LMFDB - Embedded newform 722.2.a.n.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [722,2,Mod(1,722)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(722, 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("722.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 722 = 2 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	722.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:	$5.76519902594$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{20})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 5x^{2} + 5 $ x^4 - 5*x^2 + 5
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$1.90211$ of defining polynomial
Character	$\chi$	$=$	722.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +2.79360 q^{3} +1.00000 q^{4} -2.34458 q^{5} +2.79360 q^{6} -1.28408 q^{7} +1.00000 q^{8} +4.80423 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +2.79360 q^{3} +1.00000 q^{4} -2.34458 q^{5} +2.79360 q^{6} -1.28408 q^{7} +1.00000 q^{8} +4.80423 q^{9} -2.34458 q^{10} +5.75621 q^{11} +2.79360 q^{12} +0.304282 q^{13} -1.28408 q^{14} -6.54982 q^{15} +1.00000 q^{16} +4.18619 q^{17} +4.80423 q^{18} -2.34458 q^{20} -3.58721 q^{21} +5.75621 q^{22} -6.47684 q^{23} +2.79360 q^{24} +0.497039 q^{25} +0.304282 q^{26} +5.04029 q^{27} -1.28408 q^{28} -3.12756 q^{29} -6.54982 q^{30} +6.44246 q^{31} +1.00000 q^{32} +16.0806 q^{33} +4.18619 q^{34} +3.01062 q^{35} +4.80423 q^{36} -3.97980 q^{37} +0.850045 q^{39} -2.34458 q^{40} -5.01719 q^{41} -3.58721 q^{42} -0.989378 q^{43} +5.75621 q^{44} -11.2639 q^{45} -6.47684 q^{46} -4.39445 q^{47} +2.79360 q^{48} -5.35114 q^{49} +0.497039 q^{50} +11.6946 q^{51} +0.304282 q^{52} +3.29064 q^{53} +5.04029 q^{54} -13.4959 q^{55} -1.28408 q^{56} -3.12756 q^{58} +3.31375 q^{59} -6.54982 q^{60} -10.9615 q^{61} +6.44246 q^{62} -6.16901 q^{63} +1.00000 q^{64} -0.713414 q^{65} +16.0806 q^{66} -4.38081 q^{67} +4.18619 q^{68} -18.0937 q^{69} +3.01062 q^{70} -4.41570 q^{71} +4.80423 q^{72} -2.26689 q^{73} -3.97980 q^{74} +1.38853 q^{75} -7.39144 q^{77} +0.850045 q^{78} +8.57659 q^{79} -2.34458 q^{80} -0.332090 q^{81} -5.01719 q^{82} -9.76464 q^{83} -3.58721 q^{84} -9.81485 q^{85} -0.989378 q^{86} -8.73716 q^{87} +5.75621 q^{88} -15.0765 q^{89} -11.2639 q^{90} -0.390723 q^{91} -6.47684 q^{92} +17.9977 q^{93} -4.39445 q^{94} +2.79360 q^{96} +17.3522 q^{97} -5.35114 q^{98} +27.6542 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} + 2 q^{3} + 4 q^{4} - 2 q^{5} + 2 q^{6} - 2 q^{7} + 4 q^{8} + 4 q^{9}+O(q^{10}) $ 4 * q + 4 * q^2 + 2 * q^3 + 4 * q^4 - 2 * q^5 + 2 * q^6 - 2 * q^7 + 4 * q^8 + 4 * q^9	\( 4 q + 4 q^{2} + 2 q^{3} + 4 q^{4} - 2 q^{5} + 2 q^{6} - 2 q^{7} + 4 q^{8} + 4 q^{9} - 2 q^{10} + 2 q^{11} + 2 q^{12} + 18 q^{13} - 2 q^{14} + 4 q^{15} + 4 q^{16} + 6 q^{17} + 4 q^{18} - 2 q^{20} + 4 q^{21} + 2 q^{22} - 10 q^{23} + 2 q^{24} + 6 q^{25} + 18 q^{26} - 4 q^{27} - 2 q^{28} - 2 q^{29} + 4 q^{30} + 26 q^{31} + 4 q^{32} + 16 q^{33} + 6 q^{34} + 6 q^{35} + 4 q^{36} + 4 q^{37} - 6 q^{39} - 2 q^{40} - 12 q^{41} + 4 q^{42} - 10 q^{43} + 2 q^{44} - 22 q^{45} - 10 q^{46} - 12 q^{47} + 2 q^{48} - 12 q^{49} + 6 q^{50} - 2 q^{51} + 18 q^{52} + 8 q^{53} - 4 q^{54} - 26 q^{55} - 2 q^{56} - 2 q^{58} - 8 q^{59} + 4 q^{60} + 26 q^{62} - 22 q^{63} + 4 q^{64} - 4 q^{65} + 16 q^{66} + 10 q^{67} + 6 q^{68} - 20 q^{69} + 6 q^{70} + 4 q^{72} - 14 q^{73} + 4 q^{74} + 8 q^{75} + 4 q^{77} - 6 q^{78} + 22 q^{79} - 2 q^{80} - 4 q^{81} - 12 q^{82} - 12 q^{83} + 4 q^{84} - 18 q^{85} - 10 q^{86} - 26 q^{87} + 2 q^{88} - 16 q^{89} - 22 q^{90} - 4 q^{91} - 10 q^{92} + 8 q^{93} - 12 q^{94} + 2 q^{96} + 28 q^{97} - 12 q^{98} + 22 q^{99}+O(q^{100}) \) 4 * q + 4 * q^2 + 2 * q^3 + 4 * q^4 - 2 * q^5 + 2 * q^6 - 2 * q^7 + 4 * q^8 + 4 * q^9 - 2 * q^10 + 2 * q^11 + 2 * q^12 + 18 * q^13 - 2 * q^14 + 4 * q^15 + 4 * q^16 + 6 * q^17 + 4 * q^18 - 2 * q^20 + 4 * q^21 + 2 * q^22 - 10 * q^23 + 2 * q^24 + 6 * q^25 + 18 * q^26 - 4 * q^27 - 2 * q^28 - 2 * q^29 + 4 * q^30 + 26 * q^31 + 4 * q^32 + 16 * q^33 + 6 * q^34 + 6 * q^35 + 4 * q^36 + 4 * q^37 - 6 * q^39 - 2 * q^40 - 12 * q^41 + 4 * q^42 - 10 * q^43 + 2 * q^44 - 22 * q^45 - 10 * q^46 - 12 * q^47 + 2 * q^48 - 12 * q^49 + 6 * q^50 - 2 * q^51 + 18 * q^52 + 8 * q^53 - 4 * q^54 - 26 * q^55 - 2 * q^56 - 2 * q^58 - 8 * q^59 + 4 * q^60 + 26 * q^62 - 22 * q^63 + 4 * q^64 - 4 * q^65 + 16 * q^66 + 10 * q^67 + 6 * q^68 - 20 * q^69 + 6 * q^70 + 4 * q^72 - 14 * q^73 + 4 * q^74 + 8 * q^75 + 4 * q^77 - 6 * q^78 + 22 * q^79 - 2 * q^80 - 4 * q^81 - 12 * q^82 - 12 * q^83 + 4 * q^84 - 18 * q^85 - 10 * q^86 - 26 * q^87 + 2 * q^88 - 16 * q^89 - 22 * q^90 - 4 * q^91 - 10 * q^92 + 8 * q^93 - 12 * q^94 + 2 * q^96 + 28 * q^97 - 12 * q^98 + 22 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	2.79360	1.61289	0.806444	−	0.591310i	$-0.201389\pi$
$3$	2.79360	1.61289	0.806444	+	0.591310i	$0.201389\pi$
$4$	1.00000	0.500000
$5$	−2.34458	−1.04853	−0.524263	−	0.851556i	$-0.675659\pi$
$5$	−2.34458	−1.04853	−0.524263	+	0.851556i	$0.675659\pi$
$6$	2.79360	1.14048
$7$	−1.28408	−0.485336	−0.242668	−	0.970109i	$-0.578023\pi$
$7$	−1.28408	−0.485336	−0.242668	+	0.970109i	$0.578023\pi$
$8$	1.00000	0.353553
$9$	4.80423	1.60141
$10$	−2.34458	−0.741420
$11$	5.75621	1.73556	0.867782	−	0.496945i	$-0.165545\pi$
$11$	5.75621	1.73556	0.867782	+	0.496945i	$0.165545\pi$
$12$	2.79360	0.806444
$13$	0.304282	0.0843928	0.0421964	−	0.999109i	$-0.486564\pi$
$13$	0.304282	0.0843928	0.0421964	+	0.999109i	$0.486564\pi$
$14$	−1.28408	−0.343185
$15$	−6.54982	−1.69116
$16$	1.00000	0.250000
$17$	4.18619	1.01530	0.507650	−	0.861563i	$-0.330514\pi$
$17$	4.18619	1.01530	0.507650	+	0.861563i	$0.330514\pi$
$18$	4.80423	1.13237
$19$	0	0
$19$	0	0
$20$	−2.34458	−0.524263
$21$	−3.58721	−0.782793
$22$	5.75621	1.22723
$23$	−6.47684	−1.35051	−0.675257	−	0.737583i	$-0.735967\pi$
$23$	−6.47684	−1.35051	−0.675257	+	0.737583i	$0.735967\pi$
$24$	2.79360	0.570242
$25$	0.497039	0.0994078
$26$	0.304282	0.0596747
$27$	5.04029	0.970005
$28$	−1.28408	−0.242668
$29$	−3.12756	−0.580773	−0.290387	−	0.956909i	$-0.593784\pi$
$29$	−3.12756	−0.580773	−0.290387	+	0.956909i	$0.593784\pi$
$30$	−6.54982	−1.19583
$31$	6.44246	1.15710	0.578550	−	0.815647i	$-0.303619\pi$
$31$	6.44246	1.15710	0.578550	+	0.815647i	$0.303619\pi$
$32$	1.00000	0.176777
$33$	16.0806	2.79927
$34$	4.18619	0.717926
$35$	3.01062	0.508888
$36$	4.80423	0.800704
$37$	−3.97980	−0.654275	−0.327137	−	0.944977i	$-0.606084\pi$
$37$	−3.97980	−0.654275	−0.327137	+	0.944977i	$0.606084\pi$
$38$	0	0
$39$	0.850045	0.136116
$40$	−2.34458	−0.370710
$41$	−5.01719	−0.783553	−0.391776	−	0.920060i	$-0.628139\pi$
$41$	−5.01719	−0.783553	−0.391776	+	0.920060i	$0.628139\pi$
$42$	−3.58721	−0.553518
$43$	−0.989378	−0.150879	−0.0754394	−	0.997150i	$-0.524036\pi$
$43$	−0.989378	−0.150879	−0.0754394	+	0.997150i	$0.524036\pi$
$44$	5.75621	0.867782
$45$	−11.2639	−1.67912
$46$	−6.47684	−0.954957
$47$	−4.39445	−0.640997	−0.320498	−	0.947249i	$-0.603850\pi$
$47$	−4.39445	−0.640997	−0.320498	+	0.947249i	$0.603850\pi$
$48$	2.79360	0.403222
$49$	−5.35114	−0.764449
$50$	0.497039	0.0702919
$51$	11.6946	1.63757
$52$	0.304282	0.0421964
$53$	3.29064	0.452005	0.226002	−	0.974127i	$-0.427434\pi$
$53$	3.29064	0.452005	0.226002	+	0.974127i	$0.427434\pi$
$54$	5.04029	0.685897
$55$	−13.4959	−1.81978
$56$	−1.28408	−0.171592
$57$	0	0
$58$	−3.12756	−0.410669
$59$	3.31375	0.431414	0.215707	−	0.976458i	$-0.430794\pi$
$59$	3.31375	0.431414	0.215707	+	0.976458i	$0.430794\pi$
$60$	−6.54982	−0.845578
$61$	−10.9615	−1.40347	−0.701735	−	0.712438i	$-0.747591\pi$
$61$	−10.9615	−1.40347	−0.701735	+	0.712438i	$0.747591\pi$
$62$	6.44246	0.818194
$63$	−6.16901	−0.777222
$64$	1.00000	0.125000
$65$	−0.713414	−0.0884881
$66$	16.0806	1.97938
$67$	−4.38081	−0.535202	−0.267601	−	0.963530i	$-0.586231\pi$
$67$	−4.38081	−0.535202	−0.267601	+	0.963530i	$0.586231\pi$
$68$	4.18619	0.507650
$69$	−18.0937	−2.17823
$70$	3.01062	0.359838
$71$	−4.41570	−0.524047	−0.262023	−	0.965062i	$-0.584390\pi$
$71$	−4.41570	−0.524047	−0.262023	+	0.965062i	$0.584390\pi$
$72$	4.80423	0.566183
$73$	−2.26689	−0.265320	−0.132660	−	0.991162i	$-0.542352\pi$
$73$	−2.26689	−0.265320	−0.132660	+	0.991162i	$0.542352\pi$
$74$	−3.97980	−0.462642
$75$	1.38853	0.160334
$76$	0	0
$77$	−7.39144	−0.842332
$78$	0.850045	0.0962486
$79$	8.57659	0.964941	0.482471	−	0.875912i	$-0.339739\pi$
$79$	8.57659	0.964941	0.482471	+	0.875912i	$0.339739\pi$
$80$	−2.34458	−0.262132
$81$	−0.332090	−0.0368989
$82$	−5.01719	−0.554056
$83$	−9.76464	−1.07181	−0.535904	−	0.844279i	$-0.680029\pi$
$83$	−9.76464	−1.07181	−0.535904	+	0.844279i	$0.680029\pi$
$84$	−3.58721	−0.391397
$85$	−9.81485	−1.06457
$86$	−0.989378	−0.106687
$87$	−8.73716	−0.936722
$88$	5.75621	0.613615
$89$	−15.0765	−1.59811	−0.799055	−	0.601259i	$-0.794666\pi$
$89$	−15.0765	−1.59811	−0.799055	+	0.601259i	$0.794666\pi$
$90$	−11.2639	−1.18732
$91$	−0.390723	−0.0409589
$92$	−6.47684	−0.675257
$93$	17.9977	1.86627
$94$	−4.39445	−0.453253
$95$	0	0
$96$	2.79360	0.285121
$97$	17.3522	1.76185	0.880924	−	0.473259i	$-0.156922\pi$
$97$	17.3522	1.76185	0.880924	+	0.473259i	$0.156922\pi$
$98$	−5.35114	−0.540547
$99$	27.6542	2.77935
$100$	0.497039	0.0497039
$101$	3.67667	0.365842	0.182921	−	0.983128i	$-0.441445\pi$
$101$	3.67667	0.365842	0.182921	+	0.983128i	$0.441445\pi$
$102$	11.6946	1.15793
$103$	19.0135	1.87346	0.936729	−	0.350055i	$-0.113837\pi$
$103$	19.0135	1.87346	0.936729	+	0.350055i	$0.113837\pi$
$104$	0.304282	0.0298374
$105$	8.41049	0.820779
$106$	3.29064	0.319616
$107$	10.0373	0.970340	0.485170	−	0.874420i	$-0.338758\pi$
$107$	10.0373	0.970340	0.485170	+	0.874420i	$0.338758\pi$
$108$	5.04029	0.485003
$109$	−8.84348	−0.847052	−0.423526	−	0.905884i	$-0.639208\pi$
$109$	−8.84348	−0.847052	−0.423526	+	0.905884i	$0.639208\pi$
$110$	−13.4959	−1.28678
$111$	−11.1180	−1.05527
$112$	−1.28408	−0.121334
$113$	−14.2502	−1.34055	−0.670275	−	0.742113i	$-0.733824\pi$
$113$	−14.2502	−1.34055	−0.670275	+	0.742113i	$0.733824\pi$
$114$	0	0
$115$	15.1854	1.41605
$116$	−3.12756	−0.290387
$117$	1.46184	0.135147
$118$	3.31375	0.305056
$119$	−5.37540	−0.492762
$120$	−6.54982	−0.597914
$121$	22.1340	2.01218
$122$	−10.9615	−0.992404
$123$	−14.0160	−1.26378
$124$	6.44246	0.578550
$125$	10.5575	0.944295
$126$	−6.16901	−0.549579
$127$	2.23015	0.197893	0.0989467	−	0.995093i	$-0.468453\pi$
$127$	2.23015	0.197893	0.0989467	+	0.995093i	$0.468453\pi$
$128$	1.00000	0.0883883
$129$	−2.76393	−0.243351
$130$	−0.713414	−0.0625705
$131$	1.52265	0.133035	0.0665175	−	0.997785i	$-0.478811\pi$
$131$	1.52265	0.133035	0.0665175	+	0.997785i	$0.478811\pi$
$132$	16.0806	1.39964
$133$	0	0
$134$	−4.38081	−0.378445
$135$	−11.8174	−1.01708
$136$	4.18619	0.358963
$137$	10.7118	0.915167	0.457583	−	0.889167i	$-0.348715\pi$
$137$	10.7118	0.915167	0.457583	+	0.889167i	$0.348715\pi$
$138$	−18.0937	−1.54024
$139$	−10.8143	−0.917260	−0.458630	−	0.888627i	$-0.651660\pi$
$139$	−10.8143	−0.917260	−0.458630	+	0.888627i	$0.651660\pi$
$140$	3.01062	0.254444
$141$	−12.2764	−1.03386
$142$	−4.41570	−0.370557
$143$	1.75152	0.146469
$144$	4.80423	0.400352
$145$	7.33280	0.608956
$146$	−2.26689	−0.187609
$147$	−14.9490	−1.23297
$148$	−3.97980	−0.327137
$149$	−9.33384	−0.764658	−0.382329	−	0.924026i	$-0.624878\pi$
$149$	−9.33384	−0.764658	−0.382329	+	0.924026i	$0.624878\pi$
$150$	1.38853	0.113373
$151$	19.8232	1.61319	0.806593	−	0.591107i	$-0.201309\pi$
$151$	19.8232	1.61319	0.806593	+	0.591107i	$0.201309\pi$
$152$	0	0
$153$	20.1114	1.62591
$154$	−7.39144	−0.595619
$155$	−15.1048	−1.21325
$156$	0.850045	0.0680581
$157$	13.8676	1.10676	0.553379	−	0.832930i	$-0.313338\pi$
$157$	13.8676	1.10676	0.553379	+	0.832930i	$0.313338\pi$
$158$	8.57659	0.682317
$159$	9.19276	0.729033
$160$	−2.34458	−0.185355
$161$	8.31677	0.655453
$162$	−0.332090	−0.0260915
$163$	14.2496	1.11611	0.558057	−	0.829803i	$-0.311547\pi$
$163$	14.2496	1.11611	0.558057	+	0.829803i	$0.311547\pi$
$164$	−5.01719	−0.391776
$165$	−37.7022	−2.93511
$166$	−9.76464	−0.757883
$167$	11.5901	0.896870	0.448435	−	0.893815i	$-0.351982\pi$
$167$	11.5901	0.896870	0.448435	+	0.893815i	$0.351982\pi$
$168$	−3.58721	−0.276759
$169$	−12.9074	−0.992878
$170$	−9.81485	−0.752764
$171$	0	0
$172$	−0.989378	−0.0754394
$173$	3.98353	0.302862	0.151431	−	0.988468i	$-0.451612\pi$
$173$	3.98353	0.302862	0.151431	+	0.988468i	$0.451612\pi$
$174$	−8.73716	−0.662363
$175$	−0.638237	−0.0482462
$176$	5.75621	0.433891
$177$	9.25731	0.695822
$178$	−15.0765	−1.13003
$179$	−8.45089	−0.631649	−0.315825	−	0.948818i	$-0.602281\pi$
$179$	−8.45089	−0.631649	−0.315825	+	0.948818i	$0.602281\pi$
$180$	−11.2639	−0.839560
$181$	8.48526	0.630705	0.315352	−	0.948975i	$-0.397877\pi$
$181$	8.48526	0.630705	0.315352	+	0.948975i	$0.397877\pi$
$182$	−0.390723	−0.0289623
$183$	−30.6220	−2.26364
$184$	−6.47684	−0.477479
$185$	9.33094	0.686024
$186$	17.9977	1.31966
$187$	24.0966	1.76212
$188$	−4.39445	−0.320498
$189$	−6.47214	−0.470779
$190$	0	0
$191$	−22.3790	−1.61929	−0.809644	−	0.586921i	$-0.800340\pi$
$191$	−22.3790	−1.61929	−0.809644	+	0.586921i	$0.800340\pi$
$192$	2.79360	0.201611
$193$	7.42811	0.534687	0.267344	−	0.963601i	$-0.413854\pi$
$193$	7.42811	0.534687	0.267344	+	0.963601i	$0.413854\pi$
$194$	17.3522	1.24581
$195$	−1.99300	−0.142721
$196$	−5.35114	−0.382224
$197$	8.53554	0.608132	0.304066	−	0.952651i	$-0.401656\pi$
$197$	8.53554	0.608132	0.304066	+	0.952651i	$0.401656\pi$
$198$	27.6542	1.96530
$199$	−6.35926	−0.450796	−0.225398	−	0.974267i	$-0.572368\pi$
$199$	−6.35926	−0.450796	−0.225398	+	0.974267i	$0.572368\pi$
$200$	0.497039	0.0351460
$201$	−12.2383	−0.863220
$202$	3.67667	0.258689
$203$	4.01603	0.281870
$204$	11.6946	0.818783
$205$	11.7632	0.821576
$206$	19.0135	1.32474
$207$	−31.1162	−2.16272
$208$	0.304282	0.0210982
$209$	0	0
$210$	8.41049	0.580379
$211$	−13.9578	−0.960894	−0.480447	−	0.877024i	$-0.659526\pi$
$211$	−13.9578	−0.960894	−0.480447	+	0.877024i	$0.659526\pi$
$212$	3.29064	0.226002
$213$	−12.3357	−0.845229
$214$	10.0373	0.686134
$215$	2.31967	0.158200
$216$	5.04029	0.342949
$217$	−8.27263	−0.561583
$218$	−8.84348	−0.598956
$219$	−6.33280	−0.427931
$220$	−13.4959	−0.909892
$221$	1.27378	0.0856840
$222$	−11.1180	−0.746190
$223$	8.92400	0.597595	0.298798	−	0.954317i	$-0.403414\pi$
$223$	8.92400	0.597595	0.298798	+	0.954317i	$0.403414\pi$
$224$	−1.28408	−0.0857961
$225$	2.38789	0.159193
$226$	−14.2502	−0.947912
$227$	−0.659796	−0.0437922	−0.0218961	−	0.999760i	$-0.506970\pi$
$227$	−0.659796	−0.0437922	−0.0218961	+	0.999760i	$0.506970\pi$
$228$	0	0
$229$	−6.97208	−0.460728	−0.230364	−	0.973105i	$-0.573992\pi$
$229$	−6.97208	−0.460728	−0.230364	+	0.973105i	$0.573992\pi$
$230$	15.1854	1.00130
$231$	−20.6487	−1.35859
$232$	−3.12756	−0.205334
$233$	−29.6097	−1.93980	−0.969898	−	0.243512i	$-0.921700\pi$
$233$	−29.6097	−1.93980	−0.969898	+	0.243512i	$0.921700\pi$
$234$	1.46184	0.0955636
$235$	10.3031	0.672102
$236$	3.31375	0.215707
$237$	23.9596	1.55634
$238$	−5.37540	−0.348436
$239$	−24.7034	−1.59793	−0.798965	−	0.601378i	$-0.794619\pi$
$239$	−24.7034	−1.59793	−0.798965	+	0.601378i	$0.794619\pi$
$240$	−6.54982	−0.422789
$241$	27.5586	1.77521	0.887604	−	0.460607i	$-0.152368\pi$
$241$	27.5586	1.77521	0.887604	+	0.460607i	$0.152368\pi$
$242$	22.1340	1.42283
$243$	−16.0486	−1.02952
$244$	−10.9615	−0.701735
$245$	12.5462	0.801545
$246$	−14.0160	−0.893630
$247$	0	0
$248$	6.44246	0.409097
$249$	−27.2786	−1.72871
$250$	10.5575	0.667717
$251$	−2.98855	−0.188636	−0.0943179	−	0.995542i	$-0.530067\pi$
$251$	−2.98855	−0.188636	−0.0943179	+	0.995542i	$0.530067\pi$
$252$	−6.16901	−0.388611
$253$	−37.2821	−2.34390
$254$	2.23015	0.139932
$255$	−27.4188	−1.71703
$256$	1.00000	0.0625000
$257$	14.1323	0.881546	0.440773	−	0.897619i	$-0.354704\pi$
$257$	14.1323	0.881546	0.440773	+	0.897619i	$0.354704\pi$
$258$	−2.76393	−0.172075
$259$	5.11037	0.317543
$260$	−0.713414	−0.0442440
$261$	−15.0255	−0.930055
$262$	1.52265	0.0940699
$263$	7.56887	0.466717	0.233358	−	0.972391i	$-0.425029\pi$
$263$	7.56887	0.466717	0.233358	+	0.972391i	$0.425029\pi$
$264$	16.0806	0.989692
$265$	−7.71517	−0.473939
$266$	0	0
$267$	−42.1179	−2.57757
$268$	−4.38081	−0.267601
$269$	−7.67074	−0.467694	−0.233847	−	0.972273i	$-0.575131\pi$
$269$	−7.67074	−0.467694	−0.233847	+	0.972273i	$0.575131\pi$
$270$	−11.8174	−0.719181
$271$	11.6649	0.708592	0.354296	−	0.935133i	$-0.384721\pi$
$271$	11.6649	0.708592	0.354296	+	0.935133i	$0.384721\pi$
$272$	4.18619	0.253825
$273$	−1.09152	−0.0660621
$274$	10.7118	0.647121
$275$	2.86106	0.172529
$276$	−18.0937	−1.08911
$277$	27.4405	1.64874	0.824370	−	0.566052i	$-0.191530\pi$
$277$	27.4405	1.64874	0.824370	+	0.566052i	$0.191530\pi$
$278$	−10.8143	−0.648601
$279$	30.9511	1.85299
$280$	3.01062	0.179919
$281$	16.2715	0.970675	0.485338	−	0.874327i	$-0.338697\pi$
$281$	16.2715	0.970675	0.485338	+	0.874327i	$0.338697\pi$
$282$	−12.2764	−0.731047
$283$	3.39374	0.201737	0.100868	−	0.994900i	$-0.467838\pi$
$283$	3.39374	0.201737	0.100868	+	0.994900i	$0.467838\pi$
$284$	−4.41570	−0.262023
$285$	0	0
$286$	1.75152	0.103569
$287$	6.44246	0.380287
$288$	4.80423	0.283092
$289$	0.524204	0.0308355
$290$	7.33280	0.430597
$291$	48.4751	2.84166
$292$	−2.26689	−0.132660
$293$	23.3783	1.36578	0.682888	−	0.730523i	$-0.260724\pi$
$293$	23.3783	1.36578	0.682888	+	0.730523i	$0.260724\pi$
$294$	−14.9490	−0.871842
$295$	−7.76934	−0.452349
$296$	−3.97980	−0.231321
$297$	29.0130	1.68351
$298$	−9.33384	−0.540695
$299$	−1.97079	−0.113974
$300$	1.38853	0.0801668
$301$	1.27044	0.0732270
$302$	19.8232	1.14069
$303$	10.2712	0.590062
$304$	0	0
$305$	25.7000	1.47158
$306$	20.1114	1.14969
$307$	−1.38802	−0.0792185	−0.0396093	−	0.999215i	$-0.512611\pi$
$307$	−1.38802	−0.0792185	−0.0396093	+	0.999215i	$0.512611\pi$
$308$	−7.39144	−0.421166
$309$	53.1163	3.02168
$310$	−15.1048	−0.857898
$311$	−12.1902	−0.691246	−0.345623	−	0.938374i	$-0.612332\pi$
$311$	−12.1902	−0.691246	−0.345623	+	0.938374i	$0.612332\pi$
$312$	0.850045	0.0481243
$313$	16.5314	0.934411	0.467205	−	0.884149i	$-0.345261\pi$
$313$	16.5314	0.934411	0.467205	+	0.884149i	$0.345261\pi$
$314$	13.8676	0.782596
$315$	14.4637	0.814938
$316$	8.57659	0.482471
$317$	2.68811	0.150979	0.0754897	−	0.997147i	$-0.475948\pi$
$317$	2.68811	0.150979	0.0754897	+	0.997147i	$0.475948\pi$
$318$	9.19276	0.515504
$319$	−18.0029	−1.00797
$320$	−2.34458	−0.131066
$321$	28.0402	1.56505
$322$	8.31677	0.463475
$323$	0	0
$324$	−0.332090	−0.0184495
$325$	0.151240	0.00838930
$326$	14.2496	0.789212
$327$	−24.7052	−1.36620
$328$	−5.01719	−0.277028
$329$	5.64282	0.311099
$330$	−37.7022	−2.07544
$331$	5.21303	0.286534	0.143267	−	0.989684i	$-0.454239\pi$
$331$	5.21303	0.286534	0.143267	+	0.989684i	$0.454239\pi$
$332$	−9.76464	−0.535904
$333$	−19.1198	−1.04776
$334$	11.5901	0.634183
$335$	10.2712	0.561173
$336$	−3.58721	−0.195698
$337$	−26.7275	−1.45594	−0.727969	−	0.685610i	$-0.759536\pi$
$337$	−26.7275	−1.45594	−0.727969	+	0.685610i	$0.759536\pi$
$338$	−12.9074	−0.702071
$339$	−39.8095	−2.16216
$340$	−9.81485	−0.532285
$341$	37.0842	2.00822
$342$	0	0
$343$	15.8598	0.856351
$344$	−0.989378	−0.0533437
$345$	42.4221	2.28393
$346$	3.98353	0.214156
$347$	−32.6682	−1.75372	−0.876860	−	0.480745i	$-0.840366\pi$
$347$	−32.6682	−1.75372	−0.876860	+	0.480745i	$0.840366\pi$
$348$	−8.73716	−0.468361
$349$	−29.1058	−1.55800	−0.778998	−	0.627026i	$-0.784272\pi$
$349$	−29.1058	−1.55800	−0.778998	+	0.627026i	$0.784272\pi$
$350$	−0.638237	−0.0341152
$351$	1.53367	0.0818614
$352$	5.75621	0.306807
$353$	−14.3049	−0.761372	−0.380686	−	0.924704i	$-0.624312\pi$
$353$	−14.3049	−0.761372	−0.380686	+	0.924704i	$0.624312\pi$
$354$	9.25731	0.492021
$355$	10.3529	0.549477
$356$	−15.0765	−0.799055
$357$	−15.0167	−0.794770
$358$	−8.45089	−0.446644
$359$	19.6707	1.03818	0.519090	−	0.854720i	$-0.326271\pi$
$359$	19.6707	1.03818	0.519090	+	0.854720i	$0.326271\pi$
$360$	−11.2639	−0.593658
$361$	0	0
$362$	8.48526	0.445976
$363$	61.8337	3.24543
$364$	−0.390723	−0.0204794
$365$	5.31490	0.278195
$366$	−30.6220	−1.60064
$367$	9.55053	0.498534	0.249267	−	0.968435i	$-0.419810\pi$
$367$	9.55053	0.498534	0.249267	+	0.968435i	$0.419810\pi$
$368$	−6.47684	−0.337628
$369$	−24.1037	−1.25479
$370$	9.33094	0.485092
$371$	−4.22545	−0.219374
$372$	17.9977	0.933137
$373$	3.64010	0.188477	0.0942387	−	0.995550i	$-0.469958\pi$
$373$	3.64010	0.188477	0.0942387	+	0.995550i	$0.469958\pi$
$374$	24.0966	1.24601
$375$	29.4936	1.52304
$376$	−4.39445	−0.226627
$377$	−0.951662	−0.0490131
$378$	−6.47214	−0.332891
$379$	8.34741	0.428778	0.214389	−	0.976748i	$-0.431224\pi$
$379$	8.34741	0.428778	0.214389	+	0.976748i	$0.431224\pi$
$380$	0	0
$381$	6.23015	0.319180
$382$	−22.3790	−1.14501
$383$	−9.48566	−0.484695	−0.242347	−	0.970190i	$-0.577917\pi$
$383$	−9.48566	−0.484695	−0.242347	+	0.970190i	$0.577917\pi$
$384$	2.79360	0.142561
$385$	17.3298	0.883208
$386$	7.42811	0.378081
$387$	−4.75320	−0.241619
$388$	17.3522	0.880924
$389$	36.0480	1.82770	0.913852	−	0.406047i	$-0.133093\pi$
$389$	36.0480	1.82770	0.913852	+	0.406047i	$0.133093\pi$
$390$	−1.99300	−0.100919
$391$	−27.1133	−1.37118
$392$	−5.35114	−0.270273
$393$	4.25369	0.214570
$394$	8.53554	0.430014
$395$	−20.1085	−1.01177
$396$	27.6542	1.38967
$397$	−6.40906	−0.321662	−0.160831	−	0.986982i	$-0.551417\pi$
$397$	−6.40906	−0.321662	−0.160831	+	0.986982i	$0.551417\pi$
$398$	−6.35926	−0.318761
$399$	0	0
$400$	0.497039	0.0248520
$401$	0.187660	0.00937128	0.00468564	−	0.999989i	$-0.498509\pi$
$401$	0.187660	0.00937128	0.00468564	+	0.999989i	$0.498509\pi$
$402$	−12.2383	−0.610389
$403$	1.96033	0.0976509
$404$	3.67667	0.182921
$405$	0.778611	0.0386895
$406$	4.01603	0.199312
$407$	−22.9086	−1.13554
$408$	11.6946	0.578967
$409$	17.2663	0.853762	0.426881	−	0.904308i	$-0.359612\pi$
$409$	17.2663	0.853762	0.426881	+	0.904308i	$0.359612\pi$
$410$	11.7632	0.580942
$411$	29.9244	1.47606
$412$	19.0135	0.936729
$413$	−4.25512	−0.209381
$414$	−31.1162	−1.52928
$415$	22.8940	1.12382
$416$	0.304282	0.0149187
$417$	−30.2110	−1.47944
$418$	0	0
$419$	−1.72572	−0.0843068	−0.0421534	−	0.999111i	$-0.513422\pi$
$419$	−1.72572	−0.0843068	−0.0421534	+	0.999111i	$0.513422\pi$
$420$	8.41049	0.410390
$421$	32.7546	1.59636	0.798180	−	0.602420i	$-0.205797\pi$
$421$	32.7546	1.59636	0.798180	+	0.602420i	$0.205797\pi$
$422$	−13.9578	−0.679455
$423$	−21.1119	−1.02650
$424$	3.29064	0.159808
$425$	2.08070	0.100929
$426$	−12.3357	−0.597667
$427$	14.0754	0.681155
$428$	10.0373	0.485170
$429$	4.89304	0.236238
$430$	2.31967	0.111865
$431$	−25.5119	−1.22887	−0.614433	−	0.788969i	$-0.710615\pi$
$431$	−25.5119	−1.22887	−0.614433	+	0.788969i	$0.710615\pi$
$432$	5.04029	0.242501
$433$	24.4834	1.17660	0.588299	−	0.808644i	$-0.299798\pi$
$433$	24.4834	1.17660	0.588299	+	0.808644i	$0.299798\pi$
$434$	−8.27263	−0.397099
$435$	20.4849	0.982178
$436$	−8.84348	−0.423526
$437$	0	0
$438$	−6.33280	−0.302593
$439$	−30.8388	−1.47186	−0.735928	−	0.677060i	$-0.763254\pi$
$439$	−30.8388	−1.47186	−0.735928	+	0.677060i	$0.763254\pi$
$440$	−13.4959	−0.643391
$441$	−25.7081	−1.22419
$442$	1.27378	0.0605878
$443$	10.7047	0.508595	0.254297	−	0.967126i	$-0.418156\pi$
$443$	10.7047	0.508595	0.254297	+	0.967126i	$0.418156\pi$
$444$	−11.1180	−0.527636
$445$	35.3481	1.67566
$446$	8.92400	0.422564
$447$	−26.0751	−1.23331
$448$	−1.28408	−0.0606670
$449$	2.31562	0.109281	0.0546403	−	0.998506i	$-0.482599\pi$
$449$	2.31562	0.109281	0.0546403	+	0.998506i	$0.482599\pi$
$450$	2.38789	0.112566
$451$	−28.8800	−1.35991
$452$	−14.2502	−0.670275
$453$	55.3781	2.60189
$454$	−0.659796	−0.0309657
$455$	0.916079	0.0429465
$456$	0	0
$457$	−0.0521810	−0.00244092	−0.00122046	−	0.999999i	$-0.500388\pi$
$457$	−0.0521810	−0.00244092	−0.00122046	+	0.999999i	$0.500388\pi$
$458$	−6.97208	−0.325784
$459$	21.0996	0.984847
$460$	15.1854	0.708025
$461$	39.4720	1.83840	0.919198	−	0.393796i	$-0.128838\pi$
$461$	39.4720	1.83840	0.919198	+	0.393796i	$0.128838\pi$
$462$	−20.6487	−0.960667
$463$	−6.19056	−0.287700	−0.143850	−	0.989600i	$-0.545948\pi$
$463$	−6.19056	−0.287700	−0.143850	+	0.989600i	$0.545948\pi$
$464$	−3.12756	−0.145193
$465$	−42.1970	−1.95684
$466$	−29.6097	−1.37164
$467$	−20.9962	−0.971586	−0.485793	−	0.874074i	$-0.661469\pi$
$467$	−20.9962	−0.971586	−0.485793	+	0.874074i	$0.661469\pi$
$468$	1.46184	0.0675737
$469$	5.62531	0.259753
$470$	10.3031	0.475248
$471$	38.7407	1.78508
$472$	3.31375	0.152528
$473$	−5.69507	−0.261860
$474$	23.9596	1.10050
$475$	0	0
$476$	−5.37540	−0.246381
$477$	15.8090	0.723844
$478$	−24.7034	−1.12991
$479$	15.5229	0.709261	0.354631	−	0.935006i	$-0.384607\pi$
$479$	15.5229	0.709261	0.354631	+	0.935006i	$0.384607\pi$
$480$	−6.54982	−0.298957
$481$	−1.21098	−0.0552160
$482$	27.5586	1.25526
$483$	23.2338	1.05717
$484$	22.1340	1.00609
$485$	−40.6835	−1.84734
$486$	−16.0486	−0.727980
$487$	−28.6065	−1.29629	−0.648143	−	0.761519i	$-0.724454\pi$
$487$	−28.6065	−1.29629	−0.648143	+	0.761519i	$0.724454\pi$
$488$	−10.9615	−0.496202
$489$	39.8077	1.80017
$490$	12.5462	0.566778
$491$	−30.3488	−1.36962	−0.684812	−	0.728720i	$-0.740116\pi$
$491$	−30.3488	−1.36962	−0.684812	+	0.728720i	$0.740116\pi$
$492$	−14.0160	−0.631892
$493$	−13.0926	−0.589659
$494$	0	0
$495$	−64.8373	−2.91422
$496$	6.44246	0.289275
$497$	5.67010	0.254339
$498$	−27.2786	−1.22238
$499$	8.77624	0.392878	0.196439	−	0.980516i	$-0.437062\pi$
$499$	8.77624	0.392878	0.196439	+	0.980516i	$0.437062\pi$
$500$	10.5575	0.472147
$501$	32.3782	1.44655
$502$	−2.98855	−0.133386
$503$	−21.1043	−0.940996	−0.470498	−	0.882401i	$-0.655926\pi$
$503$	−21.1043	−0.940996	−0.470498	+	0.882401i	$0.655926\pi$
$504$	−6.16901	−0.274789
$505$	−8.62023	−0.383595
$506$	−37.2821	−1.65739
$507$	−36.0582	−1.60140
$508$	2.23015	0.0989467
$509$	22.2212	0.984936	0.492468	−	0.870331i	$-0.336095\pi$
$509$	22.2212	0.984936	0.492468	+	0.870331i	$0.336095\pi$
$510$	−27.4188	−1.21412
$511$	2.91087	0.128769
$512$	1.00000	0.0441942
$513$	0	0
$514$	14.1323	0.623347
$515$	−44.5787	−1.96437
$516$	−2.76393	−0.121675
$517$	−25.2954	−1.11249
$518$	5.11037	0.224537
$519$	11.1284	0.488482
$520$	−0.713414	−0.0312853
$521$	10.0332	0.439563	0.219782	−	0.975549i	$-0.429466\pi$
$521$	10.0332	0.439563	0.219782	+	0.975549i	$0.429466\pi$
$522$	−15.0255	−0.657648
$523$	29.2823	1.28042	0.640212	−	0.768198i	$-0.278846\pi$
$523$	29.2823	1.28042	0.640212	+	0.768198i	$0.278846\pi$
$524$	1.52265	0.0665175
$525$	−1.78298	−0.0778158
$526$	7.56887	0.330018
$527$	26.9694	1.17481
$528$	16.0806	0.699818
$529$	18.9494	0.823887
$530$	−7.71517	−0.335125
$531$	15.9200	0.690870
$532$	0	0
$533$	−1.52664	−0.0661262
$534$	−42.1179	−1.82262
$535$	−23.5332	−1.01743
$536$	−4.38081	−0.189222
$537$	−23.6085	−1.01878
$538$	−7.67074	−0.330709
$539$	−30.8023	−1.32675
$540$	−11.8174	−0.508538
$541$	−37.8404	−1.62688	−0.813442	−	0.581646i	$-0.802409\pi$
$541$	−37.8404	−1.62688	−0.813442	+	0.581646i	$0.802409\pi$
$542$	11.6649	0.501050
$543$	23.7045	1.01726
$544$	4.18619	0.179482
$545$	20.7342	0.888156
$546$	−1.09152	−0.0467130
$547$	−14.4976	−0.619871	−0.309936	−	0.950758i	$-0.600308\pi$
$547$	−14.4976	−0.619871	−0.309936	+	0.950758i	$0.600308\pi$
$548$	10.7118	0.457583
$549$	−52.6613	−2.24753
$550$	2.86106	0.121996
$551$	0	0
$552$	−18.0937	−0.770120
$553$	−11.0130	−0.468321
$554$	27.4405	1.16583
$555$	26.0669	1.10648
$556$	−10.8143	−0.458630
$557$	−4.33801	−0.183807	−0.0919037	−	0.995768i	$-0.529295\pi$
$557$	−4.33801	−0.183807	−0.0919037	+	0.995768i	$0.529295\pi$
$558$	30.9511	1.31026
$559$	−0.301051	−0.0127331
$560$	3.01062	0.127222
$561$	67.3164	2.84210
$562$	16.2715	0.686371
$563$	−27.2936	−1.15029	−0.575144	−	0.818052i	$-0.695054\pi$
$563$	−27.2936	−1.15029	−0.575144	+	0.818052i	$0.695054\pi$
$564$	−12.2764	−0.516928
$565$	33.4108	1.40560
$566$	3.39374	0.142650
$567$	0.426430	0.0179084
$568$	−4.41570	−0.185278
$569$	−7.19043	−0.301439	−0.150719	−	0.988577i	$-0.548159\pi$
$569$	−7.19043	−0.301439	−0.150719	+	0.988577i	$0.548159\pi$
$570$	0	0
$571$	42.0134	1.75821	0.879103	−	0.476631i	$-0.158142\pi$
$571$	42.0134	1.75821	0.879103	+	0.476631i	$0.158142\pi$
$572$	1.75152	0.0732345
$573$	−62.5181	−2.61173
$574$	6.44246	0.268903
$575$	−3.21924	−0.134252
$576$	4.80423	0.200176
$577$	21.6713	0.902190	0.451095	−	0.892476i	$-0.351034\pi$
$577$	21.6713	0.902190	0.451095	+	0.892476i	$0.351034\pi$
$578$	0.524204	0.0218040
$579$	20.7512	0.862391
$580$	7.33280	0.304478
$581$	12.5386	0.520188
$582$	48.4751	2.00936
$583$	18.9417	0.784483
$584$	−2.26689	−0.0938047
$585$	−3.42740	−0.141706
$586$	23.3783	0.965749
$587$	−1.26864	−0.0523626	−0.0261813	−	0.999657i	$-0.508335\pi$
$587$	−1.26864	−0.0523626	−0.0261813	+	0.999657i	$0.508335\pi$
$588$	−14.9490	−0.616485
$589$	0	0
$590$	−7.76934	−0.319859
$591$	23.8449	0.980849
$592$	−3.97980	−0.163569
$593$	21.5600	0.885363	0.442682	−	0.896679i	$-0.354027\pi$
$593$	21.5600	0.885363	0.442682	+	0.896679i	$0.354027\pi$
$594$	29.0130	1.19042
$595$	12.6030	0.516674
$596$	−9.33384	−0.382329
$597$	−17.7652	−0.727083
$598$	−1.97079	−0.0805915
$599$	−28.6417	−1.17027	−0.585135	−	0.810936i	$-0.698958\pi$
$599$	−28.6417	−1.17027	−0.585135	+	0.810936i	$0.698958\pi$
$600$	1.38853	0.0566865
$601$	7.55865	0.308324	0.154162	−	0.988046i	$-0.450732\pi$
$601$	7.55865	0.308324	0.154162	+	0.988046i	$0.450732\pi$
$602$	1.27044	0.0517793
$603$	−21.0464	−0.857076
$604$	19.8232	0.806593
$605$	−51.8949	−2.10983
$606$	10.2712	0.417237
$607$	1.72737	0.0701117	0.0350558	−	0.999385i	$-0.488839\pi$
$607$	1.72737	0.0701117	0.0350558	+	0.999385i	$0.488839\pi$
$608$	0	0
$609$	11.2192	0.454625
$610$	25.7000	1.04056
$611$	−1.33715	−0.0540955
$612$	20.1114	0.812956
$613$	−27.4169	−1.10736	−0.553680	−	0.832730i	$-0.686777\pi$
$613$	−27.4169	−1.10736	−0.553680	+	0.832730i	$0.686777\pi$
$614$	−1.38802	−0.0560160
$615$	32.8617	1.32511
$616$	−7.39144	−0.297809
$617$	10.6275	0.427847	0.213924	−	0.976850i	$-0.431376\pi$
$617$	10.6275	0.427847	0.213924	+	0.976850i	$0.431376\pi$
$618$	53.1163	2.13665
$619$	8.36008	0.336020	0.168010	−	0.985785i	$-0.446266\pi$
$619$	8.36008	0.336020	0.168010	+	0.985785i	$0.446266\pi$
$620$	−15.1048	−0.606625
$621$	−32.6452	−1.31000
$622$	−12.1902	−0.488784
$623$	19.3595	0.775620
$624$	0.850045	0.0340290
$625$	−27.2381	−1.08953
$626$	16.5314	0.660728
$627$	0	0
$628$	13.8676	0.553379
$629$	−16.6602	−0.664285
$630$	14.4637	0.576248
$631$	24.5301	0.976530	0.488265	−	0.872696i	$-0.337630\pi$
$631$	24.5301	0.976530	0.488265	+	0.872696i	$0.337630\pi$
$632$	8.57659	0.341158
$633$	−38.9926	−1.54982
$634$	2.68811	0.106759
$635$	−5.22875	−0.207497
$636$	9.19276	0.364517
$637$	−1.62826	−0.0645139
$638$	−18.0029	−0.712742
$639$	−21.2140	−0.839213
$640$	−2.34458	−0.0926775
$641$	−6.97270	−0.275405	−0.137703	−	0.990474i	$-0.543972\pi$
$641$	−6.97270	−0.275405	−0.137703	+	0.990474i	$0.543972\pi$
$642$	28.0402	1.10666
$643$	−9.09024	−0.358484	−0.179242	−	0.983805i	$-0.557365\pi$
$643$	−9.09024	−0.358484	−0.179242	+	0.983805i	$0.557365\pi$
$644$	8.31677	0.327727
$645$	6.48025	0.255160
$646$	0	0
$647$	30.0074	1.17971	0.589856	−	0.807509i	$-0.299185\pi$
$647$	30.0074	1.17971	0.589856	+	0.807509i	$0.299185\pi$
$648$	−0.332090	−0.0130457
$649$	19.0747	0.748746
$650$	0.151240	0.00593213
$651$	−23.1105	−0.905770
$652$	14.2496	0.558057
$653$	10.4191	0.407732	0.203866	−	0.978999i	$-0.434649\pi$
$653$	10.4191	0.407732	0.203866	+	0.978999i	$0.434649\pi$
$654$	−24.7052	−0.966049
$655$	−3.56998	−0.139491
$656$	−5.01719	−0.195888
$657$	−10.8907	−0.424885
$658$	5.64282	0.219980
$659$	−26.3756	−1.02745	−0.513724	−	0.857956i	$-0.671734\pi$
$659$	−26.3756	−1.02745	−0.513724	+	0.857956i	$0.671734\pi$
$660$	−37.7022	−1.46755
$661$	−24.6939	−0.960483	−0.480242	−	0.877136i	$-0.659451\pi$
$661$	−24.6939	−0.960483	−0.480242	+	0.877136i	$0.659451\pi$
$662$	5.21303	0.202610
$663$	3.55845	0.138199
$664$	−9.76464	−0.378942
$665$	0	0
$666$	−19.1198	−0.740879
$667$	20.2567	0.784342
$668$	11.5901	0.448435
$669$	24.9301	0.963854
$670$	10.2712	0.396809
$671$	−63.0965	−2.43581
$672$	−3.58721	−0.138380
$673$	−9.77380	−0.376752	−0.188376	−	0.982097i	$-0.560322\pi$
$673$	−9.77380	−0.376752	−0.188376	+	0.982097i	$0.560322\pi$
$674$	−26.7275	−1.02950
$675$	2.50522	0.0964261
$676$	−12.9074	−0.496439
$677$	−21.5747	−0.829184	−0.414592	−	0.910007i	$-0.636076\pi$
$677$	−21.5747	−0.829184	−0.414592	+	0.910007i	$0.636076\pi$
$678$	−39.8095	−1.52888
$679$	−22.2816	−0.855088
$680$	−9.81485	−0.376382
$681$	−1.84321	−0.0706319
$682$	37.0842	1.42003
$683$	33.2509	1.27231	0.636155	−	0.771561i	$-0.280524\pi$
$683$	33.2509	1.27231	0.636155	+	0.771561i	$0.280524\pi$
$684$	0	0
$685$	−25.1145	−0.959576
$686$	15.8598	0.605532
$687$	−19.4772	−0.743103
$688$	−0.989378	−0.0377197
$689$	1.00129	0.0381459
$690$	42.4221	1.61498
$691$	4.80932	0.182955	0.0914776	−	0.995807i	$-0.470841\pi$
$691$	4.80932	0.182955	0.0914776	+	0.995807i	$0.470841\pi$
$692$	3.98353	0.151431
$693$	−35.5101	−1.34892
$694$	−32.6682	−1.24007
$695$	25.3550	0.961772
$696$	−8.73716	−0.331181
$697$	−21.0029	−0.795542
$698$	−29.1058	−1.10167
$699$	−82.7178	−3.12867
$700$	−0.638237	−0.0241231
$701$	3.46466	0.130859	0.0654293	−	0.997857i	$-0.479158\pi$
$701$	3.46466	0.130859	0.0654293	+	0.997857i	$0.479158\pi$
$702$	1.53367	0.0578848
$703$	0	0
$704$	5.75621	0.216946
$705$	28.7829	1.08403
$706$	−14.3049	−0.538371
$707$	−4.72113	−0.177556
$708$	9.25731	0.347911
$709$	20.5743	0.772684	0.386342	−	0.922356i	$-0.373738\pi$
$709$	20.5743	0.772684	0.386342	+	0.922356i	$0.373738\pi$
$710$	10.3529	0.388539
$711$	41.2039	1.54527
$712$	−15.0765	−0.565017
$713$	−41.7268	−1.56268
$714$	−15.0167	−0.561988
$715$	−4.10656	−0.153577
$716$	−8.45089	−0.315825
$717$	−69.0115	−2.57728
$718$	19.6707	0.734104
$719$	24.1885	0.902080	0.451040	−	0.892504i	$-0.351053\pi$
$719$	24.1885	0.902080	0.451040	+	0.892504i	$0.351053\pi$
$720$	−11.2639	−0.419780
$721$	−24.4149	−0.909257
$722$	0	0
$723$	76.9880	2.86321
$724$	8.48526	0.315352
$725$	−1.55452	−0.0577334
$726$	61.8337	2.29486
$727$	18.1276	0.672317	0.336158	−	0.941806i	$-0.390872\pi$
$727$	18.1276	0.672317	0.336158	+	0.941806i	$0.390872\pi$
$728$	−0.390723	−0.0144811
$729$	−43.8372	−1.62360
$730$	5.31490	0.196713
$731$	−4.14173	−0.153187
$732$	−30.6220	−1.13182
$733$	22.7363	0.839785	0.419893	−	0.907574i	$-0.362068\pi$
$733$	22.7363	0.839785	0.419893	+	0.907574i	$0.362068\pi$
$734$	9.55053	0.352517
$735$	35.0490	1.29280
$736$	−6.47684	−0.238739
$737$	−25.2169	−0.928877
$738$	−24.1037	−0.887269
$739$	15.1787	0.558356	0.279178	−	0.960239i	$-0.409938\pi$
$739$	15.1787	0.558356	0.279178	+	0.960239i	$0.409938\pi$
$740$	9.33094	0.343012
$741$	0	0
$742$	−4.22545	−0.155121
$743$	−3.27625	−0.120194	−0.0600970	−	0.998193i	$-0.519141\pi$
$743$	−3.27625	−0.120194	−0.0600970	+	0.998193i	$0.519141\pi$
$744$	17.9977	0.659828
$745$	21.8839	0.801764
$746$	3.64010	0.133274
$747$	−46.9116	−1.71640
$748$	24.0966	0.881060
$749$	−12.8887	−0.470941
$750$	29.4936	1.07695
$751$	52.2323	1.90598	0.952992	−	0.302995i	$-0.0979866\pi$
$751$	52.2323	1.90598	0.952992	+	0.302995i	$0.0979866\pi$
$752$	−4.39445	−0.160249
$753$	−8.34884	−0.304248
$754$	−0.951662	−0.0346575
$755$	−46.4769	−1.69147
$756$	−6.47214	−0.235389
$757$	−24.2342	−0.880807	−0.440404	−	0.897800i	$-0.645165\pi$
$757$	−24.2342	−0.880807	−0.440404	+	0.897800i	$0.645165\pi$
$758$	8.34741	0.303192
$759$	−104.151	−3.78045
$760$	0	0
$761$	−24.8054	−0.899195	−0.449597	−	0.893231i	$-0.648433\pi$
$761$	−24.8054	−0.899195	−0.449597	+	0.893231i	$0.648433\pi$
$762$	6.23015	0.225694
$763$	11.3557	0.411105
$764$	−22.3790	−0.809644
$765$	−47.1527	−1.70481
$766$	−9.48566	−0.342731
$767$	1.00832	0.0364082
$768$	2.79360	0.100806
$769$	9.64289	0.347732	0.173866	−	0.984769i	$-0.444374\pi$
$769$	9.64289	0.347732	0.173866	+	0.984769i	$0.444374\pi$
$770$	17.3298	0.624522
$771$	39.4799	1.42184
$772$	7.42811	0.267344
$773$	1.28731	0.0463014	0.0231507	−	0.999732i	$-0.492630\pi$
$773$	1.28731	0.0463014	0.0231507	+	0.999732i	$0.492630\pi$
$774$	−4.75320	−0.170850
$775$	3.20216	0.115025
$776$	17.3522	0.622907
$777$	14.2764	0.512162
$778$	36.0480	1.29238
$779$	0	0
$780$	−1.99300	−0.0713607
$781$	−25.4177	−0.909517
$782$	−27.1133	−0.969569
$783$	−15.7638	−0.563353
$784$	−5.35114	−0.191112
$785$	−32.5137	−1.16046
$786$	4.25369	0.151724
$787$	−16.3446	−0.582624	−0.291312	−	0.956628i	$-0.594092\pi$
$787$	−16.3446	−0.582624	−0.291312	+	0.956628i	$0.594092\pi$
$788$	8.53554	0.304066
$789$	21.1444	0.752762
$790$	−20.1085	−0.715427
$791$	18.2984	0.650617
$792$	27.6542	0.982648
$793$	−3.33538	−0.118443
$794$	−6.40906	−0.227449
$795$	−21.5531	−0.764410
$796$	−6.35926	−0.225398
$797$	−15.6884	−0.555712	−0.277856	−	0.960623i	$-0.589624\pi$
$797$	−15.6884	−0.555712	−0.277856	+	0.960623i	$0.589624\pi$
$798$	0	0
$799$	−18.3960	−0.650804
$800$	0.497039	0.0175730
$801$	−72.4311	−2.55923
$802$	0.187660	0.00662650
$803$	−13.0487	−0.460479
$804$	−12.2383	−0.431610
$805$	−19.4993	−0.687260
$806$	1.96033	0.0690496
$807$	−21.4290	−0.754337
$808$	3.67667	0.129345
$809$	−11.5248	−0.405192	−0.202596	−	0.979262i	$-0.564938\pi$
$809$	−11.5248	−0.405192	−0.202596	+	0.979262i	$0.564938\pi$
$810$	0.778611	0.0273576
$811$	−8.30102	−0.291488	−0.145744	−	0.989322i	$-0.546558\pi$
$811$	−8.30102	−0.291488	−0.145744	+	0.989322i	$0.546558\pi$
$812$	4.01603	0.140935
$813$	32.5871	1.14288
$814$	−22.9086	−0.802945
$815$	−33.4093	−1.17028
$816$	11.6946	0.409392
$817$	0	0
$818$	17.2663	0.603701
$819$	−1.87712	−0.0655919
$820$	11.7632	0.410788
$821$	−33.7112	−1.17653	−0.588265	−	0.808668i	$-0.700189\pi$
$821$	−33.7112	−1.17653	−0.588265	+	0.808668i	$0.700189\pi$
$822$	29.9244	1.04373
$823$	21.8678	0.762262	0.381131	−	0.924521i	$-0.375535\pi$
$823$	21.8678	0.762262	0.381131	+	0.924521i	$0.375535\pi$
$824$	19.0135	0.662368
$825$	7.99268	0.278269
$826$	−4.25512	−0.148055
$827$	39.1695	1.36206	0.681028	−	0.732257i	$-0.261533\pi$
$827$	39.1695	1.36206	0.681028	+	0.732257i	$0.261533\pi$
$828$	−31.1162	−1.08136
$829$	−14.4176	−0.500743	−0.250371	−	0.968150i	$-0.580553\pi$
$829$	−14.4176	−0.500743	−0.250371	+	0.968150i	$0.580553\pi$
$830$	22.8940	0.794661
$831$	76.6579	2.65923
$832$	0.304282	0.0105491
$833$	−22.4009	−0.776145
$834$	−30.2110	−1.04612
$835$	−27.1739	−0.940392
$836$	0	0
$837$	32.4719	1.12239
$838$	−1.72572	−0.0596139
$839$	20.9532	0.723385	0.361693	−	0.932297i	$-0.382199\pi$
$839$	20.9532	0.723385	0.361693	+	0.932297i	$0.382199\pi$
$840$	8.41049	0.290189
$841$	−19.2184	−0.662702
$842$	32.7546	1.12880
$843$	45.4561	1.56559
$844$	−13.9578	−0.480447
$845$	30.2624	1.04106
$846$	−21.1119	−0.725844
$847$	−28.4218	−0.976585
$848$	3.29064	0.113001
$849$	9.48077	0.325379
$850$	2.08070	0.0713675
$851$	25.7765	0.883607
$852$	−12.3357	−0.422614
$853$	51.9553	1.77892	0.889458	−	0.457017i	$-0.151082\pi$
$853$	51.9553	1.77892	0.889458	+	0.457017i	$0.151082\pi$
$854$	14.0754	0.481650
$855$	0	0
$856$	10.0373	0.343067
$857$	29.1835	0.996888	0.498444	−	0.866922i	$-0.333905\pi$
$857$	29.1835	0.996888	0.498444	+	0.866922i	$0.333905\pi$
$858$	4.89304	0.167046
$859$	21.9913	0.750335	0.375168	−	0.926957i	$-0.377585\pi$
$859$	21.9913	0.750335	0.375168	+	0.926957i	$0.377585\pi$
$860$	2.31967	0.0791002
$861$	17.9977	0.613360
$862$	−25.5119	−0.868939
$863$	−35.8157	−1.21918	−0.609590	−	0.792717i	$-0.708666\pi$
$863$	−35.8157	−1.21918	−0.609590	+	0.792717i	$0.708666\pi$
$864$	5.04029	0.171474
$865$	−9.33968	−0.317559
$866$	24.4834	0.831980
$867$	1.46442	0.0497343
$868$	−8.27263	−0.280791
$869$	49.3687	1.67472
$870$	20.4849	0.694505
$871$	−1.33300	−0.0451671
$872$	−8.84348	−0.299478
$873$	83.3638	2.82144
$874$	0	0
$875$	−13.5567	−0.458300
$876$	−6.33280	−0.213966
$877$	7.82483	0.264226	0.132113	−	0.991235i	$-0.457824\pi$
$877$	7.82483	0.264226	0.132113	+	0.991235i	$0.457824\pi$
$878$	−30.8388	−1.04076
$879$	65.3097	2.20284
$880$	−13.4959	−0.454946
$881$	−14.4829	−0.487941	−0.243970	−	0.969783i	$-0.578450\pi$
$881$	−14.4829	−0.487941	−0.243970	+	0.969783i	$0.578450\pi$
$882$	−25.7081	−0.865636
$883$	−23.5529	−0.792619	−0.396310	−	0.918117i	$-0.629709\pi$
$883$	−23.5529	−0.792619	−0.396310	+	0.918117i	$0.629709\pi$
$884$	1.27378	0.0428420
$885$	−21.7045	−0.729588
$886$	10.7047	0.359631
$887$	−15.8736	−0.532982	−0.266491	−	0.963837i	$-0.585864\pi$
$887$	−15.8736	−0.532982	−0.266491	+	0.963837i	$0.585864\pi$
$888$	−11.1180	−0.373095
$889$	−2.86368	−0.0960449
$890$	35.3481	1.18487
$891$	−1.91158	−0.0640404
$892$	8.92400	0.298798
$893$	0	0
$894$	−26.0751	−0.872081
$895$	19.8138	0.662301
$896$	−1.28408	−0.0428981
$897$	−5.50560	−0.183827
$898$	2.31562	0.0772731
$899$	−20.1492	−0.672013
$900$	2.38789	0.0795963
$901$	13.7753	0.458921
$902$	−28.8800	−0.961599
$903$	3.54911	0.118107
$904$	−14.2502	−0.473956
$905$	−19.8944	−0.661311
$906$	55.3781	1.83981
$907$	45.0127	1.49462	0.747311	−	0.664474i	$-0.231344\pi$
$907$	45.0127	1.49462	0.747311	+	0.664474i	$0.231344\pi$
$908$	−0.659796	−0.0218961
$909$	17.6635	0.585863
$910$	0.916079	0.0303677
$911$	−2.75901	−0.0914100	−0.0457050	−	0.998955i	$-0.514553\pi$
$911$	−2.75901	−0.0914100	−0.0457050	+	0.998955i	$0.514553\pi$
$912$	0	0
$913$	−56.2074	−1.86019
$914$	−0.0521810	−0.00172599
$915$	71.7956	2.37349
$916$	−6.97208	−0.230364
$917$	−1.95521	−0.0645667
$918$	21.0996	0.696392
$919$	−39.3083	−1.29666	−0.648331	−	0.761359i	$-0.724533\pi$
$919$	−39.3083	−1.29666	−0.648331	+	0.761359i	$0.724533\pi$
$920$	15.1854	0.500649
$921$	−3.87758	−0.127771
$922$	39.4720	1.29994
$923$	−1.34362	−0.0442258
$924$	−20.6487	−0.679294
$925$	−1.97811	−0.0650400
$926$	−6.19056	−0.203435
$927$	91.3453	3.00017
$928$	−3.12756	−0.102667
$929$	−29.7417	−0.975795	−0.487897	−	0.872901i	$-0.662236\pi$
$929$	−29.7417	−0.975795	−0.487897	+	0.872901i	$0.662236\pi$
$930$	−42.1970	−1.38369
$931$	0	0
$932$	−29.6097	−0.969898
$933$	−34.0547	−1.11490
$934$	−20.9962	−0.687015
$935$	−56.4964	−1.84763
$936$	1.46184	0.0477818
$937$	37.7211	1.23229	0.616147	−	0.787631i	$-0.288693\pi$
$937$	37.7211	1.23229	0.616147	+	0.787631i	$0.288693\pi$
$938$	5.62531	0.183673
$939$	46.1822	1.50710
$940$	10.3031	0.336051
$941$	−6.47652	−0.211129	−0.105564	−	0.994412i	$-0.533665\pi$
$941$	−6.47652	−0.211129	−0.105564	+	0.994412i	$0.533665\pi$
$942$	38.7407	1.26224
$943$	32.4955	1.05820
$944$	3.31375	0.107853
$945$	15.1744	0.493624
$946$	−5.69507	−0.185163
$947$	16.2913	0.529396	0.264698	−	0.964331i	$-0.414728\pi$
$947$	16.2913	0.529396	0.264698	+	0.964331i	$0.414728\pi$
$948$	23.9596	0.778171
$949$	−0.689776	−0.0223911
$950$	0	0
$951$	7.50953	0.243513
$952$	−5.37540	−0.174218
$953$	−34.6213	−1.12150	−0.560748	−	0.827987i	$-0.689486\pi$
$953$	−34.6213	−1.12150	−0.560748	+	0.827987i	$0.689486\pi$
$954$	15.8090	0.511835
$955$	52.4693	1.69787
$956$	−24.7034	−0.798965
$957$	−50.2930	−1.62574
$958$	15.5229	0.501523
$959$	−13.7547	−0.444164
$960$	−6.54982	−0.211395
$961$	10.5053	0.338882
$962$	−1.21098	−0.0390436
$963$	48.2213	1.55391
$964$	27.5586	0.887604
$965$	−17.4158	−0.560634
$966$	23.2338	0.747534
$967$	−48.9105	−1.57286	−0.786428	−	0.617682i	$-0.788072\pi$
$967$	−48.9105	−1.57286	−0.786428	+	0.617682i	$0.788072\pi$
$968$	22.1340	0.711414
$969$	0	0
$970$	−40.6835	−1.30627
$971$	6.07592	0.194986	0.0974928	−	0.995236i	$-0.468918\pi$
$971$	6.07592	0.194986	0.0974928	+	0.995236i	$0.468918\pi$
$972$	−16.0486	−0.514759
$973$	13.8865	0.445180
$974$	−28.6065	−0.916613
$975$	0.422505	0.0135310
$976$	−10.9615	−0.350868
$977$	57.0477	1.82512	0.912559	−	0.408944i	$-0.134103\pi$
$977$	57.0477	1.82512	0.912559	+	0.408944i	$0.134103\pi$
$978$	39.8077	1.27291
$979$	−86.7838	−2.77362
$980$	12.5462	0.400772
$981$	−42.4861	−1.35648
$982$	−30.3488	−0.968470
$983$	0.186519	0.00594905	0.00297452	−	0.999996i	$-0.499053\pi$
$983$	0.186519	0.00594905	0.00297452	+	0.999996i	$0.499053\pi$
$984$	−14.0160	−0.446815
$985$	−20.0122	−0.637642
$986$	−13.0926	−0.416952
$987$	15.7638	0.501768
$988$	0	0
$989$	6.40804	0.203764
$990$	−64.8373	−2.06066
$991$	−46.2398	−1.46886	−0.734428	−	0.678686i	$-0.762550\pi$
$991$	−46.2398	−1.46886	−0.734428	+	0.678686i	$0.762550\pi$
$992$	6.44246	0.204548
$993$	14.5631	0.462147
$994$	5.67010	0.179845
$995$	14.9098	0.472671
$996$	−27.2786	−0.864354
$997$	−20.8490	−0.660295	−0.330147	−	0.943929i	$-0.607098\pi$
$997$	−20.8490	−0.660295	−0.330147	+	0.943929i	$0.607098\pi$
$998$	8.77624	0.277807
$999$	−20.0593	−0.634650

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	722.2.a.n.1.4	yes	4
3.2	odd	2		6498.2.a.bx.1.3		4
4.3	odd	2		5776.2.a.bt.1.1		4
19.2	odd	18		722.2.e.s.99.1		24
19.3	odd	18		722.2.e.s.389.1		24
19.4	even	9		722.2.e.r.415.1		24
19.5	even	9		722.2.e.r.595.1		24
19.6	even	9		722.2.e.r.245.4		24
19.7	even	3		722.2.c.m.429.1		8
19.8	odd	6		722.2.c.n.653.4		8
19.9	even	9		722.2.e.r.423.4		24
19.10	odd	18		722.2.e.s.423.1		24
19.11	even	3		722.2.c.m.653.1		8
19.12	odd	6		722.2.c.n.429.4		8
19.13	odd	18		722.2.e.s.245.1		24
19.14	odd	18		722.2.e.s.595.4		24
19.15	odd	18		722.2.e.s.415.4		24
19.16	even	9		722.2.e.r.389.4		24
19.17	even	9		722.2.e.r.99.4		24
19.18	odd	2		722.2.a.m.1.1	✓	4
57.56	even	2		6498.2.a.ca.1.3		4
76.75	even	2		5776.2.a.bv.1.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
722.2.a.m.1.1	✓	4	19.18	odd	2
722.2.a.n.1.4	yes	4	1.1	even	1	trivial
722.2.c.m.429.1		8	19.7	even	3
722.2.c.m.653.1		8	19.11	even	3
722.2.c.n.429.4		8	19.12	odd	6
722.2.c.n.653.4		8	19.8	odd	6
722.2.e.r.99.4		24	19.17	even	9
722.2.e.r.245.4		24	19.6	even	9
722.2.e.r.389.4		24	19.16	even	9
722.2.e.r.415.1		24	19.4	even	9
722.2.e.r.423.4		24	19.9	even	9
722.2.e.r.595.1		24	19.5	even	9
722.2.e.s.99.1		24	19.2	odd	18
722.2.e.s.245.1		24	19.13	odd	18
722.2.e.s.389.1		24	19.3	odd	18
722.2.e.s.415.4		24	19.15	odd	18
722.2.e.s.423.1		24	19.10	odd	18
722.2.e.s.595.4		24	19.14	odd	18
5776.2.a.bt.1.1		4	4.3	odd	2
5776.2.a.bv.1.4		4	76.75	even	2
6498.2.a.bx.1.3		4	3.2	odd	2
6498.2.a.ca.1.3		4	57.56	even	2

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:	\( N \)	\(=\)	\( 722 = 2 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	722.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +2.79360 q^{3} +1.00000 q^{4} -2.34458 q^{5} +2.79360 q^{6} -1.28408 q^{7} +1.00000 q^{8} +4.80423 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +2.79360 q^{3} +1.00000 q^{4} -2.34458 q^{5} +2.79360 q^{6} -1.28408 q^{7} +1.00000 q^{8} +4.80423 q^{9} -2.34458 q^{10} +5.75621 q^{11} +2.79360 q^{12} +0.304282 q^{13} -1.28408 q^{14} -6.54982 q^{15} +1.00000 q^{16} +4.18619 q^{17} +4.80423 q^{18} -2.34458 q^{20} -3.58721 q^{21} +5.75621 q^{22} -6.47684 q^{23} +2.79360 q^{24} +0.497039 q^{25} +0.304282 q^{26} +5.04029 q^{27} -1.28408 q^{28} -3.12756 q^{29} -6.54982 q^{30} +6.44246 q^{31} +1.00000 q^{32} +16.0806 q^{33} +4.18619 q^{34} +3.01062 q^{35} +4.80423 q^{36} -3.97980 q^{37} +0.850045 q^{39} -2.34458 q^{40} -5.01719 q^{41} -3.58721 q^{42} -0.989378 q^{43} +5.75621 q^{44} -11.2639 q^{45} -6.47684 q^{46} -4.39445 q^{47} +2.79360 q^{48} -5.35114 q^{49} +0.497039 q^{50} +11.6946 q^{51} +0.304282 q^{52} +3.29064 q^{53} +5.04029 q^{54} -13.4959 q^{55} -1.28408 q^{56} -3.12756 q^{58} +3.31375 q^{59} -6.54982 q^{60} -10.9615 q^{61} +6.44246 q^{62} -6.16901 q^{63} +1.00000 q^{64} -0.713414 q^{65} +16.0806 q^{66} -4.38081 q^{67} +4.18619 q^{68} -18.0937 q^{69} +3.01062 q^{70} -4.41570 q^{71} +4.80423 q^{72} -2.26689 q^{73} -3.97980 q^{74} +1.38853 q^{75} -7.39144 q^{77} +0.850045 q^{78} +8.57659 q^{79} -2.34458 q^{80} -0.332090 q^{81} -5.01719 q^{82} -9.76464 q^{83} -3.58721 q^{84} -9.81485 q^{85} -0.989378 q^{86} -8.73716 q^{87} +5.75621 q^{88} -15.0765 q^{89} -11.2639 q^{90} -0.390723 q^{91} -6.47684 q^{92} +17.9977 q^{93} -4.39445 q^{94} +2.79360 q^{96} +17.3522 q^{97} -5.35114 q^{98} +27.6542 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} + 2 q^{3} + 4 q^{4} - 2 q^{5} + 2 q^{6} - 2 q^{7} + 4 q^{8} + 4 q^{9}+O(q^{10}) \) 4 * q + 4 * q^2 + 2 * q^3 + 4 * q^4 - 2 * q^5 + 2 * q^6 - 2 * q^7 + 4 * q^8 + 4 * q^9	\( 4 q + 4 q^{2} + 2 q^{3} + 4 q^{4} - 2 q^{5} + 2 q^{6} - 2 q^{7} + 4 q^{8} + 4 q^{9} - 2 q^{10} + 2 q^{11} + 2 q^{12} + 18 q^{13} - 2 q^{14} + 4 q^{15} + 4 q^{16} + 6 q^{17} + 4 q^{18} - 2 q^{20} + 4 q^{21} + 2 q^{22} - 10 q^{23} + 2 q^{24} + 6 q^{25} + 18 q^{26} - 4 q^{27} - 2 q^{28} - 2 q^{29} + 4 q^{30} + 26 q^{31} + 4 q^{32} + 16 q^{33} + 6 q^{34} + 6 q^{35} + 4 q^{36} + 4 q^{37} - 6 q^{39} - 2 q^{40} - 12 q^{41} + 4 q^{42} - 10 q^{43} + 2 q^{44} - 22 q^{45} - 10 q^{46} - 12 q^{47} + 2 q^{48} - 12 q^{49} + 6 q^{50} - 2 q^{51} + 18 q^{52} + 8 q^{53} - 4 q^{54} - 26 q^{55} - 2 q^{56} - 2 q^{58} - 8 q^{59} + 4 q^{60} + 26 q^{62} - 22 q^{63} + 4 q^{64} - 4 q^{65} + 16 q^{66} + 10 q^{67} + 6 q^{68} - 20 q^{69} + 6 q^{70} + 4 q^{72} - 14 q^{73} + 4 q^{74} + 8 q^{75} + 4 q^{77} - 6 q^{78} + 22 q^{79} - 2 q^{80} - 4 q^{81} - 12 q^{82} - 12 q^{83} + 4 q^{84} - 18 q^{85} - 10 q^{86} - 26 q^{87} + 2 q^{88} - 16 q^{89} - 22 q^{90} - 4 q^{91} - 10 q^{92} + 8 q^{93} - 12 q^{94} + 2 q^{96} + 28 q^{97} - 12 q^{98} + 22 q^{99}+O(q^{100}) \) 4 * q + 4 * q^2 + 2 * q^3 + 4 * q^4 - 2 * q^5 + 2 * q^6 - 2 * q^7 + 4 * q^8 + 4 * q^9 - 2 * q^10 + 2 * q^11 + 2 * q^12 + 18 * q^13 - 2 * q^14 + 4 * q^15 + 4 * q^16 + 6 * q^17 + 4 * q^18 - 2 * q^20 + 4 * q^21 + 2 * q^22 - 10 * q^23 + 2 * q^24 + 6 * q^25 + 18 * q^26 - 4 * q^27 - 2 * q^28 - 2 * q^29 + 4 * q^30 + 26 * q^31 + 4 * q^32 + 16 * q^33 + 6 * q^34 + 6 * q^35 + 4 * q^36 + 4 * q^37 - 6 * q^39 - 2 * q^40 - 12 * q^41 + 4 * q^42 - 10 * q^43 + 2 * q^44 - 22 * q^45 - 10 * q^46 - 12 * q^47 + 2 * q^48 - 12 * q^49 + 6 * q^50 - 2 * q^51 + 18 * q^52 + 8 * q^53 - 4 * q^54 - 26 * q^55 - 2 * q^56 - 2 * q^58 - 8 * q^59 + 4 * q^60 + 26 * q^62 - 22 * q^63 + 4 * q^64 - 4 * q^65 + 16 * q^66 + 10 * q^67 + 6 * q^68 - 20 * q^69 + 6 * q^70 + 4 * q^72 - 14 * q^73 + 4 * q^74 + 8 * q^75 + 4 * q^77 - 6 * q^78 + 22 * q^79 - 2 * q^80 - 4 * q^81 - 12 * q^82 - 12 * q^83 + 4 * q^84 - 18 * q^85 - 10 * q^86 - 26 * q^87 + 2 * q^88 - 16 * q^89 - 22 * q^90 - 4 * q^91 - 10 * q^92 + 8 * q^93 - 12 * q^94 + 2 * q^96 + 28 * q^97 - 12 * q^98 + 22 * q^99

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