LMFDB - Embedded newform 6022.2.a.b.1.16

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			1.16
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)

$f(q)$	$=$	$q+1.00000 q^{2} -1.62746 q^{3} +1.00000 q^{4} +2.10353 q^{5} -1.62746 q^{6} -4.91169 q^{7} +1.00000 q^{8} -0.351369 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.62746 q^{3} +1.00000 q^{4} +2.10353 q^{5} -1.62746 q^{6} -4.91169 q^{7} +1.00000 q^{8} -0.351369 q^{9} +2.10353 q^{10} +6.08737 q^{11} -1.62746 q^{12} -2.56497 q^{13} -4.91169 q^{14} -3.42342 q^{15} +1.00000 q^{16} -1.82198 q^{17} -0.351369 q^{18} +4.19930 q^{19} +2.10353 q^{20} +7.99359 q^{21} +6.08737 q^{22} -2.07878 q^{23} -1.62746 q^{24} -0.575144 q^{25} -2.56497 q^{26} +5.45422 q^{27} -4.91169 q^{28} +2.40083 q^{29} -3.42342 q^{30} -4.74126 q^{31} +1.00000 q^{32} -9.90696 q^{33} -1.82198 q^{34} -10.3319 q^{35} -0.351369 q^{36} -0.748878 q^{37} +4.19930 q^{38} +4.17439 q^{39} +2.10353 q^{40} -10.1621 q^{41} +7.99359 q^{42} -2.08697 q^{43} +6.08737 q^{44} -0.739117 q^{45} -2.07878 q^{46} -2.10375 q^{47} -1.62746 q^{48} +17.1247 q^{49} -0.575144 q^{50} +2.96519 q^{51} -2.56497 q^{52} -0.927999 q^{53} +5.45422 q^{54} +12.8050 q^{55} -4.91169 q^{56} -6.83420 q^{57} +2.40083 q^{58} +6.13896 q^{59} -3.42342 q^{60} +15.3036 q^{61} -4.74126 q^{62} +1.72582 q^{63} +1.00000 q^{64} -5.39550 q^{65} -9.90696 q^{66} -14.3117 q^{67} -1.82198 q^{68} +3.38313 q^{69} -10.3319 q^{70} -5.63182 q^{71} -0.351369 q^{72} +8.23490 q^{73} -0.748878 q^{74} +0.936025 q^{75} +4.19930 q^{76} -29.8993 q^{77} +4.17439 q^{78} +0.616466 q^{79} +2.10353 q^{80} -7.82243 q^{81} -10.1621 q^{82} -13.4711 q^{83} +7.99359 q^{84} -3.83259 q^{85} -2.08697 q^{86} -3.90725 q^{87} +6.08737 q^{88} -2.37643 q^{89} -0.739117 q^{90} +12.5983 q^{91} -2.07878 q^{92} +7.71621 q^{93} -2.10375 q^{94} +8.83338 q^{95} -1.62746 q^{96} -16.4587 q^{97} +17.1247 q^{98} -2.13891 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−1.62746	−0.939615	−0.469808	−	0.882769i	$-0.655677\pi$
$3$	−1.62746	−0.939615	−0.469808	+	0.882769i	$0.655677\pi$
$4$	1.00000	0.500000
$5$	2.10353	0.940729	0.470365	−	0.882472i	$-0.344122\pi$
$5$	2.10353	0.940729	0.470365	+	0.882472i	$0.344122\pi$
$6$	−1.62746	−0.664408
$7$	−4.91169	−1.85645	−0.928223	−	0.372025i	$-0.878664\pi$
$7$	−4.91169	−1.85645	−0.928223	+	0.372025i	$0.878664\pi$
$8$	1.00000	0.353553
$9$	−0.351369	−0.117123
$10$	2.10353	0.665196
$11$	6.08737	1.83541	0.917705	−	0.397261i	$-0.130039\pi$
$11$	6.08737	1.83541	0.917705	+	0.397261i	$0.130039\pi$
$12$	−1.62746	−0.469808
$13$	−2.56497	−0.711395	−0.355697	−	0.934601i	$-0.615757\pi$
$13$	−2.56497	−0.711395	−0.355697	+	0.934601i	$0.615757\pi$
$14$	−4.91169	−1.31271
$15$	−3.42342	−0.883923
$16$	1.00000	0.250000
$17$	−1.82198	−0.441894	−0.220947	−	0.975286i	$-0.570915\pi$
$17$	−1.82198	−0.441894	−0.220947	+	0.975286i	$0.570915\pi$
$18$	−0.351369	−0.0828185
$19$	4.19930	0.963386	0.481693	−	0.876340i	$-0.340022\pi$
$19$	4.19930	0.963386	0.481693	+	0.876340i	$0.340022\pi$
$20$	2.10353	0.470365
$21$	7.99359	1.74434
$22$	6.08737	1.29783
$23$	−2.07878	−0.433455	−0.216727	−	0.976232i	$-0.569538\pi$
$23$	−2.07878	−0.433455	−0.216727	+	0.976232i	$0.569538\pi$
$24$	−1.62746	−0.332204
$25$	−0.575144	−0.115029
$26$	−2.56497	−0.503032
$27$	5.45422	1.04967
$28$	−4.91169	−0.928223
$29$	2.40083	0.445822	0.222911	−	0.974839i	$-0.428444\pi$
$29$	2.40083	0.445822	0.222911	+	0.974839i	$0.428444\pi$
$30$	−3.42342	−0.625028
$31$	−4.74126	−0.851555	−0.425778	−	0.904828i	$-0.639999\pi$
$31$	−4.74126	−0.851555	−0.425778	+	0.904828i	$0.639999\pi$
$32$	1.00000	0.176777
$33$	−9.90696	−1.72458
$34$	−1.82198	−0.312466
$35$	−10.3319	−1.74641
$36$	−0.351369	−0.0585615
$37$	−0.748878	−0.123115	−0.0615574	−	0.998104i	$-0.519607\pi$
$37$	−0.748878	−0.123115	−0.0615574	+	0.998104i	$0.519607\pi$
$38$	4.19930	0.681217
$39$	4.17439	0.668437
$40$	2.10353	0.332598
$41$	−10.1621	−1.58705	−0.793524	−	0.608538i	$-0.791756\pi$
$41$	−10.1621	−1.58705	−0.793524	+	0.608538i	$0.791756\pi$
$42$	7.99359	1.23344
$43$	−2.08697	−0.318260	−0.159130	−	0.987258i	$-0.550869\pi$
$43$	−2.08697	−0.318260	−0.159130	+	0.987258i	$0.550869\pi$
$44$	6.08737	0.917705
$45$	−0.739117	−0.110181
$46$	−2.07878	−0.306499
$47$	−2.10375	−0.306864	−0.153432	−	0.988159i	$-0.549033\pi$
$47$	−2.10375	−0.306864	−0.153432	+	0.988159i	$0.549033\pi$
$48$	−1.62746	−0.234904
$49$	17.1247	2.44639
$50$	−0.575144	−0.0813377
$51$	2.96519	0.415210
$52$	−2.56497	−0.355697
$53$	−0.927999	−0.127471	−0.0637353	−	0.997967i	$-0.520301\pi$
$53$	−0.927999	−0.127471	−0.0637353	+	0.997967i	$0.520301\pi$
$54$	5.45422	0.742226
$55$	12.8050	1.72662
$56$	−4.91169	−0.656353
$57$	−6.83420	−0.905212
$58$	2.40083	0.315244
$59$	6.13896	0.799224	0.399612	−	0.916684i	$-0.369145\pi$
$59$	6.13896	0.799224	0.399612	+	0.916684i	$0.369145\pi$
$60$	−3.42342	−0.441962
$61$	15.3036	1.95942	0.979712	−	0.200411i	$-0.0642279\pi$
$61$	15.3036	1.95942	0.979712	+	0.200411i	$0.0642279\pi$
$62$	−4.74126	−0.602140
$63$	1.72582	0.217432
$64$	1.00000	0.125000
$65$	−5.39550	−0.669230
$66$	−9.90696	−1.21946
$67$	−14.3117	−1.74845	−0.874223	−	0.485524i	$-0.838629\pi$
$67$	−14.3117	−1.74845	−0.874223	+	0.485524i	$0.838629\pi$
$68$	−1.82198	−0.220947
$69$	3.38313	0.407281
$70$	−10.3319	−1.23490
$71$	−5.63182	−0.668374	−0.334187	−	0.942507i	$-0.608462\pi$
$71$	−5.63182	−0.668374	−0.334187	+	0.942507i	$0.608462\pi$
$72$	−0.351369	−0.0414092
$73$	8.23490	0.963823	0.481911	−	0.876220i	$-0.339943\pi$
$73$	8.23490	0.963823	0.481911	+	0.876220i	$0.339943\pi$
$74$	−0.748878	−0.0870553
$75$	0.936025	0.108083
$76$	4.19930	0.481693
$77$	−29.8993	−3.40734
$78$	4.17439	0.472657
$79$	0.616466	0.0693578	0.0346789	−	0.999399i	$-0.488959\pi$
$79$	0.616466	0.0693578	0.0346789	+	0.999399i	$0.488959\pi$
$80$	2.10353	0.235182
$81$	−7.82243	−0.869159
$82$	−10.1621	−1.12221
$83$	−13.4711	−1.47864	−0.739321	−	0.673353i	$-0.764854\pi$
$83$	−13.4711	−1.47864	−0.739321	+	0.673353i	$0.764854\pi$
$84$	7.99359	0.872172
$85$	−3.83259	−0.415702
$86$	−2.08697	−0.225044
$87$	−3.90725	−0.418902
$88$	6.08737	0.648916
$89$	−2.37643	−0.251901	−0.125950	−	0.992037i	$-0.540198\pi$
$89$	−2.37643	−0.251901	−0.125950	+	0.992037i	$0.540198\pi$
$90$	−0.739117	−0.0779097
$91$	12.5983	1.32067
$92$	−2.07878	−0.216727
$93$	7.71621	0.800134
$94$	−2.10375	−0.216985
$95$	8.83338	0.906285
$96$	−1.62746	−0.166102
$97$	−16.4587	−1.67113	−0.835566	−	0.549390i	$-0.814860\pi$
$97$	−16.4587	−1.67113	−0.835566	+	0.549390i	$0.814860\pi$
$98$	17.1247	1.72986
$99$	−2.13891	−0.214969
$100$	−0.575144	−0.0575144
$101$	5.11511	0.508972	0.254486	−	0.967076i	$-0.418094\pi$
$101$	5.11511	0.508972	0.254486	+	0.967076i	$0.418094\pi$
$102$	2.96519	0.293598
$103$	−10.0348	−0.988762	−0.494381	−	0.869245i	$-0.664605\pi$
$103$	−10.0348	−0.988762	−0.494381	+	0.869245i	$0.664605\pi$
$104$	−2.56497	−0.251516
$105$	16.8148	1.64096
$106$	−0.927999	−0.0901353
$107$	−3.22024	−0.311313	−0.155656	−	0.987811i	$-0.549749\pi$
$107$	−3.22024	−0.311313	−0.155656	+	0.987811i	$0.549749\pi$
$108$	5.45422	0.524833
$109$	2.98188	0.285612	0.142806	−	0.989751i	$-0.454387\pi$
$109$	2.98188	0.285612	0.142806	+	0.989751i	$0.454387\pi$
$110$	12.8050	1.22091
$111$	1.21877	0.115681
$112$	−4.91169	−0.464111
$113$	12.1139	1.13958	0.569790	−	0.821790i	$-0.307024\pi$
$113$	12.1139	1.13958	0.569790	+	0.821790i	$0.307024\pi$
$114$	−6.83420	−0.640082
$115$	−4.37278	−0.407763
$116$	2.40083	0.222911
$117$	0.901251	0.0833207
$118$	6.13896	0.565137
$119$	8.94899	0.820352
$120$	−3.42342	−0.312514
$121$	26.0561	2.36873
$122$	15.3036	1.38552
$123$	16.5384	1.49122
$124$	−4.74126	−0.425778
$125$	−11.7275	−1.04894
$126$	1.72582	0.153748
$127$	−7.72151	−0.685173	−0.342586	−	0.939486i	$-0.611303\pi$
$127$	−7.72151	−0.685173	−0.342586	+	0.939486i	$0.611303\pi$
$128$	1.00000	0.0883883
$129$	3.39646	0.299042
$130$	−5.39550	−0.473217
$131$	5.57445	0.487042	0.243521	−	0.969896i	$-0.421698\pi$
$131$	5.57445	0.487042	0.243521	+	0.969896i	$0.421698\pi$
$132$	−9.90696	−0.862290
$133$	−20.6257	−1.78847
$134$	−14.3117	−1.23634
$135$	11.4731	0.987451
$136$	−1.82198	−0.156233
$137$	−19.5939	−1.67402	−0.837008	−	0.547190i	$-0.815697\pi$
$137$	−19.5939	−1.67402	−0.837008	+	0.547190i	$0.815697\pi$
$138$	3.38313	0.287991
$139$	−16.6257	−1.41018	−0.705089	−	0.709119i	$-0.749093\pi$
$139$	−16.6257	−1.41018	−0.705089	+	0.709119i	$0.749093\pi$
$140$	−10.3319	−0.873206
$141$	3.42377	0.288334
$142$	−5.63182	−0.472612
$143$	−15.6139	−1.30570
$144$	−0.351369	−0.0292807
$145$	5.05022	0.419398
$146$	8.23490	0.681525
$147$	−27.8699	−2.29867
$148$	−0.748878	−0.0615574
$149$	16.8774	1.38265	0.691325	−	0.722544i	$-0.257027\pi$
$149$	16.8774	1.38265	0.691325	+	0.722544i	$0.257027\pi$
$150$	0.936025	0.0764261
$151$	−23.6125	−1.92156	−0.960778	−	0.277319i	$-0.910554\pi$
$151$	−23.6125	−1.92156	−0.960778	+	0.277319i	$0.910554\pi$
$152$	4.19930	0.340608
$153$	0.640186	0.0517559
$154$	−29.8993	−2.40935
$155$	−9.97340	−0.801083
$156$	4.17439	0.334219
$157$	3.22173	0.257122	0.128561	−	0.991702i	$-0.458964\pi$
$157$	3.22173	0.257122	0.128561	+	0.991702i	$0.458964\pi$
$158$	0.616466	0.0490434
$159$	1.51028	0.119773
$160$	2.10353	0.166299
$161$	10.2103	0.804685
$162$	−7.82243	−0.614588
$163$	−20.9435	−1.64042	−0.820211	−	0.572061i	$-0.806144\pi$
$163$	−20.9435	−1.64042	−0.820211	+	0.572061i	$0.806144\pi$
$164$	−10.1621	−0.793524
$165$	−20.8396	−1.62236
$166$	−13.4711	−1.04556
$167$	3.00473	0.232513	0.116256	−	0.993219i	$-0.462911\pi$
$167$	3.00473	0.232513	0.116256	+	0.993219i	$0.462911\pi$
$168$	7.99359	0.616719
$169$	−6.42093	−0.493918
$170$	−3.83259	−0.293946
$171$	−1.47550	−0.112835
$172$	−2.08697	−0.159130
$173$	−4.77399	−0.362960	−0.181480	−	0.983395i	$-0.558089\pi$
$173$	−4.77399	−0.362960	−0.181480	+	0.983395i	$0.558089\pi$
$174$	−3.90725	−0.296208
$175$	2.82493	0.213545
$176$	6.08737	0.458853
$177$	−9.99092	−0.750963
$178$	−2.37643	−0.178121
$179$	7.06775	0.528269	0.264134	−	0.964486i	$-0.414914\pi$
$179$	7.06775	0.528269	0.264134	+	0.964486i	$0.414914\pi$
$180$	−0.739117	−0.0550905
$181$	−6.71928	−0.499440	−0.249720	−	0.968318i	$-0.580339\pi$
$181$	−6.71928	−0.499440	−0.249720	+	0.968318i	$0.580339\pi$
$182$	12.5983	0.933852
$183$	−24.9060	−1.84110
$184$	−2.07878	−0.153249
$185$	−1.57529	−0.115818
$186$	7.71621	0.565780
$187$	−11.0910	−0.811057
$188$	−2.10375	−0.153432
$189$	−26.7895	−1.94865
$190$	8.83338	0.640840
$191$	−0.598372	−0.0432967	−0.0216483	−	0.999766i	$-0.506891\pi$
$191$	−0.598372	−0.0432967	−0.0216483	+	0.999766i	$0.506891\pi$
$192$	−1.62746	−0.117452
$193$	−3.15849	−0.227353	−0.113676	−	0.993518i	$-0.536263\pi$
$193$	−3.15849	−0.227353	−0.113676	+	0.993518i	$0.536263\pi$
$194$	−16.4587	−1.18167
$195$	8.78097	0.628818
$196$	17.1247	1.22320
$197$	−3.64879	−0.259966	−0.129983	−	0.991516i	$-0.541492\pi$
$197$	−3.64879	−0.259966	−0.129983	+	0.991516i	$0.541492\pi$
$198$	−2.13891	−0.152006
$199$	−2.42187	−0.171682	−0.0858409	−	0.996309i	$-0.527358\pi$
$199$	−2.42187	−0.171682	−0.0858409	+	0.996309i	$0.527358\pi$
$200$	−0.575144	−0.0406688
$201$	23.2917	1.64287
$202$	5.11511	0.359898
$203$	−11.7921	−0.827645
$204$	2.96519	0.207605
$205$	−21.3763	−1.49298
$206$	−10.0348	−0.699160
$207$	0.730417	0.0507675
$208$	−2.56497	−0.177849
$209$	25.5627	1.76821
$210$	16.8148	1.16033
$211$	−26.5310	−1.82647	−0.913234	−	0.407435i	$-0.866423\pi$
$211$	−26.5310	−1.82647	−0.913234	+	0.407435i	$0.866423\pi$
$212$	−0.927999	−0.0637353
$213$	9.16557	0.628014
$214$	−3.22024	−0.220131
$215$	−4.39001	−0.299396
$216$	5.45422	0.371113
$217$	23.2876	1.58087
$218$	2.98188	0.201958
$219$	−13.4020	−0.905622
$220$	12.8050	0.863312
$221$	4.67331	0.314361
$222$	1.21877	0.0817985
$223$	−3.47260	−0.232543	−0.116271	−	0.993217i	$-0.537094\pi$
$223$	−3.47260	−0.232543	−0.116271	+	0.993217i	$0.537094\pi$
$224$	−4.91169	−0.328176
$225$	0.202088	0.0134725
$226$	12.1139	0.805805
$227$	9.16574	0.608351	0.304176	−	0.952616i	$-0.401619\pi$
$227$	9.16574	0.608351	0.304176	+	0.952616i	$0.401619\pi$
$228$	−6.83420	−0.452606
$229$	−8.04944	−0.531922	−0.265961	−	0.963984i	$-0.585689\pi$
$229$	−8.04944	−0.531922	−0.265961	+	0.963984i	$0.585689\pi$
$230$	−4.37278	−0.288332
$231$	48.6600	3.20159
$232$	2.40083	0.157622
$233$	−6.16587	−0.403939	−0.201970	−	0.979392i	$-0.564734\pi$
$233$	−6.16587	−0.403939	−0.201970	+	0.979392i	$0.564734\pi$
$234$	0.901251	0.0589166
$235$	−4.42531	−0.288675
$236$	6.13896	0.399612
$237$	−1.00327	−0.0651697
$238$	8.94899	0.580077
$239$	16.5965	1.07354	0.536770	−	0.843729i	$-0.319644\pi$
$239$	16.5965	1.07354	0.536770	+	0.843729i	$0.319644\pi$
$240$	−3.42342	−0.220981
$241$	−24.1815	−1.55767	−0.778835	−	0.627229i	$-0.784189\pi$
$241$	−24.1815	−1.55767	−0.778835	+	0.627229i	$0.784189\pi$
$242$	26.0561	1.67495
$243$	−3.63196	−0.232991
$244$	15.3036	0.979712
$245$	36.0225	2.30139
$246$	16.5384	1.05445
$247$	−10.7711	−0.685348
$248$	−4.74126	−0.301070
$249$	21.9237	1.38936
$250$	−11.7275	−0.741713
$251$	−1.62315	−0.102452	−0.0512261	−	0.998687i	$-0.516313\pi$
$251$	−1.62315	−0.102452	−0.0512261	+	0.998687i	$0.516313\pi$
$252$	1.72582	0.108716
$253$	−12.6543	−0.795568
$254$	−7.72151	−0.484490
$255$	6.23739	0.390600
$256$	1.00000	0.0625000
$257$	15.4127	0.961415	0.480708	−	0.876881i	$-0.340380\pi$
$257$	15.4127	0.961415	0.480708	+	0.876881i	$0.340380\pi$
$258$	3.39646	0.211454
$259$	3.67826	0.228556
$260$	−5.39550	−0.334615
$261$	−0.843576	−0.0522161
$262$	5.57445	0.344391
$263$	8.83067	0.544522	0.272261	−	0.962223i	$-0.412229\pi$
$263$	8.83067	0.544522	0.272261	+	0.962223i	$0.412229\pi$
$264$	−9.90696	−0.609731
$265$	−1.95208	−0.119915
$266$	−20.6257	−1.26464
$267$	3.86755	0.236690
$268$	−14.3117	−0.874223
$269$	−15.7764	−0.961906	−0.480953	−	0.876746i	$-0.659709\pi$
$269$	−15.7764	−0.961906	−0.480953	+	0.876746i	$0.659709\pi$
$270$	11.4731	0.698233
$271$	−24.7262	−1.50201	−0.751004	−	0.660298i	$-0.770430\pi$
$271$	−24.7262	−1.50201	−0.751004	+	0.660298i	$0.770430\pi$
$272$	−1.82198	−0.110473
$273$	−20.5033	−1.24092
$274$	−19.5939	−1.18371
$275$	−3.50112	−0.211125
$276$	3.38313	0.203640
$277$	1.65492	0.0994345	0.0497173	−	0.998763i	$-0.484168\pi$
$277$	1.65492	0.0994345	0.0497173	+	0.998763i	$0.484168\pi$
$278$	−16.6257	−0.997146
$279$	1.66593	0.0997367
$280$	−10.3319	−0.617450
$281$	26.3455	1.57164	0.785820	−	0.618456i	$-0.212241\pi$
$281$	26.3455	1.57164	0.785820	+	0.618456i	$0.212241\pi$
$282$	3.42377	0.203883
$283$	−23.5673	−1.40093	−0.700464	−	0.713688i	$-0.747023\pi$
$283$	−23.5673	−1.40093	−0.700464	+	0.713688i	$0.747023\pi$
$284$	−5.63182	−0.334187
$285$	−14.3760	−0.851559
$286$	−15.6139	−0.923270
$287$	49.9130	2.94627
$288$	−0.351369	−0.0207046
$289$	−13.6804	−0.804730
$290$	5.05022	0.296559
$291$	26.7860	1.57022
$292$	8.23490	0.481911
$293$	−6.77970	−0.396074	−0.198037	−	0.980194i	$-0.563457\pi$
$293$	−6.77970	−0.396074	−0.198037	+	0.980194i	$0.563457\pi$
$294$	−27.8699	−1.62540
$295$	12.9135	0.751853
$296$	−0.748878	−0.0435277
$297$	33.2019	1.92657
$298$	16.8774	0.977681
$299$	5.33200	0.308357
$300$	0.936025	0.0540414
$301$	10.2506	0.590832
$302$	−23.6125	−1.35875
$303$	−8.32464	−0.478238
$304$	4.19930	0.240846
$305$	32.1916	1.84329
$306$	0.640186	0.0365970
$307$	18.4427	1.05258	0.526292	−	0.850304i	$-0.323582\pi$
$307$	18.4427	1.05258	0.526292	+	0.850304i	$0.323582\pi$
$308$	−29.8993	−1.70367
$309$	16.3313	0.929056
$310$	−9.97340	−0.566451
$311$	11.1406	0.631727	0.315863	−	0.948805i	$-0.397706\pi$
$311$	11.1406	0.631727	0.315863	+	0.948805i	$0.397706\pi$
$312$	4.17439	0.236328
$313$	4.88378	0.276048	0.138024	−	0.990429i	$-0.455925\pi$
$313$	4.88378	0.276048	0.138024	+	0.990429i	$0.455925\pi$
$314$	3.22173	0.181813
$315$	3.63031	0.204545
$316$	0.616466	0.0346789
$317$	17.8658	1.00344	0.501722	−	0.865029i	$-0.332700\pi$
$317$	17.8658	1.00344	0.501722	+	0.865029i	$0.332700\pi$
$318$	1.51028	0.0846925
$319$	14.6147	0.818267
$320$	2.10353	0.117591
$321$	5.24082	0.292514
$322$	10.2103	0.568998
$323$	−7.65103	−0.425714
$324$	−7.82243	−0.434580
$325$	1.47523	0.0818309
$326$	−20.9435	−1.15995
$327$	−4.85289	−0.268365
$328$	−10.1621	−0.561106
$329$	10.3330	0.569676
$330$	−20.8396	−1.14718
$331$	−5.79924	−0.318755	−0.159378	−	0.987218i	$-0.550949\pi$
$331$	−5.79924	−0.318755	−0.159378	+	0.987218i	$0.550949\pi$
$332$	−13.4711	−0.739321
$333$	0.263133	0.0144196
$334$	3.00473	0.164411
$335$	−30.1051	−1.64481
$336$	7.99359	0.436086
$337$	23.6398	1.28774	0.643872	−	0.765134i	$-0.277327\pi$
$337$	23.6398	1.28774	0.643872	+	0.765134i	$0.277327\pi$
$338$	−6.42093	−0.349252
$339$	−19.7149	−1.07077
$340$	−3.83259	−0.207851
$341$	−28.8618	−1.56295
$342$	−1.47550	−0.0797861
$343$	−49.7296	−2.68515
$344$	−2.08697	−0.112522
$345$	7.11652	0.383141
$346$	−4.77399	−0.256652
$347$	−10.4978	−0.563552	−0.281776	−	0.959480i	$-0.590924\pi$
$347$	−10.4978	−0.563552	−0.281776	+	0.959480i	$0.590924\pi$
$348$	−3.90725	−0.209451
$349$	−20.0434	−1.07290	−0.536448	−	0.843933i	$-0.680234\pi$
$349$	−20.0434	−1.07290	−0.536448	+	0.843933i	$0.680234\pi$
$350$	2.82493	0.150999
$351$	−13.9899	−0.746727
$352$	6.08737	0.324458
$353$	−22.6094	−1.20338	−0.601688	−	0.798731i	$-0.705505\pi$
$353$	−22.6094	−1.20338	−0.601688	+	0.798731i	$0.705505\pi$
$354$	−9.99092	−0.531011
$355$	−11.8467	−0.628759
$356$	−2.37643	−0.125950
$357$	−14.5641	−0.770815
$358$	7.06775	0.373542
$359$	9.10833	0.480719	0.240360	−	0.970684i	$-0.422735\pi$
$359$	9.10833	0.480719	0.240360	+	0.970684i	$0.422735\pi$
$360$	−0.739117	−0.0389549
$361$	−1.36586	−0.0718874
$362$	−6.71928	−0.353157
$363$	−42.4052	−2.22570
$364$	12.5983	0.660333
$365$	17.3224	0.906696
$366$	−24.9060	−1.30186
$367$	24.9073	1.30015	0.650075	−	0.759870i	$-0.274737\pi$
$367$	24.9073	1.30015	0.650075	+	0.759870i	$0.274737\pi$
$368$	−2.07878	−0.108364
$369$	3.57064	0.185880
$370$	−1.57529	−0.0818955
$371$	4.55805	0.236642
$372$	7.71621	0.400067
$373$	32.6470	1.69040	0.845199	−	0.534452i	$-0.179482\pi$
$373$	32.6470	1.69040	0.845199	+	0.534452i	$0.179482\pi$
$374$	−11.0910	−0.573504
$375$	19.0861	0.985600
$376$	−2.10375	−0.108493
$377$	−6.15805	−0.317156
$378$	−26.7895	−1.37790
$379$	11.3859	0.584855	0.292427	−	0.956288i	$-0.405537\pi$
$379$	11.3859	0.584855	0.292427	+	0.956288i	$0.405537\pi$
$380$	8.83338	0.453143
$381$	12.5665	0.643799
$382$	−0.598372	−0.0306154
$383$	−0.140984	−0.00720396	−0.00360198	−	0.999994i	$-0.501147\pi$
$383$	−0.140984	−0.00720396	−0.00360198	+	0.999994i	$0.501147\pi$
$384$	−1.62746	−0.0830510
$385$	−62.8942	−3.20538
$386$	−3.15849	−0.160763
$387$	0.733296	0.0372755
$388$	−16.4587	−0.835566
$389$	−33.0013	−1.67323	−0.836617	−	0.547789i	$-0.815470\pi$
$389$	−33.0013	−1.67323	−0.836617	+	0.547789i	$0.815470\pi$
$390$	8.78097	0.444642
$391$	3.78748	0.191541
$392$	17.1247	0.864930
$393$	−9.07220	−0.457632
$394$	−3.64879	−0.183824
$395$	1.29676	0.0652469
$396$	−2.13891	−0.107484
$397$	−9.91371	−0.497555	−0.248777	−	0.968561i	$-0.580029\pi$
$397$	−9.91371	−0.497555	−0.248777	+	0.968561i	$0.580029\pi$
$398$	−2.42187	−0.121397
$399$	33.5675	1.68048
$400$	−0.575144	−0.0287572
$401$	23.8601	1.19151	0.595757	−	0.803164i	$-0.296852\pi$
$401$	23.8601	1.19151	0.595757	+	0.803164i	$0.296852\pi$
$402$	23.2917	1.16168
$403$	12.1612	0.605792
$404$	5.11511	0.254486
$405$	−16.4548	−0.817643
$406$	−11.7921	−0.585234
$407$	−4.55870	−0.225966
$408$	2.96519	0.146799
$409$	5.23304	0.258757	0.129379	−	0.991595i	$-0.458702\pi$
$409$	5.23304	0.258757	0.129379	+	0.991595i	$0.458702\pi$
$410$	−21.3763	−1.05570
$411$	31.8883	1.57293
$412$	−10.0348	−0.494381
$413$	−30.1527	−1.48372
$414$	0.730417	0.0358981
$415$	−28.3369	−1.39100
$416$	−2.56497	−0.125758
$417$	27.0578	1.32502
$418$	25.5627	1.25031
$419$	−26.7199	−1.30535	−0.652676	−	0.757637i	$-0.726354\pi$
$419$	−26.7199	−1.30535	−0.652676	+	0.757637i	$0.726354\pi$
$420$	16.8148	0.820478
$421$	25.5872	1.24704	0.623521	−	0.781806i	$-0.285702\pi$
$421$	25.5872	1.24704	0.623521	+	0.781806i	$0.285702\pi$
$422$	−26.5310	−1.29151
$423$	0.739193	0.0359408
$424$	−0.927999	−0.0450676
$425$	1.04790	0.0508305
$426$	9.16557	0.444073
$427$	−75.1665	−3.63756
$428$	−3.22024	−0.155656
$429$	25.4111	1.22686
$430$	−4.39001	−0.211705
$431$	4.83298	0.232797	0.116398	−	0.993203i	$-0.462865\pi$
$431$	4.83298	0.232797	0.116398	+	0.993203i	$0.462865\pi$
$432$	5.45422	0.262416
$433$	−6.29757	−0.302642	−0.151321	−	0.988485i	$-0.548353\pi$
$433$	−6.29757	−0.302642	−0.151321	+	0.988485i	$0.548353\pi$
$434$	23.2876	1.11784
$435$	−8.21904	−0.394073
$436$	2.98188	0.142806
$437$	−8.72941	−0.417584
$438$	−13.4020	−0.640372
$439$	−27.3404	−1.30489	−0.652443	−	0.757838i	$-0.726256\pi$
$439$	−27.3404	−1.30489	−0.652443	+	0.757838i	$0.726256\pi$
$440$	12.8050	0.610454
$441$	−6.01710	−0.286529
$442$	4.67331	0.222287
$443$	25.4810	1.21064	0.605320	−	0.795982i	$-0.293045\pi$
$443$	25.4810	1.21064	0.605320	+	0.795982i	$0.293045\pi$
$444$	1.21877	0.0578403
$445$	−4.99890	−0.236971
$446$	−3.47260	−0.164433
$447$	−27.4673	−1.29916
$448$	−4.91169	−0.232056
$449$	−32.7123	−1.54379	−0.771894	−	0.635751i	$-0.780690\pi$
$449$	−32.7123	−1.54379	−0.771894	+	0.635751i	$0.780690\pi$
$450$	0.202088	0.00952651
$451$	−61.8603	−2.91289
$452$	12.1139	0.569790
$453$	38.4284	1.80552
$454$	9.16574	0.430169
$455$	26.5011	1.24239
$456$	−6.83420	−0.320041
$457$	7.22567	0.338003	0.169001	−	0.985616i	$-0.445946\pi$
$457$	7.22567	0.338003	0.169001	+	0.985616i	$0.445946\pi$
$458$	−8.04944	−0.376125
$459$	−9.93746	−0.463841
$460$	−4.37278	−0.203882
$461$	−4.02279	−0.187360	−0.0936800	−	0.995602i	$-0.529863\pi$
$461$	−4.02279	−0.187360	−0.0936800	+	0.995602i	$0.529863\pi$
$462$	48.6600	2.26387
$463$	6.05720	0.281502	0.140751	−	0.990045i	$-0.455048\pi$
$463$	6.05720	0.281502	0.140751	+	0.990045i	$0.455048\pi$
$464$	2.40083	0.111456
$465$	16.2313	0.752710
$466$	−6.16587	−0.285628
$467$	−10.7642	−0.498108	−0.249054	−	0.968490i	$-0.580120\pi$
$467$	−10.7642	−0.498108	−0.249054	+	0.968490i	$0.580120\pi$
$468$	0.901251	0.0416603
$469$	70.2945	3.24590
$470$	−4.42531	−0.204124
$471$	−5.24324	−0.241596
$472$	6.13896	0.282568
$473$	−12.7042	−0.584138
$474$	−1.00327	−0.0460819
$475$	−2.41520	−0.110817
$476$	8.94899	0.410176
$477$	0.326070	0.0149297
$478$	16.5965	0.759107
$479$	−29.9899	−1.37027	−0.685137	−	0.728414i	$-0.740258\pi$
$479$	−29.9899	−1.37027	−0.685137	+	0.728414i	$0.740258\pi$
$480$	−3.42342	−0.156257
$481$	1.92085	0.0875832
$482$	−24.1815	−1.10144
$483$	−16.6169	−0.756095
$484$	26.0561	1.18437
$485$	−34.6215	−1.57208
$486$	−3.63196	−0.164749
$487$	30.4453	1.37961	0.689803	−	0.723997i	$-0.257697\pi$
$487$	30.4453	1.37961	0.689803	+	0.723997i	$0.257697\pi$
$488$	15.3036	0.692761
$489$	34.0848	1.54137
$490$	36.0225	1.62733
$491$	−9.48169	−0.427903	−0.213951	−	0.976844i	$-0.568633\pi$
$491$	−9.48169	−0.427903	−0.213951	+	0.976844i	$0.568633\pi$
$492$	16.5384	0.745608
$493$	−4.37425	−0.197006
$494$	−10.7711	−0.484614
$495$	−4.49928	−0.202227
$496$	−4.74126	−0.212889
$497$	27.6618	1.24080
$498$	21.9237	0.982423
$499$	7.74378	0.346659	0.173330	−	0.984864i	$-0.444547\pi$
$499$	7.74378	0.346659	0.173330	+	0.984864i	$0.444547\pi$
$500$	−11.7275	−0.524470
$501$	−4.89008	−0.218473
$502$	−1.62315	−0.0724446
$503$	−13.3211	−0.593956	−0.296978	−	0.954884i	$-0.595979\pi$
$503$	−13.3211	−0.593956	−0.296978	+	0.954884i	$0.595979\pi$
$504$	1.72582	0.0768740
$505$	10.7598	0.478805
$506$	−12.6543	−0.562551
$507$	10.4498	0.464093
$508$	−7.72151	−0.342586
$509$	11.3024	0.500969	0.250485	−	0.968121i	$-0.419410\pi$
$509$	11.3024	0.500969	0.250485	+	0.968121i	$0.419410\pi$
$510$	6.23739	0.276196
$511$	−40.4473	−1.78928
$512$	1.00000	0.0441942
$513$	22.9039	1.01123
$514$	15.4127	0.679823
$515$	−21.1086	−0.930157
$516$	3.39646	0.149521
$517$	−12.8063	−0.563221
$518$	3.67826	0.161613
$519$	7.76949	0.341043
$520$	−5.39550	−0.236608
$521$	−38.5423	−1.68857	−0.844285	−	0.535894i	$-0.819975\pi$
$521$	−38.5423	−1.68857	−0.844285	+	0.535894i	$0.819975\pi$
$522$	−0.843576	−0.0369223
$523$	4.59991	0.201140	0.100570	−	0.994930i	$-0.467933\pi$
$523$	4.59991	0.201140	0.100570	+	0.994930i	$0.467933\pi$
$524$	5.57445	0.243521
$525$	−4.59747	−0.200650
$526$	8.83067	0.385035
$527$	8.63846	0.376297
$528$	−9.90696	−0.431145
$529$	−18.6787	−0.812117
$530$	−1.95208	−0.0847929
$531$	−2.15704	−0.0936075
$532$	−20.6257	−0.894237
$533$	26.0654	1.12902
$534$	3.86755	0.167365
$535$	−6.77389	−0.292861
$536$	−14.3117	−0.618169
$537$	−11.5025	−0.496369
$538$	−15.7764	−0.680170
$539$	104.245	4.49013
$540$	11.4731	0.493726
$541$	12.1740	0.523403	0.261702	−	0.965149i	$-0.415716\pi$
$541$	12.1740	0.523403	0.261702	+	0.965149i	$0.415716\pi$
$542$	−24.7262	−1.06208
$543$	10.9354	0.469281
$544$	−1.82198	−0.0781166
$545$	6.27248	0.268684
$546$	−20.5033	−0.877461
$547$	23.4256	1.00161	0.500803	−	0.865561i	$-0.333038\pi$
$547$	23.4256	1.00161	0.500803	+	0.865561i	$0.333038\pi$
$548$	−19.5939	−0.837008
$549$	−5.37721	−0.229494
$550$	−3.50112	−0.149288
$551$	10.0818	0.429499
$552$	3.38313	0.143995
$553$	−3.02789	−0.128759
$554$	1.65492	0.0703108
$555$	2.56373	0.108824
$556$	−16.6257	−0.705089
$557$	−13.9913	−0.592832	−0.296416	−	0.955059i	$-0.595791\pi$
$557$	−13.9913	−0.592832	−0.296416	+	0.955059i	$0.595791\pi$
$558$	1.66593	0.0705245
$559$	5.35301	0.226408
$560$	−10.3319	−0.436603
$561$	18.0502	0.762082
$562$	26.3455	1.11132
$563$	−7.93251	−0.334315	−0.167158	−	0.985930i	$-0.553459\pi$
$563$	−7.93251	−0.334315	−0.167158	+	0.985930i	$0.553459\pi$
$564$	3.42377	0.144167
$565$	25.4820	1.07204
$566$	−23.5673	−0.990605
$567$	38.4214	1.61355
$568$	−5.63182	−0.236306
$569$	37.7534	1.58271	0.791353	−	0.611360i	$-0.209377\pi$
$569$	37.7534	1.58271	0.791353	+	0.611360i	$0.209377\pi$
$570$	−14.3760	−0.602143
$571$	−46.1078	−1.92955	−0.964775	−	0.263076i	$-0.915263\pi$
$571$	−46.1078	−1.92955	−0.964775	+	0.263076i	$0.915263\pi$
$572$	−15.6139	−0.652851
$573$	0.973828	0.0406822
$574$	49.9130	2.08333
$575$	1.19560	0.0498598
$576$	−0.351369	−0.0146404
$577$	−1.86629	−0.0776945	−0.0388472	−	0.999245i	$-0.512369\pi$
$577$	−1.86629	−0.0776945	−0.0388472	+	0.999245i	$0.512369\pi$
$578$	−13.6804	−0.569030
$579$	5.14031	0.213624
$580$	5.05022	0.209699
$581$	66.1658	2.74502
$582$	26.7860	1.11031
$583$	−5.64908	−0.233961
$584$	8.23490	0.340763
$585$	1.89581	0.0783822
$586$	−6.77970	−0.280067
$587$	12.6273	0.521186	0.260593	−	0.965449i	$-0.416082\pi$
$587$	12.6273	0.521186	0.260593	+	0.965449i	$0.416082\pi$
$588$	−27.8699	−1.14933
$589$	−19.9100	−0.820376
$590$	12.9135	0.531641
$591$	5.93827	0.244268
$592$	−0.748878	−0.0307787
$593$	34.8637	1.43168	0.715841	−	0.698264i	$-0.246044\pi$
$593$	34.8637	1.43168	0.715841	+	0.698264i	$0.246044\pi$
$594$	33.2019	1.36229
$595$	18.8245	0.771729
$596$	16.8774	0.691325
$597$	3.94150	0.161315
$598$	5.33200	0.218042
$599$	−17.7578	−0.725564	−0.362782	−	0.931874i	$-0.618173\pi$
$599$	−17.7578	−0.725564	−0.362782	+	0.931874i	$0.618173\pi$
$600$	0.936025	0.0382131
$601$	19.3559	0.789545	0.394772	−	0.918779i	$-0.370823\pi$
$601$	19.3559	0.789545	0.394772	+	0.918779i	$0.370823\pi$
$602$	10.2506	0.417781
$603$	5.02867	0.204783
$604$	−23.6125	−0.960778
$605$	54.8098	2.22834
$606$	−8.32464	−0.338166
$607$	17.7050	0.718622	0.359311	−	0.933218i	$-0.383012\pi$
$607$	17.7050	0.718622	0.359311	+	0.933218i	$0.383012\pi$
$608$	4.19930	0.170304
$609$	19.1912	0.777668
$610$	32.1916	1.30340
$611$	5.39606	0.218301
$612$	0.640186	0.0258780
$613$	−23.3412	−0.942742	−0.471371	−	0.881935i	$-0.656241\pi$
$613$	−23.3412	−0.942742	−0.471371	+	0.881935i	$0.656241\pi$
$614$	18.4427	0.744289
$615$	34.7890	1.40283
$616$	−29.8993	−1.20468
$617$	44.0215	1.77224	0.886119	−	0.463459i	$-0.153392\pi$
$617$	44.0215	1.77224	0.886119	+	0.463459i	$0.153392\pi$
$618$	16.3313	0.656942
$619$	−45.6397	−1.83441	−0.917207	−	0.398411i	$-0.869562\pi$
$619$	−45.6397	−1.83441	−0.917207	+	0.398411i	$0.869562\pi$
$620$	−9.97340	−0.400541
$621$	−11.3381	−0.454983
$622$	11.1406	0.446698
$623$	11.6723	0.467640
$624$	4.17439	0.167109
$625$	−21.7935	−0.871740
$626$	4.88378	0.195195
$627$	−41.6023	−1.66144
$628$	3.22173	0.128561
$629$	1.36444	0.0544037
$630$	3.63031	0.144635
$631$	37.3381	1.48641	0.743204	−	0.669065i	$-0.233305\pi$
$631$	37.3381	1.48641	0.743204	+	0.669065i	$0.233305\pi$
$632$	0.616466	0.0245217
$633$	43.1782	1.71618
$634$	17.8658	0.709542
$635$	−16.2425	−0.644562
$636$	1.51028	0.0598866
$637$	−43.9244	−1.74035
$638$	14.6147	0.578602
$639$	1.97885	0.0782819
$640$	2.10353	0.0831495
$641$	−11.5380	−0.455725	−0.227863	−	0.973693i	$-0.573174\pi$
$641$	−11.5380	−0.455725	−0.227863	+	0.973693i	$0.573174\pi$
$642$	5.24082	0.206839
$643$	−45.1682	−1.78126	−0.890630	−	0.454728i	$-0.849736\pi$
$643$	−45.1682	−1.78126	−0.890630	+	0.454728i	$0.849736\pi$
$644$	10.2103	0.402343
$645$	7.14457	0.281317
$646$	−7.65103	−0.301026
$647$	6.38067	0.250850	0.125425	−	0.992103i	$-0.459971\pi$
$647$	6.38067	0.250850	0.125425	+	0.992103i	$0.459971\pi$
$648$	−7.82243	−0.307294
$649$	37.3701	1.46690
$650$	1.47523	0.0578632
$651$	−37.8997	−1.48541
$652$	−20.9435	−0.820211
$653$	−11.2083	−0.438615	−0.219307	−	0.975656i	$-0.570380\pi$
$653$	−11.2083	−0.438615	−0.219307	+	0.975656i	$0.570380\pi$
$654$	−4.85289	−0.189763
$655$	11.7260	0.458174
$656$	−10.1621	−0.396762
$657$	−2.89349	−0.112886
$658$	10.3330	0.402821
$659$	−18.9514	−0.738240	−0.369120	−	0.929382i	$-0.620341\pi$
$659$	−18.9514	−0.738240	−0.369120	+	0.929382i	$0.620341\pi$
$660$	−20.8396	−0.811181
$661$	13.8090	0.537106	0.268553	−	0.963265i	$-0.413455\pi$
$661$	13.8090	0.537106	0.268553	+	0.963265i	$0.413455\pi$
$662$	−5.79924	−0.225394
$663$	−7.60564	−0.295378
$664$	−13.4711	−0.522779
$665$	−43.3868	−1.68247
$666$	0.263133	0.0101962
$667$	−4.99078	−0.193244
$668$	3.00473	0.116256
$669$	5.65153	0.218501
$670$	−30.1051	−1.16306
$671$	93.1586	3.59635
$672$	7.99359	0.308360
$673$	−15.7900	−0.608659	−0.304329	−	0.952567i	$-0.598432\pi$
$673$	−15.7900	−0.608659	−0.304329	+	0.952567i	$0.598432\pi$
$674$	23.6398	0.910572
$675$	−3.13697	−0.120742
$676$	−6.42093	−0.246959
$677$	46.7503	1.79676	0.898380	−	0.439219i	$-0.144745\pi$
$677$	46.7503	1.79676	0.898380	+	0.439219i	$0.144745\pi$
$678$	−19.7149	−0.757147
$679$	80.8403	3.10237
$680$	−3.83259	−0.146973
$681$	−14.9169	−0.571616
$682$	−28.8618	−1.10518
$683$	5.27155	0.201710	0.100855	−	0.994901i	$-0.467842\pi$
$683$	5.27155	0.201710	0.100855	+	0.994901i	$0.467842\pi$
$684$	−1.47550	−0.0564173
$685$	−41.2164	−1.57480
$686$	−49.7296	−1.89869
$687$	13.1001	0.499802
$688$	−2.08697	−0.0795650
$689$	2.38029	0.0906819
$690$	7.11652	0.270921
$691$	−21.1385	−0.804146	−0.402073	−	0.915608i	$-0.631710\pi$
$691$	−21.1385	−0.804146	−0.402073	+	0.915608i	$0.631710\pi$
$692$	−4.77399	−0.181480
$693$	10.5057	0.399078
$694$	−10.4978	−0.398491
$695$	−34.9728	−1.32660
$696$	−3.90725	−0.148104
$697$	18.5150	0.701307
$698$	−20.0434	−0.758652
$699$	10.0347	0.379548
$700$	2.82493	0.106772
$701$	19.0372	0.719027	0.359513	−	0.933140i	$-0.382943\pi$
$701$	19.0372	0.719027	0.359513	+	0.933140i	$0.382943\pi$
$702$	−13.9899	−0.528016
$703$	−3.14477	−0.118607
$704$	6.08737	0.229426
$705$	7.20202	0.271244
$706$	−22.6094	−0.850915
$707$	−25.1239	−0.944880
$708$	−9.99092	−0.375482
$709$	35.7998	1.34449	0.672245	−	0.740329i	$-0.265330\pi$
$709$	35.7998	1.34449	0.672245	+	0.740329i	$0.265330\pi$
$710$	−11.8467	−0.444599
$711$	−0.216607	−0.00812339
$712$	−2.37643	−0.0890604
$713$	9.85601	0.369111
$714$	−14.5641	−0.545049
$715$	−32.8444	−1.22831
$716$	7.06775	0.264134
$717$	−27.0102	−1.00871
$718$	9.10833	0.339920
$719$	37.4400	1.39628	0.698138	−	0.715963i	$-0.254012\pi$
$719$	37.4400	1.39628	0.698138	+	0.715963i	$0.254012\pi$
$720$	−0.739117	−0.0275453
$721$	49.2881	1.83558
$722$	−1.36586	−0.0508321
$723$	39.3545	1.46361
$724$	−6.71928	−0.249720
$725$	−1.38082	−0.0512824
$726$	−42.4052	−1.57381
$727$	6.89714	0.255801	0.127900	−	0.991787i	$-0.459176\pi$
$727$	6.89714	0.255801	0.127900	+	0.991787i	$0.459176\pi$
$728$	12.5983	0.466926
$729$	29.3782	1.08808
$730$	17.3224	0.641131
$731$	3.80241	0.140637
$732$	−24.9060	−0.920552
$733$	−45.7875	−1.69120	−0.845600	−	0.533817i	$-0.820757\pi$
$733$	−45.7875	−1.69120	−0.845600	+	0.533817i	$0.820757\pi$
$734$	24.9073	0.919346
$735$	−58.6252	−2.16242
$736$	−2.07878	−0.0766247
$737$	−87.1203	−3.20912
$738$	3.57064	0.131437
$739$	−17.0564	−0.627431	−0.313716	−	0.949517i	$-0.601574\pi$
$739$	−17.0564	−0.627431	−0.313716	+	0.949517i	$0.601574\pi$
$740$	−1.57529	−0.0579088
$741$	17.5295	0.643963
$742$	4.55805	0.167331
$743$	4.07022	0.149322	0.0746610	−	0.997209i	$-0.476213\pi$
$743$	4.07022	0.149322	0.0746610	+	0.997209i	$0.476213\pi$
$744$	7.71621	0.282890
$745$	35.5022	1.30070
$746$	32.6470	1.19529
$747$	4.73332	0.173183
$748$	−11.0910	−0.405528
$749$	15.8169	0.577935
$750$	19.0861	0.696925
$751$	−36.4893	−1.33151	−0.665757	−	0.746169i	$-0.731891\pi$
$751$	−36.4893	−1.33151	−0.665757	+	0.746169i	$0.731891\pi$
$752$	−2.10375	−0.0767159
$753$	2.64161	0.0962657
$754$	−6.15805	−0.224263
$755$	−49.6696	−1.80766
$756$	−26.7895	−0.974324
$757$	40.3930	1.46811	0.734054	−	0.679091i	$-0.237626\pi$
$757$	40.3930	1.46811	0.734054	+	0.679091i	$0.237626\pi$
$758$	11.3859	0.413555
$759$	20.5943	0.747527
$760$	8.83338	0.320420
$761$	33.1457	1.20153	0.600766	−	0.799425i	$-0.294862\pi$
$761$	33.1457	1.20153	0.600766	+	0.799425i	$0.294862\pi$
$762$	12.5665	0.455235
$763$	−14.6461	−0.530223
$764$	−0.598372	−0.0216483
$765$	1.34665	0.0486883
$766$	−0.140984	−0.00509397
$767$	−15.7462	−0.568564
$768$	−1.62746	−0.0587260
$769$	−42.6930	−1.53955	−0.769774	−	0.638317i	$-0.779631\pi$
$769$	−42.6930	−1.53955	−0.769774	+	0.638317i	$0.779631\pi$
$770$	−62.8942	−2.26655
$771$	−25.0835	−0.903360
$772$	−3.15849	−0.113676
$773$	16.3364	0.587578	0.293789	−	0.955870i	$-0.405084\pi$
$773$	16.3364	0.587578	0.293789	+	0.955870i	$0.405084\pi$
$774$	0.733296	0.0263578
$775$	2.72691	0.0979534
$776$	−16.4587	−0.590835
$777$	−5.98623	−0.214755
$778$	−33.0013	−1.18315
$779$	−42.6736	−1.52894
$780$	8.78097	0.314409
$781$	−34.2830	−1.22674
$782$	3.78748	0.135440
$783$	13.0947	0.467965
$784$	17.1247	0.611598
$785$	6.77702	0.241882
$786$	−9.07220	−0.323595
$787$	39.5231	1.40885	0.704423	−	0.709781i	$-0.251206\pi$
$787$	39.5231	1.40885	0.704423	+	0.709781i	$0.251206\pi$
$788$	−3.64879	−0.129983
$789$	−14.3716	−0.511642
$790$	1.29676	0.0461365
$791$	−59.4998	−2.11557
$792$	−2.13891	−0.0760030
$793$	−39.2532	−1.39392
$794$	−9.91371	−0.351824
$795$	3.17693	0.112674
$796$	−2.42187	−0.0858409
$797$	−4.72650	−0.167421	−0.0837106	−	0.996490i	$-0.526677\pi$
$797$	−4.72650	−0.167421	−0.0837106	+	0.996490i	$0.526677\pi$
$798$	33.5675	1.18828
$799$	3.83298	0.135601
$800$	−0.575144	−0.0203344
$801$	0.835003	0.0295034
$802$	23.8601	0.842528
$803$	50.1289	1.76901
$804$	23.2917	0.821434
$805$	21.4777	0.756991
$806$	12.1612	0.428359
$807$	25.6755	0.903821
$808$	5.11511	0.179949
$809$	20.5935	0.724030	0.362015	−	0.932172i	$-0.382089\pi$
$809$	20.5935	0.724030	0.362015	+	0.932172i	$0.382089\pi$
$810$	−16.4548	−0.578161
$811$	0.753826	0.0264704	0.0132352	−	0.999912i	$-0.495787\pi$
$811$	0.753826	0.0264704	0.0132352	+	0.999912i	$0.495787\pi$
$812$	−11.7921	−0.413823
$813$	40.2409	1.41131
$814$	−4.55870	−0.159782
$815$	−44.0554	−1.54319
$816$	2.96519	0.103803
$817$	−8.76381	−0.306607
$818$	5.23304	0.182969
$819$	−4.42667	−0.154680
$820$	−21.3763	−0.746491
$821$	35.6945	1.24575	0.622874	−	0.782322i	$-0.285965\pi$
$821$	35.6945	1.24575	0.622874	+	0.782322i	$0.285965\pi$
$822$	31.8883	1.11223
$823$	49.6993	1.73241	0.866204	−	0.499691i	$-0.166553\pi$
$823$	49.6993	1.73241	0.866204	+	0.499691i	$0.166553\pi$
$824$	−10.0348	−0.349580
$825$	5.69793	0.198376
$826$	−30.1527	−1.04915
$827$	−24.2223	−0.842290	−0.421145	−	0.906993i	$-0.638372\pi$
$827$	−24.2223	−0.842290	−0.421145	+	0.906993i	$0.638372\pi$
$828$	0.730417	0.0253838
$829$	35.7462	1.24152	0.620758	−	0.784002i	$-0.286825\pi$
$829$	35.7462	1.24152	0.620758	+	0.784002i	$0.286825\pi$
$830$	−28.3369	−0.983587
$831$	−2.69332	−0.0934302
$832$	−2.56497	−0.0889243
$833$	−31.2008	−1.08105
$834$	27.0578	0.936934
$835$	6.32054	0.218731
$836$	25.5627	0.884105
$837$	−25.8599	−0.893848
$838$	−26.7199	−0.923024
$839$	−38.7273	−1.33702	−0.668508	−	0.743705i	$-0.733067\pi$
$839$	−38.7273	−1.33702	−0.668508	+	0.743705i	$0.733067\pi$
$840$	16.8148	0.580166
$841$	−23.2360	−0.801242
$842$	25.5872	0.881792
$843$	−42.8762	−1.47674
$844$	−26.5310	−0.913234
$845$	−13.5066	−0.464643
$846$	0.739193	0.0254140
$847$	−127.979	−4.39743
$848$	−0.927999	−0.0318676
$849$	38.3548	1.31633
$850$	1.04790	0.0359426
$851$	1.55675	0.0533647
$852$	9.16557	0.314007
$853$	25.8142	0.883861	0.441930	−	0.897049i	$-0.354294\pi$
$853$	25.8142	0.883861	0.441930	+	0.897049i	$0.354294\pi$
$854$	−75.1665	−2.57215
$855$	−3.10377	−0.106147
$856$	−3.22024	−0.110066
$857$	0.385373	0.0131641	0.00658205	−	0.999978i	$-0.497905\pi$
$857$	0.385373	0.0131641	0.00658205	+	0.999978i	$0.497905\pi$
$858$	25.4111	0.867519
$859$	−57.3482	−1.95670	−0.978348	−	0.206964i	$-0.933642\pi$
$859$	−57.3482	−1.95670	−0.978348	+	0.206964i	$0.933642\pi$
$860$	−4.39001	−0.149698
$861$	−81.2315	−2.76836
$862$	4.83298	0.164612
$863$	−40.2864	−1.37136	−0.685682	−	0.727901i	$-0.740496\pi$
$863$	−40.2864	−1.37136	−0.685682	+	0.727901i	$0.740496\pi$
$864$	5.45422	0.185556
$865$	−10.0423	−0.341447
$866$	−6.29757	−0.214000
$867$	22.2643	0.756136
$868$	23.2876	0.790433
$869$	3.75265	0.127300
$870$	−8.21904	−0.278652
$871$	36.7090	1.24384
$872$	2.98188	0.100979
$873$	5.78309	0.195728
$874$	−8.72941	−0.295277
$875$	57.6019	1.94730
$876$	−13.4020	−0.452811
$877$	20.4596	0.690872	0.345436	−	0.938442i	$-0.387731\pi$
$877$	20.4596	0.690872	0.345436	+	0.938442i	$0.387731\pi$
$878$	−27.3404	−0.922693
$879$	11.0337	0.372158
$880$	12.8050	0.431656
$881$	13.8805	0.467647	0.233823	−	0.972279i	$-0.424876\pi$
$881$	13.8805	0.467647	0.233823	+	0.972279i	$0.424876\pi$
$882$	−6.01710	−0.202606
$883$	50.8272	1.71047	0.855235	−	0.518240i	$-0.173413\pi$
$883$	50.8272	1.71047	0.855235	+	0.518240i	$0.173413\pi$
$884$	4.67331	0.157181
$885$	−21.0162	−0.706453
$886$	25.4810	0.856051
$887$	31.3763	1.05351	0.526756	−	0.850016i	$-0.323408\pi$
$887$	31.3763	1.05351	0.526756	+	0.850016i	$0.323408\pi$
$888$	1.21877	0.0408993
$889$	37.9257	1.27199
$890$	−4.99890	−0.167563
$891$	−47.6180	−1.59526
$892$	−3.47260	−0.116271
$893$	−8.83428	−0.295628
$894$	−27.4673	−0.918644
$895$	14.8673	0.496958
$896$	−4.91169	−0.164088
$897$	−8.67762	−0.289737
$898$	−32.7123	−1.09162
$899$	−11.3829	−0.379642
$900$	0.202088	0.00673626
$901$	1.69079	0.0563284
$902$	−61.8603	−2.05972
$903$	−16.6824	−0.555155
$904$	12.1139	0.402903
$905$	−14.1342	−0.469838
$906$	38.4284	1.27670
$907$	25.8715	0.859048	0.429524	−	0.903055i	$-0.358681\pi$
$907$	25.8715	0.859048	0.429524	+	0.903055i	$0.358681\pi$
$908$	9.16574	0.304176
$909$	−1.79729	−0.0596124
$910$	26.5011	0.878501
$911$	25.6667	0.850375	0.425187	−	0.905105i	$-0.360208\pi$
$911$	25.6667	0.850375	0.425187	+	0.905105i	$0.360208\pi$
$912$	−6.83420	−0.226303
$913$	−82.0034	−2.71392
$914$	7.22567	0.239004
$915$	−52.3906	−1.73198
$916$	−8.04944	−0.265961
$917$	−27.3800	−0.904167
$918$	−9.93746	−0.327985
$919$	−12.0754	−0.398329	−0.199165	−	0.979966i	$-0.563823\pi$
$919$	−12.0754	−0.398329	−0.199165	+	0.979966i	$0.563823\pi$
$920$	−4.37278	−0.144166
$921$	−30.0149	−0.989023
$922$	−4.02279	−0.132484
$923$	14.4454	0.475478
$924$	48.6600	1.60079
$925$	0.430713	0.0141618
$926$	6.05720	0.199052
$927$	3.52593	0.115807
$928$	2.40083	0.0788110
$929$	18.6748	0.612701	0.306351	−	0.951919i	$-0.400892\pi$
$929$	18.6748	0.612701	0.306351	+	0.951919i	$0.400892\pi$
$930$	16.2313	0.532246
$931$	71.9119	2.35682
$932$	−6.16587	−0.201970
$933$	−18.1309	−0.593580
$934$	−10.7642	−0.352216
$935$	−23.3304	−0.762985
$936$	0.901251	0.0294583
$937$	−43.9879	−1.43702	−0.718511	−	0.695516i	$-0.755176\pi$
$937$	−43.9879	−1.43702	−0.718511	+	0.695516i	$0.755176\pi$
$938$	70.2945	2.29520
$939$	−7.94817	−0.259379
$940$	−4.42531	−0.144338
$941$	21.9641	0.716010	0.358005	−	0.933720i	$-0.383457\pi$
$941$	21.9641	0.716010	0.358005	+	0.933720i	$0.383457\pi$
$942$	−5.24324	−0.170834
$943$	21.1247	0.687914
$944$	6.13896	0.199806
$945$	−56.3526	−1.83315
$946$	−12.7042	−0.413048
$947$	−1.19233	−0.0387454	−0.0193727	−	0.999812i	$-0.506167\pi$
$947$	−1.19233	−0.0387454	−0.0193727	+	0.999812i	$0.506167\pi$
$948$	−1.00327	−0.0325848
$949$	−21.1223	−0.685658
$950$	−2.41520	−0.0783596
$951$	−29.0759	−0.942852
$952$	8.94899	0.290038
$953$	−6.46085	−0.209287	−0.104644	−	0.994510i	$-0.533370\pi$
$953$	−6.46085	−0.209287	−0.104644	+	0.994510i	$0.533370\pi$
$954$	0.326070	0.0105569
$955$	−1.25870	−0.0407305
$956$	16.5965	0.536770
$957$	−23.7849	−0.768857
$958$	−29.9899	−0.968931
$959$	96.2390	3.10772
$960$	−3.42342	−0.110490
$961$	−8.52047	−0.274854
$962$	1.92085	0.0619307
$963$	1.13149	0.0364619
$964$	−24.1815	−0.778835
$965$	−6.64398	−0.213877
$966$	−16.6169	−0.534640
$967$	−2.08419	−0.0670231	−0.0335115	−	0.999438i	$-0.510669\pi$
$967$	−2.08419	−0.0670231	−0.0335115	+	0.999438i	$0.510669\pi$
$968$	26.0561	0.837474
$969$	12.4517	0.400008
$970$	−34.6215	−1.11163
$971$	−24.3534	−0.781537	−0.390768	−	0.920489i	$-0.627791\pi$
$971$	−24.3534	−0.781537	−0.390768	+	0.920489i	$0.627791\pi$
$972$	−3.63196	−0.116495
$973$	81.6606	2.61792
$974$	30.4453	0.975529
$975$	−2.40088	−0.0768896
$976$	15.3036	0.489856
$977$	23.6675	0.757191	0.378595	−	0.925562i	$-0.376407\pi$
$977$	23.6675	0.757191	0.378595	+	0.925562i	$0.376407\pi$
$978$	34.0848	1.08991
$979$	−14.4662	−0.462342
$980$	36.0225	1.15070
$981$	−1.04774	−0.0334517
$982$	−9.48169	−0.302573
$983$	52.8811	1.68665	0.843323	−	0.537407i	$-0.180596\pi$
$983$	52.8811	1.68665	0.843323	+	0.537407i	$0.180596\pi$
$984$	16.5384	0.527224
$985$	−7.67536	−0.244557
$986$	−4.37425	−0.139304
$987$	−16.8165	−0.535276
$988$	−10.7711	−0.342674
$989$	4.33834	0.137951
$990$	−4.49928	−0.142996
$991$	3.97811	0.126369	0.0631844	−	0.998002i	$-0.479874\pi$
$991$	3.97811	0.126369	0.0631844	+	0.998002i	$0.479874\pi$
$992$	−4.74126	−0.150535
$993$	9.43804	0.299507
$994$	27.6618	0.877378
$995$	−5.09449	−0.161506
$996$	21.9237	0.694678
$997$	−32.6625	−1.03443	−0.517216	−	0.855855i	$-0.673031\pi$
$997$	−32.6625	−1.03443	−0.517216	+	0.855855i	$0.673031\pi$
$998$	7.74378	0.245125
$999$	−4.08455	−0.129229

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6022.2.a.b.1.16	✓	54

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6022.2.a.b.1.16	✓	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.62746 q^{3} +1.00000 q^{4} +2.10353 q^{5} -1.62746 q^{6} -4.91169 q^{7} +1.00000 q^{8} -0.351369 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.62746 q^{3} +1.00000 q^{4} +2.10353 q^{5} -1.62746 q^{6} -4.91169 q^{7} +1.00000 q^{8} -0.351369 q^{9} +2.10353 q^{10} +6.08737 q^{11} -1.62746 q^{12} -2.56497 q^{13} -4.91169 q^{14} -3.42342 q^{15} +1.00000 q^{16} -1.82198 q^{17} -0.351369 q^{18} +4.19930 q^{19} +2.10353 q^{20} +7.99359 q^{21} +6.08737 q^{22} -2.07878 q^{23} -1.62746 q^{24} -0.575144 q^{25} -2.56497 q^{26} +5.45422 q^{27} -4.91169 q^{28} +2.40083 q^{29} -3.42342 q^{30} -4.74126 q^{31} +1.00000 q^{32} -9.90696 q^{33} -1.82198 q^{34} -10.3319 q^{35} -0.351369 q^{36} -0.748878 q^{37} +4.19930 q^{38} +4.17439 q^{39} +2.10353 q^{40} -10.1621 q^{41} +7.99359 q^{42} -2.08697 q^{43} +6.08737 q^{44} -0.739117 q^{45} -2.07878 q^{46} -2.10375 q^{47} -1.62746 q^{48} +17.1247 q^{49} -0.575144 q^{50} +2.96519 q^{51} -2.56497 q^{52} -0.927999 q^{53} +5.45422 q^{54} +12.8050 q^{55} -4.91169 q^{56} -6.83420 q^{57} +2.40083 q^{58} +6.13896 q^{59} -3.42342 q^{60} +15.3036 q^{61} -4.74126 q^{62} +1.72582 q^{63} +1.00000 q^{64} -5.39550 q^{65} -9.90696 q^{66} -14.3117 q^{67} -1.82198 q^{68} +3.38313 q^{69} -10.3319 q^{70} -5.63182 q^{71} -0.351369 q^{72} +8.23490 q^{73} -0.748878 q^{74} +0.936025 q^{75} +4.19930 q^{76} -29.8993 q^{77} +4.17439 q^{78} +0.616466 q^{79} +2.10353 q^{80} -7.82243 q^{81} -10.1621 q^{82} -13.4711 q^{83} +7.99359 q^{84} -3.83259 q^{85} -2.08697 q^{86} -3.90725 q^{87} +6.08737 q^{88} -2.37643 q^{89} -0.739117 q^{90} +12.5983 q^{91} -2.07878 q^{92} +7.71621 q^{93} -2.10375 q^{94} +8.83338 q^{95} -1.62746 q^{96} -16.4587 q^{97} +17.1247 q^{98} -2.13891 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 54 q + 54 q^{2} - 22 q^{3} + 54 q^{4} - 14 q^{5} - 22 q^{6} - 20 q^{7} + 54 q^{8} + 32 q^{9}+O(q^{10}) \) 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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