LMFDB - Embedded newform 6022.2.a.b.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6022,2,Mod(1,6022)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6022, 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("6022.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6022 = 2 \cdot 3011 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6022.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:	$48.0859120972$
Analytic rank:	$1$
Dimension:	$54$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Character	$\chi$	$=$	6022.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -2.46224 q^{3} +1.00000 q^{4} -1.05561 q^{5} -2.46224 q^{6} +2.87810 q^{7} +1.00000 q^{8} +3.06261 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.46224 q^{3} +1.00000 q^{4} -1.05561 q^{5} -2.46224 q^{6} +2.87810 q^{7} +1.00000 q^{8} +3.06261 q^{9} -1.05561 q^{10} +6.18577 q^{11} -2.46224 q^{12} +0.417204 q^{13} +2.87810 q^{14} +2.59915 q^{15} +1.00000 q^{16} -4.57818 q^{17} +3.06261 q^{18} -5.47986 q^{19} -1.05561 q^{20} -7.08657 q^{21} +6.18577 q^{22} -0.803349 q^{23} -2.46224 q^{24} -3.88570 q^{25} +0.417204 q^{26} -0.154168 q^{27} +2.87810 q^{28} -10.3368 q^{29} +2.59915 q^{30} +3.70756 q^{31} +1.00000 q^{32} -15.2308 q^{33} -4.57818 q^{34} -3.03814 q^{35} +3.06261 q^{36} -9.14227 q^{37} -5.47986 q^{38} -1.02726 q^{39} -1.05561 q^{40} -9.50822 q^{41} -7.08657 q^{42} +5.20566 q^{43} +6.18577 q^{44} -3.23291 q^{45} -0.803349 q^{46} +8.42645 q^{47} -2.46224 q^{48} +1.28346 q^{49} -3.88570 q^{50} +11.2726 q^{51} +0.417204 q^{52} +12.1992 q^{53} -0.154168 q^{54} -6.52973 q^{55} +2.87810 q^{56} +13.4927 q^{57} -10.3368 q^{58} -3.07139 q^{59} +2.59915 q^{60} -7.18489 q^{61} +3.70756 q^{62} +8.81451 q^{63} +1.00000 q^{64} -0.440403 q^{65} -15.2308 q^{66} -1.91366 q^{67} -4.57818 q^{68} +1.97804 q^{69} -3.03814 q^{70} +13.5210 q^{71} +3.06261 q^{72} -9.78968 q^{73} -9.14227 q^{74} +9.56751 q^{75} -5.47986 q^{76} +17.8033 q^{77} -1.02726 q^{78} -12.0839 q^{79} -1.05561 q^{80} -8.80824 q^{81} -9.50822 q^{82} -9.67676 q^{83} -7.08657 q^{84} +4.83275 q^{85} +5.20566 q^{86} +25.4516 q^{87} +6.18577 q^{88} -11.9101 q^{89} -3.23291 q^{90} +1.20076 q^{91} -0.803349 q^{92} -9.12890 q^{93} +8.42645 q^{94} +5.78457 q^{95} -2.46224 q^{96} +15.0019 q^{97} +1.28346 q^{98} +18.9446 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 54 q + 54 q^{2} - 22 q^{3} + 54 q^{4} - 14 q^{5} - 22 q^{6} - 20 q^{7} + 54 q^{8} + 32 q^{9}+O(q^{10}) $ 54 * q + 54 * q^2 - 22 * q^3 + 54 * q^4 - 14 * q^5 - 22 * q^6 - 20 * q^7 + 54 * q^8 + 32 * q^9	\( 54 q + 54 q^{2} - 22 q^{3} + 54 q^{4} - 14 q^{5} - 22 q^{6} - 20 q^{7} + 54 q^{8} + 32 q^{9} - 14 q^{10} - 22 q^{11} - 22 q^{12} - 24 q^{13} - 20 q^{14} - 32 q^{15} + 54 q^{16} - 67 q^{17} + 32 q^{18} - 54 q^{19} - 14 q^{20} - 18 q^{21} - 22 q^{22} - 52 q^{23} - 22 q^{24} + 20 q^{25} - 24 q^{26} - 82 q^{27} - 20 q^{28} - 30 q^{29} - 32 q^{30} - 78 q^{31} + 54 q^{32} - 48 q^{33} - 67 q^{34} - 71 q^{35} + 32 q^{36} - 15 q^{37} - 54 q^{38} - 39 q^{39} - 14 q^{40} - 61 q^{41} - 18 q^{42} - 53 q^{43} - 22 q^{44} - 14 q^{45} - 52 q^{46} - 96 q^{47} - 22 q^{48} + 6 q^{49} + 20 q^{50} - 13 q^{51} - 24 q^{52} - 39 q^{53} - 82 q^{54} - 75 q^{55} - 20 q^{56} - 17 q^{57} - 30 q^{58} - 78 q^{59} - 32 q^{60} - 23 q^{61} - 78 q^{62} - 52 q^{63} + 54 q^{64} - 43 q^{65} - 48 q^{66} - 54 q^{67} - 67 q^{68} + 7 q^{69} - 71 q^{70} - 41 q^{71} + 32 q^{72} - 62 q^{73} - 15 q^{74} - 81 q^{75} - 54 q^{76} - 85 q^{77} - 39 q^{78} - 45 q^{79} - 14 q^{80} + 22 q^{81} - 61 q^{82} - 117 q^{83} - 18 q^{84} - 53 q^{86} - 84 q^{87} - 22 q^{88} - 60 q^{89} - 14 q^{90} - 60 q^{91} - 52 q^{92} + 26 q^{93} - 96 q^{94} - 44 q^{95} - 22 q^{96} - 48 q^{97} + 6 q^{98} + 7 q^{99}+O(q^{100}) \) 54 * q + 54 * q^2 - 22 * q^3 + 54 * q^4 - 14 * q^5 - 22 * q^6 - 20 * q^7 + 54 * q^8 + 32 * q^9 - 14 * q^10 - 22 * q^11 - 22 * q^12 - 24 * q^13 - 20 * q^14 - 32 * q^15 + 54 * q^16 - 67 * q^17 + 32 * q^18 - 54 * q^19 - 14 * q^20 - 18 * q^21 - 22 * q^22 - 52 * q^23 - 22 * q^24 + 20 * q^25 - 24 * q^26 - 82 * q^27 - 20 * q^28 - 30 * q^29 - 32 * q^30 - 78 * q^31 + 54 * q^32 - 48 * q^33 - 67 * q^34 - 71 * q^35 + 32 * q^36 - 15 * q^37 - 54 * q^38 - 39 * q^39 - 14 * q^40 - 61 * q^41 - 18 * q^42 - 53 * q^43 - 22 * q^44 - 14 * q^45 - 52 * q^46 - 96 * q^47 - 22 * q^48 + 6 * q^49 + 20 * q^50 - 13 * q^51 - 24 * q^52 - 39 * q^53 - 82 * q^54 - 75 * q^55 - 20 * q^56 - 17 * q^57 - 30 * q^58 - 78 * q^59 - 32 * q^60 - 23 * q^61 - 78 * q^62 - 52 * q^63 + 54 * q^64 - 43 * q^65 - 48 * q^66 - 54 * q^67 - 67 * q^68 + 7 * q^69 - 71 * q^70 - 41 * q^71 + 32 * q^72 - 62 * q^73 - 15 * q^74 - 81 * q^75 - 54 * q^76 - 85 * q^77 - 39 * q^78 - 45 * q^79 - 14 * q^80 + 22 * q^81 - 61 * q^82 - 117 * q^83 - 18 * q^84 - 53 * q^86 - 84 * q^87 - 22 * q^88 - 60 * q^89 - 14 * q^90 - 60 * q^91 - 52 * q^92 + 26 * q^93 - 96 * q^94 - 44 * q^95 - 22 * q^96 - 48 * q^97 + 6 * q^98 + 7 * 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 $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−2.46224	−1.42157	−0.710787	−	0.703408i	$-0.751661\pi$
$3$	−2.46224	−1.42157	−0.710787	+	0.703408i	$0.751661\pi$
$4$	1.00000	0.500000
$5$	−1.05561	−0.472081	−0.236040	−	0.971743i	$-0.575850\pi$
$5$	−1.05561	−0.472081	−0.236040	+	0.971743i	$0.575850\pi$
$6$	−2.46224	−1.00520
$7$	2.87810	1.08782	0.543910	−	0.839144i	$-0.316943\pi$
$7$	2.87810	1.08782	0.543910	+	0.839144i	$0.316943\pi$
$8$	1.00000	0.353553
$9$	3.06261	1.02087
$10$	−1.05561	−0.333812
$11$	6.18577	1.86508	0.932540	−	0.361067i	$-0.117588\pi$
$11$	6.18577	1.86508	0.932540	+	0.361067i	$0.117588\pi$
$12$	−2.46224	−0.710787
$13$	0.417204	0.115712	0.0578558	−	0.998325i	$-0.481574\pi$
$13$	0.417204	0.115712	0.0578558	+	0.998325i	$0.481574\pi$
$14$	2.87810	0.769205
$15$	2.59915	0.671098
$16$	1.00000	0.250000
$17$	−4.57818	−1.11037	−0.555186	−	0.831726i	$-0.687353\pi$
$17$	−4.57818	−1.11037	−0.555186	+	0.831726i	$0.687353\pi$
$18$	3.06261	0.721865
$19$	−5.47986	−1.25717	−0.628583	−	0.777742i	$-0.716365\pi$
$19$	−5.47986	−1.25717	−0.628583	+	0.777742i	$0.716365\pi$
$20$	−1.05561	−0.236040
$21$	−7.08657	−1.54642
$22$	6.18577	1.31881
$23$	−0.803349	−0.167510	−0.0837549	−	0.996486i	$-0.526691\pi$
$23$	−0.803349	−0.167510	−0.0837549	+	0.996486i	$0.526691\pi$
$24$	−2.46224	−0.502602
$25$	−3.88570	−0.777140
$26$	0.417204	0.0818204
$27$	−0.154168	−0.0296697
$28$	2.87810	0.543910
$29$	−10.3368	−1.91949	−0.959747	−	0.280866i	$-0.909378\pi$
$29$	−10.3368	−1.91949	−0.959747	+	0.280866i	$0.909378\pi$
$30$	2.59915	0.474538
$31$	3.70756	0.665898	0.332949	−	0.942945i	$-0.391956\pi$
$31$	3.70756	0.665898	0.332949	+	0.942945i	$0.391956\pi$
$32$	1.00000	0.176777
$33$	−15.2308	−2.65135
$34$	−4.57818	−0.785152
$35$	−3.03814	−0.513539
$36$	3.06261	0.510436
$37$	−9.14227	−1.50298	−0.751490	−	0.659744i	$-0.770665\pi$
$37$	−9.14227	−1.50298	−0.751490	+	0.659744i	$0.770665\pi$
$38$	−5.47986	−0.888951
$39$	−1.02726	−0.164493
$40$	−1.05561	−0.166906
$41$	−9.50822	−1.48493	−0.742467	−	0.669883i	$-0.766344\pi$
$41$	−9.50822	−1.48493	−0.742467	+	0.669883i	$0.766344\pi$
$42$	−7.08657	−1.09348
$43$	5.20566	0.793856	0.396928	−	0.917850i	$-0.370076\pi$
$43$	5.20566	0.793856	0.396928	+	0.917850i	$0.370076\pi$
$44$	6.18577	0.932540
$45$	−3.23291	−0.481934
$46$	−0.803349	−0.118447
$47$	8.42645	1.22912	0.614562	−	0.788868i	$-0.289333\pi$
$47$	8.42645	1.22912	0.614562	+	0.788868i	$0.289333\pi$
$48$	−2.46224	−0.355393
$49$	1.28346	0.183352
$50$	−3.88570	−0.549521
$51$	11.2726	1.57848
$52$	0.417204	0.0578558
$53$	12.1992	1.67570	0.837848	−	0.545904i	$-0.183814\pi$
$53$	12.1992	1.67570	0.837848	+	0.545904i	$0.183814\pi$
$54$	−0.154168	−0.0209796
$55$	−6.52973	−0.880469
$56$	2.87810	0.384602
$57$	13.4927	1.78715
$58$	−10.3368	−1.35729
$59$	−3.07139	−0.399861	−0.199931	−	0.979810i	$-0.564072\pi$
$59$	−3.07139	−0.399861	−0.199931	+	0.979810i	$0.564072\pi$
$60$	2.59915	0.335549
$61$	−7.18489	−0.919931	−0.459966	−	0.887937i	$-0.652138\pi$
$61$	−7.18489	−0.919931	−0.459966	+	0.887937i	$0.652138\pi$
$62$	3.70756	0.470861
$63$	8.81451	1.11052
$64$	1.00000	0.125000
$65$	−0.440403	−0.0546252
$66$	−15.2308	−1.87479
$67$	−1.91366	−0.233790	−0.116895	−	0.993144i	$-0.537294\pi$
$67$	−1.91366	−0.233790	−0.116895	+	0.993144i	$0.537294\pi$
$68$	−4.57818	−0.555186
$69$	1.97804	0.238128
$70$	−3.03814	−0.363127
$71$	13.5210	1.60465	0.802323	−	0.596890i	$-0.203597\pi$
$71$	13.5210	1.60465	0.802323	+	0.596890i	$0.203597\pi$
$72$	3.06261	0.360932
$73$	−9.78968	−1.14580	−0.572898	−	0.819627i	$-0.694181\pi$
$73$	−9.78968	−1.14580	−0.572898	+	0.819627i	$0.694181\pi$
$74$	−9.14227	−1.06277
$75$	9.56751	1.10476
$76$	−5.47986	−0.628583
$77$	17.8033	2.02887
$78$	−1.02726	−0.116314
$79$	−12.0839	−1.35954	−0.679771	−	0.733424i	$-0.737921\pi$
$79$	−12.0839	−1.35954	−0.679771	+	0.733424i	$0.737921\pi$
$80$	−1.05561	−0.118020
$81$	−8.80824	−0.978693
$82$	−9.50822	−1.05001
$83$	−9.67676	−1.06216	−0.531081	−	0.847321i	$-0.678214\pi$
$83$	−9.67676	−1.06216	−0.531081	+	0.847321i	$0.678214\pi$
$84$	−7.08657	−0.773208
$85$	4.83275	0.524186
$86$	5.20566	0.561341
$87$	25.4516	2.72870
$88$	6.18577	0.659405
$89$	−11.9101	−1.26247	−0.631233	−	0.775593i	$-0.717451\pi$
$89$	−11.9101	−1.26247	−0.631233	+	0.775593i	$0.717451\pi$
$90$	−3.23291	−0.340779
$91$	1.20076	0.125873
$92$	−0.803349	−0.0837549
$93$	−9.12890	−0.946623
$94$	8.42645	0.869122
$95$	5.78457	0.593485
$96$	−2.46224	−0.251301
$97$	15.0019	1.52321	0.761607	−	0.648040i	$-0.224411\pi$
$97$	15.0019	1.52321	0.761607	+	0.648040i	$0.224411\pi$
$98$	1.28346	0.129649
$99$	18.9446	1.90401
$100$	−3.88570	−0.388570
$101$	−12.2274	−1.21667	−0.608336	−	0.793680i	$-0.708163\pi$
$101$	−12.2274	−1.21667	−0.608336	+	0.793680i	$0.708163\pi$
$102$	11.2726	1.11615
$103$	−12.3130	−1.21324	−0.606620	−	0.794992i	$-0.707475\pi$
$103$	−12.3130	−1.21324	−0.606620	+	0.794992i	$0.707475\pi$
$104$	0.417204	0.0409102
$105$	7.48062	0.730033
$106$	12.1992	1.18490
$107$	8.82744	0.853381	0.426690	−	0.904398i	$-0.359679\pi$
$107$	8.82744	0.853381	0.426690	+	0.904398i	$0.359679\pi$
$108$	−0.154168	−0.0148348
$109$	16.6334	1.59319	0.796597	−	0.604511i	$-0.206631\pi$
$109$	16.6334	1.59319	0.796597	+	0.604511i	$0.206631\pi$
$110$	−6.52973	−0.622585
$111$	22.5105	2.13660
$112$	2.87810	0.271955
$113$	5.90392	0.555394	0.277697	−	0.960669i	$-0.410429\pi$
$113$	5.90392	0.555394	0.277697	+	0.960669i	$0.410429\pi$
$114$	13.4927	1.26371
$115$	0.848020	0.0790782
$116$	−10.3368	−0.959747
$117$	1.27773	0.118127
$118$	−3.07139	−0.282745
$119$	−13.1765	−1.20788
$120$	2.59915	0.237269
$121$	27.2637	2.47852
$122$	−7.18489	−0.650490
$123$	23.4115	2.11094
$124$	3.70756	0.332949
$125$	9.37979	0.838954
$126$	8.81451	0.785259
$127$	0.261361	0.0231921	0.0115960	−	0.999933i	$-0.496309\pi$
$127$	0.261361	0.0231921	0.0115960	+	0.999933i	$0.496309\pi$
$128$	1.00000	0.0883883
$129$	−12.8176	−1.12852
$130$	−0.440403	−0.0386259
$131$	13.3693	1.16808	0.584042	−	0.811723i	$-0.301470\pi$
$131$	13.3693	1.16808	0.584042	+	0.811723i	$0.301470\pi$
$132$	−15.2308	−1.32567
$133$	−15.7716	−1.36757
$134$	−1.91366	−0.165315
$135$	0.162741	0.0140065
$136$	−4.57818	−0.392576
$137$	−13.8039	−1.17934	−0.589671	−	0.807643i	$-0.700743\pi$
$137$	−13.8039	−1.17934	−0.589671	+	0.807643i	$0.700743\pi$
$138$	1.97804	0.168382
$139$	−8.13465	−0.689972	−0.344986	−	0.938608i	$-0.612116\pi$
$139$	−8.13465	−0.689972	−0.344986	+	0.938608i	$0.612116\pi$
$140$	−3.03814	−0.256769
$141$	−20.7479	−1.74729
$142$	13.5210	1.13466
$143$	2.58073	0.215811
$144$	3.06261	0.255218
$145$	10.9116	0.906157
$146$	−9.78968	−0.810200
$147$	−3.16019	−0.260648
$148$	−9.14227	−0.751490
$149$	8.60952	0.705320	0.352660	−	0.935752i	$-0.385277\pi$
$149$	8.60952	0.705320	0.352660	+	0.935752i	$0.385277\pi$
$150$	9.56751	0.781184
$151$	−18.3363	−1.49219	−0.746094	−	0.665841i	$-0.768073\pi$
$151$	−18.3363	−1.49219	−0.746094	+	0.665841i	$0.768073\pi$
$152$	−5.47986	−0.444476
$153$	−14.0212	−1.13355
$154$	17.8033	1.43463
$155$	−3.91372	−0.314358
$156$	−1.02726	−0.0822463
$157$	12.5615	1.00252	0.501258	−	0.865298i	$-0.332871\pi$
$157$	12.5615	1.00252	0.501258	+	0.865298i	$0.332871\pi$
$158$	−12.0839	−0.961342
$159$	−30.0374	−2.38212
$160$	−1.05561	−0.0834529
$161$	−2.31212	−0.182221
$162$	−8.80824	−0.692041
$163$	−5.51504	−0.431971	−0.215986	−	0.976397i	$-0.569296\pi$
$163$	−5.51504	−0.431971	−0.215986	+	0.976397i	$0.569296\pi$
$164$	−9.50822	−0.742467
$165$	16.0777	1.25165
$166$	−9.67676	−0.751062
$167$	−23.8913	−1.84876	−0.924380	−	0.381472i	$-0.875417\pi$
$167$	−23.8913	−1.84876	−0.924380	+	0.381472i	$0.875417\pi$
$168$	−7.08657	−0.546740
$169$	−12.8259	−0.986611
$170$	4.83275	0.370655
$171$	−16.7827	−1.28341
$172$	5.20566	0.396928
$173$	−13.8697	−1.05449	−0.527246	−	0.849713i	$-0.676775\pi$
$173$	−13.8697	−1.05449	−0.527246	+	0.849713i	$0.676775\pi$
$174$	25.4516	1.92948
$175$	−11.1834	−0.845388
$176$	6.18577	0.466270
$177$	7.56250	0.568432
$178$	−11.9101	−0.892699
$179$	10.4993	0.784755	0.392378	−	0.919804i	$-0.371653\pi$
$179$	10.4993	0.784755	0.392378	+	0.919804i	$0.371653\pi$
$180$	−3.23291	−0.240967
$181$	−7.20422	−0.535486	−0.267743	−	0.963490i	$-0.586278\pi$
$181$	−7.20422	−0.535486	−0.267743	+	0.963490i	$0.586278\pi$
$182$	1.20076	0.0890059
$183$	17.6909	1.30775
$184$	−0.803349	−0.0592237
$185$	9.65063	0.709529
$186$	−9.12890	−0.669364
$187$	−28.3196	−2.07093
$188$	8.42645	0.614562
$189$	−0.443711	−0.0322752
$190$	5.78457	0.419657
$191$	−6.38139	−0.461741	−0.230871	−	0.972984i	$-0.574157\pi$
$191$	−6.38139	−0.461741	−0.230871	+	0.972984i	$0.574157\pi$
$192$	−2.46224	−0.177697
$193$	5.98956	0.431138	0.215569	−	0.976489i	$-0.430839\pi$
$193$	5.98956	0.431138	0.215569	+	0.976489i	$0.430839\pi$
$194$	15.0019	1.07707
$195$	1.08438	0.0776538
$196$	1.28346	0.0916758
$197$	−19.4204	−1.38365	−0.691824	−	0.722066i	$-0.743193\pi$
$197$	−19.4204	−1.38365	−0.691824	+	0.722066i	$0.743193\pi$
$198$	18.9446	1.34634
$199$	7.72778	0.547808	0.273904	−	0.961757i	$-0.411685\pi$
$199$	7.72778	0.547808	0.273904	+	0.961757i	$0.411685\pi$
$200$	−3.88570	−0.274760
$201$	4.71188	0.332350
$202$	−12.2274	−0.860317
$203$	−29.7503	−2.08806
$204$	11.2726	0.789238
$205$	10.0369	0.701009
$206$	−12.3130	−0.857890
$207$	−2.46035	−0.171006
$208$	0.417204	0.0289279
$209$	−33.8972	−2.34472
$210$	7.48062	0.516212
$211$	21.9110	1.50841	0.754207	−	0.656637i	$-0.228022\pi$
$211$	21.9110	1.50841	0.754207	+	0.656637i	$0.228022\pi$
$212$	12.1992	0.837848
$213$	−33.2919	−2.28112
$214$	8.82744	0.603431
$215$	−5.49512	−0.374764
$216$	−0.154168	−0.0104898
$217$	10.6707	0.724377
$218$	16.6334	1.12656
$219$	24.1045	1.62883
$220$	−6.52973	−0.440234
$221$	−1.91004	−0.128483
$222$	22.5105	1.51080
$223$	12.2407	0.819701	0.409850	−	0.912153i	$-0.365581\pi$
$223$	12.2407	0.819701	0.409850	+	0.912153i	$0.365581\pi$
$224$	2.87810	0.192301
$225$	−11.9004	−0.793359
$226$	5.90392	0.392723
$227$	−27.0038	−1.79230	−0.896152	−	0.443748i	$-0.853649\pi$
$227$	−27.0038	−1.79230	−0.896152	+	0.443748i	$0.853649\pi$
$228$	13.4927	0.893577
$229$	−13.3244	−0.880503	−0.440251	−	0.897875i	$-0.645111\pi$
$229$	−13.3244	−0.880503	−0.440251	+	0.897875i	$0.645111\pi$
$230$	0.848020	0.0559168
$231$	−43.8359	−2.88419
$232$	−10.3368	−0.678644
$233$	0.716424	0.0469345	0.0234672	−	0.999725i	$-0.492529\pi$
$233$	0.716424	0.0469345	0.0234672	+	0.999725i	$0.492529\pi$
$234$	1.27773	0.0835281
$235$	−8.89501	−0.580246
$236$	−3.07139	−0.199931
$237$	29.7534	1.93269
$238$	−13.1765	−0.854104
$239$	−11.7759	−0.761721	−0.380860	−	0.924633i	$-0.624372\pi$
$239$	−11.7759	−0.761721	−0.380860	+	0.924633i	$0.624372\pi$
$240$	2.59915	0.167774
$241$	−10.1021	−0.650732	−0.325366	−	0.945588i	$-0.605487\pi$
$241$	−10.1021	−0.650732	−0.325366	+	0.945588i	$0.605487\pi$
$242$	27.2637	1.75258
$243$	22.1505	1.42095
$244$	−7.18489	−0.459966
$245$	−1.35483	−0.0865568
$246$	23.4115	1.49266
$247$	−2.28622	−0.145469
$248$	3.70756	0.235431
$249$	23.8265	1.50994
$250$	9.37979	0.593230
$251$	−1.40810	−0.0888785	−0.0444392	−	0.999012i	$-0.514150\pi$
$251$	−1.40810	−0.0888785	−0.0444392	+	0.999012i	$0.514150\pi$
$252$	8.81451	0.555262
$253$	−4.96933	−0.312419
$254$	0.261361	0.0163993
$255$	−11.8994	−0.745168
$256$	1.00000	0.0625000
$257$	3.39708	0.211904	0.105952	−	0.994371i	$-0.466211\pi$
$257$	3.39708	0.211904	0.105952	+	0.994371i	$0.466211\pi$
$258$	−12.8176	−0.797987
$259$	−26.3124	−1.63497
$260$	−0.440403	−0.0273126
$261$	−31.6576	−1.95956
$262$	13.3693	0.825960
$263$	−18.9886	−1.17089	−0.585444	−	0.810713i	$-0.699080\pi$
$263$	−18.9886	−1.17089	−0.585444	+	0.810713i	$0.699080\pi$
$264$	−15.2308	−0.937393
$265$	−12.8776	−0.791064
$266$	−15.7716	−0.967019
$267$	29.3255	1.79469
$268$	−1.91366	−0.116895
$269$	−28.4671	−1.73567	−0.867834	−	0.496854i	$-0.834489\pi$
$269$	−28.4671	−1.73567	−0.867834	+	0.496854i	$0.834489\pi$
$270$	0.162741	0.00990408
$271$	25.3634	1.54072	0.770358	−	0.637612i	$-0.220078\pi$
$271$	25.3634	1.54072	0.770358	+	0.637612i	$0.220078\pi$
$272$	−4.57818	−0.277593
$273$	−2.95654	−0.178938
$274$	−13.8039	−0.833921
$275$	−24.0360	−1.44943
$276$	1.97804	0.119064
$277$	3.17087	0.190519	0.0952595	−	0.995452i	$-0.469632\pi$
$277$	3.17087	0.190519	0.0952595	+	0.995452i	$0.469632\pi$
$278$	−8.13465	−0.487884
$279$	11.3548	0.679796
$280$	−3.03814	−0.181563
$281$	−6.09063	−0.363337	−0.181668	−	0.983360i	$-0.558150\pi$
$281$	−6.09063	−0.363337	−0.181668	+	0.983360i	$0.558150\pi$
$282$	−20.7479	−1.23552
$283$	4.28563	0.254754	0.127377	−	0.991854i	$-0.459344\pi$
$283$	4.28563	0.254754	0.127377	+	0.991854i	$0.459344\pi$
$284$	13.5210	0.802323
$285$	−14.2430	−0.843682
$286$	2.58073	0.152602
$287$	−27.3656	−1.61534
$288$	3.06261	0.180466
$289$	3.95976	0.232927
$290$	10.9116	0.640749
$291$	−36.9383	−2.16536
$292$	−9.78968	−0.572898
$293$	12.3167	0.719548	0.359774	−	0.933040i	$-0.382854\pi$
$293$	12.3167	0.719548	0.359774	+	0.933040i	$0.382854\pi$
$294$	−3.16019	−0.184306
$295$	3.24218	0.188767
$296$	−9.14227	−0.531384
$297$	−0.953648	−0.0553363
$298$	8.60952	0.498736
$299$	−0.335161	−0.0193828
$300$	9.56751	0.552380
$301$	14.9824	0.863572
$302$	−18.3363	−1.05514
$303$	30.1068	1.72959
$304$	−5.47986	−0.314292
$305$	7.58441	0.434282
$306$	−14.0212	−0.801539
$307$	14.9481	0.853132	0.426566	−	0.904457i	$-0.359723\pi$
$307$	14.9481	0.853132	0.426566	+	0.904457i	$0.359723\pi$
$308$	17.8033	1.01444
$309$	30.3176	1.72471
$310$	−3.91372	−0.222285
$311$	7.58223	0.429949	0.214974	−	0.976620i	$-0.431033\pi$
$311$	7.58223	0.429949	0.214974	+	0.976620i	$0.431033\pi$
$312$	−1.02726	−0.0581569
$313$	18.8063	1.06299	0.531496	−	0.847061i	$-0.321630\pi$
$313$	18.8063	1.06299	0.531496	+	0.847061i	$0.321630\pi$
$314$	12.5615	0.708885
$315$	−9.30464	−0.524257
$316$	−12.0839	−0.679771
$317$	−21.0444	−1.18197	−0.590984	−	0.806683i	$-0.701260\pi$
$317$	−21.0444	−1.18197	−0.590984	+	0.806683i	$0.701260\pi$
$318$	−30.0374	−1.68442
$319$	−63.9410	−3.58001
$320$	−1.05561	−0.0590101
$321$	−21.7352	−1.21314
$322$	−2.31212	−0.128849
$323$	25.0878	1.39592
$324$	−8.80824	−0.489347
$325$	−1.62113	−0.0899240
$326$	−5.51504	−0.305450
$327$	−40.9555	−2.26484
$328$	−9.50822	−0.525003
$329$	24.2522	1.33707
$330$	16.0777	0.885051
$331$	−3.81327	−0.209596	−0.104798	−	0.994494i	$-0.533420\pi$
$331$	−3.81327	−0.209596	−0.104798	+	0.994494i	$0.533420\pi$
$332$	−9.67676	−0.531081
$333$	−27.9992	−1.53435
$334$	−23.8913	−1.30727
$335$	2.02007	0.110368
$336$	−7.08657	−0.386604
$337$	−16.7706	−0.913552	−0.456776	−	0.889582i	$-0.650996\pi$
$337$	−16.7706	−0.913552	−0.456776	+	0.889582i	$0.650996\pi$
$338$	−12.8259	−0.697639
$339$	−14.5368	−0.789533
$340$	4.83275	0.262093
$341$	22.9341	1.24195
$342$	−16.7827	−0.907504
$343$	−16.4528	−0.888366
$344$	5.20566	0.280670
$345$	−2.08803	−0.112416
$346$	−13.8697	−0.745639
$347$	−4.17069	−0.223894	−0.111947	−	0.993714i	$-0.535709\pi$
$347$	−4.17069	−0.223894	−0.111947	+	0.993714i	$0.535709\pi$
$348$	25.4516	1.36435
$349$	35.3830	1.89401	0.947005	−	0.321217i	$-0.104092\pi$
$349$	35.3830	1.89401	0.947005	+	0.321217i	$0.104092\pi$
$350$	−11.1834	−0.597779
$351$	−0.0643196	−0.00343312
$352$	6.18577	0.329703
$353$	−2.01709	−0.107359	−0.0536795	−	0.998558i	$-0.517095\pi$
$353$	−2.01709	−0.107359	−0.0536795	+	0.998558i	$0.517095\pi$
$354$	7.56250	0.401942
$355$	−14.2728	−0.757523
$356$	−11.9101	−0.631233
$357$	32.4436	1.71710
$358$	10.4993	0.554906
$359$	−7.89658	−0.416766	−0.208383	−	0.978047i	$-0.566820\pi$
$359$	−7.89658	−0.416766	−0.208383	+	0.978047i	$0.566820\pi$
$360$	−3.23291	−0.170389
$361$	11.0289	0.580468
$362$	−7.20422	−0.378645
$363$	−67.1298	−3.52340
$364$	1.20076	0.0629367
$365$	10.3340	0.540908
$366$	17.6909	0.924719
$367$	−29.3876	−1.53402	−0.767010	−	0.641636i	$-0.778256\pi$
$367$	−29.3876	−1.53402	−0.767010	+	0.641636i	$0.778256\pi$
$368$	−0.803349	−0.0418775
$369$	−29.1200	−1.51593
$370$	9.65063	0.501712
$371$	35.1107	1.82285
$372$	−9.12890	−0.473312
$373$	−13.4497	−0.696398	−0.348199	−	0.937421i	$-0.613207\pi$
$373$	−13.4497	−0.696398	−0.348199	+	0.937421i	$0.613207\pi$
$374$	−28.3196	−1.46437
$375$	−23.0953	−1.19263
$376$	8.42645	0.434561
$377$	−4.31255	−0.222108
$378$	−0.443711	−0.0228220
$379$	15.6535	0.804069	0.402034	−	0.915625i	$-0.368303\pi$
$379$	15.6535	0.804069	0.402034	+	0.915625i	$0.368303\pi$
$380$	5.78457	0.296742
$381$	−0.643534	−0.0329692
$382$	−6.38139	−0.326500
$383$	23.3546	1.19337	0.596683	−	0.802477i	$-0.296485\pi$
$383$	23.3546	1.19337	0.596683	+	0.802477i	$0.296485\pi$
$384$	−2.46224	−0.125651
$385$	−18.7932	−0.957791
$386$	5.98956	0.304860
$387$	15.9429	0.810424
$388$	15.0019	0.761607
$389$	−24.3530	−1.23474	−0.617372	−	0.786671i	$-0.711803\pi$
$389$	−24.3530	−1.23474	−0.617372	+	0.786671i	$0.711803\pi$
$390$	1.08438	0.0549095
$391$	3.67788	0.185998
$392$	1.28346	0.0648246
$393$	−32.9185	−1.66052
$394$	−19.4204	−0.978387
$395$	12.7558	0.641814
$396$	18.9446	0.952003
$397$	4.63734	0.232741	0.116371	−	0.993206i	$-0.462874\pi$
$397$	4.63734	0.232741	0.116371	+	0.993206i	$0.462874\pi$
$398$	7.72778	0.387359
$399$	38.8334	1.94410
$400$	−3.88570	−0.194285
$401$	8.65569	0.432245	0.216122	−	0.976366i	$-0.430659\pi$
$401$	8.65569	0.432245	0.216122	+	0.976366i	$0.430659\pi$
$402$	4.71188	0.235007
$403$	1.54681	0.0770521
$404$	−12.2274	−0.608336
$405$	9.29802	0.462023
$406$	−29.7503	−1.47648
$407$	−56.5520	−2.80318
$408$	11.2726	0.558075
$409$	−24.7273	−1.22269	−0.611343	−	0.791366i	$-0.709370\pi$
$409$	−24.7273	−1.22269	−0.611343	+	0.791366i	$0.709370\pi$
$410$	10.0369	0.495688
$411$	33.9884	1.67652
$412$	−12.3130	−0.606620
$413$	−8.83978	−0.434977
$414$	−2.46035	−0.120919
$415$	10.2148	0.501427
$416$	0.417204	0.0204551
$417$	20.0294	0.980846
$418$	−33.8972	−1.65796
$419$	8.02324	0.391961	0.195980	−	0.980608i	$-0.437211\pi$
$419$	8.02324	0.391961	0.195980	+	0.980608i	$0.437211\pi$
$420$	7.48062	0.365017
$421$	31.0305	1.51233	0.756167	−	0.654379i	$-0.227070\pi$
$421$	31.0305	1.51233	0.756167	+	0.654379i	$0.227070\pi$
$422$	21.9110	1.06661
$423$	25.8070	1.25478
$424$	12.1992	0.592448
$425$	17.7894	0.862914
$426$	−33.2919	−1.61300
$427$	−20.6788	−1.00072
$428$	8.82744	0.426690
$429$	−6.35436	−0.306792
$430$	−5.49512	−0.264998
$431$	22.0764	1.06338	0.531692	−	0.846938i	$-0.321556\pi$
$431$	22.0764	1.06338	0.531692	+	0.846938i	$0.321556\pi$
$432$	−0.154168	−0.00741742
$433$	−0.156908	−0.00754051	−0.00377026	−	0.999993i	$-0.501200\pi$
$433$	−0.156908	−0.00754051	−0.00377026	+	0.999993i	$0.501200\pi$
$434$	10.6707	0.512212
$435$	−26.8669	−1.28817
$436$	16.6334	0.796597
$437$	4.40224	0.210588
$438$	24.1045	1.15176
$439$	3.02494	0.144373	0.0721863	−	0.997391i	$-0.477002\pi$
$439$	3.02494	0.144373	0.0721863	+	0.997391i	$0.477002\pi$
$440$	−6.52973	−0.311293
$441$	3.93075	0.187178
$442$	−1.91004	−0.0908512
$443$	−14.3152	−0.680135	−0.340067	−	0.940401i	$-0.610450\pi$
$443$	−14.3152	−0.680135	−0.340067	+	0.940401i	$0.610450\pi$
$444$	22.5105	1.06830
$445$	12.5723	0.595987
$446$	12.2407	0.579616
$447$	−21.1987	−1.00266
$448$	2.87810	0.135977
$449$	32.2249	1.52079	0.760393	−	0.649463i	$-0.225006\pi$
$449$	32.2249	1.52079	0.760393	+	0.649463i	$0.225006\pi$
$450$	−11.9004	−0.560990
$451$	−58.8156	−2.76952
$452$	5.90392	0.277697
$453$	45.1483	2.12125
$454$	−27.0038	−1.26735
$455$	−1.26752	−0.0594224
$456$	13.4927	0.631855
$457$	−7.48145	−0.349968	−0.174984	−	0.984571i	$-0.555987\pi$
$457$	−7.48145	−0.349968	−0.174984	+	0.984571i	$0.555987\pi$
$458$	−13.3244	−0.622610
$459$	0.705810	0.0329444
$460$	0.848020	0.0395391
$461$	24.0932	1.12213	0.561066	−	0.827771i	$-0.310392\pi$
$461$	24.0932	1.12213	0.561066	+	0.827771i	$0.310392\pi$
$462$	−43.8359	−2.03943
$463$	−31.6641	−1.47155	−0.735777	−	0.677224i	$-0.763183\pi$
$463$	−31.6641	−1.47155	−0.735777	+	0.677224i	$0.763183\pi$
$464$	−10.3368	−0.479873
$465$	9.63652	0.446883
$466$	0.716424	0.0331877
$467$	−21.4071	−0.990602	−0.495301	−	0.868721i	$-0.664942\pi$
$467$	−21.4071	−0.990602	−0.495301	+	0.868721i	$0.664942\pi$
$468$	1.27773	0.0590633
$469$	−5.50770	−0.254322
$470$	−8.89501	−0.410296
$471$	−30.9294	−1.42515
$472$	−3.07139	−0.141372
$473$	32.2010	1.48060
$474$	29.7534	1.36662
$475$	21.2931	0.976994
$476$	−13.1765	−0.603942
$477$	37.3616	1.71067
$478$	−11.7759	−0.538618
$479$	38.5963	1.76351	0.881755	−	0.471708i	$-0.156362\pi$
$479$	38.5963	1.76351	0.881755	+	0.471708i	$0.156362\pi$
$480$	2.59915	0.118634
$481$	−3.81419	−0.173912
$482$	−10.1021	−0.460137
$483$	5.69299	0.259040
$484$	27.2637	1.23926
$485$	−15.8361	−0.719080
$486$	22.1505	1.00477
$487$	−11.2081	−0.507886	−0.253943	−	0.967219i	$-0.581728\pi$
$487$	−11.2081	−0.507886	−0.253943	+	0.967219i	$0.581728\pi$
$488$	−7.18489	−0.325245
$489$	13.5793	0.614079
$490$	−1.35483	−0.0612049
$491$	23.6515	1.06738	0.533690	−	0.845680i	$-0.320805\pi$
$491$	23.6515	1.06738	0.533690	+	0.845680i	$0.320805\pi$
$492$	23.4115	1.05547
$493$	47.3237	2.13135
$494$	−2.28622	−0.102862
$495$	−19.9980	−0.898845
$496$	3.70756	0.166475
$497$	38.9147	1.74557
$498$	23.8265	1.06769
$499$	10.7102	0.479452	0.239726	−	0.970841i	$-0.422942\pi$
$499$	10.7102	0.479452	0.239726	+	0.970841i	$0.422942\pi$
$500$	9.37979	0.419477
$501$	58.8259	2.62815
$502$	−1.40810	−0.0628466
$503$	−22.9981	−1.02544	−0.512718	−	0.858557i	$-0.671361\pi$
$503$	−22.9981	−1.02544	−0.512718	+	0.858557i	$0.671361\pi$
$504$	8.81451	0.392629
$505$	12.9073	0.574368
$506$	−4.96933	−0.220914
$507$	31.5805	1.40254
$508$	0.261361	0.0115960
$509$	1.38829	0.0615349	0.0307674	−	0.999527i	$-0.490205\pi$
$509$	1.38829	0.0615349	0.0307674	+	0.999527i	$0.490205\pi$
$510$	−11.8994	−0.526914
$511$	−28.1757	−1.24642
$512$	1.00000	0.0441942
$513$	0.844820	0.0372997
$514$	3.39708	0.149839
$515$	12.9977	0.572747
$516$	−12.8176	−0.564262
$517$	52.1241	2.29241
$518$	−26.3124	−1.15610
$519$	34.1504	1.49904
$520$	−0.440403	−0.0193129
$521$	−36.7916	−1.61187	−0.805934	−	0.592005i	$-0.798336\pi$
$521$	−36.7916	−1.61187	−0.805934	+	0.592005i	$0.798336\pi$
$522$	−31.6576	−1.38562
$523$	−3.49761	−0.152940	−0.0764699	−	0.997072i	$-0.524365\pi$
$523$	−3.49761	−0.152940	−0.0764699	+	0.997072i	$0.524365\pi$
$524$	13.3693	0.584042
$525$	27.5363	1.20178
$526$	−18.9886	−0.827942
$527$	−16.9739	−0.739395
$528$	−15.2308	−0.662837
$529$	−22.3546	−0.971940
$530$	−12.8776	−0.559367
$531$	−9.40649	−0.408207
$532$	−15.7716	−0.683785
$533$	−3.96687	−0.171824
$534$	29.3255	1.26904
$535$	−9.31829	−0.402865
$536$	−1.91366	−0.0826574
$537$	−25.8518	−1.11559
$538$	−28.4671	−1.22730
$539$	7.93920	0.341965
$540$	0.162741	0.00700324
$541$	−37.9225	−1.63041	−0.815207	−	0.579170i	$-0.803377\pi$
$541$	−37.9225	−1.63041	−0.815207	+	0.579170i	$0.803377\pi$
$542$	25.3634	1.08945
$543$	17.7385	0.761232
$544$	−4.57818	−0.196288
$545$	−17.5583	−0.752117
$546$	−2.95654	−0.126528
$547$	29.3414	1.25455	0.627274	−	0.778799i	$-0.284171\pi$
$547$	29.3414	1.25455	0.627274	+	0.778799i	$0.284171\pi$
$548$	−13.8039	−0.589671
$549$	−22.0045	−0.939131
$550$	−24.0360	−1.02490
$551$	56.6442	2.41312
$552$	1.97804	0.0841908
$553$	−34.7786	−1.47894
$554$	3.17087	0.134717
$555$	−23.7621	−1.00865
$556$	−8.13465	−0.344986
$557$	−22.3150	−0.945515	−0.472757	−	0.881193i	$-0.656741\pi$
$557$	−22.3150	−0.945515	−0.472757	+	0.881193i	$0.656741\pi$
$558$	11.3548	0.480688
$559$	2.17182	0.0918583
$560$	−3.03814	−0.128385
$561$	69.7295	2.94398
$562$	−6.09063	−0.256918
$563$	1.51026	0.0636501	0.0318250	−	0.999493i	$-0.489868\pi$
$563$	1.51026	0.0636501	0.0318250	+	0.999493i	$0.489868\pi$
$564$	−20.7479	−0.873645
$565$	−6.23221	−0.262191
$566$	4.28563	0.180138
$567$	−25.3510	−1.06464
$568$	13.5210	0.567328
$569$	29.8124	1.24980	0.624901	−	0.780704i	$-0.285139\pi$
$569$	29.8124	1.24980	0.624901	+	0.780704i	$0.285139\pi$
$570$	−14.2430	−0.596573
$571$	−5.24439	−0.219471	−0.109735	−	0.993961i	$-0.535000\pi$
$571$	−5.24439	−0.219471	−0.109735	+	0.993961i	$0.535000\pi$
$572$	2.58073	0.107906
$573$	15.7125	0.656399
$574$	−27.3656	−1.14222
$575$	3.12157	0.130179
$576$	3.06261	0.127609
$577$	−13.7921	−0.574173	−0.287087	−	0.957905i	$-0.592687\pi$
$577$	−13.7921	−0.574173	−0.287087	+	0.957905i	$0.592687\pi$
$578$	3.95976	0.164704
$579$	−14.7477	−0.612894
$580$	10.9116	0.453078
$581$	−27.8507	−1.15544
$582$	−36.9383	−1.53114
$583$	75.4617	3.12531
$584$	−9.78968	−0.405100
$585$	−1.34878	−0.0557653
$586$	12.3167	0.508797
$587$	1.00550	0.0415015	0.0207507	−	0.999785i	$-0.493394\pi$
$587$	1.00550	0.0415015	0.0207507	+	0.999785i	$0.493394\pi$
$588$	−3.16019	−0.130324
$589$	−20.3169	−0.837145
$590$	3.24218	0.133478
$591$	47.8177	1.96696
$592$	−9.14227	−0.375745
$593$	−44.3220	−1.82009	−0.910043	−	0.414513i	$-0.863952\pi$
$593$	−44.3220	−1.82009	−0.910043	+	0.414513i	$0.863952\pi$
$594$	−0.953648	−0.0391287
$595$	13.9091	0.570220
$596$	8.60952	0.352660
$597$	−19.0276	−0.778749
$598$	−0.335161	−0.0137057
$599$	−13.6143	−0.556263	−0.278132	−	0.960543i	$-0.589715\pi$
$599$	−13.6143	−0.556263	−0.278132	+	0.960543i	$0.589715\pi$
$600$	9.56751	0.390592
$601$	17.1986	0.701546	0.350773	−	0.936460i	$-0.385919\pi$
$601$	17.1986	0.701546	0.350773	+	0.936460i	$0.385919\pi$
$602$	14.9824	0.610637
$603$	−5.86079	−0.238670
$604$	−18.3363	−0.746094
$605$	−28.7797	−1.17006
$606$	30.1068	1.22300
$607$	−24.0759	−0.977209	−0.488604	−	0.872505i	$-0.662494\pi$
$607$	−24.0759	−0.977209	−0.488604	+	0.872505i	$0.662494\pi$
$608$	−5.47986	−0.222238
$609$	73.2524	2.96834
$610$	7.58441	0.307084
$611$	3.51555	0.142224
$612$	−14.0212	−0.566773
$613$	−16.1416	−0.651953	−0.325977	−	0.945378i	$-0.605693\pi$
$613$	−16.1416	−0.651953	−0.325977	+	0.945378i	$0.605693\pi$
$614$	14.9481	0.603255
$615$	−24.7133	−0.996536
$616$	17.8033	0.717314
$617$	−7.34223	−0.295587	−0.147793	−	0.989018i	$-0.547217\pi$
$617$	−7.34223	−0.295587	−0.147793	+	0.989018i	$0.547217\pi$
$618$	30.3176	1.21955
$619$	14.0693	0.565492	0.282746	−	0.959195i	$-0.408755\pi$
$619$	14.0693	0.565492	0.282746	+	0.959195i	$0.408755\pi$
$620$	−3.91372	−0.157179
$621$	0.123851	0.00496996
$622$	7.58223	0.304020
$623$	−34.2784	−1.37334
$624$	−1.02726	−0.0411231
$625$	9.52713	0.381085
$626$	18.8063	0.751649
$627$	83.4629	3.33319
$628$	12.5615	0.501258
$629$	41.8550	1.66887
$630$	−9.30464	−0.370706
$631$	45.7064	1.81954	0.909772	−	0.415108i	$-0.136256\pi$
$631$	45.7064	1.81954	0.909772	+	0.415108i	$0.136256\pi$
$632$	−12.0839	−0.480671
$633$	−53.9500	−2.14432
$634$	−21.0444	−0.835778
$635$	−0.275894	−0.0109485
$636$	−30.0374	−1.19106
$637$	0.535465	0.0212159
$638$	−63.9410	−2.53145
$639$	41.4095	1.63814
$640$	−1.05561	−0.0417265
$641$	−38.3487	−1.51468	−0.757341	−	0.653020i	$-0.773502\pi$
$641$	−38.3487	−1.51468	−0.757341	+	0.653020i	$0.773502\pi$
$642$	−21.7352	−0.857822
$643$	0.0761333	0.00300241	0.00150120	−	0.999999i	$-0.499522\pi$
$643$	0.0761333	0.00300241	0.00150120	+	0.999999i	$0.499522\pi$
$644$	−2.31212	−0.0911103
$645$	13.5303	0.532755
$646$	25.0878	0.987067
$647$	4.85018	0.190680	0.0953400	−	0.995445i	$-0.469606\pi$
$647$	4.85018	0.190680	0.0953400	+	0.995445i	$0.469606\pi$
$648$	−8.80824	−0.346020
$649$	−18.9989	−0.745773
$650$	−1.62113	−0.0635859
$651$	−26.2739	−1.02976
$652$	−5.51504	−0.215986
$653$	−42.3399	−1.65689	−0.828443	−	0.560073i	$-0.810773\pi$
$653$	−42.3399	−1.65689	−0.828443	+	0.560073i	$0.810773\pi$
$654$	−40.9555	−1.60149
$655$	−14.1127	−0.551430
$656$	−9.50822	−0.371233
$657$	−29.9820	−1.16971
$658$	24.2522	0.945448
$659$	14.2773	0.556164	0.278082	−	0.960557i	$-0.410301\pi$
$659$	14.2773	0.556164	0.278082	+	0.960557i	$0.410301\pi$
$660$	16.0777	0.625825
$661$	40.0837	1.55907	0.779537	−	0.626356i	$-0.215454\pi$
$661$	40.0837	1.55907	0.779537	+	0.626356i	$0.215454\pi$
$662$	−3.81327	−0.148207
$663$	4.70296	0.182648
$664$	−9.67676	−0.375531
$665$	16.6486	0.645604
$666$	−27.9992	−1.08495
$667$	8.30405	0.321534
$668$	−23.8913	−0.924380
$669$	−30.1396	−1.16527
$670$	2.02007	0.0780420
$671$	−44.4441	−1.71574
$672$	−7.08657	−0.273370
$673$	17.8722	0.688925	0.344462	−	0.938800i	$-0.388061\pi$
$673$	17.8722	0.688925	0.344462	+	0.938800i	$0.388061\pi$
$674$	−16.7706	−0.645979
$675$	0.599051	0.0230575
$676$	−12.8259	−0.493305
$677$	−7.45491	−0.286515	−0.143258	−	0.989685i	$-0.545758\pi$
$677$	−7.45491	−0.286515	−0.143258	+	0.989685i	$0.545758\pi$
$678$	−14.5368	−0.558284
$679$	43.1770	1.65698
$680$	4.83275	0.185328
$681$	66.4897	2.54789
$682$	22.9341	0.878193
$683$	8.74250	0.334522	0.167261	−	0.985913i	$-0.446508\pi$
$683$	8.74250	0.334522	0.167261	+	0.985913i	$0.446508\pi$
$684$	−16.7827	−0.641703
$685$	14.5714	0.556745
$686$	−16.4528	−0.628170
$687$	32.8079	1.25170
$688$	5.20566	0.198464
$689$	5.08958	0.193897
$690$	−2.08803	−0.0794898
$691$	−19.7488	−0.751278	−0.375639	−	0.926766i	$-0.622577\pi$
$691$	−19.7488	−0.751278	−0.375639	+	0.926766i	$0.622577\pi$
$692$	−13.8697	−0.527246
$693$	54.5245	2.07121
$694$	−4.17069	−0.158317
$695$	8.58698	0.325723
$696$	25.4516	0.964742
$697$	43.5303	1.64883
$698$	35.3830	1.33927
$699$	−1.76401	−0.0667208
$700$	−11.1834	−0.422694
$701$	9.72461	0.367293	0.183647	−	0.982992i	$-0.441210\pi$
$701$	9.72461	0.367293	0.183647	+	0.982992i	$0.441210\pi$
$702$	−0.0643196	−0.00242759
$703$	50.0984	1.88950
$704$	6.18577	0.233135
$705$	21.9016	0.824863
$706$	−2.01709	−0.0759143
$707$	−35.1917	−1.32352
$708$	7.56250	0.284216
$709$	33.3532	1.25261	0.626303	−	0.779580i	$-0.284567\pi$
$709$	33.3532	1.25261	0.626303	+	0.779580i	$0.284567\pi$
$710$	−14.2728	−0.535649
$711$	−37.0082	−1.38792
$712$	−11.9101	−0.446349
$713$	−2.97847	−0.111545
$714$	32.4436	1.21417
$715$	−2.72423	−0.101880
$716$	10.4993	0.392378
$717$	28.9951	1.08284
$718$	−7.89658	−0.294698
$719$	−25.5601	−0.953231	−0.476616	−	0.879112i	$-0.658137\pi$
$719$	−25.5601	−0.953231	−0.476616	+	0.879112i	$0.658137\pi$
$720$	−3.23291	−0.120483
$721$	−35.4381	−1.31979
$722$	11.0289	0.410453
$723$	24.8737	0.925063
$724$	−7.20422	−0.267743
$725$	40.1656	1.49171
$726$	−67.1298	−2.49142
$727$	−17.8381	−0.661577	−0.330789	−	0.943705i	$-0.607315\pi$
$727$	−17.8381	−0.661577	−0.330789	+	0.943705i	$0.607315\pi$
$728$	1.20076	0.0445029
$729$	−28.1150	−1.04130
$730$	10.3340	0.382480
$731$	−23.8325	−0.881475
$732$	17.6909	0.653875
$733$	−26.9934	−0.997025	−0.498513	−	0.866882i	$-0.666120\pi$
$733$	−26.9934	−0.997025	−0.498513	+	0.866882i	$0.666120\pi$
$734$	−29.3876	−1.08472
$735$	3.33591	0.123047
$736$	−0.803349	−0.0296118
$737$	−11.8374	−0.436038
$738$	−29.1200	−1.07192
$739$	23.8019	0.875567	0.437783	−	0.899080i	$-0.355764\pi$
$739$	23.8019	0.875567	0.437783	+	0.899080i	$0.355764\pi$
$740$	9.65063	0.354764
$741$	5.62922	0.206795
$742$	35.1107	1.28895
$743$	13.0527	0.478857	0.239429	−	0.970914i	$-0.423040\pi$
$743$	13.0527	0.478857	0.239429	+	0.970914i	$0.423040\pi$
$744$	−9.12890	−0.334682
$745$	−9.08826	−0.332968
$746$	−13.4497	−0.492427
$747$	−29.6362	−1.08433
$748$	−28.3196	−1.03547
$749$	25.4063	0.928324
$750$	−23.0953	−0.843320
$751$	−5.07184	−0.185074	−0.0925370	−	0.995709i	$-0.529498\pi$
$751$	−5.07184	−0.185074	−0.0925370	+	0.995709i	$0.529498\pi$
$752$	8.42645	0.307281
$753$	3.46708	0.126347
$754$	−4.31255	−0.157054
$755$	19.3559	0.704433
$756$	−0.443711	−0.0161376
$757$	3.40039	0.123589	0.0617946	−	0.998089i	$-0.480318\pi$
$757$	3.40039	0.123589	0.0617946	+	0.998089i	$0.480318\pi$
$758$	15.6535	0.568562
$759$	12.2357	0.444127
$760$	5.78457	0.209828
$761$	0.677298	0.0245520	0.0122760	−	0.999925i	$-0.496092\pi$
$761$	0.677298	0.0245520	0.0122760	+	0.999925i	$0.496092\pi$
$762$	−0.643534	−0.0233128
$763$	47.8727	1.73311
$764$	−6.38139	−0.230871
$765$	14.8009	0.535126
$766$	23.3546	0.843837
$767$	−1.28140	−0.0462686
$768$	−2.46224	−0.0888483
$769$	−1.78756	−0.0644612	−0.0322306	−	0.999480i	$-0.510261\pi$
$769$	−1.78756	−0.0644612	−0.0322306	+	0.999480i	$0.510261\pi$
$770$	−18.7932	−0.677261
$771$	−8.36442	−0.301237
$772$	5.98956	0.215569
$773$	42.1183	1.51489	0.757445	−	0.652900i	$-0.226448\pi$
$773$	42.1183	1.51489	0.757445	+	0.652900i	$0.226448\pi$
$774$	15.9429	0.573056
$775$	−14.4065	−0.517496
$776$	15.0019	0.538537
$777$	64.7873	2.32423
$778$	−24.3530	−0.873096
$779$	52.1037	1.86681
$780$	1.08438	0.0388269
$781$	83.6377	2.99279
$782$	3.67788	0.131521
$783$	1.59360	0.0569507
$784$	1.28346	0.0458379
$785$	−13.2600	−0.473268
$786$	−32.9185	−1.17416
$787$	−21.1841	−0.755132	−0.377566	−	0.925983i	$-0.623239\pi$
$787$	−21.1841	−0.755132	−0.377566	+	0.925983i	$0.623239\pi$
$788$	−19.4204	−0.691824
$789$	46.7544	1.66450
$790$	12.7558	0.453831
$791$	16.9921	0.604168
$792$	18.9446	0.673168
$793$	−2.99757	−0.106447
$794$	4.63734	0.164573
$795$	31.7077	1.12456
$796$	7.72778	0.273904
$797$	−38.1755	−1.35224	−0.676122	−	0.736790i	$-0.736341\pi$
$797$	−38.1755	−1.35224	−0.676122	+	0.736790i	$0.736341\pi$
$798$	38.8334	1.37469
$799$	−38.5778	−1.36479
$800$	−3.88570	−0.137380
$801$	−36.4760	−1.28882
$802$	8.65569	0.305643
$803$	−60.5567	−2.13700
$804$	4.71188	0.166175
$805$	2.44069	0.0860229
$806$	1.54681	0.0544841
$807$	70.0927	2.46738
$808$	−12.2274	−0.430159
$809$	8.40234	0.295410	0.147705	−	0.989031i	$-0.452811\pi$
$809$	8.40234	0.295410	0.147705	+	0.989031i	$0.452811\pi$
$810$	9.29802	0.326699
$811$	31.1319	1.09319	0.546595	−	0.837397i	$-0.315924\pi$
$811$	31.1319	1.09319	0.546595	+	0.837397i	$0.315924\pi$
$812$	−29.7503	−1.04403
$813$	−62.4507	−2.19024
$814$	−56.5520	−1.98215
$815$	5.82170	0.203925
$816$	11.2726	0.394619
$817$	−28.5263	−0.998009
$818$	−24.7273	−0.864569
$819$	3.67745	0.128500
$820$	10.0369	0.350505
$821$	−32.8756	−1.14737	−0.573684	−	0.819077i	$-0.694486\pi$
$821$	−32.8756	−1.14737	−0.573684	+	0.819077i	$0.694486\pi$
$822$	33.9884	1.18548
$823$	−4.93077	−0.171876	−0.0859379	−	0.996300i	$-0.527389\pi$
$823$	−4.93077	−0.171876	−0.0859379	+	0.996300i	$0.527389\pi$
$824$	−12.3130	−0.428945
$825$	59.1824	2.06047
$826$	−8.83978	−0.307575
$827$	−30.9467	−1.07612	−0.538061	−	0.842906i	$-0.680843\pi$
$827$	−30.9467	−1.07612	−0.538061	+	0.842906i	$0.680843\pi$
$828$	−2.46035	−0.0855030
$829$	2.61976	0.0909880	0.0454940	−	0.998965i	$-0.485514\pi$
$829$	2.61976	0.0909880	0.0454940	+	0.998965i	$0.485514\pi$
$830$	10.2148	0.354562
$831$	−7.80743	−0.270837
$832$	0.417204	0.0144639
$833$	−5.87592	−0.203589
$834$	20.0294	0.693563
$835$	25.2197	0.872765
$836$	−33.8972	−1.17236
$837$	−0.571588	−0.0197570
$838$	8.02324	0.277158
$839$	−36.1307	−1.24737	−0.623684	−	0.781676i	$-0.714365\pi$
$839$	−36.1307	−1.24737	−0.623684	+	0.781676i	$0.714365\pi$
$840$	7.48062	0.258106
$841$	77.8493	2.68446
$842$	31.0305	1.06938
$843$	14.9966	0.516510
$844$	21.9110	0.754207
$845$	13.5391	0.465760
$846$	25.8070	0.887262
$847$	78.4678	2.69618
$848$	12.1992	0.418924
$849$	−10.5522	−0.362152
$850$	17.7894	0.610173
$851$	7.34444	0.251764
$852$	−33.2919	−1.14056
$853$	−35.8191	−1.22642	−0.613212	−	0.789918i	$-0.710123\pi$
$853$	−35.8191	−1.22642	−0.613212	+	0.789918i	$0.710123\pi$
$854$	−20.6788	−0.707615
$855$	17.7159	0.605871
$856$	8.82744	0.301716
$857$	41.0004	1.40055	0.700273	−	0.713875i	$-0.253061\pi$
$857$	41.0004	1.40055	0.700273	+	0.713875i	$0.253061\pi$
$858$	−6.35436	−0.216934
$859$	54.7221	1.86710	0.933548	−	0.358453i	$-0.116696\pi$
$859$	54.7221	1.86710	0.933548	+	0.358453i	$0.116696\pi$
$860$	−5.49512	−0.187382
$861$	67.3806	2.29632
$862$	22.0764	0.751926
$863$	−42.3404	−1.44129	−0.720643	−	0.693307i	$-0.756153\pi$
$863$	−42.3404	−1.44129	−0.720643	+	0.693307i	$0.756153\pi$
$864$	−0.154168	−0.00524491
$865$	14.6409	0.497806
$866$	−0.156908	−0.00533195
$867$	−9.74986	−0.331123
$868$	10.6707	0.362189
$869$	−74.7481	−2.53565
$870$	−26.8669	−0.910872
$871$	−0.798386	−0.0270523
$872$	16.6334	0.563279
$873$	45.9450	1.55500
$874$	4.40224	0.148908
$875$	26.9960	0.912630
$876$	24.1045	0.814416
$877$	−14.4458	−0.487799	−0.243899	−	0.969801i	$-0.578427\pi$
$877$	−14.4458	−0.487799	−0.243899	+	0.969801i	$0.578427\pi$
$878$	3.02494	0.102087
$879$	−30.3266	−1.02289
$880$	−6.52973	−0.220117
$881$	−41.2163	−1.38861	−0.694306	−	0.719679i	$-0.744289\pi$
$881$	−41.2163	−1.38861	−0.694306	+	0.719679i	$0.744289\pi$
$882$	3.93075	0.132355
$883$	−34.2417	−1.15232	−0.576162	−	0.817335i	$-0.695450\pi$
$883$	−34.2417	−1.15232	−0.576162	+	0.817335i	$0.695450\pi$
$884$	−1.91004	−0.0642415
$885$	−7.98302	−0.268346
$886$	−14.3152	−0.480928
$887$	17.9631	0.603140	0.301570	−	0.953444i	$-0.402489\pi$
$887$	17.9631	0.603140	0.301570	+	0.953444i	$0.402489\pi$
$888$	22.5105	0.755401
$889$	0.752224	0.0252288
$890$	12.5723	0.421426
$891$	−54.4857	−1.82534
$892$	12.2407	0.409850
$893$	−46.1758	−1.54521
$894$	−21.1987	−0.708990
$895$	−11.0831	−0.370468
$896$	2.87810	0.0961506
$897$	0.825245	0.0275541
$898$	32.2249	1.07536
$899$	−38.3243	−1.27819
$900$	−11.9004	−0.396680
$901$	−55.8504	−1.86065
$902$	−58.8156	−1.95835
$903$	−36.8902	−1.22763
$904$	5.90392	0.196361
$905$	7.60481	0.252793
$906$	45.1483	1.49995
$907$	29.5643	0.981668	0.490834	−	0.871253i	$-0.336692\pi$
$907$	29.5643	0.981668	0.490834	+	0.871253i	$0.336692\pi$
$908$	−27.0038	−0.896152
$909$	−37.4478	−1.24207
$910$	−1.26752	−0.0420180
$911$	52.2296	1.73045	0.865223	−	0.501388i	$-0.167177\pi$
$911$	52.2296	1.73045	0.865223	+	0.501388i	$0.167177\pi$
$912$	13.4927	0.446789
$913$	−59.8582	−1.98102
$914$	−7.48145	−0.247464
$915$	−18.6746	−0.617364
$916$	−13.3244	−0.440251
$917$	38.4783	1.27066
$918$	0.705810	0.0232952
$919$	27.6448	0.911919	0.455959	−	0.890001i	$-0.349296\pi$
$919$	27.6448	0.911919	0.455959	+	0.890001i	$0.349296\pi$
$920$	0.848020	0.0279584
$921$	−36.8057	−1.21279
$922$	24.0932	0.793467
$923$	5.64101	0.185676
$924$	−43.8359	−1.44209
$925$	35.5241	1.16803
$926$	−31.6641	−1.04055
$927$	−37.7101	−1.23856
$928$	−10.3368	−0.339322
$929$	−14.1209	−0.463291	−0.231646	−	0.972800i	$-0.574411\pi$
$929$	−14.1209	−0.463291	−0.231646	+	0.972800i	$0.574411\pi$
$930$	9.63652	0.315994
$931$	−7.03319	−0.230504
$932$	0.716424	0.0234672
$933$	−18.6692	−0.611204
$934$	−21.4071	−0.700461
$935$	29.8943	0.977648
$936$	1.27773	0.0417641
$937$	−18.3553	−0.599643	−0.299821	−	0.953995i	$-0.596927\pi$
$937$	−18.3553	−0.599643	−0.299821	+	0.953995i	$0.596927\pi$
$938$	−5.50770	−0.179833
$939$	−46.3055	−1.51112
$940$	−8.89501	−0.290123
$941$	24.9026	0.811802	0.405901	−	0.913917i	$-0.366958\pi$
$941$	24.9026	0.811802	0.405901	+	0.913917i	$0.366958\pi$
$942$	−30.9294	−1.00773
$943$	7.63842	0.248741
$944$	−3.07139	−0.0999654
$945$	0.468384	0.0152365
$946$	32.2010	1.04694
$947$	41.7484	1.35664	0.678320	−	0.734767i	$-0.262709\pi$
$947$	41.7484	1.35664	0.678320	+	0.734767i	$0.262709\pi$
$948$	29.7534	0.966345
$949$	−4.08430	−0.132582
$950$	21.2931	0.690839
$951$	51.8162	1.68026
$952$	−13.1765	−0.427052
$953$	41.9841	1.36000	0.680000	−	0.733213i	$-0.261980\pi$
$953$	41.9841	1.36000	0.680000	+	0.733213i	$0.261980\pi$
$954$	37.3616	1.20963
$955$	6.73623	0.217979
$956$	−11.7759	−0.380860
$957$	157.438	5.08925
$958$	38.5963	1.24699
$959$	−39.7289	−1.28291
$960$	2.59915	0.0838872
$961$	−17.2540	−0.556580
$962$	−3.81419	−0.122975
$963$	27.0350	0.871192
$964$	−10.1021	−0.325366
$965$	−6.32261	−0.203532
$966$	5.69299	0.183169
$967$	−7.10546	−0.228496	−0.114248	−	0.993452i	$-0.536446\pi$
$967$	−7.10546	−0.228496	−0.114248	+	0.993452i	$0.536446\pi$
$968$	27.2637	0.876290
$969$	−61.7721	−1.98441
$970$	−15.8361	−0.508466
$971$	−5.07989	−0.163021	−0.0815107	−	0.996672i	$-0.525974\pi$
$971$	−5.07989	−0.163021	−0.0815107	+	0.996672i	$0.525974\pi$
$972$	22.1505	0.710477
$973$	−23.4123	−0.750565
$974$	−11.2081	−0.359130
$975$	3.99160	0.127834
$976$	−7.18489	−0.229983
$977$	23.0992	0.739008	0.369504	−	0.929229i	$-0.379528\pi$
$977$	23.0992	0.739008	0.369504	+	0.929229i	$0.379528\pi$
$978$	13.5793	0.434219
$979$	−73.6730	−2.35460
$980$	−1.35483	−0.0432784
$981$	50.9418	1.62645
$982$	23.6515	0.754751
$983$	30.4547	0.971353	0.485676	−	0.874139i	$-0.338573\pi$
$983$	30.4547	0.971353	0.485676	+	0.874139i	$0.338573\pi$
$984$	23.4115	0.746331
$985$	20.5003	0.653194
$986$	47.3237	1.50709
$987$	−59.7146	−1.90074
$988$	−2.28622	−0.0727344
$989$	−4.18196	−0.132979
$990$	−19.9980	−0.635579
$991$	43.2227	1.37301	0.686506	−	0.727124i	$-0.259143\pi$
$991$	43.2227	1.37301	0.686506	+	0.727124i	$0.259143\pi$
$992$	3.70756	0.117715
$993$	9.38916	0.297956
$994$	38.9147	1.23430
$995$	−8.15748	−0.258610
$996$	23.8265	0.754971
$997$	6.19637	0.196241	0.0981206	−	0.995175i	$-0.468717\pi$
$997$	6.19637	0.196241	0.0981206	+	0.995175i	$0.468717\pi$
$998$	10.7102	0.339024
$999$	1.40945	0.0445929

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6022.2.a.b.1.10	✓	54

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6022.2.a.b.1.10	✓	54	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:	\( N \)	\(=\)	\( 6022 = 2 \cdot 3011 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6022.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.46224 q^{3} +1.00000 q^{4} -1.05561 q^{5} -2.46224 q^{6} +2.87810 q^{7} +1.00000 q^{8} +3.06261 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.46224 q^{3} +1.00000 q^{4} -1.05561 q^{5} -2.46224 q^{6} +2.87810 q^{7} +1.00000 q^{8} +3.06261 q^{9} -1.05561 q^{10} +6.18577 q^{11} -2.46224 q^{12} +0.417204 q^{13} +2.87810 q^{14} +2.59915 q^{15} +1.00000 q^{16} -4.57818 q^{17} +3.06261 q^{18} -5.47986 q^{19} -1.05561 q^{20} -7.08657 q^{21} +6.18577 q^{22} -0.803349 q^{23} -2.46224 q^{24} -3.88570 q^{25} +0.417204 q^{26} -0.154168 q^{27} +2.87810 q^{28} -10.3368 q^{29} +2.59915 q^{30} +3.70756 q^{31} +1.00000 q^{32} -15.2308 q^{33} -4.57818 q^{34} -3.03814 q^{35} +3.06261 q^{36} -9.14227 q^{37} -5.47986 q^{38} -1.02726 q^{39} -1.05561 q^{40} -9.50822 q^{41} -7.08657 q^{42} +5.20566 q^{43} +6.18577 q^{44} -3.23291 q^{45} -0.803349 q^{46} +8.42645 q^{47} -2.46224 q^{48} +1.28346 q^{49} -3.88570 q^{50} +11.2726 q^{51} +0.417204 q^{52} +12.1992 q^{53} -0.154168 q^{54} -6.52973 q^{55} +2.87810 q^{56} +13.4927 q^{57} -10.3368 q^{58} -3.07139 q^{59} +2.59915 q^{60} -7.18489 q^{61} +3.70756 q^{62} +8.81451 q^{63} +1.00000 q^{64} -0.440403 q^{65} -15.2308 q^{66} -1.91366 q^{67} -4.57818 q^{68} +1.97804 q^{69} -3.03814 q^{70} +13.5210 q^{71} +3.06261 q^{72} -9.78968 q^{73} -9.14227 q^{74} +9.56751 q^{75} -5.47986 q^{76} +17.8033 q^{77} -1.02726 q^{78} -12.0839 q^{79} -1.05561 q^{80} -8.80824 q^{81} -9.50822 q^{82} -9.67676 q^{83} -7.08657 q^{84} +4.83275 q^{85} +5.20566 q^{86} +25.4516 q^{87} +6.18577 q^{88} -11.9101 q^{89} -3.23291 q^{90} +1.20076 q^{91} -0.803349 q^{92} -9.12890 q^{93} +8.42645 q^{94} +5.78457 q^{95} -2.46224 q^{96} +15.0019 q^{97} +1.28346 q^{98} +18.9446 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 54 q + 54 q^{2} - 22 q^{3} + 54 q^{4} - 14 q^{5} - 22 q^{6} - 20 q^{7} + 54 q^{8} + 32 q^{9}+O(q^{10}) \) 54 * q + 54 * q^2 - 22 * q^3 + 54 * q^4 - 14 * q^5 - 22 * q^6 - 20 * q^7 + 54 * q^8 + 32 * q^9	\( 54 q + 54 q^{2} - 22 q^{3} + 54 q^{4} - 14 q^{5} - 22 q^{6} - 20 q^{7} + 54 q^{8} + 32 q^{9} - 14 q^{10} - 22 q^{11} - 22 q^{12} - 24 q^{13} - 20 q^{14} - 32 q^{15} + 54 q^{16} - 67 q^{17} + 32 q^{18} - 54 q^{19} - 14 q^{20} - 18 q^{21} - 22 q^{22} - 52 q^{23} - 22 q^{24} + 20 q^{25} - 24 q^{26} - 82 q^{27} - 20 q^{28} - 30 q^{29} - 32 q^{30} - 78 q^{31} + 54 q^{32} - 48 q^{33} - 67 q^{34} - 71 q^{35} + 32 q^{36} - 15 q^{37} - 54 q^{38} - 39 q^{39} - 14 q^{40} - 61 q^{41} - 18 q^{42} - 53 q^{43} - 22 q^{44} - 14 q^{45} - 52 q^{46} - 96 q^{47} - 22 q^{48} + 6 q^{49} + 20 q^{50} - 13 q^{51} - 24 q^{52} - 39 q^{53} - 82 q^{54} - 75 q^{55} - 20 q^{56} - 17 q^{57} - 30 q^{58} - 78 q^{59} - 32 q^{60} - 23 q^{61} - 78 q^{62} - 52 q^{63} + 54 q^{64} - 43 q^{65} - 48 q^{66} - 54 q^{67} - 67 q^{68} + 7 q^{69} - 71 q^{70} - 41 q^{71} + 32 q^{72} - 62 q^{73} - 15 q^{74} - 81 q^{75} - 54 q^{76} - 85 q^{77} - 39 q^{78} - 45 q^{79} - 14 q^{80} + 22 q^{81} - 61 q^{82} - 117 q^{83} - 18 q^{84} - 53 q^{86} - 84 q^{87} - 22 q^{88} - 60 q^{89} - 14 q^{90} - 60 q^{91} - 52 q^{92} + 26 q^{93} - 96 q^{94} - 44 q^{95} - 22 q^{96} - 48 q^{97} + 6 q^{98} + 7 q^{99}+O(q^{100}) \) 54 * q + 54 * q^2 - 22 * q^3 + 54 * q^4 - 14 * q^5 - 22 * q^6 - 20 * q^7 + 54 * q^8 + 32 * q^9 - 14 * q^10 - 22 * q^11 - 22 * q^12 - 24 * q^13 - 20 * q^14 - 32 * q^15 + 54 * q^16 - 67 * q^17 + 32 * q^18 - 54 * q^19 - 14 * q^20 - 18 * q^21 - 22 * q^22 - 52 * q^23 - 22 * q^24 + 20 * q^25 - 24 * q^26 - 82 * q^27 - 20 * q^28 - 30 * q^29 - 32 * q^30 - 78 * q^31 + 54 * q^32 - 48 * q^33 - 67 * q^34 - 71 * q^35 + 32 * q^36 - 15 * q^37 - 54 * q^38 - 39 * q^39 - 14 * q^40 - 61 * q^41 - 18 * q^42 - 53 * q^43 - 22 * q^44 - 14 * q^45 - 52 * q^46 - 96 * q^47 - 22 * q^48 + 6 * q^49 + 20 * q^50 - 13 * q^51 - 24 * q^52 - 39 * q^53 - 82 * q^54 - 75 * q^55 - 20 * q^56 - 17 * q^57 - 30 * q^58 - 78 * q^59 - 32 * q^60 - 23 * q^61 - 78 * q^62 - 52 * q^63 + 54 * q^64 - 43 * q^65 - 48 * q^66 - 54 * q^67 - 67 * q^68 + 7 * q^69 - 71 * q^70 - 41 * q^71 + 32 * q^72 - 62 * q^73 - 15 * q^74 - 81 * q^75 - 54 * q^76 - 85 * q^77 - 39 * q^78 - 45 * q^79 - 14 * q^80 + 22 * q^81 - 61 * q^82 - 117 * q^83 - 18 * q^84 - 53 * q^86 - 84 * q^87 - 22 * q^88 - 60 * q^89 - 14 * q^90 - 60 * q^91 - 52 * q^92 + 26 * q^93 - 96 * q^94 - 44 * q^95 - 22 * q^96 - 48 * q^97 + 6 * q^98 + 7 * q^99

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