LMFDB - Embedded newform 4010.2.a.n.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4010,2,Mod(1,4010)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4010, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("4010.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4010 = 2 \cdot 5 \cdot 401 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4010.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:	$32.0200112105$
Analytic rank:	$0$
Dimension:	$22$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Character	$\chi$	$=$	4010.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.81588 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.81588 q^{6} -3.01167 q^{7} +1.00000 q^{8} +0.297426 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.81588 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.81588 q^{6} -3.01167 q^{7} +1.00000 q^{8} +0.297426 q^{9} +1.00000 q^{10} -5.40145 q^{11} -1.81588 q^{12} -2.18325 q^{13} -3.01167 q^{14} -1.81588 q^{15} +1.00000 q^{16} +6.31643 q^{17} +0.297426 q^{18} -6.91000 q^{19} +1.00000 q^{20} +5.46883 q^{21} -5.40145 q^{22} -7.90080 q^{23} -1.81588 q^{24} +1.00000 q^{25} -2.18325 q^{26} +4.90755 q^{27} -3.01167 q^{28} -2.41854 q^{29} -1.81588 q^{30} +6.61521 q^{31} +1.00000 q^{32} +9.80840 q^{33} +6.31643 q^{34} -3.01167 q^{35} +0.297426 q^{36} +10.6311 q^{37} -6.91000 q^{38} +3.96451 q^{39} +1.00000 q^{40} +9.90366 q^{41} +5.46883 q^{42} +8.47818 q^{43} -5.40145 q^{44} +0.297426 q^{45} -7.90080 q^{46} -12.7860 q^{47} -1.81588 q^{48} +2.07014 q^{49} +1.00000 q^{50} -11.4699 q^{51} -2.18325 q^{52} -6.09536 q^{53} +4.90755 q^{54} -5.40145 q^{55} -3.01167 q^{56} +12.5477 q^{57} -2.41854 q^{58} +0.568413 q^{59} -1.81588 q^{60} +6.77344 q^{61} +6.61521 q^{62} -0.895747 q^{63} +1.00000 q^{64} -2.18325 q^{65} +9.80840 q^{66} -3.56039 q^{67} +6.31643 q^{68} +14.3469 q^{69} -3.01167 q^{70} +4.92770 q^{71} +0.297426 q^{72} +13.1341 q^{73} +10.6311 q^{74} -1.81588 q^{75} -6.91000 q^{76} +16.2674 q^{77} +3.96451 q^{78} +16.2146 q^{79} +1.00000 q^{80} -9.80381 q^{81} +9.90366 q^{82} +12.2377 q^{83} +5.46883 q^{84} +6.31643 q^{85} +8.47818 q^{86} +4.39179 q^{87} -5.40145 q^{88} +3.75242 q^{89} +0.297426 q^{90} +6.57521 q^{91} -7.90080 q^{92} -12.0124 q^{93} -12.7860 q^{94} -6.91000 q^{95} -1.81588 q^{96} -9.37889 q^{97} +2.07014 q^{98} -1.60653 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q + 22 q^{2} + q^{3} + 22 q^{4} + 22 q^{5} + q^{6} + 22 q^{8} + 43 q^{9}+O(q^{10}) $ 22 * q + 22 * q^2 + q^3 + 22 * q^4 + 22 * q^5 + q^6 + 22 * q^8 + 43 * q^9	\( 22 q + 22 q^{2} + q^{3} + 22 q^{4} + 22 q^{5} + q^{6} + 22 q^{8} + 43 q^{9} + 22 q^{10} + 12 q^{11} + q^{12} + 10 q^{13} + q^{15} + 22 q^{16} + 24 q^{17} + 43 q^{18} + 13 q^{19} + 22 q^{20} + 13 q^{21} + 12 q^{22} + 7 q^{23} + q^{24} + 22 q^{25} + 10 q^{26} - 5 q^{27} + 22 q^{29} + q^{30} + 14 q^{31} + 22 q^{32} + 31 q^{33} + 24 q^{34} + 43 q^{36} + 35 q^{37} + 13 q^{38} + 4 q^{39} + 22 q^{40} + 29 q^{41} + 13 q^{42} + 7 q^{43} + 12 q^{44} + 43 q^{45} + 7 q^{46} - 21 q^{47} + q^{48} + 32 q^{49} + 22 q^{50} - 6 q^{51} + 10 q^{52} + 29 q^{53} - 5 q^{54} + 12 q^{55} - 13 q^{57} + 22 q^{58} + 12 q^{59} + q^{60} + 24 q^{61} + 14 q^{62} - 8 q^{63} + 22 q^{64} + 10 q^{65} + 31 q^{66} + 25 q^{67} + 24 q^{68} + 3 q^{69} + 31 q^{71} + 43 q^{72} + 30 q^{73} + 35 q^{74} + q^{75} + 13 q^{76} + 10 q^{77} + 4 q^{78} + 35 q^{79} + 22 q^{80} + 74 q^{81} + 29 q^{82} - 33 q^{83} + 13 q^{84} + 24 q^{85} + 7 q^{86} - 24 q^{87} + 12 q^{88} + 38 q^{89} + 43 q^{90} - 32 q^{91} + 7 q^{92} + 3 q^{93} - 21 q^{94} + 13 q^{95} + q^{96} + 11 q^{97} + 32 q^{98} - 41 q^{99}+O(q^{100}) \) 22 * q + 22 * q^2 + q^3 + 22 * q^4 + 22 * q^5 + q^6 + 22 * q^8 + 43 * q^9 + 22 * q^10 + 12 * q^11 + q^12 + 10 * q^13 + q^15 + 22 * q^16 + 24 * q^17 + 43 * q^18 + 13 * q^19 + 22 * q^20 + 13 * q^21 + 12 * q^22 + 7 * q^23 + q^24 + 22 * q^25 + 10 * q^26 - 5 * q^27 + 22 * q^29 + q^30 + 14 * q^31 + 22 * q^32 + 31 * q^33 + 24 * q^34 + 43 * q^36 + 35 * q^37 + 13 * q^38 + 4 * q^39 + 22 * q^40 + 29 * q^41 + 13 * q^42 + 7 * q^43 + 12 * q^44 + 43 * q^45 + 7 * q^46 - 21 * q^47 + q^48 + 32 * q^49 + 22 * q^50 - 6 * q^51 + 10 * q^52 + 29 * q^53 - 5 * q^54 + 12 * q^55 - 13 * q^57 + 22 * q^58 + 12 * q^59 + q^60 + 24 * q^61 + 14 * q^62 - 8 * q^63 + 22 * q^64 + 10 * q^65 + 31 * q^66 + 25 * q^67 + 24 * q^68 + 3 * q^69 + 31 * q^71 + 43 * q^72 + 30 * q^73 + 35 * q^74 + q^75 + 13 * q^76 + 10 * q^77 + 4 * q^78 + 35 * q^79 + 22 * q^80 + 74 * q^81 + 29 * q^82 - 33 * q^83 + 13 * q^84 + 24 * q^85 + 7 * q^86 - 24 * q^87 + 12 * q^88 + 38 * q^89 + 43 * q^90 - 32 * q^91 + 7 * q^92 + 3 * q^93 - 21 * q^94 + 13 * q^95 + q^96 + 11 * q^97 + 32 * q^98 - 41 * 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
$3$	−1.81588	−1.04840	−0.524200	−	0.851595i	$-0.675636\pi$
$3$	−1.81588	−1.04840	−0.524200	+	0.851595i	$0.675636\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−1.81588	−0.741331
$7$	−3.01167	−1.13830	−0.569152	−	0.822232i	$-0.692728\pi$
$7$	−3.01167	−1.13830	−0.569152	+	0.822232i	$0.692728\pi$
$8$	1.00000	0.353553
$9$	0.297426	0.0991419
$10$	1.00000	0.316228
$11$	−5.40145	−1.62860	−0.814300	−	0.580444i	$-0.802879\pi$
$11$	−5.40145	−1.62860	−0.814300	+	0.580444i	$0.802879\pi$
$12$	−1.81588	−0.524200
$13$	−2.18325	−0.605523	−0.302762	−	0.953066i	$-0.597909\pi$
$13$	−2.18325	−0.605523	−0.302762	+	0.953066i	$0.597909\pi$
$14$	−3.01167	−0.804902
$15$	−1.81588	−0.468859
$16$	1.00000	0.250000
$17$	6.31643	1.53196	0.765980	−	0.642865i	$-0.222254\pi$
$17$	6.31643	1.53196	0.765980	+	0.642865i	$0.222254\pi$
$18$	0.297426	0.0701039
$19$	−6.91000	−1.58526	−0.792631	−	0.609702i	$-0.791289\pi$
$19$	−6.91000	−1.58526	−0.792631	+	0.609702i	$0.791289\pi$
$20$	1.00000	0.223607
$21$	5.46883	1.19340
$22$	−5.40145	−1.15159
$23$	−7.90080	−1.64743	−0.823715	−	0.567004i	$-0.808102\pi$
$23$	−7.90080	−1.64743	−0.823715	+	0.567004i	$0.808102\pi$
$24$	−1.81588	−0.370665
$25$	1.00000	0.200000
$26$	−2.18325	−0.428170
$27$	4.90755	0.944459
$28$	−3.01167	−0.569152
$29$	−2.41854	−0.449112	−0.224556	−	0.974461i	$-0.572093\pi$
$29$	−2.41854	−0.449112	−0.224556	+	0.974461i	$0.572093\pi$
$30$	−1.81588	−0.331533
$31$	6.61521	1.18813	0.594063	−	0.804418i	$-0.297523\pi$
$31$	6.61521	1.18813	0.594063	+	0.804418i	$0.297523\pi$
$32$	1.00000	0.176777
$33$	9.80840	1.70742
$34$	6.31643	1.08326
$35$	−3.01167	−0.509065
$36$	0.297426	0.0495709
$37$	10.6311	1.74775	0.873875	−	0.486151i	$-0.161600\pi$
$37$	10.6311	1.74775	0.873875	+	0.486151i	$0.161600\pi$
$38$	−6.91000	−1.12095
$39$	3.96451	0.634830
$40$	1.00000	0.158114
$41$	9.90366	1.54669	0.773346	−	0.633984i	$-0.218582\pi$
$41$	9.90366	1.54669	0.773346	+	0.633984i	$0.218582\pi$
$42$	5.46883	0.843859
$43$	8.47818	1.29291	0.646455	−	0.762952i	$-0.276251\pi$
$43$	8.47818	1.29291	0.646455	+	0.762952i	$0.276251\pi$
$44$	−5.40145	−0.814300
$45$	0.297426	0.0443376
$46$	−7.90080	−1.16491
$47$	−12.7860	−1.86503	−0.932517	−	0.361126i	$-0.882392\pi$
$47$	−12.7860	−1.86503	−0.932517	+	0.361126i	$0.882392\pi$
$48$	−1.81588	−0.262100
$49$	2.07014	0.295735
$50$	1.00000	0.141421
$51$	−11.4699	−1.60611
$52$	−2.18325	−0.302762
$53$	−6.09536	−0.837262	−0.418631	−	0.908156i	$-0.637490\pi$
$53$	−6.09536	−0.837262	−0.418631	+	0.908156i	$0.637490\pi$
$54$	4.90755	0.667834
$55$	−5.40145	−0.728332
$56$	−3.01167	−0.402451
$57$	12.5477	1.66199
$58$	−2.41854	−0.317570
$59$	0.568413	0.0740011	0.0370005	−	0.999315i	$-0.488220\pi$
$59$	0.568413	0.0740011	0.0370005	+	0.999315i	$0.488220\pi$
$60$	−1.81588	−0.234429
$61$	6.77344	0.867250	0.433625	−	0.901093i	$-0.357234\pi$
$61$	6.77344	0.867250	0.433625	+	0.901093i	$0.357234\pi$
$62$	6.61521	0.840132
$63$	−0.895747	−0.112854
$64$	1.00000	0.125000
$65$	−2.18325	−0.270798
$66$	9.80840	1.20733
$67$	−3.56039	−0.434970	−0.217485	−	0.976064i	$-0.569785\pi$
$67$	−3.56039	−0.434970	−0.217485	+	0.976064i	$0.569785\pi$
$68$	6.31643	0.765980
$69$	14.3469	1.72716
$70$	−3.01167	−0.359963
$71$	4.92770	0.584810	0.292405	−	0.956295i	$-0.405544\pi$
$71$	4.92770	0.584810	0.292405	+	0.956295i	$0.405544\pi$
$72$	0.297426	0.0350519
$73$	13.1341	1.53723	0.768614	−	0.639713i	$-0.220947\pi$
$73$	13.1341	1.53723	0.768614	+	0.639713i	$0.220947\pi$
$74$	10.6311	1.23585
$75$	−1.81588	−0.209680
$76$	−6.91000	−0.792631
$77$	16.2674	1.85384
$78$	3.96451	0.448893
$79$	16.2146	1.82428	0.912140	−	0.409878i	$-0.134429\pi$
$79$	16.2146	1.82428	0.912140	+	0.409878i	$0.134429\pi$
$80$	1.00000	0.111803
$81$	−9.80381	−1.08931
$82$	9.90366	1.09368
$83$	12.2377	1.34326	0.671632	−	0.740885i	$-0.265594\pi$
$83$	12.2377	1.34326	0.671632	+	0.740885i	$0.265594\pi$
$84$	5.46883	0.596699
$85$	6.31643	0.685113
$86$	8.47818	0.914225
$87$	4.39179	0.470849
$88$	−5.40145	−0.575797
$89$	3.75242	0.397756	0.198878	−	0.980024i	$-0.436270\pi$
$89$	3.75242	0.397756	0.198878	+	0.980024i	$0.436270\pi$
$90$	0.297426	0.0313514
$91$	6.57521	0.689269
$92$	−7.90080	−0.823715
$93$	−12.0124	−1.24563
$94$	−12.7860	−1.31878
$95$	−6.91000	−0.708951
$96$	−1.81588	−0.185333
$97$	−9.37889	−0.952282	−0.476141	−	0.879369i	$-0.657965\pi$
$97$	−9.37889	−0.952282	−0.476141	+	0.879369i	$0.657965\pi$
$98$	2.07014	0.209116
$99$	−1.60653	−0.161462
$100$	1.00000	0.100000
$101$	9.35521	0.930878	0.465439	−	0.885080i	$-0.345896\pi$
$101$	9.35521	0.930878	0.465439	+	0.885080i	$0.345896\pi$
$102$	−11.4699	−1.13569
$103$	−4.66195	−0.459356	−0.229678	−	0.973267i	$-0.573767\pi$
$103$	−4.66195	−0.459356	−0.229678	+	0.973267i	$0.573767\pi$
$104$	−2.18325	−0.214085
$105$	5.46883	0.533703
$106$	−6.09536	−0.592034
$107$	−8.11296	−0.784309	−0.392154	−	0.919899i	$-0.628270\pi$
$107$	−8.11296	−0.784309	−0.392154	+	0.919899i	$0.628270\pi$
$108$	4.90755	0.472230
$109$	−16.5797	−1.58805	−0.794024	−	0.607886i	$-0.792018\pi$
$109$	−16.5797	−1.58805	−0.794024	+	0.607886i	$0.792018\pi$
$110$	−5.40145	−0.515008
$111$	−19.3049	−1.83234
$112$	−3.01167	−0.284576
$113$	−3.07698	−0.289458	−0.144729	−	0.989471i	$-0.546231\pi$
$113$	−3.07698	−0.289458	−0.144729	+	0.989471i	$0.546231\pi$
$114$	12.5477	1.17520
$115$	−7.90080	−0.736753
$116$	−2.41854	−0.224556
$117$	−0.649353	−0.0600327
$118$	0.568413	0.0523267
$119$	−19.0230	−1.74383
$120$	−1.81588	−0.165767
$121$	18.1757	1.65234
$122$	6.77344	0.613238
$123$	−17.9839	−1.62155
$124$	6.61521	0.594063
$125$	1.00000	0.0894427
$126$	−0.895747	−0.0797995
$127$	10.1725	0.902659	0.451330	−	0.892357i	$-0.350950\pi$
$127$	10.1725	0.902659	0.451330	+	0.892357i	$0.350950\pi$
$128$	1.00000	0.0883883
$129$	−15.3954	−1.35549
$130$	−2.18325	−0.191483
$131$	10.0143	0.874951	0.437475	−	0.899230i	$-0.355873\pi$
$131$	10.0143	0.874951	0.437475	+	0.899230i	$0.355873\pi$
$132$	9.80840	0.853712
$133$	20.8106	1.80451
$134$	−3.56039	−0.307570
$135$	4.90755	0.422375
$136$	6.31643	0.541629
$137$	−18.2497	−1.55918	−0.779589	−	0.626291i	$-0.784572\pi$
$137$	−18.2497	−1.55918	−0.779589	+	0.626291i	$0.784572\pi$
$138$	14.3469	1.22129
$139$	−15.3259	−1.29993	−0.649965	−	0.759964i	$-0.725216\pi$
$139$	−15.3259	−1.29993	−0.649965	+	0.759964i	$0.725216\pi$
$140$	−3.01167	−0.254532
$141$	23.2179	1.95530
$142$	4.92770	0.413523
$143$	11.7927	0.986155
$144$	0.297426	0.0247855
$145$	−2.41854	−0.200849
$146$	13.1341	1.08698
$147$	−3.75914	−0.310048
$148$	10.6311	0.873875
$149$	−6.79135	−0.556369	−0.278185	−	0.960528i	$-0.589733\pi$
$149$	−6.79135	−0.556369	−0.278185	+	0.960528i	$0.589733\pi$
$150$	−1.81588	−0.148266
$151$	1.17369	0.0955134	0.0477567	−	0.998859i	$-0.484793\pi$
$151$	1.17369	0.0955134	0.0477567	+	0.998859i	$0.484793\pi$
$152$	−6.91000	−0.560475
$153$	1.87867	0.151881
$154$	16.2674	1.31086
$155$	6.61521	0.531346
$156$	3.96451	0.317415
$157$	−10.7628	−0.858966	−0.429483	−	0.903075i	$-0.641304\pi$
$157$	−10.7628	−0.858966	−0.429483	+	0.903075i	$0.641304\pi$
$158$	16.2146	1.28996
$159$	11.0685	0.877786
$160$	1.00000	0.0790569
$161$	23.7946	1.87528
$162$	−9.80381	−0.770260
$163$	−0.816290	−0.0639367	−0.0319684	−	0.999489i	$-0.510178\pi$
$163$	−0.816290	−0.0639367	−0.0319684	+	0.999489i	$0.510178\pi$
$164$	9.90366	0.773346
$165$	9.80840	0.763583
$166$	12.2377	0.949831
$167$	21.9666	1.69983	0.849915	−	0.526920i	$-0.176653\pi$
$167$	21.9666	1.69983	0.849915	+	0.526920i	$0.176653\pi$
$168$	5.46883	0.421930
$169$	−8.23344	−0.633342
$170$	6.31643	0.484448
$171$	−2.05521	−0.157166
$172$	8.47818	0.646455
$173$	−17.8206	−1.35488	−0.677438	−	0.735580i	$-0.736910\pi$
$173$	−17.8206	−1.35488	−0.677438	+	0.735580i	$0.736910\pi$
$174$	4.39179	0.332941
$175$	−3.01167	−0.227661
$176$	−5.40145	−0.407150
$177$	−1.03217	−0.0775827
$178$	3.75242	0.281256
$179$	12.0222	0.898578	0.449289	−	0.893387i	$-0.351677\pi$
$179$	12.0222	0.898578	0.449289	+	0.893387i	$0.351677\pi$
$180$	0.297426	0.0221688
$181$	20.6568	1.53541	0.767705	−	0.640803i	$-0.221398\pi$
$181$	20.6568	1.53541	0.767705	+	0.640803i	$0.221398\pi$
$182$	6.57521	0.487387
$183$	−12.2998	−0.909225
$184$	−7.90080	−0.582454
$185$	10.6311	0.781617
$186$	−12.0124	−0.880794
$187$	−34.1179	−2.49495
$188$	−12.7860	−0.932517
$189$	−14.7799	−1.07508
$190$	−6.91000	−0.501304
$191$	4.67169	0.338032	0.169016	−	0.985613i	$-0.445941\pi$
$191$	4.67169	0.338032	0.169016	+	0.985613i	$0.445941\pi$
$192$	−1.81588	−0.131050
$193$	−8.07217	−0.581048	−0.290524	−	0.956868i	$-0.593830\pi$
$193$	−8.07217	−0.581048	−0.290524	+	0.956868i	$0.593830\pi$
$194$	−9.37889	−0.673365
$195$	3.96451	0.283905
$196$	2.07014	0.147867
$197$	11.1515	0.794514	0.397257	−	0.917707i	$-0.369962\pi$
$197$	11.1515	0.794514	0.397257	+	0.917707i	$0.369962\pi$
$198$	−1.60653	−0.114171
$199$	12.3680	0.876744	0.438372	−	0.898794i	$-0.355555\pi$
$199$	12.3680	0.876744	0.438372	+	0.898794i	$0.355555\pi$
$200$	1.00000	0.0707107
$201$	6.46524	0.456023
$202$	9.35521	0.658230
$203$	7.28385	0.511226
$204$	−11.4699	−0.803053
$205$	9.90366	0.691702
$206$	−4.66195	−0.324814
$207$	−2.34990	−0.163329
$208$	−2.18325	−0.151381
$209$	37.3240	2.58176
$210$	5.46883	0.377385
$211$	−15.2620	−1.05068	−0.525339	−	0.850893i	$-0.676062\pi$
$211$	−15.2620	−1.05068	−0.525339	+	0.850893i	$0.676062\pi$
$212$	−6.09536	−0.418631
$213$	−8.94811	−0.613115
$214$	−8.11296	−0.554590
$215$	8.47818	0.578207
$216$	4.90755	0.333917
$217$	−19.9228	−1.35245
$218$	−16.5797	−1.12292
$219$	−23.8499	−1.61163
$220$	−5.40145	−0.364166
$221$	−13.7903	−0.927637
$222$	−19.3049	−1.29566
$223$	4.37811	0.293180	0.146590	−	0.989197i	$-0.453170\pi$
$223$	4.37811	0.293180	0.146590	+	0.989197i	$0.453170\pi$
$224$	−3.01167	−0.201226
$225$	0.297426	0.0198284
$226$	−3.07698	−0.204678
$227$	25.3945	1.68549	0.842746	−	0.538311i	$-0.180937\pi$
$227$	25.3945	1.68549	0.842746	+	0.538311i	$0.180937\pi$
$228$	12.5477	0.830994
$229$	19.7475	1.30495	0.652475	−	0.757810i	$-0.273731\pi$
$229$	19.7475	1.30495	0.652475	+	0.757810i	$0.273731\pi$
$230$	−7.90080	−0.520963
$231$	−29.5396	−1.94357
$232$	−2.41854	−0.158785
$233$	5.39852	0.353669	0.176834	−	0.984241i	$-0.443414\pi$
$233$	5.39852	0.353669	0.176834	+	0.984241i	$0.443414\pi$
$234$	−0.649353	−0.0424495
$235$	−12.7860	−0.834069
$236$	0.568413	0.0370005
$237$	−29.4437	−1.91258
$238$	−19.0230	−1.23308
$239$	13.4073	0.867247	0.433623	−	0.901094i	$-0.357235\pi$
$239$	13.4073	0.867247	0.433623	+	0.901094i	$0.357235\pi$
$240$	−1.81588	−0.117215
$241$	−10.2946	−0.663136	−0.331568	−	0.943431i	$-0.607578\pi$
$241$	−10.2946	−0.663136	−0.331568	+	0.943431i	$0.607578\pi$
$242$	18.1757	1.16838
$243$	3.07990	0.197576
$244$	6.77344	0.433625
$245$	2.07014	0.132257
$246$	−17.9839	−1.14661
$247$	15.0862	0.959913
$248$	6.61521	0.420066
$249$	−22.2222	−1.40828
$250$	1.00000	0.0632456
$251$	5.96246	0.376347	0.188173	−	0.982136i	$-0.439743\pi$
$251$	5.96246	0.376347	0.188173	+	0.982136i	$0.439743\pi$
$252$	−0.895747	−0.0564268
$253$	42.6758	2.68300
$254$	10.1725	0.638276
$255$	−11.4699	−0.718272
$256$	1.00000	0.0625000
$257$	7.14153	0.445476	0.222738	−	0.974878i	$-0.428501\pi$
$257$	7.14153	0.445476	0.222738	+	0.974878i	$0.428501\pi$
$258$	−15.3954	−0.958473
$259$	−32.0175	−1.98947
$260$	−2.18325	−0.135399
$261$	−0.719337	−0.0445259
$262$	10.0143	0.618684
$263$	24.6160	1.51789	0.758943	−	0.651157i	$-0.225716\pi$
$263$	24.6160	1.51789	0.758943	+	0.651157i	$0.225716\pi$
$264$	9.80840	0.603665
$265$	−6.09536	−0.374435
$266$	20.8106	1.27598
$267$	−6.81395	−0.417007
$268$	−3.56039	−0.217485
$269$	−6.72613	−0.410099	−0.205050	−	0.978752i	$-0.565736\pi$
$269$	−6.72613	−0.410099	−0.205050	+	0.978752i	$0.565736\pi$
$270$	4.90755	0.298664
$271$	−5.89106	−0.357856	−0.178928	−	0.983862i	$-0.557263\pi$
$271$	−5.89106	−0.357856	−0.178928	+	0.983862i	$0.557263\pi$
$272$	6.31643	0.382990
$273$	−11.9398	−0.722630
$274$	−18.2497	−1.10251
$275$	−5.40145	−0.325720
$276$	14.3469	0.863582
$277$	9.74267	0.585380	0.292690	−	0.956207i	$-0.405450\pi$
$277$	9.74267	0.585380	0.292690	+	0.956207i	$0.405450\pi$
$278$	−15.3259	−0.919189
$279$	1.96753	0.117793
$280$	−3.01167	−0.179982
$281$	31.9484	1.90588	0.952940	−	0.303159i	$-0.0980413\pi$
$281$	31.9484	1.90588	0.952940	+	0.303159i	$0.0980413\pi$
$282$	23.2179	1.38261
$283$	−18.7617	−1.11527	−0.557634	−	0.830087i	$-0.688291\pi$
$283$	−18.7617	−1.11527	−0.557634	+	0.830087i	$0.688291\pi$
$284$	4.92770	0.292405
$285$	12.5477	0.743264
$286$	11.7927	0.697317
$287$	−29.8265	−1.76060
$288$	0.297426	0.0175260
$289$	22.8973	1.34690
$290$	−2.41854	−0.142022
$291$	17.0310	0.998372
$292$	13.1341	0.768614
$293$	−22.7410	−1.32854	−0.664272	−	0.747491i	$-0.731258\pi$
$293$	−22.7410	−1.32854	−0.664272	+	0.747491i	$0.731258\pi$
$294$	−3.75914	−0.219237
$295$	0.568413	0.0330943
$296$	10.6311	0.617923
$297$	−26.5079	−1.53815
$298$	−6.79135	−0.393412
$299$	17.2494	0.997557
$300$	−1.81588	−0.104840
$301$	−25.5335	−1.47172
$302$	1.17369	0.0675382
$303$	−16.9879	−0.975932
$304$	−6.91000	−0.396315
$305$	6.77344	0.387846
$306$	1.87867	0.107396
$307$	−4.61072	−0.263148	−0.131574	−	0.991306i	$-0.542003\pi$
$307$	−4.61072	−0.263148	−0.131574	+	0.991306i	$0.542003\pi$
$308$	16.2674	0.926920
$309$	8.46556	0.481589
$310$	6.61521	0.375719
$311$	21.5195	1.22026	0.610131	−	0.792301i	$-0.291117\pi$
$311$	21.5195	1.22026	0.610131	+	0.792301i	$0.291117\pi$
$312$	3.96451	0.224446
$313$	−7.49420	−0.423597	−0.211799	−	0.977313i	$-0.567932\pi$
$313$	−7.49420	−0.423597	−0.211799	+	0.977313i	$0.567932\pi$
$314$	−10.7628	−0.607381
$315$	−0.895747	−0.0504696
$316$	16.2146	0.912140
$317$	−15.0791	−0.846925	−0.423463	−	0.905914i	$-0.639186\pi$
$317$	−15.0791	−0.846925	−0.423463	+	0.905914i	$0.639186\pi$
$318$	11.0685	0.620688
$319$	13.0637	0.731424
$320$	1.00000	0.0559017
$321$	14.7322	0.822269
$322$	23.7946	1.32602
$323$	−43.6465	−2.42856
$324$	−9.80381	−0.544656
$325$	−2.18325	−0.121105
$326$	−0.816290	−0.0452101
$327$	30.1068	1.66491
$328$	9.90366	0.546838
$329$	38.5073	2.12297
$330$	9.80840	0.539935
$331$	23.0299	1.26584	0.632919	−	0.774218i	$-0.281856\pi$
$331$	23.0299	1.26584	0.632919	+	0.774218i	$0.281856\pi$
$332$	12.2377	0.671632
$333$	3.16197	0.173275
$334$	21.9666	1.20196
$335$	−3.56039	−0.194525
$336$	5.46883	0.298349
$337$	−4.43941	−0.241830	−0.120915	−	0.992663i	$-0.538583\pi$
$337$	−4.43941	−0.241830	−0.120915	+	0.992663i	$0.538583\pi$
$338$	−8.23344	−0.447840
$339$	5.58744	0.303468
$340$	6.31643	0.342557
$341$	−35.7317	−1.93498
$342$	−2.05521	−0.111133
$343$	14.8471	0.801667
$344$	8.47818	0.457113
$345$	14.3469	0.772412
$346$	−17.8206	−0.958042
$347$	−19.6593	−1.05537	−0.527683	−	0.849441i	$-0.676939\pi$
$347$	−19.6593	−1.05537	−0.527683	+	0.849441i	$0.676939\pi$
$348$	4.39179	0.235425
$349$	14.3939	0.770489	0.385244	−	0.922815i	$-0.374117\pi$
$349$	14.3939	0.770489	0.385244	+	0.922815i	$0.374117\pi$
$350$	−3.01167	−0.160980
$351$	−10.7144	−0.571892
$352$	−5.40145	−0.287898
$353$	−6.66992	−0.355004	−0.177502	−	0.984120i	$-0.556802\pi$
$353$	−6.66992	−0.355004	−0.177502	+	0.984120i	$0.556802\pi$
$354$	−1.03217	−0.0548592
$355$	4.92770	0.261535
$356$	3.75242	0.198878
$357$	34.5435	1.82824
$358$	12.0222	0.635390
$359$	15.9354	0.841039	0.420519	−	0.907284i	$-0.361848\pi$
$359$	15.9354	0.841039	0.420519	+	0.907284i	$0.361848\pi$
$360$	0.297426	0.0156757
$361$	28.7480	1.51305
$362$	20.6568	1.08570
$363$	−33.0049	−1.73231
$364$	6.57521	0.344635
$365$	13.1341	0.687469
$366$	−12.2998	−0.642919
$367$	−6.75272	−0.352489	−0.176245	−	0.984346i	$-0.556395\pi$
$367$	−6.75272	−0.352489	−0.176245	+	0.984346i	$0.556395\pi$
$368$	−7.90080	−0.411857
$369$	2.94560	0.153342
$370$	10.6311	0.552687
$371$	18.3572	0.953059
$372$	−12.0124	−0.622816
$373$	−9.82636	−0.508789	−0.254395	−	0.967100i	$-0.581876\pi$
$373$	−9.82636	−0.508789	−0.254395	+	0.967100i	$0.581876\pi$
$374$	−34.1179	−1.76420
$375$	−1.81588	−0.0937717
$376$	−12.7860	−0.659389
$377$	5.28028	0.271948
$378$	−14.7799	−0.760197
$379$	35.3746	1.81707	0.908535	−	0.417810i	$-0.137202\pi$
$379$	35.3746	1.81707	0.908535	+	0.417810i	$0.137202\pi$
$380$	−6.91000	−0.354475
$381$	−18.4720	−0.946348
$382$	4.67169	0.239025
$383$	−10.4960	−0.536323	−0.268161	−	0.963374i	$-0.586416\pi$
$383$	−10.4960	−0.536323	−0.268161	+	0.963374i	$0.586416\pi$
$384$	−1.81588	−0.0926663
$385$	16.2674	0.829063
$386$	−8.07217	−0.410863
$387$	2.52163	0.128182
$388$	−9.37889	−0.476141
$389$	−23.7589	−1.20462	−0.602311	−	0.798262i	$-0.705753\pi$
$389$	−23.7589	−1.20462	−0.602311	+	0.798262i	$0.705753\pi$
$390$	3.96451	0.200751
$391$	−49.9048	−2.52380
$392$	2.07014	0.104558
$393$	−18.1847	−0.917298
$394$	11.1515	0.561806
$395$	16.2146	0.815843
$396$	−1.60653	−0.0807312
$397$	−6.13836	−0.308076	−0.154038	−	0.988065i	$-0.549228\pi$
$397$	−6.13836	−0.308076	−0.154038	+	0.988065i	$0.549228\pi$
$398$	12.3680	0.619952
$399$	−37.7896	−1.89185
$400$	1.00000	0.0500000
$401$	1.00000	0.0499376
$401$	1.00000	0.0499376
$402$	6.46524	0.322457
$403$	−14.4426	−0.719438
$404$	9.35521	0.465439
$405$	−9.80381	−0.487155
$406$	7.28385	0.361492
$407$	−57.4236	−2.84638
$408$	−11.4699	−0.567844
$409$	15.0255	0.742962	0.371481	−	0.928440i	$-0.378850\pi$
$409$	15.0255	0.742962	0.371481	+	0.928440i	$0.378850\pi$
$410$	9.90366	0.489107
$411$	33.1393	1.63464
$412$	−4.66195	−0.229678
$413$	−1.71187	−0.0842357
$414$	−2.34990	−0.115491
$415$	12.2377	0.600726
$416$	−2.18325	−0.107042
$417$	27.8301	1.36285
$418$	37.3240	1.82558
$419$	−8.78504	−0.429177	−0.214589	−	0.976705i	$-0.568841\pi$
$419$	−8.78504	−0.429177	−0.214589	+	0.976705i	$0.568841\pi$
$420$	5.46883	0.266852
$421$	3.60306	0.175602	0.0878012	−	0.996138i	$-0.472016\pi$
$421$	3.60306	0.175602	0.0878012	+	0.996138i	$0.472016\pi$
$422$	−15.2620	−0.742942
$423$	−3.80289	−0.184903
$424$	−6.09536	−0.296017
$425$	6.31643	0.306392
$426$	−8.94811	−0.433538
$427$	−20.3994	−0.987194
$428$	−8.11296	−0.392154
$429$	−21.4141	−1.03388
$430$	8.47818	0.408854
$431$	6.47029	0.311663	0.155831	−	0.987784i	$-0.450194\pi$
$431$	6.47029	0.311663	0.155831	+	0.987784i	$0.450194\pi$
$432$	4.90755	0.236115
$433$	−24.2026	−1.16310	−0.581551	−	0.813510i	$-0.697554\pi$
$433$	−24.2026	−1.16310	−0.581551	+	0.813510i	$0.697554\pi$
$434$	−19.9228	−0.956326
$435$	4.39179	0.210570
$436$	−16.5797	−0.794024
$437$	54.5945	2.61161
$438$	−23.8499	−1.13959
$439$	30.0419	1.43382	0.716911	−	0.697164i	$-0.245555\pi$
$439$	30.0419	1.43382	0.716911	+	0.697164i	$0.245555\pi$
$440$	−5.40145	−0.257504
$441$	0.615714	0.0293197
$442$	−13.7903	−0.655939
$443$	−19.6662	−0.934370	−0.467185	−	0.884160i	$-0.654732\pi$
$443$	−19.6662	−0.934370	−0.467185	+	0.884160i	$0.654732\pi$
$444$	−19.3049	−0.916170
$445$	3.75242	0.177882
$446$	4.37811	0.207310
$447$	12.3323	0.583297
$448$	−3.01167	−0.142288
$449$	−35.9117	−1.69478	−0.847388	−	0.530974i	$-0.821826\pi$
$449$	−35.9117	−1.69478	−0.847388	+	0.530974i	$0.821826\pi$
$450$	0.297426	0.0140208
$451$	−53.4942	−2.51894
$452$	−3.07698	−0.144729
$453$	−2.13128	−0.100136
$454$	25.3945	1.19182
$455$	6.57521	0.308251
$456$	12.5477	0.587601
$457$	37.9370	1.77462	0.887309	−	0.461176i	$-0.152572\pi$
$457$	37.9370	1.77462	0.887309	+	0.461176i	$0.152572\pi$
$458$	19.7475	0.922739
$459$	30.9982	1.44687
$460$	−7.90080	−0.368376
$461$	−26.1979	−1.22016	−0.610080	−	0.792340i	$-0.708863\pi$
$461$	−26.1979	−1.22016	−0.610080	+	0.792340i	$0.708863\pi$
$462$	−29.5396	−1.37431
$463$	20.3556	0.946005	0.473002	−	0.881061i	$-0.343170\pi$
$463$	20.3556	0.946005	0.473002	+	0.881061i	$0.343170\pi$
$464$	−2.41854	−0.112278
$465$	−12.0124	−0.557063
$466$	5.39852	0.250082
$467$	16.6218	0.769167	0.384584	−	0.923090i	$-0.374345\pi$
$467$	16.6218	0.769167	0.384584	+	0.923090i	$0.374345\pi$
$468$	−0.649353	−0.0300164
$469$	10.7227	0.495128
$470$	−12.7860	−0.589776
$471$	19.5440	0.900540
$472$	0.568413	0.0261633
$473$	−45.7945	−2.10563
$474$	−29.4437	−1.35239
$475$	−6.91000	−0.317052
$476$	−19.0230	−0.871917
$477$	−1.81292	−0.0830078
$478$	13.4073	0.613236
$479$	−0.732653	−0.0334758	−0.0167379	−	0.999860i	$-0.505328\pi$
$479$	−0.732653	−0.0334758	−0.0167379	+	0.999860i	$0.505328\pi$
$480$	−1.81588	−0.0828833
$481$	−23.2104	−1.05830
$482$	−10.2946	−0.468908
$483$	−43.2081	−1.96604
$484$	18.1757	0.826169
$485$	−9.37889	−0.425874
$486$	3.07990	0.139707
$487$	10.3545	0.469205	0.234603	−	0.972091i	$-0.424621\pi$
$487$	10.3545	0.469205	0.234603	+	0.972091i	$0.424621\pi$
$488$	6.77344	0.306619
$489$	1.48229	0.0670313
$490$	2.07014	0.0935196
$491$	29.8674	1.34790	0.673949	−	0.738777i	$-0.264597\pi$
$491$	29.8674	1.34790	0.673949	+	0.738777i	$0.264597\pi$
$492$	−17.9839	−0.810776
$493$	−15.2766	−0.688022
$494$	15.0862	0.678761
$495$	−1.60653	−0.0722082
$496$	6.61521	0.297032
$497$	−14.8406	−0.665691
$498$	−22.2222	−0.995803
$499$	−7.95934	−0.356309	−0.178154	−	0.984003i	$-0.557013\pi$
$499$	−7.95934	−0.356309	−0.178154	+	0.984003i	$0.557013\pi$
$500$	1.00000	0.0447214
$501$	−39.8888	−1.78210
$502$	5.96246	0.266117
$503$	−34.7770	−1.55063	−0.775316	−	0.631574i	$-0.782409\pi$
$503$	−34.7770	−1.55063	−0.775316	+	0.631574i	$0.782409\pi$
$504$	−0.895747	−0.0398998
$505$	9.35521	0.416301
$506$	42.6758	1.89717
$507$	14.9510	0.663995
$508$	10.1725	0.451330
$509$	17.8749	0.792290	0.396145	−	0.918188i	$-0.370348\pi$
$509$	17.8749	0.792290	0.396145	+	0.918188i	$0.370348\pi$
$510$	−11.4699	−0.507895
$511$	−39.5555	−1.74983
$512$	1.00000	0.0441942
$513$	−33.9112	−1.49722
$514$	7.14153	0.314999
$515$	−4.66195	−0.205430
$516$	−15.3954	−0.677743
$517$	69.0631	3.03739
$518$	−32.0175	−1.40677
$519$	32.3601	1.42045
$520$	−2.18325	−0.0957416
$521$	6.00181	0.262944	0.131472	−	0.991320i	$-0.458030\pi$
$521$	6.00181	0.262944	0.131472	+	0.991320i	$0.458030\pi$
$522$	−0.719337	−0.0314845
$523$	30.3121	1.32545	0.662727	−	0.748861i	$-0.269399\pi$
$523$	30.3121	1.32545	0.662727	+	0.748861i	$0.269399\pi$
$524$	10.0143	0.437475
$525$	5.46883	0.238679
$526$	24.6160	1.07331
$527$	41.7845	1.82016
$528$	9.80840	0.426856
$529$	39.4226	1.71402
$530$	−6.09536	−0.264766
$531$	0.169061	0.00733661
$532$	20.8106	0.902254
$533$	−21.6221	−0.936558
$534$	−6.81395	−0.294869
$535$	−8.11296	−0.350754
$536$	−3.56039	−0.153785
$537$	−21.8308	−0.942069
$538$	−6.72613	−0.289984
$539$	−11.1818	−0.481634
$540$	4.90755	0.211188
$541$	16.5749	0.712613	0.356306	−	0.934369i	$-0.384036\pi$
$541$	16.5749	0.712613	0.356306	+	0.934369i	$0.384036\pi$
$542$	−5.89106	−0.253043
$543$	−37.5104	−1.60972
$544$	6.31643	0.270815
$545$	−16.5797	−0.710197
$546$	−11.9398	−0.510976
$547$	−10.0311	−0.428898	−0.214449	−	0.976735i	$-0.568796\pi$
$547$	−10.0311	−0.428898	−0.214449	+	0.976735i	$0.568796\pi$
$548$	−18.2497	−0.779589
$549$	2.01459	0.0859808
$550$	−5.40145	−0.230319
$551$	16.7121	0.711961
$552$	14.3469	0.610645
$553$	−48.8329	−2.07658
$554$	9.74267	0.413926
$555$	−19.3049	−0.819447
$556$	−15.3259	−0.649965
$557$	−14.9893	−0.635117	−0.317558	−	0.948239i	$-0.602863\pi$
$557$	−14.9893	−0.635117	−0.317558	+	0.948239i	$0.602863\pi$
$558$	1.96753	0.0832923
$559$	−18.5099	−0.782887
$560$	−3.01167	−0.127266
$561$	61.9541	2.61570
$562$	31.9484	1.34766
$563$	16.9542	0.714536	0.357268	−	0.934002i	$-0.383708\pi$
$563$	16.9542	0.714536	0.357268	+	0.934002i	$0.383708\pi$
$564$	23.2179	0.977650
$565$	−3.07698	−0.129450
$566$	−18.7617	−0.788613
$567$	29.5258	1.23997
$568$	4.92770	0.206762
$569$	−11.2145	−0.470136	−0.235068	−	0.971979i	$-0.575531\pi$
$569$	−11.2145	−0.470136	−0.235068	+	0.971979i	$0.575531\pi$
$570$	12.5477	0.525567
$571$	−12.4873	−0.522575	−0.261288	−	0.965261i	$-0.584147\pi$
$571$	−12.4873	−0.522575	−0.261288	+	0.965261i	$0.584147\pi$
$572$	11.7927	0.493078
$573$	−8.48324	−0.354392
$574$	−29.8265	−1.24494
$575$	−7.90080	−0.329486
$576$	0.297426	0.0123927
$577$	−29.3557	−1.22209	−0.611046	−	0.791595i	$-0.709251\pi$
$577$	−29.3557	−1.22209	−0.611046	+	0.791595i	$0.709251\pi$
$578$	22.8973	0.952402
$579$	14.6581	0.609170
$580$	−2.41854	−0.100425
$581$	−36.8559	−1.52904
$582$	17.0310	0.705956
$583$	32.9238	1.36357
$584$	13.1341	0.543492
$585$	−0.649353	−0.0268474
$586$	−22.7410	−0.939423
$587$	−23.3695	−0.964561	−0.482281	−	0.876017i	$-0.660191\pi$
$587$	−23.3695	−0.964561	−0.482281	+	0.876017i	$0.660191\pi$
$588$	−3.75914	−0.155024
$589$	−45.7111	−1.88349
$590$	0.568413	0.0234012
$591$	−20.2499	−0.832969
$592$	10.6311	0.436937
$593$	−21.9318	−0.900630	−0.450315	−	0.892870i	$-0.648688\pi$
$593$	−21.9318	−0.900630	−0.450315	+	0.892870i	$0.648688\pi$
$594$	−26.5079	−1.08763
$595$	−19.0230	−0.779867
$596$	−6.79135	−0.278185
$597$	−22.4588	−0.919178
$598$	17.2494	0.705379
$599$	6.67451	0.272713	0.136357	−	0.990660i	$-0.456461\pi$
$599$	6.67451	0.272713	0.136357	+	0.990660i	$0.456461\pi$
$600$	−1.81588	−0.0741331
$601$	−20.1528	−0.822051	−0.411025	−	0.911624i	$-0.634829\pi$
$601$	−20.1528	−0.822051	−0.411025	+	0.911624i	$0.634829\pi$
$602$	−25.5335	−1.04067
$603$	−1.05895	−0.0431238
$604$	1.17369	0.0477567
$605$	18.1757	0.738948
$606$	−16.9879	−0.690088
$607$	0.936778	0.0380226	0.0190113	−	0.999819i	$-0.493948\pi$
$607$	0.936778	0.0380226	0.0190113	+	0.999819i	$0.493948\pi$
$608$	−6.91000	−0.280237
$609$	−13.2266	−0.535969
$610$	6.77344	0.274249
$611$	27.9150	1.12932
$612$	1.87867	0.0759407
$613$	−8.57889	−0.346498	−0.173249	−	0.984878i	$-0.555427\pi$
$613$	−8.57889	−0.346498	−0.173249	+	0.984878i	$0.555427\pi$
$614$	−4.61072	−0.186073
$615$	−17.9839	−0.725180
$616$	16.2674	0.655432
$617$	10.8140	0.435354	0.217677	−	0.976021i	$-0.430152\pi$
$617$	10.8140	0.435354	0.217677	+	0.976021i	$0.430152\pi$
$618$	8.46556	0.340535
$619$	−23.7336	−0.953935	−0.476967	−	0.878921i	$-0.658264\pi$
$619$	−23.7336	−0.953935	−0.476967	+	0.878921i	$0.658264\pi$
$620$	6.61521	0.265673
$621$	−38.7736	−1.55593
$622$	21.5195	0.862855
$623$	−11.3010	−0.452767
$624$	3.96451	0.158708
$625$	1.00000	0.0400000
$626$	−7.49420	−0.299528
$627$	−67.7760	−2.70671
$628$	−10.7628	−0.429483
$629$	67.1509	2.67748
$630$	−0.895747	−0.0356874
$631$	5.90574	0.235104	0.117552	−	0.993067i	$-0.462495\pi$
$631$	5.90574	0.235104	0.117552	+	0.993067i	$0.462495\pi$
$632$	16.2146	0.644981
$633$	27.7140	1.10153
$634$	−15.0791	−0.598867
$635$	10.1725	0.403681
$636$	11.0685	0.438893
$637$	−4.51963	−0.179074
$638$	13.0637	0.517195
$639$	1.46562	0.0579792
$640$	1.00000	0.0395285
$641$	29.6628	1.17161	0.585805	−	0.810452i	$-0.300779\pi$
$641$	29.6628	1.17161	0.585805	+	0.810452i	$0.300779\pi$
$642$	14.7322	0.581432
$643$	8.36934	0.330055	0.165027	−	0.986289i	$-0.447229\pi$
$643$	8.36934	0.330055	0.165027	+	0.986289i	$0.447229\pi$
$644$	23.7946	0.937638
$645$	−15.3954	−0.606192
$646$	−43.6465	−1.71725
$647$	19.4599	0.765046	0.382523	−	0.923946i	$-0.375055\pi$
$647$	19.4599	0.765046	0.382523	+	0.923946i	$0.375055\pi$
$648$	−9.80381	−0.385130
$649$	−3.07026	−0.120518
$650$	−2.18325	−0.0856339
$651$	36.1775	1.41791
$652$	−0.816290	−0.0319684
$653$	−43.1133	−1.68715	−0.843577	−	0.537008i	$-0.819554\pi$
$653$	−43.1133	−1.68715	−0.843577	+	0.537008i	$0.819554\pi$
$654$	30.1068	1.17727
$655$	10.0143	0.391290
$656$	9.90366	0.386673
$657$	3.90641	0.152404
$658$	38.5073	1.50117
$659$	−0.0191090	−0.000744381 0	−0.000372191	−	1.00000i	$-0.500118\pi$
$659$	−0.0191090	−0.000744381 0	−0.000372191		1.00000i	$0.500118\pi$
$660$	9.80840	0.381791
$661$	34.2330	1.33151	0.665754	−	0.746171i	$-0.268110\pi$
$661$	34.2330	1.33151	0.665754	+	0.746171i	$0.268110\pi$
$662$	23.0299	0.895083
$663$	25.0416	0.972535
$664$	12.2377	0.474916
$665$	20.8106	0.807001
$666$	3.16197	0.122524
$667$	19.1084	0.739881
$668$	21.9666	0.849915
$669$	−7.95014	−0.307370
$670$	−3.56039	−0.137550
$671$	−36.5864	−1.41240
$672$	5.46883	0.210965
$673$	10.2976	0.396942	0.198471	−	0.980107i	$-0.436402\pi$
$673$	10.2976	0.396942	0.198471	+	0.980107i	$0.436402\pi$
$674$	−4.43941	−0.171000
$675$	4.90755	0.188892
$676$	−8.23344	−0.316671
$677$	19.2778	0.740906	0.370453	−	0.928851i	$-0.379202\pi$
$677$	19.2778	0.740906	0.370453	+	0.928851i	$0.379202\pi$
$678$	5.58744	0.214584
$679$	28.2461	1.08399
$680$	6.31643	0.242224
$681$	−46.1134	−1.76707
$682$	−35.7317	−1.36824
$683$	−25.5930	−0.979287	−0.489644	−	0.871923i	$-0.662873\pi$
$683$	−25.5930	−0.979287	−0.489644	+	0.871923i	$0.662873\pi$
$684$	−2.05521	−0.0785829
$685$	−18.2497	−0.697286
$686$	14.8471	0.566864
$687$	−35.8591	−1.36811
$688$	8.47818	0.323227
$689$	13.3077	0.506982
$690$	14.3469	0.546177
$691$	−18.9217	−0.719817	−0.359908	−	0.932988i	$-0.617192\pi$
$691$	−18.9217	−0.719817	−0.359908	+	0.932988i	$0.617192\pi$
$692$	−17.8206	−0.677438
$693$	4.83834	0.183793
$694$	−19.6593	−0.746257
$695$	−15.3259	−0.581346
$696$	4.39179	0.166470
$697$	62.5558	2.36947
$698$	14.3939	0.544818
$699$	−9.80308	−0.370786
$700$	−3.01167	−0.113830
$701$	20.9720	0.792101	0.396050	−	0.918229i	$-0.370381\pi$
$701$	20.9720	0.792101	0.396050	+	0.918229i	$0.370381\pi$
$702$	−10.7144	−0.404389
$703$	−73.4611	−2.77064
$704$	−5.40145	−0.203575
$705$	23.2179	0.874437
$706$	−6.66992	−0.251026
$707$	−28.1748	−1.05962
$708$	−1.03217	−0.0387913
$709$	−49.7059	−1.86675	−0.933373	−	0.358908i	$-0.883149\pi$
$709$	−49.7059	−1.86675	−0.933373	+	0.358908i	$0.883149\pi$
$710$	4.92770	0.184933
$711$	4.82263	0.180863
$712$	3.75242	0.140628
$713$	−52.2654	−1.95735
$714$	34.5435	1.29276
$715$	11.7927	0.441022
$716$	12.0222	0.449289
$717$	−24.3461	−0.909221
$718$	15.9354	0.594704
$719$	1.66011	0.0619117	0.0309559	−	0.999521i	$-0.490145\pi$
$719$	1.66011	0.0619117	0.0309559	+	0.999521i	$0.490145\pi$
$720$	0.297426	0.0110844
$721$	14.0403	0.522887
$722$	28.7480	1.06989
$723$	18.6938	0.695231
$724$	20.6568	0.767705
$725$	−2.41854	−0.0898225
$726$	−33.0049	−1.22493
$727$	26.8027	0.994057	0.497029	−	0.867734i	$-0.334424\pi$
$727$	26.8027	0.994057	0.497029	+	0.867734i	$0.334424\pi$
$728$	6.57521	0.243694
$729$	23.8187	0.882174
$730$	13.1341	0.486114
$731$	53.5518	1.98069
$732$	−12.2998	−0.454612
$733$	31.3252	1.15702	0.578511	−	0.815674i	$-0.303634\pi$
$733$	31.3252	1.15702	0.578511	+	0.815674i	$0.303634\pi$
$734$	−6.75272	−0.249248
$735$	−3.75914	−0.138658
$736$	−7.90080	−0.291227
$737$	19.2313	0.708393
$738$	2.94560	0.108429
$739$	46.5838	1.71361	0.856806	−	0.515638i	$-0.172445\pi$
$739$	46.5838	1.71361	0.856806	+	0.515638i	$0.172445\pi$
$740$	10.6311	0.390809
$741$	−27.3948	−1.00637
$742$	18.3572	0.673914
$743$	−19.8996	−0.730047	−0.365023	−	0.930998i	$-0.618939\pi$
$743$	−19.8996	−0.730047	−0.365023	+	0.930998i	$0.618939\pi$
$744$	−12.0124	−0.440397
$745$	−6.79135	−0.248816
$746$	−9.82636	−0.359768
$747$	3.63981	0.133174
$748$	−34.1179	−1.24747
$749$	24.4335	0.892782
$750$	−1.81588	−0.0663066
$751$	−33.1244	−1.20872	−0.604362	−	0.796710i	$-0.706572\pi$
$751$	−33.1244	−1.20872	−0.604362	+	0.796710i	$0.706572\pi$
$752$	−12.7860	−0.466258
$753$	−10.8271	−0.394562
$754$	5.28028	0.192296
$755$	1.17369	0.0427149
$756$	−14.7799	−0.537541
$757$	−9.71471	−0.353087	−0.176544	−	0.984293i	$-0.556492\pi$
$757$	−9.71471	−0.353087	−0.176544	+	0.984293i	$0.556492\pi$
$758$	35.3746	1.28486
$759$	−77.4942	−2.81286
$760$	−6.91000	−0.250652
$761$	−20.5537	−0.745072	−0.372536	−	0.928018i	$-0.621512\pi$
$761$	−20.5537	−0.745072	−0.372536	+	0.928018i	$0.621512\pi$
$762$	−18.4720	−0.669169
$763$	49.9326	1.80768
$764$	4.67169	0.169016
$765$	1.87867	0.0679234
$766$	−10.4960	−0.379237
$767$	−1.24098	−0.0448094
$768$	−1.81588	−0.0655250
$769$	33.0178	1.19065	0.595325	−	0.803485i	$-0.297023\pi$
$769$	33.0178	1.19065	0.595325	+	0.803485i	$0.297023\pi$
$770$	16.2674	0.586236
$771$	−12.9682	−0.467037
$772$	−8.07217	−0.290524
$773$	18.4219	0.662589	0.331295	−	0.943527i	$-0.392515\pi$
$773$	18.4219	0.662589	0.331295	+	0.943527i	$0.392515\pi$
$774$	2.52163	0.0906380
$775$	6.61521	0.237625
$776$	−9.37889	−0.336683
$777$	58.1399	2.08576
$778$	−23.7589	−0.851796
$779$	−68.4342	−2.45191
$780$	3.96451	0.141952
$781$	−26.6167	−0.952422
$782$	−49.9048	−1.78459
$783$	−11.8691	−0.424168
$784$	2.07014	0.0739337
$785$	−10.7628	−0.384141
$786$	−18.1847	−0.648628
$787$	37.5608	1.33890	0.669449	−	0.742858i	$-0.266530\pi$
$787$	37.5608	1.33890	0.669449	+	0.742858i	$0.266530\pi$
$788$	11.1515	0.397257
$789$	−44.6997	−1.59135
$790$	16.2146	0.576888
$791$	9.26686	0.329491
$792$	−1.60653	−0.0570856
$793$	−14.7881	−0.525140
$794$	−6.13836	−0.217842
$795$	11.0685	0.392558
$796$	12.3680	0.438372
$797$	23.7942	0.842833	0.421416	−	0.906867i	$-0.361533\pi$
$797$	23.7942	0.842833	0.421416	+	0.906867i	$0.361533\pi$
$798$	−37.7896	−1.33774
$799$	−80.7621	−2.85716
$800$	1.00000	0.0353553
$801$	1.11607	0.0394343
$802$	1.00000	0.0353112
$803$	−70.9432	−2.50353
$804$	6.46524	0.228011
$805$	23.7946	0.838648
$806$	−14.4426	−0.508720
$807$	12.2139	0.429948
$808$	9.35521	0.329115
$809$	17.0734	0.600269	0.300135	−	0.953897i	$-0.402968\pi$
$809$	17.0734	0.600269	0.300135	+	0.953897i	$0.402968\pi$
$810$	−9.80381	−0.344471
$811$	−19.5229	−0.685542	−0.342771	−	0.939419i	$-0.611365\pi$
$811$	−19.5229	−0.685542	−0.342771	+	0.939419i	$0.611365\pi$
$812$	7.28385	0.255613
$813$	10.6975	0.375177
$814$	−57.4236	−2.01270
$815$	−0.816290	−0.0285934
$816$	−11.4699	−0.401526
$817$	−58.5842	−2.04960
$818$	15.0255	0.525354
$819$	1.95564	0.0683355
$820$	9.90366	0.345851
$821$	23.3171	0.813773	0.406887	−	0.913479i	$-0.366614\pi$
$821$	23.3171	0.813773	0.406887	+	0.913479i	$0.366614\pi$
$822$	33.1393	1.15587
$823$	−20.4840	−0.714028	−0.357014	−	0.934099i	$-0.616205\pi$
$823$	−20.4840	−0.714028	−0.357014	+	0.934099i	$0.616205\pi$
$824$	−4.66195	−0.162407
$825$	9.80840	0.341485
$826$	−1.71187	−0.0595636
$827$	23.7625	0.826304	0.413152	−	0.910662i	$-0.364428\pi$
$827$	23.7625	0.826304	0.413152	+	0.910662i	$0.364428\pi$
$828$	−2.34990	−0.0816646
$829$	29.7912	1.03469	0.517345	−	0.855777i	$-0.326920\pi$
$829$	29.7912	1.03469	0.517345	+	0.855777i	$0.326920\pi$
$830$	12.2377	0.424777
$831$	−17.6915	−0.613712
$832$	−2.18325	−0.0756904
$833$	13.0759	0.453054
$834$	27.8301	0.963678
$835$	21.9666	0.760187
$836$	37.3240	1.29088
$837$	32.4645	1.12214
$838$	−8.78504	−0.303474
$839$	−47.6827	−1.64619	−0.823095	−	0.567904i	$-0.807755\pi$
$839$	−47.6827	−1.64619	−0.823095	+	0.567904i	$0.807755\pi$
$840$	5.46883	0.188693
$841$	−23.1506	−0.798298
$842$	3.60306	0.124170
$843$	−58.0145	−1.99812
$844$	−15.2620	−0.525339
$845$	−8.23344	−0.283239
$846$	−3.80289	−0.130746
$847$	−54.7392	−1.88086
$848$	−6.09536	−0.209316
$849$	34.0690	1.16925
$850$	6.31643	0.216652
$851$	−83.9945	−2.87929
$852$	−8.94811	−0.306557
$853$	47.2478	1.61773	0.808866	−	0.587992i	$-0.200082\pi$
$853$	47.2478	1.61773	0.808866	+	0.587992i	$0.200082\pi$
$854$	−20.3994	−0.698051
$855$	−2.05521	−0.0702867
$856$	−8.11296	−0.277295
$857$	−22.2105	−0.758696	−0.379348	−	0.925254i	$-0.623852\pi$
$857$	−22.2105	−0.758696	−0.379348	+	0.925254i	$0.623852\pi$
$858$	−21.4141	−0.731067
$859$	−36.4784	−1.24463	−0.622314	−	0.782768i	$-0.713807\pi$
$859$	−36.4784	−1.24463	−0.622314	+	0.782768i	$0.713807\pi$
$860$	8.47818	0.289103
$861$	54.1615	1.84582
$862$	6.47029	0.220379
$863$	−24.3125	−0.827609	−0.413804	−	0.910366i	$-0.635800\pi$
$863$	−24.3125	−0.827609	−0.413804	+	0.910366i	$0.635800\pi$
$864$	4.90755	0.166958
$865$	−17.8206	−0.605919
$866$	−24.2026	−0.822437
$867$	−41.5788	−1.41209
$868$	−19.9228	−0.676224
$869$	−87.5822	−2.97102
$870$	4.39179	0.148896
$871$	7.77319	0.263385
$872$	−16.5797	−0.561460
$873$	−2.78952	−0.0944111
$874$	54.5945	1.84669
$875$	−3.01167	−0.101813
$876$	−23.8499	−0.805815
$877$	36.2777	1.22501	0.612506	−	0.790466i	$-0.290162\pi$
$877$	36.2777	1.22501	0.612506	+	0.790466i	$0.290162\pi$
$878$	30.0419	1.01387
$879$	41.2950	1.39285
$880$	−5.40145	−0.182083
$881$	15.7596	0.530953	0.265477	−	0.964117i	$-0.414471\pi$
$881$	15.7596	0.530953	0.265477	+	0.964117i	$0.414471\pi$
$882$	0.615714	0.0207322
$883$	13.0973	0.440759	0.220380	−	0.975414i	$-0.429270\pi$
$883$	13.0973	0.440759	0.220380	+	0.975414i	$0.429270\pi$
$884$	−13.7903	−0.463819
$885$	−1.03217	−0.0346960
$886$	−19.6662	−0.660699
$887$	−55.7675	−1.87249	−0.936245	−	0.351348i	$-0.885723\pi$
$887$	−55.7675	−1.87249	−0.936245	+	0.351348i	$0.885723\pi$
$888$	−19.3049	−0.647830
$889$	−30.6360	−1.02750
$890$	3.75242	0.125781
$891$	52.9549	1.77405
$892$	4.37811	0.146590
$893$	88.3514	2.95657
$894$	12.3323	0.412453
$895$	12.0222	0.401856
$896$	−3.01167	−0.100613
$897$	−31.3228	−1.04584
$898$	−35.9117	−1.19839
$899$	−15.9992	−0.533602
$900$	0.297426	0.00991419
$901$	−38.5009	−1.28265
$902$	−53.4942	−1.78116
$903$	46.3657	1.54295
$904$	−3.07698	−0.102339
$905$	20.6568	0.686657
$906$	−2.13128	−0.0708070
$907$	−1.82491	−0.0605950	−0.0302975	−	0.999541i	$-0.509645\pi$
$907$	−1.82491	−0.0605950	−0.0302975	+	0.999541i	$0.509645\pi$
$908$	25.3945	0.842746
$909$	2.78248	0.0922890
$910$	6.57521	0.217966
$911$	36.5006	1.20932	0.604660	−	0.796484i	$-0.293309\pi$
$911$	36.5006	1.20932	0.604660	+	0.796484i	$0.293309\pi$
$912$	12.5477	0.415497
$913$	−66.1015	−2.18764
$914$	37.9370	1.25484
$915$	−12.2998	−0.406618
$916$	19.7475	0.652475
$917$	−30.1597	−0.995960
$918$	30.9982	1.02309
$919$	−4.56464	−0.150574	−0.0752868	−	0.997162i	$-0.523987\pi$
$919$	−4.56464	−0.150574	−0.0752868	+	0.997162i	$0.523987\pi$
$920$	−7.90080	−0.260482
$921$	8.37252	0.275884
$922$	−26.1979	−0.862783
$923$	−10.7584	−0.354116
$924$	−29.5396	−0.971783
$925$	10.6311	0.349550
$926$	20.3556	0.668926
$927$	−1.38659	−0.0455414
$928$	−2.41854	−0.0793926
$929$	−13.3671	−0.438560	−0.219280	−	0.975662i	$-0.570371\pi$
$929$	−13.3671	−0.438560	−0.219280	+	0.975662i	$0.570371\pi$
$930$	−12.0124	−0.393903
$931$	−14.3047	−0.468817
$932$	5.39852	0.176834
$933$	−39.0769	−1.27932
$934$	16.6218	0.543884
$935$	−34.1179	−1.11578
$936$	−0.649353	−0.0212248
$937$	21.8481	0.713745	0.356873	−	0.934153i	$-0.383843\pi$
$937$	21.8481	0.713745	0.356873	+	0.934153i	$0.383843\pi$
$938$	10.7227	0.350109
$939$	13.6086	0.444099
$940$	−12.7860	−0.417034
$941$	8.71108	0.283973	0.141986	−	0.989869i	$-0.454651\pi$
$941$	8.71108	0.283973	0.141986	+	0.989869i	$0.454651\pi$
$942$	19.5440	0.636778
$943$	−78.2468	−2.54807
$944$	0.568413	0.0185003
$945$	−14.7799	−0.480791
$946$	−45.7945	−1.48891
$947$	−6.69199	−0.217460	−0.108730	−	0.994071i	$-0.534678\pi$
$947$	−6.69199	−0.217460	−0.108730	+	0.994071i	$0.534678\pi$
$948$	−29.4437	−0.956288
$949$	−28.6749	−0.930828
$950$	−6.91000	−0.224190
$951$	27.3818	0.887916
$952$	−19.0230	−0.616539
$953$	27.3771	0.886831	0.443416	−	0.896316i	$-0.353767\pi$
$953$	27.3771	0.886831	0.443416	+	0.896316i	$0.353767\pi$
$954$	−1.81292	−0.0586954
$955$	4.67169	0.151172
$956$	13.4073	0.433623
$957$	−23.7221	−0.766825
$958$	−0.732653	−0.0236710
$959$	54.9621	1.77482
$960$	−1.81588	−0.0586073
$961$	12.7610	0.411644
$962$	−23.2104	−0.748333
$963$	−2.41300	−0.0777579
$964$	−10.2946	−0.331568
$965$	−8.07217	−0.259852
$966$	−43.2081	−1.39020
$967$	38.3011	1.23168	0.615841	−	0.787871i	$-0.288817\pi$
$967$	38.3011	1.23168	0.615841	+	0.787871i	$0.288817\pi$
$968$	18.1757	0.584189
$969$	79.2569	2.54610
$970$	−9.37889	−0.301138
$971$	−11.7577	−0.377321	−0.188661	−	0.982042i	$-0.560415\pi$
$971$	−11.7577	−0.377321	−0.188661	+	0.982042i	$0.560415\pi$
$972$	3.07990	0.0987879
$973$	46.1567	1.47971
$974$	10.3545	0.331778
$975$	3.96451	0.126966
$976$	6.77344	0.216813
$977$	−3.80149	−0.121621	−0.0608103	−	0.998149i	$-0.519368\pi$
$977$	−3.80149	−0.121621	−0.0608103	+	0.998149i	$0.519368\pi$
$978$	1.48229	0.0473983
$979$	−20.2685	−0.647785
$980$	2.07014	0.0661283
$981$	−4.93123	−0.157442
$982$	29.8674	0.953108
$983$	−32.8165	−1.04669	−0.523343	−	0.852122i	$-0.675315\pi$
$983$	−32.8165	−1.04669	−0.523343	+	0.852122i	$0.675315\pi$
$984$	−17.9839	−0.573305
$985$	11.1515	0.355318
$986$	−15.2766	−0.486505
$987$	−69.9246	−2.22573
$988$	15.0862	0.479956
$989$	−66.9843	−2.12998
$990$	−1.60653	−0.0510589
$991$	26.4225	0.839339	0.419670	−	0.907677i	$-0.362146\pi$
$991$	26.4225	0.839339	0.419670	+	0.907677i	$0.362146\pi$
$992$	6.61521	0.210033
$993$	−41.8196	−1.32711
$994$	−14.8406	−0.470715
$995$	12.3680	0.392092
$996$	−22.2222	−0.704139
$997$	−30.8465	−0.976919	−0.488460	−	0.872587i	$-0.662441\pi$
$997$	−30.8465	−0.976919	−0.488460	+	0.872587i	$0.662441\pi$
$998$	−7.95934	−0.251948
$999$	52.1729	1.65068

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4010.2.a.n.1.6	✓	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4010.2.a.n.1.6	✓	22	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:	\( N \)	\(=\)	\( 4010 = 2 \cdot 5 \cdot 401 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4010.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.81588 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.81588 q^{6} -3.01167 q^{7} +1.00000 q^{8} +0.297426 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.81588 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.81588 q^{6} -3.01167 q^{7} +1.00000 q^{8} +0.297426 q^{9} +1.00000 q^{10} -5.40145 q^{11} -1.81588 q^{12} -2.18325 q^{13} -3.01167 q^{14} -1.81588 q^{15} +1.00000 q^{16} +6.31643 q^{17} +0.297426 q^{18} -6.91000 q^{19} +1.00000 q^{20} +5.46883 q^{21} -5.40145 q^{22} -7.90080 q^{23} -1.81588 q^{24} +1.00000 q^{25} -2.18325 q^{26} +4.90755 q^{27} -3.01167 q^{28} -2.41854 q^{29} -1.81588 q^{30} +6.61521 q^{31} +1.00000 q^{32} +9.80840 q^{33} +6.31643 q^{34} -3.01167 q^{35} +0.297426 q^{36} +10.6311 q^{37} -6.91000 q^{38} +3.96451 q^{39} +1.00000 q^{40} +9.90366 q^{41} +5.46883 q^{42} +8.47818 q^{43} -5.40145 q^{44} +0.297426 q^{45} -7.90080 q^{46} -12.7860 q^{47} -1.81588 q^{48} +2.07014 q^{49} +1.00000 q^{50} -11.4699 q^{51} -2.18325 q^{52} -6.09536 q^{53} +4.90755 q^{54} -5.40145 q^{55} -3.01167 q^{56} +12.5477 q^{57} -2.41854 q^{58} +0.568413 q^{59} -1.81588 q^{60} +6.77344 q^{61} +6.61521 q^{62} -0.895747 q^{63} +1.00000 q^{64} -2.18325 q^{65} +9.80840 q^{66} -3.56039 q^{67} +6.31643 q^{68} +14.3469 q^{69} -3.01167 q^{70} +4.92770 q^{71} +0.297426 q^{72} +13.1341 q^{73} +10.6311 q^{74} -1.81588 q^{75} -6.91000 q^{76} +16.2674 q^{77} +3.96451 q^{78} +16.2146 q^{79} +1.00000 q^{80} -9.80381 q^{81} +9.90366 q^{82} +12.2377 q^{83} +5.46883 q^{84} +6.31643 q^{85} +8.47818 q^{86} +4.39179 q^{87} -5.40145 q^{88} +3.75242 q^{89} +0.297426 q^{90} +6.57521 q^{91} -7.90080 q^{92} -12.0124 q^{93} -12.7860 q^{94} -6.91000 q^{95} -1.81588 q^{96} -9.37889 q^{97} +2.07014 q^{98} -1.60653 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + 22 q^{2} + q^{3} + 22 q^{4} + 22 q^{5} + q^{6} + 22 q^{8} + 43 q^{9}+O(q^{10}) \) 22 * q + 22 * q^2 + q^3 + 22 * q^4 + 22 * q^5 + q^6 + 22 * q^8 + 43 * q^9	\( 22 q + 22 q^{2} + q^{3} + 22 q^{4} + 22 q^{5} + q^{6} + 22 q^{8} + 43 q^{9} + 22 q^{10} + 12 q^{11} + q^{12} + 10 q^{13} + q^{15} + 22 q^{16} + 24 q^{17} + 43 q^{18} + 13 q^{19} + 22 q^{20} + 13 q^{21} + 12 q^{22} + 7 q^{23} + q^{24} + 22 q^{25} + 10 q^{26} - 5 q^{27} + 22 q^{29} + q^{30} + 14 q^{31} + 22 q^{32} + 31 q^{33} + 24 q^{34} + 43 q^{36} + 35 q^{37} + 13 q^{38} + 4 q^{39} + 22 q^{40} + 29 q^{41} + 13 q^{42} + 7 q^{43} + 12 q^{44} + 43 q^{45} + 7 q^{46} - 21 q^{47} + q^{48} + 32 q^{49} + 22 q^{50} - 6 q^{51} + 10 q^{52} + 29 q^{53} - 5 q^{54} + 12 q^{55} - 13 q^{57} + 22 q^{58} + 12 q^{59} + q^{60} + 24 q^{61} + 14 q^{62} - 8 q^{63} + 22 q^{64} + 10 q^{65} + 31 q^{66} + 25 q^{67} + 24 q^{68} + 3 q^{69} + 31 q^{71} + 43 q^{72} + 30 q^{73} + 35 q^{74} + q^{75} + 13 q^{76} + 10 q^{77} + 4 q^{78} + 35 q^{79} + 22 q^{80} + 74 q^{81} + 29 q^{82} - 33 q^{83} + 13 q^{84} + 24 q^{85} + 7 q^{86} - 24 q^{87} + 12 q^{88} + 38 q^{89} + 43 q^{90} - 32 q^{91} + 7 q^{92} + 3 q^{93} - 21 q^{94} + 13 q^{95} + q^{96} + 11 q^{97} + 32 q^{98} - 41 q^{99}+O(q^{100}) \) 22 * q + 22 * q^2 + q^3 + 22 * q^4 + 22 * q^5 + q^6 + 22 * q^8 + 43 * q^9 + 22 * q^10 + 12 * q^11 + q^12 + 10 * q^13 + q^15 + 22 * q^16 + 24 * q^17 + 43 * q^18 + 13 * q^19 + 22 * q^20 + 13 * q^21 + 12 * q^22 + 7 * q^23 + q^24 + 22 * q^25 + 10 * q^26 - 5 * q^27 + 22 * q^29 + q^30 + 14 * q^31 + 22 * q^32 + 31 * q^33 + 24 * q^34 + 43 * q^36 + 35 * q^37 + 13 * q^38 + 4 * q^39 + 22 * q^40 + 29 * q^41 + 13 * q^42 + 7 * q^43 + 12 * q^44 + 43 * q^45 + 7 * q^46 - 21 * q^47 + q^48 + 32 * q^49 + 22 * q^50 - 6 * q^51 + 10 * q^52 + 29 * q^53 - 5 * q^54 + 12 * q^55 - 13 * q^57 + 22 * q^58 + 12 * q^59 + q^60 + 24 * q^61 + 14 * q^62 - 8 * q^63 + 22 * q^64 + 10 * q^65 + 31 * q^66 + 25 * q^67 + 24 * q^68 + 3 * q^69 + 31 * q^71 + 43 * q^72 + 30 * q^73 + 35 * q^74 + q^75 + 13 * q^76 + 10 * q^77 + 4 * q^78 + 35 * q^79 + 22 * q^80 + 74 * q^81 + 29 * q^82 - 33 * q^83 + 13 * q^84 + 24 * q^85 + 7 * q^86 - 24 * q^87 + 12 * q^88 + 38 * q^89 + 43 * q^90 - 32 * q^91 + 7 * q^92 + 3 * q^93 - 21 * q^94 + 13 * q^95 + q^96 + 11 * q^97 + 32 * q^98 - 41 * q^99

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