LMFDB - Embedded newform 4022.2.a.d.1.12

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:	$37$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
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)

$f(q)$	$=$	$q-1.00000 q^{2} -1.41095 q^{3} +1.00000 q^{4} -3.55049 q^{5} +1.41095 q^{6} -3.54920 q^{7} -1.00000 q^{8} -1.00921 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.41095 q^{3} +1.00000 q^{4} -3.55049 q^{5} +1.41095 q^{6} -3.54920 q^{7} -1.00000 q^{8} -1.00921 q^{9} +3.55049 q^{10} +4.87426 q^{11} -1.41095 q^{12} -3.10664 q^{13} +3.54920 q^{14} +5.00958 q^{15} +1.00000 q^{16} -4.40999 q^{17} +1.00921 q^{18} +1.30368 q^{19} -3.55049 q^{20} +5.00776 q^{21} -4.87426 q^{22} -3.42341 q^{23} +1.41095 q^{24} +7.60600 q^{25} +3.10664 q^{26} +5.65681 q^{27} -3.54920 q^{28} +8.36390 q^{29} -5.00958 q^{30} -3.07353 q^{31} -1.00000 q^{32} -6.87736 q^{33} +4.40999 q^{34} +12.6014 q^{35} -1.00921 q^{36} +7.52404 q^{37} -1.30368 q^{38} +4.38333 q^{39} +3.55049 q^{40} -4.62618 q^{41} -5.00776 q^{42} -4.44441 q^{43} +4.87426 q^{44} +3.58319 q^{45} +3.42341 q^{46} -10.5112 q^{47} -1.41095 q^{48} +5.59684 q^{49} -7.60600 q^{50} +6.22229 q^{51} -3.10664 q^{52} +8.60185 q^{53} -5.65681 q^{54} -17.3060 q^{55} +3.54920 q^{56} -1.83944 q^{57} -8.36390 q^{58} +14.4047 q^{59} +5.00958 q^{60} +7.09958 q^{61} +3.07353 q^{62} +3.58188 q^{63} +1.00000 q^{64} +11.0301 q^{65} +6.87736 q^{66} +15.1672 q^{67} -4.40999 q^{68} +4.83027 q^{69} -12.6014 q^{70} +8.37428 q^{71} +1.00921 q^{72} +5.90803 q^{73} -7.52404 q^{74} -10.7317 q^{75} +1.30368 q^{76} -17.2997 q^{77} -4.38333 q^{78} -8.39855 q^{79} -3.55049 q^{80} -4.95388 q^{81} +4.62618 q^{82} -6.84408 q^{83} +5.00776 q^{84} +15.6576 q^{85} +4.44441 q^{86} -11.8011 q^{87} -4.87426 q^{88} -2.84661 q^{89} -3.58319 q^{90} +11.0261 q^{91} -3.42341 q^{92} +4.33661 q^{93} +10.5112 q^{94} -4.62872 q^{95} +1.41095 q^{96} +0.0168333 q^{97} -5.59684 q^{98} -4.91914 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 37 q - 37 q^{2} - 5 q^{3} + 37 q^{4} - 13 q^{5} + 5 q^{6} - 22 q^{7} - 37 q^{8} + 32 q^{9}+O(q^{10}) $ 37 * q - 37 * q^2 - 5 * q^3 + 37 * q^4 - 13 * q^5 + 5 * q^6 - 22 * q^7 - 37 * q^8 + 32 * q^9	\( 37 q - 37 q^{2} - 5 q^{3} + 37 q^{4} - 13 q^{5} + 5 q^{6} - 22 q^{7} - 37 q^{8} + 32 q^{9} + 13 q^{10} + 12 q^{11} - 5 q^{12} - 36 q^{13} + 22 q^{14} - 7 q^{15} + 37 q^{16} + 4 q^{17} - 32 q^{18} - 10 q^{19} - 13 q^{20} - 11 q^{21} - 12 q^{22} - q^{23} + 5 q^{24} + 8 q^{25} + 36 q^{26} - 20 q^{27} - 22 q^{28} - 6 q^{29} + 7 q^{30} - 23 q^{31} - 37 q^{32} - 27 q^{33} - 4 q^{34} + 24 q^{35} + 32 q^{36} - 46 q^{37} + 10 q^{38} + 5 q^{39} + 13 q^{40} + 11 q^{41} + 11 q^{42} - 22 q^{43} + 12 q^{44} - 57 q^{45} + q^{46} - 18 q^{47} - 5 q^{48} - q^{49} - 8 q^{50} + 18 q^{51} - 36 q^{52} - 25 q^{53} + 20 q^{54} - 25 q^{55} + 22 q^{56} - 25 q^{57} + 6 q^{58} + 24 q^{59} - 7 q^{60} - 40 q^{61} + 23 q^{62} - 38 q^{63} + 37 q^{64} + 14 q^{65} + 27 q^{66} - 49 q^{67} + 4 q^{68} - 19 q^{69} - 24 q^{70} + 27 q^{71} - 32 q^{72} - 87 q^{73} + 46 q^{74} - 5 q^{75} - 10 q^{76} - 50 q^{77} - 5 q^{78} + 11 q^{79} - 13 q^{80} + 5 q^{81} - 11 q^{82} - 9 q^{83} - 11 q^{84} - 68 q^{85} + 22 q^{86} - 12 q^{87} - 12 q^{88} - 3 q^{89} + 57 q^{90} - 19 q^{91} - q^{92} - 69 q^{93} + 18 q^{94} + 27 q^{95} + 5 q^{96} - 98 q^{97} + q^{98} + 33 q^{99}+O(q^{100}) \) 37 * q - 37 * q^2 - 5 * q^3 + 37 * q^4 - 13 * q^5 + 5 * q^6 - 22 * q^7 - 37 * q^8 + 32 * q^9 + 13 * q^10 + 12 * q^11 - 5 * q^12 - 36 * q^13 + 22 * q^14 - 7 * q^15 + 37 * q^16 + 4 * q^17 - 32 * q^18 - 10 * q^19 - 13 * q^20 - 11 * q^21 - 12 * q^22 - q^23 + 5 * q^24 + 8 * q^25 + 36 * q^26 - 20 * q^27 - 22 * q^28 - 6 * q^29 + 7 * q^30 - 23 * q^31 - 37 * q^32 - 27 * q^33 - 4 * q^34 + 24 * q^35 + 32 * q^36 - 46 * q^37 + 10 * q^38 + 5 * q^39 + 13 * q^40 + 11 * q^41 + 11 * q^42 - 22 * q^43 + 12 * q^44 - 57 * q^45 + q^46 - 18 * q^47 - 5 * q^48 - q^49 - 8 * q^50 + 18 * q^51 - 36 * q^52 - 25 * q^53 + 20 * q^54 - 25 * q^55 + 22 * q^56 - 25 * q^57 + 6 * q^58 + 24 * q^59 - 7 * q^60 - 40 * q^61 + 23 * q^62 - 38 * q^63 + 37 * q^64 + 14 * q^65 + 27 * q^66 - 49 * q^67 + 4 * q^68 - 19 * q^69 - 24 * q^70 + 27 * q^71 - 32 * q^72 - 87 * q^73 + 46 * q^74 - 5 * q^75 - 10 * q^76 - 50 * q^77 - 5 * q^78 + 11 * q^79 - 13 * q^80 + 5 * q^81 - 11 * q^82 - 9 * q^83 - 11 * q^84 - 68 * q^85 + 22 * q^86 - 12 * q^87 - 12 * q^88 - 3 * q^89 + 57 * q^90 - 19 * q^91 - q^92 - 69 * q^93 + 18 * q^94 + 27 * q^95 + 5 * q^96 - 98 * q^97 + q^98 + 33 * 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
$3$	−1.41095	−0.814615	−0.407307	−	0.913291i	$-0.633532\pi$
$3$	−1.41095	−0.814615	−0.407307	+	0.913291i	$0.633532\pi$
$4$	1.00000	0.500000
$5$	−3.55049	−1.58783	−0.793914	−	0.608029i	$-0.791960\pi$
$5$	−3.55049	−1.58783	−0.793914	+	0.608029i	$0.791960\pi$
$6$	1.41095	0.576020
$7$	−3.54920	−1.34147	−0.670736	−	0.741696i	$-0.734022\pi$
$7$	−3.54920	−1.34147	−0.670736	+	0.741696i	$0.734022\pi$
$8$	−1.00000	−0.353553
$9$	−1.00921	−0.336403
$10$	3.55049	1.12276
$11$	4.87426	1.46964	0.734822	−	0.678260i	$-0.237266\pi$
$11$	4.87426	1.46964	0.734822	+	0.678260i	$0.237266\pi$
$12$	−1.41095	−0.407307
$13$	−3.10664	−0.861628	−0.430814	−	0.902441i	$-0.641773\pi$
$13$	−3.10664	−0.861628	−0.430814	+	0.902441i	$0.641773\pi$
$14$	3.54920	0.948564
$15$	5.00958	1.29347
$16$	1.00000	0.250000
$17$	−4.40999	−1.06958	−0.534790	−	0.844985i	$-0.679609\pi$
$17$	−4.40999	−1.06958	−0.534790	+	0.844985i	$0.679609\pi$
$18$	1.00921	0.237873
$19$	1.30368	0.299085	0.149543	−	0.988755i	$-0.452220\pi$
$19$	1.30368	0.299085	0.149543	+	0.988755i	$0.452220\pi$
$20$	−3.55049	−0.793914
$21$	5.00776	1.09278
$22$	−4.87426	−1.03920
$23$	−3.42341	−0.713830	−0.356915	−	0.934137i	$-0.616171\pi$
$23$	−3.42341	−0.713830	−0.356915	+	0.934137i	$0.616171\pi$
$24$	1.41095	0.288010
$25$	7.60600	1.52120
$26$	3.10664	0.609263
$27$	5.65681	1.08865
$28$	−3.54920	−0.670736
$29$	8.36390	1.55314	0.776569	−	0.630032i	$-0.216958\pi$
$29$	8.36390	1.55314	0.776569	+	0.630032i	$0.216958\pi$
$30$	−5.00958	−0.914621
$31$	−3.07353	−0.552022	−0.276011	−	0.961154i	$-0.589013\pi$
$31$	−3.07353	−0.552022	−0.276011	+	0.961154i	$0.589013\pi$
$32$	−1.00000	−0.176777
$33$	−6.87736	−1.19719
$34$	4.40999	0.756307
$35$	12.6014	2.13003
$36$	−1.00921	−0.168201
$37$	7.52404	1.23694	0.618472	−	0.785807i	$-0.287752\pi$
$37$	7.52404	1.23694	0.618472	+	0.785807i	$0.287752\pi$
$38$	−1.30368	−0.211485
$39$	4.38333	0.701895
$40$	3.55049	0.561382
$41$	−4.62618	−0.722487	−0.361244	−	0.932471i	$-0.617648\pi$
$41$	−4.62618	−0.722487	−0.361244	+	0.932471i	$0.617648\pi$
$42$	−5.00776	−0.772715
$43$	−4.44441	−0.677766	−0.338883	−	0.940829i	$-0.610049\pi$
$43$	−4.44441	−0.677766	−0.338883	+	0.940829i	$0.610049\pi$
$44$	4.87426	0.734822
$45$	3.58319	0.534150
$46$	3.42341	0.504754
$47$	−10.5112	−1.53322	−0.766610	−	0.642113i	$-0.778058\pi$
$47$	−10.5112	−1.53322	−0.766610	+	0.642113i	$0.778058\pi$
$48$	−1.41095	−0.203654
$49$	5.59684	0.799549
$50$	−7.60600	−1.07565
$51$	6.22229	0.871296
$52$	−3.10664	−0.430814
$53$	8.60185	1.18155	0.590777	−	0.806835i	$-0.298821\pi$
$53$	8.60185	1.18155	0.590777	+	0.806835i	$0.298821\pi$
$54$	−5.65681	−0.769794
$55$	−17.3060	−2.33354
$56$	3.54920	0.474282
$57$	−1.83944	−0.243639
$58$	−8.36390	−1.09823
$59$	14.4047	1.87533	0.937667	−	0.347535i	$-0.112981\pi$
$59$	14.4047	1.87533	0.937667	+	0.347535i	$0.112981\pi$
$60$	5.00958	0.646735
$61$	7.09958	0.909008	0.454504	−	0.890745i	$-0.349817\pi$
$61$	7.09958	0.909008	0.454504	+	0.890745i	$0.349817\pi$
$62$	3.07353	0.390339
$63$	3.58188	0.451275
$64$	1.00000	0.125000
$65$	11.0301	1.36812
$66$	6.87736	0.846544
$67$	15.1672	1.85297	0.926483	−	0.376337i	$-0.122817\pi$
$67$	15.1672	1.85297	0.926483	+	0.376337i	$0.122817\pi$
$68$	−4.40999	−0.534790
$69$	4.83027	0.581496
$70$	−12.6014	−1.50616
$71$	8.37428	0.993845	0.496922	−	0.867795i	$-0.334463\pi$
$71$	8.37428	0.993845	0.496922	+	0.867795i	$0.334463\pi$
$72$	1.00921	0.118936
$73$	5.90803	0.691482	0.345741	−	0.938330i	$-0.387628\pi$
$73$	5.90803	0.691482	0.345741	+	0.938330i	$0.387628\pi$
$74$	−7.52404	−0.874652
$75$	−10.7317	−1.23919
$76$	1.30368	0.149543
$77$	−17.2997	−1.97149
$78$	−4.38333	−0.496314
$79$	−8.39855	−0.944911	−0.472456	−	0.881354i	$-0.656632\pi$
$79$	−8.39855	−0.944911	−0.472456	+	0.881354i	$0.656632\pi$
$80$	−3.55049	−0.396957
$81$	−4.95388	−0.550431
$82$	4.62618	0.510876
$83$	−6.84408	−0.751236	−0.375618	−	0.926775i	$-0.622569\pi$
$83$	−6.84408	−0.751236	−0.375618	+	0.926775i	$0.622569\pi$
$84$	5.00776	0.546392
$85$	15.6576	1.69831
$86$	4.44441	0.479253
$87$	−11.8011	−1.26521
$88$	−4.87426	−0.519598
$89$	−2.84661	−0.301740	−0.150870	−	0.988554i	$-0.548208\pi$
$89$	−2.84661	−0.301740	−0.150870	+	0.988554i	$0.548208\pi$
$90$	−3.58319	−0.377701
$91$	11.0261	1.15585
$92$	−3.42341	−0.356915
$93$	4.33661	0.449685
$94$	10.5112	1.08415
$95$	−4.62872	−0.474896
$96$	1.41095	0.144005
$97$	0.0168333	0.00170916	0.000854581	−	1.00000i	$-0.499728\pi$
$97$	0.0168333	0.00170916	0.000854581		1.00000i	$0.499728\pi$
$98$	−5.59684	−0.565367
$99$	−4.91914	−0.494392
$100$	7.60600	0.760600
$101$	−13.9213	−1.38522	−0.692611	−	0.721311i	$-0.743540\pi$
$101$	−13.9213	−1.38522	−0.692611	+	0.721311i	$0.743540\pi$
$102$	−6.22229	−0.616099
$103$	−10.5639	−1.04089	−0.520446	−	0.853894i	$-0.674234\pi$
$103$	−10.5639	−1.04089	−0.520446	+	0.853894i	$0.674234\pi$
$104$	3.10664	0.304631
$105$	−17.7800	−1.73515
$106$	−8.60185	−0.835485
$107$	5.80725	0.561408	0.280704	−	0.959794i	$-0.409432\pi$
$107$	5.80725	0.561408	0.280704	+	0.959794i	$0.409432\pi$
$108$	5.65681	0.544327
$109$	2.07069	0.198336	0.0991682	−	0.995071i	$-0.468382\pi$
$109$	2.07069	0.198336	0.0991682	+	0.995071i	$0.468382\pi$
$110$	17.3060	1.65006
$111$	−10.6161	−1.00763
$112$	−3.54920	−0.335368
$113$	13.0548	1.22809	0.614045	−	0.789271i	$-0.289541\pi$
$113$	13.0548	1.22809	0.614045	+	0.789271i	$0.289541\pi$
$114$	1.83944	0.172279
$115$	12.1548	1.13344
$116$	8.36390	0.776569
$117$	3.13525	0.289854
$118$	−14.4047	−1.32606
$119$	15.6520	1.43481
$120$	−5.00958	−0.457310
$121$	12.7584	1.15985
$122$	−7.09958	−0.642766
$123$	6.52732	0.588549
$124$	−3.07353	−0.276011
$125$	−9.25260	−0.827578
$126$	−3.58188	−0.319100
$127$	−4.97278	−0.441263	−0.220631	−	0.975357i	$-0.570812\pi$
$127$	−4.97278	−0.441263	−0.220631	+	0.975357i	$0.570812\pi$
$128$	−1.00000	−0.0883883
$129$	6.27085	0.552118
$130$	−11.0301	−0.967405
$131$	17.5208	1.53080	0.765398	−	0.643557i	$-0.222542\pi$
$131$	17.5208	1.53080	0.765398	+	0.643557i	$0.222542\pi$
$132$	−6.87736	−0.598597
$133$	−4.62704	−0.401215
$134$	−15.1672	−1.31024
$135$	−20.0845	−1.72860
$136$	4.40999	0.378154
$137$	−0.430605	−0.0367891	−0.0183945	−	0.999831i	$-0.505855\pi$
$137$	−0.430605	−0.0367891	−0.0183945	+	0.999831i	$0.505855\pi$
$138$	−4.83027	−0.411180
$139$	−7.61036	−0.645502	−0.322751	−	0.946484i	$-0.604608\pi$
$139$	−7.61036	−0.645502	−0.322751	+	0.946484i	$0.604608\pi$
$140$	12.6014	1.06501
$141$	14.8309	1.24898
$142$	−8.37428	−0.702754
$143$	−15.1426	−1.26629
$144$	−1.00921	−0.0841007
$145$	−29.6960	−2.46612
$146$	−5.90803	−0.488952
$147$	−7.89689	−0.651325
$148$	7.52404	0.618472
$149$	14.3921	1.17905	0.589524	−	0.807751i	$-0.299315\pi$
$149$	14.3921	1.17905	0.589524	+	0.807751i	$0.299315\pi$
$150$	10.7317	0.876242
$151$	7.09338	0.577251	0.288625	−	0.957442i	$-0.406802\pi$
$151$	7.09338	0.577251	0.288625	+	0.957442i	$0.406802\pi$
$152$	−1.30368	−0.105743
$153$	4.45060	0.359810
$154$	17.2997	1.39405
$155$	10.9125	0.876517
$156$	4.38333	0.350947
$157$	−13.5488	−1.08131	−0.540657	−	0.841243i	$-0.681824\pi$
$157$	−13.5488	−1.08131	−0.540657	+	0.841243i	$0.681824\pi$
$158$	8.39855	0.668153
$159$	−12.1368	−0.962512
$160$	3.55049	0.280691
$161$	12.1504	0.957583
$162$	4.95388	0.389213
$163$	−24.8029	−1.94271	−0.971356	−	0.237631i	$-0.923629\pi$
$163$	−24.8029	−1.94271	−0.971356	+	0.237631i	$0.923629\pi$
$164$	−4.62618	−0.361244
$165$	24.4180	1.90094
$166$	6.84408	0.531204
$167$	−2.80230	−0.216848	−0.108424	−	0.994105i	$-0.534580\pi$
$167$	−2.80230	−0.216848	−0.108424	+	0.994105i	$0.534580\pi$
$168$	−5.00776	−0.386357
$169$	−3.34877	−0.257598
$170$	−15.6576	−1.20089
$171$	−1.31569	−0.100613
$172$	−4.44441	−0.338883
$173$	−17.6503	−1.34193	−0.670965	−	0.741489i	$-0.734120\pi$
$173$	−17.6503	−1.34193	−0.670965	+	0.741489i	$0.734120\pi$
$174$	11.8011	0.894638
$175$	−26.9953	−2.04065
$176$	4.87426	0.367411
$177$	−20.3244	−1.52768
$178$	2.84661	0.213362
$179$	−21.2215	−1.58617	−0.793086	−	0.609110i	$-0.791527\pi$
$179$	−21.2215	−1.58617	−0.793086	+	0.609110i	$0.791527\pi$
$180$	3.58319	0.267075
$181$	−18.4044	−1.36799	−0.683994	−	0.729488i	$-0.739759\pi$
$181$	−18.4044	−1.36799	−0.683994	+	0.729488i	$0.739759\pi$
$182$	−11.0261	−0.817309
$183$	−10.0172	−0.740491
$184$	3.42341	0.252377
$185$	−26.7141	−1.96406
$186$	−4.33661	−0.317976
$187$	−21.4954	−1.57190
$188$	−10.5112	−0.766610
$189$	−20.0772	−1.46040
$190$	4.62872	0.335802
$191$	0.459681	0.0332614	0.0166307	−	0.999862i	$-0.494706\pi$
$191$	0.459681	0.0332614	0.0166307	+	0.999862i	$0.494706\pi$
$192$	−1.41095	−0.101827
$193$	18.1383	1.30562	0.652810	−	0.757522i	$-0.273590\pi$
$193$	18.1383	1.30562	0.652810	+	0.757522i	$0.273590\pi$
$194$	−0.0168333	−0.00120856
$195$	−15.5630	−1.11449
$196$	5.59684	0.399775
$197$	3.39155	0.241638	0.120819	−	0.992675i	$-0.461448\pi$
$197$	3.39155	0.241638	0.120819	+	0.992675i	$0.461448\pi$
$198$	4.91914	0.349588
$199$	−15.4214	−1.09319	−0.546596	−	0.837396i	$-0.684077\pi$
$199$	−15.4214	−1.09319	−0.546596	+	0.837396i	$0.684077\pi$
$200$	−7.60600	−0.537826
$201$	−21.4002	−1.50945
$202$	13.9213	0.979500
$203$	−29.6852	−2.08349
$204$	6.22229	0.435648
$205$	16.4252	1.14719
$206$	10.5639	0.736022
$207$	3.45493	0.240134
$208$	−3.10664	−0.215407
$209$	6.35449	0.439549
$210$	17.7800	1.22694
$211$	−2.01995	−0.139059	−0.0695295	−	0.997580i	$-0.522150\pi$
$211$	−2.01995	−0.139059	−0.0695295	+	0.997580i	$0.522150\pi$
$212$	8.60185	0.590777
$213$	−11.8157	−0.809601
$214$	−5.80725	−0.396975
$215$	15.7798	1.07618
$216$	−5.65681	−0.384897
$217$	10.9086	0.740522
$218$	−2.07069	−0.140245
$219$	−8.33596	−0.563292
$220$	−17.3060	−1.16677
$221$	13.7003	0.921580
$222$	10.6161	0.712504
$223$	12.9784	0.869096	0.434548	−	0.900649i	$-0.356908\pi$
$223$	12.9784	0.869096	0.434548	+	0.900649i	$0.356908\pi$
$224$	3.54920	0.237141
$225$	−7.67604	−0.511736
$226$	−13.0548	−0.868391
$227$	22.0386	1.46275	0.731377	−	0.681973i	$-0.238878\pi$
$227$	22.0386	1.46275	0.731377	+	0.681973i	$0.238878\pi$
$228$	−1.83944	−0.121820
$229$	4.90645	0.324227	0.162114	−	0.986772i	$-0.448169\pi$
$229$	4.90645	0.324227	0.162114	+	0.986772i	$0.448169\pi$
$230$	−12.1548	−0.801463
$231$	24.4091	1.60600
$232$	−8.36390	−0.549117
$233$	21.6221	1.41651	0.708255	−	0.705957i	$-0.249483\pi$
$233$	21.6221	1.41651	0.708255	+	0.705957i	$0.249483\pi$
$234$	−3.13525	−0.204958
$235$	37.3200	2.43449
$236$	14.4047	0.937667
$237$	11.8500	0.769739
$238$	−15.6520	−1.01457
$239$	1.95463	0.126435	0.0632173	−	0.998000i	$-0.479864\pi$
$239$	1.95463	0.126435	0.0632173	+	0.998000i	$0.479864\pi$
$240$	5.00958	0.323367
$241$	−19.5504	−1.25935	−0.629676	−	0.776858i	$-0.716812\pi$
$241$	−19.5504	−1.25935	−0.629676	+	0.776858i	$0.716812\pi$
$242$	−12.7584	−0.820141
$243$	−9.98074	−0.640265
$244$	7.09958	0.454504
$245$	−19.8716	−1.26955
$246$	−6.52732	−0.416167
$247$	−4.05008	−0.257700
$248$	3.07353	0.195169
$249$	9.65669	0.611968
$250$	9.25260	0.585186
$251$	28.1558	1.77718	0.888590	−	0.458703i	$-0.151686\pi$
$251$	28.1558	1.77718	0.888590	+	0.458703i	$0.151686\pi$
$252$	3.58188	0.225638
$253$	−16.6866	−1.04908
$254$	4.97278	0.312020
$255$	−22.0922	−1.38347
$256$	1.00000	0.0625000
$257$	−8.44885	−0.527025	−0.263512	−	0.964656i	$-0.584881\pi$
$257$	−8.44885	−0.527025	−0.263512	+	0.964656i	$0.584881\pi$
$258$	−6.27085	−0.390406
$259$	−26.7043	−1.65933
$260$	11.0301	0.684059
$261$	−8.44092	−0.522480
$262$	−17.5208	−1.08244
$263$	−5.69334	−0.351066	−0.175533	−	0.984474i	$-0.556165\pi$
$263$	−5.69334	−0.351066	−0.175533	+	0.984474i	$0.556165\pi$
$264$	6.87736	0.423272
$265$	−30.5408	−1.87611
$266$	4.62704	0.283702
$267$	4.01644	0.245802
$268$	15.1672	0.926483
$269$	26.0560	1.58866	0.794330	−	0.607486i	$-0.207822\pi$
$269$	26.0560	1.58866	0.794330	+	0.607486i	$0.207822\pi$
$270$	20.0845	1.22230
$271$	−19.5199	−1.18575	−0.592875	−	0.805295i	$-0.702007\pi$
$271$	−19.5199	−1.18575	−0.592875	+	0.805295i	$0.702007\pi$
$272$	−4.40999	−0.267395
$273$	−15.5573	−0.941573
$274$	0.430605	0.0260138
$275$	37.0736	2.23562
$276$	4.83027	0.290748
$277$	−12.2204	−0.734255	−0.367128	−	0.930171i	$-0.619659\pi$
$277$	−12.2204	−0.734255	−0.367128	+	0.930171i	$0.619659\pi$
$278$	7.61036	0.456439
$279$	3.10183	0.185702
$280$	−12.6014	−0.753079
$281$	−28.0016	−1.67044	−0.835218	−	0.549919i	$-0.814658\pi$
$281$	−28.0016	−1.67044	−0.835218	+	0.549919i	$0.814658\pi$
$282$	−14.8309	−0.883165
$283$	29.0198	1.72505	0.862525	−	0.506014i	$-0.168881\pi$
$283$	29.0198	1.72505	0.862525	+	0.506014i	$0.168881\pi$
$284$	8.37428	0.496922
$285$	6.53091	0.386858
$286$	15.1426	0.895400
$287$	16.4192	0.969197
$288$	1.00921	0.0594682
$289$	2.44802	0.144001
$290$	29.6960	1.74381
$291$	−0.0237510	−0.00139231
$292$	5.90803	0.345741
$293$	−22.8832	−1.33685	−0.668425	−	0.743779i	$-0.733031\pi$
$293$	−22.8832	−1.33685	−0.668425	+	0.743779i	$0.733031\pi$
$294$	7.89689	0.460556
$295$	−51.1439	−2.97771
$296$	−7.52404	−0.437326
$297$	27.5728	1.59993
$298$	−14.3921	−0.833712
$299$	10.6353	0.615055
$300$	−10.7317	−0.619596
$301$	15.7741	0.909204
$302$	−7.09338	−0.408178
$303$	19.6423	1.12842
$304$	1.30368	0.0747713
$305$	−25.2070	−1.44335
$306$	−4.45060	−0.254424
$307$	10.5841	0.604064	0.302032	−	0.953298i	$-0.402335\pi$
$307$	10.5841	0.604064	0.302032	+	0.953298i	$0.402335\pi$
$308$	−17.2997	−0.985744
$309$	14.9052	0.847927
$310$	−10.9125	−0.619791
$311$	29.3365	1.66352	0.831760	−	0.555135i	$-0.187334\pi$
$311$	29.3365	1.66352	0.831760	+	0.555135i	$0.187334\pi$
$312$	−4.38333	−0.248157
$313$	11.4087	0.644859	0.322430	−	0.946593i	$-0.395500\pi$
$313$	11.4087	0.644859	0.322430	+	0.946593i	$0.395500\pi$
$314$	13.5488	0.764604
$315$	−12.7175	−0.716548
$316$	−8.39855	−0.472456
$317$	−24.7302	−1.38899	−0.694493	−	0.719499i	$-0.744371\pi$
$317$	−24.7302	−1.38899	−0.694493	+	0.719499i	$0.744371\pi$
$318$	12.1368	0.680599
$319$	40.7678	2.28256
$320$	−3.55049	−0.198479
$321$	−8.19376	−0.457331
$322$	−12.1504	−0.677114
$323$	−5.74923	−0.319896
$324$	−4.95388	−0.275215
$325$	−23.6291	−1.31071
$326$	24.8029	1.37370
$327$	−2.92165	−0.161568
$328$	4.62618	0.255438
$329$	37.3065	2.05677
$330$	−24.4180	−1.34417
$331$	−25.3655	−1.39421	−0.697107	−	0.716967i	$-0.745530\pi$
$331$	−25.3655	−1.39421	−0.697107	+	0.716967i	$0.745530\pi$
$332$	−6.84408	−0.375618
$333$	−7.59332	−0.416111
$334$	2.80230	0.153335
$335$	−53.8510	−2.94219
$336$	5.00776	0.273196
$337$	0.00442850	0.000241236 0	0.000120618	−	1.00000i	$-0.499962\pi$
$337$	0.00442850	0.000241236 0	0.000120618		1.00000i	$0.499962\pi$
$338$	3.34877	0.182149
$339$	−18.4197	−1.00042
$340$	15.6576	0.849155
$341$	−14.9812	−0.811276
$342$	1.31569	0.0711442
$343$	4.98009	0.268899
$344$	4.44441	0.239626
$345$	−17.1498	−0.923317
$346$	17.6503	0.948888
$347$	7.15668	0.384191	0.192095	−	0.981376i	$-0.438472\pi$
$347$	7.15668	0.384191	0.192095	+	0.981376i	$0.438472\pi$
$348$	−11.8011	−0.632605
$349$	28.1892	1.50893	0.754467	−	0.656338i	$-0.227896\pi$
$349$	28.1892	1.50893	0.754467	+	0.656338i	$0.227896\pi$
$350$	26.9953	1.44296
$351$	−17.5737	−0.938014
$352$	−4.87426	−0.259799
$353$	−11.8993	−0.633334	−0.316667	−	0.948537i	$-0.602564\pi$
$353$	−11.8993	−0.633334	−0.316667	+	0.948537i	$0.602564\pi$
$354$	20.3244	1.08023
$355$	−29.7328	−1.57806
$356$	−2.84661	−0.150870
$357$	−22.0842	−1.16882
$358$	21.2215	1.12159
$359$	16.3254	0.861621	0.430810	−	0.902442i	$-0.358228\pi$
$359$	16.3254	0.861621	0.430810	+	0.902442i	$0.358228\pi$
$360$	−3.58319	−0.188851
$361$	−17.3004	−0.910548
$362$	18.4044	0.967314
$363$	−18.0015	−0.944835
$364$	11.0261	0.577925
$365$	−20.9764	−1.09796
$366$	10.0172	0.523607
$367$	6.82315	0.356165	0.178083	−	0.984016i	$-0.443011\pi$
$367$	6.82315	0.356165	0.178083	+	0.984016i	$0.443011\pi$
$368$	−3.42341	−0.178457
$369$	4.66877	0.243047
$370$	26.7141	1.38880
$371$	−30.5297	−1.58502
$372$	4.33661	0.224843
$373$	−0.238489	−0.0123485	−0.00617425	−	0.999981i	$-0.501965\pi$
$373$	−0.238489	−0.0123485	−0.00617425	+	0.999981i	$0.501965\pi$
$374$	21.4954	1.11150
$375$	13.0550	0.674157
$376$	10.5112	0.542075
$377$	−25.9837	−1.33823
$378$	20.0772	1.03266
$379$	−21.0929	−1.08347	−0.541735	−	0.840550i	$-0.682232\pi$
$379$	−21.0929	−1.08347	−0.541735	+	0.840550i	$0.682232\pi$
$380$	−4.62872	−0.237448
$381$	7.01637	0.359459
$382$	−0.459681	−0.0235194
$383$	−0.540163	−0.0276011	−0.0138005	−	0.999905i	$-0.504393\pi$
$383$	−0.540163	−0.0276011	−0.0138005	+	0.999905i	$0.504393\pi$
$384$	1.41095	0.0720025
$385$	61.4226	3.13039
$386$	−18.1383	−0.923213
$387$	4.48533	0.228002
$388$	0.0168333	0.000854581 0
$389$	10.4360	0.529128	0.264564	−	0.964368i	$-0.414772\pi$
$389$	10.4360	0.529128	0.264564	+	0.964368i	$0.414772\pi$
$390$	15.5630	0.788063
$391$	15.0972	0.763498
$392$	−5.59684	−0.282683
$393$	−24.7210	−1.24701
$394$	−3.39155	−0.170864
$395$	29.8190	1.50036
$396$	−4.91914	−0.247196
$397$	−11.9864	−0.601578	−0.300789	−	0.953691i	$-0.597250\pi$
$397$	−11.9864	−0.601578	−0.300789	+	0.953691i	$0.597250\pi$
$398$	15.4214	0.773004
$399$	6.52854	0.326836
$400$	7.60600	0.380300
$401$	30.1565	1.50594	0.752971	−	0.658053i	$-0.228620\pi$
$401$	30.1565	1.50594	0.752971	+	0.658053i	$0.228620\pi$
$402$	21.4002	1.06734
$403$	9.54836	0.475637
$404$	−13.9213	−0.692611
$405$	17.5887	0.873990
$406$	29.6852	1.47325
$407$	36.6741	1.81787
$408$	−6.22229	−0.308049
$409$	19.8210	0.980086	0.490043	−	0.871698i	$-0.336981\pi$
$409$	19.8210	0.980086	0.490043	+	0.871698i	$0.336981\pi$
$410$	−16.4252	−0.811183
$411$	0.607564	0.0299689
$412$	−10.5639	−0.520446
$413$	−51.1253	−2.51571
$414$	−3.45493	−0.169801
$415$	24.2999	1.19283
$416$	3.10664	0.152316
$417$	10.7379	0.525835
$418$	−6.35449	−0.310808
$419$	−5.07857	−0.248104	−0.124052	−	0.992276i	$-0.539589\pi$
$419$	−5.07857	−0.248104	−0.124052	+	0.992276i	$0.539589\pi$
$420$	−17.7800	−0.867577
$421$	−7.00190	−0.341252	−0.170626	−	0.985336i	$-0.554579\pi$
$421$	−7.00190	−0.341252	−0.170626	+	0.985336i	$0.554579\pi$
$422$	2.01995	0.0983295
$423$	10.6080	0.515779
$424$	−8.60185	−0.417743
$425$	−33.5424	−1.62705
$426$	11.8157	0.572474
$427$	−25.1979	−1.21941
$428$	5.80725	0.280704
$429$	21.3655	1.03154
$430$	−15.7798	−0.760971
$431$	−14.1636	−0.682235	−0.341117	−	0.940021i	$-0.610805\pi$
$431$	−14.1636	−0.682235	−0.341117	+	0.940021i	$0.610805\pi$
$432$	5.65681	0.272163
$433$	−15.2992	−0.735235	−0.367617	−	0.929977i	$-0.619826\pi$
$433$	−15.2992	−0.735235	−0.367617	+	0.929977i	$0.619826\pi$
$434$	−10.9086	−0.523628
$435$	41.8997	2.00894
$436$	2.07069	0.0991682
$437$	−4.46304	−0.213496
$438$	8.33596	0.398307
$439$	−16.0493	−0.765989	−0.382995	−	0.923751i	$-0.625107\pi$
$439$	−16.0493	−0.765989	−0.382995	+	0.923751i	$0.625107\pi$
$440$	17.3060	0.825032
$441$	−5.64838	−0.268970
$442$	−13.7003	−0.651655
$443$	17.2194	0.818118	0.409059	−	0.912508i	$-0.365857\pi$
$443$	17.2194	0.818118	0.409059	+	0.912508i	$0.365857\pi$
$444$	−10.6161	−0.503817
$445$	10.1069	0.479112
$446$	−12.9784	−0.614543
$447$	−20.3066	−0.960469
$448$	−3.54920	−0.167684
$449$	−26.5008	−1.25065	−0.625326	−	0.780363i	$-0.715034\pi$
$449$	−26.5008	−1.25065	−0.625326	+	0.780363i	$0.715034\pi$
$450$	7.67604	0.361852
$451$	−22.5492	−1.06180
$452$	13.0548	0.614045
$453$	−10.0084	−0.470237
$454$	−22.0386	−1.03432
$455$	−39.1481	−1.83529
$456$	1.83944	0.0861395
$457$	−27.6757	−1.29461	−0.647306	−	0.762230i	$-0.724104\pi$
$457$	−27.6757	−1.29461	−0.647306	+	0.762230i	$0.724104\pi$
$458$	−4.90645	−0.229263
$459$	−24.9465	−1.16440
$460$	12.1548	0.566720
$461$	20.7484	0.966351	0.483176	−	0.875523i	$-0.339483\pi$
$461$	20.7484	0.966351	0.483176	+	0.875523i	$0.339483\pi$
$462$	−24.4091	−1.13562
$463$	6.62320	0.307806	0.153903	−	0.988086i	$-0.450816\pi$
$463$	6.62320	0.307806	0.153903	+	0.988086i	$0.450816\pi$
$464$	8.36390	0.388284
$465$	−15.3971	−0.714023
$466$	−21.6221	−1.00162
$467$	−36.5099	−1.68948	−0.844738	−	0.535180i	$-0.820244\pi$
$467$	−36.5099	−1.68948	−0.844738	+	0.535180i	$0.820244\pi$
$468$	3.13525	0.144927
$469$	−53.8314	−2.48570
$470$	−37.3200	−1.72144
$471$	19.1168	0.880854
$472$	−14.4047	−0.663031
$473$	−21.6632	−0.996075
$474$	−11.8500	−0.544287
$475$	9.91582	0.454969
$476$	15.6520	0.717406
$477$	−8.68105	−0.397478
$478$	−1.95463	−0.0894027
$479$	−6.98856	−0.319315	−0.159658	−	0.987172i	$-0.551039\pi$
$479$	−6.98856	−0.319315	−0.159658	+	0.987172i	$0.551039\pi$
$480$	−5.00958	−0.228655
$481$	−23.3745	−1.06579
$482$	19.5504	0.890497
$483$	−17.1436	−0.780061
$484$	12.7584	0.579927
$485$	−0.0597665	−0.00271386
$486$	9.98074	0.452735
$487$	−30.4726	−1.38085	−0.690424	−	0.723405i	$-0.742576\pi$
$487$	−30.4726	−1.38085	−0.690424	+	0.723405i	$0.742576\pi$
$488$	−7.09958	−0.321383
$489$	34.9957	1.58256
$490$	19.8716	0.897705
$491$	13.3296	0.601557	0.300779	−	0.953694i	$-0.402753\pi$
$491$	13.3296	0.601557	0.300779	+	0.953694i	$0.402753\pi$
$492$	6.52732	0.294274
$493$	−36.8847	−1.66120
$494$	4.05008	0.182222
$495$	17.4654	0.785010
$496$	−3.07353	−0.138006
$497$	−29.7220	−1.33322
$498$	−9.65669	−0.432727
$499$	34.0841	1.52581	0.762907	−	0.646508i	$-0.223771\pi$
$499$	34.0841	1.52581	0.762907	+	0.646508i	$0.223771\pi$
$500$	−9.25260	−0.413789
$501$	3.95392	0.176648
$502$	−28.1558	−1.25666
$503$	8.60981	0.383893	0.191946	−	0.981405i	$-0.438520\pi$
$503$	8.60981	0.383893	0.191946	+	0.981405i	$0.438520\pi$
$504$	−3.58188	−0.159550
$505$	49.4275	2.19950
$506$	16.6866	0.741809
$507$	4.72496	0.209843
$508$	−4.97278	−0.220631
$509$	−12.1547	−0.538747	−0.269373	−	0.963036i	$-0.586817\pi$
$509$	−12.1547	−0.538747	−0.269373	+	0.963036i	$0.586817\pi$
$510$	22.0922	0.978260
$511$	−20.9688	−0.927605
$512$	−1.00000	−0.0441942
$513$	7.37469	0.325600
$514$	8.44885	0.372663
$515$	37.5071	1.65276
$516$	6.27085	0.276059
$517$	−51.2344	−2.25329
$518$	26.7043	1.17332
$519$	24.9038	1.09316
$520$	−11.0301	−0.483703
$521$	−25.4950	−1.11696	−0.558478	−	0.829520i	$-0.688614\pi$
$521$	−25.4950	−1.11696	−0.558478	+	0.829520i	$0.688614\pi$
$522$	8.44092	0.369449
$523$	14.6183	0.639213	0.319606	−	0.947550i	$-0.396449\pi$
$523$	14.6183	0.639213	0.319606	+	0.947550i	$0.396449\pi$
$524$	17.5208	0.765398
$525$	38.0891	1.66234
$526$	5.69334	0.248241
$527$	13.5542	0.590432
$528$	−6.87736	−0.299299
$529$	−11.2803	−0.490447
$530$	30.5408	1.32661
$531$	−14.5374	−0.630867
$532$	−4.62704	−0.200607
$533$	14.3719	0.622515
$534$	−4.01644	−0.173808
$535$	−20.6186	−0.891419
$536$	−15.1672	−0.655122
$537$	29.9426	1.29212
$538$	−26.0560	−1.12335
$539$	27.2805	1.17505
$540$	−20.0845	−0.864298
$541$	−19.6667	−0.845536	−0.422768	−	0.906238i	$-0.638941\pi$
$541$	−19.6667	−0.845536	−0.422768	+	0.906238i	$0.638941\pi$
$542$	19.5199	0.838451
$543$	25.9678	1.11438
$544$	4.40999	0.189077
$545$	−7.35198	−0.314924
$546$	15.5573	0.665792
$547$	−22.9251	−0.980206	−0.490103	−	0.871665i	$-0.663041\pi$
$547$	−22.9251	−0.980206	−0.490103	+	0.871665i	$0.663041\pi$
$548$	−0.430605	−0.0183945
$549$	−7.16495	−0.305793
$550$	−37.0736	−1.58083
$551$	10.9039	0.464521
$552$	−4.83027	−0.205590
$553$	29.8082	1.26757
$554$	12.2204	0.519197
$555$	37.6923	1.59995
$556$	−7.61036	−0.322751
$557$	16.5098	0.699543	0.349771	−	0.936835i	$-0.386259\pi$
$557$	16.5098	0.699543	0.349771	+	0.936835i	$0.386259\pi$
$558$	−3.10183	−0.131311
$559$	13.8072	0.583982
$560$	12.6014	0.532507
$561$	30.3291	1.28049
$562$	28.0016	1.18118
$563$	27.0678	1.14077	0.570387	−	0.821376i	$-0.306793\pi$
$563$	27.0678	1.14077	0.570387	+	0.821376i	$0.306793\pi$
$564$	14.8309	0.624492
$565$	−46.3509	−1.95000
$566$	−29.0198	−1.21980
$567$	17.5823	0.738388
$568$	−8.37428	−0.351377
$569$	8.50576	0.356580	0.178290	−	0.983978i	$-0.442943\pi$
$569$	8.50576	0.356580	0.178290	+	0.983978i	$0.442943\pi$
$570$	−6.53091	−0.273550
$571$	−24.9616	−1.04461	−0.522306	−	0.852758i	$-0.674928\pi$
$571$	−24.9616	−1.04461	−0.522306	+	0.852758i	$0.674928\pi$
$572$	−15.1426	−0.633143
$573$	−0.648590	−0.0270952
$574$	−16.4192	−0.685326
$575$	−26.0385	−1.08588
$576$	−1.00921	−0.0420503
$577$	−13.2846	−0.553044	−0.276522	−	0.961008i	$-0.589182\pi$
$577$	−13.2846	−0.553044	−0.276522	+	0.961008i	$0.589182\pi$
$578$	−2.44802	−0.101824
$579$	−25.5923	−1.06358
$580$	−29.6960	−1.23306
$581$	24.2910	1.00776
$582$	0.0237510	0.000984511 0
$583$	41.9276	1.73646
$584$	−5.90803	−0.244476
$585$	−11.1317	−0.460238
$586$	22.8832	0.945296
$587$	1.48498	0.0612916	0.0306458	−	0.999530i	$-0.490244\pi$
$587$	1.48498	0.0612916	0.0306458	+	0.999530i	$0.490244\pi$
$588$	−7.89689	−0.325662
$589$	−4.00691	−0.165102
$590$	51.1439	2.10556
$591$	−4.78532	−0.196842
$592$	7.52404	0.309236
$593$	39.1951	1.60955	0.804776	−	0.593579i	$-0.202286\pi$
$593$	39.1951	1.60955	0.804776	+	0.593579i	$0.202286\pi$
$594$	−27.5728	−1.13132
$595$	−55.5722	−2.27824
$596$	14.3921	0.589524
$597$	21.7589	0.890531
$598$	−10.6353	−0.434910
$599$	41.7786	1.70703	0.853514	−	0.521070i	$-0.174467\pi$
$599$	41.7786	1.70703	0.853514	+	0.521070i	$0.174467\pi$
$600$	10.7317	0.438121
$601$	−35.7094	−1.45661	−0.728307	−	0.685250i	$-0.759693\pi$
$601$	−35.7094	−1.45661	−0.728307	+	0.685250i	$0.759693\pi$
$602$	−15.7741	−0.642904
$603$	−15.3068	−0.623343
$604$	7.09338	0.288625
$605$	−45.2986	−1.84165
$606$	−19.6423	−0.797916
$607$	34.0318	1.38131	0.690654	−	0.723185i	$-0.257323\pi$
$607$	34.0318	1.38131	0.690654	+	0.723185i	$0.257323\pi$
$608$	−1.30368	−0.0528713
$609$	41.8844	1.69724
$610$	25.2070	1.02060
$611$	32.6546	1.32106
$612$	4.45060	0.179905
$613$	−24.6308	−0.994830	−0.497415	−	0.867513i	$-0.665717\pi$
$613$	−24.6308	−0.994830	−0.497415	+	0.867513i	$0.665717\pi$
$614$	−10.5841	−0.427138
$615$	−23.1752	−0.934515
$616$	17.2997	0.697026
$617$	11.9634	0.481628	0.240814	−	0.970571i	$-0.422586\pi$
$617$	11.9634	0.481628	0.240814	+	0.970571i	$0.422586\pi$
$618$	−14.9052	−0.599575
$619$	37.3296	1.50041	0.750203	−	0.661208i	$-0.229956\pi$
$619$	37.3296	1.50041	0.750203	+	0.661208i	$0.229956\pi$
$620$	10.9125	0.438258
$621$	−19.3656	−0.777113
$622$	−29.3365	−1.17629
$623$	10.1032	0.404776
$624$	4.38333	0.175474
$625$	−5.17872	−0.207149
$626$	−11.4087	−0.455984
$627$	−8.96589	−0.358063
$628$	−13.5488	−0.540657
$629$	−33.1809	−1.32301
$630$	12.7175	0.506676
$631$	−36.6238	−1.45797	−0.728986	−	0.684529i	$-0.760008\pi$
$631$	−36.6238	−1.45797	−0.728986	+	0.684529i	$0.760008\pi$
$632$	8.39855	0.334077
$633$	2.85005	0.113279
$634$	24.7302	0.982162
$635$	17.6558	0.700650
$636$	−12.1368	−0.481256
$637$	−17.3874	−0.688914
$638$	−40.7678	−1.61401
$639$	−8.45140	−0.334332
$640$	3.55049	0.140346
$641$	−22.7189	−0.897343	−0.448672	−	0.893697i	$-0.648103\pi$
$641$	−22.7189	−0.897343	−0.448672	+	0.893697i	$0.648103\pi$
$642$	8.19376	0.323382
$643$	31.3065	1.23461	0.617304	−	0.786725i	$-0.288225\pi$
$643$	31.3065	1.23461	0.617304	+	0.786725i	$0.288225\pi$
$644$	12.1504	0.478792
$645$	−22.2646	−0.876669
$646$	5.74923	0.226200
$647$	30.1532	1.18544	0.592722	−	0.805407i	$-0.298053\pi$
$647$	30.1532	1.18544	0.592722	+	0.805407i	$0.298053\pi$
$648$	4.95388	0.194607
$649$	70.2123	2.75607
$650$	23.6291	0.926811
$651$	−15.3915	−0.603241
$652$	−24.8029	−0.971356
$653$	−0.226271	−0.00885469	−0.00442734	−	0.999990i	$-0.501409\pi$
$653$	−0.226271	−0.00885469	−0.00442734	+	0.999990i	$0.501409\pi$
$654$	2.92165	0.114246
$655$	−62.2074	−2.43064
$656$	−4.62618	−0.180622
$657$	−5.96243	−0.232616
$658$	−37.3065	−1.45436
$659$	19.7945	0.771082	0.385541	−	0.922691i	$-0.374015\pi$
$659$	19.7945	0.771082	0.385541	+	0.922691i	$0.374015\pi$
$660$	24.4180	0.950470
$661$	−37.9991	−1.47799	−0.738997	−	0.673709i	$-0.764700\pi$
$661$	−37.9991	−1.47799	−0.738997	+	0.673709i	$0.764700\pi$
$662$	25.3655	0.985858
$663$	−19.3304	−0.750732
$664$	6.84408	0.265602
$665$	16.4283	0.637061
$666$	7.59332	0.294235
$667$	−28.6330	−1.10868
$668$	−2.80230	−0.108424
$669$	−18.3119	−0.707978
$670$	53.8510	2.08044
$671$	34.6052	1.33592
$672$	−5.00776	−0.193179
$673$	31.6221	1.21894	0.609471	−	0.792808i	$-0.291382\pi$
$673$	31.6221	1.21894	0.609471	+	0.792808i	$0.291382\pi$
$674$	−0.00442850	−0.000170579 0
$675$	43.0257	1.65606
$676$	−3.34877	−0.128799
$677$	31.6862	1.21780	0.608900	−	0.793247i	$-0.291611\pi$
$677$	31.6862	1.21780	0.608900	+	0.793247i	$0.291611\pi$
$678$	18.4197	0.707404
$679$	−0.0597448	−0.00229279
$680$	−15.6576	−0.600443
$681$	−31.0955	−1.19158
$682$	14.9812	0.573659
$683$	3.37186	0.129020	0.0645102	−	0.997917i	$-0.479451\pi$
$683$	3.37186	0.129020	0.0645102	+	0.997917i	$0.479451\pi$
$684$	−1.31569	−0.0503066
$685$	1.52886	0.0584148
$686$	−4.98009	−0.190141
$687$	−6.92278	−0.264120
$688$	−4.44441	−0.169441
$689$	−26.7229	−1.01806
$690$	17.1498	0.652884
$691$	−26.6468	−1.01369	−0.506845	−	0.862037i	$-0.669188\pi$
$691$	−26.6468	−1.01369	−0.506845	+	0.862037i	$0.669188\pi$
$692$	−17.6503	−0.670965
$693$	17.4590	0.663214
$694$	−7.15668	−0.271664
$695$	27.0205	1.02495
$696$	11.8011	0.447319
$697$	20.4014	0.772758
$698$	−28.1892	−1.06698
$699$	−30.5078	−1.15391
$700$	−26.9953	−1.02032
$701$	−39.3889	−1.48770	−0.743849	−	0.668348i	$-0.767002\pi$
$701$	−39.3889	−1.48770	−0.743849	+	0.668348i	$0.767002\pi$
$702$	17.5737	0.663276
$703$	9.80896	0.369952
$704$	4.87426	0.183706
$705$	−52.6569	−1.98317
$706$	11.8993	0.447835
$707$	49.4096	1.85824
$708$	−20.3244	−0.763838
$709$	17.2579	0.648134	0.324067	−	0.946034i	$-0.394950\pi$
$709$	17.2579	0.648134	0.324067	+	0.946034i	$0.394950\pi$
$710$	29.7328	1.11585
$711$	8.47589	0.317871
$712$	2.84661	0.106681
$713$	10.5219	0.394050
$714$	22.0842	0.826480
$715$	53.7636	2.01065
$716$	−21.2215	−0.793086
$717$	−2.75789	−0.102995
$718$	−16.3254	−0.609258
$719$	33.0010	1.23073	0.615365	−	0.788243i	$-0.289009\pi$
$719$	33.0010	1.23073	0.615365	+	0.788243i	$0.289009\pi$
$720$	3.58319	0.133537
$721$	37.4935	1.39633
$722$	17.3004	0.643855
$723$	27.5847	1.02589
$724$	−18.4044	−0.683994
$725$	63.6159	2.36263
$726$	18.0015	0.668099
$727$	40.9403	1.51839	0.759196	−	0.650862i	$-0.225592\pi$
$727$	40.9403	1.51839	0.759196	+	0.650862i	$0.225592\pi$
$728$	−11.0261	−0.408655
$729$	28.9440	1.07200
$730$	20.9764	0.776372
$731$	19.5998	0.724924
$732$	−10.0172	−0.370246
$733$	8.06332	0.297825	0.148913	−	0.988850i	$-0.452423\pi$
$733$	8.06332	0.297825	0.148913	+	0.988850i	$0.452423\pi$
$734$	−6.82315	−0.251847
$735$	28.0379	1.03419
$736$	3.42341	0.126188
$737$	73.9287	2.72320
$738$	−4.66877	−0.171860
$739$	28.7319	1.05692	0.528460	−	0.848958i	$-0.322769\pi$
$739$	28.7319	1.05692	0.528460	+	0.848958i	$0.322769\pi$
$740$	−26.7141	−0.982028
$741$	5.71447	0.209926
$742$	30.5297	1.12078
$743$	−54.1359	−1.98605	−0.993026	−	0.117892i	$-0.962386\pi$
$743$	−54.1359	−1.98605	−0.993026	+	0.117892i	$0.962386\pi$
$744$	−4.33661	−0.158988
$745$	−51.0991	−1.87213
$746$	0.238489	0.00873171
$747$	6.90710	0.252718
$748$	−21.4954	−0.785951
$749$	−20.6111	−0.753113
$750$	−13.0550	−0.476701
$751$	−11.0799	−0.404312	−0.202156	−	0.979353i	$-0.564795\pi$
$751$	−11.0799	−0.404312	−0.202156	+	0.979353i	$0.564795\pi$
$752$	−10.5112	−0.383305
$753$	−39.7266	−1.44772
$754$	25.9837	0.946269
$755$	−25.1850	−0.916576
$756$	−20.0772	−0.730199
$757$	−47.8781	−1.74016	−0.870079	−	0.492912i	$-0.835932\pi$
$757$	−47.8781	−1.74016	−0.870079	+	0.492912i	$0.835932\pi$
$758$	21.0929	0.766128
$759$	23.5440	0.854593
$760$	4.62872	0.167901
$761$	9.49250	0.344103	0.172051	−	0.985088i	$-0.444960\pi$
$761$	9.49250	0.344103	0.172051	+	0.985088i	$0.444960\pi$
$762$	−7.01637	−0.254176
$763$	−7.34931	−0.266063
$764$	0.459681	0.0166307
$765$	−15.8018	−0.571316
$766$	0.540163	0.0195169
$767$	−44.7503	−1.61584
$768$	−1.41095	−0.0509134
$769$	−31.8160	−1.14731	−0.573657	−	0.819096i	$-0.694476\pi$
$769$	−31.8160	−1.14731	−0.573657	+	0.819096i	$0.694476\pi$
$770$	−61.4226	−2.21352
$771$	11.9209	0.429322
$772$	18.1383	0.652810
$773$	−18.7584	−0.674693	−0.337347	−	0.941380i	$-0.609529\pi$
$773$	−18.7584	−0.674693	−0.337347	+	0.941380i	$0.609529\pi$
$774$	−4.48533	−0.161222
$775$	−23.3773	−0.839736
$776$	−0.0168333	−0.000604280 0
$777$	37.6786	1.35171
$778$	−10.4360	−0.374150
$779$	−6.03107	−0.216085
$780$	−15.5630	−0.557244
$781$	40.8184	1.46060
$782$	−15.0972	−0.539875
$783$	47.3130	1.69083
$784$	5.59684	0.199887
$785$	48.1050	1.71694
$786$	24.7210	0.881769
$787$	30.3425	1.08159	0.540797	−	0.841153i	$-0.318123\pi$
$787$	30.3425	1.08159	0.540797	+	0.841153i	$0.318123\pi$
$788$	3.39155	0.120819
$789$	8.03304	0.285984
$790$	−29.8190	−1.06091
$791$	−46.3341	−1.64745
$792$	4.91914	0.174794
$793$	−22.0559	−0.783226
$794$	11.9864	0.425380
$795$	43.0917	1.52830
$796$	−15.4214	−0.546596
$797$	15.8061	0.559879	0.279940	−	0.960018i	$-0.409686\pi$
$797$	15.8061	0.559879	0.279940	+	0.960018i	$0.409686\pi$
$798$	−6.52854	−0.231108
$799$	46.3544	1.63990
$800$	−7.60600	−0.268913
$801$	2.87282	0.101506
$802$	−30.1565	−1.06486
$803$	28.7973	1.01623
$804$	−21.4002	−0.754727
$805$	−43.1398	−1.52048
$806$	−9.54836	−0.336326
$807$	−36.7638	−1.29415
$808$	13.9213	0.489750
$809$	49.2585	1.73184	0.865918	−	0.500186i	$-0.166735\pi$
$809$	49.2585	1.73184	0.865918	+	0.500186i	$0.166735\pi$
$810$	−17.5887	−0.618004
$811$	−18.1179	−0.636207	−0.318103	−	0.948056i	$-0.603046\pi$
$811$	−18.1179	−0.636207	−0.318103	+	0.948056i	$0.603046\pi$
$812$	−29.6852	−1.04175
$813$	27.5417	0.965929
$814$	−36.6741	−1.28543
$815$	88.0625	3.08469
$816$	6.22229	0.217824
$817$	−5.79410	−0.202710
$818$	−19.8210	−0.693025
$819$	−11.1276	−0.388831
$820$	16.4252	0.573593
$821$	10.3796	0.362249	0.181124	−	0.983460i	$-0.442026\pi$
$821$	10.3796	0.362249	0.181124	+	0.983460i	$0.442026\pi$
$822$	−0.607564	−0.0211912
$823$	−34.4477	−1.20077	−0.600385	−	0.799711i	$-0.704986\pi$
$823$	−34.4477	−1.20077	−0.600385	+	0.799711i	$0.704986\pi$
$824$	10.5639	0.368011
$825$	−52.3092	−1.82117
$826$	51.1253	1.77888
$827$	−22.5874	−0.785439	−0.392720	−	0.919658i	$-0.628466\pi$
$827$	−22.5874	−0.785439	−0.392720	+	0.919658i	$0.628466\pi$
$828$	3.45493	0.120067
$829$	14.6821	0.509929	0.254965	−	0.966950i	$-0.417936\pi$
$829$	14.6821	0.509929	0.254965	+	0.966950i	$0.417936\pi$
$830$	−24.2999	−0.843461
$831$	17.2425	0.598135
$832$	−3.10664	−0.107703
$833$	−24.6820	−0.855181
$834$	−10.7379	−0.371822
$835$	9.94954	0.344318
$836$	6.35449	0.219775
$837$	−17.3864	−0.600961
$838$	5.07857	0.175436
$839$	−40.6042	−1.40181	−0.700906	−	0.713253i	$-0.747221\pi$
$839$	−40.6042	−1.40181	−0.700906	+	0.713253i	$0.747221\pi$
$840$	17.7800	0.613469
$841$	40.9549	1.41224
$842$	7.00190	0.241301
$843$	39.5090	1.36076
$844$	−2.01995	−0.0695295
$845$	11.8898	0.409021
$846$	−10.6080	−0.364711
$847$	−45.2821	−1.55591
$848$	8.60185	0.295389
$849$	−40.9457	−1.40525
$850$	33.5424	1.15050
$851$	−25.7579	−0.882968
$852$	−11.8157	−0.404800
$853$	40.7804	1.39630	0.698148	−	0.715954i	$-0.254008\pi$
$853$	40.7804	1.39630	0.698148	+	0.715954i	$0.254008\pi$
$854$	25.1979	0.862253
$855$	4.67134	0.159756
$856$	−5.80725	−0.198488
$857$	14.7251	0.502998	0.251499	−	0.967858i	$-0.419076\pi$
$857$	14.7251	0.502998	0.251499	+	0.967858i	$0.419076\pi$
$858$	−21.3655	−0.729406
$859$	−0.000964852 0	−3.29203e−5 0	−1.64602e−5	−	1.00000i	$-0.500005\pi$
$859$	−0.000964852 0	−3.29203e−5 0	−1.64602e−5		1.00000i	$0.500005\pi$
$860$	15.7798	0.538088
$861$	−23.1668	−0.789522
$862$	14.1636	0.482413
$863$	13.9157	0.473696	0.236848	−	0.971547i	$-0.423886\pi$
$863$	13.9157	0.473696	0.236848	+	0.971547i	$0.423886\pi$
$864$	−5.65681	−0.192449
$865$	62.6674	2.13076
$866$	15.2992	0.519890
$867$	−3.45404	−0.117305
$868$	10.9086	0.370261
$869$	−40.9367	−1.38868
$870$	−41.8997	−1.42053
$871$	−47.1190	−1.59657
$872$	−2.07069	−0.0701225
$873$	−0.0169883	−0.000574967 0
$874$	4.46304	0.150965
$875$	32.8394	1.11017
$876$	−8.33596	−0.281646
$877$	−42.5889	−1.43812	−0.719062	−	0.694946i	$-0.755428\pi$
$877$	−42.5889	−1.43812	−0.719062	+	0.694946i	$0.755428\pi$
$878$	16.0493	0.541636
$879$	32.2871	1.08902
$880$	−17.3060	−0.583386
$881$	−19.0428	−0.641569	−0.320784	−	0.947152i	$-0.603946\pi$
$881$	−19.0428	−0.641569	−0.320784	+	0.947152i	$0.603946\pi$
$882$	5.64838	0.190191
$883$	26.2311	0.882747	0.441374	−	0.897323i	$-0.354491\pi$
$883$	26.2311	0.882747	0.441374	+	0.897323i	$0.354491\pi$
$884$	13.7003	0.460790
$885$	72.1616	2.42569
$886$	−17.2194	−0.578497
$887$	39.3016	1.31962	0.659809	−	0.751433i	$-0.270637\pi$
$887$	39.3016	1.31962	0.659809	+	0.751433i	$0.270637\pi$
$888$	10.6161	0.356252
$889$	17.6494	0.591942
$890$	−10.1069	−0.338783
$891$	−24.1465	−0.808937
$892$	12.9784	0.434548
$893$	−13.7033	−0.458564
$894$	20.3066	0.679154
$895$	75.3469	2.51857
$896$	3.54920	0.118571
$897$	−15.0059	−0.501033
$898$	26.5008	0.884345
$899$	−25.7067	−0.857366
$900$	−7.67604	−0.255868
$901$	−37.9341	−1.26377
$902$	22.5492	0.750805
$903$	−22.2565	−0.740651
$904$	−13.0548	−0.434196
$905$	65.3447	2.17213
$906$	10.0084	0.332508
$907$	−15.7617	−0.523359	−0.261680	−	0.965155i	$-0.584276\pi$
$907$	−15.7617	−0.523359	−0.261680	+	0.965155i	$0.584276\pi$
$908$	22.0386	0.731377
$909$	14.0495	0.465993
$910$	39.1481	1.29775
$911$	−1.38440	−0.0458671	−0.0229336	−	0.999737i	$-0.507301\pi$
$911$	−1.38440	−0.0458671	−0.0229336	+	0.999737i	$0.507301\pi$
$912$	−1.83944	−0.0609098
$913$	−33.3598	−1.10405
$914$	27.6757	0.915429
$915$	35.5659	1.17577
$916$	4.90645	0.162114
$917$	−62.1848	−2.05352
$918$	24.9465	0.823356
$919$	26.5566	0.876022	0.438011	−	0.898970i	$-0.355683\pi$
$919$	26.5566	0.876022	0.438011	+	0.898970i	$0.355683\pi$
$920$	−12.1548	−0.400731
$921$	−14.9336	−0.492079
$922$	−20.7484	−0.683314
$923$	−26.0159	−0.856324
$924$	24.4091	0.803002
$925$	57.2279	1.88164
$926$	−6.62320	−0.217652
$927$	10.6612	0.350159
$928$	−8.36390	−0.274559
$929$	15.0611	0.494139	0.247070	−	0.968998i	$-0.420532\pi$
$929$	15.0611	0.494139	0.247070	+	0.968998i	$0.420532\pi$
$930$	15.3971	0.504891
$931$	7.29651	0.239133
$932$	21.6221	0.708255
$933$	−41.3924	−1.35513
$934$	36.5099	1.19464
$935$	76.3194	2.49591
$936$	−3.13525	−0.102479
$937$	17.9110	0.585127	0.292563	−	0.956246i	$-0.405492\pi$
$937$	17.9110	0.585127	0.292563	+	0.956246i	$0.405492\pi$
$938$	53.8314	1.75766
$939$	−16.0972	−0.525312
$940$	37.3200	1.21725
$941$	10.8314	0.353095	0.176547	−	0.984292i	$-0.443507\pi$
$941$	10.8314	0.353095	0.176547	+	0.984292i	$0.443507\pi$
$942$	−19.1168	−0.622858
$943$	15.8373	0.515733
$944$	14.4047	0.468834
$945$	71.2838	2.31886
$946$	21.6632	0.704331
$947$	−38.1275	−1.23898	−0.619489	−	0.785005i	$-0.712660\pi$
$947$	−38.1275	−1.23898	−0.619489	+	0.785005i	$0.712660\pi$
$948$	11.8500	0.384869
$949$	−18.3541	−0.595800
$950$	−9.91582	−0.321712
$951$	34.8932	1.13149
$952$	−15.6520	−0.507283
$953$	−24.4855	−0.793162	−0.396581	−	0.918000i	$-0.629803\pi$
$953$	−24.4855	−0.793162	−0.396581	+	0.918000i	$0.629803\pi$
$954$	8.68105	0.281059
$955$	−1.63210	−0.0528134
$956$	1.95463	0.0632173
$957$	−57.5215	−1.85941
$958$	6.98856	0.225790
$959$	1.52831	0.0493516
$960$	5.00958	0.161684
$961$	−21.5534	−0.695272
$962$	23.3745	0.753624
$963$	−5.86072	−0.188859
$964$	−19.5504	−0.629676
$965$	−64.3998	−2.07310
$966$	17.1436	0.551587
$967$	1.39487	0.0448558	0.0224279	−	0.999748i	$-0.492860\pi$
$967$	1.39487	0.0448558	0.0224279	+	0.999748i	$0.492860\pi$
$968$	−12.7584	−0.410070
$969$	8.11190	0.260592
$970$	0.0597665	0.00191899
$971$	43.5137	1.39642	0.698210	−	0.715893i	$-0.253980\pi$
$971$	43.5137	1.39642	0.698210	+	0.715893i	$0.253980\pi$
$972$	−9.98074	−0.320132
$973$	27.0107	0.865923
$974$	30.4726	0.976406
$975$	33.3396	1.06772
$976$	7.09958	0.227252
$977$	54.7997	1.75320	0.876598	−	0.481223i	$-0.159807\pi$
$977$	54.7997	1.75320	0.876598	+	0.481223i	$0.159807\pi$
$978$	−34.9957	−1.11904
$979$	−13.8751	−0.443451
$980$	−19.8716	−0.634774
$981$	−2.08976	−0.0667209
$982$	−13.3296	−0.425365
$983$	−59.7534	−1.90584	−0.952918	−	0.303228i	$-0.901936\pi$
$983$	−59.7534	−1.90584	−0.952918	+	0.303228i	$0.901936\pi$
$984$	−6.52732	−0.208083
$985$	−12.0417	−0.383679
$986$	36.8847	1.17465
$987$	−52.6377	−1.67548
$988$	−4.05008	−0.128850
$989$	15.2150	0.483809
$990$	−17.4654	−0.555086
$991$	−4.54814	−0.144476	−0.0722381	−	0.997387i	$-0.523014\pi$
$991$	−4.54814	−0.144476	−0.0722381	+	0.997387i	$0.523014\pi$
$992$	3.07353	0.0975846
$993$	35.7895	1.13575
$994$	29.7220	0.942726
$995$	54.7535	1.73580
$996$	9.65669	0.305984
$997$	46.1929	1.46294	0.731472	−	0.681872i	$-0.238834\pi$
$997$	46.1929	1.46294	0.731472	+	0.681872i	$0.238834\pi$
$998$	−34.0841	−1.07891
$999$	42.5621	1.34660

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4022.2.a.d.1.12	✓	37

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4022.2.a.d.1.12	✓	37	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.41095 q^{3} +1.00000 q^{4} -3.55049 q^{5} +1.41095 q^{6} -3.54920 q^{7} -1.00000 q^{8} -1.00921 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.41095 q^{3} +1.00000 q^{4} -3.55049 q^{5} +1.41095 q^{6} -3.54920 q^{7} -1.00000 q^{8} -1.00921 q^{9} +3.55049 q^{10} +4.87426 q^{11} -1.41095 q^{12} -3.10664 q^{13} +3.54920 q^{14} +5.00958 q^{15} +1.00000 q^{16} -4.40999 q^{17} +1.00921 q^{18} +1.30368 q^{19} -3.55049 q^{20} +5.00776 q^{21} -4.87426 q^{22} -3.42341 q^{23} +1.41095 q^{24} +7.60600 q^{25} +3.10664 q^{26} +5.65681 q^{27} -3.54920 q^{28} +8.36390 q^{29} -5.00958 q^{30} -3.07353 q^{31} -1.00000 q^{32} -6.87736 q^{33} +4.40999 q^{34} +12.6014 q^{35} -1.00921 q^{36} +7.52404 q^{37} -1.30368 q^{38} +4.38333 q^{39} +3.55049 q^{40} -4.62618 q^{41} -5.00776 q^{42} -4.44441 q^{43} +4.87426 q^{44} +3.58319 q^{45} +3.42341 q^{46} -10.5112 q^{47} -1.41095 q^{48} +5.59684 q^{49} -7.60600 q^{50} +6.22229 q^{51} -3.10664 q^{52} +8.60185 q^{53} -5.65681 q^{54} -17.3060 q^{55} +3.54920 q^{56} -1.83944 q^{57} -8.36390 q^{58} +14.4047 q^{59} +5.00958 q^{60} +7.09958 q^{61} +3.07353 q^{62} +3.58188 q^{63} +1.00000 q^{64} +11.0301 q^{65} +6.87736 q^{66} +15.1672 q^{67} -4.40999 q^{68} +4.83027 q^{69} -12.6014 q^{70} +8.37428 q^{71} +1.00921 q^{72} +5.90803 q^{73} -7.52404 q^{74} -10.7317 q^{75} +1.30368 q^{76} -17.2997 q^{77} -4.38333 q^{78} -8.39855 q^{79} -3.55049 q^{80} -4.95388 q^{81} +4.62618 q^{82} -6.84408 q^{83} +5.00776 q^{84} +15.6576 q^{85} +4.44441 q^{86} -11.8011 q^{87} -4.87426 q^{88} -2.84661 q^{89} -3.58319 q^{90} +11.0261 q^{91} -3.42341 q^{92} +4.33661 q^{93} +10.5112 q^{94} -4.62872 q^{95} +1.41095 q^{96} +0.0168333 q^{97} -5.59684 q^{98} -4.91914 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 37 q - 37 q^{2} - 5 q^{3} + 37 q^{4} - 13 q^{5} + 5 q^{6} - 22 q^{7} - 37 q^{8} + 32 q^{9}+O(q^{10}) \) 37 * q - 37 * q^2 - 5 * q^3 + 37 * q^4 - 13 * q^5 + 5 * q^6 - 22 * q^7 - 37 * q^8 + 32 * q^9	\( 37 q - 37 q^{2} - 5 q^{3} + 37 q^{4} - 13 q^{5} + 5 q^{6} - 22 q^{7} - 37 q^{8} + 32 q^{9} + 13 q^{10} + 12 q^{11} - 5 q^{12} - 36 q^{13} + 22 q^{14} - 7 q^{15} + 37 q^{16} + 4 q^{17} - 32 q^{18} - 10 q^{19} - 13 q^{20} - 11 q^{21} - 12 q^{22} - q^{23} + 5 q^{24} + 8 q^{25} + 36 q^{26} - 20 q^{27} - 22 q^{28} - 6 q^{29} + 7 q^{30} - 23 q^{31} - 37 q^{32} - 27 q^{33} - 4 q^{34} + 24 q^{35} + 32 q^{36} - 46 q^{37} + 10 q^{38} + 5 q^{39} + 13 q^{40} + 11 q^{41} + 11 q^{42} - 22 q^{43} + 12 q^{44} - 57 q^{45} + q^{46} - 18 q^{47} - 5 q^{48} - q^{49} - 8 q^{50} + 18 q^{51} - 36 q^{52} - 25 q^{53} + 20 q^{54} - 25 q^{55} + 22 q^{56} - 25 q^{57} + 6 q^{58} + 24 q^{59} - 7 q^{60} - 40 q^{61} + 23 q^{62} - 38 q^{63} + 37 q^{64} + 14 q^{65} + 27 q^{66} - 49 q^{67} + 4 q^{68} - 19 q^{69} - 24 q^{70} + 27 q^{71} - 32 q^{72} - 87 q^{73} + 46 q^{74} - 5 q^{75} - 10 q^{76} - 50 q^{77} - 5 q^{78} + 11 q^{79} - 13 q^{80} + 5 q^{81} - 11 q^{82} - 9 q^{83} - 11 q^{84} - 68 q^{85} + 22 q^{86} - 12 q^{87} - 12 q^{88} - 3 q^{89} + 57 q^{90} - 19 q^{91} - q^{92} - 69 q^{93} + 18 q^{94} + 27 q^{95} + 5 q^{96} - 98 q^{97} + q^{98} + 33 q^{99}+O(q^{100}) \) 37 * q - 37 * q^2 - 5 * q^3 + 37 * q^4 - 13 * q^5 + 5 * q^6 - 22 * q^7 - 37 * q^8 + 32 * q^9 + 13 * q^10 + 12 * q^11 - 5 * q^12 - 36 * q^13 + 22 * q^14 - 7 * q^15 + 37 * q^16 + 4 * q^17 - 32 * q^18 - 10 * q^19 - 13 * q^20 - 11 * q^21 - 12 * q^22 - q^23 + 5 * q^24 + 8 * q^25 + 36 * q^26 - 20 * q^27 - 22 * q^28 - 6 * q^29 + 7 * q^30 - 23 * q^31 - 37 * q^32 - 27 * q^33 - 4 * q^34 + 24 * q^35 + 32 * q^36 - 46 * q^37 + 10 * q^38 + 5 * q^39 + 13 * q^40 + 11 * q^41 + 11 * q^42 - 22 * q^43 + 12 * q^44 - 57 * q^45 + q^46 - 18 * q^47 - 5 * q^48 - q^49 - 8 * q^50 + 18 * q^51 - 36 * q^52 - 25 * q^53 + 20 * q^54 - 25 * q^55 + 22 * q^56 - 25 * q^57 + 6 * q^58 + 24 * q^59 - 7 * q^60 - 40 * q^61 + 23 * q^62 - 38 * q^63 + 37 * q^64 + 14 * q^65 + 27 * q^66 - 49 * q^67 + 4 * q^68 - 19 * q^69 - 24 * q^70 + 27 * q^71 - 32 * q^72 - 87 * q^73 + 46 * q^74 - 5 * q^75 - 10 * q^76 - 50 * q^77 - 5 * q^78 + 11 * q^79 - 13 * q^80 + 5 * q^81 - 11 * q^82 - 9 * q^83 - 11 * q^84 - 68 * q^85 + 22 * q^86 - 12 * q^87 - 12 * q^88 - 3 * q^89 + 57 * q^90 - 19 * q^91 - q^92 - 69 * q^93 + 18 * q^94 + 27 * q^95 + 5 * q^96 - 98 * q^97 + q^98 + 33 * q^99

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