LMFDB - Embedded newform 4010.2.a.n.1.1

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			1.1
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)

$f(q)$	$=$	$q+1.00000 q^{2} -3.32876 q^{3} +1.00000 q^{4} +1.00000 q^{5} -3.32876 q^{6} +2.40644 q^{7} +1.00000 q^{8} +8.08065 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -3.32876 q^{3} +1.00000 q^{4} +1.00000 q^{5} -3.32876 q^{6} +2.40644 q^{7} +1.00000 q^{8} +8.08065 q^{9} +1.00000 q^{10} -5.27965 q^{11} -3.32876 q^{12} +6.65331 q^{13} +2.40644 q^{14} -3.32876 q^{15} +1.00000 q^{16} +5.66099 q^{17} +8.08065 q^{18} +7.64311 q^{19} +1.00000 q^{20} -8.01048 q^{21} -5.27965 q^{22} -2.99716 q^{23} -3.32876 q^{24} +1.00000 q^{25} +6.65331 q^{26} -16.9123 q^{27} +2.40644 q^{28} -2.63490 q^{29} -3.32876 q^{30} +6.35433 q^{31} +1.00000 q^{32} +17.5747 q^{33} +5.66099 q^{34} +2.40644 q^{35} +8.08065 q^{36} -7.37615 q^{37} +7.64311 q^{38} -22.1473 q^{39} +1.00000 q^{40} +3.95921 q^{41} -8.01048 q^{42} +6.05327 q^{43} -5.27965 q^{44} +8.08065 q^{45} -2.99716 q^{46} +2.62634 q^{47} -3.32876 q^{48} -1.20903 q^{49} +1.00000 q^{50} -18.8441 q^{51} +6.65331 q^{52} -0.218753 q^{53} -16.9123 q^{54} -5.27965 q^{55} +2.40644 q^{56} -25.4421 q^{57} -2.63490 q^{58} -9.80905 q^{59} -3.32876 q^{60} -6.45762 q^{61} +6.35433 q^{62} +19.4456 q^{63} +1.00000 q^{64} +6.65331 q^{65} +17.5747 q^{66} +3.10361 q^{67} +5.66099 q^{68} +9.97682 q^{69} +2.40644 q^{70} +3.85168 q^{71} +8.08065 q^{72} +7.88377 q^{73} -7.37615 q^{74} -3.32876 q^{75} +7.64311 q^{76} -12.7052 q^{77} -22.1473 q^{78} -6.19901 q^{79} +1.00000 q^{80} +32.0550 q^{81} +3.95921 q^{82} -12.2324 q^{83} -8.01048 q^{84} +5.66099 q^{85} +6.05327 q^{86} +8.77096 q^{87} -5.27965 q^{88} +13.9135 q^{89} +8.08065 q^{90} +16.0108 q^{91} -2.99716 q^{92} -21.1520 q^{93} +2.62634 q^{94} +7.64311 q^{95} -3.32876 q^{96} +3.82434 q^{97} -1.20903 q^{98} -42.6630 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−3.32876	−1.92186	−0.960931	−	0.276789i	$-0.910730\pi$
$3$	−3.32876	−1.92186	−0.960931	+	0.276789i	$0.910730\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−3.32876	−1.35896
$7$	2.40644	0.909550	0.454775	−	0.890606i	$-0.349720\pi$
$7$	2.40644	0.909550	0.454775	+	0.890606i	$0.349720\pi$
$8$	1.00000	0.353553
$9$	8.08065	2.69355
$10$	1.00000	0.316228
$11$	−5.27965	−1.59187	−0.795937	−	0.605380i	$-0.793021\pi$
$11$	−5.27965	−1.59187	−0.795937	+	0.605380i	$0.793021\pi$
$12$	−3.32876	−0.960931
$13$	6.65331	1.84530	0.922648	−	0.385643i	$-0.126020\pi$
$13$	6.65331	1.84530	0.922648	+	0.385643i	$0.126020\pi$
$14$	2.40644	0.643149
$15$	−3.32876	−0.859483
$16$	1.00000	0.250000
$17$	5.66099	1.37299	0.686495	−	0.727134i	$-0.259148\pi$
$17$	5.66099	1.37299	0.686495	+	0.727134i	$0.259148\pi$
$18$	8.08065	1.90463
$19$	7.64311	1.75345	0.876725	−	0.480993i	$-0.159724\pi$
$19$	7.64311	1.75345	0.876725	+	0.480993i	$0.159724\pi$
$20$	1.00000	0.223607
$21$	−8.01048	−1.74803
$22$	−5.27965	−1.12562
$23$	−2.99716	−0.624951	−0.312475	−	0.949926i	$-0.601158\pi$
$23$	−2.99716	−0.624951	−0.312475	+	0.949926i	$0.601158\pi$
$24$	−3.32876	−0.679481
$25$	1.00000	0.200000
$26$	6.65331	1.30482
$27$	−16.9123	−3.25477
$28$	2.40644	0.454775
$29$	−2.63490	−0.489289	−0.244645	−	0.969613i	$-0.578671\pi$
$29$	−2.63490	−0.489289	−0.244645	+	0.969613i	$0.578671\pi$
$30$	−3.32876	−0.607746
$31$	6.35433	1.14127	0.570635	−	0.821204i	$-0.306697\pi$
$31$	6.35433	1.14127	0.570635	+	0.821204i	$0.306697\pi$
$32$	1.00000	0.176777
$33$	17.5747	3.05936
$34$	5.66099	0.970851
$35$	2.40644	0.406763
$36$	8.08065	1.34678
$37$	−7.37615	−1.21263	−0.606316	−	0.795224i	$-0.707353\pi$
$37$	−7.37615	−1.21263	−0.606316	+	0.795224i	$0.707353\pi$
$38$	7.64311	1.23988
$39$	−22.1473	−3.54640
$40$	1.00000	0.158114
$41$	3.95921	0.618325	0.309162	−	0.951009i	$-0.399951\pi$
$41$	3.95921	0.618325	0.309162	+	0.951009i	$0.399951\pi$
$42$	−8.01048	−1.23604
$43$	6.05327	0.923115	0.461557	−	0.887110i	$-0.347291\pi$
$43$	6.05327	0.923115	0.461557	+	0.887110i	$0.347291\pi$
$44$	−5.27965	−0.795937
$45$	8.08065	1.20459
$46$	−2.99716	−0.441907
$47$	2.62634	0.383091	0.191545	−	0.981484i	$-0.438650\pi$
$47$	2.62634	0.383091	0.191545	+	0.981484i	$0.438650\pi$
$48$	−3.32876	−0.480465
$49$	−1.20903	−0.172718
$50$	1.00000	0.141421
$51$	−18.8441	−2.63870
$52$	6.65331	0.922648
$53$	−0.218753	−0.0300480	−0.0150240	−	0.999887i	$-0.504782\pi$
$53$	−0.218753	−0.0300480	−0.0150240	+	0.999887i	$0.504782\pi$
$54$	−16.9123	−2.30147
$55$	−5.27965	−0.711907
$56$	2.40644	0.321575
$57$	−25.4421	−3.36989
$58$	−2.63490	−0.345980
$59$	−9.80905	−1.27703	−0.638515	−	0.769610i	$-0.720451\pi$
$59$	−9.80905	−1.27703	−0.638515	+	0.769610i	$0.720451\pi$
$60$	−3.32876	−0.429741
$61$	−6.45762	−0.826814	−0.413407	−	0.910546i	$-0.635661\pi$
$61$	−6.45762	−0.826814	−0.413407	+	0.910546i	$0.635661\pi$
$62$	6.35433	0.807000
$63$	19.4456	2.44992
$64$	1.00000	0.125000
$65$	6.65331	0.825242
$66$	17.5747	2.16329
$67$	3.10361	0.379167	0.189583	−	0.981865i	$-0.439286\pi$
$67$	3.10361	0.379167	0.189583	+	0.981865i	$0.439286\pi$
$68$	5.66099	0.686495
$69$	9.97682	1.20107
$70$	2.40644	0.287625
$71$	3.85168	0.457110	0.228555	−	0.973531i	$-0.426600\pi$
$71$	3.85168	0.457110	0.228555	+	0.973531i	$0.426600\pi$
$72$	8.08065	0.952314
$73$	7.88377	0.922726	0.461363	−	0.887211i	$-0.347361\pi$
$73$	7.88377	0.922726	0.461363	+	0.887211i	$0.347361\pi$
$74$	−7.37615	−0.857460
$75$	−3.32876	−0.384372
$76$	7.64311	0.876725
$77$	−12.7052	−1.44789
$78$	−22.1473	−2.50769
$79$	−6.19901	−0.697444	−0.348722	−	0.937226i	$-0.613384\pi$
$79$	−6.19901	−0.697444	−0.348722	+	0.937226i	$0.613384\pi$
$80$	1.00000	0.111803
$81$	32.0550	3.56167
$82$	3.95921	0.437222
$83$	−12.2324	−1.34268	−0.671338	−	0.741152i	$-0.734280\pi$
$83$	−12.2324	−1.34268	−0.671338	+	0.741152i	$0.734280\pi$
$84$	−8.01048	−0.874015
$85$	5.66099	0.614020
$86$	6.05327	0.652741
$87$	8.77096	0.940346
$88$	−5.27965	−0.562812
$89$	13.9135	1.47483	0.737416	−	0.675439i	$-0.236046\pi$
$89$	13.9135	1.47483	0.737416	+	0.675439i	$0.236046\pi$
$90$	8.08065	0.851776
$91$	16.0108	1.67839
$92$	−2.99716	−0.312475
$93$	−21.1520	−2.19336
$94$	2.62634	0.270886
$95$	7.64311	0.784166
$96$	−3.32876	−0.339740
$97$	3.82434	0.388303	0.194151	−	0.980972i	$-0.437805\pi$
$97$	3.82434	0.388303	0.194151	+	0.980972i	$0.437805\pi$
$98$	−1.20903	−0.122130
$99$	−42.6630	−4.28779
$100$	1.00000	0.100000
$101$	−1.47829	−0.147095	−0.0735476	−	0.997292i	$-0.523432\pi$
$101$	−1.47829	−0.147095	−0.0735476	+	0.997292i	$0.523432\pi$
$102$	−18.8441	−1.86584
$103$	−15.2695	−1.50455	−0.752274	−	0.658850i	$-0.771043\pi$
$103$	−15.2695	−1.50455	−0.752274	+	0.658850i	$0.771043\pi$
$104$	6.65331	0.652411
$105$	−8.01048	−0.781743
$106$	−0.218753	−0.0212471
$107$	−12.4022	−1.19896	−0.599481	−	0.800389i	$-0.704626\pi$
$107$	−12.4022	−1.19896	−0.599481	+	0.800389i	$0.704626\pi$
$108$	−16.9123	−1.62739
$109$	5.67491	0.543557	0.271779	−	0.962360i	$-0.412388\pi$
$109$	5.67491	0.543557	0.271779	+	0.962360i	$0.412388\pi$
$110$	−5.27965	−0.503394
$111$	24.5534	2.33051
$112$	2.40644	0.227388
$113$	−11.3175	−1.06466	−0.532330	−	0.846537i	$-0.678684\pi$
$113$	−11.3175	−1.06466	−0.532330	+	0.846537i	$0.678684\pi$
$114$	−25.4421	−2.38287
$115$	−2.99716	−0.279486
$116$	−2.63490	−0.244645
$117$	53.7631	4.97040
$118$	−9.80905	−0.902996
$119$	13.6228	1.24880
$120$	−3.32876	−0.303873
$121$	16.8747	1.53406
$122$	−6.45762	−0.584646
$123$	−13.1793	−1.18833
$124$	6.35433	0.570635
$125$	1.00000	0.0894427
$126$	19.4456	1.73236
$127$	−9.41065	−0.835060	−0.417530	−	0.908663i	$-0.637104\pi$
$127$	−9.41065	−0.835060	−0.417530	+	0.908663i	$0.637104\pi$
$128$	1.00000	0.0883883
$129$	−20.1499	−1.77410
$130$	6.65331	0.583534
$131$	3.17192	0.277132	0.138566	−	0.990353i	$-0.455751\pi$
$131$	3.17192	0.277132	0.138566	+	0.990353i	$0.455751\pi$
$132$	17.5747	1.52968
$133$	18.3927	1.59485
$134$	3.10361	0.268111
$135$	−16.9123	−1.45558
$136$	5.66099	0.485425
$137$	−6.60284	−0.564119	−0.282059	−	0.959397i	$-0.591018\pi$
$137$	−6.60284	−0.564119	−0.282059	+	0.959397i	$0.591018\pi$
$138$	9.97682	0.849284
$139$	−3.51203	−0.297887	−0.148943	−	0.988846i	$-0.547587\pi$
$139$	−3.51203	−0.297887	−0.148943	+	0.988846i	$0.547587\pi$
$140$	2.40644	0.203382
$141$	−8.74245	−0.736247
$142$	3.85168	0.323226
$143$	−35.1271	−2.93748
$144$	8.08065	0.673388
$145$	−2.63490	−0.218817
$146$	7.88377	0.652466
$147$	4.02456	0.331940
$148$	−7.37615	−0.606316
$149$	9.73491	0.797515	0.398757	−	0.917057i	$-0.369442\pi$
$149$	9.73491	0.797515	0.398757	+	0.917057i	$0.369442\pi$
$150$	−3.32876	−0.271792
$151$	9.77443	0.795432	0.397716	−	0.917509i	$-0.369803\pi$
$151$	9.77443	0.795432	0.397716	+	0.917509i	$0.369803\pi$
$152$	7.64311	0.619938
$153$	45.7445	3.69822
$154$	−12.7052	−1.02381
$155$	6.35433	0.510392
$156$	−22.1473	−1.77320
$157$	2.44718	0.195306	0.0976530	−	0.995221i	$-0.468866\pi$
$157$	2.44718	0.195306	0.0976530	+	0.995221i	$0.468866\pi$
$158$	−6.19901	−0.493167
$159$	0.728176	0.0577481
$160$	1.00000	0.0790569
$161$	−7.21249	−0.568424
$162$	32.0550	2.51848
$163$	23.0340	1.80416	0.902082	−	0.431566i	$-0.142039\pi$
$163$	23.0340	1.80416	0.902082	+	0.431566i	$0.142039\pi$
$164$	3.95921	0.309162
$165$	17.5747	1.36819
$166$	−12.2324	−0.949415
$167$	2.32456	0.179880	0.0899400	−	0.995947i	$-0.471332\pi$
$167$	2.32456	0.179880	0.0899400	+	0.995947i	$0.471332\pi$
$168$	−8.01048	−0.618022
$169$	31.2665	2.40512
$170$	5.66099	0.434178
$171$	61.7613	4.72300
$172$	6.05327	0.461557
$173$	21.3907	1.62630	0.813151	−	0.582053i	$-0.197750\pi$
$173$	21.3907	1.62630	0.813151	+	0.582053i	$0.197750\pi$
$174$	8.77096	0.664925
$175$	2.40644	0.181910
$176$	−5.27965	−0.397968
$177$	32.6520	2.45427
$178$	13.9135	1.04286
$179$	6.86725	0.513282	0.256641	−	0.966507i	$-0.417384\pi$
$179$	6.86725	0.513282	0.256641	+	0.966507i	$0.417384\pi$
$180$	8.08065	0.602296
$181$	16.9534	1.26014	0.630068	−	0.776540i	$-0.283027\pi$
$181$	16.9534	1.26014	0.630068	+	0.776540i	$0.283027\pi$
$182$	16.0108	1.18680
$183$	21.4959	1.58902
$184$	−2.99716	−0.220953
$185$	−7.37615	−0.542305
$186$	−21.1520	−1.55094
$187$	−29.8880	−2.18563
$188$	2.62634	0.191545
$189$	−40.6985	−2.96038
$190$	7.64311	0.554489
$191$	8.39188	0.607215	0.303608	−	0.952797i	$-0.401809\pi$
$191$	8.39188	0.607215	0.303608	+	0.952797i	$0.401809\pi$
$192$	−3.32876	−0.240233
$193$	22.2863	1.60420	0.802100	−	0.597189i	$-0.203716\pi$
$193$	22.2863	1.60420	0.802100	+	0.597189i	$0.203716\pi$
$194$	3.82434	0.274571
$195$	−22.1473	−1.58600
$196$	−1.20903	−0.0863590
$197$	−27.6372	−1.96907	−0.984533	−	0.175200i	$-0.943943\pi$
$197$	−27.6372	−1.96907	−0.984533	+	0.175200i	$0.943943\pi$
$198$	−42.6630	−3.03193
$199$	8.54215	0.605537	0.302769	−	0.953064i	$-0.402089\pi$
$199$	8.54215	0.605537	0.302769	+	0.953064i	$0.402089\pi$
$200$	1.00000	0.0707107
$201$	−10.3312	−0.728706
$202$	−1.47829	−0.104012
$203$	−6.34075	−0.445033
$204$	−18.8441	−1.31935
$205$	3.95921	0.276523
$206$	−15.2695	−1.06388
$207$	−24.2190	−1.68334
$208$	6.65331	0.461324
$209$	−40.3529	−2.79127
$210$	−8.01048	−0.552776
$211$	−10.2696	−0.706987	−0.353494	−	0.935437i	$-0.615006\pi$
$211$	−10.2696	−0.706987	−0.353494	+	0.935437i	$0.615006\pi$
$212$	−0.218753	−0.0150240
$213$	−12.8213	−0.878503
$214$	−12.4022	−0.847794
$215$	6.05327	0.412829
$216$	−16.9123	−1.15074
$217$	15.2913	1.03804
$218$	5.67491	0.384353
$219$	−26.2432	−1.77335
$220$	−5.27965	−0.355954
$221$	37.6643	2.53357
$222$	24.5534	1.64792
$223$	5.18677	0.347332	0.173666	−	0.984805i	$-0.444439\pi$
$223$	5.18677	0.347332	0.173666	+	0.984805i	$0.444439\pi$
$224$	2.40644	0.160787
$225$	8.08065	0.538710
$226$	−11.3175	−0.752829
$227$	19.3840	1.28656	0.643282	−	0.765630i	$-0.277572\pi$
$227$	19.3840	1.28656	0.643282	+	0.765630i	$0.277572\pi$
$228$	−25.4421	−1.68494
$229$	−20.8692	−1.37908	−0.689538	−	0.724250i	$-0.742186\pi$
$229$	−20.8692	−1.37908	−0.689538	+	0.724250i	$0.742186\pi$
$230$	−2.99716	−0.197627
$231$	42.2925	2.78264
$232$	−2.63490	−0.172990
$233$	−8.40040	−0.550328	−0.275164	−	0.961397i	$-0.588732\pi$
$233$	−8.40040	−0.550328	−0.275164	+	0.961397i	$0.588732\pi$
$234$	53.7631	3.51460
$235$	2.62634	0.171323
$236$	−9.80905	−0.638515
$237$	20.6350	1.34039
$238$	13.6228	0.883038
$239$	28.8205	1.86425	0.932123	−	0.362142i	$-0.117954\pi$
$239$	28.8205	1.86425	0.932123	+	0.362142i	$0.117954\pi$
$240$	−3.32876	−0.214871
$241$	0.193530	0.0124664	0.00623318	−	0.999981i	$-0.498016\pi$
$241$	0.193530	0.0124664	0.00623318	+	0.999981i	$0.498016\pi$
$242$	16.8747	1.08474
$243$	−55.9666	−3.59026
$244$	−6.45762	−0.413407
$245$	−1.20903	−0.0772419
$246$	−13.1793	−0.840279
$247$	50.8520	3.23563
$248$	6.35433	0.403500
$249$	40.7186	2.58044
$250$	1.00000	0.0632456
$251$	−22.4668	−1.41809	−0.709046	−	0.705162i	$-0.750874\pi$
$251$	−22.4668	−1.41809	−0.709046	+	0.705162i	$0.750874\pi$
$252$	19.4456	1.22496
$253$	15.8239	0.994842
$254$	−9.41065	−0.590477
$255$	−18.8441	−1.18006
$256$	1.00000	0.0625000
$257$	−19.1811	−1.19648	−0.598242	−	0.801315i	$-0.704134\pi$
$257$	−19.1811	−1.19648	−0.598242	+	0.801315i	$0.704134\pi$
$258$	−20.1499	−1.25448
$259$	−17.7503	−1.10295
$260$	6.65331	0.412621
$261$	−21.2917	−1.31793
$262$	3.17192	0.195962
$263$	−14.7625	−0.910294	−0.455147	−	0.890416i	$-0.650413\pi$
$263$	−14.7625	−0.910294	−0.455147	+	0.890416i	$0.650413\pi$
$264$	17.5747	1.08165
$265$	−0.218753	−0.0134379
$266$	18.3927	1.12773
$267$	−46.3149	−2.83442
$268$	3.10361	0.189583
$269$	25.3355	1.54473	0.772366	−	0.635178i	$-0.219073\pi$
$269$	25.3355	1.54473	0.772366	+	0.635178i	$0.219073\pi$
$270$	−16.9123	−1.02925
$271$	7.00862	0.425743	0.212872	−	0.977080i	$-0.431718\pi$
$271$	7.00862	0.425743	0.212872	+	0.977080i	$0.431718\pi$
$272$	5.66099	0.343248
$273$	−53.2962	−3.22563
$274$	−6.60284	−0.398892
$275$	−5.27965	−0.318375
$276$	9.97682	0.600534
$277$	−15.1870	−0.912500	−0.456250	−	0.889852i	$-0.650808\pi$
$277$	−15.1870	−0.912500	−0.456250	+	0.889852i	$0.650808\pi$
$278$	−3.51203	−0.210638
$279$	51.3471	3.07407
$280$	2.40644	0.143813
$281$	−13.8554	−0.826546	−0.413273	−	0.910607i	$-0.635614\pi$
$281$	−13.8554	−0.826546	−0.413273	+	0.910607i	$0.635614\pi$
$282$	−8.74245	−0.520605
$283$	22.2872	1.32484	0.662418	−	0.749134i	$-0.269530\pi$
$283$	22.2872	1.32484	0.662418	+	0.749134i	$0.269530\pi$
$284$	3.85168	0.228555
$285$	−25.4421	−1.50706
$286$	−35.1271	−2.07711
$287$	9.52762	0.562398
$288$	8.08065	0.476157
$289$	15.0468	0.885103
$290$	−2.63490	−0.154727
$291$	−12.7303	−0.746264
$292$	7.88377	0.461363
$293$	−17.7935	−1.03951	−0.519754	−	0.854316i	$-0.673976\pi$
$293$	−17.7935	−1.03951	−0.519754	+	0.854316i	$0.673976\pi$
$294$	4.02456	0.234717
$295$	−9.80905	−0.571105
$296$	−7.37615	−0.428730
$297$	89.2909	5.18118
$298$	9.73491	0.563928
$299$	−19.9410	−1.15322
$300$	−3.32876	−0.192186
$301$	14.5668	0.839619
$302$	9.77443	0.562455
$303$	4.92087	0.282697
$304$	7.64311	0.438362
$305$	−6.45762	−0.369762
$306$	45.7445	2.61504
$307$	7.48351	0.427106	0.213553	−	0.976931i	$-0.431496\pi$
$307$	7.48351	0.427106	0.213553	+	0.976931i	$0.431496\pi$
$308$	−12.7052	−0.723944
$309$	50.8285	2.89153
$310$	6.35433	0.360902
$311$	19.1108	1.08367	0.541836	−	0.840484i	$-0.317729\pi$
$311$	19.1108	1.08367	0.541836	+	0.840484i	$0.317729\pi$
$312$	−22.1473	−1.25384
$313$	−14.7020	−0.831009	−0.415504	−	0.909591i	$-0.636395\pi$
$313$	−14.7020	−0.831009	−0.415504	+	0.909591i	$0.636395\pi$
$314$	2.44718	0.138102
$315$	19.4456	1.09564
$316$	−6.19901	−0.348722
$317$	14.5979	0.819902	0.409951	−	0.912108i	$-0.365546\pi$
$317$	14.5979	0.819902	0.409951	+	0.912108i	$0.365546\pi$
$318$	0.728176	0.0408341
$319$	13.9114	0.778886
$320$	1.00000	0.0559017
$321$	41.2838	2.30424
$322$	−7.21249	−0.401937
$323$	43.2675	2.40747
$324$	32.0550	1.78083
$325$	6.65331	0.369059
$326$	23.0340	1.27574
$327$	−18.8904	−1.04464
$328$	3.95921	0.218611
$329$	6.32013	0.348440
$330$	17.5747	0.967454
$331$	−8.28683	−0.455485	−0.227743	−	0.973721i	$-0.573135\pi$
$331$	−8.28683	−0.455485	−0.227743	+	0.973721i	$0.573135\pi$
$332$	−12.2324	−0.671338
$333$	−59.6041	−3.26628
$334$	2.32456	0.127194
$335$	3.10361	0.169569
$336$	−8.01048	−0.437007
$337$	−15.8247	−0.862029	−0.431015	−	0.902345i	$-0.641844\pi$
$337$	−15.8247	−0.862029	−0.431015	+	0.902345i	$0.641844\pi$
$338$	31.2665	1.70068
$339$	37.6733	2.04613
$340$	5.66099	0.307010
$341$	−33.5486	−1.81676
$342$	61.7613	3.33967
$343$	−19.7546	−1.06665
$344$	6.05327	0.326370
$345$	9.97682	0.537134
$346$	21.3907	1.14997
$347$	−2.10811	−0.113169	−0.0565846	−	0.998398i	$-0.518021\pi$
$347$	−2.10811	−0.113169	−0.0565846	+	0.998398i	$0.518021\pi$
$348$	8.77096	0.470173
$349$	−2.18344	−0.116877	−0.0584386	−	0.998291i	$-0.518612\pi$
$349$	−2.18344	−0.116877	−0.0584386	+	0.998291i	$0.518612\pi$
$350$	2.40644	0.128630
$351$	−112.523	−6.00602
$352$	−5.27965	−0.281406
$353$	−19.7256	−1.04989	−0.524943	−	0.851137i	$-0.675913\pi$
$353$	−19.7256	−1.04989	−0.524943	+	0.851137i	$0.675913\pi$
$354$	32.6520	1.73543
$355$	3.85168	0.204426
$356$	13.9135	0.737416
$357$	−45.3472	−2.40003
$358$	6.86725	0.362945
$359$	25.2519	1.33274	0.666372	−	0.745619i	$-0.267846\pi$
$359$	25.2519	1.33274	0.666372	+	0.745619i	$0.267846\pi$
$360$	8.08065	0.425888
$361$	39.4171	2.07458
$362$	16.9534	0.891051
$363$	−56.1717	−2.94825
$364$	16.0108	0.839195
$365$	7.88377	0.412656
$366$	21.4959	1.12361
$367$	−13.6044	−0.710142	−0.355071	−	0.934839i	$-0.615543\pi$
$367$	−13.6044	−0.710142	−0.355071	+	0.934839i	$0.615543\pi$
$368$	−2.99716	−0.156238
$369$	31.9930	1.66549
$370$	−7.37615	−0.383468
$371$	−0.526416	−0.0273302
$372$	−21.1520	−1.09668
$373$	20.8198	1.07801	0.539003	−	0.842304i	$-0.318801\pi$
$373$	20.8198	1.07801	0.539003	+	0.842304i	$0.318801\pi$
$374$	−29.8880	−1.54547
$375$	−3.32876	−0.171897
$376$	2.62634	0.135443
$377$	−17.5308	−0.902884
$378$	−40.6985	−2.09330
$379$	−16.1963	−0.831948	−0.415974	−	0.909376i	$-0.636559\pi$
$379$	−16.1963	−0.831948	−0.415974	+	0.909376i	$0.636559\pi$
$380$	7.64311	0.392083
$381$	31.3258	1.60487
$382$	8.39188	0.429366
$383$	−19.7265	−1.00798	−0.503989	−	0.863710i	$-0.668135\pi$
$383$	−19.7265	−1.00798	−0.503989	+	0.863710i	$0.668135\pi$
$384$	−3.32876	−0.169870
$385$	−12.7052	−0.647516
$386$	22.2863	1.13434
$387$	48.9144	2.48646
$388$	3.82434	0.194151
$389$	15.2103	0.771193	0.385597	−	0.922667i	$-0.373996\pi$
$389$	15.2103	0.771193	0.385597	+	0.922667i	$0.373996\pi$
$390$	−22.1473	−1.12147
$391$	−16.9669	−0.858051
$392$	−1.20903	−0.0610651
$393$	−10.5586	−0.532609
$394$	−27.6372	−1.39234
$395$	−6.19901	−0.311906
$396$	−42.6630	−2.14390
$397$	−25.3122	−1.27039	−0.635193	−	0.772354i	$-0.719079\pi$
$397$	−25.3122	−1.27039	−0.635193	+	0.772354i	$0.719079\pi$
$398$	8.54215	0.428179
$399$	−61.2249	−3.06508
$400$	1.00000	0.0500000
$401$	1.00000	0.0499376
$401$	1.00000	0.0499376
$402$	−10.3312	−0.515273
$403$	42.2773	2.10598
$404$	−1.47829	−0.0735476
$405$	32.0550	1.59283
$406$	−6.34075	−0.314686
$407$	38.9434	1.93036
$408$	−18.8441	−0.932921
$409$	15.7689	0.779722	0.389861	−	0.920874i	$-0.372523\pi$
$409$	15.7689	0.779722	0.389861	+	0.920874i	$0.372523\pi$
$410$	3.95921	0.195531
$411$	21.9793	1.08416
$412$	−15.2695	−0.752274
$413$	−23.6049	−1.16152
$414$	−24.2190	−1.19030
$415$	−12.2324	−0.600463
$416$	6.65331	0.326205
$417$	11.6907	0.572497
$418$	−40.3529	−1.97372
$419$	−14.7141	−0.718832	−0.359416	−	0.933178i	$-0.617024\pi$
$419$	−14.7141	−0.718832	−0.359416	+	0.933178i	$0.617024\pi$
$420$	−8.01048	−0.390871
$421$	28.1408	1.37150	0.685748	−	0.727839i	$-0.259475\pi$
$421$	28.1408	1.37150	0.685748	+	0.727839i	$0.259475\pi$
$422$	−10.2696	−0.499915
$423$	21.2225	1.03187
$424$	−0.218753	−0.0106236
$425$	5.66099	0.274598
$426$	−12.8213	−0.621195
$427$	−15.5399	−0.752029
$428$	−12.4022	−0.599481
$429$	116.930	5.64542
$430$	6.05327	0.291914
$431$	18.8169	0.906379	0.453189	−	0.891414i	$-0.350286\pi$
$431$	18.8169	0.906379	0.453189	+	0.891414i	$0.350286\pi$
$432$	−16.9123	−0.813693
$433$	3.25749	0.156545	0.0782725	−	0.996932i	$-0.475060\pi$
$433$	3.25749	0.156545	0.0782725	+	0.996932i	$0.475060\pi$
$434$	15.2913	0.734007
$435$	8.77096	0.420536
$436$	5.67491	0.271779
$437$	−22.9076	−1.09582
$438$	−26.2432	−1.25395
$439$	−10.9482	−0.522529	−0.261265	−	0.965267i	$-0.584140\pi$
$439$	−10.9482	−0.522529	−0.261265	+	0.965267i	$0.584140\pi$
$440$	−5.27965	−0.251697
$441$	−9.76972	−0.465225
$442$	37.6643	1.79151
$443$	−19.4685	−0.924978	−0.462489	−	0.886625i	$-0.653043\pi$
$443$	−19.4685	−0.924978	−0.462489	+	0.886625i	$0.653043\pi$
$444$	24.5534	1.16525
$445$	13.9135	0.659565
$446$	5.18677	0.245601
$447$	−32.4052	−1.53271
$448$	2.40644	0.113694
$449$	−26.9386	−1.27131	−0.635655	−	0.771973i	$-0.719270\pi$
$449$	−26.9386	−1.27131	−0.635655	+	0.771973i	$0.719270\pi$
$450$	8.08065	0.380926
$451$	−20.9032	−0.984295
$452$	−11.3175	−0.532330
$453$	−32.5367	−1.52871
$454$	19.3840	0.909738
$455$	16.0108	0.750599
$456$	−25.4421	−1.19143
$457$	−11.1153	−0.519951	−0.259976	−	0.965615i	$-0.583715\pi$
$457$	−11.1153	−0.519951	−0.259976	+	0.965615i	$0.583715\pi$
$458$	−20.8692	−0.975154
$459$	−95.7402	−4.46877
$460$	−2.99716	−0.139743
$461$	−16.6344	−0.774743	−0.387371	−	0.921924i	$-0.626617\pi$
$461$	−16.6344	−0.774743	−0.387371	+	0.921924i	$0.626617\pi$
$462$	42.2925	1.96762
$463$	−27.0627	−1.25771	−0.628854	−	0.777523i	$-0.716476\pi$
$463$	−27.0627	−1.25771	−0.628854	+	0.777523i	$0.716476\pi$
$464$	−2.63490	−0.122322
$465$	−21.1520	−0.980902
$466$	−8.40040	−0.389141
$467$	33.0726	1.53042	0.765208	−	0.643783i	$-0.222636\pi$
$467$	33.0726	1.53042	0.765208	+	0.643783i	$0.222636\pi$
$468$	53.7631	2.48520
$469$	7.46868	0.344871
$470$	2.62634	0.121144
$471$	−8.14607	−0.375351
$472$	−9.80905	−0.451498
$473$	−31.9591	−1.46948
$474$	20.6350	0.947799
$475$	7.64311	0.350690
$476$	13.6228	0.624402
$477$	−1.76766	−0.0809358
$478$	28.8205	1.31822
$479$	12.5633	0.574032	0.287016	−	0.957926i	$-0.407337\pi$
$479$	12.5633	0.574032	0.287016	+	0.957926i	$0.407337\pi$
$480$	−3.32876	−0.151936
$481$	−49.0758	−2.23766
$482$	0.193530	0.00881505
$483$	24.0087	1.09243
$484$	16.8747	0.767030
$485$	3.82434	0.173654
$486$	−55.9666	−2.53870
$487$	40.2031	1.82178	0.910888	−	0.412654i	$-0.135398\pi$
$487$	40.2031	1.82178	0.910888	+	0.412654i	$0.135398\pi$
$488$	−6.45762	−0.292323
$489$	−76.6747	−3.46735
$490$	−1.20903	−0.0546182
$491$	5.28440	0.238482	0.119241	−	0.992865i	$-0.461954\pi$
$491$	5.28440	0.238482	0.119241	+	0.992865i	$0.461954\pi$
$492$	−13.1793	−0.594167
$493$	−14.9161	−0.671790
$494$	50.8520	2.28794
$495$	−42.6630	−1.91756
$496$	6.35433	0.285318
$497$	9.26885	0.415765
$498$	40.7186	1.82464
$499$	−4.34120	−0.194339	−0.0971693	−	0.995268i	$-0.530979\pi$
$499$	−4.34120	−0.194339	−0.0971693	+	0.995268i	$0.530979\pi$
$500$	1.00000	0.0447214
$501$	−7.73791	−0.345704
$502$	−22.4668	−1.00274
$503$	−19.0214	−0.848122	−0.424061	−	0.905634i	$-0.639396\pi$
$503$	−19.0214	−0.848122	−0.424061	+	0.905634i	$0.639396\pi$
$504$	19.4456	0.866178
$505$	−1.47829	−0.0657830
$506$	15.8239	0.703460
$507$	−104.079	−4.62230
$508$	−9.41065	−0.417530
$509$	41.4457	1.83705	0.918524	−	0.395366i	$-0.129382\pi$
$509$	41.4457	1.83705	0.918524	+	0.395366i	$0.129382\pi$
$510$	−18.8441	−0.834429
$511$	18.9719	0.839266
$512$	1.00000	0.0441942
$513$	−129.262	−5.70707
$514$	−19.1811	−0.846042
$515$	−15.2695	−0.672854
$516$	−20.1499	−0.887049
$517$	−13.8661	−0.609832
$518$	−17.7503	−0.779903
$519$	−71.2044	−3.12553
$520$	6.65331	0.291767
$521$	19.4558	0.852375	0.426187	−	0.904635i	$-0.359856\pi$
$521$	19.4558	0.852375	0.426187	+	0.904635i	$0.359856\pi$
$522$	−21.2917	−0.931914
$523$	3.00894	0.131572	0.0657860	−	0.997834i	$-0.479045\pi$
$523$	3.00894	0.131572	0.0657860	+	0.997834i	$0.479045\pi$
$524$	3.17192	0.138566
$525$	−8.01048	−0.349606
$526$	−14.7625	−0.643675
$527$	35.9718	1.56695
$528$	17.5747	0.764840
$529$	−14.0170	−0.609437
$530$	−0.218753	−0.00950201
$531$	−79.2635	−3.43974
$532$	18.3927	0.797425
$533$	26.3419	1.14099
$534$	−46.3149	−2.00424
$535$	−12.4022	−0.536192
$536$	3.10361	0.134056
$537$	−22.8594	−0.986457
$538$	25.3355	1.09229
$539$	6.38323	0.274945
$540$	−16.9123	−0.727789
$541$	−30.0469	−1.29182	−0.645908	−	0.763415i	$-0.723521\pi$
$541$	−30.0469	−1.29182	−0.645908	+	0.763415i	$0.723521\pi$
$542$	7.00862	0.301046
$543$	−56.4339	−2.42181
$544$	5.66099	0.242713
$545$	5.67491	0.243086
$546$	−53.2962	−2.28087
$547$	−28.2391	−1.20742	−0.603708	−	0.797205i	$-0.706311\pi$
$547$	−28.2391	−1.20742	−0.603708	+	0.797205i	$0.706311\pi$
$548$	−6.60284	−0.282059
$549$	−52.1818	−2.22707
$550$	−5.27965	−0.225125
$551$	−20.1388	−0.857944
$552$	9.97682	0.424642
$553$	−14.9176	−0.634360
$554$	−15.1870	−0.645235
$555$	24.5534	1.04224
$556$	−3.51203	−0.148943
$557$	9.06474	0.384085	0.192043	−	0.981387i	$-0.438489\pi$
$557$	9.06474	0.384085	0.192043	+	0.981387i	$0.438489\pi$
$558$	51.3471	2.17370
$559$	40.2743	1.70342
$560$	2.40644	0.101691
$561$	99.4900	4.20047
$562$	−13.8554	−0.584456
$563$	−7.00966	−0.295422	−0.147711	−	0.989031i	$-0.547191\pi$
$563$	−7.00966	−0.295422	−0.147711	+	0.989031i	$0.547191\pi$
$564$	−8.74245	−0.368124
$565$	−11.3175	−0.476131
$566$	22.2872	0.936801
$567$	77.1386	3.23952
$568$	3.85168	0.161613
$569$	−46.4551	−1.94750	−0.973749	−	0.227626i	$-0.926904\pi$
$569$	−46.4551	−1.94750	−0.973749	+	0.227626i	$0.926904\pi$
$570$	−25.4421	−1.06565
$571$	−9.42541	−0.394441	−0.197221	−	0.980359i	$-0.563192\pi$
$571$	−9.42541	−0.394441	−0.197221	+	0.980359i	$0.563192\pi$
$572$	−35.1271	−1.46874
$573$	−27.9346	−1.16698
$574$	9.52762	0.397675
$575$	−2.99716	−0.124990
$576$	8.08065	0.336694
$577$	21.3868	0.890344	0.445172	−	0.895445i	$-0.353142\pi$
$577$	21.3868	0.890344	0.445172	+	0.895445i	$0.353142\pi$
$578$	15.0468	0.625863
$579$	−74.1857	−3.08305
$580$	−2.63490	−0.109408
$581$	−29.4365	−1.22123
$582$	−12.7303	−0.527688
$583$	1.15494	0.0478326
$584$	7.88377	0.326233
$585$	53.7631	2.22283
$586$	−17.7935	−0.735042
$587$	25.0504	1.03394	0.516971	−	0.856003i	$-0.327060\pi$
$587$	25.0504	1.03394	0.516971	+	0.856003i	$0.327060\pi$
$588$	4.02456	0.165970
$589$	48.5668	2.00116
$590$	−9.80905	−0.403832
$591$	91.9975	3.78427
$592$	−7.37615	−0.303158
$593$	−29.8548	−1.22599	−0.612995	−	0.790087i	$-0.710035\pi$
$593$	−29.8548	−1.22599	−0.612995	+	0.790087i	$0.710035\pi$
$594$	89.2909	3.66365
$595$	13.6228	0.558482
$596$	9.73491	0.398757
$597$	−28.4348	−1.16376
$598$	−19.9410	−0.815449
$599$	−40.3594	−1.64904	−0.824520	−	0.565833i	$-0.808555\pi$
$599$	−40.3594	−1.64904	−0.824520	+	0.565833i	$0.808555\pi$
$600$	−3.32876	−0.135896
$601$	47.1041	1.92142	0.960708	−	0.277561i	$-0.0895260\pi$
$601$	47.1041	1.92142	0.960708	+	0.277561i	$0.0895260\pi$
$602$	14.5668	0.593700
$603$	25.0792	1.02131
$604$	9.77443	0.397716
$605$	16.8747	0.686052
$606$	4.92087	0.199897
$607$	−45.1230	−1.83149	−0.915743	−	0.401764i	$-0.868397\pi$
$607$	−45.1230	−1.83149	−0.915743	+	0.401764i	$0.868397\pi$
$608$	7.64311	0.309969
$609$	21.1068	0.855292
$610$	−6.45762	−0.261461
$611$	17.4738	0.706916
$612$	45.7445	1.84911
$613$	42.5422	1.71826	0.859132	−	0.511754i	$-0.171004\pi$
$613$	42.5422	1.71826	0.859132	+	0.511754i	$0.171004\pi$
$614$	7.48351	0.302010
$615$	−13.1793	−0.531439
$616$	−12.7052	−0.511906
$617$	−11.5026	−0.463077	−0.231539	−	0.972826i	$-0.574376\pi$
$617$	−11.5026	−0.463077	−0.231539	+	0.972826i	$0.574376\pi$
$618$	50.8285	2.04462
$619$	−25.3762	−1.01996	−0.509978	−	0.860187i	$-0.670347\pi$
$619$	−25.3762	−1.01996	−0.509978	+	0.860187i	$0.670347\pi$
$620$	6.35433	0.255196
$621$	50.6888	2.03407
$622$	19.1108	0.766273
$623$	33.4822	1.34143
$624$	−22.1473	−0.886601
$625$	1.00000	0.0400000
$626$	−14.7020	−0.587612
$627$	134.325	5.36443
$628$	2.44718	0.0976530
$629$	−41.7563	−1.66493
$630$	19.4456	0.774733
$631$	13.3347	0.530845	0.265423	−	0.964132i	$-0.414489\pi$
$631$	13.3347	0.530845	0.265423	+	0.964132i	$0.414489\pi$
$632$	−6.19901	−0.246584
$633$	34.1850	1.35873
$634$	14.5979	0.579758
$635$	−9.41065	−0.373450
$636$	0.728176	0.0288740
$637$	−8.04403	−0.318716
$638$	13.9114	0.550756
$639$	31.1241	1.23125
$640$	1.00000	0.0395285
$641$	40.6777	1.60667	0.803337	−	0.595524i	$-0.203056\pi$
$641$	40.6777	1.60667	0.803337	+	0.595524i	$0.203056\pi$
$642$	41.2838	1.62934
$643$	9.77067	0.385318	0.192659	−	0.981266i	$-0.438289\pi$
$643$	9.77067	0.385318	0.192659	+	0.981266i	$0.438289\pi$
$644$	−7.21249	−0.284212
$645$	−20.1499	−0.793401
$646$	43.2675	1.70234
$647$	−12.5737	−0.494323	−0.247162	−	0.968974i	$-0.579498\pi$
$647$	−12.5737	−0.494323	−0.247162	+	0.968974i	$0.579498\pi$
$648$	32.0550	1.25924
$649$	51.7883	2.03287
$650$	6.65331	0.260964
$651$	−50.9012	−1.99498
$652$	23.0340	0.902082
$653$	−19.5288	−0.764221	−0.382110	−	0.924117i	$-0.624803\pi$
$653$	−19.5288	−0.764221	−0.382110	+	0.924117i	$0.624803\pi$
$654$	−18.8904	−0.738673
$655$	3.17192	0.123937
$656$	3.95921	0.154581
$657$	63.7060	2.48541
$658$	6.32013	0.246384
$659$	35.1384	1.36880	0.684398	−	0.729109i	$-0.260065\pi$
$659$	35.1384	1.36880	0.684398	+	0.729109i	$0.260065\pi$
$660$	17.5747	0.684094
$661$	−28.0073	−1.08936	−0.544678	−	0.838645i	$-0.683348\pi$
$661$	−28.0073	−1.08936	−0.544678	+	0.838645i	$0.683348\pi$
$662$	−8.28683	−0.322077
$663$	−125.375	−4.86918
$664$	−12.2324	−0.474707
$665$	18.3927	0.713239
$666$	−59.6041	−2.30961
$667$	7.89722	0.305782
$668$	2.32456	0.0899400
$669$	−17.2655	−0.667524
$670$	3.10361	0.119903
$671$	34.0940	1.31618
$672$	−8.01048	−0.309011
$673$	−31.9710	−1.23239	−0.616196	−	0.787593i	$-0.711327\pi$
$673$	−31.9710	−1.23239	−0.616196	+	0.787593i	$0.711327\pi$
$674$	−15.8247	−0.609547
$675$	−16.9123	−0.650954
$676$	31.2665	1.20256
$677$	−23.1293	−0.888930	−0.444465	−	0.895796i	$-0.646606\pi$
$677$	−23.1293	−0.888930	−0.444465	+	0.895796i	$0.646606\pi$
$678$	37.6733	1.44683
$679$	9.20305	0.353181
$680$	5.66099	0.217089
$681$	−64.5248	−2.47260
$682$	−33.5486	−1.28464
$683$	−9.10179	−0.348270	−0.174135	−	0.984722i	$-0.555713\pi$
$683$	−9.10179	−0.348270	−0.174135	+	0.984722i	$0.555713\pi$
$684$	61.7613	2.36150
$685$	−6.60284	−0.252282
$686$	−19.7546	−0.754233
$687$	69.4686	2.65039
$688$	6.05327	0.230779
$689$	−1.45543	−0.0554475
$690$	9.97682	0.379811
$691$	−29.3840	−1.11782	−0.558910	−	0.829228i	$-0.688780\pi$
$691$	−29.3840	−1.11782	−0.558910	+	0.829228i	$0.688780\pi$
$692$	21.3907	0.813151
$693$	−102.666	−3.89996
$694$	−2.10811	−0.0800227
$695$	−3.51203	−0.133219
$696$	8.77096	0.332463
$697$	22.4130	0.848954
$698$	−2.18344	−0.0826446
$699$	27.9629	1.05765
$700$	2.40644	0.0909550
$701$	30.4837	1.15135	0.575676	−	0.817678i	$-0.304739\pi$
$701$	30.4837	1.15135	0.575676	+	0.817678i	$0.304739\pi$
$702$	−112.523	−4.24689
$703$	−56.3767	−2.12629
$704$	−5.27965	−0.198984
$705$	−8.74245	−0.329260
$706$	−19.7256	−0.742382
$707$	−3.55742	−0.133791
$708$	32.6520	1.22714
$709$	−36.3906	−1.36668	−0.683339	−	0.730101i	$-0.739473\pi$
$709$	−36.3906	−1.36668	−0.683339	+	0.730101i	$0.739473\pi$
$710$	3.85168	0.144551
$711$	−50.0921	−1.87860
$712$	13.9135	0.521432
$713$	−19.0449	−0.713238
$714$	−45.3472	−1.69708
$715$	−35.1271	−1.31368
$716$	6.86725	0.256641
$717$	−95.9367	−3.58282
$718$	25.2519	0.942393
$719$	17.5994	0.656348	0.328174	−	0.944617i	$-0.393567\pi$
$719$	17.5994	0.656348	0.328174	+	0.944617i	$0.393567\pi$
$720$	8.08065	0.301148
$721$	−36.7452	−1.36846
$722$	39.4171	1.46695
$723$	−0.644215	−0.0239586
$724$	16.9534	0.630068
$725$	−2.63490	−0.0978578
$726$	−56.1717	−2.08473
$727$	33.7020	1.24994	0.624969	−	0.780650i	$-0.285112\pi$
$727$	33.7020	1.24994	0.624969	+	0.780650i	$0.285112\pi$
$728$	16.0108	0.593400
$729$	90.1345	3.33831
$730$	7.88377	0.291792
$731$	34.2675	1.26743
$732$	21.4959	0.794511
$733$	−12.8954	−0.476301	−0.238151	−	0.971228i	$-0.576541\pi$
$733$	−12.8954	−0.476301	−0.238151	+	0.971228i	$0.576541\pi$
$734$	−13.6044	−0.502146
$735$	4.02456	0.148448
$736$	−2.99716	−0.110477
$737$	−16.3860	−0.603586
$738$	31.9930	1.17768
$739$	−8.97666	−0.330212	−0.165106	−	0.986276i	$-0.552797\pi$
$739$	−8.97666	−0.330212	−0.165106	+	0.986276i	$0.552797\pi$
$740$	−7.37615	−0.271153
$741$	−169.274	−6.21844
$742$	−0.526416	−0.0193253
$743$	29.2503	1.07309	0.536544	−	0.843872i	$-0.319729\pi$
$743$	29.2503	1.07309	0.536544	+	0.843872i	$0.319729\pi$
$744$	−21.1520	−0.775471
$745$	9.73491	0.356659
$746$	20.8198	0.762266
$747$	−98.8454	−3.61656
$748$	−29.8880	−1.09281
$749$	−29.8451	−1.09052
$750$	−3.32876	−0.121549
$751$	3.77210	0.137646	0.0688230	−	0.997629i	$-0.478076\pi$
$751$	3.77210	0.137646	0.0688230	+	0.997629i	$0.478076\pi$
$752$	2.62634	0.0957726
$753$	74.7867	2.72538
$754$	−17.5308	−0.638435
$755$	9.77443	0.355728
$756$	−40.6985	−1.48019
$757$	−11.6198	−0.422329	−0.211164	−	0.977451i	$-0.567726\pi$
$757$	−11.6198	−0.422329	−0.211164	+	0.977451i	$0.567726\pi$
$758$	−16.1963	−0.588276
$759$	−52.6741	−1.91195
$760$	7.64311	0.277245
$761$	−9.54402	−0.345970	−0.172985	−	0.984924i	$-0.555341\pi$
$761$	−9.54402	−0.345970	−0.172985	+	0.984924i	$0.555341\pi$
$762$	31.3258	1.13481
$763$	13.6563	0.494393
$764$	8.39188	0.303608
$765$	45.7445	1.65389
$766$	−19.7265	−0.712748
$767$	−65.2627	−2.35650
$768$	−3.32876	−0.120116
$769$	−10.0380	−0.361978	−0.180989	−	0.983485i	$-0.557930\pi$
$769$	−10.0380	−0.361978	−0.180989	+	0.983485i	$0.557930\pi$
$770$	−12.7052	−0.457863
$771$	63.8493	2.29948
$772$	22.2863	0.802100
$773$	−23.0946	−0.830657	−0.415328	−	0.909672i	$-0.636333\pi$
$773$	−23.0946	−0.830657	−0.415328	+	0.909672i	$0.636333\pi$
$774$	48.9144	1.75819
$775$	6.35433	0.228254
$776$	3.82434	0.137286
$777$	59.0865	2.11972
$778$	15.2103	0.545316
$779$	30.2607	1.08420
$780$	−22.1473	−0.793000
$781$	−20.3355	−0.727662
$782$	−16.9669	−0.606734
$783$	44.5622	1.59252
$784$	−1.20903	−0.0431795
$785$	2.44718	0.0873435
$786$	−10.5586	−0.376612
$787$	−22.3723	−0.797488	−0.398744	−	0.917062i	$-0.630554\pi$
$787$	−22.3723	−0.797488	−0.398744	+	0.917062i	$0.630554\pi$
$788$	−27.6372	−0.984533
$789$	49.1408	1.74946
$790$	−6.19901	−0.220551
$791$	−27.2349	−0.968363
$792$	−42.6630	−1.51596
$793$	−42.9646	−1.52572
$794$	−25.3122	−0.898298
$795$	0.728176	0.0258257
$796$	8.54215	0.302769
$797$	12.3982	0.439166	0.219583	−	0.975594i	$-0.429530\pi$
$797$	12.3982	0.439166	0.219583	+	0.975594i	$0.429530\pi$
$798$	−61.2249	−2.16734
$799$	14.8677	0.525980
$800$	1.00000	0.0353553
$801$	112.431	3.97254
$802$	1.00000	0.0353112
$803$	−41.6235	−1.46886
$804$	−10.3312	−0.364353
$805$	−7.21249	−0.254207
$806$	42.2773	1.48915
$807$	−84.3358	−2.96876
$808$	−1.47829	−0.0520060
$809$	18.3013	0.643439	0.321719	−	0.946835i	$-0.395739\pi$
$809$	18.3013	0.643439	0.321719	+	0.946835i	$0.395739\pi$
$810$	32.0550	1.12630
$811$	−1.27041	−0.0446100	−0.0223050	−	0.999751i	$-0.507100\pi$
$811$	−1.27041	−0.0446100	−0.0223050	+	0.999751i	$0.507100\pi$
$812$	−6.34075	−0.222517
$813$	−23.3300	−0.818219
$814$	38.9434	1.36497
$815$	23.0340	0.806846
$816$	−18.8441	−0.659674
$817$	46.2658	1.61863
$818$	15.7689	0.551347
$819$	129.378	4.52083
$820$	3.95921	0.138262
$821$	−45.0442	−1.57205	−0.786027	−	0.618192i	$-0.787865\pi$
$821$	−45.0442	−1.57205	−0.786027	+	0.618192i	$0.787865\pi$
$822$	21.9793	0.766616
$823$	−8.82010	−0.307449	−0.153725	−	0.988114i	$-0.549127\pi$
$823$	−8.82010	−0.307449	−0.153725	+	0.988114i	$0.549127\pi$
$824$	−15.2695	−0.531938
$825$	17.5747	0.611872
$826$	−23.6049	−0.821321
$827$	−11.7091	−0.407164	−0.203582	−	0.979058i	$-0.565258\pi$
$827$	−11.7091	−0.407164	−0.203582	+	0.979058i	$0.565258\pi$
$828$	−24.2190	−0.841668
$829$	−34.1749	−1.18694	−0.593471	−	0.804855i	$-0.702243\pi$
$829$	−34.1749	−1.18694	−0.593471	+	0.804855i	$0.702243\pi$
$830$	−12.2324	−0.424591
$831$	50.5540	1.75370
$832$	6.65331	0.230662
$833$	−6.84428	−0.237140
$834$	11.6907	0.404817
$835$	2.32456	0.0804447
$836$	−40.3529	−1.39563
$837$	−107.466	−3.71457
$838$	−14.7141	−0.508291
$839$	−31.7920	−1.09758	−0.548791	−	0.835959i	$-0.684912\pi$
$839$	−31.7920	−1.09758	−0.548791	+	0.835959i	$0.684912\pi$
$840$	−8.01048	−0.276388
$841$	−22.0573	−0.760596
$842$	28.1408	0.969795
$843$	46.1214	1.58851
$844$	−10.2696	−0.353494
$845$	31.2665	1.07560
$846$	21.2225	0.729645
$847$	40.6079	1.39530
$848$	−0.218753	−0.00751200
$849$	−74.1888	−2.54615
$850$	5.66099	0.194170
$851$	22.1075	0.757835
$852$	−12.8213	−0.439251
$853$	−53.0992	−1.81808	−0.909041	−	0.416707i	$-0.863184\pi$
$853$	−53.0992	−1.81808	−0.909041	+	0.416707i	$0.863184\pi$
$854$	−15.5399	−0.531765
$855$	61.7613	2.11219
$856$	−12.4022	−0.423897
$857$	−29.2533	−0.999275	−0.499637	−	0.866235i	$-0.666533\pi$
$857$	−29.2533	−0.999275	−0.499637	+	0.866235i	$0.666533\pi$
$858$	116.930	3.99192
$859$	20.5619	0.701562	0.350781	−	0.936457i	$-0.385916\pi$
$859$	20.5619	0.701562	0.350781	+	0.936457i	$0.385916\pi$
$860$	6.05327	0.206415
$861$	−31.7152	−1.08085
$862$	18.8169	0.640907
$863$	−0.646643	−0.0220120	−0.0110060	−	0.999939i	$-0.503503\pi$
$863$	−0.646643	−0.0220120	−0.0110060	+	0.999939i	$0.503503\pi$
$864$	−16.9123	−0.575368
$865$	21.3907	0.727305
$866$	3.25749	0.110694
$867$	−50.0871	−1.70105
$868$	15.2913	0.519022
$869$	32.7286	1.11024
$870$	8.77096	0.297364
$871$	20.6493	0.699675
$872$	5.67491	0.192177
$873$	30.9031	1.04591
$874$	−22.9076	−0.774861
$875$	2.40644	0.0813527
$876$	−26.2432	−0.886676
$877$	−32.2439	−1.08880	−0.544400	−	0.838826i	$-0.683242\pi$
$877$	−32.2439	−1.08880	−0.544400	+	0.838826i	$0.683242\pi$
$878$	−10.9482	−0.369484
$879$	59.2303	1.99779
$880$	−5.27965	−0.177977
$881$	8.24040	0.277626	0.138813	−	0.990319i	$-0.455671\pi$
$881$	8.24040	0.277626	0.138813	+	0.990319i	$0.455671\pi$
$882$	−9.76972	−0.328964
$883$	1.36228	0.0458445	0.0229223	−	0.999737i	$-0.492703\pi$
$883$	1.36228	0.0458445	0.0229223	+	0.999737i	$0.492703\pi$
$884$	37.6643	1.26679
$885$	32.6520	1.09758
$886$	−19.4685	−0.654058
$887$	34.6021	1.16183	0.580913	−	0.813966i	$-0.302696\pi$
$887$	34.6021	1.16183	0.580913	+	0.813966i	$0.302696\pi$
$888$	24.5534	0.823959
$889$	−22.6462	−0.759530
$890$	13.9135	0.466383
$891$	−169.239	−5.66972
$892$	5.18677	0.173666
$893$	20.0734	0.671730
$894$	−32.4052	−1.08379
$895$	6.86725	0.229547
$896$	2.40644	0.0803937
$897$	66.3789	2.21633
$898$	−26.9386	−0.898952
$899$	−16.7430	−0.558411
$900$	8.08065	0.269355
$901$	−1.23836	−0.0412556
$902$	−20.9032	−0.696001
$903$	−48.4896	−1.61363
$904$	−11.3175	−0.376414
$905$	16.9534	0.563550
$906$	−32.5367	−1.08096
$907$	56.7849	1.88551	0.942755	−	0.333485i	$-0.108225\pi$
$907$	56.7849	1.88551	0.942755	+	0.333485i	$0.108225\pi$
$908$	19.3840	0.643282
$909$	−11.9455	−0.396209
$910$	16.0108	0.530753
$911$	−27.4121	−0.908204	−0.454102	−	0.890950i	$-0.650040\pi$
$911$	−27.4121	−0.908204	−0.454102	+	0.890950i	$0.650040\pi$
$912$	−25.4421	−0.842472
$913$	64.5825	2.13737
$914$	−11.1153	−0.367661
$915$	21.4959	0.710632
$916$	−20.8692	−0.689538
$917$	7.63305	0.252066
$918$	−95.7402	−3.15990
$919$	9.49316	0.313151	0.156575	−	0.987666i	$-0.449955\pi$
$919$	9.49316	0.313151	0.156575	+	0.987666i	$0.449955\pi$
$920$	−2.99716	−0.0988134
$921$	−24.9108	−0.820839
$922$	−16.6344	−0.547826
$923$	25.6264	0.843504
$924$	42.2925	1.39132
$925$	−7.37615	−0.242526
$926$	−27.0627	−0.889334
$927$	−123.388	−4.05258
$928$	−2.63490	−0.0864949
$929$	−17.0232	−0.558512	−0.279256	−	0.960217i	$-0.590088\pi$
$929$	−17.0232	−0.558512	−0.279256	+	0.960217i	$0.590088\pi$
$930$	−21.1520	−0.693603
$931$	−9.24072	−0.302852
$932$	−8.40040	−0.275164
$933$	−63.6152	−2.08267
$934$	33.0726	1.08217
$935$	−29.8880	−0.977442
$936$	53.7631	1.75730
$937$	10.1135	0.330394	0.165197	−	0.986261i	$-0.447174\pi$
$937$	10.1135	0.330394	0.165197	+	0.986261i	$0.447174\pi$
$938$	7.46868	0.243861
$939$	48.9396	1.59708
$940$	2.62634	0.0856617
$941$	−9.38543	−0.305956	−0.152978	−	0.988230i	$-0.548886\pi$
$941$	−9.38543	−0.305956	−0.152978	+	0.988230i	$0.548886\pi$
$942$	−8.14607	−0.265413
$943$	−11.8664	−0.386422
$944$	−9.80905	−0.319257
$945$	−40.6985	−1.32392
$946$	−31.9591	−1.03908
$947$	39.2260	1.27467	0.637336	−	0.770586i	$-0.280036\pi$
$947$	39.2260	1.27467	0.637336	+	0.770586i	$0.280036\pi$
$948$	20.6350	0.670195
$949$	52.4532	1.70270
$950$	7.64311	0.247975
$951$	−48.5930	−1.57574
$952$	13.6228	0.441519
$953$	54.1121	1.75286	0.876432	−	0.481525i	$-0.159917\pi$
$953$	54.1121	1.75286	0.876432	+	0.481525i	$0.159917\pi$
$954$	−1.76766	−0.0572303
$955$	8.39188	0.271555
$956$	28.8205	0.932123
$957$	−46.3076	−1.49691
$958$	12.5633	0.405902
$959$	−15.8894	−0.513095
$960$	−3.32876	−0.107435
$961$	9.37747	0.302499
$962$	−49.0758	−1.58227
$963$	−100.218	−3.22946
$964$	0.193530	0.00623318
$965$	22.2863	0.717420
$966$	24.0087	0.772466
$967$	−22.7045	−0.730127	−0.365064	−	0.930983i	$-0.618953\pi$
$967$	−22.7045	−0.730127	−0.365064	+	0.930983i	$0.618953\pi$
$968$	16.8747	0.542372
$969$	−144.027	−4.62682
$970$	3.82434	0.122792
$971$	51.8738	1.66471	0.832354	−	0.554244i	$-0.186993\pi$
$971$	51.8738	1.66471	0.832354	+	0.554244i	$0.186993\pi$
$972$	−55.9666	−1.79513
$973$	−8.45151	−0.270943
$974$	40.2031	1.28819
$975$	−22.1473	−0.709281
$976$	−6.45762	−0.206703
$977$	36.0767	1.15420	0.577098	−	0.816675i	$-0.304185\pi$
$977$	36.0767	1.15420	0.577098	+	0.816675i	$0.304185\pi$
$978$	−76.6747	−2.45179
$979$	−73.4586	−2.34775
$980$	−1.20903	−0.0386209
$981$	45.8569	1.46410
$982$	5.28440	0.168632
$983$	53.2300	1.69777	0.848886	−	0.528575i	$-0.177274\pi$
$983$	53.2300	1.69777	0.848886	+	0.528575i	$0.177274\pi$
$984$	−13.1793	−0.420140
$985$	−27.6372	−0.880593
$986$	−14.9161	−0.475027
$987$	−21.0382	−0.669654
$988$	50.8520	1.61782
$989$	−18.1426	−0.576901
$990$	−42.6630	−1.35592
$991$	9.09258	0.288835	0.144418	−	0.989517i	$-0.453869\pi$
$991$	9.09258	0.288835	0.144418	+	0.989517i	$0.453869\pi$
$992$	6.35433	0.201750
$993$	27.5849	0.875380
$994$	9.26885	0.293990
$995$	8.54215	0.270804
$996$	40.7186	1.29022
$997$	19.5157	0.618069	0.309035	−	0.951051i	$-0.399994\pi$
$997$	19.5157	0.618069	0.309035	+	0.951051i	$0.399994\pi$
$998$	−4.34120	−0.137418
$999$	124.748	3.94684

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4010.2.a.n.1.1	✓	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -3.32876 q^{3} +1.00000 q^{4} +1.00000 q^{5} -3.32876 q^{6} +2.40644 q^{7} +1.00000 q^{8} +8.08065 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -3.32876 q^{3} +1.00000 q^{4} +1.00000 q^{5} -3.32876 q^{6} +2.40644 q^{7} +1.00000 q^{8} +8.08065 q^{9} +1.00000 q^{10} -5.27965 q^{11} -3.32876 q^{12} +6.65331 q^{13} +2.40644 q^{14} -3.32876 q^{15} +1.00000 q^{16} +5.66099 q^{17} +8.08065 q^{18} +7.64311 q^{19} +1.00000 q^{20} -8.01048 q^{21} -5.27965 q^{22} -2.99716 q^{23} -3.32876 q^{24} +1.00000 q^{25} +6.65331 q^{26} -16.9123 q^{27} +2.40644 q^{28} -2.63490 q^{29} -3.32876 q^{30} +6.35433 q^{31} +1.00000 q^{32} +17.5747 q^{33} +5.66099 q^{34} +2.40644 q^{35} +8.08065 q^{36} -7.37615 q^{37} +7.64311 q^{38} -22.1473 q^{39} +1.00000 q^{40} +3.95921 q^{41} -8.01048 q^{42} +6.05327 q^{43} -5.27965 q^{44} +8.08065 q^{45} -2.99716 q^{46} +2.62634 q^{47} -3.32876 q^{48} -1.20903 q^{49} +1.00000 q^{50} -18.8441 q^{51} +6.65331 q^{52} -0.218753 q^{53} -16.9123 q^{54} -5.27965 q^{55} +2.40644 q^{56} -25.4421 q^{57} -2.63490 q^{58} -9.80905 q^{59} -3.32876 q^{60} -6.45762 q^{61} +6.35433 q^{62} +19.4456 q^{63} +1.00000 q^{64} +6.65331 q^{65} +17.5747 q^{66} +3.10361 q^{67} +5.66099 q^{68} +9.97682 q^{69} +2.40644 q^{70} +3.85168 q^{71} +8.08065 q^{72} +7.88377 q^{73} -7.37615 q^{74} -3.32876 q^{75} +7.64311 q^{76} -12.7052 q^{77} -22.1473 q^{78} -6.19901 q^{79} +1.00000 q^{80} +32.0550 q^{81} +3.95921 q^{82} -12.2324 q^{83} -8.01048 q^{84} +5.66099 q^{85} +6.05327 q^{86} +8.77096 q^{87} -5.27965 q^{88} +13.9135 q^{89} +8.08065 q^{90} +16.0108 q^{91} -2.99716 q^{92} -21.1520 q^{93} +2.62634 q^{94} +7.64311 q^{95} -3.32876 q^{96} +3.82434 q^{97} -1.20903 q^{98} -42.6630 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + 22 q^{2} + q^{3} + 22 q^{4} + 22 q^{5} + q^{6} + 22 q^{8} + 43 q^{9}+O(q^{10}) \) 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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