LMFDB - Embedded newform 4022.2.a.c.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4022,2,Mod(1,4022)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4022, 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("4022.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4022 = 2 \cdot 2011 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4022.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:	$32.1158316930$
Analytic rank:	$1$
Dimension:	$31$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Character	$\chi$	$=$	4022.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -3.04963 q^{3} +1.00000 q^{4} -0.453463 q^{5} -3.04963 q^{6} +2.87005 q^{7} +1.00000 q^{8} +6.30022 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -3.04963 q^{3} +1.00000 q^{4} -0.453463 q^{5} -3.04963 q^{6} +2.87005 q^{7} +1.00000 q^{8} +6.30022 q^{9} -0.453463 q^{10} +4.55403 q^{11} -3.04963 q^{12} -2.73733 q^{13} +2.87005 q^{14} +1.38289 q^{15} +1.00000 q^{16} -7.16654 q^{17} +6.30022 q^{18} -3.68033 q^{19} -0.453463 q^{20} -8.75259 q^{21} +4.55403 q^{22} -6.31159 q^{23} -3.04963 q^{24} -4.79437 q^{25} -2.73733 q^{26} -10.0644 q^{27} +2.87005 q^{28} +1.63467 q^{29} +1.38289 q^{30} +9.35349 q^{31} +1.00000 q^{32} -13.8881 q^{33} -7.16654 q^{34} -1.30146 q^{35} +6.30022 q^{36} -0.591277 q^{37} -3.68033 q^{38} +8.34784 q^{39} -0.453463 q^{40} -2.96995 q^{41} -8.75259 q^{42} -1.90913 q^{43} +4.55403 q^{44} -2.85692 q^{45} -6.31159 q^{46} +1.48290 q^{47} -3.04963 q^{48} +1.23721 q^{49} -4.79437 q^{50} +21.8553 q^{51} -2.73733 q^{52} +6.93275 q^{53} -10.0644 q^{54} -2.06508 q^{55} +2.87005 q^{56} +11.2236 q^{57} +1.63467 q^{58} -9.46594 q^{59} +1.38289 q^{60} -1.11562 q^{61} +9.35349 q^{62} +18.0820 q^{63} +1.00000 q^{64} +1.24128 q^{65} -13.8881 q^{66} -7.91081 q^{67} -7.16654 q^{68} +19.2480 q^{69} -1.30146 q^{70} -2.51842 q^{71} +6.30022 q^{72} +8.48903 q^{73} -0.591277 q^{74} +14.6210 q^{75} -3.68033 q^{76} +13.0703 q^{77} +8.34784 q^{78} -7.22101 q^{79} -0.453463 q^{80} +11.7921 q^{81} -2.96995 q^{82} +1.41425 q^{83} -8.75259 q^{84} +3.24976 q^{85} -1.90913 q^{86} -4.98512 q^{87} +4.55403 q^{88} +1.60826 q^{89} -2.85692 q^{90} -7.85629 q^{91} -6.31159 q^{92} -28.5246 q^{93} +1.48290 q^{94} +1.66889 q^{95} -3.04963 q^{96} -16.4270 q^{97} +1.23721 q^{98} +28.6914 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 31 q + 31 q^{2} - 14 q^{3} + 31 q^{4} - 13 q^{5} - 14 q^{6} - 29 q^{7} + 31 q^{8} + 27 q^{9}+O(q^{10}) $ 31 * q + 31 * q^2 - 14 * q^3 + 31 * q^4 - 13 * q^5 - 14 * q^6 - 29 * q^7 + 31 * q^8 + 27 * q^9	\( 31 q + 31 q^{2} - 14 q^{3} + 31 q^{4} - 13 q^{5} - 14 q^{6} - 29 q^{7} + 31 q^{8} + 27 q^{9} - 13 q^{10} - 29 q^{11} - 14 q^{12} - 23 q^{13} - 29 q^{14} - 14 q^{15} + 31 q^{16} - 19 q^{17} + 27 q^{18} - 36 q^{19} - 13 q^{20} - 29 q^{22} - 24 q^{23} - 14 q^{24} + 4 q^{25} - 23 q^{26} - 65 q^{27} - 29 q^{28} + 18 q^{29} - 14 q^{30} - 41 q^{31} + 31 q^{32} - 18 q^{33} - 19 q^{34} - 28 q^{35} + 27 q^{36} - 31 q^{37} - 36 q^{38} - 31 q^{39} - 13 q^{40} - 51 q^{41} - 14 q^{43} - 29 q^{44} - 34 q^{45} - 24 q^{46} - 64 q^{47} - 14 q^{48} + 8 q^{49} + 4 q^{50} - 17 q^{51} - 23 q^{52} + 3 q^{53} - 65 q^{54} - 50 q^{55} - 29 q^{56} - 19 q^{57} + 18 q^{58} - 58 q^{59} - 14 q^{60} - 14 q^{61} - 41 q^{62} - 66 q^{63} + 31 q^{64} + 6 q^{65} - 18 q^{66} - 55 q^{67} - 19 q^{68} + q^{69} - 28 q^{70} - 42 q^{71} + 27 q^{72} - 83 q^{73} - 31 q^{74} - 49 q^{75} - 36 q^{76} + 18 q^{77} - 31 q^{78} - 56 q^{79} - 13 q^{80} + 3 q^{81} - 51 q^{82} - 43 q^{83} + 4 q^{85} - 14 q^{86} - 76 q^{87} - 29 q^{88} + 17 q^{89} - 34 q^{90} - 49 q^{91} - 24 q^{92} - 24 q^{93} - 64 q^{94} - 43 q^{95} - 14 q^{96} - 98 q^{97} + 8 q^{98} - q^{99}+O(q^{100}) \) 31 * q + 31 * q^2 - 14 * q^3 + 31 * q^4 - 13 * q^5 - 14 * q^6 - 29 * q^7 + 31 * q^8 + 27 * q^9 - 13 * q^10 - 29 * q^11 - 14 * q^12 - 23 * q^13 - 29 * q^14 - 14 * q^15 + 31 * q^16 - 19 * q^17 + 27 * q^18 - 36 * q^19 - 13 * q^20 - 29 * q^22 - 24 * q^23 - 14 * q^24 + 4 * q^25 - 23 * q^26 - 65 * q^27 - 29 * q^28 + 18 * q^29 - 14 * q^30 - 41 * q^31 + 31 * q^32 - 18 * q^33 - 19 * q^34 - 28 * q^35 + 27 * q^36 - 31 * q^37 - 36 * q^38 - 31 * q^39 - 13 * q^40 - 51 * q^41 - 14 * q^43 - 29 * q^44 - 34 * q^45 - 24 * q^46 - 64 * q^47 - 14 * q^48 + 8 * q^49 + 4 * q^50 - 17 * q^51 - 23 * q^52 + 3 * q^53 - 65 * q^54 - 50 * q^55 - 29 * q^56 - 19 * q^57 + 18 * q^58 - 58 * q^59 - 14 * q^60 - 14 * q^61 - 41 * q^62 - 66 * q^63 + 31 * q^64 + 6 * q^65 - 18 * q^66 - 55 * q^67 - 19 * q^68 + q^69 - 28 * q^70 - 42 * q^71 + 27 * q^72 - 83 * q^73 - 31 * q^74 - 49 * q^75 - 36 * q^76 + 18 * q^77 - 31 * q^78 - 56 * q^79 - 13 * q^80 + 3 * q^81 - 51 * q^82 - 43 * q^83 + 4 * q^85 - 14 * q^86 - 76 * q^87 - 29 * q^88 + 17 * q^89 - 34 * q^90 - 49 * q^91 - 24 * q^92 - 24 * q^93 - 64 * q^94 - 43 * q^95 - 14 * q^96 - 98 * q^97 + 8 * q^98 - 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
$3$	−3.04963	−1.76070	−0.880351	−	0.474323i	$-0.842693\pi$
$3$	−3.04963	−1.76070	−0.880351	+	0.474323i	$0.842693\pi$
$4$	1.00000	0.500000
$5$	−0.453463	−0.202795	−0.101398	−	0.994846i	$-0.532331\pi$
$5$	−0.453463	−0.202795	−0.101398	+	0.994846i	$0.532331\pi$
$6$	−3.04963	−1.24500
$7$	2.87005	1.08478	0.542389	−	0.840127i	$-0.317520\pi$
$7$	2.87005	1.08478	0.542389	+	0.840127i	$0.317520\pi$
$8$	1.00000	0.353553
$9$	6.30022	2.10007
$10$	−0.453463	−0.143398
$11$	4.55403	1.37309	0.686545	−	0.727087i	$-0.259126\pi$
$11$	4.55403	1.37309	0.686545	+	0.727087i	$0.259126\pi$
$12$	−3.04963	−0.880351
$13$	−2.73733	−0.759200	−0.379600	−	0.925151i	$-0.623938\pi$
$13$	−2.73733	−0.759200	−0.379600	+	0.925151i	$0.623938\pi$
$14$	2.87005	0.767054
$15$	1.38289	0.357062
$16$	1.00000	0.250000
$17$	−7.16654	−1.73814	−0.869071	−	0.494688i	$-0.835282\pi$
$17$	−7.16654	−1.73814	−0.869071	+	0.494688i	$0.835282\pi$
$18$	6.30022	1.48498
$19$	−3.68033	−0.844325	−0.422162	−	0.906520i	$-0.638729\pi$
$19$	−3.68033	−0.844325	−0.422162	+	0.906520i	$0.638729\pi$
$20$	−0.453463	−0.101398
$21$	−8.75259	−1.90997
$22$	4.55403	0.970922
$23$	−6.31159	−1.31606	−0.658029	−	0.752993i	$-0.728610\pi$
$23$	−6.31159	−1.31606	−0.658029	+	0.752993i	$0.728610\pi$
$24$	−3.04963	−0.622502
$25$	−4.79437	−0.958874
$26$	−2.73733	−0.536835
$27$	−10.0644	−1.93690
$28$	2.87005	0.542389
$29$	1.63467	0.303550	0.151775	−	0.988415i	$-0.451501\pi$
$29$	1.63467	0.303550	0.151775	+	0.988415i	$0.451501\pi$
$30$	1.38289	0.252481
$31$	9.35349	1.67994	0.839968	−	0.542636i	$-0.182574\pi$
$31$	9.35349	1.67994	0.839968	+	0.542636i	$0.182574\pi$
$32$	1.00000	0.176777
$33$	−13.8881	−2.41760
$34$	−7.16654	−1.22905
$35$	−1.30146	−0.219988
$36$	6.30022	1.05004
$37$	−0.591277	−0.0972054	−0.0486027	−	0.998818i	$-0.515477\pi$
$37$	−0.591277	−0.0972054	−0.0486027	+	0.998818i	$0.515477\pi$
$38$	−3.68033	−0.597028
$39$	8.34784	1.33672
$40$	−0.453463	−0.0716989
$41$	−2.96995	−0.463829	−0.231914	−	0.972736i	$-0.574499\pi$
$41$	−2.96995	−0.463829	−0.231914	+	0.972736i	$0.574499\pi$
$42$	−8.75259	−1.35055
$43$	−1.90913	−0.291139	−0.145569	−	0.989348i	$-0.546501\pi$
$43$	−1.90913	−0.291139	−0.145569	+	0.989348i	$0.546501\pi$
$44$	4.55403	0.686545
$45$	−2.85692	−0.425884
$46$	−6.31159	−0.930593
$47$	1.48290	0.216303	0.108152	−	0.994134i	$-0.465507\pi$
$47$	1.48290	0.216303	0.108152	+	0.994134i	$0.465507\pi$
$48$	−3.04963	−0.440176
$49$	1.23721	0.176744
$50$	−4.79437	−0.678026
$51$	21.8553	3.06035
$52$	−2.73733	−0.379600
$53$	6.93275	0.952286	0.476143	−	0.879368i	$-0.342034\pi$
$53$	6.93275	0.952286	0.476143	+	0.879368i	$0.342034\pi$
$54$	−10.0644	−1.36959
$55$	−2.06508	−0.278456
$56$	2.87005	0.383527
$57$	11.2236	1.48660
$58$	1.63467	0.214642
$59$	−9.46594	−1.23236	−0.616180	−	0.787605i	$-0.711321\pi$
$59$	−9.46594	−1.23236	−0.616180	+	0.787605i	$0.711321\pi$
$60$	1.38289	0.178531
$61$	−1.11562	−0.142841	−0.0714205	−	0.997446i	$-0.522753\pi$
$61$	−1.11562	−0.142841	−0.0714205	+	0.997446i	$0.522753\pi$
$62$	9.35349	1.18789
$63$	18.0820	2.27811
$64$	1.00000	0.125000
$65$	1.24128	0.153962
$66$	−13.8881	−1.70950
$67$	−7.91081	−0.966459	−0.483230	−	0.875494i	$-0.660536\pi$
$67$	−7.91081	−0.966459	−0.483230	+	0.875494i	$0.660536\pi$
$68$	−7.16654	−0.869071
$69$	19.2480	2.31719
$70$	−1.30146	−0.155555
$71$	−2.51842	−0.298882	−0.149441	−	0.988771i	$-0.547747\pi$
$71$	−2.51842	−0.298882	−0.149441	+	0.988771i	$0.547747\pi$
$72$	6.30022	0.742488
$73$	8.48903	0.993566	0.496783	−	0.867875i	$-0.334514\pi$
$73$	8.48903	0.993566	0.496783	+	0.867875i	$0.334514\pi$
$74$	−0.591277	−0.0687346
$75$	14.6210	1.68829
$76$	−3.68033	−0.422162
$77$	13.0703	1.48950
$78$	8.34784	0.945207
$79$	−7.22101	−0.812427	−0.406214	−	0.913778i	$-0.633151\pi$
$79$	−7.22101	−0.812427	−0.406214	+	0.913778i	$0.633151\pi$
$80$	−0.453463	−0.0506988
$81$	11.7921	1.31023
$82$	−2.96995	−0.327976
$83$	1.41425	0.155234	0.0776170	−	0.996983i	$-0.475269\pi$
$83$	1.41425	0.155234	0.0776170	+	0.996983i	$0.475269\pi$
$84$	−8.75259	−0.954986
$85$	3.24976	0.352486
$86$	−1.90913	−0.205866
$87$	−4.98512	−0.534461
$88$	4.55403	0.485461
$89$	1.60826	0.170475	0.0852374	−	0.996361i	$-0.472835\pi$
$89$	1.60826	0.170475	0.0852374	+	0.996361i	$0.472835\pi$
$90$	−2.85692	−0.301146
$91$	−7.85629	−0.823563
$92$	−6.31159	−0.658029
$93$	−28.5246	−2.95787
$94$	1.48290	0.152949
$95$	1.66889	0.171225
$96$	−3.04963	−0.311251
$97$	−16.4270	−1.66791	−0.833953	−	0.551836i	$-0.813928\pi$
$97$	−16.4270	−1.66791	−0.833953	+	0.551836i	$0.813928\pi$
$98$	1.23721	0.124977
$99$	28.6914	2.88359
$100$	−4.79437	−0.479437
$101$	4.32150	0.430005	0.215003	−	0.976613i	$-0.431024\pi$
$101$	4.32150	0.430005	0.215003	+	0.976613i	$0.431024\pi$
$102$	21.8553	2.16399
$103$	−8.92122	−0.879034	−0.439517	−	0.898234i	$-0.644850\pi$
$103$	−8.92122	−0.879034	−0.439517	+	0.898234i	$0.644850\pi$
$104$	−2.73733	−0.268418
$105$	3.96898	0.387333
$106$	6.93275	0.673368
$107$	8.66869	0.838034	0.419017	−	0.907978i	$-0.362375\pi$
$107$	8.66869	0.838034	0.419017	+	0.907978i	$0.362375\pi$
$108$	−10.0644	−0.968450
$109$	0.665302	0.0637244	0.0318622	−	0.999492i	$-0.489856\pi$
$109$	0.665302	0.0637244	0.0318622	+	0.999492i	$0.489856\pi$
$110$	−2.06508	−0.196898
$111$	1.80317	0.171150
$112$	2.87005	0.271195
$113$	−0.754723	−0.0709983	−0.0354992	−	0.999370i	$-0.511302\pi$
$113$	−0.754723	−0.0709983	−0.0354992	+	0.999370i	$0.511302\pi$
$114$	11.2236	1.05119
$115$	2.86208	0.266890
$116$	1.63467	0.151775
$117$	−17.2458	−1.59437
$118$	−9.46594	−0.871411
$119$	−20.5684	−1.88550
$120$	1.38289	0.126240
$121$	9.73916	0.885378
$122$	−1.11562	−0.101004
$123$	9.05724	0.816664
$124$	9.35349	0.839968
$125$	4.44139	0.397250
$126$	18.0820	1.61087
$127$	−4.30638	−0.382130	−0.191065	−	0.981577i	$-0.561194\pi$
$127$	−4.30638	−0.382130	−0.191065	+	0.981577i	$0.561194\pi$
$128$	1.00000	0.0883883
$129$	5.82212	0.512609
$130$	1.24128	0.108868
$131$	5.80627	0.507296	0.253648	−	0.967297i	$-0.418370\pi$
$131$	5.80627	0.507296	0.253648	+	0.967297i	$0.418370\pi$
$132$	−13.8881	−1.20880
$133$	−10.5627	−0.915905
$134$	−7.91081	−0.683390
$135$	4.56385	0.392794
$136$	−7.16654	−0.614526
$137$	−15.2169	−1.30006	−0.650032	−	0.759907i	$-0.725244\pi$
$137$	−15.2169	−1.30006	−0.650032	+	0.759907i	$0.725244\pi$
$138$	19.2480	1.63850
$139$	−8.89045	−0.754078	−0.377039	−	0.926197i	$-0.623058\pi$
$139$	−8.89045	−0.754078	−0.377039	+	0.926197i	$0.623058\pi$
$140$	−1.30146	−0.109994
$141$	−4.52229	−0.380845
$142$	−2.51842	−0.211341
$143$	−12.4659	−1.04245
$144$	6.30022	0.525018
$145$	−0.741261	−0.0615584
$146$	8.48903	0.702557
$147$	−3.77303	−0.311194
$148$	−0.591277	−0.0486027
$149$	6.50634	0.533020	0.266510	−	0.963832i	$-0.414129\pi$
$149$	6.50634	0.533020	0.266510	+	0.963832i	$0.414129\pi$
$150$	14.6210	1.19380
$151$	2.91552	0.237262	0.118631	−	0.992938i	$-0.462149\pi$
$151$	2.91552	0.237262	0.118631	+	0.992938i	$0.462149\pi$
$152$	−3.68033	−0.298514
$153$	−45.1508	−3.65022
$154$	13.0703	1.05323
$155$	−4.24146	−0.340683
$156$	8.34784	0.668362
$157$	−15.8644	−1.26612	−0.633060	−	0.774103i	$-0.718201\pi$
$157$	−15.8644	−1.26612	−0.633060	+	0.774103i	$0.718201\pi$
$158$	−7.22101	−0.574473
$159$	−21.1423	−1.67669
$160$	−0.453463	−0.0358494
$161$	−18.1146	−1.42763
$162$	11.7921	0.926473
$163$	−4.15350	−0.325327	−0.162663	−	0.986682i	$-0.552008\pi$
$163$	−4.15350	−0.325327	−0.162663	+	0.986682i	$0.552008\pi$
$164$	−2.96995	−0.231914
$165$	6.29773	0.490278
$166$	1.41425	0.109767
$167$	−13.0110	−1.00682	−0.503412	−	0.864047i	$-0.667922\pi$
$167$	−13.0110	−1.00682	−0.503412	+	0.864047i	$0.667922\pi$
$168$	−8.75259	−0.675277
$169$	−5.50701	−0.423616
$170$	3.24976	0.249246
$171$	−23.1869	−1.77314
$172$	−1.90913	−0.145569
$173$	3.57137	0.271526	0.135763	−	0.990741i	$-0.456651\pi$
$173$	3.57137	0.271526	0.135763	+	0.990741i	$0.456651\pi$
$174$	−4.98512	−0.377921
$175$	−13.7601	−1.04017
$176$	4.55403	0.343273
$177$	28.8676	2.16982
$178$	1.60826	0.120544
$179$	23.8324	1.78132	0.890659	−	0.454672i	$-0.150244\pi$
$179$	23.8324	1.78132	0.890659	+	0.454672i	$0.150244\pi$
$180$	−2.85692	−0.212942
$181$	−6.69679	−0.497769	−0.248884	−	0.968533i	$-0.580064\pi$
$181$	−6.69679	−0.497769	−0.248884	+	0.968533i	$0.580064\pi$
$182$	−7.85629	−0.582347
$183$	3.40223	0.251500
$184$	−6.31159	−0.465297
$185$	0.268123	0.0197128
$186$	−28.5246	−2.09153
$187$	−32.6366	−2.38663
$188$	1.48290	0.108152
$189$	−28.8854	−2.10111
$190$	1.66889	0.121074
$191$	−5.59871	−0.405109	−0.202554	−	0.979271i	$-0.564924\pi$
$191$	−5.59871	−0.405109	−0.202554	+	0.979271i	$0.564924\pi$
$192$	−3.04963	−0.220088
$193$	−2.33981	−0.168423	−0.0842116	−	0.996448i	$-0.526837\pi$
$193$	−2.33981	−0.168423	−0.0842116	+	0.996448i	$0.526837\pi$
$194$	−16.4270	−1.17939
$195$	−3.78544	−0.271081
$196$	1.23721	0.0883721
$197$	−4.81323	−0.342928	−0.171464	−	0.985190i	$-0.554850\pi$
$197$	−4.81323	−0.342928	−0.171464	+	0.985190i	$0.554850\pi$
$198$	28.6914	2.03901
$199$	−22.2060	−1.57414	−0.787070	−	0.616864i	$-0.788403\pi$
$199$	−22.2060	−1.57414	−0.787070	+	0.616864i	$0.788403\pi$
$200$	−4.79437	−0.339013
$201$	24.1250	1.70165
$202$	4.32150	0.304060
$203$	4.69158	0.329284
$204$	21.8553	1.53017
$205$	1.34676	0.0940621
$206$	−8.92122	−0.621571
$207$	−39.7644	−2.76382
$208$	−2.73733	−0.189800
$209$	−16.7603	−1.15933
$210$	3.96898	0.273886
$211$	7.45337	0.513111	0.256555	−	0.966530i	$-0.417412\pi$
$211$	7.45337	0.513111	0.256555	+	0.966530i	$0.417412\pi$
$212$	6.93275	0.476143
$213$	7.68025	0.526242
$214$	8.66869	0.592580
$215$	0.865719	0.0590415
$216$	−10.0644	−0.684797
$217$	26.8450	1.82236
$218$	0.665302	0.0450600
$219$	−25.8884	−1.74937
$220$	−2.06508	−0.139228
$221$	19.6172	1.31960
$222$	1.80317	0.121021
$223$	−7.21849	−0.483386	−0.241693	−	0.970353i	$-0.577703\pi$
$223$	−7.21849	−0.483386	−0.241693	+	0.970353i	$0.577703\pi$
$224$	2.87005	0.191764
$225$	−30.2056	−2.01371
$226$	−0.754723	−0.0502034
$227$	−3.78258	−0.251058	−0.125529	−	0.992090i	$-0.540063\pi$
$227$	−3.78258	−0.251058	−0.125529	+	0.992090i	$0.540063\pi$
$228$	11.2236	0.743302
$229$	23.2749	1.53805	0.769024	−	0.639220i	$-0.220743\pi$
$229$	23.2749	1.53805	0.769024	+	0.639220i	$0.220743\pi$
$230$	2.86208	0.188720
$231$	−39.8595	−2.62256
$232$	1.63467	0.107321
$233$	28.2350	1.84973	0.924867	−	0.380290i	$-0.124176\pi$
$233$	28.2350	1.84973	0.924867	+	0.380290i	$0.124176\pi$
$234$	−17.2458	−1.12739
$235$	−0.672441	−0.0438652
$236$	−9.46594	−0.616180
$237$	22.0214	1.43044
$238$	−20.5684	−1.33325
$239$	−29.4096	−1.90235	−0.951174	−	0.308654i	$-0.900121\pi$
$239$	−29.4096	−1.90235	−0.951174	+	0.308654i	$0.900121\pi$
$240$	1.38289	0.0892654
$241$	19.2396	1.23933	0.619667	−	0.784865i	$-0.287268\pi$
$241$	19.2396	1.23933	0.619667	+	0.784865i	$0.287268\pi$
$242$	9.73916	0.626057
$243$	−5.76815	−0.370027
$244$	−1.11562	−0.0714205
$245$	−0.561029	−0.0358428
$246$	9.05724	0.577469
$247$	10.0743	0.641011
$248$	9.35349	0.593947
$249$	−4.31293	−0.273321
$250$	4.44139	0.280898
$251$	−14.3492	−0.905714	−0.452857	−	0.891583i	$-0.649595\pi$
$251$	−14.3492	−0.905714	−0.452857	+	0.891583i	$0.649595\pi$
$252$	18.0820	1.13906
$253$	−28.7432	−1.80707
$254$	−4.30638	−0.270206
$255$	−9.91056	−0.620624
$256$	1.00000	0.0625000
$257$	−27.9600	−1.74410	−0.872048	−	0.489420i	$-0.837208\pi$
$257$	−27.9600	−1.74410	−0.872048	+	0.489420i	$0.837208\pi$
$258$	5.82212	0.362469
$259$	−1.69700	−0.105446
$260$	1.24128	0.0769810
$261$	10.2987	0.637476
$262$	5.80627	0.358712
$263$	−26.8324	−1.65455	−0.827277	−	0.561794i	$-0.810111\pi$
$263$	−26.8324	−1.65455	−0.827277	+	0.561794i	$0.810111\pi$
$264$	−13.8881	−0.854752
$265$	−3.14375	−0.193119
$266$	−10.5627	−0.647643
$267$	−4.90458	−0.300155
$268$	−7.91081	−0.483230
$269$	−11.1783	−0.681555	−0.340778	−	0.940144i	$-0.610690\pi$
$269$	−11.1783	−0.681555	−0.340778	+	0.940144i	$0.610690\pi$
$270$	4.56385	0.277747
$271$	−27.4597	−1.66806	−0.834028	−	0.551722i	$-0.813971\pi$
$271$	−27.4597	−1.66806	−0.834028	+	0.551722i	$0.813971\pi$
$272$	−7.16654	−0.434535
$273$	23.9588	1.45005
$274$	−15.2169	−0.919284
$275$	−21.8337	−1.31662
$276$	19.2480	1.15859
$277$	6.50586	0.390899	0.195449	−	0.980714i	$-0.437383\pi$
$277$	6.50586	0.390899	0.195449	+	0.980714i	$0.437383\pi$
$278$	−8.89045	−0.533214
$279$	58.9290	3.52799
$280$	−1.30146	−0.0777774
$281$	17.6111	1.05059	0.525296	−	0.850920i	$-0.323955\pi$
$281$	17.6111	1.05059	0.525296	+	0.850920i	$0.323955\pi$
$282$	−4.52229	−0.269298
$283$	15.8386	0.941507	0.470753	−	0.882265i	$-0.343982\pi$
$283$	15.8386	0.941507	0.470753	+	0.882265i	$0.343982\pi$
$284$	−2.51842	−0.149441
$285$	−5.08950	−0.301476
$286$	−12.4659	−0.737123
$287$	−8.52392	−0.503151
$288$	6.30022	0.371244
$289$	34.3593	2.02114
$290$	−0.741261	−0.0435284
$291$	50.0961	2.93669
$292$	8.48903	0.496783
$293$	−16.5947	−0.969471	−0.484736	−	0.874661i	$-0.661084\pi$
$293$	−16.5947	−0.969471	−0.484736	+	0.874661i	$0.661084\pi$
$294$	−3.77303	−0.220047
$295$	4.29246	0.249917
$296$	−0.591277	−0.0343673
$297$	−45.8337	−2.65954
$298$	6.50634	0.376902
$299$	17.2769	0.999151
$300$	14.6210	0.844146
$301$	−5.47929	−0.315821
$302$	2.91552	0.167769
$303$	−13.1790	−0.757111
$304$	−3.68033	−0.211081
$305$	0.505894	0.0289674
$306$	−45.1508	−2.58110
$307$	−27.4375	−1.56594	−0.782971	−	0.622059i	$-0.786296\pi$
$307$	−27.4375	−1.56594	−0.782971	+	0.622059i	$0.786296\pi$
$308$	13.0703	0.744750
$309$	27.2064	1.54772
$310$	−4.24146	−0.240899
$311$	12.3634	0.701067	0.350533	−	0.936550i	$-0.386000\pi$
$311$	12.3634	0.701067	0.350533	+	0.936550i	$0.386000\pi$
$312$	8.34784	0.472604
$313$	22.5087	1.27227	0.636133	−	0.771579i	$-0.280533\pi$
$313$	22.5087	1.27227	0.636133	+	0.771579i	$0.280533\pi$
$314$	−15.8644	−0.895282
$315$	−8.19951	−0.461990
$316$	−7.22101	−0.406214
$317$	−20.9641	−1.17746	−0.588731	−	0.808329i	$-0.700372\pi$
$317$	−20.9641	−1.17746	−0.588731	+	0.808329i	$0.700372\pi$
$318$	−21.1423	−1.18560
$319$	7.44431	0.416801
$320$	−0.453463	−0.0253494
$321$	−26.4363	−1.47553
$322$	−18.1146	−1.00949
$323$	26.3752	1.46756
$324$	11.7921	0.655116
$325$	13.1238	0.727977
$326$	−4.15350	−0.230041
$327$	−2.02892	−0.112200
$328$	−2.96995	−0.163988
$329$	4.25600	0.234641
$330$	6.29773	0.346679
$331$	27.6536	1.51998	0.759991	−	0.649934i	$-0.225203\pi$
$331$	27.6536	1.51998	0.759991	+	0.649934i	$0.225203\pi$
$332$	1.41425	0.0776170
$333$	−3.72517	−0.204138
$334$	−13.0110	−0.711931
$335$	3.58726	0.195993
$336$	−8.75259	−0.477493
$337$	3.80005	0.207002	0.103501	−	0.994629i	$-0.466996\pi$
$337$	3.80005	0.207002	0.103501	+	0.994629i	$0.466996\pi$
$338$	−5.50701	−0.299542
$339$	2.30162	0.125007
$340$	3.24976	0.176243
$341$	42.5960	2.30670
$342$	−23.1869	−1.25380
$343$	−16.5395	−0.893050
$344$	−1.90913	−0.102933
$345$	−8.72826	−0.469914
$346$	3.57137	0.191998
$347$	21.7371	1.16691	0.583455	−	0.812146i	$-0.301701\pi$
$347$	21.7371	1.16691	0.583455	+	0.812146i	$0.301701\pi$
$348$	−4.98512	−0.267230
$349$	26.4543	1.41607	0.708033	−	0.706179i	$-0.249583\pi$
$349$	26.4543	1.41607	0.708033	+	0.706179i	$0.249583\pi$
$350$	−13.7601	−0.735508
$351$	27.5497	1.47049
$352$	4.55403	0.242730
$353$	−3.66225	−0.194922	−0.0974609	−	0.995239i	$-0.531072\pi$
$353$	−3.66225	−0.194922	−0.0974609	+	0.995239i	$0.531072\pi$
$354$	28.8676	1.53429
$355$	1.14201	0.0606118
$356$	1.60826	0.0852374
$357$	62.7258	3.31980
$358$	23.8324	1.25958
$359$	−14.5568	−0.768276	−0.384138	−	0.923276i	$-0.625501\pi$
$359$	−14.5568	−0.768276	−0.384138	+	0.923276i	$0.625501\pi$
$360$	−2.85692	−0.150573
$361$	−5.45519	−0.287115
$362$	−6.69679	−0.351976
$363$	−29.7008	−1.55889
$364$	−7.85629	−0.411782
$365$	−3.84947	−0.201490
$366$	3.40223	0.177838
$367$	−20.4525	−1.06761	−0.533807	−	0.845606i	$-0.679239\pi$
$367$	−20.4525	−1.06761	−0.533807	+	0.845606i	$0.679239\pi$
$368$	−6.31159	−0.329014
$369$	−18.7113	−0.974074
$370$	0.268123	0.0139390
$371$	19.8974	1.03302
$372$	−28.5246	−1.47893
$373$	−19.6067	−1.01520	−0.507599	−	0.861593i	$-0.669467\pi$
$373$	−19.6067	−1.01520	−0.507599	+	0.861593i	$0.669467\pi$
$374$	−32.6366	−1.68760
$375$	−13.5446	−0.699439
$376$	1.48290	0.0764747
$377$	−4.47463	−0.230455
$378$	−28.8854	−1.48571
$379$	−22.8504	−1.17375	−0.586874	−	0.809678i	$-0.699642\pi$
$379$	−22.8504	−1.17375	−0.586874	+	0.809678i	$0.699642\pi$
$380$	1.66889	0.0856124
$381$	13.1329	0.672816
$382$	−5.59871	−0.286455
$383$	6.77952	0.346417	0.173209	−	0.984885i	$-0.444586\pi$
$383$	6.77952	0.346417	0.173209	+	0.984885i	$0.444586\pi$
$384$	−3.04963	−0.155626
$385$	−5.92690	−0.302063
$386$	−2.33981	−0.119093
$387$	−12.0279	−0.611413
$388$	−16.4270	−0.833953
$389$	13.8181	0.700604	0.350302	−	0.936637i	$-0.386079\pi$
$389$	13.8181	0.700604	0.350302	+	0.936637i	$0.386079\pi$
$390$	−3.78544	−0.191683
$391$	45.2323	2.28749
$392$	1.23721	0.0624885
$393$	−17.7069	−0.893197
$394$	−4.81323	−0.242487
$395$	3.27447	0.164756
$396$	28.6914	1.44179
$397$	−1.81347	−0.0910157	−0.0455078	−	0.998964i	$-0.514491\pi$
$397$	−1.81347	−0.0910157	−0.0455078	+	0.998964i	$0.514491\pi$
$398$	−22.2060	−1.11308
$399$	32.2124	1.61264
$400$	−4.79437	−0.239719
$401$	5.23744	0.261545	0.130773	−	0.991412i	$-0.458254\pi$
$401$	5.23744	0.261545	0.130773	+	0.991412i	$0.458254\pi$
$402$	24.1250	1.20325
$403$	−25.6036	−1.27541
$404$	4.32150	0.215003
$405$	−5.34728	−0.265708
$406$	4.69158	0.232839
$407$	−2.69269	−0.133472
$408$	21.8553	1.08200
$409$	−21.0305	−1.03989	−0.519945	−	0.854200i	$-0.674047\pi$
$409$	−21.0305	−1.03989	−0.519945	+	0.854200i	$0.674047\pi$
$410$	1.34676	0.0665120
$411$	46.4057	2.28902
$412$	−8.92122	−0.439517
$413$	−27.1678	−1.33684
$414$	−39.7644	−1.95431
$415$	−0.641310	−0.0314807
$416$	−2.73733	−0.134209
$417$	27.1126	1.32771
$418$	−16.7603	−0.819773
$419$	−16.1708	−0.789996	−0.394998	−	0.918682i	$-0.629255\pi$
$419$	−16.1708	−0.789996	−0.394998	+	0.918682i	$0.629255\pi$
$420$	3.96898	0.193666
$421$	23.3469	1.13786	0.568929	−	0.822386i	$-0.307358\pi$
$421$	23.3469	1.13786	0.568929	+	0.822386i	$0.307358\pi$
$422$	7.45337	0.362824
$423$	9.34259	0.454252
$424$	6.93275	0.336684
$425$	34.3591	1.66666
$426$	7.68025	0.372109
$427$	−3.20190	−0.154951
$428$	8.66869	0.419017
$429$	38.0163	1.83544
$430$	0.865719	0.0417487
$431$	−10.4709	−0.504365	−0.252183	−	0.967680i	$-0.581148\pi$
$431$	−10.4709	−0.504365	−0.252183	+	0.967680i	$0.581148\pi$
$432$	−10.0644	−0.484225
$433$	12.4024	0.596022	0.298011	−	0.954562i	$-0.403677\pi$
$433$	12.4024	0.596022	0.298011	+	0.954562i	$0.403677\pi$
$434$	26.8450	1.28860
$435$	2.26057	0.108386
$436$	0.665302	0.0318622
$437$	23.2287	1.11118
$438$	−25.8884	−1.23699
$439$	−36.1823	−1.72688	−0.863442	−	0.504447i	$-0.831696\pi$
$439$	−36.1823	−1.72688	−0.863442	+	0.504447i	$0.831696\pi$
$440$	−2.06508	−0.0984490
$441$	7.79469	0.371176
$442$	19.6172	0.933096
$443$	1.43636	0.0682434	0.0341217	−	0.999418i	$-0.489137\pi$
$443$	1.43636	0.0682434	0.0341217	+	0.999418i	$0.489137\pi$
$444$	1.80317	0.0855748
$445$	−0.729285	−0.0345714
$446$	−7.21849	−0.341805
$447$	−19.8419	−0.938489
$448$	2.87005	0.135597
$449$	39.4854	1.86343	0.931715	−	0.363191i	$-0.118313\pi$
$449$	39.4854	1.86343	0.931715	+	0.363191i	$0.118313\pi$
$450$	−30.2056	−1.42390
$451$	−13.5252	−0.636879
$452$	−0.754723	−0.0354992
$453$	−8.89125	−0.417747
$454$	−3.78258	−0.177525
$455$	3.56254	0.167015
$456$	11.2236	0.525594
$457$	17.0198	0.796153	0.398077	−	0.917352i	$-0.369678\pi$
$457$	17.0198	0.796153	0.398077	+	0.917352i	$0.369678\pi$
$458$	23.2749	1.08756
$459$	72.1271	3.36661
$460$	2.86208	0.133445
$461$	10.9267	0.508907	0.254453	−	0.967085i	$-0.418104\pi$
$461$	10.9267	0.508907	0.254453	+	0.967085i	$0.418104\pi$
$462$	−39.8595	−1.85443
$463$	36.3480	1.68923	0.844617	−	0.535371i	$-0.179828\pi$
$463$	36.3480	1.68923	0.844617	+	0.535371i	$0.179828\pi$
$464$	1.63467	0.0758874
$465$	12.9349	0.599841
$466$	28.2350	1.30796
$467$	10.1138	0.468013	0.234007	−	0.972235i	$-0.424816\pi$
$467$	10.1138	0.468013	0.234007	+	0.972235i	$0.424816\pi$
$468$	−17.2458	−0.797187
$469$	−22.7045	−1.04839
$470$	−0.672441	−0.0310174
$471$	48.3806	2.22926
$472$	−9.46594	−0.435705
$473$	−8.69421	−0.399760
$474$	22.0214	1.01148
$475$	17.6449	0.809601
$476$	−20.5684	−0.942749
$477$	43.6778	1.99987
$478$	−29.4096	−1.34516
$479$	−12.6139	−0.576342	−0.288171	−	0.957579i	$-0.593047\pi$
$479$	−12.6139	−0.576342	−0.288171	+	0.957579i	$0.593047\pi$
$480$	1.38289	0.0631202
$481$	1.61852	0.0737983
$482$	19.2396	0.876341
$483$	55.2428	2.51363
$484$	9.73916	0.442689
$485$	7.44903	0.338243
$486$	−5.76815	−0.261649
$487$	−4.50109	−0.203964	−0.101982	−	0.994786i	$-0.532518\pi$
$487$	−4.50109	−0.203964	−0.101982	+	0.994786i	$0.532518\pi$
$488$	−1.11562	−0.0505019
$489$	12.6666	0.572804
$490$	−0.561029	−0.0253447
$491$	−1.67997	−0.0758161	−0.0379080	−	0.999281i	$-0.512069\pi$
$491$	−1.67997	−0.0758161	−0.0379080	+	0.999281i	$0.512069\pi$
$492$	9.05724	0.408332
$493$	−11.7149	−0.527612
$494$	10.0743	0.453263
$495$	−13.0105	−0.584778
$496$	9.35349	0.419984
$497$	−7.22801	−0.324221
$498$	−4.31293	−0.193267
$499$	−14.1116	−0.631721	−0.315860	−	0.948806i	$-0.602293\pi$
$499$	−14.1116	−0.631721	−0.315860	+	0.948806i	$0.602293\pi$
$500$	4.44139	0.198625
$501$	39.6787	1.77272
$502$	−14.3492	−0.640436
$503$	39.3447	1.75429	0.877147	−	0.480222i	$-0.159444\pi$
$503$	39.3447	1.75429	0.877147	+	0.480222i	$0.159444\pi$
$504$	18.0820	0.805435
$505$	−1.95964	−0.0872029
$506$	−28.7432	−1.27779
$507$	16.7943	0.745861
$508$	−4.30638	−0.191065
$509$	−14.2591	−0.632024	−0.316012	−	0.948755i	$-0.602344\pi$
$509$	−14.2591	−0.632024	−0.316012	+	0.948755i	$0.602344\pi$
$510$	−9.91056	−0.438847
$511$	24.3640	1.07780
$512$	1.00000	0.0441942
$513$	37.0404	1.63537
$514$	−27.9600	−1.23326
$515$	4.04545	0.178264
$516$	5.82212	0.256304
$517$	6.75316	0.297004
$518$	−1.69700	−0.0745618
$519$	−10.8913	−0.478077
$520$	1.24128	0.0544338
$521$	−13.8915	−0.608598	−0.304299	−	0.952577i	$-0.598422\pi$
$521$	−13.8915	−0.608598	−0.304299	+	0.952577i	$0.598422\pi$
$522$	10.2987	0.450764
$523$	8.89964	0.389154	0.194577	−	0.980887i	$-0.437667\pi$
$523$	8.89964	0.389154	0.194577	+	0.980887i	$0.437667\pi$
$524$	5.80627	0.253648
$525$	41.9632	1.83142
$526$	−26.8324	−1.16995
$527$	−67.0321	−2.91997
$528$	−13.8881	−0.604401
$529$	16.8362	0.732008
$530$	−3.14375	−0.136556
$531$	−59.6375	−2.58805
$532$	−10.5627	−0.457953
$533$	8.12975	0.352139
$534$	−4.90458	−0.212242
$535$	−3.93094	−0.169949
$536$	−7.91081	−0.341695
$537$	−72.6799	−3.13637
$538$	−11.1783	−0.481932
$539$	5.63429	0.242686
$540$	4.56385	0.196397
$541$	−19.5634	−0.841096	−0.420548	−	0.907270i	$-0.638162\pi$
$541$	−19.5634	−0.841096	−0.420548	+	0.907270i	$0.638162\pi$
$542$	−27.4597	−1.17949
$543$	20.4227	0.876423
$544$	−7.16654	−0.307263
$545$	−0.301690	−0.0129230
$546$	23.9588	1.02534
$547$	16.2089	0.693043	0.346522	−	0.938042i	$-0.387363\pi$
$547$	16.2089	0.693043	0.346522	+	0.938042i	$0.387363\pi$
$548$	−15.2169	−0.650032
$549$	−7.02867	−0.299976
$550$	−21.8337	−0.930992
$551$	−6.01610	−0.256295
$552$	19.2480	0.819249
$553$	−20.7247	−0.881304
$554$	6.50586	0.276407
$555$	−0.817673	−0.0347083
$556$	−8.89045	−0.377039
$557$	−13.2372	−0.560876	−0.280438	−	0.959872i	$-0.590480\pi$
$557$	−13.2372	−0.560876	−0.280438	+	0.959872i	$0.590480\pi$
$558$	58.9290	2.49466
$559$	5.22591	0.221033
$560$	−1.30146	−0.0549969
$561$	99.5295	4.20214
$562$	17.6111	0.742880
$563$	−19.2881	−0.812898	−0.406449	−	0.913674i	$-0.633233\pi$
$563$	−19.2881	−0.812898	−0.406449	+	0.913674i	$0.633233\pi$
$564$	−4.52229	−0.190423
$565$	0.342239	0.0143981
$566$	15.8386	0.665746
$567$	33.8439	1.42131
$568$	−2.51842	−0.105671
$569$	−26.7053	−1.11954	−0.559772	−	0.828647i	$-0.689111\pi$
$569$	−26.7053	−1.11954	−0.559772	+	0.828647i	$0.689111\pi$
$570$	−5.08950	−0.213176
$571$	−40.2551	−1.68463	−0.842313	−	0.538989i	$-0.818806\pi$
$571$	−40.2551	−1.68463	−0.842313	+	0.538989i	$0.818806\pi$
$572$	−12.4659	−0.521225
$573$	17.0740	0.713276
$574$	−8.52392	−0.355782
$575$	30.2601	1.26193
$576$	6.30022	0.262509
$577$	−32.2349	−1.34196	−0.670978	−	0.741477i	$-0.734126\pi$
$577$	−32.2349	−1.34196	−0.670978	+	0.741477i	$0.734126\pi$
$578$	34.3593	1.42916
$579$	7.13555	0.296543
$580$	−0.741261	−0.0307792
$581$	4.05897	0.168395
$582$	50.0961	2.07655
$583$	31.5719	1.30758
$584$	8.48903	0.351279
$585$	7.82034	0.323331
$586$	−16.5947	−0.685520
$587$	−20.4732	−0.845018	−0.422509	−	0.906359i	$-0.638850\pi$
$587$	−20.4732	−0.845018	−0.422509	+	0.906359i	$0.638850\pi$
$588$	−3.77303	−0.155597
$589$	−34.4239	−1.41841
$590$	4.29246	0.176718
$591$	14.6785	0.603795
$592$	−0.591277	−0.0243013
$593$	−23.3784	−0.960037	−0.480019	−	0.877258i	$-0.659370\pi$
$593$	−23.3784	−0.960037	−0.480019	+	0.877258i	$0.659370\pi$
$594$	−45.8337	−1.88058
$595$	9.32700	0.382370
$596$	6.50634	0.266510
$597$	67.7199	2.77159
$598$	17.2769	0.706506
$599$	−10.0186	−0.409347	−0.204674	−	0.978830i	$-0.565613\pi$
$599$	−10.0186	−0.409347	−0.204674	+	0.978830i	$0.565613\pi$
$600$	14.6210	0.596901
$601$	38.7817	1.58194	0.790968	−	0.611857i	$-0.209577\pi$
$601$	38.7817	1.58194	0.790968	+	0.611857i	$0.209577\pi$
$602$	−5.47929	−0.223319
$603$	−49.8398	−2.02963
$604$	2.91552	0.118631
$605$	−4.41635	−0.179550
$606$	−13.1790	−0.535358
$607$	−6.63523	−0.269316	−0.134658	−	0.990892i	$-0.542994\pi$
$607$	−6.63523	−0.269316	−0.134658	+	0.990892i	$0.542994\pi$
$608$	−3.68033	−0.149257
$609$	−14.3076	−0.579772
$610$	0.505894	0.0204831
$611$	−4.05919	−0.164217
$612$	−45.1508	−1.82511
$613$	−33.9782	−1.37237	−0.686183	−	0.727429i	$-0.740715\pi$
$613$	−33.9782	−1.37237	−0.686183	+	0.727429i	$0.740715\pi$
$614$	−27.4375	−1.10729
$615$	−4.10713	−0.165615
$616$	13.0703	0.526617
$617$	9.18032	0.369586	0.184793	−	0.982777i	$-0.440839\pi$
$617$	9.18032	0.369586	0.184793	+	0.982777i	$0.440839\pi$
$618$	27.2064	1.09440
$619$	−21.7546	−0.874390	−0.437195	−	0.899367i	$-0.644028\pi$
$619$	−21.7546	−0.874390	−0.437195	+	0.899367i	$0.644028\pi$
$620$	−4.24146	−0.170341
$621$	63.5225	2.54907
$622$	12.3634	0.495729
$623$	4.61578	0.184927
$624$	8.34784	0.334181
$625$	21.9578	0.878314
$626$	22.5087	0.899628
$627$	51.1127	2.04124
$628$	−15.8644	−0.633060
$629$	4.23741	0.168957
$630$	−8.19951	−0.326676
$631$	14.0266	0.558389	0.279195	−	0.960235i	$-0.409933\pi$
$631$	14.0266	0.558389	0.279195	+	0.960235i	$0.409933\pi$
$632$	−7.22101	−0.287236
$633$	−22.7300	−0.903435
$634$	−20.9641	−0.832591
$635$	1.95279	0.0774940
$636$	−21.1423	−0.838346
$637$	−3.38666	−0.134184
$638$	7.44431	0.294723
$639$	−15.8666	−0.627674
$640$	−0.453463	−0.0179247
$641$	34.8021	1.37460	0.687301	−	0.726373i	$-0.258795\pi$
$641$	34.8021	1.37460	0.687301	+	0.726373i	$0.258795\pi$
$642$	−26.4363	−1.04336
$643$	35.9005	1.41578	0.707888	−	0.706325i	$-0.249648\pi$
$643$	35.9005	1.41578	0.707888	+	0.706325i	$0.249648\pi$
$644$	−18.1146	−0.713815
$645$	−2.64012	−0.103955
$646$	26.3752	1.03772
$647$	−6.74504	−0.265175	−0.132588	−	0.991171i	$-0.542329\pi$
$647$	−6.74504	−0.265175	−0.132588	+	0.991171i	$0.542329\pi$
$648$	11.7921	0.463237
$649$	−43.1081	−1.69214
$650$	13.1238	0.514757
$651$	−81.8672	−3.20863
$652$	−4.15350	−0.162663
$653$	44.2483	1.73157	0.865785	−	0.500416i	$-0.166819\pi$
$653$	44.2483	1.73157	0.865785	+	0.500416i	$0.166819\pi$
$654$	−2.02892	−0.0793372
$655$	−2.63293	−0.102877
$656$	−2.96995	−0.115957
$657$	53.4827	2.08656
$658$	4.25600	0.165916
$659$	0.217285	0.00846421	0.00423210	−	0.999991i	$-0.498653\pi$
$659$	0.217285	0.00846421	0.00423210	+	0.999991i	$0.498653\pi$
$660$	6.29773	0.245139
$661$	−12.1669	−0.473239	−0.236619	−	0.971602i	$-0.576039\pi$
$661$	−12.1669	−0.473239	−0.236619	+	0.971602i	$0.576039\pi$
$662$	27.6536	1.07479
$663$	−59.8251	−2.32342
$664$	1.41425	0.0548835
$665$	4.78982	0.185741
$666$	−3.72517	−0.144348
$667$	−10.3173	−0.399489
$668$	−13.0110	−0.503412
$669$	22.0137	0.851098
$670$	3.58726	0.138588
$671$	−5.08058	−0.196134
$672$	−8.75259	−0.337638
$673$	−7.87831	−0.303686	−0.151843	−	0.988405i	$-0.548521\pi$
$673$	−7.87831	−0.303686	−0.151843	+	0.988405i	$0.548521\pi$
$674$	3.80005	0.146372
$675$	48.2526	1.85724
$676$	−5.50701	−0.211808
$677$	6.95370	0.267252	0.133626	−	0.991032i	$-0.457338\pi$
$677$	6.95370	0.267252	0.133626	+	0.991032i	$0.457338\pi$
$678$	2.30162	0.0883933
$679$	−47.1463	−1.80931
$680$	3.24976	0.124623
$681$	11.5354	0.442039
$682$	42.5960	1.63109
$683$	−4.61647	−0.176644	−0.0883222	−	0.996092i	$-0.528151\pi$
$683$	−4.61647	−0.176644	−0.0883222	+	0.996092i	$0.528151\pi$
$684$	−23.1869	−0.886572
$685$	6.90029	0.263646
$686$	−16.5395	−0.631482
$687$	−70.9797	−2.70804
$688$	−1.90913	−0.0727847
$689$	−18.9772	−0.722976
$690$	−8.72826	−0.332279
$691$	−35.8001	−1.36190	−0.680950	−	0.732330i	$-0.738433\pi$
$691$	−35.8001	−1.36190	−0.680950	+	0.732330i	$0.738433\pi$
$692$	3.57137	0.135763
$693$	82.3457	3.12806
$694$	21.7371	0.825129
$695$	4.03150	0.152923
$696$	−4.98512	−0.188960
$697$	21.2843	0.806200
$698$	26.4543	1.00131
$699$	−86.1061	−3.25683
$700$	−13.7601	−0.520083
$701$	25.3996	0.959331	0.479665	−	0.877452i	$-0.340758\pi$
$701$	25.3996	0.959331	0.479665	+	0.877452i	$0.340758\pi$
$702$	27.5497	1.03980
$703$	2.17609	0.0820729
$704$	4.55403	0.171636
$705$	2.05069	0.0772335
$706$	−3.66225	−0.137830
$707$	12.4029	0.466460
$708$	28.8676	1.08491
$709$	−31.8496	−1.19614	−0.598069	−	0.801445i	$-0.704065\pi$
$709$	−31.8496	−1.19614	−0.598069	+	0.801445i	$0.704065\pi$
$710$	1.14201	0.0428590
$711$	−45.4939	−1.70616
$712$	1.60826	0.0602719
$713$	−59.0354	−2.21089
$714$	62.7258	2.34745
$715$	5.65282	0.211404
$716$	23.8324	0.890659
$717$	89.6883	3.34947
$718$	−14.5568	−0.543253
$719$	27.5615	1.02787	0.513935	−	0.857829i	$-0.328187\pi$
$719$	27.5615	1.02787	0.513935	+	0.857829i	$0.328187\pi$
$720$	−2.85692	−0.106471
$721$	−25.6044	−0.953557
$722$	−5.45519	−0.203021
$723$	−58.6736	−2.18210
$724$	−6.69679	−0.248884
$725$	−7.83719	−0.291066
$726$	−29.7008	−1.10230
$727$	−29.2378	−1.08437	−0.542184	−	0.840260i	$-0.682403\pi$
$727$	−29.2378	−1.08437	−0.542184	+	0.840260i	$0.682403\pi$
$728$	−7.85629	−0.291174
$729$	−17.7855	−0.658723
$730$	−3.84947	−0.142475
$731$	13.6818	0.506041
$732$	3.40223	0.125750
$733$	−35.3766	−1.30667	−0.653333	−	0.757071i	$-0.726630\pi$
$733$	−35.3766	−1.30667	−0.653333	+	0.757071i	$0.726630\pi$
$734$	−20.4525	−0.754917
$735$	1.71093	0.0631086
$736$	−6.31159	−0.232648
$737$	−36.0260	−1.32704
$738$	−18.7113	−0.688774
$739$	−32.7619	−1.20517	−0.602583	−	0.798056i	$-0.705862\pi$
$739$	−32.7619	−1.20517	−0.602583	+	0.798056i	$0.705862\pi$
$740$	0.268123	0.00985638
$741$	−30.7228	−1.12863
$742$	19.8974	0.730455
$743$	35.7986	1.31332	0.656662	−	0.754185i	$-0.271968\pi$
$743$	35.7986	1.31332	0.656662	+	0.754185i	$0.271968\pi$
$744$	−28.5246	−1.04576
$745$	−2.95039	−0.108094
$746$	−19.6067	−0.717854
$747$	8.91008	0.326003
$748$	−32.6366	−1.19331
$749$	24.8796	0.909082
$750$	−13.5446	−0.494578
$751$	−2.93259	−0.107012	−0.0535058	−	0.998568i	$-0.517040\pi$
$751$	−2.93259	−0.107012	−0.0535058	+	0.998568i	$0.517040\pi$
$752$	1.48290	0.0540758
$753$	43.7597	1.59469
$754$	−4.47463	−0.162956
$755$	−1.32208	−0.0481155
$756$	−28.8854	−1.05055
$757$	35.9870	1.30797	0.653986	−	0.756507i	$-0.273096\pi$
$757$	35.9870	1.30797	0.653986	+	0.756507i	$0.273096\pi$
$758$	−22.8504	−0.829966
$759$	87.6559	3.18171
$760$	1.66889	0.0605371
$761$	−26.4943	−0.960419	−0.480210	−	0.877154i	$-0.659439\pi$
$761$	−26.4943	−0.960419	−0.480210	+	0.877154i	$0.659439\pi$
$762$	13.1329	0.475753
$763$	1.90945	0.0691269
$764$	−5.59871	−0.202554
$765$	20.4742	0.740247
$766$	6.77952	0.244954
$767$	25.9114	0.935608
$768$	−3.04963	−0.110044
$769$	−44.4651	−1.60345	−0.801726	−	0.597691i	$-0.796085\pi$
$769$	−44.4651	−1.60345	−0.801726	+	0.597691i	$0.796085\pi$
$770$	−5.92690	−0.213591
$771$	85.2675	3.07083
$772$	−2.33981	−0.0842116
$773$	23.5939	0.848613	0.424306	−	0.905519i	$-0.360518\pi$
$773$	23.5939	0.848613	0.424306	+	0.905519i	$0.360518\pi$
$774$	−12.0279	−0.432334
$775$	−44.8441	−1.61085
$776$	−16.4270	−0.589694
$777$	5.17521	0.185659
$778$	13.8181	0.495402
$779$	10.9304	0.391622
$780$	−3.78544	−0.135541
$781$	−11.4690	−0.410392
$782$	45.2323	1.61750
$783$	−16.4520	−0.587945
$784$	1.23721	0.0441861
$785$	7.19394	0.256763
$786$	−17.7069	−0.631585
$787$	−5.26560	−0.187698	−0.0938492	−	0.995586i	$-0.529917\pi$
$787$	−5.26560	−0.187698	−0.0938492	+	0.995586i	$0.529917\pi$
$788$	−4.81323	−0.171464
$789$	81.8287	2.91318
$790$	3.27447	0.116500
$791$	−2.16610	−0.0770175
$792$	28.6914	1.01950
$793$	3.05383	0.108445
$794$	−1.81347	−0.0643578
$795$	9.58726	0.340025
$796$	−22.2060	−0.787070
$797$	6.16162	0.218256	0.109128	−	0.994028i	$-0.465194\pi$
$797$	6.16162	0.218256	0.109128	+	0.994028i	$0.465194\pi$
$798$	32.2124	1.14031
$799$	−10.6273	−0.375965
$800$	−4.79437	−0.169507
$801$	10.1324	0.358009
$802$	5.23744	0.184940
$803$	38.6593	1.36426
$804$	24.1250	0.850824
$805$	8.21431	0.289516
$806$	−25.6036	−0.901849
$807$	34.0897	1.20002
$808$	4.32150	0.152030
$809$	28.1518	0.989763	0.494882	−	0.868960i	$-0.335211\pi$
$809$	28.1518	0.989763	0.494882	+	0.868960i	$0.335211\pi$
$810$	−5.34728	−0.187884
$811$	37.0502	1.30101	0.650504	−	0.759503i	$-0.274558\pi$
$811$	37.0502	1.30101	0.650504	+	0.759503i	$0.274558\pi$
$812$	4.69158	0.164642
$813$	83.7417	2.93695
$814$	−2.69269	−0.0943788
$815$	1.88346	0.0659747
$816$	21.8553	0.765087
$817$	7.02621	0.245816
$818$	−21.0305	−0.735313
$819$	−49.4964	−1.72954
$820$	1.34676	0.0470311
$821$	29.8671	1.04237	0.521185	−	0.853444i	$-0.325490\pi$
$821$	29.8671	1.04237	0.521185	+	0.853444i	$0.325490\pi$
$822$	46.4057	1.61858
$823$	−15.1188	−0.527010	−0.263505	−	0.964658i	$-0.584878\pi$
$823$	−15.1188	−0.527010	−0.263505	+	0.964658i	$0.584878\pi$
$824$	−8.92122	−0.310786
$825$	66.5846	2.31818
$826$	−27.1678	−0.945287
$827$	11.3486	0.394628	0.197314	−	0.980340i	$-0.436778\pi$
$827$	11.3486	0.394628	0.197314	+	0.980340i	$0.436778\pi$
$828$	−39.7644	−1.38191
$829$	50.4621	1.75262	0.876311	−	0.481746i	$-0.159997\pi$
$829$	50.4621	1.75262	0.876311	+	0.481746i	$0.159997\pi$
$830$	−0.641310	−0.0222602
$831$	−19.8404	−0.688257
$832$	−2.73733	−0.0949000
$833$	−8.86651	−0.307206
$834$	27.1126	0.938831
$835$	5.90002	0.204179
$836$	−16.7603	−0.579667
$837$	−94.1375	−3.25387
$838$	−16.1708	−0.558611
$839$	31.8200	1.09855	0.549274	−	0.835642i	$-0.314904\pi$
$839$	31.8200	1.09855	0.549274	+	0.835642i	$0.314904\pi$
$840$	3.96898	0.136943
$841$	−26.3279	−0.907858
$842$	23.3469	0.804588
$843$	−53.7073	−1.84978
$844$	7.45337	0.256555
$845$	2.49723	0.0859072
$846$	9.34259	0.321205
$847$	27.9519	0.960439
$848$	6.93275	0.238072
$849$	−48.3018	−1.65771
$850$	34.3591	1.17851
$851$	3.73190	0.127928
$852$	7.68025	0.263121
$853$	23.6983	0.811414	0.405707	−	0.914003i	$-0.367025\pi$
$853$	23.6983	0.811414	0.405707	+	0.914003i	$0.367025\pi$
$854$	−3.20190	−0.109567
$855$	10.5144	0.359585
$856$	8.66869	0.296290
$857$	41.8186	1.42850	0.714248	−	0.699893i	$-0.246769\pi$
$857$	41.8186	1.42850	0.714248	+	0.699893i	$0.246769\pi$
$858$	38.0163	1.29785
$859$	−30.1696	−1.02937	−0.514687	−	0.857378i	$-0.672092\pi$
$859$	−30.1696	−1.02937	−0.514687	+	0.857378i	$0.672092\pi$
$860$	0.865719	0.0295208
$861$	25.9948	0.885900
$862$	−10.4709	−0.356640
$863$	−13.9441	−0.474661	−0.237331	−	0.971429i	$-0.576273\pi$
$863$	−13.9441	−0.474661	−0.237331	+	0.971429i	$0.576273\pi$
$864$	−10.0644	−0.342399
$865$	−1.61949	−0.0550642
$866$	12.4024	0.421451
$867$	−104.783	−3.55862
$868$	26.8450	0.911179
$869$	−32.8847	−1.11554
$870$	2.26057	0.0766405
$871$	21.6545	0.733736
$872$	0.665302	0.0225300
$873$	−103.493	−3.50272
$874$	23.2287	0.785723
$875$	12.7470	0.430928
$876$	−25.8884	−0.874687
$877$	−36.2540	−1.22421	−0.612105	−	0.790776i	$-0.709677\pi$
$877$	−36.2540	−1.22421	−0.612105	+	0.790776i	$0.709677\pi$
$878$	−36.1823	−1.22109
$879$	50.6075	1.70695
$880$	−2.06508	−0.0696140
$881$	7.48027	0.252017	0.126008	−	0.992029i	$-0.459783\pi$
$881$	7.48027	0.252017	0.126008	+	0.992029i	$0.459783\pi$
$882$	7.79469	0.262461
$883$	30.3677	1.02196	0.510978	−	0.859594i	$-0.329283\pi$
$883$	30.3677	1.02196	0.510978	+	0.859594i	$0.329283\pi$
$884$	19.6172	0.659798
$885$	−13.0904	−0.440029
$886$	1.43636	0.0482553
$887$	7.43283	0.249570	0.124785	−	0.992184i	$-0.460176\pi$
$887$	7.43283	0.249570	0.124785	+	0.992184i	$0.460176\pi$
$888$	1.80317	0.0605105
$889$	−12.3595	−0.414526
$890$	−0.729285	−0.0244457
$891$	53.7014	1.79907
$892$	−7.21849	−0.241693
$893$	−5.45755	−0.182630
$894$	−19.8419	−0.663612
$895$	−10.8071	−0.361242
$896$	2.87005	0.0958818
$897$	−52.6882	−1.75921
$898$	39.4854	1.31764
$899$	15.2898	0.509944
$900$	−30.2056	−1.00685
$901$	−49.6838	−1.65521
$902$	−13.5252	−0.450341
$903$	16.7098	0.556067
$904$	−0.754723	−0.0251017
$905$	3.03675	0.100945
$906$	−8.89125	−0.295392
$907$	−20.8105	−0.691002	−0.345501	−	0.938418i	$-0.612291\pi$
$907$	−20.8105	−0.691002	−0.345501	+	0.938418i	$0.612291\pi$
$908$	−3.78258	−0.125529
$909$	27.2264	0.903042
$910$	3.56254	0.118097
$911$	8.11655	0.268913	0.134457	−	0.990919i	$-0.457071\pi$
$911$	8.11655	0.268913	0.134457	+	0.990919i	$0.457071\pi$
$912$	11.2236	0.371651
$913$	6.44053	0.213150
$914$	17.0198	0.562965
$915$	−1.54279	−0.0510030
$916$	23.2749	0.769024
$917$	16.6643	0.550303
$918$	72.1271	2.38055
$919$	31.0123	1.02300	0.511501	−	0.859283i	$-0.329090\pi$
$919$	31.0123	1.02300	0.511501	+	0.859283i	$0.329090\pi$
$920$	2.86208	0.0943598
$921$	83.6741	2.75716
$922$	10.9267	0.359851
$923$	6.89377	0.226911
$924$	−39.8595	−1.31128
$925$	2.83480	0.0932077
$926$	36.3480	1.19447
$927$	−56.2056	−1.84604
$928$	1.63467	0.0536605
$929$	14.2428	0.467291	0.233645	−	0.972322i	$-0.424935\pi$
$929$	14.2428	0.467291	0.233645	+	0.972322i	$0.424935\pi$
$930$	12.9349	0.424151
$931$	−4.55334	−0.149230
$932$	28.2350	0.924867
$933$	−37.7039	−1.23437
$934$	10.1138	0.330935
$935$	14.7995	0.483996
$936$	−17.2458	−0.563696
$937$	28.9501	0.945759	0.472880	−	0.881127i	$-0.343215\pi$
$937$	28.9501	0.945759	0.472880	+	0.881127i	$0.343215\pi$
$938$	−22.7045	−0.741327
$939$	−68.6431	−2.24008
$940$	−0.672441	−0.0219326
$941$	−10.8952	−0.355175	−0.177587	−	0.984105i	$-0.556829\pi$
$941$	−10.8952	−0.355175	−0.177587	+	0.984105i	$0.556829\pi$
$942$	48.3806	1.57633
$943$	18.7451	0.610425
$944$	−9.46594	−0.308090
$945$	13.0985	0.426094
$946$	−8.69421	−0.282673
$947$	38.3702	1.24686	0.623432	−	0.781878i	$-0.285738\pi$
$947$	38.3702	1.24686	0.623432	+	0.781878i	$0.285738\pi$
$948$	22.0214	0.715221
$949$	−23.2373	−0.754315
$950$	17.6449	0.572475
$951$	63.9326	2.07316
$952$	−20.5684	−0.666624
$953$	35.0246	1.13456	0.567278	−	0.823526i	$-0.307996\pi$
$953$	35.0246	1.13456	0.567278	+	0.823526i	$0.307996\pi$
$954$	43.6778	1.41412
$955$	2.53881	0.0821540
$956$	−29.4096	−0.951174
$957$	−22.7024	−0.733863
$958$	−12.6139	−0.407536
$959$	−43.6732	−1.41028
$960$	1.38289	0.0446327
$961$	56.4877	1.82218
$962$	1.61852	0.0521833
$963$	54.6147	1.75993
$964$	19.2396	0.619667
$965$	1.06102	0.0341554
$966$	55.2428	1.77741
$967$	−27.3595	−0.879822	−0.439911	−	0.898041i	$-0.644990\pi$
$967$	−27.3595	−0.879822	−0.439911	+	0.898041i	$0.644990\pi$
$968$	9.73916	0.313028
$969$	−80.4345	−2.58393
$970$	7.44903	0.239174
$971$	8.07358	0.259094	0.129547	−	0.991573i	$-0.458648\pi$
$971$	8.07358	0.259094	0.129547	+	0.991573i	$0.458648\pi$
$972$	−5.76815	−0.185014
$973$	−25.5161	−0.818008
$974$	−4.50109	−0.144224
$975$	−40.0227	−1.28175
$976$	−1.11562	−0.0357102
$977$	32.0512	1.02541	0.512704	−	0.858565i	$-0.328644\pi$
$977$	32.0512	1.02541	0.512704	+	0.858565i	$0.328644\pi$
$978$	12.6666	0.405033
$979$	7.32404	0.234077
$980$	−0.561029	−0.0179214
$981$	4.19155	0.133826
$982$	−1.67997	−0.0536101
$983$	22.0362	0.702846	0.351423	−	0.936217i	$-0.385698\pi$
$983$	22.0362	0.702846	0.351423	+	0.936217i	$0.385698\pi$
$984$	9.05724	0.288734
$985$	2.18262	0.0695442
$986$	−11.7149	−0.373078
$987$	−12.9792	−0.413133
$988$	10.0743	0.320506
$989$	12.0496	0.383156
$990$	−13.0105	−0.413500
$991$	10.3307	0.328167	0.164083	−	0.986446i	$-0.447533\pi$
$991$	10.3307	0.328167	0.164083	+	0.986446i	$0.447533\pi$
$992$	9.35349	0.296973
$993$	−84.3333	−2.67623
$994$	−7.22801	−0.229259
$995$	10.0696	0.319228
$996$	−4.31293	−0.136660
$997$	39.1478	1.23982	0.619911	−	0.784672i	$-0.287169\pi$
$997$	39.1478	1.23982	0.619911	+	0.784672i	$0.287169\pi$
$998$	−14.1116	−0.446694
$999$	5.95086	0.188277

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4022.2.a.c.1.3	✓	31

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4022.2.a.c.1.3	✓	31	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:	\( N \)	\(=\)	\( 4022 = 2 \cdot 2011 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4022.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -3.04963 q^{3} +1.00000 q^{4} -0.453463 q^{5} -3.04963 q^{6} +2.87005 q^{7} +1.00000 q^{8} +6.30022 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -3.04963 q^{3} +1.00000 q^{4} -0.453463 q^{5} -3.04963 q^{6} +2.87005 q^{7} +1.00000 q^{8} +6.30022 q^{9} -0.453463 q^{10} +4.55403 q^{11} -3.04963 q^{12} -2.73733 q^{13} +2.87005 q^{14} +1.38289 q^{15} +1.00000 q^{16} -7.16654 q^{17} +6.30022 q^{18} -3.68033 q^{19} -0.453463 q^{20} -8.75259 q^{21} +4.55403 q^{22} -6.31159 q^{23} -3.04963 q^{24} -4.79437 q^{25} -2.73733 q^{26} -10.0644 q^{27} +2.87005 q^{28} +1.63467 q^{29} +1.38289 q^{30} +9.35349 q^{31} +1.00000 q^{32} -13.8881 q^{33} -7.16654 q^{34} -1.30146 q^{35} +6.30022 q^{36} -0.591277 q^{37} -3.68033 q^{38} +8.34784 q^{39} -0.453463 q^{40} -2.96995 q^{41} -8.75259 q^{42} -1.90913 q^{43} +4.55403 q^{44} -2.85692 q^{45} -6.31159 q^{46} +1.48290 q^{47} -3.04963 q^{48} +1.23721 q^{49} -4.79437 q^{50} +21.8553 q^{51} -2.73733 q^{52} +6.93275 q^{53} -10.0644 q^{54} -2.06508 q^{55} +2.87005 q^{56} +11.2236 q^{57} +1.63467 q^{58} -9.46594 q^{59} +1.38289 q^{60} -1.11562 q^{61} +9.35349 q^{62} +18.0820 q^{63} +1.00000 q^{64} +1.24128 q^{65} -13.8881 q^{66} -7.91081 q^{67} -7.16654 q^{68} +19.2480 q^{69} -1.30146 q^{70} -2.51842 q^{71} +6.30022 q^{72} +8.48903 q^{73} -0.591277 q^{74} +14.6210 q^{75} -3.68033 q^{76} +13.0703 q^{77} +8.34784 q^{78} -7.22101 q^{79} -0.453463 q^{80} +11.7921 q^{81} -2.96995 q^{82} +1.41425 q^{83} -8.75259 q^{84} +3.24976 q^{85} -1.90913 q^{86} -4.98512 q^{87} +4.55403 q^{88} +1.60826 q^{89} -2.85692 q^{90} -7.85629 q^{91} -6.31159 q^{92} -28.5246 q^{93} +1.48290 q^{94} +1.66889 q^{95} -3.04963 q^{96} -16.4270 q^{97} +1.23721 q^{98} +28.6914 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 31 q + 31 q^{2} - 14 q^{3} + 31 q^{4} - 13 q^{5} - 14 q^{6} - 29 q^{7} + 31 q^{8} + 27 q^{9}+O(q^{10}) \) 31 * q + 31 * q^2 - 14 * q^3 + 31 * q^4 - 13 * q^5 - 14 * q^6 - 29 * q^7 + 31 * q^8 + 27 * q^9	\( 31 q + 31 q^{2} - 14 q^{3} + 31 q^{4} - 13 q^{5} - 14 q^{6} - 29 q^{7} + 31 q^{8} + 27 q^{9} - 13 q^{10} - 29 q^{11} - 14 q^{12} - 23 q^{13} - 29 q^{14} - 14 q^{15} + 31 q^{16} - 19 q^{17} + 27 q^{18} - 36 q^{19} - 13 q^{20} - 29 q^{22} - 24 q^{23} - 14 q^{24} + 4 q^{25} - 23 q^{26} - 65 q^{27} - 29 q^{28} + 18 q^{29} - 14 q^{30} - 41 q^{31} + 31 q^{32} - 18 q^{33} - 19 q^{34} - 28 q^{35} + 27 q^{36} - 31 q^{37} - 36 q^{38} - 31 q^{39} - 13 q^{40} - 51 q^{41} - 14 q^{43} - 29 q^{44} - 34 q^{45} - 24 q^{46} - 64 q^{47} - 14 q^{48} + 8 q^{49} + 4 q^{50} - 17 q^{51} - 23 q^{52} + 3 q^{53} - 65 q^{54} - 50 q^{55} - 29 q^{56} - 19 q^{57} + 18 q^{58} - 58 q^{59} - 14 q^{60} - 14 q^{61} - 41 q^{62} - 66 q^{63} + 31 q^{64} + 6 q^{65} - 18 q^{66} - 55 q^{67} - 19 q^{68} + q^{69} - 28 q^{70} - 42 q^{71} + 27 q^{72} - 83 q^{73} - 31 q^{74} - 49 q^{75} - 36 q^{76} + 18 q^{77} - 31 q^{78} - 56 q^{79} - 13 q^{80} + 3 q^{81} - 51 q^{82} - 43 q^{83} + 4 q^{85} - 14 q^{86} - 76 q^{87} - 29 q^{88} + 17 q^{89} - 34 q^{90} - 49 q^{91} - 24 q^{92} - 24 q^{93} - 64 q^{94} - 43 q^{95} - 14 q^{96} - 98 q^{97} + 8 q^{98} - q^{99}+O(q^{100}) \) 31 * q + 31 * q^2 - 14 * q^3 + 31 * q^4 - 13 * q^5 - 14 * q^6 - 29 * q^7 + 31 * q^8 + 27 * q^9 - 13 * q^10 - 29 * q^11 - 14 * q^12 - 23 * q^13 - 29 * q^14 - 14 * q^15 + 31 * q^16 - 19 * q^17 + 27 * q^18 - 36 * q^19 - 13 * q^20 - 29 * q^22 - 24 * q^23 - 14 * q^24 + 4 * q^25 - 23 * q^26 - 65 * q^27 - 29 * q^28 + 18 * q^29 - 14 * q^30 - 41 * q^31 + 31 * q^32 - 18 * q^33 - 19 * q^34 - 28 * q^35 + 27 * q^36 - 31 * q^37 - 36 * q^38 - 31 * q^39 - 13 * q^40 - 51 * q^41 - 14 * q^43 - 29 * q^44 - 34 * q^45 - 24 * q^46 - 64 * q^47 - 14 * q^48 + 8 * q^49 + 4 * q^50 - 17 * q^51 - 23 * q^52 + 3 * q^53 - 65 * q^54 - 50 * q^55 - 29 * q^56 - 19 * q^57 + 18 * q^58 - 58 * q^59 - 14 * q^60 - 14 * q^61 - 41 * q^62 - 66 * q^63 + 31 * q^64 + 6 * q^65 - 18 * q^66 - 55 * q^67 - 19 * q^68 + q^69 - 28 * q^70 - 42 * q^71 + 27 * q^72 - 83 * q^73 - 31 * q^74 - 49 * q^75 - 36 * q^76 + 18 * q^77 - 31 * q^78 - 56 * q^79 - 13 * q^80 + 3 * q^81 - 51 * q^82 - 43 * q^83 + 4 * q^85 - 14 * q^86 - 76 * q^87 - 29 * q^88 + 17 * q^89 - 34 * q^90 - 49 * q^91 - 24 * q^92 - 24 * q^93 - 64 * q^94 - 43 * q^95 - 14 * q^96 - 98 * q^97 + 8 * q^98 - q^99

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