LMFDB - Embedded newform 6033.2.a.b.1.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6033,2,Mod(1,6033)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6033, 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("6033.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6033 = 3 \cdot 2011 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6033.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$48.1737475394$
Analytic rank:	$1$
Dimension:	$71$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
Character	$\chi$	$=$	6033.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.79990 q^{2} +1.00000 q^{3} +1.23964 q^{4} -2.94789 q^{5} -1.79990 q^{6} +0.174421 q^{7} +1.36857 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.79990 q^{2} +1.00000 q^{3} +1.23964 q^{4} -2.94789 q^{5} -1.79990 q^{6} +0.174421 q^{7} +1.36857 q^{8} +1.00000 q^{9} +5.30591 q^{10} -1.75281 q^{11} +1.23964 q^{12} -2.27496 q^{13} -0.313941 q^{14} -2.94789 q^{15} -4.94257 q^{16} +6.75399 q^{17} -1.79990 q^{18} +1.18839 q^{19} -3.65432 q^{20} +0.174421 q^{21} +3.15489 q^{22} +3.20650 q^{23} +1.36857 q^{24} +3.69006 q^{25} +4.09469 q^{26} +1.00000 q^{27} +0.216219 q^{28} -7.06451 q^{29} +5.30591 q^{30} -5.36774 q^{31} +6.15899 q^{32} -1.75281 q^{33} -12.1565 q^{34} -0.514175 q^{35} +1.23964 q^{36} +5.10795 q^{37} -2.13899 q^{38} -2.27496 q^{39} -4.03440 q^{40} -0.416693 q^{41} -0.313941 q^{42} -6.51045 q^{43} -2.17286 q^{44} -2.94789 q^{45} -5.77138 q^{46} -0.116538 q^{47} -4.94257 q^{48} -6.96958 q^{49} -6.64174 q^{50} +6.75399 q^{51} -2.82013 q^{52} +4.19484 q^{53} -1.79990 q^{54} +5.16710 q^{55} +0.238708 q^{56} +1.18839 q^{57} +12.7154 q^{58} -1.00213 q^{59} -3.65432 q^{60} +7.68309 q^{61} +9.66139 q^{62} +0.174421 q^{63} -1.20042 q^{64} +6.70632 q^{65} +3.15489 q^{66} +7.42331 q^{67} +8.37251 q^{68} +3.20650 q^{69} +0.925463 q^{70} -0.642126 q^{71} +1.36857 q^{72} -2.23420 q^{73} -9.19381 q^{74} +3.69006 q^{75} +1.47318 q^{76} -0.305728 q^{77} +4.09469 q^{78} -5.06919 q^{79} +14.5702 q^{80} +1.00000 q^{81} +0.750005 q^{82} +17.3335 q^{83} +0.216219 q^{84} -19.9100 q^{85} +11.7182 q^{86} -7.06451 q^{87} -2.39885 q^{88} +6.92598 q^{89} +5.30591 q^{90} -0.396801 q^{91} +3.97491 q^{92} -5.36774 q^{93} +0.209757 q^{94} -3.50325 q^{95} +6.15899 q^{96} +1.39417 q^{97} +12.5445 q^{98} -1.75281 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 71 q - 11 q^{2} + 71 q^{3} + 53 q^{4} - 8 q^{5} - 11 q^{6} - 46 q^{7} - 33 q^{8} + 71 q^{9}+O(q^{10}) $ 71 * q - 11 * q^2 + 71 * q^3 + 53 * q^4 - 8 * q^5 - 11 * q^6 - 46 * q^7 - 33 * q^8 + 71 * q^9	\( 71 q - 11 q^{2} + 71 q^{3} + 53 q^{4} - 8 q^{5} - 11 q^{6} - 46 q^{7} - 33 q^{8} + 71 q^{9} - 41 q^{10} - 18 q^{11} + 53 q^{12} - 67 q^{13} - 7 q^{14} - 8 q^{15} + 21 q^{16} - 25 q^{17} - 11 q^{18} - 43 q^{19} - 8 q^{20} - 46 q^{21} - 49 q^{22} - 75 q^{23} - 33 q^{24} + 19 q^{25} + 71 q^{27} - 89 q^{28} - 35 q^{29} - 41 q^{30} - 82 q^{31} - 62 q^{32} - 18 q^{33} - 28 q^{34} - 51 q^{35} + 53 q^{36} - 66 q^{37} - 29 q^{38} - 67 q^{39} - 102 q^{40} + q^{41} - 7 q^{42} - 112 q^{43} - 25 q^{44} - 8 q^{45} - 36 q^{46} - 67 q^{47} + 21 q^{48} + 7 q^{49} - 24 q^{50} - 25 q^{51} - 134 q^{52} - 40 q^{53} - 11 q^{54} - 112 q^{55} + 9 q^{56} - 43 q^{57} - 47 q^{58} - 18 q^{59} - 8 q^{60} - 144 q^{61} - 19 q^{62} - 46 q^{63} - 17 q^{64} - 31 q^{65} - 49 q^{66} - 85 q^{67} - 22 q^{68} - 75 q^{69} - 11 q^{70} - 44 q^{71} - 33 q^{72} - 98 q^{73} + 6 q^{74} + 19 q^{75} - 85 q^{76} - 39 q^{77} - 126 q^{79} + 21 q^{80} + 71 q^{81} - 69 q^{82} - 43 q^{83} - 89 q^{84} - 112 q^{85} + 32 q^{86} - 35 q^{87} - 85 q^{88} + 8 q^{89} - 41 q^{90} - 40 q^{91} - 96 q^{92} - 82 q^{93} - 99 q^{94} - 103 q^{95} - 62 q^{96} - 67 q^{97} - 11 q^{98} - 18 q^{99}+O(q^{100}) \) 71 * q - 11 * q^2 + 71 * q^3 + 53 * q^4 - 8 * q^5 - 11 * q^6 - 46 * q^7 - 33 * q^8 + 71 * q^9 - 41 * q^10 - 18 * q^11 + 53 * q^12 - 67 * q^13 - 7 * q^14 - 8 * q^15 + 21 * q^16 - 25 * q^17 - 11 * q^18 - 43 * q^19 - 8 * q^20 - 46 * q^21 - 49 * q^22 - 75 * q^23 - 33 * q^24 + 19 * q^25 + 71 * q^27 - 89 * q^28 - 35 * q^29 - 41 * q^30 - 82 * q^31 - 62 * q^32 - 18 * q^33 - 28 * q^34 - 51 * q^35 + 53 * q^36 - 66 * q^37 - 29 * q^38 - 67 * q^39 - 102 * q^40 + q^41 - 7 * q^42 - 112 * q^43 - 25 * q^44 - 8 * q^45 - 36 * q^46 - 67 * q^47 + 21 * q^48 + 7 * q^49 - 24 * q^50 - 25 * q^51 - 134 * q^52 - 40 * q^53 - 11 * q^54 - 112 * q^55 + 9 * q^56 - 43 * q^57 - 47 * q^58 - 18 * q^59 - 8 * q^60 - 144 * q^61 - 19 * q^62 - 46 * q^63 - 17 * q^64 - 31 * q^65 - 49 * q^66 - 85 * q^67 - 22 * q^68 - 75 * q^69 - 11 * q^70 - 44 * q^71 - 33 * q^72 - 98 * q^73 + 6 * q^74 + 19 * q^75 - 85 * q^76 - 39 * q^77 - 126 * q^79 + 21 * q^80 + 71 * q^81 - 69 * q^82 - 43 * q^83 - 89 * q^84 - 112 * q^85 + 32 * q^86 - 35 * q^87 - 85 * q^88 + 8 * q^89 - 41 * q^90 - 40 * q^91 - 96 * q^92 - 82 * q^93 - 99 * q^94 - 103 * q^95 - 62 * q^96 - 67 * q^97 - 11 * q^98 - 18 * 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 $

$2$	−1.79990	−1.27272	−0.636361	−	0.771392i	$-0.719561\pi$
$2$	−1.79990	−1.27272	−0.636361	+	0.771392i	$0.719561\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.23964	0.619820
$5$	−2.94789	−1.31834	−0.659168	−	0.751995i	$-0.729092\pi$
$5$	−2.94789	−1.31834	−0.659168	+	0.751995i	$0.729092\pi$
$6$	−1.79990	−0.734806
$7$	0.174421	0.0659250	0.0329625	−	0.999457i	$-0.489506\pi$
$7$	0.174421	0.0659250	0.0329625	+	0.999457i	$0.489506\pi$
$8$	1.36857	0.483863
$9$	1.00000	0.333333
$10$	5.30591	1.67788
$11$	−1.75281	−0.528493	−0.264246	−	0.964455i	$-0.585123\pi$
$11$	−1.75281	−0.528493	−0.264246	+	0.964455i	$0.585123\pi$
$12$	1.23964	0.357853
$13$	−2.27496	−0.630959	−0.315480	−	0.948932i	$-0.602165\pi$
$13$	−2.27496	−0.630959	−0.315480	+	0.948932i	$0.602165\pi$
$14$	−0.313941	−0.0839042
$15$	−2.94789	−0.761142
$16$	−4.94257	−1.23564
$17$	6.75399	1.63808	0.819041	−	0.573734i	$-0.194506\pi$
$17$	6.75399	1.63808	0.819041	+	0.573734i	$0.194506\pi$
$18$	−1.79990	−0.424240
$19$	1.18839	0.272636	0.136318	−	0.990665i	$-0.456473\pi$
$19$	1.18839	0.272636	0.136318	+	0.990665i	$0.456473\pi$
$20$	−3.65432	−0.817131
$21$	0.174421	0.0380618
$22$	3.15489	0.672624
$23$	3.20650	0.668602	0.334301	−	0.942466i	$-0.391500\pi$
$23$	3.20650	0.668602	0.334301	+	0.942466i	$0.391500\pi$
$24$	1.36857	0.279359
$25$	3.69006	0.738012
$26$	4.09469	0.803035
$27$	1.00000	0.192450
$28$	0.216219	0.0408616
$29$	−7.06451	−1.31185	−0.655923	−	0.754828i	$-0.727721\pi$
$29$	−7.06451	−1.31185	−0.655923	+	0.754828i	$0.727721\pi$
$30$	5.30591	0.968722
$31$	−5.36774	−0.964074	−0.482037	−	0.876151i	$-0.660103\pi$
$31$	−5.36774	−0.964074	−0.482037	+	0.876151i	$0.660103\pi$
$32$	6.15899	1.08877
$33$	−1.75281	−0.305125
$34$	−12.1565	−2.08482
$35$	−0.514175	−0.0869114
$36$	1.23964	0.206607
$37$	5.10795	0.839742	0.419871	−	0.907584i	$-0.362075\pi$
$37$	5.10795	0.839742	0.419871	+	0.907584i	$0.362075\pi$
$38$	−2.13899	−0.346990
$39$	−2.27496	−0.364284
$40$	−4.03440	−0.637895
$41$	−0.416693	−0.0650765	−0.0325382	−	0.999470i	$-0.510359\pi$
$41$	−0.416693	−0.0650765	−0.0325382	+	0.999470i	$0.510359\pi$
$42$	−0.313941	−0.0484421
$43$	−6.51045	−0.992834	−0.496417	−	0.868084i	$-0.665351\pi$
$43$	−6.51045	−0.992834	−0.496417	+	0.868084i	$0.665351\pi$
$44$	−2.17286	−0.327570
$45$	−2.94789	−0.439446
$46$	−5.77138	−0.850944
$47$	−0.116538	−0.0169989	−0.00849943	−	0.999964i	$-0.502705\pi$
$47$	−0.116538	−0.0169989	−0.00849943	+	0.999964i	$0.502705\pi$
$48$	−4.94257	−0.713399
$49$	−6.96958	−0.995654
$50$	−6.64174	−0.939283
$51$	6.75399	0.945748
$52$	−2.82013	−0.391081
$53$	4.19484	0.576205	0.288103	−	0.957600i	$-0.406976\pi$
$53$	4.19484	0.576205	0.288103	+	0.957600i	$0.406976\pi$
$54$	−1.79990	−0.244935
$55$	5.16710	0.696731
$56$	0.238708	0.0318987
$57$	1.18839	0.157407
$58$	12.7154	1.66962
$59$	−1.00213	−0.130466	−0.0652330	−	0.997870i	$-0.520779\pi$
$59$	−1.00213	−0.130466	−0.0652330	+	0.997870i	$0.520779\pi$
$60$	−3.65432	−0.471771
$61$	7.68309	0.983719	0.491860	−	0.870674i	$-0.336317\pi$
$61$	7.68309	0.983719	0.491860	+	0.870674i	$0.336317\pi$
$62$	9.66139	1.22700
$63$	0.174421	0.0219750
$64$	−1.20042	−0.150053
$65$	6.70632	0.831817
$66$	3.15489	0.388340
$67$	7.42331	0.906902	0.453451	−	0.891281i	$-0.350193\pi$
$67$	7.42331	0.906902	0.453451	+	0.891281i	$0.350193\pi$
$68$	8.37251	1.01532
$69$	3.20650	0.386018
$70$	0.925463	0.110614
$71$	−0.642126	−0.0762063	−0.0381032	−	0.999274i	$-0.512132\pi$
$71$	−0.642126	−0.0762063	−0.0381032	+	0.999274i	$0.512132\pi$
$72$	1.36857	0.161288
$73$	−2.23420	−0.261494	−0.130747	−	0.991416i	$-0.541738\pi$
$73$	−2.23420	−0.261494	−0.130747	+	0.991416i	$0.541738\pi$
$74$	−9.19381	−1.06876
$75$	3.69006	0.426091
$76$	1.47318	0.168985
$77$	−0.305728	−0.0348409
$78$	4.09469	0.463633
$79$	−5.06919	−0.570328	−0.285164	−	0.958479i	$-0.592048\pi$
$79$	−5.06919	−0.570328	−0.285164	+	0.958479i	$0.592048\pi$
$80$	14.5702	1.62899
$81$	1.00000	0.111111
$82$	0.750005	0.0828242
$83$	17.3335	1.90260	0.951299	−	0.308270i	$-0.0997499\pi$
$83$	17.3335	1.90260	0.951299	+	0.308270i	$0.0997499\pi$
$84$	0.216219	0.0235915
$85$	−19.9100	−2.15954
$86$	11.7182	1.26360
$87$	−7.06451	−0.757395
$88$	−2.39885	−0.255718
$89$	6.92598	0.734152	0.367076	−	0.930191i	$-0.380359\pi$
$89$	6.92598	0.734152	0.367076	+	0.930191i	$0.380359\pi$
$90$	5.30591	0.559292
$91$	−0.396801	−0.0415960
$92$	3.97491	0.414413
$93$	−5.36774	−0.556608
$94$	0.209757	0.0216348
$95$	−3.50325	−0.359426
$96$	6.15899	0.628600
$97$	1.39417	0.141556	0.0707781	−	0.997492i	$-0.477452\pi$
$97$	1.39417	0.141556	0.0707781	+	0.997492i	$0.477452\pi$
$98$	12.5445	1.26719
$99$	−1.75281	−0.176164
$100$	4.57434	0.457434
$101$	1.98205	0.197221	0.0986106	−	0.995126i	$-0.468560\pi$
$101$	1.98205	0.197221	0.0986106	+	0.995126i	$0.468560\pi$
$102$	−12.1565	−1.20367
$103$	5.58525	0.550331	0.275166	−	0.961397i	$-0.411267\pi$
$103$	5.58525	0.550331	0.275166	+	0.961397i	$0.411267\pi$
$104$	−3.11344	−0.305298
$105$	−0.514175	−0.0501783
$106$	−7.55029	−0.733349
$107$	−11.7663	−1.13749	−0.568744	−	0.822514i	$-0.692571\pi$
$107$	−11.7663	−1.13749	−0.568744	+	0.822514i	$0.692571\pi$
$108$	1.23964	0.119284
$109$	−13.4639	−1.28961	−0.644805	−	0.764347i	$-0.723061\pi$
$109$	−13.4639	−1.28961	−0.644805	+	0.764347i	$0.723061\pi$
$110$	−9.30026	−0.886745
$111$	5.10795	0.484826
$112$	−0.862089	−0.0814598
$113$	7.35350	0.691759	0.345879	−	0.938279i	$-0.387581\pi$
$113$	7.35350	0.691759	0.345879	+	0.938279i	$0.387581\pi$
$114$	−2.13899	−0.200335
$115$	−9.45242	−0.881443
$116$	−8.75745	−0.813109
$117$	−2.27496	−0.210320
$118$	1.80373	0.166047
$119$	1.17804	0.107991
$120$	−4.03440	−0.368289
$121$	−7.92765	−0.720696
$122$	−13.8288	−1.25200
$123$	−0.416693	−0.0375719
$124$	−6.65406	−0.597552
$125$	3.86156	0.345389
$126$	−0.313941	−0.0279681
$127$	1.25046	0.110960	0.0554802	−	0.998460i	$-0.482331\pi$
$127$	1.25046	0.110960	0.0554802	+	0.998460i	$0.482331\pi$
$128$	−10.1573	−0.897791
$129$	−6.51045	−0.573213
$130$	−12.0707	−1.05867
$131$	12.1916	1.06519	0.532594	−	0.846371i	$-0.321217\pi$
$131$	12.1916	1.06519	0.532594	+	0.846371i	$0.321217\pi$
$132$	−2.17286	−0.189123
$133$	0.207281	0.0179735
$134$	−13.3612	−1.15423
$135$	−2.94789	−0.253714
$136$	9.24332	0.792608
$137$	1.20637	0.103067	0.0515334	−	0.998671i	$-0.483589\pi$
$137$	1.20637	0.103067	0.0515334	+	0.998671i	$0.483589\pi$
$138$	−5.77138	−0.491293
$139$	−9.69410	−0.822243	−0.411121	−	0.911581i	$-0.634863\pi$
$139$	−9.69410	−0.822243	−0.411121	+	0.911581i	$0.634863\pi$
$140$	−0.637391	−0.0538694
$141$	−0.116538	−0.00981430
$142$	1.15576	0.0969895
$143$	3.98757	0.333457
$144$	−4.94257	−0.411881
$145$	20.8254	1.72946
$146$	4.02134	0.332809
$147$	−6.96958	−0.574841
$148$	6.33202	0.520489
$149$	6.10476	0.500121	0.250061	−	0.968230i	$-0.419549\pi$
$149$	6.10476	0.500121	0.250061	+	0.968230i	$0.419549\pi$
$150$	−6.64174	−0.542295
$151$	−7.16834	−0.583352	−0.291676	−	0.956517i	$-0.594213\pi$
$151$	−7.16834	−0.583352	−0.291676	+	0.956517i	$0.594213\pi$
$152$	1.62640	0.131919
$153$	6.75399	0.546028
$154$	0.550279	0.0443427
$155$	15.8235	1.27097
$156$	−2.82013	−0.225791
$157$	4.53840	0.362204	0.181102	−	0.983464i	$-0.442034\pi$
$157$	4.53840	0.362204	0.181102	+	0.983464i	$0.442034\pi$
$158$	9.12403	0.725869
$159$	4.19484	0.332672
$160$	−18.1560	−1.43536
$161$	0.559282	0.0440776
$162$	−1.79990	−0.141413
$163$	10.0040	0.783570	0.391785	−	0.920057i	$-0.371858\pi$
$163$	10.0040	0.783570	0.391785	+	0.920057i	$0.371858\pi$
$164$	−0.516549	−0.0403357
$165$	5.16710	0.402258
$166$	−31.1986	−2.42148
$167$	−16.2610	−1.25831	−0.629157	−	0.777279i	$-0.716600\pi$
$167$	−16.2610	−1.25831	−0.629157	+	0.777279i	$0.716600\pi$
$168$	0.238708	0.0184167
$169$	−7.82458	−0.601891
$170$	35.8360	2.74850
$171$	1.18839	0.0908787
$172$	−8.07061	−0.615378
$173$	5.69845	0.433245	0.216623	−	0.976255i	$-0.430496\pi$
$173$	5.69845	0.433245	0.216623	+	0.976255i	$0.430496\pi$
$174$	12.7154	0.963953
$175$	0.643624	0.0486534
$176$	8.66340	0.653028
$177$	−1.00213	−0.0753245
$178$	−12.4661	−0.934371
$179$	20.4790	1.53068	0.765338	−	0.643629i	$-0.222572\pi$
$179$	20.4790	1.53068	0.765338	+	0.643629i	$0.222572\pi$
$180$	−3.65432	−0.272377
$181$	−3.71590	−0.276200	−0.138100	−	0.990418i	$-0.544100\pi$
$181$	−3.71590	−0.276200	−0.138100	+	0.990418i	$0.544100\pi$
$182$	0.714201	0.0529401
$183$	7.68309	0.567951
$184$	4.38833	0.323512
$185$	−15.0577	−1.10706
$186$	9.66139	0.708407
$187$	−11.8385	−0.865715
$188$	−0.144466	−0.0105362
$189$	0.174421	0.0126873
$190$	6.30551	0.457450
$191$	−19.8670	−1.43752	−0.718762	−	0.695256i	$-0.755291\pi$
$191$	−19.8670	−1.43752	−0.718762	+	0.695256i	$0.755291\pi$
$192$	−1.20042	−0.0866332
$193$	−0.0599317	−0.00431398	−0.00215699	−	0.999998i	$-0.500687\pi$
$193$	−0.0599317	−0.00431398	−0.00215699	+	0.999998i	$0.500687\pi$
$194$	−2.50936	−0.180162
$195$	6.70632	0.480250
$196$	−8.63977	−0.617126
$197$	16.7168	1.19102	0.595512	−	0.803347i	$-0.296949\pi$
$197$	16.7168	1.19102	0.595512	+	0.803347i	$0.296949\pi$
$198$	3.15489	0.224208
$199$	−22.5842	−1.60095	−0.800477	−	0.599363i	$-0.795421\pi$
$199$	−22.5842	−1.60095	−0.800477	+	0.599363i	$0.795421\pi$
$200$	5.05011	0.357097
$201$	7.42331	0.523600
$202$	−3.56749	−0.251008
$203$	−1.23220	−0.0864835
$204$	8.37251	0.586193
$205$	1.22836	0.0857927
$206$	−10.0529	−0.700418
$207$	3.20650	0.222867
$208$	11.2441	0.779640
$209$	−2.08303	−0.144086
$210$	0.925463	0.0638630
$211$	−21.9492	−1.51104	−0.755521	−	0.655124i	$-0.772616\pi$
$211$	−21.9492	−1.51104	−0.755521	+	0.655124i	$0.772616\pi$
$212$	5.20009	0.357144
$213$	−0.642126	−0.0439978
$214$	21.1781	1.44771
$215$	19.1921	1.30889
$216$	1.36857	0.0931195
$217$	−0.936247	−0.0635566
$218$	24.2337	1.64131
$219$	−2.23420	−0.150973
$220$	6.40534	0.431848
$221$	−15.3650	−1.03356
$222$	−9.19381	−0.617048
$223$	9.63701	0.645342	0.322671	−	0.946511i	$-0.395419\pi$
$223$	9.63701	0.645342	0.322671	+	0.946511i	$0.395419\pi$
$224$	1.07426	0.0717769
$225$	3.69006	0.246004
$226$	−13.2356	−0.880416
$227$	7.98024	0.529667	0.264834	−	0.964294i	$-0.414683\pi$
$227$	7.98024	0.529667	0.264834	+	0.964294i	$0.414683\pi$
$228$	1.47318	0.0975637
$229$	−12.3184	−0.814026	−0.407013	−	0.913422i	$-0.633430\pi$
$229$	−12.3184	−0.814026	−0.407013	+	0.913422i	$0.633430\pi$
$230$	17.0134	1.12183
$231$	−0.305728	−0.0201154
$232$	−9.66829	−0.634754
$233$	28.2070	1.84790	0.923950	−	0.382514i	$-0.124942\pi$
$233$	28.2070	1.84790	0.923950	+	0.382514i	$0.124942\pi$
$234$	4.09469	0.267678
$235$	0.343542	0.0224102
$236$	−1.24228	−0.0808654
$237$	−5.06919	−0.329279
$238$	−2.12035	−0.137442
$239$	−20.9946	−1.35803	−0.679015	−	0.734124i	$-0.737593\pi$
$239$	−20.9946	−1.35803	−0.679015	+	0.734124i	$0.737593\pi$
$240$	14.5702	0.940500
$241$	−8.23978	−0.530771	−0.265386	−	0.964142i	$-0.585499\pi$
$241$	−8.23978	−0.530771	−0.265386	+	0.964142i	$0.585499\pi$
$242$	14.2690	0.917245
$243$	1.00000	0.0641500
$244$	9.52427	0.609729
$245$	20.5456	1.31261
$246$	0.750005	0.0478186
$247$	−2.70354	−0.172022
$248$	−7.34613	−0.466480
$249$	17.3335	1.09847
$250$	−6.95043	−0.439584
$251$	−13.1347	−0.829057	−0.414529	−	0.910036i	$-0.636054\pi$
$251$	−13.1347	−0.829057	−0.414529	+	0.910036i	$0.636054\pi$
$252$	0.216219	0.0136205
$253$	−5.62040	−0.353351
$254$	−2.25070	−0.141222
$255$	−19.9100	−1.24681
$256$	20.6830	1.29269
$257$	−13.3318	−0.831614	−0.415807	−	0.909453i	$-0.636501\pi$
$257$	−13.3318	−0.831614	−0.415807	+	0.909453i	$0.636501\pi$
$258$	11.7182	0.729540
$259$	0.890935	0.0553600
$260$	8.31342	0.515577
$261$	−7.06451	−0.437282
$262$	−21.9437	−1.35569
$263$	4.79635	0.295756	0.147878	−	0.989006i	$-0.452756\pi$
$263$	4.79635	0.295756	0.147878	+	0.989006i	$0.452756\pi$
$264$	−2.39885	−0.147639
$265$	−12.3659	−0.759633
$266$	−0.373085	−0.0228753
$267$	6.92598	0.423863
$268$	9.20223	0.562116
$269$	−18.3812	−1.12072	−0.560360	−	0.828249i	$-0.689337\pi$
$269$	−18.3812	−1.12072	−0.560360	+	0.828249i	$0.689337\pi$
$270$	5.30591	0.322907
$271$	−21.4156	−1.30090	−0.650452	−	0.759547i	$-0.725420\pi$
$271$	−21.4156	−1.30090	−0.650452	+	0.759547i	$0.725420\pi$
$272$	−33.3821	−2.02409
$273$	−0.396801	−0.0240155
$274$	−2.17134	−0.131175
$275$	−6.46798	−0.390034
$276$	3.97491	0.239261
$277$	13.8826	0.834125	0.417062	−	0.908878i	$-0.363060\pi$
$277$	13.8826	0.834125	0.417062	+	0.908878i	$0.363060\pi$
$278$	17.4484	1.04649
$279$	−5.36774	−0.321358
$280$	−0.703685	−0.0420532
$281$	−14.0794	−0.839907	−0.419953	−	0.907546i	$-0.637954\pi$
$281$	−14.0794	−0.839907	−0.419953	+	0.907546i	$0.637954\pi$
$282$	0.209757	0.0124909
$283$	−25.5729	−1.52015	−0.760076	−	0.649835i	$-0.774838\pi$
$283$	−25.5729	−1.52015	−0.760076	+	0.649835i	$0.774838\pi$
$284$	−0.796005	−0.0472342
$285$	−3.50325	−0.207515
$286$	−7.17722	−0.424398
$287$	−0.0726801	−0.00429017
$288$	6.15899	0.362922
$289$	28.6164	1.68332
$290$	−37.4836	−2.20112
$291$	1.39417	0.0817275
$292$	−2.76961	−0.162079
$293$	−22.6692	−1.32435	−0.662175	−	0.749349i	$-0.730366\pi$
$293$	−22.6692	−1.32435	−0.662175	+	0.749349i	$0.730366\pi$
$294$	12.5445	0.731613
$295$	2.95416	0.171998
$296$	6.99060	0.406321
$297$	−1.75281	−0.101708
$298$	−10.9880	−0.636515
$299$	−7.29465	−0.421861
$300$	4.57434	0.264100
$301$	−1.13556	−0.0654526
$302$	12.9023	0.742444
$303$	1.98205	0.113866
$304$	−5.87372	−0.336881
$305$	−22.6489	−1.29687
$306$	−12.1565	−0.694941
$307$	−16.8561	−0.962026	−0.481013	−	0.876714i	$-0.659731\pi$
$307$	−16.8561	−0.962026	−0.481013	+	0.876714i	$0.659731\pi$
$308$	−0.378992	−0.0215951
$309$	5.58525	0.317734
$310$	−28.4807	−1.61760
$311$	−17.6904	−1.00313	−0.501564	−	0.865120i	$-0.667242\pi$
$311$	−17.6904	−1.00313	−0.501564	+	0.865120i	$0.667242\pi$
$312$	−3.11344	−0.176264
$313$	−17.7443	−1.00297	−0.501483	−	0.865167i	$-0.667212\pi$
$313$	−17.7443	−1.00297	−0.501483	+	0.865167i	$0.667212\pi$
$314$	−8.16867	−0.460985
$315$	−0.514175	−0.0289705
$316$	−6.28397	−0.353501
$317$	1.38952	0.0780433	0.0390216	−	0.999238i	$-0.487576\pi$
$317$	1.38952	0.0780433	0.0390216	+	0.999238i	$0.487576\pi$
$318$	−7.55029	−0.423399
$319$	12.3828	0.693301
$320$	3.53872	0.197821
$321$	−11.7663	−0.656729
$322$	−1.00665	−0.0560985
$323$	8.02640	0.446601
$324$	1.23964	0.0688689
$325$	−8.39472	−0.465655
$326$	−18.0061	−0.997267
$327$	−13.4639	−0.744556
$328$	−0.570274	−0.0314881
$329$	−0.0203268	−0.00112065
$330$	−9.30026	−0.511962
$331$	15.9210	0.875095	0.437547	−	0.899195i	$-0.355847\pi$
$331$	15.9210	0.875095	0.437547	+	0.899195i	$0.355847\pi$
$332$	21.4873	1.17927
$333$	5.10795	0.279914
$334$	29.2682	1.60148
$335$	−21.8831	−1.19560
$336$	−0.862089	−0.0470308
$337$	19.0936	1.04009	0.520047	−	0.854137i	$-0.325914\pi$
$337$	19.0936	1.04009	0.520047	+	0.854137i	$0.325914\pi$
$338$	14.0835	0.766039
$339$	7.35350	0.399387
$340$	−24.6813	−1.33853
$341$	9.40863	0.509506
$342$	−2.13899	−0.115663
$343$	−2.43659	−0.131564
$344$	−8.91001	−0.480396
$345$	−9.45242	−0.508901
$346$	−10.2566	−0.551400
$347$	18.6177	0.999451	0.499726	−	0.866184i	$-0.333434\pi$
$347$	18.6177	0.999451	0.499726	+	0.866184i	$0.333434\pi$
$348$	−8.75745	−0.469449
$349$	5.01530	0.268463	0.134231	−	0.990950i	$-0.457143\pi$
$349$	5.01530	0.268463	0.134231	+	0.990950i	$0.457143\pi$
$350$	−1.15846	−0.0619223
$351$	−2.27496	−0.121428
$352$	−10.7956	−0.575405
$353$	−18.6165	−0.990858	−0.495429	−	0.868648i	$-0.664989\pi$
$353$	−18.6165	−0.990858	−0.495429	+	0.868648i	$0.664989\pi$
$354$	1.80373	0.0958672
$355$	1.89292	0.100466
$356$	8.58572	0.455042
$357$	1.17804	0.0623484
$358$	−36.8602	−1.94812
$359$	7.48588	0.395090	0.197545	−	0.980294i	$-0.436703\pi$
$359$	7.48588	0.395090	0.197545	+	0.980294i	$0.436703\pi$
$360$	−4.03440	−0.212632
$361$	−17.5877	−0.925670
$362$	6.68824	0.351526
$363$	−7.92765	−0.416094
$364$	−0.491890	−0.0257820
$365$	6.58618	0.344737
$366$	−13.8288	−0.722843
$367$	−7.37972	−0.385218	−0.192609	−	0.981276i	$-0.561695\pi$
$367$	−7.37972	−0.385218	−0.192609	+	0.981276i	$0.561695\pi$
$368$	−15.8484	−0.826154
$369$	−0.416693	−0.0216922
$370$	27.1023	1.40898
$371$	0.731669	0.0379863
$372$	−6.65406	−0.344997
$373$	−13.8715	−0.718237	−0.359118	−	0.933292i	$-0.616923\pi$
$373$	−13.8715	−0.718237	−0.359118	+	0.933292i	$0.616923\pi$
$374$	21.3081	1.10181
$375$	3.86156	0.199410
$376$	−0.159491	−0.00822513
$377$	16.0714	0.827722
$378$	−0.313941	−0.0161474
$379$	14.0973	0.724130	0.362065	−	0.932153i	$-0.382072\pi$
$379$	14.0973	0.724130	0.362065	+	0.932153i	$0.382072\pi$
$380$	−4.34277	−0.222780
$381$	1.25046	0.0640630
$382$	35.7586	1.82957
$383$	12.7135	0.649631	0.324815	−	0.945777i	$-0.394698\pi$
$383$	12.7135	0.649631	0.324815	+	0.945777i	$0.394698\pi$
$384$	−10.1573	−0.518340
$385$	0.901251	0.0459320
$386$	0.107871	0.00549050
$387$	−6.51045	−0.330945
$388$	1.72826	0.0877393
$389$	−22.5642	−1.14405	−0.572025	−	0.820236i	$-0.693842\pi$
$389$	−22.5642	−1.14405	−0.572025	+	0.820236i	$0.693842\pi$
$390$	−12.0707	−0.611224
$391$	21.6567	1.09523
$392$	−9.53837	−0.481760
$393$	12.1916	0.614987
$394$	−30.0886	−1.51584
$395$	14.9434	0.751885
$396$	−2.17286	−0.109190
$397$	2.02312	0.101537	0.0507687	−	0.998710i	$-0.483833\pi$
$397$	2.02312	0.101537	0.0507687	+	0.998710i	$0.483833\pi$
$398$	40.6494	2.03757
$399$	0.207281	0.0103770
$400$	−18.2384	−0.911919
$401$	−6.32320	−0.315766	−0.157883	−	0.987458i	$-0.550467\pi$
$401$	−6.32320	−0.315766	−0.157883	+	0.987458i	$0.550467\pi$
$402$	−13.3612	−0.666397
$403$	12.2114	0.608291
$404$	2.45703	0.122242
$405$	−2.94789	−0.146482
$406$	2.21784	0.110069
$407$	−8.95328	−0.443798
$408$	9.24332	0.457613
$409$	4.53196	0.224091	0.112046	−	0.993703i	$-0.464260\pi$
$409$	4.53196	0.224091	0.112046	+	0.993703i	$0.464260\pi$
$410$	−2.21093	−0.109190
$411$	1.20637	0.0595056
$412$	6.92370	0.341106
$413$	−0.174792	−0.00860097
$414$	−5.77138	−0.283648
$415$	−51.0972	−2.50826
$416$	−14.0114	−0.686967
$417$	−9.69410	−0.474722
$418$	3.74925	0.183382
$419$	15.1830	0.741736	0.370868	−	0.928686i	$-0.379060\pi$
$419$	15.1830	0.741736	0.370868	+	0.928686i	$0.379060\pi$
$420$	−0.637391	−0.0311015
$421$	29.9855	1.46140	0.730702	−	0.682697i	$-0.239193\pi$
$421$	29.9855	1.46140	0.730702	+	0.682697i	$0.239193\pi$
$422$	39.5063	1.92314
$423$	−0.116538	−0.00566629
$424$	5.74094	0.278805
$425$	24.9226	1.20892
$426$	1.15576	0.0559969
$427$	1.34009	0.0648517
$428$	−14.5859	−0.705038
$429$	3.98757	0.192522
$430$	−34.5438	−1.66585
$431$	−24.1966	−1.16551	−0.582754	−	0.812649i	$-0.698025\pi$
$431$	−24.1966	−1.16551	−0.582754	+	0.812649i	$0.698025\pi$
$432$	−4.94257	−0.237800
$433$	−18.6288	−0.895244	−0.447622	−	0.894223i	$-0.647729\pi$
$433$	−18.6288	−0.895244	−0.447622	+	0.894223i	$0.647729\pi$
$434$	1.68515	0.0808898
$435$	20.8254	0.998502
$436$	−16.6904	−0.799326
$437$	3.81059	0.182285
$438$	4.02134	0.192147
$439$	−27.0373	−1.29042	−0.645211	−	0.764004i	$-0.723231\pi$
$439$	−27.0373	−1.29042	−0.645211	+	0.764004i	$0.723231\pi$
$440$	7.07154	0.337123
$441$	−6.96958	−0.331885
$442$	27.6555	1.31544
$443$	−35.1952	−1.67217	−0.836087	−	0.548597i	$-0.815162\pi$
$443$	−35.1952	−1.67217	−0.836087	+	0.548597i	$0.815162\pi$
$444$	6.33202	0.300505
$445$	−20.4170	−0.967860
$446$	−17.3456	−0.821340
$447$	6.10476	0.288745
$448$	−0.209380	−0.00989225
$449$	11.7971	0.556740	0.278370	−	0.960474i	$-0.410206\pi$
$449$	11.7971	0.556740	0.278370	+	0.960474i	$0.410206\pi$
$450$	−6.64174	−0.313094
$451$	0.730384	0.0343924
$452$	9.11569	0.428766
$453$	−7.16834	−0.336798
$454$	−14.3636	−0.674119
$455$	1.16972	0.0548375
$456$	1.62640	0.0761633
$457$	−32.1838	−1.50549	−0.752747	−	0.658310i	$-0.771272\pi$
$457$	−32.1838	−1.50549	−0.752747	+	0.658310i	$0.771272\pi$
$458$	22.1720	1.03603
$459$	6.75399	0.315249
$460$	−11.7176	−0.546336
$461$	11.3529	0.528757	0.264379	−	0.964419i	$-0.414833\pi$
$461$	11.3529	0.528757	0.264379	+	0.964419i	$0.414833\pi$
$462$	0.550279	0.0256013
$463$	33.8452	1.57292	0.786460	−	0.617641i	$-0.211912\pi$
$463$	33.8452	1.57292	0.786460	+	0.617641i	$0.211912\pi$
$464$	34.9169	1.62097
$465$	15.8235	0.733797
$466$	−50.7697	−2.35186
$467$	12.7685	0.590857	0.295429	−	0.955365i	$-0.404538\pi$
$467$	12.7685	0.590857	0.295429	+	0.955365i	$0.404538\pi$
$468$	−2.82013	−0.130360
$469$	1.29478	0.0597875
$470$	−0.618342	−0.0285220
$471$	4.53840	0.209118
$472$	−1.37148	−0.0631277
$473$	11.4116	0.524705
$474$	9.12403	0.419081
$475$	4.38524	0.201209
$476$	1.46034	0.0669348
$477$	4.19484	0.192068
$478$	37.7883	1.72839
$479$	2.63002	0.120169	0.0600843	−	0.998193i	$-0.480863\pi$
$479$	2.63002	0.120169	0.0600843	+	0.998193i	$0.480863\pi$
$480$	−18.1560	−0.828706
$481$	−11.6204	−0.529843
$482$	14.8308	0.675524
$483$	0.559282	0.0254482
$484$	−9.82743	−0.446702
$485$	−4.10985	−0.186619
$486$	−1.79990	−0.0816451
$487$	−17.4082	−0.788842	−0.394421	−	0.918930i	$-0.629055\pi$
$487$	−17.4082	−0.788842	−0.394421	+	0.918930i	$0.629055\pi$
$488$	10.5149	0.475986
$489$	10.0040	0.452395
$490$	−36.9799	−1.67058
$491$	−0.989168	−0.0446405	−0.0223203	−	0.999751i	$-0.507105\pi$
$491$	−0.989168	−0.0446405	−0.0223203	+	0.999751i	$0.507105\pi$
$492$	−0.516549	−0.0232878
$493$	−47.7136	−2.14891
$494$	4.86611	0.218936
$495$	5.16710	0.232244
$496$	26.5304	1.19125
$497$	−0.112000	−0.00502390
$498$	−31.1986	−1.39804
$499$	−20.6473	−0.924300	−0.462150	−	0.886802i	$-0.652922\pi$
$499$	−20.6473	−0.924300	−0.462150	+	0.886802i	$0.652922\pi$
$500$	4.78695	0.214079
$501$	−16.2610	−0.726487
$502$	23.6412	1.05516
$503$	−18.2183	−0.812316	−0.406158	−	0.913803i	$-0.633132\pi$
$503$	−18.2183	−0.812316	−0.406158	+	0.913803i	$0.633132\pi$
$504$	0.238708	0.0106329
$505$	−5.84286	−0.260004
$506$	10.1162	0.449718
$507$	−7.82458	−0.347502
$508$	1.55012	0.0687755
$509$	−18.0297	−0.799152	−0.399576	−	0.916700i	$-0.630843\pi$
$509$	−18.0297	−0.799152	−0.399576	+	0.916700i	$0.630843\pi$
$510$	35.8360	1.58685
$511$	−0.389692	−0.0172390
$512$	−16.9127	−0.747444
$513$	1.18839	0.0524689
$514$	23.9959	1.05841
$515$	−16.4647	−0.725522
$516$	−8.07061	−0.355289
$517$	0.204270	0.00898377
$518$	−1.60359	−0.0704579
$519$	5.69845	0.250134
$520$	9.17808	0.402486
$521$	−32.2317	−1.41209	−0.706047	−	0.708165i	$-0.749523\pi$
$521$	−32.2317	−1.41209	−0.706047	+	0.708165i	$0.749523\pi$
$522$	12.7154	0.556538
$523$	26.1230	1.14228	0.571140	−	0.820853i	$-0.306501\pi$
$523$	26.1230	1.14228	0.571140	+	0.820853i	$0.306501\pi$
$524$	15.1132	0.660225
$525$	0.643624	0.0280901
$526$	−8.63296	−0.376415
$527$	−36.2536	−1.57923
$528$	8.66340	0.377026
$529$	−12.7183	−0.552971
$530$	22.2574	0.966801
$531$	−1.00213	−0.0434886
$532$	0.256954	0.0111404
$533$	0.947958	0.0410606
$534$	−12.4661	−0.539459
$535$	34.6857	1.49959
$536$	10.1593	0.438817
$537$	20.4790	0.883736
$538$	33.0843	1.42637
$539$	12.2164	0.526196
$540$	−3.65432	−0.157257
$541$	21.8619	0.939917	0.469958	−	0.882689i	$-0.344269\pi$
$541$	21.8619	0.939917	0.469958	+	0.882689i	$0.344269\pi$
$542$	38.5459	1.65569
$543$	−3.71590	−0.159464
$544$	41.5978	1.78349
$545$	39.6901	1.70014
$546$	0.714201	0.0305650
$547$	42.7391	1.82739	0.913695	−	0.406400i	$-0.133216\pi$
$547$	42.7391	1.82739	0.913695	+	0.406400i	$0.133216\pi$
$548$	1.49546	0.0638829
$549$	7.68309	0.327906
$550$	11.6417	0.496404
$551$	−8.39542	−0.357657
$552$	4.38833	0.186780
$553$	−0.884174	−0.0375989
$554$	−24.9873	−1.06161
$555$	−15.0577	−0.639163
$556$	−12.0172	−0.509642
$557$	−30.3762	−1.28708	−0.643541	−	0.765412i	$-0.722535\pi$
$557$	−30.3762	−1.28708	−0.643541	+	0.765412i	$0.722535\pi$
$558$	9.66139	0.408999
$559$	14.8110	0.626438
$560$	2.54135	0.107391
$561$	−11.8385	−0.499821
$562$	25.3415	1.06897
$563$	−11.2932	−0.475951	−0.237975	−	0.971271i	$-0.576484\pi$
$563$	−11.2932	−0.475951	−0.237975	+	0.971271i	$0.576484\pi$
$564$	−0.144466	−0.00608310
$565$	−21.6773	−0.911971
$566$	46.0287	1.93473
$567$	0.174421	0.00732500
$568$	−0.878796	−0.0368735
$569$	−26.5612	−1.11350	−0.556752	−	0.830678i	$-0.687953\pi$
$569$	−26.5612	−1.11350	−0.556752	+	0.830678i	$0.687953\pi$
$570$	6.30551	0.264109
$571$	−28.5399	−1.19436	−0.597179	−	0.802108i	$-0.703712\pi$
$571$	−28.5399	−1.19436	−0.597179	+	0.802108i	$0.703712\pi$
$572$	4.94315	0.206683
$573$	−19.8670	−0.829955
$574$	0.130817	0.00546019
$575$	11.8322	0.493436
$576$	−1.20042	−0.0500177
$577$	4.40797	0.183506	0.0917531	−	0.995782i	$-0.470753\pi$
$577$	4.40797	0.183506	0.0917531	+	0.995782i	$0.470753\pi$
$578$	−51.5066	−2.14239
$579$	−0.0599317	−0.00249068
$580$	25.8160	1.07195
$581$	3.02333	0.125429
$582$	−2.50936	−0.104016
$583$	−7.35276	−0.304520
$584$	−3.05767	−0.126527
$585$	6.70632	0.277272
$586$	40.8023	1.68553
$587$	−31.1008	−1.28367	−0.641833	−	0.766844i	$-0.721826\pi$
$587$	−31.1008	−1.28367	−0.641833	+	0.766844i	$0.721826\pi$
$588$	−8.63977	−0.356298
$589$	−6.37898	−0.262841
$590$	−5.31720	−0.218906
$591$	16.7168	0.687638
$592$	−25.2464	−1.03762
$593$	30.1604	1.23854	0.619270	−	0.785178i	$-0.287429\pi$
$593$	30.1604	1.23854	0.619270	+	0.785178i	$0.287429\pi$
$594$	3.15489	0.129447
$595$	−3.47273	−0.142368
$596$	7.56770	0.309985
$597$	−22.5842	−0.924311
$598$	13.1296	0.536911
$599$	12.4015	0.506713	0.253357	−	0.967373i	$-0.418465\pi$
$599$	12.4015	0.506713	0.253357	+	0.967373i	$0.418465\pi$
$600$	5.05011	0.206170
$601$	−11.7435	−0.479025	−0.239513	−	0.970893i	$-0.576988\pi$
$601$	−11.7435	−0.479025	−0.239513	+	0.970893i	$0.576988\pi$
$602$	2.04389	0.0833029
$603$	7.42331	0.302301
$604$	−8.88617	−0.361573
$605$	23.3698	0.950119
$606$	−3.56749	−0.144919
$607$	−15.3740	−0.624012	−0.312006	−	0.950080i	$-0.601001\pi$
$607$	−15.3740	−0.624012	−0.312006	+	0.950080i	$0.601001\pi$
$608$	7.31931	0.296837
$609$	−1.23220	−0.0499313
$610$	40.7658	1.65056
$611$	0.265120	0.0107256
$612$	8.37251	0.338439
$613$	6.68157	0.269866	0.134933	−	0.990855i	$-0.456918\pi$
$613$	6.68157	0.269866	0.134933	+	0.990855i	$0.456918\pi$
$614$	30.3392	1.22439
$615$	1.22836	0.0495324
$616$	−0.418410	−0.0168582
$617$	−15.2833	−0.615283	−0.307642	−	0.951502i	$-0.599540\pi$
$617$	−15.2833	−0.615283	−0.307642	+	0.951502i	$0.599540\pi$
$618$	−10.0529	−0.404387
$619$	24.4408	0.982359	0.491180	−	0.871058i	$-0.336566\pi$
$619$	24.4408	0.982359	0.491180	+	0.871058i	$0.336566\pi$
$620$	19.6154	0.787775
$621$	3.20650	0.128673
$622$	31.8409	1.27670
$623$	1.20804	0.0483990
$624$	11.2441	0.450126
$625$	−29.8338	−1.19335
$626$	31.9380	1.27650
$627$	−2.08303	−0.0831882
$628$	5.62598	0.224501
$629$	34.4991	1.37557
$630$	0.925463	0.0368713
$631$	33.2525	1.32376	0.661880	−	0.749610i	$-0.269759\pi$
$631$	33.2525	1.32376	0.661880	+	0.749610i	$0.269759\pi$
$632$	−6.93755	−0.275961
$633$	−21.9492	−0.872401
$634$	−2.50100	−0.0993274
$635$	−3.68622	−0.146283
$636$	5.20009	0.206197
$637$	15.8555	0.628217
$638$	−22.2877	−0.882379
$639$	−0.642126	−0.0254021
$640$	29.9427	1.18359
$641$	6.51913	0.257490	0.128745	−	0.991678i	$-0.458905\pi$
$641$	6.51913	0.257490	0.128745	+	0.991678i	$0.458905\pi$
$642$	21.1781	0.835833
$643$	−33.1770	−1.30837	−0.654187	−	0.756332i	$-0.726989\pi$
$643$	−33.1770	−1.30837	−0.654187	+	0.756332i	$0.726989\pi$
$644$	0.693308	0.0273202
$645$	19.1921	0.755687
$646$	−14.4467	−0.568398
$647$	−2.81435	−0.110643	−0.0553217	−	0.998469i	$-0.517618\pi$
$647$	−2.81435	−0.110643	−0.0553217	+	0.998469i	$0.517618\pi$
$648$	1.36857	0.0537626
$649$	1.75654	0.0689503
$650$	15.1097	0.592649
$651$	−0.936247	−0.0366944
$652$	12.4013	0.485673
$653$	−20.2338	−0.791811	−0.395905	−	0.918291i	$-0.629569\pi$
$653$	−20.2338	−0.791811	−0.395905	+	0.918291i	$0.629569\pi$
$654$	24.2337	0.947613
$655$	−35.9396	−1.40428
$656$	2.05953	0.0804113
$657$	−2.23420	−0.0871645
$658$	0.0365861	0.00142628
$659$	12.5571	0.489155	0.244578	−	0.969630i	$-0.421351\pi$
$659$	12.5571	0.489155	0.244578	+	0.969630i	$0.421351\pi$
$660$	6.40534	0.249328
$661$	−36.0351	−1.40160	−0.700802	−	0.713356i	$-0.747174\pi$
$661$	−36.0351	−1.40160	−0.700802	+	0.713356i	$0.747174\pi$
$662$	−28.6561	−1.11375
$663$	−15.3650	−0.596728
$664$	23.7221	0.920597
$665$	−0.611042	−0.0236952
$666$	−9.19381	−0.356253
$667$	−22.6524	−0.877103
$668$	−20.1578	−0.779928
$669$	9.63701	0.372588
$670$	39.3874	1.52167
$671$	−13.4670	−0.519888
$672$	1.07426	0.0414404
$673$	24.7881	0.955512	0.477756	−	0.878493i	$-0.341450\pi$
$673$	24.7881	0.955512	0.477756	+	0.878493i	$0.341450\pi$
$674$	−34.3666	−1.32375
$675$	3.69006	0.142030
$676$	−9.69966	−0.373064
$677$	−23.4220	−0.900179	−0.450090	−	0.892983i	$-0.648608\pi$
$677$	−23.4220	−0.900179	−0.450090	+	0.892983i	$0.648608\pi$
$678$	−13.2356	−0.508309
$679$	0.243172	0.00933209
$680$	−27.2483	−1.04492
$681$	7.98024	0.305804
$682$	−16.9346	−0.648459
$683$	−19.3399	−0.740019	−0.370010	−	0.929028i	$-0.620646\pi$
$683$	−19.3399	−0.740019	−0.370010	+	0.929028i	$0.620646\pi$
$684$	1.47318	0.0563284
$685$	−3.55623	−0.135877
$686$	4.38562	0.167444
$687$	−12.3184	−0.469978
$688$	32.1784	1.22679
$689$	−9.54307	−0.363562
$690$	17.0134	0.647689
$691$	16.4309	0.625060	0.312530	−	0.949908i	$-0.398823\pi$
$691$	16.4309	0.625060	0.312530	+	0.949908i	$0.398823\pi$
$692$	7.06402	0.268534
$693$	−0.305728	−0.0116136
$694$	−33.5100	−1.27202
$695$	28.5771	1.08399
$696$	−9.66829	−0.366476
$697$	−2.81434	−0.106601
$698$	−9.02703	−0.341678
$699$	28.2070	1.06689
$700$	0.797863	0.0301564
$701$	21.9832	0.830295	0.415148	−	0.909754i	$-0.363730\pi$
$701$	21.9832	0.830295	0.415148	+	0.909754i	$0.363730\pi$
$702$	4.09469	0.154544
$703$	6.07026	0.228944
$704$	2.10412	0.0793020
$705$	0.343542	0.0129385
$706$	33.5079	1.26109
$707$	0.345711	0.0130018
$708$	−1.24228	−0.0466877
$709$	−37.8799	−1.42261	−0.711305	−	0.702883i	$-0.751896\pi$
$709$	−37.8799	−1.42261	−0.711305	+	0.702883i	$0.751896\pi$
$710$	−3.40706	−0.127865
$711$	−5.06919	−0.190109
$712$	9.47870	0.355229
$713$	−17.2117	−0.644582
$714$	−2.12035	−0.0793522
$715$	−11.7549	−0.439609
$716$	25.3866	0.948743
$717$	−20.9946	−0.784059
$718$	−13.4738	−0.502839
$719$	−28.6312	−1.06776	−0.533881	−	0.845560i	$-0.679267\pi$
$719$	−28.6312	−1.06776	−0.533881	+	0.845560i	$0.679267\pi$
$720$	14.5702	0.542998
$721$	0.974186	0.0362806
$722$	31.6561	1.17812
$723$	−8.23978	−0.306441
$724$	−4.60637	−0.171195
$725$	−26.0685	−0.968158
$726$	14.2690	0.529572
$727$	−22.0267	−0.816924	−0.408462	−	0.912775i	$-0.633935\pi$
$727$	−22.0267	−0.816924	−0.408462	+	0.912775i	$0.633935\pi$
$728$	−0.543050	−0.0201268
$729$	1.00000	0.0370370
$730$	−11.8545	−0.438754
$731$	−43.9715	−1.62634
$732$	9.52427	0.352027
$733$	−50.3392	−1.85932	−0.929660	−	0.368418i	$-0.879900\pi$
$733$	−50.3392	−1.85932	−0.929660	+	0.368418i	$0.879900\pi$
$734$	13.2828	0.490276
$735$	20.5456	0.757834
$736$	19.7488	0.727951
$737$	−13.0117	−0.479291
$738$	0.750005	0.0276081
$739$	−13.4372	−0.494294	−0.247147	−	0.968978i	$-0.579493\pi$
$739$	−13.4372	−0.494294	−0.247147	+	0.968978i	$0.579493\pi$
$740$	−18.6661	−0.686180
$741$	−2.70354	−0.0993171
$742$	−1.31693	−0.0483460
$743$	−16.5244	−0.606221	−0.303110	−	0.952955i	$-0.598025\pi$
$743$	−16.5244	−0.606221	−0.303110	+	0.952955i	$0.598025\pi$
$744$	−7.34613	−0.269322
$745$	−17.9962	−0.659328
$746$	24.9672	0.914115
$747$	17.3335	0.634199
$748$	−14.6754	−0.536587
$749$	−2.05229	−0.0749889
$750$	−6.95043	−0.253794
$751$	−17.5119	−0.639019	−0.319509	−	0.947583i	$-0.603518\pi$
$751$	−17.5119	−0.639019	−0.319509	+	0.947583i	$0.603518\pi$
$752$	0.575999	0.0210045
$753$	−13.1347	−0.478656
$754$	−28.9270	−1.05346
$755$	21.1315	0.769054
$756$	0.216219	0.00786383
$757$	39.0056	1.41768	0.708841	−	0.705368i	$-0.249218\pi$
$757$	39.0056	1.41768	0.708841	+	0.705368i	$0.249218\pi$
$758$	−25.3737	−0.921615
$759$	−5.62040	−0.204007
$760$	−4.79446	−0.173913
$761$	26.6983	0.967812	0.483906	−	0.875120i	$-0.339218\pi$
$761$	26.6983	0.967812	0.483906	+	0.875120i	$0.339218\pi$
$762$	−2.25070	−0.0815344
$763$	−2.34839	−0.0850175
$764$	−24.6279	−0.891006
$765$	−19.9100	−0.719848
$766$	−22.8831	−0.826799
$767$	2.27980	0.0823187
$768$	20.6830	0.746335
$769$	−0.203941	−0.00735430	−0.00367715	−	0.999993i	$-0.501170\pi$
$769$	−0.203941	−0.00735430	−0.00367715	+	0.999993i	$0.501170\pi$
$770$	−1.62216	−0.0584587
$771$	−13.3318	−0.480133
$772$	−0.0742938	−0.00267389
$773$	−8.86603	−0.318889	−0.159444	−	0.987207i	$-0.550970\pi$
$773$	−8.86603	−0.318889	−0.159444	+	0.987207i	$0.550970\pi$
$774$	11.7182	0.421200
$775$	−19.8073	−0.711498
$776$	1.90802	0.0684938
$777$	0.890935	0.0319621
$778$	40.6133	1.45606
$779$	−0.495195	−0.0177422
$780$	8.31342	0.297668
$781$	1.12553	0.0402745
$782$	−38.9799	−1.39392
$783$	−7.06451	−0.252465
$784$	34.4476	1.23027
$785$	−13.3787	−0.477507
$786$	−21.9437	−0.782707
$787$	30.9914	1.10473	0.552363	−	0.833604i	$-0.313726\pi$
$787$	30.9914	1.10473	0.552363	+	0.833604i	$0.313726\pi$
$788$	20.7228	0.738220
$789$	4.79635	0.170755
$790$	−26.8966	−0.956940
$791$	1.28261	0.0456042
$792$	−2.39885	−0.0852394
$793$	−17.4787	−0.620687
$794$	−3.64141	−0.129229
$795$	−12.3659	−0.438574
$796$	−27.9963	−0.992304
$797$	−46.2436	−1.63803	−0.819017	−	0.573769i	$-0.805481\pi$
$797$	−46.2436	−1.63803	−0.819017	+	0.573769i	$0.805481\pi$
$798$	−0.373085	−0.0132071
$799$	−0.787099	−0.0278455
$800$	22.7270	0.803522
$801$	6.92598	0.244717
$802$	11.3811	0.401882
$803$	3.91614	0.138197
$804$	9.20223	0.324538
$805$	−1.64870	−0.0581091
$806$	−21.9792	−0.774185
$807$	−18.3812	−0.647049
$808$	2.71258	0.0954281
$809$	22.6540	0.796472	0.398236	−	0.917283i	$-0.369622\pi$
$809$	22.6540	0.796472	0.398236	+	0.917283i	$0.369622\pi$
$810$	5.30591	0.186431
$811$	−20.7145	−0.727385	−0.363693	−	0.931519i	$-0.618484\pi$
$811$	−20.7145	−0.727385	−0.363693	+	0.931519i	$0.618484\pi$
$812$	−1.52748	−0.0536042
$813$	−21.4156	−0.751077
$814$	16.1150	0.564831
$815$	−29.4906	−1.03301
$816$	−33.3821	−1.16861
$817$	−7.73697	−0.270682
$818$	−8.15708	−0.285205
$819$	−0.396801	−0.0138653
$820$	1.52273	0.0531760
$821$	−1.71327	−0.0597935	−0.0298967	−	0.999553i	$-0.509518\pi$
$821$	−1.71327	−0.0597935	−0.0298967	+	0.999553i	$0.509518\pi$
$822$	−2.17134	−0.0757341
$823$	14.9115	0.519783	0.259891	−	0.965638i	$-0.416313\pi$
$823$	14.9115	0.519783	0.259891	+	0.965638i	$0.416313\pi$
$824$	7.64382	0.266285
$825$	−6.46798	−0.225186
$826$	0.314609	0.0109466
$827$	28.1663	0.979438	0.489719	−	0.871880i	$-0.337099\pi$
$827$	28.1663	0.979438	0.489719	+	0.871880i	$0.337099\pi$
$828$	3.97491	0.138138
$829$	−13.7757	−0.478448	−0.239224	−	0.970964i	$-0.576893\pi$
$829$	−13.7757	−0.478448	−0.239224	+	0.970964i	$0.576893\pi$
$830$	91.9699	3.19232
$831$	13.8826	0.481582
$832$	2.73091	0.0946774
$833$	−47.0724	−1.63096
$834$	17.4484	0.604189
$835$	47.9356	1.65888
$836$	−2.58221	−0.0893075
$837$	−5.36774	−0.185536
$838$	−27.3278	−0.944023
$839$	−3.41169	−0.117785	−0.0588923	−	0.998264i	$-0.518757\pi$
$839$	−3.41169	−0.117785	−0.0588923	+	0.998264i	$0.518757\pi$
$840$	−0.703685	−0.0242794
$841$	20.9073	0.720941
$842$	−53.9709	−1.85996
$843$	−14.0794	−0.484920
$844$	−27.2091	−0.936574
$845$	23.0660	0.793494
$846$	0.209757	0.00721161
$847$	−1.38275	−0.0475119
$848$	−20.7333	−0.711984
$849$	−25.5729	−0.877660
$850$	−44.8582	−1.53862
$851$	16.3787	0.561454
$852$	−0.796005	−0.0272707
$853$	−23.8801	−0.817639	−0.408820	−	0.912615i	$-0.634060\pi$
$853$	−23.8801	−0.817639	−0.408820	+	0.912615i	$0.634060\pi$
$854$	−2.41204	−0.0825382
$855$	−3.50325	−0.119809
$856$	−16.1030	−0.550389
$857$	−16.6752	−0.569615	−0.284808	−	0.958585i	$-0.591930\pi$
$857$	−16.6752	−0.569615	−0.284808	+	0.958585i	$0.591930\pi$
$858$	−7.17722	−0.245026
$859$	6.13355	0.209274	0.104637	−	0.994510i	$-0.466632\pi$
$859$	6.13355	0.209274	0.104637	+	0.994510i	$0.466632\pi$
$860$	23.7913	0.811276
$861$	−0.0726801	−0.00247693
$862$	43.5514	1.48337
$863$	−7.77031	−0.264505	−0.132252	−	0.991216i	$-0.542221\pi$
$863$	−7.77031	−0.264505	−0.132252	+	0.991216i	$0.542221\pi$
$864$	6.15899	0.209533
$865$	−16.7984	−0.571163
$866$	33.5300	1.13940
$867$	28.6164	0.971863
$868$	−1.16061	−0.0393936
$869$	8.88533	0.301414
$870$	−37.4836	−1.27081
$871$	−16.8877	−0.572218
$872$	−18.4263	−0.623995
$873$	1.39417	0.0471854
$874$	−6.85868	−0.231998
$875$	0.673539	0.0227698
$876$	−2.76961	−0.0935763
$877$	30.2054	1.01996	0.509982	−	0.860185i	$-0.329652\pi$
$877$	30.2054	1.01996	0.509982	+	0.860185i	$0.329652\pi$
$878$	48.6645	1.64235
$879$	−22.6692	−0.764614
$880$	−25.5388	−0.860911
$881$	12.7391	0.429192	0.214596	−	0.976703i	$-0.431157\pi$
$881$	12.7391	0.429192	0.214596	+	0.976703i	$0.431157\pi$
$882$	12.5445	0.422397
$883$	−25.4623	−0.856873	−0.428437	−	0.903572i	$-0.640935\pi$
$883$	−25.4623	−0.856873	−0.428437	+	0.903572i	$0.640935\pi$
$884$	−19.0471	−0.640623
$885$	2.95416	0.0993031
$886$	63.3478	2.12821
$887$	21.9460	0.736875	0.368437	−	0.929653i	$-0.379893\pi$
$887$	21.9460	0.736875	0.368437	+	0.929653i	$0.379893\pi$
$888$	6.99060	0.234589
$889$	0.218107	0.00731507
$890$	36.7486	1.23182
$891$	−1.75281	−0.0587214
$892$	11.9464	0.399996
$893$	−0.138493	−0.00463450
$894$	−10.9880	−0.367492
$895$	−60.3700	−2.01795
$896$	−1.77166	−0.0591869
$897$	−7.29465	−0.243561
$898$	−21.2336	−0.708575
$899$	37.9204	1.26472
$900$	4.57434	0.152478
$901$	28.3319	0.943872
$902$	−1.31462	−0.0437720
$903$	−1.13556	−0.0377891
$904$	10.0638	0.334717
$905$	10.9541	0.364125
$906$	12.9023	0.428650
$907$	14.5492	0.483097	0.241548	−	0.970389i	$-0.422345\pi$
$907$	14.5492	0.483097	0.241548	+	0.970389i	$0.422345\pi$
$908$	9.89263	0.328298
$909$	1.98205	0.0657404
$910$	−2.10539	−0.0697929
$911$	−36.3955	−1.20584	−0.602919	−	0.797802i	$-0.705996\pi$
$911$	−36.3955	−1.20584	−0.602919	+	0.797802i	$0.705996\pi$
$912$	−5.87372	−0.194498
$913$	−30.3823	−1.00551
$914$	57.9276	1.91608
$915$	−22.6489	−0.748750
$916$	−15.2704	−0.504550
$917$	2.12648	0.0702226
$918$	−12.1565	−0.401224
$919$	−25.4492	−0.839490	−0.419745	−	0.907642i	$-0.637881\pi$
$919$	−25.4492	−0.839490	−0.419745	+	0.907642i	$0.637881\pi$
$920$	−12.9363	−0.426498
$921$	−16.8561	−0.555426
$922$	−20.4341	−0.672960
$923$	1.46081	0.0480831
$924$	−0.378992	−0.0124679
$925$	18.8486	0.619740
$926$	−60.9180	−2.00189
$927$	5.58525	0.183444
$928$	−43.5103	−1.42829
$929$	8.13671	0.266957	0.133478	−	0.991052i	$-0.457385\pi$
$929$	8.13671	0.266957	0.133478	+	0.991052i	$0.457385\pi$
$930$	−28.4807	−0.933920
$931$	−8.28260	−0.271451
$932$	34.9665	1.14537
$933$	−17.6904	−0.579156
$934$	−22.9821	−0.751997
$935$	34.8985	1.14130
$936$	−3.11344	−0.101766
$937$	−12.6893	−0.414542	−0.207271	−	0.978284i	$-0.566458\pi$
$937$	−12.6893	−0.414542	−0.207271	+	0.978284i	$0.566458\pi$
$938$	−2.33048	−0.0760929
$939$	−17.7443	−0.579063
$940$	0.425869	0.0138903
$941$	−1.19595	−0.0389870	−0.0194935	−	0.999810i	$-0.506205\pi$
$941$	−1.19595	−0.0389870	−0.0194935	+	0.999810i	$0.506205\pi$
$942$	−8.16867	−0.266150
$943$	−1.33613	−0.0435103
$944$	4.95309	0.161209
$945$	−0.514175	−0.0167261
$946$	−20.5397	−0.667804
$947$	11.2657	0.366085	0.183043	−	0.983105i	$-0.441405\pi$
$947$	11.2657	0.366085	0.183043	+	0.983105i	$0.441405\pi$
$948$	−6.28397	−0.204094
$949$	5.08271	0.164992
$950$	−7.89300	−0.256083
$951$	1.38952	0.0450583
$952$	1.61223	0.0522527
$953$	−41.9060	−1.35747	−0.678735	−	0.734384i	$-0.737471\pi$
$953$	−41.9060	−1.35747	−0.678735	+	0.734384i	$0.737471\pi$
$954$	−7.55029	−0.244450
$955$	58.5657	1.89514
$956$	−26.0258	−0.841735
$957$	12.3828	0.400278
$958$	−4.73377	−0.152941
$959$	0.210416	0.00679468
$960$	3.53872	0.114212
$961$	−2.18740	−0.0705614
$962$	20.9155	0.674343
$963$	−11.7663	−0.379163
$964$	−10.2144	−0.328983
$965$	0.176672	0.00568728
$966$	−1.00665	−0.0323885
$967$	46.3026	1.48899	0.744496	−	0.667627i	$-0.232690\pi$
$967$	46.3026	1.48899	0.744496	+	0.667627i	$0.232690\pi$
$968$	−10.8496	−0.348718
$969$	8.02640	0.257845
$970$	7.39732	0.237514
$971$	−45.2839	−1.45323	−0.726615	−	0.687045i	$-0.758907\pi$
$971$	−45.2839	−1.45323	−0.726615	+	0.687045i	$0.758907\pi$
$972$	1.23964	0.0397615
$973$	−1.69086	−0.0542064
$974$	31.3331	1.00398
$975$	−8.39472	−0.268846
$976$	−37.9743	−1.21553
$977$	41.7499	1.33570	0.667849	−	0.744297i	$-0.267215\pi$
$977$	41.7499	1.33570	0.667849	+	0.744297i	$0.267215\pi$
$978$	−18.0061	−0.575772
$979$	−12.1399	−0.387994
$980$	25.4691	0.813580
$981$	−13.4639	−0.429870
$982$	1.78040	0.0568150
$983$	−43.4974	−1.38735	−0.693676	−	0.720287i	$-0.744010\pi$
$983$	−43.4974	−1.38735	−0.693676	+	0.720287i	$0.744010\pi$
$984$	−0.570274	−0.0181797
$985$	−49.2793	−1.57017
$986$	85.8797	2.73497
$987$	−0.0203268	−0.000647008 0
$988$	−3.35142	−0.106623
$989$	−20.8758	−0.663811
$990$	−9.30026	−0.295582
$991$	9.22473	0.293033	0.146517	−	0.989208i	$-0.453194\pi$
$991$	9.22473	0.293033	0.146517	+	0.989208i	$0.453194\pi$
$992$	−33.0598	−1.04965
$993$	15.9210	0.505236
$994$	0.201590	0.00639403
$995$	66.5759	2.11060
$996$	21.4873	0.680851
$997$	40.5073	1.28288	0.641440	−	0.767174i	$-0.278338\pi$
$997$	40.5073	1.28288	0.641440	+	0.767174i	$0.278338\pi$
$998$	37.1631	1.17638
$999$	5.10795	0.161609

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6033.2.a.b.1.16	✓	71

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6033.2.a.b.1.16	✓	71	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 6033 = 3 \cdot 2011 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6033.a (trivial)

\(f(q)\)	\(=\)	\(q-1.79990 q^{2} +1.00000 q^{3} +1.23964 q^{4} -2.94789 q^{5} -1.79990 q^{6} +0.174421 q^{7} +1.36857 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.79990 q^{2} +1.00000 q^{3} +1.23964 q^{4} -2.94789 q^{5} -1.79990 q^{6} +0.174421 q^{7} +1.36857 q^{8} +1.00000 q^{9} +5.30591 q^{10} -1.75281 q^{11} +1.23964 q^{12} -2.27496 q^{13} -0.313941 q^{14} -2.94789 q^{15} -4.94257 q^{16} +6.75399 q^{17} -1.79990 q^{18} +1.18839 q^{19} -3.65432 q^{20} +0.174421 q^{21} +3.15489 q^{22} +3.20650 q^{23} +1.36857 q^{24} +3.69006 q^{25} +4.09469 q^{26} +1.00000 q^{27} +0.216219 q^{28} -7.06451 q^{29} +5.30591 q^{30} -5.36774 q^{31} +6.15899 q^{32} -1.75281 q^{33} -12.1565 q^{34} -0.514175 q^{35} +1.23964 q^{36} +5.10795 q^{37} -2.13899 q^{38} -2.27496 q^{39} -4.03440 q^{40} -0.416693 q^{41} -0.313941 q^{42} -6.51045 q^{43} -2.17286 q^{44} -2.94789 q^{45} -5.77138 q^{46} -0.116538 q^{47} -4.94257 q^{48} -6.96958 q^{49} -6.64174 q^{50} +6.75399 q^{51} -2.82013 q^{52} +4.19484 q^{53} -1.79990 q^{54} +5.16710 q^{55} +0.238708 q^{56} +1.18839 q^{57} +12.7154 q^{58} -1.00213 q^{59} -3.65432 q^{60} +7.68309 q^{61} +9.66139 q^{62} +0.174421 q^{63} -1.20042 q^{64} +6.70632 q^{65} +3.15489 q^{66} +7.42331 q^{67} +8.37251 q^{68} +3.20650 q^{69} +0.925463 q^{70} -0.642126 q^{71} +1.36857 q^{72} -2.23420 q^{73} -9.19381 q^{74} +3.69006 q^{75} +1.47318 q^{76} -0.305728 q^{77} +4.09469 q^{78} -5.06919 q^{79} +14.5702 q^{80} +1.00000 q^{81} +0.750005 q^{82} +17.3335 q^{83} +0.216219 q^{84} -19.9100 q^{85} +11.7182 q^{86} -7.06451 q^{87} -2.39885 q^{88} +6.92598 q^{89} +5.30591 q^{90} -0.396801 q^{91} +3.97491 q^{92} -5.36774 q^{93} +0.209757 q^{94} -3.50325 q^{95} +6.15899 q^{96} +1.39417 q^{97} +12.5445 q^{98} -1.75281 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 71 q - 11 q^{2} + 71 q^{3} + 53 q^{4} - 8 q^{5} - 11 q^{6} - 46 q^{7} - 33 q^{8} + 71 q^{9}+O(q^{10}) \) 71 * q - 11 * q^2 + 71 * q^3 + 53 * q^4 - 8 * q^5 - 11 * q^6 - 46 * q^7 - 33 * q^8 + 71 * q^9	\( 71 q - 11 q^{2} + 71 q^{3} + 53 q^{4} - 8 q^{5} - 11 q^{6} - 46 q^{7} - 33 q^{8} + 71 q^{9} - 41 q^{10} - 18 q^{11} + 53 q^{12} - 67 q^{13} - 7 q^{14} - 8 q^{15} + 21 q^{16} - 25 q^{17} - 11 q^{18} - 43 q^{19} - 8 q^{20} - 46 q^{21} - 49 q^{22} - 75 q^{23} - 33 q^{24} + 19 q^{25} + 71 q^{27} - 89 q^{28} - 35 q^{29} - 41 q^{30} - 82 q^{31} - 62 q^{32} - 18 q^{33} - 28 q^{34} - 51 q^{35} + 53 q^{36} - 66 q^{37} - 29 q^{38} - 67 q^{39} - 102 q^{40} + q^{41} - 7 q^{42} - 112 q^{43} - 25 q^{44} - 8 q^{45} - 36 q^{46} - 67 q^{47} + 21 q^{48} + 7 q^{49} - 24 q^{50} - 25 q^{51} - 134 q^{52} - 40 q^{53} - 11 q^{54} - 112 q^{55} + 9 q^{56} - 43 q^{57} - 47 q^{58} - 18 q^{59} - 8 q^{60} - 144 q^{61} - 19 q^{62} - 46 q^{63} - 17 q^{64} - 31 q^{65} - 49 q^{66} - 85 q^{67} - 22 q^{68} - 75 q^{69} - 11 q^{70} - 44 q^{71} - 33 q^{72} - 98 q^{73} + 6 q^{74} + 19 q^{75} - 85 q^{76} - 39 q^{77} - 126 q^{79} + 21 q^{80} + 71 q^{81} - 69 q^{82} - 43 q^{83} - 89 q^{84} - 112 q^{85} + 32 q^{86} - 35 q^{87} - 85 q^{88} + 8 q^{89} - 41 q^{90} - 40 q^{91} - 96 q^{92} - 82 q^{93} - 99 q^{94} - 103 q^{95} - 62 q^{96} - 67 q^{97} - 11 q^{98} - 18 q^{99}+O(q^{100}) \) 71 * q - 11 * q^2 + 71 * q^3 + 53 * q^4 - 8 * q^5 - 11 * q^6 - 46 * q^7 - 33 * q^8 + 71 * q^9 - 41 * q^10 - 18 * q^11 + 53 * q^12 - 67 * q^13 - 7 * q^14 - 8 * q^15 + 21 * q^16 - 25 * q^17 - 11 * q^18 - 43 * q^19 - 8 * q^20 - 46 * q^21 - 49 * q^22 - 75 * q^23 - 33 * q^24 + 19 * q^25 + 71 * q^27 - 89 * q^28 - 35 * q^29 - 41 * q^30 - 82 * q^31 - 62 * q^32 - 18 * q^33 - 28 * q^34 - 51 * q^35 + 53 * q^36 - 66 * q^37 - 29 * q^38 - 67 * q^39 - 102 * q^40 + q^41 - 7 * q^42 - 112 * q^43 - 25 * q^44 - 8 * q^45 - 36 * q^46 - 67 * q^47 + 21 * q^48 + 7 * q^49 - 24 * q^50 - 25 * q^51 - 134 * q^52 - 40 * q^53 - 11 * q^54 - 112 * q^55 + 9 * q^56 - 43 * q^57 - 47 * q^58 - 18 * q^59 - 8 * q^60 - 144 * q^61 - 19 * q^62 - 46 * q^63 - 17 * q^64 - 31 * q^65 - 49 * q^66 - 85 * q^67 - 22 * q^68 - 75 * q^69 - 11 * q^70 - 44 * q^71 - 33 * q^72 - 98 * q^73 + 6 * q^74 + 19 * q^75 - 85 * q^76 - 39 * q^77 - 126 * q^79 + 21 * q^80 + 71 * q^81 - 69 * q^82 - 43 * q^83 - 89 * q^84 - 112 * q^85 + 32 * q^86 - 35 * q^87 - 85 * q^88 + 8 * q^89 - 41 * q^90 - 40 * q^91 - 96 * q^92 - 82 * q^93 - 99 * q^94 - 103 * q^95 - 62 * q^96 - 67 * q^97 - 11 * q^98 - 18 * q^99

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