi$
$912$	−58.9461	−1.95190
$913$	0.279491	0.00924979
$914$	−34.8027	−1.15117
$915$	−141.177	−4.66718
$916$	−38.6073	−1.27562
$917$	−31.3678	−1.03585
$918$	10.7205	0.353830
$919$	33.2812	1.09785	0.548923	−	0.835873i	$-0.315038\pi$
$919$	33.2812	1.09785	0.548923	+	0.835873i	$0.315038\pi$
$920$	129.446	4.26772
$921$	−7.87550	−0.259506
$922$	89.8634	2.95949
$923$	−60.7233	−1.99873
$924$	−4.05542	−0.133413
$925$	−16.4935	−0.542303
$926$	−1.92803	−0.0633589
$927$	2.26427	0.0743683
$928$	−108.221	−3.55253
$929$	18.1904	0.596806	0.298403	−	0.954440i	$-0.403546\pi$
$929$	18.1904	0.596806	0.298403	+	0.954440i	$0.403546\pi$
$930$	0.778083	0.0255144
$931$	−7.42508	−0.243347
$932$	−51.6285	−1.69115
$933$	−8.60938	−0.281858
$934$	72.7103	2.37915
$935$	2.29395	0.0750200
$936$	−86.4484	−2.82565
$937$	−9.19420	−0.300361	−0.150181	−	0.988659i	$-0.547986\pi$
$937$	−9.19420	−0.300361	−0.150181	+	0.988659i	$0.547986\pi$
$938$	7.96935	0.260208
$939$	45.8758	1.49710
$940$	212.372	6.92682
$941$	−4.11910	−0.134279	−0.0671394	−	0.997744i	$-0.521387\pi$
$941$	−4.11910	−0.134279	−0.0671394	+	0.997744i	$0.521387\pi$
$942$	21.4808	0.699883
$943$	35.6156	1.15980
$944$	−76.3442	−2.48479
$945$	−12.1297	−0.394579
$946$	−0.130556	−0.00424475
$947$	−6.07670	−0.197466	−0.0987332	−	0.995114i	$-0.531479\pi$
$947$	−6.07670	−0.197466	−0.0987332	+	0.995114i	$0.531479\pi$
$948$	−104.091	−3.38071
$949$	−57.2327	−1.85785
$950$	−93.4742	−3.03270
$951$	−74.2008	−2.40612
$952$	−45.1060	−1.46189
$953$	31.4429	1.01853	0.509267	−	0.860609i	$-0.329917\pi$
$953$	31.4429	1.01853	0.509267	+	0.860609i	$0.329917\pi$
$954$	−10.1974	−0.330154
$955$	31.3738	1.01523
$956$	17.9826	0.581599
$957$	4.06556	0.131421
$958$	30.9096	0.998645
$959$	11.2673	0.363840
$960$	−90.2581	−2.91307
$961$	−30.9991	−0.999972
$962$	14.8296	0.478127
$963$	−48.0199	−1.54742
$964$	−76.8120	−2.47395
$965$	21.5882	0.694948
$966$	48.9091	1.57363
$967$	−36.0454	−1.15914	−0.579570	−	0.814922i	$-0.696780\pi$
$967$	−36.0454	−1.15914	−0.579570	+	0.814922i	$0.696780\pi$
$968$	82.2158	2.64252
$969$	17.6824	0.568040
$970$	−56.7769	−1.82300
$971$	0.134950	0.00433076	0.00216538	−	0.999998i	$-0.499311\pi$
$971$	0.134950	0.00433076	0.00216538	+	0.999998i	$0.499311\pi$
$972$	97.7888	3.13658
$973$	−29.3001	−0.939319
$974$	−83.8269	−2.68599
$975$	−155.410	−4.97711
$976$	138.207	4.42390
$977$	38.5139	1.23217	0.616084	−	0.787680i	$-0.288718\pi$
$977$	38.5139	1.23217	0.616084	+	0.787680i	$0.288718\pi$
$978$	−126.158	−4.03410
$979$	−3.20327	−0.102377
$980$	−61.4480	−1.96288
$981$	44.1348	1.40912
$982$	93.8669	2.99541
$983$	4.00470	0.127730	0.0638650	−	0.997959i	$-0.479657\pi$
$983$	4.00470	0.127730	0.0638650	+	0.997959i	$0.479657\pi$
$984$	−156.503	−4.98913
$985$	−61.2225	−1.95071
$986$	76.8237	2.44657
$987$	47.2305	1.50336
$988$	59.5471	1.89445
$989$	1.11559	0.0354736
$990$	4.86685	0.154679
$991$	39.6704	1.26017	0.630087	−	0.776525i	$-0.283019\pi$
$991$	39.6704	1.26017	0.630087	+	0.776525i	$0.283019\pi$
$992$	−0.321879	−0.0102197
$993$	−27.9421	−0.886715
$994$	−67.2198	−2.13208
$995$	41.1886	1.30577
$996$	17.8292	0.564939
$997$	16.2184	0.513641	0.256820	−	0.966459i	$-0.417325\pi$
$997$	16.2184	0.513641	0.256820	+	0.966459i	$0.417325\pi$
$998$	−75.4094	−2.38704
$999$	−1.62716	−0.0514810

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6011.2.a.f.1.13	✓	275

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6011.2.a.f.1.13	✓	275	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:	\( N \)	\(=\)	\( 6011 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6011.a (trivial)

\(f(q)\)	\(=\)	\(q-2.61945 q^{2} -2.32553 q^{3} +4.86151 q^{4} +4.35353 q^{5} +6.09159 q^{6} -2.02403 q^{7} -7.49557 q^{8} +2.40807 q^{9} +O(q^{10})\)	\(q-2.61945 q^{2} -2.32553 q^{3} +4.86151 q^{4} +4.35353 q^{5} +6.09159 q^{6} -2.02403 q^{7} -7.49557 q^{8} +2.40807 q^{9} -11.4039 q^{10} -0.177226 q^{11} -11.3056 q^{12} +4.78943 q^{13} +5.30183 q^{14} -10.1243 q^{15} +9.91124 q^{16} -2.97313 q^{17} -6.30781 q^{18} +2.55745 q^{19} +21.1647 q^{20} +4.70692 q^{21} +0.464235 q^{22} -3.96683 q^{23} +17.4311 q^{24} +13.9532 q^{25} -12.5457 q^{26} +1.37655 q^{27} -9.83982 q^{28} +9.86443 q^{29} +26.5199 q^{30} +0.0293395 q^{31} -10.9708 q^{32} +0.412144 q^{33} +7.78795 q^{34} -8.81166 q^{35} +11.7068 q^{36} -1.18205 q^{37} -6.69910 q^{38} -11.1379 q^{39} -32.6322 q^{40} -8.97836 q^{41} -12.3295 q^{42} -0.281229 q^{43} -0.861586 q^{44} +10.4836 q^{45} +10.3909 q^{46} +10.0343 q^{47} -23.0488 q^{48} -2.90332 q^{49} -36.5498 q^{50} +6.91408 q^{51} +23.2838 q^{52} +1.61664 q^{53} -3.60580 q^{54} -0.771560 q^{55} +15.1712 q^{56} -5.94741 q^{57} -25.8394 q^{58} -7.70280 q^{59} -49.2191 q^{60} +13.9445 q^{61} -0.0768534 q^{62} -4.87399 q^{63} +8.91504 q^{64} +20.8509 q^{65} -1.07959 q^{66} +1.50313 q^{67} -14.4539 q^{68} +9.22496 q^{69} +23.0817 q^{70} -12.6786 q^{71} -18.0498 q^{72} -11.9498 q^{73} +3.09633 q^{74} -32.4486 q^{75} +12.4330 q^{76} +0.358710 q^{77} +29.1752 q^{78} +9.20705 q^{79} +43.1489 q^{80} -10.4254 q^{81} +23.5183 q^{82} -1.57703 q^{83} +22.8827 q^{84} -12.9436 q^{85} +0.736665 q^{86} -22.9400 q^{87} +1.32841 q^{88} +18.0745 q^{89} -27.4613 q^{90} -9.69392 q^{91} -19.2848 q^{92} -0.0682299 q^{93} -26.2842 q^{94} +11.1339 q^{95} +25.5129 q^{96} +4.97875 q^{97} +7.60509 q^{98} -0.426773 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 275 q + 16 q^{2} + 9 q^{3} + 316 q^{4} + 36 q^{5} + 30 q^{6} + 41 q^{7} + 36 q^{8} + 322 q^{9}+O(q^{10}) \) 275 * q + 16 * q^2 + 9 * q^3 + 316 * q^4 + 36 * q^5 + 30 * q^6 + 41 * q^7 + 36 * q^8 + 322 * q^9	\( 275 q + 16 q^{2} + 9 q^{3} + 316 q^{4} + 36 q^{5} + 30 q^{6} + 41 q^{7} + 36 q^{8} + 322 q^{9} + 44 q^{10} + 42 q^{11} + 26 q^{12} + 97 q^{13} + 24 q^{14} + 46 q^{15} + 386 q^{16} + 35 q^{17} + 47 q^{18} + 101 q^{19} + 60 q^{20} + 187 q^{21} + 72 q^{22} + 35 q^{23} + 73 q^{24} + 373 q^{25} + 21 q^{26} + 27 q^{27} + 97 q^{28} + 162 q^{29} + 13 q^{30} + 113 q^{31} + 58 q^{32} + 16 q^{33} + 52 q^{34} + 23 q^{35} + 426 q^{36} + 257 q^{37} + 8 q^{38} + 87 q^{39} + 126 q^{40} + 77 q^{41} - 7 q^{42} + 107 q^{43} + 133 q^{44} + 140 q^{45} + 207 q^{46} + 24 q^{47} + 4 q^{48} + 418 q^{49} + 65 q^{50} + 94 q^{51} + 142 q^{52} + 81 q^{53} + 79 q^{54} + 26 q^{55} + 62 q^{56} + 112 q^{57} + 44 q^{58} + 30 q^{59} + 83 q^{60} + 347 q^{61} + 5 q^{62} + 97 q^{63} + 508 q^{64} + 94 q^{65} + 4 q^{66} + 98 q^{67} + 28 q^{68} + 91 q^{69} + 17 q^{70} + 58 q^{71} + 99 q^{72} + 157 q^{73} + 80 q^{74} + 83 q^{75} + 264 q^{76} + 61 q^{77} + 5 q^{78} + 282 q^{79} + 49 q^{80} + 403 q^{81} + 46 q^{82} + 43 q^{83} + 318 q^{84} + 396 q^{85} + 57 q^{86} + 31 q^{87} + 180 q^{88} + 98 q^{89} + 67 q^{90} + 195 q^{91} + 97 q^{92} + 83 q^{93} + 96 q^{94} + 28 q^{95} + 127 q^{96} + 167 q^{97} + 24 q^{98} + 133 q^{99}+O(q^{100}) \) 275 * q + 16 * q^2 + 9 * q^3 + 316 * q^4 + 36 * q^5 + 30 * q^6 + 41 * q^7 + 36 * q^8 + 322 * q^9 + 44 * q^10 + 42 * q^11 + 26 * q^12 + 97 * q^13 + 24 * q^14 + 46 * q^15 + 386 * q^16 + 35 * q^17 + 47 * q^18 + 101 * q^19 + 60 * q^20 + 187 * q^21 + 72 * q^22 + 35 * q^23 + 73 * q^24 + 373 * q^25 + 21 * q^26 + 27 * q^27 + 97 * q^28 + 162 * q^29 + 13 * q^30 + 113 * q^31 + 58 * q^32 + 16 * q^33 + 52 * q^34 + 23 * q^35 + 426 * q^36 + 257 * q^37 + 8 * q^38 + 87 * q^39 + 126 * q^40 + 77 * q^41 - 7 * q^42 + 107 * q^43 + 133 * q^44 + 140 * q^45 + 207 * q^46 + 24 * q^47 + 4 * q^48 + 418 * q^49 + 65 * q^50 + 94 * q^51 + 142 * q^52 + 81 * q^53 + 79 * q^54 + 26 * q^55 + 62 * q^56 + 112 * q^57 + 44 * q^58 + 30 * q^59 + 83 * q^60 + 347 * q^61 + 5 * q^62 + 97 * q^63 + 508 * q^64 + 94 * q^65 + 4 * q^66 + 98 * q^67 + 28 * q^68 + 91 * q^69 + 17 * q^70 + 58 * q^71 + 99 * q^72 + 157 * q^73 + 80 * q^74 + 83 * q^75 + 264 * q^76 + 61 * q^77 + 5 * q^78 + 282 * q^79 + 49 * q^80 + 403 * q^81 + 46 * q^82 + 43 * q^83 + 318 * q^84 + 396 * q^85 + 57 * q^86 + 31 * q^87 + 180 * q^88 + 98 * q^89 + 67 * q^90 + 195 * q^91 + 97 * q^92 + 83 * q^93 + 96 * q^94 + 28 * q^95 + 127 * q^96 + 167 * q^97 + 24 * q^98 + 133 * q^99

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