LMFDB - Embedded newform 671.2.a.d.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [671,2,Mod(1,671)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(671, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("671.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 671 = 11 \cdot 61 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	671.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:	$5.35796197563$
Analytic rank:	$0$
Dimension:	$21$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Character	$\chi$	$=$	671.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.19302 q^{2} +1.13601 q^{3} +2.80936 q^{4} -3.87665 q^{5} -2.49129 q^{6} +3.34814 q^{7} -1.77494 q^{8} -1.70949 q^{9} +O(q^{10})$	\(q-2.19302 q^{2} +1.13601 q^{3} +2.80936 q^{4} -3.87665 q^{5} -2.49129 q^{6} +3.34814 q^{7} -1.77494 q^{8} -1.70949 q^{9} +8.50160 q^{10} -1.00000 q^{11} +3.19145 q^{12} +3.33150 q^{13} -7.34255 q^{14} -4.40390 q^{15} -1.72622 q^{16} +2.42548 q^{17} +3.74895 q^{18} -7.48304 q^{19} -10.8909 q^{20} +3.80351 q^{21} +2.19302 q^{22} +6.20068 q^{23} -2.01635 q^{24} +10.0285 q^{25} -7.30607 q^{26} -5.35001 q^{27} +9.40612 q^{28} -2.67585 q^{29} +9.65787 q^{30} +8.31622 q^{31} +7.33554 q^{32} -1.13601 q^{33} -5.31914 q^{34} -12.9796 q^{35} -4.80257 q^{36} +5.59361 q^{37} +16.4105 q^{38} +3.78461 q^{39} +6.88084 q^{40} +0.632514 q^{41} -8.34118 q^{42} +5.14454 q^{43} -2.80936 q^{44} +6.62710 q^{45} -13.5982 q^{46} +6.95884 q^{47} -1.96100 q^{48} +4.21003 q^{49} -21.9926 q^{50} +2.75536 q^{51} +9.35939 q^{52} -10.8778 q^{53} +11.7327 q^{54} +3.87665 q^{55} -5.94275 q^{56} -8.50078 q^{57} +5.86821 q^{58} +0.797395 q^{59} -12.3721 q^{60} +1.00000 q^{61} -18.2377 q^{62} -5.72361 q^{63} -12.6346 q^{64} -12.9151 q^{65} +2.49129 q^{66} +13.0038 q^{67} +6.81405 q^{68} +7.04401 q^{69} +28.4645 q^{70} +15.1395 q^{71} +3.03425 q^{72} +4.09379 q^{73} -12.2669 q^{74} +11.3924 q^{75} -21.0225 q^{76} -3.34814 q^{77} -8.29974 q^{78} +11.2765 q^{79} +6.69197 q^{80} -0.949176 q^{81} -1.38712 q^{82} +6.06669 q^{83} +10.6854 q^{84} -9.40276 q^{85} -11.2821 q^{86} -3.03979 q^{87} +1.77494 q^{88} +16.4725 q^{89} -14.5334 q^{90} +11.1543 q^{91} +17.4199 q^{92} +9.44728 q^{93} -15.2609 q^{94} +29.0092 q^{95} +8.33321 q^{96} -3.95096 q^{97} -9.23269 q^{98} +1.70949 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 21 q + 3 q^{3} + 32 q^{4} + 7 q^{5} + 5 q^{6} + 5 q^{7} - 6 q^{8} + 40 q^{9}+O(q^{10}) $ 21 * q + 3 * q^3 + 32 * q^4 + 7 * q^5 + 5 * q^6 + 5 * q^7 - 6 * q^8 + 40 * q^9	\( 21 q + 3 q^{3} + 32 q^{4} + 7 q^{5} + 5 q^{6} + 5 q^{7} - 6 q^{8} + 40 q^{9} + q^{10} - 21 q^{11} + 6 q^{12} + 20 q^{13} + 17 q^{14} + 18 q^{15} + 50 q^{16} + q^{17} - 5 q^{18} + 15 q^{19} - 2 q^{20} + 16 q^{21} + 11 q^{23} - 16 q^{24} + 48 q^{25} - 5 q^{26} + 12 q^{27} - 16 q^{28} - 9 q^{29} + 16 q^{30} + 22 q^{31} + 3 q^{32} - 3 q^{33} + 33 q^{34} - 39 q^{35} + 57 q^{36} + 21 q^{37} + 11 q^{38} - 28 q^{39} - 16 q^{40} + 7 q^{41} - 55 q^{42} + 16 q^{43} - 32 q^{44} + 44 q^{45} - 3 q^{46} + 5 q^{47} - 71 q^{48} + 80 q^{49} - 33 q^{50} - 19 q^{51} + 60 q^{52} + 9 q^{53} + 13 q^{54} - 7 q^{55} + 44 q^{56} + 39 q^{57} - 27 q^{58} + 13 q^{59} + 70 q^{60} + 21 q^{61} - 23 q^{62} + 24 q^{63} + 66 q^{64} + 25 q^{65} - 5 q^{66} + 38 q^{67} - 74 q^{68} - 17 q^{69} - 33 q^{70} + 12 q^{71} - 75 q^{72} + 20 q^{73} - 12 q^{74} - 10 q^{75} + 59 q^{76} - 5 q^{77} - 14 q^{78} + q^{79} - 38 q^{80} + 89 q^{81} + 7 q^{82} - 19 q^{83} - 14 q^{84} + 38 q^{85} - 3 q^{86} + 4 q^{87} + 6 q^{88} + 37 q^{89} - 174 q^{90} + 24 q^{91} + 31 q^{92} - 15 q^{93} - 64 q^{94} - 43 q^{95} - 38 q^{96} + 68 q^{97} - 2 q^{98} - 40 q^{99}+O(q^{100}) \) 21 * q + 3 * q^3 + 32 * q^4 + 7 * q^5 + 5 * q^6 + 5 * q^7 - 6 * q^8 + 40 * q^9 + q^10 - 21 * q^11 + 6 * q^12 + 20 * q^13 + 17 * q^14 + 18 * q^15 + 50 * q^16 + q^17 - 5 * q^18 + 15 * q^19 - 2 * q^20 + 16 * q^21 + 11 * q^23 - 16 * q^24 + 48 * q^25 - 5 * q^26 + 12 * q^27 - 16 * q^28 - 9 * q^29 + 16 * q^30 + 22 * q^31 + 3 * q^32 - 3 * q^33 + 33 * q^34 - 39 * q^35 + 57 * q^36 + 21 * q^37 + 11 * q^38 - 28 * q^39 - 16 * q^40 + 7 * q^41 - 55 * q^42 + 16 * q^43 - 32 * q^44 + 44 * q^45 - 3 * q^46 + 5 * q^47 - 71 * q^48 + 80 * q^49 - 33 * q^50 - 19 * q^51 + 60 * q^52 + 9 * q^53 + 13 * q^54 - 7 * q^55 + 44 * q^56 + 39 * q^57 - 27 * q^58 + 13 * q^59 + 70 * q^60 + 21 * q^61 - 23 * q^62 + 24 * q^63 + 66 * q^64 + 25 * q^65 - 5 * q^66 + 38 * q^67 - 74 * q^68 - 17 * q^69 - 33 * q^70 + 12 * q^71 - 75 * q^72 + 20 * q^73 - 12 * q^74 - 10 * q^75 + 59 * q^76 - 5 * q^77 - 14 * q^78 + q^79 - 38 * q^80 + 89 * q^81 + 7 * q^82 - 19 * q^83 - 14 * q^84 + 38 * q^85 - 3 * q^86 + 4 * q^87 + 6 * q^88 + 37 * q^89 - 174 * q^90 + 24 * q^91 + 31 * q^92 - 15 * q^93 - 64 * q^94 - 43 * q^95 - 38 * q^96 + 68 * q^97 - 2 * q^98 - 40 * 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 $

$2$	−2.19302	−1.55070	−0.775351	−	0.631530i	$-0.782427\pi$
$2$	−2.19302	−1.55070	−0.775351	+	0.631530i	$0.782427\pi$
$3$	1.13601	0.655874	0.327937	−	0.944700i	$-0.393647\pi$
$3$	1.13601	0.655874	0.327937	+	0.944700i	$0.393647\pi$
$4$	2.80936	1.40468
$5$	−3.87665	−1.73369	−0.866846	−	0.498575i	$-0.833857\pi$
$5$	−3.87665	−1.73369	−0.866846	+	0.498575i	$0.833857\pi$
$6$	−2.49129	−1.01706
$7$	3.34814	1.26548	0.632739	−	0.774365i	$-0.281931\pi$
$7$	3.34814	1.26548	0.632739	+	0.774365i	$0.281931\pi$
$8$	−1.77494	−0.627537
$9$	−1.70949	−0.569830
$10$	8.50160	2.68844
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	3.19145	0.921292
$13$	3.33150	0.923993	0.461996	−	0.886882i	$-0.347133\pi$
$13$	3.33150	0.923993	0.461996	+	0.886882i	$0.347133\pi$
$14$	−7.34255	−1.96238
$15$	−4.40390	−1.13708
$16$	−1.72622	−0.431556
$17$	2.42548	0.588266	0.294133	−	0.955765i	$-0.404969\pi$
$17$	2.42548	0.588266	0.294133	+	0.955765i	$0.404969\pi$
$18$	3.74895	0.883637
$19$	−7.48304	−1.71673	−0.858364	−	0.513041i	$-0.828519\pi$
$19$	−7.48304	−1.71673	−0.858364	+	0.513041i	$0.828519\pi$
$20$	−10.8909	−2.43528
$21$	3.80351	0.829993
$22$	2.19302	0.467554
$23$	6.20068	1.29293	0.646466	−	0.762943i	$-0.276246\pi$
$23$	6.20068	1.29293	0.646466	+	0.762943i	$0.276246\pi$
$24$	−2.01635	−0.411585
$25$	10.0285	2.00569
$26$	−7.30607	−1.43284
$27$	−5.35001	−1.02961
$28$	9.40612	1.77759
$29$	−2.67585	−0.496893	−0.248447	−	0.968646i	$-0.579920\pi$
$29$	−2.67585	−0.496893	−0.248447	+	0.968646i	$0.579920\pi$
$30$	9.65787	1.76328
$31$	8.31622	1.49364	0.746819	−	0.665028i	$-0.231580\pi$
$31$	8.31622	1.49364	0.746819	+	0.665028i	$0.231580\pi$
$32$	7.33554	1.29675
$33$	−1.13601	−0.197753
$34$	−5.31914	−0.912226
$35$	−12.9796	−2.19395
$36$	−4.80257	−0.800428
$37$	5.59361	0.919584	0.459792	−	0.888027i	$-0.347924\pi$
$37$	5.59361	0.919584	0.459792	+	0.888027i	$0.347924\pi$
$38$	16.4105	2.66213
$39$	3.78461	0.606022
$40$	6.88084	1.08796
$41$	0.632514	0.0987820	0.0493910	−	0.998780i	$-0.484272\pi$
$41$	0.632514	0.0987820	0.0493910	+	0.998780i	$0.484272\pi$
$42$	−8.34118	−1.28707
$43$	5.14454	0.784535	0.392267	−	0.919851i	$-0.371691\pi$
$43$	5.14454	0.784535	0.392267	+	0.919851i	$0.371691\pi$
$44$	−2.80936	−0.423527
$45$	6.62710	0.987910
$46$	−13.5982	−2.00495
$47$	6.95884	1.01505	0.507526	−	0.861637i	$-0.330560\pi$
$47$	6.95884	1.01505	0.507526	+	0.861637i	$0.330560\pi$
$48$	−1.96100	−0.283046
$49$	4.21003	0.601432
$50$	−21.9926	−3.11023
$51$	2.75536	0.385828
$52$	9.35939	1.29791
$53$	−10.8778	−1.49418	−0.747091	−	0.664721i	$-0.768550\pi$
$53$	−10.8778	−1.49418	−0.747091	+	0.664721i	$0.768550\pi$
$54$	11.7327	1.59662
$55$	3.87665	0.522728
$56$	−5.94275	−0.794134
$57$	−8.50078	−1.12596
$58$	5.86821	0.770534
$59$	0.797395	0.103812	0.0519060	−	0.998652i	$-0.483470\pi$
$59$	0.797395	0.103812	0.0519060	+	0.998652i	$0.483470\pi$
$60$	−12.3721	−1.59724
$61$	1.00000	0.128037
$61$	1.00000	0.128037
$62$	−18.2377	−2.31619
$63$	−5.72361	−0.721107
$64$	−12.6346	−1.57932
$65$	−12.9151	−1.60192
$66$	2.49129	0.306657
$67$	13.0038	1.58867	0.794336	−	0.607479i	$-0.207819\pi$
$67$	13.0038	1.58867	0.794336	+	0.607479i	$0.207819\pi$
$68$	6.81405	0.826325
$69$	7.04401	0.847999
$70$	28.4645	3.40216
$71$	15.1395	1.79673	0.898367	−	0.439246i	$-0.144754\pi$
$71$	15.1395	1.79673	0.898367	+	0.439246i	$0.144754\pi$
$72$	3.03425	0.357589
$73$	4.09379	0.479142	0.239571	−	0.970879i	$-0.422993\pi$
$73$	4.09379	0.479142	0.239571	+	0.970879i	$0.422993\pi$
$74$	−12.2669	−1.42600
$75$	11.3924	1.31548
$76$	−21.0225	−2.41145
$77$	−3.34814	−0.381556
$78$	−8.29974	−0.939761
$79$	11.2765	1.26870	0.634352	−	0.773045i	$-0.281267\pi$
$79$	11.2765	1.26870	0.634352	+	0.773045i	$0.281267\pi$
$80$	6.69197	0.748185
$81$	−0.949176	−0.105464
$82$	−1.38712	−0.153182
$83$	6.06669	0.665906	0.332953	−	0.942943i	$-0.391955\pi$
$83$	6.06669	0.665906	0.332953	+	0.942943i	$0.391955\pi$
$84$	10.6854	1.16587
$85$	−9.40276	−1.01987
$86$	−11.2821	−1.21658
$87$	−3.03979	−0.325899
$88$	1.77494	0.189210
$89$	16.4725	1.74608	0.873041	−	0.487647i	$-0.162145\pi$
$89$	16.4725	1.74608	0.873041	+	0.487647i	$0.162145\pi$
$90$	−14.5334	−1.53195
$91$	11.1543	1.16929
$92$	17.4199	1.81615
$93$	9.44728	0.979637
$94$	−15.2609	−1.57404
$95$	29.0092	2.97628
$96$	8.33321	0.850505
$97$	−3.95096	−0.401159	−0.200579	−	0.979677i	$-0.564282\pi$
$97$	−3.95096	−0.401159	−0.200579	+	0.979677i	$0.564282\pi$
$98$	−9.23269	−0.932643
$99$	1.70949	0.171810
$100$	28.1735	2.81735
$101$	4.24862	0.422753	0.211377	−	0.977405i	$-0.432205\pi$
$101$	4.24862	0.422753	0.211377	+	0.977405i	$0.432205\pi$
$102$	−6.04258	−0.598305
$103$	−11.0222	−1.08605	−0.543026	−	0.839716i	$-0.682722\pi$
$103$	−11.0222	−1.08605	−0.543026	+	0.839716i	$0.682722\pi$
$104$	−5.91323	−0.579840
$105$	−14.7449	−1.43895
$106$	23.8553	2.31703
$107$	10.4279	1.00810	0.504052	−	0.863673i	$-0.331842\pi$
$107$	10.4279	1.00810	0.504052	+	0.863673i	$0.331842\pi$
$108$	−15.0301	−1.44627
$109$	−5.49290	−0.526124	−0.263062	−	0.964779i	$-0.584732\pi$
$109$	−5.49290	−0.526124	−0.263062	+	0.964779i	$0.584732\pi$
$110$	−8.50160	−0.810596
$111$	6.35438	0.603131
$112$	−5.77963	−0.546124
$113$	−12.2934	−1.15647	−0.578234	−	0.815871i	$-0.696258\pi$
$113$	−12.2934	−1.15647	−0.578234	+	0.815871i	$0.696258\pi$
$114$	18.6424	1.74602
$115$	−24.0379	−2.24155
$116$	−7.51743	−0.697976
$117$	−5.69517	−0.526519
$118$	−1.74871	−0.160981
$119$	8.12085	0.744437
$120$	7.81668	0.713562
$121$	1.00000	0.0909091
$122$	−2.19302	−0.198547
$123$	0.718539	0.0647885
$124$	23.3632	2.09808
$125$	−19.4936	−1.74356
$126$	12.5520	1.11822
$127$	−2.89882	−0.257228	−0.128614	−	0.991695i	$-0.541053\pi$
$127$	−2.89882	−0.257228	−0.128614	+	0.991695i	$0.541053\pi$
$128$	13.0368	1.15231
$129$	5.84423	0.514555
$130$	28.3231	2.48410
$131$	−12.2543	−1.07066	−0.535331	−	0.844642i	$-0.679813\pi$
$131$	−12.2543	−1.07066	−0.535331	+	0.844642i	$0.679813\pi$
$132$	−3.19145	−0.277780
$133$	−25.0543	−2.17248
$134$	−28.5177	−2.46356
$135$	20.7401	1.78503
$136$	−4.30509	−0.369159
$137$	17.8925	1.52866	0.764332	−	0.644823i	$-0.223069\pi$
$137$	17.8925	1.52866	0.764332	+	0.644823i	$0.223069\pi$
$138$	−15.4477	−1.31499
$139$	−12.6337	−1.07158	−0.535788	−	0.844353i	$-0.679985\pi$
$139$	−12.6337	−1.07158	−0.535788	+	0.844353i	$0.679985\pi$
$140$	−36.4643	−3.08179
$141$	7.90529	0.665745
$142$	−33.2014	−2.78620
$143$	−3.33150	−0.278594
$144$	2.95096	0.245913
$145$	10.3734	0.861461
$146$	−8.97779	−0.743007
$147$	4.78262	0.394464
$148$	15.7145	1.29172
$149$	−18.7862	−1.53903	−0.769513	−	0.638632i	$-0.779501\pi$
$149$	−18.7862	−1.53903	−0.769513	+	0.638632i	$0.779501\pi$
$150$	−24.9838	−2.03992
$151$	−14.2055	−1.15602	−0.578012	−	0.816028i	$-0.696171\pi$
$151$	−14.2055	−1.15602	−0.578012	+	0.816028i	$0.696171\pi$
$152$	13.2820	1.07731
$153$	−4.14634	−0.335211
$154$	7.34255	0.591680
$155$	−32.2391	−2.58951
$156$	10.6323	0.851267
$157$	0.168712	0.0134647	0.00673235	−	0.999977i	$-0.497857\pi$
$157$	0.168712	0.0134647	0.00673235	+	0.999977i	$0.497857\pi$
$158$	−24.7296	−1.96738
$159$	−12.3573	−0.979995
$160$	−28.4373	−2.24817
$161$	20.7607	1.63617
$162$	2.08157	0.163543
$163$	7.00919	0.549002	0.274501	−	0.961587i	$-0.411487\pi$
$163$	7.00919	0.549002	0.274501	+	0.961587i	$0.411487\pi$
$164$	1.77696	0.138757
$165$	4.40390	0.342843
$166$	−13.3044	−1.03262
$167$	14.2000	1.09883	0.549414	−	0.835550i	$-0.314851\pi$
$167$	14.2000	1.09883	0.549414	+	0.835550i	$0.314851\pi$
$168$	−6.75100	−0.520851
$169$	−1.90108	−0.146237
$170$	20.6205	1.58152
$171$	12.7922	0.978243
$172$	14.4528	1.10202
$173$	−19.2874	−1.46639	−0.733196	−	0.680017i	$-0.761972\pi$
$173$	−19.2874	−1.46639	−0.733196	+	0.680017i	$0.761972\pi$
$174$	6.66633	0.505373
$175$	33.5766	2.53816
$176$	1.72622	0.130119
$177$	0.905845	0.0680875
$178$	−36.1246	−2.70765
$179$	14.6949	1.09835	0.549175	−	0.835708i	$-0.314942\pi$
$179$	14.6949	1.09835	0.549175	+	0.835708i	$0.314942\pi$
$180$	18.6179	1.38770
$181$	5.00787	0.372232	0.186116	−	0.982528i	$-0.440410\pi$
$181$	5.00787	0.372232	0.186116	+	0.982528i	$0.440410\pi$
$182$	−24.4617	−1.81322
$183$	1.13601	0.0839760
$184$	−11.0059	−0.811362
$185$	−21.6845	−1.59428
$186$	−20.7181	−1.51913
$187$	−2.42548	−0.177369
$188$	19.5499	1.42582
$189$	−17.9126	−1.30295
$190$	−63.6178	−4.61532
$191$	−0.913661	−0.0661102	−0.0330551	−	0.999454i	$-0.510524\pi$
$191$	−0.913661	−0.0661102	−0.0330551	+	0.999454i	$0.510524\pi$
$192$	−14.3529	−1.03583
$193$	−11.2144	−0.807229	−0.403614	−	0.914929i	$-0.632246\pi$
$193$	−11.2144	−0.807229	−0.403614	+	0.914929i	$0.632246\pi$
$194$	8.66455	0.622078
$195$	−14.6716	−1.05066
$196$	11.8275	0.844820
$197$	13.0173	0.927441	0.463721	−	0.885981i	$-0.346514\pi$
$197$	13.0173	0.927441	0.463721	+	0.885981i	$0.346514\pi$
$198$	−3.74895	−0.266427
$199$	−9.78075	−0.693339	−0.346669	−	0.937987i	$-0.612687\pi$
$199$	−9.78075	−0.693339	−0.346669	+	0.937987i	$0.612687\pi$
$200$	−17.7999	−1.25864
$201$	14.7724	1.04197
$202$	−9.31733	−0.655565
$203$	−8.95913	−0.628807
$204$	7.74080	0.541965
$205$	−2.45204	−0.171258
$206$	24.1720	1.68414
$207$	−10.6000	−0.736751
$208$	−5.75092	−0.398754
$209$	7.48304	0.517613
$210$	32.3359	2.23139
$211$	3.72562	0.256482	0.128241	−	0.991743i	$-0.459067\pi$
$211$	3.72562	0.256482	0.128241	+	0.991743i	$0.459067\pi$
$212$	−30.5597	−2.09885
$213$	17.1986	1.17843
$214$	−22.8687	−1.56327
$215$	−19.9436	−1.36014
$216$	9.49596	0.646118
$217$	27.8439	1.89016
$218$	12.0461	0.815862
$219$	4.65058	0.314257
$220$	10.8909	0.734265
$221$	8.08050	0.543553
$222$	−13.9353	−0.935277
$223$	−18.0723	−1.21021	−0.605105	−	0.796146i	$-0.706869\pi$
$223$	−18.0723	−1.21021	−0.605105	+	0.796146i	$0.706869\pi$
$224$	24.5604	1.64101
$225$	−17.1435	−1.14290
$226$	26.9598	1.79334
$227$	−7.30933	−0.485137	−0.242569	−	0.970134i	$-0.577990\pi$
$227$	−7.30933	−0.485137	−0.242569	+	0.970134i	$0.577990\pi$
$228$	−23.8817	−1.58161
$229$	−3.38255	−0.223525	−0.111763	−	0.993735i	$-0.535650\pi$
$229$	−3.38255	−0.223525	−0.111763	+	0.993735i	$0.535650\pi$
$230$	52.7157	3.47597
$231$	−3.80351	−0.250252
$232$	4.74949	0.311819
$233$	−3.58756	−0.235029	−0.117514	−	0.993071i	$-0.537493\pi$
$233$	−3.58756	−0.235029	−0.117514	+	0.993071i	$0.537493\pi$
$234$	12.4897	0.816474
$235$	−26.9770	−1.75979
$236$	2.24017	0.145822
$237$	12.8102	0.832109
$238$	−17.8092	−1.15440
$239$	−20.9385	−1.35440	−0.677200	−	0.735799i	$-0.736807\pi$
$239$	−20.9385	−1.35440	−0.677200	+	0.735799i	$0.736807\pi$
$240$	7.60212	0.490715
$241$	−14.8021	−0.953488	−0.476744	−	0.879042i	$-0.658183\pi$
$241$	−14.8021	−0.953488	−0.476744	+	0.879042i	$0.658183\pi$
$242$	−2.19302	−0.140973
$243$	14.9718	0.960439
$244$	2.80936	0.179851
$245$	−16.3208	−1.04270
$246$	−1.57577	−0.100468
$247$	−24.9298	−1.58624
$248$	−14.7608	−0.937313
$249$	6.89180	0.436750
$250$	42.7499	2.70374
$251$	19.9160	1.25709	0.628543	−	0.777775i	$-0.283652\pi$
$251$	19.9160	1.25709	0.628543	+	0.777775i	$0.283652\pi$
$252$	−16.0797	−1.01292
$253$	−6.20068	−0.389833
$254$	6.35718	0.398885
$255$	−10.6816	−0.668907
$256$	−3.32100	−0.207562
$257$	−22.2211	−1.38612	−0.693059	−	0.720881i	$-0.743737\pi$
$257$	−22.2211	−1.38612	−0.693059	+	0.720881i	$0.743737\pi$
$258$	−12.8165	−0.797923
$259$	18.7282	1.16371
$260$	−36.2831	−2.25018
$261$	4.57434	0.283145
$262$	26.8740	1.66028
$263$	−1.12178	−0.0691721	−0.0345860	−	0.999402i	$-0.511011\pi$
$263$	−1.12178	−0.0691721	−0.0345860	+	0.999402i	$0.511011\pi$
$264$	2.01635	0.124098
$265$	42.1695	2.59045
$266$	54.9446	3.36887
$267$	18.7129	1.14521
$268$	36.5324	2.23157
$269$	3.27958	0.199960	0.0999798	−	0.994989i	$-0.468122\pi$
$269$	3.27958	0.199960	0.0999798	+	0.994989i	$0.468122\pi$
$270$	−45.4836	−2.76805
$271$	−0.586170	−0.0356073	−0.0178036	−	0.999842i	$-0.505667\pi$
$271$	−0.586170	−0.0356073	−0.0178036	+	0.999842i	$0.505667\pi$
$272$	−4.18692	−0.253870
$273$	12.6714	0.766908
$274$	−39.2388	−2.37050
$275$	−10.0285	−0.604738
$276$	19.7892	1.19117
$277$	15.1268	0.908882	0.454441	−	0.890777i	$-0.349839\pi$
$277$	15.1268	0.908882	0.454441	+	0.890777i	$0.349839\pi$
$278$	27.7060	1.66170
$279$	−14.2165	−0.851119
$280$	23.0380	1.37678
$281$	5.88779	0.351236	0.175618	−	0.984458i	$-0.443808\pi$
$281$	5.88779	0.351236	0.175618	+	0.984458i	$0.443808\pi$
$282$	−17.3365	−1.03237
$283$	29.5862	1.75872	0.879358	−	0.476160i	$-0.157972\pi$
$283$	29.5862	1.75872	0.879358	+	0.476160i	$0.157972\pi$
$284$	42.5324	2.52383
$285$	32.9546	1.95206
$286$	7.30607	0.432017
$287$	2.11774	0.125006
$288$	−12.5400	−0.738928
$289$	−11.1170	−0.653943
$290$	−22.7490	−1.33587
$291$	−4.48831	−0.263110
$292$	11.5009	0.673041
$293$	5.73008	0.334755	0.167378	−	0.985893i	$-0.446470\pi$
$293$	5.73008	0.334755	0.167378	+	0.985893i	$0.446470\pi$
$294$	−10.4884	−0.611696
$295$	−3.09122	−0.179978
$296$	−9.92834	−0.577073
$297$	5.35001	0.310439
$298$	41.1986	2.38657
$299$	20.6576	1.19466
$300$	32.0053	1.84783
$301$	17.2246	0.992811
$302$	31.1529	1.79265
$303$	4.82646	0.277273
$304$	12.9174	0.740864
$305$	−3.87665	−0.221977
$306$	9.09302	0.519813
$307$	20.2593	1.15626	0.578129	−	0.815946i	$-0.303783\pi$
$307$	20.2593	1.15626	0.578129	+	0.815946i	$0.303783\pi$
$308$	−9.40612	−0.535963
$309$	−12.5213	−0.712313
$310$	70.7012	4.01556
$311$	−3.07029	−0.174100	−0.0870502	−	0.996204i	$-0.527744\pi$
$311$	−3.07029	−0.174100	−0.0870502	+	0.996204i	$0.527744\pi$
$312$	−6.71746	−0.380302
$313$	27.3010	1.54314	0.771572	−	0.636142i	$-0.219471\pi$
$313$	27.3010	1.54314	0.771572	+	0.636142i	$0.219471\pi$
$314$	−0.369990	−0.0208798
$315$	22.1884	1.25018
$316$	31.6797	1.78212
$317$	−1.40786	−0.0790732	−0.0395366	−	0.999218i	$-0.512588\pi$
$317$	−1.40786	−0.0790732	−0.0395366	+	0.999218i	$0.512588\pi$
$318$	27.0998	1.51968
$319$	2.67585	0.149819
$320$	48.9798	2.73806
$321$	11.8462	0.661189
$322$	−45.5288	−2.53722
$323$	−18.1500	−1.00989
$324$	−2.66658	−0.148143
$325$	33.4098	1.85324
$326$	−15.3713	−0.851339
$327$	−6.23997	−0.345071
$328$	−1.12268	−0.0619894
$329$	23.2992	1.28452
$330$	−9.65787	−0.531648
$331$	−13.6295	−0.749147	−0.374573	−	0.927197i	$-0.622211\pi$
$331$	−13.6295	−0.749147	−0.374573	+	0.927197i	$0.622211\pi$
$332$	17.0435	0.935384
$333$	−9.56222	−0.524006
$334$	−31.1409	−1.70396
$335$	−50.4114	−2.75427
$336$	−6.56570	−0.358188
$337$	−23.0887	−1.25772	−0.628861	−	0.777518i	$-0.716479\pi$
$337$	−23.0887	−1.25772	−0.628861	+	0.777518i	$0.716479\pi$
$338$	4.16913	0.226771
$339$	−13.9654	−0.758497
$340$	−26.4157	−1.43259
$341$	−8.31622	−0.450349
$342$	−28.0536	−1.51696
$343$	−9.34122	−0.504378
$344$	−9.13126	−0.492324
$345$	−27.3072	−1.47017
$346$	42.2977	2.27394
$347$	−17.8829	−0.960006	−0.480003	−	0.877267i	$-0.659365\pi$
$347$	−17.8829	−0.960006	−0.480003	+	0.877267i	$0.659365\pi$
$348$	−8.53985	−0.457784
$349$	−16.5158	−0.884071	−0.442036	−	0.896997i	$-0.645744\pi$
$349$	−16.5158	−0.884071	−0.442036	+	0.896997i	$0.645744\pi$
$350$	−73.6344	−3.93592
$351$	−17.8236	−0.951352
$352$	−7.33554	−0.390985
$353$	8.23829	0.438480	0.219240	−	0.975671i	$-0.429642\pi$
$353$	8.23829	0.438480	0.219240	+	0.975671i	$0.429642\pi$
$354$	−1.98654	−0.105583
$355$	−58.6908	−3.11498
$356$	46.2772	2.45268
$357$	9.22534	0.488257
$358$	−32.2263	−1.70321
$359$	−7.15090	−0.377410	−0.188705	−	0.982034i	$-0.560429\pi$
$359$	−7.15090	−0.377410	−0.188705	+	0.982034i	$0.560429\pi$
$360$	−11.7627	−0.619950
$361$	36.9959	1.94715
$362$	−10.9824	−0.577222
$363$	1.13601	0.0596249
$364$	31.3365	1.64248
$365$	−15.8702	−0.830686
$366$	−2.49129	−0.130222
$367$	−29.7118	−1.55094	−0.775472	−	0.631382i	$-0.782488\pi$
$367$	−29.7118	−1.55094	−0.775472	+	0.631382i	$0.782488\pi$
$368$	−10.7038	−0.557972
$369$	−1.08128	−0.0562890
$370$	47.5546	2.47225
$371$	−36.4204	−1.89085
$372$	26.5408	1.37608
$373$	15.5940	0.807428	0.403714	−	0.914885i	$-0.367719\pi$
$373$	15.5940	0.807428	0.403714	+	0.914885i	$0.367719\pi$
$374$	5.31914	0.275046
$375$	−22.1448	−1.14355
$376$	−12.3515	−0.636982
$377$	−8.91461	−0.459126
$378$	39.2827	2.02048
$379$	3.93071	0.201907	0.100954	−	0.994891i	$-0.467811\pi$
$379$	3.93071	0.201907	0.100954	+	0.994891i	$0.467811\pi$
$380$	81.4972	4.18072
$381$	−3.29308	−0.168709
$382$	2.00368	0.102517
$383$	7.69912	0.393407	0.196703	−	0.980463i	$-0.436976\pi$
$383$	7.69912	0.393407	0.196703	+	0.980463i	$0.436976\pi$
$384$	14.8099	0.755767
$385$	12.9796	0.661500
$386$	24.5934	1.25177
$387$	−8.79453	−0.447051
$388$	−11.0997	−0.563500
$389$	12.4596	0.631727	0.315863	−	0.948805i	$-0.397706\pi$
$389$	12.4596	0.631727	0.315863	+	0.948805i	$0.397706\pi$
$390$	32.1752	1.62926
$391$	15.0396	0.760587
$392$	−7.47256	−0.377421
$393$	−13.9210	−0.702219
$394$	−28.5472	−1.43819
$395$	−43.7150	−2.19954
$396$	4.80257	0.241338
$397$	16.8597	0.846164	0.423082	−	0.906091i	$-0.360948\pi$
$397$	16.8597	0.846164	0.423082	+	0.906091i	$0.360948\pi$
$398$	21.4494	1.07516
$399$	−28.4618	−1.42487
$400$	−17.3113	−0.865567
$401$	10.0010	0.499425	0.249712	−	0.968320i	$-0.419664\pi$
$401$	10.0010	0.499425	0.249712	+	0.968320i	$0.419664\pi$
$402$	−32.3963	−1.61578
$403$	27.7055	1.38011
$404$	11.9359	0.593833
$405$	3.67963	0.182842
$406$	19.6476	0.975093
$407$	−5.59361	−0.277265
$408$	−4.89061	−0.242121
$409$	3.37679	0.166972	0.0834859	−	0.996509i	$-0.473395\pi$
$409$	3.37679	0.166972	0.0834859	+	0.996509i	$0.473395\pi$
$410$	5.37738	0.265570
$411$	20.3260	1.00261
$412$	−30.9654	−1.52556
$413$	2.66979	0.131372
$414$	23.2461	1.14248
$415$	−23.5185	−1.15448
$416$	24.4384	1.19819
$417$	−14.3520	−0.702818
$418$	−16.4105	−0.802664
$419$	−23.0855	−1.12780	−0.563899	−	0.825844i	$-0.690699\pi$
$419$	−23.0855	−1.12780	−0.563899	+	0.825844i	$0.690699\pi$
$420$	−41.4236	−2.02127
$421$	−6.13654	−0.299077	−0.149538	−	0.988756i	$-0.547779\pi$
$421$	−6.13654	−0.299077	−0.149538	+	0.988756i	$0.547779\pi$
$422$	−8.17037	−0.397727
$423$	−11.8961	−0.578407
$424$	19.3075	0.937655
$425$	24.3238	1.17988
$426$	−37.7170	−1.82740
$427$	3.34814	0.162028
$428$	29.2958	1.41606
$429$	−3.78461	−0.182723
$430$	43.7368	2.10918
$431$	33.6449	1.62062	0.810308	−	0.586005i	$-0.199300\pi$
$431$	33.6449	1.62062	0.810308	+	0.586005i	$0.199300\pi$
$432$	9.23531	0.444334
$433$	20.6095	0.990427	0.495214	−	0.868771i	$-0.335090\pi$
$433$	20.6095	0.990427	0.495214	+	0.868771i	$0.335090\pi$
$434$	−61.0623	−2.93108
$435$	11.7842	0.565009
$436$	−15.4315	−0.739036
$437$	−46.4000	−2.21961
$438$	−10.1988	−0.487319
$439$	13.1005	0.625254	0.312627	−	0.949876i	$-0.398791\pi$
$439$	13.1005	0.625254	0.312627	+	0.949876i	$0.398791\pi$
$440$	−6.88084	−0.328031
$441$	−7.19700	−0.342714
$442$	−17.7207	−0.842890
$443$	24.8810	1.18213	0.591067	−	0.806623i	$-0.298707\pi$
$443$	24.8810	1.18213	0.591067	+	0.806623i	$0.298707\pi$
$444$	17.8517	0.847205
$445$	−63.8582	−3.02717
$446$	39.6330	1.87668
$447$	−21.3412	−1.00941
$448$	−42.3023	−1.99859
$449$	35.4096	1.67108	0.835542	−	0.549427i	$-0.185154\pi$
$449$	35.4096	1.67108	0.835542	+	0.549427i	$0.185154\pi$
$450$	37.5962	1.77230
$451$	−0.632514	−0.0297839
$452$	−34.5367	−1.62447
$453$	−16.1375	−0.758206
$454$	16.0295	0.752303
$455$	−43.2415	−2.02719
$456$	15.0884	0.706579
$457$	−5.00611	−0.234176	−0.117088	−	0.993122i	$-0.537356\pi$
$457$	−5.00611	−0.234176	−0.117088	+	0.993122i	$0.537356\pi$
$458$	7.41801	0.346621
$459$	−12.9764	−0.605684
$460$	−67.5311	−3.14865
$461$	−31.9040	−1.48592	−0.742958	−	0.669338i	$-0.766578\pi$
$461$	−31.9040	−1.48592	−0.742958	+	0.669338i	$0.766578\pi$
$462$	8.34118	0.388067
$463$	2.91706	0.135567	0.0677837	−	0.997700i	$-0.478407\pi$
$463$	2.91706	0.135567	0.0677837	+	0.997700i	$0.478407\pi$
$464$	4.61912	0.214437
$465$	−36.6238	−1.69839
$466$	7.86760	0.364459
$467$	34.3642	1.59018	0.795092	−	0.606488i	$-0.207422\pi$
$467$	34.3642	1.59018	0.795092	+	0.606488i	$0.207422\pi$
$468$	−15.9998	−0.739590
$469$	43.5386	2.01043
$470$	59.1613	2.72891
$471$	0.191658	0.00883115
$472$	−1.41533	−0.0651458
$473$	−5.14454	−0.236546
$474$	−28.0930	−1.29035
$475$	−75.0433	−3.44322
$476$	22.8144	1.04570
$477$	18.5955	0.851430
$478$	45.9187	2.10027
$479$	22.7117	1.03772	0.518862	−	0.854858i	$-0.326356\pi$
$479$	22.7117	1.03772	0.518862	+	0.854858i	$0.326356\pi$
$480$	−32.3050	−1.47451
$481$	18.6351	0.849689
$482$	32.4614	1.47858
$483$	23.5843	1.07312
$484$	2.80936	0.127698
$485$	15.3165	0.695486
$486$	−32.8334	−1.48936
$487$	−13.7426	−0.622738	−0.311369	−	0.950289i	$-0.600787\pi$
$487$	−13.7426	−0.622738	−0.311369	+	0.950289i	$0.600787\pi$
$488$	−1.77494	−0.0803479
$489$	7.96248	0.360076
$490$	35.7920	1.61692
$491$	−18.5437	−0.836867	−0.418434	−	0.908247i	$-0.637421\pi$
$491$	−18.5437	−0.836867	−0.418434	+	0.908247i	$0.637421\pi$
$492$	2.01863	0.0910071
$493$	−6.49024	−0.292305
$494$	54.6716	2.45979
$495$	−6.62710	−0.297866
$496$	−14.3557	−0.644588
$497$	50.6893	2.27373
$498$	−15.1139	−0.677270
$499$	33.2925	1.49038	0.745190	−	0.666853i	$-0.232359\pi$
$499$	33.2925	1.49038	0.745190	+	0.666853i	$0.232359\pi$
$500$	−54.7644	−2.44914
$501$	16.1313	0.720693
$502$	−43.6762	−1.94937
$503$	23.1519	1.03229	0.516146	−	0.856501i	$-0.327366\pi$
$503$	23.1519	1.03229	0.516146	+	0.856501i	$0.327366\pi$
$504$	10.1591	0.452521
$505$	−16.4704	−0.732924
$506$	13.5982	0.604516
$507$	−2.15964	−0.0959132
$508$	−8.14382	−0.361323
$509$	−26.7406	−1.18526	−0.592629	−	0.805476i	$-0.701910\pi$
$509$	−26.7406	−1.18526	−0.592629	+	0.805476i	$0.701910\pi$
$510$	23.4250	1.03728
$511$	13.7066	0.606344
$512$	−18.7907	−0.830438
$513$	40.0344	1.76756
$514$	48.7315	2.14946
$515$	42.7294	1.88288
$516$	16.4185	0.722785
$517$	−6.95884	−0.306050
$518$	−41.0714	−1.80457
$519$	−21.9106	−0.961768
$520$	22.9235	1.00526
$521$	8.78354	0.384814	0.192407	−	0.981315i	$-0.438371\pi$
$521$	8.78354	0.384814	0.192407	+	0.981315i	$0.438371\pi$
$522$	−10.0316	−0.439073
$523$	−43.4482	−1.89986	−0.949928	−	0.312470i	$-0.898844\pi$
$523$	−43.4482	−1.89986	−0.949928	+	0.312470i	$0.898844\pi$
$524$	−34.4267	−1.50394
$525$	38.1433	1.66471
$526$	2.46010	0.107265
$527$	20.1709	0.878656
$528$	1.96100	0.0853416
$529$	15.4484	0.671671
$530$	−92.4788	−4.01702
$531$	−1.36314	−0.0591551
$532$	−70.3864	−3.05164
$533$	2.10722	0.0912739
$534$	−41.0378	−1.77588
$535$	−40.4254	−1.74774
$536$	−23.0811	−0.996950
$537$	16.6935	0.720378
$538$	−7.19220	−0.310078
$539$	−4.21003	−0.181339
$540$	58.2665	2.50739
$541$	0.244343	0.0105051	0.00525256	−	0.999986i	$-0.498328\pi$
$541$	0.244343	0.0105051	0.00525256	+	0.999986i	$0.498328\pi$
$542$	1.28549	0.0552163
$543$	5.68898	0.244137
$544$	17.7922	0.762835
$545$	21.2941	0.912138
$546$	−27.7887	−1.18925
$547$	−6.46011	−0.276214	−0.138107	−	0.990417i	$-0.544102\pi$
$547$	−6.46011	−0.276214	−0.138107	+	0.990417i	$0.544102\pi$
$548$	50.2666	2.14728
$549$	−1.70949	−0.0729592
$550$	21.9926	0.937769
$551$	20.0235	0.853031
$552$	−12.5027	−0.532151
$553$	37.7552	1.60551
$554$	−33.1735	−1.40941
$555$	−24.6337	−1.04564
$556$	−35.4926	−1.50522
$557$	24.5456	1.04003	0.520015	−	0.854157i	$-0.325926\pi$
$557$	24.5456	1.04003	0.520015	+	0.854157i	$0.325926\pi$
$558$	31.1771	1.31983
$559$	17.1390	0.724904
$560$	22.4056	0.946811
$561$	−2.75536	−0.116332
$562$	−12.9121	−0.544663
$563$	−10.3692	−0.437009	−0.218504	−	0.975836i	$-0.570118\pi$
$563$	−10.3692	−0.437009	−0.218504	+	0.975836i	$0.570118\pi$
$564$	22.2088	0.935159
$565$	47.6574	2.00496
$566$	−64.8833	−2.72725
$567$	−3.17797	−0.133462
$568$	−26.8718	−1.12752
$569$	−37.4636	−1.57055	−0.785277	−	0.619144i	$-0.787480\pi$
$569$	−37.4636	−1.57055	−0.785277	+	0.619144i	$0.787480\pi$
$570$	−72.2703	−3.02707
$571$	30.5449	1.27826	0.639132	−	0.769097i	$-0.279294\pi$
$571$	30.5449	1.27826	0.639132	+	0.769097i	$0.279294\pi$
$572$	−9.35939	−0.391336
$573$	−1.03792	−0.0433599
$574$	−4.64426	−0.193848
$575$	62.1832	2.59322
$576$	21.5987	0.899944
$577$	−25.3268	−1.05437	−0.527184	−	0.849751i	$-0.676752\pi$
$577$	−25.3268	−1.05437	−0.527184	+	0.849751i	$0.676752\pi$
$578$	24.3799	1.01407
$579$	−12.7396	−0.529440
$580$	29.1425	1.21008
$581$	20.3121	0.842689
$582$	9.84298	0.408005
$583$	10.8778	0.450513
$584$	−7.26625	−0.300680
$585$	22.0782	0.912822
$586$	−12.5662	−0.519106
$587$	34.2550	1.41385	0.706927	−	0.707287i	$-0.250081\pi$
$587$	34.2550	1.41385	0.706927	+	0.707287i	$0.250081\pi$
$588$	13.4361	0.554095
$589$	−62.2307	−2.56417
$590$	6.77913	0.279092
$591$	14.7877	0.608284
$592$	−9.65582	−0.396852
$593$	−15.8516	−0.650945	−0.325473	−	0.945551i	$-0.605523\pi$
$593$	−15.8516	−0.650945	−0.325473	+	0.945551i	$0.605523\pi$
$594$	−11.7327	−0.481399
$595$	−31.4817	−1.29063
$596$	−52.7772	−2.16184
$597$	−11.1110	−0.454743
$598$	−45.3026	−1.85256
$599$	−11.4422	−0.467515	−0.233757	−	0.972295i	$-0.575102\pi$
$599$	−11.4422	−0.467515	−0.233757	+	0.972295i	$0.575102\pi$
$600$	−20.2208	−0.825512
$601$	−26.8268	−1.09429	−0.547144	−	0.837039i	$-0.684285\pi$
$601$	−26.8268	−1.09429	−0.547144	+	0.837039i	$0.684285\pi$
$602$	−37.7740	−1.53955
$603$	−22.2299	−0.905272
$604$	−39.9082	−1.62384
$605$	−3.87665	−0.157608
$606$	−10.5845	−0.429968
$607$	11.8113	0.479404	0.239702	−	0.970847i	$-0.422950\pi$
$607$	11.8113	0.479404	0.239702	+	0.970847i	$0.422950\pi$
$608$	−54.8921	−2.22617
$609$	−10.1776	−0.412418
$610$	8.50160	0.344220
$611$	23.1834	0.937900
$612$	−11.6485	−0.470865
$613$	17.6434	0.712609	0.356305	−	0.934370i	$-0.384037\pi$
$613$	17.6434	0.712609	0.356305	+	0.934370i	$0.384037\pi$
$614$	−44.4291	−1.79301
$615$	−2.78553	−0.112323
$616$	5.94275	0.239440
$617$	−22.6740	−0.912823	−0.456411	−	0.889769i	$-0.650865\pi$
$617$	−22.6740	−0.912823	−0.456411	+	0.889769i	$0.650865\pi$
$618$	27.4596	1.10459
$619$	−2.14696	−0.0862936	−0.0431468	−	0.999069i	$-0.513738\pi$
$619$	−2.14696	−0.0862936	−0.0431468	+	0.999069i	$0.513738\pi$
$620$	−90.5712	−3.63743
$621$	−33.1737	−1.33121
$622$	6.73323	0.269978
$623$	55.1522	2.20963
$624$	−6.53308	−0.261532
$625$	25.4276	1.01710
$626$	−59.8718	−2.39296
$627$	8.50078	0.339489
$628$	0.473973	0.0189136
$629$	13.5672	0.540960
$630$	−48.6598	−1.93865
$631$	16.4001	0.652876	0.326438	−	0.945219i	$-0.394151\pi$
$631$	16.4001	0.652876	0.326438	+	0.945219i	$0.394151\pi$
$632$	−20.0151	−0.796158
$633$	4.23232	0.168220
$634$	3.08747	0.122619
$635$	11.2377	0.445955
$636$	−34.7160	−1.37658
$637$	14.0257	0.555719
$638$	−5.86821	−0.232325
$639$	−25.8809	−1.02383
$640$	−50.5394	−1.99774
$641$	17.2072	0.679645	0.339823	−	0.940490i	$-0.389633\pi$
$641$	17.2072	0.679645	0.339823	+	0.940490i	$0.389633\pi$
$642$	−25.9790	−1.02531
$643$	45.8874	1.80962	0.904811	−	0.425813i	$-0.140012\pi$
$643$	45.8874	1.80962	0.904811	+	0.425813i	$0.140012\pi$
$644$	58.3243	2.29830
$645$	−22.6560	−0.892081
$646$	39.8034	1.56604
$647$	−44.5350	−1.75085	−0.875426	−	0.483351i	$-0.839419\pi$
$647$	−44.5350	−1.75085	−0.875426	+	0.483351i	$0.839419\pi$
$648$	1.68473	0.0661826
$649$	−0.797395	−0.0313005
$650$	−73.2686	−2.87383
$651$	31.6308	1.23971
$652$	19.6913	0.771172
$653$	−5.57274	−0.218078	−0.109039	−	0.994037i	$-0.534777\pi$
$653$	−5.57274	−0.218078	−0.109039	+	0.994037i	$0.534777\pi$
$654$	13.6844	0.535102
$655$	47.5057	1.85620
$656$	−1.09186	−0.0426300
$657$	−6.99830	−0.273030
$658$	−51.0956	−1.99192
$659$	−39.3284	−1.53202	−0.766008	−	0.642831i	$-0.777760\pi$
$659$	−39.3284	−1.53202	−0.766008	+	0.642831i	$0.777760\pi$
$660$	12.3721	0.481585
$661$	−2.51038	−0.0976426	−0.0488213	−	0.998808i	$-0.515546\pi$
$661$	−2.51038	−0.0976426	−0.0488213	+	0.998808i	$0.515546\pi$
$662$	29.8899	1.16170
$663$	9.17950	0.356502
$664$	−10.7680	−0.417881
$665$	97.1267	3.76641
$666$	20.9702	0.812578
$667$	−16.5921	−0.642449
$668$	39.8929	1.54350
$669$	−20.5302	−0.793744
$670$	110.553	4.27105
$671$	−1.00000	−0.0386046
$672$	27.9007	1.07629
$673$	−21.9820	−0.847343	−0.423671	−	0.905816i	$-0.639259\pi$
$673$	−21.9820	−0.847343	−0.423671	+	0.905816i	$0.639259\pi$
$674$	50.6341	1.95035
$675$	−53.6523	−2.06508
$676$	−5.34083	−0.205416
$677$	−18.2538	−0.701552	−0.350776	−	0.936459i	$-0.614082\pi$
$677$	−18.2538	−0.701552	−0.350776	+	0.936459i	$0.614082\pi$
$678$	30.6265	1.17620
$679$	−13.2283	−0.507657
$680$	16.6894	0.640008
$681$	−8.30344	−0.318189
$682$	18.2377	0.698357
$683$	−12.3322	−0.471877	−0.235938	−	0.971768i	$-0.575816\pi$
$683$	−12.3322	−0.471877	−0.235938	+	0.971768i	$0.575816\pi$
$684$	35.9378	1.37412
$685$	−69.3632	−2.65023
$686$	20.4855	0.782141
$687$	−3.84260	−0.146604
$688$	−8.88062	−0.338570
$689$	−36.2395	−1.38061
$690$	59.8854	2.27980
$691$	−26.4275	−1.00535	−0.502675	−	0.864476i	$-0.667651\pi$
$691$	−26.4275	−1.00535	−0.502675	+	0.864476i	$0.667651\pi$
$692$	−54.1852	−2.05981
$693$	5.72361	0.217422
$694$	39.2177	1.48868
$695$	48.9765	1.85778
$696$	5.39545	0.204514
$697$	1.53415	0.0581101
$698$	36.2196	1.37093
$699$	−4.07549	−0.154149
$700$	94.3288	3.56529
$701$	47.3706	1.78916	0.894582	−	0.446904i	$-0.147473\pi$
$701$	47.3706	1.78916	0.894582	+	0.446904i	$0.147473\pi$
$702$	39.0875	1.47526
$703$	−41.8572	−1.57868
$704$	12.6346	0.476183
$705$	−30.6461	−1.15420
$706$	−18.0668	−0.679952
$707$	14.2250	0.534985
$708$	2.54484	0.0956411
$709$	37.5265	1.40934	0.704668	−	0.709537i	$-0.251096\pi$
$709$	37.5265	1.40934	0.704668	+	0.709537i	$0.251096\pi$
$710$	128.710	4.83041
$711$	−19.2770	−0.722945
$712$	−29.2377	−1.09573
$713$	51.5662	1.93117
$714$	−20.2314	−0.757141
$715$	12.9151	0.482997
$716$	41.2833	1.54283
$717$	−23.7863	−0.888316
$718$	15.6821	0.585251
$719$	−15.3971	−0.574216	−0.287108	−	0.957898i	$-0.592694\pi$
$719$	−15.3971	−0.574216	−0.287108	+	0.957898i	$0.592694\pi$
$720$	−11.4399	−0.426338
$721$	−36.9039	−1.37437
$722$	−81.1330	−3.01946
$723$	−16.8153	−0.625368
$724$	14.0689	0.522867
$725$	−26.8347	−0.996614
$726$	−2.49129	−0.0924604
$727$	−28.1185	−1.04286	−0.521428	−	0.853295i	$-0.674600\pi$
$727$	−28.1185	−1.04286	−0.521428	+	0.853295i	$0.674600\pi$
$728$	−19.7983	−0.733774
$729$	19.8555	0.735390
$730$	34.8038	1.28815
$731$	12.4780	0.461515
$732$	3.19145	0.117959
$733$	10.9059	0.402817	0.201409	−	0.979507i	$-0.435448\pi$
$733$	10.9059	0.402817	0.201409	+	0.979507i	$0.435448\pi$
$734$	65.1587	2.40505
$735$	−18.5406	−0.683879
$736$	45.4853	1.67661
$737$	−13.0038	−0.479002
$738$	2.37126	0.0872874
$739$	−21.1774	−0.779021	−0.389511	−	0.921022i	$-0.627356\pi$
$739$	−21.1774	−0.779021	−0.389511	+	0.921022i	$0.627356\pi$
$740$	−60.9195	−2.23945
$741$	−28.3204	−1.04038
$742$	79.8709	2.93215
$743$	−16.2063	−0.594552	−0.297276	−	0.954792i	$-0.596078\pi$
$743$	−16.2063	−0.594552	−0.297276	+	0.954792i	$0.596078\pi$
$744$	−16.7684	−0.614759
$745$	72.8276	2.66820
$746$	−34.1981	−1.25208
$747$	−10.3709	−0.379453
$748$	−6.81405	−0.249146
$749$	34.9141	1.27573
$750$	48.5641	1.77331
$751$	3.82560	0.139598	0.0697991	−	0.997561i	$-0.477764\pi$
$751$	3.82560	0.139598	0.0697991	+	0.997561i	$0.477764\pi$
$752$	−12.0125	−0.438051
$753$	22.6247	0.824489
$754$	19.5500	0.711968
$755$	55.0697	2.00419
$756$	−50.3228	−1.83022
$757$	−11.4027	−0.414437	−0.207219	−	0.978295i	$-0.566441\pi$
$757$	−11.4027	−0.414437	−0.207219	+	0.978295i	$0.566441\pi$
$758$	−8.62015	−0.313098
$759$	−7.04401	−0.255681
$760$	−51.4896	−1.86772
$761$	−8.00618	−0.290224	−0.145112	−	0.989415i	$-0.546354\pi$
$761$	−8.00618	−0.290224	−0.145112	+	0.989415i	$0.546354\pi$
$762$	7.22180	0.261618
$763$	−18.3910	−0.665798
$764$	−2.56680	−0.0928636
$765$	16.0739	0.581154
$766$	−16.8844	−0.610057
$767$	2.65652	0.0959215
$768$	−3.77267	−0.136135
$769$	8.44893	0.304676	0.152338	−	0.988328i	$-0.451320\pi$
$769$	8.44893	0.304676	0.152338	+	0.988328i	$0.451320\pi$
$770$	−28.4645	−1.02579
$771$	−25.2434	−0.909117
$772$	−31.5052	−1.13390
$773$	−13.9443	−0.501542	−0.250771	−	0.968046i	$-0.580684\pi$
$773$	−13.9443	−0.501542	−0.250771	+	0.968046i	$0.580684\pi$
$774$	19.2866	0.693244
$775$	83.3988	2.99577
$776$	7.01272	0.251742
$777$	21.2753	0.763248
$778$	−27.3242	−0.979621
$779$	−4.73313	−0.169582
$780$	−41.2178	−1.47584
$781$	−15.1395	−0.541736
$782$	−32.9823	−1.17944
$783$	14.3158	0.511606
$784$	−7.26744	−0.259552
$785$	−0.654039	−0.0233437
$786$	30.5290	1.08893
$787$	−6.62789	−0.236259	−0.118129	−	0.992998i	$-0.537690\pi$
$787$	−6.62789	−0.236259	−0.118129	+	0.992998i	$0.537690\pi$
$788$	36.5702	1.30276
$789$	−1.27435	−0.0453681
$790$	95.8681	3.41083
$791$	−41.1601	−1.46348
$792$	−3.03425	−0.107817
$793$	3.33150	0.118305
$794$	−36.9738	−1.31215
$795$	47.9048	1.69901
$796$	−27.4776	−0.973919
$797$	−6.86668	−0.243230	−0.121615	−	0.992577i	$-0.538807\pi$
$797$	−6.86668	−0.243230	−0.121615	+	0.992577i	$0.538807\pi$
$798$	62.4174	2.20955
$799$	16.8786	0.597120
$800$	73.5641	2.60088
$801$	−28.1596	−0.994970
$802$	−21.9324	−0.774460
$803$	−4.09379	−0.144467
$804$	41.5011	1.46363
$805$	−80.4822	−2.83662
$806$	−60.7589	−2.14014
$807$	3.72562	0.131148
$808$	−7.54105	−0.265293
$809$	−22.2319	−0.781633	−0.390817	−	0.920469i	$-0.627807\pi$
$809$	−22.2319	−0.781633	−0.390817	+	0.920469i	$0.627807\pi$
$810$	−8.06952	−0.283534
$811$	17.0512	0.598750	0.299375	−	0.954135i	$-0.403222\pi$
$811$	17.0512	0.598750	0.299375	+	0.954135i	$0.403222\pi$
$812$	−25.1694	−0.883273
$813$	−0.665893	−0.0233539
$814$	12.2669	0.429956
$815$	−27.1722	−0.951801
$816$	−4.75637	−0.166506
$817$	−38.4968	−1.34683
$818$	−7.40539	−0.258924
$819$	−19.0682	−0.666297
$820$	−6.88865	−0.240562
$821$	13.7365	0.479406	0.239703	−	0.970846i	$-0.422950\pi$
$821$	13.7365	0.479406	0.239703	+	0.970846i	$0.422950\pi$
$822$	−44.5755	−1.55475
$823$	31.3223	1.09183	0.545914	−	0.837841i	$-0.316183\pi$
$823$	31.3223	1.09183	0.545914	+	0.837841i	$0.316183\pi$
$824$	19.5638	0.681538
$825$	−11.3924	−0.396632
$826$	−5.85491	−0.203718
$827$	29.3223	1.01964	0.509819	−	0.860282i	$-0.329712\pi$
$827$	29.3223	1.01964	0.509819	+	0.860282i	$0.329712\pi$
$828$	−29.7792	−1.03490
$829$	18.2233	0.632920	0.316460	−	0.948606i	$-0.397506\pi$
$829$	18.2233	0.632920	0.316460	+	0.948606i	$0.397506\pi$
$830$	51.5766	1.79025
$831$	17.1842	0.596112
$832$	−42.0921	−1.45928
$833$	10.2113	0.353802
$834$	31.4742	1.08986
$835$	−55.0485	−1.90503
$836$	21.0225	0.727080
$837$	−44.4919	−1.53786
$838$	50.6270	1.74888
$839$	−9.21238	−0.318047	−0.159023	−	0.987275i	$-0.550834\pi$
$839$	−9.21238	−0.318047	−0.159023	+	0.987275i	$0.550834\pi$
$840$	26.1713	0.902996
$841$	−21.8398	−0.753097
$842$	13.4576	0.463779
$843$	6.68857	0.230366
$844$	10.4666	0.360275
$845$	7.36985	0.253530
$846$	26.0884	0.896937
$847$	3.34814	0.115043
$848$	18.7775	0.644823
$849$	33.6101	1.15350
$850$	−53.3428	−1.82964
$851$	34.6842	1.18896
$852$	48.3171	1.65532
$853$	−1.71618	−0.0587608	−0.0293804	−	0.999568i	$-0.509353\pi$
$853$	−1.71618	−0.0587608	−0.0293804	+	0.999568i	$0.509353\pi$
$854$	−7.34255	−0.251257
$855$	−49.5909	−1.69597
$856$	−18.5090	−0.632623
$857$	48.1201	1.64375	0.821876	−	0.569667i	$-0.192928\pi$
$857$	48.1201	1.64375	0.821876	+	0.569667i	$0.192928\pi$
$858$	8.29974	0.283349
$859$	−53.3428	−1.82003	−0.910016	−	0.414573i	$-0.863931\pi$
$859$	−53.3428	−1.82003	−0.910016	+	0.414573i	$0.863931\pi$
$860$	−56.0287	−1.91056
$861$	2.40577	0.0819884
$862$	−73.7840	−2.51309
$863$	−11.8351	−0.402872	−0.201436	−	0.979502i	$-0.564561\pi$
$863$	−11.8351	−0.402872	−0.201436	+	0.979502i	$0.564561\pi$
$864$	−39.2452	−1.33515
$865$	74.7705	2.54227
$866$	−45.1970	−1.53586
$867$	−12.6290	−0.428904
$868$	78.2234	2.65507
$869$	−11.2765	−0.382528
$870$	−25.8430	−0.876161
$871$	43.3223	1.46792
$872$	9.74958	0.330162
$873$	6.75412	0.228592
$874$	101.756	3.44196
$875$	−65.2671	−2.20643
$876$	13.0651	0.441430
$877$	−31.0985	−1.05012	−0.525062	−	0.851064i	$-0.675958\pi$
$877$	−31.0985	−1.05012	−0.525062	+	0.851064i	$0.675958\pi$
$878$	−28.7298	−0.969583
$879$	6.50941	0.219557
$880$	−6.69197	−0.225586
$881$	−0.502655	−0.0169349	−0.00846744	−	0.999964i	$-0.502695\pi$
$881$	−0.502655	−0.0169349	−0.00846744	+	0.999964i	$0.502695\pi$
$882$	15.7832	0.531448
$883$	38.2265	1.28642	0.643211	−	0.765689i	$-0.277602\pi$
$883$	38.2265	1.28642	0.643211	+	0.765689i	$0.277602\pi$
$884$	22.7010	0.763518
$885$	−3.51165	−0.118043
$886$	−54.5647	−1.83314
$887$	−55.2883	−1.85640	−0.928200	−	0.372081i	$-0.878644\pi$
$887$	−55.2883	−1.85640	−0.928200	+	0.372081i	$0.878644\pi$
$888$	−11.2787	−0.378487
$889$	−9.70564	−0.325517
$890$	140.043	4.69424
$891$	0.949176	0.0317986
$892$	−50.7715	−1.69996
$893$	−52.0733	−1.74257
$894$	46.8019	1.56529
$895$	−56.9671	−1.90420
$896$	43.6492	1.45822
$897$	23.4671	0.783545
$898$	−77.6542	−2.59135
$899$	−22.2530	−0.742179
$900$	−48.1623	−1.60541
$901$	−26.3839	−0.878977
$902$	1.38712	0.0461860
$903$	19.5673	0.651158
$904$	21.8201	0.725727
$905$	−19.4138	−0.645336
$906$	35.3899	1.17575
$907$	30.6802	1.01872	0.509359	−	0.860554i	$-0.329882\pi$
$907$	30.6802	1.01872	0.509359	+	0.860554i	$0.329882\pi$
$908$	−20.5345	−0.681462
$909$	−7.26297	−0.240897
$910$	94.8297	3.14357
$911$	−0.197413	−0.00654057	−0.00327029	−	0.999995i	$-0.501041\pi$
$911$	−0.197413	−0.00654057	−0.00327029	+	0.999995i	$0.501041\pi$
$912$	14.6742	0.485913
$913$	−6.06669	−0.200778
$914$	10.9785	0.363137
$915$	−4.40390	−0.145589
$916$	−9.50279	−0.313981
$917$	−41.0291	−1.35490
$918$	28.4575	0.939236
$919$	−44.9844	−1.48390	−0.741950	−	0.670456i	$-0.766099\pi$
$919$	−44.9844	−1.48390	−0.741950	+	0.670456i	$0.766099\pi$
$920$	42.6659	1.40665
$921$	23.0147	0.758359
$922$	69.9662	2.30421
$923$	50.4375	1.66017
$924$	−10.6854	−0.351524
$925$	56.0953	1.84440
$926$	−6.39719	−0.210225
$927$	18.8424	0.618865
$928$	−19.6288	−0.644347
$929$	−7.20796	−0.236485	−0.118243	−	0.992985i	$-0.537726\pi$
$929$	−7.20796	−0.236485	−0.118243	+	0.992985i	$0.537726\pi$
$930$	80.3170	2.63370
$931$	−31.5038	−1.03250
$932$	−10.0787	−0.330140
$933$	−3.48787	−0.114188
$934$	−75.3615	−2.46590
$935$	9.40276	0.307503
$936$	10.1086	0.330410
$937$	−10.8511	−0.354489	−0.177245	−	0.984167i	$-0.556718\pi$
$937$	−10.8511	−0.354489	−0.177245	+	0.984167i	$0.556718\pi$
$938$	−95.4813	−3.11758
$939$	31.0141	1.01211
$940$	−75.7881	−2.47194
$941$	−32.0924	−1.04618	−0.523092	−	0.852276i	$-0.675221\pi$
$941$	−32.0924	−1.04618	−0.523092	+	0.852276i	$0.675221\pi$
$942$	−0.420311	−0.0136945
$943$	3.92201	0.127718
$944$	−1.37648	−0.0448006
$945$	69.4408	2.25891
$946$	11.2821	0.366813
$947$	−17.1736	−0.558068	−0.279034	−	0.960281i	$-0.590014\pi$
$947$	−17.1736	−0.558068	−0.279034	+	0.960281i	$0.590014\pi$
$948$	35.9883	1.16885
$949$	13.6385	0.442724
$950$	164.572	5.33942
$951$	−1.59934	−0.0518620
$952$	−14.4140	−0.467162
$953$	−12.5624	−0.406937	−0.203468	−	0.979082i	$-0.565221\pi$
$953$	−12.5624	−0.406937	−0.203468	+	0.979082i	$0.565221\pi$
$954$	−40.7804	−1.32031
$955$	3.54195	0.114615
$956$	−58.8238	−1.90250
$957$	3.03979	0.0982623
$958$	−49.8073	−1.60920
$959$	59.9067	1.93449
$960$	55.6414	1.79582
$961$	38.1596	1.23095
$962$	−40.8673	−1.31762
$963$	−17.8264	−0.574448
$964$	−41.5844	−1.33934
$965$	43.4743	1.39949
$966$	−51.7210	−1.66410
$967$	−7.96396	−0.256104	−0.128052	−	0.991767i	$-0.540872\pi$
$967$	−7.96396	−0.256104	−0.128052	+	0.991767i	$0.540872\pi$
$968$	−1.77494	−0.0570488
$969$	−20.6185	−0.662362
$970$	−33.5895	−1.07849
$971$	−5.74776	−0.184454	−0.0922272	−	0.995738i	$-0.529399\pi$
$971$	−5.74776	−0.184454	−0.0922272	+	0.995738i	$0.529399\pi$
$972$	42.0610	1.34911
$973$	−42.2993	−1.35605
$974$	30.1379	0.965681
$975$	37.9538	1.21549
$976$	−1.72622	−0.0552550
$977$	38.5935	1.23472	0.617358	−	0.786682i	$-0.288203\pi$
$977$	38.5935	1.23472	0.617358	+	0.786682i	$0.288203\pi$
$978$	−17.4619	−0.558371
$979$	−16.4725	−0.526463
$980$	−45.8510	−1.46466
$981$	9.39005	0.299801
$982$	40.6669	1.29773
$983$	−59.6227	−1.90167	−0.950835	−	0.309698i	$-0.899772\pi$
$983$	−59.6227	−1.90167	−0.950835	+	0.309698i	$0.899772\pi$
$984$	−1.27537	−0.0406572
$985$	−50.4634	−1.60790
$986$	14.2332	0.453279
$987$	26.4680	0.842486
$988$	−70.0367	−2.22816
$989$	31.8996	1.01435
$990$	14.5334	0.461902
$991$	12.3426	0.392076	0.196038	−	0.980596i	$-0.437192\pi$
$991$	12.3426	0.392076	0.196038	+	0.980596i	$0.437192\pi$
$992$	61.0039	1.93688
$993$	−15.4832	−0.491346
$994$	−111.163	−3.52587
$995$	37.9166	1.20204
$996$	19.3615	0.613494
$997$	28.6925	0.908699	0.454350	−	0.890823i	$-0.349872\pi$
$997$	28.6925	0.908699	0.454350	+	0.890823i	$0.349872\pi$
$998$	−73.0114	−2.31113
$999$	−29.9259	−0.946813

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	671.2.a.d.1.5	✓	21
3.2	odd	2		6039.2.a.l.1.17		21
11.10	odd	2		7381.2.a.j.1.17		21

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
671.2.a.d.1.5	✓	21	1.1	even	1	trivial
6039.2.a.l.1.17		21	3.2	odd	2
7381.2.a.j.1.17		21	11.10	odd	2

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:	\( N \)	\(=\)	\( 671 = 11 \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	671.a (trivial)

\(f(q)\)	\(=\)	\(q-2.19302 q^{2} +1.13601 q^{3} +2.80936 q^{4} -3.87665 q^{5} -2.49129 q^{6} +3.34814 q^{7} -1.77494 q^{8} -1.70949 q^{9} +O(q^{10})\)	\(q-2.19302 q^{2} +1.13601 q^{3} +2.80936 q^{4} -3.87665 q^{5} -2.49129 q^{6} +3.34814 q^{7} -1.77494 q^{8} -1.70949 q^{9} +8.50160 q^{10} -1.00000 q^{11} +3.19145 q^{12} +3.33150 q^{13} -7.34255 q^{14} -4.40390 q^{15} -1.72622 q^{16} +2.42548 q^{17} +3.74895 q^{18} -7.48304 q^{19} -10.8909 q^{20} +3.80351 q^{21} +2.19302 q^{22} +6.20068 q^{23} -2.01635 q^{24} +10.0285 q^{25} -7.30607 q^{26} -5.35001 q^{27} +9.40612 q^{28} -2.67585 q^{29} +9.65787 q^{30} +8.31622 q^{31} +7.33554 q^{32} -1.13601 q^{33} -5.31914 q^{34} -12.9796 q^{35} -4.80257 q^{36} +5.59361 q^{37} +16.4105 q^{38} +3.78461 q^{39} +6.88084 q^{40} +0.632514 q^{41} -8.34118 q^{42} +5.14454 q^{43} -2.80936 q^{44} +6.62710 q^{45} -13.5982 q^{46} +6.95884 q^{47} -1.96100 q^{48} +4.21003 q^{49} -21.9926 q^{50} +2.75536 q^{51} +9.35939 q^{52} -10.8778 q^{53} +11.7327 q^{54} +3.87665 q^{55} -5.94275 q^{56} -8.50078 q^{57} +5.86821 q^{58} +0.797395 q^{59} -12.3721 q^{60} +1.00000 q^{61} -18.2377 q^{62} -5.72361 q^{63} -12.6346 q^{64} -12.9151 q^{65} +2.49129 q^{66} +13.0038 q^{67} +6.81405 q^{68} +7.04401 q^{69} +28.4645 q^{70} +15.1395 q^{71} +3.03425 q^{72} +4.09379 q^{73} -12.2669 q^{74} +11.3924 q^{75} -21.0225 q^{76} -3.34814 q^{77} -8.29974 q^{78} +11.2765 q^{79} +6.69197 q^{80} -0.949176 q^{81} -1.38712 q^{82} +6.06669 q^{83} +10.6854 q^{84} -9.40276 q^{85} -11.2821 q^{86} -3.03979 q^{87} +1.77494 q^{88} +16.4725 q^{89} -14.5334 q^{90} +11.1543 q^{91} +17.4199 q^{92} +9.44728 q^{93} -15.2609 q^{94} +29.0092 q^{95} +8.33321 q^{96} -3.95096 q^{97} -9.23269 q^{98} +1.70949 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 21 q + 3 q^{3} + 32 q^{4} + 7 q^{5} + 5 q^{6} + 5 q^{7} - 6 q^{8} + 40 q^{9}+O(q^{10}) \) 21 * q + 3 * q^3 + 32 * q^4 + 7 * q^5 + 5 * q^6 + 5 * q^7 - 6 * q^8 + 40 * q^9	\( 21 q + 3 q^{3} + 32 q^{4} + 7 q^{5} + 5 q^{6} + 5 q^{7} - 6 q^{8} + 40 q^{9} + q^{10} - 21 q^{11} + 6 q^{12} + 20 q^{13} + 17 q^{14} + 18 q^{15} + 50 q^{16} + q^{17} - 5 q^{18} + 15 q^{19} - 2 q^{20} + 16 q^{21} + 11 q^{23} - 16 q^{24} + 48 q^{25} - 5 q^{26} + 12 q^{27} - 16 q^{28} - 9 q^{29} + 16 q^{30} + 22 q^{31} + 3 q^{32} - 3 q^{33} + 33 q^{34} - 39 q^{35} + 57 q^{36} + 21 q^{37} + 11 q^{38} - 28 q^{39} - 16 q^{40} + 7 q^{41} - 55 q^{42} + 16 q^{43} - 32 q^{44} + 44 q^{45} - 3 q^{46} + 5 q^{47} - 71 q^{48} + 80 q^{49} - 33 q^{50} - 19 q^{51} + 60 q^{52} + 9 q^{53} + 13 q^{54} - 7 q^{55} + 44 q^{56} + 39 q^{57} - 27 q^{58} + 13 q^{59} + 70 q^{60} + 21 q^{61} - 23 q^{62} + 24 q^{63} + 66 q^{64} + 25 q^{65} - 5 q^{66} + 38 q^{67} - 74 q^{68} - 17 q^{69} - 33 q^{70} + 12 q^{71} - 75 q^{72} + 20 q^{73} - 12 q^{74} - 10 q^{75} + 59 q^{76} - 5 q^{77} - 14 q^{78} + q^{79} - 38 q^{80} + 89 q^{81} + 7 q^{82} - 19 q^{83} - 14 q^{84} + 38 q^{85} - 3 q^{86} + 4 q^{87} + 6 q^{88} + 37 q^{89} - 174 q^{90} + 24 q^{91} + 31 q^{92} - 15 q^{93} - 64 q^{94} - 43 q^{95} - 38 q^{96} + 68 q^{97} - 2 q^{98} - 40 q^{99}+O(q^{100}) \) 21 * q + 3 * q^3 + 32 * q^4 + 7 * q^5 + 5 * q^6 + 5 * q^7 - 6 * q^8 + 40 * q^9 + q^10 - 21 * q^11 + 6 * q^12 + 20 * q^13 + 17 * q^14 + 18 * q^15 + 50 * q^16 + q^17 - 5 * q^18 + 15 * q^19 - 2 * q^20 + 16 * q^21 + 11 * q^23 - 16 * q^24 + 48 * q^25 - 5 * q^26 + 12 * q^27 - 16 * q^28 - 9 * q^29 + 16 * q^30 + 22 * q^31 + 3 * q^32 - 3 * q^33 + 33 * q^34 - 39 * q^35 + 57 * q^36 + 21 * q^37 + 11 * q^38 - 28 * q^39 - 16 * q^40 + 7 * q^41 - 55 * q^42 + 16 * q^43 - 32 * q^44 + 44 * q^45 - 3 * q^46 + 5 * q^47 - 71 * q^48 + 80 * q^49 - 33 * q^50 - 19 * q^51 + 60 * q^52 + 9 * q^53 + 13 * q^54 - 7 * q^55 + 44 * q^56 + 39 * q^57 - 27 * q^58 + 13 * q^59 + 70 * q^60 + 21 * q^61 - 23 * q^62 + 24 * q^63 + 66 * q^64 + 25 * q^65 - 5 * q^66 + 38 * q^67 - 74 * q^68 - 17 * q^69 - 33 * q^70 + 12 * q^71 - 75 * q^72 + 20 * q^73 - 12 * q^74 - 10 * q^75 + 59 * q^76 - 5 * q^77 - 14 * q^78 + q^79 - 38 * q^80 + 89 * q^81 + 7 * q^82 - 19 * q^83 - 14 * q^84 + 38 * q^85 - 3 * q^86 + 4 * q^87 + 6 * q^88 + 37 * q^89 - 174 * q^90 + 24 * q^91 + 31 * q^92 - 15 * q^93 - 64 * q^94 - 43 * q^95 - 38 * q^96 + 68 * q^97 - 2 * q^98 - 40 * q^99

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