LMFDB - Embedded newform 619.2.a.a.1.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [619,2,Mod(1,619)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(619, 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("619.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 619 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	619.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:	$4.94273988512$
Analytic rank:	$1$
Dimension:	$21$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.19
Character	$\chi$	$=$	619.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.61466 q^{2} -2.35583 q^{3} +0.607120 q^{4} +0.981279 q^{5} -3.80386 q^{6} -0.0820085 q^{7} -2.24902 q^{8} +2.54995 q^{9} +O(q^{10})$	\(q+1.61466 q^{2} -2.35583 q^{3} +0.607120 q^{4} +0.981279 q^{5} -3.80386 q^{6} -0.0820085 q^{7} -2.24902 q^{8} +2.54995 q^{9} +1.58443 q^{10} -0.0155165 q^{11} -1.43027 q^{12} -4.49441 q^{13} -0.132416 q^{14} -2.31173 q^{15} -4.84565 q^{16} +0.0424957 q^{17} +4.11730 q^{18} -7.23140 q^{19} +0.595754 q^{20} +0.193198 q^{21} -0.0250538 q^{22} +4.78934 q^{23} +5.29833 q^{24} -4.03709 q^{25} -7.25693 q^{26} +1.06024 q^{27} -0.0497890 q^{28} -7.53183 q^{29} -3.73265 q^{30} +6.01931 q^{31} -3.32601 q^{32} +0.0365542 q^{33} +0.0686161 q^{34} -0.0804732 q^{35} +1.54813 q^{36} -6.28717 q^{37} -11.6762 q^{38} +10.5881 q^{39} -2.20692 q^{40} -6.87805 q^{41} +0.311949 q^{42} -12.4977 q^{43} -0.00942036 q^{44} +2.50221 q^{45} +7.73314 q^{46} +11.9620 q^{47} +11.4155 q^{48} -6.99327 q^{49} -6.51852 q^{50} -0.100113 q^{51} -2.72865 q^{52} -2.68677 q^{53} +1.71193 q^{54} -0.0152260 q^{55} +0.184439 q^{56} +17.0360 q^{57} -12.1613 q^{58} +4.85711 q^{59} -1.40350 q^{60} +15.2013 q^{61} +9.71913 q^{62} -0.209118 q^{63} +4.32092 q^{64} -4.41027 q^{65} +0.0590225 q^{66} +2.90529 q^{67} +0.0258000 q^{68} -11.2829 q^{69} -0.129937 q^{70} +9.70183 q^{71} -5.73490 q^{72} +6.12979 q^{73} -10.1516 q^{74} +9.51071 q^{75} -4.39033 q^{76} +0.00127248 q^{77} +17.0961 q^{78} +13.6930 q^{79} -4.75493 q^{80} -10.1476 q^{81} -11.1057 q^{82} +2.76246 q^{83} +0.117295 q^{84} +0.0417002 q^{85} -20.1796 q^{86} +17.7437 q^{87} +0.0348969 q^{88} -16.5137 q^{89} +4.04021 q^{90} +0.368580 q^{91} +2.90770 q^{92} -14.1805 q^{93} +19.3145 q^{94} -7.09602 q^{95} +7.83553 q^{96} +10.2707 q^{97} -11.2917 q^{98} -0.0395662 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 21 q - 9 q^{2} - 5 q^{3} + 15 q^{4} - 21 q^{5} - 6 q^{6} - 4 q^{7} - 21 q^{8} + 6 q^{9}+O(q^{10}) $ 21 * q - 9 * q^2 - 5 * q^3 + 15 * q^4 - 21 * q^5 - 6 * q^6 - 4 * q^7 - 21 * q^8 + 6 * q^9	\( 21 q - 9 q^{2} - 5 q^{3} + 15 q^{4} - 21 q^{5} - 6 q^{6} - 4 q^{7} - 21 q^{8} + 6 q^{9} + q^{10} - 27 q^{11} - 8 q^{12} - 11 q^{13} - 19 q^{14} - 10 q^{15} + 11 q^{16} - 14 q^{17} - 14 q^{18} - 15 q^{19} - 25 q^{20} - 42 q^{21} + 12 q^{22} - 14 q^{23} - 8 q^{24} + 16 q^{25} - 11 q^{26} - 5 q^{27} + q^{28} - 78 q^{29} + q^{30} - 8 q^{31} - 41 q^{32} - 6 q^{33} + 7 q^{34} - 3 q^{35} - q^{36} - 23 q^{37} + 21 q^{38} - 4 q^{39} + 12 q^{40} - 59 q^{41} + 39 q^{42} + 2 q^{43} - 50 q^{44} - 36 q^{45} - 15 q^{46} - 12 q^{47} + 10 q^{48} + 17 q^{49} - 23 q^{50} - 8 q^{51} + 18 q^{52} - 36 q^{53} - 4 q^{54} + 23 q^{55} - 28 q^{56} - 24 q^{57} + 46 q^{58} - 17 q^{59} + 8 q^{60} - 22 q^{61} + 42 q^{62} - 6 q^{63} + 49 q^{64} - 53 q^{65} + 29 q^{66} + 15 q^{67} - 16 q^{68} - 30 q^{69} + 44 q^{70} - 56 q^{71} + 12 q^{72} - 2 q^{73} - 12 q^{74} + 2 q^{75} - 4 q^{76} - 47 q^{77} + 36 q^{78} + 5 q^{79} + 15 q^{80} - 19 q^{81} + 47 q^{82} - q^{83} - 20 q^{84} - 29 q^{85} - 23 q^{86} + 44 q^{87} + 61 q^{88} - 12 q^{89} + 91 q^{90} + 5 q^{91} + 35 q^{92} - 15 q^{93} + 34 q^{94} - 17 q^{95} + 14 q^{96} + 21 q^{97} + 24 q^{98} - 38 q^{99}+O(q^{100}) \) 21 * q - 9 * q^2 - 5 * q^3 + 15 * q^4 - 21 * q^5 - 6 * q^6 - 4 * q^7 - 21 * q^8 + 6 * q^9 + q^10 - 27 * q^11 - 8 * q^12 - 11 * q^13 - 19 * q^14 - 10 * q^15 + 11 * q^16 - 14 * q^17 - 14 * q^18 - 15 * q^19 - 25 * q^20 - 42 * q^21 + 12 * q^22 - 14 * q^23 - 8 * q^24 + 16 * q^25 - 11 * q^26 - 5 * q^27 + q^28 - 78 * q^29 + q^30 - 8 * q^31 - 41 * q^32 - 6 * q^33 + 7 * q^34 - 3 * q^35 - q^36 - 23 * q^37 + 21 * q^38 - 4 * q^39 + 12 * q^40 - 59 * q^41 + 39 * q^42 + 2 * q^43 - 50 * q^44 - 36 * q^45 - 15 * q^46 - 12 * q^47 + 10 * q^48 + 17 * q^49 - 23 * q^50 - 8 * q^51 + 18 * q^52 - 36 * q^53 - 4 * q^54 + 23 * q^55 - 28 * q^56 - 24 * q^57 + 46 * q^58 - 17 * q^59 + 8 * q^60 - 22 * q^61 + 42 * q^62 - 6 * q^63 + 49 * q^64 - 53 * q^65 + 29 * q^66 + 15 * q^67 - 16 * q^68 - 30 * q^69 + 44 * q^70 - 56 * q^71 + 12 * q^72 - 2 * q^73 - 12 * q^74 + 2 * q^75 - 4 * q^76 - 47 * q^77 + 36 * q^78 + 5 * q^79 + 15 * q^80 - 19 * q^81 + 47 * q^82 - q^83 - 20 * q^84 - 29 * q^85 - 23 * q^86 + 44 * q^87 + 61 * q^88 - 12 * q^89 + 91 * q^90 + 5 * q^91 + 35 * q^92 - 15 * q^93 + 34 * q^94 - 17 * q^95 + 14 * q^96 + 21 * q^97 + 24 * q^98 - 38 * 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 $

$2$	1.61466	1.14174	0.570868	−	0.821042i	$-0.306607\pi$
$2$	1.61466	1.14174	0.570868	+	0.821042i	$0.306607\pi$
$3$	−2.35583	−1.36014	−0.680070	−	0.733147i	$-0.738051\pi$
$3$	−2.35583	−1.36014	−0.680070	+	0.733147i	$0.738051\pi$
$4$	0.607120	0.303560
$5$	0.981279	0.438841	0.219421	−	0.975630i	$-0.429583\pi$
$5$	0.981279	0.438841	0.219421	+	0.975630i	$0.429583\pi$
$6$	−3.80386	−1.55292
$7$	−0.0820085	−0.0309963	−0.0154982	−	0.999880i	$-0.504933\pi$
$7$	−0.0820085	−0.0309963	−0.0154982	+	0.999880i	$0.504933\pi$
$8$	−2.24902	−0.795150
$9$	2.54995	0.849983
$10$	1.58443	0.501041
$11$	−0.0155165	−0.00467839	−0.00233920	−	0.999997i	$-0.500745\pi$
$11$	−0.0155165	−0.00467839	−0.00233920	+	0.999997i	$0.500745\pi$
$12$	−1.43027	−0.412885
$13$	−4.49441	−1.24652	−0.623262	−	0.782013i	$-0.714193\pi$
$13$	−4.49441	−1.24652	−0.623262	+	0.782013i	$0.714193\pi$
$14$	−0.132416	−0.0353896
$15$	−2.31173	−0.596886
$16$	−4.84565	−1.21141
$17$	0.0424957	0.0103067	0.00515337	−	0.999987i	$-0.498360\pi$
$17$	0.0424957	0.0103067	0.00515337	+	0.999987i	$0.498360\pi$
$18$	4.11730	0.970456
$19$	−7.23140	−1.65900	−0.829499	−	0.558508i	$-0.811374\pi$
$19$	−7.23140	−1.65900	−0.829499	+	0.558508i	$0.811374\pi$
$20$	0.595754	0.133215
$21$	0.193198	0.0421593
$22$	−0.0250538	−0.00534148
$23$	4.78934	0.998646	0.499323	−	0.866416i	$-0.333582\pi$
$23$	4.78934	0.998646	0.499323	+	0.866416i	$0.333582\pi$
$24$	5.29833	1.08152
$25$	−4.03709	−0.807418
$26$	−7.25693	−1.42320
$27$	1.06024	0.204044
$28$	−0.0497890	−0.00940924
$29$	−7.53183	−1.39863	−0.699313	−	0.714815i	$-0.746511\pi$
$29$	−7.53183	−1.39863	−0.699313	+	0.714815i	$0.746511\pi$
$30$	−3.73265	−0.681486
$31$	6.01931	1.08110	0.540550	−	0.841312i	$-0.318216\pi$
$31$	6.01931	1.08110	0.540550	+	0.841312i	$0.318216\pi$
$32$	−3.32601	−0.587961
$33$	0.0365542	0.00636327
$34$	0.0686161	0.0117676
$35$	−0.0804732	−0.0136025
$36$	1.54813	0.258021
$37$	−6.28717	−1.03360	−0.516802	−	0.856105i	$-0.672878\pi$
$37$	−6.28717	−1.03360	−0.516802	+	0.856105i	$0.672878\pi$
$38$	−11.6762	−1.89414
$39$	10.5881	1.69545
$40$	−2.20692	−0.348945
$41$	−6.87805	−1.07417	−0.537085	−	0.843528i	$-0.680475\pi$
$41$	−6.87805	−1.07417	−0.537085	+	0.843528i	$0.680475\pi$
$42$	0.311949	0.0481348
$43$	−12.4977	−1.90589	−0.952944	−	0.303146i	$-0.901963\pi$
$43$	−12.4977	−1.90589	−0.952944	+	0.303146i	$0.901963\pi$
$44$	−0.00942036	−0.00142017
$45$	2.50221	0.373008
$46$	7.73314	1.14019
$47$	11.9620	1.74484	0.872418	−	0.488761i	$-0.162551\pi$
$47$	11.9620	1.74484	0.872418	+	0.488761i	$0.162551\pi$
$48$	11.4155	1.64769
$49$	−6.99327	−0.999039
$50$	−6.51852	−0.921858
$51$	−0.100113	−0.0140186
$52$	−2.72865	−0.378395
$53$	−2.68677	−0.369057	−0.184528	−	0.982827i	$-0.559076\pi$
$53$	−2.68677	−0.369057	−0.184528	+	0.982827i	$0.559076\pi$
$54$	1.71193	0.232965
$55$	−0.0152260	−0.00205307
$56$	0.184439	0.0246467
$57$	17.0360	2.25647
$58$	−12.1613	−1.59686
$59$	4.85711	0.632342	0.316171	−	0.948702i	$-0.397603\pi$
$59$	4.85711	0.632342	0.316171	+	0.948702i	$0.397603\pi$
$60$	−1.40350	−0.181191
$61$	15.2013	1.94633	0.973163	−	0.230118i	$-0.0739113\pi$
$61$	15.2013	1.94633	0.973163	+	0.230118i	$0.0739113\pi$
$62$	9.71913	1.23433
$63$	−0.209118	−0.0263463
$64$	4.32092	0.540115
$65$	−4.41027	−0.547026
$66$	0.0590225	0.00726517
$67$	2.90529	0.354938	0.177469	−	0.984126i	$-0.443209\pi$
$67$	2.90529	0.354938	0.177469	+	0.984126i	$0.443209\pi$
$68$	0.0258000	0.00312871
$69$	−11.2829	−1.35830
$70$	−0.129937	−0.0155304
$71$	9.70183	1.15140	0.575698	−	0.817663i	$-0.304731\pi$
$71$	9.70183	1.15140	0.575698	+	0.817663i	$0.304731\pi$
$72$	−5.73490	−0.675864
$73$	6.12979	0.717438	0.358719	−	0.933446i	$-0.383214\pi$
$73$	6.12979	0.717438	0.358719	+	0.933446i	$0.383214\pi$
$74$	−10.1516	−1.18010
$75$	9.51071	1.09820
$76$	−4.39033	−0.503606
$77$	0.00127248	0.000145013 0
$78$	17.0961	1.93575
$79$	13.6930	1.54059	0.770293	−	0.637690i	$-0.220110\pi$
$79$	13.6930	1.54059	0.770293	+	0.637690i	$0.220110\pi$
$80$	−4.75493	−0.531617
$81$	−10.1476	−1.12751
$82$	−11.1057	−1.22642
$83$	2.76246	0.303219	0.151610	−	0.988440i	$-0.451554\pi$
$83$	2.76246	0.303219	0.151610	+	0.988440i	$0.451554\pi$
$84$	0.117295	0.0127979
$85$	0.0417002	0.00452302
$86$	−20.1796	−2.17602
$87$	17.7437	1.90233
$88$	0.0348969	0.00372002
$89$	−16.5137	−1.75044	−0.875222	−	0.483721i	$-0.839285\pi$
$89$	−16.5137	−1.75044	−0.875222	+	0.483721i	$0.839285\pi$
$90$	4.04021	0.425876
$91$	0.368580	0.0386377
$92$	2.90770	0.303149
$93$	−14.1805	−1.47045
$94$	19.3145	1.99214
$95$	−7.09602	−0.728036
$96$	7.83553	0.799710
$97$	10.2707	1.04284	0.521418	−	0.853302i	$-0.325403\pi$
$97$	10.2707	1.04284	0.521418	+	0.853302i	$0.325403\pi$
$98$	−11.2917	−1.14064
$99$	−0.0395662	−0.00397655
$100$	−2.45100	−0.245100
$101$	8.92005	0.887578	0.443789	−	0.896131i	$-0.353634\pi$
$101$	8.92005	0.887578	0.443789	+	0.896131i	$0.353634\pi$
$102$	−0.161648	−0.0160055
$103$	−11.0422	−1.08802	−0.544011	−	0.839078i	$-0.683095\pi$
$103$	−11.0422	−1.08802	−0.544011	+	0.839078i	$0.683095\pi$
$104$	10.1080	0.991174
$105$	0.189581	0.0185013
$106$	−4.33822	−0.421365
$107$	−2.90349	−0.280691	−0.140346	−	0.990103i	$-0.544821\pi$
$107$	−2.90349	−0.280691	−0.140346	+	0.990103i	$0.544821\pi$
$108$	0.643696	0.0619397
$109$	1.28135	0.122731	0.0613653	−	0.998115i	$-0.480455\pi$
$109$	1.28135	0.122731	0.0613653	+	0.998115i	$0.480455\pi$
$110$	−0.0245847	−0.00234406
$111$	14.8115	1.40585
$112$	0.397384	0.0375493
$113$	1.02230	0.0961697	0.0480848	−	0.998843i	$-0.484688\pi$
$113$	1.02230	0.0961697	0.0480848	+	0.998843i	$0.484688\pi$
$114$	27.5073	2.57629
$115$	4.69968	0.438247
$116$	−4.57273	−0.424567
$117$	−11.4605	−1.05952
$118$	7.84257	0.721967
$119$	−0.00348501	−0.000319471 0
$120$	5.19913	0.474614
$121$	−10.9998	−0.999978
$122$	24.5449	2.22219
$123$	16.2035	1.46102
$124$	3.65445	0.328179
$125$	−8.86791	−0.793170
$126$	−0.337653	−0.0300805
$127$	−12.5963	−1.11774	−0.558870	−	0.829255i	$-0.688765\pi$
$127$	−12.5963	−1.11774	−0.558870	+	0.829255i	$0.688765\pi$
$128$	13.6288	1.20463
$129$	29.4426	2.59228
$130$	−7.12107	−0.624560
$131$	−13.7455	−1.20095	−0.600477	−	0.799642i	$-0.705023\pi$
$131$	−13.7455	−1.20095	−0.600477	+	0.799642i	$0.705023\pi$
$132$	0.0221928	0.00193163
$133$	0.593037	0.0514228
$134$	4.69106	0.405246
$135$	1.04040	0.0895430
$136$	−0.0955740	−0.00819540
$137$	12.7486	1.08919	0.544595	−	0.838699i	$-0.316683\pi$
$137$	12.7486	1.08919	0.544595	+	0.838699i	$0.316683\pi$
$138$	−18.2180	−1.55082
$139$	−16.9196	−1.43510	−0.717552	−	0.696505i	$-0.754738\pi$
$139$	−16.9196	−1.43510	−0.717552	+	0.696505i	$0.754738\pi$
$140$	−0.0488569	−0.00412916
$141$	−28.1805	−2.37322
$142$	15.6651	1.31459
$143$	0.0697373	0.00583173
$144$	−12.3561	−1.02968
$145$	−7.39083	−0.613775
$146$	9.89751	0.819124
$147$	16.4750	1.35883
$148$	−3.81707	−0.313761
$149$	−0.690746	−0.0565881	−0.0282941	−	0.999600i	$-0.509007\pi$
$149$	−0.690746	−0.0565881	−0.0282941	+	0.999600i	$0.509007\pi$
$150$	15.3566	1.25386
$151$	−13.2215	−1.07595	−0.537976	−	0.842960i	$-0.680811\pi$
$151$	−13.2215	−1.07595	−0.537976	+	0.842960i	$0.680811\pi$
$152$	16.2636	1.31915
$153$	0.108362	0.00876055
$154$	0.00205462	0.000165566 0
$155$	5.90662	0.474431
$156$	6.42824	0.514671
$157$	−5.52835	−0.441210	−0.220605	−	0.975363i	$-0.570803\pi$
$157$	−5.52835	−0.441210	−0.220605	+	0.975363i	$0.570803\pi$
$158$	22.1096	1.75894
$159$	6.32959	0.501969
$160$	−3.26374	−0.258022
$161$	−0.392766	−0.0309543
$162$	−16.3849	−1.28732
$163$	17.9642	1.40707	0.703533	−	0.710663i	$-0.251605\pi$
$163$	17.9642	1.40707	0.703533	+	0.710663i	$0.251605\pi$
$164$	−4.17580	−0.326075
$165$	0.0358699	0.00279246
$166$	4.46043	0.346196
$167$	7.76654	0.600993	0.300496	−	0.953783i	$-0.402848\pi$
$167$	7.76654	0.600993	0.300496	+	0.953783i	$0.402848\pi$
$168$	−0.434508	−0.0335230
$169$	7.19971	0.553824
$170$	0.0673315	0.00516409
$171$	−18.4397	−1.41012
$172$	−7.58763	−0.578552
$173$	−9.89445	−0.752261	−0.376131	−	0.926567i	$-0.622746\pi$
$173$	−9.89445	−0.752261	−0.376131	+	0.926567i	$0.622746\pi$
$174$	28.6501	2.17196
$175$	0.331076	0.0250270
$176$	0.0751873	0.00566745
$177$	−11.4425	−0.860074
$178$	−26.6639	−1.99854
$179$	−24.8984	−1.86100	−0.930498	−	0.366296i	$-0.880626\pi$
$179$	−24.8984	−1.86100	−0.930498	+	0.366296i	$0.880626\pi$
$180$	1.51914	0.113230
$181$	2.95642	0.219749	0.109875	−	0.993945i	$-0.464955\pi$
$181$	2.95642	0.219749	0.109875	+	0.993945i	$0.464955\pi$
$182$	0.595130	0.0441140
$183$	−35.8117	−2.64728
$184$	−10.7713	−0.794074
$185$	−6.16946	−0.453588
$186$	−22.8966	−1.67886
$187$	−0.000659384 0	−4.82189e−5 0
$188$	7.26237	0.529663
$189$	−0.0869491	−0.00632462
$190$	−11.4576	−0.831225
$191$	−25.8995	−1.87402	−0.937012	−	0.349297i	$-0.886420\pi$
$191$	−25.8995	−1.87402	−0.937012	+	0.349297i	$0.886420\pi$
$192$	−10.1794	−0.734633
$193$	1.78447	0.128449	0.0642246	−	0.997935i	$-0.479543\pi$
$193$	1.78447	0.128449	0.0642246	+	0.997935i	$0.479543\pi$
$194$	16.5837	1.19064
$195$	10.3899	0.744033
$196$	−4.24576	−0.303268
$197$	13.0116	0.927037	0.463518	−	0.886087i	$-0.346587\pi$
$197$	13.0116	0.927037	0.463518	+	0.886087i	$0.346587\pi$
$198$	−0.0638859	−0.00454017
$199$	−12.3706	−0.876932	−0.438466	−	0.898748i	$-0.644478\pi$
$199$	−12.3706	−0.876932	−0.438466	+	0.898748i	$0.644478\pi$
$200$	9.07952	0.642019
$201$	−6.84439	−0.482766
$202$	14.4028	1.01338
$203$	0.617674	0.0433522
$204$	−0.0607806	−0.00425549
$205$	−6.74928	−0.471390
$206$	−17.8294	−1.24223
$207$	12.2126	0.848832
$208$	21.7783	1.51005
$209$	0.112206	0.00776144
$210$	0.306109	0.0211235
$211$	−20.7916	−1.43136	−0.715678	−	0.698431i	$-0.753882\pi$
$211$	−20.7916	−1.43136	−0.715678	+	0.698431i	$0.753882\pi$
$212$	−1.63119	−0.112031
$213$	−22.8559	−1.56606
$214$	−4.68815	−0.320475
$215$	−12.2638	−0.836382
$216$	−2.38452	−0.162246
$217$	−0.493635	−0.0335101
$218$	2.06893	0.140126
$219$	−14.4408	−0.975816
$220$	−0.00924400	−0.000623230 0
$221$	−0.190993	−0.0128476
$222$	23.9155	1.60511
$223$	11.0328	0.738810	0.369405	−	0.929269i	$-0.379562\pi$
$223$	11.0328	0.738810	0.369405	+	0.929269i	$0.379562\pi$
$224$	0.272761	0.0182246
$225$	−10.2944	−0.686292
$226$	1.65066	0.109800
$227$	6.95850	0.461852	0.230926	−	0.972971i	$-0.425824\pi$
$227$	6.95850	0.461852	0.230926	+	0.972971i	$0.425824\pi$
$228$	10.3429	0.684974
$229$	9.78633	0.646699	0.323350	−	0.946280i	$-0.395191\pi$
$229$	9.78633	0.646699	0.323350	+	0.946280i	$0.395191\pi$
$230$	7.58837	0.500362
$231$	−0.00299776	−0.000197238 0
$232$	16.9393	1.11212
$233$	−22.7290	−1.48902	−0.744512	−	0.667609i	$-0.767318\pi$
$233$	−22.7290	−1.48902	−0.744512	+	0.667609i	$0.767318\pi$
$234$	−18.5048	−1.20970
$235$	11.7380	0.765706
$236$	2.94885	0.191954
$237$	−32.2585	−2.09541
$238$	−0.00562710	−0.000364751 0
$239$	16.3959	1.06056	0.530281	−	0.847822i	$-0.322086\pi$
$239$	16.3959	1.06056	0.530281	+	0.847822i	$0.322086\pi$
$240$	11.2018	0.723074
$241$	−13.0962	−0.843601	−0.421801	−	0.906689i	$-0.638602\pi$
$241$	−13.0962	−0.843601	−0.421801	+	0.906689i	$0.638602\pi$
$242$	−17.7608	−1.14171
$243$	20.7253	1.32953
$244$	9.22901	0.590827
$245$	−6.86235	−0.438420
$246$	26.1632	1.66810
$247$	32.5009	2.06798
$248$	−13.5376	−0.859637
$249$	−6.50790	−0.412421
$250$	−14.3186	−0.905590
$251$	9.84460	0.621386	0.310693	−	0.950510i	$-0.399439\pi$
$251$	9.84460	0.621386	0.310693	+	0.950510i	$0.399439\pi$
$252$	−0.126959	−0.00799770
$253$	−0.0743136	−0.00467206
$254$	−20.3387	−1.27616
$255$	−0.0982386	−0.00615194
$256$	13.3641	0.835254
$257$	2.51314	0.156766	0.0783828	−	0.996923i	$-0.475024\pi$
$257$	2.51314	0.156766	0.0783828	+	0.996923i	$0.475024\pi$
$258$	47.5397	2.95969
$259$	0.515601	0.0320379
$260$	−2.67756	−0.166055
$261$	−19.2058	−1.18881
$262$	−22.1943	−1.37117
$263$	−4.22833	−0.260730	−0.130365	−	0.991466i	$-0.541615\pi$
$263$	−4.22833	−0.260730	−0.130365	+	0.991466i	$0.541615\pi$
$264$	−0.0822113	−0.00505975
$265$	−2.63647	−0.161957
$266$	0.957551	0.0587112
$267$	38.9034	2.38085
$268$	1.76386	0.107745
$269$	−10.2205	−0.623152	−0.311576	−	0.950221i	$-0.600857\pi$
$269$	−10.2205	−0.623152	−0.311576	+	0.950221i	$0.600857\pi$
$270$	1.67988	0.102234
$271$	16.1490	0.980981	0.490491	−	0.871447i	$-0.336818\pi$
$271$	16.1490	0.980981	0.490491	+	0.871447i	$0.336818\pi$
$272$	−0.205919	−0.0124857
$273$	−0.868312	−0.0525527
$274$	20.5847	1.24357
$275$	0.0626414	0.00377742
$276$	−6.85007	−0.412325
$277$	−3.92890	−0.236065	−0.118032	−	0.993010i	$-0.537659\pi$
$277$	−3.92890	−0.236065	−0.118032	+	0.993010i	$0.537659\pi$
$278$	−27.3194	−1.63851
$279$	15.3489	0.918917
$280$	0.180986	0.0108160
$281$	7.15274	0.426697	0.213348	−	0.976976i	$-0.431563\pi$
$281$	7.15274	0.426697	0.213348	+	0.976976i	$0.431563\pi$
$282$	−45.5018	−2.70959
$283$	15.6051	0.927628	0.463814	−	0.885933i	$-0.346481\pi$
$283$	15.6051	0.927628	0.463814	+	0.885933i	$0.346481\pi$
$284$	5.89018	0.349518
$285$	16.7170	0.990232
$286$	0.112602	0.00665829
$287$	0.564059	0.0332953
$288$	−8.48116	−0.499757
$289$	−16.9982	−0.999894
$290$	−11.9337	−0.700769
$291$	−24.1961	−1.41840
$292$	3.72152	0.217785
$293$	24.4615	1.42905	0.714527	−	0.699608i	$-0.246642\pi$
$293$	24.4615	1.42905	0.714527	+	0.699608i	$0.246642\pi$
$294$	26.6015	1.55143
$295$	4.76618	0.277498
$296$	14.1400	0.821870
$297$	−0.0164512	−0.000954598 0
$298$	−1.11532	−0.0646087
$299$	−21.5252	−1.24484
$300$	5.77415	0.333371
$301$	1.02492	0.0590755
$302$	−21.3482	−1.22845
$303$	−21.0141	−1.20723
$304$	35.0408	2.00973
$305$	14.9167	0.854128
$306$	0.174968	0.0100022
$307$	6.64750	0.379393	0.189696	−	0.981843i	$-0.439250\pi$
$307$	6.64750	0.379393	0.189696	+	0.981843i	$0.439250\pi$
$308$	0.000772550 0	4.40201e−5 0
$309$	26.0136	1.47986
$310$	9.53718	0.541675
$311$	4.81740	0.273170	0.136585	−	0.990628i	$-0.456387\pi$
$311$	4.81740	0.273170	0.136585	+	0.990628i	$0.456387\pi$
$312$	−23.8128	−1.34814
$313$	16.7884	0.948937	0.474469	−	0.880272i	$-0.342640\pi$
$313$	16.7884	0.948937	0.474469	+	0.880272i	$0.342640\pi$
$314$	−8.92639	−0.503745
$315$	−0.205203	−0.0115619
$316$	8.31332	0.467661
$317$	−34.4252	−1.93351	−0.966757	−	0.255697i	$-0.917695\pi$
$317$	−34.4252	−1.93351	−0.966757	+	0.255697i	$0.917695\pi$
$318$	10.2201	0.573116
$319$	0.116867	0.00654332
$320$	4.24003	0.237025
$321$	6.84015	0.381780
$322$	−0.634184	−0.0353417
$323$	−0.307304	−0.0170988
$324$	−6.16082	−0.342268
$325$	18.1443	1.00647
$326$	29.0061	1.60650
$327$	−3.01864	−0.166931
$328$	15.4689	0.854127
$329$	−0.980985	−0.0540835
$330$	0.0579175	0.00318826
$331$	25.6915	1.41213	0.706066	−	0.708146i	$-0.250468\pi$
$331$	25.6915	1.41213	0.706066	+	0.708146i	$0.250468\pi$
$332$	1.67715	0.0920453
$333$	−16.0320	−0.878546
$334$	12.5403	0.686175
$335$	2.85090	0.155762
$336$	−0.936171	−0.0510723
$337$	−27.5794	−1.50234	−0.751172	−	0.660107i	$-0.770511\pi$
$337$	−27.5794	−1.50234	−0.751172	+	0.660107i	$0.770511\pi$
$338$	11.6251	0.632321
$339$	−2.40836	−0.130804
$340$	0.0253170	0.00137301
$341$	−0.0933984	−0.00505781
$342$	−29.7738	−1.60998
$343$	1.14757	0.0619628
$344$	28.1077	1.51547
$345$	−11.0717	−0.596078
$346$	−15.9762	−0.858883
$347$	−11.2397	−0.603378	−0.301689	−	0.953406i	$-0.597550\pi$
$347$	−11.2397	−0.603378	−0.301689	+	0.953406i	$0.597550\pi$
$348$	10.7726	0.577471
$349$	12.7366	0.681775	0.340888	−	0.940104i	$-0.389272\pi$
$349$	12.7366	0.681775	0.340888	+	0.940104i	$0.389272\pi$
$350$	0.534574	0.0285742
$351$	−4.76517	−0.254346
$352$	0.0516079	0.00275071
$353$	−26.8755	−1.43044	−0.715220	−	0.698900i	$-0.753673\pi$
$353$	−26.8755	−1.43044	−0.715220	+	0.698900i	$0.753673\pi$
$354$	−18.4758	−0.981977
$355$	9.52020	0.505280
$356$	−10.0258	−0.531365
$357$	0.00821011	0.000434525 0
$358$	−40.2025	−2.12477
$359$	1.70221	0.0898391	0.0449196	−	0.998991i	$-0.485697\pi$
$359$	1.70221	0.0898391	0.0449196	+	0.998991i	$0.485697\pi$
$360$	−5.62753	−0.296597
$361$	33.2932	1.75227
$362$	4.77361	0.250896
$363$	25.9136	1.36011
$364$	0.223772	0.0117289
$365$	6.01503	0.314841
$366$	−57.8236	−3.02249
$367$	−6.88555	−0.359423	−0.179712	−	0.983719i	$-0.557516\pi$
$367$	−6.88555	−0.359423	−0.179712	+	0.983719i	$0.557516\pi$
$368$	−23.2074	−1.20977
$369$	−17.5387	−0.913027
$370$	−9.96157	−0.517878
$371$	0.220338	0.0114394
$372$	−8.60927	−0.446370
$373$	−0.567772	−0.0293981	−0.0146991	−	0.999892i	$-0.504679\pi$
$373$	−0.567772	−0.0293981	−0.0146991	+	0.999892i	$0.504679\pi$
$374$	−0.00106468	−5.50532e−5 0
$375$	20.8913	1.07882
$376$	−26.9028	−1.38741
$377$	33.8511	1.74342
$378$	−0.140393	−0.00722104
$379$	9.98779	0.513038	0.256519	−	0.966539i	$-0.417424\pi$
$379$	9.98779	0.513038	0.256519	+	0.966539i	$0.417424\pi$
$380$	−4.30814	−0.221003
$381$	29.6748	1.52028
$382$	−41.8189	−2.13964
$383$	−8.27774	−0.422973	−0.211486	−	0.977381i	$-0.567830\pi$
$383$	−8.27774	−0.422973	−0.211486	+	0.977381i	$0.567830\pi$
$384$	−32.1073	−1.63847
$385$	0.00124866	6.36376e−5 0
$386$	2.88131	0.146655
$387$	−31.8686	−1.61997
$388$	6.23557	0.316563
$389$	−1.19458	−0.0605678	−0.0302839	−	0.999541i	$-0.509641\pi$
$389$	−1.19458	−0.0605678	−0.0302839	+	0.999541i	$0.509641\pi$
$390$	16.7761	0.849489
$391$	0.203526	0.0102928
$392$	15.7280	0.794386
$393$	32.3822	1.63347
$394$	21.0093	1.05843
$395$	13.4367	0.676073
$396$	−0.0240214	−0.00120712
$397$	19.6311	0.985257	0.492628	−	0.870240i	$-0.336036\pi$
$397$	19.6311	0.985257	0.492628	+	0.870240i	$0.336036\pi$
$398$	−19.9744	−1.00122
$399$	−1.39710	−0.0699422
$400$	19.5623	0.978116
$401$	−4.13156	−0.206320	−0.103160	−	0.994665i	$-0.532895\pi$
$401$	−4.13156	−0.206320	−0.103160	+	0.994665i	$0.532895\pi$
$402$	−11.0513	−0.551191
$403$	−27.0533	−1.34762
$404$	5.41554	0.269433
$405$	−9.95763	−0.494799
$406$	0.997333	0.0494968
$407$	0.0975546	0.00483560
$408$	0.225156	0.0111469
$409$	−28.6690	−1.41759	−0.708796	−	0.705413i	$-0.750762\pi$
$409$	−28.6690	−1.41759	−0.708796	+	0.705413i	$0.750762\pi$
$410$	−10.8978	−0.538203
$411$	−30.0337	−1.48145
$412$	−6.70395	−0.330280
$413$	−0.398324	−0.0196003
$414$	19.7191	0.969142
$415$	2.71074	0.133065
$416$	14.9485	0.732908
$417$	39.8598	1.95194
$418$	0.181174	0.00886151
$419$	−8.99898	−0.439629	−0.219814	−	0.975542i	$-0.570545\pi$
$419$	−8.99898	−0.439629	−0.219814	+	0.975542i	$0.570545\pi$
$420$	0.115099	0.00561624
$421$	−38.5589	−1.87925	−0.939623	−	0.342212i	$-0.888824\pi$
$421$	−38.5589	−1.87925	−0.939623	+	0.342212i	$0.888824\pi$
$422$	−33.5714	−1.63423
$423$	30.5025	1.48308
$424$	6.04262	0.293456
$425$	−0.171559	−0.00832184
$426$	−36.9044	−1.78803
$427$	−1.24663	−0.0603289
$428$	−1.76277	−0.0852067
$429$	−0.164290	−0.00793197
$430$	−19.8018	−0.954927
$431$	−26.9587	−1.29856	−0.649278	−	0.760551i	$-0.724929\pi$
$431$	−26.9587	−1.29856	−0.649278	+	0.760551i	$0.724929\pi$
$432$	−5.13757	−0.247181
$433$	31.8649	1.53133	0.765664	−	0.643241i	$-0.222411\pi$
$433$	31.8649	1.53133	0.765664	+	0.643241i	$0.222411\pi$
$434$	−0.797051	−0.0382597
$435$	17.4116	0.834820
$436$	0.777931	0.0372561
$437$	−34.6336	−1.65675
$438$	−23.3169	−1.11412
$439$	6.84647	0.326764	0.163382	−	0.986563i	$-0.447760\pi$
$439$	6.84647	0.326764	0.163382	+	0.986563i	$0.447760\pi$
$440$	0.0342436	0.00163250
$441$	−17.8325	−0.849166
$442$	−0.308389	−0.0146686
$443$	−40.0638	−1.90349	−0.951744	−	0.306894i	$-0.900710\pi$
$443$	−40.0638	−1.90349	−0.951744	+	0.306894i	$0.900710\pi$
$444$	8.99237	0.426759
$445$	−16.2045	−0.768167
$446$	17.8142	0.843525
$447$	1.62728	0.0769678
$448$	−0.354352	−0.0167416
$449$	19.1086	0.901791	0.450895	−	0.892577i	$-0.351105\pi$
$449$	19.1086	0.901791	0.450895	+	0.892577i	$0.351105\pi$
$450$	−16.6219	−0.783564
$451$	0.106723	0.00502539
$452$	0.620658	0.0291933
$453$	31.1477	1.46345
$454$	11.2356	0.527313
$455$	0.361680	0.0169558
$456$	−38.3143	−1.79423
$457$	10.0808	0.471559	0.235779	−	0.971807i	$-0.424236\pi$
$457$	10.0808	0.471559	0.235779	+	0.971807i	$0.424236\pi$
$458$	15.8016	0.738359
$459$	0.0450559	0.00210303
$460$	2.85327	0.133034
$461$	−26.7647	−1.24656	−0.623278	−	0.782000i	$-0.714199\pi$
$461$	−26.7647	−1.24656	−0.623278	+	0.782000i	$0.714199\pi$
$462$	−0.00484035	−0.000225193 0
$463$	15.9368	0.740648	0.370324	−	0.928903i	$-0.379247\pi$
$463$	15.9368	0.740648	0.370324	+	0.928903i	$0.379247\pi$
$464$	36.4966	1.69431
$465$	−13.9150	−0.645293
$466$	−36.6995	−1.70007
$467$	−4.23484	−0.195965	−0.0979825	−	0.995188i	$-0.531239\pi$
$467$	−4.23484	−0.195965	−0.0979825	+	0.995188i	$0.531239\pi$
$468$	−6.95791	−0.321630
$469$	−0.238259	−0.0110018
$470$	18.9529	0.874233
$471$	13.0239	0.600108
$472$	−10.9238	−0.502807
$473$	0.193921	0.00891649
$474$	−52.0864	−2.39241
$475$	29.1938	1.33951
$476$	−0.00211582	−9.69785e−5 0
$477$	−6.85114	−0.313692
$478$	26.4738	1.21088
$479$	−24.0604	−1.09935	−0.549673	−	0.835380i	$-0.685248\pi$
$479$	−24.0604	−1.09935	−0.549673	+	0.835380i	$0.685248\pi$
$480$	7.68884	0.350946
$481$	28.2571	1.28841
$482$	−21.1459	−0.963169
$483$	0.925292	0.0421023
$484$	−6.67818	−0.303553
$485$	10.0785	0.457639
$486$	33.4643	1.51797
$487$	2.39559	0.108555	0.0542773	−	0.998526i	$-0.482715\pi$
$487$	2.39559	0.108555	0.0542773	+	0.998526i	$0.482715\pi$
$488$	−34.1881	−1.54762
$489$	−42.3207	−1.91381
$490$	−11.0804	−0.500559
$491$	−14.7040	−0.663580	−0.331790	−	0.943353i	$-0.607653\pi$
$491$	−14.7040	−0.663580	−0.331790	+	0.943353i	$0.607653\pi$
$492$	9.83750	0.443509
$493$	−0.320071	−0.0144153
$494$	52.4778	2.36109
$495$	−0.0388255	−0.00174507
$496$	−29.1675	−1.30966
$497$	−0.795632	−0.0356890
$498$	−10.5080	−0.470876
$499$	13.9696	0.625364	0.312682	−	0.949858i	$-0.398773\pi$
$499$	13.9696	0.625364	0.312682	+	0.949858i	$0.398773\pi$
$500$	−5.38389	−0.240775
$501$	−18.2967	−0.817435
$502$	15.8957	0.709458
$503$	42.0594	1.87533	0.937667	−	0.347534i	$-0.112981\pi$
$503$	42.0594	1.87533	0.937667	+	0.347534i	$0.112981\pi$
$504$	0.470310	0.0209493
$505$	8.75305	0.389506
$506$	−0.119991	−0.00533425
$507$	−16.9613	−0.753279
$508$	−7.64746	−0.339301
$509$	13.0276	0.577440	0.288720	−	0.957414i	$-0.406770\pi$
$509$	13.0276	0.577440	0.288720	+	0.957414i	$0.406770\pi$
$510$	−0.158622	−0.00702389
$511$	−0.502695	−0.0222379
$512$	−5.67928	−0.250991
$513$	−7.66706	−0.338509
$514$	4.05787	0.178985
$515$	−10.8355	−0.477469
$516$	17.8752	0.786912
$517$	−0.185608	−0.00816302
$518$	0.832520	0.0365788
$519$	23.3097	1.02318
$520$	9.91880	0.434968
$521$	−23.9020	−1.04717	−0.523584	−	0.851974i	$-0.675405\pi$
$521$	−23.9020	−1.04717	−0.523584	+	0.851974i	$0.675405\pi$
$522$	−31.0108	−1.35731
$523$	−21.5279	−0.941351	−0.470675	−	0.882306i	$-0.655990\pi$
$523$	−21.5279	−0.941351	−0.470675	+	0.882306i	$0.655990\pi$
$524$	−8.34520	−0.364562
$525$	−0.779960	−0.0340402
$526$	−6.82730	−0.297685
$527$	0.255795	0.0111426
$528$	−0.177129	−0.00770854
$529$	−0.0622411	−0.00270613
$530$	−4.25700	−0.184912
$531$	12.3854	0.537480
$532$	0.360045	0.0156099
$533$	30.9128	1.33898
$534$	62.8157	2.71830
$535$	−2.84914	−0.123179
$536$	−6.53408	−0.282229
$537$	58.6566	2.53122
$538$	−16.5025	−0.711475
$539$	0.108511	0.00467390
$540$	0.631645	0.0271817
$541$	24.8816	1.06974	0.534871	−	0.844934i	$-0.320360\pi$
$541$	24.8816	1.06974	0.534871	+	0.844934i	$0.320360\pi$
$542$	26.0751	1.12002
$543$	−6.96484	−0.298890
$544$	−0.141341	−0.00605996
$545$	1.25736	0.0538593
$546$	−1.40203	−0.0600012
$547$	4.13933	0.176985	0.0884924	−	0.996077i	$-0.471795\pi$
$547$	4.13933	0.176985	0.0884924	+	0.996077i	$0.471795\pi$
$548$	7.73996	0.330635
$549$	38.7625	1.65434
$550$	0.101144	0.00431281
$551$	54.4657	2.32032
$552$	25.3755	1.08005
$553$	−1.12295	−0.0477525
$554$	−6.34383	−0.269524
$555$	14.5342	0.616944
$556$	−10.2723	−0.435641
$557$	−19.5016	−0.826310	−0.413155	−	0.910661i	$-0.635573\pi$
$557$	−19.5016	−0.826310	−0.413155	+	0.910661i	$0.635573\pi$
$558$	24.7833	1.04916
$559$	56.1700	2.37574
$560$	0.389945	0.0164782
$561$	0.00155340	6.55845e−5 0
$562$	11.5492	0.487175
$563$	3.55466	0.149811	0.0749055	−	0.997191i	$-0.476134\pi$
$563$	3.55466	0.149811	0.0749055	+	0.997191i	$0.476134\pi$
$564$	−17.1089	−0.720416
$565$	1.00316	0.0422032
$566$	25.1969	1.05911
$567$	0.832190	0.0349487
$568$	−21.8196	−0.915532
$569$	−7.61372	−0.319184	−0.159592	−	0.987183i	$-0.551018\pi$
$569$	−7.61372	−0.319184	−0.159592	+	0.987183i	$0.551018\pi$
$570$	26.9923	1.13058
$571$	30.7549	1.28705	0.643526	−	0.765424i	$-0.277471\pi$
$571$	30.7549	1.28705	0.643526	+	0.765424i	$0.277471\pi$
$572$	0.0423390	0.00177028
$573$	61.0150	2.54894
$574$	0.910762	0.0380145
$575$	−19.3350	−0.806325
$576$	11.0181	0.459089
$577$	−1.64770	−0.0685946	−0.0342973	−	0.999412i	$-0.510919\pi$
$577$	−1.64770	−0.0685946	−0.0342973	+	0.999412i	$0.510919\pi$
$578$	−27.4463	−1.14161
$579$	−4.20392	−0.174709
$580$	−4.48712	−0.186318
$581$	−0.226545	−0.00939868
$582$	−39.0685	−1.61944
$583$	0.0416892	0.00172659
$584$	−13.7860	−0.570471
$585$	−11.2460	−0.464963
$586$	39.4969	1.63160
$587$	−14.0294	−0.579057	−0.289528	−	0.957169i	$-0.593498\pi$
$587$	−14.0294	−0.579057	−0.289528	+	0.957169i	$0.593498\pi$
$588$	10.0023	0.412488
$589$	−43.5281	−1.79354
$590$	7.69575	0.316829
$591$	−30.6531	−1.26090
$592$	30.4654	1.25212
$593$	−24.4493	−1.00401	−0.502005	−	0.864864i	$-0.667404\pi$
$593$	−24.4493	−1.00401	−0.502005	+	0.864864i	$0.667404\pi$
$594$	−0.0265631	−0.00108990
$595$	−0.00341977	−0.000140197 0
$596$	−0.419366	−0.0171779
$597$	29.1432	1.19275
$598$	−34.7559	−1.42127
$599$	15.1556	0.619240	0.309620	−	0.950860i	$-0.399798\pi$
$599$	15.1556	0.619240	0.309620	+	0.950860i	$0.399798\pi$
$600$	−21.3898	−0.873236
$601$	12.7928	0.521829	0.260915	−	0.965362i	$-0.415976\pi$
$601$	12.7928	0.521829	0.260915	+	0.965362i	$0.415976\pi$
$602$	1.65490	0.0674486
$603$	7.40835	0.301691
$604$	−8.02705	−0.326616
$605$	−10.7938	−0.438832
$606$	−33.9306	−1.37834
$607$	−36.8214	−1.49454	−0.747268	−	0.664523i	$-0.768635\pi$
$607$	−36.8214	−1.49454	−0.747268	+	0.664523i	$0.768635\pi$
$608$	24.0517	0.975426
$609$	−1.45514	−0.0589652
$610$	24.0854	0.975188
$611$	−53.7621	−2.17498
$612$	0.0657888	0.00265935
$613$	4.89286	0.197621	0.0988104	−	0.995106i	$-0.468496\pi$
$613$	4.89286	0.197621	0.0988104	+	0.995106i	$0.468496\pi$
$614$	10.7334	0.433166
$615$	15.9002	0.641157
$616$	−0.00286184	−0.000115307 0
$617$	30.6926	1.23564	0.617818	−	0.786321i	$-0.288017\pi$
$617$	30.6926	1.23564	0.617818	+	0.786321i	$0.288017\pi$
$618$	42.0031	1.68961
$619$	−1.00000	−0.0401934
$619$	−1.00000	−0.0401934
$620$	3.58603	0.144018
$621$	5.07787	0.203768
$622$	7.77845	0.311887
$623$	1.35426	0.0542573
$624$	−51.3061	−2.05389
$625$	11.4836	0.459343
$626$	27.1075	1.08344
$627$	−0.264338	−0.0105566
$628$	−3.35637	−0.133934
$629$	−0.267178	−0.0106531
$630$	−0.331332	−0.0132006
$631$	−0.0884091	−0.00351951	−0.00175976	−	0.999998i	$-0.500560\pi$
$631$	−0.0884091	−0.00351951	−0.00175976	+	0.999998i	$0.500560\pi$
$632$	−30.7960	−1.22500
$633$	48.9816	1.94685
$634$	−55.5850	−2.20756
$635$	−12.3605	−0.490510
$636$	3.84282	0.152378
$637$	31.4306	1.24533
$638$	0.188701	0.00747074
$639$	24.7392	0.978666
$640$	13.3737	0.528641
$641$	−43.3449	−1.71202	−0.856010	−	0.516960i	$-0.827064\pi$
$641$	−43.3449	−1.71202	−0.856010	+	0.516960i	$0.827064\pi$
$642$	11.0445	0.435892
$643$	25.2727	0.996658	0.498329	−	0.866988i	$-0.333947\pi$
$643$	25.2727	0.996658	0.498329	+	0.866988i	$0.333947\pi$
$644$	−0.238456	−0.00939650
$645$	28.8914	1.13760
$646$	−0.496191	−0.0195224
$647$	23.6113	0.928256	0.464128	−	0.885768i	$-0.346368\pi$
$647$	23.6113	0.928256	0.464128	+	0.885768i	$0.346368\pi$
$648$	22.8222	0.896541
$649$	−0.0753652	−0.00295834
$650$	29.2969	1.14912
$651$	1.16292	0.0455785
$652$	10.9064	0.427129
$653$	36.3837	1.42381	0.711903	−	0.702278i	$-0.247834\pi$
$653$	36.3837	1.42381	0.711903	+	0.702278i	$0.247834\pi$
$654$	−4.87406	−0.190591
$655$	−13.4882	−0.527028
$656$	33.3286	1.30126
$657$	15.6307	0.609810
$658$	−1.58396	−0.0617490
$659$	−24.4126	−0.950982	−0.475491	−	0.879721i	$-0.657730\pi$
$659$	−24.4126	−0.950982	−0.475491	+	0.879721i	$0.657730\pi$
$660$	0.0217773	0.000847681 0
$661$	34.8393	1.35509	0.677545	−	0.735481i	$-0.263044\pi$
$661$	34.8393	1.35509	0.677545	+	0.735481i	$0.263044\pi$
$662$	41.4830	1.61228
$663$	0.449948	0.0174745
$664$	−6.21284	−0.241105
$665$	0.581934	0.0225664
$666$	−25.8861	−1.00307
$667$	−36.0725	−1.39673
$668$	4.71522	0.182437
$669$	−25.9914	−1.00489
$670$	4.60323	0.177838
$671$	−0.235870	−0.00910567
$672$	−0.642580	−0.0247881
$673$	13.4451	0.518271	0.259135	−	0.965841i	$-0.416562\pi$
$673$	13.4451	0.518271	0.259135	+	0.965841i	$0.416562\pi$
$674$	−44.5312	−1.71528
$675$	−4.28031	−0.164749
$676$	4.37109	0.168119
$677$	−19.6238	−0.754202	−0.377101	−	0.926172i	$-0.623079\pi$
$677$	−19.6238	−0.754202	−0.377101	+	0.926172i	$0.623079\pi$
$678$	−3.88868	−0.149344
$679$	−0.842288	−0.0323240
$680$	−0.0937847	−0.00359648
$681$	−16.3931	−0.628184
$682$	−0.150807	−0.00577468
$683$	32.5631	1.24599	0.622995	−	0.782226i	$-0.285916\pi$
$683$	32.5631	1.24599	0.622995	+	0.782226i	$0.285916\pi$
$684$	−11.1951	−0.428056
$685$	12.5100	0.477981
$686$	1.85293	0.0707452
$687$	−23.0550	−0.879602
$688$	60.5596	2.30881
$689$	12.0755	0.460038
$690$	−17.8769	−0.680563
$691$	−26.9237	−1.02423	−0.512113	−	0.858918i	$-0.671137\pi$
$691$	−26.9237	−1.02423	−0.512113	+	0.858918i	$0.671137\pi$
$692$	−6.00712	−0.228356
$693$	0.00324476	0.000123258 0
$694$	−18.1482	−0.688898
$695$	−16.6029	−0.629783
$696$	−39.9061	−1.51264
$697$	−0.292288	−0.0110712
$698$	20.5653	0.778407
$699$	53.5456	2.02528
$700$	0.201003	0.00759720
$701$	−41.3044	−1.56005	−0.780024	−	0.625750i	$-0.784793\pi$
$701$	−41.3044	−1.56005	−0.780024	+	0.625750i	$0.784793\pi$
$702$	−7.69412	−0.290396
$703$	45.4650	1.71475
$704$	−0.0670454	−0.00252687
$705$	−27.6529	−1.04147
$706$	−43.3948	−1.63318
$707$	−0.731520	−0.0275116
$708$	−6.94700	−0.261084
$709$	14.0800	0.528787	0.264394	−	0.964415i	$-0.414828\pi$
$709$	14.0800	0.528787	0.264394	+	0.964415i	$0.414828\pi$
$710$	15.3719	0.576896
$711$	34.9165	1.30947
$712$	37.1396	1.39187
$713$	28.8285	1.07964
$714$	0.0132565	0.000496113 0
$715$	0.0684318	0.00255920
$716$	−15.1163	−0.564924
$717$	−38.6260	−1.44251
$718$	2.74849	0.102573
$719$	33.7949	1.26034	0.630168	−	0.776459i	$-0.282986\pi$
$719$	33.7949	1.26034	0.630168	+	0.776459i	$0.282986\pi$
$720$	−12.1248	−0.451866
$721$	0.905555	0.0337246
$722$	53.7571	2.00063
$723$	30.8525	1.14742
$724$	1.79490	0.0667071
$725$	30.4067	1.12928
$726$	41.8416	1.55289
$727$	18.0793	0.670525	0.335263	−	0.942125i	$-0.391175\pi$
$727$	18.0793	0.670525	0.335263	+	0.942125i	$0.391175\pi$
$728$	−0.828945	−0.0307227
$729$	−18.3826	−0.680837
$730$	9.71222	0.359465
$731$	−0.531101	−0.0196435
$732$	−21.7420	−0.803608
$733$	−43.3711	−1.60195	−0.800974	−	0.598700i	$-0.795684\pi$
$733$	−43.3711	−1.60195	−0.800974	+	0.598700i	$0.795684\pi$
$734$	−11.1178	−0.410366
$735$	16.1666	0.596312
$736$	−15.9294	−0.587165
$737$	−0.0450799	−0.00166054
$738$	−28.3190	−1.04244
$739$	−46.8227	−1.72240	−0.861200	−	0.508265i	$-0.830287\pi$
$739$	−46.8227	−1.72240	−0.861200	+	0.508265i	$0.830287\pi$
$740$	−3.74561	−0.137691
$741$	−76.5667	−2.81275
$742$	0.355771	0.0130608
$743$	40.6857	1.49261	0.746307	−	0.665602i	$-0.231825\pi$
$743$	40.6857	1.49261	0.746307	+	0.665602i	$0.231825\pi$
$744$	31.8923	1.16923
$745$	−0.677814	−0.0248332
$746$	−0.916758	−0.0335649
$747$	7.04413	0.257731
$748$	−0.000400325 0	−1.46373e−5 0
$749$	0.238111	0.00870040
$750$	33.7323	1.23173
$751$	−25.3303	−0.924315	−0.462158	−	0.886798i	$-0.652925\pi$
$751$	−25.3303	−0.924315	−0.462158	+	0.886798i	$0.652925\pi$
$752$	−57.9636	−2.11371
$753$	−23.1922	−0.845172
$754$	54.6580	1.99053
$755$	−12.9740	−0.472172
$756$	−0.0527886	−0.00191990
$757$	−4.11119	−0.149424	−0.0747119	−	0.997205i	$-0.523804\pi$
$757$	−4.11119	−0.149424	−0.0747119	+	0.997205i	$0.523804\pi$
$758$	16.1269	0.585754
$759$	0.175070	0.00635465
$760$	15.9591	0.578898
$761$	−23.1277	−0.838378	−0.419189	−	0.907899i	$-0.637685\pi$
$761$	−23.1277	−0.838378	−0.419189	+	0.907899i	$0.637685\pi$
$762$	47.9146	1.73576
$763$	−0.105081	−0.00380420
$764$	−15.7241	−0.568879
$765$	0.106333	0.00384449
$766$	−13.3657	−0.482923
$767$	−21.8298	−0.788230
$768$	−31.4835	−1.13606
$769$	−19.0675	−0.687591	−0.343795	−	0.939045i	$-0.611713\pi$
$769$	−19.0675	−0.687591	−0.343795	+	0.939045i	$0.611713\pi$
$770$	0.00201616	7.26573e−5 0
$771$	−5.92054	−0.213223
$772$	1.08339	0.0389921
$773$	29.1828	1.04963	0.524816	−	0.851216i	$-0.324134\pi$
$773$	29.1828	1.04963	0.524816	+	0.851216i	$0.324134\pi$
$774$	−51.4569	−1.84958
$775$	−24.3005	−0.872900
$776$	−23.0991	−0.829211
$777$	−1.21467	−0.0435761
$778$	−1.92884	−0.0691524
$779$	49.7380	1.78205
$780$	6.30789	0.225859
$781$	−0.150538	−0.00538668
$782$	0.328626	0.0117516
$783$	−7.98559	−0.285382
$784$	33.8869	1.21025
$785$	−5.42485	−0.193621
$786$	52.2862	1.86499
$787$	1.18127	0.0421078	0.0210539	−	0.999778i	$-0.493298\pi$
$787$	1.18127	0.0421078	0.0210539	+	0.999778i	$0.493298\pi$
$788$	7.89959	0.281411
$789$	9.96123	0.354629
$790$	21.6956	0.771896
$791$	−0.0838371	−0.00298090
$792$	0.0889853	0.00316196
$793$	−68.3208	−2.42614
$794$	31.6975	1.12490
$795$	6.21109	0.220285
$796$	−7.51047	−0.266202
$797$	−40.8345	−1.44643	−0.723217	−	0.690621i	$-0.757337\pi$
$797$	−40.8345	−1.44643	−0.723217	+	0.690621i	$0.757337\pi$
$798$	−2.25583	−0.0798555
$799$	0.508334	0.0179836
$800$	13.4274	0.474731
$801$	−42.1090	−1.48785
$802$	−6.67105	−0.235563
$803$	−0.0951127	−0.00335645
$804$	−4.15537	−0.146548
$805$	−0.385413	−0.0135840
$806$	−43.6817	−1.53862
$807$	24.0777	0.847575
$808$	−20.0614	−0.705758
$809$	21.3990	0.752350	0.376175	−	0.926549i	$-0.377239\pi$
$809$	21.3990	0.752350	0.376175	+	0.926549i	$0.377239\pi$
$810$	−16.0782	−0.564929
$811$	−43.1351	−1.51468	−0.757339	−	0.653022i	$-0.773501\pi$
$811$	−43.1351	−1.51468	−0.757339	+	0.653022i	$0.773501\pi$
$812$	0.375003	0.0131600
$813$	−38.0443	−1.33427
$814$	0.157517	0.00552098
$815$	17.6279	0.617478
$816$	0.485111	0.0169823
$817$	90.3762	3.16186
$818$	−46.2907	−1.61852
$819$	0.939860	0.0328414
$820$	−4.09763	−0.143095
$821$	−0.762945	−0.0266270	−0.0133135	−	0.999911i	$-0.504238\pi$
$821$	−0.762945	−0.0266270	−0.0133135	+	0.999911i	$0.504238\pi$
$822$	−48.4941	−1.69143
$823$	12.7820	0.445551	0.222776	−	0.974870i	$-0.428488\pi$
$823$	12.7820	0.445551	0.222776	+	0.974870i	$0.428488\pi$
$824$	24.8342	0.865140
$825$	−0.147573	−0.00513782
$826$	−0.643157	−0.0223783
$827$	−44.3929	−1.54369	−0.771846	−	0.635810i	$-0.780666\pi$
$827$	−44.3929	−1.54369	−0.771846	+	0.635810i	$0.780666\pi$
$828$	7.41450	0.257672
$829$	−39.7844	−1.38177	−0.690884	−	0.722965i	$-0.742779\pi$
$829$	−39.7844	−1.38177	−0.690884	+	0.722965i	$0.742779\pi$
$830$	4.37692	0.151925
$831$	9.25584	0.321081
$832$	−19.4200	−0.673267
$833$	−0.297184	−0.0102968
$834$	64.3600	2.22860
$835$	7.62114	0.263740
$836$	0.0681224	0.00235606
$837$	6.38194	0.220592
$838$	−14.5303	−0.501940
$839$	−30.1833	−1.04204	−0.521022	−	0.853543i	$-0.674449\pi$
$839$	−30.1833	−1.04204	−0.521022	+	0.853543i	$0.674449\pi$
$840$	−0.426373	−0.0147113
$841$	27.7285	0.956156
$842$	−62.2594	−2.14560
$843$	−16.8507	−0.580367
$844$	−12.6230	−0.434502
$845$	7.06493	0.243041
$846$	49.2511	1.69329
$847$	0.902074	0.0309956
$848$	13.0192	0.447080
$849$	−36.7630	−1.26170
$850$	−0.277009	−0.00950135
$851$	−30.1114	−1.03220
$852$	−13.8763	−0.475393
$853$	19.5863	0.670621	0.335311	−	0.942108i	$-0.391159\pi$
$853$	19.5863	0.670621	0.335311	+	0.942108i	$0.391159\pi$
$854$	−2.01289	−0.0688796
$855$	−18.0945	−0.618819
$856$	6.53003	0.223192
$857$	20.8053	0.710697	0.355349	−	0.934734i	$-0.384362\pi$
$857$	20.8053	0.710697	0.355349	+	0.934734i	$0.384362\pi$
$858$	−0.265271	−0.00905622
$859$	57.5982	1.96523	0.982613	−	0.185667i	$-0.0594445\pi$
$859$	57.5982	1.96523	0.982613	+	0.185667i	$0.0594445\pi$
$860$	−7.44558	−0.253892
$861$	−1.32883	−0.0452863
$862$	−43.5291	−1.48261
$863$	−1.39588	−0.0475164	−0.0237582	−	0.999718i	$-0.507563\pi$
$863$	−1.39588	−0.0475164	−0.0237582	+	0.999718i	$0.507563\pi$
$864$	−3.52639	−0.119970
$865$	−9.70921	−0.330123
$866$	51.4508	1.74837
$867$	40.0449	1.36000
$868$	−0.299696	−0.0101723
$869$	−0.212467	−0.00720746
$870$	28.1137	0.953144
$871$	−13.0576	−0.442439
$872$	−2.88178	−0.0975893
$873$	26.1899	0.886392
$874$	−55.9215	−1.89157
$875$	0.727244	0.0245853
$876$	−8.76728	−0.296219
$877$	21.7368	0.733998	0.366999	−	0.930221i	$-0.380385\pi$
$877$	21.7368	0.733998	0.366999	+	0.930221i	$0.380385\pi$
$878$	11.0547	0.373078
$879$	−57.6271	−1.94371
$880$	0.0737797	0.00248711
$881$	−28.9334	−0.974790	−0.487395	−	0.873182i	$-0.662053\pi$
$881$	−28.9334	−0.974790	−0.487395	+	0.873182i	$0.662053\pi$
$882$	−28.7934	−0.969523
$883$	26.7524	0.900288	0.450144	−	0.892956i	$-0.351373\pi$
$883$	26.7524	0.900288	0.450144	+	0.892956i	$0.351373\pi$
$884$	−0.115956	−0.00390002
$885$	−11.2283	−0.377436
$886$	−64.6893	−2.17328
$887$	−14.8214	−0.497652	−0.248826	−	0.968548i	$-0.580045\pi$
$887$	−14.8214	−0.497652	−0.248826	+	0.968548i	$0.580045\pi$
$888$	−33.3115	−1.11786
$889$	1.03300	0.0346458
$890$	−26.1647	−0.877044
$891$	0.157455	0.00527494
$892$	6.69823	0.224273
$893$	−86.5020	−2.89468
$894$	2.62750	0.0878769
$895$	−24.4323	−0.816682
$896$	−1.11768	−0.0373391
$897$	50.7099	1.69315
$898$	30.8539	1.02961
$899$	−45.3365	−1.51206
$900$	−6.24993	−0.208331
$901$	−0.114176	−0.00380377
$902$	0.172321	0.00573767
$903$	−2.41454	−0.0803510
$904$	−2.29917	−0.0764693
$905$	2.90108	0.0964350
$906$	50.2928	1.67087
$907$	−24.4359	−0.811380	−0.405690	−	0.914011i	$-0.632969\pi$
$907$	−24.4359	−0.811380	−0.405690	+	0.914011i	$0.632969\pi$
$908$	4.22465	0.140200
$909$	22.7457	0.754426
$910$	0.583989	0.0193590
$911$	5.16681	0.171184	0.0855920	−	0.996330i	$-0.472722\pi$
$911$	5.16681	0.171184	0.0855920	+	0.996330i	$0.472722\pi$
$912$	−82.5503	−2.73351
$913$	−0.0428636	−0.00141858
$914$	16.2770	0.538396
$915$	−35.1413	−1.16173
$916$	5.94148	0.196312
$917$	1.12725	0.0372251
$918$	0.0727498	0.00240110
$919$	−26.7241	−0.881548	−0.440774	−	0.897618i	$-0.645296\pi$
$919$	−26.7241	−0.881548	−0.440774	+	0.897618i	$0.645296\pi$
$920$	−10.5697	−0.348472
$921$	−15.6604	−0.516028
$922$	−43.2158	−1.42324
$923$	−43.6040	−1.43524
$924$	−0.00182000	−5.98735e−5 0
$925$	25.3819	0.834551
$926$	25.7326	0.845624
$927$	−28.1571	−0.924800
$928$	25.0510	0.822338
$929$	−15.5891	−0.511462	−0.255731	−	0.966748i	$-0.582316\pi$
$929$	−15.5891	−0.511462	−0.255731	+	0.966748i	$0.582316\pi$
$930$	−22.4680	−0.736754
$931$	50.5712	1.65740
$932$	−13.7992	−0.452008
$933$	−11.3490	−0.371549
$934$	−6.83782	−0.223740
$935$	−0.000647039 0	−2.11604e−5 0
$936$	25.7750	0.842481
$937$	−0.475211	−0.0155245	−0.00776223	−	0.999970i	$-0.502471\pi$
$937$	−0.475211	−0.0155245	−0.00776223	+	0.999970i	$0.502471\pi$
$938$	−0.384707	−0.0125611
$939$	−39.5507	−1.29069
$940$	7.12641	0.232438
$941$	−8.05058	−0.262442	−0.131221	−	0.991353i	$-0.541890\pi$
$941$	−8.05058	−0.262442	−0.131221	+	0.991353i	$0.541890\pi$
$942$	21.0291	0.685165
$943$	−32.9413	−1.07272
$944$	−23.5358	−0.766026
$945$	−0.0853213	−0.00277550
$946$	0.313116	0.0101803
$947$	−27.5803	−0.896239	−0.448120	−	0.893974i	$-0.647906\pi$
$947$	−27.5803	−0.896239	−0.448120	+	0.893974i	$0.647906\pi$
$948$	−19.5848	−0.636084
$949$	−27.5498	−0.894304
$950$	47.1381	1.52936
$951$	81.1001	2.62985
$952$	0.00783788	0.000254027 0
$953$	19.7094	0.638449	0.319225	−	0.947679i	$-0.396578\pi$
$953$	19.7094	0.638449	0.319225	+	0.947679i	$0.396578\pi$
$954$	−11.0622	−0.358153
$955$	−25.4147	−0.822399
$956$	9.95428	0.321945
$957$	−0.275320	−0.00889984
$958$	−38.8492	−1.25516
$959$	−1.04550	−0.0337609
$960$	−9.98880	−0.322387
$961$	5.23212	0.168778
$962$	45.6256	1.47103
$963$	−7.40376	−0.238583
$964$	−7.95098	−0.256084
$965$	1.75107	0.0563688
$966$	1.49403	0.0480696
$967$	6.90731	0.222124	0.111062	−	0.993813i	$-0.464575\pi$
$967$	6.90731	0.222124	0.111062	+	0.993813i	$0.464575\pi$
$968$	24.7387	0.795133
$969$	0.723957	0.0232568
$970$	16.2733	0.522503
$971$	45.7189	1.46719	0.733595	−	0.679587i	$-0.237841\pi$
$971$	45.7189	1.46719	0.733595	+	0.679587i	$0.237841\pi$
$972$	12.5828	0.403593
$973$	1.38755	0.0444829
$974$	3.86806	0.123941
$975$	−42.7450	−1.36894
$976$	−73.6600	−2.35780
$977$	45.8247	1.46606	0.733031	−	0.680195i	$-0.238105\pi$
$977$	45.8247	1.46606	0.733031	+	0.680195i	$0.238105\pi$
$978$	−68.3334	−2.18506
$979$	0.256234	0.00818926
$980$	−4.16627	−0.133087
$981$	3.26737	0.104319
$982$	−23.7419	−0.757633
$983$	19.0136	0.606441	0.303220	−	0.952920i	$-0.401938\pi$
$983$	19.0136	0.606441	0.303220	+	0.952920i	$0.401938\pi$
$984$	−36.4421	−1.16173
$985$	12.7680	0.406822
$986$	−0.516805	−0.0164584
$987$	2.31104	0.0735611
$988$	19.7319	0.627757
$989$	−59.8559	−1.90331
$990$	−0.0626898	−0.00199241
$991$	44.8465	1.42460	0.712299	−	0.701877i	$-0.247654\pi$
$991$	44.8465	1.42460	0.712299	+	0.701877i	$0.247654\pi$
$992$	−20.0203	−0.635645
$993$	−60.5249	−1.92070
$994$	−1.28467	−0.0407474
$995$	−12.1391	−0.384834
$996$	−3.95107	−0.125195
$997$	12.2537	0.388078	0.194039	−	0.980994i	$-0.437841\pi$
$997$	12.2537	0.388078	0.194039	+	0.980994i	$0.437841\pi$
$998$	22.5561	0.714000
$999$	−6.66594	−0.210901

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	619.2.a.a.1.19	✓	21
3.2	odd	2		5571.2.a.e.1.3		21
4.3	odd	2		9904.2.a.j.1.18		21

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
619.2.a.a.1.19	✓	21	1.1	even	1	trivial
5571.2.a.e.1.3		21	3.2	odd	2
9904.2.a.j.1.18		21	4.3	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:	\( N \)	\(=\)	\( 619 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	619.a (trivial)

\(f(q)\)	\(=\)	\(q+1.61466 q^{2} -2.35583 q^{3} +0.607120 q^{4} +0.981279 q^{5} -3.80386 q^{6} -0.0820085 q^{7} -2.24902 q^{8} +2.54995 q^{9} +O(q^{10})\)	\(q+1.61466 q^{2} -2.35583 q^{3} +0.607120 q^{4} +0.981279 q^{5} -3.80386 q^{6} -0.0820085 q^{7} -2.24902 q^{8} +2.54995 q^{9} +1.58443 q^{10} -0.0155165 q^{11} -1.43027 q^{12} -4.49441 q^{13} -0.132416 q^{14} -2.31173 q^{15} -4.84565 q^{16} +0.0424957 q^{17} +4.11730 q^{18} -7.23140 q^{19} +0.595754 q^{20} +0.193198 q^{21} -0.0250538 q^{22} +4.78934 q^{23} +5.29833 q^{24} -4.03709 q^{25} -7.25693 q^{26} +1.06024 q^{27} -0.0497890 q^{28} -7.53183 q^{29} -3.73265 q^{30} +6.01931 q^{31} -3.32601 q^{32} +0.0365542 q^{33} +0.0686161 q^{34} -0.0804732 q^{35} +1.54813 q^{36} -6.28717 q^{37} -11.6762 q^{38} +10.5881 q^{39} -2.20692 q^{40} -6.87805 q^{41} +0.311949 q^{42} -12.4977 q^{43} -0.00942036 q^{44} +2.50221 q^{45} +7.73314 q^{46} +11.9620 q^{47} +11.4155 q^{48} -6.99327 q^{49} -6.51852 q^{50} -0.100113 q^{51} -2.72865 q^{52} -2.68677 q^{53} +1.71193 q^{54} -0.0152260 q^{55} +0.184439 q^{56} +17.0360 q^{57} -12.1613 q^{58} +4.85711 q^{59} -1.40350 q^{60} +15.2013 q^{61} +9.71913 q^{62} -0.209118 q^{63} +4.32092 q^{64} -4.41027 q^{65} +0.0590225 q^{66} +2.90529 q^{67} +0.0258000 q^{68} -11.2829 q^{69} -0.129937 q^{70} +9.70183 q^{71} -5.73490 q^{72} +6.12979 q^{73} -10.1516 q^{74} +9.51071 q^{75} -4.39033 q^{76} +0.00127248 q^{77} +17.0961 q^{78} +13.6930 q^{79} -4.75493 q^{80} -10.1476 q^{81} -11.1057 q^{82} +2.76246 q^{83} +0.117295 q^{84} +0.0417002 q^{85} -20.1796 q^{86} +17.7437 q^{87} +0.0348969 q^{88} -16.5137 q^{89} +4.04021 q^{90} +0.368580 q^{91} +2.90770 q^{92} -14.1805 q^{93} +19.3145 q^{94} -7.09602 q^{95} +7.83553 q^{96} +10.2707 q^{97} -11.2917 q^{98} -0.0395662 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 21 q - 9 q^{2} - 5 q^{3} + 15 q^{4} - 21 q^{5} - 6 q^{6} - 4 q^{7} - 21 q^{8} + 6 q^{9}+O(q^{10}) \) 21 * q - 9 * q^2 - 5 * q^3 + 15 * q^4 - 21 * q^5 - 6 * q^6 - 4 * q^7 - 21 * q^8 + 6 * q^9	\( 21 q - 9 q^{2} - 5 q^{3} + 15 q^{4} - 21 q^{5} - 6 q^{6} - 4 q^{7} - 21 q^{8} + 6 q^{9} + q^{10} - 27 q^{11} - 8 q^{12} - 11 q^{13} - 19 q^{14} - 10 q^{15} + 11 q^{16} - 14 q^{17} - 14 q^{18} - 15 q^{19} - 25 q^{20} - 42 q^{21} + 12 q^{22} - 14 q^{23} - 8 q^{24} + 16 q^{25} - 11 q^{26} - 5 q^{27} + q^{28} - 78 q^{29} + q^{30} - 8 q^{31} - 41 q^{32} - 6 q^{33} + 7 q^{34} - 3 q^{35} - q^{36} - 23 q^{37} + 21 q^{38} - 4 q^{39} + 12 q^{40} - 59 q^{41} + 39 q^{42} + 2 q^{43} - 50 q^{44} - 36 q^{45} - 15 q^{46} - 12 q^{47} + 10 q^{48} + 17 q^{49} - 23 q^{50} - 8 q^{51} + 18 q^{52} - 36 q^{53} - 4 q^{54} + 23 q^{55} - 28 q^{56} - 24 q^{57} + 46 q^{58} - 17 q^{59} + 8 q^{60} - 22 q^{61} + 42 q^{62} - 6 q^{63} + 49 q^{64} - 53 q^{65} + 29 q^{66} + 15 q^{67} - 16 q^{68} - 30 q^{69} + 44 q^{70} - 56 q^{71} + 12 q^{72} - 2 q^{73} - 12 q^{74} + 2 q^{75} - 4 q^{76} - 47 q^{77} + 36 q^{78} + 5 q^{79} + 15 q^{80} - 19 q^{81} + 47 q^{82} - q^{83} - 20 q^{84} - 29 q^{85} - 23 q^{86} + 44 q^{87} + 61 q^{88} - 12 q^{89} + 91 q^{90} + 5 q^{91} + 35 q^{92} - 15 q^{93} + 34 q^{94} - 17 q^{95} + 14 q^{96} + 21 q^{97} + 24 q^{98} - 38 q^{99}+O(q^{100}) \) 21 * q - 9 * q^2 - 5 * q^3 + 15 * q^4 - 21 * q^5 - 6 * q^6 - 4 * q^7 - 21 * q^8 + 6 * q^9 + q^10 - 27 * q^11 - 8 * q^12 - 11 * q^13 - 19 * q^14 - 10 * q^15 + 11 * q^16 - 14 * q^17 - 14 * q^18 - 15 * q^19 - 25 * q^20 - 42 * q^21 + 12 * q^22 - 14 * q^23 - 8 * q^24 + 16 * q^25 - 11 * q^26 - 5 * q^27 + q^28 - 78 * q^29 + q^30 - 8 * q^31 - 41 * q^32 - 6 * q^33 + 7 * q^34 - 3 * q^35 - q^36 - 23 * q^37 + 21 * q^38 - 4 * q^39 + 12 * q^40 - 59 * q^41 + 39 * q^42 + 2 * q^43 - 50 * q^44 - 36 * q^45 - 15 * q^46 - 12 * q^47 + 10 * q^48 + 17 * q^49 - 23 * q^50 - 8 * q^51 + 18 * q^52 - 36 * q^53 - 4 * q^54 + 23 * q^55 - 28 * q^56 - 24 * q^57 + 46 * q^58 - 17 * q^59 + 8 * q^60 - 22 * q^61 + 42 * q^62 - 6 * q^63 + 49 * q^64 - 53 * q^65 + 29 * q^66 + 15 * q^67 - 16 * q^68 - 30 * q^69 + 44 * q^70 - 56 * q^71 + 12 * q^72 - 2 * q^73 - 12 * q^74 + 2 * q^75 - 4 * q^76 - 47 * q^77 + 36 * q^78 + 5 * q^79 + 15 * q^80 - 19 * q^81 + 47 * q^82 - q^83 - 20 * q^84 - 29 * q^85 - 23 * q^86 + 44 * q^87 + 61 * q^88 - 12 * q^89 + 91 * q^90 + 5 * q^91 + 35 * q^92 - 15 * q^93 + 34 * q^94 - 17 * q^95 + 14 * q^96 + 21 * q^97 + 24 * q^98 - 38 * q^99

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